Cordic Trig Functions with PicBasic Pro

This include file allows you to perform the arctangent (atan2) & hypotenuse or sine & cosine. It uses an cordic equation, written in assembly to get to a quick 16 bit solution. This solution is accurate within 0.01%, according to the original author. The results of sin and cos are returned as a pair, in the same step. Also, the results of atan2, and the hypotenuse is also given as a pair in one step. See www.chiefdelphi.com/media/papers/2016 for more information. Using the code from Pat Fairbank, I modified it to work with PicBasic Pro, on a PIC18F device. (This was done with a lot of help from Darrel Taylor). The original code was touted to be 90 times faster than math.h, if you are into C.

Atan2 can be used to calculate distance and heading to lat and long co-ordinates, and also to calculate tilt, among many other equations.

Examples for use:
sincos example:

ang : input angle in degrees.dd example: ang = 3000 (= 30.00 degrees)
call sincos
result : x = 15004 , y = 25981
so, 15004/30000 = sin(ang) = 0.5001 and 25981/30000 = cos(ang) = 0.8660

atan2 example:
input x,y co-ordinates
x = 25981, y = 15000
call atan2
result: x = 29998 = hypotenuse or distance to x,y, y = angle to x,y in degrees.dd = 5998 (=59.98 degrees), ang = 5463 = radians 0 to 65535

For more info, see the thread here www.picbasic.co.uk/forum/showthread.php

Quoted from www.dspguru.com/info/faqs/cordic.htm :
"CORDIC is an acronym that stands for COordinate Rotation DIgital Computer, and was coined
by Volder [Volder 59]. Its concepts have been further developed to include calculation of the Discrete
Fourier Transform [Despain 74], exponential, logarithm, forward and inverse circular and hyperbolic
functions, ratios and square roots [Chen 72] [Walther 71], and has been applied to the antialiasing
of lines and polygons [Turkowski 82].

It is an iterative fixed-point technique that achieves approximately one more bit of accuracy with
each iteration. In spite of merely linear convergence, the inner loop is very simple, with arithmetic
that consists of only shifts and adds, so it is competitive with (and even outperforms) floating-
point techniques with quadratic convergence, for the accuracy typically required for 2-dimensional
raster graphics."

by scalerobotics