1 /* $NetBSD: n_asinh.c,v 1.5 2002/06/15 00:10:17 matt 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[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* ASINH(X) 42 * RETURN THE INVERSE HYPERBOLIC SINE OF X 43 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 44 * CODED IN C BY K.C. NG, 2/16/85; 45 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. 46 * 47 * Required system supported functions : 48 * copysign(x,y) 49 * sqrt(x) 50 * 51 * Required kernel function: 52 * log1p(x) ...return log(1+x) 53 * 54 * Method : 55 * Based on 56 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 57 * we have 58 * asinh(x) := x if 1+x*x=1, 59 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else 60 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) 61 * 62 * Accuracy: 63 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. 64 * In a test run with 52,000 random arguments on a VAX, the maximum 65 * observed error was 1.58 ulps (units in the last place). 66 * 67 * Constants: 68 * The hexadecimal values are the intended ones for the following constants. 69 * The decimal values may be used, provided that the compiler will convert 70 * from decimal to binary accurately enough to produce the hexadecimal values 71 * shown. 72 */ 73 #define _LIBM_STATIC 74 #include "mathimpl.h" 75 76 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 77 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 78 79 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 80 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 81 82 #ifdef vccast 83 #define ln2hi vccast(ln2hi) 84 #define ln2lo vccast(ln2lo) 85 #endif 86 87 double 88 asinh(double x) 89 { 90 double t,s; 91 const static double small=1.0E-10, /* fl(1+small*small) == 1 */ 92 big =1.0E20, /* fl(1+big) == big */ 93 one =1.0 ; 94 95 #if !defined(__vax__)&&!defined(tahoe) 96 if(x!=x) return(x); /* x is NaN */ 97 #endif /* !defined(__vax__)&&!defined(tahoe) */ 98 if((t=copysign(x,one))>small) 99 if(t<big) { 100 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } 101 else /* if |x| > big */ 102 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} 103 else /* if |x| < small */ 104 return(x); 105 } 106