Inexpensive correctly rounded floating-point division and square root with input scaling

Recent embedded DSPs are incorporating IEEE-compliant floating point arithmetic to ease the development of, e.g., multiple antenna MIMO in software-defined radio. An obvious choice of FPU architecture in DSP is to include a fused multiply-add (FMA) operation, which accelerates most DSP applications. Another advantage of FMA is that it enables fast software algorithms for, e.g., division and square root without much additional hardware. However, these algorithms are nontrivial to perform at the target accuracy to get the correctly rounded result without danger of overflow. Previous FMA-based systems either rely on a power-hungry wide intermediate format or forego correct rounding. A wide format is unattractive in a power-sensitive embedded environment since it requires enlarged register files, wider data buses and possibly a larger multiplier. We present provably correct algorithms for efficient IEEE-compliant division and square root with only a 32-bit format using hardware prescaling and postscaling steps. The required hardware has approximately 8% of area and power footprint of a single FMA unit.