As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. Exploiting this feature, we demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We illustrate how this symbolic system improves numerical computing tasks by showcasing an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.
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Managing code transformations for better performance portability
Code optimization is an intricate task that is getting more complex as computing systems evolve. Managing the program optimization process, including the implementation and evaluation of code variants, is tedious, inefficient, and errors are likely to be introduced in the process. Moreover, because each platform typically requires a different sequence of transformations to fully harness its computing power, the optimization process complexity grows as new platforms are adopted. To address these issues, systems and frameworks have been proposed to automate the code optimization process. They, however, have not been widely adopted and are primarily used by experts with deep knowledge about underlying architecture and compiler intricacies. This article describes the requirements that we believe necessary for making automatic performance tuning more broadly used, especially in complex, long-lived high-performance computing applications. Besides discussing limitations of current systems and strategies to overcome these, we describe the design of a system that is able to semi-automatically generate efficient platform-specific code. In the proposed system, the code optimization is programmer-guided, separately from application code, on an external file in what we call optimization programming. The language to program the optimization process is able to represent complex collections of transformations and, as a result, generate efficient platform-specific code. A database manages different optimized versions of code regions, providing a pragmatic approach to performance portability, and the framework itself has separate components, allowing the optimized code to be used on systems without installing all of the modules required for the code generation. We present experiments on two different platforms to illustrate the generation of efficient platform-specific code that performs comparable to hand-optimized, vendor-provided code.
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- Award ID(s):
- 1725729
- NSF-PAR ID:
- 10297762
- Date Published:
- Journal Name:
- The International Journal of High Performance Computing Applications
- Volume:
- 33
- Issue:
- 6
- ISSN:
- 1094-3420
- Page Range / eLocation ID:
- 1290 to 1306
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/1094342019865606
