20 General utilities library [utilities]

20.10 Compile-time rational arithmetic [ratio]

20.10.3 Class template ratio [ratio.ratio]

namespace std {
  template <intmax_t N, intmax_t D = 1>
  class ratio {
    typedef ratio<num, den> type;
    static constexpr intmax_t num;
    static constexpr intmax_t 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.