21 Metaprogramming library [meta]

21.4 Compile-time rational arithmetic [ratio]

21.4.3 Class template ratio [ratio.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>; }; }
If the template argument D is zero or the absolute values of either of the template arguments N and D is not representable by type intmax_t, the program is ill-formed.
[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.
This excludes the most negative value.
— end note]
The static data members num and den shall have the following values, where gcd represents the greatest common divisor of the absolute values of N and D:
  • num shall have the value sgn(N) * sgn(D) * abs(N) / gcd.
  • den shall have the value abs(D) / gcd.