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f964490f | 1 | /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. |
b168057a | 2 | Copyright (C) 1999-2015 Free Software Foundation, Inc. |
f964490f RM |
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 | |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
f964490f | 19 | |
ad39cce0 | 20 | #include <float.h> |
1ed0291c RH |
21 | #include <math.h> |
22 | #include <math_private.h> | |
f964490f RM |
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 | /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) | |
42 | x in <0,0.1484375> */ | |
43 | #define COS1 c[6] | |
44 | #define COS2 c[7] | |
45 | #define COS3 c[8] | |
46 | #define COS4 c[9] | |
47 | #define COS5 c[10] | |
48 | #define COS6 c[11] | |
49 | #define COS7 c[12] | |
50 | #define COS8 c[13] | |
51 | -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ | |
52 | 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ | |
53 | -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ | |
54 | 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ | |
55 | -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ | |
56 | 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ | |
57 | -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ | |
58 | 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ | |
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 | /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) | |
74 | x in <0,0.1484375> */ | |
75 | #define SIN1 c[19] | |
76 | #define SIN2 c[20] | |
77 | #define SIN3 c[21] | |
78 | #define SIN4 c[22] | |
79 | #define SIN5 c[23] | |
80 | #define SIN6 c[24] | |
81 | #define SIN7 c[25] | |
82 | #define SIN8 c[26] | |
83 | -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ | |
84 | 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ | |
85 | -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ | |
86 | 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ | |
87 | -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ | |
88 | 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ | |
89 | -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ | |
90 | 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ | |
91 | }; | |
92 | ||
93 | #define SINCOSL_COS_HI 0 | |
94 | #define SINCOSL_COS_LO 1 | |
95 | #define SINCOSL_SIN_HI 2 | |
96 | #define SINCOSL_SIN_LO 3 | |
97 | extern const long double __sincosl_table[]; | |
98 | ||
99 | void | |
100 | __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy) | |
101 | { | |
102 | long double h, l, z, sin_l, cos_l_m1; | |
103 | int64_t ix; | |
4ebd120c AM |
104 | uint32_t tix, hix, index; |
105 | double xhi, hhi; | |
106 | ||
107 | xhi = ldbl_high (x); | |
108 | EXTRACT_WORDS64 (ix, xhi); | |
109 | tix = ((uint64_t)ix) >> 32; | |
f964490f RM |
110 | tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ |
111 | if (tix < 0x3fc30000) /* |x| < 0.1484375 */ | |
112 | { | |
113 | /* Argument is small enough to approximate it by a Chebyshev | |
114 | polynomial of degree 16(17). */ | |
115 | if (tix < 0x3c600000) /* |x| < 2^-57 */ | |
ad39cce0 JM |
116 | { |
117 | if (fabsl (x) < LDBL_MIN) | |
118 | { | |
119 | long double force_underflow = x * x; | |
120 | math_force_eval (force_underflow); | |
121 | } | |
122 | if (!((int)x)) /* generate inexact */ | |
123 | { | |
124 | *sinx = x; | |
125 | *cosx = ONE; | |
126 | return; | |
127 | } | |
128 | } | |
f964490f RM |
129 | z = x * x; |
130 | *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ | |
131 | z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); | |
132 | *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ | |
133 | z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); | |
134 | } | |
135 | else | |
136 | { | |
137 | /* So that we don't have to use too large polynomial, we find | |
138 | l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
139 | possible values for h. We look up cosl(h) and sinl(h) in | |
140 | pre-computed tables, compute cosl(l) and sinl(l) using a | |
141 | Chebyshev polynomial of degree 10(11) and compute | |
142 | sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and | |
143 | cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ | |
16f0eced RM |
144 | int six = tix; |
145 | tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; | |
146 | index = 0x3ffe - (tix >> 16); | |
147 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); | |
148 | x = fabsl (x); | |
149 | switch (index) | |
150 | { | |
151 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; | |
152 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; | |
153 | default: | |
154 | case 2: index = (hix - 0x3ffc3000) >> 10; break; | |
155 | } | |
156 | hix = (hix << 4) & 0x3fffffff; | |
157 | /* | |
158 | The following should work for double but generates the wrong index. | |
159 | For now the code above converts double to ieee extended to compute | |
9c84384c JM |
160 | the index back to double for the h value. |
161 | ||
16f0eced | 162 | |
f964490f RM |
163 | index = 0x3fe - (tix >> 20); |
164 | hix = (tix + (0x2000 << index)) & (0xffffc000 << index); | |
c0df8e69 JM |
165 | if (signbit (x)) |
166 | { | |
167 | x = -x; | |
168 | y = -y; | |
169 | } | |
f964490f RM |
170 | switch (index) |
171 | { | |
172 | case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; | |
173 | case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; | |
174 | default: | |
175 | case 2: index = (hix - 0x3fc30000) >> 14; break; | |
176 | } | |
16f0eced | 177 | */ |
4ebd120c AM |
178 | INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); |
179 | h = hhi; | |
f964490f RM |
180 | if (iy) |
181 | l = y - (h - x); | |
182 | else | |
183 | l = x - h; | |
184 | z = l * l; | |
185 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
186 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
187 | z = __sincosl_table [index + SINCOSL_SIN_HI] | |
188 | + (__sincosl_table [index + SINCOSL_SIN_LO] | |
189 | + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) | |
190 | + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); | |
191 | *sinx = (ix < 0) ? -z : z; | |
192 | *cosx = __sincosl_table [index + SINCOSL_COS_HI] | |
193 | + (__sincosl_table [index + SINCOSL_COS_LO] | |
194 | - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l | |
195 | - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); | |
196 | } | |
197 | } |