1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> 4<title>Arithmetic Operations Can Overflow Silently</title> 5<link rel="stylesheet" href="../boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Safe Numerics"> 8<link rel="up" href="../tutorial.html" title="Tutorial and Motivating Examples"> 9<link rel="prev" href="1.html" title="Arithmetic Expressions Can Yield Incorrect Results"> 10<link rel="next" href="3.html" title="Arithmetic on Unsigned Integers Can Yield Incorrect Results"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img href="index.html" height="164px" src="pre-boost.jpg" alt="Library Documentation Index"></td> 15<td><h2>Safe Numerics</h2></td> 16</tr></table> 17<div class="spirit-nav"> 18<a accesskey="p" href="1.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="3.html"><img src="../images/next.png" alt="Next"></a> 19</div> 20<div class="section"> 21<div class="titlepage"><div><div><h3 class="title"> 22<a name="safe_numerics.tutorial.2"></a>Arithmetic Operations Can Overflow Silently</h3></div></div></div> 23<p>A variation of the above is when a value is incremented/decremented 24 beyond its domain.</p> 25<pre class="programlisting"><span class="comment">// Copyright (c) 2018 Robert Ramey</span> 26<span class="comment">//</span> 27<span class="comment">// Distributed under the Boost Software License, Version 1.0. (See</span> 28<span class="comment">// accompanying file LICENSE_1_0.txt or copy at</span> 29<span class="comment">// http://www.boost.org/LICENSE_1_0.txt)</span> 30 31<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 32 33<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> 34 35<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> 36 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"example 2:"</span><span class="special">;</span> 37 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"undetected overflow in data type"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 38 <span class="comment">// problem: undetected overflow</span> 39 <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> 40 <span class="keyword">try</span><span class="special">{</span> 41 <span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">INT_MAX</span><span class="special">;</span> 42 <span class="comment">// the following silently produces an incorrect result</span> 43 <span class="special">++</span><span class="identifier">x</span><span class="special">;</span> 44 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">x</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="identifier">INT_MAX</span> <span class="special"><<</span> <span class="string">" + 1"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 45 <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> 46 <span class="special">}</span> 47 <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> 48 <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> 49 <span class="special">}</span> 50 <span class="comment">// solution: replace int with safe<int></span> 51 <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> 52 <span class="keyword">try</span><span class="special">{</span> 53 <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> 54 <span class="identifier">safe</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="identifier">INT_MAX</span><span class="special">;</span> 55 <span class="comment">// throws exception when result is past maximum possible </span> 56 <span class="special">++</span><span class="identifier">x</span><span class="special">;</span> 57 <span class="identifier">assert</span><span class="special">(</span><span class="keyword">false</span><span class="special">)</span><span class="special">;</span> <span class="comment">// never arrive here</span> 58 <span class="special">}</span> 59 <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> 60 <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> 61 <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> 62 <span class="special">}</span> 63 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 64<span class="special">}</span> 65</pre> 66<pre class="screen">example 2:undetected overflow in data type 67Not using safe numerics 68-2147483648 != 2147483647 + 1 69error NOT detected! 70Using safe numerics 71addition result too large 72error detected!</pre> 73<p>When variables of unsigned integer type are decremented below zero, 74 they "roll over" to the highest possible unsigned version of that integer 75 type. This is a common problem which is generally never detected.</p> 76</div> 77<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 78<td align="left"></td> 79<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 80 Software License</a></p> 81</div></td> 82</tr></table> 83<hr> 84<div class="spirit-nav"> 85<a accesskey="p" href="1.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="3.html"><img src="../images/next.png" alt="Next"></a> 86</div> 87</body> 88</html> 89
