sysdeps/ieee754/ldbl-128/e_atanhl.c

   1 /* s_atanhl.c -- long double version of s_atan.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 /* __ieee754_atanhl(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  *      atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  23  *                   2             1 - x                      1 - x
  24  *
  25  *      For x<0.5
  26  *      atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
  27  *
  28  * Special cases:
  29  *      atanhl(x) is NaN if |x| > 1 with signal;
  30  *      atanhl(NaN) is that NaN with no signal;
  31  *      atanhl(+-1) is +-INF with signal.
  32  *
  33  */
  34
  35 #include <float.h>
  36 #include <math.h>
  37 #include <math_private.h>
  38
  39 static const long double one = 1.0L, huge = 1e4900L;
  40
  41 static const long double zero = 0.0L;
  42
  43 long double
  44 __ieee754_atanhl(long double x)
  45 {
  46         long double t;
  47         u_int32_t jx, ix;
  48         ieee854_long_double_shape_type u;
  49
  50         u.value = x;
  51         jx = u.parts32.w0;
  52         ix = jx & 0x7fffffff;
  53         u.parts32.w0 = ix;
  54         if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
  55           {
  56             if (u.value == one)
  57               return x/zero;
  58             else
  59               return (x-x)/(x-x);
  60           }
  61         if(ix<0x3fc60000 && (huge+x)>zero)      /* x < 2^-57 */
  62           {
  63             if (fabsl (x) < LDBL_MIN)
  64               {
  65                 long double force_underflow = x * x;
  66                 math_force_eval (force_underflow);
  67               }
  68             return x;
  69           }
  70
  71         if(ix<0x3ffe0000) {             /* x < 0.5 */
  72             t = u.value+u.value;
  73             t = 0.5*__log1pl(t+t*u.value/(one-u.value));
  74         } else
  75             t = 0.5*__log1pl((u.value+u.value)/(one-u.value));
  76         if(jx & 0x80000000) return -t; else return t;
  77 }
  78 strong_alias (__ieee754_atanhl, __atanhl_finite)