English

Counting Ones Without Broadword Operations

Computational Complexity 2016-01-19 v2

Abstract

A lower time bound Ω(min(ν(x),nν(x))\Omega(\min(\nu(x), n-\nu(x)) for counting the number of ones in a binary input word xx of length nn is presented, where ν(x)\nu(x) is the number of ones. The operations available are increment, decrement, bit-wise logical operations, and assignment. The only constant available is zero. An almost matching upper bound is also obtained.

Cite

@article{arxiv.1511.05210,
  title  = {Counting Ones Without Broadword Operations},
  author = {Holger Petersen},
  journal= {arXiv preprint arXiv:1511.05210},
  year   = {2016}
}
R2 v1 2026-06-22T11:46:54.840Z