boost/numeric/ublas/traits.hpp
// // 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> #include <boost/typeof/typeof.hpp> #include <boost/utility/enable_if.hpp> #include <boost/type_traits/is_float.hpp> #include <boost/type_traits/is_integral.hpp> #include <boost/mpl/and.hpp> // 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; }; template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator+ (I in1, std::complex<R> const& in2 ) { return R (in1) + in2; } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator+ (std::complex<R> const& in1, I in2) { return in1 + R (in2); } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator- (I in1, std::complex<R> const& in2) { return R (in1) - in2; } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator- (std::complex<R> const& in1, I in2) { return in1 - R (in2); } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator* (I in1, std::complex<R> const& in2) { return R (in1) * in2; } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator* (std::complex<R> const& in1, I in2) { return in1 * R(in2); } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator/ (I in1, std::complex<R> const& in2) { return R(in1) / in2; } template<typename R, typename I> typename boost::enable_if< mpl::and_< boost::is_float<R>, boost::is_integral<I> >, std::complex<R> >::type inline operator/ (std::complex<R> const& in1, I in2) { return in1 / R (in2); } // 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 self_type::type_abs (t); // original computation has been replaced because a complex number should behave like a scalar type // 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 self_type::type_abs (t); // original computation has been replaced because a complex number should behave like a scalar type // 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<> struct type_traits<std::complex<double> > : complex_traits<std::complex<double> >{ typedef type_traits<std::complex<double> > self_type; typedef std::complex<double> value_type; typedef const value_type &const_reference; typedef value_type &reference; typedef double real_type; typedef std::complex<long double> precision_type; }; template<> struct type_traits<std::complex<long double> > : complex_traits<std::complex<long double> > { typedef type_traits<std::complex<long double> > self_type; typedef std::complex<long double> value_type; typedef const value_type &const_reference; typedef value_type &reference; typedef long double real_type; typedef value_type precision_type; }; #ifdef BOOST_UBLAS_USE_INTERVAL // Define scalar interval type traits template<> struct type_traits<boost::numeric::interval<float> > : scalar_traits<boost::numeric::interval<float> > { typedef type_traits<boost::numeric::interval<float> > self_type; typedef boost::numeric::interval<float> value_type; typedef const value_type &const_reference; typedef value_type &reference; typedef value_type real_type; typedef boost::numeric::interval<double> precision_type; }; template<> struct type_traits<boost::numeric::interval<double> > : scalar_traits<boost::numeric::interval<double> > { typedef type_traits<boost::numeric::interval<double> > self_type; typedef boost::numeric::interval<double> value_type; typedef const value_type &const_reference; typedef value_type &reference; typedef value_type real_type; typedef boost::numeric::interval<long double> precision_type; }; template<> struct type_traits<boost::numeric::interval<long double> > : scalar_traits<boost::numeric::interval<long double> > { typedef type_traits<boost::numeric::interval<long double> > self_type; typedef boost::numeric::interval<long double> value_type; typedef const value_type &const_reference; typedef value_type &reference; typedef value_type real_type; typedef value_type precision_type; }; #endif // Storage tags -- hierarchical definition of storage characteristics struct unknown_storage_tag {}; struct sparse_proxy_tag: public unknown_storage_tag {}; struct sparse_tag: public sparse_proxy_tag {}; struct packed_proxy_tag: public sparse_proxy_tag {}; struct packed_tag: public packed_proxy_tag {}; struct dense_proxy_tag: public packed_proxy_tag {}; struct dense_tag: public dense_proxy_tag {}; template<class S1, class S2> struct storage_restrict_traits { typedef S1 storage_category; }; template<> struct storage_restrict_traits<sparse_tag, dense_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<sparse_tag, packed_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<sparse_tag, sparse_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<packed_tag, dense_proxy_tag> { typedef packed_proxy_tag storage_category; }; template<> struct storage_restrict_traits<packed_tag, packed_proxy_tag> { typedef packed_proxy_tag storage_category; }; template<> struct storage_restrict_traits<packed_tag, sparse_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<packed_proxy_tag, sparse_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<dense_tag, dense_proxy_tag> { typedef dense_proxy_tag storage_category; }; template<> struct storage_restrict_traits<dense_tag, packed_proxy_tag> { typedef packed_proxy_tag storage_category; }; template<> struct storage_restrict_traits<dense_tag, sparse_proxy_tag> { typedef sparse_proxy_tag storage_category; }; template<> struct storage_restrict_traits<dense_proxy_tag, packed_proxy_tag> { typedef packed_proxy_tag storage_category; }; template<> struct storage_restrict_traits<dense_proxy_tag, sparse_proxy_tag> { typedef sparse_proxy_tag storage_category; }; // Iterator tags -- hierarchical definition of storage characteristics struct sparse_bidirectional_iterator_tag : public std::bidirectional_iterator_tag {}; struct packed_random_access_iterator_tag : public std::random_access_iterator_tag {}; struct dense_random_access_iterator_tag : public packed_random_access_iterator_tag {}; // Thanks to Kresimir Fresl for convincing Comeau with iterator_base_traits ;-) template<class IC> struct iterator_base_traits {}; template<> struct iterator_base_traits<std::forward_iterator_tag> { template<class I, class T> struct iterator_base { typedef forward_iterator_base<std::forward_iterator_tag, I, T> type; }; }; template<> struct iterator_base_traits<std::bidirectional_iterator_tag> { template<class I, class T> struct iterator_base { typedef bidirectional_iterator_base<std::bidirectional_iterator_tag, I, T> type; }; }; template<> struct iterator_base_traits<sparse_bidirectional_iterator_tag> { template<class I, class T> struct iterator_base { typedef bidirectional_iterator_base<sparse_bidirectional_iterator_tag, I, T> type; }; }; template<> struct iterator_base_traits<std::random_access_iterator_tag> { template<class I, class T> struct iterator_base { typedef random_access_iterator_base<std::random_access_iterator_tag, I, T> type; }; }; template<> struct iterator_base_traits<packed_random_access_iterator_tag> { template<class I, class T> struct iterator_base { typedef random_access_iterator_base<packed_random_access_iterator_tag, I, T> type; }; }; template<> struct iterator_base_traits<dense_random_access_iterator_tag> { template<class I, class T> struct iterator_base { typedef random_access_iterator_base<dense_random_access_iterator_tag, I, T> type; }; }; template<class I1, class I2> struct iterator_restrict_traits { typedef I1 iterator_category; }; template<> struct iterator_restrict_traits<packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag> { typedef sparse_bidirectional_iterator_tag iterator_category; }; template<> struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag> { typedef sparse_bidirectional_iterator_tag iterator_category; }; template<> struct iterator_restrict_traits<dense_random_access_iterator_tag, sparse_bidirectional_iterator_tag> { typedef sparse_bidirectional_iterator_tag iterator_category; }; template<> struct iterator_restrict_traits<sparse_bidirectional_iterator_tag, dense_random_access_iterator_tag> { typedef sparse_bidirectional_iterator_tag iterator_category; }; template<> struct iterator_restrict_traits<dense_random_access_iterator_tag, packed_random_access_iterator_tag> { typedef packed_random_access_iterator_tag iterator_category; }; template<> struct iterator_restrict_traits<packed_random_access_iterator_tag, dense_random_access_iterator_tag> { typedef packed_random_access_iterator_tag iterator_category; }; template<class I> BOOST_UBLAS_INLINE void increment (I &it, const I &it_end, typename I::difference_type compare, packed_random_access_iterator_tag) { it += (std::min) (compare, it_end - it); } template<class I> BOOST_UBLAS_INLINE void increment (I &it, const I &/* it_end */, typename I::difference_type /* compare */, sparse_bidirectional_iterator_tag) { ++ it; } template<class I> BOOST_UBLAS_INLINE void increment (I &it, const I &it_end, typename I::difference_type compare) { increment (it, it_end, compare, typename I::iterator_category ()); } template<class I> BOOST_UBLAS_INLINE void increment (I &it, const I &it_end) { #if BOOST_UBLAS_TYPE_CHECK I cit (it); while (cit != it_end) { BOOST_UBLAS_CHECK (*cit == typename I::value_type/*zero*/(), internal_logic ()); ++ cit; } #endif it = it_end; } namespace detail { // specialisation which define whether a type has a trivial constructor // or not. This is used by array types. template<typename T> struct has_trivial_constructor : public boost::has_trivial_constructor<T> {}; template<typename T> struct has_trivial_destructor : public boost::has_trivial_destructor<T> {}; template<typename FLT> struct has_trivial_constructor<std::complex<FLT> > : public boost::true_type {}; template<typename FLT> struct has_trivial_destructor<std::complex<FLT> > : public boost::true_type {}; } /** \brief Traits class to extract type information from a constant matrix or vector CONTAINER. * */ template < class E > struct container_view_traits { /// type of indices typedef typename E::size_type size_type; /// type of differences of indices typedef typename E::difference_type difference_type; /// storage category: \c unknown_storage_tag, \c dense_tag, \c packed_tag, ... typedef typename E::storage_category storage_category; /// type of elements typedef typename E::value_type value_type; /// const reference to an element typedef typename E::const_reference const_reference; /// type used in expressions to mark a reference to this class (usually a const container_reference<const E> or the class itself) typedef typename E::const_closure_type const_closure_type; }; /** \brief Traits class to extract additional type information from a mutable matrix or vector CONTAINER. * */ template < class E > struct mutable_container_traits { /// reference to an element typedef typename E::reference reference; /// type used in expressions to mark a reference to this class (usually a container_reference<E> or the class itself) typedef typename E::closure_type closure_type; }; /** \brief Traits class to extract type information from a matrix or vector CONTAINER. * */ template < class E > struct container_traits : container_view_traits<E>, mutable_container_traits<E> { }; /** \brief Traits class to extract type information from a constant MATRIX. * */ template < class MATRIX > struct matrix_view_traits : container_view_traits <MATRIX> { /// orientation of the matrix, either \c row_major_tag, \c column_major_tag or \c unknown_orientation_tag typedef typename MATRIX::orientation_category orientation_category; /// row iterator for the matrix typedef typename MATRIX::const_iterator1 const_iterator1; /// column iterator for the matrix typedef typename MATRIX::const_iterator2 const_iterator2; }; /** \brief Traits class to extract additional type information from a mutable MATRIX. * */ template < class MATRIX > struct mutable_matrix_traits : mutable_container_traits <MATRIX> { /// row iterator for the matrix typedef typename MATRIX::iterator1 iterator1; /// column iterator for the matrix typedef typename MATRIX::iterator2 iterator2; }; /** \brief Traits class to extract type information from a MATRIX. * */ template < class MATRIX > struct matrix_traits : matrix_view_traits <MATRIX>, mutable_matrix_traits <MATRIX> { }; /** \brief Traits class to extract type information from a VECTOR. * */ template < class VECTOR > struct vector_view_traits : container_view_traits <VECTOR> { /// iterator for the VECTOR typedef typename VECTOR::const_iterator const_iterator; /// iterator pointing to the first element static const_iterator begin(const VECTOR & v) { return v.begin(); } /// iterator pointing behind the last element static const_iterator end(const VECTOR & v) { return v.end(); } }; /** \brief Traits class to extract type information from a VECTOR. * */ template < class VECTOR > struct mutable_vector_traits : mutable_container_traits <VECTOR> { /// iterator for the VECTOR typedef typename VECTOR::iterator iterator; /// iterator pointing to the first element static iterator begin(VECTOR & v) { return v.begin(); } /// iterator pointing behind the last element static iterator end(VECTOR & v) { return v.end(); } }; /** \brief Traits class to extract type information from a VECTOR. * */ template < class VECTOR > struct vector_traits : vector_view_traits <VECTOR>, mutable_vector_traits <VECTOR> { }; // Note: specializations for T[N] and T[M][N] have been moved to traits/c_array.hpp }}} #endif