Understanding performance stairs

Abstract

How do experts navigate the huge space of implementations for a given specification to find an efficient choice with minimal searching? Answer: They use "heuristics" -rules of thumb that are more street wisdom than scientific fact. We provide a scientific justification for Dense Linear Algebra (DLA) heuristics by showing that only a few decisions (out of many possible) are critical to performance; once these decisions are made, the die is cast and only relatively minor performance improvements are possible. The (implementation × performance) space of DLA is stair-stepped. Each stair is a set of implementations with very similar performance and (surprisingly) share key design decision(s). High-performance stairs align with heuristics that prescribe certain decisions in a particular context. Stairs also tell us how to tailor the search engine of a DLA code generator to reduce the time it needs to find implementations that are as good or better than those crafted by experts.

Deriving Correct High-Performance Algorithms

“…Details go beyond the scope of this paper. What is important is that in a study that explores the design space that is created [28], it is shown that the design decision that has the greatest impact on performance is what algorithm from the family of algorithms to use.…”

From software extensions to product lines of dataflow programs

“…Dataflow programs (DfP) abound in today's world. They are fault-tolerant servers [14,46], relational query execution plans [20,46], dense linear algebra kernels [39,38], virtual instruments [53, 49,26], stream processing applications [26,54], and large-scale cloud data processing applications [13,25]. A Df P is a directed graph: nodes called boxes are components or computations; edges indicate the flow of data.…”

“…Reverse engineering legacy systems to extract and systematize the transformations (knowledge) used to build them is only the first step of a larger process. The knowledge gathered and encoded can later be used to mechanize/automate forward engineering [39,38], i.e., to generate new programs. Extensions provided a mechanism to ease the process of extracting knowledge from legacy systems, and allowed us to improve the tools to assist experts in this task.…”