1. An apparatus for extending the precision of a complex multiplication with accumulation, the apparatus comprising: a reduced precision storage unit for storing at least two complex operands, a reduced-precision real value, and a reduced-precision imaginary value; multipliers for multiplication of the two complex operands accessed from the reduced-precision storage unit to produce real and imaginary components of a complex product; adders for addition and subtraction of the real and imaginary components of the complex product to produce a real result and an imaginary result; an extended-precision storage unit for holding an extended-precision real component and an extended-precision imaginary component; an accumulator for computing a real component of the complex multiplication with accumulation by adding an extended-precision real value with the real result producing an accumulated real result, the extended-precision real value formed by a concatenation of the extended-precision real component with the reduced-precision real value, and the accumulated real result made available for storing back an updated extended-precision real component in the extended-precision storage unit and an updated reduced-precision real value in the reduced-precision storage unit; and an accumulator for computing an imaginary component of the complex multiplication with accumulation by adding an extended-precision imaginary value with the imaginary result producing an accumulated imaginary result, the extended-precision imaginary value formed by a concatenation of the extended-precision imaginary component with the reduced-precision imaginary value, and the accumulated imaginary result made available for storing back an updated extended-precision imaginary component in the extended-precision storage unit and an updated reduced-precision imaginary value in the reduced-precision storage unit.