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<title>Issue 3801: cartesian_product_view::iterator::distance-from ignores the size of last underlying range</title>
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<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#C++23">C++23</a> status.</em></p>
<h3 id="3801"><a href="lwg-defects.html#3801">3801</a>. <code>cartesian_product_view::<i>iterator</i>::<i>distance-from</i></code> ignores the size of last underlying range</h3>
<p><b>Section:</b> 25.7.33.3 <a href="https://wg21.link/range.cartesian.iterator">[range.cartesian.iterator]</a> <b>Status:</b> <a href="lwg-active.html#C++23">C++23</a>
 <b>Submitter:</b> Patrick Palka <b>Opened:</b> 2022-10-25 <b>Last modified:</b> 2023-11-22</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all other</b> <a href="lwg-index.html#range.cartesian.iterator">issues</a> in [range.cartesian.iterator].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#C++23">C++23</a> status.</p>
<p><b>Discussion:</b></p>
<p>
The helper <code><i>scaled-size</i>(<i>N</i>)</code> from the wording for <a href="https://wg21.link/P2374R4" title=" views::cartesian_product">P2374R4</a>'s
<code>cartesian_product_view::<i>iterator</i>::<i>distance-from</i></code> is recursively 
specified as:
</p>
<blockquote>
<p>
Let <code><i>scaled-size</i>(<i>N</i>)</code> be the product of
<code>static_cast&lt;difference_type&gt;(ranges::size(std::get&lt;<i>N</i>&gt;(<i>parent_</i>-&gt;<i>bases_</i>)))</code>
and <code><i>scaled-size</i>(<i>N</i> + 1)</code> if <code><i>N</i> &lt; sizeof...(Vs)</code>, otherwise
<code>static_cast&lt;difference_type&gt;(1)</code>;
</p>
</blockquote>
<p>
Intuitively, <code><i>scaled-size</i>(<i>N</i>)</code> is the size of the cartesian product of all
but the first <code><i>N</i></code> underlying ranges. Thus <code><i>scaled-size</i>(sizeof...(Vs))</code> 
ought to just yield the size of the last underlying range (since there are
<code>1 + sizeof...(Vs)</code> underlying ranges), but according to this definition it
yields <code>1</code>. Similarly at the other extreme, <code><i>scaled-size</i>(0)</code> should yield
the product of the sizes of all the underlying ranges, but it instead yields that of all but 
the last underlying range.
<p/>
For <code>cartesian_product_view</code>s of two or more underlying ranges, this
causes the relevant <code>operator-</code> overloads to compute wrong distances, e.g.
</p>
<blockquote><pre>
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
</pre></blockquote>
<p>
The recursive condition should probably use <code>&lt;=</code> instead of <code>&lt;</code>.
</p>

<p><i>[2022-11-04; Reflector poll]</i></p>

<p>
Set status to Tentatively Ready after seven votes in favour during reflector poll.
</p>

<p><i>[2022-11-12 Approved at November 2022 meeting in Kona. Status changed: Voting &rarr; WP.]</i></p>



<p id="res-3801"><b>Proposed resolution:</b></p>
<p>
This wording is relative to <a href="https://wg21.link/N4917" title=" Working Draft, Standard for Programming Language C++">N4917</a>.
</p>

<ol>
<li><p>Modify  [ranges.cartesian.iterator] as indicated:</p>

<blockquote>
<pre>
template&lt;class Tuple&gt;
  constexpr difference_type <i>distance-from</i>(Tuple t);
</pre>
<blockquote>
<p>
-7- Let:
</p>
<ol style="list-style-type: none">
<li><p>(7.1) &mdash; <code><i>scaled-size</i>(<i>N</i>)</code> be the product of 
<code>static_cast&lt;difference_type&gt;(ranges::size(std::get&lt;<i>N</i>&gt;(<i>parent_</i>-&gt;<i>bases_</i>)))</code> 
and <code><i>scaled-size</i>(<i>N</i> + 1)</code> if <code><i>N</i> <ins>&le;</ins><del>&lt;</del> sizeof...(Vs)</code>, otherwise 
<code>static_cast&lt;difference_type&gt;(1)</code>;</p></li>
<li><p>(7.2) &mdash; <code><i>scaled-distance</i>(<i>N</i>)</code> be the product of 
<code>static_cast&lt;difference_type&gt;(std::get&lt;<i>N</i>&gt;(<i>current_</i>) - std::get&lt;<i>N</i>&gt;(t))</code> 
and <code><i>scaled-size</i>(<i>N</i> + 1)</code>; and</p></li>
<li><p>(7.3) &mdash; <code><i>scaled-sum</i></code> be the sum of <code><i>scaled-distance</i>(<i>N</i>)</code> for every 
integer <code>0 &le; N &le; sizeof...(Vs)</code>.</p></li>
</ol>
</blockquote>
</blockquote>
</li>

</ol>





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