sysdeps/ieee754/ldbl-128ibm/k_sincosl.c

   1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999,2004,2006 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, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const long double c[] = {
  24 #define ONE c[0]
  25  1.00000000000000000000000000000000000E+00L, /* 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-01L, /* bffe0000000000000000000000000000 */
  35  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
  36 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
  37  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  38 -2.75573112601362126593516899592158083E-07L, /* 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-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 */
  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-01L, /* bffc5555555555555555555555555555 */
  67  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
  68 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
  69  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  70 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
  71
  72 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  73    x in <0,0.1484375>  */
  74 #define SIN1 c[19]
  75 #define SIN2 c[20]
  76 #define SIN3 c[21]
  77 #define SIN4 c[22]
  78 #define SIN5 c[23]
  79 #define SIN6 c[24]
  80 #define SIN7 c[25]
  81 #define SIN8 c[26]
  82 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
  83  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
  84 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
  85  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
  86 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
  87  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
  88 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  89  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
  90 };
  91
  92 #define SINCOSL_COS_HI 0
  93 #define SINCOSL_COS_LO 1
  94 #define SINCOSL_SIN_HI 2
  95 #define SINCOSL_SIN_LO 3
  96 extern const long double __sincosl_table[];
  97
  98 void
  99 __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
 100 {
 101   long double h, l, z, sin_l, cos_l_m1;
 102   int64_t ix;
 103   u_int32_t tix, hix, index;
 104   GET_LDOUBLE_MSW64 (ix, x);
 105   tix = ((u_int64_t)ix) >> 32;
 106   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 107   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
 108     {
 109       /* Argument is small enough to approximate it by a Chebyshev
 110          polynomial of degree 16(17).  */
 111       if (tix < 0x3c600000)             /* |x| < 2^-57 */
 112         if (!((int)x))                  /* generate inexact */
 113           {
 114             *sinx = x;
 115             *cosx = ONE;
 116             return;
 117           }
 118       z = x * x;
 119       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 120                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 121       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 122                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 123     }
 124   else
 125     {
 126       /* So that we don't have to use too large polynomial,  we find
 127          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 128          possible values for h.  We look up cosl(h) and sinl(h) in
 129          pre-computed tables,  compute cosl(l) and sinl(l) using a
 130          Chebyshev polynomial of degree 10(11) and compute
 131          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
 132          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 133       int six = tix;
 134       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 135       index = 0x3ffe - (tix >> 16);
 136       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 137       x = fabsl (x);
 138       switch (index)
 139         {
 140         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 141         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 142         default:
 143         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 144         }
 145       hix = (hix << 4) & 0x3fffffff;
 146 /*
 147     The following should work for double but generates the wrong index.
 148     For now the code above converts double to ieee extended to compute
 149     the index back to double for the h value.
 150
 151
 152       index = 0x3fe - (tix >> 20);
 153       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
 154       x = fabsl (x);
 155       switch (index)
 156         {
 157         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 158         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 159         default:
 160         case 2: index = (hix - 0x3fc30000) >> 14; break;
 161         }
 162 */
 163       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
 164       if (iy)
 165         l = y - (h - x);
 166       else
 167         l = x - h;
 168       z = l * l;
 169       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 170       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 171       z = __sincosl_table [index + SINCOSL_SIN_HI]
 172           + (__sincosl_table [index + SINCOSL_SIN_LO]
 173              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 174              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 175       *sinx = (ix < 0) ? -z : z;
 176       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
 177               + (__sincosl_table [index + SINCOSL_COS_LO]
 178                  - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 179                     - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 180     }
 181 }