A scaling-less Newton-Raphson pipelined implementation for a fixed-point inverse square root operator

Abstract

The inverse square root is a common operation in digital signal processing architectures, in particular when matrix inversions are required. The Newton-Raphson algorithm is usually used, either in floating or in fixed-point formats. With the former format, the well-known fast inverse square root computation is based on a 32-bit integer constant, which is allowed by the standardized format of the mantissa. For the fixed-point format, there are many possibilities, which usually force a design with scaling of the input in order to respect a pre-determined work range. Having the input in a known range makes it possible to compute a first approximation with coefficients stored in memory. In this paper, a novel generic architecture which does not require scaling is proposed. This design is totally pipelined, ROM-less and can be directly used in any architecture. The implementation is optimized to reach the maximum clock frequency offered by the DSP cells of Xilinx FPGAs. This frequency is higher than the one available by using memory blocks.