Hardware Support for Interval Arithmetic

Hardware Support for Interval Arithmetic

A hardware unit for interval arithmetic (including division by an interval that contains zero) is described in this paper. After a brief introduction an instruction set for interval arithmetic is defined which is attractive from the mathematical point of view. These instructions consist of the basic arithmetic operations and comparisons for intervals including the relevant lattice operations. T...

Diagrammatic Representation for Interval Arithmetic

The paper presents a diagrammatic representation of a standard interval space (the so-called MR-diagram), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined ...

A Hardware Approximation to Interval Arithmetic for Sine and Cosine Function

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

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. ...

Function Interval Arithmetic

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation sol...