A coprocessor for accurate and reliable numerical computations

Abstract

This paper presents the architecture and hardware design of a special-purpose coprocessor that performs variable-precision, interval arithmetic. Variable-precision arithmetic allows the precision of the computation to be specified, based on the problem to be solved and the required accuracy of the results. Interval arithmetic produces two values for each result, such that the true result is guaranteed to be between the two values. The coprocessor gives the programmer the ability to specify the precision of the computation, determine the accuracy of the results, and recompute inaccurate results with higher precision. Direct hardware support for variable-precision, interval arithmetic greatly improves the accuracy and reliability of numerical computations. Execution time estimates indicate that the coprocessor is two to three orders of magnitude faster than an existing software package for variable-precision, interval arithmetic.