* [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions
@ 2018-06-27 13:04 Szabolcs Nagy
2018-06-27 13:06 ` [PATCH 1/5] Use uint32_t sign argument to math error functions Szabolcs Nagy
` (5 more replies)
0 siblings, 6 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:04 UTC (permalink / raw)
To: newlib; +Cc: nd
The implementations are based on code from
https://github.com/ARM-software/optimized-routines
and provided here under 3 clause BSD license.
Tested on aarch64 and arm targets.
(I'll reply with git format-patch attached because git
send email does not work for me and thunderbird mangles
things if i inline).
Szabolcs Nagy (5):
Use uint32_t sign argument to math error functions
New exp and exp2 implementations
New log implementation
New log2 implementation
New pow implementation
newlib/libc/include/machine/ieeefp.h | 23 ++
newlib/libm/common/Makefile.am | 4 +-
newlib/libm/common/Makefile.in | 75 ++++-
newlib/libm/common/exp.c | 165 ++++++++++
newlib/libm/common/exp2.c | 152 +++++++++
newlib/libm/common/exp_data.c | 611 +++++++++++++++++++++++++++++++++++
newlib/libm/common/fdlibm.h | 3 +
newlib/libm/common/log.c | 175 ++++++++++
newlib/libm/common/log2.c | 157 +++++++++
newlib/libm/common/log2_data.c | 208 ++++++++++++
newlib/libm/common/log_data.c | 510 +++++++++++++++++++++++++++++
newlib/libm/common/math_config.h | 125 ++++++-
newlib/libm/common/math_err.c | 101 ++++++
newlib/libm/common/math_errf.c | 12 +-
newlib/libm/common/pow.c | 377 +++++++++++++++++++++
newlib/libm/common/pow_log_data.c | 187 +++++++++++
newlib/libm/common/s_log2.c | 2 +
newlib/libm/common/sf_pow.c | 6 +-
newlib/libm/math/e_exp.c | 2 +
newlib/libm/math/e_log.c | 2 +
newlib/libm/math/e_pow.c | 2 +
newlib/libm/math/w_exp.c | 2 +
newlib/libm/math/w_exp2.c | 2 +
newlib/libm/math/w_log.c | 2 +
newlib/libm/math/w_pow.c | 3 +-
25 files changed, 2889 insertions(+), 19 deletions(-)
create mode 100644 newlib/libm/common/exp.c
create mode 100644 newlib/libm/common/exp2.c
create mode 100644 newlib/libm/common/exp_data.c
create mode 100644 newlib/libm/common/log.c
create mode 100644 newlib/libm/common/log2.c
create mode 100644 newlib/libm/common/log2_data.c
create mode 100644 newlib/libm/common/log_data.c
create mode 100644 newlib/libm/common/math_err.c
create mode 100644 newlib/libm/common/pow.c
create mode 100644 newlib/libm/common/pow_log_data.c
--.
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* [PATCH 1/5] Use uint32_t sign argument to math error functions
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
@ 2018-06-27 13:06 ` Szabolcs Nagy
2018-06-27 13:07 ` [PATCH 2/5] New exp and exp2 implementations Szabolcs Nagy
` (4 subsequent siblings)
5 siblings, 0 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:06 UTC (permalink / raw)
To: newlib; +Cc: nd
[-- Attachment #1: Type: text/plain, Size: 0 bytes --]
[-- Attachment #2: 0001-Use-uint32_t-sign-argument-to-math-error-functions.patch --]
[-- Type: text/x-patch, Size: 4167 bytes --]
From ba4ec32f6e531edb6cb39c755c980a86d3d2517c Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Mon, 25 Jun 2018 17:39:27 +0100
Subject: [PATCH 1/5] Use uint32_t sign argument to math error functions
This change is equivalent to the commit
https://github.com/ARM-software/optimized-routines/commit/c65db17340782d647c49e17cbba244862dc38402
and only affects code that is from the Arm optimized-routines project.
It does not affect the observable behaviour, but the code generation
can be different on 64bit targets. The intention is to make the
portable semantics of the code obvious by using a fixed size type.
---
newlib/libm/common/math_config.h | 8 ++++----
newlib/libm/common/math_errf.c | 12 ++++++------
newlib/libm/common/sf_pow.c | 6 +++---
3 files changed, 13 insertions(+), 13 deletions(-)
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
index 6d87376ab..e4b53fcdd 100644
--- a/newlib/libm/common/math_config.h
+++ b/newlib/libm/common/math_config.h
@@ -199,10 +199,10 @@ eval_as_double (double x)
# define unlikely(x) (x)
#endif
-HIDDEN float __math_oflowf (unsigned long);
-HIDDEN float __math_uflowf (unsigned long);
-HIDDEN float __math_may_uflowf (unsigned long);
-HIDDEN float __math_divzerof (unsigned long);
+HIDDEN float __math_oflowf (uint32_t);
+HIDDEN float __math_uflowf (uint32_t);
+HIDDEN float __math_may_uflowf (uint32_t);
+HIDDEN float __math_divzerof (uint32_t);
HIDDEN float __math_invalidf (float);
/* Shared between expf, exp2f and powf. */
diff --git a/newlib/libm/common/math_errf.c b/newlib/libm/common/math_errf.c
index 60b1bb3f2..92eaf883e 100644
--- a/newlib/libm/common/math_errf.c
+++ b/newlib/libm/common/math_errf.c
@@ -1,5 +1,5 @@
/* Single-precision math error handling.
- Copyright (c) 2017 ARM Ltd. All rights reserved.
+ Copyright (c) 2017-2018 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
@@ -45,14 +45,14 @@ with_errnof (float y, int e)
/* NOINLINE prevents fenv semantics breaking optimizations. */
NOINLINE static float
-xflowf (unsigned long sign, float y)
+xflowf (uint32_t sign, float y)
{
y = (sign ? -y : y) * y;
return with_errnof (y, ERANGE);
}
HIDDEN float
-__math_uflowf (unsigned long sign)
+__math_uflowf (uint32_t sign)
{
return xflowf (sign, 0x1p-95f);
}
@@ -61,20 +61,20 @@ __math_uflowf (unsigned long sign)
/* Underflows to zero in some non-nearest rounding mode, setting errno
is valid even if the result is non-zero, but in the subnormal range. */
HIDDEN float
-__math_may_uflowf (unsigned long sign)
+__math_may_uflowf (uint32_t sign)
{
return xflowf (sign, 0x1.4p-75f);
}
#endif
HIDDEN float
-__math_oflowf (unsigned long sign)
+__math_oflowf (uint32_t sign)
{
return xflowf (sign, 0x1p97f);
}
HIDDEN float
-__math_divzerof (unsigned long sign)
+__math_divzerof (uint32_t sign)
{
float y = 0;
return with_errnof ((sign ? -1 : 1) / y, ERANGE);
diff --git a/newlib/libm/common/sf_pow.c b/newlib/libm/common/sf_pow.c
index 6741a349b..2aa91c9b8 100644
--- a/newlib/libm/common/sf_pow.c
+++ b/newlib/libm/common/sf_pow.c
@@ -1,5 +1,5 @@
/* Single-precision pow function.
- Copyright (c) 2017 ARM Ltd. All rights reserved.
+ Copyright (c) 2017-2018 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
@@ -93,7 +93,7 @@ log2_inline (uint32_t ix)
(in case of fast toint intrinsics) or not. The unscaled xd must be
in [-1021,1023], sign_bias sets the sign of the result. */
static inline double_t
-exp2_inline (double_t xd, unsigned long sign_bias)
+exp2_inline (double_t xd, uint32_t sign_bias)
{
uint64_t ki, ski, t;
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
@@ -152,7 +152,7 @@ zeroinfnan (uint32_t ix)
float
powf (float x, float y)
{
- unsigned long sign_bias = 0;
+ uint32_t sign_bias = 0;
uint32_t ix, iy;
ix = asuint (x);
--
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* [PATCH 3/5] New log implementation
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
2018-06-27 13:06 ` [PATCH 1/5] Use uint32_t sign argument to math error functions Szabolcs Nagy
2018-06-27 13:07 ` [PATCH 2/5] New exp and exp2 implementations Szabolcs Nagy
@ 2018-06-27 13:07 ` Szabolcs Nagy
2018-06-27 13:08 ` [PATCH 4/5] New log2 implementation Szabolcs Nagy
` (2 subsequent siblings)
5 siblings, 0 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:07 UTC (permalink / raw)
To: newlib; +Cc: nd
[-- Attachment #1: Type: text/plain, Size: 1 bytes --]
[-- Attachment #2: 0003-New-log-implementation.patch --]
[-- Type: text/x-patch, Size: 37382 bytes --]
From 91999470975110d15a1f3beddb37f1c57730fe50 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Tue, 26 Jun 2018 15:27:50 +0100
Subject: [PATCH 3/5] New log implementation
The new implementations are provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.519 ULP with inlined fma and fma contraction. It uses
a 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1703 bytes. The w_log.c wrapper is disabled since error handling is
inline in the new code.
New __HAVE_FAST_FMA and __HAVE_FAST_FMA_DEFAULT feature macros were
added to enable selecting between the code path that uses fma and the
one that does not. Targets supposed to set __HAVE_FAST_FMA_DEFAULT
if they have single instruction fma and the compiler can actually
inline it (gcc has __FP_FAST_FMA macro but that does not guarantee
inlining with -fno-builtin-fma).
Improvements on Cortex-A72:
latency: 1.9x
thruput: 2.3x
---
newlib/libc/include/machine/ieeefp.h | 23 ++
newlib/libm/common/Makefile.am | 2 +-
newlib/libm/common/Makefile.in | 19 +-
newlib/libm/common/fdlibm.h | 1 +
newlib/libm/common/log.c | 175 ++++++++++++
newlib/libm/common/log_data.c | 510 +++++++++++++++++++++++++++++++++++
newlib/libm/common/math_config.h | 14 +
newlib/libm/math/e_log.c | 2 +
newlib/libm/math/w_log.c | 2 +
9 files changed, 744 insertions(+), 4 deletions(-)
create mode 100644 newlib/libm/common/log.c
create mode 100644 newlib/libm/common/log_data.c
diff --git a/newlib/libc/include/machine/ieeefp.h b/newlib/libc/include/machine/ieeefp.h
index 2fb2268ce..88b83f68c 100644
--- a/newlib/libc/include/machine/ieeefp.h
+++ b/newlib/libc/include/machine/ieeefp.h
@@ -65,6 +65,17 @@
double and single precision arithmetics has similar latency and it
has no legacy SVID matherr support, only POSIX errno and fenv
exception based error handling.
+
+ __HAVE_FAST_FMA_DEFAULT
+
+ Default value for __HAVE_FAST_FMA if that's not set by the user.
+ It should be set here based on predefined feature macros.
+
+ __HAVE_FAST_FMA
+
+ It should be set to 1 if the compiler can inline an fma call as a
+ single instruction. Some math code has a separate faster code
+ path assuming the target has single instruction fma.
*/
#if (defined(__arm__) || defined(__thumb__)) && !defined(__MAVERICK__)
@@ -80,6 +91,9 @@
# endif
# if __ARM_FP & 0x8
# define __OBSOLETE_MATH_DEFAULT 0
+# if __ARM_FEATURE_FMA
+# define __HAVE_FAST_FMA_DEFAULT 1
+# endif
# endif
#else
# define __IEEE_BIG_ENDIAN
@@ -96,6 +110,7 @@
#define __IEEE_BIG_ENDIAN
#endif
#define __OBSOLETE_MATH_DEFAULT 0
+#define __HAVE_FAST_FMA_DEFAULT 1
#endif
#ifdef __epiphany__
@@ -460,6 +475,14 @@
#define __OBSOLETE_MATH __OBSOLETE_MATH_DEFAULT
#endif
+#ifndef __HAVE_FAST_FMA_DEFAULT
+/* Assume slow fma by default. */
+#define __HAVE_FAST_FMA_DEFAULT 0
+#endif
+#ifndef __HAVE_FAST_FMA
+#define __HAVE_FAST_FMA __HAVE_FAST_FMA_DEFAULT
+#endif
+
#ifndef __IEEE_BIG_ENDIAN
#ifndef __IEEE_LITTLE_ENDIAN
#error Endianess not declared!!
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am
index d7c479117..257a03c5c 100644
--- a/newlib/libm/common/Makefile.am
+++ b/newlib/libm/common/Makefile.am
@@ -13,7 +13,7 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in
index c35ada3ec..856e01185 100644
--- a/newlib/libm/common/Makefile.in
+++ b/newlib/libm/common/Makefile.in
@@ -95,7 +95,8 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
lib_a-s_scalbln.$(OBJEXT) lib_a-s_signbit.$(OBJEXT) \
lib_a-s_trunc.$(OBJEXT) lib_a-exp.$(OBJEXT) \
lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
- lib_a-math_err.$(OBJEXT)
+ lib_a-math_err.$(OBJEXT) lib_a-log.$(OBJEXT) \
+ lib_a-log_data.$(OBJEXT)
am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -165,7 +166,7 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
- exp_data.lo math_err.lo
+ exp_data.lo math_err.lo log.lo log_data.lo
am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
@@ -356,7 +357,7 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
@@ -724,6 +725,18 @@ lib_a-math_err.o: math_err.c
lib_a-math_err.obj: math_err.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_err.obj `if test -f 'math_err.c'; then $(CYGPATH_W) 'math_err.c'; else $(CYGPATH_W) '$(srcdir)/math_err.c'; fi`
+lib_a-log.o: log.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log.o `test -f 'log.c' || echo '$(srcdir)/'`log.c
+
+lib_a-log.obj: log.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log.obj `if test -f 'log.c'; then $(CYGPATH_W) 'log.c'; else $(CYGPATH_W) '$(srcdir)/log.c'; fi`
+
+lib_a-log_data.o: log_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log_data.o `test -f 'log_data.c' || echo '$(srcdir)/'`log_data.c
+
+lib_a-log_data.obj: log_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log_data.obj `if test -f 'log_data.c'; then $(CYGPATH_W) 'log_data.c'; else $(CYGPATH_W) '$(srcdir)/log_data.c'; fi`
+
lib_a-sf_finite.o: sf_finite.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
diff --git a/newlib/libm/common/fdlibm.h b/newlib/libm/common/fdlibm.h
index f6c3740e3..ae85569ad 100644
--- a/newlib/libm/common/fdlibm.h
+++ b/newlib/libm/common/fdlibm.h
@@ -232,6 +232,7 @@ extern float __ieee754_scalbf __P((float,float));
extern symbol is reserved whenever the caller is reserved)
and there are no observable error handling side effects. */
# define __ieee754_exp(x) exp(x)
+# define __ieee754_log(x) log(x)
# define __ieee754_expf(x) expf(x)
# define __ieee754_logf(x) logf(x)
# define __ieee754_powf(x,y) powf(x,y)
diff --git a/newlib/libm/common/log.c b/newlib/libm/common/log.c
new file mode 100644
index 000000000..32752f55c
--- /dev/null
+++ b/newlib/libm/common/log.c
@@ -0,0 +1,175 @@
+/* Double-precision log(x) function.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log_data.tab
+#define T2 __log_data.tab2
+#define B __log_data.poly1
+#define A __log_data.poly
+#define Ln2hi __log_data.ln2hi
+#define Ln2lo __log_data.ln2lo
+#define N (1 << LOG_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+static inline uint32_t
+top16 (double x)
+{
+ return asuint64 (x) >> 48;
+}
+
+double
+log (double x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
+ uint64_t ix, iz, tmp;
+ uint32_t top;
+ int k, i;
+
+ ix = asuint64 (x);
+ top = top16 (x);
+
+#if LOG_POLY1_ORDER == 10 || LOG_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1p-5)
+# define HI asuint64 (1.0 + 0x1.1p-5)
+#elif LOG_POLY1_ORDER == 12
+# define LO asuint64 (1.0 - 0x1p-4)
+# define HI asuint64 (1.0 + 0x1.09p-4)
+#endif
+ if (unlikely (ix - LO < HI - LO))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+ return 0;
+ r = x - 1.0;
+ r2 = r*r;
+ r3 = r*r2;
+#if LOG_POLY1_ORDER == 10
+ /* Worst-case error is around 0.516 ULP. */
+ y = r3*(B[1] + r*B[2] + r2*B[3]
+ + r3*(B[4] + r*B[5] + r2*B[6] + r3*(B[7] + r*B[8])));
+ w = B[0]*r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+#elif LOG_POLY1_ORDER == 11
+ /* Worst-case error is around 0.516 ULP. */
+ y = r3*(B[1] + r*B[2]
+ + r2*(B[3] + r*B[4] + r2*B[5]
+ + r3*(B[6] + r*B[7] + r2*B[8] + r3*B[9])));
+ w = B[0]*r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+#elif LOG_POLY1_ORDER == 12
+ y = r3*(B[1] + r*B[2] + r2*B[3]
+ + r3*(B[4] + r*B[5] + r2*B[6]
+ + r3*(B[7] + r*B[8] + r2*B[9] + r3*B[10])));
+# if N <= 64
+ /* Worst-case error is around 0.532 ULP. */
+ w = B[0]*r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+# else
+ /* Worst-case error is around 0.507 ULP. */
+ w = r*0x1p27;
+ double_t rhi = r + w - w;
+ double_t rlo = r - rhi;
+ w = rhi*rhi*B[0]; /* B[0] == -0.5. */
+ hi = r + w;
+ lo = r - hi + w;
+ lo += B[0]*rlo*(rhi + r);
+ y += lo;
+ y += hi;
+# endif
+#endif
+ return y;
+ }
+ if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzero (1);
+ if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
+ return x;
+ if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+ return __math_invalid (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint64 (x * 0x1p52);
+ ix -= 52ULL << 52;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = asdouble (iz);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
+ /* r ~= z/c - 1, |r| < 1/(2*N). */
+#if __HAVE_FAST_FMA
+ /* rounding error: 0x1p-55/N. */
+ r = fma (z, invc, -1.0);
+#else
+ /* rounding error: 0x1p-55/N + 0x1p-66. */
+ r = (z - T2[i].chi - T2[i].clo)*invc;
+#endif
+ kd = (double_t) k;
+
+ /* hi + lo = r + log(c) + k*Ln2. */
+ w = kd*Ln2hi + logc;
+ hi = w + r;
+ lo = w - hi + r + kd*Ln2lo;
+
+ /* log(x) = lo + (log1p(r) - r) + hi. */
+ r2 = r * r; /* rounding error: 0x1p-54/N^2. */
+ /* Worst case error if |y| > 0x1p-5:
+ 0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
+ Worst case error if |y| > 0x1p-4:
+ 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
+#if LOG_POLY_ORDER == 6
+ y = lo + r2*A[0] + r*r2*(A[1] + r*A[2] + r2*(A[3] + r*A[4])) + hi;
+#elif LOG_POLY_ORDER == 7
+ y = lo + r2*(A[0] + r*A[1] + r2*(A[2] + r*A[3]) + r2*r2*(A[4] + r*A[5])) + hi;
+#endif
+ return y;
+}
+#endif
diff --git a/newlib/libm/common/log_data.c b/newlib/libm/common/log_data.c
new file mode 100644
index 000000000..ef62677ca
--- /dev/null
+++ b/newlib/libm/common/log_data.c
@@ -0,0 +1,510 @@
+/* Data for log.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << LOG_TABLE_BITS)
+
+const struct log_data __log_data = {
+.ln2hi = 0x1.62e42fefa3800p-1,
+.ln2lo = 0x1.ef35793c76730p-45,
+.poly1 = {
+#if LOG_POLY1_ORDER == 10
+// relative error: 0x1.32eccc6p-62
+// in -0x1p-5 0x1.1p-5 (|log(1+x)| > 0x1p-5 outside this interval)
+-0x1p-1,
+0x1.55555555554e5p-2,
+-0x1.0000000000af2p-2,
+0x1.9999999bbe436p-3,
+-0x1.55555537f9cdep-3,
+0x1.24922fc8127cfp-3,
+-0x1.0000b7d6bb612p-3,
+0x1.c806ee1ddbcafp-4,
+-0x1.972335a9c2d6ep-4,
+#elif LOG_POLY1_ORDER == 11
+// relative error: 0x1.52c8b708p-68
+// in -0x1p-5 0x1.1p-5 (|log(1+x)| > 0x1p-5 outside this interval)
+-0x1p-1,
+0x1.5555555555555p-2,
+-0x1.ffffffffffea9p-3,
+0x1.999999999c4d4p-3,
+-0x1.55555557f5541p-3,
+0x1.249248fbe33e4p-3,
+-0x1.ffffc9a3c825bp-4,
+0x1.c71e1f204435dp-4,
+-0x1.9a7f26377d06ep-4,
+0x1.71c30cf8f7364p-4,
+#elif LOG_POLY1_ORDER == 12
+// relative error: 0x1.c04d76cp-63
+// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
+-0x1p-1,
+0x1.5555555555577p-2,
+-0x1.ffffffffffdcbp-3,
+0x1.999999995dd0cp-3,
+-0x1.55555556745a7p-3,
+0x1.24924a344de3p-3,
+-0x1.fffffa4423d65p-4,
+0x1.c7184282ad6cap-4,
+-0x1.999eb43b068ffp-4,
+0x1.78182f7afd085p-4,
+-0x1.5521375d145cdp-4,
+#endif
+},
+.poly = {
+#if N == 64 && LOG_POLY_ORDER == 7
+// relative error: 0x1.906eb8ap-58
+// abs error: 0x1.d2cad5a8p-67
+// in -0x1.fp-8 0x1.fp-8
+-0x1.0000000000027p-1,
+0x1.555555555556ap-2,
+-0x1.fffffff0440bap-3,
+0x1.99999991906c3p-3,
+-0x1.555c8d7e8201ep-3,
+0x1.24978c59151fap-3,
+#elif N == 128 && LOG_POLY_ORDER == 6
+// relative error: 0x1.926199e8p-56
+// abs error: 0x1.882ff33p-65
+// in -0x1.fp-9 0x1.fp-9
+-0x1.0000000000001p-1,
+0x1.555555551305bp-2,
+-0x1.fffffffeb459p-3,
+0x1.999b324f10111p-3,
+-0x1.55575e506c89fp-3,
+#elif N == 128 && LOG_POLY_ORDER == 7
+// relative error: 0x1.649fc4bp-64
+// abs error: 0x1.c3b5769p-74
+// in -0x1.fp-9 0x1.fp-9
+-0x1.0000000000001p-1,
+0x1.5555555555556p-2,
+-0x1.fffffffea1a8p-3,
+0x1.99999998e9139p-3,
+-0x1.555776801b968p-3,
+0x1.2493c29331a5cp-3,
+#endif
+},
+.tab = {
+#if N == 64
+{0x1.7242886495cd8p+0, -0x1.79e267bdfe000p-2},
+{0x1.6e1f769340dc9p+0, -0x1.6e60ee0ecb000p-2},
+{0x1.6a13ccc8f195cp+0, -0x1.63002fdbf6000p-2},
+{0x1.661ec72e86f3ap+0, -0x1.57bf76c597000p-2},
+{0x1.623fa6c447b16p+0, -0x1.4c9e07f0d2000p-2},
+{0x1.5e75bbca31702p+0, -0x1.419b42f027000p-2},
+{0x1.5ac05655adb10p+0, -0x1.36b67660e6000p-2},
+{0x1.571ed3e940191p+0, -0x1.2bef0839e4800p-2},
+{0x1.539094ac0fbbfp+0, -0x1.21445727cb000p-2},
+{0x1.5015007e7fc42p+0, -0x1.16b5ca3c3d000p-2},
+{0x1.4cab877c31cf9p+0, -0x1.0c42d3805f800p-2},
+{0x1.49539e76a88d3p+0, -0x1.01eae61b60800p-2},
+{0x1.460cbc12211dap+0, -0x1.ef5adb9fb0000p-3},
+{0x1.42d6624debe3ap+0, -0x1.db13daab99000p-3},
+{0x1.3fb0144f0d462p+0, -0x1.c6ffbe896e000p-3},
+{0x1.3c995a1f9a9b4p+0, -0x1.b31d84722d000p-3},
+{0x1.3991c23952500p+0, -0x1.9f6c3cf6eb000p-3},
+{0x1.3698df35eaa14p+0, -0x1.8beafe7f13000p-3},
+{0x1.33ae463091760p+0, -0x1.7898db878d000p-3},
+{0x1.30d190aae3d72p+0, -0x1.6574efe4ec000p-3},
+{0x1.2e025c9203c89p+0, -0x1.527e620845000p-3},
+{0x1.2b404a7244988p+0, -0x1.3fb457d798000p-3},
+{0x1.288b01dc19544p+0, -0x1.2d1615a077000p-3},
+{0x1.25e2268085f69p+0, -0x1.1aa2b431e5000p-3},
+{0x1.23456812abb74p+0, -0x1.08598f1d2b000p-3},
+{0x1.20b4703174157p+0, -0x1.ec738fee40000p-4},
+{0x1.1e2ef308b4e9bp+0, -0x1.c885768862000p-4},
+{0x1.1bb4a36b70a3fp+0, -0x1.a4e75b6a46000p-4},
+{0x1.194538e960658p+0, -0x1.8197efba9a000p-4},
+{0x1.16e0692a10ac8p+0, -0x1.5e95ad734e000p-4},
+{0x1.1485f1ba1568bp+0, -0x1.3bdf67117c000p-4},
+{0x1.12358e123ed6fp+0, -0x1.1973b744f0000p-4},
+{0x1.0fef01de37c8dp+0, -0x1.eea33446bc000p-5},
+{0x1.0db20b82be414p+0, -0x1.aaef4ab304000p-5},
+{0x1.0b7e6f67f69b3p+0, -0x1.67c962fd2c000p-5},
+{0x1.0953f342fc108p+0, -0x1.252f29acf8000p-5},
+{0x1.0732604ec956bp+0, -0x1.c63d19e9c0000p-6},
+{0x1.051980117f9b0p+0, -0x1.432ab6a388000p-6},
+{0x1.03091aa6810f1p+0, -0x1.8244357f50000p-7},
+{0x1.01010152cf066p+0, -0x1.0080a711c0000p-8},
+{0x1.fc07ef6b6e30bp-1, 0x1.fe03018e80000p-8},
+{0x1.f4465aa1024afp-1, 0x1.7b91986450000p-6},
+{0x1.ecc07a8fd3f5ep-1, 0x1.39e88608c8000p-5},
+{0x1.e573ad856b537p-1, 0x1.b42dc6e624000p-5},
+{0x1.de5d6dc7b8057p-1, 0x1.165372ec20000p-4},
+{0x1.d77b6498bddf7p-1, 0x1.51b07a0170000p-4},
+{0x1.d0cb580315c0fp-1, 0x1.8c3465c7ea000p-4},
+{0x1.ca4b30d1cf449p-1, 0x1.c5e544a290000p-4},
+{0x1.c3f8ef4810d8ep-1, 0x1.fec91aa0a6000p-4},
+{0x1.bdd2b8b311f44p-1, 0x1.1b72acdc5c000p-3},
+{0x1.b7d6c2eeac054p-1, 0x1.371fc65a98000p-3},
+{0x1.b20363474c8f5p-1, 0x1.526e61c1aa000p-3},
+{0x1.ac570165eeab1p-1, 0x1.6d60ffc240000p-3},
+{0x1.a6d019f331df4p-1, 0x1.87fa08a013000p-3},
+{0x1.a16d3ebc9e3c3p-1, 0x1.a23bc630c3000p-3},
+{0x1.9c2d14567ef45p-1, 0x1.bc286a3512000p-3},
+{0x1.970e4efae9169p-1, 0x1.d5c2195697000p-3},
+{0x1.920fb3bd0b802p-1, 0x1.ef0ae132d3000p-3},
+{0x1.8d3018b58699ap-1, 0x1.040259974e000p-2},
+{0x1.886e5ff170ee6p-1, 0x1.1058bd40e2000p-2},
+{0x1.83c977ad35d27p-1, 0x1.1c898c1137800p-2},
+{0x1.7f405ed16c520p-1, 0x1.2895a3e65b000p-2},
+{0x1.7ad220d0335c4p-1, 0x1.347dd8f6bd000p-2},
+{0x1.767dce53474fdp-1, 0x1.4043083cb3800p-2},
+#elif N == 128
+{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2},
+{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2},
+{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2},
+{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2},
+{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2},
+{0x1.69147332f0cbap+0, -0x1.602d076180000p-2},
+{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2},
+{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2},
+{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2},
+{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2},
+{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2},
+{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2},
+{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2},
+{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2},
+{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2},
+{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2},
+{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2},
+{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2},
+{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2},
+{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2},
+{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2},
+{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2},
+{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2},
+{0x1.4880524d48434p+0, -0x1.feb224586f000p-3},
+{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3},
+{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3},
+{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3},
+{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3},
+{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3},
+{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3},
+{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3},
+{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3},
+{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3},
+{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3},
+{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3},
+{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3},
+{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3},
+{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3},
+{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3},
+{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3},
+{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3},
+{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3},
+{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3},
+{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3},
+{0x1.293726014b530p+0, -0x1.31b996b490000p-3},
+{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3},
+{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3},
+{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3},
+{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3},
+{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3},
+{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4},
+{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4},
+{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4},
+{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4},
+{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4},
+{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4},
+{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4},
+{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4},
+{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4},
+{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4},
+{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4},
+{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4},
+{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4},
+{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4},
+{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5},
+{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5},
+{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5},
+{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5},
+{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5},
+{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5},
+{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5},
+{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5},
+{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6},
+{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6},
+{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6},
+{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6},
+{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7},
+{0x1.02865137932a9p+0, -0x1.419355daa0000p-7},
+{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8},
+{0x1.008040614b195p+0, -0x1.0040979240000p-9},
+{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9},
+{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7},
+{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6},
+{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6},
+{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5},
+{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5},
+{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5},
+{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5},
+{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4},
+{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4},
+{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4},
+{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4},
+{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4},
+{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4},
+{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4},
+{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4},
+{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4},
+{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3},
+{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3},
+{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3},
+{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3},
+{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3},
+{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3},
+{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3},
+{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3},
+{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3},
+{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3},
+{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3},
+{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3},
+{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3},
+{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3},
+{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3},
+{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3},
+{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3},
+{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3},
+{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3},
+{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2},
+{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2},
+{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2},
+{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2},
+{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2},
+{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2},
+{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2},
+{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2},
+{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2},
+{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2},
+{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2},
+{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2},
+#endif
+},
+#if !__HAVE_FAST_FMA
+.tab2 = {
+# if N == 64
+{0x1.61ffff94c4fecp-1, -0x1.9fe4fc998f325p-56},
+{0x1.66000020377ddp-1, 0x1.e804c7a9519f2p-55},
+{0x1.6a00004c41678p-1, 0x1.902c675d9ecfep-55},
+{0x1.6dffff7384f87p-1, -0x1.2fd6b95e55043p-56},
+{0x1.720000b37216ep-1, 0x1.802bc8d437043p-55},
+{0x1.75ffffbeb3c9dp-1, 0x1.6047ad0a0d4e4p-57},
+{0x1.7a0000628daep-1, -0x1.e00434b49313dp-56},
+{0x1.7dffffd7abd1ap-1, -0x1.6015f8a083576p-56},
+{0x1.81ffffdf40c54p-1, 0x1.7f54bf76a42c9p-57},
+{0x1.860000f334e11p-1, 0x1.60054cb5344d7p-56},
+{0x1.8a0001238aca7p-1, 0x1.c03c9bd132f55p-57},
+{0x1.8dffffb81d212p-1, -0x1.001e519f2764fp-55},
+{0x1.92000086adc7cp-1, 0x1.1fe40f88f49c6p-55},
+{0x1.960000135d8eap-1, -0x1.f832268dc3095p-55},
+{0x1.99ffff9435acp-1, 0x1.7031d8b835edcp-56},
+{0x1.9e00003478565p-1, -0x1.0030b221ce3eep-58},
+{0x1.a20000b592948p-1, 0x1.8fd2f1dbd4639p-55},
+{0x1.a600000ad0bcfp-1, 0x1.901d6a974e6bep-55},
+{0x1.a9ffff55953a5p-1, 0x1.a07556192db98p-57},
+{0x1.adffff29ce03dp-1, -0x1.fff0717ec71c2p-56},
+{0x1.b1ffff34f3ac8p-1, 0x1.8005573de89d1p-57},
+{0x1.b60000894c55bp-1, -0x1.ff2fb51b044c7p-57},
+{0x1.b9fffef45ec7dp-1, -0x1.9ff7c4e8730fp-56},
+{0x1.be0000cda7b2ap-1, 0x1.57d058dbf3c1dp-55},
+{0x1.c1ffff2c57917p-1, 0x1.7e66d7e48dbc9p-58},
+{0x1.c60000ea5b82ap-1, -0x1.47f5e132ed4bep-55},
+{0x1.ca0001121ae98p-1, -0x1.40958c8d5e00ap-58},
+{0x1.ce0000f9241cbp-1, -0x1.7da063caa81c8p-59},
+{0x1.d1fffe8be95a4p-1, -0x1.82e3a411afcd9p-59},
+{0x1.d5ffff035932bp-1, -0x1.00f901b3fe87dp-58},
+{0x1.d9fffe8b54ba7p-1, 0x1.ffef55d6e3a4p-55},
+{0x1.de0000ad95d19p-1, 0x1.5feb2efd4c7c7p-55},
+{0x1.e1fffe925ce47p-1, 0x1.c8085484eaf08p-55},
+{0x1.e5fffe3ddf853p-1, -0x1.fd5ed02c5cadp-60},
+{0x1.e9fffed0a0e5fp-1, -0x1.a80aaef411586p-55},
+{0x1.ee00008f82eep-1, -0x1.b000aeaf97276p-55},
+{0x1.f20000a22d2f4p-1, -0x1.8f8906e13eba3p-56},
+{0x1.f5fffee35b57dp-1, 0x1.1fdd33b2d3714p-57},
+{0x1.fa00014eec3a6p-1, -0x1.3ee0b7a18c1a5p-58},
+{0x1.fdffff5daa89fp-1, -0x1.c1e24c8e3b503p-58},
+{0x1.0200005b93349p+0, -0x1.50197fe6bedcap-54},
+{0x1.05ffff9d597acp+0, 0x1.20160d062d0dcp-55},
+{0x1.0a00005687a63p+0, -0x1.27f3f9307696ep-54},
+{0x1.0dffff779164ep+0, 0x1.b7eb40bb9c4f4p-54},
+{0x1.12000044a0aa8p+0, 0x1.efbc914d512c4p-55},
+{0x1.16000069685bcp+0, -0x1.c0bea3eb2d82cp-57},
+{0x1.1a000093f0d78p+0, 0x1.1fecbf1e8c52p-54},
+{0x1.1dffffb2b1457p+0, -0x1.3fc91365637d6p-55},
+{0x1.2200008824a1p+0, -0x1.dff7e9feb578ap-54},
+{0x1.25ffffeef953p+0, -0x1.b00a61ec912f7p-55},
+{0x1.2a0000a1e7783p+0, 0x1.60048318b0483p-56},
+{0x1.2e0000853d4c7p+0, -0x1.77fbedf2c8cf3p-54},
+{0x1.320000324c55bp+0, 0x1.f81983997354fp-54},
+{0x1.360000594f796p+0, -0x1.cfe4beff900a9p-54},
+{0x1.3a0000a4c1c0fp+0, 0x1.07dbb2e268d0ep-54},
+{0x1.3e0000751c61bp+0, 0x1.80583ed1c566ep-56},
+{0x1.42000069e8a9fp+0, 0x1.f01f1edf82045p-54},
+{0x1.460000b5a1e34p+0, -0x1.dfdf0cf45c14ap-55},
+{0x1.4a0000187e513p+0, 0x1.401306b83a98dp-55},
+{0x1.4dffff3ba420bp+0, 0x1.9fc6539a6454ep-56},
+{0x1.51fffffe391c9p+0, -0x1.601ef3353ac83p-54},
+{0x1.560000e342455p+0, 0x1.3fb7fac8ac151p-55},
+{0x1.59ffffc39676fp+0, 0x1.4fe7dd6659cc2p-55},
+{0x1.5dfffff10ef42p+0, -0x1.48154cb592bcbp-54},
+# elif N == 128
+{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56},
+{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55},
+{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55},
+{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57},
+{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56},
+{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55},
+{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55},
+{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56},
+{0x1.710000e86978p-1, 0x1.bff6671097952p-56},
+{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55},
+{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57},
+{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57},
+{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55},
+{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56},
+{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55},
+{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55},
+{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55},
+{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55},
+{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55},
+{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55},
+{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55},
+{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56},
+{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55},
+{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55},
+{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55},
+{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56},
+{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55},
+{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56},
+{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55},
+{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55},
+{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60},
+{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55},
+{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56},
+{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55},
+{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55},
+{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55},
+{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55},
+{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57},
+{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55},
+{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57},
+{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58},
+{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56},
+{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56},
+{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55},
+{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56},
+{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57},
+{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57},
+{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55},
+{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55},
+{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57},
+{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55},
+{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55},
+{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56},
+{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57},
+{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55},
+{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55},
+{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56},
+{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55},
+{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58},
+{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56},
+{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56},
+{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55},
+{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55},
+{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57},
+{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56},
+{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56},
+{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56},
+{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58},
+{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55},
+{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56},
+{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58},
+{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55},
+{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59},
+{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55},
+{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55},
+{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57},
+{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56},
+{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57},
+{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56},
+{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57},
+{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55},
+{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54},
+{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54},
+{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55},
+{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57},
+{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54},
+{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55},
+{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56},
+{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55},
+{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54},
+{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54},
+{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55},
+{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54},
+{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54},
+{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57},
+{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54},
+{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54},
+{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54},
+{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56},
+{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56},
+{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56},
+{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54},
+{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55},
+{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55},
+{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55},
+{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54},
+{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54},
+{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55},
+{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54},
+{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55},
+{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56},
+{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54},
+{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57},
+{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55},
+{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55},
+{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54},
+{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54},
+{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54},
+{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54},
+{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54},
+{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57},
+{0x1.530001605277ap+0, -0x1.6bfcece233209p-54},
+{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55},
+{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54},
+{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55},
+{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54},
+{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54},
+{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54},
+#endif
+},
+#endif /* !__HAVE_FAST_FMA */
+};
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
index 0fa1de8a2..b8295b2a5 100644
--- a/newlib/libm/common/math_config.h
+++ b/newlib/libm/common/math_config.h
@@ -326,4 +326,18 @@ extern const struct exp_data {
uint64_t tab[2*(1 << EXP_TABLE_BITS)];
} __exp_data HIDDEN;
+#define LOG_TABLE_BITS 7
+#define LOG_POLY_ORDER 6
+#define LOG_POLY1_ORDER 12
+extern const struct log_data {
+ double ln2hi;
+ double ln2lo;
+ double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ double poly1[LOG_POLY1_ORDER - 1];
+ struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
+#if !__HAVE_FAST_FMA
+ struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
+#endif
+} __log_data HIDDEN;
+
#endif
diff --git a/newlib/libm/math/e_log.c b/newlib/libm/math/e_log.c
index 72cddb2f8..ac4a95068 100644
--- a/newlib/libm/math/e_log.c
+++ b/newlib/libm/math/e_log.c
@@ -63,6 +63,7 @@
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#ifndef _DOUBLE_IS_32BITS
@@ -144,3 +145,4 @@ static double zero = 0.0;
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /*__OBSOLETE_MATH */
diff --git a/newlib/libm/math/w_log.c b/newlib/libm/math/w_log.c
index 2e7e6c00c..5f66d26ad 100644
--- a/newlib/libm/math/w_log.c
+++ b/newlib/libm/math/w_log.c
@@ -49,6 +49,7 @@ PORTABILITY
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#include <errno.h>
#ifndef _DOUBLE_IS_32BITS
@@ -106,3 +107,4 @@ PORTABILITY
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
--
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* [PATCH 2/5] New exp and exp2 implementations
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
2018-06-27 13:06 ` [PATCH 1/5] Use uint32_t sign argument to math error functions Szabolcs Nagy
@ 2018-06-27 13:07 ` Szabolcs Nagy
2018-06-29 12:35 ` Sebastian Huber
2018-06-27 13:07 ` [PATCH 3/5] New log implementation Szabolcs Nagy
` (3 subsequent siblings)
5 siblings, 1 reply; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:07 UTC (permalink / raw)
To: newlib; +Cc: nd
[-- Attachment #1: Type: text/plain, Size: 0 bytes --]
[-- Attachment #2: 0002-New-exp-and-exp2-implementations.patch --]
[-- Type: text/x-patch, Size: 50273 bytes --]
From e7d979273d6628ad43192fbe72edf638629d91a3 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Fri, 22 Jun 2018 18:12:26 +0100
Subject: [PATCH 2/5] New exp and exp2 implementations
The new implementations are provided under !__OBSOLETE_MATH, they use
ISO C99 code. There are several settings, with the default one the
worst case error in nearest rounding mode is 0.509 ULP for exp and
0.507 ULP for exp2 when a multiply and add is contracted into an fma.
They use a shared 2 KB lookup table, on aarch64 .text+.rodata size
of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled
for the new code as it takes care of error handling inline.
The old exp2(x) code used to be just pow(2,x) so the speedup there
is more significant.
The file name has no special prefix to avoid any name collision with
existing files.
Improvements on Cortex-A72:
exp latency: 3.2x
exp thruput: 4.1x
exp2 latency: 7.8x
exp2 thruput: 18.8x
---
newlib/libm/common/Makefile.am | 3 +-
newlib/libm/common/Makefile.in | 34 ++-
newlib/libm/common/exp.c | 165 +++++++++++
newlib/libm/common/exp2.c | 152 ++++++++++
newlib/libm/common/exp_data.c | 611 +++++++++++++++++++++++++++++++++++++++
newlib/libm/common/fdlibm.h | 1 +
newlib/libm/common/math_config.h | 70 ++++-
newlib/libm/common/math_err.c | 101 +++++++
newlib/libm/math/e_exp.c | 2 +
newlib/libm/math/w_exp.c | 2 +
newlib/libm/math/w_exp2.c | 2 +
11 files changed, 1138 insertions(+), 5 deletions(-)
create mode 100644 newlib/libm/common/exp.c
create mode 100644 newlib/libm/common/exp2.c
create mode 100644 newlib/libm/common/exp_data.c
create mode 100644 newlib/libm/common/math_err.c
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am
index 97b24315b..d7c479117 100644
--- a/newlib/libm/common/Makefile.am
+++ b/newlib/libm/common/Makefile.am
@@ -12,7 +12,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_fdim.c s_fma.c s_fmax.c s_fmin.c s_fpclassify.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
- s_signbit.c s_trunc.c
+ s_signbit.c s_trunc.c \
+ exp.c exp2.c exp_data.c math_err.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in
index c944ac790..c35ada3ec 100644
--- a/newlib/libm/common/Makefile.in
+++ b/newlib/libm/common/Makefile.in
@@ -93,7 +93,9 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
lib_a-s_llround.$(OBJEXT) lib_a-s_nearbyint.$(OBJEXT) \
lib_a-s_remquo.$(OBJEXT) lib_a-s_round.$(OBJEXT) \
lib_a-s_scalbln.$(OBJEXT) lib_a-s_signbit.$(OBJEXT) \
- lib_a-s_trunc.$(OBJEXT)
+ lib_a-s_trunc.$(OBJEXT) lib_a-exp.$(OBJEXT) \
+ lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
+ lib_a-math_err.$(OBJEXT)
am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -162,7 +164,8 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo s_fma.lo \
s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
- s_scalbln.lo s_signbit.lo s_trunc.lo
+ s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
+ exp_data.lo math_err.lo
am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
@@ -352,7 +355,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_fdim.c s_fma.c s_fmax.c s_fmin.c s_fpclassify.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
- s_signbit.c s_trunc.c
+ s_signbit.c s_trunc.c \
+ exp.c exp2.c exp_data.c math_err.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
@@ -696,6 +700,30 @@ lib_a-s_trunc.o: s_trunc.c
lib_a-s_trunc.obj: s_trunc.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-s_trunc.obj `if test -f 's_trunc.c'; then $(CYGPATH_W) 's_trunc.c'; else $(CYGPATH_W) '$(srcdir)/s_trunc.c'; fi`
+lib_a-exp.o: exp.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp.o `test -f 'exp.c' || echo '$(srcdir)/'`exp.c
+
+lib_a-exp.obj: exp.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp.obj `if test -f 'exp.c'; then $(CYGPATH_W) 'exp.c'; else $(CYGPATH_W) '$(srcdir)/exp.c'; fi`
+
+lib_a-exp2.o: exp2.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp2.o `test -f 'exp2.c' || echo '$(srcdir)/'`exp2.c
+
+lib_a-exp2.obj: exp2.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp2.obj `if test -f 'exp2.c'; then $(CYGPATH_W) 'exp2.c'; else $(CYGPATH_W) '$(srcdir)/exp2.c'; fi`
+
+lib_a-exp_data.o: exp_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp_data.o `test -f 'exp_data.c' || echo '$(srcdir)/'`exp_data.c
+
+lib_a-exp_data.obj: exp_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp_data.obj `if test -f 'exp_data.c'; then $(CYGPATH_W) 'exp_data.c'; else $(CYGPATH_W) '$(srcdir)/exp_data.c'; fi`
+
+lib_a-math_err.o: math_err.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_err.o `test -f 'math_err.c' || echo '$(srcdir)/'`math_err.c
+
+lib_a-math_err.obj: math_err.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_err.obj `if test -f 'math_err.c'; then $(CYGPATH_W) 'math_err.c'; else $(CYGPATH_W) '$(srcdir)/math_err.c'; fi`
+
lib_a-sf_finite.o: sf_finite.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
diff --git a/newlib/libm/common/exp.c b/newlib/libm/common/exp.c
new file mode 100644
index 000000000..f295b6173
--- /dev/null
+++ b/newlib/libm/common/exp.c
@@ -0,0 +1,165 @@
+/* Double-precision e^x function.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define InvLn2N __exp_data.invln2N
+#define NegLn2hiN __exp_data.negln2hiN
+#define NegLn2loN __exp_data.negln2loN
+#define Shift __exp_data.shift
+#define T __exp_data.tab
+#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
+#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
+#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
+#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
+#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
+
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by <= 460. */
+ sbits -= 1009ull << 52;
+ scale = asdouble (sbits);
+ y = 0x1p1009 * (scale + scale * tmp);
+ return check_oflow (y);
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (y < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo;
+ lo = scale - y + scale * tmp;
+ hi = 1.0 + y;
+ lo = 1.0 - hi + y + lo;
+ y = eval_as_double (hi + lo) - 1.0;
+ /* Avoid -0.0 with downward rounding. */
+ if (WANT_ROUNDING && y == 0.0)
+ y = 0.0;
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (y);
+}
+
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+double
+exp (double x)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, z, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ return WANT_ROUNDING ? 1.0 + x : 1.0;
+ if (abstop >= top12 (1024.0))
+ {
+ if (asuint64 (x) == asuint64 (-INFINITY))
+ return 0.0;
+ if (abstop >= top12 (INFINITY))
+ return 1.0 + x;
+ if (asuint64 (x) >> 63)
+ return __math_uflow (0);
+ else
+ return __math_oflow (0);
+ }
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
+ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
+ z = InvLn2N * x;
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#elif EXP_USE_TOINT_NARROW
+ /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd) >> 16;
+ kd = (double_t) (int32_t) ki;
+#else
+ /* z - kd is in [-1, 1] in non-nearest rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd);
+ kd -= Shift;
+#endif
+ r = x + kd*NegLn2hiN + kd*NegLn2loN;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2*(ki % N);
+ top = ki << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r*r;
+ /* Without fma the worst case error is 0.25/N ulp larger. */
+ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
+#if EXP_POLY_ORDER == 4
+ tmp = tail + r + r2*C2 + r*r2*(C3 + r*C4);
+#elif EXP_POLY_ORDER == 5
+ tmp = tail + r + r2*(C2 + r*C3) + r2*r2*(C4 + r*C5);
+#elif EXP_POLY_ORDER == 6
+ tmp = tail + r + r2*(0.5 + r*C3) + r2*r2*(C4 + r*C5 + r2*C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
+ is no spurious underflow here even without fma. */
+ return scale + scale * tmp;
+}
+#endif
diff --git a/newlib/libm/common/exp2.c b/newlib/libm/common/exp2.c
new file mode 100644
index 000000000..6579e16fd
--- /dev/null
+++ b/newlib/libm/common/exp2.c
@@ -0,0 +1,152 @@
+/* Double-precision 2^x function.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define Shift __exp_data.exp2_shift
+#define T __exp_data.tab
+#define C1 __exp_data.exp2_poly[0]
+#define C2 __exp_data.exp2_poly[1]
+#define C3 __exp_data.exp2_poly[2]
+#define C4 __exp_data.exp2_poly[3]
+#define C5 __exp_data.exp2_poly[4]
+#define C6 __exp_data.exp2_poly[5]
+
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by 1. */
+ sbits -= 1ull << 52;
+ scale = asdouble (sbits);
+ y = 2 * (scale + scale * tmp);
+ return check_oflow (y);
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (y < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo;
+ lo = scale - y + scale * tmp;
+ hi = 1.0 + y;
+ lo = 1.0 - hi + y + lo;
+ y = eval_as_double (hi + lo) - 1.0;
+ /* Avoid -0.0 with downward rounding. */
+ if (WANT_ROUNDING && y == 0.0)
+ y = 0.0;
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (y);
+}
+
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+double
+exp2 (double x)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ return WANT_ROUNDING ? 1.0 + x : 1.0;
+ if (abstop >= top12 (1024.0))
+ {
+ if (asuint64 (x) == asuint64 (-INFINITY))
+ return 0.0;
+ if (abstop >= top12 (INFINITY))
+ return 1.0 + x;
+ if (!(asuint64 (x) >> 63))
+ return __math_oflow (0);
+ else if (asuint64 (x) >= asuint64 (-1075.0))
+ return __math_uflow (0);
+ }
+ if (2 * asuint64 (x) > 2 * asuint64 (928.0))
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */
+ /* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */
+ kd = eval_as_double (x + Shift);
+ ki = asuint64 (kd); /* k. */
+ kd -= Shift; /* k/N for int k. */
+ r = x - kd;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2*(ki % N);
+ top = ki << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r*r;
+ /* Without fma the worst case error is 0.5/N ulp larger. */
+ /* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */
+#if EXP2_POLY_ORDER == 4
+ tmp = tail + r*C1 + r2*C2 + r*r2*(C3 + r*C4);
+#elif EXP2_POLY_ORDER == 5
+ tmp = tail + r*C1 + r2*(C2 + r*C3) + r2*r2*(C4 + r*C5);
+#elif EXP2_POLY_ORDER == 6
+ tmp = tail + r*C1 + r2*(0.5 + r*C3) + r2*r2*(C4 + r*C5 + r2*C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there
+ is no spurious underflow here even without fma. */
+ return scale + scale * tmp;
+}
+#endif
diff --git a/newlib/libm/common/exp_data.c b/newlib/libm/common/exp_data.c
new file mode 100644
index 000000000..3b60f87ef
--- /dev/null
+++ b/newlib/libm/common/exp_data.c
@@ -0,0 +1,611 @@
+/* Shared data between exp, exp2 and pow.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+
+const struct exp_data __exp_data = {
+// N/ln2
+.invln2N = 0x1.71547652b82fep0 * N,
+// -ln2/N
+#if N == 64
+.negln2hiN = -0x1.62e42fefa0000p-7,
+.negln2loN = -0x1.cf79abc9e3b3ap-46,
+#elif N == 128
+.negln2hiN = -0x1.62e42fefa0000p-8,
+.negln2loN = -0x1.cf79abc9e3b3ap-47,
+#elif N == 256
+.negln2hiN = -0x1.62e42fefc0000p-9,
+.negln2loN = 0x1.c610ca86c3899p-45,
+#endif
+// Used for rounding when !TOINT_INTRINSICS
+#if EXP_USE_TOINT_NARROW
+.shift = 0x1800000000.8p0,
+#else
+.shift = 0x1.8p52,
+#endif
+// exp polynomial coefficients.
+.poly = {
+#if N == 64 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
+// abs error: 1.5543*2^-60
+// ulp error: 0.529 (0.533 without fma)
+// if |x| < ln2/128+eps
+// abs error if |x| < ln2/64: 1.7157*2^-50
+0x1.fffffffffdbcdp-2,
+0x1.555555555444cp-3,
+0x1.555573c6a9f7dp-5,
+0x1.1111266d28935p-7,
+#elif N == 64 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
+// abs error: 1.6735*2^-64
+// ulp error: 0.518 (0.522 without fma)
+// if |x| < ln2/64
+0x1.5555555548f9ap-3,
+0x1.555555554bf5dp-5,
+0x1.11115b75f0f4dp-7,
+0x1.6c171a6b6303ep-10,
+#elif N == 128 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
+// abs error: 1.555*2^-66
+// ulp error: 0.509 (0.511 without fma)
+// if |x| < ln2/256+eps
+// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
+// abs error if |x| < ln2/128: 1.7145*2^-56
+0x1.ffffffffffdbdp-2,
+0x1.555555555543cp-3,
+0x1.55555cf172b91p-5,
+0x1.1111167a4d017p-7,
+#elif N == 128 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
+// abs error: 1.5542*2^-60
+// ulp error: 0.521 (0.523 without fma)
+// if |x| < ln2/128
+0x1.fffffffffdbcep-2,
+0x1.55555555543c2p-3,
+0x1.555573c64f2e3p-5,
+0x1.111126b4eff73p-7,
+#elif N == 128 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
+// abs error: 1.6861*2^-71
+// ulp error: 0.509 (0.511 without fma)
+// if |x| < ln2/128
+0x1.55555555548fdp-3,
+0x1.555555555658fp-5,
+0x1.111123a859bb6p-7,
+0x1.6c16ba6920cabp-10,
+#elif N == 256 && EXP_POLY_ORDER == 4 && !EXP_POLY_WIDE
+// abs error: 1.43*2^-58
+// ulp error: 0.549 (0.550 without fma)
+// if |x| < ln2/512
+0x1p0, // unused
+0x1.fffffffffffd4p-2,
+0x1.5555571d6ef9p-3,
+0x1.5555576a5adcep-5,
+#elif N == 256 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
+// abs error: 1.5547*2^-66
+// ulp error: 0.505 (0.506 without fma)
+// if |x| < ln2/256
+0x1.ffffffffffdbdp-2,
+0x1.555555555543cp-3,
+0x1.55555cf16e1edp-5,
+0x1.1111167a4b553p-7,
+#endif
+},
+.exp2_shift = 0x1.8p52 / N,
+// exp2 polynomial coefficients.
+.exp2_poly = {
+#if N == 64 && EXP2_POLY_ORDER == 6 && EXP2_POLY_WIDE
+// abs error: 1.3054*2^-63
+// ulp error: 0.515
+// if |x| < 1/64
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c58fp-3,
+0x1.c6b08d7045cf1p-5,
+0x1.3b2ab6fb8fd0ep-7,
+0x1.5d884afec48d7p-10,
+0x1.43097dc684ae1p-13,
+#elif N == 128 && EXP2_POLY_ORDER == 5 && !EXP2_POLY_WIDE
+// abs error: 1.2195*2^-65
+// ulp error: 0.507 (0.511 without fma)
+// if |x| < 1/256
+// abs error if |x| < 1/128: 1.9941*2^-56
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c424p-3,
+0x1.c6b08d70cf4b5p-5,
+0x1.3b2abd24650ccp-7,
+0x1.5d7e09b4e3a84p-10,
+#elif N == 256 && EXP2_POLY_ORDER == 5 && EXP2_POLY_WIDE
+// abs error: 1.2195*2^-65
+// ulp error: 0.504 (0.508 without fma)
+// if |x| < 1/256
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c424p-3,
+0x1.c6b08d70cf4b5p-5,
+0x1.3b2abd24650ccp-7,
+0x1.5d7e09b4e3a84p-10,
+#endif
+},
+// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
+// tab[2*k] = asuint64(T[k])
+// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
+.tab = {
+#if N == 64
+0x0, 0x3ff0000000000000,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0xbc93cedd78565858, 0x3feea23882552225,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+#elif N == 128
+0x0, 0x3ff0000000000000,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc93cedd78565858, 0x3feea23882552225,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+#elif N == 256
+0x0, 0x3ff0000000000000,
+0xbc84e82fc61851ac, 0x3feffb1afa5abcbf,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0xbc82985dd8521d32, 0x3feff168143b0281,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0x3c651e617061bfbd, 0x3fefe7d42e11bbcc,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c845fad437fa426, 0x3fefde5f72f654b1,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0xbc954529642b232f, 0x3fefd50a0e3c1f89,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0x3c8293708ef5c32e, 0x3fefcbd42b72a836,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0xbc95b9280905b2a4, 0x3fefc2bdf66607e0,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c84f31f32c4b7e7, 0x3fefb9c79b1f3919,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c9407fb30d06420, 0x3fefb0f145e46c85,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0xbc9a5d04b3b9911b, 0x3fefa83b23395dec,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc937a01f0739546, 0x3fef9fa55fdfa9c5,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0x3c8b8268b04ef0a5, 0x3fef973028d7233e,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc9ac46e44a2ebcc, 0x3fef8edbab5e2ab6,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc65704e90c9f860, 0x3fef86a814f204ab,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0xbc897cea57e46280, 0x3fef7e95934f312e,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0x3c56f01429e2b9d2, 0x3fef76a45471c3c2,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0x3c6e653b2459034b, 0x3fef6ed48695bbc0,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c92cc7ea345b7dc, 0x3fef672658375d2f,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0x3c957bfb2876ea9e, 0x3fef5f99f8138a1c,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c8cdc1873af2155, 0x3fef582f95281c6b,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc9493684653a131, 0x3fef50e75eb44027,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0xbc98e2899077520a, 0x3fef49c18438ce4d,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c9120fcd4f59273, 0x3fef42be3578a819,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c89b788c188c9b8, 0x3fef3bdda27912d1,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c877afbca90ef84, 0x3fef351ffb82140a,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c91512f082876ee, 0x3fef2e85711ece75,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0x3c9a02f0c7d75ec6, 0x3fef280e341ddf29,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0xbc803297e78260bf, 0x3fef21ba7591bb70,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc95b77e5ccd9fbf, 0x3fef1b8a66d10f13,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0xbc91e75c40b4251e, 0x3fef157e39771b2f,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c98a911f1f7785a, 0x3fef0f961f641589,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0xbc61e7c998db7dbb, 0x3fef09d24abd886b,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c85425c11faadf4, 0x3fef0432edeeb2fd,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0xbc979517a03e2847, 0x3feefeb83ba8ea32,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc800e2a46da4bee, 0x3feef96266e3fa2d,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0xbc87430803972b34, 0x3feef431a2de883b,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc954de30ae02d94, 0x3feeef26231e754a,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0xbc94f2487e1c03ec, 0x3feeea401b7140ef,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0x3c914a5432fcb2f4, 0x3feee57fbfec6cf4,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c79c3bba5562a2f, 0x3feee0e544ede173,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc85a71612e21658, 0x3feedc70df1c5175,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0x3c86421f6f1d24d6, 0x3feed822c367a024,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc9348a6815fce65, 0x3feed3fb2709468a,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0x3c835c43984d9871, 0x3feecffa3f84b9d4,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0xbc632afc8d9473a0, 0x3feecc2042a7d232,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0xbc95fc5e44de020e, 0x3feec86d668b3237,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0xbc7ea0148327c42f, 0x3feec4e1e192aed2,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0xbc7a843ad1a88022, 0x3feec17dea6db7d7,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c892ca3bf144e63, 0x3feebe41b817c114,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0xbc902c99b04aa8b0, 0x3feebb2d81d8abff,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0x3c73e34f67e67118, 0x3feeb8417f4531ee,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc75a3b1197ba0f0, 0x3feeb57de83f4eef,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0x3c81bd2888075068, 0x3feeb2e2f4f6ad27,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0xbc896be8ae89ef8f, 0x3feeb070dde910d2,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0xbc88e6ac90348602, 0x3feeae27dbe2c4cf,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0xbc91af7f1365c3ac, 0x3feeac0827ff07cc,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0xbc943a3540d1898a, 0x3feeaa11fba87a03,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0xbc951f58ddaa8090, 0x3feea84590998b93,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc82e1648e50a17c, 0x3feea6a320dceb71,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0x3c95f30eda98a575, 0x3feea52ae6cdf6f4,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0x3c917ecda8a72159, 0x3feea3dd1d1929fd,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc9345f3cee1ae6e, 0x3feea2b9febc8fb7,
+0xbc93cedd78565858, 0x3feea23882552225,
+0xbc85c33fdf910406, 0x3feea1c1c70833f6,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0x3c81079ab5789604, 0x3feea0f4b19e9538,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0x3c727df161cd7778, 0x3feea052fa75173e,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0x3c93f9924a05b767, 0x3fee9fdcddd47645,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc87557939a8b5ef, 0x3fee9f9298593ae5,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0x3c51ed2f56fa9d1a, 0x3fee9f7466f42e87,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc88e67a9006c909, 0x3fee9f8286ead08a,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0x3c86597566977ac8, 0x3fee9fbd35d7cbfd,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c92c0b7028a5c3a, 0x3feea024b1ab6e09,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0x3c8a30faf49cc78c, 0x3feea0b938ac1cf6,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0xbc92dad3519d7b5b, 0x3feea17b0976cfdb,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0x3c87d51410fd15c2, 0x3feea26a62ff86f0,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc760a3629969871, 0x3feea3878491c491,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0x3c8b18c6e3fdef5d, 0x3feea4d2add106d9,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0x3c90ec1ddcb1390a, 0x3feea64c1eb941f7,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0xbc522cea4f3afa1e, 0x3feea7f4179f5b21,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c7c88549b958471, 0x3feea9cad931a436,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c931143962f7877, 0x3feeabd0a478580f,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0x3c93e9e96f112479, 0x3feeae05bad61778,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0xbc8dac42a4a38df0, 0x3feeb06a5e0866d9,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0x3c8b99dd98b1ed84, 0x3feeb2fed0282c8a,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc7885ad50cbb750, 0x3feeb5c353aa2fe2,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc82d5e85f3e0301, 0x3feeb8b82b5f98e5,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0xbc51669428996971, 0x3feebbdd9a7670b3,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0x3c71f2b2c1c4c014, 0x3feebf33e47a22a2,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0xbc9294f304f166b6, 0x3feec2bb4d53fe0d,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0xbc8a1e58414c07d3, 0x3feec674194bb8d5,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0xbc79740b58a20091, 0x3feeca5e8d07f29e,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c9165830a2b96c2, 0x3feece7aed8eb8bb,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0xbc903d5cbe27874b, 0x3feed2c980460ad8,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c5986178980fce0, 0x3feed74a8af46052,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0xbc89472975b1f2a5, 0x3feedbfe53c12e59,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0x3c7d8157a34b7e7f, 0x3feee0e521356eba,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0x3c8c8a4e231ebb7d, 0x3feee5ff3a3c2774,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc888c8d11a142e5, 0x3feeeb4ce622f2ff,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0x3c889c2ea41433c7, 0x3feef0ce6c9a8952,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc7274aedac8ff80, 0x3feef68415b749b1,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0x3c85c620ce76df06, 0x3feefc6e29f1c52a,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc8fda52e1b51e41, 0x3fef028cf22749e4,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0xbc32141a7b3e2cd8, 0x3fef08e0b79a6f1f,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc302899507554e5, 0x3fef0f69c3f3a207,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0xbc80dda2d4c0010c, 0x3fef16286141b33d,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0xbc8a007daadf8d68, 0x3fef1d1cd9fa652c,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0x3c836909391181d3, 0x3fef244778fafb22,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0xbc811cd7dbdf9547, 0x3fef2ba88988c933,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0xbc7ac28b7bef6621, 0x3fef33405751c4db,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc7030587207b9e1, 0x3fef3b0f2e6d1675,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0xbc8cc734592af7fc, 0x3fef43155b5bab74,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0x3c87752a44f587e8, 0x3fef4b532b08c968,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0x3c85b66fefeef52e, 0x3fef53c8eacaa1d6,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0x3c5159d9d908a96e, 0x3fef5c76e862e6d3,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0x3c8c254d16117a68, 0x3fef655d71ff6075,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0xbc8d8c329fbd0e03, 0x3fef6e7cd63a8315,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0xbc8ea6e6fbd5f2a6, 0x3fef77d5641c0658,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc63e8e3eab2cbb4, 0x3fef81676b197d17,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0xbc8b7966cd0d2cd9, 0x3fef8b333b16ee12,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0xbc776caa4c2ff1cf, 0x3fef953924676d76,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc81d5fc525d9940, 0x3fef9f7977cdb740,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0x3c855cd8aaea3d21, 0x3fefa9f4867cca6e,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0x3c8269947c2bed4a, 0x3fefb4aaa2188510,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0xbc83b6137e9afe9e, 0x3fefbf9c1cb6412a,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0xbc69fa74878ba7c7, 0x3fefcac948dd7274,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0x3c901f3a75ee0efe, 0x3fefd632798844f8,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0xbc516a9ce6ed84fa, 0x3fefe1d802243c89,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0xbc699c7db2effc76, 0x3fefedba3692d514,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+0x3c64b458677f9840, 0x3feff9d96b2a23d9,
+#endif
+},
+};
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/common/fdlibm.h b/newlib/libm/common/fdlibm.h
index 4523e8b2a..f6c3740e3 100644
--- a/newlib/libm/common/fdlibm.h
+++ b/newlib/libm/common/fdlibm.h
@@ -231,6 +231,7 @@ extern float __ieee754_scalbf __P((float,float));
This is valid as long as there are no namespace issues (the
extern symbol is reserved whenever the caller is reserved)
and there are no observable error handling side effects. */
+# define __ieee754_exp(x) exp(x)
# define __ieee754_expf(x) expf(x)
# define __ieee754_logf(x) logf(x)
# define __ieee754_powf(x,y) powf(x,y)
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
index e4b53fcdd..0fa1de8a2 100644
--- a/newlib/libm/common/math_config.h
+++ b/newlib/libm/common/math_config.h
@@ -147,8 +147,21 @@ issignalingf_inline (float x)
return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
}
-/* Force the evaluation of a floating-point expression for its side-effect. */
#if __aarch64__ && __GNUC__
+/* Prevent the optimization of a floating-point expression. */
+static inline float
+opt_barrier_float (float x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+ return x;
+}
+static inline double
+opt_barrier_double (double x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+ return x;
+}
+/* Force the evaluation of a floating-point expression for its side-effect. */
static inline void
force_eval_float (float x)
{
@@ -160,6 +173,18 @@ force_eval_double (double x)
__asm__ __volatile__ ("" : "+w" (x));
}
#else
+static inline float
+opt_barrier_float (float x)
+{
+ volatile float y = x;
+ return y;
+}
+static inline double
+opt_barrier_double (double x)
+{
+ volatile double y = x;
+ return y;
+}
static inline void
force_eval_float (float x)
{
@@ -199,11 +224,33 @@ eval_as_double (double x)
# define unlikely(x) (x)
#endif
+/* Error handling tail calls for special cases, with sign argument. */
HIDDEN float __math_oflowf (uint32_t);
HIDDEN float __math_uflowf (uint32_t);
HIDDEN float __math_may_uflowf (uint32_t);
HIDDEN float __math_divzerof (uint32_t);
+HIDDEN double __math_oflow (uint32_t);
+HIDDEN double __math_uflow (uint32_t);
+HIDDEN double __math_may_uflow (uint32_t);
+HIDDEN double __math_divzero (uint32_t);
+/* Error handling using input checking. */
HIDDEN float __math_invalidf (float);
+HIDDEN double __math_invalid (double);
+/* Error handling using output checking, only for errno setting. */
+HIDDEN double __math_check_oflow (double);
+HIDDEN double __math_check_uflow (double);
+
+static inline double
+check_oflow (double x)
+{
+ return WANT_ERRNO ? __math_check_oflow (x) : x;
+}
+
+static inline double
+check_uflow (double x)
+{
+ return WANT_ERRNO ? __math_check_uflow (x) : x;
+}
/* Shared between expf, exp2f and powf. */
#define EXP2F_TABLE_BITS 5
@@ -258,4 +305,25 @@ extern const struct powf_log2_data
double poly[POWF_LOG2_POLY_ORDER];
} __powf_log2_data HIDDEN;
+#define EXP_TABLE_BITS 7
+#define EXP_POLY_ORDER 5
+/* Use polynomial that is optimized for a wider input range. This may be
+ needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */
+#define EXP_POLY_WIDE 0
+/* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be
+ needed for good precision in non-nearest rouning and !EXP_POLY_WIDE. */
+#define EXP_USE_TOINT_NARROW 0
+#define EXP2_POLY_ORDER 5
+#define EXP2_POLY_WIDE 0
+extern const struct exp_data {
+ double invln2N;
+ double shift;
+ double negln2hiN;
+ double negln2loN;
+ double poly[4]; /* Last four coefficients. */
+ double exp2_shift;
+ double exp2_poly[EXP2_POLY_ORDER];
+ uint64_t tab[2*(1 << EXP_TABLE_BITS)];
+} __exp_data HIDDEN;
+
#endif
diff --git a/newlib/libm/common/math_err.c b/newlib/libm/common/math_err.c
new file mode 100644
index 000000000..e9d2a5c82
--- /dev/null
+++ b/newlib/libm/common/math_err.c
@@ -0,0 +1,101 @@
+/* Double-precision math error handling.
+ Copyright (c) 2018 ARM Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "math_config.h"
+
+#if WANT_ERRNO
+#include <errno.h>
+/* NOINLINE reduces code size and avoids making math functions non-leaf
+ when the error handling is inlined. */
+NOINLINE static double
+with_errno (double y, int e)
+{
+ errno = e;
+ return y;
+}
+#else
+#define with_errno(x, e) (x)
+#endif
+
+/* NOINLINE reduces code size. */
+NOINLINE static double
+xflow (uint32_t sign, double y)
+{
+ y = opt_barrier_double (sign ? -y : y) * y;
+ return with_errno (y, ERANGE);
+}
+
+HIDDEN double
+__math_uflow (uint32_t sign)
+{
+ return xflow (sign, 0x1p-767);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+ is valid even if the result is non-zero, but in the subnormal range. */
+HIDDEN double
+__math_may_uflow (uint32_t sign)
+{
+ return xflow (sign, 0x1.8p-538);
+}
+#endif
+
+HIDDEN double
+__math_oflow (uint32_t sign)
+{
+ return xflow (sign, 0x1p769);
+}
+
+HIDDEN double
+__math_divzero (uint32_t sign)
+{
+ double y = opt_barrier_double (sign ? -1.0 : 1.0) / 0.0;
+ return with_errno (y, ERANGE);
+}
+
+HIDDEN double
+__math_invalid (double x)
+{
+ double y = (x - x) / (x - x);
+ return isnan (x) ? y : with_errno (y, EDOM);
+}
+
+/* Check result and set errno if necessary. */
+
+HIDDEN double
+__math_check_uflow (double y)
+{
+ return y == 0.0 ? with_errno (y, ERANGE) : y;
+}
+
+HIDDEN double
+__math_check_oflow (double y)
+{
+ return isinf (y) ? with_errno (y, ERANGE) : y;
+}
diff --git a/newlib/libm/math/e_exp.c b/newlib/libm/math/e_exp.c
index e7455eef6..81ea64dfb 100644
--- a/newlib/libm/math/e_exp.c
+++ b/newlib/libm/math/e_exp.c
@@ -75,6 +75,7 @@
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#ifndef _DOUBLE_IS_32BITS
@@ -164,3 +165,4 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/w_exp.c b/newlib/libm/math/w_exp.c
index 9cd607e4e..0c4467712 100644
--- a/newlib/libm/math/w_exp.c
+++ b/newlib/libm/math/w_exp.c
@@ -53,6 +53,7 @@ PORTABILITY
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#include <errno.h>
#ifndef _DOUBLE_IS_32BITS
@@ -126,3 +127,4 @@ u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/w_exp2.c b/newlib/libm/math/w_exp2.c
index 3e41dfc79..c48bdf699 100644
--- a/newlib/libm/math/w_exp2.c
+++ b/newlib/libm/math/w_exp2.c
@@ -52,6 +52,7 @@ PORTABILITY
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#include <errno.h>
#include <math.h>
@@ -68,3 +69,4 @@ PORTABILITY
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
--
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* [PATCH 4/5] New log2 implementation
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
` (2 preceding siblings ...)
2018-06-27 13:07 ` [PATCH 3/5] New log implementation Szabolcs Nagy
@ 2018-06-27 13:08 ` Szabolcs Nagy
2018-06-27 13:09 ` [PATCH 5/5] New pow implementation Szabolcs Nagy
2018-06-27 13:55 ` [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Corinna Vinschen
5 siblings, 0 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:08 UTC (permalink / raw)
To: newlib; +Cc: nd
[-- Attachment #1: Type: text/plain, Size: 1 bytes --]
[-- Attachment #2: 0004-New-log2-implementation.patch --]
[-- Type: text/x-patch, Size: 20557 bytes --]
From d38f924efd91dd33e7df12f5267ce63b0051b6f9 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Tue, 26 Jun 2018 16:06:54 +0100
Subject: [PATCH 4/5] New log2 implementation
The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.547 ULP with inlined fma and fma contraction. It uses
a 1 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1584 bytes.
Note that the math.h header defines log2(x) to be log(x)/Ln2, this is
not changed, so the new code is only used if that macro is suppressed.
Improvements on Cortex-A72:
latency: 2.0x
thruput: 2.2x
---
newlib/libm/common/Makefile.am | 2 +-
newlib/libm/common/Makefile.in | 20 +++-
newlib/libm/common/log2.c | 157 +++++++++++++++++++++++++++++
newlib/libm/common/log2_data.c | 208 +++++++++++++++++++++++++++++++++++++++
newlib/libm/common/math_config.h | 14 +++
newlib/libm/common/s_log2.c | 2 +
6 files changed, 399 insertions(+), 4 deletions(-)
create mode 100644 newlib/libm/common/log2.c
create mode 100644 newlib/libm/common/log2_data.c
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am
index 257a03c5c..7fb3cc2e9 100644
--- a/newlib/libm/common/Makefile.am
+++ b/newlib/libm/common/Makefile.am
@@ -13,7 +13,7 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c log.c log_data.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in
index 856e01185..97dddbd47 100644
--- a/newlib/libm/common/Makefile.in
+++ b/newlib/libm/common/Makefile.in
@@ -96,7 +96,8 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
lib_a-s_trunc.$(OBJEXT) lib_a-exp.$(OBJEXT) \
lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
lib_a-math_err.$(OBJEXT) lib_a-log.$(OBJEXT) \
- lib_a-log_data.$(OBJEXT)
+ lib_a-log_data.$(OBJEXT) lib_a-log2.$(OBJEXT) \
+ lib_a-log2_data.$(OBJEXT)
am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -166,7 +167,8 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
- exp_data.lo math_err.lo log.lo log_data.lo
+ exp_data.lo math_err.lo log.lo log_data.lo log2.lo \
+ log2_data.lo
am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
@@ -357,7 +359,7 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c log.c log_data.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
@@ -737,6 +739,18 @@ lib_a-log_data.o: log_data.c
lib_a-log_data.obj: log_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log_data.obj `if test -f 'log_data.c'; then $(CYGPATH_W) 'log_data.c'; else $(CYGPATH_W) '$(srcdir)/log_data.c'; fi`
+lib_a-log2.o: log2.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2.o `test -f 'log2.c' || echo '$(srcdir)/'`log2.c
+
+lib_a-log2.obj: log2.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2.obj `if test -f 'log2.c'; then $(CYGPATH_W) 'log2.c'; else $(CYGPATH_W) '$(srcdir)/log2.c'; fi`
+
+lib_a-log2_data.o: log2_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2_data.o `test -f 'log2_data.c' || echo '$(srcdir)/'`log2_data.c
+
+lib_a-log2_data.obj: log2_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2_data.obj `if test -f 'log2_data.c'; then $(CYGPATH_W) 'log2_data.c'; else $(CYGPATH_W) '$(srcdir)/log2_data.c'; fi`
+
lib_a-sf_finite.o: sf_finite.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
diff --git a/newlib/libm/common/log2.c b/newlib/libm/common/log2.c
new file mode 100644
index 000000000..64617de6c
--- /dev/null
+++ b/newlib/libm/common/log2.c
@@ -0,0 +1,157 @@
+/* Double-precision log2(x) function.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log2_data.tab
+#define T2 __log2_data.tab2
+#define B __log2_data.poly1
+#define A __log2_data.poly
+#define InvLn2hi __log2_data.invln2hi
+#define InvLn2lo __log2_data.invln2lo
+#define N (1 << LOG2_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+static inline uint32_t
+top16 (double x)
+{
+ return asuint64 (x) >> 48;
+}
+
+double
+(log2) (double x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
+ uint64_t ix, iz, tmp;
+ uint32_t top;
+ int k, i;
+
+ ix = asuint64 (x);
+ top = top16 (x);
+
+#if LOG2_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1.5b51p-5)
+# define HI asuint64 (1.0 + 0x1.6ab2p-5)
+#endif
+ if (unlikely (ix - LO < HI - LO))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+ return 0;
+ r = x - 1.0;
+#if __HAVE_FAST_FMA
+ hi = r*InvLn2hi;
+ lo = r*InvLn2lo + fma (r, InvLn2hi, -hi);
+#else
+ double_t rhi, rlo;
+ rhi = asdouble (asuint64 (r) & -1ULL<<32);
+ rlo = r - rhi;
+ hi = rhi*InvLn2hi;
+ lo = rlo*InvLn2hi + r*InvLn2lo;
+#endif
+ r2 = r * r; /* rounding error: 0x1p-62. */
+ r4 = r2 * r2;
+#if LOG2_POLY1_ORDER == 11
+ /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
+ p = r2*(B[0] + r*B[1]);
+ y = hi + p;
+ lo += hi - y + p;
+ lo += r4*(B[2] + r*B[3] + r2*(B[4] + r*B[5])
+ + r4*(B[6] + r*B[7] + r2*(B[8] + r*B[9])));
+ y += lo;
+#endif
+ return y;
+ }
+ if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzero (1);
+ if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
+ return x;
+ if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+ return __math_invalid (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint64 (x * 0x1p52);
+ ix -= 52ULL << 52;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = asdouble (iz);
+ kd = (double_t) k;
+
+ /* log2(x) = log2(z/c) + log2(c) + k. */
+ /* r ~= z/c - 1, |r| < 1/(2*N). */
+#if __HAVE_FAST_FMA
+ /* rounding error: 0x1p-55/N. */
+ r = fma (z, invc, -1.0);
+ t1 = r*InvLn2hi;
+ t2 = r*InvLn2lo + fma (r, InvLn2hi, -t1);
+#else
+ double_t rhi, rlo;
+ /* rounding error: 0x1p-55/N + 0x1p-65. */
+ r = (z - T2[i].chi - T2[i].clo)*invc;
+ rhi = asdouble (asuint64 (r) & -1ULL << 32);
+ rlo = r - rhi;
+ t1 = rhi*InvLn2hi;
+ t2 = rlo*InvLn2hi + r*InvLn2lo;
+#endif
+
+ /* hi + lo = r/ln2 + log2(c) + k. */
+ t3 = kd + logc;
+ hi = t3 + t1;
+ lo = t3 - hi + t1 + t2;
+
+ /* log2(r+1) = r/ln2 + r^2*poly(r). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r * r; /* rounding error: 0x1p-54/N^2. */
+ r4 = r2 * r2;
+#if LOG2_POLY_ORDER == 7
+ /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
+ ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
+ p = A[0] + r*A[1] + r2*(A[2] + r*A[3]) + r4*(A[4] + r*A[5]);
+ y = lo + r2*p + hi;
+#endif
+ return y;
+}
+#endif
diff --git a/newlib/libm/common/log2_data.c b/newlib/libm/common/log2_data.c
new file mode 100644
index 000000000..c3e5fa688
--- /dev/null
+++ b/newlib/libm/common/log2_data.c
@@ -0,0 +1,208 @@
+/* Data for log2.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << LOG2_TABLE_BITS)
+
+const struct log2_data __log2_data = {
+// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0
+.invln2hi = 0x1.7154765200000p+0,
+.invln2lo = 0x1.705fc2eefa200p-33,
+.poly1 = {
+#if LOG2_POLY1_ORDER == 11
+// relative error: 0x1.2fad8188p-63
+// in -0x1.5b51p-5 0x1.6ab2p-5
+-0x1.71547652b82fep-1,
+0x1.ec709dc3a03f7p-2,
+-0x1.71547652b7c3fp-2,
+0x1.2776c50f05be4p-2,
+-0x1.ec709dd768fe5p-3,
+0x1.a61761ec4e736p-3,
+-0x1.7153fbc64a79bp-3,
+0x1.484d154f01b4ap-3,
+-0x1.289e4a72c383cp-3,
+0x1.0b32f285aee66p-3,
+#endif
+},
+.poly = {
+#if N == 64 && LOG2_POLY_ORDER == 7
+// relative error: 0x1.a72c2bf8p-58
+// abs error: 0x1.67a552c8p-66
+// in -0x1.f45p-8 0x1.f45p-8
+-0x1.71547652b8339p-1,
+0x1.ec709dc3a04bep-2,
+-0x1.7154764702ffbp-2,
+0x1.2776c50034c48p-2,
+-0x1.ec7b328ea92bcp-3,
+0x1.a6225e117f92ep-3,
+#endif
+},
+.tab = {
+#if N == 64
+{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
+{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
+{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
+{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
+{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
+{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
+{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
+{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
+{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
+{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
+{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
+{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
+{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
+{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
+{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
+{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
+{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
+{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
+{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
+{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
+{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
+{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
+{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
+{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
+{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
+{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
+{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
+{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
+{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
+{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
+{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
+{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
+{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
+{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
+{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
+{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
+{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
+{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
+{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
+{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
+{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
+{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
+{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
+{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
+{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
+{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
+{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
+{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
+{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
+{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
+{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
+{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
+{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
+{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
+{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
+{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
+{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
+{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
+{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
+{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
+{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
+{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
+{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
+{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2},
+#endif
+},
+#if !__HAVE_FAST_FMA
+.tab2 = {
+# if N == 64
+{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
+{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
+{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
+{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
+{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
+{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
+{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
+{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
+{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
+{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
+{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
+{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
+{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
+{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
+{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
+{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
+{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
+{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
+{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
+{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
+{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
+{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
+{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
+{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
+{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
+{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
+{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
+{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
+{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
+{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
+{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
+{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
+{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
+{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
+{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
+{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
+{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
+{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
+{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
+{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
+{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
+{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
+{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
+{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
+{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
+{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
+{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
+{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
+{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
+{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
+{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
+{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
+{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
+{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
+{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
+{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
+{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
+{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
+{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
+{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
+{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
+{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
+{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
+{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54},
+# endif
+},
+#endif /* !__HAVE_FAST_FMA */
+};
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
index b8295b2a5..32439f78b 100644
--- a/newlib/libm/common/math_config.h
+++ b/newlib/libm/common/math_config.h
@@ -340,4 +340,18 @@ extern const struct log_data {
#endif
} __log_data HIDDEN;
+#define LOG2_TABLE_BITS 6
+#define LOG2_POLY_ORDER 7
+#define LOG2_POLY1_ORDER 11
+extern const struct log2_data {
+ double invln2hi;
+ double invln2lo;
+ double poly[LOG2_POLY_ORDER - 1];
+ double poly1[LOG2_POLY1_ORDER - 1];
+ struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
+#if !__HAVE_FAST_FMA
+ struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
+#endif
+} __log2_data HIDDEN;
+
#endif
diff --git a/newlib/libm/common/s_log2.c b/newlib/libm/common/s_log2.c
index 3655778e8..0b1ec1d63 100644
--- a/newlib/libm/common/s_log2.c
+++ b/newlib/libm/common/s_log2.c
@@ -66,6 +66,7 @@ C99, POSIX, System V Interface Definition (Issue 6).
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#include <errno.h>
#include <math.h>
#undef log2
@@ -83,3 +84,4 @@ C99, POSIX, System V Interface Definition (Issue 6).
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
--
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* [PATCH 5/5] New pow implementation
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
` (3 preceding siblings ...)
2018-06-27 13:08 ` [PATCH 4/5] New log2 implementation Szabolcs Nagy
@ 2018-06-27 13:09 ` Szabolcs Nagy
2018-06-27 13:55 ` [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Corinna Vinschen
5 siblings, 0 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-06-27 13:09 UTC (permalink / raw)
To: newlib; +Cc: nd
[-- Attachment #1: Type: text/plain, Size: 1 bytes --]
[-- Attachment #2: 0005-New-pow-implementation.patch --]
[-- Type: text/x-patch, Size: 31145 bytes --]
From d1fa3a7c841acbbc7bfbc64b758a535616a70144 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Tue, 26 Jun 2018 16:25:12 +0100
Subject: [PATCH 5/5] New pow implementation
The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses
a 4 KB lookup table in addition to the table in exp_data.c, on aarch64
.text+.rodata size of libm.a is increased by 2295 bytes.
Improvements on Cortex-A72:
latency: 3.3x
thruput: 4.9x
---
newlib/libm/common/Makefile.am | 3 +-
newlib/libm/common/Makefile.in | 20 +-
newlib/libm/common/fdlibm.h | 1 +
newlib/libm/common/math_config.h | 19 ++
newlib/libm/common/pow.c | 377 ++++++++++++++++++++++++++++++++++++++
newlib/libm/common/pow_log_data.c | 187 +++++++++++++++++++
newlib/libm/math/e_pow.c | 2 +
newlib/libm/math/w_pow.c | 3 +-
8 files changed, 607 insertions(+), 5 deletions(-)
create mode 100644 newlib/libm/common/pow.c
create mode 100644 newlib/libm/common/pow_log_data.c
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am
index 7fb3cc2e9..b0856715b 100644
--- a/newlib/libm/common/Makefile.am
+++ b/newlib/libm/common/Makefile.am
@@ -13,7 +13,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c \
+ pow.c pow_log_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in
index 97dddbd47..a777a3466 100644
--- a/newlib/libm/common/Makefile.in
+++ b/newlib/libm/common/Makefile.in
@@ -97,7 +97,8 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
lib_a-math_err.$(OBJEXT) lib_a-log.$(OBJEXT) \
lib_a-log_data.$(OBJEXT) lib_a-log2.$(OBJEXT) \
- lib_a-log2_data.$(OBJEXT)
+ lib_a-log2_data.$(OBJEXT) lib_a-pow.$(OBJEXT) \
+ lib_a-pow_log_data.$(OBJEXT)
am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -168,7 +169,7 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
exp_data.lo math_err.lo log.lo log_data.lo log2.lo \
- log2_data.lo
+ log2_data.lo pow.lo pow_log_data.lo
am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
@@ -359,7 +360,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
s_lrint.c s_llrint.c \
s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
s_signbit.c s_trunc.c \
- exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
+ exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c \
+ pow.c pow_log_data.c
fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
@@ -751,6 +753,18 @@ lib_a-log2_data.o: log2_data.c
lib_a-log2_data.obj: log2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2_data.obj `if test -f 'log2_data.c'; then $(CYGPATH_W) 'log2_data.c'; else $(CYGPATH_W) '$(srcdir)/log2_data.c'; fi`
+lib_a-pow.o: pow.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-pow.o `test -f 'pow.c' || echo '$(srcdir)/'`pow.c
+
+lib_a-pow.obj: pow.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-pow.obj `if test -f 'pow.c'; then $(CYGPATH_W) 'pow.c'; else $(CYGPATH_W) '$(srcdir)/pow.c'; fi`
+
+lib_a-pow_log_data.o: pow_log_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-pow_log_data.o `test -f 'pow_log_data.c' || echo '$(srcdir)/'`pow_log_data.c
+
+lib_a-pow_log_data.obj: pow_log_data.c
+ $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-pow_log_data.obj `if test -f 'pow_log_data.c'; then $(CYGPATH_W) 'pow_log_data.c'; else $(CYGPATH_W) '$(srcdir)/pow_log_data.c'; fi`
+
lib_a-sf_finite.o: sf_finite.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
diff --git a/newlib/libm/common/fdlibm.h b/newlib/libm/common/fdlibm.h
index ae85569ad..2155f5194 100644
--- a/newlib/libm/common/fdlibm.h
+++ b/newlib/libm/common/fdlibm.h
@@ -233,6 +233,7 @@ extern float __ieee754_scalbf __P((float,float));
and there are no observable error handling side effects. */
# define __ieee754_exp(x) exp(x)
# define __ieee754_log(x) log(x)
+# define __ieee754_pow(x,y) pow(x,y)
# define __ieee754_expf(x) expf(x)
# define __ieee754_logf(x) logf(x)
# define __ieee754_powf(x,y) powf(x,y)
diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h
index 32439f78b..3a8cebbe3 100644
--- a/newlib/libm/common/math_config.h
+++ b/newlib/libm/common/math_config.h
@@ -147,6 +147,15 @@ issignalingf_inline (float x)
return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
}
+static inline int
+issignaling_inline (double x)
+{
+ uint64_t ix = asuint64 (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
+ return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
+}
+
#if __aarch64__ && __GNUC__
/* Prevent the optimization of a floating-point expression. */
static inline float
@@ -354,4 +363,14 @@ extern const struct log2_data {
#endif
} __log2_data HIDDEN;
+#define POW_LOG_TABLE_BITS 7
+#define POW_LOG_POLY_ORDER 8
+extern const struct pow_log_data {
+ double ln2hi;
+ double ln2lo;
+ double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ /* Note: the pad field is unused, but allows slightly faster indexing. */
+ struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
+} __pow_log_data HIDDEN;
+
#endif
diff --git a/newlib/libm/common/pow.c b/newlib/libm/common/pow.c
new file mode 100644
index 000000000..da7081cb4
--- /dev/null
+++ b/newlib/libm/common/pow.c
@@ -0,0 +1,377 @@
+/* Double-precision x^y function.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+Worst-case error: 0.54 ULP (~= ulperr_exp + 1024*Ln2*relerr_log*2^53)
+relerr_log: 1.3 * 2^-68 (Relative error of log, 1.5 * 2^-68 without fma)
+ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma)
+*/
+
+#define T __pow_log_data.tab
+#define A __pow_log_data.poly
+#define Ln2hi __pow_log_data.ln2hi
+#define Ln2lo __pow_log_data.ln2lo
+#define N (1 << POW_LOG_TABLE_BITS)
+#define OFF 0x3fe6955500000000
+
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+static inline double_t
+log_inline (uint64_t ix, double_t *tail)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
+ uint64_t iz, tmp;
+ int k, i;
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ z = asdouble (iz);
+ kd = (double_t) k;
+
+ /* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */
+ invc = T[i].invc;
+ logc = T[i].logc;
+ logctail = T[i].logctail;
+
+ /* r = z/c - 1, arranged to be exact. */
+#if __HAVE_FAST_FMA
+ r = fma (z, invc, -1.0);
+#else
+ double_t zhi = asdouble (iz & (-1ULL << 32));
+ double_t zlo = z - zhi;
+ double_t rhi = zhi * invc - 1.0;
+ double_t rlo = zlo * invc;
+ r = rhi + rlo;
+#endif
+
+ /* k*Ln2 + log(c) + r. */
+ t1 = kd * Ln2hi + logc;
+ t2 = t1 + r;
+ lo1 = kd * Ln2lo + logctail;
+ lo2 = t1 - t2 + r;
+
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ double_t ar, ar2, ar3, lo3, lo4;
+ ar = A[0] * r; /* A[0] = -0.5. */
+ ar2 = r * ar;
+ ar3 = r * ar2;
+ /* k*Ln2 + log(c) + r + A[0]*r*r. */
+#if __HAVE_FAST_FMA
+ hi = t2 + ar2;
+ lo3 = fma (ar, r, -ar2);
+ lo4 = t2 - hi + ar2;
+#else
+ double_t arhi = A[0] * rhi;
+ double_t arhi2 = rhi * arhi;
+ hi = t2 + arhi2;
+ lo3 = rlo * (ar + arhi);
+ lo4 = t2 - hi + arhi2;
+#endif
+ /* p = log1p(r) - r - A[0]*r*r. */
+#if POW_LOG_POLY_ORDER == 8
+ p = ar3*(A[1] + r*A[2] + ar2*(A[3] + r*A[4] + ar2*(A[5] + r*A[6])));
+#endif
+ lo = lo1 + lo2 + lo3 + lo4 + p;
+ y = hi + lo;
+ *tail = hi - y + lo;
+ return y;
+}
+
+#undef N
+#undef T
+#define N (1 << EXP_TABLE_BITS)
+#define InvLn2N __exp_data.invln2N
+#define NegLn2hiN __exp_data.negln2hiN
+#define NegLn2loN __exp_data.negln2loN
+#define Shift __exp_data.shift
+#define T __exp_data.tab
+#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
+#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
+#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
+#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
+#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
+
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by <= 460. */
+ sbits -= 1009ull << 52;
+ scale = asdouble (sbits);
+ y = 0x1p1009 * (scale + scale * tmp);
+ return check_oflow (y);
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ /* Note: sbits is signed scale. */
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (fabs (y) < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo, one = 1.0;
+ if (y < 0.0)
+ one = -1.0;
+ lo = scale - y + scale * tmp;
+ hi = one + y;
+ lo = one - hi + y + lo;
+ y = eval_as_double (hi + lo) - one;
+ /* Fix the sign of 0. */
+ if (y == 0.0)
+ y = asdouble (sbits & 0x8000000000000000);
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (y);
+}
+
+#define SIGN_BIAS (0x800 << EXP_TABLE_BITS)
+
+static inline double
+exp_inline (double x, double xtail, uint32_t sign_bias)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, z, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ {
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ double_t one = WANT_ROUNDING ? 1.0 + x : 1.0;
+ return sign_bias ? -one : one;
+ }
+ if (abstop >= top12 (1024.0))
+ {
+ /* Note: inf and nan are already handled. */
+ if (asuint64 (x) >> 63)
+ return __math_uflow (sign_bias);
+ else
+ return __math_oflow (sign_bias);
+ }
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
+ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
+ z = InvLn2N * x;
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#elif EXP_USE_TOINT_NARROW
+ /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd) >> 16;
+ kd = (double_t) (int32_t) ki;
+#else
+ /* z - kd is in [-1, 1] in non-nearest rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd);
+ kd -= Shift;
+#endif
+ r = x + kd*NegLn2hiN + kd*NegLn2loN;
+ /* The code assumes 2^-200 < |xtail| < 2^-8/N. */
+ r += xtail;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2*(ki % N);
+ top = (ki + sign_bias) << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r*r;
+ /* Without fma the worst case error is 0.25/N ulp larger. */
+ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
+#if EXP_POLY_ORDER == 4
+ tmp = tail + r + r2*C2 + r*r2*(C3 + r*C4);
+#elif EXP_POLY_ORDER == 5
+ tmp = tail + r + r2*(C2 + r*C3) + r2*r2*(C4 + r*C5);
+#elif EXP_POLY_ORDER == 6
+ tmp = tail + r + r2*(0.5 + r*C3) + r2*r2*(C4 + r*C5 + r2*C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
+ is no spurious underflow here even without fma. */
+ return scale + scale * tmp;
+}
+
+/* Returns 0 if not int, 1 if odd int, 2 if even int. */
+static inline int
+checkint (uint64_t iy)
+{
+ int e = iy >> 52 & 0x7ff;
+ if (e < 0x3ff)
+ return 0;
+ if (e > 0x3ff + 52)
+ return 2;
+ if (iy & ((1ULL << (0x3ff + 52 - e)) - 1))
+ return 0;
+ if (iy & (1ULL << (0x3ff + 52 - e)))
+ return 1;
+ return 2;
+}
+
+static inline int
+zeroinfnan (uint64_t i)
+{
+ return 2 * i - 1 >= 2 * asuint64 (INFINITY) - 1;
+}
+
+double
+pow (double x, double y)
+{
+ uint32_t sign_bias = 0;
+ uint64_t ix, iy;
+ uint32_t topx, topy;
+
+ ix = asuint64 (x);
+ iy = asuint64 (y);
+ topx = top12 (x);
+ topy = top12 (y);
+ if (unlikely (topx - 0x001 >= 0x7ff - 0x001
+ || (topy & 0x7ff) - 0x3be >= 0x43e - 0x3be))
+ {
+ /* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0
+ and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1. */
+ /* Special cases: (x < 0x1p-126 or inf or nan) or
+ (|y| < 0x1p-65 or |y| >= 0x1p63 or nan). */
+ if (unlikely (zeroinfnan (iy)))
+ {
+ if (2 * iy == 0)
+ return issignaling_inline (x) ? x + y : 1.0;
+ if (ix == asuint64 (1.0))
+ return issignaling_inline (y) ? x + y : 1.0;
+ if (2 * ix > 2 * asuint64 (INFINITY)
+ || 2 * iy > 2 * asuint64 (INFINITY))
+ return x + y;
+ if (2 * ix == 2 * asuint64 (1.0))
+ return 1.0;
+ if ((2 * ix < 2 * asuint64 (1.0)) == !(iy >> 63))
+ return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
+ return y * y;
+ }
+ if (unlikely (zeroinfnan (ix)))
+ {
+ double_t x2 = x * x;
+ if (ix >> 63 && checkint (iy) == 1)
+ {
+ x2 = -x2;
+ sign_bias = 1;
+ }
+ if (WANT_ERRNO && 2 * ix == 0 && iy >> 63)
+ return __math_divzero (sign_bias);
+ /* Without the barrier some versions of clang hoist the 1/x2 and
+ thus division by zero exception can be signaled spuriously. */
+ return iy >> 63 ? opt_barrier_double (1 / x2) : x2;
+ }
+ /* Here x and y are non-zero finite. */
+ if (ix >> 63)
+ {
+ /* Finite x < 0. */
+ int yint = checkint (iy);
+ if (yint == 0)
+ return __math_invalid (x);
+ if (yint == 1)
+ sign_bias = SIGN_BIAS;
+ ix &= 0x7fffffffffffffff;
+ topx &= 0x7ff;
+ }
+ if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be)
+ {
+ /* Note: sign_bias == 0 here because y is not odd. */
+ if (ix == asuint64 (1.0))
+ return 1.0;
+ if ((topy & 0x7ff) < 0x3be)
+ {
+ /* |y| < 2^-65, x^y ~= 1 + y*log(x). */
+ if (WANT_ROUNDING)
+ return ix > asuint64 (1.0) ? 1.0 + y : 1.0 - y;
+ else
+ return 1.0;
+ }
+ return (ix > asuint64 (1.0)) == (topy < 0x800) ? __math_oflow (0)
+ : __math_uflow (0);
+ }
+ if (topx == 0)
+ {
+ /* Normalize subnormal x so exponent becomes negative. */
+ ix = asuint64 (x * 0x1p52);
+ ix &= 0x7fffffffffffffff;
+ ix -= 52ULL << 52;
+ }
+ }
+
+ double_t lo;
+ double_t hi = log_inline (ix, &lo);
+ double_t ehi, elo;
+#if __HAVE_FAST_FMA
+ ehi = y * hi;
+ elo = y * lo + fma (y, hi, -ehi);
+#else
+ double_t yhi = asdouble (iy & -1ULL << 27);
+ double_t ylo = y - yhi;
+ double_t lhi = asdouble (asuint64 (hi) & -1ULL << 27);
+ double_t llo = hi - lhi + lo;
+ ehi = yhi * lhi;
+ elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */
+#endif
+ return exp_inline (ehi, elo, sign_bias);
+}
+#endif
diff --git a/newlib/libm/common/pow_log_data.c b/newlib/libm/common/pow_log_data.c
new file mode 100644
index 000000000..9b94f5e4b
--- /dev/null
+++ b/newlib/libm/common/pow_log_data.c
@@ -0,0 +1,187 @@
+/* Data for the log part of pow.
+ Copyright (c) 2018 Arm Ltd. All rights reserved.
+
+ SPDX-License-Identifier: BSD-3-Clause
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ 3. The name of the company may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << POW_LOG_TABLE_BITS)
+
+const struct pow_log_data __pow_log_data = {
+.ln2hi = 0x1.62e42fefa3800p-1,
+.ln2lo = 0x1.ef35793c76730p-45,
+.poly = {
+#if N == 128 && POW_LOG_POLY_ORDER == 8
+// relative error: 0x1.11922ap-70
+// in -0x1.6bp-8 0x1.6bp-8
+// Coefficients are scaled to match the scaling during evaluation.
+-0x1p-1,
+0x1.555555555556p-2 * -2,
+-0x1.0000000000006p-2 * -2,
+0x1.999999959554ep-3 * 4,
+-0x1.555555529a47ap-3 * 4,
+0x1.2495b9b4845e9p-3 * -8,
+-0x1.0002b8b263fc3p-3 * -8,
+#endif
+},
+.tab = {
+#if N == 128
+#define A(a,b,c) {a,0,b,c},
+A(0x1.6a00000000000p+0, -0x1.62c82f2b9c800p-2, 0x1.ab42428375680p-48)
+A(0x1.6800000000000p+0, -0x1.5d1bdbf580800p-2, -0x1.ca508d8e0f720p-46)
+A(0x1.6600000000000p+0, -0x1.5767717455800p-2, -0x1.362a4d5b6506dp-45)
+A(0x1.6400000000000p+0, -0x1.51aad872df800p-2, -0x1.684e49eb067d5p-49)
+A(0x1.6200000000000p+0, -0x1.4be5f95777800p-2, -0x1.41b6993293ee0p-47)
+A(0x1.6000000000000p+0, -0x1.4618bc21c6000p-2, 0x1.3d82f484c84ccp-46)
+A(0x1.5e00000000000p+0, -0x1.404308686a800p-2, 0x1.c42f3ed820b3ap-50)
+A(0x1.5c00000000000p+0, -0x1.3a64c55694800p-2, 0x1.0b1c686519460p-45)
+A(0x1.5a00000000000p+0, -0x1.347dd9a988000p-2, 0x1.5594dd4c58092p-45)
+A(0x1.5800000000000p+0, -0x1.2e8e2bae12000p-2, 0x1.67b1e99b72bd8p-45)
+A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
+A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
+A(0x1.5400000000000p+0, -0x1.22941fbcf7800p-2, -0x1.65a242853da76p-46)
+A(0x1.5200000000000p+0, -0x1.1c898c1699800p-2, -0x1.fafbc68e75404p-46)
+A(0x1.5000000000000p+0, -0x1.1675cababa800p-2, 0x1.f1fc63382a8f0p-46)
+A(0x1.4e00000000000p+0, -0x1.1058bf9ae4800p-2, -0x1.6a8c4fd055a66p-45)
+A(0x1.4c00000000000p+0, -0x1.0a324e2739000p-2, -0x1.c6bee7ef4030ep-47)
+A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
+A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
+A(0x1.4800000000000p+0, -0x1.fb9186d5e4000p-3, 0x1.d572aab993c87p-47)
+A(0x1.4600000000000p+0, -0x1.ef0adcbdc6000p-3, 0x1.b26b79c86af24p-45)
+A(0x1.4400000000000p+0, -0x1.e27076e2af000p-3, -0x1.72f4f543fff10p-46)
+A(0x1.4200000000000p+0, -0x1.d5c216b4fc000p-3, 0x1.1ba91bbca681bp-45)
+A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
+A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
+A(0x1.3e00000000000p+0, -0x1.bc286742d9000p-3, 0x1.94eb0318bb78fp-46)
+A(0x1.3c00000000000p+0, -0x1.af3c94e80c000p-3, 0x1.a4e633fcd9066p-52)
+A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
+A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
+A(0x1.3800000000000p+0, -0x1.9525a9cf45000p-3, -0x1.ad1d904c1d4e3p-45)
+A(0x1.3600000000000p+0, -0x1.87fa06520d000p-3, 0x1.bbdbf7fdbfa09p-45)
+A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
+A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
+A(0x1.3200000000000p+0, -0x1.6d60fe719d000p-3, -0x1.0e46aa3b2e266p-46)
+A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
+A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
+A(0x1.2e00000000000p+0, -0x1.526e5e3a1b000p-3, -0x1.0de8b90075b8fp-45)
+A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
+A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
+A(0x1.2a00000000000p+0, -0x1.371fc201e9000p-3, 0x1.178864d27543ap-48)
+A(0x1.2800000000000p+0, -0x1.29552f81ff000p-3, -0x1.48d301771c408p-45)
+A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
+A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
+A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
+A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
+A(0x1.2200000000000p+0, -0x1.fec9131dbe000p-4, -0x1.575545ca333f2p-45)
+A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
+A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
+A(0x1.1e00000000000p+0, -0x1.c5e548f5bc000p-4, -0x1.d0c57585fbe06p-46)
+A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
+A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
+A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
+A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
+A(0x1.1800000000000p+0, -0x1.6f0d28ae56000p-4, -0x1.69737c93373dap-45)
+A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
+A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
+A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
+A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
+A(0x1.1200000000000p+0, -0x1.16536eea38000p-4, 0x1.47c5e768fa309p-46)
+A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
+A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
+A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
+A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
+A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
+A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
+A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
+A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
+A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
+A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
+A(0x1.0600000000000p+0, -0x1.7b91b07d58000p-6, -0x1.88d5493faa639p-45)
+A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
+A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
+A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
+A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
+A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
+A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
+A(0x1.fc00000000000p-1, 0x1.0101575890000p-7, -0x1.0c76b999d2be8p-46)
+A(0x1.f800000000000p-1, 0x1.0205658938000p-6, -0x1.3dc5b06e2f7d2p-45)
+A(0x1.f400000000000p-1, 0x1.8492528c90000p-6, -0x1.aa0ba325a0c34p-45)
+A(0x1.f000000000000p-1, 0x1.0415d89e74000p-5, 0x1.111c05cf1d753p-47)
+A(0x1.ec00000000000p-1, 0x1.466aed42e0000p-5, -0x1.c167375bdfd28p-45)
+A(0x1.e800000000000p-1, 0x1.894aa149fc000p-5, -0x1.97995d05a267dp-46)
+A(0x1.e400000000000p-1, 0x1.ccb73cdddc000p-5, -0x1.a68f247d82807p-46)
+A(0x1.e200000000000p-1, 0x1.eea31c006c000p-5, -0x1.e113e4fc93b7bp-47)
+A(0x1.de00000000000p-1, 0x1.1973bd1466000p-4, -0x1.5325d560d9e9bp-45)
+A(0x1.da00000000000p-1, 0x1.3bdf5a7d1e000p-4, 0x1.cc85ea5db4ed7p-45)
+A(0x1.d600000000000p-1, 0x1.5e95a4d97a000p-4, -0x1.c69063c5d1d1ep-45)
+A(0x1.d400000000000p-1, 0x1.700d30aeac000p-4, 0x1.c1e8da99ded32p-49)
+A(0x1.d000000000000p-1, 0x1.9335e5d594000p-4, 0x1.3115c3abd47dap-45)
+A(0x1.cc00000000000p-1, 0x1.b6ac88dad6000p-4, -0x1.390802bf768e5p-46)
+A(0x1.ca00000000000p-1, 0x1.c885801bc4000p-4, 0x1.646d1c65aacd3p-45)
+A(0x1.c600000000000p-1, 0x1.ec739830a2000p-4, -0x1.dc068afe645e0p-45)
+A(0x1.c400000000000p-1, 0x1.fe89139dbe000p-4, -0x1.534d64fa10afdp-45)
+A(0x1.c000000000000p-1, 0x1.1178e8227e000p-3, 0x1.1ef78ce2d07f2p-45)
+A(0x1.be00000000000p-1, 0x1.1aa2b7e23f000p-3, 0x1.ca78e44389934p-45)
+A(0x1.ba00000000000p-1, 0x1.2d1610c868000p-3, 0x1.39d6ccb81b4a1p-47)
+A(0x1.b800000000000p-1, 0x1.365fcb0159000p-3, 0x1.62fa8234b7289p-51)
+A(0x1.b400000000000p-1, 0x1.4913d8333b000p-3, 0x1.5837954fdb678p-45)
+A(0x1.b200000000000p-1, 0x1.527e5e4a1b000p-3, 0x1.633e8e5697dc7p-45)
+A(0x1.ae00000000000p-1, 0x1.6574ebe8c1000p-3, 0x1.9cf8b2c3c2e78p-46)
+A(0x1.ac00000000000p-1, 0x1.6f0128b757000p-3, -0x1.5118de59c21e1p-45)
+A(0x1.aa00000000000p-1, 0x1.7898d85445000p-3, -0x1.c661070914305p-46)
+A(0x1.a600000000000p-1, 0x1.8beafeb390000p-3, -0x1.73d54aae92cd1p-47)
+A(0x1.a400000000000p-1, 0x1.95a5adcf70000p-3, 0x1.7f22858a0ff6fp-47)
+A(0x1.a000000000000p-1, 0x1.a93ed3c8ae000p-3, -0x1.8724350562169p-45)
+A(0x1.9e00000000000p-1, 0x1.b31d8575bd000p-3, -0x1.c358d4eace1aap-47)
+A(0x1.9c00000000000p-1, 0x1.bd087383be000p-3, -0x1.d4bc4595412b6p-45)
+A(0x1.9a00000000000p-1, 0x1.c6ffbc6f01000p-3, -0x1.1ec72c5962bd2p-48)
+A(0x1.9600000000000p-1, 0x1.db13db0d49000p-3, -0x1.aff2af715b035p-45)
+A(0x1.9400000000000p-1, 0x1.e530effe71000p-3, 0x1.212276041f430p-51)
+A(0x1.9200000000000p-1, 0x1.ef5ade4dd0000p-3, -0x1.a211565bb8e11p-51)
+A(0x1.9000000000000p-1, 0x1.f991c6cb3b000p-3, 0x1.bcbecca0cdf30p-46)
+A(0x1.8c00000000000p-1, 0x1.07138604d5800p-2, 0x1.89cdb16ed4e91p-48)
+A(0x1.8a00000000000p-1, 0x1.0c42d67616000p-2, 0x1.7188b163ceae9p-45)
+A(0x1.8800000000000p-1, 0x1.1178e8227e800p-2, -0x1.c210e63a5f01cp-45)
+A(0x1.8600000000000p-1, 0x1.16b5ccbacf800p-2, 0x1.b9acdf7a51681p-45)
+A(0x1.8400000000000p-1, 0x1.1bf99635a6800p-2, 0x1.ca6ed5147bdb7p-45)
+A(0x1.8200000000000p-1, 0x1.214456d0eb800p-2, 0x1.a87deba46baeap-47)
+A(0x1.7e00000000000p-1, 0x1.2bef07cdc9000p-2, 0x1.a9cfa4a5004f4p-45)
+A(0x1.7c00000000000p-1, 0x1.314f1e1d36000p-2, -0x1.8e27ad3213cb8p-45)
+A(0x1.7a00000000000p-1, 0x1.36b6776be1000p-2, 0x1.16ecdb0f177c8p-46)
+A(0x1.7800000000000p-1, 0x1.3c25277333000p-2, 0x1.83b54b606bd5cp-46)
+A(0x1.7600000000000p-1, 0x1.419b423d5e800p-2, 0x1.8e436ec90e09dp-47)
+A(0x1.7400000000000p-1, 0x1.4718dc271c800p-2, -0x1.f27ce0967d675p-45)
+A(0x1.7200000000000p-1, 0x1.4c9e09e173000p-2, -0x1.e20891b0ad8a4p-45)
+A(0x1.7000000000000p-1, 0x1.522ae0738a000p-2, 0x1.ebe708164c759p-45)
+A(0x1.6e00000000000p-1, 0x1.57bf753c8d000p-2, 0x1.fadedee5d40efp-46)
+A(0x1.6c00000000000p-1, 0x1.5d5bddf596000p-2, -0x1.a0b2a08a465dcp-47)
+#endif
+},
+};
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/e_pow.c b/newlib/libm/math/e_pow.c
index cad6737a1..6d2a501a1 100644
--- a/newlib/libm/math/e_pow.c
+++ b/newlib/libm/math/e_pow.c
@@ -58,6 +58,7 @@
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#ifndef _DOUBLE_IS_32BITS
@@ -313,3 +314,4 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
}
#endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/w_pow.c b/newlib/libm/math/w_pow.c
index fc38f68ec..9d1e396a5 100644
--- a/newlib/libm/math/w_pow.c
+++ b/newlib/libm/math/w_pow.c
@@ -52,6 +52,7 @@ PORTABILITY
*/
#include "fdlibm.h"
+#if __OBSOLETE_MATH
#include <errno.h>
#ifndef _DOUBLE_IS_32BITS
@@ -207,7 +208,7 @@ PORTABILITY
}
#endif /* defined(_DOUBLE_IS_32BITS) */
-
+#endif /* __OBSOLETE_MATH */
--
2.14.1
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
` (4 preceding siblings ...)
2018-06-27 13:09 ` [PATCH 5/5] New pow implementation Szabolcs Nagy
@ 2018-06-27 13:55 ` Corinna Vinschen
5 siblings, 0 replies; 9+ messages in thread
From: Corinna Vinschen @ 2018-06-27 13:55 UTC (permalink / raw)
To: newlib
[-- Attachment #1: Type: text/plain, Size: 673 bytes --]
On Jun 27 14:04, Szabolcs Nagy wrote:
> The implementations are based on code from
> https://github.com/ARM-software/optimized-routines
> and provided here under 3 clause BSD license.
>
> Tested on aarch64 and arm targets.
>
> (I'll reply with git format-patch attached because git
> send email does not work for me and thunderbird mangles
> things if i inline).
>
> Szabolcs Nagy (5):
> Use uint32_t sign argument to math error functions
> New exp and exp2 implementations
> New log implementation
> New log2 implementation
> New pow implementation
Series pushed.
Thanks,
Corinna
--
Corinna Vinschen
Cygwin Maintainer
Red Hat
[-- Attachment #2: signature.asc --]
[-- Type: application/pgp-signature, Size: 833 bytes --]
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: [PATCH 2/5] New exp and exp2 implementations
2018-06-27 13:07 ` [PATCH 2/5] New exp and exp2 implementations Szabolcs Nagy
@ 2018-06-29 12:35 ` Sebastian Huber
2018-07-04 15:49 ` Szabolcs Nagy
0 siblings, 1 reply; 9+ messages in thread
From: Sebastian Huber @ 2018-06-29 12:35 UTC (permalink / raw)
To: Szabolcs Nagy, newlib; +Cc: nd
Hello,
On 27/06/18 15:06, Szabolcs Nagy wrote:
> + THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
is there a typo in this line of the license?
--
Sebastian Huber, embedded brains GmbH
Address : Dornierstr. 4, D-82178 Puchheim, Germany
Phone : +49 89 189 47 41-16
Fax : +49 89 189 47 41-09
E-Mail : sebastian.huber@embedded-brains.de
PGP : Public key available on request.
Diese Nachricht ist keine geschäftliche Mitteilung im Sinne des EHUG.
^ permalink raw reply [flat|nested] 9+ messages in thread
* Re: [PATCH 2/5] New exp and exp2 implementations
2018-06-29 12:35 ` Sebastian Huber
@ 2018-07-04 15:49 ` Szabolcs Nagy
0 siblings, 0 replies; 9+ messages in thread
From: Szabolcs Nagy @ 2018-07-04 15:49 UTC (permalink / raw)
To: Sebastian Huber, newlib; +Cc: nd
On 29/06/18 12:22, Sebastian Huber wrote:
> Hello,
>
> On 27/06/18 15:06, Szabolcs Nagy wrote:
>> +Â Â THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
>
> is there a typo in this line of the license?
>
it is not a typo.
i think either using all uppercase name or the official
name of the company are both fine, the BSD license template
has "THE COPYRIGHT HOLDERS AND CONTRIBUTORS" here but you
are supposed to put an actual name there to be clear, it
seems others tend to use all uppercase name, but i doubt
that makes a legal difference and using the official name
is generally better in legal text (this is just a quirk of
the bsd license that it has too many configurable bits and
everybody does it slightly differently).
^ permalink raw reply [flat|nested] 9+ messages in thread
end of thread, other threads:[~2018-07-04 15:34 UTC | newest]
Thread overview: 9+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2018-06-27 13:04 [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Szabolcs Nagy
2018-06-27 13:06 ` [PATCH 1/5] Use uint32_t sign argument to math error functions Szabolcs Nagy
2018-06-27 13:07 ` [PATCH 2/5] New exp and exp2 implementations Szabolcs Nagy
2018-06-29 12:35 ` Sebastian Huber
2018-07-04 15:49 ` Szabolcs Nagy
2018-06-27 13:07 ` [PATCH 3/5] New log implementation Szabolcs Nagy
2018-06-27 13:08 ` [PATCH 4/5] New log2 implementation Szabolcs Nagy
2018-06-27 13:09 ` [PATCH 5/5] New pow implementation Szabolcs Nagy
2018-06-27 13:55 ` [PATCH 0/5] New double precision exp, exp2, log, log2 and pow functions Corinna Vinschen
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