/* @(#)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.
 * ====================================================
 */

/* __fdlibm_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) := hugev*hugev (overflow)
 *
 * Special cases:
 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
 *	only cosh(0)=1 is exact for finite x.
 */

#include "math.h"

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

double __fdlibm_cosh(double x) {
	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(tinyv) = 1 */
		return one + (t * t) / (w + w);
	}

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

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

	/* |x| in [log(maxdouble), overflowthresold] */
	lx = *((((*(unsigned*)&one) >> 29)) + (unsigned*)&x);
	if(ix < 0x408633CE ||
	   (ix == 0x408633ce) && (lx <= (unsigned)0x8fb9f87d)) {
		w = __fdlibm_exp(half * fabs(x));
		t = half * w;
		return t * w;
	}

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