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Traditional workload analysis uses discrete times measured by data accesses. An example is the classic independent reference model (IRM). Effective solutions have been developed to model workloads with stochastic access patterns, but they incur a high cost for Zipfian workloads, which may contain millions of items each accessed with a different frequency. This paper first presents a continuous-time model of locality for workloads with stochastic access patterns. It shows that two previous techniques by Dan and Towsley and by Denning and Schwartz can be interpreted as a single model using different discrete times. Using continuous time, it derives a closed-form solution for an item and a general solution that is a differentiable function. In addition, the paper presents an approximation technique by grouping items into partitions. When evaluated using Zipfian workloads, it shows that a workload with millions of items can be approximated using a small number of partitions, and the continuous-time model has greater accuracy and is faster to compute numerically. For the largest data size verifiable using trace generation and simulation, the new techniques reduce the time of locality analysis by 6 orders of magnitude. 

Cache replacement policies typically use some form of statistics on past access behavior. As a common limitation, how- ever, the extent of the history being recorded is limited to either just the data in cache or, more recently, a larger but still finite-length window of accesses, because the cost of keeping a long history can easily outweigh its benefit. This paper presents a statistical method to keep track of instruction pointer-based access reuse intervals of arbitrary length and uses this information to identify the Least Ex- pected Use (LEU) blocks for replacement. LEU uses dynamic sampling supported by novel hardware that maintains a state to record arbitrarily long reuse intervals. LEU is evaluated using the Cache Replacement Championship simulator, tested on PolyBench and SPEC, and compared with five policies including a recent technique that approximates optimal caching using a fixed-length history. By maintaining statistics for an arbitrary history, LEU outperforms previous techniques for a broad range of scientific kernels, whose data reuses are longer than those in traces traditionally used in computer architecture studies. 

Cache management is important in exploiting locality and reducing data movement. This article studies a new type of programmable cache called the lease cache. By assigning leases, software exerts the primary control on when and how long data stays in the cache. Previous work has shown an optimal solution for an ideal lease cache. This article develops and evaluates a set of practical solutions for a physical lease cache emulated in FPGA with the full suite of PolyBench benchmarks. Compared to automatic caching, lease programming can further reduce data movement by 10% to over 60% when the data size is 16 times to 3,000 times the cache size, and the techniques in this article realize over 80% of this potential. Moreover, lease programming can reduce data movement by another 0.8% to 20% after polyhedral locality optimization.