1 /* $NetBSD: n_acosh.c,v 1.1 1995/10/10 23:36:33 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[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* ACOSH(X) 40 * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85. 44 * 45 * Required system supported functions : 46 * sqrt(x) 47 * 48 * Required kernel function: 49 * log1p(x) ...return log(1+x) 50 * 51 * Method : 52 * Based on 53 * acosh(x) = log [ x + sqrt(x*x-1) ] 54 * we have 55 * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else 56 * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . 57 * These formulae avoid the over/underflow complication. 58 * 59 * Special cases: 60 * acosh(x) is NaN with signal if x<1. 61 * acosh(NaN) is NaN without signal. 62 * 63 * Accuracy: 64 * acosh(x) returns the exact inverse hyperbolic cosine of x nearly 65 * rounded. In a test run with 512,000 random arguments on a VAX, the 66 * maximum observed error was 3.30 ulps (units of the last place) at 67 * x=1.0070493753568216 . 68 * 69 * Constants: 70 * The hexadecimal values are the intended ones for the following constants. 71 * The decimal values may be used, provided that the compiler will convert 72 * from decimal to binary accurately enough to produce the hexadecimal values 73 * shown. 74 */ 75 76 #include "mathimpl.h" 77 78 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 79 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 80 81 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 82 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) 83 84 #ifdef vccast 85 #define ln2hi vccast(ln2hi) 86 #define ln2lo vccast(ln2lo) 87 #endif 88 89 double 90 acosh(x) 91 double x; 92 { 93 double t,big=1.E20; /* big+1==big */ 94 95 #if !defined(vax)&&!defined(tahoe) 96 if(x!=x) return(x); /* x is NaN */ 97 #endif /* !defined(vax)&&!defined(tahoe) */ 98 99 /* return log1p(x) + log(2) if x is large */ 100 if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 101 102 t=sqrt(x-1.0); 103 return(log1p(t*(t+sqrt(x+1.0)))); 104 } 105