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We show that Boolean matrix multiplication, computed as a sum of products ofcolumn vectors with row vectors, is essentially the same as Warshall'salgorithm for computing the transitive closure matrix of a graph from itsadjacency matrix.  Warshall's algorithm can be generalized to Floyd's algorithm for computingthe distance matrix of a graph with weighted edges. We will generalize Booleanmatrices in the same way, keeping matrix multiplication essentially equivalentto the Floyd-Warshall algorithm. This way, we get matrices over a semiring,which are similar to the so-called "funny matrices".  We discuss our implementation of operations on Boolean matrices and on theirgeneralization, which make use of vector instructions.

Fast algorithms for anti-distance matrices as a generalization of Boolean matrices