1 /* $NetBSD: n_atanh.c,v 1.5 1999/07/02 15:37:36 simonb 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 #if 0 37 static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* ATANH(X) 42 * RETURN THE HYPERBOLIC ARC TANGENT OF X 43 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 44 * CODED IN C BY K.C. NG, 1/8/85; 45 * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85. 46 * 47 * Required kernel function: 48 * log1p(x) ...return log(1+x) 49 * 50 * Method : 51 * Return 52 * 1 2x x 53 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 54 * 2 1 - x 1 - x 55 * 56 * Special cases: 57 * atanh(x) is NaN if |x| > 1 with signal; 58 * atanh(NaN) is that NaN with no signal; 59 * atanh(+-1) is +-INF with signal. 60 * 61 * Accuracy: 62 * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. 63 * In a test run with 512,000 random arguments on a VAX, the maximum 64 * observed error was 1.87 ulps (units in the last place) at 65 * x= -3.8962076028810414000e-03. 66 */ 67 #include "mathimpl.h" 68 69 #if defined(__vax__)||defined(tahoe) 70 #include <errno.h> 71 #endif /* defined(__vax__)||defined(tahoe) */ 72 73 double atanh(x) 74 double x; 75 { 76 double z; 77 z = copysign(0.5,x); 78 x = copysign(x,1.0); 79 #if defined(__vax__)||defined(tahoe) 80 if (x == 1.0) { 81 return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ 82 } 83 #endif /* defined(__vax__)||defined(tahoe) */ 84 x = x/(1.0-x); 85 return( z*log1p(x+x) ); 86 } 87