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<title>Issue 2792: [fund.ts.v2] gcd and lcm should support a wider range of input values</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#TS">TS</a> status.</em></p>
<h3 id="2792"><a href="lwg-defects.html#2792">2792</a>. [fund.ts.v2] <code>gcd</code> and <code>lcm</code> should support a wider range of input values</h3>
<p><b>Section:</b> 13.1.2 <a href="https://cplusplus.github.io/fundamentals-ts/v2.html#numeric.ops.gcd">[fund.ts.v2::numeric.ops.gcd]</a>, 13.1.3 <a href="https://cplusplus.github.io/fundamentals-ts/v2.html#numeric.ops.lcm">[fund.ts.v2::numeric.ops.lcm]</a> <b>Status:</b> <a href="lwg-active.html#TS">TS</a>
 <b>Submitter:</b> Marshall Clow <b>Opened:</b> 2016-11-09 <b>Last modified:</b> 2020-09-06</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all other</b> <a href="lwg-index.html#fund.ts.v2::numeric.ops.gcd">issues</a> in [fund.ts.v2::numeric.ops.gcd].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#TS">TS</a> status.</p>
<p><b>Discussion:</b></p>
<p>
<b>Addresses fund.ts.v2: JP 010, JP 011</b>
<p/>
By the current definition, <code>gcd((int64_t)1234, (int32_t)-2147483648)</code> is 
ill-formed (because <code>2147483648</code> is not representable as a value of <code>int32_t</code>.)
We want to change this case to be well-formed. As long as both <code>|m|</code> and <code>|n|</code> 
are representable as values of the common type, absolute values can 
be calculate <code>d</code> without causing unspecified behavior, by converting <code>m</code> and <code>n</code> 
to the common type before taking the negation.
<p/>
Suggested resolution:
</p>
<blockquote><p>
<del><code>|m|</code> shall be representable as a value of type <code>M</code> and <code>|n|</code> shall 
be representable as a value of type <code>N</code></del><ins><code>|m|</code> and <code>|n|</code> shall be 
representable as a value of <code>common_type_t&lt;M, N&gt;</code></ins>.
</p></blockquote>

<p><i>[Issues Telecon 16-Dec-2016]</i></p>

<p>Resolved by N4616</p>


<p id="res-2792"><b>Proposed resolution:</b></p>
<p>This wording is relative to <a href="https://wg21.link/n4600">N4600</a>.</p>

<ol>
<li><p>Edit 13.1.2 <a href="https://cplusplus.github.io/fundamentals-ts/v2.html#numeric.ops.gcd">[fund.ts.v2::numeric.ops.gcd]</a> as indicated:</p>
<blockquote>
<pre>
template&lt;class M, class N&gt;
  constexpr common_type_t&lt;M, N&gt; gcd(M m, N n);
</pre>
<blockquote>
<p>
-2- <i>Requires:</i> <del><code>|m|</code> shall be representable as a value of type <code>M</code> and <code>|n|</code> shall 
be representable as a value of type <code>N</code></del><ins><code>|m|</code> and <code>|n|</code> shall be representable as 
a value of <code>common_type_t&lt;M, N&gt;</code></ins>. [<i>Note:</i> These requirements ensure, for example, that 
<code>gcd(m, m) = |m|</code> is representable as a value of type <code>M</code>. &mdash; <i>end note</i>] 
</p>
</blockquote>
</blockquote>
</li>

<li><p>Edit 13.1.3 <a href="https://cplusplus.github.io/fundamentals-ts/v2.html#numeric.ops.lcm">[fund.ts.v2::numeric.ops.lcm]</a> as indicated:</p>
<blockquote>
<pre>
template&lt;class M, class N&gt;
  constexpr common_type_t&lt;M, N&gt; lcm(M m, N n);
</pre>
<blockquote>
<p>
-2- <i>Requires:</i> <del><code>|m|</code> shall be representable as a value of type <code>M</code> and <code>|n|</code> shall 
be representable as a value of type <code>N</code></del><ins><code>|m|</code> and <code>|n|</code> shall be representable as 
a value of <code>common_type_t&lt;M, N&gt;</code></ins>. The least common multiple of <code>|m|</code> and <code>|n|</code> shall 
be representable as a value of type <code>common_type_t&lt;M, N&gt;</code>.
</p>
</blockquote>
</blockquote>
</li>
</ol>






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