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

   1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2019 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    <https://www.gnu.org/licenses/>.  */
  19
  20 #include <float.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <math-underflow.h>
  24
  25 static const long double c[] = {
  26 #define ONE c[0]
  27  1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
  28
  29 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  30    x in <0,1/256>  */
  31 #define SCOS1 c[1]
  32 #define SCOS2 c[2]
  33 #define SCOS3 c[3]
  34 #define SCOS4 c[4]
  35 #define SCOS5 c[5]
  36 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
  37  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
  38 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
  39  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  40 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
  41
  42 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  43    x in <0,0.1484375>  */
  44 #define COS1 c[6]
  45 #define COS2 c[7]
  46 #define COS3 c[8]
  47 #define COS4 c[9]
  48 #define COS5 c[10]
  49 #define COS6 c[11]
  50 #define COS7 c[12]
  51 #define COS8 c[13]
  52 -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
  53  4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
  54 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
  55  2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  56 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
  57  2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
  58 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
  59  4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  60
  61 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  62    x in <0,1/256>  */
  63 #define SSIN1 c[14]
  64 #define SSIN2 c[15]
  65 #define SSIN3 c[16]
  66 #define SSIN4 c[17]
  67 #define SSIN5 c[18]
  68 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
  69  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
  70 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
  71  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  72 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
  73
  74 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  75    x in <0,0.1484375>  */
  76 #define SIN1 c[19]
  77 #define SIN2 c[20]
  78 #define SIN3 c[21]
  79 #define SIN4 c[22]
  80 #define SIN5 c[23]
  81 #define SIN6 c[24]
  82 #define SIN7 c[25]
  83 #define SIN8 c[26]
  84 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
  85  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
  86 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
  87  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
  88 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
  89  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
  90 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  91  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
  92 };
  93
  94 #define SINCOSL_COS_HI 0
  95 #define SINCOSL_COS_LO 1
  96 #define SINCOSL_SIN_HI 2
  97 #define SINCOSL_SIN_LO 3
  98 extern const long double __sincosl_table[];
  99
 100 void
 101 __kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
 102 {
 103   long double h, l, z, sin_l, cos_l_m1;
 104   int64_t ix;
 105   uint32_t tix, hix, index;
 106   double xhi, hhi;
 107
 108   xhi = ldbl_high (x);
 109   EXTRACT_WORDS64 (ix, xhi);
 110   tix = ((uint64_t)ix) >> 32;
 111   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 112   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
 113     {
 114       /* Argument is small enough to approximate it by a Chebyshev
 115          polynomial of degree 16(17).  */
 116       if (tix < 0x3c600000)             /* |x| < 2^-57 */
 117         {
 118           math_check_force_underflow (x);
 119           if (!((int)x))                        /* generate inexact */
 120             {
 121               *sinx = x;
 122               *cosx = ONE;
 123               return;
 124             }
 125         }
 126       z = x * x;
 127       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 128                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 129       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 130                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 131     }
 132   else
 133     {
 134       /* So that we don't have to use too large polynomial,  we find
 135          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 136          possible values for h.  We look up cosl(h) and sinl(h) in
 137          pre-computed tables,  compute cosl(l) and sinl(l) using a
 138          Chebyshev polynomial of degree 10(11) and compute
 139          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
 140          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 141       int six = tix;
 142       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 143       index = 0x3ffe - (tix >> 16);
 144       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 145       x = fabsl (x);
 146       switch (index)
 147         {
 148         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 149         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 150         default:
 151         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 152         }
 153       hix = (hix << 4) & 0x3fffffff;
 154 /*
 155     The following should work for double but generates the wrong index.
 156     For now the code above converts double to ieee extended to compute
 157     the index back to double for the h value.
 158
 159
 160       index = 0x3fe - (tix >> 20);
 161       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
 162       if (signbit (x))
 163         {
 164           x = -x;
 165           y = -y;
 166         }
 167       switch (index)
 168         {
 169         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 170         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 171         default:
 172         case 2: index = (hix - 0x3fc30000) >> 14; break;
 173         }
 174 */
 175       INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
 176       h = hhi;
 177       if (iy)
 178         l = y - (h - x);
 179       else
 180         l = x - h;
 181       z = l * l;
 182       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 183       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 184       z = __sincosl_table [index + SINCOSL_SIN_HI]
 185           + (__sincosl_table [index + SINCOSL_SIN_LO]
 186              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 187              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 188       *sinx = (ix < 0) ? -z : z;
 189       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
 190               + (__sincosl_table [index + SINCOSL_COS_LO]
 191                  - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 192                     - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 193     }
 194 }