< cpp‎ | numeric‎ | ratio
Defined in header <ratio>
template< class R1, class R2 >
using ratio_subtract = /* see below */;

The alias template std::ratio_subtract denotes the result of subtracting two exact rational fractions represented by the std::ratio specializations R1 and R2.

The result is a std::ratio specialization std::ratio<U, V>, such that given Num == R1::num * R2::den - R2::num * R1::den and Denom == R1::den * R2::den (computed without arithmetic overflow), U is std::ratio<Num, Denom>::num and V is std::ratio<Num, Denom>::den.

[edit] Notes

If U or V is not representable in std::intmax_t, the program is ill-formed. If Num or Denom is not representable in std::intmax_t, the program is ill-formed unless the implementation yields correct values for U and V.

The above definition requires that the result of std::ratio_subtract<R1, R2> be already reduced to lowest terms; for example, std::ratio_subtract<std::ratio<1, 2>, std::ratio<1, 6>> is the same type as std::ratio<1, 3>.

[edit] Example

#include <iostream>
#include <ratio>
int main()
    typedef std::ratio<2, 3> two_third;
    typedef std::ratio<1, 6> one_sixth;
    typedef std::ratio_subtract<two_third, one_sixth> diff;
    std::cout << "2/3 - 1/6 = " << diff::num << '/' << diff::den << '\n';


2/3 - 1/6 = 1/2