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) */
atanh(double x)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