libquadmath/math/atanhq.c

   1 /* s_atanhl.c -- __float128 version of s_atan.c.
   2  * Conversion to __float128 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 /* atanhq(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 "quadmath-imp.h"
  36
  37 static const __float128 one = 1.0Q, huge = 1e4900Q;
  38 static const __float128 zero = 0.0Q;
  39
  40 __float128
  41 atanhq (__float128 x)
  42 {
  43         __float128 t;
  44         uint32_t jx, ix;
  45         ieee854_float128 u;
  46
  47         u.value = x;
  48         jx = u.words32.w0;
  49         ix = jx & 0x7fffffff;
  50         u.words32.w0 = ix;
  51         if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
  52           {
  53             if (u.value == one)
  54               return x/zero;
  55             else
  56               return (x-x)/(x-x);
  57           }
  58         if(ix<0x3fc60000 && (huge+x)>zero) return x;    /* x < 2^-57 */
  59
  60         if(ix<0x3ffe0000) {             /* x < 0.5 */
  61             t = u.value+u.value;
  62             t = 0.5*log1pq(t+t*u.value/(one-u.value));
  63         } else
  64             t = 0.5*log1pq((u.value+u.value)/(one-u.value));
  65         if(jx & 0x80000000) return -t; else return t;
  66 }