Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915888272244736 |
|---|---|
| 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 |