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8848d99d | 1 | /* Quad-precision floating point sine on <-pi/4,pi/4>. |
6d7e8eda | 2 | Copyright (C) 1999-2023 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 | /* The polynomials have not been optimized for extended-precision and | |
20 | may contain more terms than needed. */ | |
21 | ||
ad39cce0 | 22 | #include <float.h> |
8848d99d JM |
23 | #include <math.h> |
24 | #include <math_private.h> | |
8f5b00d3 | 25 | #include <math-underflow.h> |
8848d99d JM |
26 | |
27 | /* The polynomials have not been optimized for extended-precision and | |
28 | may contain more terms than needed. */ | |
29 | ||
30 | static const long double c[] = { | |
31 | #define ONE c[0] | |
32 | 1.00000000000000000000000000000000000E+00L, | |
33 | ||
34 | /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) | |
35 | x in <0,1/256> */ | |
36 | #define SCOS1 c[1] | |
37 | #define SCOS2 c[2] | |
38 | #define SCOS3 c[3] | |
39 | #define SCOS4 c[4] | |
40 | #define SCOS5 c[5] | |
41 | -5.00000000000000000000000000000000000E-01L, | |
42 | 4.16666666666666666666666666556146073E-02L, | |
43 | -1.38888888888888888888309442601939728E-03L, | |
44 | 2.48015873015862382987049502531095061E-05L, | |
45 | -2.75573112601362126593516899592158083E-07L, | |
46 | ||
47 | /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) | |
48 | x in <0,0.1484375> */ | |
49 | #define SIN1 c[6] | |
50 | #define SIN2 c[7] | |
51 | #define SIN3 c[8] | |
52 | #define SIN4 c[9] | |
53 | #define SIN5 c[10] | |
54 | #define SIN6 c[11] | |
55 | #define SIN7 c[12] | |
56 | #define SIN8 c[13] | |
57 | -1.66666666666666666666666666666666538e-01L, | |
58 | 8.33333333333333333333333333307532934e-03L, | |
59 | -1.98412698412698412698412534478712057e-04L, | |
60 | 2.75573192239858906520896496653095890e-06L, | |
61 | -2.50521083854417116999224301266655662e-08L, | |
62 | 1.60590438367608957516841576404938118e-10L, | |
63 | -7.64716343504264506714019494041582610e-13L, | |
64 | 2.81068754939739570236322404393398135e-15L, | |
65 | ||
66 | /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) | |
67 | x in <0,1/256> */ | |
68 | #define SSIN1 c[14] | |
69 | #define SSIN2 c[15] | |
70 | #define SSIN3 c[16] | |
71 | #define SSIN4 c[17] | |
72 | #define SSIN5 c[18] | |
73 | -1.66666666666666666666666666666666659E-01L, | |
74 | 8.33333333333333333333333333146298442E-03L, | |
75 | -1.98412698412698412697726277416810661E-04L, | |
76 | 2.75573192239848624174178393552189149E-06L, | |
77 | -2.50521016467996193495359189395805639E-08L, | |
78 | }; | |
79 | ||
80 | #define SINCOSL_COS_HI 0 | |
81 | #define SINCOSL_COS_LO 1 | |
82 | #define SINCOSL_SIN_HI 2 | |
83 | #define SINCOSL_SIN_LO 3 | |
84 | extern const long double __sincosl_table[]; | |
85 | ||
86 | long double | |
87 | __kernel_sinl(long double x, long double y, int iy) | |
88 | { | |
89 | long double absx, h, l, z, sin_l, cos_l_m1; | |
90 | int index; | |
91 | ||
92 | absx = fabsl (x); | |
93 | if (absx < 0.1484375L) | |
94 | { | |
95 | /* Argument is small enough to approximate it by a Chebyshev | |
96 | polynomial of degree 17. */ | |
97 | if (absx < 0x1p-33L) | |
ad39cce0 | 98 | { |
d96164c3 | 99 | math_check_force_underflow (x); |
ad39cce0 JM |
100 | if (!((int)x)) return x; /* generate inexact */ |
101 | } | |
8848d99d JM |
102 | z = x * x; |
103 | return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ | |
104 | z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); | |
105 | } | |
106 | else | |
107 | { | |
108 | /* So that we don't have to use too large polynomial, we find | |
109 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
110 | possible values for h. We look up cosl(h) and sinl(h) in | |
111 | pre-computed tables, compute cosl(l) and sinl(l) using a | |
112 | Chebyshev polynomial of degree 10(11) and compute | |
113 | sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ | |
114 | index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L))); | |
115 | h = 0.1484375L + index / 128.0; | |
116 | index *= 4; | |
117 | if (iy) | |
118 | l = (x < 0 ? -y : y) - (h - absx); | |
119 | else | |
120 | l = absx - h; | |
121 | z = l * l; | |
122 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
123 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
124 | z = __sincosl_table [index + SINCOSL_SIN_HI] | |
125 | + (__sincosl_table [index + SINCOSL_SIN_LO] | |
126 | + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) | |
127 | + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); | |
128 | return (x < 0) ? -z : z; | |
129 | } | |
130 | } |