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Using alternative cache indexing/hashing functions is a popular technique to reduce conflict misses by achieving a more uniform cache access distribution across the sets in the cache. Although various alternative hashing functions have been demonstrated to eliminate the worst-case conflict behavior, no study has really analyzed the pathological behavior of such hashing functions that often results in performance slowdown. In this paper, we present an in-depth analysis of the pathological behavior of cache hashing functions. Based on the analysis, we propose two new hashing functions, prime modulo and odd-multiplier displacement, that are resistant to pathological behavior and yet are able to eliminate the worst-case conflict behavior in the L2 cache. We show that these two schemes can be implemented in fast hardware using a set of narrow addition operations, with negligible fragmentation in the L2 cache. We evaluate the schemes on 23 memory intensive applications. For applications that have nonuniform cache accesses, both prime modulo and odd-multiplier displacement hashing achieve an average speedup of 1.27 compared to traditional hashing, without slowing down any of the 23 benchmarks. We also evaluate using odd-multiplier displacement function with multiple multipliers in conjunction with a skewed associative L2 cache. The skewed associative cache achieves a better average speedup at the cost of some pathological behavior that slows down four applications by up to 7 percent.
Cache hashing, cache indexing, prime modulo, odd-multiplier displacement, conflict misses.

J. Lee, M. Kharbutli and Y. Solihin, "Eliminating Conflict Misses Using Prime Number-Based Cache Indexing," in IEEE Transactions on Computers, vol. 54, no. , pp. 573-586, 2005.
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