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<title>Numeric&lt;T&gt;</title>
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<td><h2>Safe Numerics</h2></td>
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<div class="titlepage"><div><div><h3 class="title">
<a name="safe_numerics.numeric"></a>Numeric&lt;T&gt;</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="numeric.html#safe_numerics.numeric.description">Description</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130204085440">Notation</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130204078192">Associated Types</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130204072896">Valid Expressions</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130203973088">Models</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130203971280">Header</a></span></dt>
<dt><span class="section"><a href="numeric.html#idm130203969088">Note on Usage of <code class="computeroutput">std::numeric_limits</code></a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="safe_numerics.numeric.description"></a>Description</h4></div></div></div>
<p>A type is Numeric if it has the properties of a number.</p>
<p>More specifically, a type T is Numeric if there exists a
    specialization of <code class="computeroutput">std::numeric_limits&lt;T&gt;</code>. See the
    documentation for the standard library class <code class="computeroutput">numeric_limits</code>.
    The standard library includes such specializations for all the built-in
    numeric types. Note that this concept is distinct from the C++ standard
    library type traits <code class="computeroutput">is_integral</code> and
    <code class="computeroutput">is_arithmetic</code>. These latter fulfill the requirement of the
    concept Numeric. But there are types T which fulfill this concept for
    which <code class="computeroutput">is_arithmetic&lt;T&gt;::value == false</code>. For example see
    <code class="computeroutput">safe_signed_integer&lt;int&gt;</code>.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130204085440"></a>Notation</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col align="left">
<col align="left">
</colgroup>
<tbody>
<tr>
<td align="left"><code class="computeroutput">T, U, V</code></td>
<td align="left">A type that is a model of Numeric</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t, u</code></td>
<td align="left">An object of a type modeling Numeric</td>
</tr>
</tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130204078192"></a>Associated Types</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col align="left">
<col align="left">
</colgroup>
<tbody><tr>
<td align="left"><code class="computeroutput">std::numeric_limits&lt;T&gt;</code></td>
<td align="left">The numeric_limits class template provides a C++ program
            with information about various properties of the implementation's
            representation of the arithmetic types. See C++ standard
            18.3.2.2.</td>
</tr></tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130204072896"></a>Valid Expressions</h4></div></div></div>
<p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/Assignable.html" target="_top">Assignable</a> the
    following expressions must be valid. Any operations which result in
    integers which cannot be represented as some Numeric type will throw an
    exception.</p>
<div class="table">
<a name="idm130204071072"></a><p class="title"><b>Table&#160;1.&#160;General</b></p>
<div class="table-contents"><table class="table" summary="General">
<colgroup>
<col align="left">
<col align="left">
<col align="left">
</colgroup>
<thead><tr>
<th align="left">Expression</th>
<th align="left">Return Type</th>
<th align="left">Return Value</th>
</tr></thead>
<tbody>
<tr>
<td align="left"><code class="computeroutput">std::numeric_limits&lt;T&gt;::is_bounded
              </code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">std::numeric_limits&lt;T&gt;::is_integer</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">std::numeric_limits&lt;T&gt;::is_signed</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">std::numeric_limits&lt;T&gt;::is_specialized
              </code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left"><code class="computeroutput">true</code></td>
</tr>
</tbody>
</table></div>
</div>
<p><br class="table-break"></p>
<div class="table">
<a name="idm130204050048"></a><p class="title"><b>Table&#160;2.&#160;Unary Operators</b></p>
<div class="table-contents"><table class="table" summary="Unary Operators">
<colgroup>
<col align="left">
<col align="left">
<col align="left">
</colgroup>
<thead><tr>
<th align="left">Expression</th>
<th align="left">Return Type</th>
<th align="left">Semantics</th>
</tr></thead>
<tbody>
<tr>
<td align="left"><code class="computeroutput">-t</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">Invert sign</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">+t</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">unary plus - a no op</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t--</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">post decrement</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t++</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">post increment</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">--t</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">pre decrement</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">++t</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">pre increment</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="idm130204029296"></a><p class="title"><b>Table&#160;3.&#160;Binary Operators</b></p>
<div class="table-contents"><table class="table" summary="Binary Operators">
<colgroup>
<col align="left">
<col align="left">
<col align="left">
</colgroup>
<thead><tr>
<th align="left">Expression</th>
<th align="left">Return Type</th>
<th align="left">Semantics</th>
</tr></thead>
<tbody>
<tr>
<td align="left"><code class="computeroutput">t - u</code></td>
<td align="left"><code class="computeroutput">V</code></td>
<td align="left">subtract u from t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t + u</code></td>
<td align="left"><code class="computeroutput">V</code></td>
<td align="left">add u to t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t * u</code></td>
<td align="left"><code class="computeroutput">V</code></td>
<td align="left">multiply t by u</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t / u</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">divide t by u</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t % u</code></td>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">t modulus u</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t &lt; u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t less than u, <code class="computeroutput">false</code>
            otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t &lt;= u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t less than or equal to u,
            <code class="computeroutput">false</code> otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t &gt; u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t greater than u, <code class="computeroutput">false</code>
            otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t &gt;= u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t greater than or equal to u,
            <code class="computeroutput">false</code> otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t == u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t equal to u, <code class="computeroutput">false</code>
            otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t != u</code></td>
<td align="left"><code class="computeroutput">bool</code></td>
<td align="left">
<code class="computeroutput">true</code> if t not equal to u, <code class="computeroutput">false</code>
            otherwise</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t = u</code></td>
<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
<td align="left">assign value of u to t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t += u</code></td>
<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
<td align="left">add u to t and assign to t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t -= u</code></td>
<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
<td align="left">subtract u from t and assign to t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t *= u</code></td>
<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
<td align="left">multiply t by u and assign to t</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">t /= u</code></td>
<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
<td align="left">divide t by u and assign to t</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203973088"></a>Models</h4></div></div></div>
<p><code class="computeroutput">int, float, safe_signed_integer&lt;int&gt;,
    safe_signed_range&lt;int&gt;, checked_result&lt;int&gt;,
    etc.</code></p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203971280"></a>Header</h4></div></div></div>
<p><a href="../../include/concept/numeric.hpp" target="_top"><code class="computeroutput">#include
    &lt;boost/numeric/safe_numerics/concepts/numeric.hpp&gt;
    </code></a></p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203969088"></a>Note on Usage of <code class="computeroutput">std::numeric_limits</code>
</h4></div></div></div>
<p>We define the word "Numeric" in terms of the operations which are
    supported by "Numeric" types. This is in line with the current and
    historical usage of the word "concept" in the context of C++. It is also
    common to define compile time predicates such as
    "<code class="computeroutput">is_numeric&lt;T&gt;</code>" to permit one to include expressions in
    his code which will generated a compile time error if the specified type
    (T) does not support the operations required. But this is not always true.
    In the C++ standard library there is a predicate
    <code class="computeroutput">is_arithmetic&lt;T&gt;</code> whose name might suggest that it
    should return <code class="computeroutput">true</code> for any type which supports the operations
    above. But this is not the case. The standard defines
    <code class="computeroutput">is_arithmetic&lt;T&gt;</code> as <code class="computeroutput">true</code> for any of the
    builtin types <code class="computeroutput">int</code>, <code class="computeroutput">long</code>, <code class="computeroutput">float</code>,
    <code class="computeroutput">double</code>, etc and <code class="computeroutput">false</code> for any other types. So
    even if a user defined type U were to support the operations above,
    <code class="computeroutput">is_arithmetic&lt;U&gt;</code> would still return <code class="computeroutput">false</code>.
    This is quite unintuitive and not a good match for our purposes. Hence we
    define our own term "Numeric" to designate any type T which:</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem"><p>Supports the operations above</p></li>
<li class="listitem"><p>Specializes the standard type numeric_limits</p></li>
</ul></div>
<p>while following the C++ standard in using
    <code class="computeroutput">is_arithmetic&lt;T&gt;</code>, <code class="computeroutput">is_integral&lt;T&gt;</code> to
    detect specific types only. The standard types are useful in various
    aspects of the implementation - which of course is done in terms of the
    standard types.</p>
<p>This in turn raises another question: Is it "legal" to specialize
    <code class="computeroutput">std::numeric_limits</code> for one's own types such as
    <code class="computeroutput">safe&lt;int&gt;</code>. In my view the standard is ambiguous on
    this. See various interpretations: </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem"><p><a href="https://stackoverflow.com/questions/16122912/is-it-ok-to-specialize-stdnumeric-limitst-for-user-defined-number-like-class" target="_top">is-it-ok-to-specialize-stdnumeric-limitst-for-user-defined-number-like-class</a></p></li>
<li class="listitem"><p><a href="https://en.cppreference.com/w/cpp/types/numeric_limits" target="_top">cppreference.com/w/cpp/types/numeric_limits</a></p></li>
</ul></div>
<p>In any case, it seems pretty clear that no harm will come of it. In
    spite of the consideration given to this issue, it turns out that the
    found no real need to implement these predicates. For example, there is no
    "is_numeric&lt;T&gt;" implemented as part of the safe numerics library.
    This may change in the future though. Even if not used, defining and
    maintaining these type requirements in this document has been very
    valuable in keeping the concepts and code more unified and
    understandable.</p>
<p>Remember that above considerations apply to other numeric types used
    in this library even though we don't explicitly repeat this information
    for every case.</p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2012-2018 Robert Ramey<p><a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Subject to Boost
      Software License</a></p>
</div></td>
</tr></table>
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