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### 3801. `cartesian_product_view::`*iterator*::*distance-from* ignores the size of last underlying range

**Section:** 26.7.32.3 [range.cartesian.iterator] **Status:** WP
**Submitter:** Patrick Palka **Opened:** 2022-10-25 **Last modified:** 2023-02-07

**Priority: **Not Prioritized

**View all other** issues in [range.cartesian.iterator].

**View all issues with** WP status.

**Discussion:**

The helper *scaled-size*(*N*) from the wording for P2374R4's
`cartesian_product_view::`*iterator*::*distance-from* is recursively
specified as:

Let *scaled-size*(*N*) be the product of
`static_cast<difference_type>(ranges::size(std::get<`*N*>(*parent_*->*bases_*)))
and *scaled-size*(*N* + 1) if *N* < sizeof...(Vs), otherwise
`static_cast<difference_type>(1)`;

Intuitively, *scaled-size*(*N*) is the size of the cartesian product of all
but the first *N* underlying ranges. Thus *scaled-size*(sizeof...(Vs))
ought to just yield the size of the last underlying range (since there are
`1 + sizeof...(Vs)` underlying ranges), but according to this definition it
yields `1`. Similarly at the other extreme, *scaled-size*(0) should yield
the product of the sizes of all the underlying ranges, but it instead yields that of all but
the last underlying range.

For `cartesian_product_view`s of two or more underlying ranges, this
causes the relevant `operator-` overloads to compute wrong distances, e.g.

int x[] = {1, 2, 3};
auto v = views::cartesian_product(x, x);
auto i = v.begin() + 5; // *i == {2, 3}
assert(*i == tuple{2, 3});
assert(i - v.begin() == 5); // fails, expects 3, because:
// scaled-sum = scaled-distance(0) + scaled-distance(1)
// = ((1 - 0) * scaled-size(1)) + ((2 - 0) * scaled-size(2))
// = 1 + 2 instead of 3 + 2

The recursive condition should probably use `<=` instead of `<`.

*[2022-11-04; Reflector poll]*

Set status to Tentatively Ready after seven votes in favour during reflector poll.

*[2022-11-12 Approved at November 2022 meeting in Kona. Status changed: Voting → WP.]*

**Proposed resolution:**

This wording is relative to N4917.

Modify [ranges.cartesian.iterator] as indicated:

template<class Tuple>
constexpr difference_type *distance-from*(Tuple t);

-7- Let:

(7.1) — *scaled-size*(*N*) be the product of
`static_cast<difference_type>(ranges::size(std::get<`*N*>(*parent_*->*bases_*)))
and *scaled-size*(*N* + 1) if *N* ≤~~<~~ sizeof...(Vs), otherwise
`static_cast<difference_type>(1)`;

(7.2) — *scaled-distance*(*N*) be the product of
`static_cast<difference_type>(std::get<`*N*>(*current_*) - std::get<*N*>(t))
and *scaled-size*(*N* + 1); and

(7.3) — *scaled-sum* be the sum of *scaled-distance*(*N*) for every
integer `0 ≤ N ≤ sizeof...(Vs)`.