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    union {
6        float f;
7        uint32_t i;
8    } u = {.f = x};
9    unsigned s = u.i >> 31;
10    float_t y;
11
12    /* |x| */
13    u.i &= 0x7fffffff;
14    y = u.f;
15
16    if (u.i < 0x3f800000 - (1 << 23)) {
17        if (u.i < 0x3f800000 - (32 << 23)) {
18            /* handle underflow */
19            if (u.i < (1 << 23))
20                FORCE_EVAL((float)(y * y));
21        } else {
22            /* |x| < 0.5, up to 1.7ulp error */
23            y = 0.5f * log1pf(2 * y + 2 * y * y / (1 - y));
24        }
25    } else {
26        /* avoid overflow */
27        y = 0.5f * log1pf(2 * (y / (1 - y)));
28    }
29    return s ? -y : y;
30}
31