sysdeps/ieee754/ldbl-128/k_cosl.c

   1 /* Quad-precision floating point cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999 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 "math.h"
  22 #include "math_private.h"
  23
  24 static const long double c[] = {
  25 #define ONE c[0]
  26  1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
  27
  28 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  29    x in <0,1/256>  */
  30 #define SCOS1 c[1]
  31 #define SCOS2 c[2]
  32 #define SCOS3 c[3]
  33 #define SCOS4 c[4]
  34 #define SCOS5 c[5]
  35 -5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
  36  4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
  37 -1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
  38  2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  39 -2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
  40
  41 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  42    x in <0,0.1484375>  */
  43 #define COS1 c[6]
  44 #define COS2 c[7]
  45 #define COS3 c[8]
  46 #define COS4 c[9]
  47 #define COS5 c[10]
  48 #define COS6 c[11]
  49 #define COS7 c[12]
  50 #define COS8 c[13]
  51 -4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
  52  4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
  53 -1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
  54  2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  55 -2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
  56  2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
  57 -1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
  58  4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  59
  60 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  61    x in <0,1/256>  */
  62 #define SSIN1 c[14]
  63 #define SSIN2 c[15]
  64 #define SSIN3 c[16]
  65 #define SSIN4 c[17]
  66 #define SSIN5 c[18]
  67 -1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
  68  8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
  69 -1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
  70  2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
  71 -2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
  72 };
  73
  74 #define SINCOSL_COS_HI 0
  75 #define SINCOSL_COS_LO 1
  76 #define SINCOSL_SIN_HI 2
  77 #define SINCOSL_SIN_LO 3
  78 extern const long double __sincosl_table[];
  79
  80 long double
  81 __kernel_cosl(long double x, long double y)
  82 {
  83   long double h, l, z, sin_l, cos_l_m1;
  84   int64_t ix;
  85   u_int32_t tix, hix, index;
  86   GET_LDOUBLE_MSW64 (ix, x);
  87   tix = ((u_int64_t)ix) >> 32;
  88   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  89   if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */
  90     {
  91       /* Argument is small enough to approximate it by a Chebyshev
  92          polynomial of degree 16.  */
  93       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
  94         if (!((int)x)) return ONE;      /* generate inexact */
  95       z = x * x;
  96       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
  97                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
  98     }
  99   else
 100     {
 101       /* So that we don't have to use too large polynomial,  we find
 102          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 103          possible values for h.  We look up cosl(h) and sinl(h) in
 104          pre-computed tables,  compute cosl(l) and sinl(l) using a
 105          Chebyshev polynomial of degree 10(11) and compute
 106          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 107       index = 0x3ffe - (tix >> 16);
 108       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 109       x = fabsl (x);
 110       switch (index)
 111         {
 112         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 113         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 114         default:
 115         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 116         }
 117
 118       SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
 119       l = y - (h - x);
 120       z = l * l;
 121       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 122       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 123       return __sincosl_table [index + SINCOSL_COS_HI]
 124              + (__sincosl_table [index + SINCOSL_COS_LO]
 125                 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 126                    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 127     }
 128 }