cordic

Demonstration of the working of the CORDIC algorithms.

Introduction

CORDIC is a set of hardware optimized implmentations of many calculator functions. This implementation emphasizes on decimal calculations.

The CORDIC loop

All functions use the same loop that consists of only the following operations:

• addition and subtraction
• shifting (per digit) of values
• table lookup (only four tables of 6 entries for the whole program!)
• check the sign of a value This is why CORDIC is still used today in hardware optimized evaluation on FPGAs.

Implemented functions

This program implements:

• multiplication and division
• sin, cos in degrees and radians
• atan in degrees and radians
• sinh and cosh
• atanh
• tan and tanh (using two CORDIC operations)
• hypot (sqrt(x2+y2) using two CORDIC operations
• exp, log, sqrt

Goal of the file

The goal is to showcase the working of CORDIC. That's why there is a very limited class Fixed that defines fixed point numbers with only a few operations:

• addition
• subtraction, negation
• shifting to the right (with proper rounding)
• comparing with a given value giving the difference as a number of digits (for accuracy measurements)
• comparing "greater than 0" and nothing else
• (left) multiplication with -1, 0 and 1

All the operations above are calculated using Fixed numbers. Setup is using regular floats, of course.