One of the important advantages FPGA architectures offer to designers of DSP-based algorithms is the possibility of doing what has come to be known as distributed arithmetic.16

Distributed Arithmetic (DA), along with Modulo Arithmetic, is a computational algorithm that performs multiplication with look-up table-based (LUT) schemes instead of actually doing the calculations using multiplier and adder circuits. DA specifically targets the sum of products (sometimes called the inner product or dot product of multidimensional vectors) a computation that is at the heart of many important filtering and frequency-transforming functions used in DSP. The LUTs can be spread all over the die for all practical purposes inside numerous CLBs thereby allowing a better utilization of placement and routing resources, while enabling an unprecedented flexibility in embedding algorithms inside an FPGA that had not been contemplated until recently.

The derivation of the DA algorithm is most simple, but its applications are extremely broad.