Computer and Calculator Computation of Elementary Functions (UMAP)

This module considers methods used to approximate the elementary functions on digital computers and electronic calculators. The requirements for such approximations are discussed, with brief comments on hardware and error. Range reduction, polynomial approximations, and especially CORDIC techniques are emphasized. The square root, trigonometric, exponential, and logarithmic functions are treated in detail.

Table of Contents:

INTRODUCTION

BACKGROUND INFORMATION
Hardware Aspects
The base used for number representation
Integers vs. real-number representation and arithmetic
Hardware vs. software implementation of operations
Requirements of Function Evaluation Routines
Error Considerations

THE SQUARE ROOT
Calculator Computation of Square Root
Computer Computation of the Square Root

ELEMENTARY FUNCTIONS OF COMPUTERS
Preliminary Remarks
Computation of Elementary Functions
Computation of the exponential function
Evaluation of the natural logarithm

ELEMENTARY FUNCTIONS ON CALCULATORS
Sines, Cosines, and Tangents via CORDIC
The CORDIC algorithm for tangent
The CORDIC computation of sines and cosines
A CORDIC Algorithm for Arctangent
Derivation of the CORDIC algorithm for arctangent

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHORS