A Non-Oblivious Reduction of Counting Ones to Multiplication

TL;DR

This paper introduces an efficient algorithm for counting ones in a binary word using only logical operations and multiplication, achieving a time complexity of O(log log b).

Contribution

It presents a novel non-oblivious method that reduces counting ones to multiplication, improving efficiency over previous approaches.

Findings

Runs in time O(log log b)

Uses only logical operations and multiplication

Offers a new approach to counting ones

Abstract

An algorithm counting the number of ones in a binary word is presented running in time $O(\log\log b)$ where $b$ is the number of ones. The operations available include bit-wise logical operations and multiplication.