Optimization of Fixed-Point Circuits Represented by Taylor Series and Real-Valued Polynomials Including Analysis of Precision and Range

In this thesis, our research focuses on fixed-point arithmetic circuits. Fixed-point representation is important in low power Application-Specific Integrated Circuits (ASICs) and in Programmable Logic Devices (PLDs). There are two aspects of the data representation problem: the precision problem and the range problem. Both of these are addressed in this thesis. We use the new technique based on Arithmetic Transform (AT) which is a canonical and efficient representation for digital circuits to avoid the disadvantages of past methods, and design an efficient algorithm which can compose detached modules to obtain the overall AT for a complex circuit.;The proposed algorithms in the thesis overcome disadvantages of past explorations. They are more flexible in processing both Taylor series and multivariate polynomials and obtain more precise results, resulting in better implementations under various constraints.;First the precision problem is processed. The typical imprecise circuits expressed in terms of Taylor series are addressed in our research. Imprecise factors including finite terms and input quantization are analyzed by AT, and algorithms are designed to verify and optimize imprecise circuits in terms of different constraints. A hybrid method performs range analysis to handle the range problem and allocates the smallest integer bit-widths. Having devised the individual methods for precision and range analysis, we then combine the two together to find the optimized implementation. Furthermore, we extend the method to analyze floating-point circuits and feedback circuits.