/* @(#)e_sinh.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_sinh(x)
 * Method :
 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
 *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
 *	2.
 *		                                    E + E/(E+1)
 *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
 *			       			        2
 *
 *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
 *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
 *	    ln2ovft  <  x	    :  sinh(x) := x*shugev (overflow)
 *
 * Special cases:
 *	sinh(x) is |x| if x is +INF, -INF, or NaN.
 *	only sinh(0)=0 is exact for finite x.
 */

#include "math.h"

static const double one = 1.0, shugev = 1.0e307;

double __fdlibm_sinh(double x) {
	double	 t, w, h;
	int	 ix, jx;
	unsigned lx;

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

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

	h = 0.5;
	if(jx < 0) h = -h;
	/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
	if(ix < 0x40360000) {			       /* |x|<22 */
		if(ix < 0x3e300000)		       /* |x|<2**-28 */
			if(shugev + x > one) return x; /* sinh(tinyv) = tinyv with inexact */
		t = expm1(fabs(x));
		if(ix < 0x3ff00000) return h * (2.0 * t - t * t / (t + one));
		return h * (t + t / (t + one));
	}

	/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
	if(ix < 0x40862E42) return h * __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(0.5 * fabs(x));
		t = h * w;
		return t * w;
	}

	/* |x| > overflowthresold, sinh(x) overflow */
	return x * shugev;
}