On Faster Integer Calculations using Non-Arithmetic Primitives

TL;DR

This paper explores how non-arithmetic primitives like division with remainder and bitwise operations can significantly improve the efficiency of integer decision algorithms, demonstrating concrete benefits through new algorithms.

Contribution

It introduces and analyzes fast algorithms that leverage non-arithmetic primitives, showing their advantages over traditional arithmetic-only approaches.

Findings

Non-arithmetic primitives can reduce algorithm complexity.

Concrete problems benefit from these primitives.

New algorithms demonstrate improved performance.

Abstract

The unit cost model is both convenient and largely realistic for describing integer decision algorithms over (+,*). Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware, may lead to a considerable drop in complexity. We show a variety of concrete problems to benefit from such NON-arithmetic primitives by presenting and analyzing corresponding fast algorithms.