libquadmath/math/sinq_kernel.c

   1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2013 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 "quadmath-imp.h"
  22
  23 static const __float128 c[] = {
  24 #define ONE c[0]
  25  1.00000000000000000000000000000000000E+00Q, /* 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-01Q, /* bffe0000000000000000000000000000 */
  35  4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
  36 -1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
  37  2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  38 -2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
  39
  40 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  41    x in <0,0.1484375>  */
  42 #define SIN1 c[6]
  43 #define SIN2 c[7]
  44 #define SIN3 c[8]
  45 #define SIN4 c[9]
  46 #define SIN5 c[10]
  47 #define SIN6 c[11]
  48 #define SIN7 c[12]
  49 #define SIN8 c[13]
  50 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
  51  8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
  52 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
  53  2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
  54 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
  55  1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
  56 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  57  2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
  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-01Q, /* bffc5555555555555555555555555555 */
  67  8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
  68 -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
  69  2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  70 -2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
  71 };
  72
  73 #define SINCOSQ_COS_HI 0
  74 #define SINCOSQ_COS_LO 1
  75 #define SINCOSQ_SIN_HI 2
  76 #define SINCOSQ_SIN_LO 3
  77 extern const __float128 __sincosq_table[];
  78
  79 __float128
  80 __quadmath_kernel_sinq (__float128 x, __float128 y, int iy)
  81 {
  82   __float128 h, l, z, sin_l, cos_l_m1;
  83   int64_t ix;
  84   uint32_t tix, hix, index;
  85   GET_FLT128_MSW64 (ix, x);
  86   tix = ((uint64_t)ix) >> 32;
  87   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  88   if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */
  89     {
  90       /* Argument is small enough to approximate it by a Chebyshev
  91          polynomial of degree 17.  */
  92       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
  93         if (!((int)x)) return x;        /* generate inexact */
  94       z = x * x;
  95       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
  96                        z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
  97     }
  98   else
  99     {
 100       /* So that we don't have to use too large polynomial,  we find
 101          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 102          possible values for h.  We look up cosq(h) and sinq(h) in
 103          pre-computed tables,  compute cosq(l) and sinq(l) using a
 104          Chebyshev polynomial of degree 10(11) and compute
 105          sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l).  */
 106       index = 0x3ffe - (tix >> 16);
 107       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 108       x = fabsq (x);
 109       switch (index)
 110         {
 111         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 112         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 113         default:
 114         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 115         }
 116
 117       SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
 118       if (iy)
 119         l = (ix < 0 ? -y : y) - (h - x);
 120       else
 121         l = x - h;
 122       z = l * l;
 123       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 124       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 125       z = __sincosq_table [index + SINCOSQ_SIN_HI]
 126           + (__sincosq_table [index + SINCOSQ_SIN_LO]
 127              + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
 128              + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
 129       return (ix < 0) ? -z : z;
 130     }
 131 }