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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="Content-Language" content="en-us">
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<meta name="GENERATOR" content="Microsoft FrontPage 6.0">
<meta name="Author" content="Kevlin Henney">
<meta name="KeyWords" content=
"C++, Reference Counting, Advanced Techniques, Smart Pointers, Patterns">
<title>Counted Body Techniques</title>
</head>
<body bgcolor="#FFFFFF" text="#000000">
<h1 align="center"><i><font size="+4">Counted Body Techniques</font></i></h1>
<center>
<p><b><font size="+1"><a href="../people/kevlin_henney.htm">Kevlin Henney</a><br></font>
(<a href=
"mailto:kevlin@acm.org">kevlin@acm.org</a>, <a href=
"mailto:khenney@qatraining.com">khenney@qatraining.com</a>)</b></p>
</center>
<div style="margin-left: 2em">
<p>Reference counting techniques? Nothing new, you might think. Every good
C++ text that takes you to an intermediate or advanced level will
introduce the concept. It has been explored with such thoroughness in the
past that you might be forgiven for thinking that everything that can be
said has been said. Well, let's start from first principles and see if we
can unearth something new....</p>
</div>
<hr width="100%">
<h2>And then there were none...</h2>
<div style="margin-left: 2em">
<p>The principle behind reference counting is to keep a running usage
count of an object so that when it falls to zero we know the object is
unused. This is normally used to simplify the memory management for
dynamically allocated objects: keep a count of the number of references
held to that object and, on zero, delete the object.</p>
<p>How to keep a track of the number of users of an object? Well, normal
pointers are quite dumb, and so an extra level of indirection is required
to manage the count. This is essentially the P<font size="-1">ROXY</font>
pattern described in <i>Design Patterns</i> [Gamma, Helm, Johnson &amp;
Vlissides, Addison-Wesley, <font size="-1">ISBN</font> 0-201-63361-2]. The
intent is given as</p>
<div style="margin-left: 2em">
<p><i>Provide a surrogate or placeholder for another object to control
access to it.</i></p>
</div>
<p>Coplien [<i>Advanced C++ Programming Styles and Idioms</i>,
Addison-Wesley, <font size="-1">ISBN</font> 0-201-56365-7] defines a set
of idioms related to this essential separation of a handle and a body
part. The <i>Taligent Guide to Designing Programs</i> [Addison-Wesley,
<font size="-1">ISBN</font> 0-201-40888-0] identifies a number of specific
categories for proxies (aka surrogates). Broadly speaking they fall into
two general categories:</p>
<ul>
<li><i>Hidden</i>: The handle is the object of interest, hiding the body
itself. The functionality of the handle is obtained by delegation to the
body, and the user of the handle is unaware of the body. Reference
counted strings offer a transparent optimisation. The body is shared
between copies of a string until such a time as a change is needed, at
which point a copy is made. Such a C<font size=
"-1">OPY</font> <font size="-1">ON</font> W<font size="-1">RITE</font>
pattern (a specialisation of L<font size="-1">AZY</font> E<font size=
"-1">VALUATION</font>) requires the use of a hidden reference counted
body.</li>
<li><i>Explicit</i>: Here the body is of interest and the handle merely
provides intelligence for its access and housekeeping. In C++ this is
often implemented as the S<font size="-1">MART</font> P<font size=
"-1">OINTER</font> idiom. One such application is that of reference
counted smart pointers that collaborate to keep a count of an object,
deleting it when the count falls to zero.</li>
</ul>
</div>
<hr width="100%">
<h2>Attached vs detached</h2>
<div style="margin-left: 2em">
<p>For reference counted smart pointers there are two places the count can
exist, resulting in two different patterns, both outlined in
<i>Software Patterns</i> [Coplien, SIGS, <font size="-1">ISBN</font>
0-884842-50-X]:</p>
<ul>
<li>C<font size="-1">OUNTED</font> B<font size="-1">ODY</font> or A<font size="-1">TTACHED</font>
C<font size="-1">OUNTED</font>
H<font size="-1">ANDLE</font>/B<font size="-1">ODY</font> places the
count within the object being counted. The benefits are that
countability is a part of the object being counted, and that reference
counting does not require an additional object. The drawbacks are
clearly that this is intrusive, and that the space for the reference
count is wasted when the object is not heap based. Therefore the
reference counting ties you to a particular implementation and style of
use.</li>
<li>D<font size="-1">ETACHED</font> C<font size="-1">OUNTED</font>
H<font size="-1">ANDLE</font>/B<font size="-1">ODY</font> places the
count outside the object being counted, such that they are handled
together. The clear benefit of this is that this technique is completely
unintrusive, with all of the intelligence and support apparatus in the
smart pointer, and therefore can be used on classes created
independently of the reference counted pointer. The main disadvantage is
that frequent use of this can lead to a proliferation of small objects,
i.e. the counter, being created on the heap.</li>
</ul>
<p>Even with this simple analysis, it seems that the D<font size=
"-1">ETACHED</font> C<font size="-1">OUNTED</font> H<font size=
"-1">ANDLE</font>/B<font size="-1">ODY</font> approach is ahead. Indeed,
with the increasing use of templates this is often the favourite, and is
the principle behind the common - but not standard - <tt><font size=
"+1">counted_ptr</font></tt>. <i>[The Boost name is <a href=
"../libs/smart_ptr/shared_ptr.htm"><tt><font size=
"+1">shared_ptr</font></tt></a> rather than <tt><font size=
"+1">counted_ptr</font></tt>.]</i></p>
<p>A common implementation of C<font size="-1">OUNTED</font> B<font size=
"-1">ODY</font> is to provide the counting mechanism in a base class that
the counted type is derived from. Either that, or the reference counting
mechanism is provided anew for each class that needs it. Both of these
approaches are unsatisfactory because they are quite closed, coupling a
class into a particular framework. Added to this the non-cohesiveness of
having the count lying dormant in a non-counted object, and you get the
feeling that excepting its use in widespread object models such as COM and
CORBA the C<font size="-1">OUNTED</font> B<font size="-1">ODY</font>
approach is perhaps only of use in specialised situations.</p>
</div>
<hr width="100%">
<h2>A requirements based approach</h2>
<div style="margin-left: 2em">
<p>It is the question of openness that convinced me to revisit the
problems with the C<font size="-1">OUNTED</font> B<font size=
"-1">ODY</font> idiom. Yes, there is a certain degree of intrusion
expected when using this idiom, but is there anyway to minimise this and
decouple the choice of counting mechanism from the smart pointer type
used?</p>
<p>In recent years the most instructive body of code and specification for
constructing open general purpose components has been the Stepanov and
Lee's STL (Standard Template Library), now part of the C++ standard
library. The STL approach makes extensive use of compile time polymorphism
based on well defined operational requirements for types. For instance,
each container, contained and iterator type is defined by the operations
that should be performable on an object of that type, often with
annotations describing additional constraints. Compile time polymorphism,
as its name suggests, resolves functions at compile time based on function
name and argument usage, i.e. overloading. This is less intrusive,
although less easily diagnosed if incorrect, than runtime poymorphism that
is based on types, names and function signatures.</p>
<p>This requirements based approach can be applied to reference counting.
The operations we need for a type to be <i>Countable</i> are loosely:</p>
<ul>
<li>An <tt><font size="+1">acquire</font></tt> operation that registers
interest in a <i>Countable</i> object.</li>
<li>A <tt><font size="+1">release</font></tt> operation unregisters
interest in a <i>Countable</i> object.</li>
<li>An <tt><font size="+1">acquired</font></tt> query that returns
whether or not a <i>Countable</i> object is currently acquired.</li>
<li>A <tt><font size="+1">dispose</font></tt> operation that is
responsible for disposing of an object that is no longer acquired.</li>
</ul>
<p>Note that the count is deduced as a part of the abstract state of this
type, and is not mentioned or defined in any other way. The openness of
this approach derives in part from the use of global functions, meaning
that no particular member functions are implied; a perfect way to wrap up
an existing counted body class without modifying the class itself. The
other aspect to the openness comes from a more precise specification of
the operations.</p>
<p>For a type to be <i>Countable</i> it must satisfy the following
requirements, where <tt><font size="+1">ptr</font></tt> is a non-null
pointer to a single object (i.e. not an array) of the type, and
<i><tt><font size="+1">#function</font></tt></i> indicates number of calls
to <tt><font size="+1"><i>function(</i>ptr<i>)</i></font></tt>:</p>
<center>
<table border="1" cellspacing="2" cellpadding="2" summary="">
<tr>
<td><i>Expression</i></td>
<td><i>Return type</i></td>
<td><i>Semantics and notes</i></td>
</tr>
<tr>
<td><tt><font size="+1">acquire(ptr)</font></tt></td>
<td>no requirement</td>
<td><i>post</i>: <tt><font size="+1">acquired(ptr)</font></tt></td>
</tr>
<tr>
<td><tt><font size="+1">release(ptr)</font></tt></td>
<td>no requirement</td>
<td><i>pre</i>: <tt><font size="+1">acquired(ptr)<br></font></tt>
<i>post</i>: <tt><font size="+1">acquired(ptr) == #acquire -
#release</font></tt></td>
</tr>
<tr>
<td><tt><font size="+1">acquired(ptr)</font></tt></td>
<td>convertible to <tt><font size="+1">bool</font></tt></td>
<td><i>return</i>: <tt><font size="+1">#acquire &gt; #release</font></tt></td>
</tr>
<tr>
<td><tt><font size="+1">dispose(ptr, ptr)</font></tt></td>
<td>no requirement</td>
<td><i>pre</i>: <tt><font size="+1">!acquired(ptr)<br></font></tt>
<i>post</i>: <tt><font size="+1">*ptr</font></tt> no longer usable</td>
</tr>
</table>
</center>
<p>Note that the two arguments to <tt><font size="+1">dispose</font></tt>
are to support selection of the appropriate type safe version of the
function to be called. In the general case the intent is that the first
argument determines the type to be deleted, and would typically be
templated, while the second selects which template to use, e.g. by
conforming to a specific base class.</p>
<p>In addition the following requirements must also be satisfied, where
<tt><font size="+1">null</font></tt> is a null pointer to the
<i>Countable</i> type:</p>
<center>
<table border="1" summary="">
<tr>
<td><i>Expression</i></td>
<td><i>Return type</i></td>
<td><i>Semantics and notes</i></td>
</tr>
<tr>
<td><tt><font size="+1">acquire(null)</font></tt></td>
<td>no requirement</td>
<td><i>action</i>: none</td>
</tr>
<tr>
<td><tt><font size="+1">release(null)</font></tt></td>
<td>no requirement</td>
<td><i>action</i>: none</td>
</tr>
<tr>
<td><tt><font size="+1">acquired(null)</font></tt></td>
<td>convertible to <tt><font size="+1">bool</font></tt></td>
<td><i>return</i>: <tt><font size="+1">false</font></tt></td>
</tr>
<tr>
<td><tt><font size="+1">dispose(null, null)</font></tt></td>
<td>no requirement</td>
<td><i>action</i>: none</td>
</tr>
</table>
</center>
<p>Note that there are no requirements on these functions in terms of
exceptions thrown or not thrown, except that if exceptions are thrown the
functions themselves should be exception safe.</p>
</div>
<hr width="100%">
<h2>Getting smart</h2>
<div style="margin-left: 2em">
<p>Given the <i>Countable</i> requirements for a type, it is possible to
define a generic smart pointer type that uses them for reference counting:</p>
<div style="margin-left: 2em">
<pre>
<tt>template&lt;typename countable_type&gt;
class countable_ptr
{
public: // construction and destruction
explicit countable_ptr(countable_type *);
countable_ptr(const countable_ptr &amp;);
~countable_ptr();
public: // access
countable_type *operator-&gt;() const;
countable_type &amp;operator*() const;
countable_type *get() const;
public: // modification
countable_ptr &amp;clear();
countable_ptr &amp;assign(countable_type *);
countable_ptr &amp;assign(const countable_ptr &amp;);
countable_ptr &amp;operator=(const countable_ptr &amp;);
private: // representation
countable_type *body;
};
</tt>
</pre>
</div>
<p>The interface to this class has been kept intentionally simple, e.g.
member templates and <tt><font size="+1">throw</font></tt> specs have been
omitted, for exposition. The majority of the functions are quite simple in
implementation, relying very much on the <tt><font size=
"+1">assign</font></tt> member as a keystone function:</p>
<div style="margin-left: 2em">
<pre>
<tt>template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt;::countable_ptr(countable_type *initial)
: body(initial)
{
acquire(body);
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt;::countable_ptr(const countable_ptr &amp;other)
: body(other.body)
{
acquire(body);
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt;::~countable_ptr()
{
clear();
}
template&lt;typename countable_type&gt;
countable_type *countable_ptr&lt;countable_type&gt;::operator-&gt;() const
{
return body;
}
template&lt;typename countable_type&gt;
countable_type &amp;countable_ptr&lt;countable_type&gt;::operator*() const
{
return *body;
}
template&lt;typename countable_type&gt;
countable_type *countable_ptr&lt;countable_type&gt;::get() const
{
return body;
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt; &amp;countable_ptr&lt;countable_type&gt;::clear()
{
return assign(0);
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt; &amp;countable_ptr&lt;countable_type&gt;::assign(countable_type *rhs)
{
// set to rhs (uses Copy Before Release idiom which is self assignment safe)
acquire(rhs);
countable_type *old_body = body;
body = rhs;
// tidy up
release(old_body);
if(!acquired(old_body))
{
dispose(old_body, old_body);
}
return *this;
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt; &amp;countable_ptr&lt;countable_type&gt;::assign(const countable_ptr &amp;rhs)
{
return assign(rhs.body);
}
template&lt;typename countable_type&gt;
countable_ptr&lt;countable_type&gt; &amp;countable_ptr&lt;countable_type&gt;::operator=(const countable_ptr &amp;rhs)
{
return assign(rhs);
}
</tt>
</pre>
</div>
</div>
<hr width="100%">
<h2>Public accountability</h2>
<div style="margin-left: 2em">
<p>Conformance to the requirements means that a type can be used with
<tt><font size="+1">countable_ptr</font></tt>. Here is an implementation
mix-in class (<i>mix-imp</i>) that confers countability on its derived
classes through member functions. This class can be used as a class
adaptor:</p>
<div style="margin-left: 2em">
<pre>
<tt>class countability
{
public: // manipulation
void acquire() const;
void release() const;
size_t acquired() const;
protected: // construction and destruction
countability();
~countability();
private: // representation
mutable size_t count;
private: // prevention
countability(const countability &amp;);
countability &amp;operator=(const countability &amp;);
};
</tt>
</pre>
</div>
<p>Notice that the manipulation functions are <tt><font size=
"+1">const</font></tt> and that the <tt><font size="+1">count</font></tt>
member itself is <tt><font size="+1">mutable</font></tt>. This is because
countability is not a part of an object's abstract state: memory
management does not depend on the <tt><font size=
"+1">const</font></tt>-ness or otherwise of an object. I won't include the
definitions of the member functions here as you can probably guess them:
increment, decrement and return the current count, respectively for the
manipulation functions. In a multithreaded environment you should ensure
that such read and write operations are atomic.</p>
<p>So how do we make this class <i>Countable</i>? A simple set of
forwarding functions does the job:</p>
<div style="margin-left: 2em">
<pre>
<tt>void acquire(const countability *ptr)
{
if(ptr)
{
ptr-&gt;acquire();
}
}
void release(const countability *ptr)
{
if(ptr)
{
ptr-&gt;release();
}
}
size_t acquired(const countability *ptr)
{
return ptr ? ptr-&gt;acquired() : 0;
}
template&lt;class countability_derived&gt;
void dispose(const countability_derived *ptr, const countability *)
{
delete ptr;
}
</tt>
</pre>
</div>
<p>Any type that now derives from <tt><font size=
"+1">countability</font></tt> may now be used with <tt><font size=
"+1">countable_ptr</font></tt>:</p>
<div style="margin-left: 2em">
<pre>
<tt>class example : public countability
{
...
};
void simple()
{
countable_ptr&lt;example&gt; ptr(new example);
countable_ptr&lt;example&gt; qtr(ptr);
ptr.clear(); // set ptr to point to null
} // allocated object deleted when qtr destructs
</tt>
</pre>
</div>
</div>
<hr width="100%">
<h2>Runtime mixin</h2>
<div style="margin-left: 2em">
<p>The challenge is to apply C<font size="-1">OUNTED</font> B<font size=
"-1">ODY</font> in a non-intrusive fashion, such that there is no overhead
when an object is not counted. What we would like to do is confer this
capability on a per object rather than on a per class basis. Effectively
we are after <i>Countability</i> on any object, i.e. anything pointed to
by a <tt><font size="+1">void *</font></tt>! It goes without saying that <tt><font size="+1">
void</font></tt> is perhaps the least committed of any type.</p>
<p>The forces to resolve on this are quite interesting, to say the least.
Interesting, but not insurmountable. Given that the class of a runtime
object cannot change dynamically in any well defined manner, and the
layout of the object must be fixed, we have to find a new place and time
to add the counting state. The fact that this must be added only on heap
creation suggests the following solution:</p>
<div style="margin-left: 2em">
<pre>
<tt>struct countable_new;
extern const countable_new countable;
void *operator new(size_t, const countable_new &amp;);
void operator delete(void *, const countable_new &amp;);</tt>
</pre>
</div>
<p>We have overloaded <tt><font size="+1">operator new</font></tt> with a
dummy argument to distinguish it from the regular global <tt><font size=
"+1">operator new</font></tt>. This is comparable to the use of the
<tt><font size="+1">std::nothrow_t</font></tt> type and <tt><font size=
"+1">std::nothrow</font></tt> object in the standard library. The
placement <tt><font size="+1">operator delete</font></tt> is there to
perform any tidy up in the event of failed construction. Note that this is
not yet supported on all that many compilers.</p>
<p>The result of a <tt><font size="+1">new</font></tt> expression using
<tt><font size="+1">countable</font></tt> is an object allocated on the
heap that has a header block that holds the count, i.e. we have extended
the object by prefixing it. We can provide a couple of features in an
anonymous namespace (not shown) in the implementation file for for
supporting the count and its access from a raw pointer:</p>
<div style="margin-left: 2em">
<pre>
<tt>struct count
{
size_t value;
};
count *header(const void *ptr)
{
return const_cast&lt;count *&gt;(static_cast&lt;const count *&gt;(ptr) - 1);
}
</tt>
</pre>
</div>
<p>An important constraint to observe here is the alignment of
<tt><font size="+1">count</font></tt> should be such that it is suitably
aligned for any type. For the definition shown this will be the case on
almost all platforms. However, you may need to add a padding member for
those that don't, e.g. using an anonymous <tt><font size=
"+1">union</font></tt> to coalign <tt><font size="+1">count</font></tt>
and the most aligned type. Unfortunately, there is no portable way of
specifying this such that the minimum alignment is also observed - this is
a common problem when specifying your own allocators that do not directly
use the results of either <tt><font size="+1">new</font></tt> or
<tt><font size="+1">malloc</font></tt>.</p>
<p>Again, note that the count is not considered to be a part of the
logical state of the object, and hence the conversion from
<tt><font size="+1">const</font></tt> to non-<tt><font size=
"+1">const</font></tt> - <tt><font size="+1">count</font></tt> is in
effect a <tt><font size="+1">mutable</font></tt> type.</p>
<p>The allocator functions themselves are fairly straightforward:</p>
<div style="margin-left: 2em">
<pre>
<tt>void *operator new(size_t size, const countable_new &amp;)
{
count *allocated = static_cast&lt;count *&gt;(::operator new(sizeof(count) + size));
*allocated = count(); // initialise the header
return allocated + 1; // adjust result to point to the body
}
void operator delete(void *ptr, const countable_new &amp;)
{
::operator delete(header(ptr));
}
</tt>
</pre>
</div>
<p>Given a correctly allocated header, we now need the <i>Countable</i>
functions to operate on <tt><font size="+1">const void *</font></tt> to
complete the picture:</p>
<div style="margin-left: 2em">
<pre>
<tt>void acquire(const void *ptr)
{
if(ptr)
{
++header(ptr)-&gt;value;
}
}
void release(const void *ptr)
{
if(ptr)
{
--header(ptr)-&gt;value;
}
}
size_t acquired(const void *ptr)
{
return ptr ? header(ptr)-&gt;value : 0;
}
template&lt;typename countable_type&gt;
void dispose(const countable_type *ptr, const void *)
{
ptr-&gt;~countable_type();
operator delete(const_cast&lt;countable_type *&gt;(ptr), countable);
}
</tt>
</pre>
</div>
<p>The most complex of these is the <tt><font size=
"+1">dispose</font></tt> function that must ensure that the correct type
is destructed and also that the memory is collected from the correct
offset. It uses the value and type of first argument to perform this
correctly, and the second argument merely acts as a strategy selector,
i.e. the use of <tt><font size="+1">const void *</font></tt>
distinguishes it from the earlier dispose shown for <tt><font size=
"+1">const countability *</font></tt>.</p>
</div>
<hr width="100%">
<h2>Getting smarter</h2>
<div style="margin-left: 2em">
<p>Now that we have a way of adding countability at creation for objects
of any type, what extra is needed to make this work with the
<tt><font size="+1">countable_ptr</font></tt> we defined earlier? Good
news: nothing!</p>
<div style="margin-left: 2em">
<pre>
<tt>class example
{
...
};
void simple()
{
countable_ptr&lt;example&gt; ptr(new(countable) example);
countable_ptr&lt;example&gt; qtr(ptr);
ptr.clear(); // set ptr to point to null
} // allocated object deleted when qtr destructs
</tt>
</pre>
</div>
<p>The <tt><font size="+1">new(countable)</font></tt> expression defines a
different policy for allocation and deallocation and, in common with other
allocators, any attempt to mix your allocation policies, e.g. call
<tt><font size="+1">delete</font></tt> on an object allocated with
<tt><font size="+1">new(countable)</font></tt>, results in undefined
behaviour. This is similar to what happens when you mix <tt><font size=
"+1">new[]</font></tt> with <tt><font size="+1">delete</font></tt> or
<tt><font size="+1">malloc</font></tt> with <tt><font size=
"+1">delete</font></tt>. The whole point of <i>Countable</i> conformance
is that <i>Countable</i> objects are used with <tt><font size=
"+1">countable_ptr</font></tt>, and this ensures the correct use.</p>
<p>However, accidents will happen, and inevitably you may forget to
allocate using <tt><font size="+1">new(countable)</font></tt> and instead
use <tt><font size="+1">new</font></tt>. This error and others can be
detected in most cases by extending the code shown here to add a check
member to the <tt><font size="+1">count</font></tt>, validating the check
on every access. A benefit of ensuring clear separation between header and
implementation source files means that you can introduce a checking
version of this allocator without having to recompile your code.</p>
</div>
<hr width="100%">
<h2>Conclusion</h2>
<div style="margin-left: 2em">
<p>There are two key concepts that this article has introduced:</p>
<ul>
<li>The use of a generic requirements based approach to simplify and
adapt the use of the C<font size="-1">OUNTED</font> B<font size=
"-1">ODY</font> pattern.</li>
<li>The ability, through control of allocation, to dynamically and
non-intrusively add capabilities to fixed types using the R<font size=
"-1">UNTIME</font> M<font size="-1">IXIN</font> pattern.</li>
</ul>
<p>The application of the two together gives rise to a new variant of the
essential C<font size="-1">OUNTED</font> B<font size="-1">ODY</font>
pattern, U<font size="-1">NINTRUSIVE</font> C<font size=
"-1">OUNTED</font> B<font size="-1">ODY</font>. You can take this theme
even further and contrive a simple garbage collection system for C++.</p>
<p>The complete code for <tt><font size="+1">countable_ptr</font></tt>,
<tt><font size="+1">countability</font></tt>, and the <tt><font size=
"+1">countable new</font></tt> is also available.</p>
</div>
<div align="right">
<hr width="100%">
<font size="-1"><i>First published in</i> <a href=
"http://www.accu.org/c++sig/public/Overload.html">Overload</a> <i>25,
April 1998, ISSN 1354-3172</i></font>
</div>
<p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src=
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<p>Revised
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->04 December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38514" --></p>
<p><i>Copyright &copy; 1998-1999 Kevlin Henney</i></p>
<p><i>Distributed under the Boost Software License, Version 1.0. (See
accompanying file <a href="../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy
at <a href=
"http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p>
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