[ratio.comparison]

# 21 Metaprogramming library [[meta]](./#meta)

## 21.5 Compile-time rational arithmetic [[ratio]](ratio#comparison)

### 21.5.5 Comparison of ratios [ratio.comparison]

[ð](#lib:ratio_equal)

`template<class R1, class R2>
  struct ratio_equal : bool_constant<R1::num == R2::num && R1::den == R2::den> { };
`

[ð](#lib:ratio_not_equal)

`template<class R1, class R2>
  struct ratio_not_equal : bool_constant<!ratio_equal_v<R1, R2>> { };
`

[ð](#lib:ratio_less)

`template<class R1, class R2>
  struct ratio_less : bool_constant<see below> { };
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/meta.tex#L7242)

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 frombool_constant<false>[.](#1.sentence-1)

Implementations may use other algorithms to
compute this relationship to avoid overflow[.](#1.sentence-2)

If overflow occurs, the program is ill-formed[.](#1.sentence-3)

[ð](#lib:ratio_less_equal)

`template<class R1, class R2>
  struct ratio_less_equal : bool_constant<!ratio_less_v<R2, R1>> { };
`

[ð](#lib:ratio_greater)

`template<class R1, class R2>
  struct ratio_greater : bool_constant<ratio_less_v<R2, R1>> { };
`

[ð](#lib:ratio_greater_equal)

`template<class R1, class R2>
  struct ratio_greater_equal : bool_constant<!ratio_less_v<R1, R2>> { };
`
