The table maker's quantum search

TL;DR

This paper demonstrates how quantum search algorithms can efficiently determine the minimum precision needed to correctly round elementary functions over floating-point inputs, offering asymptotic speedups for certain functions.

Contribution

It introduces a quantum approach to compute the hardness to round for elementary functions, improving over classical methods in specific cases.

Findings

Quantum search computes rounding hardness in  O(2^{n/2} \, log(1/\delta)) time.

Quantum algorithms outperform classical heuristics for periodic functions in large binades.

The method applies to exponential-related functions and provides probabilistic guarantees.

Abstract

We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target precision of $n$ digits for all possible precision-$n$ floating-point inputs in a given interval. For elementary functions $f$ related to the exponential function, quantum search takes time $\tilde O(2^{n/2} \log (1/\delta))$ to return, with probability $1-\delta$, the hardness to round $f$ over all $n$-bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics.