Variable-precision, interval arithmetic coprocessors

This paper presents hardware designs, arithmetic algorithms, and numerical applications for variable-precision, interval arithmetic coprocessors. These coprocessors give the programmer the ability to set the initial precision of the computation, determine the accuracy of the results, and recompute inaccurate results with higher precision. Variable-precision, interval arithmetic algorithms are used to reduce the execution times of numerical applications. Three hardware designs with data paths of 16, 32, and 64 bits are examined. These designs are compared based on their estimated chip area, cycle time, and execution times for various numerical applications. Each coprocessor can be implemented on a single chip with a cycle time that is comparable to IEEE double-precision floating point coprocessors. For certain numerical applications, the coprocessors are two to four orders of magnitude faster than a conventional software package for variable-precision, interval arithmetic.AbstractПредставлены конструкция аппаратуры, испояьзуемые арифметические алгоритмы и приложения к решению численных задач для интервальных арифметических сопроцессоров переменной разрядности. Эти сопроцессоры позволяют программисту устанавливать начальную разрядность вычислений, определять точность результатов и заново вычислять неточные результаты с большей разрядностью. Для уменьшения времени выполнения в численных приложениях используются пнтервально-арифмети ческие алгоритмы переменной разрядности. Рассмотрены три аппаратные схемы с щиной данных щириной 16, 32 и 64 бита. Эти схемы сравниваются по требуемой площади крисгалла, продолжительности рабочего пикяа и быстродействию в различных численных приложениях. Каджый из этих сопроцессоров может быть реализован на одном кристалле с рабочей частотой, сравнимой с сопроцессорами плавающей точки двойной точности стандарта IEEE. В некоторых численных приложениях наши сопроцессоры на два-четыре порядка быстрее, чем распространенные программные пакеты, реализующие интервальную арифметику переменной разрядности.

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