Is Cache Oblivious DGEMM a Viable Alternative?

We present an in-depth study of various implementations of DGEMM, using both the recursive and iterative programming styles. Recursive algorithms for DGEMM are usually cache-oblivious and they automatically block DGEMM’s operands A, B, C for the memory hierarchy. Iterative algorithms for DGEMM explicitly block A, B, C for the L1 cache, higher caches and memory. Our study shows that recursive DGEMM implementations cannot achieve the high performance of blocked iterative algorithms. 1 A study of Recursive and Interative Algorithms for DGEMM The performance of DGEMM on modern computers is limited by the performance of the memory system in two ways. First, the latency of memory accesses can be many hundreds of cycles, so the processor may be stalled most of the time, waiting for reads to complete. Second, the bandwidth from memory is usually far less than the rate at which the processor can consume data. This contribution examines in depth these limitations for both recursive and iterative programming styles. We describe the results of a study of the performance of highly-optimized cache-oblivious and cache-conscious programs for DGEMM on four modern architectures: IBM Power 5, Sun UltraSPARC IIIi, Intel Itanium 2, and Intel Pentium 4 Xeon. These programs are generated by a domain-specific compiler we are building called BRILA (Block Recursive Implementation of Linear Algebra). The compiler takes recursive descriptions of linear algebra problems, and produces optimized iterative or recursive programs as output. Our main finding is that there is a significant gap between the performance of cache-oblivious and cache-conscious algorithms in this domain. We also provide insights into why this gap exists. We are not aware of any similar study in the literature. First we motivate approximate blocking by giving a quantitative analysis of how blocking can reduce the required bandwidth from memory. This analysis provides a novel way of looking at the memory hierarchy behavior of cacheoblivious programs.