#ifndef GRID_MATH_ARITH_H
#define GRID_MATH_ARITH_H

namespace Grid {

    
    ///////////////////////////////////////////////////////////////////////////////////////////////////
    /////////////////////////////////////////// ADD         ///////////////////////////////////////////
    ///////////////////////////////////////////////////////////////////////////////////////////////////
    

// ADD is simple for now; cannot mix types and straightforward template
// Scalar +/- Scalar
// Vector +/- Vector
// Matrix +/- Matrix
  template<class vtype,class ltype,class rtype> inline void add(iScalar<vtype> * __restrict__ ret,
								const iScalar<ltype> * __restrict__ lhs,
								const iScalar<rtype> * __restrict__ rhs)
  {
    add(&ret->_internal,&lhs->_internal,&rhs->_internal);
  }
  template<class vtype,class ltype,class rtype,int N> inline void add(iVector<vtype,N> * __restrict__ ret,
								      const iVector<ltype,N> * __restrict__ lhs,
								      const iVector<rtype,N> * __restrict__ rhs)
  {
    for(int c=0;c<N;c++){
      ret->_internal[c]=lhs->_internal[c]+rhs->_internal[c];
    }
    return;
  }
  
  template<class vtype,class ltype,class rtype, int N> inline  void add(iMatrix<vtype,N> * __restrict__ ret,
									const iMatrix<ltype,N> * __restrict__ lhs,
									const iMatrix<rtype,N> * __restrict__ rhs)
  {
    for(int c2=0;c2<N;c2++){
      for(int c1=0;c1<N;c1++){
        add(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal[c1][c2]);
      }}
    return;
  }
  template<class vtype,class ltype,class rtype, int N> inline  void add(iMatrix<vtype,N> * __restrict__ ret,
									const iScalar<ltype>   * __restrict__ lhs,
									const iMatrix<rtype,N> * __restrict__ rhs)
  {
    for(int c2=0;c2<N;c2++){
      for(int c1=0;c1<N;c1++){
        add(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
      }}
    return;
  }
  template<class vtype,class ltype,class rtype, int N> inline  void add(iMatrix<vtype,N> * __restrict__ ret,
									const iMatrix<ltype,N> * __restrict__ lhs,
									const iScalar<rtype>   * __restrict__ rhs)
  {
    for(int c2=0;c2<N;c2++){
      for(int c1=0;c1<N;c1++){
        if ( c1==c2)
	  add(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
        else
	  ret->_internal[c1][c2]=lhs->_internal[c1][c2];
      }}
    return;
  }

  // Need to figure multi-precision.
  template<class Mytype>  Mytype timesI(Mytype &r)
    {
      iScalar<Complex> i;
      i._internal = Complex(0,1);
      return r*i;
    }

  // + operator for scalar, vector, matrix
  template<class ltype,class rtype>
    //inline auto operator + (iScalar<ltype>& lhs,iScalar<rtype>&& rhs) -> iScalar<decltype(lhs._internal + rhs._internal)>
    inline auto operator + (const iScalar<ltype>& lhs,const iScalar<rtype>& rhs) -> iScalar<decltype(lhs._internal + rhs._internal)>
  {
    typedef iScalar<decltype(lhs._internal+rhs._internal)> ret_t;
    ret_t ret;
    add(&ret,&lhs,&rhs);
    return ret;
  }
  template<class ltype,class rtype,int N>
    inline auto operator + (const iVector<ltype,N>& lhs,const iVector<rtype,N>& rhs) ->iVector<decltype(lhs._internal[0]+rhs._internal[0]),N>
    {
      typedef iVector<decltype(lhs._internal[0]+rhs._internal[0]),N> ret_t;
    ret_t ret;
    add(&ret,&lhs,&rhs);
    return ret;
    }
  template<class ltype,class rtype,int N>
    inline auto operator + (const iMatrix<ltype,N>& lhs,const iMatrix<rtype,N>& rhs) ->iMatrix<decltype(lhs._internal[0][0]+rhs._internal[0][0]),N>
    {
      typedef iMatrix<decltype(lhs._internal[0][0]+rhs._internal[0][0]),N> ret_t;
      ret_t ret;
      add(&ret,&lhs,&rhs);
      return ret;
    }
  template<class ltype,class rtype,int N>
inline auto operator + (const iScalar<ltype>& lhs,const iMatrix<rtype,N>& rhs)->iMatrix<decltype(lhs._internal+rhs._internal[0][0]),N>
    {
      typedef iMatrix<decltype(lhs._internal+rhs._internal[0][0]),N> ret_t;
      ret_t ret;
      add(&ret,&lhs,&rhs);
      return ret;
    }

  template<class ltype,class rtype,int N>
    inline auto operator + (const iMatrix<ltype,N>& lhs,const iScalar<rtype>& rhs)->iMatrix<decltype(lhs._internal[0][0]+rhs._internal),N>
    {
      typedef iMatrix<decltype(lhs._internal[0][0]+rhs._internal),N> ret_t;
      ret_t ret;
      add(&ret,&lhs,&rhs);
      return ret;
    }


    ///////////////////////////////////////////////////////////////////////////////////////////////////
    /////////////////////////////////////////// SUB         ///////////////////////////////////////////
    ///////////////////////////////////////////////////////////////////////////////////////////////////
    

// SUB is simple for now; cannot mix types and straightforward template
// Scalar +/- Scalar
// Vector +/- Vector
// Matrix +/- Matrix
// Matrix /- scalar
template<class vtype,class ltype,class rtype> inline void sub(iScalar<vtype> * __restrict__ ret,
                                                              const iScalar<ltype> * __restrict__ lhs,
                                                              const iScalar<rtype> * __restrict__ rhs)
{
    sub(&ret->_internal,&lhs->_internal,&rhs->_internal);
}

template<class vtype,class ltype,class rtype,int N> inline void sub(iVector<vtype,N> * __restrict__ ret,
                                                                    const iVector<ltype,N> * __restrict__ lhs,
                                                                    const iVector<rtype,N> * __restrict__ rhs)
{
    for(int c=0;c<N;c++){
        ret->_internal[c]=lhs->_internal[c]-rhs->_internal[c];
    }
    return;
}
template<class vtype,class ltype,class rtype, int N> inline void sub(iMatrix<vtype,N> * __restrict__ ret,
                                                                     const iMatrix<ltype,N> * __restrict__ lhs,
                                                                     const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        sub(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal[c1][c2]);
    }}
    return;
}
template<class vtype,class ltype,class rtype, int N> inline void sub(iMatrix<vtype,N> * __restrict__ ret,
                                                                     const iScalar<ltype> * __restrict__ lhs,
                                                                     const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        if ( c1!=c2) {
            sub(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
        } else {
            // Fails -- need unary minus. Catalogue other unops?
            ret->_internal[c1][c2]=zero;
            ret->_internal[c1][c2]=ret->_internal[c1][c2]-rhs->_internal[c1][c2];

        }
    }}
    return;
}
template<class vtype,class ltype,class rtype, int N> inline void sub(iMatrix<vtype,N> * __restrict__ ret,
                                                                     const iMatrix<ltype,N> * __restrict__ lhs,
                                                                     const iScalar<rtype> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        if ( c1!=c2)
            sub(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
        else
            ret->_internal[c1][c2]=lhs->_internal[c1][c2];
    }}
    return;
}

template<class v> void vprefetch(const iScalar<v> &vv)
{
  vprefetch(vv._internal);
}
template<class v,int N> void vprefetch(const iVector<v,N> &vv)
{
  for(int i=0;i<N;i++){
    vprefetch(vv._internal[i]);
  }
}
template<class v,int N> void vprefetch(const iMatrix<v,N> &vv)
{
  for(int i=0;i<N;i++){
  for(int j=0;j<N;j++){
    vprefetch(vv._internal[i][j]);
  }}
}

    // - operator for scalar, vector, matrix
template<class ltype,class rtype> inline auto
operator - (const iScalar<ltype>& lhs, const iScalar<rtype>& rhs) -> iScalar<decltype(lhs._internal - rhs._internal)>
{
    typedef iScalar<decltype(lhs._internal-rhs._internal)> ret_t;
    ret_t ret;
    sub(&ret,&lhs,&rhs);
    return ret;
}
template<class ltype,class rtype,int N>
inline auto operator - (const iVector<ltype,N>& lhs,const iVector<rtype,N>& rhs) ->iVector<decltype(lhs._internal[0]-rhs._internal[0]),N>
{
    typedef iVector<decltype(lhs._internal[0]-rhs._internal[0]),N> ret_t;
    ret_t ret;
    sub(&ret,&lhs,&rhs);
    return ret;
}
template<class ltype,class rtype,int N>
inline auto operator - (const iMatrix<ltype,N>& lhs,const iMatrix<rtype,N>& rhs) ->iMatrix<decltype(lhs._internal[0][0]-rhs._internal[0][0]),N>
{
    typedef iMatrix<decltype(lhs._internal[0][0]-rhs._internal[0][0]),N> ret_t;
    ret_t ret;
    sub(&ret,&lhs,&rhs);
    return ret;
}
template<class ltype,class rtype,int N>
inline auto operator - (const iScalar<ltype>& lhs,const iMatrix<rtype,N>& rhs)->iMatrix<decltype(lhs._internal-rhs._internal[0][0]),N>
{
    typedef iMatrix<decltype(lhs._internal-rhs._internal[0][0]),N> ret_t;
    ret_t ret;
    sub(&ret,&lhs,&rhs);
    return ret;
}
template<class ltype,class rtype,int N>
inline auto operator - (const iMatrix<ltype,N>& lhs,const iScalar<rtype>& rhs)->iMatrix<decltype(lhs._internal[0][0]-rhs._internal),N>
{
    typedef iMatrix<decltype(lhs._internal[0][0]-rhs._internal),N> ret_t;
    ret_t ret;
    sub(&ret,&lhs,&rhs);
    return ret;
}

///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// MAC         ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////

    ///////////////////////////
    // Legal multiplication table
    ///////////////////////////
    // scal x scal = scal
    // mat x  mat  = mat
    // mat  x scal = mat
    // scal x mat  = mat
    // mat  x vec  = vec
    // vec  x scal = vec
    // scal x vec  = vec
    ///////////////////////////
template<class rtype,class vtype,class mtype>
inline  void mac(iScalar<rtype> * __restrict__ ret,const iScalar<vtype> * __restrict__ lhs,const iScalar<mtype> * __restrict__ rhs)
{
    mac(&ret->_internal,&lhs->_internal,&rhs->_internal);
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
    for(int c3=0;c3<N;c3++){
        mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
    }}}
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs){
    for(int c1=0;c1<N;c1++){
    for(int c2=0;c2<N;c2++){
        mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
    }}
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iScalar<ltype> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c1=0;c1<N;c1++){
    for(int c2=0;c2<N;c2++){
        mac(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
    }}
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iVector<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iVector<rtype,N> * __restrict__ rhs)
{
    for(int c1=0;c1<N;c1++){
    for(int c2=0;c2<N;c2++){
        mac(&ret->_internal[c1],&lhs->_internal[c1][c2],&rhs->_internal[c2]);
    }}
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iVector<rrtype,N> * __restrict__ ret,const iScalar<ltype> * __restrict__ lhs,const iVector<rtype,N> * __restrict__ rhs)
{
    for(int c1=0;c1<N;c1++){
        mac(&ret->_internal[c1],&lhs->_internal,&rhs->_internal[c1]);
    }
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mac(iVector<rrtype,N> * __restrict__ ret,const iVector<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs)
{
    for(int c1=0;c1<N;c1++){
        mac(&ret->_internal[c1],&lhs->_internal[c1],&rhs->_internal);
    }
    return;
}

    ///////////////////////////////////////////////////////////////////////////////////////////////////
    /////////////////////////////////////////// MUL         ///////////////////////////////////////////
    ///////////////////////////////////////////////////////////////////////////////////////////////////

    
template<class rtype,class vtype,class mtype>
inline void mult(iScalar<rtype> * __restrict__ ret,const iScalar<mtype> * __restrict__ lhs,const iScalar<vtype> * __restrict__ rhs){
    mult(&ret->_internal,&lhs->_internal,&rhs->_internal);
}

template<class rrtype,class ltype,class rtype,int N>
inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        mult(&ret->_internal[c1][c2],&lhs->_internal[c1][0],&rhs->_internal[0][c2]);
        for(int c3=1;c3<N;c3++){
            mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
        }
    }}
    return;
}
template<class rrtype,class ltype,class rtype,int N>
inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        mult(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
    }}
    return;
}

template<class rrtype,class ltype,class rtype, int N>
inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iScalar<ltype>   * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
    for(int c2=0;c2<N;c2++){
    for(int c1=0;c1<N;c1++){
        mult(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
    }}
    return;
}
// Matrix left multiplies vector
template<class rtype,class vtype,class mtype,int N>
inline void mult(iVector<rtype,N> * __restrict__ ret,const iMatrix<mtype,N> * __restrict__ lhs,const iVector<vtype,N> * __restrict__ rhs)
{
    for(int c1=0;c1<N;c1++){
        mult(&ret->_internal[c1],&lhs->_internal[c1][0],&rhs->_internal[0]);
        for(int c2=1;c2<N;c2++){
            mac(&ret->_internal[c1],&lhs->_internal[c1][c2],&rhs->_internal[c2]);
        }
    }
    return;
}
template<class rtype,class vtype,class mtype,int N>
inline void mult(iVector<rtype,N> * __restrict__ ret,
                 const iScalar<mtype>   * __restrict__ lhs,
                 const iVector<vtype,N> * __restrict__ rhs){
    for(int c1=0;c1<N;c1++){
        mult(&ret->_internal[c1],&lhs->_internal,&rhs->_internal[c1]);
    }
}
template<class rtype,class vtype,class mtype,int N>
inline void mult(iVector<rtype,N> * __restrict__ ret,
                 const iVector<vtype,N> * __restrict__ rhs,
                 const iScalar<mtype> * __restrict__ lhs){
    mult(ret,lhs,rhs);
}
    


template<class rtype,class vtype,class mtype,int N> inline
iVector<rtype,N> operator * (const iMatrix<mtype,N>& lhs,const iVector<vtype,N>& rhs)
{
    iVector<rtype,N> ret;
    mult(&ret,&lhs,&rhs);
    return ret;
}

template<class rtype,class vtype,class mtype,int N> inline
iVector<rtype,N> operator * (const iScalar<mtype>& lhs,const iVector<vtype,N>& rhs)
{
    iVector<rtype,N> ret;
    mult(&ret,&lhs,&rhs);
    return ret;
}

template<class rtype,class vtype,class mtype,int N> inline
iVector<rtype,N> operator * (const iVector<mtype,N>& lhs,const iScalar<vtype>& rhs)
{
    iVector<rtype,N> ret;
    mult(&ret,&lhs,&rhs);
    return ret;
}
    
    //////////////////////////////////////////////////////////////////
    // Glue operators to mult routines. Must resolve return type cleverly from typeof(internal)
    // since nesting matrix<scalar> x matrix<matrix>-> matrix<matrix>
    // while         matrix<scalar> x matrix<scalar>-> matrix<scalar>
    // so return type depends on argument types in nasty way.
    //////////////////////////////////////////////////////////////////
    // scal x scal = scal
    // mat x  mat  = mat
    // mat  x scal = mat
    // scal x mat  = mat
    // mat  x vec  = vec
    // vec  x scal = vec
    // scal x vec  = vec
    //
    // We can special case scalar_type ??
template<class l,class r>
inline auto operator * (const iScalar<l>& lhs,const iScalar<r>& rhs) -> iScalar<decltype(lhs._internal * rhs._internal)>
{
    typedef iScalar<decltype(lhs._internal*rhs._internal)> ret_t;
    ret_t ret;
    mult(&ret,&lhs,&rhs);
    return ret;
}
template<class l,class r,int N> inline
auto operator * (const iMatrix<l,N>& lhs,const iMatrix<r,N>& rhs) -> iMatrix<decltype(lhs._internal[0][0]*rhs._internal[0][0]),N>
{
    typedef decltype(lhs._internal[0][0]*rhs._internal[0][0]) ret_t;
    iMatrix<ret_t,N> ret;
    mult(&ret,&lhs,&rhs);
    return ret;
}
template<class l,class r, int N> inline
auto operator * (const iMatrix<r,N>& lhs,const iScalar<l>& rhs) -> iMatrix<decltype(lhs._internal[0][0]*rhs._internal),N>
{
    typedef decltype(lhs._internal[0][0]*rhs._internal) ret_t;
        
    iMatrix<ret_t,N> ret;
    for(int c1=0;c1<N;c1++){
    for(int c2=0;c2<N;c2++){
        mult(&ret._internal[c1][c2],&lhs._internal[c1][c2],&rhs._internal);
    }}
    return ret;
}
template<class l,class r,int N> inline
auto operator * (const iScalar<l>& lhs,const iMatrix<r,N>& rhs) -> iMatrix<decltype(lhs._internal*rhs._internal[0][0]),N>
{
    typedef decltype(lhs._internal*rhs._internal[0][0]) ret_t;
    iMatrix<ret_t,N> ret;
    for(int c1=0;c1<N;c1++){
    for(int c2=0;c2<N;c2++){
        mult(&ret._internal[c1][c2],&lhs._internal,&rhs._internal[c1][c2]);
    }}
    return ret;
}
template<class l,class r,int N> inline
auto operator * (const iMatrix<l,N>& lhs,const iVector<r,N>& rhs) -> iVector<decltype(lhs._internal[0][0]*rhs._internal[0]),N>
{
    typedef decltype(lhs._internal[0][0]*rhs._internal[0]) ret_t;
    iVector<ret_t,N> ret;
    for(int c1=0;c1<N;c1++){
        mult(&ret._internal[c1],&lhs._internal[c1][0],&rhs._internal[0]);
        for(int c2=1;c2<N;c2++){
            mac(&ret._internal[c1],&lhs._internal[c1][c2],&rhs._internal[c2]);
        }
    }
    return ret;
}
template<class l,class r,int N> inline
auto operator * (const iScalar<l>& lhs,const iVector<r,N>& rhs) -> iVector<decltype(lhs._internal*rhs._internal[0]),N>
{
    typedef decltype(lhs._internal*rhs._internal[0]) ret_t;
    iVector<ret_t,N> ret;
    for(int c1=0;c1<N;c1++){
        mult(&ret._internal[c1],&lhs._internal,&rhs._internal[c1]);
    }
    return ret;
}
template<class l,class r,int N> inline
auto operator * (const iVector<l,N>& lhs,const iScalar<r>& rhs) -> iVector<decltype(lhs._internal[0]*rhs._internal),N>
{
    typedef decltype(lhs._internal[0]*rhs._internal) ret_t;
    iVector<ret_t,N> ret;
    for(int c1=0;c1<N;c1++){
        mult(&ret._internal[c1],&lhs._internal[c1],&rhs._internal);
    }
    return ret;
}


//////////////////////////////////////////////////////////////////////////////////////////
// Must support native C++ types Integer, Complex, Real
//////////////////////////////////////////////////////////////////////////////////////////

// multiplication by fundamental scalar type
template<class l,int N> inline iScalar<l> operator * (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iScalar<l>::tensor_reduced srhs(rhs);
  return lhs*srhs;
}
template<class l,int N> inline iScalar<l> operator * (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iVector<l,N>::tensor_reduced srhs(rhs);
  return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (const typename iScalar<l>::scalar_type lhs,const iVector<l,N>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type &rhs) 
{
  typename iMatrix<l,N>::tensor_reduced srhs(rhs);
  return lhs*srhs;
}
template<class l,int N> inline iMatrix<l,N> operator * (const typename iScalar<l>::scalar_type & lhs,const iMatrix<l,N>& rhs) {  return rhs*lhs; }

////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator * (const iScalar<l>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (double lhs,const iScalar<l>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (double lhs,const iVector<l,N>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iMatrix<l,N> operator * (double lhs,const iMatrix<l,N>& rhs) {  return rhs*lhs; }

////////////////////////////////////////////////////////////////////
// Complex support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator * (const iScalar<l>& lhs,ComplexD rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (ComplexD lhs,const iScalar<l>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,ComplexD rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (ComplexD lhs,const iVector<l,N>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,ComplexD rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iMatrix<l,N> operator * (ComplexD lhs,const iMatrix<l,N>& rhs) {  return rhs*lhs; }

////////////////////////////////////////////////////////////////////
// Integer support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator * (const iScalar<l>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (Integer lhs,const iScalar<l>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (Integer lhs,const iVector<l,N>& rhs) {  return rhs*lhs; }

template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs*srhs;
}
template<class l,int N> inline iMatrix<l,N> operator * (Integer lhs,const iMatrix<l,N>& rhs) {  return rhs*lhs; }



///////////////////////////////////////////////////////////////////////////////////////////////
// addition by fundamental scalar type applies to matrix(down diag) and scalar
///////////////////////////////////////////////////////////////////////////////////////////////
template<class l,int N> inline iScalar<l> operator + (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iScalar<l>::tensor_reduced srhs(rhs);
  return lhs+srhs;
}
template<class l,int N> inline iScalar<l> operator + (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) {  return rhs+lhs; }

template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iMatrix<l,N>::tensor_reduced srhs(rhs);
  return lhs+srhs;
}
template<class l,int N> inline iMatrix<l,N> operator + (const typename iScalar<l>::scalar_type lhs,const iMatrix<l,N>& rhs) {  return rhs+lhs; }

////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator + (const iScalar<l>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs+srhs;
}
template<class l> inline iScalar<l> operator + (double lhs,const iScalar<l>& rhs) {  return rhs+lhs; }

template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs+srhs;
}
template<class l,int N> inline iMatrix<l,N> operator + (double lhs,const iMatrix<l,N>& rhs) {  return rhs+lhs; }


// Integer support cast to scalar type through constructor


template<class l> inline iScalar<l> operator + (const iScalar<l>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs+srhs;
}

template<class l> inline iScalar<l> operator + (Integer lhs,const iScalar<l>& rhs) {  return rhs+lhs; }

template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs+srhs;
}
template<class l,int N> inline iMatrix<l,N> operator + (Integer lhs,const iMatrix<l,N>& rhs) {  return rhs+lhs; }


///////////////////////////////////////////////////////////////////////////////////////////////
// subtraction of fundamental scalar type applies to matrix(down diag) and scalar
///////////////////////////////////////////////////////////////////////////////////////////////
template<class l,int N> inline iScalar<l> operator - (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iScalar<l>::tensor_reduced srhs(rhs);
  return lhs-srhs;
}
template<class l,int N> inline iScalar<l> operator - (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) 
{
  typename iScalar<l>::tensor_reduced slhs(lhs);
  return slhs-rhs;
}

template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs) 
{
  typename iScalar<l>::tensor_reduced srhs(rhs);
  return lhs-srhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const typename iScalar<l>::scalar_type lhs,const iMatrix<l,N>& rhs) 
{
  typename iScalar<l>::tensor_reduced slhs(lhs);
  return slhs-rhs;
}

////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator - (const iScalar<l>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs-srhs;
}
template<class l> inline iScalar<l> operator - (double lhs,const iScalar<l>& rhs) 
{
  typename iScalar<l>::scalar_type t(lhs);
  typename iScalar<l>::tensor_reduced slhs(t);
  return slhs-rhs;
}

template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,double rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs-srhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (double lhs,const iMatrix<l,N>& rhs) 
{
  typename iScalar<l>::scalar_type t(lhs);
  typename iScalar<l>::tensor_reduced slhs(t);
  return slhs-rhs;
}

////////////////////////////////////////////////////////////////////
// Integer support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator - (const iScalar<l>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs-srhs;
}
template<class l> inline iScalar<l> operator - (Integer lhs,const iScalar<l>& rhs) 
{
  typename iScalar<l>::scalar_type t(lhs);
  typename iScalar<l>::tensor_reduced slhs(t);
  return slhs-rhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,Integer rhs) 
{
  typename iScalar<l>::scalar_type t(rhs);
  typename iScalar<l>::tensor_reduced srhs(t);
  return lhs-srhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (Integer lhs,const iMatrix<l,N>& rhs) 
{
  typename iScalar<l>::scalar_type t(lhs);
  typename iScalar<l>::tensor_reduced slhs(t);
  return slhs-rhs;
}

}
#endif