New algorithm to test percolation conditions within the Newman-Ziff algorithm

A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman-Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman-Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.