atanh.c raw

   1  #include "libm.h"
   2  
   3  /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
   4  double atanh(double x)
   5  {
   6  	union {double f; uint64_t i;} u = {.f = x};
   7  	unsigned e = u.i >> 52 & 0x7ff;
   8  	unsigned s = u.i >> 63;
   9  	double_t y;
  10  
  11  	/* |x| */
  12  	u.i &= (uint64_t)-1/2;
  13  	y = u.f;
  14  
  15  	if (e < 0x3ff - 1) {
  16  		if (e < 0x3ff - 32) {
  17  			/* handle underflow */
  18  			if (e == 0)
  19  				FORCE_EVAL((float)y);
  20  		} else {
  21  			/* |x| < 0.5, up to 1.7ulp error */
  22  			y = 0.5*log1p(2*y + 2*y*y/(1-y));
  23  		}
  24  	} else {
  25  		/* avoid overflow */
  26  		y = 0.5*log1p(2*(y/(1-y)));
  27  	}
  28  	return s ? -y : y;
  29  }
  30