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 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* __ieee754_atanhl(x)
  22  * Method :
  23  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
  24  *    2.For x>=0.5
  25  *                   1              2x                          x
  26  *      atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  27  *                   2             1 - x                      1 - x
  28  *
  29  *      For x<0.5
  30  *      atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
  31  *
  32  * Special cases:
  33  *      atanhl(x) is NaN if |x| > 1 with signal;
  34  *      atanhl(NaN) is that NaN with no signal;
  35  *      atanhl(+-1) is +-INF with signal.
  36  *
  37  */
  38
  39 #include "math.h"
  40 #include "math_private.h"
  41
  42 #ifdef __STDC__
  43 static const long double one = 1.0L, huge = 1e4900L;
  44 #else
  45 static long double one = 1.0L, huge = 1e4900L;
  46 #endif
  47
  48 #ifdef __STDC__
  49 static const long double zero = 0.0L;
  50 #else
  51 static double long zero = 0.0L;
  52 #endif
  53
  54 #ifdef __STDC__
  55         long double __ieee754_atanhl(long double x)
  56 #else
  57         long double __ieee754_atanhl(x)
  58         long double x;
  59 #endif
  60 {
  61         long double t;
  62         u_int32_t jx, ix;
  63         ieee854_long_double_shape_type u;
  64
  65         u.value = x;
  66         jx = u.parts32.w0;
  67         ix = jx & 0x7fffffff;
  68         u.parts32.w0 = ix;
  69         if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
  70           {
  71             if (u.value == one)
  72               return x/zero;
  73             else
  74               return (x-x)/(x-x);
  75           }
  76         if(ix<0x3fc60000 && (huge+x)>zero) return x;    /* x < 2^-57 */
  77
  78         if(ix<0x3ffe0000) {             /* x < 0.5 */
  79             t = u.value+u.value;
  80             t = 0.5*__log1pl(t+t*u.value/(one-u.value));
  81         } else
  82             t = 0.5*__log1pl((u.value+u.value)/(one-u.value));
  83         if(jx & 0x80000000) return -t; else return t;
  84 }