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372 lines
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HTML
<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
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<title>Numeric<T></title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="home" href="index.html" title="Safe Numerics">
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<link rel="up" href="concepts.html" title="Type Requirements">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img href="index.html" height="164px" src="pre-boost.jpg" alt="Library Documentation Index"></td>
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<td><h2>Safe Numerics</h2></td>
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</tr></table>
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<div class="spirit-nav">
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<a accesskey="p" href="concepts.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="concepts.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="integer.html"><img src="images/next.png" alt="Next"></a>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="safe_numerics.numeric"></a>Numeric<T></h3></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="numeric.html#safe_numerics.numeric.description">Description</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720767520">Notation</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720760272">Associated Types</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720754976">Valid Expressions</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720655392">Models</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720653584">Header</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm488720651392">Note on Usage of <code class="computeroutput">std::numeric_limits</code></a></span></dt>
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</dl></div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="safe_numerics.numeric.description"></a>Description</h4></div></div></div>
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<p>A type is Numeric if it has the properties of a number.</p>
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<p>More specifically, a type T is Numeric if there exists a
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specialization of <code class="computeroutput">std::numeric_limits<T></code>. See the
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documentation for the standard library class <code class="computeroutput">numeric_limits</code>.
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The standard library includes such specializations for all the built-in
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numeric types. Note that this concept is distinct from the C++ standard
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library type traits <code class="computeroutput">is_integral</code> and
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<code class="computeroutput">is_arithmetic</code>. These latter fulfill the requirement of the
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concept Numeric. But there are types T which fulfill this concept for
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which <code class="computeroutput">is_arithmetic<T>::value == false</code>. For example see
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<code class="computeroutput">safe_signed_integer<int></code>.</p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720767520"></a>Notation</h4></div></div></div>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col align="left">
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<col align="left">
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</colgroup>
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<tbody>
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<tr>
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<td align="left"><code class="computeroutput">T, U, V</code></td>
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<td align="left">A type that is a model of Numeric</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t, u</code></td>
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<td align="left">An object of a type modeling Numeric</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720760272"></a>Associated Types</h4></div></div></div>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col align="left">
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<col align="left">
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</colgroup>
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<tbody><tr>
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<td align="left"><code class="computeroutput">std::numeric_limits<T></code></td>
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<td align="left">The numeric_limits class template provides a C++ program
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with information about various properties of the implementation's
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representation of the arithmetic types. See C++ standard
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18.3.2.2.</td>
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</tr></tbody>
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</table></div>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720754976"></a>Valid Expressions</h4></div></div></div>
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<p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/Assignable.html" target="_top">Assignable</a> the
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following expressions must be valid. Any operations which result in
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integers which cannot be represented as some Numeric type will throw an
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exception.</p>
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<div class="table">
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<a name="idm488720753152"></a><p class="title"><b>Table 1. General</b></p>
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<div class="table-contents"><table class="table" summary="General">
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<colgroup>
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<col align="left">
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<col align="left">
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<col align="left">
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</colgroup>
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<thead><tr>
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<th align="left">Expression</th>
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<th align="left">Return Type</th>
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<th align="left">Return Value</th>
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</tr></thead>
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<tbody>
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<tr>
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<td align="left"><code class="computeroutput">std::numeric_limits<T>::is_bounded
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</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
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</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">std::numeric_limits<T>::is_integer</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
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</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">std::numeric_limits<T>::is_signed</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> or <code class="computeroutput">false</code>
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</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">std::numeric_limits<T>::is_specialized
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</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left"><code class="computeroutput">true</code></td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<p><br class="table-break"></p>
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<div class="table">
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<a name="idm488720732288"></a><p class="title"><b>Table 2. Unary Operators</b></p>
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<div class="table-contents"><table class="table" summary="Unary Operators">
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<colgroup>
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<col align="left">
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<col align="left">
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<col align="left">
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</colgroup>
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<thead><tr>
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<th align="left">Expression</th>
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<th align="left">Return Type</th>
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<th align="left">Semantics</th>
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</tr></thead>
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<tbody>
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<tr>
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<td align="left"><code class="computeroutput">-t</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">Invert sign</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">+t</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">unary plus - a no op</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t--</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">post decrement</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t++</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">post increment</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">--t</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">pre decrement</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">++t</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">pre increment</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<br class="table-break"><div class="table">
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<a name="idm488720711568"></a><p class="title"><b>Table 3. Binary Operators</b></p>
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<div class="table-contents"><table class="table" summary="Binary Operators">
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<colgroup>
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<col align="left">
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<col align="left">
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<col align="left">
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</colgroup>
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<thead><tr>
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<th align="left">Expression</th>
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<th align="left">Return Type</th>
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<th align="left">Semantics</th>
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</tr></thead>
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<tbody>
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<tr>
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<td align="left"><code class="computeroutput">t - u</code></td>
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<td align="left"><code class="computeroutput">V</code></td>
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<td align="left">subtract u from t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t + u</code></td>
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<td align="left"><code class="computeroutput">V</code></td>
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<td align="left">add u to t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t * u</code></td>
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<td align="left"><code class="computeroutput">V</code></td>
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<td align="left">multiply t by u</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t / u</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">divide t by u</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t % u</code></td>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">t modulus u</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t < u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t less than u, <code class="computeroutput">false</code>
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otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t <= u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t less than or equal to u,
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<code class="computeroutput">false</code> otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t > u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t greater than u, <code class="computeroutput">false</code>
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otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t >= u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t greater than or equal to u,
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<code class="computeroutput">false</code> otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t == u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t equal to u, <code class="computeroutput">false</code>
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otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t != u</code></td>
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<td align="left"><code class="computeroutput">bool</code></td>
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<td align="left">
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<code class="computeroutput">true</code> if t not equal to u, <code class="computeroutput">false</code>
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otherwise</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t = u</code></td>
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<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
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<td align="left">assign value of u to t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t += u</code></td>
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<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
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<td align="left">add u to t and assign to t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t -= u</code></td>
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<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
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<td align="left">subtract u from t and assign to t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t *= u</code></td>
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<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
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<td align="left">multiply t by u and assign to t</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t /= u</code></td>
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<td align="left"><code class="computeroutput"><code class="computeroutput">T</code></code></td>
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<td align="left">divide t by u and assign to t</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<br class="table-break">
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720655392"></a>Models</h4></div></div></div>
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<p><code class="computeroutput">int, float, safe_signed_integer<int>,
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safe_signed_range<int>, checked_result<int>,
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etc.</code></p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720653584"></a>Header</h4></div></div></div>
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<p><a href="../../include/boost/safe_numerics/concept/numeric.hpp" target="_top"><code class="computeroutput">#include
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<boost/safe_numerics/concepts/numeric.hpp> </code></a></p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h4 class="title">
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<a name="idm488720651392"></a>Note on Usage of <code class="computeroutput">std::numeric_limits</code>
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</h4></div></div></div>
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<p>We define the word "Numeric" in terms of the operations which are
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supported by "Numeric" types. This is in line with the current and
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historical usage of the word "concept" in the context of C++. It is also
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common to define compile time predicates such as
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"<code class="computeroutput">is_numeric<T></code>" to permit one to include expressions in
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his code which will generated a compile time error if the specified type
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(T) does not support the operations required. But this is not always true.
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In the C++ standard library there is a predicate
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<code class="computeroutput">is_arithmetic<T></code> whose name might suggest that it
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should return <code class="computeroutput">true</code> for any type which supports the operations
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above. But this is not the case. The standard defines
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<code class="computeroutput">is_arithmetic<T></code> as <code class="computeroutput">true</code> for any of the
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builtin types <code class="computeroutput">int</code>, <code class="computeroutput">long</code>, <code class="computeroutput">float</code>,
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<code class="computeroutput">double</code>, etc and <code class="computeroutput">false</code> for any other types. So
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even if a user defined type U were to support the operations above,
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<code class="computeroutput">is_arithmetic<U></code> would still return <code class="computeroutput">false</code>.
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This is quite unintuitive and not a good match for our purposes. Hence we
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define our own term "Numeric" to designate any type T which:</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem"><p>Supports the operations above</p></li>
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<li class="listitem"><p>Specializes the standard type numeric_limits</p></li>
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</ul></div>
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<p>while following the C++ standard in using
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<code class="computeroutput">is_arithmetic<T></code>, <code class="computeroutput">is_integral<T></code> to
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detect specific types only. The standard types are useful in various
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aspects of the implementation - which of course is done in terms of the
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standard types.</p>
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<p>This in turn raises another question: Is it "legal" to specialize
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<code class="computeroutput">std::numeric_limits</code> for one's own types such as
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<code class="computeroutput">safe<int></code>. In my view the standard is ambiguous on
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this. See various interpretations: </p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<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>
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<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>
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</ul></div>
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<p>In any case, it seems pretty clear that no harm will come of it. In
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spite of the consideration given to this issue, it turns out that the
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found no real need to implement these predicates. For example, there is no
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"is_numeric<T>" implemented as part of the safe numerics library.
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This may change in the future though. Even if not used, defining and
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maintaining these type requirements in this document has been very
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valuable in keeping the concepts and code more unified and
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understandable.</p>
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<p>Remember that above considerations apply to other numeric types used
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in this library even though we don't explicitly repeat this information
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for every case.</p>
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</div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2012-2018 Robert Ramey<p><a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Subject to Boost
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Software License</a></p>
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</div></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="concepts.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="concepts.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="integer.html"><img src="images/next.png" alt="Next"></a>
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