TweetFollow Us on Twitter

Engineering Tips
Volume Number:4
Issue Number:2
Column Tag:The Workstation Mac

Tips for Engineering Applications

By Paul Zarchan, Cambridge, Mass.

Introduction

With the advent of the Mac 2 and many third party Macintosh speed enhancers many engineers will now consider using the Macintosh for serious computation. Many of these engineers are currently using mainframe computers where the graphics environment is primitive or nonexistant and where CPU time is expensive and has little to do with turn around time. The purpose of this article is to give a few pointers in BASIC and FORTRAN, the languages with which engineers will initially feel most comfortable, on how to make effective use of the Macintosh for both graphics and speed.

Many engineers have heard that programming on the Mac is difficult and unlike mainframe programming. This is true if the end result is a commercial product. Making a program user friendly may cause simple code to grow by more than an order of magnitude. Using the various Macintosh toolbox routines requires the learning of a new language and a new way of thinking. However ordinary engineering applications are quite easy to program on the Mac - in fact even easier to program than on a mainframe or other micro - because of the user friendly environment, superior editing tools and virtually instantaneous feedback.

This article will show how engineers can modify ordinary programs, written in FORTRAN or BASIC, which generate numerical output and enhance these programs with the addition of a few lines of code so that they can serve as input drivers to professional commercial graphics software. In this way their numerical output can easily be converted to professional quality graphs and charts with little effort. They will discover, as I did, that instantaneous graphical feedback will not only help them convey their engineering message to others quickly but will also challenge them to modify their original program to get even more useful information. In addition, techniques for generating random numbers on the Mac will be discussed so that engineers can see how easy it is to perform monte carlo and statistical analysis. Finally, for those engineers wanting to run more complex problems on the Mac in BASIC, tips will be given on how to speed up program execution tiime with minimal changes to the program.

Plotting

The powerful graphic commands in MS BASIC and the access to the Macintosh toolbox in MacFortran permit the development of plotting packages in those respective languages. However, rather than re-inventing the wheel, it is better and much easier to use a very powerful commercial graphics package for engineers that already exists - Cricket Graph. The purpose of this section is to show the few lines of code are necessary to add to existing engineering programs so that the resultant output data,whether generated in BASIC or FORTRAN, can be transferred to Cricket Graph.

Cricket Graph requires it’s numerical input to be in a tab delimited format. Unfortuneately MS BASIC writes data to a file in comma delimited format. The simple fix to the problem is to have BASIC write it’s output to the screen for viewing purposes and to also write the output to the Macintosh clipboard for eventual pasting into Cricket Graph. Listing 1 presents a sample BASIC program which computes the expressions y=i2 and z=i3 for values of i ranging between 1 and 10. The resultant output is written to both the screen and clipboard.

OPEN “CLIP:”FOR OUTPUT AS #1
FOR I=1 TO 10
Y=I*I
Z=I^3
PRINT I,Y,Z
WRITE #1,I,Y,Z
NEXT I
CLOSE #1

Listing 1 - Writing Output to Clipboard in BASIC

The code in boldface can be added to any program so that output can be written to the clipboard in tab delimited format. The next step is to quit BASIC and then open Cricket Graph and finally to use the paste command to import the data. The resultant line plot, developed with Crickett Graph and slightly enhanced in MacDraw, is shown in Fig. 1.

Figure 1 - Using Cricket Graph to Plot BASIC Output

With Cricket Graph the ranges on the abscissa and ordinate can be changed quickly by double-clicking on the axis of interest. In addition, the BASIC data can be viewed in log-log form by simply choosing the log option in Cricket Graph. Grids can be added for additional readability. Figure 2 shows the same BASIC data viewed in gridded log-log format.

Figure 2 - BASIC Output Viewed in Log-Log Format

A FORTRAN program can also be modified so that its ouput can also be placed in a tabbed delimited format. This is easier to do in FORTRAN than in BASIC because it is possible to write data to a sequential file in tabbed delimited format. In order to illustrate the technique let’s consider the Fourier Series representation of the periodic square wave shown in Fig. 3.

Figure 3 - Fourier Series Representation of Periodic Square Wave

An infinite amount of terms would yield a perfect representation of the square wave whereas a finite number of terms would approximate the square wave. This effect is known as Gibbs phenomenon. Listing 2 presents a FORTRAN program which computes the first three terms of the periodic square wave Fourier Series and also writes the output to both the screen and also to a sequential file called “SAM”.

 REAL L
 CHARACTER*1 TAB
 TAB=Z’09'
 OPEN(1,STATUS=’NEW’,FILE=’SAM’)
 L=.5
 PI=3.14159
 C1=4./PI
 DO 10 X=0,1,.01
 F1=C1*SIN(PI*X/L)
 F3=F1+C1*SIN(3.*PI*X/L)/3.
 F5=F3+C1*SIN(5.*PI*X/L)/5.
 WRITE(9,*)X,F1,F3,F5
 WRITE(1,97)X,TAB,F1,TAB,F3,TAB,F5
 97FORMAT(F8.3,A1,F8.3,A1,F8.3,A1,F8.3)
 10CONTINUE
 CLOSE(1)
 PAUSE
 END

Listing 2 - Writing Tabbed Delimited Output to File in FORTRAN

The boldfaced statements in the above listing can be added to any FORTRAN program to write the output data, in a tabbed delimited format, to a sequential file. The sequential file can then be directly opened by Cricket Graph for plotting. For this example the resultant Cricket Graph output is displayed in line chart form in Fig. 4.

Figure 4 - FORTRAN Output Displayed in Cricket Graph

Random Numbers

Random numbers play an important role in engineering applications. They form the cornerstone of monte carlo and statistical analysis. In BASIC, uniformly distributed random numbers are available with the RND statement. Other random distributions can be constructed from the uniform distribution. For example, since the RND statement creates a uniformly distributed number between 0 and 1 with variance 1/12 and mean .5, a gaussian distributed random variable with variance 1 and zero mean can be constructed, according to the central limit theorem, by adding 12 uniformly distributed numbers together (12 times 1/12 is one) and subtracting 6. Therefore the following BASIC statement generates an approximate Gaussian distributed random variable with zero mean and unity standard deviation.

X=RND+RND+RND+RND+RND+RND+RND+RND+RND+RND+RND+RND-6

The distribution is approximately Gaussian since the maximum and minimum values of the distribution are ±6 rather than ±• . If the approximate Gaussian number generator is in a program inner loop and computer running time needs to be enhanced, fewer terms can be used in the above expression to speed up the program. For example, a six term approximate Gaussian number generator with unity variance and zero mean can be constructed from

X=1.414*(RND+RND+RND+RND+RND+RND-3)

In this case the maximum and minimum values of the approximate distribution are ±3 rather than ±• .

FORTRAN, unlike BASIC does not provide a uniform random number generator. However an efficient random number generator can be constructed in FORTRAN by making one toolbox call. TOOLBX(RANDOM) generates a uniformly distributed integer between ±32768 quickly. Listing 3 presents a FORTRAN program which, by using the above toolbox call, generates approximate gaussian random numbers and then puts the numbers into bins so that a probability density function can also be constructed.

 INTEGER BIN,RANDOM,SUM
 INTEGER*4 TOOLBX
 DIMENSION H(10000),X(10000)
 PARAMETER (RANDOM=Z’86140000')
 CHARACTER*1 TAB
 TAB=Z’09'
 OPEN(2,STATUS=’NEW’,FILE=’SAM’)
 XMAX=6.
 XMIN=-6.
 RANGE=XMAX-XMIN
 TMP=1/SQRT(6.28)
 N=1000
 BIN=50
 DO 10 I=1,N
 SUM=0
      DO 14 J=1,12
      IRAN=TOOLBX(RANDOM)
      SUM=SUM+IRAN
 14  CONTINUE
     X(I)=SUM/65536.
 10CONTINUE
 DO 20 I=1,BIN
 H(I)=0
 20CONTINUE
 DO 30 I=1,N
 K=INT(((X(I)-XMIN)/RANGE)*BIN)+.99
 IF( K<1)K=1
 IF(K>BIN)K=BIN
 H(K)=H(K)+1
 30CONTINUE
 DO 40 K=1,BIN
 PDF=(H(K)/N)*BIN/RANGE
 AB=XMIN+K*RANGE/BIN
 TH=TMP*EXP(-AB*AB/2.)
 WRITE(9,*)AB,PDF,TH
 WRITE(2,97)AB,TAB,PDF,TAB,TH
 97FORMAT(F8.3,A1,F8.3,A1,F8.3)
 40CONTINUE
 CLOSE(2)
 PAUSE
 END

Listing 3 - FORTRAN Program Illustrating Random Number Generation

The highlighted terms are those statements which are required by any FORTRAN program to generate uniformly distributed or gaussian distributed random numbers. Here X(I) is the resultant gaussian distributed number. In this particular program 1000 random numbers are calculated. The accuracy of the random number generator is illustrated by viewing the program output, shown in Fig. 5, which compares the sampled probability density function to the theoretical bell-shaped curve.

Figure 5 - FORTRAN Generates Gaussian Distributed Random Numbers Accurately

Speeding Up BASIC Programs

In a previous issue MacTutor issue1 it was shown how the transient response of a sixth order Butterworth filter could be simulated in FORTRAN using the second order Runge Kutta method for integrating the six differential equations. A block diagram of the Butterworth filter is repeated here for convenience in Fig. 6. Here the “1/s” terms represent integrations.

Figure 6 - Sixth Order Butterworth Filter

The resultant six first order differential equations, which can be obtained from Fig. 6, are:

A BASIC program which can integrate the above differential equations is shown in Listing 4.

DIM X(6),XOLD(6),XD(6)
START=TIMER
B1=3.86:B2=7.46:B3=9.13:B4=7.46:B5=3.86:B6=1:W0=50
XIN=1
ORDER=6
FOR I=1 TO ORDER
X(I)=0
NEXT I
T=0
H=.0005
S=0
BEGIN:
IF T>=.5 GOTO FINISH
S=S+H
FOR I=1 TO ORDER
XOLD(I)=X(I)
NEXT I
GOSUB INTEG
FOR I=1 TO ORDER
X(I)=X(I)+H*XD(I)
NEXT I
T=T+H
GOSUB INTEG
FOR I=1 TO ORDER
X(I)=.5*(XOLD(I)+X(I)+H*XD(I))
NEXT I
IF S>.004999 THEN
S=0
PRINT T,X(1)
END IF
GOTO BEGIN
FINISH:
PRINT TIMER-START
WHILE INKEY$=””:WEND
INTEG:
XD(1)=X(2)
XD(2)=X(3)
XD(3)=X(4)
XD(4)=X(5)
XD(5)=X(6)
XD(6)=(W0^6)*(XIN-B5*X(6)/(W0^5)-B4*X(5)/(W0^4)-B3*X(4)/(W0^3)-B2*X(3)/(W0^2)-B1*X(2)/W0-X(1))/B6
RETURN
END

Listing 4 - BASIC Simulation of Butterworth Filter

We can see from the listing that the integration step size, H, is .0005 sec. The running time for this program in interpretive MS BASIC is 229 sec on a Macintosh. Halving the step size or doubling the simulation time will double the running time. The program can be speeded up by using the MS BASIC Compiler and the resultant running time will decrease to 56 sec. Other methods can also be used to further enhance speed. For example the compiler and interpreter assume that all arrays are dynamic. However we can tell the compiler, but not the interpreter, that the arrays are static (as long as we aren’t going to redimension statements during the program) and significantly decrease the running times. In addition, making loop parameters integers, as is commonly done in FORTRAN, rather than default single precision real numbers will also enhance running time - especially with the compiler. Converting real numbers to integers can easily be accomplished in BASIC by adding a percent sign to the variable. Finally eliminating repeated calculations of constants from loops will also speed up the program. For example, the derivative XD(6) has many such constant computations which can easily be moved to the beginning of the program without destroying the readability of the code. The faster running BASIC program is shown in Listing 5.

DIM X(6),XOLD(6),XD(6)
START=TIMER
B1=3.86:B2=7.46:B3=9.13:B4=7.46:B5=3.86:B6=1:W0=50
XIN=1
ORDER%=6
W02=W0*W0
W03=W02*W0
W04=W03*W0
W05=W04*W0
W06=W05*W0
FOR I%=1 TO ORDER%
X(I%)=0
NEXT I%
T=0
H=.0005
S=0
BEGIN:
IF T>=.5 GOTO FINISH
S=S+H
FOR I%=1 TO ORDER%
XOLD(I%)=X(I%)
NEXT I%
GOSUB INTEG
FOR I%=1 TO ORDER%
X(I%)=X(I%)+H*XD(I%)
NEXT I%
T=T+H
GOSUB INTEG
FOR I%=1 TO ORDER%
X(I%)=.5*(XOLD(I%)+X(I%)+H*XD(I%))
NEXT I%
IF S>.004999 THEN
S=0
PRINT T,X(1)
END IF
GOTO BEGIN
FINISH:
PRINT TIMER-START
WHILE INKEY$=””:WEND
INTEG:
XD(1)=X(2)
XD(2)=X(3)
XD(3)=X(4)
XD(4)=X(5)
XD(5)=X(6)
XD(6)=W06*(XIN-B5*X(6)/W05-B4*X(5)/W04-B3*X(4)/W03-B2*X(3)/W02-B1*X(2)/W0-X(1))/B6
RETURN
END

Listing 6 - Faster BASIC Program

The terms that were changed to speed up the program are highlighted. Table 1 documents the speedup enhancements.

Condition Interpreter Compiler

Nominal 229 sec 56 sec

Make Arrays Static 229 sec 42 sec

Use Integers in Loops 211 sec 26 sec

Move Constant Computations 120 sec 22 sec

Out of Loops

Table 1 - Improving Speed of BASIC

We can see from Table 1 that there is a big payoff in using static arrays and integers when using the compiler. On the other hand, moving constant computations out of loops is more effective, in this case, when using the interpreter. For this example we can see that the net speed-up in being careful and using the compiler, rather than the interpreter, is more than a factor of 10 with only minor modifications to the original code. The best policy is to first get the programmed debugged and running using the interpreter because errors can be found and corrections can be made virtually instaneously. The tips for speed enhancement can then be applied when the program is checked out and is ready to be compiled.

References

1. Zarchan, P. “New Mac Workstation Potential”,

MacTutor, March 1987, pp. 15-21.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

VirtualBox 5.1.10 - x86 virtualization s...
VirtualBox is a family of powerful x86 virtualization products for enterprise as well as home use. Not only is VirtualBox an extremely feature rich, high performance product for enterprise customers... Read more
Pixa 1.1.9 - Quickly and easily organize...
Pixa is an image-organizing application. The new app functions well, is easy to use, and helps people organize their images quickly and easily on their computers. For those who prefer not to use the... Read more
Civilization VI 1.0.1 - Next iteration o...
Sid Meier’s Civilization VI is the next entry in the popular Civilization franchise. Originally created by legendary game designer Sid Meier, Civilization is a strategy game in which you attempt to... Read more
Google Chrome 55.0.2883.75 - Modern and...
Google Chrome is a Web browser by Google, created to be a modern platform for Web pages and applications. It utilizes very fast loading of Web pages and has a V8 engine, which is a custom built... Read more
Chromium 55.0.2883.75 - Fast and stable...
Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all Internet users to experience the web. Version 55.0.2883.75: Security fixes: High CVE-2016... Read more
Luminar 1.0.2 - Powerful, adaptive, conf...
Luminar is the new full-featured image editor that adapts to the way you edit photos. Over 300 essential tools to fix, edit, and enhance your photos with comfort. The future of photo editing is here... Read more
Slack 2.3.3 - Collaborative communicatio...
Slack is a collaborative communication app that simplifies real-time messaging, archiving, and search for modern working teams. Version 2.3.3: Fixed window zoom jumping back-and-forth OS X 10.9... Read more
WhatRoute 2.0.10 - Geographically trace...
WhatRoute is designed to find the names of all the routers an IP packet passes through on its way from your Mac to a destination host. It also measures the round-trip time from your Mac to the router... Read more
Luminar 1.0.2 - Powerful, adaptive, conf...
Luminar is the new full-featured image editor that adapts to the way you edit photos. Over 300 essential tools to fix, edit, and enhance your photos with comfort. The future of photo editing is here... Read more
WhatRoute 2.0.10 - Geographically trace...
WhatRoute is designed to find the names of all the routers an IP packet passes through on its way from your Mac to a destination host. It also measures the round-trip time from your Mac to the router... Read more

Latest Forum Discussions

See All

Amateur Surgeon 4 Guide: Become the worl...
It's time to wield your trusty pizza cutter again, as Amateur Surgeon has returned with a whole fresh set of challenges (and some old, familiar ones, too). Starting anew isn't easy, especially when all you have at your disposal is a lighter, the... | Read more »
Le Parker: Sous Chef Extraordinaire (Ga...
Le Parker: Sous Chef Extraordinaire 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: | Read more »
Telltale Games really is working on a Gu...
Telltale Games' next episodic adventure is indeed Guardians of the Galaxy. A document tied to the voice actors strike suggested that the project was in the work, but now we have direct confirmation following an announcement at the Game Awards that... | Read more »
Amateur Surgeon returns to iOS and Andro...
Amateur Surgeon and its two sequels disappeared from the App Store some time and it was sad days for all. But now, just in time for the holidays, the Adult Swim favorite makes its joyous return in the shape of Amateur Surgeon 4, a remake with... | Read more »
The best board games on mobile
Sometimes you need to ditch all of the high speed, high action games in favor of something a little more traditional. If you don't feel like parting ways from your mobile device, though, there are still plenty of ways to get that old-school fix.... | Read more »
The best Facebook Messenger Instant Game...
Facebook's new Instant Games is now here, meaning you can play games with your friends directly via Facebook. It's a fun new way to connect with friends, of course, but it's also proving to be a solid gaming experience in its own right, with a... | Read more »
You can now play game's on Facebook...
Facebook launched its new Instant Games platform in an exciting new attempt to engage its user base. As a result, you can now play a number of different games directly through Facebook Messenger. All of these games run with HTML5, meaning you play... | Read more »
Apollo Justice Ace Attorney (Games)
Apollo Justice Ace Attorney 1.00.00 Device: iOS Universal Category: Games Price: $.99, Version: 1.00.00 (iTunes) Description: Court Is Back In Session Star as rookie defense attorney, Apollo Justice, as he visits crime scenes,... | Read more »
KORG iWAVESTATION (Music)
KORG iWAVESTATION 1.0 Device: iOS Universal Category: Music Price: $19.99, Version: 1.0 (iTunes) Description: A revolutionary new world of sound.The Wave Sequence Synthesizer for iPad - KORG iWAVESTATION | Read more »
Don't Grind Guide: Tips for becomin...
Don’t Grind is a surprising, derpy little one touch game with fun hand-drawn graphics. The goal is simple -- get the high score without being chopped to bits. That can be tough when you’re not used to the game, and that’s compounded by the fact... | Read more »

Price Scanner via MacPrices.net

13-inch Silver Touch Bar MacBook Pro in stock...
Amazon has the new 2016 13″ 2.9GHz/256GB Silver Touch Bar MacBook Pro (MLVP2LL/A) in stock today and on sale for $1749 including free shipping. That’s $50 off MSRP, and it’s the lowest price... Read more
Parallels Toolbox 1.3 for Mac Offers 25 Singl...
Parallels has launched Parallels Toolbox 1.3 for Mac, an upgrade that adds five new utilities to the stand-alone application which was released in August and is available exclusively online at http... Read more
OWC Mercury Elite Pro Dual mini Ultra-Portabl...
OWC has introduced the new OWC Mercury Elite Pro Dual mini, a powerful yet ultra-portable dual-drive RAID solution. The new Mercury Elite Pro Dual mini packs phenomenal performance into a small... Read more
Clearance 13-inch Retina MacBook Pros availab...
B&H Photo has clearance 2015 13″ Retina Apple MacBook Pros available for up to $200 off original MSRP. Shipping is free, and B&H charges NY tax only: - 13″ 2.7GHz/128GB Retina MacBook Pro: $... Read more
Roundup of 2016 13-inch 2.0GHz MacBook Pro sa...
B&H has the non-Touch Bar 13″ MacBook Pros in stock today for $50-$100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 13″ 2.0GHz MacBook Pro Space Gray (MLL42LL/A): $1449 $... Read more
New 13-inch 2.0GHz Space Gray MacBook Pro in...
Adorama has the new 13″ 2.0GHz Space Gray MacBook Pro (non-Touch Bar, MLL42LL/A) in stock for $1499 including a free 3-year AppleCare Protection Plan. Shipping is free, and Adorama charges sales tax... Read more
Finnair Adopts iOS Enterprise iPad Apps from...
Finnair and IBM have announced a first-of-its-kind agreement to utilize iOS enterprise apps from IBM to support the airline’s overall digital transformation. Finnair is focused on Asia-Europe traffic... Read more
Tech21 Launches Evo Go iPhone 7 Case Availabl...
Tech21 has announced the launch of the Evo Go case for Apple iPhone 7 and iPhone 7 Plus, exclusively at T-Mobile. Available online and at participating T-Mobile stores nationwide, Evo Go cases start... Read more
Apple Turns (RED) with More Ways to Join the...
In recognition of World AIDS Day, Apple is offering more ways than ever for customers to join (RED) in its mission to create an AIDS-free generation. Apple is the worlds largest corporate contributor... Read more
Deals on new 15-inch Touch Bar MacBook Pros,...
B&H Photo has new 2016 Apple 15″ Touch Bar MacBook Pro models in stock today with some available for $50 off MSRP, each including free shipping plus NY sales tax only: - 15″ 2.7GHz Touch Bar... Read more

Jobs Board

*Apple* Brand Ambassador (Macy's) - The...
…(T-ROC), is proud of its unprecedented relationship with our partner and client, APPLE ,in bringing amazing" APPLE ADVOCATES"to "non" Apple store locations. Read more
US- *Apple* Store Leader Program - Apple (Un...
…Summary Learn and grow as you explore the art of leadership at the Apple Store. You'll master our retail business inside and out through training, hands-on Read more
*Apple* Retail - Multiple Positions- White P...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
Automotive Detailer - *Apple* Used Autos -...
We are currently conductinginterviews and will be accepting applications for a part-time detailer. Apple Used Autos is a great place to work andstart a career. We Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.