sysdeps/libm-ieee754/e_atanh.c

   1 /* @(#)e_atanh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
  15 #endif
  16
  17 /* __ieee754_atanh(x)
  18  * Method :
  19  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  20  *    2.For x>=0.5
  21  *                  1              2x                          x
  22  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  23  *                  2             1 - x                      1 - x
  24  *
  25  *      For x<0.5
  26  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  27  *
  28  * Special cases:
  29  *      atanh(x) is NaN if |x| > 1 with signal;
  30  *      atanh(NaN) is that NaN with no signal;
  31  *      atanh(+-1) is +-INF with signal.
  32  *
  33  */
  34
  35 #include "math.h"
  36 #include "math_private.h"
  37
  38 #ifdef __STDC__
  39 static const double one = 1.0, huge = 1e300;
  40 #else
  41 static double one = 1.0, huge = 1e300;
  42 #endif
  43
  44 #ifdef __STDC__
  45 static const double zero = 0.0;
  46 #else
  47 static double zero = 0.0;
  48 #endif
  49
  50 #ifdef __STDC__
  51         double __ieee754_atanh(double x)
  52 #else
  53         double __ieee754_atanh(x)
  54         double x;
  55 #endif
  56 {
  57         double t;
  58         int32_t hx,ix;
  59         u_int32_t lx;
  60         EXTRACT_WORDS(hx,lx,x);
  61         ix = hx&0x7fffffff;
  62         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  63             return (x-x)/(x-x);
  64         if(ix==0x3ff00000)
  65             return x/zero;
  66         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  67         SET_HIGH_WORD(x,ix);
  68         if(ix<0x3fe00000) {             /* x < 0.5 */
  69             t = x+x;
  70             t = 0.5*__log1p(t+t*x/(one-x));
  71         } else
  72             t = 0.5*__log1p((x+x)/(one-x));
  73         if(hx>=0) return t; else return -t;
  74 }