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s_asinh.c
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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
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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 /* @(#)s_asinh.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 /* asinh(x)
00053  * Method :
00054  *     Based on 
00055  *            asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
00056  *     we have
00057  *     asinh(x) := x  if  1+x*x=1,
00058  *             := sign(x)*(log(x)+ln2)) for large |x|, else
00059  *             := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
00060  *             := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))  
00061  */
00062 
00063 #include "fdlibm.h"
00064 
00065 #ifdef __STDC__
00066 static const double 
00067 #else
00068 static double 
00069 #endif
00070 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
00071 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
00072 really_big=  1.00000000000000000000e+300; 
00073 
00074 #ifdef __STDC__
00075        double fd_asinh(double x)
00076 #else
00077        double fd_asinh(x)
00078        double x;
00079 #endif
00080 {      
00081         fd_twoints u;
00082        double t,w;
00083        int hx,ix;
00084         u.d = x;
00085        hx = __HI(u);
00086        ix = hx&0x7fffffff;
00087        if(ix>=0x7ff00000) return x+x;     /* x is inf or NaN */
00088        if(ix< 0x3e300000) { /* |x|<2**-28 */
00089            if(really_big+x>one) return x; /* return x inexact except 0 */
00090        } 
00091        if(ix>0x41b00000) {  /* |x| > 2**28 */
00092            w = __ieee754_log(fd_fabs(x))+ln2;
00093        } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
00094            t = fd_fabs(x);
00095            w = __ieee754_log(2.0*t+one/(fd_sqrt(x*x+one)+t));
00096        } else {             /* 2.0 > |x| > 2**-28 */
00097            t = x*x;
00098            w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
00099        }
00100        if(hx>0) return w; else return -w;
00101 }