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) */
4float 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}