/* @(#)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"

#ifdef __STDC__

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

#else

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

#endif

#ifdef __STDC__

	double __ieee754_cosh(double x)

#else

	double __ieee754_cosh(x)

	double x;

#endif

{	

	double t,w;

	int ix;

	unsigned lx;

    /* High word of |x|. */

	ix = __HI(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] */

	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&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;

}