glibc/sysdeps/ieee754/flt-32/math_config.h

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Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
/* Configuration for math routines.
Copyright (C) 2017-2022 Free Software Foundation, Inc.
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
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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
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<https://www.gnu.org/licenses/>. */
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
#ifndef _MATH_CONFIG_H
#define _MATH_CONFIG_H
#include <math.h>
#include <math_private.h>
#include <nan-high-order-bit.h>
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
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#include <stdint.h>
#ifndef WANT_ROUNDING
/* Correct special case results in non-nearest rounding modes. */
# define WANT_ROUNDING 1
#endif
#ifndef WANT_ERRNO
/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0. */
# define WANT_ERRNO 1
#endif
#ifndef WANT_ERRNO_UFLOW
/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
#endif
#ifndef TOINT_INTRINSICS
Clean up converttoint handling and document the semantics This patch currently only affects aarch64. The roundtoint and converttoint internal functions are only called with small values, so 32 bit result is enough for converttoint and it is a signed int conversion so the return type is changed to int32_t. The original idea was to help the compiler keeping the result in uint64_t, then it's clear that no sign extension is needed and there is no accidental undefined or implementation defined signed int arithmetics. But it turns out gcc does a good job with inlining so changing the type has no overhead and the semantics of the conversion is less surprising this way. Since we want to allow the asuint64 (x + 0x1.8p52) style conversion, the top bits were never usable and the existing code ensures that only the bottom 32 bits of the conversion result are used. On aarch64 the neon intrinsics (which round ties to even) are changed to round and lround (which round ties away from zero) this does not affect the results in a significant way, but more portable (relies on round and lround being inlined which works with -fno-math-errno). The TOINT_SHIFT and TOINT_RINT macros were removed, only keep separate code paths for TOINT_INTRINSICS and !TOINT_INTRINSICS. * sysdeps/aarch64/fpu/math_private.h (roundtoint): Use round. (converttoint): Use lround. * sysdeps/ieee754/flt-32/math_config.h (roundtoint): Declare and document the semantics when TOINT_INTRINSICS is set. (converttoint): Likewise. (TOINT_RINT): Remove. (TOINT_SHIFT): Remove. * sysdeps/ieee754/flt-32/e_expf.c (__expf): Remove the TOINT_RINT code path.
2018-07-04 11:29:29 +00:00
/* When set, the roundtoint and converttoint functions are provided with
the semantics documented below. */
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
# define TOINT_INTRINSICS 0
#endif
Clean up converttoint handling and document the semantics This patch currently only affects aarch64. The roundtoint and converttoint internal functions are only called with small values, so 32 bit result is enough for converttoint and it is a signed int conversion so the return type is changed to int32_t. The original idea was to help the compiler keeping the result in uint64_t, then it's clear that no sign extension is needed and there is no accidental undefined or implementation defined signed int arithmetics. But it turns out gcc does a good job with inlining so changing the type has no overhead and the semantics of the conversion is less surprising this way. Since we want to allow the asuint64 (x + 0x1.8p52) style conversion, the top bits were never usable and the existing code ensures that only the bottom 32 bits of the conversion result are used. On aarch64 the neon intrinsics (which round ties to even) are changed to round and lround (which round ties away from zero) this does not affect the results in a significant way, but more portable (relies on round and lround being inlined which works with -fno-math-errno). The TOINT_SHIFT and TOINT_RINT macros were removed, only keep separate code paths for TOINT_INTRINSICS and !TOINT_INTRINSICS. * sysdeps/aarch64/fpu/math_private.h (roundtoint): Use round. (converttoint): Use lround. * sysdeps/ieee754/flt-32/math_config.h (roundtoint): Declare and document the semantics when TOINT_INTRINSICS is set. (converttoint): Likewise. (TOINT_RINT): Remove. (TOINT_SHIFT): Remove. * sysdeps/ieee754/flt-32/e_expf.c (__expf): Remove the TOINT_RINT code path.
2018-07-04 11:29:29 +00:00
#if TOINT_INTRINSICS
/* Round x to nearest int in all rounding modes, ties have to be rounded
consistently with converttoint so the results match. If the result
would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
static inline double_t
roundtoint (double_t x);
/* Convert x to nearest int in all rounding modes, ties have to be rounded
consistently with roundtoint. If the result is not representible in an
int32_t then the semantics is unspecified. */
static inline int32_t
converttoint (double_t x);
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
#endif
static inline uint32_t
asuint (float f)
{
union
{
float f;
uint32_t i;
} u = {f};
return u.i;
}
static inline float
asfloat (uint32_t i)
{
union
{
uint32_t i;
float f;
} u = {i};
return u.f;
}
static inline uint64_t
asuint64 (double f)
{
union
{
double f;
uint64_t i;
} u = {f};
return u.i;
}
static inline double
asdouble (uint64_t i)
{
union
{
uint64_t i;
double f;
} u = {i};
return u.f;
}
static inline int
issignalingf_inline (float x)
{
uint32_t ix = asuint (x);
if (HIGH_ORDER_BIT_IS_SET_FOR_SNAN)
return (ix & 0x7fc00000) == 0x7fc00000;
return 2 * (ix ^ 0x00400000) > 2 * 0x7fc00000UL;
}
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
#define NOINLINE __attribute__ ((noinline))
attribute_hidden float __math_oflowf (uint32_t);
attribute_hidden float __math_uflowf (uint32_t);
attribute_hidden float __math_may_uflowf (uint32_t);
attribute_hidden float __math_divzerof (uint32_t);
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
attribute_hidden float __math_invalidf (float);
math: Optimized generic exp10f with wrappers It is inspired by expf and reuses its tables and internal functions. The error checks are inlined and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Result for x86_64 (i7-4790K CPU @ 4.00GHz) are: Before new code: "exp10f": { "workload-spec2017.wrf (adapted)": { "duration": 4.0414e+09, "iterations": 1.00128e+08, "reciprocal-throughput": 26.6818, "latency": 54.043, "max-throughput": 3.74787e+07, "min-throughput": 1.85038e+07 } With new code: "exp10f": { "workload-spec2017.wrf (adapted)": { "duration": 4.11951e+09, "iterations": 1.23968e+08, "reciprocal-throughput": 21.0581, "latency": 45.4028, "max-throughput": 4.74876e+07, "min-throughput": 2.20251e+07 } Result for aarch64 (A72 @ 2GHz) are: Before new code: "exp10f": { "workload-spec2017.wrf (adapted)": { "duration": 4.62362e+09, "iterations": 3.3376e+07, "reciprocal-throughput": 127.698, "latency": 149.365, "max-throughput": 7.831e+06, "min-throughput": 6.69501e+06 } With new code: "exp10f": { "workload-spec2017.wrf (adapted)": { "duration": 4.29108e+09, "iterations": 6.6752e+07, "reciprocal-throughput": 51.2111, "latency": 77.3568, "max-throughput": 1.9527e+07, "min-throughput": 1.29271e+07 } Checked on x86_64-linux-gnu, powerpc64le-linux-gnu, aarch64-linux-gnu, and sparc64-linux-gnu.
2020-04-08 20:32:28 +00:00
/* Shared between expf, exp2f, exp10f, and powf. */
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
#define EXP2F_TABLE_BITS 5
#define EXP2F_POLY_ORDER 3
extern const struct exp2f_data
{
uint64_t tab[1 << EXP2F_TABLE_BITS];
double shift_scaled;
double poly[EXP2F_POLY_ORDER];
double shift;
double invln2_scaled;
double poly_scaled[EXP2F_POLY_ORDER];
} __exp2f_data attribute_hidden;
#define LOGF_TABLE_BITS 4
#define LOGF_POLY_ORDER 4
extern const struct logf_data
{
struct
{
double invc, logc;
} tab[1 << LOGF_TABLE_BITS];
double ln2;
double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
} __logf_data attribute_hidden;
#define LOG2F_TABLE_BITS 4
#define LOG2F_POLY_ORDER 4
extern const struct log2f_data
{
struct
{
double invc, logc;
} tab[1 << LOG2F_TABLE_BITS];
double poly[LOG2F_POLY_ORDER];
} __log2f_data attribute_hidden;
#define POWF_LOG2_TABLE_BITS 4
#define POWF_LOG2_POLY_ORDER 5
#if TOINT_INTRINSICS
# define POWF_SCALE_BITS EXP2F_TABLE_BITS
#else
# define POWF_SCALE_BITS 0
#endif
#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
extern const struct powf_log2_data
{
struct
{
double invc, logc;
} tab[1 << POWF_LOG2_TABLE_BITS];
double poly[POWF_LOG2_POLY_ORDER];
} __powf_log2_data attribute_hidden;
Optimized generic expf and exp2f with wrappers Based on new expf and exp2f code from https://github.com/ARM-software/optimized-routines/ with wrapper on aarch64: expf reciprocal-throughput: 2.3x faster expf latency: 1.7x faster without wrapper on aarch64: expf reciprocal-throughput: 3.3x faster expf latency: 1.7x faster without wrapper on aarch64: exp2f reciprocal-throughput: 2.8x faster exp2f latency: 1.3x faster libm.so size on aarch64: .text size: -152 bytes .rodata size: -1740 bytes expf/exp2f worst case nearest rounding error: 0.502 ulp worst case non-nearest rounding error: 1 ulp Error checks are inline and errno setting is in separate tail called functions, but the wrappers are kept in this patch to handle the _LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls and once for __expf_finite calls on targets where the new code is used.) Double precision arithmetics is used which is expected to be faster on most targets (including soft-float) than using single precision and it is easier to get good precision result with it. Const data is kept in a separate translation unit which complicates maintenance a bit, but is expected to give good code for literal loads on most targets and allows sharing data across expf, exp2f and powf. (This data is disabled on i386, m68k and ia64 which have their own expf, exp2f and powf code.) Some details may need target specific tweaks: - best convert and round to int operation in the arg reduction may be different across targets. - code was optimized on fma target, optimal polynomial eval may be different without fma. - gcc does not always generate good code for fp bit representation access via unions or it may be inherently slow on some targets. The libm-test-ulps will need adjustment because.. - The argument reduction ideally uses nearest rounded rint, but that is not efficient on most targets, so the polynomial can get evaluated on a wider interval in non-nearest rounding mode making 1 ulp errors common in that case. - The polynomial is evaluated such that it may have 1 ulp error on negative tiny inputs with upward rounding. * math/Makefile (type-float-routines): Add math_errf and e_exp2f_data. * sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define. (roundtoint, converttoint): Likewise. * sysdeps/ieee754/flt-32/e_expf.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f.c: New implementation. * sysdeps/ieee754/flt-32/e_exp2f_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h: New file. * sysdeps/ieee754/flt-32/math_errf.c: New file. * sysdeps/ieee754/flt-32/t_exp2f.h: Remove. * sysdeps/i386/fpu/e_exp2f_data.c: New file. * sysdeps/i386/fpu/math_errf.c: New file. * sysdeps/ia64/fpu/e_exp2f_data.c: New file. * sysdeps/ia64/fpu/math_errf.c: New file. * sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
2017-09-06 16:42:00 +00:00
#endif