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diff --git a/src/boost/libs/utility/operators.htm b/src/boost/libs/utility/operators.htm new file mode 100644 index 00000000..d2c6682c --- /dev/null +++ b/src/boost/libs/utility/operators.htm @@ -0,0 +1,2144 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> + +<html> + <head> + <meta name="generator" content= + "HTML Tidy for Windows (vers 1st August 2002), see www.w3.org"> + <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="../../boost.png" alt="boost.png (6897 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> + + <li><a href="#symmetry">Symmetry 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 + is equivalent to !(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> + + <p>As Daniel Krügler pointed out, this technique violates 14.6.5/2 + and is thus non-portable. The reasoning is, that the operators injected + by the instantiation of e.g. + <code>less_than_comparable<myclass></code> can not be found + by ADL according to the rules given by 3.4.2/2, since myclass is + not an associated class of + <code>less_than_comparable<myclass></code>. + Thus only use this technique if all else fails.</p> + + <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.</p> + + <p>The primary operand type <code>T</code> needs to be of class type, + built-in types are not supported.</p> + + <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>bool operator==(const U&, const T&)</code><br> + <code>bool operator!=(const U&, const T&)</code><br> + <code>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+(const T&, const T&)</code></td> + + <td><code>T temp(t); temp += t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="addable2">addable<T, U></a></code><br> + <code>addable2<T, U></code></td> + + <td><code>T operator+(const T&, const U&)</code><br> + <code>T operator+(const U&, const T& )</code></td> + + <td><code>T temp(t); temp += u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name= + "subtractable1">subtractable<T></a></code><br> + <code>subtractable1<T></code></td> + + <td><code>T operator-(const T&, const T&)</code></td> + + <td><code>T temp(t); temp -= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="subtractable2">subtractable<T, + U></a></code><br> + <code>subtractable2<T, U></code></td> + + <td><code>T operator-(const T&, const U&)</code></td> + + <td><code>T temp(t); temp -= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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*(const T&, const T&)</code></td> + + <td><code>T temp(t); temp *= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="multipliable2">multipliable<T, + U></a></code><br> + <code>multipliable2<T, U></code></td> + + <td><code>T operator*(const T&, const U&)</code><br> + <code>T operator*(const U&, const T&)</code></td> + + <td><code>T temp(t); temp *= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="dividable1">dividable<T></a></code><br> + <code>dividable1<T></code></td> + + <td><code>T operator/(const T&, const T&)</code></td> + + <td><code>T temp(t); temp /= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="dividable2">dividable<T, U></a></code><br> + <code>dividable2<T, U></code></td> + + <td><code>T operator/(const T&, const U&)</code></td> + + <td><code>T temp(t); temp /= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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%(const T&, const T&)</code></td> + + <td><code>T temp(t); temp %= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="modable2">modable<T, U></a></code><br> + <code>modable2<T, U></code></td> + + <td><code>T operator%(const T&, const U&)</code></td> + + <td><code>T temp(t); temp %= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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|(const T&, const T&)</code></td> + + <td><code>T temp(t); temp |= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="orable2">orable<T, U></a></code><br> + <code>orable2<T, U></code></td> + + <td><code>T operator|(const T&, const U&)</code><br> + <code>T operator|(const U&, const T&)</code></td> + + <td><code>T temp(t); temp |= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="andable1">andable<T></a></code><br> + <code>andable1<T></code></td> + + <td><code>T operator&(const T&, const T&)</code></td> + + <td><code>T temp(t); temp &= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="andable2">andable<T, U></a></code><br> + <code>andable2<T, U></code></td> + + <td><code>T operator&(const T&, const U&)</code><br> + <code>T operator&(const U&, const T&)</code></td> + + <td><code>T temp(t); temp &= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="xorable1">xorable<T></a></code><br> + <code>xorable1<T></code></td> + + <td><code>T operator^(const T&, const T&)</code></td> + + <td><code>T temp(t); temp ^= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name="xorable2">xorable<T, U></a></code><br> + <code>xorable2<T, U></code></td> + + <td><code>T operator^(const T&, const U&)</code><br> + <code>T operator^(const U&, const T&)</code></td> + + <td><code>T temp(t); temp ^= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</td> + </tr> + + <tr> + <td><code><a name= + "incrementable">incrementable<T></a></code></td> + + <td><code>T operator++(T&, int)</code></td> + + <td><code>T temp(t); ++t</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&, int)</code></td> + + <td><code>T temp(t); --t;</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<<(const T&, const T&)</code></td> + + <td><code>T temp(t); temp <<= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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<<(const T&, const U&)</code></td> + + <td><code>T temp(t); temp <<= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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>>(const T&, const T&)</code></td> + + <td><code>T temp(t); temp >>= t1</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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>>(const T&, const U&)</code></td> + + <td><code>T temp(t); temp >>= u</code>.<br> + Return convertible to <code>T</code>. See the <a href= + "#symmetry">Symmetry Note</a>.</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> + + <h4><a name="symmetry">Symmetry</a> Note</h4> + + <p>Before talking about symmetry, we need to talk about optimizations to + understand the reasons for the different implementation styles of + operators. Let's have a look at <code>operator+</code> for a class + <code>T</code> as an example:</p> +<pre> +T operator+( const T& lhs, const T& rhs ) +{ + return T( lhs ) += rhs; +} +</pre> + This would be a normal implementation of <code>operator+</code>, but it + is not an efficient one. An unnamed local copy of <code>lhs</code> is + created, <code>operator+=</code> is called on it and it is copied to the + function return value (which is another unnamed object of type + <code>T</code>). The standard doesn't generally allow the intermediate + object to be optimized away: + + <blockquote> + 3.7.2/2: Automatic storage duration<br> + <br> + If a named automatic object has initialization or a destructor with + side effects, it shall not be destroyed before the end of its block, + nor shall it be eliminated as an optimization even if it appears to be + unused, except that a class object or its copy may be eliminated as + specified in 12.8. + </blockquote> + The reference to 12.8 is important for us: + + <blockquote> + 12.8/15: Copying class objects<br> + ...<br> + For a function with a class return type, if the expression in the + return statement is the name of a local object, and the cv-unqualified + type of the local object is the same as the function return type, an + implementation is permitted to omit creating the temporary object to + hold the function return value, even if the class copy constructor or + destructor has side effects. + </blockquote> + This optimization is known as the named return value optimization (NRVO), + which leads us to the following implementation for + <code>operator+</code>: +<pre> +T operator+( const T& lhs, const T& rhs ) +{ + T nrv( lhs ); + nrv += rhs; + return nrv; +} +</pre> + Given this implementation, the compiler is allowed to remove the + intermediate object. Sadly, not all compiler implement the NRVO, some + even implement it in an incorrect way which makes it useless here. + Without the NRVO, the NRVO-friendly code is no worse than the original + code showed above, but there is another possible implementation, which + has some very special properties: +<pre> +T operator+( T lhs, const T& rhs ) +{ + return lhs += rhs; +} +</pre> + The difference to the first implementation is that <code>lhs</code> is + not taken as a constant reference used to create a copy; instead, + <code>lhs</code> is a by-value parameter, thus it is already the copy + needed. This allows another optimization (12.2/2) for some cases. + Consider <code>a + b + c</code> where the result of + <code>a + b</code> is not copied when used as <code>lhs</code> + when adding <code>c</code>. This is more efficient than the original + code, but not as efficient as a compiler using the NRVO. For most people, + it is still preferable for compilers that don't implement the NRVO, but + the <code>operator+</code> now has a different function signature. Also, + the number of objects created differs for + <code>(a + b ) + c</code> and + <code>a + ( b + c )</code>. Most probably, + this won't be a problem for you, but if your code relies on the function + signature or a strict symmetric behaviour, you should set + <code>BOOST_FORCE_SYMMETRIC_OPERATORS</code> in your user-config. This + will force the NRVO-friendly implementation to be used even for compilers + that don't implement the NRVO. <br> + <br> + + <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= + "euclidean_ring_operators1">euclidean_ring_operators<T></a></code><br> + + <code>euclidean_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= + "euclidean_ring_operators2">euclidean_ring_operators<T, + U></a></code><br> + <code>euclidean_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_euclidean_ring_operators1">ordered_euclidean_ring_operators<T></a></code><br> + + <code>ordered_euclidean_ring_operators1<T></code></td> + + <td> + <ul> + <li><code><a href= + "#euclidean_ring_operators1">euclidean_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_euclidean_ring_operators2">ordered_euclidean_ring_operators<T, + U></a></code><br> + <code>ordered_euclidean_ring_operators2<T, U></code></td> + + <td> + <ul> + <li><code><a href= + "#euclidean_ring_operators2">euclidean_ring_operators<T, + U></a></code></li> + + <li><code><a href="#totally_ordered2">totally_ordered<T, + U></a></code></li> + </ul> + </td> + </tr> + </table> + + <h4>Spelling: euclidean vs. euclidian</h4> + + <p>Older versions of the Boost.Operators library used + "<code>euclidian</code>", but it was pointed out that + "<code>euclidean</code>" is the more common spelling. + To be compatible with older version, the library now supports + both spellings. + </p> + + <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="test/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 compiler status + report 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>. Address of the returned value 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> + + <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= + "../iterator/doc/function_output_iterator.html">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="test/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="http://www.boost.org/development/testing.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="http://www.boost.org/people/dave_abrahams.htm">Dave Abrahams</a></dt> + + <dd>Started the library and contributed the arithmetic operators in + <cite><a href= + "../../boost/operators.hpp">boost/operators.hpp</a></cite>.</dd> + + <dt><a href="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</a></dt> + + <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>.</dd> + + <dt><a href="http://www.boost.org/people/aleksey_gurtovoy.htm">Aleksey + Gurtovoy</a></dt> + + <dd>Contributed the code to support <a href="#chaining">base class + chaining</a> while remaining backward-compatible with old versions of + the library.</dd> + + <dt><a href="http://www.boost.org/people/beman_dawes.html">Beman Dawes</a></dt> + + <dd>Contributed <cite><a href= + "test/operators_test.cpp">operators_test.cpp</a></cite>.</dd> + + <dt><a href="http://www.boost.org/people/daryle_walker.html">Daryle Walker</a></dt> + + <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.</dd> + + <dt>Helmut Zeisel</dt> + + <dd>Contributed the 'left' operators and added some grouped operator + classes.</dd> + + <dt>Daniel Frey</dt> + + <dd>Contributed the NRVO-friendly and symmetric implementation of + arithmetic operators.</dd> + + </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: 7 Aug 2008</p> + + <p>Copyright © Beman Dawes, David Abrahams, 1999-2001.</p> + <p>Copyright © Daniel Frey, 2002-2009.</p> + <p>Use, modification, and distribution is subject to the Boost Software + License, Version 1.0. (See accompanying file + <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy at + <a href="http://www.boost.org/LICENSE_1_0.txt"> + www.boost.org/LICENSE_1_0.txt</a>)</p> + </body> +</html> + |