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

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.