traits.hpp

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//
//  Copyright (c) 2000-2002
//  Joerg Walter, Mathias Koch
//
//  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)
//
//  The authors gratefully acknowledge the support of
//  GeNeSys mbH & Co. KG in producing this work.
//

#ifndef _BOOST_UBLAS_TRAITS_
#define _BOOST_UBLAS_TRAITS_

#include <iterator>
#include <complex>
#include <boost/config/no_tr1/cmath.hpp>

#include <boost/numeric/ublas/detail/config.hpp>
#include <boost/numeric/ublas/detail/iterator.hpp>
#include <boost/numeric/ublas/detail/returntype_deduction.hpp>

#include <boost/type_traits.hpp>
#include <complex>

// anonymous namespace to avoid ADL issues
namespace {
  template<class T> T boost_numeric_ublas_sqrt (const T& t) {
    using namespace std;
    // we'll find either std::sqrt or else another version via ADL:
    return sqrt (t);
  }
  template<class T> T boost_numeric_ublas_abs (const T& t) {
    using namespace std;
    // we'll find either std::abs or else another version via ADL:
    return abs (t);
  }
}

namespace boost { namespace numeric { namespace ublas {

    // Use Joel de Guzman's return type deduction
    // uBLAS assumes a common return type for all binary arithmetic operators
    template<class X, class Y>
    struct promote_traits {
        typedef type_deduction_detail::base_result_of<X, Y> base_type;
        static typename base_type::x_type x;
        static typename base_type::y_type y;
        static const std::size_t size = sizeof (
                type_deduction_detail::test<
                    typename base_type::x_type
                  , typename base_type::y_type
                >(x + y)     // Use x+y to stand of all the arithmetic actions
            );

        static const std::size_t index = (size / sizeof (char)) - 1;
        typedef typename mpl::at_c<
            typename base_type::types, index>::type id;
        typedef typename id::type promote_type;
    };


    // Type traits - generic numeric properties and functions
    template<class T>
    struct type_traits;
        
    // Define properties for a generic scalar type
    template<class T>
    struct scalar_traits {
        typedef scalar_traits<T> self_type;
        typedef T value_type;
        typedef const T &const_reference;
        typedef T &reference;

        typedef T real_type;
        typedef real_type precision_type;       // we do not know what type has more precision then the real_type

        static const unsigned plus_complexity = 1;
        static const unsigned multiplies_complexity = 1;

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return t;
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference /*t*/) {
                return 0;
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return t;
        }

        static
        BOOST_UBLAS_INLINE
        real_type type_abs (const_reference t) {
            return boost_numeric_ublas_abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type type_sqrt (const_reference t) {
            // force a type conversion back to value_type for intgral types
            return value_type (boost_numeric_ublas_sqrt (t));
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return self_type::type_abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::type_abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return self_type::type_abs (t);
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };

    // Define default type traits, assume T is a scalar type
    template<class T>
    struct type_traits : scalar_traits <T> {
        typedef type_traits<T> self_type;
        typedef T value_type;
        typedef const T &const_reference;
        typedef T &reference;

        typedef T real_type;
        typedef real_type precision_type;
        static const unsigned multiplies_complexity = 1;

    };

    // Define real type traits
    template<>
    struct type_traits<float> : scalar_traits<float> {
        typedef type_traits<float> self_type;
        typedef float value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
        typedef double precision_type;
    };
    template<>
    struct type_traits<double> : scalar_traits<double> {
        typedef type_traits<double> self_type;
        typedef double value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
        typedef long double precision_type;
    };
    template<>
    struct type_traits<long double>  : scalar_traits<long double> {
        typedef type_traits<long double> self_type;
        typedef long double value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
        typedef value_type precision_type;
    };

    // Define properties for a generic complex type
    template<class T>
    struct complex_traits {
        typedef complex_traits<T> self_type;
        typedef T value_type;
        typedef const T &const_reference;
        typedef T &reference;

        typedef typename T::value_type real_type;
        typedef real_type precision_type;       // we do not know what type has more precision then the real_type

        static const unsigned plus_complexity = 2;
        static const unsigned multiplies_complexity = 6;

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return std::real (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return std::imag (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return std::conj (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type type_abs (const_reference t) {
                return abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type type_sqrt (const_reference t) {
                return sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return type_traits<real_type>::type_abs (self_type::real (t)) +
                   type_traits<real_type>::type_abs (self_type::imag (t));
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::type_abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return (std::max) (type_traits<real_type>::type_abs (self_type::real (t)),
                             type_traits<real_type>::type_abs (self_type::imag (t)));
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
    
    // Define complex type traits
    template<>
    struct type_traits<std::complex<float> > : complex_traits<std::complex<float> >{
        typedef type_traits<std::complex<float> > self_type;
        typedef std::complex<float> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef float real_type;
        typedef std::complex<double> precision_type;

    };
    template<>