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) */
4double 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