mirror of
https://github.com/boostorg/safe_numerics.git
synced 2026-02-09 11:22:23 +00:00
1bc0b94e65
a) made trap_exception work b) updated manual and examples to show how to use library to eliminate runtime penalty c) added in safe_literal d) made corrections of various types
221 lines
12 KiB
HTML
221 lines
12 KiB
HTML
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
|
<title>Introduction</title>
|
|
<link rel="stylesheet" href="boostbook.css" type="text/css">
|
|
<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
|
|
<link rel="home" href="index.html" title="Safe Numerics">
|
|
<link rel="up" href="index.html" title="Safe Numerics">
|
|
<link rel="prev" href="index.html" title="Safe Numerics">
|
|
<link rel="next" href="tutorial.html" title="Tutorial and Motivating Examples">
|
|
</head>
|
|
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
|
<table cellpadding="2" width="100%"><tr>
|
|
<td valign="top"><img href="index.html" height="164px" src="pre-boost.jpg" alt="Library Documentation Index"></td>
|
|
<td><h2>Safe Numerics</h2></td>
|
|
</tr></table>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="index.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="index.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="tutorial.html"><img src="images/next.png" alt="Next"></a>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="safe_numerics.introduction"></a>Introduction</h2></div></div></div>
|
|
<div class="toc"><dl>
|
|
<dt><span class="section"><a href="introduction.html#safe_numerics.introduction.problem">Problem</a></span></dt>
|
|
<dt><span class="section"><a href="introduction.html#safe_numerics.introduction.solution">Solution</a></span></dt>
|
|
<dt><span class="section"><a href="introduction.html#safe_numerics.introduction.summary">Implementation</a></span></dt>
|
|
<dt><span class="section"><a href="introduction.html#idm473864781120">Additional Features</a></span></dt>
|
|
<dt><span class="section"><a href="introduction.html#safe_numerics.introduction.requirements">Requirements</a></span></dt>
|
|
<dt><span class="section"><a href="introduction.html#safe_numerics.introduction.scope">Scope</a></span></dt>
|
|
</dl></div>
|
|
<p>All data types, type requirements, function and meta function names
|
|
are found in the name space boost::numeric . In order to make this document
|
|
more readable, we have omitted this name space qualifier.</p>
|
|
<div class="note"><table border="0" summary="Note">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="images/note.png"></td>
|
|
<th align="left">Note</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>Library code in this document resides in the name space
|
|
<code class="computeroutput">boost::numeric</code>. This name space has generally been
|
|
eliminated from text, code and examples in order to avoid
|
|
clutter.</p></td></tr>
|
|
</table></div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="safe_numerics.introduction.problem"></a>Problem</h3></div></div></div>
|
|
<p>Arithmetic operations in C++ are NOT guaranteed to yield a correct
|
|
mathematical result. This feature is inherited from the early days of C.
|
|
The behavior of <code class="computeroutput">int</code>, <code class="computeroutput">unsigned int</code> and others
|
|
were designed to map closely to the underlying hardware. Computer hardware
|
|
implements these types as a fixed number of bits. When the result of
|
|
arithmetic operations exceeds this number of bits, the result will not be
|
|
arithmetically correct. The following example illustrates this
|
|
problem.</p>
|
|
<pre class="programlisting">int f(int x, int y){
|
|
// this returns an invalid result for some legal values of x and y !
|
|
return x + y;
|
|
}
|
|
</pre>
|
|
<p>It is incumbent up the C/C++ programmer to guarantee that this
|
|
behavior does not result in incorrect or unexpected operation of the
|
|
program. There are no language facilities which do this. They have to be
|
|
explicitly addressed in the program code. There are a number of ways to do
|
|
this. See<a class="link" href="bibliography.html#INT32-C">[<a class="citation" href="bibliography.html#idm473861135168"><span class="citation">INT32-C</span></a>]</a> seems
|
|
to recommend the following approach.</p>
|
|
<pre class="programlisting">int f(int x, int y){
|
|
if (((y > 0) && (x > (INT_MAX - y)))
|
|
|| ((y < 0) && (x < (INT_MIN - x)))) {
|
|
/* Handle error */
|
|
}
|
|
return x + y;
|
|
}
|
|
</pre>
|
|
<p>This will indeed trap the error. However, it would be tedious and
|
|
laborious for a programmer to do alter his code to do. Altering code in
|
|
this way for all arithmetic operations would likely render the code
|
|
unreadable and add another source of potential programming errors. This
|
|
approach is clearly not functional when the expression is even a little
|
|
more complex as is shown in the following example.</p>
|
|
<pre class="programlisting">int f(int x, int y, int z){
|
|
// this returns an invalid result for some legal values of x and y !
|
|
return x + y * z;
|
|
}
|
|
</pre>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="safe_numerics.introduction.solution"></a>Solution</h3></div></div></div>
|
|
<p>This library implements special versions of int, unsigned, etc.
|
|
which behave exactly like the original ones EXCEPT that the results of
|
|
these operations are guaranteed to be either arithmetically correct or
|
|
invoke an error. Using this library, the above example would be rendered
|
|
as:</p>
|
|
<pre class="programlisting">#include <boost/safe_numeric/safe_integer.hpp>
|
|
|
|
safe<int> f(safe<int> x, safe<int> y){
|
|
return x + y; // throw exception if correct result cannot be returned
|
|
}
|
|
</pre>
|
|
<p>The addition expression is checked at runtime or (if possible) at
|
|
compile time to trap any possible errors resulting from incorrect
|
|
arithmetic behavior. This will permit one to write arithmetic expressions
|
|
that cannot produce an erroneous result. Instead, one and only one of the
|
|
following is guaranteed to occur.</p>
|
|
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
|
|
<li class="listitem"><p>the expression will yield the correct mathematical
|
|
result</p></li>
|
|
<li class="listitem"><p>the expression will emit a compilation error.</p></li>
|
|
<li class="listitem"><p>the expression will invoke a runtime exception.</p></li>
|
|
</ul></div>
|
|
<p>In other words, the <span class="emphasis"><em>library absolutely guarantees that no
|
|
arithmetic expression will yield incorrect results</em></span>.</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="safe_numerics.introduction.summary"></a>Implementation</h3></div></div></div>
|
|
<p>All facilities modern C++ are employed to minimize runtime overhead
|
|
required to make this guarantee. In many cases there is no runtime
|
|
overhead at all. In other cases, small changes in the program are required
|
|
to eliminate the runtime overhead. The library implements special versions
|
|
of int, unsigned, etc. named <code class="computeroutput">safe<int></code>,
|
|
<code class="computeroutput">safe<unsigned int></code> etc. These behave exactly like the
|
|
original ones EXCEPT that expressions using these types fulfill the above
|
|
guarantee. These types are meant to be "drop-in" replacements for the
|
|
built-in types they are meant to replace. So things which are legal - such
|
|
as assigning an signed to unsigned value are not trapped at compile time -
|
|
as they are legal C/C++ code - but rather checked at runtime to trap the
|
|
case where this (legal) operation would lead to an arithmetically
|
|
incorrect result.</p>
|
|
<p>Note that the library addresses arithmetical errors generated by
|
|
straightforward C/C++ expressions. Some of these arithmetic errors are
|
|
defined as conforming to C/C++ standard while others are not. So
|
|
characterizing this library as addressing undefined behavior of C/C++
|
|
numeric expressions is misleading.</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="idm473864781120"></a>Additional Features</h3></div></div></div>
|
|
<p>Operation of safe types is determined by template parameters which
|
|
specify a pair of <a class="link" href="promotion_policies.html" title="Promotion Policies">policy
|
|
classes</a> which specify the behavior for type promotion and error
|
|
handling. In addition to the usage serving as a drop-in replacement for
|
|
standard integer types, Users of the library can:</p>
|
|
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
|
|
<li class="listitem">
|
|
<p>Select or define an exception policy class to specify handling
|
|
of exceptions.</p>
|
|
<div class="itemizedlist"><ul class="itemizedlist" type="circle">
|
|
<li class="listitem"><p>throw exception or runtime, trap at compile time.</p></li>
|
|
<li class="listitem"><p>trap at compiler time all operations which might fail at
|
|
runtime.</p></li>
|
|
<li class="listitem"><p>specify custom functions which should be called at
|
|
runtime</p></li>
|
|
</ul></div>
|
|
</li>
|
|
<li class="listitem">
|
|
<p>Select or define a promotion policy class to alter the C++
|
|
type promotion rules. This can be used to </p>
|
|
<div class="itemizedlist"><ul class="itemizedlist" type="circle">
|
|
<li class="listitem"><p>use C++ native type promotion rules so that, except
|
|
throwing/trapping of exceptions, programs will operate
|
|
identically when using/not using safe types.</p></li>
|
|
<li class="listitem"><p>replace C++ native promotion rules with ones which are
|
|
arithmetically equivalent but minimize the need for runtime
|
|
checking of arithmetic results.</p></li>
|
|
<li class="listitem"><p>replace C++ native promotion rules with ones which
|
|
emulate other machine architectures. This is designed to
|
|
permit the testing of C++ code destined to be run on another
|
|
machine on one's development platform. Such a situation often
|
|
occurs while developing code for embedded systems.</p></li>
|
|
</ul></div>
|
|
</li>
|
|
<li class="listitem"><p>Enforce of other program requirements using ranged integer
|
|
types. The library includes types safe_..._range<Min, Max> and
|
|
safe_literal(...). These types can be used to improve program
|
|
correctness and performance. </p></li>
|
|
</ul></div>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="safe_numerics.introduction.requirements"></a>Requirements</h3></div></div></div>
|
|
<p>This library is composed entirely of C++ Headers. It requires a
|
|
compiler compatible with the C++14 standard.</p>
|
|
<p>The following Boost Libraries must be installed in order to use this
|
|
library</p>
|
|
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
|
|
<li class="listitem"><p>mpl</p></li>
|
|
<li class="listitem"><p>integer</p></li>
|
|
<li class="listitem"><p>config</p></li>
|
|
<li class="listitem"><p>concept checking</p></li>
|
|
<li class="listitem"><p>tribool</p></li>
|
|
<li class="listitem"><p>enable_if</p></li>
|
|
</ul></div>
|
|
<p>In order to run the test suite, the following the Boost
|
|
preprocessor library is also required.</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="safe_numerics.introduction.scope"></a>Scope</h3></div></div></div>
|
|
<p>This library currently applies only to built-in integer types.
|
|
Analogous issues arise for floating point types but they are not currently
|
|
addressed by this version of the library. User or Library defined types
|
|
such as arbitrary precision integers can also have this problem. Extension
|
|
of this library to these other types is not currently under development
|
|
but may be addressed in the future. This is one reason why the library
|
|
name is "safe numeric" rather than "safe integer" library.</p>
|
|
</div>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"></td>
|
|
<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
|
|
Software License</a></p>
|
|
</div></td>
|
|
</tr></table>
|
|
<hr>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="index.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="index.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="tutorial.html"><img src="images/next.png" alt="Next"></a>
|
|
</div>
|
|
</body>
|
|
</html>
|