Back to index

lightning-sunbird  0.9+nobinonly
e_acosh.c
Go to the documentation of this file.
00001 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
00002  *
00003  * ***** BEGIN LICENSE BLOCK *****
00004  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
00005  *
00006  * The contents of this file are subject to the Mozilla Public License Version
00007  * 1.1 (the "License"); you may not use this file except in compliance with
00008  * the License. You may obtain a copy of the License at
00009  * http://www.mozilla.org/MPL/
00010  *
00011  * Software distributed under the License is distributed on an "AS IS" basis,
00012  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
00013  * for the specific language governing rights and limitations under the
00014  * License.
00015  *
00016  * The Original Code is Mozilla Communicator client code, released
00017  * March 31, 1998.
00018  *
00019  * The Initial Developer of the Original Code is
00020  * Sun Microsystems, Inc.
00021  * Portions created by the Initial Developer are Copyright (C) 1998
00022  * the Initial Developer. All Rights Reserved.
00023  *
00024  * Contributor(s):
00025  *
00026  * Alternatively, the contents of this file may be used under the terms of
00027  * either of the GNU General Public License Version 2 or later (the "GPL"),
00028  * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
00029  * in which case the provisions of the GPL or the LGPL are applicable instead
00030  * of those above. If you wish to allow use of your version of this file only
00031  * under the terms of either the GPL or the LGPL, and not to allow others to
00032  * use your version of this file under the terms of the MPL, indicate your
00033  * decision by deleting the provisions above and replace them with the notice
00034  * and other provisions required by the GPL or the LGPL. If you do not delete
00035  * the provisions above, a recipient may use your version of this file under
00036  * the terms of any one of the MPL, the GPL or the LGPL.
00037  *
00038  * ***** END LICENSE BLOCK ***** */
00039 
00040 /* @(#)e_acosh.c 1.3 95/01/18 */
00041 /*
00042  * ====================================================
00043  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00044  *
00045  * Developed at SunSoft, a Sun Microsystems, Inc. business.
00046  * Permission to use, copy, modify, and distribute this
00047  * software is freely granted, provided that this notice 
00048  * is preserved.
00049  * ====================================================
00050  *
00051  */
00052 
00053 /* __ieee754_acosh(x)
00054  * Method :
00055  *     Based on 
00056  *            acosh(x) = log [ x + sqrt(x*x-1) ]
00057  *     we have
00058  *            acosh(x) := log(x)+ln2,     if x is large; else
00059  *            acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
00060  *            acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
00061  *
00062  * Special cases:
00063  *     acosh(x) is NaN with signal if x<1.
00064  *     acosh(NaN) is NaN without signal.
00065  */
00066 
00067 #include "fdlibm.h"
00068 
00069 #ifdef __STDC__
00070 static const double 
00071 #else
00072 static double 
00073 #endif
00074 one    = 1.0,
00075 ln2    = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
00076 
00077 #ifdef __STDC__
00078        double __ieee754_acosh(double x)
00079 #else
00080        double __ieee754_acosh(x)
00081        double x;
00082 #endif
00083 {      
00084         fd_twoints u;
00085        double t;
00086        int hx;
00087         u.d = x;
00088        hx = __HI(u);
00089        if(hx<0x3ff00000) {         /* x < 1 */
00090            return (x-x)/(x-x);
00091        } else if(hx >=0x41b00000) {       /* x > 2**28 */
00092            if(hx >=0x7ff00000) {   /* x is inf of NaN */
00093                return x+x;
00094            } else 
00095               return __ieee754_log(x)+ln2;       /* acosh(huge)=log(2x) */
00096        } else if(((hx-0x3ff00000)|__LO(u))==0) {
00097            return 0.0;                    /* acosh(1) = 0 */
00098        } else if (hx > 0x40000000) {      /* 2**28 > x > 2 */
00099            t=x*x;
00100            return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one)));
00101        } else {                    /* 1<x<2 */
00102            t = x-one;
00103            return fd_log1p(t+fd_sqrt(2.0*t+t*t));
00104        }
00105 }