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

   1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2014 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   uint32_t tix, hix, index;
 104   double xhi, hhi;
 105
 106   xhi = ldbl_high (x);
 107   EXTRACT_WORDS64 (ix, xhi);
 108   tix = ((uint64_t)ix) >> 32;
 109   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 110   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
 111     {
 112       /* Argument is small enough to approximate it by a Chebyshev
 113          polynomial of degree 16(17).  */
 114       if (tix < 0x3c600000)             /* |x| < 2^-57 */
 115         if (!((int)x))                  /* generate inexact */
 116           {
 117             *sinx = x;
 118             *cosx = ONE;
 119             return;
 120           }
 121       z = x * x;
 122       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 123                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 124       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 125                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 126     }
 127   else
 128     {
 129       /* So that we don't have to use too large polynomial,  we find
 130          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 131          possible values for h.  We look up cosl(h) and sinl(h) in
 132          pre-computed tables,  compute cosl(l) and sinl(l) using a
 133          Chebyshev polynomial of degree 10(11) and compute
 134          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
 135          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 136       int six = tix;
 137       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 138       index = 0x3ffe - (tix >> 16);
 139       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 140       x = fabsl (x);
 141       switch (index)
 142         {
 143         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 144         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 145         default:
 146         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 147         }
 148       hix = (hix << 4) & 0x3fffffff;
 149 /*
 150     The following should work for double but generates the wrong index.
 151     For now the code above converts double to ieee extended to compute
 152     the index back to double for the h value.
 153
 154
 155       index = 0x3fe - (tix >> 20);
 156       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
 157       if (signbit (x))
 158         {
 159           x = -x;
 160           y = -y;
 161         }
 162       switch (index)
 163         {
 164         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 165         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 166         default:
 167         case 2: index = (hix - 0x3fc30000) >> 14; break;
 168         }
 169 */
 170       INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
 171       h = hhi;
 172       if (iy)
 173         l = y - (h - x);
 174       else
 175         l = x - h;
 176       z = l * l;
 177       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 178       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 179       z = __sincosl_table [index + SINCOSL_SIN_HI]
 180           + (__sincosl_table [index + SINCOSL_SIN_LO]
 181              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 182              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 183       *sinx = (ix < 0) ? -z : z;
 184       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
 185               + (__sincosl_table [index + SINCOSL_COS_LO]
 186                  - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 187                     - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 188     }
 189 }