Reliable Generation of High-Performance Matrix Algebra

TL;DR

This paper introduces BTO, a domain-specific compiler that optimizes matrix algebra sequences to achieve performance close to hand-optimized code, outperforming general-purpose optimizing compilers.

Contribution

The paper presents BTO, a specialized compiler that reliably generates high-performance matrix algebra code through scalable optimization techniques.

Findings

BTO achieves 16% to 39% performance relative to hand-optimized code.

Optimizing compilers often reach only 25% of hand-optimized performance.

BTO's scalable search effectively combines loop fusion, array contraction, and multithreading.

Abstract

Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls result in suboptimal performance. The entire sequence needs to be optimized in concert. Instead of vendor-tuned BLAS, a programmer could start with source code in Fortran or C (e.g., based on the Netlib BLAS) and use a state-of-the-art optimizing compiler. However, our experiments show that optimizing compilers often attain only one-quarter the performance of hand-optimized code. In this paper we present a domain-specific compiler for matrix algebra, the Build to Order BLAS (BTO), that reliably achieves high performance using a scalable search algorithm for choosing the best combination of loop fusion, array contraction, and multithreading for data parallelism. The BTO compiler generates code that is between 16% slower and 39% faster than hand-optimized code.