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Towards Program Optimization through Automated Analysis of Numerical Precision.

Michael D Linderman1, Matthew Ho1, David L Dill1

  • 1Computer Systems Laboratory, Stanford University, Stanford, CA, USA.

Proceedings of the ... CGO : International Symposium on Code Generation and Optimization. International Symposium on Code Generation and Optimization
|August 15, 2017
PubMed
Summary
This summary is machine-generated.

Reducing arithmetic precision speeds up computations and saves power but can reduce accuracy. This study introduces a proof assistant and static analysis to bound errors, enabling verification and optimization for performance gains.

Keywords:
D.2.4 [Software Engineering]: Program Verification–ValidationD.3.4 [Programming Languages]: Processors–OptimizationDesignFixed-Point NumbersFloating-Point NumbersG.1.0 [Mathematics of Computing]: Numerical Analysis–Computer ArithmeticNumerical PrecisionPerformanceStatic Error AnalysisVerification

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Area of Science:

  • Computer Science
  • Numerical Analysis
  • Software Engineering

Background:

  • Reducing arithmetic precision offers significant performance benefits like increased speed and reduced power consumption, crucial for architectures like GPUs.
  • However, this precision reduction inherently compromises computational accuracy, posing a challenge for reliable software development.

Purpose of the Study:

  • To develop a proof assistant and static analysis techniques for bounding numerical and precision-related errors.
  • To enable programmers and compilers to verify and optimize applications for diverse configurations using these error bounds.

Main Methods:

  • Implementation of a proof assistant.
  • Development of static analysis techniques for error bounding.
  • Application of these techniques to case studies.

Main Results:

  • Demonstrated effectiveness of the proof assistant and static analysis in bounding errors.
  • Quantified performance benefits achieved through rigorous precision analysis.
  • Successful verification and optimization of case study applications.

Conclusions:

  • The developed techniques provide a rigorous method for managing precision-related errors in computations.
  • Numerical verification and optimization using bounded errors can lead to substantial performance improvements without sacrificing necessary accuracy.