N3797 has this to say on std::ratio
:
N3797 [20.11.4] [ratio.arithmetic]
2 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.
It then gives the following:
// 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");
This seems to me to suggest that if your program would overflow either the denominator or the numerator in intermediate calculations, the program is ill-formed.