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glibc  2.9
k_sincosl.c
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00001 /* Quad-precision floating point sine and 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 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
00074    x in <0,0.1484375>  */
00075 #define SIN1 c[19]
00076 #define SIN2 c[20]
00077 #define SIN3 c[21]
00078 #define SIN4 c[22]
00079 #define SIN5 c[23]
00080 #define SIN6 c[24]
00081 #define SIN7 c[25]
00082 #define SIN8 c[26]
00083 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
00084  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
00085 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
00086  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
00087 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
00088  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
00089 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
00090  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
00091 };
00092 
00093 #define SINCOSL_COS_HI 0
00094 #define SINCOSL_COS_LO 1
00095 #define SINCOSL_SIN_HI 2
00096 #define SINCOSL_SIN_LO 3
00097 extern const long double __sincosl_table[];
00098 
00099 void
00100 __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
00101 {
00102   long double h, l, z, sin_l, cos_l_m1;
00103   int64_t ix;
00104   u_int32_t tix, hix, index;
00105   GET_LDOUBLE_MSW64 (ix, x);
00106   tix = ((u_int64_t)ix) >> 32;
00107   tix &= ~0x80000000;                     /* tix = |x|'s high 32 bits */
00108   if (tix < 0x3ffc3000)                   /* |x| < 0.1484375 */
00109     {
00110       /* Argument is small enough to approximate it by a Chebyshev
00111         polynomial of degree 16(17).  */
00112       if (tix < 0x3fc60000)        /* |x| < 2^-57 */
00113        if (!((int)x))                     /* generate inexact */
00114          {
00115            *sinx = x;
00116            *cosx = ONE;
00117            return;
00118          }
00119       z = x * x;
00120       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
00121                      z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
00122       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
00123                    z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
00124     }
00125   else
00126     {
00127       /* So that we don't have to use too large polynomial,  we find
00128         l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
00129         possible values for h.  We look up cosl(h) and sinl(h) in
00130         pre-computed tables,  compute cosl(l) and sinl(l) using a
00131         Chebyshev polynomial of degree 10(11) and compute
00132         sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
00133         cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
00134       index = 0x3ffe - (tix >> 16);
00135       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
00136       x = fabsl (x);
00137       switch (index)
00138        {
00139        case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
00140        case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
00141        default:
00142        case 2: index = (hix - 0x3ffc3000) >> 10; break;
00143        }
00144 
00145       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
00146       if (iy)
00147        l = y - (h - x);
00148       else
00149        l = x - h;
00150       z = l * l;
00151       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
00152       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
00153       z = __sincosl_table [index + SINCOSL_SIN_HI]
00154          + (__sincosl_table [index + SINCOSL_SIN_LO]
00155             + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
00156             + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
00157       *sinx = (ix < 0) ? -z : z;
00158       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
00159              + (__sincosl_table [index + SINCOSL_COS_LO]
00160                - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
00161                   - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
00162     }
00163 }