Hi everybody,
I've been thinking a bit about dynamically zero-padding viennacl::matrix<>
for full hardware use ( best bandwidth for BLAS1, BLAS2, best performance
for BLAS3).
Basically, the big problem arising is that the blocking-parameter is not
dependent on the hardware or the matrix, but rather on the operation, ie :
x = prod(A,y)
C0 = prod(A,B0)
C1 = prod(trans(A), B1)
C2 = prod(B2, A)
all use the same matrix A but require different padding sizes. If we want
to handle all these cases properly, it seems like we will need an
intelligence layer to dynamically update the matrix A.
However, I believe that resizing A to fit the right padding sizes is not an
option, because the corresponding overhead would outweigh the benefits of
padding for the bandwidth-limited kernel.
Another option would be to pad A with the biggest block size required. ie,
if on the current hardware:
BLAS1 Matrix[**] requires padding 4*4
GEMM AA requires LHS padded by 32*128, RHS by 128*16
GEMM TA requires LHS padded by 16*256, RHS by 256*64
... etc..
then each matrix would be zero-padded 256*128, so that it can fit all the
context.
After that, at each operation, internal_size*() would be updated to fit the
correct block sizes. Are we really sure that the initial zeros of the
padding will remain zeros throughout the whole execution process?
[**]I've come to the conclusion that having a specific BLAS1 kernel for
matrix was necessary, in order to allow maximum bandwidth on operations
such as :
A = B + repmat(x, 1, traits::size2(B));
A = B + eye(size1,size2)...
These operations are not implemented yet, though, but the most difficult
part is precisely to have a kernel using vector4 for these operations, for
example.
Do you agree or do you think we should use a 1D kernel for matrix blas1
too? Since both views are equivalent, the autotuner should also be able to
find bandwidth-optimal 2D parameters.
Best regards,
Philippe
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