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<title>Issue 1389: Compile-time rational arithmetic and overflow</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#Resolved">Resolved</a> status.</em></p>
<h3 id="1389"><a href="lwg-defects.html#1389">1389</a>. Compile-time rational arithmetic and overflow</h3>
<p><b>Section:</b> 21.5.4 <a href="https://wg21.link/ratio.arithmetic">[ratio.arithmetic]</a> <b>Status:</b> <a href="lwg-active.html#Resolved">Resolved</a>
 <b>Submitter:</b> BSI <b>Opened:</b> 2010-08-25 <b>Last modified:</b> 2016-01-28</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all other</b> <a href="lwg-index.html#ratio.arithmetic">issues</a> in [ratio.arithmetic].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#Resolved">Resolved</a> status.</p>
<p><b>Discussion:</b></p>
<p><b>Addresses GB-89</b></p>
<p>
The alias representations of the <code>ratio</code> arithmetic templates
do not allow implementations to avoid overflow, since they
explicitly specify the form of the aliased template
instantiation. For example
<code>ratio_multiply</code>, <code>ratio&lt;2, LLONG_MAX&gt;</code> is <em>required</em> to
alias <code>ratio&lt;2*LLONG_MAX, LLONG_MAX*2&gt;</code>, which
overflows, so is ill-formed. However, this is trivially equal
to <code>ratio&lt;1, 1&gt;</code>. It also contradicts the opening statement of
21.5.4 <a href="https://wg21.link/ratio.arithmetic">[ratio.arithmetic]</a> p. 1 "implementations may use other algorithms to
compute these values".
</p>

<p><i>[
2010-10-25 Daniel adds:
]</i></p>


<blockquote><p>
Accepting <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3131.html">n3131</a> would solve this issue.
</p></blockquote>

<p><i>[Batavia: Resolved by accepting
<a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2010/n3210.pdf">n3210</a>.]</i></p>




<p id="res-1389"><b>Proposed resolution:</b></p>
<p>Change the wording in 21.5.4 <a href="https://wg21.link/ratio.arithmetic">[ratio.arithmetic]</a> p. 2-5 as follows:</p>
<blockquote><pre>
template &lt;class R1, class R2&gt; using ratio_add = <em>see below</em>;
</pre><blockquote><p>
2 The type <code>ratio_add&lt;R1, R2&gt;</code> shall be a synonym for <del><code>ratio&lt;T1, T2&gt;</code></del>
<ins><code>ratio&lt;U, V&gt;</code> such that <code>ratio&lt;U, V&gt;::num</code> and <code>ratio&lt;U, V&gt;::den</code> 
are the same as the corresponding members of <code>ratio&lt;T1, T2&gt;</code> would be in the absence of 
arithmetic overflow</ins> where <code>T1</code> has the value <code>R1::num * R2::den + R2::num * R1::den</code> 
and <code>T2</code> has the value <code>R1::den * R2::den</code>. <ins>If the required values of <code>ratio&lt;U, V&gt;::num</code> 
and <code>ratio&lt;U, V&gt;::den</code> cannot be represented in <code>intmax_t</code> then the program is ill-formed.</ins>
</p></blockquote></blockquote>
<blockquote><pre>
template &lt;class R1, class R2&gt; using ratio_subtract = <em>see below</em>;
</pre><blockquote><p>
3 The type <code>ratio_subtract&lt;R1, R2&gt;</code> shall be a synonym for <del><code>ratio&lt;T1, T2&gt;</code></del>
<ins><code>ratio&lt;U, V&gt;</code> such that <code>ratio&lt;U, V&gt;::num</code> and <code>ratio&lt;U, V&gt;::den</code> 
are the same as the corresponding members of <code>ratio&lt;T1, T2&gt;</code> would be in the absence of 
arithmetic overflow</ins> where <code>T1</code> has the value <code>R1::num * R2::den - R2::num * R1::den</code> 
and <code>T2</code> has the value <code>R1::den * R2::den</code>. <ins>If the required values of <code>ratio&lt;U, V&gt;::num</code> 
and <code>ratio&lt;U, V&gt;::den</code> cannot be represented in <code>intmax_t</code> then the program is ill-formed.</ins>
</p></blockquote></blockquote>
<blockquote><pre>
template &lt;class R1, class R2&gt; using ratio_multiply = <em>see below</em>;
</pre><blockquote><p>
4 The type <code>ratio_multiply&lt;R1, R2&gt;</code> shall be a synonym for <del><code>ratio&lt;T1, T2&gt;</code></del>
<ins><code>ratio&lt;U, V&gt;</code> such that <code>ratio&lt;U, V&gt;::num</code> and <code>ratio&lt;U, V&gt;::den</code> 
are the same as the corresponding members of <code>ratio&lt;T1, T2&gt;</code> would be in the absence of 
arithmetic overflow</ins> where <code>T1</code> has the value <code>R1::num * R2::num</code> and <code>T2</code> 
has the value <code>R1::den * R2::den</code>. <ins>If the required values of <code>ratio&lt;U, V&gt;::num</code> 
and <code>ratio&lt;U, V&gt;::den</code> cannot be represented in <code>intmax_t</code> then the program is ill-formed.</ins>
</p></blockquote></blockquote>
<blockquote><pre>
template &lt;class R1, class R2&gt; using ratio_divide = <em>see below</em>;
</pre><blockquote><p>
5 The type <code>ratio_divide&lt;R1, R2&gt;</code> shall be a synonym for <del><code>ratio&lt;T1, T2&gt;</code></del>
<ins><code>ratio&lt;U, V&gt;</code> such that <code>ratio&lt;U, V&gt;::num</code> and <code>ratio&lt;U, V&gt;::den</code> 
are the same as the corresponding members of <code>ratio&lt;T1, T2&gt;</code> would be in the absence of 
arithmetic overflow</ins> where <code>T1</code> has the value <code>R1::num * R2::den</code> and <code>T2</code> 
has the value <code>R1::den * R2::num</code>. <ins>If the required values of <code>ratio&lt;U, V&gt;::num</code> 
and <code>ratio&lt;U, V&gt;::den</code> cannot be represented in <code>intmax_t</code> then the program is ill-formed.</ins>
</p></blockquote></blockquote>





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