From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: by sourceware.org (Postfix, from userid 1888) id 24383389803C; Wed, 18 Nov 2020 14:22:39 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org 24383389803C Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit From: Patrick Palka To: gcc-cvs@gcc.gnu.org, libstdc++-cvs@gcc.gnu.org Subject: [gcc(refs/users/ppalka/heads/libstdcxx-floating-to_chars)] libstdc++: Import parts of the Ryu library X-Act-Checkin: gcc X-Git-Author: Patrick Palka X-Git-Refname: refs/users/ppalka/heads/libstdcxx-floating-to_chars X-Git-Oldrev: cb1a4876a0e724ca3962ec14dce9e7819fa72ea5 X-Git-Newrev: 9c7c1b252f8e4d76098040ea4fc52bc104d2b147 Message-Id: <20201118142239.24383389803C@sourceware.org> Date: Wed, 18 Nov 2020 14:22:39 +0000 (GMT) X-BeenThere: libstdc++-cvs@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Libstdc++-cvs mailing list List-Unsubscribe: , List-Archive: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 18 Nov 2020 14:22:39 -0000 https://gcc.gnu.org/g:9c7c1b252f8e4d76098040ea4fc52bc104d2b147 commit 9c7c1b252f8e4d76098040ea4fc52bc104d2b147 Author: Patrick Palka Date: Wed Nov 18 09:21:20 2020 -0500 libstdc++: Import parts of the Ryu library This imports the source files from the Ryu library that define d2s_buffered_n, f2s_buffered_n, d2fixed_buffered_n, d2exp_buffered_n and generic_binary_to_decimal, which we're going to use as the base 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. Diff: --- 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 +++++ libstdc++-v3/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(+) 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 +#include +#include + +#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 +#include +#include +#include +#include + +#ifdef RYU_DEBUG +#include +#include +#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 + +#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 }, + { 18332056844289122710u, 16592893013671929434u, 240246646623u }, + { 11114572877353986193u, 4549827147718617002u, 72285931760u }, + { 1703393793997526525u, 5274510003815168970u, 87112u }, + { 5082852056285196265u, 1606938044258990u, 0u }, + { 816434266573722365u, 1606938u, 0u }, + { 1u, 0u, 129530986496u }, + { 5736523019264798742u, 9794971998307800534u, 69797980545u }, + { 10129314776268243339u, 14720142899209240168u, 36233143877u }, + { 16511595775483995364u, 4300745446091561534u, 50823839524u }, + { 12367293405401453325u, 15197156861335443363u, 5708990770u }, + { 16934621733248854291u, 13078571300009428617u, 5u }, + { 10278280417769171336u, 105312291668u, 0u }, + { 5760764486226151240u, 105u, 0u }, + { 1u, 0u, 238731001856u }, + { 4128368337188369761u, 13484604155038683036u, 72453031918u }, + { 10240941003671005056u, 8356963862052375698u, 175317175368u }, + { 17933378316822368251u, 5850852848337610020u, 231147060143u }, + { 8346249813075698616u, 2712780827214982049u, 128419156711u }, + { 15906203609160902695u, 7732076577307618051u, 374144u }, + { 14525607416135386328u, 6901746346790563u, 0u }, + { 6397156777364256320u, 6901746u, 0u }, + { 1u, 0u, 34937634816u }, + { 16798760952716600048u, 17296309485351745866u, 249899825954u }, + { 2419982808370854967u, 16598859101615853087u, 50404946937u }, + { 2922947087773078956u, 7469952526870444256u, 165733552434u }, + { 15419220167069510190u, 13531654022114669523u, 77854221733u }, + { 3452124642157173416u, 15757609704383306942u, 24519928653u }, + { 5979700067267186899u, 9590990814237149589u, 24u }, + { 4913998146922579597u, 452312848583u, 0u }, + { 5771037749337678924u, 452u, 0u }, + { 1u, 0u, 8835301376u }, + { 3464734175350698519u, 15408590707489433889u, 90993782792u }, + { 9334527711335850125u, 18332056844289122709u, 170602522202u }, + { 7269882896518450106u, 11114572877353986192u, 202092341162u }, + { 1372511258182263196u, 1703393793997526524u, 174275541962u }, 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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 }, + { 0u, 17827675094632103936u, 123785264354u }, + { 0u, 7347197909193981952u, 226966440203u }, + { 0u, 13677404030777688064u, 11398292396u }, + { 0u, 3810326759732150272u, 172741453558u }, + { 0u, 9943947977234055168u, 246206558227u }, + { 0u, 0u, 19539062500u }, + { 0u, 0u, 228000000000u }, + { 12945425605062557696u, 909494u, 0u }, + { 4388757836872548352u, 909494701772928u, 0u }, + { 1152921504606846976u, 14878706826214591391u, 49303u }, + { 0u, 4387341015746028192u, 151806576313u }, + { 0u, 651726680428265472u, 185237838233u }, + { 0u, 2570638187944738816u, 153035330174u }, + { 0u, 7419175577111756800u, 126139354575u }, + { 0u, 17299322326264840192u, 207402194313u }, + { 0u, 7990511638862102528u, 137937798142u }, + { 0u, 16717361816799281152u, 254433166503u }, + { 0u, 0u, 167906250000u }, + { 0u, 0u, 16000000000u }, + { 16192327041775828992u, 13u, 0u }, + { 15024075324038053888u, 13877787807u, 0u }, + { 5449091666327633920u, 13877787807814456755u, 0u }, + { 2494994193563254784u, 9707857417284919307u, 752316384u }, + { 4611686018427387904u, 1844515466944871826u, 224526264005u }, + { 0u, 15167599819856275072u, 197099991383u }, + { 0u, 14830185305589481472u, 87822237233u }, + { 0u, 6163721531743535104u, 49803945956u }, + { 0u, 14122847407012052992u, 228334136013u }, + { 0u, 335491783960035328u, 205765601092u }, + { 0u, 941252322120433664u, 68018187046u }, + { 0u, 11529215046068469760u, 38051025390u }, + { 0u, 0u, 238625000000u }, + { 0u, 0u, 64000000000u }, + { 4368439412768899072u, 211758u, 0u }, + { 1563676642168012800u, 211758236813575u, 0u }, + { 11532349341402398720u, 8061591463141767016u, 11479u }, + { 9048364970084925440u, 16628725344207857142u, 215437019748u }, + { 16609275425742389248u, 3555541870038531535u, 100901445007u }, + { 0u, 18316647450161853665u, 143192746310u }, + { 0u, 16709574568378075648u, 70992947447u }, + { 0u, 7696022835795591168u, 247905827852u }, + { 0u, 16664449640376041472u, 12417202233u }, + { 0u, 3109186955116544000u, 57903381625u }, + { 0u, 10515518101817131008u, 121168549362u }, + { 0u, 9961962375743537152u, 242570047378u }, + { 0u, 9223372036854775808u, 146540039062u }, + { 0u, 0u, 150500000000u }, + { 14485570586272534528u, 3231174267u, 0u }, + { 17827675094632103936u, 3231174267785264354u, 0u }, + { 7347197909193981952u, 748977172262750475u, 175162308u }, + { 13677404030777688064u, 15965033457315095468u, 196040602133u }, + { 3810326759732150272u, 16809402149066729206u, 21865466197u }, + { 9943947977234055168u, 7563769067065700371u, 85911239516u }, + { 0u, 13550322810840051428u, 92410032742u }, + { 0u, 8663209637545764864u, 102734564471u }, + { 0u, 8969247575312957440u, 119469633535u }, + { 0u, 6193172891660451840u, 255486223885u }, + { 0u, 3427954273864908800u, 13335732575u }, + { 0u, 10058367555266936832u, 95185829773u }, + { 0u, 13907115649320091648u, 141545265197u }, + { 0u, 0u, 45753906250u }, + { 0u, 0u, 74000000000u }, + { 14878706826214591391u, 49303u, 0u }, + { 4387341015746028192u, 49303806576313u, 0u }, + { 651726680428265472u, 14106411361315920281u, 2672u }, + { 2570638187944738816u, 3609034283485221502u, 112764710092u }, + { 7419175577111756800u, 9896072247338192335u, 204195646140u }, + { 17299322326264840192u, 8889095178479228297u, 188536467151u }, + { 7990511638862102528u, 3631796911038383102u, 207481878815u }, + { 16717361816799281152u, 898318840772166823u, 31196880105u }, + { 0u, 17293677953982795024u, 233048697961u }, + { 0u, 7353628266884669440u, 105937492160u }, + { 0u, 2404693032470315008u, 192398640987u }, + { 0u, 9191155893041889280u, 91130358670u }, + { 0u, 6353946855033798656u, 142498253559u }, + { 0u, 3767824038248841216u, 247344448149u }, + { 0u, 7205759403792793600u, 149204254150u }, + { 0u, 0u, 198390625000u }, + { 0u, 0u, 232000000000u }, + { 9707857417284919307u, 752316384u, 0u }, + { 1844515466944871826u, 752316384526264005u, 0u }, + { 15167599819856275072u, 17063068157692817751u, 40783152u }, + { 14830185305589481472u, 5385330256507239985u, 48924990778u }, + { 6163721531743535104u, 3373050282752075748u, 58291939338u }, + { 14122847407012052992u, 4116064001262906061u, 10182853422u }, + { 335491783960035328u, 11306582046748043076u, 46223132276u }, + { 941252322120433664u, 17035410946089626406u, 116612931040u }, + { 11529215046068469760u, 15618595715183448558u, 224923491477u }, + { 0u, 5141740092277295680u, 149846685770u }, + { 0u, 16973644291514990592u, 74278734288u }, + { 0u, 14625255268443750400u, 208920143100u }, + { 0u, 14021170507320131584u, 252792836676u 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4250043307981877118u, 11545396528u }, + { 18088011566435813579u, 7075646198054337199u, 48230395309u }, + { 15008862380698848893u, 18141738384245531503u, 173383571548u }, + { 18160498644611827812u, 8174370508376809531u, 92983465608u }, + { 3604680497457231965u, 3581964982731575596u, 136443133513u }, + { 5957615565551495921u, 14798509948722114761u, 73194178710u }, + { 17528455034961565995u, 14713923334885122090u, 150802228831u }, + { 8503772325120113809u, 5042978054260414139u, 95797643382u }, + { 8501492578048509537u, 2052996319372883413u, 118273380388u }, + { 2296237701094386060u, 8825683007899981588u, 36111293153u }, + { 3753593040591076946u, 9992196755378745151u, 225478441234u }, + { 8518075399775653155u, 9301073417573669950u, 18541678071u }, + { 12757855675959554597u, 5331614769144850592u, 247504212200u }, + { 121631169379748595u, 14354009428310052102u, 232289027415u }, + { 16679062494579173314u, 5581221063029119078u, 87778132410u }, + { 10739912744743898054u, 1529260335339476189u, 186302558600u }, + { 9367340677776287570u, 16483061525949201148u, 136082901368u }, + { 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 +#include +#include +#include +#include + +#ifdef RYU_DEBUG +#include +#include +#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 }, + { 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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 +#include + +// 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 + +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 +#include +#include +#include +#include +#include + +#ifdef RYU_DEBUG +#include +#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