Self-Alignment Schemes for the Implementation of Addition-Related Floating-Point Operators
Advances in semiconductor technology brings to the market incredibly dense devices, capable of handling tens to hundreds floating-point operators on a single chip; so do the latest field programmable gate arrays (FPGAs). In order to alleviate the complexity of resorting to these devices in computationally intensive applications, this article proposes hardware schemes for the realization of addition-related floating-point operators based on the self-alignment technique (SAT). The article demonstrates that the schemes guarantee an accuracy as if summation was computed accurately in the precision of operator's internal mantissa, then faithfully rounded to working precision. To achieve such performance, the article adopts the redundant high radix carry-save (HRCS) format for the rapid addition of wide mantissas. Implementation results show that combining the SAT and the HRCS format allows the implementation of complex operators with reduced area and latency, more so when a fused-path approach is adopted. The article also proposes a new hardware operator for performing endomorphic HRCS additions and presents a new technique for speeding up the conversion from the redundant HRCS to a conventional binary format.
floating-point fpga self-alignment technique summation design algorithms redundant arithmetic accumulator