path: root/src/math/asinh.c

/* origin: FreeBSD /usr/src/lib/msun/src/s_asinh.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.
 * ====================================================
 */
/* asinh(x)
 * Method :
 *      Based on
 *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
 *      we have
 *      asinh(x) := x  if  1+x*x=1,
 *               := sign(x)*(log(x)+ln2)) for large |x|, else
 *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
 *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
 */

#include "libm.h"

static const double
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge= 1.00000000000000000000e+300;

double asinh(double x)
{
	double t,w;
	int32_t hx,ix;

	GET_HIGH_WORD(hx, x);
	ix = hx & 0x7fffffff;
	if (ix >= 0x7ff00000)   /* x is inf or NaN */
		return x+x;
	if (ix < 0x3e300000) {  /* |x| < 2**-28 */
		/* return x inexact except 0 */
		if (huge+x > 1.0)
			return x;
	}
	if (ix > 0x41b00000) {  /* |x| > 2**28 */
		w = log(fabs(x)) + ln2;
	} else if (ix > 0x40000000) {  /* 2**28 > |x| > 2.0 */
		t = fabs(x);
		w = log(2.0*t + 1.0/(sqrt(x*x+1.0)+t));
	} else {                /* 2.0 > |x| > 2**-28 */
		t = x*x;
		w =log1p(fabs(x) + t/(1.0+sqrt(1.0+t)));
	}
	if (hx > 0)
		return w;
	return -w;
}