Simplified floating-point division and square root

Digital Signal Processing (DSP) algorithms on low-power embedded platforms are often implemented using fixed-point arithmetic due to expected power and area savings over floating-point computation. However, recent research shows that floating-point arithmetic can be made competitive by using a reduced-precision format instead of, e.g., IEEE standard single precision, thereby avoiding the algorithm design and implementation difficulties associated with fixed-point arithmetic. This paper investigates the effects of simplified floating-point arithmetic applied to an FMA-based floating-point unit and the associated software division and square root operations. Software operations are proposed which attain near-exact precision with twice the performance of exact algorithms and resolve overflow-related errors with inexpensive exponent-manipulation special instructions.