Реализация высокоточных вычислений в базисе модулярно-интервальной арифметики

Реализация высокоточных вычислений в базисе модулярно-интервальной арифметики

Автор: Коржавина Анастасия Сергеевна, Князьков Владимир Сергеевич

Журнал: Программные системы: теория и приложения @programmnye-sistemy

Рубрика: Математические основы программирования

Статья в выпуске: 3 (42) т.10, 2019 года.

Бесплатный доступ

Проблема влияния ошибок округления возникает в большом количестве задач в различных областях знаний, включая вычислительную математику, математическую физику, биохимию, квантовую механику, математическое программирование. Для решения таких задач может потребоваться точность в 100-1000 десятичных цифр. В рамках данного исследования разработаны новые способы представления числовой информации - модулярно-позиционные интервально-логарифмические системы счисления, а также методы выполнения арифметических операций для повышения скорости высокоточных вычислений.

Модулярная арифметика, гибридные системы счисления, логарифмическая интервальная характеристика, высокоточные вычисления, длинная арифметика

Короткий адрес: https://sciup.org/143169803

IDR: 143169803   |   УДК: 004.222.3:681.5.07+004.421.4   |   DOI: 10.25209/2079-3316-2019-10-3-81-127

High-precision computations using residue-interval arithmetic on FPGAS

The problem of round-off errors arises in a large number of issues in various fields of knowledge, including computational mathematics, mathematical physics, biochemistry, quantum mechanics, mathematical programming. Today, experts place particular emphasis on accuracy, fault tolerance, stability, and reproducibility of computation results of numerical models when solving a wide range of industrial and scientific problems, such as: mathematical modeling and structural designs of aircrafts, cars, ships; process modeling and computations for solving large-scale problems in the field of nuclear physics, aerodynamics, gas, and hydrodynamics; problems on reliable predictive modeling of climatic processes and forecasting of global changes in the atmosphere and water environments; faithful modeling of chemical processes and synthesis of pharmaceuticals, etc.Floating-point arithmetic is the dominant choice for most scientific applications. However, there are a lot of unsolvable with double-precision arithmetic problems...

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