musl/src/math/sinhl.c

/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/* sinhl(x)
 * Method :
 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
 *      1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
 *      2.
 *                                                   E + E/(E+1)
 *          0        <= x <= 25     :  sinhl(x) := --------------, E=expm1l(x)
 *                                                       2
 *
 *          25       <= x <= lnovft :  sinhl(x) := expl(x)/2
 *          lnovft   <= x <= ln2ovft:  sinhl(x) := expl(x/2)/2 * expl(x/2)
 *          ln2ovft  <  x           :  sinhl(x) := x*huge (overflow)
 *
 * Special cases:
 *      sinhl(x) is |x| if x is +INF, -INF, or NaN.
 *      only sinhl(0)=0 is exact for finite x.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double sinhl(long double x)
{
	return sinh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double huge = 1.0e4931L;

long double sinhl(long double x)
{
	long double t,w,h;
	uint32_t jx,ix,i0,i1;

	/* Words of |x|. */
	GET_LDOUBLE_WORDS(jx, i0, i1, x);
	ix = jx & 0x7fff;

	/* x is INF or NaN */
	if (ix == 0x7fff) return x + x;

	h = 0.5;
	if (jx & 0x8000)
		h = -h;
	/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
	if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
		if (ix < 0x3fdf)  /* |x|<2**-32 */
			if (huge + x > 1.0)
				return x;/* sinh(tiny) = tiny with inexact */
		t = expm1l(fabsl(x));
		if (ix < 0x3fff)
			return h*(2.0*t - t*t/(t + 1.0));
		return h*(t + t/(t + 1.0));
	}

	/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
	if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
		return h*expl(fabsl(x));

	/* |x| in [log(maxdouble), overflowthreshold] */
	if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
	     (i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
		w = expl(0.5*fabsl(x));
		t = h*w;
		return t*w;
	}

	/* |x| > overflowthreshold, sinhl(x) overflow */
	return x*huge;
}
#endif