mirror of
https://github.com/boostorg/safe_numerics.git
synced 2026-02-09 11:22:23 +00:00
1bc0b94e65
a) made trap_exception work b) updated manual and examples to show how to use library to eliminate runtime penalty c) added in safe_literal d) made corrections of various types
366 lines
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366 lines
13 KiB
HTML
<html>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>Numeric<T></title>
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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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<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>
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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>
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<dt><span class="section"><a href="numeric.html#idm473861967648">Description</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm473861962416">Notation</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm473861952624">Associated Types</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm473861947552">Valid Expressions</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm473861856208">Header</a></span></dt>
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<dt><span class="section"><a href="numeric.html#idm473861854208">Models</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="idm473861967648"></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
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specialization of <code class="computeroutput">std::numeric_limits<T></code>. See the
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documentation for standard library class numeric_limits. The standard
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library includes such specializations for all the primitive numeric types.
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Note that this concept is distinct from the C++ standard library type
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traits <code class="computeroutput">is_integral</code> and <code class="computeroutput">is_arithmetic</code>. These
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latter fulfill the requirement of the concept Numeric. But there are types
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T which fulfill this concept for which <code class="computeroutput">is_arithmetic<T>::value
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== 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="idm473861962416"></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 the 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 type modeling Numeric</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">os</code></td>
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<td align="left">An object of type std::base_ostreami</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">is</code></td>
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<td align="left">An object of type std::base_istream</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="idm473861952624"></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="idm473861947552"></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="idm473861945872"></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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</colgroup>
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<thead><tr>
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<th align="left">Expression</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">true</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">true</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput"><td align="left">os << T</td></code></td>
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<td align="left">os &i</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput"><td align="left">is >> T</td></code></td>
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<td align="left">is &</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="idm473861934064"></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">T</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">T</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">T</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">T</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">T</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">T</td>
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<td align="left">pre increment</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">~</code></td>
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<td align="left">T</td>
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<td align="left">complement</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="idm473861915280"></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">V</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">V</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">V</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">T</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">T</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">T</td>
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<td align="left">shift t left u bits</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">T</td>
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<td align="left">shift t right by u bits</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">bool</td>
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<td align="left">true if t less than u, false 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">bool</td>
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<td align="left">true if t less than or equal to u, false 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">bool</td>
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<td align="left">true if t greater than u, false 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">bool</td>
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<td align="left">true if t greater than or equal to u, false
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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">bool</td>
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<td align="left">true if t equal to u, false 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">bool</td>
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<td align="left">true if t not equal to u, false 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">V</td>
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<td align="left">and of t and u padded out max # bits in t, 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">V</td>
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<td align="left">or of t and u padded out max # bits in t, 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">V</td>
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<td align="left">exclusive or of t and u padded out max # bits in t,
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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">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">T</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">T</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">T</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">T</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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<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">and t with 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">T</td>
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<td align="left">left shift the value of t by u bits</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">T</td>
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<td align="left">right shift the value of t by u bits</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">T</td>
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<td align="left">and the value of t with 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">T</td>
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<td align="left">or the value of t with 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">T</td>
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<td align="left">exclusive or the value of t with 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="idm473861856208"></a>Header</h4></div></div></div>
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<p><a href="../../include/concept/numeric.hpp" target="_top"><code class="computeroutput">#include
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<safe_numerics/include/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="idm473861854208"></a>Models</h4></div></div></div>
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<p><code class="computeroutput">int, safe_signed_integer<int>,
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safe_signed_range<int>, etc.</code></p>
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<p>The definition of this concept</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 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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</html>
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