Research On Higher-order Derivation Algorithm Of Ternary Optical Computer Based On Taylor Series Expansion

As people's demand for structural calculations gradually increases,and the efficiency of electronic computers in this regard is limited,researchers are forced to start looking for other solutions.Since the ternary optical computer(TOC)is now mature,in addition to the characteristics of high-symbols with light and high parallelism,it also has the characteristics of a large number of data bits and a reconfigurable processor.Therefore,when the problem solved by the electronic computer is more complicated or difficult to solve,people hope that it can be solved in combination with the TOC.Higher-order derivation is an important tool in the field of mathematics,which is widely used in differentials,quantum mechanics,and engineering applications.Due to the carry in the calculation of the electronic computer,the calculation efficiency is low when solving the higher-order derivation problem.For this problem,this paper uses the advantages of the TOC without carry,combined with the relevant characteristics of the TOC,by constructing multipliers and adders on the TOC platform,and copying multiple composite operator units,to solve the higher-order derivation problem of complex calculations.This paper first analyzes the higher-order derivation of the polynomial function of the Taylor series expansion,and deduces the principle of the higher-order derivation algorithm,and then discusses in detail the algorithm design based on the higher-order derivation of the TOC,the reconstruction process of the multiplier and the adder,the design of the composite operator unit.Secondly,the higher-order derivation algorithm in the actual operation process is designed,the number of multipliers and adders required in the implementation process is given,and the hardware resources,clock cycles and reconfigurable schemes are analyzed.Finally,the experimental simulation verifies the feasibility of the scheme,and it also proves the correctness of the higher-order derivation algorithm for fast and accurate parallel calculation on the ternary optical platform.Compared with the traditional higher-order derivation,the higher-order derivation based on the TOC is better in time,operation efficiency and complex operation processing,and has certain application significance.There are three main innovations in the thesis,which are as follows:Realize the higher-order derivation algorithm design based on the TOC,which provides a new solution for the research of complex problems,and also provides an expansion direction for the mathematical application of the TOC.Propose the reconstruction scheme of the multiplier and the adder,and realize the bit allocation technology,and analyze various hardware resources in detail.Using the TOC processor's numerous bits and reconfigurable characteristics,the reconstructed multiple multipliers are packaged into a composite operator unit,which can support the higher-order derivation operation of large-scale numerical values,which provides a foundation for the upper application of the TOC.