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<title>Issue 613: max_digits10 missing from numeric_limits</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#CD1">CD1</a> status.</em></p>
<h3 id="613"><a href="lwg-defects.html#613">613</a>. max_digits10 missing from numeric_limits</h3>
<p><b>Section:</b> 17.3.5.3 <a href="https://wg21.link/numeric.special">[numeric.special]</a> <b>Status:</b> <a href="lwg-active.html#CD1">CD1</a>
 <b>Submitter:</b> Bo Persson <b>Opened:</b> 2006-11-20 <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#numeric.special">issues</a> in [numeric.special].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#CD1">CD1</a> status.</p>
<p><b>Discussion:</b></p>
<p>
Section 17.3.5.3 <a href="https://wg21.link/numeric.special">[numeric.special]</a> starts out by saying that "All members shall be provided 
for all specializations."
</p>
<p>
Then it goes on to show specializations for float and bool, where one member 
is missing (max_digits10).
</p>

<p>
Maarten Kronenburg adds:
</p>

<p>
I agree, just adding the comment that the exact number of decimal digits
is digits * ln(radix) / ln(10), where probably this real number is
rounded downward for digits10, and rounded upward for max_digits10
(when radix=10, then digits10=max_digits10).
Why not add this exact definition also to the standard, so the user
knows what these numbers exactly mean.
</p>

<p>
Howard adds:
</p>

<p>
For reference, here are the correct formulas from
<a href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1822.pdf">N1822</a>:
</p>

<blockquote><pre>
digits10 = floor((digits-1) * log10(2))
max_digits10 = ceil((1 + digits) * log10(2))
</pre></blockquote>

<p>
We are also missing a statement regarding for what specializations this member has meaning.
</p>



<p id="res-613"><b>Proposed resolution:</b></p>
<p>
Change and add after 17.3.5.2 <a href="https://wg21.link/numeric.limits.members">[numeric.limits.members]</a>, p11:
</p>

<blockquote>
<pre>static const int max_digits10;</pre>
<blockquote>
<p>
-11- Number of base 10 digits required to ensure that values which
differ <del>by only one epsilon</del> are always differentiated.
</p>
<p><ins>
-12- Meaningful for all floating point types.
</ins></p>
</blockquote>
</blockquote>

<p>
Change 17.3.5.3 <a href="https://wg21.link/numeric.special">[numeric.special]</a>, p2:
</p>

<blockquote><pre>
template&lt;&gt; class numeric_limits&lt;float&gt; { 
public: 
  static const bool is_specialized = true; 
  ...
  static const int digits10 = 6;
  <ins>static const int max_digits10 = 9</ins>;
  ...
</pre></blockquote>

<p>
Change 17.3.5.3 <a href="https://wg21.link/numeric.special">[numeric.special]</a>, p3:
</p>

<blockquote><pre>
template&lt;&gt; class numeric_limits&lt;bool&gt; { 
public: 
  static const bool is_specialized = true; 
  ...
  static const int digits10 = 0;
  <ins>static const int max_digits10 = 0</ins>;
  ...
</pre></blockquote>







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