1/* Quad-precision floating point sine on <-pi/4,pi/4>. 2 Copyright (C) 1999 Free Software Foundation, Inc. 3 This file is part of the GNU C Library. 4 Contributed by Jakub Jelinek <jj@ultra.linux.cz> 5 6 The GNU C Library is free software; you can redistribute it and/or 7 modify it under the terms of the GNU Lesser General Public 8 License as published by the Free Software Foundation; either 9 version 2.1 of the License, or (at your option) any later version. 10 11 The GNU C Library is distributed in the hope that it will be useful, 12 but WITHOUT ANY WARRANTY; without even the implied warranty of 13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 14 Lesser General Public License for more details. 15 16 You should have received a copy of the GNU Lesser General Public 17 License along with the GNU C Library; if not, write to the Free 18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 19 02111-1307 USA. */ 20 21#include "quadmath-imp.h" 22 23static const __float128 c[] = { 24#define ONE c[0] 25 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */ 26 27/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) 28 x in <0,1/256> */ 29#define SCOS1 c[1] 30#define SCOS2 c[2] 31#define SCOS3 c[3] 32#define SCOS4 c[4] 33#define SCOS5 c[5] 34-5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */ 35 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */ 36-1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */ 37 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ 38-2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */ 39 40/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) 41 x in <0,0.1484375> */ 42#define SIN1 c[6] 43#define SIN2 c[7] 44#define SIN3 c[8] 45#define SIN4 c[9] 46#define SIN5 c[10] 47#define SIN6 c[11] 48#define SIN7 c[12] 49#define SIN8 c[13] 50-1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */ 51 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */ 52-1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */ 53 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */ 54-2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */ 55 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */ 56-7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ 57 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */ 58 59/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) 60 x in <0,1/256> */ 61#define SSIN1 c[14] 62#define SSIN2 c[15] 63#define SSIN3 c[16] 64#define SSIN4 c[17] 65#define SSIN5 c[18] 66-1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */ 67 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */ 68-1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */ 69 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */ 70-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */ 71}; 72 73#define SINCOSQ_COS_HI 0 74#define SINCOSQ_COS_LO 1 75#define SINCOSQ_SIN_HI 2 76#define SINCOSQ_SIN_LO 3 77extern const __float128 __sincosq_table[]; 78 79__float128 80__quadmath_kernel_sinq (__float128 x, __float128 y, int iy) 81{ 82 __float128 h, l, z, sin_l, cos_l_m1; 83 int64_t ix; 84 uint32_t tix, hix, index; 85 GET_FLT128_MSW64 (ix, x); 86 tix = ((uint64_t)ix) >> 32; 87 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ 88 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ 89 { 90 /* Argument is small enough to approximate it by a Chebyshev 91 polynomial of degree 17. */ 92 if (tix < 0x3fc60000) /* |x| < 2^-57 */ 93 if (!((int)x)) return x; /* generate inexact */ 94 z = x * x; 95 return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ 96 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); 97 } 98 else 99 { 100 /* So that we don't have to use too large polynomial, we find 101 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 102 possible values for h. We look up cosq(h) and sinq(h) in 103 pre-computed tables, compute cosq(l) and sinq(l) using a 104 Chebyshev polynomial of degree 10(11) and compute 105 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l). */ 106 index = 0x3ffe - (tix >> 16); 107 hix = (tix + (0x200 << index)) & (0xfffffc00 << index); 108 x = fabsq (x); 109 switch (index) 110 { 111 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; 112 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; 113 default: 114 case 2: index = (hix - 0x3ffc3000) >> 10; break; 115 } 116 117 SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0); 118 if (iy) 119 l = (ix < 0 ? -y : y) - (h - x); 120 else 121 l = x - h; 122 z = l * l; 123 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); 124 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); 125 z = __sincosq_table [index + SINCOSQ_SIN_HI] 126 + (__sincosq_table [index + SINCOSQ_SIN_LO] 127 + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1) 128 + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l)); 129 return (ix < 0) ? -z : z; 130 } 131} 132