glibc/sysdeps/ieee754/dbl-64/math_err.c

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Add new exp and exp2 implementations Optimized exp and exp2 implementations using a lookup table for fractional powers of 2. There are several variants, see e_exp_data.c, they can be selected by modifying math_config.h allowing different tradeoffs. The default selection should be acceptable as generic libm code. Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on aarch64 the rodata size is 2160 bytes, shared between exp and exp2. On aarch64 .text + .rodata size decreased by 24912 bytes. The non-nearest rounding error is less than 1 ULP even on targets without efficient round implementation (although the error rate is higher in that case). Targets with single instruction, rounding mode independent, to nearest integer rounding and conversion can use them by setting TOINT_INTRINSICS and adding the necessary code to their math_private.h. The __exp1 code uses the same algorithm, so the error bound of pow increased a bit. New double precision error handling code was added following the style of the single precision error handling code. Improvements on Cortex-A72 compared to current glibc master: exp thruput: 1.61x in [-9.9 9.9] exp latency: 1.53x in [-9.9 9.9] exp thruput: 1.13x in [0.5 1] exp latency: 1.30x in [0.5 1] exp2 thruput: 2.03x in [-9.9 9.9] exp2 latency: 1.64x in [-9.9 9.9] For small (< 1) inputs the current exp code uses a separate algorithm so the speed up there is less. Was tested on aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets, only non-nearest rounding ulp errors increase and they are within acceptable bounds (ulp updates are in separate patches). * NEWS: Mention exp and exp2 improvements. * math/Makefile (libm-support): Remove t_exp. (type-double-routines): Add math_err and e_exp_data. * sysdeps/aarch64/libm-test-ulps: Update. * sysdeps/arm/libm-test-ulps: Update. * sysdeps/i386/fpu/e_exp_data.c: New file. * sysdeps/i386/fpu/math_err.c: New file. * sysdeps/i386/fpu/t_exp.c: Remove. * sysdeps/ia64/fpu/e_exp_data.c: New file. * sysdeps/ia64/fpu/math_err.c: New file. * sysdeps/ia64/fpu/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/e_exp.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp_data.c: New file. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound. * sysdeps/ieee754/dbl-64/eexp.tbl: Remove. * sysdeps/ieee754/dbl-64/math_config.h: New file. * sysdeps/ieee754/dbl-64/math_err.c: New file. * sysdeps/ieee754/dbl-64/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/t_exp2.h: Remove. * sysdeps/ieee754/dbl-64/uexp.h: Remove. * sysdeps/ieee754/dbl-64/uexp.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_err.c: New file. * sysdeps/m68k/m680x0/fpu/t_exp.c: Remove. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
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/* Double-precision math error handling.
Copyright (C) 2018-2021 Free Software Foundation, Inc.
Add new exp and exp2 implementations Optimized exp and exp2 implementations using a lookup table for fractional powers of 2. There are several variants, see e_exp_data.c, they can be selected by modifying math_config.h allowing different tradeoffs. The default selection should be acceptable as generic libm code. Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on aarch64 the rodata size is 2160 bytes, shared between exp and exp2. On aarch64 .text + .rodata size decreased by 24912 bytes. The non-nearest rounding error is less than 1 ULP even on targets without efficient round implementation (although the error rate is higher in that case). Targets with single instruction, rounding mode independent, to nearest integer rounding and conversion can use them by setting TOINT_INTRINSICS and adding the necessary code to their math_private.h. The __exp1 code uses the same algorithm, so the error bound of pow increased a bit. New double precision error handling code was added following the style of the single precision error handling code. Improvements on Cortex-A72 compared to current glibc master: exp thruput: 1.61x in [-9.9 9.9] exp latency: 1.53x in [-9.9 9.9] exp thruput: 1.13x in [0.5 1] exp latency: 1.30x in [0.5 1] exp2 thruput: 2.03x in [-9.9 9.9] exp2 latency: 1.64x in [-9.9 9.9] For small (< 1) inputs the current exp code uses a separate algorithm so the speed up there is less. Was tested on aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets, only non-nearest rounding ulp errors increase and they are within acceptable bounds (ulp updates are in separate patches). * NEWS: Mention exp and exp2 improvements. * math/Makefile (libm-support): Remove t_exp. (type-double-routines): Add math_err and e_exp_data. * sysdeps/aarch64/libm-test-ulps: Update. * sysdeps/arm/libm-test-ulps: Update. * sysdeps/i386/fpu/e_exp_data.c: New file. * sysdeps/i386/fpu/math_err.c: New file. * sysdeps/i386/fpu/t_exp.c: Remove. * sysdeps/ia64/fpu/e_exp_data.c: New file. * sysdeps/ia64/fpu/math_err.c: New file. * sysdeps/ia64/fpu/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/e_exp.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp_data.c: New file. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound. * sysdeps/ieee754/dbl-64/eexp.tbl: Remove. * sysdeps/ieee754/dbl-64/math_config.h: New file. * sysdeps/ieee754/dbl-64/math_err.c: New file. * sysdeps/ieee754/dbl-64/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/t_exp2.h: Remove. * sysdeps/ieee754/dbl-64/uexp.h: Remove. * sysdeps/ieee754/dbl-64/uexp.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_err.c: New file. * sysdeps/m68k/m680x0/fpu/t_exp.c: Remove. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
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This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
Prefer https to http for gnu.org and fsf.org URLs Also, change sources.redhat.com to sourceware.org. This patch was automatically generated by running the following shell script, which uses GNU sed, and which avoids modifying files imported from upstream: sed -ri ' s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g ' \ $(find $(git ls-files) -prune -type f \ ! -name '*.po' \ ! -name 'ChangeLog*' \ ! -path COPYING ! -path COPYING.LIB \ ! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \ ! -path manual/texinfo.tex ! -path scripts/config.guess \ ! -path scripts/config.sub ! -path scripts/install-sh \ ! -path scripts/mkinstalldirs ! -path scripts/move-if-change \ ! -path INSTALL ! -path locale/programs/charmap-kw.h \ ! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \ ! '(' -name configure \ -execdir test -f configure.ac -o -f configure.in ';' ')' \ ! '(' -name preconfigure \ -execdir test -f preconfigure.ac ';' ')' \ -print) and then by running 'make dist-prepare' to regenerate files built from the altered files, and then executing the following to cleanup: chmod a+x sysdeps/unix/sysv/linux/riscv/configure # Omit irrelevant whitespace and comment-only changes, # perhaps from a slightly-different Autoconf version. git checkout -f \ sysdeps/csky/configure \ sysdeps/hppa/configure \ sysdeps/riscv/configure \ sysdeps/unix/sysv/linux/csky/configure # Omit changes that caused a pre-commit check to fail like this: # remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines git checkout -f \ sysdeps/powerpc/powerpc64/ppc-mcount.S \ sysdeps/unix/sysv/linux/s390/s390-64/syscall.S # Omit change that caused a pre-commit check to fail like this: # remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
2019-09-07 05:40:42 +00:00
<https://www.gnu.org/licenses/>. */
Add new exp and exp2 implementations Optimized exp and exp2 implementations using a lookup table for fractional powers of 2. There are several variants, see e_exp_data.c, they can be selected by modifying math_config.h allowing different tradeoffs. The default selection should be acceptable as generic libm code. Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on aarch64 the rodata size is 2160 bytes, shared between exp and exp2. On aarch64 .text + .rodata size decreased by 24912 bytes. The non-nearest rounding error is less than 1 ULP even on targets without efficient round implementation (although the error rate is higher in that case). Targets with single instruction, rounding mode independent, to nearest integer rounding and conversion can use them by setting TOINT_INTRINSICS and adding the necessary code to their math_private.h. The __exp1 code uses the same algorithm, so the error bound of pow increased a bit. New double precision error handling code was added following the style of the single precision error handling code. Improvements on Cortex-A72 compared to current glibc master: exp thruput: 1.61x in [-9.9 9.9] exp latency: 1.53x in [-9.9 9.9] exp thruput: 1.13x in [0.5 1] exp latency: 1.30x in [0.5 1] exp2 thruput: 2.03x in [-9.9 9.9] exp2 latency: 1.64x in [-9.9 9.9] For small (< 1) inputs the current exp code uses a separate algorithm so the speed up there is less. Was tested on aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets, only non-nearest rounding ulp errors increase and they are within acceptable bounds (ulp updates are in separate patches). * NEWS: Mention exp and exp2 improvements. * math/Makefile (libm-support): Remove t_exp. (type-double-routines): Add math_err and e_exp_data. * sysdeps/aarch64/libm-test-ulps: Update. * sysdeps/arm/libm-test-ulps: Update. * sysdeps/i386/fpu/e_exp_data.c: New file. * sysdeps/i386/fpu/math_err.c: New file. * sysdeps/i386/fpu/t_exp.c: Remove. * sysdeps/ia64/fpu/e_exp_data.c: New file. * sysdeps/ia64/fpu/math_err.c: New file. * sysdeps/ia64/fpu/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/e_exp.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp_data.c: New file. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound. * sysdeps/ieee754/dbl-64/eexp.tbl: Remove. * sysdeps/ieee754/dbl-64/math_config.h: New file. * sysdeps/ieee754/dbl-64/math_err.c: New file. * sysdeps/ieee754/dbl-64/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/t_exp2.h: Remove. * sysdeps/ieee754/dbl-64/uexp.h: Remove. * sysdeps/ieee754/dbl-64/uexp.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_err.c: New file. * sysdeps/m68k/m680x0/fpu/t_exp.c: Remove. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
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#include <math-barriers.h>
#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 = math_opt_barrier (sign ? -y : y) * y;
return with_errno (y, ERANGE);
}
attribute_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. */
attribute_hidden double
__math_may_uflow (uint32_t sign)
{
return xflow (sign, 0x1.8p-538);
}
#endif
attribute_hidden double
__math_oflow (uint32_t sign)
{
return xflow (sign, 0x1p769);
}
attribute_hidden double
__math_divzero (uint32_t sign)
{
double y = math_opt_barrier (sign ? -1.0 : 1.0) / 0.0;
return with_errno (y, ERANGE);
}
attribute_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. */
attribute_hidden double
__math_check_uflow (double y)
{
return y == 0.0 ? with_errno (y, ERANGE) : y;
}
attribute_hidden double
__math_check_oflow (double y)
{
return isinf (y) ? with_errno (y, ERANGE) : y;
}