Adaptation of Double-Precision Matrix Multiplication to the Cell Broadband Engine Architecture

This paper presents an approach to adaptation of the double-precision matrix multiplication to the architecture of Cell processors. The algorithm used for the adaptation on a single SPE is based on

C

 = 

C

 + 

A

*

B

operation performed for matrices of size 64 ×64; these matrices are further divided into smaller submatrices which correspond to micro-kernel operations. Our approach is based on a performance model which is constructed as a function of submatrix size. The model accounts for such factors as size of local storage, number of registers, properties of double-precision operations, balance between pipelines, etc. This approach allows us to take into consideration properties of the first generation of Cell processors and its successor - PowerXCell 8i.

This adaptation is followed by an optimization phase which includes loop transformations, kernel implementation with SIMD instructions, and other transformations necessary to achieve balance between even and odd pipelines. Finally we present hand-tunings performed with the IBM Assembly Visualizer tool. The proposed adaptation and optimizations allow us to achieve about 96% of the peak performance.