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194 lines
7.3 KiB
C
194 lines
7.3 KiB
C
/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
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Copyright (C) 1999-2024 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 <float.h>
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#include <math.h>
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#include <math_private.h>
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#include <math-underflow.h>
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static const long double c[] = {
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#define ONE c[0]
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1.00000000000000000000000000000000000E+00L, /* 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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-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
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4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
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-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
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2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
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-2.75573112601362126593516899592158083E-07L, /* 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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-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
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4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
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-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
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2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
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-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
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2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
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-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
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4.77810092804389587579843296923533297E-14L, /* 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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-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
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8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
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-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
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2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
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-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
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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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-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
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8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
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-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
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2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
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-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
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1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
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-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
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2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
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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 long double __sincosl_table[];
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void
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__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
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{
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long double 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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double xhi, hhi;
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xhi = ldbl_high (x);
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EXTRACT_WORDS64 (ix, xhi);
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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 < 0x3fc30000) /* |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 < 0x3c600000) /* |x| < 2^-57 */
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{
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math_check_force_underflow (x);
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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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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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int six = tix;
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tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
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index = 0x3ffe - (tix >> 16);
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hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
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x = fabsl (x);
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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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hix = (hix << 4) & 0x3fffffff;
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/*
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The following should work for double but generates the wrong index.
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For now the code above converts double to ieee extended to compute
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the index back to double for the h value.
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index = 0x3fe - (tix >> 20);
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hix = (tix + (0x2000 << index)) & (0xffffc000 << 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 << 14) + hix - 0x3fe00000) >> 12; break;
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case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
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default:
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case 2: index = (hix - 0x3fc30000) >> 14; break;
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}
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*/
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INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
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h = hhi;
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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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