1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2014 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, see
18 <http://www.gnu.org/licenses/>. */
21 #include <math_private.h>
23 static const long double c
[] = {
25 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
27 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
34 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
35 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
36 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
37 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
38 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
40 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
50 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
51 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
52 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
53 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
54 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
55 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
56 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
57 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
59 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
66 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
67 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
68 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
69 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
70 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
73 #define SINCOSL_COS_HI 0
74 #define SINCOSL_COS_LO 1
75 #define SINCOSL_SIN_HI 2
76 #define SINCOSL_SIN_LO 3
77 extern const long double __sincosl_table
[];
80 __kernel_sinl(long double x
, long double y
, int iy
)
82 long double h
, l
, z
, sin_l
, cos_l_m1
;
84 u_int32_t tix
, hix
, index
;
88 EXTRACT_WORDS64 (ix
, xhi
);
89 tix
= ((u_int64_t
)ix
) >> 32;
90 tix
&= ~0x80000000; /* tix = |x|'s high 32 bits */
91 if (tix
< 0x3fc30000) /* |x| < 0.1484375 */
93 /* Argument is small enough to approximate it by a Chebyshev
94 polynomial of degree 17. */
95 if (tix
< 0x3c600000) /* |x| < 2^-57 */
96 if (!((int)x
)) return x
; /* generate inexact */
98 return x
+ (x
* (z
*(SIN1
+z
*(SIN2
+z
*(SIN3
+z
*(SIN4
+
99 z
*(SIN5
+z
*(SIN6
+z
*(SIN7
+z
*SIN8
)))))))));
103 /* So that we don't have to use too large polynomial, we find
104 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
105 possible values for h. We look up cosl(h) and sinl(h) in
106 pre-computed tables, compute cosl(l) and sinl(l) using a
107 Chebyshev polynomial of degree 10(11) and compute
108 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
110 tix
= ((six
- 0x3ff00000) >> 4) + 0x3fff0000;
111 index
= 0x3ffe - (tix
>> 16);
112 hix
= (tix
+ (0x200 << index
)) & (0xfffffc00 << index
);
116 case 0: index
= ((45 << 10) + hix
- 0x3ffe0000) >> 8; break;
117 case 1: index
= ((13 << 11) + hix
- 0x3ffd0000) >> 9; break;
119 case 2: index
= (hix
- 0x3ffc3000) >> 10; break;
121 hix
= (hix
<< 4) & 0x3fffffff;
123 The following should work for double but generates the wrong index.
124 For now the code above converts double to ieee extended to compute
125 the index back to double for the h value.
127 index = 0x3fe - (tix >> 20);
128 hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
132 case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
133 case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
135 case 2: index = (hix - 0x3fc30000) >> 14; break;
138 INSERT_WORDS64 (hhi
, ((uint64_t)hix
) << 32);
141 l
= (ix
< 0 ? -y
: y
) - (h
- x
);
145 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
146 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
147 z
= __sincosl_table
[index
+ SINCOSL_SIN_HI
]
148 + (__sincosl_table
[index
+ SINCOSL_SIN_LO
]
149 + (__sincosl_table
[index
+ SINCOSL_SIN_HI
] * cos_l_m1
)
150 + (__sincosl_table
[index
+ SINCOSL_COS_HI
] * sin_l
));
151 return (ix
< 0) ? -z
: z
;