1/* Extended-precision floating point cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Based on quad-precision cosine by Jakub Jelinek <jj@ultra.linux.cz>
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include <math.h>
21#include <math_private.h>
22
23/* The polynomials have not been optimized for extended-precision and
24 may contain more terms than needed. */
25
26static const long double c[] = {
27#define ONE c[0]
28 1.00000000000000000000000000000000000E+00L,
29
30/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
31 x in <0,1/256> */
32#define SCOS1 c[1]
33#define SCOS2 c[2]
34#define SCOS3 c[3]
35#define SCOS4 c[4]
36#define SCOS5 c[5]
37-5.00000000000000000000000000000000000E-01L,
38 4.16666666666666666666666666556146073E-02L,
39-1.38888888888888888888309442601939728E-03L,
40 2.48015873015862382987049502531095061E-05L,
41-2.75573112601362126593516899592158083E-07L,
42
43/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
44 x in <0,0.1484375> */
45#define COS1 c[6]
46#define COS2 c[7]
47#define COS3 c[8]
48#define COS4 c[9]
49#define COS5 c[10]
50#define COS6 c[11]
51#define COS7 c[12]
52#define COS8 c[13]
53-4.99999999999999999999999999999999759E-01L,
54 4.16666666666666666666666666651287795E-02L,
55-1.38888888888888888888888742314300284E-03L,
56 2.48015873015873015867694002851118210E-05L,
57-2.75573192239858811636614709689300351E-07L,
58 2.08767569877762248667431926878073669E-09L,
59-1.14707451049343817400420280514614892E-11L,
60 4.77810092804389587579843296923533297E-14L,
61
62/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
63 x in <0,1/256> */
64#define SSIN1 c[14]
65#define SSIN2 c[15]
66#define SSIN3 c[16]
67#define SSIN4 c[17]
68#define SSIN5 c[18]
69-1.66666666666666666666666666666666659E-01L,
70 8.33333333333333333333333333146298442E-03L,
71-1.98412698412698412697726277416810661E-04L,
72 2.75573192239848624174178393552189149E-06L,
73-2.50521016467996193495359189395805639E-08L,
74};
75
76#define SINCOSL_COS_HI 0
77#define SINCOSL_COS_LO 1
78#define SINCOSL_SIN_HI 2
79#define SINCOSL_SIN_LO 3
80extern const long double __sincosl_table[];
81
82long double
83__kernel_cosl(long double x, long double y)
84{
85 long double h, l, z, sin_l, cos_l_m1;
86 int index;
87
88 if (signbit (x))
89 {
90 x = -x;
91 y = -y;
92 }
93 if (x < 0.1484375L)
94 {
95 /* Argument is small enough to approximate it by a Chebyshev
96 polynomial of degree 16. */
97 if (x < 0x1p-33L)
98 if (!((int)x)) return ONE; /* generate inexact */
99 z = x * x;
100 return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
101 z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
102 }
103 else
104 {
105 /* So that we don't have to use too large polynomial, we find
106 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
107 possible values for h. We look up cosl(h) and sinl(h) in
108 pre-computed tables, compute cosl(l) and sinl(l) using a
109 Chebyshev polynomial of degree 10(11) and compute
110 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
111 index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L)));
112 h = 0.1484375L + index / 128.0;
113 index *= 4;
114 l = y - (h - x);
115 z = l * l;
116 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
117 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
118 return __sincosl_table [index + SINCOSL_COS_HI]
119 + (__sincosl_table [index + SINCOSL_COS_LO]
120 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
121 - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
122 }
123}
124