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-1- BOOLEAN OPERATIONS IN BASIC LANGUAGE It was like digging skeletons out of the closet. I knew that old college algebra book was somewhere, but we had just moved and all of the family's books were stored in no less than 24 sealed boxes. Of course, after hours of digging, I found it...in the next to the last box. For years I have used comparison and logical operations in my Basic programs without knowing the underlying theory; but if I was going to write an article to help beginner Basic programmers transition to intermediate programming, I'd better have a reference. Finally on page 236, I found a brief section on Boolean algebra. In the simple world of Boole, everything is either black or white; that is, it is either TRUE or FALSE. You can reduce a series of IF-THEN logical operations to a single line of code using Boolean algebra, thus adding speed to the program and reducing the length of the source code. The examples in this tutorial are written in the popular GFA BASIC, my favorite language for the ST series, but the ideas on Boolean comparisons can be universally applied to any Basic language program. BOOLEAN BASICS Boolean algebra looks at a mathematical comparison and -2- determines if it is TRUE or FALSE, and then assigns a value to the result. In GFA BASIC, TRUE = negative one(-1) and FALSE = zero(0). You have to be careful because all Basic languages are not identical. For example, in Atari-800 Basic, TRUE = positive one(+1) and FALSE = zero(0). Let's begin with this mathematical comparison: X=12 As a simple mathematical comparison function, X is equated to twelve. But in Boolean algebra, if X is equal to twelve, then the condition is TRUE and the statement is assigned the value of negative one; or if X is not equal to twelve, then the condition is FALSE and the statement is assigned the value of zero. Putting this into Basic code, consider the brief program below: Let X=5 Let Y=5 Z = (X=12) + (Y<10) Print "Z equals ";Z As a beginner basic programmer, comparing a variable (Z) to other comparison statements (X=12, Y<10) combined with arithmetic functions (plus sign) made me scratch my head because the equation looked like nonsense; but this is a classic basic Boolean operation. We know that X=5 and Y=5 by -3- previous initialization or calculation. So what does Z equal by Boolean algebra? X equals five, so (X=12) is FALSE and has a value of zero. Y also equals five, so (Y<10) is TRUE and has a value of negative one. Therefore, Z equals zero plus negative one for a total value of negative one. As demonstrated, you can utilize any of the comparison functions with Boolean algebra; equals (=), less than (<), greater than (>), not equal to (<>), greater than or equal to (>=), and less than or equal to (<=). If you haven't caught on to the potential power of Boolean operations yet, don't worry. You'll find that the following program examples and descriptive text will give you concrete guidelines for the practical use of Boolean operations. REPLACING CONDITIONAL IF-THEN STATEMENTS A common use of Boolean operations is to replace a series of related conditional IF-THEN statements with a streamlined Boolean statement. If there are a large number of IF-THEN statements in the subroutine, then the savings in Basic source code space can be significant. The easiest example of this concept is when IF-THEN statements are used to elicit a TRUE or FALSE response, such as setting flags. Study the following example and note how IF-THEN statements can be replaced by one line of Boolean code: -4- Do Print "Select 'Y' to turn flag TRUE" Repeat Z$=Inkey$ Until Z$<>"" If Z$="Y" Then Flag=True Endif If Z$<>"Y" Then Flag=False Endif Print "Flag value = ";Flag Loop Using a Boolean operation, this program can be changed to: Do Print "Select 'Y' to turn Flag TRUE" Repeat Z$=Inkey$ Until Z$<>"" Flag=(Z$="Y") !BOOLEAN OPERATION Print "Flag value = ";Flag Loop The REPEAT-UNTIL loop waits until you select a key. If you select "Y", then Z$="Y" is TRUE and the value of the Flag is -5- set to negative one(-1). If you select another letter, such as "N", then Z$="Y" is FALSE and the value of the Flag variable is set to zero(0). Okay, this is only a minor change in code; but let's consider a more lengthy comparison you might have embedded in a program: If Z=10 Then X=1 Endif If Z=15 Then X=2 Endif If Z=20 Then X=4 Endif If Z=25 Then X=8 Endif With Boolean operations to the rescue, this series of conditional IF-THEN's is reduced to: X = ABS((Z=10) + 2*(Z=15) + 4*(Z=20) + 8*(Z=25)) "Pretty compact now," I would say. One disadvantage is that this Boolean contraction is visually distracting, -6- increasing the chances for hidden bugs, compared to the orderly layout of IF-THEN statements. Fortunately, the GFA BASIC Editor won't let you get away with incorrect usage of mathematical symbols. I usually write the program with the modular IF-THEN statements first. If the program is running well, I will go back into the source code and apply Boolean operations where I can, testing the program after each change, before finally compiling the code. The calculation of this Boolean operation above would be as follows: If Z is not 10,15,20, or 25, then the expression would be: X equals the absolute value of (0+2*(0)+4*(0)+8*(0)), or X equals zero. If Z equals 10, then the expression would be: X equals the absolute value of ((-1)+2*(0)+4*(0)+8*(0)), or X equals one. If Z equals 15, then the expression would be: X equals the absolute value of (0+2*(-1)+4*(0)+8*(0)), or X equals two. If Z equals 20, then the expression would be: X equals the absolute value of (0+2*(0)+4*(-1)+8*(0)), or X equals four. If Z equals 25..., well, I'll let you derive this condition as a Boolean exercise, because you will be doing similar calculations in the following practical examples of an error trapping subroutine and a menu click detection subroutine. -7- ERROR TRAPPING SUBROUTINE Study the "***ERROR TRAPPING SUBROUTINE ***" below written in GFA BASIC. The subroutine catches errors as they occur in the main program and converts some of the more commonly occuring error numbers into English text in an Alert Box. Since the error numbers that I selected for the conversion to English are random, irregular positive and negative numbers, I could not quickly dream up an algebraic routine to point to the English error message by an offset value. I'm not a mathematical genius! So, normally the Basic programmer would develop a series of conditional IF-THEN statements to handle the conversion of an error number to English. A few of these IF-THEN statements might be as follows: If En%=22 Then Error_message$="FILE ALREADY OPEN" Endif If En%=24 Then Error_message$="FILE NOT OPENED" Endif ' !...ONE STATEMENT FOR EACH ERROR NUMBER... If En%=(-39) Then Error_message$="MEMORY FULL" Endif ' !...AND SO ON... -8- Sixteen IF-THEN statements were removed by applying Boolean logic to the subroutine. It is funny how things happen, but after I wrote this routine for my GFA BASIC programs, I discovered that "OPTION E+" in the GFA BASIC COMPILER inserts a subroutine into compiled GFA BASIC programs that converts error number messages into English text! ' *** ERROR TRAPPPING SUBROUTINE *** Procedure Er_trap Close !CLOSE EVERYTHING En%=Err !Err RETURNS ERROR NUMBER TO INTEGER VARIABLE En% '!BOOLEAN OPERATION REPLACES SIXTEEN IF-THEN STATEMENTS '!Er_dif% VARIABLE IS OFFSET TO ERROR NAME IN DATA SET BELOW Er_pnt% = Abs((En%=22)+2*(En%=24)+3*(En%=37)+4*(En%=50)) Add Er_pnt%,Abs(5*(En%=48)+6*(En%=51)+7*(En%=52)) Add Er_pnt%,Abs(8*(En%=53)+9*(En%=54)+10*(En%=55)) Add Er_pnt%,Abs(11*(En%=-10)+12*(En%=-11)+13*(En%=-13)) Add Er_pnt%,Abs(14*(En%=-33)+15*(En%=-34)+16*(En%=-39)) If Er_pnt%=0 !IF ERROR NOT COMMON Err#, PRINT THE NUMBER Error_message$="ERROR # "+Str$(En%)+" OCCURRED" Alert 1,Error_message$,1,"CONT",B% Else Restore Er_data !IF ERROR IS COMMON Err NUMBER, For I%=1 To Er_pnt% !FIND ENGLISH TEXT IN DATA SET Read Error_message$ -9- Next I% !AND SEND TEXT TO THE ALERT BOX Alert 1,Error_message$,1,"CONT",B% Endif On Error Gosub Er_trap !RESET ERROR HANDLER Clr En% !CLEAR ERROR NUMBER VARIABLE Resume Begin_again !RESTART FILESELECT PROC. IN MAIN PRG Er_data: !DATA SET OF COMMON ERRORS Data "FILE ALREADY OPENED","FILE NOT OPENED" Data "DISKETTE FULL","NOT AN 'R' FILE" Data "OPEN 'R' FILE | RECORD LENGTH WRONG" Data "ONLY ONE FIELD PER | OPEN 'R' ALLOWED" Data "FIELDS LARGER THAN | RECORD LENGTH" Data "TOO MANY FIELDS (MAX=9)" Data "GET/PUT FIELDS | STRING LENGTH WRONG" Data "GET/PUT RECORD | NUMBER WRONG ","WRITE FAULT" Data "READ FAULT","DISKETTE WRITE PROTECTED" Data "FILE NOT FOUND","PATH NOT FOUND","MEMORY FULL" Return To demonstrate how the Boolean operation works in this error trapping subroutine, let's presume that you are utilizing a FILESELECT subroutine in your program to send a data array, such as a series of names and addresses, from RAM to a sequential disk file. You've selected the filename, and clicked "Enter"; but your diskette cannot receive the data since the Write-Protection Tab is in the "write-protect-on" position. This will generate an error number that is trapped -10- by the error trapping subroutine. The GFA BASIC manual, page 240 (version 2.0), notes that such an error will generate a TOS error number of (-13). Therefore, the only TRUE comparison in the Boolean operation above is (En%=-13). So the absolute value of 13*(En%=-13) equals ABS(13*(-1)), or thirteen. All of the other comparisons are FALSE, resulting in zeros for the rest of the Boolean equation. Therefore, adding up all of the results of these Boolean comparisons gives the variable, Er_pnt%, a value of 13. The READ-DATA subroutine will then put the thirteenth English text error message into the Alert Box. If the error number had been (51), then the sixth English text error message would have been put into the Alert Box. I hope by now you are catching onto the idea of using Boolean operations. HANDLING MENU CLICKS Every GFA BASIC program that uses pull-down menus is accompanied by a subroutine to conditionally read the "click" on a menu item, referring the program to another subroutine. When studying the source code with the GFA BASIC EDITOR, you will usually see several screenfuls of menu click conditional IF-THEN statements, such as: If Menu(0)=20 Then Gosub Procedure_three -11- Endif ' !... AND SO ON ... A whole series of IF-THEN statements can be changed to a line or two of "ON-(integer variable)-GOSUB-(routine)" statements using Boolean comparisons. Study the " *** MENU CLICK DETECTION SUBROUTINE ***" below: ' *** MENU CLICK DETECTION SUBROUTINE *** Procedure Menclick Q%=Menu(0) !VARIABLE, Q%, HOLDS # OF MENU ITEM CLICKED ' REPLACE TWELVE IF-ENDIF's WITH BOOLEAN OPERATION Z%=Abs(1*(Q%=15)+2*(Q%=16)+3*(Q%=18)+4*(Q%=21) +5*(Q%=22)+6*(Q%=23)+7*(Q%=26)+8*(Q%=27) +9*(Q%=28)+10*(Q%=29)+11*(Q%=32))+12*(Q%=34)) On Z% Gosub Loadfont,Savefont,Quitprog,Printerreset, Dlfont,Testfont,Createchar,Editchar, Copychar,Deletechar,Restorechar,Asciibox Return Now that you are getting more in tune with the Boolean way of thinking, I'll just give a quick example for the routine above. Suppose that you clicked the menu item "Printerreset". The integer variable, Z%, would equal the absolute value of (1*(0)+2*(0)+3*(0)+4*(-1)+5*(0)...+12*(0)), or four. The next line of code states, "On four, gosub Printerreset." -12- READING JOYSTICKS AND CHECKING BOUNDARIES For this final example, you will find it helpful to refer to figure 1., which shows all of the ST-joystick position values. When the joystick is centered, a value of zero is returned. When the joystick is moved to the upper-right position, a value of nine is returned. Let's say you wanted to move a Sprite about the screen, but wanted to keep it inside a box. The X,Y coordinates of the upper-left corner of the box are 50,50; and the X,Y coordinates of the lower-right corner of the box are 500,150. The joystick is read to determine which way the Sprite should move. To move the Sprite, you will be incrementing X by one for any joystick inputs to the right and you will be incrementing Y by one for any joystick inputs downward. Decrementing the X and Y values with joystick inputs will move the Sprite in the corresponding opposite directions. To read the joystick, you would have to set up eight conditional IF-THEN statements, such as: If Joystick%=10 Then X=X+1 !MOVE THE SPRITE DOWN AND RIGHT Y=Y+1 Endif -13- To check the boundaries, you would have to set up four conditional IF-THEN statements, such as: If X>500 Then X=500 !KEEP 'X' INSIDE RIGHT BORDER Endif That adds about forty lines of IF-THEN-ENDIF statements to your source code. Study the next example of Boolean logic and follow the explanation of how it works. This subroutine is integrated into the brief GFA BASIC program listing accompanying this tutorial, so you can have fun moving the Sprite around "The Sprite Corral." If S%>0 ! JOYSTICK MOVED FROM CENTER POSTION '!TESTS FOR 8 JOYSTICK POSITIONS AND CHECKS BOUNDARIES '!BOOLEAN COMPARISONS REPLACE 12 IF-THEN STATEMENTS Add X%,(S%>7 And S%<11)*(X%<500)-(S%>3 And S%<7)*(X%>50) Add Y%,(S% Mod 4=2)*(Y%<150)-(S% Mod 4=1)*(Y%>50) Endif Sprite S$,X%,Y% ! POSITIONS SPRITE All joystick inputs to the right return the values of 9, 8, or 10; that is: (S%>7 And S%<11). All joystick inputs to the left return values that are: (S%>3 And S%<7). All joystick inputs upward return the values of 5,1, or 9, which are divisible by four with a remainder of one; that is: (S% Mod -14- 4=1). All joystick inputs downward return values that are divisible by four with a remainder of 2: (S% Mod 4=2). These four comparisons are unique to each of the four cardinal directions of joystick input. Let's do the Boolean calculations for a given situation. The Sprite is at X,Y coordinates of 100,125. You move the joystick to the right, returning a value of S%=8. The comparisons (S%>7 And S%<11), (X%<500), (X%>50), (Y%<150), and (Y%>50) are TRUE and are assigned the value of (-1). All other Boolean comparisons are FALSE and are assigned the value of (0). The calculation is then: Add X%,(-1*-1) - (0*-1) or Add X%,1 Add Y%,(0*-1) - (0*-1) or Add Y%,0 This moves the Sprite to the right by one with new X,Y coordinates of 101,125. To show how boundaries are checked, keep pushing the Sprite to the right until the X coordinate is 500. Stop. Now try to move the Sprite to the right, returning a joystick position value of S%=8. Again the comparisons (S%>7 And S%<11), (X%>50), (Y%<150), and (Y%>50) are TRUE and are assigned a value of (-1). But now the comparison (X%<500) is FALSE and is assigned a value of (0). The other comparisons remain FALSE. The calculation is now: Add X%,(-1*0) - (0*-1) or Add X%,0 Add Y%,(0*-1) - (0*-1) or Add Y%,0 The Sprite will not move past the right X boundary of 500 despite your joystick input to the right. -15- A more complicated and final situation might find the Sprite at X,Y coordinates of 100,150. You push the joystick downward and to the left, returning a joystick position value of S%=6. The comparisons (S% Mod 4=2), (S%>3 And S%<7), (X%>50), (X%<500), and (Y%>50) are TRUE and are assigned a value of (-1). The other comparisons are FALSE and are assigned a value of (0). The Boolean calculations are: Add X%,(0*-1) - (-1*-1) or Add X%,(-1) Add Y%,(-1*0) - (0*-1) or Add Y%,0 The Sprite moves to the left, but is unable to move below the lower Y boundary of 150. The new Sprite X,Y coordinates are 99,150. With the assistance of this tutorial, the beginner GFA BASIC programmer should have a better understanding of Boolean operations and will be able to employ them in future programming efforts to reduce the object code length and improve the speed of program execution. Of course, Boolean algebra is an unusual way of calculating equations, so don't feel overwhelmed if you have to read this tutorial over again. I had to read that section in my algebra book three times. GFA BASIC LISTING ' *** MOVE SPRITE WITH JOYSTICK IN PORT 1 *** Sp$=Mki$(1)+Mki$(1)+Mki$(0)+Mki$(0)+Mki$(1) ! DEFINE SPRITE For I%=1 To 16 -16- Sp$=Sp$+Mki$(0)+Mki$(65535) Next I% Deffill 3,2,6 !DRAW THE BOX TO HOLD THE SPRITE Pbox 50,49,514,164 Print At(30,14);Chr$(27);"c2";"The Sprite Corral"; X%=50 !PUT SPRITE IN BOX Y%=50 Print At(1,24);"Press any key to quit"; Hidem ' Repeat !Peek $FFFC02 = QUICK READ JOYSTICK POSITION @Readjoy(Peek(&HFFFC02)) Until Inkey$<>"" !PRESS ANY KEY TO QUIT GFA BASIC ROUTINE Out 4,&H8 ! TURN MOUSE BACK ON WHEN EXIT PROGRAM ' Procedure Readjoy(S%)!PASS VALUE Peek $FFFC02 TO VARIABLE S% If S%>0 ! JOYSTICK MOVED FROM CENTER POSTION ' TESTS FOR 8 JOYSTICK POSITIONS AND CHECKS BOUNDARIES ' !REPLACES 12 IF-THEN STATEMENTS Add X%,(S%>7 And S%<11)*(X%<500)-(S%>3 And S%<7)*(X%>50) Add Y%,(S% Mod 4=2)*(Y%<150)-(S% Mod 4=1)*(Y%>50) Endif Vsync ! REMOVES ANIMATION FLICKER Sprite S$,X%,Y% ! POSITIONS SPRITE Return