21 Metaprogramming library [meta]

21.4 Compile-time rational arithmetic [ratio]

21.4.4 Arithmetic on ratios [ratio.arithmetic]

Each of the alias templates ratio_add, ratio_subtract, ratio_multiply, and ratio_divide denotes the result of an arithmetic computation on two ratios R1 and R2.

With X and Y computed (in the absence of arithmetic overflow) as specified by Table 56, each alias denotes a ratio<U, V> such that U is the same as ratio<X, Y>::num and V is the same as ratio<X, Y>::den.

If it is not possible to represent U or V with intmax_t, the program is ill-formed.

Otherwise, an implementation should yield correct values of U and V.

If it is not possible to represent X or Y with intmax_t, the program is ill-formed unless the implementation yields correct values of U and V.

Table 56: Expressions used to perform ratio arithmetic [tab:ratio.arithmetic]

🔗	Type	Value of X	Value of Y
🔗	ratio_add<R1, R2>	R1::num * R2::den +	R1::den * R2::den
🔗		R2::num * R1::den
🔗	ratio_subtract<R1, R2>	R1::num * R2::den -	R1::den * R2::den
🔗		R2::num * R1::den
🔗	ratio_multiply<R1, R2>	R1::num * R2::num	R1::den * R2::den
🔗	ratio_divide<R1, R2>	R1::num * R2::den	R1::den * R2::num

[Example 1: static_assert(ratio_add<ratio<1, 3>, ratio<1, 6>>::num == 1, "1/3+1/6 == 1/2"); static_assert(ratio_add<ratio<1, 3>, ratio<1, 6>>::den == 2, "1/3+1/6 == 1/2"); static_assert(ratio_multiply<ratio<1, 3>, ratio<3, 2>>::num == 1, "1/3*3/2 == 1/2"); static_assert(ratio_multiply<ratio<1, 3>, ratio<3, 2>>::den == 2, "1/3*3/2 == 1/2"); // The following cases may cause the program to be ill-formed under some implementations static_assert(ratio_add<ratio<1, INT_MAX>, ratio<1, INT_MAX>>::num == 2, "1/MAX+1/MAX == 2/MAX"); static_assert(ratio_add<ratio<1, INT_MAX>, ratio<1, INT_MAX>>::den == INT_MAX, "1/MAX+1/MAX == 2/MAX"); static_assert(ratio_multiply<ratio<1, INT_MAX>, ratio<INT_MAX, 2>>::num == 1, "1/MAX * MAX/2 == 1/2"); static_assert(ratio_multiply<ratio<1, INT_MAX>, ratio<INT_MAX, 2>>::den == 2, "1/MAX * MAX/2 == 1/2"); — end example]