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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.4"></a>Implicit Conversions Can Lead to Erroneous Results</h3></div></div></div>
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<p>At CPPCon 2016 Jon Kalb gave a very entertaining (and disturbing
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example) <a href="https://www.youtube.com/watch?v=wvtFGa6XJDU" target="_top">lightening talk</a>
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related to C++ expressions.</p>
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<p>The talk included a very, very simple example similar to the
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following:</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="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="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 4: "</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">"implicit conversions change data values"</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: implicit conversions change data values</span>
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<span class="keyword">try</span><span class="special">{</span>
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<span class="keyword">signed</span> <span class="keyword">int</span> <span class="identifier">a</span><span class="special">{</span><span class="special">-</span><span class="number">1</span><span class="special">}</span><span class="special">;</span>
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<span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">b</span><span class="special">{</span><span class="number">1</span><span class="special">}</span><span class="special">;</span>
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<span class="keyword">if</span><span class="special">(</span><span class="identifier">a</span> <span class="special"><</span> <span class="identifier">b</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">"a is less than b\n"</span><span class="special">;</span>
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<span class="special">}</span>
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<span class="keyword">else</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">"b is less than a\n"</span><span class="special">;</span>
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<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="comment">// never arrive here - just produce the wrong answer!</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> and char with safe<char></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="keyword">signed</span> <span class="keyword">int</span><span class="special">></span> <span class="identifier">a</span><span class="special">{</span><span class="special">-</span><span class="number">1</span><span class="special">}</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">b</span><span class="special">{</span><span class="number">1</span><span class="special">}</span><span class="special">;</span>
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<span class="keyword">if</span><span class="special">(</span><span class="identifier">a</span> <span class="special"><</span> <span class="identifier">b</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">"a is less than b\n"</span><span class="special">;</span>
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<span class="special">}</span>
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<span class="keyword">else</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">"b is less than a\n"</span><span class="special">;</span>
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<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">// never arrive here - just produce the correct answer!</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="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="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>A normal person reads the above code and has to be dumbfounded by
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this. The code doesn't do what the text - according to the rules of
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algebra - says it does. But C++ doesn't follow the rules of algebra - it
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has it's own rules. There is generally no compile time error. You can get
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a compile time warning if you set some specific compile time switches. The
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explanation lies in reviewing how C++ reconciles binary expressions
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(<code class="computeroutput">a < b</code> is an expression here) where operands are different
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types. In processing this expression, the compiler:</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem"><p>Determines the "best" common type for the two operands. In
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this case, application the the rules in the C++ standard dictate
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that this type will be an <code class="computeroutput">unsigned int</code>.</p></li>
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<li class="listitem"><p>Converts each operand to this common type. The signed value of
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-1 is converted to an unsigned value with the same bit-wise
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contents, 0xFFFFFFFF, on a machine with 32 bit integers. This
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corresponds to a decimal value of 4294967295.</p></li>
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<li class="listitem"><p>Performs the calculation - in this case it's,
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<code class="computeroutput"><</code>, the "less than" operation. Since 1 is less than
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4294967295 the program prints "b is less than a".</p></li>
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</ul></div>
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<p>In order for a programmer to detect and understand this error he
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should be pretty familiar with the implicit conversion rules of the C++
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standard. These are available in a copy of the standard and also in the
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canonical reference book <em class="citetitle"><a class="link" href="bibliography.html#stroustrup" title="The C++ Programming Language Fourth Edition">The C++
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Programming Language</a></em> . (both are over 1200 pages
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long!). Even experienced programmers won't spot this issue and know to
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take precautions to avoid it. And this is a relatively easy one to spot.
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In the more general case this will use integers which don't correspond to
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easily recognizable numbers and/or will be buried as a part of some more
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complex expression.</p>
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<p>This example generated a good amount of web traffic along with every
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one's pet suggestions. See for example <a href="https://bulldozer00.com/2016/10/16/the-unsigned-conundrum/" target="_top">a blog
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post with every one's favorite "solution"</a>. All the proposed
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"solutions" have disadvantages and attempts to agree on how handle this
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are ultimately fruitless in spite of, or maybe because of, the <a href="https://twitter.com/robertramey1/status/795742870045016065" target="_top">emotional
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content</a>. Our solution is by far the simplest: Just use the safe
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numerics library as shown in the example above.</p>
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<p>Note that in this particular case, there is absolutely no extra
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overhead in using the safe integer library. Code generated will either
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equal or exceed the efficiency of using primitive integer types.</p>
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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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