musl/src/math/atanhl.c

/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_atanh.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.
 * ====================================================
 */
/* atanhl(x)
 * Method :
 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
 *    2.For x>=0.5
 *                   1              2x                          x
 *      atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
 *                   2             1 - x                      1 - x
 *
 *      For x<0.5
 *      atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
 *
 * Special cases:
 *      atanhl(x) is NaN if |x| > 1 with signal;
 *      atanhl(NaN) is that NaN with no signal;
 *      atanhl(+-1) is +-INF with signal.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atanhl(long double x)
{
	return atanh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double huge = 1e4900L;

long double atanhl(long double x)
{
	long double t;
	int32_t ix;
	uint32_t se,i0,i1;

	GET_LDOUBLE_WORDS(se, i0, i1, x);
	ix = se & 0x7fff;
	if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31)) > 0x3fff)
		/* |x| > 1 */
		return (x-x)/(x-x);
	if (ix == 0x3fff)
		return x/0.0;
	if (ix < 0x3fe3 && huge+x > 0.0)  /* x < 2**-28 */
		return x;
	SET_LDOUBLE_EXP(x, ix);
	if (ix < 0x3ffe) {  /* x < 0.5 */
		t = x + x;
		t = 0.5*log1pl(t + t*x/(1.0 - x));
	} else
		t = 0.5*log1pl((x + x)/(1.0 - x));
	if (se <= 0x7fff)
		return t;
	return -t;
}
#endif