The Art of C++ / Operators is a zero-dependency C++11 single-header library that provides highly efficient, move aware operators for arithmetic data types.
Preface
Rationale
Example
Requirements
Installation
Provided Templates
Commutativity
RValue References
noexcept
Changelog
License
The Art of C++ / Operators is the next logical step in the evolution of the Boost.Operators library, whose maintainer I became in 2002. Since then, C++ has changed significiantly and with C++11, the time has come for a complete rewrite and to get rid of some very old legacy code and work-arounds.
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 ≡ !(x < y)).
Replicating these operators for multiple classes is both tedious and error-prone. The Art of C++ / Operators templates help by generating operators for you based on other operators you've defined in your class.
The generated operators are overloaded to take full advantage of move-aware types
and are carefully written to allow the compiler to apply important optimizations
to avoid unneccessary temporary objects. All generated operators are automatically
marked noexcept when the underlying base operations are themself marked as
noexcept.
#include <tao/operators.hpp>
class MyInt
: tao::operators::commutative_addable< MyInt >,
tao::operators::multipliable< MyInt, double >
{
public:
// create a new instance of MyInt
MyInt( const int v ) noexcept;
// copy and move constructor
MyInt( const MyInt& v ) noexcept;
MyInt( MyInt&& v ) noexcept; // optional
// copy and move assignment
MyInt& operator=( const MyInt& v ) noexcept;
MyInt& operator=( MyInt&& v ) noexcept; // optional
// addition of another MyInt
MyInt& operator+=( const MyInt& v ) noexcept;
MyInt& operator+=( MyInt&& v ) noexcept; // optional
// multiplication by a scalar
MyInt& operator*=( const double v ) noexcept;
};then the library's templates generate the following operators:
// generated by tao::operators::commutative_addable< MyInt >
MyInt operator+( const MyInt& lhs, const MyInt& rhs ) noexcept;
MyInt&& operator+( const MyInt& lhs, MyInt&& rhs ) noexcept;
MyInt&& operator+( MyInt&& lhs, const MyInt& rhs ) noexcept;
MyInt&& operator+( MyInt&& lhs, MyInt&& rhs ) noexcept;
// generated by tao::operators::multipliable< MyInt, double >
MyInt operator*( const MyInt& lhs, const double& rhs ) noexcept;
MyInt operator*( const MyInt& lhs, double&& rhs ) noexcept;
MyInt&& operator*( MyInt&& lhs, const double& rhs ) noexcept;
MyInt&& operator*( MyInt&& lhs, double&& rhs ) noexcept;Note: The
// optionalinclass MyIntabove marks methods that you typically only add when your class benefits from an rvalue reference parameter. If there is no benefit for the implementation, you can just omit these methods. If you leave them out, The Art of C++ / Operators will simply call the corresponding non-movable version that takes the parameter by const lvalue reference.
Requires C++11 or newer. Tested with:
- GCC 4.7+
- Clang 3.2+
- Visual Studio 2015+
Remember to enable C++11, e.g., provide -std=c++11 or similar options.
Note: If you use or test the library with other compilers/versions, e.g., Visual C++, Intel C++, or any other compiler we'd like to hear from you.
Note: For compilers that don't support
noexcept, see chapter noexcept.
The Art of C++ / Operators is a single-header library. There is nothing to build or install, just copy the header somewhere and include it in your code.
The following table gives an overview of the available templates. Note that the "Provides" and "Requires" columns are just a basic overview. Multiple overloads per provided operator might exist to ensure the most efficient implementation for each case, exploiting move-semantics when possible and (unless explicitly disabled) pass-through of temporary values to avoid creating new temporaries.
Each overload of an operator is marked noexcept when the required operation(s)
that are used to implement it are also marked noexcept.
| Template | Provides | Requires |
|---|---|---|
equality_comparable< T >
|
T != T
|
T == T
|
equality_comparable< T, U >
|
T != UU == TU != T
|
T == U
|
less_than_comparable< T >
|
T > TT <= TT >= T
|
T < T
|
less_than_comparable< T, U >
|
T <= UT >= UU < TU > TU <= TU >= T
|
T < UT > U
|
equivalent< T >
|
T == T
|
T < T
|
equivalent< T, U >
|
T == U
|
T < UT > U
|
partially_ordered< T >
|
T > TT <= TT >= T
|
T < TT == T
|
partially_ordered< T, U >
|
T <= UT >= UU < TU > TU <= TU >= T
|
T < UT > UT == U
|
commutative_addable< T >
|
T + T
|
T += T
|
commutative_addable< T, U >
|
T + UU + T
|
T += U
|
addable< T >
|
T + T
|
T += T
|
addable< T, U >
|
T + U
|
T += U
|
addable_left< T, U >
|
U + T
|
T( U )T += T
|
subtractable< T >
|
T - T
|
T -= T
|
subtractable< T, U >
|
T - U
|
T -= U
|
subtractable_left< T, U >
|
U - T
|
T( U )T -= T
|
commutative_multipliable< T >
|
T * T
|
T *= T
|
commutative_multipliable< T, U >
|
T * UU * T
|
T *= U
|
multipliable< T >
|
T * T
|
T *= T
|
multipliable< T, U >
|
T * U
|
T *= U
|
multipliable_left< T, U >
|
U * T
|
T( U )T *= T
|
dividable< T >
|
T / T
|
T /= T
|
dividable< T, U >
|
T / U
|
T /= U
|
dividable_left< T, U >
|
U / T
|
T( U )T /= T
|
modable< T >
|
T % T
|
T %= T
|
modable< T, U >
|
T % U
|
T %= U
|
modable_left< T, U >
|
U % T
|
T( U )T %= T
|
commutative_andable< T >
|
T & T
|
T &= T
|
commutative_andable< T, U >
|
T & UU & T
|
T &= U
|
andable< T >
|
T & T
|
T &= T
|
andable< T, U >
|
T & U
|
T &= U
|
andable_left< T, U >
|
U & T
|
T( U )T &= T
|
commutative_orable< T >
|
T | T
|
T |= T
|
commutative_orable< T, U >
|
T | UU | T
|
T |= U
|
orable< T >
|
T | T
|
T |= T
|
orable< T, U >
|
T | U
|
T |= U
|
orable_left< T, U >
|
U | T
|
T( U )T |= T
|
commutative_xorable< T >
|
T ^ T
|
T ^= T
|
commutative_xorable< T, U >
|
T ^ UU ^ T
|
T ^= U
|
xorable< T >
|
T ^ T
|
T ^= T
|
xorable< T, U >
|
T ^ U
|
T ^= U
|
xorable_left< T, U >
|
U ^ T
|
T( U )T ^= T
|
left_shiftable< T >
|
T << T
|
T <<= T
|
left_shiftable< T, U >
|
T << U
|
T <<= U
|
right_shiftable< T >
|
T >> T
|
T >>= T
|
right_shiftable< T, U >
|
T >> U
|
T >>= U
|
incrementable< T >
|
T++
|
++T
|
decrementable< T >
|
T--
|
--T
|
The following templates provide common groups of related operations.
For example, since a type which is left shiftable is usually also
right shiftable, the shiftable template provides the combined operators
of both.
| Template | Provides |
|---|---|
totally_ordered< T >
|
equality_comparable< T >less_than_comparable< T >
|
totally_ordered< T, U >
|
equality_comparable< T, U >less_than_comparable< T, U >
|
commutative_ring< T >
|
commutative_addable< T >subtractable< T >commutative_multipliable< T >
|
commutative_ring< T, U >
|
commutative_addable< T, U >subtractable< T, U >subtractable_left< T, U >commutative_multipliable< T, U >
|
ring< T >
|
commutative_addable< T >subtractable< T >multipliable< T >
|
ring< T, U >
|
commutative_addable< T, U >subtractable< T, U >subtractable_left< T, U >multipliable< T, U >
|
field< T >
|
commutative_ring< T >dividable< T >
|
field< T, U >
|
commutative_ring< T, U >dividable< T, U >dividable_left< T, U >
|
ordered_commutative_ring< T >
|
commutative_ring< T >totally_ordered< T >
|
ordered_commutative_ring< T, U >
|
commutative_ring< T, U >totally_ordered< T, U >
|
ordered_ring< T >
|
ring< T >totally_ordered< T >
|
ordered_ring< T, U >
|
ring< T, U >totally_ordered< T, U >
|
ordered_field< T >
|
field< T >totally_ordered< T >
|
ordered_field< T, U >
|
field< T, U >totally_ordered< T, U >
|
commutative_bitwise< T >
|
commutative_andable< T >commutative_orable< T >commutative_xorable< T >
|
commutative_bitwise< T, U >
|
commutative_andable< T, U >commutative_orable< T, U >commutative_xorable< T, U >
|
bitwise< T >
|
andable< T >orable< T >xorable< T >
|
bitwise< T, U >
|
andable< T, U >orable< T, U >xorable< T, U >
|
bitwise_left< T, U >
|
andable_left< T, U >orable_left< T, U >xorable_left< T, U >
|
shiftable< T >
|
left_shiftable< T >right_shiftable< T >
|
shiftable< T, U >
|
left_shiftable< T, U >right_shiftable< T, U >
|
unit_steppable< T >
|
incrementable< T >decrementable< T >
|
For some templates, there are both commutative
and non-commutative versions available. If the class you are writing is
commutative wrt an operation, you should prefer the commutative template,
i.e., the one which has commutative_ at the beginning.
It will be more efficient in some cases because it can avoid to create an extra temporary for the result and it has fewer requirements.
The one-argument version of the commutative template provides the same
operators as the non-commutative one, but you can see from the result type
in which cases creating a temporary (returning T) can be avoided
(returning T&&).
For the two-argument version, commutative_{OP}< T, U > provides the operators
of both {OP}< T, U > and {OP}_left< T, U >, again the return type indicates
those cases where an extra temporary is avoided.
As you can see above, several overloads of some operators return rvalue references. This helps to eliminate temporaries in more complicated expressions, but some people consider it dangerous. The argument against returning rvalue references usually is something like:
const auto& result = a + b + c;where they expect a temporary to be returned from the expression a + b + c,
and the lifetime of the temporary can be extended by binding it to a reference.
While this would work if an actual temporary value is returned, it does not work with
the second operator + returning an rvalue reference to the intermediate temporary
created by the first operator +.
I consider the above code bad style that has no place in modern C++. It should be replaced by
const auto result = a + b + c;and the problem goes away. Also, if you expect an expression to return a temporary value, but you don't verify your assumption, it is your fault for basing your code on those assumptions.
There is, however, one problem where the above binding to a references happens behind the scenes, i.e. without being immediately visible. It may happen if you are using a range-based for-loop. The problem in this case is not limited to returning rvalue references, hence you should always make sure that you do not mix any kind of expression other than directly naming a variable when using a range-based for-loop. Example:
// instead of this:
for( const auto& e : a + b + c ) { ... }
// always use something like this:
const auto r = a + b + c;
for( const auto& e : r ) { ... }With all that said, you can disable returning rvalue references by defining
TAO_OPERATORS_NO_RVALUE_REFERENCE_RESULTS. If it is set, all operators will
return a value (an rvalue) instead of rvalue references.
If your compiler does not support noexcept, the following might be a viable
work-around:
#include <utility> // make sure it's included before the following!
#define noexcept(...)
#include <tao/operators.hpp>
#undef noexceptWith this little hack, The Art of C++ / Operators can be used with GCC 4.4+.
Released 2018-02-13
- Initial release.
The Art of C++ is certified Open Source software. It may be used for any purpose, including commercial purposes, at absolutely no cost. It is distributed under the terms of the MIT license reproduced here.
Copyright (c) 2013-2018 Daniel Frey
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