An exact method for estimating maximum errors of multi-mode floating-point iterative booth multiplier

With the rapid growth of floating-point FP arithmetic, FP multipliers have become the main energy consumers in embedded systems. Many FP applications allow a slight output distortion, thereby we can trade output quality with energy consumption via reducing the precision of FP multiplication operations to be less accurate than IEEE single-precision FP multiplication. In this paper, we propose a sort of multi-mode FP iterative booth multiplier which can provide multiple precision modes PMs. However, the maximum error of each PM with respect to IEEE single-precision FP multiplication is very difficult to compute by using exhaustive simulation. To efficiently assign each multiplication operation in an application to a proper PM for satisfying output error constraint and achieving more energy saving, an exact analysis method is proposed to estimate the maximum error of each PM. Experimental results show that the proposed method can get 46% to 63% reduction in the estimated value of the maximum error, leading to up to 24% more energy saving than previous work.