3.1 KiB
[ratio.arithmetic]
21 Metaprogramming library [meta]
21.5 Compile-time rational arithmetic [ratio]
21.5.4 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 tworatios R1 and R2.
With X and Y computed (in the absence of arithmetic overflow) as specified by Table 65, each alias denotes a ratio<U, V> such that U is the same as ratio<X, Y>::num andV 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 andV.
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 andV.
Table 65 — Expressions used to perform ratio arithmetic [tab:ratio.arithmetic]
| ð Type |
Value of X | Value of Y |
|---|---|---|
| ð ratio_add<R1, R2> |
R1::num * R2::den + | R1::den * R2::den |
| ð | R2::num * R1::den | |
| ð ratio_subtract<R1, R2> |
R1::num * R2::den - | R1::den * R2::den |
| ð | R2::num * R1::den | |
| ð ratio_multiply<R1, R2> |
R1::num * R2::num | R1::den * R2::den |
| ð 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, "1/33/2 == 1/2");static_assert(ratio_multiply<ratio<1, 3>, ratio<3, 2>>::den == 2, "1/33/2 == 1/2");
// The following cases may cause the program to be ill-formed under some implementationsstatic_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"); â end example]