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Numerical Methods
Real-Time and Embedded Systems Programming
Author : Don Morgan
Publisher : M&T Publishing, Inc.
ISBN l-5585l-232-2

Overview
If you work with microprocessors or microcontrollers, you work with numbers. Whether it is a simple embedded machine-tool controller that does little more than drive displays, or interpret thumbwheel settings, or is a DSP functioning in a realtime system, you must deal with some form of numerics. Even an application that lacks special requirements for code size or speed might need to perform an occasional fractional multiply or divide for a D/A converter or another peripheral accepting binary parameters. And though the real bit twiddling may hide under the hood of a higher-level language, the individual responsible for that code must know how that operation differs from other forms of arithmetic to perform it correctly.

Embedded systems work involves all kinds of microprocessors and microcontrollers, and much of the programming is done in assembler because of the speed benefits or the resulting smaller code size. Unfortunately, few references are written to specifically address assembly language programming. One of the major reasons for this might be that assembly-language routines are not easily ported from one processor to another. As a result, most of the material devoted to assembler programming is written by the companies that make the processors. The code and algorithms in these cases are then tailored to the particular advantages (or to overcoming the particular disadvantages) of the product. The documentation that does exist contains very little about writing floating-point routines or elementary functions.

This book has two purposes. The first and primary aim is to present a spectrum of topics involving numerics and provide the information necessary to understand the fundamentals as well as write the routines themselves. Along with this information are examples of their implementation in 8086 assembler and pseudocode that show each algorithm in component steps, so you can port the operation to another target. A secondary, but by no means minor, goal is to introduce you to the benefits of binary arithmetic on a binary machine. The decimal numbering system is so pervasive that it is often difficult to think of numbers in any other format, but doing arithmetic in decimal on a binary machine can mean an enormous number of wasted machine cycles, undue complexity, and bloated programs. As you proceed through this book, you should become less dependent on blind libraries and more able to write fast, efficient routines in the native base of your machine.

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