Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging
Provides a practical, accurate, and fast debugging tool for floating-point errors in numerical software.
EXPLANIFLOAT combines double-double oracles and condition numbers to achieve 80.0% precision and 96.1% recall on 546 numeric benchmarks, avoiding correlated errors and handling over/underflow.
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.