libquadmath/math/cosq_kernel.c

   1 /* Quad-precision floating point cosine 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 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  40    x in <0,0.1484375>  */
  41 #define COS1 c[6]
  42 #define COS2 c[7]
  43 #define COS3 c[8]
  44 #define COS4 c[9]
  45 #define COS5 c[10]
  46 #define COS6 c[11]
  47 #define COS7 c[12]
  48 #define COS8 c[13]
  49 -4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */
  50  4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
  51 -1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
  52  2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  53 -2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
  54  2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
  55 -1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
  56  4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  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_cosq(__float128 x, __float128 y)
  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 16.  */
  91       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
  92         if (!((int)x)) return ONE;      /* generate inexact */
  93       z = x * x;
  94       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
  95                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
  96     }
  97   else
  98     {
  99       /* So that we don't have to use too large polynomial,  we find
 100          l and h such that x = l + h,  where fabsq(l) <= 1.0/256 with 83
 101          possible values for h.  We look up cosq(h) and sinq(h) in
 102          pre-computed tables,  compute cosq(l) and sinq(l) using a
 103          Chebyshev polynomial of degree 10(11) and compute
 104          cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l).  */
 105       index = 0x3ffe - (tix >> 16);
 106       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 107       if (signbitq (x))
 108         {
 109           x = -x;
 110           y = -y;
 111         }
 112       switch (index)
 113         {
 114         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 115         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 116         default:
 117         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 118         }
 119
 120       SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
 121       l = y - (h - x);
 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       return __sincosq_table [index + SINCOSL_COS_HI]
 126              + (__sincosq_table [index + SINCOSL_COS_LO]
 127                 - (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
 128                    - __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
 129     }
 130 }