public static function ristretto255_sqrt_ratio_m1(
        ParagonIE_Sodium_Core_Curve25519_Fe $u,
        ParagonIE_Sodium_Core_Curve25519_Fe $v
    ) {
        $sqrtm1 = ParagonIE_Sodium_Core_Curve25519_Fe::ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1);

        $v3 = self::fe_mul(
            self::fe_sq($v),
            $v
        ); /* v3 = v^3 */
        $x = self::fe_mul(
            self::fe_mul(
                self::fe_sq($v3),
                $u
            ),
            $v
        ); /* x = uv^7 */

        $x = self::fe_mul(
            self::fe_mul(
                self::fe_pow22523($x), /* x = (uv^7)^((q-5)/8) */
                $v3
            ),
            $u
        ); /* x = uv^3(uv^7)^((q-5)/8) */

        $vxx = self::fe_mul(
            self::fe_sq($x),
            $v
        ); /* vx^2 */

        $m_root_check = self::fe_sub($vxx, $u); /* vx^2-u */
        $p_root_check = self::fe_add($vxx, $u); /* vx^2+u */
        $f_root_check = self::fe_mul($u, $sqrtm1); /* u*sqrt(-1) */
        $f_root_check = self::fe_add($vxx, $f_root_check); /* vx^2+u*sqrt(-1) */

        $has_m_root = self::fe_iszero($m_root_check);
        $has_p_root = self::fe_iszero($p_root_check);
        $has_f_root = self::fe_iszero($f_root_check);

        $x_sqrtm1 = self::fe_mul($x, $sqrtm1); /* x*sqrt(-1) */

        $x = self::fe_abs(
            self::fe_cmov($x, $x_sqrtm1, $has_p_root | $has_f_root)
        );
        return array(
            'x' => $x,
            'nonsquare' => $has_m_root | $has_p_root
        );
    }