1999-07-15 18:26:25 +00:00
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/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
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2021-01-02 19:32:25 +00:00
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Copyright (C) 1999-2021 Free Software Foundation, Inc.
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1999-07-15 18:26:25 +00:00
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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2001-07-06 04:58:11 +00:00
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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1999-07-15 18:26:25 +00:00
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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2001-07-06 04:58:11 +00:00
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Lesser General Public License for more details.
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1999-07-15 18:26:25 +00:00
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2001-07-06 04:58:11 +00:00
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You should have received a copy of the GNU Lesser General Public
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2012-02-09 23:18:22 +00:00
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License along with the GNU C Library; if not, see
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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
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<https://www.gnu.org/licenses/>. */
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1999-07-15 18:26:25 +00:00
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2015-06-23 22:24:20 +00:00
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#include <float.h>
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2012-03-09 19:29:16 +00:00
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#include <math.h>
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#include <math_private.h>
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2018-05-10 00:53:04 +00:00
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#include <math-underflow.h>
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1999-07-15 18:26:25 +00:00
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2016-07-20 20:20:51 +00:00
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static const _Float128 c[] = {
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1999-07-15 18:26:25 +00:00
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#define ONE c[0]
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2016-09-02 16:01:07 +00:00
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L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */
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1999-07-15 18:26:25 +00:00
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/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
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x in <0,1/256> */
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#define SCOS1 c[1]
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#define SCOS2 c[2]
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#define SCOS3 c[3]
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#define SCOS4 c[4]
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#define SCOS5 c[5]
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2016-09-02 16:01:07 +00:00
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L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */
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L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */
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L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */
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L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */
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L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */
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1999-07-15 18:26:25 +00:00
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/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
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x in <0,0.1484375> */
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#define COS1 c[6]
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#define COS2 c[7]
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#define COS3 c[8]
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#define COS4 c[9]
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#define COS5 c[10]
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#define COS6 c[11]
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#define COS7 c[12]
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#define COS8 c[13]
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2016-09-02 16:01:07 +00:00
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L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */
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L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */
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L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */
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L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
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L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */
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L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */
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L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */
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L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
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1999-07-15 18:26:25 +00:00
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/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
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x in <0,1/256> */
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#define SSIN1 c[14]
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#define SSIN2 c[15]
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#define SSIN3 c[16]
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#define SSIN4 c[17]
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#define SSIN5 c[18]
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2016-09-02 16:01:07 +00:00
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L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */
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L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */
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L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */
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L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */
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L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */
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1999-07-15 18:26:25 +00:00
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/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
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x in <0,0.1484375> */
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#define SIN1 c[19]
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#define SIN2 c[20]
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#define SIN3 c[21]
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#define SIN4 c[22]
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#define SIN5 c[23]
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#define SIN6 c[24]
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#define SIN7 c[25]
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#define SIN8 c[26]
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2016-09-02 16:01:07 +00:00
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L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */
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L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */
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L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */
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L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */
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L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */
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L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */
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L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */
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L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */
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1999-07-15 18:26:25 +00:00
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};
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#define SINCOSL_COS_HI 0
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#define SINCOSL_COS_LO 1
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#define SINCOSL_SIN_HI 2
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#define SINCOSL_SIN_LO 3
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2016-07-20 20:20:51 +00:00
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extern const _Float128 __sincosl_table[];
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1999-07-15 18:26:25 +00:00
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void
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2016-07-20 20:20:51 +00:00
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__kernel_sincosl(_Float128 x, _Float128 y, _Float128 *sinx, _Float128 *cosx, int iy)
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1999-07-15 18:26:25 +00:00
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{
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2016-07-20 20:20:51 +00:00
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_Float128 h, l, z, sin_l, cos_l_m1;
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1999-07-15 18:26:25 +00:00
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int64_t ix;
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2017-08-03 19:55:04 +00:00
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uint32_t tix, hix, index;
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1999-07-15 18:26:25 +00:00
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GET_LDOUBLE_MSW64 (ix, x);
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2017-08-03 19:55:04 +00:00
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tix = ((uint64_t)ix) >> 32;
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1999-07-15 18:26:25 +00:00
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tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
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if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
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{
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/* Argument is small enough to approximate it by a Chebyshev
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polynomial of degree 16(17). */
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if (tix < 0x3fc60000) /* |x| < 2^-57 */
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2015-06-23 22:24:20 +00:00
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{
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2015-09-23 22:42:30 +00:00
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math_check_force_underflow (x);
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2015-06-23 22:24:20 +00:00
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if (!((int)x)) /* generate inexact */
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{
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*sinx = x;
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*cosx = ONE;
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return;
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}
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}
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1999-07-15 18:26:25 +00:00
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z = x * x;
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*sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
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z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
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*cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
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z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
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}
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else
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{
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/* So that we don't have to use too large polynomial, we find
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l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
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possible values for h. We look up cosl(h) and sinl(h) in
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pre-computed tables, compute cosl(l) and sinl(l) using a
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Chebyshev polynomial of degree 10(11) and compute
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sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
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cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
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index = 0x3ffe - (tix >> 16);
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hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
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2012-03-22 12:52:50 +00:00
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if (signbit (x))
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{
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x = -x;
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y = -y;
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}
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1999-07-15 18:26:25 +00:00
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switch (index)
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{
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case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
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case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
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default:
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case 2: index = (hix - 0x3ffc3000) >> 10; break;
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}
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2017-08-03 19:55:04 +00:00
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SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
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1999-07-15 18:26:25 +00:00
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if (iy)
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l = y - (h - x);
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else
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l = x - h;
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z = l * l;
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sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
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cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
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z = __sincosl_table [index + SINCOSL_SIN_HI]
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+ (__sincosl_table [index + SINCOSL_SIN_LO]
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+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
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+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
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*sinx = (ix < 0) ? -z : z;
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*cosx = __sincosl_table [index + SINCOSL_COS_HI]
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+ (__sincosl_table [index + SINCOSL_COS_LO]
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- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
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- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
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}
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}
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