1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- 2 * 3 * ***** BEGIN LICENSE BLOCK ***** 4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 5 * 6 * The contents of this file are subject to the Mozilla Public License Version 7 * 1.1 (the "License"); you may not use this file except in compliance with 8 * the License. You may obtain a copy of the License at 9 * http://www.mozilla.org/MPL/ 10 * 11 * Software distributed under the License is distributed on an "AS IS" basis, 12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License 13 * for the specific language governing rights and limitations under the 14 * License. 15 * 16 * The Original Code is Mozilla Communicator client code, released 17 * March 31, 1998. 18 * 19 * The Initial Developer of the Original Code is 20 * Sun Microsystems, Inc. 21 * Portions created by the Initial Developer are Copyright (C) 1998 22 * the Initial Developer. All Rights Reserved. 23 * 24 * Contributor(s): 25 * 26 * Alternatively, the contents of this file may be used under the terms of 27 * either of the GNU General Public License Version 2 or later (the "GPL"), 28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 29 * in which case the provisions of the GPL or the LGPL are applicable instead 30 * of those above. If you wish to allow use of your version of this file only 31 * under the terms of either the GPL or the LGPL, and not to allow others to 32 * use your version of this file under the terms of the MPL, indicate your 33 * decision by deleting the provisions above and replace them with the notice 34 * and other provisions required by the GPL or the LGPL. If you do not delete 35 * the provisions above, a recipient may use your version of this file under 36 * the terms of any one of the MPL, the GPL or the LGPL. 37 * 38 * ***** END LICENSE BLOCK ***** */ 39 40 /* @(#)e_acosh.c 1.3 95/01/18 */ 41 /* 42 * ==================================================== 43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 44 * 45 * Developed at SunSoft, a Sun Microsystems, Inc. business. 46 * Permission to use, copy, modify, and distribute this 47 * software is freely granted, provided that this notice 48 * is preserved. 49 * ==================================================== 50 * 51 */ 52 53 /* __ieee754_acosh(x) 54 * Method : 55 * Based on 56 * acosh(x) = log [ x + sqrt(x*x-1) ] 57 * we have 58 * acosh(x) := log(x)+ln2, if x is large; else 59 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 60 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 61 * 62 * Special cases: 63 * acosh(x) is NaN with signal if x<1. 64 * acosh(NaN) is NaN without signal. 65 */ 66 67 #include "fdlibm.h" 68 69 #ifdef __STDC__ 70 static const double 71 #else 72 static double 73 #endif 74 one = 1.0, 75 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 76 77 #ifdef __STDC__ __ieee754_acosh(double x)78 double __ieee754_acosh(double x) 79 #else 80 double __ieee754_acosh(x) 81 double x; 82 #endif 83 { 84 fd_twoints u; 85 double t; 86 int hx; 87 u.d = x; 88 hx = __HI(u); 89 if(hx<0x3ff00000) { /* x < 1 */ 90 return (x-x)/(x-x); 91 } else if(hx >=0x41b00000) { /* x > 2**28 */ 92 if(hx >=0x7ff00000) { /* x is inf of NaN */ 93 return x+x; 94 } else 95 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 96 } else if(((hx-0x3ff00000)|__LO(u))==0) { 97 return 0.0; /* acosh(1) = 0 */ 98 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 99 t=x*x; 100 return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one))); 101 } else { /* 1<x<2 */ 102 t = x-one; 103 return fd_log1p(t+fd_sqrt(2.0*t+t*t)); 104 } 105 } 106