1620_Users_Group_Western_Region_196406 1620 Users Group Western Region 196406

1620_Users_Group_Western_Region_196406 1620_Users_Group_Western_Region_196406

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1620 USERS GROUP
WESTERN REGION
MINUTES OF THE MEETING
JUNE 17-19, 1964

DENVER, COLORADO

ROBERT R. WHITE
WESTERN REGION SECRETARY

:_*_ _
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1'

o

CONTENTS

1.

Roster of Attendees

2.

Minutes of the Eighth Meeting of the Western Region 1620
Users Group

3.

Sound-off Session

4.

Agenda

5.

A Least Squares Solution tor a Range Measuring Instrumentation System; Oliver Lee Kingsley and Burton L. Williams

6. Boundary Value Problems in Ordinary Differential Equations

with Constant Coefficients; Riohard Rosanoft and Gordon Nab

7. a)
b)
8.

9.

o

Reader; R. C. Steinbaoh
A 519 Simulator; R. C. Steinbach

Simultaneous Linear Equations with Complex Coefficients;

H. Kuffel

Applications of Numerical Filters in the Power Spectral
Analysis of Stationary Time Series; Alexander A. J. Hoffman

10.

IBM 1620 Assists Student Counselors at Junior College;

11.

1620 Computer Utilization in a Wind Tunnel Data Acquisition
System; Stanley E. Wisniewski

12.

1620 1PL-V; Wendell T. Beyer

13.

Petroleum Exploration and Production Application for the
IBM 1620 and Plotter; Jack L. Morrison

14.

A Control System Approach to Automatic Jet Engine Testing;
Aubrey D. Wood

15.

Generalized Filter Hetwork A/C Steady State Analysis
Program; D. H. O'Herren

16.

FORTRAN II - Debugging Techniques and Aids; Leon P. Goldberg

17 •

FORTRAN II and the 1443; Lanny L. Hotfman

18.

A Survey ot the Beginning Programming

Paul S. Chan

Cou~se;

Clarence B.

Germain

19.

FORTRAN "Teach" Problems; Wendell L. Pope

1

.. ------.--,~~~~~~----.------~--~----

._---

20.

A Load-and-Go SPS with Monitor Control; Kenneth M. Lochner
and Glenn R. Ingram

21.

Examples of 1620 Use in College Administration; Noel T. Smith

22.

Automatic Processing of Autospot and Automap Programs with
the 1620-1311 Disk System; Jack T. Dunn and Ernie G. Moore

23.

General Ray Trace Program; D. H. O'Herren (presented at
Tempe, Arizona, December 1963)
.

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WESTERN' REGION
SUMMER MEET J NG
.JUL. Y 1:7. 18. 1.9. 1·964
DlENYER.CfLOR,AOO

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ROSTER OF ATT9C)EES
1032

MRS. BETTY CJLSICl(

1084

GEORGIA STATE COLL.
ATLANTA ,GA.
1118

NANCY PAQUIN

PATRICK
1118

PUeL l'e tEAL TH SERV.

LANNY L. HOFFMAN
GUGGENHEIM LABS

1177

1258

1.290

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3016

RENe: SEUIGNY ..JR.
HAYES INTERNATIONAL.
HUNTSVILLE-ALA.

1238

FRANCES K. DURKAN

1273

S. HAMER

..JUDITH KOERNER

ARGONNE NAT. L.AB.

NEW YORK.N.Y.

IDAHO FALLS • l'OAtiO

ROBERT D. WEEMS
N.C,. STATE CQL.LEGE
RALE I,GH. N.C.

1352

THOMAS P. SODANO

3041

EUGENE C. EWING

MEMPHIS. TENN.
ARTHUR P. WOODS 4R.
ARMCO STEEL CORP

MIDOL..ETOWN. orn 0

3055

BARNEY T. WATSON

VA HO:SPITAl..
OMAHA ,NEB.

Me PHERSON.KAN.
..J. RICHARD BURROWS
H.O.+R •• ENG! NEERS
OMAHA. NE:a.

WALKER R. HURD
OP I ,BOARO OF EOUC.

NAT cooP REFINERY AS
3082

PAUL A,. BlCIiCFORO
. OU MED RES COMP CNTR
OtlLLO. TEX.

.LAS YEGAS.NEV.

LOWELL A. RASMUSSEN
~AMAUSER CO.
TACCMA ••ASH.

5096

BURTON L. WILL'lAMS

5;104

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CLAIII<

,CHASE JR.

5'117

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WEteELL ·,·L. 'POPE
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GEORGE V.COPLAND
MALLr,tattRTGN CO'.

DUNCaN,.'GKt.,A.

IJUNCAN,.~OIUGHL t N
FT RAYS tleasuring Squipment
or s i 7TIp 1 y

D>~~.

An ins trune nta t ion Ry ste.:n cap.1;) 1e <)f gi vi ng Sue 1 i dean

three s?ace position 2sti::1ates is termed as a :xr?tJ~'·!E system.
ca 1

;):'m/D>;'~

A typi-

system usually consi sts of three non-coli near instrument

or eq'.lip:11e'l1t si tes used to neasure range.

The typical solution equations are the classical deterministic set
that rejects th,c minor image solution.

A four or more T)?-1E system

presents a problem because a slisht error in any range
~ill

not produce a set of

classical approach.

ho~ogeneous

~ea~urenent

space position estimates by the

There is a need for a good method to combine

o

15

Leu

iii.tila.iSaaE:::

alii:

hUM

$Ii

the set of overdetermined measurements into a single space paint
estimate.

The least squares method will provide the required space

point estimate if the set of measurements are unhiased.

The least squares equations developed ~inimize the sumS of squares of
the error set of range measurements.

The observational equation from "C:.]hich the error equati.on is derived
is written:
(1)

R •
ml

=

R. + E .
1

ml

o

where R • denotes the measured range from the i -th 'J:··18 to the
ml

tracked vehicle.
denotes the true range frdm

~.
1

the

i -.th

DHZ

to the tracked

vehicle.
B

Tn

i denotes the measurement error associ ated vli th th·e observa-

tion taken from the i-th D>fE.
The error equation is easily obtained from the

ob~ervational

equation,

thus:
(2)

Eml.

= :l . ml

Ri

The true value needs to be replaced by

so~e

suitable spproximation.

Later, the true value td 11 be estimated by t1:'? fin:!l soilltion or

16

. - - - - - - - -....•

--~ . . . . .-

...~.. ---.-~.--.- ......

- - -.......

~. . .

o

reduction equ.qtions.

The assu:nption is made that the true value can

be represented by the linear terms of a Taylor series about some
nearby poi nt R , 'o1here:
o

R0
=0
~ (X, Y , Z )
000

(3)

From the i-th DHE, the range to the point (X0
, 0
Y ,0
Z ) is written:

(4a) R .

/1/(X

a

01

0

_ Xi)2 + (y

_ 1.)2 + (z
0

1

Z )2

_

i

0

For any space position (X, Y, Z), the equation becomes:

=

(4b) Ri

1\,
'veX - Xi):! +

.-

(Y: Yi)~

-:r

+ (Z ... Zi)

The linear Taylor series representation is written:

=.~.
+~1i
I
01
2> X

:to

(5)

1

(x- X)
0

o

+~RIH
-d

Y

I

(Z-~)

o

0

0

where

~ TU~
x
(.'j
"

=

(X

o

(Y

The

1

01

0

Ri/
Z 0

(zo - z0 ) /Po. 01•

=

'~ighted

- Y. )/R i

010

=

;~
c;::

- X.) /R .

error sums of squares for k measurements from k DME

sites is written:
(6a)

k

~

i-1

... 2
J!,mi

k

=

2i-1

2

10

17

I
I

==_i,SMMweU;';:" ,mIMi. ,1.,".*=140£4",4; IUki.

4¥ to

. ,14

$,

. ' .. ; .. A4GUP

o
where

wi

is the weight given to each measurement.

The errors sums of

squares for equally weighted measurements is written:
(6b)

k

k

~

i·1

E2.
mt

=

~i -~

:2i=l

2

Generally, the components of the instrumentation system are near enough
alike in performance and behavior that equation (6b) is applicable.
For a system that consists of heterogeneous distance measuring equipment (system components), each weight that would be inversely proportional to the equipments range variance would be appropriate.

The error sums of squares are minimized

~vi

th respect to the range

measurement parameter which is a function of the three orthogonal components X, Y and Z.

o

The three resulting equations thus formed are
A

'"

~

called the normal equations from which the estimates X, Y and Z are
obtained:
(7a)
(7b)

~x ~l
d
~l
';;>Y

(7c)

~
~z

~l

(R .

ml

-Ria

(R . -

mt

(Rml. -

=0

Ri~

=

R.0

=0

1

0

o
18

II

'",HlltP '9IWt"i"'

\

t 7$ e

»t htHtt

:!!indtt t'dtritt*HWt:dYitf tl ..

- '"¥tnar!

j

o
The constant terms not involving (X-So), (Y-Y ) and (2-2 ) are placed
o
0
on the

rig~t

(8a)(f,2
~~:?.

Ex

hand side of the equation:
-K. )(X

0

1

0

-x. )~X

+ (Y -1 )(X -X.) 61 + (.Z

1

1

0

0

1

.0

-z.

1

)(X -X.
0

1

)j)-;;~
J

01

~
(')282

(Sb

-. ~.
K

--

T,2
:\oi

C>
f'\.

•

if}

+ (y -Yo )(Y -y.) 61 + (Z

-,~.)A
X
t.rz;.'''0 -X.)(.2
1
0
1

+ (Y -Y.)( 7, -3.).6 Y + (2 -ZI )(Z -Zi

0

1

0

0

1

1

0

0

1

0

0

)A~1j<'.
:J

=c 2

=c 3

01

'ti.lere

[

1<
C

-Z~)(Y..-l.)6-;)
1
0
1 :J

r(X 0 -:\i)(Y0 -Yo1 ).6X
C"

1 =~
i=l

(., . - -.. i) (X - 1\.
"

')

m1

•

0

k

C2

=ii=l

f

.... 3

r~ro1

=.t

i =1
/"\,

L~ ~{

=

,"'

....

l\

=

/'0

?;

) /

d

I.. 01.

D

J

J

.}(.7.0 - 2.1 ) /'l 01

01

-X

0

L\ Y = '"
Y ..
..,

1

.-R 01.}(y0 -Y.)/?.
1
01

ml

.-;:

k

,..

U'

0

-

Y

a

7

'''0

o

19

lOW

_

saawZlaa:i1::aiii:aS::i4iQAi Itiil mal%1I.:.';. ;:;;AQP4ii. i.UXA

:.

- - ----

--.........-...--

---- "-~-----------~--.--~~~..............

The equations can be written in coapact fora by matrix notation:

-

(9a)

or
(9b)

SolYing tor

A

A

-

If.. equation

c
(9b):

(10)

The final solution tor X, Y, and Z can be written:

o

(11)

The necessar,r start point (X.'Yo,Zo') can be obtained fram a
deterministic solution for three range measureaents*.

The

region for convergent solutions has not been tully explored
at this tiae.

* Armijo, Larry, "Determination of Trajectories Using Range
Data from Three Non-Co1inear Radar Stations", Technical Memorandua ,.66, USASMSA, Sept. 1960, WSMR,N.M.

0'
20

o
III

A

NEr~OD

FOR ESrrIAT.l!N-;

IN~ENTA.TION

SYSTErvl PRECISION

The term precision estimate refers to the standard deviation estimates
for the coordinate data X, Y and Z from the instrumentation system.

If

there exi sts a cormnon range measur.ement vari ance (II"~), then by use of
the relative variance-covariance matrix, A

-1

, from equation (10) esti-

mates of the component variances can be obtained.

The diagonal elements

A-1 are used to estimate the component variance:

from the

0

0

A22

0

(12)
=

/\2

.1

= 0

1

If no such set of C i exist the functions 

()

w

X

X

s-

a>

-0
s-

O

-

..c
c
a>
>
a>
V')

I

a>
C

0

a::
X

a>

a..
E
0
U

CI

a>

..c
C

en

0
0

0::::
~

0

Q.

0

~

X

X

M

.

~

::>

.2'

u..

o
- 12 -

32

1$

tit

NniM"tt'"

I

IV.

0

BASIS FUNCTIONS AND BOUNDARY CONDITIONS

1

1

1

The solution of a homogenous fourth order ordinary differential
equation' with constant coefficients whose characteristic polynomial has the
roots ± a ± i (3 can be represented as a linear combination of the functions.

te

(a

+ i(3)x'
. "

e

(a -

i~)x

(- Q' + i~)x
(- a - iB)x\
, e" e

(4. 1.)

Of course, this is not the only set which could have been selected. Such a
set is called a system or basis of functions if the member functions are
linearly independent. A test for the linear independence is provided by
the Wronskian determinant. This is a determinant whose first row is the
system itself and whose jth row is made up of J-Ist derivative of the function
in the corresponding column.
We shall have a great deal more to say about linear independence in
the next section of the paper. For the present, we wish to show how the
programming and del?ugging of the problem are simplified by writing the
derivative boundary conditions in terms of the Wronskian. Recall the form
of the derivative boundary conditions.
n - 1

i
j

=

L=

1

2, n

.
J

1

h.. d -. T
1, J
dx J at x

=

~x)

0

= F.

(4. 2)

1

and x

c

=L

We see that

.
1
d J - T (x)
j - 1

(4.2a)

dx

is a column vector. We also see that recognition of the boundary conditions
in the form (4. 2) permits us to deal separately 'with the specification of
boundary conditions (bij) and the determination of the vector (4.2a).
For our 11 th order problem the matrix (b i , j) was computed from a coded
input. This provided a flexibility which waf? most useful when numerical
difficulties were seen in the boundary conditions themselves. Such a scheme
suggests the pos sibility of writing a generalized program.

o
- 13 -

33

Notice the vector (4.2a) is a function of X and exists in an N space.
On the other hand, the matrix (b i , j) can be written as N linearly
independent conditions at either X = 0 or, X = L. Thus~ for the two-point
boundary value, problem N conditions must be selected from 2N derivative
conditions and possibly some integral conditions. This draws attention to
the fact the boundary conditions selected must be such as to specify a
unique solution. We shall not give adequate coverage to this problem
in this paper. Let us now examine the vector (4. 2a). It has a physical
meaning without regard to the basis or coordinate system in which the
solution is written. That is to say it could be written at various values
of X as a table of numbers which would be independent of the manner in
which it was obtained. To analyze it symbolically, however, we must
assume a basis of functions, say {¢iJ. The first element of (4. 2a)

(j

= 1)

is the zeroth derivative, or the function
(4. 3)

where the a
are the constants of integration to be determined by the
K
equations 4. 2. But:
.
1
d J - T (x)

C"

dx

j - I

n
=

2:

k = 1

d

J.

1
-

CP'k (x)

j - I
dx

a

W{x)a
k
k =

(4.4)

where W{x) is the matrix of functions from the Wronskian determinant.
The recognition of these matrix products is the key to relieving the
program of unmanageable detail. As will be seen later, a factor in the
choice of the basis is the ease with which the Wronskian may be developed
by a simple set of do loops. The (bi, j) matrix may be checked separately.
Any linear independence may be displayed in easier-to-recognize form.
The program has pattern.
As we have indicated, the specification of boundary conditions which
are sufficient and compatible involves more than we can discuss here.
The reader is referred to Ref. 19·

o
- 14 -

II

"ill
"'I

v. SELECTION OF THE SYSTEM OR
BASIS FUNC TIONS FOR THE SOL UT10N
Given an ordinary differential equation whose characteristic polynomial contains the non-repeated roots ± a ± iB there are many choice s of
functions for the solution. Consider, for example, the se four base s or
systems:
e

{a

+ iB}x

e

{Q' - iB)x

e

{- a

+ iB}x

e{- a - iB}x

I

(5. t)

Cosh(ax} Cos(Bx}, Sinh{ax} Cos(6x}, Cosh(ax}Sin{Bx},
Sinh{ax} Sin{ Bx}

I

{5.

~}

{5. 3}
and:

Z

=L

I

- X

fe

-ax

cos{Bx), e

-ax,
-az
-az
J
sin(Bx}, e
cos{Bz}, e
sin{Bz}

(5.4)

The question arises, is there a choice? If these functions are
mathematically equivalent, which they are, can one set be superior to
another for digital programming? The answer is yes. Let us first
dispose of (5. 1) on the arbitrary basis that we prefer not to.perform
complex arithmetic if we can avoid it.
The usual textbook treatment is to point out that the functions must
be linearly independent. For the mathematician, this con,dition is me t for
all of the bases under discussion. For the digital programmer, however,
this situation may be quite different. If the domain L of the solution is
large enough, all of the sets of functions expressed in the computer number
set become linearly dependent:
Lim
aL . -

co

, I

sinh{aL} = 1
cosh{aL}

Lim
-aL
-aL. (({L)
e
cos(6L} = a, Lim
e
SIn tJ
aL -co
L _ co

=

Lim -aL ± iBL
e
aL - co

=

0

(5. 5)

o
- 15 -

35

Ott> t

o

In the machine , this breakdown in linear independence becomes exact.
That is to say, we may have coshaL = sinhaL to the last digit. Of course
one may expect computational difficultie s long before the los s of the last
tragic digit.
Is there any way out of this dilemma? Again the answer is yes. The
moment we realize that the finite number of digits in the calculation limits
our ability to produce the "exact" solution we begin to consider analogies
with approximate methods. We seek functions to represent our solution
which "look like" the solution. Clearly basis (5.4) is greatly superior in
this light. Only (5.4) of the bases considered, directly represents a
function which arises at disturbances at the boundaries and is damped as
it proceeds to the interior of the region.
Comparing basis (5.4) with basis (5.2) it is seen that the functions
of (5. 2) approach each other in exactly the range in which they become
large. The functions of (5.4), on the other hand, approach each other in
exac tly the range in which they drop out of the solution.
It is not surprising that the basis (5.4) is superior when we take
note of the fact that it contains more physical information. Only basis
(5.4) is cognizant of the location of the disturbance caused by mismatching
strains at X = L.

o

Let us inquire into the physical significance of positive real parts of
characteristic polynomial roots. In the initial value problem, with time
as the independent variable, positive real parts have been used as criteria
of stability. When space is made the independent variable, and the
problem is formulated as an initial value problem, a numerical instability
is quickly associated with positive real parts. Consider for example,
the differential equation
(5. 6)

which is the homogenous equation for the deflection of a railroad track.
Ref. 15, the solution is shown in several form s including the me thod of
initial conditions.

In

o
- 16 -

36

t

',~',

",

y(;x)

= yo

c osh(A. x) co's (A. ;x)

e

+ 2~' fcoS h (>-";x) sin{>-..;x) + sinh{>-";x) cos{>-..
~Q

2o s inh(>-";x) s in{>-..;x) 30
2>-" EI
4>-.. EI

{c

o

X)}

osh(>-";x) sin(>-,,;xl - sinh(>-";x) cos {>-.. ;xl I
(5. 7)

where

Yo

= displacement at

e0 =
~

Q

0

0

slope at origin

= bending
=

origin

moment at origin

shear ,at origin

In fac t, the solution is damped as one in ove s away from a local load or
disturbance. The method of initial conditions, however, requires that
this damped function be composed of a linear combination of rapidly
e;xpanding func tions.

c

In the finite arithmetic of the digital computer, this means that if
I
a fly settles on the railroad track in Denver and the initial conditions are
determined to the full capacity of the computer number set some place
this side of Los Angeles, the railroad tracks will be ripped and torn in
the most terrible carnage since World War II.
With time as the independent variable, the model is realis tic.
Positive e;xponentials mean positive feedback. The rate of growth of the
function is proportional to the function with a positive coefficient of
proportionality. lilt takes money to make money. II "Population growth
is e;xplosive in a favorable environment"-"chemical reactions become
e;xplosive if the rate of the reaction increases with the reaction products"
(including the final ene-rgy as a product). But time moves on. Functions
do not have causes today and develop into effects yesterday.
Space coordinate s, however, are quite arbitrary. One does not
need to establish a coordinate system to pull a glued joint. Thus, the
physical meaning of the positive e;xponential in our glue line problem is
seen to be a stereotyped pattern of coordinate system specification.

o
- 17 -

37
..

- - - - - - - - - -..---

.~~~--~~-

'$

o

It is well known that the choice of a coordinate system can make
the solution of a problem easier or more difficult (Ref. 21). In at least
some problems it has great numerical consequences (Ref. 5). Interestingly enough, since the boundary conditions supply the information for
the evaluation of the constants of integration, we see that they contain
vital information about the origion of the coordinate system. One of
the problem s in specifying boundary conditions is to make sure they
produce a unique solution in a defined coordinate system.
Stres s analysts have traditionally handled positive exponentials by
testing such a parameter as a over the domain. If aL is large (say
aL > 6), he uses basis (5.3) as a special b~sis. He sets the arbitrary
constants associated with positive exponentials equal to zero (when
aL> 6) and calls his solution the semi-infinite case. We think the
choice of basis (5.4) is superior for several reasons. For one thing,
the characteristic polynomial may contain more than one set of complex
roots with positive real parts. One set may correspond to a semiinfinite case and another to a short case. This situation actually occurs
in our 11 th order problem. Additionally, we should like to pick one
basis and avoid programming more than one basis of functions.

o

If our mission in this paper were only to show that the basis (5.4)
is superior for our problem, we could certainly bring this discussion
to a close now. Our interest, however, is broader. We wish to explore
the relative merits of bases in hopes that we may obtain criteria which
help us in the solution of some other problem.
We have identified part of our numerical difficulties as arlslng
from a breakdown in linear independence due to the finite nature of the
computer number set. Linear independence is established if there are
non-zero values of the Wronskian and Gramian. For basis (5.3) or
(5.4), we rediscovered an ancient device for writing the Nth derivative
which will render our discussion easier. Consider one of the functions,
say e -axcos «(3x)
~

dn-.

~=

-ae

= e -ax cos«(3x)

-ax

cos«(3x) - (3e

o
- 18 -

-ax

sin(f3x)

(5.8)

But ide ntify
a

+

iB= R(cos(e)

+

c

i sin(e) )

-ax

R cos (Bx - e)

(5. 9)

It can be shown that:
J -ax
d e · cos(Bx}
-ax
j
.
------ = e
(-R) cos(Bx - je}
j
dx

(5.10)

And since

Z

=

J -QZ
d e
cos(Bz)
---~-j
dx
j
d e

-QZ

dx

dz

L - X

sin(Bz)
j

d;Z

=

-1

=

= e

(5.11)

-az j
R sin(je

+

c

Bz)

In the seventh order problem we used the basis

e

-a z
-a z
-aZz
1 cos((\z), e
1 sin(B1z), e

I

1

,

d¢> = e -axR (-c os (e) cos (Bx) - sin( e) sin( B:x»
df{
= - e

l

(5.1Z)

o
- 19 -

39

·

t*t

t

The jth row of the Wronskian determinant for this basis is:

o

(5. 13)
Consider this .Wronskian if L is large. When X = L, the first three
columns of the determinant become very small. If X = 0, the last three
become very small. It is shown in Ref. 22 that for an Nth order differential equation which does not contain the (N - 1st) derivative, the Wronskian
is constant through the domain. To see that this is the fact for this
Wronskian, it is helpful to factor the Wronskian into the three factors.
= [R]

[ W (X) ]

o

[T (X) ]

[E (X ) ]

(5. 14)

Where [R 1 is the diagonal determinant whose elements are Rl j, [E(X)l
is the diagonal determinant whose elements are the exponential terms
-0:'
e

1

-0:'

Z

e

1

Z

and T (x) is the remaining determinant whose jth row may be written

(5.15)

then
[R 1

'" R (l
1

+

+

0:'1

-(0:'1

2

+

+

3

+4 +

5

+

z)

0:'2) (x

[E(X) 1 = e

+ 6)

'" R 21
1

(5.16)

o
- 20 -

4u

t'

tt

* ••t

"

Iii I
'I
I

With considerable manipulation of rows, the IT(X)] determinant can be
seen to contain factors of the form
2

cos (/3x)

+

c

sin 2«(3x)

The Wronskian of basis (5. 2) is less manageable, as may be seen from
the single term:
w ,7
1

324.
= (a 5
- lOa (3 + 5a (3 ) Slnh(ax)

cos«(3x)

4
2 3
5
.
- (5a /3 - lOa /3 + /3 )cosh(crx) sln(/3x)

(5.17)

Numerical difficulties arise because columns 1 and 2 and columns 5 and 6
of the complete basis may be obtained from each other 'by replacing
sinhcrx w~th coshax or vice versa. Thus, the linear independence depends
upon the ability to distinguish the hyperbolic functions at large values of
X with a computer number set. Through considerable algebra the
Wronskian may be shown to contain the factors (cosh2(ax) - sinh 2(ax)
and (cos 2 (/3x) + sin2(/3x) ).
The difficulties with basis (5.3) interestingly eno,ugh do not arise
in the same manner as with (5.2). Except for a minor phase difference
in angles /3x and 6z the most significant difference between (5.3) and (5.4)
lies in their respective[E(X)ldeterminants. For basis (5.3), this
becomes
(-a
e

l

- a

1

- a

2

+ cr 1 +

a

1

+ ( 2 )x

0

=

e

=

1

so that on this consideration the basis is seen to be at least as good as
basis (5.4). A similar pattern is observed if we consider the Gramian
determinant.
For a basis of functions (i)' the Gramian determinate is given by
L

G.. =

1,J

J

o

. . dx
1

J

(5~18)

-21 -

41

C

'I"

N"f ' ,)

\!:Iiriei'M. 'ribW'Wrii'iliit""Nfl'!W't"!![t"WM1f'l"ifHt"H\"ij"I"'HfW,'*\8*WillNNWW'''j"''' U1 fW'+':i1I:Wlli''mW'¥"J

""'111,""11"

W"'lftl'ij"eHWUtfltt""tlbiWN!wH" 'U"I!!'W

t

'IIIetlllfUUlfU,,",.,'Mltt",

1

ttt

h

$

tttt rMtI

....... tt±ris·t*rt:tW#rt.

we prefer. to normalize the Gramian as to.

o

L

J
o

G~:C

=

i,j

1>. 1>. dx
1
J

(5.. 19)

L

L

f

f

1>.2 dx
1

o

o

1>.
J

2

dx

In this form we may think of the functions 1>i and 1>j as being coordinate
vectors in a function space. The terms Gi . are then cosines of angles
between the coordinate vectors. One may ~~so think of them as simple
correlation coefficients between the base functions.
Now consider the functions e-axcos(f3x) and e- az cos(f3z).
Then
L

f
G~:C

o

1, 3

e

-ax

cos (f3x) e

-az

cos ( Bz) dx

o

=

L

L

f

e

-2ax

2
cos (f3x)dx

J

e

-2az

2

cos (f3z )dx

o

o

L
e

-ax

.f

cos(f3x) cos(6z) dx

0

=

L

J

e

-2ax

2
cos «(3x) dx

(5. 20)

0

If L is great the definite integral in the denominator will be approximated
by the lower limit so that the order of magnitude of G 1 3 is e -aL. Thus,
in this basis the functions separate into nearly orthogo~al sets as sociated
with the respective boundaries.

o
- 22 -

42

A similar situation holds for basis (5.3). The exponentials f(ill
out of the numerator before integration and the denominator contains
e aL . For basis (5.2), however:

o

L

J
G*

1,2

cosh(ax) cos(0x} sinh(ax} <;:os(0x)dx

o

=

L

L

f

2
2
cosh (ax) cos (Bx)dx

.22
sInh (ax) cos (Bx}dx

o

L

J

(e

2ax

- e

- 2ax

2
) cos (0x)dx

o

=
L

J

(e

2ax

+ 2+ e

-2ax

2
) cos (0x}dx

(e

2ax

-2+e

-2ax

2
) cos (0x}dx

o

---_t

(5. 21)

1

How may we distinguish between basis (5. 3) and (5. 4)?
recall that our solution is in the form
T

(x) =

~

(5.22)

a. . (x)
1

Let us

1

o

This can be seen to be the vector T (x) in a function space, written in terms
of its components ai along the coordinate axes i(x}. We have seen that
basis (5. 2) is unattractive because the axes i become parallel. For the
basis (5.3), the problem is the scaling of the axes. The length of the
coordinate vectors is exactly the integral in the denominator of the
Gramian. Thus, for a basis with distinct axes, such as (5.3), the choice
of a second coordinate origin essentially normalizes the coordinate vectors.
Let us now consider the full matrix for the derivative boundary conditions. We may partition th is matrix into four partitions as

,
-- - -----,--------

,

S 21

I

S 22

(5.23)

o

- 23 -

43

,t

t

"\!!ii"'iillif'H'd'lli:ill:l!l:tlYf!l¥t:H±l"W!!'!tW$!!'tttt eln"Wnr!l!!!!WM'Ilf¥l!fIll'"w"W',,!'!t,,'rt!lI!!!!I11WnN'MH'ltI"

o

II",,'' ' !!

"f'IW"",'''$7''

1m

••

hila

tt

t

• tt

' •.

"$ *>

Where above the horizontal line we write the conditions to be met at
X = 0 and below the conditions to be met at X = L. To the left of the
vertical line we write solution components associated with exponentials
with negative real parts and to the right exponentials with .positive real
parts (or for basis 5. 4 solution components in Z).
We have two matrix e,quations (at X = 0 and X
represented as:
[ B1

[R 1

[T (X

n

[E (X ) 1

=

= L).

They may be

(5. 24)

[51

The matrice s [B 1 are rectangular. They and the matrice s [R 1 are
unchanged from basis (5.3) to (5.4). The changes in [T(X)l are only
differences in phase angle of the trigonometric functions. The matrix
[E (X)l , however, is very different. A t X = 0, the E matrix for basis
(5.3) is the identity matrix. The E matrix for basis (5.4) is the diagonal
matrix

L

-Q'

I

1,1,1, e

-0:'

1

e

1

L

This same matrix multiplies the E matrix of (5. 3) at X

= L.

To give the E matrix of basis (5.4)

o

-0:'

e

1

L

-Q'

e

2

L

If we denote the complete matrix for the boundary conditions for basis
(5. 3) as S and the diagonal transformation matrix

L

-0:'

1,1,1, e

I

1

-0:'

e

1

L

as C, we may write the boundary conditions in basis (5.4) as

[51 [Cl [Al

=

[Fl

except for the difference s in phase angle noted above.
If we chose to pre-multiply [A 1 , rather than post-multiply [Cl J it
is seen that C represents a scaling of the coefficients [A 1. This problem
is identified by Lanczos (Ref. 5) as artificial ill-conditioning. His
recommendation is just the sort of rescaling accomplished by the choice
of basis (5.4).

o
- 24 -

!,:I
"1
I

I

o

VI. REMARKS AND CONCLUSIONS

Using basis (5.4), we finally see the boundary condition equations in
the partitioned form of the previous section in a physical light. The
matrix Sll represents the semi-infinite problem at X = 0_ The matrix
S22 represents the semi-infinite problem at X = L. The matrices S12
and S21 represent cross-coupling between the semi-infinite solutions.
The final four figures show the solution and components for the
seventh order problem solved with basis (5.4). Figure 4 is a plot of the
shear stress for a typical joint. Figure 5 shows the components of the
shear stress for this particular problem. The components associated
with complex roots were too small to show on the same scale. Notice
that the physical problem - two transients moving in from the boundaries,
the solution, the solution components and the partitioned form of the
matrix - all reflect the same pattern.
Figure 6 shows the peel stress solution. ~Figure 7 shows the
components of the peel stress. Rl is the absolute value of the complex
root 0'1 + i f3 1 - R2 is the value of 0'2. Recall with basis (5. 4) the
derivatives contain successively higher powers of the moduli RiO Now Rl
is 6. 78, whereas, R2 is 1. 77. One is not too surprised, then, when
a-which is given by

_£

a- (X)

2

CJ

dT(X))
dx

contains larger components or the functions associated with the roots
±O'l ± i f31Notice, also, that the magnitude of the real parts serve to determine how local the effects will be. Notice the components associated
with ±O'1 ±i-f31 are much more rapidly damped than the components
associated with 0' 2This same problem was solved using basis (5.2). An interesting
comparison of the numerical difficulties is p,rovided by comparison of
the conditioning number of the matrices which had to be inverted. The
conditioning number is the ratio of the largest Eigenvalue to'the lowest.

o
- 25 -

45

#dbtt'J'J.tLtW'

rittH±>tbW'

HIt"'.*' '11

lb

.t

o

The logarithm of the conditioning number provides an estimate of the
number of digits which will be lost in the inversion. For the basis (5.2)
solution, a 6 x 6 matrix was inverted. The conditioning number was
2.6. 10 8 • For the basis (5.4), two 3 x 3 matrices are inverted (solution
by partioning Ref. 10). Their conditioning numbers were 1.10.10 2 •
Our conclusions follow HaITlming' s beautiful statement (Ref. 1):
"The Purpose of computing is insight, not numbers." Recognition of
matrix products added tremendously to our insight and provided an
unusual opportunity to see the nature of our numerical difficulties.
We confess to a strong interest in writing more solvable equations.
The work which has been done on best approaches to the problem of
solving poor equations, while very useful, has already run its course.
Nothing but more digits will improve on the best methods available.
The problem of writing better equations is certainly not simple.
Nor do we feel that we now know how. We do believe that the close
imitation of the physical problem is a good clue. Further, for this
problem we identified two mechanisms which could affect the equations.
The basis (5. 2) led to badly skew axes, the basis (5. 3) to badly scaled
axes. The double coordinate system improved the scaling. It is
interesting to note that the normal equations of a least square approximation problem become highly skewed"if the coordinate origin is very
distant from the center of gravity of the function being approximated.
The pos sibili ty of writing a gene ralized program for the clas s of
problems treated here looks good. If we were to write it, the first
thing we should like to do is be very sure of our polynomial root routines.
Another difficulty would be choosing the boundary conditions before the
nature of the characteristic polynomial was established.

o
- 26 -

46

o

E
Cl)

::0
0
d:

~

~

Cl)

-0
~

0

-

...c:
c
Cl)

>

Cl)

Vl

M

Cl)

...c:
' +-

0

C

0

::J

C

0

Vl
~

N

0

Cl)

...c:
Vl

.

""¢

Cl)
~

::J

.~

u..
~

0
0
0
0

an

0
0
0

~

0
0
0

(W)

0
0
0

N

0
0
0

~

0
- 27 -

47

o

o
/ase

o

1.77X

a

4000

7

9 -1.77 Z

/i

3000

~

2000
1000 ---I

o
~
(7

o

" ~

1

ff

2

3

4

5 • 'Ti(X)

Figure 5. Components of Shear Solution (Note: Complex Components Were Too Small for Scale)

~~

6000
5000
4000
3000
N
.~

2000
1000
0

-1000

1 \

o

..

/

1
Figure 6.

"'c.o"'

o

2

3

II

5 • U(X)

4

Peel Stress Sol ution Curve for Seventh Order Problem

c
~-~ ~

-------

o

o

o
1 cos (til :x)

e

5000

o

-C1/ X

R1=6.78
R2=1.77
011 =4.796
til =4.794
012=1.77

4000
3000

Ui (:x:)

3 Ti (x:)
- lE.a (d.ci:x:
:3

1i(:X:»)

_t ci
c;,l ci:x:

2000
IN

o

1000

o
-1000
c.n
e

-OIl X sin (til :x: )
e- OiaX
Il'C

o

E<

»

1

2

3

4

./11

5

Figure 7. Components of Peel Stress Sol ution, Seventh Order Problem *

·Curves are labeled with corresponding functions from the basis of the shear solution. As can be seen
from peel stress expression, the true functions of this diagram are linear combinations of high order
derivatives of the respective shear basis functions.

o

REFERENCES

1.

Ham.m.ing, R. W. Num.erica.! Methods for Scientists and Engineer s.
New York: McGraw-Hill Book Co .. Inc. (1962).

2.

Goland, M., and Eric Reisner. "The Stre sses in Cem.ented Joints, "
Journal of Applied Mechanics (March 1944), pp. A17-A27.

3.

National Physical Laboratory. Modern Com.puting Methods.
Edition, London: Her Majesty's Stationery Office (1961).

4.

Burnside, W. S., and A. W. Panton. The Theory of Equations, Vol. I.
New York: Dover Publications, Inc. (1928).

5.

Lanczos, C. Applied Analysis.
Inc. (1956).

6.

Wilkinson, J.H. "The Evaluation of the Zeros of IlI-CondltJ.;,)ned
Polynom.ials," Num.erische Mathem.atik, Vol. I, pp. 150-180.

7•

Lance, G. N. Num.erical Methods for High-Speed Com.puter s.
Iliffe & Sons, Ltd. (1960).

8.

Golom.b, M., and M. Shanks. Elem.ents of Ordinary Differential
Equations. New York: McGraw-Hill Book Co., Inc. (1950).

9.

Kaplan, W. Advanced Calculus.
Publishing Co., Inc. (1953).

Second

Englewood Cliffs, N. J.: Prentice Hall,

Cam.bridge:

London:

o

Addison Wesley

10.

Fadeeva, V.N. Com.putational Methods of Linear Algebra.
Dover Publications, Inc. (1958).

New York:

11.

Kaplan, W. Ordinary Differential Equations.
Publishing Co., Inc. (1958).

12.

Ralston, A., and Henry Wil£' Mathem.atical Methods for Digital
Com.puters. New York: John Wiley & Sons, Inc. (1960).

13.

Hildebrand, F. B. Introduction to Num.erical Analysis.
McGraw-Hill Book Co" Inc. (1956).

Palo Alto: Addison Wesley

New York:

o
- 31 -

51

rr_ I I,,,,,,, IMIM

o

0,
:'1

. ·1

1''ILi'''NIfI''Iopl'i''!!1

2' I

, "

't.t,'

'1IfPf'?1I

tt

.,

t

I

1Ft

, t h

II tttttttwitrrrbtt

14.

Householder, A. S. Principles of Numerical Analysis.
McGraw-Hill Book Co., Inc. (1953).

New York:

15.

Hetenyi, M. Beams on Elastic Foundation.
University of Michigan Press (1946).

16.

Courant, R. Differential and Integral Calculus, Vol. 1.
Inter scienc p Publisher s, Inc. (1934).

17.

Pa ige, L. J., and J. D. Swift.
Ginn and Company (1961).

18.

Churchill, R. V. Fourier Series and Boundary Value Problems.
New York: McGraw-Hill Book Co., Inc. (1941).

19.

Lanczos, C. Linear Differential Operators.
D. Van Nostrand Co., Ltd. (1961).

20.

Edwards, J. An Elementary Treatise on the Differential Calculus.
London: MacMillan and Co. (1892).

21.

Morse, P. M., and H. Feshbach. Methods of Theoretical Physics.
New York: McGraw-Hill Book Co., Inc. (1953).

22.

Ince, E. L. Ordinary Differential Equations.
Publications, Inc. (1926).

23.

Ford, L. R. Differential Equations.
Co., In c • (1 9 55) •

Ann Arbor:

The

New York:

Elements of Linear Algebra.

o
- 32 -

New York:

New York:

New York:

Dover

New York: McGraw-Hill Book

READER
A program to read and execute elementary
machine language laboratory exercises
R. C. Steinbach (5145)
Introduction
Grossmont College is one of California's many public two-year colleges.
These colleges provide three educational programs:

(1) General education

courses for the community, (2) Technical-vocational courses, (3) Transfer
courses for students going on to four year institutions.

Within the techni-

cal-vocational area Grossmont College has a data processing program containing a one year (four units per semester) computer programming course which
begins with machine language.

Students are capable of writing miniature

machine language programs after approximately two lecture hours.

The pro-

gram described here monitors the student programs, allowing the student to

C

see his program executed and relieving the instructor of the job of reading
machine language programs.
Student Program Format
During the first six weeks of the programming course the students are assigned
specific problems to code.
end of this paper.
as follows:

Examples of these problems can be found at the

For each problem, each student hands in a deck of cards

(See Figure 1)

each student's program.

The first card or Header Card is used to identify

This card contains the student's name beginning in

column one and ending with a record mark.

It also contains a five digit

identification number beginning in column 75 and a record mark in column 80.
Reader uses this latter record mark to recognize the header card.
~a~

Cards follow the header card.

The Pro-

The student machine language program is

punched 72 digits (6 instructions) per card into as many cards as is necessary
to a maximum of ten.

A record mark in column 73 of a program card indicates

52

o

.et

to" \

't

t»

tt

rt

••

t

t.

t

.j

I

eM

trW $\

d"

t

•

1

j

t • H.....

* t" tt. rt ee

UH¢&ttss' trbtMt* htritnaz

Page 2.

o

that column one of the next card follows column 72 of the card just read.
Thus the last card (it may be the first and hence the only card of the program) has no record mark in column 73.
All programs return control to READER with a branch to 00000.

This allows

a manual restart (INSERT, RELEASE, START) if the student program hangs up
and has not destroyed the READER program.
OPTIONS
During the time that the student has no knowledge of input/output instructions
READER outputs the work area so that the student (and the instructor) may
check the program results.

This output may be suppressed using console

switch 3 after the student is familiar with output instructions.

The output

device, either card punch or typewriter, for READER may be selected using
console switch 4.

This latter option allows remarks from READER to be output

on the same device required of the student in a given problem.
A TYPICAL RUN
For each problem, the programs written by the students form a single deck
which follows the READER object deck and four special data cards.

(See

Figure 2)
The first speciaL data card contains program identification, console switch
settings and tabulator information for the operator.

The next three cards

contain data for the student work area, e.g. numbers to add or subtract,
negative numbers to count.
It is advisable to add an instructor written solution to this deck of 4
special data cards so that the students can see the right answers and see

o

one way of writing the program.
first student program.

As far as READER is concerned, this is the

Note that the 4 special data cards and the instructor

53

Iii
I,

Page 3.
written program form a package which separates the reader object deck from

o

the deck of student programs and which is easy to include for any given
assignment.
READER types the program identification and operator message and halts.

It

then reads the three data cards. initializes the student work area and reads
and executes the student programs as follows:
1.

Search for Header Card.

(Go to 3 when found; go to 2 on last

card indicator.)
2.

Type "All programs read" and halt.

Press start to read next 4

special data cards and new batch of student programs.
3.

Type student identification number.

4.

Input student program. output student name and number of cards
required for program.

5.

Branch to student program.

Return to 6 is automatic by student

o

or manual by operator.
6.

Output work area if switch 3 is on.

7.

Initialize student work area.

8.

Go to 1.

REMARKS
One should list the student program deck before doing anything else so that
there is a permanent record of who turned in what.

This is at least a par-

tial defense against a charge of deck shuffling at execution time.
A clumsy student can wipe out core with a TF or TR.

The only thing to do is

reload the READER. but at least you have his identification number on the
typewriter.
A loopt checkstoPt or bad operation code can be noted by hand on the typewriter output and the READER restarted manually.

o

it &sttdt

t

t ••

tttt

tnt

t

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,

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Page 4.

o

It is possible for a student to read the next student's program as data.
As soon as this is obvious, a STOP, INSERT, R/S, will restart the READER.
A comparison of the initial listing and the run listing will determine who
was left out and his (their) program(s) can be placed at the end of the
student program deck.
Conclusion
I would appreciate comments and criticism from any interested person.

I do

not plan to submit this to the Users Group Library until at least one more
class has tried the system; they may think up new ways of giving the READER
trouble.

o
55

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56

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/

STUDENT

PROGRAMS
,d I

/

Ii

INSTRUCTOR'S PROGRAM
DATA

:1

,tI
ill

(3 CARDS)

i

PROGRAM

I D, OPERATOR MESSAGE
------

(

READER

OBJECT

DECK

~

I

III

I

----------------------Y

L -__
~

-'1

FIGURE

2

i ji

1IIIjli '

I

~I
I

LAB EXERCISE I

Numbers, described below, are in storage with the most significant digit
flagged.
Address of least
Number
Number of Digits
significant digit
A

1.1

B

6
2

C
D

3

4

7006
7010
7016
7021

Assume no overflow, numbers are integers.

Replace A by A+B
Replace C by C-B
Replace D by D-658
1.2

Assume no overflow, numbers are integers.

Replace A by the integer A-2B+C-D
1.3

Assume no overflow.

o

Assume decimal locations as follows:

xxx. xxx
.xx
C = x.xxx
D = xx.x

A =
B =

Replace A by A - D
Replace D by C + D
Replace C by C + 2.93

o
58

trh t

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_.ew

LAB EXERCISE 3
Note:

Memory addresses above 11000 are available for your use.
digit of your program is in 07300.

The first

3.1 Return the carriage on the typewriter. Type out the numerical contents
of 7001 - 7009, space the typewriter, type out the alphameric contents of
7030 - 7047. Return the carriage and type the numeric contents of 7030 - 7047.
There are no record marks in place.
3.2 Return the carriage, type your name (25 oharacter maximum), tabulate and
type your code number.

3.3 As input to your program have one card with your name beginning in col. 1,
and the words "1620 I/O PROGRAM" in col. 32-47, and a second card with 5 zeros,
5 ones, 5 twos, etc., and 5 nines in col. 1-50. Duplicate the two cards.
3.4 I will supply you with 3 cards which you will use as input to your program.
Each card will have the following format:

o

A five digit number A in col. 6 - 10.
A nine digit number B in col. 17 - 25.
You are to punch out three cards with the following format:
A and B as above
A+B with low order digit in col. 40
A.B with low order digit in col. 60
There are no flags on the input cards, and there should be no flags on the
output cards.

o
59

et.

'I
I

o
LAB EXERCISE 5

5.1

Type a message to turn on console switch 2 and then halt.
If the switch is not set properly repeat the message and
halt. Continue this process until the switch is on.

5.2

Two flagged 4 digit integers have their units position in
7005, and 7010 respectively. If the n-th integer is
less than 2222}
equal to 2222
greater than 2222

put a

{I }
2
3

in 7011 + n

5.3

35 flagged 4 digit integers have their units position in
7004, 7008, ••• , 7000 + 4n, ••• , 7140. Tabulate the typewriter and type the number of negative numbers in the list.

5.4

Three 5 digit integers are located in 7005, 7010, and 7015
respectively; arrange them in ascending order in locations
7020, 7025, 7030.

c

o
60

,*.' rirttfri

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A 519 Simulator
R. C. Steinbach (5145)

o
Introduction

Card reproduction on the 1620 is not new;
approach is to insert 371111100500

391111100400

the most straight forward
4900000 R/S.

The problem

becomes slightly more complex if information is to be deleted, the columns
permuted, sequence numbers added, and/or information gang punched into the
cards.

This paper describes one method of handling these other possibi1i-

ties.
Method
During the first phase, 'the simulator sets up a table of source
addresses.

The first entry in the table is the address of the two digit

field to be placed in column one of the output deck; the second entry
addresses the source field for column two; etc.

During the second phase,

a card is read into an input buffer, 80 two-digit fields are transmitted
from the appropriate source (the source table is addressed indirectly)
sequentially into an output buffer.

A card is punched and the next card

read, and so on.
Format Cards
The deck to be reproduced is preceded by three format cards called
INPUT, OUTPUT, and EMIT.

All three cards must be there, however, the INPUT

and EMIT cards may be blank.

The input format card identifies the source of

characters from the deck to be reproduced; the output format card identifies
the destination of all characters to be punched in the new deck; the emit
format card contains characters to be gang punched into all cards of the

o

new deck.
The simulator produces the source table by scanning the output format

61

=-=

.. ",,' "' .... '''''.'''"-'-'--,,~."'''''."=,
... "=."

Page #2.

card.

All c,olumns that are blank in the output format card will be blank

in the new, or output, deck.

A field of l's in the OUTPUT card indicates

that the source is the same field on the old, or input, deck.

A fIeld of 2's

(up to 5) indicates a sequence number field on the output deck.

Note that

this requires the OUTPUT card to be scanned from right to left. ' A field
of 3's indicates that characters are to be emitted from the corresponding
columns of the EMIT card.

If a field of any other character, e.g. AAA or

»»),

is encountered on the OUTPUT card, then the INPUT card is searched for a
corresponding field.

The location of the field on the INPUT card determines

the columns to be picked up in the old deck; the location of the field on the
OUTPUT card determines the destination in the new deck.

If the OUTPUT card

contains a character other than the four special characters (blank, 1, 2, 3),
that same character must appear on the input format card; furthermore, the
field length defined must be the same.
"Format card mismatch" is typed
cards.

an~

If either of these conditions fail,

c

the program will then accept new format

Figure 1 shows an eKample of the three format cards.

Anomalies
Although it is not immediately obvious, the method chosen to set up the
source table allows one field of the input deck to be placed in more than one
field of the output deck.

To accomplish this, a field indication on the INPUT

card appears in several (non-adjacent) fields of the OUTPUT card.

Two non-

adjacent fields on the input card designated by the same non-special character
will not be correctly interpreted.
Sequence numbers (even of different length) may also be punched in several
non-adjacent fields.

o

Modifications
Often, one wishes to change the emit characters whenever a master card is

62

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.

,

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Page #3.

o

detected.

The variety of ways in which a master card may be indicated, and

the number of possible reactions to a master card suggests one of the following manual solutions to the problem rather than a fully automated system.
If there are just a few decks headed by master cards, the same INPUT
and OUTPUT cards may be used with a different EMIT card.

The Master card

may be used for an EMIT card if the master card is not to be duplicated and
the characters to be emitted are in the correct columns.
If there are many master cards in a particular run, they may be detected
using a compare or compare immediate after each card is read.

A special

routine is then added to the source deck to transmit characters from the
Master card to the EMIT card image.

The bulk of the routine can be instruc-

t ions of the form TF ENIT-2+2 1:ecn, IN-2+21:mcn where ecn stands for emit column
number and mcn stands for master column number.

o

With the d'lZ~tect routine and

transmit routine added, the source deck is reassembled.
Conclusions
Any suggestions on ways to improve this program will be greatly appreciated.

It will be submitted to the Users Group Library after these improve-

ments are incorporated.

o
63

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o
GOOOIiEAR
GOODYEAR AEROSPACE
CORPORATION
AR I ZONA

DIVISION

LITCHFIELD PARK. ARIZONA

o
SIMULTANEOUS LINEAR

~UATIONS

WITH CCIU'LEX COEFFICIENTS

N. Kuffel

AAP-18906

May 1, 1961&

o
65

SIMULTANEOUS LINEAR EQUATIONS
WITH CClWLEX COEFFICIENTS

N.

Kuffel

INTRODUCTIOIf
This program 801T•• a1ll1ltaneoue linear equations with complex coefficient.

resulting in complex roote. It vas original~ developed to aolve large
8.18tema and baa applications in mechanical and electrical engineering
problema.
Ot the I1UJIlerOU8 programs available for

ma~ix

inversion and simul taneoua

o

'equationa, very fev take into account the under-and-overfiow problems ,
. encountered on large matrix qatema. There are no }rograma published at
the present time tor the 1620 tor solutions of complex simultaneous
tiona, and 'fiery fev available even tor other machines.
are available on the 162~ tor real systems.

e~a­

Several. progr81U

'1'h1a program w1ll 80lTe up to 20 aillul taneous linear equftioDS with oomplex
coetticients. Two tOJ'IU ot output results, A+jB and Ke j , are available
. tor either a 8pecified limited DUJlber of unknowns, or for all unknowna up
to 20.

The progr_ 18 written in Fortran with Format and requires

40

K

IlSOr.r.

Qi"D a I178tea

ot H 81Dltaneoua linear' equationa, in N unknowns, v1th

coaplex (or real) coeftioients, the progra solves forth. desired nuaber
of unknowns in terms ot complex numbers. In certainaituatioDs, onlY a
tew ot w.rous unkn01lD8 are needed. Tho8e desired can be rearranged to
appear tirst in the equations. By ap8city1ng the muaber desired, only'

o

that DWIber v11l. be solved tor, saving considerable coapt tar time in the
cue ot large systems.

66

----_*_____H_tt_.h_.______
~

-*-r--_._____ t.____. *___

-..

M_t_~_·

.'M.'_*_____________tt_t_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _

* __

"".,.,

o

.tr

II

%'1• •

SIMULTANEOUS LINEAR PltUATICJlS WITH C()fPLEX COEFFICIENTS

Those equations to be solved are set in determinants of the fonal

IZI

•

la'

+j

where a and b are the coefficients.

Ibi

The' application of Cramer.' Rule gives
~I

IZI

•

fel

+j

1-1

+j

• ( 1& I ICI

Idl
Ib J
+

USI

•

~I

1&,2

,a,

-j

Ibl

lal

-j

Ibl

leil )

(,a,

+ ~
+

lei,

~I

Ie I)

11'12

where Z 1. the determinant ot the coefficients and

is the same determinant
with the coefficients or the desired unknown replaced by the constant terms.
(&)

All determinants are evaluated by the triangular method, in which all elements
to one side or the leading diagonal are computed to be zero. The determinant
i8 equal to the product of the eleMents in the leading diagonal of the triangular determinant. This method of evaluation is preferable to that of expansion
in terms of ainors or the pivotal method because of the storage and time problem
imolved in the large complex systems.
Previous programs have made it necessary to do a manual rearrangement ot data
when a sero element is encountered on the diagonal, resulting e1 ther trom the
original coetficients or trom subsequent compltat1ons.

This program will check

elements in the same column of the remaming rows of the determinant for a
non-sero element. It such a value 18 found, a row interchange is performed,
changing also the sign ot the determinant. It no non-sero element is found
we 'haye the case of a sero determinant. It this occurs for the coetficient
detena1nant, a me8sage 1s typed out ani a different _thod of solution JIlUst
be found for this cue of a nonsingular solution. A .ero nu.rator determinant evaluates an unknown equal to zero, which is the correct result.

o

o.-er and underflow proble.. are quite common in matrix problems when dOing
accumulative operations J such .a coml'Qting t.he product ot the diagonal
e1811l8nt& oftha deterJlinant. A scaling procedure baa eliminated such ditt1culties in this program. Before mul t1plying, each diagonal element 1.IJ scaled
to the range between .1 and 1.0, storing an accumulative characteristic
-2-

67

SDlTLTANEOUS LINEAR EQUATIONS WITH COMPLEICOEFFICIENTS

o

(or power· of 'ten) tor the determinant, which is ()utput with the product
and then applied in the final division ot deteminants 80 that the end
'results have the correct magnitude.
EepeciaJ.q :Ill the case ot large 87Ste1l8, this program has been found to
be as 8tt1ci~nt even for real systems as most existing programs, particu-

larly because of the row interchange and scaling procedures.
As many as 20 eQ.uations in 20 unlmOWllS may be handledby' this program on
a hOI machine, which is minimum core for the program. The largest system
. run up to this time baa been 18 equations, but no difficulties can ,be
foreeeen on 8.l\Y larger problems because of the 8Caling procedure.
The reeul.ta are indicated in two forms.

The actual outputs are the real

and imaginary parts of the 8olution, as well as the magnitude and phase

angle.

These will give results in the tormal
A + jB and Ke

jt

G

where

A • real part

B • imaginar,y part
I • magnitude
t • phase 8l'Igl, in degrees

t • tan-1

B

I

SUMMARY

This program has been used numerous tim·es for several months nov, on systelft8
trom 3 equations to 18, both partial. and complete solutions.
on the 1620 MOD II have runa

Execution tiIles

3rd and bth order - 1 lIlin.
lSth order -

20 Ilin.

17th order -

29 Ilin.

o

It ehould be noted that theae times are dependent on the original set up

ot the coefficients

and how m&ny' row interchanges are nece8slll7.

68
-3-

*:

!

,.1,..,r""Miur

,t

t

.....

"

t

r

r

r

tt:

r

t

ztt

In

t.

t,)

*'

tt

hi

_

$ ht

de

HMstrttsttitstt· "m

tiM

tt)L

SIMULTANEOUS LINEAR I!XtUATIONS WITH COMPLEX COEFFICIENTS

The program. is written in Fortran with Format and uses an ABSOLUTE VALUE
aubrout1ne. Thi8can be easily changed in the 80urce program it the
subroutine 18 not relld1:q available. Although the program Jresently begins at 6600,
there 18 _ple storage to recompile with a starting position of 8)00 for other
_chine configurations.

It would be a silllple matter to change input and output

DIOdes to tit other needs and equ1pnent.

No serise switches are used.

SUIple input and output data follow in Appendix A and a JrOgram listing is
in Appendix B.

o

o

69
-1&-

APPENDIX A
Sample inplt and output data listing tollow.

Input data tollows the aame

o

sequence tor all programs although Case 1 will be the only one described.
.

.~

Case 1 - 3
Input

.

1

order complex system, canplete solution
st

Card - NSOL • 3 (number of solutions desired) - 13 format
Note statements 500 and 101 in program listing (Appendix B)

2nd Card - N· • :3 (order

or· system)

- I3 format

ot the
coefficients) - both values are on the same card in Elh.8

N X N (9) Cards - AR and AI (real and imagin&J7 parts

format and are entered row-wise.
Note statement 100 in Appendix B.
N(:3) Cards - FR and FI (real and imaginary parts or the constanta) both values on the same card as were the coefficients.
output

Real and imaginary parts ot the input coefricients
Real and imaginary parts otthe input constanta
Real and imaginary diagonal produots, value of the
coefficient determinant, scale factors for the produots
and the determinant, phase angle and magnitude.
Real am imaginary diagonal products, value of the determinant
and scale factors for NSOL(:3) solutions which include real and
imaginary
(A an~ B), phase angle (t) and magnitude (X).

parJ

CatSe 2 - 4th order real system, complete solution

ease :3 - 4th order real system, partial solution
Case

4-

'fd

order real system, sero determinant

o
7U

LN'i#!Htt"i:i!.1·dt6·H"JWi~WMlJjJ""tMiMWi

"•.•,# fW'bwrw'i#tPtiJliH¥t' ""fit W'litiiW*Mtw "'w'\\tiriW ""'iib' tit" '.' b' 1fut'W'J/,'i"i:iINibtt' 'It 'f 'il'YrrWwlttW''b' HfW 'f'IWWifY-B'm"tfiJ'''twt2'',eiilI''!'tmnUWW'H IPl/W II pmllr:"r' ,
Wi

'"rnltl"""Wm',

!

t

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rt

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wrtrris

Sample Case 1
Page 2

o

Input

3
3

+.20110300E+04+.13140000~+03
-.20~50000£+04-.22700000E+Ol

+.OOOOOOOOE-99+.0000000 0E - 99
-.20550000E+04-.22700000E+Ol·
+.161U2980E+U5+.21747GOOE+03
-.14170000E+05-.1b~OOOOOE+03

+.00000000E-99+.00000000E-99
-.14170000E+05-.18500000E+03
+.22498000E+OS+.13500000E+03
+.OOOOOOOO~-99+.000000UOE-99

+.OUOOOOOOE-99+.00000000E-99
+.G3300000E+04+.00000000~-Y9

o
7I

t•

...._ ..

Page 3

Sample

Output

C~~e,

"

1

o

SOLUTIO~

OF SIMULTANEOUS LINEAR EQUATIONS
WITH COMPLEX CUEFFICIENTS
PROG. 223-63

ORDER

3

REAL

I r'lAGI NARY

.20110300E+04
-.20550000E+04
.000000001:-99
-.20550000E+04
• 16 10298 0 E +0 5
-.14170000E+05

.OOOOOOOOE-99
-.1'-:-170000E+05
.22498000E+05

.131'tOOOOE+03
-.22700000E+Ol
.OOOOOOOOE-99
-.22700000E+Ol
.21747000E+03
-.18500000E+03
.OOOOOOOOc-99
-.1i3500000E+03
.185UOOOOE+03

c O~,j ST td'J T S
.OOOOOOOOE-99
.OOOOOOOOE-99
• [j 3300 000 E +0'+

.OOOOOOOOE-99
.OOOOOOOOE-99
.OOOOuOOOt-99

REAL PROD.
.22940795E-OI

IMAG PROO.
DETERMINANT
.25515200[-02
.53279032E-03
0
f'~UlTIPLY REt\L ANO H,'IAGIf,u\R.Y PRODUCTS BY I.OF
(·':UL T I PLY OETE;':j'·jJ NAi'JT BY 1.0E
26

= • (, 3 4 6':,. 6 L t: +OlD f ~ R t: E S
= • 2 308 22 5 1 E- () 1 ~~ 1. a~

PH A S E td ~ G L E
i"i A GNIT U 0 r~

REA L P RU D •

t l"

I Iii AG PRO D •

1. 3

L)

ET E Ri',( I NA1'1 T

.2425606P.E-Ol
.34347995E-03
.Sd847480E-03
1
MULTIPLY REAL AND IMAGI~ARY P~OOUCTS BY I.OE
MULTIPLY UETERMINANT BY I.eE
26

REAL P~OD.
.23717163E-Ol

IMAG PROD.

13

DETERMI~ANT

.lH60~040E-n2

.56596678E-03
2
r-'ULTIPLY REAL AND Ii:1l\GIi'JAkY Pi.{ODUCTS dY l.OE
tl: Ul TIP LY 0 ET E:;( ;'<1 I /.! Ar\J T BY l. 0 E
26

REAL PROD.
INAG PROD.
DETE~MIN~NT
.23433940E-ul
.21191024E-02
.55364013E-03
3
j'' l UL TIP LY REA LAN [) I r;;~ GIL ARY PRO UUCTS d Y 1. 0 ~
~llJ L TIP LY 0 ET ER~!I :"J Ar·JT BY 1. () E
26

13

1J

SOLUTIONS OF THE SIMULTANEOUS LINEAR EQUATIUNS
ORDER

3

REAL

I r;At;I NARY

PHASE AiJGLE

~;'iA(~f"!

o

I TUDE

72

Page

o

b

met

tri±it tittbstt·

r o_..sri
t

r

th

WI teeti

tnrM,. . . . .

trtr #&

ttt

tt

4

.10460585[:+01

-.10137221f:-OO

.10301~13E+Jl

- • 3 3 it- :; 4 it-:~ 1 E- 0 1

• 10 1 <) 1 (, 2 Gt: +0 1

-.209t~0622E-Ol

-.553:'1769E+Ol
-.18600954E+Ol
-.11793317E+Ol

.J.05095BHE+Ol
.103066~·3F.+Ol
• J_

0 1 C) 3 7 i5t) E + 0 1

o

o
73

Page

5

Sample Case 2
Input

4
4
+.30000000E+Ol+.OOOOOOOO~-99

+.20000000E+Ol+.OOOOOOOOE-99
-.10000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+Ol+.OOOOOOOOt-99
+.10000000E+Ol+.00000000E-99
-.10000000E+Ol+.UOOOOOOOE-99
-.20000000E+Ol+.OOOOOOOOE-99
+.40000000E+Ol+.OOOOOOOOE-99
+.20000000E+Ol+.OOOOOOOOE-99
+.30000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+Ol+.OOOOOOOOE-99
-.20000000E+Ol+.OOOOOOOGE-99
+.50000000E+Ol+.OOOOOOOOc-99
-.20000000E+Ol+.OOOOOOOOE-S9
+.30000000E+Ol+.00000000E-99
+.20000000E+Ul+.000000UO~-99

+.lOOUOOOOE+Oi+.OOOOOOOOE-99
+.30000000E+Ol+.OOOOOOOOE-99
-.20000000E+Ol+.OOOOOOOOE-99
+.OOOOOOOOE-99+.00000000E-99

o

o

-

.rrttt ... rMn

II

Page

rt

ttt

·W'U'EW'

t

h

r d

•

t

ttt

st

trtt dtt

*:

trte H

*•

ttr_..

Sample Case 2
Output

6

o

SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
WITH COMPLEX COEFFICIENTS
PROG. 223-63
ORDER

I t-\A GI NAR Y

REAL

.30000000t:+0 1
.20000000E+()1
-.lOOOOOOOE+Ol
.100U0000f+Ol
.10000000E+Ol
-.10000000E+Ol
-.20000000E+C 1
.40000000E+Ol
.20000000E+Ol
.3()OOOOOOc+{J1
.100000001::+01
- • 20 0000 00 [-: + 0 1
.500000001::+01
-.20()()OOOOE+Ol
.300000001::+01
.20000000[:+01

.OOOOOOOOl:-99
.OOOOOOOOt-99
.OOOOOOOOE-99
.000000001.:-99
.OOOOOOOOt-99

.OOOOOOOOE-99
.OOOOOOOOE-99
• OOU 00000 c- C1 9
.OOOOOOOOE-99
.OOOOOOOOE-99
.OUOOOOOOl-99

.()()OOOOOOF.-99
.OOOOOOOOt-99
.OOOOOOUQE-99

.OOOOOUOGE-09
.OOOOOOOOE-SY

C l) N S T A~! T S

.10000000E+Ul
.30000000E+Ol
-. ~~ 00 00000 E +0 1
.OOOOOOCOF:-99

REAL PROD.

• OOOOOOOl) \:-99

.OOOOOOOOi::-99
.00000000 r:-9<;

.00000000l:-99

IMAG PROO.

DfTFRMINANT

.49999993E-02
.nOOOOOOOf-99
.24999993E-04
0
t.1 UL TIP l Y Ret, L A1'1 D I jVl AG 11\1 A~), Y P FJJ Due T S BY 1. 0 E
1"1 Ul TIP LY D~.: T ER 1'"1 I j\J I~ (~ T BY 1. 0 E
8
PHASE

Af'JGLE

MAGNITUDE

=

=

.(;OOOOOOOE:-99DEGREES
.49~99992E-02
1.DE

*

4

REAL PROD.
I~1AG FRUD.
DET~::r-(;'lIi'JANT
.19000000E-OO
.00000000E-99
.3610000UE-Ol
1
i.~, UL TIP LY n. cAL t\ !'J D I fll' AG I I\! ARY P t;( [J l") UCT S E Y 1. a f:
t': U LTIP L Y D~: T ER t'-'1 I Nt, NT B Y 1. 0 E

REA L PRO D•
-.28999992E-02

I 1'1: i~ G PRUD•
.J0000000t-99

....,
i.

4

DET L: ;~ f.'; I NAN T
.84099953E-05

2

MULTIPLY REAL AND IMAGINARY PPUOUCTS BY I.OE
MULTIPLY DETERMINANT BY l.OE
8

o

4

REA.L PROD.
rr"1AG PP,OD.
DETERMI!~t\NT
-.50999986E-02
.OOOOOOOOE-99
.26009985E-04
3
MULTIPLY PlAL AND IMAGINARY PRODUCTS BY 1.DE
~ULTIPLY DETERMINANT BY 1.OE
3

4

4

75

....&

'r

""1

.;.;.~~

'r"~p

•

'~·-·t

'-'----t'j·..

'-·'·!··,e!·-t··''''·!·''·--.-·····t·-.·--"-..

Page

~·.~.-,

7

o

RcAL PPCO.
I j"lAG PROD.
DETER~·: I:\~ANT
.48999998E-02
.OOOOOOOOE-99
.24009998E-04
4
MULTIPLY REAL !.\NO H"1AGINAr~Y PRODljCTS l3Y 1.OF.
MU L TIP L Y 0 E T Ek f--i I rJ tHJ T b Y 1. 0 E
- c)
SOL UTI OI'J S 0 F THE S I ;~ UL TAI'd: f) US L I f\! EAR E QUA T I UN5
ORDER

4

REAL

.38000004E-OO
-.:57999987E-OO
-.10199998E+Ol
.98000006E-07

I!\iAGINARY
-.DOOOOOOOE-99
-.OOOOOOOOE-99
-.00000000 F:-99
-.00000000E-99

PHt\SE ANGLE

!·itiGi\' I TUDE

.OOOOOOOOE-99
.OOOOOOOOE-99
.OOOOOOOOE-99
.OOOOOOOOE-99

.380n0003E-OO
.579999[~6E-OO

.10199997t:+Ol
.9?()nC00:5f:-07

o
76

=

re.sr1 "ts

WsttH j" _

t

t

t rSrz

t

t.

=

1m

rtn',

•

Sample Case 3
Input
'

Page 8

o
4
4

+.30000000E+Ol+.OOOOOOOOE-99
+.20000000E+Ol+.OOOOOOOOE-99
-.10000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+Ol+.OOOOQOOOE-99
+.lOOOOOOOE+Ol+.OooodoOOE-99
-.lOOOOOOOE+Ol+.OOOOOOOOE-99
-.20000000E+Ol+.OOOOOOOOE-99
+.40000000~+Ol+.OOOOOOOOE-99

c

+.20000000E+Ol+.OOOOOOOOc-99
+.30000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+Ol+.OQOOOOOOE-99
-.?OOOOOOOE+Ol+.OOOOOOOOE-99
+.50000000E+Ol+.OOOOOOOOE-9 Q
-.20000000E+Ol+.OOOOOOOOE-99
+.30000000E+Ol+.OOOOOOOOE-99
+.20000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+Ol+.OOOOOOOOc-99
+.30000000E+Ol+.OOOOOOOOE-99
-.20000DOOE+Ol+.OOOOOOOOE-9~

+.OOOOOOOOE-99+.00000000E-99

o
77

"

.

r~

."_

Page

9

Sample Case 3
OUtput

0 '·
'

Ii\iEAR EUU/~T IOi'lS
COEFFICIENTS

SOLUTlfJN UF S I~~UL T/ i'EOLiS L

WITH

COMPL~X

PROG.
or~DER

I

2~~3-63

4

REAL

I t-I/\ GIN AR Y
.00000000[:-99
.OOOOOOOOt-99
.OOOOOOOOE-S9
.OOOOOOOOE-99
.ClOOOOOOOE-99
.OOOOOOOOE-99
.00000000[-99
.OOOOOOOOE-99
.OOOOOOOOE-99
.00000000c-99
.OOOOOOOO!:-99
.OOOOOOOOE-99
.OOOOOOQOE-99
.OOOOOOOOE-99
.OOOOOOOOE-99

• 30000000E -C) 2
.20000000[-()2
-. lOOOOOOOE -0 2
.lOOOOOOOE-01
.lOOOOOOOE-02
-.lOOOOOOOE-02
-.20000000E-02
.lrOOOOOOOE~02

.200()OOOOE-02
.3000(lOOOE-U2
.lOOOOOOOt:-02
-.20000000E-02
.5 0000000 E -0 2
-.?OOOOOOOE-LJ2
.30000000E-02
.20000000E-02

• noo OCO(jO E-; TNAf~ T

I [vi AG P PJ J D•

-.28999992E-02
.OOOOQOOOE-99
.84099953E-052
t., U L T I ;:) LY I-' EA L Af\j D I ~1;\ G I !. L-\ !~ Y P R() [) UC T S UY 1. 0 E
~1 UL TIP L YJ rJ E T ER H I NI~ f\J T ~) Y 1. 0 E
- 16
SOLUTIONS OF THE
ORDER

SIMULTA~EUUS

.'
-c·

LI~fAR

-8

o

EQUATIUNS

4

78
------

.-.--.--~--------.-~-.--.--~-~-.-.--.-~---

--

-~-

~

~

-~~-

m

'!!!!!¥I'UPWMWlIP'IIIH"W

,I,.

•

tt· •

t

H.

t

rt

tr the

trW

=

Page 10

IiJ,GINARY

.3800000 l tE-OO
-.57999987i:-OO

-.OOOOO()OOf--99
-.OOOUOOOOE-99

PHASE !\I\JGL E

.OOOOOOOOE-99
.OOOOOf)OOE-99

~1

AGiJ I T UDE

.3G000003E-OO
.~7999Yd6F-OO

o

o
79

' I'

...

Page II

Sample Case

Input

. • ........ , ~,

,to - . . . ,..-

4

o

3
3

+.lOOOOOOQE+Ol+.OOOOOOOOE-99
+.20000000E+Ol+.OOQOOOOOE-99
+.20000000E+Ul+.oodpoOOOE-99
+.30000000E+Ol+.00000000E-99
+.lOOOOOOOE+Ol+.OO~OOOOOE-99

+.10000000E+Ol+.00000000E-99
+.20000000E+Ol+.OOOOOOOOE-99
+.20000000E+Ol+.OOOOOOPOE-99
+.20000000E+Ol+.OOOOOOOOE-99
+.lOOOOOOOE+02+.00000000E-99
+.50000000E+Ol+.OOOOOOOOE-99
+.15000000E+02+.00000000E-99

C''-' '
~

'\

o
8U

we

ttttrsttttttt • • •1 thr«
1

t

mi't

_*

",=,U,,'!!W'!J[!W5Ll5"

rt ' . "

t

Page 12

ew·''':"''',, tiS" l' .M"',,·I"2 rr"'rrf)5fWfYtYWWltW"!

Sample Case

OUtput

4

o
SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
WITH COMPLEX COEFFICIENTS
PROG. 223-63
D,RDER

3

Rt:AL

I 1-1,.,\ GIN ARY
.OOOOOOOOE-99
.00000000 [:::-99
.OOOOOOOOE-99

.10000000E+Ol
.200UOOOOE+Ol
.20000000E+Ol

.3()OOOOOOE+Ol

.OOOOOUOOt-99
.OOOO()OOOE:-99

.10()OOOOOE+Ol
.10000000E+Ol

.00000000[-99

• 2CJOOOOOO[~ +() 1
.2uOOOOOOE+Ol
.2000000Uf-:+Ol

.O'JOOOOOOE-99
.OOOOOOOOE-99
• OOOOGOOO E-(~'':1

CUNS TAI\TS
.lOOUOOUOE+02
.50UIJOOOUt:+Ol
.150000COE+02

o

J

Z E RU DE T E R MI j\J A t ~ T -

.COClOOOOOE-99
• 0 0 (J lJ 0 0 0 0 t: - 99

.OOOOOOOOE-99
US t

UI F FER EN T ~1f: THO D 0 F S () L UTI 0 ;\1

o
81

APPENDIX B

PAGE 01
SOURCE PROGRArll]

07000 C

SOL UTI 0 ;\1

07000 C

S I HUL TAN E 0 US LIN EAR E CUt\ T I Ur,; S trJ I THe II tv; P LEX

(J F

COEFFICIENTS USING CRAMERS RULE

07000 C

PROG NO 223-63

07000 C

o E T E R'''11 NAN T S

07000 C

E L E,.,1 E NT SEN T ERE D R0 \.J - \..' I S E

E V !~ L U ATE 0 B Y THE

T R I A N GU L.4 R

:'1 ET t-l (J [)

07000 C
07000 C

AR-REAL PART OF DETERMINANT

07000 C

A I - I ~1 AGIN A~~ Y PAR T

07000 C

REA LAN D Hi; AGIN ARY PAR T S 0 F A C (j F. F FIe lEN T E ~~ T ERE D

07000 C

FR-REAL PART OF CONSTANT

07000 C

FI-If·1AGINARY PART CF CONSTAt-.!T

07000 C

N-ORDER OF

07000 C

N SOL . -

07000

o It·') ENS ION

07000

DIMENSION XR(20), XI(20)

07000

CONV

07048
07072
07096
07118
07142

•

07296
07320

(J F

Ut: T t=. R ~/I I NAi'.J T
~:lf'\

S AI·H:: C .~ R j)

TERM
TER~~

THE SY STEt'i

N U MB ER 0 F S (J L UTI 0 f\J S fH:': S I

~

E D (E qUA L T 0

[j R

AR ( 2 0 , 2 0 ) , h I ( 2 () , 2 a ) , F R ( ;: 0) , F I ( ? 0 ) ,

~.! R (

L F: :-; S T H A f'~ f'J)
2 0 , 2 () ) , \,.r I ( 2 0 , 2 0 )

= 180./3.14159265

500 READ 101, NSOL

READ 101, N
10 1 FOR t~ AT (I 3 )
PUNCH 104
104 FOR tv, A T (I / 1 5 X 41 H S[) L UTI 0 N 0 F S I MU L T A j\j E LJ U S LIN EAR t: 0 U :4 T I

(J (\J

S)

PUNCH 105
105 FORMAT (22X, 25HwltH COMPLEX CUEFFICIENTS/29X12HPROG. 223-63/)

o

I

07552
07576

07712 C

PUNCH 119, N
,

119 FORMAT{5HORDER,I31/5X,4HREAL,11X,9HIMAGINARY)
INPUT AND PUNCH MATRIX

82

p"

o

t

"J'P!!SP*W'fttMW!!'NP'

"t

., nmwW',w.m.Inni.uRn W' "'Ynrrm'Hl''tW·h'' '2fif"#rWij[ddS'HiflW'PW.... ··MEWWFiiiE'S·W-Y·!Wwi fijiMHi·WI .t'''ttffl'fm" ]HZ' 'Nrnil!!'!'" .·Mt!'W'BW'''\'''!l"··fHf 'MfflWt''t'Urt'tN M! "8 nffYf'l'lm." .wlm WilE j7' J5!F"liWw 'Pt'i ['i?
t

[!

PAGE 02

07712

DO 1 I

07724

DO 1 J

07736

RE/~D

07892

=
=

1, N

1, N

100,

AR(I,J),

AI(I,J)

100 FORMAT (E14.8, EI4.B)
AR ( I , J ),

AI ( I , J )

0"7 92 0

P U i\l CHI 16,

08076 C

SET UP WORKING MATRIX

08076

08232

WI ( I , J)

08388

1 CO I'll T I ~.J UE
PUI\!CH

08460

c·

103

084B4
08532

AI ( I , J )

~

103

FOR ;·i AT

(/9 H CON S T t\ N T S )

I N PUT AND P Uf\; CH CO r·J S T i~ NT S

C

08532

DO 2 I = 1, N

08544

READ

08628

2

100, FP,{I),

PUf'~Cr!

116, FR(I),

FItI)

Fl(I)

4

08748
08784
08832

=0
LIM = N-l
SIGN = 1.0

MN

50

08868 C

DIAGONALIZATION UF Ut:TU<.:·'iI~jANT

08868

DO 25 I

=

1,Llr'~

08880
OB916

08964

o

09300

L = 1+1

1 8 0 E N = WR ( NUH , I ) ~:~ vJ R ( 1': ur"l, I ) + \. .J I ( NUM, I ) ::~ ~,I I (N U""\ , I )
IF(OEN)

14,

15,

14

09356

14 If(NUM-I) 914,914, 24

09424

15 NUr-'1

=

NUi';+ 1

83

"

, . mm,...i,,,

PAGE 03

o

09472

IF

(NUtvi-f'J)

09540

53 I F (f·1 N· ) 4 ,

09596

4 PUNCH 110

09620

PRINT 110

09644
09788

18,

4,

18,

53

5

110 FORMAT(//42HZERO DETERMINANT - USE DIFFERENT METHOD OF9H SOLUTION)
STOP

09836

24 DO 16 J

;::

1, N

09848

WRT

;::

WR(I,J)

09944

vJ I T

;::

WI(I,J)

10040

WR(I,J)

:::

WR ( NUt:i , J )

10196

~~

:::

~~

10352

WR ( N Ut·l t J )

;::

10448

16 WIH.JUM,J)

I (I , J )

I ( NLJ t:j , J )
~'!R

T

C'·'
,

10580 C

;::

WIT

.

I

CHANGE SIGN OF DETERMINANT IF ROWS ARE INTERCHANGED

10Seo

SIGN;:: -SIGN

10628

914 DO 23 J

10640

WRT

:::

WR(J,I)

10736

WIT ==

~~I(J,I}

10832

DO 23 K

==

10844

Xl

;::

WR T t-J R ( I , K ) - WI ( I ,K ) ::q'J I T

*

11072

X2

;::

WR(I,K>*WIT+WI(I,K)*WRT

==

L, N

I , N

11288
11660

12020

WI ( J , K)

23 CONTINUE

1.2128 C
12128

;:: ~J I ( ,-I· t K ) - ( WR ( I , I ):~ X2 - \~ I ( I , I ) ~:, Xl) IDE N

ADJUST ,"4AGNITUOE TO AVUID OVER OR U~~DERFLO~J
5

IS;:: 0

o

ts

O>AGE

tt

't

, In

PII""YPMP=Y'R"fll!flNtMPWUW W "f!!1'"!W'E'l'iI'f1f'P'flHiff'YR!P"MJ!'!"M!UWI'E'P ''''wi'f',,'1'1 INS n 'PWw.;iI&WbkWr r ,WiWWM""#tt""'1!prWWtiitMi1tl"ffiltn "'15ft'mCW JI 'fl'i'MTI'IMWMlWifW'Pi:'1*iI'!!f·'''' I'.

04

12176

=

DO 200 I

12164

220 AB\4R

=

1, N

ABSF(WR(I,I)

I F ( AS ~~ R ) 200, ·200, 213

12272

211, 200, 210

12328

213 IF(ABWR-1.)

12396

211 IF(ABWR-.l) 212, 200, 200

12464

212 TTEN

=

=

10.

12500

IS

12548

GU TO 214

12556

210 TTEN = • 1

12592

1 S = I S+ 1,

12640
012808
12976
12984

214

15-1

\~R(I,I)

= WR(I,I)*TTEN

WI ( I , I )

= WI(I,I)*TTEN

GO TO 220
200 CONTINUE

13020 C

EVALUTION OF DETERMINANT TAKING PRODUCT OF DIAGONAL ELEMENTS

13020

DO 7 I

13032

J

13080

PROD R

13428

PRO D I

13764

\tJ R ( I , I)

13860

0

r

• -riP t d '

= 2,

N

;: 1-1

=(WK ( J , J ) *\-J R ( I , I ) - WI ( J, ,J ) ::q~ I ( I , I ) )
=(~J R ( I , I ) ~('fJ I ( J , J ) + ~'I I ( I , I ) ~:~ WR ( J , J ) )
;: PRO 0 R

7 WI ( I , I) = P ROD I

= PRODR*SIGN

13992

PRODR

14040

PRODI ;: PRODI*SIGN

14088

DET

14184

IF (DET), Ill, 121, III

14240

= PRODR*PRODR+PRODI*PROOI

121 IF(MN) 4, 4, 111

·e
8. t.t

c

PAGE 05
14296

111 PUNCH 115

14320

115 FORMAT (/2X, lOHREAL PROD., 7X, lOHIMAG PROD. 7X, 11HDETERMINANT)

14478

PUNCH 116, PRODR, PRODI, DET, MN

14538

116 FORMAT (E14.8, 3X, E14.8, 3X, EI4.8,

=

14602

ISO

14650

PUNCH 117, IS

14674

IS+IS

117 FORMAT (lOX,44HMULTIPLY REAL AND IMAGINARY PRODUCTS BY I.OE, 15)

14818

14842

IS)

PU~·jCH

118, I SD

11 8 FOR j\1 /..\ T (lOX, 28 Ht·1 ULTIP L Y 0 ET E Rt·1 I Nt~ i" T 3 Y 1. () E,

I5 )

14954

IFU'lN) 8, 9,8

15010 C

DETERMINANT OF THE COEFFICIENTS IS SAVED FOR LATER COMPUTATIONS

15010

9

BOT ::

=

DET

15046

ISZ

15082

PRDIZ :: PROD!

15118

PRDRZ

15154

PHID =ATAN~(PRODI/PRODR)*CO~V

15226

AMAG = SQRTF(DET)

15262

PUNCH 109, PHID

15286

109

15368
15404
15486 C
15486 C

IS

=

PR()OR

FUR~AT(/13HPHASE

ANGLE

=,

E14.8, 7HDEGREES)

PUNCH 125, AMAG, IS
125

FORMAT(llH~AGNITUOE

=,

E14.8, 7H

SET UP DETERMINANTS WITH

*

1.0E,I5/)

COE~FICIENTS

OF

UNKNO~NS

REPLACED BY

KN OvJN T ER ~1S

15486

DO 10 MN

15498

DO 11 I

15510

DO 11 J

= 1, NSOL
= 1, N
= 1, N

86

tttttnttttrttttrs rts

0

•

s

•

tt _ tsn"

, WI "'j'ffii"B'WP'5M IL'S"),IY'.H"'rr!P'w

:l!WJYIII8!·"''ij'''!m'

N' ,

r::" MNW/.'MDMI'H'fW'tMrW''!'Wf!!!

Itt

n "M.5BM.' TIl! 'c"'r:"lJIl',!,U"MnfB'" !IY"FWF2!"'f'".'N"WW'W'WW+rt' I' ''l"!I!!'UmWMMII'f-rru'tUH'''fP'm:r

'Yn!'fltwmP(":

PAGE 06
~~ R (

15522

= AR ( I , J )
= AI(I,J)
= 1, N

I,J)

15678

11 WI ( I , J )

15906

DO 12 J

15918

~,

16038

12 WI ( J

R ( J , t~1 N )
,(if: I'~

)

=

FR(J)

;:

F I ( ,J)

16194

GO TO 50

16202 C

SOLUTION OF THE UNKNOWNS

16202 C

POWER OF 10 READJUSTS

16202

8

VAL

=

=
=

XR(hN)

16430

XI(MN)

16574

10 CONTINUE
PUI'JCH

~AGNITUDE

(lO.**(IS-ISZ)/SOT

16298

016610

TocnR~ECT

(PRODR*PRDRl+PROUI*PRUIZ)*VAL
(PRORZ*PRODI-PROOR*PRDIZ)*VAL

106

1 0 6 F 0 Kt·1 AT (I /1+ 6 H S () L UTI Uj'J S DF THE S I t'-i Ul T!\ ~\! E 0 US lIN FAR. E (~1 UJ'. T ION S / )

PUNCH 3, N

1676h

16790

3FURMAT(5HORDERI4//~X4HREAL1IX9~II~AGINARY7X11HPHASE

=

17026

DO 13 I

17038

IF(XR(I»

17118

123 PHID

1715't

GO TO

17162

1 2 2 PHI 0

17282

1 24

17486
17594
01767()

17706
17730

=

ANGLE7X9HMAGNITUDL/}

1, NSUL
122, 123, 122

90.

124

=

ATAN F ( X I ( I ) / XR ( I ) ) ~:: CON V

Ar", AG :;: S(.) RTF ( XR ( I ) ;:~ XR ( I ) + XI ( I ) ;:' XI ( I ) )

PUN CH 1 20, XR ( I ), XI . ( I ), PHI 0, A1\1 AG
120 FORMAT(E14.8, 3X, E14.b, 3X, F14.8, 3X, E14.8)

13 CONTINUE
PRINT 900

gOO FORMAT(31HPAUSf, PUSH START FOR NEXT CASE)

8"

o

PAGE 07

17816

PAUSE

17828

GO TO 500

17836

END

SYMBOL TABLE
39999 SIN
399b9

SINF

39979 COS
39969 CDSF
39959 ATAN
39949

ATANF

39939 EXP
39929

EXPF

39919
39909
39899
39889
39879

LOG
LOGF
SQRT
SQRTF

39869

39859
35859
31859
31659

ABSF
ABSFF
AR
AI
FR
FI

31459 WR
27459 ~~I
23459 XR

XI
23059 CONV

23259

23049
23039
23029
23019
23009
22999

35869

31869
31669
31469
27 L.. 69

c

23469

23269
23069

18000000+03
31 Lt15926+01

000
),'<0500

*0101
*0101

221)89 NSOL
22979 N

22969 *0104
22959 *0104
22949 ::::0105
22939 ~::o 105
22929 l!~O 119
22919 ~~o 119
22909 :::0001
22899 I
22889 J
22879 *0100
22.869 ~:~O 100
22859 ~:(o 116
22849 ~(O 116

o

>tt

ttt

OPAGE 08

22839
22829
22819
22809
22199
22789
22779
22769
22759
22749
22139
22729
22719
22709

103
103
'::0002

~::O

;:~o

MN
0000
L I ~1
0001
)::0050

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o
APPLICATIONS OF NUMERICAL FILTERS IN
THE POWER SPECTRAL ANALYSIS OF STATIONARY
TIME SERIES

BY

ALEXANDER A. J. HOFFMAN
TEXAS CHRISTIAN UNIVERSITY
FORT WORTH, TEXAS

o

Presented At
Western Region 1620 Users Group Meeting
Denver, Colorado

June 17, 1964

o
91

o

We will focus our attention on the spectral analysis

of finite length recordings of a physical process which

is assumed to be random in nature.

For deterministic

functions such as periodic and aperiodic functions a

harmonic analysis is usually carried out by Fourier

series analysis and by Fourier integral analysis,

respectively.

The discrete line spectrum for a periodic

function and the continuous spectrum for the aperiodic

C~·i
I

function may be determined analytically because these

deterministic functions are "known for all values of

time".

Random series are a class of functions which are

not deterministic and do not lend themselves to the same

harmonic analysis techniques used for deterministic

functions: that is, statistical methods must be used.

The Tukey techniquei which is used here, is

applicable

o

to random time series which very closely approximate a

~2

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-2-

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stationary random ergodic process.

This computational

procedure yields the variance spectrum of a time series.

Other names for the resultant computation are power density

spectrum, second-degree spectrum, or quadratic

~ll

spect~umi

of which refer to the distribution of variance as a

function of frequency.

One begins with a recording of a physical process

which is assumed to represent a sample of a random process.

o

The record must be free of "pure tone" or periodic

components and transients.

After sampling the record

at equi-spaced intervals the linear trends and average

should be removed.

Briefly, the Tukey method consists of computation

of statistical estimates of the spectrum of a finite

discrete time series by a numerical approximation of the

o

Wiener-Khinchine equations.

The procedure involves two

93

-3steps.

First, one computes a set of mean lagged products

of the time series.

Another hame for the set of mean

lagged products is the autocorrelation function.

The

raw power spectral estimates are computed by application

of a discrete finite Fourier cosine transform to the

autocorrelation function.

This transformation gives the

desired frequency domain representation of the time series.

Systematic statistical errors resulting from use of a

finite amount of data appear in the raw power spectral

estimates.

c

The Tukey technique to obtain improved

spectral estimates involves a smoothing or refining

operation performed on the raw estimates.

Slide 1 shows the Tukey equations.

Slide 2 shows an example of a time series to which

one might apply the Tukey analysis.

Slide 3 shows the power densi ty spec-truro of the time

o

r

tttt

st.

1"z

-4-

o

series.

Eighty percent confidence intervals are shown.

Your attention is directed to the fact that the

power density qraph has an upper bound at a point marked

fN and that no power estimates of higher frequency are

plotted.

This upper band set is known as the Nyguist

frequency and is a function of the length of the sampling

interval.

A full discussion of sampling theory is

beyond the scope of this presentation.

However, a few

brief remarks are in order.

When a continuous function is sampled at equi-spaced

intervals, the question should be asked: "How well will

the discrete set of sampled values represent the original

function?"

A continuous function of time is completely

determined by its values at equally spaced intervals

provided that the continuous function contains no

o

frequenctes higher than, say, W cycles per second, and

·
9 t.)

~

-5-

the ordinates are given at points spaced 1/2 W seconds

apart, the series extending for all time.

G

This is a

statement of the popularly referred to Shannon theorem.

Under consideration here is an analysis which is to be

based on sampled values obtained from continuous records

which are not infinite in extent and are not band limited.

Analysis based on finite amounts of data is common to

statistical work.

c

Of immediate concern is the selection of the sampling

interval and the problem of aliasing.

Consider two sine

waves of equal amplitude, but different frequencies.

(See Slide 4)

Attention here is directed to a particular set of

sine waves, differ¥ing in frequency, but having a common

set of equally spaced sample values.

Thus, given only

the sampled values, a sine wave of a given frequency may

o

..

m•

t

t

-6-

o

be confused with a sine wave of higher frequency.

Specifically, if a harmonic time function X(t) is

sampled at equally spaced time intervals At, then a

frequency

=_1_
2~t

called the Nyguist or folding frequency, exists such

that the functions with frequencies

f + nfN ' for n = 0,2,4, .•. ,

o

are not distinguishable.

Obviously, then, power contributed to a power spectrum

at a given frequency f cannot be distinguished from

powers contributed by frequencies f + n f

of frequencies is known as aliasing.

N

.

This translation

If the data

actually contain power at frequencies greater than f N ,
this power will be "folded back" into the principal band

which extends from 0 to f N .

o

Power that is folded back

results in a distortion of the true power spectrum in

97

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_ _ _ _ _ _ _ __

-7-

o

the principal band.

To make the effect of aliasing negligible it is

necessary to select a sampling interval IIsmall enough

ll

to place the Nyguist frequency beyond all significant

power contributi ons.

Associated with each spectral estimate there is a

confidence interval which depends on the number of

degrees of freedom in the computation.

If one assumes

o

the distribution of the data to be Gaussian and that the

distribution of the variability in the spectral estimates

follows the so called "chi-square" distribution, then

the number of degrees of freedom may be computed

by the convenient formula:

k

= m~

(N -

~

)

where k = number of degr~es
N = number of sampled values
m = number of the maximum log

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The confidence intervals are then computed using

the number of degrees of freedom.

As the number of

degrees of freedom is increased the confidence intervals

decrease in size and the computed estimates are more

reliable.

The number of degrees of freedom is, generally

speaking, directly proportional to the number of data

points and inversely proportional to the maximum

o

number of lags.

Acquisition of more data may be impossible

or economically unfeasible and reducing the number of

lags reduces the number of spectral points in the

frequency range from zero to the Nyguist frequency.

This brings us to the point of this paper.

In many physical processes the power density decreases

very rapidly with increasing frequency.

Often at the

higher frequencies the power density of the process under

o
investigation is of the same order of magnitude as the

-9-

noise background.

o

One must sample the processes often

enough to avoid aliasing which would cause the noise to

"fold back" into the frequency range of interest.

Then

one must take many lags and compute many power density

estimates in order to have a good look at the lower

frequencies.

The consequences of this are large

confidence intervals and much computation.

In order to get around this problem one can operate

o

on the original sampled data with a linear operator which

is often called a numerical filter because of its

mathematical resemblance to an electrical filter.

Through

use of filters one can change the frequency spectrum in

a known and desireable way.

In particular, a low-pass

filter may be used to suppress the power near the

Nyguist frequency and not significantly disturb the low

frequency spectrum of a time

o

series~

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Slide 5 shows a' power density spectrum computed

before and after low-pass filtering.

Slide 6 shows a comparison between the mathematical

model of an electrical filter which operates on a

continuous electrical signal and a linear operator

(a numerical filter) which operates on a set of equi-

spaced sample values of a time series.

Note that the

time domain representation of the electrical filter is

characterized by W, the impulse response or memory of the

filter.

The time domain representation of the linear

operator is simply an array of numbers.

In the

frequency domain both the electrical and numerical filters

have representations called the frequency response.

It

can be shown that the numerical filter is simply a

numerical approximation to the mathematical model of

o

the electrical filter.

i 0

j

-11-

o

Slide 7 shows a plot of the coefficients of a

low-pass filter.

Slide 8 shows the frequency response of both a

high-pass and a low-pass filter.

After the time series has been operated on by say,

a low-pass filter, the new time series may be resampled

usina a larger sampling interval.

That is, the set of

sampled values may be decimated by taking every other

value, every third value, etc.

c

A new lower Nyguist

frequency is associated with the power spectrum of the

new time series since the new sampling interval is larger

than the original one.

The low-pass filter has suppressed

the power at the higher frequencies and thus all but

eliminated possible distortion caused by aliasing.

Now

the low frequency range may be investigateQ using fewer

lags and thus keep the size of the confidence intervals small.

1 t) 2

o

-12-

o

After the power spectrum has been computed the effect

of the filter is removed using the frequency domain

representation of the filter.

In various applications high-pass, band-pass as

well as low-pass filters have been used.

Such computations

are used in geophysical applications such as analysis of

temporal variations in the earth1s magnetic field and

o

in biomedical applications such as analysis of EEG

recordings.

Slide 9 shows a macro-flow chart of a computer program,

written in 1620 Fortran lIz to accomplish the computations

discussed in this presentation.
Listings of the program are available from the author.
(User 5130).

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FIGURE 9
SINE WAvES OF rlF"FERENT ~ FREOUENCIES WITH THE
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FtGlJR E 14
THE F,REOUENCY F~E. SPONSEOF LOW~ PASS'
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man

IBM 1620 ASSISTS STUDENT COUNSELORS AT JUNIOR COLLEGE

o

Paul S. Chan
IBM CORPORATION
3610 - 14th Street
Riverside, California

May 18, 1964

o
11 3

.

g'&,"'

TABLE OF CONTENTS

•
I

I

1.

Abstract

2.

Introduction

3.

Purpose of the Study

4.

Data

5.

Method of Analysis

6.

Results

7.

Sununary

8.

Appendices
(a)
(b)
(c)
(d)

Correlations between Test Scores and Final Grades
Scattergrarn of SCAT T vs. Chemis~y IA
Scattergram of Mathematics Placement vs. Chemistry lA
Smnmary of equations.

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ABSTRACT

IBM 1620 ASSISTS STUDENT COUNSELORS AT JUNIOR COLLEGE

The present study reports findings, based on the com.puted results
from the IBM 1620, concerning the extent to which test scores on the college freshman testing program - such as the ACE, SCAT, Co-operative
English Tests - are able to predict academic success or failure in specific junior college courses. Scattergrams have been created for those
correlations of highest significance to assist counselors in estimating
the incoming student I s aptitude for college level study and in making a
more accurate appraisal of the student1s competence in a particular subject area.

o

Paul S. Chan
May 15, 1964

o
11 5

*

INTRODUCTION

Unlike private colleges, the state colleges, or the state university,
California I s public junior colleges are required by law to admit any resident of their districts who is a high school graduate or who is over 18
and able to profit from instruction.
Junior college adrninistrators have interpreted this as m.eaning that
they cannot deny admission to any applicant who has reached his 18th
birthday, although virtually all now have retention policies which deny
re ... enrollm.ent to students who fail to m.aintain a "satisfactory" grade
point average ~ At one t:ii:me, many administrator s interpreted the legislative m.andate to m.ean that they could not set any qualification for registration in any class. An apparent change in legislative sentiment has
com.bined with the realities of P?st-war enrollment pressures to cause
most junior colleges to search for som.e equitable means of screening
from. classes (particularly from. transfer classes) those students who
have little opportunity to succeed.
The freshm.an testing program. has been an established practice at
Riverside City College, a public junior college, for the past years. Although the counselors and admissions officers have been m.aking extensive use of these tests to assist in laying out the academ.ic path of m.any
students, there have been no attem.pts until recently to m.ake regular
evaluations of the measuring instrum.ents in use. Recently an IBM 1620
was installed at the college. One of the first projects to use the system
was ab attem.pt to determ.ine the relationship between the test scores and
the final grades in specific courses. It is anticipated that the results
will im.prove placem.ent of students in appropriate sections or courses,
and selection of students for particular areas of concentration or preprofessional training.

-2-

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PURPOSE OF THE STUDY

The battery of tests - ACE, SCAT and others - were administered to
the in-corning new students for the dual purpose of counseling and placement. Since this investigation was the initial application, the present
study was to demonstrate the validity of the battery for these purposes.
Another aim of the study was to modify the battery to include only those
tests best suited for the screening program. Excessive overlap of abilities measured by one test and those measured by another results in a
waste of the student 1 s time. Also, too great an array of scores for academic counselors might prove more confusing than helpful.
It was anticipated, too,' that critical cut-off scores could be developed
for 'eachtest, making it both practical and possible to advise the individual student, upon the basis of his score, just what his chances for success of failure in a specific course would be.

-3-

o
1j 7

DATA
This study involved over BOO students who were enrolled in Psychology
49, a freshInan orientation course, and who had completed one or more of
2S.courses which the college wished to examine.
There were fifteen predictor s. The se included:
(1) three scores from the ACE (Quantitative, Linguistic, and Total)
(2) the R. C. C. Arithmetic Competency Test of 40 items
(3) three scores from the School and College Ability Tests
(SCAT, Quantitative, Verbal, and Total)
(4) six scores from the Cooperative English Tests, Form lA-1960
EDITION (Vocabulary, Level of Comprehension, Speed of Comprehension, Total Reading, English Expression, and Total English)
(S) overall high school grade point averages (to obtain this figure academic subjects and othe rs such as typing, speech, journalism, and
music courses were used. Physical education, military science
and driver education were not used. Shop cour ses were used where
it was the student's high school major.)
(6) academic grade point averages (to obtain this figure only solids
such as English, foreign languages, math at the algebra and higher
level, history and sciences, but not including general science,
were used.)

C

ACE and ArithInetic scores were easily obtairied because they are a part
of the placement battery of tests required of all new students. The SCAT
and Cooperative English test scores were obtained by testing in the Psycho- I
logy 49 clas ses and the two high school grade point averages were rather
tediously obtained by employing an individual to compute the figures by hand.
The courses included chiefly transfer courses with a few not-transit:-. ~
type courses and represented a cross-section of the major divisions within the college.
DEPARTMENT
Anthropology
Art
Biology
Business
Business
Business
Business
Chemistry
Chemistry

Descriptive· Title

Couroe No.
2
lA
1
lA
lBA (hour)
SOA (SlA)
BlA (SOA)
lA
2

Cultural Anthropology
History and Appreciation of Art
General Biology
Principals of Accounting
Business Law
Elementary Accounting
Business Mathematics
Chemistry
Introductory General Chemistry

o

-4-

1 1 ti

=__

·_t...t•••••____. . . .

._. . . ._ _
._._·. . . . .
1II. . ._

DEPARTMENT

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Electronics
English
Geography
History
History
History
Math
Music
Nursing
Philosophy
Physical Science
Physics
Political Science
Psychology
Sociology
Spanish

t

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m.. .. .In.•.P'.. . . . ., .t . . .St.
. . . . . . . .• ._. .• .•______
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_. . . .. . . .t .
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.

'I( _ _ _ _•_•~
_ _•
_

Descriptive Title

Course No.
51
1A
1
3
4A
6A
3A
20
1A
6A
1
2A
3
lA
1
1

Electrical Fundamentals of Electr onic s
English Composition
Introductory Physical Geography
American History
History of European Civilization
Political and Social History of the US
Analytic Geometry and Calculus
History and Appreciation of Music
Introduction to Nursing
Introductory Philosophy
Introduction to Physical Science
General Physics
American Political Institutions
General Psychology
Introduction to Sociology
Elementary Spanish

This battery of tests was originally selected to provide a basis for predicting over-all scholastic success and success in specific subject-matter
areas: The ACE for general scholarship, with its Q and L sub-scores for
areas of primarily quantitative and verbal content respectively; the Cooperative English Test for English and other areas which require considerable reading; the Mathematics Tests for placement in mathematics and allied physical science courses.
Final grades of the students in each of the chosen freshman courses
were compared with their scores on each of the tests, The courses were
chosen from four areas: Language, Humanities, Social Science s, and
Natural Sciences.

o
-4B-

11 9

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~=-===~.=

=~~=

c
METHOD OF ANALYSIS

Results of the test battery were separated into ten test variables:

(1)

Three scores, the Q, L, and T, were derived from the ACE;

(2)

Six scores froITl the Co-operative English Test;

(3)

Three scores, the V, Q, and T, froITl the SCAT; and

(4)

One score froITl MatheITlatics PlaceITlent Test.

All the test scores and course grades were recorded in punched cards.

An analysis prograITl was written in Fortran.
Coefficients of correlation were co:mputed by the 1620 between scores
on each of these tests and final grades in each course. To substantiate the
validity of the results, besides the correlation coefficient, regression line
coefficients, standard error of estiITlate, and standard error of regression
coefficient b, the significance of r and of b were analyzed. A SUITlma ry of
equations for these calculations can be found in Appendix D.

c

-5-

12u

-.....
N

CORRELATIONS BETWEEN TEST SCORES AND FINAL GRADES
MATH
cases

Q

ACE
L

(EXp~

297

268

326

196

233

397
491 tt
363
196
362

290
362
363
084
275

089
656 Tt
286

122
287

596~\-

407

457 11
441

018
100
404
051
144

169

488 ft

438

525 TT

612 ft

436 1:
185
217
400
121
209
342
218

326 ft
165
406 tf
348
245
376
306
241

4S3"~

433 1:
160
416 tt
439
360

334 TT
033
316 ft
421
357
457 tT
582 TT
290

295

Humanities
Anthropology
Art lA
Music 20
Philosophy 6A
average

22
18
22
24

131
488 1:
463 fT
415
399

287
009
233
117
159

Social Science
Geography

l8

201

Natural Science
Biology
Chemistry lA
Chemistry 2
Electronics
Mathematics 3A
Nursing lA
Physical Science
average

40
55
30
13
23
25
21

125

578~'"

127
534 ft
278

~':

tT

o

SCAT
5

~Tr~

044

101

CO-OP ENGLISH
3
4
~Sp~

064

599~':

2

~Le~

33

442~':

1
~Vo)

Language
Spanish

..............

T

189
386 TT
359
144
144
450 TT
218

596~\-

l33
326

458~~

6
(Tot Eng)

V

179

232

040
546 ft
389
027
251

228
7941:
404
154
495

688~':

675 Tf

449~':

379 ft
106

048
421fT
405
324
310
449
260

473~':

425
368
503 ft
377
295

Q

T

281

161

362 1T

182

478~':

737~':

091
367

382
396
065
330

049
388
330
045
203

159
519 TT
018
501 fT
299

336

548 11

616 1: 093

242

547~':

536 fT
116
598 1:
492
324
452 fT
538 ft
342

391 fT
208
411ft
392
413
579"\065
275

375 TT
266 Tf
J.24
484
126
384 11
328
232

146
551 tf
501
305
294
528 ft
320

456~~

375 fT
329 ft
405 fT
588 n
225
558"\491
385

Indicates .01 level of significance
.05 level of significance

~ndicates

o

o

o

RESULTS

The results of this study are reported in Appendix A, a table presenting
the correlations between test results and course grades. Within each curricular area, the average correlation with each test is also given. All
the correlations coefficients in Appendix A at the .0 I level of significance
are marked with an asterisk and at the .05 level with double :crimes.
Grades in some courses appear to correlate relatively well with scores
on all the tests, while those in orther courses showed low correlations
with most of the test scores. For example, biology has 12 out of 13 subscore s with correlation at either· .05 or .01 level of significance and chemistry has ten out of 13, whereas Spanish and electronics h?~Te only one out of
13 at .05 level of significance. Some explanations may be offered for this
phenomenon. One is that the differential magnitude of the correlations depends partly on the magnitude of the reliabilities of the grades in those courses. Sectionings of a course will certainly be a factor to affect the magnitude. Another factor is that grades in some courses .are based on objectivetype examinations, while in others on a more subjective basis.
The relatively high predicitive power of the mathematics placement test
in the Natural Science Division is more or less expected. However, an almost equivalent result was found in the Q part of the SCAT Test. This is
an indication that it may be possible to obtain the same predictive information from either of the tests, so duplication of student's effort can be avoided.
It is quite unexpected that Spanish correlates with only the total score of the
SCAT Test in the entire battery. Also, electronics correlates only at .05
level of significance, with Q part of the SCAT Test. It is possible that this
phenomenon is due to the fact that SCAT Tests involves not only the psychological functions commonly measured by tests of verbal ability, but als~ a
particular type of reasoning ability important in academic success which is
not assessed by any othe r tests employed in the present battery.

G

The two parts, speed of comprehension and total reading, of the Cooperative English Test show high correlation with geography. This can be
explained because of the fact that the Social Studies courses normally require more speed in reaidng and in comprehension. The significant correlation at .01 level between philosophy and the vocabulary part of the Cooperative English Test certainly implies the requirements to succeed in
the course.

-6-

c
122

o

In general, the six JR rts of the Co-operative English Test correlate relatively better than any of the three parts in the ACE Tests, with all the selected courses. This is illustrated by the ,r-values of .794 with Art, .458
with Music, etc.
The tendency was noted also for correlations to be relatively high or
low with reference to separate courses rather than to the different tests •.
It was hypothesized that this phenomenon might be the result of difference
among the courses in inter-section standardization reliability of grading,
or use of objective examinations.

o

-7-

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SUMMARY

o

In this study of the value of a battery of aptitude and achieve:ment tests
for the prediction of junior college fresh:man grades, test scores were correlated with final grades in a variety of fresh:man courses. The individual
correlations appeared s:mall, but the relative predictive power was de:monstrated clearly.

The following :major conclusions concerning the predictive significance
of the present battery appear to be warranted:
(a)

Overlapping of tests in the battery used is evidenced, suggesting
that such an extensive array of exa:minations is so:mewhat superflous and repetitive. Both over-all and individual course predic·tions could be :made with even greater accuracy with a :more abbreviated battery.

(b)

Fro:m the scattergra:m, it was found that it is feasible to deter:mine the cut-off score in screening and to obtain :more insight
in the statistical probability of achieve:ment of a student in a particular course.

(c)

o

Because of the s:mall nu:mber of cases in this particular study, a
caution against placing too :much weight on individual test scores
in guidance, selection or place:ment is in order.

-8-

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SCATTERGRAM OF SCAT T-SCORE

F

D

99-95
2

3

1

2

2

2

84-80

2

3

5

1

79-75

2

3

1

74-70

1

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4

69-65

4

1

64-60

3

1
1

1

59-55
1

49-44

TOTAL

A

1

89-85

54-50

o

B

3

94-90

C

C

1

1

14

14

19

4

3

VB.

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CHEMISTRY IA

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SCATTERGRAM OF MATHEMATICS PLACEMENT
VS.

•

CHEMISTRY lA

F

D

C

44-40

B

A

1

39-35

3

3

11

3

34-30

9

7

7

1

29-25

4

4

1

24-20

1

2

1

C:!
TOTAL

17

14

19

5

3

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-

-----------~~--------

----------- -------------

---------------------------------

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APPENDIX (D)
SUMMAR Y OF EQUA TIONS

(1)

'-

(6~)2..

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Variance s

V\

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= V\~~"1.

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_

Y\(\t\-\)
(2)· Regression Line

(3 )

V\ ~X1

- L~ 2.~
V\ L:-~ ~--=(_L>)( ") i

b

--

~

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Correlation Coefficient

f1-

~

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h

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, Ln L y.~ -{2.-,c y. Jl (\ ~ 1~ - ( 'i J)~ J

(4)

Standard Error of Estimate

(5)

Standard Error of Regression Coefficient b
/

:")~.

'- ! ~.
S I)(r-~ ~

,---'

-,,-,-<--

(6)

Signficance of r
COITlpare l.n..[ with the critical value in statistical table for 2
variables and n-2 degrees of freedom.

(7)

Signfic anc e of b
Compare
with the critical value in statistical table
for n-2 degrees of freedom.

t -:..1*

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127

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,I

1620 COMPUTER UTILIZA TION
IN A WIND TUNNEL DATA
ACQUISITION SYSTEM

by
Stanley E. Wisniewski
Programming Operations Section
NORTHROP DATA PROCESSING

Presented to the
1620 Users Grou p
Brown Palace Hotel
Denver I Colorado

18 June 1964

NORTHROP CORPORATION

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TABLE OF CONTENTS

PAGE

. . . . . . . . . . . .. . . . . . ... . . ..... . .. .. . ..... .. .. . .
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
WIND TUNNEL TESTING FACILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DATA ACQUISITION SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
COMPUTER UTILIZATION •• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
COMPUTER HARDWARE MODIFICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . .
ABSTRACT ......

_.

0,
I'

1
2
3
4
5

6

SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

. . . . . . . . . . . .. . . . . .... . . . .. . .. . . . . . . . . . .

8

RECORD FORMAT

.......................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

CONCLUDING REMARKS.

10

REFERENCES

10

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_______________________________________________ NORTHROPCORPORATION

ABSTRACT

This paper describes how the IBM 1620 computer was teamed with a high-speed digital
data acquisition system and two tape units to perform on-line processing of wind tunnel test
data. The total installation is located in the Northrop Norair wind tunnel complex comprised·
of three tunnels: subsonic, transonic-sup~rsonic, and hypersonic. The processing installation provides a central data acquisition and reduction function for all three tunnels, even
simultaneously when necessary.
The high-speed data acquisition section scans, measures, and digitizes test data, in- .
troduces identification information, and records the data on magnetic tape for instantaneous
reading by the 1620, in a read-after-write manner. The 1620 then reduces the data into
tabulations meaningful to the aerodynamics research engineers, enabling them to make early
evaluation of test run results and to proceed with model changes if called for.
During off-line operations, the computer is available for other applications, and has
full control of the tape units.

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130
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INTRODUCTION

Today, more than ever, competition in the aerospace industry is very keen and time
is one of the most important elements to be utilized. For this reason, a company that makes
use of wind tunnels nlust also have a satisfactory test data acquisition system and a means of
automatically reducing the collected data as soon as it becomes available.
In the following paragraphs you will learn how we at Northrop have improved our techniques in this area. Our wind tunnels will be described as well as our data acquisition system to which a 1620 computer is coupled. Also of interest will be the changes we designed
into the 1620 computer to make it suitable for our applications and the programs we have
written to fulfill our objectives.
To the general public, wind tunnels are environmental chambers used to test model
planes,but to the aerodynamicist, wind tunnels are probably the most superior devices
used in aeronautical and aerospace research and development. Because of modern wind
tunnels, today's test pilots are no longer the nerveless stunt men of the past, but professional engineers. Wind tunnels offer both fast and accurate data as well as the ability to
simulate the different types of atmospheric conditions of any time of day or year. However,
they are by no means new tools. Years before the Wright Brothers famed flight at Kitty
Hawk, wind tunnels, crude as they were, gave valuable aerodynamics data which proved the
feasibility of powered flight. The original wind tunnel employed by Orville and Wilbur
Wright is on exhibit at the Air Force Museum, Wright- Patterson Air Force Base in Dayton,
Ohio.

o
131
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WIND TUNNEL TESTING FACILITIES

Dominated by its 100,000-cubic-foot vacuum sphere is the supersonic-hypersonic wind
tunnel facility at Hawthorne, California. This space age test facility provides test velocities from Mach 0.5 to Mach 14 with temperatures to 3000 degrees and simulated altitudes to
200,000 feet. To my knowledge, no privately-owned wind tunnel in the United States can
produce the combined heat, pressure, velocity and run time that are obtainable with the
one at Hawthorne. This relatively new, dual-circuit facility provides a greatly expanded
capability for aerodynamics testing on advanced aircraft, missiles and space systems. It
consists of two separate wind tunnel circuits: transonic-supersonic (Mach 0.5 through
Mach 5) and hypersonic (Mach 6 through Mach 14). Design models can be tested for periods
of at least 30 seconds in the supersonic circuit and up to one minute in the hypersonic circuit. The hypersonic tunnel can accommodate up to six 30-second runs each eight-hour
shift. More test runs of proportionately shorter duration are possible.
Test sections, in which the models are mounted for aerodynamic study, measure two feet
square in the supersonic circuit and 30 inches in diameter in the hypersonic circuit. A
special "free jet" section in the hypersonic circuit allows removal of a model from the air
flow while air flow is being established, thus protecting the model from excessive heat
loads. The pressing of a button promptly injects the model into the flow stream. In a
transonic or supersonic run, air passes from storage through a settling chamber (to smooth
the airflow and remove any turbulence), is expanded through a nozzle (to establish Mach
number), flows through the test section and then is forced through a "second throat" to reduce its velocity and to recompress it to atmospheric pressure before it exhausts through a
muffler.

C>

In a hypersonic run, air must be expanded so much (to achieve the higher velocities)
that its temperature could actually be reduced to a point where the air would turn to liquid.
To prevent liquefaction, an electrically fired heater containing a 16-ton bed of 3/8-inch
alumina pebbles heats the air to temperatures as high as 3000 degrees Fahrenheit before it
reaches the hypersonic nozzle. When the air is cooled by expansion, its temperature is
therefore still high enough to keep it from liquefying.
From the test section, the hypersonic air passes through a "second throat" as in the
supersonic circuit, to reduce velocity and then through a cooler to remove heat. It is then
discharged into a large 100,000 cubic-foot vacuum sphere. The vacuum sphere is essential
to hypersonic operations in order to achieve the high velocities desired in the test section.
With storage pressure fixed at 3,200 pounds per square inch, the required pressure ratio
obviously cannot be met by discharging the "used" air to atmospheric pressure (14.7 pounds
per square inch). A low-pressure atmosphere is necessary and this is the function of the
vacuum sphere.
About 100 feet from the supersonic-hypersonic facility and in another building is the'
7' x 10' subsonic wind tunnel which went into operation in the year 1956 and was used in the
very successful development of the Northrop T-38 Talon supersonic trainer, F- 5 fighter,
and Laminar Flow Control (LFC) airplane. During those tests, the output of test data was
punched onto cards, carried to a remotely-located IBM 704 computer installation, processed
and returned in a relatively-long turn-around time (normally about three days; on emergency
basis about four hours).

3

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132

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--------------------.----------------------------NDRTHROPCDRPORATION

DATA ACQUISITION SYSTEM

Today in the same building that houses the subsonic tunnel, is the data acquisition
system, which we are very proud to possess. It was designed and built to our specifications
by the Astrodata Corp. It serves all three of our wind tunnels. The data from any two of
the three remotely-located tunnels can be transmitted to this center simultaneously.

o

The analog data, supplied by transducers at each of the tunnels is digitized by an
analog-to-digital converter (ADC) in the central data system. The digital data from the
ADC is then sent to the formatting generator where it is joined by other digital data from
the model-position encoders, the time-of-day clock and also the switch settings from both
the transmitting site and the central data system. The switch settings provide fixed information such as the barometric pressure, the test number, the run number and the date.
The formatting generator then assembles and prepares the data for recording on magnetic
tape. The records produced by the formatting generator are of variable length and automatically padded to contain an integral multiple of six characters, so that the resulting
magnetic tape recordings can be used with both the 7090 and 1620 mM computers. The
ability to read the system-generated tapes by the 7090 computer proved very valuable during system checkout, because the 1620 computer was not adapted to handle magnetic tapes
until later.
There are two types of records produced by the data acquisition system. The first of
these is the title run record which identifies the test run by a test number, a run number,
four parameters, the barometric pressure, the day and the time of day, and the model position by roll, yaw and pitch. The activation of the title push button switch will initiate output
of a title run record consisting mainly of the above information provided through manuallyset, thunlbwheel switches. The second of the two types of records produced by this system
is the data record. A data record is generated when the data circuit is closed (manually or
automatically). The data record consists of an identification header, the time of day, the
model position, and data from all site input channels programmed for the specific test.

o
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- - - - - - - - - - - - - - - - - - - -_ _ _ _ _ NORTHROP CORPORATION

o

COMPUTER UTILIZATION

The 1620 computer employed is a Mod I with 40,000 core storage positions. It is
equipped with most of the special, built-in features (indirect addressing, hardware divide,
and floating point arithmetic). This computer is attached to the data acquisition system by
an umbilical cord; it has been programmed to read and reduce the data as it is being recorded on anyone of the two magnetic tape units. The reading is accomplished in a readafter-write manner, termed "eavesdropping." The information is introduced into the computer by the read gap, which is pOSitioned a distance of .300-inch behind the write gap of a
two-gap read-write head, almost immediately after the information is written onto the tape
by the system. The normal function of the read gap, which is to provide parity checking
during the recording process, was extended to make this possible. The two magnetic tape
units used are Datamec D2020. These units are IBM compatible, using either 200 bpi or
556 bpi tape formats at 30 ips tape speed. The Central Data System (CDS) records at the
556 bpi density.
Eavesdropping allows the computer to sample the data as it is being recorded without
interfering with the recording process itself. During the eavesdropping or on-line mode,
as it is sometimes called, all the tape units are under the control of the CDS. Upon receipt
of a signal from the 1620, the CDS causes the first character and associated parity bit to be
transmitted to the 1620. Each character and associated parity bit continues to be transmitted until the longitudinal redundancy check character (LRCC) is encountered. The corAputer cannot initiate tape movement by attempting to read a tape while in this mode; therefore, a read tape instruction hangs up the computer until the CDS moves the tape to record
new information. Besides the eavesdropping mode, the computer is also able to operate in
an off-line mode. During the off-line mode, a selected tape unit (any of the two) may be
read or written by the 1620 as if it were its own. These two modes of operation are manually
selected.

C'

Reduced punched card data is generally generated and plotted off-line during tests. An
IBIVI 407 printer is also available in this center and is used to print much of the punched card
output.

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COMPUTER HARDWARE MODIFICATIONS

The 1620 computer performing the data reduction is unique. Three new instructions
had to be designed and the computer modified to permit their use for this special application. The design and implementation of these instructions into the computer required .
several months. In addition, other instructions were adapted to permit the reading, writing
and other handling of magnetic tapes.
The three new instructions pertain specifically to the use of magnetic tape.
BST,

backspace magnetic tape (36XXXXX01300),

REW,

rewind magnetic tape (36XXXXX02300) and

WEF, write end of file (36XXXXX01200)
Two instructions that refer to paper tape normally, RNPT, read numerically paper
tape and WNPT, write numerically paper tape, were modified to read magnetic tape (RMT)
and write magnetic tape (WMT), in the numerical mode.

0

'1

,I

RMT,

read magnetic tape (36YYYYY00300) and

WMT, write magnetic tape (38YYYYY00200)
In order to allow for tape redundancy and end of file testing, the functions of the
following sense switch testing codes were extended.
BC 1,

branch console switch 1 on (46YYYYY00100) and

BC2,

branch console switch 2 on (46YYYYY00200)

When a BC1 instruction is executed, a branch takes place if either sense switch 1 is
on or if a tape redundancy occurs. Likewise, the BC2 instruction also serves two purposes:
a branch will occur if either sense switch 2 is on or an end of file mark is sep..sed. These
two sense switches must be in their off position during magnetic tape operations. The redundancy and end of file indicators are not reset by any of these two instructions; they are reset
only when the selected tape is pet into motion again.

o
135
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1
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- - - - - - - - - - . - - - - - - - - - -_ _ _ _ NORTHROP CORPORATION

SOFTWARE

Although the rnagnetic tapes normally may be read and written with FORTRAN coded
programs by utilization of the paper tape statements, the tapes produced by this system can
only be read by SPS or machine type programs. This is due to the various field widths contained within the records written by the system. The problem of reading tapes was quickly
resolved by the writing of an SPS subprogram that could be called by and loaded with
FORTRAN coded programs.
The SPS subprogram was designed to operate in two modes. The first of these modes,
as directed by the arguments of the FORTRAN program, causes a compacted system record
to be read from the tape. Each of the fields of the record is then extracted and expanded to
a six-character field width. Flags are placed over the leftmost positions of each of the
fields and the fields are then transmitted to their prescribed COMMON locations as integers.
The second of the two modes requires the subprogram to search through the tape (not used
during the on-line operation) for a particular title run record that agrees with the run and
test numbers indicated in the arguments of the calling program. When the appropriate
record is found, the information fronl the record is processed in the same manner as it
was in the first mode. If the record is not found an indicator is placed in a communication
field, reserved in COMMON for this purpose.
The two tape reading modes of the subprogram~ described above, are very useful and
make the 1620 an even more important asset to the overall system. The first of these two
modes provides the user with integer data that. is FORTRAN-compatible. The second mode,
in addition to performing the same task as the first mode~ assists in retrieving previously
recorded data.

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RECORD FORMAT

The formatting generator produces t\·vo types of records and these are the title run
record and the data record. The purpose of t he title run record is to provide identification
for the data records that follow it. The title run record consists of 54 characters of the
following information:
Characters 1 - 5
Characters 6 - 12
Characters 13 - 24
Characters 25 - 32
Characters 33 - 35
Characters 36 - 40
Characters 41 - 48
Characters 49 - 54

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Information Retrieval Aid (IRA)
Time of Day (TOD)
Model Position (Pitch, Yaw and Roll)
Parameters from the CDS to be used for
computations or further identification
Day (00 1 thru 366)
Barometric Pressure
Paran1eters from the transmitting site to
be used for computations or identification
Test and Run numbers

The IRA indicates the record type and identifies the test site.
also gives the number of channels (data words) that were recorded.

In the data record, it

The data records produced by the formatting generator are of a variable length. The
length varies with the number of data words that are recorded. Characters 1 - 24 of the data
record are of the same format as those of the title run record. Characters 25 and above
represent data words. Each data word consists of four characters. As many as 100 data
words can be recorded in one record. The record is automatically padded to contain an
integral multiple of six characters.

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PARA. 2

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PARA 2

50 49 48
X X X
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X X X
X X X X X X X

36 35 34 33
X X X X
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X X X X
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X X X X X X X X X X X X X X X X X X X X X X
X LX X X X_~ X X X X X X X X X X X X X~ ~~

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58 57 56 55 54 53 52 51
X X X X
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CENTRAL
(FIXED DATA SWITCHES!

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(FIXED DATA SWITCHES)

47 46 45
X X X
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44 43 42
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41
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32 31
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30 29 28
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27 26 25
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24 23 22
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21 20 19 18
X X X X
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X X X X
X~ ~~ X~ ~>< L~~ ~ X X X X

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17
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16 15 14
X X X
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X X X X X X X X· X X
X X X X X X X X X X
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6

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TITLE RUN RECORD

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ NORTHROP CORPORATION

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CONCLUDING REMARKS

This paper has described how an automatic data acquisition and processing system
was developed to perform a vital function in the modern wind tunnel complex at Northrop
Norair. The major benefits of this computerized system can be stated as follows:
1.

It reduces wind tunnel data immediately when it is most needed.

2.

It permits quicker and more effective adjustments to be made to the model
within the test chamber.

3.

It shortens the time spent in carrying out a series of tests.

REFERENCES

"The Programming Gap in Real Time Systems", R. V. Head,
Datamation, February 1963.
"Pitfalls & Safeguards in Real Time Digital Systems", W. A. Hosier,
Datamation, May 1962.
"Air in a Hurry", H. M. Karaszewski, Compressed Air, February
1963.
"Flight Simulation Without Forward Velocity", Henry M. Karaszewski,
Compressed Air, December 1959.
"Northrop Inaugurates Mach 14 Wind Tunnel", Northrop Technical
Digest, November 1962.

o
10

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_ _ _ _ _-.-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ NORTHROP CORPORATION

°1

1043

OVERALL VIEW OF WIND TUNNEL COMPLEX, SHOWING SUPERSONIC AT LEFT AND SUBSONIC AT EXTREME RIGHT

HYPERSONIC FACILITY

C''\,
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12113

MODEL OF SUPERSONIC -

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HYPERSONIC CIRCUIT

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CENTRAL DATA ACQUISITION SYSTEM

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SIGNAL CONDITIONING CABINET AT SUPERSONIC SITE

12

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o

1

1620 IPL-V

A NON- NUMERIC PROBLEM SOLVING TOOL
by
Wendell Terry Beyer

c

An essay
submitted to the Department of Mathematics
of the University of Oregon
in partial fulfillment
of the requirements for the degree of
Master of Arts
Apr i 1 1964

1 li -')

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r __ =_'tt

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-

Acknowledgments

The development of the 1620 IPL-V system was done
in part while the author was an IBM/WDPC Research Assistant
at the University of Oregon.

This assistantship was

provided by the western Data Processing Center at the
University of California.

Many long hours on an IBM 1620

computer were freely provided by the University of Oregon
Statistical Laboratory and Computing Center.

o

o
1 43

o

Preface

This paper is composed of three section.
Section I introduces the need for computer languages
similar to IPL-V, section II outlines the IPL-V
language, and section III describes the IPL-V implementation for the IBM 1620 computer.

A detailed

description of the IPL-V instructions and a sample
problem are contained in the appendix.

A list of

selected references is given at the end.

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III

I

Stored program digital computers were initially
developed as devices for performing complex arithmetic
calculations at high speeds.

At first, the task of

programming these machines was burdensome because all
programming was done in machine language.

However,

programming languages were soon developed as an aid to
the programmer, beginning with low level assembly
languages for specific machines and eventually evolving
into high level, machine independent languages such as
FORTRAN, ALGOL, and COBOL.

Due to the arithmetic origins

of the computer, these languages were designed to assist

o

the programmer in the coding of arithmetic or numeric
prob 1ems.
For a long time, however, it had been known that
the digital computer, with its ability to analyze data
and take differential action, was not inherently
limited in scope to numeric problems.

Indeed the problem

of translating source statements from a high level
language like FORTRAN into machine code is itself a
problem basically non-numeric in nature.

Other problems

for which computer solutions were sought include chess,
bridge, analytic differentiation and integration,
language translation, pattern recognition, study of learning and self-organizing systems, information retrival,

o
1 45

2

1

Q

theorem proving, and most recently theory developing.

1

As interest in these and similar problems grew,
certain questions arose.

Is the present form of digital

computer, designed with numeric computations in mind,
It

necessarily the best for non-numeric problems?
what better designs might there be?

If not,

Is it in fact

possible to believe that one design will be capable
of handling the majority of non-numeric problems?

Is

it possible to develop a high level language which will
do for non-numeric computation what FORTRAN does for
numeric computation?
Today these questions remain largely unanswered.
No one has succeeded in developing a high level language
designed for non-numeric computing although work is
being carried on in this area.

Some computer designs

have been developed which seem to yield a better method
of attack on non-numeric problems than that afforded by
numeric computers.
To more fully appreciate the problems confronting
the designer of a non-numeric computer, it is necessary to
examine some of the common characteristics of the nonnumeric problems listed above.

These problems cover a

wide variety of topics and one might suspect that there
is little in common among them; however, four character-.
istics do appear in most of the problems.
First, each problem is non-numeric in part or .in

146

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whole.

The great computational power of modern numeric

computers is not needed.
Second, in most of the problems there is a need
for a unit of data more complex than a simple number or
array of numbers.

For example in analytic differentiation,

some method of representing algebraic formulae is needed.
In language translation or theorem proving some method
of representing syntax or theoretical relationships must
be provided.
Third, in many of the problems the assrgnment of
specific areas of memory to contain certain types of
information is difficult or impossible since the form,

o

structure, and amount of information is not known at the
time a program is set in action.

For example, in many

cases it is not known what form a self-organizing
system will take, or what concepts, and hence information.
a theory developing program will yield.
Fourth, it is often desirable to have certain
portions of a program call on themselves as subroutines.
This

is called recursion and is useful in differentiation

or game playing where a routine may call on itself to
look ahead a move.
A successful non-numeric computer, if it is to
have general applicability, must be designed to meet
these four needs.

o

numeric work

Similarly, any language aimed at non-

must fill these needs.

1 Ii 7

. - _. _.__ .""-'.-."""-

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~~='"~~-~--""=~--.--

4

IPL-V is an abbreviation for Information Processing Language V, a highly successful and widely used
language designed for non-numeric computing.

The IPL

languages were developed at the RAND Corporation by
Newell, Shaw and Simon, beginning in 1954 with IPL-I,
a language for playing chess.

Of the IPL languages,

IPL-V is the only one which has seen widespread use.
The language is well-documented and a manual for programmers is available. 1 In the next section IPL-V is outlined
and the manner in which it meets the four problems
posed above is discussed.

o

lSee reference [3J.

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148

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II

The IPL-V language may be regarded as an assembly
language for a non-numeric computer, the IPL computer,
or as a medium level language which is machine independent
and is executed on numeric computers by an interpreter
program.

It is interesting to note that an IPL computer

has never been built, and all work done in IPL-V is
accomplished by means of interpreters.

Nevertheless it

is useful to describe the IPL-V language in terms of
the IPL computer.
It is the function of the IPL computer to manipu-

o

1ate symbol s, that is, to accept as data, members of a
certain set of symbols, to store these symbols in memory,
move the symbols from one location to another, compare
the symbols', make decisions

bas~d

on these comparisons.

organize the symbols in memory in a meaningful manner
and produce as output a sequence of symbols.

For this

reason IPL-V is often referred to as a symbol-manipulation
language.
The memory of the IPL computer is divided into
cells. and it is the addresses of these cells which
form the symbol manipulated by the computer.

That is,

an IPL symbol is the address of a cell in the IPL
memor y.

o

trary.

The meaning assigned to these symbols is arbiThus regardless of the contents of cell 14613,

-5-

149

6

the address 14613 may represent New york City in a
military problem, Act II of Hamlet in a literature
analysis. or the principle of mathematical induction in
a theorem proving problem.
Since it is inconvenient for a programmer to deal
directly with memory addresses, the IPL-V language
allows a more convenient external representation of
The thirty-six characters ABC ••• Z $

symbols.
-

"I"

/

)

(

and, are called regional characters.

=.

+

At the

beginning of his program a programmer may assign to each
regional character a continuous block of cells in
memory.

The block of cells assigned to say A is called

the A region and the individual cells in this region are
referred to by the symbols AD (or simply A) for the first
cell, A1 for the second cell, etc.

Any symbol naming

a cell in one of the thirty-six regions is called a
regional symbol.

The assembler translates regional

symbols into the corresponding addresses.

In addition

the IPL computer has the ability to transform the address
of any regional cell into the correct regional symbol
during output operations.

The address of any cell not

assigned to a region is a non-regional symbol, and may
be represented by the programmer in a variety of ways.
Each cell in the IPL memory contains two digits
called the P and Q digits and two addresses called the
SYMB for symbol and the LINK.

A typical cell in memory

150

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is represented by the following diagram:

, ,
P Q SYMB

LINK

The individual portions of a cell are not addressable.
Cells may be used for one of three purposes: to
contain an instruction for the IPL computer, to contain
data, or to contain information necessary to the functioning of the IPL computer.
There are a fixed number of cells of the third
type and three regions are automatically set aside to
contain them.

The H, W, and J regions always contain

the same cells in memory.

o

The cells of the H region

function as registers and indicators in the IPL computer.
The W region contains some cells usable by the programmer
as temporary storage and other cells used in exercising
a certain degree of control over the operation of the
computer.

Each cell in the J region represents

~nd

contains the first instruction of a built in subroutine,
of which there are 188 in a complete system.
With the exception of the H, W, and J cells, any
cell in memory may be used to contain data or an
instruction, and during the course of a program. may
contain both.
A cell containing data may be of two types.

o

A

data term is a cell containing special alphanumeric or

151

8
numeric information. while the P and Q digits indicate
the type of information~

o

A standard data cell is a cell

used to store an IPL symbol.

The symbol is stored in

the SYMB and the P and Q digits indicate the type of
symbol. 3 The LINK of a standard data cell also contains
a symbol, the use of which will be described below.
data cell containing the symbol

I0

I

0 I 1461 3

"+"

A

might look as follows:

00000

P Q SYMB

LINK

where 14613 is the address of the first cell in the "+"
region.

Unless attention is to be called to the P and

Q di gi ts, thi s wi 11 be represented by
+

,0 1

•

o

2All data terms have a Q digit of 1 which serves
to distinguish them from standard data cells which have
a Q digit of 0, 2, or 4. The P digit of a data term
indicates the type of information stored in the data
term as fo 11 ows :
P=O
Decimal integer
P=l
Floating point number
P=2
Alphanumeric
Octal number
P=3
3Standard data cells usually have a P digit of 0
although they may be specially marked by a P digit of 1.
The Q digit indicates the type of symbol contained in
SYMB as follows:
Q=O

Q=2
Q=4

SYMB is regional
SYMB is local
SYMB is internal

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The data terms playa rather minor role in the computer,
usually serving as storage locations for numeric
information; while the role of the standard data cell is
central to the operation of the computer.
In dealing with symbols of arbitrary meaning, the
IPL computer answers the first need of a non-numeric
computer, that of dealing with non-numeric information.
These symbols do double duty, serving sometimes as the
addresses of cells in memory and at other times representing the concept assigned by

th~

programmer.

However,

the IPL symbol, being an address, is basically no more
complex than a number.

o

The need for a complex unit of data is fulfilled
by the list, a basic unit of data in the IPL computer.
A list is a sequence of data cells whicharejoined
together by having the link of each cell contain the
address or name of the following cell.

A list of the

symbols Al, 87, c4, and Al in that order would be
represented by the following diagram;
M4 ->/ A1

,-+-->/

87

,--+-/-->/

c4

-1---->/ Al ,0/.

where the arrows indicate the cell referenced by the LINK
of a cell.

Note the use of the symbol 0 in the link of

the 1as t ce 11 •

Th iss ymbo 1 i s ca 11 ed the ter mi na t i on

symbol and indicates that the list terminates at that

o

point.

The name of the first cell in the above list is

153

10

o

M4 and the list is also referred to by that symbol.
Given cell M4, any symbol on the list may be reached by
passing from link to link.
Far more complex structures may be created by using
the SYMB of some cells on a list to contain the names of
other lists.

The Q digit of a cellon a list may be used

to indicate whether the SYMB contains an abstract symbol
or the name of a sublist which is to be considered part
of the structure. 4 The number of structures possible is
limited only by the programmer's imagination, but for
simplicity only lists will be considered below.
Because of the list, IPL-V is called a listprocessing language, as are other languages which use
the same concept.

The language contains subroutines for

c

list manipulations such as copying, printing, searching,
or erasing lists.

An example is a subroutine which will

4 For example., the algebraic expression A-1'B+C/(D+A)
may be represented by the structure El below which
expresses the structure of the expression in a manner not
possible in a linear list representation.

El->/

->1

,0/

>1

+

>1

1_.>1

C

>/ L

>I~

1_>1

0

>1

>1

A

>1

"it:

+

>1

B

A

,01

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test whether a given symbol occurs

on a list or not.

consider again the list:

M4 -> I

A1

,-+---> I 87 ,-11-----:> I C4 ,-11--> I

A 1 ,0 I

The location of the first cell of the list is important.
Since the name of the list is M4, the firSt cell of the
list must be cell M4, but the location of the remaining
three cells is unimportant to the structure of the list.
This fact has important consequences.
When inserting a new symbol on a list, it is not
necessary to disturb the original cells of the list.

For

example, the symbol D5 may be inserted between 87 and

o

C4 on list M4 above by finding any unused cell anywhere
in memory, placing the symbol D5 in that cell, and
rearranging the links as follows:

M4->1 Al

'----'----I

>I~

r>/

->/05

1

C4

1-+-1->1

Al

,01

+=1

In this way a solution is achieved for the third
problem of non-numeric computers, memory assignment.

A

block of memory need not be reserved for expansion of a
data structure, since in expanding, a data structure may
make use of any unused cells in memory, whether they lie
in a continuous block or not.

Even the names

data structures may be kept on lists.

of new

Onl) the total

o
155

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-

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~

-~.

..

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. -- .•. .__ ....•. -

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12

number of cells in memory is of concern to the IPL-V

'-~.-

... '

...... ... ---..• - ....
"

~

--

....... ...

o

programmer.
It might. seem that locating an unused cell in
memory would be difficult, but this problem is handled
in an elegant and efficient manner.

After assembly, all

unused cells are linked together to form a list named
H2 and called the available

space~.

During processing

when a cell is needed, one is removed from H2 for use;
and when a cell is no longer needed by the programmer,
it is returned to H2.
The list organization also allows cells to be used
as though they were capable of storing more than one
symbol.

Suppose for the moment we have a symbol stored

in cell WO, say A7, and we need to temporarily store a
second symbol, say 83, also in WOe

We execute an IPL instruction causing the computer
to push down cell WOe

That is, an unused cell is

removed from H2, inserted behind cell WO, and a copy of
the symbol in WO is placed in the new cell, creating
the following list:
WO->I A7 , -+--~>IA7

,01

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Now that a copy of A7 has been made, B3 may be placed
in WOe
WO - > /._B..:;..3--&-=--> 1 A7 ,0 I

We may go even further and store C8 in WO before removing B3, by pushing down WO again, then storing C8.
WO ->1 C8

I

-+--->1

B3

-+----->1

A7

,01

The list created in this manner is called a push down
list but is no different from any other list.
When the symbol c4 is no longer needed in cell WO,
a pop up instruction is executed.

c;

This operation copies

the second symbol on the list into the first cell and
removes the second cell from the list. returning it to

H2.

wo->I B3 1-+1-.....;>/ A7 ,0/
One more pop up, and WO is returned to its original
state.

wo->I A7 ,0/
The preceeding sequence of events may be summarized
by writing the push down list vertically.
push
store
A7 down> A7
B3
A7

o

:>

push
store
8 pop
B3 down> B3 C8 > C up >
A7
B3
B3
A7
A7

-

-

E'

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14

The push down and pop up instructions enable a
subroutine and main routine to use the same storage
cefls.

A set of working cells, WO through W9, are

provided for temporary storage.

When a subroutine needs

temporary storage, some of these cell s are pushed down,
then used as storage.

Any information stored by the

main routine in these cells is preserved by the push
down operation.

Before terminating, the subroutine pops

up these cells, returning them to their original state.
The ability of the IPL computer to allow recursion,
the fourth need of a non-numeric computer, is also based
on the push down operation.

The cell Hl, called the

current instruction address cell

t

contains at any given

c

time the address of the instruction currently being
executed by the IPL computer.

When an instruction is

completed, the address of the next instruction is
obtained and placed in Hl.

Like any other cell in the

memory, H1 may be pushed down.

When one routine calls

on another as a subroutine, Hl is pushed down by the
computer;. saving the address of the instruction in the
main routine where processing is suspended.

The address

of the first instruction in the subroutine is placed in
Hl and that instruction is executed.

Processing now

continues along the subroutine and the computer is said
to have descended a level.

Before terminating. the

subroutine may call on itself or another subroutine.

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Again Hl is pushed down, saving the point at which processing was suspended in the subroutine, and processing
continues at a lower level.

When a subroutine terminates.

Hl is popped up and the routine one level up resumes
action.

A combination of the manner in which Hl is used

and the ability of the working cells to keep the
contents of routines on different levels from becoming
mixed, allows a subroutine to call on itself.
The instructions in the IPL computer are kept in
lists.

The p, Q, and SYMB of a cell make up the

instruction and the LINK indicates the next instruction.
The IPL computer follows instructions from cell to cell

o

down a list rather than executing instructions sequentially in memory.

I

This allows routines to be manipulated

with the list processing subroutines.

It is conceivable

that a main routine could construct a subroutine using
list processing subroutines, execute that subroutine,
then erase it, that i~ return all of its cells to the
available space list.
In communicating information to a subroutine. a
special cell HO, the communication cell, is used.

The

symbols required as inputs by the subroutine are placed
in HO using the push down operation.

The subroutine

accepts these inputs, removing them from HO, and before
terminating, places all output symbols in HO where they

o

are recovered by the maintroutine.

15 9

16

0

In addition to producing output symbols, some
subroutines produce a yes or no answer.

"+"

/

For this purpose

a cell called the test cell, H5, is provided.
cell may be in one of two states,

'1

The test

or, "_"., and an

instruction is provided to allow conditional branches
or transfers within the program on the basis of the state
of the test cell.
There are only eight basic instructions in IPL-V,
most of the processing being done by the numerous subroutines.

Two instructions are used for placing symbols

in HO, one instruction
instructions
each

for calling on subroutines, two

for removing symbols from HO, one instruction

for popping up cells or pushing down cells, and one

instruction

for conditional branching on the status of

t he test cell.

The P digit determines the type of

instruction and SYMB contains a symbol, the name of a
cell, or the name of a subroutine, depending on the context.
The Q digit is used in connection with SYMB for three
levels of addressing.

For more complete information

concerning instructions and a sample routine, see the
appendi x.
,The external form of IPL-V is quite simple.

Lists,

instructions or data, are written vertically on the coding
sheet.

Each line represents a cell and space is provided

to indicate the name of the cell and the P, Q, SYMB, and

o

"

LINK of the ce 11 .

I f ali nk i s 1eft b,l ank, the ce 11 i s

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17

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assumed to link to the cellon the following line of the
coding sheet and the name of the following cell may
also be left blank if its memory location is unimportant.
Thus to create the list
T4->1

+

-4----,>1 z28

,_ _--L--.!

~->I z29

,01

we write on the coding sheet

NAME
T4

PQ SYMB

LINK

+

z28
Z29

0

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o
161

S

7"

c

III
The University of Oregon IPL-V system for the IBM
1620 computer, developed and written by the author and
John D. MacDonald, was designed with two objectives in
mind.

It was intended first as an educational device to

acquaint students with list processing and symbol
manipulation problems, and second as a system for checking out IPL-V programs before running them on larger
computers.

In view of the educational aim, operating

speed was sometimes sacrificed for operating ease and
additional safeguards.

Because of the speed and size

of the 1620, the system was never intended as a production
tool.

o

The 1620 system is based on the specifications of
IPL-V set forth in the manualS and is fully compatible
with those specifications, though not all options are
available on the 1620 system.

Operating on any 1620

equipped with card I/O, indirect addressing, automatic
divide, and special instructions, the system provides
approximately 640 IPL cells at run time with a 20K
memory.

An additional 1,660 cells are available with each

additional 20K of memory.

The system operates at approx-

imately 80 IPL instructions per second and is equipped
Ssee reference [3].

,.,.,

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-18-

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19

with all tracing and monitoring features specified by
the manual.

These features include operator or program

controlled trace with output on any unit, automatic
trapping on error conditions, and flexibility in trap
recovery.
The system consists of three decks, the assembler,
subroutines, and the interpreter, which are loaded in
that order with the source deck placed between the
assembler and subroutines.

The assembler loads into the

lower portion of memory and assembles the source deck
directly into the upper portion, producing an assembly
listing on option.

o

Next the subroutine deck i.s read by

the assembler and those subroutines called for are
loaded into memory.

After the last card of the subroutine

deck has been read, the interpreter loads into the lower
portion of memory, occupying the space previously occupied
by the assembler; the computer halts; and execution
begins when START is pressed.
The internal form of an IPL cell is a twelve
digit field with an odd address.

From low to high

address the cell contains the P, Q, SYMB (five digits),
and LINK (five digits).
Provisions are made for writing additional
subroutines in SPS and including them in the source
deck.

It is also possible to reserve blocks of space

in the 1620 memory for use by other systems.

Methods

163

20
of setting_ up linkage between systems are described in
the documentation.
The documentation is in the form of an appendix to
the'manua1 6 with cross references. A master copy of the
documentation is maintained on cards for easy editing
and reproduction.
During the summer and fall of 1963, a preliminary
version of the system was written.

This version was

distributed to approximately twenty participating users
for field testing and was used in a one term seminar in
IPL-V programming at the University of Oregon.

Students

in this seminar used the system for problems such as
analyzing poetical structure, construction of Farey
sequences of numbers, calculation of all closed paths in
a planar graph, and construction of a machine for
playing Hex.

The system has also been used for map

coloring and analytic differentiation.
The preliminary version does not contain block
handling, auxillary storage, read/write, floating point,
save for restart, or post mortem dump routines.

During

the summer of 1964, a final version will be written, which
will include all features except auxillary storage
processes.

The final version will be submitted to the

1620 Users Group's General Program Library for distribution.

6See reference [3].

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Appendix
The IPL-V Instruction
The Q digit of an instruction operates on the
SYMB to produce a transformed symbol S as follows:
Q=O

S is SYMB.

Q=l

S is the symbol contained in
the cell whose name is SYMB.

Q=2

S is the symbol in the cell
whose name is contained in
the cell named SYMB.

For example, if we have the following cells in memory,
Al -~I T4 101
T4->1 J8 101

c

and the SYMB of the instruction contains Al. the Q
digit produces the following transformations:

.fQ SYMB
oAt

S

Al

T4
J8

1 A1

2 Al

The transformed symbol S is stored in a register; the
SYMB portion of the original instruction is never
altered in memory.
After the transformed symbol has been obtained the
P digit determines the action as follows:

o

p=o

call on the subroutine whose
fir s tin s t r uc t ion i sin ce 1 1 S.

P=l

push down HO and place a copy
of the symbol S in HO.

-21-

165

22

P=2

copy the symbol in HO into
cell S, then pop up HO.

P=3

pop up cell S.

p=4

push down cell S.

P=5

same as P=l except HO is
not pushed down first.

p=6

same as P=2 except HO is
not popped up afterward.

P=7

if H5 is -, transfer to
cell S for the next instruction. if H5 is +, continue.

Sample Problem
As an example of how the instructions are used, we
will write a short subroutine below.

It will be necessary

to understand the operation of two of the J routines.
J2 accepts two inputs in HO.
symbol.

Each input is a

J2 compares the symbols and sets H5 "+" if

they are equal and "-", if not.

J2 leaves no symbols

as output in HO and the two input symbols are no longer
in HO after J2 terminates.
J60 accepts one input which is the name of a cell
on a list.

If that cell is the last cellon the list,

J60 sets H5 "-" and leaves the input as output.

If the

ce 11 i s not the 1as t ce 11 on the 1 i s t, J60 places the
name of the following ce 11 in HO and sets H5 "+".
We now code the routine E4.

E4 i s a routine which

eva 1u.a tes a function of X at a given point.

More

clearly, E4 accepts a symbol representing a given point,

1 6 ti

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say A, and a second s ymbo 1 assumed to
list representing a function of X.

be the name of a

For example, the list

Fl below:
Fl

X
~t~

L

0
G
(

B

/

X
)

II
"xlog (~)
x
E4 then evaluates the function at A by replacing every

0

occurrence of the symbol X on the list by the symbol A
to yield the list:
Fl

A
~I,

o

L
0
G
(

B

/

A
)

"alog(~)"
a

0

In addition since

E4 should leave no output i n HO.

E4 does not set H5 as part of its output, the status of
H5 should be the same after execution of E4 as before.
But E4 must call on J2, which does reset H5.

For this

reason, it will be necessary to push down H5 at the
beginning of E4 to save its status, then to pop it up
at the end to restore its status.
WO and WI will also be needed.

o

Two storage cells,

It is assumed that the

routine which called on E4 input the name of the function

'"'

24

list first, then the symbol representing the point.
A little study and liberal use of a black board as a
simulator will make the operation of E4 clear.

The

symbols 9-1,9-2, and 9-3 are called local symbols and
are used for internal branching within the routine.
Name

PQ SYMB

E4

40 H5
40 wo
40 Wl
20 WO

9 -1

1 2 HO

10
00
70
60
11

9-2
9-3

LINK

21
00
70
30
30
30
30

X
J2
9-2
Wl
WO
W1
J60
9-3
WO
W1
H5
HO

9-1
0

Comments
Preserve H5
Preserve WO
Preserve W1
Move "point" to WO
Input symbol in list cell
Input X
Compare symbols
Go to 9-2 if not equal
Copy list cell address in Wl
Input point symbol
Move point symbol to list cell
Find next list cell
If no list cell, clean up
Restore WO
Restore Wl
Restore H5
Pop up HO, terminate

o

160

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*

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Selected References
IPL-V, Primary Sources
[1 ]

Dupchak. Robert, TIFi..: Teach Informatioil Processing
Language, The RA:\lO Cor~()ratlont'--"'Rt-:il-3819-PR, --October 1963.

[2 ]

Newell, Allen, "Doc 'Tlentation of IPL-Vt', Comm. ACtvl,
vol. 6, No.3, March 1963. pp. 86-8~.

[3 ]

Newell. Allen, et al., Information Processing
Language-V Manua 1, (Second Edl tl on-) , Prenti ceHall, Inc .. "Englewood C'iiffs, New Jersey.,
January 1964.

IPL-V. Applications

0,

[4 ]

Newell, Allen, A Guide to the G2neral Problem-Solver
Program GPS-2-2, The RAND torporatlon, RM-3337PR, February 1963.

[5 ]

Newell, Allen, and H. A. Simon, tIGPS, A Program
that Simulates Human Thought," Lernende
Automaten, H. Billings (ed.), Oldenbourg,
Munlch, 1961.

[6 ]

Newe 1 1, All en, and H. A. Sima n , " The Log i c The 0 r y
Machine: A Complex Information Processing
System", IRE Trans. Info. Theory, Vol. IT-2,
No.3, September 1956, pp. 61-79.

[7 ]

S i mo n, H.A., " Ex per i me n t s wi t h a He uri s tic Com p i 1e r , "
J. ACM , vol. 10, No.4, 0 c to b e r 196 3, p p. 493 - 506 •

[8 ]

Stefferud, Einar, The Logic Theory Machine: A Model
Heuristic Program, The RAND Corporatlon,
RM-3731-CC, June 1963.

f·,.II

General Informati on on Lists

o

[9 ]

Baecker, H. D., "Happed List Structures," Comm. ACM,
vol. 6, No.8, August 1963, pp. 435-4~

[10 ]

Banerji, R. B., "The Description List of Concepts,"
Comm. ACM, vol. 5, No.8, August 1962,
pp. 426-432.
-25-

1 6 !J

26
[11]

Bow1den, H. J., "A List-Type Storage Technique
for Alphanumeric Information,Jr Comm. ACM,
Vol. 6, No.8, August 1963. pp. 433-434.

[ 12 ]

Weizenbaum, J .. "Knotted List Structures." Comm.
ACM, Vol. 5, No.3, March 1962, pp. 161-165.

Other List-Processing Languages
.[13]

Bobrow, O. G., and Bertram Raphael, A Comparison
of List-Processing Computer Languages. Comm.
AeM , V0 I. I, No. 4 , Apr 1 I I 964 , p p . 2 3 1 - 240 •

[t4]

Cooper, O. C., and H. Whitfield. "ALP: An Autocode List-Processing Language," Comp. J .•
Vol. 5. No.1. April 1962. pp 28-32.

[15]

Gelernter, H., J. R. Hansen, and C. L. Gerberich.
"A FORTRAN-Compiled List-Processing Language,"
J. ACM , Vol. 7, No.2, Apr i l l 960 p p . 87 - 10 1 •
t

[16]

Green, 8. F., Jr. "Computer Languages for Symbol
Manipulation," IRE Trans. on Human Factors
in Electronics, Vol. HFE-2, No. I, March 1961,
pp. 3-8.

[17]

Mccarthy, J., et al., LISP 1.5 Programmer's Manual,
MIT Computatlon Center and Research Laboratory
of Electronics, Cambridge, Massachusetts, 1962.

[18]

Weizenbaum, J., "Symmetric List Processor," Comm.
ACM, Vol. 6, No.9, September 1963. pp. 524-

57+4.

[19]

Introduction to COMIT Programming, Research Laboratory of Electronlcs and MIT Computation
Center, MIT Press, Cambridge. Massachusetts,
1961 •

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PETROLEUM EXPLORATION AND PRODUCTION APPLICATION
FOR THE IBM 1620 AND PLOTTER

By
Jack L. Morrison
Oil Information Center
University of Oklahoma Research Institute
Norman, Oklahoma

Delivered at:
IBM 1620 Users Group
Western Region Meeting
Denver, Colorado
June 17-19, 1964

o
17 1

It was refreshing to h~r Dr. Edward N. Brandt, of the Un iversity of Oklahoma
Medical School Biostatistical Laboratory I say in his keynote address that the
problems dealing with computers in the field of medicine are such that they are
basically related to and parallel the problems which are encountered in the oil
industry. Dr. Brandt also related that the use of computers in medicine has
required that the users better define their problems, which gives them a better
understanding of the overall situation. The same can be said about the use of
computers in the oil industry.

In the next 15-20 minutes, I plan to tell you a little about the Oil Information

o

Center which is an integral part of the University of Oklahoma Research Institute. I will discuss the Oi I Information Center:
1. Why and how it was established
2. The goa Is and objectives
3. How it is connected with the University computer usage genera I Iy
and the IBM 1620 specifically
4. What we are presently doing, 'and

5. Where we are going
I. GENESIS OF THE OIL INFORMATION CENTER'

Two independent oil men in Oklahoma, Mr. Ward Merrick, Ardmore, and Mr ..
Howard McCasland, Iv\ack Oil Company I Duncan, were concerned about three

172

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apparently unrelated situations and problem areas in Oklahoma. lhese three
probl em areas were:
1. No attempt had ever been made to gather groups of oi l.field related
information on a J ibrary basis.

20 The Oklahoma Corporation ·Commission needed an assist in, some of
their data processing problems and engineering ca leu lations

0

3. The computers at the University of Oklahoma were not being utilized
as much as could be reasonably expected by local industries, particularly the oil industry.

The concern of these two independent oil operators led .them to the concept of
the Oi I Information Center and as a direct result they furn ishedthe impetus by

o

suppl ying financia I assistance through the medium of their personal foundations ~
A two-year budget was set up for the in itia I phase of this Center.

One obvious obiective of the Oi I Information Center was that sooner or later it
must become self-supporting from earned income. It was felt by all concerned
that these problem areas just mentioned would be the strong nucleus upon which
the objective of self-support would be reached.

After a series of conferences, oil industry executives and University people agreed
that the log ica I central location for libraries of oil information wou Id be on the
campus at the University of Oklahoma. The categories of information which seemed
desirable to collect were electric logs, scout tickets, drillstem tests, sample logs,

o
2

1·73

and Oklahoma Corporation Commission completion forms~ The University of
Oklahoma has been famous for years in the quality and quantity of graduates
pointed toward the oil industry. The University has probably turned out as
many petroleum geologists, petroleum geophysicists and petroleum engineers
as any university in the United States.

The Oil and Gas Conservation Department of the Oklahoma Corporation. Commission needed assistance with some data processing problems . They wished to
work directly with a group who could help them in their work, on whose integrity they could rely and in whom they could have confidence. The Oil Information Center devised a plan to prepare computer programs to assist with
some of these problems, and Commission representatives gladly accepted this
plan.

II. OPERATIONS OF OIL INFORMATION CENTER
A. Introduction to University Relations
The actual operation of the Oi II nformation Center is concerned with various
areas of effort. A ma jor area is connected with university activities. These
are:
1. The graduate program of the University of Oklahoma
2. The Oklahoma Geologic,a I Survey, The University of Oklahoma
Schools of Geology and Petroleum Engineering

3

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.

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3. Conducting seminars on oil related topics
4. Attracting people in the oil industry to the campus

Geology Graduate Student
In checking the records I found no evidence indicating that any geology graduate
student had used the computers or plotter to assist them in their master's thesis
work. I sought out someone who might be ·interested in using the computer and
found a Humble Oil geologist, on leave from his company to do master's work,
and who was wi II ing to work with me. Since the geologist was not a programmer,
arrangements were made for his programs to be written for him and through the
cooperation of the Computer Lab his key punching was accomplished. This graduate student's thesis was on the geology of an oi I field in North Central Texas.
His study of the electric logs on each well furnished him with formation tops,
well elevations, etc. for his study of 25 different formations. With this information punched into cards he was ready to use the 1620 and plotter to prepare his
isopach and subsea calculations and his many maps. The computer program as
written was general enough that calculations could be made for isopach.thicknesses, subsea formation tops, and sandshc;J Ie-I imestone ratios. This is an example
of what can be done in working with graduate students and we hope to encourage
others a long these lines.

o
4

175
-~-~-~----------.--

"I

1

,I
I

I:

o·
Oklahoma Geological Survey and University of Oklahoma
Schools of Geology and Petroleum Engineering
The Oil Information Center has attempted to work closely with the Oklahoma
Geological Survey and the University of Oklahoma Schools of Geology and
Petroleum Engineering. The I ibraries of oi I field information being gathered
by the Oil Information Center are a valuable complement to the Core and
Sample Libraries now existing at the University of Oklahoma. The Geological
Survey uses the electric logs, sample logs, drillstem tests, etc. in their statewide geologic investigations. The Schools of Geology and Petroleum Engineering can use the same information as teaching aids.

c

Conducted Symposiums
An important acti vity in the university phase of our operation is the conduction
of symposiums. The Oil Information Center, in conjunction with our libraries
of informaHon and computer services, has conducted two symposiums on the campus. One was related to our Drillstem Test library to which we were able to
get good industry speakers from a II over the Southwest.

The second symposium was directly connected with the Mid-Continent Well Data
System in Oklahoma City. In addition to the speakers .at this meeting, the Oi I
Information· Center in cooperation with the Un'iversity of Oklahoma Computer
lab demonstrated an information retrieval program. I $hall discuss this demonstra-

01
5

176

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tion in more detail in a few minutes. These symposiums have been extremely
helpful in our relationsh ip with oi I industry people, particularly on the operating level. The sharing of new ideas and approaches is always helpful.

Bring People to the Campus
Directly through the efforts of the Oil Information Center a large number of
people have been directed to or through the University of Oklahoma campus.
Our seminar on drillstem testing attracted 148 people for two days ot meetings.
The Mid-Continent Well Data System Symposium was for one day and was attended by 65 peop Ie.

o

Major oil company and consulting geologists from Tulsa, Ardmore, Norman, Ada,
and Oklahoma City have been to the Oil Information Center libraries for various
reasons. Maior oil company representatives have also been to our computer installations using our computer and plotter services. Others have investigated the
services which we have to offer in order to determine how this information could
be beneficially used by their company.

Industry Effort
To the best of my knowledge, this is the first industry wide effort of information
gathering undertaken by the University of Oklahoma. Acceptance of ,the oil
Iibraries could well lead to the establishment of the gathering of information in

o

other fields of endeavor.

6

17 i

P""S'''"E''hl''

Oi I Industry in Oklahoma
With the advent of oil industry data retrieval pilot studies in West Texas, the
Oil Information Center found it advisable to conduct their own pilot project on
the digitizing of scout tickets and a retrieval program to recover this information.
The Autwinefield in Kay County, Oklahoma, was chosen for this study for several reasons. The field has more than one producing zone; it produces both oil
and water; both major oi I compan ies and independent

0

iI operators have wells in

the field. Scout tickets were received on 122 wells which included some surrounding dry holes, and the information was keypunched to our predetermined
format.

A computer program was written for our 1410 to retrieve certain information from
these cards. The program was written to gather certain usable groups of information:
1. list the wells which cored the Red Fork formation,
2~

List the wells and the detailed results of all drillstem tests in the
Red Fork formation,

3. list the casing programs in each well,
4. List the formation tops from some wells,
5. list each well that penetrated the Mississippi formation, and
6. List the details of the acid and fracture treatments on each producing Red Fork well.
These are some of the categories of information chosen to be retrieved for this
demonstration. This information is typical of that which is used by the exploration geologist and the petroleum eng ineer in some of their everyday problems.

7

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170

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Oklahoma Corporation Commission
Preparation of Oklahoma Guymon-Hugoton Gas Allowable Schedule:
Due to the large amount of paper work which they process, and .their general
work load, Gas Conservation Department personnel ·often were two or three
months late in the preparation and distribution of the Guymon-Hugoton Gas
Allowable Schedu Ie. ' By the time the operators of the well and the purchasers
of .the gas received the schedules they were practically of no value.

The Oi I Information Center worked as .1 iaison between Corporation Commission
engineers and the Computer Lab programmer so that a computer program could

o

be written to calculate the monthly gas allowable for each well in the field.
When Corporation Commission personnel prepared this gas allowable schedule
on a desk calculator, they required approximately 70-75 manhours per month.
After an estimated five hours of keypunching and keyverifying per month, the
IBM 1410 makes these calculations to prepare this gas allowable schedule in

0.4 hours per month.

Calculate one-point back pressure test:
An Oklahoma Corporation Commission statewide rule makes it mandatory for all
allocated gas wells to annually report a one-point back pressure test. This information is used in assigning per we II gas allowables for the following year.

o
8

1 '7

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An estimated 1,800 - 2,000 of these tests are filed with the Commission each
year and the Gas Engineer is required to check each of the calculations. The
Gas Engineer informed me that with no interruptions he could check five or
six of these calculations per hour. This meant that two or two and one-half
man-months per year was spent in checking these previously calculated tests.
An O.U. Computer Lab programmer wrote a program for our 1410 to make
these calculations. The 1410 processes these tests in 4.25 hours, which is a
significant dollar saving estimated at 3-1/2: 1. This Gas Engineer is now
freed to do more productive and original work for the Commission, which represents the true saving.

c

B. Introduction to· Commerc ia I Appl ications
Our other major effort is the industrial commercial activities. We have worked
directly with:
1. t-Aa jor oil companies
2. Independent oil operators
3. Oil-field service companies
4. Petroleum consultants

In mid-1963 IBM released a group of programs from their 1620 library, which
are called the Petroleum Package. These programs were written by experienced
petroleum engineers, geophysicists, and geologists for a rather wide range of

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commonly encountered exploration and engineering problems. The engineering
programs deal with primary oi I recovery, secondary recovery, economic eva luations, casing design, gas production rates, flash calculations, etc. The exploration programs deal mainly with geophysics, but are also related to map contouring,
electric log analysis, dipmeter calculations, map preparation, etc.

In the past ten years petroleum oriented companies have become more dollar conscious and overall economics have played an ever increasing part in top management decisions. Computers are being used more and more to funnel detailed geophysical, geological and petroleum engineering information to these top management people for their perusal in making their decisions.

In the recent past it was not feasible to make many groups of calculations in the
fields of geophysics, geology and petroleum engineering. These calculations were
known applications and approaches to their problems but were too detailed and too
time consuming for the engineer or geologist toiustify spending the time from his
oth~r doily duties.

With the advent of computers, it became more realistic to

consider making some of these calculations. Also, in the pQst, the necessary data
to make these calculations were not gathered knowing that they would never be
used. Such is not the case now, and it should be pointed out that the gathering
of these data in many cases makes for a more efficient operation on all levels.

o
10

181

"UW:,.":"

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In several application areas the use of digital computers is becoming more
valuable as magnetic tape recording devices are used.inthe field. Some of
.these instances are:
1. Electric logs (and their companion logs)
2. Dipmeter surveys
3. Geophysical field surveys
Many of the large oi I field service companies are instal.ling magnetic tape
recording devices in their field trucks. This will lead to a more detailed study
of data now being received but not efficiently used.

However, most of the commercial work which we have done in our 1620 Lab

·c\
L/

. is related to geophysical problems. The reason is rather obvious when the users
were questioned. In many-instances geophysic ists were not making certain
known approaches to their problems because of the number of manhours requ ired to prepare the data I make the ca Icu lations and plot certa in information.
The use of computers and digital plotters now makes it more practical to better
utilize data gathered in the field by geophysical crews.

As some of you know, a reflection seismograph crew costs an oil company between $15,000 to $60,000 per month depending on the overall services rendered and the field equipment involved. As in most any other service operation, reflection seismograph field crews can and do have certain problems.

c
11

182

'W!"'YUr";;"ii*)'fliMdW'ijlij'¥f'''WitlitHWWI'''!J!J"'!im,r!!p' nj,.t!LTtPlfM

WNU

JT PPUZ"''W:!'HilSl''*'HtWMfllfw'Mi!iiQWlWHliiUi'W ""M'''rern.'tltl·l1' P'III ,,'Yi!'f"WbiWlN'Mt¥f "P!lU7ll1'' Ii 1M
lf

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If the field data are being processed on computers as work progresses, the
errors can quite easi Iy be rectified. However, if there is a large time lag
between the error and its discovery, it may not be so easy to make the necessary adiustments.

A geophysical group of a maior oil company in Oklahoma City has been our
largest user of commercial time on our 1620 and plotter. This District office
is responsible for the geophysical work in all of Oklahoma, all of Kansas, the
Texas Panhandle, North Central Texas and the northern 2/3 of Arkansas. In
addition to the reflection seismograph field crews gathering new data, they

o

are continually reviewing old seismic records previousl y shot by themselves
or by other companies.

One geophysicist pointed out the following,relative to the information gathered
from 300 shot .... poi nts. The time requ ired to hand ca Icu late and hand plot this
data frqm 300 shot-points would be an estimated two man-months. To use computers, this same amount of work would require an experienced geophysicist
one week, another week to key-punch, one to one and one-half hours on the
1620 for calculation, and five and one-half to six hours on the 1620 dnd online plotter. This represents a vast saving of time as well as money.

One geophysic ist pointed out that the use of our 1620 computer on their reflec-

o

tion seismograph field data makes it possible for them to better uti! ize the

12

183

information which ~ be gathered from seismic records. He said that they can
now prepare ten to twelve useful sub-surface maps where previously they were
fortunate if they were able to get five to six maps from a set of seismic records.

Dan Merriom of the Kansas Geological Survey and John Harbaugh of Stanford
University through their joint effort developed a computer program to assist in
the location of mineral deposits. (1) Based on certain known geologicQI land/or
geophysical information and certain mathematical computations trend surfaces
are fitted so that the sum of the squared deviations is the least possible value.
The trend surface analysis may be used to:
1 . Predict projected depths to geological units within an area,

c!

2. Del ineate unconformities or changes in structural patterns, and,
3. Extend better "geologic guesses" into adjacent unknown areas of
no control.

Close agreement exists between loca I structural features and trend-surface residuals. The residual maps were found to stress or emphasize trend relationships
not otherwise clearly observed from original data and to emphasize the local
component of the structural pattern by essentially removing the regional component or regional dip. Inasmuch as in many regions the oil and gas producing
areas are systematica fly assoc iated with structura I features, there is the possibi I ity that a study of the residuals will indicate previously overlooked areas
favorable for additional oi I exploration.

13

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The Oil Information· Center plans to take advantage of the existence of this
program but we plan to rewrite the program to use the IBM 1620 and plotter
rather than using the printer to prepare the map.

John P. Dowds, a successful petroleum consultant in Oklahoma City, has
worked on the laws of probabi Iities and the appl ication of statistical methods
to help analyze the problem of obtaining commercial oil or gas production.
Dowds, in a recent paper, stressed that "exploration geologists and geophysicists need to become statistically minded and to think of locating oil and gas
fields as a problem in applied possibilities. II (2)

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Dowds uses entropy for his mathematical model to learn of favorable trends
and patterns in searching for logical locations for drilling new oil or gas exploration wells.

Dowds determined a long time ago that his calculations were too difficult and
the number of these calculations required were too many to be done by hand.
An Oil Information Center programmer recently wrote programs to Dowds' formulae for his entrop), calculations. These are now being run on our 1620 and
plotter. The final output to be studied for purposes of exploration is a series
of contour maps. Dowds is representing a large independent oil operation in
Oklahoma City in their search for sizable oil or gas reserves.

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185

James M. Forgotson, Jr., research geologist with Pan American Petroleum Corporation in Tulsa, said in a recent Oil and Gas Journal article that the use of
electronic computers to evaluate electric logs is very practical. He said, "The
speed with which these computations can be performed makes the analysis of many
z ones or formations in thousands of wells practical. II Forgotsonwent on to point.
out that IIwithout the aid of the computer, approximately eight manhours are required to calculate shaliness, saturation ratio, and favorability criterion for four
~ones

in one well. II He also made ar interesting co mpa.ri son stating that "with

the use of computers approximately one and one-half man-months would be required to process four zones in 1,000 wells while without the use of computers

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fifty-·four man-months would be consumed. II (3)

III. SUMMARY
The Oil Information Center is serving a useful purpose to the University of Oklahoma, to the Oklahoma Corporation Commission, and to the oil industry in general
in Oklahoma.

With the 1410, 1620 and the plotter now in the University of Oklahoma Computer
Lab, we are able to offer computer services to:
1. Maior oil companies
2. Independent oil operators
3. Consultant geologists and petroleum engineers

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4. Oil field service companies
15

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Using the 1620 Petroleum Package of programs has proven successful up to a
point even though the large maiority of commercial time which we are able
to sell has been to companies who have written their own progrdms.

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REFERENCES

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1.

Merriam, D. and Harbaugh, J. "Balgol Program for Trend-Surface Mapping", distributed by the Kansas Geological Survey (Special Distribution
Publication #3).

2.

Dowds, John P. "Application of Information Theory in Establishing Oil
Field Trends", presented in June 1963 at Stanford University during the
3rd Annua I Conference on Computers in the Minera I Industries.

3.

Forgotson, J.M., Jr. II How Computers Help Find Oil II, Oil and Gas
Journa I, March 18, 1963.

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187

o

A CONTROL SYSTEM APPROACH
TO
AUTOMATIC JET ENGINE TESTING

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1620 User's Group
western Region
June 17,18,19 - 1964

Aubrey D. Wood
IBM Systems Engineer
Oklahoma City, Oklahoma

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TABLE OF CONTENTS

I.

INTRODUCTION TO THE PROBLEM
A.
B.

II.

HISTORY OF JET ENGINE TESTING
PRESENT TEST PROBLEMS
1. Present Test Techniques
2. Testing Techniques
3 . Instrumentation
4. Human Errors
5. Rerun Statistics
6. Capacity
7. Safety

SOLUTION TO THE PROBLEM
A. INTRODUCTION
B. PREVIOUS WORK
1. Data Logging
2. Research and Development - Jet Engine Test
3. Industrial Testing Systems - Discrete Process
C. AUTOMATIC JET ENGINE TEST CONTROL SYSTEM
1. System Design Requirements
2. Control System and Interface Description

III.

ECONOMIC JUSTIFICATIONS
A. TANGIBLE
B. INTANGIBLE

IV.

SUMMARY AND CONCLUSIONS

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A. History of Jet Engine Testing:
.After the first jet propelled airplane was captured from Germany by the United
states in World War II, development of the jet type aircraft has proceeded in rapid fire
fashion.
The first truly great use of the jet airplane came about as a result of the Korean
War. In a few short years since the early 1950's, the development and production of
the jet engine has proceeded at an amazing rate.
With the production of the first jet also came problems in the maintenance and
overhaul of these complex, high thrust engines. At the beginning, especially during the
Korean War, maintenance and repair was carried out in the remote airstrip locations
and centralized repair facilities using the out-moded piston engine repair and test facilities. The piston engines had not required the highly substantial and instrumented test
facilities that the newer high thrust jet engines were requiring; so, many of the first
tests were performed in a crude makeshift manner.
In the initial stages, many of the repair personnel became engine test personnel.
Because the jet engine development had proceeded in a hurried fashion, adequate testing
procedures were lacking; so many of the first test cell personnel found themselves preparing their own through pooling, interchanging and accumulating their experiences.
Many of the basic principles of these early testing technical procedures are still in use
today. Also, the great majority of today's test cells are modified piston engine of low
thrust jet engine test cells and their instrumentation leaves a lot to be desired. Much
of the instrumentation was installed on a "guess and try" basis.

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Since the early 1950's the production rate and number of jet engines in the air
has risen considerably. With these increases also came increases in the number of
engines to be overhauled and repaired. The test facilities in many instances have been
updated with new instruments. The engine manufacturers have also been allowed time
to adequately prepare better testing procedures. Even with all of these improvements
there still remains two pressing problems. They are: (1) the large number of engines
awaiting the testing facility and (2) the advent of the higher thrust (turbo fan, J75, etc.)
jet engine has again outdated the test facilities.
B. Present Test Problems:
Because of the rapid expansion of the test facilities to accomodate the increased
workload of jet engines and the complexities of the higher thrust engines, many problems
arose in acquiring an adequate balance between the production and quality control functions.
These problems are presented in the following sections. They are grouped into
areas in order to present a detailed view of each. It should, however, be noted that the
problems actually overlap into other areas and even overlap each other. Many times a

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particular problem arises because of testing techniques, instrumentation, and the
facilities being used.
1. Present Testing Methods

In order to fully understand the problems associated with the present testing
techniques, the following is submitted as a general discussion of the overall testing
procedure.
The typical jet engine test cell has two or three men assigned to it. During
the initial installation phases two men perform all necessary physical connections.
This will include steps (a) and (b) of the test procedure. During the running/testing
of the engine, one of these men will control the throttle and instrumentation necessary
to run the engine and make recordings while the other man makes the balance of the
necessary recordings at the appropriate times and places. A third man acts as an inspector. His job is to observe the readings being made and perform a reasonableness
check on certain limits to see if recording errors have been made. He also takes observed readings and corrects them to a standard day (sea level or other) condition for
comparison with the technical order specifications.
On the final analysis he either accepts or rejects the engine based upon its
performance within the limits and specifications of the manufacturer's technical
order. As the engine is routed to test from final assembly it is complete as required
by technical order to the final piece of safety wire.
a. Dres sdown
Upon receiving the engine at the test area, numerous steps are necessary in
order to prepare the engine for testing. The first step is checking for possible external damage which might have occurred during transportation. The engine normally
is assigned to a particular test cell prior to dressing for test. Special plugs, fittings,
and some harness have to be removed in order to install test equipment. Special test
harness is installed in order to obtain individual thermocouple readings for temperature
spread checks. Various pressure taps are installed throughout the engine in order to
obtain internal air, oil and fuel pressures. Engines are so designed that internal
pressures must meet certain limits. If engine internal ratios are below values outlined by engine manufacturer, it becomes necessary to change some specific internal
clearance in order to obtain required ratios.

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The next step is to install a workhorse tail cone or afterburner. Altogether,
there are approximately ten test fittings and adapters that must be installed in addition
to temperature harness. Engine mounting adapters and bellmouth adapter rings are
installed. Finally the engine oil tank is filled to capacity. This about completes the
initial dressing. If the engine is designed for an after-burner, then an AB is attached.
There are additional functions of preparations to be performed after the engine enters
the test cell.
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b. Preliminary Check
After installation of the engine in the test stand, it is necessary to perform
some inspections at particular times. This will include such inspections as freedom of compressor rotation and making sure no foreign objects are present in the
compressor inlet. It is necessary to accomplish this type inspection prior to installing the bellmouth and inlet screen. If an inspection is performed after installation of the bellmouth, it is quite easy to overlook some small item which might result
in compressor damage.
c. Preliminary Shakedown
After engine is properly secured in the test stand with all pressure and
temperature connections, attached, a complete shakedown is accomplished by a
quality inspector. This shakedown is necessary to pick up anything which may have
been overlooked during the engine installation.
d. Functional Component Check
The next step is a functional component check out. This consists of selecting
the main fuel control emergency system, afterburner system, and anti-icing valves
for functional operation. These checks are necessary prior to starting the engine in
order to replace such items that may be faulty.

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e. Dry Run
Prior to starting the engine a dry run is performed in order to flush preservative oil from the fuel components, pressure fuel and oil system. Leaks are
sometimes found during this check. Afterwards, the dry run oil system is replenished
and the pressurizing valve sense line reconnected.
f. Running Prior to Acceptance
The engine is then ready for a start. After the engine has started and reached
idle R. P. M. a complete shakedown is made to check for air, oil and fuel leaks. If no
abnormal conditions are found, power is advanced toward top power and preliminary
checks are made on oil pressure, E. G. T. and vibration.
g. Performance Runs
After the preliminary run has been completed, the engine is ready for a performance test run. This test run consists of numerous functions in order to test the
basic engine and its attached components as a complete assembly.

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Other checks that follow during the actual performance test are acceleration
checks, simulated afterburner runs, emergency system runs, oil consumption check
and performance calclilations.
The test run begins with an initial power advance after start to approximately
nine thousand RPM. This is necessary in order to obtain specific data for test run
calculations and warm up the engine oil. The engine oil must be heated to actual
operating temperature in order to obtain valid consumption during test run. Oil temperature must be noted at the time oil level is checked on a sight gauge and again at
completion of the test run. Oil temperature at the time of the final check must be
within ± 2 degrees F. of the initial temperature. Oil consumption is actually determined by visually observing a sight gauge. This sight gauge is calibrated to the
engine oil tank and actually seeks the oil level within the engine tank. The oil level
sight gauge is marked with ten increments to the inch and each increment represents
a specific amount of oil.
The data collected during the initial warm up period is used to determine the
exact power position required for various test runs. Four power runs ranging between seventy-five per cent and take off are required in order to help determine the
quality of the engine.
Test run power positions are determined by charts representing given thrust
positions. All data from such charts represent standard day conditions biased for
temperature variation. Actual thrust requirements are subtracted from points corresponding to various power positions by using compressor inlet temperatures. Once
having obtained required corrected thrust output, this data must be converted to actual
time conditions. This correction is a function of present time condition variations
from a standard day and test cell correction factors.
Each individual run has a time duration of five to twenty minutes depending
upon the position of power. Recordings of internal pressures from compressor inlet to turbine discharge are made. Temperatures of air inlet, oil, fuel and turbine
discharge air are logged. Other recordings such as fuel flow, thrust, turbine discharge pressure, RPM and vibration are necessary.

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All data logged directly related with the functional operation of the engine must
be corrected to a standard day condition. This data is also corrected for compressor
inlet temperature, barometric pressure and test cell correction factors. There are
approximately 175 calculations performed during the test run. Thirty-five points are
plotted on special graphs in order to determine if any maximum limit; has been exceeded.
Also plot points are necessary in ot;der to determine minimum RPM required to obtain
guaranteed rated thrust. Other correction factors which are necessary pertain to the
emergency fuel flow and cooling air ratio. Other checks of the emergency system
consist of acceleration procedures and engine starts. Such steps are necessary in
order to determine if the emergency system has the ability to operate properly and
take over engine operation in the event the main system fail.
Cooling air ratio is a necessary factor in order to determine if a sufficient
4

amount of air is being furnished to the hot section parts. If the air ratio is below
values outlined by the engine manufacturer, damage could occur to some parts .

.

h. Simulated AB Runs
After completing the necessary performance checks, the engine afterburner
system is simulated. The complete afterburner system is subjected to all functions
of operation without actual firing. The method used is simply to rout afterfurner
regulator fuel back to the pump inlet. The ignitor valve will fire, nozzle control
will function and afterburner regulator will meter fuel. This system actually is
quite practical insofar as all fuel is returned to the inlet supply.
2. Testing Techniques
Jet Engine Testing has many problems associated with the techniques encountered using the present manual methods. Some of these problems can be directly associated with human capabilities and reactions during the test cycle. These
represent man's inability to cope with the complex situations and the split-second
decisions at a speed and with the accuracy required for maintaining a high quality
test procedure.
other problems can be attributed to inaccuracies in the existing mechanical
and electrical means of transmitting test data to the test cell personnel from its
primary source on the engine. These problems are created because a primary
signal in the form of an electrical pulse, voltage or current, pressures, and temperatures must be converted to a mechanical means of display for use by the test
operator.
a. Standard Tests
A standard test is defined as one in which the test procedure for each type,
model, and series engine is conducted in the same manner each time it is conducted,
e. g. all data are gathered the same, analyzed the same, and all decisions are made
under the same rules without variance. This does not mean that the magnitude of
each number in the recorded data will be the same each time, but the manner and intervals at which the recordings are made remain constant.
If an engine is tested and found to be acceptable under one set of ambient
conditions, it should also be acceptable when tested under another set of changed
ambient conditions. The procedure for testing after overhaul contains the necessary
charts and calculations to correct all recordings to a standard day condition; thus,
all data should be acceptable under the standard test limits each time it is taken, if
it is acceptable at anyone of the times.

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Even though the testing instructions gives a description of the major procedures to be followed in testing a jet engine, it would become an insurmountable
task to specify to the test cell personnel all the exact steps to be taken during the
test.
Located at the test facility are many different operators and inspectors,
(quality personnel). Because each man is capable of thinking and making individual
decisions, he will conduct a jet engine test in a different manner. Because the
technical order allows the variations in the manner in which a major test step may
be conducted, each operator will not perform each step the same. This situation
as well as inconsistencies in the test cell instrumentation will create many different
techniques in testing and a possible multiple variations on the acceptance or rejection of an engine under varying conditions.
Not all of the problems associated with the Jet Engine Test can be completely
removed by achieving the standard test alone. However, in the process of achieving
this standard test many of the "ills" of the present method of testing would have to be
eliminated.
The achievement of a standard test can only be realized after correction of
the problems in the forthcoming sections.

c

b. Correlation of Test Cells
In most test facilities there are two or more test cells. In order to obtain
a standard set of test data on a engine test in one or more of these cells, it is
necessary to inter-correlate the cells.
Either a "gold plated" or standard engine that has been tested in the manufacturer's cells is tested in the production cells. This process is commonly known
as calibrating a cell. It involves running the standard engine in the production cell,
comparing the data gathered with the instrument recordings made in the manufacturer's
cells. This will produce a correlation or correction factor to be used with each cell.
The correlation of one cell may require from five to eight hours to completelonger if trouble is encountered. Trouble is common. Difficulties arise from changing
cell ambient conditions (air temperature, humidity, etc.) inaccuracies of data from
readout mechanisms, changing of test cell personnel, etc.
The accuracy of the data acquired in a final test phase will be directly dependent upon the degree of accuracy obtained in calculations of each cells correlation
factor. Not only are the inaccuracies involved a problem, but there are extra manhours, fuel costs, and engine wear characteristics encurred.

o

Rather than correlating every ninety days as is now required, X (average) and
R (range or deviation) charts of all instrument reading deviations from those readings
6

195

of the production correlator engine would· produce cell correction factors. This
would allow a constant updating of the cell correction or correlating factor as well
as indicating trending abnormalities that may be developing.
Using the present
techniques of testing jet engines; it is impossible to gather sufficient data, calculate the X and R's of the recordings, and do the correlating.
The data recordings must be gathered and analyzed over a sufficient period
of time to detect trending conditions. This usually involves such things as EPR's,
EGT's, Nl and N2 speeds and their average and range deviations from the standard
engine recordings.
Even if it were possible to gather the data, the magnitude of the calculation
and analysis is enormous and would require many manhours.
c. Penalty Runs
It may become desirable after either a major test or a test segment completion, to conduct a penalty run. The penalty run would involve running a small
segment of the test, several test segments, or the complete test.

After the completed test and the performance calculations have been made,
the engine results could indicate an off specification; thus, requiring the need for a
recheck of the calculations and test recordings.
Many times when a borderline situation exists, the inspector will call for I
the same recheck. Because of the inconsistency in testing methods, calculations,
and decisions, the inspector may feel it necessary to repeat a portion of the test in
order to gather additional data for analysis, or verification of calculations and recordings. Even when a penalty run is made, conditions may exist (the need for
simultaneous readings) that cause the data accuracy to be insufficient, e. g., it is
impossible to obtain simultaneous recordings under the manual methods. Because
the operator and inspector know of the inconsistencies that exist, several extra
minutes or hours along with many extra gallons of fuel may be consumed in conducting the penalty run in order to obtain suffieiently accurate data for a correct test.

c

3. Instrumentation
There are many and varied problems in the instrumentation areas. The
sensing elements on most instruments are reliable and accurate. However, the
actual readout mechanism is very difficult to keep within the calibration limits.
Because most readout mechanisms present problems of nonlinearity in changing
from one setting to another, time and manpower must be spent on a periodic
(usually monthly or bimonthly) basis to insure accurate calibration. Many tirnes
an instrument can become erradic in its reading and the test cell personnel not
become aware of it until a new calibration is made. In the mean time many "good"
engines have been rejected and many possible "rejects" are flying or in storage.

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4. Human Error
Throughout the test procedure recordings are being made on a second
timing intervals. Many of these readings should be made simultaneously, but
because of the human inability to observe and record on a "split" second basis
many of the reading~ will change by large increments before they can all be
recorded. This is especially true during acceleration and deacceleration of the
engine.
Because all the instruments are not located at a 90 0 angle with the eyes
of the man making the recording and because many of his recordings are made at
a fast rate, it has been found that many recordings have been made with large
errors (sometimes a completely gross transition error- is made). A 5 lb. pressure
error or 5% temperature error is enough in some readings to reject a "good"
engine or accept a "bad" engine.
5. Rerun Statistics

o

If after the sequence of test events, calculations and plotting of data the
engine does not perform according to the technical specifications it is not always
rejected and sent to the rework area immediately. After a series of checks on the
calculations made by himself, gross range errors on readings,or minor detectable
instrument error, the inspector will apply his knowledge in conjunction with the
trouble shooting points listed in the TO to diagnosing the area of trouble in the engine. These diagnostics will then be sent back with the engine to the rework area
(overhaul line).
If he feels that some element of doubt is present in a reading or calculation,
portions of the test or the complete test may be performed again. This re-running
may consist of re-trimming the engine, re-running the performance runs, or giving
an AB function check. Many times the ability to diagnose the problem area relys
solely upon the experience and background of the inspector in charge of the test.
The majority of the inspection personnel have not gained this type of experience.
Because of this inexperience, many of the engines may be re-run or rejected needlessly. If the engine must be re-run several times in order to find the source of
trouble, large quantities of time and fuel are consumed.
If we consider the price of a complete overhaul of an engine ranging from
$12,000 to $15,000, the needless reject of a good engine or the improper diagnostic
of an engine for overhaul becomes an expensive waste.

o

Because of the advance in design of the jet type engine year by year, itbecomes a large task to keep the test personnel updated on the new techniques accompanying the advance design engines. During the period of time when the modernization of the cell and training of personnel are being done, many costly errors are
made.
8

If we consider a facility that tests 2, 000 engines per year, the annual fuel
bill will be approximately $550,000 per year. It has been estimated that 40 per
cent of this fuel bill can be attributed to running reworked engines or performing
a portion of a test over again (because of improper readings or calcuation errors).
The preceding sections describe in general the testing procedures and some
of its existing problems. Do not be "misled" by the seemingly simple test procedures described. There are many things not covered in as minute a detail as
possible; also not mentioned are the many splitsecond decisions that must be made
during the course of the test and at times when possible malfunctions occur.
6. Capacity
In cases of national emergency, or increased workload responsibility, the
need for increased test capacity in the high thrust cells could develop into it major
production "bottleneck. "
Pressure could be relieved in these situations by creating extra shifts of
men to handle testing and facilities maintenance; however, the increased utilization
of the cells under the present test time and procedures would increase many fold
the manhours of ~aintenance as well as cause the quality of the engines released
to the field to be inferior because of this increased pressure.
In either case, the cost of an increased workload under these conditions,
can become enormous.
7. Safety
There are several events that could take place to endanger the lives of
personnel working in the test cell while an engine is running. No "concrete"
solution will be found to completely remove all these danger areas. The technical
order regulations specify where and at what time personnel may be in the cells
while the engine is running. Because of unusual circumstances, the rules are many
times "bent" to fit the situation. In many of these cases, danger may be at its peak.
Examination of the possible dangers of these situations reveals that there
is a possibility of fuel leaks and thus flash fire while trimming. The bleed valve
may also dump excess air overboard while decelerating. The force of this air
can be enough to knock a man off his feet. There are also dangers from any engine part or accessories not being securely fastened and thus breaking away.

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II. SOLUTION TO THE PROBLEM
A. Introduction
Some of the problems existing in testing a turbo jet engine have been discussed
in the first section of this paper. Not all of the intangible problems were brought out,
but inference was made to them.
The forthcoming discussion is submitted as a possible approach to the solution
of many of the problems that act as a plague to the efficient and correct testing of a jet
engine.
There are many alternatives to the degree of automation that can be applied by
the use of a computer in a jet test cell. The primary problem rests on two factors:
(1) What degree of control should the system have and (2) Whether the system should
be a primary "slave" to the operator or the operator a "slave" to the computer.
The one chosen discusses a completely closed loop operation (In this instance,
the running of the test including start-up shut-down via an IBM 1710 Control System,
related hardware and any special features). The advantages and disavantages of
operating in a manual and open-loop mode as compared to the chosen approach are discussed.

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A great majority of the following information has been derived by working with
prospective customers in the jet engine test area; however, due to reasons which will
not be discussed, customers' names will not be mentioned. *
B. Previous Work
1. Data Logging
One of the first attempts at applying an on-line device for the logging and reduction of engine test data was tried by the U. S. Naval Airforce. A special device
for these purposes was built by Gilmore Industries (3) to perform such a function.
The primary design of this device was for gathering piston type engine data.
Many of these were later modified to receive data from test cells geared for jet
engines.
The data logger was usually located in a prototype cell where certain special
test runs could be made.
The data logger was primarily an analog type sensing device. Its primary
readouts were instrument faces, graphical x-y plotting and type writer data that had

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Contact author for further information.

10

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been convert~d by an analog-to-digital converter to a scaled digital form. The
number of channels or sensing and readout elements depended upon the elaborateness
of the model ordered. The acceptance of this system was "poor" especially in commercial installations (where a few are found war surplus) where the price/performance ratio was much too great.

0

This piece of equipment contained the same hinderances as the analog computer does. No logical ability coupled with an "exponential" increase in price for
flexibility, plus inadequate readout accuracy. Enough of this type of gear to log
data in one cell often times cost as much as the digital computer components to
control multi-cells.
2. Research and Development Jet Engine Testing
One of the first companies to apply a computer to the role of gathering and
reducing test data was Pratt and Whitney. The computer is·an IBM 1410 with a
special interface (Analog-to-Digital Converter) to take data gathered during tests
conducted for research purposes. The system acts as a data monitor. It logs and
reduces data only during the time the engine is in the performance run phases.
Special instrumentation has been added to detect malfunction of components at
high temperatures and fast speeds. After one test has been conducted, the instrument leads are then automatically connected to an engine awaiting test in another
cell.

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Because the purpose of this system was to do only a data logging and data
reduction job, no further effort has been made to perform a close-loop function.
Cases of research and development do not readily adapt themselves to a
close-loop operation. There are many times when extraordinary or special tests
need to be conducted which would not be compatible with the programs that had
been written for test.
There are also under development in the NASA Space Program the adaptation
of fast general purpose computer to missile checkout. This program like all other
programs in jet engine control is in its infancy.
3. Industrial Testing Systems - Discrete Process
Industry has entered an era in which the processing of production and product
performance information must be incorporated as a part of the manufacturing oper'~,,­
tion. As the profit squeeze continues along with the need for increased production~
the cost of manufacturing the product must be reduced to maintain or improve the
profit position. Much has been done and is being done to reduce the cost of making
the product through advances in technology and by automation. However, the costly
operation of quality assurance which continues to receive more demanding tasks is
not keeping abreast of its production counterpart. To parallel the giant step made in
manufacturing through automation, the quality assurance program in industry has
11

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made and continues to make drastic advances through in-process test and inspection systems. Some of the industrial testing applications using industrial
process control systems are:

1. Space Vehicles - Analog to digital converter used in logging, reducing and analyzing data on space vehicles in environmental
chambers.
2. Potentiometers - Final testing of potentiometers.
3. Automobiles - On -line quality control to determine defects in
assembly as they happen.
4. Aerospace Nose Cones - FM Tape playback of data telemetered
from missiles.
5. Nuclear Research - On -line recording of information from a
spark chamber.
6. Atomic Powered Naval Ships - On-line measurements and computation of shielding experiments.

o

In general Industrial Testing with control systems controls plant test
procedure, analyzes product test data and contributes to production test equipment the capabilities of:
1. Testing dynamically at prod~ction speeds.
2. Correlating the test data for each product.
3. Determining the classification of each produced unit based upon
specification.
4. Sorting product unit after final test.
5. Storing test data for future analysis.
6. Initiating reports during production runs.
7. Checking and calibrating of test equipment during production runs.
8. Scheduling produced product.
9. Determining critical trends as they develop. 1
The prece~ing paragraphs have shown the development of automatic control
systems in the continuous process industries and manufacturing operations involving discrete processes. In each case one of the main objectives is increasing the
quality of the end product. It can also be clearly seen that automatic testing is not
an idea with unproven results but the missing link between production and quality.

o

1. IBM Application Brief, No. K20-1725

12

·20

o

C. Automatic Jet Engine Test Control System
1. System Design Requirements
In the preceding sections of this report the various phases of the actual jet
engine test were discussed in moderate detail. These are functions performed by
the operator, recorder, and inspector.
The following describes the functions the control system will perform in
regard to the various test phases. The functions are necessary to deliver a high
quality engine with minimum cost.
a.

Control of the Independent Variables to Set Up and Sequence Tests

The jet engine control system will select various test phases for an individual type, model and serial number engine -use information gathered from the
engine in the test cell, such as pressures, temperatures, flows, etc., and determine appropriate test sequences and procedures taken from the Technical Order
to send control signals to the engine in the cell.
By designing the test phases as a series of logical steps, the system will
use each test phase as a sub-program and execute the over-all series of sub-programs
under control of a master monitor routine.
b.

Data Acquisition and Control

c

Each instrument pick-up will be connected to a transducer which will be
connected to a transducer which will be connected to a multiplexer and terminal
unit which will be connected to an analog-to-digital converter. The analog-todigital converter will provide a digital voltage to the control system main frame.
The main frame will scan all instrument leads for each pressure, temperature,
flow, etc and convert these by the use of equations into meaningful engineering
values. These values will then be used to control the system.
The system will also convert a digital value to an analog voltage for control
of the throttle, trimmer and other relay switches in order to control the speed,
thrust, fuel flow, and other controllable variables.
c.

Calculation of Performance Parameters

After gathering all data (instrument readings), one of the test phases will
correct all data to a standard day (usually sea level) condition in order that all
parameters may be compared against the T. o. limits for trimming and reject
status.

o

13

202

St.'

o

d.

t.o_

Operator Guide for Engine Adjustment

Such things as warning messages, trim guides, test status, etc, will be
logged for the operator. Any transducer reading will be available upon operator
demand.
Any time the engine must be stopped or shut down by the control system,
a message will be logged on the typewriter giving the reason, a complete diagnostic,
and recommendations for repair or rework.
e.

Automatic Instrument Calibration
This can be done by either or both of the following:
1. Comparison of a known standard signal with the transducer output from
this signal.
2.

o

f.

Comparison of the transducer output to other related signals. This will,
in essence, tell if the signal is abnormal (too high, too low, or fluctuating).
From this an automatic calibration can be done. This will insure against
catastrophic results from a faulty transducer.

Check Calibration of Installed Engine Transducers

Many pick-ups are installed on the engine during dress-down, thermocouples, tachometers, etc. It is possible for one of these to be faulty (disconnecttion or off speCification in the thermocouple not detected during test). By using
the calibrate feature, control system abnormalities may be detected before the
actual test.
g.

Conduct Penalty Runs

After the major test phases are completed and the acceptability of the engine
is ascertained, it may be necessary to re-conduct portions of the major test or call
upon special penalty run procedures to be executed. This need arises when certain
T. o. limits have been exceeded or an engine has been accepted on a marginal condition. This will insure correctness.of data and calculations as well as insuring
that an out-of-limit condition was not a transient. The ability to automatically select and execute these routines under control of the automatic system will improve
both speed and accuracy of the over-all test.
.
h.

o

Engine Diagnostics

During the running of a sub-portion of the test or aft~r completion of the
major test, conditions may arise that will indicate off specifications in the engine

14

1III

J,I

I,

or one of its components. By gathering data at high speeds, using past historical
data on engine rejects, failure incidents and rework data, and building a series
of logical steps or a mathematical model of certain sections of the engine, it will
be possible to determine the exact cause of the abnormality and make recommendations for repair.
There will be a learning process by the system.
is gathered, the logical model will improve.

o

As more and better data

The ultimate aim of the system is to furnish complete re-work information
to the engine penalty line. In many cases, this will save time and prevent unnecessary rework of an engine.
i.

Logging and/or Punch-Out of Test Data and Engine Data

After a major test has been completed, all instrument readings, calculations,
and diagnostics remarks will be stored on the disk storage unit. The operator in the
cell control room will execute a request to the central control system room via the
manual entry control. The control system then will print a completed log or run
sheet giving the three items above for each test phase.
The log may be used by the operator to select penalty or re-runs if it appears
that a componm t or recording is marginal to the limit.
Several carbon copies may be produced so that copies may be sent to all authorized personnel.
An engine data plate card will be printed to accompany the engine and a military run data card punched for Quality Analysis.
j.

Store Test Programs and Parameters for All Type, Model and Serial Number
Engines

The control system will use a mass random access unit for storage of the
test parameters and limits for all engine models, types and serial number that will
be tested. This type storage insures immediate access to all types of engine programs for complete asynchronous testing and control for the test facility.
Mass storage will allow the system to be open ended ~or expansion to future
cells. By the use of this mass storage, a better and more complete engine diagnostic
can be performed (as pointed out in the previous section). The system will be designed to allow the updating of all engine technical orders on a daily basis.
As a secondary function, statistical data will be stored for analysis. By
storing summary data, critical trends can be detected early. All causes for rejects
or defects can be stored by type, model, and serial number. Summary data will be
quickly available upon management request.

15

0,

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I

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tr.

t&rtMtzd

. t+rl

Detect Emergency and Unsafe Conditions and Take Appropriate Action

The fast instrument scanning speed of the control system permits dangerous
trends to be detected in many of the instrument readings and appropriate corrective
action to be initiated to prevent occurence of out-of-limit conditions. In out-oflimit situations, the system will quickly bring the test and engine to a halt to prevent
serious damage.
One of the most important things to consider when designing the actual control system is achieving a high degree of reliability. Two types of failures can occur.
The failures and corrective actions are:
Type I - Transient Failures
These are internal system transmission errors and occur on a transient
basis. In this case, the system will record the failure and try twice more to perform the operation. The recording will be used by maintenance engineers for regular preventive maintenance (once per week). A transient type error will usually
be eliminated in three attempts.
Type IT - Complete Component Failure

o

In this case, the system will try to by-pass the bad component switching to
manual control or bring the engine to a safe stop. A by-pass procedure will be incorporated for' emergency action.
1.

Quality Analysis
1) The system will use store data to perform reliability calculations for engine
and individual components.
2) The quality analysis will produce data assurance for a better test engine.

m.

Production
1) Scheduling - Using advanced techniques such as linear programming, a
master plan will be prepared for scheduling the cells.
2) Planning - Better methods of machine and manpower utilization can be prepared.

2. Control System and Interface Description

o

To approach the problem of determining the necessary hardware, one must
keep three factors in mind. They are (1) design functions as determined in the meeting
of section 1 (2) instrumentation-present and future, (3) and layout of the basic test
cell.

16

--~------

..

---.,.--

If we notice the basic test cell layout as shown in illustration I, it shows
the location of the control room as being between two test cells. If there are
more than two cells (there are usually several more) then it is logical there will
be two or more control rooms. Because a typical control system will control
more than two cells, it will be necessary to locate the computer in either a remote location or in the rear of one of the test cells. When this is done, there
arises necessity for remote communication devices.

0 ,'
,

Attention should be drawn to the design function to operate in conjunction
with this communications device. Whether the operator or the central computer
system is the "slave". It will be necessary to place a device for the operator
(inspector, etc.) to select the particular test function he wishes to perform. It
will also be necessary for him to get return information from the instrument
readings, pertinent calculations and emergency or troubleshooting messages.
Many times it will be necessary for the test cell foreman to have information
concerning phases of test of engines in each cell in order to coordinate the overall
movement of engines in test. He will also need access to stored statistical information pertaining to reject, re-run and other engine test functions. Many times
upper level management will inquire of the cell foreman on these statistics. Things
that could be available on an inquiry basis would be:
1.
2.
3.
4.
5.

Number of rejects/month on a certain model number.
Major cause of rejects.
What was done for correction.
Ranges and standard deviations from set standard operating limits.
Etc.

Using the system described in illustration 2 and treating the requirement as
8 test cells, each component and its function will be discussed.
a.

Central Computer (1620 Model IT)

Because of the speed needed to accomplish the sampling of the necessary instrument leads" making all necessary calculations, actually sending output signals,
for control and receiving feedback input signals for correction, the 1620 Model IT
with a 60,000 position memory was chosen. The 1620 as the heart of the 1710 Control
System contains the necessary machine instructions and programming systems (Executive System-e. g., monitor) to operate in conjunction with an asynchronous test
system design.
b.

Auxiliary storage (2-1311 Disc Files)

Even though the majority of the skeleton test functions are the same for all
engines, there still remains different test parameters for each engine model. Each
of thes~ parameters must be stored for immediate access. Because no central computer memory would be large enough to contain all test program phases, these must
17

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1712 D

1712

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1712

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STORAGE
WORK TABLE

1625

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1620

1622

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1712 IV. V • VI • VIII

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--

DESK

CONTROL ROOM

I

I

also be stored for immediate access as they are called by the skeleton control program. Also contained in auxiliary storage would be necessary diagnostic routines
available upon request, as well as emergency limit and correction routines.
A second disc file would be used as in intermediate store area for input/
output information, if all input/output devices are busy and they would be available
to store quality and production control data gained as a by-product of each test.
This data would be available upon inquiry from management.
c.

Interface Equipment (1711 and 1712's)

In order to attach all necessary points for 8 cell (see Appendix B) and con-'
vert the analog (electrical) signal into a digital form in a sufficient time period, the
analog to digital converter (1711) has the ability to convert 200 pOints/second. In
order to handle all necessary analog input points, analog output points, contact indicating and operating relays for an eight (8) test cell facility, it is necessary to
have three (3) multiplexing and terminal units (1712's) to the system.
d.

Test Cell Input/Output Gear (1713, 1715, 1717)

Located adjacent to each instrument control panel will be an IBM 1713, 1715
and 1717.
The operator will have the option with the IBM 1713 manual entry devicethrough a set of coded instructions -to dial in either the command for a complete
test or portions of a test. The command will be dialed through the use of twelve (12)
rotary knobs with zero (0) to nine (9) selection ability.
An enter key will be hit, the information will go via the SIOC channel and
interrupt the computer, the computer will read the rotary knobs and start the processing.
e.

Interface

All instruments that furnish an electric signal of a standard form will be
sent via shielded cabling to the 1712 multiplexing unit, all non standard (pulsed, etc)
and pressure type signals will be transformed via transducers (in the test cell
control room) to an electrical form and ~e~t to the central system complex.
All pickup signals from the engine are easily adjusted to the standard 1710
signals; however, more specialized servos must be bought or designed to control
the throttle and trimming mechanism. There are several types of stepping motors
or feedback systems on the market today that can handle these tasks.

c
19

o

All existing cell instruments will remain intact as man;ual back-up for the
system. Through a specially designed panel, the operator will be allowed the
option of switching to either automatic or manual system at any time.

m.

ECONOMIC JUSTIFICATIONS
The justifications for considering the "Control Systems Approach to Jet Engine
Testing" can be broken into tangible, intangible and possible savings categories. The
justifications can vary depending upon the application. Some of each are listed as
follows:

A.

Tangible
1. Increased Engine Throughput:
This can be accomplished by
a. Simplifying the testing procedure.
b. Decreasing delay in such things as trimming and shakedown.
c. Operator Guide Print-Out for prompt emergency and testing actions.

o

The best time estimate for engine throughput with no major hindrances is
5 hours 55 minutes. As previously mentioned, the average throughput is approximately eight (8) hours for an engine with time running up to twelve (12) hours if
there are several re-runs or persistent trouble exists.
The control system would increase the capability of the cells to take on
added workload without added facilities. This need would arise in wartime emergency for federal customers and with added contractual obligations for both commercial and federal.
2. Reduced Manpower Requirement/Engine
This would free inspection' and operating personnel for a greater engine
throughput. One operator would be substantial for testing procedures, where the
present system utilizes an inspector and two (2) shops or production personnel.
3. Avoiding Re-Run of Engines

o

a.

By eliminating bad instrument calibration--erroneous transducer signal.

b.

Bad instrument reading--can be eliminated. The signal will originate completely at the transducer and eliminate' the nonlinearity of the instrument .
read-out mechanism. Operator error in reading will also be eliminated,
e. g., simultaneous reading of instruments.
21

4. Decreased Ftlel Costs
This can be saved with automatic trim procedures and avoidances of excess
penalty runs.
5. Decreased Calibration Costs
By automatically calibrating the transducers the computer will give a
correction or tare factor for the back-up reading devices. The time between calibrations will decrease. The maintenance costs will correspondingly decrease.

B. Intangible·s
1. Better Engine Quality
a. Better checked out engines through more certain detection of off-specification
units.
b. Simultaneous recording of the instruments, thus insuring proper data for checking
limit parameters.
c. Consistent methods of testing, thus insuring proper acceptance or rejection of an
engine.
2. Decreased Re-Work Costs Through Better Diagnostics
As mentioned previously, the system with its on-line mass storage can furnish
pinpoint diagnostics to eliminate complete overhaul for minor abnormalities or defects.
3. Data .Assurance
This assurance can be derived through getting simultaneous readings or reliability in instrument calibration and will result in better customer (the pilot or
branch of the armed services) satisfaction.
4. Increased Safety for Personnel, Equipment and Property
5. Increased Readiness Program on First Line Aircraft
6. Reduced Paperwork Handling
Complete and accurate unit performance logging. Here we have better customer
satisfaction through hard copy records. Diagnostics are automatically printed to be
sent back for re-work.·
-,
22

2i 0

·,

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b

IV. SUMMARY AND CONCLUSIONS
This paper has attempted to discuss one particular approach to the application
of a digital computer to the closed loop control of a jet engine test cell.
As has been pointed out, there are many approaches to consider in designing a
system for a particular application. In summary, the things that must be considered
are repeated and listed as follows:
1. Degree of Control Desired-Open or Closed Loop

2. How Much the Operator is "Slave" to the Computer or Vise Versa
3. How Many Test Cells Must Be Controlled Simultaneously
4. The Functions that the Customer Wishes the System to Perform
The justifications for a control system can be varied, depending upon what the
customer wishes to accomplish; however, the "state of the art" of automatic control
in jet engine testing is in its infancy and there are many justifications in all cases.

o

It should be pointed out that the general approaches and ideas used are appli-

cable to many other industries and are not limited to jet engine testing.

23

o

BIBLIOGRAPHY

1.

o

Industrial Testing Systems at the IBM Components Division
Poughkeepsie, New York.
Application Brief, No. K20-1725

2.

Sales Guide Industrial Testing Systems
IBM Internal

3.

Introduction to Control Systems
General Information Manual F26-5577-0

24

o

o
GOOO/iE4R
GOODYEAR

AEROSPACE

CORPOR,\TION
ARI10NA

DIVI~ION

lITCHF IELD PARK ARllONA

GENERALIZED

C"'·,

FILTF~

NETWORK

I,IJ

ALe

STEADY STATE ANALYSIS PROGRAM

by

D. Ho O'Herren

AAP-18911

o

May 1, 1964

I~l

l i1
II
I

o
TABLE OF CONTENTS

I

Generalized Filter Network

Alc

Stea~

State

Analysis Program • • • • • • • • • • • • • • • • • • •

1

II

Program Input Data • • • • • • • • • • • • • • • • • •

6

III

Sample Problema

8

• • • • • • • • • • • • • • • • • • •

-.

8

a.

Sample Problem 1 • • •

b.

Sample Problem 2 • •

•

11

o.

Sample Problem 3 • • • • • • • • • • • • • • • •

16

d.

Input Data Problem 1 • • • • • • • • • • • • • 0

22

e.

Output Problem 1 • • • •

• • • • •

23

to

Input Data Problem 2 • • • • • • • • • • • • • •

24

g.

Output Problem 2 • • • • • • • • • • • • • • • •

2,

h.

Input Data Problem 3 • • • • • • • • • • • • •

27

10

Output Problem 3 • • •

• • • • • • • • • • • •

·• •

• • • • • • • •

·•

·•

• • •

• • • • • • • • •

· . .' .

IV

APPENDIX A

v

Li sting of Fo rtran II Source Program

•

•

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GENERALIZED FILTER NE'IWORK

Ale

STEADY STATE ANALYSIS PROORAM

This program has· heen written to make possible comprehensive surveys of
theoretical filter designs. It opens up a more sophisticated range of
filters to theoretical consideration and evaluation. The program' input
is general enough that almost any filter network consisting of cascaded
inverted-L or symmetrical lattice sections may be handled easily.
The minimum machine requirements are a 1620 with La K core storage, auto
divide, and indirect addressing.
The source language is Fortran II.
There are 6 au bprograms plus the mainline program.
~
Filter design has been speeded in recent years with the advent of tables
of normalized low-pass filter element values*. Even if these tables are
used, this program allows the desiener to compute the effects of component
tolerances, finite Q's, and mismatched terminations. These introductory
remarks have centered around. .filter design, rut it will be apparent that
the program is useful for analyzin~ any RLe network, e.g., amplitude or
phase equalizers.
The filter designer needs to know how a proposed design will perform over
a particular range of frequencies before making recommendations to those
who will implement the design. Manual 0.

1.

o

PROGRAiVi

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15.4715
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26.4500
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29.3887
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32.0716
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BETA

76.462
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114.502
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138.993
156.885
156.901
170.717
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0

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13.2695
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20.9877
20.9950
28.1290
28.1360
34.9788
34.9855
41.6625
41.6691
48.2434
48.2500
54.1565
54.7630
61.2225
61.2289

T(F)

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.81361108E-01
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.15999999E-07
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o
-23-

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SAMPLE PROBLEM 2 NETWORK ANALYSIS PROGRAM
50.

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211
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o

GENERAL NETWORK ANALYSIS PROGRAM
SAMPLE PROBLEM 2 NETWORK ANALYSIS PROGRAM

1MAY64

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50.0000
50.001Q
52.0000
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54.0000
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56.0000
56.0010
58.0000
58.0010
60.0000
60.0010
62.0000
62.0010
64.0000
64.0010
66.0000
66.0010
68.0000
68.0010
70.0000
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72.0000
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14.0000
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76.0000
76.0010
78.0000

=

MP=
1
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DB
21.6168
21.6170
21.9569
21.9511

22.2846
22.2848
22.6008
22.6009
22.9061
22.9063
23.2015
23.2016
23.4874
23.4875
23.7646
23.7647
24.0334
24.0336
24.2946

24.2947
24.5484
24.5485
24.79:>3
24.7954
25.0356
25.0358

25.2698
25.2699
25.498,2

BETA

89.216
89.216
89.613
89.613
89.994
89.994
90.361
90.361
90.716
90.716
91.060
91.060
91.393
91.394
91.718
91.718
92.033
92.034
92.341
92.342
92.642

92.643
92.937
92.931
93. 225
93.226
93.508
93.509
93.786

0

L

=

1 ORDERS

.50000000E+Ol

=

C( 1 , 3 , 1 )

o

1

=

.OOOOOOOOE-99
.OOOOOOOOE-99 R:::
.OOOOOOOOE-99 R = .OOOOOOOOE-99
.OOOOOOOOE-99
.10000000E-06 R
1 ORDERS
.50000000E+01

=

R:: .OOOOOOOOE-99
R = .OOOOOOOOE-~9

.OOOOOOOOE-99
.00000000E-99
.150000001:-06

R

=

.OOOOOOOOE-99

.OOOOOOOOE-99

R

=

.lOOOOOOOE+03

ZREAL

5.2596
5.2596
5.2426
5.2425
5.2274
5.2274
5.2138
5.2138
5.2016
5.2016
5.1906
5.1906
5.1806
5.1806
5.1715
5.1715
5.1633
5.1633
5.1558
5.1557
5.14A8
5.1-488
5.1425
5.1425
5.1367
5.1367
5.1313
5.1313
5.1263

ZIMAG
-4.8518
-4.8517
-4.6662
-4.6661
-4.4943
-4.4943
-4.3347
-4.3346
-4.1859
-4.1859
-4.0471
-4.0470
-3.9172
-3.9171
-3.7953
-3.7953
-3.6809
-3.6808
-3.5731
-3.5731
-3.4715'
-3.4714
,-3.3755
'-3.3755
-3.2847
-3.2847
-3.1987
-3.1986
-3.1170

T(F )

.55555554E-09
.55833331t-09
.52499998l:::-09

.52777776E-09
.472222201::-09

.472222201:-09
.47222220E-09
.41666665E-09

.41666665E-09
.44444443c-09

.416666651:-09
.41666665E-09
.38888887E-09

.38888887E-09

-25-

78.0010
80.0000
80.0010
82.0000
82.0010
84.0000
84.0010
86.0000
86.0010
8S.0000
88.0010
90.0000
90.0010
92.0000
92.0010
94.0000
94.0010
96.0000
96.0010
98.0000
98.0010
100.0000
100.0010

25.4983
25.7209
25.7210
25.9384
25.9385
26.1509
26.1510
26.3585
26.3586
26.5616
26.5617
26.1604
26.7605
26.9549
26.9550
27·1455
27.1456
27.3323
21.3324
27.5154

21.5155
27.6950
27.6951

93.786
94.059
94.059
94.32R
94.328
94.593
94.593
94.853
94.853
95.110
95.110
95.364

5.1263
5.1211
5.1217
5.1174
5.1174
5.1134
5.1134
5.1097
5.1097
5.1062
5.1062
5.1030

95.364

5.1030

95.614
95.615
95.862
95.862
96.107
96.107
96.349
96.349
96.588
96.588

5.1000
5.1000

5.0971
5.0971
5.0944
5.0944
5.0919
5.0919
5.0896
5.0896

-3.1170
-3.0395
-3.0394
-2.9657
-2.9657
-2.8954
-2.8954
-2.8284
-2.8284
-2.7645
-2.1644
-2.7033
-2.7033
-2.6449
-2.6449
-2.5889
-2.5889
-2.5353
-2.5352
-2.4838
-2.4838
-2.4344
-2.4344

.38888887E-09

0

.36111110E-09
.36111110E-09
.36111110E-09
.38888887E-09
.36111110E-09
.36111110E-09
.36111110E-09
.33333332E-09
.361111101:-09
.33333332E-09
.33333332E-09

o

01
239

SAMPLE PROBLEM 3 NETWORK ANALYSIS PROGRAM

O?·

5.
2
1
1

2

o

2

100.

100.

2

1
+.lOOOOOOOE-05
+.OOOOOOOOE-99+.00000000E-99+.10000000E+04
3
1
3
+.lOOOOOOOE-ll+.OOOOOOOOE-99+.10000000E+07
+.30000000E-06+.20000000E-12+.10000000E+04
+.lOOOOOOOE-ll
+.OOOOOOOOE-99+.10000000E-05+.100000QOE+03

+.lOOOOOOOE-12+.00000000E-99+.50000000E+02
+.OOOOOOOOE~99+.20000000E-12+.10000000E+03

o
1
+.50000000E-OB+.IOOOOOOOE-07+.10000000E+03
1
3

0

+.OOOOOOOOE-99+.50000000E-06
+.OOOOOOOOE-99+.00000000E-99+.10000000E+03
+.lOOOOOOOE-05+.00000000E-99+.1000QOOOE+Ob

o

o

4MAY64
1•

0.0

"~"~!!W\'~--' .. ~

.. -.. '.~~;"'::':";.. ~' .. ";"~,;:':;'

-.",..... ,.. , ..."",,"............. =:.--..:..-~..::..:.-.;..----

'I
GENERAL

ANALYSIS

NETWORK

PROGRAM

SAMPLE PROBLEM 3 NETWORK ANALYSIS
~OR=

VORa

100.000

SECTIONS=

lIS

ORDER

Kc

t

1

t

1

ORDER

K=

,
,

,
,
,

,
2
,

K=
C( 2
C( 4

f

K=

2

C( 2

t

2

t

2

t

2
2
2

t

,
,

C( 1
C( 3
5

t

cc

1
1
1
1

::

)

::
::

)
)

::

2
)

J::

)

::

)

::

1

1=

1

3
3
3

F

5.0000
5.0010
10.0000
10.0010
15.0000
15.0010
20.0000
20.0010
25.0000
25.0010
30.0000
30.0010
35.0000
35.0010
40.0000
40.0010
45.0000
45.0010
50.0000

,
,

,

R
R

::

=

.OOOOOOOOE-99
.10000000E+04

R

::

R

::

R =
R '::

.10000000E+07
.10000000E+04
.OOOOOOOOE-99
.10000000E+03

.OOOOOOOOE-99
.20000000E-12

R ::
R =

.50000000E+02
.10000000[+03

.lOOOOOOOE-07

R

.lOOOOOOOE+03

.OOOOOOOOE-99
.OOOOOOOOE-99

1

)

3

=

=

::

L
l

2:

.1OOOOOOOE-ll

L

=

.OOOOOOOOE-99
0
MQ=
MP=
.lOOOOOOOE-12
.OOOOOOOOE-99

L

::

0

2
L =

L

MQ=

;:

L =

MQ=
3
.OOOOOOOOE-99
.OOOOOOOOE-99
.10000000E-05

0

DB
180.7194
180.7228
192.0992

192.1008
198.3916
198.3926
202.1228
202.7236
206.0672
206.0678
208.8217
208.8282
211.1986
211.1991
213.2865
213.2869
215.1560
215.1563
216.8501

.B ETA

180.838
180.838

182.003
182.004
182.824
182.825
183.368
183.368
183.685
183.685
183."835
183.835
183.869
183.869
183.'828
183.828
183.741
18:3.741
183.628

.OOOOOOOOE-99
.200000001:-12
.OOOOOOOOE-99
.10000000E-05

1

.50000000E-08

MP=

1 ) =
1 )

MQ:::
1
.1OOOOOOOE-ll
.30aOOOOOE-06

MP=

3
3

3IS
3

2

1
L =
L =

MP=

)

1=

2

::

1

,
,
1=
, 2
, 2

2

0.000

3

I::

ORDER

K-

1

=

)
)

MQ=
1
.10000000E-05
.OOOOOOOOE-99

MP=

1

1

2IS
2

C( 1
C( 2
C( 4
C( 6

Neyel::

2

0

4MAY64

1

Ie:

1

C( 1
C( 2

VOI=

1.000

lETTR::

2

PROGRAM

L
L
L

::

0
==
==

=

.50000000E-06
.OOOOOOOOE-99
.OOOOOOOOE-99
ZREAL

1065.2886
1065.2887
1066.2497
1066.2501
1067.7597
1067.7601
1069.6027
1069.6031
1071.5953
1071.5957
1073.5931
1073.5935
1075.4981
1015.49B5
1077.2542
1077.2546
1078.8370
1078.8373
1080.2430

R =
R ::

R

::

ZIMAG
.2987
.2999
4.5705
4.5712
7.4989
1.4994
9.6923
9.6927
11.2RIO
11.2812
12.3601
12.3602
13.0270
13.0271
13.3159

.OOOOOOOOE-99
.10000000E+03
.10000000E+06
T(F)

.77777775E-09

.55555554l:-09
.38888887E-09

!"

.22222221E-09
.13888888E-09
.55555554E-I0
.OOOOOOOOE-99

13.3760

-.27777777E-IO

13.4893
13.4893
13.4347

-.55555554E-IO

241

0

_

0

50.0010
55.0000
55.0010
60.0000
60.0010
65.0000
65.0010
70.0000
70.0010
75.0000
75.0010
80.0000
80.0010
85.0000
85.0010
90.0000
90.0010
95.0000
95.0010
100.0000
100.0010

216.8505
218.3995
218.3998
219.8269
219.8272
221.1500
221.1502
222.3827
222.3829
223.5363
223.5365
224.6202
224.6204
225.6422
225.6424
226.6089
226.6091
227.5257
221.5259
228.3976
228.3977

183.628
183.501
183.501
183.369
183.369
183.237
183.237
183.108
183.108
182.985
182.985
182.867
182.867
182.757
182.757
182.653
182.653
182.555
182.555
182.464
182.464

.. htrn

1080.2433
1081.4807
1081.4R09
1082.5648
1082.5651
1083.5125
1083.5127
1084.3404
1084.3405
1085.0647
1085.0649
1085.6991
1085.6998
1086.2579
1086.2580
1086.7501
1086.7502
10207.1857
1087.1857
1087.5724
1087.5725

13.4347
13.2648
13.2647
13.0190
13.0189
12'.7260
12.7260
12.4067
12.4066
12.0753
12.0752
11.7419
11.7418
11.4133
11.4132
11.0938
11.0937
10.1862
10.7862
10.4922
lO.'t922

-.55555554E-10
-.55555554E-IO
-.5555~554t:-1O

-.83333331t-1O
-.555555541::-10
-.55555554E-10
-.5555~554t-1O

-.55555554E-1O
-.55555S54t=-lO
-.55555554E-1O
-.55555554E-IO

o
M4 _ _• •

::;,=

----.---~-.--~-'~~-

--

o

APPENDIX A

The following paragraphs will outlin~ the equations programmed for the
vari.ous subprograms. These assume steady state conditions on the imaginary
axis (5· jel) with linear, lumped, bilateral, passive elements. The program
processes basic sections starting with that section nearest the output
termination. Regardless of section type, this section will have ZA and ZB
impedances •.

The DRPTZ subprogram calculates the impedances and admittances for a single
order as in Figqre 8 for both the ZA and ZB impedance.
The number of parallel branches, or resonators 8S they are called in the
Westinghouse report, allowed is a function of available core storage. As
written, three resonators per order are allowed although this could be
increased by reallocating storage, i .•. , reducing the number of orders fer
basic section impedance or the number of basic sections. The impedance for
a single branch or resonator i8:
1
1
Zl • l1. + j001:L + ~ • ~ + j(~ -

COCi)

o

1

•
R..

--~

YRLl •

2

+

(Ca)

R2
1 + (tAl ~ -

Ll -

1

~

4-)2
VI

Ca)

)2

o

~

o

I
I

t

I

I

I

I

LJ~

FI(;{Tf.' B .. "

Sl~0LF

Onnfn

M~

I

I
I

t
I
I

f

I

onrFn 2

o

I

:=

2
~(

Z(2) -

..c.---

:L

1) -

~

Z(~)

Z(3) -

o

onrrRS
&2

1

OPlwr 3

-31-

Em

MiJSUSSUi a

., IlliX)

1$

lIIffttit'dHillti'

_____ .. _._._. ___ ...... "..".'"'·'·"'''.r.·''.'''''.''"" ....... _,,~··_~r;,;.J..oo""""'"~.......,~.

'WitH 'rlN&'

ttl """WJ.tIii:o i

" .... _.'-'

•

Summing admittances for all k parallel branches in an order gives:
k

L

mI;. •

YRLi

i-l
k
YIMT -

y

T

L
i-1

YIM i

•

The DRPTZ subprogram stores values of ZRL-. and ZIM.r impedances.

control is then given to the ORDER

SUb~ra.m.

Program

The ORDER subprogram first stores the impedance values just computed by

DRPTZ as subSCripted impedances Z(I), with the order counter I set at 1.

Control is returned to the main line which determines if either the ZA or
ZB basic section impedance consists of more than one order.

If not, control

It there are more than one
order in either ZA or ZB' the counter is incremented to 2 and con trol 18
returned to mpTZ.
is given to the proper recursion subprogram.

The DRPTZ subprogram then zeros the variables

YRLr

and

YIHr

and repeats the

process described above using the element values for the second orders of
the appropriate basic section impedances.

Control is then given to the

OHDER subprogram.

The ORDER subproeram determines i f the order counter I equals 2 or 3.

If

I is 2, ORDER simply sums the impedances ZT just computed by Dlli)TZ with those
previously stored as subscripted ·impedances when I equalled 1.
illustrates the situation.

Figure 9

C

o

Z(l) • ZTRL(l) + jZTIM(l)
Z(2) • Z(l) +ZT • Z'ffiL(l) + jZTIM(l) + ZFLT + jZ~
ZTP~(2) • ZTRL(l) + ZRL
T

ZTIM(2) • ZTIM(l)

+

-ZTRL(2) + jZTIM(2)

ZIMT

If the order eounter I is.3, the ORDER subproBram has the 51 tuation in
Figure 10.

IT for the

DRPTZ again has comj::u ted the impedance ZT and admittance

third order.

Y • YRLT + jYIM.r (for Order 3)
T

Y(3) • 1/Z(3) •
•

~

IT· ZTRL(2}

+

ZTRL(2) ~ jZTIM(2)

+

IRLr

+

jZTIM(2)

+

IT

+ j y~

where

o

y(3) •

i ~ [ZTRL(2)

+ A(YRL T)] +j

r(YIM.r) - ZTIM(2)] }

Let B • ZTRL(2) + A(YB~)
C - A(YIMT) - ZTIM(2)

Z(3) • 1/Y(3).

A

B+

3c

•

A(B - jC)

B2

+

c2

Control is returned. to the main line.

If there are no further orders to

be processed in the particular basic section impedances, control is

eiven to

the appropriate recursion subprogram LADDER or LATTICE.
The LADDER subprQgram has the a1 tuation in Figure 11.
computation proceeds from right to lett.

As n;:;ntioned previously

The first step is to pick up the

complex values of impedance just comp.tted by the DRPTZ and ORDER subprograms,
and the voltage and impedance existing at. the

being considered.

4C)

au tput of the particular section

If the first section to the left of the output termination

is being processed, these latter two values are Vo and R.
0

In the general

case t he7 are V _ and ZK_lo

K1

VK_1 • ~-1 + jV~_l
-)J~

$

V·

1...

""

I\TlT Vk

-

ZBk

SFCTIO~

k

~

TFiN

Zk-

c

V_
k.-.

--

Z"k
-. ... _ _ _ _ ...._ _ _............_ _..6

..-

-

fIGCnr. 11 - C \SC.\DEO

l..u~nF.n SFCTln~s

7,\;_1 -

. FICtlW

l~

v·1

-

-

SY\~~FT!lIC'L l.~TTlr.f. srcflo~

V

--

ZT

Z

""

-.

fHTPF 11 • F II TF!~

~FTWOnK

T~nv.I'f~TIO'\l

Z ",' n I ~prT

2 ''{ ~40

ZT

-341,1,

I'i:'I'
1,'1

Note that Z~ and Z\ are equal to the appropriate Z(I) values determined
in DRPl'Z and ORDER where I is the maximum order of the kth section.

The LATTICE subprogram has the situation presented in Figure 12.
It will be noted that s,ymmetrioal resistive pi sections are placed at
each end ot the basic s.ymmetrical lattice section to permit a definite

4:)

amount

or

attenuation or isolation between sections.

8trective~

This feature can

be eliminated by inserting zero values tor the series e1ernents

ZAx

R B and very large values tor the shunt RA elements. Again
and Z~
have been COMplted by the DRPTZ and ORDER subprogra..~ and are equal to
the appropriate Z(I) values where I is the ma.,,

•

".aaUiM.::I;;: 1M

., •. --.-~."--~~.--~~~~----

14, 3X2HI=t 14, 3X3HMP=,

112 FORMAT (2HK=,

14, 3X3HMQ=, 14)

IREC • MP(K,I)
L

=1

9 IF (IREC-l) 7, 8, 8

8 INOX

= 2*L-l

c
C

READ 103, C(INDX,K,I), AL( INDX,K,I), R( INDX,K,I)
READ C(FARAOS),l(HENRIES),AND R(OHMS) VALUES OF ZA TYPE IMPEDANCE

C

C

WHICH IS PARALLEL ARM FOR INVERTED-L SECTIONS AND IS SERIES

C

ARM FOR LATTICE SECTIONS.

c
c
PUNCH 101, INDX, K,

107 FORMAT ( 2HC ( ,

1£14.8, 2X4HR

I, C(INDX,K,I), AL(INDX,K,I), R(INOX,K,I)

,,

12, 2H
::

,

12, 5H )

12, 2H "

=,

E14.8, 2X4HL

=•

EI4.8)

L = l+l
GO T09
7

IREe = MQ(K,I)
L = 1

10 IF (IREC-l) 2, 11, 11

11 INOX= 2*L
C
C

REA D 1 0 3 , C ( 1 NO X, K, I ), Al ,( I NO X, K , I ), R ( I NDX, K ,I )

C

READ

C(FARADS),L(HENR,IES~fANO

R(OHMS)

OF IB TYPE IMPEDANCE

v~HICH

C

IS SERIES ARM FOR INVERTEO-L SECTIONS AND IS PARALLEL ARM FOR

C

LATTICE SECTIONS.

255
-L2-

"--~-"-.----

o

........-

......._

..............

_......

.._-_.....

-_ .. ..

I

~I'

fw,r"'''''WlffiiiM!.ltMiJeSli:/iZiW"W"Y

Hlp"'",,!"

5

t, •

r.

oc
PUNCH 107, INOX, K,

I, C(INDX,K,I), AL(INDX,K,I), R(INDX,K,I)

L :: L+1
GO TO 10

2

CONTINUE
FCOUN
KKLL

= FMIN
=1

JFREQ = 1

"
NSECT
20 ZRL

=

NSECT-l

lOR

c

101=0.

0

ZIM

= 0.0

VRL

= VOR

= VOl
IREC = 0

VIM

K

= 1

I

z:

1

N :x

1

GO TO (42,43),lETTR

c
C

CALCULATE DROP FOR PI PAD PRECEDING FIRST SECTION.

c
42 CALL

LATTIS

43 IREC

&:

F

10

F2

I
!

N

2

= (FCOUN*1.OE+6)*PI2
&:

=1

F*F

256

il
,--j

I

i

K

:=

0

1

=

25 lORD

IOROR (K)

=1

I

22 CALL QRPTZ

CALL ORDER

IF ( IORO-I ) 3, 3, 21

,21

=

I

1+1

GO TO 22
3 GO TO (36.,.37},lETTR
36

CALL LATTIS
GO TO 38

37

CALL LAODER

38 IF(NSECT-K) 27, 21, 24

24 K

C

= K+l

GO TO 25
21 IF(NCYCL-N) 30, 30, 29
29 N
K

:;

N+l

=

1

GO TO 25
30

CONTINUE

GO TO (99,44),

LETTR

99 ZRLN == ZPRL

lIMN

=

ZPIM

GO TO ( 97 ,98 ) t KKLL
44 ZRLN

&:

ZRL

lIMN :: ZIM

257

GO TO (97,98), KKLl
91 PUNCH 109

, I

-.j!~

---

- -

--

~---

-------

- --

..

0

I

• he

KKLL

0C

=

rrt. .rttsttssri

2

C
C
98 K

:::

SET

C

NSECT+l
K AND I VALUES PERTAINING TO INPUT TERMINAL

C

BE EQUAL TO NSECT+l, I

C

IA TYPE.

= 1,

IMPEDANCE. K WILL

WHERE THE IMPEDANCE IS CONSIDER~D

C

I

=1

CALL T ERMIN
32 GO TO (33,34). JFREQ
C

=2

33 JFREQ

CALL BETAD8

C

CALCULATE DB AND BETA.

c

c
BETAl = BETA
C

C

ZRLN AND lIMN ARE IMPEDANCE VALUES OF INSERTED 'NETWORK WITH OUTPUT

TERMINATION ZOR. THESE INCLUDE PI PADS FOR LATTICE SECTIONS.
PUNCH 108, FCOUN, DB, BETA, ZRLN, lIMN

c
C

INCREMENT F BY 1000 CYCLES AND REPEAT ENTIRE PROCEDURE IN ORDER

TO OBTAIN TIME DELAY.

C

Q

258
FCOUN

= FCOUN+O.OOl

-45-

_cuaciU,M

',1
/II

II

GO TO 20
34 CALL BETADB
T

= (BETA-BETAl)*CONST

JFREQ :: 1

PUNCH 108, FCOUN, DB, BETA, ZRLN, lIMN, T

c
C

DECREMENT FREQUENCY BY 1000 CYCLES.

c
FCOUN

= FCOUN-O.OOI

C

C

IS FREQUENCY AT MAXIMUM VALUE.

c
IF(FMAX-FCOUN) 12, 12, 35
C

()

c

NO. INCREMENT BY AMOUNT AT INPUT AND REPEAT CALCULATIONS.

c
35 FCOUN

= FCDUN+FDEL

GO TO 20
C

C

YES. GO TO START TO READ IN NEXT COMPLETE FILTER PRObLEM.

C

108 FORMAT (F9.4, 2XF9.4, 2XFIO.3, 2XFIO.4, 2XFIO.4, 2XE14.8)
I

109 FORMAT C/4XIHF t lOX2HDB, 8X4HBETA, 8X5HZREAL, 7X5HZIMAG,9X4HT(F)/)
END

25U

-------

-~-~--

0

HfU'W"W#"ttWliIllW'w'W'rrM'Y"''PZF

oc

-

tr

1U

.'!$=

,

!

'"

SUBROUTINE BETADB
CALCULATES BETA(RADIANS) AND DB FOR FREQUENCY
DIMENSION C(6,5,3), R(6,5,3), AL(6,5,3}, MP(5,3), MQ(5,3),

IRA(5), RB{S), IORDR(5)t ZAKRl(3), ZBKRL(3), ZAKIM(3), ZBKIM(3)
COMMON C, R, AL, MP, MQ, RAt RB, ZAKRL, ZBKRL, ZAKIM, ZBKIM, YARL,
lYBRL, YAIM, YBIM, ZARL, ZBRL, ZAIM,
2 VPR L ,

VP 1M, Z R l

t

Z 1M, VRL, V 1M, K,

ZBIH, F, F2, IREe, ZPRL, ZPIM,
I,

I P UNC, R A0, . R B0, 0 EN,

L,

3INDX, REAL, AIMGt RlOEN, ANMIN, RLNUM, DENIM, A, B, QUAN, IORDR,
4LETTR, VAR1, lORD, ZARLK, ZBRLK, ZAIMK, ZBIMK,NSECT, NT
COMMON XK, RK, lOR, lOI, VOR, VOl, BETA, DB, XIMAG
PI

= 3.14159265

PI2

= 6.2831853

CONY :: lSO.O/PI

4()

BETA

= (ATANF(VPIM/VPRL»*CONV

c
C

MAKE BETA POSITIVE ANGLE BETWEEN 0 AND 360 DEGREES.

c
IF(VPRL) 1, 2, 2
1 BETA

= BETA+lSO.O

GO TO 4
2 IF(BETA)

3, 4, 4

= BETA+360.0

3 BETA

= ZOR*VPRL-ZOI*VPIM
XIMAG = VPRL*ZOI+ZOR*VPIM
XNUM = SQRTF(RNUM*RNUM+XIMAG*XIMAG)

4 RNUM

RLDEN

o

= RK*VOR+ZOR*VOR-XK*VOI-ZOI*VOI

XIMAD = XK*VOR+ZOI*VOR+RK*VOI+ZOR*VOI
DEN

26U

= SQRTFlRLOEN*RLDEN+XIMAO*XIMAD)

I; ,

"

DB

=

.

"_.~

__ .".~ .• ".,,_w

. .~_ _ _ .

2.0*4.3429448*LOGF(XNUM IDEN)

o

RETURN
END

o

261

01I.
I

-48.

rt

o
, C

nttr

rrt

SUBROUTINE LATTI$
RECURSION FORMULAE FOR SYMMETRICAL LATTICE SECTION

c

CALCULATES lRL, lIM, ZPRL, ZPIM, VKL, VIM, VPRL, VPIM
DIMENSION C(6,5,3), R(6,5,3), AL(6,5,3), MP(5,]}, MQ(5,3),

lRA(S), RB(5), IORDR(S), ZAKRL(3), lBKRL(3), ZAKIM(3), ZBKIM(31
COMMON C, R, AL,
1 Y BR L, Y AI tvl , YBIl"l ,

VP I 1"1, l R L,

2 VP R L ,

MP,

MQ,

Z AR L ,

RA,

RB,

ZAKRl, lBKRL, ZAKIM, ZBKltII, YARL,

Z ARL, ZA 1M,

Z 1M, VRL, V I ~"

K,

7 B 1M, F, F 2,

I,

IRE C,

ZP R l ,

I P U(\j C, RA0, R 80, DEN,

l P If-1 ,

L,

3INDX, REAL, AIMG, RLDEN, ANMIN, RLNUM, DENIM, A, B, QUAN, IORnR,
4LETTR, VARl, lORD, ZARLK, ZBRlK, ZAIMK, lBIMK,N~FCT, NT
COMMON XK, RK, lOR, lOI, VDR, VOl, BETA, DB, XIMAG

o

REAL

= I.O/RAO

AIHG

= RBO

C

C

IF FIKST SECTION, GO TO 4022 TO CALCULATE INTIIAL PI PAD

D~OP.

C

COME BACK TO CALCULATE FIRST SECTION AND FOLLOWING PI

C

PAD DROP.

c
IF(IREC> 4021, 4022, 4021
4021 ZARLK ::: ZAKR L ( I )

=
=

ZBRLK
ZAIMK

l BKR L ( I )

ZAKIM( I)

ZBIMK = Z BK 1M ( I )

0

REAL

=

Z AR LK+Z BR LK

AIMG

;;:

ZAIMK+ZBIMK

RLNUM

=

ZPRL*REAL- ZPIM*AIMG

')

,')

')

;;.ij:.",

RLNUM

o

RLNUM+2.0*(ZARLK*ZBRLK-ZAIMK*ZBIMK)

RlDEN

=

2.0* lPRL+REAL

-u9-

II.! 1

I'!

c

ANMIN

=
=

ANMIN

= ANMIN+2.0*(ZARlK*ZBIMK+ZAIMK*ZBRLKJ

DENIM

2.0* ZPIM+AIMG
ZPIM*REAL+ ZPRL*AIMG

DEN

= 1.O/(RLDEN*RlDEN+DENIM*DENIM)

ZRL

= (RLNUM*RLOEN+DENIM*ANMIN>*DEN
= (RLDEN*ANMIN-RLNUM*OENIM)*OEN

lIM

/

= ZBRLK-ZARlK
= ZBIMK-ZAIMK

REAL
AIMG

=
=

RlOEN
DENIM
DEN

ZPRL#REAL- ZPIM*AIMG
ZPIM*REAL+ ZPRL*AIMG

= 1.O/(RlDEN*RLDEN+DENIM*OENIM)

A

= VPRL*RLNUM-VPIM*ANMIN

B

= VPIM*RLNUM+VPRl*ANMIN

VRl :

(A*RLOEN+DENIM*B)*OEN

= (RLDEN*B-A*DENIM)*DEN
REAL = l.O/RA(K)

VIM

= RB(K)

AIMG
4022 DEN

l.O/(ZRl*ZRL+ZIM*ZIM)

c

RLNUM

= 1.O+REAL*AIMG+AIMG*ZRl*DEN

ANMIN

=

RLOEN

= 2.0*REAL+AIMG*REAL*REAL+(ZRl*REAL*AIMG+ZRL>*DEN

DENIM

=

DEN

= 1.O/(RLDEN*RLDEN+DENIM*DENIM)

AIMG*ZIM*OEN

(REAl*AIMG*ZIM+ZIM}*DEN

ZPRl

~

(RLNUM*RlDEN+OENIM*ANMIN)*DEN

ZPIM

=

(-RLDEN*ANMIN+RLNUM*DENIMJ*OEN

= 1.0/ (ZRl*ZRL + ZIM*ZIM)
VPRL = VRL+VRL*REAL*AIMG+(VRl*AIMG*ZRL+VIM*ZIM*AIMG)*OEN
VPIM = VIM+VIM*AIMG*REAL+(VIM*AIMG*ZRL-VRL*ZIM*AIMG)*OEN
DEN

o

263

I

I

I

II
Iii

I:

0

1

,.,j

W $ rim Mrirzw

4002 RETURN

END

o

o
-51 . .

==:WJ£iiiSiliii1JS:S:S(t!kiil$ X(, ti ; Q '

... ,- ..•".-.•.•"...• ,_._I..• _"- . . . -~.~'-······"·····-

o

SUBROUTINE ORDER

C

COMPUTES TOTAL COMPLEX IMPEDANCE FOR BASIC SECTION IMPEDANCES

C

ZA AND ZS FROM INDIVIDUAL ORDERS.

lRA(S), RB(5), IORDR(5), ZAKRL(3), lBKRL(3), ZAKIM(311 ZBKIM(3)
COMMON C, R, AL, MP, MQ,

RA, RB, ZAKRL, ZBKRL, ZAKIM, ZBKIM, YARL,

lYBRl, VAIM, YBIM, ZARL, ZBRL, ZAIM, Z81M, F, F2, IREe, ZPRl, ZPIM,
2 VP RL, VP 1M, ZR L, Z 1M, VRL, V 1M, K,

I,

I P UNC, RA0, R B0, DEN, L,

3INDX, REAL, AIMG, RLDEN, ANMIN, RLNUM, DENIM, A, B, QUAN, IORDR,

4lETTR, VARl, tORD, ZARLK, lBRLK, ZAIMK, ZBIMK,NSECT, NT
COMMON XK, RK, lOR, lOI, VDR, VOl, BETA, DB, XIMAG
IVAL ;: 1-1

IF(IVAL) 5001, 5002, 5001
5002 ZAKRL(I) = ZARl

IAKIM(I) :;: ZAIM
lBKRL(I) ::: ZBRL
Z8K 1M ( I) ::: Z B 1M

GO TO 5006
5001 IF(I-(I/2)*2} 5007, 5004, 5007

5004 ZAKRl(I)

= ZARL+lAKRL(IVAl)

lAKIM{I)

= ZAIM+ZAKIM(IVAl)

ZBKRL(I)

=

ZBKIM(ll

= lBIM+ZBKIM( IVAl}

ZBRL+ZBKRl(IVAL)

GO TO 5006

5007 RlNUM

= ZAKRL(IVAL)

DENIM

= ZAKIM(IVAL)

QUAN =RLNUM*RLNUM+DENIM*OENIM
B = YARL*QUAN+RlNUM

?
I'fII

{~ r'

V

t.t

.. 52-

o

4C)

A

= YAIM*QUAN-DENIM

DEN

~

1.O/(8*B+A*A)

ZAKRL(I)

= S*QUAN*OEN

ZAKIM(I)

= -A*QUAN*OEN

RLNUM • ZBKRL(IVAL)
DENIM. lBKIM(IVAL)

QUAN =RlNUM*RLNUM+OENIM*OENIM
B

= YBRL*QUAN+RlNUM

A • YBIM*QUAN-OENIM

DEN

= 1.O/(S*B+A*Al

ZBKRL(I) • B*QUAN*OEN
Z8KIM(I) • -A*QUAN*OEN
5006 RETURN

END

o

266
-53-

L .£itau

a

&*144,4$1.4

o

SUBROUTINE TERMIN

C

CALCULATES IMPEDANCE AND VOLTAGE AT INPUT TO

I~PUT

TERMINATION.

DIMENSION C(6,5,3), RC6j5,3), AL(6,5,3), MP(5,3t, "0(5,3),
iRA.'), R8(S), IOROR(5), ZAKRl(3), ZBKRL(3), ZAKIM(3J, IBKIM13)

C, R, AL, HP, MQ, RAt Ra, ZAKRl, ZBKRL, ZAKIM, ZBKIM, YARL,

tOMMO~

lYBRl, VAIM, YBIM, ZARL, ZBRl, ZAIM, 18IM, F, F2, IREe, ZPRL, ZPIM,
2VPRL, VPIM, IRL, lIM, VRl, VIM, K, I, IPUNC, RAO, RBO, DEN, L,
31NDX, REAL, AIMG,

RLOEN, ANMIN, RlNUM, QENIM, A, 8, QUAN,. IORDR,

4LETTR, VARl, lORD, ZARLK, Z8RLK, ZAIMK, ZBIMK,NSECT, NT
COMMON XK, RK, lOR, lOl, VOR, VOl, BETA, DB, XIMAG
GO TO (5,6), LETTR
5 ZTRL

= ZPRL

ZTIM

= ZP 1M

GO TO 1
6 ZTRL

1TIM

ZRL

:I

= ZIM

c
C

USE ORPTZ TO CALCULATE INPUT TERMINATION IMPEDANCE.

C

7 CAll DRPTZ

Z8TRL •

lT~l+ZARL

= ZTIM+ZAIM

zaTIM
RI(

II:

ZARL

XK

==

lAIH

REAL

&I:

VPRl*ZBTRL-VPIM*ZBTIM

XIHAG- VPIM*Z6TRL+VPRl*ZBTiM

OEN • ZTRl*ZTRL+ZTIM*ZTIM

267
I

1

1 F eDEN)

1, 2, 1

-54-

\.\
.•

\

I'

z&s

4C) ,

HI

en

2 PUNCH 101

101 FORMAT (41HERROR .DENO" I-NATOR IN TERM IN eQUAL TO ZERO)

PAuse
c
C

CALCULATE INPUT VOLTAGE REQUIRED TO PRODUCE SPECIFIED OUTPUT

C

TERMINATION VOLTAGE.

c
1 VKRL

a

(REAl*ZTRL+XIMAG*ZTIM)/OEN

VKIM =

(ZTRL.XIMAG-ZTIM~REAL)/OEN

VPRL

z;

VKRl

VPIM

I:

VKIM

RETURN

END

o
-ssdAiM

., .•...,•..,.,'.••"•••.~......c.-..._ _,

o

SUBROUTINE LADDER

lRA(S), RB(S), IORDR(SJ, ZAKRl(3), ZBKRl(3), ZAKIM(3), ZBKIM(3)
COMMON C, R, ALt MP. HQ, RA, RB, ZAKRl, lBKRL, ZAKIM, ZBKIM, YARl,

lY8RL, YAIM, YBIM, ZARl,ZBRl, ZAIM, ZBIM, F, FZ, tREe, ZPRL, ZPIM,
2VPRl, VPIM, ZRL, lIM, VRL, VIM, K, It IPUNC, RAO, RBO, DEN, L,
3INOX, REAL, AIMG, RlDEN, ANMIN, RLNUM, DENIM, A, S, QUAN, IOROR,
4LETTR, VAR1, lORD, ZARLK, Z8RLK, ZAIMK, ZSIMK,NSECT, NT
COMMON XK, RK, lOR, 101, VOR, VOl, BETA, DB, XIMAG
C

COMPUTES RECURSION EQUATIONS FOR LADDER SECTIONS.

C

CALCULATES ZRL, lIM, ZPRL, ZPIM, VRL, VIM, VPRL, VPIM.
ZARlK • ZAKRL(I)

ZAfMK

= ZAKIM(I)

ZBRlK

= IBKRL(I)

o

ZBIMK = ZBKIM(I)
VPRL

:II:

VPIM

= VIM

RlOEN

VRL

= ZARlK+ZRL

DENIM • lAIMK+ZIM
DEN

= RLDEN*RLDEN+DENIM*DENIM

RlNUM
XIMAG

= ZARlK*ZRL-ZAIMK*ZIM
= ZAIMK*ZRL+ZIM*ZARlK

RNUM

= RlNUM*RlOEN+XIMAG*OENIM

XMAG

=XIMAG*RLDEN-RLNUM*OENIM

IF(OEN) 1, 2, 1
2 PUNCH

101

101 FORMAT (32HERROR,ZERO DENOMINATOR IN LADDER)

2 6 ~..l

PAUSE

-56-

l~

!I
-

--~-~-----

sr

c:;

1 ZPRL • RNUM/DEN

ZPIM
, ZRL

ZIM
DEN

XMAG/DEN

2&

= ZPRL+ZBRLK
= ZPIM+ZBIMK
= ZPRL*ZPRL+ZPIM*ZPIM

IF(DEN)

= 1.O+(Z8RlK*ZPRL+ZBIMK*ZPIM)/DEN

3 REAL

=

XIMAG

VRL

3, 2, 3

(ZBIMK*ZPRL-ZPIM*ZBRLK)/OEN

= VPRl*REAL-VPIM*XIMAG

= VPRL*XIMAG+VPIM*REAL
VPRL = VRL

VIM

VPIM

C"
)

o

=

VIM

RETURN
END

270
-57-

auZS4iSUili h:.uti Zi4 ; _

C

SU8ROUTINE

ORPTZ

CA~tULATES

IMPEOANCE AND ADMITTANCE FOR A TWO-TERMINAL IMPEDANCE

c

iOROER).

C

IE. YARL, VAl", rBRl, Y8IM, ZARL, ZAIM, IBRL, ZBIM

1£. YARl, VAIM, VBRl,
OIMENSION C(6,5.3),

Y~IM,

Rt~",3),

ZARL, ZAIM, ZBRl, 181M
AL(6,5,3), MP(5,3), MQCS,3),

lRA(5), R8(S,t, IORDRt5), ZAKRL(3', lBKRL(3), ZAKIMC3!, ZBKIM(3)

COMMON C,R9 AL, HP, MQ, RAt RB, ZAKRL, ZBKRL, ZAKIM, Z6KIM, YARl,

lY8Rl, YAIM, YBI", ZARL, ZBRL, ZAIM, lSIN, F, F2, IREe, ZPRL, ZPIM.
2VPRL, VPIM, ZRl, lIM,

VR~,

VIM, K, I, IPUNC, RAO, RBO, DEN, L,

3JNDX, REAL. AIMG, RlO£N,ANMIN, RlNUM, DENIM, A, 8, QUAN, IOROR,

4LETTR, VAR1, lORD, ZARlK, Z8RLK, ZAIMK, 18IMKtNSECT, NT
COMMON lK, RKt lOR, lOI, VOR, VOl, SETA, DB,

IVAL

~IMAG

MPCK,!)

I:

G

'tARt- 0.0
.,AIM

0.0

c

L • 1
11 IF CIVAL-L) 9, 10, 10
10 INDX

III

.L* 2-1

VARl •

R'INDX,K~I)

QUAN

F2*tCINOX,K,I)

c

IF CQUAN) S, 4, 3

4 QUAN = AL(INOX,K,I)*F
TO

GO

J QUAN
~

~
·(Al(INDX,Kfl)-l~O/OUAN)*F

OEN • 1.O/(VAR1*VAR1+QU4N*QUAN)

YARL = YARL+VAR1.OEN

YAJM • yAIM-QUAN*DEN
1.

c

L+l

271
-$8-

tt

o

..

*=

GO TO 11
~

9 OEN

VARL*VARL + YAIM*VAIM

I F (D EN)

12 t

1 3 ,. 12

= l.O/DEN

12 DEN
13 ZARl

a

YARL*OEN

ZAIM

II:

-YAIM*OEN

IVAL

= MQ(K,I)

YBRL :: 0.0
YSIM ::: 0.0
l

1

lit

16 IF (IVAL-L) 14, 15, 15
15 INDX

o

= 2*L

VARI ::: R(INDX,K,I)

= F2*C(INDX,K,I)

QUAN

IF(QUAN) 6, 7, 6
7 QUAN : AL(INDX,K,I)*F
GO TO 8

6 QUAN =(Al(INDX,K,I)-l.O/QUAN)*F
8 DEN

R

1.O/(VAR1*VAR1+QUAN*QUAN)

YBRL ::: VBRl+VAR1*OEN
Y81M ::: YBIM-QUAN*OEN
l

= L+l

GO TO 16

14 OEN =

Y8RL~YBRL

+ VBIM*VBIM

IF (DEN) 17, 18, 17

o

17 DEN = 1.O/DEN
18 ZBRL ::: Y8RL.OEN
ZSIM ::: -YBIM*OEN

272
-59-

o

RETURN
END

o

273

o
I

-60-

il
I:

3.'

o

1620 USERS GROUP
WESTERN REGION MEETING
June

o

18, 1964

FORTRAN II - DEBUGGING TECHNIQUES AND AIDS

Leon P. Goldberg
Technical Staff
Princeton University

o
.=_.UiMi,a:eit:

~I

I
I

I

!

o

FORTPAN II

fLo A.--t \'t"\C:r

!.

\'\'r"\v,\)'i'; i\K\":.

NON RET-sOCABLE SUBROUTINES

.Address

Subroutine na.me

Function

01510

SHe

r/o
r/o
rio
r/o
r/o
r/o
rio

01768
03158
03182
01418
01574
00986
01022
01058
01800
02052
02152
02380
03280
03300
06020
06052
06528
07316
07348
07416
07440
07484
07570·

07604
07698
.07932 .
08152 .

. 08586
09044
09356
09504

09528
09740

.09808
09856

09952
10000
Q(,""(to

Otz.Sf.:,
Oo+~5

COi'.fPLT
RJi...TY

RAPT
Men
SLlillH

HATY
ltlAPT
\-lACD

HTYPE
REDO
fu,~

ITYPE·

FTYPE
ETYPE
XTlPE
ATYPE
H.4.TRIX
FXA

FXSR
FXS

F.XH
FXD
F'LDR

RSGl{
FLOAT
FIX
·FIXI

FAX!
FAX8
FT1FAC

I/O

r/o

Irollertth conversion
Multiple field specs.
Multiple parenthesized specs.
I specification
F specification
E specification
X specification
A specification
Reading arrays

I+J
-(J-l<-K)+I

I-J
r-t:-J

r/J
l/(r/J)
-I or -A

A==I·

I=A
I**J
A~~-I

A~"*B

FAC to A

FSB
FAD
FSBR
F1vrP

A+B
-(P.*B)+C
A-X-B

FD

AlB

FDVR

TOFAC

C

A-B

I/(A/B)

A to FAC

T~\<':.t

"?~~?EJ\\ (\\~~)
t=t\~

0
275

'bin

o

:r.

- up.

INTERACTION OF tOMMON AND EQUIVALENCE IN UNDIMENSIONED VARIABLES.
COfvlMON X, Y, Z
EQUIVALENCE (X,A),(Y,B,C),(Z,L)

C

A=4.15273 LJ.1
8=2."k A
R=X+2.

S=B+R

Z=X+Y+S

STOP
END
TURN SW 1 ON FOR SYMBOL TABLE, PRESS START
11043 41527301
110 51 2~1(100Qj01
59999
X
59999
A
59991
59991
59991

Y
B
C

59983
S9983

Z

11~159

11067

L

R

s

END OF PASS I

o
276

c

COMMON STORAGE IN DIMENSIONED VARIABLES.
Y(2 ,5), Z(3 ,4,5 )
CO/lIMON x, Y
STOP

o1t1E NS ION X(5)-,

END
TURNSW 1

ON FOR SYM~OL
59959
. X 59999
59859
y -5991~9
11045
Z 11635
END OF PASS- I

TA8[E,PR~SS

o

START

Oi
277

1et

EXAMPLES TO DEMONSTRATE THE COMPLEX INTERACTION OF EQUIVALENCE AN·D
COMMON STORAGE ASSlGNMENTIN DIMENSIONED VARIABLES.
DIMENSIONX(5), Y(2,5), Z(3,4,S)
COMMON X
.
EQUIVALENCE (Y,Z)
STOP
END
TURN SW 1 ON fOR SYMBOL .TABLE, PRESS START
X ~9999
59959
Y 11135
11045
Z 11635
11045
END OF PASS .1

ENTER

o

PRESS START
DIMENSIONX(5), ·Y(2.,5), Z(3,4,5)
COMMON X
EQU I VALENCE. (X(S), Y(10) ,Z(60»
STOP
END
TURNSW 1 ON FOR SYMBOLTABLE,~?~ESS START
SOURCEPROGRAM~

X ~9~99
Y S9999
~9409
Z 59999
END OF P'ASS' I

39959
59909

ENTER SOURCE PROGRAM,' PRESS START .
DIMENSION XeS), Y(2,S), Z(3,4 5)
EQU I VALENCE· . (y( 10) ,X(5},Z(60~)
STOP
END
TURN SWl ON 'FOR SYMBOL TABLE, PRESS START
T104SZ11635
11545
Y 11635
11595
X 11635
END OF PASS I '

o
27~
• _ _ Ail.

C

EXAMPLES TO DEMONSTRATE THE COMPLEX INTERACTION OF EQUIVALENCE AND'

COt~i''10N STORAGE ASSfGNt~ENT !t4 DfHENS!ONED VARIABLES.
D f ME ~!S ION X ( 5 ), Y ( 2 , 5), Z (3 ,4, 5 )
EQU r VA LE f\ CE ( Z ( 6 ~1 ) ,X (5);; Y( 1 0 ) )

C

0.

STOP
END
TURN SW 1 ON FOR SYMBOL TABLE, PRESS START

Z 11635
X T1635
Y 11635 .

11045

T1595

T1545
Er~D

OF PASS I

ENTER

SQURCEPROGRAM, PRESS START
DIMENSION X(5)~ Y(2,5), Z(3,4,5)

c0 r!!

TF
BNF
CF
TF
A(v1
TF
8NF
CF
TF
AM
TF
BI\JF
CF
TF
Alv1
BT
BT
BT
BT
BT
BT
B

5

XPGM-l,5,010
A,XPGH-l,Olll
*+36,A,()l
A, ,0
A,A,Olll
XPGlvi-I , 5, 010
B, XPG~'i-l ,0 III
~~+36,B,01

B, ,0
B,B,0111
XPGf 1-1,5,010
C,XPGt"i-1,0111

o

v

~,"+36,C,Ol

C, ,0
C,C,0111
XPGM-l,5,010
D, XPG~,'i - 1 , III
*+36,0,01
D, ,0
0,0,0111
XPG("'1-1 , 1 , 010
TOFAC,A,l
FAD,B,l
t=RrvlFAC, C, 1
TOFAC,A,l
FSB,B,l
FRfviFAC, 0, 1
XPGM-l,,06

°

I

I'

FLAG CONVENTION •••••••••••

°

IF P IS RELOCATABLE, FLAG OPERAND IS
IF Q IS RELOCATABLE, FLAG OPERAND IS 1

NORMAL FLAG OPERANDS ARE STILL IN EFFECT FOR
IMMEDIATE AND INDIRECT ADDRESSING.
FLAGS ARE USED OVER THE OPERATION CODE TO DENOTE RELOCATION TO
THE LOADER. THESE FLAGS DO NOT ALTER THE OPERATION OF
THE INSTRUCTION.

0 (,\
,1;1

T EST

c
C

10

P i-< UC; R Af-/I

FUR

1,4 Lt· 3

[) R If,! T F 1<'

P un,

S p.1

(X)

\I

s. x.

U I f'/I EJ\j S I U hi X ( 5 00 ) , Y ( ~ 0 0 )
P R II"lT 1 0
F CJ k i·1 A T ( 1 H 1 )
T=O.
DU 1 I=1,200
X ( I ) =T
Y(I)=SINF(T)
T=T+.01-::-3.14159

1 C 0 i\! T I [\! U C
PAUSE
CALL PLOT (X, 10., U., 5, Y, 1., -1.,10,2(0)
STUP

E 1\1 [)

o

o
_

:a:tii2i4iIiJ:

C

FURTkt\f\i SUBRUUTli\]E FOR 1443 t>RII\ITER PLDTTI/\jG,

C
C

B Y L.

o

H[j F F [i! i\ ,\J, GUGG E i\J H F I i'v1 L I~ BS •

SUBRUUTINE PLUT(X,XMAX,XMIN,NX,Y,YMAX,YMIN,NY,N)
DIMENSION OUMMY(2),OUTPUT(102),X(2),Y(2)
XCHtd~=. 20
YCHAk=.71
CHAR=.14
BL ,Lj,I\lK=O.
XNU=100.
NOX=XNU+1.
YL AS EL=Yt'lAX
DX=(XMAX-XMIN)/XNO
DY=(YMAX-YMIN)/50.
MOVE MAX DOWN BY ONE-HALF bOX ••••
YYfll,AX=YHAX+. 5{~OY
XXr'HI\J=Xfv1Ij\J-. 5~~DX

C
C

KY=O
i\IX l=/\')X+ 1
DO 1 1=1,51
C
CALL INIT(OUTPUT,SLANK)
DO III II2=I,NUX
III
OUTPUT ( 112) =BLAhli<
C
CALL GRIO(OUTPUT,DX,OY,NX,NY,KY,I,XCHAR,YCHAk,IND)
IND=O
IF(I-1-50*KY/NY)211,222,211
222
OD 332 JJ=l,NClX
332
OUTPUT(JJ)=XCHAR
1 ~JD= 1

211
Lr·44

C

2221
3331

1121
H

10
2
11

3

12
1

KY=KY+l
DO 444 JJ=l,NXl
12=( (JJ-l)~~(NOX-l) )/NX
OUTPUT(12+1)=YCHAk
ZI=I
UP=YYMAX-(ZI-l.)*OY
OUWI\J=UP-DY
CALL FINDY(X,Y,UP,OOWN,OUTPUT,N,DX,Dy,XMAX,XMIN,CHAR)
DO 1121 IF=l,!'\')
IF(Y(IF)-UP)2221,112l,ll2l
IF(Y(IF)-DUWN)112l,333l,333l
CUNT I j\jUE
JJ=(X(IF)-XXMIN)/UX
JJ=JJ+l
DUTPUT (J"J) =CHAR.
CONTINUE
IF (U\jD) 10, 10, 11
PRINT 2, (OUTPUT(J) ,J=l,f\!UX)
FURMAT(12X,50Al,5lAl)
GO TU 12
PRINT 3,YLABEL,(OUTPUT(J),J=l,NOX)
FORMAT(lX,EI0.3,lX,50Al,51Al)
YLABEL=YLABEL-DY
C(Ji'\JTIi\JUE
RETURN

o

EI"~O

11
----.---.---~.-.-

J".rp*rrIlUIZ'N"

..

liz

M

FDRTRAI\J I I S P S S lJ BR0 UTI [\1 F. S, L. H[) F Fiv) A'\1, GlJ GGEf\I HE I 1\1 l 1\ b S •

0

1

ASS EfVI Bl Y Af\J D F I [\1 ALP HAS e UF S P S SUB S. FIJ R Fj\\ I I •
1) USE 1620/1710 SPS TO ASSEMBLE AND COMPRESS THE SPS PROGRAM.
2) ReMUVE THE FIRST TWO (2) AND THE LAST SEVEN (7) CARDS FROM THE
COM P f<. ESSE D DEC K• (T HIS Dn ES i\1 0 T I f\I CLI J DF THE Th' n Rl A. 1\1 K CAR 0 SAT THE
ENO OF THE DECK)
3) AOD HEADER CARD AS NO.1.
4) ADD TRAILER CARD TO END OF DF.CK.
5) CORRECT DSA'S , IF ANY,USED IN THF SPS PROGRAM,nTHERWISE, GO TO 7.
6) PUNCH A FlAGG~D ZERO IN CUlUMN 62 OF All ORJECT DECK CAR[lS
PRODUCED BY DSA'S IN SPS PROGRAM.
7) CHECK FOR RElOCATABlE CONSTANTS, IF NONE, THEN GO TO 9.
8) PUNCH A FLAGGED 1 IN COLUMN 62 OF All CONSTANTS NOT TO BE
RELOCATED.
9) PUN CH NE\Ai CAR D I\i O. I 1\1 TRAI l ERe ARn T[) C(1 1\1 TIN lJ F S FqUE 1'-1 C Ir'\! G•
10) THE DECK CAN NOW BE USED WITH A FORTRAN CALL STATEMENT.

THE HEADER CARD ••••••••••••••••••• •••••
COlS. 1-12

C\

COlS.
COlS.
COlS.
COlS.
COlS.
COlS.

13-20 .
21-22
23-24
25-62
63
64-80

SUBROUTINE NAME IN TWO-DIGIT ALPHANUMERIC FORM WITH FLAG
OVER HIGH ORDER DIGIT AND RIGHT JUSTIFIED.
BLANK
FF, lENGTH OF FLOATING MANTISSA, FLAG OVER HIGH ORDER DIGIT.
KK, lENGTH OF FIXED MANTISSA, FLAG OVER HIGH ORDER DIGIT.
BLANK
RECORD NARK (0-2-e)
BLANK, EXCEPT FLAG IN COL. 7A

THE TRAILER CARD •••••••••••••••• ••••••
COlS. 1~62
COlS. 63
COlS. 64-80

BLANK
FLAGGED 1
BLANK, EXCEPT FOR CARD NO. IN COL. 78-80.

o
_au

Ztili.l2UC&fU:;

a:iII $II (J&\l Jf

•

-- - '••;.,:",:..j~ ... .:i:.~~~"~,
----------,,-'---~".''-~

1:\

,

PLOT FOR 1443 PRINTER, L. HOFFMAN GUGGENHEIM LABS.

*
*
*

I

I

!

AN EXAfvlPLE OF AN SPS SUBROUTINE FOR FN I I

.

~-

11036
11040
11045
11050
11055
11060
11065
11070
11075
11080
11085
11092
11094
11106
11118
11130
11142
11154
11166
11178
11190
11202
11214
11226
11238
11250
11262
11274
11286
11298
11310
11322
11334
11346
11358
11370
11382
11394
11406
11418
11430
11442
11454
11466
11478
11490
11502
11514
11526
11538
11550
11562
11574
11586
11598
11610

4/24
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO

00005
00005
00005
00005
00005
00005
00005
00005
00005
00005
00007
J1
KO
tvlfvl

L3
KO
Jl
KO
lvJM

L3
KO
J1
KO
MM
L3
KO
Jl
KO
~~111J

L3
KO
J1
KG
fvlM

L3
KO
Jl
KO
M~I

L3
KO
J1
KO
MM
L3
KO
Jl
KO
MM
'L3
KO
J1
KO
MM
l3

11093
11045
11154
11045
11045
11093
11050
11214
11050
11050
11093
11055
11274
11055
11055
11093
11060
11334
11060
11060
11093
11065
11394
11065
11065
11093
11070
11454
11070'
11070
11093
11075
11514
11075
11075
11093
11080
11574
11080
11080
11093
11085
11634
11085
l.

000-5
1109L
11045
00000
1104N
000-5
1109L
11050
00000
1105000-5
1109L
11055
00000
1105N
000-5
1109L
11060
00000
1106000-5
1109L
11065
00000
1106N
000-5
1109L
11070
00000
1107000-5
1109L
11075
00000
11071\J
000-5
1109L
11080
00000
1108000-5
1109l
11085
00000

AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTLJ
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO
AUTO

PLOT
X
XHAX
XMIN
NX
Y
Yfl-1AX
YfVl IN
NY
N
*
START

DORG
OS
OS
OS
OS
OS
DS
OS
OS
OS
OS
OS
AM
TF
BNF
CF
TF
AM
TF
BNF
CF
TF
A~'l

TF
BNF
CF
TF
A~1

TF
BNF
CF
TF
AM
TF
BNF
CF
TF
AM
TF
BNF
CF
TF
AT·1
TF
BNF
CF
TF
At4
TF
BNF
CF
TF
AM
TF
BNF
CF

11036
5
5
5
5
5
5
5
5
5
5
7
END OF ARGUMENT ADDRESSES/
START-l,5,010
X
,START-1,01ll
,01
*+36,X
,,0
X
,X
X
,0111
START-1,5,010
X(v;A X ,START-1,0111
*+36, XfvJAX
,01
XiVlAX , ,0
XfvlAX , Xf'1AX
,0111
START-l,5,01O
X/\'I I I"
,START-1,Ol11
*+36,Xr'1!N ,01
XMIN , ,0
Xivi IN
, Xf'vl IN
,0111
START-l,5,010
NX
,START-1,0111
,01
*+36,NX
, ,0
NX
,NX
NX
,0111
START-1,5,010
Y
,START-1,0111
,01
*+36,Y
, ,0
Y
,Y
Y
,0111
START-1,5,010
Yt-1AX ,START-I,0111
*+36,YMAX ,0 1
YMAX , ,0
yrv1AX , Yf~AX
,0 111
START-1,5,010
yrvJIN ,START-l,0111
*+36, yr-1 IN ,0 1
Yjl/lIN ,,0
YMIN ,Yf'1IN ,0111
START-1,5,010
NY
,S TAR T-1., III
,01
*+36,NY
, ,0
NY
,NY
NY
,0111
START-1,5,010
,START-1,0111
N
,01
*+36,N
307
N

0

Ie

°

,,°

0

1
....-..---..-~~~~~..............--.-------~~-~---

11622
11631.;·

0

1

11646
1165 i j-

i< II
Jl
1,:9

T~

1\:

!\. tJTl.l

l . ! 'i

ST/J.L~.T-l,?,UlU

12 {) 11.;·

UUUUU

/\UT l.,

/\ IZ Ii t.1 i· i; ,
H
Di) l~. c; .;:--3
S Y:·it'.iIL

, ".J
j

I JT (l
.~:~

FF

3/17
3/17

KK

1)5

, :)

O()Ll'OS

f= t.',C

!)S

, it K ~)

01402
016:32

(lU()()O

uoouu

LrJ 2."3
Lf/2. 3

DS
US

,1(')';7

U2336

UU()f.)O

U2112
01772
0135H

OO()UU
(JOO()O

uouoo

03u()2

OUO()()

02 Lj·30

uoooo

02336

()OOOO
00000
00000

U3'+3 i +

i)S
DS

,2336
,2117
,1772

i)S

,

FIX

't/23
4/"2.3
4/23

US

,3 OC) 2

DS

,2430
,2336

US
DS
DS
DS
DS

L-:/23

CflHPLT

DS

,56~)O

uooo:.:;

4/23

Fj'"T

00003

4/23

DC
DC
DC
DC
DC
DC

~ , 5 -( C) 4
3,002
5,7,')50
3,010

4/23
4/23
4/23

00003
00005
00012
U0102
00001
00005

Lt

3/13
3/22
3/22
3/25
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22

OOOOLt

00003
OU005
00005
00(:)10
00010
00010
00005
00008
00002
00010
00010
00010
00010
00001
00005
00008
00002
00008
00002
00008
00002
00005
00010
01314

/23

"-/2'+

-l}*~:.-::--~

**eJ~~--::-

J2038

3/22
3/22
3/22
3/22
3/22
3/25
3/22

DC
DC
UUf'.' OUT D.t·.C
OUTPUT D.l\ S
Df-IC
KEDO

I

JJ
112
12

IF
ZI
UP

o[l\tI}i\1

COUNT
1-11-\ L F 1
HALF
YYHAX
DY

5,62HO
12,
102
1, •

DS

4
3

DS

5
5
FF
FF
FF

DS

5

DC
DC

B,5()OOOOOO
2,00
FF
FF
FF
FF
1
KK

DC

8,10000000

DC

2,03
8,10000000
2,01

[) i\l E 1

DC

ClI'JE

DC
DC

F1
FIFTY
KY
XXfv1 IN

2,03
5,57 C)L'r
3,OOZ

K'/i'-

OS
DS
OX
OS
YLABEL OS
I h!\)
DS
NUX
OS
Xf\IOl
Xf\!(l

,6066

DS
DS
DS
OS
DS
US

DC
OS
DS

AR.OUND BTn

H I:: ~~.

, 131 /j-

4/23

~·/Z3

ST;\i':TS

,321H
, ::iOIH

00005

i\ !'iI ) Cll

, 3 Lt3 <';-

DS
DS

00003
00002
00005

r.-:

,30 1: 6

TY
S\'IC

oouoo

i\UL

1 .:)?
-, ('".:.

I·.! /\

00000

1P

1)5

FLDi\T
Fi·:F/.I.C
.FSfl ,
FlI.D
FSbl-(
Fi·.ip
FDV
FDVr<
Tf"lF t\c

T

, iLI-U2

R S(;I\

4/2.3

4/23

OOOOU

IlbrA

C r-

F)(l)

41 Z:j
L1·I 2 3
LI-/23
5()12
1.1-/23

00000
00000

0131 LI0502£3
06066
0565U
11658
11661
11666
11669
11671
11676
11679
116b7
11711
11<,)15
11920
11924
11 '127
11932
11937
11947
11957
11967
11972
11980
11982
11992
12002
12012
12022
12023
12028
12036
12038
12046
'.2048
12056
12058
12063
12073
1207'+

!.~/:~ 3
1.1-/23

Tf<,:~

US

,(1

, 1 ()

"3/1-(

030<,;-6
U321d

0

i\UTi)

U()U-;~

UUUUO
(Juno:)
UUUUU

OUU l):;

OJ

11 U h\i

1109~~,

/~

OCOlU

,0111

110d:J

8,50000000

2,02

KK
FF
TOFAC, Xi\![), 17

308

j:

·"" .......

.!

•

'"I t;: .......~" .• ~~~", ...••

............".... .......
~."

,~''".~,

lilil

"I
~I~I

12086
12098
12110
12122
12134
12146
12158
12170

1P
17
K6
2P
1P
2P
1P
1P

02430
01772,
12028
01314
01402
03002
03218
01402

J2048
000-0
00485
11070
J2022
11075
J2058
J2002

12182
12194
12206
12218

2P
2P
1P
1P

01314
03002,
03218
01402

11050
11055
J2038
J2012

12230
12242
12254
12266
12278
12290
12302

1P
2P
1P
1P
1P
2P
1P

03046
02336
01402
01314
03046
02430
01402

J1982
11055
J2073
J2002'
J1982
11070
J1992

12314
12326
12338
12350
12362
12374
12386
12398
12410
12422
12434

"J6
J6
J6
JO
KJ
KJ
J6
J1
KM
M6
J5

12063
11920
11927
11972
11972
11972
1197K
11927
12028
12350
12023

0-000
00-01
00-01
J1711
11927
11927
000-0
000-1
11927
01300
00000

12446 J3
12458 32
12470 26
12482 ' 2P
12494 12
12506 2J
12518 14
12530 M7

12063
00095
00485
0'1652
00485
00485
00485
12662

-00500000
00099
11080
000-1
11920
0-000
01200

12542
12554
12566
12578
12590
12602
12614
12'626

J6 11924
JO 11972
KJ- - 11972
KJ 11972
J6 1197K
Jl 11924
KM 12028
M6 12554

00-01
J1711
11924
11924
OOOKO
000-1
11924
01300-

1263~8

J5
J1

12023
12063

00001
000-1

12662 J6
12674 20
12686' 12

11924
00485
00485

00-00
12028.
000-1

12650

3/22
3/22
3/2,2
3/22
3/24
3/22
3/22
3/24
3/22
3/22
3/22
3/22 '
3/24
3/22
3/25
3/25
3/25
3/25
3/22
3/22
3/24
3/22
3/22
3/22
3/25
3/22
3/22
3/22
3/22
3/22
3/24
3,/24
3/22
3/22
3/22
3/23
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/25
3/22
3/22
3/22
3/22
3/22
3/24'
3/24
3/22
3/22
3/22
3/22
3/22
3/22
3/25

BlM
BTM
TF
,BT
BTM
BT
BTM
. BTM

*

*

*

FAD,ONE,17
FIX;0,10
NOX,FAC,O
TOFAC,YMAX,l
TRACE,YLABELj17
FSB,YMIN,l
FDV,FIFTY,17
TRACE,DY,17

BT
BT
8TM
BTM

TOFAC,XMAX,l
FSB,XMIN,l
FDV,XNO,17
TRACE,DX,17

BTM
8T
BTM
BTM
BTM
BT
BTM

FMP,HALF,17
FSBR,XMIN,l
TRACE,XXMIN,17
TOFAC,DY,17
FMP,HALF,17
FAD,YMAX,l
TRACE,YYMAX,17

0

KY,0,08
1,1,09
112,1,09
COUNT,OUTPUT,017
COUNT,II2,01
COUNT,II2,01
COUNT,0,0610
112,1,010
NOX,112,01
'c
BNN RTN111,,0
TDM IND,Q,O
GR I D•••' ••••••
KY,50,0711
MM
SF
99-KK+1
FAC,99
TF
FXD,NY,l
BT
FAC,1,10
SM
FAC,I,1
A
FAC,0,8
eM
BNE 1211,,0

TFM
TFM
RTN1
TFM
RTN111 TFM
A
A
TFM
AM

*

*1222

TFM
RTN332 TFM
A
A
TFM
AM
C
BNN

*
*1211

TOM
AM

TFM
RTN444 TF
SM

0

JJ,1,09
COUNl,OUTPHT,017
COUNT,JJ,Ol
COUNT,JJ,Ol
COUNT,20,0610
JJ,1,010
NOX,JJ,Ol
RTN332,,0
INO,l,O
KY,1,010
JJ,0,09
FAC,NOX,l
FAC,1,10

3U9

0

·"W"ri'flftnml'Bwn'''" t

0

7

12698 2L
12710 32
12722 26
12734 . 2P
12746 JO
12758 Kl
12770 Kl
12782 Jl
12794 J6
12806 J1
12818 KM
12830 M6
12842
12854
12866
12878
12890
12902
12914
12926
12938
12950
12962

0

0

-

tt

00485
00095
00485
01652
11932
11932'
11932
11932
1193K
11924
110612674

20 00485
33 00483
32 00481
17 02112
1P 01402
1P '03002
1P 03046
IP 02336
1P 01402
1P 03002
1P 01402

11924
00000
00099
11060
J1711
00485
00485
000-2
OOOPI
000-1
11924'
01300
11920
00000
00000
000-0
J1941
J2048
J2002
J1992
J1957
J2002
J1967

12974
12986
12998
13010
13022
13034
13046
13058
1.3070
13082
13094
13106
13114
13114
13126
13138
13150
13162
13174
13186
13198
13210
13222
13234
, 13246
13258
13270
13282
13294
13306
13318

J6
J3
2J
27
IP
M4
J3
2J
27
IP
M4
M9

11937 00-01
11937 OOOJO
00099 11065
01314 00099
03002 JI957
13246 00483
11937 OOOJO
00099 11065
01314 . 00099
03002· J1967
13114 00483
13246 00000

J3
2J
27
1P
IP
17
11
13.
32·
1J
16
Jl
KM
M6
ML
L9
M9
L9

11937
OOQ99
01314
03002
03218
01772
00485
00485
00095
00099
0009R
11937
1108N
12986
13318
11687
13366
11687

OOOJO
11045
00099
J2073
J2012
000-0
000-1
-0002
0'0000
J1711
000J4
000-1
11937
01300
12023
00900
00000
00901

13330
13342
13354
13366

IP
IP
17
IP

05028
06066
05650
01314

J1653
J2022
000-0
J2022

3/22
3/23
3/25
3/22

3/22
3/22
3/25
3/22
3/22
3/22
3/24
3/24
3/22'
3/22
3/24
3/24
3/22
3/22
3/22
3/22
3/22
3/24
3/22
3/24
3/22
3/22
3/22
3/22
3/22
3/22
3/25
.3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22
3/22

*

*

M,
SF
TF
BT
TFM
A
A
AM
TFM
AM
C
BNN

FAC,JJ,1
99-KK+l
FAC,99
FXD,NX,l
12 ,OUTPUT, 0 1 7
12,FAC,0
12,FAC,0
12,2,010
12,71,0610
JJ,1,010
NX,JJ,016
RTN444, ,0

TF
CF
SF
BTM
BTM
BTM
BTM
BTM
BTM
BTM
BTM

FAC,I,l
FAC-2
FAC-KK+1
FLOAT,0,10
TRACE,ZI,17
FSB,ONE,17
FMP,DY,17
FSBR,YYMAX,17
TRACE,UP,17
FSB,DY,17
TRACE,DOWN,17

IF,I,09
IF,FF,010
99,Y,1
TOFAC,99
FSB,UP,17
11121,FAC-2,0
IF,FF,010
99,Y,1
A
TOFAC,99 .
BT
BTM FSB,DOWN,17
BNF 13331,FAC-2,0
11121,,0
B
DORG *-3
IF,FF,OlO
MM
99,X,,1
A
TOFAC,99
BT
BTM FSB,XXMIN,17
BTM FDV,DX,17
BTM FIX,0,10
FAC,l,10
AM
FAC,2,7
MM
SF
95·
99,OUTPUT,17
AM
TFM 99,14,610
IF,I,010
AM
C,
. N, IF,016,
BNN RTN121"O
Il1,IND,Ol
BO
OUTPUT-24,00900,O
WA
112,,0
B
OUTPUT-24,00901,0
WA
ADD YLABEL OUTPUT • • • • •
BTM WATY,FMT-5,17
BTM SWC,YLABEL,17
BTM COMPLT,0,10
310
BIM . TOFAC,YLABEL,17

TFM
RTN121 MM
A
BT
BTM
BNF
12221 MM

13331

3/22

·3/25
3/22
3/22
3/22
3/22
3/22,
3/22
3/22
3/22., . I 11-2-1
3/24
3/24
3/22
4/2
110
3/13
4/2
III
3/13
*
4/24
4/2
4/2
3/13
112

U_

=Uki:UJiitCeaUtii.ilii¢

_ _ _ _ _ _,, _ _

13378
13390
13402
13414
13426
13438
00000

~~,,

1P
1P
Jl
J4
M7
M9

_______

03002
01402
11920
"11920
12338
1109L

J2002
J2022
000-1

OOONI
01100
00000

~~

_ _ _ _ _ _ _ _ _""""''''''''''''''''''''''M't''''''"'-........
,,"t"""",,'··t"""'·
..

7..::=-"··-·~~~~

3/13
3/13
3/13
3/13
3/13
3/13
3/13

'BTM - FSB, DY, 17
BTM TRACE,YLABEL,17
AM
1,1,010
1,51,010
eM
BNP -RTN1,-,0
START-1,,06
~
DEND

0

c

i

II

I

31

-----~~---~~-~---~-----~--

o

j\J Ui"li:

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k I eLI S T I 1\1 G UF Ut) J EC T f.lt: C K 0 F S P S P L UT S (JEHU JUT I h! F F CJ f{ F i\1
L.

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(; LJ C; GE I\! H E p1

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L A r~ S •

OUO 0 575356630000000008050 OOOl}OO OOOUOOOO 00000 0 OUO UOOOOOOOOOOUOOR 00 OUU UOOOU OUOO 001.

11110930000526110451109344111541104533110450000026110451104~k0011109411154000002
111109300005261105011093441121411050331105000000261105Ol105UkOOll11541l214()00003
1 1 11 093 000 05 26 11 0 5 5 11 () 9 344 1 1 2 7 if 1 1 0 5 5 3 3 11 0 ') ') 00 () 002 6 1 1 0 5 5 1 1. 0 ::> ~) ROO 1 1 1 ? 1 '-I. 1 1 2"7 4 000 () 0 4
1111093000052611060110934411334110603311060000002 611 0601106 UkOO 111 2741133 LtUOOOO 1)
1 III 093 00005 26 1 1 06 5 1 1 09 3 44 11 39 411 0 6 5 3 3 1 1 06 5 000002 6 1 1 06 5 1 1 () 6 :; ROO 11 1 3 3 L~ 1 1 39 1+ 0000 () 6

111109300005261107011093441145411070331107000000261107011C)70R001113941145400U007
1111 09300005 26 11075 110934411 5 1 4110 7533 11 0750000026 11 075 1 1 () 7 5 ROO 1 11/+ 5 4 11 5 1 L~ 0 0000 H

o

11110930000526110801109344115741108033110R000000261108OllOeOROOll151411574000009
11110930000526110851109344116341108533110A500000261108511085R0011157411634000U10
111109300002491207400000kOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0000000001116341165bUOOOll

0579400207850010030579400206280ROOOOOOOOOOOOOOOOOOOOOO00000001011165411685000012
OOOOOOOOOOOOOOOOOOOOOOOOROOOOOOOOOOOOOOOOOOOOOOOOOOOOO00000001011168611710000013
OROOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO00000001011191411916000014

5000000000ROOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO()000001011197311983000015

l00000000310000000015000000002ROOOOOOOOOOOOOOOOOOOOOOO00000001011202912059000016

170131412038170243012048170177200000261202800485270131411070R0011207412134000017
170140212022270300211075170321812058170140212002270131411050R0011213412194000018

o

312

270300211055170321812038170140212012170304611982270233611055R0011219412254000019
1701402120731701314120021703046119b2270243011070170140211992R0011225412314000020

o

161206300000161192000001161192700001161197211711211197211927R0011231412374000021
211197211927161197200000111192700001241202811927461235001300R0011237412434000022
151202300000131206300050320009500000260048500099270165211080R0011243412494000023
1200485000U1210048511920140048500000471266201200161192400001R0011249412554000024
161197211711211197211924211197211924161197200020111192400001ROOl1255412614000025
241202811924461255401300151202300001111206300001161192400000R0011261412674000026
26004851202d120048500001230048511924320009500000260048500099ROOl1267412734000027
2701652110b0161193211711211193200485211193200485111193200002R0011273412794000028
16119 32000711111924000U 124110601192446126740 13002600lt·8 511920kOO 112794128 540000 29
33004830000032004H100000170211200000170140211947170300212048R0011285412914000030
1703046121)U2170233611992170140211957170300212002170140211967R0011291412974000031
16119370000113119370001021U009911065270131400099170300211957R0011297413034000032
441324600483131193700010210009911065270131400099170300211967R0011303413094000033
441311400483491324600000kOOOOOOOOOOOOOOOOOOOOOOOOOOOOO00000000011309413118000034
1 3 1 1 9 370 () 0 102 10 () 09 Y11 0 L~ :> 270 1 3 14000 I.) 91 -, 03002 1 2073 1 7 032 18 120 1 2 ROO 11 3 1141 3 1 7 400003 5
1701772000UOI1004e~000011300485000U2320009500000110009911711R0011317413234000036

160009900U1411119370000124110H51193746129A601300431331R12023R0011323413294000037
391i687009U04913~66000U03YI168-'00901170502811653170606612022ROOl1329413354000038

313

0

o

170565000000170131412022170300212002170140212022111192000001R0011335413414000039
141192000051471233801100491109300000 ROOOOOO 0000000000000 0000000 113 f t 14134500000 'to
00000000000000000000000000000000000000000000000000000000000000100000000000000041

o

o

AUTOf\'iATIC

C
C
C
C

I

Ii'JI<.AGE GENERATOR FOR SPS SUBS. FOR FN I I.

o

L. HUFFMAN, GUGGENHEIM LABS.

*1205
C

27
1
2

4
3

S P S - F j\J I I LIN 1<./..\ GE A1\1 [) C0 [\! S TAf\.I TAl JT ni'vl ATIC GE~,j ER;~\ TOR ••••••
DIMENSION VAR(20)
RI?'AD 1, N
FORteIAT(I5}
READ 2,(VAR{I},I=I,N)
FORlviAT (A6 )
TYPE 3
FORMAT(22H TYPE SUBROUTINE NAME. )
A CCE P T 2, S j\! A f,l E
I F ( Si\J A/"'1 E ) 5 , 4 , 5

5 PUNCH 6

PRINT 6
6 FORMAT{5HAUTU ,6X,9HDURGl1036)
PUNCH 7, Si\iA/'JIE
PR I 1\IT 7, SNAI"iE
7 FORMAT(5HAUTO ,A6,5HDS
5)
DO 8 1=1, I\J
P lH\j C H 9, VAR ( I )

PRINT 9,VAR{I)
9 FORMAT(5HAUTO
8 COi\JTIi\lUE

,A6,5hDS

PUf\ICH 10
PRINT 10
10 FORivlAT (5HAUTO ,6X,5HDS
PUNCH 30
PRINT 30
PUNCH 31
PRINT 31
PUNCH 32
PRINT 32
PUNCH 45
PR Ii'll 45
PUNCH 38
PRINT 38
PUNCH 33
PR !f\lT 33
PUNCH 34
PRINT 34
PUNCH 37
PRINT 37
PUI\lCH 36
PRINT 36
PUNCH 35
PR lr'~T 35
PUNCH 41
PRINT 41
PUNCH 40
PRINT 40
PUNCH 39
PRINT 39
PUNCH 42
PRINT 42
PUNCH 43
PRINT 43
PUNCH 44
PRINT 44

5)

7)

0

0
315

------~--~.-~~~~---

. - - - - - -----------------

--------_._------_. ---

0

0

I'; "~

PUNCH 46
PRINT 46
PUNCH 49
PRINT 49
PUNCH 48
PRINT 48
PUNCH 47
PRINT 47
,4HDS ,6H,10
30 FORfvlA T { 5HAUTO ,6HFF
,4HDS ,6H,5
31 FORfvlAT (5HAUTU ,6HKK
,4HDS ,6H,485
32 FORIV1AT ( 5HAUTU ,6HFAC
,4HDS ,6H,1314
,6HTOFAC
FORlvlAT
{5HAUTO
45
38 FORfvlA T ( 5HAUTO ,6HFI'IFAC ,4HDS ,6H,1358
33 FORfv1AT (5 HAUTO ,6HTRACE ,4HDS ,6H,1402
,4HDS ,6H,1652
34 FORMAT(5HAUTO ,6HFXD
,4HDS ,6H,1772
37 FORfv1AT {5 HAUTO ,6HFIX
,4HDS ,6H,2112
,6HFLOAT
36 FORIViA T ( 5HAUTO
,6H,2336
,4HDS
,6HRSGN
FORt-iAT
(5
HAUTO
35
41 FOR~'lA T { 5HAUTO ,6HFSBR ,4HDS ,6H,2336
,4HDS , 6H, 2L~30
40 FORI-/iAT (5HAUTO ,6HFAD
,4HDS ,6H,3002
,6HFSB
FORfvlA
T
(
5HAUTO
39
,4HDS ,6H,3046
42 FORMAT(5HAUTO ,6HFl'iiP
,4HDS ,6H,3218
43 FORfvlAT ( 5HAUTO ,6HFDV
,4HDS ,6H,3434
,6HFDVR
FORfvlAT
(5HAUTO
44
46 FOR/viAT ( 5HAUTO , 6 H\"J ATY ,4HDS ,6H,4920
,4HDS ,6H,5028
49 FORjvlAT (5HAUTO ,6HPRA
,4HDS 6H,5650
,
6HCOfvlPL
T
48 FORfvlAT ( 5HAUTO
,6H,6066
,4HDS
,6HSWC
47 FORMAT(5HAUTO
PUNCH 11
PRINT 11
11 FORMAT(5X,IH*,12X,25HEND OF ARGUI'~Ef\lT ADDRESSES/5X,lH*,14X,14HSTART
I I I LINKAGE. )
START=.6263415963
BLANK=O.
DO 12 1=1, N
IF(I-l)13,14,13
14 PUNCH 15,START
PRINT 15,START
15 FORIVIA T ( 5HAUTO , A6, 4HAlvi ,13HSTART-1,5,010)
GO TO 16
13 PUNCH 15,BLANK
PRINT 15,BLANK
16 PUNCH 17, VAR ( I )
PRINT 17,VAR(I)
17 FORMAT(5HAUTO ,6X,4HTF ,A6,13H,START-l,Olll)
PUNCH 18,VAR(I)
PRINT ·18,VAR( I)
18 FORI"lAT (5HAUTO ,6X,4HBbJF ,5H*+36"A6,3H,Ol)
PUNCH 19,VAR(I)
PRINT 19,VAR(I)
19 FOR~1AT ( 5HAUTO ,6X,4HCF ,A6,3H"O)
PUNCH 20,VAR(I),VAR(I)
PRINT 20,VAR(I),VAR(I)
20 FORMAT{5HAUTO ,6X,4HTF ,~6,lH"A6,5H,OlI1)
12 CONTINUE
M=N/2
M=M·~2

0

I F ( fVl-N ) 2 1 , 22 , 2 1
22 PUNCH 23
PRINT 23
23 FORMAT(5HAUTO , 6X, 4HA~1

,13HSTART-l,I,OlO)

316

GO TO 24
21 PUNCH 25
PRINT 25
25 FORMAT(5HAUTO ,6X,4HAM ,13HSTART-l,2,010)
24 PUNCH 26
PRINT 26
26 FORMAT(5HAUTO ,6X,4HB
,9HAROUND"O/5HAUTO ,bX,4HDORG,3H*-3/
261 5X,1H*,12X,36HSYMBOL TABLE AND CONSTANTS HERE •••
)
GO TO 27
END
_DATA FOR AUTO-LINK.
9

X

XMAX
XMIN
NX
Y

YMAX
YMIN
NY
N

317

---~

o

- - - - - - - - - - - - - ------------- -----------------------

1,,. t

tr

t

trm.tm.

If -

A SURVEY OF THE BEGINNING PROGRAMMING COURSE

o

Clarence B. Germain
College of St. Thomas
February 20, 1964
Last Fall, a questionaire was sent to the 280 schools which are members of the
qSERS Group. 175 schools responded. The results are tabulated on the following pages.
1.

No allowance has been made for non-respondents.

This does bias the results.

2.

Since the survey covers only schools baving 1620's, the figures for the end of
1964 do not reflect the influence of schools which will acquire their first 1620
during the year.

3.

A suprising number of respondents gave incoaistent answers; e.g., they indicated
floating-point hardware, 'but not divie hardware, or they indicated that 35% of
their students run their own SPS programs, while they taught SPS only to 20%
of their students.

4.

Figures for index registers, binary capabilities, and the 1627 plotter may not
be indicative since the questionaire was circulated too soon after announcement
of these features.

5. Average enrollment in the beginning programming courses in 170 students per'
school per year.

6. Many of the Mod.el II 1620' s will supplement existing Model I' s, not replace them.
7. Relatively few schools indicated any plans to obtain the 1443 printer.
8. The disk units willmore than double in popularity during 1964 with 1/3 of all
schools having at least one disk unit by the end of the year.

0

9.

While 3% of the schools offered no course involving Fortran, 35% of the students
were taught more than one version of Fortran.

10.

At the end of 1963, 51% of the schools had the hardware necessary to run Fortran
IIj by the end of 1964, this figure will rise to 5910.

11.

85i of the students get tlhands on experience in running their own programs on
tl

the computer. This percentage is about the same regardless of what programming
systems (SPS, GOTRAN, etc.) are taught.
12.

Jim Moore's Multi-Trace, 1.4.003, was the most commonly mentioned trace program
taught to students. However, 85% of the schools indicated that they used no
trace program in their courses.

13., The figures for textbooks are for use in at least one course. Many schools use
more than one text in a course. 31% of the schools use only IBM publications
as texts. While a wide variety of texts, many unrelated to either Fortran or
the 1620, are in use, only four commercial texts and a half-dozen IBM publications are used with any frequency. Of the non-programming type texts, numerical
analysis books, particularly Stanton's, were most "often mentioned.
14.

The textbook percentages in no way indicate sales of books; these figures are
quite different from the percentages shown here and were not a 'part of this study.

o
318
=_ _i_eaZilisa':;;iiUOU\i

iU&lliiiii

X.i

,iI

AMP;;

RESPONSES OF 175 SCHOOLS TO A SEPTEMBER 1963 QUESTIONAIRE
Results are given as a percentage of the number of schools replying to the questionaire. Probable errors do not' exceed ±3% except for items marked with an asterisk
(*) where the probable error is less than ±eJfo. Results are given for the end of 1963
and for the end of 1964. Changes for 1964 are only for equipment now on order. Slight
discrepancies in the percentages are due to rounding.
1620 Model:

1964

One

3

31
3

Special Features, ~4ode1 II (1964)
Automatic Floating-Point
65*
Index Registers
0*
Binary Capabilities
5*

1

1

31
14

31
14

1

1

3

3
1

II

11

Special Features, Model I
AFP, Div, IDA, Edit
AFP, Div, IDA
AFP, Div,
Edit
AFP, Div
Div, IDA, Edit
Div, IDA
Div,
Edit
Div
IDA, Edit

IDA
Edit
~o special features
Summary:
Autamat~c Floating-Point
Automatic Divide
Indirect Addressing
Additional (Edit) Instructions

Number of 1620's in the school:

8910

I

31

o

1

3

o

3

13

13

Type of Courses Offered:

35

Both credit and non-credit
Non-credit courses only
Credit ',courses only
No answer or no courses

64

82
82

5

Installations with Printer (1964)
No disk
23*
1 disk
15*
2 disks
54*
0·:'
3 disks
4 disks
8*

1

82
82

95%

~o

1

34

0'

5
36
13
41

o

64
Departments which offer 'courses:

Storage:
20K core,
40K core,
60K core,
GOK core,
4'oK core,
60K core,

no disk
no disk
no disk
disk
disk
disk

Input-Output:
Paper Tape only
Paper Tape and Cards
Cards only
Magnetic Tape
Paper Tape
Cards, 1622-1
Cards, 1622-2
Cards, RPQ to read 800 cpm
1443 Printer
Disk, one or more
1627 Plotter
1710

48
21
17
5
4
5
4
10

86
4
13
83
13
3
14
4
2

38

18
13
12

9
9

4
10
86
4

14
81
16
3
8

31

Engineering
Education
Mathematics
Business
Other

40
1

45
31

40

Subjects Taught:
Machine Language
Operation of the Computer
SPS
GOTRAN

FORTRAN with FORMAT
FORTRAN II or II-D
FORGO, etc.
Use of same library trace
Block Diagramming
Monitor I

32
66

29
17

47
33

35

13

63
9

4
3
1-

319

Disks:
No disk
1 disk
2 disks
3 disks
4 disks
Hardware necessary to run:
Fortran II only
Fortran II and II-D
Fortran II-D only

86

68

8
5

20
11

1

1

o

31
9
5

Students are expected to write and
run their own programs using:

SPS II
GOTRAN

o

FORTRAN with FORMAT
FORTRAN Pre-Compiler
FORTRAN II

25
15
43

28
21

29
19
11

Required or recommended texts:
IBM Publications

14

1620 Reference Manual
1110 Reference Manual
BPS Reference Manual

4

49

GOTRAN Reference Manual
1620 FORTRAN Reference Manual
1620 FORTRAN II Bulletin
FORTRAN General Information Manual

22

61
38
23

12
15

1620 Program Writing and Testing Bulletin
Introduction to IBM Data Processing Systems
Programming and Block Diagramming Techniques

12

Commercial Publications
Germain--Programming the IBM 1620
Leeson-Dimitry--Basic Programming Concepts and the IBM 1620 Computer
Gruenberger-McCracken---Introduction to Electronic Computers
Guide to FORTRAN Programming
Organick-A FORTRAN Primer
Colman-Smallwood--Computer Language
Smith-Johnson--FORTRAN Autotester

McCracke~A

27
39

6
38
38
6
3

o
320
.

aam:iSa,,;;;:

Utah State University
Logan, Utah

o
FORl'RAN ''TEACH'' PROBLEMS

by
Wendell L. Pope
These problems are designed to be of assistance in introducing the neophyte
to 1ORI'RAN. Problem sets and programs to check them are provided for arithmetic
statements, subscripted variables, fixed and floating point variables. functions
and control statements, loops and input-output~ The problems do not require
that a student be able to write a complete program. They provide a means of
acquainting him with the characteristics of FORTRAN in easy stages and help to
bridge the gap between the introduc'tion to computing and the writing of a compl4te
program. The student's statements are checked for correctness by imbedding
them in the appropriate checking program. They are checked for compilation
errors by the FORGO processor, and for accuracy by the checking program itself.
This is done by comparing the values computed by the student's statements to a
predetermined set of "correct" values. For wrong anSwers, the number of the
problem and the value computed are output, for right,answers only the number of
the problem is output.

321

C

FLOW CHART - TEACH Problem Checking Program

Read values to .
be used in this
problem set

1
Read the "right
answers for
this problem
set

f

Execute studen~
statements
evaluating ~
for each value
of i

l

o

~

~"

r-__~==~~~~ea~c~h~v~a~l~u~e~o~f__i ______________________________.
I,
No

Is X.

Store'i as
wrong

l.

Yes
Store i as
right

Punch i, X. and
l.

the right answer

I

Increment i

________ & test for
exit

i

iExit

~re

any prob-\---...-.:J. Punch the numbers 0
lems right?
of the correct problems

Are any prob,lems wrong?

I

o

lNo

B

_J

Yes_..J ~nch the numbers of
the incorrect prob-

1..J..ems....

~

__ _

322
•

Ama_LiualUiS;' !I dUI ;

C TEACH PROBLEM NO 1
PLACE STUDENT HEADER CARD IN FRONT OF THIS CARD
DIMENSION NRITE(10),NWRNG(10),RIGHT(lO),X(10)
READ,A,B,C,D,E,F,G,H,(RIGHTCI),I=1,10)
C
INSERT STUDENT STATEMENTS BEHIND THIS CARD
K=O
L=O
DO 9950 1=1,10
IF(X(I)-RIGHTCI» 9912,9914,9912

o

9912 L=L+l

NWRNG(L)=!
PUNCH 9920,I,X(I),RIGHTCI)
GO TO 9950
1914 K=K+l
NRITECK)=I
9950 CONTINUE
IFCK) 9922,9924,9922

9922 PUNCH 9923,(NRITECI),I=1,K)
9923 FORMAT(6H RIGHT,10I5)
0'24 IF(L) 9925,9~26,9925
9925 PUNCH 9927,(NWRNGCI),I=1,L)
9926 STOP
9920 FORMAT(9H PROB NOo I3,4X,9HYOUR ANS=E1608,4X,10HRIGHT ANS= E1608)
9927 FORMAT(6H WRONG, 1015)
END

10.341296 10.345599 8.6867569 ~400683394 15.683097 .0034784067
.OOOj4329602 1.1234567
~10664629E+02
0.41901625
0.84447317E+02 0.12039480E+02
.65303219E+09 0010259388E+01 Oo14580430F+Ol Oo87982136F+Ol
~46184027E+02
O.11729093E+03

323

o

h $ tt

0 ',

'11'i

ttt

*t

irittnf tritrit .

C TEACH PROBLEM NO 2
PLACE STUDENT HEADER CARD IN FRONT OF THIS CARD
DIMENSION NRITE( 5) ,NWRNG( 5) ,RIGHT( 5) ,XC 5) ,R(4) ,ft,(4,4)
READ , K, L , ( ( A( I ~ J ) ,J = 1 , 4 ) , I =1 ,4) , ( 8 ( I ) , I = 1 , 4), ( RIGHT ( I ) , I = 1 , ~ }
INSERT STUDENT STATEMENTS BEHIND THIS CAR~
C
K=O

L=O

DO 9919 1::1,5

IF(X(I)-RIGHT(I») 9912,9914,9912
9912 L=L+1
N\~RNG(L)=I

PUNCH 9920,I,X(I),RIGHT(I)
GO TO 9919
9914 K=K+l
NRITF(K)=I
9919 CONTINUE
IF(K) 9922,9924,9922
9922 PUNCH 9923,{NRITE(I)~1=1,K)

9923 FORMAT(5HRIGHT,10I5)
9924 IF(L) 9925,9926,9925
9925 PUNCH 9927,(NWRNG(I),I=1,Ll
9926 STOP
9927 FORMAT(5HWRONG,lOI5)
9920 FORMAT(8HPROB NO. 13,4X,9HYOUR ANS= E1608,4X,}OHRIGHT ANS= E1608)
END
2 '3
2.3964587
6 0 0247685

o

3 G 6241346
4 0 1024678

7.3214680

8.3469201

5 0 4673001

410125807

401357653
503751468
9 0 3704368
4913189 0 2

503422c)87
6e0347'1'12
10.437695
770104270

3.3524569
7.3107~86

-1~3579430

086225934

50312 l
0 3687946
So3420769 60046-2 0 5347962

4

C TEACH PROBLEM NO 3
PLACE STUDENT HEADER CARD IN FRONT OF ,THIS CARD
DIMENSION NRITE(10) ,NWRNG( 10) ,RIGHT! 10, ,X(10) ,8(4)
READ,K,L,(BCI),I=1,4),(RIGHT(I),I=I,5)
C
INSERT STUDENT STATEMENTS BeHIND THIS CARD
K=O

0
. '

L=O
DO 9919 1=1,5

IF(X(I)-RIGHTCI»

9912,Q914,9912

9912 L=L+1

NWRNGCL)=I
,PUNCH 9920,I,X(I),RIGHT(I)
GO TO 9919
9914 K=K+l
NRITE{K)=I
9919 CONTINUE
IFCK) 9922,9924,9922
9922 PUNCH 9923,(~RITE(I)'I=1,K)
9923 FORMAT(5HRIGHT,lOI5)
9924 IFCL) 9925,9926,9925
9925 PUNCH 9927,(NWRNG(I),I=1,L)
9926 STOP
9927 FORMAT(5HWRONG,10I5)
9920 FORMAT(8HPROB NO. 13,4X,9HYOUR ANS=

E16~8,4X,lOHRIGHT

ANS= E1608)

END

2

3

157~09495

-103579430

9 0 3704368 10 0 437695 -1 0 3579430
150915392 205 0 01975 1100

~2Q5347962

o
325
----

--.~.-.--~- .. ------------~-- ...... ~-------~-

C TEACH PROBLEM NO 4
PLACE STUDENT HEADER CARD IN FRONT OF THIS CARD
C TEACH PROBLEM NO 4
PLACE STUDENT HEADER CARD IN FRONT OF THIS C
DIMENSION NRITE(5),NWRNG(5),RIGHT (5),X(5)
READ,A,R,C,O,E,F,G,H,K,(RIGHTCI),I=1,5)
C
INSERT STUDENT STATEMENTS ~FHIND THIS CARD
K=O

L=O

DO 9919 !=1,5
IF (X(I)-RIGHT(I) )9912,9914,9912
9912 L=L+l
NWRNG(L)=I
PUNCH 9920,I,X(I),RIGHT(I)
GO TO 9919
9914 K=K+l
NRITECK)=I
9919 CONTINUE
IF(K)9922,9924,9922
9922 PUNCH 9923,(NRITE(I),I=1,K)
9923 FORMAT(SHRIGHT,10I5)
9924 IF(L)992S,9926,9925
9925 PUNCH 9927,(NWRNG(I),I=1,L)
9926 STOP
9927 FORMAT(5HWRONG,10I5)
9920 FORMAT(SHPROB NOo I3,4X,9HYOUR ANS= E1608,4X,lQHRIGHT ANS=
END
1.2457369 203580123 308609756 407602541 503025768 602047536
700367524 803205689 2
1 01161260 103001178 078878076 204429843 ~o648008P'

E1608~

I

10
I

:=a::iUSXUSll£ii

:au,::: :H;;

: !.il: ; .. &14 KZIS;; (

' " , , ".. , ........'""'...

,~~=-"-

C TEACH PROBLEM NO 5
PLACE STUDENT HEADER CARD IN FRONT OF THIS CARD
DIMENSION NRITE(S),NWRNG(5)9RIGHT(5),X(S)
REAO,A,8,C,D,E,(RIGHT(I),I=1,5)
C
INSERT STUDENT STATEMENTS BEHIND THIS CARD
K=O

o

L=O
DO 9919 1=1,5
IF (X(I}-RIGHT(I»9912,9914,9912

9912 L=L+1

NWRNGCL)=I
PUNCH 9920,I,X(I)~RIGHT(I)
GO TO 9919
9914 K=K+l
NRITECK)=I
9919 CONTINUE
IF(K)9922,9924,Q922
9922 PUNCH 9923,(NRITE B > A > H > C > F > G > 0, compute

X(9)

=A+

+

B+ C+ E + F + G+ H

to obtain the .most a.ceuracy.

o
329

'iU

••

"rf1'

mr

TEACH PROBLEM SET 2
Subscripted Variables

o
Assume the arrays A

=

andB =

are in storage. Write and keypunch correct FORTRAN statements to
evaluate each of the following expressions.
4

2.

1.

X(2) = E

a ° b.
j=l l J J

4. x(4)

where {b ! denotes the integer portion of b l •
l

o

TEACH PROBLEM SET 3
Fixed point, Floating point, and subscripted variables

Assume that values of k and Land B

are in storage •

=

..

•

b
n

Write and keypunch correct FORTRAN statements to evaluate each of the
following expressions.
4

'1.

Xl = E b~].

2.

~

i=l

3.

0

4

4. X4

X3 = . E1 bok.
].-].
l.=

5. X5

=

~ + kL

+.

=b

k

3

-5

= ~ b~
i=1

'-

k3 .;. 2

330
cai.lUi

AUIiIZUiJik!iih I.

Ii.: ,

Li,

#;

-------_. _--.--------_ . -.--

~~~-~--~-~------~-----------""""~~~!""""---."""'-.-.'="'_
.. .
, . .-._._. . _--_ .. _ - - - _ .. _

.. _. .

TEACH PROBLEM SET 4

Functions and Control Statements
Write (and keypunch) statements to evaD.uate ~, X , X and X5 according
2
4
tQ the instructions in the flow chart below. Assume A, B, C, D, E, F
an~ K to be defined.

o

i
\

A
= e

~A<'O

Test A

....

A>D

.~

VA

Xl =

"

A = 0
~JL

~= 0
,ir

"/

'*"

~

......

~-

,r.,.-

X = Arctan(A+B)
2

.
i3

'v'
= VCos(C-D~

"V

X4 = In(EoF)

!--

K = 1

Test K

K =3

X4

== ln~F-E>'

K=2
'~

~4 =
,II

It

In(E+F)
-""

i/"

"'

'V'

X5 = I \+X2+X3+X4 ,

1

c
331
..

- ..---~-.-.---.--- ..-.----.-..--~-----------

-~-----------

.------------ - -

.

--

TEACH PRO BLEM SET 5
Loops

Write (and keypunch) statements to evaluate Xl' X2 , X3 , X4 and
X5 in ·the exercises below.
3

3

1.

2
3
Xl -- 3 + 6 + 9 + 12

2.

Xi

2

+ • • • + 99 •

c

=A D
+ B

= 2, 3, 4, 5.

i

"EoX.
v
1-1

TEACH PROBLEM SET 6
Input - Output (without formats)

~ad

o

A,B,e & D

Punch A,B,C & D

i

=1
..•

'-'f"
~II

Read Z

,1,/

I~

=

AZ3+BZ2+CZ+D

,~

o

Punch Z, X.J.
,,(~

Is i <

5?

...];No

.

Yes

)

i + 1 ... i

332
:::aaama"" stli

iiililMii .SW

,
\ .Ji
0

LOAD-ANn-GO

SPS WITH MONITOR CONTROL

Kenneth M. Lochner and Glenn R. Ingram

c

o
333

urw'n"

",!!"n

P'

t

tr

t

.'.&

WEtt'

r'

MSC ASSEMBLY SYSTEM:

I.)

INTRODUCTION
This paper will discuss a monitore(l ~ load-and-co type assembler developed
at Montana state College and the conditions that prompt.en tts development. It
.is a report on work done by Ken Lochner, 'formerly of the rJSC Computing Center,
ant.l SOO!l to aSSUr1C d\1t.ie~::; as chief programmer at the Dartmouth Complltation
Center, in the actual writing of the processor.
To s~ggest some of the background reasons for this processor, it is well
to admit that I am a relative newcomer to 1620 ranks in completing my second
academic year with a 1620, after leaving a 709 :Lnstallation. Anyone who
follows this path finds himself wondering why in the world he did, and then
develops a feeling somewhat akin to tbe fellow who had a job with a circus.
This particular job consisted of followinr; behind the animals during a parade,
and cleaning the street with his little shovel. After an espeCially trying day,
he complained so bitterly that his wife asked, "If it's so bad, why don't you
quit and get another job?" The man replied, 1I1llfhat! And get out of show bu~)i­
ness?"
If t.he analogy isn't exact, it may be suggesti.ve that some things could be
cleaner in the 1620 tent.

IT.)

BACKGRQUND AND

To indicur,
reliak1ility of the test, the xank t percentile l"ank:. z""scorS;l and t-s·r:orefor

0

ll

each ;Jtuder.lt_

o
·,,4 ..·

343

EQUAtIONS USED

o

Alpha-3 =

Alpha-three:

1

ncr"3
Alpha-four:

Alpha-4

Arithmetic Mean:

X=

Pe rcentileRank:

PR =

Reliability of Test:

Rt

=

=

'n
2£

(Xi - X)3

i=1

1

no-4

100 Cn ... rank)
·n
1
Z - X (1 - X)
crZ (I - 1)

Standard Deviation:

o

T -Scor.e(Sipa Score);

T-Scor.e

= 50 +

Z -Scor.e (Standard Score.):

Z-Score

=

Le~end:

10'(Z score)

Xi - X·

I = Total Possible Points
n =.Number taking the test
N n
if nZ 30
n-l
if n< 30
Rt = Reliability of the test
Standard.Deviation
X = Arithmetic Mean
Xi Individual Score.

=

=
=

o
_UA& 'Ustail::Z1l (

a

¢#

¥4

II

1 John E. Frue~d, Modern Elemen.tary Stati!~~£.~.~fE-;ngle·wood Cliffs, 1963p,
p. (indicated a.bove)"
Z V·'lc.or
t
H . N011, .1.ld~:rOo.Lh,,~,lOU
... ".'., "' .. ~., .... { . .,•.. '0 ..J"-J·~;'U"
1' t1 ,"... 1::,.t._C
""i ·n":'.l
11.;'t
";"'~'I"'" -1"'~~
.. ,.a.. ~ ,"'d,·a
..,r.",'.I(.",:ne,.;
..;~
p. (indicated ab()ve;·..
':b

OJ>

-

_ _ ..."......-._.!,...,,~..l.,j.o. ................::Ro, ......

~

/I. >OQo.' ...... h;6J• • ............

_" _

-.~"", ••~"" ••" " , . " " . _ . _

.........

,..."-~ ...

_

"

...

~u.• _~_"

.......

_ _ .......... , ...... , ..... -........,

:~,

! ./,..,!OS"(.)
'i:."
,.}- ..
'Vi
_r

o

COMMENTS

........... ..... __ enveen:a·,c;~J~:ted group's
m~. . and a#,<,apecl(ied J·aY':;'.core. value. The'mean is o. O~:&n.d. the.taIldar.:d.
'is": :f~ 0.,

ae.tion

J"~re~ple, 8Uppf).~:;;a.:.tudeDt had a.c~r. of 49~li~f.i. to be,

cOIXlll&red wi~ his cl.·elJ.. :~~en that the mean aDd 8tandat.~, Clevia~ion are
40. ~ and 6. 0,,) re.pectivelY~> we find hi. z-.core is '(49 -40)t~' = 1. '5, whi.~)l·
co;t'r•• ponda:" at-score 0(,:$'0 + 1'0 (1.5) :: 65~ In otb.~ w~'rds. this 8tud.~ti, •
:o~~ ,is 1. 5'~tandard de~#.O.8 abO~ the mean. :Thi.~y:~18o beiJl~~.t.d
to ~••n ~t.--ite 8corftdbe~!'tba~abc)ut 93 per cent of the'l~up~

•.

o
. -8-

I, .

PREPARATION 'OF DATA

O"
J

Data Carda: Each IBM data. input· card (except the header' card) must be
prepared in the followbig manner:
Columns

Field

Student Number
Name (see Exceptions, below)
Score (fioating-pointwlth de¢~ in columD.:
,
32: may have one P~c.e.·., to right of .
.' "ecimal in columD.3:~l.

1-5
7-Z7

28-33

0
Oa

40

46-47
55-56

0 ..

64-65

o.

72.·73

O.

.

.

a~ader

tb:f)

Card;: The first card of the data nust contain in columns 2.8-33"
total poss.~ble points. CC)lu.mns 40-73 (,re punched aS8ta~d above.

Sortlns:

o

The data cards are then sorted in descending order', according to'
columns Z8-33.After sorting is completed, the header card is thell placed,
on top of theciec~j it-is the first data care.
. .
LimatiODS: The program wH'i' handle ~ lJ!aximum of SOO iDdiftdualtest a,cOr•••

Exceptions: The program is so design(d that column,s l--Z1of the data inpUt
cards may beleit blank wi~out affectillg the rest of the prog,\am.

o
aasMi!JiiUtiA I,ll i.i.iltti ii.UQn $

~.t;.,i

III
:1

OUTPUT

\

Printed. Output; The arithmetin mean. standard deviation, alpha-three, alpha ..
lour, and the reliability of the test are printed out first (in that order.) This
Information is printed regarene. 8. of the switch settings.

o

The reinainiag irdormatic)D. Ulay or may Dot be printed out. depending on
the switch settinl•.

The heading, etudeatllUmhe:r and name. score, number•. rank, percentile
rank. z-eco%'e. -and t-score is printed out neXt.
Final1 y, e«c.h ~~De of tyJjeCl output contains ~e following information "in the

indicated or01:; student ni'libber. name, .core, a "coW'lter" number, rank,
percentile rarike IS-score, and f.score .. Students receiving the ·same score are
grouped together; the type.writer double spaces between groups.-

When the last card

~8

-

been proceesed, the_ word STOP is printed.

Pun«;hed Output: The first seven cards contain the ~_rithmetic mean, 8tancm.rd
deviatioD. alpb8.-three~_ alpha-four; the reliability of the test, and two blank
, cards. 'This lnformation is punched in COlwnllS 1-35.

on

The He,adlng: Name, Sere. ~(),1 Rnk,Ptrk, Z-Scre. and T-Scre is punched
the eighth ca~d.

0

The remaming cal-dscontain the following infornu~tiot\
Field
'Student Number

C91n~Da

1-5
_1-Z7

~ama

28~33

38-40

Be'ore
A "counte r" numbe r

44 .. 49

Rank

54-59

Pe rcentile Rank
Z ...Score
T-Score

63 .. 68
71-76

Sorting PUnched Outl!ut: The punched output cards Jnay be sorted alphabetically
by sorting in ~8,<:ending order-according to columns 1-5. (This assumes that
the student nuinbers are assigned in sequence 'when the last names are in
- :alphabetical-order). The first eight ca.rds of the output will be rejected by the
sorter because columns l-S-are blank; however, save these cards to process
through the Alphabetic Interpreter.

o
J

I

-10-

349

I

-j

o

.Alphabetic Inte rpreting of Punch~d Output: The information contained in
the punched output cards may be printed at the top_ of each card by means
of the IBM 548 Alphabeticlnterpreter.
The alphameric interpreter board should be wired as follows:

Wire Read Brushes

The Print Entri.es

to

1 ... 29
30 ... 32

1-35
38-40
44 .. 49
54-59

41··~46

63,..68

48·,53

71 ...16

5~/,,60

34 ..,3Z

o
-11 ...

35U

I
I

')
:AEAIi :ail LiCSi!6t!U;;;:, $ a .!I

MACHINE REQUlREMENTS

Equlpmeat Specificadoria::: IBM
Sto~a.e .l\eqwrel1JeDta:

. ~OK"

16'20,

l6ZZ" ,

,
0
"

,'

.. Source Lang'la,e:" .Mit FORTRAN

Special Features: None

c

0,
I.
""-lZ~

351'

o

Step-by-Step Procedure: A.sUme that ·the object deck i8 compiled, and at

Then· ~.~ -

hand.

~ad

1.

Clear 1"62,Z Card

z.

Load A£i~F~rtran
in the 1622..

3.

Check S~tche8,'

Puach.

load.~.

object

clec~.

Sw~tCh

Afi~

.F9rti'an Subroutin••

STO~

PARITY.: ,Check Switch ...
1/0 Chec:~ Switch

OVERFLOW Checlt

and the

STOP
.

PROGRAM

4.lf»re •• RESET and Reader, ..,OAD,·.
5.

Set Program Switches :fol' desired option.

Switch: ..

a, ON for

PUNCHED o.tpat.

. SwitCh Z'and 3 OFF for PRINT ltD output.
Switch Z and 3 O~ fO,-",PBlNTJD and PUNCHED output.
Switch 1 :and 4:
6.Pre~8

7.·

S.TART

Place data carda' in the 162.Z an4pre88 READER START.

a.Press

9.

OF~ •

~UNCH

STARTif . neCe8$ary.

Typewri~:t· prints
aD.~lor 16ZZ
punch•••
..
. '
~.

10.

Repeat Step 7. (i.e. two pa$see are·.%equired).

II.

Typewriter printsaud/or' 16ZZ punche'8.
prOc••• ~d. the V:'0rd S·TOP 18 typed.'

When

th.la;.t .,*1'4 bas

beea.

o
I

:s:aiJiUiUZ &t4Iititi:iltiiiU

J

M.4 1M, Mi ;sa :

----.-.. . --.-"-~. --.-.-,-~~-----~--------"'"""""'''~''.,"~="~=

Expected Stops: 1£ the data .is not sorted in descending o~der, a "card
out of sequ.ence" message ~ill be pl"intedout and the. program will bl"anch
to the STOP command. The restart procedure is then neces sary.
The computer will automatic'a1ly'stop if more than 500 scores are'
read in.

o

Resta~t

Procedure: Press INSTANT STOP p RESET, INSERT g RELEASE,
START Repeat the step-bY"'step pro~edul"e for program exe«=ution.
0

o

,,,1<'1-

-~--~- .....

-----..

..

- ...--",-~------

353
--

----"",--~~----------------".---.-- ....

F.low Chart; tor .
Teet Score. AnalYsis

Format

o

Specification

tor. I/O

Set Counters
Equal to . Zero

-----~

Count. the Number
Persons Taking

ot

the Test

Yes

S'i'O.P

o
Read a
Raw. Score

PRINT Error

Compute
Arithmet1

o

Mean

-15..._IliM"::::": ; ; (( II NMM

$Ii ¥I@

. ZS $

=
.. ,.;. .:,."'"'-.-""'. . -"

;;;..;;,.
..

_ _ _ _ _ _ ..... ~.~
••
_ . _.~ _ _ _ _ _ _ _ _ _ _ _ _ _ ~~~!
. . . .__
. . . ..~.".
.
__ • .u."""'"~._~."""'._

~~~

_ _ _ _ _.

Find the Deviat1on'
ot Each Soore From

o

the Mean .

F.ind the SuP.l of the
Squared., . Cubed., and
the Fourth Power of
the Deviations From
the l-1ean

Use n tor

Oalcu.lat1on
of

No_ .-(
...a-_ _ _ _

.

Is the Number ot
Persons ?aking
the Tes~ ~ 30?

Yes

Use

~;-='--ooE!iIIooI

(n-l) tor

Calculation

of

CalcUlate the
Standard Deviation,
Alpha-3, Alpha-h,
and· the tieliability

.t>UlICH, Arithmetic
Hean, Standard

>--~----li~ Deviation,. A~lpha~3,

Alp~4, Reliability

POUCH

Head;~g'

. Off

. ott

Read Total
Possible l:'oints

355·
-16-

0

----:_ _ _ _ _-BII

o

sad .studsilt
Number, Name.
Raw ·Score· .

No

Compute Rank, ..

Percentile Rank"

. z,..score, T-score
PUHctrj: St~ent Hlmlber.
>-_On_·_____~ NalIle,ScQ~J:. No, Rank,

Oft

Pereenti1$' ·Rank.. ·· .'
~scorei.·:·T~score .

..

'

ott:

o

!O

~RlNT, student Number; ,
N~~:Sc~re~ No~ Rank,

.t
li-

Percentile .Rank,

z,;..sco~~ T~sCore

*Where ·If .~ua;ts

th8.. number· of p~ons

.

rt'

talctrig the test,.

-11-

356
,...:anawl liIat

$.

!:. :;

\

uu

i

#i

II
i

o
357
---~~~--------

\,:~

III

-18-----------------~-------------

\~
I

---_.------ .._---

t"MNtii ,*W*'Hrh "

'Ii

ffiW"nm

1!!1F7.,'!!,

P' II

En j t r

-

i

. -

PRINT 889,AMEAN

T0794
10818

o T0818

PRINT 778
PR .NT 900~ STDV sAlFA3

T0842

PRINT 778
PRINT 901,AlFA4,REl
T0938
PRINT 778
T0962
IF (SENSE SWITCH 2)39 42
10982 39 PUNCH 390

10902

0

11006

T1026

f1050

41 IF (SENSE SW ITCH
42 PR fNT 778

3)l~2j)44

'

PRINT 442

Tl'074PR~NT 443
PRINT 776
T1122 44 OLD-l000 0 0

11098
T1146

.

READ 100, TPTS& Zl 92:2, Z3, Z4f) ZS
DO 83 N-l NMBR

T1230
T1242

100,SCRE(N)"l1ltZ2~Z3&14r'ZS

READ

J-N

T1350

Tl3.74
IF IN-NHBR)Sl f)63 99
T,1.442 51JF SCRE(N)~..SCREtN+l) )16,,52962
T1554

S2 IF

J-l)99~54,S3

T1622 53 IF (SCRE(N.... t) -SCRE(N» 16 1'641)54
T1734 54 SAVEN:-N
T1758 55 N-N+l
11794
IF (N ...NMBR)S7 ;,58 99
'
11862 57 IF (SCRE(N)~"SCRElN+t» 161'55 ,58

O

il

T19.14 58 TH ISH-H
TI998
ADD-(TH'SN-SAVEN)/2 0
g

12046
12082
T2090
T2158
I12222970
4
12302
12326

SRANK-SAVEN+ADD
GO TO 64
62 IF (J-1)99t)66~63
63 IF (SCRE(N.-l)-SCRE(N»16,,64 fJ 66
64. RANKaSRANK

GO TO 61
66 RANK-N
67 ~J

T2350PtAtlK-

-

(( Ttf1BR,,4tANK)*1 0( 0) /TNMBR
0

12410
ZSCRE-(SCRE(N)eAMEAN)/STDV '
12482
TSCRE-ZSCRE*10 0+50 0
T2530
If (SENSE SWITCH 2)73,,75
12550 73 PUNCH 100,SCRE(N)"N"RANK~PRANKl)ZSCRE9TSCRE
T2658
IF' (S£NSE SWITCH 3)7Sf)82
o

T2618 1S

0

tF(OlD--SCRE(N})16~76f>78

12766 76PR iNT
12790
. GO TO
12,798 18'PR tNT
12822 19 PR 't~T

716
79
718

l00f>SCRE(N) vN&RANKe>PRANK.,ZSCRE, TSCRE

12930 82 OLD-SCRE(N)
12918 83 CONTINUE
1301'4 99 STOP
T3022 ,

o

END

END OF COMPILATION 1354113810

35~
.. 19- .
, aa:sosUiUU Ii lit:

.' .ii

IA. q

. ::44#4.1

"

"L,II

A.LFA 3

o

= alpha~;.th:t;e~

.ALFA 4

NMBR

= total number of p~rsons

taldn.g the test

PRANK

RE.L

= relia'bilityofthe test

SAlfA 3

= E.(Xi-Xb 3
i=l

n

SAFA4

seRE

= individtlal test score

(raw score}

.~

SDEV

{Xi

~

Xj

o

SSCRE

STJ)V

= stanciat'd d3viation

STDV 2

=~

STDV 3

::: 0- 3

STDV 4:

= 0-4

TNl.-iBR

= total ;tlumber of persons

TOTAL

= TNM:6R - 1.:0

TPTS

if TNMBR .:~> 30
= TNMBR
= total possible points or tdal number of test items,

:::

0-

talt~n.p'

if TNMBR

the test.
~

30

which

ever is greater.

o
359
-zo-

:,
',I·'
/I
"

TSCRE

0

VAR
Z'3CRE

Zl

- ZS

r_

oW

_.

T=SCRE
(Xi .~, X~
Z·,.SC()RE~

= DurIlmy

Var.ia.bh~s

o

o
36H
II .1 •

tI " llit! ; :, Z!ii J.

z

.Aa:WiF

ARITI+lETtC MEAN

IS

STANDARD OEV ~/rr

~ON

821) 256

VS

".,c,828

Al,PHA 3 IS

ALPHA

L~

IS

REL lAB fL·ITY OF TES1'

11 () 09 f4

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6!.i~9U J·i)I\TR iCK GERRY W~\YNr~
(f725 W~lDER RICHARD l'fNN
55475 ~tC .COy CAROL RUTH
2l}31 0

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22977 DOUGHERTY CHARLES \i:.
25383 EMMER1" R.OB E~T tARt.

76 00
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35<~OO

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69130 RAUSCH MICHAEL
73936 SANDERS JAMES W

64 0 0

36 50

36. 50

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60410

~R,~645
..,~1 c\645

330544
33 (,5 1}4

62091 NEWHARD NANCY FAYE
28065 FOLTA JAMES VI tl CE NT
STOP

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362
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~I
I

o

A

PROPOSAL FO,R AN
ADDITION IN GRADE REPORTING
PROCEDURES TO ALLOW'FOR ,
AUTOMATIC PROCESSING OF PROBA'rION STUDE'NTS

Indiana State Colle ge
Computer Center
'May S. 1964

363

o

j8 h"IbI'HWti'i%H¥'i i'NWT,!'Jii,'Mijw'trnrump""

"1"1,,"'8 '

***#

FLOW
OF

C"':
I'l

PROCEDURE

o
I II

II IliiiutM; : Ii : (

aM ;;Uti.,

II
Explanation ,of Flow Chart

o

A

All card files are merged together in alphabetical sequence by
student number.

B

Computer writes grade reports and updates student index file.
Probation cards for failing students. Store used cards.

C

Grade reports' to students and school officials.

D

Output: New student index cards and probation report writing cards.

E

New index cards go back into file for report use.

F

Probation report cards are sorted by school.

G

Probation reports are printed and sent to the deans of the schools.

H

Probation cards are stored.

o
365
-~.---.-.-------~-~~~-

----.-.---~~---~-.---

1
J

r

00
Student Grade
Card File

:-

0

0
Student Index
Card File

Student Index
Exception Card
File

8

8
Comment Card
File

Student Name
and Address
Card

grade card

o
~~ort
Ilrtm
ort
updated
index card
o Students and c. c. to
concerned.school authori"'-------I

n ex cards
index card
1ndex card
index card
ew Student
index ca rd file

o

Page 1

r 1111

,

UI, ii: :

til; ¥ 44M

IXU ::UU'.A "

robation Repor
Card FUe

o

'Schoolof
Education·
n

School of
Liberal Ar

'.

o

Business

1620
Computer

0:

L

Page 2

3·6 7

O:~
II',!'

CARD.
JUSTIFICATION

o

o
I

iUI.am;;;:

ii;

Ii.:

..

36.~.

;

$lIIUi

:.mad.

II
I

I

I

Explanation of Card File

After completion of Step A (shown by the flow chart), the input to the
computer consists of multiple card groups, one per student. It is the
purpose of this report to show the need for including each type of card.

o

The speed and efficiency of any data processing procedure are largely
dependant upon the volume of data to be processed. Because card volume
is of such importance, it is to the users advantage to keep it at a minimwn.
The five types of input data cards necessary for the student academic
progress reports follow. They are:
Card 1 - Student Clas s Grade Card
These cards enter the flow through the registration line. They are the
yellow striped cards the student submits for each clas s he attempts. After
registration, the cards are held until the instructors turn in their grades.
Each grade, with the respective grade points, is entered on the correct
grade card. The result of this activity leaves a workable file of all work
completed on punched cards.

Card 2 - Student Index Card
A continuous file of student index cards is maintained by the Computer
Center. This file records the complete scholastic history and present status
of each student. It is this card that records the amount of college work
completed, with the grade average earned for this work - on a cumulative
basis, and also on a single semester basis.
Such information as where the student lives, what social organization
does he belong to, the number of credit hours transferred in from· other
colleges, his fir~t two major areas of study, his minor area of study, and
the sex, is all recorded in a numerical code on this card.
It is the student index card that facilitates all reports on academic progressjfrom a report showing the current and cumulative index of each girl
living on the third floor of Reeve Hall, to a report of the numbe rs of hours
all Education majors carried any given semester.
Because this card is so vital to our work, and because the grade report
contains both cwnulative and current credit hours, grade points· earned, and
grade point ratio, it is necessary for this card to be re-computc::d at each
semester's end.

o
36!J

Card 3 - - Student

Requ~red

Index Exception Card

The purpose of this card file is to automate the detailed processing of
studentt; having scholastic problems. Because the student's academic
progress is of upmost concern to the college, careful monitoring and guidance
techniques are essential. The inclusion of this card greatly facilitates much
of the detailed analysis work necessary.
The student index card allows the proper school authorities to care-'
fully supervise the progress of a 'student. By submitting a probation form
to the Computer Center, a school official can stipulate exactly what scholastic level of achievement must be met. This is done by simply stating
what grade point ratio the student must earn, either on a cumulative, or
semester basis. This information is then entered into the student's card
group and allows the compute r to analyze the student's work accordingly.
If the student fails to m.eet this requirement, the computer will generate
a card from which a complete scholastic report can be written and sent to
the appropriate official.
The card is labeled "exception" because, in the absence of such a card,
the computer will use the. standard required index schedule to analyze the
student. See Probation Scaling.

o

Card 4 -- Student Name and Address Card
The name and address card allows for automatic addressing of the grade
report.
Carld 5 - - Comment Card
The comment card allows a school official a maximum of two lines
(68 characters) of comment on the student grade report. Through the use
of a comment code, the comment may be printed only if the student fails
to meet specified grade conditions. It is also possible' to print the comment
under any conditions. See Comment Printing.

o

37H

•

I

II I 'I

dSMm:a:us::ti .: ,a:

.UU.l;II.1i

Output Data Cards

o

Two types of cards are generated by the computer. The first, an
updated student index card, replaces the input student index card (see
card 2 - student index card).
The second, a probation report card (card 6), is punched for every
student falling below certain ininimum grade average requIrements.
The purpose of this 'card is to allow a file of cards to be maintained on
all probation students. A more complete description of this will be found
under Probation Report.

Comment Printing
The grade processing procedure utilizes two kinds of comments. The
first type, those entered on the comment card, may be worded as the school
official desires. However, because the probation report sent to the school
authorities should explain what kind of comment was made, and who authorized
the comment, the inclusion of an authority code, and of a comment classification code is necessary.
The classification of comments is as follows (without respect to wording):
Code
1
2

Description
Place on Probation
Contact the Dean of your
school
Contact the Re gis trar
Withdrawn from school
for scholastic reasons
Withhold Permit to Register

3
4

5

6
7
8

9

Machine generated probation
comment.

The authority codes are as follows:
Description
Registrar
Dean of Students
Business Office
Dean of the School of Ed.
Dean of the School of Lib. Arts

Code
1
2
3

4
5

o

371

-------.--~-

--

--_ ...._ . _ - - - - - - - ~--~-------------~------~-~-----

-

----~-

- - ----

.. ---.....

-~

..-----

6
7
8

Computer Center

9

It should be noted .that the presence of a comment does not necessarily
mean a student is on probation.
A special punch over the comment code will suppress printing if the
required index is met or exceeded. Thus, a code 1 and this special punch
would read J, a Z would read K, 3 - L, etc..
The second form of comment, machine-generated, are those printed on
the grade report to notify the student he is being placed on probation, or
that he is being removed from probation status. These comments will be
indentifie d by a code 9.

o

0,
",...?
tl • -

-

-=MiAZi&£ilMltiitiU i ilL i.# . 4 .$* $

=¥i4Aii

i_A

I
Probation Scaling

o

As each student i~dex card enters the computer during grade processing, the probation code found in card column 47 will be examined.
A zero in this c~lumn indicates the student is not on probation this
semester, any other digit means that the student was on probation last
semester, i. e., a 3 would indicate a probation student for the 3 preceding semesters. If the student again fails to earn a satisfactory grade
.index, the probation code will be incremented by 1. If the student earns
a satisfactory average, the probation code will be made zero.
As each student'~ grades are proces:sed and the new cumulative hours
and grade points are brought up to date, the computer will, in the absence
of a required index exception card, scale the cumulative hours and find the
required grade -point average. The scale is as follows:
Cumulative Hours

o - 16
17 - 32
33- 45

Required Grade -Point Average
1.00
1.25
1.50

1.BO

46 - 60
61 +

2.00

Any student who does not meet or exceed this scale will be automatically
placed on probation. The probation code for such students will be incremented and a "Probation Report Card" (card 6) will be generated.
The ~omputer will notify such students of this condition 1;>y - in the
absence of a comment card - printing on the grade report. See comment
printing.
Special Provisions

If a "Required Index Exception Card" (card 3) is present, their
grade -point. average will be scaled as specified by this card.

c
373

I

)'+1:')'1:*

Hritiod

.m

e

o

CARD

FORMAT

o

o
I

alliliOU SII;:,

. U1Z,AMAM 1$·· -I i. • 1.$ $

a

------.---.~.~-

....... ,•..--"---'--'-'---.:..

• •. _.

"'-'E'-'~~'-

- t""

j),

~
Card
1

CJ

Student Class Grade Card
Card Column

Description
Student Number
School
Name
Clas s ification
Curriculum
Number in Class
Department
Course Number
Section Number
Course Description
Course Number
Time Clas s Meets
Days Class Meets
Semeste r Code
Grade
Grade Points
Hours of Credit
Code 1

1-5
6
7-27
28
29
30-32
33-36
37-40
41-42
43-57
58-61
62-65
66'-70
71-72
73-74
75-77
79
80

0

o

iI

375
-

-------- -- - - - - - - - - - - - - - - - -

ITC"

Card
2
Student Index Card
Card Column
1-5

6
7-27
28-31
32-35
36-38
39-40
41-43
44-46
47
48
49
50-51
58-61
62-63
64-65

66
67-69
70
71
72-73
74-75
76-77
78
80

Description
Student Number
School
Name
Cumulative Hours
Cumulative Points
Cumulative Grade Point Ratio
Semester Hours
Seme ste r Points
Semeste r Grade Point Ratio
Probation Code
Grade Point Ratio
Hours
Housing
Total Hours Toward Graduation
Hall
House
Social Organization
Semester Code
New or Transfer Students
Teaching or Non-Teaching
Minor
Second Major
First Major
Sex
Code 2

o
376
1 I _iilUS JliJ! II . : t itA:

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N$#$i

i'~",I

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Card,
3

o

Student Required Index Exception Card
Card Column

1-5
6
7-27
28
29~31

32-34

35-37
80

Description
Student Number
School
Name
Authority
Required Cumulative Index
to be Earned
Required Serne,ster Index to
be Earned,
Semester Code
Code 4

o

o
377

PO

Card Format

o

Card
4

Student Name and Address Card
Description
Student Numbe r
School
Name
Street Address
City and State
Code 1

Card Column

1-5
6

7-27
28-51
52-72
80

o
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MtttJilitl#lU $$1.:

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Card
5

o

Comment Card
Card Column
1-5
6
7
8

9-11
12-45

46-79
80

Description
Student Number
School
Authority
Comment Code
Semester Code
First Line of Comment
Second Line of Comment
Code 5

o

o

t "'

tttttt

Card Coding For Schools

o

Card Column 6 Of All Cards

School
Education
Liberal Arts
Business
NUl"sing
Other

Code
I
2
3
4
5
Card Coding For Classification

Card Column 49 Student Index Card
Card Column 75 of Probation Report Card

0"

Code
I
2
3
4
5

Clas s ification
Freshman
Sophomore
Junior
Senior
Other

Cumulative
Number of Hours
o - 27
28 - 56
57 - 85
86 - 124

o
38U
aaz:saaiitJiza: $ ;, :

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FORMS

o

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38 1

~,

00.-

Probation and Comment Request Form

,~

To: Computer Center

/ 1964

Date:

Please

C1 Place on Probation

CJ Withhold the Permit to Register

CJ Make the Following Comment

only,
Mr. Mrs. Miss
Student Name

-----------------

a

Student Number

If a CJ cumulative
current grade-point ratio __ e _ _ __
Do Not Fill This Out For A Comment Only

is not earned.
Please make the following comment

o

1-- --- f on the Grade Report
Comment
Code

CJ if the student is plaeed on probation,

regardless of the scholastic achievement.

First Line of Comment
34 Characte rs only - Include Blank Spaces
Second Line of Comment
Classification of Comment

CJ

AUTHORITY CODE
Signature of Authority

o

o

o

~-.~----=-

o

o

o

~

Probation Report

00
C'~

After .grade processing the probation report cards will be used to generate a report of all students
currently on probation. The format of this report is as follows:

CD

g
~

~

~

~

.a
88
§.

.~

Student
Name

Total Hrs Required
Toward
Index '.
<1Hours~nts,GPR-,Ho,Yll__,E911lts,_G.ElLr.-O.ts.Ji.1..,.--rCumlC.ur,

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INDIANA STATE COLLEGE
COMPUTER CENTER

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Grade

9999'9999999999999999999999999999999999999999999999999999999999999999999999999999
1 2 3 4 5 • 1 • • 10 11 12 13 14 15 1& 17 11 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 48 47 48 48 50 51 52 53 54 55 51 51 51 SIlO 11 U 13 14 IS II .7 .... 70 71 72 73 74 7S ,. 77 71 71 •

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99999 9999999999999999999999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9' 9 999999999999999999989999 99999
12145 • 1 • • 10 11 12 13 14 15 16 17 11 11 20 21 22 23 24 25 26 27 .2I3O~3233~~36n38.~~42~44a.U484850~
-------

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99999999999999999999999999999999999999999999999999999999999999999999199999999999
1 2 3 4 5 • 7 • • 10 11 12 13 14 15 11 17 11 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3& 31 31 39 40 41 42 43 44 45 • 47 48 49 50 51 52 53 54 55 51 57 51 59 10 11 &2 63 14 IS II 81 .... 70 71
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1 2 3 4 5 • 7 • 9 1011 12 13 14'15 16 17 18 192021 22 23 24 25 26 2728 29 30 31:32 33 34 35!36 37~38 • 40 41 4243 44 45 48 47 48 41 50151 52:53 54 55156 575159 80 61 62 63 &4 65 16 87 II It 70 71 7273 74 ~5 78 n 7t 711.

Probation Report

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INDIANA STATE COLLEGE
COMPUTER CENTER

999 999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ~ 9 9 9 9 9 9 9 9 9 999 999 9 9 999 9 9 9 9 9 9 9 9 9 9 9'9 9 9 9 9 9 9 9 a 9 9 g 9 9 9 9 9~9 9 999 9 9 9 9:9 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 11 18 1920 21 22 23 24 25 26 2728 29 30 31 3233 34 35 36 37 38 39
5

STUDENT ~

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55 56 57 58 59 60 61 62 63 64 65 66 6768 69 70 71 72.73747576 n 7. 7. 80
TOTAL

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1 2 3 4 5 6 7 8 9 1011 1213 14 15 16 1118 1920 21 22 23 24 25 26 27 28 29 30131 32 33 34135 36 37 38 39 40 41 42 43 44145 4& 47 48 49 so 51 525354 55 56 5758 59 601&1 62 63 64 65 66 67 .. 69 70 71 7273747578 n
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Index

999999 9 99 9 9 9 99 999 999 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 999999999999999999999999999999999999999999

1 2 3 4 5 & 7 • 9 10 11 12 13 14 15 16 11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4& 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 &7 &8 • 10 71 72 73 .74 75 78 n 7878 10

STUDENT

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NAME

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II

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99999 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 999 9 999 999 9 999 9 9 9 9 9 9 9 999 9 9 9 9 9 999 999 9 9 9 9 999 9 9 9 9 9 9 9 9 9 9 9
1

12345 6 1 • 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 ~ 29 3G

w.

323334 353631

3839~~~4344454&~48495O~~53545556~585960~U6364e66V.a1071nnUn78nn7t
-_

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Exception

999999999999 9 9 9 9 9 9 9 9 99999999999999999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9.9 9 99999 9 9 9 9 999999999999:99
1 2 3 4 5 & 7 • 9 10 11 12 13 14 15 1& 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4& 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 678. a 70 71 72 73 74751.
. SrI/DENT

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SECOND

LINE OF COMMENT

FIRST

LINE

OF COMMENT

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99999 9 9 9 9 9 9 9999999999999999~999999999~9999999 999 999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 99 9
12345 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2B 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4& 4748 49 50 51 5253 54 55 56 5758 59 60 61626364 65 66 67 &8. 70 717273741576 n 7~.78 ~
---

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--

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Comment

~=----

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COST STUDY
PROGRAM ABSTRACTS

Programs 1, 2) and 3

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(1.)

PROGRAM 1
Description:
This program extends the enrolhnent and class hour figures in the
2 cards. The input, the 2 cards sorted by Depa;rtment Number, is read
from the 1622 card reader. The computer multiplies the. enrollment
figure times ~"1e clas s hour figure. The entire 2 card is reproduced for
output - containing the extended amount in card columns 26-31.

o

When a change in Department Number occurs, the machine will
genera. te a 3 card. The refore, there should be one 3 card for eve ry department entered. The 3 card will contain: The Year, Dept. No.·, Total Student
Class Figure, and the Total FTE Staff Figure. Both totals are from the 2
cards.
Error Conditions:
As the file goes through the I'n.achinc, a sequence check for equal group:>
is performed .. If a 2 card is out of order an error message will be typed or.
the typewriter ("error in Dept. sequence. "). B~cause the comput'er' recognizes
an error condition on an "Not Equal and Not High" compare break, the
department to which the error card belongs may have already passed completely through. In such a case it will be ne'cessary to:
1. Adjust the 3 card for that department.
.
2. Rerun the department ~with the card included.
Irrespective of. which method is used, the run must be started from the
firs t depa. rtm ent for which the re is no 3 card. .

Switch Settings:
I/O
- Stop
Parity
- Stop
Overflow - Stop
Console Switches:
Sw. 1
Not
Sw. 2
Not
Sw.3
See
·Sw. 4
Not

Used
Used
Ope'rating, Sugges tions
Used

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----------

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- - - - - . " - - - - ..

-~---

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(2)

0 ,'\

PROGRAM 2

,i

Des cription:
This program is used to pro-rate the number two cards. After
Program 1 is complete, the Department Total cards (3 cards) have two
total expense amounts keypunched in them. These cards are then placed
back in the file of 2 cards in front of their respective department files.
This program (Program 2) then accepts that file as data. The program
a'ccepts the data in sequential order (by Dept. No. - 3 card first, followe.d
by the two cards) and pro -rate s the two amounts from each 3 card into
each two card.
The two amounts to be allocated are found in card columns 19-24
and 25-30 of each 3 card. The first amount is pro-rated by weighting
the student class hours figure on each 2 card against the total student class
hour amount on its respective 3 card. This is then applied to the first total
(stored in the machine) for each 2 card 1 s share. The second amount is prorated on a similar basis, i. e., FTE. figures are weighted. ~he remainders
are carried into the following dividend, allowing the last card to zero-balance
the anlount to be allocated and the amount allocated.

C

1

:1

Error: Conditions:
The program tests for six error conditions during processing. If an
error condition is detected, the computer will type "Error Nil and halt.
The six error conditions follow:
Error
1
2
3
4
5

6

Sequence - 3 card
Sequence - 2 card
Amount allocated on student hours doesn It
ze ro balance
Amount allocated on FTE doesnlt zero balance
Student hours from 2 cards do J'lot equal tot~l
from 3 'card
.FTE percentages from 2 cards do not equal total
from 3 card

On any of the above conditions, except I an.d 2, it will be necessary to start
from the last departxnent not com pIe tel y proces sed.

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(3 )

PROGRAM 2

o

Switch Settings:

I/O

- Stop

Parity
- Stop
Overflow - Stop
Console Switches:
S ...v.l
Not Used
Sw.2
Not Used
Sw.3
Must be same setting as in Program 1
Sw.4
Not Used

I

I

1

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38~

1
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( 4)

PROG'RAM 3
Des cl"iption:
This program allocates the Pl"O -rated totals on the two cards to a
7 card for each course. The output fron1. Program 2 is sorted into course
within departlnent order (card columns 5-10) with the 7 cards then being
mel"ged in. If the data is in correct order, there will be one seven card
in i1 0nt of every group of 2 cards.
4

The program accepts its data through the card reader. The cornpu-;;(:r
will read all the data cards for an entire department, then punch a new 7
card with the sum of the three expense totals from the two cards (FTE
Expense + Salary Expense + Student C:ass Hours Expense) allocated to the
six different grade levels (Freshmen, Sophomore, Junior, Senior, Special,
and Graduate). The total enrollment of each class is weighted against the
remainder from each division is carried to the following dividend to zerobalance the last card of each group.
The 7 card generated, then, has the complete cost of the course
allocated to each class of students.

o

Error Conditions:
The program is extremely lilnited as to the number of error conditions
it can check. The 7 cards are presumed to have been crossfooted, and the
2 cards have been through the machine checks of Program l' and 2. Three
error ~onditions might arise. They are:
1. An urunatched two card
2. A sequence error
3. The 7 card allocation did not ze ro balance - This would happen if
a 2 card was missing.
On any error condition, the typewrite will describe the error and halt. It
is then necessary to start over, from the last course 7 card not punc;hed.
Switch Settings:
I/O
- Stop
Parity
- Stop
Ove rflow - Stop

r

Console Switch Settings:
Not Used

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(5)

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OPERATING SUGGESTIONS

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1.

Before running any program, clear the machine. This is done by:
pressing "Reset", then "Insert" on the computer console. Type
in 260000800009, then pres"S the R-S key. Wait about 1/8 of a
second and depress "Instant. Stop". Then press "Reset".

2.

After clearing the machine, place one of the object decks in the read
hopper and press "Load" (This is the yellow button). After the
machine stops reading, press the green "Reader Start" to read in
the last card. The machine will be in the manual mode at this point.
Load the data in the ·read ;hopper, and blank cards in the punch hoppe r
and press Start to begin processing.

3.

If programs one and two are used with swltch 3 off, there 'will be a
duplication of output. That is, Program 1 extends the two cards with
switch 3 off. This may be avoided by using the programs with s\vitch
3 on (Programs 1 and 2). This method will allow just Program 2 to
generate the 2 ~ards. Program 1 \vill then punch only the 3 cards
and Program 2 will extend the 2 cards as it pro-rates the:m. Irrespective

of the switch setting used, it must be the same for both programs.
See the following flow chart for a m.ore complete description.

o

o
391

\,~

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(6)
Equipment Specifications
2.0K 162.0 Computer
1622. Card/Punch Unit
Additional Feature s
TNS and TNF Ins tructions >:c
Indirect Addressing Not Used

):;These instructions greatly fac:ilitate numeric conversion, but if not
avaiiable, they "may be siInulated with several transmit digit instructions.
As an example of this substitution, Program 1, line 01090 (TNS in+lO,
Now, Dept. No. 3-6) might be changed to:
"

C

TD
TD
TD
TD
SF

Now, in+lO
Now - 1, in+8
Now - 2., in+6
Now - 3, in+4
Now - 3

This is·because a number such as 0036 will be_.+ead as 70707376.

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392
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F LOW CHART FOR S,\VITCH 3 SETTINGS
FOR PROGRAMS 1 AND 2

3 cards and extended
2 cards

Just 3 cards

1

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Program 2

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(? _ _ _ _ _

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Pro -rate d
and extended
2 cards

! I 19n
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Off;;;...,FPro-rated 2
cards

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The output from Program 1 with Switch 3 ON
This then becomes the input for Prqgram 2.

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is merged in the input flle.

393

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~
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9 9 9 9 9 9 9 999 9 9 999 9 9 9 9 9 999 9 9 9 9 999 9 9 99 9 9 99 9 9 9 9 9 9 9'9 9 9 999 9 9 9 9 9 9 9 9 9 g 9 9 9 9 9 99 9 9 9 999 9 9 !.
1 2 3 4 5 & 1 • 9 10 11 12 13 H IS 16 11 18 19 20 21 22 23 2425 2S 21 28

P£"7I
No.
No.

CQU
L5l<"

l~l9 919 ,17

t-'--t~

ADD MODI FI CA TION
TO CALL
NEXT PROGRAM

MODIFY 1/0
INSTRUCTION
FOR DISK
OPERATION

LOAD PROG.
INTO CORE
IN NORMAL
MANNER

TRANSFER
PROG. FROM
CORE TO
DISK

CALL PROG.
BACK TO
CORE WHEN
NEEDED

CHECK OUTPUT
TO BE SURE PROG.
WAS NOT ALTERED
BY MODIFICATION

o

)'#triitttsW

ht

....

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for call at any time it is needed.

It is suggested that the output of the

test run be compared with the original test data to point out any
erroneous changes which have altered the logic of the program.
We will now go back and examine the individual blocks of
this flowchart (Slide 1) in more detail.

If it were decided that our

program, when finished, should call in a second phase or program we
could simply replace the final halt with the two instructions needed
to call the next program from the disk.

In Slide 2 we have replaced

the halt at 10588 with an Op Code 34 followed by an Op Code 36.
These will transfer the next program from the disk to core.

This will

work fine if the fir st instruction of the new program is located at

o

10612.

This is because the instruction at 10612 will be the next

instruction executed.

From this, we can conclude that the Op Code

34 and 36 instructions to call the second program must be located
just in front of the address at which the first instruction in the second
program will be loaded.

This is illustrated in Slide 2 where the Op

Code 26 at location 10612 would be the first instruction executed in
the second program.
To further illustrate this point, we will take the case of an SPS
Program which has a halt at location 0 followed by a branch, in Loc 12,
to the origin or beginning of the program.

Here we have replaced the

halt at 10588 in Slide 3 with a 49, or branch, to 19976.
19976, we have placed our Op Code 34 and 36.

At location

The next instruction

executed after the Op Code 36 will be the instructiop. brought out from

o

location 0 which is normally the first instruction in an SPS Program.

I

~

17

o

MODIFICA TION TO CALL NEXT PROGRAM

CORE
LOC.

OP
CODE

I

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P&Q ADDRESS

•

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10588

48

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00000 00000

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FINAL INSTRUCTION
IN UNMODIFIED PROGRAM

C'

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10588
10600

34
36

10612

26

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19962 00701
19962 00702

FIRST MODI FI ED
INSTRUCTION

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MODIFICATION TO CALL NEXT SPS PROGRAM
OP
CODE

CORE
LOC.

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10576
10588

..... ~

LAST

-

19962
19976
19988

1000
34
36

00000
00012

41
49

P&Q ADDRESS

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INSTRUCTION IN PROG.
19976

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00200 00000
19962 00701
19962 00702
0000000000
01700

_....

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Now that the new program is in core, this is also the first
instruction of our second phase or second program.

This takes

advantage of the wrap around feature which allows us to execute the
instruction at location 0 J after the instruction located at 19988 is
executed.

This also takes advantage of the fact that very seldom are

instructions located in the upper end of core in the 19900 area.

This

allows us to use this area.
Let us now examine the block labeled "Modify I/O Instructions
for Disk".

Slide 4 is an enlargement of this block.

The first

decision block asks,'!Al-ethe're 300 to 500 core locations available?"
This figure,

300~500

is rather broad and varies depending on the

number of read or write statements in the program which are to be
modified.

If we have this number of core positions available, then

we go to the next decision block which asks, "Does the program read
into or write from an area beginning with an odd address?" If this
answer is "yes", then our modifications will require an additional
200 locations.

These additional 200 locations are used to program

the transfer of data so that the disk works out of or into an area
beginning with an even address.

If this is not done, the first or last

digit of the data will be lost in a disk transfer.

The transfer of data

to core is made prior to a write disk or following a read disk
instruction usi ng a transmit record so that record marks and
special characters would also be transferred; thus not altering the
data in any respect.

Once we find that sufficient core storage is

available, we proceed to the writing of the modification program.

o

I - 18

---------~----~--~----

--~

o

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1/0 MODIFICATIONS
SLIDE # 1

YES SIDE OF WILL PROG.
USE DISK FOR DATA.

YES

SUFFICIENT CORE
LOCATIONS ARE
AVAILABLE TO
PROCEED WITH
MODI FICATIONS.

~
~.......

USE TWO ROUTINES,
ONE OVERLAYING THE
OTHER. THESE 100 LOC.
WILL BE FOR CONTROL
OF ROUTINE IN. CORE.

USE TWO OVERLAYED
PROGRAMS WITH EACH,
AT ITS COMPLETION,
CALLING THE OTHER IN.

1/0 MODIFICATIONS
YES

USE FALSE B.TM·
16
ADR. OF RETURN TO PROG.
49 TO DISK I/O
FOR EACH EXIT.

NO

USE UNCONDITIONAL
BRANCH (49) TO MODIFICATIONS
FOR DISK OPERATION AND A (49)
BACK TO ORIGINAL PROGRAM.

OK TO USE BTM
TO GO TO DISK
MODIFICATIONS FROM
ORIGINAL PROGRAM.

NO

PROGRAM MUST
KEEP COUNT OR
MODIFY LAST CARD
TO STOP READING.

WRITE PROGRAM CONSIDERING
THE ABOVE TO READ, WRITE
DATA AND KEEP TRACK OF
DATA LOC. ON DISK.

NO
ON SLIDE #1 .
CLEAR ALL FLAGS
FROM DATA PRIOR
TO WRITING DATA
ON DISK .

~

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LOAD PROG.

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tri.o.M'#

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Ifs in the first block in Slide

4, we had found that sufficient

core was not available, we would have gone out the no side to the
next decision box which asks, "Are there at least 100 locations
available?"

These 100 locations will be necessary for a control

program which will control a section of core storage calling either
the I/O routine or the main program whenever either is needed.

In

other words, a portion of core will be shared by both the I/O program and
the program which normally resides in this area.

This way we can actually

use a program which fills practically all of core and still have available
the additional programming necessary to take care of reading and
writing on the disk.

o

cannot be found.

There are very few cases where 100 locations

In many cases, an output error message may be

modified or abbreviated . . The locations acquired in this manner may be
used for control purposes.

The locations from 0

area may sometimes be used.

=

80 in the product

By dumping the program out on the

typewriter, there may be other areas which will become evident.

In

this way, sufficient area may be found to contain the instructions
necessary to call the alternate program and control whichever program
is in core at the present time.

If we reach a situation where fewer

than 100 cores are available, and if the logic of the program will allow,
the best solution would be to have each of the two overlayed programs,
a t its completion, call its counterpart in on top of the existing program.
In this way, you are alternating back and forth and each program, when
executed, will automatically call the next.

o
442
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=

19

o
The next decision block asks, "Are branch and transmit
instructions used to go from the original program to its "read a card" or
"punch a card" routine?" If the answer to this is "ye s" we will not be
able to use branch and transmit type instructions to branch our disk
routines.

And, in the case of this, we go out the left side of this block

to the next block which asks, "Is there more than one place where the
original program branches to its read or write routines?"

The point

here is: If branch and transmit instructions had been used by the original
program to go into its routine which, after modification, we will be
branching

from~

we may not use a branch and transmit again prior to

reaching the branch back.

Thus, in cases where the branch and transmit

instruction is used by the original pr~gram to branch to its I/O routine,
we must use a 49 'type branch to branch to disk routine.

c!

But, if the

original program had not used a branch and transmit instruction, we
maY9 in turn, use branch and transmit instructions to get to and from
the disk routine.
The next block says, "Does the program recognize the last card
of data?" With card operation, when the last data card has been read,
the card reader will stop, but the disk will continue to read sectors
beyond the last data unless provisions are made to sense this last data.
If the answer to this decision block is "no", then some provision must
be made so that the program will not read the disk completely never
knowing when it has finished the last card.

This may be accomplished

in two ways:

o
I

=

20

S'ttt'=_

t=

o
1.

A count can be maintained of the number of cards stored
on the disk when the data was originally written on the
disk.

This count can be checked as the data is read back

for the last position.
20

Or, the position following the last data segment on the
disk could be loaded with a special indicator which the
next, or following, program will recognize as the last
data area.

In the case of AUTOSPOT AND AUTOMAP, the program already made
provisions for the last card by placing a fini card at the end of the data
a s it is written.

o

This fini card contained a 99 and was recognized by

the following program as terminating the data.
From here, we go to the next decision block which checks for
input in alphanumeric form.

Again, in this block we run into a uniqueness

of the disk which in some cases would be an advantage~but which we must
watch for.

When we read the disk or write disk in alpha, flags are

transferred with the data.
cards.
data.

This is contrary to reading or writing on

Thus, we must make provisions to remove the flags left in the
The programs with which we are working assumed that there

would be no flags in the input data and went on to set flags in the input
area which were later used for data transfer.

The extra flags left by the

disk can cause serious errors if allowed to remain.

To correct this,

we used a clear flag instruction to clear al1 flags from the 80 positions
of data prior to writing on the disk.

o

In this way, no flags were read

back from the disk into the input area.

I

~

21

o
Coming down through the flowchart (Slide 1)1I we have now reached
the point which says load program into core in normal manner.

The

modifications which we have described up until now may be inserted into
the original program deck in two ways:
1.

We can modify the original deck prior to loading the
program into core by repunching the necessary cards.

2.

We can load the program in with no modifications and
then write a "trailer program" which will load the
modifications on top of the normal program.

Either method is satisfactory.
Now it becomes necessary to transfer the complete modified
program onto the disk for recall at a later time.

Again, there are a

((l\.\,

~I

number of ways in which this can be done.

1.

This can be done by placing the two neces sary disk
instructions into the input area.

After we had loaded the

program with the modifications, we would branch to these
instructions which in turn would load the program on the
disk.

When the program is read back from the disk

these two instructions (34 and 38) would still be in the
input area but the assumption is that the first data read
into this area would be read over these instructions and
they would have no affect on the program.
2.

If we had used the trailer program to load in our
modifications after the initial program had been already
loaded into core, we would have included these two

I - 22

o

tt

$'

j"TI

o
instructions.

Again, either way is satisfactory.

The main

point is to get the program on the disk with the modifications.
Now all that remains is to have the program called in from the
disk.

Here, we may use the same philosophy which we had used when

we had one program calling the following program.

The main thing to

remember here is that the Op Code 36 instruction must be located just
in front of the first instruction to be executed in our next program.
SPS programs, we used the call routine illustrated on Slide 5.
an Op Code 41 followed by an Op Code 34, 16 and 49.
into location O.

The Op Code 41 will do nothing.

In

We have here

The program is read

We go to the 34 which

will seek the disk address which we specified in the control word
located at 44..

The 16 transmits immediately the 36 to location 0 and 1.

We then branch back to 0 and exe cute this instruction which will now be
a 36 or "read a disk".

The new program will be read in and the next

instruction executed, after the instruction located at location 0, will be
the instruction located at 12 which, in the case of SPS program, will
be a b ranch to the or igin of the pro gram.
In the case of non=SPS programs where the branch is not located
in position 12, we may use the program similar to the one in the second
part of Slide 50

Again, this program is read into location 0: the first

instruction is a 34,

Ii

seek the disk".

The second instruction, an Op

Code 26, will transfer the Op Code 36, instruction 9 located at 0046,
to a location just in front of where the next program will start after it
is read in.

The third instruction Op Code 49 will branch to and execute

o
I

=

23

,-----~--~~~---...........-

-=
.

------"
.....",
..."',.""'-.-"' ......
""...""""
... ---~~~
.. -~---=."-'''''''-'
........ '--'"-=
..-'='---..=--'
.. -=."'=-."-"""""'--"".. ---"=------""'-',
........
- =~~

o

TWO CALL PROGRAMS TO CALL AND
START PROGRAM ON DISK
CORE
LOC.

OP
CODE

00000
00012
00024
00036
00044

41
34
16
49

00000
00012
00024
00032

34
26
49

00046
00058

36

,
I

•

CONTENTS OF
P&Q ADDRESS
00044
00702
00044
00701
00001
00036
00000
105000 200 00000
(DISK CONTROL WORD)

rr"t

IV;

00032
00701
START ·1 00057
START·12
105000 200 00000
(DISK CONTROL WORD)
00032
00702

o
,

.~

....

L1'1 ,

- - ..

-----------------.---.--~~

....

~-~---~~

hli

1

r

$ t

±bi . zHziWtirt

- !

'II

r

II

o
the Op Code 36 instruction.

The Op Code 36 instruction will be executed

reading in the new program and the following instruction which will be
the first instruction in the new program will be the next one executed.
The final block on Slide 1 points out the advisability of checking
the finished program by comparing its output with the output from the
program prior to any modifications.

In this way, we can be relatively

sure we Ive not altered the main philosophy of the program in any way.
I have included in the appendix a typical set of modifications for
your reference.

I might add one precaution

modified programs get on the Monitor Disk.

~-

DO NOT let any of your

Probably Monitor would

have to be reloaded and your program most likely would not run any way.

o

In concluding, let me say that I hope I have brought to your
attention an area of disk operation which has receiveq. very little
publicity in the past.

You must realize that there are very definite

limitations to the use of the disk with programs modified in this manner.
The program must be in a complete core image and if programs are
linked together with each calling the next, the sequence is restricted
and there can be little deviation without rewriting the modifications.
But, for programs which will run in the same sequence, or for a
single program that is run very often, a considerable savings can
result.

The resulting program is fast, economical and easy to

operate.
I realize we have covered some rather technical material here
in a rather short time.

o

Therefore, I invite your questions either now or

this afternoon during our workshop when we hope to s it down with you

I

~

24

and help you modify your post-processors or any other programs which
you have to modify.

Please bring a copy of your program listing and

find out the last location that your program uses in core.

Anytime in

the near future that I maybe of as si stance, please feel free to contact
me through the Huntsville Branch Office.
our workshop this afternoon.
Now, are there any questions?

I

- - - - --_._--

_.. _ - - _.. __. __. __•..._

...

25

~

_ _._--_. ._ - - -

-

---

I hope to see many

6f·y~u

in

o

dr.

t zib

• tt

o
II

Appendix

1

OF Code Reference Table
and
Disc Word Explanation

o

o

o
CODE

MNEMONIC

TYPE OPERATION

11

AM

Add Immediate

12

SM

Subtract Immediate

13

MM

Multiply Immediate

14

CM

Compare Immediate

15

TDM

Transmit Digit Immediate

16

TFM

Transmit Field Immediate

17

BTM

Branch and Transmit Immediate

21

A

Add

22

S

Subtract

23

M

Multiply

24

C

Compare

25

TD

Transmit Digit

26

TF

Transmit Field

27

BT

Branch and Transmit

31

TR

Transmit Record

32

SF

Set Flag

33

CF

Clear Flag

34

SK

Seek (0 :: x~7xl)

34

K

Control

35

DN

Dump Numerically

* 36

RN

Read Numerically

37

RA

Read Alphamerically

* 38

WN

Write Numerically

39

WA

Write Alphamerically

o

o
451

11-1

.-~--.-

•...-.. -~.-.-.-----~~

jM

•

un

0

r

t···

r "b. .±it'st. ttibtHb#ttttt

1

CODE

TYPE OPERATION

MNEMONIC

41

NOP

No Operation

42

BB

Branch Back

43

BD

B ranch Digit

44

BNF

Branch No Flag

45

BNR

Branch No Record Mark

46

BI

Branch Indicator

47

BNI

B ranch No Indicator

48

H

Halt

49

B

Branch

55

BNG

Branch No Group Mark

C)
*Read- Write disk modifiers on next page.

o
11-2

o

DISK CONTROL FIELD

In order to read from or write on the disk there are four things
that must be known.
(1)

The se are;

The disk drive number if more than one drive is attached to
the system.

(2)

The five position disk sector address.

(3)

The number of sectors to be written or read.

(4)

The starting core location.

The disk control field incorporates all four of the above items into
a 14 position field.

Thus:

F l' F 2 ' F 3' F 4 ' F 5

S 6' S7' S 8

M 9 , M 1¢' M 11 ' M 12' M 1 3

The disk drive number is located in F~.

This drive code number

varies with the number of drives attached to the system.
used.

For drive ¢ a I is

For drive 1 a 3 is used.
A sector on the disk is equal to 1¢¢ positions of core storage.

are 2¢, ¢¢¢ sectors on each disk.
from ¢~¢¢¢ ~. 19999.

These sectors are numbered sequentially

The disk control field F 1 ~ F5 contains the sector address.

This sector address determines

where~

on the disk, the write or read will start.

Next is the number of sectors to be read or written.
S6 ~ S8.

There

This is located in

The maximum number of sectors that can be read ·or written is 2~¢

and the minimum number is ¢¢l.

The method for reading or writing fewer

than 1¢¢ core locations is explained on the next page in "R ead~ Write Disk

o

Modifiers".

----.--~

...--

('

,....

(1\

if

~)

tj

rl

!

-

HtttrifflH

o
M9

~

M 13 contains the core location of the leftmost position of the

data transferred to or from the disk.

This core location must be an even

number.
In a seek, read? or write disk instruction the "P" address is the core
location of the leftmost position of the disk control field.

This leftmost

position must be in an even location.
The "Q" address of the disk instructions contains ~7 in Q8 and Q9
and a modifier in Qll.
modifier in

read~write

The modifier in all seek instructions is a 1.
instructions is explained in "Read- Write Disk

Modifiers" .

o
11-4

The

o

READ- WRITE DISK MODIFIERS

All read-write disk instructions must have a "Q" address of
where M is the modifier.

"x~7xM"

The modifier determines whether or not a group

mark (*) will have any effect on the data being transferred.
The write disk instruction (38) with a modifier of ~ will be
determined after the first group mark encountered in core has been
transferred to the disk.

If no group mark is encountered the instruction

will be terminated when the sector count has been decremented to ~~~.
The read disk instruction (36) with a modifier of ~ will be terminated
after the first group mark encountered on the disk has been transferred into
core or, if no group mark is encountered, when the sector has been
decremented to ~~j1.
The read or write disk instruction with a modifier of 2 will treat the
group mark as data and transfer data until the sector count has been decremented
to _~j1.

o
11-5

o
III

Appendix 2

Machine Language Modifications
to AUTOSPOT, AUTOMAP and
Milwaukee Matic Post- Processor

o

Note:
The post-processor included here is Users
Group Library number 10.4. 004 - the
"Computer Routines for the Milwaukee
Matic Solid State Contro:ITed Machining Centers".

o
456

AUTOMAP PHASE I

Statement number 1 is a five position field for the indirect address which shows
from where to start the transmis sion of the record (statement #2).

This is done

because there are two write statements in the main program and each writes
from a different location.

As each of the two locations are odd numbered, they

must be moved to an even location and, since the only locations left are
11~~~~

- ~~~8~,

these will be used.

Statements #2 and #3 move the data from the

odd numbered program output area into even numbered locations.

Statement #4

writes the output data on the disk.

Statements 5, 6, and 7 check indicators; address check,wrong-Iength record/
read back check and write check respectively and, if either the address check or
write check indicator is on. a branch to a "seek" instruction (statement flIp) and
then a branch (statement #l~) to the write instruction is made.

C

If the WLR/RBC

indicator is on a branch to the next instruction is made simply to turn off the
WLR/RBC console light.

This is done due to the fact that this indicator is

turned on each time a record wi th length unequal to 100 character multiples is
read or written.

Statement 8 adds one (1) to the sector address.

Return to the main program is

accomplished by a branch back (statement #9).

Statement H12 is the write output data disk word.

Statements 14 - 19 type the message "FIN!" to indicate the end of phase 1 and
to set up the calling of the next program.

457
111-1

o

mm

trt±tt***"

o

**

j"

"Ms

Statements

rim

2~

r

_ 25 are changes to the main program.

disk output area.

2~

and 22 clear the

21 and 23 branch to the write disk routine and transmit the

starting address into the area reserved by statement #1.
a group mark after the

8~th

Statements 26 _ 31 dump

Statement 25 insures

position to terminate the write disk instruction.

the program on the disk in a core image.

Statements 32 _ 39 load the modifications, read the first program loader card
and branch to continue loading the main program.

o

o
111-2

0

AUTOMAPPHl
WRITE DISK
STATEMENT NUMBER

CORE LOCATION OPCODE P·ADDRESS

QADDRESS

1

19802

00

0000

2

19808

31

00000

19807

~

19820

26

00079

15390

4

19832

38

19914

00700

5

19844

46

19894

03600

6

19856

46

19868

03700

7

19868

46

19894

00700

8

19880

11

19919

00001

9

19892

42

10

19894

34

19914

00701

11

19906

49

19832

0

12

19914

10

00000

01000

13

19926

00

14

19928

10

42002

00000

15

19940

00

46495

.6490r

16

19952

39

19943

00100

17

19964

34

19928

00701

18

19976

48

00000

00000

19

19988

36

19928

00702

-

C:

0
,

~

,;

.

111-3

45H

\'ff

tt

0

ht

tdbtitrttittrii

AUTOMAP PHI
LOADER AND CHANGES TO MAIN PROGRAM

1

STATEMENT NUMBER

0

o

CORE LOCATION OPCODE

PADDRESS Q ADDRESS

20

02504

31

00000

15982

21

02516

17

19808

16063

22

11086

31

00000

15982

23

11098

17

19808

16065

24

11182

49

19952

00000

25

16062

:I:

26

15402

34

15440

00701

27

15414

16

00004

-41000

28

15426

38

15440

00702

29

15438

48

30

15440

10

40002

00000

31

15452

00

32

00000

36

00080

00500

33

00012

36

15402

00500

34·

00024

36

19802

00500

35

00036

36

19882

00500

36

00048

36

19962

00500

37

00060

49

00080

38

00080

36

00000

39

00092

49

00000

111-4

-

00500

PHASE I SPECIFICATION SECTION OF

0

AUTOSPOT - MODIFICATIONS FOR DISK OPERATION

LOAD
00000
00012
00024
00036
00048
00060
00072

PROGRAM
36 19522
36 19680
36 19840
36 19600
36 19760
36 19920
49 19626

19522
19534
19546

31 19648 05819
49 19976 05914
10500020000000

00500
00500
00500
00500
00500
00500
9

Load the modifications into co re

Save data for next phase
Branch to ftc all next program"
Disk control for this phase

FALSE BRANCH & TRANSMIT
19560 10520014904948
Disk control next phase
19574 15 19969 00009 Change 42 to a 49
19586 16 19821 [0701 Transfer "write from" address
19598 49 19822 0
Go to entry of program
19606 15 19969 00002 Change 49 to 42
19618 49 10660 0
Return to program

Ci

MODIFICATIONS TO PROGRAM
19526 36 00000 00500 Reset location 0 to 80
19538 26 10654 19785 Modify unit instruction to branch to unit on disk routine
19550 26 07755 19759
19562 26 09039 19771
19574 26 06368 19778 Modify end of program
19586 15 05911 0000:t Used to save jata for machining section
19698 32 07751 00000
19710 32 09035 00000
19722 34 19546 00701 Write program on disk
19734 38 19546 00702
19746 48
19748 27 19822 02753
19760 17 19822 10877 Modified instructions to be inserted in program
19772 49 19976
19779 49 19574
19786
19798
19810
19822
19834

11
11

19821
19816
25 19626
14 19816
47 19878

00001
00001
00000
19785
01200

Increase address and transmit qigit

C'

,.J

Has all data been moved?
,

oj

l.! lj

III-5

--------------------------------- - -----

---_.------------_._--._-----------------

i

1

wa..

*t

±it'. . . tif& )""

tit""'

" ... "!"! "

PHASE I SPECIFICATION SECTION OF

0

AUTOSPOT - MODIFICATIONS FOR DISK OPERATION

19846
19858
19870
19878
19890
19898
19912
19924
19936
19948
19956
19968
19976
19988
00000

16 19840 19878
16 19816 19626
49 19912 0
16 19840 19786
49 19810 0
10000000119626
38 19898 00702
47 19956 03600
34 19898 00701
49 19912 011 19903 00001
42 19606 0
34 19560 00701
36 19560 00702

Prepares this section for return pass

1st pass set-up

Write data on disk
Rewrite if we had an address check
Increase sector address by one
Return to Program
C all next program

o

o
1II-6

· PHASE I MACHINE SECTION

Same as Phase I specification with these exceptions
19522 41 00000 00000
19534 49 19976 04948 Branch to end of program
19546 10520014919746
Disk address for this phase
19560 10540020000000
Disk address for next phase
19626
19638
19650
19662
19674
19686
19698
19700
19712
19720

41 00000
26 15929
26 07595
32 15913
34 19546
38 19546
48
49 19574
49 19534

19746 31
19758 49

00500
19711 Modify write instruction
19719 Modify end of program
00000
00701
00702 Load this program on disk
00000

05819 19648
04984 0

To transmit record left by specification section of Phase 1

(~:
~

o
111-7

11

tie tdrr't

o

.....

=&W [

MODIFICATION TO PHASE 2 OF AUTOSPOT TO
RUN FROM DISK

PATCH PROGRAM
19466 26 13225 12033
19478 11 13225 00010
19490 26 13225 12055
19502 11 13225 00004
19514 49 11226 0
·19522 34 19560 00701
19534 49 19976 06850
19546 10540020000000
19560 10535001001900
19574 bbbbbbbbbb

0

Program patch that was in the way moved to here
End of this phase.;.. seek for next phase
Disk control word this section
Disk control word next section

MODIFICATION TO ORIGINAL PROGRAM
19584 36 00000 00500 Read in last cards of modification
19596 36 19680 00500
19608 26 01762 19712 Modify "read a card" instruction
19620 26 03219 19705 Modify error routine
19632 41 00000 00000 NoOp
19644 26 11780 19720 Modify "write a card" instructioq
19656 26 12024 19727 Modify end to call next program
19668 34 19546 00701
19680 38 19546 00702 Write these modifications all on the disk
19692 48
19694 46 19466 01200
19706 49 197420
19714 49 19912 4919522
READ DISK DATA
19728 10000000119600
19742 36 19728 00702 Read a card from disk & seek if necessary then go back
and read again
19754 47 19786 03600
19766 34 19728 00701
19778 49 19742 0
19786 11 19733 OOOQl Increase sector address by one

0

TRANSFER FIELD JUST
19798 25 13056 19600
19810 14 19809 19679
19822 46 19866 01200
19834 11 19809 00001
19846 11 19804 00001
19858 49 19798 0

READ TO EVEN LOCATION
Transfer data to area beginning with an even address
Check for last transfer
Increase disc location by one

46

Repeat

nI-B

i~

MODIFICATIONS TO PHASE 2 of AUTOSPOT
TO RUN FROM DISK

o

TRANSFER FIELD -JUST READ TO EVEN LOCATION
19866 16 19809 19600 Housekeep because all data is transferred now
19878 16 19804 13056
Return to program
19890 49 01768 0
-

WRITE DATA ON DISK
19898 10200000113136
19912 38 19898 00702
19924 47 19956 -03600
19936 34 19898 00701
19948 49 19912 0
19956 11 19903 00001
19968 49 11786 0
19976
19988

36
49

19560
02318

Write data on disk
If addree; check - seek first then write data

Increase sectoraddress by one
Return to program

00702 End of this phase - read in control program for next phase
00000

Load program to load in modifications into core 00000
00012
00024
00036
00048
00060
00072

36
36
36
36
36
36
49

19466
19546
19626
19760
19840
19920
19584

00500
00500
00500
00500
00500
00500
0

Load modifications into core and branch to the first modificatid{;!

o
111-9

•

htrttritt"itt***· ..

MODIFICATIONS TO AUTOSPOT PHASE 3 FOR DISK OPERATION

0
READ DATA FROM THE DISK
18312 36 01984 00702 Read data from disk
18324
18336
18348
18356
18368

47
34
49

11
25

18380 14
18392 46
18404 n
18416 11
18428 49
18436 16
18448 16
18460 49

18356
01984
18312
01989
13411

03600
00701
0
00001
18626

If not correct cylinder seek and go back to read

Add one to sector address
Transfer data to data read in area which start with an odd
address. Use transmit digit 80 times.

18379 18705
18436 01200
18374 00001
18379 00001
18368 0
Housekeep transfer data routine and return to program
18374 13411
18379 18626
13334 00000

CALL OVERLAYED ROUTINE "FLOAT" & CONTROL WORDS
18472 16 19964 f0292 If program branches to FSIN or FCOS set at to call FlDAT and
go to 18786

0

18484
18496
18508
18520
18fi34
18546
18560

49 18786 00000
16 19964 10376
49 18786 00000
00000000000000
41 00000 01700
10560020000000
1053500100190000

Orgin of program 01700
Disk address this program
Disk address of next program

ROUTINE TO MODIFY ORIGINAL PHASE 3 PROGRAM BEFORE IT IS PLACED ON DISK
ALSO 18626 to 18705 ARE USED-FOR A TRANSFER OF DATA AREA
18576 36 00000 00500 Read in a- card and branch to it
18588 49
18596 26
18608 26
18620 36
18632 36
18644 16
18656 16
18668 16
18680 36
18692 36
18704 34

00000
13801
13329
13298
13620
10322
10406
12882
13272
00000
18546

0
00063
00071
00500
00500
19966
02590
02570
00500
00500
00701

Modify write data instruction
Modify read data instruction
Read in another card
Read Modification into 13620
Modification to original program to call float
Read modifications into 13272
Read ori.ginal information into 06000
Write complete program disk

0

,

111-10

.',

Lj- \)

:-

h

MODIFICATIONS TO AUl'OSPOT. PHASE 3 FOR DISK OPERATION

o

ROUTINE TO MODIFY ORIGINAL PHASE 3 PROGRAM BEFORE IT IS PLACED ON DISK
ALSO 18626 TO 18705 ARE USED FOR A TRANSFER OF DATA AREA
18716 38 18546 00702
18728 34 13280 00701 Write "read/write data on disk" routine on disk
18740 38 13280 00702
18752 48 20 - O's
IF PROGRAM NEEDS FATN CALL IN FIDAT ROUTINE
18774· 16 19964 12852
18786 34 00000.00701 Seek float and go to 19946 which will read It in
18798 49 19946 0
WHITE OUTPUT DATA ON DISK FOR NEXT PROGRAM
18806 16 18841 13847 Housekeep transmit digit
18818 16 1.8836 18626
18830 25 18626 13847 Transmit digit 80 times
18842 14 18836 18705 Have we transmitted digit 80 times?
18854 46 18912 01200
18862 11 18836 00001 Increase count· or transmit digit and write data
18878 11 18841 00001
18890 49 18830 0
18902 00000000000000
18912 38 19986 00702 Write data on disk
18924 47 18956 0360()
18936 34 19986 00701 If at wrong cylinder seek and rewrite
18948 49 18912 0
18956 11 19991 00001 Increase sector count by one and return to program
1~968 49 13806 0
18980

0)

INSTRUCTION FOR IDCATION 0 TO 80
00000 49 01700 000· Branch to origin of program
00010 44 18312 18966
00022 36 13280 00702 If the read/write disk routine is in core go to R/W if not call it in
00034 49 18312 0
00042 44 18806 18966
00054 36 13280 00702
00066 49 18806 otn042M3
00080
INSTRUCTION FOR LOCATION 02528 TO 02610
02528 39 02559 00100
02540 26 17043 16793 Error message - no tool card:
02552 49 02634 0
02560 55 56634 30F

"NO

Te"

III-II

-.--~~~.-----------

---_.. _-_ .. _--

-

-~

-

-----~--

-

-~-------~------

0

1

II'S

mtirttrimr

T

fts#S

!'

.•

p

J'I'

MODIFICATIONS TO AUTOS POT PHASE 3 FOR DISK OPERATION

02570 44
02582 49

18774
18668

18966
0

02590 44
02602 49
02610

18496 18966
17676 0

Check to see is "float" routine is in core - if not call it in

INSTRUCTIONS FOR LOCATION 19946 to 00000
19946 36 13628 00602 Call in float and branch

to proper location

19958
19966

49 00000 0
44: 18472 18966

Check to see that float is in core if not prepare to call it in

19978
19986

49 17708 0
10200000118626

Control word for read data from disk

00000

o

o
Ill-12

MODIFICATIONS TO AUTOSPOT PHASE 3 FOR DISK
OPERATION

0

Load cards for phase 3 modifications
00000
00012
00024
00036
00048
00056.

34 00056 00701
38 00056 00702
36 18552 00500
36 18632 00500
49 18576'"0
10536700718312

00000
00012
00024
00036
00048
00060
00072
00080

36
36
36
36
36
36
49

18312
18392
18472
18712
18792
18872
18576

00500 Load in s Ix modification cards
00500
00500
00500
00500
00500
0
Call in next card

00000
00012
00024
00036
00048
00056
00064
00072

36
36
36
36
49
49

18930
19892
02530
01936
18596
00042
00010

00500
00500
00500
00500
0
0
0

49

Load "flmt" on to disk
Load in two modification cards
Call in next card
Control word for float

Load in 4 modification cards

0

Return to Modification program
Modification for write a card
Modification for read a card

o
111-13

'm

rtt'tr'tz

.t.

.

-

. II

!

T

I

W

_

TRAILER CONTROL PROGRAM FOR AUTOSPOT

DISK CONTROL WORDS
01900
01914
01928
01942
01956
01970

xX

XXXX2 0000000 Control word to call post process~r
10560020000000
Disk control word to call phase 3
10200000110000
Disk control word to punch out put
10000000000000
Disk control word for last data written by last phase
10200010010000
Disk control word for write - X .per data
10000010010000
Disk control word for read trace per data

TRANSFER DATA FROM SECTOR 100000 TO 102000 SO POST PROCESSOR WILL FIND DATA
01984
01996
02008
02020
02032
02044
02056
02068
02080

o

26
34
36
34
38
11
11
24
47

01947
01970
01970
01956
01956
01975
01961
01975
01996

19991
00701
00702 Transfer data, 10,000 location at a time
00701
00702
00100 Increase sector address for transfer by 100
00100
01947 If more data still - so back & transfer again
01100

CHECK FOR CARD OUTPUT
02092 34
02104 39
02116 34
02128 48
02140 47

00000 00102
02375 00100 Type out instructions
00000 00102
00000 00000
02224·00100 Check switch

PUNCH OUTPUT ON CARDS FROM DISK
02152 34 01928 00701 Read from the disk one card at a time & punch it
02164 36 01928
02176 38 10000
02188 11 01933
02200 24 01933
02212 47 02152

00702
00400
00001
01947 If not finished, get next card
01100

CALL IN NEXT PROGRAM
02224 26 01927 01913 Enter here from phase 3
02236 34 00000 00102 Enter here from phase 2
02248 39 02441 00100 Set up switches for next program

0

02260
02272
02284
02296
02304
02316

48
34
26
49
36
00

00000
01914
19999
19988
01914

00000
00701
02317 C all in next program from disk and branch to its start
0
00702

111-14

470

c

TRAILER CONTROL PROGRAM FOR AUTOS POT

CHECK SWITCH 3
02318 34 00000
02330 39 02645
02342 48 00000
02354 46 02236
02366 4!l 02092
PRINT AREA
02374 62 66007
. 02386 55 00465
02398 43 41594
02410 64 63215
02422 45 63006
02434 59 630ts
02446 64 57006
02458 46 56590
02470 67 63005
02482 47 20594
02494 63 00626
02506 63 ot
02540 10 00

00102 Check switch 3 for either phase 3 call or card output·
00100
00000
00300
0

10056
65900
40056
94562
26341
24563
26600
05545
75956
56245
34159

SW 10

TYPE OUT AREA:
NbFORb
CARDbo
UT!RES
ETbSTA
RT/SET
UPbSWb
FORbNE
XTbPRO
G-RESE
TbSTAR

G

TI

LOAD CORE & DISK
02544 41 02220 00500
02556 36 02300 00500 Call the remainder of the program into core and load the
whole program disk with a correct halt at 02628
02568 36 02380 00500
02580 36 02460 00500
02592 36 02620 00500
02604 34 02630 00701
02616 36 02630 00702
02628 48
02630 10535001001900
02644 62 66007 30056 SWb3bO
02656 55 00465 65900 NbFORb
02668 57 48007 32159 PHb31R
02680 45 62456 30062 ESETbS
02692 63 41596 301
TART
LOAD
00000
00012
00024
00036
00048

ROUTINE -TO LOAD PROGRAM INTO CORE
36 01900 00500
36 01980 00500
36 02000 00500
36 02140 00500
36 02220 00500

0
Ii 7

III -15
.----~-----

....--..

-----.---------~-

..

----~------

1

1

o
TRAILER CONTROL PROGRAM FOR AUTOSPOT

WAD ROUTINE. - TO WAD PROGRAM INTO CORE
00060 36 02540 00500
00072 49 02544 0

o
111-16

472

II

~II

I

0

A UTOMAP PHASE II

This phase is loaded on the disk in t,-vo sections.

This is done because all

core locations are taken and the "read in" area is defined as "DC" rather
than "OS".

Statements 1 - 14 load the first section and 15 - 23 load the

second section.

Statements 24 - 31 are changes to the main program.

Statement 24 branches

to the read disk routine and statement 25 adds one (1) to the read sector
address upon returning to the main program.

Statement 26 transmits the field

of numerical blanks to location ¢~¢¢~ rather than to the output area.
branches to the write disk routine.
"END" typeout to a "no op".

Number 27

Number 28 changes the halt after the

Statements 29 - 31 change record marks to group

marks to insure termination of the write disk instruction after the transfer
of 8¢ characters.

Statements 32 - 42 are the read disk routine.

The program branches to the

read instruction (#33) and if an address check or write check occurs a branch
to the seek instruction (#32) is made.
statement 37 checks for a "FINI" code.

Upon completion of the read operation,
Upon finding a "FINI", statement 39

sets up a branch to end of program routine.

Statement 4¢ branches to the

main program.

Statements 43 - 56 are the write disk instructions.

The program branches to

statement 44, which gives the option of either; (1) putting the output on the
disk or (2) punching it in cards.

Statements 45 and 46 move the output from the

odd numbered core location to an even location.

III-17

Statement 47 writes on the

li 7 3

o

o
disk.

Statements 48, 49, and

if necessary.

5~

check indicators and seeks (statement

4~)

Statement 51 adds one (1) to the sector address and statement

52 returns to the main program.

Statement 53 in the punch statement and

statement 54 returns to the main program.

The "End of Job" message is contained in statements 57, 58, and 59.
Statements 62, 63, 64 and 65 type "End of Job" and call the next program.

o

o
111-18

0

AUTOMAP PH2
CORE TO DISK
STATEMENT NUMBER

CORE LOCATION OP CODE

PADDRESS

QADDRESS

1

00000

36

19640

00500

2

00012

36

19720

00500

3

00024

36

00080

00500

4

00036

36

19900

00500

5

00048

49

00080

6

00080

36

00000

7

00092

49

00000

00500

R-W DISK

C'
_ Il~,.:

CARDS

-

8

19900

16

00004

41000

9

19912

16

00009

00000

10

199~4

34

19950

00701

11

19936

38

19950

00702

12

19948

48

13

19950

10

42001

98000

14

19962

00

15

00000

36

15000

00500

16

00012

36

19800

00500

17

00024

36

19840

00500

111-19

-

o

llu""tmM'pNtI.i

$." _*_.. 'rid...

'UU

t

tit,

-

•

"j

AUTOMAP PH2
CORE TO DISK
STATEMENT NUMBER

CORE LOCATION

OP CODE P ADDRESS

00036

18
19

36

19920

49

15000

Q ADDRESS

00500

20

15000

34

15026

00701

21

15012

38

15026

00702

22

15024

48

23

15026

10

43980

02198

00
FROM R-W

C\
i

0

DISK CARDS

24

01714

49

19652

00000

25

01726

11

19749

00001

26

01854

31

00000

11372

27

01866

49

19770

00000

28

07872

41

29

11290

~

30

11371

1=

31

04603

..~.

32

19640

34

19744

00701

33

19652

36

19744

00700

34

1~664

46

19640

03600

35

19676

46

19688

03700

III-20

-

[i 76

!.

0

U

AUTOMAP PH2
CORE TO DISK

1

STATEMENT NUMBER

0

CORE LOCATION

OP CODE

P ADDRESS Q ADDRESS

57

19908

00

57487

20062

58

19920

63

41596

30043

59

19932

56

550;!::

60

19938

10

44000

72000

61

19950

00

62

19952

39

19909

00100

63

19964

48

00000

00000

64

19976

34

19938

00701

65

19988

36

19938

00702

'I,.

10
1II-22

~

____

~

__

~,

.~

_ _ _"""""",_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

.IfIiJ,"._""""'W".'=:i'."''''~''I\;

___

''''''''''''""''''*"_"

_-=""""""=

h""",'-"","",,",,'',""""","'"'"""'"".........

c

POST PROCESSOR PHASE I

Statements 1 - 7 are changes to the main program.

Statement 1 branches on

indicator (equal) when the "FINI" card is read to initialize the starting sector
address.

Statement 2 branches to the read disk routine.

to the write disk routine.
rather than Phase 3.

Statement 3 branches

Statement 4 branches to set up the calling of Phase 2

Statement 5 branches to call the next program.

Statement 6 changes the message from "Reload G. P. Output" to "Starting Pass
Two." Statement 7 changes another message.

The old message was, "Use

Phase 2, Contouring", the new message is "Calling Ph 2, Contouring".

Statements 8 - 12 load the program on the disk.
If-"","

~I

Statements 13 - 21 load the changes into core.

Statements 22 - 31 are the read disk routines.

Number 22 is a two position

field to receive the transmission from the BTM entry_

The group mark on the

disk is the 81st character and this program only has 8; positions defined for
the read in area so that the first character beyond the read in area must be saved.
Statement 24 accomplishes this.

Statement 25 then reads disk.

Statement 26

turns off WLB/RBC console light, and statement 27 returns the digit moved by
statement 24.

Statement 29 returns to the main program.

Statements 34 - 44 are the write disk routine.

Again in order to get all 8_

positions on the disk the 81st character must be moved ('36) anp a group mark
placed in the 81st position ('37).

Statement 38 writes on the disk, statement 39

111-23

- - - - - _ . _ - - - - - _.. --_ .. _ - - - - -

479

o

'7

tt

o

•

-turns off the WLR/RBC light and statement

4P

replaces the digit moved.

Statement 41 adds one (1) to the sector address and statement 41 returns to
the main program.

Statements 43 - 48 set up the program to call Phase 2 rather than Phase 3 if
desired.

Statements 49 - 54 call the next program.

o

o
III~24

...M

.

\;6"\;'/-'· .... ·

_ ..... "._.,.

,

.. ··:...It.;~.:.:.;w~oIil...;..;...j,..;~_·_"c •

i:li'l
I

I

POST PROCESSOR'PHl

C

READ-WRITE DISK
STATEMENT NUMBER

CORE LOCATION

OP CODE

PADDRESS

Q ADDRESS

1

11132

46

19784

01200

2

11556

17

19696

00000

3

19512

17

19806

00000

4

19596

17

19908

00000

5

19620

17

' 19952

00000

6

02033

STARTING PASS TWO
(Alphamerically Coded)

7

01985

CALLING PH 2
(Alphamerical1y Coded)

-

-

CORE TO DISK

(;\1

8

01770

34

01808

00701

9

01782

16

00004

41000

10

01794

38

01808

00702

11

01806

48

12

01808

10

58002

00000

00

WADER

13

00000

36

19694

00500

14

00012

36

19774

00500

15

00024

36

19854

00500

1II-25

~~~--

_ _ _ _ _ _ I_~_. __ -----------~--.-.------.. - ..----.-~ ______..____ ._~.. ____ ~ ____. _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _

o
, 8 (1

L!

0

POST PROCESSOR PH!
READ-WRITE DISK
STATEMENT NUMBER

0

CORE LOCATION

OP CODE

PADDRESS

Q ADDRESS

16

00036

36

19934

00500

17

00048

36

01770

-00500

18

00060

36

00080

00500

19

00072

49

00080

20

00080

36

00000

21

00092

49

00000

22

19694

00

23

19696

34

19770

00701

24

19708

25

19703

01850

25

19720

36

19770

00700

26

19732

46

19744

03700

27

19744

25

01850

19703

28

19756

11

19775-

00001

29

19768

42

30

19770

10

20000

-01017

31

19782

70

32

19784

16

19775

02000

33

19796

49

11496

0

34

19804

00

0

00500

-

III- 26

,f
l..!

8 ')_

0

POST PROCESSOR PHI
READ-WRITE DISK
STATEMENT NUMBER

CORE LOCATION

OPCODE

PADDRESS

QADDRESS

35

19806

34

19892

00701

36

19818

25

19837

10086

37

19830

15

10086

OOOOF"

38

19842

38

19892

00700

39

19854

46

19866

03700

40

19866

25

10086

19837

41

19878

11

19897

00001

42

19890

42

43

19892

10

44

19904

06

45

19906

00

46

19908

16

19939

06000

47

19920

39

01985

00100

48

19932

42

49

19934

10

62002

00000

50

19946

00

0000

51

19952

39

01931

00100

52

19964

48

00000

00000

53

19976

34

19934

00701

54

-

00000

01100

~~

'"

-

19988

36
IIT-27

-

-

19934

00702

li83

0

I

. 'nrittritr ' .

o

*.

POST PROCESSOR PHASE II

Statements 1 - 16 are the read disk routine.

The main program branches to

the read statement (1#4), then checks indicators (statements 5, 6, and 7).

If

the disk address check or read check indicator is on a branch to a seek (#13) is
made.

Following a correct transfer from disk to core the input data is

transferred to the odd input address.

Statements 8 - 12 are needed for this.

Upon completion of transfer of the 8_th character, statements 13 and 14
initialize the transmit digit instruction (##8).

Statement 15 adds one (I) to the

sector address and ##16 returns to the main program.

Statements 17 - 29 are the write disk routine.

Since there are only 8~

positions defined as an output area, the 8lst position must be saved (#121) in
order to set a group mark (#l22) to terminate the read instruction of the next
program.

Following this is the write disk instruction (1123), indicator checking

instructions (statements 24, 25, and 26) and a branch to a seek (1119), if
necessary.

After the seek the digit is transmitted to the 81st position (112_>

before returning to statement 21.

Upon completion of the transfer from core

to disk, the 81st digit is replaced (1I27), one (I) is added to the sector address

(1#28) and statement 29 returns to the main program •

. Because Phase 2 is not always used and only two areas are defined on the
disk for input-output, it is necessary to move the data output by Phase 2 so
that input for programs to come will be properly oriented.

Statements 34 - 60

do this.

o
111-28

..

~

Statements

3~

- 33 move the output exchange statements to the high end of

core, out of the way of incoming data.

0

On completion of the exchange,

statements 61 - 7~ set up the call of the next program.

Statements 71 - 73 are changes to the main program.
read routine.

#71 branches to the

#72 branches to the write routine and 73 branches to end of

job routine.

Statements 74 - 79 load the program on the disk.

Statements 8~ - 94 load the changes into core.

o
III-29

--.----------------~~~~

: &#$ mtb

*iriririrt

mzt

0

POST PROCESSOR PH2
READ-WRITE DISK
STATEMENT NUMBER

CI

CORE LOCATION

OP CODE

PADDRESS

Q ADDRESS

00000

01150

34

10720

00701

10746

36

10720

00700

5

10758

46

10734

03600

6

10770

46

10782

03700

7

10782

46

10734

00600

8

10794

25

02365

15000

9

10806

11

10800

00001

10

10818

11

10805

00001

11

10830

14

10805

15080

12

10842

47

10794

01200

13

10854

16

10800

02365

14

10866

16

10805

15000

15

10878

11

10725

00001

16

10890

49

01844

0

17

10898

10

20000

01024

18

10910 '

70

19

.10912

34

10898

00701

1

10720

10

2

10732

00

3

10734

4

-

"
I

-

0
III-3D

48\)

0

POST PROCESSOR PH2
READ WRITE DISK
STATEMENT NUMBER

CORE LOCATION . OP CODE

PADDRESS

Q ADDRESS

20

10924

15

02550

00000

21

10936

25

10935

02550

22

10948

15

02550

OOO~

23

10960

38

10898

00700

24

10972

46

10912

03600

25

10984

46

10996

03700

26

10996

46

10912

00700

27

11008

25

02550

10935

28

11020

11

10903

00001

29

11032

49

03264

0

30

11040

31

19618

11084

31

11052

31

19938

11404

32

11064

39

03475

00100

33

11076

49

19626

0

34

11084

(19618)

00

0

35

11087

(19621)

00

000

36

11092

(19626)

26

19625

10903

37

11104

(19638)

12

19625

02100

38

11116

(19650)

11

19620

00001

39

11128

(19662)

14

19625

00000

1II-31

----~~---.-----~-----

.-

-

C;

C)
!

48 'l
--------._-

.... _--------

-------"._----------- -

· '11'11

POST PROCESSOR PH2

0

READ WRITE DISK
STATEMENT NUMBER

0

0

CORE LOCATION

OP CODE

PADDRESS

Q ADDRESS

40

11140

(19674)

47

19734

01300

41

11152

(19686)

12

19625

00100

42

11164

(19698)

11

19620

00001

43

11176

(19710)

14

19625

00000

44

11188

(19722)

46

19686

01100

45

11200

34

19888

00701

46

11212

(19746)

36

19888

00702

47

11224

(19758)

46

19734

00600

48

11236

(19770)

34

19874

00701

49

11248

(19782)

38

19874

00702

50

11260

(19794)

46

19770

00700

51

11272

(19806)

11

19879

00100

52

11284

(19818)

11

19893

00100

53

11296

(19830)

12

19620

00001

54

11308

(19842)

14

19620

00000

55

11320

(19854)

47

19734

.01200

56

11332

(19866)

49

19952

0

57

11340

(19874)

10

00001

00005

58

11352

(19886)

00

59

113q4

(19888)

10

20001

00005

60

11366

(19900)

00

( 19734)

111-32

-

[i

8b

0

POST PROCESSOR PH2
READ WRITE DISK
STATEMENT NUMBER

CORE LOCATION OP CODE

PADDRESS

Q ADDRESS

61

11368

(19902)

00

59456

24563

62

11380

(19914)

00

62634

15963

63

11392

(19926)

23

00574

8730;7!-

64

11404

(19938)

10

62002

00000

65

11416

(19950)

00

66

11418

(19952)

39

19901

00100

67

11430

(19964)

48

00000

00000

68

11442

(19976)

34

19938

00701

69

11454

(19988)

36

19938

00702

70

11466

C

..1"

CHANGE TO MAIN PROGRAM

71

01832

49

10758

00000

72

03252

49

10936

00400

73

03372

49

11040

00000

74

15000

34

15038

00701

75

15012

16

00004

41000

76

15024

38

15038

00702

77

15036

48

CORE TO DISK

-

111-33

0
48 ~J

--------~---

---~~--

----~-

_

"Ii

±""

rit ri

de&" t "bit"

"".. 'ibritarictbhftp"-'

0

If! "

POST PROCESSOR PH2
READ WRITE DISK
STATEMENT NUMBER

C

CORE LOCATION

OP CODE

P ADDRESS Q ADDRESS
60001

20000

36

00080

00500

00012

36

00160

00500

82

00024

36

15000

00500

83

00036

36

10720

00500

84

00048

36

10800

00500

85

00060

36

10880

00500

86

00072

36

10960

00500

87

00084

36

11040

00500

88

00096

36

11120

00500

89

00108

36

11200

00500

90

00120

36

11280

00500

91

00132

36

11360

00500

92

00144

36

11440

00500

93

00156

36

00000

00500

94

00168

49

00000

78

15038

10

79

15050

00

80

00000

81

o
1II-34

490

POST PROCESSOR PHASE III

Statements 1 - 18 are the read routine.

The main program branches to the

read instruction (#5) and transmits the starting core location into the disk word

(II 3 and 4).

Statements 6, 7, and 8 check indicators and branch to "seek" (#1)

if necessary.

Statements 9 - 14 transfer the input data to the odd input address.

Statem ents 15 and 16 initialize statement 9.

Statement 18 returns to the main

program.

Statements 19 - 32 are the output routine.

The main program branches to #23,

checks indicator (program switch 2) and if it is on punches a card (#31) then
returns to the main program (#32).

If program switch 2 is off the program will write

the output on the disk and return to the main program (#3~).

o

Statements 33 - 35 are !'fill in zeros".

Statements 38 - 4¢ are the end of job message.

Statements 41 - 45 type end of job and call the next program.

Statements 46 - 51 are changes to the main program.

Statement 46 "branches

and transmits" to the read routine and 47, 48; 49, and 51 branch and transmit to
the write routine.

Statement 5¢ branches to the end of job routine.

Statements 52 - 57 transfer a core image to the disk.

o

Statements 58 - 67 load the changes into core.

III-35

49

m

!

•

r,.,."· .

r

OJ

POST PROCESSOR PH3
READ WRITE DISK
SATEMENT NUMBER

0

o

CORE LOCATION OP CORE

PADDRESS

Q ADDRESS

1

19524

34

19544

00701

2

19536

49

19558

0

3

19544

10

00000

01000

4

19556

00

5

19558

36

19544

00700

6

19570

46

19582

03700

7

19582

46

19524

03600

8

19594

46

19524

00600

9

19606

25

03653

00000

10

19618

14

19612

03732

11

19630

46

19674

01200

12

19642

11

19612

00001

13

19654

11

19617

00001

14

19666

49

19606

0

15

19674

16

19612

03653

16

19686

16

19617

00000

17

19698

11

19549

00001

18

19710

42

19

19712

34

19732

00701

20

19724

49

19746

o

1II-36

-

492

POST PROCESSOR PH3

0

READ WRITE DISK
STATEMENT NUMBER

CORE LOCATION

OP CORE

. 21

19732

10

22

19744

78

23

19746

24

PADDRESS

Q ADDRESS

20000

02039

46

19832

00200

19758

15

04139

OOOQ.L

25

19770

38

19732

00700

26

19782

46

19794

03700

27

19794

46

19712

03600

28

19806

46

19712

00700

29

19818

11

19737

00002

30

19830

42

31

19832

39

03979

00400

32

19844

42

00000

00000

33

19856

00

00000

00000

34

19868

00

00000

00000

35

19880

00

00000

000

36

19890

10

64001

70000

37

19902

00

38

19904

59

45624

56300

39

19916

62

63415

96323

40

19928

00

43565

56501="

41

19940

39

03085

00100

42

19952

39

19901

00100

0

III-37

--.--~~"-.~.-----

-

-

~----,~-

.. - - - - - ..

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0
4~3

"'!!Jw!f"!II'!!lmS"'!!!!I,?"!!!i'VUSII",,'

_

tr

... 1

o

&d

,

IT'

POST PROCESSOR PH3
READ WRITE DISK
STATEMENT NUMBER

CORE LOCATION

OP CORE

P ADDRESS

Q ADDRESS

43

19964

48

00000

00000

44

19976

34

19890

00701

45

19988

36

19890

00702

CHANGE TO MAIN PROGRAM

0

-

46

01940

17

19558

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47

02536

17

19746

03978

48

11754

17

19746

03978

49

12546

17

19746

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50

12570

49

19940

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51

13894

17

19746

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52

03654

34

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53

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41000

54

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38

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55

03690

48

!;()

036H2

10

{)2002

00000

57

0:.n04

00

CORE TO DISK

0
III - 3H

C'

POST PROCESSOR PH3
LOADER
STATEMENT NUMBER

CORE LOCATION

OP CORE

PADDRESS

QADDRESS

58

00000

36

00080

00500

59

00012

36

03654

00500

60

00024

36

19524

00500

61

00036

36

19604

00500

62

00048

36

19684

00500

63

00060

36

19764

00500

64

00072

36

19844

00500

65

00084

36

19924

00500

66

00096

36

00000

00500

67

00108

49

00000

C)

o
111-39

•

If!

o
IV

Appendix 3

Sample Problem

o

o
4U6

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. - ........-_.-.-- ·-·------4

_ _ _ _ _ _ _ _-ilr.2;.,1;.:8~1:-----~Z;---::l'71t:-...---------------------__t
121113
2 l6
I
..... --~ '--'-" - ... ~
-11221~··98 -05
~ "-O'?O.'O-O'

...

16

~

L

... -'~H .-.------.-......

gn~

:~ :Z'i~ ~:~-:i~+---::~- ~:~g
IIC

Z Jl

2 38
... ~ ~9r'- -.-..- ....-- ..... -..... -.-.....-.--...----...-.. -.-... -..'-"'-1

12166
2 1(0
----------,tr.Z'l-:1;-:f,;'-;8:-----ii2, . ; ; k C ; ; 9 ; - - - - - - - - - - - - - - - - -......-

......Qf... __..l.!!!~ __._ _.__. ______.___.________

H;'ji,'i '>IJIH')

5~~·Jn~~-----· .. ---:-·--· -.-....~ ... --.-.--..------~

1215"

~~.

I Ii)

.. 1,)'·:..:0000 .. -·· ..-·- .. •·· ..- ..... -------... -.,--.----.•,---.. ~,

". . IHU·

.-.. . . -.......

2, lH

1 II )'}
~C;
2,111
'1 ·ii;j'i ..·.. · .--- .. l'iE.. ~.-.-------.

o

·IH81

} ~~:~'.:

nt

j

5 -OOUO

12182

1 01\)

"HO

10

12l71·

5,~()OUn

iZ7'th
.1[.22-"1'6~00'

I

-------ro .--.-.-----------..------.. --.--.---.--.- ,

-.... -12164..
12110\

j

I 04h PTtNr
l oltl, RtcNI

ltd
1

---..-.--.-.- ....-~ ..-.,.--....--.... -... - ... - ·-··----··-··-·---·---···· .. -····1-2104""
····-·-·~j2.... -·-·-··--·----·--:-------·--~------i
12\0" ....·---- -21""'--'"
1
·
,
!
-.- .... -.-- ...... --.... --.-.. ---..----.--.....- -.---.... --.-----. ---· .. -· ..-·.. --IHill·
--'-'
-------.-----~.

UC
2,1)'0
..--- -r;no Tvrr--lE"'-"
~

.

..----.. --. -----.... - ·----·-riH 1'8 ··\"9s685·ji·..aifeei-----49-19522···---·-----·---·

....-.. -..

llnKli .-It

. ----.. ----.. --.-------

7 -0

3-0

11 1l,ENIl P"A~f2iJ

to

N~qOI)OOI)Ob •
10 NllunOIlOOO __ . ___ ..__ . ____.. H_. ______._.__

- .. -Ti1hir--·---·-To"NTnmm 1U i o ·
li~?OOOOOO

l.F,O"
ll',I'}

lu H·Il.".S3l<))
10

l3',;>

0

for D

<:

Q

Z

-=:

0

for D

:>

a

Therefore it is possible to represent three types of surfaces with the single equation:
.. Z

.. D

=

0

The constants A, B, C, D, and E are program input data o

o

mil

b#ttt

- 3 -

o

GENERAL RAY TRACE
INPUT
A header card and

3 cards for each surface are required inputo

Ray information

may be entered in 2 ways, either one ray per card or as a fan of rays.

To enter

single rays, switch No o 1 must be ono
CODE
REFR (1)

HEADER CARD:

Cols. 1 - 11

Initial index of refraction (may appear aqywhere in Cols o 1 - 11).

•

Ex •• If the initial medium is air, the number 1.0 can be
punched in Cols. 1 - 3.

Col. 12
NOSUR

Blank

Cols o 13 - 14 Number of surfaces.

If the number of surfaces is 9 or less,

puneh it in Col. 14 and leave Colo 13 blank.

o

TOL

Cols. 15 - 29

Iteration tolerance in form + O.lOOOOOOOE.YI.

This number i.

used to establish a criterion for convergence of the iteration
processo

Convergence is assumed when the increment magnitude

il leIS than the tolerance. It is recommended that +O olOOOOOOOE-06
(01 X 10-6 • 10.7 ) be used, as onlY 8 places are carried in
computationo It

may

so_times be necessary to relax the

tolerance to + O. lOOOOOOOE-05 , either to obtain convergence
or to .peed up the program.
Cols. )0 - 80 Blank

·0

518

-4-

o

SURFACE CARDS:

Card A:

IO(I)

Col. 1 - 11

x ...

coordinate of origin of local system" punched

in 8a..

~

as the initial index of refraction

on the "adar card.

YO(I)

Cols. 12 - 22

Y - coordinate ot origin at local system, punched in

aame tashion as X - coord1na'te

ZO(I)

Cole. 2.3-"

z-

coordinate of origiJl of local system" punched in

a. .a tashion as X .. coerdina'te.
Alpba(I)

Cola. 34 ..

lab Y &xia euler

a~l.

(C)() in decimal degrees, pUl'lchad in

aaM tashion as X - coordinate.

Beta(I)

Cola. 4S -SS

X axia euler angle

(/3> in decillal degr.es" punched iJt

c

alUll8 ruhiGll as I - coordiRa'te.
Cela. 56 .. 66

zan.

euler angle

(7' in decimal d~gree., punched ill

aame ta.hion as X • coordina'e.
Cola. 61 - 1T

Blank.

Cola. 78 ... 80 It i. 8Uggea'ed, but Rot required, that the surface carda
be punched Oll .. OlB .. OlC, W, 02B, etc., in Cola. 18 - 80
\0 eneure that t hey are kept in the correct order.

Card B:
'l'he tirat tift tielda gi... the ooettie1enta in the aUrface equatiOil

r

.-AXI

+ BIt

• CZ! + Z • D

u.2 + yt •

0,

a.

tollows:

.1(1)

Cola. 1 .. ~ A (punched in _tubioa a. X .. coordinate on Card A)

B(I)

Cola. 12 .. -2f,B (punched in __ ta.hion as A).

C(I)

Cola.

23 .. 3lP (punched in a... tasbion as A).

D(I)

Cola.

lb ....w..p (punched in a_ tashion as

B(l)

Cob.

16 -

.A).

5~ (pancbecl ill a_tashion as A).

519

-----------

o

HNUrnM'

y-

•• : sr.

tst

ft" "

T·

- S•

o
Refr(I)

Cols o S6 - 66

Index of refraction of medium following the surface, except
in the case of reflection, when the

negati~

of the index

of refraction for the previous surface is us.do

(Field is

punched in same fashion as A)o
Cols o 67 - 77

Blank

Cols o 78 - 80 May be punched

8S

suggested for Card

Ao

Card C:
APl(I)

Cols o 1 - 11

X - coordinate of center of

circular-~nnular

aperture or

coordinate of center of hyperbolic aperture or X lower
bound of base of rectangular-trapezoidal aperture o
AP2(I)

Cols e 12 - 22 Y - coordinate of center of circular-annular aperture or
coordinate of center of qyperbolic aperture or X upper bound

o

of base of rectangular-trapezoidal apertureo
AP3(I}

Cols. 23 - 33

Inner radius of circular-annular aperture or length of
semi-major axis of hyperbolic aperture or Y lower bound
for rectangular-trapezoidal apertureo

AP4(I)

Cols o 34 - 44

Outer radius of circular-annular aperture or length of
semi-minor axis of hyperbolic aperture or Y upper bound
for :rectangular-trapezoidal apertureo

APS(I)

Cols o 4S - SS

Y lower bound for hyperbolic aperture or reciprocal
slope of left hand side of
aperture 0

o

recta~lar-trapezoidal

Enter 0. for c ircular-anJilular apertureo

52U

- 6 -

Co18 0 56 - 66

o
Y upper bound for hyperbolic aperture or reciprocal
slope 0f right hand side of reetanular-trapezoidal
ape,rture o Enter Oofor circular...annular apertureo

NAP (I)

NOUT(I)

Cols o 61

Blank

Colo 68

Ape rture code
circular - annular

1:

rectangular-trapezoidal

2:

hyperbolic

Colo 69

Blank

Colo 70

Output code

Cols
RAY INPUT

Blank:

0

71 - 77

Blank:

no output a t surface

1:

output at surface

Blank

C·\

1

(Single ray per card, switch Ion)

One record, either typed or punched, is used for each ray.
with a bar over them are system coordinateso

NOTE:

Coordinate.

Those without a bar are local

coordinates 0

x- coordinate of 1st point on rayo

XA

Cols o 1 - 11

YA

Cols o 12 - 22 I . coordinate of lat point on rayo

ZA

Cols o 23 - .3.3

Z ""

coordinate of 1st point on ray.

RPAR 1

Cols o 34 - 44

X-

coordinate of 2nd point 0n ray.

or! direction cosine of ray at 1st point.
RPAR 2

Cols o 45 - 55 Y - coordinate of 2nd point on ray
or

RPAR .3

Y direction

cosine of ray at 1st pointo

Cola 0 56 - 66 Z - coordinate of 2nd point on ray
or ! direction cosine of ray at 1st pointo
Colo 67

.---------~-.--~---~--

Blank

521

'±z btt"j

- 7-

o

Input code

Colo 68

NIN

NAXIN

Blank:

2 points

1:

1 point and direction cosine

Colo 69

Blank

Colo 10

Optical axis intersection computation code
Blank:

b,ypas8 computation of intersection of image ray
with optical axis o

1:
Cols o 71 - 13

IRAY

Perform aboTe computation

Ray identification number (right justified)

Cols o 14 - 80 Blank.
(Fans of rays on 2 cards)

RAY INPUT
Card 1

Cols o 1 - 11

FXUl, the maximum

Cols o 12 - 22

FZ1, the

Cols o 23

0[010

X coordinate at t he 1st pointo

Z coordinate at the 1st pointo

3) XGAP1,the X spacing between fans at 1st pointo

Xcoordinate

Cols o 34 - 44

FXP2,

Cols o 45 ... 55

FZ2, the! coordinate at t he 2nd point.

Cols. S6 - 66

XGAP2, the X spacing between rays at the 2nd pOint.

the maximum

of each fan at the 2nd pointo

Card 2
Co1s. 1,·'11

FYU2, the maximum

Y coordinate

at the 2nd pointo

Cola. 12 - 22 YGAP2, theY spacing between rays at .he 2nd point.
All fans are assumed 'to originate ~t 1 :II: 0 at the 1st pointo
The following sample ray trace problem will better illustrate the useage of the

Horn

pro gram 0

o

The surface

s.Yste~

to be traced is as follows:

522

Ii'

OBJECT

0.0000

SURFACE III

3.0000

SURFACE

3.5000

c

- - - - -

R

SURFACE

112

3.8525

113

= 1.15

' - R = .85

- --

4.3525

SURFACE

4.8525
4.9525

------ - --

114

-- --- ---- ----

e

.500 l+l

/ELLIPTICAL
LENS

6.0000
6.5000
6.7500

1.000

IMAGE

NOT

1'0

-..f

8.0000 -

x

SCALE

y

z

z
FIGURE

• SAMPLE RAY TRACE SYSTEM

..

------

...._---_..

-_.--- .... _._-- --'--'-

I

01
523

r

iW

$1

#rim

•

- 9 -

o

DATA INPUT TO GENERAL RAY TRACE
PROGRAM FOR SAMPLE PROBLEM

SURFACE

DATA

SURFACES 1

&

2

These are both spherical surfaceso
F = AX2

=L..
2

+ By2
X2

...

CZ2 + Z

1
+ -y2

R

a:

.. L..

2 R

2

The surface equation becomes:

R

0

Z2 + Z ==

= - 0435 x2 - 0435y2 - 0435 z2

..

Z ==

0

0

(Surface #1)

= 0588 x2 ... 0588 y2 + 0588 z2 ... Z = 0 (Surface #2)
These are not coneso

o

Therefore D

=E

= 0

The vertex planes for these surfaces are perpendicular to the Z (optical)
axis 0

Therefore Ct. ,

J3,

and

r

are zeroo

The vertex coordinates are:
Surface #1

(0, 0, 3 00)

5\lrface #2

(0, 0, 3050)

0

The index of refraction following Surface #1 is 10523, that following Surface

#2 is 1 0 00 0
The apertature on both surfaces is a circle of 005 inches diametero

o

- 10 -

o

Surfaces .3 & 4
Both surfaces are planes arranged to constitute a prism o

The first, No o .3,

is arranged so that rays are deflected in the negative X direction o

The

second surface, No o 41 is perpendicular to the optic axis o
The surface equation for both surfaces is:

F = Z = 0
A=B=C=

D=E=O

Surface No o .3 is rotated 45 degrees when positioned in the system o To
accomplish this rotation, it is necessary to specify the angle alpha equal
to 45_degreeso

The rotation angles, alpha, beta, and gamma are defined:

o
~~

yt =

yw

Zt

xt

____

~yl

Jlro----~

X"

y

xt

= Xl'

o

"Ell

m

tr

$

r

it

- 11 -

o

The specified apertature is a square 1" xl" 0

Therefore the minimum and maximum

allowable x and y values are (0 0 5, 0 0 5) and (-005 9 0 0 5) respective1yo

These

After rotation of surface No o 3,

values apply to the surfaces before rotation o

the actual minimum and maximum x apertature values will be corrected by the
program to (~005/

0 0 5/

-{2,

-{2).

AP5 and AP6 are the inverse slopes of the

left and right edgee of the apertature as viewed from the object point (positive
Y up)o

In the sample, these slopes are reciprocal infinity or zeroo

equal to 1 to specify a rectangular apertature o
output data at the surfaceso

NAP is set

NOUT is set equal to 1 to obtain

The index of refraction of the prism is 1 0 60

Surface 5 & 6
Surface

5 is an elliptical cylindero Surface 6 is a simple plane with input

similar to surface No o

y2

0

a

2

+

The equa tion of the ellipse in the YZ plane is:

40

Z2
2 == 1
b

a

==

b

1

==

005

The surface equation, adjusted so that the origin is at the point nearest the
object point, is:

F == -0 0 25 y
Therefore A

=

D

2

=

E

=

0,

B

=

-0 0 25,

C = -1 0 00 0

Note that surface

No o 5 is a cylinder with rulings in the X direction o If it had been desired
to translate this surface off the optic axis in the Y direction, then YO would
be specified according1yo
This

pro~ram

was originally written by William Webb of Goodyear Aerospace

Corporation, Akron, Ohio and to that gentlemen goes the credit for t his signifi-

o

cant contribution to the lens desiGner's kit of toolso

The program ha s been

altered slightly to suit current needs and is being maintained b:y the writero

-----------------------------------------------------

~~--'

1:1

- 12 -

SAMPLE PROBLEM DATA INPUT

SAMPlF PROBLEM. PROGR.M NO.

14~'A-6~

•

1~/(1f'-/63

C'

7+0.1000~000f-~6

1 •."-'

0.0

0.P

3.0

0.'"

0.0

0.0

lA

-.435

-.435

-.435

9.0

0.0

1.5~'

18

0.0

0.0

0.0

18.5

0.0

0.0

0.

121.

3.5

0.0

0.0

0.0

2A

0.588

0.~e8

0.588

0.pj

91.0

1.0

28

0.0

0.9

0.0

0.5

0.0

0.0

0.0

"'.0

4.352'5

-45.~

0.0

0.0

3A

0.e

0.0

0.0

0.0

0.0

1.6

3B

-0.5

121.5

-0.5

9.5

0.0

0.0

0.0

4.9525

0.0

0.0

e.0
e.e

0.0

0.0

0.0

13.0

0.0

1.Jlf

-0.5

e.5

-0.5

0.5

0.0

tIJ.0

0.

0.0

6.0

0.0

"'.-tIJ

0.0

5A

0.0

-0.25

-1.(21

tIJ.0

121.0

1.5

58

-2.0
.

2."

-1.0

1.Ci'J

0.8

0.0

0.'"

0.13

6.75

0.0

0.0

0.0

6A

0.0

0.0

fJ.fJ

0.0

0.0

1.0

68

-2.13

2.0

-l.et

1.0

ttJ.ttJ

0.0

13.0

tIJ.0

8.0

0.0

0.13

0.fJ

7A

0.0

0.0

0.0

0.0

0.13

1.0

78

0.0

0.0

13.0

121."

0.fJ

0.8

0.1

0.0

0.1

0.3

3.0

0.!

0.1

0.~

,

o

o

lC

1

2C

1

1 1

3C
4A

4B

4C

1 1

1 1

5C

1 1

e

C'

6C

1

7C

o
521

Oh

0

t

rtrr

rirbH rirlt

- 13 .;.

SAMPLE PROBLEM DATA OUTPtrl'

SAMPLE PROBLEM, PROGRAM NO. 143A-63.

OBJ PT

RAY SURF
1
1

1
1
1
2

1
2

4

5 NO INCIDENCE
~

0

2

3

2

4

2

.3"'568

-.~55S9

.30fl'CfI'~

.30e~2

-."'35e9

ZOR M

.0~PJ0'"

~.08521

.99781

XOR K

X OR K

.100091

.~00~0

y~

L
Z OR M

• "''''C'J00

.309J~

.28848
.29772
3.39209
-."4675
-.01308
4.30574
-.42369
-.15807

-.32813

Y OR L
Z OR M

.10000
.""000
• "0QJ00
.10000
.0001'30
.0000O

3.0t'WJ&2'0
.30"'0"

.OO~00

3.00"'P0

4.9525~

X OR K

.10"0
.00000
.00000
.10000
.00000
.0M00
.10"'00
.00000
.00000
.10000
.QJ000QJ

.80000
• 30D)00
3.00fJ00

-.00136
.30409
3.04095

.rlJ~00

-.01~C'J6

.3Bf1fJ0
3.00C'J00
.00000
.3009."0

.29198
!.44-823
-.03302
.06923
4.31947
-.26404

I(

2

y OR L

l OR
X OR
y OR
Z OR
X OR
Y OR
Z OR
X OR

5

M
K.
L

M
K

,..l
K

Y OR l
Z OR M
XOR K
YOR l

6
7

NO IMT W/OPT AX

2
'3

3

2

3

'3

'3

,.

'3

0

1

3

5
6

• 000t2J0

• 10.fJ9.JfJ
.00000
.0fJ0011
.10000

.3e0~0
3.0~000

.,0fJ0fJ
.30900

3.00~t""

3.~012J

.0000fJ
• ~l'J0f'0
3.1JfJN0
~0"'fl'00
.3~"

,.0QJ00QJ

.0PJfI01J

.fJ0tHJf8

.30000

X OR IC.
Y OR L

.QJ0000
.1000fJ
• 00P100

Z OR

.00fl'0~

S.9fJOO0
.0rm.!J00
.30"''''0

lOR fit
2

DIR COS

.300"0

Z OR M
)( OR K

2

tNT PT

.100~0

Y OR L
2

PT/DC

.0000121

X OR

3

2D

X OR K
Y OR L

Y OR L
lOR M

1

12/02/63

M

X OR K
y OR l
Z OR M
X OR K
Y OR L
Z O~ M
X ~ K
y OR l
Z OR M
X OR K
y OR L
Z OR "4
X OR K
y OR l
l 09' M
X OR K

.10000
.80f/J0flJ
.89000
.10000

• 00000
.00000
.10C"091
.00000
.00080

.1emJ0
.00000
.00900

.1f2'000

3.~00

-.30000
.311000
3 .80f/J0flJ

-''''~633

4.95250
-.99486
-.;7026
6.03553
-1.272!9
-.43702
6.75000
-2.08!77
-.63295
8.0Pft09J

-.300fJ0

-.31159
.30869
3.08697
-.30660

.3000'0

.l'?55

~.00000

3.38486
-."'1229
-.02183
4. 34192 {'I
-.14898
-.14338
4.95250
-.58127
-.5278"

-.'M00
.''''000
!.m00021

-.3""'"
• 30fJCJJ0
3.00000
-.30000
.3fJ~

.0fM'0fJ
.0t'K'J0('J

3.0(?J000

,10000

-.391fJ00

6.07531
-.74N0

-.3QJ4~3
.894~9

-.494!5
-.19014
.84810
- • ..,9091
-.3042'
.53fJ8S
-."'211~

- •.0.2."1
.99933
-.92552
-.24762
.96851
-.'1870
-.15416
.928~7

-.'4192
-.24"62
.8e'311
-.36128
-.08675
.92140
-.54192
-.1301~

.83028
-.54192
-.13181'
.83tt28

.01673
-.03736

.99916
.28045

-.3",.,•
.91~'34

-.21391}
-.19fJ21
.95815
-.~4225

--.3fJ434
.!8895

-.22816
-.fJ8569
.96984

-.3.125

528

;"iI'

- 14 ..
y

:Z
:3

•
It

4

,.
4
5
5

5

5
~

5

X C!JR·K

7

Y OR(
NO tNT W/Op·T

3

OA l

.DR M

Z

M~

X

~

~X

1

~

y OR L.
Z OR M

X OR
Y OR

2

,

l

em

X OR
"fOR
z OR
X OR
Y OR
Z OR

4

5 APERTVRE STOP
1

6

6

6
6
6

1

2
3
4

5

, •.,.e

.J.,..
.s.,..

J.00fJefJ·
.3~fJ
.J~

'~fJ86"8

-'t'~t~~

- •• "!~
.,~ft'·'
- ....1"2

, .29166·
,.• Z'166

~.1"'12·

'.51'49
..... "21126

·~ •••·1"

-.82,,26
•• "!2.3
-.'6'll

_,"2"1"

·-.t."
."~,.·1

.0eff00

.~

.00080

.000fJ0
.00080

.,~

• 304fJ9

3.~fJ

!.QJ4.'~

OR K

~0QJ0fJ0

.~

• f)~

• Nfl•

YOR l
Z OR M
X OPt K
"f OR L
OR M
X OR f(

.1¥'0f&fJ

.3fJ1J08

.292'.,1

-.,24751·

l
M.

f(

OR L

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GENERAL RAY TRACE PROGRAM

o

21.

CARD '/0

DIMENSION

XOC~~).YO(35).ZO(~~)tAlPHA(~~)tAETA(35}tGAMMA(3~)tAC~5)

DIMENSION

RFFR(36).APIC35).AP2(3~)tAP!(~S).AP4(~5).AP~f35),AP6C'5'

DIMENStON

NAP(35),NOUTC35).CK8A~(35',ClBA~f35J,CM~ARf35JtX~eAR'3~'

DIMENSION

Y~BAR(35Jtl~BAR(35)tB(35),C~35).D(1~Jt~t3~)

DI~ENSION

KKK

R(35),KSURC35)

1

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GO TO (813. 803), KKK
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803 PRINT 115

115 FORMAT (20HlOAD DATA,PUSH START)
PAUSE
813 KKK •

2

o

READ TITLE CARD
READ ?
2FORMATC49H

,8H

PUNCH 2
PUNCH 100
JB

= 50

PUNCH 1
,PUNCH 1.00
PUNCH 10'"
PI

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3.14159265

CONY • P1/180.
C

READ HEADER CARD
1'-'12 FORMAT
READ

CFl1.5,I3,E15~8)

1~2,

REFR(l),NOSUR,TOl

C

REFR • INITIAL INDEX OF RfFR

C

TOl

= MIN.

LIMIT ON

NOSUR • NOSUR+l

ITERAT~ON

,NOSUR. NO. OF SURFACES

o

JNC~FMFNT

539

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o
00 203 I

c

~

25

2. NOSUR

READ SURFACE DATA
103 FORMAT CFl1.S. FIt.5. FIl.5, FII.5, FIl.5, Fll.5.J2.12,13)
REAO 103, XOtIJ,YO(I),lO(I).ALPHACIl.RETA(t).GAMMACI)

c

XO. YO, AND ZO ARE LOCAL SYSTEM SURFACE VERTEX COORDINATES.

c

ALPHA, BETA, AND GAMMA ARE EULER ROTATIONAL ANGLES.
READ 1?!3.Af I) .~( I) tC(!) ,DC I) .F"( I' .RFF'~( J)

a, c. D. AND
REFR = INDEX OF

A.

c

c
203

C

REAO

o

c

REFRACTION FOLLOWING SURFACf.

1~3'AP1(t,.AP2(I)'AP3(1).AP4(I),AP5(1).AP6(I)'NAP(IJ,NOUTCI)

API, AP2, AP3, AP4. AP5, AND AP6 SPECIFY APERTURE DIMENSIONS. SEE

C
C

E ARE SURFACF FQUATTON COEFFICIENTS.

INPUT WRITE UP.
NAP • 0 FOR CIRCULAR-ANNULAR APERTU~E. • 1 FOP RECT-TRAPElOIDAL
APERTURE,

=2

FOR HYPERAOLYC

APE~TURE.

c

NOUT

=0

FOR NO OUTPUT AT SURFACE, = 1 OTHERWISE.

C

QFAD

QAV

nATA

C

SWITCH 1 ON TO USE SINGLE RAY
IF(SENSE SWITCH 1)
2~5 READ 10~t

2~5,

CA~D

INPUT

201

XA.YAfZA,RPARl,RPAR2.RPAR!.NI~,NAXIN.IRAY

C

XA, VA. AND ZA ARE RAY COORDINATES AT FIRST POINT

C

RPARl, RPAR2. RPAR3 ARE RAY COORDINATES AT SECOND POINT

C

OR RAY DIRECTION COSINES AT FIRST POINT

C

MIN

C

NIH-. 1 IF RAYS ARr SPEC. BY 1 POINT AND

C

NAXIN

C

=0
c

IF PAYS ARE sPtc.

~Y

2 POINTS
Dt~. COSJM~S.

1 FOR COMPUTATION OF INTERSECTION OF RAY WITH OPTICAL

AXIS. • 0 OTHERWISE

I~~Y

= RAY

NUMBER.

GO TO 206

~

201 READ 116. FXU1. FZl. XGAP1; FXU2t FZ2. XGAP2
READ 116, FYU2f YGAP2

Po 26

C

RAY INPUT DATA, FXUl • MAX.XR. FZl • lR. FXU2 • MAX. X AT POINT 2

C

XGAPI • X SPACING AT POINT I, XGAP2 • X SPACING AT POINT 2

C

FZ2 - Z

C

FYU2

COOROINAT~

o

AT POINT 2

MAX Y COORDINATE AT 2ND POINT, YGAP2 • Y SPACING AT POINT 2

II

116 FORMATtFll.'.Fl1.5,Fll.5.'11.5,Fll,5.Fll.5)
IRAY • 0

GAP3-flJ.
RPARZ-'VU2
e12

~PAR2=~PA.2-GAP3
IF(RPAR2+FYU2)~0,,814.et4

814 GAP'3.YGAP2
GAP! - fJ.

XA • FXUl
4 XA - XA"!""GAPl

o

IFfXA+FXUl)~l2,8~4,804

804 GAPl • XGAPI

GAPZ •. fIJ.
~PARI
~

FXU~

•

RPA_l • RPARI-GAP2
IF(RPARl+FXU2)_.e0~,8~5

8"5 GAP2

XGAP2

1;

YA • 0.0

ZA

II

R9AR~

FIl
• FZ2

NUt • fJ

NAXIN • 1
IRAY • IRAY .... 1
206 NIN • NIN+1
GO TO (287.288). NIN

o

P. 27

0

208

CKf'ARfll • RPARl
CLeARC1) • ftPAR2

• RP.'"

C~AA~(t)

GO TO 2St

2m.., xo •

~ttARI-XA

YD • Rf'Aft2-VA
ZD • RPA~~·ZA
RALE" • SOATeXD*XD+YD*YD+ZD*ZD)
CKeA~(l)

•

XO/~Al~"

CleAR{ll • YD/tltALfN
CM~Aft

(1) • lO/'AlEN

209 .",eARll) • XA

Y0eARfl) • YA
ZfJ8AR(1) •

O

DO 15

lA-

I • 2. NOSUR

IMl • 1-1
SA • SIN(CONV*ALPHAftt,
CA

• costCONV*ALPHA{t,'

se • SJNCCONV*8ETA(1))
CB • COS(CONV*BETAfJt,
56 • S!"tCOMV*GAMMA(I)
COSCCONV*GA~MA(I)t

CG •

Xl • X88AR{IMlt-xoCt)
Yl • V.BARf IMl '-VO( r I

Zl • l""ARCIMIl-ZOCI)
Rl1 • CA*Cr,+SA*SA*S(;
Jt'l~ •

Rl'

0

-Cl*SG

• c.. Sft*SG-SA*CG

ft21 • CA*SG-SA*s8*CG

5 ft 2

P. 28
R22

= C8*CG

R23

E

-CSA*SG+CA*SB*CG)

R31

==

~A*CB

R32

II:

58

R33

lit

CA*CS

X"" .::

Xl*Rl1+Yl*~12+Z1*RI3

YCi7

::I

Xl*R21+Yl*R22+Z1*R23

Z0 •

Xl*R31+Yl*R~2+Z1*R33

CK a

CKBAR(IMl)*Rl1+CLBAR(IM1)*R12+CMBA~(IMl)*R13

CL

s

CKBARfIMl)*R21+CLBARrl~1)*R22+CMAAR(IMl)*R23

II:

CKBARCIM1)*R31+CLBAR(IMl)*R32+CM~ARCIM1~*~~3

eM
J

0

t

IF(OtI))
31~

Z2

C

II:

31~.311.~02

-ZC!1

C:

IF(CM) 6210. 10,60~
6"0 X0
Y~

11:

X0-2.*CK*Z0/CM

• Y0-2.*CL*Z0/CM

GO TO 211

311 IF(CMl
210 X0
y~

210,3~2.21~

31:

)(l'J-CK*Z0/CM

•

yt?l-Cl"'l~/CM

Z2 • 0.
GO TO 211
3t2!2 Z2

• Z0

211 S

II

0.

5 J

:r:

J+l

X • X0+Ck*S
y •

Y"'+CL*S

Z • Z2+CM*S

543

0

P.29

o

IFeDfI))

l12.21~,214

212 IF fl) 7.6,6

7 Z

-Z

ft

IF (CM) 4e0
4~~

10, 400

= X0+CK*(Z-Z2)/CM
V = Y0+CLc.l-Z2)./CM

X

21~,216.216

6 IFf V)
715 V

= -V

IF(CL)

4~1,

1~.

4~1

401 X

= X0+CK*tY-V0)/Cl

Z

= Z2+CM*CY-V0,/CL

216 DO • Del)*otI)

F • ffll*OO*X*X+OO*V*V-Z*Z

FX • 2.*X*ECl)*OD

o

~V

= 2.*V 4 DO

Fl

c

-2.*Z

GO TO 8
214 IFtl) 6.6,7
213 F • AfIl*X*X+BfI'*V*V+CCI)*Z*Z+Z

FX .2.*A(It*X

FV • 2.*Sf.'l*V
FZ

e

e

DET~T

2.*C(r'*Z+1.

= CK*FX+CL*FY+CM*Fl

IFfOETMT) 218,217,218
217 IF(F) 10.9.10

10 PUftCH 104, tRAY. IMl
11

CONTINU~

IF (SENSE SWITCH 1)205,3

o

218 OElS

= -F/DETMT

,

~

'il

p.30

o

D~LS*DElS

DELS2 •

TOL2 • TOl*TOl
IF(DEl52-TOl2) 9. 9, 219
219 IF(J-JB) 220,10,10
220 S • S+DfLS
GO TO 5
9

t~{D(I)1

320.321.301

320 IF(S-2.*Z0/CMJ 221. 222. 222
'21 IF(CM)

!p,e.·~~lt'0f/.f

'~1

IFtS)

221t222,~'2

~00

IF(5-l~/CM'

221 PUNCH 105.

221,222.222
t~AYt

IMI

GO TO 11
222 lAP • NAPtll+l
GO TO
223 RHSO •

(Z2't224.22~),KAP

(X.APlft,)*CX-APIC!)+fY-AP'CI»)*CV-AP'Cltt

IFCRHSQ-AP'fl'*AP3(I») 12. 226,
12 'UNCH 106.

t~AY.

c

~26

1M!

GO TO 11
226 IF(RHSQ-AP4(1'*AP4(I»

13, 12. 12

224 IFfY-AP3(ltt 12,12.227

227 IFtY-AP4(I'J 2l8.12.12

?2S

tFfX-(AP~fr)*tY-AP3(lt)+AP1(t).)

2?9 tFtX-fAP6(1'*fY-AP3ft))+AP2(I,t.
225 IFfY-AP5Cl.,

12.1'.229
1~.12tl~

12t12t23~

230 IFfY-AP6CItl 231.12.12
~~1

FFF • fX-APlfl))/AP3fI)
FFFl • "F*FFF

666 • fV-AP2CI)t/AP4(It

o

Po

o

GGG2

= GGG*GGG

IF(FFF'-GG~2-1.)

13 RAT

ALe

1~.

12, 1?

= ~FFR(TMl)/PFFPfl'

= (RAT*DETMT)/(FX*FX+FY*FY+F7*~Zt

IF (REFR(I'+REFRCIM1») 232,233.232
23~

GAMUC • 2.*ALC
RAT

=

1.

GO TO 14
232 BLC

= fRAT*RAT-l.)/fFX*FX+FY*FY+FZ*FZ)

DIS( • ALe-ALC-PLC
IF(DISC)

234,235,2~5

234 PUNCH 1?7,

I~AYt

IMl

GO TO 11

o

235 DISC = SORTfOISC)
IFfALC) 236.10,231
236 DISC • -DISC

= DISC-Ale

237 GAMUC

14 CK • RAT*CK+GAMUC*FX
CL • RAT*Cl+GAMUC*FY
CfIIl •

RAT*C~+GAMlJC"'FZ

X0BAR(I) • R11*X+R21*Y+R31*Z+XOCI,
Y~8AR(J)

• R12*X+R22*V+R32*Z+YO(I)

Z0BAR(I) • Rl,*X+R23*V+R33*Z+ZO("
CKBAR(J)

= Rl1*CK+RZl*Cl+R31*CM

CL8ARtIl •

R12*CK+R~2*CL+R32*CM

CM8AR(I' •

Rl~*CK+R2~*CL+R33*CM

KOUT • NOUTfI,+l
GO TO

o

16 PUNCH

(l~,lb).KOUT

108tI~AY.IMl.XA,RP~Rl.X~RAR.l),(KBAR(I)

31

P. 32
PUNCH

109.YA,RPAR2,Y0RA~(1),CLeAR(I)

PUNCH

11~.lAtRPAR~.ZmAAR(Il,CMeA~(J)

c

15 CONTINUE

NAXIN • NAXIN+l
GO TO (17.239"HAXIN
239

IF(CKB~R(N05UR)'

240,241.24~

'41

rF(X~~AR(N05UR))

18.242.1e

Ie PUNCH 111, fRAY
GO TO 1'1

242 S

c

-y~eARfNOSU~)

IFf CLeAR(NOSuP) , 243.244.243
244

IF(Y?BA~(NOSU~)'

24~

s

c

18,245,le

5/CLBAP.(NOSU~)

GO TO 245

240 S

= -X~8AR(NOSU~'/CKBAR("O~UR)

IF(ClSAR(N05UR)

246,244,246

246 IF(5+Y0BARtN05UR)/CLeARCN05UR1) 18,245,le
245 AXIN

PUNCH

=

Z0BA~{NOSU~)+S*C~BAR(NOSUR)

112,I~AV.AXIN

11 PUNCH 1"'0

IFfSFN5F 5wtTCH 1) l05,

~

1 FORM.Tt!HRAY SUPF,2~X6HOeJ PT,4XSH'D PT/OC.~X6HI"T PT,6X7HOIR COSt
leJe

FOR"AT flXt

104 FORMAT f I ~ , I ~ t 13H

NO INCIDENCE)

Ifl15 FORMAT f13,J3.13H VIRTUAL PATH)
106 FORMAT (13,t3,14H APERTURE STOP)
1~7

FORMAT (I3t13,14H NO REFRACTION)

1~8

FORMAT fI3,Il,16X,8HX OR

10.'19 !="OPMAT

(22XfeH~

OP l

f(

,Fl1.~,lX,Fl1.~91X.F114~.lX,Fl1.~)

,Fl1.5,IX,Fl1.5,lX,Fll.5.1X.Fll.5)

o

o

Po

110

FO~~AT

(22X,!HZ

O~

M

.F11.5.1X,Fl1.~,lX,'11.5.1X.Fl1.5)

111 FORMAT fI3,4X.15HNO tNT W/OPT AX)
112 FORMAT (I3.4X.23HOPT AX
£ND

c

o

INTERS~CTION

Z =.F11.5)

33

o



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