#include "libm.h"

/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
double atanh(double x)
{
        union {double f; uint64_t i;} u = {.f = x};
        unsigned e = u.i >> 52 & 0x7ff;
        unsigned s = u.i >> 63;
        double_t y;

        /* |x| */
        u.i &= (uint64_t)-1/2;
        y = u.f;

        if (e < 0x3ff - 1) {
                if (e < 0x3ff - 32) {
                        /* handle underflow */
                        if (e == 0)
                                FORCE_EVAL((float)y);
                } else {
                        /* |x| < 0.5, up to 1.7ulp error */
                        y = 0.5*log1p(2*y + 2*y*y/(1-y));
                }
        } else {
                /* avoid overflow */
                y = 0.5*log1p(2*(y/(1-y)));
        }
        return s ? -y : y;
}