Lecture Notes in Computer Science 4917

Drug Design Issues on the Cell BE 181
Fig. 2. Eklundh matrix transposition idea for a 4 × 4matrix
one SPE, no synchronization is needed in order to DMA transfer (swap) the
submatrices to main memory after being transposed in the SPE. Indeed, double
buffering can be implemented overlapping the DMA transfers (put or get) of one
submatrix and the transposition of the other submatrix. In this case, blocksize
B can be up to 64 since one SPE has to keep two B × B submatrices in its LS.
In the case of using two SPEs, those have to be synchronized to DMA transfer
(swap) the submatrices transposed to main memory. The synchronization is done
by using the atomic read intrinsic of the IBM SDK. In this case, blocksize B
can be up to 128 since each SPE has to keep one B × B submatrix in the LS.
In any case, for 128 × 128 planes, one SPE can locally transpose a complete
plane since a plane fits in the LS of the SPE. Moreover, in this case, Steps 1, 2,
and 3, and Steps 4 and 5 of the 3D FFT can be performed together in the same
SPE before transfering the data back to main memory.
Sumarizing, our 3D FFT may follow different execution paths depending on
the plane transposition strategy (one or two SPEs swapping submatrices) and
the B blocksize algorithm parameter:
1. Case B×B submatrix is not the complete plane and/or does not fit in the LS
of a SPE. Plane transposition is done by blocking. We evaluate two different
strategies:
(a) One SPE transposes two B ×B submatrices in its LS and DMA transfers
(swaps) them to main memory. B blocksize can be up to 64.
(b) Two SPEs transpose two B ×B submatrices, and synchronize each other
to DMA transfer them to main memory. B blocksize can be up to 128.
2. Case 128×128 planes and B blocksize is 128. One SPE can locally transpose
a complete plane. Steps 1, 2 and 3 of the 3D FFT are done together in a
SPE. Steps 4 and 5 are also done together.
Finally, Steps 6 and 7 of the 3D FFT are optional in the context of FTDock
because the complex multiplication ((F ∗ A )(FB)) can be done using the element
orientation obtained on the matrix transposition of Step 4 of the 3D FFT. Therefore,
we do not have to perform Steps 6 and 7 for each 3D FFT in our FTDock