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 spedfy the predsion 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 gready 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 d0uble-predsion floating point processors. 1-IporpaMMHl IntroductionAdvances in VLSI technology and computer architecture have lead to increasingly faster digital computers. During each of the last three decades, the computational speeds of the fastest computers increased by a factor of roughly 100 [1]. This increase in computing power has lead to the development of computer systems which perform billions of arithmetic operations per second and has given researchers the ability to solve previously intractable problems. The large number of arithmetic operations, however, has made it extremely important to keep track of and control errors in numerical computations.

A family of variable-precision interval arithmetic processors

“…Conclusions are presented in Section 5. This paper is an extension of the research presented in [27], [28]. More detailed information about the processors is given in [29].…”

Variable-precision, interval arithmetic coprocessors

“…To facilitate the use of interval arithmetic, these processors provide the four rounding modes specified by the IEEE 754 floating point standard [15]. A software interface to the VPL~Cs is presented in [29]. Although these processors improve the speed of variable-predsion computations, they do not provide special instructions for inte~wat arithmetic or vector and matrix operations.…”