/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. Copyright (C) 1999-2016 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek 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 . */ #include #include #include static const long double c[] = { #define ONE c[0] 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) x in <0,1/256> */ #define SCOS1 c[1] #define SCOS2 c[2] #define SCOS3 c[3] #define SCOS4 c[4] #define SCOS5 c[5] -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) x in <0,0.1484375> */ #define COS1 c[6] #define COS2 c[7] #define COS3 c[8] #define COS4 c[9] #define COS5 c[10] #define COS6 c[11] #define COS7 c[12] #define COS8 c[13] -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) x in <0,1/256> */ #define SSIN1 c[14] #define SSIN2 c[15] #define SSIN3 c[16] #define SSIN4 c[17] #define SSIN5 c[18] -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) x in <0,0.1484375> */ #define SIN1 c[19] #define SIN2 c[20] #define SIN3 c[21] #define SIN4 c[22] #define SIN5 c[23] #define SIN6 c[24] #define SIN7 c[25] #define SIN8 c[26] -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ }; #define SINCOSL_COS_HI 0 #define SINCOSL_COS_LO 1 #define SINCOSL_SIN_HI 2 #define SINCOSL_SIN_LO 3 extern const long double __sincosl_table[]; void __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy) { long double h, l, z, sin_l, cos_l_m1; int64_t ix; uint32_t tix, hix, index; double xhi, hhi; xhi = ldbl_high (x); EXTRACT_WORDS64 (ix, xhi); tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3fc30000) /* |x| < 0.1484375 */ { /* Argument is small enough to approximate it by a Chebyshev polynomial of degree 16(17). */ if (tix < 0x3c600000) /* |x| < 2^-57 */ { math_check_force_underflow (x); if (!((int)x)) /* generate inexact */ { *sinx = x; *cosx = ONE; return; } } z = x * x; *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); } else { /* So that we don't have to use too large polynomial, we find l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 possible values for h. We look up cosl(h) and sinl(h) in pre-computed tables, compute cosl(l) and sinl(l) using a Chebyshev polynomial of degree 10(11) and compute sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ int six = tix; tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; index = 0x3ffe - (tix >> 16); hix = (tix + (0x200 << index)) & (0xfffffc00 << index); x = fabsl (x); switch (index) { case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; default: case 2: index = (hix - 0x3ffc3000) >> 10; break; } hix = (hix << 4) & 0x3fffffff; /* The following should work for double but generates the wrong index. For now the code above converts double to ieee extended to compute the index back to double for the h value. index = 0x3fe - (tix >> 20); hix = (tix + (0x2000 << index)) & (0xffffc000 << index); if (signbit (x)) { x = -x; y = -y; } switch (index) { case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; default: case 2: index = (hix - 0x3fc30000) >> 14; break; } */ INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); h = hhi; if (iy) l = y - (h - x); else l = x - h; z = l * l; sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); z = __sincosl_table [index + SINCOSL_SIN_HI] + (__sincosl_table [index + SINCOSL_SIN_LO] + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); *sinx = (ix < 0) ? -z : z; *cosx = __sincosl_table [index + SINCOSL_COS_HI] + (__sincosl_table [index + SINCOSL_COS_LO] - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); } }