Boost C++ Libraries of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

This is the documentation for an old version of Boost. Click here to view this page for the latest version.
Front Page / Metafunctions / Concepts / Numeric Metafunction

Numeric Metafunction


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 and subsequent specifications, op is a placeholder token for the actual Numeric Metafunction's name, and x, y and x1,x2,... xn are arbitrary numeric types.

Expression Type Complexity
op_tag<x>::type Integral Constant Amortized constant time.
   , op_tag<y>::type
Any type Unspecified.
op<x1,x2,... xn>::type Any type Unspecified.

Expression semantics

typedef op_tag<x>::type tag;
Semantics:tag is a tag type for x for op. tag::value is x's conversion rank.
typedef op_impl<
    , op_tag<y>::type
    >::apply<x,y>::type r;
Semantics:r is the result of op application on arguments x and y.
typedef op<x1,x2,... xn>::type r;
Semantics:r is the result of op application on arguments x1,x2,... xn.


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 {

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 );


See also

Tag Dispatched Metafunction, Metafunctions, numeric_cast