double rsqrt(double x) {
    double left, right;
    if (x < 1.0) {
        if (x < 0.0) {
            long long nan = 0x7ff8000000000000L;
            return *(double*)&nan;
        }
        left = x;
        right = 1.0;
    } else {
        left = 1.0;
        right = x;
    }
    double root = 1.0, oldRoot = 1.0;
    for (;;) {
        double root = (right + left) / 2.0;
        if (root == oldRoot) return root;
        if (root * root > x) right = root;
        else left = root;
        oldRoot = root;
    }
}