Precision Modeling and Bit-width Optimization of Floating-Point Applications

We present a floating-point precision modeling methodology that can be used to develop application adaptive arithmetic precision models for variable bitwidth floating-point computing. We also developed optimization algorithms that minimize the total bit-width for the application such that the output accuracy meets user-defined requirements. The methodology supports different bit-widths for different variables in the datapath. Computing using floating-point (FP) representations provides a wide dynamic range of real numbers, freeing programmers from writing the manual scaling code required for fixed-point representation. Nevertheless, floating-point operations have always been considered beyond the capabilities of custom or re-configurable hardware implementation. IEEE standard precision floating-point operations cost too much in power and area to be practical on many devices. A promising solution to reduce the cost of FP implementation is to reduce the bit-width of the FP representation. Research results show that it is feasible and beneficial to use reduced bit-width FP representation in modern multimedia and streaming application workloads [1]. By taking advantage of bit-width information during architectural synthesis, area is reduced by 15-86%, clock speed improved by 3-249%, and power consumption reduced by 46-73% [2]. The optimal bit-widths are the smallest bit-widths that satisfy the accuracy requirement. They can be obtained through simulation-based searching or modelbased optimization. Simulation-based bit-width searching is a process that simulates using all possible bit-widths, and finds the best solution. It is a straight-forward method to determine the minimal bit-width, but it does not provide any intelligent optimization, and it can consume enormous computation time, especially when the target applications are large designs or a large input space is involved. As a better approach, model-based bit-width optimization eliminates the need for exhaustive simulation, and automatically analyzes and adapts the level of precision according to the need of an application.