1 /* Quad-precision floating point cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2022 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 static const _Float128 c[] = {
23 #define ONE c[0]
24 L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */
25
26 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
27 x in <0,1/256> */
28 #define SCOS1 c[1]
29 #define SCOS2 c[2]
30 #define SCOS3 c[3]
31 #define SCOS4 c[4]
32 #define SCOS5 c[5]
33 L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */
34 L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */
35 L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */
36 L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */
37 L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */
38
39 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
40 x in <0,0.1484375> */
41 #define COS1 c[6]
42 #define COS2 c[7]
43 #define COS3 c[8]
44 #define COS4 c[9]
45 #define COS5 c[10]
46 #define COS6 c[11]
47 #define COS7 c[12]
48 #define COS8 c[13]
49 L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */
50 L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */
51 L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */
52 L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
53 L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */
54 L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */
55 L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */
56 L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
57
58 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
59 x in <0,1/256> */
60 #define SSIN1 c[14]
61 #define SSIN2 c[15]
62 #define SSIN3 c[16]
63 #define SSIN4 c[17]
64 #define SSIN5 c[18]
65 L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */
66 L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */
67 L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */
68 L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */
69 L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */
70 };
71
72 #define SINCOSL_COS_HI 0
73 #define SINCOSL_COS_LO 1
74 #define SINCOSL_SIN_HI 2
75 #define SINCOSL_SIN_LO 3
76 extern const _Float128 __sincosl_table[];
77
78 _Float128
__kernel_cosl(_Float128 x,_Float128 y)79 __kernel_cosl(_Float128 x, _Float128 y)
80 {
81 _Float128 h, l, z, sin_l, cos_l_m1;
82 int64_t ix;
83 uint32_t tix, hix, index;
84 GET_LDOUBLE_MSW64 (ix, x);
85 tix = ((uint64_t)ix) >> 32;
86 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
87 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
88 {
89 /* Argument is small enough to approximate it by a Chebyshev
90 polynomial of degree 16. */
91 if (tix < 0x3fc60000) /* |x| < 2^-57 */
92 if (!((int)x)) return ONE; /* generate inexact */
93 z = x * x;
94 return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
95 z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
96 }
97 else
98 {
99 /* So that we don't have to use too large polynomial, we find
100 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
101 possible values for h. We look up cosl(h) and sinl(h) in
102 pre-computed tables, compute cosl(l) and sinl(l) using a
103 Chebyshev polynomial of degree 10(11) and compute
104 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
105 index = 0x3ffe - (tix >> 16);
106 hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
107 if (signbit (x))
108 {
109 x = -x;
110 y = -y;
111 }
112 switch (index)
113 {
114 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
115 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
116 default:
117 case 2: index = (hix - 0x3ffc3000) >> 10; break;
118 }
119
120 SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
121 l = y - (h - x);
122 z = l * l;
123 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
124 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
125 return __sincosl_table [index + SINCOSL_COS_HI]
126 + (__sincosl_table [index + SINCOSL_COS_LO]
127 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
128 - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
129 }
130 }
131