Fast bit-accurate reciprocal square root

The reciprocal square root (RSR) is an operation extensively used in signal processing algorithms, where it is necessary the design of RSR architectures in fixed-point (FxP) representation for using in mobile devices. Currently, RSR implementations are mainly focused on floating point format, which requires long execution time and large area resources. In this paper, an algorithm for designing FxP RSR architectures is proposed, which achieves bit-accurate results in two clock cycles of execution time. The proposed algorithm is based on the Newton–Raphson method, where the seed is provided through piecewise polynomial approximation. A comparison between this RSR proposal and the straightforward approach shows that the proposed algorithm achieves an approximately 10-fold gain in execution time, which allows a speed-up of signal processing algorithms.