1 /* Quad-precision floating point cosine 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/>. */
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 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
50 -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
51 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
52 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
53 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
54 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
55 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
56 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
57 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
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_cosl(long double x
, long double y
)
82 long double h
, l
, z
, sin_l
, cos_l_m1
;
84 uint32_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 16. */
95 if (tix
< 0x3c600000) /* |x| < 2^-57 */
96 if (!((int)x
)) return ONE
; /* generate inexact */
98 return ONE
+ (z
*(COS1
+z
*(COS2
+z
*(COS3
+z
*(COS4
+
99 z
*(COS5
+z
*(COS6
+z
*(COS7
+z
*COS8
))))))));
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 cosl(h+l) = cosl(h)cosl(l) - sinl(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 + (0x200 << index)) & (0xfffffc00 << 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);
146 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
147 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
148 return __sincosl_table
[index
+ SINCOSL_COS_HI
]
149 + (__sincosl_table
[index
+ SINCOSL_COS_LO
]
150 - (__sincosl_table
[index
+ SINCOSL_SIN_HI
] * sin_l
151 - __sincosl_table
[index
+ SINCOSL_COS_HI
] * cos_l_m1
));