# Computer and Calculator Computation of Elementary Functions (UMAP)

### Author: Richard J. Pulskamp and James Delaney

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:INTRODUCTIONBACKGROUND 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

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHORS

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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