glibc/sysdeps/ieee754/flt-32/s_sincosf_data.c

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Improve performance of sincosf This patch is a complete rewrite of sincosf. The new version is significantly faster, as well as simple and accurate. The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over all 4 billion inputs. In non-nearest rounding modes the error is 1ULP. The algorithm uses 3 main cases: small inputs which don't need argument reduction, small inputs which need a simple range reduction and large inputs requiring complex range reduction. The code uses approximate integer comparisons to quickly decide between these cases. The small range reducer uses a single reduction step to handle values up to 120.0. It is fastest on targets which support inlined round instructions. The large range reducer uses integer arithmetic for simplicity. It does a 32x96 bit multiply to compute a 64-bit modulo result. This is more than accurate enough to handle the worst-case cancellation for values close to an integer multiple of PI/4. It could be further optimized, however it is already much faster than necessary. sincosf throughput gains on Cortex-A72: * |x| < 0x1p-12 : 1.6x * |x| < M_PI_4 : 1.7x * |x| < 2 * M_PI: 1.5x * |x| < 120.0 : 1.8x * |x| < Inf : 2.3x * math/Makefile: Add s_sincosf_data.c. * sysdeps/ia64/fpu/s_sincosf_data.c: New file. * sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function. (sincosf_poly): Likewise. (reduce_small): Likewise. (reduce_large): Likewise. * sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite. * sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data. * sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file. * sysdeps/x86_64/fpu/s_sincosf_data.c: New file.
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/* Compute sine and cosine of argument.
Copyright (C) 2018-2021 Free Software Foundation, Inc.
Improve performance of sincosf This patch is a complete rewrite of sincosf. The new version is significantly faster, as well as simple and accurate. The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over all 4 billion inputs. In non-nearest rounding modes the error is 1ULP. The algorithm uses 3 main cases: small inputs which don't need argument reduction, small inputs which need a simple range reduction and large inputs requiring complex range reduction. The code uses approximate integer comparisons to quickly decide between these cases. The small range reducer uses a single reduction step to handle values up to 120.0. It is fastest on targets which support inlined round instructions. The large range reducer uses integer arithmetic for simplicity. It does a 32x96 bit multiply to compute a 64-bit modulo result. This is more than accurate enough to handle the worst-case cancellation for values close to an integer multiple of PI/4. It could be further optimized, however it is already much faster than necessary. sincosf throughput gains on Cortex-A72: * |x| < 0x1p-12 : 1.6x * |x| < M_PI_4 : 1.7x * |x| < 2 * M_PI: 1.5x * |x| < 120.0 : 1.8x * |x| < Inf : 2.3x * math/Makefile: Add s_sincosf_data.c. * sysdeps/ia64/fpu/s_sincosf_data.c: New file. * sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function. (sincosf_poly): Likewise. (reduce_small): Likewise. (reduce_large): Likewise. * sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite. * sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data. * sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file. * sysdeps/x86_64/fpu/s_sincosf_data.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
2019-09-07 05:40:42 +00:00
<https://www.gnu.org/licenses/>. */
Improve performance of sincosf This patch is a complete rewrite of sincosf. The new version is significantly faster, as well as simple and accurate. The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over all 4 billion inputs. In non-nearest rounding modes the error is 1ULP. The algorithm uses 3 main cases: small inputs which don't need argument reduction, small inputs which need a simple range reduction and large inputs requiring complex range reduction. The code uses approximate integer comparisons to quickly decide between these cases. The small range reducer uses a single reduction step to handle values up to 120.0. It is fastest on targets which support inlined round instructions. The large range reducer uses integer arithmetic for simplicity. It does a 32x96 bit multiply to compute a 64-bit modulo result. This is more than accurate enough to handle the worst-case cancellation for values close to an integer multiple of PI/4. It could be further optimized, however it is already much faster than necessary. sincosf throughput gains on Cortex-A72: * |x| < 0x1p-12 : 1.6x * |x| < M_PI_4 : 1.7x * |x| < 2 * M_PI: 1.5x * |x| < 120.0 : 1.8x * |x| < Inf : 2.3x * math/Makefile: Add s_sincosf_data.c. * sysdeps/ia64/fpu/s_sincosf_data.c: New file. * sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function. (sincosf_poly): Likewise. (reduce_small): Likewise. (reduce_large): Likewise. * sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite. * sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data. * sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file. * sysdeps/x86_64/fpu/s_sincosf_data.c: New file.
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#include <stdint.h>
#include <math.h>
#include "math_config.h"
#include "s_sincosf.h"
/* The constants and polynomials for sine and cosine. The 2nd entry
computes -cos (x) rather than cos (x) to get negation for free. */
const sincos_t __sincosf_table[2] =
{
{
{ 1.0, -1.0, -1.0, 1.0 },
#if TOINT_INTRINSICS
0x1.45F306DC9C883p-1,
#else
0x1.45F306DC9C883p+23,
#endif
0x1.921FB54442D18p0,
0x1p0,
-0x1.ffffffd0c621cp-2,
0x1.55553e1068f19p-5,
-0x1.6c087e89a359dp-10,
0x1.99343027bf8c3p-16,
-0x1.555545995a603p-3,
0x1.1107605230bc4p-7,
-0x1.994eb3774cf24p-13
},
{
{ 1.0, -1.0, -1.0, 1.0 },
#if TOINT_INTRINSICS
0x1.45F306DC9C883p-1,
#else
0x1.45F306DC9C883p+23,
#endif
0x1.921FB54442D18p0,
-0x1p0,
0x1.ffffffd0c621cp-2,
-0x1.55553e1068f19p-5,
0x1.6c087e89a359dp-10,
-0x1.99343027bf8c3p-16,
-0x1.555545995a603p-3,
0x1.1107605230bc4p-7,
-0x1.994eb3774cf24p-13
}
};
/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
only 8 new bits are added per entry, making the table 4 times larger. */
const uint32_t __inv_pio4[24] =
{
0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
};