Abstract
As an important tool in the field of mathematics, higher-order derivation problems are widely used in differentials, quantum mechanics, and engineering applications. However, in the electronic computer (EC), due to the existence of the carry in the calculation, the computational efficiency is low when solving the higher-order derivation problem. In response to this problem, the ternary optical computer (TOC) has the advantages of no carry-in and the characteristics of numerous data bits, reconfigurable processors and parallel computing. Solve the higher-order derivation problems with complex operations by constructing multipliers and adders on the TOC platform, and copying multiple composite operator units (COUs). This article introduces the design of the higher-order derivative algorithm based on TOC in detail, the reconfiguration process of the multiplier and adder, and the number of bits of the multiplier and adder required in the implementation is given. Besides, the hardware resources and clock cycles in the operation are analyzed. The feasibility of the implementation scheme is verified by experiments. Compared with the traditional higher-order derivative, the higher-order derivative based on the TOC is superior in time performance, computational efficiency, and processing of complex operations. Due to the limitation of the research stage, the algorithm is only applicable to the function of polynomials, which lays a foundation for the further research of higher-order derivative algorithms, and has certain application significance.
Highlights
Internet technology has experienced the rise of the late 20th century, and the rapid development at the beginning of this century
Input the divided multiplier and multiplicand, and pass them to the Modified Signed-Digit (MSD) multiplier of the minimum module (MM) reconstructed by the processor of the ternary optical computer (TOC) for parallel calculation; Step 3: According to the weights of the two basic units in their original data, perform a zero-padding operation on the obtained results, and add them to obtain the product of two multi-digit numbers [38]
After the calculation of each coefficient is completed, if you need to calculate the value of the specific point of the higher-order derivative, it is necessary to multiply each coefficient by the power of the point and add the products of each item, which increase the amount of data, making the calculation amount complicated and the computational efficiency is low
Summary
Internet technology has experienced the rise of the late 20th century, and the rapid development at the beginning of this century. Operation, the logical relationship is ‘‘XOR’’, the same is 0, the difference is 1, the result of ‘‘XOR’’ is the value of the local sum, and determine whether to perform the carry according to the operation requirements; subtraction is a complement-addition operation; multiplication operations use shift-addition or a large amount of hardware for logic operations; division is performed by shift-subtraction and performing a complement-addition operation This process is repeated multiple times to complete the update of the higherorder derivative [2]. A ternary optical processor with multiple data bits is used to solve the higher-order derivative problem of complex calculations by constructing multipliers, adders, and replicating multiple composite operator units (COUs), and computational efficiency is analyzed
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