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This paper presents a high-throughput, low-latency, hardware-efficient fixed-point implementation of the fast affine projection (FAP) algorithm. The proposed architecture utilizes reusable distributed arithmetic (RDA) in combination with optimizations in the update process to enable the coefficients to be updated in a fixed number of cycles independent of filter length. Fixed-point simulations show that the effect of replacing some of the multiplications with arithmetic shifts is minor, with RDA-FAP maintaining a faster convergence rate than NLMS. The proposed design is also compared against a multiplier-based design in terms of number of computations and number of clock cycles needed for a single FAP update cycle.