]>
Commit | Line | Data |
---|---|---|
1ec601bf | 1 | /* Quad-precision floating point sine on <-pi/4,pi/4>. |
4239f144 | 2 | Copyright (C) 1999-2018 Free Software Foundation, Inc. |
1ec601bf FXC |
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 | |
4239f144 JM |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
1ec601bf FXC |
19 | |
20 | #include "quadmath-imp.h" | |
21 | ||
22 | static const __float128 c[] = { | |
23 | #define ONE c[0] | |
24 | 1.00000000000000000000000000000000000E+00Q, /* 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 | -5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */ | |
34 | 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */ | |
35 | -1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */ | |
36 | 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ | |
37 | -2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */ | |
38 | ||
39 | /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) | |
40 | x in <0,0.1484375> */ | |
41 | #define SIN1 c[6] | |
42 | #define SIN2 c[7] | |
43 | #define SIN3 c[8] | |
44 | #define SIN4 c[9] | |
45 | #define SIN5 c[10] | |
46 | #define SIN6 c[11] | |
47 | #define SIN7 c[12] | |
48 | #define SIN8 c[13] | |
49 | -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */ | |
50 | 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */ | |
51 | -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */ | |
52 | 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */ | |
53 | -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */ | |
54 | 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */ | |
55 | -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ | |
56 | 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */ | |
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 | -1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */ | |
66 | 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */ | |
67 | -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */ | |
68 | 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */ | |
69 | -2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */ | |
70 | }; | |
71 | ||
4239f144 JM |
72 | #define SINCOSL_COS_HI 0 |
73 | #define SINCOSL_COS_LO 1 | |
74 | #define SINCOSL_SIN_HI 2 | |
75 | #define SINCOSL_SIN_LO 3 | |
1ec601bf FXC |
76 | extern const __float128 __sincosq_table[]; |
77 | ||
78 | __float128 | |
4239f144 | 79 | __quadmath_kernel_sinq(__float128 x, __float128 y, int iy) |
1ec601bf FXC |
80 | { |
81 | __float128 h, l, z, sin_l, cos_l_m1; | |
82 | int64_t ix; | |
83 | uint32_t tix, hix, index; | |
84 | GET_FLT128_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 17. */ | |
91 | if (tix < 0x3fc60000) /* |x| < 2^-57 */ | |
1eba0867 JJ |
92 | { |
93 | math_check_force_underflow (x); | |
94 | if (!((int)x)) return x; /* generate inexact */ | |
95 | } | |
1ec601bf FXC |
96 | z = x * x; |
97 | return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ | |
98 | z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); | |
99 | } | |
100 | else | |
101 | { | |
102 | /* So that we don't have to use too large polynomial, we find | |
4239f144 | 103 | l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83 |
f029f4be TB |
104 | possible values for h. We look up cosq(h) and sinq(h) in |
105 | pre-computed tables, compute cosq(l) and sinq(l) using a | |
1ec601bf | 106 | Chebyshev polynomial of degree 10(11) and compute |
f029f4be | 107 | sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l). */ |
1ec601bf FXC |
108 | index = 0x3ffe - (tix >> 16); |
109 | hix = (tix + (0x200 << index)) & (0xfffffc00 << index); | |
110 | x = fabsq (x); | |
111 | switch (index) | |
112 | { | |
113 | case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; | |
114 | case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; | |
115 | default: | |
116 | case 2: index = (hix - 0x3ffc3000) >> 10; break; | |
117 | } | |
118 | ||
119 | SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0); | |
120 | if (iy) | |
f029f4be | 121 | l = (ix < 0 ? -y : y) - (h - x); |
1ec601bf FXC |
122 | else |
123 | l = x - h; | |
124 | z = l * l; | |
125 | sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
126 | cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
4239f144 JM |
127 | z = __sincosq_table [index + SINCOSL_SIN_HI] |
128 | + (__sincosq_table [index + SINCOSL_SIN_LO] | |
129 | + (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1) | |
130 | + (__sincosq_table [index + SINCOSL_COS_HI] * sin_l)); | |
1ec601bf FXC |
131 | return (ix < 0) ? -z : z; |
132 | } | |
133 | } |