A processing device determines a scope indicating at least a portion of the processing system and target data from atomic memory operation to be performed. Based on the scope, the processing device determines one or more hardware parameters for at least a portion of the processing system. The processing device then compares the hardware parameters to the scope and target data to determine one or more corrections. The processing device then provides the scope, target data, hardware parameters, and corrections to a plurality of hardware lookup tables. The hardware lookup tables are configured to receive the scope, target data, hardware parameters, and corrections as inputs and output values indicating one or more coherency actions and one or more orderings. The processing device then executes one or more of the indicated coherency actions and the atomic memory operation based on the indicated ordering.