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source: downloads/boost_1_34_1/libs/utility/operators.htm @ 29

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9	<title>Header <boost/operators.hpp> Documentation</title>
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13	<h1><img src="../../boost.png" alt="boost.png (6897 bytes)" align=
14	"middle" width="277" height="86">Header <cite><<a href=
15	"../../boost/operators.hpp">boost/operators.hpp</a>></cite></h1>
16
17	<p>The header <cite><<a href=
18	"../../boost/operators.hpp">boost/operators.hpp</a>></cite> supplies
19	several sets of class templates (in namespace <code>boost</code>). These
20	templates define operators at namespace scope in terms of a minimal
21	number of fundamental operators provided by the class.</p>
22
23	<h2><a name="contents">Contents</a></h2>
24
25	<ul>
26	<li><a href="#contents">Contents</a></li>
27
28	<li>
29	<a href="#rationale">Rationale</a>
30
31	<ul>
32	<li><a href="#semantics">Summary of Template Semantics</a></li>
33
34	<li><a href="#concepts_note">Use of <i>concepts</i></a></li>
35	</ul>
36	</li>
37
38	<li>
39	<a href="#usage">Usage</a>
40
41	<ul>
42	<li>
43	<a href="#two_arg">Two-Argument Template Forms</a>
44
45	<ul>
46	<li><a href="#two_arg_gen">General Considerations</a></li>
47
48	<li><a href="#mixed_arithmetics">Mixed arithmetics</a></li>
49	</ul>
50	</li>
51
52	<li><a href="#chaining">Base Class Chaining and Object
53	Size</a></li>
54
55	<li><a href="#explicit_instantiation">Separate, Explicit
56	Instantiation</a></li>
57
58	<li><a href="#portability">Requirement Portability</a></li>
59	</ul>
60	</li>
61
62	<li><a href="#example">Example</a></li>
63
64	<li>
65	<a href="#arithmetic">Arithmetic operators</a>
66
67	<ul>
68	<li>
69	<a href="#smpl_oprs">Simple Arithmetic Operators</a>
70
71	<ul>
72	<li><a href="#ordering">Ordering Note</a></li>
73
74	<li><a href="#symmetry">Symmetry Note</a></li>
75	</ul>
76	</li>
77
78	<li><a href="#grpd_oprs">Grouped Arithmetic Operators</a></li>
79
80	<li><a href="#ex_oprs">Example Templates</a></li>
81
82	<li><a href="#a_demo">Arithmetic Operators Demonstration and Test
83	Program</a></li>
84	</ul>
85	</li>
86
87	<li>
88	<a href="#deref">Dereference Operators and Iterator Helpers</a>
89
90	<ul>
91	<li><a href="#dereference">Dereference operators</a></li>
92
93	<li><a href="#grpd_iter_oprs">Grouped Iterator Operators</a></li>
94
95	<li>
96	<a href="#iterator">Iterator Helpers</a>
97
98	<ul>
99	<li><a href="#iterator_helpers_notes">Iterator Helper
100	Notes</a></li>
101	</ul>
102	</li>
103
104	<li><a href="#i_demo">Iterator Demonstration and Test
105	Program</a></li>
106	</ul>
107	</li>
108
109	<li><a href="#contributors">Contributors</a></li>
110
111	<li><a href="#old_lib_note">Note for Users of Older Versions</a></li>
112	</ul>
113
114	<h2><a name="rationale">Rationale</a></h2>
115
116	<p>Overloaded operators for class types typically occur in groups. If you
117	can write <code>x + y</code>, you probably also want to be able
118	to write <code>x += y</code>. If you can write <code>x < y,</code> you
119	also want <code>x > y, x >= y,</code> and <code>x <= y</code>.
120	Moreover, unless your class has really surprising behavior, some of these
121	related operators can be defined in terms of others (e.g. <code>x >= y
122	<=> !(x < y)</code>). Replicating this boilerplate for multiple
123	classes is both tedious and error-prone. The <cite><a href=
124	"../../boost/operators.hpp">boost/operators.hpp</a></cite> templates help
125	by generating operators for you at namespace scope based on other
126	operators you've defined in your class.</p>
127
128	<p>If, for example, you declare a class like this:</p>
129
130	<blockquote>
131	<pre>
132	class MyInt
133	: boost::operators<MyInt>
134	{
135	bool operator<(const MyInt& x) const;
136	bool operator==(const MyInt& x) const;
137	MyInt& operator+=(const MyInt& x);
138	MyInt& operator-=(const MyInt& x);
139	MyInt& operator*=(const MyInt& x);
140	MyInt& operator/=(const MyInt& x);
141	MyInt& operator%=(const MyInt& x);
142	MyInt& operator\|=(const MyInt& x);
143	MyInt& operator&=(const MyInt& x);
144	MyInt& operator^=(const MyInt& x);
145	MyInt& operator++();
146	MyInt& operator--();
147	};
148	</pre>
149	</blockquote>
150
151	<p>then the <code><a href="#operators1">operators<></a></code>
152	template adds more than a dozen additional operators, such as
153	<code>operator></code>, <code><=</code>, <code>>=</code>, and
154	(binary) <code>+</code>. <a href="#two_arg">Two-argument forms</a> of the
155	templates are also provided to allow interaction with other types.</p>
156
157	<h3>Summary of Template <a name="semantics">Semantics</a></h3>
158
159	<ol>
160	<li>Each operator template completes the concept(s) it describes by
161	defining overloaded operators for its target class.</li>
162
163	<li>The name of an operator class template indicates the <a href=
164	"#concepts_note">concept</a> that its target class will model.</li>
165
166	<li>Usually, the target class uses an instantation of the operator
167	class template as a base class. Some operator templates support an <a
168	href="#explicit_instantiation">alternate method</a>.</li>
169
170	<li>The concept can be compound, <i>i.e.</i> it may represent a common
171	combination of other, simpler concepts.</li>
172
173	<li>Most operator templates require their target class to support
174	operations related to the operators supplied by the template. In
175	accordance with widely accepted <a href=
176	"http://www.gotw.ca/gotw/004.htm">coding style recommendations</a>, the
177	target class is often required to supply the assignment counterpart
178	operator of the concept's "main operator." For example, the
179	<code>addable</code> template requires <code>operator+=(T
180	const&)</code> and in turn supplies <code>operator+(T const&, T
181	const&)</code>.</li>
182	</ol>
183
184	<h3>Use of <i><a name="concepts_note">concepts</a></i></h3>
185
186	<p>The discussed concepts are not necessarily the standard library's
187	concepts (CopyConstructible, <i>etc.</i>), although some of them could
188	be; they are what we call <i>concepts with a small 'c'</i>. In
189	particular, they are different from the former ones in that they <em>do
190	not</em> describe precise semantics of the operators they require to be
191	defined, except the requirements that (a) the semantics of the operators
192	grouped in one concept should be consistent (<i>e.g.</i> effects of
193	evaluating of <code>a += b</code> and
194	<code>a = a + b</code> expressions should be the
195	same), and (b) that the return types of the operators should follow
196	semantics of return types of corresponding operators for built-in types
197	(<i>e.g.</i> <code>operator<</code> should return a type convertible
198	to <code>bool</code>, and <code>T::operator-=</code> should return type
199	convertible to <code>T</code>). Such "loose" requirements make operators
200	library applicable to broader set of target classes from different
201	domains, <i>i.e.</i> eventually more useful.</p>
202
203	<h2><a name="usage">Usage</a></h2>
204
205	<h3><a name="two_arg">Two-Argument</a> Template Forms</h3>
206
207	<h4><a name="two_arg_gen">General Considerations</a></h4>
208
209	<p>The arguments to a binary operator commonly have identical types, but
210	it is not unusual to want to define operators which combine different
211	types. For <a href="#example">example</a>, one might want to multiply a
212	mathematical vector by a scalar. The two-argument template forms of the
213	arithmetic operator templates are supplied for this purpose. When
214	applying the two-argument form of a template, the desired return type of
215	the operators typically determines which of the two types in question
216	should be derived from the operator template. For example, if the result
217	of <code>T + U</code> is of type <code>T</code>, then
218	<code>T</code> (not <code>U</code>) should be derived from <code><a href=
219	"#addable2">addable<T, U></a></code>. The comparison templates
220	(<code><a href="#less_than_comparable2">less_than_comparable<T,
221	U></a></code>, <code><a href=
222	"#equality_comparable2">equality_comparable<T, U></a></code>,
223	<code><a href="#equivalent2">equivalent<T, U></a></code>, and
224	<code><a href="#partially_ordered2">partially_ordered<T,
225	U></a></code>) are exceptions to this guideline, since the return type
226	of the operators they define is <code>bool</code>.</p>
227
228	<p>On compilers which do not support partial specialization, the
229	two-argument forms must be specified by using the names shown below with
230	the trailing <code>'2'</code>. The single-argument forms with the
231	trailing <code>'1'</code> are provided for symmetry and to enable certain
232	applications of the <a href="#chaining">base class chaining</a>
233	technique.</p>
234
235	<h4><a name="mixed_arithmetics">Mixed Arithmetics</a></h4>
236
237	<p>Another application of the two-argument template forms is for mixed
238	arithmetics between a type <code>T</code> and a type <code>U</code> that
239	is convertible to <code>T</code>. In this case there are two ways where
240	the two-argument template forms are helpful: one is to provide the
241	respective signatures for operator overloading, the second is
242	performance.</p>
243
244	<p>With respect to the operator overloading assume <i>e.g.</i> that
245	<code>U</code> is <code>int</code>, that <code>T</code> is an
246	user-defined unlimited integer type, and that <code>double
247	operator-(double, const T&)</code> exists. If one wants to compute
248	<code>int - T</code> and does not provide <code>T operator-(int, const
249	T&)</code>, the compiler will consider <code>double operator-(double,
250	const T&)</code> to be a better match than <code>T operator-(const
251	T&, const T&)</code>, which will probably be different from the
252	user's intention. To define a complete set of operator signatures,
253	additional 'left' forms of the two-argument template forms are provided
254	(<code><a href="#subtractable2_left">subtractable2_left<T,
255	U></a></code>, <code><a href="#dividable2_left">dividable2_left<T,
256	U></a></code>, <code><a href="#modable2_left">modable2_left<T,
257	U></a></code>) that define the signatures for non-commutative
258	operators where <code>U</code> appears on the left hand side
259	(<code>operator-(const U&, const T&)</code>,
260	<code>operator/(const U&, const T&)</code>, <code>operator%(const
261	U&, const T&)</code>).</p>
262
263	<p>With respect to the performance observe that when one uses the single
264	type binary operator for mixed type arithmetics, the type <code>U</code>
265	argument has to be converted to type <code>T</code>. In practice,
266	however, there are often more efficient implementations of, say
267	<code>T::operator-=(const U&)</code> that avoid unnecessary
268	conversions from <code>U</code> to <code>T</code>. The two-argument
269	template forms of the arithmetic operator create additional operator
270	interfaces that use these more efficient implementations. There is,
271	however, no performance gain in the 'left' forms: they still need a
272	conversion from <code>U</code> to <code>T</code> and have an
273	implementation equivalent to the code that would be automatically created
274	by the compiler if it considered the single type binary operator to be
275	the best match.</p>
276
277	<h3>Base Class <a name="chaining">Chaining</a> and Object Size</h3>
278
279	<p>Every operator class template, except the <a href=
280	"#ex_oprs">arithmetic examples</a> and the <a href="#iterator">iterator
281	helpers</a>, has an additional, but optional, template type parameter
282	<code>B</code>. This parameter will be a publicly-derived base class of
283	the instantiated template. This means it must be a class type. It can be
284	used to avoid the bloating of object sizes that is commonly associated
285	with multiple-inheritance from several empty base classes (see the <a
286	href="#old_lib_note">note for users of older versions</a> for more
287	details). To provide support for a group of operators, use the
288	<code>B</code> parameter to chain operator templates into a single-base
289	class hierarchy, demostrated in the <a href="#example">usage example</a>.
290	The technique is also used by the composite operator templates to group
291	operator definitions. If a chain becomes too long for the compiler to
292	support, try replacing some of the operator templates with a single
293	grouped operator template that chains the old templates together; the
294	length limit only applies to the number of templates directly in the
295	chain, not those hidden in group templates.</p>
296
297	<p><strong>Caveat:</strong> to chain to a base class which is
298	<em>not</em> a Boost operator template when using the <a href=
299	"#two_arg">single-argument form</a> of a Boost operator template, you
300	must specify the operator template with the trailing <code>'1'</code> in
301	its name. Otherwise the library will assume you mean to define a binary
302	operation combining the class you intend to use as a base class and the
303	class you're deriving.</p>
304
305	<h3>Separate, <a name="explicit_instantiation">Explicit
306	Instantiation</a></h3>
307
308	<p>On some compilers (<i>e.g.</i> Borland, GCC) even single-inheritance
309	seems to cause an increase in object size in some cases. If you are not
310	defining a class template, you may get better object-size performance by
311	avoiding derivation altogether, and instead explicitly instantiating the
312	operator template as follows:</p>
313
314	<blockquote>
315	<pre>
316	class myclass // lose the inheritance...
317	{
318	//...
319	};
320
321	// explicitly instantiate the operators I need.
322	template struct less_than_comparable<myclass>;
323	template struct equality_comparable<myclass>;
324	template struct incrementable<myclass>;
325	template struct decrementable<myclass>;
326	template struct addable<myclass,long>;
327	template struct subtractable<myclass,long>;
328	</pre>
329	</blockquote>
330
331	<p>Note that some operator templates cannot use this workaround and must
332	be a base class of their primary operand type. Those templates define
333	operators which must be member functions, and the workaround needs the
334	operators to be independent friend functions. The relevant templates
335	are:</p>
336
337	<ul>
338	<li><code><a href=
339	"#dereferenceable">dereferenceable<></a></code></li>
340
341	<li><code><a href="#indexable">indexable<></a></code></li>
342
343	<li>Any composite operator template that includes at least one of the
344	above</li>
345	</ul>
346
347	<p>As Daniel Krügler pointed out, this technique violates 14.6.5/2
348	and is thus non-portable. The reasoning is, that the operators injected
349	by the instantiation of e.g.
350	<code>less_than_comparable<myclass></code> can not be found
351	by ADL according to the rules given by 3.4.2/2, since myclass is
352	not an associated class of
353	<code>less_than_comparable<myclass></code>.
354	Thus only use this technique if all else fails.</p>
355
356	<h3>Requirement <a name="portability">Portability</a></h3>
357
358	<p>Many compilers (<i>e.g.</i> MSVC 6.3, GCC 2.95.2) will not enforce the
359	requirements in the operator template tables unless the operations which
360	depend on them are actually used. This is not standard-conforming
361	behavior. In particular, although it would be convenient to derive all
362	your classes which need binary operators from the <code><a href=
363	"#operators1">operators<></a></code> and <code><a href=
364	"#operators2">operators2<></a></code> templates, regardless of
365	whether they implement all the requirements of those templates, this
366	shortcut is not portable. Even if this currently works with your
367	compiler, it may not work later.</p>
368
369	<h2><a name="example">Example</a></h2>
370
371	<p>This example shows how some of the <a href="#arithmetic">arithmetic
372	operator templates</a> can be used with a geometric point class
373	(template).</p>
374	<pre>
375	template <class T>
376	class point // note: private inheritance is OK here!
377	: boost::addable< point<T> // point + point
378	, boost::subtractable< point<T> // point - point
379	, boost::dividable2< point<T>, T // point / T
380	, boost::multipliable2< point<T>, T // point * T, T * point
381	> > > >
382	{
383	public:
384	point(T, T);
385	T x() const;
386	T y() const;
387
388	point operator+=(const point&);
389	// point operator+(point, const point&) automatically
390	// generated by addable.
391
392	point operator-=(const point&);
393	// point operator-(point, const point&) automatically
394	// generated by subtractable.
395
396	point operator*=(T);
397	// point operator*(point, const T&) and
398	// point operator*(const T&, point) auto-generated
399	// by multipliable.
400
401	point operator/=(T);
402	// point operator/(point, const T&) auto-generated
403	// by dividable.
404	private:
405	T x_;
406	T y_;
407	};
408
409	// now use the point<> class:
410
411	template <class T>
412	T length(const point<T> p)
413	{
414	return sqrt(p.x()p.x() + p.y()p.y());
415	}
416
417	const point<float> right(0, 1);
418	const point<float> up(1, 0);
419	const point<float> pi_over_4 = up + right;
420	const point<float> pi_over_4_normalized = pi_over_4 / length(pi_over_4);
421	</pre>
422
423	<h2><a name="arithmetic">Arithmetic</a> Operators</h2>
424
425	<p>The arithmetic operator templates ease the task of creating a custom
426	numeric type. Given a core set of operators, the templates add related
427	operators to the numeric class. These operations are like the ones the
428	standard arithmetic types have, and may include comparisons, adding,
429	incrementing, logical and bitwise manipulations, <i>etc</i>. Further,
430	since most numeric types need more than one of these operators, some
431	templates are provided to combine several of the basic operator templates
432	in one declaration.</p>
433
434	<p>The requirements for the types used to instantiate the simple operator
435	templates are specified in terms of expressions which must be valid and
436	the expression's return type. The composite operator templates only list
437	what other templates they use. The supplied operations and requirements
438	of the composite operator templates can be inferred from the operations
439	and requirements of the listed components.</p>
440
441	<h3><a name="smpl_oprs">Simple Arithmetic Operators</a></h3>
442
443	<p>These templates are "simple" since they provide operators based on a
444	single operation the base type has to provide. They have an additional
445	optional template parameter <code>B</code>, which is not shown, for the
446	<a href="#chaining">base class chaining</a> technique.</p>
447
448	<table cellpadding="5" border="1" align="center">
449	<caption>
450	Simple Arithmetic Operator Template Classes
451	</caption>
452
453	<tr>
454	<td colspan="3">
455	<table align="center" border="1">
456	<caption>
457	<em>Key</em>
458	</caption>
459
460	<tr>
461	<td><code>T</code>: primary operand type</td>
462
463	<td><code>U</code>: alternate operand type</td>
464	</tr>
465
466	<tr>
467	<td><code>t</code>, <code>t1</code>: values of type
468	<code>T</code></td>
469
470	<td><code>u</code>: value of type <code>U</code></td>
471	</tr>
472	</table>
473	</td>
474	</tr>
475
476	<tr>
477	<th>Template</th>
478
479	<th>Supplied Operations</th>
480
481	<th>Requirements</th>
482	</tr>
483
484	<tr>
485	<td><code><a name=
486	"less_than_comparable1">less_than_comparable<T></a></code><br>
487	<code>less_than_comparable1<T></code></td>
488
489	<td><code>bool operator>(const T&, const T&)</code><br>
490	<code>bool operator<=(const T&, const T&)</code><br>
491	<code>bool operator>=(const T&, const T&)</code></td>
492
493	<td><code>t < t1</code>.<br>
494	Return convertible to <code>bool</code>. See the <a href=
495	"#ordering">Ordering Note</a>.</td>
496	</tr>
497
498	<tr>
499	<td><code><a name="less_than_comparable2">less_than_comparable<T,
500	U></a></code><br>
501	<code>less_than_comparable2<T, U></code></td>
502
503	<td><code>bool operator<=(const T&, const U&)</code><br>
504	<code>bool operator>=(const T&, const U&)</code><br>
505	<code>bool operator>(const U&, const T&)</code><br>
506	<code>bool operator<(const U&, const T&)</code><br>
507	<code>bool operator<=(const U&, const T&)</code><br>
508	<code>bool operator>=(const U&, const T&)</code></td>
509
510	<td><code>t < u</code>. <code>t > u</code>.<br>
511	Returns convertible to <code>bool</code>. See the <a href=
512	"#ordering">Ordering Note</a>.</td>
513	</tr>
514
515	<tr>
516	<td><code><a name=
517	"equality_comparable1">equality_comparable<T></a></code><br>
518	<code>equality_comparable1<T></code></td>
519
520	<td><code>bool operator!=(const T&, const T&)</code></td>
521
522	<td><code>t == t1</code>.<br>
523	Return convertible to <code>bool</code>.</td>
524	</tr>
525
526	<tr>
527	<td><code><a name="equality_comparable2">equality_comparable<T,
528	U></a></code><br>
529	<code>equality_comparable2<T, U></code></td>
530
531	<td><code>bool operator==(const U&, const T&)</code><br>
532	<code>bool operator!=(const U&, const T&)</code><br>
533	<code>bool operator!=(const T&, const U&)</code></td>
534
535	<td><code>t == u</code>.<br>
536	Return convertible to <code>bool</code>.</td>
537	</tr>
538
539	<tr>
540	<td><code><a name="addable1">addable<T></a></code><br>
541	<code>addable1<T></code></td>
542
543	<td><code>T operator+(const T&, const T&)</code></td>
544
545	<td><code>T temp(t); temp += t1</code>.<br>
546	Return convertible to <code>T</code>. See the <a href=
547	"#symmetry">Symmetry Note</a>.</td>
548	</tr>
549
550	<tr>
551	<td><code><a name="addable2">addable<T, U></a></code><br>
552	<code>addable2<T, U></code></td>
553
554	<td><code>T operator+(const T&, const U&)</code><br>
555	<code>T operator+(const U&, const T& )</code></td>
556
557	<td><code>T temp(t); temp += u</code>.<br>
558	Return convertible to <code>T</code>. See the <a href=
559	"#symmetry">Symmetry Note</a>.</td>
560	</tr>
561
562	<tr>
563	<td><code><a name=
564	"subtractable1">subtractable<T></a></code><br>
565	<code>subtractable1<T></code></td>
566
567	<td><code>T operator-(const T&, const T&)</code></td>
568
569	<td><code>T temp(t); temp -= t1</code>.<br>
570	Return convertible to <code>T</code>. See the <a href=
571	"#symmetry">Symmetry Note</a>.</td>
572	</tr>
573
574	<tr>
575	<td><code><a name="subtractable2">subtractable<T,
576	U></a></code><br>
577	<code>subtractable2<T, U></code></td>
578
579	<td><code>T operator-(const T&, const U&)</code></td>
580
581	<td><code>T temp(t); temp -= u</code>.<br>
582	Return convertible to <code>T</code>. See the <a href=
583	"#symmetry">Symmetry Note</a>.</td>
584	</tr>
585
586	<tr>
587	<td><code><a name="subtractable2_left">subtractable2_left<T,
588	U></a></code></td>
589
590	<td><code>T operator-(const U&, const T&)</code></td>
591
592	<td><code>T temp(u); temp -= t</code>.<br>
593	Return convertible to <code>T</code>.</td>
594	</tr>
595
596	<tr>
597	<td><code><a name=
598	"multipliable1">multipliable<T></a></code><br>
599	<code>multipliable1<T></code></td>
600
601	<td><code>T operator*(const T&, const T&)</code></td>
602
603	<td><code>T temp(t); temp *= t1</code>.<br>
604	Return convertible to <code>T</code>. See the <a href=
605	"#symmetry">Symmetry Note</a>.</td>
606	</tr>
607
608	<tr>
609	<td><code><a name="multipliable2">multipliable<T,
610	U></a></code><br>
611	<code>multipliable2<T, U></code></td>
612
613	<td><code>T operator*(const T&, const U&)</code><br>
614	<code>T operator*(const U&, const T&)</code></td>
615
616	<td><code>T temp(t); temp *= u</code>.<br>
617	Return convertible to <code>T</code>. See the <a href=
618	"#symmetry">Symmetry Note</a>.</td>
619	</tr>
620
621	<tr>
622	<td><code><a name="dividable1">dividable<T></a></code><br>
623	<code>dividable1<T></code></td>
624
625	<td><code>T operator/(const T&, const T&)</code></td>
626
627	<td><code>T temp(t); temp /= t1</code>.<br>
628	Return convertible to <code>T</code>. See the <a href=
629	"#symmetry">Symmetry Note</a>.</td>
630	</tr>
631
632	<tr>
633	<td><code><a name="dividable2">dividable<T, U></a></code><br>
634	<code>dividable2<T, U></code></td>
635
636	<td><code>T operator/(const T&, const U&)</code></td>
637
638	<td><code>T temp(t); temp /= u</code>.<br>
639	Return convertible to <code>T</code>. See the <a href=
640	"#symmetry">Symmetry Note</a>.</td>
641	</tr>
642
643	<tr>
644	<td><code><a name="dividable2_left">dividable2_left<T,
645	U></a></code></td>
646
647	<td><code>T operator/(const U&, const T&)</code></td>
648
649	<td><code>T temp(u); temp /= t</code>.<br>
650	Return convertible to <code>T</code>.</td>
651	</tr>
652
653	<tr>
654	<td><code><a name="modable1">modable<T></a></code><br>
655	<code>modable1<T></code></td>
656
657	<td><code>T operator%(const T&, const T&)</code></td>
658
659	<td><code>T temp(t); temp %= t1</code>.<br>
660	Return convertible to <code>T</code>. See the <a href=
661	"#symmetry">Symmetry Note</a>.</td>
662	</tr>
663
664	<tr>
665	<td><code><a name="modable2">modable<T, U></a></code><br>
666	<code>modable2<T, U></code></td>
667
668	<td><code>T operator%(const T&, const U&)</code></td>
669
670	<td><code>T temp(t); temp %= u</code>.<br>
671	Return convertible to <code>T</code>. See the <a href=
672	"#symmetry">Symmetry Note</a>.</td>
673	</tr>
674
675	<tr>
676	<td><code><a name="modable2_left">modable2_left<T,
677	U></a></code></td>
678
679	<td><code>T operator%(const U&, const T&)</code></td>
680
681	<td><code>T temp(u); temp %= t</code>.<br>
682	Return convertible to <code>T</code>.</td>
683	</tr>
684
685	<tr>
686	<td><code><a name="orable1">orable<T></a></code><br>
687	<code>orable1<T></code></td>
688
689	<td><code>T operator\|(const T&, const T&)</code></td>
690
691	<td><code>T temp(t); temp \|= t1</code>.<br>
692	Return convertible to <code>T</code>. See the <a href=
693	"#symmetry">Symmetry Note</a>.</td>
694	</tr>
695
696	<tr>
697	<td><code><a name="orable2">orable<T, U></a></code><br>
698	<code>orable2<T, U></code></td>
699
700	<td><code>T operator\|(const T&, const U&)</code><br>
701	<code>T operator\|(const U&, const T&)</code></td>
702
703	<td><code>T temp(t); temp \|= u</code>.<br>
704	Return convertible to <code>T</code>. See the <a href=
705	"#symmetry">Symmetry Note</a>.</td>
706	</tr>
707
708	<tr>
709	<td><code><a name="andable1">andable<T></a></code><br>
710	<code>andable1<T></code></td>
711
712	<td><code>T operator&(const T&, const T&)</code></td>
713
714	<td><code>T temp(t); temp &= t1</code>.<br>
715	Return convertible to <code>T</code>. See the <a href=
716	"#symmetry">Symmetry Note</a>.</td>
717	</tr>
718
719	<tr>
720	<td><code><a name="andable2">andable<T, U></a></code><br>
721	<code>andable2<T, U></code></td>
722
723	<td><code>T operator&(const T&, const U&)</code><br>
724	<code>T operator&(const U&, const T&)</code></td>
725
726	<td><code>T temp(t); temp &= u</code>.<br>
727	Return convertible to <code>T</code>. See the <a href=
728	"#symmetry">Symmetry Note</a>.</td>
729	</tr>
730
731	<tr>
732	<td><code><a name="xorable1">xorable<T></a></code><br>
733	<code>xorable1<T></code></td>
734
735	<td><code>T operator^(const T&, const T&)</code></td>
736
737	<td><code>T temp(t); temp ^= t1</code>.<br>
738	Return convertible to <code>T</code>. See the <a href=
739	"#symmetry">Symmetry Note</a>.</td>
740	</tr>
741
742	<tr>
743	<td><code><a name="xorable2">xorable<T, U></a></code><br>
744	<code>xorable2<T, U></code></td>
745
746	<td><code>T operator^(const T&, const U&)</code><br>
747	<code>T operator^(const U&, const T&)</code></td>
748
749	<td><code>T temp(t); temp ^= u</code>.<br>
750	Return convertible to <code>T</code>. See the <a href=
751	"#symmetry">Symmetry Note</a>.</td>
752	</tr>
753
754	<tr>
755	<td><code><a name=
756	"incrementable">incrementable<T></a></code></td>
757
758	<td><code>T operator++(T&, int)</code></td>
759
760	<td><code>T temp(t); ++t</code><br>
761	Return convertible to <code>T</code>.</td>
762	</tr>
763
764	<tr>
765	<td><code><a name=
766	"decrementable">decrementable<T></a></code></td>
767
768	<td><code>T operator--(T&, int)</code></td>
769
770	<td><code>T temp(t); --t;</code><br>
771	Return convertible to <code>T</code>.</td>
772	</tr>
773
774	<tr>
775	<td><code><a name=
776	"left_shiftable1">left_shiftable<T></a></code><br>
777	<code>left_shiftable1<T></code></td>
778
779	<td><code>T operator<<(const T&, const T&)</code></td>
780
781	<td><code>T temp(t); temp <<= t1</code>.<br>
782	Return convertible to <code>T</code>. See the <a href=
783	"#symmetry">Symmetry Note</a>.</td>
784	</tr>
785
786	<tr>
787	<td><code><a name="left_shiftable2">left_shiftable<T,
788	U></a></code><br>
789	<code>left_shiftable2<T, U></code></td>
790
791	<td><code>T operator<<(const T&, const U&)</code></td>
792
793	<td><code>T temp(t); temp <<= u</code>.<br>
794	Return convertible to <code>T</code>. See the <a href=
795	"#symmetry">Symmetry Note</a>.</td>
796	</tr>
797
798	<tr>
799	<td><code><a name=
800	"right_shiftable1">right_shiftable<T></a></code><br>
801	<code>right_shiftable1<T></code></td>
802
803	<td><code>T operator>>(const T&, const T&)</code></td>
804
805	<td><code>T temp(t); temp >>= t1</code>.<br>
806	Return convertible to <code>T</code>. See the <a href=
807	"#symmetry">Symmetry Note</a>.</td>
808	</tr>
809
810	<tr>
811	<td><code><a name="right_shiftable2">right_shiftable<T,
812	U></a></code><br>
813	<code>right_shiftable2<T, U></code></td>
814
815	<td><code>T operator>>(const T&, const U&)</code></td>
816
817	<td><code>T temp(t); temp >>= u</code>.<br>
818	Return convertible to <code>T</code>. See the <a href=
819	"#symmetry">Symmetry Note</a>.</td>
820	</tr>
821
822	<tr>
823	<td><code><a name="equivalent1">equivalent<T></a></code><br>
824	<code>equivalent1<T></code></td>
825
826	<td><code>bool operator==(const T&, const T&)</code></td>
827
828	<td><code>t < t1</code>.<br>
829	Return convertible to <code>bool</code>. See the <a href=
830	"#ordering">Ordering Note</a>.</td>
831	</tr>
832
833	<tr>
834	<td><code><a name="equivalent2">equivalent<T, U></a></code><br>
835	<code>equivalent2<T, U></code></td>
836
837	<td><code>bool operator==(const T&, const U&)</code></td>
838
839	<td><code>t < u</code>. <code>t > u</code>.<br>
840	Returns convertible to <code>bool</code>. See the <a href=
841	"#ordering">Ordering Note</a>.</td>
842	</tr>
843
844	<tr>
845	<td><code><a name=
846	"partially_ordered1">partially_ordered<T></a></code><br>
847	<code>partially_ordered1<T></code></td>
848
849	<td><code>bool operator>(const T&, const T&)</code><br>
850	<code>bool operator<=(const T&, const T&)</code><br>
851	<code>bool operator>=(const T&, const T&)</code></td>
852
853	<td><code>t < t1</code>. <code>t == t1</code>.<br>
854	Returns convertible to <code>bool</code>. See the <a href=
855	"#ordering">Ordering Note</a>.</td>
856	</tr>
857
858	<tr>
859	<td><code><a name="partially_ordered2">partially_ordered<T,
860	U></a></code><br>
861	<code>partially_ordered2<T, U></code></td>
862
863	<td><code>bool operator<=(const T&, const U&)</code><br>
864	<code>bool operator>=(const T&, const U&)</code><br>
865	<code>bool operator>(const U&, const T&)</code><br>
866	<code>bool operator<(const U&, const T&)</code><br>
867	<code>bool operator<=(const U&, const T&)</code><br>
868	<code>bool operator>=(const U&, const T&)</code></td>
869
870	<td><code>t < u</code>. <code>t > u</code>. <code>t ==
871	u</code>.<br>
872	Returns convertible to <code>bool</code>. See the <a href=
873	"#ordering">Ordering Note</a>.</td>
874	</tr>
875	</table>
876
877	<h4><a name="ordering">Ordering</a> Note</h4>
878
879	<p>The <code><a href=
880	"#less_than_comparable1">less_than_comparable<T></a></code> and
881	<code><a href="#partially_ordered1">partially_ordered<T></a></code>
882	templates provide the same set of operations. However, the workings of
883	<code><a href=
884	"#less_than_comparable1">less_than_comparable<T></a></code> assume
885	that all values of type <code>T</code> can be placed in a total order. If
886	that is not true (<i>e.g.</i> Not-a-Number values in IEEE floating point
887	arithmetic), then <code><a href=
888	"#partially_ordered1">partially_ordered<T></a></code> should be
889	used. The <code><a href=
890	"#partially_ordered1">partially_ordered<T></a></code> template can
891	be used for a totally-ordered type, but it is not as efficient as
892	<code><a href=
893	"#less_than_comparable1">less_than_comparable<T></a></code>. This
894	rule also applies for <code><a href=
895	"#less_than_comparable2">less_than_comparable<T, U></a></code> and
896	<code><a href="#partially_ordered2">partially_ordered<T,
897	U></a></code> with respect to the ordering of all <code>T</code> and
898	<code>U</code> values, and for both versions of <code><a href=
899	"#equivalent1">equivalent<></a></code>. The solution for <code><a
900	href="#equivalent1">equivalent<></a></code> is to write a custom
901	<code>operator==</code> for the target class.</p>
902
903	<h4><a name="symmetry">Symmetry</a> Note</h4>
904
905	<p>Before talking about symmetry, we need to talk about optimizations to
906	understand the reasons for the different implementation styles of
907	operators. Let's have a look at <code>operator+</code> for a class
908	<code>T</code> as an example:</p>
909	<pre>
910	T operator+( const T& lhs, const T& rhs )
911	{
912	return T( lhs ) += rhs;
913	}
914	</pre>
915	This would be a normal implementation of <code>operator+</code>, but it
916	is not an efficient one. An unnamed local copy of <code>lhs</code> is
917	created, <code>operator+=</code> is called on it and it is copied to the
918	function return value (which is another unnamed object of type
919	<code>T</code>). The standard doesn't generally allow the intermediate
920	object to be optimized away:
921
922	<blockquote>
923	3.7.2/2: Automatic storage duration<br>
924	<br>
925	If a named automatic object has initialization or a destructor with
926	side effects, it shall not be destroyed before the end of its block,
927	nor shall it be eliminated as an optimization even if it appears to be
928	unused, except that a class object or its copy may be eliminated as
929	specified in 12.8.
930	</blockquote>
931	The reference to 12.8 is important for us:
932
933	<blockquote>
934	12.8/15: Copying class objects<br>
935	...<br>
936	For a function with a class return type, if the expression in the
937	return statement is the name of a local object, and the cv-unqualified
938	type of the local object is the same as the function return type, an
939	implementation is permitted to omit creating the temporary object to
940	hold the function return value, even if the class copy constructor or
941	destructor has side effects.
942	</blockquote>
943	This optimization is known as the named return value optimization (NRVO),
944	which leads us to the following implementation for
945	<code>operator+</code>:
946	<pre>
947	T operator+( const T& lhs, const T& rhs )
948	{
949	T nrv( lhs );
950	nrv += rhs;
951	return nrv;
952	}
953	</pre>
954	Given this implementation, the compiler is allowed to remove the
955	intermediate object. Sadly, not all compiler implement the NRVO, some
956	even implement it in an incorrect way which makes it useless here.
957	Without the NRVO, the NRVO-friendly code is no worse than the original
958	code showed above, but there is another possible implementation, which
959	has some very special properties:
960	<pre>
961	T operator+( T lhs, const T& rhs )
962	{
963	return lhs += rhs;
964	}
965	</pre>
966	The difference to the first implementation is that <code>lhs</code> is
967	not taken as a constant reference used to create a copy; instead,
968	<code>lhs</code> is a by-value parameter, thus it is already the copy
969	needed. This allows another optimization (12.2/2) for some cases.
970	Consider <code>a + b + c</code> where the result of
971	<code>a + b</code> is not copied when used as <code>lhs</code>
972	when adding <code>c</code>. This is more efficient than the original
973	code, but not as efficient as a compiler using the NRVO. For most people,
974	it is still preferable for compilers that don't implement the NRVO, but
975	the <code>operator+</code> now has a different function signature. Also,
976	the number of objects created differs for
977	<code>(a + b ) + c</code> and
978	<code>a + ( b + c )</code>. Most probably,
979	this won't be a problem for you, but if your code relies on the function
980	signature or a strict symmetric behaviour, you should set
981	<code>BOOST_FORCE_SYMMETRIC_OPERATORS</code> in your user-config. This
982	will force the NRVO-friendly implementation to be used even for compilers
983	that don't implement the NRVO. <br>
984	<br>
985
986	<h3><a name="grpd_oprs">Grouped Arithmetic Operators</a></h3>
987
988	<p>The following templates provide common groups of related operations.
989	For example, since a type which is addable is usually also subractable,
990	the <code><a href="#additive1">additive</a></code> template provides the
991	combined operators of both. The grouped operator templates have an
992	additional optional template parameter <code>B</code>, which is not
993	shown, for the <a href="#chaining">base class chaining</a> technique.</p>
994
995	<table cellpadding="5" border="1" align="center">
996	<caption>
997	Grouped Arithmetic Operator Template Classes
998	</caption>
999
1000	<tr>
1001	<td colspan="2">
1002	<table align="center" border="1">
1003	<caption>
1004	<em>Key</em>
1005	</caption>
1006
1007	<tr>
1008	<td><code>T</code>: primary operand type</td>
1009
1010	<td><code>U</code>: alternate operand type</td>
1011	</tr>
1012	</table>
1013	</td>
1014	</tr>
1015
1016	<tr>
1017	<th>Template</th>
1018
1019	<th>Component Operator Templates</th>
1020	</tr>
1021
1022	<tr>
1023	<td><code><a name=
1024	"totally_ordered1">totally_ordered<T></a></code><br>
1025	<code>totally_ordered1<T></code></td>
1026
1027	<td>
1028	<ul>
1029	<li><code><a href=
1030	"#less_than_comparable1">less_than_comparable<T></a></code></li>
1031
1032	<li><code><a href=
1033	"#equality_comparable1">equality_comparable<T></a></code></li>
1034	</ul>
1035	</td>
1036	</tr>
1037
1038	<tr>
1039	<td><code><a name="totally_ordered2">totally_ordered<T,
1040	U></a></code><br>
1041	<code>totally_ordered2<T, U></code></td>
1042
1043	<td>
1044	<ul>
1045	<li><code><a href=
1046	"#less_than_comparable2">less_than_comparable<T,
1047	U></a></code></li>
1048
1049	<li><code><a href=
1050	"#equality_comparable2">equality_comparable<T,
1051	U></a></code></li>
1052	</ul>
1053	</td>
1054	</tr>
1055
1056	<tr>
1057	<td><code><a name="additive1">additive<T></a></code><br>
1058	<code>additive1<T></code></td>
1059
1060	<td>
1061	<ul>
1062	<li><code><a href="#addable1">addable<T></a></code></li>
1063
1064	<li><code><a href=
1065	"#subtractable1">subtractable<T></a></code></li>
1066	</ul>
1067	</td>
1068	</tr>
1069
1070	<tr>
1071	<td><code><a name="additive2">additive<T, U></a></code><br>
1072	<code>additive2<T, U></code></td>
1073
1074	<td>
1075	<ul>
1076	<li><code><a href="#addable2">addable<T, U></a></code></li>
1077
1078	<li><code><a href="#subtractable2">subtractable<T,
1079	U></a></code></li>
1080	</ul>
1081	</td>
1082	</tr>
1083
1084	<tr>
1085	<td><code><a name=
1086	"multiplicative1">multiplicative<T></a></code><br>
1087	<code>multiplicative1<T></code></td>
1088
1089	<td>
1090	<ul>
1091	<li><code><a href=
1092	"#multipliable1">multipliable<T></a></code></li>
1093
1094	<li><code><a href=
1095	"#dividable1">dividable<T></a></code></li>
1096	</ul>
1097	</td>
1098	</tr>
1099
1100	<tr>
1101	<td><code><a name="multiplicative2">multiplicative<T,
1102	U></a></code><br>
1103	<code>multiplicative2<T, U></code></td>
1104
1105	<td>
1106	<ul>
1107	<li><code><a href="#multipliable2">multipliable<T,
1108	U></a></code></li>
1109
1110	<li><code><a href="#dividable2">dividable<T,
1111	U></a></code></li>
1112	</ul>
1113	</td>
1114	</tr>
1115
1116	<tr>
1117	<td><code><a name=
1118	"integer_multiplicative1">integer_multiplicative<T></a></code><br>
1119
1120	<code>integer_multiplicative1<T></code></td>
1121
1122	<td>
1123	<ul>
1124	<li><code><a href=
1125	"#multiplicative1">multiplicative<T></a></code></li>
1126
1127	<li><code><a href="#modable1">modable<T></a></code></li>
1128	</ul>
1129	</td>
1130	</tr>
1131
1132	<tr>
1133	<td><code><a name=
1134	"integer_multiplicative2">integer_multiplicative<T,
1135	U></a></code><br>
1136	<code>integer_multiplicative2<T, U></code></td>
1137
1138	<td>
1139	<ul>
1140	<li><code><a href="#multiplicative2">multiplicative<T,
1141	U></a></code></li>
1142
1143	<li><code><a href="#modable2">modable<T, U></a></code></li>
1144	</ul>
1145	</td>
1146	</tr>
1147
1148	<tr>
1149	<td><code><a name="arithmetic1">arithmetic<T></a></code><br>
1150	<code>arithmetic1<T></code></td>
1151
1152	<td>
1153	<ul>
1154	<li><code><a href="#additive1">additive<T></a></code></li>
1155
1156	<li><code><a href=
1157	"#multiplicative1">multiplicative<T></a></code></li>
1158	</ul>
1159	</td>
1160	</tr>
1161
1162	<tr>
1163	<td><code><a name="arithmetic2">arithmetic<T, U></a></code><br>
1164	<code>arithmetic2<T, U></code></td>
1165
1166	<td>
1167	<ul>
1168	<li><code><a href="#additive2">additive<T,
1169	U></a></code></li>
1170
1171	<li><code><a href="#multiplicative2">multiplicative<T,
1172	U></a></code></li>
1173	</ul>
1174	</td>
1175	</tr>
1176
1177	<tr>
1178	<td><code><a name=
1179	"integer_arithmetic1">integer_arithmetic<T></a></code><br>
1180	<code>integer_arithmetic1<T></code></td>
1181
1182	<td>
1183	<ul>
1184	<li><code><a href="#additive1">additive<T></a></code></li>
1185
1186	<li><code><a href=
1187	"#integer_multiplicative1">integer_multiplicative<T></a></code></li>
1188	</ul>
1189	</td>
1190	</tr>
1191
1192	<tr>
1193	<td><code><a name="integer_arithmetic2">integer_arithmetic<T,
1194	U></a></code><br>
1195	<code>integer_arithmetic2<T, U></code></td>
1196
1197	<td>
1198	<ul>
1199	<li><code><a href="#additive2">additive<T,
1200	U></a></code></li>
1201
1202	<li><code><a href=
1203	"#integer_multiplicative2">integer_multiplicative<T,
1204	U></a></code></li>
1205	</ul>
1206	</td>
1207	</tr>
1208
1209	<tr>
1210	<td><code><a name="bitwise1">bitwise<T></a></code><br>
1211	<code>bitwise1<T></code></td>
1212
1213	<td>
1214	<ul>
1215	<li><code><a href="#xorable1">xorable<T></a></code></li>
1216
1217	<li><code><a href="#andable1">andable<T></a></code></li>
1218
1219	<li><code><a href="#orable1">orable<T></a></code></li>
1220	</ul>
1221	</td>
1222	</tr>
1223
1224	<tr>
1225	<td><code><a name="bitwise2">bitwise<T, U></a></code><br>
1226	<code>bitwise2<T, U></code></td>
1227
1228	<td>
1229	<ul>
1230	<li><code><a href="#xorable2">xorable<T, U></a></code></li>
1231
1232	<li><code><a href="#andable2">andable<T, U></a></code></li>
1233
1234	<li><code><a href="#orable2">orable<T, U></a></code></li>
1235	</ul>
1236	</td>
1237	</tr>
1238
1239	<tr>
1240	<td><code><a name=
1241	"unit_steppable">unit_steppable<T></a></code></td>
1242
1243	<td>
1244	<ul>
1245	<li><code><a href=
1246	"#incrementable">incrementable<T></a></code></li>
1247
1248	<li><code><a href=
1249	"#decrementable">decrementable<T></a></code></li>
1250	</ul>
1251	</td>
1252	</tr>
1253
1254	<tr>
1255	<td><code><a name="shiftable1">shiftable<T></a></code><br>
1256	<code>shiftable1<T></code></td>
1257
1258	<td>
1259	<ul>
1260	<li><code><a href=
1261	"#left_shiftable1">left_shiftable<T></a></code></li>
1262
1263	<li><code><a href=
1264	"#right_shiftable1">right_shiftable<T></a></code></li>
1265	</ul>
1266	</td>
1267	</tr>
1268
1269	<tr>
1270	<td><code><a name="shiftable2">shiftable<T, U></a></code><br>
1271	<code>shiftable2<T, U></code></td>
1272
1273	<td>
1274	<ul>
1275	<li><code><a href="#left_shiftable2">left_shiftable<T,
1276	U></a></code></li>
1277
1278	<li><code><a href="#right_shiftable2">right_shiftable<T,
1279	U></a></code></li>
1280	</ul>
1281	</td>
1282	</tr>
1283
1284	<tr>
1285	<td><code><a name=
1286	"ring_operators1">ring_operators<T></a></code><br>
1287	<code>ring_operators1<T></code></td>
1288
1289	<td>
1290	<ul>
1291	<li><code><a href="#additive1">additive<T></a></code></li>
1292
1293	<li><code><a href=
1294	"#multipliable1">multipliable<T></a></code></li>
1295	</ul>
1296	</td>
1297	</tr>
1298
1299	<tr>
1300	<td><code><a name="ring_operators2">ring_operators<T,
1301	U></a></code><br>
1302	<code>ring_operators2<T, U></code></td>
1303
1304	<td>
1305	<ul>
1306	<li><code><a href="#additive2">additive<T,
1307	U></a></code></li>
1308
1309	<li><code><a href="#subtractable2_left">subtractable2_left<T,
1310	U></a></code></li>
1311
1312	<li><code><a href="#multipliable2">multipliable<T,
1313	U></a></code></li>
1314	</ul>
1315	</td>
1316	</tr>
1317
1318	<tr>
1319	<td><code><a name=
1320	"ordered_ring_operators1">ordered_ring_operators<T></a></code><br>
1321
1322	<code>ordered_ring_operators1<T></code></td>
1323
1324	<td>
1325	<ul>
1326	<li><code><a href=
1327	"#ring_operators1">ring_operators<T></a></code></li>
1328
1329	<li><code><a href=
1330	"#totally_ordered1">totally_ordered<T></a></code></li>
1331	</ul>
1332	</td>
1333	</tr>
1334
1335	<tr>
1336	<td><code><a name=
1337	"ordered_ring_operators2">ordered_ring_operators<T,
1338	U></a></code><br>
1339	<code>ordered_ring_operators2<T, U></code></td>
1340
1341	<td>
1342	<ul>
1343	<li><code><a href="#ring_operators2">ring_operators<T,
1344	U></a></code></li>
1345
1346	<li><code><a href="#totally_ordered2">totally_ordered<T,
1347	U></a></code></li>
1348	</ul>
1349	</td>
1350	</tr>
1351
1352	<tr>
1353	<td><code><a name=
1354	"field_operators1">field_operators<T></a></code><br>
1355	<code>field_operators1<T></code></td>
1356
1357	<td>
1358	<ul>
1359	<li><code><a href=
1360	"#ring_operators1">ring_operators<T></a></code></li>
1361
1362	<li><code><a href=
1363	"#dividable1">dividable<T></a></code></li>
1364	</ul>
1365	</td>
1366	</tr>
1367
1368	<tr>
1369	<td><code><a name="field_operators2">field_operators<T,
1370	U></a></code><br>
1371	<code>field_operators2<T, U></code></td>
1372
1373	<td>
1374	<ul>
1375	<li><code><a href="#ring_operators2">ring_operators<T,
1376	U></a></code></li>
1377
1378	<li><code><a href="#dividable2">dividable<T,
1379	U></a></code></li>
1380
1381	<li><code><a href="#dividable2_left">dividable2_left<T,
1382	U></a></code></li>
1383	</ul>
1384	</td>
1385	</tr>
1386
1387	<tr>
1388	<td><code><a name=
1389	"ordered_field_operators1">ordered_field_operators<T></a></code><br>
1390
1391	<code>ordered_field_operators1<T></code></td>
1392
1393	<td>
1394	<ul>
1395	<li><code><a href=
1396	"#field_operators1">field_operators<T></a></code></li>
1397
1398	<li><code><a href=
1399	"#totally_ordered1">totally_ordered<T></a></code></li>
1400	</ul>
1401	</td>
1402	</tr>
1403
1404	<tr>
1405	<td><code><a name=
1406	"ordered_field_operators2">ordered_field_operators<T,
1407	U></a></code><br>
1408	<code>ordered_field_operators2<T, U></code></td>
1409
1410	<td>
1411	<ul>
1412	<li><code><a href="#field_operators2">field_operators<T,
1413	U></a></code></li>
1414
1415	<li><code><a href="#totally_ordered2">totally_ordered<T,
1416	U></a></code></li>
1417	</ul>
1418	</td>
1419	</tr>
1420
1421	<tr>
1422	<td><code><a name=
1423	"euclidian_ring_operators1">euclidian_ring_operators<T></a></code><br>
1424
1425	<code>euclidian_ring_operators1<T></code></td>
1426
1427	<td>
1428	<ul>
1429	<li><code><a href=
1430	"#ring_operators1">ring_operators<T></a></code></li>
1431
1432	<li><code><a href=
1433	"#dividable1">dividable<T></a></code></li>
1434
1435	<li><code><a href="#modable1">modable<T></a></code></li>
1436	</ul>
1437	</td>
1438	</tr>
1439
1440	<tr>
1441	<td><code><a name=
1442	"euclidian_ring_operators2">euclidian_ring_operators<T,
1443	U></a></code><br>
1444	<code>euclidian_ring_operators2<T, U></code></td>
1445
1446	<td>
1447	<ul>
1448	<li><code><a href="#ring_operators2">ring_operators<T,
1449	U></a></code></li>
1450
1451	<li><code><a href="#dividable2">dividable<T,
1452	U></a></code></li>
1453
1454	<li><code><a href="#dividable2_left">dividable2_left<T,
1455	U></a></code></li>
1456
1457	<li><code><a href="#modable2">modable<T, U></a></code></li>
1458
1459	<li><code><a href="#modable2_left">modable2_left<T,
1460	U></a></code></li>
1461	</ul>
1462	</td>
1463	</tr>
1464
1465	<tr>
1466	<td><code><a name=
1467	"ordered_euclidian_ring_operators1">ordered_euclidian_ring_operators<T></a></code><br>
1468
1469	<code>ordered_euclidian_ring_operators1<T></code></td>
1470
1471	<td>
1472	<ul>
1473	<li><code><a href=
1474	"#euclidian_ring_operators1">euclidian_ring_operators<T></a></code></li>
1475
1476	<li><code><a href=
1477	"#totally_ordered1">totally_ordered<T></a></code></li>
1478	</ul>
1479	</td>
1480	</tr>
1481
1482	<tr>
1483	<td><code><a name=
1484	"ordered_euclidian_ring_operators2">ordered_euclidian_ring_operators<T,
1485	U></a></code><br>
1486	<code>ordered_euclidian_ring_operators2<T, U></code></td>
1487
1488	<td>
1489	<ul>
1490	<li><code><a href=
1491	"#euclidian_ring_operators2">euclidian_ring_operators<T,
1492	U></a></code></li>
1493
1494	<li><code><a href="#totally_ordered2">totally_ordered<T,
1495	U></a></code></li>
1496	</ul>
1497	</td>
1498	</tr>
1499	</table>
1500
1501	<h3><a name="ex_oprs">Example</a> Templates</h3>
1502
1503	<p>The arithmetic operator class templates <code><a href=
1504	"#operators1">operators<></a></code> and <code><a href=
1505	"#operators2">operators2<></a></code> are examples of
1506	non-extensible operator grouping classes. These legacy class templates,
1507	from previous versions of the header, cannot be used for <a href=
1508	"#chaining">base class chaining</a>.</p>
1509
1510	<table cellpadding="5" border="1" align="center">
1511	<caption>
1512	Final Arithmetic Operator Template Classes
1513	</caption>
1514
1515	<tr>
1516	<td colspan="2">
1517	<table align="center" border="1">
1518	<caption>
1519	<em>Key</em>
1520	</caption>
1521
1522	<tr>
1523	<td><code>T</code>: primary operand type</td>
1524
1525	<td><code>U</code>: alternate operand type</td>
1526	</tr>
1527	</table>
1528	</td>
1529	</tr>
1530
1531	<tr>
1532	<th>Template</th>
1533
1534	<th>Component Operator Templates</th>
1535	</tr>
1536
1537	<tr>
1538	<td><code><a name="operators1">operators<T></a></code></td>
1539
1540	<td>
1541	<ul>
1542	<li><code><a href=
1543	"#totally_ordered1">totally_ordered<T></a></code></li>
1544
1545	<li><code><a href=
1546	"#integer_arithmetic1">integer_arithmetic<T></a></code></li>
1547
1548	<li><code><a href="#bitwise1">bitwise<T></a></code></li>
1549
1550	<li><code><a href=
1551	"#unit_steppable">unit_steppable<T></a></code></li>
1552	</ul>
1553	</td>
1554	</tr>
1555
1556	<tr>
1557	<td><code><a name="operators2">operators<T, U></a></code><br>
1558	<code>operators2<T, U></code></td>
1559
1560	<td>
1561	<ul>
1562	<li><code><a href="#totally_ordered2">totally_ordered<T,
1563	U></a></code></li>
1564
1565	<li><code><a href="#integer_arithmetic2">integer_arithmetic<T,
1566	U></a></code></li>
1567
1568	<li><code><a href="#bitwise2">bitwise<T, U></a></code></li>
1569	</ul>
1570	</td>
1571	</tr>
1572	</table>
1573
1574	<h3><a name="a_demo">Arithmetic Operators Demonstration</a> and Test
1575	Program</h3>
1576
1577	<p>The <cite><a href="operators_test.cpp">operators_test.cpp</a></cite>
1578	program demonstrates the use of the arithmetic operator templates, and
1579	can also be used to verify correct operation. Check the <a href=
1580	"../../status/compiler_status.html">compiler status report</a> for the
1581	test results with selected platforms.</p>
1582
1583	<h2><a name="deref">Dereference</a> Operators and Iterator Helpers</h2>
1584
1585	<p>The <a href="#iterator">iterator helper</a> templates ease the task of
1586	creating a custom iterator. Similar to arithmetic types, a complete
1587	iterator has many operators that are "redundant" and can be implemented
1588	in terms of the core set of operators.</p>
1589
1590	<p>The <a href="#dereference">dereference operators</a> were motivated by
1591	the <a href="#iterator">iterator helpers</a>, but are often useful in
1592	non-iterator contexts as well. Many of the redundant iterator operators
1593	are also arithmetic operators, so the iterator helper classes borrow many
1594	of the operators defined above. In fact, only two new operators need to
1595	be defined (the pointer-to-member <code>operator-></code> and the
1596	subscript <code>operator[]</code>)!</p>
1597
1598	<p>The requirements for the types used to instantiate the dereference
1599	operators are specified in terms of expressions which must be valid and
1600	their return type. The composite operator templates list their component
1601	templates, which the instantiating type must support, and possibly other
1602	requirements.</p>
1603
1604	<h3><a name="dereference">Dereference</a> Operators</h3>
1605
1606	<p>All the dereference operator templates in this table accept an
1607	optional template parameter (not shown) to be used for <a href=
1608	"#chaining">base class chaining</a>.</p>
1609
1610	<table cellpadding="5" border="1" align="center">
1611	<caption>
1612	Dereference Operator Template Classes
1613	</caption>
1614
1615	<tr>
1616	<td colspan="3">
1617	<table align="center" border="1">
1618	<caption>
1619	<em>Key</em>
1620	</caption>
1621
1622	<tr>
1623	<td><code>T</code>: operand type</td>
1624
1625	<td><code>P</code>: <code>pointer</code> type</td>
1626	</tr>
1627
1628	<tr>
1629	<td><code>D</code>: <code>difference_type</code></td>
1630
1631	<td><code>R</code>: <code>reference</code> type</td>
1632	</tr>
1633
1634	<tr>
1635	<td><code>i</code>: object of type <code>T</code> (an
1636	iterator)</td>
1637
1638	<td><code>n</code>: object of type <code>D</code> (an
1639	index)</td>
1640	</tr>
1641	</table>
1642	</td>
1643	</tr>
1644
1645	<tr>
1646	<th>Template</th>
1647
1648	<th>Supplied Operations</th>
1649
1650	<th>Requirements</th>
1651	</tr>
1652
1653	<tr>
1654	<td><code><a name="dereferenceable">dereferenceable<T,
1655	P></a></code></td>
1656
1657	<td><code>P operator->() const</code></td>
1658
1659	<td><code>(&*i)</code>. Return convertible to
1660	<code>P</code>.</td>
1661	</tr>
1662
1663	<tr>
1664	<td><code><a name="indexable">indexable<T, D,
1665	R></a></code></td>
1666
1667	<td><code>R operator[](D n) const</code></td>
1668
1669	<td><code>*(i + n)</code>. Return of type
1670	<code>R</code>.</td>
1671	</tr>
1672	</table>
1673
1674	<h3><a name="grpd_iter_oprs">Grouped Iterator Operators</a></h3>
1675
1676	<p>There are five iterator operator class templates, each for a different
1677	category of iterator. The following table shows the operator groups for
1678	any category that a custom iterator could define. These class templates
1679	have an additional optional template parameter <code>B</code>, which is
1680	not shown, to support <a href="#chaining">base class chaining</a>.</p>
1681
1682	<table cellpadding="5" border="1" align="center">
1683	<caption>
1684	Iterator Operator Class Templates
1685	</caption>
1686
1687	<tr>
1688	<td colspan="2">
1689	<table align="center" border="1">
1690	<caption>
1691	<em>Key</em>
1692	</caption>
1693
1694	<tr>
1695	<td><code>T</code>: operand type</td>
1696
1697	<td><code>P</code>: <code>pointer</code> type</td>
1698	</tr>
1699
1700	<tr>
1701	<td><code>D</code>: <code>difference_type</code></td>
1702
1703	<td><code>R</code>: <code>reference</code> type</td>
1704	</tr>
1705
1706	<tr>
1707	<td><code>V</code>: <code>value_type</code></td>
1708
1709	<td>
1710	</td>
1711	</tr>
1712	</table>
1713	</td>
1714	</tr>
1715
1716	<tr>
1717	<th>Template</th>
1718
1719	<th>Component Operator Templates</th>
1720	</tr>
1721
1722	<tr>
1723	<td><code><a name="input_iteratable">input_iteratable<T,
1724	P></a></code></td>
1725
1726	<td>
1727	<ul>
1728	<li><code><a href=
1729	"#equality_comparable1">equality_comparable<T></a></code></li>
1730
1731	<li><code><a href=
1732	"#incrementable">incrementable<T></a></code></li>
1733
1734	<li><code><a href="#dereferenceable">dereferenceable<T,
1735	P></a></code></li>
1736	</ul>
1737	</td>
1738	</tr>
1739
1740	<tr>
1741	<td><code><a name=
1742	"output_iteratable">output_iteratable<T></a></code></td>
1743
1744	<td>
1745	<ul>
1746	<li><code><a href=
1747	"#incrementable">incrementable<T></a></code></li>
1748	</ul>
1749	</td>
1750	</tr>
1751
1752	<tr>
1753	<td><code><a name="forward_iteratable">forward_iteratable<T,
1754	P></a></code></td>
1755
1756	<td>
1757	<ul>
1758	<li><code><a href="#input_iteratable">input_iteratable<T,
1759	P></a></code></li>
1760	</ul>
1761	</td>
1762	</tr>
1763
1764	<tr>
1765	<td><code><a name=
1766	"bidirectional_iteratable">bidirectional_iteratable<T,
1767	P></a></code></td>
1768
1769	<td>
1770	<ul>
1771	<li><code><a href="#forward_iteratable">forward_iteratable<T,
1772	P></a></code></li>
1773
1774	<li><code><a href=
1775	"#decrementable">decrementable<T></a></code></li>
1776	</ul>
1777	</td>
1778	</tr>
1779
1780	<tr>
1781	<td><code><a name=
1782	"random_access_iteratable">random_access_iteratable<T, P, D,
1783	R></a></code></td>
1784
1785	<td>
1786	<ul>
1787	<li><code><a href=
1788	"#bidirectional_iteratable">bidirectional_iteratable<T,
1789	P></a></code></li>
1790
1791	<li><code><a href=
1792	"#totally_ordered1">totally_ordered<T></a></code></li>
1793
1794	<li><code><a href="#additive2">additive<T,
1795	D></a></code></li>
1796
1797	<li><code><a href="#indexable">indexable<T, D,
1798	R></a></code></li>
1799	</ul>
1800	</td>
1801	</tr>
1802	</table>
1803
1804	<h3><a name="iterator">Iterator</a> Helpers</h3>
1805
1806	<p>There are also five iterator helper class templates, each
1807	corresponding to a different iterator category. These classes cannot be
1808	used for <a href="#chaining">base class chaining</a>. The following
1809	summaries show that these class templates supply both the iterator
1810	operators from the <a href="#grpd_iter_oprs">iterator operator class
1811	templates</a> and the iterator typedef's required by the C++ standard
1812	(<code>iterator_category</code>, <code>value_type</code>,
1813	<i>etc.</i>).</p>
1814
1815	<table cellpadding="5" border="1" align="center">
1816	<caption>
1817	Iterator Helper Class Templates
1818	</caption>
1819
1820	<tr>
1821	<td colspan="2">
1822	<table align="center" border="1">
1823	<caption>
1824	<em>Key</em>
1825	</caption>
1826
1827	<tr>
1828	<td><code>T</code>: operand type</td>
1829
1830	<td><code>P</code>: <code>pointer</code> type</td>
1831	</tr>
1832
1833	<tr>
1834	<td><code>D</code>: <code>difference_type</code></td>
1835
1836	<td><code>R</code>: <code>reference</code> type</td>
1837	</tr>
1838
1839	<tr>
1840	<td><code>V</code>: <code>value_type</code></td>
1841
1842	<td><code>x1, x2</code>: objects of type <code>T</code></td>
1843	</tr>
1844	</table>
1845	</td>
1846	</tr>
1847
1848	<tr>
1849	<th>Template</th>
1850
1851	<th>Operations & Requirements</th>
1852	</tr>
1853
1854	<tr valign="baseline">
1855	<td><code><a name="input_iterator_helper">input_iterator_helper<T,
1856	V, D, P, R></a></code></td>
1857
1858	<td>
1859	Supports the operations and has the requirements of
1860
1861	<ul>
1862	<li><code><a href="#input_iteratable">input_iteratable<T,
1863	P></a></code></li>
1864	</ul>
1865	</td>
1866	</tr>
1867
1868	<tr valign="baseline">
1869	<td><code><a name=
1870	"output_iterator_helper">output_iterator_helper<T></a></code></td>
1871
1872	<td>
1873	Supports the operations and has the requirements of
1874
1875	<ul>
1876	<li><code><a href=
1877	"#output_iteratable">output_iteratable<T></a></code></li>
1878	</ul>
1879	See also [<a href="#1">1</a>], [<a href="#2">2</a>].
1880	</td>
1881	</tr>
1882
1883	<tr valign="baseline">
1884	<td><code><a name=
1885	"forward_iterator_helper">forward_iterator_helper<T, V, D, P,
1886	R></a></code></td>
1887
1888	<td>
1889	Supports the operations and has the requirements of
1890
1891	<ul>
1892	<li><code><a href="#forward_iteratable">forward_iteratable<T,
1893	P></a></code></li>
1894	</ul>
1895	</td>
1896	</tr>
1897
1898	<tr valign="baseline">
1899	<td><code><a name=
1900	"bidirectional_iterator_helper">bidirectional_iterator_helper<T,
1901	V, D, P, R></a></code></td>
1902
1903	<td>
1904	Supports the operations and has the requirements of
1905
1906	<ul>
1907	<li><code><a href=
1908	"#bidirectional_iteratable">bidirectional_iteratable<T,
1909	P></a></code></li>
1910	</ul>
1911	</td>
1912	</tr>
1913
1914	<tr valign="baseline">
1915	<td><code><a name=
1916	"random_access_iterator_helper">random_access_iterator_helper<T,
1917	V, D, P, R></a></code></td>
1918
1919	<td>
1920	Supports the operations and has the requirements of
1921
1922	<ul>
1923	<li><code><a href=
1924	"#random_access_iteratable">random_access_iteratable<T, P, D,
1925	R></a></code></li>
1926	</ul>
1927	To satisfy <cite><a href=
1928	"http://www.sgi.com/tech/stl/RandomAccessIterator.html">RandomAccessIterator</a></cite>,
1929	<code>x1 - x2</code> with return convertible to <code>D</code> is
1930	also required.
1931	</td>
1932	</tr>
1933	</table>
1934
1935	<h4><a name="iterator_helpers_notes">Iterator Helper Notes</a></h4>
1936
1937	<p><a name="1">[1]</a> Unlike other iterator helpers templates,
1938	<code>output_iterator_helper</code> takes only one template parameter -
1939	the type of its target class. Although to some it might seem like an
1940	unnecessary restriction, the standard requires
1941	<code>difference_type</code> and <code>value_type</code> of any output
1942	iterator to be <code>void</code> (24.3.1 [lib.iterator.traits]), and
1943	<code>output_iterator_helper</code> template respects this requirement.
1944	Also, output iterators in the standard have void <code>pointer</code> and
1945	<code>reference</code> types, so the <code>output_iterator_helper</code>
1946	does the same.</p>
1947
1948	<p><a name="2">[2]</a> As self-proxying is the easiest and most common
1949	way to implement output iterators (see, for example, insert [24.4.2] and
1950	stream iterators [24.5] in the standard library),
1951	<code>output_iterator_helper</code> supports the idiom by defining
1952	<code>operator*</code> and <code>operator++</code> member functions which
1953	just return a non-const reference to the iterator itself. Support for
1954	self-proxying allows us, in many cases, to reduce the task of writing an
1955	output iterator to writing just two member functions - an appropriate
1956	constructor and a copy-assignment operator. For example, here is a
1957	possible implementation of <code><a href=
1958	"../iterator/doc/function_output_iterator.html">boost::function_output_iterator</a></code>
1959	adaptor:</p>
1960	<pre>
1961	template<class UnaryFunction>
1962	struct function_output_iterator
1963	: boost::output_iterator_helper< function_output_iterator<UnaryFunction> >
1964	{
1965	explicit function_output_iterator(UnaryFunction const& f = UnaryFunction())
1966	: func(f) {}
1967
1968	template<typename T>
1969	function_output_iterator& operator=(T const& value)
1970	{
1971	this->func(value);
1972	return *this;
1973	}
1974
1975	private:
1976	UnaryFunction func;
1977	};
1978	</pre>
1979
1980	<p>Note that support for self-proxying does not prevent you from using
1981	<code>output_iterator_helper</code> to ease any other, different kind of
1982	output iterator's implementation. If
1983	<code>output_iterator_helper</code>'s target type provides its own
1984	definition of <code>operator*</code> or/and <code>operator++</code>, then
1985	these operators will get used and the ones supplied by
1986	<code>output_iterator_helper</code> will never be instantiated.</p>
1987
1988	<h3><a name="i_demo">Iterator Demonstration</a> and Test Program</h3>
1989
1990	<p>The <cite><a href="iterators_test.cpp">iterators_test.cpp</a></cite>
1991	program demonstrates the use of the iterator templates, and can also be
1992	used to verify correct operation. The following is the custom iterator
1993	defined in the test program. It demonstrates a correct (though trivial)
1994	implementation of the core operations that must be defined in order for
1995	the iterator helpers to "fill in" the rest of the iterator
1996	operations.</p>
1997
1998	<blockquote>
1999	<pre>
2000	template <class T, class R, class P>
2001	struct test_iter
2002	: public boost::random_access_iterator_helper<
2003	test_iter<T,R,P>, T, std::ptrdiff_t, P, R>
2004	{
2005	typedef test_iter self;
2006	typedef R Reference;
2007	typedef std::ptrdiff_t Distance;
2008
2009	public:
2010	explicit test_iter(T* i =0);
2011	test_iter(const self& x);
2012	self& operator=(const self& x);
2013	Reference operator*() const;
2014	self& operator++();
2015	self& operator--();
2016	self& operator+=(Distance n);
2017	self& operator-=(Distance n);
2018	bool operator==(const self& x) const;
2019	bool operator<(const self& x) const;
2020	friend Distance operator-(const self& x, const self& y);
2021	};
2022	</pre>
2023	</blockquote>
2024
2025	<p>Check the <a href="../../status/compiler_status.html">compiler status
2026	report</a> for the test results with selected platforms.</p>
2027	<hr>
2028
2029	<h2><a name="contributors">Contributors</a></h2>
2030
2031	<dl>
2032	<dt><a href="../../people/dave_abrahams.htm">Dave Abrahams</a></dt>
2033
2034	<dd>Started the library and contributed the arithmetic operators in
2035	<cite><a href=
2036	"../../boost/operators.hpp">boost/operators.hpp</a></cite>.</dd>
2037
2038	<dt><a href="../../people/jeremy_siek.htm">Jeremy Siek</a></dt>
2039
2040	<dd>Contributed the <a href="#deref">dereference operators and iterator
2041	helpers</a> in <cite><a href=
2042	"../../boost/operators.hpp">boost/operators.hpp</a></cite>. Also
2043	contributed <cite><a href=
2044	"iterators_test.cpp">iterators_test.cpp</a></cite>.</dd>
2045
2046	<dt><a href="../../people/aleksey_gurtovoy.htm">Aleksey
2047	Gurtovoy</a></dt>
2048
2049	<dd>Contributed the code to support <a href="#chaining">base class
2050	chaining</a> while remaining backward-compatible with old versions of
2051	the library.</dd>
2052
2053	<dt><a href="../../people/beman_dawes.html">Beman Dawes</a></dt>
2054
2055	<dd>Contributed <cite><a href=
2056	"operators_test.cpp">operators_test.cpp</a></cite>.</dd>
2057
2058	<dt><a href="../../people/daryle_walker.html">Daryle Walker</a></dt>
2059
2060	<dd>Contributed classes for the shift operators, equivalence, partial
2061	ordering, and arithmetic conversions. Added the grouped operator
2062	classes. Added helper classes for input and output iterators.</dd>
2063
2064	<dt>Helmut Zeisel</dt>
2065
2066	<dd>Contributed the 'left' operators and added some grouped operator
2067	classes.</dd>
2068
2069	<dt>Daniel Frey</dt>
2070
2071	<dd>Contributed the NRVO-friendly and symmetric implementation of
2072	arithmetic operators.</dd>
2073
2074	</dl>
2075
2076	<h2>Note for Users of <a name="old_lib_note">Older Versions</a></h2>
2077
2078	<p>The <a href="#chaining">changes in the library interface and
2079	recommended usage</a> were motivated by some practical issues described
2080	below. The new version of the library is still backward-compatible with
2081	the former one (so you're not <em>forced</em> change any existing code),
2082	but the old usage is deprecated. Though it was arguably simpler and more
2083	intuitive than using <a href="#chaining">base class chaining</a>, it has
2084	been discovered that the old practice of deriving from multiple operator
2085	templates can cause the resulting classes to be much larger than they
2086	should be. Most modern C++ compilers significantly bloat the size of
2087	classes derived from multiple empty base classes, even though the base
2088	classes themselves have no state. For instance, the size of
2089	<code>point<int></code> from the <a href="#example">example</a>
2090	above was 12-24 bytes on various compilers for the Win32 platform,
2091	instead of the expected 8 bytes.</p>
2092
2093	<p>Strictly speaking, it was not the library's fault--the language rules
2094	allow the compiler to apply the empty base class optimization in that
2095	situation. In principle an arbitrary number of empty base classes can be
2096	allocated at the same offset, provided that none of them have a common
2097	ancestor (see section 10.5 [class.derived] paragraph 5 of the standard).
2098	But the language definition also doesn't <em>require</em> implementations
2099	to do the optimization, and few if any of today's compilers implement it
2100	when multiple inheritance is involved. What's worse, it is very unlikely
2101	that implementors will adopt it as a future enhancement to existing
2102	compilers, because it would break binary compatibility between code
2103	generated by two different versions of the same compiler. As Matt Austern
2104	said, "One of the few times when you have the freedom to do this sort of
2105	thing is when you're targeting a new architecture...". On the other hand,
2106	many common compilers will use the empty base optimization for single
2107	inheritance hierarchies.</p>
2108
2109	<p>Given the importance of the issue for the users of the library (which
2110	aims to be useful for writing light-weight classes like
2111	<code>MyInt</code> or <code>point<></code>), and the forces
2112	described above, we decided to change the library interface so that the
2113	object size bloat could be eliminated even on compilers that support only
2114	the simplest form of the empty base class optimization. The current
2115	library interface is the result of those changes. Though the new usage is
2116	a bit more complicated than the old one, we think it's worth it to make
2117	the library more useful in real world. Alexy Gurtovoy contributed the
2118	code which supports the new usage idiom while allowing the library remain
2119	backward-compatible.</p>
2120	<hr>
2121
2122	<p>Revised: 29 Oct 2004</p>
2123
2124	<p>Copyright © Beman Dawes, David Abrahams, 1999-2001.</p>
2125	<p>Copyright © Daniel Frey, 2002-2004.</p>
2126	<p>Use, modification, and distribution is subject to the Boost Software
2127	License, Version 1.0. (See accompanying file
2128	<a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy at
2129	<a href="http://www.boost.org/LICENSE_1_0.txt">
2130	www.boost.org/LICENSE_1_0.txt</a>)</p>
2131	</body>
2132	</html>
2133

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