Formal Modeling and Verification of Controllers for a Family of DRAM Caches

Abstract

Die-stacking technology enables the use of a high density DRAM as a cache. Major processor vendors have recently started using these stacked DRAM modules as the last level cache of their products. These stacked DRAM modules provide high bandwidth with relatively low latency compared to the off-package DRAM modules. Recent studies on DRAM caches propose several variants to optimize performance and power of the systems. However, none of the existing works discuss its design and verification aspect. DRAM cache controller (DCC) design is significantly complex in comparison to a conventional DRAM-based main memory controller. This is because it involves controlling both the timing aspect of DRAM system as well as the functional aspect of cache. Therefore, without rigorous modeling and verification of such designs, it would be difficult to ensure correctness. In the current research, we focus on the design and verification issues of DCC. We select a common variant of DRAM cache and build a formal model of its controller in terms of interacting state machines; we term the common variant as the baseline and its model as the base model. We then verify safety, liveness, and timing properties of this variant using model checking. Next, we demonstrate how the formal models and the associated properties of other variants of DCCs can be derived from the base model in a systematic way. Analyzing the individual DRAM cache variations, we observe that most of the variants exhibit product-line characteristics.