Dynamic data layouts for cache-conscious factorization of DFT

Abstract

Effective utilization of cache memories is a key factor in achieving high performance in computing the Discrete Fourier Transform (DFT). Most optimization techniques for computing the DFT rely on either modifying the computation and data access order or exploiting low level platform specific details, while keeping the data layout in memory static. In this paper, we propose a high level optimization technique, dynamic data layout (DDL). In DDL, data reorganization is performed between computations to effectively utilize the cache. This cache-conscious factorization of the DFT including the data reorganization steps is automatically computed by using efficient techniques in our approach. An analytical model of the cache miss pattern is utilized to predict the performance and explore the search space of factorizations. Our technique results in up to a factor of 4 improvement over standard FFT implementations and up to 33% improvement over other optimization techniques such as copying on SUN UltraSPARC-II, DEC Alpha and Intel Pentium III.

Optimizing graph algorithms for improved cache performance

“…Chatterjee et al discuss layout optimizations for a suite of dense matrix kernels in [7]. Park and Prasanna discuss dynamic data remapping to improve cache performance for the DFT in [31]. One characteristic that all these problems share is a very regular memory accesses that are known at compile time.…”

“…While memory density has been growing rapidly, the speed of memory has been far outpaced by the speed of modern processors [32]. This phenomenon has resulted in severe application level performance degradation on high-end systems and has been well studied for many dense linear algebra problems like matrix multiplication and FFT [31][41] [45]. A number of groups are attempting to improve performance by performing computations in memory [6] [25].…”

SPIRAL: Code Generation for DSP Transforms

“…The idea of platform adaptive loop body interleaving is introduced in [23] as an extension to FFTW and as an example of a general adaptation idea for divide and conquer algorithms [24]. Another variant of computing the DFT studies adaptation through runtime permutations versus re-addressing [25], [26]. Adaptive libraries for the related Walsh-Hadamard transform (WHT), based on similar ideas, have been developed in [27].…”

Cache-friendly implementations of transitive closure

“…Frigo and others discuss the cache performance of cache oblivious algorithms for matrix transpose, FFT, and sorting in [9]. Park and Prasanna discuss dynamic data remapping to improve cache performance for the DFT in [13]. One characteristic that these problems share is a very regular memory accesses that are known at compile time.…”