6.1 Introduction

The Fortran 95 floating-point environment on SPARC processors implements the arithmetic model specified by the IEEE Standard 754 for Binary Floating Point Arithmetic. This environment enables you to develop robust, high-performance, portable numerical applications. It also provides tools to investigate any unusual behavior by a numerical program.

In numerical programs, there are many potential sources for computational error:

• The computational model could be wrong

• The algorithm used could be numerically unstable

• The data could be ill-conditioned

• The hardware could be producing unexpected results

Finding the source of the errors in a numerical computation that has gone wrong can be extremely difficult. The chance of coding errors can be reduced by using commercially available and tested library packages whenever possible. Choice of algorithms is another critical issue. Using the appropriate computer arithmetic is another.

This chapter makes no attempt to teach or explain numerical error analysis. The material presented here is intended to introduce the IEEE floating-point model as implemented by Fortran 95.