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}