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

   1 /* Quad-precision floating point cosine 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, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <math.h>
  21 #include <math_private.h>
  22
  23 static const long double c[] = {
  24 #define ONE c[0]
  25  1.00000000000000000000000000000000000E+00L, /* 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-01L, /* bffe0000000000000000000000000000 */
  35  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
  36 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
  37  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  38 -2.75573112601362126593516899592158083E-07L, /* 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-01L, /* bffdfffffffffffffffffffffffffffb */
  51  4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
  52 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
  53  2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  54 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
  55  2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
  56 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
  57  4.77810092804389587579843296923533297E-14L, /* 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-01L, /* bffc5555555555555555555555555555 */
  67  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
  68 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
  69  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  70 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
  71 };
  72
  73 #define SINCOSL_COS_HI 0
  74 #define SINCOSL_COS_LO 1
  75 #define SINCOSL_SIN_HI 2
  76 #define SINCOSL_SIN_LO 3
  77 extern const long double __sincosl_table[];
  78
  79 long double
  80 __kernel_cosl(long double x, long double y)
  81 {
  82   long double h, l, z, sin_l, cos_l_m1;
  83   int64_t ix;
  84   u_int32_t tix, hix, index;
  85   GET_LDOUBLE_MSW64 (ix, x);
  86   tix = ((u_int64_t)ix) >> 32;
  87   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  88   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
  89     {
  90       /* Argument is small enough to approximate it by a Chebyshev
  91          polynomial of degree 16.  */
  92       if (tix < 0x3c600000)             /* |x| < 2^-57 */
  93         if (!((int)x)) return ONE;      /* generate inexact */
  94       z = x * x;
  95       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
  96                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
  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 cosl(h) and sinl(h) in
 103          pre-computed tables,  compute cosl(l) and sinl(l) using a
 104          Chebyshev polynomial of degree 10(11) and compute
 105          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 106       int six = tix;
 107       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 108       index = 0x3ffe - (tix >> 16);
 109       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 110       x = fabsl (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       hix = (hix << 4) & 0x3fffffff;
 119 /*
 120     The following should work for double but generates the wrong index.
 121     For now the code above converts double to ieee extended to compute
 122     the index back to double for the h value.
 123
 124       index = 0x3fe - (tix >> 20);
 125       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 126       if (signbit (x))
 127         {
 128           x = -x;
 129           y = -y;
 130         }
 131       switch (index)
 132         {
 133         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 134         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 135         default:
 136         case 2: index = (hix - 0x3fc30000) >> 14; break;
 137         }
 138 */
 139       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
 140       l = y - (h - x);
 141       z = l * l;
 142       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 143       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 144       return __sincosl_table [index + SINCOSL_COS_HI]
 145              + (__sincosl_table [index + SINCOSL_COS_LO]
 146                 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 147                    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 148     }
 149 }