Automatic Accuracy-Guaranteed Bit-Width Optimization for Fixed and Floating-Point Systems

In this paper we present Minibit+, an approach that optimizes the bit-widths of fixed-point and floating-point designs, while guaranteeing accuracy. Our approach adopts different levels of analysis giving the designer the opportunity to terminate it at any stage to obtain a result. Range analysis is achieved using a combined affine and interval arithmetic approach to reduce the number of bits. Precision analysis involves a coarse-grain and fine-grain analysis. The best representation, in fixed-point or floating-point, for the numbers is then chosen based on the range, precision and latency. Three case studies are used: discrete cosine transform, B-Splines and RGB to YCbCr color conversion. Our analysis can run over 200 times faster than current approaches to this problem while producing more accurate results, on average within 2-3% of an exhaustive search.