Multiplicative Square Root Algorithms for FPGAs

Most current square root implementations for FPGAs use a digit recurrence algorithm which is well suited to their LUT structure. However, recent computing-oriented FPGAs include embedded multipliers and RAM blocks which can also be used to implement quadratic convergence algorithms, very high radix digit recurrences, or polynomial approximation algorithms. The cost of these solutions is evaluated and compared, and a complete implementation of a polynomial approach is presented within the open-source FloPoCo framework. This polynomial approach allows a shorter latency and higher frequency than the digit recurrence approach, and improves over previous multiplicative approaches. However, the cost of IEEE-compliant correct rounding is shown to be very high.