Section: New Results

On Characterizing the Data Access Complexity (IO) of Programs and Using it for Architectural Design Exploration

Participants : Venmugil Elango [OSU] , Naser Sedaghati [OSU] , Fabrice Rastello, Louis-Noël Pouchet [UCLA] , J. Ramanujam [LSU] , Radu Teodorescu [OSU] , P. Sadayappan [OSU] .

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a fundamental characterization of data access complexity will be increasingly important. The problem of developing lower bounds for data access complexity has been modeled using the formalism of Hong & Kung's red/blue pebble game for computational directed acyclic graphs (CDAGs). However, previously developed approaches to lower bounds analysis for the red/blue pebble game are very limited in effectiveness when applied to CDAGs of real programs, with computations comprised of multiple sub-computations with differing DAG structure. We address this problem by developing an approach for effectively composing lower bounds based on graph decomposition. We also develop a static analysis algorithm to derive the asymptotic data-access lower bounds of programs, as a function of the problem size and cache size.

The roofline model is a popular approach to “bounds and bottleneck” performance analysis. It focuses on the limits to performance of processors because of limited bandwidth to off-chip memory. It models upper bounds on performance as a function of operational intensity, the ratio of computational operations per byte of data moved from/to memory. While operational intensity can be directly measured for a specific implementation of an algorithm on a particular target platform, it is of interest to obtain broader insights on bottlenecks, where various semantically equivalent implementations of an algorithm are considered, along with analysis for variations in architectural parameters. This is currently very cumbersome and requires performance modeling and analysis of many variants.

We alleviate this problem by using the roofline model in conjunction with upper bounds on the operational intensity of computations as a function of cache capacity, derived using lower bounds on data movement. This enables bottleneck analysis that holds across all dependence-preserving semantically equivalent implementations of an algorithm. We demonstrate the utility of the approach in in assessing fundamental limits to performance and energy efficiency for several benchmark algorithms across a design space of architectural variations.

This work is the fruit of the collaboration  9.4 with OSU. The first contribution (static analysis for lower bound) will be presented at ACM POPL'15 [10] . The second contribution (architectural exploration) is to be published at ACM TACO'15 [3] .