/*
* Copyright (c) 1985 Regents of the University of California.
*
* Use and reproduction of this software are granted in accordance with
* the terms and conditions specified in the Berkeley Software License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that all recipients should regard themselves as participants in an
* ongoing research project and hence should feel obligated to report
* their experiences (good or bad) with these elementary function codes,
* using "sendbug 4bsd-bugs@BERKELEY", to the authors.
*/
#ifndef lint
static char sccsid[] = "@(#)atanh.c 1.2 (Berkeley) 8/21/85";
#endif not lint
/* ATANH(X)
* RETURN THE HYPERBOLIC ARC TANGENT OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
*
* Required kernel function:
* log1p(x) ...return log(1+x)
*
* Method :
* Return
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - 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.
*
* Accuracy:
* atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
* In a test run with 512,000 random arguments on a VAX, the maximum
* observed error was 1.87 ulps (units in the last place) at
* x= -3.8962076028810414000e-03.
*/
#ifdef VAX
#include
#endif
double atanh(x)
double x;
{
double copysign(),log1p(),z;
z = copysign(0.5,x);
x = copysign(x,1.0);
#ifdef VAX
if (x == 1.0) {
extern double infnan();
return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */
}
#endif
x = x/(1.0-x);
return( z*log1p(x+x) );
}