[ratio.ratio]

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

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

### 21.5.3 Class template ratio [ratio.ratio]

[ð](#lib:ratio)

namespace std {template<intmax_t N, intmax_t D = 1> class ratio {public:static constexpr intmax_t num; static constexpr intmax_t den; using type = ratio<num, den>; };}

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/meta.tex#L7127)

If the template argument D is zero or the absolute values of either of the
template arguments N and D is not representable by typeintmax_t, the program is ill-formed[.](#1.sentence-1)

[*Note [1](#note-1)*:

These rules ensure that infinite
ratios are avoided and that for any negative input, there exists a representable value
of its absolute value which is positive[.](#1.sentence-2)

This excludes the most negative value[.](#1.sentence-3)

â *end note*]

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/meta.tex#L7139)

The static data members num and den shall have the following values,
where gcd represents the greatest common divisor of the absolute values ofN and D:

- [(2.1)](#2.1)

  num shall have the value sgn(N) * sgn(D) * abs(N) / gcd[.](#2.1.sentence-1)

- [(2.2)](#2.2)

  den shall have the value abs(D) / gcd[.](#2.2.sentence-1)
