1 /* Extended-precision floating point cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2023 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 /* 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 }