lib/libm/src/s_cos.c

   1 /* @(#)s_cos.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: s_cos.c,v 1.11 2007/08/20 16:01:39 drochner Exp $");
  16 #endif
  17
  18 /* cos(x)
  19  * Return cosine function of x.
  20  *
  21  * kernel function:
  22  *      __kernel_sin            ... sine function on [-pi/4,pi/4]
  23  *      __kernel_cos            ... cosine function on [-pi/4,pi/4]
  24  *      __ieee754_rem_pio2      ... argument reduction routine
  25  *
  26  * Method.
  27  *      Let S,C and T denote the sin, cos and tan respectively on
  28  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  29  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  30  *      We have
  31  *
  32  *          n        sin(x)      cos(x)        tan(x)
  33  *     ----------------------------------------------------------
  34  *          0          S           C             T
  35  *          1          C          -S            -1/T
  36  *          2         -S          -C             T
  37  *          3         -C           S            -1/T
  38  *     ----------------------------------------------------------
  39  *
  40  * Special cases:
  41  *      Let trig be any of sin, cos, or tan.
  42  *      trig(+-INF)  is NaN, with signals;
  43  *      trig(NaN)    is that NaN;
  44  *
  45  * Accuracy:
  46  *      TRIG(x) returns trig(x) nearly rounded
  47  */
  48
  49 #include "namespace.h"
  50 #include "math.h"
  51 #include "math_private.h"
  52
  53 #if 0 /* notyet */
  54 #ifdef __weak_alias
  55 __weak_alias(cos, _cos)
  56 #endif
  57 #endif
  58
  59 double
  60 cos(double x)
  61 {
  62         double y[2],z=0.0;
  63         int32_t n, ix;
  64
  65     /* High word of x. */
  66         GET_HIGH_WORD(ix,x);
  67
  68     /* |x| ~< pi/4 */
  69         ix &= 0x7fffffff;
  70         if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
  71
  72     /* cos(Inf or NaN) is NaN */
  73         else if (ix>=0x7ff00000) return x-x;
  74
  75     /* argument reduction needed */
  76         else {
  77             n = __ieee754_rem_pio2(x,y);
  78             switch(n&3) {
  79                 case 0: return  __kernel_cos(y[0],y[1]);
  80                 case 1: return -__kernel_sin(y[0],y[1],1);
  81                 case 2: return -__kernel_cos(y[0],y[1]);
  82                 default:
  83                         return  __kernel_sin(y[0],y[1],1);
  84             }
  85         }
  86 }