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Showing content from https://timsong-cpp.github.io/cppwp/n4140/ratio.comparison below:

[ratio.comparison]

20.11.5 Comparison of ratios [ratio.comparison]

template <class R1, class R2> struct ratio_equal : integral_constant<bool, see below> { };

If R1::num == R2::num and R1::den == R2::den, ratio_equal<R1, R2> shall be derived from
integral_constant<bool, true>; otherwise it shall be derived from integral_constant<bool, false>.

template <class R1, class R2> struct ratio_not_equal : integral_constant<bool, !ratio_equal<R1, R2>::value> { };

template <class R1, class R2> struct ratio_less : integral_constant<bool, see below> { };

If R1::num * R2::den < R2::num * R1::den, ratio_less<R1, R2> shall be derived from integral_constant<bool, true>; otherwise it shall be derived from integral_constant<bool, 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 : integral_constant<bool, !ratio_less<R2, R1>::value> { };

template <class R1, class R2> struct ratio_greater : integral_constant<bool, ratio_less<R2, R1>::value> { };

template <class R1, class R2> struct ratio_greater_equal : integral_constant<bool, !ratio_less<R1, R2>::value> { };


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