Algorithms for estimating modular numbers in floating-point arithmetic
In the residue number system (RNS), the operations of addition, subtraction, and multiplication are executed in parallel for different digits (residues) of the modular numbers. Therefore, RNS is used for reaching the maximum performance in many high-speed computer arithmetic applications. However, R...
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| Main Author: | |
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| Format: | Article |
| Language: | Russian |
| Published: |
North-Caucasus Federal University
2022-09-01
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| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/294 |
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| Summary: | In the residue number system (RNS), the operations of addition, subtraction, and multiplication are executed in parallel for different digits (residues) of the modular numbers. Therefore, RNS is used for reaching the maximum performance in many high-speed computer arithmetic applications. However, RNS has disadvantages, especially in issues like estimating the magnitudes of modular numbers. Traditional methods for estimating the magnitudes in RNS that are based on the Chinese remainder theorem, or on the Mixed-Radix Conversion, result in rather slow and inefficient implementation. For solving this problem, the interval floating-point characteristic (IFC) method was proposed. This paper describes direct and stepwise algorithms for IFC computation in fixed-precision floating-point arithmetic. Time complexity (in terms of the elementary arithmetic operations) and accuracy are assessed for each algorithm. |
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| ISSN: | 2308-4758 |