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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="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 results in a result which exceeds the capacity
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of a data variable to hold it, the result is undefined. This is called
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"overflow". Since word size can differ between machines, code which
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produces correct results in one set of circumstances may fail when
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re-compiled on a machine with different hardware. When this occurs, Most
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C++ compilers will continue to execute with no indication that the results
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are wrong. It is the programmer's responsibility to ensure such undefined
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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 <code class="computeroutput">char</code> type with <code class="computeroutput">safe<char></code>
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type.</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cassert</span><span class="special">></span>
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<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">cstdint</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="string">"../include/safe_integer.hpp"</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="identifier">argc</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span> <span class="identifier">argv</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="comment">// problem: arithmetic operations can yield incorrect results.</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="comment">// but assert fails to detect it since C++ implicitly</span>
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<span class="comment">// converts variables to int before evaluating he expression!</span>
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<span class="comment">// assert(z == x + y);</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="keyword">static_cast</span><span class="special"><</span><span class="keyword">int</span><span class="special">></span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="identifier">x</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="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="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="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 std::int8_t with safe<std::int8_t></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">numeric</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="number">127</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 and 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="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 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="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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<p>Note that I've used <code class="computeroutput">char</code> types in this example to make
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the problem and solution easier to see. The exact same example could have
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been done with <code class="computeroutput">int</code> types albeit with different values.</p>
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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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