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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Header <boost/operators.hpp> Documentation</title>
</head>
<body text="black" bgcolor="white" link="blue" vlink="purple" alink="red">
<h1><img src="../../c++boost.gif" alt="c++boost.gif (8819 bytes)"
align="middle" width="277" height="86">Header <cite><<a
href="../../boost/operators.hpp">boost/operators.hpp</a>></cite></h1>
<p>The header <cite><<a
href="../../boost/operators.hpp">boost/operators.hpp</a>></cite>
supplies several sets of class templates (in namespace
<code>boost</code>). These templates define operators at namespace
scope in terms of a minimal number of fundamental operators
provided by the class.</p>
<h2><a name="contents">Contents</a></h2>
<ul>
<li><a href="#contents">Contents</a></li>
<li><a href="#rationale">Rationale</a>
<ul>
<li><a href="#semantics">Summary of Template Semantics</a></li>
<li><a href="#concepts_note">Use of <i>concepts</i></a></li>
</ul></li>
<li><a href="#usage">Usage</a>
<ul>
<li><a href="#two_arg">Two-Argument Template Forms</a>
<ul>
<li><a href="#two_arg_gen">General Considerations</a></li>
<li><a href="#mixed_arithmetics">Mixed arithmetics</a></li>
</ul></li>
<li><a href="#chaining">Base Class Chaining and Object Size</a></li>
<li><a href="#explicit_instantiation">Separate, Explicit
Instantiation</a></li>
<li><a href="#portability">Requirement Portability</a></li>
</ul></li>
<li><a href="#example">Example</a></li>
<li><a href="#arithmetic">Arithmetic operators</a>
<ul>
<li><a href="#smpl_oprs">Simple Arithmetic Operators</a>
<ul>
<li><a href="#ordering">Ordering Note</a></li>
</ul></li>
<li><a href="#grpd_oprs">Grouped Arithmetic Operators</a></li>
<li><a href="#ex_oprs">Example Templates</a></li>
<li><a href="#a_demo">Arithmetic Operators Demonstration
and Test Program</a></li>
</ul></li>
<li><a href="#deref">Dereference Operators and Iterator
Helpers</a>
<ul>
<li><a href="#dereference">Dereference operators</a></li>
<li><a href="#grpd_iter_oprs">Grouped Iterator Operators</a></li>
<li><a href="#iterator">Iterator Helpers</a>
<ul>
<li><a href="#iterator_helpers_notes">Iterator Helper
Notes</a></li>
</ul></li>
<li><a href="#i_demo">Iterator Demonstration and Test
Program</a></li>
</ul></li>
<li><a href="#contributors">Contributors</a></li>
<li><a href="#old_lib_note">Note for Users of Older Versions</a></li>
</ul>
<h2><a name="rationale">Rationale</a></h2>
<p>Overloaded operators for class types typically occur in groups. If
you can write <code>x + y</code>, you probably also want to be able to
write <code>x += y</code>. If you can write <code>x < y,</code> you
also want <code>x > y, x >= y,</code> and <code>x <= y</code>.
Moreover, unless your class has really surprising behavior, some of
these related operators can be defined in terms of others (e.g. <code>x
>= y <=> !(x < y)</code>). Replicating this boilerplate for
multiple classes is both tedious and error-prone. The <cite><a
href="../../boost/operators.hpp">boost/operators.hpp</a></cite>
templates help by generating operators for you at namespace scope based
on other operators you've defined in your class.</p>
<p>If, for example, you declare a class like this:</p>
<blockquote>
<pre>class MyInt
: boost::operators<MyInt>
{
bool operator<(const MyInt& x) const;
bool operator==(const MyInt& x) const;
MyInt& operator+=(const MyInt& x);
MyInt& operator-=(const MyInt& x);
MyInt& operator*=(const MyInt& x);
MyInt& operator/=(const MyInt& x);
MyInt& operator%=(const MyInt& x);
MyInt& operator|=(const MyInt& x);
MyInt& operator&=(const MyInt& x);
MyInt& operator^=(const MyInt& x);
MyInt& operator++();
MyInt& operator--();
};</pre>
</blockquote>
<p>then the <code><a href="#operators1">operators<></a></code>
template adds more than a dozen additional operators, such as
<code>operator></code>, <code><=</code>, <code>>=</code>, and
(binary) <code>+</code>. <a href="#two_arg">Two-argument forms</a> of
the templates are also provided to allow interaction with other types.</p>
<h3>Summary of Template <a name="semantics">Semantics</a></h3>
<ol>
<li>Each operator template completes the concept(s) it describes by
defining overloaded operators for its target class.</li>
<li>The name of an operator class template indicates the <a
href="#concepts_note">concept</a> that its target class will
model.</li>
<li>Usually, the target class uses an instantation of the operator class
template as a base class. Some operator templates support an
<a href="#explicit_instantiation">alternate method</a>.</li>
<li>The concept can be compound, <i>i.e.</i> it may represent a
common combination of other, simpler concepts.</li>
<li>Most operator templates require their target class to support
operations related to the operators supplied by the template. In
accordance with widely accepted <a
href="http://www.gotw.ca/gotw/004.htm">coding style
recommendations</a>, the target class is often required to
supply the assignment counterpart operator of the concept's
"main operator." For example, the <code>addable</code>
template requires <code>operator+=(T const&)</code> and
in turn supplies <code>operator+(T const&, T
const&)</code>.</li>
</ol>
<h3>Use of <i><a name="concepts_note">concepts</a></i></h3>
<p>The discussed concepts are not necessarily the standard library's
concepts (CopyConstructible, <i>etc.</i>), although some of them could
be; they are what we call <i>concepts with a small 'c'</i>. In
particular, they are different from the former ones in that they <em>do
not</em> describe precise semantics of the operators they require to
be defined, except the requirements that (a) the semantics of the
operators grouped in one concept should be consistent (<i>e.g.</i>
effects of evaluating of <code>a += b</code> and <code>a = a + b</code>
expressions should be the same), and (b) that the return types of the
operators should follow semantics of return types of corresponding
operators for built-in types (<i>e.g.</i> <code>operator<</code>
should return a type convertible to <code>bool</code>, and
<code>T::operator-=</code> should return type convertible to
<code>T</code>). Such "loose" requirements make operators
library applicable to broader set of target classes from different
domains, <i>i.e.</i> eventually more useful.</p>
<h2><a name="usage">Usage</a></h2>
<h3><a name="two_arg">Two-Argument</a> Template Forms</h3>
<h4><a name="two_arg_gen">General Considerations</a></h4>
<p>The arguments to a binary operator commonly have identical types, but
it is not unusual to want to define operators which combine different
types. For <a href="#example">example</a>, one might want to multiply a
mathematical vector by a scalar. The two-argument template forms of the
arithmetic operator templates are supplied for this purpose. When
applying the two-argument form of a template, the desired return type of
the operators typically determines which of the two types in question
should be derived from the operator template. For example, if the
result of <code>T + U</code> is of type <code>T</code>, then
<code>T</code> (not <code>U</code>) should be derived from <code><a
href="#addable2">addable<T, U></a></code>. The comparison
templates (<code><a href="#less_than_comparable2">less_than_comparable<T,
U></a></code>, <code><a href="#equality_comparable2">equality_comparable<T,
U></a></code>, <code><a href="#equivalent2">equivalent<T, U></a></code>,
and <code><a href="#partially_ordered2">partially_ordered<T, U></a></code>)
are exceptions to this guideline, since the return type of the operators
they define is <code>bool</code>.</p>
<p>On compilers which do not support partial specialization, the
two-argument forms must be specified by using the names shown below with
the trailing <code>'2'</code>. The single-argument forms with the
trailing <code>'1'</code> are provided for symmetry and to enable
certain applications of the <a href="#chaining">base class chaining</a>
technique.</p>
<h4><a name="mixed_arithmetics">Mixed Arithmetics</a></h4>
<p>Another application of the two-argument template forms is for
mixed arithmetics between a type <code>T</code> and a type <code>U</code>
that is convertible to <code>T</code>. In this case there are two ways
where the two-argument template forms are helpful: one is to provide
the respective signatures for operator overloading, the second is
performance.</p>
<p>With respect to the operator overloading assume <i>e.g.</i> that
<code>U</code> is <code>int</code>, that <code>T</code> is an user-defined
unlimited integer type, and that <code>double operator-(double, const
T&)</code> exists. If one wants to compute <code>int - T</code> and
does not provide <code>T operator-(int, const T&)</code>, the
compiler will consider <code>double operator-(double, const T&)</code>
to be a better match than <code>T operator-(const T&, const
T&)</code>, which will probably be different from the user's intention.
To define a complete set of operator signatures, additional 'left' forms
of the two-argument template forms are provided (<code><a
href="#subtractable2_left">subtractable2_left<T, U></a></code>,
<code><a href="#dividable2_left">dividable2_left<T, U></a></code>,
<code><a href="#modable2_left">modable2_left<T, U></a></code>) that
define the signatures for non-commutative operators where <code>U</code>
appears on the left hand side (<code>operator-(const U&, const
T&)</code>, <code>operator/(const U&, const T&)</code>,
<code>operator%(const U&, const T&)</code>).</p>
<p>With respect to the performance observe that when one uses the
single type binary operator for mixed type arithmetics, the type
<code>U</code> argument has to be converted to type <code>T</code>. In
practice, however, there are often more efficient implementations of,
say <code>T::operator-=(const U&)</code> that avoid unnecessary
conversions from <code>U</code> to <code>T</code>. The two-argument
template forms of the arithmetic operator create additional operator
interfaces that use these more efficient implementations. There is, however,
no performance gain in the 'left' forms: they still need a conversion
from <code>U</code> to <code>T</code> and have an implementation
equivalent to the code that would be automatically created by the compiler
if it considered the single type binary operator to be the best match.</p>
<h3>Base Class <a name="chaining">Chaining</a> and Object Size</h3>
<p>Every operator class template, except the <a href="#ex_oprs">arithmetic
examples</a> and the <a href="#iterator">iterator helpers</a>, has an
additional, but optional, template type parameter <code>B</code>. This
parameter will be a publicly-derived base class of the instantiated template.
This means it must be a class type. It can be used to avoid the bloating of
object sizes that is commonly associated with multiple-inheritance from
several empty base classes (see the <a href="#old_lib_note">note for users of
older versions</a> for more details). To provide support for a group of
operators, use the <code>B</code> parameter to chain operator templates
into a single-base class hierarchy, demostrated in the <a href="#example">usage
example</a>. The technique is also used by the composite operator templates
to group operator definitions. If a chain becomes too long for the compiler to
support, try replacing some of the operator templates with a single grouped
operator template that chains the old templates together; the length limit only
applies to the number of templates directly in the chain, not those hidden in
group templates.</p>
<p><strong>Caveat:</strong> to chain to a base class which is
<em>not</em> a Boost operator template when using the <a
href="#two_arg">single-argument form</a> of a Boost operator template,
you must specify the operator template with the trailing
<code>'1'</code> in its name. Otherwise the library will assume you
mean to define a binary operation combining the class you intend to use
as a base class and the class you're deriving.</p>
<h3>Separate, <a name="explicit_instantiation">Explicit Instantiation</a></h3>
<p>On some compilers (<i>e.g.</i> Borland, GCC) even single-inheritance seems
to cause an increase in object size in some cases. If you are not defining
a class template, you may get better object-size performance by avoiding
derivation altogether, and instead explicitly instantiating the operator
template as follows:</p>
<blockquote><pre>
class myclass // lose the inheritance...
{
//...
};
// explicitly instantiate the operators I need.
template struct less_than_comparable<myclass>;
template struct equality_comparable<myclass>;
template struct incrementable<myclass>;
template struct decrementable<myclass>;
template struct addable<myclass,long>;
template struct subtractable<myclass,long>;
</pre></blockquote>
<p>Note that some operator templates cannot use this workaround and must
be a base class of their primary operand type. Those templates define
operators which must be member functions, and the workaround needs the
operators to be independent friend functions. The relevant templates are:</p>
<ul>
<li><code><a href="#dereferenceable">dereferenceable<></a></code></li>
<li><code><a href="#indexable">indexable<></a></code></li>
<li>Any composite operator template that includes at least one of the
above</li>
</ul>
<h3>Requirement <a name="portability">Portability</a></h3>
<p>Many compilers (<i>e.g.</i> MSVC 6.3, GCC 2.95.2) will not enforce
the requirements in the operator template tables unless the operations
which depend on them are actually used. This is not standard-conforming
behavior. In particular, although it would be convenient to derive all
your classes which need binary operators from the
<code><a href="#operators1">operators<></a></code>
and <code><a href="#operators2">operators2<></a></code>
templates, regardless of whether they implement all the requirements
of those templates, this shortcut is not portable. Even if this currently
works with your compiler, it may not work later.</p>
<h2><a name="example">Example</a></h2>
<p>This example shows how some of the <a href="#arithmetic">arithmetic
operator templates</a> can be used with a geometric point class (template).</p>
<pre>
template <class T>
class point // note: private inheritance is OK here!
: boost::addable< point<T> // point + point
, boost::subtractable< point<T> // point - point
, boost::dividable2< point<T>, T // point / T
, boost::multipliable2< point<T>, T // point * T, T * point
> > > >
{
public:
point(T, T);
T x() const;
T y() const;
point operator+=(const point&);
// point operator+(point, const point&) automatically
// generated by addable.
point operator-=(const point&);
// point operator-(point, const point&) automatically
// generated by subtractable.
point operator*=(T);
// point operator*(point, const T&) and
// point operator*(const T&, point) auto-generated
// by multipliable.
point operator/=(T);
// point operator/(point, const T&) auto-generated
// by dividable.
private:
T x_;
T y_;
};
// now use the point<> class:
template <class T>
T length(const point<T> p)
{
return sqrt(p.x()*p.x() + p.y()*p.y());
}
const point<float> right(0, 1);
const point<float> up(1, 0);
const point<float> pi_over_4 = up + right;
const point<float> pi_over_4_normalized = pi_over_4 / length(pi_over_4);
</pre>
<h2><a name="arithmetic">Arithmetic</a> Operators</h2>
<p>The arithmetic operator templates ease the task of creating a custom
numeric type. Given a core set of operators, the templates add related
operators to the numeric class. These operations are like the ones the
standard arithmetic types have, and may include comparisons, adding,
incrementing, logical and bitwise manipulations, <i>etc</i>. Further, since
most numeric types need more than one of these operators, some
templates are provided to combine several of the basic operator
templates in one declaration.</p>
<p>The requirements for the types used to instantiate the simple operator
templates are specified in terms of expressions which must be valid and
the expression's return type. The composite operator templates only list
what other templates they use. The supplied operations and requirements
of the composite operator templates can be inferred from the operations and
requirements of the listed components.</p>
<h3><a name="smpl_oprs">Simple Arithmetic Operators</a></h3>
<p>These templates are "simple" since they provide operators
based on a single operation the base type has to provide. They have an
additional optional template parameter <code>B</code>, which is not shown,
for the <a href="#chaining">base class chaining</a> technique.
<table cellpadding="5" border="1" align="center">
<caption>Simple Arithmetic Operator Template Classes</caption>
<tr>
<td colspan="3"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: primary operand type</td>
<td><code>U</code>: alternate operand type</td>
</tr>
<tr>
<td><code>t</code>, <code>t1</code>: values of type
<code>T</code></td>
<td><code>u</code>: value of type <code>U</code></td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Supplied Operations</th>
<th>Requirements</th>
</tr>
<tr>
<td><code><a name="less_than_comparable1">less_than_comparable<T></a></code><br>
<code>less_than_comparable1<T></code></td>
<td><code>bool operator>(const T&, const T&)</code><br>
<code>bool operator<=(const T&, const T&)</code><br>
<code>bool operator>=(const T&, const T&)</code></td>
<td><code>t < t1</code>.<br>
Return convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
<tr>
<td><code><a name="less_than_comparable2">less_than_comparable<T, U></a></code><br>
<code>less_than_comparable2<T, U></code></td>
<td><code>bool operator<=(const T&, const U&)</code><br>
<code>bool operator>=(const T&, const U&)</code><br>
<code>bool operator>(const U&, const T&)</code><br>
<code>bool operator<(const U&, const T&)</code><br>
<code>bool operator<=(const U&, const T&)</code><br>
<code>bool operator>=(const U&, const T&)</code></td>
<td><code>t < u</code>. <code>t > u</code>.<br>
Returns convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
<tr>
<td><code><a name="equality_comparable1">equality_comparable<T></a></code><br>
<code>equality_comparable1<T></code></td>
<td><code>bool operator!=(const T&, const T&)</code></td>
<td><code>t == t1</code>.<br>
Return convertible to <code>bool</code>.</td>
</tr>
<tr>
<td><code><a name="equality_comparable2">equality_comparable<T, U></a></code><br>
<code>equality_comparable2<T, U></code></td>
<td><code>friend bool operator==(const U&, const T&)</code><br>
<code>friend bool operator!=(const U&, const T&)</code><br>
<code>friend bool operator!=( const T&, const U&)</code></td>
<td><code>t == u</code>.<br>
Return convertible to <code>bool</code>.</td>
</tr>
<tr>
<td><code><a name="addable1">addable<T></a></code><br>
<code>addable1<T></code></td>
<td><code>T operator+(T, const T&)</code></td>
<td><code>t += t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="addable2">addable<T, U></a></code><br>
<code>addable2<T, U></code></td>
<td><code>T operator+(T, const U&)</code><br>
<code>T operator+(const U&, T )</code></td>
<td><code>t += u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="subtractable1">subtractable<T></a></code><br>
<code>subtractable1<T></code></td>
<td><code>T operator-(T, const T&)</code></td>
<td><code>t -= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="subtractable2">subtractable<T, U></a></code><br>
<code>subtractable2<T, U></code></td>
<td><code>T operator-(T, const U&)</code></td>
<td><code>t -= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="subtractable2_left">subtractable2_left<T, U></a></code></td>
<td><code>T operator-(const U&, const T&)</code></td>
<td><code>T temp(u); temp -= t</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="multipliable1">multipliable<T></a></code><br>
<code>multipliable1<T></code></td>
<td><code>T operator*(T, const T&)</code></td>
<td><code>t *= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="multipliable2">multipliable<T, U></a></code><br>
<code>multipliable2<T, U></code></td>
<td><code>T operator*(T, const U&)</code><br>
<code>T operator*(const U&, T )</code></td>
<td><code>t *= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="dividable1">dividable<T></a></code><br>
<code>dividable1<T></code></td>
<td><code>T operator/(T, const T&)</code></td>
<td><code>t /= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="dividable2">dividable<T, U></a></code><br>
<code>dividable2<T, U></code></td>
<td><code>T operator/(T, const U&)</code></td>
<td><code>t /= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="dividable2_left">dividable2_left<T, U></a></code></td>
<td><code>T operator/(const U&, const T&)</code></td>
<td><code>T temp(u); temp /= t</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="modable1">modable<T></a></code><br>
<code>modable1<T></code></td>
<td><code>T operator%(T, const T&)</code></td>
<td><code>t %= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="modable2">modable<T, U></a></code><br>
<code>modable2<T, U></code></td>
<td><code>T operator%(T, const U&)</code></td>
<td><code>t %= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="modable2_left">modable2_left<T, U></a></code></td>
<td><code>T operator%(const U&, const T&)</code></td>
<td><code>T temp(u); temp %= t</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="orable1">orable<T></a></code><br>
<code>orable1<T></code></td>
<td><code>T operator|(T, const T&)</code></td>
<td><code>t |= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="orable2">orable<T, U></a></code><br>
<code>orable2<T, U></code></td>
<td><code>T operator|(T, const U&)</code><br>
<code>T operator|(const U&, T )</code></td>
<td><code>t |= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="andable1">andable<T></a></code><br>
<code>andable1<T></code></td>
<td><code>T operator&(T, const T&)</code></td>
<td><code>t &= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="andable2">andable<T, U></a></code><br>
<code>andable2<T, U></code></td>
<td><code>T operator&(T, const U&)</code><br>
<code>T operator&(const U&, T)</code></td>
<td><code>t &= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="xorable1">xorable<T></a></code><br>
<code>xorable1<T></code></td>
<td><code>T operator^(T, const T&)</code></td>
<td><code>t ^= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="xorable2">xorable<T, U></a></code><br>
<code>xorable2<T, U></code></td>
<td><code>T operator^(T, const U&)</code><br>
<code>T operator^(const U&, T )</code></td>
<td><code>t ^= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="incrementable">incrementable<T></a></code></td>
<td><code>T operator++(T& x, int)</code></td>
<td><code>T temp(x); ++x; return temp;</code><br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="decrementable">decrementable<T></a></code></td>
<td><code>T operator--(T& x, int)</code></td>
<td><code>T temp(x); --x; return temp;</code><br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="left_shiftable1">left_shiftable<T></a></code><br>
<code>left_shiftable1<T></code></td>
<td><code>T operator<<(T, const T&)</code></td>
<td><code>t <<= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="left_shiftable2">left_shiftable<T, U></a></code><br>
<code>left_shiftable2<T, U></code></td>
<td><code>T operator<<(T, const U&)</code></td>
<td><code>t <<= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="right_shiftable1">right_shiftable<T></a></code><br>
<code>right_shiftable1<T></code></td>
<td><code>T operator>>(T, const T&)</code></td>
<td><code>t >>= t1</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="right_shiftable2">right_shiftable<T, U></a></code><br>
<code>right_shiftable2<T, U></code></td>
<td><code>T operator>>(T, const U&)</code></td>
<td><code>t >>= u</code>.<br>
Return convertible to <code>T</code>.</td>
</tr>
<tr>
<td><code><a name="equivalent1">equivalent<T></a></code><br>
<code>equivalent1<T></code></td>
<td><code>bool operator==(const T&, const T&)</code></td>
<td><code>t < t1</code>.<br>
Return convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
<tr>
<td><code><a name="equivalent2">equivalent<T, U></a></code><br>
<code>equivalent2<T, U></code></td>
<td><code>bool operator==(const T&, const U&)</code></td>
<td><code>t < u</code>. <code>t > u</code>.<br>
Returns convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
<tr>
<td><code><a name="partially_ordered1">partially_ordered<T></a></code><br>
<code>partially_ordered1<T></code></td>
<td><code>bool operator>(const T&, const T&)</code><br>
<code>bool operator<=(const T&, const T&)</code><br>
<code>bool operator>=(const T&, const T&)</code></td>
<td><code>t < t1</code>. <code>t == t1</code>.<br>
Returns convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
<tr>
<td><code><a name="partially_ordered2">partially_ordered<T, U></a></code><br>
<code>partially_ordered2<T, U></code></td>
<td><code>bool operator<=(const T&, const U&)</code><br>
<code>bool operator>=(const T&, const U&)</code><br>
<code>bool operator>(const U&, const T&)</code><br>
<code>bool operator<(const U&, const T&)</code><br>
<code>bool operator<=(const U&, const T&)</code><br>
<code>bool operator>=(const U&, const T&)</code></td>
<td><code>t < u</code>. <code>t > u</code>. <code>t == u</code>.<br>
Returns convertible to <code>bool</code>. See the <a
href="#ordering">Ordering Note</a>.</td>
</tr>
</table>
<h4><a name="ordering">Ordering</a> Note</h4>
<p>The <code><a href="#less_than_comparable1">less_than_comparable<T></a></code>
and <code><a href="#partially_ordered1">partially_ordered<T></a></code>
templates provide the same set of operations. However, the workings of
<code><a href="#less_than_comparable1">less_than_comparable<T></a></code>
assume that all values of type <code>T</code> can be placed in a total order. If
that is not true (<i>e.g.</i> Not-a-Number values in IEEE floating point
arithmetic), then
<code><a href="#partially_ordered1">partially_ordered<T></a></code>
should be used. The
<code><a href="#partially_ordered1">partially_ordered<T></a></code>
template can be used for a totally-ordered type, but it is not as efficient as
<code><a href="#less_than_comparable1">less_than_comparable<T></a></code>.
This rule also applies for
<code><a href="#less_than_comparable2">less_than_comparable<T,
U></a></code> and <code><a href="#partially_ordered2">partially_ordered<T,
U></a></code> with respect to the ordering of all <code>T</code> and
<code>U</code> values, and for both versions of
<code><a href="#equivalent1">equivalent<></a></code>. The solution for
<code><a href="#equivalent1">equivalent<></a></code> is to write a
custom <code>operator==</code> for the target class.</p>
<h3><a name="grpd_oprs">Grouped Arithmetic Operators</a></h3>
<p>The following templates provide common groups of related operations.
For example, since a type which is addable is usually also subractable, the
<code><a href="#additive1">additive</a></code> template provides the combined
operators of both. The grouped operator templates have an additional
optional template parameter <code>B</code>, which is not shown, for the
<a href="#chaining">base class chaining</a> technique.</p>
<table cellpadding="5" border="1" align="center">
<caption>Grouped Arithmetic Operator Template Classes</caption>
<tr>
<td colspan="2"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: primary operand type</td>
<td><code>U</code>: alternate operand type</td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Component Operator Templates</th>
</tr>
<tr>
<td><code><a name="totally_ordered1">totally_ordered<T></a></code><br>
<code>totally_ordered1<T></code></td>
<td><ul>
<li><code><a href="#less_than_comparable1">less_than_comparable<T></a></code></li>
<li><code><a href="#equality_comparable1">equality_comparable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="totally_ordered2">totally_ordered<T, U></a></code><br>
<code>totally_ordered2<T, U></code></td>
<td><ul>
<li><code><a href="#less_than_comparable2">less_than_comparable<T, U></a></code></li>
<li><code><a href="#equality_comparable2">equality_comparable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="additive1">additive<T></a></code><br>
<code>additive1<T></code></td>
<td><ul>
<li><code><a href="#addable1">addable<T></a></code></li>
<li><code><a href="#subtractable1">subtractable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="additive2">additive<T, U></a></code><br>
<code>additive2<T, U></code></td>
<td><ul>
<li><code><a href="#addable2">addable<T, U></a></code></li>
<li><code><a href="#subtractable2">subtractable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="multiplicative1">multiplicative<T></a></code><br>
<code>multiplicative1<T></code></td>
<td><ul>
<li><code><a href="#multipliable1">multipliable<T></a></code></li>
<li><code><a href="#dividable1">dividable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="multiplicative2">multiplicative<T, U></a></code><br>
<code>multiplicative2<T, U></code></td>
<td><ul>
<li><code><a href="#multipliable2">multipliable<T, U></a></code></li>
<li><code><a href="#dividable2">dividable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="integer_multiplicative1">integer_multiplicative<T></a></code><br>
<code>integer_multiplicative1<T></code></td>
<td><ul>
<li><code><a href="#multiplicative1">multiplicative<T></a></code></li>
<li><code><a href="#modable1">modable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="integer_multiplicative2">integer_multiplicative<T, U></a></code><br>
<code>integer_multiplicative2<T, U></code></td>
<td><ul>
<li><code><a href="#multiplicative2">multiplicative<T, U></a></code></li>
<li><code><a href="#modable2">modable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="arithmetic1">arithmetic<T></a></code><br>
<code>arithmetic1<T></code></td>
<td><ul>
<li><code><a href="#additive1">additive<T></a></code></li>
<li><code><a href="#multiplicative1">multiplicative<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="arithmetic2">arithmetic<T, U></a></code><br>
<code>arithmetic2<T, U></code></td>
<td><ul>
<li><code><a href="#additive2">additive<T, U></a></code></li>
<li><code><a href="#multiplicative2">multiplicative<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="integer_arithmetic1">integer_arithmetic<T></a></code><br>
<code>integer_arithmetic1<T></code></td>
<td><ul>
<li><code><a href="#additive1">additive<T></a></code></li>
<li><code><a href="#integer_multiplicative1">integer_multiplicative<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="integer_arithmetic2">integer_arithmetic<T, U></a></code><br>
<code>integer_arithmetic2<T, U></code></td>
<td><ul>
<li><code><a href="#additive2">additive<T, U></a></code></li>
<li><code><a href="#integer_multiplicative2">integer_multiplicative<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="bitwise1">bitwise<T></a></code><br>
<code>bitwise1<T></code></td>
<td><ul>
<li><code><a href="#xorable1">xorable<T></a></code></li>
<li><code><a href="#andable1">andable<T></a></code></li>
<li><code><a href="#orable1">orable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="bitwise2">bitwise<T, U></a></code><br>
<code>bitwise2<T, U></code></td>
<td><ul>
<li><code><a href="#xorable2">xorable<T, U></a></code></li>
<li><code><a href="#andable2">andable<T, U></a></code></li>
<li><code><a href="#orable2">orable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="unit_steppable">unit_steppable<T></a></code></td>
<td><ul>
<li><code><a href="#incrementable">incrementable<T></a></code></li>
<li><code><a href="#decrementable">decrementable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="shiftable1">shiftable<T></a></code><br>
<code>shiftable1<T></code></td>
<td><ul>
<li><code><a href="#left_shiftable1">left_shiftable<T></a></code></li>
<li><code><a href="#right_shiftable1">right_shiftable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="shiftable2">shiftable<T, U></a></code><br>
<code>shiftable2<T, U></code></td>
<td><ul>
<li><code><a href="#left_shiftable2">left_shiftable<T, U></a></code></li>
<li><code><a href="#right_shiftable2">right_shiftable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ring_operators1">ring_operators<T></a></code><br>
<code>ring_operators1<T></code></td>
<td><ul>
<li><code><a href="#additive1">additive<T></a></code></li>
<li><code><a href="#multipliable1">multipliable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ring_operators2">ring_operators<T, U></a></code><br>
<code>ring_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#additive2">additive<T, U></a></code></li>
<li><code><a href="#subtractable2_left">subtractable2_left<T, U></a></code></li>
<li><code><a href="#multipliable2">multipliable<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_ring_operators1">ordered_ring_operators<T></a></code><br>
<code>ordered_ring_operators1<T></code></td>
<td><ul>
<li><code><a href="#ring_operators1">ring_operators<T></a></code></li>
<li><code><a href="#totally_ordered1">totally_ordered<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_ring_operators2">ordered_ring_operators<T, U></a></code><br>
<code>ordered_ring_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#ring_operators2">ring_operators<T, U></a></code></li>
<li><code><a href="#totally_ordered2">totally_ordered<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="field_operators1">field_operators<T></a></code><br>
<code>field_operators1<T></code></td>
<td><ul>
<li><code><a href="#ring_operators1">ring_operators<T></a></code></li>
<li><code><a href="#dividable1">dividable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="field_operators2">field_operators<T, U></a></code><br>
<code>field_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#ring_operators2">ring_operators<T, U></a></code></li>
<li><code><a href="#dividable2">dividable<T, U></a></code></li>
<li><code><a href="#dividable2_left">dividable2_left<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_field_operators1">ordered_field_operators<T></a></code><br>
<code>ordered_field_operators1<T></code></td>
<td><ul>
<li><code><a href="#field_operators1">field_operators<T></a></code></li>
<li><code><a href="#totally_ordered1">totally_ordered<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_field_operators2">ordered_field_operators<T, U></a></code><br>
<code>ordered_field_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#field_operators2">field_operators<T, U></a></code></li>
<li><code><a href="#totally_ordered2">totally_ordered<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="euclidian_ring_operators1">euclidian_ring_operators<T></a></code><br>
<code>euclidian_ring_operators1<T></code></td>
<td><ul>
<li><code><a href="#ring_operators1">ring_operators<T></a></code></li>
<li><code><a href="#dividable1">dividable<T></a></code></li>
<li><code><a href="#modable1">modable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="euclidian_ring_operators2">euclidian_ring_operators<T, U></a></code><br>
<code>euclidian_ring_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#ring_operators2">ring_operators<T, U></a></code></li>
<li><code><a href="#dividable2">dividable<T, U></a></code></li>
<li><code><a href="#dividable2_left">dividable2_left<T, U></a></code></li>
<li><code><a href="#modable2">modable<T, U></a></code></li>
<li><code><a href="#modable2_left">modable2_left<T, U></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_euclidian_ring_operators1">ordered_euclidian_ring_operators<T></a></code><br>
<code>ordered_euclidian_ring_operators1<T></code></td>
<td><ul>
<li><code><a href="#euclidian_ring_operators1">euclidian_ring_operators<T></a></code></li>
<li><code><a href="#totally_ordered1">totally_ordered<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="ordered_euclidian_ring_operators2">ordered_euclidian_ring_operators<T, U></a></code><br>
<code>ordered_euclidian_ring_operators2<T, U></code></td>
<td><ul>
<li><code><a href="#euclidian_ring_operators2">euclidian_ring_operators<T, U></a></code></li>
<li><code><a href="#totally_ordered2">totally_ordered<T, U></a></code></li>
</ul></td>
</tr>
</table>
<h3><a name="ex_oprs">Example</a> Templates</h3>
<p>The arithmetic operator class templates <code><a
href="#operators1">operators<></a></code> and <code><a
href="#operators2">operators2<></a></code> are examples of
non-extensible operator grouping classes. These legacy class templates,
from previous versions of the header, cannot be used for
<a href="#chaining">base class chaining</a>.</p>
<table cellpadding="5" border="1" align="center">
<caption>Final Arithmetic Operator Template Classes</caption>
<tr>
<td colspan="2"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: primary operand type</td>
<td><code>U</code>: alternate operand type</td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Component Operator Templates</th>
</tr>
<tr>
<td><code><a name="operators1">operators<T></a></code></td>
<td><ul>
<li><code><a href="#totally_ordered1">totally_ordered<T></a></code></li>
<li><code><a href="#integer_arithmetic1">integer_arithmetic<T></a></code></li>
<li><code><a href="#bitwise1">bitwise<T></a></code></li>
<li><code><a href="#unit_steppable">unit_steppable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="operators2">operators<T, U></a></code><br>
<code>operators2<T, U></code></td>
<td><ul>
<li><code><a href="#totally_ordered2">totally_ordered<T, U></a></code></li>
<li><code><a href="#integer_arithmetic2">integer_arithmetic<T, U></a></code></li>
<li><code><a href="#bitwise2">bitwise<T, U></a></code></li>
</ul></td>
</tr>
</table>
<h3><a name="a_demo">Arithmetic Operators Demonstration</a> and Test Program</h3>
<p>The <cite><a href="operators_test.cpp">operators_test.cpp</a></cite>
program demonstrates the use of the arithmetic operator templates, and
can also be used to verify correct operation. Check the <a
href="../../status/compiler_status.html">compiler status report</a> for the test results
with selected platforms.</p>
<h2><a name="deref">Dereference</a> Operators and Iterator Helpers</h2>
<p>The <a href="#iterator">iterator helper</a> templates ease the task
of creating a custom iterator. Similar to arithmetic types, a complete
iterator has many operators that are "redundant" and can be
implemented in terms of the core set of operators.</p>
<p>The <a href="#dereference">dereference operators</a> were motivated
by the <a href="#iterator">iterator helpers</a>, but are often useful in
non-iterator contexts as well. Many of the redundant iterator operators
are also arithmetic operators, so the iterator helper classes borrow
many of the operators defined above. In fact, only two new operators
need to be defined (the pointer-to-member <code>operator-></code> and
the subscript <code>operator[]</code>)!</p>
<p>The requirements for the types used to instantiate the dereference
operators are specified in terms of expressions which must be valid and
their return type. The composite operator templates list their component
templates, which the instantiating type must support, and possibly other
requirements.</p>
<h3><a name="dereference">Dereference</a> Operators</h3>
<p>All the dereference operator templates in this table accept an
optional template parameter (not shown) to be used for <a
href="#chaining">base class chaining</a>.</p>
<table cellpadding="5" border="1" align="center">
<caption>Dereference Operator Template Classes</caption>
<tr>
<td colspan="3"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: operand type</td>
<td><code>P</code>: <code>pointer</code> type</td>
</tr>
<tr>
<td><code>D</code>: <code>difference_type</code></td>
<td><code>R</code>: <code>reference</code> type</td>
</tr>
<tr>
<td><code>i</code>: object of type <code>T</code> (an iterator)</td>
<td><code>n</code>: object of type <code>D</code> (an index)</td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Supplied Operations</th>
<th>Requirements</th>
</tr>
<tr>
<td><code><a name="dereferenceable">dereferenceable<T, P></a></code></td>
<td><code>P operator->() const</code></td>
<td><code>(&*i)</code>. Return convertible to <code>P</code>.</td>
</tr>
<tr>
<td><code><a name="indexable">indexable<T, D, R></a></code></td>
<td><code>R operator[](D n) const</code></td>
<td><code>*(i + n)</code>. Return of type <code>R</code>.</td>
</tr>
</table>
<h3><a name="grpd_iter_oprs">Grouped Iterator Operators</a></h3>
<p>There are five iterator operator class templates, each for a different
category of iterator. The following table shows the operator groups
for any category that a custom iterator could define. These class
templates have an additional optional template parameter <code>B</code>,
which is not shown, to support <a href="#chaining">base class chaining</a>.</p>
<table cellpadding="5" border="1" align="center">
<caption>Iterator Operator Class Templates</caption>
<tr>
<td colspan="2"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: operand type</td>
<td><code>P</code>: <code>pointer</code> type</td>
</tr>
<tr>
<td><code>D</code>: <code>difference_type</code></td>
<td><code>R</code>: <code>reference</code> type</td>
</tr>
<tr>
<td><code>V</code>: <code>value_type</code></td>
<td></td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Component Operator Templates</th>
</tr>
<tr>
<td><code><a name="input_iteratable">input_iteratable<T, P></a></code></td>
<td><ul>
<li><code><a href="#equality_comparable1">equality_comparable<T></a></code></li>
<li><code><a href="#incrementable">incrementable<T></a></code></li>
<li><code><a href="#dereferenceable">dereferenceable<T, P></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="output_iteratable">output_iteratable<T></a></code></td>
<td><ul>
<li><code><a href="#incrementable">incrementable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="forward_iteratable">forward_iteratable<T, P></a></code></td>
<td><ul>
<li><code><a href="#input_iteratable">input_iteratable<T, P></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="bidirectional_iteratable">bidirectional_iteratable<T, P></a></code></td>
<td><ul>
<li><code><a href="#forward_iteratable">forward_iteratable<T, P></a></code></li>
<li><code><a href="#decrementable">decrementable<T></a></code></li>
</ul></td>
</tr>
<tr>
<td><code><a name="random_access_iteratable">random_access_iteratable<T, P, D, R></a></code></td>
<td><ul>
<li><code><a href="#bidirectional_iteratable">bidirectional_iteratable<T, P></a></code></li>
<li><code><a href="#totally_ordered1">totally_ordered<T></a></code></li>
<li><code><a href="#additive2">additive<T, D></a></code></li>
<li><code><a href="#indexable">indexable<T, D, R></a></code></li>
</ul></td>
</tr>
</table>
<h3><a name="iterator">Iterator</a> Helpers</h3>
<p>There are also five iterator helper class templates, each corresponding
to a different iterator category. These classes cannot be used for <a
href="#chaining">base class chaining</a>. The following summaries
show that these class templates supply both the iterator operators from
the <a href="#grpd_iter_oprs">iterator operator class templates</a> and
the iterator typedef's required by the C++ standard (<code>iterator_category</code>,
<code>value_type</code>, <i>etc.</i>).</p>
<table cellpadding="5" border="1" align="center">
<caption>Iterator Helper Class Templates</caption>
<tr>
<td colspan="2"><table align="center" border="1">
<caption><em>Key</em></caption>
<tr>
<td><code>T</code>: operand type</td>
<td><code>P</code>: <code>pointer</code> type</td>
</tr>
<tr>
<td><code>D</code>: <code>difference_type</code></td>
<td><code>R</code>: <code>reference</code> type</td>
</tr>
<tr>
<td><code>V</code>: <code>value_type</code></td>
<td><code>x1, x2</code>: objects of type <code>T</code></td>
</tr>
</table></td>
</tr>
<tr>
<th>Template</th>
<th>Operations & Requirements</th>
</tr>
<tr valign="baseline">
<td><code><a name="input_iterator_helper">input_iterator_helper<T, V, D, P, R></a></code></td>
<td>Supports the operations and has the requirements of
<ul>
<li><code><a href="#input_iteratable">input_iteratable<T, P></a></code></li>
</ul></td>
</tr>
<tr valign="baseline">
<td><code><a name="output_iterator_helper">output_iterator_helper<T></a></code></td>
<td>Supports the operations and has the requirements of
<ul>
<li><code><a href="#output_iteratable">output_iteratable<T></a></code></li>
</ul>
See also [<a href="#1">1</a>], [<a href="#2">2</a>].
</td>
</tr>
<tr valign="baseline">
<td><code><a name="forward_iterator_helper">forward_iterator_helper<T, V, D, P, R></a></code></td>
<td>Supports the operations and has the requirements of
<ul>
<li><code><a href="#forward_iteratable">forward_iteratable<T, P></a></code></li>
</ul></td>
</tr>
<tr valign="baseline">
<td><code><a name="bidirectional_iterator_helper">bidirectional_iterator_helper<T, V, D, P, R></a></code></td>
<td>Supports the operations and has the requirements of
<ul>
<li><code><a href="#bidirectional_iteratable">bidirectional_iteratable<T, P></a></code></li>
</ul></td>
</tr>
<tr valign="baseline">
<td><code><a name="random_access_iterator_helper">random_access_iterator_helper<T, V, D, P, R></a></code></td>
<td>Supports the operations and has the requirements of
<ul>
<li><code><a href="#random_access_iteratable">random_access_iteratable<T, P, D, R></a></code></li>
</ul>
To satisfy <cite><a href="http://www.sgi.com/tech/stl/RandomAccessIterator.html">RandomAccessIterator</a></cite>,
<code>x1 - x2</code> with return convertible to <code>D</code>
is also required.</td>
</tr>
</table>
<h4><a name="iterator_helpers_notes">Iterator Helper Notes</a></h4>
<p><a name="1">[1]</a> Unlike other iterator helpers templates,
<code>output_iterator_helper</code> takes only one template parameter - the type of
its target class. Although to some it might seem like an unnecessary
restriction, the standard requires <code>difference_type</code> and
<code>value_type</code> of any output iterator to be
<code>void</code> (24.3.1 [lib.iterator.traits]), and
<code>output_iterator_helper</code> template respects this
requirement. Also, output iterators in the standard have void <code>pointer</code> and
<code>reference</code> types, so the <code>output_iterator_helper</code> does the
same.
<p><a name="2">[2]</a> As self-proxying is the easiest and most common way to
implement output iterators (see, for example, insert [24.4.2] and stream
iterators [24.5] in the standard library), <code>output_iterator_helper</code>
supports the idiom by defining <code>operator*</code>
and <code>operator++</code> member functions which just return a
non-const reference to the iterator itself. Support for
self-proxying allows us, in many cases, to reduce the task of writing an output
iterator to writing just two member functions - an appropriate
constructor and a copy-assignment operator. For example, here is a possible
implementation of <code><a href="function_output_iterator.htm">boost::function_output_iterator</a></code>
adaptor:</p>
<pre>
template<class UnaryFunction>
struct function_output_iterator
: boost::output_iterator_helper< function_output_iterator<UnaryFunction> >
{
explicit function_output_iterator(UnaryFunction const& f = UnaryFunction())
: func(f) {}
template<typename T>
function_output_iterator& operator=(T const& value)
{
this->func(value);
return *this;
}
private:
UnaryFunction func;
};
</pre>
<p>Note that support for self-proxying does not prevent you from using <code>output_iterator_helper</code> to ease any other, different kind of output iterator's implementation. If <code>output_iterator_helper</code>'s target type provides its own definition of <code>operator*</code> or/and <code>operator++</code>, then these operators will get used and the ones supplied by <code>output_iterator_helper</code> will never be instantiated.</p>
<h3><a name="i_demo">Iterator Demonstration</a> and Test Program</h3>
<p>The <cite><a href="iterators_test.cpp">iterators_test.cpp</a></cite>
program demonstrates the use of the iterator templates, and can also be
used to verify correct operation. The following is the custom iterator
defined in the test program. It demonstrates a correct (though trivial)
implementation of the core operations that must be defined in order for
the iterator helpers to "fill in" the rest of the iterator
operations.</p>
<blockquote>
<pre>template <class T, class R, class P>
struct test_iter
: public boost::random_access_iterator_helper<
test_iter<T,R,P>, T, std::ptrdiff_t, P, R>
{
typedef test_iter self;
typedef R Reference;
typedef std::ptrdiff_t Distance;
public:
explicit test_iter(T* i =0);
test_iter(const self& x);
self& operator=(const self& x);
Reference operator*() const;
self& operator++();
self& operator--();
self& operator+=(Distance n);
self& operator-=(Distance n);
bool operator==(const self& x) const;
bool operator<(const self& x) const;
friend Distance operator-(const self& x, const self& y);
};</pre>
</blockquote>
<p>Check the <a href="../../status/compiler_status.html">compiler status report</a> for
the test results with selected platforms.</p>
<hr>
<h2><a name="contributors">Contributors</a></h2>
<dl>
<dt><a href="../../people/dave_abrahams.htm">Dave Abrahams</a>
<dd>Started the library and contributed the arithmetic operators in
<cite><a
href="../../boost/operators.hpp">boost/operators.hpp</a></cite>.
<dt><a href="../../people/jeremy_siek.htm">Jeremy Siek</a>
<dd>Contributed the <a href="#deref">dereference operators and
iterator helpers</a> in <cite><a
href="../../boost/operators.hpp">boost/operators.hpp</a></cite>.
Also contributed <cite><a
href="iterators_test.cpp">iterators_test.cpp</a></cite>.
<dt><a href="../../people/aleksey_gurtovoy.htm">Aleksey Gurtovoy</a>
<dd>Contributed the code to support <a href="#chaining">base class
chaining</a> while remaining backward-compatible with old
versions of the library.
<dt><a href="../../people/beman_dawes.html">Beman Dawes</a>
<dd>Contributed <cite><a href="operators_test.cpp">operators_test.cpp</a></cite>.
<dt><a href="../../people/daryle_walker.html">Daryle Walker</a>
<dd>Contributed classes for the shift operators, equivalence,
partial ordering, and arithmetic conversions. Added the
grouped operator classes. Added helper classes for
input and output iterators.
<dt>Helmut Zeisel
<dd>Contributed the 'left' operators and added some
grouped operator classes.
</dl>
<h2>Note for Users of <a name="old_lib_note">Older Versions</a></h2>
<p>The <a href="#chaining">changes in the library interface and
recommended usage</a> were motivated by some practical issues described
below. The new version of the library is still backward-compatible with
the former one (so you're not <em>forced</em> change any existing code),
but the old usage is deprecated. Though it was arguably simpler and
more intuitive than using <a href="#chaining">base class chaining</a>,
it has been discovered that the old practice of deriving from multiple
operator templates can cause the resulting classes to be much larger
than they should be. Most modern C++ compilers significantly bloat the
size of classes derived from multiple empty base classes, even though
the base classes themselves have no state. For instance, the size of
<code>point<int></code> from the <a href="#example">example</a>
above was 12-24 bytes on various compilers for the Win32 platform,
instead of the expected 8 bytes.</p>
<p>Strictly speaking, it was not the library's fault--the language
rules allow the compiler to apply the empty base class optimization in
that situation. In principle an arbitrary number of empty base classes
can be allocated at the same offset, provided that none of them have a
common ancestor (see section 10.5 [class.derived] paragraph 5 of the
standard). But the language definition also doesn't <em>require</em>
implementations to do the optimization, and few if any of today's
compilers implement it when multiple inheritance is involved. What's
worse, it is very unlikely that implementors will adopt it as a future
enhancement to existing compilers, because it would break binary
compatibility between code generated by two different versions of the
same compiler. As Matt Austern said, "One of the few times when you
have the freedom to do this sort of thing is when you're targeting a new
architecture...". On the other hand, many common compilers will use
the empty base optimization for single inheritance hierarchies.</p>
<p>Given the importance of the issue for the users of the library (which
aims to be useful for writing light-weight classes like
<code>MyInt</code> or <code>point<></code>), and the forces
described above, we decided to change the library interface so that the
object size bloat could be eliminated even on compilers that support
only the simplest form of the empty base class optimization. The
current library interface is the result of those changes. Though the
new usage is a bit more complicated than the old one, we think it's
worth it to make the library more useful in real world. Alexy Gurtovoy
contributed the code which supports the new usage idiom while allowing
the library remain backward-compatible.</p>
<hr>
<p>Revised: 30 Oct 2001</p>
<p>Copyright © David Abrahams and Beman Dawes 1999-2001.
Permission to copy, use, modify, sell and distribute this document is
granted provided this copyright notice appears in all copies. This
document is provided "as is" without express or implied
warranty, and with no claim as to its suitability for any purpose.</p>
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