a06d9f7a69
added tests for check result < and == operations correct implementation of some checked result types added constexpr example
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<title>Arithmetic Expressions Can Yield Incorrect Results</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="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="safe_numerics.tutorial.1"></a>Arithmetic Expressions Can Yield Incorrect Results</h3></div></div></div>
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<p>When some operation on signed integer types results in a result
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which exceeds the capacity of a data variable to hold it, the result is
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undefined. In the case of unsigned integer types a similar situation
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results in a value wrap as per modulo arithmetic. In either case the
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result is different than in integer number arithmetic in the mathematical
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sense. This is called "overflow". Since word size can differ between
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machines, code which produces mathematically correct results in one set of
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circumstances may fail when re-compiled on a machine with different
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hardware. When this occurs, most C++ programs will continue to execute
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with no indication that the results are wrong. It is the programmer's
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responsibility to ensure such undefined behavior is avoided.</p>
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<p>This program demonstrates this problem. The solution is to replace
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instances of built in integer types with corresponding safe types.</p>
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<pre class="programlisting"><span class="comment">// Copyright (c) 2018 Robert Ramey</span>
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<span class="comment">//</span>
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<span class="comment">// Distributed under the Boost Software License, Version 1.0. (See</span>
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<span class="comment">// accompanying file LICENSE_1_0.txt or copy at</span>
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<span class="comment">// http://www.boost.org/LICENSE_1_0.txt)</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">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="special">[</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">cout</span> <span class="special"><<</span> <span class="string">"example 1:"</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="string">"undetected erroneous expression evaluation"</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="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Not using safe numerics"</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="keyword">try</span><span class="special">{</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">127</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span> <span class="identifier">z</span><span class="special">;</span>
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<span class="comment">// this produces an invalid result !</span>
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<span class="identifier">z</span> <span class="special">=</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">y</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="string">"error NOT detected!"</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="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">z</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">x</span> <span class="special"><<</span> <span class="string">" + "</span> <span class="special"><<</span> <span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">y</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="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</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">cout</span> <span class="special"><<</span> <span class="string">"error detected!"</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="comment">// solution: replace int with safe<int></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="string">"Using safe numerics"</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="keyword">try</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">safe_numerics</span><span class="special">;</span>
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<span class="identifier">safe</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span><span class="special">></span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">INT_MAX</span><span class="special">;</span>
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<span class="identifier">safe</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span><span class="special">></span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
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<span class="identifier">safe</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int8_t</span><span class="special">></span> <span class="identifier">z</span><span class="special">;</span>
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<span class="comment">// rather than producing an invalid result an exception is thrown</span>
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<span class="identifier">z</span> <span class="special">=</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">y</span><span class="special">;</span>
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<span class="special">}</span>
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<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</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="comment">// which we can catch here</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="string">"error detected:"</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="keyword">return</span> <span class="number">0</span><span class="special">;</span>
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<span class="special">}</span>
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</pre>
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<pre class="screen">example 1:undetected erroneous expression evaluation
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Not using safe numerics
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error NOT detected!
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-127 != 127 + 2
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Using safe numerics
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error detected:converted signed value too large: positive overflow error
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Program ended with exit code: 0</pre>
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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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