1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
2 Copyright (C) 1999 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Jakub Jelinek <jj@ultra.linux.cz>
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.
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.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, write to the Free
18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
21 #include "quadmath-imp.h"
23 static const __float128 c
[] = {
25 1.00000000000000000000000000000000000E+00Q
, /* 3fff0000000000000000000000000000 */
27 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
34 -5.00000000000000000000000000000000000E-01Q
, /* bffe0000000000000000000000000000 */
35 4.16666666666666666666666666556146073E-02Q
, /* 3ffa5555555555555555555555395023 */
36 -1.38888888888888888888309442601939728E-03Q
, /* bff56c16c16c16c16c16a566e42c0375 */
37 2.48015873015862382987049502531095061E-05Q
, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
38 -2.75573112601362126593516899592158083E-07Q
, /* bfe927e4f5dce637cb0b54908754bde0 */
40 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
50 -4.99999999999999999999999999999999759E-01Q
, /* bffdfffffffffffffffffffffffffffb */
51 4.16666666666666666666666666651287795E-02Q
, /* 3ffa5555555555555555555555516f30 */
52 -1.38888888888888888888888742314300284E-03Q
, /* bff56c16c16c16c16c16c16a463dfd0d */
53 2.48015873015873015867694002851118210E-05Q
, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
54 -2.75573192239858811636614709689300351E-07Q
, /* bfe927e4fb7789f5aa8142a22044b51f */
55 2.08767569877762248667431926878073669E-09Q
, /* 3fe21eed8eff881d1e9262d7adff4373 */
56 -1.14707451049343817400420280514614892E-11Q
, /* bfda9397496922a9601ed3d4ca48944b */
57 4.77810092804389587579843296923533297E-14Q
, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
59 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
66 -1.66666666666666666666666666666666659E-01Q
, /* bffc5555555555555555555555555555 */
67 8.33333333333333333333333333146298442E-03Q
, /* 3ff81111111111111111111110fe195d */
68 -1.98412698412698412697726277416810661E-04Q
, /* bff2a01a01a01a01a019e7121e080d88 */
69 2.75573192239848624174178393552189149E-06Q
, /* 3fec71de3a556c640c6aaa51aa02ab41 */
70 -2.50521016467996193495359189395805639E-08Q
, /* bfe5ae644ee90c47dc71839de75b2787 */
72 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
82 -1.66666666666666666666666666666666538e-01Q
, /* bffc5555555555555555555555555550 */
83 8.33333333333333333333333333307532934e-03Q
, /* 3ff811111111111111111111110e7340 */
84 -1.98412698412698412698412534478712057e-04Q
, /* bff2a01a01a01a01a01a019e7a626296 */
85 2.75573192239858906520896496653095890e-06Q
, /* 3fec71de3a556c7338fa38527474b8f5 */
86 -2.50521083854417116999224301266655662e-08Q
, /* bfe5ae64567f544e16c7de65c2ea551f */
87 1.60590438367608957516841576404938118e-10Q
, /* 3fde6124613a811480538a9a41957115 */
88 -7.64716343504264506714019494041582610e-13Q
, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
89 2.81068754939739570236322404393398135e-15Q
, /* 3fce9510115aabf87aceb2022a9a9180 */
92 #define SINCOSQ_COS_HI 0
93 #define SINCOSQ_COS_LO 1
94 #define SINCOSQ_SIN_HI 2
95 #define SINCOSQ_SIN_LO 3
96 extern const __float128 __sincosq_table
[];
99 __kernel_sincosq(__float128 x
, __float128 y
, __float128
*sinx
, __float128
*cosx
, int iy
)
101 __float128 h
, l
, z
, sin_l
, cos_l_m1
;
103 uint32_t tix
, hix
, index
;
104 GET_FLT128_MSW64 (ix
, x
);
105 tix
= ((uint64_t)ix
) >> 32;
106 tix
&= ~0x80000000; /* tix = |x|'s high 32 bits */
107 if (tix
< 0x3ffc3000) /* |x| < 0.1484375 */
109 /* Argument is small enough to approximate it by a Chebyshev
110 polynomial of degree 16(17). */
111 if (tix
< 0x3fc60000) /* |x| < 2^-57 */
112 if (!((int)x
)) /* generate inexact */
119 *sinx
= x
+ (x
* (z
*(SIN1
+z
*(SIN2
+z
*(SIN3
+z
*(SIN4
+
120 z
*(SIN5
+z
*(SIN6
+z
*(SIN7
+z
*SIN8
)))))))));
121 *cosx
= ONE
+ (z
*(COS1
+z
*(COS2
+z
*(COS3
+z
*(COS4
+
122 z
*(COS5
+z
*(COS6
+z
*(COS7
+z
*COS8
))))))));
126 /* So that we don't have to use too large polynomial, we find
127 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
128 possible values for h. We look up cosl(h) and sinl(h) in
129 pre-computed tables, compute cosl(l) and sinl(l) using a
130 Chebyshev polynomial of degree 10(11) and compute
131 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
132 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
133 index
= 0x3ffe - (tix
>> 16);
134 hix
= (tix
+ (0x200 << index
)) & (0xfffffc00 << index
);
138 case 0: index
= ((45 << 10) + hix
- 0x3ffe0000) >> 8; break;
139 case 1: index
= ((13 << 11) + hix
- 0x3ffd0000) >> 9; break;
141 case 2: index
= (hix
- 0x3ffc3000) >> 10; break;
144 SET_FLT128_WORDS64(h
, ((uint64_t)hix
) << 32, 0);
150 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
151 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
152 z
= __sincosq_table
[index
+ SINCOSQ_SIN_HI
]
153 + (__sincosq_table
[index
+ SINCOSQ_SIN_LO
]
154 + (__sincosq_table
[index
+ SINCOSQ_SIN_HI
] * cos_l_m1
)
155 + (__sincosq_table
[index
+ SINCOSQ_COS_HI
] * sin_l
));
156 *sinx
= (ix
< 0) ? -z
: z
;
157 *cosx
= __sincosq_table
[index
+ SINCOSQ_COS_HI
]
158 + (__sincosq_table
[index
+ SINCOSQ_COS_LO
]
159 - (__sincosq_table
[index
+ SINCOSQ_SIN_HI
] * sin_l
160 - __sincosq_table
[index
+ SINCOSQ_COS_HI
] * cos_l_m1
));