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The header <boost/operators.hpp>
supplies several sets of class templates in namespace
boost
. These templates define
operators at namespace scope in terms of a minimal number of fundamental
operators provided by the class.
Overloaded operators for class types typically occur in groups. If you
can write x +
y
, you probably also want to
be able to write x +=
y
. If you can write x < y,
you
also want x >
y
, x
>= y,
and x
<= y
.
Moreover, unless your class has really surprising behavior, some of these
related operators can be defined in terms of others (e.g. x >= y
is equivalent to !(x < y)
).
Replicating this boilerplate for multiple classes is both tedious and error-prone.
The <boost/operators.hpp>
templates help by generating operators for you at namespace scope based
on other operators you have defined in your class.
If, for example, you declare a class like this:
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--();
};
then the operators
<>
template adds more than a dozen additional operators, such as operator>
,
operator<=
,
operator>=
,
and the binary operator+
.
Two-argument forms of the templates are also provided to allow interaction with other types.
This is a Summary of Template Semantics:
addable
template requires operator+=(T const&)
and in turn supplies operator+(T const&,
T const&)
.
Note on the use of concepts:
The discussed concepts are not necessarily the standard library's concepts,
such as CopyConstructible,
although some of them could be; they are what we call concepts
with a small 'c'. In particular, they are different from the
former ones in that they do not 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
(e.g. effects of evaluating of a
+= b
and a =
a +
b
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 (e.g. operator<
should return a type convertible to bool
,
and T::operator-=
should return type convertible to T
).
Such "loose" requirements make operators
library applicable to broader set of target classes from different domains,
i.e. eventually more useful.
This example shows how some of the arithmetic operator templates can be used with a geometric point class template.
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);
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 example, 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 T
+ U
is of type T
, then T
(not U
)
should be derived from addable<T, U>
.
The comparison templates less_than_comparable<T,U>
, equality_comparable<T, U>
, equivalent<T, U>
, and partially_ordered<T, U>
are exceptions to this guideline,
since the return type of the operators they define is bool
.
On compilers which do not support partial specialization, the two-argument
forms must be specified by using the names shown below with the trailing
'2'
. The single-argument forms
with the trailing '1'
are provided
for symmetry and to enable certain applications of the base
class chaining technique.
Mixed Arithmetics:
Another application of the two-argument template forms is for mixed arithmetics
between a type T
and a
type U
that is convertible
to T
. 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.
With respect to the operator overloading assume e.g. that U
is int
,
that T
is an user-defined
unlimited integer type, and that double
operator-(double, const T&)
exists.
If one wants to compute int - T
and
does not provide T operator-(int,
const T&)
, the compiler will consider double operator-(double, const T&)
to be a better match than T operator-(const T&, const T&)
,
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 subtractable2_left<T, U>
, dividable2_left<T, U>
, and modable2_left<T, U>
that define the signatures for
non-commutative operators where U
appears on the left hand side (operator-(const U&, const T&)
, operator/(const U&, const T&)
, operator%(const U&, const T&)
).
With respect to the performance observe that when one uses the single type
binary operator for mixed type arithmetics, the type U
argument has to be converted to type T
.
In practice, however, there are often more efficient implementations of,
say T::operator-=(const U&)
that avoid unnecessary conversions
from U
to T
.
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 U
to T
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.
Every operator class template, except the arithmetic
examples and the iterator helpers,
has an additional, but optional, template type parameter B
. 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 note for users of older versions
for more details.
To provide support for a group of operators, use the B
parameter to chain operator templates into a single-base class hierarchy,
demostrated in the usage example. 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.
Caveat: to chain to a base class which is not
a Boost operator template when using the single-argument
form of a Boost operator template, you must specify the operator
template with the trailing '1'
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.
On some compilers (e.g. 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:
class my_class // lose the inheritance... { //... }; // explicitly instantiate the operators I need. template struct less_than_comparable<my_class>; template struct equality_comparable<my_class>; template struct incrementable<my_class>; template struct decrementable<my_class>; template struct addable<my_class,long>; template struct subtractable<my_class,long>;
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:
dereferenceable<>
indexable<>
As Daniel Krugler pointed out, this technique violates C++11 §14.6.5/2 [temp.inject]
and is thus non-portable. The reasoning is, that the operators injected
by the instantiation of e.g. less_than_comparable<my_class>
can not be found by ADL according to
the rules given by C++11 §3.4.2/2 [basic.lookup.argdep], since my_class
is not an associated class of
less_than_comparable<my_class>
.
Thus only use this technique if all else fails.
Many compilers (e.g. 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 operators<>
and operators2<>
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.
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, etc. 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.
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.
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 B
,
which is not shown, for the base class chaining
technique.
The primary operand type T
needs to be of class type, built-in types are not supported.
Table 1.6. Notation
Key |
Description |
---|---|
|
primary operand type |
|
values of type |
|
alternate operand type |
|
value of type |
Table 1.7. Simple Arithmetic Operator Template Classes
Template |
Supplied Operations |
Requirements |
Propagates constexpr |
---|---|---|---|
|
Return convertible to |
Since |
|
|
|
Returns convertible to |
Since |
|
Return convertible to |
Since |
|
|
|
Return convertible to |
Since |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
Return convertible to |
No |
|
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
Return convertible to |
No |
|
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
Return convertible to |
No |
|
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
No |
|
|
Return convertible to |
Since |
|
|
Returns convertible to |
Since |
|
Returns convertible to |
Since |
|
|
|
Returns convertible to |
Since |
Ordering Note: The less_than_comparable<T>
and partially_ordered<T>
templates provide the same set of operations. However, the workings of
less_than_comparable<T>
assume that all values of type
T
can be placed in a total
order. If that is not true (e.g. Not-a-Number values in IEEE floating point
arithmetic), then partially_ordered<T>
should be used. The partially_ordered<T>
template can be used for a totally-ordered type, but it is not as efficient
as less_than_comparable<T>
. This rule also applies for
less_than_comparable<T, U>
and partially_ordered<T,U>
with respect to the ordering of all T
and U
values, and for both
versions of equivalent<>
. The solution for equivalent<>
is to write a custom operator==
for the target class.
Symmetry Note: 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 operator+
for a class T
as an example:
T operator+( const T& lhs, const T& rhs ) { return T( lhs ) += rhs; }
This would be a normal implementation of operator+
, but it is not an efficient one. An unnamed
local copy of lhs
is created,
operator+=
is called on it and it is copied to the function return value (which is
another unnamed object of type T
).
The standard doesn't generally allow the intermediate object to be optimized
away:
C++11 §3.7.3/3 [basic.stc.auto]: Automatic storage duration: If a variable with automatic storage duration 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/move may be eliminated as specified in 12.8.
The reference to §12.8 is important for us:
C++11 §12.8/31 [class.copy]: Copying and moving class objects: When certain criteria are met, an implementation is allowed to omit the copy/move construction of a class object, even if the copy/move constructor and/or destructor for the object have side effects. (…) This elision of copy/move operations, called copy elision, is permitted in the following circumstances (which may be combined to eliminate multiple copies):
— in a
return
statement in a function with a class return type, when the expression is the name of a non-volatile automatic object (other than a function or catch-clause parameter) with the same cv- unqualified type as the function return type, the copy/move operation can be omitted by constructing the automatic object directly into the function's return value(…)
This optimization is known as the named return value optimization (NRVO),
which leads us to the following implementation for operator+
:
T operator+( const T& lhs, const T& rhs ) { T nrv( lhs ); nrv += rhs; return nrv; }
Given this implementation, the compiler is allowed to remove the intermediate object. Sadly, not all compilers 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:
T operator+( T lhs, const T& rhs ) { return lhs += rhs; }
The difference to the first implementation is that lhs
is not taken as a constant reference used to create a copy; instead, lhs
is a by-value parameter, thus it
is already the copy needed. This allows another optimization (C++11 §12.2/2
[class.temporary]) for some cases.
Consider a +
b +
c
where the result of a + b
is not copied when used as lhs
when adding c
.
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 operator+
now has a different function signature.
Also, the number of objects created differs for (a + b ) + c
and
a +
( b
+ c
)
.
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
BOOST_FORCE_SYMMETRIC_OPERATORS
in your user-config. This will force the NRVO-friendly implementation to
be used even for compilers that do not implement the NRVO.
The following templates provide common groups of related operations. For
example, since a type which is addable is usually also subtractable, the
additive
template provides the combined operators of both. The grouped operator
templates have an additional optional template parameter B
, which is not shown, for the base class chaining technique.
Table 1.9. Grouped Arithmetic Operator Template Classes
Template |
Component Operator Templates |
---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Spelling: euclidean vs. euclidian: Older versions
of the Boost.Operators library used "euclidian
",
but it was pointed out that "euclidean
"
is the more common spelling. To be compatible with older version, the library
now supports both spellings.
The arithmetic operator class templates operators<>
and operators2<>
are examples of non-extensible
operator grouping classes. These legacy class templates, from previous
versions of the header, cannot be used for base
class chaining.
Table 1.11. Final Arithmetic Operator Template Classes
Template |
Component Operator Templates |
---|---|
|
|
|
Arithmetic Operators Demonstration and
Test Program: The operators_test.cpp
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.
The iterator helper 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.
The dereference operators were motivated
by the iterator helpers, 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 operator->
and the subscript operator[]
.
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.
All the dereference operator templates in this table accept an optional template parameter (not shown) to be used for base class chaining.
Table 1.12. Notation
Key |
Description |
---|---|
|
operand type |
|
|
|
object of type |
|
|
|
|
|
object of type |
Table 1.13. Dereference Operator Template Classes
Template |
Supplied Operations |
Requirements |
---|---|---|
|
|
|
|
|
|
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 B
,
which is not shown, to support base class
chaining.
Table 1.14. Notation
Key |
Description |
---|---|
|
operand type |
|
|
|
|
|
|
|
|
Table 1.15. Iterator Operator Class Templates
Template |
Component Operator Templates |
---|---|
|
|
|
|
|
There are also five iterator helper class templates, each corresponding
to a different iterator category. These classes cannot be used for base class chaining. The following summaries
show that these class templates supply both the iterator operators from
the iterator operator class templates
and the iterator typedef
s
required by the C++ standard, such as iterator_category
and value_type
.
Table 1.16. Notation
Key |
Description |
---|---|
|
operand type |
|
|
|
|
|
|
|
|
|
objects of type |
Table 1.17. Helper Class Templates
Template |
Operations and Requirements |
---|---|
|
Supports the operations and has the requirements of |
Supports the operations and has the requirements of |
|
|
Supports the operations and has the requirements of |
|
Supports the operations and has the requirements of |
|
Supports the operations and has the requirements of
To satisfy RandomAccessIterator,
|
output_iterator_helper
takes only one template parameter - the type of its target class. Although
to some it might seem like an unnecessary restriction, the standard
requires difference_type
and value_type
of any
output iterator to be void
(C++11 §24.4.1 [lib.iterator.traits]), and output_iterator_helper
template
respects this requirement. Also, output iterators in the standard have
void pointer
and reference
types, so the output_iterator_helper
does
the same.
output_iterator_helper
supports
the idiom by defining operator*
and operator++
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 boost::function_output_iterator
adaptor:
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;
};
Note that support for self-proxying does not prevent you from using output_iterator_helper
to ease any other, different kind of output iterator's implementation.
If output_iterator_helper
's
target type provides its own definition of operator*
or/and operator++
, then these operators will get used and
the ones supplied by output_iterator_helper
will never be instantiated.
The iterators_test.cpp
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.
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; typedefstd::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); };
Check the compiler status report for the test results with selected platforms.
The changes in the library interface and recommended usage were motivated by some practical issues described below. The new version of the library is still backward-compatible with the former one, so you are not forced to change any existing code, but the old usage is deprecated.
Though it was arguably simpler and more intuitive than using base
class chaining, 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 point<int>
from the example above was 12-24 bytes
on various compilers for the Win32 platform, instead of the expected 8
bytes.
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 §10 [class.derived] paragraph 8 of the C++11 standard).
But the language definition also does not require 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 are targeting a new architecture…". On the other hand, many common compilers will use the empty base optimization for single inheritance hierarchies.
Given the importance of the issue for the users of the library (which aims
to be useful for writing light-weight classes like MyInt
or point<>
),
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
to remain backward-compatible.
boost/operators.hpp
.
operators_test.cpp
.