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< title > The MPL Reference Manual: Numeric Metafunction</ title >
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< body class = "docframe refmanual" >
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< table class = "header" >< tr class = "header" >< td class = "header-group navigation-bar" >< span class = "navigation-group" >< a href = "./tag-dispatched-metafunction.html" class = "navigation-link" > Prev</ a > < a href = "./trivial-metafunction.html" class = "navigation-link" > Next</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./tag-dispatched-metafunction.html" class = "navigation-link" > Back</ a > < a href = "./trivial-metafunction.html" class = "navigation-link" > Along</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./metafunctions-concepts.html" class = "navigation-link" > Up</ a > < a href = "../refmanual.html" class = "navigation-link" > Home</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./refmanual_toc.html" class = "navigation-link" > Full TOC</ a ></ span ></ td >
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< td class = "header-group page-location" >< a href = "../refmanual.html" class = "navigation-link" > Front Page</ a > / < a href = "./metafunctions.html" class = "navigation-link" > Metafunctions</ a > / < a href = "./metafunctions-concepts.html" class = "navigation-link" > Concepts</ a > / < a href = "./numeric-metafunction.html" class = "navigation-link" > Numeric Metafunction</ a ></ td >
</ tr ></ table >< div class = "header-separator" ></ div >
< div class = "section" id = "numeric-metafunction" >
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< h1 >< a class = "toc-backref" href = "./metafunctions-concepts.html#id1517" > Numeric Metafunction</ a ></ h1 >
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< div class = "section" id = "id847" >
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< h3 >< a class = "subsection-title" href = "#description" name = "description" > Description</ a ></ h3 >
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< p > A < a class = "reference internal" href = "./numeric-metafunction.html" > Numeric Metafunction</ a > is a < a class = "reference internal" href = "./tag-dispatched-metafunction.html" > Tag Dispatched Metafunction</ a > that provides
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a built-in infrastructure for easy implementation of mixed-type operations.</ p >
</ div >
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< div class = "section" id = "id848" >
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< h3 >< a class = "subsection-title" href = "#expression-requirements" name = "expression-requirements" > Expression requirements</ a ></ h3 >
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< p > In the following table and subsequent specifications, < tt class = "literal" >< span class = "pre" > op</ span ></ tt > is a placeholder token for the actual
< a class = "reference internal" href = "./numeric-metafunction.html" > Numeric Metafunction</ a > 's name, and < tt class = "literal" >< span class = "pre" > x</ span ></ tt > , < tt class = "literal" >< span class = "pre" > y</ span ></ tt > and < em > x</ em >< sub > 1</ sub > ,< em > x</ em >< sub > 2</ sub > ,... < em > x</ em >< sub > n</ sub > are
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arbitrary numeric types.</ p >
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< table border = "1" class = "docutils table" >
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< colgroup >
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< col width = "25%" />
< col width = "29%" />
</ colgroup >
< thead valign = "bottom" >
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< tr >< th class = "head" > Expression</ th >
< th class = "head" > Type</ th >
< th class = "head" > Complexity</ th >
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</ tr >
</ thead >
< tbody valign = "top" >
< tr >< td >< tt class = "literal" >< span class = "pre" > op_tag< x> ::type</ span ></ tt ></ td >
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< td >< a class = "reference internal" href = "./integral-constant.html" > Integral Constant</ a ></ td >
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< td > Amortized constant time.</ td >
</ tr >
< tr >< td >< pre class = "first last literal-block" >
op_impl<
op_tag< x> ::type
, op_tag< y> ::type
> ::< a href = "./apply.html" class = "identifier" > apply</ a > < x,y> ::type
</ pre >
</ td >
< td > Any type</ td >
< td > Unspecified.</ td >
</ tr >
< tr >< td >< tt class = "literal" >< span class = "pre" > op< </ span ></ tt >< em > x</ em >< sub > 1</ sub > ,< em > x</ em >< sub > 2</ sub > ,... < em > x</ em >< sub > n</ sub >< tt class = "literal" >< span class = "pre" > > ::type</ span ></ tt ></ td >
< td > Any type</ td >
< td > Unspecified.</ td >
</ tr >
</ tbody >
</ table >
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< div class = "section" id = "id849" >
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< h3 >< a class = "subsection-title" href = "#expression-semantics" name = "expression-semantics" > Expression semantics</ a ></ h3 >
< pre class = "literal-block" >
typedef op_tag< x> ::type tag;
</ pre >
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< table class = "docutils field-list" frame = "void" rules = "none" >
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< col class = "field-name" />
< col class = "field-body" />
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< tr class = "field" >< th class = "field-name" > Semantics:</ th >< td class = "field-body" >< tt class = "literal" >< span class = "pre" > tag</ span ></ tt > is a tag type for < tt class = "literal" >< span class = "pre" > x</ span ></ tt > for < tt class = "literal" >< span class = "pre" > op</ span ></ tt > .
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< tt class = "literal" >< span class = "pre" > tag::value</ span ></ tt > is < tt class = "literal" >< span class = "pre" > x</ span ></ tt > 's < em > conversion rank</ em > .</ td >
</ tr >
</ tbody >
</ table >
<!-- .......................................................................... -->
< pre class = "literal-block" >
typedef op_impl<
op_tag< x> ::type
, op_tag< y> ::type
> ::< a href = "./apply.html" class = "identifier" > apply</ a > < x,y> ::type r;
</ pre >
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< table class = "docutils field-list" frame = "void" rules = "none" >
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< col class = "field-name" />
< col class = "field-body" />
< tbody valign = "top" >
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< tr class = "field" >< th class = "field-name" > Semantics:</ th >< td class = "field-body" >< tt class = "literal" >< span class = "pre" > r</ span ></ tt > is the result of < tt class = "literal" >< span class = "pre" > op</ span ></ tt > application on arguments < tt class = "literal" >< span class = "pre" > x</ span ></ tt >
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and < tt class = "literal" >< span class = "pre" > y</ span ></ tt > .</ td >
</ tr >
</ tbody >
</ table >
<!-- .......................................................................... -->
< pre class = "literal-block" >
typedef op< < em > x</ em >< sub > 1</ sub > ,< em > x</ em >< sub > 2</ sub > ,... < em > x</ em >< sub > n</ sub > > ::type r;
</ pre >
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< table class = "docutils field-list" frame = "void" rules = "none" >
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< col class = "field-name" />
< col class = "field-body" />
< tbody valign = "top" >
< tr class = "field" >< th class = "field-name" > Semantics:</ th >< td class = "field-body" >< tt class = "literal" >< span class = "pre" > r</ span ></ tt > is the result of < tt class = "literal" >< span class = "pre" > op</ span ></ tt > application on arguments < em > x</ em >< sub > 1</ sub > ,< em > x</ em >< sub > 2</ sub > ,... < em > x</ em >< sub > n</ sub > .</ td >
</ tr >
</ tbody >
</ table >
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< div class = "section" id = "id850" >
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< h3 >< a class = "subsection-title" href = "#example" name = "example" > Example</ a ></ h3 >
< pre class = "literal-block" >
struct complex_tag : < a href = "./int.html" class = "identifier" > int_</ a > < 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 < a href = "./apply.html" class = "identifier" > apply</ a >
: complex<
< a href = "./plus.html" class = "identifier" > plus</ a > < typename N1::real, typename N2::real >
, < a href = "./plus.html" class = "identifier" > plus</ a > < typename N1::imag, typename N2::imag >
>
{
};
};
}}
typedef complex< < a href = "./int.html" class = "identifier" > int_</ a > < 5> , < a href = "./int.html" class = "identifier" > int_</ a > < -1> > c1;
typedef complex< < a href = "./int.html" class = "identifier" > int_</ a > < -5> , < a href = "./int.html" class = "identifier" > int_</ a > < 1> > c2;
typedef < a href = "./plus.html" class = "identifier" > plus</ a > < c1,c2> r1;
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( real< r1> ::value, ==, 0 );
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( imag< r1> ::value, ==, 0 );
typedef < a href = "./plus.html" class = "identifier" > plus</ a > < c1,c1> r2;
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( real< r2> ::value, ==, 10 );
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( imag< r2> ::value, ==, -2 );
typedef < a href = "./plus.html" class = "identifier" > plus</ a > < c2,c2> r3;
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( real< r3> ::value, ==, -10 );
< a href = "./assert-relation.html" class = "identifier" > BOOST_MPL_ASSERT_RELATION</ a > ( imag< r3> ::value, ==, 2 );
</ pre >
</ div >
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< div class = "section" id = "id851" >
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< h3 >< a class = "subsection-title" href = "#models" name = "models" > Models</ a ></ h3 >
< ul class = "simple" >
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< li >< a class = "reference internal" href = "./plus.html" > plus</ a ></ li >
< li >< a class = "reference internal" href = "./minus.html" > minus</ a ></ li >
< li >< a class = "reference internal" href = "./times.html" > times</ a ></ li >
< li >< a class = "reference internal" href = "./divides.html" > divides</ a ></ li >
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</ ul >
</ div >
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< div class = "section" id = "id852" >
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< h3 >< a class = "subsection-title" href = "#see-also" name = "see-also" > See also</ a ></ h3 >
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< p >< a class = "reference internal" href = "./tag-dispatched-metafunction.html" > Tag Dispatched Metafunction</ a > , < a class = "reference internal" href = "./metafunctions.html" > Metafunctions</ a > , < a class = "reference internal" href = "./numeric-cast.html" > numeric_cast</ a ></ p >
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<!-- Metafunctions/Concepts//Trivial Metafunction |70 -->
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< table class = "footer" >< tr class = "footer" >< td class = "header-group navigation-bar" >< span class = "navigation-group" >< a href = "./tag-dispatched-metafunction.html" class = "navigation-link" > Prev</ a > < a href = "./trivial-metafunction.html" class = "navigation-link" > Next</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./tag-dispatched-metafunction.html" class = "navigation-link" > Back</ a > < a href = "./trivial-metafunction.html" class = "navigation-link" > Along</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./metafunctions-concepts.html" class = "navigation-link" > Up</ a > < a href = "../refmanual.html" class = "navigation-link" > Home</ a ></ span >< span class = "navigation-group-separator" > | </ span >< span class = "navigation-group" >< a href = "./refmanual_toc.html" class = "navigation-link" > Full TOC</ a ></ span ></ td >
< td >< div class = "copyright-footer" >< div class = "copyright" > Copyright © 2001-2009 Aleksey Gurtovoy and David Abrahams</ div >
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at < a class = "reference external" href = "http://www.boost.org/LICENSE_1_0.txt" target = "_top" > http://www.boost.org/LICENSE_1_0.txt</ a > )</ div ></ td ></ tr ></ table ></ body >
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