CORDIC algorithms

[MaxCuriosus]

Does anyone know where I can find examples of CORDIC algorithms written in Pascal?

[Thaddy]

I used a CORDIC implementation in UCSD Pascal on an Apple 2e while teaching computer science introduction in programming at University in 1982 ... So a little over 41 years ago.
I also wrote one in TurboPascal in 1989 based on the UCSD code.
I do no have the code anymore, but I can write a CORDIC easily, since it is not very difficult. So if you can not find it, ping me.

I think you can find a CORDIC for Pascal anyway since it is quite common to use.
edit
On Rosetta code is a quite good example in C that will easily translate. It is not a full task yet. Google Rosetta code cordic. The C code will translate in minutes, not hours.It uses look/up tables for some of the trigonometric functions so it is fast.
This afternoon I have some time left so I will add it here if there isn´t a link or code yet.

[avra]

I did Taylor series for AvrCo fixed point lib, so if needed ping me

[BlueIcaro]

Hello, I found this C code. https://people.math.sc.edu/Burkardt/c_src/fn/fn.html
It has a lot of comments. I think I't we easy port to Pascal

/BlueIcaro

[Thaddy]

I am close to clean up the C  translated code from Rosetta code and will post it tomorrow. Just need to fix the example, basically Pascalify it, but the core function  is ready and did not take too much time, as I expected.

BTW the UCSD version from 41 years ago showed up in Google....
For good measure, though.
I used the ucsd version for teaching purposes, but did not write it.
I wrote a TurboPascal version

A good reader would have understood that.

[AlexTP]

@Thaddy,
1. let's create the wiki page, and post examples there. Easy for future users to google it.

2. what function is discussed: sin, cos, tan, sqrt, other?

[Thaddy]

I will open a wiki subject and when verified also post it to Rosetta code.
Strange to visit the subject after 40 odd years.

[MarkMLl]

Strange to visit the subject after 40 odd years.

Maybe, maybe not. We're all of us getting older, and that sometimes leads us to revisit and tidy up- or at least explore- "loose ends".

http://www.hp9825.com/html/osborne_s_story.html

https://hackaday.com/2013/08/30/ken-shirriff-completely-reverse-engineers-the-1974-sinclair-scientific-calculator/

We might not do it for the right reasons, but at least we do it.

MarkMLl

[MaxCuriosus]

1) Publishing CORDIC algorithms in Pascal is a good idea. It is one more opportunity to highlight the excellence of the Pascal language.

2) The reason of my original post is to see the algorithm to compute the square root and to compare it with the various non-CORDIC based ones.

3) Is there a snowball chance that somebody know or remember the square root algorithm type used in the math package (assembler) used in DEC PDP11? In the late 70s I saw the source printout of that routine but I don't remember the algorithm type. 

[jamie]

Well I know how to do it on paper and its been a while since I have done it.

But I remember you had to add 2 zeros to each remainder and go from there.

[MathMan]

...

2) The reason of my original post is to see the algorithm to compute the square root and to compare it with the various non-CORDIC based ones.

3) Is there a snowball chance that somebody know or remember the square root algorithm type used in the math package (assembler) used in DEC PDP11? In the late 70s I saw the source printout of that routine but I don't remember the algorithm type.

2) You'll probably be disappointed - FP math libraries have seen tremenduous improvements over the last 20 years.

3) Maybe this - http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf - it at least references the PDP11 as using it.

Cheers,
MathMan

[Thaddy]

Hello, I found this C code. https://people.math.sc.edu/Burkardt/c_src/fn/fn.html
It has a lot of comments. I think I't we easy port to Pascal

/BlueIcaro

I am impressed by the cleanliness of that code, but I would suggest not to translate it, but compile it into a library and add just a pascal header.
Just compile in C and translate cordic.h with h2pas seems enough at first glance. Looks a bit of overkill to translate cordic.c to Pascal, although that can be done. There should not be many issues with h2pas, except maybe some type declarations like int4 which means a 32 bit integer type. I believe cint is already always 32 bit.

FYI the Rosetta code translation will follow later today, I hope. That is less clean but works.

[Curt Carpenter]

For a nice short review of the math, see https://www.allaboutcircuits.com/technical-articles/an-introduction-to-the-cordic-algorithm/

[Thaddy]

Here's 'a' version of a CORDIC function, but it still is not what I have in mind. But it does NOT work as advertised and is reasonably compact. It contains a bug that I have to recover from and discovered after posting.

Code: Pascal  [Select][+][-]

1. {$mode objfpc}
2. uses math;
3. const
4.   ArctanTable: array[0..29] of double = (
5.     0.7853981633974483, 0.4636476090008061, 0.24497866312686414,
6.     0.12435499454676144, 0.06241880999595735, 0.031239833430268277,
7.     0.015623728620476831, 0.007812341060101111, 0.0039062301319669718,
8.     0.0019531225164788188, 0.0009765621895593195, 0.0004882812111948983,
9.     0.00024414062014936177, 0.00012207031189367021, 6.103515617420877e-05,
10.     3.0517578115526096e-05, 1.5258789061315762e-05, 7.62939453110197e-06,
11.     3.814697265606496e-06, 1.907348632810187e-06, 9.536743164059608e-07,
12.     4.7683715820308884e-07, 2.3841857910155797e-07, 1.1920928955078068e-07,
13.     5.960464477539055e-08, 2.9802322387695303e-08, 1.4901161193847655e-08,
14.     7.450580596923828e-09, 3.725290298461914e-09, 1.862645149230957e-09
15.   );
16.  
17. // function CORDIC(var x, y: double;const  n: Integer): double; //todo
18. function CORDIC(x, y: double;const  n: Integer): double;
19. var
20.   i: Integer;
21.   d, tx, ty: double;
22. begin
23.   if x = 0 then
24.   begin
25.     Result := y;
26.     Exit; // get rid of exit
27.   end;
28.   if y = 0 then
29.   begin
30.     Result := x;
31.     Exit;// get rid of exit
32.   end;
33.   if x < 0 then
34.   begin
35.     x := -x;
36.     y := -y;
37.   end;
38.   d := 1;
39.   tx := x;
40.   ty := y;
41.   for i := 0 to n - 1 do
42.   begin
43.     if ty < 0 then
44.     begin
45.       x := x + d * ty;
46.       y := y - d * tx;
47.       ArctanTable[i] := ArctanTable[i] - ArctanTable[i];
48.     end
49.     else
50.     begin
51.       x := x - d * ty;
52.       y := y + d * tx;
53.     end;
54.     d := d / 2;
55.     tx := tx / 2;
56.     ty := ty / 2;
57.   end;
58.   Result := x;
59. end;
60. begin
61. end.

Examples will follow, but I think the internals can still be improved.

[BlueIcaro]

Hello, I found this C code. https://people.math.sc.edu/Burkardt/c_src/fn/fn.html
It has a lot of comments. I think I't we easy port to Pascal

/BlueIcaro

I am impressed by the cleanliness of that code, but I would suggest not to translate it, but compile it into a library and add just a pascal header.
Just compile in C and translate cordic.h with h2pas seems enough at first glance. Looks a bit of overkill to translate cordic.c to Pascal, although that can be done. There should not be many issues with h2pas, except maybe some type declarations like int4 which means a 32 bit integer type. I believe cint is already always 32 bit.

FYI the Rosetta code translation will follow later today, I hope. That is less clean but works.

Hi, that's true, and better idea than nime.
/BlueIcaro