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3fe4dc41 | 1 | /* Quad-precision floating point sine on <-pi/4,pi/4>. |
688903eb | 2 | Copyright (C) 1999-2018 Free Software Foundation, Inc. |
3fe4dc41 UD |
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 | |
41bdb6e2 AJ |
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. | |
3fe4dc41 UD |
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 | |
41bdb6e2 | 14 | Lesser General Public License for more details. |
3fe4dc41 | 15 | |
41bdb6e2 | 16 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
3fe4dc41 | 19 | |
ad39cce0 | 20 | #include <float.h> |
1ed0291c RH |
21 | #include <math.h> |
22 | #include <math_private.h> | |
8f5b00d3 | 23 | #include <math-underflow.h> |
3fe4dc41 | 24 | |
15089e04 | 25 | static const _Float128 c[] = { |
3fe4dc41 | 26 | #define ONE c[0] |
02bbfb41 | 27 | L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ |
3fe4dc41 UD |
28 | |
29 | /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) | |
30 | x in <0,1/256> */ | |
31 | #define SCOS1 c[1] | |
32 | #define SCOS2 c[2] | |
33 | #define SCOS3 c[3] | |
34 | #define SCOS4 c[4] | |
35 | #define SCOS5 c[5] | |
02bbfb41 PM |
36 | L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ |
37 | L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ | |
38 | L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ | |
39 | L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ | |
40 | L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ | |
3fe4dc41 UD |
41 | |
42 | /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) | |
43 | x in <0,0.1484375> */ | |
44 | #define SIN1 c[6] | |
45 | #define SIN2 c[7] | |
46 | #define SIN3 c[8] | |
47 | #define SIN4 c[9] | |
48 | #define SIN5 c[10] | |
49 | #define SIN6 c[11] | |
50 | #define SIN7 c[12] | |
51 | #define SIN8 c[13] | |
02bbfb41 PM |
52 | L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */ |
53 | L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */ | |
54 | L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */ | |
55 | L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */ | |
56 | L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */ | |
57 | L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */ | |
58 | L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */ | |
59 | L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */ | |
3fe4dc41 UD |
60 | |
61 | /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) | |
62 | x in <0,1/256> */ | |
63 | #define SSIN1 c[14] | |
64 | #define SSIN2 c[15] | |
65 | #define SSIN3 c[16] | |
66 | #define SSIN4 c[17] | |
67 | #define SSIN5 c[18] | |
02bbfb41 PM |
68 | L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ |
69 | L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ | |
70 | L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ | |
71 | L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ | |
72 | L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ | |
3fe4dc41 UD |
73 | }; |
74 | ||
75 | #define SINCOSL_COS_HI 0 | |
76 | #define SINCOSL_COS_LO 1 | |
77 | #define SINCOSL_SIN_HI 2 | |
78 | #define SINCOSL_SIN_LO 3 | |
15089e04 | 79 | extern const _Float128 __sincosl_table[]; |
3fe4dc41 | 80 | |
15089e04 PM |
81 | _Float128 |
82 | __kernel_sinl(_Float128 x, _Float128 y, int iy) | |
3fe4dc41 | 83 | { |
15089e04 | 84 | _Float128 h, l, z, sin_l, cos_l_m1; |
3fe4dc41 | 85 | int64_t ix; |
24ab7723 | 86 | uint32_t tix, hix, index; |
3fe4dc41 | 87 | GET_LDOUBLE_MSW64 (ix, x); |
24ab7723 | 88 | tix = ((uint64_t)ix) >> 32; |
3fe4dc41 UD |
89 | tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ |
90 | if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ | |
91 | { | |
92 | /* Argument is small enough to approximate it by a Chebyshev | |
93 | polynomial of degree 17. */ | |
94 | if (tix < 0x3fc60000) /* |x| < 2^-57 */ | |
ad39cce0 | 95 | { |
d96164c3 | 96 | math_check_force_underflow (x); |
ad39cce0 JM |
97 | if (!((int)x)) return x; /* generate inexact */ |
98 | } | |
3fe4dc41 UD |
99 | z = x * x; |
100 | return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ | |
101 | z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); | |
102 | } | |
103 | else | |
104 | { | |
105 | /* So that we don't have to use too large polynomial, we find | |
106 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
107 | possible values for h. We look up cosl(h) and sinl(h) in | |
108 | pre-computed tables, compute cosl(l) and sinl(l) using a | |
109 | Chebyshev polynomial of degree 10(11) and compute | |
110 | sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ | |
111 | index = 0x3ffe - (tix >> 16); | |
112 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); | |
113 | x = fabsl (x); | |
114 | switch (index) | |
115 | { | |
116 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; | |
117 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; | |
118 | default: | |
119 | case 2: index = (hix - 0x3ffc3000) >> 10; break; | |
120 | } | |
121 | ||
24ab7723 | 122 | SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0); |
3fe4dc41 | 123 | if (iy) |
c0df8e69 | 124 | l = (ix < 0 ? -y : y) - (h - x); |
3fe4dc41 UD |
125 | else |
126 | l = x - h; | |
127 | z = l * l; | |
128 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
129 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
130 | z = __sincosl_table [index + SINCOSL_SIN_HI] | |
131 | + (__sincosl_table [index + SINCOSL_SIN_LO] | |
132 | + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) | |
133 | + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); | |
134 | return (ix < 0) ? -z : z; | |
135 | } | |
136 | } |