1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. 2 Copyright (C) 1999-2018 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, see 18 <http://www.gnu.org/licenses/>. */ 19 20 #include "quadmath-imp.h" 21 22 static const __float128 c[] = { 23 #define ONE c[0] 24 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */ 25 26 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) 27 x in <0,1/256> */ 28 #define SCOS1 c[1] 29 #define SCOS2 c[2] 30 #define SCOS3 c[3] 31 #define SCOS4 c[4] 32 #define SCOS5 c[5] 33 -5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */ 34 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */ 35 -1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */ 36 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ 37 -2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */ 38 39 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) 40 x in <0,0.1484375> */ 41 #define COS1 c[6] 42 #define COS2 c[7] 43 #define COS3 c[8] 44 #define COS4 c[9] 45 #define COS5 c[10] 46 #define COS6 c[11] 47 #define COS7 c[12] 48 #define COS8 c[13] 49 -4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */ 50 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */ 51 -1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */ 52 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ 53 -2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */ 54 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */ 55 -1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */ 56 4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ 57 58 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) 59 x in <0,1/256> */ 60 #define SSIN1 c[14] 61 #define SSIN2 c[15] 62 #define SSIN3 c[16] 63 #define SSIN4 c[17] 64 #define SSIN5 c[18] 65 -1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */ 66 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */ 67 -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */ 68 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */ 69 -2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */ 70 71 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) 72 x in <0,0.1484375> */ 73 #define SIN1 c[19] 74 #define SIN2 c[20] 75 #define SIN3 c[21] 76 #define SIN4 c[22] 77 #define SIN5 c[23] 78 #define SIN6 c[24] 79 #define SIN7 c[25] 80 #define SIN8 c[26] 81 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */ 82 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */ 83 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */ 84 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */ 85 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */ 86 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */ 87 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ 88 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */ 89 }; 90 91 #define SINCOSL_COS_HI 0 92 #define SINCOSL_COS_LO 1 93 #define SINCOSL_SIN_HI 2 94 #define SINCOSL_SIN_LO 3 95 extern const __float128 __sincosq_table[]; 96 97 void 98 __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx, __float128 *cosx, int iy) 99 { 100 __float128 h, l, z, sin_l, cos_l_m1; 101 int64_t ix; 102 uint32_t tix, hix, index; 103 GET_FLT128_MSW64 (ix, x); 104 tix = ((uint64_t)ix) >> 32; 105 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ 106 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ 107 { 108 /* Argument is small enough to approximate it by a Chebyshev 109 polynomial of degree 16(17). */ 110 if (tix < 0x3fc60000) /* |x| < 2^-57 */ 111 { 112 math_check_force_underflow (x); 113 if (!((int)x)) /* generate inexact */ 114 { 115 *sinx = x; 116 *cosx = ONE; 117 return; 118 } 119 } 120 z = x * x; 121 *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ 122 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); 123 *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ 124 z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); 125 } 126 else 127 { 128 /* So that we don't have to use too large polynomial, we find 129 l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83 130 possible values for h. We look up cosq(h) and sinq(h) in 131 pre-computed tables, compute cosq(l) and sinq(l) using a 132 Chebyshev polynomial of degree 10(11) and compute 133 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and 134 cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l). */ 135 index = 0x3ffe - (tix >> 16); 136 hix = (tix + (0x200 << index)) & (0xfffffc00 << index); 137 if (signbitq (x)) 138 { 139 x = -x; 140 y = -y; 141 } 142 switch (index) 143 { 144 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; 145 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; 146 default: 147 case 2: index = (hix - 0x3ffc3000) >> 10; break; 148 } 149 150 SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0); 151 if (iy) 152 l = y - (h - x); 153 else 154 l = x - h; 155 z = l * l; 156 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); 157 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); 158 z = __sincosq_table [index + SINCOSL_SIN_HI] 159 + (__sincosq_table [index + SINCOSL_SIN_LO] 160 + (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1) 161 + (__sincosq_table [index + SINCOSL_COS_HI] * sin_l)); 162 *sinx = (ix < 0) ? -z : z; 163 *cosx = __sincosq_table [index + SINCOSL_COS_HI] 164 + (__sincosq_table [index + SINCOSL_COS_LO] 165 - (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l 166 - __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1)); 167 } 168 } 169