lib/cosl.c

   1 /* s_cosl.c -- long double version of s_sin.c.
   2  * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include <config.h>
  17
  18 /* Specification.  */
  19 #include <math.h>
  20
  21 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
  22
  23 long double
  24 cosl (long double x)
  25 {
  26   return cos (x);
  27 }
  28
  29 #else
  30
  31 /* Code based on glibc/sysdeps/ieee754/ldbl-128/s_cosl.c.  */
  32
  33 /* cosl(x)
  34  * Return cosine function of x.
  35  *
  36  * kernel function:
  37  *      __kernel_sinl           ... sine function on [-pi/4,pi/4]
  38  *      __kernel_cosl           ... cosine function on [-pi/4,pi/4]
  39  *      __ieee754_rem_pio2l     ... argument reduction routine
  40  *
  41  * Method.
  42  *      Let S,C and T denote the sin, cos and tan respectively on
  43  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  44  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  45  *      We have
  46  *
  47  *          n        sin(x)      cos(x)        tan(x)
  48  *     ----------------------------------------------------------
  49  *          0          S           C             T
  50  *          1          C          -S            -1/T
  51  *          2         -S          -C             T
  52  *          3         -C           S            -1/T
  53  *     ----------------------------------------------------------
  54  *
  55  * Special cases:
  56  *      Let trig be any of sin, cos, or tan.
  57  *      trig(+-INF)  is NaN, with signals;
  58  *      trig(NaN)    is that NaN;
  59  *
  60  * Accuracy:
  61  *      TRIG(x) returns trig(x) nearly rounded
  62  */
  63
  64 # include "trigl.h"
  65
  66 long double
  67 cosl (long double x)
  68 {
  69   long double y[2],z=0.0L;
  70   int n;
  71
  72   /* cosl(NaN) is NaN */
  73   if (isnanl (x))
  74     return x;
  75
  76   /* |x| ~< pi/4 */
  77   if (x >= -0.7853981633974483096156608458198757210492
  78       && x <= 0.7853981633974483096156608458198757210492)
  79     return kernel_cosl(x, z);
  80
  81   /* cosl(Inf) is NaN, cosl(0) is 1 */
  82   else if (x + x == x && x != 0.0)
  83     return x - x;           /* NaN */
  84
  85   /* argument reduction needed */
  86   else
  87     {
  88       n = ieee754_rem_pio2l (x, y);
  89       switch (n & 3)
  90         {
  91         case 0:
  92           return  kernel_cosl (y[0], y[1]);
  93         case 1:
  94           return -kernel_sinl (y[0], y[1], 1);
  95         case 2:
  96           return -kernel_cosl (y[0], y[1]);
  97         default:
  98           return  kernel_sinl (y[0], y[1], 1);
  99         }
 100     }
 101 }
 102
 103 #endif
 104
 105 #if 0
 106 int
 107 main (void)
 108 {
 109   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492));
 110   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *29));
 111   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *2));
 112   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *30));
 113   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *4));
 114   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *32));
 115   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *2/3));
 116   printf ("%.16Lg\n", cosl (0.7853981633974483096156608458198757210492 *4/3));
 117 }
 118 #endif