ceph/src/boost/libs/mpl/doc/src/refmanual/NumericMetafunction.rst

   1 .. Metafunctions/Concepts//Numeric Metafunction |60
   2
   3 Numeric Metafunction
   4 ====================
   5
   6 Description
   7 -----------
   8
   9 A |Numeric Metafunction| is a |tag dispatched metafunction| that provides
  10 a built-in infrastructure for easy implementation of mixed-type operations.
  11
  12
  13 Expression requirements
  14 -----------------------
  15
  16 |In the following table...| ``op`` is a placeholder token for the actual
  17 |Numeric Metafunction|'s name, and ``x``, ``y`` and |x1...xn| are
  18 arbitrary numeric types.
  19
  20 +-------------------------------------------+-----------------------+---------------------------+
  21 | Expression                                | Type                  | Complexity                |
  22 +===========================================+=======================+===========================+
  23 |``op_tag<x>::type``                        | |Integral Constant|   | Amortized constant time.  |
  24 +-------------------------------------------+-----------------------+---------------------------+
  25 | .. parsed-literal::                       | Any type              | Unspecified.              |
  26 |                                           |                       |                           |
  27 |    op_impl<                               |                       |                           |
  28 |         op_tag<x>::type                   |                       |                           |
  29 |       , op_tag<y>::type                   |                       |                           |
  30 |       >::apply<x,y>::type                 |                       |                           |
  31 +-------------------------------------------+-----------------------+---------------------------+
  32 |``op<``\ |x1...xn|\ ``>::type``            | Any type              | Unspecified.              |
  33 +-------------------------------------------+-----------------------+---------------------------+
  34
  35
  36 Expression semantics
  37 --------------------
  38
  39 .. parsed-literal::
  40
  41     typedef op_tag<x>::type tag;
  42
  43 :Semantics:
  44     ``tag`` is a tag type for ``x`` for ``op``.
  45     ``tag::value`` is ``x``\ 's *conversion rank*.
  46
  47
  48 .. ..........................................................................
  49
  50 .. parsed-literal::
  51
  52     typedef op_impl<
  53           op_tag<x>::type
  54         , op_tag<y>::type
  55         >::apply<x,y>::type r;
  56
  57 :Semantics:
  58     ``r`` is the result of ``op`` application on arguments ``x``
  59     and ``y``.
  60
  61
  62 .. ..........................................................................
  63
  64 .. parsed-literal::
  65
  66     typedef op<\ |x1...xn|\ >::type r;
  67
  68 :Semantics:
  69     ``r`` is the result of ``op`` application on arguments |x1...xn|.
  70
  71
  72
  73
  74 Example
  75 -------
  76
  77 .. parsed-literal::
  78
  79
  80     struct complex_tag : int_<10> {};
  81
  82     template< typename Re, typename Im > struct complex
  83     {
  84         typedef complex_tag tag;
  85         typedef complex type;
  86         typedef Re real;
  87         typedef Im imag;
  88     };
  89
  90     template< typename C > struct real : C::real {};
  91     template< typename C > struct imag : C::imag {};
  92
  93     namespace boost { namespace mpl {
  94
  95     template<>
  96     struct plus_impl< complex_tag,complex_tag >
  97     {
  98         template< typename N1, typename N2 > struct apply
  99             : complex<
 100                   plus< typename N1::real, typename N2::real >
 101                 , plus< typename N1::imag, typename N2::imag >
 102                 >
 103         {
 104         };
 105     };
 106
 107     }}
 108
 109     typedef complex< int_<5>, int_<-1> > c1;
 110     typedef complex< int_<-5>, int_<1> > c2;
 111
 112     typedef plus<c1,c2> r1;
 113     BOOST_MPL_ASSERT_RELATION( real<r1>::value, ==, 0 );
 114     BOOST_MPL_ASSERT_RELATION( imag<r1>::value, ==, 0 );
 115
 116     typedef plus<c1,c1> r2;
 117     BOOST_MPL_ASSERT_RELATION( real<r2>::value, ==, 10 );
 118     BOOST_MPL_ASSERT_RELATION( imag<r2>::value, ==, -2 );
 119
 120     typedef plus<c2,c2> r3;
 121     BOOST_MPL_ASSERT_RELATION( real<r3>::value, ==, -10 );
 122     BOOST_MPL_ASSERT_RELATION( imag<r3>::value, ==, 2 );
 123
 124
 125
 126 Models
 127 ------
 128
 129 * |plus|
 130 * |minus|
 131 * |times|
 132 * |divides|
 133
 134
 135 See also
 136 --------
 137
 138 |Tag Dispatched Metafunction|, |Metafunctions|, |numeric_cast|
 139
 140
 141 .. copyright:: Copyright ©  2001-2009 Aleksey Gurtovoy and David Abrahams
 142    Distributed under the Boost Software License, Version 1.0. (See accompanying
 143    file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)