1 /* $NetBSD: n_asinh.c,v 1.1 1995/10/10 23:36:35 ragge 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 static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* ASINH(X) 40 * RETURN THE INVERSE HYPERBOLIC SINE OF X 41 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 42 * CODED IN C BY K.C. NG, 2/16/85; 43 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. 44 * 45 * Required system supported functions : 46 * copysign(x,y) 47 * sqrt(x) 48 * 49 * Required kernel function: 50 * log1p(x) ...return log(1+x) 51 * 52 * Method : 53 * Based on 54 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 55 * we have 56 * asinh(x) := x if 1+x*x=1, 57 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else 58 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) 59 * 60 * Accuracy: 61 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. 62 * In a test run with 52,000 random arguments on a VAX, the maximum 63 * observed error was 1.58 ulps (units in the last place). 64 * 65 * Constants: 66 * The hexadecimal values are the intended ones for the following constants. 67 * The decimal values may be used, provided that the compiler will convert 68 * from decimal to binary accurately enough to produce the hexadecimal values 69 * shown. 70 */ 71 #include "mathimpl.h" 72 73 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 74 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 75 76 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 77 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 78 79 #ifdef vccast 80 #define ln2hi vccast(ln2hi) 81 #define ln2lo vccast(ln2lo) 82 #endif 83 84 double asinh(x) 85 double x; 86 { 87 double t,s; 88 const static double small=1.0E-10, /* fl(1+small*small) == 1 */ 89 big =1.0E20, /* fl(1+big) == big */ 90 one =1.0 ; 91 92 #if !defined(vax)&&!defined(tahoe) 93 if(x!=x) return(x); /* x is NaN */ 94 #endif /* !defined(vax)&&!defined(tahoe) */ 95 if((t=copysign(x,one))>small) 96 if(t<big) { 97 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } 98 else /* if |x| > big */ 99 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} 100 else /* if |x| < small */ 101 return(x); 102 } 103