libquadmath/math/sinq_kernel.c

   1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2018 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 "quadmath-imp.h"
  21
  22 static const __float128 c[] = {
  23 #define ONE c[0]
  24  1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
  25
  26 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  27    x in <0,1/256>  */
  28 #define SCOS1 c[1]
  29 #define SCOS2 c[2]
  30 #define SCOS3 c[3]
  31 #define SCOS4 c[4]
  32 #define SCOS5 c[5]
  33 -5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */
  34  4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
  35 -1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
  36  2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  37 -2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
  38
  39 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  40    x in <0,0.1484375>  */
  41 #define SIN1 c[6]
  42 #define SIN2 c[7]
  43 #define SIN3 c[8]
  44 #define SIN4 c[9]
  45 #define SIN5 c[10]
  46 #define SIN6 c[11]
  47 #define SIN7 c[12]
  48 #define SIN8 c[13]
  49 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
  50  8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
  51 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
  52  2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
  53 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
  54  1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
  55 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  56  2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
  57
  58 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  59    x in <0,1/256>  */
  60 #define SSIN1 c[14]
  61 #define SSIN2 c[15]
  62 #define SSIN3 c[16]
  63 #define SSIN4 c[17]
  64 #define SSIN5 c[18]
  65 -1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */
  66  8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
  67 -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
  68  2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  69 -2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
  70 };
  71
  72 #define SINCOSL_COS_HI 0
  73 #define SINCOSL_COS_LO 1
  74 #define SINCOSL_SIN_HI 2
  75 #define SINCOSL_SIN_LO 3
  76 extern const __float128 __sincosq_table[];
  77
  78 __float128
  79 __quadmath_kernel_sinq(__float128 x, __float128 y, int iy)
  80 {
  81   __float128 h, l, z, sin_l, cos_l_m1;
  82   int64_t ix;
  83   uint32_t tix, hix, index;
  84   GET_FLT128_MSW64 (ix, x);
  85   tix = ((uint64_t)ix) >> 32;
  86   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  87   if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */
  88     {
  89       /* Argument is small enough to approximate it by a Chebyshev
  90          polynomial of degree 17.  */
  91       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
  92         {
  93           math_check_force_underflow (x);
  94           if (!((int)x)) return x;      /* generate inexact */
  95         }
  96       z = x * x;
  97       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
  98                        z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
  99     }
 100   else
 101     {
 102       /* So that we don't have to use too large polynomial,  we find
 103          l and h such that x = l + h,  where fabsq(l) <= 1.0/256 with 83
 104          possible values for h.  We look up cosq(h) and sinq(h) in
 105          pre-computed tables,  compute cosq(l) and sinq(l) using a
 106          Chebyshev polynomial of degree 10(11) and compute
 107          sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l).  */
 108       index = 0x3ffe - (tix >> 16);
 109       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 110       x = fabsq (x);
 111       switch (index)
 112         {
 113         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 114         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 115         default:
 116         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 117         }
 118
 119       SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
 120       if (iy)
 121         l = (ix < 0 ? -y : y) - (h - x);
 122       else
 123         l = x - h;
 124       z = l * l;
 125       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 126       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 127       z = __sincosq_table [index + SINCOSL_SIN_HI]
 128           + (__sincosq_table [index + SINCOSL_SIN_LO]
 129              + (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 130              + (__sincosq_table [index + SINCOSL_COS_HI] * sin_l));
 131       return (ix < 0) ? -z : z;
 132     }
 133 }