1 /* $NetBSD: n_acosh.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[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* ACOSH(X) 42 * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85. 46 * 47 * Required system supported functions : 48 * sqrt(x) 49 * 50 * Required kernel function: 51 * log1p(x) ...return log(1+x) 52 * 53 * Method : 54 * Based on 55 * acosh(x) = log [ x + sqrt(x*x-1) ] 56 * we have 57 * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else 58 * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . 59 * These formulae avoid the over/underflow complication. 60 * 61 * Special cases: 62 * acosh(x) is NaN with signal if x<1. 63 * acosh(NaN) is NaN without signal. 64 * 65 * Accuracy: 66 * acosh(x) returns the exact inverse hyperbolic cosine of x nearly 67 * rounded. In a test run with 512,000 random arguments on a VAX, the 68 * maximum observed error was 3.30 ulps (units of the last place) at 69 * x=1.0070493753568216 . 70 * 71 * Constants: 72 * The hexadecimal values are the intended ones for the following constants. 73 * The decimal values may be used, provided that the compiler will convert 74 * from decimal to binary accurately enough to produce the hexadecimal values 75 * shown. 76 */ 77 78 #define _LIBM_STATIC 79 #include "mathimpl.h" 80 81 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 82 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 83 84 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 85 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) 86 87 #ifdef vccast 88 #define ln2hi vccast(ln2hi) 89 #define ln2lo vccast(ln2lo) 90 #endif 91 92 double 93 acosh(double x) 94 { 95 double t,big=1.E20; /* big+1==big */ 96 97 #if !defined(__vax__)&&!defined(tahoe) 98 if(x!=x) return(x); /* x is NaN */ 99 #endif /* !defined(__vax__)&&!defined(tahoe) */ 100 101 /* return log1p(x) + log(2) if x is large */ 102 if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 103 104 t=sqrt(x-1.0); 105 return(log1p(t*(t+sqrt(x+1.0)))); 106 } 107