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<title>safe<T, PP = boost::numeric::native, EP = boost::numeric::throw_exception></title>
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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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<div class="titlepage"><div><div><h3 class="title">
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<a name="safe_numerics.safe"></a>safe<T, PP = boost::numeric::native, EP =
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boost::numeric::throw_exception></h3></div></div></div>
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<div class="toc"><dl>
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<dt><span class="section"><a href="safe.html#idm413203968448">Description</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203966480">Notation</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203959104">Associated Types</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203952064">Template Parameters</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203934320">Model of</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203931728">Valid Expressions</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203929440">Header</a></span></dt>
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<dt><span class="section"><a href="safe.html#idm413203927328">Examples of use</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="idm413203968448"></a>Description</h4></div></div></div>
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<p>A <code class="computeroutput">safe<T, PP , EP></code> can be used anywhere a type T
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can be used. Any expression which uses this type is guaranteed to return
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an arithmetically correct value or trap in some way.</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="idm413203966480"></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><tr>
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<td align="left"><code class="computeroutput">T</code></td>
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<td align="left">Underlying type from which a safe type is being
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derived</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="idm413203959104"></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>
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<tr>
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<td align="left"><code class="computeroutput">PP</code></td>
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<td align="left">A type which specifies the result type of an expression
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using safe types.</td>
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</tr>
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<tr>
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<td align="left"><code class="computeroutput">EP</code></td>
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<td align="left">A type containing members which are called when a correct
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result cannot be returned</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="idm413203952064"></a>Template Parameters</h4></div></div></div>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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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">Parameter</th>
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<th align="left">Type Requirements</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><code class="computeroutput">T</code></td>
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<td align="left"><a href="http://en.cppreference.com/w/cpp/types/is_integral" target="_top">Integer<T></a></td>
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<td align="left"><p>The underlying type. Currently only integer types
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supported</p></td>
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</tr>
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<tr>
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<td><code class="computeroutput">PP</code></td>
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<td align="left"><a class="link" href="numeric.html" title="Numeric<T>"><a class="link" href="promotion_policy.html" title="PromotionPolicy<PP>">PromotionPolicy<PP></a></a></td>
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<td align="left"><p>Default value is <a class="link" href="promotion_policy.html#safe_numerics.promotion_policy.models.native">boost::numeric::native</a></p></td>
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</tr>
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<tr>
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<td><code class="computeroutput">EP</code></td>
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<td align="left"><a class="link" href="numeric.html" title="Numeric<T>"><a class="link" href="exception_policy.html" title="ExceptionPolicy<EP>">Exception
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Policy<EP></a></a></td>
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<td align="left"><p>Default value is <a class="link" href="exception_policy.html#safe_numerics.exception_policy.models.thow_exception">boost::numeric::throw_exception</a></p></td>
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</tr>
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</tbody>
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</table></div>
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<p>See examples below.</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="idm413203934320"></a>Model of</h4></div></div></div>
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<p><a class="link" href="numeric.html" title="Numeric<T>">Integer</a></p>
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<p><a class="link" href="safe_numeric_concept.html" title="SafeNumeric<T>">SafeNumeric</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="idm413203931728"></a>Valid Expressions</h4></div></div></div>
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<p>Implements all expressions and only those expressions defined by the
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<a class="link" href="safe_numeric_concept.html" title="SafeNumeric<T>">SafeNumeric</a> type
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requirements. This, the result type of such an expression will be another
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safe type. The actual type of the result of such an expression will depend
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upon the specific promotion policy template parameter.</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="idm413203929440"></a>Header</h4></div></div></div>
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<p><code class="filename"><a href="../../include/safe_integer.hpp" target="_top">#include
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<boost/safe_numerics/safe_integer.hpp></a></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="idm413203927328"></a>Examples of use</h4></div></div></div>
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<p>The most common usage would be safe<T> which uses the default
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promotion and exception policies. This type is meant to be a "drop-in"
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replacement of the intrinsic integer types. That is, expressions involving
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these types will be evaluated into result types which reflect the standard
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rules for evaluation of C++ expressions. Should it occur that such
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evaluation cannot return a correct result, an exception will be
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thrown.</p>
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<p>There are two aspects of the operation of this type which can be
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customized with a policy. The first is the result type of an arithmetic
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operation. C++ defines the rules which define this result type in terms of
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the constituent types of the operation. Here we refer to these rules a
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"type promotion" rules. These rules will sometimes result in a type which
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cannot hold the actual arithmetic result of the operation. This is the
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main motivation for making this library in the first place. One way to
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deal with this problem is to substitute our own type promotion rules for
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the C++ ones.</p>
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<div class="section">
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<div class="titlepage"><div><div><h5 class="title">
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<a name="idm413203924240"></a>Drop-in replacement for standard integer type.</h5></div></div></div>
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<p>The following program will throw an exception and emit a error
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message at runtime if any of several events result in an incorrect
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arithmetic type. Behavior of this program could vary according to the
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machine architecture in question.</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">exception</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">safe</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">void</span> <span class="identifier">f</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
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<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
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<span class="identifier">safe</span><span class="special"><</span><span class="keyword">int</span><span class="special">></span> <span class="identifier">j</span><span class="special">;</span>
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<span class="keyword">try</span> <span class="special">{</span>
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<span class="identifier">safe</span><span class="special"><</span><span class="keyword">int</span><span class="special">></span> <span class="identifier">i</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">>></span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could overflow !</span>
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<span class="identifier">j</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could overflow</span>
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<span class="special">}</span>
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<span class="keyword">catch</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span> <span class="special">&</span> <span class="identifier">e</span><span class="special">)</span><span class="special">{</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">(</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
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<span class="special">}</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">j</span><span class="special">;</span>
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<span class="special">}</span></pre>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h5 class="title">
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<a name="idm413203856016"></a>Guarantee correct behavior at compile time.</h5></div></div></div>
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<p>In some instance catching an error at run time is not sufficient.
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We want to be sure that the program can never fail. To achieve this, use
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the trap_exception exception policy rather than the default throw
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exception policy.</p>
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<p>The following program will emit a compile error at any statement
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which might possibly result in incorrect behavior.</p>
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<p>This is because there is no way to guarantee that the expression i
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* i will return an arithmetically correct result. Since we know that the
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program cannot compile if there is any possibility of arithmetic error,
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we can dispense with the exception handling used above.</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">safe</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">void</span> <span class="identifier">f</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
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<span class="keyword">using</span> <span class="identifier">safe_int</span> <span class="special">=</span> <span class="identifier">safe</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">native</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">trap_exception</span><span class="special">></span><span class="special">;</span>
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<span class="identifier">safe_int</span> <span class="identifier">i</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">>></span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could throw exception here !!!</span>
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<span class="identifier">safe_int</span> <span class="identifier">j</span><span class="special">;</span>
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<span class="identifier">j</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could throw exception here !!!</span>
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<span class="special">}</span></pre>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h5 class="title">
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<a name="idm413203819168"></a>Adjust type promotion rules.</h5></div></div></div>
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<p>Another way to avoid arithmetic errors like overflow is to promote
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types to larger sizes before doing the arithmetic. This can be justified
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by the observe</p>
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<p>Stepping back, we can see that many of the cases of invalid
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arithmetic are wouldn't exist if results types were larger. So we can
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avoid these problems by replacing the C++ type promotion rules for
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expressions with our own rules. This can be done by specifying a
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non-default type promotion policy automatic. The policy stores the
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result of an expression in the smallest size that can accommodate the
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largest value that an expression can yield. All the work is done at
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compile time - checking for exceptions necessary (input is of course an
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exception). The following example illustrates this.</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">safe</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
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<span class="keyword">void</span> <span class="identifier">f</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
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<span class="keyword">using</span> <span class="identifier">safe_int</span> <span class="special">=</span> <span class="identifier">safe</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">automatic</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">throw_exception</span><span class="special">></span><span class="special">;</span>
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<span class="identifier">safe_int</span> <span class="identifier">i</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">>></span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// might throw exception</span>
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<span class="keyword">auto</span> <span class="identifier">j</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// won't ever trap - result type can hold the maximum value of i * i</span>
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<span class="identifier">static_assert</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">is_safe</span><span class="special"><</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">j</span><span class="special">)</span><span class="special">></span><span class="special">::</span><span class="identifier">value</span><span class="special">)</span><span class="special">;</span> <span class="comment">// result is another safe type</span>
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<span class="identifier">static_assert</span><span class="special">(</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">)</span><span class="special">></span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span> <span class="special">>=</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">safe_int</span><span class="special">></span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">safe_int</span><span class="special">></span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span>
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<span class="special">)</span><span class="special">;</span> <span class="comment">// always true</span>
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<span class="special">}</span></pre>
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</div>
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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="types.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="types.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="safe_range.html"><img src="images/next.png" alt="Next"></a>
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