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3fe4dc41 | 1 | /* Quad-precision floating point cosine on <-pi/4,pi/4>. |
581c785b | 2 | Copyright (C) 1999-2022 Free Software Foundation, Inc. |
3fe4dc41 | 3 | This file is part of the GNU C Library. |
3fe4dc41 UD |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or | |
41bdb6e2 AJ |
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. | |
3fe4dc41 UD |
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 | |
41bdb6e2 | 13 | Lesser General Public License for more details. |
3fe4dc41 | 14 | |
41bdb6e2 | 15 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 | 16 | License along with the GNU C Library; if not, see |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
3fe4dc41 | 18 | |
1ed0291c RH |
19 | #include <math.h> |
20 | #include <math_private.h> | |
3fe4dc41 | 21 | |
15089e04 | 22 | static const _Float128 c[] = { |
3fe4dc41 | 23 | #define ONE c[0] |
02bbfb41 | 24 | L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ |
3fe4dc41 UD |
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] | |
02bbfb41 PM |
33 | L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ |
34 | L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ | |
35 | L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ | |
36 | L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ | |
37 | L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ | |
3fe4dc41 UD |
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] | |
02bbfb41 PM |
49 | L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */ |
50 | L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */ | |
51 | L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */ | |
52 | L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ | |
53 | L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */ | |
54 | L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */ | |
55 | L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */ | |
56 | L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ | |
3fe4dc41 UD |
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] | |
02bbfb41 PM |
65 | L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ |
66 | L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ | |
67 | L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ | |
68 | L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ | |
69 | L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ | |
3fe4dc41 UD |
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 | |
15089e04 | 76 | extern const _Float128 __sincosl_table[]; |
3fe4dc41 | 77 | |
15089e04 PM |
78 | _Float128 |
79 | __kernel_cosl(_Float128 x, _Float128 y) | |
3fe4dc41 | 80 | { |
15089e04 | 81 | _Float128 h, l, z, sin_l, cos_l_m1; |
3fe4dc41 | 82 | int64_t ix; |
24ab7723 | 83 | uint32_t tix, hix, index; |
3fe4dc41 | 84 | GET_LDOUBLE_MSW64 (ix, x); |
24ab7723 | 85 | tix = ((uint64_t)ix) >> 32; |
3fe4dc41 UD |
86 | tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ |
87 | if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ | |
88 | { | |
89 | /* Argument is small enough to approximate it by a Chebyshev | |
90 | polynomial of degree 16. */ | |
91 | if (tix < 0x3fc60000) /* |x| < 2^-57 */ | |
92 | if (!((int)x)) return ONE; /* generate inexact */ | |
93 | z = x * x; | |
94 | return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ | |
95 | z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); | |
96 | } | |
97 | else | |
98 | { | |
99 | /* So that we don't have to use too large polynomial, we find | |
100 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
101 | possible values for h. We look up cosl(h) and sinl(h) in | |
102 | pre-computed tables, compute cosl(l) and sinl(l) using a | |
103 | Chebyshev polynomial of degree 10(11) and compute | |
104 | cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ | |
105 | index = 0x3ffe - (tix >> 16); | |
106 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); | |
c0df8e69 JM |
107 | if (signbit (x)) |
108 | { | |
109 | x = -x; | |
110 | y = -y; | |
111 | } | |
3fe4dc41 UD |
112 | switch (index) |
113 | { | |
114 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; | |
115 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; | |
116 | default: | |
117 | case 2: index = (hix - 0x3ffc3000) >> 10; break; | |
118 | } | |
119 | ||
24ab7723 | 120 | SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0); |
3fe4dc41 UD |
121 | l = y - (h - x); |
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 | return __sincosl_table [index + SINCOSL_COS_HI] | |
126 | + (__sincosl_table [index + SINCOSL_COS_LO] | |
127 | - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l | |
128 | - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); | |
129 | } | |
130 | } |