a06d9f7a69
added tests for check result < and == operations correct implementation of some checked result types added constexpr example
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<title>Arithmetic on Unsigned Integers Can Yield Incorrect Results</title>
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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.3"></a>Arithmetic on Unsigned Integers Can Yield Incorrect Results</h3></div></div></div>
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<p>Subtracting two unsigned values of the same size will result in an
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unsigned value. If the first operand is less than the second the result
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will be arithmetically in correct. But if the size of the unsigned types
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is less than that of an <code class="computeroutput">unsigned int</code>, C/C++ will promote the
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types to <code class="computeroutput">signed int</code> before subtracting resulting in an
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correct result. In either case, there is no indication of an error.
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Somehow, the programmer is expected to avoid this behavior. Advice usually
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takes the form of "Don't use unsigned integers for arithmetic". This is
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well and good, but often not practical. C/C++ itself uses unsigned for
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<code class="computeroutput">sizeof(T)</code> which is then used by users in arithmetic.</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"><p><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 8:"</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="keyword">unsigned</span> <span class="keyword">int</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="keyword">unsigned</span> <span class="keyword">int</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="keyword">unsigned</span> <span class="keyword">int</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">y</span> <span class="special">-</span> <span class="identifier">x</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="identifier">z</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="identifier">y</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">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="keyword">unsigned</span> <span class="keyword">int</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="keyword">unsigned</span> <span class="keyword">int</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="keyword">unsigned</span> <span class="keyword">int</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">y</span> <span class="special">-</span> <span class="identifier">x</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="identifier">z</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="identifier">y</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">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="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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</p></pre>
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<pre class="screen">example 8:undetected erroneous expression evaluation
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Not using safe numerics
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error NOT detected!
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4294967171 != 2 - 127
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Using safe numerics
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error detected:subtraction result cannot be negative: negative overflow error
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Program ended with exit code: 0</pre>
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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 © 2012-2018 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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