.. Metafunctions/Concepts//Numeric Metafunction |60

Numeric Metafunction

Description

A |Numeric Metafunction| is a |tag dispatched metafunction| that provides a built-in infrastructure for easy implementation of mixed-type operations.

Expression requirements

|In the following table...| op is a placeholder token for the actual |Numeric Metafunction|'s name, and x, y and |x1...xn| are arbitrary numeric types.

+-------------------------------------------+-----------------------+---------------------------+ | Expression | Type | Complexity | +===========================================+=======================+===========================+ |op_tag<x>::type | |Integral Constant| | Amortized constant time. | +-------------------------------------------+-----------------------+---------------------------+ | .. parsed-literal:: | Any type | Unspecified. | | | | | | op_impl< | | | | op_tag<x>::type | | | | , op_tag<y>::type | | | | >::apply<x,y>::type | | | +-------------------------------------------+-----------------------+---------------------------+ |op<\ |x1...xn|\ >::type | Any type | Unspecified. | +-------------------------------------------+-----------------------+---------------------------+

Expression semantics

.. parsed-literal::

typedef op_tag<x>::type tag;

:Semantics: tag is a tag type for x for op. tag::value is x\ 's conversion rank.

.. ..........................................................................

.. parsed-literal::

typedef op_impl<
      op_tag<x>::type
    , op_tag<y>::type
    >::apply<x,y>::type r;

:Semantics: r is the result of op application on arguments x and y.

.. ..........................................................................

.. parsed-literal::

typedef op<\ |x1...xn|\ >::type r;

:Semantics: r is the result of op application on arguments |x1...xn|.

Example

.. parsed-literal::

struct complex_tag : int_<10> {};

template< typename Re, typename Im > struct complex
{
    typedef complex_tag tag;
    typedef complex type;
    typedef Re real;
    typedef Im imag;
};

template< typename C > struct real : C::real {};
template< typename C > struct imag : C::imag {};

namespace boost { namespace mpl {

template<>
struct plus_impl< complex_tag,complex_tag >
{
    template< typename N1, typename N2 > struct apply
        : complex<
              plus< typename N1::real, typename N2::real >
            , plus< typename N1::imag, typename N2::imag >
            >
    {
    };
};

}}

typedef complex< int_<5>, int_<-1> > c1;
typedef complex< int_<-5>, int_<1> > c2;

typedef plus<c1,c2> r1;
BOOST_MPL_ASSERT_RELATION( real<r1>::value, ==, 0 );
BOOST_MPL_ASSERT_RELATION( imag<r1>::value, ==, 0 );

typedef plus<c1,c1> r2;
BOOST_MPL_ASSERT_RELATION( real<r2>::value, ==, 10 );
BOOST_MPL_ASSERT_RELATION( imag<r2>::value, ==, -2 );

typedef plus<c2,c2> r3;
BOOST_MPL_ASSERT_RELATION( real<r3>::value, ==, -10 );
BOOST_MPL_ASSERT_RELATION( imag<r3>::value, ==, 2 );

Models

• |plus|
• |minus|
• |times|
• |divides|

See also

|Tag Dispatched Metafunction|, |Metafunctions|, |numeric_cast|

.. copyright:: Copyright 2001-2009 Aleksey Gurtovoy and David Abrahams Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)