libquadmath/math/sincosq_kernel.c

   1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2017 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 /* 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-01Q, /* bffdfffffffffffffffffffffffffffb */
  51  4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
  52 -1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
  53  2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  54 -2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
  55  2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
  56 -1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
  57  4.77810092804389587579843296923533297E-14Q, /* 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-01Q, /* bffc5555555555555555555555555555 */
  67  8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
  68 -1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
  69  2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  70 -2.50521016467996193495359189395805639E-08Q, /* 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-01Q, /* bffc5555555555555555555555555550 */
  83  8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
  84 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
  85  2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
  86 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
  87  1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
  88 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  89  2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
  90 };
  91
  92 #define SINCOSQ_COS_HI 0
  93 #define SINCOSQ_COS_LO 1
  94 #define SINCOSQ_SIN_HI 2
  95 #define SINCOSQ_SIN_LO 3
  96 extern const __float128 __sincosq_table[];
  97
  98 void
  99 __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
 100                           __float128 *cosx, int iy)
 101 {
 102   __float128 h, l, z, sin_l, cos_l_m1;
 103   int64_t ix;
 104   uint32_t tix, hix, index;
 105   GET_FLT128_MSW64 (ix, x);
 106   tix = ((uint64_t)ix) >> 32;
 107   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 108   if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */
 109     {
 110       /* Argument is small enough to approximate it by a Chebyshev
 111          polynomial of degree 16(17).  */
 112       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
 113         {
 114           math_check_force_underflow (x);
 115           if (!((int)x))                        /* generate inexact */
 116             {
 117               *sinx = x;
 118               *cosx = ONE;
 119               return;
 120             }
 121         }
 122       z = x * x;
 123       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 124                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 125       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 126                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 127     }
 128   else
 129     {
 130       /* So that we don't have to use too large polynomial,  we find
 131          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 132          possible values for h.  We look up cosq(h) and sinq(h) in
 133          pre-computed tables,  compute cosq(l) and sinq(l) using a
 134          Chebyshev polynomial of degree 10(11) and compute
 135          sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and
 136          cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l).  */
 137       index = 0x3ffe - (tix >> 16);
 138       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 139       if (signbitq (x))
 140        {
 141          x = -x;
 142          y = -y;
 143        }
 144       switch (index)
 145         {
 146         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 147         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 148         default:
 149         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 150         }
 151
 152       SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
 153       if (iy)
 154         l = y - (h - x);
 155       else
 156         l = x - h;
 157       z = l * l;
 158       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 159       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 160       z = __sincosq_table [index + SINCOSQ_SIN_HI]
 161           + (__sincosq_table [index + SINCOSQ_SIN_LO]
 162              + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
 163              + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
 164       *sinx = (ix < 0) ? -z : z;
 165       *cosx = __sincosq_table [index + SINCOSQ_COS_HI]
 166               + (__sincosq_table [index + SINCOSQ_COS_LO]
 167                  - (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l
 168                     - __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));
 169     }
 170 }