1/* Quad-precision floating point cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2021 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed 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
23static const _Float128 c[] = {
24#define ONE c[0]
25 L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */
26
27/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
28 x in <0,1/256> */
29#define SCOS1 c[1]
30#define SCOS2 c[2]
31#define SCOS3 c[3]
32#define SCOS4 c[4]
33#define SCOS5 c[5]
34L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */
35 L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */
36L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */
37 L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */
38L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */
39
40/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
41 x in <0,0.1484375> */
42#define COS1 c[6]
43#define COS2 c[7]
44#define COS3 c[8]
45#define COS4 c[9]
46#define COS5 c[10]
47#define COS6 c[11]
48#define COS7 c[12]
49#define COS8 c[13]
50L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */
51 L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */
52L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */
53 L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
54L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */
55 L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */
56L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */
57 L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
58
59/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
60 x in <0,1/256> */
61#define SSIN1 c[14]
62#define SSIN2 c[15]
63#define SSIN3 c[16]
64#define SSIN4 c[17]
65#define SSIN5 c[18]
66L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */
67 L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */
68L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */
69 L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */
70L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */
71};
72
73#define SINCOSL_COS_HI 0
74#define SINCOSL_COS_LO 1
75#define SINCOSL_SIN_HI 2
76#define SINCOSL_SIN_LO 3
77extern const _Float128 __sincosl_table[];
78
79_Float128
80__kernel_cosl(_Float128 x, _Float128 y)
81{
82 _Float128 h, l, z, sin_l, cos_l_m1;
83 int64_t ix;
84 uint32_t tix, hix, index;
85 GET_LDOUBLE_MSW64 (ix, x);
86 tix = ((uint64_t)ix) >> 32;
87 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
88 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
89 {
90 /* Argument is small enough to approximate it by a Chebyshev
91 polynomial of degree 16. */
92 if (tix < 0x3fc60000) /* |x| < 2^-57 */
93 if (!((int)x)) return ONE; /* generate inexact */
94 z = x * x;
95 return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
96 z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
97 }
98 else
99 {
100 /* So that we don't have to use too large polynomial, we find
101 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
102 possible values for h. We look up cosl(h) and sinl(h) in
103 pre-computed tables, compute cosl(l) and sinl(l) using a
104 Chebyshev polynomial of degree 10(11) and compute
105 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
106 index = 0x3ffe - (tix >> 16);
107 hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
108 if (signbit (x))
109 {
110 x = -x;
111 y = -y;
112 }
113 switch (index)
114 {
115 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
116 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
117 default:
118 case 2: index = (hix - 0x3ffc3000) >> 10; break;
119 }
120
121 SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
122 l = y - (h - x);
123 z = l * l;
124 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
125 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
126 return __sincosl_table [index + SINCOSL_COS_HI]
127 + (__sincosl_table [index + SINCOSL_COS_LO]
128 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
129 - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
130 }
131}
132