1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999,2004,2006 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
22 #include "math_private.h"
24 static const long double c
[] = {
26 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
28 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
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 */
41 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
51 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
52 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
53 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
54 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
55 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
56 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
57 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
58 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
60 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
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 */
74 #define SINCOSL_COS_HI 0
75 #define SINCOSL_COS_LO 1
76 #define SINCOSL_SIN_HI 2
77 #define SINCOSL_SIN_LO 3
78 extern const long double __sincosl_table
[];
81 __kernel_sinl(long double x
, long double y
, int iy
)
83 long double h
, l
, z
, sin_l
, cos_l_m1
;
85 u_int32_t tix
, hix
, index
;
86 GET_LDOUBLE_MSW64 (ix
, x
);
87 tix
= ((u_int64_t
)ix
) >> 32;
88 tix
&= ~0x80000000; /* tix = |x|'s high 32 bits */
89 if (tix
< 0x3fc30000) /* |x| < 0.1484375 */
91 /* Argument is small enough to approximate it by a Chebyshev
92 polynomial of degree 17. */
93 if (tix
< 0x3c600000) /* |x| < 2^-57 */
94 if (!((int)x
)) return x
; /* generate inexact */
96 return x
+ (x
* (z
*(SIN1
+z
*(SIN2
+z
*(SIN3
+z
*(SIN4
+
97 z
*(SIN5
+z
*(SIN6
+z
*(SIN7
+z
*SIN8
)))))))));
101 /* So that we don't have to use too large polynomial, we find
102 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
103 possible values for h. We look up cosl(h) and sinl(h) in
104 pre-computed tables, compute cosl(l) and sinl(l) using a
105 Chebyshev polynomial of degree 10(11) and compute
106 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
107 index
= 0x3fe - (tix
>> 20);
108 hix
= (tix
+ (0x2000 << index
)) & (0xffffc000 << index
);
112 case 0: index
= ((45 << 14) + hix
- 0x3fe00000) >> 12; break;
113 case 1: index
= ((13 << 15) + hix
- 0x3fd00000) >> 13; break;
115 case 2: index
= (hix
- 0x3fc30000) >> 14; break;
118 SET_LDOUBLE_WORDS64(h
, ((u_int64_t
)hix
) << 32, 0);
124 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
125 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
126 z
= __sincosl_table
[index
+ SINCOSL_SIN_HI
]
127 + (__sincosl_table
[index
+ SINCOSL_SIN_LO
]
128 + (__sincosl_table
[index
+ SINCOSL_SIN_HI
] * cos_l_m1
)
129 + (__sincosl_table
[index
+ SINCOSL_COS_HI
] * sin_l
));
130 return (ix
< 0) ? -z
: z
;