Multi-digit arithmetic in sequential, parallel and quantum computational models
Keywords:
багаторозрядна арифметика,послідовна модель обчислень,паралельна модель обчислень, квантова модель обчисленьAbstract
Various computational models for the implementation of multi–digit arithmetic operations are considered. The division into sequential, parallel and quantum computing models is to consider the features of the architecture of the devices on which the programs will be executed. The work presents the features of the implementation of algorithms for different computational models. The main criteria to get the complexity for different computational models are presented. It is said about restrictions that should be considered in the case of the implementation.
References
V. K. Zadiraka and A. M. Tereshchenko, Computer Arithmetic of Multi-Bit Numbers in Sequential and Parallel Computational Models [in Ukrainian], Naukova Dumka, Kyiv (2021).
Schonhage A., Straßen V. Schnelle Multiplikation großen Zahlen. Computing. 1971. 7, N 3–4. P. 281–292. DOI: 10.1007/BF02242355.
A. A. Karatsuba and Yu. P. Ofman, Multiplication of multi-digit numbers using automata, Doklady SSSR, Vol. 145, No. 2, 293–294 (1962).
Amdahl G.M. Validity of the single processor approach to achieving large-scale computing capabilities. AFIPS Conf. Proc. 30. 1967. P. 483–485.
Larasati H.T. Awaludin A.M., Ji J. Kim H. Quantum Circuit Design of Toom 3-Way Multiplication. Appl. Sci. 2021. 11, 3752. DOI: 10.3390/app11093752.
