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, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const long double c[] = {
  25 #define ONE c[0]
  26  1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
  27
  28 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  29    x in <0,1/256>  */
  30 #define SCOS1 c[1]
  31 #define SCOS2 c[2]
  32 #define SCOS3 c[3]
  33 #define SCOS4 c[4]
  34 #define SCOS5 c[5]
  35 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
  36  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
  37 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
  38  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  39 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
  40
  41 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  42    x in <0,0.1484375>  */
  43 #define COS1 c[6]
  44 #define COS2 c[7]
  45 #define COS3 c[8]
  46 #define COS4 c[9]
  47 #define COS5 c[10]
  48 #define COS6 c[11]
  49 #define COS7 c[12]
  50 #define COS8 c[13]
  51 -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
  52  4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
  53 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
  54  2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  55 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
  56  2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
  57 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
  58  4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  59
  60 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  61    x in <0,1/256>  */
  62 #define SSIN1 c[14]
  63 #define SSIN2 c[15]
  64 #define SSIN3 c[16]
  65 #define SSIN4 c[17]
  66 #define SSIN5 c[18]
  67 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
  68  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
  69 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
  70  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  71 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
  72
  73 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  74    x in <0,0.1484375>  */
  75 #define SIN1 c[19]
  76 #define SIN2 c[20]
  77 #define SIN3 c[21]
  78 #define SIN4 c[22]
  79 #define SIN5 c[23]
  80 #define SIN6 c[24]
  81 #define SIN7 c[25]
  82 #define SIN8 c[26]
  83 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
  84  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
  85 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
  86  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
  87 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
  88  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
  89 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  90  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
  91 };
  92
  93 #define SINCOSL_COS_HI 0
  94 #define SINCOSL_COS_LO 1
  95 #define SINCOSL_SIN_HI 2
  96 #define SINCOSL_SIN_LO 3
  97 extern const long double __sincosl_table[];
  98
  99 void
 100 __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
 101 {
 102   long double h, l, z, sin_l, cos_l_m1;
 103   int64_t ix;
 104   u_int32_t tix, hix, index;
 105   GET_LDOUBLE_MSW64 (ix, x);
 106   tix = ((u_int64_t)ix) >> 32;
 107   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 108   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
 109     {
 110       /* Argument is small enough to approximate it by a Chebyshev
 111          polynomial of degree 16(17).  */
 112       if (tix < 0x3c600000)             /* |x| < 2^-57 */
 113         if (!((int)x))                  /* generate inexact */
 114           {
 115             *sinx = x;
 116             *cosx = ONE;
 117             return;
 118           }
 119       z = x * x;
 120       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 121                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 122       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 123                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 124     }
 125   else
 126     {
 127       /* So that we don't have to use too large polynomial,  we find
 128          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 129          possible values for h.  We look up cosl(h) and sinl(h) in
 130          pre-computed tables,  compute cosl(l) and sinl(l) using a
 131          Chebyshev polynomial of degree 10(11) and compute
 132          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
 133          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 134       int six = tix;
 135       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 136       index = 0x3ffe - (tix >> 16);
 137       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 138       x = fabsl (x);
 139       switch (index)
 140         {
 141         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 142         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 143         default:
 144         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 145         }
 146       hix = (hix << 4) & 0x3fffffff;
 147 /*
 148     The following should work for double but generates the wrong index.
 149     For now the code above converts double to ieee extended to compute
 150     the index back to double for the h value.
 151
 152
 153       index = 0x3fe - (tix >> 20);
 154       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
 155       x = fabsl (x);
 156       switch (index)
 157         {
 158         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 159         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 160         default:
 161         case 2: index = (hix - 0x3fc30000) >> 14; break;
 162         }
 163 */
 164       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
 165       if (iy)
 166         l = y - (h - x);
 167       else
 168         l = x - h;
 169       z = l * l;
 170       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 171       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 172       z = __sincosl_table [index + SINCOSL_SIN_HI]
 173           + (__sincosl_table [index + SINCOSL_SIN_LO]
 174              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 175              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 176       *sinx = (ix < 0) ? -z : z;
 177       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
 178               + (__sincosl_table [index + SINCOSL_COS_LO]
 179                  - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 180                     - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 181     }
 182 }