template <class R1, class R2>
struct ratio_equal : bool_constant<R1::num == R2::num && R1::den == R2::den> { };
template <class R1, class R2>
struct ratio_not_equal : bool_constant<!ratio_equal_v<R1, R2>> { };
template <class R1, class R2>
struct ratio_less : bool_constant<see below> { };
If R1::num × R2::den is less than R2::num × R1::den, ratio_less<R1, R2> shall be derived from bool_constant<true>; otherwise it shall be derived from bool_constant<false>. Implementations may use other algorithms to compute this relationship to avoid overflow. If overflow occurs, the program is ill-formed.
template <class R1, class R2>
struct ratio_less_equal : bool_constant<!ratio_less_v<R2, R1>> { };
template <class R1, class R2>
struct ratio_greater : bool_constant<ratio_less_v<R2, R1>> { };
template <class R1, class R2>
struct ratio_greater_equal : bool_constant<!ratio_less_v<R1, R2>> { };