Classification and Analysis of Predictable Memory Patterns

The verification complexity of real-time requirements in embedded systems grows exponentially with the number of applications, as resource sharing prevents independent verification using simulation-based approaches. Formal verification is a promising alternative, although its applicability is limited to systems with predictable hardware and software. SDRAM memories are common examples of essential hardware components with unpredictable timing behavior, typically preventing use of formal approaches. A predictable SDRAM controller has been proposed that provides guarantees on bandwidth and latency by dynamically scheduling memory patterns, which are statically computed sequences of SDRAM commands. However, the proposed patterns become increasingly inefficient as memories become faster, making them unsuitable for DDR3 SDRAM. This paper extends the memory pattern concept in two ways. Firstly, we introduce a burst count parameter that enables patterns to have multiple SDRAM bursts per bank, which is required for DDR3 memories to be used efficiently. Secondly, we present a classification of memory pattern sets into four categories based on the combination of patterns that cause worst-case bandwidth and latency to be provided. Bounds on bandwidth and latency are derived that apply to all pattern types and burst counts, as opposed to the single case covered by earlier work. Experimental results show that these extensions are required to support the most efficient pattern sets for many use-cases. We also demonstrate that the burst count parameter increases efficiency in presence of large requests and enables a wider range of real-time requirements to be satisfied.