1 /* Quad-precision floating point sine 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 <float.h>
20 #include <math.h>
21 #include <math_private.h>
22 #include <math-underflow.h>
23
24 static const long double c[] = {
25 #define ONE c[0]
26 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
27
28 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
29 x in <0,1/256> */
30 #define SCOS1 c[1]
31 #define SCOS2 c[2]
32 #define SCOS3 c[3]
33 #define SCOS4 c[4]
34 #define SCOS5 c[5]
35 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
36 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
37 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
38 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
39 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
40
41 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
42 x in <0,0.1484375> */
43 #define SIN1 c[6]
44 #define SIN2 c[7]
45 #define SIN3 c[8]
46 #define SIN4 c[9]
47 #define SIN5 c[10]
48 #define SIN6 c[11]
49 #define SIN7 c[12]
50 #define SIN8 c[13]
51 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
52 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
53 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
54 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
55 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
56 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
57 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
58 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
59
60 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
61 x in <0,1/256> */
62 #define SSIN1 c[14]
63 #define SSIN2 c[15]
64 #define SSIN3 c[16]
65 #define SSIN4 c[17]
66 #define SSIN5 c[18]
67 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
68 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
69 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
70 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
71 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
72 };
73
74 #define SINCOSL_COS_HI 0
75 #define SINCOSL_COS_LO 1
76 #define SINCOSL_SIN_HI 2
77 #define SINCOSL_SIN_LO 3
78 extern const long double __sincosl_table[];
79
80 long double
81 __kernel_sinl(long double x, long double y, int iy)
82 {
83 long double h, l, z, sin_l, cos_l_m1;
84 int64_t ix;
85 uint32_t tix, hix, index;
86 double xhi, hhi;
87
88 xhi = ldbl_high (x);
89 EXTRACT_WORDS64 (ix, xhi);
90 tix = ((uint64_t)ix) >> 32;
91 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
92 if (tix < 0x3fc30000) /* |x| < 0.1484375 */
93 {
94 /* Argument is small enough to approximate it by a Chebyshev
95 polynomial of degree 17. */
96 if (tix < 0x3c600000) /* |x| < 2^-57 */
97 {
98 math_check_force_underflow (x);
99 if (!((int)x)) return x; /* generate inexact */
100 }
101 z = x * x;
102 return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
103 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
104 }
105 else
106 {
107 /* So that we don't have to use too large polynomial, we find
108 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
109 possible values for h. We look up cosl(h) and sinl(h) in
110 pre-computed tables, compute cosl(l) and sinl(l) using a
111 Chebyshev polynomial of degree 10(11) and compute
112 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
113 int six = tix;
114 tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
115 index = 0x3ffe - (tix >> 16);
116 hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
117 x = fabsl (x);
118 switch (index)
119 {
120 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
121 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
122 default:
123 case 2: index = (hix - 0x3ffc3000) >> 10; break;
124 }
125 hix = (hix << 4) & 0x3fffffff;
126 /*
127 The following should work for double but generates the wrong index.
128 For now the code above converts double to ieee extended to compute
129 the index back to double for the h value.
130
131 index = 0x3fe - (tix >> 20);
132 hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
133 x = fabsl (x);
134 switch (index)
135 {
136 case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
137 case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
138 default:
139 case 2: index = (hix - 0x3fc30000) >> 14; break;
140 }
141 */
142 INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
143 h = hhi;
144 if (iy)
145 l = (ix < 0 ? -y : y) - (h - x);
146 else
147 l = x - h;
148 z = l * l;
149 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
150 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
151 z = __sincosl_table [index + SINCOSL_SIN_HI]
152 + (__sincosl_table [index + SINCOSL_SIN_LO]
153 + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
154 + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
155 return (ix < 0) ? -z : z;
156 }
157 }