1. In a data processing system that executes a program of instructions, a method for performing a complex digital filter on a plurality of data samples and a set of complex coefficients comprising the computer implemented steps of: A) for each corresponding relationship in a plurality of corresponding relationships between said complex coefficients in said set of complex coefficients and said data samples in said plurality of data samples, wherein each of said plurality of corresponding relationships is used in said complex digital filter, performing the steps of: A1) for each complex coefficient in said set of complex coefficients, performing the steps of: a) determining a corresponding data sample for said complex coefficient according to said corresponding relationship; b) receiving an instruction; c) in response to said instruction, performing the steps of: c1) reading eight data elements stored as packed data, a first subset of said eight data elements including two representations of each of the components of said complex coefficient, a second subset of said eight data elements including two representations of each of the components of said corresponding data sample, wherein each representation of said components either represents the positive or negative of said component; and c2) generating a currently calculated complex number representing the product of said complex coefficient and corresponding data sample using said first and second subsets; d) adding the real component of said currently calculated complex number to a first data element of an accumulation packed data item for said corresponding relationship; and e) adding the imaginary component of said currently calculated complex number to a second data element of said accumulation packed data item for said corresponding relationship.