usr/src/lib/libm/common_source/atanh.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms are permitted
 * provided that this notice is preserved and that due credit is given
 * to the University of California at Berkeley. The name of the University
 * may not be used to endorse or promote products derived from this
 * software without specific prior written permission. This software
 * is provided ``as is'' without express or implied warranty.
 *
 * 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
 * the sendbug(8) program, to the authors.
 */

#ifndef lint
static char sccsid[] = "@(#)atanh.c     5.2 (Berkeley) %G%";
#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.
 */
#if defined(vax)||defined(tahoe)
#include <errno.h>
#endif  /* defined(vax)||defined(tahoe) */

double atanh(x)
double x;
{
        double copysign(),log1p(),z;
        z = copysign(0.5,x);
        x = copysign(x,1.0);
#if defined(vax)||defined(tahoe)
        if (x == 1.0) {
            extern double infnan();
            return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
        }
#endif  /* defined(vax)||defined(tahoe) */
        x = x/(1.0-x);
        return( z*log1p(x+x) );
}