Re: Matrix Multiplication

[Gautier <Gautier.deMontmollin@maths.unine.ch>]

> Intrigued about the 'renames' bit.  I thought the renames was just a
> compiler overhead and had no run-time effect at all.

IIRC the renames takes `aliases' the its target its present state.
E.g.
  declare
    x: thing renames complicated(i,j).k;
  begin
    -- i,j could change, doesn't affect x

The ARM gurus will comment better...

Anyway it is a way to obtain a direct pointer to `complicated(i,j).k',
not just a syntaxic alias. On my tests with sparse matrices,
`renames' in the matrix-vector multiplication simply *halves* the computation
time of the whole BiCGStab algorithm (compiled on Compaq (DEC) Ada)!

The `renames' are

  procedure Mult( A: in out CRS_matrix; u: vector; w: in out vector ) is
   deb, fin, jaj: index;
   ui, wi, wi_sum: real;
   rows: constant index:= A.rows;
   val: vector renames A.val;
   col_ind: index_array renames A.col_ind;
   row_ptr: index_array renames A.row_ptr;

   begin

      if  not A.symmetric  then
         -- *** la matrice est memorisee sous forme non symetrique

         for i in 1..rows loop
            deb := row_ptr(i);
            fin := row_ptr(i + 1) - 1;
            wi_sum := 0.0;
            for j in deb .. fin loop
               wi_sum := wi_sum + val(j) * u(col_ind(j));
            end loop;
            w(i) := wi_sum;
         end loop;
...

GNAT optimizer (-O2) is smarter for memorizing these addresses,
but sometimes one has to help it too with a small `renames'
(testings for textured 3D)...
 
-- 
Gautier

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