ecency-mobile/ios/Pods/boost-for-react-native/boost/qvm/vec_operations.hpp

//Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc.

//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)

#ifndef UUID_384AFF3AD23A11DFA80B754FE0D72085
#define UUID_384AFF3AD23A11DFA80B754FE0D72085

#include <boost/qvm/vec_operations2.hpp>
#include <boost/qvm/vec_operations3.hpp>
#include <boost/qvm/vec_operations4.hpp>
#include <boost/qvm/assert.hpp>
#include <boost/qvm/scalar_traits.hpp>
#include <string>

namespace
boost
    {
    namespace
    qvm
        {
        namespace
        qvm_detail
            {
            BOOST_QVM_INLINE_CRITICAL
            void const *
            get_valid_ptr_vec_operations()
                {
                static int const obj=0;
                return &obj;
                }
            }

        ////////////////////////////////////////////////

        namespace
        qvm_to_string_detail
            {
            template <class T>
            std::string to_string( T const & x );
            }

        namespace
        qvm_detail
            {
            template <int D>
            struct
            to_string_v_defined
                {
                static bool const value=false;
                };

            template <int I,int DimMinusOne>
            struct
            to_string_vector_elements
                {
                template <class A>
                static
                std::string
                f( A const & a )
                    {
                    using namespace qvm_to_string_detail;
                    return to_string(vec_traits<A>::template read_element<I>(a))+','+to_string_vector_elements<I+1,DimMinusOne>::f(a);
                    }
                };

            template <int DimMinusOne>
            struct
            to_string_vector_elements<DimMinusOne,DimMinusOne>
                {
                template <class A>
                static
                std::string
                f( A const & a )
                    {
                    using namespace qvm_to_string_detail;
                    return to_string(vec_traits<A>::template read_element<DimMinusOne>(a));
                    }
                };
            }

        template <class A>
        inline
        typename boost::enable_if_c<
            is_vec<A>::value  &&
            !qvm_detail::to_string_v_defined<vec_traits<A>::dim>::value,
            std::string>::type
        to_string( A const & a )
            {
            return '('+qvm_detail::to_string_vector_elements<0,vec_traits<A>::dim-1>::f(a)+')';
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            assign_vv_defined
                {
                static bool const value=false;
                };

            template <int I,int N>
            struct
            copy_vector_elements
                {
                template <class A,class B>
                static
                void
                f( A & a, B const & b )
                    {
                    vec_traits<A>::template write_element<I>(a)=vec_traits<B>::template read_element<I>(b);
                    copy_vector_elements<I+1,N>::f(a,b);
                    }
                };

            template <int N>
            struct
            copy_vector_elements<N,N>
                {
                template <class A,class B>
                static
                void
                f( A &, B const & )
                    {
                    }
                };
            }

        template <class A,class B>
        inline
        typename boost::enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::assign_vv_defined<vec_traits<A>::dim>::value,
            A &>::type
        assign( A & a, B const & b )
            {
            qvm_detail::copy_vector_elements<0,vec_traits<A>::dim>::f(a,b);
            return a;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            convert_to_v_defined
                {
                static bool const value=false;
                };
            }

        template <class R,class A>
        BOOST_QVM_INLINE_TRIVIAL
        typename enable_if_c<
            is_vec<R>::value && is_vec<A>::value &&
            vec_traits<R>::dim==vec_traits<A>::dim &&
            !qvm_detail::convert_to_v_defined<vec_traits<R>::dim>::value,
            R>::type
        convert_to( A const & a )
            {
            R r; assign(r,a);
            return r;
            }

        ////////////////////////////////////////////////

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==3 && vec_traits<B>::dim==3,
            deduce_vec2<A,B,3> >::type
        cross( A const & a, B const & b )
            {
            typedef typename deduce_vec2<A,B,3>::type R;
            R r;
            vec_traits<R>::template write_element<0>(r)=
                vec_traits<A>::template read_element<1>(a)*vec_traits<B>::template read_element<2>(b)-
                vec_traits<A>::template read_element<2>(a)*vec_traits<B>::template read_element<1>(b);
            vec_traits<R>::template write_element<1>(r)=
                vec_traits<A>::template read_element<2>(a)*vec_traits<B>::template read_element<0>(b)-
                vec_traits<A>::template read_element<0>(a)*vec_traits<B>::template read_element<2>(b);
            vec_traits<R>::template write_element<2>(r)=
                vec_traits<A>::template read_element<0>(a)*vec_traits<B>::template read_element<1>(b)-
                vec_traits<A>::template read_element<1>(a)*vec_traits<B>::template read_element<0>(b);
            return r;
            }

        ////////////////////////////////////////////////

        template <class A,class B,class Cmp>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim,
            bool>::type
        cmp( A const & a, B const & b, Cmp f )
            {
            typedef typename deduce_scalar<
                typename vec_traits<A>::scalar_type,
                typename vec_traits<B>::scalar_type>::type T;
            int const dim=vec_traits<A>::dim;
            T v1[dim]; assign(v1,a);
            T v2[dim]; assign(v2,b);
            for( int i=0; i!=dim; ++i )
                if( !f(v1[i],v2[i]) )
                    return false;
            return true;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <class T,int Dim>
            class
            zero_vec_
                {
                zero_vec_( zero_vec_ const & );
                zero_vec_ & operator=( zero_vec_ const & );
                ~zero_vec_();

                public:

                template <class R>
                BOOST_QVM_INLINE_TRIVIAL
                operator R() const
                    {
                    R r;
                    assign(r,*this);
                    return r;
                    }
                };
            }

        template <class V>
        struct vec_traits;

        template <class T,int Dim>
        struct
        vec_traits< qvm_detail::zero_vec_<T,Dim> >
            {
            typedef qvm_detail::zero_vec_<T,Dim> this_vector;
            typedef T scalar_type;
            static int const dim=Dim;

            template <int I>
            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element( this_vector const & x )
                {
                BOOST_QVM_STATIC_ASSERT(I>=0);
                BOOST_QVM_STATIC_ASSERT(I<Dim);
                return scalar_traits<scalar_type>::value(0);
                }

            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element_idx( int i, this_vector const & x )
                {
                BOOST_QVM_ASSERT(i>=0);
                BOOST_QVM_ASSERT(i<Dim);
                return scalar_traits<scalar_type>::value(0);
                }
            };

        template <class T,int Dim,int D>
        struct
        deduce_vec<qvm_detail::zero_vec_<T,Dim>,D>
            {
            typedef vec<T,D> type;
            };

        template <class T,int Dim>
        BOOST_QVM_INLINE_TRIVIAL
        qvm_detail::zero_vec_<T,Dim> const &
        zero_vec()
            {
            return *(qvm_detail::zero_vec_<T,Dim> const *)qvm_detail::get_valid_ptr_vec_operations();
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value,
            void>::type
        set_zero( A & a )
            {
            assign(a,zero_vec<typename vec_traits<A>::scalar_type,vec_traits<A>::dim>());
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <class OriginalType,class Scalar>
            class
            vector_scalar_cast_
                {
                vector_scalar_cast_( vector_scalar_cast_ const & );
                vector_scalar_cast_ & operator=( vector_scalar_cast_ const & );
                ~vector_scalar_cast_();

                public:

                template <class T>
                BOOST_QVM_INLINE_TRIVIAL
                vector_scalar_cast_ &
                operator=( T const & x )
                    {
                    assign(*this,x);
                    return *this;
                    }

                template <class R>
                BOOST_QVM_INLINE_TRIVIAL
                operator R() const
                    {
                    R r;
                    assign(r,*this);
                    return r;
                    }
                };

            template <bool> struct scalar_cast_vector_filter { };
            template <> struct scalar_cast_vector_filter<true> { typedef int type; };
            }

        template <class OriginalType,class Scalar>
        struct
        vec_traits< qvm_detail::vector_scalar_cast_<OriginalType,Scalar> >
            {
            typedef Scalar scalar_type;
            typedef qvm_detail::vector_scalar_cast_<OriginalType,Scalar> this_vector;
            static int const dim=vec_traits<OriginalType>::dim;

            template <int I>
            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element( this_vector const & x )
                {
                BOOST_QVM_STATIC_ASSERT(I>=0);
                BOOST_QVM_STATIC_ASSERT(I<dim);
                return scalar_type(vec_traits<OriginalType>::template read_element<I>(reinterpret_cast<OriginalType const &>(x)));
                }

            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element_idx( int i, this_vector const & x )
                {
                BOOST_QVM_ASSERT(i>=0);
                BOOST_QVM_ASSERT(i<dim);
                return scalar_type(vec_traits<OriginalType>::read_element_idx(i,reinterpret_cast<OriginalType const &>(x)));
                }
            };

        template <class OriginalType,class Scalar,int D>
        struct
        deduce_vec<qvm_detail::vector_scalar_cast_<OriginalType,Scalar>,D>
            {
            typedef vec<Scalar,D> type;
            };

        template <class Scalar,class T>
        BOOST_QVM_INLINE_TRIVIAL
        qvm_detail::vector_scalar_cast_<T,Scalar> const &
        scalar_cast( T const & x, typename qvm_detail::scalar_cast_vector_filter<is_vec<T>::value>::type=0 )
            {
            return reinterpret_cast<qvm_detail::vector_scalar_cast_<T,Scalar> const &>(x);
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            div_eq_vs_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_scalar<B>::value &&
            !qvm_detail::div_eq_vs_defined<vec_traits<A>::dim>::value,
            A &>::type
        operator/=( A & a, B b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<A>::write_element_idx(i,a)/=b;
            return a;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            div_vs_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_scalar<B>::value &&
            !qvm_detail::div_vs_defined<vec_traits<A>::dim>::value,
            deduce_vec<A> >::type
        operator/( A const & a, B b )
            {
            typedef typename deduce_vec<A>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=vec_traits<A>::read_element_idx(i,a)/b;
            return r;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            dot_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::dot_vv_defined<vec_traits<A>::dim>::value,
            deduce_scalar<typename vec_traits<A>::scalar_type,typename vec_traits<B>::scalar_type> >::type
        dot( A const & a, B const & b )
            {
            typedef typename deduce_scalar<typename vec_traits<A>::scalar_type,typename vec_traits<B>::scalar_type>::type T;
            T m(scalar_traits<T>::value(0));
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                m+=vec_traits<A>::read_element_idx(i,a)*vec_traits<B>::read_element_idx(i,b);
            return m;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            eq_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::eq_vv_defined<vec_traits<A>::dim>::value,
            bool>::type
        operator==( A const & a, B const & b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                if( vec_traits<A>::read_element_idx(i,a)!=vec_traits<B>::read_element_idx(i,b) )
                    return false;
            return true;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            mag_sqr_v_defined
                {
                static bool const value=false;
                };
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value &&
            !qvm_detail::mag_sqr_v_defined<vec_traits<A>::dim>::value,
            typename vec_traits<A>::scalar_type>::type
        mag_sqr( A const & a )
            {
            typedef typename vec_traits<A>::scalar_type T;
            T m(scalar_traits<T>::value(0));
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                {
                T x=vec_traits<A>::read_element_idx(i,a);
                m+=x*x;
                }
            return m;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            mag_v_defined
                {
                static bool const value=false;
                };
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value &&
            !qvm_detail::mag_v_defined<vec_traits<A>::dim>::value,
            typename vec_traits<A>::scalar_type>::type
        mag( A const & a )
            {
            typedef typename vec_traits<A>::scalar_type T;
            T m(scalar_traits<T>::value(0));
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                {
                T x=vec_traits<A>::read_element_idx(i,a);
                m+=x*x;
                }
            return sqrt<T>(m);
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            minus_eq_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::minus_eq_vv_defined<vec_traits<A>::dim>::value,
            A &>::type
        operator-=( A & a, B const & b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<A>::write_element_idx(i,a)-=vec_traits<B>::read_element_idx(i,b);
            return a;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            minus_v_defined
                {
                static bool const value=false;
                };
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value &&
            !qvm_detail::minus_v_defined<vec_traits<A>::dim>::value,
            deduce_vec<A> >::type
        operator-( A const & a )
            {
            typedef typename deduce_vec<A>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=-vec_traits<A>::read_element_idx(i,a);
            return r;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            minus_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::minus_vv_defined<vec_traits<A>::dim>::value,
            deduce_vec2<A,B,vec_traits<A>::dim> >::type
        operator-( A const & a, B const & b )
            {
            typedef typename deduce_vec2<A,B,vec_traits<A>::dim>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=vec_traits<A>::read_element_idx(i,a)-vec_traits<B>::read_element_idx(i,b);
            return r;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            mul_eq_vs_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_scalar<B>::value &&
            !qvm_detail::mul_eq_vs_defined<vec_traits<A>::dim>::value,
            A &>::type
        operator*=( A & a, B b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<A>::write_element_idx(i,a)*=b;
            return a;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            mul_vs_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_scalar<B>::value &&
            !qvm_detail::mul_vs_defined<vec_traits<A>::dim>::value,
            deduce_vec<A> >::type
        operator*( A const & a, B b )
            {
            typedef typename deduce_vec<A>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=vec_traits<A>::read_element_idx(i,a)*b;
            return r;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            neq_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::neq_vv_defined<vec_traits<A>::dim>::value,
            bool>::type
        operator!=( A const & a, B const & b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                if( vec_traits<A>::read_element_idx(i,a)!=vec_traits<B>::read_element_idx(i,b) )
                    return true;
            return false;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            normalize_v_defined
                {
                static bool const value=false;
                };
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value &&
            !qvm_detail::normalize_v_defined<vec_traits<A>::dim>::value,
            deduce_vec<A> >::type
        normalized( A const & a )
            {
            typedef typename vec_traits<A>::scalar_type T;
            T m(scalar_traits<T>::value(0));
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                {
                T x=vec_traits<A>::read_element_idx(i,a);
                m+=x*x;
                }
            if( m==scalar_traits<T>::value(0) )
                BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
            T rm=scalar_traits<T>::value(1)/sqrt<T>(m);
            typedef typename deduce_vec<A>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=vec_traits<A>::read_element_idx(i,a)*rm;
            return r;
            }

        template <class A>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value &&
            !qvm_detail::normalize_v_defined<vec_traits<A>::dim>::value,
            void>::type
        normalize( A & a )
            {
            typedef typename vec_traits<A>::scalar_type T;
            T m(scalar_traits<T>::value(0));
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                {
                T x=vec_traits<A>::read_element_idx(i,a);
                m+=x*x;
                }
            if( m==scalar_traits<T>::value(0) )
                BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
            T rm=scalar_traits<T>::value(1)/sqrt<T>(m);
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<A>::write_element_idx(i,a)*=rm;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            plus_eq_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::plus_eq_vv_defined<vec_traits<A>::dim>::value,
            A &>::type
        operator+=( A & a, B const & b )
            {
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<A>::write_element_idx(i,a)+=vec_traits<B>::read_element_idx(i,b);
            return a;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <int D>
            struct
            plus_vv_defined
                {
                static bool const value=false;
                };
            }

        template <class A,class B>
        BOOST_QVM_INLINE_OPERATIONS
        typename lazy_enable_if_c<
            is_vec<A>::value && is_vec<B>::value &&
            vec_traits<A>::dim==vec_traits<B>::dim &&
            !qvm_detail::plus_vv_defined<vec_traits<A>::dim>::value,
            deduce_vec2<A,B,vec_traits<A>::dim> >::type
        operator+( A const & a, B const & b )
            {
            typedef typename deduce_vec2<A,B,vec_traits<A>::dim>::type R;
            R r;
            for( int i=0; i!=vec_traits<A>::dim; ++i )
                vec_traits<R>::write_element_idx(i,r)=vec_traits<A>::read_element_idx(i,a)+vec_traits<B>::read_element_idx(i,b);
            return r;
            }

        ////////////////////////////////////////////////

        namespace
        qvm_detail
            {
            template <class T>
            class
            vref_
                {
                vref_( vref_ const & );
                vref_ & operator=( vref_ const & );
                ~vref_();

                public:

                template <class R>
                BOOST_QVM_INLINE_TRIVIAL
                vref_ &
                operator=( R const & x )
                    {
                    assign(*this,x);
                    return *this;
                    }

                template <class R>
                BOOST_QVM_INLINE_TRIVIAL
                operator R() const
                    {
                    R r;
                    assign(r,*this);
                    return r;
                    }
                };
            }

        template <class V>
        struct
        vec_traits< qvm_detail::vref_<V> >
            {
            typedef typename vec_traits<V>::scalar_type scalar_type;
            typedef qvm_detail::vref_<V> this_vector;
            static int const dim=vec_traits<V>::dim;

            template <int I>
            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element( this_vector const & x )
                {
                BOOST_QVM_STATIC_ASSERT(I>=0);
                BOOST_QVM_STATIC_ASSERT(I<dim);
                return vec_traits<V>::template read_element<I>(reinterpret_cast<V const &>(x));
                }

            template <int I>
            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type &
            write_element( this_vector & x )
                {
                BOOST_QVM_STATIC_ASSERT(I>=0);
                BOOST_QVM_STATIC_ASSERT(I<dim);
                return vec_traits<V>::template write_element<I>(reinterpret_cast<V &>(x));
                }

            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type
            read_element_idx( int i, this_vector const & x )
                {
                BOOST_QVM_ASSERT(i>=0);
                BOOST_QVM_ASSERT(i<dim);
                return vec_traits<V>::read_element_idx(i,reinterpret_cast<V const &>(x));
                }

            static
            BOOST_QVM_INLINE_CRITICAL
            scalar_type &
            write_element_idx( int i, this_vector & x )
                {
                BOOST_QVM_ASSERT(i>=0);
                BOOST_QVM_ASSERT(i<dim);
                return vec_traits<V>::write_element_idx(i,reinterpret_cast<V &>(x));
                }
            };

        template <class V,int D>
        struct
        deduce_vec<qvm_detail::vref_<V>,D>
            {
            typedef vec<typename vec_traits<V>::scalar_type,D> type;
            };

        template <class V>
        BOOST_QVM_INLINE_TRIVIAL
        typename enable_if_c<
            is_vec<V>::value,
            qvm_detail::vref_<V> const &>::type
        vref( V const & a )
            {
            return reinterpret_cast<qvm_detail::vref_<V> const &>(a);
            }

        template <class V>
        BOOST_QVM_INLINE_TRIVIAL
        typename enable_if_c<
            is_vec<V>::value,
            qvm_detail::vref_<V> &>::type
        vref( V & a )
            {
            return reinterpret_cast<qvm_detail::vref_<V> &>(a);
            }

        ////////////////////////////////////////////////

        namespace
        sfinae
            {
            using ::boost::qvm::to_string;
            using ::boost::qvm::assign;
            using ::boost::qvm::convert_to;
            using ::boost::qvm::cross;
            using ::boost::qvm::cmp;
            using ::boost::qvm::set_zero;
            using ::boost::qvm::scalar_cast;
            using ::boost::qvm::operator/=;
            using ::boost::qvm::operator/;
            using ::boost::qvm::dot;
            using ::boost::qvm::operator==;
            using ::boost::qvm::mag_sqr;
            using ::boost::qvm::mag;
            using ::boost::qvm::operator-=;
            using ::boost::qvm::operator-;
            using ::boost::qvm::operator*=;
            using ::boost::qvm::operator*;
            using ::boost::qvm::operator!=;
            using ::boost::qvm::normalized;
            using ::boost::qvm::normalize;
            using ::boost::qvm::operator+=;
            using ::boost::qvm::operator+;
            using ::boost::qvm::vref;
            }

        ////////////////////////////////////////////////
        }
    }

#endif