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223 lines
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<html>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>SafeNumeric<T></title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
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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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<a accesskey="p" href="integer.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="promotion_policy.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.safe_numeric_concept"></a>SafeNumeric<T></h3></div></div></div>
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<div class="toc"><dl>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041753872">Description</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041752480">Refinement of</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041750976">Notation</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041735120">Valid Expressions</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041705392">Complexity Guarantees</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041704080">Invariants</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041702496">Header</a></span></dt>
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<dt><span class="section"><a href="safe_numeric_concept.html#idm531041700384">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="idm531041753872"></a>Description</h4></div></div></div>
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<p>This holds an arithmetic value which can be used as a replacement
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for built-in C++ arithmetic values. These types differ from their built-in
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counter parts in that the are guaranteed not to produce invalid arithmetic
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results.</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="idm531041752480"></a>Refinement of</h4></div></div></div>
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<p><a class="link" href="numeric.html" title="Numeric<T>">Numeric</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="idm531041750976"></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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<thead><tr>
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<th align="left">Symbol</th>
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<th align="left">Description</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">Types fulfilling <a class="link" href="numeric.html" title="Numeric<T>">Numeric</a> type
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requirements</td>
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</tr>
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<tr>
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<td align="left">t, u</td>
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<td align="left">objects of types T, U</td>
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</tr>
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<tr>
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<td align="left">S</td>
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<td align="left">A type fulfilling SafeNumeric type requirements</td>
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</tr>
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<tr>
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<td align="left">s, s1, s2</td>
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<td align="left">objects of types S</td>
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</tr>
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<tr>
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<td align="left">op</td>
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<td align="left">C++ infix operator</td>
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</tr>
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<tr>
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<td align="left">prefix_op</td>
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<td align="left">C++ prefix operator</td>
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</tr>
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<tr>
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<td align="left">postfix_op</td>
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<td align="left">C++ postfix operator</td>
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</tr>
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<tr>
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<td align="left">assign_op</td>
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<td align="left">C++ assignment operator</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="idm531041735120"></a>Valid Expressions</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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<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">Result Type</th>
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<th align="left">Description</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">s op u</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">t op s</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">s1 op s2</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">s1 assign_op s2</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">prefix_op S</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">S postfix_op</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>invoke safe C++ operator op and return another
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SafeNumeric type</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">S(t)</code></td>
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<td align="left">unspecified S</td>
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<td align="left"><p>construct a instance of S from a value
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t</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">S</code></td>
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<td align="left">S</td>
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<td align="left"><p>construct a uninitialized instance of
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S</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">is_safe<S></code></td>
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<td align="left">std::true_type or std::false_type</td>
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<td align="left"><p>type trait to query whether any type T fulfills the
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requirements for a SafeNumeric type.</p></td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">static_cast<T>(s)</code></td>
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<td align="left">T</td>
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<td align="left"><p>convert the value of s to type T. If the value of s
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cannot be correctly represented as a type T, it is an
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error.</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>The key fact documented in the above table is that the result of any
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binary operation where one or both of the operands is a SafeNumeric type
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is also a SafeNumeric type. Also note that all the expressions in the
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above table are <code class="computeroutput">constexpr</code> expressions. So that if they are
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invoked with constant values, the result will be available a compile
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time.</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="idm531041705392"></a>Complexity Guarantees</h4></div></div></div>
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<p>There are no explicit complexity guarantees here. However, it would
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be very surprising if any implementation were to be more complex that
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O(0);</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="idm531041704080"></a>Invariants</h4></div></div></div>
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<p>The fundamental requirement of a SafeNumeric type is that implements
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all C++ operations permitted on it's base type in a way the prevents the
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return of an incorrect arithmetic result. Various implementations of this
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concept may handle circumstances which produce such results differently (
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throw exception, compile time trap, etc..) no implementation should return
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an arithmetically incorrect result.</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="idm531041702496"></a>Header</h4></div></div></div>
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<p><a href="../../include/concept/exception_policy.hpp" target="_top"><code class="computeroutput">#include
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<safe_numerics/include/concepts/safe_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="idm531041700384"></a>Models</h4></div></div></div>
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<p>boost::numeric::safe<T></p>
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<p>boost::numeric::safe_signed_range<-11, 11></p>
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<p>boost::numeric::safe_unsigned_range<0, 11></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="integer.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="promotion_policy.html"><img src="images/next.png" alt="Next"></a>
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