* software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

static const double ln2 =  6.93147180559945286227E-01;
static const double huge = 1E+300;
static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
static const double two_pow_p28 = 268435456.0; /* 2**28 */
static const double zero = 0.0;

/* 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)))  
 */

#ifndef HAVE_ASINH
double
asinh(double x)
{	
	double w;
	double absx = fabs(x);

	if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
		return x+x;
	}
	if (absx < two_pow_m28) {	/* |x| < 2**-28 */
		if ((huge + x) > 1.0)
			return x;	/* return x inexact except 0 */
	} 
	if (absx > two_pow_p28) {	/* |x| > 2**28 */
		w = log(absx)+ln2;
	}
	else if (absx > 2.0) {		/* 2 < |x| < 2**28 */
		w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
	}
	else {				/* 2**-28 <= |x| < 2= */
		double t = x*x;
		w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
	}
	return copysign(w, x);
	
}
#endif /* HAVE_ASINH */

/* acosh(x)
 * Method :
 *      Based on
 *	      acosh(x) = log [ x + sqrt(x*x-1) ]
 *      we have
 *	      acosh(x) := log(x)+ln2, if x is large; else
 *	      acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
 *	      acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
 *
 * Special cases:
 *      acosh(x) is NaN with signal if x<1.
 *      acosh(NaN) is NaN without signal.
 */

#ifndef HAVE_ACOSH
double
acosh(double x)
{
	if (Py_IS_NAN(x)) {
		return x+x;
	}

	if (x < 1.) {			/* x < 1;  return a NaN */
		return (x-x)/(x-x);
	}
	else if (x >= two_pow_p28) {	/* x > 2**28 */
		if (Py_IS_INFINITY(x)) {
			return x+x;
		} else {
			return log(x)+ln2;	/* acosh(huge)=log(2x) */
		}
	}
	else if (x == 1.) {
		return 0.0;			/* acosh(1) = 0 */
	} else if (x > 2.) {			/* 2 < x < 2**28 */
		double t = x*x;
		return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
	} else {				/* 1 < x <= 2 */
		double t = x - 1.0;
		return log1p(t + sqrt(2.0*t + t*t));
	}
}
#endif /* HAVE_ACOSH */

/* atanh(x)
 * Method :
 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
 *    2.For x>=0.5
 *		  1	      2x			  x
 *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
 *		  2	     1 - x		      1 - x
 *
 *      For x<0.5
 *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
 *
 * Special cases:
 *      atanh(x) is NaN if |x| > 1 with signal;
 *      atanh(NaN) is that NaN with no signal;
 *      [atanh(+-1) is +-INF with signal.]
 *      Python: atanh(+-1) raises a ValueError
 *
 */

#ifndef HAVE_ATANH
double
atanh(double x)
{
	double absx;
	double t;

	if (Py_IS_NAN(x)) {
		return x+x;
	}

	absx = fabs(x);
	if (absx == 1.) {
		return x/zero;
	}
	if (absx > 1.) {		/* XXX |x| >= 1 */
		return (x-x)/(x-x);
	}
	if (absx < two_pow_m28) {	/* |x| < 2**-28 */
		return x;
	}
	if (absx < 0.5) {		/* |x| < 0.5 */
		t = absx+absx;
		t = 0.5 * log1p(t + t*absx / (1.0 - absx));
	} 
	else {				/* 0.5 <= |x| <= 1.0 */
		t = 0.5 * log1p((absx + absx) / (1.0 - absx));
	}

	return copysign(t, x);
}
#endif /* HAVE_ATANH */