1 /* $NetBSD: n_atanh.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #ifndef lint 32 #if 0 33 static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93"; 34 #endif 35 #endif /* not lint */ 36 37 /* ATANH(X) 38 * RETURN THE HYPERBOLIC ARC TANGENT OF X 39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 40 * CODED IN C BY K.C. NG, 1/8/85; 41 * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85. 42 * 43 * Required kernel function: 44 * log1p(x) ...return log(1+x) 45 * 46 * Method : 47 * Return 48 * 1 2x x 49 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 50 * 2 1 - x 1 - x 51 * 52 * Special cases: 53 * atanh(x) is NaN if |x| > 1 with signal; 54 * atanh(NaN) is that NaN with no signal; 55 * atanh(+-1) is +-INF with signal. 56 * 57 * Accuracy: 58 * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. 59 * In a test run with 512,000 random arguments on a VAX, the maximum 60 * observed error was 1.87 ulps (units in the last place) at 61 * x= -3.8962076028810414000e-03. 62 */ 63 #include "mathimpl.h" 64 65 #if defined(__vax__)||defined(tahoe) 66 #include <errno.h> 67 #endif /* defined(__vax__)||defined(tahoe) */ 68 69 double 70 atanh(double x) 71 { 72 double z; 73 z = copysign(0.5,x); 74 x = copysign(x,1.0); 75 #if defined(__vax__)||defined(tahoe) 76 if (x == 1.0) { 77 return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ 78 } 79 #endif /* defined(__vax__)||defined(tahoe) */ 80 x = x/(1.0-x); 81 return( z*log1p(x+x) ); 82 } 83