Variable-precision, interval arithmetic coprocessors

This chapter presents the design and analysis of variable-precision, interval arithmetic processors. The processors give the user the ability to specify the precision of the computation, determine the accuracy of the results, and recompute inaccurate results with higher precision. The processors support a wide variety of arithmetic operations on variable-precision oating point numbers and intervals. EEcient hardware algorithms and specially designed functional units increase the speed, accuracy, and reliability of numerical computations. Area and delay estimates indicate that the processors can be implemented with areas and cycle times that are comparable to conventional IEEE double-precision oating point coprocessors. Execution time estimates indicate that the processors are two to three orders of magnitude faster than a conventional software package for variable-precision, interval arithmetic. 1.1 INTRODUCTION Floating point arithmetic provides a high-speed method for performing sci-entiic computations. Modern personal computers and workstations perform millions of oating point operations per second 1-1], 1-2]. Unfortunately, however, roundoo error and catastrophic cancellation in oating point computations can quickly lead to results that are completely inaccurate 1-3], 1-4]. Consequently, a method is needed for monitoring and controlling errors in oat-ing point computations. Most computer systems, however, do not provide an eecient mechanism to specify the precision of the computation or determine the accuracy of the results.