[PATCH 1/4] libstdc++: Import parts of the Ryu library

[PATCH 1/4] libstdc++: Import parts of the Ryu library

[Patrick Palka]

This imports the source files from the Ryu library that define
d2s_buffered_n, f2s_buffered_n, d2fixed_buffered_n and d2exp_buffered_n
and generic_binary_to_decimal, which we're going to need as part of our
std::to_chars implementation.

libstdc++-v3/ChangeLog:

	* src/c++17/ryu/MERGE: New file.
	* src/c++17/ryu/common.h, src/c++17/ryu/d2fixed.c,
	src/c++17/ryu/d2fixed_full_table.h, src/c++17/ryu/d2s.c,
	src/c++17/ryu/d2s_full_table.h, src/c++17/ryu/d2s_intrinsics.h,
	src/c++17/ryu/digit_table.h, src/c++17/ryu/f2s.c,
	src/c++17/ryu/f2s_instrinsics.h,
	src/c++17/ryu/generic_128.c, src/c++17/ryu/generic_128.h,
	src/c++17/ryu/ryu_generic_128.h: Import these files from the
	Ryu library.
---
 libstdc++-v3/src/c++17/ryu/MERGE              |    4 +
 libstdc++-v3/src/c++17/ryu/common.h           |  114 +
 libstdc++-v3/src/c++17/ryu/d2fixed.c          |  819 +++
 .../src/c++17/ryu/d2fixed_full_table.h        | 4420 +++++++++++++++++
 libstdc++-v3/src/c++17/ryu/d2s.c              |  509 ++
 libstdc++-v3/src/c++17/ryu/d2s_full_table.h   |  367 ++
 libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h   |  358 ++
 libstdc++-v3/src/c++17/ryu/digit_table.h      |   35 +
 libstdc++-v3/src/c++17/ryu/f2s.c              |  345 ++
 libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h   |  128 +
 libstdc++-v3/src/c++17/ryu/generic_128.c      |  338 ++
 libstdc++-v3/src/c++17/ryu/generic_128.h      |  517 ++
 libstdc++-v3/src/c++17/ryu/ryu_generic_128.h  |   70 +
 13 files changed, 8024 insertions(+)
 create mode 100644 libstdc++-v3/src/c++17/ryu/MERGE
 create mode 100644 libstdc++-v3/src/c++17/ryu/common.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/d2fixed.c
 create mode 100644 libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/d2s.c
 create mode 100644 libstdc++-v3/src/c++17/ryu/d2s_full_table.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/digit_table.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/f2s.c
 create mode 100644 libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/generic_128.c
 create mode 100644 libstdc++-v3/src/c++17/ryu/generic_128.h
 create mode 100644 libstdc++-v3/src/c++17/ryu/ryu_generic_128.h

diff --git a/libstdc++-v3/src/c++17/ryu/MERGE b/libstdc++-v3/src/c++17/ryu/MERGE
new file mode 100644
index 00000000000..0ea65add2ff
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/MERGE
@@ -0,0 +1,4 @@
+22c887c017a8512abcd4a8f6bfcdb2742829cd7d
+
+The first line of this file holds the git revision number of the
+last merge done from the master library sources.
diff --git a/libstdc++-v3/src/c++17/ryu/common.h b/libstdc++-v3/src/c++17/ryu/common.h
new file mode 100644
index 00000000000..7dc130947ac
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/common.h
@@ -0,0 +1,114 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#include <assert.h>
+#include <stdint.h>
+#include <string.h>
+
+#if defined(_M_IX86) || defined(_M_ARM)
+#define RYU_32_BIT_PLATFORM
+#endif
+
+// Returns the number of decimal digits in v, which must not contain more than 9 digits.
+static inline uint32_t decimalLength9(const uint32_t v) {
+  // Function precondition: v is not a 10-digit number.
+  // (f2s: 9 digits are sufficient for round-tripping.)
+  // (d2fixed: We print 9-digit blocks.)
+  assert(v < 1000000000);
+  if (v >= 100000000) { return 9; }
+  if (v >= 10000000) { return 8; }
+  if (v >= 1000000) { return 7; }
+  if (v >= 100000) { return 6; }
+  if (v >= 10000) { return 5; }
+  if (v >= 1000) { return 4; }
+  if (v >= 100) { return 3; }
+  if (v >= 10) { return 2; }
+  return 1;
+}
+
+// Returns e == 0 ? 1 : [log_2(5^e)]; requires 0 <= e <= 3528.
+static inline int32_t log2pow5(const int32_t e) {
+  // This approximation works up to the point that the multiplication overflows at e = 3529.
+  // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
+  // than 2^9297.
+  assert(e >= 0);
+  assert(e <= 3528);
+  return (int32_t) ((((uint32_t) e) * 1217359) >> 19);
+}
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
+static inline int32_t pow5bits(const int32_t e) {
+  // This approximation works up to the point that the multiplication overflows at e = 3529.
+  // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
+  // than 2^9297.
+  assert(e >= 0);
+  assert(e <= 3528);
+  return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
+}
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
+static inline int32_t ceil_log2pow5(const int32_t e) {
+  return log2pow5(e) + 1;
+}
+
+// Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
+static inline uint32_t log10Pow2(const int32_t e) {
+  // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
+  assert(e >= 0);
+  assert(e <= 1650);
+  return (((uint32_t) e) * 78913) >> 18;
+}
+
+// Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
+static inline uint32_t log10Pow5(const int32_t e) {
+  // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
+  assert(e >= 0);
+  assert(e <= 2620);
+  return (((uint32_t) e) * 732923) >> 20;
+}
+
+static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) {
+  if (mantissa) {
+    memcpy(result, "NaN", 3);
+    return 3;
+  }
+  if (sign) {
+    result[0] = '-';
+  }
+  if (exponent) {
+    memcpy(result + sign, "Infinity", 8);
+    return sign + 8;
+  }
+  memcpy(result + sign, "0E0", 3);
+  return sign + 3;
+}
+
+static inline uint32_t float_to_bits(const float f) {
+  uint32_t bits = 0;
+  memcpy(&bits, &f, sizeof(float));
+  return bits;
+}
+
+static inline uint64_t double_to_bits(const double d) {
+  uint64_t bits = 0;
+  memcpy(&bits, &d, sizeof(double));
+  return bits;
+}
+
+#endif // RYU_COMMON_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed.c b/libstdc++-v3/src/c++17/ryu/d2fixed.c
new file mode 100644
index 00000000000..5f479abb91b
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed.c
@@ -0,0 +1,819 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+//
+// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
+//     depending on your compiler.
+//
+// -DRYU_AVOID_UINT128 Avoid using uint128_t. Slower, depending on your compiler.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef RYU_DEBUG
+#include <inttypes.h>
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define POW10_ADDITIONAL_BITS 120
+
+#if defined(HAS_UINT128)
+static inline uint128_t umul256(const uint128_t a, const uint64_t bHi, const uint64_t bLo, uint128_t* const productHi) {
+  const uint64_t aLo = (uint64_t)a;
+  const uint64_t aHi = (uint64_t)(a >> 64);
+
+  const uint128_t b00 = (uint128_t)aLo * bLo;
+  const uint128_t b01 = (uint128_t)aLo * bHi;
+  const uint128_t b10 = (uint128_t)aHi * bLo;
+  const uint128_t b11 = (uint128_t)aHi * bHi;
+
+  const uint64_t b00Lo = (uint64_t)b00;
+  const uint64_t b00Hi = (uint64_t)(b00 >> 64);
+
+  const uint128_t mid1 = b10 + b00Hi;
+  const uint64_t mid1Lo = (uint64_t)(mid1);
+  const uint64_t mid1Hi = (uint64_t)(mid1 >> 64);
+
+  const uint128_t mid2 = b01 + mid1Lo;
+  const uint64_t mid2Lo = (uint64_t)(mid2);
+  const uint64_t mid2Hi = (uint64_t)(mid2 >> 64);
+
+  const uint128_t pHi = b11 + mid1Hi + mid2Hi;
+  const uint128_t pLo = ((uint128_t)mid2Lo << 64) | b00Lo;
+
+  *productHi = pHi;
+  return pLo;
+}
+
+// Returns the high 128 bits of the 256-bit product of a and b.
+static inline uint128_t umul256_hi(const uint128_t a, const uint64_t bHi, const uint64_t bLo) {
+  // Reuse the umul256 implementation.
+  // Optimizers will likely eliminate the instructions used to compute the
+  // low part of the product.
+  uint128_t hi;
+  umul256(a, bHi, bLo, &hi);
+  return hi;
+}
+
+// Unfortunately, gcc/clang do not automatically turn a 128-bit integer division
+// into a multiplication, so we have to do it manually.
+static inline uint32_t uint128_mod1e9(const uint128_t v) {
+  // After multiplying, we're going to shift right by 29, then truncate to uint32_t.
+  // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting.
+  const uint64_t multiplied = (uint64_t) umul256_hi(v, 0x89705F4136B4A597u, 0x31680A88F8953031u);
+
+  // For uint32_t truncation, see the mod1e9() comment in d2s_intrinsics.h.
+  const uint32_t shifted = (uint32_t) (multiplied >> 29);
+
+  return ((uint32_t) v) - 1000000000 * shifted;
+}
+
+// Best case: use 128-bit type.
+static inline uint32_t mulShift_mod1e9(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+  const uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
+  const uint128_t b1 = ((uint128_t) m) * mul[1]; // 64
+  const uint128_t b2 = ((uint128_t) m) * mul[2]; // 128
+#ifdef RYU_DEBUG
+  if (j < 128 || j > 180) {
+    printf("%d\n", j);
+  }
+#endif
+  assert(j >= 128);
+  assert(j <= 180);
+  // j: [128, 256)
+  const uint128_t mid = b1 + (uint64_t) (b0 >> 64); // 64
+  const uint128_t s1 = b2 + (uint64_t) (mid >> 64); // 128
+  return uint128_mod1e9(s1 >> (j - 128));
+}
+
+#else // HAS_UINT128
+
+#if defined(HAS_64_BIT_INTRINSICS)
+// Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b.
+static inline uint64_t umul256_hi128_lo64(
+  const uint64_t aHi, const uint64_t aLo, const uint64_t bHi, const uint64_t bLo) {
+  uint64_t b00Hi;
+  const uint64_t b00Lo = umul128(aLo, bLo, &b00Hi);
+  uint64_t b01Hi;
+  const uint64_t b01Lo = umul128(aLo, bHi, &b01Hi);
+  uint64_t b10Hi;
+  const uint64_t b10Lo = umul128(aHi, bLo, &b10Hi);
+  uint64_t b11Hi;
+  const uint64_t b11Lo = umul128(aHi, bHi, &b11Hi);
+  (void) b00Lo; // unused
+  (void) b11Hi; // unused
+  const uint64_t temp1Lo = b10Lo + b00Hi;
+  const uint64_t temp1Hi = b10Hi + (temp1Lo < b10Lo);
+  const uint64_t temp2Lo = b01Lo + temp1Lo;
+  const uint64_t temp2Hi = b01Hi + (temp2Lo < b01Lo);
+  return b11Lo + temp1Hi + temp2Hi;
+}
+
+static inline uint32_t uint128_mod1e9(const uint64_t vHi, const uint64_t vLo) {
+  // After multiplying, we're going to shift right by 29, then truncate to uint32_t.
+  // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting.
+  const uint64_t multiplied = umul256_hi128_lo64(vHi, vLo, 0x89705F4136B4A597u, 0x31680A88F8953031u);
+
+  // For uint32_t truncation, see the mod1e9() comment in d2s_intrinsics.h.
+  const uint32_t shifted = (uint32_t) (multiplied >> 29);
+
+  return ((uint32_t) vLo) - 1000000000 * shifted;
+}
+#endif // HAS_64_BIT_INTRINSICS
+
+static inline uint32_t mulShift_mod1e9(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+  uint64_t high0;                                   // 64
+  const uint64_t low0 = umul128(m, mul[0], &high0); // 0
+  uint64_t high1;                                   // 128
+  const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+  uint64_t high2;                                   // 192
+  const uint64_t low2 = umul128(m, mul[2], &high2); // 128
+  const uint64_t s0low = low0;              // 0
+  (void) s0low; // unused
+  const uint64_t s0high = low1 + high0;     // 64
+  const uint32_t c1 = s0high < low1;
+  const uint64_t s1low = low2 + high1 + c1; // 128
+  const uint32_t c2 = s1low < low2; // high1 + c1 can't overflow, so compare against low2
+  const uint64_t s1high = high2 + c2;       // 192
+#ifdef RYU_DEBUG
+  if (j < 128 || j > 180) {
+    printf("%d\n", j);
+  }
+#endif
+  assert(j >= 128);
+  assert(j <= 180);
+#if defined(HAS_64_BIT_INTRINSICS)
+  const uint32_t dist = (uint32_t) (j - 128); // dist: [0, 52]
+  const uint64_t shiftedhigh = s1high >> dist;
+  const uint64_t shiftedlow = shiftright128(s1low, s1high, dist);
+  return uint128_mod1e9(shiftedhigh, shiftedlow);
+#else // HAS_64_BIT_INTRINSICS
+  if (j < 160) { // j: [128, 160)
+    const uint64_t r0 = mod1e9(s1high);
+    const uint64_t r1 = mod1e9((r0 << 32) | (s1low >> 32));
+    const uint64_t r2 = ((r1 << 32) | (s1low & 0xffffffff));
+    return mod1e9(r2 >> (j - 128));
+  } else { // j: [160, 192)
+    const uint64_t r0 = mod1e9(s1high);
+    const uint64_t r1 = ((r0 << 32) | (s1low >> 32));
+    return mod1e9(r1 >> (j - 160));
+  }
+#endif // HAS_64_BIT_INTRINSICS
+}
+#endif // HAS_UINT128
+
+// Convert `digits` to a sequence of decimal digits. Append the digits to the result.
+// The caller has to guarantee that:
+//   10^(olength-1) <= digits < 10^olength
+// e.g., by passing `olength` as `decimalLength9(digits)`.
+static inline void append_n_digits(const uint32_t olength, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+  printf("DIGITS=%u\n", digits);
+#endif
+
+  uint32_t i = 0;
+  while (digits >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+    const uint32_t c = digits % 10000;
+#endif
+    digits /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + olength - i - 2, DIGIT_TABLE + c0, 2);
+    memcpy(result + olength - i - 4, DIGIT_TABLE + c1, 2);
+    i += 4;
+  }
+  if (digits >= 100) {
+    const uint32_t c = (digits % 100) << 1;
+    digits /= 100;
+    memcpy(result + olength - i - 2, DIGIT_TABLE + c, 2);
+    i += 2;
+  }
+  if (digits >= 10) {
+    const uint32_t c = digits << 1;
+    memcpy(result + olength - i - 2, DIGIT_TABLE + c, 2);
+  } else {
+    result[0] = (char) ('0' + digits);
+  }
+}
+
+// Convert `digits` to a sequence of decimal digits. Print the first digit, followed by a decimal
+// dot '.' followed by the remaining digits. The caller has to guarantee that:
+//   10^(olength-1) <= digits < 10^olength
+// e.g., by passing `olength` as `decimalLength9(digits)`.
+static inline void append_d_digits(const uint32_t olength, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+  printf("DIGITS=%u\n", digits);
+#endif
+
+  uint32_t i = 0;
+  while (digits >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+    const uint32_t c = digits % 10000;
+#endif
+    digits /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + olength + 1 - i - 2, DIGIT_TABLE + c0, 2);
+    memcpy(result + olength + 1 - i - 4, DIGIT_TABLE + c1, 2);
+    i += 4;
+  }
+  if (digits >= 100) {
+    const uint32_t c = (digits % 100) << 1;
+    digits /= 100;
+    memcpy(result + olength + 1 - i - 2, DIGIT_TABLE + c, 2);
+    i += 2;
+  }
+  if (digits >= 10) {
+    const uint32_t c = digits << 1;
+    result[2] = DIGIT_TABLE[c + 1];
+    result[1] = '.';
+    result[0] = DIGIT_TABLE[c];
+  } else {
+    result[1] = '.';
+    result[0] = (char) ('0' + digits);
+  }
+}
+
+// Convert `digits` to decimal and write the last `count` decimal digits to result.
+// If `digits` contains additional digits, then those are silently ignored.
+static inline void append_c_digits(const uint32_t count, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+  printf("DIGITS=%u\n", digits);
+#endif
+  // Copy pairs of digits from DIGIT_TABLE.
+  uint32_t i = 0;
+  for (; i < count - 1; i += 2) {
+    const uint32_t c = (digits % 100) << 1;
+    digits /= 100;
+    memcpy(result + count - i - 2, DIGIT_TABLE + c, 2);
+  }
+  // Generate the last digit if count is odd.
+  if (i < count) {
+    const char c = (char) ('0' + (digits % 10));
+    result[count - i - 1] = c;
+  }
+}
+
+// Convert `digits` to decimal and write the last 9 decimal digits to result.
+// If `digits` contains additional digits, then those are silently ignored.
+static inline void append_nine_digits(uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+  printf("DIGITS=%u\n", digits);
+#endif
+  if (digits == 0) {
+    memset(result, '0', 9);
+    return;
+  }
+
+  for (uint32_t i = 0; i < 5; i += 4) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+    const uint32_t c = digits % 10000;
+#endif
+    digits /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + 7 - i, DIGIT_TABLE + c0, 2);
+    memcpy(result + 5 - i, DIGIT_TABLE + c1, 2);
+  }
+  result[0] = (char) ('0' + digits);
+}
+
+static inline uint32_t indexForExponent(const uint32_t e) {
+  return (e + 15) / 16;
+}
+
+static inline uint32_t pow10BitsForIndex(const uint32_t idx) {
+  return 16 * idx + POW10_ADDITIONAL_BITS;
+}
+
+static inline uint32_t lengthForIndex(const uint32_t idx) {
+  // +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9
+  return (log10Pow2(16 * (int32_t) idx) + 1 + 16 + 8) / 9;
+}
+
+static inline int copy_special_str_printf(char* const result, const bool sign, const uint64_t mantissa) {
+#if defined(_MSC_VER)
+  // TODO: Check that -nan is expected output on Windows.
+  if (sign) {
+    result[0] = '-';
+  }
+  if (mantissa) {
+    if (mantissa < (1ull << (DOUBLE_MANTISSA_BITS - 1))) {
+      memcpy(result + sign, "nan(snan)", 9);
+      return sign + 9;
+    }
+    memcpy(result + sign, "nan", 3);
+    return sign + 3;
+  }
+#else
+  if (mantissa) {
+    memcpy(result, "nan", 3);
+    return 3;
+  }
+  if (sign) {
+    result[0] = '-';
+  }
+#endif
+  memcpy(result + sign, "Infinity", 8);
+  return sign + 8;
+}
+
+int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
+  const uint64_t bits = double_to_bits(d);
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 63; bit >= 0; --bit) {
+    printf("%d", (int) ((bits >> bit) & 1));
+  }
+  printf("\n");
+#endif
+
+  // Decode bits into sign, mantissa, and exponent.
+  const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+  const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+  const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+  // Case distinction; exit early for the easy cases.
+  if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
+    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+  }
+  if (ieeeExponent == 0 && ieeeMantissa == 0) {
+    int index = 0;
+    if (ieeeSign) {
+      result[index++] = '-';
+    }
+    result[index++] = '0';
+    if (precision > 0) {
+      result[index++] = '.';
+      memset(result + index, '0', precision);
+      index += precision;
+    }
+    return index;
+  }
+
+  int32_t e2;
+  uint64_t m2;
+  if (ieeeExponent == 0) {
+    e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+    m2 = ieeeMantissa;
+  } else {
+    e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+    m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  }
+
+#ifdef RYU_DEBUG
+  printf("-> %" PRIu64 " * 2^%d\n", m2, e2);
+#endif
+
+  int index = 0;
+  bool nonzero = false;
+  if (ieeeSign) {
+    result[index++] = '-';
+  }
+  if (e2 >= -52) {
+    const uint32_t idx = e2 < 0 ? 0 : indexForExponent((uint32_t) e2);
+    const uint32_t p10bits = pow10BitsForIndex(idx);
+    const int32_t len = (int32_t) lengthForIndex(idx);
+#ifdef RYU_DEBUG
+    printf("idx=%u\n", idx);
+    printf("len=%d\n", len);
+#endif
+    for (int32_t i = len - 1; i >= 0; --i) {
+      const uint32_t j = p10bits - e2;
+      // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+      // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+      const uint32_t digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] + i], (int32_t) (j + 8));
+      if (nonzero) {
+        append_nine_digits(digits, result + index);
+        index += 9;
+      } else if (digits != 0) {
+        const uint32_t olength = decimalLength9(digits);
+        append_n_digits(olength, digits, result + index);
+        index += olength;
+        nonzero = true;
+      }
+    }
+  }
+  if (!nonzero) {
+    result[index++] = '0';
+  }
+  if (precision > 0) {
+    result[index++] = '.';
+  }
+#ifdef RYU_DEBUG
+  printf("e2=%d\n", e2);
+#endif
+  if (e2 < 0) {
+    const int32_t idx = -e2 / 16;
+#ifdef RYU_DEBUG
+    printf("idx=%d\n", idx);
+#endif
+    const uint32_t blocks = precision / 9 + 1;
+    // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
+    int roundUp = 0;
+    uint32_t i = 0;
+    if (blocks <= MIN_BLOCK_2[idx]) {
+      i = blocks;
+      memset(result + index, '0', precision);
+      index += precision;
+    } else if (i < MIN_BLOCK_2[idx]) {
+      i = MIN_BLOCK_2[idx];
+      memset(result + index, '0', 9 * i);
+      index += 9 * i;
+    }
+    for (; i < blocks; ++i) {
+      const int32_t j = ADDITIONAL_BITS_2 + (-e2 - 16 * idx);
+      const uint32_t p = POW10_OFFSET_2[idx] + i - MIN_BLOCK_2[idx];
+      if (p >= POW10_OFFSET_2[idx + 1]) {
+        // If the remaining digits are all 0, then we might as well use memset.
+        // No rounding required in this case.
+        const uint32_t fill = precision - 9 * i;
+        memset(result + index, '0', fill);
+        index += fill;
+        break;
+      }
+      // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+      // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+      uint32_t digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j + 8);
+#ifdef RYU_DEBUG
+      printf("digits=%u\n", digits);
+#endif
+      if (i < blocks - 1) {
+        append_nine_digits(digits, result + index);
+        index += 9;
+      } else {
+        const uint32_t maximum = precision - 9 * i;
+        uint32_t lastDigit = 0;
+        for (uint32_t k = 0; k < 9 - maximum; ++k) {
+          lastDigit = digits % 10;
+          digits /= 10;
+        }
+#ifdef RYU_DEBUG
+        printf("lastDigit=%u\n", lastDigit);
+#endif
+        if (lastDigit != 5) {
+          roundUp = lastDigit > 5;
+        } else {
+          // Is m * 10^(additionalDigits + 1) / 2^(-e2) integer?
+          const int32_t requiredTwos = -e2 - (int32_t) precision - 1;
+          const bool trailingZeros = requiredTwos <= 0
+            || (requiredTwos < 60 && multipleOfPowerOf2(m2, (uint32_t) requiredTwos));
+          roundUp = trailingZeros ? 2 : 1;
+#ifdef RYU_DEBUG
+          printf("requiredTwos=%d\n", requiredTwos);
+          printf("trailingZeros=%s\n", trailingZeros ? "true" : "false");
+#endif
+        }
+        if (maximum > 0) {
+          append_c_digits(maximum, digits, result + index);
+          index += maximum;
+        }
+        break;
+      }
+    }
+#ifdef RYU_DEBUG
+    printf("roundUp=%d\n", roundUp);
+#endif
+    if (roundUp != 0) {
+      int roundIndex = index;
+      int dotIndex = 0; // '.' can't be located at index 0
+      while (true) {
+        --roundIndex;
+        char c;
+        if (roundIndex == -1 || (c = result[roundIndex], c == '-')) {
+          result[roundIndex + 1] = '1';
+          if (dotIndex > 0) {
+            result[dotIndex] = '0';
+            result[dotIndex + 1] = '.';
+          }
+          result[index++] = '0';
+          break;
+        }
+        if (c == '.') {
+          dotIndex = roundIndex;
+          continue;
+        } else if (c == '9') {
+          result[roundIndex] = '0';
+          roundUp = 1;
+          continue;
+        } else {
+          if (roundUp == 2 && c % 2 == 0) {
+            break;
+          }
+          result[roundIndex] = c + 1;
+          break;
+        }
+      }
+    }
+  } else {
+    memset(result + index, '0', precision);
+    index += precision;
+  }
+  return index;
+}
+
+void d2fixed_buffered(double d, uint32_t precision, char* result) {
+  const int len = d2fixed_buffered_n(d, precision, result);
+  result[len] = '\0';
+}
+
+char* d2fixed(double d, uint32_t precision) {
+  char* const buffer = (char*)malloc(2000);
+  const int index = d2fixed_buffered_n(d, precision, buffer);
+  buffer[index] = '\0';
+  return buffer;
+}
+
+
+
+int d2exp_buffered_n(double d, uint32_t precision, char* result) {
+  const uint64_t bits = double_to_bits(d);
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 63; bit >= 0; --bit) {
+    printf("%d", (int) ((bits >> bit) & 1));
+  }
+  printf("\n");
+#endif
+
+  // Decode bits into sign, mantissa, and exponent.
+  const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+  const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+  const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+  // Case distinction; exit early for the easy cases.
+  if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
+    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+  }
+  if (ieeeExponent == 0 && ieeeMantissa == 0) {
+    int index = 0;
+    if (ieeeSign) {
+      result[index++] = '-';
+    }
+    result[index++] = '0';
+    if (precision > 0) {
+      result[index++] = '.';
+      memset(result + index, '0', precision);
+      index += precision;
+    }
+    memcpy(result + index, "e+00", 4);
+    index += 4;
+    return index;
+  }
+
+  int32_t e2;
+  uint64_t m2;
+  if (ieeeExponent == 0) {
+    e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+    m2 = ieeeMantissa;
+  } else {
+    e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+    m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  }
+
+#ifdef RYU_DEBUG
+  printf("-> %" PRIu64 " * 2^%d\n", m2, e2);
+#endif
+
+  const bool printDecimalPoint = precision > 0;
+  ++precision;
+  int index = 0;
+  if (ieeeSign) {
+    result[index++] = '-';
+  }
+  uint32_t digits = 0;
+  uint32_t printedDigits = 0;
+  uint32_t availableDigits = 0;
+  int32_t exp = 0;
+  if (e2 >= -52) {
+    const uint32_t idx = e2 < 0 ? 0 : indexForExponent((uint32_t) e2);
+    const uint32_t p10bits = pow10BitsForIndex(idx);
+    const int32_t len = (int32_t) lengthForIndex(idx);
+#ifdef RYU_DEBUG
+    printf("idx=%u\n", idx);
+    printf("len=%d\n", len);
+#endif
+    for (int32_t i = len - 1; i >= 0; --i) {
+      const uint32_t j = p10bits - e2;
+      // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+      // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+      digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] + i], (int32_t) (j + 8));
+      if (printedDigits != 0) {
+        if (printedDigits + 9 > precision) {
+          availableDigits = 9;
+          break;
+        }
+        append_nine_digits(digits, result + index);
+        index += 9;
+        printedDigits += 9;
+      } else if (digits != 0) {
+        availableDigits = decimalLength9(digits);
+        exp = i * 9 + (int32_t) availableDigits - 1;
+        if (availableDigits > precision) {
+          break;
+        }
+        if (printDecimalPoint) {
+          append_d_digits(availableDigits, digits, result + index);
+          index += availableDigits + 1; // +1 for decimal point
+        } else {
+          result[index++] = (char) ('0' + digits);
+        }
+        printedDigits = availableDigits;
+        availableDigits = 0;
+      }
+    }
+  }
+
+  if (e2 < 0 && availableDigits == 0) {
+    const int32_t idx = -e2 / 16;
+#ifdef RYU_DEBUG
+    printf("idx=%d, e2=%d, min=%d\n", idx, e2, MIN_BLOCK_2[idx]);
+#endif
+    for (int32_t i = MIN_BLOCK_2[idx]; i < 200; ++i) {
+      const int32_t j = ADDITIONAL_BITS_2 + (-e2 - 16 * idx);
+      const uint32_t p = POW10_OFFSET_2[idx] + (uint32_t) i - MIN_BLOCK_2[idx];
+      // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+      // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+      digits = (p >= POW10_OFFSET_2[idx + 1]) ? 0 : mulShift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j + 8);
+#ifdef RYU_DEBUG
+      printf("exact=%" PRIu64 " * (%" PRIu64 " + %" PRIu64 " << 64) >> %d\n", m2, POW10_SPLIT_2[p][0], POW10_SPLIT_2[p][1], j);
+      printf("digits=%u\n", digits);
+#endif
+      if (printedDigits != 0) {
+        if (printedDigits + 9 > precision) {
+          availableDigits = 9;
+          break;
+        }
+        append_nine_digits(digits, result + index);
+        index += 9;
+        printedDigits += 9;
+      } else if (digits != 0) {
+        availableDigits = decimalLength9(digits);
+        exp = -(i + 1) * 9 + (int32_t) availableDigits - 1;
+        if (availableDigits > precision) {
+          break;
+        }
+        if (printDecimalPoint) {
+          append_d_digits(availableDigits, digits, result + index);
+          index += availableDigits + 1; // +1 for decimal point
+        } else {
+          result[index++] = (char) ('0' + digits);
+        }
+        printedDigits = availableDigits;
+        availableDigits = 0;
+      }
+    }
+  }
+
+  const uint32_t maximum = precision - printedDigits;
+#ifdef RYU_DEBUG
+  printf("availableDigits=%u\n", availableDigits);
+  printf("digits=%u\n", digits);
+  printf("maximum=%u\n", maximum);
+#endif
+  if (availableDigits == 0) {
+    digits = 0;
+  }
+  uint32_t lastDigit = 0;
+  if (availableDigits > maximum) {
+    for (uint32_t k = 0; k < availableDigits - maximum; ++k) {
+      lastDigit = digits % 10;
+      digits /= 10;
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("lastDigit=%u\n", lastDigit);
+#endif
+  // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
+  int roundUp = 0;
+  if (lastDigit != 5) {
+    roundUp = lastDigit > 5;
+  } else {
+    // Is m * 2^e2 * 10^(precision + 1 - exp) integer?
+    // precision was already increased by 1, so we don't need to write + 1 here.
+    const int32_t rexp = (int32_t) precision - exp;
+    const int32_t requiredTwos = -e2 - rexp;
+    bool trailingZeros = requiredTwos <= 0
+      || (requiredTwos < 60 && multipleOfPowerOf2(m2, (uint32_t) requiredTwos));
+    if (rexp < 0) {
+      const int32_t requiredFives = -rexp;
+      trailingZeros = trailingZeros && multipleOfPowerOf5(m2, (uint32_t) requiredFives);
+    }
+    roundUp = trailingZeros ? 2 : 1;
+#ifdef RYU_DEBUG
+    printf("requiredTwos=%d\n", requiredTwos);
+    printf("trailingZeros=%s\n", trailingZeros ? "true" : "false");
+#endif
+  }
+  if (printedDigits != 0) {
+    if (digits == 0) {
+      memset(result + index, '0', maximum);
+    } else {
+      append_c_digits(maximum, digits, result + index);
+    }
+    index += maximum;
+  } else {
+    if (printDecimalPoint) {
+      append_d_digits(maximum, digits, result + index);
+      index += maximum + 1; // +1 for decimal point
+    } else {
+      result[index++] = (char) ('0' + digits);
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("roundUp=%d\n", roundUp);
+#endif
+  if (roundUp != 0) {
+    int roundIndex = index;
+    while (true) {
+      --roundIndex;
+      char c;
+      if (roundIndex == -1 || (c = result[roundIndex], c == '-')) {
+        result[roundIndex + 1] = '1';
+        ++exp;
+        break;
+      }
+      if (c == '.') {
+        continue;
+      } else if (c == '9') {
+        result[roundIndex] = '0';
+        roundUp = 1;
+        continue;
+      } else {
+        if (roundUp == 2 && c % 2 == 0) {
+          break;
+        }
+        result[roundIndex] = c + 1;
+        break;
+      }
+    }
+  }
+  result[index++] = 'e';
+  if (exp < 0) {
+    result[index++] = '-';
+    exp = -exp;
+  } else {
+    result[index++] = '+';
+  }
+
+  if (exp >= 100) {
+    const int32_t c = exp % 10;
+    memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+    result[index + 2] = (char) ('0' + c);
+    index += 3;
+  } else {
+    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+    index += 2;
+  }
+
+  return index;
+}
+
+void d2exp_buffered(double d, uint32_t precision, char* result) {
+  const int len = d2exp_buffered_n(d, precision, result);
+  result[len] = '\0';
+}
+
+char* d2exp(double d, uint32_t precision) {
+  char* const buffer = (char*)malloc(2000);
+  const int index = d2exp_buffered_n(d, precision, buffer);
+  buffer[index] = '\0';
+  return buffer;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
new file mode 100644
index 00000000000..70857652161
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
@@ -0,0 +1,4420 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2FIXED_FULL_TABLE_H
+#define RYU_D2FIXED_FULL_TABLE_H
+
+#include <stdint.h>
+
+#define TABLE_SIZE 64
+
+static const uint16_t POW10_OFFSET[TABLE_SIZE] = {
+  0, 2, 5, 8, 12, 16, 21, 26, 32, 39,
+  46, 54, 62, 71, 80, 90, 100, 111, 122, 134,
+  146, 159, 173, 187, 202, 217, 233, 249, 266, 283,
+  301, 319, 338, 357, 377, 397, 418, 440, 462, 485,
+  508, 532, 556, 581, 606, 632, 658, 685, 712, 740,
+  769, 798, 828, 858, 889, 920, 952, 984, 1017, 1050,
+  1084, 1118, 1153, 1188
+};
+
+static const uint64_t POW10_SPLIT[1224][3] = {
+  {                    1u,    72057594037927936u,                    0u },
+  {   699646928636035157u,             72057594u,                    0u },
+  {                    1u,                    0u,                  256u },
+  { 11902091922964236229u,        4722366482869u,                    0u },
+  {  6760415703743915872u,                 4722u,                    0u },
+  {                    1u,                    0u,             16777216u },
+  { 13369850649504950658u,   309485009821345068u,                    0u },
+  { 15151142278969419334u,            309485009u,                    0u },
+  {                    1u,                    0u,          75511627776u },
+  {  4635408826454083567u,  9437866644873197963u,                 1099u },
+  { 12367138975830625353u,       20282409603651u,                    0u },
+  {  7555853734021184432u,                20282u,                    0u },
+  {                    1u,                    0u,         250037927936u },
+  {  5171444645924616995u,   699646928636035156u,             72057594u },
+  { 16672297533003297786u,  1329227995784915872u,                    0u },
+  { 14479142226848862515u,           1329227995u,                    0u },
+  {                    1u,                    0u,         181645213696u },
+  { 12214193123817091081u, 11902091922964236228u,         114366482869u },
+  { 16592893013671929435u,  6760415703743915871u,                 4722u },
+  {  4549827147718617003u,       87112285931760u,                    0u },
+  {  5274510003815168971u,                87112u,                    0u },
+  {                    1u,                    0u,          44724781056u },
+  {  9794971998307800535u, 13369850649504950657u,         209821345068u },
+  { 14720142899209240169u, 15151142278969419333u,            309485009u },
+  {  4300745446091561535u,  5708990770823839524u,                    0u },
+  { 15197156861335443364u,           5708990770u,                    0u },
+  {                    1u,                    0u,         139251286016u },
+  { 13484604155038683037u,  4635408826454083566u,          67670423947u },
+  {  8356963862052375699u, 12367138975830625352u,          58409603651u },
+  {  5850852848337610021u,  7555853734021184431u,                20282u },
+  {  2712780827214982050u,      374144419156711u,                    0u },
+  {  7732076577307618052u,               374144u,                    0u },
+  {                    1u,                    0u,          84280344576u },
+  { 17296309485351745867u,  5171444645924616994u,         160903807060u },
+  { 16598859101615853088u, 16672297533003297785u,         219784915872u },
+  {  7469952526870444257u, 14479142226848862514u,           1329227995u },
+  { 13531654022114669524u,  6073184580144670117u,                    1u },
+  { 15757609704383306943u,          24519928653u,                    0u },
+  {  9590990814237149590u,                   24u,                    0u },
+  {                    1u,                    0u,         196662132736u },
+  { 15408590707489433890u, 12214193123817091080u,          95899502532u },
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+  { 14296661839130179261u,  1600562031807691889u,         223367281473u },
+  {  9254773150378118248u,  6775147337046626723u,         217855008735u },
+  { 12174712433727875143u, 15772127322106297821u,         113224509657u },
+  {   705653145340915199u,  4141472200527441473u,          20989118065u },
+  { 17763928858962481812u, 18246007807879281266u,         143052082196u },
+  {  3982836567612046296u,   960746958654787122u,          68615608975u },
+  { 12730849277561967739u, 11355981212264408476u,         140085276740u },
+  { 17314488764367235908u,  1573078209576251480u,          64338558092u },
+  { 15951418930590301119u,  6245294478780491366u,         145407838528u },
+  {  7193356087283467261u,  7523292955659721509u,          59783592849u },
+  { 17592945625696089446u, 14454736751015226504u,          25391385403u },
+  {  3554461664875361428u,  7219786377781411315u,          97574471193u },
+  {  2213779057785318208u, 10597123082209392430u,         128375261537u },
+  {  3880940796082421148u,  6922353544343010713u,         104776154496u },
+  {  4528237545358141043u, 14317523356293377429u,         133219971944u },
+  { 11681196539088147363u,  4057766168681892716u,          25824757125u },
+  {  9835005502912643017u, 15214083611901244044u,           8454853657u },
+  {  4964088126040986696u,  8390569016883950720u,          66578989576u },
+  {  3355564873147047622u, 10680472538208175054u,          45659930434u },
+  {  1853093467828272927u, 12173567833130544926u,         213075153709u },
+  { 14755341584803008677u,  1386341248286610025u,         240676937941u },
+  {  4701571132542556621u, 12487300952797237351u,         245141746416u },
+  {  6128849686644853851u,  2614759871804869719u,          79460481781u },
+  { 12026867901170202094u,  8494389567327729476u,              8863311u },
+  { 17909760324981426303u,   163499238157084246u,                    0u },
+  {  2897692901883393664u,            163499238u,                    0u },
+  {                    1u,                    0u,         159339380736u },
+  { 12323704802554838154u,  6260469580539185877u,           8965946783u },
+  {  7135886931147821732u, 17818573101084525840u,         164119318024u },
+  { 15341283120292884947u,  2201029069927307149u,          62563676580u },
+  {  3092789040392634166u, 10397997613804897038u,         206773573694u },
+  {  8811761390822097865u, 14269915965770103740u,         171909436366u },
+  { 16870860798610218169u, 16776139909196366726u,          54338624171u },
+  { 17452041453591904833u,  6246513436385199719u,           6158620214u },
+  { 10314783684009874908u,  2926026498821554287u,         225852481030u },
+  {  4932636630789274903u, 15725499391028340981u,         121464937185u },
+  { 18143884346082124480u,  8576577277771450826u,          54841522553u },
+  {  2823209155405527322u, 15523351176022259334u,          85258861878u },
+  { 16195396106620226251u,  4775158829429176133u,         152549789013u },
+  {  1150544491807648944u, 10141817222123532461u,         212696472984u },
+  {  7767455475523884824u, 12847658900242624585u,         171743122900u },
+  { 15204378045683991808u, 13708197964460514654u,         104105793195u },
+  { 17239732561718805622u,  1951540006613246931u,         153540978792u },
+  { 12886430624522800062u,  9979297327280092198u,          49833822361u },
+  { 18162250541178258136u, 15381307706282553683u,          16544130097u },
+  { 17028935366700158084u, 10037428657543061176u,          17140126480u },
+  { 16075467823964198637u,  2584877324547208667u,         178061074449u },
+  {  9803858825574498304u,  1126624732730703575u,          80081372850u },
+  { 17464070808143041817u,  1501064139624981019u,          35282958416u },
+  { 17682703471239266776u,  5219661484955306108u,         113289319203u },
+  { 18147688354161351336u,  5336997298570282211u,          56660882545u },
+  {  6663423873348080051u, 12191131175733833361u,         241200960568u },
+  {  9417270363716235133u,  3707068178994436535u,          61273516273u },
+  {  9295013721571344179u,  5045484691732942021u,          75804906301u },
+  {  6199479138350037783u, 14847900542908711231u,          73493163339u },
+  {   887603005365085688u,  9097257915916965134u,         226134008905u },
+  {   333989628642975696u,  2472027983230314216u,          68865979874u },
+  {  4620735991403939439u, 15974509111133272204u,                  580u },
+  { 12418523063962801201u,       10715086071862u,                    0u },
+  {  1587745622680169419u,                10715u,                    0u },
+  {                    1u,                    0u,         225655914496u },
+  { 10968905082284365638u, 12099486841948187398u,          72288392929u },
+  { 14076907092801977812u,  5319910566029976327u,         139626084168u },
+  {  3438322122816124202u, 11549214421017285863u,          77108354699u },
+  { 14645413324829073676u,  1998791413186046699u,           8925646925u },
+  { 12271281439492289999u, 17075171930090011209u,         208821732872u },
+  {  6233751789862708246u, 15158296003813501473u,         176073730256u },
+  {  1962644459455827991u,  1360083178079384114u,         155334366896u },
+  {  8726934184642952500u,  6167980558592741157u,          60196792475u },
+  {  4531087719737475147u,  3630180428124865652u,           6123412028u },
+  {   481513520412720775u,  2276550099763657676u,         110022063878u },
+  {   992149349835802669u,   407006713016100654u,          68772091758u },
+  { 11165474436676191361u, 14242579061653496001u,         190972772932u },
+  { 10240785855143707184u, 17944493332678643703u,          76053515454u },
+  { 10059329918238932466u,   987185901870869451u,          61302420044u },
+  { 14791716450947031886u,  5578665155415167744u,          21262876221u },
+  { 15378882314737417403u,  4849210377429577535u,         125586119445u },
+  { 14726970229242271128u, 10811995403388891861u,         117382285949u },
+  {  5090110549507128156u,  7051931074990177293u,          76110091637u },
+  { 17185220781106503841u,  2030832259446664274u,         223329028940u },
+  {  9858517691519529306u,  6069512651054767895u,         162575098847u },
+  {  5595905546638020703u, 10608701253763958798u,         212851101602u },
+  { 15555173226968030256u, 15700053443426906716u,         111962756308u },
+  { 10745236628845355771u, 17759719234725541221u,          16823306351u },
+  {  9973314042399760760u, 15187321568916405209u,          47598488080u },
+  {  4374506813558796576u, 11040156458113129593u,         114151827759u },
+  { 15960826480426749933u,  2800727824598008496u,           5162480498u },
+  {  9636454862798615738u,  2997236166375604478u,          14339360261u },
+  { 17973331528911319269u,  6260091886451512840u,          63952637454u },
+  {  7366495200039369602u, 17573059315228347473u,          78407630399u },
+  { 10505831326526933399u,  7519453664590169250u,         176857031246u },
+  {  2803218632575724145u, 15809436065653866528u,             38067632u },
+  {  8425731874431741636u,   702223880805592151u,                    0u },
+  { 14860552245711912111u,            702223880u,                    0u },
+  {                    1u,                    0u,         234012409856u },
+  {  6993664200669526994u,   228921437623588921u,         212119037930u },
+  {  4065363582031999356u,  2195862230003073883u,          71052052948u },
+  {  6899780515342669867u,   960207412233973687u,         189133594695u },
+  { 17713500890201844939u,  2464387149230492478u,         247196883901u },
+  {  6445781125105107086u,  3631866936444955212u,          93085560055u },
+  { 13563044070717478571u,  1578304441149380226u,         223986111069u },
+  { 13167612994149348885u, 18190538519673445180u,         153068901087u },
+  {  5505463469596727288u,  1271000736479934748u,          96991663513u },
+  { 12125446212518819372u, 18292963032817745633u,         151930679904u },
+  { 12537707724735421794u, 17168014021925537454u,         165978316695u },
+  { 15173675086703777069u, 18046757712870378948u,         167805453733u },
+  { 13535510174093048476u, 14857998893911743219u,           7646922151u },
+  { 10698912997087096629u, 11933607369968684574u,         179188857095u },
+  { 16952559548431933861u,  3483798509902859161u,         107400007091u },
+  { 13528255827744249993u,  7378828438829845830u,          75856039275u },
+  { 14122167436324771955u, 15791137430347699564u,          11923964747u },
+  { 13071007137740038297u, 17044141236829932640u,         221491992075u },
+  { 13011887609328904025u,  9075651910862456483u,          46965547485u },
+  {  3116434332871336590u, 17811207355884564094u,          59240619054u },
+  {  9050993820536772770u,  4438638126207305936u,          57678058555u },
+  { 11993719123438634238u, 12507972635512950184u,         225794626361u },
+  {  1414857165879849301u, 14658269128098109407u,         119197456865u },
+  { 13819438220812375094u,  3642436268910286110u,         196205082231u },
+  {  6073063033888264440u,  3783099432964819560u,          54514864836u },
+  {  6828883869150720294u,  9497579866027539637u,         222184053046u },
+  {  4548265621068768345u,  3395179445046271360u,         152321926878u },
+  { 10422524923581371874u,  5938502732309497275u,         224314075544u },
+  {  1858996082510682634u,  5793671185917606254u,         224048207584u },
+  {   890276727450878316u,   889272970253526587u,          90465891296u },
+  {  3886008133802710905u,  8594177504370135500u,         102399764570u },
+  {   612074409233016757u,  7374354721120724711u,         190800386918u },
+  {  3927020336901729264u, 14764532643665507566u,                 2494u },
+  {  5298603480094474942u,       46020944252475u,                    0u },
+  { 17418383752590430025u,                46020u,                    0u },
+  {                    1u,                    0u,          45292322816u },
+  {  8973799690601597929u,  5392404173658087694u,         121269781293u },
+  {  1343055462055792431u,  4976586473237854315u,          83342007929u },
+  { 17425118728683169659u,  6308932742419013568u,          51261934931u },
+  { 18389781726026675967u,  4831846642430703058u,         102983344691u },
+  {   272526939565961561u, 18139507855949846900u,         231263777382u },
+  { 11293026845930963228u,  4865833876326628409u,         113775023591u },
+  { 13997416438903902597u, 14296661839130179260u,         163501702257u },
+  {  6186605805999441184u,  9254773150378118247u,         221659992483u },
+  {  4401776373281836138u, 12174712433727875142u,          65038253533u },
+  { 16338917089754547008u,   705653145340915198u,         114962984513u },
+  { 13337700757935003056u, 17763928858962481811u,          50215910002u },
+  { 14612496890816348693u,  3982836567612046295u,         156690140722u },
+  {  3219935399907691719u, 12730849277561967738u,          88938620316u },
+  { 10887238730052330387u, 17314488764367235907u,         102864728152u },
+  {   360256418697768294u, 15951418930590301118u,          37389952614u },
+  {   321440824631118565u,  7193356087283467260u,         136953715493u },
+  { 10069228080701402580u, 17592945625696089445u,         243192687752u },
+  {  9428069607611622975u,  3554461664875361427u,          46120009203u },
+  { 14736799017468812344u,  2213779057785318207u,         153210386222u },
+  { 10875332567307979280u,  3880940796082421147u,         149245476249u },
+  {  4611492910339012807u,  4528237545358141042u,         108633238933u },
+  { 10743508637597314786u, 11681196539088147362u,         140533156716u },
+  {  9356196315668016028u,  9835005502912643016u,         128269103756u },
+  { 15755598617722189347u,  4964088126040986695u,         206181905536u },
+  {  1275276394173375542u,  3355564873147047621u,          30100456398u },
+  { 12644999363867216251u,  1853093467828272926u,         105799888670u },
+  {  4553830511509832021u, 14755341584803008676u,         103254872681u },
+  {  8869400642218174412u,  4701571132542556620u,          87332245607u },
+  { 16570849151159054040u,  6128849686644853850u,          68651977815u },
+  { 16127119334101797673u, 12026867901170202093u,          86970890052u },
+  {  9686867250420930550u, 17909760324981426302u,         230157084246u },
+  { 10678226869774428035u,  2897692901883393663u,            163499238u },
+  {  7767227962910162068u,  3016028602530220424u,                    0u },
+  {  9780840471948993674u,           3016028602u,                    0u },
+  {                    1u,                    0u,         213668069376u },
+  {  6288709332106746357u, 12323704802554838153u,          16386837205u },
+  {  9066785620141948673u,  7135886931147821731u,         141831652624u },
+  {  8442375916704414909u, 15341283120292884946u,          14167660429u },
+  { 11604629218100425803u,  3092789040392634165u,         188477686542u },
+  {  3877248044010875762u,  8811761390822097864u,         134914571196u },
+  { 16435137704395217283u, 16870860798610218168u,         103946077062u },
+  { 14994442577577813271u, 17452041453591904832u,         111559165543u },
+  {  4410105917142436089u, 10314783684009874907u,         245267398767u },
+  {  4632574728444936970u,  4932636630789274902u,         202983581941u },
+  {  9117147535650050359u, 18143884346082124479u,         134153046474u },
+  {   588939301256904809u,  2823209155405527321u,          69877954182u },
+  {   324393982565305683u, 16195396106620226250u,         173062371141u },
+  {  9380909186923521175u,  1150544491807648943u,          73421074605u },
+  {  4463385697777230217u,  7767455475523884823u,          94824230985u },
+  { 16378985502426333808u, 15204378045683991807u,         211934567774u },
+  { 18210894922387834354u, 17239732561718805621u,          38698574803u },
+  {  1555748035329493205u, 12886430624522800061u,          83984577574u },
+  {  4277055533891898507u, 18162250541178258135u,         184923140435u },
+  { 11574429772510874408u, 17028935366700158083u,         219871452856u },
+  { 17391099253493808815u, 16075467823964198636u,         215531468251u },
+  {  5791212393959129882u,  9803858825574498303u,          27946729175u },
+  { 11254268231455680880u, 17464070808143041816u,         124958581275u },
+  { 16355477587312235322u, 17682703471239266775u,         227983788156u },
+  {  2411485149249320633u, 18147688354161351335u,         145361224931u },
+  { 12763114642070638360u,  6663423873348080050u,         183510511249u },
+  {  1147543073987366419u,  9417270363716235132u,         197503883703u },
+  {  8410777835225272692u,  9295013721571344178u,          63336074437u },
+  {  8134725822306818018u,  6199479138350037782u,          14048117055u },
+  {  8899607004752328377u,   887603005365085687u,         232018105614u },
+  {   690976506652396830u,   333989628642975695u,         140250490600u },
+  { 12281570945595192074u,  4620735991403939438u,          54673209484u },
+  { 12592957291365552899u, 12418523063962801200u,         219086071862u },
+  { 13595807339013970272u,  1587745622680169418u,                10715u },
+  {  9698096389749839992u,      197658450495420u,                    0u },
+  {  8310173728816391804u,               197658u,                    0u },
+};
+
+#define TABLE_SIZE_2 69
+#define ADDITIONAL_BITS_2 120
+
+static const uint16_t POW10_OFFSET_2[TABLE_SIZE_2] = {
+     0,    2,    6,   12,   20,   29,   40,   52,   66,   80,
+    95,  112,  130,  150,  170,  192,  215,  240,  265,  292,
+   320,  350,  381,  413,  446,  480,  516,  552,  590,  629,
+   670,  712,  755,  799,  845,  892,  940,  989, 1040, 1092,
+  1145, 1199, 1254, 1311, 1369, 1428, 1488, 1550, 1613, 1678,
+  1743, 1810, 1878, 1947, 2017, 2088, 2161, 2235, 2311, 2387,
+  2465, 2544, 2625, 2706, 2789, 2873, 2959, 3046, 3133
+};
+
+static const uint8_t MIN_BLOCK_2[TABLE_SIZE_2] = {
+     0,    0,    0,    0,    0,    0,    1,    1,    2,    3,
+     3,    4,    4,    5,    5,    6,    6,    7,    7,    8,
+     8,    9,    9,   10,   11,   11,   12,   12,   13,   13,
+    14,   14,   15,   15,   16,   16,   17,   17,   18,   19,
+    19,   20,   20,   21,   21,   22,   22,   23,   23,   24,
+    24,   25,   26,   26,   27,   27,   28,   28,   29,   29,
+    30,   30,   31,   31,   32,   32,   33,   34,    0
+};
+
+static const uint64_t POW10_SPLIT_2[3133][3] = {
+  {                    0u,                    0u,              3906250u },
+  {                    0u,                    0u,         202000000000u },
+  {                    0u, 11153727427136454656u,                   59u },
+  {                    0u,  7205759403792793600u,          59604644775u },
+  {                    0u,                    0u,         167390625000u },
+  {                    0u,                    0u,         232000000000u },
+  {                    0u,    16777216000000000u,                    0u },
+  {                    0u, 12945425605062557696u,               909494u },
+  {                    0u,  4388757836872548352u,         182701772928u },
+  {                    0u,  1152921504606846976u,         128237915039u },
+  {                    0u,                    0u,         159062500000u },
+  {                    0u,                    0u,         160000000000u },
+  {                    0u,         256000000000u,                    0u },
+  {                    0u, 16192327041775828992u,                   13u },
+  {                    0u, 15024075324038053888u,          13877787807u },
+  {                    0u,  5449091666327633920u,         159814456755u },
+  {                    0u,  2494994193563254784u,         179295395851u },
+  {                    0u,  4611686018427387904u,          11135253906u },
+  {                    0u,                    0u,         146250000000u },
+  {                    0u,                    0u,         128000000000u },
+  {                    0u,              3906250u,                    0u },
+  {                    0u,     3906250000000000u,                    0u },
+  {                    0u,  4368439412768899072u,               211758u },
+  {                    0u,  1563676642168012800u,          46236813575u },
+  {                    0u, 11532349341402398720u,           7084767080u },
+  {                    0u,  9048364970084925440u,         104625169910u },
+  {                    0u, 16609275425742389248u,         246490512847u },
+  {                    0u,                    0u,         207900390625u },
+  {                    0u,                    0u,         225000000000u },
+  { 11153727427136454656u,                   59u,                    0u },
+  {  7205759403792793600u,          59604644775u,                    0u },
+  {                    0u,  4264412554261970152u,                    3u },
+  {                    0u, 14485570586272534528u,           3231174267u },
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+  { 12227321512794715397u, 14431217812333089675u,         120893548555u },
+  {  7241061891859170651u,  3452349151135392267u,          11782317885u },
+  { 13148571323079237489u,  9075317899834447999u,          61187152222u },
+  { 12509763434355012654u,  2764331337978901575u,          94491973969u },
+  { 11812768946960181977u,  1942890683708857202u,          81149854702u },
+  { 14170358803552564832u,   165089169728028447u,         238105324315u },
+  { 18179989524780635952u, 15193620741871233073u,          27008949501u },
+  { 17091718978514754901u, 14995000835194145926u,         253823647830u },
+  {  7394768384359232459u,  1788823614552255558u,          86812880624u },
+  {  6778628272692852803u,  8384901184618498845u,         240096972322u },
+  { 18193335045875234320u,   405511217862281310u,          34454546404u },
+  {  1378519212560967521u,  3111530463755196557u,         228021982807u },
+  {  4677732610631043584u,  7893558450035460812u,          87168676404u },
+  { 17296098591070486528u,   156573858237402216u,          52427910661u },
+  {  7343735382392963072u, 15915324019419451223u,           5008487885u },
+  { 14525996728454217728u, 16293363012778802804u,         205862771443u },
+  {  9691359370008330240u, 14342105318291351412u,         243883264978u },
+  {  3044433348102455296u,  3788398842525387052u,         210777487087u },
+  {  9223372036854775808u, 14118764407048307670u,         239205369512u },
+  {                    0u,  2705021334614720768u,         168765379752u },
+  {                    0u,  7017988973805568000u,         168146639500u },
+  {                    0u, 10956732053634154496u,         140380445944u },
+  {                    0u, 14657517938546835456u,         248593965634u },
+  {                    0u, 11268868284797157376u,          66794585639u },
+  {                    0u, 14600669991935148032u,          39610886573u },
+  {                    0u,  4611686018427387904u,         173791503906u },
+  {                    0u,                    0u,          34250000000u },
+  {                    0u,                    0u,         128000000000u },
+  {  8201586317771250746u,           1424047269u,                    0u },
+  {  3278889188817135834u,  1424047269444608885u,                    0u },
+  {  1710725240251040430u,  3001188830946823627u,             77197757u },
+  {  1850175733663425006u,  9732296932705387049u,         189162694772u },
+  {  9147599666163914249u, 16337535782679529459u,         116527588873u },
+  { 10221885933644344166u,  7969742269895046547u,           9885659589u },
+  { 14901479793736678101u,  2923592083903829642u,         197432040594u },
+  {  5181831442059703136u,  8144196241160608534u,         146158488244u },
+  {  6396246577759793483u, 16431078457793424253u,         180441497762u },
+  { 14167229556464870447u,   202362949592775653u,         162890730548u },
+  {  2969982933326311854u,  8835125248522947981u,          52010970117u },
+  {  7892677766222018881u,  7959873808777345113u,           5478953099u },
+  {   798698968922663621u, 14929747122315126151u,         139431505623u },
+  { 15926812109043458972u,  4310328817360515349u,         215809343213u },
+  {  8663842590352697437u,  7294899422760201126u,         237233663393u },
+  { 17093523026636671168u,  2047461597291187207u,         161395457290u },
+  {   839764004742743203u, 10942374468813517900u,          10110993115u },
+  { 16894643909298232323u, 10364795403063433969u,         219593187308u },
+  {  9066702926218949317u, 12330859528790939137u,         236561876684u },
+  {  9119392417260546810u,  8973160144879916806u,         204668457234u },
+  {  9723021096578315109u,  2895354388547509877u,          18486435986u },
+  { 14787464248751217597u, 16766844772497556429u,         146156957475u },
+  {  3733434565920249133u,  7442407174620948827u,          35908932476u },
+  {  6643788868836820841u,  6683013428676659077u,         124403453701u },
+  {  4729646697422664063u, 16713703375071907588u,           5362286883u },
+  {  4090144564201555829u,  8791044883080637861u,          35906051675u },
+  {  2109480737093400002u,   602844107089214413u,          91476563498u },
+  { 16577155033369419739u,  9754832281172880875u,          42032680244u },
+  {   745377248603805917u, 10587846778003503903u,          52528810517u },
+  { 11305561465807999667u, 17206244172922947013u,          21573968323u },
+  {  2211245518782892177u, 11620628420699303875u,         195932752365u },
+  { 14170095199249735666u, 17864732368219338611u,         237629955528u },
+  { 17849973668116118927u,  4146383014621345887u,         200968449082u },
+  {  9020960204585720001u, 11445705075042688243u,          58224775873u },
+  { 10807134002871850916u,  7369147888966546592u,         193620472915u },
+  {  3925122626254791201u,  9762476865090597796u,          83399482307u },
+  { 17208463291312718997u,  5507001428194242827u,         195529224931u },
+  {  5145077219589447653u, 11371471148365328344u,         227298535145u },
+  { 17602397765035489468u,  3148788104946538618u,         233616448686u },
+  { 16422643262490753377u,  3762722308424507574u,         174170696145u },
+  {  2902509461400906224u,  1156171244825745915u,         209203977585u },
+  {  3422418805967265206u, 14208921674868257865u,         113062676168u },
+  {  4228874576277237392u,  7903080886897905503u,         200770267187u },
+  {  2553488530807495751u,  6367240794154270982u,          51428426873u },
+  { 11546099176912486413u,  1623672396662369850u,         121345168815u },
+  { 10460791037534167991u, 18323231215381674394u,         175088019456u },
+  {  8127117908566000904u,  9842279843006544554u,            993304354u },
+  { 11541304458088287306u,  7376839231308610600u,          34533551059u },
+  {  6249718665174839700u,   609751749293657672u,         211399899256u },
+  { 13102508413386290995u, 10386457966860989799u,         120033054708u },
+  {  6274675218640661911u, 11160336020836149780u,         244563051014u },
+  {  3404497118599817167u, 17947559933847409193u,           6605003027u },
+  { 11258566093988562335u, 10229787001712704590u,          19972939173u },
+  { 16762592482501635397u, 10441677090043619866u,         165554557864u },
+  {  5550125446725071998u,  4996681336392922375u,         168566044449u },
+  {  6370033225258510318u,   124497102381021895u,          33270870638u },
+  {  1503521728674735398u,  8180812057779384577u,         110006749001u },
+  {  4250415082606384364u,  5294232873532946716u,          73443482710u },
+  {  6020091901030562974u,  2885620189169448039u,          86287000939u },
+  { 16288222967151527138u, 16662526875008170507u,         107156429783u },
+  {  6377016228656203782u, 15663095032402672480u,         215903277391u },
+  {  8378856515587563750u,  1824281504410546614u,          79849098083u },
+  { 15812881490200838483u,  9506565509584809953u,          99098894498u },
+  {  4548570371183413652u, 16941136942345070055u,         162515351948u },
+  { 16731431495283420383u, 15924115693705937725u,         140918380873u },
+  { 14737727629551135532u,  9247807690406628462u,          73863248041u },
+  { 12413722258104293893u,  7993916633864834871u,         169501324659u },
+  {   800899742400762438u,  1018504409177639408u,         115433351089u },
+  {   603197008376033550u, 12097800686634130718u,         177055213234u },
+  {  6380777281587743935u,  6221488888422637551u,         178655823089u },
+  { 10001440249018225388u,  8229322865256080421u,         241337267588u },
+  {  5505914461980436708u,  7927745108183101786u,         132446112486u },
+  {  1105464290051876864u,  8488683721235326653u,         230429763923u },
+  {  4500443576769970176u, 11165516518170922283u,          83460172466u },
+  {  2843045143185981440u,  5463648141113596927u,         178605283863u },
+  {   660949699682893824u,  3958440403860778042u,          23296184959u },
+  {   276549164618219520u,  5091534813990256011u,         127214587484u },
+  {  4683743612465315840u,  6100166970623291280u,          92276012655u },
+  {                    0u,  1913011027739012426u,         111330690714u },
+  {                    0u, 11310957650604221440u,         154103704535u },
+  {                    0u, 16303817257009020928u,         215613168242u },
+  {                    0u,  9090406322154766336u,         114883831704u },
+  {                    0u,  3003279315069566976u,         152492791914u },
+  {                    0u, 16582887146675765248u,         106162808097u },
+  {                    0u,  9691746398101307392u,          33898960113u },
+  {                    0u,                    0u,         241525390625u },
+  {                    0u,                    0u,          33000000000u },
+};
+
+#endif // RYU_D2FIXED_FULL_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2s.c b/libstdc++-v3/src/c++17/ryu/d2s.c
new file mode 100644
index 00000000000..aa0da52da71
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s.c
@@ -0,0 +1,509 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+//
+// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
+//     depending on your compiler.
+//
+// -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every
+//     required power of 5, only store every 26th entry, and compute
+//     intermediate values with a multiplication. This reduces the lookup table
+//     size by about 10x (only one case, and only double) at the cost of some
+//     performance. Currently requires MSVC intrinsics.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef RYU_DEBUG
+#include <inttypes.h>
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+
+// Include either the small or the full lookup tables depending on the mode.
+#if defined(RYU_OPTIMIZE_SIZE)
+#include "ryu/d2s_small_table.h"
+#else
+#include "ryu/d2s_full_table.h"
+#endif
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+static inline uint32_t decimalLength17(const uint64_t v) {
+  // This is slightly faster than a loop.
+  // The average output length is 16.38 digits, so we check high-to-low.
+  // Function precondition: v is not an 18, 19, or 20-digit number.
+  // (17 digits are sufficient for round-tripping.)
+  assert(v < 100000000000000000L);
+  if (v >= 10000000000000000L) { return 17; }
+  if (v >= 1000000000000000L) { return 16; }
+  if (v >= 100000000000000L) { return 15; }
+  if (v >= 10000000000000L) { return 14; }
+  if (v >= 1000000000000L) { return 13; }
+  if (v >= 100000000000L) { return 12; }
+  if (v >= 10000000000L) { return 11; }
+  if (v >= 1000000000L) { return 10; }
+  if (v >= 100000000L) { return 9; }
+  if (v >= 10000000L) { return 8; }
+  if (v >= 1000000L) { return 7; }
+  if (v >= 100000L) { return 6; }
+  if (v >= 10000L) { return 5; }
+  if (v >= 1000L) { return 4; }
+  if (v >= 100L) { return 3; }
+  if (v >= 10L) { return 2; }
+  return 1;
+}
+
+// A floating decimal representing m * 10^e.
+typedef struct floating_decimal_64 {
+  uint64_t mantissa;
+  // Decimal exponent's range is -324 to 308
+  // inclusive, and can fit in a short if needed.
+  int32_t exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
+  int32_t e2;
+  uint64_t m2;
+  if (ieeeExponent == 0) {
+    // We subtract 2 so that the bounds computation has 2 additional bits.
+    e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+    m2 = ieeeMantissa;
+  } else {
+    e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+    m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  }
+  const bool even = (m2 & 1) == 0;
+  const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+  printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
+#endif
+
+  // Step 2: Determine the interval of valid decimal representations.
+  const uint64_t mv = 4 * m2;
+  // Implicit bool -> int conversion. True is 1, false is 0.
+  const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+  // We would compute mp and mm like this:
+  // uint64_t mp = 4 * m2 + 2;
+  // uint64_t mm = mv - 1 - mmShift;
+
+  // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+  uint64_t vr, vp, vm;
+  int32_t e10;
+  bool vmIsTrailingZeros = false;
+  bool vrIsTrailingZeros = false;
+  if (e2 >= 0) {
+    // I tried special-casing q == 0, but there was no effect on performance.
+    // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
+    const uint32_t q = log10Pow2(e2) - (e2 > 3);
+    e10 = (int32_t) q;
+    const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
+    const int32_t i = -e2 + (int32_t) q + k;
+#if defined(RYU_OPTIMIZE_SIZE)
+    uint64_t pow5[2];
+    double_computeInvPow5(q, pow5);
+    vr = mulShiftAll64(m2, pow5, i, &vp, &vm, mmShift);
+#else
+    vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+    if (q <= 21) {
+      // This should use q <= 22, but I think 21 is also safe. Smaller values
+      // may still be safe, but it's more difficult to reason about them.
+      // Only one of mp, mv, and mm can be a multiple of 5, if any.
+      const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
+      if (mvMod5 == 0) {
+        vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+      } else if (acceptBounds) {
+        // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+        // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+        // <=> true && pow5Factor(mm) >= q, since e2 >= q.
+        vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+      } else {
+        // Same as min(e2 + 1, pow5Factor(mp)) >= q.
+        vp -= multipleOfPowerOf5(mv + 2, q);
+      }
+    }
+  } else {
+    // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+    const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
+    e10 = (int32_t) q + e2;
+    const int32_t i = -e2 - (int32_t) q;
+    const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+    const int32_t j = (int32_t) q - k;
+#if defined(RYU_OPTIMIZE_SIZE)
+    uint64_t pow5[2];
+    double_computePow5(i, pow5);
+    vr = mulShiftAll64(m2, pow5, j, &vp, &vm, mmShift);
+#else
+    vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
+    printf("%u %d %d %d\n", q, i, k, j);
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+    if (q <= 1) {
+      // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+      // mv = 4 * m2, so it always has at least two trailing 0 bits.
+      vrIsTrailingZeros = true;
+      if (acceptBounds) {
+        // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+        vmIsTrailingZeros = mmShift == 1;
+      } else {
+        // mp = mv + 2, so it always has at least one trailing 0 bit.
+        --vp;
+      }
+    } else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
+      // We want to know if the full product has at least q trailing zeros.
+      // We need to compute min(p2(mv), p5(mv) - e2) >= q
+      // <=> p2(mv) >= q && p5(mv) - e2 >= q
+      // <=> p2(mv) >= q (because -e2 >= q)
+      vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
+#ifdef RYU_DEBUG
+      printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("e10=%d\n", e10);
+  printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+  printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+  printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+  // Step 4: Find the shortest decimal representation in the interval of valid representations.
+  int32_t removed = 0;
+  uint8_t lastRemovedDigit = 0;
+  uint64_t output;
+  // On average, we remove ~2 digits.
+  if (vmIsTrailingZeros || vrIsTrailingZeros) {
+    // General case, which happens rarely (~0.7%).
+    for (;;) {
+      const uint64_t vpDiv10 = div10(vp);
+      const uint64_t vmDiv10 = div10(vm);
+      if (vpDiv10 <= vmDiv10) {
+        break;
+      }
+      const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+      const uint64_t vrDiv10 = div10(vr);
+      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+      vmIsTrailingZeros &= vmMod10 == 0;
+      vrIsTrailingZeros &= lastRemovedDigit == 0;
+      lastRemovedDigit = (uint8_t) vrMod10;
+      vr = vrDiv10;
+      vp = vpDiv10;
+      vm = vmDiv10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+    printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+    if (vmIsTrailingZeros) {
+      for (;;) {
+        const uint64_t vmDiv10 = div10(vm);
+        const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+        if (vmMod10 != 0) {
+          break;
+        }
+        const uint64_t vpDiv10 = div10(vp);
+        const uint64_t vrDiv10 = div10(vr);
+        const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+        vrIsTrailingZeros &= lastRemovedDigit == 0;
+        lastRemovedDigit = (uint8_t) vrMod10;
+        vr = vrDiv10;
+        vp = vpDiv10;
+        vm = vmDiv10;
+        ++removed;
+      }
+    }
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
+      // Round even if the exact number is .....50..0.
+      lastRemovedDigit = 4;
+    }
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+  } else {
+    // Specialized for the common case (~99.3%). Percentages below are relative to this.
+    bool roundUp = false;
+    const uint64_t vpDiv100 = div100(vp);
+    const uint64_t vmDiv100 = div100(vm);
+    if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
+      const uint64_t vrDiv100 = div100(vr);
+      const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
+      roundUp = vrMod100 >= 50;
+      vr = vrDiv100;
+      vp = vpDiv100;
+      vm = vmDiv100;
+      removed += 2;
+    }
+    // Loop iterations below (approximately), without optimization above:
+    // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
+    // Loop iterations below (approximately), with optimization above:
+    // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+    for (;;) {
+      const uint64_t vpDiv10 = div10(vp);
+      const uint64_t vmDiv10 = div10(vm);
+      if (vpDiv10 <= vmDiv10) {
+        break;
+      }
+      const uint64_t vrDiv10 = div10(vr);
+      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+      roundUp = vrMod10 >= 5;
+      vr = vrDiv10;
+      vp = vpDiv10;
+      vm = vmDiv10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + (vr == vm || roundUp);
+  }
+  const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+  printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+  printf("O=%" PRIu64 "\n", output);
+  printf("EXP=%d\n", exp);
+#endif
+
+  floating_decimal_64 fd;
+  fd.exponent = exp;
+  fd.mantissa = output;
+  return fd;
+}
+
+static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
+  // Step 5: Print the decimal representation.
+  int index = 0;
+  if (sign) {
+    result[index++] = '-';
+  }
+
+  uint64_t output = v.mantissa;
+  const uint32_t olength = decimalLength17(output);
+
+#ifdef RYU_DEBUG
+  printf("DIGITS=%" PRIu64 "\n", v.mantissa);
+  printf("OLEN=%u\n", olength);
+  printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+  // Print the decimal digits.
+  // The following code is equivalent to:
+  // for (uint32_t i = 0; i < olength - 1; ++i) {
+  //   const uint32_t c = output % 10; output /= 10;
+  //   result[index + olength - i] = (char) ('0' + c);
+  // }
+  // result[index] = '0' + output % 10;
+
+  uint32_t i = 0;
+  // We prefer 32-bit operations, even on 64-bit platforms.
+  // We have at most 17 digits, and uint32_t can store 9 digits.
+  // If output doesn't fit into uint32_t, we cut off 8 digits,
+  // so the rest will fit into uint32_t.
+  if ((output >> 32) != 0) {
+    // Expensive 64-bit division.
+    const uint64_t q = div1e8(output);
+    uint32_t output2 = ((uint32_t) output) - 100000000 * ((uint32_t) q);
+    output = q;
+
+    const uint32_t c = output2 % 10000;
+    output2 /= 10000;
+    const uint32_t d = output2 % 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    const uint32_t d0 = (d % 100) << 1;
+    const uint32_t d1 = (d / 100) << 1;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+    memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+    memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+    i += 8;
+  }
+  uint32_t output2 = (uint32_t) output;
+  while (output2 >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = output2 - 10000 * (output2 / 10000);
+#else
+    const uint32_t c = output2 % 10000;
+#endif
+    output2 /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+    i += 4;
+  }
+  if (output2 >= 100) {
+    const uint32_t c = (output2 % 100) << 1;
+    output2 /= 100;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+    i += 2;
+  }
+  if (output2 >= 10) {
+    const uint32_t c = output2 << 1;
+    // We can't use memcpy here: the decimal dot goes between these two digits.
+    result[index + olength - i] = DIGIT_TABLE[c + 1];
+    result[index] = DIGIT_TABLE[c];
+  } else {
+    result[index] = (char) ('0' + output2);
+  }
+
+  // Print decimal point if needed.
+  if (olength > 1) {
+    result[index + 1] = '.';
+    index += olength + 1;
+  } else {
+    ++index;
+  }
+
+  // Print the exponent.
+  result[index++] = 'E';
+  int32_t exp = v.exponent + (int32_t) olength - 1;
+  if (exp < 0) {
+    result[index++] = '-';
+    exp = -exp;
+  }
+
+  if (exp >= 100) {
+    const int32_t c = exp % 10;
+    memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+    result[index + 2] = (char) ('0' + c);
+    index += 3;
+  } else if (exp >= 10) {
+    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+    index += 2;
+  } else {
+    result[index++] = (char) ('0' + exp);
+  }
+
+  return index;
+}
+
+static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
+  floating_decimal_64* const v) {
+  const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+  const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+  if (e2 > 0) {
+    // f = m2 * 2^e2 >= 2^53 is an integer.
+    // Ignore this case for now.
+    return false;
+  }
+
+  if (e2 < -52) {
+    // f < 1.
+    return false;
+  }
+
+  // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
+  // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
+  const uint64_t mask = (1ull << -e2) - 1;
+  const uint64_t fraction = m2 & mask;
+  if (fraction != 0) {
+    return false;
+  }
+
+  // f is an integer in the range [1, 2^53).
+  // Note: mantissa might contain trailing (decimal) 0's.
+  // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
+  v->mantissa = m2 >> -e2;
+  v->exponent = 0;
+  return true;
+}
+
+int d2s_buffered_n(double f, char* result) {
+  // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
+  const uint64_t bits = double_to_bits(f);
+
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 63; bit >= 0; --bit) {
+    printf("%d", (int) ((bits >> bit) & 1));
+  }
+  printf("\n");
+#endif
+
+  // Decode bits into sign, mantissa, and exponent.
+  const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+  const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+  const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+  // Case distinction; exit early for the easy cases.
+  if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
+    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+  }
+
+  floating_decimal_64 v;
+  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+  if (isSmallInt) {
+    // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
+    // For scientific notation we need to move these zeros into the exponent.
+    // (This is not needed for fixed-point notation, so it might be beneficial to trim
+    // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
+    for (;;) {
+      const uint64_t q = div10(v.mantissa);
+      const uint32_t r = ((uint32_t) v.mantissa) - 10 * ((uint32_t) q);
+      if (r != 0) {
+        break;
+      }
+      v.mantissa = q;
+      ++v.exponent;
+    }
+  } else {
+    v = d2d(ieeeMantissa, ieeeExponent);
+  }
+
+  return to_chars(v, ieeeSign, result);
+}
+
+void d2s_buffered(double f, char* result) {
+  const int index = d2s_buffered_n(f, result);
+
+  // Terminate the string.
+  result[index] = '\0';
+}
+
+char* d2s(double f) {
+  char* const result = (char*) malloc(25);
+  d2s_buffered(f, result);
+  return result;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_full_table.h b/libstdc++-v3/src/c++17/ryu/d2s_full_table.h
new file mode 100644
index 00000000000..c8629eef1b2
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s_full_table.h
@@ -0,0 +1,367 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+// These tables are generated by PrintDoubleLookupTable.
+#define DOUBLE_POW5_INV_BITCOUNT 125
+#define DOUBLE_POW5_BITCOUNT 125
+
+#define DOUBLE_POW5_INV_TABLE_SIZE 342
+#define DOUBLE_POW5_TABLE_SIZE 326
+
+static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = {
+  {                    1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u },
+  {  5165088340638674453u, 1475739525896764129u }, {  7821419487252849886u, 1180591620717411303u },
+  {  8824922364862649494u, 1888946593147858085u }, {  7059937891890119595u, 1511157274518286468u },
+  { 13026647942995916322u, 1208925819614629174u }, {  9774590264567735146u, 1934281311383406679u },
+  { 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u },
+  { 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u },
+  {  9162556910162266299u, 1267650600228229401u }, {  7281393426775805432u, 2028240960365167042u },
+  { 16893161185646375315u, 1622592768292133633u }, {  2446482504291369283u, 1298074214633706907u },
+  {  7603720821608101175u, 2076918743413931051u }, {  2393627842544570617u, 1661534994731144841u },
+  { 16672297533003297786u, 1329227995784915872u }, { 11918280793837635165u, 2126764793255865396u },
+  {  5845275820328197809u, 1701411834604692317u }, { 15744267100488289217u, 1361129467683753853u },
+  {  3054734472329800808u, 2177807148294006166u }, { 17201182836831481939u, 1742245718635204932u },
+  {  6382248639981364905u, 1393796574908163946u }, {  2832900194486363201u, 2230074519853062314u },
+  {  5955668970331000884u, 1784059615882449851u }, {  1075186361522890384u, 1427247692705959881u },
+  { 12788344622662355584u, 2283596308329535809u }, { 13920024512871794791u, 1826877046663628647u },
+  {  3757321980813615186u, 1461501637330902918u }, { 10384555214134712795u, 1169201309864722334u },
+  {  5547241898389809503u, 1870722095783555735u }, {  4437793518711847602u, 1496577676626844588u },
+  { 10928932444453298728u, 1197262141301475670u }, { 17486291911125277965u, 1915619426082361072u },
+  {  6610335899416401726u, 1532495540865888858u }, { 12666966349016942027u, 1225996432692711086u },
+  { 12888448528943286597u, 1961594292308337738u }, { 17689456452638449924u, 1569275433846670190u },
+  { 14151565162110759939u, 1255420347077336152u }, {  7885109000409574610u, 2008672555323737844u },
+  {  9997436015069570011u, 1606938044258990275u }, {  7997948812055656009u, 1285550435407192220u },
+  { 12796718099289049614u, 2056880696651507552u }, {  2858676849947419045u, 1645504557321206042u },
+  { 13354987924183666206u, 1316403645856964833u }, { 17678631863951955605u, 2106245833371143733u },
+  {  3074859046935833515u, 1684996666696914987u }, { 13527933681774397782u, 1347997333357531989u },
+  { 10576647446613305481u, 2156795733372051183u }, { 15840015586774465031u, 1725436586697640946u },
+  {  8982663654677661702u, 1380349269358112757u }, { 18061610662226169046u, 2208558830972980411u },
+  { 10759939715039024913u, 1766847064778384329u }, { 12297300586773130254u, 1413477651822707463u },
+  { 15986332124095098083u, 2261564242916331941u }, {  9099716884534168143u, 1809251394333065553u },
+  { 14658471137111155161u, 1447401115466452442u }, {  4348079280205103483u, 1157920892373161954u },
+  { 14335624477811986218u, 1852673427797059126u }, {  7779150767507678651u, 1482138742237647301u },
+  {  2533971799264232598u, 1185710993790117841u }, { 15122401323048503126u, 1897137590064188545u },
+  { 12097921058438802501u, 1517710072051350836u }, {  5988988032009131678u, 1214168057641080669u },
+  { 16961078480698431330u, 1942668892225729070u }, { 13568862784558745064u, 1554135113780583256u },
+  {  7165741412905085728u, 1243308091024466605u }, { 11465186260648137165u, 1989292945639146568u },
+  { 16550846638002330379u, 1591434356511317254u }, { 16930026125143774626u, 1273147485209053803u },
+  {  4951948911778577463u, 2037035976334486086u }, {   272210314680951647u, 1629628781067588869u },
+  {  3907117066486671641u, 1303703024854071095u }, {  6251387306378674625u, 2085924839766513752u },
+  { 16069156289328670670u, 1668739871813211001u }, {  9165976216721026213u, 1334991897450568801u },
+  {  7286864317269821294u, 2135987035920910082u }, { 16897537898041588005u, 1708789628736728065u },
+  { 13518030318433270404u, 1367031702989382452u }, {  6871453250525591353u, 2187250724783011924u },
+  {  9186511415162383406u, 1749800579826409539u }, { 11038557946871817048u, 1399840463861127631u },
+  { 10282995085511086630u, 2239744742177804210u }, {  8226396068408869304u, 1791795793742243368u },
+  { 13959814484210916090u, 1433436634993794694u }, { 11267656730511734774u, 2293498615990071511u },
+  {  5324776569667477496u, 1834798892792057209u }, {  7949170070475892320u, 1467839114233645767u },
+  { 17427382500606444826u, 1174271291386916613u }, {  5747719112518849781u, 1878834066219066582u },
+  { 15666221734240810795u, 1503067252975253265u }, { 12532977387392648636u, 1202453802380202612u },
+  {  5295368560860596524u, 1923926083808324180u }, {  4236294848688477220u, 1539140867046659344u },
+  {  7078384693692692099u, 1231312693637327475u }, { 11325415509908307358u, 1970100309819723960u },
+  {  9060332407926645887u, 1576080247855779168u }, { 14626963555825137356u, 1260864198284623334u },
+  { 12335095245094488799u, 2017382717255397335u }, {  9868076196075591040u, 1613906173804317868u },
+  { 15273158586344293478u, 1291124939043454294u }, { 13369007293925138595u, 2065799902469526871u },
+  {  7005857020398200553u, 1652639921975621497u }, { 16672732060544291412u, 1322111937580497197u },
+  { 11918976037903224966u, 2115379100128795516u }, {  5845832015580669650u, 1692303280103036413u },
+  { 12055363241948356366u, 1353842624082429130u }, {   841837113407818570u, 2166148198531886609u },
+  {  4362818505468165179u, 1732918558825509287u }, { 14558301248600263113u, 1386334847060407429u },
+  { 12225235553534690011u, 2218135755296651887u }, {  2401490813343931363u, 1774508604237321510u },
+  {  1921192650675145090u, 1419606883389857208u }, { 17831303500047873437u, 2271371013423771532u },
+  {  6886345170554478103u, 1817096810739017226u }, {  1819727321701672159u, 1453677448591213781u },
+  { 16213177116328979020u, 1162941958872971024u }, { 14873036941900635463u, 1860707134196753639u },
+  { 15587778368262418694u, 1488565707357402911u }, {  8780873879868024632u, 1190852565885922329u },
+  {  2981351763563108441u, 1905364105417475727u }, { 13453127855076217722u, 1524291284333980581u },
+  {  7073153469319063855u, 1219433027467184465u }, { 11317045550910502167u, 1951092843947495144u },
+  { 12742985255470312057u, 1560874275157996115u }, { 10194388204376249646u, 1248699420126396892u },
+  {  1553625868034358140u, 1997919072202235028u }, {  8621598323911307159u, 1598335257761788022u },
+  { 17965325103354776697u, 1278668206209430417u }, { 13987124906400001422u, 2045869129935088668u },
+  {   121653480894270168u, 1636695303948070935u }, {    97322784715416134u, 1309356243158456748u },
+  { 14913111714512307107u, 2094969989053530796u }, {  8241140556867935363u, 1675975991242824637u },
+  { 17660958889720079260u, 1340780792994259709u }, { 17189487779326395846u, 2145249268790815535u },
+  { 13751590223461116677u, 1716199415032652428u }, { 18379969808252713988u, 1372959532026121942u },
+  { 14650556434236701088u, 2196735251241795108u }, {   652398703163629901u, 1757388200993436087u },
+  { 11589965406756634890u, 1405910560794748869u }, {  7475898206584884855u, 2249456897271598191u },
+  {  2291369750525997561u, 1799565517817278553u }, {  9211793429904618695u, 1439652414253822842u },
+  { 18428218302589300235u, 2303443862806116547u }, {  7363877012587619542u, 1842755090244893238u },
+  { 13269799239553916280u, 1474204072195914590u }, { 10615839391643133024u, 1179363257756731672u },
+  {  2227947767661371545u, 1886981212410770676u }, { 16539753473096738529u, 1509584969928616540u },
+  { 13231802778477390823u, 1207667975942893232u }, {  6413489186596184024u, 1932268761508629172u },
+  { 16198837793502678189u, 1545815009206903337u }, {  5580372605318321905u, 1236652007365522670u },
+  {  8928596168509315048u, 1978643211784836272u }, { 18210923379033183008u, 1582914569427869017u },
+  {  7190041073742725760u, 1266331655542295214u }, {   436019273762630246u, 2026130648867672343u },
+  {  7727513048493924843u, 1620904519094137874u }, {  9871359253537050198u, 1296723615275310299u },
+  {  4726128361433549347u, 2074757784440496479u }, {  7470251503888749801u, 1659806227552397183u },
+  { 13354898832594820487u, 1327844982041917746u }, { 13989140502667892133u, 2124551971267068394u },
+  { 14880661216876224029u, 1699641577013654715u }, { 11904528973500979224u, 1359713261610923772u },
+  {  4289851098633925465u, 2175541218577478036u }, { 18189276137874781665u, 1740432974861982428u },
+  {  3483374466074094362u, 1392346379889585943u }, {  1884050330976640656u, 2227754207823337509u },
+  {  5196589079523222848u, 1782203366258670007u }, { 15225317707844309248u, 1425762693006936005u },
+  {  5913764258841343181u, 2281220308811097609u }, {  8420360221814984868u, 1824976247048878087u },
+  { 17804334621677718864u, 1459980997639102469u }, { 17932816512084085415u, 1167984798111281975u },
+  { 10245762345624985047u, 1868775676978051161u }, {  4507261061758077715u, 1495020541582440929u },
+  {  7295157664148372495u, 1196016433265952743u }, {  7982903447895485668u, 1913626293225524389u },
+  { 10075671573058298858u, 1530901034580419511u }, {  4371188443704728763u, 1224720827664335609u },
+  { 14372599139411386667u, 1959553324262936974u }, { 15187428126271019657u, 1567642659410349579u },
+  { 15839291315758726049u, 1254114127528279663u }, {  3206773216762499739u, 2006582604045247462u },
+  { 13633465017635730761u, 1605266083236197969u }, { 14596120828850494932u, 1284212866588958375u },
+  {  4907049252451240275u, 2054740586542333401u }, {   236290587219081897u, 1643792469233866721u },
+  { 14946427728742906810u, 1315033975387093376u }, { 16535586736504830250u, 2104054360619349402u },
+  {  5849771759720043554u, 1683243488495479522u }, { 15747863852001765813u, 1346594790796383617u },
+  { 10439186904235184007u, 2154551665274213788u }, { 15730047152871967852u, 1723641332219371030u },
+  { 12584037722297574282u, 1378913065775496824u }, {  9066413911450387881u, 2206260905240794919u },
+  { 10942479943902220628u, 1765008724192635935u }, {  8753983955121776503u, 1412006979354108748u },
+  { 10317025513452932081u, 2259211166966573997u }, {   874922781278525018u, 1807368933573259198u },
+  {  8078635854506640661u, 1445895146858607358u }, { 13841606313089133175u, 1156716117486885886u },
+  { 14767872471458792434u, 1850745787979017418u }, {   746251532941302978u, 1480596630383213935u },
+  {   597001226353042382u, 1184477304306571148u }, { 15712597221132509104u, 1895163686890513836u },
+  {  8880728962164096960u, 1516130949512411069u }, { 10793931984473187891u, 1212904759609928855u },
+  { 17270291175157100626u, 1940647615375886168u }, {  2748186495899949531u, 1552518092300708935u },
+  {  2198549196719959625u, 1242014473840567148u }, { 18275073973719576693u, 1987223158144907436u },
+  { 10930710364233751031u, 1589778526515925949u }, { 12433917106128911148u, 1271822821212740759u },
+  {  8826220925580526867u, 2034916513940385215u }, {  7060976740464421494u, 1627933211152308172u },
+  { 16716827836597268165u, 1302346568921846537u }, { 11989529279587987770u, 2083754510274954460u },
+  {  9591623423670390216u, 1667003608219963568u }, { 15051996368420132820u, 1333602886575970854u },
+  { 13015147745246481542u, 2133764618521553367u }, {  3033420566713364587u, 1707011694817242694u },
+  {  6116085268112601993u, 1365609355853794155u }, {  9785736428980163188u, 2184974969366070648u },
+  { 15207286772667951197u, 1747979975492856518u }, {  1097782973908629988u, 1398383980394285215u },
+  {  1756452758253807981u, 2237414368630856344u }, {  5094511021344956708u, 1789931494904685075u },
+  {  4075608817075965366u, 1431945195923748060u }, {  6520974107321544586u, 2291112313477996896u },
+  {  1527430471115325346u, 1832889850782397517u }, { 12289990821117991246u, 1466311880625918013u },
+  { 17210690286378213644u, 1173049504500734410u }, {  9090360384495590213u, 1876879207201175057u },
+  { 18340334751822203140u, 1501503365760940045u }, { 14672267801457762512u, 1201202692608752036u },
+  { 16096930852848599373u, 1921924308174003258u }, {  1809498238053148529u, 1537539446539202607u },
+  { 12515645034668249793u, 1230031557231362085u }, {  1578287981759648052u, 1968050491570179337u },
+  { 12330676829633449412u, 1574440393256143469u }, { 13553890278448669853u, 1259552314604914775u },
+  {  3239480371808320148u, 2015283703367863641u }, { 17348979556414297411u, 1612226962694290912u },
+  {  6500486015647617283u, 1289781570155432730u }, { 10400777625036187652u, 2063650512248692368u },
+  { 15699319729512770768u, 1650920409798953894u }, { 16248804598352126938u, 1320736327839163115u },
+  {  7551343283653851484u, 2113178124542660985u }, {  6041074626923081187u, 1690542499634128788u },
+  { 12211557331022285596u, 1352433999707303030u }, {  1091747655926105338u, 2163894399531684849u },
+  {  4562746939482794594u, 1731115519625347879u }, {  7339546366328145998u, 1384892415700278303u },
+  {  8053925371383123274u, 2215827865120445285u }, {  6443140297106498619u, 1772662292096356228u },
+  { 12533209867169019542u, 1418129833677084982u }, {  5295740528502789974u, 2269007733883335972u },
+  { 15304638867027962949u, 1815206187106668777u }, {  4865013464138549713u, 1452164949685335022u },
+  { 14960057215536570740u, 1161731959748268017u }, {  9178696285890871890u, 1858771135597228828u },
+  { 14721654658196518159u, 1487016908477783062u }, {  4398626097073393881u, 1189613526782226450u },
+  {  7037801755317430209u, 1903381642851562320u }, {  5630241404253944167u, 1522705314281249856u },
+  {   814844308661245011u, 1218164251424999885u }, {  1303750893857992017u, 1949062802279999816u },
+  { 15800395974054034906u, 1559250241823999852u }, {  5261619149759407279u, 1247400193459199882u },
+  { 12107939454356961969u, 1995840309534719811u }, {  5997002748743659252u, 1596672247627775849u },
+  {  8486951013736837725u, 1277337798102220679u }, {  2511075177753209390u, 2043740476963553087u },
+  { 13076906586428298482u, 1634992381570842469u }, { 14150874083884549109u, 1307993905256673975u },
+  {  4194654460505726958u, 2092790248410678361u }, { 18113118827372222859u, 1674232198728542688u },
+  {  3422448617672047318u, 1339385758982834151u }, { 16543964232501006678u, 2143017214372534641u },
+  {  9545822571258895019u, 1714413771498027713u }, { 15015355686490936662u, 1371531017198422170u },
+  {  5577825024675947042u, 2194449627517475473u }, { 11840957649224578280u, 1755559702013980378u },
+  { 16851463748863483271u, 1404447761611184302u }, { 12204946739213931940u, 2247116418577894884u },
+  { 13453306206113055875u, 1797693134862315907u }, {  3383947335406624054u, 1438154507889852726u },
+  { 16482362180876329456u, 2301047212623764361u }, {  9496540929959153242u, 1840837770099011489u },
+  { 11286581558709232917u, 1472670216079209191u }, {  5339916432225476010u, 1178136172863367353u },
+  {  4854517476818851293u, 1885017876581387765u }, {  3883613981455081034u, 1508014301265110212u },
+  { 14174937629389795797u, 1206411441012088169u }, { 11611853762797942306u, 1930258305619341071u },
+  {  5600134195496443521u, 1544206644495472857u }, { 15548153800622885787u, 1235365315596378285u },
+  {  6430302007287065643u, 1976584504954205257u }, { 16212288050055383484u, 1581267603963364205u },
+  { 12969830440044306787u, 1265014083170691364u }, {  9683682259845159889u, 2024022533073106183u },
+  { 15125643437359948558u, 1619218026458484946u }, {  8411165935146048523u, 1295374421166787957u },
+  { 17147214310975587960u, 2072599073866860731u }, { 10028422634038560045u, 1658079259093488585u },
+  {  8022738107230848036u, 1326463407274790868u }, {  9147032156827446534u, 2122341451639665389u },
+  { 11006974540203867551u, 1697873161311732311u }, {  5116230817421183718u, 1358298529049385849u },
+  { 15564666937357714594u, 2173277646479017358u }, {  1383687105660440706u, 1738622117183213887u },
+  { 12174996128754083534u, 1390897693746571109u }, {  8411947361780802685u, 2225436309994513775u },
+  {  6729557889424642148u, 1780349047995611020u }, {  5383646311539713719u, 1424279238396488816u },
+  {  1235136468979721303u, 2278846781434382106u }, { 15745504434151418335u, 1823077425147505684u },
+  { 16285752362063044992u, 1458461940118004547u }, {  5649904260166615347u, 1166769552094403638u },
+  {  5350498001524674232u, 1866831283351045821u }, {   591049586477829062u, 1493465026680836657u },
+  { 11540886113407994219u, 1194772021344669325u }, {    18673707743239135u, 1911635234151470921u },
+  { 14772334225162232601u, 1529308187321176736u }, {  8128518565387875758u, 1223446549856941389u },
+  {  1937583260394870242u, 1957514479771106223u }, {  8928764237799716840u, 1566011583816884978u },
+  { 14521709019723594119u, 1252809267053507982u }, {  8477339172590109297u, 2004494827285612772u },
+  { 17849917782297818407u, 1603595861828490217u }, {  6901236596354434079u, 1282876689462792174u },
+  { 18420676183650915173u, 2052602703140467478u }, {  3668494502695001169u, 1642082162512373983u },
+  { 10313493231639821582u, 1313665730009899186u }, {  9122891541139893884u, 2101865168015838698u },
+  { 14677010862395735754u, 1681492134412670958u }, {   673562245690857633u, 1345193707530136767u }
+};
+
+static const uint64_t DOUBLE_POW5_SPLIT[DOUBLE_POW5_TABLE_SIZE][2] = {
+  {                    0u, 1152921504606846976u }, {                    0u, 1441151880758558720u },
+  {                    0u, 1801439850948198400u }, {                    0u, 2251799813685248000u },
+  {                    0u, 1407374883553280000u }, {                    0u, 1759218604441600000u },
+  {                    0u, 2199023255552000000u }, {                    0u, 1374389534720000000u },
+  {                    0u, 1717986918400000000u }, {                    0u, 2147483648000000000u },
+  {                    0u, 1342177280000000000u }, {                    0u, 1677721600000000000u },
+  {                    0u, 2097152000000000000u }, {                    0u, 1310720000000000000u },
+  {                    0u, 1638400000000000000u }, {                    0u, 2048000000000000000u },
+  {                    0u, 1280000000000000000u }, {                    0u, 1600000000000000000u },
+  {                    0u, 2000000000000000000u }, {                    0u, 1250000000000000000u },
+  {                    0u, 1562500000000000000u }, {                    0u, 1953125000000000000u },
+  {                    0u, 1220703125000000000u }, {                    0u, 1525878906250000000u },
+  {                    0u, 1907348632812500000u }, {                    0u, 1192092895507812500u },
+  {                    0u, 1490116119384765625u }, {  4611686018427387904u, 1862645149230957031u },
+  {  9799832789158199296u, 1164153218269348144u }, { 12249790986447749120u, 1455191522836685180u },
+  { 15312238733059686400u, 1818989403545856475u }, { 14528612397897220096u, 2273736754432320594u },
+  { 13692068767113150464u, 1421085471520200371u }, { 12503399940464050176u, 1776356839400250464u },
+  { 15629249925580062720u, 2220446049250313080u }, {  9768281203487539200u, 1387778780781445675u },
+  {  7598665485932036096u, 1734723475976807094u }, {   274959820560269312u, 2168404344971008868u },
+  {  9395221924704944128u, 1355252715606880542u }, {  2520655369026404352u, 1694065894508600678u },
+  { 12374191248137781248u, 2117582368135750847u }, { 14651398557727195136u, 1323488980084844279u },
+  { 13702562178731606016u, 1654361225106055349u }, {  3293144668132343808u, 2067951531382569187u },
+  { 18199116482078572544u, 1292469707114105741u }, {  8913837547316051968u, 1615587133892632177u },
+  { 15753982952572452864u, 2019483917365790221u }, { 12152082354571476992u, 1262177448353618888u },
+  { 15190102943214346240u, 1577721810442023610u }, {  9764256642163156992u, 1972152263052529513u },
+  { 17631875447420442880u, 1232595164407830945u }, {  8204786253993389888u, 1540743955509788682u },
+  {  1032610780636961552u, 1925929944387235853u }, {  2951224747111794922u, 1203706215242022408u },
+  {  3689030933889743652u, 1504632769052528010u }, { 13834660704216955373u, 1880790961315660012u },
+  { 17870034976990372916u, 1175494350822287507u }, { 17725857702810578241u, 1469367938527859384u },
+  {  3710578054803671186u, 1836709923159824231u }, {    26536550077201078u, 2295887403949780289u },
+  { 11545800389866720434u, 1434929627468612680u }, { 14432250487333400542u, 1793662034335765850u },
+  {  8816941072311974870u, 2242077542919707313u }, { 17039803216263454053u, 1401298464324817070u },
+  { 12076381983474541759u, 1751623080406021338u }, {  5872105442488401391u, 2189528850507526673u },
+  { 15199280947623720629u, 1368455531567204170u }, {  9775729147674874978u, 1710569414459005213u },
+  { 16831347453020981627u, 2138211768073756516u }, {  1296220121283337709u, 1336382355046097823u },
+  { 15455333206886335848u, 1670477943807622278u }, { 10095794471753144002u, 2088097429759527848u },
+  {  6309871544845715001u, 1305060893599704905u }, { 12499025449484531656u, 1631326116999631131u },
+  { 11012095793428276666u, 2039157646249538914u }, { 11494245889320060820u, 1274473528905961821u },
+  {   532749306367912313u, 1593091911132452277u }, {  5277622651387278295u, 1991364888915565346u },
+  {  7910200175544436838u, 1244603055572228341u }, { 14499436237857933952u, 1555753819465285426u },
+  {  8900923260467641632u, 1944692274331606783u }, { 12480606065433357876u, 1215432671457254239u },
+  { 10989071563364309441u, 1519290839321567799u }, {  9124653435777998898u, 1899113549151959749u },
+  {  8008751406574943263u, 1186945968219974843u }, {  5399253239791291175u, 1483682460274968554u },
+  { 15972438586593889776u, 1854603075343710692u }, {   759402079766405302u, 1159126922089819183u },
+  { 14784310654990170340u, 1448908652612273978u }, {  9257016281882937117u, 1811135815765342473u },
+  { 16182956370781059300u, 2263919769706678091u }, {  7808504722524468110u, 1414949856066673807u },
+  {  5148944884728197234u, 1768687320083342259u }, {  1824495087482858639u, 2210859150104177824u },
+  {  1140309429676786649u, 1381786968815111140u }, {  1425386787095983311u, 1727233711018888925u },
+  {  6393419502297367043u, 2159042138773611156u }, { 13219259225790630210u, 1349401336733506972u },
+  { 16524074032238287762u, 1686751670916883715u }, { 16043406521870471799u, 2108439588646104644u },
+  {   803757039314269066u, 1317774742903815403u }, { 14839754354425000045u, 1647218428629769253u },
+  {  4714634887749086344u, 2059023035787211567u }, {  9864175832484260821u, 1286889397367007229u },
+  { 16941905809032713930u, 1608611746708759036u }, {  2730638187581340797u, 2010764683385948796u },
+  { 10930020904093113806u, 1256727927116217997u }, { 18274212148543780162u, 1570909908895272496u },
+  {  4396021111970173586u, 1963637386119090621u }, {  5053356204195052443u, 1227273366324431638u },
+  { 15540067292098591362u, 1534091707905539547u }, { 14813398096695851299u, 1917614634881924434u },
+  { 13870059828862294966u, 1198509146801202771u }, { 12725888767650480803u, 1498136433501503464u },
+  { 15907360959563101004u, 1872670541876879330u }, { 14553786618154326031u, 1170419088673049581u },
+  {  4357175217410743827u, 1463023860841311977u }, { 10058155040190817688u, 1828779826051639971u },
+  {  7961007781811134206u, 2285974782564549964u }, { 14199001900486734687u, 1428734239102843727u },
+  { 13137066357181030455u, 1785917798878554659u }, { 11809646928048900164u, 2232397248598193324u },
+  { 16604401366885338411u, 1395248280373870827u }, { 16143815690179285109u, 1744060350467338534u },
+  { 10956397575869330579u, 2180075438084173168u }, {  6847748484918331612u, 1362547148802608230u },
+  { 17783057643002690323u, 1703183936003260287u }, { 17617136035325974999u, 2128979920004075359u },
+  { 17928239049719816230u, 1330612450002547099u }, { 17798612793722382384u, 1663265562503183874u },
+  { 13024893955298202172u, 2079081953128979843u }, {  5834715712847682405u, 1299426220705612402u },
+  { 16516766677914378815u, 1624282775882015502u }, { 11422586310538197711u, 2030353469852519378u },
+  { 11750802462513761473u, 1268970918657824611u }, { 10076817059714813937u, 1586213648322280764u },
+  { 12596021324643517422u, 1982767060402850955u }, {  5566670318688504437u, 1239229412751781847u },
+  {  2346651879933242642u, 1549036765939727309u }, {  7545000868343941206u, 1936295957424659136u },
+  {  4715625542714963254u, 1210184973390411960u }, {  5894531928393704067u, 1512731216738014950u },
+  { 16591536947346905892u, 1890914020922518687u }, { 17287239619732898039u, 1181821263076574179u },
+  { 16997363506238734644u, 1477276578845717724u }, {  2799960309088866689u, 1846595723557147156u },
+  { 10973347230035317489u, 1154122327223216972u }, { 13716684037544146861u, 1442652909029021215u },
+  { 12534169028502795672u, 1803316136286276519u }, { 11056025267201106687u, 2254145170357845649u },
+  { 18439230838069161439u, 1408840731473653530u }, { 13825666510731675991u, 1761050914342066913u },
+  {  3447025083132431277u, 2201313642927583642u }, {  6766076695385157452u, 1375821026829739776u },
+  {  8457595869231446815u, 1719776283537174720u }, { 10571994836539308519u, 2149720354421468400u },
+  {  6607496772837067824u, 1343575221513417750u }, { 17482743002901110588u, 1679469026891772187u },
+  { 17241742735199000331u, 2099336283614715234u }, { 15387775227926763111u, 1312085177259197021u },
+  {  5399660979626290177u, 1640106471573996277u }, { 11361262242960250625u, 2050133089467495346u },
+  { 11712474920277544544u, 1281333180917184591u }, { 10028907631919542777u, 1601666476146480739u },
+  {  7924448521472040567u, 2002083095183100924u }, { 14176152362774801162u, 1251301934489438077u },
+  {  3885132398186337741u, 1564127418111797597u }, {  9468101516160310080u, 1955159272639746996u },
+  { 15140935484454969608u, 1221974545399841872u }, {   479425281859160394u, 1527468181749802341u },
+  {  5210967620751338397u, 1909335227187252926u }, { 17091912818251750210u, 1193334516992033078u },
+  { 12141518985959911954u, 1491668146240041348u }, { 15176898732449889943u, 1864585182800051685u },
+  { 11791404716994875166u, 1165365739250032303u }, { 10127569877816206054u, 1456707174062540379u },
+  {  8047776328842869663u, 1820883967578175474u }, {   836348374198811271u, 2276104959472719343u },
+  {  7440246761515338900u, 1422565599670449589u }, { 13911994470321561530u, 1778206999588061986u },
+  {  8166621051047176104u, 2222758749485077483u }, {  2798295147690791113u, 1389224218428173427u },
+  { 17332926989895652603u, 1736530273035216783u }, { 17054472718942177850u, 2170662841294020979u },
+  {  8353202440125167204u, 1356664275808763112u }, { 10441503050156459005u, 1695830344760953890u },
+  {  3828506775840797949u, 2119787930951192363u }, {    86973725686804766u, 1324867456844495227u },
+  { 13943775212390669669u, 1656084321055619033u }, {  3594660960206173375u, 2070105401319523792u },
+  {  2246663100128858359u, 1293815875824702370u }, { 12031700912015848757u, 1617269844780877962u },
+  {  5816254103165035138u, 2021587305976097453u }, {  5941001823691840913u, 1263492066235060908u },
+  {  7426252279614801142u, 1579365082793826135u }, {  4671129331091113523u, 1974206353492282669u },
+  {  5225298841145639904u, 1233878970932676668u }, {  6531623551432049880u, 1542348713665845835u },
+  {  3552843420862674446u, 1927935892082307294u }, { 16055585193321335241u, 1204959932551442058u },
+  { 10846109454796893243u, 1506199915689302573u }, { 18169322836923504458u, 1882749894611628216u },
+  { 11355826773077190286u, 1176718684132267635u }, {  9583097447919099954u, 1470898355165334544u },
+  { 11978871809898874942u, 1838622943956668180u }, { 14973589762373593678u, 2298278679945835225u },
+  {  2440964573842414192u, 1436424174966147016u }, {  3051205717303017741u, 1795530218707683770u },
+  { 13037379183483547984u, 2244412773384604712u }, {  8148361989677217490u, 1402757983365377945u },
+  { 14797138505523909766u, 1753447479206722431u }, { 13884737113477499304u, 2191809349008403039u },
+  { 15595489723564518921u, 1369880843130251899u }, { 14882676136028260747u, 1712351053912814874u },
+  {  9379973133180550126u, 2140438817391018593u }, { 17391698254306313589u, 1337774260869386620u },
+  {  3292878744173340370u, 1672217826086733276u }, {  4116098430216675462u, 2090272282608416595u },
+  {   266718509671728212u, 1306420176630260372u }, {   333398137089660265u, 1633025220787825465u },
+  {  5028433689789463235u, 2041281525984781831u }, { 10060300083759496378u, 1275800953740488644u },
+  { 12575375104699370472u, 1594751192175610805u }, {  1884160825592049379u, 1993438990219513507u },
+  { 17318501580490888525u, 1245899368887195941u }, {  7813068920331446945u, 1557374211108994927u },
+  {  5154650131986920777u, 1946717763886243659u }, {   915813323278131534u, 1216698602428902287u },
+  { 14979824709379828129u, 1520873253036127858u }, {  9501408849870009354u, 1901091566295159823u },
+  { 12855909558809837702u, 1188182228934474889u }, {  2234828893230133415u, 1485227786168093612u },
+  {  2793536116537666769u, 1856534732710117015u }, {  8663489100477123587u, 1160334207943823134u },
+  {  1605989338741628675u, 1450417759929778918u }, { 11230858710281811652u, 1813022199912223647u },
+  {  9426887369424876662u, 2266277749890279559u }, { 12809333633531629769u, 1416423593681424724u },
+  { 16011667041914537212u, 1770529492101780905u }, {  6179525747111007803u, 2213161865127226132u },
+  { 13085575628799155685u, 1383226165704516332u }, { 16356969535998944606u, 1729032707130645415u },
+  { 15834525901571292854u, 2161290883913306769u }, {  2979049660840976177u, 1350806802445816731u },
+  { 17558870131333383934u, 1688508503057270913u }, {  8113529608884566205u, 2110635628821588642u },
+  {  9682642023980241782u, 1319147268013492901u }, { 16714988548402690132u, 1648934085016866126u },
+  { 11670363648648586857u, 2061167606271082658u }, { 11905663298832754689u, 1288229753919426661u },
+  {  1047021068258779650u, 1610287192399283327u }, { 15143834390605638274u, 2012858990499104158u },
+  {  4853210475701136017u, 1258036869061940099u }, {  1454827076199032118u, 1572546086327425124u },
+  {  1818533845248790147u, 1965682607909281405u }, {  3442426662494187794u, 1228551629943300878u },
+  { 13526405364972510550u, 1535689537429126097u }, {  3072948650933474476u, 1919611921786407622u },
+  { 15755650962115585259u, 1199757451116504763u }, { 15082877684217093670u, 1499696813895630954u },
+  {  9630225068416591280u, 1874621017369538693u }, {  8324733676974063502u, 1171638135855961683u },
+  {  5794231077790191473u, 1464547669819952104u }, {  7242788847237739342u, 1830684587274940130u },
+  { 18276858095901949986u, 2288355734093675162u }, { 16034722328366106645u, 1430222333808546976u },
+  {  1596658836748081690u, 1787777917260683721u }, {  6607509564362490017u, 2234722396575854651u },
+  {  1823850468512862308u, 1396701497859909157u }, {  6891499104068465790u, 1745876872324886446u },
+  { 17837745916940358045u, 2182346090406108057u }, {  4231062170446641922u, 1363966306503817536u },
+  {  5288827713058302403u, 1704957883129771920u }, {  6611034641322878003u, 2131197353912214900u },
+  { 13355268687681574560u, 1331998346195134312u }, { 16694085859601968200u, 1664997932743917890u },
+  { 11644235287647684442u, 2081247415929897363u }, {  4971804045566108824u, 1300779634956185852u },
+  {  6214755056957636030u, 1625974543695232315u }, {  3156757802769657134u, 2032468179619040394u },
+  {  6584659645158423613u, 1270292612261900246u }, { 17454196593302805324u, 1587865765327375307u },
+  { 17206059723201118751u, 1984832206659219134u }, {  6142101308573311315u, 1240520129162011959u },
+  {  3065940617289251240u, 1550650161452514949u }, {  8444111790038951954u, 1938312701815643686u },
+  {   665883850346957067u, 1211445438634777304u }, {   832354812933696334u, 1514306798293471630u },
+  { 10263815553021896226u, 1892883497866839537u }, { 17944099766707154901u, 1183052186166774710u },
+  { 13206752671529167818u, 1478815232708468388u }, { 16508440839411459773u, 1848519040885585485u },
+  { 12623618533845856310u, 1155324400553490928u }, { 15779523167307320387u, 1444155500691863660u },
+  {  1277659885424598868u, 1805194375864829576u }, {  1597074856780748586u, 2256492969831036970u },
+  {  5609857803915355770u, 1410308106144398106u }, { 16235694291748970521u, 1762885132680497632u },
+  {  1847873790976661535u, 2203606415850622041u }, { 12684136165428883219u, 1377254009906638775u },
+  { 11243484188358716120u, 1721567512383298469u }, {   219297180166231438u, 2151959390479123087u },
+  {  7054589765244976505u, 1344974619049451929u }, { 13429923224983608535u, 1681218273811814911u },
+  { 12175718012802122765u, 2101522842264768639u }, { 14527352785642408584u, 1313451776415480399u },
+  { 13547504963625622826u, 1641814720519350499u }, { 12322695186104640628u, 2052268400649188124u },
+  { 16925056528170176201u, 1282667750405742577u }, {  7321262604930556539u, 1603334688007178222u },
+  { 18374950293017971482u, 2004168360008972777u }, {  4566814905495150320u, 1252605225005607986u },
+  { 14931890668723713708u, 1565756531257009982u }, {  9441491299049866327u, 1957195664071262478u },
+  {  1289246043478778550u, 1223247290044539049u }, {  6223243572775861092u, 1529059112555673811u },
+  {  3167368447542438461u, 1911323890694592264u }, {  1979605279714024038u, 1194577431684120165u },
+  {  7086192618069917952u, 1493221789605150206u }, { 18081112809442173248u, 1866527237006437757u },
+  { 13606538515115052232u, 1166579523129023598u }, {  7784801107039039482u, 1458224403911279498u },
+  {   507629346944023544u, 1822780504889099373u }, {  5246222702107417334u, 2278475631111374216u },
+  {  3278889188817135834u, 1424047269444608885u }, {  8710297504448807696u, 1780059086805761106u }
+};
+
+#endif // RYU_D2S_FULL_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
new file mode 100644
index 00000000000..ea590a60d25
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
@@ -0,0 +1,358 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#include <assert.h>
+#include <stdint.h>
+
+// Defines RYU_32_BIT_PLATFORM if applicable.
+#include "ryu/common.h"
+
+// ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
+// Let's do the same for now.
+#if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
+#define HAS_UINT128
+#elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#if defined(HAS_UINT128)
+typedef __uint128_t uint128_t;
+#endif
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
+  return _umul128(a, b, productHi);
+}
+
+// Returns the lower 64 bits of (hi*2^64 + lo) >> dist, with 0 < dist < 64.
+static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
+  // For the __shiftright128 intrinsic, the shift value is always
+  // modulo 64.
+  // In the current implementation of the double-precision version
+  // of Ryu, the shift value is always < 64. (In the case
+  // RYU_OPTIMIZE_SIZE == 0, the shift value is in the range [49, 58].
+  // Otherwise in the range [2, 59].)
+  // However, this function is now also called by s2d, which requires supporting
+  // the larger shift range (TODO: what is the actual range?).
+  // Check this here in case a future change requires larger shift
+  // values. In this case this function needs to be adjusted.
+  assert(dist < 64);
+  return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else // defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
+  // The casts here help MSVC to avoid calls to the __allmul library function.
+  const uint32_t aLo = (uint32_t)a;
+  const uint32_t aHi = (uint32_t)(a >> 32);
+  const uint32_t bLo = (uint32_t)b;
+  const uint32_t bHi = (uint32_t)(b >> 32);
+
+  const uint64_t b00 = (uint64_t)aLo * bLo;
+  const uint64_t b01 = (uint64_t)aLo * bHi;
+  const uint64_t b10 = (uint64_t)aHi * bLo;
+  const uint64_t b11 = (uint64_t)aHi * bHi;
+
+  const uint32_t b00Lo = (uint32_t)b00;
+  const uint32_t b00Hi = (uint32_t)(b00 >> 32);
+
+  const uint64_t mid1 = b10 + b00Hi;
+  const uint32_t mid1Lo = (uint32_t)(mid1);
+  const uint32_t mid1Hi = (uint32_t)(mid1 >> 32);
+
+  const uint64_t mid2 = b01 + mid1Lo;
+  const uint32_t mid2Lo = (uint32_t)(mid2);
+  const uint32_t mid2Hi = (uint32_t)(mid2 >> 32);
+
+  const uint64_t pHi = b11 + mid1Hi + mid2Hi;
+  const uint64_t pLo = ((uint64_t)mid2Lo << 32) | b00Lo;
+
+  *productHi = pHi;
+  return pLo;
+}
+
+static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
+  // We don't need to handle the case dist >= 64 here (see above).
+  assert(dist < 64);
+  assert(dist > 0);
+  return (hi << (64 - dist)) | (lo >> dist);
+}
+
+#endif // defined(HAS_64_BIT_INTRINSICS)
+
+#if defined(RYU_32_BIT_PLATFORM)
+
+// Returns the high 64 bits of the 128-bit product of a and b.
+static inline uint64_t umulh(const uint64_t a, const uint64_t b) {
+  // Reuse the umul128 implementation.
+  // Optimizers will likely eliminate the instructions used to compute the
+  // low part of the product.
+  uint64_t hi;
+  umul128(a, b, &hi);
+  return hi;
+}
+
+// On 32-bit platforms, compilers typically generate calls to library
+// functions for 64-bit divisions, even if the divisor is a constant.
+//
+// E.g.:
+// https://bugs.llvm.org/show_bug.cgi?id=37932
+// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+//
+// The functions here perform division-by-constant using multiplications
+// in the same way as 64-bit compilers would do.
+//
+// NB:
+// The multipliers and shift values are the ones generated by clang x64
+// for expressions like x/5, x/10, etc.
+
+static inline uint64_t div5(const uint64_t x) {
+  return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64_t div10(const uint64_t x) {
+  return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64_t div100(const uint64_t x) {
+  return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64_t div1e8(const uint64_t x) {
+  return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+static inline uint64_t div1e9(const uint64_t x) {
+  return umulh(x >> 9, 0x44B82FA09B5A53u) >> 11;
+}
+
+static inline uint32_t mod1e9(const uint64_t x) {
+  // Avoid 64-bit math as much as possible.
+  // Returning (uint32_t) (x - 1000000000 * div1e9(x)) would
+  // perform 32x64-bit multiplication and 64-bit subtraction.
+  // x and 1000000000 * div1e9(x) are guaranteed to differ by
+  // less than 10^9, so their highest 32 bits must be identical,
+  // so we can truncate both sides to uint32_t before subtracting.
+  // We can also simplify (uint32_t) (1000000000 * div1e9(x)).
+  // We can truncate before multiplying instead of after, as multiplying
+  // the highest 32 bits of div1e9(x) can't affect the lowest 32 bits.
+  return ((uint32_t) x) - 1000000000 * ((uint32_t) div1e9(x));
+}
+
+#else // defined(RYU_32_BIT_PLATFORM)
+
+static inline uint64_t div5(const uint64_t x) {
+  return x / 5;
+}
+
+static inline uint64_t div10(const uint64_t x) {
+  return x / 10;
+}
+
+static inline uint64_t div100(const uint64_t x) {
+  return x / 100;
+}
+
+static inline uint64_t div1e8(const uint64_t x) {
+  return x / 100000000;
+}
+
+static inline uint64_t div1e9(const uint64_t x) {
+  return x / 1000000000;
+}
+
+static inline uint32_t mod1e9(const uint64_t x) {
+  return (uint32_t) (x - 1000000000 * div1e9(x));
+}
+
+#endif // defined(RYU_32_BIT_PLATFORM)
+
+static inline uint32_t pow5Factor(uint64_t value) {
+  uint32_t count = 0;
+  for (;;) {
+    assert(value != 0);
+    const uint64_t q = div5(value);
+    const uint32_t r = ((uint32_t) value) - 5 * ((uint32_t) q);
+    if (r != 0) {
+      break;
+    }
+    value = q;
+    ++count;
+  }
+  return count;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) {
+  // I tried a case distinction on p, but there was no performance difference.
+  return pow5Factor(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) {
+  assert(value != 0);
+  assert(p < 64);
+  // __builtin_ctzll doesn't appear to be faster here.
+  return (value & ((1ull << p) - 1)) == 0;
+}
+
+// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+// Multiplication:
+//   The 64-bit factor is variable and passed in, the 128-bit factor comes
+//   from a lookup table. We know that the 64-bit factor only has 55
+//   significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+//   factor only has 124 significant bits (i.e., the 4 topmost bits are
+//   zeros).
+// Shift:
+//   In principle, the multiplication result requires 55 + 124 = 179 bits to
+//   represent. However, we then shift this value to the right by j, which is
+//   at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
+//   bits. This means that we only need the topmost 64 significant bits of
+//   the 64x128-bit multiplication.
+//
+// There are several ways to do this:
+// 1. Best case: the compiler exposes a 128-bit type.
+//    We perform two 64x64-bit multiplications, add the higher 64 bits of the
+//    lower result to the higher result, and shift by j - 64 bits.
+//
+//    We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+//    that these are only 64-bit inputs, and can map these to the best
+//    possible sequence of assembly instructions.
+//    x64 machines happen to have matching assembly instructions for
+//    64x64-bit multiplications and 128-bit shifts.
+//
+// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
+//    instructions mentioned in 1.
+//
+// 3. We only have 64x64 bit instructions that return the lower 64 bits of
+//    the result, i.e., we have to use plain C.
+//    Our inputs are less than the full width, so we have three options:
+//    a. Ignore this fact and just implement the intrinsics manually.
+//    b. Split both into 31-bit pieces, which guarantees no internal overflow,
+//       but requires extra work upfront (unless we change the lookup table).
+//    c. Split only the first factor into 31-bit pieces, which also guarantees
+//       no internal overflow, but requires extra work since the intermediate
+//       results are not perfectly aligned.
+#if defined(HAS_UINT128)
+
+// Best case: use 128-bit type.
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+  const uint128_t b0 = ((uint128_t) m) * mul[0];
+  const uint128_t b2 = ((uint128_t) m) * mul[1];
+  return (uint64_t) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
+  uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+//  m <<= 2;
+//  uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
+//  uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
+//
+//  uint128_t hi = (b0 >> 64) + b2;
+//  uint128_t lo = b0 & 0xffffffffffffffffull;
+//  uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
+//  uint128_t vpLo = lo + (factor << 1);
+//  *vp = (uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
+//  uint128_t vmLo = lo - (factor << mmShift);
+//  *vm = (uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
+//  return (uint64_t) (hi >> (j - 64));
+  *vp = mulShift64(4 * m + 2, mul, j);
+  *vm = mulShift64(4 * m - 1 - mmShift, mul, j);
+  return mulShift64(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+  // m is maximum 55 bits
+  uint64_t high1;                                   // 128
+  const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+  uint64_t high0;                                   // 64
+  umul128(m, mul[0], &high0);                       // 0
+  const uint64_t sum = high0 + low1;
+  if (sum < high0) {
+    ++high1; // overflow into high1
+  }
+  return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
+  uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+  *vp = mulShift64(4 * m + 2, mul, j);
+  *vm = mulShift64(4 * m - 1 - mmShift, mul, j);
+  return mulShift64(4 * m, mul, j);
+}
+
+#else // !defined(HAS_UINT128) && !defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+  // m is maximum 55 bits
+  uint64_t high1;                                   // 128
+  const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+  uint64_t high0;                                   // 64
+  umul128(m, mul[0], &high0);                       // 0
+  const uint64_t sum = high0 + low1;
+  if (sum < high0) {
+    ++high1; // overflow into high1
+  }
+  return shiftright128(sum, high1, j - 64);
+}
+
+// This is faster if we don't have a 64x64->128-bit multiplication.
+static inline uint64_t mulShiftAll64(uint64_t m, const uint64_t* const mul, const int32_t j,
+  uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+  m <<= 1;
+  // m is maximum 55 bits
+  uint64_t tmp;
+  const uint64_t lo = umul128(m, mul[0], &tmp);
+  uint64_t hi;
+  const uint64_t mid = tmp + umul128(m, mul[1], &hi);
+  hi += mid < tmp; // overflow into hi
+
+  const uint64_t lo2 = lo + mul[0];
+  const uint64_t mid2 = mid + mul[1] + (lo2 < lo);
+  const uint64_t hi2 = hi + (mid2 < mid);
+  *vp = shiftright128(mid2, hi2, (uint32_t) (j - 64 - 1));
+
+  if (mmShift == 1) {
+    const uint64_t lo3 = lo - mul[0];
+    const uint64_t mid3 = mid - mul[1] - (lo3 > lo);
+    const uint64_t hi3 = hi - (mid3 > mid);
+    *vm = shiftright128(mid3, hi3, (uint32_t) (j - 64 - 1));
+  } else {
+    const uint64_t lo3 = lo + lo;
+    const uint64_t mid3 = mid + mid + (lo3 < lo);
+    const uint64_t hi3 = hi + hi + (mid3 < mid);
+    const uint64_t lo4 = lo3 - mul[0];
+    const uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
+    const uint64_t hi4 = hi3 - (mid4 > mid3);
+    *vm = shiftright128(mid4, hi4, (uint32_t) (j - 64));
+  }
+
+  return shiftright128(mid, hi, (uint32_t) (j - 64 - 1));
+}
+
+#endif // HAS_64_BIT_INTRINSICS
+
+#endif // RYU_D2S_INTRINSICS_H
diff --git a/libstdc++-v3/src/c++17/ryu/digit_table.h b/libstdc++-v3/src/c++17/ryu/digit_table.h
new file mode 100644
index 00000000000..02219bc6d53
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/digit_table.h
@@ -0,0 +1,35 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+// A table of all two-digit numbers. This is used to speed up decimal digit
+// generation by copying pairs of digits into the final output.
+static const char DIGIT_TABLE[200] = {
+  '0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9',
+  '1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9',
+  '2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9',
+  '3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9',
+  '4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9',
+  '5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9',
+  '6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9',
+  '7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9',
+  '8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9',
+  '9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9'
+};
+
+#endif // RYU_DIGIT_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/f2s.c b/libstdc++-v3/src/c++17/ryu/f2s.c
new file mode 100644
index 00000000000..255ecbe599c
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/f2s.c
@@ -0,0 +1,345 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+
+#ifdef RYU_DEBUG
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+// A floating decimal representing m * 10^e.
+typedef struct floating_decimal_32 {
+  uint32_t mantissa;
+  // Decimal exponent's range is -45 to 38
+  // inclusive, and can fit in a short if needed.
+  int32_t exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent) {
+  int32_t e2;
+  uint32_t m2;
+  if (ieeeExponent == 0) {
+    // We subtract 2 so that the bounds computation has 2 additional bits.
+    e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+    m2 = ieeeMantissa;
+  } else {
+    e2 = (int32_t) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+    m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+  }
+  const bool even = (m2 & 1) == 0;
+  const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+  printf("-> %u * 2^%d\n", m2, e2 + 2);
+#endif
+
+  // Step 2: Determine the interval of valid decimal representations.
+  const uint32_t mv = 4 * m2;
+  const uint32_t mp = 4 * m2 + 2;
+  // Implicit bool -> int conversion. True is 1, false is 0.
+  const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+  const uint32_t mm = 4 * m2 - 1 - mmShift;
+
+  // Step 3: Convert to a decimal power base using 64-bit arithmetic.
+  uint32_t vr, vp, vm;
+  int32_t e10;
+  bool vmIsTrailingZeros = false;
+  bool vrIsTrailingZeros = false;
+  uint8_t lastRemovedDigit = 0;
+  if (e2 >= 0) {
+    const uint32_t q = log10Pow2(e2);
+    e10 = (int32_t) q;
+    const int32_t k = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
+    const int32_t i = -e2 + (int32_t) q + k;
+    vr = mulPow5InvDivPow2(mv, q, i);
+    vp = mulPow5InvDivPow2(mp, q, i);
+    vm = mulPow5InvDivPow2(mm, q, i);
+#ifdef RYU_DEBUG
+    printf("%u * 2^%d / 10^%u\n", mv, e2, q);
+    printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+#endif
+    if (q != 0 && (vp - 1) / 10 <= vm / 10) {
+      // We need to know one removed digit even if we are not going to loop below. We could use
+      // q = X - 1 above, except that would require 33 bits for the result, and we've found that
+      // 32-bit arithmetic is faster even on 64-bit machines.
+      const int32_t l = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) (q - 1)) - 1;
+      lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + (int32_t) q - 1 + l) % 10);
+    }
+    if (q <= 9) {
+      // The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well.
+      // Only one of mp, mv, and mm can be a multiple of 5, if any.
+      if (mv % 5 == 0) {
+        vrIsTrailingZeros = multipleOfPowerOf5_32(mv, q);
+      } else if (acceptBounds) {
+        vmIsTrailingZeros = multipleOfPowerOf5_32(mm, q);
+      } else {
+        vp -= multipleOfPowerOf5_32(mp, q);
+      }
+    }
+  } else {
+    const uint32_t q = log10Pow5(-e2);
+    e10 = (int32_t) q + e2;
+    const int32_t i = -e2 - (int32_t) q;
+    const int32_t k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+    int32_t j = (int32_t) q - k;
+    vr = mulPow5divPow2(mv, (uint32_t) i, j);
+    vp = mulPow5divPow2(mp, (uint32_t) i, j);
+    vm = mulPow5divPow2(mm, (uint32_t) i, j);
+#ifdef RYU_DEBUG
+    printf("%u * 5^%d / 10^%u\n", mv, -e2, q);
+    printf("%u %d %d %d\n", q, i, k, j);
+    printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+#endif
+    if (q != 0 && (vp - 1) / 10 <= vm / 10) {
+      j = (int32_t) q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+      lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, (uint32_t) (i + 1), j) % 10);
+    }
+    if (q <= 1) {
+      // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+      // mv = 4 * m2, so it always has at least two trailing 0 bits.
+      vrIsTrailingZeros = true;
+      if (acceptBounds) {
+        // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+        vmIsTrailingZeros = mmShift == 1;
+      } else {
+        // mp = mv + 2, so it always has at least one trailing 0 bit.
+        --vp;
+      }
+    } else if (q < 31) { // TODO(ulfjack): Use a tighter bound here.
+      vrIsTrailingZeros = multipleOfPowerOf2_32(mv, q - 1);
+#ifdef RYU_DEBUG
+      printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("e10=%d\n", e10);
+  printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+  printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+  printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+  // Step 4: Find the shortest decimal representation in the interval of valid representations.
+  int32_t removed = 0;
+  uint32_t output;
+  if (vmIsTrailingZeros || vrIsTrailingZeros) {
+    // General case, which happens rarely (~4.0%).
+    while (vp / 10 > vm / 10) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=23106
+      // The compiler does not realize that vm % 10 can be computed from vm / 10
+      // as vm - (vm / 10) * 10.
+      vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+#else
+      vmIsTrailingZeros &= vm % 10 == 0;
+#endif
+      vrIsTrailingZeros &= lastRemovedDigit == 0;
+      lastRemovedDigit = (uint8_t) (vr % 10);
+      vr /= 10;
+      vp /= 10;
+      vm /= 10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+    printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+    if (vmIsTrailingZeros) {
+      while (vm % 10 == 0) {
+        vrIsTrailingZeros &= lastRemovedDigit == 0;
+        lastRemovedDigit = (uint8_t) (vr % 10);
+        vr /= 10;
+        vp /= 10;
+        vm /= 10;
+        ++removed;
+      }
+    }
+#ifdef RYU_DEBUG
+    printf("%u %d\n", vr, lastRemovedDigit);
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
+      // Round even if the exact number is .....50..0.
+      lastRemovedDigit = 4;
+    }
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+  } else {
+    // Specialized for the common case (~96.0%). Percentages below are relative to this.
+    // Loop iterations below (approximately):
+    // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+    while (vp / 10 > vm / 10) {
+      lastRemovedDigit = (uint8_t) (vr % 10);
+      vr /= 10;
+      vp /= 10;
+      vm /= 10;
+      ++removed;
+    }
+#ifdef RYU_DEBUG
+    printf("%u %d\n", vr, lastRemovedDigit);
+    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    // We need to take vr + 1 if vr is outside bounds or we need to round up.
+    output = vr + (vr == vm || lastRemovedDigit >= 5);
+  }
+  const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+  printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+  printf("O=%u\n", output);
+  printf("EXP=%d\n", exp);
+#endif
+
+  floating_decimal_32 fd;
+  fd.exponent = exp;
+  fd.mantissa = output;
+  return fd;
+}
+
+static inline int to_chars(const floating_decimal_32 v, const bool sign, char* const result) {
+  // Step 5: Print the decimal representation.
+  int index = 0;
+  if (sign) {
+    result[index++] = '-';
+  }
+
+  uint32_t output = v.mantissa;
+  const uint32_t olength = decimalLength9(output);
+
+#ifdef RYU_DEBUG
+  printf("DIGITS=%u\n", v.mantissa);
+  printf("OLEN=%u\n", olength);
+  printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+  // Print the decimal digits.
+  // The following code is equivalent to:
+  // for (uint32_t i = 0; i < olength - 1; ++i) {
+  //   const uint32_t c = output % 10; output /= 10;
+  //   result[index + olength - i] = (char) ('0' + c);
+  // }
+  // result[index] = '0' + output % 10;
+  uint32_t i = 0;
+  while (output >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+    const uint32_t c = output - 10000 * (output / 10000);
+#else
+    const uint32_t c = output % 10000;
+#endif
+    output /= 10000;
+    const uint32_t c0 = (c % 100) << 1;
+    const uint32_t c1 = (c / 100) << 1;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+    i += 4;
+  }
+  if (output >= 100) {
+    const uint32_t c = (output % 100) << 1;
+    output /= 100;
+    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+    i += 2;
+  }
+  if (output >= 10) {
+    const uint32_t c = output << 1;
+    // We can't use memcpy here: the decimal dot goes between these two digits.
+    result[index + olength - i] = DIGIT_TABLE[c + 1];
+    result[index] = DIGIT_TABLE[c];
+  } else {
+    result[index] = (char) ('0' + output);
+  }
+
+  // Print decimal point if needed.
+  if (olength > 1) {
+    result[index + 1] = '.';
+    index += olength + 1;
+  } else {
+    ++index;
+  }
+
+  // Print the exponent.
+  result[index++] = 'E';
+  int32_t exp = v.exponent + (int32_t) olength - 1;
+  if (exp < 0) {
+    result[index++] = '-';
+    exp = -exp;
+  }
+
+  if (exp >= 10) {
+    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+    index += 2;
+  } else {
+    result[index++] = (char) ('0' + exp);
+  }
+
+  return index;
+}
+
+int f2s_buffered_n(float f, char* result) {
+  // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
+  const uint32_t bits = float_to_bits(f);
+
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 31; bit >= 0; --bit) {
+    printf("%u", (bits >> bit) & 1);
+  }
+  printf("\n");
+#endif
+
+  // Decode bits into sign, mantissa, and exponent.
+  const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+  const uint32_t ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+  const uint32_t ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+  // Case distinction; exit early for the easy cases.
+  if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
+    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+  }
+
+  const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+  return to_chars(v, ieeeSign, result);
+}
+
+void f2s_buffered(float f, char* result) {
+  const int index = f2s_buffered_n(f, result);
+
+  // Terminate the string.
+  result[index] = '\0';
+}
+
+char* f2s(float f) {
+  char* const result = (char*) malloc(16);
+  f2s_buffered(f, result);
+  return result;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
new file mode 100644
index 00000000000..bb822c9a0c0
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
@@ -0,0 +1,128 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_F2S_INTRINSICS_H
+#define RYU_F2S_INTRINSICS_H
+
+// Defines RYU_32_BIT_PLATFORM if applicable.
+#include "ryu/common.h"
+
+#if defined(RYU_FLOAT_FULL_TABLE)
+
+#include "ryu/f2s_full_table.h"
+
+#else
+
+#if defined(RYU_OPTIMIZE_SIZE)
+#include "ryu/d2s_small_table.h"
+#else
+#include "ryu/d2s_full_table.h"
+#endif
+#define FLOAT_POW5_INV_BITCOUNT (DOUBLE_POW5_INV_BITCOUNT - 64)
+#define FLOAT_POW5_BITCOUNT (DOUBLE_POW5_BITCOUNT - 64)
+
+#endif
+
+static inline uint32_t pow5factor_32(uint32_t value) {
+  uint32_t count = 0;
+  for (;;) {
+    assert(value != 0);
+    const uint32_t q = value / 5;
+    const uint32_t r = value % 5;
+    if (r != 0) {
+      break;
+    }
+    value = q;
+    ++count;
+  }
+  return count;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5_32(const uint32_t value, const uint32_t p) {
+  return pow5factor_32(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2_32(const uint32_t value, const uint32_t p) {
+  // __builtin_ctz doesn't appear to be faster here.
+  return (value & ((1u << p) - 1)) == 0;
+}
+
+// It seems to be slightly faster to avoid uint128_t here, although the
+// generated code for uint128_t looks slightly nicer.
+static inline uint32_t mulShift32(const uint32_t m, const uint64_t factor, const int32_t shift) {
+  assert(shift > 32);
+
+  // The casts here help MSVC to avoid calls to the __allmul library
+  // function.
+  const uint32_t factorLo = (uint32_t)(factor);
+  const uint32_t factorHi = (uint32_t)(factor >> 32);
+  const uint64_t bits0 = (uint64_t)m * factorLo;
+  const uint64_t bits1 = (uint64_t)m * factorHi;
+
+#if defined(RYU_32_BIT_PLATFORM)
+  // On 32-bit platforms we can avoid a 64-bit shift-right since we only
+  // need the upper 32 bits of the result and the shift value is > 32.
+  const uint32_t bits0Hi = (uint32_t)(bits0 >> 32);
+  uint32_t bits1Lo = (uint32_t)(bits1);
+  uint32_t bits1Hi = (uint32_t)(bits1 >> 32);
+  bits1Lo += bits0Hi;
+  bits1Hi += (bits1Lo < bits0Hi);
+  if (shift >= 64) {
+    // s2f can call this with a shift value >= 64, which we have to handle.
+    // This could now be slower than the !defined(RYU_32_BIT_PLATFORM) case.
+    return (uint32_t)(bits1Hi >> (shift - 64));
+  } else {
+    const int32_t s = shift - 32;
+    return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+  }
+#else // RYU_32_BIT_PLATFORM
+  const uint64_t sum = (bits0 >> 32) + bits1;
+  const uint64_t shiftedSum = sum >> (shift - 32);
+  assert(shiftedSum <= UINT32_MAX);
+  return (uint32_t) shiftedSum;
+#endif // RYU_32_BIT_PLATFORM
+}
+
+static inline uint32_t mulPow5InvDivPow2(const uint32_t m, const uint32_t q, const int32_t j) {
+#if defined(RYU_FLOAT_FULL_TABLE)
+  return mulShift32(m, FLOAT_POW5_INV_SPLIT[q], j);
+#elif defined(RYU_OPTIMIZE_SIZE)
+  // The inverse multipliers are defined as [2^x / 5^y] + 1; the upper 64 bits from the double lookup
+  // table are the correct bits for [2^x / 5^y], so we have to add 1 here. Note that we rely on the
+  // fact that the added 1 that's already stored in the table never overflows into the upper 64 bits.
+  uint64_t pow5[2];
+  double_computeInvPow5(q, pow5);
+  return mulShift32(m, pow5[1] + 1, j);
+#else
+  return mulShift32(m, DOUBLE_POW5_INV_SPLIT[q][1] + 1, j);
+#endif
+}
+
+static inline uint32_t mulPow5divPow2(const uint32_t m, const uint32_t i, const int32_t j) {
+#if defined(RYU_FLOAT_FULL_TABLE)
+  return mulShift32(m, FLOAT_POW5_SPLIT[i], j);
+#elif defined(RYU_OPTIMIZE_SIZE)
+  uint64_t pow5[2];
+  double_computePow5(i, pow5);
+  return mulShift32(m, pow5[1], j);
+#else
+  return mulShift32(m, DOUBLE_POW5_SPLIT[i][1], j);
+#endif
+}
+
+#endif // RYU_F2S_INTRINSICS_H
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.c b/libstdc++-v3/src/c++17/ryu/generic_128.c
new file mode 100644
index 00000000000..2eb8da8aba8
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.c
@@ -0,0 +1,338 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+
+
+
+
+#ifdef RYU_DEBUG
+static char* s(uint128_t v) {
+  int len = decimalLength(v);
+  char* b = (char*) malloc((len + 1) * sizeof(char));
+  for (int i = 0; i < len; i++) {
+    const uint32_t c = (uint32_t) (v % 10);
+    v /= 10;
+    b[len - 1 - i] = (char) ('0' + c);
+  }
+  b[len] = 0;
+  return b;
+}
+#endif
+
+#define ONE ((uint128_t) 1)
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+
+struct floating_decimal_128 float_to_fd128(float f) {
+  uint32_t bits = 0;
+  memcpy(&bits, &f, sizeof(float));
+  return generic_binary_to_decimal(bits, FLOAT_MANTISSA_BITS, FLOAT_EXPONENT_BITS, false);
+}
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+
+struct floating_decimal_128 double_to_fd128(double d) {
+  uint64_t bits = 0;
+  memcpy(&bits, &d, sizeof(double));
+  return generic_binary_to_decimal(bits, DOUBLE_MANTISSA_BITS, DOUBLE_EXPONENT_BITS, false);
+}
+
+#define LONG_DOUBLE_MANTISSA_BITS 64
+#define LONG_DOUBLE_EXPONENT_BITS 15
+
+struct floating_decimal_128 long_double_to_fd128(long double d) {
+  uint128_t bits = 0;
+  memcpy(&bits, &d, sizeof(long double));
+#ifdef RYU_DEBUG
+  // For some odd reason, this ends up with noise in the top 48 bits. We can
+  // clear out those bits with the following line; this is not required, the
+  // conversion routine should ignore those bits, but the debug output can be
+  // confusing if they aren't 0s.
+  bits &= (ONE << 80) - 1;
+#endif
+  return generic_binary_to_decimal(bits, LONG_DOUBLE_MANTISSA_BITS, LONG_DOUBLE_EXPONENT_BITS, true);
+}
+
+struct floating_decimal_128 generic_binary_to_decimal(
+    const uint128_t bits, const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit) {
+#ifdef RYU_DEBUG
+  printf("IN=");
+  for (int32_t bit = 127; bit >= 0; --bit) {
+    printf("%u", (uint32_t) ((bits >> bit) & 1));
+  }
+  printf("\n");
+#endif
+
+  const uint32_t bias = (1u << (exponentBits - 1)) - 1;
+  const bool ieeeSign = ((bits >> (mantissaBits + exponentBits)) & 1) != 0;
+  const uint128_t ieeeMantissa = bits & ((ONE << mantissaBits) - 1);
+  const uint32_t ieeeExponent = (uint32_t) ((bits >> mantissaBits) & ((ONE << exponentBits) - 1u));
+
+  if (ieeeExponent == 0 && ieeeMantissa == 0) {
+    struct floating_decimal_128 fd;
+    fd.mantissa = 0;
+    fd.exponent = 0;
+    fd.sign = ieeeSign;
+    return fd;
+  }
+  if (ieeeExponent == ((1u << exponentBits) - 1u)) {
+    struct floating_decimal_128 fd;
+    fd.mantissa = explicitLeadingBit ? ieeeMantissa & ((ONE << (mantissaBits - 1)) - 1) : ieeeMantissa;
+    fd.exponent = FD128_EXCEPTIONAL_EXPONENT;
+    fd.sign = ieeeSign;
+    return fd;
+  }
+
+  int32_t e2;
+  uint128_t m2;
+  // We subtract 2 in all cases so that the bounds computation has 2 additional bits.
+  if (explicitLeadingBit) {
+    // mantissaBits includes the explicit leading bit, so we need to correct for that here.
+    if (ieeeExponent == 0) {
+      e2 = 1 - bias - mantissaBits + 1 - 2;
+    } else {
+      e2 = ieeeExponent - bias - mantissaBits + 1 - 2;
+    }
+    m2 = ieeeMantissa;
+  } else {
+    if (ieeeExponent == 0) {
+      e2 = 1 - bias - mantissaBits - 2;
+      m2 = ieeeMantissa;
+    } else {
+      e2 = ieeeExponent - bias - mantissaBits - 2;
+      m2 = (ONE << mantissaBits) | ieeeMantissa;
+    }
+  }
+  const bool even = (m2 & 1) == 0;
+  const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+  printf("-> %s %s * 2^%d\n", ieeeSign ? "-" : "+", s(m2), e2 + 2);
+#endif
+
+  // Step 2: Determine the interval of legal decimal representations.
+  const uint128_t mv = 4 * m2;
+  // Implicit bool -> int conversion. True is 1, false is 0.
+  const uint32_t mmShift =
+      (ieeeMantissa != (explicitLeadingBit ? ONE << (mantissaBits - 1) : 0))
+      || (ieeeExponent == 0);
+
+  // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+  uint128_t vr, vp, vm;
+  int32_t e10;
+  bool vmIsTrailingZeros = false;
+  bool vrIsTrailingZeros = false;
+  if (e2 >= 0) {
+    // I tried special-casing q == 0, but there was no effect on performance.
+    // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
+    const uint32_t q = log10Pow2(e2) - (e2 > 3);
+    e10 = q;
+    const int32_t k = FLOAT_128_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+    const int32_t i = -e2 + q + k;
+    uint64_t pow5[4];
+    generic_computeInvPow5(q, pow5);
+    vr = mulShift(4 * m2, pow5, i);
+    vp = mulShift(4 * m2 + 2, pow5, i);
+    vm = mulShift(4 * m2 - 1 - mmShift, pow5, i);
+#ifdef RYU_DEBUG
+    printf("%s * 2^%d / 10^%d\n", s(mv), e2, q);
+    printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+#endif
+    // floor(log_5(2^128)) = 55, this is very conservative
+    if (q <= 55) {
+      // Only one of mp, mv, and mm can be a multiple of 5, if any.
+      if (mv % 5 == 0) {
+        vrIsTrailingZeros = multipleOfPowerOf5(mv, q - 1);
+      } else if (acceptBounds) {
+        // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+        // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+        // <=> true && pow5Factor(mm) >= q, since e2 >= q.
+        vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+      } else {
+        // Same as min(e2 + 1, pow5Factor(mp)) >= q.
+        vp -= multipleOfPowerOf5(mv + 2, q);
+      }
+    }
+  } else {
+    // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+    const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
+    e10 = q + e2;
+    const int32_t i = -e2 - q;
+    const int32_t k = pow5bits(i) - FLOAT_128_POW5_BITCOUNT;
+    const int32_t j = q - k;
+    uint64_t pow5[4];
+    generic_computePow5(i, pow5);
+    vr = mulShift(4 * m2, pow5, j);
+    vp = mulShift(4 * m2 + 2, pow5, j);
+    vm = mulShift(4 * m2 - 1 - mmShift, pow5, j);
+#ifdef RYU_DEBUG
+    printf("%s * 5^%d / 10^%d\n", s(mv), -e2, q);
+    printf("%d %d %d %d\n", q, i, k, j);
+    printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+#endif
+    if (q <= 1) {
+      // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+      // mv = 4 m2, so it always has at least two trailing 0 bits.
+      vrIsTrailingZeros = true;
+      if (acceptBounds) {
+        // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+        vmIsTrailingZeros = mmShift == 1;
+      } else {
+        // mp = mv + 2, so it always has at least one trailing 0 bit.
+        --vp;
+      }
+    } else if (q < 127) { // TODO(ulfjack): Use a tighter bound here.
+      // We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q-1
+      // <=> ntz(mv) >= q-1  &&  pow5Factor(mv) - e2 >= q-1
+      // <=> ntz(mv) >= q-1    (e2 is negative and -e2 >= q)
+      // <=> (mv & ((1 << (q-1)) - 1)) == 0
+      // We also need to make sure that the left shift does not overflow.
+      vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+#ifdef RYU_DEBUG
+      printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("e10=%d\n", e10);
+  printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+  printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+  printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+  // Step 4: Find the shortest decimal representation in the interval of legal representations.
+  uint32_t removed = 0;
+  uint8_t lastRemovedDigit = 0;
+  uint128_t output;
+
+  while (vp / 10 > vm / 10) {
+    vmIsTrailingZeros &= vm % 10 == 0;
+    vrIsTrailingZeros &= lastRemovedDigit == 0;
+    lastRemovedDigit = (uint8_t) (vr % 10);
+    vr /= 10;
+    vp /= 10;
+    vm /= 10;
+    ++removed;
+  }
+#ifdef RYU_DEBUG
+  printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+  printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+  if (vmIsTrailingZeros) {
+    while (vm % 10 == 0) {
+      vrIsTrailingZeros &= lastRemovedDigit == 0;
+      lastRemovedDigit = (uint8_t) (vr % 10);
+      vr /= 10;
+      vp /= 10;
+      vm /= 10;
+      ++removed;
+    }
+  }
+#ifdef RYU_DEBUG
+  printf("%s %d\n", s(vr), lastRemovedDigit);
+  printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+  if (vrIsTrailingZeros && (lastRemovedDigit == 5) && (vr % 2 == 0)) {
+    // Round even if the exact numbers is .....50..0.
+    lastRemovedDigit = 4;
+  }
+  // We need to take vr+1 if vr is outside bounds or we need to round up.
+  output = vr +
+      ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || (lastRemovedDigit >= 5));
+  const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+  printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+  printf("O=%s\n", s(output));
+  printf("EXP=%d\n", exp);
+#endif
+
+  struct floating_decimal_128 fd;
+  fd.mantissa = output;
+  fd.exponent = exp;
+  fd.sign = ieeeSign;
+  return fd;
+}
+
+static inline int copy_special_str(char * const result, const struct floating_decimal_128 fd) {
+  if (fd.mantissa) {
+    memcpy(result, "NaN", 3);
+    return 3;
+  }
+  if (fd.sign) {
+    result[0] = '-';
+  }
+  memcpy(result + fd.sign, "Infinity", 8);
+  return fd.sign + 8;
+}
+
+int generic_to_chars(const struct floating_decimal_128 v, char* const result) {
+  if (v.exponent == FD128_EXCEPTIONAL_EXPONENT) {
+    return copy_special_str(result, v);
+  }
+
+  // Step 5: Print the decimal representation.
+  int index = 0;
+  if (v.sign) {
+    result[index++] = '-';
+  }
+
+  uint128_t output = v.mantissa;
+  const uint32_t olength = decimalLength(output);
+
+#ifdef RYU_DEBUG
+  printf("DIGITS=%s\n", s(v.mantissa));
+  printf("OLEN=%u\n", olength);
+  printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+  for (uint32_t i = 0; i < olength - 1; ++i) {
+    const uint32_t c = (uint32_t) (output % 10);
+    output /= 10;
+    result[index + olength - i] = (char) ('0' + c);
+  }
+  result[index] = '0' + (uint32_t) (output % 10); // output should be < 10 by now.
+
+  // Print decimal point if needed.
+  if (olength > 1) {
+    result[index + 1] = '.';
+    index += olength + 1;
+  } else {
+    ++index;
+  }
+
+  // Print the exponent.
+  result[index++] = 'E';
+  int32_t exp = v.exponent + olength - 1;
+  if (exp < 0) {
+    result[index++] = '-';
+    exp = -exp;
+  }
+
+  uint32_t elength = decimalLength(exp);
+  for (uint32_t i = 0; i < elength; ++i) {
+    const uint32_t c = exp % 10;
+    exp /= 10;
+    result[index + elength - 1 - i] = (char) ('0' + c);
+  }
+  index += elength;
+  return index;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.h b/libstdc++-v3/src/c++17/ryu/generic_128.h
new file mode 100644
index 00000000000..88e96776664
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.h
@@ -0,0 +1,517 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_GENERIC128_H
+#define RYU_GENERIC128_H
+
+
+typedef __uint128_t uint128_t;
+
+#define FLOAT_128_POW5_INV_BITCOUNT 249
+#define FLOAT_128_POW5_BITCOUNT 249
+#define POW5_TABLE_SIZE 56
+
+// These tables are ~4.5 kByte total, compared to ~160 kByte for the full tables.
+
+// There's no way to define 128-bit constants in C, so we use little-endian
+// pairs of 64-bit constants.
+static const uint64_t GENERIC_POW5_TABLE[POW5_TABLE_SIZE][2] = {
+ {                    1u,                    0u },
+ {                    5u,                    0u },
+ {                   25u,                    0u },
+ {                  125u,                    0u },
+ {                  625u,                    0u },
+ {                 3125u,                    0u },
+ {                15625u,                    0u },
+ {                78125u,                    0u },
+ {               390625u,                    0u },
+ {              1953125u,                    0u },
+ {              9765625u,                    0u },
+ {             48828125u,                    0u },
+ {            244140625u,                    0u },
+ {           1220703125u,                    0u },
+ {           6103515625u,                    0u },
+ {          30517578125u,                    0u },
+ {         152587890625u,                    0u },
+ {         762939453125u,                    0u },
+ {        3814697265625u,                    0u },
+ {       19073486328125u,                    0u },
+ {       95367431640625u,                    0u },
+ {      476837158203125u,                    0u },
+ {     2384185791015625u,                    0u },
+ {    11920928955078125u,                    0u },
+ {    59604644775390625u,                    0u },
+ {   298023223876953125u,                    0u },
+ {  1490116119384765625u,                    0u },
+ {  7450580596923828125u,                    0u },
+ {   359414837200037393u,                    2u },
+ {  1797074186000186965u,                   10u },
+ {  8985370930000934825u,                   50u },
+ {  8033366502585570893u,                  252u },
+ {  3273344365508751233u,                 1262u },
+ { 16366721827543756165u,                 6310u },
+ {  8046632842880574361u,                31554u },
+ {  3339676066983768573u,               157772u },
+ { 16698380334918842865u,               788860u },
+ {  9704925379756007861u,              3944304u },
+ { 11631138751360936073u,             19721522u },
+ {  2815461535676025517u,             98607613u },
+ { 14077307678380127585u,            493038065u },
+ { 15046306170771983077u,           2465190328u },
+ {  1444554559021708921u,          12325951644u },
+ {  7222772795108544605u,          61629758220u },
+ { 17667119901833171409u,         308148791101u },
+ { 14548623214327650581u,        1540743955509u },
+ { 17402883850509598057u,        7703719777548u },
+ { 13227442957709783821u,       38518598887744u },
+ { 10796982567420264257u,      192592994438723u },
+ { 17091424689682218053u,      962964972193617u },
+ { 11670147153572883801u,     4814824860968089u },
+ {  3010503546735764157u,    24074124304840448u },
+ { 15052517733678820785u,   120370621524202240u },
+ {  1475612373555897461u,   601853107621011204u },
+ {  7378061867779487305u,  3009265538105056020u },
+ { 18443565265187884909u, 15046327690525280101u }
+};
+
+static const uint64_t GENERIC_POW5_SPLIT[89][4] = {
+ {                    0u,                    0u,                    0u,    72057594037927936u },
+ {                    0u,  5206161169240293376u,  4575641699882439235u,    73468396926392969u },
+ {  3360510775605221349u,  6983200512169538081u,  4325643253124434363u,    74906821675075173u },
+ { 11917660854915489451u,  9652941469841108803u,   946308467778435600u,    76373409087490117u },
+ {  1994853395185689235u, 16102657350889591545u,  6847013871814915412u,    77868710555449746u },
+ {   958415760277438274u, 15059347134713823592u,  7329070255463483331u,    79393288266368765u },
+ {  2065144883315240188u,  7145278325844925976u, 14718454754511147343u,    80947715414629833u },
+ {  8980391188862868935u, 13709057401304208685u,  8230434828742694591u,    82532576417087045u },
+ {   432148644612782575u,  7960151582448466064u, 12056089168559840552u,    84148467132788711u },
+ {   484109300864744403u, 15010663910730448582u, 16824949663447227068u,    85795995087002057u },
+ { 14793711725276144220u, 16494403799991899904u, 10145107106505865967u,    87475779699624060u },
+ { 15427548291869817042u, 12330588654550505203u, 13980791795114552342u,    89188452518064298u },
+ {  9979404135116626552u, 13477446383271537499u, 14459862802511591337u,    90934657454687378u },
+ { 12385121150303452775u,  9097130814231585614u,  6523855782339765207u,    92715051028904201u },
+ {  1822931022538209743u, 16062974719797586441u,  3619180286173516788u,    94530302614003091u },
+ { 12318611738248470829u, 13330752208259324507u, 10986694768744162601u,    96381094688813589u },
+ { 13684493829640282333u,  7674802078297225834u, 15208116197624593182u,    98268123094297527u },
+ {  5408877057066295332u,  6470124174091971006u, 15112713923117703147u,   100192097295163851u },
+ { 11407083166564425062u, 18189998238742408185u,  4337638702446708282u,   102153740646605557u },
+ {  4112405898036935485u,   924624216579956435u, 14251108172073737125u,   104153790666259019u },
+ { 16996739107011444789u, 10015944118339042475u,  2395188869672266257u,   106192999311487969u },
+ {  4588314690421337879u,  5339991768263654604u, 15441007590670620066u,   108272133262096356u },
+ {  2286159977890359825u, 14329706763185060248u,  5980012964059367667u,   110391974208576409u },
+ {  9654767503237031099u, 11293544302844823188u, 11739932712678287805u,   112553319146000238u },
+ { 11362964448496095896u,  7990659682315657680u,   251480263940996374u,   114756980673665505u },
+ {  1423410421096377129u, 14274395557581462179u, 16553482793602208894u,   117003787300607788u },
+ {  2070444190619093137u, 11517140404712147401u, 11657844572835578076u,   119294583757094535u },
+ {  7648316884775828921u, 15264332483297977688u,   247182277434709002u,   121630231312217685u },
+ { 17410896758132241352u, 10923914482914417070u, 13976383996795783649u,   124011608097704390u },
+ {  9542674537907272703u,  3079432708831728956u, 14235189590642919676u,   126439609438067572u },
+ { 10364666969937261816u,  8464573184892924210u, 12758646866025101190u,   128915148187220428u },
+ { 14720354822146013883u, 11480204489231511423u,  7449876034836187038u,   131439155071681461u },
+ {  1692907053653558553u, 17835392458598425233u,  1754856712536736598u,   134012579040499057u },
+ {  5620591334531458755u, 11361776175667106627u, 13350215315297937856u,   136636387622027174u },
+ { 17455759733928092601u, 10362573084069962561u, 11246018728801810510u,   139311567287686283u },
+ {  2465404073814044982u, 17694822665274381860u,  1509954037718722697u,   142039123822846312u },
+ {  2152236053329638369u, 11202280800589637091u, 16388426812920420176u,    72410041352485523u },
+ { 17319024055671609028u, 10944982848661280484u,  2457150158022562661u,    73827744744583080u },
+ { 17511219308535248024u,  5122059497846768077u,  2089605804219668451u,    75273205100637900u },
+ { 10082673333144031533u, 14429008783411894887u, 12842832230171903890u,    76746965869337783u },
+ { 16196653406315961184u, 10260180891682904501u, 10537411930446752461u,    78249581139456266u },
+ { 15084422041749743389u,   234835370106753111u, 16662517110286225617u,    79781615848172976u },
+ {  8199644021067702606u,  3787318116274991885u,  7438130039325743106u,    81343645993472659u },
+ { 12039493937039359765u,  9773822153580393709u,  5945428874398357806u,    82936258850702722u },
+ {   984543865091303961u,  7975107621689454830u,  6556665988501773347u,    84560053193370726u },
+ {  9633317878125234244u, 16099592426808915028u,  9706674539190598200u,    86215639518264828u },
+ {  6860695058870476186u,  4471839111886709592u,  7828342285492709568u,    87903640274981819u },
+ { 14583324717644598331u,  4496120889473451238u,  5290040788305728466u,    89624690099949049u },
+ { 18093669366515003715u, 12879506572606942994u, 18005739787089675377u,    91379436055028227u },
+ { 17997493966862379937u, 14646222655265145582u, 10265023312844161858u,    93168537870790806u },
+ { 12283848109039722318u, 11290258077250314935u,  9878160025624946825u,    94992668194556404u },
+ {  8087752761883078164u,  5262596608437575693u, 11093553063763274413u,    96852512843287537u },
+ { 15027787746776840781u, 12250273651168257752u,  9290470558712181914u,    98748771061435726u },
+ { 15003915578366724489u,  2937334162439764327u,  5404085603526796602u,   100682155783835929u },
+ {  5225610465224746757u, 14932114897406142027u,  2774647558180708010u,   102653393903748137u },
+ { 17112957703385190360u, 12069082008339002412u,  3901112447086388439u,   104663226546146909u },
+ {  4062324464323300238u,  3992768146772240329u, 15757196565593695724u,   106712409346361594u },
+ {  5525364615810306701u, 11855206026704935156u, 11344868740897365300u,   108801712734172003u },
+ {  9274143661888462646u,  4478365862348432381u, 18010077872551661771u,   110931922223466333u },
+ { 12604141221930060148u,  8930937759942591500u,  9382183116147201338u,   113103838707570263u },
+ { 14513929377491886653u,  1410646149696279084u,   587092196850797612u,   115318278760358235u },
+ {  2226851524999454362u,  7717102471110805679u,  7187441550995571734u,   117576074943260147u },
+ {  5527526061344932763u,  2347100676188369132u, 16976241418824030445u,   119878076118278875u },
+ {  6088479778147221611u, 17669593130014777580u, 10991124207197663546u,   122225147767136307u },
+ { 11107734086759692041u,  3391795220306863431u, 17233960908859089158u,   124618172316667879u },
+ {  7913172514655155198u, 17726879005381242552u,   641069866244011540u,   127058049470587962u },
+ { 12596991768458713949u, 15714785522479904446u,  6035972567136116512u,   129545696547750811u },
+ { 16901996933781815980u,  4275085211437148707u, 14091642539965169063u,   132082048827034281u },
+ {  7524574627987869240u, 15661204384239316051u,  2444526454225712267u,   134668059898975949u },
+ {  8199251625090479942u,  6803282222165044067u, 16064817666437851504u,   137304702024293857u },
+ {  4453256673338111920u, 15269922543084434181u,  3139961729834750852u,   139992966499426682u },
+ { 15841763546372731299u,  3013174075437671812u,  4383755396295695606u,   142733864029230733u },
+ {  9771896230907310329u,  4900659362437687569u, 12386126719044266361u,    72764212553486967u },
+ {  9420455527449565190u,  1859606122611023693u,  6555040298902684281u,    74188850200884818u },
+ {  5146105983135678095u,  2287300449992174951u,  4325371679080264751u,    75641380576797959u },
+ { 11019359372592553360u,  8422686425957443718u,  7175176077944048210u,    77122349788024458u },
+ { 11005742969399620716u,  4132174559240043701u,  9372258443096612118u,    78632314633490790u },
+ {  8887589641394725840u,  8029899502466543662u, 14582206497241572853u,    80171842813591127u },
+ {   360247523705545899u, 12568341805293354211u, 14653258284762517866u,    81741513143625247u },
+ { 12314272731984275834u,  4740745023227177044u,  6141631472368337539u,    83341915771415304u },
+ {   441052047733984759u,  7940090120939869826u, 11750200619921094248u,    84973652399183278u },
+ {  3436657868127012749u,  9187006432149937667u, 16389726097323041290u,    86637336509772529u },
+ { 13490220260784534044u, 15339072891382896702u,  8846102360835316895u,    88333593597298497u },
+ {  4125672032094859833u,   158347675704003277u, 10592598512749774447u,    90063061402315272u },
+ { 12189928252974395775u,  2386931199439295891u,  7009030566469913276u,    91826390151586454u },
+ {  9256479608339282969u,  2844900158963599229u, 11148388908923225596u,    93624242802550437u },
+ { 11584393507658707408u,  2863659090805147914u,  9873421561981063551u,    95457295292572042u },
+ { 13984297296943171390u,  1931468383973130608u, 12905719743235082319u,    97326236793074198u },
+ {  5837045222254987499u, 10213498696735864176u, 14893951506257020749u,    99231769968645227u }
+};
+
+// Unfortunately, the results are sometimes off by one or two. We use an additional
+// lookup table to store those cases and adjust the result.
+static const uint64_t POW5_ERRORS[156] = {
+ 0x0000000000000000u, 0x0000000000000000u, 0x0000000000000000u, 0x9555596400000000u,
+ 0x65a6569525565555u, 0x4415551445449655u, 0x5105015504144541u, 0x65a69969a6965964u,
+ 0x5054955969959656u, 0x5105154515554145u, 0x4055511051591555u, 0x5500514455550115u,
+ 0x0041140014145515u, 0x1005440545511051u, 0x0014405450411004u, 0x0414440010500000u,
+ 0x0044000440010040u, 0x5551155000004001u, 0x4554555454544114u, 0x5150045544005441u,
+ 0x0001111400054501u, 0x6550955555554554u, 0x1504159645559559u, 0x4105055141454545u,
+ 0x1411541410405454u, 0x0415555044545555u, 0x0014154115405550u, 0x1540055040411445u,
+ 0x0000000500000000u, 0x5644000000000000u, 0x1155555591596555u, 0x0410440054569565u,
+ 0x5145100010010005u, 0x0555041405500150u, 0x4141450455140450u, 0x0000000144000140u,
+ 0x5114004001105410u, 0x4444100404005504u, 0x0414014410001015u, 0x5145055155555015u,
+ 0x0141041444445540u, 0x0000100451541414u, 0x4105041104155550u, 0x0500501150451145u,
+ 0x1001050000004114u, 0x5551504400141045u, 0x5110545410151454u, 0x0100001400004040u,
+ 0x5040010111040000u, 0x0140000150541100u, 0x4400140400104110u, 0x5011014405545004u,
+ 0x0000000044155440u, 0x0000000010000000u, 0x1100401444440001u, 0x0040401010055111u,
+ 0x5155155551405454u, 0x0444440015514411u, 0x0054505054014101u, 0x0451015441115511u,
+ 0x1541411401140551u, 0x4155104514445110u, 0x4141145450145515u, 0x5451445055155050u,
+ 0x4400515554110054u, 0x5111145104501151u, 0x565a655455500501u, 0x5565555555525955u,
+ 0x0550511500405695u, 0x4415504051054544u, 0x6555595965555554u, 0x0100915915555655u,
+ 0x5540001510001001u, 0x5450051414000544u, 0x1405010555555551u, 0x5555515555644155u,
+ 0x5555055595496555u, 0x5451045004415000u, 0x5450510144040144u, 0x5554155555556455u,
+ 0x5051555495415555u, 0x5555554555555545u, 0x0000000010005455u, 0x4000005000040000u,
+ 0x5565555555555954u, 0x5554559555555505u, 0x9645545495552555u, 0x4000400055955564u,
+ 0x0040000000000001u, 0x4004100100000000u, 0x5540040440000411u, 0x4565555955545644u,
+ 0x1140659549651556u, 0x0100000410010000u, 0x5555515400004001u, 0x5955545555155255u,
+ 0x5151055545505556u, 0x5051454510554515u, 0x0501500050415554u, 0x5044154005441005u,
+ 0x1455445450550455u, 0x0010144055144545u, 0x0000401100000004u, 0x1050145050000010u,
+ 0x0415004554011540u, 0x1000510100151150u, 0x0100040400001144u, 0x0000000000000000u,
+ 0x0550004400000100u, 0x0151145041451151u, 0x0000400400005450u, 0x0000100044010004u,
+ 0x0100054100050040u, 0x0504400005410010u, 0x4011410445500105u, 0x0000404000144411u,
+ 0x0101504404500000u, 0x0000005044400400u, 0x0000000014000100u, 0x0404440414000000u,
+ 0x5554100410000140u, 0x4555455544505555u, 0x5454105055455455u, 0x0115454155454015u,
+ 0x4404110000045100u, 0x4400001100101501u, 0x6596955956966a94u, 0x0040655955665965u,
+ 0x5554144400100155u, 0xa549495401011041u, 0x5596555565955555u, 0x5569965959549555u,
+ 0x969565a655555456u, 0x0000001000000000u, 0x0000000040000140u, 0x0000040100000000u,
+ 0x1415454400000000u, 0x5410415411454114u, 0x0400040104000154u, 0x0504045000000411u,
+ 0x0000001000000010u, 0x5554000000001040u, 0x5549155551556595u, 0x1455541055515555u,
+ 0x0510555454554541u, 0x9555555555540455u, 0x6455456555556465u, 0x4524565555654514u,
+ 0x5554655255559545u, 0x9555455441155556u, 0x0000000051515555u, 0x0010005040000550u,
+ 0x5044044040000000u, 0x1045040440010500u, 0x0000400000040000u, 0x0000000000000000u
+};
+
+static const uint64_t GENERIC_POW5_INV_SPLIT[89][4] = {
+ {                    0u,                    0u,                    0u,   144115188075855872u },
+ {  1573859546583440065u,  2691002611772552616u,  6763753280790178510u,   141347765182270746u },
+ { 12960290449513840412u, 12345512957918226762u, 18057899791198622765u,   138633484706040742u },
+ {  7615871757716765416u,  9507132263365501332u,  4879801712092008245u,   135971326161092377u },
+ {  7869961150745287587u,  5804035291554591636u,  8883897266325833928u,   133360288657597085u },
+ {  2942118023529634767u, 15128191429820565086u, 10638459445243230718u,   130799390525667397u },
+ { 14188759758411913794u,  5362791266439207815u,  8068821289119264054u,   128287668946279217u },
+ {  7183196927902545212u,  1952291723540117099u, 12075928209936341512u,   125824179589281448u },
+ {  5672588001402349748u, 17892323620748423487u,  9874578446960390364u,   123407996258356868u },
+ {  4442590541217566325u,  4558254706293456445u, 10343828952663182727u,   121038210542800766u },
+ {  3005560928406962566u,  2082271027139057888u, 13961184524927245081u,   118713931475986426u },
+ { 13299058168408384786u, 17834349496131278595u,  9029906103900731664u,   116434285200389047u },
+ {  5414878118283973035u, 13079825470227392078u, 17897304791683760280u,   114198414639042157u },
+ { 14609755883382484834u, 14991702445765844156u,  3269802549772755411u,   112005479173303009u },
+ { 15967774957605076027u,  2511532636717499923u, 16221038267832563171u,   109854654326805788u },
+ {  9269330061621627145u,  3332501053426257392u, 16223281189403734630u,   107745131455483836u },
+ { 16739559299223642282u,  1873986623300664530u,  6546709159471442872u,   105676117443544318u },
+ { 17116435360051202055u,  1359075105581853924u,  2038341371621886470u,   103646834405281051u },
+ { 17144715798009627550u,  3201623802661132408u,  9757551605154622431u,   101656519392613377u },
+ { 17580479792687825857u,  6546633380567327312u, 15099972427870912398u,    99704424108241124u },
+ {  9726477118325522902u, 14578369026754005435u, 11728055595254428803u,    97789814624307808u },
+ {   134593949518343635u,  5715151379816901985u,  1660163707976377376u,    95911971106466306u },
+ {  5515914027713859358u,  7124354893273815720u,  5548463282858794077u,    94070187543243255u },
+ {  6188403395862945512u,  5681264392632320838u, 15417410852121406654u,    92263771480600430u },
+ { 15908890877468271457u, 10398888261125597540u,  4817794962769172309u,    90492043761593298u },
+ {  1413077535082201005u, 12675058125384151580u,  7731426132303759597u,    88754338271028867u },
+ {  1486733163972670293u, 11369385300195092554u, 11610016711694864110u,    87050001685026843u },
+ {  8788596583757589684u,  3978580923851924802u,  9255162428306775812u,    85378393225389919u },
+ {  7203518319660962120u, 15044736224407683725u,  2488132019818199792u,    83738884418690858u },
+ {  4004175967662388707u, 18236988667757575407u, 15613100370957482671u,    82130858859985791u },
+ { 18371903370586036463u,    53497579022921640u, 16465963977267203307u,    80553711981064899u },
+ { 10170778323887491315u,  1999668801648976001u, 10209763593579456445u,    79006850823153334u },
+ { 17108131712433974546u, 16825784443029944237u,  2078700786753338945u,    77489693813976938u },
+ { 17221789422665858532u, 12145427517550446164u,  5391414622238668005u,    76001670549108934u },
+ {  4859588996898795878u,  1715798948121313204u,  3950858167455137171u,    74542221577515387u },
+ { 13513469241795711526u,   631367850494860526u, 10517278915021816160u,    73110798191218799u },
+ { 11757513142672073111u,  2581974932255022228u, 17498959383193606459u,   143413724438001539u },
+ { 14524355192525042817u,  5640643347559376447u,  1309659274756813016u,   140659771648132296u },
+ {  2765095348461978538u, 11021111021896007722u,  3224303603779962366u,   137958702611185230u },
+ { 12373410389187981037u, 13679193545685856195u, 11644609038462631561u,   135309501808182158u },
+ { 12813176257562780151u,  3754199046160268020u,  9954691079802960722u,   132711173221007413u },
+ { 17557452279667723458u,  3237799193992485824u, 17893947919029030695u,   130162739957935629u },
+ { 14634200999559435155u,  4123869946105211004u,  6955301747350769239u,   127663243886350468u },
+ {  2185352760627740240u,  2864813346878886844u, 13049218671329690184u,   125211745272516185u },
+ {  6143438674322183002u, 10464733336980678750u,  6982925169933978309u,   122807322428266620u },
+ {  1099509117817174576u, 10202656147550524081u,   754997032816608484u,   120449071364478757u },
+ {  2410631293559367023u, 17407273750261453804u, 15307291918933463037u,   118136105451200587u },
+ { 12224968375134586697u,  1664436604907828062u, 11506086230137787358u,   115867555084305488u },
+ {  3495926216898000888u, 18392536965197424288u, 10992889188570643156u,   113642567358547782u },
+ {  8744506286256259680u,  3966568369496879937u, 18342264969761820037u,   111460305746896569u },
+ {  7689600520560455039u,  5254331190877624630u,  9628558080573245556u,   109319949786027263u },
+ { 11862637625618819436u,  3456120362318976488u, 14690471063106001082u,   107220694767852583u },
+ {  5697330450030126444u, 12424082405392918899u,   358204170751754904u,   105161751436977040u },
+ { 11257457505097373622u, 15373192700214208870u,   671619062372033814u,   103142345693961148u },
+ { 16850355018477166700u,  1913910419361963966u,  4550257919755970531u,   101161718304283822u },
+ {  9670835567561997011u, 10584031339132130638u,  3060560222974851757u,    99219124612893520u },
+ {  7698686577353054710u, 11689292838639130817u, 11806331021588878241u,    97313834264240819u },
+ { 12233569599615692137u,  3347791226108469959u, 10333904326094451110u,    95445130927687169u },
+ { 13049400362825383933u, 17142621313007799680u,  3790542585289224168u,    93612312028186576u },
+ { 12430457242474442072u,  5625077542189557960u, 14765055286236672238u,    91814688482138969u },
+ {  4759444137752473128u,  2230562561567025078u,  4954443037339580076u,    90051584438315940u },
+ {  7246913525170274758u,  8910297835195760709u,  4015904029508858381u,    88322337023761438u },
+ { 12854430245836432067u,  8135139748065431455u, 11548083631386317976u,    86626296094571907u },
+ {  4848827254502687803u,  4789491250196085625u,  3988192420450664125u,    84962823991462151u },
+ {  7435538409611286684u,   904061756819742353u, 14598026519493048444u,    83331295300025028u },
+ { 11042616160352530997u,  8948390828345326218u, 10052651191118271927u,    81731096615594853u },
+ { 11059348291563778943u, 11696515766184685544u,  3783210511290897367u,    80161626312626082u },
+ {  7020010856491885826u,  5025093219346041680u,  8960210401638911765u,    78622294318500592u },
+ { 17732844474490699984u,  7820866704994446502u,  6088373186798844243u,    77112521891678506u },
+ {   688278527545590501u,  3045610706602776618u,  8684243536999567610u,    75631741404109150u },
+ {  2734573255120657297u,  3903146411440697663u,  9470794821691856713u,    74179396127820347u },
+ { 15996457521023071259u,  4776627823451271680u, 12394856457265744744u,    72754940025605801u },
+ { 13492065758834518331u,  7390517611012222399u,  1630485387832860230u,   142715675091463768u },
+ { 13665021627282055864u,  9897834675523659302u, 17907668136755296849u,   139975126841173266u },
+ {  9603773719399446181u, 10771916301484339398u, 10672699855989487527u,   137287204938390542u },
+ {  3630218541553511265u,  8139010004241080614u,  2876479648932814543u,   134650898807055963u },
+ {  8318835909686377084u,  9525369258927993371u,  2796120270400437057u,   132065217277054270u },
+ { 11190003059043290163u, 12424345635599592110u, 12539346395388933763u,   129529188211565064u },
+ {  8701968833973242276u,   820569587086330727u,  2315591597351480110u,   127041858141569228u },
+ {  5115113890115690487u, 16906305245394587826u,  9899749468931071388u,   124602291907373862u },
+ { 15543535488939245974u, 10945189844466391399u,  3553863472349432246u,   122209572307020975u },
+ {  7709257252608325038u,  1191832167690640880u, 15077137020234258537u,   119862799751447719u },
+ {  7541333244210021737u,  9790054727902174575u,  5160944773155322014u,   117561091926268545u },
+ { 12297384708782857832u,  1281328873123467374u,  4827925254630475769u,   115303583460052092u },
+ { 13243237906232367265u, 15873887428139547641u,  3607993172301799599u,   113089425598968120u },
+ { 11384616453739611114u, 15184114243769211033u, 13148448124803481057u,   110917785887682141u },
+ { 17727970963596660683u,  1196965221832671990u, 14537830463956404138u,   108787847856377790u },
+ { 17241367586707330931u,  8880584684128262874u, 11173506540726547818u,   106698810713789254u },
+ {  7184427196661305643u, 14332510582433188173u, 14230167953789677901u,   104649889046128358u }
+};
+
+static const uint64_t POW5_INV_ERRORS[154] = {
+ 0x1144155514145504u, 0x0000541555401141u, 0x0000000000000000u, 0x0154454000000000u,
+ 0x4114105515544440u, 0x0001001111500415u, 0x4041411410011000u, 0x5550114515155014u,
+ 0x1404100041554551u, 0x0515000450404410u, 0x5054544401140004u, 0x5155501005555105u,
+ 0x1144141000105515u, 0x0541500000500000u, 0x1104105540444140u, 0x4000015055514110u,
+ 0x0054010450004005u, 0x4155515404100005u, 0x5155145045155555u, 0x1511555515440558u,
+ 0x5558544555515555u, 0x0000000000000010u, 0x5004000000000050u, 0x1415510100000010u,
+ 0x4545555444514500u, 0x5155151555555551u, 0x1441540144044554u, 0x5150104045544400u,
+ 0x5450545401444040u, 0x5554455045501400u, 0x4655155555555145u, 0x1000010055455055u,
+ 0x1000004000055004u, 0x4455405104000005u, 0x4500114504150545u, 0x0000000014000000u,
+ 0x5450000000000000u, 0x5514551511445555u, 0x4111501040555451u, 0x4515445500054444u,
+ 0x5101500104100441u, 0x1545115155545055u, 0x0000000000000000u, 0x1554000000100000u,
+ 0x5555545595551555u, 0x5555051851455955u, 0x5555555555555559u, 0x0000400011001555u,
+ 0x0000004400040000u, 0x5455511555554554u, 0x5614555544115445u, 0x6455156145555155u,
+ 0x5455855455415455u, 0x5515555144555545u, 0x0114400000145155u, 0x0000051000450511u,
+ 0x4455154554445100u, 0x4554150141544455u, 0x65955555559a5965u, 0x5555555854559559u,
+ 0x9569654559616595u, 0x1040044040005565u, 0x1010010500011044u, 0x1554015545154540u,
+ 0x4440555401545441u, 0x1014441450550105u, 0x4545400410504145u, 0x5015111541040151u,
+ 0x5145051154000410u, 0x1040001044545044u, 0x4001400000151410u, 0x0540000044040000u,
+ 0x0510555454411544u, 0x0400054054141550u, 0x1001041145001100u, 0x0000000140000000u,
+ 0x0000000014100000u, 0x1544005454000140u, 0x4050055505445145u, 0x0011511104504155u,
+ 0x5505544415045055u, 0x1155154445515554u, 0x0000000000004555u, 0x0000000000000000u,
+ 0x5101010510400004u, 0x1514045044440400u, 0x5515519555515555u, 0x4554545441555545u,
+ 0x1551055955551515u, 0x0150000011505515u, 0x0044005040400000u, 0x0004001004010050u,
+ 0x0000051004450414u, 0x0114001101001144u, 0x0401000001000001u, 0x4500010001000401u,
+ 0x0004100000005000u, 0x0105000441101100u, 0x0455455550454540u, 0x5404050144105505u,
+ 0x4101510540555455u, 0x1055541411451555u, 0x5451445110115505u, 0x1154110010101545u,
+ 0x1145140450054055u, 0x5555565415551554u, 0x1550559555555555u, 0x5555541545045141u,
+ 0x4555455450500100u, 0x5510454545554555u, 0x1510140115045455u, 0x1001050040111510u,
+ 0x5555454555555504u, 0x9954155545515554u, 0x6596656555555555u, 0x0140410051555559u,
+ 0x0011104010001544u, 0x965669659a680501u, 0x5655a55955556955u, 0x4015111014404514u,
+ 0x1414155554505145u, 0x0540040011051404u, 0x1010000000015005u, 0x0010054050004410u,
+ 0x5041104014000100u, 0x4440010500100001u, 0x1155510504545554u, 0x0450151545115541u,
+ 0x4000100400110440u, 0x1004440010514440u, 0x0000115050450000u, 0x0545404455541500u,
+ 0x1051051555505101u, 0x5505144554544144u, 0x4550545555515550u, 0x0015400450045445u,
+ 0x4514155400554415u, 0x4555055051050151u, 0x1511441450001014u, 0x4544554510404414u,
+ 0x4115115545545450u, 0x5500541555551555u, 0x5550010544155015u, 0x0144414045545500u,
+ 0x4154050001050150u, 0x5550511111000145u, 0x1114504055000151u, 0x5104041101451040u,
+ 0x0010501401051441u, 0x0010501450504401u, 0x4554585440044444u, 0x5155555951450455u,
+ 0x0040000400105555u, 0x0000000000000001u,
+};
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 32768.
+static inline uint32_t pow5bits(const int32_t e) {
+  assert(e >= 0);
+  assert(e <= 1 << 15);
+  return (uint32_t) (((e * 163391164108059ull) >> 46) + 1);
+}
+
+static inline void mul_128_256_shift(
+    const uint64_t* const a, const uint64_t* const b, const uint32_t shift, const uint32_t corr, uint64_t* const result) {
+  assert(shift > 0);
+  assert(shift < 256);
+  const uint128_t b00 = ((uint128_t) a[0]) * b[0]; // 0
+  const uint128_t b01 = ((uint128_t) a[0]) * b[1]; // 64
+  const uint128_t b02 = ((uint128_t) a[0]) * b[2]; // 128
+  const uint128_t b03 = ((uint128_t) a[0]) * b[3]; // 196
+  const uint128_t b10 = ((uint128_t) a[1]) * b[0]; // 64
+  const uint128_t b11 = ((uint128_t) a[1]) * b[1]; // 128
+  const uint128_t b12 = ((uint128_t) a[1]) * b[2]; // 196
+  const uint128_t b13 = ((uint128_t) a[1]) * b[3]; // 256
+
+  const uint128_t s0 = b00;       // 0   x
+  const uint128_t s1 = b01 + b10; // 64  x
+  const uint128_t c1 = s1 < b01;  // 196 x
+  const uint128_t s2 = b02 + b11; // 128 x
+  const uint128_t c2 = s2 < b02;  // 256 x
+  const uint128_t s3 = b03 + b12; // 196 x
+  const uint128_t c3 = s3 < b03;  // 324 x
+
+  const uint128_t p0 = s0 + (s1 << 64);                                // 0
+  const uint128_t d0 = p0 < b00;                                       // 128
+  const uint128_t q1 = s2 + (s1 >> 64) + (s3 << 64);                   // 128
+  const uint128_t d1 = q1 < s2;                                        // 256
+  const uint128_t p1 = q1 + (c1 << 64) + d0;                           // 128
+  const uint128_t d2 = p1 < q1;                                        // 256
+  const uint128_t p2 = b13 + (s3 >> 64) + c2 + (c3 << 64) + d1 + d2;   // 256
+
+  if (shift < 128) {
+    const uint128_t r0 = corr + ((p0 >> shift) | (p1 << (128 - shift)));
+    const uint128_t r1 = ((p1 >> shift) | (p2 << (128 - shift))) + (r0 < corr);
+    result[0] = (uint64_t) r0;
+    result[1] = (uint64_t) (r0 >> 64);
+    result[2] = (uint64_t) r1;
+    result[3] = (uint64_t) (r1 >> 64);
+  } else if (shift == 128) {
+    const uint128_t r0 = corr + p1;
+    const uint128_t r1 = p2 + (r0 < corr);
+    result[0] = (uint64_t) r0;
+    result[1] = (uint64_t) (r0 >> 64);
+    result[2] = (uint64_t) r1;
+    result[3] = (uint64_t) (r1 >> 64);
+  } else {
+    const uint128_t r0 = corr + ((p1 >> (shift - 128)) | (p2 << (256 - shift)));
+    const uint128_t r1 = (p2 >> (shift - 128)) + (r0 < corr);
+    result[0] = (uint64_t) r0;
+    result[1] = (uint64_t) (r0 >> 64);
+    result[2] = (uint64_t) r1;
+    result[3] = (uint64_t) (r1 >> 64);
+  }
+}
+
+// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
+static inline void generic_computePow5(const uint32_t i, uint64_t* const result) {
+  const uint32_t base = i / POW5_TABLE_SIZE;
+  const uint32_t base2 = base * POW5_TABLE_SIZE;
+  const uint64_t* const mul = GENERIC_POW5_SPLIT[base];
+  if (i == base2) {
+    result[0] = mul[0];
+    result[1] = mul[1];
+    result[2] = mul[2];
+    result[3] = mul[3];
+  } else {
+    const uint32_t offset = i - base2;
+    const uint64_t* const m = GENERIC_POW5_TABLE[offset];
+    const uint32_t delta = pow5bits(i) - pow5bits(base2);
+    const uint32_t corr = (uint32_t) ((POW5_ERRORS[i / 32] >> (2 * (i % 32))) & 3);
+    mul_128_256_shift(m, mul, delta, corr, result);
+  }
+}
+
+// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
+static inline void generic_computeInvPow5(const uint32_t i, uint64_t* const result) {
+  const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
+  const uint32_t base2 = base * POW5_TABLE_SIZE;
+  const uint64_t* const mul = GENERIC_POW5_INV_SPLIT[base]; // 1/5^base2
+  if (i == base2) {
+    result[0] = mul[0] + 1;
+    result[1] = mul[1];
+    result[2] = mul[2];
+    result[3] = mul[3];
+  } else {
+    const uint32_t offset = base2 - i;
+    const uint64_t* const m = GENERIC_POW5_TABLE[offset]; // 5^offset
+    const uint32_t delta = pow5bits(base2) - pow5bits(i);
+    const uint32_t corr = (uint32_t) ((POW5_INV_ERRORS[i / 32] >> (2 * (i % 32))) & 3) + 1;
+    mul_128_256_shift(m, mul, delta, corr, result);
+  }
+}
+
+static inline uint32_t pow5Factor(uint128_t value) {
+  for (uint32_t count = 0; value > 0; ++count) {
+    if (value % 5 != 0) {
+      return count;
+    }
+    value /= 5;
+  }
+  return 0;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5(const uint128_t value, const uint32_t p) {
+  // I tried a case distinction on p, but there was no performance difference.
+  return pow5Factor(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2(const uint128_t value, const uint32_t p) {
+  return (value & ((((uint128_t) 1) << p) - 1)) == 0;
+}
+
+static inline uint128_t mulShift(const uint128_t m, const uint64_t* const mul, const int32_t j) {
+  assert(j > 128);
+  uint64_t a[2];
+  a[0] = (uint64_t) m;
+  a[1] = (uint64_t) (m >> 64);
+  uint64_t result[4];
+  mul_128_256_shift(a, mul, j, 0, result);
+  return (((uint128_t) result[1]) << 64) | result[0];
+}
+
+static inline uint32_t decimalLength(const uint128_t v) {
+  static uint128_t LARGEST_POW10 = (((uint128_t) 5421010862427522170ull) << 64) | 687399551400673280ull;
+  uint128_t p10 = LARGEST_POW10;
+  for (uint32_t i = 39; i > 0; i--) {
+    if (v >= p10) {
+      return i;
+    }
+    p10 /= 10;
+  }
+  return 1;
+}
+
+// Returns floor(log_10(2^e)).
+static inline uint32_t log10Pow2(const int32_t e) {
+  // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
+  assert(e >= 0);
+  assert(e <= 1 << 15);
+  return (uint32_t) ((((uint64_t) e) * 169464822037455ull) >> 49);
+}
+
+// Returns floor(log_10(5^e)).
+static inline uint32_t log10Pow5(const int32_t e) {
+  // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
+  assert(e >= 0);
+  assert(e <= 1 << 15);
+  return (uint32_t) ((((uint64_t) e) * 196742565691928ull) >> 48);
+}
+
+#endif // RYU_GENERIC128_H
diff --git a/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h b/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h
new file mode 100644
index 00000000000..f5d476343b6
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h
@@ -0,0 +1,70 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+//    (See accompanying file LICENSE-Apache or copy at
+//     http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE-Boost or copy at
+//     https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_GENERIC_128_H
+#define RYU_GENERIC_128_H
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// This is a generic 128-bit implementation of float to shortest conversion
+// using the Ryu algorithm. It can handle any IEEE-compatible floating-point
+// type up to 128 bits. In order to use this correctly, you must use the
+// appropriate *_to_fd128 function for the underlying type - DO NOT CAST your
+// input to another floating-point type, doing so will result in incorrect
+// output!
+//
+// For any floating-point type that is not natively defined by the compiler,
+// you can use generic_binary_to_decimal to work directly on the underlying bit
+// representation.
+
+#define FD128_EXCEPTIONAL_EXPONENT 0x7FFFFFFF
+
+// A floating decimal representing (-1)^s * m * 10^e.
+struct floating_decimal_128 {
+  __uint128_t mantissa;
+  int32_t exponent;
+  bool sign;
+};
+
+struct floating_decimal_128 float_to_fd128(float f);
+struct floating_decimal_128 double_to_fd128(double d);
+
+// According to wikipedia (https://en.wikipedia.org/wiki/Long_double), this likely only works on
+// x86 with specific compilers (clang?). May need an ifdef.
+struct floating_decimal_128 long_double_to_fd128(long double d);
+
+// Converts the given binary floating point number to the shortest decimal floating point number
+// that still accurately represents it.
+struct floating_decimal_128 generic_binary_to_decimal(
+    const __uint128_t bits, const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit);
+
+// Converts the given decimal floating point number to a string, writing to result, and returning
+// the number characters written. Does not terminate the buffer with a 0. In the worst case, this
+// function can write up to 53 characters.
+//
+// Maximal char buffer requirement:
+// sign + mantissa digits + decimal dot + 'E' + exponent sign + exponent digits
+// = 1 + 39 + 1 + 1 + 1 + 10 = 53
+int generic_to_chars(const struct floating_decimal_128 v, char* const result);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // RYU_GENERIC_128_H
-- 
2.28.0.rc0

[PATCH 2/4] libstdc++: Apply modifications to our local copy of Ryu

[Patrick Palka]

This performs the following modifications to our local copy of Ryu in
order to make it more easily usable for our std::to_chars implementation:

  * Remove all #includes
  * Remove copy_special_str routines
  * Adjust the exponent formatting to match printf
  * Remove some functions we're not going to use
  * Add an out-parameter to d2exp_buffered_n for the scientific exponent
  * Store the sign bit inside struct floating_decimal_[32|64]
  * Rename [df]2s_buffered_n and change their return type

libstdc++-v3/ChangeLog:

	* src/c++17/ryu/common.h, src/c++17/ryu/d2fixed.c,
	src/c++17/ryu/d2fixed_full_table.h, src/c++17/ryu/d2s.c,
	src/c++17/ryu/d2s_intrinsics.h, src/c++17/ryu/f2s.c,
	src/c++17/ryu/f2s_intrinsics.h: Apply local modifications.
---
 libstdc++-v3/src/c++17/ryu/common.h           | 19 ----
 libstdc++-v3/src/c++17/ryu/d2fixed.c          | 98 ++-----------------
 .../src/c++17/ryu/d2fixed_full_table.h        |  1 -
 libstdc++-v3/src/c++17/ryu/d2s.c              | 56 +++--------
 libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h   |  4 -
 libstdc++-v3/src/c++17/ryu/f2s.c              | 52 +++-------
 libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h   |  4 -
 libstdc++-v3/src/c++17/ryu/generic_128.c      |  7 +-
 8 files changed, 43 insertions(+), 198 deletions(-)

diff --git a/libstdc++-v3/src/c++17/ryu/common.h b/libstdc++-v3/src/c++17/ryu/common.h
index 7dc130947ac..f8ee147db04 100644
--- a/libstdc++-v3/src/c++17/ryu/common.h
+++ b/libstdc++-v3/src/c++17/ryu/common.h
@@ -17,9 +17,6 @@
 #ifndef RYU_COMMON_H
 #define RYU_COMMON_H
 
-#include <assert.h>
-#include <stdint.h>
-#include <string.h>
 
 #if defined(_M_IX86) || defined(_M_ARM)
 #define RYU_32_BIT_PLATFORM
@@ -83,22 +80,6 @@ static inline uint32_t log10Pow5(const int32_t e) {
   return (((uint32_t) e) * 732923) >> 20;
 }
 
-static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) {
-  if (mantissa) {
-    memcpy(result, "NaN", 3);
-    return 3;
-  }
-  if (sign) {
-    result[0] = '-';
-  }
-  if (exponent) {
-    memcpy(result + sign, "Infinity", 8);
-    return sign + 8;
-  }
-  memcpy(result + sign, "0E0", 3);
-  return sign + 3;
-}
-
 static inline uint32_t float_to_bits(const float f) {
   uint32_t bits = 0;
   memcpy(&bits, &f, sizeof(float));
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed.c b/libstdc++-v3/src/c++17/ryu/d2fixed.c
index 5f479abb91b..642a29d3010 100644
--- a/libstdc++-v3/src/c++17/ryu/d2fixed.c
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed.c
@@ -23,23 +23,11 @@
 //
 // -DRYU_AVOID_UINT128 Avoid using uint128_t. Slower, depending on your compiler.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
 
 #ifdef RYU_DEBUG
-#include <inttypes.h>
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/digit_table.h"
-#include "ryu/d2fixed_full_table.h"
-#include "ryu/d2s_intrinsics.h"
 
 #define DOUBLE_MANTISSA_BITS 52
 #define DOUBLE_EXPONENT_BITS 11
@@ -328,33 +316,6 @@ static inline uint32_t lengthForIndex(const uint32_t idx) {
   return (log10Pow2(16 * (int32_t) idx) + 1 + 16 + 8) / 9;
 }
 
-static inline int copy_special_str_printf(char* const result, const bool sign, const uint64_t mantissa) {
-#if defined(_MSC_VER)
-  // TODO: Check that -nan is expected output on Windows.
-  if (sign) {
-    result[0] = '-';
-  }
-  if (mantissa) {
-    if (mantissa < (1ull << (DOUBLE_MANTISSA_BITS - 1))) {
-      memcpy(result + sign, "nan(snan)", 9);
-      return sign + 9;
-    }
-    memcpy(result + sign, "nan", 3);
-    return sign + 3;
-  }
-#else
-  if (mantissa) {
-    memcpy(result, "nan", 3);
-    return 3;
-  }
-  if (sign) {
-    result[0] = '-';
-  }
-#endif
-  memcpy(result + sign, "Infinity", 8);
-  return sign + 8;
-}
-
 int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
   const uint64_t bits = double_to_bits(d);
 #ifdef RYU_DEBUG
@@ -372,20 +333,10 @@ int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
-    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+    __builtin_abort();
   }
   if (ieeeExponent == 0 && ieeeMantissa == 0) {
-    int index = 0;
-    if (ieeeSign) {
-      result[index++] = '-';
-    }
-    result[index++] = '0';
-    if (precision > 0) {
-      result[index++] = '.';
-      memset(result + index, '0', precision);
-      index += precision;
-    }
-    return index;
+    __builtin_abort();
   }
 
   int32_t e2;
@@ -549,21 +500,9 @@ int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
   return index;
 }
 
-void d2fixed_buffered(double d, uint32_t precision, char* result) {
-  const int len = d2fixed_buffered_n(d, precision, result);
-  result[len] = '\0';
-}
-
-char* d2fixed(double d, uint32_t precision) {
-  char* const buffer = (char*)malloc(2000);
-  const int index = d2fixed_buffered_n(d, precision, buffer);
-  buffer[index] = '\0';
-  return buffer;
-}
-
 
 
-int d2exp_buffered_n(double d, uint32_t precision, char* result) {
+int d2exp_buffered_n(double d, uint32_t precision, char* result, int* exp_out) {
   const uint64_t bits = double_to_bits(d);
 #ifdef RYU_DEBUG
   printf("IN=");
@@ -580,22 +519,10 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
-    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+    __builtin_abort();
   }
   if (ieeeExponent == 0 && ieeeMantissa == 0) {
-    int index = 0;
-    if (ieeeSign) {
-      result[index++] = '-';
-    }
-    result[index++] = '0';
-    if (precision > 0) {
-      result[index++] = '.';
-      memset(result + index, '0', precision);
-      index += precision;
-    }
-    memcpy(result + index, "e+00", 4);
-    index += 4;
-    return index;
+    __builtin_abort();
   }
 
   int32_t e2;
@@ -785,6 +712,9 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
       }
     }
   }
+  if (exp_out) {
+    *exp_out = exp;
+  }
   result[index++] = 'e';
   if (exp < 0) {
     result[index++] = '-';
@@ -805,15 +735,3 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
 
   return index;
 }
-
-void d2exp_buffered(double d, uint32_t precision, char* result) {
-  const int len = d2exp_buffered_n(d, precision, result);
-  result[len] = '\0';
-}
-
-char* d2exp(double d, uint32_t precision) {
-  char* const buffer = (char*)malloc(2000);
-  const int index = d2exp_buffered_n(d, precision, buffer);
-  buffer[index] = '\0';
-  return buffer;
-}
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
index 70857652161..1fa252959e6 100644
--- a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
@@ -17,7 +17,6 @@
 #ifndef RYU_D2FIXED_FULL_TABLE_H
 #define RYU_D2FIXED_FULL_TABLE_H
 
-#include <stdint.h>
 
 #define TABLE_SIZE 64
 
diff --git a/libstdc++-v3/src/c++17/ryu/d2s.c b/libstdc++-v3/src/c++17/ryu/d2s.c
index aa0da52da71..3225808c463 100644
--- a/libstdc++-v3/src/c++17/ryu/d2s.c
+++ b/libstdc++-v3/src/c++17/ryu/d2s.c
@@ -27,28 +27,15 @@
 //     size by about 10x (only one case, and only double) at the cost of some
 //     performance. Currently requires MSVC intrinsics.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
 
 #ifdef RYU_DEBUG
-#include <inttypes.h>
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/digit_table.h"
-#include "ryu/d2s_intrinsics.h"
 
 // Include either the small or the full lookup tables depending on the mode.
 #if defined(RYU_OPTIMIZE_SIZE)
-#include "ryu/d2s_small_table.h"
 #else
-#include "ryu/d2s_full_table.h"
 #endif
 
 #define DOUBLE_MANTISSA_BITS 52
@@ -86,9 +73,10 @@ typedef struct floating_decimal_64 {
   // Decimal exponent's range is -324 to 308
   // inclusive, and can fit in a short if needed.
   int32_t exponent;
+  bool sign;
 } floating_decimal_64;
 
-static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
+static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign) {
   int32_t e2;
   uint64_t m2;
   if (ieeeExponent == 0) {
@@ -308,13 +296,14 @@ static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_
   floating_decimal_64 fd;
   fd.exponent = exp;
   fd.mantissa = output;
+  fd.sign = ieeeSign;
   return fd;
 }
 
-static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
+static inline int to_chars(const floating_decimal_64 v, char* const result) {
   // Step 5: Print the decimal representation.
   int index = 0;
-  if (sign) {
+  if (v.sign) {
     result[index++] = '-';
   }
 
@@ -397,29 +386,28 @@ static inline int to_chars(const floating_decimal_64 v, const bool sign, char* c
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + (int32_t) olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
+  } else
+    result[index++] = '+';
 
   if (exp >= 100) {
     const int32_t c = exp % 10;
     memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
     result[index + 2] = (char) ('0' + c);
     index += 3;
-  } else if (exp >= 10) {
+  } else {
     memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
     index += 2;
-  } else {
-    result[index++] = (char) ('0' + exp);
   }
 
   return index;
 }
 
-static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
+static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign,
   floating_decimal_64* const v) {
   const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
   const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
@@ -448,10 +436,11 @@ static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t iee
   // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
   v->mantissa = m2 >> -e2;
   v->exponent = 0;
+  v->sign = ieeeSign;
   return true;
 }
 
-int d2s_buffered_n(double f, char* result) {
+floating_decimal_64 floating_to_fd64(double f) {
   // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
   const uint64_t bits = double_to_bits(f);
 
@@ -469,11 +458,11 @@ int d2s_buffered_n(double f, char* result) {
   const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
-    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+    __builtin_abort();
   }
 
   floating_decimal_64 v;
-  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, ieeeSign, &v);
   if (isSmallInt) {
     // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
     // For scientific notation we need to move these zeros into the exponent.
@@ -489,21 +478,8 @@ int d2s_buffered_n(double f, char* result) {
       ++v.exponent;
     }
   } else {
-    v = d2d(ieeeMantissa, ieeeExponent);
+    v = d2d(ieeeMantissa, ieeeExponent, ieeeSign);
   }
 
-  return to_chars(v, ieeeSign, result);
-}
-
-void d2s_buffered(double f, char* result) {
-  const int index = d2s_buffered_n(f, result);
-
-  // Terminate the string.
-  result[index] = '\0';
-}
-
-char* d2s(double f) {
-  char* const result = (char*) malloc(25);
-  d2s_buffered(f, result);
-  return result;
+  return v;
 }
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
index ea590a60d25..fa993e6fad6 100644
--- a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
+++ b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
@@ -17,11 +17,8 @@
 #ifndef RYU_D2S_INTRINSICS_H
 #define RYU_D2S_INTRINSICS_H
 
-#include <assert.h>
-#include <stdint.h>
 
 // Defines RYU_32_BIT_PLATFORM if applicable.
-#include "ryu/common.h"
 
 // ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
 // Let's do the same for now.
@@ -37,7 +34,6 @@ typedef __uint128_t uint128_t;
 
 #if defined(HAS_64_BIT_INTRINSICS)
 
-#include <intrin.h>
 
 static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
   return _umul128(a, b, productHi);
diff --git a/libstdc++-v3/src/c++17/ryu/f2s.c b/libstdc++-v3/src/c++17/ryu/f2s.c
index 255ecbe599c..5e635958aa1 100644
--- a/libstdc++-v3/src/c++17/ryu/f2s.c
+++ b/libstdc++-v3/src/c++17/ryu/f2s.c
@@ -18,22 +18,11 @@
 // Runtime compiler options:
 // -DRYU_DEBUG Generate verbose debugging output to stdout.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
-#include <limits.h>
 
 #ifdef RYU_DEBUG
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/f2s_intrinsics.h"
-#include "ryu/digit_table.h"
 
 #define FLOAT_MANTISSA_BITS 23
 #define FLOAT_EXPONENT_BITS 8
@@ -45,9 +34,10 @@ typedef struct floating_decimal_32 {
   // Decimal exponent's range is -45 to 38
   // inclusive, and can fit in a short if needed.
   int32_t exponent;
+  bool sign;
 } floating_decimal_32;
 
-static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent) {
+static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign) {
   int32_t e2;
   uint32_t m2;
   if (ieeeExponent == 0) {
@@ -224,13 +214,14 @@ static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_
   floating_decimal_32 fd;
   fd.exponent = exp;
   fd.mantissa = output;
+  fd.sign = ieeeSign;
   return fd;
 }
 
-static inline int to_chars(const floating_decimal_32 v, const bool sign, char* const result) {
+static inline int to_chars(const floating_decimal_32 v, char* const result) {
   // Step 5: Print the decimal representation.
   int index = 0;
-  if (sign) {
+  if (v.sign) {
     result[index++] = '-';
   }
 
@@ -288,24 +279,22 @@ static inline int to_chars(const floating_decimal_32 v, const bool sign, char* c
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + (int32_t) olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
-
-  if (exp >= 10) {
-    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
-    index += 2;
   } else {
-    result[index++] = (char) ('0' + exp);
+    result[index++] = '+';
   }
 
+  memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+  index += 2;
+
   return index;
 }
 
-int f2s_buffered_n(float f, char* result) {
+floating_decimal_32 floating_to_fd32(float f) {
   // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
   const uint32_t bits = float_to_bits(f);
 
@@ -324,22 +313,9 @@ int f2s_buffered_n(float f, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
-    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+    __builtin_abort();
   }
 
-  const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
-  return to_chars(v, ieeeSign, result);
-}
-
-void f2s_buffered(float f, char* result) {
-  const int index = f2s_buffered_n(f, result);
-
-  // Terminate the string.
-  result[index] = '\0';
-}
-
-char* f2s(float f) {
-  char* const result = (char*) malloc(16);
-  f2s_buffered(f, result);
-  return result;
+  const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent, ieeeSign);
+  return v;
 }
diff --git a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
index bb822c9a0c0..db751a41329 100644
--- a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
+++ b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
@@ -18,18 +18,14 @@
 #define RYU_F2S_INTRINSICS_H
 
 // Defines RYU_32_BIT_PLATFORM if applicable.
-#include "ryu/common.h"
 
 #if defined(RYU_FLOAT_FULL_TABLE)
 
-#include "ryu/f2s_full_table.h"
 
 #else
 
 #if defined(RYU_OPTIMIZE_SIZE)
-#include "ryu/d2s_small_table.h"
 #else
-#include "ryu/d2s_full_table.h"
 #endif
 #define FLOAT_POW5_INV_BITCOUNT (DOUBLE_POW5_INV_BITCOUNT - 64)
 #define FLOAT_POW5_BITCOUNT (DOUBLE_POW5_BITCOUNT - 64)
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.c b/libstdc++-v3/src/c++17/ryu/generic_128.c
index 2eb8da8aba8..fca6ecb8412 100644
--- a/libstdc++-v3/src/c++17/ryu/generic_128.c
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.c
@@ -320,14 +320,17 @@ int generic_to_chars(const struct floating_decimal_128 v, char* const result) {
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
+  } else
+    result[index++] = '+';
 
   uint32_t elength = decimalLength(exp);
+  if (elength == 1)
+    ++elength;
   for (uint32_t i = 0; i < elength; ++i) {
     const uint32_t c = exp % 10;
     exp /= 10;
-- 
2.28.0.rc0

Re: [PATCH 2/4] libstdc++: Apply modifications to our local copy of Ryu

[Patrick Palka]

On Tue, 14 Jul 2020, Patrick Palka wrote:

> This performs the following modifications to our local copy of Ryu in
> order to make it more easily usable for our std::to_chars implementation:
> 
>   * Remove all #includes
>   * Remove copy_special_str routines
>   * Adjust the exponent formatting to match printf
>   * Remove some functions we're not going to use
>   * Add an out-parameter to d2exp_buffered_n for the scientific exponent
>   * Store the sign bit inside struct floating_decimal_[32|64]
>   * Rename [df]2s_buffered_n and change their return type

Here is v2 of this patch, which applies another modification to Ryu that 
v2 of the third patch in the series depends on:

-- >8 --

Subject: [PATCH 2/4] libstdc++: Apply modifications to our local copy of Ryu

This performs the following modifications to our local copy of Ryu in
order to make it more easily usable in our std::to_chars implementation:

  * Remove all #includes
  * Remove copy_special_str routines
  * Adjust the exponent formatting to match printf
  * Remove some functions we're not going to use
  * Add an out-parameter to d2exp_buffered_n for the scientific exponent
  * Store the sign bit inside struct floating_decimal_[32|64]
  * Rename [df]2s_buffered_n and change their return type
  * Make generic_binary_to_decimal take the bit representation in parts

libstdc++-v3/ChangeLog:

	* src/c++17/ryu/common.h, src/c++17/ryu/d2fixed.c,
	src/c++17/ryu/d2fixed_full_table.h, src/c++17/ryu/d2s.c,
	src/c++17/ryu/d2s_intrinsics.h, src/c++17/ryu/f2s.c,
	src/c++17/ryu/f2s_intrinsics.h: Apply local modifications.
---
 libstdc++-v3/src/c++17/ryu/common.h           | 19 ----
 libstdc++-v3/src/c++17/ryu/d2fixed.c          | 98 ++-----------------
 .../src/c++17/ryu/d2fixed_full_table.h        |  1 -
 libstdc++-v3/src/c++17/ryu/d2s.c              | 56 +++--------
 libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h   |  4 -
 libstdc++-v3/src/c++17/ryu/f2s.c              | 52 +++-------
 libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h   |  4 -
 libstdc++-v3/src/c++17/ryu/generic_128.c      | 47 ++-------
 8 files changed, 45 insertions(+), 236 deletions(-)

diff --git a/libstdc++-v3/src/c++17/ryu/common.h b/libstdc++-v3/src/c++17/ryu/common.h
index 7dc130947ac..f8ee147db04 100644
--- a/libstdc++-v3/src/c++17/ryu/common.h
+++ b/libstdc++-v3/src/c++17/ryu/common.h
@@ -17,9 +17,6 @@
 #ifndef RYU_COMMON_H
 #define RYU_COMMON_H
 
-#include <assert.h>
-#include <stdint.h>
-#include <string.h>
 
 #if defined(_M_IX86) || defined(_M_ARM)
 #define RYU_32_BIT_PLATFORM
@@ -83,22 +80,6 @@ static inline uint32_t log10Pow5(const int32_t e) {
   return (((uint32_t) e) * 732923) >> 20;
 }
 
-static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) {
-  if (mantissa) {
-    memcpy(result, "NaN", 3);
-    return 3;
-  }
-  if (sign) {
-    result[0] = '-';
-  }
-  if (exponent) {
-    memcpy(result + sign, "Infinity", 8);
-    return sign + 8;
-  }
-  memcpy(result + sign, "0E0", 3);
-  return sign + 3;
-}
-
 static inline uint32_t float_to_bits(const float f) {
   uint32_t bits = 0;
   memcpy(&bits, &f, sizeof(float));
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed.c b/libstdc++-v3/src/c++17/ryu/d2fixed.c
index 5f479abb91b..642a29d3010 100644
--- a/libstdc++-v3/src/c++17/ryu/d2fixed.c
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed.c
@@ -23,23 +23,11 @@
 //
 // -DRYU_AVOID_UINT128 Avoid using uint128_t. Slower, depending on your compiler.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
 
 #ifdef RYU_DEBUG
-#include <inttypes.h>
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/digit_table.h"
-#include "ryu/d2fixed_full_table.h"
-#include "ryu/d2s_intrinsics.h"
 
 #define DOUBLE_MANTISSA_BITS 52
 #define DOUBLE_EXPONENT_BITS 11
@@ -328,33 +316,6 @@ static inline uint32_t lengthForIndex(const uint32_t idx) {
   return (log10Pow2(16 * (int32_t) idx) + 1 + 16 + 8) / 9;
 }
 
-static inline int copy_special_str_printf(char* const result, const bool sign, const uint64_t mantissa) {
-#if defined(_MSC_VER)
-  // TODO: Check that -nan is expected output on Windows.
-  if (sign) {
-    result[0] = '-';
-  }
-  if (mantissa) {
-    if (mantissa < (1ull << (DOUBLE_MANTISSA_BITS - 1))) {
-      memcpy(result + sign, "nan(snan)", 9);
-      return sign + 9;
-    }
-    memcpy(result + sign, "nan", 3);
-    return sign + 3;
-  }
-#else
-  if (mantissa) {
-    memcpy(result, "nan", 3);
-    return 3;
-  }
-  if (sign) {
-    result[0] = '-';
-  }
-#endif
-  memcpy(result + sign, "Infinity", 8);
-  return sign + 8;
-}
-
 int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
   const uint64_t bits = double_to_bits(d);
 #ifdef RYU_DEBUG
@@ -372,20 +333,10 @@ int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
-    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+    __builtin_abort();
   }
   if (ieeeExponent == 0 && ieeeMantissa == 0) {
-    int index = 0;
-    if (ieeeSign) {
-      result[index++] = '-';
-    }
-    result[index++] = '0';
-    if (precision > 0) {
-      result[index++] = '.';
-      memset(result + index, '0', precision);
-      index += precision;
-    }
-    return index;
+    __builtin_abort();
   }
 
   int32_t e2;
@@ -549,21 +500,9 @@ int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
   return index;
 }
 
-void d2fixed_buffered(double d, uint32_t precision, char* result) {
-  const int len = d2fixed_buffered_n(d, precision, result);
-  result[len] = '\0';
-}
-
-char* d2fixed(double d, uint32_t precision) {
-  char* const buffer = (char*)malloc(2000);
-  const int index = d2fixed_buffered_n(d, precision, buffer);
-  buffer[index] = '\0';
-  return buffer;
-}
-
 
 
-int d2exp_buffered_n(double d, uint32_t precision, char* result) {
+int d2exp_buffered_n(double d, uint32_t precision, char* result, int* exp_out) {
   const uint64_t bits = double_to_bits(d);
 #ifdef RYU_DEBUG
   printf("IN=");
@@ -580,22 +519,10 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
-    return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+    __builtin_abort();
   }
   if (ieeeExponent == 0 && ieeeMantissa == 0) {
-    int index = 0;
-    if (ieeeSign) {
-      result[index++] = '-';
-    }
-    result[index++] = '0';
-    if (precision > 0) {
-      result[index++] = '.';
-      memset(result + index, '0', precision);
-      index += precision;
-    }
-    memcpy(result + index, "e+00", 4);
-    index += 4;
-    return index;
+    __builtin_abort();
   }
 
   int32_t e2;
@@ -785,6 +712,9 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
       }
     }
   }
+  if (exp_out) {
+    *exp_out = exp;
+  }
   result[index++] = 'e';
   if (exp < 0) {
     result[index++] = '-';
@@ -805,15 +735,3 @@ int d2exp_buffered_n(double d, uint32_t precision, char* result) {
 
   return index;
 }
-
-void d2exp_buffered(double d, uint32_t precision, char* result) {
-  const int len = d2exp_buffered_n(d, precision, result);
-  result[len] = '\0';
-}
-
-char* d2exp(double d, uint32_t precision) {
-  char* const buffer = (char*)malloc(2000);
-  const int index = d2exp_buffered_n(d, precision, buffer);
-  buffer[index] = '\0';
-  return buffer;
-}
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
index 70857652161..1fa252959e6 100644
--- a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
@@ -17,7 +17,6 @@
 #ifndef RYU_D2FIXED_FULL_TABLE_H
 #define RYU_D2FIXED_FULL_TABLE_H
 
-#include <stdint.h>
 
 #define TABLE_SIZE 64
 
diff --git a/libstdc++-v3/src/c++17/ryu/d2s.c b/libstdc++-v3/src/c++17/ryu/d2s.c
index aa0da52da71..3225808c463 100644
--- a/libstdc++-v3/src/c++17/ryu/d2s.c
+++ b/libstdc++-v3/src/c++17/ryu/d2s.c
@@ -27,28 +27,15 @@
 //     size by about 10x (only one case, and only double) at the cost of some
 //     performance. Currently requires MSVC intrinsics.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
 
 #ifdef RYU_DEBUG
-#include <inttypes.h>
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/digit_table.h"
-#include "ryu/d2s_intrinsics.h"
 
 // Include either the small or the full lookup tables depending on the mode.
 #if defined(RYU_OPTIMIZE_SIZE)
-#include "ryu/d2s_small_table.h"
 #else
-#include "ryu/d2s_full_table.h"
 #endif
 
 #define DOUBLE_MANTISSA_BITS 52
@@ -86,9 +73,10 @@ typedef struct floating_decimal_64 {
   // Decimal exponent's range is -324 to 308
   // inclusive, and can fit in a short if needed.
   int32_t exponent;
+  bool sign;
 } floating_decimal_64;
 
-static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
+static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign) {
   int32_t e2;
   uint64_t m2;
   if (ieeeExponent == 0) {
@@ -308,13 +296,14 @@ static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_
   floating_decimal_64 fd;
   fd.exponent = exp;
   fd.mantissa = output;
+  fd.sign = ieeeSign;
   return fd;
 }
 
-static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
+static inline int to_chars(const floating_decimal_64 v, char* const result) {
   // Step 5: Print the decimal representation.
   int index = 0;
-  if (sign) {
+  if (v.sign) {
     result[index++] = '-';
   }
 
@@ -397,29 +386,28 @@ static inline int to_chars(const floating_decimal_64 v, const bool sign, char* c
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + (int32_t) olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
+  } else
+    result[index++] = '+';
 
   if (exp >= 100) {
     const int32_t c = exp % 10;
     memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
     result[index + 2] = (char) ('0' + c);
     index += 3;
-  } else if (exp >= 10) {
+  } else {
     memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
     index += 2;
-  } else {
-    result[index++] = (char) ('0' + exp);
   }
 
   return index;
 }
 
-static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
+static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign,
   floating_decimal_64* const v) {
   const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
   const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
@@ -448,10 +436,11 @@ static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t iee
   // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
   v->mantissa = m2 >> -e2;
   v->exponent = 0;
+  v->sign = ieeeSign;
   return true;
 }
 
-int d2s_buffered_n(double f, char* result) {
+floating_decimal_64 floating_to_fd64(double f) {
   // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
   const uint64_t bits = double_to_bits(f);
 
@@ -469,11 +458,11 @@ int d2s_buffered_n(double f, char* result) {
   const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
-    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+    __builtin_abort();
   }
 
   floating_decimal_64 v;
-  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+  const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, ieeeSign, &v);
   if (isSmallInt) {
     // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
     // For scientific notation we need to move these zeros into the exponent.
@@ -489,21 +478,8 @@ int d2s_buffered_n(double f, char* result) {
       ++v.exponent;
     }
   } else {
-    v = d2d(ieeeMantissa, ieeeExponent);
+    v = d2d(ieeeMantissa, ieeeExponent, ieeeSign);
   }
 
-  return to_chars(v, ieeeSign, result);
-}
-
-void d2s_buffered(double f, char* result) {
-  const int index = d2s_buffered_n(f, result);
-
-  // Terminate the string.
-  result[index] = '\0';
-}
-
-char* d2s(double f) {
-  char* const result = (char*) malloc(25);
-  d2s_buffered(f, result);
-  return result;
+  return v;
 }
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
index ea590a60d25..fa993e6fad6 100644
--- a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
+++ b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
@@ -17,11 +17,8 @@
 #ifndef RYU_D2S_INTRINSICS_H
 #define RYU_D2S_INTRINSICS_H
 
-#include <assert.h>
-#include <stdint.h>
 
 // Defines RYU_32_BIT_PLATFORM if applicable.
-#include "ryu/common.h"
 
 // ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
 // Let's do the same for now.
@@ -37,7 +34,6 @@ typedef __uint128_t uint128_t;
 
 #if defined(HAS_64_BIT_INTRINSICS)
 
-#include <intrin.h>
 
 static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
   return _umul128(a, b, productHi);
diff --git a/libstdc++-v3/src/c++17/ryu/f2s.c b/libstdc++-v3/src/c++17/ryu/f2s.c
index 255ecbe599c..5e635958aa1 100644
--- a/libstdc++-v3/src/c++17/ryu/f2s.c
+++ b/libstdc++-v3/src/c++17/ryu/f2s.c
@@ -18,22 +18,11 @@
 // Runtime compiler options:
 // -DRYU_DEBUG Generate verbose debugging output to stdout.
 
-#include "ryu/ryu.h"
 
-#include <assert.h>
-#include <stdbool.h>
-#include <stdint.h>
-#include <stdlib.h>
-#include <string.h>
-#include <limits.h>
 
 #ifdef RYU_DEBUG
-#include <stdio.h>
 #endif
 
-#include "ryu/common.h"
-#include "ryu/f2s_intrinsics.h"
-#include "ryu/digit_table.h"
 
 #define FLOAT_MANTISSA_BITS 23
 #define FLOAT_EXPONENT_BITS 8
@@ -45,9 +34,10 @@ typedef struct floating_decimal_32 {
   // Decimal exponent's range is -45 to 38
   // inclusive, and can fit in a short if needed.
   int32_t exponent;
+  bool sign;
 } floating_decimal_32;
 
-static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent) {
+static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign) {
   int32_t e2;
   uint32_t m2;
   if (ieeeExponent == 0) {
@@ -224,13 +214,14 @@ static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_
   floating_decimal_32 fd;
   fd.exponent = exp;
   fd.mantissa = output;
+  fd.sign = ieeeSign;
   return fd;
 }
 
-static inline int to_chars(const floating_decimal_32 v, const bool sign, char* const result) {
+static inline int to_chars(const floating_decimal_32 v, char* const result) {
   // Step 5: Print the decimal representation.
   int index = 0;
-  if (sign) {
+  if (v.sign) {
     result[index++] = '-';
   }
 
@@ -288,24 +279,22 @@ static inline int to_chars(const floating_decimal_32 v, const bool sign, char* c
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + (int32_t) olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
-
-  if (exp >= 10) {
-    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
-    index += 2;
   } else {
-    result[index++] = (char) ('0' + exp);
+    result[index++] = '+';
   }
 
+  memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+  index += 2;
+
   return index;
 }
 
-int f2s_buffered_n(float f, char* result) {
+floating_decimal_32 floating_to_fd32(float f) {
   // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
   const uint32_t bits = float_to_bits(f);
 
@@ -324,22 +313,9 @@ int f2s_buffered_n(float f, char* result) {
 
   // Case distinction; exit early for the easy cases.
   if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
-    return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+    __builtin_abort();
   }
 
-  const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
-  return to_chars(v, ieeeSign, result);
-}
-
-void f2s_buffered(float f, char* result) {
-  const int index = f2s_buffered_n(f, result);
-
-  // Terminate the string.
-  result[index] = '\0';
-}
-
-char* f2s(float f) {
-  char* const result = (char*) malloc(16);
-  f2s_buffered(f, result);
-  return result;
+  const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent, ieeeSign);
+  return v;
 }
diff --git a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
index bb822c9a0c0..db751a41329 100644
--- a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
+++ b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
@@ -18,18 +18,14 @@
 #define RYU_F2S_INTRINSICS_H
 
 // Defines RYU_32_BIT_PLATFORM if applicable.
-#include "ryu/common.h"
 
 #if defined(RYU_FLOAT_FULL_TABLE)
 
-#include "ryu/f2s_full_table.h"
 
 #else
 
 #if defined(RYU_OPTIMIZE_SIZE)
-#include "ryu/d2s_small_table.h"
 #else
-#include "ryu/d2s_full_table.h"
 #endif
 #define FLOAT_POW5_INV_BITCOUNT (DOUBLE_POW5_INV_BITCOUNT - 64)
 #define FLOAT_POW5_BITCOUNT (DOUBLE_POW5_BITCOUNT - 64)
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.c b/libstdc++-v3/src/c++17/ryu/generic_128.c
index 2eb8da8aba8..17c1567a6a1 100644
--- a/libstdc++-v3/src/c++17/ryu/generic_128.c
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.c
@@ -37,42 +37,9 @@ static char* s(uint128_t v) {
 
 #define ONE ((uint128_t) 1)
 
-#define FLOAT_MANTISSA_BITS 23
-#define FLOAT_EXPONENT_BITS 8
-
-struct floating_decimal_128 float_to_fd128(float f) {
-  uint32_t bits = 0;
-  memcpy(&bits, &f, sizeof(float));
-  return generic_binary_to_decimal(bits, FLOAT_MANTISSA_BITS, FLOAT_EXPONENT_BITS, false);
-}
-
-#define DOUBLE_MANTISSA_BITS 52
-#define DOUBLE_EXPONENT_BITS 11
-
-struct floating_decimal_128 double_to_fd128(double d) {
-  uint64_t bits = 0;
-  memcpy(&bits, &d, sizeof(double));
-  return generic_binary_to_decimal(bits, DOUBLE_MANTISSA_BITS, DOUBLE_EXPONENT_BITS, false);
-}
-
-#define LONG_DOUBLE_MANTISSA_BITS 64
-#define LONG_DOUBLE_EXPONENT_BITS 15
-
-struct floating_decimal_128 long_double_to_fd128(long double d) {
-  uint128_t bits = 0;
-  memcpy(&bits, &d, sizeof(long double));
-#ifdef RYU_DEBUG
-  // For some odd reason, this ends up with noise in the top 48 bits. We can
-  // clear out those bits with the following line; this is not required, the
-  // conversion routine should ignore those bits, but the debug output can be
-  // confusing if they aren't 0s.
-  bits &= (ONE << 80) - 1;
-#endif
-  return generic_binary_to_decimal(bits, LONG_DOUBLE_MANTISSA_BITS, LONG_DOUBLE_EXPONENT_BITS, true);
-}
-
 struct floating_decimal_128 generic_binary_to_decimal(
-    const uint128_t bits, const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit) {
+    const uint128_t ieeeMantissa, const uint32_t ieeeExponent, const bool ieeeSign,
+    const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit) {
 #ifdef RYU_DEBUG
   printf("IN=");
   for (int32_t bit = 127; bit >= 0; --bit) {
@@ -82,9 +49,6 @@ struct floating_decimal_128 generic_binary_to_decimal(
 #endif
 
   const uint32_t bias = (1u << (exponentBits - 1)) - 1;
-  const bool ieeeSign = ((bits >> (mantissaBits + exponentBits)) & 1) != 0;
-  const uint128_t ieeeMantissa = bits & ((ONE << mantissaBits) - 1);
-  const uint32_t ieeeExponent = (uint32_t) ((bits >> mantissaBits) & ((ONE << exponentBits) - 1u));
 
   if (ieeeExponent == 0 && ieeeMantissa == 0) {
     struct floating_decimal_128 fd;
@@ -320,14 +284,17 @@ int generic_to_chars(const struct floating_decimal_128 v, char* const result) {
   }
 
   // Print the exponent.
-  result[index++] = 'E';
+  result[index++] = 'e';
   int32_t exp = v.exponent + olength - 1;
   if (exp < 0) {
     result[index++] = '-';
     exp = -exp;
-  }
+  } else
+    result[index++] = '+';
 
   uint32_t elength = decimalLength(exp);
+  if (elength == 1)
+    ++elength;
   for (uint32_t i = 0; i < elength; ++i) {
     const uint32_t c = exp % 10;
     exp /= 10;
-- 
2.28.0.rc0

Re: [PATCH 2/4] libstdc++: Apply modifications to our local copy of Ryu

[Jonathan Wakely]

On 15/07/20 14:12 -0400, Patrick Palka via Libstdc++ wrote:
>On Tue, 14 Jul 2020, Patrick Palka wrote:
>
>> This performs the following modifications to our local copy of Ryu in
>> order to make it more easily usable for our std::to_chars implementation:
>>
>>   * Remove all #includes
>>   * Remove copy_special_str routines
>>   * Adjust the exponent formatting to match printf
>>   * Remove some functions we're not going to use
>>   * Add an out-parameter to d2exp_buffered_n for the scientific exponent
>>   * Store the sign bit inside struct floating_decimal_[32|64]
>>   * Rename [df]2s_buffered_n and change their return type
>
>Here is v2 of this patch, which applies another modification to Ryu that
>v2 of the third patch in the series depends on:

OK, thanks.

[PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing fixed and scientific
formatting of float and double. For formatting long double with an
explicit precision argument we use a printf fallback.  Hexadecimal
formatting for float, double and long double is implemented from
scratch.

The supported long double binary formats are float64 (same as double),
float80 (x86 extended precision), float128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length before
the fact, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer (if the
output range is smaller than the upper bound).

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu, and
where we also take care to avoid having to format the string a second
time when the general formatting mode resolves to fixed.

Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.

libstdc++-v3/ChangeLog:

	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
	* config/abi/pre/gnu.ver: Add new exports.
	* configure: Regenerate.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	* testsuite/20_util/to_chars/long_double.cc: New test.
	* testsuite/util/testsuite_abi.cc: Add new symbol version.
---
 libstdc++-v3/acinclude.m4                     |    2 +-
 libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
 libstdc++-v3/configure                        |    2 +-
 libstdc++-v3/include/std/charconv             |   21 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    5 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1488 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
 9 files changed, 1726 insertions(+), 5 deletions(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
index ee5e0336f2c..e3926e1c9c2 100644
--- a/libstdc++-v3/acinclude.m4
+++ b/libstdc++-v3/acinclude.m4
@@ -3846,7 +3846,7 @@ changequote([,])dnl
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index edf4485e607..9a1bcfd25d1 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
 
 } GLIBCXX_3.4.27;
 
+GLIBCXX_3.4.29 {
+    # to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[fdeg];
+
+    # to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[fdeg]St12chars_format;
+
+    # to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
+
+} GLIBCXX_3.4.28;
+
 # Symbols in the support library (libsupc++) have their own tag.
 CXXABI_1.3 {
 
diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
index dd54bd406a9..73f771e7335 100755
--- a/libstdc++-v3/configure
+++ b/libstdc++-v3/configure
@@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index cc7dd0e3758..042cc4fbcca 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -688,6 +688,27 @@ namespace __detail
   operator^=(chars_format& __lhs, chars_format __rhs) noexcept
   { return __lhs = __lhs ^ __rhs; }
 
+  // Floating-point std::to_chars
+
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 85e31fbd91f..6637c5b4500 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -50,6 +50,7 @@ inst_sources =
 endif
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index de605a3f6a6..3b3b0d93a2c 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,8 +124,8 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = fs_dir.lo fs_ops.lo fs_path.lo memory_resource.lo \
-	$(am__objects_1)
+am__objects_2 = floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
 @ENABLE_EXTERN_TEMPLATE_TRUE@	string-inst.lo $(am__objects_3)
@@ -435,6 +435,7 @@ headers =
 @ENABLE_EXTERN_TEMPLATE_TRUE@	$(extra_string_inst_sources)
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..1bafdd8bf29
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1488 @@
+// floating-point std::to_chars implementation -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_DEBUG
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+namespace
+{
+  namespace __ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+    namespace __generic128
+    {
+      // Put the generic Ryu definitions in its own namespace to avoid name
+      // conflicts.
+#include "ryu/ryu_generic_128.h"
+#include "ryu/generic_128.h"
+#include "ryu/generic_128.c"
+    } // namespace __generic128
+
+    using __generic128::floating_decimal_128;
+    using __generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return __generic128::generic_to_chars(v, result); }
+  } // namespace __ryu
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+  static optional<to_chars_result>
+  __handle_special_value(char* first, char* const last, const T value,
+			 const chars_format fmt, const int precision)
+  {
+    __glibcxx_assert(precision >= 0);
+
+    string_view str;
+    switch (fpclassify(value))
+      {
+      case FP_INFINITE:
+	str = "-inf";
+	break;
+
+      case FP_NAN:
+	str = "-nan";
+	break;
+
+      case FP_ZERO:
+	break;
+
+      default:
+      case FP_SUBNORMAL:
+      case FP_NORMAL: [[likely]]
+	return nullopt;
+      }
+
+    if (!str.empty()) [[unlikely]]
+      {
+	if (!signbit(value))
+	  str.remove_prefix(strlen("-"));
+
+	if (last - first < (int)str.length())
+	  return {{last, errc::value_too_large}};
+
+	memcpy(first, &str[0], str.length());
+	first += str.length();
+	return {{first, errc{}}};
+      }
+
+    __glibcxx_assert(value == 0);
+    const bool neg_zero_p = signbit(value);
+    int output_length;
+    switch (fmt)
+      {
+      case chars_format::fixed:
+      case chars_format::scientific:
+      case chars_format::hex:
+	output_length = neg_zero_p + 1;
+	if (precision)
+	  output_length += strlen(".") + precision;
+	if (fmt == chars_format::scientific)
+	  output_length += strlen("e+00");
+	else if (fmt == chars_format::hex)
+	  output_length += strlen("p+0");
+	if (last - first < output_length)
+	  return {{last, errc::value_too_large}};
+
+	if (neg_zero_p)
+	  *first++ = '-';
+	*first++ = '0';
+	if (precision)
+	  {
+	    *first++ = '.';
+	    memset(first, '0', precision);
+	    first += precision;
+	  }
+	if (fmt == chars_format::scientific)
+	  {
+	    memcpy(first, "e+00", 4);
+	    first += 4;
+	  }
+	else if (fmt == chars_format::hex)
+	  {
+	    memcpy(first, "p+0", 3);
+	    first += 3;
+	  }
+	return {{first, errc{}}};
+
+      default:
+	__glibcxx_assert(fmt == chars_format::general || fmt == chars_format{});
+	output_length = neg_zero_p + 1;
+	if (last - first < output_length)
+	  return {{last, errc::value_too_large}};
+
+	if (neg_zero_p)
+	  *first++ = '-';
+	*first++ = '0';
+	return {{first, errc{}}};
+      }
+  }
+
+  namespace
+  {
+    enum class __long_double_kind
+    {
+      float80,     // x86 extended precision
+      ibm128,      // ibm 128bit (encoded as a pair of doubles)
+      float128,    // ieee binary128
+      float64,     // ieee binary64, same as double
+      unsupported, // unsupported/unknown
+    };
+
+    // Determine the binary format of our 'long double' type, if we support it.
+    // If the binary format is 'unsupported' or 'float64', then we make the long
+    // double to_chars overloads just go through double.
+    constexpr __long_double_kind __ldk
+      = (__LDBL_MANT_DIG__ == 64 ? __long_double_kind::float80
+	 : __LDBL_MANT_DIG__ == 106 ? __long_double_kind::ibm128
+	 : __LDBL_MANT_DIG__ == 113 ? __long_double_kind::float128
+	 : __LDBL_MANT_DIG__ == __DBL_MANT_DIG__ ? __long_double_kind::float64
+	 : __long_double_kind::unsupported);
+
+    // A traits class that contains pertinent information about the binary
+    // format of each of the floating-point types we support.
+    template<typename T, __long_double_kind ldk = __ldk>
+      struct __floating_type_traits
+      { };
+
+    template<>
+      struct __floating_type_traits<float>
+      {
+	// We (and Ryu) assume float has the IEEE binary32 format.
+	static_assert(__FLT_MANT_DIG__ == 24);
+
+	using bitrep_t = uint32_t;
+	static constexpr int mantissa_bits = 23;
+	static constexpr int exponent_bits = 8;
+	static constexpr bool has_implicit_leading_bit = true;
+
+	using shortest_scientific_t = __ryu::floating_decimal_32;
+	static constexpr uint64_t pow10_adjustment_tab[]
+	  = { 0b0000000000011101011100110101100101101110000000000000000000000000,
+	    };
+      };
+
+    template<>
+      struct __floating_type_traits<double>
+      {
+	// We (and Ryu) assume double has the IEEE binary64 format.
+	static_assert(__DBL_MANT_DIG__ == 53);
+
+	using bitrep_t = uint64_t;
+	static constexpr int mantissa_bits = 52;
+	static constexpr int exponent_bits = 11;
+	static constexpr bool has_implicit_leading_bit = true;
+
+	using shortest_scientific_t = __ryu::floating_decimal_64;
+	static constexpr uint64_t pow10_adjustment_tab[]
+	  = { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	      0b0111100011110101011000011110000000110110010101011000001110011111,
+	      0b0101101100000000011100100100111100110110110100010001010101110000,
+	      0b0011110010111000101111110101100011101100010001010000000101100111,
+	      0b0001010000011001011100100001010000010101101000001101000000000000,
+	    };
+      };
+
+    template<>
+      struct __floating_type_traits<long double, __long_double_kind::float64>
+      {
+	// These traits are deliberately empty since we'll make the exported
+	// long double overloads just call the double overloads.
+      };
+
+    template<>
+      struct __floating_type_traits<long double, __long_double_kind::float80>
+      {
+	using bitrep_t = unsigned __int128;
+	static constexpr int mantissa_bits = 64;
+	static constexpr int exponent_bits = 15;
+	static constexpr bool has_implicit_leading_bit = false;
+
+	using shortest_scientific_t = __ryu::floating_decimal_128;
+	static constexpr uint64_t pow10_adjustment_tab[]
+	  = { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	      0b1001100101001111010011011111101000101111110001011001011101110000,
+	      0b0000101111111011110010001000001010111101011110111111010100011001,
+	      0b0011100000011111001101101011111001111100100010000101001111101001,
+	      0b0100100100000000100111010010101110011000110001101101110011001010,
+	      0b0111100111100010100000010011000010010110101111110101000011110100,
+	      0b1010100111100010011110000011011101101100010110000110101010101010,
+	      0b0000001111001111000000101100111011011000101000110011101100110010,
+	      0b0111000011100100101101010100001101111110101111001000010011111111,
+	      0b0010111000100110100100100010101100111010110001101010010111001000,
+	      0b0000100000010110000011001001000111000001111010100101101000001111,
+	      0b0010101011101000111100001011000010011101000101010010010000101111,
+	      0b1011111011101101110010101011010001111000101000101101011001100011,
+	      0b1010111011011011110111110011001010000010011001110100101101000101,
+	      0b0011000001110110011010010000011100100011001011001100001101010110,
+	      0b0100011111011000111111101000011110000010111110101001000000001001,
+	      0b1110000001110001001101101110011000100000001010000111100010111010,
+	      0b1110001001010011101000111000001000010100110000010110100011110000,
+	      0b0000011010110000110001111000011111000011001101001101001001000110,
+	      0b1010010111001000101001100101010110100100100010010010000101000010,
+	      0b1011001110000111100010100110000011100011111001110111001100000101,
+	      0b0110101001001000010110001000010001010101110101100001111100011001,
+	      0b1111100011110101011110011010101001010010100011000010110001101001,
+	      0b0100000100001000111101011100010011011111011001000000001100011000,
+	      0b1110111111000111100101110111110000000011001110011100011011011001,
+	      0b1100001100100000010001100011011000111011110000110011010101000011,
+	      0b1111111011100111011101001111111000010000001111010111110010000100,
+	      0b1110111001111110101111000101000000001010001110011010001000111010,
+	      0b1000010001011000101111111010110011111101110101101001111000111010,
+	      0b0100000111101001000111011001101000001010111011101001101111000100,
+	      0b0000011100110001000111011100111100110001101111111010110111100000,
+	      0b0000011101011100100110010011110101010100010011110010010111010000,
+	      0b0011011001100111110101111100001001101110101101001110110011110110,
+	      0b1011000101000001110100111001100100111100110011110000000001101000,
+	      0b1011100011110100001001110101010110111001000000001011101001011110,
+	      0b1111001010010010100000010110101010101011101000101000000000001100,
+	      0b1000001111100100111001110101100001010011111111000001000011110000,
+	      0b0001011101001000010000101101111000001110101100110011001100110111,
+	      0b1110011100000010101011011111001010111101111110100000011100000011,
+	      0b1001110110011100101010011110100010110001001110110000101011100110,
+	      0b1001101000100011100111010000011011100001000000110101100100001001,
+	      0b1010111000101000101101010111000010001100001010100011111100000100,
+	      0b0111101000100011000101101011111011100010001101110111001111001011,
+	      0b1110100111010110001110110110000000010110100011110000010001111100,
+	      0b1100010100011010001011001000111001010101011110100101011001000000,
+	      0b0000110001111001100110010110111010101101001101000000000010010101,
+	      0b0001110111101000001111101010110010010000111110111100000111110100,
+	      0b0111110111001001111000110001101101001010101110110101111110000100,
+	      0b0000111110111010101111100010111010011100010110011011011001000001,
+	      0b1010010100100100101110111111111000101100000010111111101101000110,
+	      0b1000100111111101100011001101000110001000000100010101010100001101,
+	      0b1100101010101000111100101100001000110001110010100000000010110101,
+	      0b1010000100111101100100101010010110100010000000110101101110000100,
+	      0b1011111011110001110000100100000000001010111010001101100000100100,
+	      0b0111101101100011001110011100000001000101101101111000100111011111,
+	      0b0100111010010011011001010011110100001100111010010101111111100011,
+	      0b0010001001011000111000001100110111110111110010100011000110110110,
+	      0b0101010110000000010000100000110100111011111101000100000111010010,
+	      0b0110000011011101000001010100110101101110011100110101000000001001,
+	      0b1101100110100000011000001111000100100100110001100110101010101100,
+	      0b0010100101010110010010001010101000011111111111001011001010001111,
+	      0b0111001010001111001100111001010101001000110101000011110000001000,
+	      0b0110010011001001001111110001010010001011010010001101110110110011,
+	      0b0110010100111011000100111000001001101011111001110010111110111111,
+	      0b0101110111001001101100110100101001110010101110011001101110001000,
+	      0b0100110101010111011010001100010111100011010011111001010100111000,
+	      0b0111000110110111011110100100010111000110000110110110110001111110,
+	      0b1000101101010100100100111110100011110110110010011001110011110101,
+	      0b1001101110101001010100111101101011000101000010110101101111110000,
+	      0b0100100101001011011001001011000010001101001010010001010110101000,
+	      0b0010100001001011100110101000010110000111000111000011100101011011,
+	      0b0110111000011001111101101011111010001000000010101000101010011110,
+	      0b1000110110100001111011000001111100001001000000010110010100100100,
+	      0b1001110100011111100111101011010000010101011100101000010010100110,
+	      0b0001010110101110100010101010001110110110100011101010001001111100,
+	      0b1010100101101100000010110011100110100010010000100100001110000100,
+	      0b0001000000010000001010000010100110000001110100111001110111101101,
+	      0b1100000000000000000000000000000000000000000000000000000000000000,
+	    };
+      };
+
+    template<>
+      struct __floating_type_traits<long double, __long_double_kind::ibm128>
+      {
+	using bitrep_t = unsigned __int128;
+	static constexpr int mantissa_bits = 105;
+	static constexpr int exponent_bits = 11;
+	static constexpr bool has_implicit_leading_bit = true;
+
+	using shortest_scientific_t = __ryu::floating_decimal_128;
+	static constexpr uint64_t pow10_adjustment_tab[]
+	  = { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	      0b0000000000000000000100000000000000000000001000000000000000000010,
+	      0b0000100000000000000000001001000000000000000001100100000000000000,
+	      0b0011000000000000000000000000000001110000010000000000000000000000,
+	      0b0000100000000000001000000000000000000000000000100000000000000000,
+	    };
+      };
+
+    template<>
+      struct __floating_type_traits<long double, __long_double_kind::float128>
+      {
+	using bitrep_t = unsigned __int128;
+	static constexpr int mantissa_bits = 112;
+	static constexpr int exponent_bits = 15;
+	static constexpr bool has_implicit_leading_bit = true;
+
+	using shortest_scientific_t = __ryu::floating_decimal_128;
+	static constexpr uint64_t pow10_adjustment_tab[]
+	  = { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	      0b1011001111110100000100010101101110011100100110000110010110011000,
+	      0b1010100010001101111111000000001101010010100010010000111011110111,
+	      0b1011111001110001111000011111000010110111000111110100101010100101,
+	      0b0110100110011110011011000011000010011001110001001001010011100011,
+	      0b0000011111110010101111101011101010000110011111100111001110100111,
+	      0b0100010101010110000010111011110100000010011001001010001110111101,
+	      0b1101110111000010001101100000110100000111001001101011000101011011,
+	      0b0100111011101101010000001101011000101100101110010010110000101011,
+	      0b0100000110111000000110101000010011101000110100010110000011101101,
+	      0b1011001101001000100001010001100100001111011101010101110001010110,
+	      0b1000000001000000101001110010110010001111101101010101001100000110,
+	      0b0101110110100110000110000001001010111110001110010000111111010011,
+	      0b1010001111100111000100011100100100111100100101000001011001000111,
+	      0b1010011000011100110101100111001011100101111111100001110100000100,
+	      0b1100011100100010100000110001001010000000100000001001010111011101,
+	      0b0101110000100011001111101101000000100110000010010111010001111010,
+	      0b0100111100011010110111101000100110000111001001101100000001111100,
+	      0b1100100100111110101011000100000101011010110111000111110100110101,
+	      0b0110010000010111010100110011000000111010000010111011010110000100,
+	      0b0101001001010010110111010111000101011100000111100111000001110010,
+	      0b1101111111001011101010110001000111011010111101001011010110100100,
+	      0b0001000100110000011111101011001101110010110110010000000011100100,
+	      0b0001000000000101001001001000000000011000100011001110101001001110,
+	      0b0010010010001000111010011011100001000110011011011110110100111000,
+	      0b0000100110101100000111100010100100011100110111011100001111001100,
+	      0b1011111010001110001100000011110111111111100000001011111111101100,
+	      0b0000011100001111010101110000100110111100101101110111101001000001,
+	      0b1100010001110110111100001001001101101000011100000010110101001011,
+	      0b0100101001101011111001011110101101100011011111011100101010101111,
+	      0b0001101001111001110000101101101100001011010001011110011101000010,
+	      0b1111000000101001101111011010110011101110100001011011001011100010,
+	      0b0101001010111101101100001111100010010110001101001000001101100100,
+	      0b0101100101011110001100101011111000111001111001001001101101100001,
+	      0b1111001101010010100100011011000110110010001111000111010001001101,
+	      0b0001110010011000000001000110110111011000011100001000011001110111,
+	      0b0100001011011011011011110011101100100101111111101100101000001110,
+	      0b0101011110111101010111100111101111000101111111111110100011011010,
+	      0b1110101010001001110100000010110111010111111010111110100110010110,
+	      0b1010001111100001001100101000110100001100011100110010000011010111,
+	      0b1111111101101111000100111100000101011000001110011011101010111001,
+	      0b1111101100001110100101111101011001000100000101110000110010100011,
+	      0b1001010110110101101101000101010001010000101011011111010011010000,
+	      0b0111001110110011101001100111000001000100001010110000010000001101,
+	      0b0101111100111110100111011001111001111011011110010111010011101010,
+	      0b1110111000000001100100111001100100110001011011001110101111110111,
+	      0b0001010001001101010111101010011111000011110001101101011001111111,
+	      0b0101000011100011010010001101100001011101011010100110101100100010,
+	      0b0001000101011000100101111100110110000101101101111000110001001011,
+	      0b0101100101001011011000010101000000010100011100101101000010011111,
+	      0b1000010010001011101001011010100010111011110100110011011000100111,
+	      0b1000011011100001010111010111010011101100100010010010100100101001,
+	      0b1001001001010111110101000010111010000000101111010100001010010010,
+	      0b0011011110110010010101111011000001000000000011011111000011111011,
+	      0b1011000110100011001110000001000100000001011100010111010010011110,
+	      0b0111101110110101110111110000011000000100011100011000101101101110,
+	      0b1001100101111011011100011110101011001111100111101010101010110111,
+	      0b1100110010010001100011001111010000000100011101001111011101001111,
+	      0b1000111001111010100101000010000100000001001100101010001011001101,
+	      0b0011101011110000110010100101010100110010100001000010101011111101,
+	      0b1100000000000110000010101011000000011101000110011111100010111111,
+	      0b0010100110000011011100010110111100010110101100110011101110001101,
+	      0b0010111101010011111000111001111100110111111100100011110001101110,
+	      0b1001110111001001101001001001011000010100110001000000100011010110,
+	      0b0011110101100111011011111100001000011001010100111100100101111010,
+	      0b0010001101000011000010100101110000010101101000100110000100001010,
+	      0b0010000010100110010101100101110011101111000111111111001001100001,
+	      0b0100111111011011011011100111111011000010011101101111011111110110,
+	      0b1111111111010110101011101000100101110100001110001001101011100111,
+	      0b1011111101000101110000111100100010111010100001010000010010110010,
+	      0b1111010101001011101011101010000100110110001110111100100110111111,
+	      0b1011001101000001001101000010101010010110010001100001011100011010,
+	      0b0101001011011101010001110100010000010001111100100100100001001101,
+	      0b0010100000111001100011000101100101000001111100111001101000000010,
+	      0b1011001111010101011001000100100110100100110111110100000110111000,
+	      0b0101011111010011100011010010111101110010100001111111100010001001,
+	      0b0010111011101100100000000000001111111010011101100111100001001101,
+	      0b1101000000000000000000000000000000000000000000000000000000000000,
+	    };
+      };
+  } // anon namespace
+
+  // Returns the bit representation of the floating-point value argument that
+  // is compatible with the canonical IEEE format.
+  template<typename T>
+    static typename __floating_type_traits<T>::bitrep_t
+    __get_canonical_bitrep(const T value)
+    {
+      typename __floating_type_traits<T>::bitrep_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+      return value_bits;
+    }
+
+  template<>
+    typename __floating_type_traits<long double>::bitrep_t
+    __get_canonical_bitrep(const long double value)
+    {
+      if constexpr (__ldk != __long_double_kind::ibm128)
+	{
+	  typename __floating_type_traits<long double>::bitrep_t value_bits = 0;
+	  memcpy(&value_bits, &value, sizeof(value));
+	  return value_bits;
+	}
+      else
+	{
+	  // The layout of __ibm128 isn't compatible with the canonical IEEE
+	  // format.  So we transform it into an IEEE-compatible format,
+	  // suitable for consumption by the generic Ryu API, with an 11-bit
+	  // exponent and 105-bit mantissa (with an implicit leading bit).
+	  // We keep the exponent and sign of the high part, and merge the
+	  // mantissa of the high part with the mantissa (and the implicit
+	  // leading bit) of the low part.
+	  using bitrep_t = unsigned __int128;
+	  bitrep_t value_bits = 0;
+	  memcpy(&value_bits, &value, sizeof(value_bits));
+
+	  const uint64_t value_hi = value_bits;
+	  const uint64_t value_lo = value_bits >> 64;
+
+	  uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+	  unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+	  const int sign_hi = (value_hi >> 63) & 1;
+
+	  uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+	  const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+	  const int sign_lo = (value_lo >> 63) & 1;
+
+	    {
+	      // The following code for adjusting the low-part mantissa to
+	      // combine it with the high-part mantissa is taken from the glibc
+	      // source file sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	      mantissa_lo <<= 7;
+	      if (exponent_lo != 0)
+		mantissa_lo |= (1ull << (52 + 7));
+	      else
+		mantissa_lo <<= 1;
+
+	      const int ediff = exponent_hi - exponent_lo - 53;
+	      if (ediff > 63)
+		mantissa_lo = 0;
+	      else if (ediff > 0)
+		mantissa_lo >>= ediff;
+	      else if (ediff < 0)
+		mantissa_lo <<= -ediff;
+
+	      if (sign_lo != sign_hi && mantissa_lo != 0)
+		{
+		  mantissa_lo = (1ull << 60) - mantissa_lo;
+		  if (mantissa_hi == 0)
+		    {
+		      mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		      mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		      exponent_hi--;
+		    }
+		  else
+		    mantissa_hi--;
+		}
+	    }
+
+	  const int ieee_sign = sign_hi;
+	  const unsigned ieee_exponent = exponent_hi;
+	  const bitrep_t ieee_mantissa = ((bitrep_t{mantissa_hi} << 64)
+					  | (bitrep_t{mantissa_lo} << 4)) >> 11;
+
+	  bitrep_t ieee_bits = 0;
+	  if (ieee_sign)
+	    ieee_bits |= bitrep_t{1} << (11+105);
+	  ieee_bits |= bitrep_t{ieee_exponent} << 105;
+	  ieee_bits |= ieee_mantissa;
+	  return ieee_bits;
+	}
+    }
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392. has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can trust the shortest scientific exponent to determine the
+  // length of the exact value, but for these powers of 10 the length of the
+  // exact value is one smaller than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    static bool
+    __is_rounded_up_pow10_p(const typename
+			    __floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= __floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64] & (1ull<<(63-fd.exponent%64)));
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* last, const T value,
+			    std::optional<int> precision)
+    {
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = __floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= __floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = __floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using bitrep_t = typename __floating_type_traits<T>::bitrep_t;
+
+      if (precision && *precision < 0)
+	precision = nullopt;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto value_bits = __get_canonical_bitrep(value);
+      const bool sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      const bitrep_t ieee_mantissa = value_bits & ((bitrep_t{1} << mantissa_bits)
+						   - 1u);
+      const uint32_t biased_exponent
+	= (value_bits >> mantissa_bits) & ((bitrep_t{1} << exponent_bits) - 1u);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      bitrep_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= bitrep_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (bitrep_t{1} << (mantissa_bits
+								   - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = bitrep_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  if (should_round & (bitrep_t{1} << dropped_bits))
+	    // Round up the least significant printed hexit.
+	    effective_mantissa += bitrep_t{1} << dropped_bits;
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits,
+	  effective_mantissa <<= dropped_bits;
+	  if constexpr (!has_implicit_leading_bit)
+	    if (effective_mantissa == bitrep_t{1} << rounded_mantissa_bits)
+	      {
+		// We rounded the leading nibble up and it overflowed,
+		// e.g f.ffp+10 with precision=1 became 10.0p+10.  Absorb the
+		// extra hexit into the exponent to obtain 1.0p+14.
+		effective_mantissa >>= 4;
+		written_exponent += 4;
+	      }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(bitrep_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(bitrep_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_printed_exponent = abs(written_exponent);
+      expected_output_length += (abs_printed_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_printed_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_printed_exponent >= 100 ? strlen("p+ddd")
+				 : abs_printed_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first [[maybe_unused]] = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits - 4;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+
+	       effective_mantissa &= ~(bitrep_t{0b1111} << nibble_offset);
+	       nibble_offset -= 4;
+	    }
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      auto result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point value.
+  template<typename T>
+    static typename __floating_type_traits<T>::shortest_scientific_t
+    __floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (is_same_v<T, float>)
+	return __ryu::floating_to_fd32(value);
+      else if constexpr (is_same_v<T, double>)
+	return __ryu::floating_to_fd64(value);
+      else if constexpr (is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = __floating_type_traits<long double>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = __floating_type_traits<long double>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = __floating_type_traits<long double>::has_implicit_leading_bit;
+
+	  const auto value_bits = __get_canonical_bitrep(value);
+	  return __ryu::generic_binary_to_decimal(value_bits,
+						  mantissa_bits, exponent_bits,
+						  !has_implicit_leading_bit);
+	}
+    }
+
+  static int
+  __mantissa_length(__ryu::floating_decimal_32 fd)
+  { return __ryu::decimalLength9(fd.mantissa); }
+
+  static int
+  __mantissa_length(__ryu::floating_decimal_64 fd)
+  { return __ryu::decimalLength17(fd.mantissa); }
+
+  static int
+  __mantissa_length(__ryu::floating_decimal_128 fd)
+  { return __ryu::__generic128::decimalLength(fd.mantissa); }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = __floating_to_shortest_scientific(value);
+      const int mantissa_length = __mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+NNNN")
+				     : abs_exponent >= 100 ? strlen("e+NNN")
+				     : strlen("e+NN"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = __ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa that what the
+	  // shortest scientific form given by Ryu contains.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (__is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // Adding some wiggle room due to rounding yields the condition
+	  // value_fits_inside_mantissa below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < __floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length [[maybe_unused]]
+		= fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = __ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length [[maybe_unused]] = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point at the appropriate
+	      // spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length [[maybe_unused]]
+		= result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = __floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = __floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using bitrep_t = typename __floating_type_traits<T>::bitrep_t;
+
+      // Extract the sign and exponent from the value.
+      const auto value_bits = __get_canonical_bitrep(value);
+      const bool sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      const uint32_t biased_exponent
+	= (value_bits >> mantissa_bits) & ((bitrep_t{1} << exponent_bits) - 1u);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+    // Ryu doesn't support formatting floating-point types larger than double
+    // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward obvious upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is "far away" from +-100.  Otherwise, our
+	  // floor(log2) is too coarse-grained and doesn't consider
+	  // precision-dependent rounding in order to distinguish between a
+	  // scientific exponent of +-100 or +-99.
+	  // We handle this edge case by first writing the result to a
+	  // sufficiently sized output buffer.
+	  const bool scientific_exponent_near_100
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+	  int output_length;
+	  if (scientific_exponent_near_100) [[unlikely]]
+	    {
+	      const int output_length_upper_bound
+		= strlen("-d.") + effective_precision + strlen("e+ddd");
+	      char buffer[output_length_upper_bound];
+	      output_length = __ryu::d2exp_buffered_n(value, effective_precision,
+						      buffer, nullptr);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    {
+	      // Compute the output length exactly, perform a bounds check,
+	      // and write the result directly into the range.
+	      int expected_output_length = sign + strlen("d");
+	      if (effective_precision > 0)
+		expected_output_length += strlen(".") + effective_precision;
+	      expected_output_length
+		+= ((floor_log2_value >= 332 || floor_log2_value <= -333)
+		    ? strlen("e+ddd") : strlen("e+dd"));
+	      if (last - first < expected_output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      output_length = __ryu::d2exp_buffered_n(value, effective_precision,
+						      first, nullptr);
+	      __glibcxx_assert(output_length == expected_output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice in the excess zeros to the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // It is harder to compute the exact output length with fixed
+	  // formatting, so we instead compute an upper bound and write to an
+	  // intermediate buffer if necessary.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      output_length
+		= __ryu::d2fixed_buffered_n(value, effective_precision, first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      char buffer[output_length_upper_bound];
+	      output_length
+		= __ryu::d2fixed_buffered_n(value, effective_precision, buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific string such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = __ryu::d2exp_buffered_n(value, effective_precision - 1,
+				      buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+    if constexpr (__ldk == __long_double_kind::float64
+		  || __ldk == __long_double_kind::unsupported)
+      return __floating_to_chars_shortest(first, last, (double)value,
+					  chars_format{});
+    else
+      return __floating_to_chars_shortest(first, last, value, chars_format{});
+  }
+
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+    if constexpr (__ldk == __long_double_kind::float64
+		  || __ldk == __long_double_kind::unsupported)
+      return __floating_to_chars_shortest(first, last, (double)value, fmt);
+    else
+      return __floating_to_chars_shortest(first, last, value, fmt);
+  }
+
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+    if constexpr (__ldk == __long_double_kind::float64
+		  || __ldk == __long_double_kind::unsupported)
+      return __floating_to_chars_precision(first, last, (double)value,
+					   fmt, precision);
+    else
+      return __floating_to_chars_precision(first, last, value, fmt, precision);
+  }
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..f6a73cf4b88
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the other formatting modes, which go through printf.
+void
+test02()
+{
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (const long double start : {2.0L, 0x1.ffffffffffffffffffffffffffffp+0L})
+      for (long double __value = start; !isinf(__value); __value *= __value)
+	for (const long double value : {__value, 1.0L/__value})
+	  {
+	    for (const int precision : {-1, 0, 10, 100, 10000})
+	      {
+		const char* const printf_specifier
+		  = (fmt == chars_format::fixed ? "%.*Lf"
+		     : fmt == chars_format::scientific ? "%.*Le"
+		     : fmt == chars_format::general ? "%.*Lg"
+		     : fmt == chars_format::hex ? "%.*La"
+		     : nullptr);
+		unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						  precision, value);
+
+		char printf_buffer[output_length+1];
+		snprintf(printf_buffer, output_length+1, printf_specifier,
+			 precision, value);
+
+		char to_chars_buffer[output_length];
+		auto result = to_chars(to_chars_buffer,
+				       to_chars_buffer+output_length,
+				       value, fmt, precision);
+		VERIFY( result.ec == errc{} );
+		VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+		result = to_chars(to_chars_buffer,
+				  to_chars_buffer+output_length-1,
+				  value, fmt, precision);
+		VERIFY( result.ec == errc::value_too_large );
+	      }
+
+	    // Verify that the nearby values have a different shortest form.
+	    char to_chars_buffer[50000];
+	    auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				   value, fmt);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    char nearby_buffer[50000];
+	      {
+		const long double smaller = nextdownl(value);
+		result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				  smaller, fmt);
+		VERIFY( result.ec == errc{} );
+		*result.ptr = '\0';
+		VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	      }
+
+	      {
+		long double larger = nextupl(value);
+		result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				  larger, fmt);
+		VERIFY( result.ec == errc{} );
+		*result.ptr = '\0';
+		VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	      }
+	  }
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
diff --git a/libstdc++-v3/testsuite/util/testsuite_abi.cc b/libstdc++-v3/testsuite/util/testsuite_abi.cc
index aedb6561ed4..4b73604cc74 100644
--- a/libstdc++-v3/testsuite/util/testsuite_abi.cc
+++ b/libstdc++-v3/testsuite/util/testsuite_abi.cc
@@ -209,6 +209,7 @@ check_version(symbol& test, bool added)
       known_versions.push_back("GLIBCXX_3.4.26");
       known_versions.push_back("GLIBCXX_3.4.27");
       known_versions.push_back("GLIBCXX_3.4.28");
+      known_versions.push_back("GLIBCXX_3.4.29");
       known_versions.push_back("CXXABI_1.3");
       known_versions.push_back("CXXABI_LDBL_1.3");
       known_versions.push_back("CXXABI_1.3.1");
@@ -240,7 +241,7 @@ check_version(symbol& test, bool added)
 	test.version_status = symbol::incompatible;
 
       // Check that added symbols are added in the latest pre-release version.
-      bool latestp = (test.version_name == "GLIBCXX_3.4.28"
+      bool latestp = (test.version_name == "GLIBCXX_3.4.29"
 		     || test.version_name == "CXXABI_1.3.12"
 		     || test.version_name == "CXXABI_FLOAT128"
 		     || test.version_name == "CXXABI_TM_1");
-- 
2.28.0.rc0

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Tue, 14 Jul 2020, Patrick Palka wrote:

> This implements the floating-point std::to_chars overloads for float,
> double and long double.  We use the Ryu library to compute the shortest
> round-trippable fixed and scientific forms of a number for float, double
> and long double.  We also use Ryu for performing fixed and scientific
> formatting of float and double. For formatting long double with an
> explicit precision argument we use a printf fallback.  Hexadecimal
> formatting for float, double and long double is implemented from
> scratch.
> 
> The supported long double binary formats are float64 (same as double),
> float80 (x86 extended precision), float128 and ibm128.
> 
> Much of the complexity of the implementation is in computing the exact
> output length before handing it off to Ryu (which doesn't do bounds
> checking).  In some cases it's hard to compute the output length before
> the fact, so in these cases we instead compute an upper bound on the
> output length and use a sufficiently-sized intermediate buffer (if the
> output range is smaller than the upper bound).
> 
> Another source of complexity is in the general-with-precision formatting
> mode, where we need to do zero-trimming of the string returned by Ryu, and
> where we also take care to avoid having to format the string a second
> time when the general formatting mode resolves to fixed.
> 
> Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> 
> libstdc++-v3/ChangeLog:
> 
> 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> 	* config/abi/pre/gnu.ver: Add new exports.
> 	* configure: Regenerate.
> 	* include/std/charconv (to_chars): Declare the floating-point
> 	overloads for float, double and long double.
> 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> 	* src/c++17/Makefile.in: Regenerate.
> 	* src/c++17/floating_to_chars.cc: New file.
> 	* testsuite/20_util/to_chars/long_double.cc: New test.
> 	* testsuite/util/testsuite_abi.cc: Add new symbol version.

Here is v2 of this patch, which fixes a build failure on i386 due to
__int128 being unavailable, by refactoring the long double binary format
selection to avoid referring to __int128 when it doesn't exist.  The
patch also makes the hex formatting for 80-bit long double use uint64_t
instead of __int128 since the mantissa has exactly 64 bits in this case.

-- >8 --

Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
 implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing fixed and scientific
formatting of float and double. For formatting long double with an
explicit precision argument we use a printf fallback.  Hexadecimal
formatting for float, double and long double is implemented from
scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length before
the fact, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer (if the
output range is smaller than the upper bound).

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu, and
where we also take care to avoid having to format the string a second
time when the general formatting mode resolves to fixed.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's approach of being consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form of 1.08p+0 is 2.1p-1, but we output the former instead of the
   latter, as does printf.

2. The Ryu routines for doing shortest formatting on types larger than
   binary64 use the __int128 type, and some targets (e.g.  i386) have a
   large long double type but lack __int128.  For such targets we make
   the long double to_chars overloads go through the double overloads,
   which means we lose precision in the output.  (The mantissa of long
   double is 64 bits on i386, so I think we could potentially fix this
   writing a specialized version of the generic Ryu formatting
   routine which works with uint64_t instead of __int128.)

3. The __ibm128 shortest formatting routines don't guarantee
   round-trippability if the exponent difference between the low-order
   and high-order parts is too large.  This is because we treat the type
   as if it has a contiguous 105-bit mantissa by merging the high-order
   and low-order mantissas, so we potentially lose precision from the
   low-order part.  Although this precision-dropping behavior is
   non-conforming, it seems consistent with how printf formats __ibm128.

Tested so far on x86_64-pc-linux-gnu and on powerpc64-unknown-linux-gnu.

libstdc++-v3/ChangeLog:

	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
	* config/abi/pre/gnu.ver: Add new exports.
	* configure: Regenerate.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	* testsuite/20_util/to_chars/long_double.cc: New test.
	* testsuite/util/testsuite_abi.cc: Add new symbol version.
---
 libstdc++-v3/acinclude.m4                     |    2 +-
 libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
 libstdc++-v3/configure                        |    2 +-
 libstdc++-v3/include/std/charconv             |   21 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    5 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1515 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
 9 files changed, 1753 insertions(+), 5 deletions(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
index ee5e0336f2c..e3926e1c9c2 100644
--- a/libstdc++-v3/acinclude.m4
+++ b/libstdc++-v3/acinclude.m4
@@ -3846,7 +3846,7 @@ changequote([,])dnl
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index edf4485e607..9a1bcfd25d1 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
 
 } GLIBCXX_3.4.27;
 
+GLIBCXX_3.4.29 {
+    # to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[fdeg];
+
+    # to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[fdeg]St12chars_format;
+
+    # to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
+
+} GLIBCXX_3.4.28;
+
 # Symbols in the support library (libsupc++) have their own tag.
 CXXABI_1.3 {
 
diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
index dd54bd406a9..73f771e7335 100755
--- a/libstdc++-v3/configure
+++ b/libstdc++-v3/configure
@@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index cc7dd0e3758..042cc4fbcca 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -688,6 +688,27 @@ namespace __detail
   operator^=(chars_format& __lhs, chars_format __rhs) noexcept
   { return __lhs = __lhs ^ __rhs; }
 
+  // Floating-point std::to_chars
+
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 85e31fbd91f..6637c5b4500 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -50,6 +50,7 @@ inst_sources =
 endif
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index de605a3f6a6..3b3b0d93a2c 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,8 +124,8 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = fs_dir.lo fs_ops.lo fs_path.lo memory_resource.lo \
-	$(am__objects_1)
+am__objects_2 = floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
 @ENABLE_EXTERN_TEMPLATE_TRUE@	string-inst.lo $(am__objects_3)
@@ -435,6 +435,7 @@ headers =
 @ENABLE_EXTERN_TEMPLATE_TRUE@	$(extra_string_inst_sources)
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..fd83537110f
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1515 @@
+// floating-point std::to_chars implementation -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_DEBUG
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We currently support the binary64, float80 (i.e. x86 80-bit extended
+// precision), binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#   define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu stuff in its own namespace to avoid name conflicts.
+#include "ryu/generic_128.h"
+#include "ryu/ryu_generic_128.h"
+#include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_rep;
+      ieee_rep.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_rep.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_rep.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_rep;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (with an implicit leading bit).  We keep the exponent and sign
+      // of the high part, and merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_rep;
+      ieee_rep.mantissa = ((uint_t{mantissa_hi} << 64)
+			   | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_rep.biased_exponent = exponent_hi;
+      ieee_rep.sign = sign_hi;
+      return ieee_rep;
+    }
+#endif
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can trust the shortest scientific exponent to determine the
+  // length of the exact value, but for these powers of 10 the length of the
+  // exact value is one smaller than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+    static optional<to_chars_result>
+    __handle_special_value(char* first, char* const last, const T value,
+			   const chars_format fmt, const int precision)
+    {
+      __glibcxx_assert(precision >= 0);
+
+      string_view str;
+      switch (fpclassify(value))
+	{
+	case FP_INFINITE:
+	  str = "-inf";
+	  break;
+
+	case FP_NAN:
+	  str = "-nan";
+	  break;
+
+	case FP_ZERO:
+	  break;
+
+	default:
+	case FP_SUBNORMAL:
+	case FP_NORMAL: [[likely]]
+	  return nullopt;
+	}
+
+      if (!str.empty())
+	{
+	  if (!signbit(value))
+	    str.remove_prefix(strlen("-"));
+
+	  if (last - first < (int)str.length())
+	    return {{last, errc::value_too_large}};
+
+	  memcpy(first, &str[0], str.length());
+	  first += str.length();
+	  return {{first, errc{}}};
+	}
+
+      __glibcxx_assert(value == 0);
+      const bool neg_zero_p = signbit(value);
+      int output_length;
+      switch (fmt)
+	{
+	case chars_format::fixed:
+	case chars_format::scientific:
+	case chars_format::hex:
+	  output_length = neg_zero_p + 1;
+	  if (precision)
+	    output_length += strlen(".") + precision;
+	  if (fmt == chars_format::scientific)
+	    output_length += strlen("e+00");
+	  else if (fmt == chars_format::hex)
+	    output_length += strlen("p+0");
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  if (precision)
+	    {
+	      *first++ = '.';
+	      memset(first, '0', precision);
+	      first += precision;
+	    }
+	  if (fmt == chars_format::scientific)
+	    {
+	      memcpy(first, "e+00", 4);
+	      first += 4;
+	    }
+	  else if (fmt == chars_format::hex)
+	    {
+	      memcpy(first, "p+0", 3);
+	      first += 3;
+	    }
+	  return {{first, errc{}}};
+
+	default:
+	  __glibcxx_assert(fmt == chars_format::general
+			   || fmt == chars_format{});
+	  output_length = neg_zero_p + 1;
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  return {{first, errc{}}};
+	}
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* last, const T value,
+			    std::optional<int> precision)
+    {
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+      constexpr int mantissa_t_width = sizeof(mantissa_t)*__CHAR_BIT__;
+
+      if (precision && *precision < 0)
+	precision = nullopt;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      static_assert(mantissa_t_width >= rounded_mantissa_bits);
+      mantissa_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								     - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = mantissa_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits;
+	  effective_mantissa <<= dropped_bits;
+	  if (should_round & (mantissa_t{1} << dropped_bits))
+	    {
+	      // Round up the least significant nibble.
+	      effective_mantissa += mantissa_t{1} << dropped_bits;
+	      // Check and adjust for overflow of the leading nibble.  When the
+	      // type has an implicit leading bit, then the leading nibble
+	      // before rounding is either 0 or 1, so it can't overflow.
+	      if constexpr (!has_implicit_leading_bit)
+		{
+		  // The only floating type with explicit leading mantissa bit
+		  // that we currently support is x86 80-bit extended precision.
+		  // So we hardcode the below overflow check for this type.
+		  static_assert(mantissa_t_width == 64
+				&& rounded_mantissa_bits == 64);
+		  if (effective_mantissa == 0)
+		    {
+		      // We rounded up the least significant nibble and the
+		      // mantissa overflowed, e.g f.fcp+10 with precision=1
+		      // became 10.0p+10.  Absorb the extra hexit into the
+		      // exponent to obtain 1.0p+14.
+		      effective_mantissa
+			= mantissa_t{1} << (rounded_mantissa_bits - 4);
+		      written_exponent += 4;
+		    }
+		}
+	    }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_printed_exponent = abs(written_exponent);
+      expected_output_length += (abs_printed_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_printed_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_printed_exponent >= 100 ? strlen("p+ddd")
+				 : abs_printed_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first [[maybe_unused]] = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits - 4;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+
+	       effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	       nibble_offset -= 4;
+	    }
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      auto result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point value.
+  template<typename T>
+    static typename floating_type_traits<T>::shortest_scientific_t
+    __floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						  mantissa_bits, exponent_bits,
+						  !has_implicit_leading_bit);
+	}
+#else
+      static_assert(!is_same_v<T, long double>);
+#endif
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = __floating_to_shortest_scientific(value);
+      const int mantissa_length = get_mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+NNNN")
+				     : abs_exponent >= 100 ? strlen("e+NNN")
+				     : strlen("e+NN"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa that what the
+	  // shortest scientific form given by Ryu contains.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // Adding some wiggle room due to rounding yields the condition
+	  // value_fits_inside_mantissa below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length [[maybe_unused]]
+		= fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length [[maybe_unused]] = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point at the appropriate
+	      // spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length [[maybe_unused]]
+		= result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+      // Extract the sign and exponent from the value.
+      const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+    // Ryu doesn't support formatting floating-point types larger than double
+    // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward obvious upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is "far away" from +-100.  Otherwise, our
+	  // floor(log2) is too coarse-grained and doesn't consider
+	  // precision-dependent rounding in order to distinguish between a
+	  // scientific exponent of +-100 or +-99.
+	  // We handle this edge case by first writing the result to a
+	  // sufficiently sized output buffer.
+	  const bool scientific_exponent_near_100
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+	  int output_length;
+	  if (scientific_exponent_near_100) [[unlikely]]
+	    {
+	      const int output_length_upper_bound
+		= strlen("-d.") + effective_precision + strlen("e+ddd");
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    buffer, nullptr);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    {
+	      // Compute the output length exactly, perform a bounds check,
+	      // and write the result directly into the range.
+	      int expected_output_length = sign + strlen("d");
+	      if (effective_precision > 0)
+		expected_output_length += strlen(".") + effective_precision;
+	      expected_output_length
+		+= ((floor_log2_value >= 332 || floor_log2_value <= -333)
+		    ? strlen("e+ddd") : strlen("e+dd"));
+	      if (last - first < expected_output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    first, nullptr);
+	      __glibcxx_assert(output_length == expected_output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice in the excess zeros to the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // It is harder to compute the exact output length with fixed
+	  // formatting, so we instead compute an upper bound and write to an
+	  // intermediate buffer if necessary.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific string such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = ryu::d2exp_buffered_n(value, effective_precision - 1,
+				    buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_shortest(first, last,
+					static_cast<double>(value),
+					chars_format{});
+#else
+    return __floating_to_chars_shortest(first, last, value, chars_format{});
+#endif
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_shortest(first, last,
+					static_cast<double>(value),
+					fmt);
+#else
+    return __floating_to_chars_shortest(first, last, value, fmt);
+#endif
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_precision(first, last,
+					 static_cast<double>(value),
+					 fmt, precision);
+#else
+    return __floating_to_chars_precision(first, last, value, fmt, precision);
+#endif
+  }
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..d995aa02d09
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
diff --git a/libstdc++-v3/testsuite/util/testsuite_abi.cc b/libstdc++-v3/testsuite/util/testsuite_abi.cc
index aedb6561ed4..4b73604cc74 100644
--- a/libstdc++-v3/testsuite/util/testsuite_abi.cc
+++ b/libstdc++-v3/testsuite/util/testsuite_abi.cc
@@ -209,6 +209,7 @@ check_version(symbol& test, bool added)
       known_versions.push_back("GLIBCXX_3.4.26");
       known_versions.push_back("GLIBCXX_3.4.27");
       known_versions.push_back("GLIBCXX_3.4.28");
+      known_versions.push_back("GLIBCXX_3.4.29");
       known_versions.push_back("CXXABI_1.3");
       known_versions.push_back("CXXABI_LDBL_1.3");
       known_versions.push_back("CXXABI_1.3.1");
@@ -240,7 +241,7 @@ check_version(symbol& test, bool added)
 	test.version_status = symbol::incompatible;
 
       // Check that added symbols are added in the latest pre-release version.
-      bool latestp = (test.version_name == "GLIBCXX_3.4.28"
+      bool latestp = (test.version_name == "GLIBCXX_3.4.29"
 		     || test.version_name == "CXXABI_1.3.12"
 		     || test.version_name == "CXXABI_FLOAT128"
 		     || test.version_name == "CXXABI_TM_1");
-- 
2.28.0.rc0

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Wed, 15 Jul 2020, Patrick Palka wrote:

> On Tue, 14 Jul 2020, Patrick Palka wrote:
> 
> > This implements the floating-point std::to_chars overloads for float,
> > double and long double.  We use the Ryu library to compute the shortest
> > round-trippable fixed and scientific forms of a number for float, double
> > and long double.  We also use Ryu for performing fixed and scientific
> > formatting of float and double. For formatting long double with an
> > explicit precision argument we use a printf fallback.  Hexadecimal
> > formatting for float, double and long double is implemented from
> > scratch.
> > 
> > The supported long double binary formats are float64 (same as double),
> > float80 (x86 extended precision), float128 and ibm128.
> > 
> > Much of the complexity of the implementation is in computing the exact
> > output length before handing it off to Ryu (which doesn't do bounds
> > checking).  In some cases it's hard to compute the output length before
> > the fact, so in these cases we instead compute an upper bound on the
> > output length and use a sufficiently-sized intermediate buffer (if the
> > output range is smaller than the upper bound).
> > 
> > Another source of complexity is in the general-with-precision formatting
> > mode, where we need to do zero-trimming of the string returned by Ryu, and
> > where we also take care to avoid having to format the string a second
> > time when the general formatting mode resolves to fixed.
> > 
> > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > 
> > libstdc++-v3/ChangeLog:
> > 
> > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > 	* config/abi/pre/gnu.ver: Add new exports.
> > 	* configure: Regenerate.
> > 	* include/std/charconv (to_chars): Declare the floating-point
> > 	overloads for float, double and long double.
> > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > 	* src/c++17/Makefile.in: Regenerate.
> > 	* src/c++17/floating_to_chars.cc: New file.
> > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> 
> Here is v2 of this patch, which fixes a build failure on i386 due to
> __int128 being unavailable, by refactoring the long double binary format
> selection to avoid referring to __int128 when it doesn't exist.  The
> patch also makes the hex formatting for 80-bit long double use uint64_t
> instead of __int128 since the mantissa has exactly 64 bits in this case.

Here's v3 which just makes some minor stylistic adjustments, and most
notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
since we just want to enable __glibcxx_assert and not all of debug mode.

-- >8 --

Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
 implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing explicit-precision
fixed and scientific formatting of float and double. For
explicit-precision formatting of long double we fall back to using
printf.  Hexadecimal formatting for float, double and long double is
implemented from scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length
beforehand, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer if
necessary.

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu,
and where we also take care to avoid having to format the string a
second time when the general formatting mode resolves to fixed.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's approach of being consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form of 1.08p+0 is 2.1p-1, but we output the former instead of the
   latter, as does printf.

2. The Ryu routines for doing shortest formatting on types larger than
   binary64 use the __int128 type, and some targets (e.g. i386) have a
   large long double type but lack __int128.  For these targets we make
   the long double to_chars overloads go through the double overloads,
   which means we lose precision in the output.  (The mantissa of long
   double is 64 bits on i386, so I think we could potentially fix this
   by writing a specialized version of the generic Ryu formatting
   routine which works with uint64_t instead of __int128.)

3. The __ibm128 shortest formatting routines don't guarantee
   round-trippability if the difference between the high- and low-order
   exponent is too large.  This is because we treat the type as if it
   has a contiguous 105-bit mantissa by merging the high- and low-order
   mantissas, so we potentially lose precision from the low-order part.
   Although this precision-dropping behavior is non-conforming, it seems
   consistent with how printf formats __ibm128.

libstdc++-v3/ChangeLog:

	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
	* config/abi/pre/gnu.ver: Add new exports.
	* configure: Regenerate.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	* testsuite/20_util/to_chars/long_double.cc: New test.
	* testsuite/util/testsuite_abi.cc: Add new symbol version.
---
 libstdc++-v3/acinclude.m4                     |    2 +-
 libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
 libstdc++-v3/configure                        |    2 +-
 libstdc++-v3/include/std/charconv             |   21 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    5 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
 9 files changed, 1752 insertions(+), 5 deletions(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
index ee5e0336f2c..e3926e1c9c2 100644
--- a/libstdc++-v3/acinclude.m4
+++ b/libstdc++-v3/acinclude.m4
@@ -3846,7 +3846,7 @@ changequote([,])dnl
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index edf4485e607..9a1bcfd25d1 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
 
 } GLIBCXX_3.4.27;
 
+GLIBCXX_3.4.29 {
+    # to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[fdeg];
+
+    # to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[fdeg]St12chars_format;
+
+    # to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
+
+} GLIBCXX_3.4.28;
+
 # Symbols in the support library (libsupc++) have their own tag.
 CXXABI_1.3 {
 
diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
index dd54bd406a9..73f771e7335 100755
--- a/libstdc++-v3/configure
+++ b/libstdc++-v3/configure
@@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index cc7dd0e3758..042cc4fbcca 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -688,6 +688,27 @@ namespace __detail
   operator^=(chars_format& __lhs, chars_format __rhs) noexcept
   { return __lhs = __lhs ^ __rhs; }
 
+  // Floating-point std::to_chars
+
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 85e31fbd91f..6637c5b4500 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -50,6 +50,7 @@ inst_sources =
 endif
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index de605a3f6a6..3b3b0d93a2c 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,8 +124,8 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = fs_dir.lo fs_ops.lo fs_path.lo memory_resource.lo \
-	$(am__objects_1)
+am__objects_2 = floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
 @ENABLE_EXTERN_TEMPLATE_TRUE@	string-inst.lo $(am__objects_3)
@@ -435,6 +435,7 @@ headers =
 @ENABLE_EXTERN_TEMPLATE_TRUE@	$(extra_string_inst_sources)
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..64e4a378fc2
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1514 @@
+// floating-point std::to_chars implementation -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_ASSERTIONS
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We currently support the binary64, float80 (i.e. x86 80-bit extended
+// precision), binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#   define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu stuff in its own namespace to avoid name conflicts.
+#include "ryu/generic_128.h"
+#include "ryu/ryu_generic_128.h"
+#include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_rep;
+      ieee_rep.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_rep.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_rep.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_rep;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (with an implicit leading bit).  We keep the exponent and sign
+      // of the high part, and merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_rep;
+      ieee_rep.mantissa = ((uint_t{mantissa_hi} << 64)
+			   | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_rep.biased_exponent = exponent_hi;
+      ieee_rep.sign = sign_hi;
+      return ieee_rep;
+    }
+#endif
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can trust the shortest scientific exponent to determine the
+  // length of the exact value, but for these powers of 10 the length of the
+  // exact value is one smaller than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(const ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+    static optional<to_chars_result>
+    __handle_special_value(char* first, char* const last, const T value,
+			   const chars_format fmt, const int precision)
+    {
+      __glibcxx_assert(precision >= 0);
+
+      string_view str;
+      switch (fpclassify(value))
+	{
+	case FP_INFINITE:
+	  str = "-inf";
+	  break;
+
+	case FP_NAN:
+	  str = "-nan";
+	  break;
+
+	case FP_ZERO:
+	  break;
+
+	default:
+	case FP_SUBNORMAL:
+	case FP_NORMAL: [[likely]]
+	  return nullopt;
+	}
+
+      if (!str.empty())
+	{
+	  if (!signbit(value))
+	    str.remove_prefix(strlen("-"));
+
+	  if (last - first < (int)str.length())
+	    return {{last, errc::value_too_large}};
+
+	  memcpy(first, &str[0], str.length());
+	  first += str.length();
+	  return {{first, errc{}}};
+	}
+
+      __glibcxx_assert(value == 0);
+      const bool neg_zero_p = signbit(value);
+      int output_length;
+      switch (fmt)
+	{
+	case chars_format::fixed:
+	case chars_format::scientific:
+	case chars_format::hex:
+	  output_length = neg_zero_p + 1;
+	  if (precision)
+	    output_length += strlen(".") + precision;
+	  if (fmt == chars_format::scientific)
+	    output_length += strlen("e+00");
+	  else if (fmt == chars_format::hex)
+	    output_length += strlen("p+0");
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  if (precision)
+	    {
+	      *first++ = '.';
+	      memset(first, '0', precision);
+	      first += precision;
+	    }
+	  if (fmt == chars_format::scientific)
+	    {
+	      memcpy(first, "e+00", 4);
+	      first += 4;
+	    }
+	  else if (fmt == chars_format::hex)
+	    {
+	      memcpy(first, "p+0", 3);
+	      first += 3;
+	    }
+	  return {{first, errc{}}};
+
+	default:
+	  __glibcxx_assert(fmt == chars_format::general
+			   || fmt == chars_format{});
+	  output_length = neg_zero_p + 1;
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  return {{first, errc{}}};
+	}
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* last, const T value,
+			    optional<int> precision)
+    {
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+      constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__;
+
+      if (precision && *precision < 0)
+	precision = nullopt;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      static_assert(mantissa_t_width >= rounded_mantissa_bits);
+      mantissa_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								     - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = mantissa_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits;
+	  effective_mantissa <<= dropped_bits;
+	  if (should_round & (mantissa_t{1} << dropped_bits))
+	    {
+	      // Round up the least significant nibble.
+	      effective_mantissa += mantissa_t{1} << dropped_bits;
+	      // Check and adjust for overflow of the leading nibble.  When the
+	      // type has an implicit leading bit, then the leading nibble
+	      // before rounding is either 0 or 1, so it can't overflow.
+	      if constexpr (!has_implicit_leading_bit)
+		{
+		  // The only floating type with explicit leading mantissa bit
+		  // that we currently support is x86 80-bit extended precision.
+		  // So we hardcode the below overflow check for this type.
+		  static_assert(mantissa_t_width == 64
+				&& rounded_mantissa_bits == 64);
+		  if (effective_mantissa == 0)
+		    {
+		      // We rounded up the least significant nibble and the
+		      // mantissa overflowed, e.g f.fcp+10 with precision=1
+		      // became 10.0p+10.  Absorb the extra hexit into the
+		      // exponent to obtain 1.0p+14.
+		      effective_mantissa
+			= mantissa_t{1} << (rounded_mantissa_bits - 4);
+		      written_exponent += 4;
+		    }
+		}
+	    }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_written_exponent = abs(written_exponent);
+      expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_written_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_written_exponent >= 100 ? strlen("p+ddd")
+				 : abs_written_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first [[maybe_unused]] = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits - 4;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+
+	       effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	       nibble_offset -= 4;
+	    }
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      const to_chars_result result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point number.
+  template<typename T>
+    static typename floating_type_traits<T>::shortest_scientific_t
+    __floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						  mantissa_bits, exponent_bits,
+						  !has_implicit_leading_bit);
+	}
+#endif
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = __floating_to_shortest_scientific(value);
+      const int mantissa_length = get_mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+NNNN")
+				     : abs_exponent >= 100 ? strlen("e+NNN")
+				     : strlen("e+NN"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa that what the
+	  // shortest scientific form given by Ryu contains.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // Adding some wiggle room due to rounding yields the condition
+	  // value_fits_inside_mantissa below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length [[maybe_unused]]
+		= fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length [[maybe_unused]] = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point at the appropriate
+	      // spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length [[maybe_unused]]
+		= result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* const last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+      // Extract the sign and exponent from the value.
+      const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+    // Ryu doesn't support formatting floating-point types larger than double
+    // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward obvious upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is "far away" from +-100.  Otherwise, our
+	  // floor(log2) is too coarse-grained and doesn't consider
+	  // precision-dependent rounding in order to distinguish between a
+	  // scientific exponent of +-100 or +-99.
+	  // We handle this edge case by first writing the result to a
+	  // sufficiently sized output buffer.
+	  const bool scientific_exponent_near_100
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+	  int output_length;
+	  if (scientific_exponent_near_100) [[unlikely]]
+	    {
+	      const int output_length_upper_bound
+		= strlen("-d.") + effective_precision + strlen("e+ddd");
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    buffer, nullptr);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    {
+	      // Compute the output length exactly, perform a bounds check,
+	      // and write the result directly into the range.
+	      int expected_output_length = sign + strlen("d");
+	      if (effective_precision > 0)
+		expected_output_length += strlen(".") + effective_precision;
+	      expected_output_length
+		+= ((floor_log2_value >= 332 || floor_log2_value <= -333)
+		    ? strlen("e+ddd") : strlen("e+dd"));
+	      if (last - first < expected_output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    first, nullptr);
+	      __glibcxx_assert(output_length == expected_output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice in the excess zeros to the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // It is harder to compute the exact output length with fixed
+	  // formatting, so we instead compute an upper bound and write to an
+	  // intermediate buffer if necessary.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific string such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = ryu::d2exp_buffered_n(value, effective_precision - 1,
+				    buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_shortest(first, last,
+					static_cast<double>(value),
+					chars_format{});
+#else
+    return __floating_to_chars_shortest(first, last, value, chars_format{});
+#endif
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_shortest(first, last,
+					static_cast<double>(value),
+					fmt);
+#else
+    return __floating_to_chars_shortest(first, last, value, fmt);
+#endif
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+#if LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED
+    return __floating_to_chars_precision(first, last,
+					 static_cast<double>(value),
+					 fmt, precision);
+#else
+    return __floating_to_chars_precision(first, last, value, fmt, precision);
+#endif
+  }
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..d995aa02d09
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
diff --git a/libstdc++-v3/testsuite/util/testsuite_abi.cc b/libstdc++-v3/testsuite/util/testsuite_abi.cc
index aedb6561ed4..4b73604cc74 100644
--- a/libstdc++-v3/testsuite/util/testsuite_abi.cc
+++ b/libstdc++-v3/testsuite/util/testsuite_abi.cc
@@ -209,6 +209,7 @@ check_version(symbol& test, bool added)
       known_versions.push_back("GLIBCXX_3.4.26");
       known_versions.push_back("GLIBCXX_3.4.27");
       known_versions.push_back("GLIBCXX_3.4.28");
+      known_versions.push_back("GLIBCXX_3.4.29");
       known_versions.push_back("CXXABI_1.3");
       known_versions.push_back("CXXABI_LDBL_1.3");
       known_versions.push_back("CXXABI_1.3.1");
@@ -240,7 +241,7 @@ check_version(symbol& test, bool added)
 	test.version_status = symbol::incompatible;
 
       // Check that added symbols are added in the latest pre-release version.
-      bool latestp = (test.version_name == "GLIBCXX_3.4.28"
+      bool latestp = (test.version_name == "GLIBCXX_3.4.29"
 		     || test.version_name == "CXXABI_1.3.12"
 		     || test.version_name == "CXXABI_FLOAT128"
 		     || test.version_name == "CXXABI_TM_1");
-- 
2.28.0.rc0.12.gb6a658bd00

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Fri, 17 Jul 2020, Patrick Palka wrote:

> On Wed, 15 Jul 2020, Patrick Palka wrote:
> 
> > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > 
> > > This implements the floating-point std::to_chars overloads for float,
> > > double and long double.  We use the Ryu library to compute the shortest
> > > round-trippable fixed and scientific forms of a number for float, double
> > > and long double.  We also use Ryu for performing fixed and scientific
> > > formatting of float and double. For formatting long double with an
> > > explicit precision argument we use a printf fallback.  Hexadecimal
> > > formatting for float, double and long double is implemented from
> > > scratch.
> > > 
> > > The supported long double binary formats are float64 (same as double),
> > > float80 (x86 extended precision), float128 and ibm128.
> > > 
> > > Much of the complexity of the implementation is in computing the exact
> > > output length before handing it off to Ryu (which doesn't do bounds
> > > checking).  In some cases it's hard to compute the output length before
> > > the fact, so in these cases we instead compute an upper bound on the
> > > output length and use a sufficiently-sized intermediate buffer (if the
> > > output range is smaller than the upper bound).
> > > 
> > > Another source of complexity is in the general-with-precision formatting
> > > mode, where we need to do zero-trimming of the string returned by Ryu, and
> > > where we also take care to avoid having to format the string a second
> > > time when the general formatting mode resolves to fixed.
> > > 
> > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > 
> > > libstdc++-v3/ChangeLog:
> > > 
> > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > 	* configure: Regenerate.
> > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > 	overloads for float, double and long double.
> > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > 	* src/c++17/Makefile.in: Regenerate.
> > > 	* src/c++17/floating_to_chars.cc: New file.
> > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > 
> > Here is v2 of this patch, which fixes a build failure on i386 due to
> > __int128 being unavailable, by refactoring the long double binary format
> > selection to avoid referring to __int128 when it doesn't exist.  The
> > patch also makes the hex formatting for 80-bit long double use uint64_t
> > instead of __int128 since the mantissa has exactly 64 bits in this case.
> 
> Here's v3 which just makes some minor stylistic adjustments, and most
> notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> since we just want to enable __glibcxx_assert and not all of debug mode.

Here's v4, which should now correctly support using <charconv> with
-mlong-double-64 on targets with a large default long double type.
This is done by defining the long double to_chars overloads as inline
wrappers around the double overloads within <charconv> whenever
__DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.

-- >8 --

Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
 implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing explicit-precision
fixed and scientific formatting of float and double. For
explicit-precision formatting of long double we fall back to using
printf.  Hexadecimal formatting for float, double and long double is
implemented from scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length
beforehand, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer if
necessary.

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu,
and where we also take care to avoid having to format the string a
second time when the general formatting mode resolves to fixed.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's approach of being consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form of 1.08p+0 is 2.1p-1, but we output the former instead of the
   latter, as does printf.

2. The Ryu routines for doing shortest formatting on types larger than
   binary64 use the __int128 type, and some targets (e.g. i386) have a
   large long double type but lack __int128.  For such targets we make
   the long double to_chars overloads go through the double overloads,
   which means we lose precision in the output.  (The mantissa of long
   double is 64 bits on i386, so I think we could potentially fix this
   by writing a specialized version of the generic Ryu formatting
   routine which works with uint64_t instead of __int128.)

3. The __ibm128 shortest formatting routines don't guarantee
   round-trippability if the difference between the high- and low-order
   exponent is too large.  This is because we treat the type as if it
   has a contiguous 105-bit mantissa by merging the high- and low-order
   mantissas, so we potentially lose precision from the low-order part.
   Although this precision-dropping behavior is non-conforming, it seems
   consistent with how printf formats __ibm128.

libstdc++-v3/ChangeLog:

	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
	* config/abi/pre/gnu.ver: Add new exports.
	* configure: Regenerate.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	* testsuite/20_util/to_chars/long_double.cc: New test.
	* testsuite/util/testsuite_abi.cc: Add new symbol version.
---
 libstdc++-v3/acinclude.m4                     |    2 +-
 libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
 libstdc++-v3/configure                        |    2 +-
 libstdc++-v3/include/std/charconv             |   43 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    5 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
 9 files changed, 1774 insertions(+), 5 deletions(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
index ee5e0336f2c..e3926e1c9c2 100644
--- a/libstdc++-v3/acinclude.m4
+++ b/libstdc++-v3/acinclude.m4
@@ -3846,7 +3846,7 @@ changequote([,])dnl
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index edf4485e607..9a1bcfd25d1 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
 
 } GLIBCXX_3.4.27;
 
+GLIBCXX_3.4.29 {
+    # to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[fdeg];
+
+    # to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[fdeg]St12chars_format;
+
+    # to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
+
+} GLIBCXX_3.4.28;
+
 # Symbols in the support library (libsupc++) have their own tag.
 CXXABI_1.3 {
 
diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
index dd54bd406a9..73f771e7335 100755
--- a/libstdc++-v3/configure
+++ b/libstdc++-v3/configure
@@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index cc7dd0e3758..bd59924f7e7 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -688,6 +688,49 @@ namespace __detail
   operator^=(chars_format& __lhs, chars_format __rhs) noexcept
   { return __lhs = __lhs ^ __rhs; }
 
+  // Floating-point std::to_chars
+
+  // Overloads for float.
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for double.
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for long double.
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // If long double has the same binary format as double, then we just define
+  // the long double overloads as wrappers around the corresponding double
+  // overloads.
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+  inline to_chars_result
+  to_chars(char* __first, char* __last, long double __value) noexcept
+  { return to_chars(__first, __last, double(__value)); }
+
+  inline to_chars_result
+  to_chars(char* __first, char* __last, long double __value,
+	   chars_format __fmt) noexcept
+  { return to_chars(__first, __last, double(__value), __fmt); }
+
+  inline to_chars_result
+  to_chars(char* __first, char* __last, long double __value,
+	   chars_format __fmt, int __precision) noexcept
+  { return to_chars(__first, __last, double(__value), __fmt, __precision); }
+#endif
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 85e31fbd91f..6637c5b4500 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -50,6 +50,7 @@ inst_sources =
 endif
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index de605a3f6a6..3b3b0d93a2c 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,8 +124,8 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = fs_dir.lo fs_ops.lo fs_path.lo memory_resource.lo \
-	$(am__objects_1)
+am__objects_2 = floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
 @ENABLE_EXTERN_TEMPLATE_TRUE@	string-inst.lo $(am__objects_3)
@@ -435,6 +435,7 @@ headers =
 @ENABLE_EXTERN_TEMPLATE_TRUE@	$(extra_string_inst_sources)
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..62aea809fc0
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1514 @@
+// floating-point std::to_chars implementation -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_ASSERTIONS
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We currently support the binary64, float80 (i.e. x86 80-bit extended
+// precision), binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#   define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu bits in their own namespace to avoid name conflicts.
+# include "ryu/generic_128.h"
+# include "ryu/ryu_generic_128.h"
+# include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_rep;
+      ieee_rep.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_rep.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_rep.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_rep;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (with an implicit leading bit).  We keep the exponent and sign
+      // of the high part, and merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_rep;
+      ieee_rep.mantissa = ((uint_t{mantissa_hi} << 64)
+			   | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_rep.biased_exponent = exponent_hi;
+      ieee_rep.sign = sign_hi;
+      return ieee_rep;
+    }
+#endif
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point number.
+  template<typename T>
+    typename floating_type_traits<T>::shortest_scientific_t
+    floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (std::is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (std::is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (std::is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						mantissa_bits, exponent_bits,
+						!has_implicit_leading_bit);
+	}
+#endif
+    }
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can trust the shortest scientific exponent to determine the
+  // length of the exact value, but for these powers of 10 the length of the
+  // exact value is one smaller than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(const ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+    static optional<to_chars_result>
+    __handle_special_value(char* first, char* const last, const T value,
+			   const chars_format fmt, const int precision)
+    {
+      __glibcxx_assert(precision >= 0);
+
+      string_view str;
+      switch (__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL,
+				   FP_ZERO, value))
+	{
+	case FP_INFINITE:
+	  str = "-inf";
+	  break;
+
+	case FP_NAN:
+	  str = "-nan";
+	  break;
+
+	case FP_ZERO:
+	  break;
+
+	default:
+	case FP_SUBNORMAL:
+	case FP_NORMAL: [[likely]]
+	  return nullopt;
+	}
+
+      if (!str.empty())
+	{
+	  if (!__builtin_signbit(value))
+	    str.remove_prefix(strlen("-"));
+
+	  if (last - first < (int)str.length())
+	    return {{last, errc::value_too_large}};
+
+	  memcpy(first, &str[0], str.length());
+	  first += str.length();
+	  return {{first, errc{}}};
+	}
+
+      __glibcxx_assert(value == 0);
+      const bool neg_zero_p = __builtin_signbit(value);
+      int output_length;
+      switch (fmt)
+	{
+	case chars_format::fixed:
+	case chars_format::scientific:
+	case chars_format::hex:
+	  output_length = neg_zero_p + 1;
+	  if (precision)
+	    output_length += strlen(".") + precision;
+	  if (fmt == chars_format::scientific)
+	    output_length += strlen("e+00");
+	  else if (fmt == chars_format::hex)
+	    output_length += strlen("p+0");
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  if (precision)
+	    {
+	      *first++ = '.';
+	      memset(first, '0', precision);
+	      first += precision;
+	    }
+	  if (fmt == chars_format::scientific)
+	    {
+	      memcpy(first, "e+00", 4);
+	      first += 4;
+	    }
+	  else if (fmt == chars_format::hex)
+	    {
+	      memcpy(first, "p+0", 3);
+	      first += 3;
+	    }
+	  return {{first, errc{}}};
+
+	default:
+	  __glibcxx_assert(fmt == chars_format::general
+			   || fmt == chars_format{});
+	  output_length = neg_zero_p + 1;
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  return {{first, errc{}}};
+	}
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* last, const T value,
+			    optional<int> precision)
+    {
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+      constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__;
+
+      if (precision && *precision < 0)
+	precision = nullopt;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      static_assert(mantissa_t_width >= rounded_mantissa_bits);
+      mantissa_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								     - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = mantissa_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits;
+	  effective_mantissa <<= dropped_bits;
+	  if (should_round & (mantissa_t{1} << dropped_bits))
+	    {
+	      // Round up the least significant nibble.
+	      effective_mantissa += mantissa_t{1} << dropped_bits;
+	      // Check and adjust for overflow of the leading nibble.  When the
+	      // type has an implicit leading bit, then the leading nibble
+	      // before rounding is either 0 or 1, so it can't overflow.
+	      if constexpr (!has_implicit_leading_bit)
+		{
+		  // The only floating type with explicit leading mantissa bit
+		  // that we currently support is x86 80-bit extended precision.
+		  // So we hardcode the below overflow check for this type.
+		  static_assert(mantissa_t_width == 64
+				&& rounded_mantissa_bits == 64);
+		  if (effective_mantissa == 0)
+		    {
+		      // We rounded up the least significant nibble and the
+		      // mantissa overflowed, e.g f.fcp+10 with precision=1
+		      // became 10.0p+10.  Absorb the extra hexit into the
+		      // exponent to obtain 1.0p+14.
+		      effective_mantissa
+			= mantissa_t{1} << (rounded_mantissa_bits - 4);
+		      written_exponent += 4;
+		    }
+		}
+	    }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_written_exponent = abs(written_exponent);
+      expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_written_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_written_exponent >= 100 ? strlen("p+ddd")
+				 : abs_written_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first [[maybe_unused]] = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits - 4;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+
+	       effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	       nibble_offset -= 4;
+	    }
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      const to_chars_result result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = floating_to_shortest_scientific(value);
+      const int mantissa_length = get_mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+NNNN")
+				     : abs_exponent >= 100 ? strlen("e+NNN")
+				     : strlen("e+NN"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa that what the
+	  // shortest scientific form given by Ryu contains.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // Adding some wiggle room due to rounding yields the condition
+	  // value_fits_inside_mantissa below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length [[maybe_unused]]
+		= fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length [[maybe_unused]] = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point at the appropriate
+	      // spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length [[maybe_unused]]
+		= result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* const last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+      // Extract the sign and exponent from the value.
+      const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+    // Ryu doesn't support formatting floating-point types larger than double
+    // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward obvious upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is "far away" from +-100.  Otherwise, our
+	  // floor(log2) is too coarse-grained and doesn't consider
+	  // precision-dependent rounding in order to distinguish between a
+	  // scientific exponent of +-100 or +-99.
+	  // We handle this edge case by first writing the result to a
+	  // sufficiently sized output buffer.
+	  const bool scientific_exponent_near_100
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+	  int output_length;
+	  if (scientific_exponent_near_100) [[unlikely]]
+	    {
+	      const int output_length_upper_bound
+		= strlen("-d.") + effective_precision + strlen("e+ddd");
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    buffer, nullptr);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    {
+	      // Compute the output length exactly, perform a bounds check,
+	      // and write the result directly into the range.
+	      int expected_output_length = sign + strlen("d");
+	      if (effective_precision > 0)
+		expected_output_length += strlen(".") + effective_precision;
+	      expected_output_length
+		+= ((floor_log2_value >= 332 || floor_log2_value <= -333)
+		    ? strlen("e+ddd") : strlen("e+dd"));
+	      if (last - first < expected_output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    first, nullptr);
+	      __glibcxx_assert(output_length == expected_output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice in the excess zeros to the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // It is harder to compute the exact output length with fixed
+	  // formatting, so we instead compute an upper bound and write to an
+	  // intermediate buffer if necessary.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific string such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = ryu::d2exp_buffered_n(value, effective_precision - 1,
+				    buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  // Define the overloads for float.
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for double.
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for double, if they haven't already been defined
+  // inline in <charconv>.
+#if LONG_DOUBLE_KIND != LDK_BINARY64
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value),
+					  chars_format{});
+    else
+      return __floating_to_chars_shortest(first, last, value, chars_format{});
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value), fmt);
+    else
+      return __floating_to_chars_shortest(first, last, value, fmt);
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_precision(first, last, double(value), fmt,
+					   precision);
+    else
+      return __floating_to_chars_precision(first, last, value, fmt, precision);
+  }
+#endif
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..d995aa02d09
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
diff --git a/libstdc++-v3/testsuite/util/testsuite_abi.cc b/libstdc++-v3/testsuite/util/testsuite_abi.cc
index aedb6561ed4..4b73604cc74 100644
--- a/libstdc++-v3/testsuite/util/testsuite_abi.cc
+++ b/libstdc++-v3/testsuite/util/testsuite_abi.cc
@@ -209,6 +209,7 @@ check_version(symbol& test, bool added)
       known_versions.push_back("GLIBCXX_3.4.26");
       known_versions.push_back("GLIBCXX_3.4.27");
       known_versions.push_back("GLIBCXX_3.4.28");
+      known_versions.push_back("GLIBCXX_3.4.29");
       known_versions.push_back("CXXABI_1.3");
       known_versions.push_back("CXXABI_LDBL_1.3");
       known_versions.push_back("CXXABI_1.3.1");
@@ -240,7 +241,7 @@ check_version(symbol& test, bool added)
 	test.version_status = symbol::incompatible;
 
       // Check that added symbols are added in the latest pre-release version.
-      bool latestp = (test.version_name == "GLIBCXX_3.4.28"
+      bool latestp = (test.version_name == "GLIBCXX_3.4.29"
 		     || test.version_name == "CXXABI_1.3.12"
 		     || test.version_name == "CXXABI_FLOAT128"
 		     || test.version_name == "CXXABI_TM_1");
-- 
2.28.0.rc0.12.gb6a658bd00

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Fri, 17 Jul 2020, Patrick Palka wrote:

> On Fri, 17 Jul 2020, Patrick Palka wrote:
> 
> > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > 
> > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > 
> > > > This implements the floating-point std::to_chars overloads for float,
> > > > double and long double.  We use the Ryu library to compute the shortest
> > > > round-trippable fixed and scientific forms of a number for float, double
> > > > and long double.  We also use Ryu for performing fixed and scientific
> > > > formatting of float and double. For formatting long double with an
> > > > explicit precision argument we use a printf fallback.  Hexadecimal
> > > > formatting for float, double and long double is implemented from
> > > > scratch.
> > > > 
> > > > The supported long double binary formats are float64 (same as double),
> > > > float80 (x86 extended precision), float128 and ibm128.
> > > > 
> > > > Much of the complexity of the implementation is in computing the exact
> > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > checking).  In some cases it's hard to compute the output length before
> > > > the fact, so in these cases we instead compute an upper bound on the
> > > > output length and use a sufficiently-sized intermediate buffer (if the
> > > > output range is smaller than the upper bound).
> > > > 
> > > > Another source of complexity is in the general-with-precision formatting
> > > > mode, where we need to do zero-trimming of the string returned by Ryu, and
> > > > where we also take care to avoid having to format the string a second
> > > > time when the general formatting mode resolves to fixed.
> > > > 
> > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > 
> > > > libstdc++-v3/ChangeLog:
> > > > 
> > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > 	* configure: Regenerate.
> > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > 	overloads for float, double and long double.
> > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > 
> > > Here is v2 of this patch, which fixes a build failure on i386 due to
> > > __int128 being unavailable, by refactoring the long double binary format
> > > selection to avoid referring to __int128 when it doesn't exist.  The
> > > patch also makes the hex formatting for 80-bit long double use uint64_t
> > > instead of __int128 since the mantissa has exactly 64 bits in this case.
> > 
> > Here's v3 which just makes some minor stylistic adjustments, and most
> > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > since we just want to enable __glibcxx_assert and not all of debug mode.
> 
> Here's v4, which should now correctly support using <charconv> with
> -mlong-double-64 on targets with a large default long double type.
> This is done by defining the long double to_chars overloads as inline
> wrappers around the double overloads within <charconv> whenever
> __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.

> 
> -- >8 --
> 
> Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
>  implementation
> 
> This implements the floating-point std::to_chars overloads for float,
> double and long double.  We use the Ryu library to compute the shortest
> round-trippable fixed and scientific forms of a number for float, double
> and long double.  We also use Ryu for performing explicit-precision
> fixed and scientific formatting of float and double. For
> explicit-precision formatting of long double we fall back to using
> printf.  Hexadecimal formatting for float, double and long double is
> implemented from scratch.
> 
> The supported long double binary formats are binary64, binary80 (x86
> 80-bit extended precision), binary128 and ibm128.
> 
> Much of the complexity of the implementation is in computing the exact
> output length before handing it off to Ryu (which doesn't do bounds
> checking).  In some cases it's hard to compute the output length
> beforehand, so in these cases we instead compute an upper bound on the
> output length and use a sufficiently-sized intermediate buffer if
> necessary.
> 
> Another source of complexity is in the general-with-precision formatting
> mode, where we need to do zero-trimming of the string returned by Ryu,
> and where we also take care to avoid having to format the string a
> second time when the general formatting mode resolves to fixed.
> 
> This implementation is non-conforming in a couple of ways:
> 
> 1. For the shortest hexadecimal formatting, we currently follow the
>    Microsoft implementation's approach of being consistent with the
>    output of printf's '%a' specifier at the expense of sometimes not
>    printing the shortest representation.  For example, the shortest hex
>    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
>    latter, as does printf.
> 
> 2. The Ryu routines for doing shortest formatting on types larger than
>    binary64 use the __int128 type, and some targets (e.g. i386) have a
>    large long double type but lack __int128.  For such targets we make
>    the long double to_chars overloads go through the double overloads,
>    which means we lose precision in the output.  (The mantissa of long
>    double is 64 bits on i386, so I think we could potentially fix this
>    by writing a specialized version of the generic Ryu formatting
>    routine which works with uint64_t instead of __int128.)
> 
> 3. The __ibm128 shortest formatting routines don't guarantee
>    round-trippability if the difference between the high- and low-order
>    exponent is too large.  This is because we treat the type as if it
>    has a contiguous 105-bit mantissa by merging the high- and low-order
>    mantissas, so we potentially lose precision from the low-order part.
>    Although this precision-dropping behavior is non-conforming, it seems
>    consistent with how printf formats __ibm128.
> 
> libstdc++-v3/ChangeLog:
> 
> 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> 	* config/abi/pre/gnu.ver: Add new exports.
> 	* configure: Regenerate.
> 	* include/std/charconv (to_chars): Declare the floating-point
> 	overloads for float, double and long double.
> 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> 	* src/c++17/Makefile.in: Regenerate.
> 	* src/c++17/floating_to_chars.cc: New file.
> 	* testsuite/20_util/to_chars/long_double.cc: New test.
> 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> ---
>  libstdc++-v3/acinclude.m4                     |    2 +-
>  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
>  libstdc++-v3/configure                        |    2 +-
>  libstdc++-v3/include/std/charconv             |   43 +
>  libstdc++-v3/src/c++17/Makefile.am            |    1 +
>  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
>  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
>  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
>  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
>  9 files changed, 1774 insertions(+), 5 deletions(-)
>  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
>  create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> 
> diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> index ee5e0336f2c..e3926e1c9c2 100644
> --- a/libstdc++-v3/acinclude.m4
> +++ b/libstdc++-v3/acinclude.m4
> @@ -3846,7 +3846,7 @@ changequote([,])dnl
>  fi
>  
>  # For libtool versioning info, format is CURRENT:REVISION:AGE
> -libtool_VERSION=6:28:0
> +libtool_VERSION=6:29:0
>  
>  # Everything parsed; figure out what files and settings to use.
>  case $enable_symvers in
> diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
> index edf4485e607..9a1bcfd25d1 100644
> --- a/libstdc++-v3/config/abi/pre/gnu.ver
> +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
>  
>  } GLIBCXX_3.4.27;
>  
> +GLIBCXX_3.4.29 {
> +    # to_chars(char*, char*, [float|double|long double])
> +    _ZSt8to_charsPcS_[fdeg];
> +
> +    # to_chars(char*, char*, [float|double|long double], chars_format)
> +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> +
> +    # to_chars(char*, char*, [float|double|long double], chars_format, int)
> +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> +
> +} GLIBCXX_3.4.28;
> +
>  # Symbols in the support library (libsupc++) have their own tag.
>  CXXABI_1.3 {
>  
> diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> index dd54bd406a9..73f771e7335 100755
> --- a/libstdc++-v3/configure
> +++ b/libstdc++-v3/configure
> @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
>  fi
>  
>  # For libtool versioning info, format is CURRENT:REVISION:AGE
> -libtool_VERSION=6:28:0
> +libtool_VERSION=6:29:0
>  
>  # Everything parsed; figure out what files and settings to use.
>  case $enable_symvers in
> diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
> index cc7dd0e3758..bd59924f7e7 100644
> --- a/libstdc++-v3/include/std/charconv
> +++ b/libstdc++-v3/include/std/charconv
> @@ -688,6 +688,49 @@ namespace __detail
>    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
>    { return __lhs = __lhs ^ __rhs; }
>  
> +  // Floating-point std::to_chars
> +
> +  // Overloads for float.
> +  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, float __value,
> +			   chars_format __fmt) noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, float __value,
> +			   chars_format __fmt, int __precision) noexcept;
> +
> +  // Overloads for double.
> +  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, double __value,
> +			   chars_format __fmt) noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, double __value,
> +			   chars_format __fmt, int __precision) noexcept;
> +
> +  // Overloads for long double.
> +  to_chars_result to_chars(char* __first, char* __last, long double __value)
> +    noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, long double __value,
> +			   chars_format __fmt) noexcept;
> +  to_chars_result to_chars(char* __first, char* __last, long double __value,
> +			   chars_format __fmt, int __precision) noexcept;
> +
> +  // If long double has the same binary format as double, then we just define
> +  // the long double overloads as wrappers around the corresponding double
> +  // overloads.
> +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> +  inline to_chars_result
> +  to_chars(char* __first, char* __last, long double __value) noexcept
> +  { return to_chars(__first, __last, double(__value)); }
> +
> +  inline to_chars_result
> +  to_chars(char* __first, char* __last, long double __value,
> +	   chars_format __fmt) noexcept
> +  { return to_chars(__first, __last, double(__value), __fmt); }
> +
> +  inline to_chars_result
> +  to_chars(char* __first, char* __last, long double __value,
> +	   chars_format __fmt, int __precision) noexcept
> +  { return to_chars(__first, __last, double(__value), __fmt, __precision); }
> +#endif

Hmm, I think this approach for supporting -mlong-double-64 might
introduce an ODR violation because each long double to_chars overload
could potentially have two different definitions available in a program,
one out-of-line in floating_to_chars.cc (compiled without
-mlong-double-64) and another inline in <charconv> (compiled with
-mlong-double-64)..

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Jonathan Wakely]

On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
>On Fri, 17 Jul 2020, Patrick Palka wrote:
>
>> On Fri, 17 Jul 2020, Patrick Palka wrote:
>>
>> > On Wed, 15 Jul 2020, Patrick Palka wrote:
>> >
>> > > On Tue, 14 Jul 2020, Patrick Palka wrote:
>> > >
>> > > > This implements the floating-point std::to_chars overloads for float,
>> > > > double and long double.  We use the Ryu library to compute the shortest
>> > > > round-trippable fixed and scientific forms of a number for float, double
>> > > > and long double.  We also use Ryu for performing fixed and scientific
>> > > > formatting of float and double. For formatting long double with an
>> > > > explicit precision argument we use a printf fallback.  Hexadecimal
>> > > > formatting for float, double and long double is implemented from
>> > > > scratch.
>> > > >
>> > > > The supported long double binary formats are float64 (same as double),
>> > > > float80 (x86 extended precision), float128 and ibm128.
>> > > >
>> > > > Much of the complexity of the implementation is in computing the exact
>> > > > output length before handing it off to Ryu (which doesn't do bounds
>> > > > checking).  In some cases it's hard to compute the output length before
>> > > > the fact, so in these cases we instead compute an upper bound on the
>> > > > output length and use a sufficiently-sized intermediate buffer (if the
>> > > > output range is smaller than the upper bound).
>> > > >
>> > > > Another source of complexity is in the general-with-precision formatting
>> > > > mode, where we need to do zero-trimming of the string returned by Ryu, and
>> > > > where we also take care to avoid having to format the string a second
>> > > > time when the general formatting mode resolves to fixed.
>> > > >
>> > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
>> > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
>> > > >
>> > > > libstdc++-v3/ChangeLog:
>> > > >
>> > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> > > > 	* config/abi/pre/gnu.ver: Add new exports.
>> > > > 	* configure: Regenerate.
>> > > > 	* include/std/charconv (to_chars): Declare the floating-point
>> > > > 	overloads for float, double and long double.
>> > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> > > > 	* src/c++17/Makefile.in: Regenerate.
>> > > > 	* src/c++17/floating_to_chars.cc: New file.
>> > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> > >
>> > > Here is v2 of this patch, which fixes a build failure on i386 due to
>> > > __int128 being unavailable, by refactoring the long double binary format
>> > > selection to avoid referring to __int128 when it doesn't exist.  The
>> > > patch also makes the hex formatting for 80-bit long double use uint64_t
>> > > instead of __int128 since the mantissa has exactly 64 bits in this case.
>> >
>> > Here's v3 which just makes some minor stylistic adjustments, and most
>> > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
>> > since we just want to enable __glibcxx_assert and not all of debug mode.
>>
>> Here's v4, which should now correctly support using <charconv> with
>> -mlong-double-64 on targets with a large default long double type.
>> This is done by defining the long double to_chars overloads as inline
>> wrappers around the double overloads within <charconv> whenever
>> __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
>
>>
>> -- >8 --
>>
>> Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
>>  implementation
>>
>> This implements the floating-point std::to_chars overloads for float,
>> double and long double.  We use the Ryu library to compute the shortest
>> round-trippable fixed and scientific forms of a number for float, double
>> and long double.  We also use Ryu for performing explicit-precision
>> fixed and scientific formatting of float and double. For
>> explicit-precision formatting of long double we fall back to using
>> printf.  Hexadecimal formatting for float, double and long double is
>> implemented from scratch.
>>
>> The supported long double binary formats are binary64, binary80 (x86
>> 80-bit extended precision), binary128 and ibm128.
>>
>> Much of the complexity of the implementation is in computing the exact
>> output length before handing it off to Ryu (which doesn't do bounds
>> checking).  In some cases it's hard to compute the output length
>> beforehand, so in these cases we instead compute an upper bound on the
>> output length and use a sufficiently-sized intermediate buffer if
>> necessary.
>>
>> Another source of complexity is in the general-with-precision formatting
>> mode, where we need to do zero-trimming of the string returned by Ryu,
>> and where we also take care to avoid having to format the string a
>> second time when the general formatting mode resolves to fixed.
>>
>> This implementation is non-conforming in a couple of ways:
>>
>> 1. For the shortest hexadecimal formatting, we currently follow the
>>    Microsoft implementation's approach of being consistent with the
>>    output of printf's '%a' specifier at the expense of sometimes not
>>    printing the shortest representation.  For example, the shortest hex
>>    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
>>    latter, as does printf.
>>
>> 2. The Ryu routines for doing shortest formatting on types larger than
>>    binary64 use the __int128 type, and some targets (e.g. i386) have a
>>    large long double type but lack __int128.  For such targets we make
>>    the long double to_chars overloads go through the double overloads,
>>    which means we lose precision in the output.  (The mantissa of long
>>    double is 64 bits on i386, so I think we could potentially fix this
>>    by writing a specialized version of the generic Ryu formatting
>>    routine which works with uint64_t instead of __int128.)
>>
>> 3. The __ibm128 shortest formatting routines don't guarantee
>>    round-trippability if the difference between the high- and low-order
>>    exponent is too large.  This is because we treat the type as if it
>>    has a contiguous 105-bit mantissa by merging the high- and low-order
>>    mantissas, so we potentially lose precision from the low-order part.
>>    Although this precision-dropping behavior is non-conforming, it seems
>>    consistent with how printf formats __ibm128.
>>
>> libstdc++-v3/ChangeLog:
>>
>> 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> 	* config/abi/pre/gnu.ver: Add new exports.
>> 	* configure: Regenerate.
>> 	* include/std/charconv (to_chars): Declare the floating-point
>> 	overloads for float, double and long double.
>> 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> 	* src/c++17/Makefile.in: Regenerate.
>> 	* src/c++17/floating_to_chars.cc: New file.
>> 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> ---
>>  libstdc++-v3/acinclude.m4                     |    2 +-
>>  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
>>  libstdc++-v3/configure                        |    2 +-
>>  libstdc++-v3/include/std/charconv             |   43 +
>>  libstdc++-v3/src/c++17/Makefile.am            |    1 +
>>  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
>>  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
>>  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
>>  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
>>  9 files changed, 1774 insertions(+), 5 deletions(-)
>>  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
>>  create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
>>
>> diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
>> index ee5e0336f2c..e3926e1c9c2 100644
>> --- a/libstdc++-v3/acinclude.m4
>> +++ b/libstdc++-v3/acinclude.m4
>> @@ -3846,7 +3846,7 @@ changequote([,])dnl
>>  fi
>>
>>  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> -libtool_VERSION=6:28:0
>> +libtool_VERSION=6:29:0
>>
>>  # Everything parsed; figure out what files and settings to use.
>>  case $enable_symvers in
>> diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
>> index edf4485e607..9a1bcfd25d1 100644
>> --- a/libstdc++-v3/config/abi/pre/gnu.ver
>> +++ b/libstdc++-v3/config/abi/pre/gnu.ver
>> @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
>>
>>  } GLIBCXX_3.4.27;
>>
>> +GLIBCXX_3.4.29 {
>> +    # to_chars(char*, char*, [float|double|long double])
>> +    _ZSt8to_charsPcS_[fdeg];
>> +
>> +    # to_chars(char*, char*, [float|double|long double], chars_format)
>> +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
>> +
>> +    # to_chars(char*, char*, [float|double|long double], chars_format, int)
>> +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
>> +
>> +} GLIBCXX_3.4.28;
>> +
>>  # Symbols in the support library (libsupc++) have their own tag.
>>  CXXABI_1.3 {
>>
>> diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
>> index dd54bd406a9..73f771e7335 100755
>> --- a/libstdc++-v3/configure
>> +++ b/libstdc++-v3/configure
>> @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
>>  fi
>>
>>  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> -libtool_VERSION=6:28:0
>> +libtool_VERSION=6:29:0
>>
>>  # Everything parsed; figure out what files and settings to use.
>>  case $enable_symvers in
>> diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
>> index cc7dd0e3758..bd59924f7e7 100644
>> --- a/libstdc++-v3/include/std/charconv
>> +++ b/libstdc++-v3/include/std/charconv
>> @@ -688,6 +688,49 @@ namespace __detail
>>    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
>>    { return __lhs = __lhs ^ __rhs; }
>>
>> +  // Floating-point std::to_chars
>> +
>> +  // Overloads for float.
>> +  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, float __value,
>> +			   chars_format __fmt) noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, float __value,
>> +			   chars_format __fmt, int __precision) noexcept;
>> +
>> +  // Overloads for double.
>> +  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, double __value,
>> +			   chars_format __fmt) noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, double __value,
>> +			   chars_format __fmt, int __precision) noexcept;
>> +
>> +  // Overloads for long double.
>> +  to_chars_result to_chars(char* __first, char* __last, long double __value)
>> +    noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, long double __value,
>> +			   chars_format __fmt) noexcept;
>> +  to_chars_result to_chars(char* __first, char* __last, long double __value,
>> +			   chars_format __fmt, int __precision) noexcept;
>> +
>> +  // If long double has the same binary format as double, then we just define
>> +  // the long double overloads as wrappers around the corresponding double
>> +  // overloads.
>> +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
>> +  inline to_chars_result
>> +  to_chars(char* __first, char* __last, long double __value) noexcept
>> +  { return to_chars(__first, __last, double(__value)); }
>> +
>> +  inline to_chars_result
>> +  to_chars(char* __first, char* __last, long double __value,
>> +	   chars_format __fmt) noexcept
>> +  { return to_chars(__first, __last, double(__value), __fmt); }
>> +
>> +  inline to_chars_result
>> +  to_chars(char* __first, char* __last, long double __value,
>> +	   chars_format __fmt, int __precision) noexcept
>> +  { return to_chars(__first, __last, double(__value), __fmt, __precision); }
>> +#endif
>
>Hmm, I think this approach for supporting -mlong-double-64 might
>introduce an ODR violation because each long double to_chars overload
>could potentially have two different definitions available in a program,
>one out-of-line in floating_to_chars.cc (compiled without
>-mlong-double-64) and another inline in <charconv> (compiled with
>-mlong-double-64)..

But they have different mangled names, so there's no ODR violation.
The 64-bit long double is mangled as 'e' and the 128-bit long double
is mangled as __float128. You *will* get an ODR violation on targets
where there's no -mlong-double-64 switch, where double and long double
are always the same representation.

What I'm doing for std::from_chars is adding this in the new
src/c++17/floating_from_chars.cc file:

#ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
#pragma GCC diagnostic ignored "-Wattribute-alias"
extern "C" from_chars_result _ZSt10from_charsPKcS0_ReSt12chars_format(double)
__attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
#endif

This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
(i.e. from_chars for 64-bit long double) as an alias of
_ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
double). 

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Mon, 20 Jul 2020, Jonathan Wakely wrote:

> On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > 
> > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > 
> > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > >
> > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > >
> > > > > > This implements the floating-point std::to_chars overloads for
> > > float,
> > > > > > double and long double.  We use the Ryu library to compute the
> > > shortest
> > > > > > round-trippable fixed and scientific forms of a number for float,
> > > double
> > > > > > and long double.  We also use Ryu for performing fixed and
> > > scientific
> > > > > > formatting of float and double. For formatting long double with an
> > > > > > explicit precision argument we use a printf fallback.  Hexadecimal
> > > > > > formatting for float, double and long double is implemented from
> > > > > > scratch.
> > > > > >
> > > > > > The supported long double binary formats are float64 (same as
> > > double),
> > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > > >
> > > > > > Much of the complexity of the implementation is in computing the
> > > exact
> > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > > > checking).  In some cases it's hard to compute the output length
> > > before
> > > > > > the fact, so in these cases we instead compute an upper bound on the
> > > > > > output length and use a sufficiently-sized intermediate buffer (if
> > > the
> > > > > > output range is smaller than the upper bound).
> > > > > >
> > > > > > Another source of complexity is in the general-with-precision
> > > formatting
> > > > > > mode, where we need to do zero-trimming of the string returned by
> > > Ryu, and
> > > > > > where we also take care to avoid having to format the string a
> > > second
> > > > > > time when the general formatting mode resolves to fixed.
> > > > > >
> > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > > >
> > > > > > libstdc++-v3/ChangeLog:
> > > > > >
> > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > 	* configure: Regenerate.
> > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > 	overloads for float, double and long double.
> > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > >
> > > > > Here is v2 of this patch, which fixes a build failure on i386 due to
> > > > > __int128 being unavailable, by refactoring the long double binary
> > > format
> > > > > selection to avoid referring to __int128 when it doesn't exist.  The
> > > > > patch also makes the hex formatting for 80-bit long double use
> > > uint64_t
> > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > case.
> > > >
> > > > Here's v3 which just makes some minor stylistic adjustments, and most
> > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > since we just want to enable __glibcxx_assert and not all of debug mode.
> > > 
> > > Here's v4, which should now correctly support using <charconv> with
> > > -mlong-double-64 on targets with a large default long double type.
> > > This is done by defining the long double to_chars overloads as inline
> > > wrappers around the double overloads within <charconv> whenever
> > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > 
> > > 
> > > -- >8 --
> > > 
> > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > >  implementation
> > > 
> > > This implements the floating-point std::to_chars overloads for float,
> > > double and long double.  We use the Ryu library to compute the shortest
> > > round-trippable fixed and scientific forms of a number for float, double
> > > and long double.  We also use Ryu for performing explicit-precision
> > > fixed and scientific formatting of float and double. For
> > > explicit-precision formatting of long double we fall back to using
> > > printf.  Hexadecimal formatting for float, double and long double is
> > > implemented from scratch.
> > > 
> > > The supported long double binary formats are binary64, binary80 (x86
> > > 80-bit extended precision), binary128 and ibm128.
> > > 
> > > Much of the complexity of the implementation is in computing the exact
> > > output length before handing it off to Ryu (which doesn't do bounds
> > > checking).  In some cases it's hard to compute the output length
> > > beforehand, so in these cases we instead compute an upper bound on the
> > > output length and use a sufficiently-sized intermediate buffer if
> > > necessary.
> > > 
> > > Another source of complexity is in the general-with-precision formatting
> > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > and where we also take care to avoid having to format the string a
> > > second time when the general formatting mode resolves to fixed.
> > > 
> > > This implementation is non-conforming in a couple of ways:
> > > 
> > > 1. For the shortest hexadecimal formatting, we currently follow the
> > >    Microsoft implementation's approach of being consistent with the
> > >    output of printf's '%a' specifier at the expense of sometimes not
> > >    printing the shortest representation.  For example, the shortest hex
> > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > >    latter, as does printf.
> > > 
> > > 2. The Ryu routines for doing shortest formatting on types larger than
> > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > >    large long double type but lack __int128.  For such targets we make
> > >    the long double to_chars overloads go through the double overloads,
> > >    which means we lose precision in the output.  (The mantissa of long
> > >    double is 64 bits on i386, so I think we could potentially fix this
> > >    by writing a specialized version of the generic Ryu formatting
> > >    routine which works with uint64_t instead of __int128.)
> > > 
> > > 3. The __ibm128 shortest formatting routines don't guarantee
> > >    round-trippability if the difference between the high- and low-order
> > >    exponent is too large.  This is because we treat the type as if it
> > >    has a contiguous 105-bit mantissa by merging the high- and low-order
> > >    mantissas, so we potentially lose precision from the low-order part.
> > >    Although this precision-dropping behavior is non-conforming, it seems
> > >    consistent with how printf formats __ibm128.
> > > 
> > > libstdc++-v3/ChangeLog:
> > > 
> > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > 	* configure: Regenerate.
> > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > 	overloads for float, double and long double.
> > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > 	* src/c++17/Makefile.in: Regenerate.
> > > 	* src/c++17/floating_to_chars.cc: New file.
> > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > ---
> > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > >  libstdc++-v3/configure                        |    2 +-
> > >  libstdc++-v3/include/std/charconv             |   43 +
> > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
> > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > >  create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > 
> > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > index ee5e0336f2c..e3926e1c9c2 100644
> > > --- a/libstdc++-v3/acinclude.m4
> > > +++ b/libstdc++-v3/acinclude.m4
> > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > >  fi
> > > 
> > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > -libtool_VERSION=6:28:0
> > > +libtool_VERSION=6:29:0
> > > 
> > >  # Everything parsed; figure out what files and settings to use.
> > >  case $enable_symvers in
> > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > index edf4485e607..9a1bcfd25d1 100644
> > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > 
> > >  } GLIBCXX_3.4.27;
> > > 
> > > +GLIBCXX_3.4.29 {
> > > +    # to_chars(char*, char*, [float|double|long double])
> > > +    _ZSt8to_charsPcS_[fdeg];
> > > +
> > > +    # to_chars(char*, char*, [float|double|long double], chars_format)
> > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > +
> > > +    # to_chars(char*, char*, [float|double|long double], chars_format,
> > > int)
> > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > +
> > > +} GLIBCXX_3.4.28;
> > > +
> > >  # Symbols in the support library (libsupc++) have their own tag.
> > >  CXXABI_1.3 {
> > > 
> > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > index dd54bd406a9..73f771e7335 100755
> > > --- a/libstdc++-v3/configure
> > > +++ b/libstdc++-v3/configure
> > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning
> > > will be disabled." >&2;}
> > >  fi
> > > 
> > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > -libtool_VERSION=6:28:0
> > > +libtool_VERSION=6:29:0
> > > 
> > >  # Everything parsed; figure out what files and settings to use.
> > >  case $enable_symvers in
> > > diff --git a/libstdc++-v3/include/std/charconv
> > > b/libstdc++-v3/include/std/charconv
> > > index cc7dd0e3758..bd59924f7e7 100644
> > > --- a/libstdc++-v3/include/std/charconv
> > > +++ b/libstdc++-v3/include/std/charconv
> > > @@ -688,6 +688,49 @@ namespace __detail
> > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > >    { return __lhs = __lhs ^ __rhs; }
> > > 
> > > +  // Floating-point std::to_chars
> > > +
> > > +  // Overloads for float.
> > > +  to_chars_result to_chars(char* __first, char* __last, float __value)
> > > noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, float __value,
> > > +			   chars_format __fmt) noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, float __value,
> > > +			   chars_format __fmt, int __precision) noexcept;
> > > +
> > > +  // Overloads for double.
> > > +  to_chars_result to_chars(char* __first, char* __last, double __value)
> > > noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, double __value,
> > > +			   chars_format __fmt) noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, double __value,
> > > +			   chars_format __fmt, int __precision) noexcept;
> > > +
> > > +  // Overloads for long double.
> > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > __value)
> > > +    noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > __value,
> > > +			   chars_format __fmt) noexcept;
> > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > __value,
> > > +			   chars_format __fmt, int __precision) noexcept;
> > > +
> > > +  // If long double has the same binary format as double, then we just
> > > define
> > > +  // the long double overloads as wrappers around the corresponding
> > > double
> > > +  // overloads.
> > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > +  inline to_chars_result
> > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > +  { return to_chars(__first, __last, double(__value)); }
> > > +
> > > +  inline to_chars_result
> > > +  to_chars(char* __first, char* __last, long double __value,
> > > +	   chars_format __fmt) noexcept
> > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > +
> > > +  inline to_chars_result
> > > +  to_chars(char* __first, char* __last, long double __value,
> > > +	   chars_format __fmt, int __precision) noexcept
> > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > __precision); }
> > > +#endif
> > 
> > Hmm, I think this approach for supporting -mlong-double-64 might
> > introduce an ODR violation because each long double to_chars overload
> > could potentially have two different definitions available in a program,
> > one out-of-line in floating_to_chars.cc (compiled without
> > -mlong-double-64) and another inline in <charconv> (compiled with
> > -mlong-double-64)..
> 
> But they have different mangled names, so there's no ODR violation.
> The 64-bit long double is mangled as 'e' and the 128-bit long double
> is mangled as __float128. You *will* get an ODR violation on targets
> where there's no -mlong-double-64 switch, where double and long double
> are always the same representation.
> 
> What I'm doing for std::from_chars is adding this in the new
> src/c++17/floating_from_chars.cc file:
> 
> #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> #pragma GCC diagnostic ignored "-Wattribute-alias"
> extern "C" from_chars_result _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> #endif
> 
> This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> (i.e. from_chars for 64-bit long double) as an alias of
> _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> double). 

Aha, that makes sense.  I'll follow suit for std::to_chars.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Jonathan Wakely]

On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
>On Mon, 20 Jul 2020, Jonathan Wakely wrote:
>
>> On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
>> > On Fri, 17 Jul 2020, Patrick Palka wrote:
>> >
>> > > On Fri, 17 Jul 2020, Patrick Palka wrote:
>> > >
>> > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
>> > > >
>> > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
>> > > > >
>> > > > > > This implements the floating-point std::to_chars overloads for
>> > > float,
>> > > > > > double and long double.  We use the Ryu library to compute the
>> > > shortest
>> > > > > > round-trippable fixed and scientific forms of a number for float,
>> > > double
>> > > > > > and long double.  We also use Ryu for performing fixed and
>> > > scientific
>> > > > > > formatting of float and double. For formatting long double with an
>> > > > > > explicit precision argument we use a printf fallback.  Hexadecimal
>> > > > > > formatting for float, double and long double is implemented from
>> > > > > > scratch.
>> > > > > >
>> > > > > > The supported long double binary formats are float64 (same as
>> > > double),
>> > > > > > float80 (x86 extended precision), float128 and ibm128.
>> > > > > >
>> > > > > > Much of the complexity of the implementation is in computing the
>> > > exact
>> > > > > > output length before handing it off to Ryu (which doesn't do bounds
>> > > > > > checking).  In some cases it's hard to compute the output length
>> > > before
>> > > > > > the fact, so in these cases we instead compute an upper bound on the
>> > > > > > output length and use a sufficiently-sized intermediate buffer (if
>> > > the
>> > > > > > output range is smaller than the upper bound).
>> > > > > >
>> > > > > > Another source of complexity is in the general-with-precision
>> > > formatting
>> > > > > > mode, where we need to do zero-trimming of the string returned by
>> > > Ryu, and
>> > > > > > where we also take care to avoid having to format the string a
>> > > second
>> > > > > > time when the general formatting mode resolves to fixed.
>> > > > > >
>> > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
>> > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
>> > > > > >
>> > > > > > libstdc++-v3/ChangeLog:
>> > > > > >
>> > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
>> > > > > > 	* configure: Regenerate.
>> > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
>> > > > > > 	overloads for float, double and long double.
>> > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> > > > > > 	* src/c++17/Makefile.in: Regenerate.
>> > > > > > 	* src/c++17/floating_to_chars.cc: New file.
>> > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> > > > >
>> > > > > Here is v2 of this patch, which fixes a build failure on i386 due to
>> > > > > __int128 being unavailable, by refactoring the long double binary
>> > > format
>> > > > > selection to avoid referring to __int128 when it doesn't exist.  The
>> > > > > patch also makes the hex formatting for 80-bit long double use
>> > > uint64_t
>> > > > > instead of __int128 since the mantissa has exactly 64 bits in this
>> > > case.
>> > > >
>> > > > Here's v3 which just makes some minor stylistic adjustments, and most
>> > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
>> > > > since we just want to enable __glibcxx_assert and not all of debug mode.
>> > >
>> > > Here's v4, which should now correctly support using <charconv> with
>> > > -mlong-double-64 on targets with a large default long double type.
>> > > This is done by defining the long double to_chars overloads as inline
>> > > wrappers around the double overloads within <charconv> whenever
>> > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
>> >
>> > >
>> > > -- >8 --
>> > >
>> > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
>> > >  implementation
>> > >
>> > > This implements the floating-point std::to_chars overloads for float,
>> > > double and long double.  We use the Ryu library to compute the shortest
>> > > round-trippable fixed and scientific forms of a number for float, double
>> > > and long double.  We also use Ryu for performing explicit-precision
>> > > fixed and scientific formatting of float and double. For
>> > > explicit-precision formatting of long double we fall back to using
>> > > printf.  Hexadecimal formatting for float, double and long double is
>> > > implemented from scratch.
>> > >
>> > > The supported long double binary formats are binary64, binary80 (x86
>> > > 80-bit extended precision), binary128 and ibm128.
>> > >
>> > > Much of the complexity of the implementation is in computing the exact
>> > > output length before handing it off to Ryu (which doesn't do bounds
>> > > checking).  In some cases it's hard to compute the output length
>> > > beforehand, so in these cases we instead compute an upper bound on the
>> > > output length and use a sufficiently-sized intermediate buffer if
>> > > necessary.
>> > >
>> > > Another source of complexity is in the general-with-precision formatting
>> > > mode, where we need to do zero-trimming of the string returned by Ryu,
>> > > and where we also take care to avoid having to format the string a
>> > > second time when the general formatting mode resolves to fixed.
>> > >
>> > > This implementation is non-conforming in a couple of ways:
>> > >
>> > > 1. For the shortest hexadecimal formatting, we currently follow the
>> > >    Microsoft implementation's approach of being consistent with the
>> > >    output of printf's '%a' specifier at the expense of sometimes not
>> > >    printing the shortest representation.  For example, the shortest hex
>> > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
>> > >    latter, as does printf.
>> > >
>> > > 2. The Ryu routines for doing shortest formatting on types larger than
>> > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
>> > >    large long double type but lack __int128.  For such targets we make
>> > >    the long double to_chars overloads go through the double overloads,
>> > >    which means we lose precision in the output.  (The mantissa of long
>> > >    double is 64 bits on i386, so I think we could potentially fix this
>> > >    by writing a specialized version of the generic Ryu formatting
>> > >    routine which works with uint64_t instead of __int128.)
>> > >
>> > > 3. The __ibm128 shortest formatting routines don't guarantee
>> > >    round-trippability if the difference between the high- and low-order
>> > >    exponent is too large.  This is because we treat the type as if it
>> > >    has a contiguous 105-bit mantissa by merging the high- and low-order
>> > >    mantissas, so we potentially lose precision from the low-order part.
>> > >    Although this precision-dropping behavior is non-conforming, it seems
>> > >    consistent with how printf formats __ibm128.
>> > >
>> > > libstdc++-v3/ChangeLog:
>> > >
>> > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> > > 	* config/abi/pre/gnu.ver: Add new exports.
>> > > 	* configure: Regenerate.
>> > > 	* include/std/charconv (to_chars): Declare the floating-point
>> > > 	overloads for float, double and long double.
>> > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> > > 	* src/c++17/Makefile.in: Regenerate.
>> > > 	* src/c++17/floating_to_chars.cc: New file.
>> > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> > > ---
>> > >  libstdc++-v3/acinclude.m4                     |    2 +-
>> > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
>> > >  libstdc++-v3/configure                        |    2 +-
>> > >  libstdc++-v3/include/std/charconv             |   43 +
>> > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
>> > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
>> > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514 +++++++++++++++++
>> > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
>> > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
>> > >  9 files changed, 1774 insertions(+), 5 deletions(-)
>> > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
>> > >  create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
>> > >
>> > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
>> > > index ee5e0336f2c..e3926e1c9c2 100644
>> > > --- a/libstdc++-v3/acinclude.m4
>> > > +++ b/libstdc++-v3/acinclude.m4
>> > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
>> > >  fi
>> > >
>> > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> > > -libtool_VERSION=6:28:0
>> > > +libtool_VERSION=6:29:0
>> > >
>> > >  # Everything parsed; figure out what files and settings to use.
>> > >  case $enable_symvers in
>> > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
>> > > b/libstdc++-v3/config/abi/pre/gnu.ver
>> > > index edf4485e607..9a1bcfd25d1 100644
>> > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
>> > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
>> > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
>> > >
>> > >  } GLIBCXX_3.4.27;
>> > >
>> > > +GLIBCXX_3.4.29 {
>> > > +    # to_chars(char*, char*, [float|double|long double])
>> > > +    _ZSt8to_charsPcS_[fdeg];
>> > > +
>> > > +    # to_chars(char*, char*, [float|double|long double], chars_format)
>> > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
>> > > +
>> > > +    # to_chars(char*, char*, [float|double|long double], chars_format,
>> > > int)
>> > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
>> > > +
>> > > +} GLIBCXX_3.4.28;
>> > > +
>> > >  # Symbols in the support library (libsupc++) have their own tag.
>> > >  CXXABI_1.3 {
>> > >
>> > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
>> > > index dd54bd406a9..73f771e7335 100755
>> > > --- a/libstdc++-v3/configure
>> > > +++ b/libstdc++-v3/configure
>> > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning
>> > > will be disabled." >&2;}
>> > >  fi
>> > >
>> > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> > > -libtool_VERSION=6:28:0
>> > > +libtool_VERSION=6:29:0
>> > >
>> > >  # Everything parsed; figure out what files and settings to use.
>> > >  case $enable_symvers in
>> > > diff --git a/libstdc++-v3/include/std/charconv
>> > > b/libstdc++-v3/include/std/charconv
>> > > index cc7dd0e3758..bd59924f7e7 100644
>> > > --- a/libstdc++-v3/include/std/charconv
>> > > +++ b/libstdc++-v3/include/std/charconv
>> > > @@ -688,6 +688,49 @@ namespace __detail
>> > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
>> > >    { return __lhs = __lhs ^ __rhs; }
>> > >
>> > > +  // Floating-point std::to_chars
>> > > +
>> > > +  // Overloads for float.
>> > > +  to_chars_result to_chars(char* __first, char* __last, float __value)
>> > > noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, float __value,
>> > > +			   chars_format __fmt) noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, float __value,
>> > > +			   chars_format __fmt, int __precision) noexcept;
>> > > +
>> > > +  // Overloads for double.
>> > > +  to_chars_result to_chars(char* __first, char* __last, double __value)
>> > > noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, double __value,
>> > > +			   chars_format __fmt) noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, double __value,
>> > > +			   chars_format __fmt, int __precision) noexcept;
>> > > +
>> > > +  // Overloads for long double.
>> > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > __value)
>> > > +    noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > __value,
>> > > +			   chars_format __fmt) noexcept;
>> > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > __value,
>> > > +			   chars_format __fmt, int __precision) noexcept;
>> > > +
>> > > +  // If long double has the same binary format as double, then we just
>> > > define
>> > > +  // the long double overloads as wrappers around the corresponding
>> > > double
>> > > +  // overloads.
>> > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
>> > > +  inline to_chars_result
>> > > +  to_chars(char* __first, char* __last, long double __value) noexcept
>> > > +  { return to_chars(__first, __last, double(__value)); }
>> > > +
>> > > +  inline to_chars_result
>> > > +  to_chars(char* __first, char* __last, long double __value,
>> > > +	   chars_format __fmt) noexcept
>> > > +  { return to_chars(__first, __last, double(__value), __fmt); }
>> > > +
>> > > +  inline to_chars_result
>> > > +  to_chars(char* __first, char* __last, long double __value,
>> > > +	   chars_format __fmt, int __precision) noexcept
>> > > +  { return to_chars(__first, __last, double(__value), __fmt,
>> > > __precision); }
>> > > +#endif
>> >
>> > Hmm, I think this approach for supporting -mlong-double-64 might
>> > introduce an ODR violation because each long double to_chars overload
>> > could potentially have two different definitions available in a program,
>> > one out-of-line in floating_to_chars.cc (compiled without
>> > -mlong-double-64) and another inline in <charconv> (compiled with
>> > -mlong-double-64)..
>>
>> But they have different mangled names, so there's no ODR violation.
>> The 64-bit long double is mangled as 'e' and the 128-bit long double
>> is mangled as __float128. You *will* get an ODR violation on targets
>> where there's no -mlong-double-64 switch, where double and long double
>> are always the same representation.
>>
>> What I'm doing for std::from_chars is adding this in the new
>> src/c++17/floating_from_chars.cc file:
>>
>> #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
>> #pragma GCC diagnostic ignored "-Wattribute-alias"
>> extern "C" from_chars_result _ZSt10from_charsPKcS0_ReSt12chars_format(double)
>> __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
>> #endif
>>
>> This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
>> (i.e. from_chars for 64-bit long double) as an alias of
>> _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
>> double).
>
>Aha, that makes sense.  I'll follow suit for std::to_chars.

Actually that should be:

#ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
extern "C" from_chars_result
_ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
					 long double& value,
					 chars_format fmt) noexcept
__attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
#endif

With the right parameter list I don't need to disable the warning.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Mon, 20 Jul 2020, Jonathan Wakely wrote:

> On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > 
> > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > >
> > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > >
> > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > > >
> > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > > > >
> > > > > > > > This implements the floating-point std::to_chars overloads for
> > > > > float,
> > > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > shortest
> > > > > > > > round-trippable fixed and scientific forms of a number for
> > > float,
> > > > > double
> > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > > > scientific
> > > > > > > > formatting of float and double. For formatting long double with
> > > an
> > > > > > > > explicit precision argument we use a printf fallback.
> > > Hexadecimal
> > > > > > > > formatting for float, double and long double is implemented from
> > > > > > > > scratch.
> > > > > > > >
> > > > > > > > The supported long double binary formats are float64 (same as
> > > > > double),
> > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > > > > >
> > > > > > > > Much of the complexity of the implementation is in computing the
> > > > > exact
> > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > bounds
> > > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > before
> > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > the
> > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > (if
> > > > > the
> > > > > > > > output range is smaller than the upper bound).
> > > > > > > >
> > > > > > > > Another source of complexity is in the general-with-precision
> > > > > formatting
> > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > by
> > > > > Ryu, and
> > > > > > > > where we also take care to avoid having to format the string a
> > > > > second
> > > > > > > > time when the general formatting mode resolves to fixed.
> > > > > > > >
> > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > > > > >
> > > > > > > > libstdc++-v3/ChangeLog:
> > > > > > > >
> > > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > > > 	* configure: Regenerate.
> > > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > > > 	overloads for float, double and long double.
> > > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > > >
> > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > to
> > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > > > format
> > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > The
> > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > > > uint64_t
> > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > > > case.
> > > > > >
> > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > most
> > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > mode.
> > > > >
> > > > > Here's v4, which should now correctly support using <charconv> with
> > > > > -mlong-double-64 on targets with a large default long double type.
> > > > > This is done by defining the long double to_chars overloads as inline
> > > > > wrappers around the double overloads within <charconv> whenever
> > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > >
> > > > >
> > > > > -- >8 --
> > > > >
> > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > > >  implementation
> > > > >
> > > > > This implements the floating-point std::to_chars overloads for float,
> > > > > double and long double.  We use the Ryu library to compute the
> > > shortest
> > > > > round-trippable fixed and scientific forms of a number for float,
> > > double
> > > > > and long double.  We also use Ryu for performing explicit-precision
> > > > > fixed and scientific formatting of float and double. For
> > > > > explicit-precision formatting of long double we fall back to using
> > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > > > implemented from scratch.
> > > > >
> > > > > The supported long double binary formats are binary64, binary80 (x86
> > > > > 80-bit extended precision), binary128 and ibm128.
> > > > >
> > > > > Much of the complexity of the implementation is in computing the exact
> > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > > checking).  In some cases it's hard to compute the output length
> > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > > > output length and use a sufficiently-sized intermediate buffer if
> > > > > necessary.
> > > > >
> > > > > Another source of complexity is in the general-with-precision
> > > formatting
> > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > > and where we also take care to avoid having to format the string a
> > > > > second time when the general formatting mode resolves to fixed.
> > > > >
> > > > > This implementation is non-conforming in a couple of ways:
> > > > >
> > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > > >    Microsoft implementation's approach of being consistent with the
> > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > > >    printing the shortest representation.  For example, the shortest
> > > hex
> > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > > >    latter, as does printf.
> > > > >
> > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > > >    large long double type but lack __int128.  For such targets we make
> > > > >    the long double to_chars overloads go through the double overloads,
> > > > >    which means we lose precision in the output.  (The mantissa of long
> > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > > >    by writing a specialized version of the generic Ryu formatting
> > > > >    routine which works with uint64_t instead of __int128.)
> > > > >
> > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > > >    round-trippability if the difference between the high- and
> > > low-order
> > > > >    exponent is too large.  This is because we treat the type as if it
> > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > low-order
> > > > >    mantissas, so we potentially lose precision from the low-order
> > > part.
> > > > >    Although this precision-dropping behavior is non-conforming, it
> > > seems
> > > > >    consistent with how printf formats __ibm128.
> > > > >
> > > > > libstdc++-v3/ChangeLog:
> > > > >
> > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > 	* configure: Regenerate.
> > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > 	overloads for float, double and long double.
> > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > ---
> > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > > >  libstdc++-v3/configure                        |    2 +-
> > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > +++++++++++++++++
> > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > >  create mode 100644
> > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > >
> > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > > --- a/libstdc++-v3/acinclude.m4
> > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > >  fi
> > > > >
> > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > -libtool_VERSION=6:28:0
> > > > > +libtool_VERSION=6:29:0
> > > > >
> > > > >  # Everything parsed; figure out what files and settings to use.
> > > > >  case $enable_symvers in
> > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > >
> > > > >  } GLIBCXX_3.4.27;
> > > > >
> > > > > +GLIBCXX_3.4.29 {
> > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > > +
> > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > chars_format)
> > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > > +
> > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > chars_format,
> > > > > int)
> > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > > +
> > > > > +} GLIBCXX_3.4.28;
> > > > > +
> > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > > >  CXXABI_1.3 {
> > > > >
> > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > > > index dd54bd406a9..73f771e7335 100755
> > > > > --- a/libstdc++-v3/configure
> > > > > +++ b/libstdc++-v3/configure
> > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > versioning
> > > > > will be disabled." >&2;}
> > > > >  fi
> > > > >
> > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > -libtool_VERSION=6:28:0
> > > > > +libtool_VERSION=6:29:0
> > > > >
> > > > >  # Everything parsed; figure out what files and settings to use.
> > > > >  case $enable_symvers in
> > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > > b/libstdc++-v3/include/std/charconv
> > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > > --- a/libstdc++-v3/include/std/charconv
> > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > >
> > > > > +  // Floating-point std::to_chars
> > > > > +
> > > > > +  // Overloads for float.
> > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > __value)
> > > > > noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > __value,
> > > > > +			   chars_format __fmt) noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > __value,
> > > > > +			   chars_format __fmt, int __precision)
> > > noexcept;
> > > > > +
> > > > > +  // Overloads for double.
> > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > __value)
> > > > > noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > __value,
> > > > > +			   chars_format __fmt) noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > __value,
> > > > > +			   chars_format __fmt, int __precision)
> > > noexcept;
> > > > > +
> > > > > +  // Overloads for long double.
> > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > __value)
> > > > > +    noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > __value,
> > > > > +			   chars_format __fmt) noexcept;
> > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > __value,
> > > > > +			   chars_format __fmt, int __precision)
> > > noexcept;
> > > > > +
> > > > > +  // If long double has the same binary format as double, then we
> > > just
> > > > > define
> > > > > +  // the long double overloads as wrappers around the corresponding
> > > > > double
> > > > > +  // overloads.
> > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > > +  inline to_chars_result
> > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > > > +
> > > > > +  inline to_chars_result
> > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > +	   chars_format __fmt) noexcept
> > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > > > +
> > > > > +  inline to_chars_result
> > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > +	   chars_format __fmt, int __precision) noexcept
> > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > > > __precision); }
> > > > > +#endif
> > > >
> > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > > introduce an ODR violation because each long double to_chars overload
> > > > could potentially have two different definitions available in a program,
> > > > one out-of-line in floating_to_chars.cc (compiled without
> > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > > -mlong-double-64)..
> > > 
> > > But they have different mangled names, so there's no ODR violation.
> > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > is mangled as __float128. You *will* get an ODR violation on targets
> > > where there's no -mlong-double-64 switch, where double and long double
> > > are always the same representation.
> > > 
> > > What I'm doing for std::from_chars is adding this in the new
> > > src/c++17/floating_from_chars.cc file:
> > > 
> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > extern "C" from_chars_result
> > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > #endif
> > > 
> > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > (i.e. from_chars for 64-bit long double) as an alias of
> > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > double).
> > 
> > Aha, that makes sense.  I'll follow suit for std::to_chars.
> 
> Actually that should be:
> 
> #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> extern "C" from_chars_result
> _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> 					 long double& value,
> 					 chars_format fmt) noexcept
> __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> #endif
> 
> With the right parameter list I don't need to disable the warning.

Sounds good.  Here's patch v5 that defines such aliases, tested so far
on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.

-- >8 --

Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
 implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing explicit-precision
fixed and scientific formatting of float and double. For
explicit-precision formatting of long double we fall back to using
printf.  Hexadecimal formatting for float, double and long double is
implemented from scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length
beforehand, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer if
necessary.

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu,
and where we also take care to avoid having to format the string a
second time when the general formatting mode resolves to fixed.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's approach of being consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form of 1.08p+0 is 2.1p-1, but we output the former instead of the
   latter, as does printf.

2. The Ryu routines for doing shortest formatting on types larger than
   binary64 use the __int128 type, and some targets (e.g. i386) have a
   large long double type but lack __int128.  For such targets we make
   the long double to_chars overloads go through the double overloads,
   which means we lose precision in the output.  (The mantissa of long
   double is 64 bits on i386, so I think we could potentially fix this
   by writing a specialized version of the generic Ryu formatting
   routine which works with uint64_t instead of __int128.)

3. The __ibm128 shortest formatting routines don't guarantee
   round-trippability if the difference between the high- and low-order
   exponent is too large.  This is because we treat the type as if it
   has a contiguous 105-bit mantissa by merging the high- and low-order
   mantissas, so we potentially lose precision from the low-order part.
   Although this precision-dropping behavior is non-conforming, it seems
   consistent with how printf formats __ibm128.

libstdc++-v3/ChangeLog:

	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
	* config/abi/pre/gnu.ver: Add new exports.
	* configure: Regenerate.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	* testsuite/20_util/to_chars/long_double.cc: New test.
	* testsuite/util/testsuite_abi.cc: Add new symbol version.
---
 libstdc++-v3/acinclude.m4                     |    2 +-
 libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
 libstdc++-v3/configure                        |    2 +-
 libstdc++-v3/include/std/charconv             |   24 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    5 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1547 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
 9 files changed, 1788 insertions(+), 5 deletions(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
index ee5e0336f2c..e3926e1c9c2 100644
--- a/libstdc++-v3/acinclude.m4
+++ b/libstdc++-v3/acinclude.m4
@@ -3846,7 +3846,7 @@ changequote([,])dnl
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index edf4485e607..9a1bcfd25d1 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
 
 } GLIBCXX_3.4.27;
 
+GLIBCXX_3.4.29 {
+    # to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[fdeg];
+
+    # to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[fdeg]St12chars_format;
+
+    # to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
+
+} GLIBCXX_3.4.28;
+
 # Symbols in the support library (libsupc++) have their own tag.
 CXXABI_1.3 {
 
diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
index dd54bd406a9..73f771e7335 100755
--- a/libstdc++-v3/configure
+++ b/libstdc++-v3/configure
@@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol versioning will be disabled." >&2;}
 fi
 
 # For libtool versioning info, format is CURRENT:REVISION:AGE
-libtool_VERSION=6:28:0
+libtool_VERSION=6:29:0
 
 # Everything parsed; figure out what files and settings to use.
 case $enable_symvers in
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index cc7dd0e3758..a1767a4ab2e 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -688,6 +688,30 @@ namespace __detail
   operator^=(chars_format& __lhs, chars_format __rhs) noexcept
   { return __lhs = __lhs ^ __rhs; }
 
+  // Floating-point std::to_chars
+
+  // Overloads for float.
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for double.
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for long double.
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 85e31fbd91f..6637c5b4500 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -50,6 +50,7 @@ inst_sources =
 endif
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index de605a3f6a6..3b3b0d93a2c 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,8 +124,8 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = fs_dir.lo fs_ops.lo fs_path.lo memory_resource.lo \
-	$(am__objects_1)
+am__objects_2 = floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
 @ENABLE_EXTERN_TEMPLATE_TRUE@	string-inst.lo $(am__objects_3)
@@ -435,6 +435,7 @@ headers =
 @ENABLE_EXTERN_TEMPLATE_TRUE@	$(extra_string_inst_sources)
 
 sources = \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..eb7cdf13e8b
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1547 @@
+// Floating-point std::to_chars implementation -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_ASSERTIONS
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We currently support the binary64, float80 (i.e. x86 80-bit extended
+// precision), binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#  define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu bits in their own namespace to avoid name conflicts.
+# include "ryu/generic_128.h"
+# include "ryu/ryu_generic_128.h"
+# include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_rep;
+      ieee_rep.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_rep.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_rep.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_rep;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (with an implicit leading bit).  We keep the exponent and sign
+      // of the high part, and merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_rep;
+      ieee_rep.mantissa = ((uint_t{mantissa_hi} << 64)
+			   | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_rep.biased_exponent = exponent_hi;
+      ieee_rep.sign = sign_hi;
+      return ieee_rep;
+    }
+#endif
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point number.
+  template<typename T>
+    typename floating_type_traits<T>::shortest_scientific_t
+    floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (std::is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (std::is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (std::is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						mantissa_bits, exponent_bits,
+						!has_implicit_leading_bit);
+	}
+#endif
+    }
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can trust the shortest scientific exponent to determine the
+  // length of the exact value, but for these powers of 10 the length of the
+  // exact value is one smaller than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(const ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+    static optional<to_chars_result>
+    __handle_special_value(char* first, char* const last, const T value,
+			   const chars_format fmt, const int precision)
+    {
+      __glibcxx_assert(precision >= 0);
+
+      string_view str;
+      switch (__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL,
+				   FP_ZERO, value))
+	{
+	case FP_INFINITE:
+	  str = "-inf";
+	  break;
+
+	case FP_NAN:
+	  str = "-nan";
+	  break;
+
+	case FP_ZERO:
+	  break;
+
+	default:
+	case FP_SUBNORMAL:
+	case FP_NORMAL: [[likely]]
+	  return nullopt;
+	}
+
+      if (!str.empty())
+	{
+	  if (!__builtin_signbit(value))
+	    str.remove_prefix(strlen("-"));
+
+	  if (last - first < (int)str.length())
+	    return {{last, errc::value_too_large}};
+
+	  memcpy(first, &str[0], str.length());
+	  first += str.length();
+	  return {{first, errc{}}};
+	}
+
+      __glibcxx_assert(value == 0);
+      const bool neg_zero_p = __builtin_signbit(value);
+      int output_length;
+      switch (fmt)
+	{
+	case chars_format::fixed:
+	case chars_format::scientific:
+	case chars_format::hex:
+	  output_length = neg_zero_p + 1;
+	  if (precision)
+	    output_length += strlen(".") + precision;
+	  if (fmt == chars_format::scientific)
+	    output_length += strlen("e+00");
+	  else if (fmt == chars_format::hex)
+	    output_length += strlen("p+0");
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  if (precision)
+	    {
+	      *first++ = '.';
+	      memset(first, '0', precision);
+	      first += precision;
+	    }
+	  if (fmt == chars_format::scientific)
+	    {
+	      memcpy(first, "e+00", 4);
+	      first += 4;
+	    }
+	  else if (fmt == chars_format::hex)
+	    {
+	      memcpy(first, "p+0", 3);
+	      first += 3;
+	    }
+	  return {{first, errc{}}};
+
+	default:
+	  __glibcxx_assert(fmt == chars_format::general
+			   || fmt == chars_format{});
+	  output_length = neg_zero_p + 1;
+	  if (last - first < output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (neg_zero_p)
+	    *first++ = '-';
+	  *first++ = '0';
+	  return {{first, errc{}}};
+	}
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* last, const T value,
+			    optional<int> precision)
+    {
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+      constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__;
+
+      if (precision && *precision < 0)
+	precision = nullopt;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      static_assert(mantissa_t_width >= rounded_mantissa_bits);
+      mantissa_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								     - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = mantissa_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits;
+	  effective_mantissa <<= dropped_bits;
+	  if (should_round & (mantissa_t{1} << dropped_bits))
+	    {
+	      // Round up the least significant nibble.
+	      effective_mantissa += mantissa_t{1} << dropped_bits;
+	      // Check and adjust for overflow of the leading nibble.  When the
+	      // type has an implicit leading bit, then the leading nibble
+	      // before rounding is either 0 or 1, so it can't overflow.
+	      if constexpr (!has_implicit_leading_bit)
+		{
+		  // The only floating type with explicit leading mantissa bit
+		  // that we currently support is x86 80-bit extended precision.
+		  // So we hardcode the below overflow check for this type.
+		  static_assert(mantissa_t_width == 64
+				&& rounded_mantissa_bits == 64);
+		  if (effective_mantissa == 0)
+		    {
+		      // We rounded up the least significant nibble and the
+		      // mantissa overflowed, e.g f.fcp+10 with precision=1
+		      // became 10.0p+10.  Absorb the extra hexit into the
+		      // exponent to obtain 1.0p+14.
+		      effective_mantissa
+			= mantissa_t{1} << (rounded_mantissa_bits - 4);
+		      written_exponent += 4;
+		    }
+		}
+	    }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_written_exponent = abs(written_exponent);
+      expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_written_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_written_exponent >= 100 ? strlen("p+ddd")
+				 : abs_written_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits - 4;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+
+	       effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	       nibble_offset -= 4;
+	    }
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      const to_chars_result result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = floating_to_shortest_scientific(value);
+      const int mantissa_length = get_mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+NNNN")
+				     : abs_exponent >= 100 ? strlen("e+NNN")
+				     : strlen("e+NN"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa that what the
+	  // shortest scientific form given by Ryu contains.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // Adding some wiggle room due to rounding yields the condition
+	  // value_fits_inside_mantissa below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length = fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point at the appropriate
+	      // spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length = result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* const last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+      // Extract the sign and exponent from the value.
+      const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+      // Ryu doesn't support formatting floating-point types larger than double
+      // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is far enough away from +-100.  But if it's
+	  // near +-100, then our log2 approximation is too coarse (and doesn't
+	  // consider precision-dependent rounding) in order to accurately
+	  // distinguish between a scientific exponent of +-100 and +-99.
+	  const bool scientific_exponent_near_100_p
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+
+	  // Compute an upper bound on the output length.  TODO: Maybe also
+	  // consider a lower bound on the output length.
+	  int output_length_upper_bound = sign + strlen("d");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  if (scientific_exponent_near_100_p
+	      || (floor_log2_value >= 332 || floor_log2_value <= -333))
+	    output_length_upper_bound += strlen("e+ddd");
+	  else
+	    output_length_upper_bound += strlen("e+dd");
+
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      // The result will definitely fit into the output range, so we can
+	      // write directly into it.
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    first, nullptr);
+	      __glibcxx_assert(output_length == output_length_upper_bound
+			       || (scientific_exponent_near_100_p
+				   && (output_length
+				       == output_length_upper_bound - 1)));
+	    }
+	  else if (scientific_exponent_near_100_p)
+	    {
+	      // Write the result of d2exp_buffered_n into an intermediate
+	      // buffer, do a bounds check, and copy the result into the output
+	      // range.
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    buffer, nullptr);
+	      __glibcxx_assert(output_length == output_length_upper_bound - 1
+			       || output_length == output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    // If the scientific exponent is not near 100, then the upper bound
+	    // is actually the exact length, and so the result will definitely
+	    // not fit into the output range.
+	    return {last, errc::value_too_large};
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice the excess zeros into the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // Compute an upper bound on the output length.  TODO: Maybe also
+	  // consider a lower bound on the output length.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      // The result will definitely fit into the output range, so we can
+	      // write directly into it.
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // Write the result of d2fixed_buffered_n into an intermediate
+	      // buffer, do a bounds check, and copy the result into the output
+	      // range.
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific form such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = ryu::d2exp_buffered_n(value, effective_precision - 1,
+				    buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  // Define the overloads for float.
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for double.
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for double.
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value),
+					  chars_format{});
+    else
+      return __floating_to_chars_shortest(first, last, value, chars_format{});
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value), fmt);
+    else
+      return __floating_to_chars_shortest(first, last, value, fmt);
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_precision(first, last, double(value), fmt,
+					   precision);
+    else
+      return __floating_to_chars_precision(first, last, value, fmt, precision);
+  }
+
+#ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
+  // Map the -mlong-double-64 long double overloads to the double overloads.
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_e(char* first, char* last, double value) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_d")));
+
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_eSt12chars_format(char* first, char* last, double value,
+				     chars_format fmt) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_format")));
+
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_eSt12chars_formati(char* first, char* last, double value,
+				      chars_format fmt, int precision) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_formati")));
+#endif
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..d995aa02d09
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
diff --git a/libstdc++-v3/testsuite/util/testsuite_abi.cc b/libstdc++-v3/testsuite/util/testsuite_abi.cc
index aedb6561ed4..4b73604cc74 100644
--- a/libstdc++-v3/testsuite/util/testsuite_abi.cc
+++ b/libstdc++-v3/testsuite/util/testsuite_abi.cc
@@ -209,6 +209,7 @@ check_version(symbol& test, bool added)
       known_versions.push_back("GLIBCXX_3.4.26");
       known_versions.push_back("GLIBCXX_3.4.27");
       known_versions.push_back("GLIBCXX_3.4.28");
+      known_versions.push_back("GLIBCXX_3.4.29");
       known_versions.push_back("CXXABI_1.3");
       known_versions.push_back("CXXABI_LDBL_1.3");
       known_versions.push_back("CXXABI_1.3.1");
@@ -240,7 +241,7 @@ check_version(symbol& test, bool added)
 	test.version_status = symbol::incompatible;
 
       // Check that added symbols are added in the latest pre-release version.
-      bool latestp = (test.version_name == "GLIBCXX_3.4.28"
+      bool latestp = (test.version_name == "GLIBCXX_3.4.29"
 		     || test.version_name == "CXXABI_1.3.12"
 		     || test.version_name == "CXXABI_FLOAT128"
 		     || test.version_name == "CXXABI_TM_1");
-- 
2.28.0.rc1

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Mon, 20 Jul 2020, Patrick Palka wrote:

> On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> 
> > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > 
> > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > >
> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > >
> > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > > > >
> > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > > > > >
> > > > > > > > > This implements the floating-point std::to_chars overloads for
> > > > > > float,
> > > > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > > shortest
> > > > > > > > > round-trippable fixed and scientific forms of a number for
> > > > float,
> > > > > > double
> > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > > > > scientific
> > > > > > > > > formatting of float and double. For formatting long double with
> > > > an
> > > > > > > > > explicit precision argument we use a printf fallback.
> > > > Hexadecimal
> > > > > > > > > formatting for float, double and long double is implemented from
> > > > > > > > > scratch.
> > > > > > > > >
> > > > > > > > > The supported long double binary formats are float64 (same as
> > > > > > double),
> > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > > > > > >
> > > > > > > > > Much of the complexity of the implementation is in computing the
> > > > > > exact
> > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > > bounds
> > > > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > > before
> > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > > the
> > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > > (if
> > > > > > the
> > > > > > > > > output range is smaller than the upper bound).
> > > > > > > > >
> > > > > > > > > Another source of complexity is in the general-with-precision
> > > > > > formatting
> > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > > by
> > > > > > Ryu, and
> > > > > > > > > where we also take care to avoid having to format the string a
> > > > > > second
> > > > > > > > > time when the general formatting mode resolves to fixed.
> > > > > > > > >
> > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > > > > > >
> > > > > > > > > libstdc++-v3/ChangeLog:
> > > > > > > > >
> > > > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > > > > 	* configure: Regenerate.
> > > > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > > > > 	overloads for float, double and long double.
> > > > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > > > >
> > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > > to
> > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > > > > format
> > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > > The
> > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > > > > uint64_t
> > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > > > > case.
> > > > > > >
> > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > > most
> > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > > mode.
> > > > > >
> > > > > > Here's v4, which should now correctly support using <charconv> with
> > > > > > -mlong-double-64 on targets with a large default long double type.
> > > > > > This is done by defining the long double to_chars overloads as inline
> > > > > > wrappers around the double overloads within <charconv> whenever
> > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > > >
> > > > > >
> > > > > > -- >8 --
> > > > > >
> > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > > > >  implementation
> > > > > >
> > > > > > This implements the floating-point std::to_chars overloads for float,
> > > > > > double and long double.  We use the Ryu library to compute the
> > > > shortest
> > > > > > round-trippable fixed and scientific forms of a number for float,
> > > > double
> > > > > > and long double.  We also use Ryu for performing explicit-precision
> > > > > > fixed and scientific formatting of float and double. For
> > > > > > explicit-precision formatting of long double we fall back to using
> > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > > > > implemented from scratch.
> > > > > >
> > > > > > The supported long double binary formats are binary64, binary80 (x86
> > > > > > 80-bit extended precision), binary128 and ibm128.
> > > > > >
> > > > > > Much of the complexity of the implementation is in computing the exact
> > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > > > checking).  In some cases it's hard to compute the output length
> > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > > > > output length and use a sufficiently-sized intermediate buffer if
> > > > > > necessary.
> > > > > >
> > > > > > Another source of complexity is in the general-with-precision
> > > > formatting
> > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > > > and where we also take care to avoid having to format the string a
> > > > > > second time when the general formatting mode resolves to fixed.
> > > > > >
> > > > > > This implementation is non-conforming in a couple of ways:
> > > > > >
> > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > > > >    Microsoft implementation's approach of being consistent with the
> > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > > > >    printing the shortest representation.  For example, the shortest
> > > > hex
> > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > > > >    latter, as does printf.
> > > > > >
> > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > > > >    large long double type but lack __int128.  For such targets we make
> > > > > >    the long double to_chars overloads go through the double overloads,
> > > > > >    which means we lose precision in the output.  (The mantissa of long
> > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > > > >    by writing a specialized version of the generic Ryu formatting
> > > > > >    routine which works with uint64_t instead of __int128.)
> > > > > >
> > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > > > >    round-trippability if the difference between the high- and
> > > > low-order
> > > > > >    exponent is too large.  This is because we treat the type as if it
> > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > > low-order
> > > > > >    mantissas, so we potentially lose precision from the low-order
> > > > part.
> > > > > >    Although this precision-dropping behavior is non-conforming, it
> > > > seems
> > > > > >    consistent with how printf formats __ibm128.
> > > > > >
> > > > > > libstdc++-v3/ChangeLog:
> > > > > >
> > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > 	* configure: Regenerate.
> > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > 	overloads for float, double and long double.
> > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > > ---
> > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > > > >  libstdc++-v3/configure                        |    2 +-
> > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > > +++++++++++++++++
> > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > > >  create mode 100644
> > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > > >
> > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > > > --- a/libstdc++-v3/acinclude.m4
> > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > > >  fi
> > > > > >
> > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > > -libtool_VERSION=6:28:0
> > > > > > +libtool_VERSION=6:29:0
> > > > > >
> > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > >  case $enable_symvers in
> > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > > >
> > > > > >  } GLIBCXX_3.4.27;
> > > > > >
> > > > > > +GLIBCXX_3.4.29 {
> > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > > > +
> > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > chars_format)
> > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > > > +
> > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > chars_format,
> > > > > > int)
> > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > > > +
> > > > > > +} GLIBCXX_3.4.28;
> > > > > > +
> > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > > > >  CXXABI_1.3 {
> > > > > >
> > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > > > > index dd54bd406a9..73f771e7335 100755
> > > > > > --- a/libstdc++-v3/configure
> > > > > > +++ b/libstdc++-v3/configure
> > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > > versioning
> > > > > > will be disabled." >&2;}
> > > > > >  fi
> > > > > >
> > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > > -libtool_VERSION=6:28:0
> > > > > > +libtool_VERSION=6:29:0
> > > > > >
> > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > >  case $enable_symvers in
> > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > > > b/libstdc++-v3/include/std/charconv
> > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > > > --- a/libstdc++-v3/include/std/charconv
> > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > > >
> > > > > > +  // Floating-point std::to_chars
> > > > > > +
> > > > > > +  // Overloads for float.
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > __value)
> > > > > > noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > __value,
> > > > > > +			   chars_format __fmt) noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > __value,
> > > > > > +			   chars_format __fmt, int __precision)
> > > > noexcept;
> > > > > > +
> > > > > > +  // Overloads for double.
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > __value)
> > > > > > noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > __value,
> > > > > > +			   chars_format __fmt) noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > __value,
> > > > > > +			   chars_format __fmt, int __precision)
> > > > noexcept;
> > > > > > +
> > > > > > +  // Overloads for long double.
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > __value)
> > > > > > +    noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > __value,
> > > > > > +			   chars_format __fmt) noexcept;
> > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > __value,
> > > > > > +			   chars_format __fmt, int __precision)
> > > > noexcept;
> > > > > > +
> > > > > > +  // If long double has the same binary format as double, then we
> > > > just
> > > > > > define
> > > > > > +  // the long double overloads as wrappers around the corresponding
> > > > > > double
> > > > > > +  // overloads.
> > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > > > +  inline to_chars_result
> > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > > > > +
> > > > > > +  inline to_chars_result
> > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > > +	   chars_format __fmt) noexcept
> > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > > > > +
> > > > > > +  inline to_chars_result
> > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > > +	   chars_format __fmt, int __precision) noexcept
> > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > > > > __precision); }
> > > > > > +#endif
> > > > >
> > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > > > introduce an ODR violation because each long double to_chars overload
> > > > > could potentially have two different definitions available in a program,
> > > > > one out-of-line in floating_to_chars.cc (compiled without
> > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > > > -mlong-double-64)..
> > > > 
> > > > But they have different mangled names, so there's no ODR violation.
> > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > > is mangled as __float128. You *will* get an ODR violation on targets
> > > > where there's no -mlong-double-64 switch, where double and long double
> > > > are always the same representation.
> > > > 
> > > > What I'm doing for std::from_chars is adding this in the new
> > > > src/c++17/floating_from_chars.cc file:
> > > > 
> > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > > extern "C" from_chars_result
> > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > #endif
> > > > 
> > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > > (i.e. from_chars for 64-bit long double) as an alias of
> > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > > double).
> > > 
> > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > 
> > Actually that should be:
> > 
> > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > extern "C" from_chars_result
> > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > 					 long double& value,
> > 					 chars_format fmt) noexcept
> > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > #endif
> > 
> > With the right parameter list I don't need to disable the warning.
> 
> Sounds good.  Here's patch v5 that defines such aliases, tested so far
> on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.

Here's v6 which is rebased against the floating-point from_chars patch
and which also works around a false-positive -Wmaybe-uninitialized
warning in __floating_to_chars_hex, as well as performs some minor
commentary/style cleanups:

-- >8 --

Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
 implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms of a number for float, double
and long double.  We also use Ryu for performing explicit-precision
fixed and scientific formatting of float and double. For
explicit-precision formatting of long double we fall back to using
printf.  Hexadecimal formatting for float, double and long double is
implemented from scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length
beforehand, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer if
necessary.

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu,
and where we also take care to avoid having to format the string a
second time when the general formatting mode resolves to fixed.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's approach of being consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form of 1.08p+0 is 2.1p-1, but we output the former instead of the
   latter, as does printf.

2. The Ryu routines for doing shortest formatting on types larger than
   binary64 use the __int128 type, and some targets (e.g. i386) have a
   large long double type but lack __int128.  For such targets we make
   the long double to_chars overloads go through the double overloads,
   which means we lose precision in the output.  (The mantissa of long
   double is 64 bits on i386, so I think we could potentially fix this
   by writing a specialized version of the generic Ryu formatting
   routine which works with uint64_t instead of __int128.)

3. The __ibm128 shortest formatting routines don't guarantee
   round-trippability if the difference between the high- and low-order
   exponent is too large.  This is because we treat the type as if it
   has a contiguous 105-bit mantissa by merging the high- and low-order
   mantissas, so we potentially lose precision from the low-order part.
   Although this precision-dropping behavior is non-conforming, it seems
   consistent with how printf formats __ibm128.

libstdc++-v3/ChangeLog:

	* config/abi/pre/gnu.ver: Add new exports.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	(to_chars): Define for float, double and long double.
	* testsuite/20_util/to_chars/long_double.cc: New test.
---
 libstdc++-v3/config/abi/pre/gnu.ver           |    9 +
 libstdc++-v3/include/std/charconv             |   24 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    3 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1552 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  197 +++
 6 files changed, 1785 insertions(+), 1 deletion(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index 17aff5d907b..9be022d319a 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2304,6 +2304,15 @@ GLIBCXX_3.4.29 {
     # std::from_chars
     _ZSt10from_charsPKcS0_R[def]St12chars_format;
 
+    # std::to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[defg];
+
+    # std::to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[defg]St12chars_format;
+
+    # std::to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[defg]St12chars_formati;
+
 } GLIBCXX_3.4.28;
 
 # Symbols in the support library (libsupc++) have their own tag.
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index be668c1939e..b0f8a6106bc 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -702,6 +702,30 @@ namespace __detail
 	     chars_format __fmt = chars_format::general);
 #endif
 
+  // Floating-point std::to_chars
+
+  // Overloads for float.
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for double.
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for long double.
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 642efb976ac..0f5b7eb8e56 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -51,6 +51,7 @@ endif
 
 sources = \
 	floating_from_chars.cc \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index ce08eb3ff11..bf291d7f236 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,7 +124,7 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = floating_from_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+am__objects_2 = floating_from_chars.lo floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
 	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
@@ -436,6 +436,7 @@ headers =
 
 sources = \
 	floating_from_chars.cc \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..be8784336b7
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1552 @@
+// std::to_chars implementation for floating-point types -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file.
+#define _GLIBCXX_ASSERTIONS
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We currently support the binary64, float80 (i.e. x86 80-bit extended
+// precision), binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#  define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu bits in their own namespace to avoid name conflicts.
+# include "ryu/generic_128.h"
+# include "ryu/ryu_generic_128.h"
+# include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_repr;
+      ieee_repr.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_repr.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_repr.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_repr;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (plus an implicit leading bit).  We use the exponent and sign
+      // of the high part, and we merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_repr;
+      ieee_repr.mantissa = ((uint_t{mantissa_hi} << 64)
+			    | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_repr.biased_exponent = exponent_hi;
+      ieee_repr.sign = sign_hi;
+      return ieee_rep;
+    }
+#endif
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point number.
+  template<typename T>
+    typename floating_type_traits<T>::shortest_scientific_t
+    floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (std::is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (std::is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (std::is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						mantissa_bits, exponent_bits,
+						!has_implicit_leading_bit);
+	}
+#endif
+    }
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can rely on the shortest scientific exponent to determine the
+  // length of the exact fixed form, but for these powers of 10 the length of
+  // the fixed form is one less than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(const ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+  // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+  // all formatting modes.
+  template<typename T>
+    static optional<to_chars_result>
+    __handle_special_value(char* first, char* const last, const T value,
+			   const chars_format fmt, const int precision)
+    {
+      __glibcxx_assert(precision >= 0);
+
+      string_view str;
+      switch (__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL,
+				   FP_ZERO, value))
+	{
+	case FP_INFINITE:
+	  str = "-inf";
+	  break;
+
+	case FP_NAN:
+	  str = "-nan";
+	  break;
+
+	case FP_ZERO:
+	  break;
+
+	default:
+	case FP_SUBNORMAL:
+	case FP_NORMAL: [[likely]]
+	  return nullopt;
+	}
+
+      if (!str.empty())
+	{
+	  // We're formatting +-inf or +-nan.
+	  if (!__builtin_signbit(value))
+	    str.remove_prefix(strlen("-"));
+
+	  if (last - first < (int)str.length())
+	    return {{last, errc::value_too_large}};
+
+	  memcpy(first, &str[0], str.length());
+	  first += str.length();
+	  return {{first, errc{}}};
+	}
+
+      // We're formatting 0.
+      __glibcxx_assert(value == 0);
+      const bool sign = __builtin_signbit(value);
+      int expected_output_length;
+      const char* orig_first = first;
+      switch (fmt)
+	{
+	case chars_format::fixed:
+	case chars_format::scientific:
+	case chars_format::hex:
+	  expected_output_length = sign + 1;
+	  if (precision)
+	    expected_output_length += strlen(".") + precision;
+	  if (fmt == chars_format::scientific)
+	    expected_output_length += strlen("e+00");
+	  else if (fmt == chars_format::hex)
+	    expected_output_length += strlen("p+0");
+	  if (last - first < expected_output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (sign)
+	    *first++ = '-';
+	  *first++ = '0';
+	  if (precision)
+	    {
+	      *first++ = '.';
+	      memset(first, '0', precision);
+	      first += precision;
+	    }
+	  if (fmt == chars_format::scientific)
+	    {
+	      memcpy(first, "e+00", 4);
+	      first += 4;
+	    }
+	  else if (fmt == chars_format::hex)
+	    {
+	      memcpy(first, "p+0", 3);
+	      first += 3;
+	    }
+	  break;
+
+	case chars_format::general:
+	default: // case chars_format{}:
+	  expected_output_length = sign + 1;
+	  if (last - first < expected_output_length)
+	    return {{last, errc::value_too_large}};
+
+	  if (sign)
+	    *first++ = '-';
+	  *first++ = '0';
+	  break;
+	}
+      __glibcxx_assert(first - orig_first == expected_output_length);
+      return {{first, errc{}}};
+    }
+
+  // This subroutine of the floating-point to_chars overloads performs
+  // hexadecimal formatting.
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_hex(char* first, char* const last, const T value,
+			    const optional<int> precision)
+    {
+      if (precision && *precision < 0) [[unlikely]]
+	// A negative precision argument is treated as if it is omitted.
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_requires_valid_range(first, last);
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr bool has_implicit_leading_bit
+	= floating_type_traits<T>::has_implicit_leading_bit;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+      using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+      constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       chars_format::hex,
+					       precision.value_or(0)))
+	return *result;
+
+      // Extract the sign, mantissa and exponent from the value.
+      const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Shift the mantissa so that its bitwidth is a multiple of 4.
+      constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+      static_assert(mantissa_t_width >= rounded_mantissa_bits);
+      mantissa_t effective_mantissa
+	= ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+      if (is_normal_number)
+	{
+	  if constexpr (has_implicit_leading_bit)
+	    // Restore the mantissa's implicit leading bit.
+	    effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+	  else
+	    // The explicit mantissa bit should already be set.
+	    __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								     - 1u)));
+	}
+
+      // Compute the shortest precision needed to print this value exactly,
+      // disregarding trailing zeros.
+      constexpr int full_hex_precision = (has_implicit_leading_bit
+					  ? (mantissa_bits + 3) / 4
+					  // With an explicit leading bit, we
+					  // use the four leading nibbles as the
+					  // hexit before the decimal point.
+					  : (mantissa_bits - 4 + 3) / 4);
+      const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+      const int shortest_full_precision = full_hex_precision - trailing_zeros;
+      __glibcxx_assert(shortest_full_precision >= 0);
+
+      int written_exponent = unbiased_exponent;
+      const int effective_precision = precision.value_or(shortest_full_precision);
+      if (effective_precision < shortest_full_precision)
+	{
+	  // When limiting the precision, we need to determine how to round the
+	  // least significant printed hexit.  The following branchless
+	  // bit-level-parallel technique computes whether to round up the
+	  // mantissa bit at index N (according to round-to-nearest rules) when
+	  // dropping N bits of precision, for each index N in the bit vector.
+	  // This technique is borrowed from the MSVC implementation.
+	  using bitvec = mantissa_t;
+	  const bitvec round_bit = effective_mantissa << 1;
+	  const bitvec has_tail_bits = round_bit - 1;
+	  const bitvec lsb_bit = effective_mantissa;
+	  const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+	  const int dropped_bits = 4*(full_hex_precision - effective_precision);
+	  // Mask out the dropped nibbles.
+	  effective_mantissa >>= dropped_bits;
+	  effective_mantissa <<= dropped_bits;
+	  if (should_round & (mantissa_t{1} << dropped_bits))
+	    {
+	      // Round up the least significant nibble.
+	      effective_mantissa += mantissa_t{1} << dropped_bits;
+	      // Check and adjust for overflow of the leading nibble.  When the
+	      // type has an implicit leading bit, then the leading nibble
+	      // before rounding is either 0 or 1, so it can't overflow.
+	      if constexpr (!has_implicit_leading_bit)
+		{
+		  // The only supported floating-point type with explicit
+		  // leading mantissa bit is LDK_FLOAT80, i.e. x86 80-bit
+		  // extended precision, and so we hardcode the below overflow
+		  // check+adjustment for this type.
+		  static_assert(mantissa_t_width == 64
+				&& rounded_mantissa_bits == 64);
+		  if (effective_mantissa == 0)
+		    {
+		      // We rounded up the least significant nibble and the
+		      // mantissa overflowed, e.g f.fcp+10 with precision=1
+		      // became 10.0p+10.  Absorb this extra hexit into the
+		      // exponent to obtain 1.0p+14.
+		      effective_mantissa
+			= mantissa_t{1} << (rounded_mantissa_bits - 4);
+		      written_exponent += 4;
+		    }
+		}
+	    }
+	}
+
+      // Compute the leading hexit and mask it out from the mantissa.
+      char leading_hexit;
+      if constexpr (has_implicit_leading_bit)
+	{
+	  const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+	  __glibcxx_assert(nibble <= 2);
+	  leading_hexit = '0' + nibble;
+	  effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+	}
+      else
+	{
+	  const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+	  __glibcxx_assert(nibble < 16);
+	  leading_hexit = "0123456789abcdef"[nibble];
+	  effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+	  written_exponent -= 3;
+	}
+
+      // Now before we start writing the string, determine the total length of
+      // the output string and perform a single bounds check.
+      int expected_output_length = sign + 1;
+      if (effective_precision != 0)
+	expected_output_length += strlen(".") + effective_precision;
+      const int abs_written_exponent = abs(written_exponent);
+      expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd")
+				 : abs_written_exponent >= 1000 ? strlen("p+dddd")
+				 : abs_written_exponent >= 100 ? strlen("p+ddd")
+				 : abs_written_exponent >= 10 ? strlen("p+dd")
+				 : strlen("p+d"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const auto saved_first = first;
+      // Write the negative sign and the leading hexit.
+      if (sign)
+	*first++ = '-';
+      *first++ = leading_hexit;
+
+      if (effective_precision > 0)
+	{
+	  *first++ = '.';
+	  int written_hexits = 0;
+	  // Extract and mask out the leading nibble after the decimal point,
+	  // write its corresponding hexit, and repeat until the mantissa is
+	  // empty.
+	  int nibble_offset = rounded_mantissa_bits;
+	  if constexpr (!has_implicit_leading_bit)
+	    // We already printed the entire leading hexit.
+	    nibble_offset -= 4;
+	  while (effective_mantissa != 0)
+	    {
+	      nibble_offset -= 4;
+	      const unsigned nibble = effective_mantissa >> nibble_offset;
+	      __glibcxx_assert(nibble < 16);
+	      *first++ = "0123456789abcdef"[nibble];
+	      ++written_hexits;
+	       effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	    }
+	  __glibcxx_assert(nibble_offset >= 0);
+	  __glibcxx_assert(written_hexits <= effective_precision);
+	  // Since the mantissa is now empty, every hexit hereafter must be '0'.
+	  if (int remaining_hexits = effective_precision - written_hexits)
+	    {
+	      memset(first, '0', remaining_hexits);
+	      first += remaining_hexits;
+	    }
+	}
+
+      // Finally, write the exponent.
+      *first++ = 'p';
+      if (written_exponent >= 0)
+	*first++ = '+';
+      const to_chars_result result = to_chars(first, last, written_exponent);
+      __glibcxx_assert(result.ec == errc{}
+		       && result.ptr == saved_first + expected_output_length);
+      return result;
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_shortest(char* first, char* const last, const T value,
+				 chars_format fmt)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, nullopt);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general
+		       || fmt == chars_format{});
+      __glibcxx_requires_valid_range(first, last);
+
+      if (auto result = __handle_special_value(first, last, value, fmt, 0))
+	return *result;
+
+      const auto fd = floating_to_shortest_scientific(value);
+      const int mantissa_length = get_mantissa_length(fd);
+      const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+      if (fmt == chars_format::general)
+	{
+	  // Resolve the 'general' formatting mode as per the specification of
+	  // the 'g' printf output specifier.  Since there is no precision
+	  // argument, the default precision of the 'g' specifier, 6, applies.
+	  if (scientific_exponent >= -4 && scientific_exponent < 6)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+      else if (fmt == chars_format{})
+	{
+	  // The 'plain' formatting mode resolves to 'scientific' if it yields
+	  // the shorter string, and resolves to 'fixed' otherwise.  The
+	  // following lower and upper bounds on the exponent characterize when
+	  // to prefer 'fixed' over 'scientific'.
+	  int lower_bound = -(mantissa_length + 3);
+	  int upper_bound = 5;
+	  if (mantissa_length == 1)
+	    // The decimal point in scientific notation will be omitted in this
+	    // case; tighten the bounds appropriately.
+	    ++lower_bound, --upper_bound;
+
+	  if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	    fmt = chars_format::fixed;
+	  else
+	    fmt = chars_format::scientific;
+	}
+
+      if (fmt == chars_format::scientific)
+	{
+	  // Calculate the total length of the output string, perform a bounds
+	  // check, and then defer to Ryu's to_chars subroutine.
+	  int expected_output_length = fd.sign + mantissa_length;
+	  if (mantissa_length > 1)
+	    expected_output_length += strlen(".");
+	  const int abs_exponent = abs(scientific_exponent);
+	  expected_output_length += (abs_exponent >= 1000 ? strlen("e+dddd")
+				     : abs_exponent >= 100 ? strlen("e+ddd")
+				     : strlen("e+dd"));
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  const int output_length = ryu::to_chars(fd, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+      else if (fmt == chars_format::fixed && fd.exponent >= 0)
+	{
+	  // The Ryu exponent is positive, and so this number's shortest
+	  // representation is a whole number, to be formatted in fixed instead
+	  // of scientific notation "as if by std::printf".  This means we may
+	  // need to print more digits of the IEEE mantissa than what the
+	  // shortest scientific form given by Ryu provides.
+	  //
+	  // For instance, the exactly representable number
+	  // 12300000000000001048576.0 has as its shortest scientific
+	  // representation 123e+22, so in this case fd.mantissa is 123 and
+	  // fd.exponent is 22, which doesn't have enough information to format
+	  // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+	  // precision=0 to format the number in the general case here.
+
+	  // To that end, first compute the output length and perform a bounds
+	  // check.
+	  int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+	  if (is_rounded_up_pow10_p<T>(fd))
+	    --expected_output_length;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+
+	  // Optimization: if the shortest representation fits inside the IEEE
+	  // mantissa, then the number is certainly exactly-representable and
+	  // its shortest scientific form must be equal to its exact form.  So
+	  // we can write the value in fixed form exactly via fd.mantissa and
+	  // fd.exponent.
+	  //
+	  // Taking log2 of both sides of the desired condition
+	  //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+	  // we get
+	  //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+	  // where log2 10 is slightly smaller than 10/3=3.333...
+	  //
+	  // After adding some wiggle room due to rounding we get the condition
+	  // value_fits_inside_mantissa_p below.
+	  const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+	  const bool value_fits_inside_mantissa_p
+	    = (log2_mantissa + (fd.exponent*10 + 2) / 3
+	       < floating_type_traits<T>::mantissa_bits - 2);
+	  if (value_fits_inside_mantissa_p)
+	    {
+	      // Print the small exactly-represantable number in fixed form by
+	      // writing out fd.mantissa followed by fd.exponent many 0s.
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      memset(result.ptr, '0', fd.exponent);
+	      result.ptr += fd.exponent;
+	      const int output_length = fd.sign + (result.ptr - first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return result;
+	    }
+	  else if constexpr (is_same_v<T, long double>)
+	    {
+	      // We can't use d2fixed_buffered_n for types larger than double,
+	      // so we instead format larger types through sprintf.
+	      // TODO: We currently go through an intermediate buffer in order
+	      // to accomodate the mandatory null terminator of sprintf, but we
+	      // can avoid this if we use sprintf to write all but the last
+	      // digit, and carefully compute and write the last digit
+	      // ourselves.
+	      char buffer[expected_output_length+1];
+	      const int saved_rounding_mode = fegetround();
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	      const int output_length = sprintf(buffer, "%.0Lf", value);
+	      if (saved_rounding_mode != FE_TONEAREST)
+		fesetround(saved_rounding_mode);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      memcpy(first, buffer, output_length);
+	      return {first + output_length, errc{}};
+	    }
+	  else
+	    {
+	      // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	      const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	      __glibcxx_assert(output_length == expected_output_length);
+	      return {first + output_length, errc{}};
+	    }
+	}
+      else if (fmt == chars_format::fixed && fd.exponent < 0)
+	{
+	  // The Ryu exponent is negative, so fd.mantissa definitely contains
+	  // all of the whole part of the number, and therefore fd.mantissa and
+	  // fd.exponent contain all of the information needed to format the
+	  // number in fixed notation "as if by std::printf" (with precision
+	  // equal to -fd.exponent).
+	  const int whole_digits = max(mantissa_length + fd.exponent, 1);
+	  const int expected_output_length
+	    = fd.sign + whole_digits + strlen(".") + -fd.exponent;
+	  if (last - first < expected_output_length)
+	    return {last, errc::value_too_large};
+	  if (mantissa_length <= -fd.exponent)
+	    {
+	      // The magnitude of the number is less than one.  Format the
+	      // number appropriately.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      *first++ = '0';
+	      *first++ = '.';
+	      const int leading_zeros = -fd.exponent - mantissa_length;
+	      memset(first, '0', leading_zeros);
+	      first += leading_zeros;
+	      const to_chars_result result = to_chars(first, last, fd.mantissa);
+	      const int output_length = result.ptr - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length
+			       && result.ec == errc{});
+	      return result;
+	    }
+	  else
+	    {
+	      // The magnitude of the number is at least one.
+	      const char* orig_first = first;
+	      if (fd.sign)
+		*first++ = '-';
+	      to_chars_result result = to_chars(first, last, fd.mantissa);
+	      __glibcxx_assert(result.ec == errc{});
+	      // Make space for and write the decimal point in the correct spot.
+	      memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		      -fd.exponent);
+	      result.ptr[fd.exponent] = '.';
+	      const int output_length = result.ptr + 1 - orig_first;
+	      __glibcxx_assert(output_length == expected_output_length);
+	      ++result.ptr;
+	      return result;
+	    }
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  template<typename T>
+    static to_chars_result
+    __floating_to_chars_precision(char* first, char* const last, const T value,
+				  chars_format fmt, int precision)
+    {
+      if (fmt == chars_format::hex)
+	return __floating_to_chars_hex(first, last, value, precision);
+
+      __glibcxx_assert(fmt == chars_format::fixed
+		       || fmt == chars_format::scientific
+		       || fmt == chars_format::general);
+      __glibcxx_requires_valid_range(first, last);
+
+      // A negative precision argument is treated as if it were omitted, in
+      // which case the default precision of 6 applies, as per the printf
+      // specification.
+      if (precision < 0)
+	precision = 6;
+
+      if (auto result = __handle_special_value(first, last, value,
+					       fmt, precision))
+	return *result;
+
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+      // Extract the sign and exponent from the value.
+      const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+      const bool is_normal_number = (biased_exponent != 0);
+
+      // Calculate the unbiased exponent.
+      const int32_t unbiased_exponent = (is_normal_number
+					 ? biased_exponent - exponent_bias
+					 : 1 - exponent_bias);
+
+      // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+      const int floor_log2_value = unbiased_exponent;
+      // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+      const int approx_log10_value = (floor_log2_value >= 0
+				      ? (floor_log2_value*301 + 999)/1000
+				      : (floor_log2_value*301 - 999)/1000);
+
+      // Compute (an upper bound of) the number's effective precision when it is
+      // formatted in scientific and fixed notation.  Beyond this precision all
+      // digits are definitely zero, and this fact allows us to bound the sizes
+      // of any local output buffers that we may need to use.  TODO: Consider
+      // the number of trailing zero bits in the mantissa to obtain finer upper
+      // bounds.
+      // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+      // bounds below is necessary only for __ibm128, it seems.  Even though the
+      // type has 105 bits of precision, printf may output 106 fractional digits
+      // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+      const int max_eff_scientific_precision
+	= (floor_log2_value >= 0
+	   ? max(mantissa_bits + 1, approx_log10_value + 1)
+	   : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_scientific_precision > 0);
+
+      const int max_eff_fixed_precision
+	= (floor_log2_value >= 0
+	   ? mantissa_bits + 1
+	   : -floor_log2_value + mantissa_bits + 1);
+      __glibcxx_assert(max_eff_fixed_precision > 0);
+
+      // Ryu doesn't support formatting floating-point types larger than double
+      // with an explicit precision, so instead we just go through printf.
+      if constexpr (is_same_v<T, long double>)
+	{
+	  int effective_precision;
+	  const char* output_specifier;
+	  if (fmt == chars_format::scientific)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Le";
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      effective_precision = min(precision, max_eff_fixed_precision);
+	      output_specifier = "%.*Lf";
+	    }
+	  else if (fmt == chars_format::general)
+	    {
+	      effective_precision = min(precision, max_eff_scientific_precision);
+	      output_specifier = "%.*Lg";
+	    }
+	  const int excess_precision = (fmt != chars_format::general
+					? precision - effective_precision : 0);
+
+	  // Since the output of printf is locale-sensitive, we need to be able
+	  // to handle a radix point that's different from '.'.
+	  char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+	  if (effective_precision > 0)
+	    // ???: Can nl_langinfo() ever return null?
+	    if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	      {
+		strncpy(radix, radix_ptr, sizeof(radix)-1);
+		// We accept only radix points which are at most 4 bytes (one
+		// UTF-8 character) wide.
+		__glibcxx_assert(radix[4] == '\0');
+	      }
+
+	  // Compute straightforward upper bounds on the output length.
+	  int output_length_upper_bound;
+	  if (fmt == chars_format::scientific || fmt == chars_format::general)
+	    output_length_upper_bound = (strlen("-d") + sizeof(radix)
+					 + effective_precision
+					 + strlen("e+dddd"));
+	  else if (fmt == chars_format::fixed)
+	    {
+	      if (approx_log10_value >= 0)
+		output_length_upper_bound = sign + approx_log10_value + 1;
+	      else
+		output_length_upper_bound = sign + strlen("0");
+	      output_length_upper_bound += sizeof(radix) + effective_precision;
+	    }
+
+	  // Do the sprintf into the local buffer.
+	  char buffer[output_length_upper_bound+1];
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+	  int output_length
+	    = sprintf(buffer, output_specifier, effective_precision, value);
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  if (effective_precision > 0)
+	    // We need to replace a radix that is different from '.' with '.'.
+	    if (const string_view radix_sv = {radix}; radix_sv != ".")
+	      {
+		const string_view buffer_sv = {buffer, (size_t)output_length};
+		const size_t radix_index = buffer_sv.find(radix_sv);
+		if (radix_index != string_view::npos)
+		  {
+		    buffer[radix_index] = '.';
+		    if (radix_sv.length() > 1)
+		      {
+			memmove(&buffer[radix_index + 1],
+				&buffer[radix_index + radix_sv.length()],
+				output_length - radix_index - radix_sv.length());
+			output_length -= radix_sv.length() - 1;
+		      }
+		  }
+	      }
+
+	  // Copy the string from the buffer over to the output range.
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	  first += output_length;
+
+	  // Add the excess 0s to the result.
+	  if (excess_precision > 0)
+	    {
+	      if (fmt == chars_format::scientific)
+		{
+		  char* const significand_end
+		    = (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		       : first[-5] == 'e' ? &first[-5]
+		       : &first[-4]);
+		  __glibcxx_assert(*significand_end == 'e');
+		    memmove(significand_end + excess_precision, significand_end,
+			    first - significand_end);
+		    memset(significand_end, '0', excess_precision);
+		    first += excess_precision;
+		}
+	      else if (fmt == chars_format::fixed)
+		{
+		  memset(first, '0', excess_precision);
+		  first += excess_precision;
+		}
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::scientific)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_scientific_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // We can easily compute the output length exactly whenever the
+	  // scientific exponent is far enough away from +-100.  But if it's
+	  // near +-100, then our log2 approximation is too coarse (and doesn't
+	  // consider precision-dependent rounding) in order to accurately
+	  // distinguish between a scientific exponent of +-100 and +-99.
+	  const bool scientific_exponent_near_100_p
+	    = abs(abs(floor_log2_value) - 332) <= 4;
+
+	  // Compute an upper bound on the output length.  TODO: Maybe also
+	  // consider a lower bound on the output length.
+	  int output_length_upper_bound = sign + strlen("d");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+	  if (scientific_exponent_near_100_p
+	      || (floor_log2_value >= 332 || floor_log2_value <= -333))
+	    output_length_upper_bound += strlen("e+ddd");
+	  else
+	    output_length_upper_bound += strlen("e+dd");
+
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      // The result will definitely fit into the output range, so we can
+	      // write directly into it.
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    first, nullptr);
+	      __glibcxx_assert(output_length == output_length_upper_bound
+			       || (scientific_exponent_near_100_p
+				   && (output_length
+				       == output_length_upper_bound - 1)));
+	    }
+	  else if (scientific_exponent_near_100_p)
+	    {
+	      // Write the result of d2exp_buffered_n into an intermediate
+	      // buffer, do a bounds check, and copy the result into the output
+	      // range.
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						    buffer, nullptr);
+	      __glibcxx_assert(output_length == output_length_upper_bound - 1
+			       || output_length == output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  else
+	    // If the scientific exponent is not near 100, then the upper bound
+	    // is actually the exact length, and so the result will definitely
+	    // not fit into the output range.
+	    return {last, errc::value_too_large};
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Splice the excess zeros into the result.
+	      char* const significand_end = (first[-5] == 'e'
+					     ? &first[-5] : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+	      memmove(significand_end + excess_precision, significand_end,
+		      first - significand_end);
+	      memset(significand_end, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  const int effective_precision
+	    = min(precision, max_eff_fixed_precision);
+	  const int excess_precision = precision - effective_precision;
+
+	  // Compute an upper bound on the output length.  TODO: Maybe also
+	  // consider a lower bound on the output length.
+	  int output_length_upper_bound;
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  if (effective_precision > 0)
+	    output_length_upper_bound += strlen(".") + effective_precision;
+
+	  int output_length;
+	  if (last - first >= output_length_upper_bound + excess_precision)
+	    {
+	      // The result will definitely fit into the output range, so we can
+	      // write directly into it.
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      first);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // Write the result of d2fixed_buffered_n into an intermediate
+	      // buffer, do a bounds check, and copy the result into the output
+	      // range.
+	      char buffer[output_length_upper_bound];
+	      output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						      buffer);
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	      if (last - first < output_length + excess_precision)
+		return {last, errc::value_too_large};
+	      memcpy(first, buffer, output_length);
+	    }
+	  first += output_length;
+	  if (excess_precision > 0)
+	    {
+	      // Append the excess zeros into the result.
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	  return {first, errc{}};
+	}
+      else if (fmt == chars_format::general)
+	{
+	  // Handle the 'general' formatting mode as per C11 printf's %g output
+	  // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+	  // an intermediate buffer and manually perform zero-trimming there
+	  // before copying the result over to the output range.
+	  int effective_precision
+	    = min(precision, max_eff_scientific_precision + 1);
+	  const int output_length_upper_bound
+	    = strlen("-d.") + effective_precision + strlen("e+ddd");
+	  // The four bytes of headroom is to avoid needing to do a memmove when
+	  // rewriting a scientific form such as 1.00e-2 into the equivalent
+	  // fixed form 0.001.
+	  char buffer[4 + output_length_upper_bound];
+
+	  // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+	  if (effective_precision == 0)
+	    effective_precision = 1;
+
+	  // Perform a trial formatting in scientific form, and obtain the
+	  // scientific exponent.
+	  int scientific_exponent;
+	  char* buffer_start = buffer + 4;
+	  int output_length
+	    = ryu::d2exp_buffered_n(value, effective_precision - 1,
+				    buffer_start, &scientific_exponent);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+
+	  // 7.21.6.1/8: "Then, if a conversion with style E would have an
+	  // exponent of X:
+	  //   if P > X >= -4, the conversion is with style f and
+	  //     precision P - (X + 1).
+	  //   otherwise, the conversion is with style e and precision P - 1."
+	  const bool resolve_to_fixed_form
+	    = (scientific_exponent >= -4
+	       && scientific_exponent < effective_precision);
+	  if (resolve_to_fixed_form)
+	    {
+	      // Rather than invoking d2fixed_buffered_n to reformat the number
+	      // for us from scratch, we can just rewrite the scientific form
+	      // into fixed form in-place.  This is safe to do because whenever
+	      // %g resolves to %f, the fixed form will be no larger than the
+	      // corresponding scientific form, and it will also contain the
+	      // same significant digits as the scientific form.
+	      fmt = chars_format::fixed;
+	      if (scientific_exponent < 0)
+		{
+		  // e.g. buffer_start == "-1.234e-04"
+		  char* leading_digit = &buffer_start[sign];
+		  leading_digit[1] = leading_digit[0];
+		  // buffer_start == "-11234e-04"
+		  buffer_start -= -scientific_exponent;
+		  __glibcxx_assert(buffer_start >= buffer);
+		  // buffer_start == "????-11234e-04"
+		  char* head = buffer_start;
+		  if (sign)
+		    *head++ = '-';
+		  *head++ = '0';
+		  *head++ = '.';
+		  memset(head, '0', -scientific_exponent - 1);
+		  // buffer_start == "-0.00011234e-04"
+
+		  // Now drop the exponent suffix, and add the leading zeros to
+		  // the output length.
+		  output_length -= strlen("e-0d");
+		  output_length += -scientific_exponent;
+		  if (effective_precision - 1 == 0)
+		    // The scientific form had no decimal point, but the fixed
+		    // form now does.
+		    output_length += strlen(".");
+		}
+	      else if (effective_precision == 1)
+		{
+		  // The scientific exponent must be 0, so the fixed form
+		  // coincides with the scientific form (minus the exponent
+		  // suffix).
+		  __glibcxx_assert(scientific_exponent == 0);
+		  output_length -= strlen("e+dd");
+		}
+	      else
+		{
+		  // We are dealing with a scientific form which has a
+		  // non-empty fractional part and a nonnegative exponent,
+		  // e.g. buffer_start == "1.234e+02".
+		  __glibcxx_assert(effective_precision >= 1);
+		  char* const decimal_point = &buffer_start[sign + 1];
+		  __glibcxx_assert(*decimal_point == '.');
+		  memmove(decimal_point, decimal_point+1,
+			  scientific_exponent);
+		  // buffer_start == "123.4e+02"
+		  decimal_point[scientific_exponent] = '.';
+		  if (scientific_exponent >= 100)
+		    output_length -= strlen("e+ddd");
+		  else
+		    output_length -= strlen("e+dd");
+		  if (effective_precision - 1 == scientific_exponent)
+		    output_length -= strlen(".");
+		}
+	      effective_precision -= 1 + scientific_exponent;
+
+	      __glibcxx_assert(output_length <= output_length_upper_bound);
+	    }
+	  else
+	    {
+	      // We're sticking to the scientific form, so keep the output as-is.
+	      fmt = chars_format::scientific;
+	      effective_precision = effective_precision - 1;
+	    }
+
+	  // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+	  // the fractional portion of the result and the decimal-point
+	  // character is removed if there is no fractional portion remaining."
+	  if (effective_precision > 0)
+	    {
+	      char* decimal_point = nullptr;
+	      if (fmt == chars_format::scientific)
+		decimal_point = &buffer_start[sign + 1];
+	      else if (fmt == chars_format::fixed)
+		decimal_point
+		  = &buffer_start[output_length] - effective_precision - 1;
+	      __glibcxx_assert(*decimal_point == '.');
+
+	      char* const fractional_part_start = decimal_point + 1;
+	      char* fractional_part_end = nullptr;
+	      if (fmt == chars_format::scientific)
+		{
+		  fractional_part_end = (buffer_start[output_length-5] == 'e'
+					 ? &buffer_start[output_length-5]
+					 : &buffer_start[output_length-4]);
+		  __glibcxx_assert(*fractional_part_end == 'e');
+		}
+	      else if (fmt == chars_format::fixed)
+		fractional_part_end = &buffer_start[output_length];
+
+	      const string_view fractional_part
+		= {fractional_part_start, (size_t)(fractional_part_end
+						   - fractional_part_start) };
+	      const size_t last_nonzero_digit_pos
+		= fractional_part.find_last_not_of('0');
+
+	      char* trim_start;
+	      if (last_nonzero_digit_pos == string_view::npos)
+		trim_start = decimal_point;
+	      else
+		trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	      if (fmt == chars_format::scientific)
+		memmove(trim_start, fractional_part_end,
+			&buffer_start[output_length] - fractional_part_end);
+	      output_length -= fractional_part_end - trim_start;
+	    }
+
+	  if (last - first < output_length)
+	    return {last, errc::value_too_large};
+
+	  memcpy(first, buffer_start, output_length);
+	  return {first + output_length, errc{}};
+	}
+
+      __glibcxx_assert(false);
+      __builtin_unreachable();
+    }
+
+  // Define the overloads for float.
+  to_chars_result
+  to_chars(char* first, char* last, float value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, float value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for double.
+  to_chars_result
+  to_chars(char* first, char* last, double value) noexcept
+  { return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+  { return __floating_to_chars_shortest(first, last, value, fmt); }
+
+  to_chars_result
+  to_chars(char* first, char* last, double value, chars_format fmt,
+	   int precision) noexcept
+  { return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+  // Define the overloads for long double.
+  to_chars_result
+  to_chars(char* first, char* last, long double value) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value),
+					  chars_format{});
+    else
+      return __floating_to_chars_shortest(first, last, value, chars_format{});
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_shortest(first, last, double(value), fmt);
+    else
+      return __floating_to_chars_shortest(first, last, value, fmt);
+  }
+
+  to_chars_result
+  to_chars(char* first, char* last, long double value, chars_format fmt,
+	   int precision) noexcept
+  {
+    if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		  || LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+      return __floating_to_chars_precision(first, last, double(value), fmt,
+					   precision);
+    else
+      return __floating_to_chars_precision(first, last, value, fmt, precision);
+  }
+
+#ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
+  // Map the -mlong-double-64 long double overloads to the double overloads.
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_e(char* first, char* last, double value) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_d")));
+
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_eSt12chars_format(char* first, char* last, double value,
+				     chars_format fmt) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_format")));
+
+  extern "C" to_chars_result
+  _ZSt8to_charsPcS_eSt12chars_formati(char* first, char* last, double value,
+				      chars_format fmt, int precision) noexcept
+    __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_formati")));
+#endif
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..d995aa02d09
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,197 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cfenv>
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Test that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
-- 
2.28.0.rc1

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Wed, 22 Jul 2020, Patrick Palka wrote:

> On Mon, 20 Jul 2020, Patrick Palka wrote:
> 
> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > 
> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > 
> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > >
> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > > >
> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > > > > >
> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > > > > > >
> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> > > > > > > float,
> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > > > shortest
> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> > > > > float,
> > > > > > > double
> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > > > > > scientific
> > > > > > > > > > formatting of float and double. For formatting long double with
> > > > > an
> > > > > > > > > > explicit precision argument we use a printf fallback.
> > > > > Hexadecimal
> > > > > > > > > > formatting for float, double and long double is implemented from
> > > > > > > > > > scratch.
> > > > > > > > > >
> > > > > > > > > > The supported long double binary formats are float64 (same as
> > > > > > > double),
> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > > > > > > >
> > > > > > > > > > Much of the complexity of the implementation is in computing the
> > > > > > > exact
> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > > > bounds
> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > > > before
> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > > > the
> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > > > (if
> > > > > > > the
> > > > > > > > > > output range is smaller than the upper bound).
> > > > > > > > > >
> > > > > > > > > > Another source of complexity is in the general-with-precision
> > > > > > > formatting
> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > > > by
> > > > > > > Ryu, and
> > > > > > > > > > where we also take care to avoid having to format the string a
> > > > > > > second
> > > > > > > > > > time when the general formatting mode resolves to fixed.
> > > > > > > > > >
> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > > > > > > >
> > > > > > > > > > libstdc++-v3/ChangeLog:
> > > > > > > > > >
> > > > > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > > > > > 	* configure: Regenerate.
> > > > > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > > > > > 	overloads for float, double and long double.
> > > > > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > > > > >
> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > > > to
> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > > > > > format
> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > > > The
> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > > > > > uint64_t
> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > > > > > case.
> > > > > > > >
> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > > > most
> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > > > mode.
> > > > > > >
> > > > > > > Here's v4, which should now correctly support using <charconv> with
> > > > > > > -mlong-double-64 on targets with a large default long double type.
> > > > > > > This is done by defining the long double to_chars overloads as inline
> > > > > > > wrappers around the double overloads within <charconv> whenever
> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > > > >
> > > > > > >
> > > > > > > -- >8 --
> > > > > > >
> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > > > > >  implementation
> > > > > > >
> > > > > > > This implements the floating-point std::to_chars overloads for float,
> > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > shortest
> > > > > > > round-trippable fixed and scientific forms of a number for float,
> > > > > double
> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> > > > > > > fixed and scientific formatting of float and double. For
> > > > > > > explicit-precision formatting of long double we fall back to using
> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > > > > > implemented from scratch.
> > > > > > >
> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > > > > > >
> > > > > > > Much of the complexity of the implementation is in computing the exact
> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> > > > > > > necessary.
> > > > > > >
> > > > > > > Another source of complexity is in the general-with-precision
> > > > > formatting
> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > > > > and where we also take care to avoid having to format the string a
> > > > > > > second time when the general formatting mode resolves to fixed.
> > > > > > >
> > > > > > > This implementation is non-conforming in a couple of ways:
> > > > > > >
> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > > > > >    Microsoft implementation's approach of being consistent with the
> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > > > > >    printing the shortest representation.  For example, the shortest
> > > > > hex
> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > > > > >    latter, as does printf.
> > > > > > >
> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > > > > >    large long double type but lack __int128.  For such targets we make
> > > > > > >    the long double to_chars overloads go through the double overloads,
> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > > > > >    by writing a specialized version of the generic Ryu formatting
> > > > > > >    routine which works with uint64_t instead of __int128.)
> > > > > > >
> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > > > > >    round-trippability if the difference between the high- and
> > > > > low-order
> > > > > > >    exponent is too large.  This is because we treat the type as if it
> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > > > low-order
> > > > > > >    mantissas, so we potentially lose precision from the low-order
> > > > > part.
> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> > > > > seems
> > > > > > >    consistent with how printf formats __ibm128.
> > > > > > >
> > > > > > > libstdc++-v3/ChangeLog:
> > > > > > >
> > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
> > > > > > > 	* configure: Regenerate.
> > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
> > > > > > > 	overloads for float, double and long double.
> > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > > > 	* src/c++17/Makefile.in: Regenerate.
> > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
> > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > > > ---
> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > > > > >  libstdc++-v3/configure                        |    2 +-
> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > > > +++++++++++++++++
> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > > > >  create mode 100644
> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > > > >
> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > > > >  fi
> > > > > > >
> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > > > -libtool_VERSION=6:28:0
> > > > > > > +libtool_VERSION=6:29:0
> > > > > > >
> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > > >  case $enable_symvers in
> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > > > >
> > > > > > >  } GLIBCXX_3.4.27;
> > > > > > >
> > > > > > > +GLIBCXX_3.4.29 {
> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > > > > +
> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > > chars_format)
> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > > > > +
> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > > chars_format,
> > > > > > > int)
> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > > > > +
> > > > > > > +} GLIBCXX_3.4.28;
> > > > > > > +
> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > > > > >  CXXABI_1.3 {
> > > > > > >
> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > > > > > index dd54bd406a9..73f771e7335 100755
> > > > > > > --- a/libstdc++-v3/configure
> > > > > > > +++ b/libstdc++-v3/configure
> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > > > versioning
> > > > > > > will be disabled." >&2;}
> > > > > > >  fi
> > > > > > >
> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > > > -libtool_VERSION=6:28:0
> > > > > > > +libtool_VERSION=6:29:0
> > > > > > >
> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > > >  case $enable_symvers in
> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > > > > b/libstdc++-v3/include/std/charconv
> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > > > >
> > > > > > > +  // Floating-point std::to_chars
> > > > > > > +
> > > > > > > +  // Overloads for float.
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > __value)
> > > > > > > noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > __value,
> > > > > > > +			   chars_format __fmt) noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > __value,
> > > > > > > +			   chars_format __fmt, int __precision)
> > > > > noexcept;
> > > > > > > +
> > > > > > > +  // Overloads for double.
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > __value)
> > > > > > > noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > __value,
> > > > > > > +			   chars_format __fmt) noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > __value,
> > > > > > > +			   chars_format __fmt, int __precision)
> > > > > noexcept;
> > > > > > > +
> > > > > > > +  // Overloads for long double.
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > > __value)
> > > > > > > +    noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > > __value,
> > > > > > > +			   chars_format __fmt) noexcept;
> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > > > __value,
> > > > > > > +			   chars_format __fmt, int __precision)
> > > > > noexcept;
> > > > > > > +
> > > > > > > +  // If long double has the same binary format as double, then we
> > > > > just
> > > > > > > define
> > > > > > > +  // the long double overloads as wrappers around the corresponding
> > > > > > > double
> > > > > > > +  // overloads.
> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > > > > +  inline to_chars_result
> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > > > > > +
> > > > > > > +  inline to_chars_result
> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > > > +	   chars_format __fmt) noexcept
> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > > > > > +
> > > > > > > +  inline to_chars_result
> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > > > +	   chars_format __fmt, int __precision) noexcept
> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > > > > > __precision); }
> > > > > > > +#endif
> > > > > >
> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > > > > introduce an ODR violation because each long double to_chars overload
> > > > > > could potentially have two different definitions available in a program,
> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > > > > -mlong-double-64)..
> > > > > 
> > > > > But they have different mangled names, so there's no ODR violation.
> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> > > > > where there's no -mlong-double-64 switch, where double and long double
> > > > > are always the same representation.
> > > > > 
> > > > > What I'm doing for std::from_chars is adding this in the new
> > > > > src/c++17/floating_from_chars.cc file:
> > > > > 
> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > > > extern "C" from_chars_result
> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > > #endif
> > > > > 
> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > > > double).
> > > > 
> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > > 
> > > Actually that should be:
> > > 
> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > extern "C" from_chars_result
> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > > 					 long double& value,
> > > 					 chars_format fmt) noexcept
> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > #endif
> > > 
> > > With the right parameter list I don't need to disable the warning.
> > 
> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> 
> Here's v6 which is rebased against the floating-point from_chars patch
> and which also works around a false-positive -Wmaybe-uninitialized
> warning in __floating_to_chars_hex, as well as performs some minor
> commentary/style cleanups:

Here's v7, with the following changes:

* Remove extraneous indentation (two spaces when inside the std
  namespace, two spaces after a template header) for better consistency
  with floating_from_chars.cc
* Guard the calls to fe[gs]etround with a preprocessor test for
  _GLIBCXX_USE_C99_FENV_TR1;
* Properly XFAIL the new long_double.cc test on targets with a
  large long double type but without __int128, most notably i386
* Reword the commit message slightly.

-- >8 --

Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation

This implements the floating-point std::to_chars overloads for float,
double and long double.  We use the Ryu library to compute the shortest
round-trippable fixed and scientific forms for float, double and long
double.  We also use Ryu for performing explicit-precision fixed and
scientific formatting of float and double. For explicit-precision
formatting of long double we fall back to using printf.  Hexadecimal
formatting for float, double and long double is implemented from
scratch.

The supported long double binary formats are binary64, binary80 (x86
80-bit extended precision), binary128 and ibm128.

Much of the complexity of the implementation is in computing the exact
output length before handing it off to Ryu (which doesn't do bounds
checking).  In some cases it's hard to compute the output length
beforehand, so in these cases we instead compute an upper bound on the
output length and use a sufficiently-sized intermediate buffer only if
necessary.

Another source of complexity is in the general-with-precision formatting
mode, where we need to do zero-trimming of the string returned by Ryu,
and where we also take care to avoid having to format the number through
Ryu a second time when the general formatting mode resolves to fixed
(which we determine by doing a scientific formatting first and
inspecting the scientific exponent).  We avoid going through Ryu twice
by instead transforming the scientific form to the corresponding fixed
form via in-place string manipulation.

This implementation is non-conforming in a couple of ways:

1. For the shortest hexadecimal formatting, we currently follow the
   Microsoft implementation's decision to be consistent with the
   output of printf's '%a' specifier at the expense of sometimes not
   printing the shortest representation.  For example, the shortest hex
   form for the number 1.08p+0 is 2.1p-1, but we output the former
   instead of the latter, as does printf.

2. The Ryu routine generic_binary_to_decimal that we use for performing
   shortest formatting for large floating point types is implemented
   using the __int128 type, but some targets with a large long double
   type lack __int128 (e.g. i686), so we can't perform shortest
   formatting of long double on such targets through Ryu.  As a
   temporary stopgap this patch makes the long double to_chars overloads
   just dispatch to the double overloads on these targets, which means
   we lose precision in the output.  (We could potentially fix this by
   writing a specialized version of Ryu's generic_binary_to_decimal
   routine that uses uint64_t instead of __int128.)  [Though I wonder if
   there's a better way to work around the lack of __int128 on i686
   specifically?]

3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
   property if the difference between the high- and low-order exponent
   is large.  This is because we treat __ibm128 as if it has a
   contiguous 105-bit mantissa by merging the mantissas of the high-
   and low-order parts (using code extracted from glibc), so we
   potentially lose precision from the low-order part.  This seems to be
   consistent with how glibc printf formats __ibm128.

libstdc++-v3/ChangeLog:

	* config/abi/pre/gnu.ver: Add new exports.
	* include/std/charconv (to_chars): Declare the floating-point
	overloads for float, double and long double.
	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
	* src/c++17/Makefile.in: Regenerate.
	* src/c++17/floating_to_chars.cc: New file.
	(to_chars): Define for float, double and long double.
	* testsuite/20_util/to_chars/long_double.cc: New test.
---
 libstdc++-v3/config/abi/pre/gnu.ver           |    7 +
 libstdc++-v3/include/std/charconv             |   24 +
 libstdc++-v3/src/c++17/Makefile.am            |    1 +
 libstdc++-v3/src/c++17/Makefile.in            |    3 +-
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 1564 +++++++++++++++++
 .../testsuite/20_util/to_chars/long_double.cc |  199 +++
 6 files changed, 1797 insertions(+), 1 deletion(-)
 create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/long_double.cc

diff --git a/libstdc++-v3/config/abi/pre/gnu.ver b/libstdc++-v3/config/abi/pre/gnu.ver
index 5ffe9d95289..c1f44d42ae5 100644
--- a/libstdc++-v3/config/abi/pre/gnu.ver
+++ b/libstdc++-v3/config/abi/pre/gnu.ver
@@ -2320,6 +2320,13 @@ GLIBCXX_3.4.29 {
     _ZNSbIwSt11char_traitsIwESaIwEE7reserveEv;
     _ZNSt7__cxx1112basic_stringI[cw]St11char_traitsI[cw]ESaI[cw]EE7reserveEv;
 
+    # std::to_chars(char*, char*, [float|double|long double])
+    _ZSt8to_charsPcS_[defg];
+    # std::to_chars(char*, char*, [float|double|long double], chars_format)
+    _ZSt8to_charsPcS_[defg]St12chars_format;
+    # std::to_chars(char*, char*, [float|double|long double], chars_format, int)
+    _ZSt8to_charsPcS_[defg]St12chars_formati;
+
 } GLIBCXX_3.4.28;
 
 # Symbols in the support library (libsupc++) have their own tag.
diff --git a/libstdc++-v3/include/std/charconv b/libstdc++-v3/include/std/charconv
index be668c1939e..b0f8a6106bc 100644
--- a/libstdc++-v3/include/std/charconv
+++ b/libstdc++-v3/include/std/charconv
@@ -702,6 +702,30 @@ namespace __detail
 	     chars_format __fmt = chars_format::general);
 #endif
 
+  // Floating-point std::to_chars
+
+  // Overloads for float.
+  to_chars_result to_chars(char* __first, char* __last, float __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, float __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for double.
+  to_chars_result to_chars(char* __first, char* __last, double __value) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
+  // Overloads for long double.
+  to_chars_result to_chars(char* __first, char* __last, long double __value)
+    noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt) noexcept;
+  to_chars_result to_chars(char* __first, char* __last, long double __value,
+			   chars_format __fmt, int __precision) noexcept;
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace std
 #endif // C++14
diff --git a/libstdc++-v3/src/c++17/Makefile.am b/libstdc++-v3/src/c++17/Makefile.am
index 642efb976ac..0f5b7eb8e56 100644
--- a/libstdc++-v3/src/c++17/Makefile.am
+++ b/libstdc++-v3/src/c++17/Makefile.am
@@ -51,6 +51,7 @@ endif
 
 sources = \
 	floating_from_chars.cc \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/Makefile.in b/libstdc++-v3/src/c++17/Makefile.in
index ce08eb3ff11..bf291d7f236 100644
--- a/libstdc++-v3/src/c++17/Makefile.in
+++ b/libstdc++-v3/src/c++17/Makefile.in
@@ -124,7 +124,7 @@ LTLIBRARIES = $(noinst_LTLIBRARIES)
 libc__17convenience_la_LIBADD =
 @ENABLE_DUAL_ABI_TRUE@am__objects_1 = cow-fs_dir.lo cow-fs_ops.lo \
 @ENABLE_DUAL_ABI_TRUE@	cow-fs_path.lo
-am__objects_2 = floating_from_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
+am__objects_2 = floating_from_chars.lo floating_to_chars.lo fs_dir.lo fs_ops.lo fs_path.lo \
 	memory_resource.lo $(am__objects_1)
 @ENABLE_DUAL_ABI_TRUE@am__objects_3 = cow-string-inst.lo
 @ENABLE_EXTERN_TEMPLATE_TRUE@am__objects_4 = ostream-inst.lo \
@@ -436,6 +436,7 @@ headers =
 
 sources = \
 	floating_from_chars.cc \
+	floating_to_chars.cc \
 	fs_dir.cc \
 	fs_ops.cc \
 	fs_path.cc \
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
new file mode 100644
index 00000000000..7020c580d5f
--- /dev/null
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -0,0 +1,1564 @@
+// std::to_chars implementation for floating-point types -*- C++ -*-
+
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+// <http://www.gnu.org/licenses/>.
+
+// Activate __glibcxx_assert within this file to shake out any bugs.
+#define _GLIBCXX_ASSERTIONS
+
+#include <charconv>
+
+#include <bit>
+#include <cfenv>
+#include <cassert>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <langinfo.h>
+#include <optional>
+#include <string_view>
+#include <type_traits>
+
+// Determine the binary format of 'long double'.
+
+// We support the binary64, float80 (i.e. x86 80-bit extended precision),
+// binary128, and ibm128 formats.
+#define LDK_UNSUPPORTED 0
+#define LDK_BINARY64    1
+#define LDK_FLOAT80     2
+#define LDK_BINARY128   3
+#define LDK_IBM128      4
+
+#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
+# define LONG_DOUBLE_KIND LDK_BINARY64
+#elif defined(__SIZEOF_INT128__)
+// The Ryu routines need a 128-bit integer type in order to do shortest
+// formatting of types larger than 64-bit double, so without __int128 we can't
+// support any large long double format.  This is the case for e.g. i386.
+# if __LDBL_MANT_DIG__ == 64
+#  define LONG_DOUBLE_KIND LDK_FLOAT80
+# elif __LDBL_MANT_DIG__ == 113
+#  define LONG_DOUBLE_KIND LDK_BINARY128
+# elif __LDBL_MANT_DIG__ == 106
+#  define LONG_DOUBLE_KIND LDK_IBM128
+# endif
+#endif
+#if !defined(LONG_DOUBLE_KIND)
+# define LONG_DOUBLE_KIND LDK_UNSUPPORTED
+#endif
+
+namespace
+{
+  namespace ryu
+  {
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+#include "ryu/d2s_full_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/d2s.c"
+#include "ryu/d2fixed.c"
+#include "ryu/f2s.c"
+
+#ifdef __SIZEOF_INT128__
+    namespace generic128
+    {
+      // Put the generic Ryu bits in their own namespace to avoid name conflicts.
+# include "ryu/generic_128.h"
+# include "ryu/ryu_generic_128.h"
+# include "ryu/generic_128.c"
+    } // namespace generic128
+
+    using generic128::floating_decimal_128;
+    using generic128::generic_binary_to_decimal;
+
+    int
+    to_chars(const floating_decimal_128 v, char* const result)
+    { return generic128::generic_to_chars(v, result); }
+#endif
+  } // namespace ryu
+
+  // A traits class that contains pertinent information about the binary
+  // format of each of the floating-point types we support.
+  template<typename T>
+    struct floating_type_traits
+    { };
+
+  template<>
+    struct floating_type_traits<float>
+    {
+      // We (and Ryu) assume float has the IEEE binary32 format.
+      static_assert(__FLT_MANT_DIG__ == 24);
+      static constexpr int mantissa_bits = 23;
+      static constexpr int exponent_bits = 8;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint32_t;
+      using shortest_scientific_t = ryu::floating_decimal_32;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000011101011100110101100101101110000000000000000000000000 };
+    };
+
+  template<>
+    struct floating_type_traits<double>
+    {
+      // We (and Ryu) assume double has the IEEE binary64 format.
+      static_assert(__DBL_MANT_DIG__ == 53);
+      static constexpr int mantissa_bits = 52;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_64;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000011000110101110111000001100101110000111100,
+	    0b0111100011110101011000011110000000110110010101011000001110011111,
+	    0b0101101100000000011100100100111100110110110100010001010101110000,
+	    0b0011110010111000101111110101100011101100010001010000000101100111,
+	    0b0001010000011001011100100001010000010101101000001101000000000000 };
+    };
+
+#if LONG_DOUBLE_KIND == LDK_BINARY64
+  // When long double is equivalent to double, we just forward the long double
+  // overloads to the double overloads, so we don't need to define a a
+  // floating_type_traits<long double> specialization in this case.
+#elif LONG_DOUBLE_KIND == LDK_FLOAT80
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 64;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = false;
+      using mantissa_t = uint64_t;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000110101011111110100010100110000011101,
+	    0b1001100101001111010011011111101000101111110001011001011101110000,
+	    0b0000101111111011110010001000001010111101011110111111010100011001,
+	    0b0011100000011111001101101011111001111100100010000101001111101001,
+	    0b0100100100000000100111010010101110011000110001101101110011001010,
+	    0b0111100111100010100000010011000010010110101111110101000011110100,
+	    0b1010100111100010011110000011011101101100010110000110101010101010,
+	    0b0000001111001111000000101100111011011000101000110011101100110010,
+	    0b0111000011100100101101010100001101111110101111001000010011111111,
+	    0b0010111000100110100100100010101100111010110001101010010111001000,
+	    0b0000100000010110000011001001000111000001111010100101101000001111,
+	    0b0010101011101000111100001011000010011101000101010010010000101111,
+	    0b1011111011101101110010101011010001111000101000101101011001100011,
+	    0b1010111011011011110111110011001010000010011001110100101101000101,
+	    0b0011000001110110011010010000011100100011001011001100001101010110,
+	    0b0100011111011000111111101000011110000010111110101001000000001001,
+	    0b1110000001110001001101101110011000100000001010000111100010111010,
+	    0b1110001001010011101000111000001000010100110000010110100011110000,
+	    0b0000011010110000110001111000011111000011001101001101001001000110,
+	    0b1010010111001000101001100101010110100100100010010010000101000010,
+	    0b1011001110000111100010100110000011100011111001110111001100000101,
+	    0b0110101001001000010110001000010001010101110101100001111100011001,
+	    0b1111100011110101011110011010101001010010100011000010110001101001,
+	    0b0100000100001000111101011100010011011111011001000000001100011000,
+	    0b1110111111000111100101110111110000000011001110011100011011011001,
+	    0b1100001100100000010001100011011000111011110000110011010101000011,
+	    0b1111111011100111011101001111111000010000001111010111110010000100,
+	    0b1110111001111110101111000101000000001010001110011010001000111010,
+	    0b1000010001011000101111111010110011111101110101101001111000111010,
+	    0b0100000111101001000111011001101000001010111011101001101111000100,
+	    0b0000011100110001000111011100111100110001101111111010110111100000,
+	    0b0000011101011100100110010011110101010100010011110010010111010000,
+	    0b0011011001100111110101111100001001101110101101001110110011110110,
+	    0b1011000101000001110100111001100100111100110011110000000001101000,
+	    0b1011100011110100001001110101010110111001000000001011101001011110,
+	    0b1111001010010010100000010110101010101011101000101000000000001100,
+	    0b1000001111100100111001110101100001010011111111000001000011110000,
+	    0b0001011101001000010000101101111000001110101100110011001100110111,
+	    0b1110011100000010101011011111001010111101111110100000011100000011,
+	    0b1001110110011100101010011110100010110001001110110000101011100110,
+	    0b1001101000100011100111010000011011100001000000110101100100001001,
+	    0b1010111000101000101101010111000010001100001010100011111100000100,
+	    0b0111101000100011000101101011111011100010001101110111001111001011,
+	    0b1110100111010110001110110110000000010110100011110000010001111100,
+	    0b1100010100011010001011001000111001010101011110100101011001000000,
+	    0b0000110001111001100110010110111010101101001101000000000010010101,
+	    0b0001110111101000001111101010110010010000111110111100000111110100,
+	    0b0111110111001001111000110001101101001010101110110101111110000100,
+	    0b0000111110111010101111100010111010011100010110011011011001000001,
+	    0b1010010100100100101110111111111000101100000010111111101101000110,
+	    0b1000100111111101100011001101000110001000000100010101010100001101,
+	    0b1100101010101000111100101100001000110001110010100000000010110101,
+	    0b1010000100111101100100101010010110100010000000110101101110000100,
+	    0b1011111011110001110000100100000000001010111010001101100000100100,
+	    0b0111101101100011001110011100000001000101101101111000100111011111,
+	    0b0100111010010011011001010011110100001100111010010101111111100011,
+	    0b0010001001011000111000001100110111110111110010100011000110110110,
+	    0b0101010110000000010000100000110100111011111101000100000111010010,
+	    0b0110000011011101000001010100110101101110011100110101000000001001,
+	    0b1101100110100000011000001111000100100100110001100110101010101100,
+	    0b0010100101010110010010001010101000011111111111001011001010001111,
+	    0b0111001010001111001100111001010101001000110101000011110000001000,
+	    0b0110010011001001001111110001010010001011010010001101110110110011,
+	    0b0110010100111011000100111000001001101011111001110010111110111111,
+	    0b0101110111001001101100110100101001110010101110011001101110001000,
+	    0b0100110101010111011010001100010111100011010011111001010100111000,
+	    0b0111000110110111011110100100010111000110000110110110110001111110,
+	    0b1000101101010100100100111110100011110110110010011001110011110101,
+	    0b1001101110101001010100111101101011000101000010110101101111110000,
+	    0b0100100101001011011001001011000010001101001010010001010110101000,
+	    0b0010100001001011100110101000010110000111000111000011100101011011,
+	    0b0110111000011001111101101011111010001000000010101000101010011110,
+	    0b1000110110100001111011000001111100001001000000010110010100100100,
+	    0b1001110100011111100111101011010000010101011100101000010010100110,
+	    0b0001010110101110100010101010001110110110100011101010001001111100,
+	    0b1010100101101100000010110011100110100010010000100100001110000100,
+	    0b0001000000010000001010000010100110000001110100111001110111101101,
+	    0b1100000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_BINARY128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 112;
+      static constexpr int exponent_bits = 15;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000000100000010000000,
+	    0b1011001111110100000100010101101110011100100110000110010110011000,
+	    0b1010100010001101111111000000001101010010100010010000111011110111,
+	    0b1011111001110001111000011111000010110111000111110100101010100101,
+	    0b0110100110011110011011000011000010011001110001001001010011100011,
+	    0b0000011111110010101111101011101010000110011111100111001110100111,
+	    0b0100010101010110000010111011110100000010011001001010001110111101,
+	    0b1101110111000010001101100000110100000111001001101011000101011011,
+	    0b0100111011101101010000001101011000101100101110010010110000101011,
+	    0b0100000110111000000110101000010011101000110100010110000011101101,
+	    0b1011001101001000100001010001100100001111011101010101110001010110,
+	    0b1000000001000000101001110010110010001111101101010101001100000110,
+	    0b0101110110100110000110000001001010111110001110010000111111010011,
+	    0b1010001111100111000100011100100100111100100101000001011001000111,
+	    0b1010011000011100110101100111001011100101111111100001110100000100,
+	    0b1100011100100010100000110001001010000000100000001001010111011101,
+	    0b0101110000100011001111101101000000100110000010010111010001111010,
+	    0b0100111100011010110111101000100110000111001001101100000001111100,
+	    0b1100100100111110101011000100000101011010110111000111110100110101,
+	    0b0110010000010111010100110011000000111010000010111011010110000100,
+	    0b0101001001010010110111010111000101011100000111100111000001110010,
+	    0b1101111111001011101010110001000111011010111101001011010110100100,
+	    0b0001000100110000011111101011001101110010110110010000000011100100,
+	    0b0001000000000101001001001000000000011000100011001110101001001110,
+	    0b0010010010001000111010011011100001000110011011011110110100111000,
+	    0b0000100110101100000111100010100100011100110111011100001111001100,
+	    0b1011111010001110001100000011110111111111100000001011111111101100,
+	    0b0000011100001111010101110000100110111100101101110111101001000001,
+	    0b1100010001110110111100001001001101101000011100000010110101001011,
+	    0b0100101001101011111001011110101101100011011111011100101010101111,
+	    0b0001101001111001110000101101101100001011010001011110011101000010,
+	    0b1111000000101001101111011010110011101110100001011011001011100010,
+	    0b0101001010111101101100001111100010010110001101001000001101100100,
+	    0b0101100101011110001100101011111000111001111001001001101101100001,
+	    0b1111001101010010100100011011000110110010001111000111010001001101,
+	    0b0001110010011000000001000110110111011000011100001000011001110111,
+	    0b0100001011011011011011110011101100100101111111101100101000001110,
+	    0b0101011110111101010111100111101111000101111111111110100011011010,
+	    0b1110101010001001110100000010110111010111111010111110100110010110,
+	    0b1010001111100001001100101000110100001100011100110010000011010111,
+	    0b1111111101101111000100111100000101011000001110011011101010111001,
+	    0b1111101100001110100101111101011001000100000101110000110010100011,
+	    0b1001010110110101101101000101010001010000101011011111010011010000,
+	    0b0111001110110011101001100111000001000100001010110000010000001101,
+	    0b0101111100111110100111011001111001111011011110010111010011101010,
+	    0b1110111000000001100100111001100100110001011011001110101111110111,
+	    0b0001010001001101010111101010011111000011110001101101011001111111,
+	    0b0101000011100011010010001101100001011101011010100110101100100010,
+	    0b0001000101011000100101111100110110000101101101111000110001001011,
+	    0b0101100101001011011000010101000000010100011100101101000010011111,
+	    0b1000010010001011101001011010100010111011110100110011011000100111,
+	    0b1000011011100001010111010111010011101100100010010010100100101001,
+	    0b1001001001010111110101000010111010000000101111010100001010010010,
+	    0b0011011110110010010101111011000001000000000011011111000011111011,
+	    0b1011000110100011001110000001000100000001011100010111010010011110,
+	    0b0111101110110101110111110000011000000100011100011000101101101110,
+	    0b1001100101111011011100011110101011001111100111101010101010110111,
+	    0b1100110010010001100011001111010000000100011101001111011101001111,
+	    0b1000111001111010100101000010000100000001001100101010001011001101,
+	    0b0011101011110000110010100101010100110010100001000010101011111101,
+	    0b1100000000000110000010101011000000011101000110011111100010111111,
+	    0b0010100110000011011100010110111100010110101100110011101110001101,
+	    0b0010111101010011111000111001111100110111111100100011110001101110,
+	    0b1001110111001001101001001001011000010100110001000000100011010110,
+	    0b0011110101100111011011111100001000011001010100111100100101111010,
+	    0b0010001101000011000010100101110000010101101000100110000100001010,
+	    0b0010000010100110010101100101110011101111000111111111001001100001,
+	    0b0100111111011011011011100111111011000010011101101111011111110110,
+	    0b1111111111010110101011101000100101110100001110001001101011100111,
+	    0b1011111101000101110000111100100010111010100001010000010010110010,
+	    0b1111010101001011101011101010000100110110001110111100100110111111,
+	    0b1011001101000001001101000010101010010110010001100001011100011010,
+	    0b0101001011011101010001110100010000010001111100100100100001001101,
+	    0b0010100000111001100011000101100101000001111100111001101000000010,
+	    0b1011001111010101011001000100100110100100110111110100000110111000,
+	    0b0101011111010011100011010010111101110010100001111111100010001001,
+	    0b0010111011101100100000000000001111111010011101100111100001001101,
+	    0b1101000000000000000000000000000000000000000000000000000000000000 };
+    };
+#elif LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    struct floating_type_traits<long double>
+    {
+      static constexpr int mantissa_bits = 105;
+      static constexpr int exponent_bits = 11;
+      static constexpr bool has_implicit_leading_bit = true;
+      using mantissa_t = unsigned __int128;
+      using shortest_scientific_t = ryu::floating_decimal_128;
+
+      static constexpr uint64_t pow10_adjustment_tab[]
+	= { 0b0000000000000000000000000000000000000000000000001000000100000000,
+	    0b0000000000000000000100000000000000000000001000000000000000000010,
+	    0b0000100000000000000000001001000000000000000001100100000000000000,
+	    0b0011000000000000000000000000000001110000010000000000000000000000,
+	    0b0000100000000000001000000000000000000000000000100000000000000000 };
+    };
+#endif
+
+  // An IEEE-style decomposition of a floating-point value of type T.
+  template<typename T>
+    struct ieee_t
+    {
+      typename floating_type_traits<T>::mantissa_t mantissa;
+      uint32_t biased_exponent;
+      bool sign;
+    };
+
+  // Decompose the floating-point value into its IEEE components.
+  template<typename T>
+    ieee_t<T>
+    get_ieee_repr(const T value)
+    {
+      constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+      constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+      constexpr int total_bits = mantissa_bits + exponent_bits + 1;
+
+      constexpr auto get_uint_t = [] {
+	if constexpr (total_bits <= 32)
+	  return uint32_t{};
+	else if constexpr (total_bits <= 64)
+	  return uint64_t{};
+#ifdef __SIZEOF_INT128__
+	else if constexpr (total_bits <= 128)
+	  return (unsigned __int128){};
+#endif
+      };
+      using uint_t = decltype(get_uint_t());
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value));
+
+      ieee_t<T> ieee_repr;
+      ieee_repr.mantissa = value_bits & ((uint_t{1} << mantissa_bits) - 1u);
+      ieee_repr.biased_exponent
+	= (value_bits >> mantissa_bits) & ((uint_t{1} << exponent_bits) - 1u);
+      ieee_repr.sign = (value_bits >> (mantissa_bits + exponent_bits)) & 1;
+      return ieee_repr;
+    }
+
+#if LONG_DOUBLE_KIND == LDK_IBM128
+  template<>
+    ieee_t<long double>
+    get_ieee_repr(const long double value)
+    {
+      // The layout of __ibm128 isn't compatible with the standard IEEE format.
+      // So we transform it into an IEEE-compatible format, suitable for
+      // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit
+      // mantissa (plus an implicit leading bit).  We use the exponent and sign
+      // of the high part, and we merge the mantissa of the high part with the
+      // mantissa (and the implicit leading bit) of the low part.
+      using uint_t = unsigned __int128;
+      uint_t value_bits = 0;
+      memcpy(&value_bits, &value, sizeof(value_bits));
+
+      const uint64_t value_hi = value_bits;
+      const uint64_t value_lo = value_bits >> 64;
+
+      uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1);
+      unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1);
+      const int sign_hi = (value_hi >> 63) & 1;
+
+      uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1);
+      const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1);
+      const int sign_lo = (value_lo >> 63) & 1;
+
+	{
+	  // The following code for adjusting the low-part mantissa to combine
+	  // it with the high-part mantissa is taken from the glibc source file
+	  // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c.
+	  mantissa_lo <<= 7;
+	  if (exponent_lo != 0)
+	    mantissa_lo |= (1ull << (52 + 7));
+	  else
+	    mantissa_lo <<= 1;
+
+	  const int ediff = exponent_hi - exponent_lo - 53;
+	  if (ediff > 63)
+	    mantissa_lo = 0;
+	  else if (ediff > 0)
+	    mantissa_lo >>= ediff;
+	  else if (ediff < 0)
+	    mantissa_lo <<= -ediff;
+
+	  if (sign_lo != sign_hi && mantissa_lo != 0)
+	    {
+	      mantissa_lo = (1ull << 60) - mantissa_lo;
+	      if (mantissa_hi == 0)
+		{
+		  mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59);
+		  mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1);
+		  exponent_hi--;
+		}
+	      else
+		mantissa_hi--;
+	    }
+	}
+
+      ieee_t<long double> ieee_repr;
+      ieee_repr.mantissa = ((uint_t{mantissa_hi} << 64)
+			    | (uint_t{mantissa_lo} << 4)) >> 11;
+      ieee_repr.biased_exponent = exponent_hi;
+      ieee_repr.sign = sign_hi;
+      return ieee_repr;
+    }
+#endif
+
+  // Invoke Ryu to obtain the shortest scientific form for the given
+  // floating-point number.
+  template<typename T>
+    typename floating_type_traits<T>::shortest_scientific_t
+    floating_to_shortest_scientific(const T value)
+    {
+      if constexpr (std::is_same_v<T, float>)
+	return ryu::floating_to_fd32(value);
+      else if constexpr (std::is_same_v<T, double>)
+	return ryu::floating_to_fd64(value);
+#ifdef __SIZEOF_INT128__
+      else if constexpr (std::is_same_v<T, long double>)
+	{
+	  constexpr int mantissa_bits
+	    = floating_type_traits<T>::mantissa_bits;
+	  constexpr int exponent_bits
+	    = floating_type_traits<T>::exponent_bits;
+	  constexpr bool has_implicit_leading_bit
+	    = floating_type_traits<T>::has_implicit_leading_bit;
+
+	  const auto [mantissa, exponent, sign] = get_ieee_repr(value);
+	  return ryu::generic_binary_to_decimal(mantissa, exponent, sign,
+						mantissa_bits, exponent_bits,
+						!has_implicit_leading_bit);
+	}
+#endif
+    }
+
+  // This subroutine returns true if the shortest scientific form fd is a
+  // positive power of 10, and the floating-point number that has this shortest
+  // scientific form is smaller than this power of 10.
+  //
+  // For instance, the exactly-representable 64-bit number
+  // 99999999999999991611392.0 has the shortest scientific form 1e23, so its
+  // exact value is smaller than its shortest scientific form.
+  //
+  // Usually we can rely on the shortest scientific exponent to determine the
+  // length of the exact fixed form, but for these powers of 10 the length of
+  // the fixed form is one less than what the scientific exponent suggests.
+  //
+  // This subroutine inspects a lookup table to detect when fd is such a
+  // "rounded up" power of 10.
+  template<typename T>
+    bool
+    is_rounded_up_pow10_p(const typename
+			  floating_type_traits<T>::shortest_scientific_t fd)
+    {
+      if (fd.exponent < 0 || fd.mantissa != 1) [[likely]]
+	return false;
+
+      constexpr auto& pow10_adjustment_tab
+	= floating_type_traits<T>::pow10_adjustment_tab;
+      __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab));
+      return (pow10_adjustment_tab[fd.exponent/64]
+	      & (1ull << (63 - fd.exponent%64)));
+    }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_32 fd)
+  { return ryu::decimalLength9(fd.mantissa); }
+
+  int
+  get_mantissa_length(const ryu::floating_decimal_64 fd)
+  { return ryu::decimalLength17(fd.mantissa); }
+
+#ifdef __SIZEOF_INT128__
+  int
+  get_mantissa_length(const ryu::floating_decimal_128 fd)
+  { return ryu::generic128::decimalLength(fd.mantissa); }
+#endif
+} // anon namespace
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+// This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in
+// all formatting modes.
+template<typename T>
+static optional<to_chars_result>
+__handle_special_value(char* first, char* const last, const T value,
+		       const chars_format fmt, const int precision)
+{
+  __glibcxx_assert(precision >= 0);
+
+  string_view str;
+  switch (__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL,
+			       FP_ZERO, value))
+    {
+    case FP_INFINITE:
+      str = "-inf";
+      break;
+
+    case FP_NAN:
+      str = "-nan";
+      break;
+
+    case FP_ZERO:
+      break;
+
+    default:
+    case FP_SUBNORMAL:
+    case FP_NORMAL: [[likely]]
+      return nullopt;
+    }
+
+  if (!str.empty())
+    {
+      // We're formatting +-inf or +-nan.
+      if (!__builtin_signbit(value))
+	str.remove_prefix(strlen("-"));
+
+      if (last - first < (int)str.length())
+	return {{last, errc::value_too_large}};
+
+      memcpy(first, &str[0], str.length());
+      first += str.length();
+      return {{first, errc{}}};
+    }
+
+  // We're formatting 0.
+  __glibcxx_assert(value == 0);
+  const bool sign = __builtin_signbit(value);
+  int expected_output_length;
+  const char* orig_first = first;
+  switch (fmt)
+    {
+    case chars_format::fixed:
+    case chars_format::scientific:
+    case chars_format::hex:
+      expected_output_length = sign + 1;
+      if (precision)
+	expected_output_length += strlen(".") + precision;
+      if (fmt == chars_format::scientific)
+	expected_output_length += strlen("e+00");
+      else if (fmt == chars_format::hex)
+	expected_output_length += strlen("p+0");
+      if (last - first < expected_output_length)
+	return {{last, errc::value_too_large}};
+
+      if (sign)
+	*first++ = '-';
+      *first++ = '0';
+      if (precision)
+	{
+	  *first++ = '.';
+	  memset(first, '0', precision);
+	  first += precision;
+	}
+      if (fmt == chars_format::scientific)
+	{
+	  memcpy(first, "e+00", 4);
+	  first += 4;
+	}
+      else if (fmt == chars_format::hex)
+	{
+	  memcpy(first, "p+0", 3);
+	  first += 3;
+	}
+      break;
+
+    case chars_format::general:
+    default: // case chars_format{}:
+      expected_output_length = sign + 1;
+      if (last - first < expected_output_length)
+	return {{last, errc::value_too_large}};
+
+      if (sign)
+	*first++ = '-';
+      *first++ = '0';
+      break;
+    }
+  __glibcxx_assert(first - orig_first == expected_output_length);
+  return {{first, errc{}}};
+}
+
+// This subroutine of the floating-point to_chars overloads performs
+// hexadecimal formatting.
+template<typename T>
+static to_chars_result
+__floating_to_chars_hex(char* first, char* const last, const T value,
+			const optional<int> precision)
+{
+  if (precision.has_value() && precision.value() < 0) [[unlikely]]
+    // A negative precision argument is treated as if it were omitted.
+    return __floating_to_chars_hex(first, last, value, nullopt);
+
+  __glibcxx_requires_valid_range(first, last);
+
+  constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+  constexpr bool has_implicit_leading_bit
+    = floating_type_traits<T>::has_implicit_leading_bit;
+  constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+  constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+  using mantissa_t = typename floating_type_traits<T>::mantissa_t;
+  constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__;
+
+  if (auto result = __handle_special_value(first, last, value,
+					   chars_format::hex,
+					   precision.value_or(0)))
+    return *result;
+
+  // Extract the sign, mantissa and exponent from the value.
+  const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value);
+  const bool is_normal_number = (biased_exponent != 0);
+
+  // Calculate the unbiased exponent.
+  const int32_t unbiased_exponent = (is_normal_number
+				     ? biased_exponent - exponent_bias
+				     : 1 - exponent_bias);
+
+  // Shift the mantissa so that its bitwidth is a multiple of 4.
+  constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4;
+  static_assert(mantissa_t_width >= rounded_mantissa_bits);
+  mantissa_t effective_mantissa
+    = ieee_mantissa << (rounded_mantissa_bits - mantissa_bits);
+  if (is_normal_number)
+    {
+      if constexpr (has_implicit_leading_bit)
+	// Restore the mantissa's implicit leading bit.
+	effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits;
+      else
+	// The explicit mantissa bit should already be set.
+	__glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits
+								 - 1u)));
+    }
+
+  // Compute the shortest precision needed to print this value exactly,
+  // disregarding trailing zeros.
+  constexpr int full_hex_precision = (has_implicit_leading_bit
+				      ? (mantissa_bits + 3) / 4
+				      // With an explicit leading bit, we
+				      // use the four leading nibbles as the
+				      // hexit before the decimal point.
+				      : (mantissa_bits - 4 + 3) / 4);
+  const int trailing_zeros = __countr_zero(effective_mantissa) / 4;
+  const int shortest_full_precision = full_hex_precision - trailing_zeros;
+  __glibcxx_assert(shortest_full_precision >= 0);
+
+  int written_exponent = unbiased_exponent;
+  const int effective_precision = precision.value_or(shortest_full_precision);
+  if (effective_precision < shortest_full_precision)
+    {
+      // When limiting the precision, we need to determine how to round the
+      // least significant printed hexit.  The following branchless
+      // bit-level-parallel technique computes whether to round up the
+      // mantissa bit at index N (according to round-to-nearest rules) when
+      // dropping N bits of precision, for each index N in the bit vector.
+      // This technique is borrowed from the MSVC implementation.
+      using bitvec = mantissa_t;
+      const bitvec round_bit = effective_mantissa << 1;
+      const bitvec has_tail_bits = round_bit - 1;
+      const bitvec lsb_bit = effective_mantissa;
+      const bitvec should_round = round_bit & (has_tail_bits | lsb_bit);
+
+      const int dropped_bits = 4*(full_hex_precision - effective_precision);
+      // Mask out the dropped nibbles.
+      effective_mantissa >>= dropped_bits;
+      effective_mantissa <<= dropped_bits;
+      if (should_round & (mantissa_t{1} << dropped_bits))
+	{
+	  // Round up the least significant nibble.
+	  effective_mantissa += mantissa_t{1} << dropped_bits;
+	  // Check and adjust for overflow of the leading nibble.  When the
+	  // type has an implicit leading bit, then the leading nibble
+	  // before rounding is either 0 or 1, so it can't overflow.
+	  if constexpr (!has_implicit_leading_bit)
+	    {
+	      // The only supported floating-point type with explicit
+	      // leading mantissa bit is LDK_FLOAT80, i.e. x86 80-bit
+	      // extended precision, and so we hardcode the below overflow
+	      // check+adjustment for this type.
+	      static_assert(mantissa_t_width == 64
+			    && rounded_mantissa_bits == 64);
+	      if (effective_mantissa == 0)
+		{
+		  // We rounded up the least significant nibble and the
+		  // mantissa overflowed, e.g f.fcp+10 with precision=1
+		  // became 10.0p+10.  Absorb this extra hexit into the
+		  // exponent to obtain 1.0p+14.
+		  effective_mantissa
+		    = mantissa_t{1} << (rounded_mantissa_bits - 4);
+		  written_exponent += 4;
+		}
+	    }
+	}
+    }
+
+  // Compute the leading hexit and mask it out from the mantissa.
+  char leading_hexit;
+  if constexpr (has_implicit_leading_bit)
+    {
+      const unsigned nibble = effective_mantissa >> rounded_mantissa_bits;
+      __glibcxx_assert(nibble <= 2);
+      leading_hexit = '0' + nibble;
+      effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits);
+    }
+  else
+    {
+      const unsigned nibble = effective_mantissa >> (rounded_mantissa_bits-4);
+      __glibcxx_assert(nibble < 16);
+      leading_hexit = "0123456789abcdef"[nibble];
+      effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4));
+      written_exponent -= 3;
+    }
+
+  // Now before we start writing the string, determine the total length of
+  // the output string and perform a single bounds check.
+  int expected_output_length = sign + 1;
+  if (effective_precision != 0)
+    expected_output_length += strlen(".") + effective_precision;
+  const int abs_written_exponent = abs(written_exponent);
+  expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd")
+			     : abs_written_exponent >= 1000 ? strlen("p+dddd")
+			     : abs_written_exponent >= 100 ? strlen("p+ddd")
+			     : abs_written_exponent >= 10 ? strlen("p+dd")
+			     : strlen("p+d"));
+  if (last - first < expected_output_length)
+    return {last, errc::value_too_large};
+
+  const auto saved_first = first;
+  // Write the negative sign and the leading hexit.
+  if (sign)
+    *first++ = '-';
+  *first++ = leading_hexit;
+
+  if (effective_precision > 0)
+    {
+      *first++ = '.';
+      int written_hexits = 0;
+      // Extract and mask out the leading nibble after the decimal point,
+      // write its corresponding hexit, and repeat until the mantissa is
+      // empty.
+      int nibble_offset = rounded_mantissa_bits;
+      if constexpr (!has_implicit_leading_bit)
+	// We already printed the entire leading hexit.
+	nibble_offset -= 4;
+      while (effective_mantissa != 0)
+	{
+	  nibble_offset -= 4;
+	  const unsigned nibble = effective_mantissa >> nibble_offset;
+	  __glibcxx_assert(nibble < 16);
+	  *first++ = "0123456789abcdef"[nibble];
+	  ++written_hexits;
+	   effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset);
+	}
+      __glibcxx_assert(nibble_offset >= 0);
+      __glibcxx_assert(written_hexits <= effective_precision);
+      // Since the mantissa is now empty, every hexit hereafter must be '0'.
+      if (int remaining_hexits = effective_precision - written_hexits)
+	{
+	  memset(first, '0', remaining_hexits);
+	  first += remaining_hexits;
+	}
+    }
+
+  // Finally, write the exponent.
+  *first++ = 'p';
+  if (written_exponent >= 0)
+    *first++ = '+';
+  const to_chars_result result = to_chars(first, last, written_exponent);
+  __glibcxx_assert(result.ec == errc{}
+		   && result.ptr == saved_first + expected_output_length);
+  return result;
+}
+
+template<typename T>
+static to_chars_result
+__floating_to_chars_shortest(char* first, char* const last, const T value,
+			     chars_format fmt)
+{
+  if (fmt == chars_format::hex)
+    return __floating_to_chars_hex(first, last, value, nullopt);
+
+  __glibcxx_assert(fmt == chars_format::fixed
+		   || fmt == chars_format::scientific
+		   || fmt == chars_format::general
+		   || fmt == chars_format{});
+  __glibcxx_requires_valid_range(first, last);
+
+  if (auto result = __handle_special_value(first, last, value, fmt, 0))
+    return *result;
+
+  const auto fd = floating_to_shortest_scientific(value);
+  const int mantissa_length = get_mantissa_length(fd);
+  const int scientific_exponent = fd.exponent + mantissa_length - 1;
+
+  if (fmt == chars_format::general)
+    {
+      // Resolve the 'general' formatting mode as per the specification of
+      // the 'g' printf output specifier.  Since there is no precision
+      // argument, the default precision of the 'g' specifier, 6, applies.
+      if (scientific_exponent >= -4 && scientific_exponent < 6)
+	fmt = chars_format::fixed;
+      else
+	fmt = chars_format::scientific;
+    }
+  else if (fmt == chars_format{})
+    {
+      // The 'plain' formatting mode resolves to 'scientific' if it yields
+      // the shorter string, and resolves to 'fixed' otherwise.  The
+      // following lower and upper bounds on the exponent characterize when
+      // to prefer 'fixed' over 'scientific'.
+      int lower_bound = -(mantissa_length + 3);
+      int upper_bound = 5;
+      if (mantissa_length == 1)
+	// The decimal point in scientific notation will be omitted in this
+	// case; tighten the bounds appropriately.
+	++lower_bound, --upper_bound;
+
+      if (fd.exponent >= lower_bound && fd.exponent <= upper_bound)
+	fmt = chars_format::fixed;
+      else
+	fmt = chars_format::scientific;
+    }
+
+  if (fmt == chars_format::scientific)
+    {
+      // Calculate the total length of the output string, perform a bounds
+      // check, and then defer to Ryu's to_chars subroutine.
+      int expected_output_length = fd.sign + mantissa_length;
+      if (mantissa_length > 1)
+	expected_output_length += strlen(".");
+      const int abs_exponent = abs(scientific_exponent);
+      expected_output_length += (abs_exponent >= 1000 ? strlen("e+dddd")
+				 : abs_exponent >= 100 ? strlen("e+ddd")
+				 : strlen("e+dd"));
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      const int output_length = ryu::to_chars(fd, first);
+      __glibcxx_assert(output_length == expected_output_length);
+      return {first + output_length, errc{}};
+    }
+  else if (fmt == chars_format::fixed && fd.exponent >= 0)
+    {
+      // The Ryu exponent is positive, and so this number's shortest
+      // representation is a whole number, to be formatted in fixed instead
+      // of scientific notation "as if by std::printf".  This means we may
+      // need to print more digits of the IEEE mantissa than what the
+      // shortest scientific form given by Ryu provides.
+      //
+      // For instance, the exactly representable number
+      // 12300000000000001048576.0 has as its shortest scientific
+      // representation 123e+22, so in this case fd.mantissa is 123 and
+      // fd.exponent is 22, which doesn't have enough information to format
+      // the number exactly.  So we defer to Ryu's d2fixed_buffered_n with
+      // precision=0 to format the number in the general case here.
+
+      // To that end, first compute the output length and perform a bounds
+      // check.
+      int expected_output_length = fd.sign + mantissa_length + fd.exponent;
+      if (is_rounded_up_pow10_p<T>(fd))
+	--expected_output_length;
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+
+      // Optimization: if the shortest representation fits inside the IEEE
+      // mantissa, then the number is certainly exactly-representable and
+      // its shortest scientific form must be equal to its exact form.  So
+      // we can write the value in fixed form exactly via fd.mantissa and
+      // fd.exponent.
+      //
+      // Taking log2 of both sides of the desired condition
+      //   fd.mantissa * 10^fd.exponent < 2^mantissa_bits
+      // we get
+      //   log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits
+      // where log2 10 is slightly smaller than 10/3=3.333...
+      //
+      // After adding some wiggle room due to rounding we get the condition
+      // value_fits_inside_mantissa_p below.
+      const int log2_mantissa = __bit_width(fd.mantissa) - 1;
+      const bool value_fits_inside_mantissa_p
+	= (log2_mantissa + (fd.exponent*10 + 2) / 3
+	   < floating_type_traits<T>::mantissa_bits - 2);
+      if (value_fits_inside_mantissa_p)
+	{
+	  // Print the small exactly-represantable number in fixed form by
+	  // writing out fd.mantissa followed by fd.exponent many 0s.
+	  if (fd.sign)
+	    *first++ = '-';
+	  to_chars_result result = to_chars(first, last, fd.mantissa);
+	  __glibcxx_assert(result.ec == errc{});
+	  memset(result.ptr, '0', fd.exponent);
+	  result.ptr += fd.exponent;
+	  const int output_length = fd.sign + (result.ptr - first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return result;
+	}
+      else if constexpr (is_same_v<T, long double>)
+	{
+	  // We can't use d2fixed_buffered_n for types larger than double,
+	  // so we instead format larger types through sprintf.
+	  // TODO: We currently go through an intermediate buffer in order
+	  // to accomodate the mandatory null terminator of sprintf, but we
+	  // can avoid this if we use sprintf to write all but the last
+	  // digit, and carefully compute and write the last digit
+	  // ourselves.
+	  char buffer[expected_output_length+1];
+#if _GLIBCXX_USE_C99_FENV_TR1
+	  const int saved_rounding_mode = fegetround();
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+#endif
+	  const int output_length = sprintf(buffer, "%.0Lf", value);
+#if _GLIBCXX_USE_C99_FENV_TR1
+	  if (saved_rounding_mode != FE_TONEAREST)
+	    fesetround(saved_rounding_mode);
+#endif
+	  __glibcxx_assert(output_length == expected_output_length);
+	  memcpy(first, buffer, output_length);
+	  return {first + output_length, errc{}};
+	}
+      else
+	{
+	  // Otherwise, the number is too big, so defer to d2fixed_buffered_n.
+	  const int output_length = ryu::d2fixed_buffered_n(value, 0, first);
+	  __glibcxx_assert(output_length == expected_output_length);
+	  return {first + output_length, errc{}};
+	}
+    }
+  else if (fmt == chars_format::fixed && fd.exponent < 0)
+    {
+      // The Ryu exponent is negative, so fd.mantissa definitely contains
+      // all of the whole part of the number, and therefore fd.mantissa and
+      // fd.exponent contain all of the information needed to format the
+      // number in fixed notation "as if by std::printf" (with precision
+      // equal to -fd.exponent).
+      const int whole_digits = max(mantissa_length + fd.exponent, 1);
+      const int expected_output_length
+	= fd.sign + whole_digits + strlen(".") + -fd.exponent;
+      if (last - first < expected_output_length)
+	return {last, errc::value_too_large};
+      if (mantissa_length <= -fd.exponent)
+	{
+	  // The magnitude of the number is less than one.  Format the
+	  // number appropriately.
+	  const char* orig_first = first;
+	  if (fd.sign)
+	    *first++ = '-';
+	  *first++ = '0';
+	  *first++ = '.';
+	  const int leading_zeros = -fd.exponent - mantissa_length;
+	  memset(first, '0', leading_zeros);
+	  first += leading_zeros;
+	  const to_chars_result result = to_chars(first, last, fd.mantissa);
+	  const int output_length = result.ptr - orig_first;
+	  __glibcxx_assert(output_length == expected_output_length
+			   && result.ec == errc{});
+	  return result;
+	}
+      else
+	{
+	  // The magnitude of the number is at least one.
+	  const char* orig_first = first;
+	  if (fd.sign)
+	    *first++ = '-';
+	  to_chars_result result = to_chars(first, last, fd.mantissa);
+	  __glibcxx_assert(result.ec == errc{});
+	  // Make space for and write the decimal point in the correct spot.
+	  memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent],
+		  -fd.exponent);
+	  result.ptr[fd.exponent] = '.';
+	  const int output_length = result.ptr + 1 - orig_first;
+	  __glibcxx_assert(output_length == expected_output_length);
+	  ++result.ptr;
+	  return result;
+	}
+    }
+
+  __glibcxx_assert(false);
+  __builtin_unreachable();
+}
+
+template<typename T>
+static to_chars_result
+__floating_to_chars_precision(char* first, char* const last, const T value,
+			      chars_format fmt, const int precision)
+{
+  if (fmt == chars_format::hex)
+    return __floating_to_chars_hex(first, last, value, precision);
+
+  if (precision < 0) [[unlikely]]
+    // A negative precision argument is treated as if it were omitted, in
+    // which case the default precision of 6 applies, as per the printf
+    // specification.
+    return __floating_to_chars_precision(first, last, value, fmt, 6);
+
+  __glibcxx_assert(fmt == chars_format::fixed
+		   || fmt == chars_format::scientific
+		   || fmt == chars_format::general);
+  __glibcxx_requires_valid_range(first, last);
+
+  if (auto result = __handle_special_value(first, last, value,
+					   fmt, precision))
+    return *result;
+
+  constexpr int mantissa_bits = floating_type_traits<T>::mantissa_bits;
+  constexpr int exponent_bits = floating_type_traits<T>::exponent_bits;
+  constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1;
+
+  // Extract the sign and exponent from the value.
+  const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value);
+  const bool is_normal_number = (biased_exponent != 0);
+
+  // Calculate the unbiased exponent.
+  const int32_t unbiased_exponent = (is_normal_number
+				     ? biased_exponent - exponent_bias
+				     : 1 - exponent_bias);
+
+  // Obtain trunc(log2(abs(value))), which is just the unbiased exponent.
+  const int floor_log2_value = unbiased_exponent;
+  // This is within +-1 of log10(abs(value)).  Note that log10 2 is 0.3010..
+  const int approx_log10_value = (floor_log2_value >= 0
+				  ? (floor_log2_value*301 + 999)/1000
+				  : (floor_log2_value*301 - 999)/1000);
+
+  // Compute (an upper bound of) the number's effective precision when it is
+  // formatted in scientific and fixed notation.  Beyond this precision all
+  // digits are definitely zero, and this fact allows us to bound the sizes
+  // of any local output buffers that we may need to use.  TODO: Consider
+  // the number of trailing zero bits in the mantissa to obtain finer upper
+  // bounds.
+  // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the
+  // bounds below is necessary only for __ibm128, it seems.  Even though the
+  // type has 105 bits of precision, printf may output 106 fractional digits
+  // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0.
+  const int max_eff_scientific_precision
+    = (floor_log2_value >= 0
+       ? max(mantissa_bits + 1, approx_log10_value + 1)
+       : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1);
+  __glibcxx_assert(max_eff_scientific_precision > 0);
+
+  const int max_eff_fixed_precision
+    = (floor_log2_value >= 0
+       ? mantissa_bits + 1
+       : -floor_log2_value + mantissa_bits + 1);
+  __glibcxx_assert(max_eff_fixed_precision > 0);
+
+  // Ryu doesn't support formatting floating-point types larger than double
+  // with an explicit precision, so instead we just go through printf.
+  if constexpr (is_same_v<T, long double>)
+    {
+      int effective_precision;
+      const char* output_specifier;
+      if (fmt == chars_format::scientific)
+	{
+	  effective_precision = min(precision, max_eff_scientific_precision);
+	  output_specifier = "%.*Le";
+	}
+      else if (fmt == chars_format::fixed)
+	{
+	  effective_precision = min(precision, max_eff_fixed_precision);
+	  output_specifier = "%.*Lf";
+	}
+      else if (fmt == chars_format::general)
+	{
+	  effective_precision = min(precision, max_eff_scientific_precision);
+	  output_specifier = "%.*Lg";
+	}
+      const int excess_precision = (fmt != chars_format::general
+				    ? precision - effective_precision : 0);
+
+      // Since the output of printf is locale-sensitive, we need to be able
+      // to handle a radix point that's different from '.'.
+      char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'};
+      if (effective_precision > 0)
+	// ???: Can nl_langinfo() ever return null?
+	if (const char* const radix_ptr = nl_langinfo(RADIXCHAR))
+	  {
+	    strncpy(radix, radix_ptr, sizeof(radix)-1);
+	    // We accept only radix points which are at most 4 bytes (one
+	    // UTF-8 character) wide.
+	    __glibcxx_assert(radix[4] == '\0');
+	  }
+
+      // Compute straightforward upper bounds on the output length.
+      int output_length_upper_bound;
+      if (fmt == chars_format::scientific || fmt == chars_format::general)
+	output_length_upper_bound = (strlen("-d") + sizeof(radix)
+				     + effective_precision
+				     + strlen("e+dddd"));
+      else if (fmt == chars_format::fixed)
+	{
+	  if (approx_log10_value >= 0)
+	    output_length_upper_bound = sign + approx_log10_value + 1;
+	  else
+	    output_length_upper_bound = sign + strlen("0");
+	  output_length_upper_bound += sizeof(radix) + effective_precision;
+	}
+
+      // Do the sprintf into the local buffer.
+      char buffer[output_length_upper_bound+1];
+#if _GLIBCXX_USE_C99_FENV_TR1
+      const int saved_rounding_mode = fegetround();
+      if (saved_rounding_mode != FE_TONEAREST)
+	fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
+#endif
+      int output_length
+	= sprintf(buffer, output_specifier, effective_precision, value);
+#if _GLIBCXX_USE_C99_FENV_TR1
+      if (saved_rounding_mode != FE_TONEAREST)
+	fesetround(saved_rounding_mode);
+#endif
+      __glibcxx_assert(output_length <= output_length_upper_bound);
+
+      if (effective_precision > 0)
+	// We need to replace a radix that is different from '.' with '.'.
+	if (const string_view radix_sv = {radix}; radix_sv != ".")
+	  {
+	    const string_view buffer_sv = {buffer, (size_t)output_length};
+	    const size_t radix_index = buffer_sv.find(radix_sv);
+	    if (radix_index != string_view::npos)
+	      {
+		buffer[radix_index] = '.';
+		if (radix_sv.length() > 1)
+		  {
+		    memmove(&buffer[radix_index + 1],
+			    &buffer[radix_index + radix_sv.length()],
+			    output_length - radix_index - radix_sv.length());
+		    output_length -= radix_sv.length() - 1;
+		  }
+	      }
+	  }
+
+      // Copy the string from the buffer over to the output range.
+      if (last - first < output_length + excess_precision)
+	return {last, errc::value_too_large};
+      memcpy(first, buffer, output_length);
+      first += output_length;
+
+      // Add the excess 0s to the result.
+      if (excess_precision > 0)
+	{
+	  if (fmt == chars_format::scientific)
+	    {
+	      char* const significand_end
+		= (output_length >= 6 && first[-6] == 'e' ? &first[-6]
+		   : first[-5] == 'e' ? &first[-5]
+		   : &first[-4]);
+	      __glibcxx_assert(*significand_end == 'e');
+		memmove(significand_end + excess_precision, significand_end,
+			first - significand_end);
+		memset(significand_end, '0', excess_precision);
+		first += excess_precision;
+	    }
+	  else if (fmt == chars_format::fixed)
+	    {
+	      memset(first, '0', excess_precision);
+	      first += excess_precision;
+	    }
+	}
+      return {first, errc{}};
+    }
+  else if (fmt == chars_format::scientific)
+    {
+      const int effective_precision
+	= min(precision, max_eff_scientific_precision);
+      const int excess_precision = precision - effective_precision;
+
+      // We can easily compute the output length exactly whenever the
+      // scientific exponent is far enough away from +-100.  But if it's
+      // near +-100, then our log2 approximation is too coarse (and doesn't
+      // consider precision-dependent rounding) in order to accurately
+      // distinguish between a scientific exponent of +-100 and +-99.
+      const bool scientific_exponent_near_100_p
+	= abs(abs(floor_log2_value) - 332) <= 4;
+
+      // Compute an upper bound on the output length.  TODO: Maybe also
+      // consider a lower bound on the output length.
+      int output_length_upper_bound = sign + strlen("d");
+      if (effective_precision > 0)
+	output_length_upper_bound += strlen(".") + effective_precision;
+      if (scientific_exponent_near_100_p
+	  || (floor_log2_value >= 332 || floor_log2_value <= -333))
+	output_length_upper_bound += strlen("e+ddd");
+      else
+	output_length_upper_bound += strlen("e+dd");
+
+      int output_length;
+      if (last - first >= output_length_upper_bound + excess_precision)
+	{
+	  // The result will definitely fit into the output range, so we can
+	  // write directly into it.
+	  output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						first, nullptr);
+	  __glibcxx_assert(output_length == output_length_upper_bound
+			   || (scientific_exponent_near_100_p
+			       && (output_length
+				   == output_length_upper_bound - 1)));
+	}
+      else if (scientific_exponent_near_100_p)
+	{
+	  // Write the result of d2exp_buffered_n into an intermediate
+	  // buffer, do a bounds check, and copy the result into the output
+	  // range.
+	  char buffer[output_length_upper_bound];
+	  output_length = ryu::d2exp_buffered_n(value, effective_precision,
+						buffer, nullptr);
+	  __glibcxx_assert(output_length == output_length_upper_bound - 1
+			   || output_length == output_length_upper_bound);
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	}
+      else
+	// If the scientific exponent is not near 100, then the upper bound
+	// is actually the exact length, and so the result will definitely
+	// not fit into the output range.
+	return {last, errc::value_too_large};
+      first += output_length;
+      if (excess_precision > 0)
+	{
+	  // Splice the excess zeros into the result.
+	  char* const significand_end = (first[-5] == 'e'
+					 ? &first[-5] : &first[-4]);
+	  __glibcxx_assert(*significand_end == 'e');
+	  memmove(significand_end + excess_precision, significand_end,
+		  first - significand_end);
+	  memset(significand_end, '0', excess_precision);
+	  first += excess_precision;
+	}
+      return {first, errc{}};
+    }
+  else if (fmt == chars_format::fixed)
+    {
+      const int effective_precision
+	= min(precision, max_eff_fixed_precision);
+      const int excess_precision = precision - effective_precision;
+
+      // Compute an upper bound on the output length.  TODO: Maybe also
+      // consider a lower bound on the output length.
+      int output_length_upper_bound;
+      if (approx_log10_value >= 0)
+	output_length_upper_bound = sign + approx_log10_value + 1;
+      else
+	output_length_upper_bound = sign + strlen("0");
+      if (effective_precision > 0)
+	output_length_upper_bound += strlen(".") + effective_precision;
+
+      int output_length;
+      if (last - first >= output_length_upper_bound + excess_precision)
+	{
+	  // The result will definitely fit into the output range, so we can
+	  // write directly into it.
+	  output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						  first);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	}
+      else
+	{
+	  // Write the result of d2fixed_buffered_n into an intermediate
+	  // buffer, do a bounds check, and copy the result into the output
+	  // range.
+	  char buffer[output_length_upper_bound];
+	  output_length = ryu::d2fixed_buffered_n(value, effective_precision,
+						  buffer);
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	  if (last - first < output_length + excess_precision)
+	    return {last, errc::value_too_large};
+	  memcpy(first, buffer, output_length);
+	}
+      first += output_length;
+      if (excess_precision > 0)
+	{
+	  // Append the excess zeros into the result.
+	  memset(first, '0', excess_precision);
+	  first += excess_precision;
+	}
+      return {first, errc{}};
+    }
+  else if (fmt == chars_format::general)
+    {
+      // Handle the 'general' formatting mode as per C11 printf's %g output
+      // specifier.  Since Ryu doesn't do zero-trimming, we always write to
+      // an intermediate buffer and manually perform zero-trimming there
+      // before copying the result over to the output range.
+      int effective_precision
+	= min(precision, max_eff_scientific_precision + 1);
+      const int output_length_upper_bound
+	= strlen("-d.") + effective_precision + strlen("e+ddd");
+      // The four bytes of headroom is to avoid needing to do a memmove when
+      // rewriting a scientific form such as 1.00e-2 into the equivalent
+      // fixed form 0.001.
+      char buffer[4 + output_length_upper_bound];
+
+      // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero."
+      if (effective_precision == 0)
+	effective_precision = 1;
+
+      // Perform a trial formatting in scientific form, and obtain the
+      // scientific exponent.
+      int scientific_exponent;
+      char* buffer_start = buffer + 4;
+      int output_length
+	= ryu::d2exp_buffered_n(value, effective_precision - 1,
+				buffer_start, &scientific_exponent);
+      __glibcxx_assert(output_length <= output_length_upper_bound);
+
+      // 7.21.6.1/8: "Then, if a conversion with style E would have an
+      // exponent of X:
+      //   if P > X >= -4, the conversion is with style f and
+      //     precision P - (X + 1).
+      //   otherwise, the conversion is with style e and precision P - 1."
+      const bool resolve_to_fixed_form
+	= (scientific_exponent >= -4
+	   && scientific_exponent < effective_precision);
+      if (resolve_to_fixed_form)
+	{
+	  // Rather than invoking d2fixed_buffered_n to reformat the number
+	  // for us from scratch, we can just rewrite the scientific form
+	  // into fixed form in-place.  This is safe to do because whenever
+	  // %g resolves to %f, the fixed form will be no larger than the
+	  // corresponding scientific form, and it will also contain the
+	  // same significant digits as the scientific form.
+	  fmt = chars_format::fixed;
+	  if (scientific_exponent < 0)
+	    {
+	      // e.g. buffer_start == "-1.234e-04"
+	      char* leading_digit = &buffer_start[sign];
+	      leading_digit[1] = leading_digit[0];
+	      // buffer_start == "-11234e-04"
+	      buffer_start -= -scientific_exponent;
+	      __glibcxx_assert(buffer_start >= buffer);
+	      // buffer_start == "????-11234e-04"
+	      char* head = buffer_start;
+	      if (sign)
+		*head++ = '-';
+	      *head++ = '0';
+	      *head++ = '.';
+	      memset(head, '0', -scientific_exponent - 1);
+	      // buffer_start == "-0.00011234e-04"
+
+	      // Now drop the exponent suffix, and add the leading zeros to
+	      // the output length.
+	      output_length -= strlen("e-0d");
+	      output_length += -scientific_exponent;
+	      if (effective_precision - 1 == 0)
+		// The scientific form had no decimal point, but the fixed
+		// form now does.
+		output_length += strlen(".");
+	    }
+	  else if (effective_precision == 1)
+	    {
+	      // The scientific exponent must be 0, so the fixed form
+	      // coincides with the scientific form (minus the exponent
+	      // suffix).
+	      __glibcxx_assert(scientific_exponent == 0);
+	      output_length -= strlen("e+dd");
+	    }
+	  else
+	    {
+	      // We are dealing with a scientific form which has a
+	      // non-empty fractional part and a nonnegative exponent,
+	      // e.g. buffer_start == "1.234e+02".
+	      __glibcxx_assert(effective_precision >= 1);
+	      char* const decimal_point = &buffer_start[sign + 1];
+	      __glibcxx_assert(*decimal_point == '.');
+	      memmove(decimal_point, decimal_point+1,
+		      scientific_exponent);
+	      // buffer_start == "123.4e+02"
+	      decimal_point[scientific_exponent] = '.';
+	      if (scientific_exponent >= 100)
+		output_length -= strlen("e+ddd");
+	      else
+		output_length -= strlen("e+dd");
+	      if (effective_precision - 1 == scientific_exponent)
+		output_length -= strlen(".");
+	    }
+	  effective_precision -= 1 + scientific_exponent;
+
+	  __glibcxx_assert(output_length <= output_length_upper_bound);
+	}
+      else
+	{
+	  // We're sticking to the scientific form, so keep the output as-is.
+	  fmt = chars_format::scientific;
+	  effective_precision = effective_precision - 1;
+	}
+
+      // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from
+      // the fractional portion of the result and the decimal-point
+      // character is removed if there is no fractional portion remaining."
+      if (effective_precision > 0)
+	{
+	  char* decimal_point = nullptr;
+	  if (fmt == chars_format::scientific)
+	    decimal_point = &buffer_start[sign + 1];
+	  else if (fmt == chars_format::fixed)
+	    decimal_point
+	      = &buffer_start[output_length] - effective_precision - 1;
+	  __glibcxx_assert(*decimal_point == '.');
+
+	  char* const fractional_part_start = decimal_point + 1;
+	  char* fractional_part_end = nullptr;
+	  if (fmt == chars_format::scientific)
+	    {
+	      fractional_part_end = (buffer_start[output_length-5] == 'e'
+				     ? &buffer_start[output_length-5]
+				     : &buffer_start[output_length-4]);
+	      __glibcxx_assert(*fractional_part_end == 'e');
+	    }
+	  else if (fmt == chars_format::fixed)
+	    fractional_part_end = &buffer_start[output_length];
+
+	  const string_view fractional_part
+	    = {fractional_part_start, (size_t)(fractional_part_end
+					       - fractional_part_start) };
+	  const size_t last_nonzero_digit_pos
+	    = fractional_part.find_last_not_of('0');
+
+	  char* trim_start;
+	  if (last_nonzero_digit_pos == string_view::npos)
+	    trim_start = decimal_point;
+	  else
+	    trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1;
+	  if (fmt == chars_format::scientific)
+	    memmove(trim_start, fractional_part_end,
+		    &buffer_start[output_length] - fractional_part_end);
+	  output_length -= fractional_part_end - trim_start;
+	}
+
+      if (last - first < output_length)
+	return {last, errc::value_too_large};
+
+      memcpy(first, buffer_start, output_length);
+      return {first + output_length, errc{}};
+    }
+
+  __glibcxx_assert(false);
+  __builtin_unreachable();
+}
+
+// Define the overloads for float.
+to_chars_result
+to_chars(char* first, char* last, float value) noexcept
+{ return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+to_chars_result
+to_chars(char* first, char* last, float value, chars_format fmt) noexcept
+{ return __floating_to_chars_shortest(first, last, value, fmt); }
+
+to_chars_result
+to_chars(char* first, char* last, float value, chars_format fmt,
+	 int precision) noexcept
+{ return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+// Define the overloads for double.
+to_chars_result
+to_chars(char* first, char* last, double value) noexcept
+{ return __floating_to_chars_shortest(first, last, value, chars_format{}); }
+
+to_chars_result
+to_chars(char* first, char* last, double value, chars_format fmt) noexcept
+{ return __floating_to_chars_shortest(first, last, value, fmt); }
+
+to_chars_result
+to_chars(char* first, char* last, double value, chars_format fmt,
+	 int precision) noexcept
+{ return __floating_to_chars_precision(first, last, value, fmt, precision); }
+
+// Define the overloads for long double.
+to_chars_result
+to_chars(char* first, char* last, long double value) noexcept
+{
+  if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		|| LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+    return __floating_to_chars_shortest(first, last, double(value),
+					chars_format{});
+  else
+    return __floating_to_chars_shortest(first, last, value, chars_format{});
+}
+
+to_chars_result
+to_chars(char* first, char* last, long double value, chars_format fmt) noexcept
+{
+  if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		|| LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+    return __floating_to_chars_shortest(first, last, double(value), fmt);
+  else
+    return __floating_to_chars_shortest(first, last, value, fmt);
+}
+
+to_chars_result
+to_chars(char* first, char* last, long double value, chars_format fmt,
+	 int precision) noexcept
+{
+  if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64
+		|| LONG_DOUBLE_KIND == LDK_UNSUPPORTED)
+    return __floating_to_chars_precision(first, last, double(value), fmt,
+					 precision);
+  else
+    return __floating_to_chars_precision(first, last, value, fmt, precision);
+}
+
+#ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
+// Map the -mlong-double-64 long double overloads to the double overloads.
+extern "C" to_chars_result
+_ZSt8to_charsPcS_e(char* first, char* last, double value) noexcept
+  __attribute__((alias ("_ZSt8to_charsPcS_d")));
+
+extern "C" to_chars_result
+_ZSt8to_charsPcS_eSt12chars_format(char* first, char* last, double value,
+				   chars_format fmt) noexcept
+  __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_format")));
+
+extern "C" to_chars_result
+_ZSt8to_charsPcS_eSt12chars_formati(char* first, char* last, double value,
+				    chars_format fmt, int precision) noexcept
+  __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_formati")));
+#endif
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
diff --git a/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
new file mode 100644
index 00000000000..12ac8ae7822
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
@@ -0,0 +1,199 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// <charconv> is supported in C++14 as a GNU extension, but this test uses C++17
+// hexadecimal floating-point literals.
+// { dg-do run { target c++17 } }
+// { dg-xfail-run-if "Ryu needs __int128" { large_long_double && { ! int128 } } }
+
+#include <charconv>
+
+#include <cmath>
+#include <cstring>
+#include <iterator>
+#include <limits>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// The long double overloads of std::to_chars currently just go through printf
+// (except for the hexadecimal formatting).
+
+// Test our hand-written hexadecimal formatting implementation.
+void
+test01()
+{
+  const long double hex_testcases[]
+    = { nextdownl(numeric_limits<long double>::max()),
+	nextupl(numeric_limits<long double>::min()),
+	42.0L,
+	0x1.2p+0L,
+	0x1.23p+0L,
+	0x1.234p+0L,
+	0x1.2345p+0L,
+	0x1.23456p+0L,
+	0x1.234567p+0L,
+	0x1.2345678p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789p+0L,
+	0x1.23456789ap+0L,
+	0x1.23456789abp+0L,
+	0x1.23456789abcp+0L,
+	0x1.23456789abcdp+0L,
+	0x1.23456789abcdep+0L,
+	0x1.23456789abcdefp+0L,
+	0x1.23456789abcdef0p+0L,
+	0x1.23456789abcdef01p+0L,
+	0x1.23456789abcdef012p+0L,
+	0x1.23456789abcdef0123p+0L,
+	0x1.23456789abcdef01234p+0L,
+	0x1.23456789abcdef012345p+0L,
+	0x1.23456789abcdef0123456p+0L,
+	0x1.23456789abcdef01234567p+0L,
+	0x1.23456789abcdef012345678p+0L,
+	0x1.23456789abcdef0123456789p+0L,
+	0x1.23456789abcdef0123456789ap+0L,
+	0x1.23456789abcdef0123456789abp+0L,
+	0x1.23456789abcdef0123456789abcp+0L,
+	0x1.23456789abcdef0123456789abcdp+0L,
+    };
+
+  for (int exponent : {-11000, -3000, -300, -50, -7, 0, 7, 50, 300, 3000, 11000})
+    for (long double testcase : hex_testcases)
+      {
+	testcase = ldexpl(testcase, exponent);
+	if (testcase == 0.0L || isinf(testcase))
+	  continue;
+
+	char to_chars_buffer[1024], printf_buffer[1024];
+	memset(to_chars_buffer, '\0', sizeof(to_chars_buffer));
+	memset(printf_buffer, '\0', sizeof(printf_buffer));
+
+	auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			       testcase, chars_format::hex);
+	VERIFY( result.ec == errc{} );
+	*result.ptr = '\0';
+	sprintf(printf_buffer, "%La", testcase);
+	VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	  {
+	    // Verify that the nearby values have a different shortest form.
+	    testcase = nextdownl(testcase);
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextupl(nextupl(testcase));
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    VERIFY( strcmp(to_chars_buffer, printf_buffer+strlen("0x")) != 0);
+	    sprintf(printf_buffer, "%La", testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+
+	    testcase = nextdownl(testcase);
+	  }
+
+	for (int precision = -1; precision < 50; precision++)
+	  {
+	    result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+			      testcase, chars_format::hex, precision);
+	    VERIFY( result.ec == errc{} );
+	    *result.ptr = '\0';
+	    sprintf(printf_buffer, "%.*La", precision, testcase);
+	    VERIFY( !strcmp(to_chars_buffer, printf_buffer+strlen("0x")) );
+	  }
+      }
+}
+
+// Test the rest of the formatting modes, which go through printf.
+void
+test02()
+{
+  const long double growth_factor = 1.442695040888963407359924681001892137L;
+  for (chars_format fmt : {chars_format::fixed, chars_format::scientific,
+			   chars_format::general})
+    for (long double __value = 1.0L, count = 0; !isinf(__value);
+	 ++count <= 100.0L ? __value *= growth_factor : __value *= __value)
+      for (const long double value : {__value, 1.0L/__value})
+	{
+	  for (const int precision : {-1, 0, 10, 100, 10000})
+	    {
+	      const char* const printf_specifier
+		= (fmt == chars_format::fixed ? "%.*Lf"
+		   : fmt == chars_format::scientific ? "%.*Le"
+		   : fmt == chars_format::general ? "%.*Lg"
+		   : nullptr);
+	      unsigned output_length = snprintf(nullptr, 0, printf_specifier,
+						precision, value);
+
+	      char printf_buffer[output_length+1];
+	      snprintf(printf_buffer, output_length+1, printf_specifier,
+		       precision, value);
+
+	      char to_chars_buffer[output_length];
+	      auto result = to_chars(to_chars_buffer,
+				     to_chars_buffer+output_length,
+				     value, fmt, precision);
+	      VERIFY( result.ec == errc{} );
+	      VERIFY( !memcmp(printf_buffer, to_chars_buffer, output_length) );
+
+	      result = to_chars(to_chars_buffer,
+				to_chars_buffer+output_length-1,
+				value, fmt, precision);
+	      VERIFY( result.ec == errc::value_too_large );
+	    }
+
+	  // Verify that the nearby values have a different shortest form.
+	  char to_chars_buffer[50000];
+	  auto result = to_chars(begin(to_chars_buffer), end(to_chars_buffer),
+				 value, fmt);
+	  VERIFY( result.ec == errc{} );
+	  *result.ptr = '\0';
+	  char nearby_buffer[50000];
+	    {
+	      const long double smaller = nextdownl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				smaller, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+
+	    {
+	      long double larger = nextupl(value);
+	      result = to_chars(begin(nearby_buffer), end(nearby_buffer),
+				larger, fmt);
+	      VERIFY( result.ec == errc{} );
+	      *result.ptr = '\0';
+	      VERIFY( strcmp(to_chars_buffer, nearby_buffer) != 0 );
+	    }
+	}
+}
+
+int
+main()
+{
+  test01();
+  test02();
+}
-- 
2.28.0.258.g2befe97201

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Jonathan Wakely]

On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
>On Wed, 22 Jul 2020, Patrick Palka wrote:
>
>> On Mon, 20 Jul 2020, Patrick Palka wrote:
>>
>> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
>> >
>> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
>> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
>> > > >
>> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
>> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
>> > > > > >
>> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
>> > > > > > >
>> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
>> > > > > > > >
>> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
>> > > > > > > > >
>> > > > > > > > > > This implements the floating-point std::to_chars overloads for
>> > > > > > > float,
>> > > > > > > > > > double and long double.  We use the Ryu library to compute the
>> > > > > > > shortest
>> > > > > > > > > > round-trippable fixed and scientific forms of a number for
>> > > > > float,
>> > > > > > > double
>> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
>> > > > > > > scientific
>> > > > > > > > > > formatting of float and double. For formatting long double with
>> > > > > an
>> > > > > > > > > > explicit precision argument we use a printf fallback.
>> > > > > Hexadecimal
>> > > > > > > > > > formatting for float, double and long double is implemented from
>> > > > > > > > > > scratch.
>> > > > > > > > > >
>> > > > > > > > > > The supported long double binary formats are float64 (same as
>> > > > > > > double),
>> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
>> > > > > > > > > >
>> > > > > > > > > > Much of the complexity of the implementation is in computing the
>> > > > > > > exact
>> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
>> > > > > bounds
>> > > > > > > > > > checking).  In some cases it's hard to compute the output length
>> > > > > > > before
>> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
>> > > > > the
>> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
>> > > > > (if
>> > > > > > > the
>> > > > > > > > > > output range is smaller than the upper bound).
>> > > > > > > > > >
>> > > > > > > > > > Another source of complexity is in the general-with-precision
>> > > > > > > formatting
>> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
>> > > > > by
>> > > > > > > Ryu, and
>> > > > > > > > > > where we also take care to avoid having to format the string a
>> > > > > > > second
>> > > > > > > > > > time when the general formatting mode resolves to fixed.
>> > > > > > > > > >
>> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
>> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
>> > > > > > > > > >
>> > > > > > > > > > libstdc++-v3/ChangeLog:
>> > > > > > > > > >
>> > > > > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> > > > > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
>> > > > > > > > > > 	* configure: Regenerate.
>> > > > > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
>> > > > > > > > > > 	overloads for float, double and long double.
>> > > > > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> > > > > > > > > > 	* src/c++17/Makefile.in: Regenerate.
>> > > > > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
>> > > > > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> > > > > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> > > > > > > > >
>> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
>> > > > > to
>> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
>> > > > > > > format
>> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
>> > > > > The
>> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
>> > > > > > > uint64_t
>> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
>> > > > > > > case.
>> > > > > > > >
>> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
>> > > > > most
>> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
>> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
>> > > > > mode.
>> > > > > > >
>> > > > > > > Here's v4, which should now correctly support using <charconv> with
>> > > > > > > -mlong-double-64 on targets with a large default long double type.
>> > > > > > > This is done by defining the long double to_chars overloads as inline
>> > > > > > > wrappers around the double overloads within <charconv> whenever
>> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
>> > > > > >
>> > > > > > >
>> > > > > > > -- >8 --
>> > > > > > >
>> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
>> > > > > > >  implementation
>> > > > > > >
>> > > > > > > This implements the floating-point std::to_chars overloads for float,
>> > > > > > > double and long double.  We use the Ryu library to compute the
>> > > > > shortest
>> > > > > > > round-trippable fixed and scientific forms of a number for float,
>> > > > > double
>> > > > > > > and long double.  We also use Ryu for performing explicit-precision
>> > > > > > > fixed and scientific formatting of float and double. For
>> > > > > > > explicit-precision formatting of long double we fall back to using
>> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
>> > > > > > > implemented from scratch.
>> > > > > > >
>> > > > > > > The supported long double binary formats are binary64, binary80 (x86
>> > > > > > > 80-bit extended precision), binary128 and ibm128.
>> > > > > > >
>> > > > > > > Much of the complexity of the implementation is in computing the exact
>> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
>> > > > > > > checking).  In some cases it's hard to compute the output length
>> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
>> > > > > > > output length and use a sufficiently-sized intermediate buffer if
>> > > > > > > necessary.
>> > > > > > >
>> > > > > > > Another source of complexity is in the general-with-precision
>> > > > > formatting
>> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
>> > > > > > > and where we also take care to avoid having to format the string a
>> > > > > > > second time when the general formatting mode resolves to fixed.
>> > > > > > >
>> > > > > > > This implementation is non-conforming in a couple of ways:
>> > > > > > >
>> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
>> > > > > > >    Microsoft implementation's approach of being consistent with the
>> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
>> > > > > > >    printing the shortest representation.  For example, the shortest
>> > > > > hex
>> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
>> > > > > > >    latter, as does printf.
>> > > > > > >
>> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
>> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
>> > > > > > >    large long double type but lack __int128.  For such targets we make
>> > > > > > >    the long double to_chars overloads go through the double overloads,
>> > > > > > >    which means we lose precision in the output.  (The mantissa of long
>> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
>> > > > > > >    by writing a specialized version of the generic Ryu formatting
>> > > > > > >    routine which works with uint64_t instead of __int128.)
>> > > > > > >
>> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
>> > > > > > >    round-trippability if the difference between the high- and
>> > > > > low-order
>> > > > > > >    exponent is too large.  This is because we treat the type as if it
>> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
>> > > > > low-order
>> > > > > > >    mantissas, so we potentially lose precision from the low-order
>> > > > > part.
>> > > > > > >    Although this precision-dropping behavior is non-conforming, it
>> > > > > seems
>> > > > > > >    consistent with how printf formats __ibm128.
>> > > > > > >
>> > > > > > > libstdc++-v3/ChangeLog:
>> > > > > > >
>> > > > > > > 	* acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
>> > > > > > > 	* config/abi/pre/gnu.ver: Add new exports.
>> > > > > > > 	* configure: Regenerate.
>> > > > > > > 	* include/std/charconv (to_chars): Declare the floating-point
>> > > > > > > 	overloads for float, double and long double.
>> > > > > > > 	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>> > > > > > > 	* src/c++17/Makefile.in: Regenerate.
>> > > > > > > 	* src/c++17/floating_to_chars.cc: New file.
>> > > > > > > 	* testsuite/20_util/to_chars/long_double.cc: New test.
>> > > > > > > 	* testsuite/util/testsuite_abi.cc: Add new symbol version.
>> > > > > > > ---
>> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
>> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
>> > > > > > >  libstdc++-v3/configure                        |    2 +-
>> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
>> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
>> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
>> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
>> > > > > +++++++++++++++++
>> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
>> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
>> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
>> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
>> > > > > > >  create mode 100644
>> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
>> > > > > > >
>> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
>> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
>> > > > > > > --- a/libstdc++-v3/acinclude.m4
>> > > > > > > +++ b/libstdc++-v3/acinclude.m4
>> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
>> > > > > > >  fi
>> > > > > > >
>> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> > > > > > > -libtool_VERSION=6:28:0
>> > > > > > > +libtool_VERSION=6:29:0
>> > > > > > >
>> > > > > > >  # Everything parsed; figure out what files and settings to use.
>> > > > > > >  case $enable_symvers in
>> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
>> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
>> > > > > > > index edf4485e607..9a1bcfd25d1 100644
>> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
>> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
>> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
>> > > > > > >
>> > > > > > >  } GLIBCXX_3.4.27;
>> > > > > > >
>> > > > > > > +GLIBCXX_3.4.29 {
>> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
>> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
>> > > > > > > +
>> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
>> > > > > chars_format)
>> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
>> > > > > > > +
>> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
>> > > > > chars_format,
>> > > > > > > int)
>> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
>> > > > > > > +
>> > > > > > > +} GLIBCXX_3.4.28;
>> > > > > > > +
>> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
>> > > > > > >  CXXABI_1.3 {
>> > > > > > >
>> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
>> > > > > > > index dd54bd406a9..73f771e7335 100755
>> > > > > > > --- a/libstdc++-v3/configure
>> > > > > > > +++ b/libstdc++-v3/configure
>> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
>> > > > > versioning
>> > > > > > > will be disabled." >&2;}
>> > > > > > >  fi
>> > > > > > >
>> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
>> > > > > > > -libtool_VERSION=6:28:0
>> > > > > > > +libtool_VERSION=6:29:0
>> > > > > > >
>> > > > > > >  # Everything parsed; figure out what files and settings to use.
>> > > > > > >  case $enable_symvers in
>> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
>> > > > > > > b/libstdc++-v3/include/std/charconv
>> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
>> > > > > > > --- a/libstdc++-v3/include/std/charconv
>> > > > > > > +++ b/libstdc++-v3/include/std/charconv
>> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
>> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
>> > > > > > >    { return __lhs = __lhs ^ __rhs; }
>> > > > > > >
>> > > > > > > +  // Floating-point std::to_chars
>> > > > > > > +
>> > > > > > > +  // Overloads for float.
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
>> > > > > __value)
>> > > > > > > noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
>> > > > > __value,
>> > > > > > > +			   chars_format __fmt) noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
>> > > > > __value,
>> > > > > > > +			   chars_format __fmt, int __precision)
>> > > > > noexcept;
>> > > > > > > +
>> > > > > > > +  // Overloads for double.
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
>> > > > > __value)
>> > > > > > > noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
>> > > > > __value,
>> > > > > > > +			   chars_format __fmt) noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
>> > > > > __value,
>> > > > > > > +			   chars_format __fmt, int __precision)
>> > > > > noexcept;
>> > > > > > > +
>> > > > > > > +  // Overloads for long double.
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > > > > > __value)
>> > > > > > > +    noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > > > > > __value,
>> > > > > > > +			   chars_format __fmt) noexcept;
>> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
>> > > > > > > __value,
>> > > > > > > +			   chars_format __fmt, int __precision)
>> > > > > noexcept;
>> > > > > > > +
>> > > > > > > +  // If long double has the same binary format as double, then we
>> > > > > just
>> > > > > > > define
>> > > > > > > +  // the long double overloads as wrappers around the corresponding
>> > > > > > > double
>> > > > > > > +  // overloads.
>> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
>> > > > > > > +  inline to_chars_result
>> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
>> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
>> > > > > > > +
>> > > > > > > +  inline to_chars_result
>> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
>> > > > > > > +	   chars_format __fmt) noexcept
>> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
>> > > > > > > +
>> > > > > > > +  inline to_chars_result
>> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
>> > > > > > > +	   chars_format __fmt, int __precision) noexcept
>> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
>> > > > > > > __precision); }
>> > > > > > > +#endif
>> > > > > >
>> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
>> > > > > > introduce an ODR violation because each long double to_chars overload
>> > > > > > could potentially have two different definitions available in a program,
>> > > > > > one out-of-line in floating_to_chars.cc (compiled without
>> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
>> > > > > > -mlong-double-64)..
>> > > > >
>> > > > > But they have different mangled names, so there's no ODR violation.
>> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
>> > > > > is mangled as __float128. You *will* get an ODR violation on targets
>> > > > > where there's no -mlong-double-64 switch, where double and long double
>> > > > > are always the same representation.
>> > > > >
>> > > > > What I'm doing for std::from_chars is adding this in the new
>> > > > > src/c++17/floating_from_chars.cc file:
>> > > > >
>> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
>> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
>> > > > > extern "C" from_chars_result
>> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
>> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
>> > > > > #endif
>> > > > >
>> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
>> > > > > (i.e. from_chars for 64-bit long double) as an alias of
>> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
>> > > > > double).
>> > > >
>> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
>> > >
>> > > Actually that should be:
>> > >
>> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
>> > > extern "C" from_chars_result
>> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
>> > > 					 long double& value,
>> > > 					 chars_format fmt) noexcept
>> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
>> > > #endif
>> > >
>> > > With the right parameter list I don't need to disable the warning.
>> >
>> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
>> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
>>
>> Here's v6 which is rebased against the floating-point from_chars patch
>> and which also works around a false-positive -Wmaybe-uninitialized
>> warning in __floating_to_chars_hex, as well as performs some minor
>> commentary/style cleanups:
>
>Here's v7, with the following changes:
>
>* Remove extraneous indentation (two spaces when inside the std
>  namespace, two spaces after a template header) for better consistency
>  with floating_from_chars.cc
>* Guard the calls to fe[gs]etround with a preprocessor test for
>  _GLIBCXX_USE_C99_FENV_TR1;
>* Properly XFAIL the new long_double.cc test on targets with a
>  large long double type but without __int128, most notably i386
>* Reword the commit message slightly.
>
>-- >8 --
>
>Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
>
>This implements the floating-point std::to_chars overloads for float,
>double and long double.  We use the Ryu library to compute the shortest
>round-trippable fixed and scientific forms for float, double and long
>double.  We also use Ryu for performing explicit-precision fixed and
>scientific formatting of float and double. For explicit-precision
>formatting of long double we fall back to using printf.  Hexadecimal
>formatting for float, double and long double is implemented from
>scratch.
>
>The supported long double binary formats are binary64, binary80 (x86
>80-bit extended precision), binary128 and ibm128.
>
>Much of the complexity of the implementation is in computing the exact
>output length before handing it off to Ryu (which doesn't do bounds
>checking).  In some cases it's hard to compute the output length
>beforehand, so in these cases we instead compute an upper bound on the
>output length and use a sufficiently-sized intermediate buffer only if
>necessary.
>
>Another source of complexity is in the general-with-precision formatting
>mode, where we need to do zero-trimming of the string returned by Ryu,
>and where we also take care to avoid having to format the number through
>Ryu a second time when the general formatting mode resolves to fixed
>(which we determine by doing a scientific formatting first and
>inspecting the scientific exponent).  We avoid going through Ryu twice
>by instead transforming the scientific form to the corresponding fixed
>form via in-place string manipulation.
>
>This implementation is non-conforming in a couple of ways:
>
>1. For the shortest hexadecimal formatting, we currently follow the
>   Microsoft implementation's decision to be consistent with the
>   output of printf's '%a' specifier at the expense of sometimes not
>   printing the shortest representation.  For example, the shortest hex
>   form for the number 1.08p+0 is 2.1p-1, but we output the former
>   instead of the latter, as does printf.
>
>2. The Ryu routine generic_binary_to_decimal that we use for performing
>   shortest formatting for large floating point types is implemented
>   using the __int128 type, but some targets with a large long double
>   type lack __int128 (e.g. i686), so we can't perform shortest
>   formatting of long double on such targets through Ryu.  As a
>   temporary stopgap this patch makes the long double to_chars overloads
>   just dispatch to the double overloads on these targets, which means
>   we lose precision in the output.  (We could potentially fix this by
>   writing a specialized version of Ryu's generic_binary_to_decimal
>   routine that uses uint64_t instead of __int128.)  [Though I wonder if
>   there's a better way to work around the lack of __int128 on i686
>   specifically?]
>
>3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
>   property if the difference between the high- and low-order exponent
>   is large.  This is because we treat __ibm128 as if it has a
>   contiguous 105-bit mantissa by merging the mantissas of the high-
>   and low-order parts (using code extracted from glibc), so we
>   potentially lose precision from the low-order part.  This seems to be
>   consistent with how glibc printf formats __ibm128.
>
>libstdc++-v3/ChangeLog:
>
>	* config/abi/pre/gnu.ver: Add new exports.
>	* include/std/charconv (to_chars): Declare the floating-point
>	overloads for float, double and long double.
>	* src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
>	* src/c++17/Makefile.in: Regenerate.
>	* src/c++17/floating_to_chars.cc: New file.
>	(to_chars): Define for float, double and long double.
>	* testsuite/20_util/to_chars/long_double.cc: New test.

Sorry it took so long to review, this is OK for trunk.

The patch needs some minor changes to rebase it on the current trunk:
The linker script has additions since you send this patch, so the
context in the patch is wrong and it doesn't apply, and in <charconv>
the first line of context in the patch needs to have 'noexcept' added.
That rebase should be easy though.

I'll look at adding __float128 support for powerpc64le.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <jwakely@redhat.com> wrote:
>
> On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> >On Wed, 22 Jul 2020, Patrick Palka wrote:
> >
> >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> >>
> >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> >> >
> >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> >> > > >
> >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> >> > > > > >
> >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> >> > > > > > >
> >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> >> > > > > > > >
> >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> >> > > > > > > > >
> >> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> >> > > > > > > float,
> >> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> >> > > > > > > shortest
> >> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> >> > > > > float,
> >> > > > > > > double
> >> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> >> > > > > > > scientific
> >> > > > > > > > > > formatting of float and double. For formatting long double with
> >> > > > > an
> >> > > > > > > > > > explicit precision argument we use a printf fallback.
> >> > > > > Hexadecimal
> >> > > > > > > > > > formatting for float, double and long double is implemented from
> >> > > > > > > > > > scratch.
> >> > > > > > > > > >
> >> > > > > > > > > > The supported long double binary formats are float64 (same as
> >> > > > > > > double),
> >> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> >> > > > > > > > > >
> >> > > > > > > > > > Much of the complexity of the implementation is in computing the
> >> > > > > > > exact
> >> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> >> > > > > bounds
> >> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> >> > > > > > > before
> >> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> >> > > > > the
> >> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> >> > > > > (if
> >> > > > > > > the
> >> > > > > > > > > > output range is smaller than the upper bound).
> >> > > > > > > > > >
> >> > > > > > > > > > Another source of complexity is in the general-with-precision
> >> > > > > > > formatting
> >> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> >> > > > > by
> >> > > > > > > Ryu, and
> >> > > > > > > > > > where we also take care to avoid having to format the string a
> >> > > > > > > second
> >> > > > > > > > > > time when the general formatting mode resolves to fixed.
> >> > > > > > > > > >
> >> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> >> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> >> > > > > > > > > >
> >> > > > > > > > > > libstdc++-v3/ChangeLog:
> >> > > > > > > > > >
> >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new exports.
> >> > > > > > > > > >    * configure: Regenerate.
> >> > > > > > > > > >    * include/std/charconv (to_chars): Declare the floating-point
> >> > > > > > > > > >    overloads for float, double and long double.
> >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New file.
> >> > > > > > > > > >    * testsuite/20_util/to_chars/long_double.cc: New test.
> >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add new symbol version.
> >> > > > > > > > >
> >> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> >> > > > > to
> >> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> >> > > > > > > format
> >> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> >> > > > > The
> >> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> >> > > > > > > uint64_t
> >> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> >> > > > > > > case.
> >> > > > > > > >
> >> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> >> > > > > most
> >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> >> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> >> > > > > mode.
> >> > > > > > >
> >> > > > > > > Here's v4, which should now correctly support using <charconv> with
> >> > > > > > > -mlong-double-64 on targets with a large default long double type.
> >> > > > > > > This is done by defining the long double to_chars overloads as inline
> >> > > > > > > wrappers around the double overloads within <charconv> whenever
> >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> >> > > > > >
> >> > > > > > >
> >> > > > > > > -- >8 --
> >> > > > > > >
> >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> >> > > > > > >  implementation
> >> > > > > > >
> >> > > > > > > This implements the floating-point std::to_chars overloads for float,
> >> > > > > > > double and long double.  We use the Ryu library to compute the
> >> > > > > shortest
> >> > > > > > > round-trippable fixed and scientific forms of a number for float,
> >> > > > > double
> >> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> >> > > > > > > fixed and scientific formatting of float and double. For
> >> > > > > > > explicit-precision formatting of long double we fall back to using
> >> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> >> > > > > > > implemented from scratch.
> >> > > > > > >
> >> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> >> > > > > > >
> >> > > > > > > Much of the complexity of the implementation is in computing the exact
> >> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> >> > > > > > > checking).  In some cases it's hard to compute the output length
> >> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> >> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> >> > > > > > > necessary.
> >> > > > > > >
> >> > > > > > > Another source of complexity is in the general-with-precision
> >> > > > > formatting
> >> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> >> > > > > > > and where we also take care to avoid having to format the string a
> >> > > > > > > second time when the general formatting mode resolves to fixed.
> >> > > > > > >
> >> > > > > > > This implementation is non-conforming in a couple of ways:
> >> > > > > > >
> >> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> >> > > > > > >    Microsoft implementation's approach of being consistent with the
> >> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> >> > > > > > >    printing the shortest representation.  For example, the shortest
> >> > > > > hex
> >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> >> > > > > > >    latter, as does printf.
> >> > > > > > >
> >> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> >> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> >> > > > > > >    large long double type but lack __int128.  For such targets we make
> >> > > > > > >    the long double to_chars overloads go through the double overloads,
> >> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> >> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> >> > > > > > >    by writing a specialized version of the generic Ryu formatting
> >> > > > > > >    routine which works with uint64_t instead of __int128.)
> >> > > > > > >
> >> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> >> > > > > > >    round-trippability if the difference between the high- and
> >> > > > > low-order
> >> > > > > > >    exponent is too large.  This is because we treat the type as if it
> >> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> >> > > > > low-order
> >> > > > > > >    mantissas, so we potentially lose precision from the low-order
> >> > > > > part.
> >> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> >> > > > > seems
> >> > > > > > >    consistent with how printf formats __ibm128.
> >> > > > > > >
> >> > > > > > > libstdc++-v3/ChangeLog:
> >> > > > > > >
> >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> >> > > > > > >  * configure: Regenerate.
> >> > > > > > >  * include/std/charconv (to_chars): Declare the floating-point
> >> > > > > > >  overloads for float, double and long double.
> >> > > > > > >  * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New test.
> >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new symbol version.
> >> > > > > > > ---
> >> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> >> > > > > > >  libstdc++-v3/configure                        |    2 +-
> >> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> >> > > > > +++++++++++++++++
> >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> >> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> >> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> >> > > > > > >  create mode 100644
> >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> >> > > > > > >
> >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> >> > > > > > >  fi
> >> > > > > > >
> >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> >> > > > > > > -libtool_VERSION=6:28:0
> >> > > > > > > +libtool_VERSION=6:29:0
> >> > > > > > >
> >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> >> > > > > > >  case $enable_symvers in
> >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> >> > > > > > >
> >> > > > > > >  } GLIBCXX_3.4.27;
> >> > > > > > >
> >> > > > > > > +GLIBCXX_3.4.29 {
> >> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> >> > > > > > > +
> >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> >> > > > > chars_format)
> >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> >> > > > > > > +
> >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> >> > > > > chars_format,
> >> > > > > > > int)
> >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> >> > > > > > > +
> >> > > > > > > +} GLIBCXX_3.4.28;
> >> > > > > > > +
> >> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> >> > > > > > >  CXXABI_1.3 {
> >> > > > > > >
> >> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> >> > > > > > > index dd54bd406a9..73f771e7335 100755
> >> > > > > > > --- a/libstdc++-v3/configure
> >> > > > > > > +++ b/libstdc++-v3/configure
> >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> >> > > > > versioning
> >> > > > > > > will be disabled." >&2;}
> >> > > > > > >  fi
> >> > > > > > >
> >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> >> > > > > > > -libtool_VERSION=6:28:0
> >> > > > > > > +libtool_VERSION=6:29:0
> >> > > > > > >
> >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> >> > > > > > >  case $enable_symvers in
> >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> >> > > > > > > b/libstdc++-v3/include/std/charconv
> >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> >> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> >> > > > > > >
> >> > > > > > > +  // Floating-point std::to_chars
> >> > > > > > > +
> >> > > > > > > +  // Overloads for float.
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> >> > > > > __value)
> >> > > > > > > noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> >> > > > > __value,
> >> > > > > > > +                           chars_format __fmt) noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> >> > > > > __value,
> >> > > > > > > +                           chars_format __fmt, int __precision)
> >> > > > > noexcept;
> >> > > > > > > +
> >> > > > > > > +  // Overloads for double.
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> >> > > > > __value)
> >> > > > > > > noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> >> > > > > __value,
> >> > > > > > > +                           chars_format __fmt) noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> >> > > > > __value,
> >> > > > > > > +                           chars_format __fmt, int __precision)
> >> > > > > noexcept;
> >> > > > > > > +
> >> > > > > > > +  // Overloads for long double.
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> >> > > > > > > __value)
> >> > > > > > > +    noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> >> > > > > > > __value,
> >> > > > > > > +                           chars_format __fmt) noexcept;
> >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> >> > > > > > > __value,
> >> > > > > > > +                           chars_format __fmt, int __precision)
> >> > > > > noexcept;
> >> > > > > > > +
> >> > > > > > > +  // If long double has the same binary format as double, then we
> >> > > > > just
> >> > > > > > > define
> >> > > > > > > +  // the long double overloads as wrappers around the corresponding
> >> > > > > > > double
> >> > > > > > > +  // overloads.
> >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> >> > > > > > > +  inline to_chars_result
> >> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> >> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> >> > > > > > > +
> >> > > > > > > +  inline to_chars_result
> >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> >> > > > > > > +           chars_format __fmt) noexcept
> >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> >> > > > > > > +
> >> > > > > > > +  inline to_chars_result
> >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> >> > > > > > > +           chars_format __fmt, int __precision) noexcept
> >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> >> > > > > > > __precision); }
> >> > > > > > > +#endif
> >> > > > > >
> >> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> >> > > > > > introduce an ODR violation because each long double to_chars overload
> >> > > > > > could potentially have two different definitions available in a program,
> >> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> >> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> >> > > > > > -mlong-double-64)..
> >> > > > >
> >> > > > > But they have different mangled names, so there's no ODR violation.
> >> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> >> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> >> > > > > where there's no -mlong-double-64 switch, where double and long double
> >> > > > > are always the same representation.
> >> > > > >
> >> > > > > What I'm doing for std::from_chars is adding this in the new
> >> > > > > src/c++17/floating_from_chars.cc file:
> >> > > > >
> >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> >> > > > > extern "C" from_chars_result
> >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> >> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> >> > > > > #endif
> >> > > > >
> >> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> >> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> >> > > > > double).
> >> > > >
> >> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> >> > >
> >> > > Actually that should be:
> >> > >
> >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> >> > > extern "C" from_chars_result
> >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> >> > >                                   long double& value,
> >> > >                                   chars_format fmt) noexcept
> >> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> >> > > #endif
> >> > >
> >> > > With the right parameter list I don't need to disable the warning.
> >> >
> >> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> >>
> >> Here's v6 which is rebased against the floating-point from_chars patch
> >> and which also works around a false-positive -Wmaybe-uninitialized
> >> warning in __floating_to_chars_hex, as well as performs some minor
> >> commentary/style cleanups:
> >
> >Here's v7, with the following changes:
> >
> >* Remove extraneous indentation (two spaces when inside the std
> >  namespace, two spaces after a template header) for better consistency
> >  with floating_from_chars.cc
> >* Guard the calls to fe[gs]etround with a preprocessor test for
> >  _GLIBCXX_USE_C99_FENV_TR1;
> >* Properly XFAIL the new long_double.cc test on targets with a
> >  large long double type but without __int128, most notably i386
> >* Reword the commit message slightly.
> >
> >-- >8 --
> >
> >Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
> >
> >This implements the floating-point std::to_chars overloads for float,
> >double and long double.  We use the Ryu library to compute the shortest
> >round-trippable fixed and scientific forms for float, double and long
> >double.  We also use Ryu for performing explicit-precision fixed and
> >scientific formatting of float and double. For explicit-precision
> >formatting of long double we fall back to using printf.  Hexadecimal
> >formatting for float, double and long double is implemented from
> >scratch.
> >
> >The supported long double binary formats are binary64, binary80 (x86
> >80-bit extended precision), binary128 and ibm128.
> >
> >Much of the complexity of the implementation is in computing the exact
> >output length before handing it off to Ryu (which doesn't do bounds
> >checking).  In some cases it's hard to compute the output length
> >beforehand, so in these cases we instead compute an upper bound on the
> >output length and use a sufficiently-sized intermediate buffer only if
> >necessary.
> >
> >Another source of complexity is in the general-with-precision formatting
> >mode, where we need to do zero-trimming of the string returned by Ryu,
> >and where we also take care to avoid having to format the number through
> >Ryu a second time when the general formatting mode resolves to fixed
> >(which we determine by doing a scientific formatting first and
> >inspecting the scientific exponent).  We avoid going through Ryu twice
> >by instead transforming the scientific form to the corresponding fixed
> >form via in-place string manipulation.
> >
> >This implementation is non-conforming in a couple of ways:
> >
> >1. For the shortest hexadecimal formatting, we currently follow the
> >   Microsoft implementation's decision to be consistent with the
> >   output of printf's '%a' specifier at the expense of sometimes not
> >   printing the shortest representation.  For example, the shortest hex
> >   form for the number 1.08p+0 is 2.1p-1, but we output the former
> >   instead of the latter, as does printf.
> >
> >2. The Ryu routine generic_binary_to_decimal that we use for performing
> >   shortest formatting for large floating point types is implemented
> >   using the __int128 type, but some targets with a large long double
> >   type lack __int128 (e.g. i686), so we can't perform shortest
> >   formatting of long double on such targets through Ryu.  As a
> >   temporary stopgap this patch makes the long double to_chars overloads
> >   just dispatch to the double overloads on these targets, which means
> >   we lose precision in the output.  (We could potentially fix this by
> >   writing a specialized version of Ryu's generic_binary_to_decimal
> >   routine that uses uint64_t instead of __int128.)  [Though I wonder if
> >   there's a better way to work around the lack of __int128 on i686
> >   specifically?]
> >
> >3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
> >   property if the difference between the high- and low-order exponent
> >   is large.  This is because we treat __ibm128 as if it has a
> >   contiguous 105-bit mantissa by merging the mantissas of the high-
> >   and low-order parts (using code extracted from glibc), so we
> >   potentially lose precision from the low-order part.  This seems to be
> >   consistent with how glibc printf formats __ibm128.
> >
> >libstdc++-v3/ChangeLog:
> >
> >       * config/abi/pre/gnu.ver: Add new exports.
> >       * include/std/charconv (to_chars): Declare the floating-point
> >       overloads for float, double and long double.
> >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> >       * src/c++17/Makefile.in: Regenerate.
> >       * src/c++17/floating_to_chars.cc: New file.
> >       (to_chars): Define for float, double and long double.
> >       * testsuite/20_util/to_chars/long_double.cc: New test.
>
> Sorry it took so long to review, this is OK for trunk.
>
> The patch needs some minor changes to rebase it on the current trunk:
> The linker script has additions since you send this patch, so the
> context in the patch is wrong and it doesn't apply, and in <charconv>
> the first line of context in the patch needs to have 'noexcept' added.
> That rebase should be easy though.
>
> I'll look at adding __float128 support for powerpc64le.

Thanks a lot.  I committed the patch series just now, after rebasing
and retesting on x86_64, aarch64 and ppc64le.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Christophe Lyon]

Hi,


On Fri, 18 Dec 2020 at 05:13, Patrick Palka via Gcc-patches
<gcc-patches@gcc.gnu.org> wrote:
>
> On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <jwakely@redhat.com> wrote:
> >
> > On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> > >On Wed, 22 Jul 2020, Patrick Palka wrote:
> > >
> > >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> > >>
> > >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > >> >
> > >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > >> > > >
> > >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > >> > > > > >
> > >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > >> > > > > > >
> > >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > >> > > > > > > >
> > >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > >> > > > > > > > >
> > >> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> > >> > > > > > > float,
> > >> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> > >> > > > > > > shortest
> > >> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> > >> > > > > float,
> > >> > > > > > > double
> > >> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > >> > > > > > > scientific
> > >> > > > > > > > > > formatting of float and double. For formatting long double with
> > >> > > > > an
> > >> > > > > > > > > > explicit precision argument we use a printf fallback.
> > >> > > > > Hexadecimal
> > >> > > > > > > > > > formatting for float, double and long double is implemented from
> > >> > > > > > > > > > scratch.
> > >> > > > > > > > > >
> > >> > > > > > > > > > The supported long double binary formats are float64 (same as
> > >> > > > > > > double),
> > >> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > >> > > > > > > > > >
> > >> > > > > > > > > > Much of the complexity of the implementation is in computing the
> > >> > > > > > > exact
> > >> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > >> > > > > bounds
> > >> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> > >> > > > > > > before
> > >> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > >> > > > > the
> > >> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > >> > > > > (if
> > >> > > > > > > the
> > >> > > > > > > > > > output range is smaller than the upper bound).
> > >> > > > > > > > > >
> > >> > > > > > > > > > Another source of complexity is in the general-with-precision
> > >> > > > > > > formatting
> > >> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > >> > > > > by
> > >> > > > > > > Ryu, and
> > >> > > > > > > > > > where we also take care to avoid having to format the string a
> > >> > > > > > > second
> > >> > > > > > > > > > time when the general formatting mode resolves to fixed.
> > >> > > > > > > > > >
> > >> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > >> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > >> > > > > > > > > >
> > >> > > > > > > > > > libstdc++-v3/ChangeLog:
> > >> > > > > > > > > >
> > >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new exports.
> > >> > > > > > > > > >    * configure: Regenerate.
> > >> > > > > > > > > >    * include/std/charconv (to_chars): Declare the floating-point
> > >> > > > > > > > > >    overloads for float, double and long double.
> > >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> > >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New file.
> > >> > > > > > > > > >    * testsuite/20_util/to_chars/long_double.cc: New test.
> > >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > >> > > > > > > > >
> > >> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > >> > > > > to
> > >> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > >> > > > > > > format
> > >> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > >> > > > > The
> > >> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > >> > > > > > > uint64_t
> > >> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > >> > > > > > > case.
> > >> > > > > > > >
> > >> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > >> > > > > most
> > >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > >> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > >> > > > > mode.
> > >> > > > > > >
> > >> > > > > > > Here's v4, which should now correctly support using <charconv> with
> > >> > > > > > > -mlong-double-64 on targets with a large default long double type.
> > >> > > > > > > This is done by defining the long double to_chars overloads as inline
> > >> > > > > > > wrappers around the double overloads within <charconv> whenever
> > >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > >> > > > > >
> > >> > > > > > >
> > >> > > > > > > -- >8 --
> > >> > > > > > >
> > >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > >> > > > > > >  implementation
> > >> > > > > > >
> > >> > > > > > > This implements the floating-point std::to_chars overloads for float,
> > >> > > > > > > double and long double.  We use the Ryu library to compute the
> > >> > > > > shortest
> > >> > > > > > > round-trippable fixed and scientific forms of a number for float,
> > >> > > > > double
> > >> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> > >> > > > > > > fixed and scientific formatting of float and double. For
> > >> > > > > > > explicit-precision formatting of long double we fall back to using
> > >> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > >> > > > > > > implemented from scratch.
> > >> > > > > > >
> > >> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> > >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > >> > > > > > >
> > >> > > > > > > Much of the complexity of the implementation is in computing the exact
> > >> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > >> > > > > > > checking).  In some cases it's hard to compute the output length
> > >> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > >> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> > >> > > > > > > necessary.
> > >> > > > > > >
> > >> > > > > > > Another source of complexity is in the general-with-precision
> > >> > > > > formatting
> > >> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > >> > > > > > > and where we also take care to avoid having to format the string a
> > >> > > > > > > second time when the general formatting mode resolves to fixed.
> > >> > > > > > >
> > >> > > > > > > This implementation is non-conforming in a couple of ways:
> > >> > > > > > >
> > >> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > >> > > > > > >    Microsoft implementation's approach of being consistent with the
> > >> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > >> > > > > > >    printing the shortest representation.  For example, the shortest
> > >> > > > > hex
> > >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > >> > > > > > >    latter, as does printf.
> > >> > > > > > >
> > >> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > >> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > >> > > > > > >    large long double type but lack __int128.  For such targets we make
> > >> > > > > > >    the long double to_chars overloads go through the double overloads,
> > >> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> > >> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > >> > > > > > >    by writing a specialized version of the generic Ryu formatting
> > >> > > > > > >    routine which works with uint64_t instead of __int128.)
> > >> > > > > > >
> > >> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > >> > > > > > >    round-trippability if the difference between the high- and
> > >> > > > > low-order
> > >> > > > > > >    exponent is too large.  This is because we treat the type as if it
> > >> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > >> > > > > low-order
> > >> > > > > > >    mantissas, so we potentially lose precision from the low-order
> > >> > > > > part.
> > >> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> > >> > > > > seems
> > >> > > > > > >    consistent with how printf formats __ibm128.
> > >> > > > > > >
> > >> > > > > > > libstdc++-v3/ChangeLog:
> > >> > > > > > >
> > >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> > >> > > > > > >  * configure: Regenerate.
> > >> > > > > > >  * include/std/charconv (to_chars): Declare the floating-point
> > >> > > > > > >  overloads for float, double and long double.
> > >> > > > > > >  * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> > >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> > >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New test.
> > >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > >> > > > > > > ---
> > >> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > >> > > > > > >  libstdc++-v3/configure                        |    2 +-
> > >> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > >> > > > > +++++++++++++++++
> > >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > >> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > >> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > >> > > > > > >  create mode 100644
> > >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > >> > > > > > >
> > >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > >> > > > > > >  fi
> > >> > > > > > >
> > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > >> > > > > > > -libtool_VERSION=6:28:0
> > >> > > > > > > +libtool_VERSION=6:29:0
> > >> > > > > > >
> > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > >> > > > > > >  case $enable_symvers in
> > >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > >> > > > > > >
> > >> > > > > > >  } GLIBCXX_3.4.27;
> > >> > > > > > >
> > >> > > > > > > +GLIBCXX_3.4.29 {
> > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > >> > > > > > > +
> > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > >> > > > > chars_format)
> > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > >> > > > > > > +
> > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > >> > > > > chars_format,
> > >> > > > > > > int)
> > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > >> > > > > > > +
> > >> > > > > > > +} GLIBCXX_3.4.28;
> > >> > > > > > > +
> > >> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > >> > > > > > >  CXXABI_1.3 {
> > >> > > > > > >
> > >> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > >> > > > > > > index dd54bd406a9..73f771e7335 100755
> > >> > > > > > > --- a/libstdc++-v3/configure
> > >> > > > > > > +++ b/libstdc++-v3/configure
> > >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > >> > > > > versioning
> > >> > > > > > > will be disabled." >&2;}
> > >> > > > > > >  fi
> > >> > > > > > >
> > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > >> > > > > > > -libtool_VERSION=6:28:0
> > >> > > > > > > +libtool_VERSION=6:29:0
> > >> > > > > > >
> > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > >> > > > > > >  case $enable_symvers in
> > >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > >> > > > > > > b/libstdc++-v3/include/std/charconv
> > >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > >> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > >> > > > > > >
> > >> > > > > > > +  // Floating-point std::to_chars
> > >> > > > > > > +
> > >> > > > > > > +  // Overloads for float.
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > >> > > > > __value)
> > >> > > > > > > noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > >> > > > > __value,
> > >> > > > > > > +                           chars_format __fmt) noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > >> > > > > __value,
> > >> > > > > > > +                           chars_format __fmt, int __precision)
> > >> > > > > noexcept;
> > >> > > > > > > +
> > >> > > > > > > +  // Overloads for double.
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > >> > > > > __value)
> > >> > > > > > > noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > >> > > > > __value,
> > >> > > > > > > +                           chars_format __fmt) noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > >> > > > > __value,
> > >> > > > > > > +                           chars_format __fmt, int __precision)
> > >> > > > > noexcept;
> > >> > > > > > > +
> > >> > > > > > > +  // Overloads for long double.
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > >> > > > > > > __value)
> > >> > > > > > > +    noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > >> > > > > > > __value,
> > >> > > > > > > +                           chars_format __fmt) noexcept;
> > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > >> > > > > > > __value,
> > >> > > > > > > +                           chars_format __fmt, int __precision)
> > >> > > > > noexcept;
> > >> > > > > > > +
> > >> > > > > > > +  // If long double has the same binary format as double, then we
> > >> > > > > just
> > >> > > > > > > define
> > >> > > > > > > +  // the long double overloads as wrappers around the corresponding
> > >> > > > > > > double
> > >> > > > > > > +  // overloads.
> > >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > >> > > > > > > +  inline to_chars_result
> > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > >> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > >> > > > > > > +
> > >> > > > > > > +  inline to_chars_result
> > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > >> > > > > > > +           chars_format __fmt) noexcept
> > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > >> > > > > > > +
> > >> > > > > > > +  inline to_chars_result
> > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > >> > > > > > > +           chars_format __fmt, int __precision) noexcept
> > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > >> > > > > > > __precision); }
> > >> > > > > > > +#endif
> > >> > > > > >
> > >> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > >> > > > > > introduce an ODR violation because each long double to_chars overload
> > >> > > > > > could potentially have two different definitions available in a program,
> > >> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> > >> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > >> > > > > > -mlong-double-64)..
> > >> > > > >
> > >> > > > > But they have different mangled names, so there's no ODR violation.
> > >> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > >> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> > >> > > > > where there's no -mlong-double-64 switch, where double and long double
> > >> > > > > are always the same representation.
> > >> > > > >
> > >> > > > > What I'm doing for std::from_chars is adding this in the new
> > >> > > > > src/c++17/floating_from_chars.cc file:
> > >> > > > >
> > >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > >> > > > > extern "C" from_chars_result
> > >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > >> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > >> > > > > #endif
> > >> > > > >
> > >> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > >> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> > >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > >> > > > > double).
> > >> > > >
> > >> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > >> > >
> > >> > > Actually that should be:
> > >> > >
> > >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > >> > > extern "C" from_chars_result
> > >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > >> > >                                   long double& value,
> > >> > >                                   chars_format fmt) noexcept
> > >> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > >> > > #endif
> > >> > >
> > >> > > With the right parameter list I don't need to disable the warning.
> > >> >
> > >> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> > >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> > >>
> > >> Here's v6 which is rebased against the floating-point from_chars patch
> > >> and which also works around a false-positive -Wmaybe-uninitialized
> > >> warning in __floating_to_chars_hex, as well as performs some minor
> > >> commentary/style cleanups:
> > >
> > >Here's v7, with the following changes:
> > >
> > >* Remove extraneous indentation (two spaces when inside the std
> > >  namespace, two spaces after a template header) for better consistency
> > >  with floating_from_chars.cc
> > >* Guard the calls to fe[gs]etround with a preprocessor test for
> > >  _GLIBCXX_USE_C99_FENV_TR1;
> > >* Properly XFAIL the new long_double.cc test on targets with a
> > >  large long double type but without __int128, most notably i386
> > >* Reword the commit message slightly.
> > >
> > >-- >8 --
> > >
> > >Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
> > >
> > >This implements the floating-point std::to_chars overloads for float,
> > >double and long double.  We use the Ryu library to compute the shortest
> > >round-trippable fixed and scientific forms for float, double and long
> > >double.  We also use Ryu for performing explicit-precision fixed and
> > >scientific formatting of float and double. For explicit-precision
> > >formatting of long double we fall back to using printf.  Hexadecimal
> > >formatting for float, double and long double is implemented from
> > >scratch.
> > >
> > >The supported long double binary formats are binary64, binary80 (x86
> > >80-bit extended precision), binary128 and ibm128.
> > >
> > >Much of the complexity of the implementation is in computing the exact
> > >output length before handing it off to Ryu (which doesn't do bounds
> > >checking).  In some cases it's hard to compute the output length
> > >beforehand, so in these cases we instead compute an upper bound on the
> > >output length and use a sufficiently-sized intermediate buffer only if
> > >necessary.
> > >
> > >Another source of complexity is in the general-with-precision formatting
> > >mode, where we need to do zero-trimming of the string returned by Ryu,
> > >and where we also take care to avoid having to format the number through
> > >Ryu a second time when the general formatting mode resolves to fixed
> > >(which we determine by doing a scientific formatting first and
> > >inspecting the scientific exponent).  We avoid going through Ryu twice
> > >by instead transforming the scientific form to the corresponding fixed
> > >form via in-place string manipulation.
> > >
> > >This implementation is non-conforming in a couple of ways:
> > >
> > >1. For the shortest hexadecimal formatting, we currently follow the
> > >   Microsoft implementation's decision to be consistent with the
> > >   output of printf's '%a' specifier at the expense of sometimes not
> > >   printing the shortest representation.  For example, the shortest hex
> > >   form for the number 1.08p+0 is 2.1p-1, but we output the former
> > >   instead of the latter, as does printf.
> > >
> > >2. The Ryu routine generic_binary_to_decimal that we use for performing
> > >   shortest formatting for large floating point types is implemented
> > >   using the __int128 type, but some targets with a large long double
> > >   type lack __int128 (e.g. i686), so we can't perform shortest
> > >   formatting of long double on such targets through Ryu.  As a
> > >   temporary stopgap this patch makes the long double to_chars overloads
> > >   just dispatch to the double overloads on these targets, which means
> > >   we lose precision in the output.  (We could potentially fix this by
> > >   writing a specialized version of Ryu's generic_binary_to_decimal
> > >   routine that uses uint64_t instead of __int128.)  [Though I wonder if
> > >   there's a better way to work around the lack of __int128 on i686
> > >   specifically?]
> > >
> > >3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
> > >   property if the difference between the high- and low-order exponent
> > >   is large.  This is because we treat __ibm128 as if it has a
> > >   contiguous 105-bit mantissa by merging the mantissas of the high-
> > >   and low-order parts (using code extracted from glibc), so we
> > >   potentially lose precision from the low-order part.  This seems to be
> > >   consistent with how glibc printf formats __ibm128.
> > >
> > >libstdc++-v3/ChangeLog:
> > >
> > >       * config/abi/pre/gnu.ver: Add new exports.
> > >       * include/std/charconv (to_chars): Declare the floating-point
> > >       overloads for float, double and long double.
> > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > >       * src/c++17/Makefile.in: Regenerate.
> > >       * src/c++17/floating_to_chars.cc: New file.
> > >       (to_chars): Define for float, double and long double.
> > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> >
> > Sorry it took so long to review, this is OK for trunk.
> >
> > The patch needs some minor changes to rebase it on the current trunk:
> > The linker script has additions since you send this patch, so the
> > context in the patch is wrong and it doesn't apply, and in <charconv>
> > the first line of context in the patch needs to have 'noexcept' added.
> > That rebase should be easy though.
> >
> > I'll look at adding __float128 support for powerpc64le.
>
> Thanks a lot.  I committed the patch series just now, after rebasing
> and retesting on x86_64, aarch64 and ppc64le.
>

My newlib-based toolchains (arm-eabi, aarch64-elf) fail to build after
this commit, because:
libstdc++-v3/src/c++17/floating_to_chars.cc:951:40: error:
'FE_TONEAREST' was not declared in this scope
  951 |             if (saved_rounding_mode != FE_TONEAREST)

I'm (still) using newlib-3.3.0, and I think newlib's fenv.h was updated
this year for arm/aarch64, so I suspect bumping to 3.4.0 would
avoid the problem. However, is this something you want to support?
(I mean the possibility that FE_TONEAREST is not supported etc...)

Thanks,

Christophe

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Jonathan Wakely]

I think we can test for it with #ifdef and just provide an incorrectly
rounded result for newlib.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Fri, 18 Dec 2020, Christophe Lyon wrote:

> Hi,
> 
> 
> On Fri, 18 Dec 2020 at 05:13, Patrick Palka via Gcc-patches
> <gcc-patches@gcc.gnu.org> wrote:
> >
> > On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <jwakely@redhat.com> wrote:
> > >
> > > On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> > > >On Wed, 22 Jul 2020, Patrick Palka wrote:
> > > >
> > > >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> > > >>
> > > >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > >> >
> > > >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > > >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > >> > > >
> > > >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > >> > > > > >
> > > >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > >> > > > > > >
> > > >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > >> > > > > > > >
> > > >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > >> > > > > > > > >
> > > >> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> > > >> > > > > > > float,
> > > >> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> > > >> > > > > > > shortest
> > > >> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> > > >> > > > > float,
> > > >> > > > > > > double
> > > >> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > >> > > > > > > scientific
> > > >> > > > > > > > > > formatting of float and double. For formatting long double with
> > > >> > > > > an
> > > >> > > > > > > > > > explicit precision argument we use a printf fallback.
> > > >> > > > > Hexadecimal
> > > >> > > > > > > > > > formatting for float, double and long double is implemented from
> > > >> > > > > > > > > > scratch.
> > > >> > > > > > > > > >
> > > >> > > > > > > > > > The supported long double binary formats are float64 (same as
> > > >> > > > > > > double),
> > > >> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > >> > > > > > > > > >
> > > >> > > > > > > > > > Much of the complexity of the implementation is in computing the
> > > >> > > > > > > exact
> > > >> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > >> > > > > bounds
> > > >> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> > > >> > > > > > > before
> > > >> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > >> > > > > the
> > > >> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > >> > > > > (if
> > > >> > > > > > > the
> > > >> > > > > > > > > > output range is smaller than the upper bound).
> > > >> > > > > > > > > >
> > > >> > > > > > > > > > Another source of complexity is in the general-with-precision
> > > >> > > > > > > formatting
> > > >> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > >> > > > > by
> > > >> > > > > > > Ryu, and
> > > >> > > > > > > > > > where we also take care to avoid having to format the string a
> > > >> > > > > > > second
> > > >> > > > > > > > > > time when the general formatting mode resolves to fixed.
> > > >> > > > > > > > > >
> > > >> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > >> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > >> > > > > > > > > >
> > > >> > > > > > > > > > libstdc++-v3/ChangeLog:
> > > >> > > > > > > > > >
> > > >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new exports.
> > > >> > > > > > > > > >    * configure: Regenerate.
> > > >> > > > > > > > > >    * include/std/charconv (to_chars): Declare the floating-point
> > > >> > > > > > > > > >    overloads for float, double and long double.
> > > >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> > > >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New file.
> > > >> > > > > > > > > >    * testsuite/20_util/to_chars/long_double.cc: New test.
> > > >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > >> > > > > > > > >
> > > >> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > >> > > > > to
> > > >> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > >> > > > > > > format
> > > >> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > >> > > > > The
> > > >> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > >> > > > > > > uint64_t
> > > >> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > >> > > > > > > case.
> > > >> > > > > > > >
> > > >> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > >> > > > > most
> > > >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > >> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > >> > > > > mode.
> > > >> > > > > > >
> > > >> > > > > > > Here's v4, which should now correctly support using <charconv> with
> > > >> > > > > > > -mlong-double-64 on targets with a large default long double type.
> > > >> > > > > > > This is done by defining the long double to_chars overloads as inline
> > > >> > > > > > > wrappers around the double overloads within <charconv> whenever
> > > >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > >> > > > > >
> > > >> > > > > > >
> > > >> > > > > > > -- >8 --
> > > >> > > > > > >
> > > >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > >> > > > > > >  implementation
> > > >> > > > > > >
> > > >> > > > > > > This implements the floating-point std::to_chars overloads for float,
> > > >> > > > > > > double and long double.  We use the Ryu library to compute the
> > > >> > > > > shortest
> > > >> > > > > > > round-trippable fixed and scientific forms of a number for float,
> > > >> > > > > double
> > > >> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> > > >> > > > > > > fixed and scientific formatting of float and double. For
> > > >> > > > > > > explicit-precision formatting of long double we fall back to using
> > > >> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > >> > > > > > > implemented from scratch.
> > > >> > > > > > >
> > > >> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> > > >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > > >> > > > > > >
> > > >> > > > > > > Much of the complexity of the implementation is in computing the exact
> > > >> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > >> > > > > > > checking).  In some cases it's hard to compute the output length
> > > >> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > >> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> > > >> > > > > > > necessary.
> > > >> > > > > > >
> > > >> > > > > > > Another source of complexity is in the general-with-precision
> > > >> > > > > formatting
> > > >> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > >> > > > > > > and where we also take care to avoid having to format the string a
> > > >> > > > > > > second time when the general formatting mode resolves to fixed.
> > > >> > > > > > >
> > > >> > > > > > > This implementation is non-conforming in a couple of ways:
> > > >> > > > > > >
> > > >> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > >> > > > > > >    Microsoft implementation's approach of being consistent with the
> > > >> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > >> > > > > > >    printing the shortest representation.  For example, the shortest
> > > >> > > > > hex
> > > >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > >> > > > > > >    latter, as does printf.
> > > >> > > > > > >
> > > >> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > >> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > >> > > > > > >    large long double type but lack __int128.  For such targets we make
> > > >> > > > > > >    the long double to_chars overloads go through the double overloads,
> > > >> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> > > >> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > >> > > > > > >    by writing a specialized version of the generic Ryu formatting
> > > >> > > > > > >    routine which works with uint64_t instead of __int128.)
> > > >> > > > > > >
> > > >> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > >> > > > > > >    round-trippability if the difference between the high- and
> > > >> > > > > low-order
> > > >> > > > > > >    exponent is too large.  This is because we treat the type as if it
> > > >> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > >> > > > > low-order
> > > >> > > > > > >    mantissas, so we potentially lose precision from the low-order
> > > >> > > > > part.
> > > >> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> > > >> > > > > seems
> > > >> > > > > > >    consistent with how printf formats __ibm128.
> > > >> > > > > > >
> > > >> > > > > > > libstdc++-v3/ChangeLog:
> > > >> > > > > > >
> > > >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> > > >> > > > > > >  * configure: Regenerate.
> > > >> > > > > > >  * include/std/charconv (to_chars): Declare the floating-point
> > > >> > > > > > >  overloads for float, double and long double.
> > > >> > > > > > >  * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> > > >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> > > >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New test.
> > > >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > >> > > > > > > ---
> > > >> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > >> > > > > > >  libstdc++-v3/configure                        |    2 +-
> > > >> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > >> > > > > +++++++++++++++++
> > > >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > >> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > >> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > >> > > > > > >  create mode 100644
> > > >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > >> > > > > > >
> > > >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > > >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > >> > > > > > >  fi
> > > >> > > > > > >
> > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > >> > > > > > > -libtool_VERSION=6:28:0
> > > >> > > > > > > +libtool_VERSION=6:29:0
> > > >> > > > > > >
> > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > >> > > > > > >  case $enable_symvers in
> > > >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > >> > > > > > >
> > > >> > > > > > >  } GLIBCXX_3.4.27;
> > > >> > > > > > >
> > > >> > > > > > > +GLIBCXX_3.4.29 {
> > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > >> > > > > > > +
> > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > >> > > > > chars_format)
> > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > >> > > > > > > +
> > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > >> > > > > chars_format,
> > > >> > > > > > > int)
> > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > >> > > > > > > +
> > > >> > > > > > > +} GLIBCXX_3.4.28;
> > > >> > > > > > > +
> > > >> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > >> > > > > > >  CXXABI_1.3 {
> > > >> > > > > > >
> > > >> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > >> > > > > > > index dd54bd406a9..73f771e7335 100755
> > > >> > > > > > > --- a/libstdc++-v3/configure
> > > >> > > > > > > +++ b/libstdc++-v3/configure
> > > >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > >> > > > > versioning
> > > >> > > > > > > will be disabled." >&2;}
> > > >> > > > > > >  fi
> > > >> > > > > > >
> > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > >> > > > > > > -libtool_VERSION=6:28:0
> > > >> > > > > > > +libtool_VERSION=6:29:0
> > > >> > > > > > >
> > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > >> > > > > > >  case $enable_symvers in
> > > >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > >> > > > > > > b/libstdc++-v3/include/std/charconv
> > > >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > > >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > >> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > >> > > > > > >
> > > >> > > > > > > +  // Floating-point std::to_chars
> > > >> > > > > > > +
> > > >> > > > > > > +  // Overloads for float.
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > >> > > > > __value)
> > > >> > > > > > > noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > >> > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > >> > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > >> > > > > noexcept;
> > > >> > > > > > > +
> > > >> > > > > > > +  // Overloads for double.
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > >> > > > > __value)
> > > >> > > > > > > noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > >> > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > >> > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > >> > > > > noexcept;
> > > >> > > > > > > +
> > > >> > > > > > > +  // Overloads for long double.
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > >> > > > > > > __value)
> > > >> > > > > > > +    noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > >> > > > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > >> > > > > > > __value,
> > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > >> > > > > noexcept;
> > > >> > > > > > > +
> > > >> > > > > > > +  // If long double has the same binary format as double, then we
> > > >> > > > > just
> > > >> > > > > > > define
> > > >> > > > > > > +  // the long double overloads as wrappers around the corresponding
> > > >> > > > > > > double
> > > >> > > > > > > +  // overloads.
> > > >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > >> > > > > > > +  inline to_chars_result
> > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > >> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > >> > > > > > > +
> > > >> > > > > > > +  inline to_chars_result
> > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > >> > > > > > > +           chars_format __fmt) noexcept
> > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > >> > > > > > > +
> > > >> > > > > > > +  inline to_chars_result
> > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > >> > > > > > > +           chars_format __fmt, int __precision) noexcept
> > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > >> > > > > > > __precision); }
> > > >> > > > > > > +#endif
> > > >> > > > > >
> > > >> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > >> > > > > > introduce an ODR violation because each long double to_chars overload
> > > >> > > > > > could potentially have two different definitions available in a program,
> > > >> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> > > >> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > >> > > > > > -mlong-double-64)..
> > > >> > > > >
> > > >> > > > > But they have different mangled names, so there's no ODR violation.
> > > >> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > >> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> > > >> > > > > where there's no -mlong-double-64 switch, where double and long double
> > > >> > > > > are always the same representation.
> > > >> > > > >
> > > >> > > > > What I'm doing for std::from_chars is adding this in the new
> > > >> > > > > src/c++17/floating_from_chars.cc file:
> > > >> > > > >
> > > >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > >> > > > > extern "C" from_chars_result
> > > >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > >> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > >> > > > > #endif
> > > >> > > > >
> > > >> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > >> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> > > >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > >> > > > > double).
> > > >> > > >
> > > >> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > > >> > >
> > > >> > > Actually that should be:
> > > >> > >
> > > >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > >> > > extern "C" from_chars_result
> > > >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > > >> > >                                   long double& value,
> > > >> > >                                   chars_format fmt) noexcept
> > > >> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > >> > > #endif
> > > >> > >
> > > >> > > With the right parameter list I don't need to disable the warning.
> > > >> >
> > > >> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> > > >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> > > >>
> > > >> Here's v6 which is rebased against the floating-point from_chars patch
> > > >> and which also works around a false-positive -Wmaybe-uninitialized
> > > >> warning in __floating_to_chars_hex, as well as performs some minor
> > > >> commentary/style cleanups:
> > > >
> > > >Here's v7, with the following changes:
> > > >
> > > >* Remove extraneous indentation (two spaces when inside the std
> > > >  namespace, two spaces after a template header) for better consistency
> > > >  with floating_from_chars.cc
> > > >* Guard the calls to fe[gs]etround with a preprocessor test for
> > > >  _GLIBCXX_USE_C99_FENV_TR1;
> > > >* Properly XFAIL the new long_double.cc test on targets with a
> > > >  large long double type but without __int128, most notably i386
> > > >* Reword the commit message slightly.
> > > >
> > > >-- >8 --
> > > >
> > > >Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
> > > >
> > > >This implements the floating-point std::to_chars overloads for float,
> > > >double and long double.  We use the Ryu library to compute the shortest
> > > >round-trippable fixed and scientific forms for float, double and long
> > > >double.  We also use Ryu for performing explicit-precision fixed and
> > > >scientific formatting of float and double. For explicit-precision
> > > >formatting of long double we fall back to using printf.  Hexadecimal
> > > >formatting for float, double and long double is implemented from
> > > >scratch.
> > > >
> > > >The supported long double binary formats are binary64, binary80 (x86
> > > >80-bit extended precision), binary128 and ibm128.
> > > >
> > > >Much of the complexity of the implementation is in computing the exact
> > > >output length before handing it off to Ryu (which doesn't do bounds
> > > >checking).  In some cases it's hard to compute the output length
> > > >beforehand, so in these cases we instead compute an upper bound on the
> > > >output length and use a sufficiently-sized intermediate buffer only if
> > > >necessary.
> > > >
> > > >Another source of complexity is in the general-with-precision formatting
> > > >mode, where we need to do zero-trimming of the string returned by Ryu,
> > > >and where we also take care to avoid having to format the number through
> > > >Ryu a second time when the general formatting mode resolves to fixed
> > > >(which we determine by doing a scientific formatting first and
> > > >inspecting the scientific exponent).  We avoid going through Ryu twice
> > > >by instead transforming the scientific form to the corresponding fixed
> > > >form via in-place string manipulation.
> > > >
> > > >This implementation is non-conforming in a couple of ways:
> > > >
> > > >1. For the shortest hexadecimal formatting, we currently follow the
> > > >   Microsoft implementation's decision to be consistent with the
> > > >   output of printf's '%a' specifier at the expense of sometimes not
> > > >   printing the shortest representation.  For example, the shortest hex
> > > >   form for the number 1.08p+0 is 2.1p-1, but we output the former
> > > >   instead of the latter, as does printf.
> > > >
> > > >2. The Ryu routine generic_binary_to_decimal that we use for performing
> > > >   shortest formatting for large floating point types is implemented
> > > >   using the __int128 type, but some targets with a large long double
> > > >   type lack __int128 (e.g. i686), so we can't perform shortest
> > > >   formatting of long double on such targets through Ryu.  As a
> > > >   temporary stopgap this patch makes the long double to_chars overloads
> > > >   just dispatch to the double overloads on these targets, which means
> > > >   we lose precision in the output.  (We could potentially fix this by
> > > >   writing a specialized version of Ryu's generic_binary_to_decimal
> > > >   routine that uses uint64_t instead of __int128.)  [Though I wonder if
> > > >   there's a better way to work around the lack of __int128 on i686
> > > >   specifically?]
> > > >
> > > >3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
> > > >   property if the difference between the high- and low-order exponent
> > > >   is large.  This is because we treat __ibm128 as if it has a
> > > >   contiguous 105-bit mantissa by merging the mantissas of the high-
> > > >   and low-order parts (using code extracted from glibc), so we
> > > >   potentially lose precision from the low-order part.  This seems to be
> > > >   consistent with how glibc printf formats __ibm128.
> > > >
> > > >libstdc++-v3/ChangeLog:
> > > >
> > > >       * config/abi/pre/gnu.ver: Add new exports.
> > > >       * include/std/charconv (to_chars): Declare the floating-point
> > > >       overloads for float, double and long double.
> > > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > >       * src/c++17/Makefile.in: Regenerate.
> > > >       * src/c++17/floating_to_chars.cc: New file.
> > > >       (to_chars): Define for float, double and long double.
> > > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> > >
> > > Sorry it took so long to review, this is OK for trunk.
> > >
> > > The patch needs some minor changes to rebase it on the current trunk:
> > > The linker script has additions since you send this patch, so the
> > > context in the patch is wrong and it doesn't apply, and in <charconv>
> > > the first line of context in the patch needs to have 'noexcept' added.
> > > That rebase should be easy though.
> > >
> > > I'll look at adding __float128 support for powerpc64le.
> >
> > Thanks a lot.  I committed the patch series just now, after rebasing
> > and retesting on x86_64, aarch64 and ppc64le.
> >
> 
> My newlib-based toolchains (arm-eabi, aarch64-elf) fail to build after
> this commit, because:
> libstdc++-v3/src/c++17/floating_to_chars.cc:951:40: error:
> 'FE_TONEAREST' was not declared in this scope
>   951 |             if (saved_rounding_mode != FE_TONEAREST)
> 
> I'm (still) using newlib-3.3.0, and I think newlib's fenv.h was updated
> this year for arm/aarch64, so I suspect bumping to 3.4.0 would
> avoid the problem. However, is this something you want to support?
> (I mean the possibility that FE_TONEAREST is not supported etc...)

Thanks for the heads up.  Yes, it seems we should be testing that
FE_TONEAREST is defined before using it or fegetround()/fesetround().
This'll fix the build breakage and is also more conforming to the C
standard, which says that the latter functions work only if this macro
is defined.

Does the following patch look OK to commit?

-- >8 --

Subject: [PATCH] libstdc++: Check FE_TONEAREST is defined before using it

We need to check that FE_TONEAREST is defined before using it and
fegetround/fesetround to adjust the floating-point rounding mode
(as per the specification of fenv.h).

libstdc++-v3/ChangeLog:

	* src/c++17/floating_from_chars.cc (from_chars_impl): Check
	FE_TONEAREST is defined before adjusting the rounding mode.
	* src/c++17/floating_to_chars.cc (__floating_to_chars_precision):
	Likewise.
---
 libstdc++-v3/src/c++17/floating_from_chars.cc | 4 ++--
 libstdc++-v3/src/c++17/floating_to_chars.cc   | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc b/libstdc++-v3/src/c++17/floating_from_chars.cc
index a1943351493..86d6d0645a9 100644
--- a/libstdc++-v3/src/c++17/floating_from_chars.cc
+++ b/libstdc++-v3/src/c++17/floating_from_chars.cc
@@ -307,7 +307,7 @@ namespace
       {
 	locale_t orig = ::uselocale(loc);
 
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	const int rounding = std::fegetround();
 	if (rounding != FE_TONEAREST)
 	  std::fesetround(FE_TONEAREST);
@@ -333,7 +333,7 @@ namespace
 #endif
 	const int conv_errno = std::__exchange(errno, save_errno);
 
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	if (rounding != FE_TONEAREST)
 	  std::fesetround(rounding);
 #endif
diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
index dd83f5eea93..474e791e717 100644
--- a/libstdc++-v3/src/c++17/floating_to_chars.cc
+++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
@@ -946,13 +946,13 @@ template<typename T>
 	    // digit, and carefully compute and write the last digit
 	    // ourselves.
 	    char buffer[expected_output_length+1];
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	    const int saved_rounding_mode = fegetround();
 	    if (saved_rounding_mode != FE_TONEAREST)
 	      fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
 #endif
 	    const int output_length = sprintf(buffer, "%.0Lf", value);
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	    if (saved_rounding_mode != FE_TONEAREST)
 	      fesetround(saved_rounding_mode);
 #endif
@@ -1139,14 +1139,14 @@ template<typename T>
 
 	// Do the sprintf into the local buffer.
 	char buffer[output_length_upper_bound+1];
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	const int saved_rounding_mode = fegetround();
 	if (saved_rounding_mode != FE_TONEAREST)
 	  fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
 #endif
 	int output_length
 	  = sprintf(buffer, output_specifier, effective_precision, value);
-#if _GLIBCXX_USE_C99_FENV_TR1
+#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
 	if (saved_rounding_mode != FE_TONEAREST)
 	  fesetround(saved_rounding_mode);
 #endif
-- 
2.30.0.rc0

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Christophe Lyon]

On Fri, 18 Dec 2020 at 16:00, Patrick Palka <ppalka@redhat.com> wrote:
>
> On Fri, 18 Dec 2020, Christophe Lyon wrote:
>
> > Hi,
> >
> >
> > On Fri, 18 Dec 2020 at 05:13, Patrick Palka via Gcc-patches
> > <gcc-patches@gcc.gnu.org> wrote:
> > >
> > > On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <jwakely@redhat.com> wrote:
> > > >
> > > > On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> > > > >On Wed, 22 Jul 2020, Patrick Palka wrote:
> > > > >
> > > > >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> > > > >>
> > > > >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > >> >
> > > > >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > > > >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > >> > > >
> > > > >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > > >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > >> > > > > >
> > > > >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > >> > > > > > >
> > > > >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > >> > > > > > > >
> > > > >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > >> > > > > > > > >
> > > > >> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> > > > >> > > > > > > float,
> > > > >> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> > > > >> > > > > > > shortest
> > > > >> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> > > > >> > > > > float,
> > > > >> > > > > > > double
> > > > >> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > > >> > > > > > > scientific
> > > > >> > > > > > > > > > formatting of float and double. For formatting long double with
> > > > >> > > > > an
> > > > >> > > > > > > > > > explicit precision argument we use a printf fallback.
> > > > >> > > > > Hexadecimal
> > > > >> > > > > > > > > > formatting for float, double and long double is implemented from
> > > > >> > > > > > > > > > scratch.
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > > The supported long double binary formats are float64 (same as
> > > > >> > > > > > > double),
> > > > >> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > > Much of the complexity of the implementation is in computing the
> > > > >> > > > > > > exact
> > > > >> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > > >> > > > > bounds
> > > > >> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> > > > >> > > > > > > before
> > > > >> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > > >> > > > > the
> > > > >> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > > >> > > > > (if
> > > > >> > > > > > > the
> > > > >> > > > > > > > > > output range is smaller than the upper bound).
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > > Another source of complexity is in the general-with-precision
> > > > >> > > > > > > formatting
> > > > >> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > > >> > > > > by
> > > > >> > > > > > > Ryu, and
> > > > >> > > > > > > > > > where we also take care to avoid having to format the string a
> > > > >> > > > > > > second
> > > > >> > > > > > > > > > time when the general formatting mode resolves to fixed.
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > >> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > > libstdc++-v3/ChangeLog:
> > > > >> > > > > > > > > >
> > > > >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new exports.
> > > > >> > > > > > > > > >    * configure: Regenerate.
> > > > >> > > > > > > > > >    * include/std/charconv (to_chars): Declare the floating-point
> > > > >> > > > > > > > > >    overloads for float, double and long double.
> > > > >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> > > > >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New file.
> > > > >> > > > > > > > > >    * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > >> > > > > > > > >
> > > > >> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > > >> > > > > to
> > > > >> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > > >> > > > > > > format
> > > > >> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > > >> > > > > The
> > > > >> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > > >> > > > > > > uint64_t
> > > > >> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > > >> > > > > > > case.
> > > > >> > > > > > > >
> > > > >> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > > >> > > > > most
> > > > >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > >> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > > >> > > > > mode.
> > > > >> > > > > > >
> > > > >> > > > > > > Here's v4, which should now correctly support using <charconv> with
> > > > >> > > > > > > -mlong-double-64 on targets with a large default long double type.
> > > > >> > > > > > > This is done by defining the long double to_chars overloads as inline
> > > > >> > > > > > > wrappers around the double overloads within <charconv> whenever
> > > > >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > > >> > > > > >
> > > > >> > > > > > >
> > > > >> > > > > > > -- >8 --
> > > > >> > > > > > >
> > > > >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > > >> > > > > > >  implementation
> > > > >> > > > > > >
> > > > >> > > > > > > This implements the floating-point std::to_chars overloads for float,
> > > > >> > > > > > > double and long double.  We use the Ryu library to compute the
> > > > >> > > > > shortest
> > > > >> > > > > > > round-trippable fixed and scientific forms of a number for float,
> > > > >> > > > > double
> > > > >> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> > > > >> > > > > > > fixed and scientific formatting of float and double. For
> > > > >> > > > > > > explicit-precision formatting of long double we fall back to using
> > > > >> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > > >> > > > > > > implemented from scratch.
> > > > >> > > > > > >
> > > > >> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> > > > >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > > > >> > > > > > >
> > > > >> > > > > > > Much of the complexity of the implementation is in computing the exact
> > > > >> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > >> > > > > > > checking).  In some cases it's hard to compute the output length
> > > > >> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > > >> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> > > > >> > > > > > > necessary.
> > > > >> > > > > > >
> > > > >> > > > > > > Another source of complexity is in the general-with-precision
> > > > >> > > > > formatting
> > > > >> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > >> > > > > > > and where we also take care to avoid having to format the string a
> > > > >> > > > > > > second time when the general formatting mode resolves to fixed.
> > > > >> > > > > > >
> > > > >> > > > > > > This implementation is non-conforming in a couple of ways:
> > > > >> > > > > > >
> > > > >> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > > >> > > > > > >    Microsoft implementation's approach of being consistent with the
> > > > >> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > > >> > > > > > >    printing the shortest representation.  For example, the shortest
> > > > >> > > > > hex
> > > > >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > > >> > > > > > >    latter, as does printf.
> > > > >> > > > > > >
> > > > >> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > > >> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > > >> > > > > > >    large long double type but lack __int128.  For such targets we make
> > > > >> > > > > > >    the long double to_chars overloads go through the double overloads,
> > > > >> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> > > > >> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > > >> > > > > > >    by writing a specialized version of the generic Ryu formatting
> > > > >> > > > > > >    routine which works with uint64_t instead of __int128.)
> > > > >> > > > > > >
> > > > >> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > > >> > > > > > >    round-trippability if the difference between the high- and
> > > > >> > > > > low-order
> > > > >> > > > > > >    exponent is too large.  This is because we treat the type as if it
> > > > >> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > > >> > > > > low-order
> > > > >> > > > > > >    mantissas, so we potentially lose precision from the low-order
> > > > >> > > > > part.
> > > > >> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> > > > >> > > > > seems
> > > > >> > > > > > >    consistent with how printf formats __ibm128.
> > > > >> > > > > > >
> > > > >> > > > > > > libstdc++-v3/ChangeLog:
> > > > >> > > > > > >
> > > > >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> > > > >> > > > > > >  * configure: Regenerate.
> > > > >> > > > > > >  * include/std/charconv (to_chars): Declare the floating-point
> > > > >> > > > > > >  overloads for float, double and long double.
> > > > >> > > > > > >  * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> > > > >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> > > > >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > >> > > > > > > ---
> > > > >> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > > >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > > >> > > > > > >  libstdc++-v3/configure                        |    2 +-
> > > > >> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > > >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > > >> > > > > +++++++++++++++++
> > > > >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > > >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > > >> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > > >> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > >> > > > > > >  create mode 100644
> > > > >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > >> > > > > > >
> > > > >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > > >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > > > >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > >> > > > > > >  fi
> > > > >> > > > > > >
> > > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > >> > > > > > >
> > > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > >> > > > > > >  case $enable_symvers in
> > > > >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > >> > > > > > >
> > > > >> > > > > > >  } GLIBCXX_3.4.27;
> > > > >> > > > > > >
> > > > >> > > > > > > +GLIBCXX_3.4.29 {
> > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > >> > > > > > > +
> > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > >> > > > > chars_format)
> > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > >> > > > > > > +
> > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > >> > > > > chars_format,
> > > > >> > > > > > > int)
> > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > >> > > > > > > +
> > > > >> > > > > > > +} GLIBCXX_3.4.28;
> > > > >> > > > > > > +
> > > > >> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > > >> > > > > > >  CXXABI_1.3 {
> > > > >> > > > > > >
> > > > >> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > > >> > > > > > > index dd54bd406a9..73f771e7335 100755
> > > > >> > > > > > > --- a/libstdc++-v3/configure
> > > > >> > > > > > > +++ b/libstdc++-v3/configure
> > > > >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > > >> > > > > versioning
> > > > >> > > > > > > will be disabled." >&2;}
> > > > >> > > > > > >  fi
> > > > >> > > > > > >
> > > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > >> > > > > > >
> > > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > >> > > > > > >  case $enable_symvers in
> > > > >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > >> > > > > > > b/libstdc++-v3/include/std/charconv
> > > > >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > > > >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > >> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > > >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > >> > > > > > >
> > > > >> > > > > > > +  // Floating-point std::to_chars
> > > > >> > > > > > > +
> > > > >> > > > > > > +  // Overloads for float.
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > >> > > > > __value)
> > > > >> > > > > > > noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > >> > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > >> > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > >> > > > > noexcept;
> > > > >> > > > > > > +
> > > > >> > > > > > > +  // Overloads for double.
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > >> > > > > __value)
> > > > >> > > > > > > noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > >> > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > >> > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > >> > > > > noexcept;
> > > > >> > > > > > > +
> > > > >> > > > > > > +  // Overloads for long double.
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > >> > > > > > > __value)
> > > > >> > > > > > > +    noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > >> > > > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > >> > > > > > > __value,
> > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > >> > > > > noexcept;
> > > > >> > > > > > > +
> > > > >> > > > > > > +  // If long double has the same binary format as double, then we
> > > > >> > > > > just
> > > > >> > > > > > > define
> > > > >> > > > > > > +  // the long double overloads as wrappers around the corresponding
> > > > >> > > > > > > double
> > > > >> > > > > > > +  // overloads.
> > > > >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > >> > > > > > > +  inline to_chars_result
> > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > > >> > > > > > > +
> > > > >> > > > > > > +  inline to_chars_result
> > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > >> > > > > > > +           chars_format __fmt) noexcept
> > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > > >> > > > > > > +
> > > > >> > > > > > > +  inline to_chars_result
> > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > >> > > > > > > +           chars_format __fmt, int __precision) noexcept
> > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > > >> > > > > > > __precision); }
> > > > >> > > > > > > +#endif
> > > > >> > > > > >
> > > > >> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > > >> > > > > > introduce an ODR violation because each long double to_chars overload
> > > > >> > > > > > could potentially have two different definitions available in a program,
> > > > >> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> > > > >> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > > >> > > > > > -mlong-double-64)..
> > > > >> > > > >
> > > > >> > > > > But they have different mangled names, so there's no ODR violation.
> > > > >> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > > >> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> > > > >> > > > > where there's no -mlong-double-64 switch, where double and long double
> > > > >> > > > > are always the same representation.
> > > > >> > > > >
> > > > >> > > > > What I'm doing for std::from_chars is adding this in the new
> > > > >> > > > > src/c++17/floating_from_chars.cc file:
> > > > >> > > > >
> > > > >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > > >> > > > > extern "C" from_chars_result
> > > > >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > > >> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > >> > > > > #endif
> > > > >> > > > >
> > > > >> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > > >> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> > > > >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > > >> > > > > double).
> > > > >> > > >
> > > > >> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > > > >> > >
> > > > >> > > Actually that should be:
> > > > >> > >
> > > > >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > >> > > extern "C" from_chars_result
> > > > >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > > > >> > >                                   long double& value,
> > > > >> > >                                   chars_format fmt) noexcept
> > > > >> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > >> > > #endif
> > > > >> > >
> > > > >> > > With the right parameter list I don't need to disable the warning.
> > > > >> >
> > > > >> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> > > > >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> > > > >>
> > > > >> Here's v6 which is rebased against the floating-point from_chars patch
> > > > >> and which also works around a false-positive -Wmaybe-uninitialized
> > > > >> warning in __floating_to_chars_hex, as well as performs some minor
> > > > >> commentary/style cleanups:
> > > > >
> > > > >Here's v7, with the following changes:
> > > > >
> > > > >* Remove extraneous indentation (two spaces when inside the std
> > > > >  namespace, two spaces after a template header) for better consistency
> > > > >  with floating_from_chars.cc
> > > > >* Guard the calls to fe[gs]etround with a preprocessor test for
> > > > >  _GLIBCXX_USE_C99_FENV_TR1;
> > > > >* Properly XFAIL the new long_double.cc test on targets with a
> > > > >  large long double type but without __int128, most notably i386
> > > > >* Reword the commit message slightly.
> > > > >
> > > > >-- >8 --
> > > > >
> > > > >Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
> > > > >
> > > > >This implements the floating-point std::to_chars overloads for float,
> > > > >double and long double.  We use the Ryu library to compute the shortest
> > > > >round-trippable fixed and scientific forms for float, double and long
> > > > >double.  We also use Ryu for performing explicit-precision fixed and
> > > > >scientific formatting of float and double. For explicit-precision
> > > > >formatting of long double we fall back to using printf.  Hexadecimal
> > > > >formatting for float, double and long double is implemented from
> > > > >scratch.
> > > > >
> > > > >The supported long double binary formats are binary64, binary80 (x86
> > > > >80-bit extended precision), binary128 and ibm128.
> > > > >
> > > > >Much of the complexity of the implementation is in computing the exact
> > > > >output length before handing it off to Ryu (which doesn't do bounds
> > > > >checking).  In some cases it's hard to compute the output length
> > > > >beforehand, so in these cases we instead compute an upper bound on the
> > > > >output length and use a sufficiently-sized intermediate buffer only if
> > > > >necessary.
> > > > >
> > > > >Another source of complexity is in the general-with-precision formatting
> > > > >mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > >and where we also take care to avoid having to format the number through
> > > > >Ryu a second time when the general formatting mode resolves to fixed
> > > > >(which we determine by doing a scientific formatting first and
> > > > >inspecting the scientific exponent).  We avoid going through Ryu twice
> > > > >by instead transforming the scientific form to the corresponding fixed
> > > > >form via in-place string manipulation.
> > > > >
> > > > >This implementation is non-conforming in a couple of ways:
> > > > >
> > > > >1. For the shortest hexadecimal formatting, we currently follow the
> > > > >   Microsoft implementation's decision to be consistent with the
> > > > >   output of printf's '%a' specifier at the expense of sometimes not
> > > > >   printing the shortest representation.  For example, the shortest hex
> > > > >   form for the number 1.08p+0 is 2.1p-1, but we output the former
> > > > >   instead of the latter, as does printf.
> > > > >
> > > > >2. The Ryu routine generic_binary_to_decimal that we use for performing
> > > > >   shortest formatting for large floating point types is implemented
> > > > >   using the __int128 type, but some targets with a large long double
> > > > >   type lack __int128 (e.g. i686), so we can't perform shortest
> > > > >   formatting of long double on such targets through Ryu.  As a
> > > > >   temporary stopgap this patch makes the long double to_chars overloads
> > > > >   just dispatch to the double overloads on these targets, which means
> > > > >   we lose precision in the output.  (We could potentially fix this by
> > > > >   writing a specialized version of Ryu's generic_binary_to_decimal
> > > > >   routine that uses uint64_t instead of __int128.)  [Though I wonder if
> > > > >   there's a better way to work around the lack of __int128 on i686
> > > > >   specifically?]
> > > > >
> > > > >3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
> > > > >   property if the difference between the high- and low-order exponent
> > > > >   is large.  This is because we treat __ibm128 as if it has a
> > > > >   contiguous 105-bit mantissa by merging the mantissas of the high-
> > > > >   and low-order parts (using code extracted from glibc), so we
> > > > >   potentially lose precision from the low-order part.  This seems to be
> > > > >   consistent with how glibc printf formats __ibm128.
> > > > >
> > > > >libstdc++-v3/ChangeLog:
> > > > >
> > > > >       * config/abi/pre/gnu.ver: Add new exports.
> > > > >       * include/std/charconv (to_chars): Declare the floating-point
> > > > >       overloads for float, double and long double.
> > > > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > >       * src/c++17/Makefile.in: Regenerate.
> > > > >       * src/c++17/floating_to_chars.cc: New file.
> > > > >       (to_chars): Define for float, double and long double.
> > > > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> > > >
> > > > Sorry it took so long to review, this is OK for trunk.
> > > >
> > > > The patch needs some minor changes to rebase it on the current trunk:
> > > > The linker script has additions since you send this patch, so the
> > > > context in the patch is wrong and it doesn't apply, and in <charconv>
> > > > the first line of context in the patch needs to have 'noexcept' added.
> > > > That rebase should be easy though.
> > > >
> > > > I'll look at adding __float128 support for powerpc64le.
> > >
> > > Thanks a lot.  I committed the patch series just now, after rebasing
> > > and retesting on x86_64, aarch64 and ppc64le.
> > >
> >
> > My newlib-based toolchains (arm-eabi, aarch64-elf) fail to build after
> > this commit, because:
> > libstdc++-v3/src/c++17/floating_to_chars.cc:951:40: error:
> > 'FE_TONEAREST' was not declared in this scope
> >   951 |             if (saved_rounding_mode != FE_TONEAREST)
> >
> > I'm (still) using newlib-3.3.0, and I think newlib's fenv.h was updated
> > this year for arm/aarch64, so I suspect bumping to 3.4.0 would
> > avoid the problem. However, is this something you want to support?
> > (I mean the possibility that FE_TONEAREST is not supported etc...)
>
> Thanks for the heads up.  Yes, it seems we should be testing that
> FE_TONEAREST is defined before using it or fegetround()/fesetround().
> This'll fix the build breakage and is also more conforming to the C
> standard, which says that the latter functions work only if this macro
> is defined.
>
> Does the following patch look OK to commit?
>
> -- >8 --
>
> Subject: [PATCH] libstdc++: Check FE_TONEAREST is defined before using it
>
> We need to check that FE_TONEAREST is defined before using it and
> fegetround/fesetround to adjust the floating-point rounding mode
> (as per the specification of fenv.h).
>
> libstdc++-v3/ChangeLog:
>
>         * src/c++17/floating_from_chars.cc (from_chars_impl): Check
>         FE_TONEAREST is defined before adjusting the rounding mode.
>         * src/c++17/floating_to_chars.cc (__floating_to_chars_precision):
>         Likewise.

Thanks, that's better but not sufficient:
/libstdc++-v3/src/c++17/floating_to_chars.cc: In instantiation of
'std::to_chars_result std::__floating_to_chars_shortest(char*, char*,
T, std::chars_format) [with T = float]':
/libstdc++-v3/src/c++17/floating_to_chars.cc:1484:73:   required from here
/libstdc++-v3/src/c++17/floating_to_chars.cc:978:37: error: no
matching function for call to 'max(long int, int)'
  978 |         const int whole_digits = max(mantissa_length + fd.exponent, 1);

are we just missing a cast?

> ---
>  libstdc++-v3/src/c++17/floating_from_chars.cc | 4 ++--
>  libstdc++-v3/src/c++17/floating_to_chars.cc   | 8 ++++----
>  2 files changed, 6 insertions(+), 6 deletions(-)
>
> diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc b/libstdc++-v3/src/c++17/floating_from_chars.cc
> index a1943351493..86d6d0645a9 100644
> --- a/libstdc++-v3/src/c++17/floating_from_chars.cc
> +++ b/libstdc++-v3/src/c++17/floating_from_chars.cc
> @@ -307,7 +307,7 @@ namespace
>        {
>         locale_t orig = ::uselocale(loc);
>
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>         const int rounding = std::fegetround();
>         if (rounding != FE_TONEAREST)
>           std::fesetround(FE_TONEAREST);
> @@ -333,7 +333,7 @@ namespace
>  #endif
>         const int conv_errno = std::__exchange(errno, save_errno);
>
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>         if (rounding != FE_TONEAREST)
>           std::fesetround(rounding);
>  #endif
> diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
> index dd83f5eea93..474e791e717 100644
> --- a/libstdc++-v3/src/c++17/floating_to_chars.cc
> +++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
> @@ -946,13 +946,13 @@ template<typename T>
>             // digit, and carefully compute and write the last digit
>             // ourselves.
>             char buffer[expected_output_length+1];
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>             const int saved_rounding_mode = fegetround();
>             if (saved_rounding_mode != FE_TONEAREST)
>               fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
>  #endif
>             const int output_length = sprintf(buffer, "%.0Lf", value);
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>             if (saved_rounding_mode != FE_TONEAREST)
>               fesetround(saved_rounding_mode);
>  #endif
> @@ -1139,14 +1139,14 @@ template<typename T>
>
>         // Do the sprintf into the local buffer.
>         char buffer[output_length_upper_bound+1];
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>         const int saved_rounding_mode = fegetround();
>         if (saved_rounding_mode != FE_TONEAREST)
>           fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
>  #endif
>         int output_length
>           = sprintf(buffer, output_specifier, effective_precision, value);
> -#if _GLIBCXX_USE_C99_FENV_TR1
> +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
>         if (saved_rounding_mode != FE_TONEAREST)
>           fesetround(saved_rounding_mode);
>  #endif
> --
> 2.30.0.rc0
>

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Fri, 18 Dec 2020, Christophe Lyon wrote:

> On Fri, 18 Dec 2020 at 16:00, Patrick Palka <ppalka@redhat.com> wrote:
> >
> > On Fri, 18 Dec 2020, Christophe Lyon wrote:
> >
> > > Hi,
> > >
> > >
> > > On Fri, 18 Dec 2020 at 05:13, Patrick Palka via Gcc-patches
> > > <gcc-patches@gcc.gnu.org> wrote:
> > > >
> > > > On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <jwakely@redhat.com> wrote:
> > > > >
> > > > > On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > >On Wed, 22 Jul 2020, Patrick Palka wrote:
> > > > > >
> > > > > >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> > > > > >>
> > > > > >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > > >> >
> > > > > >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > > >> > > >
> > > > > >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > >> > > > > >
> > > > > >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > >> > > > > > >
> > > > > >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > > >> > > > > > > >
> > > > > >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > > >> > > > > > > > >
> > > > > >> > > > > > > > > > This implements the floating-point std::to_chars overloads for
> > > > > >> > > > > > > float,
> > > > > >> > > > > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > >> > > > > > > shortest
> > > > > >> > > > > > > > > > round-trippable fixed and scientific forms of a number for
> > > > > >> > > > > float,
> > > > > >> > > > > > > double
> > > > > >> > > > > > > > > > and long double.  We also use Ryu for performing fixed and
> > > > > >> > > > > > > scientific
> > > > > >> > > > > > > > > > formatting of float and double. For formatting long double with
> > > > > >> > > > > an
> > > > > >> > > > > > > > > > explicit precision argument we use a printf fallback.
> > > > > >> > > > > Hexadecimal
> > > > > >> > > > > > > > > > formatting for float, double and long double is implemented from
> > > > > >> > > > > > > > > > scratch.
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > > The supported long double binary formats are float64 (same as
> > > > > >> > > > > > > double),
> > > > > >> > > > > > > > > > float80 (x86 extended precision), float128 and ibm128.
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > > Much of the complexity of the implementation is in computing the
> > > > > >> > > > > > > exact
> > > > > >> > > > > > > > > > output length before handing it off to Ryu (which doesn't do
> > > > > >> > > > > bounds
> > > > > >> > > > > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > >> > > > > > > before
> > > > > >> > > > > > > > > > the fact, so in these cases we instead compute an upper bound on
> > > > > >> > > > > the
> > > > > >> > > > > > > > > > output length and use a sufficiently-sized intermediate buffer
> > > > > >> > > > > (if
> > > > > >> > > > > > > the
> > > > > >> > > > > > > > > > output range is smaller than the upper bound).
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > > Another source of complexity is in the general-with-precision
> > > > > >> > > > > > > formatting
> > > > > >> > > > > > > > > > mode, where we need to do zero-trimming of the string returned
> > > > > >> > > > > by
> > > > > >> > > > > > > Ryu, and
> > > > > >> > > > > > > > > > where we also take care to avoid having to format the string a
> > > > > >> > > > > > > second
> > > > > >> > > > > > > > > > time when the general formatting mode resolves to fixed.
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > > Tested on x86_64-pc-linux-gnu, aarch64-unknown-linux-gnu,
> > > > > >> > > > > > > > > > s390x-ibm-linux-gnu, and powerpc64-unknown-linux-gnu.
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > > libstdc++-v3/ChangeLog:
> > > > > >> > > > > > > > > >
> > > > > >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new exports.
> > > > > >> > > > > > > > > >    * configure: Regenerate.
> > > > > >> > > > > > > > > >    * include/std/charconv (to_chars): Declare the floating-point
> > > > > >> > > > > > > > > >    overloads for float, double and long double.
> > > > > >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> > > > > >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New file.
> > > > > >> > > > > > > > > >    * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > >> > > > > > > > >
> > > > > >> > > > > > > > > Here is v2 of this patch, which fixes a build failure on i386 due
> > > > > >> > > > > to
> > > > > >> > > > > > > > > __int128 being unavailable, by refactoring the long double binary
> > > > > >> > > > > > > format
> > > > > >> > > > > > > > > selection to avoid referring to __int128 when it doesn't exist.
> > > > > >> > > > > The
> > > > > >> > > > > > > > > patch also makes the hex formatting for 80-bit long double use
> > > > > >> > > > > > > uint64_t
> > > > > >> > > > > > > > > instead of __int128 since the mantissa has exactly 64 bits in this
> > > > > >> > > > > > > case.
> > > > > >> > > > > > > >
> > > > > >> > > > > > > > Here's v3 which just makes some minor stylistic adjustments, and
> > > > > >> > > > > most
> > > > > >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with _GLIBCXX_ASSERTIONS
> > > > > >> > > > > > > > since we just want to enable __glibcxx_assert and not all of debug
> > > > > >> > > > > mode.
> > > > > >> > > > > > >
> > > > > >> > > > > > > Here's v4, which should now correctly support using <charconv> with
> > > > > >> > > > > > > -mlong-double-64 on targets with a large default long double type.
> > > > > >> > > > > > > This is done by defining the long double to_chars overloads as inline
> > > > > >> > > > > > > wrappers around the double overloads within <charconv> whenever
> > > > > >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > > > >> > > > > >
> > > > > >> > > > > > >
> > > > > >> > > > > > > -- >8 --
> > > > > >> > > > > > >
> > > > > >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add floating-point std::to_chars
> > > > > >> > > > > > >  implementation
> > > > > >> > > > > > >
> > > > > >> > > > > > > This implements the floating-point std::to_chars overloads for float,
> > > > > >> > > > > > > double and long double.  We use the Ryu library to compute the
> > > > > >> > > > > shortest
> > > > > >> > > > > > > round-trippable fixed and scientific forms of a number for float,
> > > > > >> > > > > double
> > > > > >> > > > > > > and long double.  We also use Ryu for performing explicit-precision
> > > > > >> > > > > > > fixed and scientific formatting of float and double. For
> > > > > >> > > > > > > explicit-precision formatting of long double we fall back to using
> > > > > >> > > > > > > printf.  Hexadecimal formatting for float, double and long double is
> > > > > >> > > > > > > implemented from scratch.
> > > > > >> > > > > > >
> > > > > >> > > > > > > The supported long double binary formats are binary64, binary80 (x86
> > > > > >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > > > > >> > > > > > >
> > > > > >> > > > > > > Much of the complexity of the implementation is in computing the exact
> > > > > >> > > > > > > output length before handing it off to Ryu (which doesn't do bounds
> > > > > >> > > > > > > checking).  In some cases it's hard to compute the output length
> > > > > >> > > > > > > beforehand, so in these cases we instead compute an upper bound on the
> > > > > >> > > > > > > output length and use a sufficiently-sized intermediate buffer if
> > > > > >> > > > > > > necessary.
> > > > > >> > > > > > >
> > > > > >> > > > > > > Another source of complexity is in the general-with-precision
> > > > > >> > > > > formatting
> > > > > >> > > > > > > mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > > >> > > > > > > and where we also take care to avoid having to format the string a
> > > > > >> > > > > > > second time when the general formatting mode resolves to fixed.
> > > > > >> > > > > > >
> > > > > >> > > > > > > This implementation is non-conforming in a couple of ways:
> > > > > >> > > > > > >
> > > > > >> > > > > > > 1. For the shortest hexadecimal formatting, we currently follow the
> > > > > >> > > > > > >    Microsoft implementation's approach of being consistent with the
> > > > > >> > > > > > >    output of printf's '%a' specifier at the expense of sometimes not
> > > > > >> > > > > > >    printing the shortest representation.  For example, the shortest
> > > > > >> > > > > hex
> > > > > >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the former instead of the
> > > > > >> > > > > > >    latter, as does printf.
> > > > > >> > > > > > >
> > > > > >> > > > > > > 2. The Ryu routines for doing shortest formatting on types larger than
> > > > > >> > > > > > >    binary64 use the __int128 type, and some targets (e.g. i386) have a
> > > > > >> > > > > > >    large long double type but lack __int128.  For such targets we make
> > > > > >> > > > > > >    the long double to_chars overloads go through the double overloads,
> > > > > >> > > > > > >    which means we lose precision in the output.  (The mantissa of long
> > > > > >> > > > > > >    double is 64 bits on i386, so I think we could potentially fix this
> > > > > >> > > > > > >    by writing a specialized version of the generic Ryu formatting
> > > > > >> > > > > > >    routine which works with uint64_t instead of __int128.)
> > > > > >> > > > > > >
> > > > > >> > > > > > > 3. The __ibm128 shortest formatting routines don't guarantee
> > > > > >> > > > > > >    round-trippability if the difference between the high- and
> > > > > >> > > > > low-order
> > > > > >> > > > > > >    exponent is too large.  This is because we treat the type as if it
> > > > > >> > > > > > >    has a contiguous 105-bit mantissa by merging the high- and
> > > > > >> > > > > low-order
> > > > > >> > > > > > >    mantissas, so we potentially lose precision from the low-order
> > > > > >> > > > > part.
> > > > > >> > > > > > >    Although this precision-dropping behavior is non-conforming, it
> > > > > >> > > > > seems
> > > > > >> > > > > > >    consistent with how printf formats __ibm128.
> > > > > >> > > > > > >
> > > > > >> > > > > > > libstdc++-v3/ChangeLog:
> > > > > >> > > > > > >
> > > > > >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> > > > > >> > > > > > >  * configure: Regenerate.
> > > > > >> > > > > > >  * include/std/charconv (to_chars): Declare the floating-point
> > > > > >> > > > > > >  overloads for float, double and long double.
> > > > > >> > > > > > >  * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> > > > > >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> > > > > >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new symbol version.
> > > > > >> > > > > > > ---
> > > > > >> > > > > > >  libstdc++-v3/acinclude.m4                     |    2 +-
> > > > > >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |   12 +
> > > > > >> > > > > > >  libstdc++-v3/configure                        |    2 +-
> > > > > >> > > > > > >  libstdc++-v3/include/std/charconv             |   43 +
> > > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |    1 +
> > > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |    5 +-
> > > > > >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 1514
> > > > > >> > > > > +++++++++++++++++
> > > > > >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |  197 +++
> > > > > >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |    3 +-
> > > > > >> > > > > > >  9 files changed, 1774 insertions(+), 5 deletions(-)
> > > > > >> > > > > > >  create mode 100644 libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > > >> > > > > > >  create mode 100644
> > > > > >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > > >> > > > > > >
> > > > > >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4 b/libstdc++-v3/acinclude.m4
> > > > > >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > > >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > > > > >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > > >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > > >> > > > > > >  fi
> > > > > >> > > > > > >
> > > > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > > >> > > > > > >
> > > > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > >> > > > > > >  case $enable_symvers in
> > > > > >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > > >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > > >> > > > > > >
> > > > > >> > > > > > >  } GLIBCXX_3.4.27;
> > > > > >> > > > > > >
> > > > > >> > > > > > > +GLIBCXX_3.4.29 {
> > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double])
> > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > > >> > > > > chars_format)
> > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long double],
> > > > > >> > > > > chars_format,
> > > > > >> > > > > > > int)
> > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +} GLIBCXX_3.4.28;
> > > > > >> > > > > > > +
> > > > > >> > > > > > >  # Symbols in the support library (libsupc++) have their own tag.
> > > > > >> > > > > > >  CXXABI_1.3 {
> > > > > >> > > > > > >
> > > > > >> > > > > > > diff --git a/libstdc++-v3/configure b/libstdc++-v3/configure
> > > > > >> > > > > > > index dd54bd406a9..73f771e7335 100755
> > > > > >> > > > > > > --- a/libstdc++-v3/configure
> > > > > >> > > > > > > +++ b/libstdc++-v3/configure
> > > > > >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me: WARNING: === Symbol
> > > > > >> > > > > versioning
> > > > > >> > > > > > > will be disabled." >&2;}
> > > > > >> > > > > > >  fi
> > > > > >> > > > > > >
> > > > > >> > > > > > >  # For libtool versioning info, format is CURRENT:REVISION:AGE
> > > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > > >> > > > > > >
> > > > > >> > > > > > >  # Everything parsed; figure out what files and settings to use.
> > > > > >> > > > > > >  case $enable_symvers in
> > > > > >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > > >> > > > > > > b/libstdc++-v3/include/std/charconv
> > > > > >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > > >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > > > > >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > > >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > > >> > > > > > >    operator^=(chars_format& __lhs, chars_format __rhs) noexcept
> > > > > >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > > >> > > > > > >
> > > > > >> > > > > > > +  // Floating-point std::to_chars
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  // Overloads for float.
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > >> > > > > __value)
> > > > > >> > > > > > > noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > >> > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, float
> > > > > >> > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > > >> > > > > noexcept;
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  // Overloads for double.
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > >> > > > > __value)
> > > > > >> > > > > > > noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > >> > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, double
> > > > > >> > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > > >> > > > > noexcept;
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  // Overloads for long double.
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > >> > > > > > > __value)
> > > > > >> > > > > > > +    noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > >> > > > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt) noexcept;
> > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char* __last, long double
> > > > > >> > > > > > > __value,
> > > > > >> > > > > > > +                           chars_format __fmt, int __precision)
> > > > > >> > > > > noexcept;
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  // If long double has the same binary format as double, then we
> > > > > >> > > > > just
> > > > > >> > > > > > > define
> > > > > >> > > > > > > +  // the long double overloads as wrappers around the corresponding
> > > > > >> > > > > > > double
> > > > > >> > > > > > > +  // overloads.
> > > > > >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > > >> > > > > > > +  inline to_chars_result
> > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value) noexcept
> > > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value)); }
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  inline to_chars_result
> > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > >> > > > > > > +           chars_format __fmt) noexcept
> > > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt); }
> > > > > >> > > > > > > +
> > > > > >> > > > > > > +  inline to_chars_result
> > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long double __value,
> > > > > >> > > > > > > +           chars_format __fmt, int __precision) noexcept
> > > > > >> > > > > > > +  { return to_chars(__first, __last, double(__value), __fmt,
> > > > > >> > > > > > > __precision); }
> > > > > >> > > > > > > +#endif
> > > > > >> > > > > >
> > > > > >> > > > > > Hmm, I think this approach for supporting -mlong-double-64 might
> > > > > >> > > > > > introduce an ODR violation because each long double to_chars overload
> > > > > >> > > > > > could potentially have two different definitions available in a program,
> > > > > >> > > > > > one out-of-line in floating_to_chars.cc (compiled without
> > > > > >> > > > > > -mlong-double-64) and another inline in <charconv> (compiled with
> > > > > >> > > > > > -mlong-double-64)..
> > > > > >> > > > >
> > > > > >> > > > > But they have different mangled names, so there's no ODR violation.
> > > > > >> > > > > The 64-bit long double is mangled as 'e' and the 128-bit long double
> > > > > >> > > > > is mangled as __float128. You *will* get an ODR violation on targets
> > > > > >> > > > > where there's no -mlong-double-64 switch, where double and long double
> > > > > >> > > > > are always the same representation.
> > > > > >> > > > >
> > > > > >> > > > > What I'm doing for std::from_chars is adding this in the new
> > > > > >> > > > > src/c++17/floating_from_chars.cc file:
> > > > > >> > > > >
> > > > > >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > > >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > > > >> > > > > extern "C" from_chars_result
> > > > > >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > > > >> > > > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > > >> > > > > #endif
> > > > > >> > > > >
> > > > > >> > > > > This just defines the _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > > > >> > > > > (i.e. from_chars for 64-bit long double) as an alias of
> > > > > >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e. from_chars for 64-bit
> > > > > >> > > > > double).
> > > > > >> > > >
> > > > > >> > > > Aha, that makes sense.  I'll follow suit for std::to_chars.
> > > > > >> > >
> > > > > >> > > Actually that should be:
> > > > > >> > >
> > > > > >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > > >> > > extern "C" from_chars_result
> > > > > >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char* first, const char* last,
> > > > > >> > >                                   long double& value,
> > > > > >> > >                                   chars_format fmt) noexcept
> > > > > >> > > __attribute__((alias ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > > >> > > #endif
> > > > > >> > >
> > > > > >> > > With the right parameter list I don't need to disable the warning.
> > > > > >> >
> > > > > >> > Sounds good.  Here's patch v5 that defines such aliases, tested so far
> > > > > >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> > > > > >>
> > > > > >> Here's v6 which is rebased against the floating-point from_chars patch
> > > > > >> and which also works around a false-positive -Wmaybe-uninitialized
> > > > > >> warning in __floating_to_chars_hex, as well as performs some minor
> > > > > >> commentary/style cleanups:
> > > > > >
> > > > > >Here's v7, with the following changes:
> > > > > >
> > > > > >* Remove extraneous indentation (two spaces when inside the std
> > > > > >  namespace, two spaces after a template header) for better consistency
> > > > > >  with floating_from_chars.cc
> > > > > >* Guard the calls to fe[gs]etround with a preprocessor test for
> > > > > >  _GLIBCXX_USE_C99_FENV_TR1;
> > > > > >* Properly XFAIL the new long_double.cc test on targets with a
> > > > > >  large long double type but without __int128, most notably i386
> > > > > >* Reword the commit message slightly.
> > > > > >
> > > > > >-- >8 --
> > > > > >
> > > > > >Subject: [PATCH] libstdc++: Add floating-point std::to_chars implementation
> > > > > >
> > > > > >This implements the floating-point std::to_chars overloads for float,
> > > > > >double and long double.  We use the Ryu library to compute the shortest
> > > > > >round-trippable fixed and scientific forms for float, double and long
> > > > > >double.  We also use Ryu for performing explicit-precision fixed and
> > > > > >scientific formatting of float and double. For explicit-precision
> > > > > >formatting of long double we fall back to using printf.  Hexadecimal
> > > > > >formatting for float, double and long double is implemented from
> > > > > >scratch.
> > > > > >
> > > > > >The supported long double binary formats are binary64, binary80 (x86
> > > > > >80-bit extended precision), binary128 and ibm128.
> > > > > >
> > > > > >Much of the complexity of the implementation is in computing the exact
> > > > > >output length before handing it off to Ryu (which doesn't do bounds
> > > > > >checking).  In some cases it's hard to compute the output length
> > > > > >beforehand, so in these cases we instead compute an upper bound on the
> > > > > >output length and use a sufficiently-sized intermediate buffer only if
> > > > > >necessary.
> > > > > >
> > > > > >Another source of complexity is in the general-with-precision formatting
> > > > > >mode, where we need to do zero-trimming of the string returned by Ryu,
> > > > > >and where we also take care to avoid having to format the number through
> > > > > >Ryu a second time when the general formatting mode resolves to fixed
> > > > > >(which we determine by doing a scientific formatting first and
> > > > > >inspecting the scientific exponent).  We avoid going through Ryu twice
> > > > > >by instead transforming the scientific form to the corresponding fixed
> > > > > >form via in-place string manipulation.
> > > > > >
> > > > > >This implementation is non-conforming in a couple of ways:
> > > > > >
> > > > > >1. For the shortest hexadecimal formatting, we currently follow the
> > > > > >   Microsoft implementation's decision to be consistent with the
> > > > > >   output of printf's '%a' specifier at the expense of sometimes not
> > > > > >   printing the shortest representation.  For example, the shortest hex
> > > > > >   form for the number 1.08p+0 is 2.1p-1, but we output the former
> > > > > >   instead of the latter, as does printf.
> > > > > >
> > > > > >2. The Ryu routine generic_binary_to_decimal that we use for performing
> > > > > >   shortest formatting for large floating point types is implemented
> > > > > >   using the __int128 type, but some targets with a large long double
> > > > > >   type lack __int128 (e.g. i686), so we can't perform shortest
> > > > > >   formatting of long double on such targets through Ryu.  As a
> > > > > >   temporary stopgap this patch makes the long double to_chars overloads
> > > > > >   just dispatch to the double overloads on these targets, which means
> > > > > >   we lose precision in the output.  (We could potentially fix this by
> > > > > >   writing a specialized version of Ryu's generic_binary_to_decimal
> > > > > >   routine that uses uint64_t instead of __int128.)  [Though I wonder if
> > > > > >   there's a better way to work around the lack of __int128 on i686
> > > > > >   specifically?]
> > > > > >
> > > > > >3. Our shortest formatting for __ibm128 doesn't guarantee the round-trip
> > > > > >   property if the difference between the high- and low-order exponent
> > > > > >   is large.  This is because we treat __ibm128 as if it has a
> > > > > >   contiguous 105-bit mantissa by merging the mantissas of the high-
> > > > > >   and low-order parts (using code extracted from glibc), so we
> > > > > >   potentially lose precision from the low-order part.  This seems to be
> > > > > >   consistent with how glibc printf formats __ibm128.
> > > > > >
> > > > > >libstdc++-v3/ChangeLog:
> > > > > >
> > > > > >       * config/abi/pre/gnu.ver: Add new exports.
> > > > > >       * include/std/charconv (to_chars): Declare the floating-point
> > > > > >       overloads for float, double and long double.
> > > > > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > > > >       * src/c++17/Makefile.in: Regenerate.
> > > > > >       * src/c++17/floating_to_chars.cc: New file.
> > > > > >       (to_chars): Define for float, double and long double.
> > > > > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > >
> > > > > Sorry it took so long to review, this is OK for trunk.
> > > > >
> > > > > The patch needs some minor changes to rebase it on the current trunk:
> > > > > The linker script has additions since you send this patch, so the
> > > > > context in the patch is wrong and it doesn't apply, and in <charconv>
> > > > > the first line of context in the patch needs to have 'noexcept' added.
> > > > > That rebase should be easy though.
> > > > >
> > > > > I'll look at adding __float128 support for powerpc64le.
> > > >
> > > > Thanks a lot.  I committed the patch series just now, after rebasing
> > > > and retesting on x86_64, aarch64 and ppc64le.
> > > >
> > >
> > > My newlib-based toolchains (arm-eabi, aarch64-elf) fail to build after
> > > this commit, because:
> > > libstdc++-v3/src/c++17/floating_to_chars.cc:951:40: error:
> > > 'FE_TONEAREST' was not declared in this scope
> > >   951 |             if (saved_rounding_mode != FE_TONEAREST)
> > >
> > > I'm (still) using newlib-3.3.0, and I think newlib's fenv.h was updated
> > > this year for arm/aarch64, so I suspect bumping to 3.4.0 would
> > > avoid the problem. However, is this something you want to support?
> > > (I mean the possibility that FE_TONEAREST is not supported etc...)
> >
> > Thanks for the heads up.  Yes, it seems we should be testing that
> > FE_TONEAREST is defined before using it or fegetround()/fesetround().
> > This'll fix the build breakage and is also more conforming to the C
> > standard, which says that the latter functions work only if this macro
> > is defined.
> >
> > Does the following patch look OK to commit?
> >
> > -- >8 --
> >
> > Subject: [PATCH] libstdc++: Check FE_TONEAREST is defined before using it
> >
> > We need to check that FE_TONEAREST is defined before using it and
> > fegetround/fesetround to adjust the floating-point rounding mode
> > (as per the specification of fenv.h).
> >
> > libstdc++-v3/ChangeLog:
> >
> >         * src/c++17/floating_from_chars.cc (from_chars_impl): Check
> >         FE_TONEAREST is defined before adjusting the rounding mode.
> >         * src/c++17/floating_to_chars.cc (__floating_to_chars_precision):
> >         Likewise.
> 
> Thanks, that's better but not sufficient:
> /libstdc++-v3/src/c++17/floating_to_chars.cc: In instantiation of
> 'std::to_chars_result std::__floating_to_chars_shortest(char*, char*,
> T, std::chars_format) [with T = float]':
> /libstdc++-v3/src/c++17/floating_to_chars.cc:1484:73:   required from here
> /libstdc++-v3/src/c++17/floating_to_chars.cc:978:37: error: no
> matching function for call to 'max(long int, int)'
>   978 |         const int whole_digits = max(mantissa_length + fd.exponent, 1);
> 
> are we just missing a cast?

Ah yes, I think this was also reported earlier today as PR libstdc++/98370.
I just went ahead and committed the above FE_TONEAREST fix and the
proposed PR98370 fix under the "obvious" rule.  Does latest trunk build
for you now?

> 
> > ---
> >  libstdc++-v3/src/c++17/floating_from_chars.cc | 4 ++--
> >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 8 ++++----
> >  2 files changed, 6 insertions(+), 6 deletions(-)
> >
> > diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc b/libstdc++-v3/src/c++17/floating_from_chars.cc
> > index a1943351493..86d6d0645a9 100644
> > --- a/libstdc++-v3/src/c++17/floating_from_chars.cc
> > +++ b/libstdc++-v3/src/c++17/floating_from_chars.cc
> > @@ -307,7 +307,7 @@ namespace
> >        {
> >         locale_t orig = ::uselocale(loc);
> >
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >         const int rounding = std::fegetround();
> >         if (rounding != FE_TONEAREST)
> >           std::fesetround(FE_TONEAREST);
> > @@ -333,7 +333,7 @@ namespace
> >  #endif
> >         const int conv_errno = std::__exchange(errno, save_errno);
> >
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >         if (rounding != FE_TONEAREST)
> >           std::fesetround(rounding);
> >  #endif
> > diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc b/libstdc++-v3/src/c++17/floating_to_chars.cc
> > index dd83f5eea93..474e791e717 100644
> > --- a/libstdc++-v3/src/c++17/floating_to_chars.cc
> > +++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
> > @@ -946,13 +946,13 @@ template<typename T>
> >             // digit, and carefully compute and write the last digit
> >             // ourselves.
> >             char buffer[expected_output_length+1];
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >             const int saved_rounding_mode = fegetround();
> >             if (saved_rounding_mode != FE_TONEAREST)
> >               fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
> >  #endif
> >             const int output_length = sprintf(buffer, "%.0Lf", value);
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >             if (saved_rounding_mode != FE_TONEAREST)
> >               fesetround(saved_rounding_mode);
> >  #endif
> > @@ -1139,14 +1139,14 @@ template<typename T>
> >
> >         // Do the sprintf into the local buffer.
> >         char buffer[output_length_upper_bound+1];
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >         const int saved_rounding_mode = fegetround();
> >         if (saved_rounding_mode != FE_TONEAREST)
> >           fesetround(FE_TONEAREST); // We want round-to-nearest behavior.
> >  #endif
> >         int output_length
> >           = sprintf(buffer, output_specifier, effective_precision, value);
> > -#if _GLIBCXX_USE_C99_FENV_TR1
> > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> >         if (saved_rounding_mode != FE_TONEAREST)
> >           fesetround(saved_rounding_mode);
> >  #endif
> > --
> > 2.30.0.rc0
> >
> 
> 

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Christophe Lyon]

Le ven. 18 déc. 2020 à 18:03, Patrick Palka <ppalka@redhat.com> a écrit :

> On Fri, 18 Dec 2020, Christophe Lyon wrote:
>
> > On Fri, 18 Dec 2020 at 16:00, Patrick Palka <ppalka@redhat.com> wrote:
> > >
> > > On Fri, 18 Dec 2020, Christophe Lyon wrote:
> > >
> > > > Hi,
> > > >
> > > >
> > > > On Fri, 18 Dec 2020 at 05:13, Patrick Palka via Gcc-patches
> > > > <gcc-patches@gcc.gnu.org> wrote:
> > > > >
> > > > > On Thu, Dec 17, 2020 at 9:32 AM Jonathan Wakely <
> jwakely@redhat.com> wrote:
> > > > > >
> > > > > > On 19/08/20 17:57 -0400, Patrick Palka via Libstdc++ wrote:
> > > > > > >On Wed, 22 Jul 2020, Patrick Palka wrote:
> > > > > > >
> > > > > > >> On Mon, 20 Jul 2020, Patrick Palka wrote:
> > > > > > >>
> > > > > > >> > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > > > >> >
> > > > > > >> > > On 20/07/20 08:53 -0400, Patrick Palka via Libstdc++
> wrote:
> > > > > > >> > > > On Mon, 20 Jul 2020, Jonathan Wakely wrote:
> > > > > > >> > > >
> > > > > > >> > > > > On 19/07/20 23:37 -0400, Patrick Palka via Libstdc++
> wrote:
> > > > > > >> > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > > >> > > > > >
> > > > > > >> > > > > > > On Fri, 17 Jul 2020, Patrick Palka wrote:
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > > On Wed, 15 Jul 2020, Patrick Palka wrote:
> > > > > > >> > > > > > > >
> > > > > > >> > > > > > > > > On Tue, 14 Jul 2020, Patrick Palka wrote:
> > > > > > >> > > > > > > > >
> > > > > > >> > > > > > > > > > This implements the floating-point
> std::to_chars overloads for
> > > > > > >> > > > > > > float,
> > > > > > >> > > > > > > > > > double and long double.  We use the Ryu
> library to compute the
> > > > > > >> > > > > > > shortest
> > > > > > >> > > > > > > > > > round-trippable fixed and scientific forms
> of a number for
> > > > > > >> > > > > float,
> > > > > > >> > > > > > > double
> > > > > > >> > > > > > > > > > and long double.  We also use Ryu for
> performing fixed and
> > > > > > >> > > > > > > scientific
> > > > > > >> > > > > > > > > > formatting of float and double. For
> formatting long double with
> > > > > > >> > > > > an
> > > > > > >> > > > > > > > > > explicit precision argument we use a printf
> fallback.
> > > > > > >> > > > > Hexadecimal
> > > > > > >> > > > > > > > > > formatting for float, double and long
> double is implemented from
> > > > > > >> > > > > > > > > > scratch.
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > > The supported long double binary formats
> are float64 (same as
> > > > > > >> > > > > > > double),
> > > > > > >> > > > > > > > > > float80 (x86 extended precision), float128
> and ibm128.
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > > Much of the complexity of the
> implementation is in computing the
> > > > > > >> > > > > > > exact
> > > > > > >> > > > > > > > > > output length before handing it off to Ryu
> (which doesn't do
> > > > > > >> > > > > bounds
> > > > > > >> > > > > > > > > > checking).  In some cases it's hard to
> compute the output length
> > > > > > >> > > > > > > before
> > > > > > >> > > > > > > > > > the fact, so in these cases we instead
> compute an upper bound on
> > > > > > >> > > > > the
> > > > > > >> > > > > > > > > > output length and use a sufficiently-sized
> intermediate buffer
> > > > > > >> > > > > (if
> > > > > > >> > > > > > > the
> > > > > > >> > > > > > > > > > output range is smaller than the upper
> bound).
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > > Another source of complexity is in the
> general-with-precision
> > > > > > >> > > > > > > formatting
> > > > > > >> > > > > > > > > > mode, where we need to do zero-trimming of
> the string returned
> > > > > > >> > > > > by
> > > > > > >> > > > > > > Ryu, and
> > > > > > >> > > > > > > > > > where we also take care to avoid having to
> format the string a
> > > > > > >> > > > > > > second
> > > > > > >> > > > > > > > > > time when the general formatting mode
> resolves to fixed.
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > > Tested on x86_64-pc-linux-gnu,
> aarch64-unknown-linux-gnu,
> > > > > > >> > > > > > > > > > s390x-ibm-linux-gnu, and
> powerpc64-unknown-linux-gnu.
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > > libstdc++-v3/ChangeLog:
> > > > > > >> > > > > > > > > >
> > > > > > >> > > > > > > > > >    * acinclude.m4 (libtool_VERSION): Bump
> to 6:29:0.
> > > > > > >> > > > > > > > > >    * config/abi/pre/gnu.ver: Add new
> exports.
> > > > > > >> > > > > > > > > >    * configure: Regenerate.
> > > > > > >> > > > > > > > > >    * include/std/charconv (to_chars):
> Declare the floating-point
> > > > > > >> > > > > > > > > >    overloads for float, double and long
> double.
> > > > > > >> > > > > > > > > >    * src/c++17/Makefile.am (sources): Add
> floating_to_chars.cc.
> > > > > > >> > > > > > > > > >    * src/c++17/Makefile.in: Regenerate.
> > > > > > >> > > > > > > > > >    * src/c++17/floating_to_chars.cc: New
> file.
> > > > > > >> > > > > > > > > >    *
> testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > > >> > > > > > > > > >    * testsuite/util/testsuite_abi.cc: Add
> new symbol version.
> > > > > > >> > > > > > > > >
> > > > > > >> > > > > > > > > Here is v2 of this patch, which fixes a build
> failure on i386 due
> > > > > > >> > > > > to
> > > > > > >> > > > > > > > > __int128 being unavailable, by refactoring
> the long double binary
> > > > > > >> > > > > > > format
> > > > > > >> > > > > > > > > selection to avoid referring to __int128 when
> it doesn't exist.
> > > > > > >> > > > > The
> > > > > > >> > > > > > > > > patch also makes the hex formatting for
> 80-bit long double use
> > > > > > >> > > > > > > uint64_t
> > > > > > >> > > > > > > > > instead of __int128 since the mantissa has
> exactly 64 bits in this
> > > > > > >> > > > > > > case.
> > > > > > >> > > > > > > >
> > > > > > >> > > > > > > > Here's v3 which just makes some minor stylistic
> adjustments, and
> > > > > > >> > > > > most
> > > > > > >> > > > > > > > notably replaces the use of _GLIBCXX_DEBUG with
> _GLIBCXX_ASSERTIONS
> > > > > > >> > > > > > > > since we just want to enable __glibcxx_assert
> and not all of debug
> > > > > > >> > > > > mode.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > Here's v4, which should now correctly support
> using <charconv> with
> > > > > > >> > > > > > > -mlong-double-64 on targets with a large default
> long double type.
> > > > > > >> > > > > > > This is done by defining the long double to_chars
> overloads as inline
> > > > > > >> > > > > > > wrappers around the double overloads within
> <charconv> whenever
> > > > > > >> > > > > > > __DBL_MANT_DIG__ equals __LDBL_MANT_DIG__.
> > > > > > >> > > > > >
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > -- >8 --
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > Subject: [PATCH 3/4] libstdc++: Add
> floating-point std::to_chars
> > > > > > >> > > > > > >  implementation
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > This implements the floating-point std::to_chars
> overloads for float,
> > > > > > >> > > > > > > double and long double.  We use the Ryu library
> to compute the
> > > > > > >> > > > > shortest
> > > > > > >> > > > > > > round-trippable fixed and scientific forms of a
> number for float,
> > > > > > >> > > > > double
> > > > > > >> > > > > > > and long double.  We also use Ryu for performing
> explicit-precision
> > > > > > >> > > > > > > fixed and scientific formatting of float and
> double. For
> > > > > > >> > > > > > > explicit-precision formatting of long double we
> fall back to using
> > > > > > >> > > > > > > printf.  Hexadecimal formatting for float, double
> and long double is
> > > > > > >> > > > > > > implemented from scratch.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > The supported long double binary formats are
> binary64, binary80 (x86
> > > > > > >> > > > > > > 80-bit extended precision), binary128 and ibm128.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > Much of the complexity of the implementation is
> in computing the exact
> > > > > > >> > > > > > > output length before handing it off to Ryu (which
> doesn't do bounds
> > > > > > >> > > > > > > checking).  In some cases it's hard to compute
> the output length
> > > > > > >> > > > > > > beforehand, so in these cases we instead compute
> an upper bound on the
> > > > > > >> > > > > > > output length and use a sufficiently-sized
> intermediate buffer if
> > > > > > >> > > > > > > necessary.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > Another source of complexity is in the
> general-with-precision
> > > > > > >> > > > > formatting
> > > > > > >> > > > > > > mode, where we need to do zero-trimming of the
> string returned by Ryu,
> > > > > > >> > > > > > > and where we also take care to avoid having to
> format the string a
> > > > > > >> > > > > > > second time when the general formatting mode
> resolves to fixed.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > This implementation is non-conforming in a couple
> of ways:
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > 1. For the shortest hexadecimal formatting, we
> currently follow the
> > > > > > >> > > > > > >    Microsoft implementation's approach of being
> consistent with the
> > > > > > >> > > > > > >    output of printf's '%a' specifier at the
> expense of sometimes not
> > > > > > >> > > > > > >    printing the shortest representation.  For
> example, the shortest
> > > > > > >> > > > > hex
> > > > > > >> > > > > > >    form of 1.08p+0 is 2.1p-1, but we output the
> former instead of the
> > > > > > >> > > > > > >    latter, as does printf.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > 2. The Ryu routines for doing shortest formatting
> on types larger than
> > > > > > >> > > > > > >    binary64 use the __int128 type, and some
> targets (e.g. i386) have a
> > > > > > >> > > > > > >    large long double type but lack __int128.  For
> such targets we make
> > > > > > >> > > > > > >    the long double to_chars overloads go through
> the double overloads,
> > > > > > >> > > > > > >    which means we lose precision in the output.
> (The mantissa of long
> > > > > > >> > > > > > >    double is 64 bits on i386, so I think we could
> potentially fix this
> > > > > > >> > > > > > >    by writing a specialized version of the
> generic Ryu formatting
> > > > > > >> > > > > > >    routine which works with uint64_t instead of
> __int128.)
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > 3. The __ibm128 shortest formatting routines
> don't guarantee
> > > > > > >> > > > > > >    round-trippability if the difference between
> the high- and
> > > > > > >> > > > > low-order
> > > > > > >> > > > > > >    exponent is too large.  This is because we
> treat the type as if it
> > > > > > >> > > > > > >    has a contiguous 105-bit mantissa by merging
> the high- and
> > > > > > >> > > > > low-order
> > > > > > >> > > > > > >    mantissas, so we potentially lose precision
> from the low-order
> > > > > > >> > > > > part.
> > > > > > >> > > > > > >    Although this precision-dropping behavior is
> non-conforming, it
> > > > > > >> > > > > seems
> > > > > > >> > > > > > >    consistent with how printf formats __ibm128.
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > libstdc++-v3/ChangeLog:
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  * acinclude.m4 (libtool_VERSION): Bump to 6:29:0.
> > > > > > >> > > > > > >  * config/abi/pre/gnu.ver: Add new exports.
> > > > > > >> > > > > > >  * configure: Regenerate.
> > > > > > >> > > > > > >  * include/std/charconv (to_chars): Declare the
> floating-point
> > > > > > >> > > > > > >  overloads for float, double and long double.
> > > > > > >> > > > > > >  * src/c++17/Makefile.am (sources): Add
> floating_to_chars.cc.
> > > > > > >> > > > > > >  * src/c++17/Makefile.in: Regenerate.
> > > > > > >> > > > > > >  * src/c++17/floating_to_chars.cc: New file.
> > > > > > >> > > > > > >  * testsuite/20_util/to_chars/long_double.cc: New
> test.
> > > > > > >> > > > > > >  * testsuite/util/testsuite_abi.cc: Add new
> symbol version.
> > > > > > >> > > > > > > ---
> > > > > > >> > > > > > >  libstdc++-v3/acinclude.m4                     |
>   2 +-
> > > > > > >> > > > > > >  libstdc++-v3/config/abi/pre/gnu.ver           |
>  12 +
> > > > > > >> > > > > > >  libstdc++-v3/configure                        |
>   2 +-
> > > > > > >> > > > > > >  libstdc++-v3/include/std/charconv             |
>  43 +
> > > > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.am            |
>   1 +
> > > > > > >> > > > > > >  libstdc++-v3/src/c++17/Makefile.in            |
>   5 +-
> > > > > > >> > > > > > >  libstdc++-v3/src/c++17/floating_to_chars.cc   |
> 1514
> > > > > > >> > > > > +++++++++++++++++
> > > > > > >> > > > > > >  .../testsuite/20_util/to_chars/long_double.cc |
> 197 +++
> > > > > > >> > > > > > >  libstdc++-v3/testsuite/util/testsuite_abi.cc  |
>   3 +-
> > > > > > >> > > > > > >  9 files changed, 1774 insertions(+), 5
> deletions(-)
> > > > > > >> > > > > > >  create mode 100644
> libstdc++-v3/src/c++17/floating_to_chars.cc
> > > > > > >> > > > > > >  create mode 100644
> > > > > > >> > > > > libstdc++-v3/testsuite/20_util/to_chars/long_double.cc
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > diff --git a/libstdc++-v3/acinclude.m4
> b/libstdc++-v3/acinclude.m4
> > > > > > >> > > > > > > index ee5e0336f2c..e3926e1c9c2 100644
> > > > > > >> > > > > > > --- a/libstdc++-v3/acinclude.m4
> > > > > > >> > > > > > > +++ b/libstdc++-v3/acinclude.m4
> > > > > > >> > > > > > > @@ -3846,7 +3846,7 @@ changequote([,])dnl
> > > > > > >> > > > > > >  fi
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  # For libtool versioning info, format is
> CURRENT:REVISION:AGE
> > > > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  # Everything parsed; figure out what files and
> settings to use.
> > > > > > >> > > > > > >  case $enable_symvers in
> > > > > > >> > > > > > > diff --git a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > >> > > > > > > b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > >> > > > > > > index edf4485e607..9a1bcfd25d1 100644
> > > > > > >> > > > > > > --- a/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > >> > > > > > > +++ b/libstdc++-v3/config/abi/pre/gnu.ver
> > > > > > >> > > > > > > @@ -2299,6 +2299,18 @@ GLIBCXX_3.4.28 {
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  } GLIBCXX_3.4.27;
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > +GLIBCXX_3.4.29 {
> > > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long
> double])
> > > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg];
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long
> double],
> > > > > > >> > > > > chars_format)
> > > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_format;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +    # to_chars(char*, char*, [float|double|long
> double],
> > > > > > >> > > > > chars_format,
> > > > > > >> > > > > > > int)
> > > > > > >> > > > > > > +    _ZSt8to_charsPcS_[fdeg]St12chars_formati;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +} GLIBCXX_3.4.28;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > >  # Symbols in the support library (libsupc++)
> have their own tag.
> > > > > > >> > > > > > >  CXXABI_1.3 {
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > diff --git a/libstdc++-v3/configure
> b/libstdc++-v3/configure
> > > > > > >> > > > > > > index dd54bd406a9..73f771e7335 100755
> > > > > > >> > > > > > > --- a/libstdc++-v3/configure
> > > > > > >> > > > > > > +++ b/libstdc++-v3/configure
> > > > > > >> > > > > > > @@ -75231,7 +75231,7 @@ $as_echo "$as_me:
> WARNING: === Symbol
> > > > > > >> > > > > versioning
> > > > > > >> > > > > > > will be disabled." >&2;}
> > > > > > >> > > > > > >  fi
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  # For libtool versioning info, format is
> CURRENT:REVISION:AGE
> > > > > > >> > > > > > > -libtool_VERSION=6:28:0
> > > > > > >> > > > > > > +libtool_VERSION=6:29:0
> > > > > > >> > > > > > >
> > > > > > >> > > > > > >  # Everything parsed; figure out what files and
> settings to use.
> > > > > > >> > > > > > >  case $enable_symvers in
> > > > > > >> > > > > > > diff --git a/libstdc++-v3/include/std/charconv
> > > > > > >> > > > > > > b/libstdc++-v3/include/std/charconv
> > > > > > >> > > > > > > index cc7dd0e3758..bd59924f7e7 100644
> > > > > > >> > > > > > > --- a/libstdc++-v3/include/std/charconv
> > > > > > >> > > > > > > +++ b/libstdc++-v3/include/std/charconv
> > > > > > >> > > > > > > @@ -688,6 +688,49 @@ namespace __detail
> > > > > > >> > > > > > >    operator^=(chars_format& __lhs, chars_format
> __rhs) noexcept
> > > > > > >> > > > > > >    { return __lhs = __lhs ^ __rhs; }
> > > > > > >> > > > > > >
> > > > > > >> > > > > > > +  // Floating-point std::to_chars
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  // Overloads for float.
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, float
> > > > > > >> > > > > __value)
> > > > > > >> > > > > > > noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, float
> > > > > > >> > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt)
> noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, float
> > > > > > >> > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt,
> int __precision)
> > > > > > >> > > > > noexcept;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  // Overloads for double.
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, double
> > > > > > >> > > > > __value)
> > > > > > >> > > > > > > noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, double
> > > > > > >> > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt)
> noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, double
> > > > > > >> > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt,
> int __precision)
> > > > > > >> > > > > noexcept;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  // Overloads for long double.
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, long double
> > > > > > >> > > > > > > __value)
> > > > > > >> > > > > > > +    noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, long double
> > > > > > >> > > > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt)
> noexcept;
> > > > > > >> > > > > > > +  to_chars_result to_chars(char* __first, char*
> __last, long double
> > > > > > >> > > > > > > __value,
> > > > > > >> > > > > > > +                           chars_format __fmt,
> int __precision)
> > > > > > >> > > > > noexcept;
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  // If long double has the same binary format
> as double, then we
> > > > > > >> > > > > just
> > > > > > >> > > > > > > define
> > > > > > >> > > > > > > +  // the long double overloads as wrappers
> around the corresponding
> > > > > > >> > > > > > > double
> > > > > > >> > > > > > > +  // overloads.
> > > > > > >> > > > > > > +#if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__
> > > > > > >> > > > > > > +  inline to_chars_result
> > > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long
> double __value) noexcept
> > > > > > >> > > > > > > +  { return to_chars(__first, __last,
> double(__value)); }
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  inline to_chars_result
> > > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long
> double __value,
> > > > > > >> > > > > > > +           chars_format __fmt) noexcept
> > > > > > >> > > > > > > +  { return to_chars(__first, __last,
> double(__value), __fmt); }
> > > > > > >> > > > > > > +
> > > > > > >> > > > > > > +  inline to_chars_result
> > > > > > >> > > > > > > +  to_chars(char* __first, char* __last, long
> double __value,
> > > > > > >> > > > > > > +           chars_format __fmt, int __precision)
> noexcept
> > > > > > >> > > > > > > +  { return to_chars(__first, __last,
> double(__value), __fmt,
> > > > > > >> > > > > > > __precision); }
> > > > > > >> > > > > > > +#endif
> > > > > > >> > > > > >
> > > > > > >> > > > > > Hmm, I think this approach for supporting
> -mlong-double-64 might
> > > > > > >> > > > > > introduce an ODR violation because each long double
> to_chars overload
> > > > > > >> > > > > > could potentially have two different definitions
> available in a program,
> > > > > > >> > > > > > one out-of-line in floating_to_chars.cc (compiled
> without
> > > > > > >> > > > > > -mlong-double-64) and another inline in <charconv>
> (compiled with
> > > > > > >> > > > > > -mlong-double-64)..
> > > > > > >> > > > >
> > > > > > >> > > > > But they have different mangled names, so there's no
> ODR violation.
> > > > > > >> > > > > The 64-bit long double is mangled as 'e' and the
> 128-bit long double
> > > > > > >> > > > > is mangled as __float128. You *will* get an ODR
> violation on targets
> > > > > > >> > > > > where there's no -mlong-double-64 switch, where
> double and long double
> > > > > > >> > > > > are always the same representation.
> > > > > > >> > > > >
> > > > > > >> > > > > What I'm doing for std::from_chars is adding this in
> the new
> > > > > > >> > > > > src/c++17/floating_from_chars.cc file:
> > > > > > >> > > > >
> > > > > > >> > > > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > > > >> > > > > #pragma GCC diagnostic ignored "-Wattribute-alias"
> > > > > > >> > > > > extern "C" from_chars_result
> > > > > > >> > > > > _ZSt10from_charsPKcS0_ReSt12chars_format(double)
> > > > > > >> > > > > __attribute__((alias
> ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > > > >> > > > > #endif
> > > > > > >> > > > >
> > > > > > >> > > > > This just defines the
> _ZSt10from_charsPKcS0_ReSt12chars_format symbol
> > > > > > >> > > > > (i.e. from_chars for 64-bit long double) as an alias
> of
> > > > > > >> > > > > _ZSt10from_charsPKcS0_RdSt12chars_format (i.e.
> from_chars for 64-bit
> > > > > > >> > > > > double).
> > > > > > >> > > >
> > > > > > >> > > > Aha, that makes sense.  I'll follow suit for
> std::to_chars.
> > > > > > >> > >
> > > > > > >> > > Actually that should be:
> > > > > > >> > >
> > > > > > >> > > #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT
> > > > > > >> > > extern "C" from_chars_result
> > > > > > >> > > _ZSt10from_charsPKcS0_ReSt12chars_format(const char*
> first, const char* last,
> > > > > > >> > >                                   long double& value,
> > > > > > >> > >                                   chars_format fmt)
> noexcept
> > > > > > >> > > __attribute__((alias
> ("_ZSt10from_charsPKcS0_RdSt12chars_format")));
> > > > > > >> > > #endif
> > > > > > >> > >
> > > > > > >> > > With the right parameter list I don't need to disable the
> warning.
> > > > > > >> >
> > > > > > >> > Sounds good.  Here's patch v5 that defines such aliases,
> tested so far
> > > > > > >> > on x86_64-pc-linux-gnu and on powerpc64le-unknown-linux-gnu.
> > > > > > >>
> > > > > > >> Here's v6 which is rebased against the floating-point
> from_chars patch
> > > > > > >> and which also works around a false-positive
> -Wmaybe-uninitialized
> > > > > > >> warning in __floating_to_chars_hex, as well as performs some
> minor
> > > > > > >> commentary/style cleanups:
> > > > > > >
> > > > > > >Here's v7, with the following changes:
> > > > > > >
> > > > > > >* Remove extraneous indentation (two spaces when inside the std
> > > > > > >  namespace, two spaces after a template header) for better
> consistency
> > > > > > >  with floating_from_chars.cc
> > > > > > >* Guard the calls to fe[gs]etround with a preprocessor test for
> > > > > > >  _GLIBCXX_USE_C99_FENV_TR1;
> > > > > > >* Properly XFAIL the new long_double.cc test on targets with a
> > > > > > >  large long double type but without __int128, most notably i386
> > > > > > >* Reword the commit message slightly.
> > > > > > >
> > > > > > >-- >8 --
> > > > > > >
> > > > > > >Subject: [PATCH] libstdc++: Add floating-point std::to_chars
> implementation
> > > > > > >
> > > > > > >This implements the floating-point std::to_chars overloads for
> float,
> > > > > > >double and long double.  We use the Ryu library to compute the
> shortest
> > > > > > >round-trippable fixed and scientific forms for float, double
> and long
> > > > > > >double.  We also use Ryu for performing explicit-precision
> fixed and
> > > > > > >scientific formatting of float and double. For
> explicit-precision
> > > > > > >formatting of long double we fall back to using printf.
> Hexadecimal
> > > > > > >formatting for float, double and long double is implemented from
> > > > > > >scratch.
> > > > > > >
> > > > > > >The supported long double binary formats are binary64, binary80
> (x86
> > > > > > >80-bit extended precision), binary128 and ibm128.
> > > > > > >
> > > > > > >Much of the complexity of the implementation is in computing
> the exact
> > > > > > >output length before handing it off to Ryu (which doesn't do
> bounds
> > > > > > >checking).  In some cases it's hard to compute the output length
> > > > > > >beforehand, so in these cases we instead compute an upper bound
> on the
> > > > > > >output length and use a sufficiently-sized intermediate buffer
> only if
> > > > > > >necessary.
> > > > > > >
> > > > > > >Another source of complexity is in the general-with-precision
> formatting
> > > > > > >mode, where we need to do zero-trimming of the string returned
> by Ryu,
> > > > > > >and where we also take care to avoid having to format the
> number through
> > > > > > >Ryu a second time when the general formatting mode resolves to
> fixed
> > > > > > >(which we determine by doing a scientific formatting first and
> > > > > > >inspecting the scientific exponent).  We avoid going through
> Ryu twice
> > > > > > >by instead transforming the scientific form to the
> corresponding fixed
> > > > > > >form via in-place string manipulation.
> > > > > > >
> > > > > > >This implementation is non-conforming in a couple of ways:
> > > > > > >
> > > > > > >1. For the shortest hexadecimal formatting, we currently follow
> the
> > > > > > >   Microsoft implementation's decision to be consistent with the
> > > > > > >   output of printf's '%a' specifier at the expense of
> sometimes not
> > > > > > >   printing the shortest representation.  For example, the
> shortest hex
> > > > > > >   form for the number 1.08p+0 is 2.1p-1, but we output the
> former
> > > > > > >   instead of the latter, as does printf.
> > > > > > >
> > > > > > >2. The Ryu routine generic_binary_to_decimal that we use for
> performing
> > > > > > >   shortest formatting for large floating point types is
> implemented
> > > > > > >   using the __int128 type, but some targets with a large long
> double
> > > > > > >   type lack __int128 (e.g. i686), so we can't perform shortest
> > > > > > >   formatting of long double on such targets through Ryu.  As a
> > > > > > >   temporary stopgap this patch makes the long double to_chars
> overloads
> > > > > > >   just dispatch to the double overloads on these targets,
> which means
> > > > > > >   we lose precision in the output.  (We could potentially fix
> this by
> > > > > > >   writing a specialized version of Ryu's
> generic_binary_to_decimal
> > > > > > >   routine that uses uint64_t instead of __int128.)  [Though I
> wonder if
> > > > > > >   there's a better way to work around the lack of __int128 on
> i686
> > > > > > >   specifically?]
> > > > > > >
> > > > > > >3. Our shortest formatting for __ibm128 doesn't guarantee the
> round-trip
> > > > > > >   property if the difference between the high- and low-order
> exponent
> > > > > > >   is large.  This is because we treat __ibm128 as if it has a
> > > > > > >   contiguous 105-bit mantissa by merging the mantissas of the
> high-
> > > > > > >   and low-order parts (using code extracted from glibc), so we
> > > > > > >   potentially lose precision from the low-order part.  This
> seems to be
> > > > > > >   consistent with how glibc printf formats __ibm128.
> > > > > > >
> > > > > > >libstdc++-v3/ChangeLog:
> > > > > > >
> > > > > > >       * config/abi/pre/gnu.ver: Add new exports.
> > > > > > >       * include/std/charconv (to_chars): Declare the
> floating-point
> > > > > > >       overloads for float, double and long double.
> > > > > > >       * src/c++17/Makefile.am (sources): Add
> floating_to_chars.cc.
> > > > > > >       * src/c++17/Makefile.in: Regenerate.
> > > > > > >       * src/c++17/floating_to_chars.cc: New file.
> > > > > > >       (to_chars): Define for float, double and long double.
> > > > > > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> > > > > >
> > > > > > Sorry it took so long to review, this is OK for trunk.
> > > > > >
> > > > > > The patch needs some minor changes to rebase it on the current
> trunk:
> > > > > > The linker script has additions since you send this patch, so the
> > > > > > context in the patch is wrong and it doesn't apply, and in
> <charconv>
> > > > > > the first line of context in the patch needs to have 'noexcept'
> added.
> > > > > > That rebase should be easy though.
> > > > > >
> > > > > > I'll look at adding __float128 support for powerpc64le.
> > > > >
> > > > > Thanks a lot.  I committed the patch series just now, after
> rebasing
> > > > > and retesting on x86_64, aarch64 and ppc64le.
> > > > >
> > > >
> > > > My newlib-based toolchains (arm-eabi, aarch64-elf) fail to build
> after
> > > > this commit, because:
> > > > libstdc++-v3/src/c++17/floating_to_chars.cc:951:40: error:
> > > > 'FE_TONEAREST' was not declared in this scope
> > > >   951 |             if (saved_rounding_mode != FE_TONEAREST)
> > > >
> > > > I'm (still) using newlib-3.3.0, and I think newlib's fenv.h was
> updated
> > > > this year for arm/aarch64, so I suspect bumping to 3.4.0 would
> > > > avoid the problem. However, is this something you want to support?
> > > > (I mean the possibility that FE_TONEAREST is not supported etc...)
> > >
> > > Thanks for the heads up.  Yes, it seems we should be testing that
> > > FE_TONEAREST is defined before using it or fegetround()/fesetround().
> > > This'll fix the build breakage and is also more conforming to the C
> > > standard, which says that the latter functions work only if this macro
> > > is defined.
> > >
> > > Does the following patch look OK to commit?
> > >
> > > -- >8 --
> > >
> > > Subject: [PATCH] libstdc++: Check FE_TONEAREST is defined before using
> it
> > >
> > > We need to check that FE_TONEAREST is defined before using it and
> > > fegetround/fesetround to adjust the floating-point rounding mode
> > > (as per the specification of fenv.h).
> > >
> > > libstdc++-v3/ChangeLog:
> > >
> > >         * src/c++17/floating_from_chars.cc (from_chars_impl): Check
> > >         FE_TONEAREST is defined before adjusting the rounding mode.
> > >         * src/c++17/floating_to_chars.cc
> (__floating_to_chars_precision):
> > >         Likewise.
> >
> > Thanks, that's better but not sufficient:
> > /libstdc++-v3/src/c++17/floating_to_chars.cc: In instantiation of
> > 'std::to_chars_result std::__floating_to_chars_shortest(char*, char*,
> > T, std::chars_format) [with T = float]':
> > /libstdc++-v3/src/c++17/floating_to_chars.cc:1484:73:   required from
> here
> > /libstdc++-v3/src/c++17/floating_to_chars.cc:978:37: error: no
> > matching function for call to 'max(long int, int)'
> >   978 |         const int whole_digits = max(mantissa_length +
> fd.exponent, 1);
> >
> > are we just missing a cast?
>
> Ah yes, I think this was also reported earlier today as PR libstdc++/98370.
> I just went ahead and committed the above FE_TONEAREST fix and the
> proposed PR98370 fix under the "obvious" rule.  Does latest trunk build
> for you now?
>
> Yes, thanks !
>
> >
> > > ---
> > >  libstdc++-v3/src/c++17/floating_from_chars.cc | 4 ++--
> > >  libstdc++-v3/src/c++17/floating_to_chars.cc   | 8 ++++----
> > >  2 files changed, 6 insertions(+), 6 deletions(-)
> > >
> > > diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc
> b/libstdc++-v3/src/c++17/floating_from_chars.cc
> > > index a1943351493..86d6d0645a9 100644
> > > --- a/libstdc++-v3/src/c++17/floating_from_chars.cc
> > > +++ b/libstdc++-v3/src/c++17/floating_from_chars.cc
> > > @@ -307,7 +307,7 @@ namespace
> > >        {
> > >         locale_t orig = ::uselocale(loc);
> > >
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >         const int rounding = std::fegetround();
> > >         if (rounding != FE_TONEAREST)
> > >           std::fesetround(FE_TONEAREST);
> > > @@ -333,7 +333,7 @@ namespace
> > >  #endif
> > >         const int conv_errno = std::__exchange(errno, save_errno);
> > >
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >         if (rounding != FE_TONEAREST)
> > >           std::fesetround(rounding);
> > >  #endif
> > > diff --git a/libstdc++-v3/src/c++17/floating_to_chars.cc
> b/libstdc++-v3/src/c++17/floating_to_chars.cc
> > > index dd83f5eea93..474e791e717 100644
> > > --- a/libstdc++-v3/src/c++17/floating_to_chars.cc
> > > +++ b/libstdc++-v3/src/c++17/floating_to_chars.cc
> > > @@ -946,13 +946,13 @@ template<typename T>
> > >             // digit, and carefully compute and write the last digit
> > >             // ourselves.
> > >             char buffer[expected_output_length+1];
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >             const int saved_rounding_mode = fegetround();
> > >             if (saved_rounding_mode != FE_TONEAREST)
> > >               fesetround(FE_TONEAREST); // We want round-to-nearest
> behavior.
> > >  #endif
> > >             const int output_length = sprintf(buffer, "%.0Lf", value);
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >             if (saved_rounding_mode != FE_TONEAREST)
> > >               fesetround(saved_rounding_mode);
> > >  #endif
> > > @@ -1139,14 +1139,14 @@ template<typename T>
> > >
> > >         // Do the sprintf into the local buffer.
> > >         char buffer[output_length_upper_bound+1];
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >         const int saved_rounding_mode = fegetround();
> > >         if (saved_rounding_mode != FE_TONEAREST)
> > >           fesetround(FE_TONEAREST); // We want round-to-nearest
> behavior.
> > >  #endif
> > >         int output_length
> > >           = sprintf(buffer, output_specifier, effective_precision,
> value);
> > > -#if _GLIBCXX_USE_C99_FENV_TR1
> > > +#if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST)
> > >         if (saved_rounding_mode != FE_TONEAREST)
> > >           fesetround(saved_rounding_mode);
> > >  #endif
> > > --
> > > 2.30.0.rc0
> > >
> >
> >
>
>

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Maciej W. Rozycki]

On Thu, 17 Dec 2020, Patrick Palka via Gcc-patches wrote:

> > >libstdc++-v3/ChangeLog:
> > >
> > >       * config/abi/pre/gnu.ver: Add new exports.
> > >       * include/std/charconv (to_chars): Declare the floating-point
> > >       overloads for float, double and long double.
> > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > >       * src/c++17/Makefile.in: Regenerate.
> > >       * src/c++17/floating_to_chars.cc: New file.
> > >       (to_chars): Define for float, double and long double.
> > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> >
> > Sorry it took so long to review, this is OK for trunk.
> >
> > The patch needs some minor changes to rebase it on the current trunk:
> > The linker script has additions since you send this patch, so the
> > context in the patch is wrong and it doesn't apply, and in <charconv>
> > the first line of context in the patch needs to have 'noexcept' added.
> > That rebase should be easy though.
> >
> > I'll look at adding __float128 support for powerpc64le.
> 
> Thanks a lot.  I committed the patch series just now, after rebasing
> and retesting on x86_64, aarch64 and ppc64le.

 This breaks with the `vax-netbsdelf' target in GCC compilation:

.../libstdc++-v3/src/c++17/floating_to_chars.cc:126:38: error: static assertion failed
  126 |       static_assert(__DBL_MANT_DIG__ == 53);
      |                                      ^
make[5]: *** [Makefile:577: floating_to_chars.lo] Error 1

So what's the fallback/alternative for non-IEEE-754 FP targets?  Shouldn't 
we call into libc (possibly with a warning attribute) for the formats we 
don't have explicit handcoded support for?

  Maciej

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Patrick Palka]

On Sun, 20 Dec 2020, Maciej W. Rozycki wrote:

> On Thu, 17 Dec 2020, Patrick Palka via Gcc-patches wrote:
> 
> > > >libstdc++-v3/ChangeLog:
> > > >
> > > >       * config/abi/pre/gnu.ver: Add new exports.
> > > >       * include/std/charconv (to_chars): Declare the floating-point
> > > >       overloads for float, double and long double.
> > > >       * src/c++17/Makefile.am (sources): Add floating_to_chars.cc.
> > > >       * src/c++17/Makefile.in: Regenerate.
> > > >       * src/c++17/floating_to_chars.cc: New file.
> > > >       (to_chars): Define for float, double and long double.
> > > >       * testsuite/20_util/to_chars/long_double.cc: New test.
> > >
> > > Sorry it took so long to review, this is OK for trunk.
> > >
> > > The patch needs some minor changes to rebase it on the current trunk:
> > > The linker script has additions since you send this patch, so the
> > > context in the patch is wrong and it doesn't apply, and in <charconv>
> > > the first line of context in the patch needs to have 'noexcept' added.
> > > That rebase should be easy though.
> > >
> > > I'll look at adding __float128 support for powerpc64le.
> > 
> > Thanks a lot.  I committed the patch series just now, after rebasing
> > and retesting on x86_64, aarch64 and ppc64le.
> 
>  This breaks with the `vax-netbsdelf' target in GCC compilation:
> 
> .../libstdc++-v3/src/c++17/floating_to_chars.cc:126:38: error: static assertion failed
>   126 |       static_assert(__DBL_MANT_DIG__ == 53);
>       |                                      ^
> make[5]: *** [Makefile:577: floating_to_chars.lo] Error 1
> 
> So what's the fallback/alternative for non-IEEE-754 FP targets?  Shouldn't 
> we call into libc (possibly with a warning attribute) for the formats we 
> don't have explicit handcoded support for?

Sorry about this bootstrap breakage.  For now, we should probably just
disable the entire file/implementation on such targets until a proper
fallback could be implemented.  I posted a patch to that effect here
https://gcc.gnu.org/pipermail/gcc-patches/2020-December/562379.html
which is pending review/approval.  Until then, manually stubbing out all of
floating_to_chars.cc should probably suffice to restore bootstrap on
this target.

Re: [PATCH 3/4] libstdc++: Add floating-point std::to_chars implementation

[Maciej W. Rozycki]

On Mon, 21 Dec 2020, Patrick Palka wrote:

> >  This breaks with the `vax-netbsdelf' target in GCC compilation:
> > 
> > .../libstdc++-v3/src/c++17/floating_to_chars.cc:126:38: error: static assertion failed
> >   126 |       static_assert(__DBL_MANT_DIG__ == 53);
> >       |                                      ^
> > make[5]: *** [Makefile:577: floating_to_chars.lo] Error 1
> > 
> > So what's the fallback/alternative for non-IEEE-754 FP targets?  Shouldn't 
> > we call into libc (possibly with a warning attribute) for the formats we 
> > don't have explicit handcoded support for?
> 
> Sorry about this bootstrap breakage.  For now, we should probably just
> disable the entire file/implementation on such targets until a proper
> fallback could be implemented.  I posted a patch to that effect here
> https://gcc.gnu.org/pipermail/gcc-patches/2020-December/562379.html
> which is pending review/approval.  Until then, manually stubbing out all of
> floating_to_chars.cc should probably suffice to restore bootstrap on
> this target.

 No worries, breakage happens, especially with the more obscure areas we 
support.  Thanks for the quick fix!

  Maciej

[PATCH 4/4] libstdc++: Import MSVC floating-point std::to_chars testcases

[Patrick Palka]

libstdc++-v3/ChangeLog:

	* testsuite/20_util/to_chars/double.cc: New test, consisting of
	testcases imported from the MSVC STL testsuite.
	* testsuite/20_util/to_chars/float.cc: Likewise.
---
 .../testsuite/20_util/to_chars/double.cc      | 57000 ++++++++++++++++
 .../testsuite/20_util/to_chars/float.cc       |  4142 ++
 2 files changed, 61142 insertions(+)
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/double.cc
 create mode 100644 libstdc++-v3/testsuite/20_util/to_chars/float.cc

diff --git a/libstdc++-v3/testsuite/20_util/to_chars/double.cc b/libstdc++-v3/testsuite/20_util/to_chars/double.cc
new file mode 100644
index 00000000000..9d1f37d3026
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/to_chars/double.cc
@@ -0,0 +1,57000 @@
+// This file consists of testcases taken from the MSVC STL testsuite.
+
+// Copyright (c) Microsoft Corporation.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+
+// Copyright 2018 Ulf Adams
+// Copyright (c) Microsoft Corporation. All rights reserved.
+
+// Boost Software License - Version 1.0 - August 17th, 2003
+
+// Permission is hereby granted, free of charge, to any person or organization
+// obtaining a copy of the software and accompanying documentation covered by
+// this license (the "Software") to use, reproduce, display, distribute,
+// execute, and transmit the Software, and to prepare derivative works of the
+// Software, and to permit third-parties to whom the Software is furnished to
+// do so, all subject to the following:
+
+// The copyright notices in the Software and this entire statement, including
+// the above license grant, this restriction and the following disclaimer,
+// must be included in all copies of the Software, in whole or in part, and
+// all derivative works of the Software, unless such copies or derivative
+// works are solely in the form of machine-executable object code generated by
+// a source language processor.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+// DEALINGS IN THE SOFTWARE.
+
+// { dg-do run { target c++17 } }
+
+#include <charconv>
+
+#include <cstring>
+#include <limits>
+#include <optional>
+
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+inline constexpr double double_inf = numeric_limits<double>::infinity();
+inline constexpr double double_nan = numeric_limits<double>::quiet_NaN();
+
+struct double_to_chars_testcase {
+    double value;
+    chars_format fmt;
+    optional<int> precision;
+    const char* correct;
+
+    constexpr
+    double_to_chars_testcase(double value, chars_format fmt, const char* correct)
+      : value (value), fmt (fmt), precision (nullopt), correct (correct)
+    { }
+
+    constexpr
+    double_to_chars_testcase(double value, chars_format fmt, int precision,
+			     const char* correct)
+      : value (value), fmt (fmt), precision (precision), correct (correct)
+    { }
+};
+
+inline constexpr double_to_chars_testcase double_to_chars_test_cases[] = {
+    // Test special cases (zero, inf, nan) and an ordinary case. Also test negative signs.
+    {0.0, chars_format::scientific, "0e+00"},
+    {-0.0, chars_format::scientific, "-0e+00"},
+    {double_inf, chars_format::scientific, "inf"},
+    {-double_inf, chars_format::scientific, "-inf"},
+    {double_nan, chars_format::scientific, "nan"},
+    {-double_nan, chars_format::scientific, "-nan"},
+    {2.018, chars_format::scientific, "2.018e+00"},
+    {-2.018, chars_format::scientific, "-2.018e+00"},
+
+    // Ditto for fixed, which doesn't emit exponents.
+    {0.0, chars_format::fixed, "0"},
+    {-0.0, chars_format::fixed, "-0"},
+    {double_inf, chars_format::fixed, "inf"},
+    {-double_inf, chars_format::fixed, "-inf"},
+    {double_nan, chars_format::fixed, "nan"},
+    {-double_nan, chars_format::fixed, "-nan"},
+    {2.018, chars_format::fixed, "2.018"},
+    {-2.018, chars_format::fixed, "-2.018"},
+
+    // Ditto for general, which selects fixed for the scientific exponent 0.
+    {0.0, chars_format::general, "0"},
+    {-0.0, chars_format::general, "-0"},
+    {double_inf, chars_format::general, "inf"},
+    {-double_inf, chars_format::general, "-inf"},
+    {double_nan, chars_format::general, "nan"},
+    {-double_nan, chars_format::general, "-nan"},
+    {2.018, chars_format::general, "2.018"},
+    {-2.018, chars_format::general, "-2.018"},
+
+    // Ditto for plain, which selects fixed because it's shorter for these values.
+    {0.0, chars_format{}, "0"},
+    {-0.0, chars_format{}, "-0"},
+    {double_inf, chars_format{}, "inf"},
+    {-double_inf, chars_format{}, "-inf"},
+    {double_nan, chars_format{}, "nan"},
+    {-double_nan, chars_format{}, "-nan"},
+    {2.018, chars_format{}, "2.018"},
+    {-2.018, chars_format{}, "-2.018"},
+
+    // Ditto for hex.
+    {0.0, chars_format::hex, "0p+0"},
+    {-0.0, chars_format::hex, "-0p+0"},
+    {double_inf, chars_format::hex, "inf"},
+    {-double_inf, chars_format::hex, "-inf"},
+    {double_nan, chars_format::hex, "nan"},
+    {-double_nan, chars_format::hex, "-nan"},
+    {0x1.729p+0, chars_format::hex, "1.729p+0"},
+    {-0x1.729p+0, chars_format::hex, "-1.729p+0"},
+
+    // Ryu d2s_test.cc SwitchToSubnormal
+    {2.2250738585072014e-308, chars_format::scientific, "2.2250738585072014e-308"},
+
+    // Ryu d2s_test.cc MinAndMax
+    {0x1.fffffffffffffp+1023, chars_format::scientific, "1.7976931348623157e+308"},
+    {0x0.0000000000001p-1022, chars_format::scientific, "5e-324"},
+
+    // Ryu d2s_test.cc LotsOfTrailingZeros
+    {2.98023223876953125e-8, chars_format::scientific, "2.9802322387695312e-08"},
+
+    // Ryu d2s_test.cc Regression
+    {-2.109808898695963e16, chars_format::scientific, "-2.109808898695963e+16"},
+    {4.940656e-318, chars_format::scientific, "4.940656e-318"},
+    {1.18575755e-316, chars_format::scientific, "1.18575755e-316"},
+    {2.989102097996e-312, chars_format::scientific, "2.989102097996e-312"},
+    {9.0608011534336e15, chars_format::scientific, "9.0608011534336e+15"},
+    {4.708356024711512e18, chars_format::scientific, "4.708356024711512e+18"},
+    {9.409340012568248e18, chars_format::scientific, "9.409340012568248e+18"},
+
+    // Ryu d2s_test.cc LooksLikePow5
+    {0x1.0f0cf064dd592p+132, chars_format::scientific, "5.764607523034235e+39"},
+    {0x1.0f0cf064dd592p+133, chars_format::scientific, "1.152921504606847e+40"},
+    {0x1.0f0cf064dd592p+134, chars_format::scientific, "2.305843009213694e+40"},
+
+    // Ryu d2s_test.cc OutputLength
+    {1.0, chars_format::scientific, "1e+00"},
+    {1.2, chars_format::scientific, "1.2e+00"},
+    {1.23, chars_format::scientific, "1.23e+00"},
+    {1.234, chars_format::scientific, "1.234e+00"},
+    {1.2345, chars_format::scientific, "1.2345e+00"},
+    {1.23456, chars_format::scientific, "1.23456e+00"},
+    {1.234567, chars_format::scientific, "1.234567e+00"},
+    {1.2345678, chars_format::scientific, "1.2345678e+00"},
+    {1.23456789, chars_format::scientific, "1.23456789e+00"},
+    {1.234567895, chars_format::scientific, "1.234567895e+00"},
+    {1.2345678901, chars_format::scientific, "1.2345678901e+00"},
+    {1.23456789012, chars_format::scientific, "1.23456789012e+00"},
+    {1.234567890123, chars_format::scientific, "1.234567890123e+00"},
+    {1.2345678901234, chars_format::scientific, "1.2345678901234e+00"},
+    {1.23456789012345, chars_format::scientific, "1.23456789012345e+00"},
+    {1.234567890123456, chars_format::scientific, "1.234567890123456e+00"},
+    {1.2345678901234567, chars_format::scientific, "1.2345678901234567e+00"},
+
+    // Ryu d2s_test.cc 32-bit Chunking
+    {4.294967294, chars_format::scientific, "4.294967294e+00"},
+    {4.294967295, chars_format::scientific, "4.294967295e+00"},
+    {4.294967296, chars_format::scientific, "4.294967296e+00"},
+    {4.294967297, chars_format::scientific, "4.294967297e+00"},
+    {4.294967298, chars_format::scientific, "4.294967298e+00"},
+
+    // Ryu d2s_test.cc MinMaxShift
+    {0x1.0000000000000p-1019, chars_format::scientific, "1.7800590868057611e-307"},
+    {0x1.fffffffffffffp-1016, chars_format::scientific, "2.8480945388892175e-306"},
+    {0x1.0000000000000p-982, chars_format::scientific, "2.446494580089078e-296"},
+    {0x1.fffffffffffffp-982, chars_format::scientific, "4.8929891601781557e-296"},
+    {0x1.0000000000000p+54, chars_format::scientific, "1.8014398509481984e+16"},
+    {0x1.fffffffffffffp+54, chars_format::scientific, "3.6028797018963964e+16"},
+    {0x1.0000000000000p-716, chars_format::scientific, "2.900835519859558e-216"},
+    {0x1.fffffffffffffp-716, chars_format::scientific, "5.801671039719115e-216"},
+    {0x1.fa7161a4d6e0cp-89, chars_format::scientific, "3.196104012172126e-27"},
+
+    // Ryu d2s_test.cc SmallIntegers
+    {9007199254740991.0, chars_format::scientific, "9.007199254740991e+15"},
+    {9007199254740992.0, chars_format::scientific, "9.007199254740992e+15"},
+
+    {1.0, chars_format::scientific, "1e+00"},
+    {12.0, chars_format::scientific, "1.2e+01"},
+    {123.0, chars_format::scientific, "1.23e+02"},
+    {1234.0, chars_format::scientific, "1.234e+03"},
+    {12345.0, chars_format::scientific, "1.2345e+04"},
+    {123456.0, chars_format::scientific, "1.23456e+05"},
+    {1234567.0, chars_format::scientific, "1.234567e+06"},
+    {12345678.0, chars_format::scientific, "1.2345678e+07"},
+    {123456789.0, chars_format::scientific, "1.23456789e+08"},
+    {1234567890.0, chars_format::scientific, "1.23456789e+09"},
+    {1234567895.0, chars_format::scientific, "1.234567895e+09"},
+    {12345678901.0, chars_format::scientific, "1.2345678901e+10"},
+    {123456789012.0, chars_format::scientific, "1.23456789012e+11"},
+    {1234567890123.0, chars_format::scientific, "1.234567890123e+12"},
+    {12345678901234.0, chars_format::scientific, "1.2345678901234e+13"},
+    {123456789012345.0, chars_format::scientific, "1.23456789012345e+14"},
+    {1234567890123456.0, chars_format::scientific, "1.234567890123456e+15"},
+
+    {1.0, chars_format::scientific, "1e+00"},
+    {10.0, chars_format::scientific, "1e+01"},
+    {100.0, chars_format::scientific, "1e+02"},
+    {1000.0, chars_format::scientific, "1e+03"},
+    {10000.0, chars_format::scientific, "1e+04"},
+    {100000.0, chars_format::scientific, "1e+05"},
+    {1000000.0, chars_format::scientific, "1e+06"},
+    {10000000.0, chars_format::scientific, "1e+07"},
+    {100000000.0, chars_format::scientific, "1e+08"},
+    {1000000000.0, chars_format::scientific, "1e+09"},
+    {10000000000.0, chars_format::scientific, "1e+10"},
+    {100000000000.0, chars_format::scientific, "1e+11"},
+    {1000000000000.0, chars_format::scientific, "1e+12"},
+    {10000000000000.0, chars_format::scientific, "1e+13"},
+    {100000000000000.0, chars_format::scientific, "1e+14"},
+    {1000000000000000.0, chars_format::scientific, "1e+15"},
+
+    {1000000000000001.0, chars_format::scientific, "1.000000000000001e+15"},
+    {1000000000000010.0, chars_format::scientific, "1.00000000000001e+15"},
+    {1000000000000100.0, chars_format::scientific, "1.0000000000001e+15"},
+    {1000000000001000.0, chars_format::scientific, "1.000000000001e+15"},
+    {1000000000010000.0, chars_format::scientific, "1.00000000001e+15"},
+    {1000000000100000.0, chars_format::scientific, "1.0000000001e+15"},
+    {1000000001000000.0, chars_format::scientific, "1.000000001e+15"},
+    {1000000010000000.0, chars_format::scientific, "1.00000001e+15"},
+    {1000000100000000.0, chars_format::scientific, "1.0000001e+15"},
+    {1000001000000000.0, chars_format::scientific, "1.000001e+15"},
+    {1000010000000000.0, chars_format::scientific, "1.00001e+15"},
+    {1000100000000000.0, chars_format::scientific, "1.0001e+15"},
+    {1001000000000000.0, chars_format::scientific, "1.001e+15"},
+    {1010000000000000.0, chars_format::scientific, "1.01e+15"},
+    {1100000000000000.0, chars_format::scientific, "1.1e+15"},
+
+    {8.0, chars_format::scientific, "8e+00"},
+    {64.0, chars_format::scientific, "6.4e+01"},
+    {512.0, chars_format::scientific, "5.12e+02"},
+    {8192.0, chars_format::scientific, "8.192e+03"},
+    {65536.0, chars_format::scientific, "6.5536e+04"},
+    {524288.0, chars_format::scientific, "5.24288e+05"},
+    {8388608.0, chars_format::scientific, "8.388608e+06"},
+    {67108864.0, chars_format::scientific, "6.7108864e+07"},
+    {536870912.0, chars_format::scientific, "5.36870912e+08"},
+    {8589934592.0, chars_format::scientific, "8.589934592e+09"},
+    {68719476736.0, chars_format::scientific, "6.8719476736e+10"},
+    {549755813888.0, chars_format::scientific, "5.49755813888e+11"},
+    {8796093022208.0, chars_format::scientific, "8.796093022208e+12"},
+    {70368744177664.0, chars_format::scientific, "7.0368744177664e+13"},
+    {562949953421312.0, chars_format::scientific, "5.62949953421312e+14"},
+    {9007199254740992.0, chars_format::scientific, "9.007199254740992e+15"},
+
+    {8000.0, chars_format::scientific, "8e+03"},
+    {64000.0, chars_format::scientific, "6.4e+04"},
+    {512000.0, chars_format::scientific, "5.12e+05"},
+    {8192000.0, chars_format::scientific, "8.192e+06"},
+    {65536000.0, chars_format::scientific, "6.5536e+07"},
+    {524288000.0, chars_format::scientific, "5.24288e+08"},
+    {8388608000.0, chars_format::scientific, "8.388608e+09"},
+    {67108864000.0, chars_format::scientific, "6.7108864e+10"},
+    {536870912000.0, chars_format::scientific, "5.36870912e+11"},
+    {8589934592000.0, chars_format::scientific, "8.589934592e+12"},
+    {68719476736000.0, chars_format::scientific, "6.8719476736e+13"},
+    {549755813888000.0, chars_format::scientific, "5.49755813888e+14"},
+    {8796093022208000.0, chars_format::scientific, "8.796093022208e+15"},
+
+    // Test all exponents.
+    {7.29e-324, chars_format::scientific, "5e-324"}, // 1.729e-324 would be too small
+    {1.729e-323, chars_format::scientific, "1.5e-323"},
+    {1.729e-322, chars_format::scientific, "1.73e-322"},
+    {1.729e-321, chars_format::scientific, "1.73e-321"},
+    {1.729e-320, chars_format::scientific, "1.729e-320"},
+    {1.729e-319, chars_format::scientific, "1.729e-319"},
+    {1.729e-318, chars_format::scientific, "1.729e-318"},
+    {1.729e-317, chars_format::scientific, "1.729e-317"},
+    {1.729e-316, chars_format::scientific, "1.729e-316"},
+    {1.729e-315, chars_format::scientific, "1.729e-315"},
+    {1.729e-314, chars_format::scientific, "1.729e-314"},
+    {1.729e-313, chars_format::scientific, "1.729e-313"},
+    {1.729e-312, chars_format::scientific, "1.729e-312"},
+    {1.729e-311, chars_format::scientific, "1.729e-311"},
+    {1.729e-310, chars_format::scientific, "1.729e-310"},
+    {1.729e-309, chars_format::scientific, "1.729e-309"},
+    {1.729e-308, chars_format::scientific, "1.729e-308"},
+    {1.729e-307, chars_format::scientific, "1.729e-307"},
+    {1.729e-306, chars_format::scientific, "1.729e-306"},
+    {1.729e-305, chars_format::scientific, "1.729e-305"},
+    {1.729e-304, chars_format::scientific, "1.729e-304"},
+    {1.729e-303, chars_format::scientific, "1.729e-303"},
+    {1.729e-302, chars_format::scientific, "1.729e-302"},
+    {1.729e-301, chars_format::scientific, "1.729e-301"},
+    {1.729e-300, chars_format::scientific, "1.729e-300"},
+    {1.729e-299, chars_format::scientific, "1.729e-299"},
+    {1.729e-298, chars_format::scientific, "1.729e-298"},
+    {1.729e-297, chars_format::scientific, "1.729e-297"},
+    {1.729e-296, chars_format::scientific, "1.729e-296"},
+    {1.729e-295, chars_format::scientific, "1.729e-295"},
+    {1.729e-294, chars_format::scientific, "1.729e-294"},
+    {1.729e-293, chars_format::scientific, "1.729e-293"},
+    {1.729e-292, chars_format::scientific, "1.729e-292"},
+    {1.729e-291, chars_format::scientific, "1.729e-291"},
+    {1.729e-290, chars_format::scientific, "1.729e-290"},
+    {1.729e-289, chars_format::scientific, "1.729e-289"},
+    {1.729e-288, chars_format::scientific, "1.729e-288"},
+    {1.729e-287, chars_format::scientific, "1.729e-287"},
+    {1.729e-286, chars_format::scientific, "1.729e-286"},
+    {1.729e-285, chars_format::scientific, "1.729e-285"},
+    {1.729e-284, chars_format::scientific, "1.729e-284"},
+    {1.729e-283, chars_format::scientific, "1.729e-283"},
+    {1.729e-282, chars_format::scientific, "1.729e-282"},
+    {1.729e-281, chars_format::scientific, "1.729e-281"},
+    {1.729e-280, chars_format::scientific, "1.729e-280"},
+    {1.729e-279, chars_format::scientific, "1.729e-279"},
+    {1.729e-278, chars_format::scientific, "1.729e-278"},
+    {1.729e-277, chars_format::scientific, "1.729e-277"},
+    {1.729e-276, chars_format::scientific, "1.729e-276"},
+    {1.729e-275, chars_format::scientific, "1.729e-275"},
+    {1.729e-274, chars_format::scientific, "1.729e-274"},
+    {1.729e-273, chars_format::scientific, "1.729e-273"},
+    {1.729e-272, chars_format::scientific, "1.729e-272"},
+    {1.729e-271, chars_format::scientific, "1.729e-271"},
+    {1.729e-270, chars_format::scientific, "1.729e-270"},
+    {1.729e-269, chars_format::scientific, "1.729e-269"},
+    {1.729e-268, chars_format::scientific, "1.729e-268"},
+    {1.729e-267, chars_format::scientific, "1.729e-267"},
+    {1.729e-266, chars_format::scientific, "1.729e-266"},
+    {1.729e-265, chars_format::scientific, "1.729e-265"},
+    {1.729e-264, chars_format::scientific, "1.729e-264"},
+    {1.729e-263, chars_format::scientific, "1.729e-263"},
+    {1.729e-262, chars_format::scientific, "1.729e-262"},
+    {1.729e-261, chars_format::scientific, "1.729e-261"},
+    {1.729e-260, chars_format::scientific, "1.729e-260"},
+    {1.729e-259, chars_format::scientific, "1.729e-259"},
+    {1.729e-258, chars_format::scientific, "1.729e-258"},
+    {1.729e-257, chars_format::scientific, "1.729e-257"},
+    {1.729e-256, chars_format::scientific, "1.729e-256"},
+    {1.729e-255, chars_format::scientific, "1.729e-255"},
+    {1.729e-254, chars_format::scientific, "1.729e-254"},
+    {1.729e-253, chars_format::scientific, "1.729e-253"},
+    {1.729e-252, chars_format::scientific, "1.729e-252"},
+    {1.729e-251, chars_format::scientific, "1.729e-251"},
+    {1.729e-250, chars_format::scientific, "1.729e-250"},
+    {1.729e-249, chars_format::scientific, "1.729e-249"},
+    {1.729e-248, chars_format::scientific, "1.729e-248"},
+    {1.729e-247, chars_format::scientific, "1.729e-247"},
+    {1.729e-246, chars_format::scientific, "1.729e-246"},
+    {1.729e-245, chars_format::scientific, "1.729e-245"},
+    {1.729e-244, chars_format::scientific, "1.729e-244"},
+    {1.729e-243, chars_format::scientific, "1.729e-243"},
+    {1.729e-242, chars_format::scientific, "1.729e-242"},
+    {1.729e-241, chars_format::scientific, "1.729e-241"},
+    {1.729e-240, chars_format::scientific, "1.729e-240"},
+    {1.729e-239, chars_format::scientific, "1.729e-239"},
+    {1.729e-238, chars_format::scientific, "1.729e-238"},
+    {1.729e-237, chars_format::scientific, "1.729e-237"},
+    {1.729e-236, chars_format::scientific, "1.729e-236"},
+    {1.729e-235, chars_format::scientific, "1.729e-235"},
+    {1.729e-234, chars_format::scientific, "1.729e-234"},
+    {1.729e-233, chars_format::scientific, "1.729e-233"},
+    {1.729e-232, chars_format::scientific, "1.729e-232"},
+    {1.729e-231, chars_format::scientific, "1.729e-231"},
+    {1.729e-230, chars_format::scientific, "1.729e-230"},
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+    {1.729e87, chars_format::scientific, "1.729e+87"},
+    {1.729e88, chars_format::scientific, "1.729e+88"},
+    {1.729e89, chars_format::scientific, "1.729e+89"},
+    {1.729e90, chars_format::scientific, "1.729e+90"},
+    {1.729e91, chars_format::scientific, "1.729e+91"},
+    {1.729e92, chars_format::scientific, "1.729e+92"},
+    {1.729e93, chars_format::scientific, "1.729e+93"},
+    {1.729e94, chars_format::scientific, "1.729e+94"},
+    {1.729e95, chars_format::scientific, "1.729e+95"},
+    {1.729e96, chars_format::scientific, "1.729e+96"},
+    {1.729e97, chars_format::scientific, "1.729e+97"},
+    {1.729e98, chars_format::scientific, "1.729e+98"},
+    {1.729e99, chars_format::scientific, "1.729e+99"},
+    {1.729e100, chars_format::scientific, "1.729e+100"},
+    {1.729e101, chars_format::scientific, "1.729e+101"},
+    {1.729e102, chars_format::scientific, "1.729e+102"},
+    {1.729e103, chars_format::scientific, "1.729e+103"},
+    {1.729e104, chars_format::scientific, "1.729e+104"},
+    {1.729e105, chars_format::scientific, "1.729e+105"},
+    {1.729e106, chars_format::scientific, "1.729e+106"},
+    {1.729e107, chars_format::scientific, "1.729e+107"},
+    {1.729e108, chars_format::scientific, "1.729e+108"},
+    {1.729e109, chars_format::scientific, "1.729e+109"},
+    {1.729e110, chars_format::scientific, "1.729e+110"},
+    {1.729e111, chars_format::scientific, "1.729e+111"},
+    {1.729e112, chars_format::scientific, "1.729e+112"},
+    {1.729e113, chars_format::scientific, "1.729e+113"},
+    {1.729e114, chars_format::scientific, "1.729e+114"},
+    {1.729e115, chars_format::scientific, "1.729e+115"},
+    {1.729e116, chars_format::scientific, "1.729e+116"},
+    {1.729e117, chars_format::scientific, "1.729e+117"},
+    {1.729e118, chars_format::scientific, "1.729e+118"},
+    {1.729e119, chars_format::scientific, "1.729e+119"},
+    {1.729e120, chars_format::scientific, "1.729e+120"},
+    {1.729e121, chars_format::scientific, "1.729e+121"},
+    {1.729e122, chars_format::scientific, "1.729e+122"},
+    {1.729e123, chars_format::scientific, "1.729e+123"},
+    {1.729e124, chars_format::scientific, "1.729e+124"},
+    {1.729e125, chars_format::scientific, "1.729e+125"},
+    {1.729e126, chars_format::scientific, "1.729e+126"},
+    {1.729e127, chars_format::scientific, "1.729e+127"},
+    {1.729e128, chars_format::scientific, "1.729e+128"},
+    {1.729e129, chars_format::scientific, "1.729e+129"},
+    {1.729e130, chars_format::scientific, "1.729e+130"},
+    {1.729e131, chars_format::scientific, "1.729e+131"},
+    {1.729e132, chars_format::scientific, "1.729e+132"},
+    {1.729e133, chars_format::scientific, "1.729e+133"},
+    {1.729e134, chars_format::scientific, "1.729e+134"},
+    {1.729e135, chars_format::scientific, "1.729e+135"},
+    {1.729e136, chars_format::scientific, "1.729e+136"},
+    {1.729e137, chars_format::scientific, "1.729e+137"},
+    {1.729e138, chars_format::scientific, "1.729e+138"},
+    {1.729e139, chars_format::scientific, "1.729e+139"},
+    {1.729e140, chars_format::scientific, "1.729e+140"},
+    {1.729e141, chars_format::scientific, "1.729e+141"},
+    {1.729e142, chars_format::scientific, "1.729e+142"},
+    {1.729e143, chars_format::scientific, "1.729e+143"},
+    {1.729e144, chars_format::scientific, "1.729e+144"},
+    {1.729e145, chars_format::scientific, "1.729e+145"},
+    {1.729e146, chars_format::scientific, "1.729e+146"},
+    {1.729e147, chars_format::scientific, "1.729e+147"},
+    {1.729e148, chars_format::scientific, "1.729e+148"},
+    {1.729e149, chars_format::scientific, "1.729e+149"},
+    {1.729e150, chars_format::scientific, "1.729e+150"},
+    {1.729e151, chars_format::scientific, "1.729e+151"},
+    {1.729e152, chars_format::scientific, "1.729e+152"},
+    {1.729e153, chars_format::scientific, "1.729e+153"},
+    {1.729e154, chars_format::scientific, "1.729e+154"},
+    {1.729e155, chars_format::scientific, "1.729e+155"},
+    {1.729e156, chars_format::scientific, "1.729e+156"},
+    {1.729e157, chars_format::scientific, "1.729e+157"},
+    {1.729e158, chars_format::scientific, "1.729e+158"},
+    {1.729e159, chars_format::scientific, "1.729e+159"},
+    {1.729e160, chars_format::scientific, "1.729e+160"},
+    {1.729e161, chars_format::scientific, "1.729e+161"},
+    {1.729e162, chars_format::scientific, "1.729e+162"},
+    {1.729e163, chars_format::scientific, "1.729e+163"},
+    {1.729e164, chars_format::scientific, "1.729e+164"},
+    {1.729e165, chars_format::scientific, "1.729e+165"},
+    {1.729e166, chars_format::scientific, "1.729e+166"},
+    {1.729e167, chars_format::scientific, "1.729e+167"},
+    {1.729e168, chars_format::scientific, "1.729e+168"},
+    {1.729e169, chars_format::scientific, "1.729e+169"},
+    {1.729e170, chars_format::scientific, "1.729e+170"},
+    {1.729e171, chars_format::scientific, "1.729e+171"},
+    {1.729e172, chars_format::scientific, "1.729e+172"},
+    {1.729e173, chars_format::scientific, "1.729e+173"},
+    {1.729e174, chars_format::scientific, "1.729e+174"},
+    {1.729e175, chars_format::scientific, "1.729e+175"},
+    {1.729e176, chars_format::scientific, "1.729e+176"},
+    {1.729e177, chars_format::scientific, "1.729e+177"},
+    {1.729e178, chars_format::scientific, "1.729e+178"},
+    {1.729e179, chars_format::scientific, "1.729e+179"},
+    {1.729e180, chars_format::scientific, "1.729e+180"},
+    {1.729e181, chars_format::scientific, "1.729e+181"},
+    {1.729e182, chars_format::scientific, "1.729e+182"},
+    {1.729e183, chars_format::scientific, "1.729e+183"},
+    {1.729e184, chars_format::scientific, "1.729e+184"},
+    {1.729e185, chars_format::scientific, "1.729e+185"},
+    {1.729e186, chars_format::scientific, "1.729e+186"},
+    {1.729e187, chars_format::scientific, "1.729e+187"},
+    {1.729e188, chars_format::scientific, "1.729e+188"},
+    {1.729e189, chars_format::scientific, "1.729e+189"},
+    {1.729e190, chars_format::scientific, "1.729e+190"},
+    {1.729e191, chars_format::scientific, "1.729e+191"},
+    {1.729e192, chars_format::scientific, "1.729e+192"},
+    {1.729e193, chars_format::scientific, "1.729e+193"},
+    {1.729e194, chars_format::scientific, "1.729e+194"},
+    {1.729e195, chars_format::scientific, "1.729e+195"},
+    {1.729e196, chars_format::scientific, "1.729e+196"},
+    {1.729e197, chars_format::scientific, "1.729e+197"},
+    {1.729e198, chars_format::scientific, "1.729e+198"},
+    {1.729e199, chars_format::scientific, "1.729e+199"},
+    {1.729e200, chars_format::scientific, "1.729e+200"},
+    {1.729e201, chars_format::scientific, "1.729e+201"},
+    {1.729e202, chars_format::scientific, "1.729e+202"},
+    {1.729e203, chars_format::scientific, "1.729e+203"},
+    {1.729e204, chars_format::scientific, "1.729e+204"},
+    {1.729e205, chars_format::scientific, "1.729e+205"},
+    {1.729e206, chars_format::scientific, "1.729e+206"},
+    {1.729e207, chars_format::scientific, "1.729e+207"},
+    {1.729e208, chars_format::scientific, "1.729e+208"},
+    {1.729e209, chars_format::scientific, "1.729e+209"},
+    {1.729e210, chars_format::scientific, "1.729e+210"},
+    {1.729e211, chars_format::scientific, "1.729e+211"},
+    {1.729e212, chars_format::scientific, "1.729e+212"},
+    {1.729e213, chars_format::scientific, "1.729e+213"},
+    {1.729e214, chars_format::scientific, "1.729e+214"},
+    {1.729e215, chars_format::scientific, "1.729e+215"},
+    {1.729e216, chars_format::scientific, "1.729e+216"},
+    {1.729e217, chars_format::scientific, "1.729e+217"},
+    {1.729e218, chars_format::scientific, "1.729e+218"},
+    {1.729e219, chars_format::scientific, "1.729e+219"},
+    {1.729e220, chars_format::scientific, "1.729e+220"},
+    {1.729e221, chars_format::scientific, "1.729e+221"},
+    {1.729e222, chars_format::scientific, "1.729e+222"},
+    {1.729e223, chars_format::scientific, "1.729e+223"},
+    {1.729e224, chars_format::scientific, "1.729e+224"},
+    {1.729e225, chars_format::scientific, "1.729e+225"},
+    {1.729e226, chars_format::scientific, "1.729e+226"},
+    {1.729e227, chars_format::scientific, "1.729e+227"},
+    {1.729e228, chars_format::scientific, "1.729e+228"},
+    {1.729e229, chars_format::scientific, "1.729e+229"},
+    {1.729e230, chars_format::scientific, "1.729e+230"},
+    {1.729e231, chars_format::scientific, "1.729e+231"},
+    {1.729e232, chars_format::scientific, "1.729e+232"},
+    {1.729e233, chars_format::scientific, "1.729e+233"},
+    {1.729e234, chars_format::scientific, "1.729e+234"},
+    {1.729e235, chars_format::scientific, "1.729e+235"},
+    {1.729e236, chars_format::scientific, "1.729e+236"},
+    {1.729e237, chars_format::scientific, "1.729e+237"},
+    {1.729e238, chars_format::scientific, "1.729e+238"},
+    {1.729e239, chars_format::scientific, "1.729e+239"},
+    {1.729e240, chars_format::scientific, "1.729e+240"},
+    {1.729e241, chars_format::scientific, "1.729e+241"},
+    {1.729e242, chars_format::scientific, "1.729e+242"},
+    {1.729e243, chars_format::scientific, "1.729e+243"},
+    {1.729e244, chars_format::scientific, "1.729e+244"},
+    {1.729e245, chars_format::scientific, "1.729e+245"},
+    {1.729e246, chars_format::scientific, "1.729e+246"},
+    {1.729e247, chars_format::scientific, "1.729e+247"},
+    {1.729e248, chars_format::scientific, "1.729e+248"},
+    {1.729e249, chars_format::scientific, "1.729e+249"},
+    {1.729e250, chars_format::scientific, "1.729e+250"},
+    {1.729e251, chars_format::scientific, "1.729e+251"},
+    {1.729e252, chars_format::scientific, "1.729e+252"},
+    {1.729e253, chars_format::scientific, "1.729e+253"},
+    {1.729e254, chars_format::scientific, "1.729e+254"},
+    {1.729e255, chars_format::scientific, "1.729e+255"},
+    {1.729e256, chars_format::scientific, "1.729e+256"},
+    {1.729e257, chars_format::scientific, "1.729e+257"},
+    {1.729e258, chars_format::scientific, "1.729e+258"},
+    {1.729e259, chars_format::scientific, "1.729e+259"},
+    {1.729e260, chars_format::scientific, "1.729e+260"},
+    {1.729e261, chars_format::scientific, "1.729e+261"},
+    {1.729e262, chars_format::scientific, "1.729e+262"},
+    {1.729e263, chars_format::scientific, "1.729e+263"},
+    {1.729e264, chars_format::scientific, "1.729e+264"},
+    {1.729e265, chars_format::scientific, "1.729e+265"},
+    {1.729e266, chars_format::scientific, "1.729e+266"},
+    {1.729e267, chars_format::scientific, "1.729e+267"},
+    {1.729e268, chars_format::scientific, "1.729e+268"},
+    {1.729e269, chars_format::scientific, "1.729e+269"},
+    {1.729e270, chars_format::scientific, "1.729e+270"},
+    {1.729e271, chars_format::scientific, "1.729e+271"},
+    {1.729e272, chars_format::scientific, "1.729e+272"},
+    {1.729e273, chars_format::scientific, "1.729e+273"},
+    {1.729e274, chars_format::scientific, "1.729e+274"},
+    {1.729e275, chars_format::scientific, "1.729e+275"},
+    {1.729e276, chars_format::scientific, "1.729e+276"},
+    {1.729e277, chars_format::scientific, "1.729e+277"},
+    {1.729e278, chars_format::scientific, "1.729e+278"},
+    {1.729e279, chars_format::scientific, "1.729e+279"},
+    {1.729e280, chars_format::scientific, "1.729e+280"},
+    {1.729e281, chars_format::scientific, "1.729e+281"},
+    {1.729e282, chars_format::scientific, "1.729e+282"},
+    {1.729e283, chars_format::scientific, "1.729e+283"},
+    {1.729e284, chars_format::scientific, "1.729e+284"},
+    {1.729e285, chars_format::scientific, "1.729e+285"},
+    {1.729e286, chars_format::scientific, "1.729e+286"},
+    {1.729e287, chars_format::scientific, "1.729e+287"},
+    {1.729e288, chars_format::scientific, "1.729e+288"},
+    {1.729e289, chars_format::scientific, "1.729e+289"},
+    {1.729e290, chars_format::scientific, "1.729e+290"},
+    {1.729e291, chars_format::scientific, "1.729e+291"},
+    {1.729e292, chars_format::scientific, "1.729e+292"},
+    {1.729e293, chars_format::scientific, "1.729e+293"},
+    {1.729e294, chars_format::scientific, "1.729e+294"},
+    {1.729e295, chars_format::scientific, "1.729e+295"},
+    {1.729e296, chars_format::scientific, "1.729e+296"},
+    {1.729e297, chars_format::scientific, "1.729e+297"},
+    {1.729e298, chars_format::scientific, "1.729e+298"},
+    {1.729e299, chars_format::scientific, "1.729e+299"},
+    {1.729e300, chars_format::scientific, "1.729e+300"},
+    {1.729e301, chars_format::scientific, "1.729e+301"},
+    {1.729e302, chars_format::scientific, "1.729e+302"},
+    {1.729e303, chars_format::scientific, "1.729e+303"},
+    {1.729e304, chars_format::scientific, "1.729e+304"},
+    {1.729e305, chars_format::scientific, "1.729e+305"},
+    {1.729e306, chars_format::scientific, "1.729e+306"},
+    {1.729e307, chars_format::scientific, "1.729e+307"},
+    {1.729e308, chars_format::scientific, "1.729e+308"},
+
+    // Test all of the cases for fixed notation, including the non-Ryu fallback for large integers.
+    {1.729e-4, chars_format::fixed, "0.0001729"},
+    {1.729e-3, chars_format::fixed, "0.001729"},
+    {1.729e-2, chars_format::fixed, "0.01729"},
+    {1.729e-1, chars_format::fixed, "0.1729"},
+    {1.729e0, chars_format::fixed, "1.729"},
+    {1.729e1, chars_format::fixed, "17.29"},
+    {1.729e2, chars_format::fixed, "172.9"},
+    {1.729e3, chars_format::fixed, "1729"},
+    {1.729e4, chars_format::fixed, "17290"},
+    {1.729e5, chars_format::fixed, "172900"},
+    {1.729e6, chars_format::fixed, "1729000"},
+    {1.729e7, chars_format::fixed, "17290000"},
+    {1.729e8, chars_format::fixed, "172900000"},
+    {1.729e9, chars_format::fixed, "1729000000"},
+    {1.729e10, chars_format::fixed, "17290000000"},
+    {1.729e11, chars_format::fixed, "172900000000"},
+    {1.729e12, chars_format::fixed, "1729000000000"},
+    {1.729e13, chars_format::fixed, "17290000000000"},
+    {1.729e14, chars_format::fixed, "172900000000000"},
+    {1.729e15, chars_format::fixed, "1729000000000000"},
+    {1.729e16, chars_format::fixed, "17290000000000000"},
+    {1.729e17, chars_format::fixed, "172900000000000000"},
+    {1.729e18, chars_format::fixed, "1729000000000000000"},
+    {1.729e19, chars_format::fixed, "17290000000000000000"},
+    {1.729e20, chars_format::fixed, "172900000000000000000"},
+    {1.729e21, chars_format::fixed, "1729000000000000000000"},
+    {1.729e22, chars_format::fixed, "17289999999999999475712"},
+    {1.729e23, chars_format::fixed, "172900000000000015728640"},
+    {1.729e24, chars_format::fixed, "1728999999999999888850944"},
+    {1.729e25, chars_format::fixed, "17290000000000000499122176"},
+    {1.729e26, chars_format::fixed, "172899999999999987811352576"},
+    {1.729e27, chars_format::fixed, "1729000000000000084271955968"},
+    {1.729e28, chars_format::fixed, "17290000000000000842719559680"},
+    {1.729e29, chars_format::fixed, "172900000000000004029149085696"},
+    {1.729e30, chars_format::fixed, "1728999999999999969922746679296"},
+    {1.729e31, chars_format::fixed, "17290000000000000825127373635584"},
+    {1.729e32, chars_format::fixed, "172899999999999994740474854244352"},
+    {1.729e33, chars_format::fixed, "1729000000000000019462342580371456"},
+    {1.729e34, chars_format::fixed, "17290000000000000771084178107138048"},
+    {1.729e35, chars_format::fixed, "172900000000000003099155762643992576"},
+    {1.729e36, chars_format::fixed, "1728999999999999957204581331601719296"},
+    {1.729e37, chars_format::fixed, "17289999999999998981750002957311541248"},
+    {1.729e38, chars_format::fixed, "172900000000000018151698926790986694656"},
+    {1.729e39, chars_format::fixed, "1728999999999999879285534364252573270016"},
+    {1.729e40, chars_format::fixed, "17289999999999999397318253449840320053248"},
+    {1.729e41, chars_format::fixed, "172899999999999993973182534498403200532480"},
+    {1.729e42, chars_format::fixed, "1728999999999999978417451572652165595922432"},
+    {1.729e43, chars_format::fixed, "17290000000000001022114555011901930858348544"},
+    {1.729e44, chars_format::fixed, "172899999999999995365865078694456009793994752"},
+    {1.729e45, chars_format::fixed, "1729000000000000112114975815473235285027848192"},
+    {1.729e46, chars_format::fixed, "17289999999999999853499157926502951353575276544"},
+    {1.729e47, chars_format::fixed, "172900000000000003605593980177947119522565586944"},
+    {1.729e48, chars_format::fixed, "1728999999999999914361482179869448651542148153344"},
+    {1.729e49, chars_format::fixed, "17290000000000001090726143749254847214357604990976"},
+    {1.729e50, chars_format::fixed, "172900000000000000522667720422893215082583391469568"},
+    {1.729e51, chars_format::fixed, "1729000000000000046765052072507553179069804548456448"},
+    {1.729e52, chars_format::fixed, "17289999999999999138422524940159658886890985204219904"},
+    {1.729e53, chars_format::fixed, "172899999999999991384225249401596588868909852042199040"},
+    {1.729e54, chars_format::fixed, "1729000000000000083983435954485197620376402236306096128"},
+    {1.729e55, chars_format::fixed, "17289999999999999478704891861098122350265592635988115456"},
+    {1.729e56, chars_format::fixed, "172899999999999994787048918610981223502655926359881154560"},
+    {1.729e57, chars_format::fixed, "1729000000000000122095061049630305528274358268664135811072"},
+    {1.729e58, chars_format::fixed, "17289999999999999130255748134057135763769994625857466925056"},
+    {1.729e59, chars_format::fixed, "172900000000000002452930080605882928405559082582755422240768"},
+    {1.729e60, chars_format::fixed, "1728999999999999846123339217813844151769844644640662174564352"},
+    {1.729e61, chars_format::fixed, "17290000000000000602104931237078263105127400620649326319763456"},
+    {1.729e62, chars_format::fixed, "172899999999999994603067770723103582584986250610532172135661568"},
+    {1.729e63, chars_format::fixed, "1728999999999999991702603873821752019715013528489166085604507648"},
+    {1.729e64, chars_format::fixed, "17289999999999999917026038738217520197150135284891660856045076480"},
+    {1.729e65, chars_format::fixed, "172899999999999999170260387382175201971501352848916608560450764800"},
+    {1.729e66, chars_format::fixed, "1728999999999999898166499084643965254679184234647052827624824897536"},
+    {1.729e67, chars_format::fixed, "17290000000000000478242667473284240787365111047944340403923172982784"},
+    {1.729e68, chars_format::fixed, "172899999999999992809805261718085701949064960867652907017832337768448"},
+    {1.729e69, chars_format::fixed, "1729000000000000167550480877475991137982372600912339010606311218872320"},
+    {1.729e70, chars_format::fixed, "17289999999999998610513727042982194663129671708505022868584867821518848"},
+    {1.729e71, chars_format::fixed, "172900000000000010625065924284043680364849151489997166585674633152823296"},
+    {1.729e72, chars_format::fixed, "1729000000000000008170944627423549868714281777280183914257442511777693696"},
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+        "2408847168896930225737807976475534602049914268447524594921892157070085190159531790827520"},
+    {1.729e300, chars_format::fixed,
+        "1729000000000000010481817423448157218914651276641376931761460876112605660851141867453840620852258185492476"
+        "0005946132935188025380035176397407422424280713081526400100908727397723822830900683554148075827890911867221"
+        "12128682571397441953990644420861341612644195667042341798616666297993656260407050467540992"},
+    {1.729e301, chars_format::fixed,
+        "1729000000000000010481817423448157218914651276641376931761460876112605660851141867453840620852258185492476"
+        "0005946132935188025380035176397407422424280713081526400100908727397723822830900683554148075827890911867221"
+        "121286825713974419539906444208613416126441956670423417986166662979936562604070504675409920"},
+    {1.729e302, chars_format::fixed,
+        "1728999999999999915312735280870041199838651395047741083360807969911360281281742871233638562586378278601703"
+        "8728406068557716842154311673645116487867131973428540268529003194837222721493014309234824756525596961315624"
+        "1682015250090546076565472718067701597058986348472822448584577954892844583968606814340120576"},
+    {1.729e303, chars_format::fixed,
+        "1728999999999999991448000994932534015099451300322649762081330294872356584937262068209800209199082204114321"
+        "5750438120059693788734890475846949235512850965150929173786527620885623602563323408690283411967432121756901"
+        "73066976557299045716323460972824476484233329230579518336062488948180614176262854002713034752"},
+    {1.729e304, chars_format::fixed,
+        "1729000000000000113264426137432522519516731148762503648034166014809950670786092783371658843779408484934509"
+        "8985689402462856903263816559369881631746001351906751422198566702563065012275817967819017260674368378462945"
+        "830618950475287816373934350402604133060628744239415884964092239869840835147857113776119611392"},
+    {1.729e305, chars_format::fixed,
+        "1729000000000000064537856080432527117749819209386562093653031726834913036446560497306915389947277972606434"
+        "5691588889501591657452246125960708673252741197204422522833751069892088448390820144167523721191593875780528"
+        "1906392765143688726896544541328603857733105634659676043227052997146269577937656842765239058432"},
+    {1.729e306, chars_format::fixed,
+        "1728999999999999908612831898032541832095701003383549119633402005314792606560057181899736337684460333156593"
+        "5150467248025542870855220739051355206074308702156970044866341045344963443958827108482744394846715467196791"
+        "74270431983942825289995878606968039445389238499093310627026709121794255026067310987781764808704"},
+    {1.729e307, chars_format::fixed,
+        "1729000000000000033352851243952530060618995568185959498849105782530888950469259834225479579494714444716466"
+        "3583364561206381900132841048578837979817054698194932027240269064982663447504421537030567855922618194063780"
+        "901052285179380748731715320520224387509426927770960704712217658015290076287147169396782654291968"},
+    {1.729e308, chars_format::fixed,
+        "1729000000000000033352851243952530060618995568185959498849105782530888950469259834225479579494714444716466"
+        "3583364561206381900132841048578837979817054698194932027240269064982663447504421537030567855922618194063780"
+        "9010522851793807487317153205202243875094269277709607047122176580152900762871471693967826542919680"},
+
+    // Also test one-digit cases, where the decimal point can't appear between digits like "17.29".
+    {7e-3, chars_format::fixed, "0.007"},
+    {7e-2, chars_format::fixed, "0.07"},
+    {7e-1, chars_format::fixed, "0.7"},
+    {7e0, chars_format::fixed, "7"},
+    {7e1, chars_format::fixed, "70"},
+    {7e2, chars_format::fixed, "700"},
+    {7e3, chars_format::fixed, "7000"},
+
+    // Test the maximum value in fixed notation.
+    {0x1.fffffffffffffp+1023, chars_format::fixed,
+        "1797693134862315708145274237317043567980705675258449965989174768031572607800285387605895586327668781715404"
+        "5895351438246423432132688946418276846754670353751698604991057655128207624549009038932894407586850845513394"
+        "2304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368"},
+
+    // Test highly-trimmed powers of 2.
+    {0x1p959, chars_format::fixed,
+        "4872657005699999540176691193937594155438113428797503763433953228606474345383213051232807532941005129612652"
+        "4581157043340917295849326015470232889936481563267097656388499782365149353948277450268241763997967396091894"
+        "36842798962697437472873181807734482806413869401552138773540914294995957055488"},
+    {0x1p959, chars_format::scientific, "4.8726570057e+288"},
+    {0x1p960, chars_format::fixed,
+        "9745314011399999080353382387875188310876226857595007526867906457212948690766426102465615065882010259225304"
+        "9162314086681834591698652030940465779872963126534195312776999564730298707896554900536483527995934792183788"
+        "73685597925394874945746363615468965612827738803104277547081828589991914110976"},
+    {0x1p960, chars_format::scientific, "9.7453140114e+288"},
+
+    // Test powers of 10 that are exactly representable.
+    {1e0, chars_format::fixed, "1"},
+    {1e1, chars_format::fixed, "10"},
+    {1e2, chars_format::fixed, "100"},
+    {1e3, chars_format::fixed, "1000"},
+    {1e4, chars_format::fixed, "10000"},
+    {1e5, chars_format::fixed, "100000"},
+    {1e6, chars_format::fixed, "1000000"},
+    {1e7, chars_format::fixed, "10000000"},
+    {1e8, chars_format::fixed, "100000000"},
+    {1e9, chars_format::fixed, "1000000000"},
+    {1e10, chars_format::fixed, "10000000000"},
+    {1e11, chars_format::fixed, "100000000000"},
+    {1e12, chars_format::fixed, "1000000000000"},
+    {1e13, chars_format::fixed, "10000000000000"},
+    {1e14, chars_format::fixed, "100000000000000"},
+    {1e15, chars_format::fixed, "1000000000000000"},
+    {1e16, chars_format::fixed, "10000000000000000"},
+    {1e17, chars_format::fixed, "100000000000000000"},
+    {1e18, chars_format::fixed, "1000000000000000000"},
+    {1e19, chars_format::fixed, "10000000000000000000"},
+    {1e20, chars_format::fixed, "100000000000000000000"},
+    {1e21, chars_format::fixed, "1000000000000000000000"},
+    {1e22, chars_format::fixed, "10000000000000000000000"},
+
+    // Test powers of 10 that aren't exactly representable.
+    // This exercises the "adjustment" code.
+    {1e23, chars_format::fixed, "99999999999999991611392"},
+    {1e24, chars_format::fixed, "999999999999999983222784"},
+    {1e25, chars_format::fixed, "10000000000000000905969664"},
+    {1e26, chars_format::fixed, "100000000000000004764729344"},
+    {1e27, chars_format::fixed, "1000000000000000013287555072"},
+    {1e28, chars_format::fixed, "9999999999999999583119736832"},
+    {1e29, chars_format::fixed, "99999999999999991433150857216"},
+    {1e30, chars_format::fixed, "1000000000000000019884624838656"},
+    {1e31, chars_format::fixed, "9999999999999999635896294965248"},
+    {1e32, chars_format::fixed, "100000000000000005366162204393472"},
+    {1e33, chars_format::fixed, "999999999999999945575230987042816"},
+    {1e34, chars_format::fixed, "9999999999999999455752309870428160"},
+    {1e35, chars_format::fixed, "99999999999999996863366107917975552"},
+    {1e36, chars_format::fixed, "1000000000000000042420637374017961984"},
+    {1e37, chars_format::fixed, "9999999999999999538762658202121142272"},
+    {1e38, chars_format::fixed, "99999999999999997748809823456034029568"},
+    {1e39, chars_format::fixed, "999999999999999939709166371603178586112"},
+    {1e40, chars_format::fixed, "10000000000000000303786028427003666890752"},
+    {1e41, chars_format::fixed, "100000000000000000620008645040778319495168"},
+    {1e42, chars_format::fixed, "1000000000000000044885712678075916785549312"},
+    {1e43, chars_format::fixed, "10000000000000000139372116959414099130712064"},
+    {1e44, chars_format::fixed, "100000000000000008821361405306422640701865984"},
+    {1e45, chars_format::fixed, "999999999999999929757289024535551219930759168"},
+    {1e46, chars_format::fixed, "9999999999999999931398190359470212947659194368"},
+    {1e47, chars_format::fixed, "100000000000000004384584304507619735463404765184"},
+    {1e48, chars_format::fixed, "1000000000000000043845843045076197354634047651840"},
+    {1e49, chars_format::fixed, "9999999999999999464902769475481793196872414789632"},
+    {1e50, chars_format::fixed, "100000000000000007629769841091887003294964970946560"},
+    {1e51, chars_format::fixed, "999999999999999993220948674361627976461708441944064"},
+    {1e52, chars_format::fixed, "9999999999999999932209486743616279764617084419440640"},
+    {1e53, chars_format::fixed, "99999999999999999322094867436162797646170844194406400"},
+    {1e54, chars_format::fixed, "1000000000000000078291540404596243842305360299886116864"},
+    {1e55, chars_format::fixed, "10000000000000000102350670204085511496304388135324745728"},
+    {1e56, chars_format::fixed, "100000000000000009190283508143378238084034459715684532224"},
+    {1e57, chars_format::fixed, "1000000000000000048346692115553659057528394845890514255872"},
+    {1e58, chars_format::fixed, "9999999999999999438119489974413630815797154428513196965888"},
+    {1e59, chars_format::fixed, "99999999999999997168788049560464200849936328366177157906432"},
+    {1e60, chars_format::fixed, "999999999999999949387135297074018866963645011013410073083904"},
+    {1e61, chars_format::fixed, "9999999999999999493871352970740188669636450110134100730839040"},
+    {1e62, chars_format::fixed, "100000000000000003502199685943161173046080317798311825604870144"},
+    {1e63, chars_format::fixed, "1000000000000000057857959942726969827393378689175040438172647424"},
+    {1e64, chars_format::fixed, "10000000000000000213204190094543968723012578712679649467743338496"},
+    {1e65, chars_format::fixed, "99999999999999999209038626283633850822756121694230455365568299008"},
+    {1e66, chars_format::fixed, "999999999999999945322333868247445125709646570021247924665841614848"},
+    {1e67, chars_format::fixed, "9999999999999999827367757839185598317239782875580932278577147150336"},
+    {1e68, chars_format::fixed, "99999999999999995280522225138166806691251291352861698530421623488512"},
+    {1e69, chars_format::fixed, "1000000000000000072531436381529235126158374409646521955518210155479040"},
+    {1e70, chars_format::fixed, "10000000000000000725314363815292351261583744096465219555182101554790400"},
+    {1e71, chars_format::fixed, "100000000000000004188152556421145795899143386664033828314342771180699648"},
+    {1e72, chars_format::fixed, "999999999999999943801810948794571024057224129020550531544123892056457216"},
+    {1e73, chars_format::fixed, "9999999999999999830336967949613257980309080240684656321838454199566729216"},
+    {1e74, chars_format::fixed, "99999999999999995164818811802792197885196090803013355167206819763650035712"},
+    {1e75, chars_format::fixed, "999999999999999926539781176481198923508803215199467887262646419780362305536"},
+    {1e76, chars_format::fixed, "10000000000000000470601344959054695891559601407866630764278709534898249531392"},
+    {1e77, chars_format::fixed, "99999999999999998278261272554585856747747644714015897553975120217811154108416"},
+    {1e78, chars_format::fixed, "1000000000000000008493621433689702976148869924598760615894999102702796905906176"},
+    {1e79, chars_format::fixed, "9999999999999999673560075006595519222746403606649979913266024618633003221909504"},
+    {1e80, chars_format::fixed, "100000000000000000026609864708367276537402401181200809098131977453489758916313088"},
+    {1e81, chars_format::fixed, "999999999999999921281879895665782741935503249059183851809998224123064148429897728"},
+    {1e82, chars_format::fixed, "9999999999999999634067965630886574211027143225273567793680363843427086501542887424"},
+    {1e83, chars_format::fixed, "100000000000000003080666323096525690777025204007643346346089744069413985291331436544"},
+    {1e84, chars_format::fixed,
+        "1000000000000000057766609898115896702437267127096064137098041863234712334016924614656"},
+    {1e85, chars_format::fixed,
+        "10000000000000000146306952306748730309700429878646550592786107871697963642511482159104"},
+    {1e86, chars_format::fixed,
+        "100000000000000001463069523067487303097004298786465505927861078716979636425114821591040"},
+    {1e87, chars_format::fixed,
+        "999999999999999959416724456350362731491996089648451439669739009806703922950954425516032"},
+    {1e88, chars_format::fixed,
+        "9999999999999999594167244563503627314919960896484514396697390098067039229509544255160320"},
+    {1e89, chars_format::fixed,
+        "99999999999999999475366575191804932315794610450682175621941694731908308538307845136842752"},
+    {1e90, chars_format::fixed,
+        "999999999999999966484112715463900049825186092620125502979674597309179755437379230686511104"},
+    {1e91, chars_format::fixed,
+        "10000000000000000795623248612804971431562261401669105159386439973487930752201761134141767680"},
+    {1e92, chars_format::fixed,
+        "100000000000000004337729697461918607329029332495193931179177378933611681288968111094132375552"},
+    {1e93, chars_format::fixed,
+        "1000000000000000043377296974619186073290293324951939311791773789336116812889681110941323755520"},
+    {1e94, chars_format::fixed,
+        "10000000000000000202188791271559469885760963232143577411377768562080040049981643093586978275328"},
+    {1e95, chars_format::fixed,
+        "100000000000000002021887912715594698857609632321435774113777685620800400499816430935869782753280"},
+    {1e96, chars_format::fixed,
+        "1000000000000000049861653971908893017010268485438462151574892930611988399099305815384459015356416"},
+    {1e97, chars_format::fixed,
+        "10000000000000000735758738477112498397576062152177456799245857901351759143802190202050679656153088"},
+    {1e98, chars_format::fixed,
+        "99999999999999999769037024514370800696612547992403838920556863966097586548129676477911932478685184"},
+    {1e99, chars_format::fixed,
+        "999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056"},
+    {1e100, chars_format::fixed,
+        "10000000000000000159028911097599180468360808563945281389781327557747838772170381060813469985856815104"},
+    {1e101, chars_format::fixed,
+        "99999999999999997704951326524533662844684271992415000612999597473199345218078991130326129448151154688"},
+    {1e102, chars_format::fixed,
+        "999999999999999977049513265245336628446842719924150006129995974731993452180789911303261294481511546880"},
+    {1e103, chars_format::fixed,
+        "10000000000000000019156750857346687362159551272651920111528035145993793242039887559612361451081803235328"},
+    {1e104, chars_format::fixed,
+        "10000000000000000019156750857346687362159551272651920111528035145993793242039887559612361451081803235328"
+        "0"},
+    {1e105, chars_format::fixed,
+        "99999999999999993825830082528197854032702736447212447829441621253887149182459971363682052750390825530163"
+        "2"},
+    {1e106, chars_format::fixed,
+        "1000000000000000091035999050368435010460453995175486557154545737484090289535133415215418009754161219056435"
+        "2"},
+    {1e107, chars_format::fixed,
+        "9999999999999999688138404702992698343537126906127968940664421175279152513667064539525400239539588480525926"
+        "4"},
+    {1e108, chars_format::fixed,
+        "1000000000000000033998991713002824594943974719712898047713430714837875271723200833292741616380733445921308"
+        "672"},
+    {1e109, chars_format::fixed,
+        "9999999999999999818508707188399807864717650964328171247958398369899072554380053298205803424393137676263358"
+        "464"},
+    {1e110, chars_format::fixed,
+        "1000000000000000023569367514170255833249532795056881863129912539268281668466161732598309361592449510262314"
+        "10688"},
+    {1e111, chars_format::fixed,
+        "9999999999999999568197726416418157584051044772583782817953962156228826076211114881539429309474323220447488"
+        "90112"},
+    {1e112, chars_format::fixed,
+        "9999999999999999301199346926304397284673331501389768492615896861647229832830913903761963586894254467577228"
+        "034048"},
+    {1e113, chars_format::fixed,
+        "1000000000000000015559416129466843024268201396921061433369770580430833781164755703264985389915047447676206"
+        "28086784"},
+    {1e114, chars_format::fixed,
+        "1000000000000000015559416129466843024268201396921061433369770580430833781164755703264985389915047447676206"
+        "280867840"},
+    {1e115, chars_format::fixed,
+        "1000000000000000015559416129466843024268201396921061433369770580430833781164755703264985389915047447676206"
+        "2808678400"},
+    {1e116, chars_format::fixed,
+        "1000000000000000015559416129466843024268201396921061433369770580430833781164755703264985389915047447676206"
+        "28086784000"},
+    {1e117, chars_format::fixed,
+        "1000000000000000050555427725995033814228237030803003279020481474722232763977085405824233377105062219252417"
+        "113236701184"},
+    {1e118, chars_format::fixed,
+        "9999999999999999665649998943273759183241515094863428494587753284228752052274941196820382078490267674695111"
+        "155514343424"},
+    {1e119, chars_format::fixed,
+        "9999999999999999441675524725493338127497287038019000682423203560763798562276031100441194960474173136607361"
+        "8283536318464"},
+    {1e120, chars_format::fixed,
+        "9999999999999999800034683473942011816688051928970085181886483118307724146274287254647894349299924397547760"
+        "75181077037056"},
+    {1e121, chars_format::fixed,
+        "1000000000000000037340933747145988971939327575449182038102773041037800508067149710137861337142112641505239"
+        "9029342192009216"},
+    {1e122, chars_format::fixed,
+        "1000000000000000014405947587245273855831118622428312630137123149354989270691261316268632576257264560805054"
+        "37183296233537536"},
+    {1e123, chars_format::fixed,
+        "9999999999999999777099697314041296700579842975949215773920833226624912908898398860778665588415076316847575"
+        "22070951350501376"},
+    {1e124, chars_format::fixed,
+        "9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200"
+        "422613425626021888"},
+    {1e125, chars_format::fixed,
+        "9999999999999999248677616189928820425446708698348384614392259722252941999757930266031634937628176537515300"
+        "5841365553228283904"},
+    {1e126, chars_format::fixed,
+        "9999999999999999248677616189928820425446708698348384614392259722252941999757930266031634937628176537515300"
+        "58413655532282839040"},
+    {1e127, chars_format::fixed,
+        "9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772"
+        "377386949310916067328"},
+    {1e128, chars_format::fixed,
+        "1000000000000000075174486916518208627471429064352408213482909102357765925242415204664541101097758035428265"
+        "95503885252632667750400"},
+    {1e129, chars_format::fixed,
+        "9999999999999999982174435641852414159889288687594125004365433397299404019059046494971157661422685600097771"
+        "75966751665376232210432"},
+    {1e130, chars_format::fixed,
+        "1000000000000000059783078246051615185174929025233809070873635949832200820575113093631056034106660140344568"
+        "1992244323541365884452864"},
+    {1e131, chars_format::fixed,
+        "9999999999999999120255550095723181391285286496952573018246136855867758157690128277095993909921203475410697"
+        "4340599870111173348163584"},
+    {1e132, chars_format::fixed,
+        "9999999999999999908295674023612765636866088499824849119840922265176691516655996362010429339865415703696022"
+        "53175829982724989462249472"},
+    {1e133, chars_format::fixed,
+        "1000000000000000022351172359476859933509840930097375956047883642890026486024234359597620351184310059501015"
+        "2570837624953702918544949248"},
+    {1e134, chars_format::fixed,
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+        "275192019201707119869992081071729797163687409453914913289541779456"},
+    {1e278, chars_format::fixed,
+        "9999999999999999635068686795917855831590227478299257653231448548622174630124020581267434287082049279983778"
+        "4938001204037775189753543960218791943147793788145321066524580618236658968633362758090027700335311493754978"
+        "334367629875739137498376013657689431411868208826074951744485326848"},
+    {1e279, chars_format::fixed,
+        "1000000000000000057973292274960393763265862568545700036605220385651388108719182436946549269568487016710341"
+        "0060188467364335924481829001842443847400552403738185480928254963246837154867046197200314769922564752640282"
+        "09364937790149360843820835266007499279518823345374529865067232493568"},
+    {1e280, chars_format::fixed,
+        "1000000000000000032782245982862098248570705283021493564263333577440942603197374335927934378672411793053817"
+        "4975818241508187016346769106956959939911012930425211247788042456200658152732723551495964903285489125103006"
+        "290926013924448356521309485648260046220787856768108551057012647002112"},
+    {1e281, chars_format::fixed,
+        "1000000000000000032782245982862098248570705283021493564263333577440942603197374335927934378672411793053817"
+        "4975818241508187016346769106956959939911012930425211247788042456200658152732723551495964903285489125103006"
+        "2909260139244483565213094856482600462207878567681085510570126470021120"},
+    {1e282, chars_format::fixed,
+        "1000000000000000032782245982862098248570705283021493564263333577440942603197374335927934378672411793053817"
+        "4975818241508187016346769106956959939911012930425211247788042456200658152732723551495964903285489125103006"
+        "29092601392444835652130948564826004622078785676810855105701264700211200"},
+    {1e283, chars_format::fixed,
+        "9999999999999999553953517735361344274271821018911312812290573026184540102343798495987494338396687059809772"
+        "7966329076780975705558651098687533761031476684077544035813096345547962581760843838922021129763927973084950"
+        "24959839786965342632596166187964530344229899589832462449290116390191104"},
+    {1e284, chars_format::fixed,
+        "1000000000000000079214382508457676541256819191699710934083899342334435758975171027725445345572057645297521"
+        "6283329441806240683821311505209883878195732087635685354312082149188175289466707052058222577470946921779713"
+        "0505057184069381648545374773244373557467226310750742042216461653692645376"},
+    {1e285, chars_format::fixed,
+        "9999999999999999801591579205204428501931095198528472118000257105616503599825380852240886161861464938442861"
+        "4939722145037261932089543889369794765216645522533405937274641374814720644342089175254062058753036222027386"
+        "3006901551095990707698442841525909542472844588688081080376132618600579072"},
+    {1e286, chars_format::fixed,
+        "1000000000000000032988611034086967485427088011504507863684758314173802572778608987891478871858632441286011"
+        "7381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791"
+        "654301923722148311225012721166820834263125344653917287293299907083743789056"},
+    {1e287, chars_format::fixed,
+        "1000000000000000075252173524940187193614270804825836385192544397063524343015465710025391076396621199239392"
+        "2091755152714140104196817220558967702128769386220391563888697428719907160465407126676909922607121189796634"
+        "0736882502910990345434353553680702253338428636675464684849307718019341877248"},
+    {1e288, chars_format::fixed,
+        "1000000000000000007630473539575035660514778335511710750780086664439969510636494954611131549135839186513983"
+        "4555553952208956878605448095849998297252605948732710873996264866061464425509888400169173946264495363952086"
+        "20267012778077787723395914064607119962069483324573977857832138825282954985472"},
+    {1e289, chars_format::fixed,
+        "1000000000000000061727833527867156886994372310963011258310052850538813376539671558942539170944464796694310"
+        "4584514912613103459078543395617173821153536698722855425910210916188218613474303381375362727338596024627724"
+        "499484625789034803081540112423670420191213257583185130503608895092113260150784"},
+    {1e290, chars_format::fixed,
+        "1000000000000000061727833527867156886994372310963011258310052850538813376539671558942539170944464796694310"
+        "4584514912613103459078543395617173821153536698722855425910210916188218613474303381375362727338596024627724"
+        "4994846257890348030815401124236704201912132575831851305036088950921132601507840"},
+    {1e291, chars_format::fixed,
+        "9999999999999999578609023503462841321535518780965142838525177732290331540055724786262365370719036251480826"
+        "1289098686371420245702004200641968152637496587417778862354344999448505725826266174594802676763227561304989"
+        "6960078961318150545418464661067991669581788285529005480705688196068853638234112"},
+    {1e292, chars_format::fixed,
+        "1000000000000000013256598978357416268068656108958646003563203147794249272690425321461597941803936249972737"
+        "4638565892090988122974650007025784551738302746731685907395315255274646861058187558214617579496201832662352"
+        "585538835573636597522107561710941518560028749376834095178551288964115055725510656"},
+    {1e293, chars_format::fixed,
+        "9999999999999999246234843735396048506044893395792352520261065484899034827946607729250196942326840502532897"
+        "0231162545648343655275306678872441733790178059478330735395060467469727994972900530063978805843953102113868"
+        "000379620369084502134308975505229555772913629423636305841602377586326247764393984"},
+    {1e294, chars_format::fixed,
+        "1000000000000000066436467741248103118547156170586292454485461107376856746627884050583544890346687569804406"
+        "1207835674606680377442921610508908778753873711201997607708800780391251297994726061339549398843285746132932"
+        "05683935969567348590731356020719265634967118123751637393518591968740451429495341056"},
+    {1e295, chars_format::fixed,
+        "9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362"
+        "6970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049"
+        "02758521100414464490983962613190835886243290260424727924570510530141380583845003264"},
+    {1e296, chars_format::fixed,
+        "9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362"
+        "6970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049"
+        "027585211004144644909839626131908358862432902604247279245705105301413805838450032640"},
+    {1e297, chars_format::fixed,
+        "1000000000000000017652801462756379714374878780719864776839443139119744823869255243069012222883470359078822"
+        "0728292194112285349344027126247056154504923279794565007954563392017619494511608074472945276562227436175920"
+        "48849967890105831362861792425329827928397252374398383022243308510390698430058459037696"},
+    {1e298, chars_format::fixed,
+        "9999999999999999595662034753429788238255624467393741467120915117996487670031669885400803025551745174706847"
+        "8782311196631452228634829961492223321433823010024592147588202691169230215270582854596864146833859136224555"
+        "51313826420028155008403585629126369847605750170289266545852965785882018353801250996224"},
+    {1e299, chars_format::fixed,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "4508111903896764088007465274278014249457925878882005684283811566947219638686545940054016"},
+    {1e300, chars_format::fixed,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "45081119038967640880074652742780142494579258788820056842838115669472196386865459400540160"},
+    {1e301, chars_format::fixed,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "450811190389676408800746527427801424945792587888200568428381156694721963868654594005401600"},
+    {1e302, chars_format::fixed,
+        "1000000000000000076297030790848949253473468551506568117016017342062113802881257944841421889646917840766397"
+        "4757713854876137221038784479993829181561135051983075016764985648898162653636809541460731423515105837345898"
+        "6890825155659063617715863205282622390509284183439858617103083735673849899204570498157510656"},
+    {1e303, chars_format::fixed,
+        "1000000000000000000161765076786456438212668646231659438295495017101117499225738747865260243034213915253779"
+        "7735681803374160274458205677791996433915416060260686111507461222849761772566500442005272768073270676904621"
+        "12661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568"},
+    {1e304, chars_format::fixed,
+        "9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856"
+        "1180561621725787171937426360305302357988408668827749873014416820110410677102531624409058437198025485515990"
+        "76639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744"},
+    {1e305, chars_format::fixed,
+        "9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856"
+        "1180561621725787171937426360305302357988408668827749873014416820110410677102531624409058437198025485515990"
+        "766396825508218326595491122696079498053460349186625724064076043808459598620749043481381437440"},
+    {1e306, chars_format::fixed,
+        "1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606"
+        "1388616982910603110492255329485206969388057114406501226285146694284603569926249680283295506892241752843467"
+        "30060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208"},
+    {1e307, chars_format::fixed,
+        "9999999999999999860310597602564577717002641838126363875249660735883565852672743849064846414228960666786379"
+        "2803926546153933531728502521033362759523706153970107306916646893751785690398510731463396416232660711267200"
+        "11020169553304018596457812688561947201171488461172921822139066929851282122002676667750021070848"},
+    {1e308, chars_format::fixed,
+        "1000000000000000010979063629440455417404923096773118463368106829031575854049114915371633289784946888990612"
+        "4966972117251561159028374314008832830700919814604603127166450293302718569748969958855904333838446616500117"
+        "8426897626212945177628091195786707458122783970171784415105291802893207873272974885715430223118336"},
+
+    // These numbers have odd mantissas (unaffected by shifting)
+    // that are barely within the "max shifted mantissa" limit.
+    // They're exactly-representable multiples of powers of 10, and can use Ryu with zero-filling.
+    {1801439850948197e1, chars_format::fixed, "18014398509481970"},
+    {360287970189639e2, chars_format::fixed, "36028797018963900"},
+    {72057594037927e3, chars_format::fixed, "72057594037927000"},
+    {14411518807585e4, chars_format::fixed, "144115188075850000"},
+    {2882303761517e5, chars_format::fixed, "288230376151700000"},
+    {576460752303e6, chars_format::fixed, "576460752303000000"},
+    {115292150459e7, chars_format::fixed, "1152921504590000000"},
+    {23058430091e8, chars_format::fixed, "2305843009100000000"},
+    {4611686017e9, chars_format::fixed, "4611686017000000000"},
+    {922337203e10, chars_format::fixed, "9223372030000000000"},
+    {184467439e11, chars_format::fixed, "18446743900000000000"},
+    {36893487e12, chars_format::fixed, "36893487000000000000"},
+    {7378697e13, chars_format::fixed, "73786970000000000000"},
+    {1475739e14, chars_format::fixed, "147573900000000000000"},
+    {295147e15, chars_format::fixed, "295147000000000000000"},
+    {59029e16, chars_format::fixed, "590290000000000000000"},
+    {11805e17, chars_format::fixed, "1180500000000000000000"},
+    {2361e18, chars_format::fixed, "2361000000000000000000"},
+    {471e19, chars_format::fixed, "4710000000000000000000"},
+    {93e20, chars_format::fixed, "9300000000000000000000"},
+    {17e21, chars_format::fixed, "17000000000000000000000"},
+    {3e22, chars_format::fixed, "30000000000000000000000"},
+
+    // These numbers have odd mantissas (unaffected by shifting)
+    // that are barely above the "max shifted mantissa" limit.
+    // This activates the non-Ryu fallback for large integers.
+    {1801439850948199e1, chars_format::fixed, "18014398509481992"},
+    {360287970189641e2, chars_format::fixed, "36028797018964096"},
+    {72057594037929e3, chars_format::fixed, "72057594037928992"},
+    {14411518807587e4, chars_format::fixed, "144115188075870016"},
+    {2882303761519e5, chars_format::fixed, "288230376151900032"},
+    {576460752305e6, chars_format::fixed, "576460752304999936"},
+    {115292150461e7, chars_format::fixed, "1152921504609999872"},
+    {23058430093e8, chars_format::fixed, "2305843009299999744"},
+    {4611686019e9, chars_format::fixed, "4611686019000000512"},
+    {922337205e10, chars_format::fixed, "9223372049999998976"},
+    {184467441e11, chars_format::fixed, "18446744099999997952"},
+    {36893489e12, chars_format::fixed, "36893488999999995904"},
+    {7378699e13, chars_format::fixed, "73786990000000008192"},
+    {1475741e14, chars_format::fixed, "147574099999999983616"},
+    {295149e15, chars_format::fixed, "295148999999999967232"},
+    {59031e16, chars_format::fixed, "590310000000000065536"},
+    {11807e17, chars_format::fixed, "1180700000000000131072"},
+    {2363e18, chars_format::fixed, "2363000000000000262144"},
+    {473e19, chars_format::fixed, "4729999999999999475712"},
+    {95e20, chars_format::fixed, "9500000000000001048576"},
+    {19e21, chars_format::fixed, "19000000000000002097152"},
+    {5e22, chars_format::fixed, "49999999999999995805696"},
+
+    // Test the mantissa shifting logic.
+    // Also test a large shift, because 32-bit platforms need to simulate _BitScanForward64().
+    {302230528e15, chars_format::fixed, "302230528000000000000000"}, // 295147 * 2^10
+    {302232576e15, chars_format::fixed, "302232575999999966445568"}, // 295149 * 2^10
+    {81123342286848e18, chars_format::fixed, "81123342286848000000000000000000"}, // 2361 * 2^35
+    {81192061763584e18, chars_format::fixed, "81192061763584009007199254740992"}, // 2363 * 2^35
+
+    // Inspect all of those numbers in scientific notation.
+    // For the within-limit numbers, this verifies that Ryu is actually being used with zero-filling above.
+    // For the above-limit numbers, this tests Ryu's trimming.
+    {1801439850948197e1, chars_format::scientific, "1.801439850948197e+16"},
+    {360287970189639e2, chars_format::scientific, "3.60287970189639e+16"},
+    {72057594037927e3, chars_format::scientific, "7.2057594037927e+16"},
+    {14411518807585e4, chars_format::scientific, "1.4411518807585e+17"},
+    {2882303761517e5, chars_format::scientific, "2.882303761517e+17"},
+    {576460752303e6, chars_format::scientific, "5.76460752303e+17"},
+    {115292150459e7, chars_format::scientific, "1.15292150459e+18"},
+    {23058430091e8, chars_format::scientific, "2.3058430091e+18"},
+    {4611686017e9, chars_format::scientific, "4.611686017e+18"},
+    {922337203e10, chars_format::scientific, "9.22337203e+18"},
+    {184467439e11, chars_format::scientific, "1.84467439e+19"},
+    {36893487e12, chars_format::scientific, "3.6893487e+19"},
+    {7378697e13, chars_format::scientific, "7.378697e+19"},
+    {1475739e14, chars_format::scientific, "1.475739e+20"},
+    {295147e15, chars_format::scientific, "2.95147e+20"},
+    {59029e16, chars_format::scientific, "5.9029e+20"},
+    {11805e17, chars_format::scientific, "1.1805e+21"},
+    {2361e18, chars_format::scientific, "2.361e+21"},
+    {471e19, chars_format::scientific, "4.71e+21"},
+    {93e20, chars_format::scientific, "9.3e+21"},
+    {17e21, chars_format::scientific, "1.7e+22"},
+    {3e22, chars_format::scientific, "3e+22"},
+    {1801439850948199e1, chars_format::scientific, "1.801439850948199e+16"},
+    {360287970189641e2, chars_format::scientific, "3.60287970189641e+16"},
+    {72057594037929e3, chars_format::scientific, "7.2057594037929e+16"},
+    {14411518807587e4, chars_format::scientific, "1.4411518807587e+17"},
+    {2882303761519e5, chars_format::scientific, "2.882303761519e+17"},
+    {576460752305e6, chars_format::scientific, "5.76460752305e+17"},
+    {115292150461e7, chars_format::scientific, "1.15292150461e+18"},
+    {23058430093e8, chars_format::scientific, "2.3058430093e+18"},
+    {4611686019e9, chars_format::scientific, "4.611686019e+18"},
+    {922337205e10, chars_format::scientific, "9.22337205e+18"},
+    {184467441e11, chars_format::scientific, "1.84467441e+19"},
+    {36893489e12, chars_format::scientific, "3.6893489e+19"},
+    {7378699e13, chars_format::scientific, "7.378699e+19"},
+    {1475741e14, chars_format::scientific, "1.475741e+20"},
+    {295149e15, chars_format::scientific, "2.95149e+20"},
+    {59031e16, chars_format::scientific, "5.9031e+20"},
+    {11807e17, chars_format::scientific, "1.1807e+21"},
+    {2363e18, chars_format::scientific, "2.363e+21"},
+    {473e19, chars_format::scientific, "4.73e+21"},
+    {95e20, chars_format::scientific, "9.5e+21"},
+    {19e21, chars_format::scientific, "1.9e+22"},
+    {5e22, chars_format::scientific, "5e+22"},
+    {302230528e15, chars_format::scientific, "3.02230528e+23"},
+    {302232576e15, chars_format::scientific, "3.02232576e+23"},
+    {81123342286848e18, chars_format::scientific, "8.1123342286848e+31"},
+    {81192061763584e18, chars_format::scientific, "8.1192061763584e+31"},
+
+    // Test the switching logic of chars_format::general.
+    // C11 7.21.6.1 "The fprintf function"/8:
+    // "Let P equal [...] 6 if the precision is omitted [...].
+    // Then, if a conversion with style E would have an exponent of X:
+    // - if P > X >= -4, the conversion is with style f [...].
+    // - otherwise, the conversion is with style e [...]."
+    {1e-6, chars_format::general, "1e-06"},
+    {1e-5, chars_format::general, "1e-05"},
+    {1e-4, chars_format::general, "0.0001"},
+    {1e-3, chars_format::general, "0.001"},
+    {1e-2, chars_format::general, "0.01"},
+    {1e-1, chars_format::general, "0.1"},
+    {1e0, chars_format::general, "1"},
+    {1e1, chars_format::general, "10"},
+    {1e2, chars_format::general, "100"},
+    {1e3, chars_format::general, "1000"},
+    {1e4, chars_format::general, "10000"},
+    {1e5, chars_format::general, "100000"},
+    {1e6, chars_format::general, "1e+06"},
+    {1e7, chars_format::general, "1e+07"},
+    {1.234e-6, chars_format::general, "1.234e-06"},
+    {1.234e-5, chars_format::general, "1.234e-05"},
+    {1.234e-4, chars_format::general, "0.0001234"},
+    {1.234e-3, chars_format::general, "0.001234"},
+    {1.234e-2, chars_format::general, "0.01234"},
+    {1.234e-1, chars_format::general, "0.1234"},
+    {1.234e0, chars_format::general, "1.234"},
+    {1.234e1, chars_format::general, "12.34"},
+    {1.234e2, chars_format::general, "123.4"},
+    {1.234e3, chars_format::general, "1234"},
+    {1.234e4, chars_format::general, "12340"},
+    {1.234e5, chars_format::general, "123400"},
+    {1.234e6, chars_format::general, "1.234e+06"},
+    {1.234e7, chars_format::general, "1.234e+07"},
+    {1.234e8, chars_format::general, "1.234e+08"},
+    {1.234e9, chars_format::general, "1.234e+09"},
+    {1.234e10, chars_format::general, "1.234e+10"},
+
+    // Test the switching logic of the plain overload.
+    // N4762 19.19.2 [charconv.to.chars]/8:
+    // "The conversion specifier is f or e, chosen according to the requirement
+    // for a shortest representation (see above); a tie is resolved in favor of f."
+    {1e-6, chars_format{}, "1e-06"},
+    {1e-5, chars_format{}, "1e-05"},
+    {1e-4, chars_format{}, "1e-04"},
+    {1e-3, chars_format{}, "0.001"},
+    {1e-2, chars_format{}, "0.01"},
+    {1e-1, chars_format{}, "0.1"},
+    {1e0, chars_format{}, "1"},
+    {1e1, chars_format{}, "10"},
+    {1e2, chars_format{}, "100"},
+    {1e3, chars_format{}, "1000"},
+    {1e4, chars_format{}, "10000"},
+    {1e5, chars_format{}, "1e+05"},
+    {1e6, chars_format{}, "1e+06"},
+    {1e7, chars_format{}, "1e+07"},
+    {1.234e-6, chars_format{}, "1.234e-06"},
+    {1.234e-5, chars_format{}, "1.234e-05"},
+    {1.234e-4, chars_format{}, "0.0001234"},
+    {1.234e-3, chars_format{}, "0.001234"},
+    {1.234e-2, chars_format{}, "0.01234"},
+    {1.234e-1, chars_format{}, "0.1234"},
+    {1.234e0, chars_format{}, "1.234"},
+    {1.234e1, chars_format{}, "12.34"},
+    {1.234e2, chars_format{}, "123.4"},
+    {1.234e3, chars_format{}, "1234"},
+    {1.234e4, chars_format{}, "12340"},
+    {1.234e5, chars_format{}, "123400"},
+    {1.234e6, chars_format{}, "1234000"},
+    {1.234e7, chars_format{}, "12340000"},
+    {1.234e8, chars_format{}, "123400000"},
+    {1.234e9, chars_format{}, "1.234e+09"},
+    {1.234e10, chars_format{}, "1.234e+10"},
+
+    // GH-331 "<charconv>: Test plain shortest's large integer fallback"
+    // The exactly-representable integer 123456789012345683968 is 21 digits, but scientific shortest needs 22
+    // characters. Therefore, the plain overload must select fixed notation. Because this 21-digit number exceeds the
+    // 17-digit round-trip limit, we can't use Ryu - we need to activate the large integer fallback (Ryu Printf for
+    // double).
+    {123456789012345683968.0, chars_format::scientific, "1.2345678901234568e+20"},
+    {123456789012345683968.0, chars_format{}, "123456789012345683968"},
+
+    // Exact value is 1.9156918820264798304697...e-56, incorrectly rounded by dtoa_milo() (Grisu2).
+    {0x1.e0ffed391517ep-186, chars_format::scientific, "1.9156918820264798e-56"},
+
+    // Exact value is 6.6564021122018745286598...e+264, incorrectly rounded by dtoa_milo() (Grisu2).
+    {0x1.a6c767640cd71p+879, chars_format::scientific, "6.6564021122018745e+264"},
+
+    // Incorrectly handled by dtoa_milo() (Grisu2), which doesn't achieve shortest round-trip.
+    {4.91e-6, chars_format::scientific, "4.91e-06"},
+    {5.547e-6, chars_format::scientific, "5.547e-06"},
+
+    // Test hexfloat corner cases.
+    {0x1.728p+0, chars_format::hex, "1.728p+0"}, // instead of "2.e5p-1"
+    {0x0.0000000000001p-1022, chars_format::hex, "0.0000000000001p-1022"}, // instead of "1p-1074", min subnormal
+    {0x0.fffffffffffffp-1022, chars_format::hex, "0.fffffffffffffp-1022"}, // max subnormal
+    {0x1p-1022, chars_format::hex, "1p-1022"}, // min normal
+    {0x1.fffffffffffffp+1023, chars_format::hex, "1.fffffffffffffp+1023"}, // max normal
+
+    // Test hexfloat exponents.
+    {0x1p-1009, chars_format::hex, "1p-1009"},
+    {0x1p-999, chars_format::hex, "1p-999"},
+    {0x1p-99, chars_format::hex, "1p-99"},
+    {0x1p-9, chars_format::hex, "1p-9"},
+    {0x1p+0, chars_format::hex, "1p+0"},
+    {0x1p+9, chars_format::hex, "1p+9"},
+    {0x1p+99, chars_format::hex, "1p+99"},
+    {0x1p+999, chars_format::hex, "1p+999"},
+    {0x1p+1009, chars_format::hex, "1p+1009"},
+
+    // Test hexfloat hexits.
+    {0x1.01234567p+0, chars_format::hex, "1.01234567p+0"},
+    {0x1.89abcdefp+0, chars_format::hex, "1.89abcdefp+0"},
+
+    // Test hexfloat trimming.
+    {0x1.000000000000ap+0, chars_format::hex, "1.000000000000ap+0"},
+    {0x1.00000000000ap+0, chars_format::hex, "1.00000000000ap+0"},
+    {0x1.0000000000ap+0, chars_format::hex, "1.0000000000ap+0"},
+    {0x1.000000000ap+0, chars_format::hex, "1.000000000ap+0"},
+    {0x1.00000000ap+0, chars_format::hex, "1.00000000ap+0"},
+    {0x1.0000000ap+0, chars_format::hex, "1.0000000ap+0"},
+    {0x1.000000ap+0, chars_format::hex, "1.000000ap+0"},
+    {0x1.00000ap+0, chars_format::hex, "1.00000ap+0"},
+    {0x1.0000ap+0, chars_format::hex, "1.0000ap+0"},
+    {0x1.000ap+0, chars_format::hex, "1.000ap+0"},
+    {0x1.00ap+0, chars_format::hex, "1.00ap+0"},
+    {0x1.0ap+0, chars_format::hex, "1.0ap+0"},
+    {0x1.ap+0, chars_format::hex, "1.ap+0"},
+    {0x1p+0, chars_format::hex, "1p+0"},
+
+    // https://www.exploringbinary.com/the-shortest-decimal-string-that-round-trips-may-not-be-the-nearest/
+    // This is an exhaustive list of anomalous values.
+
+    // Because math, these values have shortest-round-trip decimal representations containing 16 significant digits,
+    // but those decimal digits aren't what would be printed by "%.15e". For ordinary values, shortest-round-trip
+    // behaves as if it can magically pick a precision for "%.*e", finding the smallest precision that round-trips.
+    // (That is, start with the exact decimal representation, and then round it as much as possible.) These anomalous
+    // values demonstrate an exception to that mental model. They aren't being "incorrectly rounded"; instead, having
+    // the shortest output that round-trips is being prioritized. (This differs by 1 in the least significant decimal
+    // digit printed, so it's a very small difference.)
+
+    // N4835 20.19.2 [charconv.to.chars]/2 demands this behavior:
+    // "The functions that take a floating-point value but not a precision parameter ensure that the string
+    // representation consists of the smallest number of characters such that there is at least one digit before the
+    // radix point (if present) and parsing the representation using the corresponding from_chars function recovers
+    // value exactly. [...] If there are several such representations, the representation with the smallest difference
+    // from the floating-point argument value is chosen, resolving any remaining ties using rounding according to
+    // round_to_nearest (17.3.4.1)."
+    {0x1p976, chars_format::scientific, "6.386688990511104e+293"},
+    {0x1p896, chars_format::scientific, "5.282945311356653e+269"},
+    {0x1p863, chars_format::scientific, "6.150157786156811e+259"},
+    {0x1p803, chars_format::scientific, "5.334411546303884e+241"},
+    {0x1p710, chars_format::scientific, "5.386379163185535e+213"},
+    {0x1p594, chars_format::scientific, "6.483618076376552e+178"},
+    {0x1p574, chars_format::scientific, "6.183260036827614e+172"},
+    {0x1p554, chars_format::scientific, "5.896816288783659e+166"},
+    {0x1p544, chars_format::scientific, "5.758609657015292e+163"},
+    {0x1p534, chars_format::scientific, "5.623642243178996e+160"},
+    {0x1p481, chars_format::scientific, "6.243497100631985e+144"},
+    {0x1p405, chars_format::scientific, "8.263199609878108e+121"},
+    {0x1p398, chars_format::scientific, "6.455624695217272e+119"},
+    {0x1p378, chars_format::scientific, "6.156563468186638e+113"},
+    {0x1p345, chars_format::scientific, "7.167183174968974e+103"},
+    {0x1p305, chars_format::scientific, "6.518515124270356e+91"},
+    {0x1p275, chars_format::scientific, "6.070840288205404e+82"},
+    {0x1p182, chars_format::scientific, "6.129982163463556e+54"},
+    {0x1p172, chars_format::scientific, "5.986310706507379e+51"},
+    {0x1p132, chars_format::scientific, "5.444517870735016e+39"},
+    {0x1p122, chars_format::scientific, "5.316911983139664e+36"},
+    {0x1p89, chars_format::scientific, "6.189700196426902e+26"},
+    {0x1p-24, chars_format::scientific, "5.960464477539063e-08"},
+    {0x1p-44, chars_format::scientific, "5.684341886080802e-14"},
+    {0x1p-77, chars_format::scientific, "6.617444900424222e-24"},
+    {0x1p-97, chars_format::scientific, "6.310887241768095e-30"},
+    {0x1p-140, chars_format::scientific, "7.174648137343064e-43"},
+    {0x1p-296, chars_format::scientific, "7.854549544476363e-90"},
+    {0x1p-366, chars_format::scientific, "6.653062250012736e-111"},
+    {0x1p-383, chars_format::scientific, "5.075883674631299e-116"},
+    {0x1p-489, chars_format::scientific, "6.256509672447191e-148"},
+    {0x1p-496, chars_format::scientific, "4.887898181599368e-150"},
+    {0x1p-509, chars_format::scientific, "5.966672584960166e-154"},
+    {0x1p-549, chars_format::scientific, "5.426657103235053e-166"},
+    {0x1p-652, chars_format::scientific, "5.351097043477547e-197"},
+    {0x1p-662, chars_format::scientific, "5.225680706521042e-200"},
+    {0x1p-695, chars_format::scientific, "6.083493012144512e-210"},
+    {0x1p-705, chars_format::scientific, "5.940911144672375e-213"},
+    {0x1p-778, chars_format::scientific, "6.290184345309701e-235"},
+    {0x1p-788, chars_format::scientific, "6.142758149716505e-238"},
+    {0x1p-791, chars_format::scientific, "7.678447687145631e-239"},
+    {0x1p-808, chars_format::scientific, "5.858190679279809e-244"},
+    {0x1p-921, chars_format::scientific, "5.641232424577593e-278"},
+    {0x1p-957, chars_format::scientific, "8.209073602596753e-289"},
+    {0x1p-1007, chars_format::scientific, "7.291122019556398e-304"},
+    {0x1p-1017, chars_format::scientific, "7.120236347223045e-307"},
+
+    // This is an exhaustive list of almost-but-not-quite-anomalous values.
+    {0x1p966, chars_format::scientific, "6.237000967296e+290"},
+    {0x1p956, chars_format::scientific, "6.090821257125e+287"},
+    {0x1p890, chars_format::scientific, "8.25460204899477e+267"},
+    {0x1p740, chars_format::scientific, "5.78358058743443e+222"},
+    {0x1p149, chars_format::scientific, "7.1362384635298e+44"},
+    {0x1p-499, chars_format::scientific, "6.10987272699921e-151"},
+    {0x1p-569, chars_format::scientific, "5.17526350329881e-172"},
+    {0x1p-645, chars_format::scientific, "6.84940421565126e-195"},
+};
+
+inline constexpr double_to_chars_testcase double_scientific_precision_to_chars_test_cases_1[] = {
+    // Test special cases (zero, inf, nan) and an ordinary case. Also test negative signs.
+    {0.0, chars_format::scientific, 4, "0.0000e+00"},
+    {-0.0, chars_format::scientific, 4, "-0.0000e+00"},
+    {double_inf, chars_format::scientific, 4, "inf"},
+    {-double_inf, chars_format::scientific, 4, "-inf"},
+    {double_nan, chars_format::scientific, 4, "nan"},
+    {-double_nan, chars_format::scientific, 4, "-nan"},
+    {1.729, chars_format::scientific, 4, "1.7290e+00"},
+    {-1.729, chars_format::scientific, 4, "-1.7290e+00"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest Basic
+    {0x1.000000001869fp+211, chars_format::scientific, 62,
+        "3.29100911471548643542566484557342614975886952410844652587974656e+63"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest Zero
+    {0.0, chars_format::scientific, 4, "0.0000e+00"},
+    {0.0, chars_format::scientific, 3, "0.000e+00"},
+    {0.0, chars_format::scientific, 2, "0.00e+00"},
+    {0.0, chars_format::scientific, 1, "0.0e+00"},
+    {0.0, chars_format::scientific, 0, "0e+00"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest MinMax
+    {0x0.0000000000001p-1022, chars_format::scientific, 750,
+        "4.9406564584124654417656879286822137236505980261432476442558568250067550727020875186529983"
+        "636163599237979656469544571773092665671035593979639877479601078187812630071319031140452784"
+        "581716784898210368871863605699873072305000638740915356498438731247339727316961514003171538"
+        "539807412623856559117102665855668676818703956031062493194527159149245532930545654440112748"
+        "012970999954193198940908041656332452475714786901472678015935523861155013480352649347201937"
+        "902681071074917033322268447533357208324319360923828934583680601060115061698097530783422773"
+        "183292479049825247307763759272478746560847782037344696995336470179726777175851256605511991"
+        "315048911014510378627381672509558373897335989936648099411642057026370902792427675445652290"
+        "87538682506419718265533447265625e-324"},
+
+    {0x1.fffffffffffffp+1023, chars_format::scientific, 308,
+        "1.7976931348623157081452742373170435679807056752584499659891747680315726078002853876058955"
+        "863276687817154045895351438246423432132688946418276846754670353751698604991057655128207624"
+        "549009038932894407586850845513394230458323690322294816580855933212334827479782620414472316"
+        "8738177180919299881250404026184124858368e+308"},
+
+    // Test more corner cases.
+    {0x0.fffffffffffffp-1022, chars_format::scientific, 766,
+        "2."
+        "2250738585072008890245868760858598876504231122409594654935248025624400092282356951787758888037591552642309"
+        "7809504343120858773871583572918219930202943792242235598198275012420417889695713117910822610439719796040004"
+        "5489739193807919893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228"
+        "6316695429105080201815926642134996606517803095075913058719846423906068637102005108723282784678843631944515"
+        "8661350412234790147923695852083215976210663754016137365830441936037147783553066828345356340050740730401356"
+        "0296804637591858316312422452159926254649430083685186171942241764645513713542013221703137049658321015465406"
+        "8035397417906022589503023501937519773030945763173210852507299305089761582519159720757232455434770912461317"
+        "493580281734466552734375e-308"}, // max subnormal
+    {0x1p-1022, chars_format::scientific, 714,
+        "2."
+        "2250738585072013830902327173324040642192159804623318305533274168872044348139181958542831590125110205640673"
+        "3973103581100515243416155346010885601238537771882113077799353200233047961014744258363607192156504694250373"
+        "4208375250806650616658158948720491179968591639648500635908770118304874799780887753749949451580451605050915"
+        "3998565824708186451135379358049921159810857660519924333521143523901487956996095912888916029926415110634663"
+        "1339366347758651302937176204732563178148566435087212282863764204484681140761391147706280168985324411002416"
+        "1447421618567166150540154285084716752901903161322778896729707373123334086988983175067838846926092773977972"
+        "858659654941091369095406136467568702398678315290680984617210924625396728515625e-308"}, // min normal
+
+    // Ryu Printf d2fixed_test.cc D2expTest RoundToEven
+    {0.125, chars_format::scientific, 2, "1.25e-01"},
+    {0.125, chars_format::scientific, 1, "1.2e-01"},
+    {0.375, chars_format::scientific, 2, "3.75e-01"},
+    {0.375, chars_format::scientific, 1, "3.8e-01"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest RoundToEvenInteger
+    {2.5, chars_format::scientific, 1, "2.5e+00"},
+    {2.5, chars_format::scientific, 0, "2e+00"},
+    {3.5, chars_format::scientific, 1, "3.5e+00"},
+    {3.5, chars_format::scientific, 0, "4e+00"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest NonRoundToEvenScenarios
+    {0.748046875, chars_format::scientific, 2, "7.48e-01"},
+    {0.748046875, chars_format::scientific, 1, "7.5e-01"},
+    {0.748046875, chars_format::scientific, 0, "7e-01"}, // 0.75 would round to "8e-01", but this is smaller
+
+    {0.2509765625, chars_format::scientific, 2, "2.51e-01"},
+    {0.2509765625, chars_format::scientific, 1, "2.5e-01"},
+    {0.2509765625, chars_format::scientific, 0, "3e-01"}, // 0.25 would round to "2e-01", but this is larger
+
+    {0x1.0000000000001p-2, chars_format::scientific, 53, "2.50000000000000055511151231257827021181583404541015625e-01"},
+    {0x1.0000000000001p-2, chars_format::scientific, 2, "2.50e-01"},
+    {0x1.0000000000001p-2, chars_format::scientific, 1, "2.5e-01"},
+    {0x1.0000000000001p-2, chars_format::scientific, 0,
+        "3e-01"}, // 0.25 would round to "2e-01", but this is larger (again)
+
+    // More rounding tests.
+    {9.5, chars_format::scientific, 1, "9.5e+00"},
+    {9.5, chars_format::scientific, 0, "1e+01"},
+    {10.5, chars_format::scientific, 2, "1.05e+01"},
+    {10.5, chars_format::scientific, 1, "1.0e+01"},
+
+    {1.241, chars_format::scientific, 3, "1.241e+00"},
+    {1.241, chars_format::scientific, 1, "1.2e+00"},
+    {1.251, chars_format::scientific, 3, "1.251e+00"},
+    {1.251, chars_format::scientific, 1, "1.3e+00"},
+    {1.261, chars_format::scientific, 3, "1.261e+00"},
+    {1.261, chars_format::scientific, 1, "1.3e+00"},
+    {1.341, chars_format::scientific, 3, "1.341e+00"},
+    {1.341, chars_format::scientific, 1, "1.3e+00"},
+    {1.351, chars_format::scientific, 3, "1.351e+00"},
+    {1.351, chars_format::scientific, 1, "1.4e+00"},
+    {1.361, chars_format::scientific, 3, "1.361e+00"},
+    {1.361, chars_format::scientific, 1, "1.4e+00"},
+
+    {2.41, chars_format::scientific, 2, "2.41e+00"},
+    {2.41, chars_format::scientific, 0, "2e+00"},
+    {2.51, chars_format::scientific, 2, "2.51e+00"},
+    {2.51, chars_format::scientific, 0, "3e+00"},
+    {2.61, chars_format::scientific, 2, "2.61e+00"},
+    {2.61, chars_format::scientific, 0, "3e+00"},
+    {3.41, chars_format::scientific, 2, "3.41e+00"},
+    {3.41, chars_format::scientific, 0, "3e+00"},
+    {3.51, chars_format::scientific, 2, "3.51e+00"},
+    {3.51, chars_format::scientific, 0, "4e+00"},
+    {3.61, chars_format::scientific, 2, "3.61e+00"},
+    {3.61, chars_format::scientific, 0, "4e+00"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest VaryingPrecision
+    {1729.142857142857, chars_format::scientific, 50, "1.72914285714285711037518922239542007446289062500000e+03"},
+    {1729.142857142857, chars_format::scientific, 49, "1.7291428571428571103751892223954200744628906250000e+03"},
+    {1729.142857142857, chars_format::scientific, 48, "1.729142857142857110375189222395420074462890625000e+03"},
+    {1729.142857142857, chars_format::scientific, 47, "1.72914285714285711037518922239542007446289062500e+03"},
+    {1729.142857142857, chars_format::scientific, 46, "1.7291428571428571103751892223954200744628906250e+03"},
+    {1729.142857142857, chars_format::scientific, 45, "1.729142857142857110375189222395420074462890625e+03"},
+    {1729.142857142857, chars_format::scientific, 44, "1.72914285714285711037518922239542007446289062e+03"},
+    {1729.142857142857, chars_format::scientific, 43, "1.7291428571428571103751892223954200744628906e+03"},
+    {1729.142857142857, chars_format::scientific, 42, "1.729142857142857110375189222395420074462891e+03"},
+    {1729.142857142857, chars_format::scientific, 41, "1.72914285714285711037518922239542007446289e+03"},
+    {1729.142857142857, chars_format::scientific, 40, "1.7291428571428571103751892223954200744629e+03"},
+    {1729.142857142857, chars_format::scientific, 39, "1.729142857142857110375189222395420074463e+03"},
+    {1729.142857142857, chars_format::scientific, 38, "1.72914285714285711037518922239542007446e+03"},
+    {1729.142857142857, chars_format::scientific, 37, "1.7291428571428571103751892223954200745e+03"},
+    {1729.142857142857, chars_format::scientific, 36, "1.729142857142857110375189222395420074e+03"},
+    {1729.142857142857, chars_format::scientific, 35, "1.72914285714285711037518922239542007e+03"},
+    {1729.142857142857, chars_format::scientific, 34, "1.7291428571428571103751892223954201e+03"},
+    {1729.142857142857, chars_format::scientific, 33, "1.729142857142857110375189222395420e+03"},
+    {1729.142857142857, chars_format::scientific, 32, "1.72914285714285711037518922239542e+03"},
+    {1729.142857142857, chars_format::scientific, 31, "1.7291428571428571103751892223954e+03"},
+    {1729.142857142857, chars_format::scientific, 30, "1.729142857142857110375189222395e+03"},
+    {1729.142857142857, chars_format::scientific, 29, "1.72914285714285711037518922240e+03"},
+    {1729.142857142857, chars_format::scientific, 28, "1.7291428571428571103751892224e+03"},
+    {1729.142857142857, chars_format::scientific, 27, "1.729142857142857110375189222e+03"},
+    {1729.142857142857, chars_format::scientific, 26, "1.72914285714285711037518922e+03"},
+    {1729.142857142857, chars_format::scientific, 25, "1.7291428571428571103751892e+03"},
+    {1729.142857142857, chars_format::scientific, 24, "1.729142857142857110375189e+03"},
+    {1729.142857142857, chars_format::scientific, 23, "1.72914285714285711037519e+03"},
+    {1729.142857142857, chars_format::scientific, 22, "1.7291428571428571103752e+03"},
+    {1729.142857142857, chars_format::scientific, 21, "1.729142857142857110375e+03"},
+    {1729.142857142857, chars_format::scientific, 20, "1.72914285714285711038e+03"},
+    {1729.142857142857, chars_format::scientific, 19, "1.7291428571428571104e+03"},
+    {1729.142857142857, chars_format::scientific, 18, "1.729142857142857110e+03"},
+    {1729.142857142857, chars_format::scientific, 17, "1.72914285714285711e+03"},
+    {1729.142857142857, chars_format::scientific, 16, "1.7291428571428571e+03"},
+    {1729.142857142857, chars_format::scientific, 15, "1.729142857142857e+03"},
+    {1729.142857142857, chars_format::scientific, 14, "1.72914285714286e+03"},
+    {1729.142857142857, chars_format::scientific, 13, "1.7291428571429e+03"},
+    {1729.142857142857, chars_format::scientific, 12, "1.729142857143e+03"},
+    {1729.142857142857, chars_format::scientific, 11, "1.72914285714e+03"},
+    {1729.142857142857, chars_format::scientific, 10, "1.7291428571e+03"},
+    {1729.142857142857, chars_format::scientific, 9, "1.729142857e+03"},
+    {1729.142857142857, chars_format::scientific, 8, "1.72914286e+03"},
+    {1729.142857142857, chars_format::scientific, 7, "1.7291429e+03"},
+    {1729.142857142857, chars_format::scientific, 6, "1.729143e+03"},
+    {1729.142857142857, chars_format::scientific, 5, "1.72914e+03"},
+    {1729.142857142857, chars_format::scientific, 4, "1.7291e+03"},
+    {1729.142857142857, chars_format::scientific, 3, "1.729e+03"},
+    {1729.142857142857, chars_format::scientific, 2, "1.73e+03"},
+    {1729.142857142857, chars_format::scientific, 1, "1.7e+03"},
+    {1729.142857142857, chars_format::scientific, 0, "2e+03"},
+
+    // Negative precision requests 6 digits of precision.
+    {1729.142857142857, chars_format::scientific, -1, "1.729143e+03"},
+    {1729.142857142857, chars_format::scientific, -2, "1.729143e+03"},
+    {1729.142857142857, chars_format::scientific, -3, "1.729143e+03"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest Carrying
+    {2.0009, chars_format::scientific, 4, "2.0009e+00"},
+    {2.0009, chars_format::scientific, 3, "2.001e+00"},
+    {2.0029, chars_format::scientific, 4, "2.0029e+00"},
+    {2.0029, chars_format::scientific, 3, "2.003e+00"},
+    {2.0099, chars_format::scientific, 4, "2.0099e+00"},
+    {2.0099, chars_format::scientific, 3, "2.010e+00"},
+    {2.0299, chars_format::scientific, 4, "2.0299e+00"},
+    {2.0299, chars_format::scientific, 3, "2.030e+00"},
+    {2.0999, chars_format::scientific, 4, "2.0999e+00"},
+    {2.0999, chars_format::scientific, 3, "2.100e+00"},
+    {2.2999, chars_format::scientific, 4, "2.2999e+00"},
+    {2.2999, chars_format::scientific, 3, "2.300e+00"},
+    {2.9999, chars_format::scientific, 4, "2.9999e+00"},
+    {2.9999, chars_format::scientific, 3, "3.000e+00"},
+    {9.9999, chars_format::scientific, 4, "9.9999e+00"},
+    {9.9999, chars_format::scientific, 3, "1.000e+01"},
+
+    {2.09, chars_format::scientific, 2, "2.09e+00"},
+    {2.09, chars_format::scientific, 1, "2.1e+00"},
+    {2.29, chars_format::scientific, 2, "2.29e+00"},
+    {2.29, chars_format::scientific, 1, "2.3e+00"},
+    {2.99, chars_format::scientific, 2, "2.99e+00"},
+    {2.99, chars_format::scientific, 1, "3.0e+00"},
+    {9.99, chars_format::scientific, 2, "9.99e+00"},
+    {9.99, chars_format::scientific, 1, "1.0e+01"},
+
+    {2.9, chars_format::scientific, 1, "2.9e+00"},
+    {2.9, chars_format::scientific, 0, "3e+00"},
+    {9.9, chars_format::scientific, 1, "9.9e+00"},
+    {9.9, chars_format::scientific, 0, "1e+01"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest Exponents
+    {9.99e-100, chars_format::scientific, 2, "9.99e-100"},
+    {9.99e-99, chars_format::scientific, 2, "9.99e-99"},
+    {9.99e-10, chars_format::scientific, 2, "9.99e-10"},
+    {9.99e-09, chars_format::scientific, 2, "9.99e-09"},
+    {9.99e-01, chars_format::scientific, 2, "9.99e-01"},
+    {9.99e+00, chars_format::scientific, 2, "9.99e+00"},
+    {9.99e+01, chars_format::scientific, 2, "9.99e+01"},
+    {9.99e+09, chars_format::scientific, 2, "9.99e+09"},
+    {9.99e+10, chars_format::scientific, 2, "9.99e+10"},
+    {9.99e+99, chars_format::scientific, 2, "9.99e+99"},
+    {9.99e+100, chars_format::scientific, 2, "9.99e+100"},
+
+    {9.99e-100, chars_format::scientific, 1, "1.0e-99"},
+    {9.99e-99, chars_format::scientific, 1, "1.0e-98"},
+    {9.99e-10, chars_format::scientific, 1, "1.0e-09"},
+    {9.99e-09, chars_format::scientific, 1, "1.0e-08"},
+    {9.99e-01, chars_format::scientific, 1, "1.0e+00"},
+    {9.99e+00, chars_format::scientific, 1, "1.0e+01"},
+    {9.99e+01, chars_format::scientific, 1, "1.0e+02"},
+    {9.99e+09, chars_format::scientific, 1, "1.0e+10"},
+    {9.99e+10, chars_format::scientific, 1, "1.0e+11"},
+    {9.99e+99, chars_format::scientific, 1, "1.0e+100"},
+    {9.99e+100, chars_format::scientific, 1, "1.0e+101"},
+
+    // Ryu Printf d2fixed_test.cc D2expTest PrintDecimalPoint
+    // These values exercise each codepath.
+    {1e+54, chars_format::scientific, 0, "1e+54"},
+    {1e+54, chars_format::scientific, 1, "1.0e+54"},
+    {1e-63, chars_format::scientific, 0, "1e-63"},
+    {1e-63, chars_format::scientific, 1, "1.0e-63"},
+    {1e+83, chars_format::scientific, 0, "1e+83"},
+    {1e+83, chars_format::scientific, 1, "1.0e+83"},
+
+    // The UCRT had trouble with rounding this value. charconv was never affected, but let's test it anyways.
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 104,
+        "1.09995565999999994887854821710219658911365648587951921896774663603198787416706536331386569598149846892544e+"
+        "104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 18, "1.099955659999999949e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 17, "1.09995565999999995e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 16, "1.0999556599999999e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 15, "1.099955660000000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 14, "1.09995566000000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 13, "1.0999556600000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 12, "1.099955660000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 11, "1.09995566000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 10, "1.0999556600e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 9, "1.099955660e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 8, "1.09995566e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 7, "1.0999557e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 6, "1.099956e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 5, "1.09996e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 4, "1.1000e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 3, "1.100e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 2, "1.10e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 1, "1.1e+104"},
+    {0x1.88e2d605edc3dp+345, chars_format::scientific, 0, "1e+104"},
+};
+
+inline constexpr double_to_chars_testcase double_scientific_precision_to_chars_test_cases_2[] = {
+    // Ryu Printf d2fixed_test.cc D2expTest AllPowersOfTen
+    // These values test every power of ten that's within the range of doubles.
+    {1e-323, chars_format::scientific, 749,
+        "9."
+        "8813129168249308835313758573644274473011960522864952885117136500135101454041750373059967272327198475959312"
+        "9390891435461853313420711879592797549592021563756252601426380622809055691634335697964207377437272113997461"
+        "4461000127748183071299687746249467945463392302800634307707961482524771311823420533171133735363740791206212"
+        "4986389054318298491065861091308880225496025941999908386397881816083312664904951429573802945356031871047722"
+        "3100269607052986944038758053621421498340666445368950667144166486387218476578691673612021202301233961950615"
+        "6684554636658495809965049461552751854495749312169556407468939399067294035945355435170251321102398263009782"
+        "2029020757254763345019116747794671979873296198823284114052741805584855350891304581750773650128394365310668"
+        "9453125e-324"},
+    {1e-322, chars_format::scientific, 749,
+        "9."
+        "8813129168249308835313758573644274473011960522864952885117136500135101454041750373059967272327198475959312"
+        "9390891435461853313420711879592797549592021563756252601426380622809055691634335697964207377437272113997461"
+        "4461000127748183071299687746249467945463392302800634307707961482524771311823420533171133735363740791206212"
+        "4986389054318298491065861091308880225496025941999908386397881816083312664904951429573802945356031871047722"
+        "3100269607052986944038758053621421498340666445368950667144166486387218476578691673612021202301233961950615"
+        "6684554636658495809965049461552751854495749312169556407468939399067294035945355435170251321102398263009782"
+        "2029020757254763345019116747794671979873296198823284114052741805584855350891304581750773650128394365310668"
+        "9453125e-323"},
+    {1e-321, chars_format::scientific, 751,
+        "9."
+        "9801260459931801923666896159380717217742080128093602413968307865136452468582167876790566945050470460718906"
+        "0684800349816471846554918998388725525087941779393815127440644429037146248550679054943849451211644835137436"
+        "0605610129025664902012684623711962624918026225828640650785041097350019024941654738502845072717378199118274"
+        "6236252944861481475976519702221969027750986201419907470261860634244145791554000943869540974809592189758199"
+        "5331272303123516813479145634157635713324073109822640173815608151251090661344478590348141414324246301570121"
+        "8251400183025080768064699956168279373040706805291251971543628793057966976304808989521953834313422245639880"
+        "0249310964827310978469307915272618699672029160811516955193269223640703904400217627568281386629678308963775"
+        "634765625e-322"},
+    {1e-320, chars_format::scientific, 750,
+        "9."
+        "9998886718268300541337523676528005766688104049139332319738542138136722671490251377536686879595124857670824"
+        "6943582132687395553181760422147911120187125822521327632643497190282764359933947726339777865966519379365430"
+        "9834532129281161268155283999204461560808953010434241919400457020315068567565301579569187340188105680700687"
+        "0486225722970118072958651424404586788201978253303907287034656397876312416883810846728688580700304253500294"
+        "9777472842337622787367223150264878556320754442713378075149896484223865098297635973695365456728848769494023"
+        "0564769292298397759684630055091384876749698303915591084358566671856101564376699700392294336955627042165899"
+        "5893369006341820505159346148768208043631775753209163523421374707251873615102000236731782933929935097694396"
+        "97265625e-321"},
+    {1e-319, chars_format::scientific, 750,
+        "9."
+        "9998886718268300541337523676528005766688104049139332319738542138136722671490251377536686879595124857670824"
+        "6943582132687395553181760422147911120187125822521327632643497190282764359933947726339777865966519379365430"
+        "9834532129281161268155283999204461560808953010434241919400457020315068567565301579569187340188105680700687"
+        "0486225722970118072958651424404586788201978253303907287034656397876312416883810846728688580700304253500294"
+        "9777472842337622787367223150264878556320754442713378075149896484223865098297635973695365456728848769494023"
+        "0564769292298397759684630055091384876749698303915591084358566671856101564376699700392294336955627042165899"
+        "5893369006341820505159346148768208043631775753209163523421374707251873615102000236731782933929935097694396"
+        "97265625e-320"},
+    {1e-318, chars_format::scientific, 754,
+        "9."
+        "9999874849559983034425876814113742209432834168744560969267393309501724022504791795040417479267848129655584"
+        "2874876041601750171714894629266707048162621742736965195169511454088992450490864069696757508040293752086570"
+        "9580676739282438749985996996081924055488407644357269925743534099929893815278419813774519051525459318108599"
+        "1107475586860661255943562083015499877004233213563327286118520376694473250010459896242984318729757813819005"
+        "4549703845033693317236663537845414770535737849377831764656567925888728970482401760612101576940871781833642"
+        "5626336137844764344642729705586000404268243261408712779922641361250092237317059153946646039468838066148529"
+        "6871589296549393052792796339935685990351574486171151756262515234669929463655509149777600441666436381638050"
+        "079345703125e-319"},
+    {1e-317, chars_format::scientific, 757,
+        "1."
+        "0000002306925373540838912978475160267584454368668534526669672098520647422515697285766597706921875662045329"
+        "8226457012793890336449486476033452643735894613076931082954841359365992666407440152120030445435135990799474"
+        "1954259843078263037226060394561354342969032583944572412669499566187211760243538754890531880822606236371978"
+        "5920066306644424273339129868180713684032457145760224028598109997351719737497945725367012867943417584786681"
+        "2026553849543810389671707959598249520266798536037749981808256864213845855131011662864961199497267523368458"
+        "5488557116467671933238644465316019273339602500503268103425725256465919083825811307197979879484581971974592"
+        "4201832234008052893493781386861080768235954429611544999118868631378263784093853548673447306782691157422959"
+        "804534912109375e-317"},
+    {1e-316, chars_format::scientific, 757,
+        "9."
+        "9999998365971443346061920956311959264775925433695214550458499705922349191381609347228383804226938538653679"
+        "2366287780216044499031536405156556539159558732763919890485263237064770961810478612616379963299515548676713"
+        "4548944815532598435214836120691606867323339473597648426536418734881746971242559593050185515442628522784588"
+        "1185131819846979153816675915341864013104515083595754786004003374046743354151291027432271285983439508858844"
+        "2646232720370702133470343586292981797312610775210888475844901856096836954505497483976693591967374658376095"
+        "0009031993538060167762492161897827345208061381095352991868150697424341071434604085640940002282989444146358"
+        "4493866832825339621246977613831620733691549327791400285367657800597186444724697763908327630133499042131006"
+        "717681884765625e-317"},
+    {1e-315, chars_format::scientific, 758,
+        "9."
+        "9999999848168380869801553486018337869440042528874622393432792982679396693408131157854639400126447623561656"
+        "3760184721079416030959336106467234733051521976644243346829052258460480303946313987131415432762626210235795"
+        "1648564032447600351437582190186923061065358655548532968545933350501169209114129270401493513009634553240699"
+        "9866063694642814968591153281329780382737718466036143916002629170014970595400981001006542729590483689199322"
+        "3303391066874746239265147746874352601633933250320885156379161863259334250313774632657068696147692692894604"
+        "4301624343806379717639929311373569268499339198531592674411496809458432057444014624821271529836759260682332"
+        "3945334163260650980068427789118371950611629025890843267716919511388313528497528027277896356395103794056922"
+        "1973419189453125e-316"},
+    {1e-314, chars_format::scientific, 759,
+        "9."
+        "9999999996388074622175516738988975729906454238392563177730222310355101443610783338917264959716398532052454"
+        "0899574415165753184152116076598302552440718301032275692463431160600051238159897524582918979708937276391703"
+        "3358525954139100543059856797136454680439560573743621422746884812063111432901286238136624312766335156286311"
+        "1734156882122398550068601017928572019701038804280182829002491749611793319525949998363969873951188107233370"
+        "1369106901525150649844628162932489682066065497831884824432587863975583979894602347525106206565724496346455"
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+        "4959839786965342632596166187964530344229899589832462449290116390191104e+282"},
+    {1e+284, chars_format::scientific, 284,
+        "1."
+        "0000000000000000792143825084576765412568191916997109340838993423344357589751710277254453455720576452975216"
+        "2833294418062406838213115052098838781957320876356853543120821491881752894667070520582225774709469217797130"
+        "505057184069381648545374773244373557467226310750742042216461653692645376e+284"},
+    {1e+285, chars_format::scientific, 284,
+        "9."
+        "9999999999999998015915792052044285019310951985284721180002571056165035998253808522408861618614649384428614"
+        "9397221450372619320895438893697947652166455225334059372746413748147206443420891752540620587530362220273863"
+        "006901551095990707698442841525909542472844588688081080376132618600579072e+284"},
+    {1e+286, chars_format::scientific, 286,
+        "1."
+        "0000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117"
+        "3816294023984005882022115176158618240811672377905911327059270770583804511182079226095749373929800486437916"
+        "54301923722148311225012721166820834263125344653917287293299907083743789056e+286"},
+    {1e+287, chars_format::scientific, 287,
+        "1."
+        "0000000000000000752521735249401871936142708048258363851925443970635243430154657100253910763966211992393922"
+        "0917551527141401041968172205589677021287693862203915638886974287199071604654071266769099226071211897966340"
+        "736882502910990345434353553680702253338428636675464684849307718019341877248e+287"},
+    {1e+288, chars_format::scientific, 288,
+        "1."
+        "0000000000000000076304735395750356605147783355117107507800866644399695106364949546111315491358391865139834"
+        "5555539522089568786054480958499982972526059487327108739962648660614644255098884001691739462644953639520862"
+        "0267012778077787723395914064607119962069483324573977857832138825282954985472e+288"},
+    {1e+289, chars_format::scientific, 289,
+        "1."
+        "0000000000000000617278335278671568869943723109630112583100528505388133765396715589425391709444647966943104"
+        "5845149126131034590785433956171738211535366987228554259102109161882186134743033813753627273385960246277244"
+        "99484625789034803081540112423670420191213257583185130503608895092113260150784e+289"},
+    {1e+290, chars_format::scientific, 289,
+        "1."
+        "0000000000000000617278335278671568869943723109630112583100528505388133765396715589425391709444647966943104"
+        "5845149126131034590785433956171738211535366987228554259102109161882186134743033813753627273385960246277244"
+        "99484625789034803081540112423670420191213257583185130503608895092113260150784e+290"},
+    {1e+291, chars_format::scientific, 290,
+        "9."
+        "9999999999999995786090235034628413215355187809651428385251777322903315400557247862623653707190362514808261"
+        "2890986863714202457020042006419681526374965874177788623543449994485057258262661745948026767632275613049896"
+        "960078961318150545418464661067991669581788285529005480705688196068853638234112e+290"},
+    {1e+292, chars_format::scientific, 292,
+        "1."
+        "0000000000000000132565989783574162680686561089586460035632031477942492726904253214615979418039362499727374"
+        "6385658920909881229746500070257845517383027467316859073953152552746468610581875582146175794962018326623525"
+        "85538835573636597522107561710941518560028749376834095178551288964115055725510656e+292"},
+    {1e+293, chars_format::scientific, 292,
+        "9."
+        "9999999999999992462348437353960485060448933957923525202610654848990348279466077292501969423268405025328970"
+        "2311625456483436552753066788724417337901780594783307353950604674697279949729005300639788058439531021138680"
+        "00379620369084502134308975505229555772913629423636305841602377586326247764393984e+292"},
+    {1e+294, chars_format::scientific, 294,
+        "1."
+        "0000000000000000664364677412481031185471561705862924544854611073768567466278840505835448903466875698044061"
+        "2078356746066803774429216105089087787538737112019976077088007803912512979947260613395493988432857461329320"
+        "5683935969567348590731356020719265634967118123751637393518591968740451429495341056e+294"},
+    {1e+295, chars_format::scientific, 294,
+        "9."
+        "9999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626"
+        "9700402258157277029368704493591001552896016804949888720722394020468419889626445633965848788795148458000490"
+        "2758521100414464490983962613190835886243290260424727924570510530141380583845003264e+294"},
+    {1e+296, chars_format::scientific, 294,
+        "9."
+        "9999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626"
+        "9700402258157277029368704493591001552896016804949888720722394020468419889626445633965848788795148458000490"
+        "2758521100414464490983962613190835886243290260424727924570510530141380583845003264e+295"},
+    {1e+297, chars_format::scientific, 297,
+        "1."
+        "0000000000000000176528014627563797143748787807198647768394431391197448238692552430690122228834703590788220"
+        "7282921941122853493440271262470561545049232797945650079545633920176194945116080744729452765622274361759204"
+        "8849967890105831362861792425329827928397252374398383022243308510390698430058459037696e+297"},
+    {1e+298, chars_format::scientific, 297,
+        "9."
+        "9999999999999995956620347534297882382556244673937414671209151179964876700316698854008030255517451747068478"
+        "7823111966314522286348299614922233214338230100245921475882026911692302152705828545968641468338591362245555"
+        "1313826420028155008403585629126369847605750170289266545852965785882018353801250996224e+297"},
+    {1e+299, chars_format::scientific, 299,
+        "1."
+        "0000000000000000525047602552044202487044685811081591549158541155118024579889081957863713750804478640437044"
+        "4383288387817694252323536043057564479218478670698284838720092657580373783023379478809005936895323497079994"
+        "508111903896764088007465274278014249457925878882005684283811566947219638686545940054016e+299"},
+    {1e+300, chars_format::scientific, 299,
+        "1."
+        "0000000000000000525047602552044202487044685811081591549158541155118024579889081957863713750804478640437044"
+        "4383288387817694252323536043057564479218478670698284838720092657580373783023379478809005936895323497079994"
+        "508111903896764088007465274278014249457925878882005684283811566947219638686545940054016e+300"},
+    {1e+301, chars_format::scientific, 299,
+        "1."
+        "0000000000000000525047602552044202487044685811081591549158541155118024579889081957863713750804478640437044"
+        "4383288387817694252323536043057564479218478670698284838720092657580373783023379478809005936895323497079994"
+        "508111903896764088007465274278014249457925878882005684283811566947219638686545940054016e+301"},
+    {1e+302, chars_format::scientific, 302,
+        "1."
+        "0000000000000000762970307908489492534734685515065681170160173420621138028812579448414218896469178407663974"
+        "7577138548761372210387844799938291815611350519830750167649856488981626536368095414607314235151058373458986"
+        "890825155659063617715863205282622390509284183439858617103083735673849899204570498157510656e+302"},
+    {1e+303, chars_format::scientific, 303,
+        "1."
+        "0000000000000000001617650767864564382126686462316594382954950171011174992257387478652602430342139152537797"
+        "7356818033741602744582056777919964339154160602606861115074612228497617725665004420052727680732706769046211"
+        "2661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568e+303"},
+    {1e+304, chars_format::scientific, 303,
+        "9."
+        "9999999999999993925355250553646218600402872201173249531907715713232045630132339028433092574405077484368561"
+        "1805616217257871719374263603053023579884086688277498730144168201104106771025316244090584371980254855159907"
+        "6639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744e+303"},
+    {1e+305, chars_format::scientific, 303,
+        "9."
+        "9999999999999993925355250553646218600402872201173249531907715713232045630132339028433092574405077484368561"
+        "1805616217257871719374263603053023579884086688277498730144168201104106771025316244090584371980254855159907"
+        "6639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744e+304"},
+    {1e+306, chars_format::scientific, 306,
+        "1."
+        "0000000000000000172160645967364548288310878250132389823288920178923806712445750479879204518754595945686061"
+        "3886169829106031104922553294852069693880571144065012262851466942846035699262496802832955068922417528434673"
+        "0060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208e+306"},
+    {1e+307, chars_format::scientific, 306,
+        "9."
+        "9999999999999998603105976025645777170026418381263638752496607358835658526727438490648464142289606667863792"
+        "8039265461539335317285025210333627595237061539701073069166468937517856903985107314633964162326607112672001"
+        "1020169553304018596457812688561947201171488461172921822139066929851282122002676667750021070848e+306"},
+    {1e+308, chars_format::scientific, 308,
+        "1."
+        "0000000000000000109790636294404554174049230967731184633681068290315758540491149153716332897849468889906124"
+        "9669721172515611590283743140088328307009198146046031271664502933027185697489699588559043338384466165001178"
+        "426897626212945177628091195786707458122783970171784415105291802893207873272974885715430223118336e+308"},
+};
+
+inline constexpr double_to_chars_testcase double_scientific_precision_to_chars_test_cases_3[] = {
+    // Ryu Printf d2fixed_test.cc D2expTest AllBinaryExponents
+    // These values test every binary exponent.
+    // The mantissas were randomly generated.
+    {0x0.63b831e8bd9d7p-1022, chars_format::scientific, 765,
+        "8."
+        "6673155601518373204745615934992065170006880827787289636461039456117181014435225731420739682086431846196084"
+        "0559717761976781401452617612090003075542930260777812518669659241729724010681746641686623499848468215594968"
+        "2021079153402945471922988971873909012440740220527800911244244822910902773084448896950002963160859062629660"
+        "9882885374947604962348974323036144310657614326754120115556509383797380330234783520222245524583876671362471"
+        "8494080431858617260899963028423305531253945552260335123939000593240656910669298632181747412649714974019858"
+        "8356285761402581880926947783051518340651609793980053160313425027619711896255545853478748493923212623215309"
+        "2624291889535798750202922731324119623206905408779063259071595105183391812893811664489504206776437911230459"
+        "57647264003753662109375e-309"},
+    {0x1.8777195166b0cp-1022, chars_format::scientific, 764,
+        "3."
+        "4024962888548891870780380223721963415936057267215768489022880931036340709664117046765987977180526441192766"
+        "7980233377849338161398396361988635343561859686478002041658296279167269633549887180398681467085048366045915"
+        "6676370951509663121515851044197786647785688189698831775149285429703757400159268959324595109001459740108998"
+        "7064349011889817819942001416735892399032878298656443356501797788246594163297203747575928614864543561706962"
+        "7150190560661004463760153276800654567748203691908193307868018274961903878508519765463087823925880361092267"
+        "9880731846129559561006152326978128322135743176002677808113397223361200222360522182681889723507749332427973"
+        "2240457324020870731250050608330505053074385990942209557473057293561320028309889744618215584592846312261826"
+        "8243968486785888671875e-308"},
+    {0x1.4668b84fe57a0p-1021, chars_format::scientific, 760,
+        "5."
+        "6740958740641631511384384536776561146340227260577357930980504423887626489617571637837441488031383754955785"
+        "4086594144651757106826827082053224819137614951757164822186954713633389739294124192094600295957101411513892"
+        "2292227756567557970015697918331549646091513808709325026828267412677470869412642816923726953169932993282696"
+        "1970700281786004455171108499583392239457705199245309170122601944018148603634684132173289075939231416021795"
+        "6773831481083699810908312929539145137356475139290129992626736771448814573026906644585538148884867233811394"
+        "2395343914793125973137539097252903908512233824086968776157212299338375466427657302566612718734454791559738"
+        "4296829871117558203187275819525974756928809649794138442664770396059164903717939140888326665645990942721255"
+        "123615264892578125e-308"},
+    {0x1.befe59a615135p-1020, chars_format::scientific, 765,
+        "1."
+        "5540526173622352375993445245662683293464994107818202403773732113997242921188175334393284236610673877760032"
+        "1140045136930880932847198094667333515588636758849652193589488647628623014759199260062387648516658758902202"
+        "4414313323949909142159529537456605070198347779192598243095403947592025125119457352938379814319820278343589"
+        "7747302961203036640889656009214261792160762451937044526624584298357832777585944388632200805521152515342330"
+        "8561170623085034646351360745189671642589380586080254484943279473962393703949926697788378603146358212695781"
+        "2370158648390166491038532530966495890940486561351377873613480311323741789526145720019072115667475187757369"
+        "0752588227109741861829975787681759234538817712508305395458670019301186211951459779169503264140139719984290"
+        "42287170886993408203125e-307"},
+    {0x1.1e3d1ff2f0c7dp-1019, chars_format::scientific, 764,
+        "1."
+        "9903200051351428805615989243193127044770722692702459361378399559534652305451954151277557670839014475339478"
+        "2867837696288408273532724825127341865493665067774242606965035835847639336549731232556074151242689053806547"
+        "2696077887804553644884150043878406627507745699995507099147377175105877153481526330603572499358626260756240"
+        "8161745031548857838580407488540228220931314580542710929232921821435828527112974792024775296802861545460264"
+        "3826566011906669643593108259028344252667022294947897471948646741545397199053445447059963324528762468428056"
+        "1552964343633309851882307590384491177630806444328543647075668536514853052975155234251635207407297067719395"
+        "3884058314203115240012536217140219386138413382468962035052024511938122187739312695493269084190401940759329"
+        "5909464359283447265625e-307"},
+    {0x1.6f434a1f8b19bp-1018, chars_format::scientific, 763,
+        "5."
+        "1074185390468469270473736828301327180750062564436661993518732867820414412582796763617494622074841605120794"
+        "6280001513512476415260093780274458550261745884171770589710369360980007788208880420310179065543732589777800"
+        "1026322540349851343686142888941809812697130982668148593939074359425039990092398040350897342987033684062247"
+        "8891910045787038724069756928395277953670595630959968898874335051527496681463133794176157145807591872109216"
+        "6144382506150797267436509897049656206429012398091894503972795298016547064662347920285527872288390895517604"
+        "4191810941642460040564082188712438936906291867000270523960550332664002210898302673308442754015967789648657"
+        "7199640058529357006968235192644651239960321968186374102417320609944271040560945042782563241257065556055749"
+        "766528606414794921875e-307"},
+    {0x1.587345c18153ep-1017, chars_format::scientific, 761,
+        "9."
+        "5803415071347647865082718369266434040574270026977809712667208404792036119580302875847883246591206937429220"
+        "0765720124757014325334439209209434046539893719315938780007431549634993916215217605362262858269407426842334"
+        "2012580732514751221293610595763003495795061946838666946253209134456556726989193259291618902375718355472162"
+        "4042439056845036040587911004852089800421901874454407994337108163738052947210061561024263715054967969591411"
+        "0270363560682828986102429968210287319178363269091390190666341835673642784686119809160641359798630514658952"
+        "9621994975436450348729144771801748911075356977674248196373371459254492612305520113008095746852968491757589"
+        "4312232673600164454503147125519469744188854742689367713126583601172208920773079707158131901323372403567191"
+        "2133693695068359375e-307"},
+    {0x1.f1b6b87277fdep-1016, chars_format::scientific, 761,
+        "2."
+        "7686246461533842708986290401534510677245449052480438452772935563477911887903937433332521175778793903095384"
+        "0412239557231923283555660292437990927601776574893980601557250737329754310915661825472040213756951830291482"
+        "6971556169842700521540676609741125857389706633023242364855348478771230295850829291438723530923932923590702"
+        "4151611338319751130631733719608246390666274473865694983392385750305737090058291815147877218349104719543513"
+        "7063089136683774947602824936693432977762482651171413713941775960038695919756102724251419600380177635071493"
+        "6245861443988258956704733318591666199586331239518529031729048520377213164363192327716960117074516227535950"
+        "9369132897727641328747183370449707056957130139385301002356826323260325258247061322707666120024327938153874"
+        "1290569305419921875e-306"},
+    {0x1.72a498409980ap-1015, chars_format::scientific, 760,
+        "4."
+        "1235396742477088973208679969440262899254505285796142223814175822702981218018251380021070120502969772416262"
+        "0356011168621659532952906006748436531426296108744371485218418489239052308056360753777114430810169989395269"
+        "5946140077164320660032095927443769046869340226546265147500705839457828617891438915581029354085740892509908"
+        "6126202065003470601897807688053820010379771148507245760602767529755342564783534772481563133530608872155816"
+        "3170273217810752940595356441071317848377916852111771962558733789348917288503698641911641096452799678633118"
+        "3241428470038337938910339876846473513908343996450852057201827354601830122948746860487681564435359569830201"
+        "2244034576878689343471222581935495027065359114155162611459186679259780987690986908851542569465209453483112"
+        "156391143798828125e-306"},
+    {0x1.ce91e910d066ap-1014, chars_format::scientific, 760,
+        "1."
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+        "1711334781978492823905176274313064600948013598950259705624044810976578137635336099364396791518714662842370"
+        "9280516241948225398658063408258944026475600604367395551060529895388440736389998513454247897588963927412199"
+        "886596463797584431228714343905526280539044788020033342657437500226579170692177128139530436608e+305"},
+    {0x1.c021a05af3889p+1016, chars_format::scientific, 306,
+        "1."
+        "2292521010494213202208392120910347371974932861996362652215354683626354286778450977056457988823406607851862"
+        "6637132565769582888977482809648230361989943269158655634268614343814815368836427061857244021348551127969781"
+        "1055580445126773330393578734970725834547100511308555559785816417647601996123490828625750523904e+306"},
+    {0x1.a0ba4fb02d02bp+1017, chars_format::scientific, 305,
+        "2."
+        "2862202954633178261723536509649685641707279850300290869803982420258862461647313576454922281065116456219182"
+        "9590977426811173756270658087196535714508685519454569812805651039956703238427854607968636622055258647292634"
+        "684121390540222150085347564627967335399432454801846311963425999483985877313898405284846501888e+306"},
+    {0x1.3f966b0ddcfd7p+1018, chars_format::scientific, 306,
+        "3."
+        "5065941308845354984753464542431391007674227604335612148522065748017825104538844307057550895580408416179424"
+        "7118416307944385786855208364451666760483209546178608196510513690039018180918045791524606584522427293544334"
+        "6243739881419482228334516326372503115386643937845878401903583322133727281304761523559911653376e+306"},
+    {0x1.f28cb9c6710a9p+1019, chars_format::scientific, 307,
+        "1."
+        "0940422247589227743316285257523446771149121608626559253104638931006152289125664762418837487890517285868544"
+        "1970842686935351143015218862511720392429343778632449186329279729720913087020406559756094832031600186601946"
+        "42090669215782471906632775672148557149263319590356475272060941885997193903260433671483161575424e+307"},
+    {0x1.c941430ebe2afp+1020, chars_format::scientific, 306,
+        "2."
+        "0068458193014485659233690965046541577150222922448876802079698749594927659484925364079051863693079922549962"
+        "3702340752679075101040300153750541846589137823389048924711303393882024589282733583930812172225616249563429"
+        "7868168967936674133963531031634950024920744675243356304584274649234115658663895314346773839872e+307"},
+    {0x1.3e04900b4e89ep+1021, chars_format::scientific, 307,
+        "2."
+        "7914963723745636433327098668092909811147302243780506069948228182283265947810001627803239111045172778906393"
+        "0987072447572980908861942482392189431390905934840154072184967491283583766051866632563025027572585713651756"
+        "30215388510334525743239925811352693280111872637884811742138711874263709333351600610928924557312e+307"},
+    {0x1.5cd1470a36d2ep+1022, chars_format::scientific, 307,
+        "6."
+        "1236992921041949817714041891928528839786938336942322084137095186042961819813936048028926723548660468971278"
+        "4969654586939917432251493887838173965737887781285740992515883352944011799461643423393002121460091055587179"
+        "85452576260185887979241983673503558946414035103004649802078842226017422195444929429676453003264e+307"},
+    {0x1.e4ed787bb244bp+1023, chars_format::scientific, 308,
+        "1."
+        "7026387749989901049352803345551957967504365590849171315485933257848664869760810216798351071186594668551262"
+        "9849272947937037080011581203332426168619415862460756069100292337181478478510557557506918137532825769631310"
+        "693972479511748662180221113394836543075210717029725044946195117678217681054268005181200990732288e+308"},
+};
+
+inline constexpr double_to_chars_testcase double_scientific_precision_to_chars_test_cases_4[] = {
+    // Test the maximum mantissa, which generates the most digits for each exponent.
+    {0x0.fffffffffffffp-1022, chars_format::scientific, 766,
+        "2."
+        "2250738585072008890245868760858598876504231122409594654935248025624400092282356951787758888037591552642309"
+        "7809504343120858773871583572918219930202943792242235598198275012420417889695713117910822610439719796040004"
+        "5489739193807919893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228"
+        "6316695429105080201815926642134996606517803095075913058719846423906068637102005108723282784678843631944515"
+        "8661350412234790147923695852083215976210663754016137365830441936037147783553066828345356340050740730401356"
+        "0296804637591858316312422452159926254649430083685186171942241764645513713542013221703137049658321015465406"
+        "8035397417906022589503023501937519773030945763173210852507299305089761582519159720757232455434770912461317"
+        "493580281734466552734375e-308"},
+    {0x1.fffffffffffffp-1022, chars_format::scientific, 766,
+        "4."
+        "4501477170144022721148195934182639518696390927032912960468522194496444440421538910330590478162701758282983"
+        "1782607924221374017287738918929105531441481564124348675997628212653465850710457376274429802596224490290377"
+        "9698114444614570510266311510031828794952795966823603998647925096578034214163701381261333311989876551545144"
+        "0315261253813266652951306000184917766328660755595837392240989947807556594098101021612198814605258742579179"
+        "0000716759993441450860872056815779154359230189103349648694206140521828924314457976051636509036065141403772"
+        "1744226256159024466852576737244643007551333245007965068671949137768847800530996396770975896584413789443379"
+        "6621993967316936280457084866613206797017728916080020698679408551343728867675409720757232455434770912461317"
+        "493580281734466552734375e-308"},
+    {0x1.fffffffffffffp-1021, chars_format::scientific, 765,
+        "8."
+        "9002954340288045442296391868365279037392781854065825920937044388992888880843077820661180956325403516565966"
+        "3565215848442748034575477837858211062882963128248697351995256425306931701420914752548859605192448980580755"
+        "9396228889229141020532623020063657589905591933647207997295850193156068428327402762522666623979753103090288"
+        "0630522507626533305902612000369835532657321511191674784481979895615113188196202043224397629210517485158358"
+        "0001433519986882901721744113631558308718460378206699297388412281043657848628915952103273018072130282807544"
+        "3488452512318048933705153474489286015102666490015930137343898275537695601061992793541951793168827578886759"
+        "3243987934633872560914169733226413594035457832160041397358817102687457735350819441514464910869541824922634"
+        "98716056346893310546875e-308"},
+    {0x1.fffffffffffffp-1020, chars_format::scientific, 765,
+        "1."
+        "7800590868057609088459278373673055807478556370813165184187408877798577776168615564132236191265080703313193"
+        "2713043169688549606915095567571642212576592625649739470399051285061386340284182950509771921038489796116151"
+        "1879245777845828204106524604012731517981118386729441599459170038631213685665480552504533324795950620618057"
+        "6126104501525306661180522400073967106531464302238334956896395979123022637639240408644879525842103497031671"
+        "6000286703997376580344348822726311661743692075641339859477682456208731569725783190420654603614426056561508"
+        "8697690502463609786741030694897857203020533298003186027468779655107539120212398558708390358633765515777351"
+        "8648797586926774512182833946645282718807091566432008279471763420537491547070163888302892982173908364984526"
+        "99743211269378662109375e-307"},
+    {0x1.fffffffffffffp-1019, chars_format::scientific, 764,
+        "3."
+        "5601181736115218176918556747346111614957112741626330368374817755597155552337231128264472382530161406626386"
+        "5426086339377099213830191135143284425153185251299478940798102570122772680568365901019543842076979592232302"
+        "3758491555691656408213049208025463035962236773458883198918340077262427371330961105009066649591901241236115"
+        "2252209003050613322361044800147934213062928604476669913792791958246045275278480817289759051684206994063343"
+        "2000573407994753160688697645452623323487384151282679718955364912417463139451566380841309207228852113123017"
+        "7395381004927219573482061389795714406041066596006372054937559310215078240424797117416780717267531031554703"
+        "7297595173853549024365667893290565437614183132864016558943526841074983094140327776605785964347816729969053"
+        "9948642253875732421875e-307"},
+    {0x1.fffffffffffffp-1018, chars_format::scientific, 763,
+        "7."
+        "1202363472230436353837113494692223229914225483252660736749635511194311104674462256528944765060322813252773"
+        "0852172678754198427660382270286568850306370502598957881596205140245545361136731802039087684153959184464604"
+        "7516983111383312816426098416050926071924473546917766397836680154524854742661922210018133299183802482472230"
+        "4504418006101226644722089600295868426125857208953339827585583916492090550556961634579518103368413988126686"
+        "4001146815989506321377395290905246646974768302565359437910729824834926278903132761682618414457704226246035"
+        "4790762009854439146964122779591428812082133192012744109875118620430156480849594234833561434535062063109407"
+        "4595190347707098048731335786581130875228366265728033117887053682149966188280655553211571928695633459938107"
+        "989728450775146484375e-307"},
+    {0x1.fffffffffffffp-1017, chars_format::scientific, 763,
+        "1."
+        "4240472694446087270767422698938444645982845096650532147349927102238862220934892451305788953012064562650554"
+        "6170434535750839685532076454057313770061274100519791576319241028049109072227346360407817536830791836892920"
+        "9503396622276662563285219683210185214384894709383553279567336030904970948532384442003626659836760496494446"
+        "0900883601220245328944417920059173685225171441790667965517116783298418110111392326915903620673682797625337"
+        "2800229363197901264275479058181049329394953660513071887582145964966985255780626552336523682891540845249207"
+        "0958152401970887829392824555918285762416426638402548821975023724086031296169918846966712286907012412621881"
+        "4919038069541419609746267157316226175045673253145606623577410736429993237656131110642314385739126691987621"
+        "597945690155029296875e-306"},
+    {0x1.fffffffffffffp-1016, chars_format::scientific, 762,
+        "2."
+        "8480945388892174541534845397876889291965690193301064294699854204477724441869784902611577906024129125301109"
+        "2340869071501679371064152908114627540122548201039583152638482056098218144454692720815635073661583673785841"
+        "9006793244553325126570439366420370428769789418767106559134672061809941897064768884007253319673520992988892"
+        "1801767202440490657888835840118347370450342883581335931034233566596836220222784653831807241347365595250674"
+        "5600458726395802528550958116362098658789907321026143775164291929933970511561253104673047365783081690498414"
+        "1916304803941775658785649111836571524832853276805097643950047448172062592339837693933424573814024825243762"
+        "9838076139082839219492534314632452350091346506291213247154821472859986475312262221284628771478253383975243"
+        "19589138031005859375e-306"},
+    {0x1.fffffffffffffp-1015, chars_format::scientific, 761,
+        "5."
+        "6961890777784349083069690795753778583931380386602128589399708408955448883739569805223155812048258250602218"
+        "4681738143003358742128305816229255080245096402079166305276964112196436288909385441631270147323167347571683"
+        "8013586489106650253140878732840740857539578837534213118269344123619883794129537768014506639347041985977784"
+        "3603534404880981315777671680236694740900685767162671862068467133193672440445569307663614482694731190501349"
+        "1200917452791605057101916232724197317579814642052287550328583859867941023122506209346094731566163380996828"
+        "3832609607883551317571298223673143049665706553610195287900094896344125184679675387866849147628049650487525"
+        "9676152278165678438985068629264904700182693012582426494309642945719972950624524442569257542956506767950486"
+        "3917827606201171875e-306"},
+    {0x1.fffffffffffffp-1014, chars_format::scientific, 761,
+        "1."
+        "1392378155556869816613938159150755716786276077320425717879941681791089776747913961044631162409651650120443"
+        "6936347628600671748425661163245851016049019280415833261055392822439287257781877088326254029464633469514336"
+        "7602717297821330050628175746568148171507915767506842623653868824723976758825907553602901327869408397195556"
+        "8720706880976196263155534336047338948180137153432534372413693426638734488089113861532722896538946238100269"
+        "8240183490558321011420383246544839463515962928410457510065716771973588204624501241869218946313232676199365"
+        "6766521921576710263514259644734628609933141310722039057580018979268825036935935077573369829525609930097505"
+        "1935230455633135687797013725852980940036538602516485298861928589143994590124904888513851508591301353590097"
+        "2783565521240234375e-305"},
+    {0x1.fffffffffffffp-1013, chars_format::scientific, 760,
+        "2."
+        "2784756311113739633227876318301511433572552154640851435759883363582179553495827922089262324819303300240887"
+        "3872695257201343496851322326491702032098038560831666522110785644878574515563754176652508058929266939028673"
+        "5205434595642660101256351493136296343015831535013685247307737649447953517651815107205802655738816794391113"
+        "7441413761952392526311068672094677896360274306865068744827386853277468976178227723065445793077892476200539"
+        "6480366981116642022840766493089678927031925856820915020131433543947176409249002483738437892626465352398731"
+        "3533043843153420527028519289469257219866282621444078115160037958537650073871870155146739659051219860195010"
+        "3870460911266271375594027451705961880073077205032970597723857178287989180249809777027703017182602707180194"
+        "556713104248046875e-305"},
+    {0x1.fffffffffffffp-1012, chars_format::scientific, 759,
+        "4."
+        "5569512622227479266455752636603022867145104309281702871519766727164359106991655844178524649638606600481774"
+        "7745390514402686993702644652983404064196077121663333044221571289757149031127508353305016117858533878057347"
+        "0410869191285320202512702986272592686031663070027370494615475298895907035303630214411605311477633588782227"
+        "4882827523904785052622137344189355792720548613730137489654773706554937952356455446130891586155784952401079"
+        "2960733962233284045681532986179357854063851713641830040262867087894352818498004967476875785252930704797462"
+        "7066087686306841054057038578938514439732565242888156230320075917075300147743740310293479318102439720390020"
+        "7740921822532542751188054903411923760146154410065941195447714356575978360499619554055406034365205414360389"
+        "11342620849609375e-305"},
+    {0x1.fffffffffffffp-1011, chars_format::scientific, 758,
+        "9."
+        "1139025244454958532911505273206045734290208618563405743039533454328718213983311688357049299277213200963549"
+        "5490781028805373987405289305966808128392154243326666088443142579514298062255016706610032235717067756114694"
+        "0821738382570640405025405972545185372063326140054740989230950597791814070607260428823210622955267177564454"
+        "9765655047809570105244274688378711585441097227460274979309547413109875904712910892261783172311569904802158"
+        "5921467924466568091363065972358715708127703427283660080525734175788705636996009934953751570505861409594925"
+        "4132175372613682108114077157877028879465130485776312460640151834150600295487480620586958636204879440780041"
+        "5481843645065085502376109806823847520292308820131882390895428713151956720999239108110812068730410828720778"
+        "2268524169921875e-305"},
+    {0x1.fffffffffffffp-1010, chars_format::scientific, 758,
+        "1."
+        "8227805048890991706582301054641209146858041723712681148607906690865743642796662337671409859855442640192709"
+        "9098156205761074797481057861193361625678430848665333217688628515902859612451003341322006447143413551222938"
+        "8164347676514128081005081194509037074412665228010948197846190119558362814121452085764642124591053435512890"
+        "9953131009561914021048854937675742317088219445492054995861909482621975180942582178452356634462313980960431"
+        "7184293584893313618272613194471743141625540685456732016105146835157741127399201986990750314101172281918985"
+        "0826435074522736421622815431575405775893026097155262492128030366830120059097496124117391727240975888156008"
+        "3096368729013017100475221961364769504058461764026376478179085742630391344199847821622162413746082165744155"
+        "6453704833984375e-304"},
+    {0x1.fffffffffffffp-1009, chars_format::scientific, 757,
+        "3."
+        "6455610097781983413164602109282418293716083447425362297215813381731487285593324675342819719710885280385419"
+        "8196312411522149594962115722386723251356861697330666435377257031805719224902006682644012894286827102445877"
+        "6328695353028256162010162389018074148825330456021896395692380239116725628242904171529284249182106871025781"
+        "9906262019123828042097709875351484634176438890984109991723818965243950361885164356904713268924627961920863"
+        "4368587169786627236545226388943486283251081370913464032210293670315482254798403973981500628202344563837970"
+        "1652870149045472843245630863150811551786052194310524984256060733660240118194992248234783454481951776312016"
+        "6192737458026034200950443922729539008116923528052752956358171485260782688399695643244324827492164331488311"
+        "290740966796875e-304"},
+    {0x1.fffffffffffffp-1008, chars_format::scientific, 756,
+        "7."
+        "2911220195563966826329204218564836587432166894850724594431626763462974571186649350685639439421770560770839"
+        "6392624823044299189924231444773446502713723394661332870754514063611438449804013365288025788573654204891755"
+        "2657390706056512324020324778036148297650660912043792791384760478233451256485808343058568498364213742051563"
+        "9812524038247656084195419750702969268352877781968219983447637930487900723770328713809426537849255923841726"
+        "8737174339573254473090452777886972566502162741826928064420587340630964509596807947963001256404689127675940"
+        "3305740298090945686491261726301623103572104388621049968512121467320480236389984496469566908963903552624033"
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+        "1.1972621413014755376696590364695917593214339111714816e+52"},
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+        "2.4519928653854219011474617066897239230902966500791943168e+55"},
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+        "3.138550867693340033468750984562846621555579712101368725504e+57"},
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+        "6.277101735386680066937501969125693243111159424202737451008e+57"},
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+        "1.2554203470773360133875003938251386486222318848405474902016e+58"},
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+        "2.5108406941546720267750007876502772972444637696810949804032e+58"},
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+        "5.0216813883093440535500015753005545944889275393621899608064e+58"},
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+        "2.00867255532373762142000063012022183779557101574487598432256e+59"},
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+        "4.01734511064747524284000126024044367559114203148975196864512e+59"},
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+        "8.03469022129495048568000252048088735118228406297950393729024e+59"},
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+        "1.606938044258990097136000504096177470236456812595900787458048e+60"},
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+        "3.213876088517980194272001008192354940472913625191801574916096e+60"},
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+        "6.427752177035960388544002016384709880945827250383603149832192e+60"},
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+        "1.2855504354071920777088004032769419761891654500767206299664384e+61"},
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+        "2.5711008708143841554176008065538839523783309001534412599328768e+61"},
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+        "5.1422017416287683108352016131077679047566618003068825198657536e+61"},
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+        "1.02844034832575366216704032262155358095133236006137650397315072e+62"},
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+        "2.05688069665150732433408064524310716190266472012275300794630144e+62"},
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+        "4.11376139330301464866816129048621432380532944024550601589260288e+62"},
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+        "8.22752278660602929733632258097242864761065888049101203178520576e+62"},
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+        "1.645504557321205859467264516194485729522131776098202406357041152e+63"},
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+        "3.291009114642411718934529032388971459044263552196404812714082304e+63"},
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+        "6.582018229284823437869058064777942918088527104392809625428164608e+63"},
+    {0x1.fffffffffffffp+212, chars_format::scientific, 64,
+        "1.3164036458569646875738116129555885836177054208785619250856329216e+64"},
+    {0x1.fffffffffffffp+213, chars_format::scientific, 64,
+        "2.6328072917139293751476232259111771672354108417571238501712658432e+64"},
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+        "5.2656145834278587502952464518223543344708216835142477003425316864e+64"},
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+        "1.05312291668557175005904929036447086689416433670284954006850633728e+65"},
+    {0x1.fffffffffffffp+216, chars_format::scientific, 65,
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+    {0x1.fffffffffffffp+1003, chars_format::scientific, 302,
+        "1."
+        "7144137714980275231793157933397708587462479355415820751086948089900709226610998035487132895733535592226072"
+        "2116007215942606278731240715201157062098220384137140321646286536485744710435953511551803661221035437711660"
+        "675605046179984043279465255100367878222272707180161212128389527493399906045198825861152768e+302"},
+    {0x1.fffffffffffffp+1004, chars_format::scientific, 302,
+        "3."
+        "4288275429960550463586315866795417174924958710831641502173896179801418453221996070974265791467071184452144"
+        "4232014431885212557462481430402314124196440768274280643292573072971489420871907023103607322442070875423321"
+        "351210092359968086558930510200735756444545414360322424256779054986799812090397651722305536e+302"},
+    {0x1.fffffffffffffp+1005, chars_format::scientific, 302,
+        "6."
+        "8576550859921100927172631733590834349849917421663283004347792359602836906443992141948531582934142368904288"
+        "8464028863770425114924962860804628248392881536548561286585146145942978841743814046207214644884141750846642"
+        "702420184719936173117861020401471512889090828720644848513558109973599624180795303444611072e+302"},
+    {0x1.fffffffffffffp+1006, chars_format::scientific, 303,
+        "1."
+        "3715310171984220185434526346718166869969983484332656600869558471920567381288798428389706316586828473780857"
+        "7692805772754085022984992572160925649678576307309712257317029229188595768348762809241442928976828350169328"
+        "5404840369439872346235722040802943025778181657441289697027116219947199248361590606889222144e+303"},
+    {0x1.fffffffffffffp+1007, chars_format::scientific, 303,
+        "2."
+        "7430620343968440370869052693436333739939966968665313201739116943841134762577596856779412633173656947561715"
+        "5385611545508170045969985144321851299357152614619424514634058458377191536697525618482885857953656700338657"
+        "0809680738879744692471444081605886051556363314882579394054232439894398496723181213778444288e+303"},
+    {0x1.fffffffffffffp+1008, chars_format::scientific, 303,
+        "5."
+        "4861240687936880741738105386872667479879933937330626403478233887682269525155193713558825266347313895123431"
+        "0771223091016340091939970288643702598714305229238849029268116916754383073395051236965771715907313400677314"
+        "1619361477759489384942888163211772103112726629765158788108464879788796993446362427556888576e+303"},
+    {0x1.fffffffffffffp+1009, chars_format::scientific, 304,
+        "1."
+        "0972248137587376148347621077374533495975986787466125280695646777536453905031038742711765053269462779024686"
+        "2154244618203268018387994057728740519742861045847769805853623383350876614679010247393154343181462680135462"
+        "83238722955518978769885776326423544206225453259530317576216929759577593986892724855113777152e+304"},
+    {0x1.fffffffffffffp+1010, chars_format::scientific, 304,
+        "2."
+        "1944496275174752296695242154749066991951973574932250561391293555072907810062077485423530106538925558049372"
+        "4308489236406536036775988115457481039485722091695539611707246766701753229358020494786308686362925360270925"
+        "66477445911037957539771552652847088412450906519060635152433859519155187973785449710227554304e+304"},
+    {0x1.fffffffffffffp+1011, chars_format::scientific, 304,
+        "4."
+        "3888992550349504593390484309498133983903947149864501122782587110145815620124154970847060213077851116098744"
+        "8616978472813072073551976230914962078971444183391079223414493533403506458716040989572617372725850720541851"
+        "32954891822075915079543105305694176824901813038121270304867719038310375947570899420455108608e+304"},
+    {0x1.fffffffffffffp+1012, chars_format::scientific, 304,
+        "8."
+        "7777985100699009186780968618996267967807894299729002245565174220291631240248309941694120426155702232197489"
+        "7233956945626144147103952461829924157942888366782158446828987066807012917432081979145234745451701441083702"
+        "65909783644151830159086210611388353649803626076242540609735438076620751895141798840910217216e+304"},
+    {0x1.fffffffffffffp+1013, chars_format::scientific, 305,
+        "1."
+        "7555597020139801837356193723799253593561578859945800449113034844058326248049661988338824085231140446439497"
+        "9446791389125228829420790492365984831588577673356431689365797413361402583486416395829046949090340288216740"
+        "531819567288303660318172421222776707299607252152485081219470876153241503790283597681820434432e+305"},
+    {0x1.fffffffffffffp+1014, chars_format::scientific, 305,
+        "3."
+        "5111194040279603674712387447598507187123157719891600898226069688116652496099323976677648170462280892878995"
+        "8893582778250457658841580984731969663177155346712863378731594826722805166972832791658093898180680576433481"
+        "063639134576607320636344842445553414599214504304970162438941752306483007580567195363640868864e+305"},
+    {0x1.fffffffffffffp+1015, chars_format::scientific, 305,
+        "7."
+        "0222388080559207349424774895197014374246315439783201796452139376233304992198647953355296340924561785757991"
+        "7787165556500915317683161969463939326354310693425726757463189653445610333945665583316187796361361152866962"
+        "127278269153214641272689684891106829198429008609940324877883504612966015161134390727281737728e+305"},
+    {0x1.fffffffffffffp+1016, chars_format::scientific, 306,
+        "1."
+        "4044477616111841469884954979039402874849263087956640359290427875246660998439729590671059268184912357151598"
+        "3557433111300183063536632393892787865270862138685145351492637930689122066789133116663237559272272230573392"
+        "4254556538306429282545379369782213658396858017219880649755767009225932030322268781454563475456e+306"},
+    {0x1.fffffffffffffp+1017, chars_format::scientific, 306,
+        "2."
+        "8088955232223682939769909958078805749698526175913280718580855750493321996879459181342118536369824714303196"
+        "7114866222600366127073264787785575730541724277370290702985275861378244133578266233326475118544544461146784"
+        "8509113076612858565090758739564427316793716034439761299511534018451864060644537562909126950912e+306"},
+    {0x1.fffffffffffffp+1018, chars_format::scientific, 306,
+        "5."
+        "6177910464447365879539819916157611499397052351826561437161711500986643993758918362684237072739649428606393"
+        "4229732445200732254146529575571151461083448554740581405970551722756488267156532466652950237089088922293569"
+        "7018226153225717130181517479128854633587432068879522599023068036903728121289075125818253901824e+306"},
+    {0x1.fffffffffffffp+1019, chars_format::scientific, 307,
+        "1."
+        "1235582092889473175907963983231522299879410470365312287432342300197328798751783672536847414547929885721278"
+        "6845946489040146450829305915114230292216689710948116281194110344551297653431306493330590047417817784458713"
+        "94036452306451434260363034958257709267174864137759045198046136073807456242578150251636507803648e+307"},
+    {0x1.fffffffffffffp+1020, chars_format::scientific, 307,
+        "2."
+        "2471164185778946351815927966463044599758820940730624574864684600394657597503567345073694829095859771442557"
+        "3691892978080292901658611830228460584433379421896232562388220689102595306862612986661180094835635568917427"
+        "88072904612902868520726069916515418534349728275518090396092272147614912485156300503273015607296e+307"},
+    {0x1.fffffffffffffp+1021, chars_format::scientific, 307,
+        "4."
+        "4942328371557892703631855932926089199517641881461249149729369200789315195007134690147389658191719542885114"
+        "7383785956160585803317223660456921168866758843792465124776441378205190613725225973322360189671271137834855"
+        "76145809225805737041452139833030837068699456551036180792184544295229824970312601006546031214592e+307"},
+    {0x1.fffffffffffffp+1022, chars_format::scientific, 307,
+        "8."
+        "9884656743115785407263711865852178399035283762922498299458738401578630390014269380294779316383439085770229"
+        "4767571912321171606634447320913842337733517687584930249552882756410381227450451946644720379342542275669711"
+        "52291618451611474082904279666061674137398913102072361584369088590459649940625202013092062429184e+307"},
+    {0x1.fffffffffffffp+1023, chars_format::scientific, 308,
+        "1."
+        "7976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045"
+        "8953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942"
+        "304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368e+308"},
+};
+
+inline constexpr double_to_chars_testcase double_fixed_precision_to_chars_test_cases_1[] = {
+    // Test special cases (zero, inf, nan) and an ordinary case. Also test negative signs.
+    {0.0, chars_format::fixed, 4, "0.0000"},
+    {-0.0, chars_format::fixed, 4, "-0.0000"},
+    {double_inf, chars_format::fixed, 4, "inf"},
+    {-double_inf, chars_format::fixed, 4, "-inf"},
+    {double_nan, chars_format::fixed, 4, "nan"},
+    {-double_nan, chars_format::fixed, 4, "-nan"},
+    {1.729, chars_format::fixed, 4, "1.7290"},
+    {-1.729, chars_format::fixed, 4, "-1.7290"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest Basic
+    {0x1.000000001869fp+211, chars_format::fixed, 0,
+        "3291009114715486435425664845573426149758869524108446525879746560"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest Zero
+    {0.0, chars_format::fixed, 4, "0.0000"},
+    {0.0, chars_format::fixed, 3, "0.000"},
+    {0.0, chars_format::fixed, 2, "0.00"},
+    {0.0, chars_format::fixed, 1, "0.0"},
+    {0.0, chars_format::fixed, 0, "0"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest MinMax
+    {0x0.0000000000001p-1022, chars_format::fixed, 1074,
+        "0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "000000000000000000000000000000000000000000000000000000049406564584124654417656879286822137"
+        "236505980261432476442558568250067550727020875186529983636163599237979656469544571773092665"
+        "671035593979639877479601078187812630071319031140452784581716784898210368871863605699873072"
+        "305000638740915356498438731247339727316961514003171538539807412623856559117102665855668676"
+        "818703956031062493194527159149245532930545654440112748012970999954193198940908041656332452"
+        "475714786901472678015935523861155013480352649347201937902681071074917033322268447533357208"
+        "324319360923828934583680601060115061698097530783422773183292479049825247307763759272478746"
+        "560847782037344696995336470179726777175851256605511991315048911014510378627381672509558373"
+        "89733598993664809941164205702637090279242767544565229087538682506419718265533447265625"},
+
+    {0x1.fffffffffffffp+1023, chars_format::fixed, 0,
+        "179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558"
+        "632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245"
+        "490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168"
+        "738177180919299881250404026184124858368"},
+
+    // Test more corner cases.
+    {0x0.fffffffffffffp-1022, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585"
+        "0720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504343"
+        "1208587738715835729182199302029437922422355981982750124204178896957131179108226104397197960400045489739193"
+        "8079198936081525613113376149842043271751033627391549782731594143828136275113838604094249464942286316695429"
+        "1050802018159266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412"
+        "2347901479236958520832159762106637540161373658304419360371477835530668283453563400507407304013560296804637"
+        "5918583163124224521599262546494300836851861719422417646455137135420132217031370496583210154654068035397417"
+        "9060225895030235019375197730309457631732108525072993050897615825191597207572324554347709124613174935802817"
+        "34466552734375"}, // max subnormal
+    {0x1p-1022, chars_format::fixed, 1022,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585"
+        "0720138309023271733240406421921598046233183055332741688720443481391819585428315901251102056406733973103581"
+        "1005152434161553460108856012385377718821130777993532002330479610147442583636071921565046942503734208375250"
+        "8066506166581589487204911799685916396485006359087701183048747997808877537499494515804516050509153998565824"
+        "7081864511353793580499211598108576605199243335211435239014879569960959128889160299264151106346631339366347"
+        "7586513029371762047325631781485664350872122828637642044846811407613911477062801689853244110024161447421618"
+        "5671661505401542850847167529019031613227788967297073731233340869889831750678388469260927739779728586596549"
+        "41091369095406136467568702398678315290680984617210924625396728515625"}, // min normal
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest RoundToEven
+    {0.125, chars_format::fixed, 3, "0.125"},
+    {0.125, chars_format::fixed, 2, "0.12"},
+    {0.375, chars_format::fixed, 3, "0.375"},
+    {0.375, chars_format::fixed, 2, "0.38"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest RoundToEvenInteger
+    {2.5, chars_format::fixed, 1, "2.5"},
+    {2.5, chars_format::fixed, 0, "2"},
+    {3.5, chars_format::fixed, 1, "3.5"},
+    {3.5, chars_format::fixed, 0, "4"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest NonRoundToEvenScenarios
+    {0.748046875, chars_format::fixed, 3, "0.748"},
+    {0.748046875, chars_format::fixed, 2, "0.75"},
+    {0.748046875, chars_format::fixed, 1, "0.7"}, // 0.75 would round to "0.8", but this is smaller
+
+    {0.2509765625, chars_format::fixed, 3, "0.251"},
+    {0.2509765625, chars_format::fixed, 2, "0.25"},
+    {0.2509765625, chars_format::fixed, 1, "0.3"}, // 0.25 would round to "0.2", but this is larger
+
+    {0x1.0000000000001p-2, chars_format::fixed, 54, "0.250000000000000055511151231257827021181583404541015625"},
+    {0x1.0000000000001p-2, chars_format::fixed, 3, "0.250"},
+    {0x1.0000000000001p-2, chars_format::fixed, 2, "0.25"},
+    {0x1.0000000000001p-2, chars_format::fixed, 1, "0.3"}, // 0.25 would round to "0.2", but this is larger (again)
+
+    // More rounding tests.
+    {9.5, chars_format::fixed, 1, "9.5"},
+    {9.5, chars_format::fixed, 0, "10"},
+    {10.5, chars_format::fixed, 1, "10.5"},
+    {10.5, chars_format::fixed, 0, "10"},
+
+    {1.241, chars_format::fixed, 3, "1.241"},
+    {1.241, chars_format::fixed, 1, "1.2"},
+    {1.251, chars_format::fixed, 3, "1.251"},
+    {1.251, chars_format::fixed, 1, "1.3"},
+    {1.261, chars_format::fixed, 3, "1.261"},
+    {1.261, chars_format::fixed, 1, "1.3"},
+    {1.341, chars_format::fixed, 3, "1.341"},
+    {1.341, chars_format::fixed, 1, "1.3"},
+    {1.351, chars_format::fixed, 3, "1.351"},
+    {1.351, chars_format::fixed, 1, "1.4"},
+    {1.361, chars_format::fixed, 3, "1.361"},
+    {1.361, chars_format::fixed, 1, "1.4"},
+
+    {2.41, chars_format::fixed, 2, "2.41"},
+    {2.41, chars_format::fixed, 0, "2"},
+    {2.51, chars_format::fixed, 2, "2.51"},
+    {2.51, chars_format::fixed, 0, "3"},
+    {2.61, chars_format::fixed, 2, "2.61"},
+    {2.61, chars_format::fixed, 0, "3"},
+    {3.41, chars_format::fixed, 2, "3.41"},
+    {3.41, chars_format::fixed, 0, "3"},
+    {3.51, chars_format::fixed, 2, "3.51"},
+    {3.51, chars_format::fixed, 0, "4"},
+    {3.61, chars_format::fixed, 2, "3.61"},
+    {3.61, chars_format::fixed, 0, "4"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest VaryingPrecision
+    {1729.142857142857, chars_format::fixed, 47, "1729.14285714285711037518922239542007446289062500000"},
+    {1729.142857142857, chars_format::fixed, 46, "1729.1428571428571103751892223954200744628906250000"},
+    {1729.142857142857, chars_format::fixed, 45, "1729.142857142857110375189222395420074462890625000"},
+    {1729.142857142857, chars_format::fixed, 44, "1729.14285714285711037518922239542007446289062500"},
+    {1729.142857142857, chars_format::fixed, 43, "1729.1428571428571103751892223954200744628906250"},
+    {1729.142857142857, chars_format::fixed, 42, "1729.142857142857110375189222395420074462890625"},
+    {1729.142857142857, chars_format::fixed, 41, "1729.14285714285711037518922239542007446289062"},
+    {1729.142857142857, chars_format::fixed, 40, "1729.1428571428571103751892223954200744628906"},
+    {1729.142857142857, chars_format::fixed, 39, "1729.142857142857110375189222395420074462891"},
+    {1729.142857142857, chars_format::fixed, 38, "1729.14285714285711037518922239542007446289"},
+    {1729.142857142857, chars_format::fixed, 37, "1729.1428571428571103751892223954200744629"},
+    {1729.142857142857, chars_format::fixed, 36, "1729.142857142857110375189222395420074463"},
+    {1729.142857142857, chars_format::fixed, 35, "1729.14285714285711037518922239542007446"},
+    {1729.142857142857, chars_format::fixed, 34, "1729.1428571428571103751892223954200745"},
+    {1729.142857142857, chars_format::fixed, 33, "1729.142857142857110375189222395420074"},
+    {1729.142857142857, chars_format::fixed, 32, "1729.14285714285711037518922239542007"},
+    {1729.142857142857, chars_format::fixed, 31, "1729.1428571428571103751892223954201"},
+    {1729.142857142857, chars_format::fixed, 30, "1729.142857142857110375189222395420"},
+    {1729.142857142857, chars_format::fixed, 29, "1729.14285714285711037518922239542"},
+    {1729.142857142857, chars_format::fixed, 28, "1729.1428571428571103751892223954"},
+    {1729.142857142857, chars_format::fixed, 27, "1729.142857142857110375189222395"},
+    {1729.142857142857, chars_format::fixed, 26, "1729.14285714285711037518922240"},
+    {1729.142857142857, chars_format::fixed, 25, "1729.1428571428571103751892224"},
+    {1729.142857142857, chars_format::fixed, 24, "1729.142857142857110375189222"},
+    {1729.142857142857, chars_format::fixed, 23, "1729.14285714285711037518922"},
+    {1729.142857142857, chars_format::fixed, 22, "1729.1428571428571103751892"},
+    {1729.142857142857, chars_format::fixed, 21, "1729.142857142857110375189"},
+    {1729.142857142857, chars_format::fixed, 20, "1729.14285714285711037519"},
+    {1729.142857142857, chars_format::fixed, 19, "1729.1428571428571103752"},
+    {1729.142857142857, chars_format::fixed, 18, "1729.142857142857110375"},
+    {1729.142857142857, chars_format::fixed, 17, "1729.14285714285711038"},
+    {1729.142857142857, chars_format::fixed, 16, "1729.1428571428571104"},
+    {1729.142857142857, chars_format::fixed, 15, "1729.142857142857110"},
+    {1729.142857142857, chars_format::fixed, 14, "1729.14285714285711"},
+    {1729.142857142857, chars_format::fixed, 13, "1729.1428571428571"},
+    {1729.142857142857, chars_format::fixed, 12, "1729.142857142857"},
+    {1729.142857142857, chars_format::fixed, 11, "1729.14285714286"},
+    {1729.142857142857, chars_format::fixed, 10, "1729.1428571429"},
+    {1729.142857142857, chars_format::fixed, 9, "1729.142857143"},
+    {1729.142857142857, chars_format::fixed, 8, "1729.14285714"},
+    {1729.142857142857, chars_format::fixed, 7, "1729.1428571"},
+    {1729.142857142857, chars_format::fixed, 6, "1729.142857"},
+    {1729.142857142857, chars_format::fixed, 5, "1729.14286"},
+    {1729.142857142857, chars_format::fixed, 4, "1729.1429"},
+    {1729.142857142857, chars_format::fixed, 3, "1729.143"},
+    {1729.142857142857, chars_format::fixed, 2, "1729.14"},
+    {1729.142857142857, chars_format::fixed, 1, "1729.1"},
+    {1729.142857142857, chars_format::fixed, 0, "1729"},
+
+    // Negative precision requests 6 digits of precision.
+    {1729.142857142857, chars_format::fixed, -1, "1729.142857"},
+    {1729.142857142857, chars_format::fixed, -2, "1729.142857"},
+    {1729.142857142857, chars_format::fixed, -3, "1729.142857"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest Carrying
+    {0.0009, chars_format::fixed, 4, "0.0009"},
+    {0.0009, chars_format::fixed, 3, "0.001"},
+    {0.0029, chars_format::fixed, 4, "0.0029"},
+    {0.0029, chars_format::fixed, 3, "0.003"},
+    {0.0099, chars_format::fixed, 4, "0.0099"},
+    {0.0099, chars_format::fixed, 3, "0.010"},
+    {0.0299, chars_format::fixed, 4, "0.0299"},
+    {0.0299, chars_format::fixed, 3, "0.030"},
+    {0.0999, chars_format::fixed, 4, "0.0999"},
+    {0.0999, chars_format::fixed, 3, "0.100"},
+    {0.2999, chars_format::fixed, 4, "0.2999"},
+    {0.2999, chars_format::fixed, 3, "0.300"},
+    {0.9999, chars_format::fixed, 4, "0.9999"},
+    {0.9999, chars_format::fixed, 3, "1.000"},
+    {2.9999, chars_format::fixed, 4, "2.9999"},
+    {2.9999, chars_format::fixed, 3, "3.000"},
+    {9.9999, chars_format::fixed, 4, "9.9999"},
+    {9.9999, chars_format::fixed, 3, "10.000"},
+    {29.9999, chars_format::fixed, 4, "29.9999"},
+    {29.9999, chars_format::fixed, 3, "30.000"},
+    {99.9999, chars_format::fixed, 4, "99.9999"},
+    {99.9999, chars_format::fixed, 3, "100.000"},
+    {299.9999, chars_format::fixed, 4, "299.9999"},
+    {299.9999, chars_format::fixed, 3, "300.000"},
+
+    {0.09, chars_format::fixed, 2, "0.09"},
+    {0.09, chars_format::fixed, 1, "0.1"},
+    {0.29, chars_format::fixed, 2, "0.29"},
+    {0.29, chars_format::fixed, 1, "0.3"},
+    {0.99, chars_format::fixed, 2, "0.99"},
+    {0.99, chars_format::fixed, 1, "1.0"},
+    {2.99, chars_format::fixed, 2, "2.99"},
+    {2.99, chars_format::fixed, 1, "3.0"},
+    {9.99, chars_format::fixed, 2, "9.99"},
+    {9.99, chars_format::fixed, 1, "10.0"},
+    {29.99, chars_format::fixed, 2, "29.99"},
+    {29.99, chars_format::fixed, 1, "30.0"},
+    {99.99, chars_format::fixed, 2, "99.99"},
+    {99.99, chars_format::fixed, 1, "100.0"},
+    {299.99, chars_format::fixed, 2, "299.99"},
+    {299.99, chars_format::fixed, 1, "300.0"},
+
+    {0.9, chars_format::fixed, 1, "0.9"},
+    {0.9, chars_format::fixed, 0, "1"},
+    {2.9, chars_format::fixed, 1, "2.9"},
+    {2.9, chars_format::fixed, 0, "3"},
+    {9.9, chars_format::fixed, 1, "9.9"},
+    {9.9, chars_format::fixed, 0, "10"},
+    {29.9, chars_format::fixed, 1, "29.9"},
+    {29.9, chars_format::fixed, 0, "30"},
+    {99.9, chars_format::fixed, 1, "99.9"},
+    {99.9, chars_format::fixed, 0, "100"},
+    {299.9, chars_format::fixed, 1, "299.9"},
+    {299.9, chars_format::fixed, 0, "300"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest RoundingResultZero
+    {0.004, chars_format::fixed, 3, "0.004"},
+    {0.004, chars_format::fixed, 2, "0.00"},
+    {0.4, chars_format::fixed, 1, "0.4"},
+    {0.4, chars_format::fixed, 0, "0"},
+    {0.5, chars_format::fixed, 1, "0.5"},
+    {0.5, chars_format::fixed, 0, "0"},
+
+    // Ryu Printf d2fixed_test.cc D2fixedTest Regression
+    {7.018232e-82, chars_format::fixed, 6, "0.000000"},
+};
+
+inline constexpr double_to_chars_testcase double_fixed_precision_to_chars_test_cases_2[] = {
+    // Ryu Printf d2fixed_test.cc D2fixedTest AllPowersOfTen
+    // These values test every power of ten that's within the range of doubles.
+    {1e-323, chars_format::fixed, 1073,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000098813129168249308835313758573644274473011960522864952885117136500135101454041750373059967272327198475"
+        "9593129390891435461853313420711879592797549592021563756252601426380622809055691634335697964207377437272113"
+        "9974614461000127748183071299687746249467945463392302800634307707961482524771311823420533171133735363740791"
+        "2062124986389054318298491065861091308880225496025941999908386397881816083312664904951429573802945356031871"
+        "0477223100269607052986944038758053621421498340666445368950667144166486387218476578691673612021202301233961"
+        "9506156684554636658495809965049461552751854495749312169556407468939399067294035945355435170251321102398263"
+        "0097822029020757254763345019116747794671979873296198823284114052741805584855350891304581750773650128394365"
+        "3106689453125"},
+    {1e-322, chars_format::fixed, 1072,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000988131291682493088353137585736442744730119605228649528851171365001351014540417503730599672723271984759"
+        "5931293908914354618533134207118795927975495920215637562526014263806228090556916343356979642073774372721139"
+        "9746144610001277481830712996877462494679454633923028006343077079614825247713118234205331711337353637407912"
+        "0621249863890543182984910658610913088802254960259419999083863978818160833126649049514295738029453560318710"
+        "4772231002696070529869440387580536214214983406664453689506671441664863872184765786916736120212023012339619"
+        "5061566845546366584958099650494615527518544957493121695564074689393990672940359453554351702513211023982630"
+        "0978220290207572547633450191167477946719798732961988232841140527418055848553508913045817507736501283943653"
+        "106689453125"},
+    {1e-321, chars_format::fixed, 1073,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0009980126045993180192366689615938071721774208012809360241396830786513645246858216787679056694505047046071"
+        "8906068480034981647184655491899838872552508794177939381512744064442903714624855067905494384945121164483513"
+        "7436060561012902566490201268462371196262491802622582864065078504109735001902494165473850284507271737819911"
+        "8274623625294486148147597651970222196902775098620141990747026186063424414579155400094386954097480959218975"
+        "8199533127230312351681347914563415763571332407310982264017381560815125109066134447859034814141432424630157"
+        "0121825140018302508076806469995616827937304070680529125197154362879305796697630480898952195383431342224563"
+        "9880024931096482731097846930791527261869967202916081151695519326922364070390440021762756828138662967830896"
+        "3775634765625"},
+    {1e-320, chars_format::fixed, 1071,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0099998886718268300541337523676528005766688104049139332319738542138136722671490251377536686879595124857670"
+        "8246943582132687395553181760422147911120187125822521327632643497190282764359933947726339777865966519379365"
+        "4309834532129281161268155283999204461560808953010434241919400457020315068567565301579569187340188105680700"
+        "6870486225722970118072958651424404586788201978253303907287034656397876312416883810846728688580700304253500"
+        "2949777472842337622787367223150264878556320754442713378075149896484223865098297635973695365456728848769494"
+        "0230564769292298397759684630055091384876749698303915591084358566671856101564376699700392294336955627042165"
+        "8995893369006341820505159346148768208043631775753209163523421374707251873615102000236731782933929935097694"
+        "39697265625"},
+    {1e-319, chars_format::fixed, 1070,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0999988867182683005413375236765280057666881040491393323197385421381367226714902513775366868795951248576708"
+        "2469435821326873955531817604221479111201871258225213276326434971902827643599339477263397778659665193793654"
+        "3098345321292811612681552839992044615608089530104342419194004570203150685675653015795691873401881056807006"
+        "8704862257229701180729586514244045867882019782533039072870346563978763124168838108467286885807003042535002"
+        "9497774728423376227873672231502648785563207544427133780751498964842238650982976359736953654567288487694940"
+        "2305647692922983977596846300550913848767496983039155910843585666718561015643766997003922943369556270421658"
+        "9958933690063418205051593461487682080436317757532091635234213747072518736151020002367317829339299350976943"
+        "9697265625"},
+    {1e-318, chars_format::fixed, 1073,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "9999987484955998303442587681411374220943283416874456096926739330950172402250479179504041747926784812965558"
+        "4287487604160175017171489462926670704816262174273696519516951145408899245049086406969675750804029375208657"
+        "0958067673928243874998599699608192405548840764435726992574353409992989381527841981377451905152545931810859"
+        "9110747558686066125594356208301549987700423321356332728611852037669447325001045989624298431872975781381900"
+        "5454970384503369331723666353784541477053573784937783176465656792588872897048240176061210157694087178183364"
+        "2562633613784476434464272970558600040426824326140871277992264136125009223731705915394664603946883806614852"
+        "9687158929654939305279279633993568599035157448617115175626251523466992946365550914977760044166643638163805"
+        "0079345703125"},
+    {1e-317, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010"
+        "0000023069253735408389129784751602675844543686685345266696720985206474225156972857665977069218756620453298"
+        "2264570127938903364494864760334526437358946130769310829548413593659926664074401521200304454351359907994741"
+        "9542598430782630372260603945613543429690325839445724126694995661872117602435387548905318808226062363719785"
+        "9200663066444242733391298681807136840324571457602240285981099973517197374979457253670128679434175847866812"
+        "0265538495438103896717079595982495202667985360377499818082568642138458551310116628649611994972675233684585"
+        "4885571164676719332386444653160192733396025005032681034257252564659190838258113071979798794845819719745924"
+        "2018322340080528934937813868610807682359544296115449991188686313782637840938535486734473067826911574229598"
+        "04534912109375"},
+    {1e-316, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000099"
+        "9999983659714433460619209563119592647759254336952145504584997059223491913816093472283838042269385386536792"
+        "3662877802160444990315364051565565391595587327639198904852632370647709618104786126163799632995155486767134"
+        "5489448155325984352148361206916068673233394735976484265364187348817469712425595930501855154426285227845881"
+        "1851318198469791538166759153418640131045150835957547860040033740467433541512910274322712859834395088588442"
+        "6462327203707021334703435862929817973126107752108884758449018560968369545054974839766935919673746583760950"
+        "0090319935380601677624921618978273452080613810953529918681506974243410714346040856409400022829894441463584"
+        "4938668328253396212469776138316207336915493277914002853676578005971864447246977639083276301334990421310067"
+        "17681884765625"},
+    {1e-315, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999"
+        "9999984816838086980155348601833786944004252887462239343279298267939669340813115785463940012644762356165637"
+        "6018472107941603095933610646723473305152197664424334682905225846048030394631398713141543276262621023579516"
+        "4856403244760035143758219018692306106535865554853296854593335050116920911412927040149351300963455324069998"
+        "6606369464281496859115328132978038273771846603614391600262917001497059540098100100654272959048368919932233"
+        "0339106687474623926514774687435260163393325032088515637916186325933425031377463265706869614769269289460443"
+        "0162434380637971763992931137356926849933919853159267441149680945843205744401462482127152983675926068233239"
+        "4533416326065098006842778911837195061162902589084326771691951138831352849752802727789635639510379405692219"
+        "73419189453125"},
+    {1e-314, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009999"
+        "9999996388074622175516738988975729906454238392563177730222310355101443610783338917264959716398532052454089"
+        "9574415165753184152116076598302552440718301032275692463431160600051238159897524582918979708937276391703335"
+        "8525954139100543059856797136454680439560573743621422746884812063111432901286238136624312766335156286311173"
+        "4156882122398550068601017928572019701038804280182829002491749611793319525949998363969873951188107233370136"
+        "9106901525150649844628162932489682066065497831884824432587863975583979894602347525106206565724496346455373"
+        "0883578833211672627673026321143460828466980275216642665831420661841156044955678739304682592136242335929789"
+        "0480896304182115950572806647047072303636995700787565951845682467426236874811053614853229021264269249513745"
+        "30792236328125"},
+    {1e-313, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000"
+        "0000013287310805879821807546636585886679620431612038734699546109582686175384116193524783693968956688140137"
+        "5540716352977559252087422693381464203581785118767706512437906713702693003503091646357646071476452635669415"
+        "5246848621505494472659507014390677520339710167910378869165274485095070275248037277953394248918430544982129"
+        "7599883717180027845159424818650742664828155549841261024871689316874103301156316092174454298782545011717304"
+        "6307626801641301972775101344275847471365727489181467010353973327923042139632713540407902463255564615170711"
+        "8588866674394044605978168193959339061045730000041082743092410352881259983203805365724543506488083910497021"
+        "9857874056331538133109738980029096933705946944523758930098881700633271540538211594184581088029517559334635"
+        "73455810546875"},
+    {1e-312, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999999"
+        "9999984653414306424254822495727998400384494798179603049566133420122111551188980872622277349738658390603661"
+        "6017469443438439328094256802746822646621526799644719490000164997455995821447379012072913768453460200785984"
+        "2506564523554753104320463194375155829195183484015334490701283289008478965323405044403142732483702404210110"
+        "7905649692216696974146511587715789684961217254373697248854313571918308886594163564317398627121032083125239"
+        "7360433366008609148270597384621394281525027380815002050113732562980691815499420536041514214523842699856175"
+        "6629431717108491072037966992019198281329518256786859176589492325403501231096999739212282309503857451372825"
+        "3432007519784245448952372271615847645051499635293291066062645927220007028099089604888938254134700400754809"
+        "37957763671875"},
+    {1e-311, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009999999"
+        "9999994753836816616511477927917844470256657499736814793090661876925865714541989788848333087337492396834329"
+        "9564388520721546473722538158536045855411592384479540534380552114130892428057327572232684630845668163768013"
+        "5027566927047722665479238893283177666153753035241799107964294452027013440391018179162227081537627087712294"
+        "7149684401750551218912852475949533812932510787775885488405715316005812990910633000601130631914738865300203"
+        "9320168310490502062186389904351023247382521319149688554563326346056647735821920228452652563270230450412699"
+        "5553552197916865708123384867766175142422964311492560020229534457444110911911051310155975850415556167325647"
+        "9466808241373590371668740244833598142522966162877208895552630351312778658273922385846255167507479200139641"
+        "76177978515625"},
+    {1e-310, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000099999999"
+        "9999996944932750289769196936057731524703811503348409363383061327826907212970624909358517403358560131942537"
+        "5440449902661182468152038295716398350514698640806187221931821854499235685101121539494695290560370356316192"
+        "0262976500977290528883924582675649786271503084114142479960098374250875666295837703332537400943138558993342"
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+        "4975818241508187016346769106956959939911012930425211247788042456200658152732723551495964903285489125103006"
+        "29092601392444835652130948564826004622078785676810855105701264700211200"},
+    {1e+283, chars_format::fixed, 0,
+        "9999999999999999553953517735361344274271821018911312812290573026184540102343798495987494338396687059809772"
+        "7966329076780975705558651098687533761031476684077544035813096345547962581760843838922021129763927973084950"
+        "24959839786965342632596166187964530344229899589832462449290116390191104"},
+    {1e+284, chars_format::fixed, 0,
+        "1000000000000000079214382508457676541256819191699710934083899342334435758975171027725445345572057645297521"
+        "6283329441806240683821311505209883878195732087635685354312082149188175289466707052058222577470946921779713"
+        "0505057184069381648545374773244373557467226310750742042216461653692645376"},
+    {1e+285, chars_format::fixed, 0,
+        "9999999999999999801591579205204428501931095198528472118000257105616503599825380852240886161861464938442861"
+        "4939722145037261932089543889369794765216645522533405937274641374814720644342089175254062058753036222027386"
+        "3006901551095990707698442841525909542472844588688081080376132618600579072"},
+    {1e+286, chars_format::fixed, 0,
+        "1000000000000000032988611034086967485427088011504507863684758314173802572778608987891478871858632441286011"
+        "7381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791"
+        "654301923722148311225012721166820834263125344653917287293299907083743789056"},
+    {1e+287, chars_format::fixed, 0,
+        "1000000000000000075252173524940187193614270804825836385192544397063524343015465710025391076396621199239392"
+        "2091755152714140104196817220558967702128769386220391563888697428719907160465407126676909922607121189796634"
+        "0736882502910990345434353553680702253338428636675464684849307718019341877248"},
+    {1e+288, chars_format::fixed, 0,
+        "1000000000000000007630473539575035660514778335511710750780086664439969510636494954611131549135839186513983"
+        "4555553952208956878605448095849998297252605948732710873996264866061464425509888400169173946264495363952086"
+        "20267012778077787723395914064607119962069483324573977857832138825282954985472"},
+    {1e+289, chars_format::fixed, 0,
+        "1000000000000000061727833527867156886994372310963011258310052850538813376539671558942539170944464796694310"
+        "4584514912613103459078543395617173821153536698722855425910210916188218613474303381375362727338596024627724"
+        "499484625789034803081540112423670420191213257583185130503608895092113260150784"},
+    {1e+290, chars_format::fixed, 0,
+        "1000000000000000061727833527867156886994372310963011258310052850538813376539671558942539170944464796694310"
+        "4584514912613103459078543395617173821153536698722855425910210916188218613474303381375362727338596024627724"
+        "4994846257890348030815401124236704201912132575831851305036088950921132601507840"},
+    {1e+291, chars_format::fixed, 0,
+        "9999999999999999578609023503462841321535518780965142838525177732290331540055724786262365370719036251480826"
+        "1289098686371420245702004200641968152637496587417778862354344999448505725826266174594802676763227561304989"
+        "6960078961318150545418464661067991669581788285529005480705688196068853638234112"},
+    {1e+292, chars_format::fixed, 0,
+        "1000000000000000013256598978357416268068656108958646003563203147794249272690425321461597941803936249972737"
+        "4638565892090988122974650007025784551738302746731685907395315255274646861058187558214617579496201832662352"
+        "585538835573636597522107561710941518560028749376834095178551288964115055725510656"},
+    {1e+293, chars_format::fixed, 0,
+        "9999999999999999246234843735396048506044893395792352520261065484899034827946607729250196942326840502532897"
+        "0231162545648343655275306678872441733790178059478330735395060467469727994972900530063978805843953102113868"
+        "000379620369084502134308975505229555772913629423636305841602377586326247764393984"},
+    {1e+294, chars_format::fixed, 0,
+        "1000000000000000066436467741248103118547156170586292454485461107376856746627884050583544890346687569804406"
+        "1207835674606680377442921610508908778753873711201997607708800780391251297994726061339549398843285746132932"
+        "05683935969567348590731356020719265634967118123751637393518591968740451429495341056"},
+    {1e+295, chars_format::fixed, 0,
+        "9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362"
+        "6970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049"
+        "02758521100414464490983962613190835886243290260424727924570510530141380583845003264"},
+    {1e+296, chars_format::fixed, 0,
+        "9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362"
+        "6970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049"
+        "027585211004144644909839626131908358862432902604247279245705105301413805838450032640"},
+    {1e+297, chars_format::fixed, 0,
+        "1000000000000000017652801462756379714374878780719864776839443139119744823869255243069012222883470359078822"
+        "0728292194112285349344027126247056154504923279794565007954563392017619494511608074472945276562227436175920"
+        "48849967890105831362861792425329827928397252374398383022243308510390698430058459037696"},
+    {1e+298, chars_format::fixed, 0,
+        "9999999999999999595662034753429788238255624467393741467120915117996487670031669885400803025551745174706847"
+        "8782311196631452228634829961492223321433823010024592147588202691169230215270582854596864146833859136224555"
+        "51313826420028155008403585629126369847605750170289266545852965785882018353801250996224"},
+    {1e+299, chars_format::fixed, 0,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "4508111903896764088007465274278014249457925878882005684283811566947219638686545940054016"},
+    {1e+300, chars_format::fixed, 0,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "45081119038967640880074652742780142494579258788820056842838115669472196386865459400540160"},
+    {1e+301, chars_format::fixed, 0,
+        "1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704"
+        "4438328838781769425232353604305756447921847867069828483872009265758037378302337947880900593689532349707999"
+        "450811190389676408800746527427801424945792587888200568428381156694721963868654594005401600"},
+    {1e+302, chars_format::fixed, 0,
+        "1000000000000000076297030790848949253473468551506568117016017342062113802881257944841421889646917840766397"
+        "4757713854876137221038784479993829181561135051983075016764985648898162653636809541460731423515105837345898"
+        "6890825155659063617715863205282622390509284183439858617103083735673849899204570498157510656"},
+    {1e+303, chars_format::fixed, 0,
+        "1000000000000000000161765076786456438212668646231659438295495017101117499225738747865260243034213915253779"
+        "7735681803374160274458205677791996433915416060260686111507461222849761772566500442005272768073270676904621"
+        "12661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568"},
+    {1e+304, chars_format::fixed, 0,
+        "9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856"
+        "1180561621725787171937426360305302357988408668827749873014416820110410677102531624409058437198025485515990"
+        "76639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744"},
+    {1e+305, chars_format::fixed, 0,
+        "9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856"
+        "1180561621725787171937426360305302357988408668827749873014416820110410677102531624409058437198025485515990"
+        "766396825508218326595491122696079498053460349186625724064076043808459598620749043481381437440"},
+    {1e+306, chars_format::fixed, 0,
+        "1000000000000000017216064596736454828831087825013238982328892017892380671244575047987920451875459594568606"
+        "1388616982910603110492255329485206969388057114406501226285146694284603569926249680283295506892241752843467"
+        "30060716088829214255439694630119794546505512415617982143262670862918816362862119154749127262208"},
+    {1e+307, chars_format::fixed, 0,
+        "9999999999999999860310597602564577717002641838126363875249660735883565852672743849064846414228960666786379"
+        "2803926546153933531728502521033362759523706153970107306916646893751785690398510731463396416232660711267200"
+        "11020169553304018596457812688561947201171488461172921822139066929851282122002676667750021070848"},
+    {1e+308, chars_format::fixed, 0,
+        "1000000000000000010979063629440455417404923096773118463368106829031575854049114915371633289784946888990612"
+        "4966972117251561159028374314008832830700919814604603127166450293302718569748969958855904333838446616500117"
+        "8426897626212945177628091195786707458122783970171784415105291802893207873272974885715430223118336"},
+};
+
+inline constexpr double_to_chars_testcase double_fixed_precision_to_chars_test_cases_3[] = {
+    // Ryu Printf d2fixed_test.cc D2fixedTest AllBinaryExponents
+    // These values test every binary exponent.
+    // The mantissas were randomly generated.
+    {0x0.63b831e8bd9d7p-1022, chars_format::fixed, 1074,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008667315560"
+        "1518373204745615934992065170006880827787289636461039456117181014435225731420739682086431846196084055971776"
+        "1976781401452617612090003075542930260777812518669659241729724010681746641686623499848468215594968202107915"
+        "3402945471922988971873909012440740220527800911244244822910902773084448896950002963160859062629660988288537"
+        "4947604962348974323036144310657614326754120115556509383797380330234783520222245524583876671362471849408043"
+        "1858617260899963028423305531253945552260335123939000593240656910669298632181747412649714974019858835628576"
+        "1402581880926947783051518340651609793980053160313425027619711896255545853478748493923212623215309262429188"
+        "9535798750202922731324119623206905408779063259071595105183391812893811664489504206776437911230459576472640"
+        "03753662109375"},
+    {0x1.8777195166b0cp-1022, chars_format::fixed, 1072,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000034024962888"
+        "5488918707803802237219634159360572672157684890228809310363407096641170467659879771805264411927667980233377"
+        "8493381613983963619886353435618596864780020416582962791672696335498871803986814670850483660459156676370951"
+        "5096631215158510441977866477856881896988317751492854297037574001592689593245951090014597401089987064349011"
+        "8898178199420014167358923990328782986564433565017977882465941632972037475759286148645435617069627150190560"
+        "6610044637601532768006545677482036919081933078680182749619038785085197654630878239258803610922679880731846"
+        "1295595610061523269781283221357431760026778081133972233612002223605221826818897235077493324279732240457324"
+        "0208707312500506083305050530743859909422095574730572935613200283098897446182155845928463122618268243968486"
+        "785888671875"},
+    {0x1.4668b84fe57a0p-1021, chars_format::fixed, 1068,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000056740958740"
+        "6416315113843845367765611463402272605773579309805044238876264896175716378374414880313837549557854086594144"
+        "6517571068268270820532248191376149517571648221869547136333897392941241920946002959571014115138922292227756"
+        "5675579700156979183315496460915138087093250268282674126774708694126428169237269531699329932826961970700281"
+        "7860044551711084995833922394577051992453091701226019440181486036346841321732890759392314160217956773831481"
+        "0836998109083129295391451373564751392901299926267367714488145730269066445855381488848672338113942395343914"
+        "7931259731375390972529039085122338240869687761572122993383754664276573025666127187344547915597384296829871"
+        "1175582031872758195259747569288096497941384426647703960591649037179391408883266656459909427212551236152648"
+        "92578125"},
+    {0x1.befe59a615135p-1020, chars_format::fixed, 1072,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000155405261736"
+        "2235237599344524566268329346499410781820240377373211399724292118817533439328423661067387776003211400451369"
+        "3088093284719809466733351558863675884965219358948864762862301475919926006238764851665875890220244143133239"
+        "4990914215952953745660507019834777919259824309540394759202512511945735293837981431982027834358977473029612"
+        "0303664088965600921426179216076245193704452662458429835783277758594438863220080552115251534233085611706230"
+        "8503464635136074518967164258938058608025448494327947396239370394992669778837860314635821269578123701586483"
+        "9016649103853253096649589094048656135137787361348031132374178952614572001907211566747518775736907525882271"
+        "0974186182997578768175923453881771250830539545867001930118621195145977916950326414013971998429042287170886"
+        "993408203125"},
+    {0x1.1e3d1ff2f0c7dp-1019, chars_format::fixed, 1071,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000199032000513"
+        "5142880561598924319312704477072269270245936137839955953465230545195415127755767083901447533947828678376962"
+        "8840827353272482512734186549366506777424260696503583584763933654973123255607415124268905380654726960778878"
+        "0455364488415004387840662750774569999550709914737717510587715348152633060357249935862626075624081617450315"
+        "4885783858040748854022822093131458054271092923292182143582852711297479202477529680286154546026438265660119"
+        "0666964359310825902834425266702229494789747194864674154539719905344544705996332452876246842805615529643436"
+        "3330985188230759038449117763080644432854364707566853651485305297515523425163520740729706771939538840583142"
+        "0311524001253621714021938613841338246896203505202451193812218773931269549326908419040194075932959094643592"
+        "83447265625"},
+    {0x1.6f434a1f8b19bp-1018, chars_format::fixed, 1070,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000510741853904"
+        "6846927047373682830132718075006256443666199351873286782041441258279676361749462207484160512079462800015135"
+        "1247641526009378027445855026174588417177058971036936098000778820888042031017906554373258977780010263225403"
+        "4985134368614288894180981269713098266814859393907435942503999009239804035089734298703368406224788919100457"
+        "8703872406975692839527795367059563095996889887433505152749668146313379417615714580759187210921661443825061"
+        "5079726743650989704965620642901239809189450397279529801654706466234792028552787228839089551760441918109416"
+        "4246004056408218871243893690629186700027052396055033266400221089830267330844275401596778964865771996400585"
+        "2935700696823519264465123996032196818637410241732060994427104056094504278256324125706555605574976652860641"
+        "4794921875"},
+    {0x1.587345c18153ep-1017, chars_format::fixed, 1068,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000958034150713"
+        "4764786508271836926643404057427002697780971266720840479203611958030287584788324659120693742922007657201247"
+        "5701432533443920920943404653989371931593878000743154963499391621521760536226285826940742684233420125807325"
+        "1475122129361059576300349579506194683866694625320913445655672698919325929161890237571835547216240424390568"
+        "4503604058791100485208980042190187445440799433710816373805294721006156102426371505496796959141102703635606"
+        "8282898610242996821028731917836326909139019066634183567364278468611980916064135979863051465895296219949754"
+        "3645034872914477180174891107535697767424819637337145925449261230552011300809574685296849175758943122326736"
+        "0016445450314712551946974418885474268936771312658360117220892077307970715813190132337240356719121336936950"
+        "68359375"},
+    {0x1.f1b6b87277fdep-1016, chars_format::fixed, 1067,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002768624646153"
+        "3842708986290401534510677245449052480438452772935563477911887903937433332521175778793903095384041223955723"
+        "1923283555660292437990927601776574893980601557250737329754310915661825472040213756951830291482697155616984"
+        "2700521540676609741125857389706633023242364855348478771230295850829291438723530923932923590702415161133831"
+        "9751130631733719608246390666274473865694983392385750305737090058291815147877218349104719543513706308913668"
+        "3774947602824936693432977762482651171413713941775960038695919756102724251419600380177635071493624586144398"
+        "8258956704733318591666199586331239518529031729048520377213164363192327716960117074516227535950936913289772"
+        "7641328747183370449707056957130139385301002356826323260325258247061322707666120024327938153874129056930541"
+        "9921875"},
+    {0x1.72a498409980ap-1015, chars_format::fixed, 1066,
+        "0."
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004123539674247"
+        "7088973208679969440262899254505285796142223814175822702981218018251380021070120502969772416262035601116862"
+        "1659532952906006748436531426296108744371485218418489239052308056360753777114430810169989395269594614007716"
+        "4320660032095927443769046869340226546265147500705839457828617891438915581029354085740892509908612620206500"
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