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8848d99d | 1 | /* Extended-precision floating point cosine on <-pi/4,pi/4>. |
dff8da6b | 2 | Copyright (C) 1999-2024 Free Software Foundation, Inc. |
8848d99d | 3 | This file is part of the GNU C Library. |
8848d99d JM |
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 | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
8848d99d JM |
18 | |
19 | #include <math.h> | |
20 | #include <math_private.h> | |
21 | ||
22 | /* The polynomials have not been optimized for extended-precision and | |
23 | may contain more terms than needed. */ | |
24 | ||
25 | static const long double c[] = { | |
26 | #define ONE c[0] | |
27 | 1.00000000000000000000000000000000000E+00L, | |
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] | |
36 | -5.00000000000000000000000000000000000E-01L, | |
37 | 4.16666666666666666666666666556146073E-02L, | |
38 | -1.38888888888888888888309442601939728E-03L, | |
39 | 2.48015873015862382987049502531095061E-05L, | |
40 | -2.75573112601362126593516899592158083E-07L, | |
41 | ||
42 | /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) | |
43 | x in <0,0.1484375> */ | |
44 | #define COS1 c[6] | |
45 | #define COS2 c[7] | |
46 | #define COS3 c[8] | |
47 | #define COS4 c[9] | |
48 | #define COS5 c[10] | |
49 | #define COS6 c[11] | |
50 | #define COS7 c[12] | |
51 | #define COS8 c[13] | |
52 | -4.99999999999999999999999999999999759E-01L, | |
53 | 4.16666666666666666666666666651287795E-02L, | |
54 | -1.38888888888888888888888742314300284E-03L, | |
55 | 2.48015873015873015867694002851118210E-05L, | |
56 | -2.75573192239858811636614709689300351E-07L, | |
57 | 2.08767569877762248667431926878073669E-09L, | |
58 | -1.14707451049343817400420280514614892E-11L, | |
59 | 4.77810092804389587579843296923533297E-14L, | |
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] | |
68 | -1.66666666666666666666666666666666659E-01L, | |
69 | 8.33333333333333333333333333146298442E-03L, | |
70 | -1.98412698412698412697726277416810661E-04L, | |
71 | 2.75573192239848624174178393552189149E-06L, | |
72 | -2.50521016467996193495359189395805639E-08L, | |
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 | |
79 | extern const long double __sincosl_table[]; | |
80 | ||
81 | long double | |
82 | __kernel_cosl(long double x, long double y) | |
83 | { | |
84 | long double h, l, z, sin_l, cos_l_m1; | |
85 | int index; | |
86 | ||
87 | if (signbit (x)) | |
88 | { | |
89 | x = -x; | |
90 | y = -y; | |
91 | } | |
92 | if (x < 0.1484375L) | |
93 | { | |
94 | /* Argument is small enough to approximate it by a Chebyshev | |
95 | polynomial of degree 16. */ | |
96 | if (x < 0x1p-33L) | |
97 | if (!((int)x)) return ONE; /* generate inexact */ | |
98 | z = x * x; | |
99 | return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ | |
100 | z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); | |
101 | } | |
102 | else | |
103 | { | |
104 | /* So that we don't have to use too large polynomial, we find | |
105 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
106 | possible values for h. We look up cosl(h) and sinl(h) in | |
107 | pre-computed tables, compute cosl(l) and sinl(l) using a | |
108 | Chebyshev polynomial of degree 10(11) and compute | |
109 | cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ | |
110 | index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L))); | |
111 | h = 0.1484375L + index / 128.0; | |
112 | index *= 4; | |
113 | l = y - (h - x); | |
114 | z = l * l; | |
115 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
116 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
117 | return __sincosl_table [index + SINCOSL_COS_HI] | |
118 | + (__sincosl_table [index + SINCOSL_COS_LO] | |
119 | - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l | |
120 | - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); | |
121 | } | |
122 | } |