lib/libm/src/e_cosh.c

   1 /* @(#)e_cosh.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  * $NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_cosh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* cosh(x)
  17  * Method :
  18  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
  19  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  20  *      2.
  21  *                                                      [ exp(x) - 1 ]^2
  22  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
  23  *                                                         2*exp(x)
  24  *
  25  *                                                exp(x) +  1/exp(x)
  26  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
  27  *                                                        2
  28  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
  29  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
  30  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
  31  *
  32  * Special cases:
  33  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  34  *      only cosh(0)=1 is exact for finite x.
  35  */
  36
  37 #include <math.h>
  38 #include "math_private.h"
  39
  40 static const double one = 1.0, half=0.5, huge = 1.0e300;
  41
  42 double
  43 cosh(double x)
  44 {
  45         double t,w;
  46         int32_t ix;
  47         u_int32_t lx;
  48
  49     /* High word of |x|. */
  50         GET_HIGH_WORD(ix,x);
  51         ix &= 0x7fffffff;
  52
  53     /* x is INF or NaN */
  54         if(ix>=0x7ff00000) return x*x;
  55
  56     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
  57         if(ix<0x3fd62e43) {
  58             t = expm1(fabs(x));
  59             w = one+t;
  60             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
  61             return one+(t*t)/(w+w);
  62         }
  63
  64     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
  65         if (ix < 0x40360000) {
  66                 t = exp(fabs(x));
  67                 return half*t+half/t;
  68         }
  69
  70     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  71         if (ix < 0x40862E42)  return half*exp(fabs(x));
  72
  73     /* |x| in [log(maxdouble), overflowthresold] */
  74         GET_LOW_WORD(lx,x);
  75         if (ix<0x408633CE ||
  76               ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  77             w = exp(half*fabs(x));
  78             t = half*w;
  79             return t*w;
  80         }
  81
  82     /* |x| > overflowthresold, cosh(x) overflow */
  83         return huge*huge;
  84 }