contrib/openbsd_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 /* atanh(x)
  14  * Method :
  15  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  16  *    2.For x>=0.5
  17  *                  1              2x                          x
  18  *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  19  *                  2             1 - x                      1 - x
  20  *
  21  *      For x<0.5
  22  *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  23  *
  24  * Special cases:
  25  *      atanh(x) is NaN if |x| > 1 with signal;
  26  *      atanh(NaN) is that NaN with no signal;
  27  *      atanh(+-1) is +-INF with signal.
  28  *
  29  */
  30
  31 #include <float.h>
  32 #include <math.h>
  33
  34 #include "math_private.h"
  35
  36 static const double one = 1.0, huge = 1e300;
  37 static const double zero = 0.0;
  38
  39 double
  40 atanh(double x)
  41 {
  42         double t;
  43         int32_t hx,ix;
  44         u_int32_t lx;
  45         EXTRACT_WORDS(hx,lx,x);
  46         ix = hx&0x7fffffff;
  47         if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  48             return (x-x)/(x-x);
  49         if(ix==0x3ff00000)
  50             return x/zero;
  51         if(ix<0x3e300000&&(huge+x)>zero) return x;      /* x<2**-28 */
  52         SET_HIGH_WORD(x,ix);
  53         if(ix<0x3fe00000) {             /* x < 0.5 */
  54             t = x+x;
  55             t = 0.5*log1p(t+t*x/(one-x));
  56         } else
  57             t = 0.5*log1p((x+x)/(one-x));
  58         if(hx>=0) return t; else return -t;
  59 }
  60
  61 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  62 __strong_alias(atanhl, atanh);
  63 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */