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A software interface and hardware design for variable-precision interval arithmetic

Программный интерфейс и конструкция аппаратуры для интервальной арифметики переменной разрядности

  • Mathematical Research
  • Published:
Reliable Computing

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Abstract

This paper presents a software interface and hardware design for variable-precision, interval arithmetic. The software interface gives the programmer the ability to specify the precision of the computation and determine the accuracy of the result Special instructions for vector and matrix operations are also provided. The hardware design directly supports variable-precision, interval arithmetic. This greatly improves the accuracy of the computation and is much faster than existing software methods for controlling numerical error. Hardware algorithms are presented for the basic arithmetic operations, exact dot products, and elementary functions. Area and delay estimates indicate that the processor can be implemented on a single chip with a cycle time that is comparable to existing IEEE double-precision floating point processors.

Abstract

Описываются программный интерфейс и конструкция аппаратуры для интервальной арифметики переменной разрядности. Программный интерфейс дает программисту возможность управлять разрядностью вычислений, определяя точность результата. Также предусмотрены специальные инструкции для векторных и матричных операций. Конструкция аппаратуры напрямую поддерживает интервальную арифметику переменной разрядности, что значительно повышает точность вычислений и обеспечивает выигрыш в скорости в сравнении с сушествуюшими программными методами управления величиной численных погрешностей. Представлены аппаратно реализованные алгоритмы для основных арифметических операций, точных скалярных произведений и элементарных функций. Оценки времени вычислений и требуемой площади кристалла покззывают, что соответствуюший процессор может быть реализован на одном кристалле с рабочей частотой, сравнимой с существующими процессорами плавающей точки двойной точности стандарта IEEE.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Texas at Austin, 78712, Austin, Texas, USA

    Michael J. Schulte & Earl E. Swartzlander Jr.

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  1. Michael J. Schulte
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  2. Earl E. Swartzlander Jr.
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Schulte, M.J., Swartzlander, E.E. A software interface and hardware design for variable-precision interval arithmetic. Reliable Comput 1, 325–342 (1995). https://doi.org/10.1007/BF02385262

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  • DOI: https://doi.org/10.1007/BF02385262

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