RTAI API: base/math/e_atanh.c Source File

00001 /* @(#)e_atanh.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice 
00009  * is preserved.
00010  * ====================================================
00011  */
00012 
00013 #if defined(LIBM_SCCS) && !defined(lint)
00014 static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
00015 #endif
00016 
00017 /* __ieee754_atanh(x)
00018  * Method :
00019  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
00020  *    2.For x>=0.5
00021  *                  1              2x                          x
00022  *  atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
00023  *                  2             1 - x                      1 - x
00024  *  
00025  *  For x<0.5
00026  *  atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
00027  *
00028  * Special cases:
00029  *  atanh(x) is NaN if |x| > 1 with signal;
00030  *  atanh(NaN) is that NaN with no signal;
00031  *  atanh(+-1) is +-INF with signal.
00032  *
00033  */
00034 
00035 #include "math.h"
00036 #include "mathP.h"
00037 
00038 #ifdef __STDC__
00039 static const double one = 1.0, huge = 1e300;
00040 #else
00041 static double one = 1.0, huge = 1e300;
00042 #endif
00043 
00044 #ifdef __STDC__
00045 static const double zero = 0.0;
00046 #else
00047 static double zero = 0.0;
00048 #endif
00049 
00050 #ifdef __STDC__
00051     double __ieee754_atanh(double x)
00052 #else
00053     double __ieee754_atanh(x)
00054     double x;
00055 #endif
00056 {
00057     double t;
00058     int32_t hx,ix;
00059     u_int32_t lx;
00060     EXTRACT_WORDS(hx,lx,x);
00061     ix = hx&0x7fffffff;
00062     if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
00063         return (x-x)/(x-x);
00064     if(ix==0x3ff00000) 
00065         return x/zero;
00066     if(ix<0x3e300000&&(huge+x)>zero) return x;  /* x<2**-28 */
00067     SET_HIGH_WORD(x,ix);
00068     if(ix<0x3fe00000) {     /* x < 0.5 */
00069         t = x+x;
00070         t = 0.5*log1p(t+t*x/(one-x));
00071     } else 
00072         t = 0.5*log1p((x+x)/(one-x));
00073     if(hx>=0) return t; else return -t;
00074 }