lib/libm/src/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 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
  16 #endif
  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 "math.h"
  37 #include "math_private.h"
  38
  39 static const double one = 1.0, huge = 1e300;
  40
  41 static const double zero = 0.0;
  42
  43 double
  44 __ieee754_atanh(double x)
  45 {
  46         double t;
  47         int32_t hx,ix;
  48         u_int32_t lx;
  49         EXTRACT_WORDS(hx,lx,x);
  50         ix = hx&0x7fffffff;
  51         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  52             return (x-x)/(x-x);
  53         if(ix==0x3ff00000)
  54             return x/zero;
  55         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  56         SET_HIGH_WORD(x,ix);
  57         if(ix<0x3fe00000) {             /* x < 0.5 */
  58             t = x+x;
  59             t = 0.5*log1p(t+t*x/(one-x));
  60         } else
  61             t = 0.5*log1p((x+x)/(one-x));
  62         if(hx>=0) return t; else return -t;
  63 }