Analysis and Detection of Stagnation in Floating-Point Summation
Abstract
Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. Here we define different types of stagnation - commonly referred to as swamping or absorption, where one operand in an addition is nearly or completely rounded off---in floating-point summation, and propose algorithms for detecting it in numerical code that uses floating-point arithmetic. Whilst cancellation in floating-point arithmetic has been studied, for example by Lam et al. in `Dynamic floating point cancellation detection', stagnation has not been exploited as a property for detecting and reporting accuracy loss in floating-point operations. We have built prototype dynamic stagnation detection tools in two languages, MATLAB and Julia, and applied them to applications ranging from basic summation of a vector, to matrix multiplication, to a fluid flow simulation model. With this tool, users are able to identify areas of their floating-point code where stagnation occurs - in those areas of the code one may need to switch to a higher precision number format, apply stochastic rounding, or use different summation algorithms such as compensated summation. To the best of our knowledge we provide a first rigorous definition of stagnation in floating-point summation.
Related
- FPScan: An Automated Constraint-Based Analyzer for Floating-Point Anomaly Detection
- Semi-similar Prandtl Flows near a Stagnation Point: Dynamical Selection and Nonlinear Stability
- The Entropy of Floating-Point Numbers
- The Rise of Low Precision Floating Point
- Performance Evaluation of an Adaptive Quadrature and a Double Exponential Formula Using Arbitrary-Precision Floating-Point Arithmetic
BibTeX
@misc{mikaitis2026analysis,
title = {{Analysis and Detection of Stagnation in Floating-Point Summation}},
author = {Mantas Mikaitis and William Woolfenden},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10819},
eprint = {2610.10819},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10819},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analysis and Detection of Stagnation in Floating-Point Summation
AU - Mantas Mikaitis
AU - William Woolfenden
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.10819
UR - https://arxiv.org/abs/2610.10819
AB - Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. Here we define different types of stagnation - commonly referred to as swamping or absorption, where one operand in an addition is nearly or completely rounded off---in floating-point summation, and propose algorithms for detecting it in numerical code that uses floating-point arithmetic. Whilst cancellation in floating-point arithmetic has been studied, for example by Lam et al. in `Dynamic floating point cancellation detection', stagnation has not been exploited as a property for detecting and reporting accuracy loss in floating-point operations. We have built prototype dynamic stagnation detection tools in two languages, MATLAB and Julia, and applied them to applications ranging from basic summation of a vector, to matrix multiplication, to a fluid flow simulation model. With this tool, users are able to identify areas of their floating-point code where stagnation occurs - in those areas of the code one may need to switch to a higher precision number format, apply stochastic rounding, or use different summation algorithms such as compensated summation. To the best of our knowledge we provide a first rigorous definition of stagnation in floating-point summation.
ER -