1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2018 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 <http://www.gnu.org/licenses/>. */
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 /* 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 -4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */
50 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
51 -1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
52 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
53 -2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
54 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
55 -1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
56 4.77810092804389587579843296923533297E-14Q, /* 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 -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 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
72 x in <0,0.1484375> */
73 #define SIN1 c[19]
74 #define SIN2 c[20]
75 #define SIN3 c[21]
76 #define SIN4 c[22]
77 #define SIN5 c[23]
78 #define SIN6 c[24]
79 #define SIN7 c[25]
80 #define SIN8 c[26]
81 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
82 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
83 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
84 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
85 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
86 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
87 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
88 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
89 };
90
91 #define SINCOSL_COS_HI 0
92 #define SINCOSL_COS_LO 1
93 #define SINCOSL_SIN_HI 2
94 #define SINCOSL_SIN_LO 3
95 extern const __float128 __sincosq_table[];
96
97 void
98 __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx, __float128 *cosx, int iy)
99 {
100 __float128 h, l, z, sin_l, cos_l_m1;
101 int64_t ix;
102 uint32_t tix, hix, index;
103 GET_FLT128_MSW64 (ix, x);
104 tix = ((uint64_t)ix) >> 32;
105 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
106 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
107 {
108 /* Argument is small enough to approximate it by a Chebyshev
109 polynomial of degree 16(17). */
110 if (tix < 0x3fc60000) /* |x| < 2^-57 */
111 {
112 math_check_force_underflow (x);
113 if (!((int)x)) /* generate inexact */
114 {
115 *sinx = x;
116 *cosx = ONE;
117 return;
118 }
119 }
120 z = x * x;
121 *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
122 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
123 *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
124 z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
125 }
126 else
127 {
128 /* So that we don't have to use too large polynomial, we find
129 l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83
130 possible values for h. We look up cosq(h) and sinq(h) in
131 pre-computed tables, compute cosq(l) and sinq(l) using a
132 Chebyshev polynomial of degree 10(11) and compute
133 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and
134 cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l). */
135 index = 0x3ffe - (tix >> 16);
136 hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
137 if (signbitq (x))
138 {
139 x = -x;
140 y = -y;
141 }
142 switch (index)
143 {
144 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
145 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
146 default:
147 case 2: index = (hix - 0x3ffc3000) >> 10; break;
148 }
149
150 SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
151 if (iy)
152 l = y - (h - x);
153 else
154 l = x - h;
155 z = l * l;
156 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
157 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
158 z = __sincosq_table [index + SINCOSL_SIN_HI]
159 + (__sincosq_table [index + SINCOSL_SIN_LO]
160 + (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1)
161 + (__sincosq_table [index + SINCOSL_COS_HI] * sin_l));
162 *sinx = (ix < 0) ? -z : z;
163 *cosx = __sincosq_table [index + SINCOSL_COS_HI]
164 + (__sincosq_table [index + SINCOSL_COS_LO]
165 - (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
166 - __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
167 }
168 }