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30891f35fa
We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
131 lines
5.1 KiB
C
131 lines
5.1 KiB
C
/* Quad-precision floating point cosine on <-pi/4,pi/4>.
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Copyright (C) 1999-2021 Free Software Foundation, Inc.
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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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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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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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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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static const _Float128 c[] = {
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#define ONE c[0]
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L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */
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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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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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/* 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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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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/* 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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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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};
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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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extern const _Float128 __sincosl_table[];
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_Float128
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__kernel_cosl(_Float128 x, _Float128 y)
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{
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_Float128 h, l, z, sin_l, cos_l_m1;
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int64_t ix;
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uint32_t tix, hix, index;
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GET_LDOUBLE_MSW64 (ix, x);
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tix = ((uint64_t)ix) >> 32;
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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. */
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if (tix < 0x3fc60000) /* |x| < 2^-57 */
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if (!((int)x)) return ONE; /* generate inexact */
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z = x * x;
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return 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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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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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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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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SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
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l = y - (h - x);
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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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return __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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