Line data    Source code

       1             : 
       2             : /* @(#)e_atanh.c 1.3 95/01/18 */
       3             : /*
       4             :  * ====================================================
       5             :  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       6             :  *
       7             :  * Developed at SunSoft, a Sun Microsystems, Inc. business.
       8             :  * Permission to use, copy, modify, and distribute this
       9             :  * software is freely granted, provided that this notice 
      10             :  * is preserved.
      11             :  * ====================================================
      12             :  *
      13             :  */
      14             : 
      15             : //#include <sys/cdefs.h>
      16             : //__FBSDID("$FreeBSD$");
      17             : 
      18             : /* __ieee754_atanh(x)
      19             :  * Method :
      20             :  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
      21             :  *    2.For x>=0.5
      22             :  *                  1              2x                          x
      23             :  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
      24             :  *                  2             1 - x                      1 - x
      25             :  *      
      26             :  *      For x<0.5
      27             :  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
      28             :  *
      29             :  * Special cases:
      30             :  *      atanh(x) is NaN if |x| > 1 with signal;
      31             :  *      atanh(NaN) is that NaN with no signal;
      32             :  *      atanh(+-1) is +-INF with signal.
      33             :  *
      34             :  */
      35             : 
      36             : #include <float.h>
      37             : 
      38             : #include "math_private.h"
      39             : 
      40             : static const double one = 1.0, huge = 1e300;
      41             : static const double zero = 0.0;
      42             : 
      43             : double
      44           0 : __ieee754_atanh(double x)
      45             : {
      46             :         double t;
      47             :         int32_t hx,ix;
      48             :         u_int32_t lx;
      49           0 :         EXTRACT_WORDS(hx,lx,x);
      50           0 :         ix = hx&0x7fffffff;
      51           0 :         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
      52           0 :             return (x-x)/(x-x);
      53           0 :         if(ix==0x3ff00000) 
      54           0 :             return x/zero;
      55           0 :         if(ix<0x3e300000&&(huge+x)>zero) return x;        /* x<2**-28 */
      56           0 :         SET_HIGH_WORD(x,ix);
      57           0 :         if(ix<0x3fe00000) {          /* x < 0.5 */
      58           0 :             t = x+x;
      59           0 :             t = 0.5*log1p(t+t*x/(one-x));
      60             :         } else 
      61           0 :             t = 0.5*log1p((x+x)/(one-x));
      62           0 :         if(hx>=0) return t; else return -t;
      63             : }