In a comment to my recent article about VARPTR, Rogelio Perea chimed in…

Still learning something new about the CoCo even after all the years, excellent article!

Would there ever be one about DEFFN? :-)

–  Rogelio Perea II, 7/19/2022

Challenge accepted.

DEF FN: Definitely Fun?

There are many features of Microsoft Color BASIC that went right over my head when I was learning to program as a junior high school kid. DEF FN was certainly one of them.

My first CoCo came with Extended Color BASIC, and that was required to use DEF FN. But what is is? According to Getting Started with Extended Color BASIC:

Extended Color BASIC has one numeric function, DEF FN, that is unlike any others we’ve talked about so far. DEF FN lets you create your own mathematical function. You can use your new function the same as any of the available functions (SIN, COS, TAN, and so on). Once you’ve used DEF FN to define a function, you may put it to work in your program by attaching the prefix FN to the name you assign to the new function. Here is the syntax for DEF FN:

DEF FN name (variable list) – formula

name is the name you assign to the function you create.
variable list contains one “dummy variable” for each variable to be used by the function.
formula defines the operation in terms of the variables given in the variable list

Note: Variable names that appear in formula serve only to define the formula; they do not affect program variables that have the same name. You may have only one argument in a formula call; therefore, DEF FN must contain only one variable.

You may use DEF FN only in a program, not in the immediate mode.

– Getting Started with Color BASIC, page 177.

I think my work here is done.

Until next time…

Okay, maybe not.

DEF FN: Define Function

There are commands in BASIC, such as PRINT and GOTO, and then there are functions that return values, such as SIN, ABS and INT.

PRINT SIN(42)
-.916521549

X=-42
PRINT ABS(X)
42

X=4.2
PRINT INT(X)
4

DEF FN allows you to create your own function that returns a value.

A simple example

We start with a simple example. What if you wanted a function that added 42 to any value you passed in? I will call this function “UA” (for “Ultimate Answer”) and define it as follows:

10 DEF FNUA(N)=N+42
20 PRINT FNUA(10)

If I run that, it will print 52. The new “function” FNUA(x) returns whatever you pass in with 42 added to it. Tada!

Function names seem to follow the same rules as variable names so you can have one or two letters (A to Z, AA to ZZ) or a letter and a number (A0 to Z9).

In the parens is a parameter that also follows the same rules of a variable. The parameter is just a placeholder so you have something to use in your new formula on the right of the equal sign. If you did DEF FNA(X) then after the equal you’d have whatever you want to happen to X. When the user calls it with FNA(123) then 123 goes to where the X was in the formula after the equals… Neat.

It’s kind of like a C function with only one parameter, now that I think about it/

// fnua(n) - return n plus 42
int fnua(float n)
{
    return n+42;
}

int main()
{
    float x = fnua(10);

    printf ("x = %f\n", x);

    return EXIT_SUCCESS;
}

You can have DEF FNA(X) or DEF FNZZ(AB) or any combination.

What can you use it for?

The manual gives an example of doing math with a long floating point value so you don’t have to have that value in your code everywhere you want to use it.

7 DEF FNR(X)=X/57.28577951
6 AA=FNR(AA): AB=FNR(AB): AC=FNR(AC)

At least I’m not the only one with code snippets that don’t really do anything.

Of course, for something like this you could have placed that number in a variable which would be faster than parsing a long number (in most cases). Still, if the formula itself is big, it could save typing, I guess.

Benchmarks, anyone?

I was curious if it would be any faster for other types of maths…

Suppose I want to use PRINT@ to put a character on the text screen, but want to use PEEK to see if it “hits” another character on the text screen. I would use the PRINT@ positions of 0-511, but I’d want to PEEK the screen memory locations of 1024-1535.

10 CLS:P=0
20 FOR I=1 TO 20:PRINT@RND(511)-1,"X";:NEXT
30 PRINT @P,"*";
40 A$=INKEY$:IF A$="" THEN 40
50 IF A$="W" THEN NP=P-32:GOTO 90
60 IF A$="A" THEN NP=P-1:GOTO 90
70 IF A$="S" THEN NP=P+32:GOTO 90
80 IF A$="D" THEN NP=P+1
90 IF NP<0 THEN 40
100 IF NP>510 THEN 40
110 IF PEEK(NP+1024)<>96 THEN 40
120 PRINT @P," ";
130 P=NP
140 GOTO 30

Above is a program that will clear the screen and put X characters in random positions. The player is an asterisk in the top left of the screen. Using the keys W (up), A (left), S (down) and D (right) will move the asterisk around the screen. Checks ensure you cannot go off the top or bottom of the screen, or run in to an X.

Line 110 does the conversion from PRINT@ position to PEEK position. Maybe we can do this:

0 ' defusr2.bas
10 CLS:P=0
15 DEF FNP(X)=X+1024
20 FOR I=1 TO 20:PRINT@RND(511)-1,"X";:NEXT
30 PRINT @P,"*";
40 A$=INKEY$:IF A$="" THEN 40
50 IF A$="W" THEN NP=P-32:GOTO 90
60 IF A$="A" THEN NP=P-1:GOTO 90
70 IF A$="S" THEN NP=P+32:GOTO 90
80 IF A$="D" THEN NP=P+1
90 IF NP<0 THEN 40
100 IF NP>510 THEN 40
110 IF PEEK(FNP(NP))<>96 THEN 40
120 PRINT @P," ";
130 P=NP
140 GOTO 30

The behavior is the same, and now I get the benefit of it not having to parse “NP+1024” each time. Parsing decimal values is slow. On Extended BASIC I could have replaced 1024 with hex &H400 and that would have been faster. For more speed, I could have used a variable and had “NP+S” or whatever.

But is it faster?

0 ' defbench1.bas
5 P=0
10 TIMER=0
20 FOR A=1 TO 1000
30 Z=P+1024
40 NEXT
50 PRINT TIMER

Doing “P+1024” 1000 times prints 481.

0 ' defbench2.bas
5 P=0
6 DEF FNP(X)=X+1024
10 TIMER=0
20 FOR A=1 TO 1000
30 Z=FNA(P)
40 NEXT
50 PRINT TIMER

That version prints 603. Not faster. The overhead of FN seems to be more than just doing it directly. In a way, this makes sense because in-lining code in assembly or C is faster than calling it as a subroutine/function.

But let’s try more… We could also include other things in the function, like the PEEK itself.

0 ' defbench3.bas
5 P=0
6 DEF FNP(X)=PEEK(X+1024)
10 TIMER=0
20 FOR A=1 TO 1000
30 Z=FNP(P)
40 NEXT
50 PRINT TIMER

That one prints 690, and if you had just done “30 Z=PEEK(P+1024)” it would have been 572.

Cool, but definitely slower. I believe this is because it’s still storing that formula in a buffer somewhere and executing it as if you’d just typed it in. Indeed, if you change the formula to use hex:

0 ' defbench3.bas
5 P=0
6 DEF FNP(X)=PEEK(X+&H400)
10 TIMER=0
20 FOR A=1 TO 1000
30 Z=FNP(P)
40 NEXT
50 PRINT TIMER

…it prints 480, which means it’s parsing that formula each time instead of converting it to a number when you define it.

Pity. It would have been really cool if this had been a way to bypass the detokenizer stuff in BASIC and speed up routines like that.

FN Conclusion

DEF FN is slower. I don’t see any example where it speeds anything up. With that said, I expect I’d use DEF FN if…

• I had a custom function I used in multiple places, and wanted to maintain it in just one spot. This would be more efficient, perhaps, than making it a GOSUB subroutine.
• I needed to save some bytes of BASIC memory.
• I wanted to write an example that fix things on small lines on the screen, just for appearances.

For anything else, I think I’d just put it in and make the program a bit faster.

Where else might one use this?

More examples

Sebastian Tepper commented to another post with a more useful example for DEF FN. There are many times when we use two PEEKs to get a 16-bit value from two bytes in memory:

V=PEEK(25)*256+PEEK(27)

Sebastian mentioned using DEF FN for this:

DEF FNP(AD)=PEEK(AD)*256+PEEK(AD+1)

V=FNP(25)

That’s very cool, and something I could see myself using. I wish I had thought of that when I was doing all my “Color BASIC memory location” articles, since I typed the double PEEK lines over and over and over…

But that’s not all…

The defined function can also use other variables. You can only pass one in, but any variable that is declared at the time the FN is used may be used. You could do this:

10 DEF FNA(X)=X*Y
20 Y=10
30 PRINT FNA(Y)
RUN
50

Above, you pass in a value for “X” and it returns the value multiplied by whatever Y is at that moment. You could create more complex formulas that way, but it kind of defeats the purpose.

Speaking of defeating the purpose, here are more silly examples. Using it to replicate PEEK:

10 DEF FNP(X)=PEEK(X)
20 PRINT FNP(1024)

How about returning if something is true or not? Like, is a memory location outside screen memory?

…but that sure looks like it would be really slow. Still neat, though. You could do:

IF FNL(L) THEN PRINT"NOT IN SCREEN MEMORY"

It does make the code look neater — especially if something is being checked multiple times (such as checking four ghost in Pac-Man or whatever).

What other examples can you think of? Leave a comment.

Until next time…

See also: part 1 and part 2.

In the first part, the following Color BASIC program was shared:

5 CLEAR 100*255
10 MX=99
20 DIM A$(MX):AL=0:DL=-1
30 SZ=RND(255):SZ=255
40 A$=STRING$(SZ,"X")
50 GOSUB 1000:GOTO 30
999 END

1000 REM
1001 REM ADD NEW STRING
1002 REM
1010 IF AL=DL THEN GOSUB 2000
1020 GOSUB 3000:IF Z<1024 THEN GOSUB 2000
1030 PRINT "ADDING";LEN(A$)"BYTES AT";AL;Z
1040 A$(AL)=A$
1050 AL=AL+1:IF AL>MX THEN AL=0
1060 IF DL=-1 THEN DL=0
1070 RETURN

2000 REM
2001 REM DELETE OLD STRING
2002 REM
2010 PRINT ,"DELETING";DL
2020 A$(DL)=""
2030 DL=DL+1:IF DL>MX THEN DL=0
2040 GOSUB 5000
2050 RETURN

3000 REM
3001 REM GET FREE STRING SPACE
3002 REM
3010 Z=(PEEK(&H23)*256+PEEK(&H24))-(PEEK(&H21)*256+PEEK(&H22))
3020 RETURN

5000 REM
5001 REM PAUSE
5002 REM
5010 PRINT"[PAUSE]";
5020 IF INKEY$="" THEN 5020
5030 PRINT STRING$(7,8);:RETURN

The program allocates enough string space to hold 100 strings of 255 bytes each. It then starts adding line after line until it detects string memory is getting low. When that happens, the oldest line is deleted (set to “”). The process continues…

The “gut feeling” was that this program should have been able to hold 100 full sized strings, but since it did use a temporary A$ (created to be 255 strings line, and the string we would be adding to the array), it seemed logical that it would have to start purging lines maybe a few entries before the end.

But instead, it starts deleting lines at around entry 47. And, the memory usage being printed out shows it drops by 510 byes each time instead of 255.

510 is an interesting number. That is 255 * 2. That makes it seem like each time we add a 255 byte string, we are using twice that memory.

And we are!

Strings may live again to see another day

The key to what is going on is in the main loop starting at line 30. We create a new A$ and set it to a string of 255 X’s. That string has to be stored somewhere, so it goes in to string memory. Then we do the GOSUB and add a string to the array, which copies our A$ in to the array A$(AL) entry.

When we go back to 30 for the next round, we create A$ again. The old copy of A$, in string memory, is deallocated, and a new A$ is created at the current string memory position. BASIC does not see if the old string space is large enough to be re-used. It just moves on to a new allocation of string space.

It looks like this… And note that strings fill from the end of the memory and move lower. Let’s say we have 16 bytes of reserved string memory (just to keep things fitting on this screen).

FRETOP points to where reserved string memory begins. MEMSIZ is the end of string memory. If we had done CLEAR 16, then FRETOP would be MEMSIZ-16.

STRTAB is where the next string will be added. It looks like this:

FRETOP                                     MEMSIZ
 |                                            |
[.][.][.][.][.][.][.][.][.][.][.][.][.][.][.][.]
                                              |
                                           STRTAB 

Let’s say we create a 4-byte A$=STRING(4, “X”) (“XXXX”) that we plan to add to an array. It will be stored in string memory:

FRETOP                                     MEMSIZ
 |                                            |
[.][.][.][.][.][.][.][.][.][.][.][.][X][X][X][X]
                                  |
                               STRTAB 

Later in the code, we assign that to the array, such as A$(0)=A$. Now A$(0) gets a copy of A$, and it looks like this (using lowercase ‘x’ to represent the copy of A$ that was put in A$(0)):

FRETOP                                     MEMSIZ
 |                                            |
[.][.][.][.][.][.][.][.][x][x][x][x][X][X][X][X]
                      |
                   STRTAB 

When we go back to do this again, a new A$ is created, and it gets stored next. The old string data is still there, but A$ has been updated to point to the new entry.

FRETOP                                     MEMSIZ
 |                                            |
[.][.][.][.][X][X][X][X][x][x][x][x][X][X][X][X]
          |
       STRTAB

…and so on. As you can see, the way this loop was written, it is creating a new A$ every time through, copying it to the array (a new entry for that) and so on. That is why we see 510 each time through instead of just 255.

Now, if the string was short, we could have done A$=”XXXXXXXXXXXXX”. If we did that, the string would exist in program space and not in string memory. But we wanted a 255 byte string, and you can’t type a line that long in BASIC so STRING$() was used instead, which requires putting the string in string memory.

However, since in THIS version we are just using the same 255 character A$ over and over again, let’s make one change so we don’t create it every time through the loop. Just change the GOTO 30 in line 50 to be GOTO 50:

30 SZ=RND(255):SZ=255
40 A$=STRING$(SZ,"X")
50 GOSUB 1000:GOTO 50

Now the program will create one A$, which will store at the start of string memory, and then loop over and over just making new entries in the array.

That small change will instantly change the results to be more like we might have expected. Now we get all the way to entry 94 before any string deleting happens:

And, from looking at that screen, each number is dropping by 255 bytes as we expected.

By the time it reached line 94, it saw that there were less than 1024 bytes of free string space left. 1024 would have held another four 255 byte strings, meaning actually had enough memory to have gotten to line 98 — just one line short of our max 99 before it rolls over. And that memory is where the initial 255-byte A$ is stored.

Tada! Mystery solved.

But wait! There’s more…

The reason I chose 1024 as a threshold was to allow for other temporary string use in the program. Things like LEFT$, MID$, STRING$ all make temporary strings. When you add two strings together it creates a third string that combines the first two. Be sure to check out my string theory article for more details on this — I learned quite a bit when researching it. I also learned that some things required strings that I did not expect to. Fun reads. Helps put you to sleep.

If I modify line 1020 to check for 255 bytes remaining instead of 1024, then re-run, I get this:

…and that is as perfect as it gets. Array is filled with strings 0-98, plus the temporary string, which is a total of 100 strings of 255-bytes each — and that is how much memory we set aside with CLEAR!

Now how much would you pay?

And because this program is self-aware when it comes to knowing how much string space is there, it can actually operate with much less string space. It will just delete old strings sooner.

You can change the CLEAR in line 5 to something smaller, like 2000, and it will still work. But, 2000/255 is 7, so it has room for the A$ plus six array entries. I expect it would DELETE every 6 lines. Let’s try…

Bingo! After lines 0-5 (six lines) it deleted and old one, then since everything was now full, it had to delete every time it added something new.

And the point is…?

Well, let’s just say I wish I knew about this back in 1983 when I wrote my cassette-based Bulletin Board System, *ALLRAM*.

I always wanted to write version 2.0.

Until next time…

See also: part 1 and part 2.

This program demonstrates Color BASIC’s string garbage collection. As strings are manipulated, string memory used will continue to grow until BASIC decides to clean up the string space and move things around a bit.

The program creates a string array and fills each entry up with string data. Using code that checks how much string space is remaining, it will delete old strings if string memory is low.

Watching it run reveals some curious things…

The Program

On an Extended or Disk BASIC system, you will need to do a PCLEAR 1 to get enough memory to run it.

• Initialization
  • Line 5 – We CLEAR enough string space to hold 100 lines at their largest size of 255 characters. Note that when you use DIM to set an array size, it is base-0. Doing a DIM A$(99) gives you A$(0) to A$(99) — 100 elements. Thus, the CLEAR uses 100, but the DIM in the next line uses 99.
  • Line 10 – MX represents the maximum number of lines in the array.
  • Line 20 – DIM A$(MX) creates an array of 0-99 entries (100). AL is set to 0, and will be the line (array entry) we will ADD next. DL will be used to track the next line (array entry) we need to delete. DL is set to -1 for “nothing to delete yet.”
• Main Loop
  • Line 30 – SZ is set to the length of the string we want to add. It has an unused RND at the start, but then SZ is hard-coded to 255. The program was designed to test random lengths of strings, but for this demo, we will be overriding that and making every string the maximum size.
  • Line 40 – GOSUB 1000 goes to a routine that will ADD a line. Then we GOTO 30 to create a new line and do it again.
• Add New String subroutine
  • Line 1010 checks to see if the ADD line has caught up to the DELETE line. If it has, we GOSUB 2000 to handle deleting the delete line.
  • Line 1020 – GOSUB 3000 will return the amount of free string space in Z. If Z is less than 104, GOSUB 2000 is called to delete a string.
  • Line 1030 – It prints how long of a string is being added to which line, followed by the current free string space before the add.
  • Line 1040 – The string is added to the A$ array at position AL.
  • Line 1050 – AL (add line) is incremented by 1, moving it to the next line of the array. If AL is larger than the MX (max array entries), it will wrap around to entry 0.
  • Line 1070 – Returns.
• Delete Old String subroutine
  • Line 2010 – Print which line is about to be deleted (set to “”).
  • Line 2020 – The A$ entry at position DL is set to “”, releasing the string memory it was using.
  • Line 2030 – DL (delete line) is incremented by one. If DL is larger than MX (max array entries), it will wrap around to entry 0.
  • Line 2040 – GOSUB 5000 is a pause routine so we can see what just happened.
• Get Free String Space routine
  • Line 3010 – Z is calculated as the difference between the FRETOP (start of string storage) memory location and the STRTAB (start of string variables) in the reserved string area. This gives us how many bytes of unused string memory is available.
  • Line 2030 – Returns.
• Pause subroutine
  • Line 510 – Print the message “[PAUSE]” with no carriage return at the end.
  • Line 5020 – If INKEY$ returns nothing (no key pressed), keep checking.
  • Line 5030 – Prints a string of 7 CHR$(8)s (backspace character) which will erase over the “[PAUSE]” prompt.

Based on the intent, one might think that running this would fill strings up to around entry 100, and then it would start deleting the old string

But is that what it will do?

Let’s run it and find out.

5 CLEAR 100*255
10 MX=99
20 DIM A$(MX):AL=0:DL=-1
30 SZ=RND(255):SZ=255
40 A$=STRING$(SZ,"X")
50 GOSUB 1000:GOTO 30
999 END

1000 REM
1001 REM ADD NEW STRING
1002 REM
1005 IF AL=DL THEN GOSUB 2000
1006 GOSUB 3000:IF Z<1024 THEN GOSUB 2000
1010 PRINT "ADDING";LEN(A$)"BYTES AT";AL;Z
1020 A$(AL)=A$
1030 AL=AL+1:IF AL>MX THEN AL=0
1040 IF DL=-1 THEN DL=0
1050 RETURN

2000 REM
2001 REM DELETE OLD STRING
2002 REM
2010 PRINT ,"DELETING";DL
2020 A$(DL)=""
2030 DL=DL+1:IF DL>MX THEN DL=0
2035 GOSUB5000
2040 RETURN

3000 REM
3001 REM GET FREE STRING SPACE
3002 REM
3010 Z=(PEEK(&H23)*256+PEEK(&H24))-(PEEK(&H21)*256+PEEK(&H22)):RETURN

5000 REM
5001 REM PAUSE
5002 REM
5010 PRINT"[PAUSE]";
5020 IF INKEY$="" THEN 5020
5030 PRINT STRING$(7,8);:RETURN

Running the Program

After a PCLEAR 1 and RUN, the program starts filling lines and we can see string memory going down. When it gets to line 47, there is only 1275 bytes of string space left.

And if we check those values, the difference between each one isn’t the 255 we might have expected. We clearly added a new 255 byte string, but memory went from 7905 to 7395 (510 bytes less) and continued down to 1785 to 1275 (510 bytes less). It appears each time we add a 255 byte string, it takes 510 bytes of string memory.

As we get to line 47, we must have had less than 1024 bytes of string memory left and the DELETE LINE subroutine is called. It deletes the oldest line, which is currently line 0. That should free up 255 bytes of string memory.

After pressing a key, we see the next few entries:

After deleting 0, memory has gone from 1275 to 756 (5120 bytes), so DELETE is called again. This time it deletes line 1.

We press a key and let it scroll a bit more until the next DELETE:

Here we see that, at some point, some string cleanup was done and our free string space grew larger. The trend of reducing by 510 bytes for each ned 255 byte string added continues…

And the process repeats, until eventually we roll over at line 99.

From here on, things get a bit more predictable, with a DELETE happening almost every line — though sometimes every two lines.

Eventually things settle in to a pattern of basically DELETING for every line ADDED.

Is it broken? Is it just poorly implemented? Or is it behaving exactly like it is supposed to?

Tune in next time for the exciting conclusion…