1/* $NetBSD: n_asinh.c,v 1.6 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 33static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93"; 34#endif 35#endif /* not lint */ 36 37/* ASINH(X) 38 * RETURN THE INVERSE HYPERBOLIC SINE OF X 39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 40 * CODED IN C BY K.C. NG, 2/16/85; 41 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. 42 * 43 * Required system supported functions : 44 * copysign(x,y) 45 * sqrt(x) 46 * 47 * Required kernel function: 48 * log1p(x) ...return log(1+x) 49 * 50 * Method : 51 * Based on 52 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 53 * we have 54 * asinh(x) := x if 1+x*x=1, 55 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else 56 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) 57 * 58 * Accuracy: 59 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. 60 * In a test run with 52,000 random arguments on a VAX, the maximum 61 * observed error was 1.58 ulps (units in the last place). 62 * 63 * Constants: 64 * The hexadecimal values are the intended ones for the following constants. 65 * The decimal values may be used, provided that the compiler will convert 66 * from decimal to binary accurately enough to produce the hexadecimal values 67 * shown. 68 */ 69#define _LIBM_STATIC 70#include "mathimpl.h" 71 72vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 73vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 74 75ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 76ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 77 78#ifdef vccast 79#define ln2hi vccast(ln2hi) 80#define ln2lo vccast(ln2lo) 81#endif 82 83double 84asinh(double x) 85{ 86 double t,s; 87 static const double small=1.0E-10, /* fl(1+small*small) == 1 */ 88 big =1.0E20, /* fl(1+big) == big */ 89 one =1.0 ; 90 91#if !defined(__vax__)&&!defined(tahoe) 92 if(x!=x) return(x); /* x is NaN */ 93#endif /* !defined(__vax__)&&!defined(tahoe) */ 94 if((t=copysign(x,one))>small) 95 if(t<big) { 96 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } 97 else /* if |x| > big */ 98 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} 99 else /* if |x| < small */ 100 return(x); 101} 102