]>
git.ipfire.org Git - thirdparty/glibc.git/blob - sysdeps/ieee754/ldbl-128ibm/k_sinl.c
1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2016 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/>. */
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
;
89 EXTRACT_WORDS64 (ix
, xhi
);
90 tix
= ((u_int64_t
)ix
) >> 32;
91 tix
&= ~0x80000000; /* tix = |x|'s high 32 bits */
92 if (tix
< 0x3fc30000) /* |x| < 0.1484375 */
94 /* Argument is small enough to approximate it by a Chebyshev
95 polynomial of degree 17. */
96 if (tix
< 0x3c600000) /* |x| < 2^-57 */
98 math_check_force_underflow (x
);
99 if (!((int)x
)) return x
; /* generate inexact */
102 return x
+ (x
* (z
*(SIN1
+z
*(SIN2
+z
*(SIN3
+z
*(SIN4
+
103 z
*(SIN5
+z
*(SIN6
+z
*(SIN7
+z
*SIN8
)))))))));
107 /* So that we don't have to use too large polynomial, we find
108 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
109 possible values for h. We look up cosl(h) and sinl(h) in
110 pre-computed tables, compute cosl(l) and sinl(l) using a
111 Chebyshev polynomial of degree 10(11) and compute
112 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
114 tix
= ((six
- 0x3ff00000) >> 4) + 0x3fff0000;
115 index
= 0x3ffe - (tix
>> 16);
116 hix
= (tix
+ (0x200 << index
)) & (0xfffffc00 << index
);
120 case 0: index
= ((45 << 10) + hix
- 0x3ffe0000) >> 8; break;
121 case 1: index
= ((13 << 11) + hix
- 0x3ffd0000) >> 9; break;
123 case 2: index
= (hix
- 0x3ffc3000) >> 10; break;
125 hix
= (hix
<< 4) & 0x3fffffff;
127 The following should work for double but generates the wrong index.
128 For now the code above converts double to ieee extended to compute
129 the index back to double for the h value.
131 index = 0x3fe - (tix >> 20);
132 hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
136 case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
137 case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
139 case 2: index = (hix - 0x3fc30000) >> 14; break;
142 INSERT_WORDS64 (hhi
, ((uint64_t)hix
) << 32);
145 l
= (ix
< 0 ? -y
: y
) - (h
- x
);
149 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
150 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
151 z
= __sincosl_table
[index
+ SINCOSL_SIN_HI
]
152 + (__sincosl_table
[index
+ SINCOSL_SIN_LO
]
153 + (__sincosl_table
[index
+ SINCOSL_SIN_HI
] * cos_l_m1
)
154 + (__sincosl_table
[index
+ SINCOSL_COS_HI
] * sin_l
));
155 return (ix
< 0) ? -z
: z
;