Design of new XOR-based hash functions for cache memories

A hash function H is a computationally efficient function that maps bitstrings of arbitrary length to bitstrings of fixed length, called hash values. Hash functions have a variety of general computational uses. They are used in processors to augment the bandwidth of an interleaved multibank memory or to enhance the utilization of a prediction table or a cache. In this paper, we design new XOR-based hash functions, which compute each set index bit as XOR of a subset of the bits in the address by using the concepts of rank and null space. These are conflict-free hash functions which are of different types according to whether m is even or odd. To apply the constructed hash functions to the skewed-associative cache, we show that the degree of interbank dispersion between two hash functions is maximal.

[1]  Koen De Bosschere,et al.  Evaluation of the performance of polynomial set index functions , 2002, ISCA 2002.

[2]  K. Kavi.  Cache Memories Cache Memories in Uniprocessors. Reading versus Writing. Improving Performance , 2022 .

[3]  Koen De Bosschere,et al.  XOR-based hash functions , 2005, IEEE Transactions on Computers.

[4]  François Bodin,et al.  Skewed Associativity Improves Program Performance and Enhances Predictability , 1997, IEEE Trans. Computers.

[5]  André Seznec,et al.  A case for two-way skewed-associative caches , 1993, ISCA '93.

[6]  André Seznec.  A New Case for Skewed-Associativity , 1997 .

[7]  Un-Sook Choi,et al.  Analysis of complemented CA derived from linear hybrid group CA , 2007, Comput. Math. Appl..

[8]  Un-Sook Choi,et al.  Computing Phase Shifts of Maximum-Length 90/150 Cellular Automata Sequences , 2004, ACRI.

[9]  Jaejin Lee,et al.  Using prime numbers for cache indexing to eliminate conflict misses , 2004, 10th International Symposium on High Performance Computer Architecture (HPCA'04).

[10]  William Jalby,et al.  XOR-Schemes: A Flexible Data Organization in Parallel Memories , 1985, ICPP.

[11]  B. Ramakrishna Rau,et al.  Pseudo-randomly interleaved memory , 1991, ISCA '91.

[12]  W. Greub.  Linear Algebra , 1981 .

[13]  Un-Sook Choi,et al.  Analysis of complemented CA derived from a linear TPMACA , 2003 .

[14]  Un-Sook Choi,et al.  Behavior of complemented CA whose complement vector is acyclic in a linear TPMACA , 2002 .

[15]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[16]  Koen De Bosschere,et al.  Efficient profile-based evaluation of randomising set index functions for cache memories , 2001, 2001 IEEE International Symposium on Performance Analysis of Systems and Software. ISPASS..