third_party/ulib/musl/src/math/atanhf.c

#include "libm.h"

/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
float atanhf(float x) {
    union {
        float f;
        uint32_t i;
    } u = {.f = x};
    unsigned s = u.i >> 31;
    float_t y;

    /* |x| */
    u.i &= 0x7fffffff;
    y = u.f;

    if (u.i < 0x3f800000 - (1 << 23)) {
        if (u.i < 0x3f800000 - (32 << 23)) {
            /* handle underflow */
            if (u.i < (1 << 23))
                FORCE_EVAL((float)(y * y));
        } else {
            /* |x| < 0.5, up to 1.7ulp error */
            y = 0.5f * log1pf(2 * y + 2 * y * y / (1 - y));
        }
    } else {
        /* avoid overflow */
        y = 0.5f * log1pf(2 * (y / (1 - y)));
    }
    return s ? -y : y;
}