TweetFollow Us on Twitter

Background TCL
Volume Number:9
Issue Number:12
Column Tag:TCL Workshop

A Piece of Apple Pi

Background processing with TCL

By Malcolm H. Teas, Rye, New Hampshire

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

About the author

Malcolm Teas has been programming the Macintosh for five years. He’s active with object programming in TCL and also uses C with Think and MPW. He lives, works, and consults from his house on the seacoast of New Hampshire.

I needed a project to test the new Think C version, since I have an interest in number theory, the project I picked was a Π calculation program. Most similar programs take over the machine while they’re at work. I wanted this one (just to keep life interesting) to optionally calculate Π in the background and let other applications continue. As the Mac doesn’t have preemptive multitasking, background applications only get time as permitted from the foreground application and vice versa. So, when we program time-intensive tasks, we’ve got to be nice to other software that may be running. The approach I took here is to let the user decide if this application should hog the system or not by setting an option in a menu. The default is to not hog.

To do this, I break the calculation up into a number of steps. The steps are implemented by a subclass of a TCL Chore object. This work is done at idle event time indirectly by the Dawdle() method of the bureaurocrats. The amount of CPU time that the calculation takes is the same if it’s done in the background or if the application hogs the system. However, the amount of time to the user is significantly longer if the work’s done in the background. This is due to the overhead of the time through the toolbox getting the idle event to run the calculation code. In addition, the calculation code is done in small steps and interspersed with other applications, etc. In the hog mode, it never leaves the calculation code at all but other apps don’t get CPU time.

Backgrounding is best for an application that’s got pre-calculation to do or can intersperse work with user input. As humans are so slow compared to the computer, the imbalance of speed can be put to good use this way.

Designing a chore for background processing

There are a couple of issues for chore-based background work. First, the chore has to be handled or know where to get all the information it needs for it’s processing. Second, if it’s work that gets completed that something else depends on, the chore has to be able to signal work complete. Last, chores need to be disposed of. One thing at a time.

In my case, my CPiChore class is a subclass of the CChore class. You’ll have to subclass the CChore class too as the standard class does nothing. The only method in CChore is the Perform() method (and of course those methods it inherits from CObject). My CPiChore subclass overrides the Perform() and Dispose() methods. It also has two new methods InitChore() and GetTicks() for setting the necessary data and getting information.

The InitChore() method takes all the necessary data as parameters. If I’d had a lot of data I could’ve passed a structure with the data loaded into it. However, as I only had four items, that seemed overkill for this project. Another alternative would’ve been for the chore to ask the necessary objects for the relevant data.

InitChore() takes the number of digits of Π to calculate, a pointer to the document object, and two flags to determine if the calculation should be timed and if hog mode is on. This data is stored locally. Note that the flags are stored in the object, but the document and the number of digits are stored in global variables that are defined and declared in the CPiChore.cp file. This makes them local to that file. The document object CAppPiDoc declares the CPiChore in it’s include file (CAppPiDoc.h). As a short-cut, I included the CAppPiDoc.h file in the CPiChore.cp file, and declared a global “document”. This means that I don’t have to type-cast as often when I use the “document” variable. The “Digits” variable is where the numDigits value is put. As this Π calculation code is ported, I didn’t convert all the calculation code to methods, instead, I left them and their global data in this CPiChore.cp file as straight C functions and data.

Perform() is the function in a chore that actually does the work. It’s called by the Idle() function in CApplication which is called every time an idle event happens. TCL considers an idle event to occur when we either receive a null event or a mouse-moved event. Note that if you’re doing background processing, you want null events while you’re app is in the background. To get them, the “Background null events” flag in the Size resource must be set. Use the SIZE flags popup in the Set Project Type dialog to do this.

The Idle() function also does some other things like check memory and do the Dawdle() method in the CBureaucrat object. Idle() runs through the chain of command to call all the Dawdle() methods there. It then runs through the list of chores to call Perform() on all the chores in the list.

When it gets to the Perform() method in CPiChore, CPiChore uses a stage counter to figure out what’s been done and what to do next. Basically, this determines and remembers what step it’s on. CPiChore uses the Machin algorithm to calculate Π (see the sidebar). The last step in the calculation stops the count of the time and tells the CAppPiDoc object that the chore is done by calling PiDone() in the document with the result of the calculation as it’s parameter.

The document gets the time the calculation took, sets flags for the state of the calculation and sends the result to the pane for display. The next time and idle event happens and the document’s Dawdle() method is called, the chore will be disposed of. This approach to deallocating the chore is known as lazy management of memory. It has the advantage that, as the Dawdle() method is called all the time, it’s more sure in deallocating the chore. The completion and the deallocation are in independent routines.

The pane to display this information isn’t a standard text edit pane. Text edit can only handle information up to around 30K of text characters. It’s easy to generate a value of Π that takes more space that this. I subclassed CPanorama to make a pane that just displayed a lot of text for this application. In addition, this CPiPane object also knows how to translate the digit numbers to text characters and how to display the time information too.

Implementation details

All the key user actions are handled through the DoCommand() method of the CAppPiDoc object. The one exception is the about box which is handled in the application’s DoCommand() method.

The number of digits is set in a dialog box that I use the regular TCL dialog classes to run. The DoCommand() method extracts the digit count from the dialog before it’s disposed. Although Symantec’s documentation states that the dialog objects must be subclassed to be really useful, I didn’t find the need to do that with the number of dialog view objects that know about the format and range of information. In this case, I used an integer text dialog view object that was told, via the template, what range of numbers to accept. Then, I use the FindViewByID() method to get that object and extract the now-conditioned value.

The time and hog (or “faster”) commands just toggle their values. In the UpdateMenus() method, these values are used to determine if those menu items are checked or not.

The start command is the important one. If the Π calculation chore is running, then this item is labeled “Stop”. If selected, it cancels and disposes of the chore. If the chore isn’t running, it starts it using the currently set number of digits and the timing and faster flags. It then assigns the chore to the application, this puts the chore in the chore list to be processed on an idle event. The chore will stay in the list until removed.

Once the chore is in the list, then the Perform() method is called with every idle event. If the faster or hog mode is on, then the Perform() method doesn’t return until the calculation is complete. Otherwise, it does one step and returns.

When the calculation is complete, the Perform() method calls the PiDone() method in the document which hands the result data off to the pane for display with the pane’s SetContent() method. This result data looks like the other data used in the calculation. It’s an array of character, but I use the characters as small integers. Actually, there’s a fair amount of wasted space as the integers range from 0-9. The calculation is carried out in decimal and there are custom routines to handle multiple place arithmetic.

The SetContent() method disposes any previous pointer to data (the data is held as pointers due to the ported code) and converts the data to characters for display. It does this by simply adding the integer value of the character zero to each number in the array.

When the Draw() method for the pane is called (it’s called automatically when the pane needs to be refreshed or when Refresh() is called), it sets the font and size of the text to draw. Draw() then creates a header line, draws it, skips down a little and draws the characters for Π. To do the drawing of the text, Draw() calls a routine called DrawWrapText() to wrap the text at the margins correctly.

DrawWrapText() takes parameters to the text, it’s size, and the margin, line information and whether or not to force a margin. This latter is similar to typing the return key to force a new line.

Listing:  CPiChore.cp
/*
 CPiChore
 Written and copyright by Malcolm H. Teas 1993.
 All rights reserved.
 
*/

#include "CAppPiDoc.h"

/*
 * Global variables
 */
int   Sign, 
 Zero, 
 Digits, 
 Pass,  /* two passes */
 Exp, /* exponent for divide */
 Divide;
static int constant[3]={0,25,239};

CAppPiDoc *document;
 
/*
 * These character arrays represent the digits for extended
 * precision arithmatic. (These may need to be int on 
 * some machines).
 */
#define DIGIT char
DIGIT *Power, *Term, *Result;

void copy (void);
void init(void);
void divi(register DIGIT *array);
void sub (void);
void add (void);

void CPiChore::Perform (long *maxSleep)
{
 long start;
 
 if (timeCalc)
 start = TickCount ();
 
 do  {
 switch (stage)  {
 case 0:
 init ();
 stage++;
 break;
 
 case 1:
 copy();
 Divide = Exp;
 divi(Term);
 if ( Sign > 0 ) 
 add();
 if ( Sign < 0 ) 
 sub();
 Exp = Exp + 2;
 Sign *= -1;
 Divide = constant[Pass];
 divi(Power);
 if (Pass == 2) 
 divi(Power);
 if (Zero == 0)
 stage++;
 break;
 
 case 2:
 Pass++;
 init ();
 stage++;
 break;
 
 case 3:
 copy();
 Divide = Exp;
 divi(Term);
 if ( Sign > 0 ) 
 add();
 if ( Sign < 0 ) 
 sub();
 Exp = Exp + 2;
 Sign *= -1;
 Divide = constant[Pass];
 divi(Power);
 if (Pass == 2) 
 divi(Power);
 if (Zero == 0)
 stage++;
 break;
 
 case 4:
 if (timeCalc)  {
 ticks += TickCount() - start;
 timeCalc = false;
 }
 document->PiDone (Result);
 stage++;
 break;
 
 case 5:
 break;
 }
 }  while (faster && stage != 5);
 
 if (timeCalc)
 ticks += TickCount() - start;
}

void CPiChore::InitChore (long numDigits, CDocument *doc, 
 Boolean timeIt, Boolean faster)
{
 stage = 0;
 Pass = 1;
 document = (CAppPiDoc *) doc;
 timeCalc = timeIt;
 ticks = 0;
 this->faster = faster;
 
 Digits = numDigits;
 FailNIL (Power = (char *) NewPtr (numDigits + 1));
 FailNIL (Term = (char *) NewPtr (numDigits + 1));
 FailNIL (Result = (char *) NewPtr (numDigits + 1));
}

long CPiChore::GetTicks (void)
{
 return ticks;
}

void CPiChore::Dispose (void)
{
 DisposPtr (Power);
 DisposPtr (Term);

 inherited::Dispose (); 
}

void add (void)
{
 register DIGIT *r, *t;
 register int sum, carry = 0;
    
 r = Result + Digits;
 t = Term + Digits;
 
 while( r >= Result )
 {
 sum = *r + *t + carry;
 carry = 0;
 if( sum >= 10 )
 {
 sum -= 10;
 carry++;
 }
 *r-- = sum;
 --t;
 }
}
 
void sub (void)
{
 register DIGIT *r, *t;
 register int diff, loan = 0; 
 
 r = Result + Digits;
 t = Term + Digits;
 
 while( r >= Result )
 {
 diff = *r - *t - loan;
 loan = 0;
 if( diff < 0 )
 {
 diff += 10;
 loan++;
 }
 *r-- = diff;
 --t;
 }
}
 
void divi(register DIGIT *array)
{
 register DIGIT *end;
 register int quotient, residue, digit = 0;
 
 Zero = 0;
 
 for( end = array + Digits; array <= end; )
 {
 digit    += *array;
 quotient =  digit / Divide;
 residue  =  digit % Divide;
 
 if((Zero !=0) || ((quotient+residue) != 0)) 
 Zero = 1;
 else 
 Zero = 0;
 
 *array++ = quotient;
 digit = 10 * residue;
 }
}
 
void init(void)
{
 register DIGIT *p, *t, *r, *end;
 
 p = Power;
 t = Term;
 r = Result;
 end = Power+Digits;
 
 while( p <= end )
 {
 *p++ = 0;
 *t++ = 0;
 
 if (Pass == 1) 
 *r++ = 0;
 }
 
 *Power = 16 / (Pass * Pass);
 
 if( Pass == 1 ) 
 {
 Divide = 5;
 }
 else
 {
 Divide = 239;
 }
 
 divi(Power);
 Exp = 1;
 Sign = 3 - (2 * Pass);
}
 
void copy (void)
{
 register DIGIT *t, *p, *end;
 
 t = Term;
 p = Power;
 end = Term + Digits;
 
 while (t <= end)
 {
 *t++ = *p++;
 }
}

How to calculate Π

The number Π in it’s simplest form, is the ratio of the circumference of a circle to that circle’s diameter. It’s an irrational number so it can’t be represented exactly by a ratio, or fraction, between two integers. As decimal numbering systems are essentially another way of expressing a fraction (i.e. the number 2.5 is actually the fraction 25/10), then Π, expressed as a decimal number, has an infinite number of places. A good reference for Π calculations is the book “History of Π” by Petr Beckmann.

The Π calculation algorithms work by interating over an approximation to Π. Each iteration, or time through the algorithm, the accuracy of the Π estimate increases. We say that we’re calculating Π, but we’re actually calculating an approximation to it. John Wallis, a sixteenth-century mathemetician, discovered a series of fractions, that when multiplied together result in Π. These are two ways to write Wallis’ product:

While this works fine, it’s also quite slow to converge or increase in accuracy, each fraction added doesn’t increase the accuracy very much. The Apple Π program in the article uses the Machin algorithm which converges much faster. It sums more complex fractions to speed up the process. More recently, mathemeticians using elliptical integrals discovered the holy grail of Π calculations: an algorithm, that while quite complex, doubles the number of accurate digits of Π for each iteration.

I ported the Machin algorithm from a version by Bryan Costales, who in turn ported it from a version by Robert Bishop. The algorithm is based on the equation:

[This is a Taylor expansion of 16 * Arctan(1/5) - 4 * Arctan(1/239). Tech. Ed.]

I use arrays of digits to implement the numbers and have written my own routines to do the arithmetic with these numbers. The calculation above is broken down into a number of steps. A step is done each time through the idle loop in the application.

Some have claimed that calculating Π to ever increasing numbers of digits (the record is around 40 million digits currently) is unecessary and not useful. However, when companies install a new supercomputer, this kind of calculation can be used for testing as it repeats intensive CPU work.

Number theorists use the results of long Π calculations to analyze the characteristics of the number, and through it, other similar numbers. Since number theory is a fundamental branch of mathematics that’s used in cryptography and computer theory this work may shed light on some aspects of mathematics that can be of practical use. Besides, it’s fun.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

OS X Server 4.1.3 - For OS X 10.10 Yosem...
Designed for OS X and iOS devices, OS X Server makes it easy to share files, schedule meetings, synchronize contacts, develop software, host your own website, publish wikis, configure Mac, iPhone,... Read more
pwSafe 4.1 - Secure password management...
pwSafe provides simple and secure password management across devices and computers. pwSafe uses iCloud to keep your password databases backed-up and synced between Macs and iOS devices. It is... Read more
Kodi 15.0.rc1 - Powerful media center to...
Kodi (was XBMC) is an award-winning free and open-source (GPL) software media player and entertainment hub that can be installed on Linux, OS X, Windows, iOS, and Android, featuring a 10-foot user... Read more
Coda 2.5.11 - One-window Web development...
Coda is a powerful Web editor that puts everything in one place. An editor. Terminal. CSS. Files. With Coda 2, we went beyond expectations. With loads of new, much-requested features, a few surprises... Read more
Bookends 12.5.7 - Reference management a...
Bookends is a full-featured bibliography/reference and information-management system for students and professionals. Access the power of Bookends directly from Mellel, Nisus Writer Pro, or MS Word (... Read more
Maya 2016 - Professional 3D modeling and...
Maya is an award-winning software and powerful, integrated 3D modeling, animation, visual effects, and rendering solution. Because Maya is based on an open architecture, all your work can be scripted... Read more
RapidWeaver 6.2.3 - Create template-base...
RapidWeaver is a next-generation Web design application to help you easily create professional-looking Web sites in minutes. No knowledge of complex code is required, RapidWeaver will take care of... Read more
MacFamilyTree 7.5.2 - Create and explore...
MacFamilyTree gives genealogy a facelift: it's modern, interactive, incredibly fast, and easy to use. We're convinced that generations of chroniclers would have loved to trade in their genealogy... Read more
Paragraphs 1.0.1 - Writing tool just for...
Paragraphs is an app just for writers. It was built for one thing and one thing only: writing. It gives you everything you need to create brilliant prose and does away with the rest. Everything in... Read more
BlueStacks App Player 0.9.21 - Run Andro...
BlueStacks App Player lets you run your Android apps fast and fullscreen on your Mac. Version 0.9.21: Note: Now requires OS X 10.8 or later running on a 64-bit Intel processor. Initial stable... Read more

Rage of Bahamut is Giving Almost All of...
The App Store isn't what it used to be back in 2012, so it's not unexpected to see some games changing their structures with the times. Now we can add Rage of Bahamut to that list with the recent announcement that the game is severely cutting back... | Read more »
Adventures of Pip (Games)
Adventures of Pip 1.0 Device: iOS iPhone Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: ** ONE WEEK ONLY — 66% OFF! *** “Adventures of Pip is a delightful little platformer full of charm, challenge and impeccable... | Read more »
Divide By Sheep - Tips, Tricks, and Stre...
Who would have thought splitting up sheep could be so involved? Anyone who’s played Divide by Sheep, that’s who! While we’re not about to give you complete solutions to everything (because that’s just cheating), we will happily give you some... | Read more »
NaturalMotion and Zynga Have Started Tea...
An official sequel to 2012's CSR Racing is officially on the way, with Zynga and NaturalMotion releasing a short teaser trailer to get everyone excited. Well, as excited as one can get from a trailer with no gameplay footage, anyway. [Read more] | Read more »
Grab a Friend and Pick up Overkill 3, Be...
Overkill 3 is a pretty enjoyable third-person shooter that was sort of begging for some online multiplayer. Fortunately the begging can stop, because its newest update has added an online co-op mode. [Read more] | Read more »
Scanner Pro's Newest Update Adds Au...
Scanner Pro is one of the most popular document scanning apps on iOS, thanks in no small part to its near-constant updates, I'm sure. Now we're up to update number six, and it adds some pretty handy new features. [Read more] | Read more »
Heroki (Games)
Heroki 1.0 Device: iOS Universal Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: CLEAR THE SKIES FOR A NEW HERO!The peaceful sky village of Levantia is in danger! The dastardly Dr. N. Forchin and his accomplice,... | Read more »
Wars of the Roses (Games)
Wars of the Roses 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
TapMon Battle (Games)
TapMon Battle 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: It's time to battle!Tap! Tap! Tap! Try tap a egg to hatch a Tapmon!Do a battle with another tapmons using your hatched tapmons! *... | Read more »
Alchemic Dungeons (Games)
Alchemic Dungeons 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: ### Release Event! ### 2.99$->0.99$ for limited time! ### Roguelike Role Playing Game! ### Alchemic Dungeons is roguelike... | Read more »

Price Scanner via MacPrices.net

Seagate Backup Plus Drives Feature 200GB of C...
Seagate Technology plc has announced that its Backup Plus family of external storage offerings will now include 200GB of OneDrive cloud storage, a major added value, and the addition of Lyve’s photo... Read more
Canon PIXMA MG3620 Wireless Inkjet All-in-One...
Canon U.S.A., Inc. has announced the PIXMA MG3620 Wireless (1) Inkjet All-in-One (AIO) printer for high-quality photo and document printing. Built with convenience in mind for the everyday home user... Read more
July 4th Holiday Weekend 13-inch MacBook Pro...
Save up to $150 on the purchase of a new 2015 13″ Retina MacBook Pro at the following resellers this weekend. Shipping is free with each model: 2.7GHz/128GB MSRP $1299 2.7GHz/... Read more
27-inch 3.5GHz 5K iMac on sale for $2149, sav...
Best Buy has the 27″ 3.5GHz 5K iMac on sale for $2149.99. Choose free shipping or free local store pickup (if available). Sale price for online orders only, in-store prices may vary. Their price is $... Read more
Apple now offering refurbished 2015 11-inch...
The Apple Store is now offering Apple Certified Refurbished 2015 11″ MacBook Airs as well as 13″ MacBook Airs (the latest models), available for up to $180 off the cost of new models. An Apple one-... Read more
15-inch 2.5GHz Retina MacBook Pro on sale for...
Amazon.com has the 15″ 2.5GHz Retina MacBook Pro on sale for $2274 including free shipping. Their price is $225 off MSRP, and it’s the lowest price available for this model. Read more
Finally Safe To Upgrade To Yosemite’?
The reason I’ve held back from upgrading my MacBook Air from OS X 10.9 Mavericks to 10.10 Yosemite for nearly a year isn’t just procrastination. Among other bugs reported, there have been persistent... Read more
Logo Pop Free Vector Logo Design App For OS X...
128bit Technologies has released of Logo Pop Free 1.2 for Mac OS X, a vector based, full-fledged, logo design app available exclusively on the Mac App Store for the agreeable price of absolutely free... Read more
21-inch 1.4GHz iMac on sale for $999, save $1...
B&H Photo has new 21″ 1.4GHz iMac on sale for $999 including free shipping plus NY sales tax only. Their price is $100 off MSRP. Best Buy has the 21″ 1.4GHz iMac on sale for $999.99 on their... Read more
16GB iPad mini 3 on sale for $339, save $60
B&H Photo has the 16GB iPad mini 3 WiFi on sale for $339 including free shipping plus NY tax only. Their price is $60 off MSRP. Read more

Jobs Board

Frameworks Engineer, *Apple* Watch - Apple...
**Job Summary** Join the team that is shaping the future of software development for Apple Watch! As a software engineer on the Apple Watch Frameworks team you will Read more
Mobile Payments Counsel, *Apple* Pay (digit...
**Job Summary** Apple is looking for an atto ey to join Apple 's Legal Department to support Apple Pay. **Key Qualifications** 4+ years of relevant experience Read more
*Apple* Solutions Consultant - Retail Sales...
**Job Summary** The ASC is an Apple employee who serves as the Apple business manager and influencer in a hyper-business critical Reseller's store which delivers Read more
Partner Marketing Manager, Merchant- *Apple*...
**Job Summary** The Apple Pay partner marketing team is looking for a marketing manager to develop and drive US marketing programs with our merchant partners. The right Read more
*Apple* Solutions Consultant - Retail Sales...
**Job Summary** As an Apple Solutions Consultant (ASC) you are the link between our customers and our products. Your role is to drive the Apple business in a retail Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.