atanhl.c raw

   1  #include "libm.h"
   2  
   3  #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
   4  long double atanhl(long double x)
   5  {
   6  	return atanh(x);
   7  }
   8  #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
   9  /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
  10  long double atanhl(long double x)
  11  {
  12  	union ldshape u = {x};
  13  	unsigned e = u.i.se & 0x7fff;
  14  	unsigned s = u.i.se >> 15;
  15  
  16  	/* |x| */
  17  	u.i.se = e;
  18  	x = u.f;
  19  
  20  	if (e < 0x3ff - 1) {
  21  		if (e < 0x3ff - LDBL_MANT_DIG/2) {
  22  			/* handle underflow */
  23  			if (e == 0)
  24  				FORCE_EVAL((float)x);
  25  		} else {
  26  			/* |x| < 0.5, up to 1.7ulp error */
  27  			x = 0.5*log1pl(2*x + 2*x*x/(1-x));
  28  		}
  29  	} else {
  30  		/* avoid overflow */
  31  		x = 0.5*log1pl(2*(x/(1-x)));
  32  	}
  33  	return s ? -x : x;
  34  }
  35  #endif
  36