1 | /* Quad-precision floating point cosine 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 <math.h> |
20 | #include <math_private.h> |
21 | |
22 | static const long double c[] = { |
23 | #define ONE c[0] |
24 | 1.00000000000000000000000000000000000E+00L, /* 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-01L, /* bffe0000000000000000000000000000 */ |
34 | 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ |
35 | -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ |
36 | 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ |
37 | -2.75573112601362126593516899592158083E-07L, /* 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-01L, /* bffdfffffffffffffffffffffffffffb */ |
50 | 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ |
51 | -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ |
52 | 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ |
53 | -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ |
54 | 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ |
55 | -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ |
56 | 4.77810092804389587579843296923533297E-14L, /* 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-01L, /* bffc5555555555555555555555555555 */ |
66 | 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ |
67 | -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ |
68 | 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ |
69 | -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ |
70 | }; |
71 | |
72 | #define SINCOSL_COS_HI 0 |
73 | #define SINCOSL_COS_LO 1 |
74 | #define SINCOSL_SIN_HI 2 |
75 | #define SINCOSL_SIN_LO 3 |
76 | extern const long double __sincosl_table[]; |
77 | |
78 | long double |
79 | __kernel_cosl(long double x, long double y) |
80 | { |
81 | long double h, l, z, sin_l, cos_l_m1; |
82 | int64_t ix; |
83 | uint32_t tix, hix, index; |
84 | double xhi, hhi; |
85 | |
86 | xhi = ldbl_high (x); |
87 | EXTRACT_WORDS64 (ix, xhi); |
88 | tix = ((uint64_t)ix) >> 32; |
89 | tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ |
90 | if (tix < 0x3fc30000) /* |x| < 0.1484375 */ |
91 | { |
92 | /* Argument is small enough to approximate it by a Chebyshev |
93 | polynomial of degree 16. */ |
94 | if (tix < 0x3c600000) /* |x| < 2^-57 */ |
95 | if (!((int)x)) return ONE; /* generate inexact */ |
96 | z = x * x; |
97 | return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ |
98 | z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); |
99 | } |
100 | else |
101 | { |
102 | /* So that we don't have to use too large polynomial, we find |
103 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 |
104 | possible values for h. We look up cosl(h) and sinl(h) in |
105 | pre-computed tables, compute cosl(l) and sinl(l) using a |
106 | Chebyshev polynomial of degree 10(11) and compute |
107 | cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ |
108 | int six = tix; |
109 | tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; |
110 | index = 0x3ffe - (tix >> 16); |
111 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); |
112 | x = fabsl (x: x); |
113 | switch (index) |
114 | { |
115 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; |
116 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; |
117 | default: |
118 | case 2: index = (hix - 0x3ffc3000) >> 10; break; |
119 | } |
120 | hix = (hix << 4) & 0x3fffffff; |
121 | /* |
122 | The following should work for double but generates the wrong index. |
123 | For now the code above converts double to ieee extended to compute |
124 | the index back to double for the h value. |
125 | |
126 | index = 0x3fe - (tix >> 20); |
127 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); |
128 | if (signbit (x)) |
129 | { |
130 | x = -x; |
131 | y = -y; |
132 | } |
133 | switch (index) |
134 | { |
135 | case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; |
136 | case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; |
137 | default: |
138 | case 2: index = (hix - 0x3fc30000) >> 14; break; |
139 | } |
140 | */ |
141 | INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); |
142 | h = hhi; |
143 | l = y - (h - x); |
144 | z = l * l; |
145 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); |
146 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); |
147 | return __sincosl_table [index + SINCOSL_COS_HI] |
148 | + (__sincosl_table [index + SINCOSL_COS_LO] |
149 | - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l |
150 | - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); |
151 | } |
152 | } |
153 | |