Inside Macintosh: PowerPC Numerics / Part 1 - The PowerPC Numerics Environment

Chapter 1 - IEEE Standard Arithmetic

This chapter describes why IEEE standard floating-point arithmetic is important and why you should use it when programming. PowerPC Numerics is an implementation of the IEEE Standard 754 for binary floating-point arithmetic as well as the standard proposed by the Floating-Point C Extensions (FPCE) branch of the Numerical C Extensions Group (NCEG). This chapter explains the benefits that PowerPC Numerics provides by conforming to these standards. It provides an overview of both the IEEE and the FPCE recommendations--describing the scope of these standards and explaining how following them improves the accuracy of your programs. It provides some examples to demonstrate how much easier programming is when the standards are followed. Finally, it describes in general how PowerPC Numerics differs from the Standard Apple Numerics Environment (SANE).

You should read this chapter if you are unfamiliar with IEEE Standard 754 or the FPCE technical report and you want to find out more about them. If you are already familiar with these standards but you would like to find out how PowerPC Numerics implements them, you can skip to the next chapter.

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Chapter Contents

About the IEEE Standard

Starting to Use IEEE Arithmetic

Careful Rounding

Exception Handling

Example: Finding Zero Return Values

Example: Searching Without Stopping

Example: Parallel Resistances

Using IEEE Arithmetic

Evaluating Continued Fractions

Computing the Area of a Triangle

About the FPCE Technical Report

PowerPC Numerics Versus SANE