23 General utilities library [utilities]

23.16 Compile-time rational arithmetic [ratio]

23.16.3 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
:
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.
In a two's complement representation, 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 sign(N) * sign(D) * abs(N) / gcd.
  • den shall have the value abs(D) / gcd.