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:: CORDIC demo 8 ::
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8b education intro for ZX Spectrum 16k

  Code: Busy soft
  Create: 25.01.2025
  Release: LoveByte 2025

This intro shows simplified CORDIC algorithm
intended for computing size of two-dimensed vector.

Now some math theory follows :)


Pythagorean Theorem
===================

It provides this computation, based od Pythagorean Theorem:

  Size = SQR(X^2+Y^2)

Where X and Y are vector coordinates.
For more info about Pythagoras, look here:
https://en.wikipedia.org/wiki/Pythagorean_theorem


CORDIC in general
=================

The CORDIC itself is based on rotating the vector.
It starts with a vector whose X coordinate is
positive whereas the Y coordinate is arbitrary.
Successive rotations have the goal of rotating the vector
to the X axis and therefore reducing the Y coordinate to zero.
When the Y is zero, the X coordinate is size of the vector.

For more info about generic CORDIC, look here:
https://en.wikipedia.org/wiki/CORDIC


Bresenham's circle drawing algorithm
====================================

For the rotating of vector,
the reverse bresenham's circle drawing algorithm is used.

Originally, it is used for successive rotations the initial
vector [X,0] - with X coordinate (it is radius) on the X asix and Y zero,
to the another vector [new_x,new_y) with the same size,
but in our case, we reverse the direction of rotating
and the goal is to get the vector to the X axis.

For more info about bresenham's circle algorithm, look here:
https://www.geeksforgeeks.org/bresenhams-circle-drawing-algorithm/


Conclusion of theory
====================

It is possible to imagine our work by this way:

Let's have a circle with unknown radius and middle at [0,0].
Let's have a point [X,Y] what is situated anywhere on the circle.
Now we move this point on the circle until its Y coordinate is not zero.
When Y coordinate of the point is zero, the X coordinate is equal
to the radius of the circle and it is our wanted size of vector [X,Y].


Implementation
==============

  Input: C = coordinate X
         B = coordinate Y

 Output: C = result = SQR(X^2+Y^2)

        ld      a,c
    L1: sub     b
        jr      nc,L2
        inc     c
        add     c
    L2: djnz    L1

 Register C contains X coordinate, what are increased by rotating vector or moving point on the circle.
 Register B is counter of iterations or successive rotations, it is initialized to coordinate Y.
 Register A holds bresenham's iterator used for computation. At begin, it is initialized to coordinate X.

To proper working of this simplified routine, a few mandatory conditions must be fulfilled:

   (X^2+Y^2) < 65536 ... Since result is 8 bit only, we must make sure to not produce overflow
   Y <= X .............. Number of iterations cannot be bigger than input coordinate X
   Y > 0 ............... Number of iterations in priciple can be zero (then result is directly X)
                         but due to using DJNZ, zero means 256 iterations and it is not good