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glibc  2.9
k_sinl.c
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00001 /* Quad-precision floating point sine on <-pi/4,pi/4>.
00002    Copyright (C) 1999,2004,2006 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 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
00042    x in <0,0.1484375>  */
00043 #define SIN1 c[6]
00044 #define SIN2 c[7]
00045 #define SIN3 c[8]
00046 #define SIN4 c[9]
00047 #define SIN5 c[10]
00048 #define SIN6 c[11]
00049 #define SIN7 c[12]
00050 #define SIN8 c[13]
00051 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
00052  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
00053 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
00054  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
00055 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
00056  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
00057 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
00058  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
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_sinl(long double x, long double y, int iy)
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 < 0x3fc30000)                   /* |x| < 0.1484375 */
00090     {
00091       /* Argument is small enough to approximate it by a Chebyshev
00092         polynomial of degree 17.  */
00093       if (tix < 0x3c600000)        /* |x| < 2^-57 */
00094        if (!((int)x)) return x;    /* generate inexact */
00095       z = x * x;
00096       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
00097                      z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
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         sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l).  */
00107       int six = tix;
00108       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
00109       index = 0x3ffe - (tix >> 16);
00110       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
00111       x = fabsl (x);
00112       switch (index)
00113        {
00114        case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
00115        case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
00116        default:
00117        case 2: index = (hix - 0x3ffc3000) >> 10; break;
00118        }
00119       hix = (hix << 4) & 0x3fffffff;
00120 /*
00121     The following should work for double but generates the wrong index.
00122     For now the code above converts double to ieee extended to compute
00123     the index back to double for the h value. 
00124     
00125       index = 0x3fe - (tix >> 20);
00126       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
00127       x = fabsl (x);
00128       switch (index)
00129        {
00130        case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
00131        case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
00132        default:
00133        case 2: index = (hix - 0x3fc30000) >> 14; break;
00134        }
00135 */
00136       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
00137       if (iy)
00138        l = y - (h - x);
00139       else
00140        l = x - h;
00141       z = l * l;
00142       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
00143       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
00144       z = __sincosl_table [index + SINCOSL_SIN_HI]
00145          + (__sincosl_table [index + SINCOSL_SIN_LO]
00146             + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
00147             + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
00148       return (ix < 0) ? -z : z;
00149     }
00150 }