]> git.proxmox.com Git - ceph.git/blobdiff - ceph/src/boost/boost/qvm/vec_operations.hpp
update ceph source to reef 18.1.2
[ceph.git] / ceph / src / boost / boost / qvm / vec_operations.hpp
index 0ed71a303f2427b24f989370a19a7cea8ec71565..de814cd00553c067912ab50dc07f8a40dd334ae5 100644 (file)
@@ -1,11 +1,11 @@
-//Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc.
-//Copyright (c) 2019 agate-pris
+#ifndef BOOST_QVM_VEC_OPERATIONS_HPP_INCLUDED
+#define BOOST_QVM_VEC_OPERATIONS_HPP_INCLUDED
 
-//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)
+// Copyright 2008-2022 Emil Dotchevski and Reverge Studios, Inc.
+// Copyright 2019 agate-pris
 
-#ifndef BOOST_QVM_384AFF3AD23A11DFA80B754FE0D72085
-#define BOOST_QVM_384AFF3AD23A11DFA80B754FE0D72085
+// 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)
 
 #include <boost/qvm/detail/vec_assign.hpp>
 #include <boost/qvm/vec_operations2.hpp>
 #include <boost/qvm/scalar_traits.hpp>
 #include <string>
 
+namespace boost { namespace qvm {
+
 namespace
-boost
+qvm_detail
     {
-    namespace
-    qvm
+    BOOST_QVM_INLINE_CRITICAL
+    void const *
+    get_valid_ptr_vec_operations()
         {
-        namespace
-        qvm_detail
-            {
-            BOOST_QVM_INLINE_CRITICAL
-            void const *
-            get_valid_ptr_vec_operations()
-                {
-                static int const obj=0;
-                return &obj;
-                }
-            }
+        static int const obj=0;
+        return &obj;
+        }
+    }
 
-        ////////////////////////////////////////////////
+////////////////////////////////////////////////
 
-        namespace
-        qvm_to_string_detail
-            {
-            template <class T>
-            std::string to_string( T const & x );
-            }
+namespace
+qvm_to_string_detail
+    {
+    template <class T>
+    std::string to_string( T const & x );
+    }
 
-        namespace
-        qvm_detail
+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 )
             {
-            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));
-                    }
-                };
+            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>
-        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 )
+        static
+        std::string
+        f( A const & a )
             {
-            return '('+qvm_detail::to_string_vector_elements<0,vec_traits<A>::dim-1>::f(a)+')';
+            using namespace qvm_to_string_detail;
+            return to_string(vec_traits<A>::template read_element<DimMinusOne>(a));
             }
+        };
+    }
 
-        ////////////////////////////////////////////////
+template <class A>
+inline
+typename 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
-            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;
-            }
+namespace
+qvm_detail
+    {
+    template <int D>
+    struct
+    convert_to_v_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        ////////////////////////////////////////////////
+template <class R,class A>
+BOOST_QVM_CONSTEXPR 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>
+BOOST_QVM_CONSTEXPR 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 )
-            {
-            for( int i=0; i!=vec_traits<A>::dim; ++i )
-                if( !f(
-                    vec_traits<A>::read_element_idx(i,a),
-                    vec_traits<B>::read_element_idx(i,b)) )
-                    return false;
-            return true;
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
+typename lazy_enable_if_c<
+    is_vec<A>::value && is_vec<B>::value &&
+    vec_traits<A>::dim==2 && vec_traits<B>::dim==2,
+    deduce_scalar<typename vec_traits<A>::scalar_type,typename vec_traits<B>::scalar_type> >::type
+cross( A const & a, B const & b )
+    {
+    typedef typename deduce_scalar<typename vec_traits<A>::scalar_type,typename vec_traits<B>::scalar_type>::type R;
+    R const 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;
+    }
 
-        ////////////////////////////////////////////////
+////////////////////////////////////////////////
 
-        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 A,class B,class Cmp>
+BOOST_QVM_CONSTEXPR 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 )
+    {
+    for( int i=0; i!=vec_traits<A>::dim; ++i )
+        if( !f(
+            vec_traits<A>::read_element_idx(i,a),
+            vec_traits<B>::read_element_idx(i,b)) )
+            return false;
+    return true;
+    }
 
-        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 & )
-                {
-                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 & )
-                {
-                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;
-            };
+namespace
+qvm_detail
+    {
+    template <class T,int Dim>
+    class
+    zero_vec_
+        {
+        zero_vec_( zero_vec_ const & );
+        zero_vec_ & operator=( zero_vec_ const & );
+        ~zero_vec_();
 
-        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();
-            }
+        public:
 
-        template <class A>
-        BOOST_QVM_INLINE_OPERATIONS
-        typename enable_if_c<
-            is_vec<A>::value,
-            void>::type
-        set_zero( A & a )
+        template <class R>
+        BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_TRIVIAL
+        operator R() const
             {
-            assign(a,zero_vec<typename vec_traits<A>::scalar_type,vec_traits<A>::dim>());
+            R r;
+            assign(r,*this);
+            return r;
             }
+        };
+    }
 
-        ////////////////////////////////////////////////
+template <class V>
+struct vec_traits;
 
-        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 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_CONSTEXPR BOOST_QVM_INLINE_CRITICAL
+    scalar_type
+    read_element( this_vector const & )
+        {
+        BOOST_QVM_STATIC_ASSERT(I>=0);
+        BOOST_QVM_STATIC_ASSERT(I<Dim);
+        return scalar_traits<scalar_type>::value(0);
+        }
 
-        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;
-            };
+    static
+    BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_CRITICAL
+    scalar_type
+    read_element_idx( int i, this_vector const & )
+        {
+        BOOST_QVM_ASSERT(i>=0);
+        BOOST_QVM_ASSERT(i<Dim);
+        return scalar_traits<scalar_type>::value(0);
+        }
+    };
 
-        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);
-            }
+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_CONSTEXPR 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();
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            div_eq_vs_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A>
+BOOST_QVM_CONSTEXPR 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>());
+    }
 
-        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 <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:
 
-        namespace
-        qvm_detail
+        template <class T>
+        BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_TRIVIAL
+        vector_scalar_cast_ &
+        operator=( T const & x )
             {
-            template <int D>
-            struct
-            div_vs_defined
-                {
-                static bool const value=false;
-                };
+            assign(*this,x);
+            return *this;
             }
 
-        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 )
+        template <class R>
+        BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_TRIVIAL
+        operator R() const
             {
-            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;
+            assign(r,*this);
             return r;
             }
+        };
 
-        ////////////////////////////////////////////////
+    template <bool> struct scalar_cast_vector_filter { };
+    template <> struct scalar_cast_vector_filter<true> { typedef int type; };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            dot_vv_defined
-                {
-                static bool const value=false;
-                };
-            }
+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_CONSTEXPR 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)));
+        }
 
-        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;
-            }
+    static
+    BOOST_QVM_CONSTEXPR 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;
+    };
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            eq_vv_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class Scalar,class T>
+BOOST_QVM_CONSTEXPR 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);
+    }
 
-        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
+    div_eq_vs_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            mag_sqr_v_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        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
+    div_vs_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            mag_v_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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_vec2<A,B,vec_traits<A>::dim> >::type
+operator/( A const & a, B 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)/b;
+    return r;
+    }
 
-        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
+    dot_vv_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            minus_eq_vv_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        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
+    eq_vv_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            minus_v_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        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
+    mag_sqr_v_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            minus_vv_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        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
+    mag_v_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            mul_eq_vs_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A>
+BOOST_QVM_CONSTEXPR 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(m);
+    }
 
-        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
+    minus_eq_vv_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            mul_vs_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        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
+    minus_v_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            mul_sv_defined
-                {
-                static bool const value=false;
-                };
-            }
+template <class A>
+BOOST_QVM_CONSTEXPR 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;
+    }
 
-        template <class A,class B>
-        BOOST_QVM_INLINE_OPERATIONS
-        typename lazy_enable_if_c<
-            is_scalar<A>::value && is_vec<B>::value &&
-            !qvm_detail::mul_sv_defined<vec_traits<B>::dim>::value,
-            deduce_vec<B> >::type
-        operator*( A a, B const & b )
-            {
-            typedef typename deduce_vec<B>::type R;
-            R r;
-            for( int i=0; i!=vec_traits<B>::dim; ++i )
-                vec_traits<R>::write_element_idx(i,r)=a*vec_traits<B>::read_element_idx(i,b);
-            return r;
-            }
+////////////////////////////////////////////////
+
+namespace
+qvm_detail
+    {
+    template <int D>
+    struct
+    minus_vv_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        ////////////////////////////////////////////////
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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
-            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
+    mul_eq_vs_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        ////////////////////////////////////////////////
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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
-            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;
-            }
+namespace
+qvm_detail
+    {
+    template <int D>
+    struct
+    mul_vs_defined
+        {
+        static bool const value=false;
+        };
+    }
 
-        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;
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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_vec2<A,B,vec_traits<A>::dim> >::type
+operator*( A const & a, B 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)*b;
+    return r;
+    }
 
-        ////////////////////////////////////////////////
+////////////////////////////////////////////////
 
-        namespace
-        qvm_detail
-            {
-            template <int D>
-            struct
-            plus_eq_vv_defined
-                {
-                static bool const value=false;
-                };
-            }
+namespace
+qvm_detail
+    {
+    template <int D>
+    struct
+    mul_sv_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;
-            }
+template <class A,class B>
+BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
+typename lazy_enable_if_c<
+    is_scalar<A>::value && is_vec<B>::value &&
+    !qvm_detail::mul_sv_defined<vec_traits<B>::dim>::value,
+    deduce_vec2<A,B,vec_traits<B>::dim> >::type
+operator*( A a, B const & b )
+    {
+    typedef typename deduce_vec2<A,B,vec_traits<B>::dim>::type R;
+    R r;
+    for( int i=0; i!=vec_traits<B>::dim; ++i )
+        vec_traits<R>::write_element_idx(i,r)=a*vec_traits<B>::read_element_idx(i,b);
+    return r;
+    }
 
-        ////////////////////////////////////////////////
+////////////////////////////////////////////////
 
-        namespace
-        qvm_detail
+namespace
+qvm_detail
+    {
+    template <int D>
+    struct
+    neq_vv_defined
+        {
+        static bool const value=false;
+        };
+    }
+
+template <class A,class B>
+BOOST_QVM_CONSTEXPR 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_CONSTEXPR 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(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_CONSTEXPR 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(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_CONSTEXPR 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_CONSTEXPR 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_CONSTEXPR BOOST_QVM_INLINE_TRIVIAL
+        vref_ &
+        operator=( R const & x )
             {
-            template <int D>
-            struct
-            plus_vv_defined
-                {
-                static bool const value=false;
-                };
+            assign(*this,x);
+            return *this;
             }
 
-        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 )
+        template <class R>
+        BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_TRIVIAL
+        operator R() const
             {
-            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);
+            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_CONSTEXPR 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));
+        }
 
-        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 <int I>
+    static
+    BOOST_QVM_CONSTEXPR 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));
+        }
 
-        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);
-            }
+    static
+    BOOST_QVM_CONSTEXPR 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));
+        }
 
-        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);
-            }
+    static
+    BOOST_QVM_CONSTEXPR 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_CONSTEXPR 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);
+    }
 
-        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;
-            }
+template <class V>
+BOOST_QVM_CONSTEXPR 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