sysdeps/ieee754/ldbl-128ibm/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 /* __ieee754_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 #include <math_private.h>
  34 #include <math-underflow.h>
  35 #include <libm-alias-finite.h>
  36
  37 static const long double one = 1.0L, huge = 1e300L;
  38
  39 static const long double zero = 0.0L;
  40
  41 long double
  42 __ieee754_atanhl(long double x)
  43 {
  44         long double t;
  45         int64_t hx,ix;
  46         double xhi;
  47
  48         xhi = ldbl_high (x);
  49         EXTRACT_WORDS64 (hx, xhi);
  50         ix = hx&0x7fffffffffffffffLL;
  51         if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */
  52             if (ix > 0x3ff0000000000000LL)
  53                 return (x-x)/(x-x);
  54             t = fabsl (x);
  55             if (t > one)
  56                 return (x-x)/(x-x);
  57             if (t == one)
  58                 return x/zero;
  59         }
  60         if(ix<0x3c70000000000000LL&&(huge+x)>zero)      /* x<2**-56 */
  61           {
  62             math_check_force_underflow (x);
  63             return x;
  64           }
  65         x = fabsl (x);
  66         if(ix<0x3fe0000000000000LL) {           /* x < 0.5 */
  67             t = x+x;
  68             t = 0.5*__log1pl(t+t*x/(one-x));
  69         } else
  70             t = 0.5*__log1pl((x+x)/(one-x));
  71         if(hx>=0) return t; else return -t;
  72 }
  73 libm_alias_finite (__ieee754_atanhl, __atanhl)