research-article

Finding root causes of floating point error

Authors:

Alex Sanchez-Stern,

Pavel Panchekha,

Zachary TatlockAuthors Info & Claims

PLDI 2018: Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

Pages 256 - 269

https://doi.org/10.1145/3192366.3192411

Published: 11 June 2018 Publication History

Abstract

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform.

This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level languages like C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to simplified program fragments whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries and tracking error across function boundaries and through the heap.

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Wang XYi XYu HHuang CPeng L(2024)Parallel Optimization for Accelerating the Generation of Correctly Rounded Elementary FunctionsProceedings of the 53rd International Conference on Parallel Processing10.1145/3673038.3673125(21-31)Online publication date: 12-Aug-2024
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Index Terms

Finding root causes of floating point error
1. Software and its engineering
  1. Software notations and tools
    1. Software maintenance tools

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Published In

cover image ACM Conferences

PLDI 2018: Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

June 2018

825 pages

ISBN:9781450356985

DOI:10.1145/3192366

General Chair:
Jeffrey S. Foster
University of Maryland at College Park, USA
,
Program Chair:
Dan Grossman
University of Washington, USA

ACM SIGPLAN Notices Volume 53, Issue 4
PLDI '18
April 2018
834 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/3296979
Editor:
Matthew Fluet
Rodchester Institude of Technology
Issue’s Table of Contents

Copyright © 2018 ACM.

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Published: 11 June 2018

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Cited By

Yi XYu HChen LMao XWang J(2024)FPCC: Detecting Floating-Point Errors via Chain ConditionsProceedings of the ACM on Programming Languages10.1145/36897648:OOPSLA2(1504-1531)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689764
Wang XYi XYu HHuang CPeng L(2024)Parallel Optimization for Accelerating the Generation of Correctly Rounded Elementary FunctionsProceedings of the 53rd International Conference on Parallel Processing10.1145/3673038.3673125(21-31)Online publication date: 12-Aug-2024
https://dl.acm.org/doi/10.1145/3673038.3673125
Xu JCui MLi FZhang ZYang HZhou BZhao JChristakis MPradel M(2024)Arfa: An Agile Regime-Based Floating-Point Optimization Approach for Rounding ErrorsProceedings of the 33rd ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3650212.3680378(1516-1528)Online publication date: 11-Sep-2024
https://dl.acm.org/doi/10.1145/3650212.3680378
Xu JSong GZhou BLi FHao JZhao JLee IChabbi MSteuwer M(2024)A Holistic Approach to Automatic Mixed-Precision Code Generation and Tuning for Affine ProgramsProceedings of the 29th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming10.1145/3627535.3638484(55-67)Online publication date: 2-Mar-2024
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Sathyavathi NBeulet P(2024)Deca-Rounding Methods for Floating Point Numbers: Error Analysis & Hardware ImplementationJournal of Signal Processing Systems10.1007/s11265-023-01899-z96:1(31-50)Online publication date: 1-Jan-2024
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Zhang ZXu JHao JQu YHe HZhou B(2024)Hierarchical search algorithm for error detection in floating-point arithmetic expressionsThe Journal of Supercomputing10.1007/s11227-023-05523-680:1(1183-1205)Online publication date: 1-Jan-2024
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Ren XKawai MHoshino TKatagiri TNagai T(2024)Auto‐Tuning Mixed‐Precision Computation by Specifying Multiple RegionsConcurrency and Computation: Practice and Experience10.1002/cpe.832637:2Online publication date: 7-Nov-2024
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Demeure NChevalier CDenis CDossantos-Uzarralde P(2023)Algorithm 1029: Encapsulated Error, a Direct Approach to Evaluate Floating-Point AccuracyACM Transactions on Mathematical Software10.1145/354920548:4(1-16)Online publication date: 22-Mar-2023
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Yu HYi XYin BLi FChen ZHuang C(2023)Efficient Generation of Floating-Point Inputs for Compiler-Induced Variability2023 IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER)10.1109/SANER56733.2023.00030(224-235)Online publication date: Mar-2023
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