Result Details
Convergence verification of the Collatz problem
This article presents a new algorithmic approach for computational convergence verification of the Collatz problem. The main contribution of the paper is the replacement of huge precomputed tables containing O(2^N) entries with small lookup tables comprising just O(N) elements. Our single-threaded CPU implementation can verify 4.2×10^9 128-bit numbers per second on Intel Xeon Gold 5218 CPU computer, and our parallel OpenCL implementation reaches the speed of 2.2×10^11 128-bit numbers per second on NVIDIA GeForce RTX 2080. Besides the convergence verification, our program also checks for path records during the convergence test.
Collatz conjecture, software optimization, parallel computing, number theory
@article{BUT168171,
author="David {Bařina}",
title="Convergence verification of the Collatz problem",
journal="JOURNAL OF SUPERCOMPUTING",
year="2021",
volume="77",
number="3",
pages="2681--2688",
doi="10.1007/s11227-020-03368-x",
issn="0920-8542",
url="https://www.fit.vut.cz/research/publication/12315/"
}
Moderní metody zpracování, analýzy a zobrazování multimediálních a 3D dat, BUT, Vnitřní projekty VUT, FIT-S-20-6460, start: 2020-03-01, end: 2023-02-28, completed