sysdeps/ieee754/ldbl-96/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 #include <math-underflow.h>
  39
  40 static const long double one = 1.0, huge = 1e4900L;
  41
  42 static const long double zero = 0.0;
  43
  44 long double
  45 __ieee754_atanhl(long double x)
  46 {
  47         long double t;
  48         int32_t ix;
  49         uint32_t se,i0,i1;
  50         GET_LDOUBLE_WORDS(se,i0,i1,x);
  51         ix = se&0x7fff;
  52         if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff)
  53           /* |x|>1 */
  54             return (x-x)/(x-x);
  55         if(ix==0x3fff)
  56             return x/zero;
  57         if(ix<0x3fdf) {
  58             math_force_eval(huge+x);
  59             math_check_force_underflow (x);
  60             return x;   /* x<2**-32 */
  61         }
  62         SET_LDOUBLE_EXP(x,ix);
  63         if(ix<0x3ffe) {         /* x < 0.5 */
  64             t = x+x;
  65             t = 0.5*__log1pl(t+t*x/(one-x));
  66         } else
  67             t = 0.5*__log1pl((x+x)/(one-x));
  68         if(se<=0x7fff) return t; else return -t;
  69 }
  70 strong_alias (__ieee754_atanhl, __atanhl_finite)