sysdeps/ieee754/ldbl-96/k_sinl.c

   1 /* Quad-precision floating point sine 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    Based on quad-precision sine 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 /* The polynomials have not been optimized for extended-precision and
  21    may contain more terms than needed.  */
  22
  23 #include <math.h>
  24 #include <math_private.h>
  25
  26 /* The polynomials have not been optimized for extended-precision and
  27    may contain more terms than needed.  */
  28
  29 static const long double c[] = {
  30 #define ONE c[0]
  31  1.00000000000000000000000000000000000E+00L,
  32
  33 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  34    x in <0,1/256>  */
  35 #define SCOS1 c[1]
  36 #define SCOS2 c[2]
  37 #define SCOS3 c[3]
  38 #define SCOS4 c[4]
  39 #define SCOS5 c[5]
  40 -5.00000000000000000000000000000000000E-01L,
  41  4.16666666666666666666666666556146073E-02L,
  42 -1.38888888888888888888309442601939728E-03L,
  43  2.48015873015862382987049502531095061E-05L,
  44 -2.75573112601362126593516899592158083E-07L,
  45
  46 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  47    x in <0,0.1484375>  */
  48 #define SIN1 c[6]
  49 #define SIN2 c[7]
  50 #define SIN3 c[8]
  51 #define SIN4 c[9]
  52 #define SIN5 c[10]
  53 #define SIN6 c[11]
  54 #define SIN7 c[12]
  55 #define SIN8 c[13]
  56 -1.66666666666666666666666666666666538e-01L,
  57  8.33333333333333333333333333307532934e-03L,
  58 -1.98412698412698412698412534478712057e-04L,
  59  2.75573192239858906520896496653095890e-06L,
  60 -2.50521083854417116999224301266655662e-08L,
  61  1.60590438367608957516841576404938118e-10L,
  62 -7.64716343504264506714019494041582610e-13L,
  63  2.81068754939739570236322404393398135e-15L,
  64
  65 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  66    x in <0,1/256>  */
  67 #define SSIN1 c[14]
  68 #define SSIN2 c[15]
  69 #define SSIN3 c[16]
  70 #define SSIN4 c[17]
  71 #define SSIN5 c[18]
  72 -1.66666666666666666666666666666666659E-01L,
  73  8.33333333333333333333333333146298442E-03L,
  74 -1.98412698412698412697726277416810661E-04L,
  75  2.75573192239848624174178393552189149E-06L,
  76 -2.50521016467996193495359189395805639E-08L,
  77 };
  78
  79 #define SINCOSL_COS_HI 0
  80 #define SINCOSL_COS_LO 1
  81 #define SINCOSL_SIN_HI 2
  82 #define SINCOSL_SIN_LO 3
  83 extern const long double __sincosl_table[];
  84
  85 long double
  86 __kernel_sinl(long double x, long double y, int iy)
  87 {
  88   long double absx, h, l, z, sin_l, cos_l_m1;
  89   int index;
  90
  91   absx = fabsl (x);
  92   if (absx < 0.1484375L)
  93     {
  94       /* Argument is small enough to approximate it by a Chebyshev
  95          polynomial of degree 17.  */
  96       if (absx < 0x1p-33L)
  97         if (!((int)x)) return x;        /* generate inexact */
  98       z = x * x;
  99       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 100                        z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 101     }
 102   else
 103     {
 104       /* So that we don't have to use too large polynomial,  we find
 105          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 106          possible values for h.  We look up cosl(h) and sinl(h) in
 107          pre-computed tables,  compute cosl(l) and sinl(l) using a
 108          Chebyshev polynomial of degree 10(11) and compute
 109          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l).  */
 110       index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L)));
 111       h = 0.1484375L + index / 128.0;
 112       index *= 4;
 113       if (iy)
 114         l = (x < 0 ? -y : y) - (h - absx);
 115       else
 116         l = absx - h;
 117       z = l * l;
 118       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 119       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 120       z = __sincosl_table [index + SINCOSL_SIN_HI]
 121           + (__sincosl_table [index + SINCOSL_SIN_LO]
 122              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 123              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 124       return (x < 0) ? -z : z;
 125     }
 126 }