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glibc  2.9
k_cosl.c
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00001 /* Quad-precision floating point cosine on <-pi/4,pi/4>.
00002    Copyright (C) 1999 Free Software Foundation, Inc.
00003    This file is part of the GNU C Library.
00004    Contributed by Jakub Jelinek <jj@ultra.linux.cz>
00005 
00006    The GNU C Library is free software; you can redistribute it and/or
00007    modify it under the terms of the GNU Lesser General Public
00008    License as published by the Free Software Foundation; either
00009    version 2.1 of the License, or (at your option) any later version.
00010 
00011    The GNU C Library is distributed in the hope that it will be useful,
00012    but WITHOUT ANY WARRANTY; without even the implied warranty of
00013    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00014    Lesser General Public License for more details.
00015 
00016    You should have received a copy of the GNU Lesser General Public
00017    License along with the GNU C Library; if not, write to the Free
00018    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
00019    02111-1307 USA.  */
00020 
00021 #include "math.h"
00022 #include "math_private.h"
00023 
00024 static const long double c[] = {
00025 #define ONE c[0]
00026  1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
00027 
00028 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
00029    x in <0,1/256>  */
00030 #define SCOS1 c[1]
00031 #define SCOS2 c[2]
00032 #define SCOS3 c[3]
00033 #define SCOS4 c[4]
00034 #define SCOS5 c[5]
00035 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
00036  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
00037 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
00038  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
00039 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
00040 
00041 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
00042    x in <0,0.1484375>  */
00043 #define COS1 c[6]
00044 #define COS2 c[7]
00045 #define COS3 c[8]
00046 #define COS4 c[9]
00047 #define COS5 c[10]
00048 #define COS6 c[11]
00049 #define COS7 c[12]
00050 #define COS8 c[13]
00051 -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
00052  4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
00053 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
00054  2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
00055 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
00056  2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
00057 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
00058  4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
00059 
00060 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
00061    x in <0,1/256>  */
00062 #define SSIN1 c[14]
00063 #define SSIN2 c[15]
00064 #define SSIN3 c[16]
00065 #define SSIN4 c[17]
00066 #define SSIN5 c[18]
00067 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
00068  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
00069 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
00070  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
00071 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
00072 };
00073 
00074 #define SINCOSL_COS_HI 0
00075 #define SINCOSL_COS_LO 1
00076 #define SINCOSL_SIN_HI 2
00077 #define SINCOSL_SIN_LO 3
00078 extern const long double __sincosl_table[];
00079 
00080 long double
00081 __kernel_cosl(long double x, long double y)
00082 {
00083   long double h, l, z, sin_l, cos_l_m1;
00084   int64_t ix;
00085   u_int32_t tix, hix, index;
00086   GET_LDOUBLE_MSW64 (ix, x);
00087   tix = ((u_int64_t)ix) >> 32;
00088   tix &= ~0x80000000;                     /* tix = |x|'s high 32 bits */
00089   if (tix < 0x3ffc3000)                   /* |x| < 0.1484375 */
00090     {
00091       /* Argument is small enough to approximate it by a Chebyshev
00092         polynomial of degree 16.  */
00093       if (tix < 0x3fc60000)        /* |x| < 2^-57 */
00094        if (!((int)x)) return ONE;  /* generate inexact */
00095       z = x * x;
00096       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
00097                   z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
00098     }
00099   else
00100     {
00101       /* So that we don't have to use too large polynomial,  we find
00102         l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
00103         possible values for h.  We look up cosl(h) and sinl(h) in
00104         pre-computed tables,  compute cosl(l) and sinl(l) using a
00105         Chebyshev polynomial of degree 10(11) and compute
00106         cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
00107       index = 0x3ffe - (tix >> 16);
00108       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
00109       x = fabsl (x);
00110       switch (index)
00111        {
00112        case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
00113        case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
00114        default:
00115        case 2: index = (hix - 0x3ffc3000) >> 10; break;
00116        }
00117 
00118       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
00119       l = y - (h - x);
00120       z = l * l;
00121       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
00122       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
00123       return __sincosl_table [index + SINCOSL_COS_HI]
00124             + (__sincosl_table [index + SINCOSL_COS_LO]
00125               - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
00126                  - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
00127     }
00128 }