sysdeps/libm-ieee754/s_cosl.c

   1 /* s_cosl.c -- long double version of s_cos.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* cosl(x)
  22  * Return cosine function of x.
  23  *
  24  * kernel function:
  25  *      __kernel_sinl           ... sine function on [-pi/4,pi/4]
  26  *      __kernel_cosl           ... cosine function on [-pi/4,pi/4]
  27  *      __ieee754_rem_pio2l     ... argument reduction routine
  28  *
  29  * Method.
  30  *      Let S,C and T denote the sin, cos and tan respectively on
  31  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  32  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  33  *      We have
  34  *
  35  *          n        sin(x)      cos(x)        tan(x)
  36  *     ----------------------------------------------------------
  37  *          0          S           C             T
  38  *          1          C          -S            -1/T
  39  *          2         -S          -C             T
  40  *          3         -C           S            -1/T
  41  *     ----------------------------------------------------------
  42  *
  43  * Special cases:
  44  *      Let trig be any of sin, cos, or tan.
  45  *      trig(+-INF)  is NaN, with signals;
  46  *      trig(NaN)    is that NaN;
  47  *
  48  * Accuracy:
  49  *      TRIG(x) returns trig(x) nearly rounded
  50  */
  51
  52 #include "math.h"
  53 #include "math_private.h"
  54
  55 #ifdef __STDC__
  56         long double __cosl(long double x)
  57 #else
  58         long double __cosl(x)
  59         long double x;
  60 #endif
  61 {
  62         long double y[2],z=0.0;
  63         int32_t n, se;
  64
  65     /* High word of x. */
  66         GET_LDOUBLE_EXP(se,x);
  67
  68     /* |x| ~< pi/4 */
  69         se &= 0x7fff;
  70         if(ix <= 0x3ffe) return __kernel_cosl(x,z);
  71
  72     /* cos(Inf or NaN) is NaN */
  73         else if (se==0x7fff) return x-x;
  74
  75     /* argument reduction needed */
  76         else {
  77             n = __ieee754_rem_pio2l(x,y);
  78             switch(n&3) {
  79                 case 0: return  __kernel_cosl(y[0],y[1]);
  80                 case 1: return -__kernel_sinl(y[0],y[1],1);
  81                 case 2: return -__kernel_cosl(y[0],y[1]);
  82                 default:
  83                         return  __kernel_sinl(y[0],y[1],1);
  84             }
  85         }
  86 }
  87 weak_alias (__cosl, cosl)