| .. 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) |
