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e_atanh.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
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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.
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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"),
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00038  * ***** END LICENSE BLOCK ***** */
00039 
00040 /* @(#)e_atanh.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_atanh(x)
00054  * Method :
00055  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
00056  *    2.For x>=0.5
00057  *                  1              2x                          x
00058  *     atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
00059  *                  2             1 - x                      1 - x
00060  *     
00061  *     For x<0.5
00062  *     atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
00063  *
00064  * Special cases:
00065  *     atanh(x) is NaN if |x| > 1 with signal;
00066  *     atanh(NaN) is that NaN with no signal;
00067  *     atanh(+-1) is +-INF with signal.
00068  *
00069  */
00070 
00071 #include "fdlibm.h"
00072 
00073 #ifdef __STDC__
00074 static const double one = 1.0, really_big = 1e300;
00075 #else
00076 static double one = 1.0, really_big = 1e300;
00077 #endif
00078 
00079 static double zero = 0.0;
00080 
00081 #ifdef __STDC__
00082        double __ieee754_atanh(double x)
00083 #else
00084        double __ieee754_atanh(x)
00085        double x;
00086 #endif
00087 {
00088        double t;
00089        int hx,ix;
00090        unsigned lx;
00091         fd_twoints u;
00092         u.d = x;
00093        hx = __HI(u);        /* high word */
00094        lx = __LO(u);        /* low word */
00095        ix = hx&0x7fffffff;
00096        if ((ix|((lx|(-(int)lx))>>31))>0x3ff00000) /* |x|>1 */
00097            return (x-x)/(x-x);
00098        if(ix==0x3ff00000) 
00099            return x/zero;
00100        if(ix<0x3e300000&&(really_big+x)>zero) return x; /* x<2**-28 */
00101         u.d = x;
00102        __HI(u) = ix;        /* x <- |x| */
00103         x = u.d;
00104        if(ix<0x3fe00000) {         /* x < 0.5 */
00105            t = x+x;
00106            t = 0.5*fd_log1p(t+t*x/(one-x));
00107        } else 
00108            t = 0.5*fd_log1p((x+x)/(one-x));
00109        if(hx>=0) return t; else return -t;
00110 }