Nox-Rhea WiKi

Hi there! I'm back, with the latest part in the series : Pregenerated arrays. This is a fairly simple concept that can treble the speed of your code, so have a look.

I still suggest that if you haven't got a copy of TEXTER that you get it.

This is shareware, written by me, that allows you to grab fonts and use them in your own programs.

I downloaded the Friendly City BBS Demo, an intro for a PE BBS, written by a new group called DamnRite, with coder Brett Step. The music was excellent, written by Kon Wilms (If I'm not mistaken, he is an Amiga weenie ). A very nice first production, and I can't wait to see more of their work. I will try con a local BBS to allow me to send Brett some fido-mail.

If you would like to contact me, or the team, there are many ways you can do it :
            1) Write a message to Grant Smith in private mail here on the Mailbox BBS.
            2) Write a message here in the Programming conference here on the Mailbox (Preferred if you have a general programming query or problem others would benefit from)
            3) Write to ASPHYXIA on the ASPHYXIA BBS.
            4) Write to Denthor, Eze or Livewire on Connectix.
            5) Write to :  Grant Smith
                           P.O.Box 270 Kloof
                           3640
                           Natal
            6) Call me (Grant Smith) at (031) 73 2129 (leave a message if you call during varsity)

NB : If you are a representative of a company or BBS, and want ASPHYXIA to do you a demo, leave mail to me; we can discuss it.

NNB : If you have done/attempted a demo, SEND IT TO ME! We are feeling quite lonely and want to meet/help out/exchange code with other demo groups. What do you have to lose? Leave a message here and we can work out how to transfer it. We really want to hear from you!

A lookup table is an imaginary table in memory where you look up the answers to certain mathematical equations instead of recalculating them each time. This may speed things up considerably. Please note that a lookup table is sometimes referred to as a pregenerated array.

One way of looking at a lookup table is as follows : Let us say that for some obscure reason you need to calculate a lot of multiplications (eg. 5*5 , 7*4 , 9*2 etc.). Instead of actually doing a slow multiply each time, you can generate a kind of bonds table, as seen below :

╔═Đ═╦═══════Đ══════Đ══════Đ══════Đ══════Đ══════Đ══════Đ══════Đ══════╗
ă─┼─Â   1   │  2   │  3   │  4   │  5   │  6   │  7   │  8   │  9   ║
ă─┴─Î═══════ě══════ě══════ě══════ě══════ě══════ě══════ě══════ě══════Á
║ 1 ║   1   │  2   │  3   │  4   │  5   │  6   │  7   │  8   │  9   │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 2 ║   2   │  4   │  6   │  8   │  10  │  12  │  14  │  16  │  18  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 3 ║   3   │  6   │  9   │  12  │  15  │  18  │  21  │  24  │  27  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 4 ║   4   │  8   │  12  │  16  │  20  │  24  │  28  │  32  │  36  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 5 ║   5   │  10  │  15  │  20  │  25  │  30  │  35  │  40  │  45  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 6 ║   6   │  12  │  18  │  24  │  30  │  36  │  42  │  48  │  54  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 7 ║   7   │  14  │  21  │  28  │  35  │  42  │  49  │  56  │  63  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 8 ║   8   │  16  │  24  │  32  │  40  │  48  │  56  │  64  │  72  │
ă───Î───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
║ 9 ║   9   │  18  │  27  │  36  │  45  │  54  │  63  │  72  │  81  │
╚═══╩───────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

This means that instead of calculating 9*4, you just find the 9 on the top and the 4 on the side, and the resulting number is the answer. This type of table is very useful when the equations are very long to do.

The example I am going to use for this part is that of circles. Cast your minds back to Part 3 on lines and circles. The circle section took quite a while to finish drawing, mainly because I had to calculate the SIN and COS for EVERY SINGLE POINT. Calculating SIN and COS is obviously very slow, and that was reflected in the speed of the section.

This is very simple. In my example, I am drawing a circle. A circle has 360 degrees, but for greater accuracy, to draw my circle I will start with zero and increase my degrees by 0.4. This means that in each circle there need to be 8000 SINs and COSes (360/0.4=8000). Putting these into the base 64k that Pascal allocates for normal variables is obviously not a happening thing, so we define them as pointers in the following manner:

        TYPE   table = Array [1..8000] of real;
 
        VAR    sintbl : ^table;
               costbl : ^table;

Then in the program we get the memory for these two pointers. Asphyxia was originally thinking of calling itself Creative Reboot Inc., mainly because we always forgot to get the necessary memory for our pointers. (Though a bit of creative assembly coding also contributed to this. We wound up rating our reboots on a scale of 1 to 10 ).

The next obvious step is to place our necessary answers into our lookup tables. This can take a bit of time, so in a demo, you would do it in the very beginning (people just think it's slow disk access or something), or after you have shown a picture (while the viewer is admiring it, you are calculating pi to its 37th degree in the background )

Another way of doing it is, after calculating it once, you save it to a file which you then load into the variable at the beginning of the program. Anyway, this is how we will calculate the table for our circle :

    Procedure Setup;
    VAR deg:real;
    BEGIN
      deg:=0;
      for loop1:=1 to 8000 do BEGIN
        deg:=deg+0.4;
        costbl^[loop1]:=cos (rad(deg));
        sintbl^[loop1]:=sin (rad(deg));
      END;
    END;

This will calculate the needed 16000 reals and place them into our two variables. The amount of time this takes is dependant on your computer.

This is very easy. In your program, wherever you put

               cos (rad(deg)),

you just replace it with :

               costbl^[deg]

Easy, no? Note that the new “deg” variable is now an integer, always between 1 and 8000.

Lookup tables may be used in many different ways. For example, when working out 3-dimensional objects, sin and cos are needed often, and are best put in a lookup table. In a game, you may pregen the course an enemy may take when attacking. Even saving a picture (for example, a plasma screen) after generating it, then loading it up later is a form of pregeneration.

When you feel that your program is going much too slow, your problems may be totally sorted out by using a table. Or, maybe not.

As you have seen above, lookup tables aren't all that exciting, but they are useful and you need to know how to use them. The attached sample program will demonstrate just how big a difference they can make.

Keep on coding, and if you finish anything, let me know about it! I never get any mail, so all mail is greatly appreciated

Sorry, no quote today, it's hot and I'm tired. Maybe next time

Denthor