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

   1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2020 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 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  43    x in <0,0.1484375>  */
  44 #define SIN1 c[6]
  45 #define SIN2 c[7]
  46 #define SIN3 c[8]
  47 #define SIN4 c[9]
  48 #define SIN5 c[10]
  49 #define SIN6 c[11]
  50 #define SIN7 c[12]
  51 #define SIN8 c[13]
  52 -1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
  53  8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
  54 -1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
  55  2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
  56 -2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
  57  1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
  58 -7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  59  2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
  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
  75 #define SINCOSL_COS_HI 0
  76 #define SINCOSL_COS_LO 1
  77 #define SINCOSL_SIN_HI 2
  78 #define SINCOSL_SIN_LO 3
  79 extern const long double __sincosl_table[];
  80
  81 long double
  82 __kernel_sinl(long double x, long double y, int iy)
  83 {
  84   long double h, l, z, sin_l, cos_l_m1;
  85   int64_t ix;
  86   uint32_t tix, hix, index;
  87   double xhi, hhi;
  88
  89   xhi = ldbl_high (x);
  90   EXTRACT_WORDS64 (ix, xhi);
  91   tix = ((uint64_t)ix) >> 32;
  92   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  93   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
  94     {
  95       /* Argument is small enough to approximate it by a Chebyshev
  96          polynomial of degree 17.  */
  97       if (tix < 0x3c600000)             /* |x| < 2^-57 */
  98         {
  99           math_check_force_underflow (x);
 100           if (!((int)x)) return x;      /* generate inexact */
 101         }
 102       z = x * x;
 103       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 104                        z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 105     }
 106   else
 107     {
 108       /* So that we don't have to use too large polynomial,  we find
 109          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 110          possible values for h.  We look up cosl(h) and sinl(h) in
 111          pre-computed tables,  compute cosl(l) and sinl(l) using a
 112          Chebyshev polynomial of degree 10(11) and compute
 113          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l).  */
 114       int six = tix;
 115       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 116       index = 0x3ffe - (tix >> 16);
 117       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 118       x = fabsl (x);
 119       switch (index)
 120         {
 121         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 122         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 123         default:
 124         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 125         }
 126       hix = (hix << 4) & 0x3fffffff;
 127 /*
 128     The following should work for double but generates the wrong index.
 129     For now the code above converts double to ieee extended to compute
 130     the index back to double for the h value.
 131
 132       index = 0x3fe - (tix >> 20);
 133       hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
 134       x = fabsl (x);
 135       switch (index)
 136         {
 137         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 138         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 139         default:
 140         case 2: index = (hix - 0x3fc30000) >> 14; break;
 141         }
 142 */
 143       INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
 144       h = hhi;
 145       if (iy)
 146         l = (ix < 0 ? -y : y) - (h - x);
 147       else
 148         l = x - h;
 149       z = l * l;
 150       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 151       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 152       z = __sincosl_table [index + SINCOSL_SIN_HI]
 153           + (__sincosl_table [index + SINCOSL_SIN_LO]
 154              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 155              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 156       return (ix < 0) ? -z : z;
 157     }
 158 }