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<title>Arithmetic operations 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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<a accesskey="p" href="../tutorial.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.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="2.html"><img src="../images/next.png" alt="Next"></a>
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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 operations 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">#include <cassert>
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#include <exception>
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#include <iostream>
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#include "../include/safe_integer.hpp"
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void detected_msg(bool detected){
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std::cout << (detected ? "error detected!" : "error NOT detected! ") << std::endl;
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}
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int main(int argc, const char * argv[]){
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std::cout << "example 1:";
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std::cout << "undetected erroneous expression evaluation" << std::endl;
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std::cout << "Not using safe numerics" << std::endl;
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try{
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char x = 127;
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char y = 2;
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char z;
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// this produces an invalid result !
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z = x + y;
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// it is the wrong result !!!
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assert(z != 129);
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// but assert fails to detect it since C++ implicitly
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// converts variables to int before evaluating he expression!
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assert(z != x + y);
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std::cout << static_cast<int>(z) << " != " << x + y << std::endl;
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detected_msg(false);
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}
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catch(std::exception){
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assert(false); // never arrive here
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}
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// solution: replace char with safe<char>
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std::cout << "Using safe numerics" << std::endl;
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try{
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using namespace boost::numeric;
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safe<char> x = 127;
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safe<char> y = 2;
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safe<char> z;
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// rather than producing and invalid result an exception is thrown
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z = x + y;
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assert(false); // never arrive here
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}
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catch(std::exception & e){
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// which can catch here
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std::cout << e.what() << std::endl;
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detected_msg(true);
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}
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return 0;
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}
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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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</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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