sysdeps/ieee754/ldbl-96/k_cosl.c

   1 /* Extended-precision floating point cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2016 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Based on quad-precision cosine 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 /* The polynomials have not been optimized for extended-precision and
  24    may contain more terms than needed.  */
  25
  26 static const long double c[] = {
  27 #define ONE c[0]
  28  1.00000000000000000000000000000000000E+00L,
  29
  30 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  31    x in <0,1/256>  */
  32 #define SCOS1 c[1]
  33 #define SCOS2 c[2]
  34 #define SCOS3 c[3]
  35 #define SCOS4 c[4]
  36 #define SCOS5 c[5]
  37 -5.00000000000000000000000000000000000E-01L,
  38  4.16666666666666666666666666556146073E-02L,
  39 -1.38888888888888888888309442601939728E-03L,
  40  2.48015873015862382987049502531095061E-05L,
  41 -2.75573112601362126593516899592158083E-07L,
  42
  43 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  44    x in <0,0.1484375>  */
  45 #define COS1 c[6]
  46 #define COS2 c[7]
  47 #define COS3 c[8]
  48 #define COS4 c[9]
  49 #define COS5 c[10]
  50 #define COS6 c[11]
  51 #define COS7 c[12]
  52 #define COS8 c[13]
  53 -4.99999999999999999999999999999999759E-01L,
  54  4.16666666666666666666666666651287795E-02L,
  55 -1.38888888888888888888888742314300284E-03L,
  56  2.48015873015873015867694002851118210E-05L,
  57 -2.75573192239858811636614709689300351E-07L,
  58  2.08767569877762248667431926878073669E-09L,
  59 -1.14707451049343817400420280514614892E-11L,
  60  4.77810092804389587579843296923533297E-14L,
  61
  62 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  63    x in <0,1/256>  */
  64 #define SSIN1 c[14]
  65 #define SSIN2 c[15]
  66 #define SSIN3 c[16]
  67 #define SSIN4 c[17]
  68 #define SSIN5 c[18]
  69 -1.66666666666666666666666666666666659E-01L,
  70  8.33333333333333333333333333146298442E-03L,
  71 -1.98412698412698412697726277416810661E-04L,
  72  2.75573192239848624174178393552189149E-06L,
  73 -2.50521016467996193495359189395805639E-08L,
  74 };
  75
  76 #define SINCOSL_COS_HI 0
  77 #define SINCOSL_COS_LO 1
  78 #define SINCOSL_SIN_HI 2
  79 #define SINCOSL_SIN_LO 3
  80 extern const long double __sincosl_table[];
  81
  82 long double
  83 __kernel_cosl(long double x, long double y)
  84 {
  85   long double h, l, z, sin_l, cos_l_m1;
  86   int index;
  87
  88   if (signbit (x))
  89     {
  90       x = -x;
  91       y = -y;
  92     }
  93   if (x < 0.1484375L)
  94     {
  95       /* Argument is small enough to approximate it by a Chebyshev
  96          polynomial of degree 16.  */
  97       if (x < 0x1p-33L)
  98         if (!((int)x)) return ONE;      /* generate inexact */
  99       z = x * x;
 100       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 101                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 102     }
 103   else
 104     {
 105       /* So that we don't have to use too large polynomial,  we find
 106          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 107          possible values for h.  We look up cosl(h) and sinl(h) in
 108          pre-computed tables,  compute cosl(l) and sinl(l) using a
 109          Chebyshev polynomial of degree 10(11) and compute
 110          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 111       index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L)));
 112       h = 0.1484375L + index / 128.0;
 113       index *= 4;
 114       l = y - (h - x);
 115       z = l * l;
 116       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 117       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 118       return __sincosl_table [index + SINCOSL_COS_HI]
 119              + (__sincosl_table [index + SINCOSL_COS_LO]
 120                 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 121                    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 122     }
 123 }