1 | /* Quad-precision floating point sine on <-pi/4,pi/4>. |
2 | Copyright (C) 1999-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <float.h> |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | #include <math-underflow.h> |
23 | |
24 | static const long double c[] = { |
25 | #define ONE c[0] |
26 | 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ |
27 | |
28 | /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) |
29 | x in <0,1/256> */ |
30 | #define SCOS1 c[1] |
31 | #define SCOS2 c[2] |
32 | #define SCOS3 c[3] |
33 | #define SCOS4 c[4] |
34 | #define SCOS5 c[5] |
35 | -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ |
36 | 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ |
37 | -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ |
38 | 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ |
39 | -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ |
40 | |
41 | /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) |
42 | x in <0,0.1484375> */ |
43 | #define SIN1 c[6] |
44 | #define SIN2 c[7] |
45 | #define SIN3 c[8] |
46 | #define SIN4 c[9] |
47 | #define SIN5 c[10] |
48 | #define SIN6 c[11] |
49 | #define SIN7 c[12] |
50 | #define SIN8 c[13] |
51 | -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ |
52 | 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ |
53 | -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ |
54 | 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ |
55 | -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ |
56 | 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ |
57 | -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ |
58 | 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ |
59 | |
60 | /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) |
61 | x in <0,1/256> */ |
62 | #define SSIN1 c[14] |
63 | #define SSIN2 c[15] |
64 | #define SSIN3 c[16] |
65 | #define SSIN4 c[17] |
66 | #define SSIN5 c[18] |
67 | -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ |
68 | 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ |
69 | -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ |
70 | 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ |
71 | -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ |
72 | }; |
73 | |
74 | #define SINCOSL_COS_HI 0 |
75 | #define SINCOSL_COS_LO 1 |
76 | #define SINCOSL_SIN_HI 2 |
77 | #define SINCOSL_SIN_LO 3 |
78 | extern const long double __sincosl_table[]; |
79 | |
80 | long double |
81 | __kernel_sinl(long double x, long double y, int iy) |
82 | { |
83 | long double h, l, z, sin_l, cos_l_m1; |
84 | int64_t ix; |
85 | uint32_t tix, hix, index; |
86 | double xhi, hhi; |
87 | |
88 | xhi = ldbl_high (x); |
89 | EXTRACT_WORDS64 (ix, xhi); |
90 | tix = ((uint64_t)ix) >> 32; |
91 | tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ |
92 | if (tix < 0x3fc30000) /* |x| < 0.1484375 */ |
93 | { |
94 | /* Argument is small enough to approximate it by a Chebyshev |
95 | polynomial of degree 17. */ |
96 | if (tix < 0x3c600000) /* |x| < 2^-57 */ |
97 | { |
98 | math_check_force_underflow (x); |
99 | if (!((int)x)) return x; /* generate inexact */ |
100 | } |
101 | z = x * x; |
102 | return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ |
103 | z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); |
104 | } |
105 | else |
106 | { |
107 | /* So that we don't have to use too large polynomial, we find |
108 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 |
109 | possible values for h. We look up cosl(h) and sinl(h) in |
110 | pre-computed tables, compute cosl(l) and sinl(l) using a |
111 | Chebyshev polynomial of degree 10(11) and compute |
112 | sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ |
113 | int six = tix; |
114 | tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; |
115 | index = 0x3ffe - (tix >> 16); |
116 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); |
117 | x = fabsl (x: x); |
118 | switch (index) |
119 | { |
120 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; |
121 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; |
122 | default: |
123 | case 2: index = (hix - 0x3ffc3000) >> 10; break; |
124 | } |
125 | hix = (hix << 4) & 0x3fffffff; |
126 | /* |
127 | The following should work for double but generates the wrong index. |
128 | For now the code above converts double to ieee extended to compute |
129 | the index back to double for the h value. |
130 | |
131 | index = 0x3fe - (tix >> 20); |
132 | hix = (tix + (0x2000 << index)) & (0xffffc000 << index); |
133 | x = fabsl (x); |
134 | switch (index) |
135 | { |
136 | case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; |
137 | case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; |
138 | default: |
139 | case 2: index = (hix - 0x3fc30000) >> 14; break; |
140 | } |
141 | */ |
142 | INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); |
143 | h = hhi; |
144 | if (iy) |
145 | l = (ix < 0 ? -y : y) - (h - x); |
146 | else |
147 | l = x - h; |
148 | z = l * l; |
149 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); |
150 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); |
151 | z = __sincosl_table [index + SINCOSL_SIN_HI] |
152 | + (__sincosl_table [index + SINCOSL_SIN_LO] |
153 | + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) |
154 | + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); |
155 | return (ix < 0) ? -z : z; |
156 | } |
157 | } |
158 | |