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 51, 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
51— Expressions used to perform ratio arithmetic
[ Example:
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"); 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 ]
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