e_cosh.c

/* @(#)e_cosh.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_cosh(x)
 * Method : 
 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
 *      1. Replace x by |x| (cosh(x) = cosh(-x)). 
 *      2. 
 *                                                      [ exp(x) - 1 ]^2 
 *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
 *                                                         2*exp(x)
 *
 *                                                exp(x) +  1/exp(x)
 *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
 *                                                        2
 *          22       <= x <= lnovft :  cosh(x) := exp(x)/2 
 *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
 *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
 *
 * Special cases:
 *      cosh(x) is |x| if x is +INF, -INF, or NaN.
 *      only cosh(0)=1 is exact for finite x.
 */

#include "fdlibm.h"

static const double one = 1.0, half=0.5, huge = 1.0e300;

double __ieee754_cosh(double x)
{       
        double t,w;
        int ix;
        unsigned lx;

    /* High word of |x|. */
        __getHI(ix,x);
        ix &= 0x7fffffff;

    /* x is INF or NaN */
        if(ix>=0x7ff00000) return x*x;  

    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
        if(ix<0x3fd62e43) {
            t = expm1(fabs(x));
            w = one+t;
            if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
            return one+(t*t)/(w+w);
        }

    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
        if (ix < 0x40360000) {
                t = __ieee754_exp(fabs(x));
                return half*t+half/t;
        }

    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
        if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
        __getLO(lx,x);
        if (ix<0x408633CE ||
              ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
            w = __ieee754_exp(half*fabs(x));
            t = half*w;
            return t*w;
        }

    /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;
}