Constructing Optimal XOR-Functions to Minimize Cache Conflict Misses

Stringent power and performance constraints, coupled with detailed knowledge of the target applications of a processor, allows for application-specific processor optimizations. It has been shown that application-specific reconfigurable hash functions eliminate a large number of cache conflict misses. These hash functions minimize conflicts by modifying the mapping of cache blocks to cache sets. This paper describes an algorithm to compute optimal XOR-functions, a particular type of hash functions based on XORs. Using this algorithm, we set an upper bound on the conflict reduction achievable with XORfunctions. We show that XOR-functions perform better than other reconfigurable hash functions studied in the literature such as bit-selecting functions. The XOR-functions are optimal for one particular execution of a program. However, we show that optimal XOR-functions are less sensitive to the characteristics of the execution than optimal bit-selecting hash functions. This again underlines that XOR-functions are the best known hash functions to implement reconfigurable hash functions.