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### 1389. Compile-time rational arithmetic and overflow

Section: 21.4.4 [ratio.arithmetic] Status: Resolved Submitter: BSI Opened: 2010-08-25 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

Addresses GB-89

The alias representations of the `ratio` arithmetic templates do not allow implementations to avoid overflow, since they explicitly specify the form of the aliased template instantiation. For example `ratio_multiply`, `ratio<2, LLONG_MAX>` is required to alias `ratio<2*LLONG_MAX, LLONG_MAX*2>`, which overflows, so is ill-formed. However, this is trivially equal to `ratio<1, 1>`. It also contradicts the opening statement of 21.4.4 [ratio.arithmetic] p. 1 "implementations may use other algorithms to compute these values".

[ 2010-10-25 Daniel adds: ]

> Accepting n3131 would solve this issue.

[Batavia: Resolved by accepting n3210.]

Proposed resolution:

Change the wording in 21.4.4 [ratio.arithmetic] p. 2-5 as follows:

>     template <class R1, class R2> using ratio_add = see below;

> > 2 The type `ratio_add<R1, R2>` shall be a synonym for `ratio<T1, T2>` `ratio<U, V>` such that `ratio<U, V>::num` and `ratio<U, V>::den` are the same as the corresponding members of `ratio<T1, T2>` would be in the absence of arithmetic overflow where `T1` has the value `R1::num * R2::den + R2::num * R1::den` and `T2` has the value `R1::den * R2::den`. If the required values of `ratio<U, V>::num` and `ratio<U, V>::den` cannot be represented in `intmax_t` then the program is ill-formed.

>     template <class R1, class R2> using ratio_subtract = see below;

> > 3 The type `ratio_subtract<R1, R2>` shall be a synonym for `ratio<T1, T2>` `ratio<U, V>` such that `ratio<U, V>::num` and `ratio<U, V>::den` are the same as the corresponding members of `ratio<T1, T2>` would be in the absence of arithmetic overflow where `T1` has the value `R1::num * R2::den - R2::num * R1::den` and `T2` has the value `R1::den * R2::den`. If the required values of `ratio<U, V>::num` and `ratio<U, V>::den` cannot be represented in `intmax_t` then the program is ill-formed.

>     template <class R1, class R2> using ratio_multiply = see below;

> > 4 The type `ratio_multiply<R1, R2>` shall be a synonym for `ratio<T1, T2>` `ratio<U, V>` such that `ratio<U, V>::num` and `ratio<U, V>::den` are the same as the corresponding members of `ratio<T1, T2>` would be in the absence of arithmetic overflow where `T1` has the value `R1::num * R2::num` and `T2` has the value `R1::den * R2::den`. If the required values of `ratio<U, V>::num` and `ratio<U, V>::den` cannot be represented in `intmax_t` then the program is ill-formed.

>     template <class R1, class R2> using ratio_divide = see below;

> > 5 The type `ratio_divide<R1, R2>` shall be a synonym for `ratio<T1, T2>` `ratio<U, V>` such that `ratio<U, V>::num` and `ratio<U, V>::den` are the same as the corresponding members of `ratio<T1, T2>` would be in the absence of arithmetic overflow where `T1` has the value `R1::num * R2::den` and `T2` has the value `R1::den * R2::num`. If the required values of `ratio<U, V>::num` and `ratio<U, V>::den` cannot be represented in `intmax_t` then the program is ill-formed.