/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";

#endif

/* __ieee754_coshl(x)

 * Method :

 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2

 *	1. Replace x by |x| (coshl(x) = coshl(-x)).

 *	2.

 *							[ exp(x) - 1 ]^2

 *	    0        <= x <= ln2/2  :  coshl(x) := 1 + -------------------

 *							   2*exp(x)

 *

 *						   exp(x) +  1/exp(x)

 *	    ln2/2    <= x <= 22     :  coshl(x) := -------------------

 *							   2

 *	    22       <= x <= lnovft :  coshl(x) := expl(x)/2

 *	    lnovft   <= x <= ln2ovft:  coshl(x) := expl(x/2)/2 * expl(x/2)

 *	    ln2ovft  <  x	    :  coshl(x) := huge*huge (overflow)

 *

 * Special cases:

 *	coshl(x) is |x| if x is +INF, -INF, or NaN.

 *	only coshl(0)=1 is exact for finite x.

 */

#include <math.h>

#include <math_private.h>

static const long double one = 1.0, half=0.5, huge = 1.0e4900L;

long double

__ieee754_coshl (long double x)

{

	long double t,w;

	int32_t ex;

	uint32_t mx,lx;

    /* High word of |x|. */

	GET_LDOUBLE_WORDS(ex,mx,lx,x);

	ex &= 0x7fff;

    /* |x| in [0,22] */

	if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {

	    /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */

		if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {

		    if (ex<0x3fbc) return one;	/* cosh(tiny) = 1 */

		    t = __expm1l(fabsl(x));

		    w = one+t;

		    return one+(t*t)/(w+w);

		}

	    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */

		t = __ieee754_expl(fabsl(x));

		return half*t+half/t;

	}

    /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */

	if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))

		return half*__ieee754_expl(fabsl(x));

    /* |x| in [log(maxdouble), log(2*maxdouble)) */

	if (ex == 0x400c && (mx < 0xb174ddc0u

			     || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))

	{

	    w = __ieee754_expl(half*fabsl(x));

	    t = half*w;

	    return t*w;

	}

    /* x is INF or NaN */

	if(ex==0x7fff) return x*x;

    /* |x| >= log(2*maxdouble), cosh(x) overflow */

	return huge*huge;

}

strong_alias (__ieee754_coshl, __coshl_finite)