Trace Pascal
 Volume Number: 5 Issue Number: 1 Column Tag: Programmer's Workshop

# Trace LightSpeed Pascal

By Alan Wootton, Santa Monica, CA, MacTutor Contributing Editor

Note: Source code files accompanying article are located on MacTech CD-ROM or source code disks.

Alan Wootton currently of MTS Informix Software, Los Angeles, is a famous early contributor of MacTutor and is well known in Mac programming circles. We welcome his return with this article.

A method of obtaining an indented listing recording the execution history, and call chain, of any LightSpeed Pascal program, is presented.

## Introduction

Once upon a time (in 1975) in a far away land (Arizona) there was a young man (your humble author) who went to a great place of learning (ASU) to seek his fame and fortune. While he was there he happened upon a course of study that involved the learning of a strange new numerical language (Fortran) that could be read and understood by a new breed of Machine Folk known as ‘Computers’. Unfortunately for the students in this class, it was necessary to learn to read and understand as Machine Folk, and the ways of the Machine Folk were strange indeed. This was a most tedious and difficult job. Surely only Wizards could train their brains to such a task!

Often was the day when these poor disciples would be presented with a riddle (translated here into a more moderne language for all ye moderne folk) such as:

```PROBLEM SET #4 (25 points) Given the procedure:

PROCEDURE A (i: integer);
begin
if i > 2 then
begin
write(i);
A(i div 2);
A(i - i div 2);
end;
end;
```

4a) Please write the the output produced by the call:

```A(123);
```

Whereupon the diligent student would, after much mental effort, correctly write:

```123 61 30 15 7 3 4 8 4 4 15 7 3 4 8 4 4 31 15 7 3 4 8 4 4 16 8 4 4 8
4 4 62 31 15 7 3 4 8 4 4 16 8 4 4 8 4 4 31 15 7 3 4 8 4 4 16 8 4 4 8
4 4
```

The result of such a wizardly task was the bestowal of the desirable, yet non-negotiable, commendation known as the ‘A’. Provided of course that the student correctly answered the other parts:

4b) How many times is the procedure A invoked?

4c) What is the maximum depth to which A recurses?

{See if you can guess. Answers at the end of the article}

As you might imagine, a great call was heard throughout the land (or at least the classroom). “Why must we learn to do the work of the machine folk when it is so admirably done by those very folk”. The answer was “so that ye may all be able to recognize the errors of the machine folk”. Errors of the machine folk? Yes, the machine folk, being of simple nature, were capable of doing only as told. When those directions were the least bit imprecise then resulting machine actions could defy all gentle reason.

At that time I thought “why don’t we teach the machines to find their own mistakes?” Being a neophyte, and not knowing the nature of the machine instructions required for such a task, I did not pursue this topic any further.

Now, things are different.

## A Goal

Often I am faced with the daunting task of understanding the execution of a large, complicated, and sometimes foreign, pieces of code. My tools are the writeln, the breakpoint, the observe window, and the rest of the fine features of the LightSpeed development environment. Additionally I usually code routines to monitor the correctness of difficult data structures. And recently, I have developed a method of using the ‘hooks’ that LightSpeed puts in its code to monitor the entire execution of a program.

Having the ability to monitor the execution of a program brings up several possibilities. One could stop at the end of every procedure and verify that all the data structures are intact, or that the heap is not damaged, or that an excessive amount of time has not elapsed. As space is limited in this article I shall present what I think is a most interesting utility: A method of producing an indented listing of all procedures called.

Given the procedure above we wish to obtain a listing such that the call: A(7) produces the result:

```BEGIN A
. BEGIN A
.  . BEGIN A
.  . END   A
.  . BEGIN A
.  . END   A
. END   A
. BEGIN A
.  . BEGIN A
.  . END   A
.  . BEGIN A
.  . END   A
. END   A
END   A
```

From this one can immediately deduce that A is called 7 times and that A recurses 2 levels deep (do you know what is output?). While I must stick with short examples, traces of complex programs can easily exceed 1,000,000 characters. For instance, it is very hard to trace through the sources of a MacApp program and observe what the execution order is. Given a trace (The MacApp debugger will do this) in the proper format (MacApp uses a very bad format, we use a better one here) one can very easily follow the path of execution and see immediately which procedure calls another one and when.

In order to obtain the desired result two things are needed. One, a way of putting ‘hooks’ into all the procedures. To obtain the format shown above we will need a hook at the start and at the end of every procedure. One way would be to type in a procedure call at the beginning and end of every procedure. Fortunately, there is a way to get LightSpeed to do this using the debug option. Second, we need a way for the ‘hooks’ to find the name of the procedure currently executing. The names option in LightSpeed (and other compilers) embeds the names in the code. Our hook routines can find, and use, these names.

## How To Work It

1) Modify your program so that it Uses the unit ‘LightTrace’.

2) Add the files ‘LightTrace.p’ and ‘LightTrace.a.lib’ to your project. Turn OFF the debug (D) option for these files. Turn ON the debug option for all files you wish traced.

3) Before any of the LightTrace routines are called you should call the routine ‘InitTracing’.

4) When you wish to start tracing, call StartTracing(false, true, true);. The first parameter specifies whether you want output in the Text (WriteLn) window. The second, if you want to open a window and show the output there. And the third, whether you want output to the file ‘Trace_File’ in the current directory.

5) (optional) Call one or more procedures or functions that may or may not have the debug option set. Try not to call StartTracing again. You may call EndTracing more than once.

6) To stop tracing you must have a call to EndTracing.

For most people this is all you need. Please skip now to the section titled “The Example:”.

## How it Works

Let’s quickly run through the procedures in LightTrace and I’ll explain their operation. Please refer to listing 1.

First, InitTracing. This simply initializes the global variables used in the unit. Mostly this prevents explosions if you inadvertently call EndTracing or WriteComment at the wrong time.

Then, one calls StartTracing. The options are saved in globals, and then windows and files are opened as needed (MakeScreenWindow: opens a small window. MakeTraceFile: creates and/or opens an MPW text file). Then some of the low memory variables, holding the locations of the code to be run when the processor encounters a TRAP instruction, are hacked. They are set to the assembly language routines ReplaceTrap7 and ReplaceTrap8. These, very short, routines go directly to TraceProcTop and TraceProcBot. The effect is one of TraceProcTop being called at the start of every procedure and TraceProcBot being called at the end of every procedure.

TraceProcTop: As mentioned, all your procedures will now call TraceProcTop as the first thing they do. TraceProcTop first gets the address of the routine that called it (GetRTS returns the address that will be returned to) and then passes this address to GetTheName. What GetTheName does is to call ScanForRTS to find the end of the routine pointed at by iP. Then, assuming that the N (names) option is turned on there should be an 8 character string at that position. This string is copied to str and GetTheName returns. Actually, some MPW programs provide 16 bit names and GetTheName is setup to handle those too. Having gotten the name of the routine TraceProcTop then calls WriteStr to output the indent, the word ‘BEGIN ‘ and then the name that was found. The indent level is incremented.

TraceProcBot does almost exactly the same thing as TraceProcTop except it prints ‘END ‘ and decrements the indent level.

WriteStr, and WriteStrLn are the output routines I use here. They go through a simple bottleneck and, according to the settings of the global variables, output is sent to the window, to the file or to the WriteLn window.

EndTracing is very simple. It closes any window or file and replaces the trap vectors. It is designed to not break even if you call it twice.

## How it Really Works

LightSpeed Pascal inserts a Trap8 instruction at the beginning of every procedure or function compiled with the debug option on. Trap7 is inserted similarily at the end. We repoint the vectors for these traps to our code named ReplaceTrap8 and ReplaceTrap7 respectively.

The goal was for the same code to run on my Mac+ and also on my MacII. In order to accomplish this I observed that, even though the exception stacks are different on the 68000 and the 68020, the value of the PC is in the same place relative to A7. So, I move the return PC to D0, and replace the return PC with the address of 88tmp. Then when the RTE is executed control is returned to 88tmp and not to the routine where the Trap8 was encountered (the target procedure). It is then a simple matter (having the old return PC in D0) to reformat the stack like a normal procedure call and jump to TraceProcTop. From the point of view of TraceProcTop it is as if TraceProcTop was called directly from the target procedure. ie. TraceProcTop will return (RTS) directly to the target procedure.

Since the stack is set for TraceProcTop to return directly to the target routine it is a simple matter to get this vector by simply fetching it from 4(A6). I use the inline function GetRTS to do this.

Having an address in the beginning of the target procedure does not automatically give us the information we need, the name of the target procedure! Assuming that the names option is on, we look for the end of the target procedure from which we can BlockMove the name to a string.

In order to find the end of the target procedure we scan down looking to recognize the return sequence. This is the function of the procedure ScanForRTS. I have incorporated into ScanForRTS every return sequence I have ever seen. A summary follows.

Procedure and Function end sequences. This list was compiled by looking at the endings produced by LightSpeed Pascal v1.11, LightSpeed C v2.0, MPW Pascal, and MPW C. I think it represents all of the possible endings produced by just about any compiler. TML and Turbo users: If you see any different endings produced by your compiler, then please let me know.

```1)    No parameter ending
UNLK
RTS    ;2 words
2) Longint parameter ending
UNLK
MOVE.L (SP)+,(SP)
RTS    ;3 words
4) General ending #1
UNLK
MOVE.L (SP)+,A0
LEA    X(SP),SP
JMP    (A0);5 words
5) Wasteful general ending
UNLK
MOVE.L (SP)+,A0
JMP    (A0);6 words
6) General ending #2
UNLK
MOVE.L (SP)+,A0
JMP    (A0);5 words
7) Wasteful no parameter ending.
UNLK
MOVE.L (SP)+,A0
JMP    (A0)
```

## Xtra for Xperts

Please note that the name at the end of the target procedure has the high bit of the first byte set. In some cases, notably MacApp method calls, a 16 byte name is supplied by the compiler. I have noticed that when 16 byte names are supplied then the high bit of the first two bytes are set. GetTheName takes this into account.

OK, so you’re wondering why I make allowances for all these other compilers when this article is for LightSpeed Pascal (works with 1.11 and 2.0). This is because I have used this code to trace code from other compilers, and I didn’t want to change it back.

MPW Pascal has an option (D++) where the compiler inserts a call to %_BP at the beginning of every procedure, and a call to %_EP at the end. If you modify StartTraceTime to hack the A5 jump table instead of the trap vectors then you can use this to trace your MPW and MacApp programs.

Furthermore, if you start a timer at StartTraceTime and pause it during TraceProcTop and TraceProcBot it is possible to get a real useful performance analysis at the same time as you get a trace.

Many other possibilities manifest themselves, given a little thought. Anyone want to do a heap scramble? How about a gadget that measures the maximum amount of stack that is used?

## The Example

The code that follows is an example, for LightSpeed Pascal, of how to trace the execution of two procedures.

Listing 1 is the text of the unit ‘LightTrace’.

Listing 2 is the source for LightTrace.a. Note that if you get the disks from MacTutor you will not need an assembler. You can just use the library LightTrace.a.lib.

Listing 3 is a short sample program. This is the way that your program should invoke tracing.

Listing 4 is the ‘Echo File’ produced by the WriteLn’s in the sample. The Text window shows the same.

Listing 5 is the trace output produced by setting the third parameter in StartTracing.

Listing 6 is the project for this example in LSP 1.11 format. This code works in the new (2.0) version also but the project is different. You will also need to convert the .lib to the new format.

```Listing 1
This is the file LightTrace.p.  It, along with LightTrace.a, contain all the code necessary
for tracing procedure and function calls in LightSpeed Pascal.

unit LightTrace;
interface

procedure InitTracing;
{ call this to init Trace vars to safe values }

procedure StartTracing
(toText, toScreen, toFile: boolean);
{ Start tracing all Subroutines }

procedure EndTracing;

procedure WriteComment (Str: str255);
{ write Str to Trace output }

{ The ‘Of’ functions are useful when formatting output }
{ that must be a Str255.  Also, try them in your observe } { window.
eg. Rectof(ThePort^.ClipRgn^^.RgnBBox) }

function IntOf (Int: longint): str255;
{ convert the Int to a Decimal Str255 }

function HexOf (lll: longint): str255;
{ convert the Int to a Hex Str255 }

function PointOf (fff: Point): str255;
{ convert the Point to a Str255 }

function RectOf (R: Rect): str255;
{ convert the Rect to a Str255 }

procedure TraceProcTop;{ don’t call this yourself}

procedure TraceProcBot;{ don’t call this yourself}

implementation

type
intsArr = array[0..16000] of integer;
intsArrP = ^intsArr;

var
indent: integer;
OldTrap7, OldTrap8: longint;
doText, doScreen, doFile, started: boolean;
ScreenWindow: grafPtr;
TracePB: paramBlockRec;

procedure ScanForRts (var iP: intsArrP);
forward;

{ see  LightTrace.asm }
procedure ReplaceTrap7;
external;
procedure ReplaceTrap8;
external;

{ retreive the addesss of the calling routine }
function GetRTS: longint;
inline
\$2EAE, \$0004;{ move.l 4(A6),(sp) }

function IntOf; {(int : longint) : str255}
var
str: str255;
begin
NumToString(int, str);
IntOf := str;
end;

function HexOf; { (lll : longint) : str255}
var
str, str2: str255;
i: integer;
c: char;
begin
if lll = 0 then
str := ‘\$0’
else
begin
str := ‘’;
while (lll <> 0) do
begin
i := lll mod 16;
if i < 10 then
c := chr(ord(‘0’) + i)
else
c := chr(ord(‘A’) + (i - 10));
str2 := ‘x’;
str2[1] := c;
str := concat(str2, str);
lll := BitShift(lll, -4);
end;
str := concat(‘\$’, str)
end;
HexOf := str;
end;

function Pointof;{  (fff :  Point) : str255}
var
str: str255;
begin
str := concat(IntOf(fff.h), ‘ ‘, IntOf(fff.v));
Pointof := str;
end;

function RectOf; {(R : Rect) : str255}
var
str: str255;
begin
with R do
str := concat(Intof(left), ‘ ‘, Intof(top), ‘ ‘,
Intof(right), ‘ ‘, Intof(bottom), ‘ ‘);
RectOf := str;
end;

{ set the globals to safe values }
procedure InitTracing;
begin
started := false;
doText := true;
doScreen := false;
doFile := false;
indent := 0;
end;

{ Open a small window in the back to see our output }
{ set ScreenWindow to point to this window }
procedure MakeScreenWindow;
var
r: rect;
OldPort: GrafPtr;
begin
getPort(OldPort);
setRect(r, 4, 40, 156, 140);
ScreenWindow := NewWindow(nil, r, ‘Trace Info’,
true, 0, nil, false, 0);
setport(ScreenWindow);
textmode(srccopy);
textFont(1);
textsize(9);
textFont(4);{monaco}
moveto(4, 16);
setport(OldPort);
end;

{ remove ScreenWindow from the screen and from}
{memory }
procedure RemoveScreenWindow;
begin
if doScreen then
DisposeWindow(ScreenWindow);
end;

{ do this to write a cr to the screen }
procedure ScreenLn;
var
ThePen, poi: point;
r: rect;
aRgn: RgnHandle;
OldPort: GrafPtr;
begin
GetPort(OldPort);
SetPort(ScreenWindow);
r := ScreenWindow^.PortRect;
GetPen(ThePen);
ThePen.h := r.left + 4;
ThePen.v := ThePen.v + 12; { move thePen down }
if (ThePen.v + 12) > r.bottom then
begin { scroll up if necessary }
aRgn := NewRgn;
ScrollRect(r, 0, -12, aRgn);
DisposeRgn(aRgn);
ThePen.v := ThePen.v - 12;
setorigin(0, 0);
repeat { pause feature }
GetMouse(poi);
until not ptInRect(poi, r);
end;
moveto(ThePen.h, ThePen.v);
setPort(OldPort);
end;

{ This does a Write to our window }
procedure WriteScreen (str: str255);
var
ThePen: point;
r: rect;
OldPort: GrafPtr;
cr: str255;
begin
cr := ‘x’;
cr[1] := chr(13);
GetPort(OldPort);
SetPort(ScreenWindow);
r := ScreenWindow^.PortRect;
GetPen(ThePen);
if (ThePen.h + stringwidth(str) > r.right) or
(pos(cr, str) > 0) then
ScreenLn;
DrawString(str);
SetPort(OldPort);
end;

{ This does a WriteLn to our window }
procedure WriteScreenLn (str: str255);
var
i: integer;
ThePen: point;
r: rect;
OldPort: GrafPtr;
begin
GetPort(OldPort);
SetPort(ScreenWindow);
WriteScreen(str);
ScreenLn;
SetPort(OldPort);
end;

procedure MakeTraceFile;
var
err: integer;
str: str255;
begin
str := ‘Trace_File’;
with TracePB do
begin
ioCompletion := nil;
ioNamePtr := @str;
ioVRefNum := 0;
ioVersNum := 0;
ioPermssn := 0;
ioMisc := nil;
err := PBOpen(@TracePB, false);
if err = fnfErr then
begin
err := PBCreate(@TracePB, false);
if err = 0 then
err := PBOpen(@TracePB, false);
end;
if err = 0 then
begin
ioMisc := pointer(0);
err := PBSetEOF(@TracePB, false);
if err = 0 then
begin
err := PBGetFInfo(@TracePB, false);
if err = 0 then
with TracePB.ioFlFndrInfo do
begin
{ we’ll make this an MPW text file }
fdType := ‘TEXT’;
fdCreator := ‘MPS ‘;
err := PBSetFInfo
(@TracePB, false);
end;{ with finder info }
end;{ if getFinfo OK }
end { if open OK }
else
doFile := false;
end; { with TracePB }
end;{ proc MakeTraceFile }

procedure CloseTraceFile;
var
err: integer;
begin
if doFile then
err := PBClose(@TracePB, false);
end;

{ same as write except the str goes to the file }
procedure WriteFile (str: str255);
var
err: integer;
eof: longint;
begin
if length(str) > 0 then
if doFile then
with TracePB do
begin
err := PBGetEof(@TracePB, false);
{ ever Fail??}
if err <> 0 then
repeat
sysbeep(1)
until button;

eof := ord(ioMisc);
ioMisc := pointer(eof + length(str));
err := PBSetEof(@TracePB, false);
if err = 0 then
begin
ioBuffer := pointer(ord(@str) + 1);
ioReqCount := length(str);
ioPosMode := fsFromstart;
ioPosOffset := eof;
err := PBWrite(@TracePB, false);
end;{ setEof OK }
end;{ with TracePB }
end;{ proc WriteFile }

{ same as writeLn(str) except output is to the file}
procedure WriteFileLn (str: str255);
begin
writeFile(str);
str := ‘x’;
str[1] := chr(13);
writeFile(str);
end;

{ These two proc’s are our output bottleneck }

procedure WriteStr (str: str255);
begin
if doText then
Write(str);
if doScreen then
WriteScreen(str);
if doFile then
WriteFile(str);
end;

procedure WriteStrLn (str: str255);
begin
if dotext then
WriteLn(str);
if doScreen then
WriteScreenLn(str);
if doFile then
WriteFileLn(str);
end;

{ Call ScanForRTS to find the end of a procedure.  iP is}
{pointed past the end (at the name) Copy the name into}
{the str.  If it is a MacApp name (16 char), then add}
{more.}
procedure GetTheName (var iP: intsArrP;
var str: str255);
begin
str := ‘12345678’;
ScanForRts(iP);
blockMove(@iP^, pointer(ord(@str) + 1), 8);
if ord(str[1]) >= 128 then
str[1] := chr(ord(str[1]) - 128);
if ord(str[2]) >= 128 then
begin
str[2] := chr(ord(str[2]) - 128);
str := concat(str, ‘12345678’);
blockMove(pointer(ord(@iP^) + 8),
pointer(ord(@str) + 9), 8);
end;
end;

procedure TraceProcTop;
var
str: str255;
iP: intsArrP;
i: integer;
begin
iP := pointer(GetRTS);
GetTheName(iP, str);
for i := 1 to indent do
writeStr(‘ . ‘);
indent := indent + 1;
writeStr(‘BEGIN ‘);
writeStrLn(str);
end;

procedure TraceProcBot;
var
str: str255;
iP: intsArrP;
i: integer;
begin
iP := pointer(GetRTS);
GetTheName(iP, str);
indent := indent - 1;
for i := 1 to indent do
writeStr(‘ . ‘);
writeStr(‘END   ‘);
writeStrLn(str);
end;

procedure WriteComment;{ (str : str255)}
var
i: integer;
begin
for i := 1 to indent do
writeStr(‘ . ‘);
writeStr(‘REM ‘);
writeStrLn(str);
end;

{ This routine moves the pointer , iP, down in memory}
{until the end sequence of a procedure or function is}
{found.  Or, it quits after 16000 bytes.  If an end }
{sequence is found then the pointer if set past the last}
{word.  If not, then the pointer is pointed at the text}
{‘unknown ‘ (8 char, including the space). See article}
{text for a list of end sequences.}

procedure ScanForRts; { (var iP : intsArrP)}
var
count, size: longint;
str: str255;
begin
count := 8000;{ max size of any procedure ??? }
size := 0;
while size = 0 do
begin
if iP^[0] = \$4E5E then   { UNLK }
begin
if (iP^[1] = \$2E9F) and (iP^[2] = \$4E75) then
size := 6
{   MOVE.l (A7)+,A7  RTS}
else if iP^[1] = \$4E75 then
size := 4{ RTS }
else if iP^[1] = \$205F then
{ MOVEA.L (A7)+,A0 }
begin
if (iP^[2] = \$4FEF) and
(iP^[4] = \$4ED0) then
{ LEA x(A7),A7  JMP (A0) }
size := 10
else if (iP^[2] = \$DFFC) and
(iP^[5] = \$4ED0) then
{ ADD.l #x,A7  JMP (A0) }
size := 12
else if (iP^[2] = \$DEFC) and
(iP^[4] = \$4ED0) then
{ ADD.w #x,A7  JMP (A0) }
size := 10
else if iP^[3] = \$4ED0 then
size := 8  {JMP (A0) }
end;
end;
count := count - 2;
if count <= 0 then
size := 22222;
if size <> 0 then
iP := pointer(ord(iP) + size)
else
iP := pointer(ord(iP) + 2)
end;{ while size=0 }
if count <= 0 then
begin
str := ‘unknown ‘;
iP := pointer(ord(@str) + 1);
end;
end; { proc scan for Rts }

procedure StartTracing;
{ (toText, toScreen, toFile : boolean)}
var
lP: ^longint;
begin
InitTracing;{ initialize global vars }
{ save the options as globals }
doText := toText;
doScreen := toScreen;
doFile := toFile;
started := true;
if doscreen then
MakeScreenWindow;
if doFile then
MakeTraceFile;
if doText then
ShowText;

lP := pointer(\$80 + 4 * 7);{ trap 7}
OldTrap7 := lP^;
lP^ := ord(@ReplaceTrap7);
lP := pointer(\$80 + 4 * 8);{ trap 8}
OldTrap8 := lP^;
lP^ := ord(@ReplaceTrap8);
end;{ proc StartTracing }

procedure EndTracing;
var
lP: ^longint;
begin
if Started then
begin
lP := pointer(\$80 + 4 * 7);{ trap 7}
lP^ := OldTrap7;
lP := pointer(\$80 + 4 * 8);{ trap 8}
lP^ := OldTrap8;
RemoveScreenWindow;
CloseTraceFile;
end;
InitTracing;
end;{ proc EndTracing }
end.{ unit lightTrace }
```
```Listing 2
This is the file LightTrace.a.  It makes the two code fragments ReplaceTrap8, and ReplaceTrap7
available to the pascal code.  What these fragments do is convert the stack from exception
(RTE or interrupt) format to subroutine (RTS) format, and then jump to TraceProcTop
(or TraceProcBot).  We take advantage of the fact that in all 680XX machines the program
counter that we RTE to is at 2(a7).  Note that the amount of stack used by the RTE can be
different depending upon processor type.

import TraceProcTop:CODE
import TraceProcBot:CODE

ReplaceTrap8 proc export

move.l 2(sp),d0 ;address to RTS to
lea    @88tmp,a0
move.l a0,2(sp) ;fake address to RTE to
RTE

@88tmp
move.l  d0,-(sp);setup stack for rts
jmp     TraceProcTop(a5)

ReplaceTrap7 proc export

move.l 2(sp),d0 ;address to RTS to
lea    @77tmp,a0
move.l a0,2(sp) ;fake address to RTE to
RTE

@77tmp
move.l  d0,-(sp);setup stack for rts
jmp     TraceProcBot(a5)

end ; of file LightTrace.a
```
```Listing 3
This is the file Test_LightTrace.p.  Here we exercise the LightTrace routines with
two short numerical  algorithms.

program test_LightTrace;
uses
LightTrace;
var
i, j: integer;

procedure Decompose (Num: integer);
{ factor Num, report smallest factors first }
var
i, factor: integer;

function check (factor: integer): boolean;
begin
if (Num div factor) * factor = Num then
check := true
else
check := false;
end;

begin
write(IntOf(Num), ‘=1’);
while check(2) and (Num > 1) do
begin
write(‘*2’);
Num := Num div 2;
end;
factor := 3;
while (Num > 1) do
begin
while check(factor) and (Num > 1) do
begin
write(‘*’, IntOf(factor));
Num := Num div factor;
end;
factor := factor + 2;
end;
writeln;
end;

procedure Reduce
(var numerator, denominator: integer);
{reduces fraction to lowest terms}
var
commonDivisor: integer;

function GCD (m, n: integer): integer;
var
r: integer;
begin
writeComment(
concat(‘GCD ‘, IntOf(m), ‘ ‘, IntOf(n)));
r := m mod n;
if r = 0 then
GCD := n
else
GCD := GCD(n, r)
end;{ funct GCD }

begin { proc reduce }
commonDivisor := GCD(numerator, denominator);
numerator := numerator div commonDivisor;
denominator := denominator div commonDivisor;
end; { proc reduce }

begin
showtext;
InitTracing;
StartTracing(false, true, true);
decompose(1 * 2 * 3 * 4 * 5);
i := 1 * 2 * 3 * 4 * 5;
j := 6 * 7 * 8 * 9;
write(IntOf(i), ‘/’, IntOf(j), ‘=’);
reduce(i, j);
writeln(IntOf(i), ‘/’, IntOf(j));
EndTracing;
end.{ of main program test_LightTrace }
```
```Listing 4
This is the file ‘Echo File’.  This is what is sent to the text window by writeln’s. It
is only two lines long and shows the result of factoring a number and reducing a fraction.

120=1*2*2*2*3*5
120/3024=5/126
```
```Listing 5
This is the file ‘Trace_File’.  It was created automatically because the third argument
to StartTracing was true.  It contains the trace output, including comments.  It does not
contain any writeln’s. Please notice that there are two sections.  The first is the trace of
the procedure Decompose. The second is the trace of the procedure Reduce, which recurses.

BEGIN DECOMPOS
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
. BEGIN CHECK
. END   CHECK
END   DECOMPOS
BEGIN REDUCE
. BEGIN GCD
.  . REM GCD 120 3024
.  . BEGIN GCD
.  .  . REM GCD 3024 120
.  .  . BEGIN GCD
.  .  .  . REM GCD 120 24
.  .  . END   GCD
.  . END   GCD
. END   GCD
END   REDUCE
```

## Listing 6

This is the project window for the example presented here. Note that the procedures to be traced must have the debug (D) and names (N) selected. Also note, The LightTrace unit must not have the debug (D) option selected.

Answers to problems 4b and 4c being, of course:127 and 6

Community Search:
MacTech Search:

## Latest Forum Discussions

Fresh From the Land Down Under – The Tou...
After a two week hiatus, we are back with another episode of The TouchArcade Show. Eli is fresh off his trip to Australia, which according to him is very similar to America but more upside down. Also kangaroos all over. Other topics this week... | Read more »
TouchArcade Game of the Week: ‘Dungeon T...
I’m a little conflicted on this week’s pick. Pretty much everyone knows the legend of Dungeon Raid, the match-3 RPG hybrid that took the world by storm way back in 2011. Everyone at the time was obsessed with it, but for whatever reason the... | Read more »
Hello gentle readers, and welcome to the SwitchArcade Round-Up for July 19th, 2024. In today’s article, we finish up the week with the unusual appearance of a review. I’ve spent my time with Hot Lap Racing, and I’m ready to give my verdict. After... | Read more »
Draknek Interview: Alan Hazelden on Thin...
Ever since I played my first release from Draknek & Friends years ago, I knew I wanted to sit down with Alan Hazelden and chat about the team, puzzle games, and much more. | Read more »
The Latest ‘Marvel Snap’ OTA Update Buff...
I don’t know about all of you, my fellow Marvel Snap (Free) players, but these days when I see a balance update I find myself clenching my… teeth and bracing for the impact to my decks. They’ve been pretty spicy of late, after all. How will the... | Read more »
‘Honkai Star Rail’ Version 2.4 “Finest D...
HoYoverse just announced the Honkai Star Rail (Free) version 2.4 “Finest Duel Under the Pristine Blue" update alongside a surprising collaboration. Honkai Star Rail 2.4 follows the 2.3 “Farewell, Penacony" update. Read about that here. | Read more »
‘Vampire Survivors+’ on Apple Arcade Wil...
Earlier this month, Apple revealed that poncle’s excellent Vampire Survivors+ () would be heading to Apple Arcade as a new App Store Great. I reached out to poncle to check in on the DLC for Vampire Survivors+ because only the first two DLCs were... | Read more »
Homerun Clash 2: Legends Derby opens for...
Since launching in 2018, Homerun Clash has performed admirably for HAEGIN, racking up 12 million players all eager to prove they could be the next baseball champions. Well, the title will soon be up for grabs again, as Homerun Clash 2: Legends... | Read more »
‘Neverness to Everness’ Is a Free To Pla...
Perfect World Games and Hotta Studio (Tower of Fantasy) announced a new free to play open world RPG in the form of Neverness to Everness a few days ago (via Gematsu). Neverness to Everness has an urban setting, and the two reveal trailers for it... | Read more »
Meditative Puzzler ‘Ouros’ Coming to iOS...
Ouros is a mediative puzzle game from developer Michael Kamm that launched on PC just a couple of months back, and today it has been revealed that the title is now heading to iOS and Android devices next month. Which is good news I say because this... | Read more »

## Price Scanner via MacPrices.net

Amazon is still selling 16-inch MacBook Pros...
Prime Day in July is over, but Amazon is still selling 16-inch Apple MacBook Pros for \$500-\$600 off MSRP. Shipping is free. These are the lowest prices available this weekend for new 16″ Apple... Read more
Walmart continues to sell clearance 13-inch M...
Walmart continues to offer clearance, but new, Apple 13″ M1 MacBook Airs (8GB RAM, 256GB SSD) online for \$699, \$300 off original MSRP, in Space Gray, Silver, and Gold colors. These are new MacBooks... Read more
Apple is offering steep discounts, up to \$600...
Apple has standard-configuration 16″ M3 Max MacBook Pros available, Certified Refurbished, starting at \$2969 and ranging up to \$600 off MSRP. Each model features a new outer case, shipping is free,... Read more
Save up to \$480 with these 14-inch M3 Pro/M3...
Apple has 14″ M3 Pro and M3 Max MacBook Pros in stock today and available, Certified Refurbished, starting at \$1699 and ranging up to \$480 off MSRP. Each model features a new outer case, shipping is... Read more
Amazon has clearance 9th-generation WiFi iPad...
Amazon has Apple’s 9th generation 10.2″ WiFi iPads on sale for \$80-\$100 off MSRP, starting only \$249. Their prices are the lowest available for new iPads anywhere: – 10″ 64GB WiFi iPad (Space Gray or... Read more
Apple is offering a \$50 discount on 2nd-gener...
Apple has Certified Refurbished White and Midnight HomePods available for \$249, Certified Refurbished. That’s \$50 off MSRP and the lowest price currently available for a full-size Apple HomePod today... Read more
The latest MacBook Pro sale at Amazon: 16-inc...
Amazon is offering instant discounts on 16″ M3 Pro and 16″ M3 Max MacBook Pros ranging up to \$400 off MSRP as part of their early July 4th sale. Shipping is free. These are the lowest prices... Read more
14-inch M3 Pro MacBook Pros with 36GB of RAM...
B&H Photo has 14″ M3 Pro MacBook Pros with 36GB of RAM and 512GB or 1TB SSDs in stock today and on sale for \$200 off Apple’s MSRP, each including free 1-2 day shipping: – 14″ M3 Pro MacBook Pro (... Read more
14-inch M3 MacBook Pros with 16GB of RAM on s...
B&H Photo has 14″ M3 MacBook Pros with 16GB of RAM and 512GB or 1TB SSDs in stock today and on sale for \$150-\$200 off Apple’s MSRP, each including free 1-2 day shipping: – 14″ M3 MacBook Pro (... Read more
Amazon is offering \$170-\$200 discounts on new...
Amazon is offering a \$170-\$200 discount on every configuration and color of Apple’s M3-powered 15″ MacBook Airs. Prices start at \$1129 for models with 8GB of RAM and 256GB of storage: – 15″ M3... Read more

## Jobs Board

*Apple* Systems Engineer - Chenega Corporati...
…LLC,** a **Chenega Professional Services** ' company, is looking for a ** Apple Systems Engineer** to support the Information Technology Operations and Maintenance Read more
Solutions Engineer - *Apple* - SHI (United...
**Job Summary** An Apple Solution Engineer's primary role is tosupport SHI customers in their efforts to select, deploy, and manage Apple operating systems and Read more
*Apple* / Mac Administrator - JAMF Pro - Ame...
Amentum is seeking an ** Apple / Mac Administrator - JAMF Pro** to provide support with the Apple Ecosystem to include hardware and software to join our team and Read more
Operations Associate - *Apple* Blossom Mall...
Operations Associate - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Read more
Cashier - *Apple* Blossom Mall - JCPenney (...
Cashier - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Blossom Mall Read more