/* $NetBSD: n_atanh.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */ /* * Copyright (c) 1985, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #ifndef lint #if 0 static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93"; #endif #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. */ #include "mathimpl.h" #if defined(__vax__)||defined(tahoe) #include <errno.h> #endif /* defined(__vax__)||defined(tahoe) */ double atanh(double x) { double z; z = copysign(0.5,x); x = copysign(x,1.0); #if defined(__vax__)||defined(tahoe) if (x == 1.0) { 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) ); } |