Templates

[chameleon]

I want to create a small library for matrices. But I want to be fast: (no OpenMP/OpenCL)
- After testing 'virtual getValue' is 5 times slower from inline.
- virtual is not compatible with SIMD technology compiler optimizations.

So I decide to make classes with no virtual members.

I want to create these classes:
DenseMatrix, DenseSummetricalMatrix (which serves also DenseUpperTriangularMatrix/DenseLowerTriangularMatrix), DenseRowMatrix (which serves DenseColumnMatrix/DenseDiagonalMatrix).

Because each of these classes must have implemented operations for any of others, code becomes super-bloated:

struct DenseMatrix // ONLY FOR MUL!!!
{
   DenseMatrix operator*(DenseMatrix &m) { ... }
   DenseMatrix operator*(DenseSymmetricalMatrix &m) { ... }
   DenseMatrix operator*(DenseDiagonalMatrix &m) { ... }
   DenseColumnMatrix operator*(DenseColumnMatrix &m) { ... }
   .......
};

I am familiar with basics of templates, but not expert.
Can I implement this with templates? (template specialization is in my mind).
Can you please write the following code with templates and without anything virtual? I write it to contain many difficult cases (for me off-course).

struct DenseMatrixBase
{
   virtual int rows() = 0;
   int columns() { return width; }
   int width;

   virtual double getValue(int x, int y) = 0;
   virtual void setValue(int x, int y, double val) = 0;

   DenseMatrixBase operator*(DenseMatrixBase &m) { ... }
   DenseMatrixBase operator+(DenseMatrixBase &m) { ... }
   ........
};


class DenseMatrix : public DenseMatrixBase
{
   virtual int rows() { return height; }
   int height;

   virtual double getValue(int x, int y) { ... }
   virtual void setValue(int x, int y, double val) { ... }
};


class DenseSymmetricalMatrix : public DenseMatrixBase
{
   virtual int rows() { return columns(); }

   virtual double getValue(int x, int y) { ... }
   virtual void setValue(int x, int y, double val) { ... }
};

[LB]

Have a look at: http://en.wikipedia.org/wiki/Template_metaprogramming#Static_polymorphism