Abstract: A data driven method for coordinating the processing of arithmetic tasks in a multiple computer system having a multiplicity of arithmetic processors by determining whether an arithmetic task is in a blocked condition or is in an execution ready condition. A source distributed processor stores data in a local memory for processing by a local processor and then transfers the processed data to a global memory for buffering in preparation for subsequent processing by a destination distributed processor. The source distributed processor generates a produce message to a destination distributed processor to indicate that the data to be transferred is available in a buffer in the global memory. The destination distributed processor loads the data to be transferred from the buffer in the global memory and then generates a consume message to the source distributed processor to indicate that the data has been transferred from the global memory and the buffer in the global memory is now available.