AIOSC: Analytical Integer Word-length Optimization based on System Characteristics for Recursive Fixed-point LTI Systems

The integer word-length optimization known as range analysis (RA) of the fixed-point designs is a challenging problem in high level synthesis and optimization of linear-time-invariant (LTI) systems. The analysis has significant effects on the resource usage, accuracy and efficiency of the final implementation, as well as the optimization time. Conventional methods in recursive LTI systems suffer from inaccurate range estimations due to dependency to symmetry or non-symmetry of the input range over zero, and involvement with parameter adjustments. The underestimations endanger the range safety, and generate a great error due to overflows. On the other hand, the overestimations increase the hardware costs, as well as weaken the signal, if the overestimated ranges are utilized in downscaling. Therefore, in this paper, we propose an efficient, safe and more precise RA method to measure the range of both recursive and non-recursive fixed-point LTI systems through analytical formulation. Our main idea is obtaining the input sequences for which variables in the LTI system would be maximum and minimum. By applying these sequences to the system, the upper and lower bounds of the intended variables are obtained as the range. The proposed method enhances the bit-widths accuracy more than 34% on average in comparison with the state-of-the-arts. The results also show about 37% and 6% savings in the area and delay, respectively.