License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ECOOP.2022.1
URN: urn:nbn:de:0030-drops-162290
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16229/
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Becker, Heiko ; Rabe, Robert ; Darulova, Eva ; Myreen, Magnus O. ; Tatlock, Zachary ; Kumar, Ramana ; Tan, Yong Kiam ; Fox, Anthony

Verified Compilation and Optimization of Floating-Point Programs in CakeML

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LIPIcs-ECOOP-2022-1.pdf (1.0 MB)

Abstract

Verified compilers such as CompCert and CakeML have become increasingly realistic over the last few years, but their support for floating-point arithmetic has thus far been limited. In particular, they lack the "fast-math-style" optimizations that unverified mainstream compilers perform. Supporting such optimizations in the setting of verified compilers is challenging because these optimizations, for the most part, do not preserve the IEEE-754 floating-point semantics. However, IEEE-754 floating-point numbers are finite approximations of the real numbers, and we argue that any compiler correctness result for fast-math optimizations should appeal to a real-valued semantics rather than the rigid IEEE-754 floating-point numbers.
This paper presents RealCake, an extension of CakeML that achieves end-to-end correctness results for fast-math-style optimized compilation of floating-point arithmetic. This result is achieved by giving CakeML a flexible floating-point semantics and integrating an external proof-producing accuracy analysis. RealCake’s end-to-end theorems relate the I/O behavior of the original source program under real-number semantics to the observable I/O behavior of the compiler generated and fast-math-optimized machine code.

BibTeX - Entry

@InProceedings{becker_et_al:LIPIcs.ECOOP.2022.1,
  author =	{Becker, Heiko and Rabe, Robert and Darulova, Eva and Myreen, Magnus O. and Tatlock, Zachary and Kumar, Ramana and Tan, Yong Kiam and Fox, Anthony},
  title =	{{Verified Compilation and Optimization of Floating-Point Programs in CakeML}},
  booktitle =	{36th European Conference on Object-Oriented Programming (ECOOP 2022)},
  pages =	{1:1--1:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-225-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{222},
  editor =	{Ali, Karim and Vitek, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16229},
  URN =		{urn:nbn:de:0030-drops-162290},
  doi =		{10.4230/LIPIcs.ECOOP.2022.1},
  annote =	{Keywords: compiler verification, compiler optimization, floating-point arithmetic}
}

Keywords: compiler verification, compiler optimization, floating-point arithmetic
Collection: 36th European Conference on Object-Oriented Programming (ECOOP 2022)
Issue Date: 2022
Date of publication: 23.06.2022
Supplementary Material: Software (ECOOP 2022 Artifact Evaluation approved artifact): https://doi.org/10.4230/DARTS.8.2.10

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