atanhf.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  float atanhf(float x)
   5  {
   6  	union {float f; uint32_t i;} u = {.f = x};
   7  	unsigned s = u.i >> 31;
   8  	float_t y;
   9  
  10  	/* |x| */
  11  	u.i &= 0x7fffffff;
  12  	y = u.f;
  13  
  14  	if (u.i < 0x3f800000 - (1<<23)) {
  15  		if (u.i < 0x3f800000 - (32<<23)) {
  16  			/* handle underflow */
  17  			if (u.i < (1<<23))
  18  				FORCE_EVAL((float)(y*y));
  19  		} else {
  20  			/* |x| < 0.5, up to 1.7ulp error */
  21  			y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
  22  		}
  23  	} else {
  24  		/* avoid overflow */
  25  		y = 0.5f*log1pf(2*(y/(1-y)));
  26  	}
  27  	return s ? -y : y;
  28  }
  29