Lesson 13

Loops

Computer programs frequently need certain operations to be repeated a specific number of times.

For example, finding the sum of ten numbers in the stack would normally take a stream of over nine statements. To a programmer's way of thinking, this makes the program several steps longer than necessary. It would be better to find a shortcut way of repeating the add operation as many times as is needed to do the job, without increasing program size with a long series of identical statements. That's where a loop construct comes in.

A loop sets up a kind of merry-go-round in your program, with a beginning and an end. At the end of the loop is an instruction that tells the program to "loop back" to the beginning of the loop. All the statements between the beginning and the end are repeated each time program execution goes through the loop.

Mops has two major categories of loops: definite and indefinite. As their names imply, each category has a different way of figuring out when to stop going around the loop. A definite loop performs only as many loops as the program specifies; an indefinite loop, on the other hand, will loop (forever) until a certain condition is met.

Let's look at each kind of loop more closely.

Definite Loops

Consider the 10-number addition problem discussed above. Since you know ahead of time that there will be exactly ten numbers on the stack before any addition takes place, you could use a definite loop to perform nine addition operations on the stack.

A definite loop in Mops consists of a DO...LOOP statement, which expects to find two numbers on the stack before the DO executes. The two numbers represent the count of the repetitions that the DO...LOOP statement is to make; the second value (on the top of the stack) is incremented before the loop begins.

DO...LOOP	( n1 n2 -- )	Increments ‘n2’ each time after performing operations between DO and LOOP; exits loop when ‘n2’ equals ‘n1’.

Because loops work only in compiled statements, you will need to put them inside colon definitions to see how they operate. Let's define a new word that adds up 10 numbers from the stack by repeatedly performing nine addition operations:

 : ADDTEN  ( n1 ... n10 -- sum )
        9 0 DO  +  LOOP  . cr ;
 

During execution, this DO...LOOP counts up from zero to nine each time through the loop. After the ninth time around, the loop stops; the top of the stack (the sum) is displayed and a carriage return is executed.

You may be wondering where Mops keeps track of the loop counter if the parameter stack is used to hold all the numbers that get added. The answer to that involves a powerful feature called indexing, which will play an increasingly important role the more you learn about Mops.

When you entered the 9 and the prior to the DO...LOOP construction in the example above, what you couldn't see was that the two numbers were automatically moved to another part of memory. The first number you typed (9) is called the limit, because that number represents the limit of how many times the loop is to be executed.

The second number (0) is called the index. This number increments by one each time through the loop. So, the first time through the DO...LOOP construction in the above example, the index number bumps up to a one; the next time to a two, and so on. Each time the index is incremented (in LOOP), a check is done to see if the index and limit numbers are equal. If so, then the DO...LOOP construction "knows" that it's time to move on and will not "loop back" (to DO) for another iteration.

What's interesting about this kind of indexing is that you can use the index number as a counter while executing a loop. By setting the limit and index numbers to integers you need to operate with inside a loop, you can copy the index number to the parameter stack each time around the loop and use that number for a calculation, a graphics plot point, a multiplication factor, or whatever.

The Mops word that copies the index to the parameter stack is "I":

I	( -- n )	Copies the current index value to the parameter stack.

Remember that this word only copies the index; it does not disturb the index in any way. Here are a couple of examples to demonstrate.

Define a word, FIVECOUNT, that displays a series of numbers from 101 to 105:

 : FIVECOUNT  106 101 DO  i .  LOOP  cr ;
 

Notice that the limit is set to 106. Remember that the index is incremented when execution reaches LOOP. The first time through, the index was 101, and the I word copied the index to the parameter stack; the . command then displayed it on the screen. On the fifth execution, 105 was the index. When execution reached LOOP, the index was incremented to 106, at which point it the index is now equal to the index so execution broke out of the loop.

You can similarly use the index number to perform operations on a number passed on the parameter stack prior to execution. Consider the following definition:

 : TIMESTABLES  { n -- }
        13 1 DO  n i *  .  LOOP  cr ;
 

If you then type '5 timestables', the program goes through twelve loops of multiplying 5 times the incrementing index number, one through twelve.

You have the flexibility in Mops to place all kinds of statements within a DO...LOOP construction, including all those conditional decision constructs we covered earlier.

There will be times when you'll want to use a DO...LOOP for the sake of compactness, but the increment you might wish to use is something other than the one automatically performed by LOOP (which can only increment by 1). For those occasions, you have the optional loop ending, +LOOP. Whatever number you place in front of the +LOOP ending will be the increment that the DO...LOOP uses to adjust the index. You can even use a negative number if you wish the loop to decrement.

+LOOP	( n -- )	Alternative word for LOOP. Increments the loop index by ‘n’ and returns execution to the nearest DO if the index and the limit are equal.

Here's how you would use +LOOP to manage a countdown:

 : COUNTDOWN
        1 10 DO  i . cr  -1 +LOOP
        ." Ignition...Liftoff!" cr ;
 

Notice that in this case, since the program loop is counting backwards, the limit is 1 and the index is 10. Each time through the loop, the index is decremented by -1. Also notice that the limit value 1 gets typed by the program. When the index is counted down and becomes equal to the limit, the loop continues and doesn't stop until the index is counted down to the limit minus 1, unlike the situation when the index is being incremented (where the loop stops when the index equals the limit). The best way to think about this is as if there is a "fence" in between the limit and one minus the limit. Whenever the index crosses the fence, in either direction, the loop stops. This will be true even if you write a program in which the increment value changes sign during the running of the loop, i.e., goes from negative to positive.

Nested Loops

It is also sometimes desirable to have more than one DO¦LOOP going on simultaneously. As with IF¦THEN constructions, DO¦LOOP operations can be nested inside one another. All you have to remember is to supply one LOOP (or +LOOP) for each DO within the colon definition.

 : NESTEDLOOP
        1 10 DO
                ." Loop: " i . cr
                        4 0 DO
                                ." Nested Loop: " i . cr
                        LOOP
        -1 +LOOP cr ;
 

Type NESTEDLOOP and watch how the inner loop iterates until completion for each iteration of the outer loop.

If you are in a nested loop and need access to the outer index, Mops has a predefined word that allows you to copy that number to the parameter stack, just like I copies the current loop index number to the stack. That word is J.

J	( -- n )	Copies to the parameter stack the index of the next outer loop from within a nested DO¦LOOP construct.

In other words, J looks up the index of the loop just outside the current DO¦LOOP construction and copies that number to the parameter stack.

 : NESTEDLOOP2
        1 10 DO
                ." Loop " i . cr
                        4 0 DO
                                ." Loop " i .
                                ." within Loop " j .
                                cr
                        LOOP
        -1 +LOOP cr ;
 

Note: If you factor out an inner loop into another definition, you can't use J”you won't get the right value. J only works with nested loops within the current definition.

Abort Loop

You may have a situation in which you need to bail out of a DO¦LOOP before its normal completion”perhaps because of some special case situation. The word LEAVE is available for this purpose.

LEAVE	( -- )	Exits the current loop immediately.

Here's our countdown example again, appropriately modified:

 : COUNTDOWN2
        1 10 DO
                i . cr
                i 7 = IF  ." Aborted!!" cr LEAVE  THEN
        -1 +LOOP ;
 

We had to remove the Ignition...Liftoff! message, otherwise it would have appeared after the countdown was aborted (which really isn't what we wanted). We'll show a better way of handling this shortly.

Indefinite Loops

An indefinite loop is another kind of loop you'll use often in a Mops program. As its name implies, an indefinite loop keeps going in circles until a certain condition exists. It can go around one time, or many thousands of times while waiting for that condition to occur. (And would continue indefinitely if allowed to.) In Mops, that condition is the presence of a flag on top of the stack.

BEGIN	( -- )	Marks the beginning of an indefinite loop.
UNTIL	( n -- )	Breaks out of an indefinite loop if ˜n' is non-zero (TRUE); otherwise returns execution to the nearest BEGIN.

Indefinite loops with BEGIN¦UNTIL can be used like this:

BEGIN  xxx  UNTIL

Operation(s) xxx will be performed repeatedly (with no end in sight) until a TRUE flag exists on the stack for UNTIL.

A useful variation of this construct uses the word NUNTIL:

NUNTIL	( n -- )	Alternative word for UNTIL. Breaks out of an indefinite loop if ˜n' is zero (FALSE); otherwise returns execution to the nearest BEGIN.

It used in the place of UNTIL in the previous example:

BEGIN  xxx  NUNTIL

As before, operation(s) xxx will be performed repeatedly, but this time the loop won't stop until a FALSE flag exists on the stack.

Here's an example of how you might use a BEGIN¦UNTIL construction. In this case, the indefinite loop will be waiting for you to enter a lower-case letter 'a' on the keyboard. The KEY operation pauses the program until you press a key, and then it pushes onto the stack a standard, equivalent code number (called an ASCII code”explained later) for the character keyed in. If the number on the stack is 97 decimal (the ASCII code number for the lower-case 'a'), then a 1 (TRUE flag) is placed on the stack, and the loop ends. Otherwise, a FALSE flag is placed on the stack, and execution returns to the beginning of the loop.

 : BEGINTEST
        BEGIN  key 97 =  UNTIL
        ." Loop broken." cr ;
 

Now, type BEGINTEST, and tap all kinds of letters on the keyboard. Until you type a lower-case letter 'a' the program keeps going around in circles.

It turns out that BEGIN also marks the beginning of another kind of infinite loop. These are the new words:

REPEAT	( -- )	Returns execution unconditionally to the nearest BEGIN.
WHILE	( n -- )	Execution continues within a loop as long as ˜n' is non-zero (TRUE).

With all three words taken together, it is called a BEGIN¦WHILE¦REPEAT loop, and naturally enough, it is used like this:

BEGIN xxx  WHILE  yyy  REPEAT

This statement will executes xxx each time through the loop, and executes yyy only if a non-zero number (TRUE) is on top of the stack when execution reaches the WHILE. If the flag at WHILE is zero, the loop is broken and yyy is not executed again.

There's also a variation on WHILE called NWHILE, which only breaks execution if the flag on the stack is zero (FALSE):

NWHILE	( n -- )	Alternative word for WHILE. Execution continues within a BEGIN¦REPEAT loop as long as ˜n' is zero (FALSE).

Here is a variation on our BEGINTEST example to show the new construct at work:

 : BEGINTEST2
        ." Type a lower-case letter 'a', please." cr
        BEGIN
                key 97 =
        NWHILE
                ." Wrong key!" cr
        REPEAT
        ." Thank you. Loop broken." cr ;
 

This example begins by printing a message prompting the user to type the letter 'a'. Unlike our first BEGINTEST, this version provides feedback to the user when they push the wrong key. If they push the right key, execution will not continue past NWHILE and print the error message, because the = will leave a TRUE on the stack (indicating that the ASCII code number of the key pushed by the user was equal to 97), and execution will break out of the loop entirely and proceed to print the final message at the end of the definition.

EXIT

While not necessarily a loop construct, this is a good place to mention another very useful operation, EXIT.

EXIT	( -- )	Terminates execution of the current word (or method).

Unlike LEAVE, EXIT exits the definition entirely. Here's a modified version of the our first BEGINTEST example that uses EXIT:

 : BEGINTEST
        BEGIN
                key 97 = IF EXIT THEN
                key 98 =
        UNTIL ;
 

This definion will keep running until you type either an 'a' (ASCII code number 97) or a 'b' (ASCII code number 98). You can also write:

 : BEGINTEST
        BEGIN
                key 97 = IF EXIT THEN
                key 98 = IF EXIT THEN
        AGAIN ;
 

Yes, we sneaked in yet another indefinite loop that uses BEGIN.

AGAIN	( -- )	Returns execution unconditionally to the nearest BEGIN.

Of course, if you write a BEGIN¦AGAIN loop, the loop must have some other way of terminating, such as EXIT.

If you write EXIT within a DO¦LOOP, you have to remember one more thing”Mops (as with any kind of Forth) keeps some extra information around to perform the DO¦LOOP, and you have to remove this information if you are going to end a DO¦LOOP in some unusual way (that is, not via LOOP, +LOOP or LEAVE). The word to use is UNLOOP.

UNLOOP	( -- )	This word will safely remove all loop information from the return stack when exiting from a DO¦LOOP.

We'll illustrate this with the countdown example again:

 : COUNTDOWN3
        1 10 DO
                i . cr
                i 7 = IF  ." Aborted!!" cr UNLOOP EXIT  THEN
        -1 +LOOP
        ." Ignition...Liftoff!" cr ;
 

You'll notice that we've been able to reinstate the Ignition...Liftoff! message, but by aborting the loop via UNLOOP and EXIT we bypass them entirely.

Warning: When you're designing loops, it is sometimes possible for an infinite loop to slip in accidentally. Try to avoid them! Double-check the stack operations of your indefinite loops to make sure that there is always at least one condition that will allow you or your program to terminate the loop. Otherwise, your program will appear to "lock up" and may be unresponsive to your keyboard input. If this happens, you'll have to force quit the Mops application.

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