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

   1 /* Quad-precision floating point cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2014 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   uint32_t tix, hix, index;
  85   double xhi, hhi;
  86
  87   xhi = ldbl_high (x);
  88   EXTRACT_WORDS64 (ix, xhi);
  89   tix = ((u_int64_t)ix) >> 32;
  90   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
  91   if (tix < 0x3fc30000)                 /* |x| < 0.1484375 */
  92     {
  93       /* Argument is small enough to approximate it by a Chebyshev
  94          polynomial of degree 16.  */
  95       if (tix < 0x3c600000)             /* |x| < 2^-57 */
  96         if (!((int)x)) return ONE;      /* generate inexact */
  97       z = x * x;
  98       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
  99                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 100     }
 101   else
 102     {
 103       /* So that we don't have to use too large polynomial,  we find
 104          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 105          possible values for h.  We look up cosl(h) and sinl(h) in
 106          pre-computed tables,  compute cosl(l) and sinl(l) using a
 107          Chebyshev polynomial of degree 10(11) and compute
 108          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 109       int six = tix;
 110       tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
 111       index = 0x3ffe - (tix >> 16);
 112       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 113       x = fabsl (x);
 114       switch (index)
 115         {
 116         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 117         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 118         default:
 119         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 120         }
 121       hix = (hix << 4) & 0x3fffffff;
 122 /*
 123     The following should work for double but generates the wrong index.
 124     For now the code above converts double to ieee extended to compute
 125     the index back to double for the h value.
 126
 127       index = 0x3fe - (tix >> 20);
 128       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 129       if (signbit (x))
 130         {
 131           x = -x;
 132           y = -y;
 133         }
 134       switch (index)
 135         {
 136         case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
 137         case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
 138         default:
 139         case 2: index = (hix - 0x3fc30000) >> 14; break;
 140         }
 141 */
 142       INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
 143       h = hhi;
 144       l = y - (h - x);
 145       z = l * l;
 146       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 147       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 148       return __sincosl_table [index + SINCOSL_COS_HI]
 149              + (__sincosl_table [index + SINCOSL_COS_LO]
 150                 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 151                    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 152     }
 153 }