Evaluation of the Performance of Polynomial Set Index Functions

Randomising set index functions, randomisation functions for short, can significantly reduce conflict misses in data caches by placing cache blocks in a conflict-free manner. XOR-based functions are a broad class of functions that generally exhibit few conflict misses. Topham and González claimed that the sub-class of functions based on division of polynomials over contains those functions that achieve the best conflict-free mapping. Furthermore, they claim that an even smaller class of functions, namely those based on irreducible polynomials, perform better still. This paper investigates these claims in a novel way, by evaluating many randomisation functions from the different classes. The minimum, maximum and average miss rates are used to compare the different classes of randomisation functions. To avoid computing miss rates for all of these functions, we estimate the miss rates using a semianalytical technique. The evaluation shows that polynomial randomisation functions are not the best possible choice, although they perform relatively well. Irreducible polynomials offer no measurable benefits over reducible polynomials, while they may be a lot more complex to implement.