Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging

Fuente: arXiv
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Main Authors: Kulkarni, Bhargav, Panchekha, Pavel
Format: Preprint
Published: 2025
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author Kulkarni, Bhargav
Panchekha, Pavel
author_facet Kulkarni, Bhargav
Panchekha, Pavel
contents Recent advances have made numeric debugging tools much faster by using double-double oracles, and numeric analysis tools much more accurate by using condition numbers. But these techniques have downsides: double-double oracles have correlated error so miss floating-point errors while condition numbers cannot cleanly handle over- and under- flow. We combine both techniques to avoid these downsides. Our combination, EXPLANIFLOAT, computes condition numbers using double-double arithmetic, which avoids correlated errors. To handle over- and under- flow, it introduces a separate logarithmic oracle. As a result, EXPLANIFLOAT achieves a precision of 80.0% and a recall of 96.1% on a collection of 546 difficult numeric benchmarks: more accurate than double-double oracles yet dramatically faster than arbitrary-precision condition number computations.
format Preprint
id arxiv_https___arxiv_org_abs_2503_11884
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging
Kulkarni, Bhargav
Panchekha, Pavel
Numerical Analysis
Recent advances have made numeric debugging tools much faster by using double-double oracles, and numeric analysis tools much more accurate by using condition numbers. But these techniques have downsides: double-double oracles have correlated error so miss floating-point errors while condition numbers cannot cleanly handle over- and under- flow. We combine both techniques to avoid these downsides. Our combination, EXPLANIFLOAT, computes condition numbers using double-double arithmetic, which avoids correlated errors. To handle over- and under- flow, it introduces a separate logarithmic oracle. As a result, EXPLANIFLOAT achieves a precision of 80.0% and a recall of 96.1% on a collection of 546 difficult numeric benchmarks: more accurate than double-double oracles yet dramatically faster than arbitrary-precision condition number computations.
title Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging
topic Numerical Analysis
url https://arxiv.org/abs/2503.11884