compiler/stdc/math/ld128/e_atanhl.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 /* atanhl(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  *      atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  19  *                   2             1 - x                      1 - x
  20  *
  21  *      For x<0.5
  22  *      atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
  23  *
  24  * Special cases:
  25  *      atanhl(x) is NaN if |x| > 1 with signal;
  26  *      atanhl(NaN) is that NaN with no signal;
  27  *      atanhl(+-1) is +-INF with signal.
  28  *
  29  */
  30
  31 #include "math.h"
  32
  33 #include "math_private.h"
  34
  35 static const long double one = 1.0L, huge = 1e4900L;
  36
  37 static const long double zero = 0.0L;
  38
  39 long double
  40 atanhl(long double x)
  41 {
  42         long double t;
  43         uint32_t jx, ix;
  44         ieee_quad_shape_type u;
  45
  46         u.value = x;
  47         jx = u.parts32.mswhi;
  48         ix = jx & 0x7fffffff;
  49         u.parts32.mswhi = ix;
  50         if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
  51           {
  52             if (u.value == one)
  53               return x/zero;
  54             else
  55               return (x-x)/(x-x);
  56           }
  57         if(ix<0x3fc60000 && (huge+x)>zero) return x;    /* x < 2^-57 */
  58
  59         if(ix<0x3ffe0000) {             /* x < 0.5 */
  60             t = u.value+u.value;
  61             t = 0.5*log1pl(t+t*u.value/(one-u.value));
  62         } else
  63             t = 0.5*log1pl((u.value+u.value)/(one-u.value));
  64         if(jx & 0x80000000) return -t; else return t;
  65 }