Mercurial > hg > CbC > CbC_gcc
comparison libquadmath/math/cosq_kernel.c @ 68:561a7518be6b
update gcc-4.6
author | Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> |
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date | Sun, 21 Aug 2011 07:07:55 +0900 |
parents | |
children | 04ced10e8804 |
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1 /* Quad-precision floating point 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> | |
5 | |
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. | |
10 | |
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. | |
15 | |
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 | |
19 02111-1307 USA. */ | |
20 | |
21 #include "quadmath-imp.h" | |
22 | |
23 static const __float128 c[] = { | |
24 #define ONE c[0] | |
25 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */ | |
26 | |
27 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) | |
28 x in <0,1/256> */ | |
29 #define SCOS1 c[1] | |
30 #define SCOS2 c[2] | |
31 #define SCOS3 c[3] | |
32 #define SCOS4 c[4] | |
33 #define SCOS5 c[5] | |
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 */ | |
39 | |
40 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) | |
41 x in <0,0.1484375> */ | |
42 #define COS1 c[6] | |
43 #define COS2 c[7] | |
44 #define COS3 c[8] | |
45 #define COS4 c[9] | |
46 #define COS5 c[10] | |
47 #define COS6 c[11] | |
48 #define COS7 c[12] | |
49 #define COS8 c[13] | |
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 */ | |
58 | |
59 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) | |
60 x in <0,1/256> */ | |
61 #define SSIN1 c[14] | |
62 #define SSIN2 c[15] | |
63 #define SSIN3 c[16] | |
64 #define SSIN4 c[17] | |
65 #define SSIN5 c[18] | |
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 */ | |
71 }; | |
72 | |
73 #define SINCOSQ_COS_HI 0 | |
74 #define SINCOSQ_COS_LO 1 | |
75 #define SINCOSQ_SIN_HI 2 | |
76 #define SINCOSQ_SIN_LO 3 | |
77 extern const __float128 __sincosq_table[]; | |
78 | |
79 __float128 | |
80 __quadmath_kernel_cosq (__float128 x, __float128 y) | |
81 { | |
82 __float128 h, l, z, sin_l, cos_l_m1; | |
83 int64_t ix; | |
84 uint32_t tix, hix, index; | |
85 GET_FLT128_MSW64 (ix, x); | |
86 tix = ((uint64_t)ix) >> 32; | |
87 tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ | |
88 if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ | |
89 { | |
90 /* Argument is small enough to approximate it by a Chebyshev | |
91 polynomial of degree 16. */ | |
92 if (tix < 0x3fc60000) /* |x| < 2^-57 */ | |
93 if (!((int)x)) return ONE; /* generate inexact */ | |
94 z = x * x; | |
95 return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ | |
96 z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); | |
97 } | |
98 else | |
99 { | |
100 /* So that we don't have to use too large polynomial, we find | |
101 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 | |
102 possible values for h. We look up cosl(h) and sinl(h) in | |
103 pre-computed tables, compute cosl(l) and sinl(l) using a | |
104 Chebyshev polynomial of degree 10(11) and compute | |
105 cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ | |
106 index = 0x3ffe - (tix >> 16); | |
107 hix = (tix + (0x200 << index)) & (0xfffffc00 << index); | |
108 x = fabsq (x); | |
109 switch (index) | |
110 { | |
111 case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; | |
112 case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; | |
113 default: | |
114 case 2: index = (hix - 0x3ffc3000) >> 10; break; | |
115 } | |
116 | |
117 SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0); | |
118 l = y - (h - x); | |
119 z = l * l; | |
120 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); | |
121 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); | |
122 return __sincosq_table [index + SINCOSQ_COS_HI] | |
123 + (__sincosq_table [index + SINCOSQ_COS_LO] | |
124 - (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l | |
125 - __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1)); | |
126 } | |
127 } |