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User Manual: PX71900-9_CentrExchNewsl#9_Jun56
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1103 CENTRAL
EXCH;~:';GE
NEWSLETTEH NUMBEH 9
June 1936
PX 71900-9
DIVISION OF SPERRY RAND CORPORATION
1902° WEST MINNEHAHA AVE.
ST. PAUL W4, MINNES9TA
Newsletter Number 9
June 1956
EDITOR'S PAGE
Coding and checkout of Trans-Use is progressing quite satisfactorily.
Trans-Use is a routine which will translate programs written in USE language
into Il03A machine language in a format ready for execution or assembly. The
USE-Compiler will be a much more powerful instrument .capable of doing a
variety of functions. For most problems, especially fixed pOint programs,
Trans-Use will be a useful instrument even when the Compiler is available.
Trans-Use is being prepared by Holloman Air Development Center.
A minimum Service Routine Library for the Il03A is about 75% complete here at St. Paul. This minimum library will include paper tape inputoutput routines and .several diagnostic routines for program debugging purposes.
On page I of the SNAP Sampler (RW-140) write-up, the last sentence
of ~aragraph b should be replaced by: "Restoring the library from magnetic
tape loads an all zero word into cell 71777bo If this word is not changed
a complete trace of all SNAP commands is automatically performedo~·
Future contributions and communications to the Central Exchange
should be addressed to Leo Kennedy, Systems Analysis Department, who has
assumed the duties of Central Exchange editor.
Leo Kennedy
Systems Analysis Department
i
NEWSLETTER NUMBER 9
JUNE 1956
REPORTS
CONVAIR
An 1103 program for computing Eigenvalues and Eigenvectors of Real, Symetric Matrices has been completed. This program
is designed to detennine all vectors Yo and all scalars A which
together with a given real, symetric mAtriX A of order N ~164 satisfy
the relationship AY i =A iY.. The mathematical technique employed
is based on the Hestenes - iarush gradient methods. The program is
made to take advantage of a matrix with large numbers of zero elements by representing it in dehydrated form, i.e., with blocks of
zero elements replaced by flags indicating the number of zeros removed.
0
RAMO-WOOLDRIDGE
A table of contents for the Ramo-Wooldridge Utility
Library fOT the 1103 is enclosed in this Newsletter. In connection
with this, the following communication was recieved from RamoWooldridge: "We nm" have our library available on a self loading
deck of binary cards. We would be glad to supply a copy of this
deck to anyone. together with complete instructions for loading
the deck in the 1103 and a list of locations occupied by each
routine. With this information the various output routines which
are part of the library could be used to obtain octal or binary
cards or bioctal paper tape for any or all rOlft ines."
-.
-
0""
.....
I
0"I
o
o
0"......
r><
0..
LOCKHEFll
As a first step in the direction of exchanging information about the organization of individual computing centers,
W. W. Leutert, Head of Mathematical and Computer Service Department
(Dept. 66-10> Lockheed Missile Systems Division has submitted an
organizational description of his department for Central Exchange
distribution. It is hoped that this first step will stimulate
the flow of such worthwhile information among the various com?uter
installations.
WRIGHT FIELD
A decimal output routine for the ERA Line Printer
has been completed. Decimal digits must be presented to the routine
in coded form and the speed of the output is limited only by the
Line printer itself (150 lines per minute, 92 characters. per line).
ii
NEWSLETTER NUMBER 9
JUNE 1956
REMINGTON RAND UNIVAC
Enclosed in this Newsletter is a report on
itA Linear Programming Routine for the .1103 Computer" which is being
developed at St. Paul.
A preliminary report on "A Multiple Correlation and
Regression Program for the 1103" is enclosed. This program has
been used successfully at St. Paul on several customer production
problems.
Also included is a description of the Utility Routine
Library for the Serial 9 1103 at St. Paul. This library (RR-126)
consists of three main parts: (1) Service Routine Library; (2)
Regional Coding Routine; (3) Library Routine.
A few inquiries have been directed to us concerning
the action of the LEFT TRANSMIT instruction (LTjkv) of the 1103A
(1) when 7~~, and (2) when k"'111. The quantity "j" in this instruction at present consists effectively of the one bit, u , in12
stead of the usual three bits, ul4, u13' u?
Hence for j = 2, 4,
or 6. effectively j = 0; and for j = 3. 5,lor 1 effectively j = 10
No anomalies arise when k~171 as is the case for the Split Instructions
and Left Shift Instructions in A and Q.
We would like to take this opportunity to review
some of the actions of the Il03A "interrupt" signal during a repeated operation. Since the Repeat Sequence by-passes Main Pulse
6 and 7, the "interrupt" will not take .effect until the Repeat
Sequence is terminated. For Normal Termination, the "interrupt"
will take effect on MP6 of the execution of the jump instruction
stored at F. When a jump condition is met during a repeated
Threshold ol Equality Jump, the "interrupt" will take effect on
MP6 of the Jump Termination Sequence. Hence, for both the Normal
and Jump termination of the Repeat Sequence, the "interrupt" does
not become effective until PAK contains the address of the next
instruction in the otherwise un-interrupted program.
--
.....
.....
.....
'-'
I
0"I
o
o
0"-
.....
t-
><
, 0...
iii
;\El~SLEl'TEn
~J{JN£
..-
.....>
00-124
Normal eerivate Routine
RW-12S
Linear Matrix Equation Solver
RR-126
Utility Routine Library. i(egional Coding Routine, library
RU-127
Multiple Hegression and Correlation Houtine
OR-128
Magnetic Drum to Magnetic Tape Dump
CV-129
Card Head and/or Punch Routine
CV-I30
Card Punch Routine
CV-131
Two Cycle Read Only Card Routine
CV-132
Solution of
CV-133
Square Root • Floating Point
CV-l34
Cube Root - Floating Point
RW-135
Fixed Point Card Output Subroutine
RW-l36
Stated Point Cdrd Output
RW-137
Octal Card Dump
\\,F-138
DIIP - a Floating Point Interpretive Subroutine
IYF-139
Polynomial Expansion,
Rl'l-140
S~AP
IfW-141
SNIP - Interpretive Floating Point Package - Complex
RW-142
Eigenvector, Eigenvalue Routine for Real Symmetric
RW-143
Floating 110int Gill Method
R\~-144
Floating Point Sine - Cosine
RW-145
Standard Atmosphere Calculation
RW-146
Manual Inspection and Insertion
'-'
I
0"-
0
NUMBER q
1qr)6
Si~ultaneous
Linear Equations by the
~=o
~~thod
0
.....
Sampler Trace
r-
><
c..
of Crout
anx'l
I
0"-
I~outine
iv
~ilatrices
RW-147
Central Exchange Sine - Cosine Routine
RW-148
Sine - Cosine Houtine (Polynomial Multiply)
RW-149
Small Angle Sine - Cosine Routine
RW-l50
Square Root
RW-151
Normally Dis tributed Pseudo Handom Numbers
RW-152
Column Heading Routine
CV-153
A Card Handling Subroutine
CV-154
Unpacked Floating Point Card Read
CV-I55
ArcSin and ArcCos, Fixed Point
CY-156
Least Squares Polynomial Approximation
CV-157
Fixed Point Charactron Output Rputine
CV-158
FLICK, A Demonstration Routine
HO-159
A Useful Instruction for Inverted Binary Numbers
HW-160
Arctan (Revised Edition of RR-26)
RW-161
Gill lv".etbod Subrol4tine (Revised Edition of aW-91)
RR-162
Pseudo-Random l\umber GenerBtor Subroutine
WF-163
Line Printer Decimal Output
CV-164
Program for Computing Eigenvalues and Eigenvectors of Real,
Symmetric Matrices
CY-165
Determinent Evaluation Package - Real
CV-166
Four Point LaGrange Interpolation for Bivariate Functions or
Their Derivatives (Fixed Point)
CY-167
Four Point LaGrange Interpolation for Trivariate Functions or
Their Derivatives (Fixed Point)
9:23
Lockheed
9:24
Table of Contents:
Ramo-Wooldridge Utility Routine LibrHry
9:25
Cumulative Errata:
Ramo-Wooldridge Library
9:26
A Linear Programming Routine for the 1103 Computer
~1issiles:
Organization of' Department 66-10
v
REVISIONS
CV-39
Floating Point Card Output
vi
OR -124
Page 1
ot'
22 March 1956
OPERATIONS RESEARCH OFFICE
7100 Connectic~t Avenue
Chevy Chase, Maryland
Title:
Normal Deviate Routine
Format:
Standard Form
Storage:
a)
b)
c)
d)
Total:
Instructions:
Constants:
Temporary Storage:
Alarm Cond! tiona:
Al~ when
01000
01000
01017
01025
-
01030,
01016,
01024,
01030,
31 octal
17 octal
6
4'
(01030) ~ 0 0
This location must be
supplied a randomly selected positive
number before th~ routine is lentered
the first time.
TLming:
12 milliseconds per deviate
Exit Condition:
(A) - deviate scaled 232
Range:
deviate will be in range 1 6
Coded and Machine Checked By:
FoR. Urbanu8
OR-124
Page 2
ot"
Description:
'!be routine provides a means for drawing "at random" from an
approximately normal distribution having a zero mean and a variance
of 1.
The routine is based on a consequence olthe Central Limit Theorem
of Mathematical Statistics, which states that a distribution of sums of
uniformly distributed random variables approaches the nonna! distribution as the nLUDber of variables
SUIIIlled
is increased.
In this routine
twelve random variables, each from the same uniform distribution and
in the
rang~ 0 to 224_1, are suamed aNI then normalized (i.e., reduced
by the theoretical mean of the distribution and divided by the square
root ot the theoretical variance of the distribution).
normalized deviates are thU8 distributed
approxL~te~
The resulting
normally with
mean 0; variance 1.
'!be accuracy ot the approximation has been Ileasured by collecting
5 samples of 1000 deviate. each and checking the distributions by
statistically testing
~
C\J
.....
'-'
I
0"-
the bJpothesis that the distributions formed
by the deviates are not significantly different from the normal distri-
bution.
For the results of these tests, see' the section titled
I
o
o
0"-
~
><
0..
"Accuracy of Approximation".
"
9-2
OR-124
Page 3 of ,
where the P's are "pseudo-random" numbers in the range 1 to 2 35 _32,
*
then the mean of S is
and the variance of the sum is
,.
~(sum) - 12
crL(uniform distribution)
r
224_1
tS
2-
(sum) - 12
12
- 224'3
i-o
The normalized sum, or deviate, is then
s
- , - st
224
Since
0 ~ S ~ 12 (2 24-1)
-6 ~ s. ~ 6
Each deviate, then, can be no larger in absolute value than
6.
Almost all (99.7%), however, can be expected to fall within the range
:t
*
3.00
The secondary modulus, 224:1, was chosen arbitrarily to provide a wide
range for the sums, and a fine gradation for the deviates. Furthermore,
it was desired to have the secondary modulus equal to 2n_l, in order to
1!educe the number of divisions required in the routine.
OR-124
Page 4 ot
b
AeeuraQY' of Approximation:
The following frequency distributions were compiled by the n03,
Each contains 1000 deviates.
The mean, variance, measure of skewness,
and measure of kurtosis for each distribution were tested statistically
and fOWld not to differ from the measures of the normal distribution
(0, 1) by a significant amount.
Deviates
-3.86
-3.47
-3.09
-2.70
-2.31
-1.93
-1.54
-1.16
-O~ 77
-0.39
0
0.39
0.77
1.16
1.54
1.93
2.31
2.70
3.09
3.47
to
-3.47
to -3.09
to
-2.70
to -2.31
to -1.93
to -1.54
to
-1.16
to -0. 'r1
to
to
to
to
to
to
to
to
to
to
to
to
-0.39
0
0.39
0.'71
1.16
1.54
1.93
2.31
2.70
3.09
3.47
3.86
(1)
(2)
(3)
(4)
(5)
0
1
2
5
18
0
0
1
2
0
13
9
36
67
99
0
44
61
103
130
155
151
137
82
56
0
6
10
25
31
65
104
112
141
147
2
4
13
12
30
61
83
139
135
164
147
90
128
64
2!}
28
11
9
21
6
0
0
6
3
0
0
101
66
38
15
7
1
1
0
144
168
152
115
85
56
36
15
7
0
0
0
0
4
3
15
37
70
101
133
145
148
109
101
74
36
15
5
Total
1
5
16
44
79
178
324
490
658
739
762
636
459
316
167
77
34
4
0
14
0
0
1
-.046
-.031
+.012
-.060
-.008
-.024
1.00
1.10
1.03
0.98
1.02
1.02
0.088
0.090
0.138
0.023
0.052
0.076
j
'(.« (skewness)
0
0-
'f~ (kurtosis)
3.07
3.00
3.18
3.08
2.78
2.90
--.....
~
Mean
.ra.
C'\I
-,
00
.....
r-
><
c..
9-4
OR-124
Page 5 ot
C,
Because it appeared that the mean of the distribution might have
some negati va bias, a further test was made in which 200 samples, each
representing the mean of 500 deviates, were compiled by the 1103.
'!he
mean of these means was +.0023, indicating that there is evidently no
reason to suspect a biased mean o
_
storage
Address
Order
H":H:Ioat't._........... _
r _ , - . . _ . · " " ' _ .- - . - - -
Function of Order
01000
37 76000 76002
Alarm exit
01001
45 O(X)()() 30000
Normal exit
01002
11 01Q17 01025
Set up index
01003
13 01020 01026
(-S)~ (01026)
01004
11 01030 20000
Random Number
01005
42 01024 01000
Alarm
01006
71 01030 01021
RN-5 13 .......(A)
01007
73 01022 10000
R.N.5 13 (mod 235_31)~A)
01010
11 20000 01030
store new R.N.
01011
11 01023 10000
Mask
01012
51 01030 01027
R.N.(mod 224-1)-7(01027)
01013
21 01026 01027
(S-S) ~ (01026)
01014
41 01025 01006
'lhro ugh 12 times?
01015
54 01026 ·00010
(S-S>-28.S'~ 232~A)
.....
01016
45 00000 01001
To Normal Exit
><
0...
01017
00 00000 00013
Index
"'....."
C\l
"-'
I
0I
0
I
--+ (A)
(01030)
~O
--+ (Q)
0
~
t-
9-5
OR-124
Page
6 ot
C
01020
00 05777 77772
S
01021
01 lO604 71625
01022
37 77777 77741
513
2 35_31
01023
00 00777 77777
224_1
01024
00 00000 00001
1
01025
[00 00000 00000]
01026
[00
00000 00000]
store &a
01027
[00
00000 00000]
Temporar.r storage
010)0
L00
00000 00000]
Current R.N.
Store index
9-6
Rl4J-125
I-ITI-O
Pg. 1 of 8
THE
RANO-~{OO1DRmGE
OORPORATION
Los Angeles 45, California
Linear Matrix Equation Solver (AX
= B)
Specifications
Identification Tag:
NTI-O
Type:
Subroutine available on cards for assembly
Storage:
217 instructions,
10NOO (OONOO )
IlNOO (OnIOO)
121,:00 (02MOO)
13MOO (03MOO)
addresses
thru 10M51
thru llli3 7
thru 121163
thru 13M62
«()!VI51)
(On·13 7 )
(02N63)
(03M62)
12 constants in program, addresses
ClNOO (CONOO) thru ClNll (OONll)
Tempor~ storage used, but not stored
in program (See Text).
229 words total program storage.
The constant pool and te~porary storage
pool are used by this routine.
Program Entrance:
Address 10N02
Program Exit:
Address 10NOl
Alarm Exit:
The alarm exit is used by this routine.
Hachine Time:
For all storage in ES time is
approxiInately (in milliseconds):
-3 n3 + -9n2m + 1~7n2 + .3~2 + 2.5nm
+ 1.8n + 1.6m + 2.7
For temporarJ storage (see text) on drum
add approximately (in milliseconds):
.. 04 [n3 + ~112m + 3n2 + lOmn] + 51
llode of Operation:
Fixed point
Coded by:
w.
Code Checked by:
\tJ" .. L. Frank
November 15, 1955
Nachine Che cked by:
lrJ ..
L. Frank
November 17, 1955
Approved by:
w.
F. Bauer
November 30, 1955
L. Frank
October 25, 1955
9-7
RW-125
l-ITI-O
Pg. 2 of 8
Description
This subroutine solves the linear matrix equation AX=B, "Where A is a nonsingular matrix of size nxn and B has the dimensions man.
I=A-IB, is a matrix of size nxm.
The solution,
For the special case, when B is the identi~y
matrix (I), one obtains the inverse of the rratrix A.
Otherwise, one can solve
m sets of n simultaneous linear equations in n unlmowns.
Considerable flexibility is afforded the programmer with respect to the
storage of the matrices A, B and the answer X.
The programmer
~
code two
auxiliary- routines -as follows:
(a)
The first must proVide successive rows of the augmented
matrix: [ A, B].
(When BaI, one only need supply rows of A).
Each row, consisting of (n+m) elements (or n elements when
BaI), must be. set up in the fixed location immediately following
the subroutine.
This data must be scaled at 2 35 and. be such,
that for all elements
~j
of
[~,BJ
18.tj .235 1~ 234
In the general case,. for B+I, the rows of [A,B] may be scaled
independently.
However, in the case of inverting a matrix,
it is necessary that the entire matrix be scaled by the same
factor.
(b)
The second auxil~ must take the successive columns of X,
found in then cells immediately following the routine, and
either store them internally or punch them out.
Since the
.'
columns of X are independently calculated, each has an associated
Bcale factor (scaled at 20 ).
This parameter positions the binary
point, (assuming the input l!2.trices are scaled at 2 3.5) and is to
be found in the (n+l)st cell following the routine.
If one has
inverted a matrix, and if the input rows were originally scaled by
lOP (or 2P ), then the output
col~~ns
must be re-scaled by lOP (or 2P ).
9-8
RW-125
NTl-O
Pg. 3 of {
These auxiliary routines are automatically entered n and m
times respectively by RJ instructions.
The subroutine sets
up these two RJ instructions from information gleaned from
the parBll1eters of the entry.
This procedure allows storage
of A,B and X on ES, MD, magnetic tape or externally on cards
or tape.
It is also possible to generate the, elements of
successive rows when a functional relation exists.
In
addition to the 229 words of storage needed by the sub-
routine , it is necessary to provide 2(n+m) cells temporary
~
(n(n+1L
iJnmed1atelY
following the subroutine, and a block of
run cells, either all on ES or all on ND.
~...
Operating Instructions
1.
Entrance to the subroutine is made by the following orders (Btl):
•
p
RJ OOM01 OOM02
p+l
00 00100 DOY01
p+2
-- uuuuu vvvvv
p+3
-- ----- xxxxx
where OOMOO is the location of the first word of· the subroutine
00100 is the location of the first word of the first auxiliary
OoYOl is the location of the second word of the second auxiliary
-
uuuuu • m (number of columns of B)
l.J'J
C\J
.....
--
0'
vvvvv
=n
o
o
XXJCCC
c::
I
(number of rows of A)
I
0'
.....
is the location of the first cell of the block of n(n+l) + run
2
t-
cells all in ES or all in 1m
><
c..
2.
to
For the case when Hal, the p + I word must be
40
OOXOO DOYOI
9-9
RW-12~j
MTI-O
Pg. 1+ of 8
3.
The auxiliary routines must be available and coded so that they can be
entered with
RJ OOXOO OOXOI
and
aoyoa
RJ
GOYOI respectively_
This implies that the first and second words of both auxiliaries are
exit and entrances respectively_
Alarm Conditions
Two alarm conditions can re suI t:
1.
A test is made to see that all elements, a
ij of the input rows are
within the limits
I
a ij '
2351~ 234
If this is violated ·the alarm routine AIR-I is entered and
oil
..
alarm -xxxxx is printed where xxxxx-3 is the address of the cell
.from which the subroutine was entered.
2.
If a singular matrix is detected in the process of inversion,
"
1/
the alarm routine AIR-I is entered and ;3ingul-wwwww is printed
wher:e
~-3
was entered.
is the address of the cell .from which the subroutine
The routine can not, however, detect all singularities
due to round-off errors (see below).
Starting again at xx:xx:x+1 will cause the rest of the main program
to be obeyed.
YJ(1chine .Time
The machine time is as indicated on the first page when all operations are
carried on in ES.
This tilne is exclusive of the times taken by the auxiliaries.
In case the block of n(n+l) + run words are stored on MD, the time must be
2
increased by the terms indicated.
TIlese times are approximate and will be a minimum in most cases.
9-10
RW-125
MTI-O
Pg.
5
of
Sample computation times for matrices of order 27 and 99 were respectively
53 seconds and 30 minutes.
l-1athematical Nethod
(Gauss elimination method)
Elementary row operations are performed on the matrix A reducing it to an upper
triangular matrix
I.
At the same time, these operations are performed on the
matrix B giving a new matrix
'B.
A partial floating point arithmetic is
maintained, in that the rows of the augmented matrix [A,B] are always kept
within the limits such that the largest element of the row (in absolute value)
lie s in the interval
In addition, before eliminating, leading elements of two rows are compared and
the element of largest magnitude becomes the pivotal point.
Next, successive columns of
13
are taken and the equation
Ax=B
is solved by
the back substitution procedure.
Singularities in"A are detected if a zero appears on the diagonal of
A.
Since
round-off errors can prevent this from occurring, one must inspect the size
of the scale factor i f A is suspected of being singular.
matrices will cause the scale factors to be very small.
III conditioned
That is, the elements
of X will be very large.
lO
....
Accuracy
C\J
-I
The accuracy in the result is a function of the condition of the matrix: A.
0"I
o
o
Seven to eight decimal place accuracy was obtained for matrices of order 10
t-
to 16.
....
0"-
><
c..
A matrix of order 39 and 99 yielded 7 and 6 place accuracy respectively.
RW-125
MTI-O
I
Pg. 6 o1'\s
D
0
D
0
D
D
D
0
D
0
.......
L'j
C\I
r-!
I
0"-
0•
0
0"-
1"'"'1
t-
><
0..
10MOO
10MOl
10M02
10MO 3
10U04
10MO 5
10M06
101.407
101.408
10M09
10Ml0
10Ml1
10M12
10M13
10M14
10U15
10"16
10M17
10M18
10 .. 19
10U20
10M21
10"22
10M23
10M24
10M25
10M26
10M27
10M28
10M29
10 ... 30
10M31
10M32
10U33
10M34
10U35
10U36
10M37
10M38
10U39
10 ... 40
10U41
10 .. 42
10M43
10M44
10M45
10'-446
10'-447
10U48
10M49
10U50
10M51
11MOO
l1Mo'l
l1M02
11M03
11M04
l1M05
11M06
llM07
l1M08
11M09
l1Ml0
l1Ml1
l1M12
l1M13
11M14
l1M15
11M16
l1M17
10 M'OO
l1MOO
12MOO
13MOO
OOMOO
01MOO
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031.400
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CONOO
37 75701
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54 OOMOl
TU AOOOO
TU AOOOO
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TU AOOOO
AT 00015
TU AOOOO
TU AOOOO
TU AOOOO
TP 00000
TU AOOOO
TV AOOOO
A T 00015
55 00016
TU AOOOO
LA AOOOO
TV AOOOO
TV 00000
TN 00016
TP 00000
TV AOOQO
TU AOOOO
AT 02Ml0
TV AOOOO
TV AOOOO
TV AOOOO
54 CON08
AT CON06
TV AOOOO
A T 02Ml0
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TV AOOOO
L. A' AOOOO
1U AOOOO
TU AOOOO
TU AOOOO
TU AOOOO
TP CONOl
AT CON06
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TP CON10
AT CON06
54 CON07
TU AOOOO
RA OOUOl
TV 03M02
TU 02"62
TU 02M62
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54 00000
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TP CON02
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TP CON07
TP 00021
TP 00000
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TP 00013
TP CON04
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TM 00000
00100
00152
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00023
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01M16
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01 ... 14
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00024
144
230
276
376
144
230
276
376
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B
BRB
ALARM AND
NORMAL E X I T
ENTRY
P-l
P-2
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SE T
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INTERCHANGE
RESET
TO
F AOORESS
SET SF INDEX
TO AUX 1
SET INDEx
TE S T FOR
I NVERS tON
BBR
AUGMENT
ROW OF
UNIT
MATRIX
CHECK I F All
ELEMENTS IN
~:Z:i
-144
145
146
147
150
151
152
153
154
155
156
157
160
161
162
163
164
165
166
167
170
171
172
173
174
175
176
177
200
201
202
203
204
205
206
207
210
211
212
213
214
215
216
217
220
221
222
223
224
225
226
227
230
231
232
233
234
235
236
237
240
241
242
243
244
245
246
247
250
251
0001°
00
00
00
00
00
00
00
00
00
00000
00000
00000
00000
00000
00000
00000
00000
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37
45
54
15
15
35
15
35
15
15
15
11
15
16
35
34
15
54
16
16
13
11
16
15
35
16
16
16
54
35
16
35
16
16
54
15
15
15
15
11
35
16
11
53
11
35
54
15
21
16
15
15
16
11
16
54
15
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37
11
11
11
46
23
75
11
11
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20017
20000 00157
20000 00241
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20000 0017;1.
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20000 00232
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20000 00245.
20000 00246
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20000 00476
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20000 00360
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00503 20000
20000 00416
00025 10000
00505 002044
00507 20000
00503 00506
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00145 00502
00400 00455
00374 00251
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00360 00231
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00025 10000
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00243 00250
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10000 00246
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C\J
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0
0
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t-
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11M18
l1M19
llM20
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11M22
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11M25
l1M26
llM27
11M28
11M29
l1M30
llM31
l1M32
11M33
l1M34
11M35
l1M36
l1M37
12MOO
12MOl
12M02
12M03
12M04
12M05
12M06
12M07
12M08
12M09
12Ml0
12Ml1
12M12
12M13
12M14
12M15
12M16
12M17
12M18
12M19
12M20
12M21
12M22
12M23
12M24
12M25
12M26
12M27
12M28
12M29
12M30
12M31
12M32
12M33
12M34
12M35
12M36
12M37
12M38
12M39
12M40
12M41
12M42
12M43
12M44
12M45
12M46
12M47
12M48
12M49
12M50
12M51
12M52
12M53
12M54
12M55
12M56
12M57
12M58
12M59
TJ
RA
IJ
RA
TP
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QS
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BOOOO AOOOO
00028 02M30
AOOOO 00028
00031 00000
02M21 00015
02M22 00015
02M30 00016
02M26 00016
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02M21 02M37
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00013 02M46
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02M44 02M41
02M47 02M42
02M46 00016
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03M56 02M46
20000 02M47
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02M49 02M51
30000 02M51
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AOOOO 02M50
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CON 09 OOM50
CON07 CON06
CON 07 00016
ROW ARE
SCALED
CORRECTLY
ADVANCE AND
SET INDEX
RESET
T
ADVANCE
X
BRB
BBR
TRANSMIT ITH
ROW TO E S
SET FOR
INVERSION
COMPARE LEAO
ELEMENTS
CONSTANT
R
INTER
0
W
CHANGE
B
NO ROW
INTER
CHANGE
OK
L
I
N
BRB
E
A
R
L
Y
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R
0
W
S
R
E
BRB
S
C
A
L
E
R
BBR
0
W
BBR
REPLACE ROW
ON DRUM I F
INTERCHANGE
TOOK PLACE
TIM E S
I
N - 1 TIMES
SET MOl
FOR INDEX
252
253
254
255
256
257
260
261
262
263
264
265
266
267
270
271
272
273
274
275
276
277
300
301
302
303
304
305
306
307
310
311·
312
313
314
315
316
317
320
321
322
323
324
325
326
327
330
331
332
333
334
335
336
337
340
341
342
343
344
345
346
347
350
351
352
353
354
355
356
357
360
361
362
363
364
365
366
367
370
371
42
21
41
21
11
53
53
45
23
23
15
16
15
21
15
15
15
15
55
16
75
11
16
16
11
11
12
12
42
47
00
71
73
21
13
45
54
73
21
11
13
11
11
54
72
45
1l.
12
42
11
11
21
21
21
21
36
47
43
16
55
44
44
21
44
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54
11
46
75
1l.
11.
11
52
54
16
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41.
23
23
00030
00251
00027
00507
00507
00261
00261
00000
00276
00353
00276
00476
00304
003,05
00305
00305
00305
00305
00305
10000
30000
00000
00430
00430
00015
00015
00000
00000
00035
00311
00000
00000
00000
00323
0050l.
00000
00000
00000
00324
00015
00030
00000
00000
00036
00037
00000
30000
30000
00034
20000
00037
00323
00324
00334
00330
00476
00323
00034
00015
00034
00352
00355
00354
00353
00466
20000
00000
00033
00357
30000
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00025
00277
00276
20000
20000
00032
00506
00504
00504
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00030
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20000
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00017
00017
00020
00020
20000
00343
00355
00354
10001
00347
00350
00020
00350
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00355
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20000
00361
00361
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10000
20000
00277
00071
00360
00262
00226
00503
00020
q-l~
RW-125
MTI-O
Pg. 8 of 8
......
If:)
C\I
r-4
I
0'
I
0
0
0"-
r-4
a-
><
Cl.4
12 .. 60
12 .. 61
12M62
12M63
13MOO
13UOl
13U02
13U03
13M04
13U05
13U06
13U07
13M08
13 .. 09
13Ul0
13M11
13M12
'13M13
13M14
13U15
13U16
13M17
13M18
13M19
13M20
13M21
13M22
13M23
13M24
13M25
13M26
13M27
13M28
13M29
13M30
13U31
13M32
13M33
13M34
13M35
13M36
13M37
13M38
13M39
13M40
13 ... 41
13M42
13M43
1.3M44
13M45
13M46
13M47
13M48
13M49
13M50
13M51
13M52
13M53
13 .... 54
13M55
13M56
13M57
13M58
13M59
13M60
13M61
13 ... 62
CINOO
C1NOl
C1Noa
C1N03
C1N04
C 1 NO 5
C1N06
C1N07
C1NOS
C1N09
C1NI0
C1Nl1
54
OS
TP
TV
TP
TU
TP
TP
QS
TP
TP
RA
RA
RS
TU
RS
RS
RP
TP
RA
TN
54
TU
TV
TP
TP
MJ
54
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TU
TV
TU
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TN
TN
TM
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54
CC
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RA
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TP
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RA
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MJ
11
MJ
RS
RP
LA
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TP
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TN
AT
MJ
24
TP
00
37
20
00
00
00
00
00
00
00
CON06
AOOOO
CON11
03M16
CON10
02MOl
CON04
00021
00013
00013
00013
00028
03U13
03M14
03U14
03M14
03M14
30000
00000
03U16
00000
03M16
AOOOO
03M02
00027
00013
00000
00030
00031
00000
BOOOO
AOOOO
00030
CON04
00000
03 .. 25
00032
03M25
03M25
03M25
00000
00030
00031
00030
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00026
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20000
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03M52
CON04
03"'60
CON04
00032
00000
14061
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00000
77777
00000
00000
0
0
a
0
20017
03 .. 55
00029
03M14
00026
03M14
00000
QOOOO
03U13
00028
00027
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03M16
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0
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00
20017
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03M25
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03M25
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03M54
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03M23
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03M42
03M54
20043
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0
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03M57
00071
03M17
000.32
03 ... 61
00032
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02M26
33411
000
00 42
77777
000 0
3
BRB
SE T
INDEX
SE T
SCALE
COUNTERS
ZERO
ADVANCE
COUNT
TO
TRANSFER
ROWS
OF UPPER
TRIANGULAR
MATRIX TO
ES
BRB
SE T
INDEX
B
BRB
A
C
K
S
U
B
S
T
RESCALE
I
T
U
T
E
RESCALE
BRB
ADVANCE
N01 TIM E S
TO
AUX
2
BRB
M-l TIMES
EXIT
SET ALARM
WORD
RESCALE
B
SINGUL
C
B
B
B
B
0
AND
TEMP
N
S
T
STORAGE
A
N
T
S
372
373
374
375
376
377
400
401
402
403
404
405
406
407
410
411
412
413
414
415
416
417
420
421
422
423
424
425
426
427
430
431
432
433
43"4
435
436
437
440
441
442
443
444
445
446
447
450
451
452
453
454
455
456
457
460
461
462
463
464
465
466
467
470
471
472
473
474
475
476
477
500
501
502
503
504
505
506
507
510
54
53
11
16
11
15
11
11
53
11
11
21
21
23
15
23
23
75
11
21
13
54
15
16
11
11
45
54
27
72
11.
11
12
42
45
23
41
15
16
15
12
13
13
12
42
45
54
27
73
21
41
11
37
21
41
45
11
45
23
75
54
46
11
46
13
3S
45
24
11
00
37
20
00
00
00
00
00
00
00
00503
20000
00510
00416
00507
00277
00501
00025
00015
00015
00015
(l0034
00413
00414
00414
00414
00414
30000
00000
00416
00000
00416
20000
00400
00033
00015
00000
00036
00037
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20000
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004i 27
00040
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004,27"
(l04'27.
00000
00036
00037
00036
00030
00000
00O~6
0003t
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00032
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0050'4
00000
00475
00000
00035
20000
00512
00462
00501
004'12
00501
00040
00000
14061
30000
00000
77777
00000
00000
00000
00000
00000
00000
00000
00000
20017
00465
00035
00414
00032
00414
00000
10000
00413
00034
00033
00017
00017
00505
00416
00020
00034
00415.
00000
00506
00000
20017
00427
00427
00040
20000
00427
20043
00015
00000
00036
00.037
20000
00435
00464
00021
004~5
00442
o 04 ~2
00452
00030'
00036
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20000
00450
00464
20043
0.0015
00000
'00020
00405
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,00000
00017
00374
0014~
75756
00144
00020
00467
00107
0041'1
00040
00473
00040
20000
00330
33411
00000
00042
77777
00000
00003
00000
00000
00000
00000
00000
00000
9-14
RW-12S
February 13, 1956
THE RAMO -WOOLDRIDGE CORPORATION
Los Angeles 45, California
Digital Computing Center
STUDY OF MATRIX INVERSION ON THE ERA-l103 EMPLOYING RO'lJfINE M'fI-O
by
Werner L Frank and Phyllis Van Liew
t
Investigations have been carried on in the inversion of matrices
of large order and/or matrices which are badly conditioned.
of this has been twofold:
The purpose
(1)
To measure the sensitivity of the routine MrI-O to ill
conditioned matrices;
( 2) '1'0 obtain some experimental experience relating to the
effect of round-ott tor large order matrices.
(We define the condition number as the ratio of the absolute
value of the largest e1genv~ue to the smallest).
It ;I., hoped that £lome conclusions will result which will answer
the foll.ow1ns questions:
(1) What is the relationship between condition number and.
result1D1 accuracy in the inverse?
(2) J'or moderatel,. well conditioned matrices what order can
'be safely inverted and what accuracy can be expected?
The _in problems considered in these investigations were the
following matrices:
(a)
J1nite sepaent of a Hilbert Matrix (Hn) where HiJ • 1+~-1
and its irlverse Tn.
(b)
Matrix aasociated·with the solution ot y"
=- y
(en)
wbere c11 • 2
13 •
C
-1 it
11-jl • 1
Cl~ • 0 all others
(c)
A s1nsular _trix (A) of order 8 studied in e. paper "The
Separation ot Close Eigenvalues ot a Real Symmetric Matrix"
by Rosser, La.nczos, Beatenes and Karush.
RW-125
Page 2
Matrix (a) has the property of being extremely ill-conditioned for n as
low as 4.
it is
a
The second matrix (b) enjoys a more moderate condition -- even though
function o:t~the square of its order (~4 n 2 ).
-r-
In addition the inverses
of both matrices are well known, the elements being given by closed algebraic
forms.
)i)re spec1fic&1.ly, a comparison of the condition of H and C can be
n
n
obta1Ded tram the following table (values are approximate):
n
C
n
Hn
2
3
16
4
10
10
40
15 1 514
0(1012 )
39
638
I1na' ].,. the
.triz (c)
mtit1e4 _trix 10-4A + 10
t
i8 s1DSUl&r and its e1pnY8l.uea are known.
-nx was 8twlied for
•
.1 + 10·n
lO-n
Xl •
1. 2 1 •••
I
10.
!!liB
Dle
_triz
•
!he accur8C7 vas checked b7 calculat1DS the product of the input _triz
8D4 it. cOJa.PUted inverse and com;paring this quantity to the identity _triz.
~
!able. 1 &D4 2 conta1n data associated with the matrices described above.
l()
....
......
N
I
0'
I
o
o
....
0'
t-
><
Co.
9-16
RW--12
Page 3
Matrix
T -1 .102
2
T3 -1.103
T4-1 .105
T -1 .106
5
T6 -1. 107
T7 -1 .109
TS-1 .1a10
&2 -1 .10
B3-1.~0
-1
&4 .10
-1
TABLE 1
Summary of Experiences on Hilbert Matrices and
_ Cn
Places
of Accuracy
Time (seconds)
Time (seconds)
With Tape Output
No Tape Output
(Rounded)
1·90
.15
8
3.65
.20
1
6.20
.45
5
9.25
.70
3
13·10
1.00
3
17.50
1.45
1
22.7
2.1
0
1.90
.15
S
3·70
.20
7
6.20
.40
5
115 .10
-1
&6 .10
9.25
.60
4
13.05
1.00
2
-1 .10
17.45
1.40
1
22.6
1.9
0
&7
lIs-l .1O
°3
°15
-. ° 27
1..")
268
53
Condition
16
15,514
16
15,,514
9
4
S
90
7
292
6
639
5
4000
C'\l
r-I
'j'
0"-
°39
I
8 °99
0"r-I
411
80 minutes
( est1lBted)
30 minutes
r><
c..
9-17
RW-125
Page 4
The Matrix lO-4A +
lO-~ = A'n
Places of .Accur8C7 in ldentlt7 Matrix
(Rounded)
lO-4A
•
•
0
Condition
00
~O
0
109
~
1
108
2
107
•
A.r
3
106
•
Ie.
.. 105
~
5
10'"
Aa.
6
103
7
102
8
10
9
1
•
As
~
•
•
I
A3
I
Az
•
~
..an
C\I
.....
I
aI
o
o
a-
.....
t-
><
0..
9-18
RR-126
9 April 1956
UfILITY ROUfINE LIBRARY {MT~)
FOR
1103 SERIAL 9 COMPUTER
The Utility Routine Library will normally be stored on
consists of the following:
(I)
MT~.
The Library
Utility Routine Loader-@ (URL-@)
This routine loads the Non-diagnostic Machine Test and transfers
control to the test
An IT START automatically transfers control
to URL-~; if (AR) is set 10, the machine test is by-passed and control is transferred to URL-l. The routine occupies blocks 1, 2 on
o
Mr~.
(2)
Non-Diagnostic Machine test
(Go~No-Go
Test)
This routine performs nine tests each of machine commands and HSS,
and four tests of the drum. A carriage return precedes the start
of each part and a 0 is typed after each successful test. A cODDDand
test failure is denoted by a printed c, a HSS test failure by a printed
e, and a drum test failure by a printed d. After each failure the
routine tries the same test over again with the same operands and
continues to do so until it obtains a successful test. Upon completion,
the routine transfers control to URL-l. The routine occupies blocks
3-32 on Mff1.
(3)
Utility Routine Loader - 1 (URL-l)
This routine loads the Service Library in the drum, 70000-75777 0
it also clears HSS, groups 4, 5, 6 and 76000-77777 on the drum. A
MJ-; is left in 00000. Upon completion, the computer is halted on a
15-; instruction'with PAK set to the entry for the Ferranti Loading
Routine. URL-l occupies blocks 33, 34 on MT~.
(4)
Service Routine Library
This is a compilation of routines of general use.
Library occ~pies blocks 35-174 on IT~.
(5)
Regional Coding Routine {RECO)
This routine occupies blocks 175-225 on
routine for deta~led description.
(6)
The Service
MT~.
See write up of this
MT~.
See write up of this
Library Routine
This routine occupies blocks 226-245 on
routine for a detailed description.
RR-126
9 April 1956
(7)
Dictionary of Subroutine Library
A list of indices tor the subroutine stored in the Subroutine
Library. This dictionary occupies blocks 246·305 on MT~.
(8)
Subroutine Library
A compilation of subroutines of general program use. The
remaining ~locks of MI't' are reserved for this library. See write up
of Library Routine for list of Subroutine in the Library.
Loaders URL-2, and URL-3 are part of the Service Library and they effect
the loading of RECO and the Library Routine respectively into HSS. The Library
Routine has a built in loader which effects the transfer of the Dictionary and
the Subroutine Library to HSS.
MT~ must be positioDed to the dead space preceding the first block on tape
before any use of the Utility Library can be made. To discourage inadvertent
writing over the Utility Library, the MT~ WRITE switch is disabled; this switch
in the DOWN position is the NORMAL condition of the computer.
9-20
RR-126
9 April 1956
GENERAL t5E OF lTfILITY ROurINE LIBRARY
I.
Normalize Computer Operation
This is an automatic operation which is designed to test the computer,
transfer the Service· Library to its drum storage, and clear HSS and the
remainder of the drum.
Operating
Instructions~
OO~
IT., positioned.
(1)
Typewriter
(2)
MASTER CLEAR: All MJ and MS selects OFF.
(3)
If the Non-diagnostic Machine Test -fsnot desired, set
(AR)~O.
IT START.
(4)
Computer halts on
(5)
Errors ~
MS~
instruction with PAK set to 70001.
{a)
Final Stop (57 77777 00000): This indicates that URL-~
has· not been transferred to HSS correctly. MASTER CLEAR,
IT START for are-transfer.
(b)
Printed "T" and MS-~ Stop: This indicates that the NonDiagnostic Machine Test has not been transferred correctly.
Push START for re-transfer of the test routine.
(c)
Final Stop (57 77777 77777): This indicates that URL-I has
not been transferred to HSS correctly. MASTER CLEAR, MT
START for are-transfer.
(d)
Printed "S" and MS-~ Stop: This indicates that the Service
Library has not been transferred correctly. Push START
. for a re-transfer of the Service Library.
NarE: .If repeated transfer errors occur and it is
suspected that the Utility Library is incorrectly
stored on MT~. the machine operator should follow
the procedure for loading the Utility Library on
MT~.
II.
Program Asse.oly
Use of the assembly routines, RECO and the Library Routine, in the
Utility Libr~ry is· accomplished by entries 70010 and 70011 respectively
in the Service Library. Entry at these points activates loaders which
read the assembly routines into their operating storage locations in HSS.
For detailed operating instructions, see descriptions of URL-2 and URL-3
in the Service Library.
9-21
RR-126
9 April 1956
III.
Starting the Computer
There are three methods of starting the computer depending upon the
amount of inform8tion stored on the drum.
(I)
If the Service Library is stored correctly on the drym. one may
use one of the routines in the library to load his program tape,
and commence program operation and/or debugging.
(2)
If the Service Library is Dot stored eorrect.ly on t be drum, give
an MT START for the Normalize Computer Operation (see description
of same). This procedure is particularly advised when one
suspects that the computer is malfunctioning.
(3)
If the Utility Library is not available on MT~ and tbe Service
Library is Dot on the drUJI, a bootstrap procedure must'be performed
by the operator (see "Procedure for Loading Utility Library on
MT~".
)
9-22
RR-126
9 A}-ril 1956
PROCEDURE FOR LOADING lJfILITY LmRARY ON
MT~
If the Utility Library is not available on Mft) follow this procedure.
This will work for a 16 interlace only.
( 1)
MASTER CLEAR
(2)
Swi tch to ABNOar.tAL DRUM
(3)
START
(4)
After FINAL STOP, switch to NORMAL DRUM
(5)
Set PAK=OOOOO and load tape I
The Ferranti Loading Routine is now on the drum.
(6) Set PAK=70001 and load tape II
The "Write Magnetic Tape _It routine is
MT~,
turn
MT~
DOW
(7)
Position
(8)
MASTER CLEAR; MD START and load tape III.
in HSS.
WRITE Switch to UP position.
The Utility Library is loaded onto MTfS.
(9)
Set PAK=DOO77 START. Tbis will cause a check sum of the information
. written an MT~ to be computed and compared with the sum computed
from paper tape. If these two sums do not check a "tttt" is printed
and computer stops. Push START for another comparison. If repeated
check sum errors occur return to step (6). Skip step (7).
(10)
After a successful loading of the Utility Library on MT~. turn MT~
WRITE switch to DOWN position. Give an Mf START to perform the
IOrmalize computer operation.
9-23
RR-l26
9 April 1956
PROGRAMMING AND OPERATION CONVENTIONS
I.
Dru. Image of H5S:
Drum cells 76000-77777 are reserved for the image of HSS. This
image is used by most servfce routines as a temporary store for H~S .
• hile the service routine operates from H5S. The programmer is advised
not to load into the image as this may result in incorrect loading of
HSS. The programmer may use this part of drum storage as a temporary
pool or work space during the operation of his program, but in so doing
deprives himself of several facilities in the Service Library for
program debugging.
II.
Drum Storage for the Service Library
Drum cells 70000-75777 are reserved for the Service Library and are
not. in general. available for program use. Loading programs into the
range 70000-70037,deprives the programmer of all facilities of the
Service Library. wbile loading into the range 70040-75777 may deprive
him of .only part of the Service Library.
III.
Storage Used in Assembly of Subroutines
The remarks .ade in I and II concerning the reserved portions of
group 7 on the drum apply also when assembling subroutines. The modified
subroutines are stored at the specified relocation addresses, and then
punched out, if the punch-out option is chosen.
IV.
. The MT' unit is reserved for the Utility Library only.
Any use of
in aD operating program must be brought to the machine operator's
attention so that he may take necessary steps to preserve the Utility
Library tape.
MT~
The NORMAL condition of the computer is indicated when the
. Switch is disabled (DOWN).
MT~
WRITE
9-24
RR-126
9 April 1956
GENERAL PROCEDURE FOR COMPUTER OPERATION
The following items should be checked before going on the computer:
(1)
List all memory used to determine if it is compatible with loading
routines and Service Library.
(2)
Do not try to load any tapes other than yellow or black.
tapes loaded at your own risk.)
(3)
Keep tape off the floor.
(4)
List library subroutines needed to determine if these routines are
in the library.
(5)
Determine which service routines will possibly be needed.
(6)
Warm up the card equipment before using (at least one hour).
(7)
Determine what peripheral equipment will be used.
(Other
When working with customers, the above information should be on hand before
they arrive. For customers, determine the amount of assistance needed and/or
wanted.
Before loading program tapes, it is suggested that the following procedure
be followed:
(1)
Check the ABNORMAL CONDITION panel.
If ABNORMAL light is on, check with the
.,.i'IRo~
.
(2)
Check the drum interlace if the drum is used in the program.
(3)
Check the Fl switch.
(4)
Check the Field III switch in the card control unit if program uses
card equipment. If the program is to use field III. (eols. 73-60),
the switch should be in NORMAL Position.
(5)
If any magnetic tape units are to be used in program, cheek to see
if the units desired are switched to RUN and are properly positioned.
(6)
If the Higb Speed Punch and/or Card equipment are not to be used in
the program, turn them OFF.
(7)
Turn Ferranti Reader OFF when not in use.
(8)
If card equipment is to be used in the program be sure to clear both
channels (read and punch) before giving 8 program START.
9-25
RR-126
9 April 1956
Upon leaving the computer, the following procedure is suggested:
(1)
Check .to see that all program tapes and output tapes are rewound
and not left in baskets or on the tables.
(2)
Clear the card equipment read, punch and receiving hoppers of all
program input and output.
(3)
If any information is stored on any of the magnetic tapes for future
use, it is the programmers responsibility to see that these tapes
are saved; otherwise it will be assumed that these tapes are usable
for other programmers.
(4)
Restore the Service Library to the drum.
CAUTION: It is advised as general practice never to Master Clear while
any of the magnetic tape units are in motion. Such clearing drops all
IT lockouts, and subsequent computer references to any moving tape will
cause trouble.
9-26
RR-126
9 April 1956
SERVICE ROUTINE LIBRARY
Service Routine Entries
70000
Final Stop
70001
Ferranti Loading Routine (FRI-O)
70002
Flex Code Loading Routine (FLEXIE)
70003
Read
70004
Write
70005
Flex Dump
70006
Bioctal Dump
70007
70010
Reco Loader (URL-2)
70011
Library Routine Loader (URL-3)
70012
70013
Changed Word Post Mortem
70014
70015
70016
Single Breakpoint Stop
70017
Automatic Sampler
70020
Restore HSS from Image
70021
Punch Check Sum
--
70036
Common Exit
---
76000- 77777
HSS Image-loading in this range results in
incorrect loading of HSS.
70v()Q -75777
Service Routine Library-loading in this range
deprives one of the service routines.
..,0
C\I
.....
I
0"I
0
0
0"-
.....
r-
~
c...
9-27
RR-126
9 Afr11 1956
PROGRAM ENrR IES TO SERV ICE ROur INES
The block of cells 70000-70037 is reserved for entries to the service
routines. Cell 70036 is reserved as the common exit from those service
routines which by their nature admit program entry and exit. For example,
the use of FRI-O as a subroutine would be effected by the instruction 37
70036 70001. All required parameter words must place in the appropriate
registers before entry is made to the particular service routine,by a Return
Jump instruction. For example, the use of the Bioctal Dump would be effected
by the following sequence:
n:
n+I:
11 (x) 10000
37 70036 70006
n+2~
where, say, (x)
=
00 00001 01777
CAUTION: Since the service routines each have only ~
entry, any inadvertent (or not) loading in the lange 7000070037 deprives one of all the service routines.
9-28
RR-126
9 AlJr11 1956
COMMENfS ON lEE OF SERVICE LIBRARY
I.
Paper Tape Preparation
a)
Bio~tal
tapes should have double 7th level at the very end of the
tape.
b)
Flex code (absolute) program tapes should have at least one 7th
level punch at the very end.
c) Flex code (RECO) program tapes should have an END. (car. ret.) or
END (car. ret.) at the end of the tape.
II.
d)
Assembled RECO program tapes are suitable for direct input via
FLEXIE. Such tapes may be converted to bioctal if so desired.
e)
Flex dump tapes are suitable for reloading via Flexie.
a 7th level punch is present at the end of the tape.
f)
Care must be taken in handling paper tapes to insure that they are
kept clean. Foreign substances on tapes uycause improper loading
into the computer.
Be sure that
Alarm Print
Many of the Subroutines contain references to the Convair
The location of this is at 75700-75777. The entries are:
37
37
75700
75700
75701
75702
Ala~
Print.
main routine
aubroutine
The alarm print in the service library is a modified version of the
Convair routine. Program, constants and working. space are in the raDge
75700-75777.
III.
-.0
N
r-!
'-'
J
0"J
Flex Constant Pool
A group of com.only used Flexowriter codes are stored in the Service
Library. in the raDge 75757-75777. This pool is used by several Service
routines; however, .it is available for general program use. The pool
consists of the following:
o
o
0"-
r-!
r-
><
~
75757
75760
75761
75762
75763
75764
00000 00037
00000 00052
00000 00074
00000 00070
3
00 00000 00064
00 00000 00062
4
5
00
00
00
00
0
1
2
9-29
RR-126
9 A}..r11 1956
75765
75766
75767
75770
75771
75772
75773
75774
75775
75776
75777
IV.
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000
00066
00072
00000
00033
00045
00004
00057
00047
00051
00042
00056
Responsibility of Restoring
6
7
8
9
Carriage Return
Space
Shift down
Shift up
Tab
Period
Minus.
Ser~ice
Library
It is the responsibility of any operator who damages the Service
Library to restore the same to the drum before leaving the computer.
v.
Loading Routines "Transfer Control" Option
The loading routines, FRI~O and FLEX IE , now have a "transfer control"
option. The following procedure will effect the transfer for either
load routine.
(1)
set program tape in reader
(2)
MASTER CLFAR
(3)
Set the cOliputer on MAIN PULSE f).
(4)
Manually insert the following into
37
7003'6
(5)
Set PAK= program start
(6)
START.
peR
70001(2)
9-30
9 April 1956-- RR-126
PROCEDURE FOR LOADING SERVICE ROUTINE LIBRARY
I.
Normal Operation
The Service Routine Library is normally stored on the drwm, 1000011177. Entry to the routines is achieved by setting PAK to one of the
low-numbered drum address, 700XX.
II.
MT Start
If the Service Library is damaged on the drum, select an MT Start.
This will effect the following:
(1)
Non-diagnostic machine test
(2)
Transfer of Service Library to the drum
(3)
Clearing of HSS and drum storage.
If (1) is not desired, set
III.
(AR)~
before the MT Start.
Bootstrap
If the Service Library is not available on magnetic tape, follow this
bootstrap procedure. This will work for a 16 interlace only.
(1)
MASTER CLEAR
(2)
Swi tch to ABNORMAL DRUM
(3)
START
(4)
After FINAL STOP t switcb to Nrmalize Computer
Q>eration.
--......
--
(b)
Machine prints "c" and halts. A check address has failed.
STARring ignores this, error and routine proceeds as though
error bad not occurred. A cheek address failure should not
be ignored as it is very likely that the ~aper tape 1, in
error.
(c)
Machine prints "m" and halts. Check sum has failed to agree
with computed sum of data read in. START to ignore t.his error
and to have routine continue read in.
-.0
C\I
I
0"I
0
0
0"-
......
r><
0..
9-32
9 AJ-ri1 1956
[FLEXIE - A Flex Code Loading Rout i ne
RR-126
1
This routine is designed to load Flex Code tape prepared on a Flexowriter
in the conventional fashion for translating to bioctal. Flexie operates in the
same fashion as the bioctal Ferranti Loading Routine. A sum check is made
whenever the input tape contains an insert to 75202, 75203.
Operating
Instru~tions~
(I)
Set PAl( = 70002; SfAHr
(2)
Computer halts on 56 00000 70002 after completing read in.
load another tape.
(3)
At least one seven-level punch should be present in the trailer to
stop the routine. If this punch is not present the following procedure may be used.
(4)
STARr to
(a)
FORCE STOP after the paper tape has passed through the reader.
(b)
MASTER CLEARi set PAl( = 00022 SfARr
Errors ~
(a) Machine prints "t" and halts. Flexie is not in HSS correctly and
must be restored. START transfers Flexie to HSS again. A second
failure indicates that Flexie is not stored in the Service Library
correctly. In this case revert to the Normalize Computer Operation.
(b)
Machine prints "c" and halts. A check address has failed. A
ignores this error and routine proceeds as if no error had
occurred.
~iART
(c) Machine prints "m and halts. A check sum has failed to agree
with computed sum of data read in. SfARr to ignore the error.
ft
This routine provides for the display of the contents of consecutive
ory locations in Q, after an initial address is stated.
~
Operation Instructions:
(1)
Enter initial address, a, in Av.
(2)
Set PAK = 70003
(3)
START.
(a) are displayed in Q. The address is· automat ica 11y advanced
for reading successive cells by repeated STARTs.
9-33
9
A~ril
1956 RR-126
[write]
This routine provides for the writing in consecutive memory locations after
an initial address is stated.
Operating Instructions:
Enter the contents for that address in Q.
(1)
Enter the address in Av.
(2)
Set PAl( = 70004
(3)
The address is automatically advanced for writing in successive cells
by repeated STARTs.
[Flex Dump
Sf ARI' •
(FLElD>J
This routine dumps the contents of consecutive storage cells on punched
paper tape only. Automatic page editing is provided and every eighth address
is given. The punched tape is suitable for re-Ioading via Flexie. A check
sum is punched out at the end of the dump. (AL>, (Aft), are not restored
or punched out. HSS is restored. This routine replaces RI-73 (Flex Dump).
Operating Instructions:
(1)
Enter in Qu the address of the first cell to be dumped.
Enter in Qv the address of the last cell to be dumped.
If a seven-level punch stop code is desired at the end of the dump
set Q35=1.
---d6
(2)
Turn ON the Higb Speed Punch.
(3)
Set PAK = 70005 SfAflf.
(4)
The machine baIts on 56 00000 70005 providing a re-entry for another
dump.
(5)
Errors:
(a)
Machine prints "t" and halts. Flexo is not in HSS correctly.
STARr transfers Flexo to HSS again. A second failure indicates
that Flexo is not stored in the Service Library correctly. In
this case revert to the ROrmalize Computer Operation.
(b)
Machine prints "pH and halts. An illegal parameter word has been
set up in Q and is displayed there. Clear Q manually and insert
correct parameter; Sl'ART.
~
..-I
~
9-34
9 Afril 1956
(6)
RR-126
Flexo dumps only one type of storage at a time, either H55 or drum.
This routine does not use the 76000-77777 image, but uses an image
70400-70715 as a temporary store for part ofHSS.
[Bioctal Dump]
This routine will dump onto paper tape in bioctal form the contents of any
specified number of consecutive storage cells in HSS or the drum except 76~
77717. A check sum is automatically punched at the end of the dump. A double
seven-level punch at the end of the tape is optional.
Operating Instructions:
(1)
Enter in Qu the address of the first cell to be dumped.
Enter in Qv the address of the last cell to be dumped.
If a double seven-level stop code is to be punched following this
dump. set ~Qp;tO.
(2)
Turn High Speed Punch
(3)
Set I'AK = 70006 SfAllf.
(4)
The stop at the end of the dump, 56 00000 70006, provides a re-ent ry
for another dump. The contents of ~,A) and t.Q; are not retained. HSS
is restored.at the end of the routine.
[ROCO II LOADER (URL-2)
ON.
1
This routine effects the transfer of REeO II from MI~ to HSS and transfers
control to RECO after a successful sum check and rewind of Mr~.
Operating Instructions:
(I)
Turn High Speed Punch and Flexowri ter ON.
(2)
Set program tape to be assembled in reader.
(3)
Set PAl( = 70010 SfARr.
RECO is transferred from the Utility Library, a routine sum check performed and MI~ rewound. Control is then transferred to REeO and
assembly begins. If no subroutines are assembled, the computer halt~
on 56 0000t 00360 providing a re-entry to the assembly routine which
is still in H55 in its correct fon.. If subroutines are assembled,
REeO transfers control to URL-3 (Library Routine Loader) and the
Computer finally halts on 56 00000 70011, providing a re-entry to URL-3.
(See writ.uP of REeO II for more detailed description of tape preparation and handling. )
9-35
9 April 1956
(4)
RR-126
Errors: Machine prints "al" , rewinds MT~ and halts. This means that
REeO has been transferred incorrectly from the Utility Library on MI;.
5'TAIlf effects anotber transfer. Repeated errors indicate that RECO
is not stored on MI~ correctly. In this case revert to tbe bootstrap
procedure described in "Procedure for Loading Utility Library on 1iT0".
[Library Q)utine Loader (URL-3)
J
This routine effects the transfer of the Library Routine from MI~ to HSS
and transfers control to the Library Routine upon completion of a successful
sum cbeck.
Operating Instructions:
(1)
Turn High Speed Punch and Flexowriter ON.
subroutines is desired set MJl select ON.
If no punch-out of assembled
(2) Set Flex code tape of subroutine assembly information in reader.
(~: When assembling REeO tapes, the END psuedo code transfers
control to URL-3; in this case the Flex tape of subroutine information must be spliced on the end of RECO tape. )
(3)
Set PAl(
= 70011
srAHI
The Library Koutine i5 transferred fromlll'fj to HSS and a routine SIlBI
check performed. Control is then transferred to. the Library Routi8e
and assembly begins. Upon completion of assembly computer halts on
56 00000 70011 providing re-entry to the Library Routine Loader.
(See write-up of Library Routine for more detailed description of
tape preparation and handling. )
(4)
-.....
. .0
N
Errors: Machine prints "a2", rewinds MI~ and halts. This means that
the Library Routine has been transferred incorrectly from MI~o srARr
effects another transfer. Repeated errors indicate that the Library
Routine is not stored on MI~ correctly. In this case revert to the
bootstrap procedure described in "Procedure for Loading Utility Library
on Mr~". For a list of errors encountered in assembly and the appropriate operating instructions for same. see wri te-up of Library Routine.
CAUIION:
Do not assemble subroutines in tbe raRge 70000-77711 •
'-"
I
0"J
~ [Changed Word Post Mortem]
.....
t-
This routine is designed to compare the contents of each word of HSS with
its image at 76000-77777. The image contsins (unless disturbed) the original
contents of H55 as read into the computer. Those words in HSS which have been
changed by the execution of the program are the only ones reported out.
9-36
9 April 1956
RR-126
Operating Instructions:
(I) Turn High Speed Punch ON.
(2)
Set PAK = 70013 STARr.
(3) Computer halts on 56 00000 70013.
The following will be punched in Flex Code.
I, the parameter word is ignored. The u-portion of each
parameter word contains the octal address, I, of a cell whose CODtents are to be sampled. If M = 20001, (AL) is sampled. If M is
not a machine address the parameter word is ignored. The v-portion
of each parameter word contains the binary scale factor, s, of the
contellts of II. 0$ s Co 70. If. ~70, "2 small" is printed.
(5)
End words - The last two words of each sublist are of the form
70 00000 00000 with the exception of the second end word of the
last sub1ist (Lf), which is 70 00000 •
SAM-O jumps to 11\
after setting up cbeck points Oft a 70017 start.
C> Output
Shown below 1s an example of sampler output where the check point
address was 00303.
00303
00075
00076
00100
00101
00102
00103
20001
10000
D)
12 34567 12340
77 03124 65432
1.23456789017
-321.098632812
993059913.000
0.43210987653
14 00000 00000
37 37373 73737
Restrictions
The word initially stored at a check point must be an instruction; it
must not be a repeat command or a repeated instruction and it may Dot
be written into or out of at any time during the course of the program.
[ Restore HSS from IlIaoe]
This routine provides for an automatic transfer of the image,
to R5S.
76~77771,
9-39
9 April 1956 RR-126
Operating Instructions:
(1)
Set PAK = 70020 STARr.
(2)
Computer halts on 56 00000 70020.
[punch Check Sum ]
This routine is to be used immediately after loading a program tape by
meaas of the Ferranti Loading Routine (FRI-O). It punches a trailer containing
the sum of the loaded program with proper insert and cbeck addresses. This
trailer can then be merged with the program tape to provide a check sum upen
subsequent loadings.
Operating Instructions:
(1)
Load tbe program tape. There must be no double seven-level punches
in the program tape. Thus after loading with FBI-O.the computer will
hang up on an External Read- FORCE sroP the computer.
(2)
lASTER CLEAR; set PAl( = 70021
(3) STARr.
IA
The following punched tape will be produced:
75202
CIECK
SlDI
75204
Double seven-level puncbes.
CA
The program will be properly loaded at the conclusion of this routine.
9-40
REl1INGTON RAND UNIVAC
REGIONAL CODING ROUTINE II (RECO II)
Introduction
RECO is a one-pass assembly routine designed to tran.late an 1103
program coded in symbolici regional address fOI"ll to 1103 machine language.
Paper tape punched in Flexowriter code is the input-output .edi ..
for HEGO.
Input is the tape of 4ECO-eoded program, to be assembled Except
for the input of decimal numbers, all nlBberiag in this progra., is r.eeorded
in the octal system.
Output is the tape of the ass,embled. progra. in octal
notation.
The output is translatable to bioctal fora via the FllA converter,
or lIay be loaded directly into the comp1lter usiag the ERA "Flexie" load
routine.
A listing of tbe asseaabl~ prograll lIay be readily obtained on a
Flexowriter.
0
RECO offers considerable flexibility in recording 1103 words..
The
1103 symbolic and numeric operation codes, as well as those of the Interpre-
tive Systell are available for use.
Addresses may be recorded fn either absolute or relative form. Relative addresses use a t"o~letter regional address
code; in addition, the one letter regional address code. A and Q refer auto.atic~lly to the accumulator and Q-register.,
A IPxi_. of., 100 distinct reg100al address codes is available in 8 REeO coded prograa. aDd tbe pseudoinstructions assigning absolute addresses to each of t,hese codes precede the
ma in progr8JJI on tbe iDput tape.
Provision is m.de for
in de~imal notation. A deei.aI
to its signed 36-bit equivaleat
floating point fora offers la.II
tbe direct input of progru
nu.ber, Nt is 88t_8tie811y
i. fixed pOint, or floating
range convers.ioD. tbe range
CODstants written
CODverted' by IlECO
point, fol'll. Tile
being J'o~gb11,
All decimal numbers are identified as sucb,by • RECO pseudo-operation
-'"
code~
The punching of insert and check addfesses Oft the output tape is
obtained by using pseudo-instructioal. A cbeck , .. of assembled 1103 word. i.
aut_atic811y puncbed out with each check address ia.tructiOD. ,A pseudoinstruction is available wbereby the progra..er caD iDsert 8 MJOv instruction in
add~esses,OOOOO and 40000;
tbis.pseudo-instructioD per-ita hi. to begin _peratiOJl of his progr_ witb 811 lID start.
C\J
.......
-I
C1'
I
o
o
C1'
.......
r><
c..
Two types of termiIJating instructions are .vailable. Tbe first of
these puncbes oat trailer aDd baits the cOIIputer.. The secoad puncta•• out
trailer and transfers control to the ERA Library Routine. ,Thus, if tbe progra..er desires the assembly of certaill subroutilles for hi. program be •• It
record the proper termiD8tingcomaaDd followed by a list of subroutine iDdices
at the end of his input .tape.
Tbis option pel'llits contilluous ass&llbl,. of the
co.plete program. The total output in this case would cODsist of two parts 011
one continuous tape:
(1) Assembled main progra.;
(2) Assembled subroatineso
Several types of progr.. errors are detected by RECO.,
The type of
9-41
RR-l26
aegional ·Coding Routine II (RECO II)
1 April 1956
error and its location on tbe input tape are printed out on the Flexowriter.
All RECO output ceases as the first program error is detected. and the RECO
input tape is processed from that point on for errors only. This error detection is lillited in the seDse that oaly the first error of a program word is
recorded.
A detail description of RECO programming is given below.
Part I
discusses the writing of regular 1103 wo~dsin symbolic for.. Part II lists
the seven RF.CO pseudo-instructions. Part III describes input-output fomat.
Part IV describes RECO error detection.
Part V lists REtO operating instructioDs.
Figure 1 of Part III is an-example of a RECO progralll. Figure 2 displays a listing of the assembled progra. given in Figure 1.
I.
1103 Words
A.
Address Portion
Addresses .y be recorded in eitber absolute or relative fona. KECO
requires that at least one digit be recorded for any absolute address. Relative
addresses appear 81 a I a 2 B, where (a 1 a 2) is a two-letter code denoting
any ODe of a .xiii. of 100 (deci.. l) addressable regioDs, and wbere (8) designates tbe sequeace Damber of tbe address within the region (a 1 a 2). The
oBly restriction .. the choice of letters in the regional address code il tbat
a 1 ~ A or Q. (8) .ay be zero, in which case only (a 1 a 2) need be recorded.
The regional portion, (a I a 2), of 8' relative address is assigned its absolute
address Yalue, 8. by MaDS of tbe KEtO p.eudo-iastfllction RE a 1 a 2 i. All
such 8s5igo.ents should be recorded at the beginning of the prograa tape.
RECO requires that 8n entry be .ade for each address portio. of every
1103 instruction and octal CODstaDt.
For' aD inst1"1Iction in wlaichan address
portion is a "j", "jn", or .tjk" DEer (e.g. RPjnv). all five octal digits
must be recorded; if j = 0, one Beed only record O. n, or k.
B. OperatioD Portion
,
.
Operation oodes are either the two digits or the two letters of the
1103 instructioD repertoire.
The n..erica1 operation codes extend from 00 to
77. In addition, tbe alpbabetica1,l1W1eric, or alpha-owaerie operatioD codes
used io the 1103 Interpretive Syste. afe recognized by RECO 811eg81 operations.
However, the operati.D code for tbe Interpretive Replace Multiply: ilrestricted
in form to either IP70 or 1470.
Thoae 1103 words which for. octal CODstaDts with absolute or"relative
address pertioDs, ••at have at least one aDd no .ore tban two digits recorded
in the operation porti08 of the word.
~
C.
ents.
Decimal Numbers
All decimal numbers are converted by REeO to signed 36-bit equivalDecimal numbers must be identified as such by the pseudo-operation code
9-42
RR-126
Regional Coding Routine II (REeO II)
1 Apri 1
1956
DE; these are the only program words for which RECO accepts numbering in the
decimal system.
There are two forms of decimal number words:
where
S,
1$ i $ 9,
0$1092
0 ~ fj $ 9,
-99 ~ P $ 99, such that
It i.fl f 2 •••
f9 f lO x loP
I
+ S< 35.
tiS" is the binary scale factor applied to
I! i.f1f 2
••• f9 flO x loP
(2) Floating Point
where 1$ is 9,
I.
"p" is the power of ten.
DE t i.flf2 ••• f9fl0
O~
fj ~ 9, -39 < p < 39.
P
F,
"F" is the
code letter denoting floating point conversion to
packed (28-8) form with biased characteristic.'
The range on
number.
L.
8
floating point decimal number, N, is roagbly 10-38
SiN I~ 1038•
The plus sign (+) is optional ou all signed quantities in the decimal
The decimal point aDd some value for P and S must always be recorded.
Sttbroatine Assembly
RECO does Dot assemble library subroutines directly: rather, it provides the option of transferring control at the end of a REeO 8ssembly to another progra. whieh assembles subroutines. The use of this option terminates
all REtO assembly aDd punehes out those subroutines listed on the input tape.
This list of subroutines must be prefaced by the RECO instruction END and .uat
comply with the input foraat of the ERA Library Routine.
The output tape resulting fra. use of this subroutine option il ODe
continuous flex code tape consisting of two parts: (1) AsseJlbled main program;
(2). assembled subroutiDes.
It is imperative that all, if any, subroQtine asseably be the final
step in a complete progra. assembly.
The reason for this is that the use of
the subroutine option in effect destroys all previous HE a 1 a 2 8 instructions,
and of course the information contained in these instructions is necessary for
proper RECO assembly.
3
q-4~
RR-126
1 April 1956
Regional Coding Routine II (KECO II)
II.
RECO Instructions or Words
A.
RE
B.
DE
c.
IA
D.
CA
E.
START
"Assign the region a 1 a 2 the value 8 tt
Tbis instruction is described in I-A above.
f9fl0
P S(F> "Decimal Number Fixed
(Floating )'t This instruct ion is described. ill
I-C above.
"Insert address at a I a 2Btt
causes a
followed
a1 a
aI
a~
This instruct ion
six-inch leader to be puncbed out
by the translated insert address.
28 •
"Cbeck address at a 1 a B" This instruction
causes the trans lated cieck address. a 1 a 28 ,
to be puncbed out, followed by a punch out of
a check sum of all 1103 words since last LA
instruction. This check· sum i l inserted at
.achine addresses 75202 and 15203 on tbe
output tape.
"Start progra at a 1 a 28" This instruction
c.u.es 8 translated MJO (a 1 a_ 28) instraction
to be inserted at addresses 00000 and 40000 OD
the asseabled progra. tape. The correct addresses aDd check
are aata.atically punched
oat. This iDstruction is optioDal.
8...
F.
00.
G.
"End REtO progr_ 8ssellbly. begin subroutine
As seJlbly"
This instruction causes a 10 inch trailer to
be punched out, aDd transfers control to the
subroutine alseably program 8S described. in
I-E above.
...0
C\J
:!
"End RECO progr.. assembly" Tbis instruction
causes 8 10 incb trailer, followed by two
periodl aDd a seventh level to be punched out.
before holting the coaputer.
III.
Input-Qutput reraat
I
0-
Figures 1 and 2 are illustrations of the horizontal and vertical
input-output 1'01'll8t5. The fonat exbibited in Figure I il strongly recOll&ended
..... for RECO progra.. ing.
Fvery 1103 aDd RECO word must be ter.inated by at least
tone
vertical
space
(i.e.
carriage return), and tbe distinct portions of any
><
c.. word .gat be separated by at least one horizontal space (i.e. space or tab).
aECO fgnorel all leader, shift uP. shift down, and delete flex codes. In particular, flex characters for "1" and 1 (one). and 0 and O(zero) are not interchangeable.
t
o
o
0-
4
9-44
RR-126
Figure 1
RE aCID
HE
HE
HE
ZA40
TQl00_
IlS50000
STAIlT
BC
IA Be
TP
TQIO A42
12
TQ6 .Q
SP
EF
TQ14 17·
0 TQ13
77
10000
20000
LA TQ5 A17
DV TQ6
TQ14
IPMP ZA ZAS
RP 30005 BC 12
TP
PR
BS ZA
0 Be
IS 30000 BC14
as 111TQ12
1473 TQI0 1014
RJ
IIJ
RSS as
0 ZA
CA BC20
IA
DE
DE
DE
DE
DE
DE
TQ5
+2.147483648 9 F
-7.3786976294 19 -36
2.9103830456 -11 35
3.14159 5 F
1.0 10 0
3.162278 -38 F
070
000
DE 1.7014118 38 F
CA TQ16
END.
9-4:1
figure 2
.000000.040000.
45 00000 00010.
00000004. 0001.
000000.075202.
00 00000 00000.
·45 00000 00010.
00000007.5204 •
• 000000.000000 •
45 00000 00010.
00000000.0001.
000000.075202.
00 00000 00000.
45 00000 00010.
00000007.5204.
be
.000000.000010.
11 00110 20042.
12 00106 10000.
31 00114 00017.
17 00000 00113.
77
54
73
14
..-..0
.....
C\J
-,
I
0"-
0
0
10000
00105
00106
71004
20000.
20017.
00114.
00045.
75 30005 00022.
11 50000 00040.
61 00000 00010 •
56 30000 00024.
23 00111 00112.
14 73011 00114.
0"-
37 50005- 50000.
t-
45 00000 00040.
.....
><
0..
00000000.0030.
000000.075202.
00 00000 00007.
70 74706 41000.
00000007.5204.
6
9-46
BR-126
Figure 2 (continued)
tq+
• 000000. 000105.
20
16
00
23
00000
77711
00000
13136
00240.
77177.
00001.
00223.
11 24021 62000.
25 41273 44004.
00 00001 ooOOOe
00 00000 00000.
31 71m 76771.
00000000.0116.
000000.075202.
00 00000 00002.
41 00470 25466.
00ooqoo1.5204.
7
RR-126
1 Apri 1 1956
Regional Coding Routine II (RECO II)
Foraat of output listing is exbibited in Figure 2. Tbis listing of
an assembled program should prove to be useful in program debugging.
The
output tape is translatable to bioctal for. or may be loaded directly into tbe
computer via the ERA "Flexie tt load routine.
s~
IV.
Flex Code stops are automatically punched by RECO after eaeh cheek
check address to facilitate bioctal translation or listing.
Error Detection
RECO detects a liaited number of progra. errors.
and their respective tags are 8S follows:
~
These error types
oc
I llega 1 operat i
HC
CA
Illegal regional address code (i.e. Aa 2 or Qa 2 )
Check address failure
RA
Unassigned relative address region
AO
Relet i ve address exceeds the vi.llle 77771
OD
Illegal octal digit flex code
FE
Decimal point missing in decimal number
FO
N\llber of fractional digits
UN
Deei.al auaber underflow (i.e. lOIS of significant digits)
DO
Illegal deci.al digit flex code
OV
Decimal number overflow (i.e. loss of Significant digits)
OIl
code
10 in decimal nwaber
RECO detects only the first error in a programaed 1103 or KECO word.
Tbis detection does Dot apply to any errors occurring in tbe lilting of subroutine indices at the end of tbe input tape; errors in this pottioa of the
input tape are detected by the subroutine progra..
C\J
......
,
~
8
~
~
><
0..
As RECO encounters a· progra. error, it prints out the error tag
followed by two decimal numbers t a group count sud 8 word count, wbicb locate
the error on the input tape.
Group 0 includes all RECO words prior to tile
first progranaed insert address instruction. wbicb i8 word 1 of group 1. Eacb
succeeding insert address begins a new group.
All output ceases as RECO detects the first program error. Bnd input
Tbis teNinetion of outtape is processed for errors only frca that point on.
put does not include that output reSUlting fra. subroutine assembly.
If the number of REeO instructions RE a I a 28 exceeds 100 (decimal)
the ca.puter will halt with an sec fault. RECO will not assemble such a program
correctly.
8
9-48
RR-126
!legional Coding Routine II (RECO II)
1 Apr!l 1956
Improper horizontal and vertical spacing is also indirectly detected
by REeO as one of the error types listed above.
v.
Operating InstructioQs
I..
Flexowrit~r
and high speed punch on.
2.
Load input tape in F~rranti reader and position the tape several
blank frames ahead of first character.
3.
Set all MJ and MS selects off; malter clear. set PAK to 10010;
START.
REDO is brought into HSS fra. magnetic tape and assembly
begins.
a.
If the instruction END. is recorded at the end of the
input tape. the computer will halt on a 56 00000 00360
instruction. If END. is oaitted. the computer must be
force stopped aiter input tape ba. pa.sed through the reader.
b.
If the subroutine option, END, is on the input tape and a
period is recorded after the last sllbroutine index, the
computer will halt on a 56 00000 70011 instruction. If the
period is a.itted, the computer ••• t be force .topped after
input tape bas passed througb the reader.
4.
To asseJlble
8 second program, and case (3)-a applies to the
preceding progra. assembly, position second tape in reader. let
PAK to 00360, aDd START.
5.
To assemble 8 second input tape making direct use of ilE a 1 a 2 8
instructions fraa the preceding tape and case (3)-a
applies. position the secoad tape in reader, set PAK to
00364 and START.
9
o
AO
RICO
RR-126
010'-1
00001
00 OQOOO
000Q2
00 00000 0IQ1I
0000'
GO 00000
0lIl5
~
00 00000
0IIaI6
~
00 00000 0IIL1
na
code. tor
CCI1Wf\Iter i.Datr\lct1on
OOOQO
OO1lO
nputo1n.
OOOOT 00 00000
~
•• 1••••••
00006 00
00010 00 OOOQO 00000
OOQU
1
00001 tbru. 00100
00 OOOOO~
000lI 00 00000 0:5007
000l..5 00 00000
O~
t)()()lA
00 00000
OlIo?
~
00 00000 .,,..
00_,--.
0001.6 .00 aoaoo· ,aoooo
00Q1,1
OOGIO 00. _ .
aoooo.
00011 OOOGGlO .....
00012 00 OOOOQ ~
au»
~
00 00000
~
00 00000 Q1.lJO
oooe
00 00000 0"'"
ooca6 00 00000 O"!50
~
..-.
-.0
00 OQOOO
0»01
000:50 00 00000 00000
N
......
....,.,
l
0'
I
0
0
0'
00031 00
000,.
~
auJI
00 00000 C8~"
......
t-
><:
0..
q-51
aoooe ~
~
00
oooe
00 OQOOO 00l0fi
00066
00 OQQOO 00l.a1
0006T
00 OQQOO ~
OOOTO 00
,
RR-li!6
OQQOO 00000
0007l 00 00000 00000
00011 00 00000 00000
ooar,
ooar-
.co
00 OQQOO 00000
00 OQQOO 00000
C)()O'O
00 00000 00000
ooar6
00 00000 00000
oocm
00 00000 00000
00100
00 00000 00000
0QlQ1
00 00000 011?2
001GI 00 00000
nex .... t .
OGIIIfUMr .....10
.,...uau.
1tIb..... 0Q101 tbn 00I0O
01M6
00l.C8 00 00000 07Iff8
~
00 OQQOO Q1I6Il.
00l.f0 00 00000 01110
00106 00 00000 0111'
00l.a1 00 00000 C1lI:JI
OQUO
,..-..
-.0
00 OQQOO
f11I'1
00Ul 00 00000
06671
001lI 00 00000
~
001U 00 00000
~
C'\I
.-4
'-"
,
OOU- 00 00000 o66a
0"J
0
0
0"-
~
00 00000
06670
l"-
00116 00 00000
0611-
OOU1 00 00000
~
()() 00000
066n
00lIl 00 00000
06171
~
i><
0..
00110
9-52
IICO
0Q1I2
00 00000
~
RR-126
06166
toll, 00 00000 0fi8le
00lI-
00
~
00 00000
OIitI:Io
00lI6 00 00000
0611~
00121 00 00000
o6eI
ooooo04ila
00lJ0 00 00000 06137
00l3l 00 00000 oQ72
00lJI 00 00000
~
001',
00 00000 Q6Ia.6i
~
00 00000 oQ64
ocn»
00 00000 ~70
0QlJ6
00 OOOQO oa7~
001Y1 00 00000
0QJ.II0
oa,.
00 00000 ~'7
00l1e.l 00 00000 07011
ocnJMI 00 00000 07066
001~'
00 00000 f1(061
001"
00 00000 OToQ.
00l1t5
00 00000 <17070
001~ . 00 00000
....0
01""
00l~1
00 00000 ·07cee
~
00 00000 070"
C\.I
.....
-I
0"I
0
0
0"-
.....
t-
><:
~
9-53
RICO
00151 00 00000 (f'f-1R
~
00 00000 07~
~,
00 00000 07Wti
ocn,a.
00 00000 07~
,
RR-126
00l.55 '00 00000 (11"70
~
00 00000 07"'711-
00l5l 00 00000 014,.
001.60 00 00000 014,.,
00161. 00 00000
oo.l68 00
~
OOOQO ~
00l6, 00 00000
~
()()l.Q
00 00000 ~
~
GO 00000 ~o
~
00 ooooo.~..
00167 00 00000
~
0Q170· 00 00000
~
00111 00 00000 0"".
00111 00 00000 0""
001." 00 00000 0 " .
ona
0011-
00 00000
001"
00 00000 0,.,,0
00176 00 00000 0:5714
.-
00l.7T 00 00000 o,-"e
...0
C\J
r-t
'-'
00I0O
00 00000 0''''''
I
0"J
0
0
0"-
t"'"'"
><
0...
9-54
00I0l 00 00000
,
0lII0
RR-126
0CJIcr. 00 OC*O. aalla·
0010'
00
14Ol5..0lIQl.
ocaoa.
00 00000 GaI20
~
00 00000
ov.;,o
00806 00 00000· 016",
00107
"all. __.ru.
AMa-.....
0GIQ1 tau 00,,-,
ooocw.1·~
00Il0 00 QOI6.~
ocml 00 OQOOO. 00000
00IlI 00
ooaoo· ooan
0GIJ3 00· 00000 -~7
00IlA 00 00000
~
at ••
«.......
o.JJ.~
. . . 01Jt61
ocxm
00 00000 ~
0CJI16 00
OOOOO.~,
0CJI11 00 GOOQO·oocel
00lIO 00 00000._'
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9-73
0U6T
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-
.,
RR-126
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GUn
u
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to ,00000.· 01Ia
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t
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9'-74
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9-75
lleO 27 RR-126
0l25'
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o~ o~
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00I0O 70011
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00000 00155
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.~ t1an Ol~27
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uan .., 00000 01'"
01l7~
0, 16121 61'30
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01177 .., 00000
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......
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9-76
~
01306 '7 005TI 00,11
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ooa~
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28 RR-126
IICOa,
O~
,,~
10012
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~,
000II
0l3M
~,
,,~
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.., 00000
013M
O~,
RR-126
" 0117" 100"
Ol,a.6 '1 00IlI 01"1
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00000
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9-78
Ilea
ooeoo
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0131'
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61
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Ol~
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01~
0lJM)5 ." .,., 0lM6
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011tCr1
uoo_~~
,ow.o u
0l.JtW I000O
01-11
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01~11
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a.'~~
'1~1Jt.
~ 01~~
oiuo
01415 U 0C86 I0000,
01",' ",",I01U7
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9-79
RR-126
23 Ju.ly, 1956
iBtrqduct10n
The ERA L1bral7 Routine tor the 110.3 Serial 9 Ccaputer extracts
subroutines tro. a library file on magnet1c tape and assemble. th. on the
drum or in high
8~eed
storage tor later U8e.
At the option ot the operator,
a flex tape ot all subroutine. assembled 1s punched out on the high speed
This routine JIJa7 be used in conj unot1on wi tb RECO II (ERA Re&1onal
Codiag Routine II) to give a continuous
nu:
tape cona18t1Dg ot °a ma1n routine
followed b,. alleubroutlnea needed in tbe execution- ot the main routine. A
deacr1ptioll ot this overall &saabl¥ procedure
DCO.
i8
giV8D 111 the vrl te.-up
It 18 alao pos.ible to uae the Ubra17 Routine eeparate17.
caee input iDtomat10n auat be provided br the opera tor in the
!h1e tape list. the subrouUnes to be
flex tape.
a.~ebled,
or
III e1 the
t011l
of a
together with
,~
infoJ.1Dat1on regardiD£ assembly mod1f'1cut1oD and storage.
Routine.
IDa)"
be
stored at a location d1fterent trom that with r,8spect to which the, are
88881bly
_OO1fied.
A detaUed description of the lnJ. ut tape is g1ven in the
section -Input Tape Format".
--
HaiR
~
......
Features ot the Ltbmrz Reut1ne
'-"
I
0-
6
o
1)
Ed t Restoration
0"-
......
r><
c..
!he Ubra17 Routine replace. the first two verds of subroutines
in -standard for.mft with the instruct1on.
37
75700
75702
45
000C()
QoOOOJ
9-80
RR-126
-2-
The first inatruction rerers to· the Convair Alara Routine which
has had its insert address changed fro. 76000t0 75100 in order to avoid
interfering with the image.
This -exit restoration" feature 18 included to facill1ta.te relocating the
!lara Print routine.
In tact, with a1nor aod1t1oationa, a difrerent atandard
preface can be .appended to subroutines in the tape 11braJ7, should thi. ever
be desired.
2)
Asaembl1' Modification
AD7 routine coded
addres8 subjeot
a)
My
be modified relatlve to &DT BSS or druIl
to the following re8trictions.
lbe routine!. coded relative to 01000.
b) All: lnatruotioD8 aDd relative operaDCla are located couecut1velT
at ·thebeginnJ ng .or the routine.
0)
All absolute constants are stored oODHoutively '-.d1atel7
after the modi.f'1able· worda.
A '118't1rlf of :routine.wh1ch·may be JaOd1t1ed b7 the 11br&l7 routine
The programmer JlU8t choose for each JDOd1tlable
1. g1yen 1n the appendix.
routine,
the starting address with respeot tovh1oh address JaOdit1oatlOll, ta
to occur, as explaiDed in detail 1n the section on -Input Tape
:3)
Storage
or
rorll&t-.
Subroutine.
1be progrumer may ohoose to store' a subroutine bepnning at 8.D7
HSS or drum a4dresa exc.pt in the 1JIage (76OfI)..77l71).
Storage in the
1JIage. vUl reault in a1JaultaDeou8 .torage ot the subroutine 1Jl the oorre8pC)Dd1ng high speed 8torage
100&tion.
It 1s the prosra-er'8 reeponaibU1ty to b. sure that .teNd
rout1nes do not overlap.
It it 1. de.ired to atore two or
lIOn
routine.
in the same locations, then the Illtra17 routine auat be applied two or .ore t.1JHa o
9-81
RR-126
-3-
The programmer .uat choose a storage location tor each routine
.etller 1 t 18 &aseab17 aod1t1able or not.
1be aetbod. ot providing 1ntormation on desired storage loca tiona
18 given 1n the section -Input Tape
Forma~".
6"
4)
'l)ped List ot Subroutines
During the operation
ot the routine, a l1st ot subroutine. "to-
gether vi th other 1ntoraation i8 typed out.
Th1e list lIJB.Y be used by the
programaer to verity that the subroutine. have 1n fact been assembled "as
he iDteDded.
S)
ror detaU. see the section -'l)ped List ot SubroutlDU -.
Flex Tape Ou.tput of Assembled Routines
The operator JI81' prooure aex tapes ot the ass-.bled subroutines
i t he desU.-ea (M. Operating lnatruct1ona).
In general eithera!l ot the
aubroutlbe8 are pmched out, or DOne ot th_ are.
The following
nex
_pe
18 punch&4 QU.'~ eaob aubrOutine (with apJ:,ropr1ate leader or traUer).
-.0
~
,
6)
a)
Inaert Address (First Storage Addres.).
b)
SUbrouU_ (aod1t1ed or not
e)
Check Address.
d)
lDaert addreaa 75202•
•)
Check aua.
t)
Oheck Address 75204.
a8
the case -7 be).
F1Dal. State after Ue1ng Routine
'-"
c r A t t e r the rout1oa baa been ueed and all' subroutines have been
o
o
~ asaeabled (and p••81b17 punched out), BSS 1. restored' to its original tora,
t-
~ except tor tho.. 100&tiona 1n which subroutines have been stored.
aubrout1nea are in their desired locations ready tor US8.
All the
Magnetic Tape
Unit 0 haa baen backed up to its starting point.
9-82
RR-126
-4-
The
Subroutine
Library
A list of subroutines currently stored on MT Unit 0 is given in
the appendix.
Preceding the first uord of each subroutine on magnetic tape
are tour "tag words".
Following the laf?t yord of each
subrout~
are enough
"all zero" words to fill out the block of :tape on whioh the last word a.ppears.
For example, a subroutine containing
tape; i.e., 4 tag worde,
"468
46s
words oocupies two blocks on the
subroutine words, and 2t8 blanks.
The four "tag "Words" preceding a subroutine g1ve the following
information a
1) •
First word abc ddddd eeeee
=0 if routine 1s assembly modifiable.
b =1 it routine 1s not assembly modifiable.
c =Oir exits are not to be restored.
c =1 1t exits are to be restored.
b
ddddd.
number of words if routine 1s assembly modifiable;
first fixed operating location if it is not •
..... a number ot modifiable words 1f' routine is assembly
modifiable J last operating location if 1 t is not.
2) • -Second Word a Check Sum (Left Part).
j). " Third Word a" Check Sum (Right Part).
4) •
Fourth Word I
This word 1 s the routinJe library index, or more simply,
Routine Index, and consists of a
nex
code of five letters,
'Which are determined by the nature of the routine and two
octal zeros to make up a 36 bit word.
a) •
lxamplesl
Central Exchange Index I RR-68 (eX - Fl08 ting Point).
Routine Index I
ex - fOl
. Routine Identification Code.
20 27 26 37 -5= 00
q-83
RR-126
-5b).
Central Exchange Index.
Routine Index I
CV 37 (Card Paokage)
cg -. 100
Routine Indentification Code.
l6 13 52 J"i 37 00
(Note that the "dash" in the index does not 8.fpear
in the identification code.)
The Library Routine is also stored on MT Unit O.
It 1s transferred
to BSS from tape by the Library Routine loader in the Service Library.
th. DictiMFY
Immed.1ately following the L1 brary Routine on MT Unit 0 1s a 40
block "dictionary". The first halt consist5 ot a 2 word check sum plu6 up
toS10 (decimal) identIfication codes of the type described in the preeed1Dg
Mction.
All words not filled with identification codes are filled with
zero••
The second half ot the dictionary consists ot a 2 word check sum
and up to 510 "control worden.
Far each identification code in the
first halt ot the dictionary, there i8 a control word in the 8Ilm8 relative
p08ition in the aecond halt; i ••• , it the identification code correspond-
ing to a given subroutine is the nth word in the first halt ot the dictionary,
~~512, then the "control word" for this subroutine 15 also in position
n, but 1n the second half
or
the dictionary.
The control word consists of
12 octal digits
op ppp qq 00000
,where
pppp is the number ot blocks of tape in MT Un!t 0
measured from its start which must be traversed to get to the start of the
subroutine,
03648~PP~20478
J
qq is the number of blocks in the subroutine, Ol~q~08.
It a subroutine is more than 208 blocks in length it is regarded as two or more separate routines, eaoh with its own "tag worde"
and "index".
9-84
RR-126
As an example, the control yord 01 2460.3 00000 calle tor a
routine whioh starts Arter l246 blocks of tape have been counted and
which is 3 blocks long.
The subroutine therefore occupies blooks l2.47, 1250,
and 1251. (octal)
Ipput
The input tape
Tape Format
ll~ts
the subroutines vb1ch a-e to be used in
a main routine together with information regarding assembly modification
and desired storage locations.
ot information tor
e~ch
The programmer must provide thEM pieces
8Ubroutine to pe assembled.
The exact format ot this information depends on whether the
routine is aeeembly modifiable.
1.)
For an5Mmbly modifiable routine,
a)
Routine Index
b)
An a8Hmbly modification a ddr.S8J 1.e. the first oper-
ating location ot the subroutine •
•
c)
A 8torag' address; i.e. the address vhere the t1rst
word of the subroutine is to be stored.
2.)
For a 8ubroutine which 1s not assembly modifiable, (1 ••• th8
subroutine i8 written with a fixed operatiDg location
or is written relative to B.S.S. location 01000 but 1s
not in -standard form").
a)
Routine Index
b)
Fixed operating addres8 (1 ••• the tirst address of the
routine.)
c)
A ·storage address
A max1mum of 16 subroutines can be aeaembl.d with one application
of the Library Routine.
Care must be taken not to store two routines in
the same location, since all subroutines are assembled and stor.d before
9-85
-7-
any ot them are punched.
RR-126
If the operator desires to :tore more than
one subroutine a. t the same location, he must use the.11brary routll2e
more than once and must have. a -separate n routine list for each appllca. tion ot this routine.
(The tape need not be separated llterally, but
must have the proper -terminating signal- betveen each routIne list.)
At the aonc1ueion
or
each routine list is a period.
This tells
the machine that all input Information· has been lIteelved and' transters
operation to the next part of -the
routin~.
If more than 16 subroutines
are called for without
a period, the input tape is automatioally stopped
.
.
atter r ea.ding in 16 indices, and the computer halts after assembling
the 16 subroutines.
Push start button to assemble the remaining sub-
routine ••
The exact format ot the tape i6 best illustrated by an.,mple.
Six subroutines are to be assembled.
The subroutine library
representation and Central kchaDge lumber.ot these subroutines are.
1) rt-tOl (RR 59)
2) opo-lOO (ev 1)
3) do-xOl(BR 47)
4) al-prl (CV )
S) ip..p01 eRR 10)
6) rt-:xOl 1BR-21)
In the above list, routines 1, 3, and 6 are written 18lat1ve to
B.S.S. address 0l000.
Routine 5 1s eo written on tape as to be 8ssemhl1
modifiable. Routines 2 and 4 operate from fixed locations.
These routines are to be operated on as followsa
1) rl-fol modified relative to 1300 and stored beginning at 51000.
2)
ope-lOO bas fixed operating location 00040 but 1s to be stored
at 42100.
9-86
RR-126
3)
do-xOl i8 not to be modified but 1s to be stored at 66300.
4)
al-pr1 has fixed operating location 75700 and is to be
stored there.
5) ip-pOl 1s not to be JIOdit1ed but i . stored at 41000.
6)
rt-xOl is to be modified relative· to OlZ72 but is to be
stored at 00300. \
The information needed on the input tape consists
ot the tolloviDg
in flex oode I
rt-fOl
01300
51000
cpo-100
00040
42100
do-xOl
01000
66300
al-prl
75700
75700
1~1
01000
41000
rt-xOl
01272
00)00
The rollowing general rules are noted I
1)
Three piece. of intormation are needed tor each subroutine.
2)
If a "standard" assembly modifiable routine ia not to be
modified, the address 01000 is the first address listedJ
otherwise the starting address is given.
3)
The first address tor a routine which has a tixed operatiDg
location is the tixed operating location.
4)
The first address for a routine written relative to 01000 but
which ie not in • standard torm" (and hence i. not modifiable)
i8 01000.
5}
The second address is always the first address at which the
subroutine 18 to be stored.
6)
.
An assembly moditiable routine may be ~tied relative
to any ·B.S.S. or drum address.
-9-
8)
RR-126
A routine may be stored anywhere in H.S.S. or on the drum.
Care BlUet be taken nct to store more thall one subroutine 111
the S8llle location.
In preparing the in!=,ut flex tape, the following rules should be
1)
There must be at least one apace between the tvo letters aDd
the three (or more) d1g! ts of the library index.
2)
There must be at Ieaat one sPace between the library index and
the f1rst address and between the flrst
~ld
second addreases o
3)
There must be a carriage return atter the secorid addr ••••
4)
Jollowbg the carriage return at the end of the laat eubrout1ne
iDtormatlon there auat be a period.
S) !be l1brar.y routine ignores extra apece., cod. de let.. and
leader on the input tape.
TYpE UPta of SUbrout1py
A8 the library' routine 18 operating on aubrout1nea taken ott
magnetic tape, it type. od iDtoraat1on tor later reterence.
1) It the eubrout1ne 18 mOdifiable and haa been modified. the
following i .
. a)
b)
typ",
11.03 L1braJ7 IDdex
Jl1aber
ot Vorda
lbaber ot Modifiable Vorde
e) MOD aaaaa
4)
where.
bbbbb
cccce
aaaaa is th. atf;rt1ng addres8
bbbbb 18 the first etorage addre ••
occco 18 the last storage addres8
9-88
RR-126
-10-
2)
If the subroutine is modifiable but has not been modified, the
S8Jne
information is typed as in 1 (except that c) 1s "BOT
MODIFIED" •
:3)
If the subroutine has a fixed operating location the following
1s typed:
a) llO3 Library Index
b) ddddd
e. . .
0) bbbbb
cecco
where I
ddddd ie the first operat11'lg location
e.... is the last operating location
bbbbband cccce are as in 1
In the example previously discussed the following would be tJ1ped
(although not necessarily in this ord.r).
rt-tol
00056
00050
mod
01300
51000
5105S.
op-1oo
0004;1
00071
42lOO
42137
do-x01
00202
00160
not modified
66300
66501
al prl
75700
7564.3
75700
756J;J
')"'
RR-126
-11-
00421
not modified
01421
01000
rt-xOl
00041
00040
mod
01272
00300
00350
The
progr~r
may quickly scan this list to see it the proper enb-
routines were aseembled and it th.re Is any overlap in storage.
Error Detection - AlArm!
The library routine detects certain errors during the course of
its operation.
encountering
The8e errors are indicated by typewritten symbols.
ODe
oftha errore described below, the machine stops.
After
In TUGet
ca ••• , several options are available to the operator, as outlined belove
r
1.
"82
ft
-
oheek sum f'ailure on transfer ot the libr8r)' routine
to BSS. NT Un!t 0 is backed to the beginning of the L1 brary
Rout1De Prese
2. "e1" - check
-
8UJIl
failure on transfer ot the first halt ot the
dictionary to B.S.S.
. .0
C'\I
I"'"of
beginning
I
a-t
or
The magnetic tape is backed to the
the dictioDnr7.
a) To retranster first halt of dictlollB.rY I
0
0
aI"'"of
b) To ignore check sum failure I set
t-
~
i:JiK1 to ratranster routine.
Press ~
PAl to 00600
3. "Ra - a non-exi8tent index has been read into
Prele STABT.
and ~
the machine.
The non-existent index i. ignored, and the program
continues.
4.
tlC2" - check sum failure on trarister of second halt
ot dict1ork"lt7
9-90
RR-126
-12-
into H.S.S.
The magnetic tape is backed to the beginning of
the second halt of the dictionary.
5.
a)
To retranster ascend half of dictionar.ya
b)
To igncre oheck sum failure:
"e,3" -
Set
check sum failure on transfer
to H.S.S.
PAl to
or
Pr•••
~
OOl?O2 and ~
subroutine from library
The magnetic tape is backed to the start of the
subroutine.
a)
To retransfer subroutinel
Press START
b)
To 1ranster next subroutine (or to proceed with program 1t
failure was on last Bubrclltine) I
Set PAX to
0)
6.
To ignore aheck
8UJA
00604.
failure.
and ~
Set
III
to
00W6
and ~
804" _ The address portion of the input flex tape is incorrect
(e.g. le8s than five ectal digit., a character 18 used other
than 0, • • ., 7).
Press
mRI
to bring in next index (or
continue program).
It an error 18 indicated (other than "Cl-),
dces not get assembled.
A look at the
ty~ed
ODe
or
the sl1brcutinea
list ot subroutines determines
which subrcu tine is missing.
. Operatips Tn'tl'l19 tiOI!
-..[)
C'\J
r-I
1) Prepare a flex tape which calle tor the 8ubroutines wanted and
'-'
I
aa$b17 modification and storage o
0'
which provides information
0
0
0'
This tape may be spliced onto the end of inl-'ut tape used tor
I
r-I
OD
t~
Cl.i
RECO II when both routines are to be used in sucoes8ion
discussion of this in the RECO II write-up).
(S. .
It this routine
is to be used alone, only the subroutine flex tap. is needed.
(For infcnht:.tion on this input flex tape 8ee the section "Input
Tape Formu t n ) •
SUBROUTINE LIBRARY APP!BDII
Subroutines Cllrrently
OD
Magnet!c Tape 0
Central
CV-l
cp-1OO
b. Alarm Print
CV-3
al-prl
o.
Card Package
C'f-37
cg-lOO
d.
Interpret!ve System, unpacked
RR-1O
1p-pO~
••
Interpret!Te SyEitem, packed
RR-1O
ip-pOl
t.
,Decimal Output
BR-2O
do-fOl
g. .Deo1mal Output Fixed. Point
RR-47
do-atOl
Square Root noat1Dg Po1nt
RB-59
rt-tol
RR-2l
rt-xOl
BoDe
ex-xCl
BR-68
ex-fOl
1. Jrca1n/ooa x, Float1Da Point
1&-'75
tg-t20
a. Arctan x, noatiDg Point
BB-74
tg-t40
n. S1nt2, 008~ x, P1xed Point
8B.-24
tg-xl~
o. Sin x,
loDe
tg-xll
1&-26
ts-x4O
. Bll-62
tg-tlO
1. Square
J.
~t
....0
....
-.-
Float1Da Point
l1xed Point
ex, rhed Point
k. .x. ftoating
C\I
I4hrarx Coda
a. Constant Pool
)l."
...-.
I g M , " Indg
C08
Point
x, l1xed Point
p • Arctan x, F1:ud Point
q.
Sin-t2,
~O.~ x, Float1Da PoiDt
I
0"I
o
o
....
0"-
A. more eubrout1nea are put ill the l1brarJ, supplements to this list will
r-
~
be 1. . .4 f'rom time to tiM.
hpj
9-92
-13RR-126
2)
Turn ON PUNCH and TYPEWRITER
J)
BE' SURE MT UNIT 0 is ON
4)
Set Jump Switch
11 ita flex tape of the aubrout1ne.
i.
-
NOT desired o
S)
If REeO II is not used, set PAX to 70011 and STAIqo
It RECO II
1s uaed, this routine will start automatieal.ly after OClllpletion
of
6)
RFl;O II.
It an alarIl
"Cl", "C2",
machine stopa.
IIC)", "04" , or
-R"
18 typed, the
For a choice of procedures, ••• the diacus8ion
ot "ERROR DEmCTION - ALARMS".
In aDT case
J.!r88Sing
the START
will caua. the Library Routine to continue; however, a 8ubroutlD8.;
may be oai tted o
7)
The routine halt. at 56
8}
To rep~t the 11brar,. routine, pres8 START after the 56 atopo
~I
00000
70011
It a per10d 18 iDadvertentl7 cm.tted at the conclu8ion at
of a Routine List, Force Stop Caa}.:uter atter Input Tape has
oOJrlJ.:letely pa8sed through reader set
PAX
tglOO52 and STAMo
RR-127
REMI~GTON
RAND UNIVAC
Information Science Division
A Multiple Regression
and
Correlation Program
for the Univac Scientific' (1103)
1 July 1956
WRITTEN AND
MACHI~E
CHECKED BY:
D. C. McGowan - California Research Corp.
Jack Rose - Remington Rand Univac
Leo Kennedy - Remington Rand Lnivae
9-94
RR-127
THE 1103 MULTIPLE REGBESSION AND CORRELATION PROGRAM
General Description
There is now available to Univac Scientific (ERA 1103)
users and service bureau customers a library progra.m for
multiple correlation (regression) analysis.
The progra.m will
handle up to m=30 variables (including the dependent) and
to n=400 observations of each.
up
The output, on punched cards,
is:
1.
The identification number of each variable used.
2.
The mean of each variable used.
3.
The standard deviation of each variable used.
(Based on n-1 degrees of freedom.)
4.
The normalized regression coefficients
(regression coefficients for each variable
reduced to standard units).
5.
The ordinary regression coefficients.
6.
The simple correlation coefficients.
7.
The partial correlation coefficients involving
the dependent variable.
(The remaining partial
correlation coefficients may be obtained if
desired. )
8.
The inverse of the correlation matrix (optional).
9.
The square of the multiple correlation
coefficient, the standard error of estimate
'.:.{based on n-m degrees of freedom), and the
.'.\
c'ons~ant
term in the regression equation.
-1-
9-95
RR-127
10. . (Opt.ional)
The back solution, in which the
regression equation just computed is used to
predict a value of the dependent variable for
each 'observation.
card
The output
for'each'ob~erv~tion
a.
consist~
of a
containing:
The number of the observation and
the identification number of the
dependent variable.
b.
The predicted value of the dependent
variable.
c.
The observed value of the dependent
variable.
d.
The difference (b-c).
Optional items 'may
be
obtained
by
making manual Jump
selections on the computer console.
There is also available a program for the back solution (10 above) in the event that the regression equation is
already known and no correlation analysis is desired •. In this
program, the output is as follows, with the numrors having the
same significance as above:
1.
Identification of variables used.
5. As before.
(Reprint of input to avoid error
or amblgui ty. )
9.
10.
As before (same).
As before.
The programs are deSigned to make good use of the
great facility of the 1103 for this type of computation.
Also,
-29-96
RR-127
they offer a number of special features, in addition to those
listed above, that make them very flexible and economical.
For these reasons they are extremely fast and. will give more
information at less cost than any other library program up to
the maximum size of problem they
~:lll
handle.
The Nature of the Problem
It frequently happens' that a dependent variable, y
or
X1,
can be considered to be a linea.r function of a number
of independent variables,
X2, X3,
e
•
e.
X m•
Then:
(1 )
where y*
= X1* 1s an
estim~te
of y (or
X1).
This implies that the effect of each x;/on y is linear and
independent of the levels of the other variables.
Ho.wever,
when .this is not the case, it is often possible to make a more
realistic mathematical model of the situation and with little
or no distortion to apply a transformation that will linearize
it to the above form.
When this is done, the
XiS
will not
generally be the directly measured experimental quantities but
functlons of them, or functions of groups of them, thus accounting for nonlinearity and interaction effects.
The multiple correlation problem proper begins when
the functions for the x's have been chosen so that an equation
in the form of (1)
ha~
been arrived at and when there are
available n observations, n>m, in each of which values of all
variables have been measured.
The problem is then to choose a
set of values for the coefficients,
lI
a ," that will best fit all
the data points.
-39-97
RR-127
Thls pro.blem 1s solved
\,/1
th the most computational ease by
classical least-squares f1 tting, wh1c,h defines aO as
m
L
aO =.Xl ~
ajXj
.
J=2
.
(2)
and
values for the regression coefficients
det~rm1nes
• • . am.
a21
a3,
Certain other statistics are also computed which
indicate how well 1n general the model has succeeded in
representing the effects of the variables and predicting the
values of
and to what extent the effect of each variable
Xl,
1s numerically important, statistically Significant, and
successfully represented by the model chosen, Equation (1).
Notation
Let y
= Xl be the dependent variable. Let
• • • xm be the independent variables.
X2, Xs,
Let the index i or J
designate the number of the variable:
i
j
=
=
1 (1) • • . m
2 (1) .
m
where m 1s the total number of variables, including the
dependent variable.
In general, the term "the Xj'S" will refer to the
variables
to x m' but not to Xl or y.
Let the index h refer to the run, or observation,
X2
number:
h
=
1 (1) • • • n
where n 1s the total number of observations of each variable •
.(For the case of micsing observations, see the section "Special
Features.")
Thus xhi is the value of the ilth variable
observed in run number h.
-4-
9-98
RR-127
Other conventions of notation will be defined as they
ar~
used.
The Method of Computation
In the 1103 program, the mean of each variable, xi'
is first computed:
n
The standard deviation, based on n-1 degrees of free-
dom,
is then computed for each variable by:
(4)
81
=
Jr.. hX~1
- Xi
~l:Ixhi
Vn-l
where
Loh designates summation over all runs with the square
roots being taken separately by the computer, and the other
arithmetic operations performed as indicated here.
The simple correlation coefficients between all pairs
of variables are then computed by:
The above computations are all computed in fixed
binary with precision to full single-word capacity being
retained.
The simple correlation coefficients are stored on
. the drum foar printing out and then converted to normalized
floating binary, mantissa 27 bits plus sign bit.
The matrix of simple correlation coefficients,
R
= (rij) is then inverted, in floating binary.
In the array
-59-99
RR-127
of this matrix, the correlation coefficients involving tne
dependent var1able
j
Row 1 and Column Ip
"1.1
that Is .. the rlj coefficients, are in
The inversion is accomplished
~y
a direct
elimination w1 thout any perm'utatlon of rows and columns.
R 1s
symmetrical, and the inverse is forced to be symmetrical,
regardless of round-off error, by computing only· the diagonal
and one triangle and assuming that the other triangle will be
The inverse so computed is Ql.
the mirror image.
Qk =R-l,
where R-l is identically equal to the inverse of Rand Qk is
the k-th approximation of R-l.
Ql, the first approximation, is
then reconverted to fixed binary.
Uhles~
R 1s badly conditioned, round-off error will
be small, but the inverse is in any event improved by the
formula
. (6)
somewhat modified.
Here 2 1s the diagonal 2 matrix.
The modi-
fication of the above formula consists of-the fact that Qk+l 1s
also forced to be symmetrical as was Ql.
Although Qk and Rare
both symmetrical, RQk J and consequently (2 - RQk)' are not
necessarily symmetrical; and, indeed, the full square matrix is
c9mputed.
When this square matrix is multiplied by Qkl however,
only one triangle of the product matriX, Qk+l, is computed.
In this improvement scheme, the square matrix (2-RQk),
which will be approximately the unit matriX, is computed in the
~
first half of each iteration cycle.
valt.~s
The sum of the absolute
of 1 minus each diagonal element of this matrix is then
c
-u-
9-100
RR-12i
. compared with the corresponding sum obtained for the matrix
(2-RQk-l).
(On the first cycle, it is compared to .a very large
arbitrary number.)
If this value is larger than for the pre-
vious iteration, the improvement method is assumed not to be
converging on the true inverse.
If it is smaller, the second
half of the iteration cycle is performed by multiplying the
square matrix (2-RQk) by the matrix Qk to form the (arbitrariiy)
symmetrical matrix Qk+l..
The same vafue,
is then compared with a "tolerance" number to see if Qk was a
sufficiently close approximation to R-l.
This tolerance number
is established by multiplying an arbitrary small number by the
number of diagonal elements in RQ; when the sum of absolute
values by the above formula 1s smaller than this· product, (qk)ij
will, on the average, equal rij to five or six correct decimal
digits to the right of the decimal pOint.
At this time, however,
Qk+l' a still better approximation of R-1, has already been
co~puted
and will be used as the final approximation.
If, on the other hand, the above test shows that the
sum of absolute values of 1 minus each diagonal element of
.-
(2-RQk) increases from one cycle to the next, the original
t-
C\I
---t
inverse, Ql, is then taken as the best approximation of R-l;
I
0"I
o
o
0"-
o
and the problem can
b~
finished using this, the typewriter
t-
indicating that this has occurred.
><
0..
for a section of code (to be written if experience proves it
~
Space is left in the program
desirable) that will apply a more powerful improvement scheme
-79-101
RR-127
on failure of the above scheme to converge.
scheme would be Qk+l.
The alternate
= Qk(RQk)-l., which is slower but which
will always converge,. unless R or Ql. is singular.
The improved inverse ·(or the unimproved inverse, if
the improvement scheme has failed ·to converge) is then used to
compute the square of the multiple correlation coefficient, the
standard error of estimate,- the normalized regression coefficients, the regular regression coefficients, and the partial
correlation coefficients.
The square of the multiple correlation coefficient is
computed by:
(rl.2,sI ••• m)2 = 1 - l/ql.l
(7 )
(qlj is the best approximation of
ri J)
The standard error of estimate, se' based on n-m
degrees of freedom, is then computed by:
r:n;L
(8)
V n-m
since Sl was based on n-1 degrees of freedom.
The normalized regression coefficients (regression
coefficients expressed in standard units) are computed by:
--.....
(9)
r-
bj
=
~qlj/ql1
The regular regression coefficients (the aj's of
C'\l
~
I
a-I
0
0
0"-
.....
r-
~
~
. Equation
1) are computed
(10)
aj
by:
= b j (S·l/S j )
The partial correlation coeft:lclents, Pij' are
computed by:
-89-102
RR-127
(11) ,
Finally', the constant term in the regression equation"
the ao of Equat10n 1, '1s computed ,by applying Equation 2.
This
completes the regression analysis proper, but if a back solution
1s desired,' Equation 1 1s then applied to each of the n obser\!ations to compute an estimated value of, y for each run.
-
l "N
-.-4
I
0'I
o
o
0'-
.-4
I"-
><
0..
-99-103
RR-127
Special Features
The 1103 multiple correlation routine has. a number
of special features designed to make 'the ,program
use-
un~sually
ful , .flexible, and econornicalof machine time. '.Some, such as
listing the normalized regression 'c'oefflcie:nts ,and the use of
a matrix inversion routine tailored specificallY'for,this
problem, are fixed parts of the code,' but others' are·optional
and under the control of the operator.
The latter are listed
here •
. 1.
Independ'ent Variables on Magnetic Tape
-
In some types of problems, a single set of independent
variables may ba used with a number of different dependent
variables.
In this case, the uS'e of each new dependent variable
constitutes an entire new problem, but important amounts of
read-in time can be saved by writing the independent variables,
the x J •s, on magnetic tape on the first proble,m and reading them
from this tape in subsequent problems.
The program is so
designed that selecting MJ No.1 will write the Xj'S on Tape
Unit 2 as they are read in from cards.
Also, it is possible in
any run to read the Xj's either from cards or from Tape Unit 2.
The y's are always read in from cards and are never written on
tape.
When the Xj'S are written on tape, they are summed, and
.........
r-
~
-.I
the sum is written as the last block of data on the tape.
When
~
they are read from
0'
......
compa~ed
><
c..
the on-line typewriter types out "Tape sum no good," or a suita-
o
o
ta~e,
they are summed again, and the sum is
with that written on the tape; if there 1s a discrepancy,
t-
ble abbreviation thereof.
Unless otherwise indicated
-10-
by
the
9-104
RR-127
typewriter, the Xj'S can be assumed to be correctly read 1n
from MT 2.2.
Elimination of Undesired Variables
The results of the correlation analysis may show that
the effects of certain independent variables on the dependent
variable are statistically inSignificant or numerically
unimportant.
It may then be desired to rerun the correlation
excluding these variables.
This is easily done 1n the program
whether the Xj'S are read in from cards or from tape.
When all-data are to be read 1n from cards, a control card is used bearing the numbers m and n.
Omission of an
undesired variable can be accomplished Simply by omitt1ng the
corresponding deck of data cards and using a new control card
with the altered value of m.
When the Xj's are to be read in from tape and only
Xl
from cards, the control deck consists of a card bearing the
number of variables to be omitted, followed by as many cards
as there are variables to be omitted, each bearing the code
number of one Xj to omit.
When no variables are to be omitted,
the control deck consists of one blank card.
--
~
......
In reading from
tape, the machine reads all the observations of one x j
,
sums
them, and then scans the list of variables to be omitted to see
'-'
I
~
whether"to reject this Xj.
In any case, the sum is retained,
o
~
......
so that the sum check on the tape reading is preserved •
r-
~
.- 3.
Treatment of Missing Observations
No missing observations among the independent varia-
bles are permitted.
If a run does not contain a full set of
-119-105
RR-127
observations, it should either be rejected or reasonable values
for the miss1ng observations should be estimated.
when a single set
or
However,
independent variables 1s used with a
number of different dependent variables, it often happens that
the sets of observations of some of the dependent variables are
not complete.
In this case,
th~
runs with missing observations'
.are rejected, but it is convenient to let the machine do this
r~Jecting
so that it can always be fed the same set of data for
the independent variables.
This 1s done by representing each
missing observation on the deck of y'8 by -0.
The machine will
scan the observations of y (but not of the Xj's) looking for
-0.
(Plus 0 1s a legitimate observation whose value happens to
be zero and will be treated normally.)
When it finds a -0 for
a Yh it changes it to normal zero, it sets all the corresponding
observations Xhj equal to zero, and it subtracts one from the
value ot n.
The effect 1n the main part of the problem is as if
that run had never been included in the data.
When the back solution is run with the data still in
the machine, y~, the predicted value of the dependent variable
~
tor a miSSing observation, 1s a O' since y* 1s computed by
Equation 1 and all the XhJ'S have been set to zero. The
('\)
~
observed value' is listed out as +0.
I
0"-
I
When the bac~ solution 1s run later, as a separate
o
o
0".....
r- problem, the tally program that rejects missing observations
><
0..
does not operate.
In this case,
Y~
assumes the value dictated
,
by Equation 1 for the set of values xhJ and for the previously
-129-106
RR-127
computed aj'Se
The observed value of Yh 1s listed as it was
punched, -0.
4.
Typing of the Square of the Multiple
Correlation Coefficient
------------------
It is sometimes convenient to'test different
func~,
tional representations of the dependent variable (y=v,. y=log:v,
"'"
y=e v , etc.,
where v is the quaritity directly measured} against
the same set of independent variables.
In this case, the choice
of functions for best fit can often be made solely on :the value
of the multiple correlation coefficient.
The square of the
multiple correlation coefficient is therefore typed out as sobn
as it is computed so that the machine can be stopped and the!
problem abandoned at this pOint if desired.
This number is
also listed on cards with the normal output of the program.
5.
SuppresSion of Most of the Partial
Correlation Coefficients
In many problems, the only partial correlation'
coefficients of interest are those between the dependent variable and the independent variables, that is, Pl.j.
The partial
correlation coefficients of the independent variables with each
other (Pij, i l l ) are usually of interest only when a
new~
mathematical model for the regression relationship is being
tested.
Therefore, to save time, the program normally computes
only the partials P1j.
However, if the remaining partials 'are
deSired, they will be. computed and listed out if manual jump
selection No. 2 is made.
The time required will be about one
second for each ten additional partials.
-139-107
RR-127
6.
Suppression of Listing the Inverse Matrix
In many routine problems, the inverse of ,the correlation matrix is not ,of particular interest, and considerable
time "is saved by not listing it out.
Therefore, the program
will 'compute but not normally list out the"inverse.
However,
when it is desired to see the i"verse, it will be listed out
by
selec'ting the manual selective jump No.3.
1.
Optional Back Solution
After completion of the correlation problem
the machine wl11 f;itoP on a' 56 00000 00430 command.
prop~r,
It it is
known at this time that a back solution Is wanted, one wll1 be
obtained simply by pushing the start button.
If this option
is not exercised, and it is decided at some later tlme that a
back solution is wanted, another program wl11 permit computation of the back solution without repeating unnecessary par,ts
ot the correlation problem.
, input is read 1n (with the
A new code 1s read in; the same
xjls
either on cards or magnetic
tape and the Jis on cards) with 'the same oontrol decks; and part
of the card output of the correlation problem (the deck bearing
the a's and the card bearing ao) 1s also read in following the
-149-108
RR-127
Machine Times
'r
To date, two runs have been made in.
ti~ing
w~ich
accurate
was recorded •. Both were made on Univac SCientific
Serial No. 9at st.
P~ul,
a magnetic core machine.
The approxi-
mate formulas for computing machine time were derived from these
two runs.
The first run consisted of a set of 16 problems run
consecutively with the same set of independent variabies.
short cuts were employed:
All
thex's were read-"in from magnetic
tape, only the partials involving the dependent variable were
computed, the inverse was not punched out, and no back solutions
were obtained.
The size of each problem was 17 variables, 91
observations.
The averag.e time per pr,ob1em was one minute and
46 seconds, exclusive of code read-in time.
Code read-in
takes 50 seconds and," of course, need be done only once for any
set of problems to be run at one time.
The second problem timed was one of 30 variables, the
maximum number, and 95 observations.
problem,
time~
From the timing of this
for the maximum case, 30 variables and 400
observations,' can be cl08.ely estimated.
The times quoted below
.
for Sections 1, 2, and 6 are so estimated; those for Sections
.
3, .4, and 5 will be unchanged from those actually measured.
All times are exclusive of code read-in time.
-159-109
RR-127
Maximum Case
Min
Sec
1.
Read all data from cards
8
50
2.
Means, standard deviation, rts
2
15
3.
Invert matrix
4
5
4.
Improve inverse
o
35 per cycle
5.
Punch Decks 1 through 9 (full)
2
10
6.
Back solution - calc and punched
Total - No Shortcuts
21
25 one imp.
cycle
When the short cuts are used, the times will be about
as follows for the maximum case:
Maximum Case
la
5a
Min
Sec
Read x's from tape,
y I S from cards
1
5
Punch Decks 1-9 omitting Deck
8 and most of partials
0
50
0
0
6a ,., Omit back solution
Total - All Shortcuts
8
50 one imp.
cycle
Times for running problems of various sizes may be
estimated from the following approximate formulas:
1.
Reading all data·from cards.
5 + (0.5)(m)(u+l) seconds
~
.....
where u is the number of cards required for n observations, at
~
I
0'
12 to the card.
This ·includes a fixed time of about 3.5 seconds
I
8 for computing constants and typing the code and input sums and
.....
0'
t-
><:
~
of 1.5 seconds for advancing the read cards and reading the
control card.
-169-110
RR-127
la.
Read~ng X'S
~a~lB,
ffom
- 5 + (0.5) (u+c) + (0.1)
y'8
from tape.
lim . . 1 ) (Y)
+ 2J
seconds
where u 1.s as above, c is the number of cards in the control
deck, and v 1.s the number of 32 word blocks required for n
observations.
This inc] udes start·-stop and computing time
during the tnpe read-in.
2.
Means, stAndard deviations, simple correlation
coefficientH.
(O.012)(m)(n)
This is quite
rough~
(lPconds
aa there 10 a time involved that depends
only on m and also one that depends on m2 n.
3.
Invert matrix.
(O.0091)(m3)
4.
Improve inverse.
(0.0013)(m~)
5.
ueconds
seconds per cycle
Compute and punch out Decks 1-9, full.
(O.0044)(m2
)
seconds for computlng
(0.25)(m) + (O.13)(m2
)
+ 3 seconds for punching.
A more accurate estimate of card punching time can be made by
computing ·the number of cardu to be punched, from the informa"""
t-
C\I
......
--,,
0'
o
o
0'
......
t-
><
0..
tion in "Card Output," and allowtng 0.5 second per card.
Sa •
Optionally omittlnp: partials not involving
dependent variable and/or punch-out of
inverse matrix.
(0.030)(m2
)
secondu (laved by omitting
extra pnrtlals
(O.058)(m2) seconds saved by omitting
inverse
-I" -
9-111
RR-127
Again a more accurate estimate can be made by computing the
exact number of 'cards saved.
6.
Back solution.
(O.0013)(m-l)(n) seconds for computing
(O.5)(n) + 1
seconds for punching
It 1s expected that these times will compare favorably
with those of any existing multiple regression and correlation
program.
-189-112
RR-127
Input - output
Scaling
All input data should be scaled
60
that the five most
significant digits are to the left of the decimal point, as the
input is in the form of integers ot five digits or less.
It is
desirable, but not absolutely necessary, that the observations
<
of a given variable be scaled so that the largest (in absolute
magnitude) has its leading significant digit appearing in the
fifth place to the left of the decimal.
However, if conveni-
ence dictates, all the observations of a variable considered
as five digit integers may contain zeros in the leading (or
possibly even the leading two) digits.
There is danger, how-
ever, that if the.dependent and independent variables are
scaled to give numbers ot very dissimilar magnitudes, considered
as integers, some of· the regression coefficients may be so small
as to lose some significant figures or so large that they overflow, in which case the problem must be rescaled to be run.
It
is therefore recommended that each variable be scaied so that
the largest observation encountered (or likely to be encountered
in subsequent problems) have
i~s
leading significant digit 1n
~
~
~
the fifth place to the left of the decimal.
The variables so
scaled are now the input variables for the problem, as far as
the machine is concerned, and the output will come out scaled
accordingly and correctly pointed off with actual printed
decimal pOints.
-199-113
RR-127
Paper Tape Input
The instruction code for the correlation program,
with optional back solution, 1s contained on a single roll of
paper tape, requiring about 50 seconds to read.
The code for
the back solution alone (correlation done previously)
shorter single roll.
Both
codes'~~e"
is
on a
completely self-contained
and need n0 other routines or Bubroutines except to load them.
Both are in bioetal code, and both may be read with either an
ERA or a Ferranti reader.
The Ferranti Load "Routine RW 63,
operating from 75170 to 75337, haa been used.
The code
occupies drum addresses 40000 through 43000 and 77074 through
77777; a load routine must be used that permits loading
t~
these addresses.
Card Input
The input data e.re :read into the machine on
cards~
As stated before, if one set of independent variables is to 'be
used for a number of problems, it may be written On magnetic
tape as it is read in from cards initially, and 1n subsequent
problems only the dependent variables need be read in from
cards.
In either case, a control deck 1s first read in,
followed immediately by a deck of cards for each variable'.
~
rh'
_
latter decks have the following format.
There are 13
C\l
~ fields on each card, starting in Column 3, each of five columns
0"
I
o
o
followed by a sign
col~mn.
The first field containa the code
0"
1"""1
t-
number
~hich
identifies the variable.
This code number may be
any integer of five digits or less, except that code numbers
for dependent variables should be positive.
-20-
The following 12
9-114
RR-127
fields of the first card in the deck contain the first 12
observations of that varIable, the
correspond~ng
12 fields of
the seoond card 1,he next 12 observations of that varIable, etc.
The observationa are exprehsed as five dIgit numbers (see
"Scaling") followed by a hlank column if the number is positive
or a column oontaining only an x (11) punch if the number is
negative.
It is not necf1ssary to punch all columns of the card,
but any blank column
exc~pt
the sign columns wil: be inter-
preted by the 1103 as a zero; thus any zero in (,ny data word
may be either punched or left blank.
Unless the number of
observations is an even multiple of 12, the last card in each
deck will not be filled, In thlscase the remaining fields may
be left blank or used tor any other purpose, as it will make
no different at all what Is In them.
that all the cards In" each deck
Since it is imperative
re~ain
1n the proper order,
the first two columns nn the card, which are not read by the
"1103, should contain the number of the card in the deck for
sorting purposes in caee of mixup.
There must be a full set of observations for all
independent variables, as any blank space will be interpreted
an observation of value zero.
However, when a number. of
dependent variables are run with one set of independent varla.bles, there may be missing observations in the dependent
variable.
These should be designatad by a minus zero (a field
of blank or zero columns followed by an x punch in the sign
colu~~)
in the proper place on the card.
A plus zero or
-219-115
RR-127
completely blank field will be interpreted as a legitimate
observation of value zero.
The machine will distinguish
between minus zero and zero only in the dependent variables; a
minus zero in an independent variable will be interpreted as an
ordinary zero.
When a dependent variable with certain observa-
tions missing is used 1n a glvenproblem with a full set of
independent variables, "n," the number of observations for the
control card (see below) is taken as the full number of
observations of the independent variables.
The machine will
scan the list of observations of the dependent variables for
minus zeros, strike out the corresponding observations of the
independent variables, and subtract 1 from "n" for every missing
observation.
When all data are to be read from cards, the control
deck consists of a Single card with "m" the number of variables
punched in Columns 10 and 11, and "n" the number of observations
punched in Columns 14, 15,. and 16.
It will make no difference
what else, if anything, is on the card from Column 18 on.
This
control card is immediately followed by the decks for the
independent variables, which are again immediately followed by
~
C'\J
the deck for the dependent variable.
It is necessary that the
r-!
~
0-
o•
o
0r-!
t-
><
0...
dependent variable be read in last (even though it will be
treated as the first variable in the matrix· and will assume the
leading position once in the drum memory), as that is the only
identification of it as being dependent.
The independent
variables, however, may be read in in any order, so long as the
cards within each deck remain in order.
The first output from
-229-116
RR-127
tl'le. probJ1em. will consist of the identlfication numbers of all
tifle variables, starting with the dependent variable' and
followed by the independent variables in the order whieh they
were entered; subsequent output will follow the same order,
so that the order in which the independent variables are
entered will be recorded and preserved 1n the output.
When the independent variables are to be read from
magnetic tlpe, the first card 1n the control deck will contain,
in Columns 1 and 2, the number of variables to be omitted, in
case it 1s not desired to use all the variables in the correlatlon.
(If none are to be omitted, a single blank card will
serve as the·control deck.)
This card will be followed by as
many cards as there are variables to be omitted, each card
bearing the code number of a variable to be omitted (in any
order) in Columns 3 through 7, with Column 8 as a sign column.
For example, if the code number of a variable to be omitted
i~
13, this number will be punched in Columns 6 and 7; if it is
minus 98745, 98745- will be punched in Columns 3 through 8.
The machine will not read anything on these cards from Column 9
on.
This control deck will be immediately followed by the deck
~
of observations of the dependent variable;
--
because when a set of independent variables is already on tape,
C\I
This system is used
-t
I
0'
I
o
o
0'
....-4
~
><
Q..
there is a1so on tape m 8.nd· n for the general case:
variables used, all observations present.
all
The control deck
will cause m to be adjusted for the particular problem, and
minus zeros in the dependent var1able observations will cause
n to be adjusted.
-239-117
RR-127
In any problem 1n which cards are used as input, it
is necessary that at least three blank cards follow the last
card to be read.
If several problems are to be run at once,
two blank cards must folIo", each problem and at least three
must follow
th~
last problem.
In some cases it is desirable
to run a number of probl("ns at a time, each with a different
dependent variable but aLl with the same set of independent
variables.
In this evert, all data are read frcm cards for
the first problem, with exactly two blank cards following the
deck for the dependent variable.
Then follows the control
deck (which may be one blank card) for the second problem,
immediately followed by the dependent variables, followed by
two blank cards, etc.
In thlsway, all the problems can be
loaded at once with no card handling on the input side after
the machine has started.
The independent variables, of course,
are written on tape during the first problem and are read from
tape in subsequent problema.
When the correlations have already been done and
only a back solution is reqUired, the independent variables
may be read in from either tape or cards as 1n the correlation
problem.
,-.,
~
The control decks and the card input for the varia-
bles are exactly as before.
The deck for the dependent varia-
,....j
'-"
~
ble is followed in this case by a deck bearing the regression
I
o
~ coeffiCients, a j ' (det.!k, 5 of the output) and then by a card
r-
~
bearing (among other things) the constant term in Equation (1),
0..
a o ' (deck 9 of the output).
Again, this card 1s followed by
at least three blanks, or exactly two blanks if another problem
-24-
9-118
RR-127
is to follow immediately.
These decks 5 and 9 will ordinarily
be the identical cards produced by the machine:when the
correlation phase of the problem was performed; their format
will be described under "Card Output."
Typewriter Output
Although the bulk of the output is on cards,the
typewriter is used to some extent as a monitor as the problem
runs.
The first act of the machine in starting the problem
is to sum the code on the drum and write the sum on the typewriter.
It would not be advisable until experience has
demonstrated conclusively that no more changes in the code are
desirable to quote this sum here or to build in an automatic
check.
In the meantime, the fact that the code is properly in
the machine can be verified by the appearance of a familiar
number as the first line of typewriter output.
The second possible item of typewriter output will
appear only if the independent variables are read in from tape
and if their sum as read in fails to agree with their sum
written on the tape.
-
In that event, there will appear on the
next line "tape sum n'o good" or a suitable abbreviation thereof.
r-
(All variables on the tape are summed as read, whether or not
--
the control deck indicates they are to be ·used in this problem,
C\I
~
I
0I
0
0
0-
so the sum should
alw~ys
be the same. )
If this appears, the
~
r><
c..
machine will stop on a 56 00000 40576 command
Pushing the
start button will cause it to attempt to read the tape again;
-259-119
RR-127
a failure repeated geveral times will indicate mechanical
difficulty in the tape or in the reading circuits.
The next item of typewriter output, on the following
line, will be the sum of all input data, including the
dependent variables.
This will normally vary from problem to
problem and aside from inspection of the general magnitude will
serve as a useful check only when difficulty is suspected and
l.t 1s desired to repeat the problem and test for trouble.
However
if only the back solution 1s to be run, this input sum
should check that written out in the correlation phase of the
problem.
The next item of typewriter output, on the following
line, will be the letter i written one or more times.
Each 1
signifies the completion of the first half of a cycle in the
improvement scheme for the inverse matrix.
If the improvement
scheme converges, the carriage will return and the typewriter
will print the next output.
If it diverges, it will write l
on the same line, "diverges. set mj 2,3. go," after which the
machine will stop on a 56 00000 00132.
Pushing the start
button will bring back the original inverse as it was before
lN
-r-4
I
~
o
o
~
the start Of the improvement scheme, and the machine will
continue the problem using that.
However, in case of divergence
it is likely that the user will want full information to indi-
I-
~
cate why this occurred.
The "set mj 2,3" is a reminder to set
these manually selected jumps, if they are not already set,
before pushing the start button if it is desired to see the
-269-120
RR-127
print ou"t of all the partial correlation coefficients (2) and
the inverse" of the correlation matrix (3).
(As indicated before,
the code has room for another and more powerful improvement
scheme that can be applied if this fails to converge.
If this
section is shown to be desirable and is wr1tten, failure of the
first method to converge will not acti v'ate the typewriter, but.
failure of both methods will cause it to write "matrix sing.try
The final item of typewriter output will be the square
of the multiple correlation coefficient.
This is written as
soon as computed because sometimes problems may differ only 1n
that alternate functions of the variables are being tried
(linear, logarithmic, higher order algebraic functions of the
basic data), and when this is the case for the dependent
variable, the choice of the function giving better fit can be
made solely on the basis of the multiple correlation coefficient.
If it turns out that the problem now in the machine
gives a coefficient lower than that for an alternate form
previously run, the problem may, if desired; be abandoned
immediately by forcing a stop at a saving of machine time.
Card Output
The card output is designed to be listed on a Type
407 tabulator using a straight
spacing being done on the cards
8~o
board, all necessary
themselves~
All numbers will
be properly pointed off with decimal pOints (8-3-12 punches on
the cards) and will be followed by minus si3ns when negative
(x or 11 punch).
It is also possible to list the output on a
-279-121
RR-127
402 tabulator without total loss of legibility, but this is
awkward because the fields are not locat-ed in the same places
in all cards.
In using a 402, a straight 80-80 board is also
used, except that there must be provision for recognition of
minus signs, and it is better to use zero suppression on the
right-hand side of the page.
Minus signs are possible in
Columns 16, 20, 24, 32, 35, 40, 47, 48, 50, 52, 56, 62, 64,
65, 72, 77, and 80.
In the 402 listing, decimal pOints will
appear as 8's {or as 9's in columns where a minus sign can
occur}, and minus signs will appear as a 9 or some other
symbol, but the output is so organized on the page that it will
not be difficult to distinguish these symbols from the legitimate numbers 8 and 9 in data words.
The output is in nine decks, exclusive of the back
solution.
,
In the first column of each card is punched the
number of the deck, and in the next two is the number of the
card in the deck.
Each deck will be briefly described below,
with the fields located with respect to the decimal pOint.
The
number of columns mentioned to the right of the decimal pOint
is exclusive of the sign
---
~
column~
which is always the right-hand
column of the field •
....-j
Deck OneThe code numbers of the variables'.
Dependent
variable first, independent variables in the order in which
they were read in.
Five numbers to a card.
No decimal pOints
printed, as all numbers are integers, but locations of hypothetical decimal pOints are in Columns 17, 32, 47, 62, and 77.
-28-
9-122
RR-127
Decks Two through Five
The means, standard deviations, normalized regression
coefficients (the bj'S of Equation 9), and tbe regular regression coefficients, respectively.
Five numbers to a card.
All
variables in the same order as the code numbers, and all lined
up directly below their respective code numbers on the page.
Decimal points in Columns 14, 29, 44, 59, and 74.
Five digits
to each side of decimal.
Decks Six
~hd
Seven
The Simple and partial correlation coefficients,
respectively.
Nine numbers on a card.
Decimal points in
Columns 10, 18, 26, 34, 42, 50, 58, 66, 74." No places to the
left of the decimal, five to the right.
coeffi~~s
As the matrix of
is symmetrical with diagonal elements unity, only
the upper right triangle without the diagonal is reproduced.
The first row of the triangle starts with the coefficient of
correlation between the dependent variable and the first
independent; succeeding elements are the coefficients between
the dependent variable and the second, third, etc.,
independent variables, in the order in which they
were read in.
-t
The second now of the triangle starts with the
coefficient between the first and second independent variables,
and continues with the coefficients between the first and" third,
fourth, etc.
Each row is one shorter than the one before.
elements of the first, row are punched on cards nine at
a
The
time;
when there are no longer nine to punch, the remaining ·spaces on
the card are filled with zeros.
This process 1s repeated with
-299-123
RR-127
.
the next row of the triangle.
of the triangle is signified
Thus the completion of each row
by
one or more words of .00000
appearing to the t'lght of a line ona page, except for those
rows containing a number of elements that is an exact multiple
of nine.
In this way, the row of the triangle is easily
identified in the printed output.
The punching out of more
than the first row of the matrix of partial correlation
coefficients is optional.
Deck Eight (Optional)
The inverse of the correlation matrix.
to a card.
Five numbers
Decimal pOints in Columns 13, 28, 43, 58, 73.
Four places to the left of the decimal, six to the right.
As
the inverse matrix is symmetrical, the same scheme i,8 used
here as with Decks 6 and 7, except that the diagonal is included,
so that each row i8
ohf\
longer than the corresponding row 'of
the matrix of correlation coefficients.
Again, the completion
of the row of the triangular matrix will be signified, except
for those rows containing a number of elements, that is a
multiple of five, by one or more words of 0.000000 appearing
to the right of a line on the page.
---
Deck Nine
.r--C'\I
Deck nine consists of one card bearing the' square of'
r-4
I
0"-
6: ' t'he",multiple correlation coefficient, the standard error of
o
, ~ , estimate ,and aO of Equation (1).
~
The decimal point 'for the
first 1s in Column 15; no places to the left, five to the
right.
The decimal point for the second is in Column 43; five
places to each side.
The decimal point for 80 is in Column 77;
eight places to the left, two to the right.
--30-
9-124
RR-127
The Back Solution (Optional)
The cards 1n the back solution each bear four numbers.
The first number on the card is a nine-digit integer starting
in Column 1.
The first five digits of this word are the code
number of the dependent variable, the. next digit is zero, and
the last three digits are the number of the observation of the
dependent variable dealt with on this card.
punched for each observation.
One card is
The next number in the card
(decimal point in Column 21, eight places to the left, two to
the right) is the value of y* computed by Equation (1).
h
The
next number (no decimal point punched, would be in Column 35,
five places to the left) is the observed value of y for
observation number h, Yh'
The last number (decimal point in
Column 49, eight places to the left, two to the right) is the
-31-
9-125
RR-127
Operat~ll)p; Instruct1011~'';
- Full Correlation Problem
The operatlng instructions will be given a sequence
designated by Roman numerals.
This sequence is based on the
assumption that no abnormal situations or mishaps will occur
at any stage in the problem.
However, there are certain check
pOints in the program at which any errors or abnormal situations
can be detected, and specific operating procedures have been
devised in case of an abnormal situation at any check pOint.
These check points will be designated by asterisks between the
lines of the normal sequence, and the procedures devised for
each point will be given following the normal sequence.
I.
Initial Preparation
A.
Set Card Unit Field III switch to Normal.
B.
Clear the read channel and place cards, prepared
as in "Card Input," in hopper.
c.
Turn on MT 1 and MT 2 and position the tapes.
D.
Turn the typewriter on.
E.
Use a 4-interlace for maximum efficiency.
II.
Load the Program
III.
Master Clear
.......
A.
Clear and MD start.
B.
Put computer on High Speed, Test Mode,
l"-
Drum Clock Source •
N
.......
'-'
I
0"I
0
0
0"-
.......
I"-
><
c...
IV.
Make Manual Jump Selections
A.
No. 1 if
B.
No. 2 if all partial correlation coefficients
XIS
are to be written on tape •
desired.
C.
No. 3 if inverse of correlation matrix is to
be punched out.
9-126
-32-
RR-127
V.
START the computer.
The typewri ter ltJill print out the code
sum and the computer will halt on a 56 00000 40100
instruction.
A.
'l'hen:
If the independent variables are to be read from
cards, START the computer.
B.
If the independent variables are to be read from
tape, set PAK=OOOOO and START the computer.
will be used.
1.
MT 2
In either case, the computer will:
Advance the cards two stations and read
control deck.
2.
Read
XiS
from cards or tape.
*
3.
Read
4.
Write input sum on typewriter.
5.
compute means, standard deviations, cross
yt~
from cards.
products (brief, characteristic scope
display for each).
6.
Invert the correlation matrix (spectacular
scope display).
rC\J
......
**
7.
Start improving matrix, using MT 1 if there
'--'
J
are more than 19 variables (scope display
0"J
o
o
0"-
char\acteristic of first half of improvement
......
r:x:
cycle) .
0...
8.
Type. out "1" after first half of each
improvement cycle.
***
-33-
9-127
RR-127
9.
lr.\.ni.bh
improving matrIx (scope display
characteristic of second half of improvement
cycle) by repeating steps 7, 8, and 9 as
often as necessary.
Frequently, once is
enough.
10.
Type out the square of the multiple correlation coefficient.
11.
Compute standard error of estimate, normalized
and regular regression coefficients, and
partial correlation coefficients (very brief
scope dis play) •
12.
Advance punch cards two stations and punch
out decks 1 through 9.
****
13.
VI.
STOP on a 56 00000 00430 instruction.
Back Solution after Correlation (Optional)
A.
If back solution is not desired, problem is
finished.
If another problem is ready in the card
rP...ad hopper (see "Card Input" for directions for
loading several problems at one time), master clear,
MD start, and go to IV.
B.
If back solution
~
deSired, START the computer.
It will:
1.
Compute back solution (very brief characteristic scope display).
2.
Advance punch cards two stations and punch out
out back solution.
*****
-34-
9-128
RR-127
3.
G.
FIN1\L STOP on a 57 00000 00000
command~
If back :Jolutlon was run and another problem-is
ready in the hopper, to to III.
*
Trouble Symptom - Typewriter writes "tape sum no good,"\--.
or a suitable abbreviation thereof, and computer
halts on a 56 00000 40576 command.
Action - START computer.
Computer will attempt to
t'.)
read tape again.
If it succeeds, it will proceed
without comment.
If it fails, the above symptom
will be repeated.
Explanation - In reading the x's from tape, the computer
will sum the data as read in and compare this sum
"!,. /
with one written on the tape.
If the sums agree,
the computer will rewind the tape while proceeding
with the problem.
If they do not, the computer
will rewind the tape while typing out the message
and then halt.
If the fault is caused- by a dropped
bit, a second reading may be successful, but this
may indicate the tape needs replacement or
regenerat.1on.
..-..
t-
C\J
I""""l
'--'
I
0I
0
0
0I""""l
tX
0....
**
Trouble Symptom - The computer halts, right after the
highly characteristic scope display indica'ting the
matrix inversion, on a 56 00000 00010 command.
Action - Master clear, MD start; set PAK = 42524, and
START.
The computer will advance the punch cards
two stations, punch out decks 1, 2, 3, and 6, and
STOP on a
57 00000 00421 command.
-35-
9-129
RR-127
Explanat10n - If the matrix is to be inverted is
singular, or nearly singular, the computer may be
unable to invert it because of overflow in the
floating pOint arithmetic or, as is more likely,
because of overflow in converting the elements of
the inverse matrix back
fixed point numbers.
~o
Such an overflow will cause the above halt.
Taking
the above action will cause the computer to print
out all the results obtained up to this pOint in
the
p~oblem,
after which it will come to a final
stop, as nothing more can be done with this problem.
The cause for the singularity of the matrix can
generally be found in the magnitude of the simple
correlation coefficients; if the explanation is not
there, it may be due to n
.",
~
m, or to a nearly perfect
fit of the regression plane.
***
Trouble Symptom - In the matrix improvement, the scope
display characteristic of the first half of the cycle
reappears after the typewriter types "1."
The type-
writer then types "diverges. set mj 2,3. go," and the
computer then halts on a 56 00000 00132 command.
Action - set manual selective jumps 2 and 3 if all the
partials and a listing of the inverse matrix are
desired.
Then START.
The computer will finish the
problem in the normal manner.
-369-130
RR-127
Eiplanation - The matrix improvement scheme has failed
to converge, probably indicating a poorly conditioned
matrix.
The computer halts to give the operator the
opportunity to set these manually selective jumps in
case full information on the inverse is desired
because of this condition, but it is not imperative
to set them.
Starting the computer will restore the
inverse as obtained directly, before the initiation
of the improvement scheme, and the problem will be
continued with this.
Divergence is usually caused
by the original inverse being not quite good enough
to meet the tolerance limit imposed but still so
good that the small improvement that can be effected
in one cycle becomes smaller than accumulated error
in the improvement scheme.
****
Trouble Symptom - 10 fault, other fault, or other
evidence of
diff~culty
Action - Clear fault.
card unit, cards.
from the punch
with card unit.
Force stop.
Check condition or
Remove frayed or warped cards
hopper~
remove punched cards.
Clear the punch channel and
See that there Is' an adequate
supply of well conditioned cards, not stuck
together, in the feed hopper. Then master clear, MD
start, see
t~at
the machine is on High Speed, Drum
Clock Source, and Test Mode.
START.
Set PAK
= 41310
and
Machine will recommence punching out results
starting with deck 1.
-379-131
RR-127
.I.~~~_planation
- During, the :punching out of the answers,
trouble can arise in the card unit because of poorly
conditioned cards l because too many punched cards have
accumulated in the output hopper, or for snme other
reason.
Since the answers are preserved on the drum,
it is possible to start over in the punch-out routine
once the cause of the difficulty has been corrected.
*****
Trouble Symptom - Same as for **** above, except that it
occurs in the punching out of the back solution.
Action - Same as above, except that PAK is set equal to
421,14 ..
EX21anation - Same as above.
-389-132
OR-128
OPERATIONS RESEARCH OFFICE
7100 Connecticut Avenue
Chevy Chase, Maryland
Complab
Coded by
S. Rigby and J. Chappell
Checked by
s.
Rigby and J. Chappell
Computer checked by
Page I of 15
Date 3 May 1956
S. Rigby and J. Chappell
Title: Magnetic Drum to Magnetic Tape Dump
Us-e:
This routine is used to dump specified portions of the
magnetic drum onto the magnetic-tape units. Returning
of the information to the drum is under control of a
routine which is written on the tape at the time of the
dumping ..
Rangst-
Anyone of the tape units may be us-ed and any number
of words from 1 to the entire dr\Ull may be dumped" Upon
restoration of the information to the drum, only the exact
words dumped are restored; the remainder of the drum is
undistubed.
Storage:
Initial storage of the routine is:
00100b - 00161b
00200b - 00540b
The entire magnetic core memory Is used for temporary
storage.
Format:
This routine is not coded in standard form, cannot be
modified,and is not self-resetting.
Parameter Words:
Parameter words for the control of this routine are
placed in A ro- i Q. See Instructions for Use, page ~.
Manual Entry f
00100b
Automatic Entry:
For use with Ferranti Read-in routines recognizing a
transfer to program code, an automatic start at 00105b
is available.
9-133
OR-128
Page 2 of 15
Description of Service
This routine is used to dump' information from the magnetic drum
onto the magnetic tapes. The information is moved from the drum into the
magnetic core before being written onto the tape. The entire corp is used for
this operation. After a start the routine first wrih~s 4 blocks of tape which
contain the routine for rCRtoring tlle information to the drum. The desired
information is then written onto the tape, containing as the first word of the
first block of information, a control word which contains the insert address
for the information and the number of locations. By resetU--g the parameter
word in Q, additional groups of information can be' dmnped, each with its own
control word. By a restart with Q ::.: 0, the signal that the last group has been
written, one additional block is written which contains a 'tnump end" control
word an~ a check sum of all dumped information. The magnetic tape is then
rewound to the original startingposition and the computer stops. All control
words contain a parity bit which will be a 0 or a 1 such as to make the number
of 1 's in every control word even.
Provision is made for the inclusion of an address to which control
of the computer will be returned after the dumped information has been restored to the drum from the tape. H such address is used, the computer will
also come to a zero stop with P AK set at this address after the dwnping bas
been completed and the tape rew~nmde At this time, the total number of
blocks that have been written will appear in Q.
To restore the information on the tape to the drum, an MT Start
is used with the appropriate J in VAK and the tape unit positioned. The undump routine is first read into core and a check sum taken on the undump
routine itself. Next the block contaIning the control word is read in and the
control word itself is subjected to a parity check. The information is then
read into core and transferred to the appropriate location in drum, where
a check sum on the information is computed. The magnetic tape is then rewound and control returned to the address designated when the information
was dumped. If no such address was design.ated, a FS results.
9-134
OR-128
Page 3 of 15
Instructions for Use of Routine
Dumping from Drum to Tape
1.
Manually dump Me. to MD, if desired.
2.
Position the magnetic tape which is being used to the position
where dumping is desired.
3.
Enter parameter word in Q:
OJ VVVVV NNNNN
J = desired tape unit
V = First Drum address of information being dumped
N = number of words to be dumped
If V + N exceeds 100000b, N is replaced by 100000b-V
(1. eo, last word dumped is 77777)
4.
Enter in AR the following:
00 00000 BBBBB
B = MD address to which control of machine should be returned
after information on tape has been restored to ~um, if any.
This may be omitted if a Final stop is desired after information is read from tape onto drum.
5.
Set PAK to 00100 and Start.
6.
If MTO has been put in the Q parameter word or if no tap~ unit has
been specified, (1. eo, J=O) , the typewriter will type out ''DltO''
and stop. If unit zero is desired, simply restart. If one of the
other tape units is desired, insert the correct J in Q and restart.
If no parameter word was inserted in. Q before starting, the typewriter will type out "set q".
7.
After dumping the information designated by the first par~eter
word, the machine will halt with Q clear. At this time additional
~
co
N
r-!
'--'
I
0"I
0
0
0"r-!
t-
:><:
0...
9-135
OR-128
Pagl~
1 of 15
groups of information may be dumped by keying into Q additional
parameter words and restarting. The parameter word in AR should
not be used after the first dump. As many groups of words may be
dumped as desired.
8.
After the last desired group of words has been dumped, the machine
should be restarted with Q = O. This will signal the routine that
the dumping is finished; the final control word and the check sum
will be written and the tape rewound. At thi.s point the machine will
come to a 0 St0P with PAK equal to the B address inserted in A in
the original dUlnp; if such was used. If no parameter word waP.
placed in AR' a Final Stop results at this pOint.
9.
At this time, the total number of blocks of tape that have been
written will appear in Q for logging purposes.
Restoring Information. to Drum
With the tape unit positioned to the same place where the dumping began,
and the appropriate tape unit keyed into UAK, an MT Start should be made. The
information dumped will be stored on the drum, check sum compared, tape rewound, and, jf no B address was used in A during the initial dump, come to a
final stop. ]f a B address was used in AR Huring the initial dump, control is
sent to B via an KSI.
Alarms and Abnormal Conditions
1.
If no tape number is keyed into the parameter word, the Flexowriter types a warning to the effect, but a restart will permit
us ing Tape unit zero.
2.
If any address other than a drum address is set for any V, the
routine will not dump the information but will repeatedly return
to a zero stop.
3.
If an address other than a drum address is used as B for the
start of the p~ogram, "a Final Stop will result at the end of both
the dump and t.he tmdump.
4.
If V + N exceedA lOOOOOb, N is replaced by lOOOOOb-V.
9-136
OR-128
Page 5 of 15
5.
"Vhen restoring the information from tape to drum, the undump
routine first performs a cheek sum on itself. If this fails, the
typewriter types out "Undump Check Sum NG". A restart reads
in the routine again and recomputes the check sum.
H
The first word of each section restored to drum is a control
word containing the insert address and number of words in that
section and a parity bit such as to make an even number of L'8
the word. Each control word is checked by the routine fnr this
feature. Should this fail, the Flexowriter types out; "Parity
check failure". A restart will repeat the read-in and parity
check.
7.
After all information has been read back into the drum, a low
order check sum of all data is made and an error cacses the
typewriter to type out ''Data check sum fault". A restart reads
the data in again.
9-137
OR-128
Page 6 of 15
SETUP ROUTINE
Storage
Location
Working
Location
00100
00100
45 00000 00101
Manual Entry
00101
00101
11 20000 01001
Store B, if used
00102
00102
11 10000 01000
Store J, V, and N
00103
00103
11 10000 20000
} Test to see if parameter
00104
00104
47 00113 00106
word was placed
00105
00105
23 10000 10000
Auto start; clear Q
00106
00106
31 00153 00052
00107
00107
61 00000 20000
00110
00110
34 20000 00006
00111
00111
47 00107 00112
00112
00112
56 00000 100101]
00113
00113
31 01001 00071
00114
00114
46 00115 )0117
00115
00115
11 00112 00521
00116
00116
45 00000 00120
00117
00117
11 00521 00201
00120
00120
16 01001 00521
00121
00121
16 01001 00201
00122
00122
11 01000 10000
Parameter word - Q
00123
00123
51 00155 20000
J-A
~ 00124
......
00124
47 00127 00125
J=O?
"-'
00125
00125
31 00154 00052
0
0
0'
00126
00126
37 00112 00107
t-
00127
00127
55 10000 00041
Shift tape unit number
00130
00130
51 00355 00356
J - 00356b
00131
00131
11 00355 10000
Jmask-Q
..-..
I
0'
I
......
><
~
~
Q
Print "set, qtl
}
Test to see if B lB lID
address
Set up exits
}
Print "IntO"
9-138
OR-128
Page 7 of 15
00132
00132
11 00100 20000
00133
00133
42 00156 00135
00134
00134
42 00157 00140
00135
00135
21 00132 00372
00136.
00136
42 00160 00132
Routine to mask tape
00137
00137
45 00000 00144
unit number into all
00140
00140
31 00132 00071
tape orders
00141
00141
16 20000 00142
00142
00142
53 00356 00000
00143
00143
45 00000 00135
00144
00144
75 10174 00146
00145
00145
21 00375 00201
00146
00146
13 00375 00375
00147
00147
65 00004 00200
Write undump routine on tape unit J
00150
00150
11 01000 10000
Parameter word - Q
00151
00151
75 30137 00001
00152
00152
11 00401 00001
00153
00153
45 24200 10435
00154
00154
07 01025 73702
00155
00155
03 00000 00000
00156
00156
63 00000 00000
00157
00157
67 70000 00000
00160
00160
11 00600 00000
}
}
Compute check sum of
undump routine
Move dump routine to
00001 - 0014Qb
Constants
,-..
co
C'\J
......
-I
0I
0
0
0-
......
t-
><
c..
9-139
OR-128
Page 8 of 15
UNDUMP R.OUTINE
00200
00000
45 OOllOO 00002
00201
00001
56 10000 1000001
Exit to math program
00202
00002
64 00003 00040
Read in remainder of undump
routine
00203
00003
75 10174 00005
00204
00004
21 00175 00001
} Test check sum of
undump routine
00205
00005
47 00007 00014
00206
00006
00 07777 00000
Constant - block mask
00207
00007
67 00004 00000
Rewind tape for new read-in
if check sum fails
00210
00010
15 00013 00132
}print out "undump
00211
00011
37 00137 00130
check sum NO"
00212
00012
64 00004 00000
00213
00013
45 00140 00003
00214
00014
15 00063 00053
Repair 00053b
00215
00015
64 00001 00177
Read in block containing control
word
00216
00016
23 00237 00237
00217
00017
11 00173 00171
00220
00020
55 00177 00001
00221
00021
11 00237 20000
Parity check
cD
C'\J
00222
00022
52 00172 00237
on
I
0'
00223
00023
41 00171 00020
control word
0
0
00224
00024:
31 00237 00070
00225
00025
46 00026 00033
00226
00026
67 00001 00000
00227
00027
41 00174 00015
00230
00030
15 00032 00132
}print out "Paritv
00231
00031
37 00137 00130
check failure"
-~
} Read in undump routine again
when check sum fails
I
0'
~
t-
><
~
9-140
OR-128
Page 9 of 15
--co
C'J
...-4
Return to read in control word
again
00232
00032
45 00144 00015
00233
00033
11 00177 20000
00234
00034
46 00044 00035
00235
00035
15 00177 00036
00236
00035
67 (00000 000001
00237
00037
11 00200 20000
00240
00040
43 00176 00001
00241
00041
15 00043 00132
00242
00042
37 00137 00130
00243
00043
45 00150 00012
00244
00044
15 00177 00170
N -00170b
00245
00045
16 00177 00053
Setup v of 00053b
00246
00046
11 00170 20000
N-A
00247
00047
42 00166 00110
N>
00250
00050
42 00167 00104
N> 1577 ?
00251
00051
64 00033 00237
Read in 1540 words
00252
00052
75 31577 00054
00253
00053
11 00200 ( OOOO~
00254
00054
37 00126 00120
Compute check sum
00255
00055
21 00053 00165
v .. 1577-v
00256
00056
23 00170 00164
N - 1577-N
00257
00057
42 00163 00070
N> 1600 ?
00260
00060
64 00034 00200
Read in 1600 words
00261
00061
16 00053 00063
Pick up current v
00262
00062
75 31600 00064
00263
00063
11 00200 100000]
} Check for final control word
}
Rewind tape
}
Test check sum, exit to
main routine if ok
}
Print "Data check sum
fault"
}
~7
?
Transfer 1577 words to MD
I
0I
0
0
0...-4
t~
}
Transfer 1600 words to MD
c..
9-141
OR-128
Page 1.0 of 15
00264
00064
37 00126 00120
Compute check sum
00265
00065
21 00053 00162
V "·1600 -
00266
00066
23 00170 00161
N - 1600 - N
00267
00067
45 00000 00057
00270
00070
21 20000 00160
N "'37-A
00271
00071
73 00157 20000
00272
00072
21 20000 00156
N"" 37
40
-A
00273
00073
15 20000 00074
00274
()O074
64 00000 00200
00275
00075
15 00155 00100
00276
00076
21 00100 00170
00277
00077
16 00053 00101
00300
00100
75 (000001 00102
00301
00101
11 00200 ,000001
00302
00102
37 00126 00120
Check sum
00303
00103
45 00000 00014
Read in next section of dumped
information
00304
00104
73 00157 20000
} J,
V
N:37 _ 0OO74b
Rearl in N" 37 blocks
40
N - 00100b
Transfer N words to MD
N
40
-A
00305
00105
35 00156 20000
00306
00106
15 20000 00107
00307
00107
64 (000001 00237
00310
00110
11 00170 20000
N
00311
00111
35 00155 20000
0-
00312
00112
15 20000 00114
0
0
0"-
00313
00113
16 00053 00115
t-
00314
00114
75 (00000] 00116
00315
00115
11 00200 f 000001
00316
00116
37 00126 00120
Compute check sum
00317
00117
45 00000 00014
Read in next section of dumped
information
.-
co
....
,
-
J; N
40
- 00107b
Read in N blocks
40
}J.
N-001l4b
f
......
><
0..
Pick up V
}Transfer N words to MD
9-142
OR-128
Page 11 of 15
00320
00120
11 00126 20000
00321
00121
34 00166 00017
00322
00122
15 20000 00124
00323
00123
11 00006 10000
00324
00124
'53 100000] 00126
00325
00125
16 00053 00127
00326
00126
75 110000](00000]
00327
00127
21 00176 100000]
00330
00130
16 00166 00171
00331
00131
16 00003 00174
00332
00132
55 00000 00006
00333
00133
61 00000 10000
00334
00134-
41 00174 00132
00335
00135
21 00132 00172
00336
00136
41 00171 00131
00337
00137
56 00000 1)0000]
00340
00140
45 47345 70622
00341
00141
34 07150 41605
00342
00142
20 16360 42434
00343
00143
07 04470 61345
00344
00144
45 47155 73012
00345
00145
14 01250 41605
00346
00146
20 16360 42630
00347
00147
14 11341 22045
00350
00150
45 47225 73001
I
00351
00151
30 04160 52016
0
0
0"-
00352
00152
36 04243 40704
00353
00153
26 30341 10145
"'0:>""'
C\J
......
--
Check sum routine
Print subroutine
-Flex code constants
I
0"-
......
r-
><
0..
9-143
OR-128
page 12 of 15
00354
00154
00 00000 00003
00355
00155
00 30000 00000
00356
00156
00 00000 00000
00357
00157
00 00000 00040
00360
00160
00 00037 00000
00361
00161
00 01600 00000
00362
00162
00 00000 01600
00363
00163
00 01600 00001
00364
00164
00 01577 00000
00365
00165
00 00000 01577
00366
00166
00 00037 00003
00367
00167
00 01577 00001
00370
00170
00 [00000] 00000
00371
00171
00 00000 r000001
00372
00172
00 00001 00000
00373
00173
00 00000 00043
00374
00174
00 00000 [00001]
00375
00175
00 00000 00000
00376
00176
00 00000 00000
00377
00177
00 00000 00000
Const.ants
and
Counters
DUMP ROllTINE
00400
ooor"
45 00000 00001
00401
00001
31 10000 00052
Parameter word - A
00402
00002
47 00014 00003
Parameter word zero ?
0
0
0-
00403
00(lrt3
23 00137 00137
Make. control word positive?
r-
.....
00404
00004
15 00012 00137
J; N ~ control word
><
0...
00405
00005
37 00040 00027
Parity bit correction
00406
00006
11 00136 00140
Move check
00407
00007
65 00001 00137
Write control word and check sum
on tape
---co
.....
C\I
,
'-'
0t
SUIn
9-144
OR-128
Page 13 of 15
--
co
00410
00010
11 00127 10000
00·111
00011
51 00012 10000
00412
00012
67 r00005] 00043
OO:t13
0001:~
45 00000 00J20
00414
00014
·46 00015 00104
00415
00015
15 10000 00051
00416
00016
31 10000 00071
00417
00017
16 20000 00137
00420
00020
31 10000 00017
00421
00021
15 20000 00130
00422
00022
31 00135 00065
100000b - A
00423
00023
16 00137 00133
Isolate N
00424
00024
34 00133 00017
100000 - N to Au
00425
00025
42 00130 00021
V -+ N > 100000b ?
00426
00026
15 00130 00137
N - control word
OQ427
00027
16 00012 00133
00043b - counter
00430
00030
23 00237 00237
o-
00431
00031
27 00137 00135
Complement parity bit
00432
00032
11 00137 10000
Control word - Q
00433
00033
55 10000 00001
Shift Q left 1 place
00434
00034
11 00237 20000
00435
00035
52 00132 00237
}Add I bit of control word
to parity sum
00436
00036
41 00133 00033
All bits added ?
00437
00037
31 00237 00070
Parity sum - A
00440
00040
46 00027 00041
Least significant bit of parity
sum zero?
00441
00041
11 00130 ·20000
N-A
00442
uuu42
15 00125 00124
1637b - 00124b
00443
00043
15 00065 00050
Setup transfer of 1637b ·words
Number of blocks - Q
Rewind tape
1." V an MD address?
}store V
} Store N
parity sum
C'J
...-4
'-'
I
'"0
0
'"
I
...-4
t-
><:
0..
OR-128
Page 14 of 15
00444
00044
16 00004 00053
Setup to write control word
00445
00045
11 00125 00131
Setup index to 1637b
00446
00046
15 00064 00134
Setup block count threshold to 40
00447
00047
42 00124 00067
N less than 1637b or 1640b ?
00450
00050
75 100000] 00052
Transfer 1637b or 1640b words
00451
00051
11 130000] 00140
00452
00052
37 00116 00105
Compute check sum
00463
00053
65 P0035] 130000]
Write words on tape
00464
00054
21 00012 00123
35 plus block count to block count
0041)5
00055
21 00051 00131
V + 1637b or 1640b - V
00456
00056
23 00130 00131
N - 1637b or
00467
00057
15 00126 00124
Set threshold to 1640b
00460
00060
15 00122 00050
Set -transfer order to 1640b words
00461
00061
16 00051 00053
Set "V" of tape write order·to 14Gb
00462
00062
11 00126 00131
Set index to 1640b
00463
00063
15 00104 00134
Set block threshold to 37
00464
00064
45 00040 00047
00465
00065
00 31637 00000
00466
00066
00 00000 00000
00467
00067
32 00134 00103
00470
00070
11 00127 10000
N +37
-A
40
Nmask-Q
00471
00071
53 20000 00102
Number of blocks - write mtJ order
00472
00072
53 00130 00074
N -OO074b
00473
00073
15 00051 00075
V-00075b
I
00474
00074
75 (30000] 00076
0"-
......
00475
00075
11 130000] 00140
><
c..
ooooe
\
.J
9-147
CV-129
ANALV...
..RKPAR£D BV
CHItCKED BV
REVISED BV
CONVAIR
Bauer and
~1n
PAGE
REPORT NO.
MODEL
SAN DIEGO
DATE
IC 007-1
ZK 491
All
3-6-56
CARD READ Al'D/Cil PUl'CH ROOTID .
'fhi. routine coabill•• the teatur•• of the card read 10 005 and the oe.rcl
p\llloh IC 006 routla.. ill orde.. tba t the operatlOl.'le of puDchiJ1g and readins
_y be perfo....d .iaultalleoue17.
fbi. routine require. u,Ol ootal word. of
IS in which to operate. con.taIlta and temporary .tonge. includecl.
operatag baat., which .ore efttciently
WI.' the card
oy(~l:.
,-'two
~ycl.
tl_. aD. po•• ibl.
the r.ading of &8 any al thirty tielela trom • oard and the pUDchiq ot III
..aT a. thirty tield. in a card .laultan.oua1,.
.....ll..bl. betwMn reterenC)ee to the routine.
al __ or for
puachia~
uc
hay.
14 -
coaput1q ti_
If the routille 1. ueed tor read1D.c
.. loa•• _ _ oarda _y contain ... many •• torv nelda.
Duriag the tlr.t tin poata ot the 18 poat oard oycle. iatorati_ to
'be puaohed i. coll'nr_cl to deol_1 and stored 111 oard code in a car4
ilia,.
J
tinal oonveraion and .oaling ot the information r.ad frca the preyloua oard
s.a
pertol"• • &lid .tored 1D specified 18 ..aoJ7 loo.tiona.
!'he r_inder of
'bile oardcyo1. i8 used for punching and reading_ row by row With the tollOldJag
, .tepa· oocurriJlg at ...ch row ot the card. cycle (beginning at row 9 and
eont1nulng through rOW' 12).
1. Puach laforatioD --.... oard _chine •
..-..
g;
3. Read intoratlon oonverted
--J.
.-4
to B. C. D. aad .tored tor tinal
oOllVer.1on during next card cycle.
I
o
~
A1 though two card eye 1.. are l1ec•••art to camp lete the opera ti0ll8 , t h •
.-4
r-
><
c..
•• t ettect 1. the COIlTerting ot one read card and the punohing ot OIle card
during eaoh card eye 1••
..........
-~
9-148
CV-129
CONVAIR
ANALYSIS
...
0· ....... '.· ...
n_
Hauser and Gerld.ll
PREPARED BY
.......
1:1.,
1) ............
1"
Ie 007-2
PAGE
;: 0 • • 0 .... ,.'0 ..
MODEL
III 491
All
DATE
3-6-56
REPORT NO.
SAN DIEGO
eMEeKED BY
REVISED BY
!he oard routine require. the following infor_tion,
1)
Binary .ealilll.
2)
Deoimal scaling.
3)
Looation ot field.
0J1
the oard••
4) Zero .uppre•• iOR (if
punching) ~
!hi. information i • •upplied the routine in a 8tandard fona called a
parameter word.
One parameter word is required tor each card field whether
reading or punohing.
If both reading and
pUDch1n~
are to be accomplished •
.. paramter word Is required tor each.
A field oem.i.ta
or
a nUJab4lr ot consecutive card colU1111U1.
The lut
oolumn ot a field i. reserved for the sien of the d.cl~AI number stored in
the field.
An 11-punoh signifie. a negative number, no punch (blank colUJlll)
signifies a positive number.
A combination 12, 3 and 8 nuneh in one eoluma
signifies a decimal point.
Fields need not be adjacent--there maV be unused colQ~8 punched or
un-punched between 1hem--nor need theY' be alike in sile.
The oonveraion operations ~re automatic.
Enty into the oard read &nd punch routine from line y is effected as
fo1lon.
,.
)
37
Omnmaa
0Jnraa
y+ 1)
AD
OPPPP
ODDDI\ Read oontro1 word
+ 2)
00
OPPPP2
ODDDD PunCh control word
2
,. +3)
XI
uuuuu
'VTV'VY
y
I
1'0 read and punch routine
Wext instruction
Ommmm repre~.nt. the ber,inning IS op~rating address of the read and
pUIlch routine.
ro....... -a
Y-fLlY
CV-129
ANALYSIS
PREPARitD BY
CONVAIR
HaUBer and Gerkin
MODEL
CHECKED BY
Ie 007-3
PAGE
REPORT NO.
SAN DIEGO
ZV 491
All
DATE
REVISED BY
The 37 command records in Ommma the address of the omtrol word.
3-6-56
The
routine i8 then entered at Ommmm and after finishing the operations the card
routine exit. to
y~
3,
the line following the second control word.
COITROL If ............ ( .
(
0 A .011 ... t
I
0
PAGE
flo
REPORT NO.
SAN DIEGO
CHECKED BY
REVISED BY
MODEL
DATE
Ie 007-6
ZV"491
All
3-6-56
!he rout ine may bs programmed in the following manner I
UlD ONLY.
37
01000
01000
10
00000
00000
00
00000
00000
37
01000
01000
11
00000
00000
00
00000
00000
37
01000
01000
11
OPPPP1 ODDDD1
00
00000
00000
37
01000
01000
20
00000
00000
00
00000
00000
37
01000
01000
20
00000
00000
00
00000
00000
I
37
01000
01000
~
22
00000
00000
00
OPPPP ODDDD
2
2
pick a read card.
piok a read card and read a oard.
piok a read oard. read a oard
and cCJ1Tert.
1IUICB OWLY I
.......
0'
C\l
piok a punch oard.
piek a punch card •
~
'-'
I
0'
0
0
0'
r-
~
a..
"0."
'.'a-"
pick .. punch card, and pundt a card.
9-153
ANA LYSI.
fIIREPAR£D BY
CHECKED BY
REVISED BY
CV-129
CONVAIR
..
0''''.'(''''
Hauser and Gerkin
0"
G.""' .... ~
o ........ .."c.,
(Q • • "
...
PAGE
T'Ofll
REPORT NO.
SAN DIEGO
MODEL
DATE
Ie 007-7
1M 491
All
3-6-56
READ and PUllCHI
37
01000
01000
30
00000
00000
00
00000
00000
37
01000
01000
31
00000
00000
pick tram both hoppers and read ..
00
00000
00000
card.
37
01000
01000
pick from both hoppe... convert. punoh
33
OPPPP
1
ODDDD
1
and read.
00
OPPPP2
ODJIDD
2
pick from both hoppers
.umbers are rouaded to the desired number of decimal digits before
punching take. plaoe.
A divide check error stop result8 if an inlufticient
number of card column8 is allowed tor the integer portion ot a field.
In ca.e of a card .ohine failure or an accidental stop in the middle ot
a card cycle. the ourrent oard may be reread or punched again,
the card8 .et 6'> A I)
=00000,
reposition
and START.
fhis routine ia ooded in standard torm.
All oonstanta are contained by the
routine.
lumber of word••
U.ed by the routine.
(;22)8:' (210)10
U.ed by temporaries immediately following routiB., (57)8 z (47)10
For " •••mbly modificatioll'
U.ed tor oonstanta I
(271)8 s ( 185)10
(31 )8:: (25)10
Thirty fields . .y~. read atid thirty fields may be punched simultaneoualy.
'~7
fielda may be read or forty field. may be punched.
14 - GOilputing
.........-"
ti_ 1. . .tWIt". be"en reterenoel to the card routia••
9-154
!fOAM NO. E T.
I
J~
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
,.
SAN DIEGO CALIFORNIA
Ie 007-8
PAGE
MODEL
ZM: 491-.2All
DATE
3-20-56
REPORT
CA~D
REA'"
ft.NI"l
PUNCH RT.
JCOO7
1~(~)
1002
11 01276 00000
15 20000 01034
16 20000 01072
1003
16 01124 00000
1004
55 20000 00003
SET EMF.~GENCY R~~UN
SHIFT FIRST f)tt:iyr ~Q)
1005
31 01273 00003
BULL CODe: • 2-2.--.-(A)
1006
1007
5'
32 20000 00001
5Lz.
(A~ )
1010
44 01011 01011
SL 1
(AL. )
1011
1012
1013
44
1014
~7
1015
41 01107 OllS?
1016
~6
1017
37 01160 010'-4
NO: SET '7C~
ALL ROWS PUNCH~D
EX!T
SET lj
1020
76 00000 01'376
READ
1021
1022
1023
76 10000 01346
45 00000 31023
A-SWITCH
1024
32 01276 00000
ADD READ CODE
102~
~1
SET 41
1026
41 01127 01076
C\J
......
1027
J
1030
16 01101 Oll~7
37 01023 ·01076
1000
1001
---.
0-
--
0J
01~17
0113~
~O()(}O
01012
16 01261 01120
44 01011 01014
01160 011'-1
00000 01016
01023 011'-1
1031
......
1032
15 01263 01253
37 01122 01016
><
c..
1033
31 01075 01034
1034
1036
55 30000 '00000
44 01036 010:37
16 01122 01075
1037
55 10000 00013
t-
1035
5TORE P1
STORE D1
E'XT~AC"
PUNCH ~
NO: SET
PICK
C~!")F~
0(3
READ?
f
ONE
~OW
76 10000 01'362
0
0
0-
CONTROL HORD
!')IGtT-l --t-I')YGTT. NF.'r--: !
SrG~ s~NTrNr:-L --+-OTr,TT
SET A~
PRESTORE MATRIX
TRANSFE~
SET B2SET CONvERSrON REPEAT
PARAMETER WOR() 1~(t)
LAST ·FIELD ~
YES: SET CONVERSION EXIT
SLl l
(0)
9-155
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5"N DIEGO
C"LIFORNIA
Ie 007-9
PAGE
MODEL
ZM 491-2.All
DATE
3-20-56
REPORT
CARn
RE~,f)
A~!!"'I
OU~!CH
1040
51 01313·200('10
~ --.".... (~
1041
1042
16 20000 01063
SET SHJFT
55 10000 00006
STORE
104'
1044
51 01~1~ ~,?~~
55 10000 00006
1045
51
01~13
1046
1047
5~
10000 00006
)
R
5iORE
l
01?'-7
STORE
1050
51 01313 01107
32 20000 00016
1051
35 01264 01052
R • 2 14(A)
SET NEXT INSTRUCTION
- 105!
00 77777 00000
5TO~E
1053
37 01053 01054
SWITCH
1054
41 01233 01247
1055
37 01260 01056
1056
41 01227 01250
1057
1060
37 01254 01061
1061
41 0110 7
SHIFT ~ DtGITS
CONVERT
L Tt::RMS
SKIP DECIMAL POINT
CONVERT
R':MAINTNCTtOMS
1062
54 01052 10107
1063
31 012;3 30000
1064
32 10000 00000
1065
73 01052 01226
.....
1066
~1
'-'
1067
51 01271
0
0
1070
.....
1071
><
c..
1072
47 01071 OlO""?
1~ 01226 01??6
11 01226 30000
VFs:-IN/. '-S
STORE RESULi
1073
21 01034 01314
ADVANCE P
1074
ADVANCE D
1076
21 01072 01276
45 00000 3107S
11 01263 01107
1077
55
;-.,
0'
N
,
,
0'
0'
r-
1075
37 01260 01061
01'~O
01254 1')1250
01~46
~oooo
00000
R
10~-1
1/2 10 R -L..-ROUNOING TERMS
'"d · lOR..
t . ,S
ADD ROUNDING
STORE I N I •
SHIFT SYGN
s reiN
r '5
S~Ni
~(A)
T~~M
2S
TN~l ~~)
N NF:G.! T rv~ ?
~N
•
,9
PRESET MATRIX STORE
~O\'J HORD
1-...('1)
9-156
FORM NO E
T
•
...
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
~
CV-129
SAN DIEGO CALIFORNIA
PAGE
Ie 007-10
MODEL
ZM 491-2,
All
DATE
3-20-56
REPORT,
CARD READ ANn PUNrH
1100
11 01312 01346
1101
1102
31
110~
44 01104 01105
llC4
32 01127 00000
1105
46 01106 01102
1106
31 20000 60000
1107
00 00000 OOCOO
1110
21 01107
1111
41 01346 01101
31 01112 0111~
1112
1113
0127~
00011
32 20000 00003
01~15
SET INDEX
3
~FNT iNrl-..,....(~L)
SL 4 (AR.) • SL 3 (AL)
BIT THtS COL. ?
YES:ADD DIG!T
SENT INEL REACHED?
YES: CLEAR (A,-)
ADO TO MATRIX
STEP MATRIX STo~r
ROW WOR~ USED UP ,
rN~TRUCTtC~~
... 6
5wITe,",
v10~O
55 0136? 00000
ROW
1114
37 01112 01100
STORE BCD
1115
C;S 01376 000;4
37 01.112 (')!101
RCf") INF='().
1116
=.
2 -,..(n )
INFO.----~1ATRIX
-f-MAT~
rx
1117
1120
16 01124 00000
SET
45 00000 31120
0(
1121
17 00000 20000
1122
1123
1124
1125
1126
1127
37 01122 01123
35 01276 01"127
5T·ART BULL
READ CONVERSION SWITCH
CLEAR PUNCH INDEX
~ET TO PJCKtJ"
NEXT CONTROL wn~D
~5
51:T FXtT
00 00000 00000
CON TROL WORn --,....(A)
1130
11 01300 01127
10~IGIT
11~1
15
1132
1133
01117
11 01107 01322
-'2 01273 00000
CLE'AP MATI!)!X AN')
CARD IMAGE'
AD!) PUNCH COOE:
1134
~7
SET
1135
15 20000 01143
STORE
1136
32 20000 00016
5L 15
1131
15 200.00 01177
STORE D2.
36 20000 01107
27 20000 01000
01275 01016
1005~
01120
010'~
EMER~~NCY
REP-UN
-SWITCH
,
0( z.
p~
(A)
9-157
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO
PAGE
CALlFOFtN'A
CA~D
MODEL
DATE
;~20"'56
11 01272 01371
1141
11 01265 01400
PRESTORE COLUMN SELECTO~
PRESTOPE ~ow SrLEr.Tn~
1142
37 01155 01143
S.ET SWITCH
1143
1144
1145
1146
1147
55 ~oooo 00000
44 01145 01161
37 01155 01161
PARAM~TFP \lIORI') ~(0)
75 30003 01151
1150
16 01020 01155
1151
1152
1153
37 01120 01154
SET
75 20003 O~154
23 01155 01276
STEP
11~4
l~ 01124 00000
1155
77 00000 30000
71 10000 30000
77 10000 "30000
45 00000 31160
SET EME~G~NCY
PUNCH
ONE
ROW
1157
1160
1167
1110
~7
1171
41 01233 012'34
1112
31 01227
:35 01270
00 00000
31 0131.
13 01052
12 '30000
1162
I
0I
0
0
0-
.....
t-
><
c..
16 01161 01107
55 10000 0OOl~
51 Ol:!13 20000
3'3 20000 00000
35 01267 01200
31 0105:3 01042
44 01220 01161
16 01231 01246
1161
0N
PUNCH
1140
1156
-.....
-
READ A,ND
1163
1164
116'
1166
1173
11".
1175
11'6
1117
01241 01171
00017
01174
Ie 001-1J
ZJl 491- Z
All
REPORT
LAST FIELD ?
SET SWITCH
SET PUNCH JNOEX
SET UP
PUNCH
ORDE~S
~1
PUNCH ORDERS
RF~U~l
l' -5Wl TCH
SLu
(Q)
S~(A)
-5 ---...(A)
SET SHIFT
STORE BtLtR. 10 ~-l
ZERO SUPPRESS ?
SE'T FOR NO ZERO SUPPRf!ss
SHIFT
B COLUMNS
L • ,15~(A)
00000
SET NEXT INSTRUCTION
STORE 10 ....
00023
2 34 __._(A)
10000
1/2.2 35 /10"-L.-ROUNDIN(; TERM
012~3
STOR~
I NI
~
28
9-158
FORM NO
E
T
1
).
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
F
SAN DIEGO CALIFORNIA
PAGE
007.1~
MODEL
DATE
3-20-56
23~(A)
N •
1200
00 00000 00000
1201
32 10000 00000
ADO ROUNDING
1202
73 01174 20000
IN' •
l~O~
~5
TER~
,3s/ 10 '-.....,...(A)
s TO ~ E" I N I . '- 36 11 ~ L
L. TIMES
THRU CONVERSION
OECIMAL POINT
1205
20000 01174
37 01241 01205
41 01227 01242
12-06
16 01262 01241
1207
1210
41 01107 0122~
41 01107 01242
AND REMA I~ INC;
1211
1212
15 01177 01216
21 01143 01314
SET TO CHECK st('N
1213
1214
1215
1216
\ 121'1
21 01177 01314
16 01155 01241
STEP 0
SET ExtT
1204
Ie
Z¥. h91-Z
All
REPORT
f
~220
-....
0'
C'l
I
0'
I
o
o
....
0'
t-
><
c..
--..,...tMAGE
STEP P
-l-.,...(A)
33 01314 00000
55
~oooo
00000
44 012~'- 01234
37 01246 01170
1221
1222
i223
43 01227 01231
Tf='qM~·
N • 2'-.....(Q)
NEGATIVr ?
SET FOR ZERO SUPPRESS
NO ZERO SUPPRESS IF L
~
0
45 00000
01?~4
01~21
00000
,
1224
3S 01400
01~26
1225
35 01274 01227
1226
00 00000 00000
1~21
00 00000
33 01320
SET FOR ~ PUNCH
SET FOR e PUNCH
STORf ! PUN'CH
STORr ~ PUNCH
SET FOR 12 PUNCH
SET NO ZERO SUp~q~S~
SET NEXT INSTRUCTION
STORE DIGIT IN IMAGE
SRI
COLUMN SELECTOq
AOVANC~ TO NEXT CARD FIELD !
YES: STEP ROW SELECTOR 12 ROWS
THIRD FIELD?
1230
1231
31
oonoo
onooo
31 01246 01232
12!2
35 01400 012)3
1233
00 00000 00000
12'4
1235
1236
55 01377
1237
0004~
44 01236 01241
21 01400 01311
42 01266 01241
--.."..(A)
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNJ"
""
4N ---.-( A)
34 20000 00063
INTEGER PART ~(R)
t)tGtT :: 0
1241
47 01231
1.6 0105j
41 01127
21 0125~
16 01240
01254
~1246
3-20-56
?
37 01254 01255
MATRIX INDEX
RESET IND~X
TRANSFE~ MATRIX WORO
SHIFT TO NF:XT DECIMAL OtGIT
SWITCH
31 01233 (')0002
4N ---."...(A)
32 01233 00001
iON -+-(~ )
52 01316 01233
10N PLUS DIGIT--+-N
~5
10000
01253
01314
01127
OOO~4
01~'2
PR~Sf!T
1264
11 01276 01052
27
0-
1265
1266
0
0
~
DATE
491- 2-
STORE FPACTrONAl PAPT
00 00000 01160
00 00000 01210
C\l
All
lON ---....( A)
1261
1262
1263
'-'
I
MODEL
45 00000 31241
45 00000 31260
-
ZM
YES: USE LAST 8 COLUMNS
31 01174 00002
32 01114 00001
11 20000 01114
5,5 01377 00010
1260
0-
Ie 007-13
REPORT
CARD READ AND PUNCH
1240
1241
1242
124'3
1244
1245
1246
1250
1251
1252
1253
1254
1255
1256
1257
PAGE
~5
01~22
0133~
01377
PRESET
PRESET
21 01363
01~71
PRESET
1267
~1
0OO4~
PRF.SET
1270
1271
1272
1273
1214
1275
1276
1217
, 1 01277 Ol174
""£S~T
00 00000 00014
12
40 00000 00000
PRESET FOR
00 000.00 00002
00 00005 00000
2
5 • ,25
51f 00000 00000
MODIFY COMMAND
00 00000 00001
00 00000 00001
1
I
0~
t-
><:
c..
012!~
~Ct.UMN
SF-LECTOR
TABLE
9-160
FORM NO E
T
I
.1'
SAN DIEGO. CALIFORNIA
00 00000 00144
1302
00 00000 01750
1303
00 00000 23420
1304
00 00003
1'305
00 00036 41100
1306
00 00461 13200
1307
CO 05753 60400
IlIO
00 73465 45000
1'11
1312
1313
11 24027 62000
00 00000 00077
EXTRACTOR
~314
00 00001 00000
tJ AOVANCF.
1315
00 00001 00001
1316
O() 00000 0001'
U AND V ADVANCE
4 BtT EXTRACTOR
1311
1320
00 00014 00000
U
00 00002 <'onoo
~ 15
1!21
1322
00 oooo~ 00000
00. 00000 00000
MATRIX WORD 1
13~'
1324
00 00000 oooon
00 00000 '00000
,
112~
~o
C"\I
11~6
00 00000 00000
•
I
1'27
00 00000 00000
1330
1331
1'92
00
C1'
......
'"
I
0
0
C1'
......
t-
o<
c..
Ie 007-t-+
ZM 491 -z
MODEL
All
DATE
3-20-56
+
1300
1301
..-
REPORT
PAGE
CARD READ AND PUNCH
"1
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
F
00 00000 00012
00 00000
00000
POWERS
OF
O~240
oooo~
TEN
~
ADV.NC~
'.2'5
2
OOO()~
5
6
7
ooono oonoo
1533
00 00000 00000
00 00000 00000
00 00000 QOOOO
1134
00 00000 00000
11
1335
00 00000 00000
0
1336
00 00000 00000
t
1337
00 00000 00000
'-
8
9
IMAGE FIELD
I ROW 12
9-161
CV-129
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OII!:GO CALlFO.-NI ...
MODEL
Ie 007 ..15
ZM 491 - 2ALL
DATE
3-20-56
PAGE
REPORT
eARn
~f"A"
ANO
~UN(H
1!40
1341
1!42
00 O()oo.o 00000
00 00000 oo~oo
4
00 00-000 00000
5
1'43
00
00
00
00
00
00000 00000
6
00000 00000
00000 00000
8
1)44
t'34~
1!46
1341
'11,0
S
.,
00000 00000
00000 00000
9
IMAGE FIELD tl
00 OOO(Jo 00000
oo-oon
~ow
12
11
1'51
00
00000
0
1352
00 00000 00000
135:3
1354
00 00000
00 00000
ooaoo
1
2
J
1'"
1'56
00 00000 00000
4
()cnoo
~
1357
00 00000 00000
1!60
00 00000 00000
6
7
1~61
no
0000(') 00000
8
1362
00
ooooe ooonn
CJ
1'63
00 00000 0(')000
1364
00 OOOO!"
oooon
IMAGE FIELD ttt ROW 12
11
1365
1366
00 00000 00000
00 00000 00000
0
1
0"
1~67
00 00000 00000
2
0
0
0"
1370
00 00000 00000
t-
1371
00 00000 00000
:4
4
1312
00 0000" Ol'n('\,.,
~
1373
00 00000 00000
6
1374
00 00000
OC'ooo
7
1375
1376
00 00000 00000
00 00000 00000
P
q
1177
00 00000
ooeon
1400
00
conoo
0(')('\1")0
--0"
C'\l
~
I
I
~
>c:
\J..f
00
oooo~
oocoo
COL tJ~N
ROW
~
E lEC Tr')P
5F.LECTO~
9-162
ANALYSIS
PREPAR£O BY
CV-130
CONVAIR
.... " ,.,.~ .. , ....••..
Hauser and Gerkin
~'\N
a ••
Icoo6-1
PAGE
.,.
ZJI 491
REPORT NO.
DlfGO
CHECKED BY
MODEL
REVISED BY
All
DATE
3-8-56
CARD PUlleR ROUTID IOOO6
fhi. routine converts apecified binary numbers into decimal and cause.
them to be punched into oarda.
It requlreeJ 245 oetal words of IS in which
to operate, constant. and temporary storage included.
It is possible to
convert and punch as many as forty fields in a card and have
17
me computing
time available between references to the punch routine.
The following information is required:
1) Binary scaling
2) Decimal sealing
3) Locations ot fields o~ the card
4)
Zero suppression
This information is 8uppiied to the card routine in a standard form
called a parameter word.
One parameter word ia required tor each field.
A field consists ot a number of conaeeutive oard columnae
The laat
column of the field is reserved f<
c..
y + 2)
Wext instruotion
I
o
o
0'
~
am..m
ODDOO
represents the beginning addres8 (IS operating address) ot the
card routine.
9-163
CONVA
ANALYSIS
PREPARED BY
CHECKED BY
'''N
Bauser and Gerkin
R
D!EGO
CV-130
PAGE IOOO6-2
REPORT NO. ZJ( 491
MODEL All
REVISED BY
;-8-56
DATE
The
37 command records
in Omumn the addre6s of the control .. ord.
routine is then entered at 0Jaamm.
'the
After finishing its operation. the card
routine exit. to y+ 2, the line following the control word.
~otrrROL-'ORD
!he control
oGmpoaltlon.i.
a8
~d
controll the operation of the eard routi..
follOWBI
J.B
1.
Ita
OPPPP
ODDDD
The fir8t octal digit, cOl'ltrol. posi tloniag of carda in the read
and punch ohannel. of the Bull Reproducer.
B.
A= 1
Piok a eard from the read hopper.
A= 2
Piok a oard from the puach hopper.
The second octal dig1 t, controls the operation to be pertonud.
B=2
puaaa a card.
opppp 18 the addreBs ot the first parameter word.
ODoon i. the addres. of the first cia ta word.
opppp aad ODDDD muat both be IS addr••• es.
J. parameter word eonslst.
ot twelve octal dig! ta divided into aix
group. ot two each r
FF 88
Pr.
BB
LL Rl
II
Flag for filial parameter word.
"'=77 octal for final word.
FF =00 otherwi •••
SS I
.i
Bina"'"
Iltaotor.
·v aA.l~-g
u
4U
{Nuaber ot bits to the right of the
binary point.,
BB.
lumber ot b~ or UDueed columns between previous field, or edge
of card, and present field.
9-164
CON
ANALYSIS
PREPAR£D BY
H!l'\Js~r
V
A
CV-130
R
PAGE
a.nd Gerkin
CHECKED BY
REVISED BY
ICOOG-3
MODEL
Zy. L91
All
DATE
3-f-56
REPORT NO.
LLI
Number of digit positions to the left of the decimal point.
RRa
Number of remaining columns in the field exclusive of sign.
RR =00 no decimal point and no decimal fraction.
zz,
Flag for zero suppression.
ZZ=77 oot8.l for Z8ro suppression.
%!::OO for no zero 8uppression.
part are suppressed.
Only zeros in the integer
A zero immediately preoedingthe decimal
pOint is not suppressed.
Total size of a field LL+ RR.l
Ra.n~
of Para.metersl
DECIMAL
00 ....(
OCTAL
sa {. 35
00 ~ BB
,
00 ~ 58 ~
63
00 t..
43
... BB '77
00 ~ LL
,
10
00 ~ LL ~ 12
00 ~
~ 11
00 ~RR ~ 1;
RR
01 ~LL +- RR
~ 11
01 ~LL -i-Rlt ~ 13
The parameter words, one for each field, ~st be stored consecutively
starting at some ES memory looation OPPPP.
There must be an equal number ot
consecutive words starting with some ES memory location ODDDD. filled with
data for the punch routine.
Punching takes place at the third card station in the punoh ohannel.
therefore. two punch cards must be advanced before pUftching can take place.
This can be done manually. or the rtmch routine can be used to pOSition the
cards as follows t
9-165
CV-130
CONVAIR
ANALYSI.
PREPARtD BY
Be. us er and Crerkin
CHECKED BY
ICOO6-4,
PAGE
REPORT NO.
MODEL
ZM h91
All
DATI:
3-8-56
REVISED BY
37
Ommmm
Ommmm
(to card routine)
20
00000
00000
(pick pUIlch card)
37
0mmRra
0maInm
(to card routine)
20
00000
00000
(piok punch card)
It should be noted that onoe a card bas entered either the read or
punch channe l i t
ccntln~.
to adTance cae card station each time the Bull
Reproducer is cycled.
lumbers are rounded to the specified number of decimal digiti after
the decimal point before punchin~ takel place.
A divide check error 8top
results if an in8uffielent number ot card columns is allowed for the
integer portion of a field.
Ia the
8Vftl1t
of a card _chi. . failure or an acreidental stop in the
lIiddl. of a oard eye 1e. the current oard _y be puached agauu
8et (p A I)
=
00000 _ and STAR!.
The routine 18 coded in standard tor., all constants are cootalaea
by the routine.
!lumber of oel18 used by the routine I
=
(201)
(129)
8
10
lu.ber of temporariea immediately following routtaol
Ok) -
(36)
8
lumber of worde tor aassmbly modifications
(153)
8
.umber of
CODe tete t
=
(26)
8
(ho)
=
10
(107)
10
(22)
10
fielda may be punched in a card.
10
17
,.0. . . , . ' .... "
me computing time available between references to punch routine.
9-166
CV-130
C;:"NVAIR - DIVISION OF GENERAL DYNAMICS CORP.
Ie 006-5
L01- 2-
PAGE
REPORT
Z~J
MODEL
A'J..i...
DATE
r.A.p~
0
C"j
0"I
0
0
0"-
~
t-
><
c..
t(""'~6
1000
71 01160 30000
1001
1002
15 20000 01027
55 2000() OO('()3
1003
32 20000
1004
15 20000 01057
lone;
~1
1006
52 01174 21'1000
CONTROL ',}O PO --."..( 1\)
SET PA~Aj\1F. TE'R PICKUP
?3~(f\) t
CONTROL "'ORD
CONTROL v,'ORD • 2 / 5 --+-(A)
~ET DATA PICKUP
qA«:'T( n!JLl f'~~E --J-( A)
EXTRACT PTCK COf)F~
1007
32 20000 ('lOCO!
.sL 2
1010
44 01011 01011
1011
44 01016 01012
SL 1
( 0J
PUNCH (
1012
17 000(')0 2of)cn
~TART
101~
~1
(1100<' 00,,00
1014
~15
Oll!'7 0'.('1 e;
1015
56 00000 01015
1016
j~
1017
17 00000 20000
1020
?1. 01201 20000
1021
7~
0115~
Ollse;
00~13
(')onC'~
oonon
.
~Ull
~f='T
t!"xtT
EX.IT
""'~
pu,.,r'-'
~TART
ro",e
8ULL
CL~A~
1004~
1022
102~
16 0115' 00000
<)F'T
1024
11 01154 01015
PRF"STOQF COlUM"'.!
IMAGE
~Me"R~FNrv
'1 ()~,!
QFQU~·'
~FLF:CTOP
1027
11 01141 01110
37 0111? "1027
55 300('0 .onooo
1030
44 01103 01.031
PARAMF,:"!"F.q WOr'D -..(1)
lt5T FIELD '?
1031
55 100eo 00(113
~Lll
1032
~1
S
1033
33 20000 00000
-~~A
1034
35 01146 01060
SET UP SHIF"T OPI")E'q
1035
55 10000 000(16
e.TC'RE"
1036
51 01175 01120
B
1037
55 10000 00006
~TORt:
1025
1026
(fj)
( ft. )
0'0'3
11 20000 01202
~
'-'
I
PUN('4 ROUT Tf!J:"
O117~
'0000
pqESTO~E
~~L~("-:Ol?
5FT 5\-1 TTCH
(0)
~A
n.
.. , ...
CV-130
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO
CALIFORNIA
1040
51 01175 01111
1041
32
'-ooo~
1042
3~
01147 01043
~ ET
1043
00
oooo~
,C':.TOPf 1nt..
1044
55 10000 000.06
STORE
1045
.
51 01·175 01043
R
1046
32 20000 00016
R • 2
1047
35 01150 01050
OC01~
O~0rn
r NSi
Neo X T
~-=O-56
~(AJ
SET NEXT !N~TqUCTln~
,.",R-l
SI!PPP!:.s ~ I (V·l
?
0105?
7 E~O
1052
16
011?~
01140
~ET
1053
37
0113~
010~4
~H!F.:r
1054
41 01120 01126
lO~5
31 01116 000?1
?34 --..,..... (/l)
1056
73 01050. 100QO
II?
1057
1060
" 3000n 011'0
00 0000~ ~nnr.~
~,TO!'E
i061
32 10000 00000
ADD ROUNDING
1062
73 01121 ?OOOO
1063
35 ?OOOO 01050
-.....
--
1064
37
M
!06-:;
41 01111 0""4
I
1066
16 01151 011 ?>",
T""I\' LI"1f"'n
~ T n P F ~ r- r p.' ~ L p r: ! ~. T
o
o
0".....
1067
41 01043 OllIS
REMAINING
t-
1070
41 01043 01134
TE~t·1~
~
1071
15 01057 01076
<;F: iO
1072
21 01027 01116
STEP
PAR:~..JlETE~
lC73
21 01057 011-76
5Tr-P
~
1074
16 OJII? 0113"
1075
33 01176 00000
1076
55 30000 nr00h
1077
44 011?4
I
i\11
1S
~1100
0"-
MODEL
DATE
que T t ()~!
~4
01.()6~
Z:! '...:.]1-,it.
L. •. ? 15 ---,.. (.~ )
1051
0113~
Ie :;0(·6
REPORT
L
~"0P~
o
PAGE
~.lf)
(0LIJMN~
n
l~-(R.l). ?3~......... qnU~~f"'lI~,lr, Tr.r"M
I'"
\"'1, •
N
~UDPI?r.:~C:T""q
7C'P0
I •
,36
,3; --..,.. (~ )
T~RM
,3; 11(11. ~(")
•
~T()RE 'N
I·
,36
lIn'"
L TI"'r:"s TJ..lRt'
cn"'v~"'~
CJ-1~r:1(
~
r ~~!
0'
~.!
nl1?~
9-168
CV-130
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S"N 01£.(,0
CAR!')
1100
17 01140
PUNCH
O~()t}3
CAt 'F"ORN'"
PAGE
Ie
REPORT
;:~~ l.~f.?l ~i!.
MODEL
~~:l
~()UTrNF."
S~T
~!O
~O~
7~R(j
s'JDo~e'~'Tf'''!
~UppqF:
ss r !"'f'~. IF" l
'1101
43 61111 01123
1102
45 00000 01126
1103
31 01112 01031
5E,T 5\4,.' r TCH
1104
75 30,)(.,3 01.101
.~t:'T
1105
11 01143 01110
1106
43 01144 01013
1107
16
011~/
OO()(jO
ALL 1:> RO~!S PUt·l CI,-I~f) ?
SFr f:M&:'R~i-Nrv P!="f'!."l'
1110
00 0000('1
OO~(\O
PUNCH
1111
00 00000 otJona
1112
00 00000 00000
1113
15 20003 01106
111h
2~
111'5
31 01177 00000·
~
1116
35 01110 01120
SET
1117
35 01156 01121
SET rop
~
1120
00 00000.00000
~TO~E
DUNCf-i
1121
00 00000 00000
II??
33
1123
37 01]40 011/4
1124
35 01110
ZERO
ONE
~ow
STEP
"U~!CH OD"~~S
--t-( 1-.)
FOR
:3 PUNCH
~
PUNCH
1125
('10 0000" OOf'()0
Ctj
.....
......,
1126
55 01015 00043
I
1127
44 01130 01133
ADVA.NeE . TO· N ~x T
-.
0
0'
I
0
0
0'
.....
r><
0..
Oll?~
II
CA.~f\
l'
F"rr.lr') ?
1130
21 01110 Ollt;,
sTr-p
1131
42 01142 01133
THr~f)
, '. ??
c;~
1133
45 00000
1134
31 OlO5f) (lOOO'?
1135
'l?
"')'-
1136
11 20000 G1050
STORE
1137
~4
TPTE'GFQ DAR T ---t-( r.. )
0101t; 00rl10
0
UP
STORE 8 PUNCH
Sr-"r FOR
l' PUN("H
Sf:'T ~JO Z f:"RO suopq~~C; 1 0".1
SET NEXT INST~UCTr0tJ
~ r(H~~ DIGIT PU~'CH
5 Q1 co LtJrv,N SELEcTnq
00000
-
PUNCH ORDERS
01110 01160
Ol~OC'
COc-~
tJ~~
PO~'I
C::FLF'crop
CAPI')
L.AST
Q
FTf-'l"'?
qOWs
C(\lUMr..'~
~1133
01050 ()()OOI
20000 00063
4N ~~A)
lOt-.!
~(A)
FRACTIONAL
P }\.R T
9-169
C\l-130
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
PAGE
CARD
MODEL
DATE
3-20-56
0
C")
r-!
'-'
I
0"I
0
0
0"-
r-!
r-
><
0...
PUNCH ROUT!NE
.
1140
47 01123 "31.140
",YGTT =0 ?
1141
27 01203 01015
PRESET
114i'
77 01~"31
0101~
f'~F:SET
1143
77 00000 01244
PRESET
1144
77 10000 01214
PRESET
1145
77 10000 01230
PRESET
1146
31 01120 0004'3
PRt"5ET
1147
ORESE'T
11~O
11 01161 01",.
11 01160 01at;0
1151
('10 onoco, (') 1 rt7()
1152
00 00000 01000
11~;
00 00014
1154
40 00000 (H100()
". '"'v ~Nce
PRESE: FO~
1155
co
00000 00002
~
1155
<"0 00005 00'1(\0
~
1157
54 00000 00000
54
1160
00
1161
00 00000 nOOOl
1162
00 0000" OOOl2
1163
tJ.64
00 00000 00144
00 00000 01750
1165
00 00000 23420
1166
00 00003 03240
1161
00 00036 41100
1170
00 00461 1;200
1171
00 05753 60400
1172
00 1'3465 45000
1173
11 2"4027 62000
1174
00 00000 0('1C'r3
1175
00
1176
00 00001 00000
1177
00 00003
oooeo
Ie 006.-·8
ZM 491-L
All
REPORT
,..,~n~r;
00001
ooaor"! oon77
noooo
o~F'SET
tJ
II
2
.
(OlU\~~·~
SFLrCTOo
15
2
30
1
TAelE
POWER5
o~
T~N
"!
rXTRAC"'OR
1 • '- 15
15
2
3
.
9-170
CV-130
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
MODEL
10 006-9
Z1f 491 -~
All
DATE
3-20-56
PAGE
REPORT
CARD PUNCH ROUTINE
no
1201
1202
00 00000 00000
00 00000 00000
FIEl.D tROW 12
11
1203
1204
1205
00 00000 00000
0
00 00000 00000
00 00000 00000
1
2
1206
00 00000 00000
~
1207
1210
1211
1212
1213
1214
1215
00 00000 00000
4
00 00000 00000
5
6
1'216
1217
1220
1221
,.....
0
C":)
r-I
I
0'
I
0
0
0"-
r-I
r-
><:"
0..
15
1200
00002
oonoo
2
CARD
00 00000 00000
.,
00 00000 00000
00 00000 00"00
00 00000 00000
00 00000 00000
00 00000 00000
00 00000 00000
00 00000 00000
8
9
CARD
Ft~lO
It ROW 12
11
0
,
1
00 00000 00000
ocnoo
122~
00 00000
122'
00 00000 00000
00 00000 00000
00 00000 00000
'6
00 00000 00000
'1
e
1230
00 00000 oonoo
00 00000 00000
1!31
00 00000 00000
1232
00 00000 00000
11
12~!
00 00000 00000
0
12~4
00 00000 00000
1
1235
1236
1237
00 00000 00000
2
00 00000 0000(1
3
00 00000 00000
4
1224
1225
1126
1227
~
4
!5
9
CARD FJELO ttt ROW
t~
9-171
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
(flQr,
PUN("'H
CV-130
PAGE
Ie 006-10
REPORT
ZII 491- 2.-
MODEL
A.l1
DATE
3-20-56
~0UT PH~'
1240
00 0000('1 00(100
~
1241
1242
00 00000 OOCOO
6
00 00000 00000
1
124~
00 0000(1 00000
e
1244
00 00000 00000
()
9-172
CV-131
CONVAIR
ANALYSIS
PREPAR£D BY
PAGE
Hauser and (".erkin
REPORT NO.
CHECKED BY
MODEL
REVISED BY
DATE
1'WO CYCLW DAD OILY CARD ROOTIII
IC 005-1
?JI h91
All
3-9-56
lC005
!'his new carel routine operates on a two eycle buis, laking B>re
un of the card cycle time than the preY'1oue rout1ne. Aa a
man)" as forty flel4a -'ybe react from each card v1thout
causing any t1a1ng difticultle.. In ..s41tlon, thi8 new routine requires
1... IS· apace than the tor.r rea4 routine.
ef~ic1ent
J;"eault, U
'1'vo baalc operatIoD8 are perfomad 1>7 this routine during the 18poiJ1t card cycl.e. The n.ret tlve pointe (about 1-.0
are used to
deeo4e the control word and to perform the tiDal· conversion of lDtor.t1on
read during the prev10W1 reM cycle. 'fhe rea1DC1.w ot the eed cycle i .
UH4 to read ~orMtlOD f'raD the preeent card aD! convert thia intonation into b1Dar7 cocled 4ecbal tora. '!'he biDary coded 4ecu.l
1n1'oration is then eormtrte4 to b1Dar7 and .eal.ed during the f'irat part
ot the next eard qcle ~ ThU8, although lt takes two card cycl•• to
eoapl.ete the operation ot rea41ng &DB. converting, the net effect is
cODYeralon of ODe eard each card cycle.
_>
A t1ae ot U alch . . 11t. _ ay be uae4 tor c~tat10n between
rererenc•• to the read routine without eauaing the bull to 8klp a cycle.
The read routIne·.ay' be ueed to perf01"ll any cOJlbination of the
i"ollav1Dgopentlona aecor41Dg to the cODtent. of a control word.
1. Pick (PriM) a read
2.
3.
card
Pick (Prs..) a punch card
Pick a read card and read
The conversion operation i. auto..tic aDd 18 always pe~0r.4
during the ear4 eycle occurring With the DGt use of the read routine.
Th1. card routine require. the following iDronatIon:
1. BiDary aeal1ug
2.
Dec1Jal acal J ng
3. toeationa of fielda on the card.
tom
'!'bl. lntoration 1. eupp11ed to the card routIne in a 8tan4ard
called • ~ word. One ~ter word 1. required for eaeh
card :t1.e14.
A f1eld conal.ta of a mDiber ot consecutIve card COllBlS. !'he
last CollSl or a field 1. reeerved for the slgn of the 4eet.l maber
stored 111 that nel.d. An 11-pun9h signifie. a negative DUIIlber, no
punch (blank colu.) 81gn1t1e. a pos1tlve nuaber. A combination 12,
, aDd 8 punCh in one col\DID -.y be UHd to repre..nt a dee1JBl point.
nelda need not be adJaeent--there may be urmaed columna, punched
or unpunehed, betwen tbem--nor need they be alike in 81se.
9-173
CON
ANALYSIS
PREPAR£D BY
Hauser and Gerkin
V
A
CV-131
R
PAGE
REPORT NO.
'a.N '''fe·,l
CHECKED BY
MODEL
REVISED BY
DATE
Ie
OO~-2
Z)!' L91
All
3-9-56
&s
Entry to
tollon.
(1')
a-
('1'0 read routine)
(y+1)
AB
OPPP.P
camD
(Control word)
(y ... 2)
BI
uuuuu
vvvvv
(next instruction)
0aIBm repreaents the beg1nning addre8S (BS operating a4dreaa)
or the card routine. '!'he control word 18 described below.
'!'he '" coaand recorda in 0DDaD. the address or the control lIOrcl.
!he routine 18 then entered at 0uIIIam. Arter :fin18hing 1ts operation,
the card rout1ne ex1 te to y ... 2, the 11ae follOW1ng the control word.
Control Word Coalpo.1t10D s
Pint octal dig1t, control. picking ot carda in either
channel ot the bull reproducer.
As
AaO Do not pick
A4 Pick read. card
A.e Pick puneh card
A-, Piek both rea4 and punch
Second octal 41g1t, controls the re&41ng operatIon.
81
BSI()
Do not read.
B-1 Read a eard
opppp
BS Addre.. ot the first paraMter word.
CIlDDD
18 Addre•• where the n\Dllber from the first card field i.
td •
iWiid.
OPPPP and ODDDD are required only it conversion 1s being performed. during the card. cycle.
One parameter word i8 required for each card :r1e14. Parameter
words 1IU8t be stored consecutively beginning at &4dreas OPPPP.
lfumbers read from the card are .tored consecutIvely begInntngat
addreal ODDDD.
.
Parameter WOrd ComposItIon:
FF
FPs
sa
BB
Il,
RR
zz
FlAg tor fInal parameter word
"-71 (octal) for final parameter word
W=OO otherwise
sa.
Binary 8ca11~ factor (nuDlber ot bits to the right of the
bInary poInt) of converted number.
138
lumber of' blank or \lJ1\lM4 card colu.l. to the lett of the
field.
PO .... , . , . - "
9-174
CV-131
CONVAIR
ANALYSIS
PREPAR£O BY
PAGE
REPORT NO.
Hauser and Gerkin
CHECKED BY
MODEL
DATE
3-Q-56
REVISED BY
LL t
Ie 005-3
ZV LL91
All
lumber ot colu.na (d1gIt poattI0D8) to the len; of the
4ec1lB1. point.
RR:
IuJiber of reaa1n1ng C01UB28 in the field, exclusIve of algn
(D\1IIber of 4ee1a1 digits to the rIght of the dect.a1 point
plus ODe for the 4ec1lBl point).
RRaOO 1Dd1catea no aee1aa1 fraCtion aDd no .a.e-1a1 po1nt.
ZZs lot ued.
Range of
~ra:
Octal
Dec1a1
as
as (. ~3
~
'5
00 ~
00 ~ BB ~
63
OO~BB~17
00 ~ IL ~ 10
OO~U.~12
OO$RR~11
00 ~ RR ~ 13
O1~LL+RR'l1
01
00 ,
~ 11, ..
RR ,13
ReadtDg takes place at the eee0n4 card atatton in the rea! channel-N84 card. a18t be a4vanee4 bef'ore rea41Dg take. place. '1'h1a laY be
done JBDUal.l.7, or -.y be clone .. f'ollowa:
ODe
37
c.-
0-
(to card routine)
10
00000
00000
(pIck read card)
The cud ~uet a4vuc~_ Y1ll. not teed turther UDle•• another order
to pick a out. 1. glftD-both pick 1IP4 rM4 ordara auat be given to
read this card.
It ahoul4 be noted that once a card enters eIther the read or punch
cbaDDel it CODt1mlee to advance OM card station each tt.. the Bul1
Reproclueer 1. cycled.
~ ~cmBtlon r..a. rro. the eard i . atond vith1D the card
routine 1D coa.t 4ec1lBl tom. ~, 1f' the aubrout1De Ie 4e8tro7e4
betwen earct C7C1.., thi. i~onatlOD w11l not be convertecl on the
following carel c1'Cle.
U.. of the read routine cauae. the aiI.1 Reproducer to -go through one
card cycle J If • •eri.. of carda 1. tOM real, there awJt be a reference
to the read. routine for -.ch card.
9-115
CV-131
CONVAIR
ANALYSIS
PREPARtD BY
HaUler
and
Gerlda
PAGE
CHECKED BY
REVISED BY
Ex_ple of coding uaed to read a .tack ot
,.,
10
,.,
,.,
11
,.,
11
11
a.- a 00000
00000 Pick carel
a.a.
a...
00000
00000
D
10 005~
fwtODEL
Dr 491
All
DATE
~-9-56
REPORT NO.
SAN DlfGO
carda.
11
Pick card 2, .read card 1
a...
a...
OPPPP
ODDDJ) Pick eard "
read card 2, CODV. card
1
a... a.OPPPP
ODDDD Pick card It.,
red card "
CODY. card 2
•
•
•
,.,
•
0.-
U
a-
OPPPP
ODDDD Pick card Dt1, read. card
Y1
a... a..a
00
OPPPP
•
ODDDD CoIlftrt card.
11,
con.... card n-1
Il
In C_ 0'1 a· card machi_ tailure or aD accidelltal atop ill the
or • caret cycle, the current card My be reread. I repoa1 tlOD the
0 . . . ., _t (PAI:)-OOOOO, ad start 110,.
aiMle
!hi, rout1ae 1e coded ill ataD4ard 'lora.
All coutaata are CODtaiDe4 by the rout1De.
Jlaber 0'1 vorU •
Uaed by the rout1ae I
usea by tapor&r1ea I
Por . . . . .lya341tication
-
Ueed tor
.....
-
CODetaDta •
Forty t1el48
I
1-.
0'
I
o
o
routlM.
0'
.....
I
My
1
• ( 116
• (12) 0
(1Jt.1~•• (97)10
( 2 ' ) . (19) 10
•
M
.....
(1OJ. ,
(1Ja. )
10
be read trca • card •
ccaput1D1 tiM afttlable between reterenee. to the .card
t-
~
,"0."
I.'.-~
9-176
CV-131
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
30~CO
C()~'TqOL
71 01142
1001
15 ?OOOO 01061
STC~F
DA~Au~T~q
1082
16 70000
~~116
~,T(,r.,:
nAT:"
1003
55 20000 oonn3
C0 ~.J T P() L
1004
31 01163 00001
BULL COD~ • ?-z ~ (f\J
100~
5/ 01156
20~OO
1006
~2
'-OO~0
00~Ol
(A )
1007
55
1~00~
00~~~
(f) )
1010
46
0,0l~
0'~'~
r.-rA'" ?
1011
~7
on00~
'00~r.
~TAP"
1012
37 01012 0]013
CO~~Vr:P$ IO~,~
1013
37 01013 01014
P E' .A f')
1014
31 0100n
nnr.o~
:n 141
01016
1016
00 00000
000n~
1017
32 01142 00000'
ADD REf\f) CODr:
1020
37 01013 01011
SET TO RE,l\,1)
1021
36 20000 01176
~TCRF.
1022
75 10011 010/4
CL':"AI;!
1023
11 20000 01164
1024
16 01140 00000
SET qERUN
1025
1026
16
Q~DrGrT
76 00000 01016
1027
76
100C~
10~0n
1030
76 10000
n~177
1031
37 01031 01032
LA,S i
lO~2
11 01136 01042
PR~SFT
1033
11 01156 b117~
SFT
1034
31 0114J 00011
T"!nr:X
~
~ F NT JNF.: l ---+ (A L
10~5
32 20000 00003
~ L4J (A R)
1036
44 01031 01040
BIT TN THIS
1037
32 01176 00000
YES: ADD-DIGIT
·35
~1034
01176
Ie 005-5
Z!.I 491
MUDEL
All
DAlE
3-20-56
-.L
'd('oD ~l~,
1000
1015
PAGE
REPORT
W0~~
I·:n.,,.,
~..' 0 I? D
--.,- (" ')
('vrLF
CA~;,
5WTT(J..I
q-.r I T (' H
~xrT
~o~,.'
:3
\"O~D
0
~ATRIX
REft,D
ONF
POW
RO\~ S\o! I TCH<
~ATRTX
~T0~~
=
)
• S L 3 (A a.J
COLU~1N
?
9-177
CV-131
CONYAIR - DIYISION OF GENERAL DYNAMICS CORP.
PAGE
REPORT
MODEL
DATE
SAN DIEGO, CALIFORNIA
Ie
oo~
Z11491-z
All
3-20-56
CARO REA!) ROUT I ~!~
1040
46 01041 01035
REACHE~
1041
31 20000
R~MOVf:
1042
1043
00 000('0 oo~oo
21 01042 01161
41 01175 01034
104 6
~
&
0
~
t-
~
~,A. Tq
STEP
ROW
',"O~D
I X STORE
EXHAU'STED
ORD~~
?
1053
41 01176 01026
DIGIT-l..r"'J!GIT. R(PFAT
1054
31 01052 01025
STORE _9'$ FOR-S IGNS
1055
37 01031 01026
R~AD
1056
37 01012 01014
SET
10'57
PRF5TOP.E
1060
15 01136 01126
37 01121 010~1
1061
55 3000n 00000
PAR.AJ·4ETE? 'NORD l--.-(a)
1'062
44 01063 01('64
LA~T
106~
16 01012 01121
SET
1064
1065
55 10000 00013
SLn
51 01157 20000
SET
1051
rl
I
AOD TO MAT~tX WORt')
1052
1050
"-
I ~Jr:L
5':'1 TCH
1047
rl
~~NT
31 01045 01046
55 01177 00000
'37 01045 01033
55 01016 00034
37 010'45 01034
37 01052 01053
1045
1046
........
0(')(')(\("
?
~FNT!N~L
1066
1067
1070
1(\71
1072
101!
1014
1015
1076
1077
POW
'."()~D
BCD Y·NF'O. -f-MATPTX
RO\·! t'/ORD 3 -..(0)
~Cfj
JN~O -+M~.tRTX
S\.<
0..
A·.t
.
. l('l~-l~ ~('IUND r ~!G
.~.!)D
~ ~~-l
.,S
•
.
51 01163 20000
<;IG~~
rIG! T
1114
IJ. 7
o",~
~Tr,N
~H-r;hT!V~
1115
13 01077 01077
11 01077 30000
YES: -N
~.~VI\N(~
1120
21 0106' 0116()
21 01116 01142
1121
45 00000 111:>1
11~2
16 011j7 O'1~O
1123
41 01176 011?7
11 01163 011·76
YES:
21 01126 01160
~TEP
TRf\NSFFR r-.! F\\'
1121
11 3000() 01164
55 01164 0000 4
ll~O
~7
"'11?'" n11-<.\1
31 01175 oooo~
~\."
1131
1132
32 0]175 00001
0"'"
~(")
3
1113
STO~E
•
TE~~·'
T~R~/
ROUNDING
37 01130 011?3
0'
I
3-20-56
PFMA!N!NG rrpM5
Ill?
1125
1126
All
DATE
I ~~~ L POP'T
STORE "!
2
. ,
SH!FT 5IGN
1124
--
"('1('\1"'11'1
I")~r
73 01077 01077
1117
MODEL
T':P~S
L
1111
O"lt:.
ZY.-1
r'T('fT5
~
41 0Il77 nl1''3
37 01130 Ol105
t"'l~17C.
IC 005-1
491- z
REPORT
P. t:" ,1\ r"l q('\UT T~.' f-
111"1",
1116
......
M
......
PAGE
~('j)
?
-f-N
RE~ULT
"
A.DVANCE D
M6T~JX
J:"~~~ ..a.U~Tt"f"
\>/"qr,
R~ Sf.T
?
Plr;rx
TPAN~FJ:P
MATQTX WQ'?I")
SHIFT TO NFXT O[c. DIGfT
4~.·
YT(""H
-+(A)
1 ("IN --..(A)
, O~I °LU~ "y(;yT --t-N
113~
5? O116?
1154
45 000"0 31114
CONVEP~
1135
1136
1.1 0114? 01077
PR~SET
35 01164 rp 1 tt~
P~F:SET
1137
(')0 00(')00 01100
I("\\!
~xrT
9-179
cv-
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SA"'4 DIEGO
CALIFORr-..IA
131
PAGE
REPORT
'MODEL
DATE
CAPr')
R~AfI
~OUT
nl('"1(,\n
!,,'1
1141
54 00000 00000
MODIFv
1142
1143
00 00000 00001
1
00 00000 00001
TABLE
1144
no
1145
CO 00000 00144
1146
00 00000 01750
1147
00 000(,)1"
~~42n
11'50
00 00003
0~~4()
1151
C)('l
1152
00 00461
115'3
00 05753 611400
1154
00 7346')
1155
11 24027 62000
1156
no oooon
!"'l('l(H"3
j
l1r;7
00 OOOf)0
t)0~77
~XTRACTOt?
1160
("0
ooonl
('l(jl'\f"('1
I.'
1161
00 00001 0()O n~.
1162
CO....,M.ANO
(1000f' n('ln12
000'36
140
PO'.·JER~
o~
TFN
1 1. 00
l~?nf)
Io!
Ciooo
/\I")V"~J(F.
.JI
ANn v- al)VANCF
00 OOOCO 00('17
lJ.
PIT r:XTPA(Tf')Q
1163
00 00000 ,)()OlO
8
1161~
00 OOO(lO Oa00n
~ATPTx
1165
(')0 00001"1
0('11'1(':0
,
1166
1"'0
o~nOil
onon,.,
'3
I
1167
()O
rotio'"
00rnil)
4
0'
111('\
"0 (')nf'lnn
('1,,('\,.,,'1
~
t-
1171
00 00000 O(iOC'O
6
1172
00 00000
00';1)('1
7
1173
("0 00000
O(,)~00
A
1174
00 0OO0()
o('loor
q
1175
()(l
00()n0 O()(,(,()
INDEx
1176
00 0OO0() O('l(iOO
DIGIT
1177
00
1"""1
(;ij
-1"""1
I
0'
0
0
'
1,,'O?n
1
1"""1
><
0..
oo()()n
00" I') f'I
ROI:!
I,•• '(')~""
OO~~
3-2C-56
I ~,~
1140
OAI')('\~
Ie
ZM LS1-z
All
'9-180
CONVAIR
ANAl.VSIS
PREPAR£D BV
PAGE
REPORT NO.
SAN DIEGO
MODEL
CHI!CKED BV
DATE
REVISEoIIv
~ OP SDIIL'1'AIIOO8 tlWAR BClJmOE
Dr !II
.iiUI 0.,
CDP1'
PARr I • III!II>IJUt'i'IO.
'!b18 PJ'08l- 1e appl10able to
fOnl
8)'8t.e ot • ..-t10118 111
+4,~ Xa. T •
+tJ.~2.. X" f
•
• •
all X,
tlal
1)
•
Xa.
D lIIlkDoaa of the
• + L2,1'11 X,.,:d, "",
#
+ a2..~X'"
.. = 4a
fI
•
n"fi
•
•
!b1. rods.. -.1078 the tloattDg po1Dt tw~ JaIIber repreHDtatloa
... the COI',"poacISIil Ar1~lc PM"'- CAOO1.
PARr II - AlALYSIS
III .a41tlOD to the
81'" ( • ..,-,ted) _trtx
all t:l., ~
a 3.1 a.1. J.
2)
•
anI
the ..tbo4
3)
~
•
-..
•
•
•
4n; ~
•
•
•
the tot_tloa of _
all
a,~
•
· •
430.1
4, a. z.
•
•
. ..
[M]
4.., n+1
•
t:tz.
•
If,
fl
4"" ~"'I
aa111u7 .tr1x
41 ~~ 1-1
aJ..
.
nI-l
ani.. /l,.,...
•
• ll"" n. 1-1
1dd.ell 18 . . . 1a I lD1 ..t1lll tbe eollltiou
X, -' X~
•
•
•
X)V
4)
5)
~ a'lie xk
- Jc'all-I
-'-,
Xl . -- tt·
l n~1
J
i = I~
:l.j •
•
.~
'1L
'J
. . . . . . 1Ibteb 1tJa4 to ~) ..t
are a•• srlbe4 1Ja a.tail 1D HCtloa 011
..u..4 of ~ 1a tbe oba)Ur _ at.ltaMoaa lfDMr ..-tloa 18
rr1ea1
lIT 1II.lM.
!•
0Ilnl..
)IrO'*"'".
!be 1Ol1It1GM aN LIpto.... 117 • NOlINi"
Sappoee the
ao1atlau tin, oMalMl b7 •• of 5) ... 4eaote4 b7·Xi. !beD ~ftecI
q8'Ma
9-:-181
CV-132
CONVAIR
ANALYSIS
.. REPAR£D BV
PAGE
REPORT NO .
SAN DIEGO
MODEL
CHECKED BV
REVISED BV
DATE
all
• + a , ,,, X. ;;,. t2, 1111 - /;,a'It"XI(
• • + d a.n. x.. :w4A 111-1- t.fZ~1( o~
•
• •
• •
•
~ t-d.lz..Xz. I- •
4..,
X, +AI-a.
. .. t
•
•
18 eo1ft1 to obta1a •
x~
nnt
·
8ft
et eon ..'lOM
'X, •
...... ..a.n.t.,...
d
('" .f.'Xk:)
a" X, -+ tt.,& Xa. + • .. • +t:t,,., x'" =d, ,,#, -EoJ IJc I(
II.~ 1.,. ~ da:... Xa. f- •. • ..,. 4~& x,... =da. ",., I - ~~... (Ox. tc .. ' KIC)
II.
•
•
•
•
••
••••
4.&J.L_.t-.4.n..& .b +. _.!_ .. ..~ .. -.~.tt1,,~.-x,.~L "'#1 -- &, 4~_~:~ x.)
... eel'N4 to oMa1a . . . . . . . . of 8OI1MU_ oX(. . . . the rl&1r'
? . (~) ottlle..a.n.t.,.... . . . ~ oloMto
lIII'0, t:be ftM1 aol1It1~ . . . obtatMCl 'b7 eMs . . tile ooneotloaa to ex,.
1Id.. JI'OtP- ~ ror ftft . . . . . . . .u . . . t tittw..,. b.7' .nt1Jal
•
-
.'
. . . . OJl'IMe cU.ttc ILII l ....ttaa
1DIa ~.
par IU - P.maIIIIDlt
1.
a.
...........
PI 1oeI8 the ~, . . . . .
All ~
AD.att
care re.t,
...u. 18
are n.4 oato tile ar..
or __
,. !be carda
".
PIIXIIAII 8!IPS
rr. tlMt
,. !be ala Nllt1lle
«IUd n.I
oato
tH.....
atoN4 a. tbe drta.
ou4 l...t ~ 1. . ._tel at (p.)
...a arl~e
6. '!be -.-tatlO1l o~ ~)
Car&
=,,.,.
paokap aN JIM4 1Dto IS.
-.ru.
7. PNlal.a..sa aa4 1. . . lIP to bec1a tIIte ..l1at1_ of aaother
Qnea of . . . .IOM.
. ..._...a:
I.vr
It 18 to cat:a1a ~ • (tbe IIUIIINr o~ row of tbe
Cl~.nrta) I'u aMI 1a 0QlJ
aat 6 With .......la1Dg oo~ blak•
• ( ..t11f.N4 __ I~) 18 ........
7'
Data out& Gl.... ..vtx 18 ........ __ . . . With a ..., car4 to 1IIeCID Il80h
( . . . . . . . ., 1dd.oh are . . . to t1U . . . . . . 1a beplJtI wlth tbe aboft
"FI lTD, an 6tlnII after .....-1a.) RIfR to I~
....
waw
!be t1Da1 eolatl. . AlII 'bU
..... - - ts.
,.0. . . . . . . - "
CI
adel.
ueoaatel
IIIdW.r to I~.
Itt:fla ani I I are puaehec1 1a
9-182
CV-132
CONVAIR
ANALYSIS
..REPAR£D BY
~11IAIJ8BR
C~ECKED BY
VAaL
~AN
PAGE
REPORT NO.
DIEGO
MODEL
REVISED BY
DATE
,. ..tart
1. Plaoe 1DJu' ORU 1D t...a
2.
Pr 1a.I JII'OSI-'
...
n..1 nop •
•
1
•
2
•
,
hower,
S 00,.'
211 ~
ALL
,j.!o~
blak ..... 1a pmoh bofie.
(1tGOOo) •
lIbr.....,... jWjJO'.'
Jbr.....,
,.,iD •••
'lo.top ~ after -.oil
.tr!x 11 • q atel.
row
or ~
em=f 1 'R7
0.. •• ;
1. AD - "
f'0tIII , ••• - "
9-183
CV-132
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CAL.IFORNIA
CROUT
PAGE
eN
75 31777 71222
STORE CAR.D INPUT qT.
11221
11 00001
71222
75 31777 71224
71223
11 71230 00001
71224
11
71225
45 00000 00300
TRANSFER CARn INPUT RT ..
TO ES
S~T FOR NF-XT Mft,TRtX RFft~
JUMP TO ~EAD ~ft,TprX
71226
45 00000 71222
PRESET
712~O
40000
STO~A(ir:
77250
00100
09 00000
~(iOOO
.L
77251
00101
00 00000
(lO00()
n
77252
77253
0010:?
00 000110 0000n
00103
00 00000 00000
(30000
( 3D 0 00
n +- 2) • 2 t 5
+ ~ n ) • 2 JS
"*" .2
00 00000 00000
7725!>
00105
00 00000 (\0000
( 2. n ( t' - 1 )
77256
no on 0 (")0
ncno~
BLAH t(
77257
"0106
00107
00 00000
nooco
k'
772f:.O
00110
no onODO
,H.,O Ii I"
K
77261
00111
('\0 00000 00000
17262
liOl12
00 Ol')ono f'lf'lQon
Ll
L2.
7726~
00113
00 00000 ('H"Ionn
n
77264
00114
00 00000 00000
2.n
7726'3
00115
00 00000 00000
2.
77266
00116
on
77267
00117
00 00000 00000
I
77210
00120
00
0'
77271
001?1
00 OOtJoh O('Of'lO
17272
00122
00 00000
O~(lO(i
77273
00123
00 00000
() (Hi () ()
2:11-+:<"-
77274
0Ol?4
00
OO()~O
000('l(,!
BLAH K
77275
00125
00 00000
O(\O()()
('h-~)
77276
00126
00 00000 00000
( n -1 )
I
0'
0
0
...-4
t-
><
c..
3-20-56
START-) .
00104
-
All
DA TE
45 00000 712?O
77254
C"')
...-4
MODEL
005
j
C'\I
z. 491
40000
71220
71?~6
CI 00,...
REPORT
00000 rH')or;n
onore noroo
+2
i- 1J
• .2
'5
"I:N 0 E:.)(
tS
n • 2
(2j-l)6Z'5
15
(Zh+l) #2-
l rys1
5 n (f n/rl ~ I
2N/n • 2'5
) :::
N
INDEX
9-184
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN r).EGO
CV-132
PAGE
C,""IFORNIA
REPORT
MODEL
DATE
Cll 005.$
ZK 491
All
3-20-56
(I?nUT
C"J
~
~
77277
00127
00 OCO(')O ()OOOr)
77100
00130
('0
O()()()~
0(')f1n~
77301
00131
00 oa<"'('o
rOooo
773'12
00132
0(') Of'l()()O 00000
17~0'3
00133
(10
77304
00134
00 00000 00000
77305
00135
00 00000 00000
77306
00136
no
77307
00137
11 01577
77310
00140
n() (\(H')('\? f'\t"O('t"
77311
00141
("10 ~OOOO ('l00(H',
77312
00142
11 40000 01600
77313
00143
il
77314
00144
7731f5
0014'5
77316
00146
11 0JS'17 0011\
11 OlC,"17 OOO'~
11 013'17 000/7
77317
n0147
on
77320
bOl130
11 00111 01577
77321
00151
11 01.577 OOC27
7732?
00 1~· 2
11 0160()
77323
00153
11 56')77 01600
773?4
001'34
11 00111
Ol~77
77325
nOl5?
00
()"ono
"12(jf)
7732A
00156
11 01377 0OO2C)
77327
(lOIS7
1 J 01 '<'7
('t()0?7
77330
00160
75 30~30
77",32
77331
00161
11
77?c..(J
OOlon
17332
00162
7C-,
3()('l~0
00164
17~33
('j016~
77334
00164
11 77(')40 oo~"n
75 30J05 00166
77335
00165
11 77175 nICOO
77336
00166
11 00140 70000
'-"
I
'"
'"t-......
I
0
0
><=
0..
OoC'()O
~('00~
OO()OO ('10000
P~~S~T'S
OOO,~
56077 01400
(H'H') 00 1"'!f"!j44
C,f:,()77
r
R'") ~.J'!" ~~ E ----fJ- F ~
r:"ERGENCY
ARITHMF:TIC
PUN('~-0UT
DACKA.GI="
--+- f!' ~
~[S
SET
9-185
CV-132
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
PAGE
REPORT
MODEL
DATE
SAN DIEGO. CALIFORNIA.':)
a. 005-'
Ell 491
All
3-20-56
CROUT
71~~7
00167
7'
00140 00101
77340
00170
~5
O()141 200<'0
77341
00],,71
15 20000 00214
77342
00172
15 20000 00216
77'43
0017:3
71 00101 00224
77344
00174
11 20000 00010
77~45
0011')
11 0('1'11
77346
00176
7~
77'347
00171
001.24 '0000
35 00074 ?OOOO
17~50
00200
71
77~51
00201
77352
00202
71353
00203
11 ?OOOO 0Ol~1
31 00121 00020
73 00101 0012?
77'354
00204
71 00041 00101
77355
00205
35 00041 00123
77356
00206
11 00101 20000
77357
00207
36 00041 00125
INDEX
77360
00210
11 00122 20000
PRESETS
77361
00211
35 00215 0021'5
77362
00212
11 00123 20000
. TO DELFTF
EXTRA
77363
00213
35 00?17 00217
7E~O~
ROW
TRANSFERS
,oonn
COMPUTF. N
2nooo 00"1"
NUM8ER OF (EllS PEQ ROW
INCLUDING
r:XT~A
NUMBEq OF CEllS PER ROW
FO~
~ATRIX
TRANSFER RO\-J OF
77364
00214
15 00000 00216
N
~
77365
00215
11 40001 01600
'-"
I
17366
00216
75 00000 00220
77367
00217
11 01600 40001
.....
77370
00220
2J 00215
n()12~
><
c..
77371
00221
21 OO?!7
0012~
77372
00222
41 00125 OO?14
All
7737'3
00223
56 10000 00227
YES! T/IX E 227
77374
00224
00
ooore oooar;
77'375
00225
no
O()I"lI"l()
n~r('\~
~L A~ll(
77376
00226
00 00(')00 00000
BLANK
.-..
.....
0'
I
0
0
0'
t-
Z:=-q~S
l¥'] TR A~ISFr:Q
[r.~]
T0 FS
TRANSFER ROW OF [r·1 ] TO DRUf-.1
EXTRA ZEROS [)~LF.T~n
STF.:P u A"ORE~~
5T~P V ADDRFS~
~O"!5
T R A ~~ 5 F J:' n q ~t"\? ~,l(j: hlrrUPN
5
q-l86
CONVAIR -
CV-132
DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNI."
P AGE
ZM 491
All
DATE
3-20-56
CRnUT
77377
71400
00227
77401
00231
("10232
17402
77403
77404
71405
77406
..-t
---aI
I
0
0
a..-t
t-
><
0..
00233
00234
00235
75 10200 00231
11 00040 76500
CLEAR AN5't,'!:R 5TORAGE
16 00623 0051-3
SET
71 OOlOl 00041
11 20000 00114
31 00114 00017
CLEAR
11 20000 00115
~WJTCH
11 00115 20000
774"7
0023 7
~~
77410
00240
75 17777 00242
77411
77412
00241
00242
11 00040 ~6100
11 00074 00100
SET ROW
71413
00243
11 on117 20000
SET
77414
00244
35 on073 20000
71415
77416
77417
0024';
~5
00246
00247
11 00115 20000
35 00141 00103
77420
007.50
00251
OO?';,
15 0('10' 1"(,)?6t;
1t; ('If\1ti' '"'0276
1 ~. r.0'()~ 004"
77423
77424
77425
0025~
15 0010'- (\(')46 ?
16 00147 00316
11 00C74 00104
77426
77427
00256
00254
00255
0" () "13
~Oll7
fl.1.d TR
IX
S"(jQAG~
INDEX
TO
00141 0010i'
TRAN.C;F~R
RO\4
ANn
C'OlUMN
TO
e~
SET SWITCH
SET
COLU~1N
00257
""1 00.100 00140
36 00140 20000
PRESET
00260
71 ?OOOO 00101
DRUM
00261
36 00073 20000
77432
77433
00262
0026:3
12 00140 00100
11 20000 00105
77434
00264
!5 00142 00266
77435
77436
00265
75 00000 00267
00266
00 00000 00000
77430
77431
III
[M )
00236
77421
774/,2
C\I
CIJ
00230
ON 005..'
MODEL
REPORT
ta,
INDEX
ADD~~5~
OF
ROW
ROW
OF (M] TO ES
TRAN5FE~
9-181
SAN OIEGO CALII'ORNIA
REPORT
el 005-8
ZM 491
MODEL
All
DATE
3-20-56
PAGE
c~nUT
77437
00267
56 10000 00270
77440
""0270
11 00104 20000
77441
00271
36 00074 20000
PRt:SET
71442
00272
71 20000 00101
DRUM
77443
00273
71 20000 00140
77444
00214
~5
0OO7~
'0000
77445
00275
~5
0014~
00')77
77446
00216
75 00000 00'300
TRAN<;F'E~
77447
00277
00 00000 00000
OF [M)
77450
00300
56 20000
77451
00301
11 00100 20000
77452
00302
4? on1.04 (\0306
77453
00303
11 00104 2000n
77454
003: 04
36 00074 00107
77455
OO~05
77456
00306
45 00000 00307
36 00074 00107
77457
0~3(,)7
ADDRESS
OF'
COLUMN
COLUMN
TO ES
(')(l3(l1
ELEMENT TO RIGHT OF D I AGONAL. {
YES: TAKE ~O6
NO: SET KI
YES: SET KI
=
77460
00310
11 O(,)("l74 ('\011"
71 00104 00140
77461
00311
!6 001173
77462
00:312
35 C'!(')144 00'31.
7746?
()O~l~
75
77464
00314
00 00000 00000
77465
00315
11 00107
?noon
71466
00316
42 on110
~C()OO
77467
00317
71 00110 00140
77470
00320
36 00073 20.00('1
77411
00321
35 00145 00321,
5,...
77472
00322
75 30002 003?.4
-t
77413
00323
00
ooono ('Inroo
a. i K. -....-
77474
00324
71 00110 00140
TRANSFER
77475
00325
36
77476
00326
35 00146 OO~'O
""\J
I'j
-4
~O(H'?
,....
I
-><
lo4
orH'~
7
1
K
TRANSFER
20()O0,.
F'L F'~t:~·1 T
(1J:'
[v]
C'031~
..,;
I
~r"
(~
INTO (111, 112~
K : K'
PRESET
>
TAK!: ?44
~
it.,K~
317
ADDQESS OF
aLk
(2.5.2..6)
'3 20000
Q.,t< j
9<-18B
CV-132
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S .... N DIEGO. CALIFORNIA
REPORT
ell 005-S
2M 1~91
MODEL
All
DATE
3-20-56
PAGE
cqnUT
77477
00327
75 3000:>
003~1
77500
00330
00
onooo
0('000
77501
00331
37 01001 01003
77502
00332
13 000'),1 0002 7
77503
00333
11 00012 00030
77504
77505
00334
11 00111
00335
17506
77507
00336
00337
77510
00340
771511
77512
00341
00342
11 OOll:? 00026
31 01001 C1OO?
11 00031 00111
11 000'32 n0112
21 OOllO 110074
45 00000 00315
77513
77514
77515
00343
00 00000
00344
J : L
00345
11 00100 20000
42 00104 00354
77516
00346
71 00104 OOD41
PR~5ET
77517
00347
36 00074 20000
77520
77521
00350
35 00150 00352
00351
75 30002
77522
00352
00 00000 00000
7752~
00:353
45 00000 00367
77524
00354
71 00100 00140
77525
00355
36 00073 20000
77526
00356
35 001S1 00360
--
77527
00357
75 30002 00361
0"-
77530
OO~60
00 00000
0
0
0"-
77531
00361
11 00111 00025
t-
775~2
00362
11 00112 00026
><
c..
7753~
00363
37 01001 01004
''''~~4
OO~64
1.1
77535
00365
17536
00366
11 00032 0011'
45 00000 00346
N
C"j
~
I
I
~
o(')o~,
OO(i"'~
noono
t NrO (27. 30)
PRODUCT OF ELEMENTS
(Lii --..... ( 25 • 2...6)
a.LJ.. - lii K. 2t k i. = L
~
- - . . (JI1J
1:1.2..)
STEP K
RETURN
SLAN$(
.
> TAKE
354
~ STORE
RESULT
E5
A!')f)RES<; FOR
[~] 5TO~AGE
~O:!t;3
OO()O~
oot'1
STORE RE~ULT
DIVIDE
BY
DJ AGON.AL
ELEMENT
OF [M]
STORF
Rf!~ULT
REiURN
9-189
CV-132
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIIII
PAGE
ex
REPORT
ZM
MODEL
All
DATE
3-20-56
005~10
491
c~nUT
11537
77540
-i3
-C\J
OO~67t;
11 00101 200(')("
77541
35 00074 20000
00371" 43 00104 00374
77542
00372
21 00104 00074
NO:
77543
00373
45 00000 00267
RETU~N
77544
00374
STORE
71545
0037t;
77546
00376
11 00101 OOll~
71 00100 00041
36 00074 20000
77547
00377
~S
001S' 00401
77550
(,)()40('l
15
~OOO2
t)04n2
77551
00401
00 00000
~oooo
77552
00402
21 00401 00114
77553
00403
21 00401 00140
77554
00404
41 00113 00400.
ROW STORED?
NO: TAKE 400
77555
00405
11 00101 ?OOOO
YES:
(A)
77556
00406
43 00100 00411
71557
00407
21 00100 00074
77560
00410
17561
00411
56 30000 00255
56 30000 00412
77562
00412
11 00101 00100
77563
00413
11 00101 20000
77564
00414
35 00074 00104
LAST ROW? YES:TAK~ 411
NO: sTEP ROW SELECTION
RETURN TO CO~PUTE NEXT f? ,.,,,,
YES: COMPUTE FINAL MATR I,X
SET UP
TO COMPUTE
FYNAl MATQIX
77565
00415
11 00101 00107
77566
00416
71 00101 00101
00370
77567
00417
54 20000 00020
J
77570
00420
35 00073 20000
......
77571
004?1
~')
><
c..
77572
00422
75 00000 00424-
77573
00423
00 OCtooO
onooo
77574
00424
11 00101
0011~
77575
00425
71 00100 0014C
77576
00426
36 00073 20000
I
0"-
0
0
0"-
t-
ROt· r
0014~
USED
Up!
YES: TAKE'
SET
'14
NEXT COL.
~L~MENT5
[M]
OF
ON
DRUM
STEP STORAGE
AD[)~ES5ES
n~
TRANSFfR
n + 1 Sf
004"
~FT
COL.
INTO ES
TFR TNOEX
TP.AN~~ER
LTH COL.
9-190
CV-132
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
REPORT
ON 005-1)
ZM 491
MODEL
All
DATE
3-20-56
PAGE
CROUT
C'\I
C"j
....-I
'-'
J
0"-
00421
35 00153 00431
rNTO
776':'0
00430
75 ?0(10?
(H)4~'
~y
77601
00 00000 COOOO
77602
00431
00432
21 00431 00115
STEP U ADDRESS
77603
0043~
21 00431 00041
5TC::P V ADDRESS
71604
00434
41 00113 00430
ROt~1 COMPLE TE? NO~TAKE
77605
00435-
11 00100 20000
YES:
776-06
00436
35 00074 00110
77607
00437
37
77610
00440
71 00100 00041
77611
()0441
36 00074 20000
77612
00442
~c:;
..1..-1
77613
00443
75 30002 00445
77614
00 00000 00000
77615
00444
004 /+5
77616
00446
47 00424 00447
LAST
Xi. COMPUTED ~ NO~TAKE 424
77617
00447
45 ('0000
YE~~
JAKE t;~4
77620
004'50
37 "'0440 70441
7762J
004-51
00 76c.OO
776'22
(i04~?
11 00074 ()O100
77623
00453
11 00074 00104
77624
00454
71 00100 (10140
77625
004'55
~6
77626
00456
71 20000 00101
77627
00457
72 00140 00100
17630
110460
:'6 0007'3 ?OOOO
OO~16
00310
00154 00444
SET
....-I
RO¥!5
4~O
tb
~TO~E
Xi
AT
E~
ADDRESS
23 00100 00074
005~4
Pt'NCH
AN<;W~~~
,noon
TRANc:t='FR
ROl\f
00140 20000
OF
J
0
0
0"-
ES
77577
[M J
0046~
t-
77631
()O4061
'::\~
><
c...
77632
00462
75 00000 00464
INTO
77633
00463
00 00000 (looon
ES
77634
00464
11 00040 00111
77635
00465
11 00040 00112
77636
00466
71 00140 00104
00142
ClEI.\R
STORAGE
TRANSFER
9-191
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-132
SAN DIEGO CALIFORNIA
CJf 005-j2"
PAGE
MODEL
Zlf 491
111
DATE
3-20-56
REPORT
C~OUT
17637
('H'l467
'6
77640
00470
35 00624 00472
77641
00471
75 30002 00473
77642
00472
77643
00473
00 00000 oceon
11 00116 20000
71644
00414
35 00157 00476
TRANSFER
ELFMENT OF
77645
004:75
75 30002 00477
(~1]
77646
004-76
1"10
of'rnn
("I!"OOO
77647
00471
37 01001
0100~
77650
00500
11 n0111 nOO25
CO~PUTE
77651
00501
11 00112 00026
NEW
77652
00502
11 00031 00027
VALUE
77653
00503
11 00032 0OO3f)
FOR
77654
00504
77655
00505
77656
OOt>06
17657
00507
01001 OIOO?
11 00031 (')0111
11 OOO'? OOll'
11 on101 ?oroo
77660
00510
43 00104
77661
00511
21 00104 00074
77662
00512
45 00000
71663
00513
11 00117 20000
77664
00514
35 00137 00516
77665
00515
75 30002 00517
77666
00516
00 00000 00000
71667
00517
13 00111 00027
0I
77670
00520
11 00112 0OO3p'
0
0
0-
77671
no!)::? 1
'37 01001 olCO::?
t-
7761'2
00S?2
75 30002
005~
><
~
71673
0052~
11
OOO~l
30()OO
OIFFF'RE"NCr:s !.IT
77674
00524
11 00101 20000
17675
00525
43 00100 00,531
71616
00;26
?1 00100 (\0074
ALL
ROWS FTNI~HFD?
NO: c:,TEP
,-.
C'I
(tj
.....
-I
.....
0OO7~
0('116
XI.
INTO
CELLS
('-~).
(')O4~6
IN TO
('7),
(~f')
~1UL T tPLY
THIS
~7
0051~
('6)
RO~!
STORE:
L
ROW FINISHED? VES:TAKt" 513
NO~ SET FOR NEXT ELEMENT
JUMP TO CO~·I T I ~lU~ ROW
YES:
TRAN~~Eq
R'1 SIDE
INTO (25) J (26)
COMPUTE
THE
nTFrF'R~~("~C;
STORE
120("1
V~S:TAK~
5~1
9-192
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
CV-132
PAGE
em
005-18
REPORT
Zy
491
MODEL
Ali \
DATE
3-20-56
C~OUT
STORAGE ADDRFS~E5
JUMP TO TRANSFER ROW
YES: PUNCH
DIFFERENCES
JUMP TO III OR TO FINAL STOP
PRESET TO STORE CORRE~TIONS
PRES~T TO PUNCH ANSWr:~S
PRE:5ET TO PUNCH nlrFE'~r:-NC~S
DUMMV
77617
00527
21
0052~
00041
77700
00530
45 00000
0045~
17701
00531
37 70440 70441
77702
00532
17703
00533
00 01200 30000
45 00000 00000
77704
00534
16 00155
77705
00535
16 00101 00451
11706
00536
16 00101
77107
005:37
45 00000 00540
77710
60540
11
77711
00541
36 00014 00126
77712
77713
00542
15 00617 00546
PRESET ADDRESS OF ANSWERS
00543
15 00621' 00550
71714
00544
16 00622 00553
77715
00545
75 30002 00547
PRESET AOORES~ OF=" COR~tCTtON~
PRESET TO STORE ANSWERS
COMPUTE
17716
00546
11 76500 OOO:? 5
77117
00547
75 30002 00551
77720
00550
11 01400 00027
77721
00551
~7
77722
00552
15 ;OOO?
77723
00553
11 00031 16t:;OO
5 TORE AN $\-JER
77724
00554
77725
00555
21 00546 00140
21 00550 00140
77726
00556
21 OOS53 00041
("'j
77727
00557
41 001?6 0054'5
I
71730
00560
45 00000 00450
77731
OO~61
57
()f1('to('
STEP ADDRf:SSES
TO COMPUTE
NEXT ANSWER
ALL ANSWERS COWDUTED1 NO:TA~~ 545
YES: JU~1P TO PUr'CH ANSWER5
F!nAL ~1'(1P
a......
7773?
00562
()01~1
TR,~,N<;F='ER
><
c..
77733
00563
"1 "filal
'31) ?0000
77734
00564
35 0("074 20000
77735
00565
35 00620 ("10567
77736
00566
75 30200 00570
,.....,
C\l
......
-a-I
0
0
t-
()~101
0052~
005~~
20000
01001 (')1002
oro()o
~ET
INDEX
CORRECTED
ANSWER
OI)S~4
2("1('00
I")rFFFRf='NC~S
TO
D~UM
9-193
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
ClAJ~2
SAN DIEGO CALIFORNIA
REPORT
01 005-~
ZI( 491
MODEL
All
DA TE
3-20-56
C~~UT
777~7
00567
77740
00570
11 01'00 ~6071
41 00614 00572
77741
00571
16
77742
00572
77743
77744
00573
.00514
75 30200 00514
11 01200 014·00
77745
O~613
OO,'~
INOEX FOR FINAL STOP
PRESET FtNAl STOP
TRANSFER COLUMN OF
DIFFERENCES INTO (1400)
SFT l' =1
00575
11 00074 00100
16 00147 OO!16
PRESET Ia
77746
00576
16 00617 00410
PRESET Il:b
77747
00'577
11 nnl01
17750
00600
35 00074 00104
77751
00601
11 00101
77752
00602
71 00100 00140
77153' 00603
36 00073 20000
77754
00604
35 00616 00606
77755
00605
75
77756
00606
11 56017 01600
77757
00607
21 00606 00041
77160
77761
00610
21 on606
00611
41 00113 00605
77762
00612
45 00000 00267
77763
0061~
77764
00614
4'5 00000 00561
00 00000 00003
77765
00615
00 ooooq.,OOOOO
ITERATIONS INDEX
BLANK
77766
00616
11 '16077 01600
PRI:5ETS
C\I
17767
00617
on
--
71770
00620
11 01200 56077
I
17171
00621
0"-
77172
00622
00 01400 00613
00 OOegO 76500
t-
77773
0062~
00 00000 00562
77774
00624
11 7(4"7 OOO?t;
77775
00625
75 00002 00016
77776
00626
17 00000 77565
('j
-t
I
a0
0
1'""4
><
0..
~OOO2
?nOnn
0011~
~F'T
TRANSFER
tND~)(
TRANSFER
TRANSP05F: OF
00607
DJFFF'RF.NC~S
tNTO (16nn •
OCll~
. .)
FINISHED TRANSF~~? NO:TAK~ 605
YES: BEGIN NEXT TTFRATTON
PR~~F:T
F'l !'-,I AL 5TOP
76500 00601
9-194
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-132
PAGE
ex 005-15
MODEL
ZII 491
All
DATE
3-20-56.
REPORT
C'pnUT
17777
(}O627
45 00000 00175
EMEP-GENCY PUNCH-nUT
77040
00630
37 70440 70441
11041
00631
00 01600 00244
77042
00632
C;6
77043
00633
37 70440 70441
11044
006~4
00 01400 00244
77045
00635
56 00000
71046
00636
77047
()O6~7
71 00101 00101
~5 00101 ?OOOO
77050
00640
45 00000 00641
77051
00641
16 20000
77052
00642
37 70440 70441
71053
0064~
00 4()OOl
oooon
77054
00644
56 00000
0064~
77055
00645
71 00101 00101
77056
~0646
~r;
77057
00647
45 009 00 00650
00000
ROW STORAGE
ti06~~
COLUMN
5TO~A(,;E
006~6
[M
1
C064~
DO'''l ?OOOO
[M1
.~
?COOO
77060
OO~50
1~
77061
00651
37 70440 70441
17062
00652
00 56100 !"'nooa
1706~
00653
56
006~'
ooooe ocooe
C'\l
C"J
~
'-'
I
a-I
77067
11 00102 20000
0
0
17070
73
r-
~
77071
~r:;
::<
77072
00074 20000
71 20000 00102
77073
71 20000 77"374-
77074
11 00102 77251
77015
11 20000 00102
77076
11 20000 00107
77077
45
a-
0..
77~74
5t:'T'
20000
UP
TO
READ
CARDS
("leono 003'-?
9-195
CV-133
CON
ANALYSIS
PREPAR£D BY
CHECKED BY
C. H. Richard.
D. B. Parker
V
~AN
A
R
PAGE
REPORT NO.
LdGCJ
MODEL
REVISED BY
DATE
CV014-1
Z)(
491
All
4-23-56
SQUARE Roar-FLOATItfO pom
(Single Preoiaion)
Given a sincle-precision floating point number, x: B.2P
c..-pute
(8ee CA 001).
-rx =fit · 2 ~:::' .-. 2P••
Initial States
(00031) = •
(00032):: P
Final State.
(00031):: ••
(00032)= p"
•• and P' are defined as follOWB.
It P i. eTen.
I'~.,
It P is octd.
W':
'or.ua usedl
'/2) P':: P t
1
Bewtone' Iteration
)' 1 :a x 1 ..,-
+ 1/2
(. t
!Xl- r' -
Firat approximation
= 235-1
Convercence i. a8.u.ed when A x
Spec1al t.atsl
P'.: p
~
X1 - i - )
(9-)
O.
It I : 0, set .": 0
• Bet 1ft ~ 9•
U It:: 9,
Alaral
It • is nepti...e.
Dna Addre...
77531 - 7156~ (25) 10:: (31)8
lIla1ber or ooaanda for a.sem'1y modification (21)10: (25)8
10 con8tanta or tempora1ie. usee.
Standard fora.
,.0 ... , . , . - "
9-196
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-l33
5""" DIEGO CALIFORNIA
PAGE
REPORT
MODEL
DATE
77537
(HOOD
37 760r'!r) 760('1,
.A.LA p~~
77540
77541
01001
45
f:XIT
01002
11 000'31
7754?
77543
f)100~
4(..
()0(H1("
'"'101"r)
B10011
?OOO~
?
f.! ~·~F~
47 01005 01001.
N;O
'-'1005
01006
17 0(,)()32 lO()"O
55 lO0na (\0043
p
EVEN
77546 ,01007
44 01n10 01nl?
p
21 00012 01n25
p
17550
01010
01011
nDn
+ 1
54 00031 ('0107
N/z
77551
(,lOl2
~5
oon41
D/?
77547
()0.()'32
77552
01013
43 01026 01001
77r;5~
01014
11 (:1(')'6
01015
F
01016
7'3
n10I7
77557, . 01020
54
77554
77555
77556
23
01021
1
Ol('l'~
00031 OelO4'?
01027'01030
OlO?7 00107
10000 01027
01027 010~O
,
,
~/()/:2
~
3?
(D')
-+ 3]
(~.l')
~
(D")
~
1"
= .,. c,;r
F
~
N : 9
-@
q ~ v.
"', -I
Y,N'~)
2.. ~ ''!Is)
~ ~
--- -7
Z.
t'
Xi. _/
X;,.-, ~
_~(N;;'_I
10:'0
J
-Xi.
o
77562
01023
11
2nnoo
00011
Xi
71563
01024
45 00000
nlool
JUMP TO rXIT
77564
01025
77565
77566
01026
00 OCOOO 00001
37 77777 ''77777
a
01027
&0
Xt -, t
77567
01030
~O ooono
~('\O(1QJ
:: A X@ -y
0
~x:
::
Q
,)
X(Xt -~ t-J'ihL-I)
<
Q
'-7/~;)7
21
01022 '.44 01015
00000 ooooQl
t.,
~
~AJd"'~;
7756n
77561
Ol02~
4-23-56
/Yo '"
£.
'Il,',
't ",.
.
r-)
fr-:
~
::
01004
77544
77545
ZII 491
All
fXIT
F.:t-'TRANCF.
rQn!"\4
CF014-2
,:l~.
.::. y.(~~
10).
7
-7 /CI S"
>.;-,
N" ~
~1
@)
1
.@
1/2X i _1
~%
<. Y.,:_,
t
x·
Co
..-.
('Ij
('Ij
f'""t
I
0"I
0
0
0"-
f'""t
t-
><
c..
9-197
CV-134
ANALYSIS
PAGE
PREPARED BY
CHECKED BV
c.
~ioharU
H.
D. B.
~AN
REPORT NO.
DIEGO
arJcer
MODEL
REVISED BY
DATE
CF013-1
ZJ(
491
All
4-23-56
CUBI ROOf-FLOATING POll!
(StnCle Precision)
Given a 8incle,""Preeis-ion floating point number;
cOBipute
~1 tial
X=
~b.
, X
State I
.:" /
p:L
.
..
•• -2;/.!:: I" .2~
(.ee CJ. 001) J
(00031) :: •
(00032)
'iDa1 St&te s
'-2P
~
p
( 00031) =r
( 00032.):: pi'
X' &lui p' are defined as 1'0110.. I
Divide p by
P.-.ula
Wle..
3. If re..inur· = 0 J
.' • ., Pt
$
P
It re-.inder :: 1 • •t,::
'1'+ ' • p'sp-t2
If remainder: 2. W':
1/2',
p'.:: pt 1
...-ton 'a IteratlO1l
1/3 (~~,
-XI.-, )
Firat approxUatioa 2 35 -1 (9),
xi C xlatf"
1-235 (-9),
ConTerpnce 18 a••uaed who . ' A x ~
Speoial testa.
.t>,
0
.'< 0
o.
It B:: 0, aet P.: 0
1
It llt:: 2 35- , aet ." :235-
-..
~
1
It It :: 1-235• set .".: 1-235
DrUID addre8S.
IUmber ot commands for assembly modificatiODs
10 oonatanta or temporaries used.
Standard fora.
Y-198
RW-135
cpo-o
THE
Pg. 1 of 8
RAM) -WOOLDRIDGE
CORPORATION
Los Angeles 45, California
Fixed Point Card Output Subroutine
Specifications
Identification Tag:
CPO-O
Type:
Subroutine
Subroutine Designation:
SUB 51641 21516 (uses 254 consecutive
cells when assembled)
Storage:
185 instructions, addresses
88800 thru 88899
88900 thru 88984
30 constants in program, addresses
88985 thru 88999
89000 thru 89014
215 words total program storage
Temporary storage used but not stored
in program. 254 consecutive cells
must be provided to assemble this
subroutine.
The constant pool and temporary storage
pool are used by this routine.
-
Program Entrance:
88802
Program Exit:
88801
Machine Time:
Card punch speed (see text)
MOde of Operation:
Fixed point
Coded by:
R. Summers
January,
Code Checked by:
R. Beach
February,
1956
Machine Checked by:
R. Beach
February,
1956
Approved by:
W. F. Bauer
March 26, 1956
I t:l
CIj
-.-t
I
C1'
I
g
C1'
1956
.-t
t-
><
0..
9-200
RW-135
CPO-O
Pg. 2 of 8
Description
This routine will output up to four fixed point numbers per card
punched.
These numbers are specified by parameter words contained in a list,
the location of which is given in the word following the RJ to this subroutine ..
This word specifies the first and last address of the parameter list.
For each output word a parameter word is required which has the
form:
xx uuuuu vvvvv
where
xx
specifies the binary exponent
uuuuu
gives the location of the output word
vvvvv
gives the address to be punched on the card and
associated with the output word.
This information suffices to convert the number to "floating decimal
form
It,
i. e. a. s.igned ten digit, normali zed rounded fraction with a signed two
digit dec imBJ. exponent.
In addition, a two digi t binary exponent. and a five
digit .decimal address are punched.
This yields a card output which meets the
specifica.tions of the card form for the SNAP RD command, CRI-2 and CPO-l..
There is no restriction on the length of the parameter list.
In case
there are not enough words to complete a card, blanks will be left in the number
fields not used.
Though the subroutine must be executed in ES, the control
word, parameter list and output words may be in ES or MD.
However, to ob;ain
full card punch speed, the parameter words and output words must be in ES.
In addition, successive entries to the routine at intervals of 8ms or less
will not interrupt the card cycle.
Hence, it is possible to employ four word
parameter lists which are successively modified by the program between
re-entries to this punch routine.
Since 6 bits are allowed to specify the binary exponent XX, the range
__ of scale f'actors (8) must be such that 0 ~ 8 ~ 63.
l!J
C'I')
...-t
'1 PrOgramming' Instructions
0"-
6
o
1.
Enter subroutine with
0"-
...-t
r-
><
c..
RJ
OOMOl
OOM02
yy
FOOOO
LOOOO
where
OOMOO is the location of the first word of this subroutine
FOOOO is the location of' the first word of the parameter list
10000 is the location of the last word of the
yy
may have any value.
parame~er
list
9-201
RW···135
CPO-O
Ps. 3 of 8
2.
Furnish parameter list.
This list is composed otparameter words of the form
xx uuuuu vvvvv
where
xx is the binary scale factor associated with the output word
uuuuu
is the location of the output word
vvvvv
is the address or identification associated with the output
number and which is placed on the card.
3.
Control is returned to the word following the control word after
punching.
4.
Routine assumes cards are positioned on the punch side of the Bull
before entry_
Accuracy
All numbers with binary exponents less than or equal to 35 are represented as ten digit decimal nUl'llbers (rounded).
All digits of the binary
number are used in the conversion so that the result is as accurate as possible.
Numbers vith binary exponents greater than 35 may have an inaccuracy in the
least significant decimal digit since an intermediate binary number (which may
be in error in its least significant bit) is used in the conversion.
10
integers in the range from 0 to 10 are converted exactly.
All
9-202
RW-135
CPO-O
Pg. 4 of 8
88800 516'41
88900 51741
89000 51841
08·800 01024
08900 01124
09000 01224
66511
02310
00 000.000000.0
00 000'('0 '0:0'00:0
88800
00 00000 00000
66511
00 000'00 0'0'000
88801
88802
MJ 00000 00000
TV 08801 08803
MP 00016 00000
TU AOOOO 08814
665·72
66513
66574
66515
66576
66517
0
D
0
D
0
0
88803
88804
88805
88806
88807
88'808
88809
88810
88811
88812
88813
88'814
88815
88816
88817
S8818
88819
88820
88821
88822
88823
88824
88825
TP AOOOO 00031
LQ 0003'1 10021
TV QOOOO 00031
66600
66601
66602
08815
08816
0901;
0002?
20036
OQ018
09000
0881~
09001
~ 88835
08817
08824
00016
09000
TP 08981
TU 08987
TU 08994
t-
88838
RS 08850
RS 08843
TV 08999
~
88839
88840
08850
08843
09016
09015
08941
08985
08983
00015
00015
08985
08983
08843
08985
08983
QOOOO
88828
88829
88830
88831
;;; 88832
~
88833
.88834
8 88836
e; 88837
88841
88842
88843
67101
02000
02144
ST 00031 00031
08998
09017
08816
08815
0881S
00023
08816
00000
08821
00016
08998
06824
00015
00016
08815
08846
08827
AOOOO
00032
888'26
88827
66735
TV
TP
TV
TU
RP
TP
08994
09000
08993
08820
30004
00000
TU 00000
TP
IJ
RA
TV
00000
00031
08801
AOOOO
MJ 00023
RA
RA
IJ
EF
RP
CC
TP
RA
TU
TU
TP
TP
TV
IJ
TV
TV
TP
08999
09017
08831
088'31
00000
66603
66604
66605
66606
66601
66610
66611
66612
66613
66614
66615
66616
06617 .
66·620
66621
66622
66623
66624
66625
66626
66627
66630
66631
66632
66633
66634
66635
66636
66637
66640
66641
66642
00
00
00
00
00000
00000
00000
00000
00000
00000
00·000
00000
45 0000'0 00000
16 02001 02003
11 00020 00000
15 20000 02016
11 20000 00037
55 00037 10'025
16
36
16
11
10000
00037
02302
02310
16 02.301
15 02024
00037
00037
02306
02331
02020
02017
75 30004 02017
11 00000 00.021
15
11
41
21
16
45
21
21
41
1;
75
27
11
21
15
15
11
11
11
15
15
23
00000 02020
00000 00000
00037
02001
20000
00021
02017
02020
023'31
00033
20044
02332
02310
02017
02021
0202'5
00020
02306
02030
OO()17
00020
02017
02056
02033
20000
00040
02311
02062
02053
02330
02:327
02215
02211
02261
02030
00020
02310
02273
02273
02302
02062 000}7
23 02053 00017
66643
16
16
41
16
16
66644
11 00000 10.000
02301
02307
02'331
02037
020~1
02211
02267
02053
02271
02267
9-203
RW-135
CPO-O
Pi. 5 of 8
88844
88845
88846
88841
QT 09002 00026
QOOOO 00005
TPBOO()() QOO74
SP
88848
rp QOOOO 08895
TP 00016 08916
88849
RJ 08982 08975
88850
Tf> 00000 AOOOO
88851
88852
88853
88854
88855
88856
88857
88858
TP 140000 OOO~O
ZJ 08855 08853
88859
88860
88861
88862
88863
88864
88865
888'6,6
8886:7
88868
88869
RP\ 10010 08923
ru
00013 09043
TP 08995 08903
SP
09004 00000
TJ
0889~
08815
S5 0889500000
TV AOOOO 08862
TV 08988 08870
TM 00030 AOaOO
LA AOOOO 00000
TP AOOOO 08895
TP 00013 089'36
TP BOOOO AOOOO
ZJ 08861 08961
TP 08996 0890:3
DV 09003 00000
SP
AOOOO 00015
888·70
TU AOOOO 00000
88871
RS 08870 00016
RA 089'36 00016
88872
88873
8·8875
88876
SP QOOOO 00000
ZJ 08868 08961
TP OOOl~ 08919
SF 00030 08919
88871
88878
ZJ 08880 08,879
88874
TN 08919 AOOOO
88879
TN 00018 AOOOO
88880
...... 88881
SA 09005 00000
SA 08895 00000
~88882
Q.. 8888;
888885
MP AOOOO 09006
TP 80000 AOOOO
TJ 09003 08886
TP 09003 AOnOO
'" 88886
~ 88887
~ 88888
ru
~a888'
a.. 88889
88890
88891
88892
88893
TN AOOOO 08936
SP AOOOO 00015
AOOOO 08892
66645
66646
66647
66650
66651
66652
66653
66654
66655
66656
66657
66660
66661
66662
66663
66664
66665
66666
66667
66670
66611
66612
66673
66674
66675
66676
66617
66700
66701
66702
66703
6670466705
66106
66707
66710
66711
66712
66713
66714
66115
66716
6671"
66120
66721
TN 08895 AOOOO
66722
AT 09007 08895
5P 00016 00000
RP 00000 08894
MP AOOOO 09003
66723
66724
66725
66726
51 02312 00032
31 10000 00005
11 300,0.0 lOll?
11 10000 02137
1'1 00·02(, 02210
31 O?~66 0225-7
11 00000 20000
11 20000 00036
47 02067 02065
75 10012 02173
15 00013 02363
11 02303 02141
31 02314 00000
42 02137 1)211'3
34 02137 00000
16 20000 02076
16 02214 02106
12 00036 20000
54 20000 00000
11 20000 02137
11 00015 02210
11 30000 20000
47 02103 02241
11 ·02'304 02147
"73 02313 10000
31 200-00 00017
15 20000 00000
23 02106 0002n
?1 02210 00020
31 10000 00000
47 02104 02241
11 00015 02~6'3
74 00036 02'263
!'3 0226'3 20000
47 0212.0 02117
13 00022 20000
31. 02~15 00000
32 021~7 00000
71 20000 O~316
11 30000 20000
42 n23~'3 021~6
11 02323 20000
13 20000 02210
-,
;>J. 20000 00017
15 20000 02134
13 02131 20000
35 02317 02137
31 00020 00000
75 00000 02136
71 20000 0231'?
9-204
RW-135
CPO-O
Pg. 6 of 8 .
88894
888q5
88896
88897
88898
88899
88900
88901
88902
88903
88904
88905
88906
88901
88908
88909
00 00000 00000
66740
RS 089'36 00016
MJ 00000 08898
66741
6'6742
't5
TP 08996 08903
00 0·0000 00000
RA 08901 00016
66743
66144
66745
66146
AOOOO
09008
QOOOO
QOOOO
TP AOOOO QOOOO
88911
88912
88913
ZJ 08912 08922
TP 00021 00000
·TU 08969 08916
00015
88914
R5 08916
88915
88916
88917
8SQ18
88919
814920
88921
88922
TJ 08989 08920
88<'126
88921
88928
8SQ29
88Q30
8SQ31
.....
66.13&
66737
1000'0
SP 80000 00015
02320
10000
10000
.2'0.000
3'0000
00 00000
23 02210
1M
QT
SP
SA
88910
8892?
~
71 2 0000' 00036
00 00000 00000
QOOOO
QOOOO
00002
00001
66727
66730
66731
66732
667'33
66·734
66135
00 00·000 00000
TP 08986 08907
TJ 08988 08898
QT 09009 AOOO.O
88923
88924
C")
MP AOOOO 00030
88 cr32
8 a 9··:~3.
--I 8893~
0' 8SQ35
I
o 88936
~ 8893-'
~
..... 88938
>< 88939
a.. 88940
88941
88942
RA 00000 00015
aT AOOOO AOOOO
EJ 09014 08914
MJ 00000 08922
TU
RA
lP
TM
SJ
00015
08936
08916
AOOOO
08925
09043
00016
AOOOO
QOOOO
'08926
RJ 08984 08QS3
':"p 00016 08936
RJ 08982 08915
TP 00030 AOOOO
SJ 08930 08931
RJ 08984 08983
TP 00021 QOOOO
TU 0899~ oaC}34
TP 08972 08979
QT 00000 ACOOO
AT OeQ·85 08936
00 00000 00000
RS 08934 00015
~A 09016 00001
IJ 09015 08948
TU 08956 09053
00 00000 OOOO()
RS 08941 0'9011
66747
66150
&6751
66752
66153
66154
667S5
667·56
66757
66760
66761
66762
66763
66764
66765
66766
66767
66710
66711
66772
66773
66714
66175
66776
66777
67000
67001
61002
67003
67004
67005
67006
67007
1
11
12
51
31
32
11
31
02212 02153
20000 10000
10000
00002
00001
0:001 7
00000
00020
00000 02142
11 02'304 02147
00 00000 00000
21 02153 00020
42 02274 02142
51 02321 20000
47 02160 02112
11 00015 10000
15 02251 02164
23 '02164 00017
42 02275 02110
·21 00000 00017
51 20000 20000
4~ '0'23:26 ,0216?
45 000.00 02112
15 00017 02363
21 02210 00020
11 02210 20000
12 20000 10000
46 02175 02176
37 02270 02267
11 00020 02210
37 02266 0225 7
11 00036 200·00
46 02202 02203
37 02270 02267
11 00025 10000
15 02301 02206
11 02254
51 00000
35 0.2271
00 00000
23 02206
Sit 02330
41 02327
15 02234
00 00000
02263
20000
02210
00000
00017
00001
02224
02375
000(';0
23 (1-2215 02323
9-205
RW-135
CPO-O
Pg. 7 of
88943
TJ 06990
9~9l}4
~s
3~q,4~
3E\94~
8 A9/f 7
r,8948
0~()1?
OqOl~
IJ OB97Q o8Q3L.
C89~6
1'0
5P 00026 OOOflQ
RJ 08982 08976
OqOl~
BRq52
IJ
OP,Q53
R;:> ~OOO3 08Q.,·5
O()O~2
088~6
6701:0 4'2 02276 022215·
61011. ')-:2 C2271 O. ~ '3 ~).?
61012 23 0.2267 o?'32?
6.101' 11 00020 0233C
61014 1'1 02'3'24 02327
610.15 . it1 02263 02206
61016 11 02'325 02210
1- _",
f\"7.017
6,7020'
~707.1
6702;?~
R ~t':~/.t.
TV 08990 08956
61023·
Ae955
"p OQOO3 08979
EW 00000 OOOO()
610_24
61025
!:'r 10fH"\a
67.026
88959
:w ~~:C
EW 10000 00000
RP 2000;~ 08997
6-7027
610:30
(;, "'O~l
88963
RS 08956 00'016
S~ C8870 0(.1015
TU AOOOO 08964
RP 30011 08965
88964
TU 00000
Oq04~
TP
QOOOC
610'3~
SP 08936 00000
610'37
88960
A8961
88962
88965
889()6
'88967
BSQ68
OAA9~
E'J OqOO! 06910
TJ 09003 08q7~
09053 .~{.if,OO
88969
TP
88970
TJ 08Q91 08922
MJ 00000 OaQ12
61032
67033
67034
61035
610'.'0
67061
61042
88972
88913
00 00000 O(,100Q
67·043
'61044
61,045
AT 089146 OS') {)'?
67046
8A97'+
Bf'975
M!J 00000 088 Q R
SP QOOOO 00000
OV 09003 QO~OO
St:) AOOOO 00015
88971
AS976
8f)q77
aSQ78
8897q
~ 88980
'I 88981
8
Tp
88950
Bii95.1
MB9S7
'3 R95B.
<:
0..
F. Bauer
9-208
RW-136
CPO-2
Page 2 of 6
4-16-56
Description
This subroutine punches six stated-point, rounded decimalnumbers per
card. Each card also contains an integer to identify the deck, and a one digit
card number.
Programming Instructions
The subroutine must be stored in high speed storage.
located at address SUBOO. To enter the subroutine use':
Assume that it is
RJ SUBOO SUBOO
followed by a control word of the form
. NN
L
M
The operation part of the control word" NN.r is two octal digits
which specify the number of numbers to be punched.
The 'ii-address part of the control word,. L, is the address of
the first cell of a list of parameter words, the make-u!> of which is
describe,d below. This list of parameter words starting at cell L
must be in high speed storage.
The v-address part of the control word t M, is the address of
an identification integer, which must be in high speed storage. The
identification integer located in cell M must be scaled 2 0 and must
be less than 10 7 . If (M) ~ 10 7 a divide check will occur.
__
~
C'j
P""'I
-I
The list of parameter words occupies NN consecutive cells in high speed
storage starting with cell L. Each parameter word, one for each number to be
punched,. contains four pieces of information in the form
ss
P
OlIFF
0"I
o
o
0"-
P""'I
r><:
0..
The operation part of the parameter word, SS., gives the binary scaling of the number to be punched. This scaling information must be expressed in two octal digits. If SS is greater than
43b (35 decimal) then n must be specified as 00.
The u-addre s s part of the parameter word,. P, is the addres s
of the number to be punched, which must be in high speed storage.
Of the five octal digits which make up the v-address part of
the parameter 'Yord the first must be zero; the ne'xt two, n" specify
the number of decimal digits to be punched in the integer part of
9-200
RW-136
CPO-2
Page 3 of 6
4-16-56
the number.
be 00.
If SS is greater than 43b (35 decimal) then II must
The last two octal digits, FF, specify the number of decimal
digits to be punched in the fractional part of the number.
The total number of decimal digits to be punched must not exceed ten
(decimal). (i. e., II + FF'::::; 12b).
If the number to be punched is too large to be expressed in the number of
digits specified a divide fault and an 10 fault will occur.
Note:
The se parameter words are similar to those used by HTO-O.
OUTPUT CARD FORM
Each card punched by this subroutine has 8 fields as follows:
Field
I
2
3
4
5
6
7
8
Columns
I
13
25
-
-
37
49
61
73
-
-
80
12
24
36
48
60
72
79
Contents
1st number
If
2nd
II
3rd
tr
4th
11
5th
'r
6th
Identifying Integer
card number
In each of the six number fields the 12th or right most column contains the
sign of the number. The 11 th column contain's the least significant digit to be
punched. The remaining digits and the decimal point occupy succeeding columns
to the left as far as required. Zeros to the left of the most significant digit or
decimal point are suppressed .
..-..
~
~
Field 7 contains the 7 digits of the identifying integer with no decimal
point.
I
'"oo
'"......
I
t-
:><
Field 8 contains a sIngle decimal digit card- number, (modulo 10). The
first card produced by each entry into the routine contains ai, the second a 2,
and so on up to 9, 0, and 1 again.
0...
TIMING
As noted above all cells referred to by this routine (namely the control
word, the identification integer, the parameter list, and all numbers to be
punched) should be in high speed storage. Successive entries at intervals of 9 rns
or less may then be made without interrupting the card cycle.
9-210
RW-136
CPO-2
Pg. 4 of 6
4/16/56
SOPOO
SIPOO
S2POO
S3POO
D
D
D
D
D
D
S4POO
oepOQ
OOPOO
OlPOO
D
D
D
0
D
0
0
D
0
TU A 0000 OlP03
TV AGOnO 04P23
SOP07
SOP08
SOP09
SOPIO
SOPtl
50P12
SOP13
SOP14
SOP15
SOP16
SOP17
SOP18
SOP19
SOP20
SlPOI
--'" SIPOO
-- SIP02
C'Ij
1""'4
80"-
1""'4
t-
:><
~
D8POC
09POO
SOPOl
SOP06
I
07POO
MP OCP03
SOP04
SOPOS
0"-
04POO
OOTOO
SOPOO
SOP02
SOP03
I
02POO
03POO
50953
SlP03
SlP04
SET FINAL
EXIT
CARD NU'¥1B£R
REDUCE N
u FOR FST WD
OCP03
OOP09
sECOND 3
U1ENT
BRR
OlP02
SN
PUNCH
BUMP lDE~r
St:T 1
EXIT
PROC PARA
ADV PAR
Loe
QOOOO 00042
oepol 00104
TU QOOOO OlP2:6
LQ QOOOO 00030
QT OCPO! 00T03
ZJ OlPl,2 OlP18
SS OCP03 00015
TU AOOQ,O oip16
QT
65311
71
65312
15 20000 02030
16 20000 02165
31 20000 000'05
11 3060·-0 ·()OO 27
16 02000 02101
21 02101 00020
65313
65314
65315
65316
65317
65320
65321
65322
653.26
65327
FIRST 3
00000 BRB
LQ OOT02 00026
11 00000 10112 B
AT OlP45 OlP28
00 00006 60:(JoO
65325
00000 B
RA OlP03 OCP02
02216
653'23
65324
OlPOQ
04POO
SlP06
SlP07
SlP08
SIP09
SIPlO
SIPll
SlP13
ENTRY
Loe PARAM
LOC IDENl
NO WORDS
TP aoooe ooroo
TV. ()OPOO OlP44
RA OlP44 OCP03
TP OCP03 OOTOl
IJ 00100 OOP09
TP OOP20 oor02
EF 00000 OlP2'S
RP 20036 OOP13
CC 07POO AOQOO
TU OOP19 02P12
RJ OlPOl OlP02
ru OlPOl 02P12
RJ OlPOl
RJ 04P11
RA 00101
45 07P02
40 00000
QJ OlPOl
45 08P02
65447
00015
02000
02025
02111
02126
02136
00027
02166
02202
00 00000 00000
00 00000 00000
0;0. 000£)0' 00000
no 0:0000 00000
00 000;00 00000
00 00000 00000
no 00000 00000
00 00000 00000
00 oaoao 00000
00 0000'0 0.0000
00 00000 00000
00 COO'OO 00000
00 Dono 0 00000
00 00000 00000
65422
65437
SP A 000'0 00005
SIPOS
SlP12
65311
65336
50914
5102.6
51039
51047
00013
0102 tf
01045
01097
01110
01118
00023
01142
01154
0116-6
00000
SHIFT INST
FD
Loe
ID
65330
65331
65332
65333
65334
65335
65336
65337
653.t.O
65341
6534'2
65343
65344
65345
65346
65347
65350
65351
65352
65353
()OO2{)
OGO() 0
11 OOO~() 00:030
41 00021· 02011
11 02024 00031
17 OOOO{) 02056.
75 2()O44 02015
27 02166 200:00
15 02023 02125
37 02026 02027
IS 02026 02'125
37 02026 02025
37 02157
21 00030
45 02170
40 00000
44 02026
45 02204
55 00031
11 00000
21 02030
33 10000
35 02102
51 0@016
15 10000
55 10000
51 00016
47 02041
34 00020
15 2000'0
02136
00020
02011
60000
02027
0-0006
00032
10112
()()()I7
00052
0206i
0003:3
02051
00036
QClO32
02047
·00017
02045
9-211
RW-136
CPO-2
Pg. 5 of 6
4/16/5 6
SlP14
SlP15
SlP16
51P17
SIP18
slPi9
SlP20
SlP21
SlP22
S1P23
SlP24
SlP25
SlP26
SlP27
SlP28
SlP29
SlP30
SlP31
SlP32
SlP33
SlP34
SlP35
6'5354
00000 OlP19
1D LESS 1
65355
65356
A 00-00 'OlP46
aoooo
ONE HALF
OlP47
11 30000 10112 B
TP 00000 OOT05
1M 00T05 Aoooo
54 20000 00153 B
AT QOOOO OlP28
SIPS1
S2POO
S2POl
S2P02
.....
t- S2P03
:>< S2POtf
S2P05
S2P06
S2P07
.:)2PC8
~;?n';9
SHIFT
02P08 01P28
lQ OlP28 00001
TV 00103 OlP34
RA OlP34 00104
LQ OOt02 00000
HA 07P02 OrJT02
LO OOTO? ,~)eo 35
65366
65367
65370
65371
65373
65314
65375
ID
FD
PaS I T IOt,'l 1
SET ZERO SUP
INTEGRL DIG
DEC f> OJ
TV
RJ
RJ
TP
RJ
TJ
ZJ 02P06 oooco
SN OCP02 00000
TV 03P06 ()2P04
AT 02P12 U2P08
65364
65365
65372
35
[IV
54 20000 00153 B
00 00000 00012 B
01 00000 00000 -01
DV 02P08 OlP28
f.tj 00008 OlP31
RJ 02Pll O~P09
M~ 00000 OlP42
SP OlP28 00002
SA 01P28 00001
TP AOOOO 01P2s
5S AOOOO 00051
__ SlP49
~ SlPSO
CI"l
PROCURE DATA
ROUNDED
SlP45
SlP47
SlP48
70
FD
45 09P02 00000
SlP46
653,60
65361
65362
65363
DIV I SOR
FD
00104 00015
1U AOOOO OlP2-=j
SP OOP20 00034
RP 00000 OlP25
MP
65357
io ZERO
OlP49 OlP30
AOOGC 02P08
SlP44
SlP41
Q..
If) NON ZERO
SlP42
SlP43
SlP31
SlP38
SlP39
SlP40
0"
I
0
0
0"
OlP48 OlP30
OlPt..6 AOOOO
OlP50 02P04
02Pll 02Pll)
02Pll 03POO
00104 00103
02Pll 02P1O
OOT05 OlP50
R.J 02PII 02P05
IJ 00100 OlPOO
RJ o4Pil 04POO
SlP36
:!,
TP
TP
RP
MP
lp
TP
SP
FD
F::~A(T
{DENT
DIG
PUNCH
eRB
TEN
35 ONt TENTH
65376
653.71
65400
65401
65402
6~403
65404
65405
65406
65407
65410
65411
65412
65413
65414
65415
65416
65,tt-11
65'+20
65421
65422
65423
65424
65425
65'.26
65'lf;21
6~"430
65431
65432
~;. :i" t~ 3 :3
11 02105 02063
11 021'03 20000
75 00000 02050
11 2000{) 02103
11 021,06 02063
11 2000'0 02121
3"'"J. 00033 00017
15 2 QOO"O 0205h
31 02024 00042
75 00000 02056
71 3000'0 021()4
11 3000:0 10112
11 0006"0 000'34
12 00034 20000
S4 200.00 00153
35 10000 02061
'1"3- (j212:1 02061
55 02061 00001
16 00032 02061
21 0206: 1 0003:3
55 OOO~l 00000
],6 02107 02115
37 02124 02123
31 02124 02126
11 00033 0OO3?
37 02124 02123
42 00034 02101
37 0212:4 02116
41 00027 02025
37 02151 (}2136
45 02220 00'000
54 20000 00153
00 OOOi:lO OOOi2
03 14631 4&3'15.
73 b2121 b2061
l £.;, 00010 02064
~ -'
37 02124 02122
45 00000 02077
31 02061 00002
32 02061 OOtlOl
11 20000 02061
34 20000 00063
47 02117 00000
33,
00011 00000
16' oii3'4 021'15
3S 62125 62t21
21 02170 OO()3i
:;.~
00031 OO(l4~~
9-212
RW-136
CPO-2
Pg. 6 of 6
4/16/56
S2PIO
IJ 0-0103 02POO
65~f3i}
S2Pll
S2~) 12
00000 00000
R~. 07P01 00T02
SN 00015 00001
AT 021'12 03P03
AT 03P07 03P04
65435
S3POO
S3POl
S3P02
S3P,03
RA
RA
S3P05
S3P06
SP 00015 00003
S4POI
S4P02
S4P03
S4P04
S4P05
S4P06
S4P07
54POB
S4P09
SlJ.PIO
S4Pl1
S4P12
S4P13
S4P14
00 00005 00000
TP OCP03 00T02
LQ 04P23 10(,15
TP
TU
RJ
TP
OlP4/~,
CIP37
OlP44 02P12
OlP37 OlP05
04P19 OlP37
SP OOTOI 00015
RJ 02Pl1 02P07
TP 04P18 QOOOO
RP 30003 04Pl1
TP 04P20 04Pl1
EW 00000 09PIO
EW 1000'0 07~10
EW 10000 08P1O
S4P}-8
RP 20'003 04P16
RS 04Pll Oepo:;
1..) 000:00 04Pll
MJ OOO()O 00000
00 00000 00011
St~P 19
RJ 02Pll 03PCO
S4P15
S4P16
S4P17
S4P20
stfP21
s4P22
S4P23
f_n,! GOODO Q9Pl1
EW 100(;:0 O}Pl1.
tW 101000 olap 1
00 70:000 OO(,{:'
l
h
65-4·,t.O
65441
654·42
21 00000 00000
65 1+A3
65444
65445
65446
21 00000 00000
31 00017 00003
45 00000 02111
00 00005 000\)0
11 00',020 00031
55 0-2165 lOO17(
11 02'101 02072
15 62101 0212':'
37 0207"2 02b32
11 02161 02072
31 0OO3() 00017
37 02124 02120
654'37
M..J 00000 02P06
SET fv1A SK
654-47
PAR ltiD T,""I
c:.;::T
.......... 1
fXIT
I
~~E. T
<~
Q
I r~AGE
GEN IMAGE
RESET
GEN I M/~GE
CARD NO
65450
65451
65452
65453
65454
6-5455
65456
65'+57
S::T TO
9
ROW
WR 11 E
WRITE
65460
65461
65462
654~63
LO'Of>
ld. 0:0.032 02111
45 ono,oo 00'000
21 02'167 60031
33 00017 00001
3$ 021'25 62131.:
35 02135 (j2132
65436
00.000 00000
00000 00000
S~P04
S3P07
S4POO
-.....
~J\,)
1] 021fJO ·10·00·0
75 300,0 3 02151
11 02162 02151
77 ooo·oe 0223Q
7~1
100:00 02'200
654'64
654,65
17 10000 02214
7.5 200.03 02156
65466
65467
23 02151 0·0020
02151
45 00000 00000
00 :;:'0000 C0oi~
37 0212/. (i2126
71 60000 02231
65470
65471
6S472
65473
65474
65475
65A76
41 ioooo
77 1000<0 02201
77 100·,0:0 02215
00 "1000-0 00000
....0
C'Ij
"-
I
0"I
0
0
0"-
.....
r-
><
~
9-213
RW-137
MDP-4
Pg. 1 of
5/1/56
THE RAMO -WOOLDRIDGE CORPORATION
Los
~les
45, California
OCTAL CARD DUMP
Specifications
Identification Tag:
MDP-4
Type:
Service 'routine (with subroutine entrance)
Special Storage:
The constant and temporary storage pools are
not used by this routine.
Service Entrance:
Address 4oo15b
Program Entrance:
Address 40015b
Program Exit:
Address 4oo20b
Alarm Exit:
The alarm exit is not used by this routine.
Machine Time:
2. 1 seconds pI us 0.5 seconds per card maximum
machine time
~~
<
\
6 words per card
..1-
(;>j
.-I
,
"-'
.
0"I
0
0
0"-
.-I
t>c!
0...
Coded by:
C. Koos
April, 1956
Machine Checked by:
C. Koos
April, 1956
Approved by:
w.
April, 1956
F. Bauer
9-214
RW-137
MDP-4
Pg. 2 of
Description
5/1/56
This routine will dump the contents of a group of consecutive ES or
MD'storage cells onto cards. Each card will contain six consecutive
octal words and the address of the cell containing the first word
on the card. The following card columns are used:
Columns
Columns
Columns
Columns
Columns
Columns
Columns
first ward
second word
third word
fourth word
fifth word
sixth word
address of first word
1 - 12
13 - 24
25 - 36
37 - 48
49 - 60
61 - 12
16 - 80
card for which all six words consist of 36 binary zeros is omitted
and the next card produced carries a punch in the 12 row of column 14.
The first and last cards of every dump will be produced even if they
contain all zeros .. Zeros will not be punched at any time in columns
31 - 12. If the last card rea.ches the end of ES or of MD before it
is filled, the remaining columns will be completed by using MD words,
beginning with address 40000.
Any
Each card carries an identifying punch in the 12 row of column 13.
This routine bootstraps itself into ES to oper.ate and then positions
cards •. At its conclusion it restores the machine to its original state,
and clears the bull.
OPERATING INSTRUCTIONS
a service routine).
1.
(to be followed when the routine is used as
Put the co .uter in test mode
s
ed (this
s~~p
is unnecessary
for a dump;.ofaJ:.l·: ES:' 9nl.y •
2.
Set PAK to 40015b and start.
3.
Computation will halt with an
a.ll zeros.
40
Manually insert the parameter word into Q.
mo
instruction and Q will contain
a.
a parameter word of all zeros will dump·ES.
b.
in all other cases, place the address of the first wora
to "be dumped in Qu and the a.ddress of the last word to be
dumped in ~
Notes: If the starting address is an ES address and the last
a.ddress is either illegal or a drum address, the routine
will dump up to the end of ES and then exit. An
immediate exit will occur and no cards will be punched
9-215
RW-137
MDP-4
Pg. 3 of
5/1/56
if the starting address is illegal or exceeds the
last address.
5. The machine will halt with an MBO instruction when the dump is
completed and the machine has been restored to its original state.
6.
If another dump is required, it is necessary only to press the
start button again to return to step 3 above.
1.
If the operator wishes to stop a dump at any time after step 3 above,
he needs only to make a forced stop, master clear, and MD start with
PAK set to 4oo40b. The machine will~then be restored to its original
state and computation will halt with the same MBO instruction mentioned
in step 5.
PROGRAMMING INSTRUCTIONS (to be followed when the routine is used as a
subroutine ) •
1.
Enter the routine with the instruction 37 40020 40015b. The word
in your program immediately folloving the RJ instruction must contain
the parameter vord (as described in step 4 of "Operating Instructions"
above). If the RJ instruction is given at address n the parameter
word will be at address n + 1 and at the conclusion of th~ dump control
will be returned to. the instruction address n + 2.
--r-
(I'J
......
I
0J
o
o
0-
......
r><
c...
9-216
WF-138
CHI P
An Interpret1ve Subroutine tor
Packed Floating Point Operands
For the ERA 1103 Computer
-
Programmed b,.:
L. Fall
P. Malo.e
9- 217
WF-138
Programmers at Wright Field have telt the need tor a compact floating
point interpret!ve coding system.
This interpret!ye system should include
basic floating point arithmetic, elapentar.r transcendental tunctions and
floating decimal Flex-coded print or punch output.
A more convenient packed floating number datini tion is desirable.
Consequently, the packed floating number definition ot the llOJAF was chosen.
A floating point "Chip" number R must satis1)' one ot the following
conditions I
1)
N. 0
2)
2
-l29 ~ 11/<2 127
The floating point word structure has the following toruu
1
8
Zl
s
c
H
I I
where S - u35
- sign
C
- u34, --- U27 - characteristic
M
- u26,
- Uo
- manti....
Sand M denote the lis complement representation ot x.227, while C 1s the
representation ot
ronn ot
L7 .J..128J scaled 27 or when S =1,
Ii 4-- 128J scaled
For N : 0, S
=C •
C is the l's complement
27.
M• all O's, or all 1'8.
For 2-129 :; R < z127 I N 1s represented in the form x.-r, where
and -128 ~ '7 ~
127.
Then, S • 0, M =" x (scaled 27), and C
= £7
i
~ x <1
1" 128J
(scaled 27).
For -2127 < H ~ _2-
129
, N is represented by' the one's complement ot
11f'.
9-218
WF-138
I
J.: __ll_I_~
Q
31
u'
t
v'
~
u' ---+ R, A, Q
32
u'
-
Vi
--+ v' , R. A.
R. A, Q
33
u'
•
v' ---+
ft, A, Q
.34
u' +
v,~
Q
35
a
06 u' + R·u' ---+ R, A, Q
36
u' + R-v'
~v',
R, A.
~ u t) • R -) R, A, Q
37
(u' + vt)
·a-+v',
R, A.
02
R
03 R
-
OS R
07 (R
J.i- _n..I_:! - -
*008
R, A.
H, A.
--+
T',
_Tt
----+
R, A. Q
42
Vi'
u' · v'
----+
R, A, Q
43
e u'
14 u' .... T' ---+
Ii, A, Q
44
In u'
-+ R, A, Q
v'~ Vi,
R, A.
v' , R, A.
12 u'
• Vi
v' ,
v',
--+
41 *8in u t
R +u'
v' , R, A.
ut
R, A, Q
R, A.
~
v' , R, A.
---+
v'
~
v',
,
R, A.
Ii,
A.
45 *t.aD ..1 \it ~ Y', ;.R, A•.
- v' -t R,
A, Q
46
Print u' (car ret it
17
Cu' ... ·v,) • R~a,
A, Q
47
Punch'u' (car ret if v'
20
Repeat
16 -u' ... R
ul-tv',
It
22
u' -tv',
R, A.
u'~v',
R, A.
R
-
24 R + U'-+yl,
2S
R
+
RI1'~v'
,
a,
=0)
+u l > •
*Rad1 ...
A.
A.
R, 1.
26 u' ... R.u I -+ v',
27 (R
Vi ;: 0)
.t;- _D_I_ ~ --
2l R t
23 R •
><
c..
40
t u' •
--4
lS
I
----+ R, A,
11 u t + v'
13
0
0
~
... aeu'
10 Repeat
'"
'"t-......
R, A,
~
• u l ----.,
04 R + u'
I
.11- _D_I __V__
Repeat
&.peat
01 R + u'
co
~
......
__
.30
00
R, A.
R.."v', R, A.
2
9-219
WF-138
The CHIP instructions are in t.he following torm.
!4_I_~I
__ ~t_
/ __Y!_
in which OP is a two-octal-digit paeudo-code and u' and yl
address reference8.
14 occupies u35, • • • u3Q;
areto~ctal-dig1t
OP occupies. u29, • • • u24J
u' occupies U2), • • • ul2; and yl occupies uU, • • • Uo.
Because ot the
tour-octal-digi t l1m1 t on address references, operands JIIlSt be located in HSS
(High-speed storage).
HSS addre.a 00005 is designated as R.
Atter
nerr
interpret!Te instruction
'.
the normaliMd, rounded, packed result 1s lett. in R and the double extension of
is lett in A.
R
The repeat order
,00,
functions in a manner analogous to regular 1103
It is coded in the forms
operation.
U23- U22' U21.
If
, j occupying
W denotes the addres8 tram which the next in8truc.tion will be
taken after the termination of the repeat.
Bspeat orders, 10, 20, 30, operate
in ex.actl1' the aaae wal" as above.
It should be noted that addresses 00003 thrQ 00016 are used as te.porary
storage.
Using 00005 as a u l or
V'
addresa v.Ul 71eld the correct reeult
except in the tollowing cases.
14 06
0005 - - - -
14 16
0005
'Y'T
14 26
'0005
v'
14 )6
:OOS v'
gives
2~
•
•
•
2Rv'
The alarm exit of 'Chip" is at 00002.
2a2
2fty'
The following ''Chip'' alarm entry has
been added to the alarm print routinl (CV-J) which places the packed operands
3
9-220
WF-138
of \he current 1natructlon in Ai and A-z
I
75750
37
00224
00224
1
31
00015
00044
2
2!7
2DOOO
00016
3
16
00000
75700
45
00000
75701
,.
For tho •• operations involving only' one· operand, the contents ot u' will
be placed in Ar when an alarm occurs.
It an alarm occurs during a repeated
instruction at addre8s 7, the address printed out will be (W-l) which mayor
may not be ,..
An alarm will occur if the result ot an interpretive operation exceeds
the llJa:I.ta of the "Chip" nuaber definition.
This Ileana that a result too
small in absolute _grdtude will also give an alarm.
By changing address
00213 from the 46 00002 00216 to 46 00214 00216 all results such that
o<
'Resultl < Z-129 will be replaeed b7 zero without an alarm.
FurthelW>re, an alarm occurs when a dirlsion by zero or b7 an unnormalised
number ia attempted, when the square root
or
a negative number is attempted)
,
U the absolute value ot the argument in the sine-cos1ne routine exeeed.a 2
it the argument in .u' i8 l •• s than ~8 or greater than In
;il27J
18.
,
or it in the
logarithm routine, the argument i. equal to or less than zero.
4.
9-221
PX 71900,.~9.=.hlaRr
FU~TION
coos
40~ 41
* Cosine,
LIMITS
Sine 'u').c:. ~
42
Square !bot
43
Rxponent.ial
44
BaturalLog 0 4C. u' <
Arc Tangent.
45
*
0 :i u' <
a1ZI
TIKI
INTERVAL fESTKD
7.a.
O(.os)
7.5.
0(100) 12,500
~8 <. u' ~ 14.9ma
iJ27 . 7.J..a
J11 t I < 2!ZI
a.om.
Addit.1on
X 2
Subtraction
X3
Multiplication
3.1 ....
X4
Division
3.6
lIS.
5.1
JU.
...0
46
Print.
47
Punch
lfewton
-T7~1) 17
.02 .02) 5.0
Band
Po~ - Sheet 56
-20(01)
, E aaxi<"l0-7
Rand
Po17 - Sheet 13
5.1 ma.
288C /word
.zfec/word
1
N
N
N
,;-27 .
Power Seriea
5.1 ms.
X7
I :!rIo(.
Rand Po17 - Sheet 16
3)
Where Emax is mu1.,.. error
Er is max4 m • rel.ative error
Xl
Multiple Orders
aa.x~ 4]fJ-7
METHOD
I hi -<.. 2-21
'Erl <. Z-27
JE jaa:xf<: lIPI
Average
Times for other Orders
X6
IE
3)
-2.5 (.02)2.5
.". Radius
X5
ERROR
s
WF-138
Pr1Jl"d or Puacbed Output - U.. of the prla. (46) or pUGh (47) order •
oaues the paob4
tl~"lDS
point
pWlche4 1D floatl. . 4801.-1
m.mber
tora. The
a' acl4r. . . "
• to
be pr1ated or
tonat tor auoh a Jll&Dlber GODta1M
tour••a obaraotera ill "he torat
ap.l.XXXXXXXapYYSP
2.3 4 5
1
6 7 8 9 10 11 12 13 14
Charaoter .. 1 thru 10 pr1a' out "he dect.l .... 1.aa aJ14 oharacter. 11 thru
13 pr1at CMlt
.lIe
power
ot
Ma b)r which the .ail• • 1. to be Bl1t1pl1e4.
1Ye17 aueh _Mr 1. to1lond b7 a apace.
'!'beJ'e
ill the y
.
whi_ • •
1. a1ao tbe option anllabl. to tl» prosra-r tor a carriage
.
.
portio. ot the prl.' or puaoh order.
M,
1t 1. po_albl. to prlat or puaeh ..yenl . . . .r. ill 00.-
B
8+1
&ta
Usu.s tbe..
or4er.~
14
:3 OOS
0 100
Jtt2
0000
eoat1m&aue of prosraa
00
14 47
• prop-....r has at his d1spoa1 a wid. wr1e'V of
poaaible toraa'. tor
o~t.puto
It ahould be acted tbat -Chip" 1.
earl•••
Ueed wi th a repeat order
~7
.wrap.
OOIUJ""
E1 a
.taJldard aubrout1u.
'l'be
pool, • •1e arltm.t10, aM tuaciloa
rout!... occupy 1A tha" order tbe tir., 700a !BS a4dr......
Whil. the choice
ot peeudo-ood•• a_iIab1e in tbe :1aterpret1Te
, . , oou1derable proan-jag tlex1bl11t7 le _chi.Ted whil. CIOJIPlctu. .
,
9-223
WF-138
00000
45 OOOOO( 30000 )
Normal EDt
00001
~5
Ent17
00002
45 00000 15750
Alarm Exit
00003
00 00000 00000
Mantiss. ot U Operand
00004.
00 00000 00000
TE)(PORARY srORAGE
Characteristic ot U Operand
.00005
00 00000 00000
Chip Accumulstor -R.· also Mantissa ot V Operand
00006
00 00000 00000
Characteristic ot V Operand
00001
00 00000 00000
U1 Address Stored in U-Portion
00010
00 00000 00000
Vl Address ~or.d in U & V-Portion.
00011
00 00000 00000
Repeat, Counter
00012
00 00000 00000
J Counter
00013
00 00000 00000
Tempohl'1 storage tor R
00014
00 00000 00000
Current
Instruction
,
00015
00 00000 00000
Packed U-Operand
00016
00 00000 00000
Packed
00011
00 04.000 00000
.5
00020
20 l~OOO 00000
Chip 1
00021
020000000000
1 Scaled 31
00022
13 05620 57731
ln 2 Scaled 34
00023
~ 00005 24110
Scaling Constant
00024
00 00000 00030
2410
00025
14 44116 65211
11'
00026
06 22011 3250lt.
1T/2
00027
00 00000 00100
64 10
00000 00100
f'
V~Op.raDd
Scaled 27
CEIl' CONsrANTS
--co
C"J
r-4
I
0'
I
0
0
0'
Scaled 32
r-4
r-
:><
Scaled 32
0...
7
9-224
WF-138
00030
00 00000(30000)
Scale Factor Storage
00031
00 00000 00200
128 10
00032
00 00000 00223
14710
00033
40 07717 77777
Mantissa Mask
00034
37 10000 00000
Characteristic Mask
0003'
00 00000
00036
00 00000 00206
13410
00031
00 00000 00045
3710
QO()40
00 00000 00000
Zero
00041
00 00000 00002
2 and ·Color Shitt-
O00lt.2
61 00000 00045
Prin, and • Car. Return-
00043
00 00000
00003
3
00044
00 00000 00004
4
00045
00 00000 00037
Flex Code 0
C>OOl4.6
00 00000 00052
Flex Code 1
00047
00 00000 00074
Flex Code 2
00<>50
00 00000 00070
Flex Code .3
000,1
00 00000
00064
nex Code 4
00052
00 00000
00062
Flex Code 5
00053
00 00000 00066
Flex Code 6
0"-
00054
00 00000
00072
Flex Code 7
r><:
0005'
OO 00000 00060
Flex Code 8
00056
00 00000 00033
Flex Code 9
00057
00 00000 00013
1110
00711
Three-Octal-Digit Extractor
~
co
C"'J
CONS!'ANT POOL
....-4
'-'
I
0"I
0
0
....-4
~
9-225
8
WF-138
00060
00 00000 00012
00061
00 00000
00056
• •
00062
31 10375 ,2421
11'/4
00063
31 46314 63146
0.110 Scaled 38
00064
00 00000 00017
Six-Bit Extractor
00065
21 6164, 24171
Degrees to Radians Scaled 40
00066
20 00000 00000
•.5 Scaled 35
00067
00 00000 00007
Octal Digit Extreo'or
00070
37 77717 77717
235 _1
00071
00 77717 00000
U Extractor
00072
00 00000 7TI71
V Extractor
00073
00 00001 00000
U Advance
00071t.
00 00000 00001
V .ld't'aD.ce
00075
00 0000l 00001
U aDd V Ad'Y8DCe
·00076
00
07177 07777
1°10
Scaled 35.
"'/2 Scaled 34
Four-Octal Digit U and V Extractors
00011
00 00000 00110
72 10
00100
11 00040 00011
Set Repeat Ctr. to Zero
00101
31
00000 00000
--
00102
34
00074 00017
--
00103
15 20000 001011-
00104
(ll (30000 10000)
Transmit Current Instruction to Q
00105
11 10000 00014
Store Current Instruction in 00014
00106
51 00076 00010
Extract V1
00101
31 20000 00011
EXPANSION
ro
ct:I
.....
I
0'
I
0
0
0'
.....
r-
><
c..c
9-226
9
WF-138
yl • 215
+
yl stored in 00010
00110
15 20000 00010
OOlll
55 10000 00003
00112
51 00016 00007
u1 • 21S Stored in U-Portion ot 00007
00113
'5 00014 10006
Shift Current Instruction Six Places in Q
00l.l4
16 00010 00225
Set up:
Store Result at yl
00115
1, 00117 00147
Set up,
R as U Operand
ooll6
15 00007 00157
Set up:
u1
00111
11 00005 00013
Store PreTiouB Result 1n 00013
00120
44 00135 00121
Test PC
00121
"' 00123 00122
00122
16 00104 00225
Test PC4
Set ups Store Result at Q
00123
"' 00124 00126
00124
1, 00007 00147
Test PC
3
DECODD«l
Set upa u l as U Operand
0012,
15 00010 00157
Set UP'
00126
44 00132 00121
00127
44 00131 00130
Test PC2
Test PCl
00130
44 00261 00231
n
XO
00131
44 OOU,7 002!5€>
X3
X2
00132
44 00134 001"
Test PCl
00133
44 00307 00246
X5 14
r-
00134
44 00311 00313
AT
><
c..
00135
31 00167 00157
Unpack tor Functions
00136
II 00016 20000
Contents ot u1 into A
00131
55 00014 10007
Shirt Current Instruotion Seven Places in Q
--co
C"j
~
'-'
I
0"I
0
0
0"-
~
8S
V Operand
PC = Pseudo-Code
S
yl
8S
V Operand
Entries tor X
= 0,
1, 2.
3.
Entries tor X = O. 1, 2, 3.
xl>
9-227
10
WF-138
00140
44 00002 00141
Alarm tor Undefined Pseudo-Codes
00141
44 00002 00142
Alar.mtor Undefined Pseudo-Cpdes
00142
44 0014, 00143
Tes' PC2
00143
44 00144 00;43
Sine-Cosine Entry
00144
44 00422 00323
En'r.J tor Exponential or Square Root
00145
4J4. 00557 00146
Print/Punch Entr.y
oolJt.6
~
Entr,r tor Arc Tan or Logeritm
00141
II (30000) 00015
00150
II 00015 10000
00151
5l. 00033 00003
Store U Manti.sa
00152
51 00034 ()(){)()4.
store U Characteristio
00153
44 00154 00156
00154-
27 00003 00031J,
00155
27 00004. 00034
00156
55 00004 00011
00151
1l(30000) 00016
00160
II 00016 10000
00161
51 0003, 00005
store V Manti ...
00162
51 00034 00006
store V Characteristio
00163
"
00164
21 00005 00034
r-
.....
00165
27 00006 00034-
><
c..
00166
'5
00161
37 OO161{OO110)
00505 00453
store U Operand
UNPAGIC
..-
Store 'f Operand
0::>
CV)
.....
'-'
I
0-.
I
0
0
0-.
00164 00166
00006 OOOll
9-228
11
WF-138
00170
21 00006 00004
00171
36
00172
71 00003 00005
00113
41 00174 00220
00174
II 00031 00005
00175
46 00176 00177
00176
13 00031 00005
00177
74 20000 00030
00200
II 20000 10000
00201
21 10000 00005
00202
43 10000 00205
00203
21 00006 00074
00204-
55 00005 10033
00205
54
00206,
11 0.00,0 20000
00207
42 00031 002ll
00210
36
00211
35 00006 20000
00212
54
00213
46 ()()()(}2·00216
00214
11 00040 20000
.....
00215
45 00000 00220
><
c..
00216
42 00070-00221
00217
45 00000 00002
a::>
C'I')
.....
MULTIPUCATION
00032 00006
NOIMALIZE, ROUND.
10000 00100
00077 20000
20000 00033
NOTE:
I
I
0
0
0'
(00002) i8 Alarm
~~~t
o ( IResultt <2-.
tor
(002J.4) Replaces Result
By Zero With No Alarm.
'-"
0'
ug
r-
I
Al8~.
12
Characteristic Too Large
9-229
WF-138
00220
11 20000 10000
00221
52 00033 00005
00222
"
00223
27 00005 00034
00224
37 00224 00225)
00225
1120000~)
00226
41 00011 00231
Repea~
00227
11 00005 20000
Result to A
00230
45 00000 00000
Jump
'0 Exit
00231
55 00012 10001
J to
Q
00232
"' 002"
00233
21 00007 00075
002:;"
44 0023' 00236
00235
21 00010 00015
00236
11."00000 0011,
002'7
11 10000 00012
Store J
00240
16 00010 00000
v to V-PortiOD ot Fl
00241
21 OOlOlt. 00073
00242
55 00014 10030
00243
51 00035 00011
00244-
41
rd
00245
45 00000 00227
Exit it n=-O
><
0..
00246
37 00167 00147
Unpack
00247
12 00005 20000
.-.
.
a::>
00223 002216-
·store Result
TEFMINATION
Instruction?
REPEAT
MODln~lTIQtf
002~
AdYance ul
AdTBnoe yl
SET. UP REPEAT
~
-......
J
0"-
0
0
J
coon
00104
Store
D
in 00011
Store n - 1 1n 00011. Jump to Next Instruction
0'
13
DIVIDE
9-230
WF-138
Alarm it Di Yisor Unnormalized or Zero
00250
42 00017 00002
00251
23 00004 00006
00252
35 00036 00006
00253
54
00254
13 00005 20000
0025'
45 00000 00173
1ump to Pack
00256
31 00167 00147
Unpack
00251
13 00005
00260
45. 00000 00262
.Jump to Add
00261
37 00167 00147
Unpa~k
00262
11 00004 20000
00263
36 00006 20000
0026J4.
46 00275 00265
00265
42 00037 00271
00266
11 00004 00006
00261
~
00270
45 00000
00271
16 20000 00272
00272
54 00003 (30000)
00213
35 00005 20000
00274
45 00000 00305
r-t
00'Z75
13 20000 20000
~
00276
42 00037 0030l
QO'ZT7
54
,-...
00003 2003'
0000'
SUB'mAc:r
Negate V Operand
~
00003 20010
00306
co
CtJ
-r-t
I
0"I
0
0
0"-
r-
,
00005 20010
9-231
WF-138
.-
co
oo}oo
45 00000 oo,a6
00301
16 20000 00302
00,02
54 00005 (30000)
0030,
3' 00003 20000
oo~
11
~
00:50'
~
20000 20010
00306
45 00000 00173
J-.p to Pack
00301
'1 00224 00147
u-v
00310
1, 00312
OO~7
Set upa
Prerioua Result 88 U
00311
1, 00164 00157
Set Upl
B a8 V
oo3l2
It., 00013 0026l
Jump to Add
00,13
1, 003].2 OOlA7
Set ups
oo3a
'7 00224 00147
U·V
0031'
1, 00007 00147
Set Upl
00316
~,
J'ump to (u + B)
00317
'7 00224 00261
U+V
00320
15 00164 OOlJt.7
Set up:
R a8 U
00321
1, 00,12 00157
Set ups
Pre.,.lou8 Be8ul t 88 V
00322
4, 00000 00141
Jump to Mu1 tip17
00323
46 00002 00324
AlarID it Argument Negative
00324
41 00325 00113
It Zero. Jump to Exit
0032'
,1 00006 00107
00326'
46 00327 00330
00321
'5 0000, 00001
00006
00000 00,11
Prerlous Reault as U
,,1
88
--,
I
0-
0
0
1
1
u • R • u or
1
u + R • yl
U
~
.-.
R + u 1 - .,1 or
R + B _ u1
(u 1 + .,1) • R
(R + u 1 ) - R
v;;.r
0-
.-.
r><
c..
9-232
WF-138
00330
35 00027 00006
00331
11 00066 ~OOOO
00332
11 10000 00003
00333
31 00005 00051
00334
73
0033'
,2 00003 00107
00336
112000010000
00331
23 20000 00003
00340
47 00332 003lt-l
00341
31 10000 00001
00342
4, 00000 00113
Jump 'to Pack
00343
11 <>00II.0 00003
store
00,"
44
0034'
11 00026 00003
oow>
23' 00006 00032
00341
46 00350
00Q()2
00350
35
~5
20000
00351
46 00352 00353
00352
11 00040 0000'
003"
36
'-"
003~
35 00023 00"5
'"
00"5
(00 00000 00000)
'"
00356
"' 00351 00360
><
e..
00"7
11 20000 20000
--,...,
co
CIj
,
I
0
0
r-I
t-
()()()03 20000
oo~
0034'
zero
1n 00003 tor Sine
SINE-COSINE
Tesi PC
o
Store 'T'f/2-
Alarm
in 00003",for Cosine
itl ull~ 218 = 262,144.
Replace u 1 By Zero
00024 10000
u 1 Into A Scaled 32
Zero Into AL it
16
ul
Scaled -Down-
9-233
WF-138
00360
35 00003 20000
00361
13 00062 10000
o
00362
11 00066 00003
8'ore Sign in 00003
00,63
"'2 00026 00361
00364
36 00025 20000
00365
"
00366
4; 00420 00363
00367
,... 20000 0004.2
00370
l' 00026 00005
00371
11 10000 10000
00'72
54 20000 000II-6
00373
11 20000 00006
x 2 Into 00006 Scaled 34
00'74
II 00421
~ Into Pi
00375
15 00366 004.01
Set u Address ot 00461
00376
11 0004:5 00013
Set Index
00377
11 00006 0000II-
i2 ·
004.00
54
00..01
" ~l'
00402
23 00401 00073
0-
00403
41 00013 00377
0
0
0-
00401t.
11 0000,
004.05
,.... 20000 00046
oQle.06
11 20000 00005
00407
11 00003 10000
...-co
('/j
r-!
-I
00003
00001
()()()()4
AR < 211 Scaled 32
~
Slltt Sip
X Into 00005 Scaled 34
Pi
20000 <>0046
()()()()4
Pi + 1
I
()()()()4
r-!
t-
><
c.
x • P
Store result in OOOOs
17
9-234
WF-138
~ll 00412
00410
"
00411
13 20000 0000'
00412
11 00031 00006
004.13
54 00005 20001
00414
45 00000 00173
lump to Pack
0041;
31 10375 52202
C1 Rand Coefficients Scaled 34
004.16
65 52~ 76452
00417
01
2'731
C3 Rand Coefficients Scaled 34
CS Rand Coefficients Scaled 34
00lJ.20
77 131" ~346
C1 Rand Coefficients Scaled 34
00II.21
00 00117 '27'7
C Rand Coefficients Scaled 34
00II.22
23 00006 00032
0011.23
46 O0t..2.. 00002
00424
'5
00425
46 00If.26 00427
ooJt.26
11 00040 00005
~27
36 , 004,1
00430
" 0002, 004,1
00431
(00 00000 00000)
00432
4J. 004" 00434
0'
00433
11 20000 20000
0
0
0'
.....
00434
73 00022 00006
><
0..
00II.'5
11 20000 00005
x Into 5
o~36
II 00Ja.52 00003
1110 Into 00003 Scaled 31
O~31
11 00021 000014-
1 Into 00004 Scaled 31
~
Examine Sign
9
EXPormlrI!L
..-..
0;:)
C'Ij
.....
-I
I
Alarm
~5 20000
Zero to 00005
10000
u l Into A Scaled 34
1
Zero to AL it u Scaled
-Down-
t-
18
9-235
WF-138
00440
11
001..41
73 00003 20000
00442
32 00066 00105
OQq.43
11 20000 00004.
004-44
23 00003 00021
00445
47 00440 00446
00446
21 00006 00031
Characteristic Into 00006
00447
31 00004 00004
eX Into A Soaled .35
00450
45 00000 00173
Go to Pack
00451
00 00000 00026
2210
00452
26 00000 00000
11 10 Scaled 31
00453
23 00006 00473
P - 1
004511-
54
2t Into A Scaled .34
0045'
36 00066 00005
2q-l Into 00005
00456
46 00002 QOls.51
Alara
00457
II 00067 00003
Set Index Equal SaYen
0014.60
1, 004 72 oo~64
Set u Address
~61
11 oo,a4 00004
8S Into Pi
00462
111 00005 ()()()()4.
0"I
00463
54 20000 000ll.6
0
0
0"-
.-4
00If.64
35 :50414 OO~
00465
(23 Q04.64 00073)
00466
41 00003
00467
71 00006 00022
00005
00004
0000, 20010
..-
co
CI'l
-.-4
I
x • Pi
Pi • 1 Into 00004 Scaled ,1
LCGe
ot 00464
x • Pi
Pi + 1
t-
><
c..
004~
(p - 1) • 111 2
19
9-236
WF-138
In u1 Into A Scaled 34
00410
35 00004 20000
00411
11 00473 00006
00472
45 00503 00113
001..13
00 00000 00201
O~74
00 00000 00000
~75
17
00II.76
10 :)0101 71550
~
Scaled 34
00477
05 23606 17663
~
Scaled 34
00500
74 11312 11627
84 80aled 34
00501
02 53533 01102
85
SOaled 34
00502
76 36303 74363
86
Scaled 34
00503
00
44750 60721
87
Scaled 34
00504
77 71310 36m
8S Soaled 34
00505
11 OOO~o 00003
Zero Into 00003
00506
23 00006 00031
Q}ar.
00507
42 00074 00516
00,10
33 00066 00024
00511
73 0000, 00005
00512
13 00006 00006
00513
II 00052 00003
00514
44 00516 0051'
0
0
0"-
00515
1, 00062 00003
t-
00516
21 00006 00031
00517
46 00520 00521
'"'"'
a;:)
C")
7TT16
10003
Go 'So Pack
a O Scaled 34
81 Scaled 34
1
ot u -
ARCTAN
2008
NegatiYe Reciprocal
Scaled 34 Into 00003
1l'/2
~
"I
0"I
-iT/2
Scaled 34 Into 00003
~
><
~
20
9-237
WF-138
11 00040 00005
00521
35 00546 00522
00522
(00 00000 00000)
u l or -1/u1 Scal.d 34 Into A
OQ52}
ll. 20000 00005
x Into 00005 Scaled 34
OO~4
71 00005 10000
OO~
~
00526
II 20000 00006
x2
~
11 ~5 00013
Be. Index Equal Six
00,,0
11 00547 ()()()()It.
C15 ID'to Pi
1, 00,a..4 00'311-
Set U Addre8s
"
0053J.
00532
--......
I
20000 (){)()46
f1l 00006
00004.
00",
54
00'34
(" 30556 oO<>Oll)
005"
21 ~34 00073
00536
1t.l 00013 005~
00537
11 0000,
00540
54 20000 00046
O~l
"
00542
,.. 0000, 20001
oo~,
11 00031 00006
00,"
1t.5 005,0 00173
00545
00 00000 00006
OO~6
54 0000, 24052
0054-7
77 73662 40,05
ID
C?
Replaoe u 1 by Zero
00520
x
2
lato 00006 Soaled34
ot 00534
• Pi
20000 oo~6
00003
()()()04
Pi + 1
x • Pi
00005
tan~
u1 Into A Scaled 35
Go to Pack
0I
0
0
0-
......
r-
><
c...
C15 Scaled
21
34
9-238
WF-138
"""'
0::>
CI"j
-.-4
00550
00 26305 45073
Cl ,3
Scaled 34
00551
17 06511 07416
ell
Scaled 34
00552
01 42561 61640
C
Scaled 34
00553
7' 61441 16451
c.,
Scaled 34
00551c-
03 14201 22666
Os
Scaled 34
00555
72 52547 44072
C.3
Scaled 34
00556
17 77777 51473
C1
Scaled 34
00551
11 oooJ4-2 00676
Set Up Print
00560
44 00561 00562
Print or Punch?
00561
21 00616 00021
Set up Punch
00562
11 00676 00565
Set up Print or Punch at 00565
0056,
16 00564 00565
Set up Print or Punch Q
0051'A
II 00670 10000
-Shirt Down- Into
0056,
(CO 00000
00566
'1 00566 (00567)
00567
II 00010 20000
yl Into .l
00570
41 00574 00512
It A Zero. Print/Punch Carriage Return
00571
00 00000 00000
Not Used
00572
U 00042 10000
-Carriage Return- Into Q
00573
'7 00566 0056'
Print/Punch Car. Ret.
0057'"
II 00016 20000
u 1 Into .A
00575
11 00044 10000
- Space- Into Q
00576
46 00577 00600
00577
ll. 00061 10000
PRINT /PQNCH
00004
I
aI
0
0
a-
.-4
t-
~
9
Q
Print/Punch Q
._- Into Q
22
9-239
WF-138
Prlnt/Punch -Speoe- or ._.
00600
31 00566 00565
00601
37 00601 ~02)
00602
47 00605 00603
0060;
16 00667 0064:5
00604
45 00000 00626
00605
12 00016 00005
Magnitude ot u l Into 00005
0~06
15 00164 00147
Set up 00005 as U
00601
15 0061; 00157
Set up 00671 as V
00610
11 00040 00617
Zero Into 00677
o0611
III 00005
20000
u 1 Equal Zero; Set up Spaoes
R(Packed) Into A
00612
42 00020 00617
It 1> N, Go to 00617
00613
42 00611 00622
It N ( 10, Go to 00622
00614
37
0061;
21 00617 00074
00616
45 00000 ooG~
00617
37 00224 00141
Nul t it»ly bJ' Tell
00620
23 00617 00074
AdJuat Deotmal Exponent
00621
45 00000 00611
...-..
co
00622
'51 00167 00147
--
00623
2, 00004 00612
00624
16 20000 00625
00625
54
00626
11 00040 00005
00627
45 00000 006;2
('Ij
r-I
I
00221~
00246
D1 'Ylde by Ten
AdJuet Decimal Exponent
UnpaoJc Normal1 zed N
0"I
0
0
0"-
r-I
r-
><
c..
00003 (30000)
N Into A Soaled
36
Set Index to Zero
23
9-240
./
WF-138
00630
11 00673 00005
Set Index to Six
00631
71 00003 00674
., • 1010 Into A
00632
11 20000 00003
f!-paction Into 00003 Scaled
36
00633
"
OOOO'OO~3
lraction Into 00003 Scaled
35
006:;'
3Jt. 20000 00044
006"
"
00636
(00 00000 00000)
00637
41 00005 00631
00640
37 -00640 (O~
00676 00636
•
';
Print/Punch Decimal Digit
'1""'?
00641
11 00675 10000
••• Into Q
00642
}7 00566 -00565
Prlnt/Punch
()()64.3
'1 00643 (0064lt)
Optional Exit tor • • 0
~
'1 00640 00630
Translate. Print/Punoh SeYen More Digits
0064,
II 00677"- 20000
"Decu.lExponent Into A
00646
37"00601 00515
Pr1l1t/Punch
00647
12 00677 20000
Magnl'tude ot Exponent Into A
00650
...7 006,1 00663
006,1
13 -00060 10000
..-..
00652
II 20000 00003
--
0065'
11 10000 20000
_ oo6~
'7 OO6It.o 00635
00655
11 0000, 20000
00656
37 00640 \)06'5
Prlilt/Punch La8~ :D1gi t ot Exponent
00657
11 00044.
10000
¥f
- Spac.- Into Q
co
C"')
,...f
w ••
W
Spece- or
w_w
Translate Exponent
I
0I
0
0
0-
,...f
r-
><
0..
I
Prlnt/Punch Pirst 'Digl t ot Exponent
24
9-241
WF-138
00660
37 00566 00565
00661
41 0000, 00660
00662
45 00000 00226
Go to
00663
11 OO~l 00005
Set Up Print/PUnch Three Spaces
~
4., 00000 006",
0066,
11 00060 oo~
00666
.., 00000 00617
(X)667
00 00000 00665
00670
00 00000 00057
Shin Do_
00671
20 11.5000 00000
Chip 10.
00072
00 00000 00167
0067'
00 00000 00006
006~
00 00000 ()O()2Jt.
006~
00·00000
~
•• •
00676
(00 00000
()()()()(j
Print or Punoh T.aporary storep
00677
po
00000 00000)
Print/Punch Space
T.~D8'ion
Set Up Prlnt/Punch Kleven Spaces
Decimal Exponent TempON17 storage
25
9-242
WF-139
110) LIBRARY SUBROUTINE
IfJfTRlES IF MORE
THAN ONE
OR NCYr STANDARD i
(------.
-_.__ ..
STANDARDs
"
n;s
X
~
COOING CHECKl
)lACHINE CHECK 2
31'.J.,F:-RESETTING:
1.
oX
or
or
Sbgument 3
tho functions
ADmESSES:
---------------------------------------------, A
-----------------------------------------------
(8)
I~truct,ion8 :_ _ _ _ _O_l_O_O_O
_ _ _ _ _throu~
(b)
Con8tanta and temporary etorage:
(e)
Con~ant.poolu8ed:~~~_O_O_O_73_·~B_O_O_O_7_4~~~~~~~~~~~~~
(d)
Temporary storage pool ~sed ____0_0....0_0_,4_-_0_:0_0_0_6_ __
01026
01025
throu~:-.._ _ _ __
----------------------------------------~-,~-- -~.
INITIAL SETTING
x< ~$t
.1
<1
(a)
Range on x:
(b)
Scaling or x and r(xJs _ _:x._<'>_2_2_8_ _ _ _~f......
CX_·...
) ~.....41t-'·2_8__
(e)
Briet
de8criptio~
of numer:i
Tf>
f.
AOOU~YJ
_.---------
OF.X~
p]
4.
NO
....;.1:.,,_ _ _~_ _ _ _ __
Location
30
MAT
BY
X
YES_
. PD
BY
Initlallooation of argument: _ _ _ _
_____
Q__
2eemisoellanz
f'lna! locat ion
2.
NO
~al
=
e'; --
meth:xl: _ _ _ _ _ _ _ _ _- - - - -
"'x +
;"'n-l
1a
Px
1 T =:n -2
___________________________________________________________
5. ALAmi- CONDITIONS FOR OOT-oF-RANGE
TES'rI _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
___K_l_ar_Dl_"_f.....;;;;:£::;;;;;....,1&.....i...
' li:_l_0_2_2_a+-I...
>_2_3_5_-_1_ _ _ _ _ _ _ _~____._,_ __
1
9-243
WF-139
6.
SPEED!
-----------------------
7 • YISCELLANY:
Address of ~ in ~u , addr~~s ofx 1n Qy •
Q~5 must be 0 or 1 according as desoending or
ascending order of location of a1.
Indox n (highest power of x) in AR•
Note:
Scale factor may be change·d by corresponding
change in shift instruction (01011).
--
0"-
M
.-I
'-"
I
C1'
I
0
0
0"-
-~
.-I
t-
><
c...
9-244
WF-139
01000
37
75700
75702
A1Hnn
01001
45
00000
(3 0000)
Exit
01002
16
10000
01024
01003
15
10000
01010
01004
16
10000
01010
01005
36
00074
00004
01006
qq
01007
01010
01007
21
01013
01026
0110110
71
01011
54
20000
00054
01012
1]
20000
00006
01013
21
01010
00073
01014
15
OlO10
01016
01015
11
00006
20000
01016
35
(3 00 00)
00005
01017
43
20000
01021
01020
45
00000
01000
Overflow elann
01021
41-
000014-
01024
Index
01022
11
00005
20000
010 23
45
00000
01001
0'
01024
71
00005
(3°000)
0
0
0"-
01025
45
00000
01011
010?6
02
00000
OCOOO
Entrance
Set 01010
0'
C"j
,....;
'-'
I
(30000) (3 0000)
Fonn (n-l)
BOX
8 nX
-+
8 n -1
I
,....;
t-
-:x:
COll.tant
0...
9-245
RW-140
FPP-O
Cover Sheet
5/25/55
THE RAMO -WOOLDRIDGE CORPORATION
Los Angeles 45, California
Interpretive Floating Point Package
FPP-O
Identification Tag:
This package consists of the following which are written
up separately:
1.
SNAP
10/10/55
2. SNAP SAMPLER TRACE
3. SNlP (SNAP Complex)
3/27/56
5/1/56
9-246
nW-140
SNAP Sampler
Page 1 of 4
March 27, 1956
SNAP
S~ler
Trace
Description
This routine monitors the course of a SNAP program by punching
out the results of those SNAP commands which are specified in a list
prepared by the programmer.
A parameter word will indicate the location
of this list.
This list has the following specifications:
a.
The list is made up of sublists of four words each.
These sublists have the form:
00
FA
LA
00
Np
Hs
00
00000 00000
00
00000 00000
FA is the address where the trace is to start and LA
the address at which it is to stop.
Np is the number
of times FA is to be passed before starting the trace,
while Hs is the number of times the section FA to LA
is to be traced.
The last two words are used by the
trace to store the blocked instructions.
b.
This list must not be placed in cells 15b thru lO7b, but
may be put on the drum.
00 Lo
In any case, a parameter word
Lf will specify its location.
Lo is the address
of the first word of the list and Lf is the address of
the last word.
cell 71777b.
This parameter word must be loaded into
In the event this word is all zero a
complete trace of the program is automatically performed.
c.
Any number of sublists may be used.
A particular address
must appear only once in the list since blocking a
blocked instruction is not possible.
d~
The storage addresses FA and LA. must be the addresses iT.
which the instructions to be blocked are actually stored
at the time the blocking routine is activated.
9-247
RW-140
SNAP Sampler
Page 2 of 4
The operation of the trace is as follows:
a.
When a. blocked FA is reached in the program, Np and
i
If N = 0, N
0 then tracing is
p
B
initiated and a start indicator placed in the word
N
S
are examined.
oontaining N and N. On the other hand, if N == 0
p
s
p
and N
0 does not occur J then no action is taken.
s
At each SNAP execution, after a trace start, the F
i
b.
register is transferred to the next available position
in the trace output hopper (last seven cells in ES).
When this hopper contains the results of six SNAP
commands (three IF instructions) then the SNAP output
routine is used to punch a. card containing the information in the trace hopper.
The identification field of
the output card. contains the address of the instruction
which produced the numbers in fields one and two.
This
address is in octal and will be 1725 if the instruction
was an FA.
The SNAP output command operation is in no
way altered during tracing.
c.
To empty the tra.ce hopper at SX1Y time J start at 12125b.
One card will be punched and the machine will stop on
JIJ 0 with PAl:
= 17717b.
8HAP must be in ES to exereise
this option.
d.
In the event the trace hopper is emptied when it contains
no information, a card will be punched containing the
address
1711
in the identification field, while the rest
of the card will be bla.nk.
e.
When a blocked LA is rea.ched in the program and if a
start indicator was set up in the word containing the
associated N and N then tracing is stopped and the trace
p
s
hopper emptied. Otherwise, no action is taken.
f.
The execution of the instruction at FA will be traced,
but that at LA will not.
9-248
RW-140
SNAP Sampler
Page 3 of 4
g.
The seven cells of ES 1 l171b -
1111'0 J cannot be used
by the programmer if the trace is to be
e~loyed.
Normal SNAP operation will not destroy the contents of
these cells.
Programming Instructions
1.
Load cell 71 717'0 with the parameter word 00 Lo
Lf
where Lo and
Lf are the locations of the first and last words of the list.
2. Load the list in form described above.
3. Start. -a.t 72000b. The routine will block the proper instructions ·as
per the list supplied J modify SNAP in order to perform the trace,
and then stop with PAl( set at 40012b.
4. • In the event no parameter word is loaded (and no list is supplied)
a start at 12000b will initiate the blocking routine to modify SNAP
on MD so that all SNAP commands will be traced.
A stop will follow
with PAX set at 40012b.
Warnings and Restrictions
1.
The list can not occupy bells 15b - 107b.
2.
Cells 171lb - 1771'0 must be reserved for the trace hopper and cannot
be used by the programmer.
3· SNAP must be in ES at the time each FA and LA is reached in the
program.
4. The instructions in FA and LA must not be read into or
o~t
of by the
program.
5. Only SNAP commands are traced.
6.
0
~
-~
I
0I
trace can only be used with SNAP and not with the complex
version.
The
7. Activating the trace modifies the copy of SNAP on Mf and destroys
0
0
0r-f
the complex arithmetic portion of SNAP.
t-
USing SNAP or its complex version, it is necessary to restore the
><
0...
library from magnetic tape.
To start another program
9-249
RW-140
SNAP Sampler
Page 4 of 4
8. An abnormality exists for the following type ot
a list:
00
FAl
IAl
00
Npl
Hsl
00
00000
00000
00
00000
00000
00
FA2
LA2
00
Np2
Ns2
00
00000
00000
00
00000
00000
Assume that Npl ' Nsl' Np2' Ns2 are such that tracing in both 8ublists
is concurrent. Further, suppose that FAl , FA2' IA2' LAl are executed
in the order given.
Bence, the traoe will be initiated at FAl and
once again at FA • When LA2 is reached, the trace will stop since it
2
was started at FAa.
The instruotions from LA2 to ~ will not be traced and the trace will
be stopped once again when ~ is reacbed. At this time the hopper will
be punched. Other unusual combinations can be analyzed in a similar
fashion.
9-250
RW-141
SNIP
Pg. 1 of 4
May 1, 1956
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Interpretive Floating Point Package - Complex
Identification:
SNIP
Type:
Service Routine (with entrance from
program available)
Storage:
Cells
634
70000b
thru
thru
1023
7166Gb This includes
SNAP
The constant pool is used by this routine.
..-..
4001~b
Service Entrance:
Address
Program Entrance:
See description
Coded by:
C. Koos
'~
""""'
'""""'
'-"
M. Perry
January, 1956
I
'"
'"r-
Code Checked by:
C. Koos
January, 1956
Machine Checked by:
C.
January, 1956
:><:
Approved by:
I
0
0
'""""'
0...
KOO8
- W. F. Bauer
April, 1956
9-251
RW-141
SNIP
Pg. 2 of 4
5/1/56
Description
SNIP is the complex arithmetic version of SNAP, a floating point
interpretive package. An understanding of the use of SNAP is presupposed.
The activation of this routine changes SNAP into SNIP on the magnetic
drum. The original version of SNAP can be obtained again only by a
transfer of the Service Routine Library from magnetic tape.
SNIP performs its operations
~n either real or complex arithmetic depending on a mode which is selected by the pre-grammer, and may be changed at
any time.
In the complex mode
1.
The complex numbers to be operated on must be in rectangular form, with
the real and imaginary parts of the number stored in consecutive cells
(For example, the complex number x + iy would be stored in the machine
with x in cello<.and y in cello<.. + 1).
2.
The floating Complex Accumulator reqUires two cells: Cell 00002, F,
is used for the real part; Cell 00003, C, is used for the iIll88inary
part, that is, the two cells 00002 and 00003 constitute the Complex
Floating Accumulator, Fc •
3. The Polynomial. Multiply command of
SNAP is changed so that its
execution will result in computing the absolute value of the number
stored in Fc •
4.
The Fix, Float, Read, Punch and No Operation connnands operate exactly
as in SNAP, while the remaining commands are changed only in the
sense that they now use both cells 00002 and 00003 for the floating
accumulator and cells 0<.. and 0<. + 1 for the argument as explained
above.
5. The machine acoumulator
A contains the rea.l part of the result after
the exeoution of any one of these operations.
6. The Replaoe and
B ..bolC options may be used 1n all cases that are
permitted by SNAP, with two consecutive cells being operated on as
desoribed. Keep in mind that the B-box must be indexed by two when
used in referencing a list of complex numbers.
7. It
18 ~ permi.sible to load Fe with TP instructions; a Load command
muat be executed tor this purpoee.
In the real mode
1.
All SNAP oommands except Polynomial Multiply operate as in SNAP
itself.
2.
The execution of the Polynomial Multiply command will give the absolute
value of (Fe) Just as it does in the complex mode.
9-252
RW-141
SNIP
Pg. 3 of h
5/1/56
SNIP commands
The Complex Accumulator, F c ' is defined as two specific electrostatic
cells which contain the complex number x + iy: cell 00002, F, contains
x and cell 00003, C, contains y. Both x and yare stored as SNAP
numbers; that is, each has its own binary exponent. The notation O~c
represents the address of a complex number x + iy, where x is stored
at 0: and y at C( + 1 J that is J (0() = x, (0( + I) = y.
The following definitions apply when in the complex mode:
Code
Result
AD 04
(F e ) +
F ;
c
(F)
~A
SU 10
(F ) - (€X ) ~ F ;
c
c
c
(F ) x (oc ) ~F ;
c
c
e
(F)
~A
(F)
~A
¢X ) -7F ;
e
c
F .
~
e'
F .
~
e'
(F)
~A
(F)
~A
(F)
~A
MP 14
(~
e
)
~
DV 20
(F )
c
PM 24
(Fc)1
30
(0( )
ST 34
(F )
e
->
O A
RT 50
i(i]
e
---?
F .
e'
(F) -7 A
LD
c
The NO (no operation), FI (fix), FL (float), RD (read data) and
The PM (polynomial multiply) instruction of SNAP is replaced by the absolute value
instruction whether operating in the real or complex arithmetic mode
if SNIP has been activated.
PO (punch data) instructions of SNAP are unaltered.
Manual Activation of SNIP
1.
Insure that both this routine and SNAP are intact on the magnetic
drum. (This can be accomplished by a transfer of the Service
Routine Library from magnetic tape).
2.
Load the problem program - The program should include the RamoWooldridge oonstant pool, and a jump to start in 4000Ob, as
supplied by RAWOOP.
Set PAX to 40013 and start--this changes SNAP into SNIP and causes
it to be read into its electrostatic locations, sets the B-box, F,
C, and output hopper to zero, supplies an appropriate jump in
cells zero and one, positions cards on both sides of the reproducer)
and gives control to cell 40000b which normally initiates execution
of the problem. program. At this time the routine is in the real
arithmetic mode.
RW-141
SNIP
Pg. 4 of
5/1/55
Programmed Activation of SNIP
Depending on the card positioning desired anyone of three different
return jump instructions may be used to activate SNIP from the program.
Each assumes that there isa manual jump instruction in cell 40000b
(such as that supplied by RAWOOP), and in each case control is returned
to the instruction immediately following the return jump.
a.
Execution of 37 40000
the reproducer.
400l3b positions cards on both sides of
b.
Execution of 37 40000
of the reproducer.
71644b feeds one card on the punch side
c.
Execution of 37 40000
71646b omits all card positioning.
otherwise the effect of programmed activation is the same as that described
in step 3 under manual activation.
Switching Modes
Activation of SNIP by any one of the methods described above leaves it
in the real arithmetic mode. At any time after SNIP has been activated the mode may be switcbed as follows:
•..
.
C
l
qe switch from the real mode to the complex mode execute the return jump
I
37 01541
.
~.J
01713b
..Jllo-switch fro.m the complex mode to. the rea.l mode execute the return jump
37 01541 017l5b
In- either case tbe desired mode change is acco.mplished, cell 00003, C,
is set to. zero, and control is returned to. the cell immediately following
-the· return jump. The real mode should crdinarily be used wherever possible
because it is ccnsiderably faster than the complex mode.
Alarms
The SNAP alarm routine is used, with the possibility of the same type
or ,alarm occurrins (!W, RT, DV, FI, RD). It is nct advisable to continue
the problem after an alarm, since either the real or imaginary part ot
& number may have caused the alarm.
9-254
RW-142
EGN-O
Page 1 of 19
May 1 ~ 1956
Eigenvector, Eigenvalue Routine
for
Real Symmetric Matrices
Identification Tag:
EGN-O
Type:
Complete package on paper tape
and/ or binary cards.
Storage:
See storage allocation chart.
Program. Entrance:
MD Start
Program Exit:
MS 0 at PAK=VAK=50270b
Alarm Exit:
See section on alarrns a.nd stops.
Machine Time:
See section on sarne.
Mode of Operation:
Fixed point
Coded by:
July. 1955, and
M. Stein
F, Meek
March~
Machine checked by:
M, Stein
F. Meek
August, 1955, and
March$ 1956
Approved by;
w.
April, 1956
Bauer
1956
9-255
RW-142
EGN-O
Page 2 of 19
May 1, 1956
De Be ription
This package consists of an input routine, a main routine, and
an output routine.
The input routine reads in the parameters and the
elements a .. , i ~ j, (the elements on and below the main diagonal) of a
1J
real symInetrie matrix A. The main routine computes the eigenvalues
of A by reducing it to diagonal form with a sequence of orthogonal row
and column operations which leave the characteristic equation invariant.
The corresponding eigenvectors are computed (also by the main routine)
by performing the same sequence of column operations on an identity
matrix.
The output routine converts and punches on cards the eigen-
values and eigenvectors in fixed point form.
rnatrices of order 2
~n
The package will handle
L38.
A special D1.ode of operation which requires a minimum number
of drum accesses is provided for use with matrices of order n L 23.
The special mode is selected by setting manually selective jump switch
1 to the ON position.
Throughout this write-up, T will be defined as
the rnatrix the coluIllI'l;s of which are the eigenvectors.
In the special
mode of operation, the number of rows 6f T to be obtained can be
varied from zero to n and must be specified in advance.
Decreasing
t.he nUlTlber of rows of T to be obtained will allow an inc rease in the
order of the eigenvalue problem. which can be solved.
Should it be de-
sired to obtain eigenvalues only, the special lTlode will be able to solve
problerns of order n
~40.
With a high speed storage capacity of 4096 words, the ordinary
m.ode of operation will. be able to accornrnodate probleITls of order
2
~n L
75, a.nd the special m.ode, problems of order n ,,/' 50.
eigenvalues are to be
found~
If only
the range of n can be extended to n
s
85.
The main routine has been written and the drum storage allocated so as
to lnake the rotitine easily ad~ptable to the 1103Ao
The rnain routine does not use the liB register ' !, the "modified
multiply add"
instruction~
or the IIpolynomial Inultiply'l instruction
found only on the Rarno-"Wooldridge 1103.
9-256
RW-142
EGN-O
Page 3 of 19
May 1, 1956
Parameters
1.
n is the order of the matrix A.
2.
In the special mode of operation, q is equal to n plus the number of
rows of T to be obtained.
In the ordinary mode of operation, q is
autom.atically set equal to n by the main routine.
In the special
mode of operation nand q must satisfy the inequality
2
+ (q-n) 2 ~ 824.
n +n
2
r.:
N is a positive integer less than 10:> associated with each matrix A
3
to be run and may be used to identify the output for a given matrix.
s is the binary scale factor used to store the matrix elements a .. ,
1J
s should be chosen such that
4.
2
33 -'
~"
n' max
i,j
See the appendix for more details in regard to scaling.
Preparation of Input Data
The input routine uses
CRI~2
to read in the parameters n, q,
s
10 Nands, scaled
i~j, scaled 2 .
1J
The first parameter card must contain n with address 00000 and a 12
a
2 ,andthematrixelementsa,.,
2
punch in column 80; for the special mode of operation, it must contain
q with address 00001.
~
.....
-I
The second card :must contain 102N with address
00000, s with address 00001, and a 12 punch in coluITln 80.
The third
card must contain
0'
I
a 11 with addre s s 00000
0'
.....
aZl willi address 00001
~
a
o
o
t-
a
22
31
with addre s s 00002
with address 00003.
9-257
RW-142
EGN-O
Page 4 of 19
May 1, 1956
The fourth card:
a
a
a
32
33
41
with address 00004
with address 00005
with address 00006
a
with address 00007
42
and so on, The last card will contain a
with address n{n+l)-2
nn
and a 12 punch in column 80, On all cards the unused fielcrs should be
left blank,
See the CRI··2 write-up (revised 12-9-55) for the details of
the card format.
If one wishes to generate the data within the 1103, or if, for any
reason, one wishes not to use the input routine, see the appendix.
Switching
Manually selective jum.p switch number one is used to select
either the ordinary mode or the special mode of operation as follows:
MSJ-1
OFF
~
ordinary mode.
MSJ-l
ON
~
special m.ode.
Manually selective jump switch number two is used to control
a monitoring typeout provided at the end of each sweep (1) as follows:
MSJ-2
OFF
---)0
MSJ-2
ON
~
typeout occurs.
typeout suppressed.
Manually selective jump switch number three is used to control
the output of the ro'ws of T as follows;
MSJ-3
OFF
--+
the rows of T are punched.
MSJ-3
ON
~
the rows of T are not punched,
The manually selective stop switches are used t.o provide stops
at the end of each of the three segments (2) of the main routine as
( 1) A sweep is defined unde r Mathematical Method.
(,2) The main routine is divided into segments I, II, and Ill.,
These
are described in detail under The Main Routine.
9-258
RW-142
EGN-O
Page 5 of 19
May l, 1956
follows;
ON ~
MSS-l
stop at conclusion of segment 1.
A
STAR T sets up segment II and jumps to entrance of that segment.
ON -----.-~
MSS-2
stop at conclusion of segment II.
A
STAR T sets up segment I and jumps to entrance of that segment.
The setting of MSJ -2 may be changed at this point.
MSS-3
ON - - }
stop at conclusion of segment III.
A
STAR T sets up segment I and jumps to entrance of that segment
Operation Instructions
1.
The package is available on binary cards and/or on paper tape.
A.
If cards are used, place the pa.ckage deck, two blank cards,
the input cards for the first rnatrix, two blank cards, the input cards for the second matrix, two blank cards 1 and so
on~
ending wiLh two or more blank cards, in the read side of the
Bull.
Manually "pick a card II and read in the package using
CRI-l (as a service routine).
B.
If paper tape is used, read in the package tape using FRI-O
(as a service routine).
Then place the input cards (as in A.
above) in the read side of the Bull.
2.
Set the MSJ and MSS switches as required.
Manually "pick a card l :,
Be sure that there are
plenty of blank cards in the punch side of the Bull.
-
3.
Start at 40000b,
It will read in the input cards for the first (next) matrix, compute
and type out twelve octal digits (with MSJ2 off) after each sweep
C\J
(see the section on Alarms 1 Stops for an explanation of the type-
~
-~
out) and finally stop on an MSS-O at PAK:::V AK:.::50000bo
I
0'
(One ITlay
I
0
0
0"~
t-
avoid this st9P by inserting 45 00000 50000b into 50552b. )
4,
Start.
It will punch the eigenvalue s and, with MSJ - 3 off, the rows
of T, and stop on an MSS-O a.t PAK=V AK=50270b ready to read in
~
the input cards for the next ITlatrix.
Set the MSJ and MSS switches
for the next rnatrix and start.
5,
Repeat 3 and 4 for the next rna trix, and so ono
9-259
RW-142
EGN-O
Page 6 of 19
May L 1956
6.
The output cards should be sorted) first on column 80, and then on
column 77, and then listed with the SNAP output-fixed point 407
panel.
Alarms, Stops
Since all transformations applied to the rnatrix A are orthogona.l.
it can be shown that S(i+l), the
S\lm
of the squares of the elements of
the lowexz triangle (including the main diagonal) of data a.t the end of a
sweep (;.::!.! orthogonal transforrnations), is equal to 5(1»
the sum at
the beginning of that sweep, plus W,the sum of the squares of all offdiagonal elements deliberately set to zero during the sweep.
The double
precision quantity S(1+1) ... S(i) .. W is formed in the accun'l.ulator and then
scale factored. The scale factor h is tested to see if the number of
'
. . 'f'lcants In
. S(i+l) - S(i) - W·U~ 1arge enoug.
h
If t h'IS 18
. not
1ea d lng
lnslgru.
the case the supervisory typewriter will type out an e (for error)
followed by the standard typeout which gives the sweep count, the scale
factor of S(i+l) _ S(i), and the scale factor of S(i+I) - S(i) - W.
puter will then halt with PAK=00210b.
depressing the start key_
The com-
The sweep may be repeated by
To ignore the alarm set PAK
= 00171b
and
depress the start key.
The scale factor h must satisfy either
h L- (50222b)
or
h? 37.
It can be proved that the sequence of S(i) is a rnonotonely increasing sequence which approaches a limit which is less than or equa.l tc
the square of the norm (3) of A., It is believed that this lirnit is equal to
-------,---'---_._--- _._--(3)
The norITI of 1\ is defined in the a.ppendix uncle r
.~~:::~_!.~~
9-260
RW-142
EGN-O
Page 7 of 19
May 1, 1956
the square of the norm of A, but the equality has never been proved for
this process.
At the conclusion of each sweep the monotonicity of the
sequence is checked by observing the sign of S(i) - S(i+l)
the process will continue.
H S(i) _ S(i+l) '- 0,
Should this not be the case, i. e., if
S(i)_ S(i+l) ~O,
the process will be assumed to have converged and the computer will
stop on an MSS-O at PAK=VAK=50000b, :r:eady to enter the output routine.
Arguments unacceptable to the square root subroutine used in the
main routine will cause the computer to halt at address 00230b.
point PAK is set to 00230b.
At this
Hence depressing the start key will not cause
a resumption of computation.
Since the input routine uses CRI-2, the paragraph under Alarm
Conditions of the CRI-2 (revised 12-9-55) write-up applies to the input
routine.
H s has been chosen too large (or much too small) a MA overflow
See
may occur or an MSS-O error stop at PAK=VAK=00062b may occur.
the appendix for more details on this.
Card Output
The output routine Uses CPO-2 to convert and punch
1.
by rows, the elements d ... , i~j, of the diagonalized m.atrix D
IJ
(the d .. are the eigenvalues of A and the d .. , i f j are the off11
1)
diagonal elements which have been reduced, essentially; to
zero);
2.
by rows, the elements of the matrix T.
Each card contains up to six consecutive elements of a row, an
identification number, I, and a one-digit card number, C.
2
The cards contairiing row i of D will have I = 10 N + i; the cards
containing row i of T will have I = l02N
+ n + i.
All of the cards Con-
taining row i of D or Twill have the same I and C will run from 1 to k
where k is the num.ber of cards required to punch row i, 6 elernents per
card.
The result of all this is that, assum.ing several m.atrices have been
9-261
RW-142
EGN-O
Page 8 of 19
May 1, 1956
run, if the output cards are sorted and listed as in 6, under Operating
Instructions, a listing will be obtained of the several matrices in the
order of the least significant digit of N.
For each matrix, the order of
the listing will be: the first six columns of D, the first six columns of T,
the second six columns of D, the second six columns of T, and so on.
Thus an eigenvector will be listed as a column directly below its corresponding eigenvalue.'
The 407 panel is so wired that the setting of an
alteration switch will cause the paper to eject to start a new sheet at the
end of each column.
To bypas s the output routine, see the appendix.
Cards, Tapes, Listings, Flow Diagrams
The complete package is available On binary cards (to be read
in using CRI-l) and On bi-octal paper tape (to be read in using FRI-O
0& the ERA paper tape reader). Also, a flexowriter dump (MDP-O)
listing of the entire package is available.
RA WOOP-assembled listings
are available for the input and output routines only.
Detailed flow dia-
grams for the entire package are on file at the Computing Center.
Mathem.atical Method
The method used by the main routine is the same method as that
described in the write-up of Illinois Code 141-MO in Illiac Library
Codes, M-Z.
That write-up stat2!3 "T,,13 operati0i.1S performed in the
routine essentially are those descrijjcd in an unpublished paper by H. H.
Goldstine, although the re are some modifications ".
The method consists of forming the sequence of ma trice s
-
A,
where R. 1 is an orthogonal matrix chosen so as to reduce to zero a
1+
pair of off-diagonal elements of D..
1
If the sequence of matrices D.
1
9-262
R\~-142
EGN-O
Page 9 of 19
May 1, 1956
c onve rge to a diagonal matrix D, i. e., if
lim D. = D,
i-t~
1
+ is
i 1
obtained from D. by a similarity transformation and the characteristic
then the elements of D are the eigenvalues of A, because D
1
equation remains unchanged.
Sirnilarly, if the sequence of rnatrices T.,
1
where
converges to a rnatrix T, i. e. ,
lim T.
i-+~
1
= T,
it can easily be shown that the columns of T are the eigenv-ectors of A,
norrnalized to unit length.
The first colurnn of T is the eigenvector
corresponding to the eigenvalue in the upper left corner of D, and so on.
+ are always chosen to reduce the largest (in
i 1
absolute
value) pair of .off-diagonal elernents of D.1 to zero, the method
.
If the rnatrices R
is called the Jacobi(4) rnethod, and it can be proved that the rnatrices D.
1
converge, and it can also be proved that if no two eigenvalues of A are
equal, then the rnatrices T. converge.
1
The rnethod used by the rnain routine (and by the llliac routine)
is not to reduce the largest pair of off-diagonal elernents to zero at each
step, but to reduce the off-diagonal elernents to zero in a definite order,
narnely, working frorn upper left to lower right below the main diagonal.
(One such sequence of reductions is called a sweep.) No proof is known
that such a "rnodified Jacobi rnethod 'l converges, but it is believed that
such a rnethod will converge for all real syrnrnetric rnatrices.
(4)C. G. J. Jacobi, "Ein leichtes Verfahren, die in der Theorie der
Sakularstorungen Vorkommenden G1eichungen llurne risch aufzu1osen",
In. reine angew.
Math., V. 30, 1846, p. 51-95.
9-263
RW-142
~GN-O
Page 10 of 19
May 1, 1956
To teduc e the pair of elements a
= a
jk
kj
(k < j) to ze ro the
orthogonal transformation R is chosen to be
kth col.
jth col.
1
1
1
kth row
cose
- sin .,
All elements
not 811.own are
1
zero,
jth row
sin 6'
1
cos 6
1
Accuracy
Several matrices have been run with the package.
Rosser (5)
constructed a matrix of order 8 with some of its eigenvalues nearly equal,
in order to compare two or three diffe rent methods of obtaining eigenvalues
and eigenvectors.
This matrix was run with the package and the largest
5
eigenvalue error was about 1'10- , which represents a relative error of
8
I' 10- . Because of the nearly equal eigenvalues, some of the eigenvectors
were less accurate than others.
The worst errors were in the components
of the vectors corresponding to the three closely-spaced eigenvalues.
-4
The largest absolute error was about 3' 10 .
(~)Ros8er,
Hestenes t Lanczos, and Karush, NBS Journal of Research,
v. 47, 195 1, pp. 291- 296.
9-264
RW-142
EGN-O
Page 11 of .l9
May 1, 1956
Hilbert matrices (6) of orders 8 and 29 were run with the package.
The results for the one of order 8 were cOlllpared with results obtained
on the Illiac (which has 4 more bits than the 1103) and the results for
the one of order 29 were compared with results obtained by the Univac
at N. Y. U., using Givens' method.
For both matrices, all of the
eigenvalues agreed through the eighth decimal place (each matrix has
for its largest eigenvalue a' number slightly less than 2).
Also, several lllatrices with all elements equal to one were run.
Such matrices have n-I eigenvalues equal to zero and one eigenvalue,
AI' equal to
n~
the order of the matrix.
digits were obtained for AI.
For n=40, 8 correct significant
For n=38, the same accuracy was obtained
for Al and all of the eigenvector components were correct through the
8th
de~imal
place.
Machine Time
The machine times
~iven
below are in seconds.
They include
card input of the data (2 +fn 8 +~ cards)(7) and card output of the results (2 +n
+ (n-6)
+ (n-12) + . . . +.(n-6k) + (q-n)
[~JcardS):(8)
(6)Matrices H with h •• = ..,......,....l----=--1J
i +j-l
(7) [~ means a if a is an integer, btl if b is the integral part of a and a
is not an integer.
(8)The last term in the series, n-6k, is the last such terlll which is
positive.
9-265
RW-142
EGN-O
Page 12 of 19
May 1, 1956
type
nutnber of
sweeps
tnode
tnachine
titne (in seconds)
n
q
22
44
all ones
special
Z
125
31
38
62
a.ll ones
ordinary
2
296
76
all ones
ordinary
471
40
40
all ones
special
2
2
8
16
Rosser
special
6
228
39
32
64
Rosser
ordinary
5
467
40
40
Rosser
special
6
311
8
16
Hilbert
special
4
29
29
58
Hilbert
ordinary
4
310
The Main Routine
Reading in the package from binary cards or paper tape places
the input routine, the three segments of the main routine, and the output routine on the drum. (9) Starting at 40000b (or at 50270b) initiates
the execution of the input routine. The input routine places the parameters,
2
n. q, 10 N. and .s, and the elements or t.ile lower triangle 01:" th~ matrix A
on the drum(10) and then initiates the execution of segment III, which runs
only once per matrix A.
The function of segment III is to set up segments
I and II for a specific value of n, make optimizing storage allotments
depending on n, and finally to form a suitable matrix of unit vectors from
which the eigenvectors can be generated.
For the ordinary case
(MSJ -1 OFF) the unit vector matrix will be stored in consecutive locations
with the first element at address 52000b.
In the special case the first
element of the unit matrix will be placed immediately following the last
element of the lower triangle of A.
Segment III concludes itself by block-
transferring segment I and data into high speed storage and jumping to
the initial line of segment I.
(9)See Storage Allocation for drum storage addresses.
(lO)See Storage Allocation for drum storage addresses.
9-266
R\v-l42
EGN-O
Page 13 of 19
May 1, 1956
Segment I proceeds through the lower triangle of the matrix
being diagonalized taking the elements and the rows in sequence.
For
+ is generi l
ated which, when applied along with R'+ to D., produces D. l' in which
1 l
1
1+
the selected pair of elements are zero. In the special mode enough high
each pair of off-diagonal elements an
~rthogonal
matrix R
speed storage (HSS) is available to store both D. and the matrix T. of
1
1
the sequence being transformed into the matrix of eigenvectors.
R. 1 may be applied directly to T. at this point and discarded.
1+
In the
1
ordinary case HSS capacity is insufficient for the storage of T..
.
Hence
1
Hence,
enough information must be preserved to reconstruct the sequence of
I
R. and apply them to T. at a later time.
1
1
This is accomplished by storing
pairs cos 6, sinG sequentially on the drum beginning at address 65000b
in a manner corresponding to the orde r in which the lower triangle was
In order to minimize the number of random drum accesses
nZ+n
nZ+n
a HSS region of length b = 01467b - -Z- or b = Ol470b (which-
swept through.
-z
ever is even) is set aside for temporary storage of the cos <9 sint9 pairs.
At the end of one sweep of (n Z - n)/Z transformations R. during which
J
1
each pair of off-diagonal elements has been set to zero once, segment I
block-transfers segment II into HSS and jumps control to the entrance line
of segment II.
In segment II an arithmetic check is made on whether the R.
1
transformation matrices have been properly generated and applied.
this is the case the latest D. is dumped on the drum.
1
detected the sweep can be repeated.
If
If a discrepancy is
In the ordinary mode of operation
I
segment II will regenerate the R. and bring the matrices T. up to date.
1
1
Convergence is then checked and if the process has been found to converge, the MSS-O stop at PAK=VAK=50000b occurs.
Otherwise, segment
I is set up and the next sweep is initiated.
The Constant Pool
The main routine does not use the R- W constant pool.
both the input and output routines do use it.
However,
It is stored at 50615b and
transferred to OOOI5b just prior to the execution of the input and output
9-267
RW-142
EGN-O
Page 14 of 19
May 1, 1956
routines.
Storage Allocation (all addresses are octal)
R- W constant pool du.:f'ing execution
00015 - - 00026
of the input and
outP'~i,
routines.
R- W temporary pool used during
00027 - - 00040
execution of the input routine.
Execution addres ses and temporary
00250 - - 00704
storage for the input routine.
00027 - - 00455 + ~
00620 - - 00617
+
Execution addresses and temporary
0
storage for the output routine.
Execution addresses for segment I and
00000 - - 00307
segment
00310 - - 00310
2
+ n +n -
'z-
1
n.
Storage for lowe r triangle of rna trix
being diagonalized (eigenvalue data)
during segment I.
Storage for matrix
being converted to eigenvectors (eigenvector data) during ordinary mode
operation of segment II.
Z
00310 + n +n
2
- - 01777
Storage for cos
~
• sin c9 pairs during
ordinary mode of operation of both
segments I and II.
Storage for eigen-
vector data during special mode of
operation.
00401 • - 00551
40000
Execll.tion addres ae s for segment III.
Storage for a jump to 50270, the entrance
of the input routine.
40001 - - 40100
Not used.
40101
Storage for parameter n.
40102
Storage for parameter q.
40103 - - 40407
Storage for segment I.
9-268
RW-142
EGN-O
Page 15 of 19
May 1, 1956
40410 - - 47777
Dump region for eigenvalue data in
ordinary mode.
Dump region for both
eigenvalue and eigenvector data in
special mode.
If n ~ 40, cells 42100
thru 47777 are not used.
50000
Storage for a jump to 50262, the
50001
entrance of the output routine.
2
Storage for parameter 10 N.
50002
Storage for parameter s.
50003 .. - 50257
Storage for segment II.
~0260
Not used.
and 50261
50262 and
.50~63
Storage for the instructions which
transfer the output routine into HS:S.
50264
Storage for the MSS-O stop after the
output routine, and a jump to 50270,
the entrance to the input routine.
50265 - .. 50267
Not used.
50270 - - 50273
Storage for the instructions which
transfer the input routine and the R- W
constant pool into HSS.
50274 - - 50372
Not used.
50373 - .. 50551
Storage for segment III.
50552
Storage for the MSS-O stop after convergence and a jump to 50000.
---C\I
~
...-t
-I
50553 .... 50614
Not used.
50615 .. - 50626
Storage for Roo W constant pool.
50627 .. - 51014
Storage for CPO-2.
51015 .... 51071
Not used.
51072 .... 51240
Storag e for output routine .
51241 .. .. 5 1247
Not used.
51250 .... 51256
Storage for input routine.
51257 - .. 51262
Not used.
51263 - - 51654
Storage for CRI-2.
0"I
0
0
0"-
...-t
t-
><
0..
9-269
RW-142
EGN-O
Page 16 of 19
May 1, 1956
51655 - - 51657
Not used.
51660 - - 51750
Storage for the scaling routine, an
addition to segment ill (see appendix).
51 751 - - 51777
Not used.
52000 - - 64777
Not used in special mode.
In ordinary
mode..J storage for eigenvector data.
"" *:...
If ..... , cells 54644 thru 64777 are
not used.
65000 - - 77777
Not used in special mode.
In ordinary
mode, storage for cos IJ, sind' pair.
for one sweep.
If n ~ 38. cells 67576
thru 77777 are not uled.
9-270
RW-142
EGN-O
Page 17 of 19
May 1, 1956
APPENDIX
Scaling
Under
l-~arameters
it was stated that s should be chosen such
that
Z33 ~ n max
1\
..
1,J
la1J.. /. Z8 <
0...
Theory. itA Process for the Step-by-Step Integration of Differential Equations
in an Automatic Digital Computing Machine Tt by S. Gill, published in Cambridge
Philosophical Society Proceedings, Vol. 47, Part I, January 1951, should be
consulted for a detailed analysis of the process on which the subroutine is
based.
Suppose we know the point (X, Y , Y2' . . 0, Y ) on the curve defined by the
l
n
system of equations
9-276
RW-143
NUI-4
Pg. 4 of 9
5/10/56
The Gill Method is a process by which we can find the next pOint on the curve:
i •e. the value of yl' Y2' • • ., y n for x = X + h.
The process can be better understood if the case where n = 1 is first considered.
We have the pOint (X-,y) on the curve ~
X + hj i.e. we want k = by such that
= f(x,y),
~
~X
and we want to find y at
=
f(X + h, Y + k).
+ h, Y + k
We derive k by making four approximations and averaging them in a particular
way.
First approximate the curve by a straight line through
(X,Y)
with the slope
~X'Y = f(X,Y), and find a first approximation to k:
k
o
=
h·f(X,Y)
Then we tra.vel a fraction m of the way along this line to the point (X+mh, Y+mk )
and find f (X + mh, Y + mk ).
0
o
This gives us a new stra.ight line through (X + mh, Y +
f(X + mh, Y + mk ), and we find
o
kl
=h
mk )
with slope
0 .
f(X + mh, Y + mk6)
We now use ko and kl to find a third point at which f is calculated:
Y +
[n-r]
(X + nh,
ko + rkl )·
k2 = h f(X + nh, Y + [n-r] ko + rk 1 )
Similarly,
~
The weighted average of ko' kl , k , and k3 is the desir~d k
2
=1,
~.y:
bY =.y(X + h)-j{X) = coko + clkl + c 2k2 + c?k~
.J -'
9-277
RW-143
NUI-4
Pg. 5 of 9
5/10/56
tor a system of equations, the same four steps given above are made for each
equation and
i = cok io +c l k il + c 2k i2 + c 3ki3 where Co + c l + c 2 + c 3 = 1.
TPe above process is, for certain values of m, n, p, s, t, co' c1 ' c 2 ' and c ,
3
the Runge-Kutta process. The Gilll..·process was derived, with application to
.,chine use iIi mind, by minimizing the . nUmber of ·.storage cells required. For
the Gill Method the above constants are
bY
m
= 1/2,
r =1
-/1/2,
c
s =
-11/2,
c'l
t = 1 + /1/2,
c
n = 1/2,
p =1
,
0
= 1/6
=(1/3) (1
-/1/2)
2 =(1/3) (1.+ 11/2)
c
= 1/6
3
The Gill process further systematizes the calculation so as to increase the
accuracy and simplifY the coding.
The Subroutine.
As used in the Gill Method Subroutine, the process is as
follows:
It is assumed that the fi(X, YlO ' Y20 , .• " • • , Yn6)
and the y. are available.
l
1st pass:
Advance x by (1/2)h
kio = h-fi (x, YIO ' Y20 , • • ., Yno )
r i1
=(1/2)k iO - qio
qil = qio + 3r il -(1/2)k iO
Yil = YiO + r il
Calculate fi (x'Yl1'Y21'
., Y ) in programmer's own coding.
nl
2nd pass:
k i1 = h f i (x, Y11' Y21' • • -, Ynl )
r i2 = (1 - {1/2) (k i1 - qi1)
qi2 = ~l + 3r i2 - (1 - 11/2)ki
Yi2 = Yi1 + r i2
Calculate fi (x, Y12' Y22 , • • ., Yn2) in programmer's own coding.
9-278
RW-143
NUI-4
Pg. 6 of 9
5/10/56
3rd pass:
Advance x by (1/2)h
ki2
=
h·f i (x'Y12'Y22' . · ., Yn2 )
ri3
= (1
qi3
=
+ /1/2) (k i2 - qi2)
qi2 + 3r i3 - (1 +
i172)
Yi3 = Yi2 + ri3
Calculate fi (x,y ,y ,
13 23
ki2
Y )
n3
4th pass:
ki3 = h.f i (x'Y13'Y23' • • oYn3)
ri4
= (1/6)(k i3
qi4
=
Yi 4
= Yi3
- 2qi3)
qi3 - 3r i 4 - (1/2)k i3
+ ri4
Calculate fi (x'Y1 4'Y 24' · • ., Yn4) in programmer's own coding.
Errors. The paper by S. Gill mentioned previously includes a detailed analysis
ot errors, both truncation error and round-off error.
The expression for the truncation error in by. is too complicated to give
here, but its dominating term, the author states, is
h5
-=iN
~rf
~l
j
~fm.
df i ]
dYl
oYm x=X
where Yo = x, f 0 = 1,
j,k,l,m
and the truncation error in bY will be approximately this when the second
i
partial derivatives are all close to zero. It is probably more useful to say
merely that the truncation error is of the order of h5 .
§
The standard deviation in Y -(1/3)qi over one step from all rounding off
i
~ errors is -(where f is the quantity mentioned in the section on notation)
0"I
o
o
0"I"'"'i
t-
1/6
r L-2f
7/3
L
l
+(1/16)h
2
u, u = the value of
one unit in the
last digit of y.
9-279
RW-143
NUI-4
Pg. 7 of 9
5/10/56
Machine Checking
The following system of two equations was solved using this routine:
dY1
dx
dyz
dx
= cos x
= -sin
x
The initial conditions, at" x = 0, were
y
1
= 0
and
y
2
= 1
The interval, ~x, used was 2~/360 radians.
were accurate to 8 decimal digits.
At
x = 360· the results
9-280
RW-143
NUI-4
Pg. 8 of 9
5/10/56
D
D
GIM01
GILOO
GIMOO
MS 00-000
M~ 00000
GIM02
GIM03
GIM04
GIMOS
M.I 00000 GtL49
MJ 00000 SILOS
RA GIL11 00016
EJ GIL69 GIL13
GIM01
GIMll
M.J 00000 GILl8
TP 00016 GILll
tu GtL72 GtL20
TP 00000 GILBS
TP 00000 O()024
67232
672:33
61234
GIM12
TP GIL.S8 00002
61:2,35
GtM13 ADHO 00024 00000
GIM14
TP 00002 GIl81
G1M1S
TP G1L1S 00031
GIM16 ADMP 00024 00031
. '61'236
612'31
'6t240
GIMOO
GtM06
GIMOS
GIM09
GIMIO
01024
51921
Gt L.OO
00000
EJ GIL'S GILOl
02000
61221
6'1'221
00 0'00·00 00000
00 000'00 00000
56 0'000:0 ;020();O
'-6'1222
61223
67224
,.5
45
45
21
43
43
45
11
15
11
11
11
67225
67226
67227
67230
67231
612,4i
alM17
TP 00002 00000
tv
61'242
GIM18
00000' GIl70
67243
GIM19
RP
30~03
Gtb21
GJM20
TP 00000 OQ02t
61244
6124$
61M21
RA GIL20
GtL61
tu GIL66 GIL25
tv Gil66 GIL.44
RP 30003 GiL.26
67246
61247
lP 00000 00026
GIM26
TP 00024 00002
G1M2? MPNO 00028 00000
612S~
GIM22
GtM23
GtM24
GtM25
GIM28
GIM29
GIM30
TP 00002 00029
TP Gtb,88 00002
MPNO 00026 00000
61M31
TP 00002 00030
-- GIM32 MPSU 00023 00029
~ GtM~3
fP O()OO2 00029
~ GtM34 AONO 00027 00000
d- GIM35 TP 00002 00021
6 GtM36 TN 00025 00002
8...... GiM31 kPAO 00030 00028
t- GIM38
TP 00002 00030
>< GIM39
TP GtLaS 00031
Q..
GtM40
TP 00029 00002
GtM41 DVAD 00031 00030
GIM42
TP 0000200028
61250
67251
6i253
6'25,4
6125;5
67-256
67251
67260
67261
67262
67263
67264
67265
67266
'0000000000
0000002061
00000 02010
0210700020
021050'2111
02104 02001
00000 02022
00020 02107
02110 02024
0OO00021ao
0'0000
021.30
14 040-30
11 0'0002
00030
00002
00000
02121
11 02113 00037
14 04030 14031
11 ooooa 00000
16 0000002106
i5 36003 02025
11 00000 ooo~1
2l 0 20240'2io ~
15 02102 02031
16 02102 02054
1536663
11 Cloaoa
62~32
OOO~2
11 90030 00002
14 14034 60006
11 00002 OQOa5
11
14
11
14
11
02130
14032
00002
14021
00002
14040;33
00002
0&000
0003,'
1()03S
00035
00006-
110,0002 006~~
13 00031 00002
14 14036 04034
61261
67270
67271
11 00002 00036
67272
672-1:3
14 '20037 0403.
1.1 02125 00031
11 00035 00002
11 00002 OOOM
9-281
RW-l43
N"JI ...4
Pgo 9 of
9
5/10/56
GIM43
RP 30003 GIL45
GIM44
TP 00026 00000
RA GiL.25 GtL67
RA 611..44 GIL69
RS GlllO 00016
ZJ Gtl24 00000
iP Gt~Ol AOOOO
LA AOOOO 00015
TU AOOOO GIL,52
TP 00000 AOOOO
GIM45
GIM46
GIM47
GIM48
GIM49
GIMSO
GIMSl
GIMS2
GIM53
GIM54
AT 00015 AOQOO
GIM56
GiM57
AOOOO GIL10
AT 00015 AOaOo
GIMS8
TU AOOOO GILl 1
TU AOOOO GIL66
GIM60
LA AOOOO 00057
TV AOOOO GtL17
GIM61
GIM62
GIM63
GtM64
~IM6~
CtM66
GfM61
GtM68
GtM;9
~tM
0
GtM7i
GtM72
GIM13
GIM14
GIM7S
GJM16
61M77
GIM78
G1M79
67275
61216
67277
61300
61301
61302
61303
67304
67305
67306
AOOOO GIl48
AOOOQ GILlS
GIM55
GIM59
~
~
"j'
tv
iU
61274-
67301
,u
61310
67311
67312
61'313
67314
67315
670316
TV A0'000 GIL66
RA GIL66 (lOO17
RA. GtLOl Q,Y016
MJ boooo G lot
00 00000 OOOO()
00
OOoo~
6732.1
61322
~
61323
60000 B
00 00000 00005
00 00000
67311
61320
oooo~
00 00000
67324
e
~
e
00000
00 00000 00000 ~
00 GIllS 00000 BAa
TP GILa7 00002
MJ 00000 GIll7
05 00000 00000 -01
01 00000 00000 00
05 00000 00000 =01
02 92893 21881 -01
02 92893 21881 -01
6132S
61326
61321
'73~O
F
F
67335
F
67336
61337
F
F
";' GiMSO
02
8 GIM81
..... GtM82
t- GIM83
01 70710 61812 00 F
01 70110 67812 00 F
01 70710 67812 00 F
01 66666 66667 -01 F
03 33333 33333 -01 F
05 00000 00000 -01 F
00 00000 00000
00 00000 00000
0"-
><
0..
GIM84
GIM85
GIM86
GIM87
GtM&s
sTARr
92893
21881
-Ol tr
e
e
61331
61332
67333
67334
67340
61341
67342
67343
67344
67345
67346
67341
67350
61'351
75 30003 02055
11 00032 00000
21 02631 o2iO~
21 02054 02105
23 02106 ,00020
41 02030 00000
11 02001 20006
54 20000 00017
15
11
16
15
35
15
35
15
15
20000
00000
20000
20000
00017
20000
00017
20000
20000
20000
20000
02064
20000
02060
02022
'20000
02012
20000
02013
02102
54
00071
16:
0,2021
16 ,200'00' 021 0 ~
21 02102 O0()21
21 02001 OOO~6
4s
60000 02001
O()OO9~O*OOO
6bo()()O~ 00000
00 00000,00005
00 00000 00003
00 0000000000
00
00 00,000 00000
00 0211300000
02127
00000
04000
14000
04000
11 14537
11
4S
20
20
20
00002
02021
00000
0'0000
00000
30314
1114531~ 30314
11 74537 30314
20 16650 11714
20 16650 11714
20 1665() 11114
17 65252 52525
17 75252 52525
20 04000 00000
00 ,00000 00000
00 00000 00000
45 00000 00000
9-282
RW-144
SIN-4
Pg. 1 of 5
5/15/56
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
FLOATING POINT SINE-COSINE
Specifications
Identification Tag:
SIN-4
Type:
Subroutine
Assembly Routine Spec:
SUB
Storage:
65 words total program storage
4
51856 06510
words temporary storage pool used,
addresses 27 b through 32 b.
The constant pool is used by this routine.
Entrance and Exit:
RJ SUBOl
SUB02
for the sine
SUB 0 3 for the cosine
RJ
SUB 01
Machine Time:
3.9
InS
Coded by:
M. Perry
May, 1956
Approved by:
w.
May 15, 1956
average, 4.8
Bauer
InS
maxim..um
9-283
RW-144
SIN-4
Pg. 2 of 5
5/15/56
Description
When supplied with an argument X in SNAP form, this routine will evaluate
sin X or cos X (depending on which of the two entrances is used) using a
Rand Polynomial Approximation, producing the answer in SNAP form.
Instructions
Pro~amming
This routine can be inserted into a program by CMP-O by the use of a "SUB tt
card in the input deck.
1. 'Place the double length extension of X in the accumulator.
X must be in radians and must be in SNAP form.
2.
3.
Return jump to the subroutine. Assuming that the subroutine -was assigned
to region SUBOO for assembly, use either the 'instruction RJ SUBOl SUB02
for the sine, or the instruction RJ SUBOl SUB03 for the cosine.
At the time of exit from the subroutine, the double length extension of
. sin' X (or cos X) in SNAP form w;'ll be in the accumulator.
Error Analysis
Sin X or cos X is oomputed to 26 bits of accuracy or to as many correct bits
as there are in the Fractional portion of !, whichever is less. For
X ~ 2 27 , this routine substitute$ zero for the argument. The alarm exit is
not U$ed.
Mathematical Method
1.
Let
Y
==
(2j,,)X, then sin X
==
sin(:rc/2)(Y)
cos X = sin(:rc/2)(Y + 1)
2.
Divide y (or y + 1) into an integral part R, and a fractional part S.
3·
R defines the quadrant into which X fall.s.
4.
RI is a number one lees than the number of the quadrant into which X falls.
5.
t-
S defines the displacement (in a position direction) within the quadrant
indicated by Rt •
~ 6.
Therefore, if RI
"qI
-----
~
Let R I be the two low order
positions of R, since in binary notation, any other positions merely
define a number of complete revolutions.
....-!
"-'
J.
80'
I
...-4
= 00
=
H' = 01
HI
10
RI = 11
Let z = S
first quadrant
Let Z = (1-8) second quadrant
third quadrant
Let Z = (-8)
Let Z = (1-8) fourth quadrant
9-284
RW-144
SIN-4
Pg. 3 of 5
5/15/56
7.
Sin (or cos) X = sin(n/2)Z.
8.
(1/z)sin(n/2)z is approximated by the Rand Polynomial Approximation
Number 16, using argument z.
9.
If x~1/2,; (2/n)x, which is in floating form, is substituted for z
before dOing step 10.
10.
Multiply the approximation from step 8 by z giving the result, sin x (.'
(or cos x).
Range of Variable
No alarm condition is recognized by this routine.
However, as X approaches
+ 227 the number of significant digits in Sine X (or Cosine X) approaches zero
and X merely defines a number of revolutions and does not significantly
designate an angle.
9-285
RW-144
SIN-4
Pg. 4 of 5
5/15/56
0
0
D
0
D
DOSOO
OOSOl
OOS02
00S03
00504
00S05
00506
00507
00S08
00509
00S10
00511
00512
D0513
00514
0"I
0
0
0"-
.....
t-
01S00 01079
DOSOO 51856
D1S00 51911
RJ 00000 00000
02067
fitJ 00000 00000
RP 20002 00504
TP 00013 02504
ALARM
NORMAL EXIT
SIN ENTRY
COS ENTRY
TU 00502 00551
seT
LA AOOOO
TM BOOOO 02S00
EXP PLUS
ooooa
LA
AOOOO 00001
LQ AOGOO 00035
MP QOOOO 01S05
TP
TP
RS
SJ
BOOOO QOOOO
QOOOO
02500
00514
SA 01507
02S01
01508
67120
61207
61120
61121
67122
69
67123
61"124
61125
67126
671:27
671'30
61131
i4
611:32
FOR .POS
200
67133
EXP
00521
00000
67134
671'35
67136
SJ OOS18 00S16
67137
AT 00S53 00S17
LA aoooo 00007
61140
00524
'-'
I
02000
00516
DOS11
~
~
00027
OOSIS
00S18
00S19
D0520
D0521
00522
00523
-.....
02500 00023
00500 01024
00525
00526
00527
00S28
00529
D0530
00531
D0532
00533
D0534
00535
TP BOOOO Qoooo
TP 02504 Aoaoo
TJ
01S07 00523
AOOOO
AOOOO 00524
QOOOO 00000
02504 00528
QOOOQ AOOOO
01S06 QOOOO
01S06 02S01
02500 Aoooo
OO;S.31 00532
00S51 00015
00533 00S35
TV
LA
IJ
TN
AT
QT
CC
QJ
RS
QJ
TP 01S06 Aoooo
Sf 02S01 02S01
TP
02S01 QOOOO
stN
15
54 200'00 00010
12 :30000
000;21
'5'4, 2'0000. 0&001
5S' 20000 0004j
'71 1'0000 02074
lil 30000 10000
11 10000 00030
23 00021 02077
46 02016 0202S
32 02076 00000
671~2
11 30000 10000,
61146
cos
37
45
75
11
000"00 0,0000
00000 00000
00000 00000
00000 00000
00000 00000
20002 02004
'OOOl'S 0003'3
02002 02063
67141
6114S
cc QOOOO
00
00000 00000
00000 00000
46 02022 02020
3:5 02065 0202l
54 10000 COCO?
61143
671"'4
ZJ 00S36 00526
00
00
00
00
671:47
611S0
67151
671'52
671:53
61154
6115$
61'1!~.
67151
61160
61161
61162
61163.
.1l 00033 200'0.0
47 0'2044 02032
42 02016 02021
21 10000 .20000
16 '2:0000 02030
54 100;00 00000
41 :00033
020~·4
:13 '10000 200'00
35 02075 10000
51 02075 ooo~O
27 00027 20000
,44 020;37 02040
23 02063 00011
44- 02041 02()43
11 02015 200·0
36 Ot)O~o 0001<1
11 OO~30 10G0O
><
0...
9-286
RW-144
SIN-4
Pg. 5 of 5
5/15/56
00536
00537
00538
00539
00540
00541
00$42
00543
00S44
00545
MP QOOOO QOOOO
SA
TP
PM'
RP
PM
01506
800,010
OlSOl:
20003
01502
00001
102502
67167
24 02070 02067
00542
02502
61170
67171
61112
67113
67174
67175
61176
61177
67200
61201
67202
67203
75
24
71
11
RA 02S00 00S54
SA 01509 00021
OOSSO
DOSS1
CC AOOOO QOOOO
RP 00000 OOSOl
TN AOOOO AOOOO
01500
01S01
01502
01503
01S04
01505
FINAL MANT33
TP BOOOIO AOOOO
ZJ 00545 00S01
00547
00554
69
68
MP BOOOO 02S01
00548
00549
00552
00553
LA aoooo 00007
00 0000000000
01 51484 19000 -04
-4 67376 55700 -03
07 96896 79280 -02
-6 45963 71106 -01
01 57079 63185
06 36619 77225 -01
01506
17 77777 77777 B
01S07
00 00000 00034
00 00000 00200 B
00 00000 00072. 8
01S08
D1S09
STA~r
34
71 10000 10000
32 02075 00001
11 300'0'00'0031
OTSOO
SF AOOO'O 00554
LA A000000021
TP 80000 aOOOo
DOS46
SQ'UARED
67164
67'165
67'166
a
67204
6?:20~
61206
38 (:9
36 C7
35 <:5
34 C3
33
34
67201
67210
61211
67212
20003
02071
30000
30000
02'052
00031
00030
20()OO
47.0205'5' 0200 r
74 20000 02066
54 200·00 00033
1130000 10000,
21 00027 02066
32 02100 00033
27 20000 10000
15 00000 02001
13 20000 20000
54 10000 00001
00 COGOOf 00006
0002366 ,51351
77 5466631.63'3
02 43150 53663.
65 52420 76451
14 44176 65102
12 13714 06667
Cl
2 oVER PI
67213
MASK
28
12B
6·7216
00 00000 OO()34
67217
00 00000 00200
61214
67215
17 77777 77177
672,20 . 00 0.00.00 00072
.s
00000 00000
9-287
RW-145
ATM-l
Page 1 of 7
May 1, 19S6
THE RAMO- WOOLDRIDGE CORPORATION
LOS ANGELES 45, CALIFORNIA
Standard Atmosphere Calculation
Spe cifi cations
Identification Tag:
ATM-I
Type:
Subroutine
Assembly Routine Spec:
SUB 50776
Storage:
79 instructions, addresses
lKLOO thru lKLll
lKROO thru lKR.33
lKPOO thru lKP3Z
13Z53
53 constants in program. addres ses
IKEOO thru lKE36
IBtFOO thru 1!ar15
13Z words total
pr~gram
storage.
7 words-tempor-
ary storage pool used, addresses
OKTOO taru OKT06
The constant pool is used by this routi~e. Program Entrance:
(See-write-up. )
Program Exit:
Address OKLOl
Alarm Exit:
The alarm exit is used by this routine. OKLO 0
Drum Assignment:
Address 65030b thru 65Z33b
Machine Time
1. 34 ms FOa TEMPERATURE
2. SZ ms FOR SPEED OF SOUND
4. 40 ma FOR DENSITY
5.48 ms FOR PRESSURE
6.76 mB FOR ALL 4 QUANTITIES
.......
...,.
ltj
--....
I
0'
I
8
....
Mode of Operation:
0'
I"-
Coded by:
~ Code Checked by:
Machine Checked by:
Approved by:
Fixed
Poin~
M. Elmore
Augu8t~
L. Kimble
L. Kimble
1955
April, 1956
April, 1956
W. F. Bauer
April, 1956
9-288
RW-14S
ATM-I
Page 2 of 7
5-1-56
Description
Given the geometric altitude Y in feet (O~ Y<
c..
l
9
3
l."'l
6
-4.806382
-4
53l5949x10
. l2033I6xI0
ZERO
ZERO
ZERO
390.2
-2
. 16Z7 33xlO
256.039
ZERO
508.79
-2
-. 1881 69xlO
ZERO
.-----='----------''--------.---~------...;....-------=--------.
Alarm Condition s
<
H the subroutine is entered with a negative argument (Y 0) it will enter
the alarm routine _ALR-l: "ATM-l" and the octal address of the RJ order with
which A TM-l was entered will print out on the flexowriter.
9-290
RW-l45
ATM-l
Page 4 of -7
5-1-56
Machine Che eking
A driver routine was written to obtain values of pressure, density, speed
of sound and temperature at 0, 1, 2, ... 91 km. in (geopotential) altitude and
these were checked against values based on the ICAO Interim Standard Atmosphere
Table.
The greatest relative error in pressure for the lower altitudes is. 002.
While the relative error for altitudes in regions 4, 5, and 6 increases sharply,
the absolute error decreases and is less than. 00008. The greatest absolute
error in density i~ very small for the entire range and is of the order of magnitude of . 0000 0004. The greatest relative error in the speed of sound for the
entire range is . 0002. The greatest relative error in temperature is . 0001.
9-291
RW-145
ATM-1
Page 5 of 7
5-1-56
OKLOO 01024
lKLOO 50776
D
D
D
D
D
D
0
D
0
D
D
lKlOO
lKL03.
lKL02
lKL03
lKlO4
lKL05
lKlO6
lKlO7
lKlO8
lKlO9
lKllO·
lKlll
lKROO
lKROl
lKR02
lKR03
lKR04
lKR05
lKR06
lKR07
lKR08
lKR09
OKROO 01036
lKROO
OKPOO
lKPOO
lKEOO
lKFOO
50788
01070
50822
50855
50892
OKEOO 01103
OKFOO 01140
OKTOO 00023
37 75701 15702 6
MJ
MJ
OKP23
MJ
OKPOO
MJ
OKR23
MJ 00000 OKR17
RJ OKP32 OKP24
TP A
OKT01
TP OKT04 A
RJ OKR33 OKR26
rp A.
OK,T03
MJ
OKL01
TP A
OKT05
TJ OOO130KR09
RP 20006 OKR12
TJ OKEOI OKR04
QT 000}4 OKRoa
MP OKFOI OKR08
AT OKRll
RP 30005
TP OKE07
OKTOO
11 OKFOb 75156 BRB
MJ
OKlOO
TP OKE07 OKTOO
tv OKR07 OKR15
TP OKE10 OKT03
TP OKEll OKT04
0
.-I
lKR16
><
c..
lKR17
lKR18
RJ OKR07 OKROO
lKR19
SP
lKR20
MM OKT05 OKT04
lKR21
TP 80000 AD 000
MJ
TV OKlll OKR33
-I
0"I
0
0"-
r-
1 :(~22
lKR23
RP 10003
TP 00013 OKTOO
TV OKLII OKR22
OKro:!
02117
02164
00027
ALARM EXIT
EXIT
PRESSURE·
DENSITY
SPEED SOUND
TEMPERATURE
All
65030
65031
65032
65033
65034
65035
65036
65037
65040
65041
65042
65·043
6st>44
65045
65046
65047,
65050
65051
OKRoe
lKRlO
lKRll
lKR12
lKR13
IkR14
lKR15
..-..
l(j
-.::r
.-I
02000
65030
02014
65044
02056
65106
6514·7
65214
ALARM
ALTITUDE
OVER 83KM
PUT IN
CONSTANT
VALUES
TMPRTR ENTRY
00034
00
00
37
45
45
45
45
45
37
11
11
37
00000 00000
00000 OCOOO
.00000 Ot'OO:;l
00000
00000
00000
00000
00000
00000
00000
00000
75701
00000
00000
00000
00000
00000
02116
20000
00033
02055
11 20000
45 ·0·0000
11 20000
42 00015
75 20006
42 02120
51 00016
71 02165
ooooe
00000
00000
00000
00000
00000
00000
00000
75702
00000
02)05
02056
02043
02035
02106
00030
20000
02046
00032
'02001
00034
02025
02030
02020
02024
02024
65052
35 02027 0202·4
65053
65054
75 30005 00000
11 02126 00027
11 02164 75756
45 00000 02000
65055
65056
65051
65060
65061
65062
65063
65064
65065
65066
65067
65070
SOUND ENTRY
00
00
00
00
00
00
00
00
00
65071
65072
65073
11
16
11
11
75
02126 00027
02023 02033
02131 00032
o2i32 00033
10003 00000
11 00015 00027
16 02013 020'+2
37 02023 0201431 00032 00042
2500034
11 30000
45 00000
16· 02013
00033
2000:';
OCOO()
02055
9-292
RW-14S
ATM-l
Page 6 of 7
5-1-56
lKR24
lKR26
lKR27
SN
!KR28
~KR29
lKR30
lKR31
lKR32
lKR33
lKPOO
lKPOl
lKP02
lKP03
lKP04
IKP05
lKP06
lKP07
lKP.o8
lKP09
lKPlO
lKPll
lKP12
lKP13
lKP14
lKP15
lKP16
lKP17
lKP18
t
...-4
t-
><
0..
65105
65106
65107
65110
65111
TV OKLll OKP21
RJ OKR07 aKROQ
SP OKF06
PM OKF07
TP BOOOO
SP OKT05
00035
OKT05
QOOOO
00033
DV QOOOO OKT06
H SCALED 15
SP OKT02 0OO3f:
PM JKTOI OKT06
PM OKTOO OKT06
TN 80000 QOODO
A2
QT
aT
65112
65113
65114
65115
65116
65111
OKF09 OKT06
MANT ISSA
65120
65121
OKF08 00000
CHARACTERSTC
65122
00047
OKP19
LQ OKT06 00010
SP OK~10 00036
RP 20004 OKP19
65123
65124
SN QOOOO
AT OKP22
EXPONENTIAL
POLYNOMIAL
65125
65126
65127
65130
ENTRY
65131
65132
65133
65134
65135
4
15
08 24472 60000
4
15
01 55380 10000
01 75261 90000
02 52624 00000
5
15
65152
5
15
5
15
65153
65154
IKP25
0
0
0"-
65103
65104
03 60891 67000
lKP24
t
65101
65102
IKEOO
lKEOl
lKP:::!3
0"-
OKF04 00027
DV OKT03 AODOO
Ai OKF02 ACOOO
LA AOOOO 00034
MM OKT03 OKF03
TP 60000 AOQOO
MJ
lKP28
lKP29
lKP30
lKP31
lKP32
lKP20
lKP21
lKP?2
...-4
.....,;
650 74
6507S
65076
65077
65100
PM OKF=ll OKT06
LA 1.,0000 00000
TP AOOOO AOQOC
MJ
LA AOOOO 00051
TV OKLl1 OKP32
RJ OKP21 OKPOI
TP AOOOO OKT02
RJ OKR22 QKR19
TP AOOOO OKT04
MP OKT04 OKT02
PM 00013 OKF15
LA AOOOO 00011
TP BOOOO AOOOO
MJ
IKP19
l.!j
~
RJ OKR22 OKRla
-p AOOOO OKT04
A: OKF05 OKT03
lKR25
lKP26
lKP27
lKE02
lKE03
lKE04
lKE05
PRES
DENS
65136
65137
TEMP
65140
65141
65142
65143
65144
65145
65146
65147
65150
65151
37 02042 020''',:-;
I I 20000 00033
35 02171 00032
33 02170 00033
73 .00032 20000
35 02166 20000
54 20000 00042
25 0003.2 02167
11 30000 2QOOO
45 00000 00000
16 02013 02103
37 02023 02014.
31 02172 OOO!..3
24 02173 0003 /,
11 30000 1000(;
31 00034 0001.:.}
73 10000 OOO'3S
31 00031 0004:i
24 00030 OOO~~')
24 00027 0003:'
13 30000 1000(;
51 02175 0OO3~;
51 02174 10000
33 10000 00057
35 02:04 021C1
55 000'35 ooo~. ?
31 02176 00044
75 20004 02101
24 02177 00035
54 20000 onooo
11 20000 2000(;
45 00000 ooooe
54 20000 00063
16 02013 02116
37 02103 02057
11 20000 00031
37 02042 0203 7
11 20000 00033
71 00033 00031
24 00015 02203
54 20000 00013
11 30000 20COc)
45 00000 00000
00 00000 00000
01 06311 12540
02 41017 20510
04 57364 06315
05 26235 71463
07 55320 00000
9-293
RW~145
ATM-l
Page 7 of 7
5-1-56
lKE06
02 75000 00000
lKE07
-4 81')6'8
11< EO'S
lKE09
--7 5062'81 6000!) -
lKElO
lKEll
03
lKE12
lKE13
lKE14
lKE15
lKE16
IKEl7
lKE18
lKE19
lKE20
lKE21
lkE22
11(£23
lKE24
lKE25
lKE26
lkE27
lKE28
5
IS
24
5
44
2
21
860
861
20000
I1(E33
lk.E34
.
-2 6269'1
-
j:
S19~2
00000
10000
1
80000 - 6
-1 26063 10000 -10
08 :38663 00000
2
-1 88169 00000 .... 3
24
44
64.
If)
~
-,
.....
t
cr0
0
0"-
.....
I-
~
lKF12
lKF13
lKF14
lKF15
75 6521' 41451
01 50652 33514
aSl
65167
74 11211 12171
A4 P
65170
77
17
00
00
A42
ZERO
2
21
840
841
ZERO
65174
02 56039 00000
2
01 62731 00000 - 3
~
-1 9653! 90000
-6 93417 20000 -
5
24
64
A32
65175
65116
65177
21
830
65200
41
24
44
A2
44
03 90200 00000
2
-8 71834 10000
-4 15298 90000 - 5
21
23184
04 18200
04 78490
01 00000
71 76000
04
BlI
65201
6'202
A21
02 04214 52625
00 4000237575
03 25230 21102
71 70021 57612
76 67224 34510
00 00000 00000
820
821
65205
ZERO
65206
00 60614 63146
00 00000 00000
At
65207
77 67226
65210
11 24347 63660
65211
14 55137 13041
810
6521.2
65213
65214
01 00651 46315
70 55271 53367
30 0107-; 652C4
Bll
ALARM
53
TAG
RE RECIP
1
24 E4
24 E3
24 E2
24 E1
1
29 R
3
2
1
12633
76 35220 47027
65203
32
00000 B
00 0171'7 77777 B
05 95618 00000 -5 15546 70000 02 38628 42000 -6 93001,28000 01 00000 00000
01 19200 00000
77 11202
436~6
00000
65204
00000
2
00000 - 8
7702C
15651
00000
ZERO
00000
5
65623
1020400000
77462
00 00000
A22
21 SOUND
35
CON
15
S'tA
21
NTS
75900
71 ?SI1' 515"1
All
Al2
30 01075 65204 B
00 00005 00000 e
01 01181 28000
:3
05 95687 00000 - 1
A3
A31
OQ
24
41
lKFlO
lkFI1
65164
65165
65166
A52
8'50
05 08190 00000
-3 56007 10000 - 3
lKF09
65163
A51
65171
65172
65173
lKE36
lkFOe
A5
65162
A41
-6 14576 40000
-9 41444 00000 - 5
01 20331 60000 ... 10
00 00000 00000
5!S'1 4b315
00 00000 00000
77 606SS. O(~ 111
ZERO
44
21
lKF06
lKF07
ZERO
5
2
lKF05
17 73143 10362
76 60545 3 1A 152
-5 31594 90000
05 18650 0,0000
IKF04
65157
65160
65161
1
-I 91052 20000 -10
lKF03
.-.
65156
A61
-1 02109 67000
lKE35
lKFOl
lKF02
A60
21
41
24
44
64
lKFOO
10 3,1070 OGeor.:
A62
6~400
lK£29
lKE30
lKE31
IKE32
65155
EXPONEN
TIAl
POLYNOM
IAL
24 EO CONSTANTS
6$215
65216
65211
65220
65221
65222
6522'
65224
65225
65226
00
oooo~
1531~
00000
01 76364 01165
23 03151 0561:'
14 72420 60441
00 64214 63146
00 31540 ~O405
04 00000 OQOOO
77 16000 00000
00 01777 77777
652~30
00 00003 03130
77 77745 46517
00 00172 13301
65231
17 77235 13422
65227
652:32· 0001000 00000
65233
05 75341 21121
9-294
RW-146
MII-O
Pg. 1 of 2
revised 5/1/56
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
MANUAL INSPECTION AND INSERTION
Designation:
MII-O
Type:
Service Routine
Special Storage:
The constant and temporary storage pools are
not used by this program.
Entrances:
Address 40002b for inspection, address 40003b
for insertion.
Exit:
Manual stop .
Coded by:
Walter F. Bauer
March 28, 1955
Machine Checked by:
Merritt Elmore
April 1, 1955
Approved by:
Wesley
..-,
-.0
~
.-.
'-'
I
0'
I
0
0
0'
.-.
t-
c.
Dixon
April 8, 1955
><
~
9-295
RW-146
MII-O
Pg. 2 of 2
revised 5/1/56
DESCRIPTION
The routine is designed to facilitate manual data read .. in and read-out by
the machine operator at the control console. With the routine, for example,
only four steps are necessary to insert a word rather than approximately
eleven without it. -The routine also facilitates the inspection (or insertion) of a succession of words. The info~tion is entered into or read
out of the machine by means of the Q~register.
OPERATING INSTRUCTIONS
The following steps should be followed to inspect program data, assuming
the computer halted at end of main pulse 6:
1.
20
30
Set PAX to·4oa02.
Set address n of word to b.e inspected into right 15 bits at
accumulator.
Start computer"
The computer will halt with the word displayed in the Q-register. Upon
restarting, the word in address n + 1 will be displayed in the Q-regiater,
thus successive starts·will c~use words in successive storage locations
to be displayed To perform step 2, the computer m.ust be in the "teat"
mode.
0
The following steps are taken to enter a word into the
the computer halted at the end of ~in pulse 6:
1.
2.
3.
4.
me~ry,
assuming
Set PAK "\;0 40003.
Set address n of word to b~ inserted into right l5 b1ts of
accumulator.
Enter word to be inserted into quotient register.
Start computer.
The computer will halt after inserting the word into addretHI n, Another
word, entered into the Q-register, will be inserted into address n + 1
upon starting the comp~ter. T~t is, upon repeating steps 3 and 4,
words are enterpo ;nto .$uccessive Ine¥llory locations, To perform steps
2 and 3, the computer ~ust be in the "test" mode.
SPECIAL WARNING
This routine does not retain the information which was in the a.ccumulator
or quotient register upon its intt1~tion.
9-296
RW-147
SIN-O
Pg. 1 of' 4
Revised May 1, 1956
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles ,45, California
CENTRAL EXCHANGE SINE -COSINE ROurINE
Specifications
Identification Tag:
SIN-O
Type:
Subroutine
Assembly Routine Specification:
SUB 49368 04008
Storage:
30 instructions
10 constants in program
No words of temporary storage used in program
40 words of total program storage
2 words temporary storage pool used,
addresses 00027b thru 00030b
Drum Assignment:
62230b thru 62217b
Entrance and Exit:
RJ SUBOI SUB03 for the Sine
RJ SUBOI SUB02 for the Cosine
Alarm:
!he alarm exit is not used
Average Machine Time:
3.63 milliseconds for Sine, 3.61 milliseconds
for Cosine
Maximum Machine Time:
4.38 milliseconds for Sine, 4.42 milliseconds
for Cosine
Mode of Operation:
Fixed point
Coded by:
A. E. Roberts, Jr.
December, 1954
Code Checked by:
Merritt Elmore
April 10, 1955
Machine Checked by:
Merritt Elmore
April 14, 1955
Approved by:
Wesley C. Dixon
May 5, 1955
RW-147
SIN-O
Pg. 2 of 4
Revised May 1, 1956
Description
When supplied with an argument X (_2 38
<.
X
< 2 38 ) scaled by
2 33 (ie. X·2 33 ) it
will compute either 2 33 • sin (.x) or 2 33 . cos (d) dependiIig on which of the
2
two possible entrances is used.
2
The Tchebycheff polynomial expansion is used.
The absolute value of the error is less than 2~32.
Programming Instructions
Assume that the subroutine is stored at S~OO and that X is the angle (in quadrants) whose sine or cosine is d.esi;red.
1.
Place X·2 33 in the accumulator
2.
Execute RJ BUBOl SUB03 for the sine, or
RJ BUBOl SUB02 for the cosine.
Control will be returned to the cell immediately following the return jump with
either
233. sin.X or 2 33 • cos.X lett in the accumulator.
2
2
Mathematical Method
Method used, sin (.X).
2
Summary.
X is transformed into· two parts:
A two bit integer q designating the
quadrant in which the angle lies; and a 33 bit fractional part y which is used
in the polynomial approximation for sin
¥.
sin (f) using the half angle formula.
Finally, sin (.X)
Cos
-¥
2
is obtained from
= :t.
cos
1m according
2
to the quadrant.
9-298
RW-147
SIN-O
Pg.. 3 of 4
revised 5,/1/56
In Detail.
1.
Make the argument positive by adding ~8 (sincelXI ~~8).
X+~8 =
O~u
U,
2.
The new argument u has an integral part and a fractional part. Throw
away all the bits of the integral part except the two immediately to
the left of the binary point (since the rest only add integral multiplies of 2". to the angle).
3.
Let q
= two
bit integral part of u.
Thus, q is one less than the
number of the quadrant in which the angle lies.
4.
5.
NOTE,
If Xl is the fractional part of u, then
= xf for
a)
y
b)
y =
sin Or'y)
zr-
=
= 01
q
~ -1 for
(:
~
LJ
or 11, and
q = 00 or 10, because sin (1( X)
a
,2i~1
y
2it1)
= cos
2
,
rr~
(X-i)] •
IYI <:'1 from above.
i=1
This is derived from the Tshebycheff expression
oc:I
sin
6.
cos ("TrY)
= 1-2
sin ~
= cos~,
sin ~
= -cos~,
--r-
One) = 2
zr-
r:J
(-1) k J
k=1
2k-1
(11'/4) [T,
2k-1
(X~ •
J
sin2 (lfY)
zr= 00
q
q
or 01
= 10
or 11
Method used, cos ('7J"X).
--r-
x4-1 replaces X and sin (1rX) is formed as above.
--r-
Machine Checking
A driver routine was used to take the sine and cosine of
68 values of
~)
--r-
and the results were checked against values obtained from the National Bureau
of Standards Table of Sines and Cosines.
9-299
RW-14-'
S[N-O
Pg. 40f 4
revised
0
0
82500
82501
82502
82S03
82504
82505
825Q6
82507
82508
82509
82510
82$11
82S12
82S13
82514
82$15
82$16
82517
82518
82519
82520
82521
82522
82523
62524
82525
82526
82527
82528
82529
82530
'8-2531
82532
82533
82534
82535
82536
82537
82500
81500
FS 000,00
MJ 00000
AT 81539
lA AOOaC
AT OOa16
QJ 81506
TP 81529
MJ 00000
TP 61526
QT 81532
QJ 81512
55 81533
MP AoooO
49368
62230
01024
00000
00000
AOOOO
00001
02000
62230
8iSOS
81528
81S09
81528
AOQOO
81511
00036
00023
00038
81S01
I
HALF
6.2254
62255
32 02041 (>0044
35 00000
21 02023
iOOCo
000i1
42 02036 02021
62256
71 10000 10000
62257
62260
71 20000 OOC21
~2
02041 00044
34 02047 QO()46
13 20{)OO 20000
36 02041 200Co
00 000>00 00000
45 00000 02001
35 02041 10000
PO! OR NEG
JUMP TO l:XIT
62264
62265
LOOP
62267
57 02043 00'066
6227()
37 77771 77774
40 00000 00000
62266
U AODRS
MASK·
~OUND
~3
62253
62261
62262
62263
00000
01 00000 00000
I
cos OF
PI v
00000
82S39
-
NEG
ONE
AOQOO
AOQOO
0
0
0"-
.....
TEST END
71
32
02035 0203·~
00000 02011
02032 0.2034
02040 20000
02014 02013
02041 00000
2boof) 10000
02041 60044
20000 00027
02037 0202'3
13
.62252
CALCULATE
44
34
OOQ2{} 10~OO
Q20.06 02oio
15
11 02'0_42 10000
71 10000 00021
0
UP iNOEX
;}~
44
11
45
11
51
62246
62250
PPLV
NOMlAL
00 00000 00000
00 oaooo 00000
57 000-00 000·00
45 00000 00000
35 02.041 20000
5t.~ 20000 00001
62247
62251
P
QOOOO QOOOO
82S38
~
LOOP
&2'240
L CALC
0
00015
TJ 81530 81517
SA 81533
MP AOOOO
55 81539
TN AOOOO
ST 81539
00 00000
MJ 00000
AT 81539
~s 81535
SCALE
A4-TO Q
~A 81519
MP
62241
62242
62243
62244
62245
st:r
SA 81533 00036
Q
AT
62236
X STAR IN A
IS QUAD £. 4
l'tO sua ONE
~OUND
STO~E
TU 81531 81519
TP 81534 QOOOO
MP QOOOO 06023
62233
62234
62235
62231
y SQUARE:
QOOOO
SA SlS33 00036
TN AOODO 00023
62t!'31
62232
VALUE FUNC
YES POS FUNC
~
00000
0"-
t-
StNE ENTRV
QAD NUM iN Q
IS QUAD 1 2
NO SET NEG
QOOOO
00000
37 77777 77774 B
40 00000 00000 e
6
02 71415 00000
1
08 04213 96000
9
01 36910 17440
01 10975 78641 10
02 69860 75408 10
.........
NO ALARM XIT
NORMAL EXiT
COSINE ENTRY
5/1/56
OFF
~6
62211
A4
A~
62212
Ai
622~5
A2
&2273·
62274
A
62216
oNE
62271
00 00i22
650}~6
00 64626 2i024
Ol. 21465 66440
12
r~
25357 1&2.21
103'15 52420
000;00 00'000
.....
t-
><
Q..
9-300
RW-148
SIN-l
Page 1 of4
Revised May 1, 1956
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Specifications
Identification Tag:
SIN-l
Type:
Subroutine
Assembly Routine Specification:
SUB 49420 04210
Storage:
32 instructions,
10 constants in program,
42 total program storage.
2 words of temporary storage pool used,
addre s se s 27b and 30b
Entrance and Exit:
RJ OOKOI OOK03 for the sine, or
RJ OOKOI OOK02 for the cosine.
Alarm:
The alarm exit is not used-but a
divide faul t may occur.
Drum Assignment:
62314b thru 62365b
Average Machine Time:
2.6 milliseconds
Maximum Machine Time:
4.0 milliseconds (estimated)
Mode of Operation:
Fixed point
Coded by:
M. Elmore
March 21, 1955
Code Checked by:
R. Beach
March 23, 1955
Machine Checked by:
M. Elmore
April 26, 1955
Approved by:
w.
May 11, 1955
co
'o:::J"
.....-I
'-'
I
0'
I
0
0
0'
.....-I
t~
Dixon
9-301
RW-148
SIlf-1.
Pg. 2 of 4
revised 5/1/56
Description
When supplied with an argument x{ ... 21t'.~2~x~21f.~2) scaled by ~ (i.e.
x·ts2) this routine will compute either t'2· s1n x or ~2·co8' x, depending on which of two entrances is used. Computation is by means o-r the Rand
approximation' using the repeat polynomial Dlll1tiply instruction. (Hence,
SIN-1 should not be used on 1103 computers not equipped with the polynomial
multiply).
The absolute error is less than ~27.
Programming and Operating Instructions
x·ZS2
1.
Place
2.
RJ to the subroutine
in A.
If the subroutine has been assigned same arbitrary region, say
then the address of the sine entrance is OOK03, the address of
sine entrance 1s OOK02, and the address of the exit is OOK01.
,should, therefore, use one of two RJ instructions to enter the
RJ
RJ
3.
OOK01
OOK01
OOK03
OOK02
OOKOO,
the coOne
routine.
to obtain the sine, or
to obtain the cosine.
At the time of exit from the routine either ~·sin x or
t'2·COS
x will
be lett in A.
4.
A divide fault occurs if x exceeds the range (see note in Mathematical
Analysis section).
Mathematical Analysis
Method used, sin x.
Summary.
..co
First x 1s reduced to a posi tive angle less than 21fJ second it
is transformed into an angle with an absolute value less than or
equal to rrk, and the sign is assigned according to the quadrant
in which the angle lies. Calculation then proceeds usi~ the
Rand approxtmation •
~
...-f
,
'-'
In Detail
0"I
0
0
1.
(a)
If x is positive and greater than 21{, 21'1s subtracted f"rom x
until x is negative, when 27f is added back iii.
(b)
If x is negative, 2lfis added to x until
0-
...-f
r-
><
c..
NOTE I
X
is positive.
The number of times that x and i 21f' are added is tallied with
If positive x does not become negative or negative x
does not become positive after six subtractions or additions
respectively, x is divided by 21f' and the remainder becomes x.
a Q-jump.
Because of this division, if Ixl>21f(2s2+6), a divide fault
will resulto
9-302
RW-14B
S1N-l
Page 3 of 4
Revised May 1, 1956
2.
If x is greater than or equal to u/2, • is subtracted until x is less than
_/2.
If this takes only one subtraction, then the negative of the newly
obtained x is used for x.
If it takes two subtractions, no further change
of sign is made.
5
3·
"
s].n x
~
= L-
1=1
a 2 "_1 x
].
2i-l
,
!
2
"x
£. ! Jfrom above.
2
This polynomial is related to the Rand Sheet No. 16 polynomial by the
following relation:
Method used, cos x.
x is replaced by x + ./2 if x is negative or by x-3-/2 if x is positive,
and sin x is found as above.
Machine Checking
TIle sin x and cos x of 34 values of x were found and the results checked
against values for the same angles found using the SIN -0 routine.
greatest error was
The
45-2- 33 (approximately .71.2-27 ).
9-303
RW-148
SIN-1
Pg. 4 of 4
revised 5/1/56
82S01
82500
81S00
FS 00000
MJ 0,0000
82S02
SJ
0
0
82S00
82504
TP
TJ
82505
82506
QJ
DV
82S07
82508
82509
82S10
SJ
82503
82511
82512
82513
82S14
82515
82516
82S17
82518
82S19
82520
8'2521
8-2522
82523
82524
82525
82$26
82S21
82528
8252'9
82S30
82$31
82$32
.-.82533
~92S34
et 82S35
~82S36
~82S37
... 82538
1'-82539
~82S40
82541
COSINE ENiRY
623,1'6
SINE ENtRV
IS )( SML NUt:
6:23l1
00 0,000'0' c),()'OOO
00 99000 00000
$,7 00000 0·0000
45 0:0000 00000
46 02011 02010
11 020>1 .10000
62320
42
tLL\,
62:321
44 02006 02013
73 0'2040 10000
46'0201b 02022
36 02040 2000.0
35 0204i 20000
45 00000 02()O3
36 02040 2eooo
4:9420
01024
00000
62'3i4
O~OO{)
6231-4
623:](5
00000
81509 81S08
81S41 QOOOO
81532 81515
81506 81S11
81532 QOOOO
81514 81S18
sua 2Pt
DIV BY 2PI
6·2322
62323
ST 81532 AOOOO
SUB
AT 81S3:3 AOOOO
M...j 000·00 81503
51 81532 AQOOO
SJ 81514 81505
QJ 81S06 81S14
ADD
2Pl
HALF PI
SUB 2Pl TIL
X GOES NEG
TLLV ADO 2Pl
AT 81532 AOOGO
ADD· 2Pl
TtL
X GOES pos
CHNGE SIGN X
SJ 81S13 81S18
TN A
A
MJ
81$22
TJ 81S33 81522
5T
JMP 10 POLV~
ts ~ 1ST QUO
NO
SUB PI
IS X SML NUF
NO
sue PI
sA 81540
41
A
SP 8153$
24
SAVE )(
X SQUARE
ROUND SCALE
5T 81S3'4 A
TJ 81533 81516
81,534 A
TP A
23
MP
23 Q
TP
RP' 2
PM
PM
TP
13
B
(9 TO I
35
stN
24
:
SCALt ANSWER
A
MJ
81501
06 28,318 53072
,~
~2
01 57619 63268
03 14159 26§36
02 60188 69075
-1 98014 14309
08 33302 51737
-1 66666 56696
09 99999 99470
01
00 70000 00000
X
P'OL YHOM tAL.
23
--B
e
6
4
:3
1
1
62332
62333
62334-
6233$
62"~36
6,23,7
62340
62341
62,'42
62343
623;44
62'34s
62,3S0
62'351
623S2
,JUMP TO
extt
oNE HALF
p·t
·62355
.
62"56
62'351
62360
62361
2P!
32 Pi
',.,.
&232'1
62330
62331
62'46
62'41
t(lMJ'UtE
4 81529
81$36
so
STOR~ )(
62324
62:'3:25
62:32'6
49 C9 SCALED 43
40 <:'7 sCALED
38 C5 SCALED 38
36 C3 SCALED 36
34 Cl SCALEO 34
ROUND OFF
02040 02611
46 02016 92005
44 02006 02($16
3S 02040 20000
46 02015 02022
-13 20009 20000
45 00000 02026
42 02041 02026
36 020-42 200,00
42 02041 02026
36 02042 20000
11 20000 00027
11" 00021 100.00
32 02050 00051
li ·~oooo OO()~O
31 02043 06043
75 20004 020:;5
24 02044 00036
24 60015 ,00021
11
~9()eO 20000'
62~64
45 000,0-0 02001
31 i0315 52421;
06 . 22071 32504
14 44116 65211
00 01272 340,41
77 63011 57010
02 10416 36646
65 25252 10030
11 77177 17645
01 00000 ooooc
6236.5
00 '70000 00000
6235,3
b23'~4
6,2362
6,2363
9-304
RW-149
SIN-2
Pg. 1 of 3
revised 5/1/56
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Small Angle Sine-Cosine Routine
Specifications
Identification Tag:
SIN-2
Type:
Subroutine
Assembly Routine Spec:
SUB
Storage:
21
instructions
9
constants in program
49770 03009
30 words total program storage
2
words temporary storage pool used,
addresses 00027b and 0OO30b
Drum Assignment:
Addresses 63052b thru 63107b
Entrance and Exit:
RJ
OOKOI
00K03
for the sine
RJ OOKOI
00K02
for the cosine
Alarm:
The alarm exit is used to print tfSIN-2"
if the argument is too large
Machine Time:
2.20
Mode of Operation:
Fixed point
Coded by:
M.
Elmore
April 22, 1955
Machine Checked by:
M. Elmore
April 29, 1955
Approved by:
w.
July 20, 1955
InS
average, 3.14 ms maximum.
pixon
9-305
RW-149
8m-2
2 o'f ,
Page
~'2-": ii:;2d
'\1' :; st
Revised 5/1/56
Description
When supplied with an argument x (- j!){ ~ x < n) scaled by ~2
(that is, X·~2) this routine will compute either 232 'sin x or
'
~2·cOS x, depending on which of two entrances is used. Computation
is by means of the Rand approximations using the repeated polynomial
multiply instruction (hence, SIN-2 should not be used on 1103
computers not equipped with the polynomial multiply instruction).
The absolute error is less than 2- 27 .
Programming Instructions
2.
If the subroutine has been assigned some
arbItrary regIon, say OOKOO, then the address of the sine
entrance is OOK03, the address of the cosine entrance is OOK02,
and the address of the exit is OOKOi. One should therefore use
one of two RJ instructions to enter the routine:
RJ to the subroutine.
RJ OOKQ1 OOK03 to obtain the sine, or
RJ OOK01 OOK02 to obtain the cosine.
3.
At the time of exit from the routine, either 232 ·sin x or
~2·COS x will be left in A.
4.
An
alarm occurs if x exceeds the range
Mathematical Analysis
Method used for sin x:
L
5
sin x
=
'qI
-r-I
I
x:2 1_ 1
i=1
,......
0'-
B2:-1
This polynomial is related to' the Rand Sheet No. 16 polynomial
by the following relation:
0'I
o
o
0'-
r-I
r-
Method used for cos x I
~
c...
x is replaced by (~) -
'xl
and sin x is found as above.
Machine Checking
The sin x and cos x of 15 values of x were found and the results were
checked against results of SIN-1 for the same angles. The answers were
identical, which is to be expected since the same polynomial was used in
both routines.
9-306
J
-
RW-149
SIN-2
Pg. 3 of 3
revised 5/1/56
D
D
82500
82501
82502
82503
82504
82505
82506
82501
82508
82509
82510
82511
82512
82513
82514
82515
82516
82517
82518
82519
82520
82521
82522
.82523
82524
82525
82526
82521
82528
82529
37
MJ
TJ
TJ
11
82500
81S00
75701
00000
81521
81521
81523
00000
81522
49770
63052
02000
63052
01024
15102 B
00000
81506
81S10
COSINE ENTRY
SINE ENTRY
ALARM lAG
TO ALR
75756 BRB
81500
MJ
81504
TJ
iM AOOOO 00023
TP 81521 AOOOO
5T 00023 AOODO
TJ 81S22 81504
TP Aooao 00023
MP 00023 QOOOO
63053
63054
63055
630'56
63057
63060
HALF PI
MINUS X
FOR COS X
63061
63062
63063
6'3064
STORE X
SA 81524 00041
TP ADOOO 00024
SP 81525 00035
RP 20004 81S18
PM 81526 00024
PM 00013 00023
TP BOOOO AOOOO
MJ 00000 81S01
01 57079 63268
-1 57079 63268
24 14065 67404 .6
01 00000 00000 B
02 60188 69075
6
-1 98074 14309
4
08 33302 51737
3
-1 66666 56696
1
09 99999 99470 - 1
--
X SQUARE
ROUND SCALE
STORE X SQ
C9 TO 6 REG
COMPUTE
SIN X
POLYNOMIAL
SCALE ANSWER
JUMP TO EXIT
32 ONE HALF PI
32
ALARM iAG
ROUND
43
40
38
36
(9
(7
C5
C3
34 (1
OFF
63065
63066
63067
63070
63071
63072
63073
63074
63075
6307·6
63077
63100
63101
63102
63103
63104
63105
63106
63107
00 00000 00000
00 00000 00000
37 15701. 75702
45 00000 OOlOOO
42 02025 02006
42 02025 02012
'11 02027 75756
45· 00000 02000
42 02026 02004
12 20000 00027
11 02025 20000
36 00027 20000
42 02026 02004
11 20000 00027
11 0002'7 10000
32 02030 00051
11 20000 00030
31 02031 000 /+3
75 20004 02022
24 02032 00030
24 00015 00027
11 30000 20000
45 00000 02001·
06 22071 32504
71 55700 45273
24 14065 67404
01 00000 00000
00 01272 34047
77 63011 57010
02 10416 3€,646
65 25252 70030
17 ·77777 77645
9-307
SQR-O
Page 1 of 3
Revised May 1, 1956
THE RAMO-WOOLDRIDGE CORPORATION
Lo s Angele s 45, California
SQUARE ROOT
Specifications
Identification Tag:
SQR-O
Type:
Subroutine
Assembly Routine Spec:
SUB 49312 04409
Storage:
34 instructions
10 constants in program
44 words of total program storage
4 words of tempora.rystorage pool used,
.a.ddress.es 00027b:-ihru 0003Zb
Entrance:
Address SUBOZ
Exit:
Address SUBOI
Alarm Exit:
The alarm exit is used.
Machine Time:
2.38 ms. maximum machine tim.e
Mode of Operation:
Fixed point
Coded by:
A. Roberts, Jr. (ERA)
"
December 1 J 1954
March 15, 1955
Code Checked by:
T. Tack
Machine Checked by:
M. Elm.ore
March 19, 1955
W. Dixon
April 29, 1955
_Approved by:
o
If)
~
---0"I
I
o
o
0"-
.-t
t-
><
Q..;
9-308
RW-150
SQR-O
Page 2 of 3
Revised May 1, 1956
Description
This routine uses a rational function approximation followed by one step
of the Newton-Raphson procedure to compute the square root.
written by A
It was
Roberts of E. R. A. and adopted for use at Ramo-Wooldridge.
·'Programming Instructions
'Assume the routine is stored at SUBOO.
square root is
desired~- place
H x is the number whose
x. 2,33 in the accumulator.
Since the
entire 7Z bits of the accumulator are used in taking the square root the
pe rmis sible range on x is
O'x<52539
ARG NEG
ARG ZERO
0153'7 01i03
SN 01538 ooOiS
T~
S2525
01S01
37 75701 75702
45 00000 00000
62141
AT
'TV
52524
01503
00 00000, O(lOOO,
00 OO()PO 00,000
0,0 0.0.0,00 00000
00 00,000 00000
EXIT
SA 0·15,35 00054
TP AOO'OO 01T02
MP 01536 01T02
52520
S-2S23
15702 B
00000
SF A 0;000 01100
TP A 00'00 AOOOO
TP A,aOaO OtTOI
52521
52522
62140
02000
000·27
00015
62140
26
50117 14640
62211
62212
20 00000 00000
24 35125 63704
62213
37 77777 77777
9-310
RW-1S1
RD-O
Pg. 1 ot 16
5/20/56
THE IWI)-WOOLDRIBGE CORPORATION
Los Angeles ·45, Calitornia
Bo~
Distributed..Pseudo.Rando. IIU1lbers
Specit1.cations
Identitication Tag:
Subroutine
.AsaeJib17 Routine Spec:
SUB 50010 02007
Storage:
20 yords tOtal . progr_ storase
2 vorda te.,or&r7 pool used, addresses
30b
1'he
:btraace ..... Exit:
am.
3lb
cOllStant pool is used.
RJ SUBOO
BUBO!
DOr.al entrance
RJ SUBOO
SOOl
reset entrance
472 + 690
o~
n llicroaeeonds (tor definition
n, see ...the_ticalJlethod).
I't n - 6 (the nor.al case) this g1ves
4612
...
-.....
-
~
o.eratioa:
~crosecond8.
F1xe4 point
1955
C04e4 07:
R. Bigelow
Jul7,
CCMle Clleclted. ])7:
•• PerI'7
July, 1955
Ilach1De Cheeked by:
R. Bigelow
lugwst, 1955
Report Written b7:
1'. Week
April, 1956
Appro'YeCl b7:
w.
111.7, 1956
t(')
~
I
0"I
g
0"-
.....
to-
Bauer
~
9-311
RW-151
IWf... Q
Pg. 2 of 16
5/20/5 6
Description
Repeated use of this subroutine produces a sequence of pseudo random
numbers from an approximately normal. distribution having mean equal to zero, and
standard deviatj,on equal to one.
Programming Instructions
Each entry to this subroutine produces in the accumulator a quantity
x.2 30 where x is a pseudo random number selected from the sequence described above.
~
obtain each x in the sequence use BJ SUBOO
SUB02.
destroyed between successive entries if the sequence of
The subroutine must not be
XIS
is to have the desired
randomness.
To restart the sequence, i.e., to obtain the first x again after the sub-
routine has been entered one or
more
times, use RJ
SUBOO
BUBOl.
The subroutine 11JfJ.y be modified to cause the sequence of XiS to more closely
approximate a normaJ. distribution.
that
5~ n ~32 and
make (SUBla) ::
To make this modificat1on choose a nUmber n such
(n - 1) _2° and make (SUB19) ::
{y 3/;;.') e2 35.
Increasing
n improves the approximat1on to a normal distribution and. increases the machine time
(see page 1).
The UXlDlOdifiedroutine uses n :: 6.
MatbemB.tical Method
Let l'i
==
52q+lYi-l· ( mod 2 s) , where q is a non-negative integer, and YO is
any ,odd positive integer less than 2
.-
~ pos~ tive
integers.
s
(~
appendix), define a sequence { Yi} of
Such sequences satisfy ma.ny- of the properties associated with
......
-
1
0'I
.
.$
sequences of random integers uniformly distributed between zero and
2.
8 many
(J'-
In fact,
such sequences have been computed and tested for Urandomness" and for "goodness
.-4
t;><
of fit" to a uniform distribution and have been found satisfactory for most purposes
0-
(see Testing).
9-312
RW-ISI
RAN-O
Pg. 3 of 16
5/20/56
If one assumes that the sequence {Yi} defined above is a sequence of
truly random integers uniformly distributed betveen zero and 2
sequence {x j
6
one can obtain a
,
~ of random numbers from a distribution which approximates the standard
(zero mean and unit standard deviation) nonnal distribution by appealing to a wellknown theorem concerning the distribution of means.
On page
69
of
[5]
there
appears the following
"Theorem:
If y has a distribution with mean m and standard deviation
a
for -which
the moment-generating function exists, then the variable
1)
x
= (y-m) rn/o
has a distribution which approaches the standard normal distribution as n becomes
infinite".
In 1),
Ydenotes
the average value of n sample values of y.
is applicable to the integers Y from the sequence lY )
i
i
exists a moment-generating function *
This theorem
because there certainly
for a unifonn distribution.
The mean m of the
is clearly
Y
i
°2 s _ 2 5 - 1
m -_ !.
2
•
2)
The standard deviation 0- is easily found to be
6'
=
1
YT
(See the appendix for a derivation of 3).)-
Let
n-1
Lk=O
4)
denote the average of n consecutive values of Y1 from the sequence [Y 'J beginning
1
with y ., j=O, 1,2, ... , and write 1) as
nJ
*
For the definition of a moment-generating funqtlon, see page 26 of
[5J
0
9-313
RW-ISI
RAJ'-O
Page
4 ot 16
5/20/56
According to the theorem, x j is the j th number in a sequence [ x
numbers from a
d1stribut~on
n becomes infinite.
6)
Xj
which approaches the
standa~
j)
of random
normal distribution as
On using 2) and 3), 5) becomes
(- I-s
= ,r.;::.
v3n y j .2
-1).
In regard to the sequence
sequence has period 2
s-2 •
[y'13 defined above,
it can be shown that such a
To obtain the longest period possible, s was chosen to be
35 for this subroutine.
Other computing installations have chosen q as large as possible, sUbject
only to the restriction that
2q
5 +l must be contained in one storage register.
Since
multiplication time on the 1103 is a direct function of the number of btnar,y ones in
2q l
one of the multiplicands, 5 + was somewhat arbitrarily chosen to be 55.
See [IJ.
In order not to introduce a bias at the beginning of the sequence, the subroutine
uses for YO the 17th integer in the sequence obtained using YO ;;; 1, namely,
13 41437 54765b.
See
[lJ
It -was stated under Programm1 ng Instructions that the unmodified subroutine
uses n
--;:::; "normal
--
= 6.
n
..-t
I
0"
I
o
o
0"
..-t
It is believed that this value of n will yield numbers sufficiently
for most purposes.
See Testing •
The subroutine does not use formulas 4) and 6) to compute x •
the following equivalent process is used:
j
Instead.
FonD.
r-
and then,
9-314
RW-151
RAN-O
Pg. 5 of 16
5/20/56
8)
Using n ;:::
6,
and s ;:::
35, it is easy
to verify that
7)
and
8) are equivalent to
4) and 6).
Testing
In the first paragraph under Mathematical Method it was stated that many
sequences
[Yi)
have been computed and tested for "randomness" and for "goodness
of tit" to a uniform. distribution.
BEAC [2]
One such testing program was carried out on the
using 2q+l ;::: 17 and s = 42 •. Another testing program was carried out on
the ORDVAC [3J using 2q+l ;::: 13 and s = 39.
A similar process tor generating pseudo-
random integers on a decimal computer, i.e., the UNIVAC, vas devised and tested
In all of' these testlngprograms, the integers generated were judged to be
tory" •
U
[4J .
sat1sfac-
But in all these testing programs q (or its analog on the UNIVAC) vas chosen
as large as possible, subject only to the particular machine register capacity.
Therefore, the small value of q used by this subroutine on the 1103 (in order to save
multiplication time) 1s somewhat questionable.
In fact, Juncosa [3Jstates that
k
k
if' 5 is used, k should be an o~d integer such that 5 iS "preferably- slightly less
than 2
..-..
II •
I'""f
-
~The
would in some sense test
Therefore, it was decided
th~
psewio normally distributed random numbers x j •
results obtained with the testing routine can be termed sati$factory.
8 details,
~
The choice of n ;::: 6 1s likewise questionable.
to write a routine, which shall hereinafter be referred to as the testing routine,
~wh1ch
I
s
For more
see the appendix.
t-
~
The subroutine , with q ;::: 2 and n
satisfactory results.
= 6,
has alread..jr been used with apparently
It was used to evaluate a :function in the form of a Fourier
series with normal.1.y distributed random. coefficients.
It was also used to simulate
9-315
RW-1Sl
RAN·O
Pg. 6 of 16
5/20/56
random and correlated radar noise.
In this
connectio~,
the theoretical distribution
of Xj was computed and plotted'* (assuming the y i to be from a truly uniform distribution) with n·= 6.
This plot is shown, along with the standard normal. distribution,
as figure 4- in the appendix.
The difference between the two curves would be con-
sidered negligible for :roost applications •
However, there is a difference which does
not show on the figure, and which might be considered important for some applications.
From 4) and 6) under Mathematical Method, one can show that
{ Xj I
for n = 6.
<
pn
<:
4.25
Hence the probabllity of obtaining an ( x j
12! 4.25
is zero.
the standard normal distribution, the probability of obtaining an
But, for
Ixl ~ 4.25' is
about one in fifty thousand •.
'*
The writer is indebted to R. Schvarz for suggesting the computation and carrying
it out.
References
1.
Pseudo-Random Humber Generator Subroutine, CV-28, Bovember, 1954, 1103 Central
Exchange Nevaletter Number 3, January, 1955.
2.
Generation of' Pseudo-random lfumbers, IBS Bepo.rt 3370, Olga Taussky and John Todd,
......
June 22, 1954.
::I 3·
Random lUmber Generation on the lmL HiSh-Speed Computing Machines,
In
BRL Report
0'
I
855,
M. L. Juncosa,
¥ay, 1953.
o
o
No.
~4.
The Generation of Pseudo-Random Numbers on a Decimal. Calculator, ACM Journal,
0'
vol:-. 1, 110 •. 2,pp. 88-91, Jack )bshman, April, 1954.
5·
Paul G. lIoel, Introduction to Mathematical Statistics, John Wiley and Sons,
New York, 1941.
9- 316
RW-151
BAi·O-' ~
Pg. T of 16
5/20/56
Derivation of 0
If the uniform distribution function t(y) is Cbosen so that the area
,
under the curve is unity, the variance6'
2
1s equal to the second moment about the
mean m, i.e.,
(J' 2 =
f2m (y-m) 2 f(y)
f(y)"
dy J
~
Y.
0
= 28 J
m = 1 •2
S
= 2s - 1
I
I
~I- - - ,
~
I
o
where 2m
~
•
ely
I
m
am
y
,,
To make the area equal to unity, f{y) must be
2
1/2m.
0
2
Thus
=
112m J2m
.
or
2
(,.2_ 2my + m ) dy,
0
0
2
2
=!L-' and 0"
3
== m
-v:sr
which is 3) under Mathematical Method.
The Testing Routine
The testing routine uses RAN-O (with q = 2 and n
= 6)
sequence any number M of sets of N x j , s, likewise in sequence.
data used in
f~s
to generate in
For example, the
1, 2, and 3, was produced using M == 512 and B == 100, so that
MN == 51,200 xj's were generated" in sequence and divided into 512 sets of 100 each.
For each set of 11 x. I s the foliowing three quantities are computed and punched on
J
cards using CPO-2:
- l'
Ii
1.
x =-
11
~x.
j=1 J
9-317
RW-151
RAJi1"{).
Pg. 8 of 16
5720/56
.
x is the sample mean and
2
is the sample variance.
6
where-B- is the actual number of Xj's for which a ~ Xj < a + , and e is the number
t
i
i l
i
of
Xj fS
for which it is expected that
ai~
Xj 2, q~ 0, s and
2q + 1_ S
" such that 5
,2.
11 of the sequence
I.
= ...k
8
-
2
8-2
{r
then the sequence Y1ll repeat 1tee1t •
the 2
S
+ 1< 2 , e.g., YO = 1, the first 2
integers
s
11 will be the 2 -2 distinct inte~rs of the form q.k + 11 and
If' YO
S1m1larly, if' YO =- 4k + 3< as, e.g. , YO = 3,
distinct 1ntegers generated w1ll be of the form 4k + 3.
9-321
PX 71900-9-(151)
.10
.09
.08
.07
,,
I
\
/'
f
.06
I
\
\
I
\
I
.05
I
.04
.03
I
I
I
I
I
I
I
I
I
\
\
\
I
\
\
.02
.01
\
\
\
\
,
"',::1
...
o
~
l ...... ~._~_
~--~~~~----~----------------------~------------------------------------------~~~----- .3-2 -.28
-:.24 -.20 -.16
-,12
-.OS -.04
.04
.16
.28
.32
.08
.20
.24
.12
o
X
FIG.
PX 71900-9-151
I
.028
,-,
,
r---'\
I
\
\
I
\
I
\
I
\
I
'\
I
I
024·
-.
I
\
\
\,
I
\
I
\
\
\
I
I
\
\
.020
\
I
I
I r
I
J'
f
I
J
.016
I
I
J
t
I
I
.012
I
I
I
I'
\
I
\
I
I
.008
\
I
\
I
I
\
\
I
I
,I
\
\
\
I
.004
'\
\
\
--..".
0
.50
.58
/
/
"
/
.66
.74
.82
.90
1.06
.98
S2
J="I~
?
1.14
1.22
"-
1.30
.~~~~
. . . . ~ :e:
ro-
1',
I'
o
...............
0 .....
.........
\JlW
0\
........
1......... --~
1.38
I.~S
0
HJ
1.54
.....
0\
UI
.....
PX 71900-9-(151)
II
.1'
.10
,
I
i
I
I
I
9
"
I
I
11
~
\
\
I
.os
\
I
I
I
f
\
I
I
,
.0"
\
'\
\
"\
f'
I
,
.0,
I
I
\
\
\
I
,I
.0&
\
\
I
w
\
,i\,
,
.04
,I
.03
"
I
I
,I
,,
I
.0 I
I
I
I
I
I
"
I
1
L~-:_/
o
2
,,
~,
I
-02.
\
4
6
8
10
t+
12.
)..2
FIG. 3
,
' ... , ....
.
. . 1 . . . --._
22
1----.-----.
24
2'
-
PX 71 900-9-(151)
I
.40~.
!
o
NORMAL DISTRIBUTION
<2> fb
(X)
f{X)
-
-0
2.0
4.0
FIG. 4
x-''''''
II-lSI
RAR-O
Pg. 16 of 16
5720/56
(lOROC OJ (,2,4(: 3. G 3 7
·n
o
0200.u
00 i:lOOOt) 00000
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OG OV(.H")O DvO(JO
i)
6:;;,'·:~2
o
t,34 i", ~f
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:)0 l,{'(L,j'C OCUt,){,,f
00 Jcr)on G~';)e0
(;0 \)0:.)00 (\0 JOO
ROUT !r-!E
reM'P ::'.T{)R
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;J~'IO l'~
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CO~) ~:'3
onG i.~;
lROO
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EXIT
lROl
lP~)-\}T03
{)OT04
EnlRAi~Cf
TP 00}05 00302
TP <.}] ({',O C~S~·:
;~~. 00104 U01'{) t:
TPO{l'fO 1 QOO(:C
Cl l\OCGO ~;O T04
[NTRAN.Cf~
lRO·2
IRO:;
lRC4
l-~{j 5
IRv€>
r
6"34·37
45 O(i{lOG 00000
1
634~.3
II 020:0 02c21
2
63434
11 620t~ 2 C0011
11 otio 1 ~ i)OO 30
71 t)2{)21 G':() t 1
11 62') 16 1 ()o.()·o
'.t:.t 20000 'O~»21
31.j· ,0:2 (.: 15 00 l 0 ~
, ~', O.O{; :3 {: o·o() 30
t.l 0003.l OZ004
ti3:'t-35
63.ft36
634·37
6·~~4/~ D
6.3 1.:41
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n
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lR12
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MP OOSOl OOTOb'
NORMALIZE
?O 9 \}t. Z: f)uti r.·\lCC
f~
~E-AH
€.
TP 00300 AOQOO'
ffiJ' OOOt'O OOR 00
'F17
j"{
Y 7.0
6'.. l~·lt :A.
63tfo·4·3
63444
63445
!~ 34i.. 6
c :)~J(;';;
j
-s
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R
R7.5ET '-(0
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00 f.i~') ~8
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.
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v
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f; ')·~5 2
634!-'3
f>.345/l
63.ffS~
11 OGQ3() 02023
1.1 30000 20000
I.t t., O"O{}.OO (0 ~! O~) C
?c: eon·V\) (}Ci~)(H)
';-.7 ,'r( I i -: "ll7-;
(4) OOiJ(H: o(~rJh 5
].~ 4- 1 ,~:. '7 5.{! '( 6 S
1~\ 1.1437 =41b'S
~t)
aoooo
00005
26 ~)O 1.:6 76:120
9-326
.
RW-152
RPH-O
Pg.1 of 3
5/23/5 6
THE RAMO-WOOLDRIOOE CORPORATION
Los Angeles 45, California
Column Heading Routine
Specifications
Identification Tag:
RPH-O
Type:
Service routine with program entrance
Entrance and Ex1t :
37 40020 40022 b to read a card
i
31 40020 40023 b to punch a card
Coded by:
R. Beach
May, 1956
Approved by:
w.
May, 1956
Bauer
RW-lS2
RPH-O
pg. 2 of 3
Description
~is routine viII
read in one card "or punCh out one card each time it
is entered. It allOYS the programmer to include column headings in
listed output when using either SlIAP output or cpo-a. The routine
stores cells 1660 b - 1171 b in the MD image.1 then bootstraps itself
into ES f'or operation. Arter completion of the read or punch function,
ES is restored and control returned to the program. A and Q are not
altered by the routine.
B:xecutiDg a read. entry causes one card to be read and a com.plete
alphanumeric card image to be stored. Executing a punch entry- results
in punching a card 'identical to the one' read in with the exception of' .
the twelve row of field three which is replaced with punches to control
the 407 (See ~rat1on). Only numeric information can be ptUlched in
f'ield three and the information in this field will be printed by the'
407 at the extreme left· of the pase, followed by 6 spaces.
A parameter word is used to specify' the first of the 36 wo:nis in
which the card image is to be loca~d upon, reading, or the first of
the 36 words trom. which the card image to be punched.
!he routine assumes that cards have been poSitioned in the Bull, but
it does not alter card. pos1tionirla ,when used. A blank card. will be
fed on tbepunch sla. ,,1len the :teati ,ent17 is executed.
Programming Instructions
1.
To read a card. Enter the routine with 37 40020 40022 b
followed by a parameter word of the form 00 00000 xxxxx where
lCOCCX i8 the a.d.dNas ot the f'irst cell in memory in which the card
image i& to be placed. Control 1s :returned to the instruction
following the par8meter word.
2.
To punch
f'ollowed
xxxxx is
image to
........
a card. Enter the routine with
by a parameter word of' the f'orm
00 OOOIY XXDX where
the address of' the first cell in memory at which the
be punched is located, and IY is:
00
thru.
19
for single spacing
20
thru
29
for double spacing
30
thru
49
for triple spacing
50
thru
89
tor page ejection
C'\I
tr,)
......
37 40020 40023 b
'-'
I
0'I
8
0'-
......
t--
~
The spacing takes place bef'ore printing the card. These page controls are identical to those used f'or SliAP with the exception
that in this routine the combinations 00 thru 09 have the
same effect as the combinations 10 thru 19-
9-328
RW-152
RPH-O
Pg. 3 of 3
The twelve row of field three of the card image will be replaced
by a row containing the page controls and a SlAP identification
punch (12 punch in column 75). It is advisable, therefore) to
use only columns 1 thru 72 of the card for heading purposes.
Only numeric i.nformation can be printed from field three. Since
the card contains a SlfAP identification punch, the word spacins
in the first 72 columns will be the same as for SNAP; that is,
four spaces are inserted after columns 12, 24, 36, 48, and 60.
The numeric information in field 3 is printed at the extreme left
of the page.
Restrictions
The card image may be located anywhere in memory except cells 1660 b 1777 b (and also with the exception of cells reserved for the R-W
library) . It is recommended that card images be placed on the drum
since the time involved in reading and punching using drum locations
is very nearly the same as that involved when the card image 1s in ES.
Suggested Use
It is suggested that the input heading cards be placed at the front
of the input deck, and that they be read in by the program before other
computation is begun. Output heading cards can then be puncbed by
the program at any time.
9-329
CV-153
PAGE
IC 010-1
REPORT NO.
ZM 491
CONVAIR
ANALYSIS
ptREPAR£D BY
C. J. Swilt
L.... Barton
CHECKED BY
SAN DIEGO
MODEL
REVISED BY
All
DATE
5-2e-56
COBTROLLER
A CARD HANDLING SUBROUTllE
I.
Ie 010
DlSCRIPTIOI
fbi. .ubroutine simplifies the reading and punching of cards
espeoially in ease. where bloeka of cards with the same format are
handled.
It will be available shortly with the service routines on
This aubroutine 'operates trom the drum and handles all necessary
block transters.
Up to
63 cards in each channel oan be handled by one
.ubroutbw reterenoe, re.diD., and punching proceeding cCIlcurrently it
d•• ired.
'l'here are thre. entrance. to this subroutine
.a
deaoribed
below.
II.
CARD FORIIATS
Bach card format ls described by a aeriea of paraaeter lIOrda ..a
de.oribed in
Ie 005. Ie 006 and Ie 001. For us. with this subroutine,
theae worda are preceded by one word, mol the number ot fielda on the
car..
TheBe for_ta _at be stored ill MD.
(0' "" :( 3'
),
I II. DTlWICBS
1.
Prime.
.ext instruction
!hl1 lubroutine 1. a1_)'8 one read oard ahead ot the ma1n progr....
It reta1na the information trom thia card within itself.
For this reason,
when a new deck of card. 1s pl~ced in the read hopper, the subroutine
must be primed
a8 . . 11 a8
the reproducer.
Both are primed by thil
entrance to the 8ubroutine.
.........
-~
9-330
CON
ANALYSIS
PREPARED eV
CHECKED t;:JV
A
V
CV-153
R
C. J. Swift
L. W. BartoD.
IC 0104
PAGE
R£PORT NO.
MODEL
REVISED BY
.QI 491
A.ll
DATE
2.
5-28.56
READ
37 00000 70402
nn j j j j j vvvvv
lext instruction
This entrance cause nn cards of format j j j j j (first address for format)
to be converted and stored in cells
.tartin~
with vvvvv. (which may be
in ES or liD).
3.
PUXCH
37 00000 70401
nn j j j j j
VTVYY
Next instruction
This entrance punch•• nn carda of format j j j j j using data atartl nc
in cell vvvvv. (which may be in ES or ID).
IV.
OPm.ATING NOTES
1.
If the -next instruction- after a punch card entrance is • read card
entrance. the operation. of reading and punching will begin simultaneously_
2.
Whenever reading occurs without 8imultaneous punching. a blank card
will appear in the output.
3. After approximately 270 words are read or punched. the reproducer
will dr0p out of operation mo~ntarily while block transfers are effected.
h.
In case of trouble with the repJ;oducer.
5. 10 007
1. contained 1n this routine.
and is modified to operate
v.
from loeation
8
tart at 00000.
It is located in eell 70656
00670.
SPECIFICATIOlfS
LOCATIONs
70400 to 71257
TEllPORAR IEB c
74001 to 75777
This subroutine is not standard and i8 not to be modified.
SUlJl
Its
j
is Calstant.
9-331
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO C.<\I..,FOR""'A
CV-153
PAGE
REPORT
MODEL
DATE
All .
CONTROLLER 6/4/56
70400
45 00000 70402
70401
45 00000 70402
70402
41 00000 00000
PICKUP ADDRESS
70403
75 31777 70405
SAVE
70404
E'S
70405
11 00001 74001
11 20000 00002
70406
31 20000 00017
70407
70410
15 20000 70411
75 30004 70412
70411
11 30004 00422
70412
75 30660 00426
70413
11 70414 00426
IN ES
STORE ADDRESS
PICK
UP
CALLING
SEQUENCE
PLACE CONTROLLER
70414
00426
15 70410 10411
RESET DRUM SUM
70415
00427
16 00002 00635
SET EXIT
70416
00430
55 00422 10042
TEST
70417
00431
44 00433 00432
70420
00432
44 00436 00621
70421
00433
11 00423 00425
70422
00434
11
70423
00435
45 00000 00441
70424
00436
31 00424 00000
;; 70425
00437
4~
00440
11 00640 00425
CLEAR NV2. 00641 TO J2
00441
23 00635 00643
ADJUST EXI.T
...... 70430
00442
15 0042:a 00466
SET FORrv1AT
70431
00443
15 00425 00464
70432
00444
70433
00445
16 00423 00510
21 00530 00644
70434
00446
42 00645 00450
70435
00447
23 00530 00644
70436
00450
31 20000 00017
70437
00451
15 20000 00550
tn
......
70426
~ 70427
'j'
0
0'-
t-
><
Co.
O()640'(\C'42~
Fr~ST
ENTRANCE
NJVl TO NJV 2
CLEAR NVI. nn641 TO Jl
TEST SIMULTANEOUS
00642 0044'
IC 010-3
491-I1
Z)(
READ
PICKUPS
TEST
AND
SET
PUNCH
PICKUP
TO PIN
9-332
5-28-56
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
CV-153
PAGE
Ie 010..q
REPORT
ZJ' '"11 ... 11
MODEL
All
DATE
5-25-56
COr-!Tr:;OLLEO 61ft/56
70440
00452
16
70441
00453
21 00530 00644
70442
00454
47 00645
...,..,
0042~
0:1530
TEST
t . :'!~
084~,6
qEA~'
r:',~T
70443
00455
70444
00456
70445
ti045
7
31 004?? 00.')52
rn TO
70446
00460
11 20000 ()O4?6
t·'6
70447
00461
31 00475 00052
70450
00467
1 1 200ClO 00423
N6
7~451
00463
75 30037 ()O465
PICKUP
70452
00464
11 0.0000 til 740
READ
70453
00465
75 30037 00461
PICKUP
70454
00466
11 00000 00430
punCH
70455
00467
55 01740 20000
Nl LESS
70456
00470
36 00430 20000
70457
00471
46 00472 00413
LARGEP
70460
00472
11 00430 10000
TO
70461
00473
31 00646 00000
70462
00474
73 1,0000 004'"
70463
00475
11 10000 00425
.l'.,rlO
70464
___ 7046-5
00476
11 00423 20000
COf'.1PUTE
00477
73 00422 004:?3
. . .J:~
noson
47 00S03 r'!"''5i'1
Tt"ST
00501
23 00423 0064)
ADJUST
70470
00502
11 00422
r- 70471
00503
11 20000 00424
STORE N4
><
0.. 70472
70473
00504
TEST
00505
11 00423 2000('j
47 00507 00506
70474
00506
11
70415
00507
11 00426 20rO()
70476
0051-0
73 0042t) 00426
r·13
70477
00511
47 00514 00512
TEST
C't)
~
70466
-- 70467
I
0'
.
L.:)
00530 00644
STORE
16 20000 00576 .
rq0~1
N~
r:'Pl
TO
F0R~1AT
FO~MAT
r-,q
Q
272 DIVI9ED py
Q
"0 N'
~~
~~
2
4 FOU.".L rFr.'1J
I
0
0
0'
....-4
004~4
20~00
004~2
N3
~J
f~ND
~·l
4
3
tJ4 TO f':?
COMPUTE
~.14
f'JIJ/l..l
lr:~O
9-333
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
CV-153
Ie 010-5
PAGE
REPORT
MODEL
All
DATE
5-28-56
ZU491-I1
CONTROlLER 6/4/56
10500
00512
70501
70502
70503
70504
70505
70506
7a501
70510
00513
23 00426 00641
11 00425 20000
ADJUsT ~:3
AND ~14
00514
00515
11 20000 f')0427
71 01740 00422
STORE M4
00516
00511
00520
00521
11 20000 10000
23 00576 10000
11 00423 00467
11 00426 00470
21 00467 00641
00522
LOWER READ
STORE BY
Nl TIMES N2
N3 TO R
M3 TO S
N3-1 TO R
M3-1 TO ~.
1 TO P
1 TO Q
SHIFT READ
FORMAT
70511
70512
0052'3
00524
70513
00525
11 00641 00471
11 00641 00472
70514
70515
00526
75 30037 00532
00521
70'516
70517
00';'30
00531
70520
70521
70522
00532
00533
00534
11 01740 0047:3
CO 00000
00 00000 00 *
45 ooono 00533
23 00412 00641
47 00560 00535
7052'3
00535
23 00410 00641
5-1 TO S
-~ 70524
~ 70525
00536
47 00537 00544
TEST
00537
46 00540 00545
TEST
70526
00540
00541
23 00611 00647
16 00650 00604
SUPPRESS PUNCHING
SET SWITCH £
16 00651 00532
45 00000 00544
SE·T SW ITCH A
~ 10531
00542
00543
70532
00544
M4 TO M2
70533
70534
10535
0054::
11 00427 00425
11 00425 00472
00546
16 00652 00612
00547
7G536
70537
00550
00551
75 30420 00560
11 (H" ('no 00002
16 "00664 01012
-~
~ 70527
....
r- 70530
21 00410 00641
$\-11 TCH A 00557
0-1 TO
Q
TEST
$\1 ITCH B 00626
M2 TO
Q
PUNCH BIN
PICKUP TO
PUNCH ~tN
PATCH
RESET
9-334
CV-153
CONY'" - OtVIStON OFGNlAl DYNAMICS CORP.
aA.N OI'GO CA~I"~"'"
IC
ZII
MODEL
All
D~ T E
5-28.56
CON:ROLl!R 6/4/56
00552
45
ooono
"07'C 7
005t:3
16 00662
01~12
00554
4~
70C\4.,
OO~SS
')0 00000 00662
7(')544
1'\0556
77 43\.''10 1('100
70545
011557
16 00652
~O612
Rr=~ET
7':)546
OO~60
45
onroo
00561
~I':
7:>540
70541
70542
IN Ie 007
CARD
SUBROUTINE
f"\f)()OO Of: 1('14
P~R.oMETEP
~JN
PUN-:~
ITCH
e
P-l tC
TFST
p
<'0605
70547
00561
23 00471 0(1641
70550
~O~62
43 0('641
70551
00563
TEST
10552
00564
41 01')610 00571
11 0:1467 20000
7055'3
0056~
i.7 00610 00566
~
705~4
00;66
11 00653 10')0"
70555
70556
Ot)~67
'53 00653 r0611
00570
45
O')OOf)
{"~61('
70557
00571
37
n~~71
00577
70560
00572
SET TO
70561
0"573
70562
00574
71 ('0473 00422
.,.., 006'54 OOC17
15 2(\1'\0') ("IOS1t)
70563
00575
75 70000 0('1577
5TO~E
70564
00576
11
-70565
C")
00577
~ 70566
00600
?3 on467 CO~41
47 on601 Q06r5
J.
70567
00601
l~
~ 10570
00602
23 00611 01656
70571
('10603
16
~ 70572
00604
37 00560 ("1(\605
SWITCH E on626t
70573
00605
11 00424 00422
Nit TO N'-
70574
00606
16 O()655 n0611
Rf5ET Rcftr.'
7057'5
00607
11 00422 00471
N2 TO P
70516
00610
37 006 7 0 00670
ENTER Ie 007
70517
00611
33 00474 01360
'-'
I
,....,
t--
j
CO~'>4
(
01'?~'"
3C"OO
6 00602 00606
,~t')650
('r.34~
TE~T
PICK
SET TO
PIJNCY (,~Rf)
ON LAST
S\'.'TTCH "
~rAD
00571
' STORE
'nl N2 WORDS
FRn:<1'
READ BIN
R-l TO R
TEST
TEST
SUPPRESS
'~ET
~,I,.!
~EADPJG
tT(H
~
~~T
swrTC~
010~
REPORT
PAGE
c
Bt,.~
CARD
9-335
491 ... 11
CONVAIR - DIVISION Of GeNEltAl DYNAMICS CORP.
!'i ......
OI~GO
(IlUf
CV-l53
MODEL
IC010-7
ZM 1J9l-1I
All
DATE
:-2~-56
PAGE
, ........
REPORT
C~~!TROLl
EP 6/4/56
5UaQOUTINE
RAISE BIN
70600
00612
00 0.0431 oaOO2
70601
00613
21 00611 00473
70602
00614
21 00612 00430
70603
0061'5
21 00576 00473
70604
00616
31 00430 00017
7f)605
00617
35 00550 00550
70606
00620
45 00000 00532
70607
00621
23 00635 00657
70610
00622
17 00000 00660
70611
C06?3
37 00670 00670
70612
00624
70613
00625
31 00556 00002
00 00000 0& *
7'1614
00626
23 ?('IOOO 20000
~UM
70615
00627
75 20011 00631
70616
00630
3'? 01212 00000
70611
00631
13 20000 01223
70620
00632
75 30012 00634
70621
00633
11 01212 71201')
70622
('0634
2.1 00635 00661
BCD
BIN
ADJUST oRU!->1
BCD AIN
TO DRUM
ADJUST EXIT
70623
006'35
75 31717 0000]
RE~TORE
10624
00636
11 74001 00001
~ 7~625
(;0637
on
:: 70626
,
00640
00 00641 00000
9'
70627
110641
('\0
~
....,
70630
00642
37 00000 70402
70631
00643
00
00644
00 00000 74000
70633
00645
00 00000 76000
70634
00646
no
70635
(')0647
'-2 oonoo
~oooo
70636
(':'065("
r'O
(,0~OO
~f')626
70631
00651
no noon!')
<'0557
lQ
0
.....
~ 70632
0('000
("11'\(')(10
orooo
*
()I"!
01
00 02
C'C'OOIJ 00420
ADD~ESSES
RAISE
STOqAGE
ADDqE'~~E~
ADJUST EXIT
PICK CARDS
PICK CA~DS
AND READ
TO BCD B tr·!
SU~1
ES
AND EXIT
C
0
N
S
T
A
N
T
~
9-336
CONVAIR - OIVtSION Of GENERAL DYNAMICS CORP.
CV-153
MODEL
IC 010-8
Lf) 1-11
All
DATE
~-28-56
PAGE
REPORTIII
CONTROLLER 6/4/56
70640
00652
00 00000
2
70641
006£33
20 0000C'
"1("\;)0(')
70642
00654
00 O(,00() 31')00()
7064~
0061)5
1")0 f')(\()OO nl~6"
70644
00656
11 00000
10645
00657
00 ("0000 ("0 03
70646
00660
('0 00000 ('"10114
70641
00661
Of')
70650
00662
75 1<"011 01013
CLEAP
70651
00663
11 00667 01212
BC~
706'52
00664
70653
00665
00 1")"'0r)O ('H"7~3
00 00000 0*
*'
70654
00666
00 00000 ('10
70655
00667
00 COOOO 00 0
10656
00670
71 01166
70657
00671
15 20000 0()724
70660
('0672
70661
OOe73
"616
70662
00614
55 20()OO ('\I)OOi
70663
00675
'31 01163 0OO0j
70664
00676
c:,.,
70655
00677
32 20000 OOO()l
-. 70666
00700
44 00701 0(1701
70667
00101
44 010:::3 0070?
0"-
70670
00702
16 011':1 (')101"
0
0
0"-
70671
00703
44 00551 0055'3
..... 70672
><
c.. 70673
·00704
37 010t::tj 01011
00705
Ij.
1°674
00706
4!5
70675
00707
37 01050 00714
70676
(10710
7~
('1"'('('('1
"1?66
70677
00711
76
1000t'
01?"~
('I'j
If:)
1"'-/
........
I
I
1"'-/
./
/
(')t'I"It'V)
~OO("lC'
("II)
(')4
[5
I
~.:
'*
~O611
'-00(')('1 ('\n76?
START OF
Ie
007 CARD
~URq()1
fiI NF
01014 ('10000
01202 70000
1 0077-r
Ol!~~
JUMP TO PATCH
!'1
CHANSE
1"'~')4;?
(,""'I
f; , ..,.
9-337
CONVAIR..;.. DIVISION OF
GEN~RAL
DYNAMICS CORP.
SA ... DIEGO CALIFORNI"
CV-153
PAGE
IC 010-9
REPORT
Zll h91-I1
MODEL
All
DATE
5-28-56
CONTROLLER 6/4/56
70100
00712
76 10000 01252
70101
00713
45 00000 00721
7J107.
00714
~'- 01166
70103
00715
57 00713 01011
70704
00716
41 01017 00766
70705
00717
16 00771 ("11011
707"6
O()7LO
n07?.1
007?2
37 00713
(H"76~
15
0114'"
?:7 01012 n0706
70711
70712
00723
37 00765 00724
00724
10713
00725
55 00511 00000
44 00726 00127
70714
00726
16 00555 ·00765
7071'3
00727
70716
00730
70717
00131
55 10000 00013
51 01203 20000
16 2.0000 ~0753
70720
00732
55
70721
00133
51 01203 01123
10122
00734
55 10000 00006
70123
00135
51 01203 Oll17
70124
00736
55 10000 00006
70725
00737
51 01203 00777
70726
00740
32 20000 00016
00741
35 01154 00142
70730
00742
00 00000 00 01
70707
7~710
"'"
It'')
..... 70727
CV':I
'-'
I
0-
0115~
InOOo
oooon
D
CHANGE
C\OOO6
I
0
0
0-
70731
00743
37 00743 00144
.....
t- 70732
00744
41
5::
70733
t')074~
37 011'10 00746
707'?J4
00746
41 01117 01140
7073')
00747
37 01144 007'51
70736
007';0
37
011~0
00751
70737
C07'il
41
007~7
01140
0112~
01137
9-338
CONVAtR - DIVISION OF GENERAL DYNAMICS CORP.
CO!'~T~OlLEC(
70740
00752
54 007·'+::' 10107
70741
00753
31 01123 00000
707 q 2",
00754
32 10000
707l~?:
1"'0755
7"
. -'
70744
?:7 01144 01140
707 1r5
00756
007')7
51 01161 20000
7r'!746
""07~(':
!~
7
('H")761 ("076')
70747
00761
1::3
rl11E- 01116
0071+
("I()7f>4
':']
7'-::75'"
00765
I!,- :,
f<'
(lrerr:
70754
007t6
11
nIls:,; 00777
70755
00767
~ ~,
r! '")
70756
00770
1.1 01':'0'" !)l?3f
70757
00771
:':1
7")760
()O772
37 ;::'"'·"("8 :)i"O-::
70,761
0')773
I~
70762
00774
";")
707f.3
70764
n0775
00776
h6 01"1-'-'r-, (',,,77')
31
?('I('I),)
r:;/)00
"0765
00777
'l.~
01'))~
1)1??3
..-. 70766
rlGOr
?l r;11777 t"l?nr:.
~lL.?7
21 0172h 01? r') '+
{;
('()"7
~r.;
0.1 11S5
()')7"'4
0116~
('~""1~
(i
('If')!) (j
(\'''lC)11
00"'7~
(11017 ('('Iroo
l.Ij
...-I
707c:
01001
4l
.~
1 :' ?f;
1"\1)77'
"
. l
I
7077':'-
11007
37
i~ll"l:'"'·?
r;10"'1
70771
~
1 CO?·
5c
(,1::-;~
"'11"\,..../)('1
...-I
7r".77'!.
"lO04
37
'l~"'!")?
"'077,.,
><
c..
7'-"77'7:
:"'l('r;r
~
",
t" 1')('\
7f'.77lJ.
01(;06
~7
r. '1 :"''' '"l
('\:)771
7'!77~'
01('~'7
16 01r..l lL
"":"'110rj
7";7,7(:
010,10
t.t
I
0
0
0"-
t-
7"'.77"7
'::1"':1 1.
5-.28-56
'? 01.116
707':)';'
--
All
DATE
(\00()(I
11 0111(;
0"-
Ie 010-10
ZK L91-I1
PAGE
REPORT
MODEL
6/4/56
70750 '- 0076?
70751 00763
M
CV-153
r
--. t. £.,
~.I-4.
5
0(!1"'')t'1
'" 1 "'~!?
17
0 rr,.,....1"\
-: ,. ,-- ;- "
9-339
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SA,... D!EGO
( "L IF ,',RN I 4
CV -153
PAGE
REPORT
MODEL
DATE
Ie 01C-11
ZM 1.)1-I1
All
:-20-56
CONTRGLLER 6/4/56
71000
01012
45 00000 0(\723
71001
01013
36 20000 ('10777
71002
01014
27 20000 00670
7100::·
01015
35 01166 01017
71004
01016
35 01165 00706
11005
01017
00 00000 OOOl1
1100(:
01020
11 011 7 0 01017
710n7
01021
75 10044 01007
71010
01022
11 00667 01223
71011
01023
32 01163
noooo
71012
01024
37 n1010
0070~
71013
01025
15 20000
010~3
71014
01026
32 20000 00016
71015
01027
15
71016
11 01162 01267
71017
01030
()1031
11 01155 01270
71020
01032
37 01045 01033
71021
71022
01033
55 00446 00000
01034
44 01035 01051
71023
01035
37 01045 01051
71024
01036
16 01051 00777
;; 71025
01037
75
01040
16 00710 01045
01041
37 01010 01044
71030
0104'
7t1 20003 rtl044
'""" 71031
r-
01043
23 01045 01"166
Ei:: 71032
71033
01044
16 01014 00000
01045
71034
01046
77 00000 01253
77 lr,OOO ~1'~3
71035
01047
77 10000 01237
71036
01050
45
71037
01t151
55 10000 1')0013
an
!: 71026
I
~
o0
0'-
71027
-
~oooo
~OOO3
onooo
0
CHANGE
CLEAR I ~~I\Gr::
ONLY L! CHANGE
01067
(')1041
()O710
9-340
CONVA'. - DIY'StaN OF GENERAL DYNAMICS CORP.
CONTROlLEP
CV-153
IC 010-12
PAGE
REPORT
MODEL
ZM 491-1I
All
0.6. TE
5-28-56
6/4/56
11040
01052
51 ') ~ 2 ,"' 3
11041
010C"3
~,
71042
010 r 4
;--:l('~~
?t)()C"" 0:"1('0""
0111)7
r-:~O"'I')
"::
O~!3'"
71('43
rl0C:S
-,..,
_ i
7104'.
010'56
1.4 "\ 1 1 If' 01""')7
71C'4c:.
OlO57
1 C.
'"11 l
i
1 01 :?!
~
-
,J
O"~
'
~ ~
;1('46
"J"I60
37
,"11. ,_,
71047
t11Cd~
1
4~
rl1")3 ()Jl?£
71:)5';
rq "'62
"]
"1
71051
~1063
-:: £:,
O',lfn
~
7105?
01064
:,7
777~7
77'530
71053
01065
31 0120 /• ('002?
71054
01066
7'>.,
""0742
~OO!"O
11055
01061
1"
o,.,1.?r
01123
710,56
01010
'1
011;'~
~a('l~ ",
71057
01071
32 100('0
~0()CO
1l0'iO
nlC7?
1" f'\lf54
?f'I""",
11061
01073
35 20C':}O C'.064
71062
01014
37
71c)63
01015
41 0111,7 nl1"2
71064
1)1076
16
01~r.;~
011~1
.- 71r.55
01077
41 f)0177
f)11~3
71066
0110C'
41 00717
o~1:2
d- 71067
g 71070
('11101
15 OlOA7 "" 1 o~
01102
21 01033 01204
21 01067 01:''")4
~l'"
011~1
"'l1"1t-'
"'0017
106 /..
f)1f)7~
(I?
~
'-'
I
0'-
;:: 71071
01103
~ 71072
01104
71073
01105
It 01"45 0 1 1'31
;3 Ol?f)4 (\"('1('1,
11('74
01106
~t;
71CJ75
01107
1:076
01110
44 011:->2 ell/,4
27 ('111£ ')1""60
710~7
01111
43 0'1117 01121
~""'l17
C'0~on
.
9-341
CONVAIR - DIVISION OF GENERAL DYNAMICS
cott"
CV-153
P4G£
~EP(·J..
M )Dt
::lATE
CONTROllE~
1')1112
45 01"000 01124
01113
:1 'J 1 :? 11 00000
71102
01114
~5
71103
01115
35 01164 01111
71104
01116
27 01244
71105
01117
~o
OC0'1() Of) 0
71106
01120
3~
01~11)
71107
01121
01122
37 r1136 01122
35 01270
011?~
01123
';17
01~t)5
01267
71112
"1124
':,5 012f.7
"O('4~
71113
71114
0112~
44 01126 01111
01126
71115
01127
71116
01130
21 nl?70 ·01 '('\7
I. "2 rn 1 C;6 ('), , 11
55 01267 00010
71117
01131
45 00000 01"'6
11120
01132
~1
01064 0('1002
71121
01133
12
010j).4
711~2
('1134
11 '0000
71123
011~~
111~1t
01136
7112'
;)
71126
I.C')
01137
011"'0
2nOOO nf)06~
47 01121 0112'
16 00743 01144
41 01017 C1143
~t 71127
01141
21
~ 71130
01142
~
...... 71131
0114'3
16 ('1110 C'1017
55 01'12 00004
71132
01144
37 01144- 01145
~,.
11134
0'145
01146
32 01123 00001
71135
01147
')2
71136
01150
45 0"000 1" 0 14 6
11137
01151
00 01')0('0 "'105('
t-
l><:
c..7113~
Ie 010-13
491-11
All
:·-26-56
ZI(
6/4/56
711"0
71101
71110
71111
T
01270 01116
01~67
("01)00
00001
~
11")6 /,
34
0114~
"11"~
01i.'04
""00'
01206 01123
9-342
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SA ... DIEGO
CO,~!TROLLER
01152
00
ooocO
71141
01153
~r::
OJ212 01/1?
71142
01154
71143
01155
11 01161, O()74~
27 01225 01267
71144
01156
77 012'33
71145
01157
Zl 01123 000 4 3
71146
01160
11 01167 01064
71147
01161
no
71150
01162
40' 00000 00000
71151
01163
00 OOO()I')
71152
01164
00 00003 00000
71153
01165
r;. 4 '"1i"'000
71154
01166
00 00000 00-::-01
11155
01167
00 00000 00*01
71156
01170
00 00000 00*12
71157
01171
00 00000 00144
71160
01172
00 00000 ()1751')
71161
01113
00 00000 23420
71162
01174
00 00003 03240
71163
01175
71164
01176
00 00036 41100
00 00461 13200
71165
01177
00 05752 60400
71166
01200
00. 73465
71167
01201
11 24027 62000
5:; 71170
01202
"0 00000 1'")"*03
71171
01203
00 00000 00077
71172
01204
no
71113
01205
00 00001 ('1,)001
71174
01206
00
71175
01207
00 00014 00000
71116
01210
no 0"002
('000('
71177
01211
0(') 0("1003
('(\no('\
I"'"of
'-'
I
0'
J
0
0
0'
I"'"of
r--
CV-153
PAGE
REPORT
MODEL
DATE
IC 010-14
Z1! 491-I1
All
1-28-56
6/4/56
71140
f2
CALlFOR"',A
OlleO
01~67
r-n00r,· r'I("\014
00001
("'(){t.02
"('::()~
4~OOO
noooo
(lonoa 0"()17
9-343
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-153
PAGE
REPORT
Ie 010-15
Zll L91-I1
MODEL
DATE
All
5-28-56
conTROLLER 6/4/56
71200
01212
(')0
OOOOD 0*
712Ql
01213
00
noooo
71?02
('0
I')"I")()"
71203
01:214
01215
71204
01216
00 000f"\0 0f) *
on 00/')('\0 ('('I f)
71205
01217
00
('\(l00()
71?~6
('I1?20
~0
('\1"1"1)1")
712('17
01221
00 OOOOr) r;
*
71210
01222
O() 0('000 00
*
71?11
('11223
1111 O"'r'!f"\O
*
BINARY
00 0
""
"*
0(',
fi
0
*
CODED
Df:C
<':' ! J ~1
P1~,L
!lIn
,\DJ"C:;T[R
........
~
.....
I
0I
o
o
0.....
r><
0..
9-344
CV-154
CONVAIR
ANALYSIS
PREPARtD
a:v L. •• 8artOll
PAGE
REPORT NO.
SAN DIEGO
CHECKED BY
MODEL
REVISED BY
DATE
UlPACDD n.OA:rIIG POm
CAll)
Ie 011 Jp 1
n 491
All
5-15-56
RIlD
!hi. routine read.8 up to tiYe deoial neati nc point nwnbera from carda and
.to.... thea
COilS f'cuti vely ill
By option the
_y b. ipcn-ed and b
DpODeftt.
724~6
Dna acldr•••
lm})aot.d fora in .1 ther 18 or liD.
-
.anti..... trMted and stored
72751 ino.
~OO - 72435 1DO.
Dr1nr
I'uaber of i!'1lJtructlema
hllber of coutant.
260
34
ootal
46
octa 1
lumber of temporari..
oc.1
01000 - 01361 inc.
B8 addr•••
COIOIdD mODe••
The subroutine ie ooded t.o .tart in 0111 01000 and Is entered by the read
37 01001 01002
.lB
tJOWO' " ' "
in oa •• of failure P A I
01000 will ju.p to last 37 read command tor repeat.
It 1. also wi th driver to
lUI. the .equeaoe
lIhi.h will .tore IS 1n 74001 -
75171 iae.. ad re.tcr e atter ue. W1 th th1.
driver sequence in oaa. of tailure P
56 .top - relea.e
,r
~30 Will re.tore IS and oome to a
will then r.,..t the la.t read cc
ad.
10 prt.e command. are lao1ud".17 00000 72433 will prt.a one read card.
A
4. 5.
or
1.
do not prints
any other number. print
B
,.01111
'.'a-"
4. 5.
or
7.
lUll
8U11
treat .antl.... as eon.ecutive integer.
9-345
C
ANALY• •
PREPAR£D BY
CHECKED8Y
REVISED BY
0
N'V A
L. 11'. B'ar-hOa
I
CV-154
R
PAO.
REPORT NO.
MODEL
$AN DIEGO
DATE
Ie 0114ZJI 491
.All
5-15-56
any Dther nuaber. nor.al~tlD' point.
mnnm
Addr••• tor atorag:. of the flrat da.ta word.
VVVVV Number ot floating point number. to be read or with option number
of mantissa. 'tored a. integer••
CARD FORK COLUMBS.
1 punchln 12 row flag for exit 1-5 otherw1 •• not
6, 21, 36, 51, 66 decimal point. punched in
7-1v, 22-31,
37~6,
U8~d
by routine.
card not uaed by routine.
52-61, 67-76 ten decimal digit manti.sa
17.32,47,62,17 lie-of mantiesa
A
pu~oh
in any row except 0 or 12 w111 read
Exponent (power ot ten) range -<:FJ to
20 , 35. 50 •
65,
a8
ner,ative.
99
80 .1p of exponent
A pbch in any row except .ore or 12 will read aa negative.
Rounding at all operatlona occura but
~nly
nine decimal
di~it
accuracy .ay be aesumed.
It the Ilantl•• a 1a .ero the exponent will be atored unc-hanged in octal
-
torm.
"1:3'
In
-
A synthetic
.....
I
~
o
sum may be printed for each series of carda oharacteristio
for t at aeri•••
~
A 12 punch in efll,. 1 wi 11 oTerride the noral count ansi caua. exit with
t-
~
the end of that oard,
In that ca •• eell 01342 will be negative (with driver
U restoration will read OYer
&13L2)
The subroutine must Ie oper.ted in IS but will .tore numbers addre.sed
to 18 or MD a8 read in.
..... ,.,.-"
9-346
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA>
CV-154
Ie 011-3
PAGE
MODEL
ZM 491
All
DATE
5-1~$6
REPORT
UNPACKED FLOAfING pOINT CARD READ
~
li,)
......
-I
aI
0
0
a......
r-
><
~
1 400
00742
56 00000 30000
EXIT
1 401
00743
75 31177 72403
STORE
1 402
00144
11 00001 74001
r:S
72403
00745
75 10352 00747
72404
00746
11 72400
12405
00747
11 00742 20000
ROUTINE
TO ES
SET
72406
00750
36 01264 72432
REPEAT
72407
00751
35 01305 20000
72410
00752
16 .20000 OC770
72411
007';3
55
SEi
EXIT
TEST FO~
72412
00754
42 00715 00756
72413
001;5
45 COOOO 007S7
72414
00756
32 00776 00000
72415
00757
72416
00760
72417
00761
55 20000 00017
37 00760 00761
16 20000 00763
72420
00762
11 00777 01024
72421
00763
11 01264 10000
72422
00764
55 20000 00006
72423
00765
~7
X
72424
00766
00760 00754
55 20000 00017
72425
00767
TP S 18RP I TOr·1E
72426
00770
37 01001 ,,1004
15 11177 30000
RESTOR!:
72427
00771
72430
00772
11 14001 00001
15 31771 12432
RESTORE! t! S
72431
00773
11 74001 00001
724~2
00114
30 00000
72433
00775
02 00000 00104
7~4~4
001 7 6
74 0(01)0
f')0!'101')
72435
00777
11 00000
OOO~(j
72436
0100l)
30 00000 00,')00
72437
01001
45 00000 30000
O~74'2
0074~
2002~
~OOOC
ES
ADDRESSES
ADDR[SS MODIFrCtTION
SEt ACQUISITION
ERASE INSTRUCTION
ACQUIRE CONTROL WO~D
t
AND EXIT
S
AND
REPEAT
REPEAT
EXI,.
9-347
CV-154
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
PAGE.
12440
01002
16 01001 01003
72441
01003
71 01264- 30000
72442
01004
13 20000 01352
7244~
01005
11 01263 01314 \
ACQUIRE CONTROL.
PRINT SUM FLAG
CLEAR
72444
OiOO-6
72445
01007
11 012t;3 01315
16 20000 01314
NUMBER OF HORDS
72446
01010
72447
01011
55 20000 00003
13 20000 01351
READ ft,S
72450
01012
~1
72451
72452
oloi3
35 01277 01227
01014
7245~
OIDIa;
724 5t~
01016
12455
01011
11 01~O5 Ol~56
11 01265 013£)7
44 01017 01022
23 01227 01313
MootFtCATINNS
72456
01020
11 01264 01356
FOR INTEGER
72457
01021
2~
72460
010.2 2
55 100"0 00021
72461
01023
724-62
01024
72463
01025
72464
01026
:;
72465
I
01027
01255 00000
01357 01261
INTEGER
SET FINAL
FL!\C;
TRANSr-:ER
SET
TP.AN~FER
STEP5
STORAGE
SeT ',DATA
0-
72467
01031
61 00000 01303
CARR I AGE RETUR'N
72470
01032
72411
72 /.72
01033
17 OelOOO 01300
11 01260 Ol~50
READ AND PICK CARe
LINE DIGIT
9
SET TEMPORARY STO~A,GE
0
0
t-!
I"-
><:
~
STORAGE
ExtT
01264
SET
01000
01264
SET REPE:AT
N-l
010:30
EX IT. IF N
010~2
SUM.TEST
72473
01034
01035
75 10011
OlO~7
CLEAI~
72474
0103.6
11
0126~
01316
MATRIX
72475
01037
76 00000 C1361
72476
01040
76 10000 10000
72'+ 77
010.41
76 l':10()O (11360
16 01256 01224
5-1-56
'"
010~O
0-
DATE
,;
72466
~
All
CI:LLs
I
.......
ZY. L~91
MODEL
\10RD
16 10000
21 01001
36 01305
23 01314
46 01001
41 01252
01230
ie 011-4
REPORT
0
9-348
CONVAIR - DIVISION OF
GENERA..~
DYNAMICS CORP.
SAN DIEGO. CAL-IFORNIA
72500
01042
37 01042 0104.3
72501
01043
54 01361 000'34
72502
01044
11 01257 01054
72503
010'1-5
72504
01046
11 01304 01327
~1 01306 00024
72505
72506
01047
01050
32 01263 00004
44 01051 01052
72507
01051
32 01350
12510
01052
46 01053 01047
72511
01053
72512
01054
12513
01055
12514
01056
31 20000 onooo
30 OOOCO OOOO{')
21 01054 01101
41 01327 01046
72515
01051
31 01057 01060
72516
0106('1
11
('Il~6C'
1 ('tljOO
72517
01061
31 01057
0104~
72520
01062
11 01361 10000
72521
0106~
~..,
72522
01064
37 01064 01065
72523·
01065
23 01:350 01264
46 01067 Oloa7
TEST -FOR 11 RO\·,
11 ROW
-
-' I
010~1
~OCOO
CV-154
PAGE Ie 011-5
REPORT ZM 491
MODEL All
DATE
5-1-56
SET 15T STORAGE
SEi IND~X
~
2 EXP 35
SHIFT 4
TEST BtT
0
ADD LIN!: D!G!T
TEST DIGITS
~
CI.,EAR A LE F'T
STORE MATRYX WOPD
STEP STORAGE
4'TIMES
01046
Re:OVCE LINE OIGrT
:; 72524
01066
~I 72525
01067
C{' 72526
01070
11 01264 013~O
37 01064 010,7
72527
~1071
37 01042 010:37
72530
01072
72531
01073
44 01073 01075
11 01102 01314
72532
01074
11 01255
O13~O
12 'ROW. DUMMY
TEST EXIT F"lAG
OVfRRIDE INDEX
SET FLAG
72533
01075
00000
N-l REMA.INDER
725~4
01076
01100
72535
01077
72536
01100
72537
01101
31 01314
42 01261
17 00000
11 01302
15 01257
TEST lAST CARD
READ AND PICK CA~D
SET INDEX FOR WORD CI-fArJG~
SET FOR 1ST EXTRACTION
lJj
0
0
CI'
po-f
r--
><
0..
01300
01'32
01123
9-349
CV-L'j4
CONVAIR - DIVISION OF GENIRAL DYNAMICS CORP.
SAN OUtGO. CAL.II"ORNIA
MODEL
Ie 011- 6
ZM '491
all
DATE
5-1-56
PAGE
AEPORT
72540
72S41
12542
,O110~
Qllo3
55 01316 00024
11 01302 01341
SHr'FT FOR I DENT NUMBER
72543
01104
01'105
42 01314 0111'
72544
01106
11 01314 013,...,
SET FOR S DATA WORDS
TEST FOR
1,..ESS THAN
~ WOROS
72545
01107
31
N-l
72546
01110
,S 01306 10000
12541
01111
~l 01~tJl
72550
01112
72~51
01113
OPTION
SE l' SMALLER
72552
01114
55 10000 OOOQl
31 01255 00000
~s 10000 01221
1255~
01115
37 01124 ,01120
12554
72555
12556
01116
01117
01120
72557
01l2'1
11 01260 013'1
11 01261 0132'
41 01312 ~11'-~
21 0112' Ol~O6
SPACE FOR PERIOD
SET TALLY
9
72560
01122
12561
Ol12~
11 01262 013:32
55 30000 00004
72~6?
01124
~,
01124
~1115
:; 72563
01125
31
01~27
00002
01126
32 01327 00001
72565
01117
'52
~ 72566
01130
41 01331 01120
TE~T
72567
01131
11 01327
7257C
01132
37 01124 011.20
SET EXPONENT
ACQUIRE
72571
01133
51 01301 20000
S~oPN
72572
01134
F"LAO
72573
01135
11 01265 01:330
47 01136 01140
72574
01136
l~
72575
01137
72576
01140
72577
01141
13 01265 013:10
37 01140 01141
11 01327 01354
It':I
:::: 12,564
I
cr
0
r-f
t-
><
0...
31 01304 00000
01~\4
01~Ol
Ol~27
00011
0111'
01327
~1:334
01334
TEST FOR
tNT~G~R
.STORAGf:
CLE'AR
TEST TO
CHANGe:
MATRIX
WORD
PSSITJON DtGIT
N X 10
ADD
D!~tT
N
CO~J~PLETF.
N
:3
TEST ~IGN
SET EXPOnENT FOR N
-FLA0
n
~1ANT
I SSf.\ X
FO~
lCl r:.xp
1~
9-350
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OIiEGO CALIFORNIA
~1ANT
1260~
01142
11 01330 01355
12601
01143
11 01264
72602
01144
37 01140 01117
72603
01145
41.
Ol~51
01217
SET TALLY
EXPONENT tNFORtvlt"TION
TEST I NTEGEH_ OPTION
726()4
01146
11
01:>6~
al~~~
CLEAR
Cl~31
REPORT
IO 011-7
ZJI L91
MODEL
All
DATE
5-1-56
I SSA FLAG
TEST N
72605 .01147
31 01354 OOOCO
72606
01150
41 01151 01223
12607
01151
23 01327 Cl~~O
EXPONE~lT
72610
01152
12 20000 20000
72611
01153
73 01265
72612
01154
31 20000 00017
ADJUSTMENT
TENS DIGYT
UNITS DIGIT
7261~
011~;
U~~TT5
72614
72615
01156
01151
01'-?4 01'1~
11 20000 01251
23 01234 01265
72616
01160
12617
01161
11 01216 Ol~27
11 Ol~10 01334
72620
01162
46 01214 01250
72621
72622
01163
01164
10 EXP 10
ADJUST AXPONENT
SIGN OF EXPONENT
ADJUST EXPONENT
7262~
01165
...... 12624
01166
01~53
CV-154
PAGE
FOR
0
4
~~
0"-
72625
01167
0
0
0"-
72626
01170
r- 726?7
01171
23 01JI. 01311
31 01~54 00000
7~ 01321 01331
31 2~OOO 00043
73 OIal7 10000
55 lOCOO 00001
32 01263 00001
El: 72630
01112
42 01327 01174
72631
01173
27 10000 01264
726:32
01174
31 10000 00044-
726!3
01175
32· 01331 00044
72634
01176
72635
01177
72636
01200
12637
01201
11 01261 011l\
14 20000 01331
11 20000 01~54
46 01202 0120'
~
l!J
-I
I
......
""O\·:F'~
OF 10
ADJU5T EXPONENT
N
N ADJUSTME~l T
FOR NEGATIVE
EXPONENT
DETERMINE
LAST
BIT
OF N
AS5E~·1P.lE
f.-t
CLEA~
SCALE FACTOR N
STORE N
TEST FOR ROU~DrNG
9-351
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN OIEGO CALfl'"ORNIA
CV-154
16 011-8
ZM 1,91
MOOEL
All
PAGE
REPORT
DATE
12640
01202
72641
01203
72642
01204
21 01354 01264
43 2QOOO 01207
32 01263 0Oln7
7264'3
01205
11 20000 01354
72644
01206
72645
01207
72646
01210
71.647
01211
72650
01212
21 01334 01264
31 (')1331 ('10000
42 01)03 01212
2'3 OlS34 01112
21 01334 01331
7265l
O121~
'37 ()1'1~ 01?14
72652
01214
41 b1353 01163
72653
01215
30 00000 00000
72654
01216
31 01213 01161
7265t;
01211
11
72656
01220
41 01355 01222
72651
01221
1~
72660
21 01315 01333
72661
01222
01223
75 10002
0122~
STORE
72662
01224
11 0123:3
~OOOO
72663
01225
-
72664
01226
0122. 013~6
01347 01115
l.(j
72665
01227
00000 00000
FINAL
"-'
I
72666
01230
0
72667
...... 12670
r>< 72671
0..
72672
72673
72674
01,231
0'
01232
21
41
30
11
21
23
46
TEMPORARY
STEP STORAGE
T£ST END OF CARD
01235
41 01352 01001
31 01263 00000
01236
75
72615
72616
01'37
01240
~'- O'~l'5 00014
12671
01241
~
......
0'
I
0
..
012S!
01234
01~t)4
Ol~~:3
l'13~~
o13'3S
ROUND
ADJUST FOR
OVe:R FlO~f
IF
NECESSARY
ADJUST
SCALE
F='A('TOR
TEST TENS DIGI'PO~'jER FOR UNITS DIGIT
ADJUST FOR UNtT~ DI('IT
N
SIGN OF N
N~f'jATrVE
SUM
0133~
3000n
5TORAGF.:
012~O
01357
StEP
T£5T FOR
01314 01261
O12~4
01033
00006 01240
5-1-56
END
tEST PRINT SUM
t:LEAR
SUM
31 20000 00030
32 01264 (')0004
9-352
CONVAIR - DIVISION Of OINEItA! DYNAMICS CORP.
72700
0121+-2
61 00000- 200nc
72701
0124)
34 2nOOO 00000
72702
72703
01244
01245
47 01241 01001
71 01354 01327
72704
01246
37 01213 01176
OF N
72705
01247
37 01247 01250
AND
72706
01250
41 01353 (')1245
72707
01251
30 00000 00000
72710
01252"
37 01247 01245
72711
01253
45
72712
01254
11 01264 01321
72713
01255
75
jOOOO
012~1
72714
01256
no
00000
()1~5~
7271'5
01?~7·
~~
01~16
O.1?1.6
72716
01260
00 00000 00*11
72717
01261
00 00000. 00005
72720
01262
0(1
72721
72722
01263
00 00000 00*0
012&4
00 00000 00001
72723
01265
00 00000 00012
7~724
01266
00 00000 00144
12725
00 00000 01750
..... 72730
01267
01270
01271
01272
72731
01273
00 00461 13200
72732
01274
72733
01275
72734
01276
00 0;753 60400
00 73465 45000
11 24021 62000
72735
01277
00 00012 00000
72736
01300
00 00000 0010e;
72737
01301
00 00000
-,
-.;;:j1
I.l'J
..... 72726
-I
0"I
0
0
0"-
t-
><
c..
72727
00
COOOO 01217
00000
CV-154
PAGE
Ie 011-9
REPORTZ» 491
MODEL All
DATE
5-1-56
SAN DIEGO. CALIFORNIA
PRINTING
ADJUSTMENT
EXPONENT
FOR
POSITIVE
SCALr:" !=" :\CTOR
CONSTANTS
OO~10
noooe 23420
CO 00003
~3240
00 00036 41100
~OO17
9-353
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CAL,,..O,.NIA
72740
72741
01102
Q130~
00 00000 00004
00 00000 0OO4~
12142
01~O4
00
7274'
013015
00 00000 00002
72744
01106
00 00001 00000
72745
01J07
72746
01~10
727'47
01!-11
00 O()OOl ·00001
-00 00000 ~OO43
00 00000 00044-
72750
01~12
72151
01 ~li;
CV-154
PAGE
REPORT
MODEL
DATE
Ie 011-10
ZII 491
All
5-1-56
00000 00003
00 00000 00110
00 00005 00000
9-354
CV-155
CON
ANALYSIS
P,REPAR£O BY
CHECKED BY
...
l)' ~
f..... (.,. .
IS
t
R. Brieger
L. Barton
..
r " .. ,
V
,A
I~ ~ till ...... , (
R
'5-
,
"., I"
.co ..
r
•
PAGE
REPORT NO.
0 ...
SAN DIEGO
MODEL
REVISED BY
DATE
ARC SIN AND ARC COS. FIXED POIV!'
Initial State I
Alarm ex! t
01001,
Exit
010021
Entry
= R. 234
where S18-& ed COl 4> &
F1u.1 STate.
'"'
5-14-56
CP015
01000 t
(A)
CF 015-1
ZII 491
All
I
•
~1
-&.233 ---+ (1)
cp. 133- - . (Q)
l.r1•••xpaulOl\ about
~
-e-:a 1!:.,..
N * + t Voft\
Y.
__ , ~.. +,
U. == 24"'-, N·~ U
~
---I
N- = #(N-Vt-H")
,a
j4
O....... genoe ia
.'.UMd lIhelt U"" < .-.
Ifaxi. . ti_.•
70.5 mill1aecODdl
.Drua addrea ••
734~ through 73551
....... of
00
(~) 10 (66) 8
Dda·.for "'••ab1)" )Iodlt1eation.
1J~ •• 60 0.11._ 1Ilclud~I1' o ... taaw
u ..
(50)10
(c.)a
t!..,..ar1 •• 01066 • 01013
1ae1u1".
.... ta1.
tea..
It _
-=
0
+1& ..... 0
,6
it ..t •
".
It
.........-"
,-, > 1
.lt.
I
extt .W Alaraa !'ria Out
, 9-355
CONVAI~
-DIVISION of GENERAL
CV-155
DYNAMICS CORP.
f!AN DIEGO. CAL!FORNIA
""'4
..to
an
.....
'-'
I
a-I
0
0
PAGE
01000
31 16000 16002
.aLARM
tS46S
01001·
45 00000 JOOf}O
EXtT
'7'1466
01002
11
·n461
0100~
47 01004 Q100l
N-
13410
01004
16 01042 0.10'5
SET FOR, POSITtVE RESULT
"'471
"1005
46 01{,)O6 nl007
H N£GATJV~?
13472
01006
16 01024 OIPS5
SET FOR NEGATIVE RESULT
1!47!
01001
12 20000 .010.61
STORE
T"J474
01010
31 01064' 00&41 .
1 2~4 ~
73475
01011
42 01067" 01·000
1&476
01012
33 01064 0'0103
1~4T7
01013
72 nlO67 \0000
"500
01014
47
73501
01015
13 20000 0106"6
.735'02
01016
34 20000 00044
7350!
01017
13 2nOOO 0101~
'3504
01020
"31 01043
.,3S05
01021
11 20000 01070
STOR!
13506
01022
31 01073 0"044
N·:t'''~(A)
7,sn?
"102!J
!? nln66
11510
01024
1~
~106~
nlot~
lo-0~O
(t'n~n
(to 000
4
MODEL
All
DATE
5-14-56
~ 35 - - . ~ISI)
oT
.,
,~
IN'
:> I~'
(A)
~
AL.ARM
.01".2" ~ (A)
(~'I+ N'j,.)·2.""--", (A)
(A)- o?
STORE (1- Hi&-)· ".''1=
a..... T3511
r><
c.. 7351"2
0102~
32 01010 't"010'
01026
11 '0000 20.,01)
11511
,01021
42 01010 O'ltJ2.1
'!~t4
01030
34
7,'1!
01031
71 20000 01062
'3'516
(')1032
54' '0000'0004'
00000
N· 2"(
_ X. - - . '(A)
X,;.
Ii /Xo --. fA)
t (ttlx. + X.)- XI
X > X. ?
4
("r -N-- - N ).
l31f.
Vo/". (N - V,-Nt.), 1'" =N*. 2.$'
~
N*.
015-2
I. 491
tt~.;nn
01010 20ftOn
~1061
If/~
cr
REPORT
2 ,t
(R)
9-356
CV-155
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
PAGE
N*"J.· 2.""
73'17
OlO3!' 71 20000 10000
73520
01034
S4 20000 00046
73521
01035
11 20000 01066
73522
01036
1'3
73S2.~
01037
11 1000" '0000
N*.2s"~tA)
7352~
01040
11 20000
~lO7~
STORE N*.2
11525
01041
11
01012
73526
01042
35 01072 01072
73527
01043
21 01067 01064
73530
01044 ·35 01065 01070
+ 2 ---+ 0 = .l...w\-'
o + 1~ P=2'W'1
73531
01045
35 01065 1')1071
Pi" 1
1'35~2
01046
71 01066
0107~
N*1. , U_-I • lot,I'
73533
~lP47
54 20000
f'~C46
N*2.· U.
73534
01050
71
7!535
01051
73 01070
735~6
01052
11 20000 01073
STORE
7"35'37
OlO5~
1~
t),.;1/fJ..hn+
1~540
01054
47 01()42 01055
..-.. 73541
01055
1~
Ol()72
0107~
SWITCH
~ 73S42
r-1056
'5l.. nlt"J72
~Ol()7
--6-
"~543
(')1057
35
10000
TT/l-~
......
73~44
01060
13 01,012 20000
><
0..
73545
01061
45 00000 01"01
73546
01062
64
73547
0106·3
14 44116 65210
1~550
01064
(H'I
7~'51
~1065
""
,
0106~
0106~
01067
2000C 01061
01071
?OO~O
,~OOO
>(A))N*.;(
STORE N*2..
Do
-
cr 015-3
REPOR-':-
ill' 491
MODEL
All
DATE
5-14-56
s.,.
,(~)
'J...'3't
... 1
IT/'1-
3
"
· l~'f
D
---It Q c2~+'
--.N*2..
>(A)
' l. 39-
(2~-')
U
""'-.
3
' :2 •
2~-1/~~ N*~. U--I
=U
4tI\
V~,
U../~+I ~ 0
~E"F.AT
LOOP
tn
,
0",
'-'
0
0
0"-
t-
~1C)63
~37~n
~1462
noooo
000.'
on,noo
~OOOl
~CA)
..e.
,",UMP TO
~(~)
~tA)
e:xtT
-V2/a. .23 ...
ir/",. · 2 s 'lo
9-357
CV-lS6
CONVAIR
ANAL.YSIS
fitREPAR£D BY
PAGE
REPORT NO.
SAN DIEGO
CHECKED BY
MODEL.
REVISED BY
DATE
eN 006-1
Z fV\ ~ 91
A I.L
3/29/S~
LU.SE SQUARES POLllfOKUL APPROXIJIATla.
Itr1'ROreCTIOI
PART I.
This routine 18 intended to enable the programmer to approximate a function
c:I
1 ot '\,...... independent variabl..
"XI)
'X. 2 ,:
v• I
P:.....
.
ot decree d if Y i. known for n+l sets ot the independent variables.
~:4 ~nd
is written for
d
=2.
'.'
~).
I, ilL
",,').
:(. XL'"
The code
By treating powers of variable. a. independent
variablel and making a few modifications in the code it i8 posaible to handle
approximations for yariOu8 combinations of
" =1
d
and
A and
d (includi~g tor example,
= 14).
PARr II. ANALYSIS
( A = 4.
,;u.,. and
d :: 2, and n .. 1 • 4- 5 ) •
Let the known ..,.lues of J b. denoted by
thoee of the independent variables by
ai
determine the
j Ie.
.L.-
80 a8
n,
L [~-. tJ· 4ihc.1.
'''''':0
( 1)
A--::..C
~x.
'J
. . .X .1" ~:J},.".
rl'.~
It 18 deaired to
to minimize
(x:' x~ x;- x~)_] z. ::
,
t".
Differentiating (1) 1ri th rel,eot to the unknown.
and settinc
the resul ta to zero yie Ida
(2)
J!,
Z. cl... [- ( x. I" t:'
.-
2.~
d....
•
"
(- ( X'
..
•
L
d..- [-( X.
",MIl
x.~
x;
X~
X; ).,-J = 0
X;J..- J = 0
•
XI-
X, ~~l
=0
J
which. it simplified becomes
9-358
CON
ANALYSIS
PREPAR£D BY
~AN
V
CV-156
A
R
PAGE
REPORT NO.
OI£GO
CH!:CKED BY
MODEL
REVISED BY
elY 006-~
2M 491
ALL
3/29/.s-~
DATE
or (in matriX-reotor form)
1-
(4)
(X~ y; ~ y;,t. ~ ( ~~ ~ ~~1:J~ -
z. (~~ r: ~;~. . . {(;t~ .r:~~X;J.,....
•
•
•
•
•
~9.(/,D~ht1'l.l
•
I , (~/1~"1; ()~
•
•
•
,
Z~'1.(I/~:~~)
The determinant of the system (4) is non-singular tuld cymmetric •. Thus.
the problem i8 completed by solving the non-homopneous linear system (4) by
Cramer's lIethod.
For the general oa8e the number -,t of equations in (4) i8
•
For the present ease
r=
15.
The Crout routine is used to 89lve
(4).
For
convenience denote'the so-called given matrix in (4) by V. and V without
summation signs by m.
PART II.
COnIIO
The code i8 developed by combining a least squares code (oalled 2,)( 4)
wi th existing ,ub-routines.
2X 4 include.
of (1) for calaulated
).
a "residual" oalculation (evaluation
The following list ~ivee th~ parts of
the tape in the order in which they appear on the tape:
Ie
003 FLOATING pom CARD INPUT
lID CLEAR
2 X
4
40000-47m
(followed by extra seventh leTel hole).
(followed by extra seventh level hole).
JPl'r.
CI . 005 CR rot
CJ. 001 TWO REG lSTER FLOATING POIlfT AR I THMET IC
IC
004
F~ATING POINT CARD OUTPUT
The rer.ister of the CROUT routine.
18 set to (17)8
71251.
indicatln~
= (15)10 and the exIt is modified to
the number of equation.
jump to the resid"al oheck
9-359
CV-156
C
ANAl_YSIS
0
N
V
A
R
PREPARE!) BY
CHECKEO SY
MODEL
REVISED BY
DATE
4
of the 2 X
There is
811
Ti'wJre is ~n MS~l at
MS:2 at
466 .. t
!J...4
()~'-3
Z~
491
ALL
3/.2. 9/.s-"
upon
~omrletlon of the feneration
which point .. has been genera ted and stored
the routine is ready to enter the CROUT
PART I I I
elY
The n index register, 50775. (\f' the 2 xL routi!'le is set to
FIT.
(5L)a::;' (1+4)10·
a.
PAGE
REPOffT NO
or
and·~
routi~8.
IIPU T - OUTPUT
Input and output is by cards in fl08.tin~, decimal format (five nu.mhers to
t he
car d) •
and
80
T~e input cards contain
I
x.,~I -'2-)I '/...J~ ~F II,., ,'1
on, with e h~8.der oard punched to start the loading at 51003.
cards contain five sets of answers
The output
in the order 0000, 1000, 0100,
0010, 0001, 2000, 1100, 1010, 1001, 0200, 0110, ••• ,0002, each set followed
by their differences (see description of CROUT routine) followed by a card
containing the residual for the last set of answera o
PART IV.
OPERATIOB
1.
Load servioe routines.
2.
Load input carda into read hopper.
3·
PT load 2 X
4. (PAl)
5. P!
4
to first extra 7th level hoI.. .
=300, start 1103.
load 2 X
4
to se~ond extra 7th level hole.
6.
)(00
to <-lear 40000-47777.
7.
PT load remaining portion of 2 X
8.
(Pu)
=50376,
4.
start 110;.
The total time for the case 1\.= b, d :: 2, n
minutes.
=44.
1s approximately twelve
9-360
CV-156
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
eN
PAGE
SA ... DIEGO C"LlFORNI"
REPORT
ALL
3-29-56
MODEL
DATE
L~AST
D('LY A"PPX
.: 0lJ,f.,PF ~
51001
?O 00000 00000
51002
00 00000 00001
1 INTO
STC>PAG~
50376
00376
75 304()O ()O400
50377
00377
11 50400 OI')4(jO
TRANSFFR POUTINE
TO r:t::.
50400
00400
75 3()O()2 ('l()40?
1
TO F<;
50401
00401
11 51001 ('llOOl
;(")402
00402
75 30010 ('l0404
Xi.
TO F:S
C;04r~
(\0401
50404
00404
()O405
75 300!)2 00406
75 30002 0041<"
5()4f"17
00406
(')0407
11 01()()3 (,)on25
50410
00410
37 00201 00203
5()411
00411
75 30()O2 ()O413
50412
()O41?
11 00031
5041~
00413
?l 00407 00770
ADVANCE
50414
00414
?1
('H) ('14 1
~,DVA~ICr:
50415
00415
41 007(-,3 1")0406
50416
00416
21 00405 00770
ADVA~~CE
sn417
00417
15 004(')5 00407
(407¥)
5n4~()
(;0420
?3 00415 00073
DI~r~!r,c,H
C;r:4?J
r:'04?1
L~
50422
00422
75 30ClO2 00424
J
t;n4?~
n04?3
11 t:1013 010j7
'"
50424
n0424
75 30040 00426
5~4?5
00425
11 01001 'i2?71
e;(~4/6
00476
1 ~.
50427
004?7
75 '?O002 00431
'i0430
00430
11 0J0()1
5040S
50406
....0
li.)
~
'-'
J
0-
0
0
~
t-
><
c..
006 - if.
z.N1491-~
,,
~1 o('r~
I"Il(')()~
X·L TO (27-30)
11 01003 000'-7
O()l~
12
0101~
1 007"'71 ()()404
007~t;
00764
('d'l0? -,
Xi TO (2 ~-26)
MULTIPLY
FL Er,1[NT OF
ffll
T0 ~S
(4 0 7tA. )
(41 ?\' )
TIMES ?
4-l
(4() 5u)
= (4 ~5u.)
(41,)",)
r-y
,
4 TI~ES ?
Y TO ES
El E~'~EN TS 01="
CHF:CK
l~T
~r'v
s TOR,~ r:r=
.~
Tn
r"F5
riJU.~L
q r /I.
SFT LOOP ! ~1~~ x
EL Er.AEN T nF
~~UL
~()Vf
l
AS
iIDlIF'"
9-361
CV-156
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO
PAGE
REPORT
MODEL
DATE
CALIFORNIA
eN (')otP-5
ZM 4-g I -Z
AL.L.
=- -;? C; - ~-6
LEAST SQUARES POLY APPqX
50431
00431
7'!: 3()()O2
50432
004~2
11 OlO()1 00025
5043~
004~3
'37 O()201
OO/O~
MUlTtPlY
50434
00434
75 30002 00436
ELEMENTS
50435
50436
00435
11 00031 01041
00436
21 00432 00770
2-15 TO E5
ADVANCE ( 43?\,)
50431
00437
'3~440
('0440
21 00435 00041
4l 00764 "'(l4~1
50441
004~1
21
~n4'30
('10770
ADVANCE (43('&.\.)
50442
00442
1~
00766
004~?
(4~i.t"l)
50443
00443
41 00767 (10426
14 ROHS OF
50444
00444
56 10000 00445
TO
50445
00445
75 30002 -00447
ACCUMUL"T~
50446
00446
11 01001 00025
50447
00447
50450
00450
75 '0002 004e;1
11 40001 nOO27
50451
00451
~7
50452
00452
75 30002 00454
50453
00453
11 OC031 01001
,)~454
00454
50455
00455
50456
(')0456
50457
00457
?1 00446
21 00450
21 00453
41 00773
-
50460
00460
75 30740 00462
II)
501+61
00461
11 01001 40001
I
50462
00462
ADVANCE (50403a.t)
50463
00463
21 50403 00772
?1 ~O4?3 0077'
......
50464
00464
21 50425 00774
><
Il..
50465
00465
41 00175
~O376
50466
00466
56 20nOO
773~(l
ADVANCE (5D42~v J
ALL !'OTNTS USE" ?
TO CROUT
5('760
00760
50761
00761
00 O()OOO 00000
00 noono noo') 1
...0
......
--
0"I
0
0
0"-
~O4~~
01'l201 (')('I?O?
ELE~1Er!TC;
OF PO\'J 1 /I, e,
MUL 1IPLICAr..JOS
OF ROWS
ADVANCE (43 5v )
()~E'
ROV! f"'lF .- CI)MOLF="Tcl"l
~
= lOOl
I)"r\.
CO~ADLrTr='f')
?
ACCUMULATION
ELEMENTS
OF ))'\.
IN AN Ec) ARF"A
PREPAPATOP,V TO
TRANSFER TO
GIVEN
00770
MAT~JX
00770
A~EA
OF
CI:?OUT
ROUTINE
00041
00445
to-
?
r~1J
TO DRUM
Ar'VANCf!
(r;n4'~a.c.)
,
X
9-362
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
LEAST
...0
-'"
1.0
-t
I
I
0
0
SQUARES
00 00000 00002
00 00000 00003
00 ().,on~ nCOt1
00 00000 00017
50762
50763
00762
00763
~tj764
50765
(')0764
00165
50766
00766
50761
00767
00 010"1 oooon
00 00000 00015
50170
00770
00 00002 00000
50771
00771
50772
00772
00 00000 00003
00 00012 00000
50773
00713
00 0(')000 n03!51
50774
00774
00 (Joooe nO()40
5077~
00775
00 00000
DATE
3 '7"2. 9
T.
C
0
N
S
T
A
N
T
S
CLEAR RESIDUAL
75 10004 56000
55771
11 00040 00664
STOR.AGE
56000
75 30060 00610
TRANSFE~
56001
11 56002 0060'-
ROUTYNF
~E5tDUAL
56002
00602
5600~
00603
00 00000 00054
00 (10040 o(,H)O()
56004
00604
00
56005
00605
56006
00606
00 00000 00016
00 00000 00016
'36007
00607
11 0("1605 00606
56010
00610
75
56011
00611
56012
00612
11 52211 COO27
15 30002 00614
56013
0061~
11 76500 00025
(25-26 )
56014
00614
31 01001 01003
MULTIPLY
56015
00615
75 30002 00617
TE~MS
~6016
00616
76~OO
~OOO2
",nooo
00612
OO()~l
noO~7
~OOO2
"0621
56n17
60617
00620
11 00664 00025
56021
006?1
n1nOl 0100/
t-
A L'-
R.
55776
><
c..' 56020
-t
Z.NJ 491
MODEL
4
OOO~4
,7
eN 006-
REPORT
POLY .A.PPRX
11
75
'",
CV-156
PAGE
SAN DIEGO. CALIFORNIA
REGt~TEPS
RE S I DUA.L Cyr::CK
TO E'S
CHt'CK
CALC!' -
lATION
CONSTANTS
SET INOF'X
POWERS TO
(27-30 )
COEFFtCIENTs TO
TO
(~7-~O)
PARTIAL ~UM
OF POLY. TO (25-26)
ACCUMlJLATF.
9-363
-;,;t
-$'~
CONVA'R - DiviSiON OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
LEAST
SQUA~ES
STORE PARTIAL
56022
00622
75 30002 00624
t;60?3
006'~
11
00664
OF POL Y""OMt AL
56024
00624
21 00611 00661
56025
00625
56026
00626
56027
00627
21 00613 00661
41 00606 00610
13 n0664 ()OO27
56030
00630
56031
ADVANCE (611 ..... )
ADVANCE (613«.)
POLY. EVALUATED
DIFFERENCE
8ETwEEN
APPROX I ~~AT I ON
ANn
FUNCTION
CALCULATION
OOO~l
ooo~n
00631
56032
00632
11
52~21
OOO'~
56033
00633
37 01001 01002
56034
00634
75 30002 00636
t;60~5
f'063t;
56036
00636
11 00031 non,?
75 30002 00640
56037
~6040
00631
00640
56041
00641
56042
00642
56043
00643
56044
00644
56045
00645
11 06666 n0025
37 01001 01002
5604~
00646
75
5"6047
00647
56050
00650
ADVANCE (632 u.)
56051
00651
11 00031 00666
21 00632 00603
15 00604 00613
56052
~O652
21 00611 00661
ADVANCP.: (611 u.)
It')
5605~
0065~
75 10002 00655
I
56054
00654
11 00040 00664
5605~
006!5IJ
41 00602 00607
..... 56056
00656·
37 70440 70441
56057
><
~
00657
00 00666 00001
56060
(")066("
Cj7
nf'lono rVHH'O
56061
('10661
no
O~O()2
...0
0I
0
0
0-
r-
eN 00l:,-1
REPORT
Z;t1491-~
MODEL
ALL
DATE
3-.2..9-.$"'
POLY APPRX
11 00665
75 30002
-.....
CV-156 PAGE
006'~
11 00031 00025
37 01001 01003
75 30002 O~643
11 00031 00027
15 30002 00645
~n(')n2
~065n
nnoon
su~
OF
THE
SQUARE
OF
ONF.'
DIFFERENCE
PARTIAL
SUM
OF
THt:"
Rl!S!DUAL.
(613..-.) =76500
CLEAR PARTIAL SUM
ALL POINT5 us~n ?
PUNCH
RES t'OtJA.L
FtNAL ~TOP
STO~.
qf:G.
INC~E~r:N"T
9-364
CV-157
1....
C.
ANALYSI.
"REPARtD BY
J.
CHECKED BY
REVISED BY
CON
" r·...
t'.
BartOll
.~ t
V
.. t .... L
A" I
"" ~ ..... ¥
,(".
'
U III
R
'!" 0 " " 1
MODEL
IF 001
ZII 491
All
DATE
6-5-56
PAGE
'0'"
SAN DIEGO
REPORT NO.
Sw1~
rInD pom CHARACTROlf OU!PUT ROUTIO
!hi8 routine prints
number~
on the eharaotron in decimal form, riven
the binary seals factor.
Drum addre81
Drinr
73032 - 7;;22 ine.
72770 - 73031 inc.
WUllllHtr of instruetiona I
213 octal
56
Constant••
octal
!uponri."
7 octal
II ..ddr••••
01000 - 01277
CtJBD IIQUDCB
'!'he lubroutine i. coded to start in cell 01000 and 18 entered by the
.equellce.
37 01000 01000
D UUt1UU ' " "
It the.trtt. 18 to be WI.d, It 1. .Zlt.r.d by the ••queno. t
!he drlTel' will Itore D ill 74001 - 7'Yf77 1110. aad r •• tore It atter
ue.
In ea •• of failve with clri.,.er •• queace, .tartinc wi th P.lI equal
to 73022 will .top priat, adftao. the fila, .... te. II, ud oome to ..
56
ltop.
Re.tartinl will thea repeat the internptecl printlJlC instruction.
D i. the axlBa DUliber ot r0W8 from the top _1eh will b. printed.
It
it 11 lero or GTeI' 32 it will b • • et equal to 3&
!be nu.ber of colUBDI 1,
4
utJOUtJ 11 the addrell o~ the 1"lr.t data word
" " ' 11 the addre.1 of the tir.t para.&ter wori
-365
C
ANALYSIS
L.
PREPAR£D BY
c.
CHECKED BY
w.
0
N
Barte
V
~AN
CV-lS1
A
R
IF 001-2
ZK491
PAGE
REPORT NO.
[j,h,Ci
J. Swi.ttJ
MODEL
All
DATE
REVISED BY
6+56
PAlLWETER WOODS
The parameter words consist of' pairs of oetal digits from left to
right corresponding to oonaecutiTe data
1fOr~.
If the value of the
4;
it i8 used as a biDary
scale factor tor the correspoading data -.rd.
It the value 1s ootal
octal digit pair is not greater than octal
77
it serves as a nag to end the parameteJ" words and exit.
v eater
than octal
43
and net equal to oota1
If it is
;-n. B will preoede that
data word whioh will have ita binary Boale tactor set equal to zero.
Parameter words are not disturbed in uae.
A. title and page number are plaoed on each page.
number of syBole up to
48.
as defined by this table.
!he ti t1_ i. -7
two octal dig! te repre.ent each aYJlbol
AnY.other pair wi 11 cause a blank .pace.
Second Octal mgit
t-
an
......
--
Digit
I
0-
(I) (3) (4) (5) .
(0)
(1)
(0)
0
1
2
,
(1)
6
7
8
9
(2)
c
D
I
p
(3)
•
J
I
(4)
-
p
(5)
u
V
J
g
4
,
•
B
G
B
L
II
Q
R
•
S
!
•
X
T
Z
Ce1l.1J 01251 - 012(i1 (or with driver 73303 - 73312) ineluaive p.re
0-
......
us~d
t-
><
c..
I
by
to store the title.
The page number ie stored in cell 01214 (and
the driv~r also in cell 7?~J'6.)
~
&<
~
9-368
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-157
S"N DIEGO, CALIFORNI"
PAGE
Ie 001-5
REPORT
III 491-II
MODEL
All
DATE
5-1-56
CHARACTRON FIXED POINT WRITE
72770
007~6
67 00001 :30000
7 171
00737
75 31771 72713
7 772
00740
00741
11 00001 74001
7 773
•
75
302~3
00743
007~6
ENTRANCE MD DRIVER
STORE ES
ROUTtNE
TO E5
SET
EXIT
7 774
00142
11 72770
7 715
00743
16 00736 00766
72776
00744
21 00766 01216
12777
55
20025
~ OO~ 00150
TEST
73000
00145
00746
73001
00747
45 00000
~O751
ES
73002
00150
32 00776 00000
73003
00751
55 ,20000 oe011
13004
00752
~7
73005
0075~
16 20000 00757
7~OO6
00754
11 00736 73026
73007
00755
11 00777 01017
SET ACQUISITION
SET REPEAT
ERASE INST
13010
007~6
16
SFT
73011
00757
011..,'
71 01216 30000
73012
00760
55 20000 00006
73013
00161
37 00152 00746
73014
00762
37 00752 00746
73015
00763
4S 00000 01001
ttn
73016
00164
11 01213 13245
'-'
J
73017
00765
11 01214 73246
CONTROL WO~D
ADJUST
ES
ADDRESSES
SO ROUTINE
RESTORE GRfD NUMRER, RETURN
RESTORE PAGt NUMrF:q ,
73020
00766
75
RESTORE
13021
00767
11 74001 00001
73022
00710
17 00000 7327:3
AOVANCE
73023
00171
15 '1777 7'3025
RESTORE
73024
00772
11 74001 00001
13025
00773
2~
73026
730~1
73026
00774
30 00000
ooaoo
73027
0071'5
02 00000 00764
--.
f"""f
'"
'"
tI
0
0
f"""f
><
Co.
007~6
00752
ADDRESS
ADJUSTMENT
0075~
0017~
~1777
FOR
30000
~XJT
E.5.
FILM
ES
REPEAT
9-369
CV-157
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5"'''' OiEGO CALIFORNIA
IF 001-6
PAGE
REPORT
ZM L91-I1
MODEL
All
DATE
5-1-56
CHARACTRON FIXED POINT WRITE
13030
00776
73031
00777
7S032
01000
730~3
01001
74 00000
11 oooot
71 C1216
15 20000
13034
01002
55 20000 00006
73035
01003
51 01231 20000
NUt·1BER OF ROWS
7~O:36
01004
13037
13040
ADD~ESS
73041
"1005
01006
01007
55 10000 00011
15 10000 01020
47 01001 01010
73042
73043
00000
0000,
30000
ACQUIRI:
01055
AODRESS
WOqn
OF 1ST DATA WORD
CONT~OL
42 01270 01011
OF 1ST (~
TEST NUMBER ~OW5
TEST NUM8ER ROW~
01010
31 01216 00005
SET
71 20000
73046
01011
01012
01013
01014
13047
01015
73050
01016
73051
01017
31 01214 00000
47 01016 01015
17 00000 01241
21 01000 (}1216
16 20000 01172
7'3052
01020
11
73053
01021
73054
01022
7~O55
01023
73044
73045
n12~4
35 01216 01273
:30000 01275
15 JI020 01102
11 0124·0 01214
EXIT
",,,
1ST
TRANSFER tD£NTITV
SET FOR PW CHANGE
FREE RUN P~tNT
TEST FOR
NEW PAGE
5ET PICKUP FOR TITLF.
PICKUP
SfT TALLY
STORr:
01025
47 01046 01026
6
73060
01026
15 01211 01027
~ 73061
r->< 73062
c..
01027
11
01030
11 01246 01211
13063
01031
73064
01032
51 01261 20000
55 10000 00006
73065
01033
32
73066
01034
77 10000 20000
SHIFT CHARACTERS
ADD po~tTION
PRINT
73067
01035
21
SHIFT RIGHT
0
~OOOO
0121~
ol'-l~
1000(t
oonoo
017.33
~2
SET
'I 73057
a--
GR!:ATf.~
CHANGE TO
DISTANCE
PAGE NUMBERS
TEST
a
ADVANCE FILM
01024
...-t
0
:32
17 00000 012'31
31 01213 00000
r---lJ"j 73056
.w.
EXTRACT
FRO~~
Q
9-370
CONVArR - DIVISION Of GENERAL DYNAMICS CORP.
SAN DIEGO. CAL'FOl'tNIA
CV-157
IF 001-
PAGE
REPORT
Z. 491-7 II
MODEL
All
DATE
5-1-56
CHARACTROi FIXED POINT RRITE
73070
13071
01037
73072
01040
73073
73075
01041
01042
01043
73076
01044
73077
01045
01046
73074
13100
11
012~4 ~121~
55 01275 00006
1:)1
O12~1
73102
43 01231 01171
73103
01051
42 01242 01055
73104
01052
73105
01053
31 0124:3 00000
11 01215 01217
7~lO6
01054
01055
73107
73110
73111
73112
,..... 73113
t; 73114
pooof
01056
01057
01060
01061
01062
37 01205
01 L1'7
~1201
11 300QO 01271
21 0105~ 01244
31 01201 00000
36 01271 01103
11 01211 20000
46 01063 01067
01063
01064
01065
01066
13 01271 01211
31 0121'2 COOOO
01067
21 01213 01233
73122
01070
71 01277 01267
73123
01071
32
73124
Ol()72
11 20000 01276
73125
01073
·73126
73127
01074
31 20000 00017
35 01212 01076
31 01262 00000
'173115
0'
6
73116
~
73117
t-
41 01271 OlO~l
21 01027 01244
42 01210 01027
21 01214 01216
11 20000 01272
11 01245 01271
37 01134 01110
01047
01050
731(')1
0
01036
>< 73120
73121
0...
01075
32 01245 00000
77 10000 20000
01236 00052
TEST TALLY
ADVANCE PICKUP
TEST END
ADVANCE PAGE NUMBER
TO rNTEGE~ STORAGE
o TO FRACTIONAL 5TC~AGE
PRINT PAGE NUMBER
SET G~rD POStT!ON
STORE SCALE FACTOR
TEST FO~
EXfT FLAG
TEST FOR OVERSIZE
E FOR SCALE FACTOR ERRO~
SET SCALt FACTOR
0
PRINT E
ACQUIRE' NUMBER
STe:P
SET BINARY
POINT SHIFT
TEST FOR SIGN
N'EGATTVE
GRID
NEGATIVE SIGN
PRINT
MOVE SIGHT
.2~~7 X BSF
.99
NUMBER FRACTIONAL
SHIFT TO U
['IIGIT~
ROU~lDING
FACTOR
9-371
CY":151
CONVAIR - DIVISION Of GENaAL DYNAMICS CORP.
SAN DIEGO. CAL.'I'"ORN'A
PA.GE
IF 001~
REPORT Z)(
L.91.i.II
MODEL
All·
DA.TE
5-1-56
CHARACTROR FIXED P0I'flT WRITE
7'134
01076
01077
01100
01101
01102
731!S
01103
731'36
01104
01105
01106
7~130
73131
73132
73133
731g1
73140
73141
73142
73141
7!t44
7'145
1'3146
73147
13150
73151
'3152
13153
01101
01110
01111
01112
0111l
01114
~n
Ito
ooono
1 01274 01103
11 01246 01274
21 01102' 01244
11 'ooot') 01275
~o 00000 00000
32 10000 0000(')
11 20000 01211
~4 20000 00044
11 20000 01272
15 2001J 01112
42 01216 01114
11 01247 01272
11 01215 10000
51 01231 01277
01·121
01122
55 01217 10011
31 01206 00000
36 10000 01124
~1 01217 00000
16 012f1 01277
31 01272 00044
13155
0112~
~2
73156
01124
73157
01125
01126
01121
;: 13154
=
01115
01116
01117
01120
It)
I
0·1
0
0
0~
t-
><
c..
TO 0
on~nft
TEST FOR PW CHANGE
RESET TALLY
ADVANC! Pw
NEXT P~I
CENTER BINARV POINT
ROUND
STORE FRACTION
STORE
tNTEG!R
JUMP IF OVERSIZE
JUMP IF SIZE OK
SET FOR MAX. INTEGER
l1-R
SET
DtvlsION
1(')
R-l NUMet!R
REPLAce
lNT£GE~
73162
7316!
73164
01130
01211 00006
30 00000 00000
11 10000 01211
73 10000 10000
55 10000 00001
22 0121$ 00001
01131
42 01212
Oll~2
27 10000 01216
ROUND
73165
0113,3
73166
011~4
73167
01135
31 01205 01204
37 01134 011~5
:31 ~1250 0000(')
PRINT tNTEGtR
OPTIONAL EXIT
PERIOD
73160
73161
0113~
DtGITS
NUMBER.
DIVISOR IN
Q
ANSWER X 2 EXP '.5
ANSWER )( 2 EXP
"
REMAINDER X 2
TEST wtTH DtVISOR
9-312
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO
CV-157
PAGE
CALIFORNIA
IC 001-9
491- 11
REPORT
Z)(
MODEL
.&.11
DATE
5-1-56
CHARACTRON FIXED POINT WRTTE
011~6
:32
73171
01137
73172
01140
73173
01141
77 10000 20000
21 0121~ Q12~1
11 01276 01211
73174
01142
37 01205 (')1204
73175
0114:3
73176
01144
73177
01145
11 01213 10000
51 01264 20000
35 01234 O121~
73200
01146
11 01263 10000
V MASK
73201
01147
73202
01150
7'203
71204
01151
73205
01153
7~206
01154
13207
01155
13210
01156
73211
01157
73212
01160
51 01211 20000
42 01273 01046
16 01234 0121)
21 0121~ 01266
15 01213 01211
31 01271 00000
42 01265 01046
17 00000 01240
11 0121~ 01213
17 00000 n1~41
VERTICAL ADJUSTMENT
JUMP IF OK
VERTICAL TO START
ADVANCE HORIZONTAL
HORIZONTAL
TO U OF A
JUMP IF OK
STOP PRINT
SET FOR NEW PAG~
ADVANCE FtLM
7321~
01161
15 01046
0116~
TEST
73214
01162
~l
01274 00000
FOR
7321r;
01163
73216
01164
-. 73217
01165
41 011'-'6 011&4
15 01102 01166
21 01166 01244
~
73220
01166
13 30000 10000
0"
73221
01167
0
0
0"-
73222
01170
t-
73223
01171
>< 73'-'-4
73225
0117?
01173
51 01261 20000
t.~ 7 01023 01172
17 00000 01240
45 00000 ~()0f)O
31 10000 00002
73226
01114
32 10000 00001
STOP PRINTING
EXIT
Q
X 10
TO A
73227
01175
11 20000 10000
REMA t NDER. TO A
t-
'-'
I
I
f'"'"4
0..
01152
Cl21~
GRID
73170
00000
PRINT PERIOD
MOVE RIGHT
CHANGE TO FRACTION TALlV
PRINT f'!RACTION
GRID
MASKED
ADVANCE
VERTICAL
END
OF
PAGE
EXIT
9-373
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
~A'" DI~G(\
CV-157
CAL'FOAN' ....
!"AGE IF 001-10
REPORT ZIIt
491-11
01116
34 20000 00102
73231
01117
42 012~5 01201
73232
01200
35 01232 20000
73233
01201
32 01213 00000
73234
01202
73235
01203
73236
01204
73237
01205
77 10000 20000
21 01'-13 0123~
41 01277 01113
45 COOOO 30000
73240
01206
55 01230 10001
73241
01207
31 01271 00044
73242
01210
11 01261 00000
73243
01211
00 01251 00000
73244
01212
73 01:216 10000
73245
0121~
73246
01214
73247
01215
73250
01216
00 00000 00*0
00 00000 00*0
00 000(')0 n('l *
00 00000 00001
73251
01217
00 00000 00012
73252
01220
00 00000 <"0144
7325~
01221
01222
00 00000 01750
00 00000 2~420
01223
00 00003 03240
~ 73256
01224
><
73257
0..
01225
41100
O{) 00461 .13200
73260
O12~6
73261
01227
13262
01230
00 0515~ 6C400
00 7~46S 45000
11 24027 62000
73263
01231
00 00000 00071
73264
01232
02 00000 00000
73265
01233
73266
01234
00 00022 00000
00 00000 00036
HORIZONTAL SPACE
VERTICAL SP,t,CE
""''''''9
I;JC.O(
01735
06 00000 00000
TEST
I 73254
0'
8 73255
"0
All
DATE
5-1-56
OVERFLOW TO POSITION
TEST FOR
ADJUSTMENT
GRID
PRtNT DIGIT
MOVE TO RIGHT
END OF WORD
13230
t;
.....
MODEL
EXIT
SUB
FOR NUMRER ADJUSTMtNT
FOR BINARY POINT SHIFT
FOR PAGt TITLE TEST
FOR ROUNDING FACTOR
GRID LOCATION
PAGE NUMBER
lFRO
POWERS
OF
OOO~6
10
MA$K
9-374
COtjVAl1 - DIVISI()N OF Gi~ERA~ OYNAMICS 'cOR'.
CV ... 157
. " ... OlitGO. CALIFO"NIA
.......
73270
73271
73272
73273
01236
01237
01241
73214
01242
00 00000 04400
00 00000 06000
00 00000 00044
73275
01243
22
73276
01244
00 00001 (')0000
73277
01245
40 00000 00000
7'3300
733(')1
73302
01246
C1247
01250
00 00000 00005
11 ~4027 61777
~o
13303
01251
44 70077 00770
73304
01252
73305
01253
73306
73307
01254
73310
01256
73311
01257
73312
01260
73313
01261
73314
01262
01 70071 00770
07 70017 00170
35 00521 72522
14 43774 $2501
44 10011 00710
07 70011 00770
07 70017 00770
71 00000 OOOO~
~7 77111 771'77
00 00000 71777
00 01400 77777
00 02000 00000
00 00400 ~OOO()
00 22221 64247
00 00000 aOO41
01240
01255
73315
01263
:;I 73316
01264
~ 73311
~ 73320
0126$
tr;
t-
73321
01266
01261
0..
73322
01270
~
><
00 77270 24366
00 COOOO 05000
O~O~O
00000
00000 00010
REPORT
MODEL
IF 001-11
ZM 491-11
All
DATE
5/1/56
PAGE
.99 X 2 EXP :30
PRIN1 FREE RUN
STOP PRINT
ADVANCE FILM
36
E
PRINT NEGATIVE SIGN
lC EXP 10 -1
PRINT PERIOD
CHARACTt:RS
FOR
PAGE
iITLE
MASK
MASK
MASK
.2a~7
X 2 cXP 30
9-375
RR-158
REMINGTON RAND UNIVAC
St. Paul, MiDD880ta
15 April, 1956
aIg. A DE!I!N~~TION BOUTINE
Descriptiop
This ro~tine enables one to display a message in Times-Square
fashion across the monitor SCQpe on tbe 1103 cODsole, or on paper tape
from the bigb speed puncb. The routine is provided with progra. eDiries'
and ex! ts for use as a subroutlneo (asS> are preserYed ID the region
76000-77777 while FLICK operates and are restored upon co.pletion of the
display.
"
Input
The routine will read a message from paper tape whicb bas been
punched in flex code directly from a Flexowriter; the routine will also
display 8 message which has been previousl, stored on the drum starting
at address 50000. In either case, the upper limit on tbe number of obaracters
per llessage is 2~1l0. A flex code-stop (octal 43) .uat te1'llinate a
Ilessage.
'Dae flex-coded claaracters recogalaed by' f1..ICI are A tllru Z,
.- tllm 9, .inus (-). equality (a), plus (+), period (.), and space.
Space codes are auta.atlcall, substituted for carriage return and tab
codes. FLICI ignores all otber flex codes, aDd paper tape leader.
In additlon~ a lIw.ber of otber characterl are Byailable for
display. !hel. oharacters canBot be punched on tape directly from 8
Flexu.riter, .Dd, be.c. u.e of tbe. requires that t~e, be read iato the
COMputer iadepeadentl, of FLICK. !be additlon.l charaoters and tbeir octal
codes are as followl:
.
...L..
·
?
••
J
%
-"If
121
122
123
•
(
124
)
125
126
r.:
127
J
r
130
I (Ilre )
m----------------____
~~
r)
f(:Rh
1
..
2
3
4
5
6
.....
...
~
It
~
"
7
______ ______________
____________
~
~
J
ltj
~
A bioctal tape of cbaracter codes for a desired Message • ., be
rJ.- loaded Into tbe COliputer, one character to 8 cell sterting at address
6 50000. !hIs for. of mes88ge iaput must of course be effected iDdependeDt11
8......
of FLICK routine •
:><
Optput
t0...
Eacb character of tbe message is displayed in 8 5x7 matrix OD
tbe scope, or on tbe paper tape. One character moyes across the scope
In approximately 3 seconds, aDd'cbaraeters are puncbed out at the rate
of 10 per second.
9-376
RR-158
Storage
The FLICK routine is located in cells 47161 tbru 47777. The
coded message Is stored in cells 50000 thru 50000+n, where II Is the number
of cbaracters in the message. Cells 54000 tbra 54000+n are used as
temporary storage. D ~04710 (37778). The FLICK routine is available in
symbolic coding (RECO) so that rearrangement of storage can be readily
performed.
Any.essage remains undisturbed on tbe drum once it is read io;
tbis enables one to redisplay a message as many times 8S Is desired until
a new message is read in.
Operatlpg Instructions
TYPE OF
PAl:
DISPLAY
SEnING·
Flex-coded
paper tape
scope
47324
37 47312 47316
DI'11II
(50000 thru
scope
47321
37 47312 47313
Flex-coded
paper tape
punch
47173
37 47161 47165
On. (50000
tllru 50000+a)
puncb
47170
37 47161 -47162
READ
MESSAGE
nOi
PROGRAM
ENTRY
50000(0)
~: It only one display is desired, lSI select s~ould be
turned ON at this point; ~therwlse tbe current display will repeat indefinitely. PrograJI entry to FLICK gl yes only.!!!. complete message
display.
AiaDs
10 If 80 illegal character code is encountered, the computer
baits on a 56 000i7 00163 commando STARTiog .i11 terminate the current
message and begin display of tbose characters wbich up to the stop point
:; bave been found to be legal ones.
~
~
I
0'
6
~
~
~
~
2. If a flex code-stop (octal 43) is o.itted from the end of
the ••ssage. FLICK rill continue to read from tape or drum until an
illegal code Is found (see alarm 10 ) . When tbe code-stop is omitted
from punched paper tape, tbe computer !!1 bang up on an Eternal Read
command: in" tbis case Force Stop, set PAl m 00136 and START. The
message is tben 8ut0.8tlc811J ter.inated and display beginso
, listing or the oode in .,..bolio-relatlw (tor assably by
RICO) and octal and/or a bioctal paper tape suitable tor reading into the
1103 _,. be obtained upon request addressed to:
lAo B. Kennedy
UrdftO Scientitic
Applioations Group
HO-159
CC - A Useful Instruction for Inverted Binary Numbers
Binary counters and converters will sometimes supply a
quanti ty -In the inverted binary or gray code. When converting
tram ordinary binary notation to gray code or vice versa,
the CC - command may be used conveniently.
Conversion fram ordinary to gray code can be done with
these 2 instructions;
LA
x
A .. 71
a + 1 CC
x
A
a
Shift ordinary numbers
1 right and leave in A
Add to each bit the following
bit modulo 2
This takes care of nmnbers up to 36 bits long. Execution time
is 228 /,P sec. The reverse process is not quite so elegant,
it uses repeated LT and CC.
SP
x
36-n
a + 1
L'l'L
o
x
a ... 2
RPV
n
a ... 4
a +
3 LTL
1
a
4 RPV
n
a +
x
T
a
6
a +-5
co
Scale up inverted numbers
Clear cell x
6
Make
a string of n shifted
}
Words
}
Add to each bit all preceding
bits modulo 2.
The size of the n\UDber to be converted i3 n.
time 1s (270. + 56n) fl see.
The
execution
Both procedures can be easily adapted to put results in
other cells.
Robert G. Tantzen,
Holloman Air Development Center
9-378
RW-160
TNI-O
Pg. 1 of 4
Revi8ed May 1, 1956
THE RAMO WOOLDRIDGE CORPORATION
Los Angeles 45, California
ARCTAN
Specifications
Identification Tag:
TNI-O
Type:
Subroutine
Assembly Routine Spec:
SUB
Storage:
58 instructions
50277 07214
14 constants in prog,am
72 words of total program storage used
or temporary storage pool used,
addresses 00027b through 00032b
4 words
Entrance and Exit:
RJ
SUBOO SUBOl
The alarm exit is not used.
Drum Assignment:
64045b through 64l54b
Machine Time:
J .. 7 ms average
Mode of Operation:
Fixed point
Coded by:
P. Johnson
December 3, 1954
8
0-
Code Checked by:
T. Tack
March 15, 1955
.....
><
~
Machine Cheeked by:
M. Elmore
March 19, 1955
Approved by:
w.
April 29, 1955
maeh1~
time
-
0
-.0
......
'-'
J
0J
......
Dixon
9-379
RW-160
TNI-0
Pg. 2 of 4.
Revised 5/1/56
Description
This routine computes F(X), an approximation to t;he arctangent of
X, by using a. polynomial approximation.
It was programmed by
Research Associates and was adopted for use at
.~ngineering
Ramo~ooldridge.
Programming Instructions
Assume the routine is stored at SUBOO, and that X is the number whose
arctangent is desired.
1.
Place X· 2 33 in the accumulator
2..
Execute
RJ
SUBOO
SUBOl
Control will be returned to the cell immediately following the return jump
.a.nd F(X)· 23~ will be left in the accumulat0:t;.
"\" 17' 16 F(X) ~
2"
1f
,.
Mathematical Method and Error Analysis
The Rand Approximation
7
Arctangent X
is used.
2i 1
C2i -1 X i=O
= F(X) =~
(See Rand Sheet 13.)
The accuracy as stated by ERA is
I
IArctangent X - F(X) ~2-25
Machine Checking
Sixteen values of the argument were tested in the range
o
~ -1225 ~ X ~ 12~5 ....
'-'
I
0"I
o
o
0"-
......
r-
><
t:l.t
9-380
RW-161
NUI-3
Pg. 1 of 9
revised 5/1/56
THE
RJ\MO~ WOOLDRIDGE
CORPORATION
Los .Angeles 1~5, California
Gill Method Subroutine
Specifications
'Identification Tag:
NUI-3
Type':
Subroutine
Assembly storage SpeC!
SUB
c~orage:
49880 07414
59 instructions, addresses
OGMOO thru ooM40
lGMOO thru 1GM17
15 constants in program, addresses
OGCOO thru OGC14
74 words total program storage, addresses
OOMOO thru OGM40
IGMOO thru 1GMl7
OOCOOt~
ooc14
10 words temporary storage pool used, 8.ddresses
0OO27b (OGTOO) thru ooo4Ob (00T09)
63230b
6334Ib
Drum Assignment:
Addresses
Program Entrances:
Addresses OOM02, OGM03, and
Program Exit:
Address OGMOl
1vBchine Time:
(lO.3n + 1.9)
thru
InS
OGMo4
per point average, where n
equals the number of equations in the system
--
Mode of Operation:
Fixed point
1""""1
-.0
~ Coded by:
I
C1'
I
J. Carlson
R. DoUthitt
14. Elmore
o
o
R. Summers
C1'
.......
t-
M. Elmore
June
8, 1955
Machine Checked by:
M- Elmore
July
7, 1955
Approved by:
lie Eauer
July 22,
>< Code Checked by:
0...
1955
9-383
RW-161
NUI-3
Pg. 2 of9
revised 5/1/56
Description
The Gil]. Method Subroutine integrates a system of first order, differential
equations using a ~tep-by-step process. Using the values of the variables at a
point and the coding for computing the derivative of each of the dependent variables
at that point, the Gill Method Subroutine produces the coordinates for the next
point of 'the solution each time it is entered.
'
A special entrance sets up the subroutine for a particular system of equations,
thus allovTing the subroutine to solve concurrently several different systems in the
same program.
The independent variable is incremented within the subroutine itself.
Notation
The system. of equations to be solved is
~' are intermediate values of the calculation ,( zero initially)
II x is the increment of the independent variable x
h is the bi'nary 8(!aling' power of x (i. e. x· 2h is in the computer)
h-l is the binary scaling power of .6x
m
i
is the binary scaling power of Yi
f is the common difference between the scaling power of Y and the scaling
i
dy
pOlqer
-.
1"""1
Ofaxi
for each i.
m - f is, the binary scaling power of
i
d.yi
a:x-
-..0
-1"""1
I
L
= 13
+ f - h
0"I
8
~
PrOgramming and
><
c..
Assign the Gill Method Subroutine to some arbitrary region, say OOMOO.
r-
Qperat~Instrtictions
In order to solve a given system, the following array of variables, derivatives,
intermediate values, and parameters should be assigned a region, say OGNOO.
9-384
CONOO
L
OGN01
00 OGN05 OGN06
RW-161
OGN02
OON03
OON04
NUI-.3
Pg • .3
n-l
6X
',,'
__ 01.,
dy1
scaled 2h-l
scaled
IIJ. -
OGN06
Y1 ·
scaled
~
OGN07
ql
initia,JJ.y zero
dy2
9
h
scaled 2
d£
oorro5
o£
revised 5/1/56
f
OGNOB
ax
scaled m - f
2
OON<
c..
(X + mh,
kl :::: h f (X + mh, Y + mk o )
He now use ko and kl to find a third point at which f is calculated:
y + [n-r ] ko + rk1 )·
k2
=h
(x + nh,
9-386
f
(X + nh, Y + [
n-r]
1-:0 + rk1 )
RW-161
NUI-3
Pg. 5 of 9
revised 5/1/56
Similarly,
=
The weighted a.verage of ko' k , kG' and k3 1s the desired k
l
6y:
Sy = Y (X + h) -y (X) = coko + clkl + c 2k2 + c3k3
,.mere Co + c
l
;- c
2
+ c3
= 1.
For a system of equations, the same four steps given above are made for each
equation and
oYi = cokio + cllti1 + c 2k i2 + C ki3 vmere Co + c l + c 2 + c = 1.
3
3
The above process is, for certain values of nt, n, p, s, t,' co' c ' c ' and c , the
l
2
3
Runge-Kutta process. The Gill process was derived, With application to machine use
in mind, by minimizing the number of storage cells required. For the Gill Method
the above conste.nts are
m
= 1/2 ,
r
= 1- 'Yi72 ,
c
n
= 1/2 ,
s
=
,
c
p
=1
if12 ,
c
,
-
t = 1 +
.(jJ2
c
0
I
=1/6
=(1/3) (1 -
(1 +
2 =(1/3)
3
=
1.I72)
Yi72)
l/e
The Gill process further systematizes the calcuJ.ation so as to increase the accuracy
and ~implify the coding.
The Subroutine
As
used in the Gill Method Subroutine, the process is as follows :
1st pass:
Advance
k io
x by (1/2)h
= h-f i (x,
Y10 ' Y20' • • • , Yno)
r il =(1/2)kio -
----
~1 = ~o
~
-0
~
~o
+ 3r i l -(1/2)kio
'-"
I
Yi l
0"I
o
o
+ r 1l
Calculate fi (x'Yll 'Y21' · • • ,
0"~
t-
:><
c..
= Yio
yrJ.' in programmer's own coding.
2nd pass:
r 12
= (I
%2 = ~
- "'1/2) (ki l - ~l)
+ 3r '12 - (1 -
Yi]2) kil
RW-161
3rd pass:
NUI-.3
. . . ,. Yn2)
r.?
= h"f1 (x'Y12'Y2'~'
= (1 + YT72) (k i2
~3
= ~2
+ 3r i3" - (1 + 'Y'I72) Iti2
Yi3
== Y:i..?
+ri3
ki2
1J
Pg. 6 of 9
revised 5/1/56
- Qi.2)
CalcuJ.ate fi (X'Y13 'Y23' • • • , Yn3 ) in programmer's own coding.
l~th
pass:
ki3
= h-fi (X,Y13 ,Y23 , · · • Yn3)
r i 4 =(1/6) (k i3 - 2%3)
~L~
==
Yi4
= Yi3
°-'13 - 31'"14 - {1/2)ki3
+ ri4
Calculate fi (x'Yl!~'Y24' · • • , Yn4) in programmer's own coding.
The ~aper by S. Gill mentioned previously. includes a detailed' analfsis of
errors, both truncation error and round-off error.
~~rors
The expression for "the truncation error in' Sy1 1s too complicated to give here, but
its d.ominating term, the author states, is
rl f'i
aYm
Jx=X
where Y == x.
~0 = 1,
0"
j,k,l,m
-. and the truncation error in Sy. 11il1 be approx1ma.tely this ,men the second partial
~
).
,lerivatives are all close to zero.
It is probably more useful to say merely that
~ the tru..."1cation error 1s of the order of 115•
o
o
0"- ~le standard deviation in y. -(1/3}a. over one step from all rounding off errors
r-!
r-!
'-"
t-
~
).
0
"'l.
is ('tfhere f is the quantity mentioned in the section on notat1on)
1/6 [. -rI3{2-2f + (l l 16)h
2
Lj~ (:~ij)x~"}ll/2 u, ~n::~t~U:h~f
last digit of y.
Machine
Chec]~ing
A driver routine solved t'tvO systems of equations both separately e.nd conctlrrently,
using the Gill Method Subroutine. The t,.,o systems Dolved are given belo", to
indiccrt;e f.~ccu.racy 2nd to serve as eX8..nrples.
9-388
RW-161
NUI-3
Pg. 7 of 9
revised 5/1/56
1.
E9.uations
dYl
= Y
d..."'{
2
equivalent to the second order
dY2
dx
-Yl
=
d
2
--1l.. +
dx
l\x
= .0812664626
:=
1(/36
2
e~lationJ
y = o.
,
= 50
Initial Conditions
Solution
Y
1
= sin
x
Accuracy
In a spot check of" the results, the greatest a.bsolute error observed was
.
-6
1.5 x 10 ~
(For x
.000000084 ) .
= 3.1415925696, Y1 = .0000015425. However, sin x =
Eauat
ions
_0
__"_-
2.
Equivalent to the third order equa.tion
'j' ax
=.1
0"I
o
o
0"-
Conditions
L~itia1
....-t
r-
:><:
At x
= .1,
0..
Y
1
= .000025,
Y2
= .001,
Y
3
= .03
Solution
Y
1
=
x
l~
"3
-x
3
b5
+
x
6000
1
120,000
Accuracy
In a spot checlc of the results, the greatest relative error observed was
(For x - .1999999975, Y = .000421t-99858. However, the solution
l
is actually .00042500002).
6
3.4 x 10-.
RW"'161
NUI-3
Pg. 8 of 9
revised 5/1/56
c ?~JtlG
r~·f'.
}C:6~l
~i?O'51
5",",
.((.98 (.:i(!
l~ 99;':::1
CO 00000 DOOOO
632.30
633() ~_
].
.:
D
11't.:::C
f)
'26i<
D
,. ('U
D
OGe
lfJBj
\~.')f'.-'''..!
v ~.·....1 f _I
lGC
49939
63323
00027
63230
63231
6::32'32
0
D
2GMOO
2GMOl
2GM02
2GM03
2GM04
2GM05
2GMO.b
2GM01
2GM08
2GM09
2GM10
2GMll
~ 1:
'lr
t
061
23
00000
00 00600
MJ
MJ
MJ
IGMOO
OGM36
TP OGMO'O QOOOO
Q.j OG~'106
OGI'-1'-·O
OJ OG:'" 38 OGr~10 7
TP QOO60 OGMO·O
RA OGH1O 06(01
RP 30003 OGMll
TP
lU
OGM15
2GM'l2
TV
OG~31
2Gr-'13
TP
RP
2GM14
2GM15
2GM16
2GM17
2GM18
2GM19
2GM20
2G~;'21
2 Gt-122
2GM23
2GM2-4
- 2GM25
:0 2GM26
OGTO!;
OGroe.
301JO~
fP
MP
LA .A
TP A
f4p OGT05
MA OGT06
LA A
TP 11
AT A
AT OGTC4
~
0..
0
2GM33
2GM34
2Gt-135
pAss
STORE C1R
UP pASs
STORE
ADDRESSES
63244
RESET
~
' I
I';'
&3:247
SHlFT
63250
63.251
63252
l
AK
Ak eo
63:253
&3'2S4
:.18
OGT'Oi+
s:roRt R
A-
2i;:
63255
63·Z;S6
63257
_....
":'0,
63'260
63261
632·62
3 lt
OGM1S OG<::ol
RA OGM31 06(02
IJ OG108 OGM14
M-J
63245
Q,32A6
STORE K.
LA ,'\
63:240
6':l'241
63:2'42
6324·3
OGT03
OGT03
OGT02
A
,63236
6'3237
PASS CONS
RESEr
CALC K
~A
0'- 2G~13
63233
63234
63235
\4HAT
OGTOO
>< 2GM32
82GM29
ENTER
RE ENTER
oGTOe
~ 2GM31
d-.
UP
TO SET
OGM16
MA CGr07 OGTC3
38
LA A
AT OGT02 OGTC2
RA OGiOl 0GT(i4
RP 30002 GG~·1J2
iP OGTOl
~ 2GM27
2Gt~28
aDono ooo:;u
on ooooe 00000
:~ /.
(j~1
D
3R
CK
OLD
V~ ... ·
00
00
00
00
00
45
00000 O()OOO
00000 00000
000·00 O(}OOO
000:00 00000
OO()OO 00000
00000 00006
45 000.00 '02051
45
11
1.. 4
44
0000:0 02044
020eo 10000
02006 O~OSO
020"46 02PC'?
lOO{lO 02000
11
21 02012 02074
75 30003 0201:3
11 00000 00034
15 OOO{tO 02017
16 OOO{)O 02031
11 o.oO(JO 00031
.15 300tr~ 0202G
11 00·0-00 00021
11 0·0000 00027
54 2~tlC!)" 00000
11 2Q(JOO ·OOO~2
().OO34 60{),32
72 00035 OOO~l
54 200'\)Q 00046
71
11 20000 06033
3S 2000() 20000
'3:~ O'OOi3 zoooo
'J
5:4 20·00{)
72
o~ao36
00042
00032
63263
63-2b l !
54 2001)0 0'0046
Y
632.65
Y AND Q
6:3267
21 0(10:;0 00033
75 30002 02640
1'1 000:30
21 020L'l 62 "lIt
21 02·037 02015
41 t;;}OO31 02016
ADD
EQUALS
N~W
Q
(~
stORE
ADVANcE
A[)f)~ESStS
CYClt: N
b~3266
63'2.70
63a11
6~212
63'213
'l'"
..... ,:?
OCC3~
nO'o3t
oogoo
45 00&60 00000
2GM36
TU OGCOO CGM10
6,3274-
2GM37
TP OGM21
'..:.I
2GM3~
RA
63275
IS 02073 02012
11 0202<
c:w
37 77717 11741
01 10604 71625
00 00000 00001
235 - 31
513
R.
--.....
C\J
-.0
---CJ"
I
I
A
(513·~I: mod p
A mod p
A
HI
1
9-392
1103 LIBHAHY SUBHOUTINE
WF-163
CENTRAL EXCHANGE INDEX:
TITLE :
Line Printer
Decima~
Output
ENTRIES IF MORE THAN ONE OR NOT STANDARJ):
x
NO
CODING CHECK:
x
BY
MACHINE CHECK:
x
BY C. S. Fluke
STA~DAHD:
YES
YES
SELF-RESETTING:
1.
Initial location of argument:
Qu=lst address of input:
=(1-92)
2.
.-
3.
Final location of argument:
00011
Location of the function:
paper
x
C. S. Fluke
NO
Qv=(no. of digits)a
10
ADDRESSES:
(a)
Instructions:
(b)
Constants and temporary storage:
(c)
Constant pool used:
(d)
Temporary storage pool used:
through
01000
01066
01065
through
01134
00040. 00057. 00073, 00074
00010 - 00017
INITIAL SETTING OF X:
C"j
...0
-r-I
(a)
Range on x:
(b)
Scaling of x and f(x):
(c)
Brief description of numerical method:
I
0'
I
0
0
0'
r-I
r-
><
0..
4.
ACCURACY:
5.
ALARM-CONDITIOi\S FOR OtT-OF-RANGE TEST:
Full 100%
ARu= illegal code;
For illegal code:
AHv = place in word of input = (1-11)8
9-393
WF-163
AL
u
= address
6.
SPEED:
7.
MISCELLANY:
of code word.
Line printer limited
Program will take parameters defining input, make card image,
and print one line starting at left most digit.
Paper is advanced
by format switches for col. #1.
Input must have information for the number of digits to be
printed, including codes' for spaces,·, 0, as well as the decimal
digits.
These codes are stored in the input as hexadecimal digits,
i.e •• 4 bits per digit, and are packed 9 digits per machine word,
going from left to right in adjoining registers.
The codes can be derived as the immediate result of a preceding
conversion routine.
They are:
Digit to be printed
8421 binary code
space
1111
0
0000
1
0001
2
0010
3
0011
4
0100
0
0
0-
5
0101
......
6
0110
7
0111
8
1000
9
1001
-
C'j
-.0
r-f
'-'
f
0f
r-f
>::
c...
•
(odd cois.)
(even cols.)
")
J
1010
9-394
CV-I64
CONVAIR
ANALYSIS
Do_ Parker
;-'. Char le. Sw1..f't
Matt Vuletioh
PREPARaD 8V
CHECKED .V
R~.D BY
A 81. . .0. 0' ••• II:••U DnlAilICI COlPOtlATlO.
SA.N DIEGO
PAGE
REPORT NO.
MODEL
pATE
\
eN 007-1
ZII 491
111
6/20/56
BV PROOIWI Clf 007
Table of Content.
1.
Introduction
2
11. Equationa
3
lll.Program Constant.
4
1V. Program Characteristics
5-7
V.
Input - Output
8-9
Vl. Operating IDitruetions
9-12
Appendix
13.14
Storage !asignmenta
15,16
'low Charts.
EV Starter
17
EV Part 1
11
IV Partp
19
IV Part 111
20
EV·Orthogonal1zation
21
III lloutine.
22
Sample Problems
Sample SOT Output
23
29 x 29
24-28
2q
Matrix A
x 29 Matrix A Dehydrated
29-31
lArP at 27 Eigell"f'alu.8
32
Eigenvector. of last 11 Eigenvalues obtain••
32-34
34-36
Code
37-70
9-395
CV-164
CONVAIR
ANALYSIS
a ...... fW . . . . . . . OBA.ac. COIIHeA'ft••
ptREPARED flY
DeIm Parker
CHECKED BV
REVISED BY
Charl•• Jwitt
llatt Vul.tioh
MN Otaoo
.'.'.
PAGE
REPORT NO.
MODEL
DATE
BY PROGRAM C1I
C. 007-2
ZK 491
All
6/20/56
007
I
1103 PR''ORAl! FOR COMPUTING EIGENVALUES AND
ETOEllVECTCRS OF REAL. SY1OIE1'RIC MATRICES
1.
INTR"DUCTIOlh
fbi. program ia designed to determine all Tectors Y1 and all .oalars
JL
1 whioh together with a given real, aymmetric matrix A ot order. ~
aati.ty the relationahlpAYi
baaed
0
= AiYi.
64
The matheatioal technique nployed ia
1
n the Hesten•• 1:aru.h gradient methode • The program performs the H••tenea-
laruah near-optimum gradient method2.
ArI.y nuaber
.ero
ei~envalu••
ma~nitud.
ot the eigenvectors and their associated posi tive. non-
aay be obtained in decreasing .equenee with respect to &l~braic
ot eigenvalue..
Extremely close eigenvalue. and eigenvalues close to
zero with reapect to the total range of eigenvalues slow. cOnYergence and in
extreme oases pre-w-ent. conTerp;ence.
the program i. made to take adn.ntage of a atrix with large Dumber.
of lero elemente by repre.enting it in dehydrated form Ie. with blocks of 'ero
element. replaced by
nag.
indicating the number of aeros removed.
For larger
..tric •• (L.O.c::.~t4), thi •• program becomes more efficient with respect,...
time
0
f solution and accuracy.
Ten deoimal digits, unpaoked floating pOint number representation i8
u.ed (See CA 001 report
,.011111 '8,a,,.
ZJ(
491).
9-396
GV-164
CONVA
ANAL-YS'S
PREPARED BY
Donn Parker
CHECKED BY
REVISED BY
11.
PAGE
A 01""011 0' CJI.I••\L DTII" ••CS COIIPOIATlOIl
REPORT NO.
.
MODEL
SAN DlaGO
Charles Swift
•
R
lfatt Vuletich
: DATE
eS' 007-3
ZM 491
All
6/2fJ/56
EQUATIOI'SI
The balic
formul~
Xi • define %1+1 by.
Give!: an approximation
may be summarized as follows.
xl+1: xi+~l~i
where ~1
: AXi-~(Xi)Xl
and }J (xl): xf .lxi/xix i
Ih8a x has
conYerged tn the eigenvector
Y,)J(X) haa
(The Rayliegh ~uoti.nt)
conver~ed
?L • The eonverr,ence tn the eigenvalue proceeds twice
to the eigenTector.
a8
fast as conv~rgenee
The program uses (3 :.8. but this can be
trom iteration to iteration.
to th~ eir,envalue
vari~d
Each eigenveotor ia obtained by
easil:!
forcin~
the
iterate xl to remain in the orthogonal compliment of the subsp&oe spanned by the
eigenve~tor8 already obtained (a 'ymmetric, real matrix has mutually orthogonal
eigenvectors).
correcti::
Thi. i . a.coompli.hed by applying the followine; orthogonalization
:o::u~a~8!e;;,:~;::;::t::::~ xi ie the 1~ iterate converging to the
eigenvector yp and Y (j:O,l ••••• p~ 1) are the p mutually orthogonal eigenvectors
j
thus
rar
obtained.
An arbi brary method of determi.ning convergence is used as follow-s.
The i terata xi and the assooiated Rayliegh quotient j1{X ) are assumed to have ~',oon
i
verged to the eigenvector y and the eigenvalue ;t respectively with d bi ts of accuracy
i
lIhenmi'ic exponent
Bui)J -
exponent [c 11 )~:>d'k: 1,2, .... ,N where
(Zi)k
18 the
k th eleme!lt of the vector Zi.
FORt.. lalZ-A
9-397
CV-164
CONVAIR
A rJ A LYSIS
PREPARED BY
CHECKED BY'
REVISED BY
111.
Donn Parker
. .. Charles Swift
Matt Vuletioh
A ....... or OUDAL DBA.a
Cll 007-4
Z1l 491
MODEL All
PAGE
co.oun ••
R.PORT NO.
flAN DlaGO
DATE
6ft.o/56
PROGR.Uf CONSTAITS AND TERMINOLOOYI
DKSCRIPTIOB
Order ot matrix
lUmber
or
PERIWIBNT L'1C ATI ON
TElIPORARY
•
4000,
00005
B
4~
oo~
40003
00003
SYHB ~L
eigenvector. in the
orthogonal compliment of converging
iterate
Bita of
s.ccurac~f"
ett.lned
00012
d
405~-L.0576
Desired bi ta of a ccuraoy
0163.,.-01636
lumber of ?ector. de. ired in output
•
00010
lUmber of cell. in IS working storage
I~
ooh06
,irat vector in IS
V1
00420 to 00417 + 2.
Secaod vector in KS
V
2
00420+ 2X
Vector in lID
Operanda tor floating arithmetic
to O~17+ III
VVD
41252 to 41451
AJID
4l..452 to ,3377
00025-000 30
OPl. 0P2
Result
S.e .eetion VI.H.
~ index 4~7
Counts interationa
IteratiaD
index
Counts iterations per accuracy teat
Test
Uadez:
Count. accuracy teata per tyPe out Typing
index
Counts iterations per
ortho~onalllatlor
Orthogonali.atl~
index
1'0"'" .ata·4
aofi!41
~7
40734
01774
40561
01621
41035
00305
9-398
CV-164
CONVA
ANALYSIS
PREPARED BY
CHECKED BY
REVISED BY
IV.
Donn Parker
Char lea Swi f't
Matt Vuletich
R
PAGE
A OI"'alO. 0,. •••••AL DY.AM.a CO.H.AnOM
REPORT NO;
eAN DIEGO
(>
eN 001-5
ZM 1~)1
MODEL
All
\ DATE
6/20/56
PR0GRAl! CHARACTERISTICS
The program will handle all matrices of order I
etora~
<
{;4. but there is
epace in MD tor only storing an undehydrated matrix ot order W<
50 le.
(11726)8 oe1la capable of storing (4753)8 two register floating elements (See
CA 001 report ZM 491).
However, the storage region may be expanded (See
appendix b.).
The program as presented ia set up to test the accuracy of convergence
every other iteration, to type the value of d every other accuracy test ie. every
fourth iteration, to orthogonalize every .ixth iteration, to compute a new
every other
ite~ation,
and to cycle
t~rough
three values
of~(al1
~
let equal to
Standard subroutines used and included on IV paper tapes.
CA 001 Two Register Single Prieilion Floating Point Arithmetic Package.
Ie 003 Decimal to Two Ref,iater Floating Binary Card Inpu.t.
This has
been modified to read dehydrated matrices.
Ie
oct.. Floating Point Card Output. Thie has been assembled and stored at
76Wo o
II 002 Alarm, Octal, and Flexprint Package.
BV SUBROUTINES
1ft' Dump and Res tore
Inner Product
Dehydrated latrix-Teetor MUltiplication
Ray1iegh Quotient
Orthogonall.ation
POIIM ,.,a·A
CV-164
COHVA
AN.L~
PR.PA.ED IIY
DoIm hrker
CHaCQD a';
*"
RtMUD IIY
R
PAGE
R&PORT NO.
MODaL
DATa
....... or .UUM. "1I11III COIIIOHW••
MN DlIOO
lwift
",1.1ob
'. Char1e1
C'I 007-6
1M 491
All
6/20/56
flaHWf PAl!!.
8un.r.
Cheok lum taken and typed.
Progr8lll ia .et up for .. given order matrix.
initial eigenvector iterates are Itored. the complete contents of the drum.
and IS i • • tored on JIl'. and the eigenvalUe and eigenvector region is .tored
on If tollowing the complete
)(I).
IS dwnp.
The .tarter is destroyed when
computation .tart••
Part I.
or.
d 1a computed. typed. and compared with
MD
a~d
Pa.rt I is Itored on
1. tranlterred to ES only when needed.
Part II. Iteration routine. It remains in ES except whep
Part II i8 restored to EB trom
)II)
orthogo~allI1ng.
for each ei("enveetor.
'Part III. Computed eigenvector and eigenvalue are stored on MD. prograza ia
.et up for the next eigenvector iteration. tinal output is cantrolled.
Part III ia stored on 1m and is transterred to E8 only
when needed •
. , COITROL.
tigen'Y8ctors. eigenvalues Illd inner products ot eigenvectors are stored
an lIT.
Program, eigenvector•• eir.envalllel, and inner products are re-
.tored tJ"om II! to lID and ES.
'fbi. acts .. a .erviee routine and
1. under
control ot the machine operator.
V1' Photo n,.pa I
duapa
After the pr..,gram
MD and ES onto MT
n.1ue. region onto
IItI
letup tor
il
10
til
liven matriX, the starter
and the initial eigenvectors and eigen-
0 and
.J1lt#
From tiM to time (about
2.
eTery half hour), at the operator. discretion. the eig.nv~ctor.
and eigenvalue. _y be dumped on· JtJ.tf 0 and
In#
2.
Then in case
ot a lailure the whole pror,ram Illd eigenvectors and eigenvalues
from the 1u" dump may be reetored to
continued from the point of the la8t
01"
)If
ES and the problem
photo dl.lDp.
By selecting
l1li2 the eigenvectors and eigenvalueF 'are
either Mr.f 2 or MT# 0 respectively_ Having the
not .electing
.tared trom
un and
re-
9-400
CV-164
CONVA
ANALYSiS
PREPARED BY
CHECKED BY
REVISED BY
DoDD Parker
• Char lea Swi f't
Matt Vuleti oh
R
PAGE
" ...... 0. 0' .IIIIE."L QY••• ICS C9."OUTIOII
REPORT NO.
SAN DIEGO
MODEL
DATE
eigenvectors &lld eigenvalues stored on two
JlJ.'
ell 007-7
IV 491
All
6/20/56
units reduces the
possibility of lo.iug the information.
The
m
dumpinp-; routine takes throe minutes forty seconds to dump
MD and ES and one minu.te ttn seconds to resto;!"e MD o.nd ES.
requires (1017)8 blocks'to store 1ID and ES
It
e.nd~7([2lfE+406)"'lJ
r
[1737
J 1>a
blocks to store the eigenvector and eigenvalue region where [
indicates "the integer part or".
]
Included in the eigenvector
and eigenvalue region are stored the inner produ~ts (dot products)
or each eigenvector with it8elf (These are uaed in the orthogonaliaation process).
IXTERJJAL COJTR~L8f
There a1"e two basic cOiltrols that are Wled during tllS computa-
tional part of thp, program.
MSf
2 at 01535 causes a atop before setting
up for the next eigenvector solution.
A.
E + 1 appears in Q and! appears in
By ohanging (Q) or (A) at this point the eigenvector to be converged
upon &ftd the number of eigenvectors desired may be changed.
Msf 1 at
01704
in Part I of the program after one or several iter~tion8 (depending on the
value of the Test Index) oausel a stop with T in Q ar,d d in A.
(Q) the desired a~cur.cy T may be altered.
By changing
I f ' ia changed. the new value
is typed on the supervilory control typewriter when the computer ia reatarted.
At an
uBI 3 atop
(there are several of them) at OO~l the mantis8a or /.3
(.xp~neDt : 0) appears in Q and may be altered for the next iteration
only.
All other external controls may be found in the operatinl instructions.
PORM '8,a-A
9-401
CV-l64
ANAL"'"
PItEPARIED BY
CHEQKIED BY
RIMSIED BY
V.
CONVAIR
1..
PAGIE
A . . . . . . or uaMAI. .,..... COUOU!I"
Dona Parker
• Cla r
8tr1 tt
. t t Vulet10h
REPORT NO.
SAN DlKao
MODEL
DATI:
01 007-8
II( 491
All
6/ao/56
I'NPUT - otTTPlJ'l'
llPUT 11 performed using the Card Input paper tape which contains
with a change to accomodate reading ill
th~
dehydrated matrix.
Ie
003
llIput consists
or the dehydrated matrix punched on cards by rowa, one row immediately 'follow-
ing the preoeding raw.
The card format and header card are described in
~c
003.
'lh. EV program may be performed without thil Input operation al long IS
the _trix ia Itored in single
prec~8ion
floating point form (see CA 001) by
row. at the addrea. 41452.
DEHYIR1TED IfATRIII
One lero element i. represented as true lero.
8everal
Zero element. in aequ_noe (row end interYening or not) are represented as
a
~.
aero repre••nting the fir.t .ero except that the exponent 18 the
nUJDber of sero ele_uta following the first zero element.
See the 8ftll1ple
problem for an example.
Alter
Weigeuwector.
the ojdaput routine where
have been obtained the program automatically exits to
all
I'l dump ie performed, and all eigenvalues are
punched in floating def1mal form on card. ( ••• Ie ~).
When the computer stOPI,
a, the number of eigenvectors wanted .tarting with the last one obtained, i.
in.erted, and when the computer ia started the~' are punohed in floating decimal
-
~
......
torm on carda in the order in which they were obtained.
The oomputer then exits
to an MIle atop.
'-'
I
S'OPERVIS'JRY C"lfTR0L tMidtI'l'ER OUn'UT:
0J
o
o
""......
the SeT type. the Talue of E and T.
~
count and d are typed.
t-
..0.... ,.,a.A
Jot the her-inning of an i teraticn pr:?cess
Every tot.dl iteration the iteration
•
When T i. "Gal1y ohanged, the new va lue of T is
9-402
CV-164
CONVA
ANALYSIS
CHECKED BY
Donn Parker
~ Charl•• Bwitt
REVISED BY
Matt Vuletich
PREPARED BY
A DIVI• • • OF
e••IIlAL
DYUIIICS
PAGE
REPORT NO.
SAN DIIEGO
MODEL
DATE
eN
007-9
Zlt 491
All
6/ID /56
When the proeeB8 haa converged (d ~T). one more iteration is per-
typed.
formed, iteration count and d are
or the
R
co..ouno.
t)~ed,
and the first three octal digits
mantiaea and last three octal digit. ot the
exp~nent
of the eigen-
yalue are typed.
Whenever a Y.T
du~p
of eigenvectors and
eigenv~lue.
is performed.
-Jrr1' i8 typed.
VI.
OPERATING INSTRUCTIONS,
A.
Paper tape start for initial starting of a problem.
1.
It il advisable to clear In to 'all leros and put
a~y
convenient
lerTiee routines in the 70000 - 77777 part of MD.
2.
Itf
#'J,
lIT
f2
should be set to the desired locations.
3. Jlatrix Input.
(Optional.
Se. aection V of this report.)
Load paper tape. • Card Read IC 003 reviled-.
Load matrix deok ot cards '(with header oard) in read hopper.
lID atart 00300. Rea.de oard., types oheck sum and "done".
4.
Load main paper tape, -IV"'.
5.
JID start at 40000.
6. At)lS
10
atop, 01017 put I x 20 ..... (Q). y x 20...... (A).
7 • Start. ., dump requires about three minutes forty aecond.. Stpp
at liS
8. Start.
B.
Output.
10 1161.
Iteration start••
When I .... eomputer .top. at 01572.
1. lumber of vectors wanted II • x 2 0 --+- (Q).
2.
c.
Intermediate 1ft' Dump.
1.
FORM'.'.·.
Start •. Stop at 01613 atter output, and Kr dump.
At _
f2
atop 01535 Set 7~30 --+ (PAl)
9-403
ANALYSI.
.tt
pREPARED BY Domt Parker
CHECKED II'Y _.. ~.
REVI• •D BY
CV-164
elf 007-10
RI:PORT NO• • 491
CONVAIR
PAGI:
A " - " Of' . . .mtAL DYIIA.u:8 COIIPOltAftOII
SAN DlIEGO
Swift
Vul.-tloh
2.
Start (lIS
3.
Start.
Ie
J&S:fe
10
Stopa MS
on).
atop 01535.
MODEL
DATE
All
6/20/56
at 01532.
low ready to continue problem or leave
oomputer toetart problem from this point at a.nother time.
D.
Continuation from 11'1' .tart.
#C. vr 1/2 .a
1.
Set JI.r
2.
,.
Load paper tape wI! Dump and Restor.-.
Jon,restore from I!
2
lIS Ie on. VJ :felott, r.atore from lIT I 0
4.
JID start at· 76370.
5.
Start.
in atep A-2.
*
Stopa at JIB
Stopa at
f
II) "
0, 01532.
2. 01535 with I :x 2° : (~) ... x 2° : (A)
ready to c . )n:tinue problem.
B.
Intermediate- atart trom MD.
1.
Ie
IE
on.
2. MD .ta~t at 40000. MS
Ie
stop 01535.1'0. ready to continue problem
from last eigennotor obtained.
P.
frouble.
trouble can ariae from one of two
ure or operator'. error.
no.)
ca••
1.
either computer tai1-
Trouble .howa up as a computer fault (seC. 1ICT.
or as a failure to cOl'l.....rge
ot trouble
Oa\1888.
al
shown on the typewriter output.
In
do the following.
Perform. .tap I.
If the laat eigenveot'Jr obtained cannot be con-
verged upon again, ___ perform the next ',tep.
2.
It II!
f
0 bas not been aet baok to ita or .:.,1t~;, back tape (1017)8
blOOD and do step D. elldtting 8ub.tep 1.
otherwis. just do atep D.
3. It .tep D fail. (ie.ft dump haa be. deetroyed). it may be possible
to atart from paper tape (etep A) end inatead of dumping the eigenyeatera and eigenvaluee on M!. re.'ore them.
P'ORIiII.,a·A
Do Itep A with M8 " 2
9-404
CV-164
CONVA
ANALYSIS
PREPAREDBY
CHECKED BY
~REVISED BY
8.1ld IIJ
R
PAGE
A • ."..0. 0' "lIlaAL DTIIA ..ca co.poRAno.
Donn Parker
~-". Charles Swift
Matt Vuletlch
REPORT NO.
BAN DIEGO
MODEL
DATE
'* 2 on a.nd with
(J-f1262 )
= 75
eN 007-11
Z)(
491
All
6/cn/;6
:;0210 76370 and (7&63) : 37 76463
7t4t1J,.
To re8tore just the eigenvectors and eigenvalues
Jtr
I
-#
0 or
2, perform step D with the following changes.
Arter substep .1e
Replace subetep
If JlT
ALARMS I
fro~ ~!T
f
Afvanoe).{T 11= 0 (1017)8 blocks.
4 with
~D start at
76374 with 2
2° in A-.
0 dump is gODlf, repeat the above steps u8ing fiT , 2.
Alarm print (se. II 002) at 01565 lndicatM I> i.
and at USC atop Ol~O,
to 1:'1 test.
~ x
J' •
(A) e
Start computer
Correot'l:!ind lJtart •. Computer jumps
Alal"!ll print any plaoe .1 •• indioates .ttempted di"!ision
by lero.
o.
Con.ergenoe control.
Bits of aoouraoy wl1l usually be negati .. tor a
number ot iterationa and when positive, they will flllCtuate, sometime.
quite violently.
The teohnique i8 to stop the iteration process after
as few iterationa as pos.ible w1th the most aceuracy.
pllshed using the IS
the ca...
#
This i8 accam-
1 stop and changing the desired accuracy to fit
8ee the sample typewriter output.
B! ts ot aoouracy required have been prestored in tle program (405&~ to
40576), six val ues
equale
801M
or T
per word in order !'rom right to lett.
When I
value, say If. and it is desired to go ba.ok to improve aome
previously obtained eigenvector ie.when E was equal to E' - S, than to
return to the oas. E : I', all eigenvectors from E' - .. to E' muat be
iterated upon to pre.eTYe orthogonalilation.
H.
Optional operationa.
1.
When starting from paper tape, MJ
#2
on eliminate8 atori~~ all onea
in the ei£eawector region as the initial iterates.
2.
..ORM ,e,a-A
IIJ
=I 3 on avoids .dumping the program on to. m. but does not
9 405
CV-164
CONVAIR
ANALY. . .
.-REPARED.Y
CHECKED BY
RP'SI:D BY
. . . . . . . . , ....... DY•••ICI COIPOU"••
JloDD. Parker
Charl•• Swift
...tt Vuletlch
.AN1)IUO
PAGIi
elf
IIEPORT NO.
1lI
MODE..
DATa
00'7-12
49i
All
6/2C/5.G
eliminate dumping the eiginvector8 and eigenvalues reGion on Y.T
and
3.
vr I
At lIS .,.
altering
2.
3
stop
00241
the mantissEl . , (J is ia Q and Cf'.n be chfl.nged by
(Q).
1. He.tenea, M.R. anrl laru8h,
w.
A Method of
Gr~dients
tor Calculation ot
Characteriati.e Roots and Vectors of' A Real Syr.rr.et:-ic Matri x, J.
NBS
2.
I 0
41, 5. (1951)
RP
Research
2227.
Stein, M.L. Gradient Methods in the Solution
or
SY8t.. of Linear EquationAl ~
J. Research ISS 48. 6, (1951) RP 2330.
,
9-406
CV-164
C ·0 N V A
ANALYSIS
PREPARE£:) BY
CHECKED BY
REVISED BY
DOnn Parker
.. Charles Swift
VattVuletich
APPDDIX AI
R
PAGE
A DIVISION 0' .INIRAL DJNAIlIc.t C:O...ORAnOM
eN 001-13
L!9l
All
REPORT NO. ZM
SAN DIEGO
MODEL
DATE
6/20/56
History and Operating Experience.
The eigenvector~igenvalue problem for large, real, e~~etrio matri.es with
many~zero
elements 1s necessary for computing the mode shapes and frequencies
of vibrations of mu1tispar wings.
The EV program for this purpose was first
coded in January, 1955 by Dr. llarvin fltein and Donn Parker, and
report, CI 001 of Repon Z II 491.
Wal
witten in February.
program hal been used to solve problema involTing
e.
1955.
preliminary
Thia tirat
37 x ;7. 35 x 35, 33 x 33,
5q x 59, 62 x 62, and 29 x 29 matrices. The program was recoded in December,
1955
by Donn Parker and is pre8ented.in thia report.
The matric•• we have had experience with have a zero eigenvalue and a large
n.gative eigenvalue which made it
.impo.8i~le
to use the conjugate
method to minimize and obtain the ".mallest eilenvalue fir.t.
~radi.nt
We are interested
in only the smallest ten eigenvalues (not including the zero and nerative valu•• )
and their associated eigenvectors, but in order to
80lve for all the larger values.
.r".. a
Investi~ation8
obte.i~
them we must first
are being carried on now to
better, more direct method.
Prov1t!on has been made to Ikip the storage of the initial iterates all of
whoae elements equal one.
If better approximations to the eigenvectors are
known, they may be placed in the eigenvector region at the same time as the
matrix input.
If the convergence i8 Tery slow tor a particular eir,envalue. increasing the
frequency of orthogonalilation otten help..
This maybe dC'ne b~{ Ina..1'lually
changing the orthogonalilation index or can be more easily done by lowering
T
.0
that the convergence 18 completed with very low accuracy. then "art
conTergenoe on the same eigenvector thu. starting with the iterate last obtained.
This otten -8hakes l008e- the itf'rate from a stagnating convergmce, and it 1s
FOR'" lela· ...
9-407
CV~164
CONVA
ANALYSt.
CH~9X"'1IY
Dorul Parker
,chari... Switb
REVISED BY
lfatt Vuletich
PREPARED IIY
• 1IMtM• . ,
.,.aM. n.ura CM,ou"oaR
SAN Dlaoo
"AClIE
REPORT NO.
MOO.L.
~TI:
CI 007-14
ZJI 491
All
6/2C/56
the relult of orthogona11zing twioe without any intermediate iterationa.
Another cause of slaw convergence i. laek ot accuracy of eigenvectors pr. .ioaly
obtained.
tor
AP~X
Convergence can be improved otten by improving the accuracy obtained
previou.l~~
B,
found eigenvectors.
Li.ted here are all reterences in the program to the matrix, eig~-
'Yl1111". e1 genTeOtora. and inner product. storage areal on the MD.
The Itorage
.'Iigamenta for thel. areal may be changed by alterlne these referenoea.
Matrix A
y.y
7t423, 7tia5, 7~71
Bigenvalues
41266
EigeD"f'ectore
-'"....
~
-I
0I
o
o
....
0t-
><
c..
...ottM
'e,a.,.
R.t. 40015. 40016
CV-164
CONVAIR
ANAL-YSIS
PREPARED BY
CHECK. . 8Y·
REVISED BY
Donn Parker
~ Charles Switt
Jlatt Vuleti ch
.AN DIEGO
MODEL
DATE
MD Storage
0
0
0
0
.
PAGE
REfIORT NO.
A DlVUIO. 0' ••• 1aM. DYllAlllca COltl'OUTlO.
EV
I
req.or"\
100
18
t~
~
IS
I~
°1
1°
\0
c
10
~
I"
j-:r-
I
6/20/56
Assignrvlents
to
Pro~ra('\
C1f 007-15
ZK 491
All
("I)
l:r
10
t:)
I~1--
I~:r
I
I
10
18
,~
I
o EI(~erivectors
o
I
o
:t-
In
I
._-,_...-_. . --.. . - - - _ I
-------.-........... --.--.;-------- ·---~·--·+-I--I
I
18
I
I
,
I
,~
I
I
:--.._. ·---·---------r------···--.'.-._.-...---'--.- ... -- .. -....
10
~
....0
......
-I
0"I
o
o
o
I~
I
,~
,-.;...---.-----.r-------
f
.
I
10
I
><
c...
tt-..l
I
o
:t-
"
'-0" .. ISla-A
E
S lrage.
I·
t
I
I
j
... -...-........... - .. ___._.__ ._. ___.[_. ___ .=.n_. __ . __._. __ ." ._.
8
I
,
I
I
I
\
----l!~ _____. . __ .___ ......
r
I
I
18
r-
I
J--- --'---
......
0"-
I
. . ·-···-1-···· .--.. - - - - · f
t!!
"CQ1d
0
~
~
....
....
~
,..
... -.----. -.. --.-.----..--...---.. -~..--.... -----.-----_4__L- --.. _.-.- -__-' __._
Ov~p4Jt
I
I'
~
,...~
_._._.-l __ ..... ~ .--.. -.-..--___.__.
ANALV. .
PR."ARIID.v
CHEcaD BY
REVIUD.v
....
CV-164
CI 007-16
ZJ( h.91
CONVAIR
........ Of''''''' O~CODO""'H
UN DlaoQ
Parker
Chari•• SWift
PAOli
REPORT NO.
All
MODEL
. t t Vuletioh
6/20/56
DATI:
ES_ StoYBge A~:s,l.~nme.,ts
,----
o
o
o
o
o
o
f Aylt,~melLc.o
!Itt
0'
I~
. . --. --t---·· __·_·- .- --- '-"-' t··-_··- --"-.-"--'-~
~--
~
. - - .. -
--t--
I
.
I
o
·,,--_·':",,···r---:..:.- ......-_._-;--- -----
I Pa.yt
I
1 - 0 _........- - _ . . _ - .
.>... - ....
. - - - - - __
..
I
--1
.-+-------+--.-"..-------+------.
.--.-.. . +-.. . . .-----.---t!
I
.
\'., ~, A?ejio"
I
to .777
I~
,=
+-- --- .-~ .
t
j-
I
..4----... ---- -- . j,' -......--
-.-..
I
--I
--
I
I
-+------
I
I
I:
I
t
--1
I
I
1£ O~1ho1·M.._ ~!ld.l-t.!.1'- i1••a~e
l
I:
I
t
-t ...... _.- . --.- - t .... - . - ...... -t . ·.... ·. ·. . ·_--t-...-.
I
cst.n·te.... I
0
;
n: . .
-t. _·--.. . .·-·. . -· .
I
I
,
Ig
I
t----·t--- ---.. -. - --,--~-"" --i--" " ·-·---f---··-·--·------l-.. -.. . . -- ......,-.-..---+----.-.-.. -I
._0-
'0t~
I
~-
I
I
I
Io~
I
I0
I
1
~
i
r------t--..---.---,-_. . .-. - . -_. . ·t-- ---'-"'--'--' --1-"'- -----+--.. . -.. ----j---.---t.------...
l ..
1-
I . ----~- -- -
t;
t
----t
I
:to
~
Pa.-vt m
-
I
t
-1- ------·---+-----.. -..-·-r--~·---·t- . ---· . ·-.--.. . - '
I
I
Pa;yt I
I
I
I
1
I
10
If
t
~
'
I
I
I
I
9-410
CONVAIR
ANALYSIS
PREPAR£D BY
CHECKED BY
REVISED BY
..
Donn Parker
Charles Swift
lfatt Vuletlch
L>
. . . . ·~· ...
f· . . . . . .
11:,
....
'.''''''0.''''0''
( ................
SAN DIEGO
CV-164
PAGE
REPORT NO.
MODEL
DATE
--------------------------------------------------------------------EV Stal'ter
eN 007-17·
Z!l }.t91
All
6/20/56
----
'*5' c.omrna..ncl
--....(t):J~
Check $Urtl
'tOO()O "1 <.,.;~o
4U05'
-
""'2.11
"1-,
'''1
S l~"Ylt.y --. E S ..
Pa.'Yt~ I J
~S
m.....
Toy e c.hc,k
$\lrrJ
0'0'"
Otol7
Bas\(. e V,
5 tOYe.
Pa.~t]I
--+'5
N" "r'
S_"tvp 13 .~i(, E V
a.nd Pa,yt 1I
Ba~it EV I
Pa:vlE
----P
01055'
MO
o-Y'thOl'S. R..... E ~
5 f.tvp O»ho~.
OY1.ho ' s.f(..... MO
O
S e.t vp P~:rll)ll
P(l.yts Lm ..... MO
011'+5
cr.a~~4l ('+0000)
c;.o" C:nttl'..,~d.
'5Ta,.y
Oll'tb
"'"'
-.::JI
--'".....
011*'
I
0"-
0
0
I
01'51
0"-
.....
t-
OlllPO
><
c..
011"1
9-411
ANALYSIS
PREPARED IIY
CHECKED 8Y
REVISED BY
CONVAIR
tJonn Parker
Gharllla Iw1 rt
att Tulet1ch
SAN DIEGO
CV-164
PAGE CI 007-18
REPORT NO. . . 491
MODEL All
DATE
6/20/56
EV
Payt I
Compvte d
OI"I;;.:3~
_ _......_ _--.
T,pe i.ttva.li.ott
numb_v.J d
O''''lra-_ _~_~~...,
Stt 'a'it i."t~T..t.tO"
'Sw~
YMO-r V.
Set t&5t &,.J••
:II:
0
t '1pt ~"dc)( - 0
OTtk • ~~~)C a 0
01'7)1
.-
.•.•-"
9-412
CONVAIR
ANALVSIS
~REPAR£D BV
CHECKED BV
REVISED BV
Donn Pa.rke~
'.. Charles Swirt:
Matt Vuletich
SAN DIEGO
CV-164
PAGE
REPORT NO.
MODEL
DATE
00101
001.10 ._ _ _--L_ _ _-,
X--+ VMD
R.yIL'J" q. s. R.
Ax'" Va. J )J(X}
!:: Ax-),J X...., V,
i ttT41i.on ~n".x + ,
001.t7
Yes
0011.3
Yes
R~set ot
lnde.x
R&1'it.1"
(t. ~·A.·)J(f)
Plc.k a.~
clUwtp",te
00150
002.',
~
13
=JI-',.....)-.p-Ot.-I
ex
Z. 491
007-19
All
6/20/56
ANALYSI.
..RS..ARI:D BY
CHECKED BY
REVISED BY .
CV-164
CONVAIR
lloml Parker
Charl•• Swift
Mitt Vule.loh
~AN
"AGE
REPORT NO.
MODEL
DATE
OliOO
EV Part
'
ON 007-20
Z1f 491
All
6/20/56
m
eV, Pa'Yts I,
U.I at. ---. £S
(3a5':t
MS #2.
Sto,o
stOY
-
0'53"
ze.
01'5,+2.
ot.570
Stl Test {ndex;: I
I tt.,~1lon
Type
()(.
3'
OY, h0
Ol5,*,1
:,
=0
=0
=0
Type C.A.,LR.JJT
X ---... v.
0 157'1
c....,el o"t~"t • '3"IV"'"~
Ournp £~ Y~q~on on MT
Ca.l"~ o",t,;(. E i9""~"1o..,~
E .... CQ.)
! .... CA}
sto
01"'1.
roall •••• -"
9-414
GV-164
CONVAIR
ANALYSIS
•
t-RE"ARtD BY
Donn Parker
CHECKED BY
Char 1e" Swi.f't
Matt Vuletloh
REVISED BY
D· ... • ... ·
t', ...
,;.
fo . . . . . . . . L
0 ....... ""'. (50
•
U ..... 0 ...... , , 0 "
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01
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II 007-26
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A.11
PAGE
DATE
6/20/56
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GV-164
SAN DIEGO CAL.IFQRNIA
PAGE
REPORT
MODEL
DATE
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9-421
CV-164
PAGE
CK 007-28
REPORT
ZM 491
All
MODEL
D,ATE
6/20/%
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CV-164
CONVAIR - DIVISION OF GENERAL DY-NAMICS CORP.
SAN (lIEG ..."'
CALIFORNIA
PAGE
-29
000505 41452
MODEL
DATE
6/20/56
29 Matrix 1 dehydrated-
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4 .5048596477- 4 .6178035335
4 .638564~884- 4 .1515033~41
3 .1144258462
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9-423
2
CONVAIR - DIVISION OF GENERAL DYNAMICS COR ...
5"N DIEGO C"LIFO .. NI"
CV-164
PAGE
REPORT
MODEL
DATE
-29
35
.4~91970185
36 .6536971121
37 .2273862205
29 Matrix A
7 .0000000000
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1 .52068300"'5 .0000000000 0
47 .0000000000 1 .1043693818 5 ,0000000000 1 .2399646300
48 ,1024655024- 0 .0000000000 · 3 .2676268826- 6 .1887073127
49 .0000000000 1 .1042037298
7 .2866537811- 6 .1427618785
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51 .0000000000 2 .5236259731- :3 .0000000000 3 .3481976210
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53 .1112163267- 6 .3354713188
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7 ,0000000000
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55 .0000000000
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58 .6856066033
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5 .0000000000 * .1576569586- 7 .165119410<;) 4
5 .1112163267- 6 ,1639B41Q41
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5 .1000440533- 7 .2~99376'310 4 .0000000000 0
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59 .0000000000
4 .1673271194
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65 .0000000000
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67 .6536977121
6 .1252089151- 5 .0000000000
68 ,7618149984
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1 ,4184782667- 5 .0000000000
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9-424
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
MODEL
CI 007-31
ZJI 471
All
DA TE
6/20/56
PAGE
REPORT
-29
X
29 latrix A dehydrated-
69 .1407101198- 5 .3153213201
5 .0000000000
2 .680Q209483- :3 .OOCOOOOOOO
2
3 .ltlS9600764- 5
70 .1930041152
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0 .3348422218- 1 .0000000000
11 .0000000000
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6 .0000000000
1 .1120507474
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72 .1000440533- 7 .2472433668
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0 .1712443284- 6 .9~21300572
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5 .1275801501- 6 .2162222531
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74 ,1762507593
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5 .5438769491
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75 .0000000000
2 .2399376310
4 ,1198305783- 7 .1117285796
5 .2251419421
5
76 .3597784223- 5 .1397444025
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4 .6237452968- 6
77 .4528849346
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80 .6301189950
5 .6496681001- 5 .7628170177
4 .3133104375- 6 .0000000000
1 .8380141004
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6 .6641036020- 5 .5339020821
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9-425
2
CV-164
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN DIEGO CALIFOANIA
PAGE
ex 007-32
REPORT
Zl{ L91
MODEL
All
DATE
6/20/;6
-29 x 29 .trix A - Largeat 'rl BigeDYalue.·
7 .4820651418
7 .3700033876
7 .3225412389
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6 .1811115067
6 .1406394162
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5 .2798447725
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429 .219358978:3 o .2018166822- 1-.5997832751 1-,1686872136- o ,6101353041- 1'05 .4541.021708- 1-.1863391329- 2-.1349249255- 1-.4557548178 2-,21677263~O- 1.'
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9-426
0
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIFOR"''''
CV-164
CW
PAGE
REPORT ZJ(
007-'3
491
MODEL
All
DATE
6/20/56
o .1619788842
0 .1447275071
0 .:3142234047
525 .2412226701- o .1401179015
0 .2.432285432
0 .4693848755- 0 .1371039500- 0
520 .2953384'03
0 ·.3534751444- 0
1-.2602498939- 0 .4556905858
0 .1924160211
0
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0
606 .1374329011- 1-.5344956371 1-.1107903066
611 .2908455711 1-,4470656228- 1-.8331004188
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0 .1116530260
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1-.3254714,aO- 1-
616 .1198812814- o .246324C048- o .2197142242
o .2178939709
0 .2041412899- 0
601 ,9872538702
o .2767826831
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0
621 .2853843273- o •.2024274199
626 .1931608232
702 .2561387440- o .3238764402
o .1390626251
o .1098771774
1-.1460346445- 1-
707 .158334e658
o .3131682609
1-.5754754076
o .1152095186
0 .8~411880("l7
1-
112 .8227234336
1-.7917191980- 1-,2729067231- 1-.1008935401
0 ,1765S52304
0
717 .1601919207
o ,1914955548- o .1272063791- o .2047718818
0 ',14<)5487239
0
722 .1918084555- o .1560439940- o .7616729855- 1-,1409317877- 0 ,4474957896
727 .9964869954
1-.1043866043- o .3308523595
o
.3120~70141-
1-.6010294681
803 .6141797102- 1-.5803298607- 1-.9705684006- 1-.8509412051- 2-.1116441731
808 .1425485252
1-.334580ae88.
o
813 .6837600983
1-.2418526175
1-.247220948C
.206105614~
o .3541688532
• 818
,2015108966- 1-,9353284944
1-
10
2-.8510108628
1-
1-.1103324698
0 ,3293018632
0
1-.1576327795
0 ,3847625000
0 ,2297059967
0
o
o
o
,2271121Cj82
.1507579325- 0 .2176791400- 0
828 .2055625735 0 .3616729594- 0 .4028024152,6369742101 0 .2:309429C04 1904 .1241868296- o .2200037762- 0 .1922119896- 2-.1862118391
0 .2q4975~q~2 1-
-
823 .1057026602
1-.3945798687
909 .4615453073
o
914 .2343719156
1-.2749795002- 1-.9006965406- 1-.1836035234- 0 .2Q1:3061208- 1-
919 .2578171128
1-.9245449~95-
.74~6527908-
'-.5319631179- 1-.1389994164- 0 .10270537551-.1601742298- o ,3353042183- 1-.2Q26734688
11-
~
...0
924 .8861986790- 1-.3590653941- 1-.3372141267
1-.4296493994
1-.3~31653875-
0'-
929 .4681'968794
1-.212732~6~4
8
1005 .1402282325
1·
3-.16167804SQ- 1-
.-4
I
1".1918261949- 1-.1331762857
I
1-.1127049421- 2-.8704605938- 2-.5376445899
1-.1?086512SQ
0'-
~ 1010 .1931098290- 3-.2492475922
1-
1-
2-.2137876390
1-.7163426069
1-.2721548472
~ 1015 .8279944112- 2-.5123606982- 2-,4697118496
1-.2279688404
0
.1262890~8a
0
1020 .1031313519- 1-.4919491178
1-.27896~4266
0 .2374814917
0 .1027065!596
0
1025 ,3272412981
o .3983715423
0 .2569282457
o .3027827199
o
.58125018'0
0
1101 .6548873728- o .1322672434
0 .4436966511
o ,24307(\1760
0 .277381418Q
0
1106 .4233536414- 3-.1411090518- 0 .21')84736623- 1-.3100173512- 0 .10<)0777226
(\
1111 .9652626801
1-.1440845923
0 .7640430626- 3-.2027671427- 1-.50972291~5
9-427
1-
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALIF!)""""
CV-164
CB 007-34
Z)( 491
411
PAGE
REPORT
MODEL
6/20/56
DATE
1116 .1041514800
0 .1455984896
1121 .1083388567
~
11-.26222S?131- 2-
0 .1542009111- 2-.2660670653- 1-.a5456630~4
.1924152284- 2-,3142390786- 1-.3320401456
1126 .3080861266- 1-.2706141637- 1-.2473936938- 2-.3564~q857a- 1-.3254114!SO- 1·
-29 z 29 .vix .l- 17 and A7 -
•
1 .2852466901
-tJ
tor 5 Lui; Big_lIftl._ and ·'Ilgenvectora Obtained-
4 .7167909440- 4 .906351413'3
2 .4086722617- 3 ,.4430918353
3 .2335918251
4 .4941644253
5 .4185 0 42341
6 .1252293543
q
-~~.
4 .2302347264
4 .8780640983
4 ,3891594201
4 .lQ86554i83
4
:3 .1610437891
5 ,3224018411
4
4 .2215584115- 4 ,763115 0 934-
,2823453282
4 ,4482887045
'+ ,5358902828- 4 .3559803496- 4 ,513043376S
4 .5367659211- 4 .4366808899- 4 .21'3150158~- 4 ,3Q4!9 0 t9!14 .2788617120 4 .2921205043· 4 .9258729738
4 ,0000000000
'4
0
.3-.58484 0 7745-
,-
~
4
4
2-.9536743164- 4-.2238154411
4-,4587173462
3-,1112222671
3-.259 0 417962
~.47242641,45
~-.104S76~492
3-.305056~719
0
3-,1618466797
...... 4 .11 9361648- 2-.' 149177551I
5 .:>1999 0 921°- 3-.14781951~O 3-,1 00 2353668
3-.5263 0 9 0 133
3·.2Q9930S125- 3:3-.4S4902~489
3·
1 ,25 4587113
2 ,1943171 0
-
24-
:3 .1322746277
2-,1255750656-
~-,1263141632
i
~
...0
.......
0I
0
0
2·.67e53~2761-
3·,4~O3726959
.
.
3-
3-
i
6 .3117322922- 4-.,354886 0 5 SO
3-,49°1885986- 3-,588417 0 532- 3- ~ OOO(H.,O{'cnO
1 .5440983961- :3 .1048014229
2 .14837e2086- 3 .1946738062
4 .1070945040- 4 .101192113~- 4 .1692379541- 4
(j
a......
r-
><
0..
4 ,2485619473
3 .5e~40B574'-
4
3 ,4~108144q7
!
!
3 .2748642092
4
4 •
3q6Q 15 1f893
4
.O('Or100()~On
0
3 .1630930404
~
,1483907992
4 .1192272509
4 .1923865984
4
4
.3593~62558
5 .6709101952
4
.5742036'509
.40053826t)7
.4217181Ci94
4 ,6175642175
4
• 1 8 If 3 1 '34 ? 2 2
3 ,6980287668
6 .2628765960- 4 .379567')600- 4
.35e431~749
4 ,630649(j416- 4
4
.~511752616-
9-428
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
1 ,4420876503
3-.655353~693-
2 .1810613952
3-.1014292240- 2-.1311376691
3 .1581385131- 3-.6322860718
3-.2121885818
3-.2524852752
PAGE
OJ
007-35
REPORT
ZJ(
491
MODEL
A.1l
DATE
6/20/56
-
4-.1532733440- 3-,2561768097
~.
3-.1082420349- 3-,1841581066- 33·.1296848058- 3-.2364650'6e
2-
,.
:;-.10567Q0352 3-.163316'12613-,2712234854- 3-.1966953217- 3-,2461611829 35 .4863739013- 3-.1 :37686729 /,.
0
6 .3905296325- 3-.1571178436- 3-.165224075'- 3-.2198219299. 3-,0000000000
4 .9267926216- 3-.1010894nS
2-.36025047~O-
1 ,3860370252- 4 .6104620982
4
.2213~O3524
3 ,11Q0178442- 4 .210e461695- .\
,7126259464- 1
3 .263536667'· 1
2 ,1842129259- 2 (1784613621 4 ,2826977963 3 ,4423348312
3 ,5577404519- 3 .1332140528- 4 ,9843081920- 2 .2246167689
4
4 ,8632015419- :3 .1759616660- 4 .2791814680- :3 .2470861891
:3 ,88606290"-
5 .1535074602- 4 .3213483627- 3 ,2804917842
~
,
.8-498887871- 3 .34·41209253- 3
.l1929a4~S8-
:3 ,4492850306
g ,0000000000
0
1 ,4743337631- 3-.3623962402- 3-.2453178161-
3·,92611~qa12
~-,1211166182
3-
3-.1343339681- 3-,4270076752- 3-,7453656290
~-
6 .3231788901
3 .4117666688
2 .1181596890- 3-.2995133400
3
3 .2039968967
3-.6852746010- 3-.2457424998-
4 .2179443836
3-.8629560470-
~-.8715689182- 4-,1202076673~
5 • .3635883~31- 5-.1727342605- 3-.3219745579-
6 .2860575914
3-.1317709684
3~.121593415~-
4-.4321~36146-
3-.7416307926· 4-.40954!5142
3-.2360116061- 23-,6519556045 33-.546~8751"o-
,....
3-.0000000000
0
,384721~~S5
2
'q"
...a
~
~
I
'"00
'"
2 .3092504680- 1 .2388179941- 2 ,1475005865
x:
3 .6838390588
I
-
l-
0...
1 ,5262494217- 2 .3670434084
2
.5836455391
2 .3316032743
2
1 .4435703933- 2 .5295424619- 0
1 ,5865302533
2 .1965289407
3
.7466571~80
2 .2211582~O5- 2
4 .1405645601- 2 .1288661291
3 ,625434:;042
~
.3464750232
~
5 .1349666774
.., .7653385296
~
3
.6515327.532
3 ,2817761727
,282Q406340- 2
:;
3 ,SQ7788S15'3
.1092935718
4 .7048841961
"3 ,8306868796
3 ,1594666481
4
6
,~OOOOOOO~O
9-429
0
CONVAIR - DIVISION Of GENERAL· DYNAMICS CORP.
SAN DIEGO CALlFO"NIA
CV-164
PAGE
CI
007-36
REPORT
ZJ(
491
MODEL
All
DATE
1 .27'3180299
2-.2706145~67
2·.125~914088
2.... 7146596908
6/20/56
3 .. ,3QI081q12~
3-
2 ,4352668766- 3-.6409106548- 3-.2651748946- 4-.5328077823- 3-,2559524146 33 • 2622641623 3-.2096276730 3-,2464428544- 3-,1937970519- 3-.2101590524 ! ....
4 .2021472901
3-.294402'2417 3-,96 l t-7011757- 4-.27~8e33427 4-.1083612442 !5 .2973526716 4-.5951523781 4-.1850426197- 3-.1238435501- 3-.2QS0429916-
,-
6 .9459257126
4-.272095.2034
4-.1901388168- 4-.146:3eQOO75
1 ,1127496843- 4 ,2277200880 3 .763897107<1 3 .4184852155
2 ,7289659832- 0 .2429425149- 3 ,3589217010- 2 .53374606123 .1315410038- 1 .~490~802323 .1661858749 :3 .2480653283
4 ,1793139050
3 .2506719238 3 ,2654883854· 1 ,45807821395 .1865230494- 3 .3312833250.- 1 ,5410145628. 2 .5716629106
6 ,5304217386- 2 .4660101890- 2 ,4259395062- 1
.61~6540591·
3-.0000000000
0
'3 .4775577502
,
'3 .lA71Q51176
2 ,8775775775
2
.1471273158
~
2
)
2 .4514717266- 1
2 .OO(}OOOOCOn
'0
4".2190023660- 3-.1531'9?''3~6 ... )...
4-.1236610114 4-.1299381256- 4-,1a8581645'- !2 ,9280181257- 4-.1234561205
3 .'013719851- 4-.8308142423- 4-.1623353455 4-.1191534102 4-,5436092615
441J1t.38061290Qe- 3...
4 .6134063005- 4",8834898472 4-.6061152089· 4-.1616589725
5 .177122652?- 3-,8745200466- 4.. ,1138821244- 4-.9864196181 4-.2568820491- 4·
6', ,6124749779- 4-,6714835763
5-.1042240765- 3-.12188771~3" 3-.0000000000 0
1 ,1210570335- 3-.1935139298
3-.7665157318
,..
9-430
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN Dti.G\."'
\"~A.lIF(l~NtA
PAGE
REPORT
MODEL
DATE
eN 007-37
ZM 491
All
6/20/56
Code
TO STARTER
40000
OOOC~
45 00000 41076
40001
00001
00
40002
00002
00 00000 00000
4oon'!
OOGf),
00 00tirO
('IOO~O
E
40004
00004
00 OOO()O 00000
E
400C5
00005
00 00000 00000
N
40006
00006
00 00000 00000
2NX2'S
40007
00007
00 00007 77777
.0010
COO10
00 00000 00000
LAST ITERATION SWITCH
INDEX
40011
00011
40012
00012
00 00000 00000
00 OQOOO 00000
40013
00013
0('1 00000 00000
40014
00014
40015
00015-
00 00000 00000
00 41452 00000
40016
00016
00 41452
41452
L
40017
40020
40021
00011
00 f)OOOO
conoo
0{
00020
00021
00 00000 00000
00 00420 00420
ooooe ooooe
JUr.1P
2N
N-l
AX
RQ
TEMPORARY
CELLS
L (MATR J x.· AMO)
(AM 0)
L (V,)
(v))
X2's
+
X2'5
L
(AMD)
1
,..
+
L (V, )
X 2 15'
+
L (v.)
X2
40022
00022
~o
40023
00023
00 00420 00420
L. (A ) X 2'5" ... L (A )
40024
00024
00 00000 00000
40025
0OO2!5
00 00000 00000
TYPING INDEX
OP 1
40026
00026
00 00(100 ('Ionco
40027
00027
00 00000 00000
400'0
00030
00 00000 00000
...0
40031
00031
00 00000 00000
RES
---0"-
40032
00032
40033
00033
40034
00034
INNER
PRODUCT
40035
0003'
00 00000 00000
00 00000 00.,00
00 00000 00000
ob 00000 00000
40036
00036
00 OrlQno ()OOOO
40037
~OO31·
00 00002 00000
~
1"""1
I
I
0
0
0"-
1"""1
r-
><
c..
00420 00420
L
OP
2
S OF Vl.
+ SV,
9-431
CONVAIR - DIVISION OF GENERAL
DY~AMICS
CORP.
CV-164
PAGE
REPORT
MO[,EL
DATE
-....
~
...0
-I
0'
I
0
0
0'
40040
00040
00 00000' 00000
40041
00041
40042
00042
40043
00043
40044
00044
00
00
00
00
40045
00045
00 00000
40046
00046
40041
00047
00 00000 00000
00 00000 00000
40050
00050
40051
40052
00051
00052
4005.3
00053
40054
00054
31 76000 76002
45 0(") 000 30000
i;·5 00000 00016
45 00000 00142
11 00027 20000
40055
00055
47 00056 00050
40056
00056
40057
00051
11 00025 20000
47 000&3 00060
40060
00060
11 00040 00031
40061
00061
40062
00062
11 00040 00032
45 00000 00051
40063
40064
0006'
00064
54 20000 00042
73 00027 10000
40065
00065
40066
00066
40067
40070
00067
00070
11
74
11
23
40071
00071
11 00025 20000
40072
00072
47 00074 00073
40073
00073
00074
21 00026 00042
45 00000 n0051
40076
.0007'
00076
40071
00077
..... 40074
t-
><
~
40075
CI 007-38
ZJ4 491
All
6/20/56
ZERO
00000 00002
00000 00()Ol
00000 00000
OOCOo 00000
oonoo
TEST INDEX
INDEX
INDEX
ITERATION COUNT
ARITHMETIC PACKAGE CA 001
00040 00025
10000 00025
20000 00031
00026 00030
11 00026 00032
11 00025 20'000
47 00100 00120
9-432
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
REPORT
CI 007-39
ZK 491
MODEL
All
DATE
6/20/56
PAGE
"qI
-.0
40100
00100
11 00027 20000
4CIOl
C~lOl
47 00105 00102
40102
00102
11 00025 00031
40103
00103
11 00026 00032
40104
00104
45 0000'. nOOS1
40105
00105
11 00026 20000
40106
00106
36 00030 00032
40107
00107
46 00116 00110
40110
00110
11 00025 20000
40111
00111
11 00021 00025
40112
00112
11 20000 00021
40113
00113
11 00026 20000
40114
11 00030 00026
40115
0011400115
40116
00116
12 00032 20000
40117
42 00141 0012'
40120
00117
00120
40121
00121
11 00030 00032
40122
00122
45 00000 00051
40123
00123
40124
00124
16 20000 Ii0124
54 0'0027 00000
40125
00125
35 00025 20000
40126
00126
11 00040 00032
40127
00127
74 20000 00032
40130
00130
40131
00131
11 20000 10031
47 00133 00132
40132
00132
13 00032 00026
40133
00133
11 00032 20000
40134
00134
42 00140 00136
40135
00135
23 00026 00207 (00.2.6) - " 0
40136
00136
21 00032 00026
40131
00137
45 00000 00051
11 20000 00030
11 00027 00031
r-f
'-'
I
<:J'I
0
0
0"-
r-f
t-
:><
c...
9-433
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
PAGE
eN
007-l~o
REPORT
Z)(
h91
MODEL
DATE
401~O
00140
00 00000 00046
40141
00141
40142
40143
00142
00143
00 00000 00043
71 00025 00027
11 00040 00025
40144
00144
74 20000 00025
·40145
40146
00145
00146
11 20000 (lon31
47 00151 00147
40147
00147
40150
00150
11 00040 00032
45 00000 00051
40151
00151
23 00025 00141
40152
00152
21 00026 00030
40153
00153
35 00025 00032
40154
00154
45 00000 00051
40155
00155
15 00022 00165
40156
00156
15 00021 00163
40157
00157
11 00002 00010
INNER PRODUCT SET
SET L (VI)
SET INDEX
N-l
40160
00160
23 00033 20000
STORE
40161
OQ161
23 00034 20000
0
40162
75 30002 00164
V,
40163
f00162
00163
11 30000 00025
~
40164
00164
7'
VJ.
40165
00165
11 30000 00027
~
40166
00166
37 00051 00053
MULTIPLY
40167
00167
75 30004 00171
RES
40170
40171
00170
11 00031 00025
INNER PRODUCT --7 OP 2
00171
37 00051 00052
ADD
0"-
40172
00172
11 00031 00033
0
0
40173
00173
11 00032 00034
r- 40174
00174
>< 40175
c..
00175
21 00163 00037
21 00165 00037
40176
00176
41 00010 0OI~
40177
00177
45 00000 30000
STORE
INNER PRODUCT
SET FOR
NEXT ELEMENT
INNER PRODUCT COMPLET[
EXIT
~
-.()
..-f
30002 00166
All
'6/20/50
L (v2 )
=
OP 1
OP 2
-10P 1
'-'
I
I
0"f"'"!
9-434
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S"N DIEGO
CALlFOFlNI"
01
ZV 491
MODEL
All
DATE
~
...0
-~
I
0'
I
0
0
0'
~
r-
><
c..
007--41
PAGE
REPORT
40200
00200
00 00000 00000
40201
100201
41 00200 00210
ORTHOGONALIZATION INDEX
EV PART II. ORTHOGONALIZE?
40202
00202
56 30000 00203
YES:
40203
00203
11.00004 20000
E
40204
00204
47 00205 00210
E
40205
00205
75 30210 00211
NO:
40206
00206
11 40740 00210
40207
00207
00 00000 00110
JUMP TO ORTHOGONALIZE
ARITHMETIC CONSTANT
40210
00210
75 30000 00212
X
40211
00211
40212
00212
11 30000 30000
37 00324 00306
40213
00213
13"00033 00035
40214
00214
11 00034 00036
40215
00215
31 00305 00260
40216
00216
21 00047 00042
S.R.
AX-;JX
ITERATION COUNT. 1
40211
00217
41 00044 00222
READY TO TEST?
40220
00220
75 30160 01640
YES:
40221
00221
11 40560 01620
40222
00222
56 30000 00223
JUMP TO TEST
NO: DUMMY
40223
00223
41 00045 00250
NEW
40224
00224
11 00247 0004S
40225
00229
37 Ob324 00306
YES: RESET ~ INDEX
R. Q.
S.R.
40226
00226
75 30004 00230
p(f) --7
40227
00221
11 00033 00025
.,.u(X) ~ OP 2
40230
002:30
37 00051 00052
ADD
40231
002~1
. 11 00031 00027
40232
00232
11 00032 00030
40233
00233
11 30000 10000
M (tJ,)
---1
40234
00234
21 00233 00257
SET FOR
Pl.
40235
00235
41 00046 00240
USED ALL {J)5?
40236
002~6
15 00304 00233
YES: RESET TO.p.
40231
00237
11 00041 00046
RESET
6/20/56
DUMMY
~(A)
-
O?
S.R.~ES
ORTHOG
---+
R.Q.
STORE
VMD
S.R.
-p(X) =5
Vl.
+
SV,
PART I
~
= S ~ V,
ES
o(?
,v(S» ,. p(
OP 1
X)
--; OP 2
{3
(Q)
INDEX
9-435
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
SIIoN DIEGO CIIoLIFO,.NIIIo
6/20/56
f1.
NO : MS ",3 STOP TO CHANGE
40241
00241
{J
40242
00242
11 10000 .00025
.23 00026 20000
40243
002~3
31 00051 00054
DIVIDE
40244
00244
11 00031 00017
STORE
40245
00245
11 00032 00020
40~46
00246
56 30000 00250
40247
OO~l
00 00000 nOO01
40250
00250
15 30000 00252
40251
00251
11 00000 00000
40252
40253
00252
00253
12 00017 00035
11 C)() 020 00036
40254
00254
37 0030S 00260
Vl.
~25'
00255
. , 00000 00256
DUM~Y
40256
·00256
RETURN TO ORTHOG TEST
40257
00257
"
30000 002.£!j
00 00001 00000
40260
00260
11 00002 00010
40261
00261
IS
40262
00262
00261
15 00022 00274
S.R. SET INDEX
V.a. + SV,
STORE L ( VI )
STORE L ( V~)
00021 00265
16 00021 00277
---+
~ tNDEX
X
---. Vl.
loci
---+ S
+.
00265
40266
00266
11 00035. 00027
40267
00261
11 00036 00030
40270
00210
37 00051 00053
MULT.
40211
00211
11 00031 00025
SV
+~
f=
X, ---7 V,
=
N-l
S
11 00032 00026
0I
40213
00273
80-
40274
00274
7'
11 30000 00021
t-
40215
00275
37 00051 00052
ADD
40276. 00276
40277 . 00277
75 30002 00300
V:al
~oooo
X
-40P 1
OO?72
11·00031
SV. ~ V,
STORE L ( VI)
V,.
40265
30002 00275
~(r)-p()(B
DUMMY
75 30002 00266
11 30000 00025
I
OP 1
~=,G
40272
0..
111
DATE
56 30000 00241
-->":
MODEL
00240
40264 100264
.....
ON 007.)4
ZM 491
40240
40263
1
.....
REPORT
PAGE
n
Vol.
~OP
2
~OP
1
--+
+
OP 2
SVu
---+ VII
9-436
CV-164
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN OIEGO C"'LI"'O~NI'"
PAGE
REPORT
MODEL
DATE
00300
40301
00301
21 00265 00037
21 00214 00037
40302
00302
21 00277 00041
FOR L
SET FOR L
40303
00303
41 00010 002~
DONE?
40304
00304
45 00410 00305
DUMMY t
40'05
00305
56 30000 30000
EXIT
40306
00306
37 00326 00330
R.a. S.R. AX ~ V1
40307
00107
40310
00310
SET FOR XX
INNER PRODUCT S.R.
40311
ori3l1
15 00021 00165
37 00177 00156
11 00033 00013
40312
00312
11 00034 00014
40313
00313
37 00171 00155
40314
00314
11 00033 00025
XX
INNER PRODUCT
XAX
40315
00315
11 00034 00026
40316
00316
11 00013 00027
40'11
00317
11 OOOl;
40320
00320
31 00051 00054
DIVIDE
40!21
00321
11 00031 0003:3
STORE
40322
00322
11 00032 00034
40323
00323
45 00000 00324-
DUMMY
40324
00324
EXIT
40325
00325
56 30000 30000
00 00000 00000
40326
00326
40327
00327
45 00000 30000
45 00000 00407
AX S.R. EXIT
JUMP TO SETUP
40~30
00330
~
4 03~'.
OO~31
15 00015 ':)0364
16 00022 00401
SET L ( AMD )
SET L (AX)
--
40332
00332
15 00405 00350
SET
40333
00333
11 00002 00010
SET
40334
00334
11 00040 00012
40335
00335
40336
00336
11 00040 00014
40337
00337
21 00012 00002
-.0
1"'"'4
I
0"I
0
0
0"-
1"'"'4
t-
><
c..
f1i
SET
L
( Vl. l )
( V. l
(M(P»)
)
X2,5
STORE
~OP
1
XX
oooso
00040 00013
6/20/56
S!T FOR L ( V,1 )
40300
.
CI 007-43
ZII 491
All
--) OP 2
j/(X)
= XAX/XX
TEMP 0( INDEX
L ( A)
INDEX=N·l
INITIAL
ZERO
SETS
SET INDEX = N-l
9-437
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP,
S .. N DIEGO
CV -164
CALIFORNIA
ZII 491
All
40340
00340
43 00002 00342
40341
00341
45 00('\00 00343
WAS INDEX ORIGINAllY ZERO?
NO; JUMP
40342
00342
15 00021 00346
YES: SET L(X,)
40343
(00343
11 00405 20000
40344-
00344
43 00350 00361
CONST ~(A)
WORKING STORAGE EXHAUSTED?
40345
00345
75 30002 00347
NO :
40346
00346
11 '30000 00025
40347
00347
75 30002 00351
403~O
00:350
40351
00:351
11 30000 00021
11 00027 20000
40352
00352
47 00365 00:353
f.1 (Au) =0;>
40353
00353
31 00030 00020
YES: 2 (FLAG) X
40354
00354
35 00346 00346
SKIP Xi·S
40355
00355
23 00012 00030
CORRECT INO!X
40~56
00356
INDEX
40357
00357
46 00357 0037!5
23 00346 00006
40'60
00360
45 00000 00375
40361
40362
00'61
00362
15 00023 00350
21 0036~ 00406
40363
75 30000 00345
40364
00'63
00364
40365
00365
37 00051 00053
40366
00366
11 00031 00025
40367
00367
11 00032 rlOO26
40370
40371
00310
00371
11 00013 00027
40312
00372
37 00051 00052
ADD
--~ 40374
00313
11 00031 00013
STORE
00374
SUM
~
40375
..-I
00375
11 00032 00014
21 00346 00037
:
40376
00376
21 00350 00037
:w 40377
00377
41 00012 003~
~
..-I
I
4037'
007
MODEL
DATE
..0
CI
PAGE
REPORT
1.1.
""'"
6/20/56
x.
~
OP 1
A"
---7 OP 2
<
0
?
2'"
-ZN)
.S"
YES: (L (Xi)
l( 2
JUMP TO NEXT ROW
YES WORKING SPACE EXHAUSTED~SET L (A)
SeT FOR NEXT BLOCK TRANSFER
BLOCK OF MATRIX
---;
11 30000 30000
ES
MULT.
Au X,
~
OP 1
(AX),
---1 OP 2
11 00014 00030
SET
FOR NEXT ELEMENT
INNER PROOUCT DONE?
9-438
CV -164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S"N DIEGO C"LII'"O,.NI"
MODEL
CI 007-45
Z)( 491
411
DATE
6~O/56
PAGE
REPORT
00400
75 30002 00402
40401
00401
11 00013 30000
40402
00402
40403
00403
21 00401 00041
41 00010 003llJ
40404
00404
45 00000
40405
00405
11 02000 00027
SET FOR (AX)l
AX COMPLETED?
YES: JUMP TO EXIT
CONST.
40406
00406
00 00000 00000
KX2'"
40407
00407
11 00040 00406
o --7 TEST INDEX
40410
00410
15 00023 00406
STO'RE
40411
00411
11 00420 20000
40412
00412
36 00406 00406
4041·~
0041~
11
40414-
00414
53 00406 00363
SET REPEAT
40415
00415
L
40416
00416
23 00015 00406
16 00023 00364
40417
00411
45 00000 00326
40420
00420
40421
00421
00 02000 00000
00 07177 00000
40422
0042~
00 00000 00000
40423"
00423
00 000-00 00000
40424
00424
00 00000 00000
40425
00425
00 00000 00000
t)() 421
003?~J
10000
40426
54 01637 10000
40427
53 20000 40564
...0
40430
16 40434 40421
I
40431
40432
11 40435 40426
45 00000 01116
'+0433
00 00000 00077
40434
><
0..
00 00000 40564
40435
54 01637 10000
40436
00
.-..
~
......
--
'"
'"......
rI
0
0
YES:
40400
oeooo
STORE
(AX),
=
NUt4BER OF ES
W.S.
K
MASK ~ (Q)
(AMD)X
2''$
-KX2's
SET L (A )
JUMP TO EXIT
CONST.
CONST.
VI
PART I PATCH TX2G.R ~(A)
STonE NEW T
RESTORE
•
(Q)
RESTORE
RETURN TO TEST
MASK
00000
9-439
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN DltGO
CV-164
CALIFORNIA
PAGE
Olf 007-46
REPORT ZM
MODEL
DATE
40437
00 00000 00000
40440
75 30274 01561
40441
40442
11 40444 01504
75 30114 01504
40443
11 40444 01504
t-+ ES. JUMP
TO INTERMEDIATE START
PART I 11-+ ES. JUMP TO
PART I I I
PART
01504
11 00033 10000
M (p) ~(Q)
40445
01505
37 01743 01734
TYPE M (J.I)
40446
01506
55 00034 10033
40447
01507
37 01743 01734
40450
01510
56 30000 01511
40451
01511
55 00004 10001
40452
01512
21 01515 10000
404S3
01513
21 01527 10000
40454
01514-
75 30002 01516
40455
01515
11 00033 30000
40456
01516
71 00001 00004
40457
01517
35 01523 01523
40460
01520
75 30000 01522
40461
01521
11 30000 30000
40462
01522
75 30000 01524
40463
01523
11 30000 30000
40464
01524
15 00021 00165
40465
01'25
37 00177 00156
40466
01526
STORE
40467
01527
75 30002 015:30
11 00033 41052
40470
01530
21 00004 00042
E
40471
01531
13 00007 00007
RESET LAST ITERATION SWITCH
40472
01532
E
4047~
01533
11 OOOOlt 10000
11 ()OOO3 20000
..... 40474
r40475
><
c..
01534
56 20000 01535
MS 112 STOP
01335
11 20000 00003
E ~(OO3)
~
-.0
.....
-I
0I
8
0-
6/20/56
II
40444
-
491
All
TYPE EXP (,v)
DUMMY
2E
~
(Q)
SET FOR E VALUE
SET FOR INNER PRODUCT
STORE
E VALUE
2NE --. (A)
SET
y
EV REGION
---? Vi
Y
--. EV REGION
SET FOR INNER PRODUCT
INNER PRODUCT
YV FOR ORTHOG
+
1
~(Q)
E ~ (A)
TO CHANGE E
9-440
CV-164
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN DIEGO CALIFORNIA
REPORT
eN 007-47
ZM 491
MODEL
All
DATE
6/20/56
PAGE
E ~(OO4)
40416
01536
11 lOOOO 00004
40417
01537
42 00004 01565
E
40500
01540
43 00004 01570
40501
O15Al
56 30000 01542
NOE E : ALARM
40526
01566
11 00003 20000
E
40527
01567
56 00000 01540
-. 40530
01510
23 10000 20000
RETURN TO Tf:ST E= E
YES E =- E OUTPUT STOP TO
;:e
40531
01571
56 00000 01572
SET M
0-
40532
01572
11 10000 00010
STORE M
8
40533
01573
16 00003 01575
SET L .. ( E VALUES)
40534
01574
31 76600 76601
OUTPUT
~ 40535
01575
00 30000 30000
~
'-'
I
I
0-
-c
"-
100~3
O15~2
> f?
=E?
E
TEST INOEX =1
ITERATION INDEX
==
=0
INDEX
INDEX
~
0
1
=0
!X2 l3 ~(Q)
2'" ~ (A )
FOR XI
---+
V,
JUMP TO TYPE T
---+
f!
(A)
VALUES
9-441
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV -164
PAGE
REPORT
MODEL
DATE
40536
01576
40537
01577
40540
01600
13 00010 10000
21 10000 00003
71 10000 00006
40541
0160}
3S 01610 01610
40542
01602
55 oeOlO 1 O'J 17
40543
01603
15 10000 01611
40544
01604
11 00000 76463
40545
01605
31 76463 16430
40546
01606
11 01612 76463
40547
C1607
37 16600 76603
40550
01610
00 30000 00000
40551
01611
00 30000 30000
40552
01612
56 00000 01532
'+ 0553
01613
37 01116 01706
40554
01614
55 01637 10033
40555
01615
37 01743 01134
40556
01616
45 1)0000 01557
40557
01617
00 00000 00000
40560
01620
40561
01621
00 00000 00"00
00 00000 00001
40562
01622
00 00000 00000
40563
01623
00 00000 00006
40564-
01624
31 37313 74042
40565
01625
35 35353 63636
40566
01626
35 35353 53535
40567
01627
34 34343 43434
40570
01630
33
33~33
33~3:3
4 as?1
01631
32 32323
2~232
40572
01632
31 31313 13131
..... 40573
40574
><
0..
40575
01633
30 30303 03030
01634
'-5
01635
20 20202 02020
"""
.....
...0
'-'
I
0"I
8
0"
r-
eN 007~
Zll 491
All
~/2'J/56
E - M ~ Ca)
(E-M) 2NX2 1S ~(A)
SET LeIST VECTOR FOR OUTPUT)
MX21~
STORE M IN OUTPUT PARAMETER
SET MT s.R.
MT DUMP EV~
RESTORE MT SIR.
OUTPUT
E VECTORS
STOP. READY TO JUMP TO MS 112
LOCATE T (IN PART r)
TX2 33 ---'(Q)
TYPE T
RETURN
PART I
TYPING INDEX
T
STORAGE
-2'>2'32 52';?'5
9-442
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
MODEL
All
DATE
6/20/56
40576
01636
14 14141 4141'+
40577
01637
40600
01640
00 00000 OOCOO
11 01774 00044
T
RESET TEST INDEX.
40601
JOi641
11 30000 20000
~(!.) ~ CA)
40602
01642
41 01643 01650
3.=O?
40603
01643
23 -30000 30000
NO: EXP (AX),- EXP(!)-+(EXP V1)
40604
01644
21 01641
SET FOR M (!l.)
40605
01645
40606
01646
21 01643 01775
41 01176 016411
SET FOR EXP(AX\-EXP(!1)
ALL EXPONENTS STORED
40607
01647
56 30000 01655
SKtP
40610
01650
55 01643 10025
YES j,=O :
40611
01651
()1652
16 10000 01652
11 01765 30000
01653
45 00000 01644
01654
00 00000 00000
21 01661 00037
40612
40613
40614
OOO~7
eN 007-1:9
h91
PAGE
REPORTZM
SA ... DIEGO CALI~O""'IA
t=O
8_
V,.
AX
-
TEST
SET
L (tXP V~)
64.
~ (EXP V~)
RETURN TO STORE EXPONENTS
FIND SMALLEST EXPONENT
SET FOR e:XP (V2 1.)
40615 fOi655
4·0616 01656
41 01777 01660
40617
01657
45 00000 01664
TESTtD ALL NUMBERS?
YES: JUMP
40620
01660
11 30000 20000
NO: EXP (V).,) --;(A)
40621
01661
42 30000 01655
40622
01662
15 01661 01660
EXP (Vl ,) <
c..
40634
01674
55 00012 10033
D X2 3) ~(Q)
40635
01675
37 01743 01134
TYPE WITH SPACE
...0
'-"
C1'
C1'
V2
< V~l.
0
DUMMY
READY TO TYPE?
YES~RESET
TY~ING
INDEX
C.R.
9-443
CV-164
CONVAIR - DIVISION OF GENERAC DYNAM'CS CORP.
5"'" 0'[(;0 CALlFO"""A
MODEL
CW 007-50
ZM 491
All
DATE
6/20/56
PAGE
REPORT
(EXIT)
40636
01676
S6 30000 01677
DUMMY)
40§37
01677
11 00001 ~OOOO
40640
01700
46 40442 01701
lAST ITERATION $vJt TCH --?(A)
l.AST ITERATION?JUMP TO PART Itl
40641
40642
01701
01102
40643
01703
23 10()OO 10000
11 00012 20000
56 10000 01104
40644
01704
11 10000 20000
40645
01705
47 01744 01706
T CHANGED?
40646
01706
11 00004 20000
NO
40641
01107
73 01623 00011
STORt E-R/6)
40650
71 20000
35 01714 01714
SET SHfFr
40652
01710
01711
01712
55 00011 00017
E-R/6X2's --+(Q)
40653
01713
21 01714 10000
SET ADORESS OF T
40654
01714
55 01624 10044
ff:X2°~{Q)
40655
01715
STORE T
40656
01716
51 01772 01637
56 30000 01717
DUMMY
40657
01717
11 00012 20000
o ~(A)
4P660
01720
42 01637 00222
0
40661
01721
11 01621 20000
40662
01722
43 00024 01724
40663
01723
37 01676 01671
NO : Jur-4p TO TYPE
40664
01724
13 00007 00007
YES:SET l.AST ITERATION SWITCH
40665
01725
15 30000 01727
X
40666
01726
11 30000 30000
40667
01727
23 00046 20000
TEST INDEX
40670
017~O
23 00024 20000
TYPE INDEX= 0
40671
01731
23 00044 20000
::I 40672
01732
56 30000 00201
ORTHOG rNDEX~O
RETURN TO ITERATE
~
40673
01733
77 71777 77771
-6
0
0-
40674
01734
61 00000 01771
4067'
01735
11 00041 00010
SPACE
SET INDEX
40651
"'""-
:g
tt
><
o
NO~
--7(Q)
0 ~(A)
STOP TO CHANGE T I,"
017~3
Q
E --+(A)
~
~ --7{A)
-6R ---+{A)
<
T?
NO:TYPING
RETURN TO tTtRATE
INDEX~{A)
(A)::. TEMP INDEX?
~VI
=0
Q.,
9-444
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
REPORT
C5 007-51
Z1I 491
MODEL
All
PAGE
5"N DIEGO C"'.. 'FORN'"
DATE
40676
r<'i 736
55 10000 00003
40677
01737
51 01773 20000
40700
01740
35 01760 01741
40101
01741
30 00('100 00(')00
40702
01742
40703
01743
4·1 00010 O11~
45 00000 30(!OO
40704
01744
11 10000 01637
40705
01745
55 10000 00033
40106
01746
37 01743 01734
40107
01747
11 00004 20000
E
40710
01750
73 01623 00013
STORE E·R/6.
40711
01751
71 200-00 01623
40712
01752
35 Q1755 0175$
40713
01753
16 01755 40426
SET SHIFT
SET
40714
01754
21 40427 00013
L
40715
01755
55 40433 20000
40716
01756 - 45 00000 40426
40717
01757
00 00000 00045
40720
01760
61 00000 01761
40721
01161
0
40722
01762
00 00000 00037
00 00000 00052
40723
01763
00 00000 00074
2
40724
01764
00 OCOOO 00070
3
40725
01765
00 00000 00064
4
40726
01166
00 00000 00062
5
40727
01767
00 00000 00066
6
~ 407~O
01770
00 0000a 00072
1
'"
80"-
40731
01711
00 00000 00004
40732
01772
t-
40733
01173
00 00000 00077
00 ooooe 00007
40734
01774
00 OO()00 00001
40735
01775
00 00002
;
...0
I
I
r-!
><
Q..
6/29/56
TYPE
EXIT
YES T CHANGED: STORE NEW T
TYPE
T=ACCURACY
~ (A)
R ~A
6R
( T)
71X2~R --1 Q
C.R.
TYPE 0
1
SPACE'
TEST INDEX
"""'''''02
9-445
CONV AIR - DIVISION Of GENEflAl DYNAMICS CORP.
CV-164
CI 007-52
REPORT ZU 491
PAGE
40736
01776
00 00000 00000
40737
01777
00 00000 00000
N-l
N-l
40740
00210
CO 00000 r;ocoo
ORTHOGONAL I ZI\ T lOr!
40741
00211
11 00317 20000
40742
00212
42 00004 00310
E )
4('743
00213
11 00305 00200
NO :
40744
00214
40745
00215
11 00004 00312
23 00312 00042
STORE E
STORE E-1
40746
00216
75 20000 00220
0
40747
00217
23
75
11
11
15
15
40750 (00220
40151
00221
40752
00222
40753
00223
40754
00224-
"'I::r
>0
.......
0J
1
L EIGf!NVECTORS
~O()OO
MD
-7 ES
00306 ct>313
S!T INDEX::. L-l
00023 00244
STORE L
00023 00165
( y)
[00225
40756 00226
56 30001 00226
40757
00227
11 00033 00025
40760
00230
{I 00034 00026
40761
00231
75 :30002 00233
yl
40762
00232
11 00322 00027
40763
00233
37 00051 00054
2
OIV. Xy'/V'yl::='K
40764
00234
11 00031 00S10
STORE
40765
00235
40766
00236
11 00032 00311
15 00022 00251
40767
00237
16 00022 00254
40770
j0240
11 00002 00314
13 00310· 00025
'-"
I
END OF ES
RESET ORTHOG INDEX
~v
30000 00222
40771 f00241
8~40772
37 00177 00156
00242
11 00311 00026
;:,40773
C'0243
75 30002 00245
:::< 40774
.....
()O244
11 30000 CC'J27
0-
6/20/56
37? PUT YV AT
SET INNER PRODUCT S.R.
DUMMY
INNER PRODUCT x.v I
FIRST ELEMENT
OP 1
40755
All
S.R.
30000 20000
:30000
MODEL
DATE
yl
--+ 01'
K,
STORE
L (V~)
SET INDEX
-K,
= N-l
~
OP 1
~
OP 2
yl
l
9-446
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
SA .. D'EGO C"l'I'O"''''''
eN 007-53
PAGE
MODEL
ZJ.f h91
All
DA TE
6/20/56
REPORT
MULT.
40775
00245
31 00051 00053
40776
00246
11 00031 00025
40777
00247
11 00032 00026
41000
00250
75 30002 00252
41001
11 30000 00027
41002
00251
00252
41001
00253
75 30002 00255
41004
00254
11 00031 30000
41005
00255
21 00244 00037
41006
0025p
21
41007
00257
21 00254 00041
41010
00260
41 00314 002411
41011
00261
21
41012
00262
41 00312 00301
DONE E VECTORS?
41013
f00263
75 30002 00265
YEs:
41014
00264
11 30000
41015
00265
15 30002 00267
41016
00266
11 30000 00027
41017
00267
37 00051 00052
41020
00270
75 30002 00272
41021
41022
00271
00272
11 00031 30000
21 00264 00037
41023
00273
21 00266 00037
41024
00274
21 00271 00041
41025
00275
41 00315
41026
"""'
~
..a
...... 41027
00276
56 30001 00277
DUMMY
00277
75 30210 00210
41030
00300
11 40210 00210
PART II ~ ES
JUMP TO PART It
41 00313 002251
L VECTORS DOME?
t-
41031
41032
00301
......
00302
YES;SET FOR NEX l VECTORS
><
41033
0030:;
21 00221 00307
56 30001 00304
41034
00304
45 00000 002161
RETURN
--
,
Ct,
0
0
Ct-
0..
-
37 00051 00052
OO~51
002~2
00037
00037
0OO2S
002~
-K, Yt
I
--1 0P 1
V2
~OP
2
ADD \/2 -K. VI'
STORE
IN V1
SET
FOR
NEXT ELEMENT
Vl. - K, Y•
SET FOR L(Y). yl)
X,
~x
---+
:::: V'-.
OP 1
fj X,
--7 OP
2
ADD
X,+ II x I
--) V,
SET
FOR
Xl.
X FORMED
DUMMY
9-447
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5"'" DIEG"
CALIFOR",'01\
REPORT
CI-007-~
ZM 491
MODEL
All
PAGE
DATE
41035
00305
00 00000 COOOS
ORTHOG INDEX
41036
41037
00306
00 00000 00000
L-l
00307
00 00000 00000
2LNX2 1S
.41040
00310
23 00306 00042
K
41041
00311
23 00307 00006
41042
00312
IS
41043
00313
75 30000 003Z0
41044
00'14
41045
00315
11 41052 02000
00 00000 COCOO
41046
00316
00 02000 00000
41047
00317
00 00000 00037
E
41050
00)20
23 00220 00006
REDUCE REPEAT
41051
00321
45 00000 00213
41052
00322
00 00000 00000
41053
00323
00 00000 OCOOO
41054
00324
00 00000 00000
41055
00325
00 00000 00000
41056
00326
00 01)000 00000
41051
OC'27
00 00000 ()OOOO
41060
OO'3~
0
00 1)0·0(\0 00000
41061
00331
00 00000 00000
41062
00312
00 00000 00000
41063
00333
00 00000 00000
41064
00334
00 00000 00000
41065
00335
41066
00336
00 00000 "(1)('0
00 00000 00000
-.0
41067
00337
00 00000 00000
I
41070
OO!40
00 00000 00000
41071
41072
00341
00 00000 00000
00342
00 00000 00000
00343
31 46314 6a146
OO~44
~l
........
oqt
-....-4
C1'
I
0
0
C1'
....-4
r41073
><
c...
41074
OO~16
00232
46;14 63146
STORAGE
6/20/56
L-2
2LN-2N
=
INDEX
E-1
INDEX =L-l
=
INDEX
STORE L ( V,I
VI)
ALL VV
..--, E5
N-l
N-l
~ {V,' yl)ES
>
CONSTANT
COMMAND
INNER PRODUCTS
OF EIGENVECTORS
STORAGE
M (;8)'-5
=.8
9-448
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
.AN DIEGO CALlFOltNIA
CV-164
CV
ZK 491
All
MODEL
DATE
4107~
00345
31 46314 63146
41076
11 40000 00000
41077
'1
16370 00000
STARTER. STO~E Ft
SUM
MT AND CARD ROUTINES
75 20576 41102
41100
SUM
41101
32 76371 00000
41102
75 21300 41104
41103
32 40000 00000
41104
11 20000 10000
MAIN PROGRAM
STORE CHECK SUM
41105
7S 30170 01103
STARTER
41106
11 41110 01010
JUMP TO ES
41101
00 OOCOO 00000
41110 (Oi010
41111 OlOll
41112 01012
5S 10000 0000'
51 01773 20000
41113
0101S
00 30000 30000
41114
01014
41 01116 010101
41115
4-1116
01015
01016
23 10000 20000
56 00000 01017
41117
01017
75 30421 01021
41120
01020
11 40001 00001
41121
01021
11 10000 00005
STORE N
41122
01022
11 20000 00003
STORE
41123
01023
55 10000 00001
STORE
01024
11 10000 00001
2N
0102!S
55 10000 00017
STORE
2NX2,$
41124
--.
~ 41125
f"""'4
~
35 01760 01013
~ES
TYPE
CHECt!!
SUM
CLEAR Qt A
STOP TO SET N~(Q), -E
CONSTANTS. PART II
-E
41126
01026
11 10000 00006
60
41127
01027
11 00005 00002
~ 41130
r>< 41131
01030
23 00002' 00042
N-l ~OO2)
01031
STORE
41132
01032
21 00022 00001
21 00022 00')06
0..
~(A)
-..-, ES
'j'
0'
007-55
PAGE
REPORT
L.(v}
9-449
6/20/56
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
PAGE
41133
41134
41135
01032
41136
41-137
01036
21 00023
21 00023
21 00023
21 00023
01037
37 00326 00327
SET UP AX
41140
01040
75 30003 01042
M(.0) lS
~
1141
01041
41142
01042
STORE l (V,)
41143
41144
01043
11 41073 00410
15 00021 OO~11
16 01164 00211
01044
15 00304 00233
L(MA)
41145
01045
15 01164 00251
L (VMD)
41146
01046
16 00022 00251
41147
01047
11 00421 10000
L (v2 )
MASK ~ (Q)
41150
01050
53 00006 00210
SET
411'1
01051
53 00006 00250
41152
01052
56 30000 0105'
41153
01053
75 30421 01055
41154
01054
11 00001 40001
41155
75
41156
41157
01055
01056
01057
54
41160
01060
13 00001 C0306
STORE L
41161
41162
41163
01061
71 00306 00006
STORE
01062
11 20000 00307
0106:3
23 00316 00006
SET L(Y' y) ES
41164
01064
STORE L-l
4116S
01065
23 00306 00042
11 00421 10000
MASK ---+(Q)
41166
01066
53 00006 00216
SET
a-
41167
01067
53 00307 00220
t-
41170
01070
53 00006 00313
41171
01071
41172
01012
15 00022 00217
lS 01165 00221
~
...0
~
'-"
01034
01035
~O113
oe001
00006
eN 007-56
MODEL
ZM 491
A] 1
DATE
6/20/56
REPORT
S'rORE
00001
01051
11 40740 00210
00406 20071
(A IN ES)
L
00006
S.R.
PART t I END
l (VMD)
REPEAT
COMMANDS
STORE CONSTANTS, PART II
MO
ORTHOG S.R.
----+ ES
K
~(A)
2NLX 2'S'
I
aI
0
0
1""'4
><
c...
REPEAT
COMMANDS
STORE L
(v,)
L(EVMD)
9-450
CV-164
COfiVAIR - DiVISION OF GENERAL DYNAMICS CORP.
SA.N DIEGO CA.UP"O.-NIA.
PAGE
41113
01073
16 00023 00221
L(W.S.)
41114
41175
41176
41111
01'014
01075
01076
15 0,0021 00264
15 00022 00266
l (VI)
01077
11 00002 00315
41200
01100
. 41201
01101
41202
01102
23 00314 00001
75 30113 01105
11 00210 40740
41203
01103
41204
DATE
6/20/56
L -(v~)
L (v,)
16 00021 00271
N-l
STORE L (v·. yl)AT END OF
STORE ORTHOG
ES
~MD
PARTS I.Itl
01104
41205
01105
11 00421 10000
MASK ---+( Q)
41206
01106
53 00006 01520
SET
41207
01101
41210
01110
53 00006 01522
S3 00006 01555
41211
01111
41212
41213
01112
01113
53 '()OOO6 01725
56 ~oooo 01113
16 01166 01515
41214
01114
15 01164 01521
41215
ol1l5
' 16 00021 01521
l (v,)
41216
01116
15 00021 01523
l (VI)
41211
01117
16 01165 01523
41220
01120
15 01165 01556
L(E VECTOR RE~ION)
L(E VECTOR REGION)
41221
01121
16 00021 01556
L (v.)
41222
01122
15 01166 01575
L (E VALUES)
41223
01123
15 01165 01610
L (E VECTORS)
41224
01124
16 00005 01611
N
41225
01125
15 00021 01641
L
0-
41226
01126
15 00022 01643
L (~1AX)
0
0
0-
41227
01127
L (M
t-
41230
01130
16 00021 01643
21 01643 01167
><
41231
01131
15 00022 01660
L (EXP
L (Vl.)
41232
01132
15 00022 01661
L (Vl.)
~
......
-I
I
......
~
007~
MODEL
15 30300 01010
11 40440 01500
..0
eN
ZK ll91
All
REPORT
---io ES
REPEAT
COMMANOS
STORE L(E VALUES)
L (VMO)
( M ~.)
r,)
AX) X2'$'+ L
(Expf)
9-451
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
Cl'·;
PAGE
REPORT ,!~'
"=:2'
-.0
....-I
'+'
'"
'"tI
0
0
....-I
><
c..
J07-58
1.jo1)1
MODEL
All
DATE
6/2;':/56
41233
01133
?1 01660 01170
L (vl.) + 1
41234
01134
21 01661 01170
L (V2)+ 1
41235
01135
15 01164 01726
L (VMO)
41236
01136
16 00021 01726
L(V, )
41237
01137
11 00002 01776
STORE N-1
41240
01140
11 00002 01777
STORE /'f-I
41241
01141
56 30000 01142
41242
01142
11 76537 76536
41243
01143
75 30300 01145
DUMMY
SET MT DUMP TO OMIT BACKING
PARTS I. III
41244
01144
11 01500 40440
41245
01145
16 01175 40000
41246
01146
45 20000 01156
41247
01147
75 17777 01151
41250
01150
11 01171 54000
41251
01151
75 17465 01151
41252 01152
41253 101153
41254 01154
11 01171 63177
21 01153 00041
41255
011SS
41 Oi173 011~
41256
01156
11 01114 10000
41257
01157
45 30000 01161
MJ 3 ON TO AVOID DUMP
41260
01160
37 76510 76500
41261
01161
11 01171 76536
41262
01162
75 30210 76430
41263
01163
11 40210 00210
MT DUMP
RESET ~T DUMP S.R. BACKING
JUMP TO DUMP EVS ON MT
PART I 1---1 es
41264
01164
00 41252 41252
L. (VMD) X 2'" t L (VMD)
41265
01165
00 54000 54000
L(E VECTOR REG t ON ON MD) X2
41266
01166
00 53600 53600
L(E VAl.UES MD)X 2'''+ L(
41267
01161
00 00001 00001
,.1270
01170
00 00001 00000
41271
01171
20 00000 00000
41212
01172
00 00000 00001
--) MO
SET MD START TO INTERMEDIATE START
M.1 '2 TO SKIP f')s ~E V REGION
ALL
11s
11 01172 54001
~
EV REGtON
1
S' ..
L(
)
1
9-452
)
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5"N DIi.GO
C .... LI"ORNIA.
i)S~EV
01173
00 00000 07631
41274
01114
00 00000
41275
01175
00 00000 40440
41276
01176
00 00000 00013
41217
01177
67 01017 00000
L (INTERMEDIATE START)
CHECK SUM INDEX
MT S.R. BACKING
76365
11 76464 76463
EV MT RESTORE
76366
11 76567 76536
16367
45 00000 76420
76370
23 10000 20000
o
76371
15 30030 76373
MT S.R.
76372
11 16550 00001
76313
37 00017 00001
ES
RESTORE MD FROM MT
76374
11 40001 40003
2NE
76375
35 76474 20000
2NE
76376
73 76415 76467
P
76377
76400
21 10000 7646~
71 10000 76473
76401
11 20000 76470
76402
75 30030 76404
76403
76404
11 76550 00001
16 76471 00014
76405
15 76410 00020
SET MT BACKING
76406
11 76467 00030
P
...a
16407
45 20000 76415
MJ #2
I
16410
76411
37 00021 00001
56 30000 76424
16412
75 31777 76365
>< 76413
11 74001 00001
MT 110
DUMMY
RESTORE'
ES
76414
S6 00000 01532
STOP) JUMP
~
-~
0J
0
0
0-
~
t-
c...
PAGE
eN
REPORT
Z!'I1
MODEL
All
DATE
6/20/56
007-~9
491
INDEX
41273
ooooe
CV-164
t
~ (Q)
--4
+ 400s~(A)
=2NE. +lfOO 11737s
P
+
1
~(Q)
(p + 1) x 31g x 2 15" ~(A)
STORE
MT S.R.
---7 ES
STORE L (EV'S)
~
MT INDEX
TO READ FROM I-1T 112
READ EVs)BACK
TO MS #2 STOP
9-453
CV-164
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
Cl~
007.«J
Z;.; h91
All
PAGE
REPORT
MODEL
DATE
76415
11 76466 10000
76416
37 00021 00022
76417
56 30000 76412
7S 30210 76414
76420
16421
11 40210 00210
16424
76425
75 30200 76412
76426
16 76477 41262
76427
45 00000 40000
76430
31 76472 00052
176431
76433
61 00000 20000
34 20000 00006
47 16431 764EJ
16434
11 40001 40003
764'35
~5
76436
73 76475 76467
76431
21 10000 76465
76440
71 10000 76473
76441
11 20000 76470
(p .,. 1) X 378 X 21"~( A)
STORE
76442
75 32000 76444
ES
76443
11 00000 74000
76444
75 30037 76446
--+ ES IMAGE
MT S.R.
76445
11 16511 00001
76446
15 76471 00003
16447
..I!'J
76450
I
0'
76451
37 O(t027 00001
0
0
76492
......
7645!
75 30037 76454
11 16511 00001
15 76471 00003
......
-I
0'
r><
0..
76454
STOP
JUMP TO STOP
STORE YYS
FOR MT DUMP
RESTORE
vv'!
11 41052 53400
76474 20000
&.
PART I I~ES
76423
11 76467 00036
15 76470 00026
~
MTH2 READ EV~)BACK
RETURN TO RESTORE ES
75 30200 76434
76432
6/2':./56
J ---)(Q)
76422
11 53400 41052
-
TYPE
MT
2NE
2NE
p:
---t ( A )
+_4008~A)
2NE
+ 4001
1137ca
P + 1 ~(Q)
- t ES
SET l (EVS)
STORE P
SET TAPE BACKING
MT DUMP ON flO
MT S.R.
--+
ES
9-454
CV -164'
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
~
-.0
-1""""1
I
0
0
C}J C07 -~',l
REPORT
,ill !;·-n
MODEL
.'All
DATE
;6/2(,/:'6
76455
11 76461 00036
76456
15 76470 00026
16451
76460
11 76466 10000
37 00027 00030
MT DUMP ON
16461
75 31717 76463
RESTORE
16462
76463
11 74001 00001
37 76463 01541
76464
56 00000 01532
76465
00 00000 00001
76466
00 20000 00000
76467
00 00000 00000
L
76470
00 00000 00000
76471
00 53400 53400
16472
04 04470 70157
l(BACKING PARAMETER)
L (EV REGION)X 2 1s + L (EV REGION)
FLEX WORD
16473
00 00037 00000
76474
00 00000 00400
76475
00 00000 01731
76476
67 01017 00000
76477
56 00000 16370
76500
75 32000 76502
16501
11 00000 74000
76502
7S 30037 00001
16503
76504
11 16511 00001
7S 30030 00001
16505
11 76550 00001
76506
75 31777 16510
76507
11 74001 00001
76510
56 00000 56510
STOP
MJ 111 TO SET
MD BLOCK
I
'"
'"t-
PAGE
2 ~J(Q)
112
e:S
STOP. JUMP TO MS'2 STOP
( P)
MT DUMP & RESTORE S.R.
STORE ES IMAGE
MT OUMP ROUTINE
--7 ES. JUMP TO ROUTINE
MT RESTORE ROUTINE
~ES. JUMP TO ROUTINE
RESTORE
E5
1""""1
><
0..
76511
00001
45 10000 00030
76512
Waoo 2
75 31737 00004
~1T
UNiT
9-455
\.VNVAIIC -
. elf :-164
UIVI)IUN Of GENERAL DYNAMICS CORP:
..... N DII:GO C ... LIf'ORNI ....
'PAGE
ZV 491
MODEL
All
DATE
.
01 007-41i
REPORT
6/20/56
~ES
76513
00('03
11 40000 00041
76514
00004
31 00041 COOO()
76515
00005
75
76516
16517
00006
00007
'2 00042 00000
11 20000 00040
76520
00010
65 00037 00040
76521
04P11
67 00037 00000
76522
00012
64 00037 00040
CHECK
SUM
MD BLOCK
STORE CHECK SUM
MO BLOCK ~ MT
BACK JAPE 36 BLOCKS
MT ~ ES MD BLOCK
76523
00013
31 00041 00000
CH~CK
76524
00014
75 21736 00016
SUM
76525
76526
00015
00016
32 00042 00000
11 20000 20000
MO BLOCK
STORE CHiCK SUM ~(A)
~6527
00017
43 00040 00023
CHECK SUMS :: ?
765'0
76531
76532
76533
00020
61 00000 Oe025
NO: TYPe- F
00021
00022
00023
67 00037 00000
BACK TAPE
MS 63 RETURN TO TRY AGAIN
SET FOR NEXT MD BLOCK
76534
00024
76535
00025
76536
76537
00026
00027
76540
00030
76541
76542
00031
00032
67 01017 00000
56 30000 76506
53 00034 00021
53 OOO~4 00026
7S 10003 00002
76543
0003~
53 00034 00010
:; 76544
00034
00 70000 00000
:: '6545
I
0;- 16546
00035
00
00036
00 00000 00020
~
r-
.,6541
00031
00 00000 00000
76550
00001
45 10000 00022
MJ Hi TO SET MT UNIT OTHER THAN 0
76551 fOoOC2
64 00037 00040
READ MD
56
21
41
56
217~6
00001
30000 00002
00063 00035
00036 00002J
30000 00026
TRANSFER COMPLETE
= (21),
T IME5
MS'3 JUMP TO RETURN TAPE
BACK TAPE TO ORIGIN
MS#3 JUMP TO RESTORE E$
SET
MT
COMMANDS
..0
o
017~7
"0000
~
><
c..
BLOCK~
ES
9-456
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
CV-164
MODEL
eN 007 ....
ZM ~91 •
All
DATE
6/20/56
PAGE
REPORT
~
---0
76552
00003
31 00041 00000
CHECK
16553
00004
75 21736 00006
SU~4
75554
00005
32 00042 00000
76555
00006
11 20000 20000
76556
00007
43 00040 00013
CHECK SUMS =..?
76557
OOCIO
61 OOOpO 00007
NO:TYPE G
76560
00011
67 00037 00000
BACK TAPE
76561
00012
56 30000 00002
MS
76562
00013
75 311'37 00015
16561
00014
76564
00015
11 00041 40000
21 00014 00027
76565
00016
76566
C0011
76567
00020
41 00030 000211
56 30000 00020
67 01017 00000
16570
76571
00021
56 30000 76506
SET FOR NEXTMD BLOCK
TRANSFER COMPLETE
MS 03 JUMP TO RETURN TAPt
BACK TAPE TO ORIGINE
MS 113 JUMP TO RESTORE ES
00022
53 00026 00002
SET
16572
00023
53
7657~
00024
53 00026 00020
76574
00025
45 00000 00002
7657'
00026
00 70000 00000
76516
00027
00 00000
76577
00030
00 00000 00020
00011
45 00000 00000
76601
16 76614 76610
76601
45 00000 76606
1660:3
16 76615 76610
76604
45 00000 76606
76605
16 76616 16610
I
76606
75 31777 76610
C'
76607
11 00001 74001
76610
15 30530 00000
I
0'
c
c
r-t
t-
;;.<
c...
BLOCK
RETURN TO TRY AGAIN
Y~S;MD BLOCK
~3
~MD
TAPE
COMMANDS
017~1
76600
r-t
~
OOO~6
MD
CARD OUTPUT Ie OC4
9-457
\'Uf'ilYAIK -
UIYI~'UN
ur
v&:NIIICAL UT NAMI\..) \..utCt'.
54N OI£GO C4I.IFO"""'4
CV -164
MODEL
CI o07-I:A
%. 491
III
DATE
6/20/56
PAGE
REPORT
76611
11 76620 00526
76612
75 31777 (')0000
7_6613
11 74001 000(")1
76614
00 00000 00744
76615
00 00000 007'1
00 00000 00733
76616
76617
76620
76621
56 00000 76605
00 00000 00037
37 77177 17717
76626
00 74000
23 00001
21 00001
21 01262
21 01207
76627
45 00000 01203
16610
00 000("0 00144
16631
00 00000
76632
76693
71 00720 30000
15 20000 00566
76634
55 20000 00011
76635
15 10000 00620
75 20044 00546
76622
76623
76624
16625
16636
00000
01262
01201
00536
00536
IJO~10
7664:5
23 00731 20000
16 00716 00000
31 00723 00001
55 10000 00030
52 OC721 20000
1664_
54 20000 00002
C1'
76645
44 00554 00554
0
0
0-
76646
44 00561
76647
17 00000 20000
21 00540 00720
16637
76640
76641
76642
..~
...a
1'"""1
'-'
I
I
1'"""1
r><
Cl.i
76650
0055~
9-458
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5 ....... D'EGO C ... l'FOR .... ' ...
CV-164
PAGE
16651
'6&~2
16 20000 00560
itS 00000 30000
16653
32 00677 00000
766S4
17 00000 20000
16655
11 00730 00650
166$6
76660
11 00714 00651
~7 00560 00566
S5 30000 00000
16661
44 00641 00570
1666Z
16663
16.64
" '666S
55
51
13
35
10000 0001'
00725 20000
7&$66
~5
10000 00006
"6&61
51 00725 0'0672
1&610
SS 10000 oooo~
Sl 00125 00665
16651
'6611
'6612
"fi13
16614
1&6'5
,16616'
" 16611
""00
,,701
i16102'
.....,
JIO!/f
J
0-
~
0'.-,
....
~
"'03
1&104
'6tO!
eN
007--~
MODEL
tM 491
All
DATE
6/20/56
REPORT
20000 20000
00715 00621
55 10000 00006
!l 00125 00713
44 00655 0060'
16 00661 00703
5' 00616 00605
41 00672 0067'
~1
00665 00011
" 00106 00704
11 20000 006S2
~1 00113 00017
31 00706 00104
16 00116. 00000
"'06
16'0'
!1 00726 00023
13 10000 10000
16110 '
Sl 00652 00107
9-4~,'
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
.... N DIEGO C"'\..'f'O"NIA
CV-164
elf
ZM
MODEL
All
DATE
76711
76712
76713
76114
1671'
16716
16717
76720
l6724
76726
15 00620 00633
S5 30000 00000
21 00566 00726
76127
21 00620 00726
16730
16 00560 00676
76731
13 00720 20000
44 00670 0061'
'7 00560 00570
16735
15 2Q014 00644
55 00761 00010
76736
75 10003 00646
16737
11 00710 00650
16 00716 00000
43 00711 00.556
00 30000 30000
76734
16740
16741
76742
-I
a--I
0
0
a-.....
t-
><:
c..
20QOO
73 00652 20000
i5 20000 00652
'37 00676 00626
41 00665 00677
41 00113 00677
76733
.....
30000
16723
76732
~
~
00672
76722
76725
6/2C/,6
10000
16 00717 00676
41 00713 00660
16721
.-..
35 10100
12 :30000
00 30000
35 10000
007-6&
491
PAGE
REPORT
7674'
76744
00 30000 30000.
16745
75 20003 00646
76746
76747
23 00650 00720
37 00703 00604
76750
43 00665 00661
00
~OOOO
30000
9-460
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN O'~GO CAL'I'"ORN'A
CV-164
PAGE
eN 001-6.7
REPORT!ll
16751
76752
45 00000 b0673
76753
00664
76755
76756
00 30000 30000
16757
00 30000 30000
16760
76764
00120
37 00103
35 00651
!5 00650
00 30000
76765
55 00650 00043
76766
44 00675 00616
76767
76773
21
45
31
32
11
76774
34 20000 00044
76775-
77001
47 00667 30000
15 20000 00706
S4 00720 10000
75 30000 3"0000
71 20000 00724
77002
77 00000 00774
77003
77 10000 00744
77004
17 10000 00760
77005
00 30000 30000
77006
53 10000 00733
77007
31 00672 00043
-77010
00 00000 00540
16754
76761
76762
76763
76770
76171
76772
76776
76177
77000
"""'
~
-.0
.....
'-'
I
0I
0
0
0"-
.....
t-
><
Co.
00721
00651
00722
00650
31
15
35
55
~3
491
MODEL
.111
DATE
6/20/56
00000
00665
00000
00001
00670
00672
00000
30000
00651 00127
00000 30000
00652 00002
00652 00001
20000 00652
9-461
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S .... N DIEGO C .... LIFORNI ..
CV-164
PAGE
MODEL
DATE
77011
00 00000 00631
77012
00 00000 00001
77013
77015
00 00000 00003
00 00000 00005
00 00000 00010
77016
00 00000
77017
00 00000 00077
77020
17022
00 00001 00000
00 00000 00014
40 00000 00000
71023
71 01206 30000
77024
15 20000 0104'
77025
11 10000 01000
11 20000 00715
17014
77021
11026
170:30
71011
11 76600 00017
, 71'032
35 00741 00741
71033
11 74000 01000
77034
21 76600 01213
1103'
45 00000 00000
77036
16 00774 76612
77037
31 00743
45 00000
16 01252
45 oooeo
77040 '
77041
__ 77042
~
~
J
I
8
~
01075
01001
77045
31 76606 00017
77047
77050
35
6/20/56
00747
77044
~ 77046
All
00737
16 00714 16612
37 00743 00737
77043
491
~OO12
16 00173 76612
41 00756 00746
71027
OC11-6t
CI'
REPORT ZJ(
00755 00755
11 74000 20000
11 20000 10000
9-462
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO CALI'-ORNIA
77051
77052
77053
770~4
1705S
em
ZM
MODEL
All
DATE
6/20/56
51 00112 00776
55 10000 00025
51 00772 00777
16 01253 01011
17060
77061
16 01255 01021
11062
16 01252 01075
77063
45 00000 01001
17064
00 00000 77177
77065
00 00000 76611
77066
00 00000 76600
17067
00
71010
00 00000 00000
77071
00 00000 00000
77012
00 00000 00000
77073
15 01000 01007
71074
11 01010 20000
77075
42 01001 01005
7707?
17071
21 01000 oo,~o
15 10500 01011
771oJO
11 01212 01300
;- 77101
00 00000 00000
17057
PAGE
REPORT
21 76600 01213
16 01254 0117,7
51 01245 20000
47 00771 00767
71056
CV-164
oeooo
00000
-.0
,:;
, 77102
00 02000 00000
0I
77103
45 00000 01216
0-
17104
71 00716 00777
77105
11 20000 01256
77106
34 01213 00020
77107
11 20000 01257
77110
11 00776 01261
0
0
'""""f
r--.
><
.:l.,
9-463
007-6.P
491
CONVAIIt - DIVISION OF GENERAL DYNAMICS COITP.
SAN OIEGO C"L'I'"OIltN'"
CY-164
PAGE
77111
17112
77113
17114
7711'
17116
17117
ZM 491
.&11
DATE
6/20/,6
,;.....
.,
11 00777 01262
00000 01023
11 00776 01262
11 01262 0126:4
11 01162 00516
l1 01046 0·0001
17121
1'1122
17123
77124
1'3 01247 20000
36 Cl21! 01'260
11 OltMt 20000
77125
77126
.,7121
" 01,47 10000
11 20800 01266
56 01213 0126'
17110
SJ 01242
11131
T 1132
171'3
13 0124-Z ,1"210
11 01266 OINt)
11134
11
71135
771'6
71131
'1 01166 80001
36 IIZ1! t"!l'2
.5 00000 Ql()~7
7"160
00 00000 001'40
17l-41
31 00'.0 OOM'
20 OOOCO 0'00""
31 00'40 0054e
20 00000 00000
15 01000 01071
15 01000 01107
11 00711 01264
77142
--cr 11143
., 1144
I
,
!55 Ot261 00020
11 OJr!' 28000
'5 01246 JOOOO
17110
8a.....
77145
~
77146
~ "147
CI 007-.7'
MODEL
REPORT
ZOa.O
23 012700111·'
zeooo
OLIn
9-464
¢V-d65
CON
ANALY. . .
..RIIPAR£O BY
CHECKED BY
J. I. 1111s
D. B. Parker
VA
~AN
I
R
PAGE
REPORT
Off GO
NO.
CI-- .
CV-165
CONVAIR
'ANALYSI.
ptREPARt=D BY
CHECKED BY
J. H. Ell1...
D. B. Parker
PAGE
REPORT NO.
MODEL
SAN DIEGO
REVISED BY
DATE
ts-. 0114
'M :491
~
The t;t-al ari th.metio, or the real ar.ithmotic and interpretive routine may
l
be used. independent of the determinant routine by chooalng the proper entrances.
For instructions on the use of real arithmetio sfte CA 001.
The interpretive
routine performs the real arithmetic operations referring to a parameter word
fo~
the locations of the mantis888 of the
oper~nd8
and result.
REAL AR ITHDT IC ·ElfTRANCI
Co 37 01001 01002 Add Ent
Co
37 01001 01003 )lul t Ent
Ce
37 01001 Ol~ 01'Y
Ent .
IlfrIRPRETIVI ROU1'ID ElTRAICB
Co 31 01001 PPPPP
C1 .u.AA BBBB
ccce .
Whereoperationa performed area
Add
(A)f(B)~(C)
P-Il06
Bubt (A)-(B)~(C) P=lllO
Vult (A)A'(B)--+(C) P-1112
DiT
(A)+(B)~C)
P$lllU
Where AAAA-location of mantissa of lat operand
BBBB-location o,f
an
......
-.0
-
mantl.~;&;
of 2nd qperand
~CCC-iocatiOft of.manti8sa of result
I
0I
DET1mJ(IJAJrr SET-{Jp
o
o
~CB
0-
......
Co 37 01001 01153
r-
><
~
C DDDD RlRR no
1
Where DODD-location ot Det. in E8
RRRI-loeation of re8ult in 18
BBII order of the determinant (octal)
....
,.,.-~
9-466
ANALYSIS
""'ARto .Y
CHaCKED .v
ItIEVlSI:O aY
J...
1111.
D. B. Parker
CONVAIR
SAN DIEGO
CV-165
0-011-.,
REPORT NO.
III 491
..AGE
MODEL
DATE 12~~
~--------------------------------------------------------------DITIRJIIWAIT IVALUATIOI EHTlWlCI
Co 37 01001 0115'
Permanent canet. used 40,
74, 77, 43. 66, 44.
Teap. storage 00003-0D932, (Al, (Q)
COJ3IIIUlda for assembly lDOdlfication
4078
(263)10
Drum Addre •• -70723-7134o
'""'
an
-.D
~
'-'
I
0"I
o
0-
0"-
~
t-
><
~
............
..
',,"
,
\1-407
CV-165
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OI£GO CAL.II'O .. N'A
Byt J. B. 1111.
Cheoked by.
no.n
PAGE
B. Parker
REPORT
OI-Ol1~
ZM 491
MODEL
DATE
ALAq"~
2-27-56
EXIT
70723
01000
37 76000 76002
70724
01001
45 00000
7 725
7 n 726
01002
45 00000 01027
~1003
45
7)72 7
01004
11 00027 20000
7"730
OlOOS
47
010~6
rqo(')('
DTVrDING RV n?
7~7~'
OlOO~
11
O(')(\?~
,"ono
NO: N~ H-4!:q ATOR ~-?'< A)
70732
0100 7
47 01014
Ot~'l(,,)
NUME'R ATO~
70733
01010
11 00040 00031
70734
01011
11 00040
70735
01012
31 01012 0101'3
70736
01013
45 00000 01001
EXIT
JUMP TO EXIT
70737
01014
54 20000 00042
NO:
70740
01015
73 00027 10000
QUOTIENT X 2:3"~
7('1741
1~
n
70742
"1016
01017
74 10000 00025
70743
01020
11 20000
OOO~l
70744
01021
2~
OOO~O
70745
"lO?2
11 0002'5 ,0000
H~A
70746
47 01025 01024
H
7(')747
01023
01024
21 00026 00074
H =
70750
01025
11 00026 00032
H
70751
01026
45 00000 01012
70752
1"\1027
70753
010:30
70754
01031
'-'
70755
01032
11
47
11
41
JUMP TO EXIT
ADD I T ION M (OPt~,6Nf") 1) ~ (,,)
0-
70756
01033
11 00025 00031
YES: M ,OPERAND 1) ~ ""(Al\lSW~~)
70757
01034
11 00026 00032
F (Op ~qAND 1) ~
70760
01035
45 00000 01012
JUMP TO EXIT
70761
0103e
11 OOOiA
NO".
A
..-...
li.I
...0
~
~OOOO
(\('\t"I4(\
00026
~~OOC
~1073
I
o
0-
,....,
,....
><
.0..
ADD ENTRANCE
MULTIDLV
DIVIDE E~ITRAnCF
YES:
"n~'~
~~T~ANCE
r.A
(0 0
= O?
ANSWER
S.~.
~ (NU~~ERATOP) X
29#~ (A)
(Q)
~,.t;
NORMALIZE IF(Q0025}=-O OR 71
NORMALIZED MANTISSA STOPEn
DIFF OF EXp.~(n0026)
01
-
0
= 11
COR~ECTF.D
EXP~ OOn32
000'25 '-0000
01031 nl051
M (OPFRAND 1) -
0J
00027 20000
NO: M (OPERAND 2)
7(A)
01036 01033
M
~')t')OO
2)~fJ.)
0
~
000~2
I
o
.EXIT
(op E~ AN"
')
= o?
r: (A~.!!;'f/E")
..
E (OPEP.A~Ir> 1)7(A)
c
9-468
CV-165
CONVAIR - DIVISION Of: GENERAL DYNAMICS CORP.
5"''''' 01£00 CALIfFOttNIA
P AGEt5-OJ.1oo5
By. J. I. 1111.
REPORT
Cheeked 'by, D. B. Parker
2-27-56
DATE
tn
-.0
...-4
'-"
I
C1"I
0
0
C1"-
...-4
r-
><
£l.4
70762
70763
010:37
01040
70764
70765
70766
01041
70767
01044
10770
01045
70711
01046
70172
01042
01043
36 00030 00032
E(op 1)
46 01047 01041
K
11 00025 20000
11 00027 00025
11 20000 00027
11 00026 ?OOOO
11 00030 C0260
YES:
AND
10773
70774
01050
42 01012 01.054
IKI
01051
11 00027 00031
70"'15
10176
0105'
11
01053
~1~12
70'177
01054
45 00000
i6 20000
110CO
01055
54 00.027
10(\nn
71001
010S6
3S 00025 20000
71C~2
01057
71003
01060
71004
01061
71005
01062
11 00040 ~OO32
74 2000~ noot2
11 20000 OOO!l
47 01064 01061
71006
01063
13 0003·2 00026
710C7
7101("1
01064
11 000'2 2COOO
42 01071 nlQ67
71011
71012
01066
01067
71013
01070
71014
01011
11015
71016
01012
71017
01074
01013
EXCHANGE.
ONE
NO;
TWO
IKI
~(A)
< ~$ !
IKI ;>
35 OR t·1( OP} 1
(op
ooo~o ooo~~
23 00026 00077
21 00032 00026
45 00000 01012
00 00000 00*46
00 00000 00*43
71 00025 00027
11 00040 OC()25
K ~ (OOO~2)
OPERAND
01047
0105~
MINUS E(OP2) =
or
">
11 20000 00o,o
12 00032 20000
0106~
ZJl 491
MODEL
-
0
2)~AN~Wr:R
TO EXIT
JU~P
<..
,~
'5? SEt ~HtFT OF 5. "ITS
M(riP'.) x ~) ~ (A}
M{OP2\ X 2A- + M (0 0 1) ~tA)
o. ~(O.O12)
NORMAL t l£ M (AN s)
=- '"i--?( t)OC! 2)
M (ANS) ~\OOO31)
o?
M(ANS) =
YES: -H~\OOO26)
H~\A)
NO:
H
<
3S?
NO', E (OP1)-~2 ~ l~OO26)
YES: E loP II PLUS H \OR
H-72)
JUMP TO EXIT
DEC
~8
oe:c
35
MUL T M (OP1)X ~
(op
2)~tA)
o~ loo.2~1
9-469
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
S"'" 011:00. CAL.IFO"NI"
C V-165
taJ-Oll-'
PAGE
B1" J. I. 111i.
Checked b7" D•. B. P&rker
Z1l 491
REPORT
MODEL
2-27-56
DATE
......,
If')
...0
.....
-I
0I
0
0
0'
....
t-
><
~
71020
01075
74 20000 00025
NORMALIZE ~.i(ANS)=34 (~~
71021
01076
11 20000 00031
M(!'NSj--+(OOO3V
71022
01077
47 01102 01100
M (ANS)
710?3
01100
YE5~"
11024
01101
11 00040 r()O~?
45 00000 01012
11025
01102
?~
71026
01103
21 00026 000"'0
71027
01104
35 00025 00032
710~O
01105
45
11031
01106
16 01147
71032
01107
45 00000 01115
71033
01110
16 01151
11034
01111
45 00000 01115
71035
01112
16 Oll?()
710.36
Olll:!
45 00000
71037
01114
71040
0111.5
. 11041
71042
("1116
,6
0002'i 0107'
oqooo
=
=
F'(ANS)
JUMP TO EXIT
NO:
H-~5 ~ (O~()2~)
011~~
AD.!)
ENTRANCE
SUBTRACT
~NT~ANCE
MULTIPLV
ENT~ANCE
0111~
01146 011!4
= n o~ -1
E COP 1) PI.U~ E ~O~ 2) ~\AH.0OO26)
E (ANS) ~O.OO32)
JUM,P TO l!XrT
01U~
o IV.rf)F
SET
01117
31 01001 00017
15 20000 01117
11 00000 011'2
71043
01120
55
~11"4
looo,
SET
71044
01121
5~
011a;~
01116
L
11045
01122
55
01152
ooo~~
5-£T
· 71045
Ol12~
55
0114~
1000~
l
71047
01124
71050
01125
11051
01126
71052
01121
11053
01130
01152 C11~t
54 01152 00014
53 011~'- Cl1~'
21 01001 00074
75 30002 011'2
71054
01131
71055
Oll~2
F:NTR.ANC~
PAQAM,!TEP
LOCATION
( Z)
( X)
5~
11 00006 00025
75 3no02 01134
H
07
01012
0113~
,35~
~f!T
L(V)
UP EXIT LOCI
X~
(op 1\
Y~
9-470
CV-165
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DI£CiO CALII"ORNIA
PAGE
BTl J ••• 1111.
REPORT
Cheotecl byl D. B. Parker
MODEL
DATE
01134
11 noooo 0002"1
31 01012 00000
01135
75 30002 01111
'l
REAL ARITH. JUMP
ANSWER
11061
01136
11 00031 00000
~ (Z)
71062
Oll~1
37
71063
01140
45 00000 01001
JUMP TO ExtT
71064
71065
71066
01141
01142
01143
13 00027 ~O027
:37 01012 01002
(nO~21)~, (0<'0'7)
JU~~P TO SU9
Jur·1P TO STORE (ANS);' EX!T
71067
('1144
01145
01146
7r056
11057
11060
01133
011~1
~1150
71074
01151
710"~
0115'
on
71076
01153
45 00000
71077
71100
71101
01154
01156
15 01405 01115
15 01'2:3 ot'114
15 01323 01177
71102
01157
111(')-'
01160
71104
01161
71105
71106
0116?
01163
11 01~''- 012'-~
11 01106 01?4'
11 01307 01244
11 01~21 01 '-5.,."
11 on066 00003
71107
01164
11 00074 00004
71110
01165
11
01~O2
0-
7111.1
01166
ti
01~14
r><
Q..
11112
01167
75 30006 01171
7111"
01170
11
71071
71072
an
...0
r-4
I
0I
0
0
r-4
01147
01155
s.~.
45 00000 011"3'
7107~
71070
00000 on777
M.• ~K
00777 10000
00000 01('\04
MASK
OOCOO
III 491
2-27-56
(op
01140
10
00
00
00
00
00
ca-ou-r
J:XtT
~10()2
00000 nl00"3
00000 01141
O()('OO
01~O/
SET UP ~. ~. ENTPY
Ot30~
01'31
013'6
ct~'~
5£1
PA~AM~'EP. L~r
SET L \All) X 2'..~ (~1114)
,5£T L (All1}'21~( 01177)
SE'T
~f!T
L(Al'
L(Al'
SfT L(.. "
.
SF'T
L{Ta.
"1')
All
A'l
T2
All
T?)
A22)
A''-)
1~
(T1 )
2X'l~~ 4
STORJ: 2 (N-l) , 2a.~
STORE COPYS
2N x. ,Ir
5TORf:
9-471
CV-165
CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
PAGE
_~
B,.t J. li. Elli...
REPORT
ZK 491
Checked bYI D. B. Parker
MODEL
DATE
71114
"'1171
'1
f'l~'~
71115
11
Ol~O5 .Ol~11
INDEX :: N-2
N-l
INDEX
(All}"'" A
71120
oli75
111~J
01176
11
11
41
15
01121 01334
71117
01112
01173
01114
'11,22
01177
71t2~
01200
01201
11116
711~4
=
or
-
01217 01166
!OOOO a1200
VES',
nooon
--+
012()~
STORF
11 00000
15 01111
A
21 01205 01326
ROW 1
tT!MP ROW)
L {ROW 2)
S"O~E
O120~
~,
n11"
'002f1i
Ol!O3
16
10~OO
012(,)~
012.04
'll~O
~1205
15 30000 01206
tl ~t'ooo ~(\~on
Til!!
01206
11l~2
01207
55 0120'
16 10000
1111'
111"
711"
7113.'
.71137
01210
7~
30000 01212
Ol211
1t
o~ooo
Ol~12
13 00001 00001
2
~T1J~ (Ttl
01'-11
:'>1 01126 0190'
2NX"~ ..,.
01214
41 013'. 011'4
15 1000~ 01'-"
TEST NEW All
1114~
71144-
012'-0
01221
..... 11145
01~22
...0
......"
I
0I
0
0
0......
00000 .20000
~' .. 1
7tt25
11126
11121
11140 "0121 ~
11141 01216
11142 01217
l,(')
n'~'l
11146
Ot22'
71147
01224
r-.
11150
01225
><
0..
711. 51
Ol~26
t!OO2~
(ROWt)
l
ROW 2
-? ROW 1
STCR£
L (RO\., ~)
01211
oooon
2-27-56
ROW
t
~
COL
(TEMP ROW)
~ow
t
~N)( fO
= '0
o --, 'DE~
11 00040 COOO3
11 01301 01~2'6
COll
=
0
'-~ 01327· 0001"..
-tN"~;(--:"
1
'-1 011" 01301
21 011"4 0131~
SET FOR
11 01310 Ol~~4
37 01111 01114
00 ooono
?1 Ol'~' 0130,"
SP."T tNDt!X
JUMP TO £xtT
~!STCR! CONSTANT
NEXT ROW
Al~/A11 ~
N-l
( A)
SET FOR Al'
9-472
CV-165
CONVAI. - DIVISION Of GENERAL DYNAMICS CORP.
SAN DI£GO CALIFO .. NIA
By. J. I. Ellie
Checked by. D. B. Parker
PAGE
~~
REPORT
Z)( 491
MODEL
DATE
01227
7115!
11154
01'-~O
012!1
71155
C12~'
71156
71157
01233
01234
11160
012~5
71161
01236
71162
01237
7l16~
01240
71164
71165
01241
01242
00
noooo
00
71166
01'4~
~7
011~7
{')tl1n
71167
01244
01245
01246
00 OOOO(} 00 *~
21 012~2 01301
21 01244 01302
11172
71173
01747
41
01250
71174
01251
01252
01253
01'42 01~~6
21 01'-44 01~~7
21 01242 01310
41
011'. 012!1
012~4
~1
011"
01255
00 00000 () OO()D
2~ 01310 00074
71110
71171
71175
11116
-,,
11177
71200
11201
01256
7120~
01257
01260
71204
t')1261
71205
xc.. 71206
It)
.J:)
.....
0"-
80"-
.....
41 O13~4 01'-24
11 Clt~'O 01~!4
11 01330 O13~S
31 01'-47 ~C'OO~·
11 01~'-4 10000
53 20000 O12!5
711~2
. 112C2
4'
01~'~
*
01241
RIAl!
SF.T
SET
tND~X=~t
-2
tNOEX=N-2
SET
( A'-1 )
L
(A'-l~(A )
(A21):: O~
YES;SET FOR NEXT ROW
JUMP TO SKIP ROW
NO',
X
A12 )(
A~l~
T
A ~'--(A~2 A2~---+ A22
SET F'OR Al'
SET FOR A2'
o -it 1 COL
2~
?~
0111~
t)1~~6 01~(')t
1ST COL 1. 0.0
X
(t )
(Al1~ T
INDEX -1
4(N+t)xt·~ ;. X ~Ja..
~130~
4 · 2""
ol~tl
SET FOR A22
01262
21 01337
21 01 '-.~5
21 OlS!1
01~15
SET
01263
11
01~~1
01242
01264
21
r.13~2
nl~'-n
l-
71207
11 00000 'OOO~
01241 012~1
21 01244 01311
45 00000 01252
37 01131 01112
2-27-56
4 · 2'·"", 4
PAPAM~TF.R~
9-473
CONVAIR -
CV-165
DIVIStaN 'OF GENERAL 'DYNAMICS CORP.
SAN OIEGO C.<\lIFOltNI.<\
lc-..oll-iG
PAGE
Bye J. I. ILLIS
REPORT
Checked by. D. B • Parker
MODEL
DATE
71210
01265
11 01312 ,01244
11211
01?~f.,
71212
0126'7
71213
01270
71214
(H271
11215
01272
'1 Ol~''3 ot~o'
21 0'12'25 01325
41 01131 01173
11 O125! !'127~
31 01137 01112
7.1216
0127'3
00
7121·7
01'274
15 01406 01115
71220
01275
15 0140'6
71221
01276
75 30002 01001
71222
01277
71223
~1300
11 00003 00000
00 0000.., 20000
71224
Ol~Ol
('10
O~OOO
O~OO~
7122!
C 130'2
' on
()20(')O
nO(\o"
71226
01303
31 01001 00017
11227
01304
71230
01305
71231
01'306
01001 00014
71232
,01 ~O7
01410 1. ()OOO
~A5K~ ('-')
71233
Ol.,le
01416 Oll&;'3
STr:JR~ ~J
712~4
01311
11235
01312
15
1.1
21
11
51
Q.l
23
5 ~ seT UP ENT
SET (L:l PA~Af>AF'T~"
PARAMETE R7(rl
EXIT PllJ~ 1
71236
0131~
~6
71237
01314
71 01:300 01153
...0
71240
0131~
I
71241
01316
11 /0000 013''''
55 01!10 1000~
71242
01317
11 '100.00 01303
STORE
2M' - 2 IT"
71243
01~20
~5
STORt. 2(N+l) . 2/'<"
71244
01321
54 20000
7124'5
Ol~?/'
11 '0000 01?-1'
,...,
lO
~
0I
0
0
0-
~
r-
><
c..
'
2-27-56
r
DE T REDUCED .
YES:
X
T -7'
~·OOOO
'Zv491
IOE'T1
RESET
INT.$J~~
011'?
20000 01'305
00000 01416
STORE
lo~TI J- EX JT
Oll~~
Ol~O4
STOR~
~1~O4
00074
OO~74
01305
.N-l
5TORf N-?
STORE
01200 "1!11
()OOO~
'N ' ,•.
~
~TO~~
2 (N + .1) . , I .:r
9-474
CV-165
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S~N
DIEGO CALI"OIllNI~
PAGE
BYI J it If. 11li.
Checked bYI D. B. Parker
REPORT
MODEL
DATE
71246
01323
II Ol153 01313
STORE
71247
01~24
?1 01'13 00014
N
712~O
Cl~2t;
71 01'301
011S~
$TO~~
O11?6
11 '0000
Ol~14
'-NX ~:a.¥
Ol~?7
,~
0140~
011,7
SE'T
71253
01~30
35 01301
Oljl~
STOR£ 2
71254
01331
STORE
71255
01332
11 01311 01116
'-1 01;16 01!~'
71256
71257
11260
01333
'-1
01~11
STO~~
01334
71 00041 011S3
STORE
01~35
35 01314 01317
2NX 2~4- 2N
71261
71262
01336
~5
01302 013,n
01337
2~
01314 01301
712'6~
Ol~40
71264
01341
01342
11 nl.l'- tOnon
11 ()1414 01306
11 01414 01301
71266
71267
01~43
~~
01344
01416 01306
53 01416 01101
71270
01345
55,(l1416
71271
01~46
11 01411 10000
71~7~
01347
5~
01416
71273
01350
11
0141~ 01~21
71274
01351
53 01416 01321
t.. (Tt}·!'~ L (Tt)
STO~E ~(Al1)·2f.a..
71275
Oi~52
11 01410 lOOOC
MASK-~(O )
"""' 71276
...... 71277
01~53
Cj~
01354
55 01416 000'0
11 01410· 10000
11
01~"~
01416 Ol~'2
71251
71252
1126.5
l{j
-.0
'-'
I
~
01~15
(')1~O6
01416 01211
71300
0
0
0-
71301
a1355
0135A
r-
71302
01357
;~
71303
01360
53 01416 n13r7
......
~
c..
2-27-56
+ 1
~
~
(N+l) . ~ ~
2X~:l4 ~ (N
r
1)
~'1f
2(Nt/ Z·
STt")RF.: 2 (N+tJ
STORE 2( N.. t)
"1A~f(~(n
~~~+- 2
'*
~
IN + 1)
. 2'J...
i'+ '- (N .,. U
.
21~
)
L (T2)
S'TORt L (T21
ST~P.~
STO~t
All
OO()~O
0I
0.-011-11
zY 491
"'A5K~
<1
STO~~ l (Atl) X'1 1.a...
STO~£
STOR~ L (InF.TI I
MASK~(OJ
01~"
STORF.
L (A1l'
9-475
CV-165
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO
CALIFORNIA
BYI J. N. Ellis
Checked by: D. B. Parker
PAGE
Cli-oll-12
REPORT
ZM
DATE
u"'J
...0
.......
1"1361
e;~
11305
01362
11 01407 10000
71~!"f
(H
~6'3
~1
01416
71307
01364
01365
01:322 01302
01306 01310
STORE l
71310
71311
71312
01366
01306 01301
01367
21
21
21
21
01307 01320
STORr: L (A12 A21 T~ J
STORE L (A22 T2 A22J
71~1~
01110
1.1
O14'~
71314
71315
01~71
5~
0130:3 01176
01372
53 01301 01204.
71316
01~73
'S~
71317
01374
Ol'-ln
15 01321 01211
71320
0137'5
71 01303 01153
71321
01376
7132'-
(11;77
35 01'11 01211
t;5 01'11 200'~
71323
"1400
16 10000 01177
11324
01401
11 01404
11325
01407
71~26
0140~
11 01407 01324
45 00000 01001
713/.7
01404
4'5
71330
01405
00 01137 00000
71331
'11406
110 OIn01 (1(\000
71332
"1407
00 07777 00000
71333
1'11410
00 Or,OOO 01717
11334
no 00717 "0000
~1.~(~
'. noon
Ol~O~
nortoo
0115~
I
71335
0
0
0-
113:315;
'11413
00 00717 00000
71337
(11414
00 (H'00n 'C007
11340
;;1415
no
.......
t-
><
0...
f\1ASK ~
~T('\~F
(Q J
L {A ll)
~A~t(-7
"r'
fA 12 All A12)
(0)
5ET
REPEAT
COMMANDS
STORE' L ~A 11)
2N;L--7 A
STORE L
(T
SET ENT
JUMP
STORF:
RO'" )
'2"S--
MA~K
JUMP TO EXIT
nl1~4
(')1411
01412
I
2-27-56
()1416 001"'11
71~n4
0-
'-'
h91
MODEL
17 71000 00000
O~I')OO
"()OO~
9-476
CV-166
ANALY"
PREPARED BY
CHECKED BY
CONVAIR
C. J. SWIFT, M. COVHERa .........." ••.lL DnAIIIeS cowouno.
D. SHU MWAY
ON 012-1
PAGE
491
REJIORT NO. ZM
SAN DIEGO
MODEL
July 10,
DATI:
REVISED BY
1956
FOUR PODI'l' LAGRANGE IITERPOLATION POR BIVARIATE fUNCTIONS
OR THEIR ImtIV ATIVES (FIlED POIIT)
I.
IESCRIPTIOH I
If trom one to five quanti tie.
r
D are each functions
ot ;two variables
x and y and are given in the tora of tabled values (not necessarily at
equal distance point.) J then this aubroutine evaluates the.. tunctiona or
one ot the first partial
'!be nearest tabled nluee
uses tallie.
r •
0 and
fto
deri~ti~s
ot
of the .. tunctions by interpolation.
x and 1 are first round.
The subroutine
s1gnity displace_nt in the x and 7 table ••
0 signifies the first tour x .alue. (Xo, Xl, X2, X).
signifies the first four 1 values (Yol
'1'
f •
0
A sixteen point grid ot
12' '').
tunction value. corresponds to the selected wJ.ues ot x'a and 7' ••
'!be Lac,range _thod for interpolation is used to evaluate the tunction.
at the gi'ftD point (x, 7) tor each F
D.
ot
The aubrout1ne is also set up to cOllplte the }:arti&! derivati..s
the tunction.
b.r the use ot control words which
are, specified as
tollows,
.,
04
44400
00000
compute
00
00044
44em
cOlllplte
00
00000
00000
cOJIpUte
~\
J-F.
d-X
- .,
J. F . Il
~~
In order to eliminate scaling probl_., the aubroutiDe computes the
partial derivatiw8
t~.
factor as the function).
an -1ncre_nt-
A
I
(stored at the .... seale
'1'be coder lIIlat di'Y1de this b7 6 ~
stored in cell 00001 vi th the au. scaling
a8
(which 18
the in4ependent variable
in'Yol'Md).
The subroutine uses a normalization process to achieve tull accuracy
wi thout overfiov.
Unless the point x, 1 lies outside the region,
DO
owr-
n.ov 'can occur.
..... ,.,a·.
'1-477
CV-166
ANALftIa
PlltEPARED IIY
.v
CHECKED BY
RtVIS&D
"C 0
N V It. I R
PAGII
REPORT NO.
MODIIL
C. J. SWIP"T, Me COV HER ...wa..........AL 1mI. . . . cCHIPOUno.
IlAN DIEGO
D. SnrTMW''''Y
flU
A
DATI:
eN 112-2
ZM 491
July 10, 1956
It the point x, l' liea wi thin the same rectangle of the X7 grid as
the previously used point, Jalcb
a saving ot over halt in
II.
ot
the cODlpltation Is not repeated with
t_.
SPECD'ICATIORSI
Loca ti-ona and Storage
A--
1.
!be aubroutiDe 18 storediD cella 01000 -
0l24'6
~(2-41). or
(1 6 7)10 celle
2.
I S TeDlpOrar1ea need are cella 0000l to
rxxrn
phia (2 0 )8 owl!.
tor each dependent twlctloza.
3.
Cells to be modifiedl {24,?)e
4. Constanta not
5.
noDe
DKXi1t1edt
Intcm-.t1on atoNd on d:nua tor each . . t ottabl...
.....,....,. aad a:JtU .....
,
Ch)
Para.tera a
1 c.U.
(e)
'l'ellpOrarieal
(24)10 o.lla
(4)
Tables
B
ot
~ iDdepeDdet Y&rlablH
Code, PullDtera Imd
..t ot
j
tro. 1 -to S fUDctlona
x
&D<
Cl.t
ALARM EXIT
EXIT
SET UP EXIT
COMPARE SIGMA
~JI TH ZERO
TEST FOR X
AT CENTER
OF GRID
. TEST FOR
UPPER
LIMIT OF
X TABLE
TEST FOR Y
AT CENTER
OF GRID
TEST FOR
UPPER
LIMIT OF
Y TABLE
TEST FOR
ZERO SIGMA
TEST FOR
ZERO RHO
SIGMA MINUS TltJO
SIGMA PLUS ONE
JUMP TO NEW VALUES
RHO MINUS TWO
RHO PLUS ONE
SET S1:!ITCH AND JUMP
SET UP FOR
DENOM I Nft. TOR
JUMP TO PQ SUBR
O_AR1
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFQRNIA
CV-166
PAGE
ON 012-6
REPORT
ZM 491-11
MODEL
DATE
BIVARIATE
INTERPOtATIO~'
01040
16 01227 01175
01041
16 '01237 01044
01042
01043
16 01240 01646
15 01237 01044
PARTIAL SWITCH TO NUM
ZERO SET TO J AND I
RIJ SET TO ROO
PI SET TO PO
01044
71 30015 30011
QJ
01045
54 20000
01046
11 20000 30054
01047
21 01046 01235
OlO5e
43 01241 01055
01051
21 01()44 01234
01052
42 01242 01044
01053
21 01044 01235
01054
45 00007 01043
01055
37 01055 30000
01056
15 01054 0117'4
01057
45 00000 01060
01060
37 01.167 01155
IJ PLUS ONE'
JUMP TO NUM AFTER LAST IJ
J PLUS ONE
TEST FOR LAST J
I PLUS ONE
INTO LOOP AGAIN
'NUM DEN SW t TCH
SET uP FOR NUM
JUMP TO PQ SUBR
SET PI TO PO
~10el
16 01237 nl066
SET
01062
75 10005 01064
PICK UP
01063
11 01236 00002
01064
15 01240 01067
01065
15 01237 01066
01066
71 30015 30011
01067
73 30054 00007
ZERO TO SUMS
00 TO rJ
SET J
OJ TIMES PI
DIVIDED BY RIJ
01070
11 01246 01076
01071
11 01232 00010
SEi UP N INDEX
01012
15 01067 01074
SET
01013
21 01074 01232
c... 01074
71 30074 00007
01075
54 20000 00047
"1076
35 30002 30002
01077
21 01076 01231
F'N-tJ
TIMES FN-IJ
PLUS
FN SUM
IJK PLUS ONE
...0
...0
.....
I
0"I
0
0
0"
......
t-
><
July 10, 1956
OO.O~7
TIMES
PI
r
9-482
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-166
PAGE
REPORT
MODEL
DATE
BIVI'~qIA.TE
N PLUS ONE
TEST FOR LAST N
RIJ PLUS ONE
arJ PLUS ONE
5 COMPARED TO J
PI PLUS ONE
5 COMPARED TO I
OUT OF INTERPOLATION
SET COORDS\1ITCH
SET FIRST
X ADDRESS
SET FIRST
Y ADDRESS
COMPUTE
ADDRESS
OF
FIRST
RO\'!
21 00010 01232
01101
42 00034 01073
01102
21 01067 01234
01103
21 01066 01234
01104
42 01242 01066
01105
21 01066 01235
01106
42 01243 01065
01107
45 00037 01001
01110
16 01244
01111
15 00035 01133
01112
21
01113
15 00036 01135
01114
21 01135 00033
01115
54 00031 10071
01116
16 01240 01140
111117
15 01107 01121
01120
11 01232 00003
1"1121
15 30('00 1"1140
01122
21 01140 01154
01123
72 10000 00032
01124
35 00033 01140
01125
45 00000 01126
01126
-
011.27
35 00031 01142
35 00031 01144
...0
...0
01130
35 00031 01146
'-'
01131
01132
45 00000 30000
75 30004 01134
..... 01133
11 30000 00044
X S
>< 01134
75 30004 01136
PICK UP
Y$
5\1 ITCH
PICK UP
I
0'
I
8a-
r-
0..
July 10, 1956
I ~!TERP0LAT ION
01100
.....
eN 012-7
ZM 491-11
0113~
011~1
00032
r"l1135
11 300('0 00050
01136
37 01131 01137
C'1137
75 30004
~1141
AND
FIRST
FUNcTION
SET TRANSFERS
FOR
F
PICK UPS
COORD SWITCH
PICK UP
FN S
9-483
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OtEGO. CA",IFORNIA
CV-166
PAGE
REPORT
MODEL
DATE
eN 012-8
ZM 491-11
July 10, 1956
BIVARIATE INTERPOLATION
FN
FUNCTION
01140
11 30000 00054
01141
01142
75 30004 01143
01143
75
01144
11 30000 00104
01145
75 30004 01147
01146
11 30000 00110
D
"'1147
01150
45 0('0"0 (11150
21 01121 01234
ADDRESS
01151
21 00003 01232
01152
42 00034 01121
01153
45 00000 01003
01154
00 00000 00020
01155
11 00024 00007
01156
75 30004 01160
01157
11 00044 00002
01160
37 01225 01170
01161
75 30004 01163
01162
11 00015 00011
01163
11 00025 00007
01164
75 30004 01166
01165
11 00050 00002
01166
37 01225 01170
01167
45 0000(' 30000
01170
11 00005 20000
::;; 01171
36 00002 00010
~ 01172
16 01243 01217
0"-
01173
75 10003 01175
..... 01174
11 30000 00021
01175
75 30003 01212
01176
23 00021 00003
01177
55 00026 00003
-..0
I
I
0
0
0"-
......
><
c..
11 30000 00100
~OOO4
01145
G
R
I
F
PLUS ~NE
REPEAT LOOP
JUMP TO BEGINNING
CONSTANT
W SET TO x
\tIN SET
TO XI
DO INNER LOOP
P S
IN PLACE
~! SET TO Y
\~N SET
iO VJ
JUMP TO INNER LOOP
EXIT SUBR
W3 MINUS \t/O
EQUALS DELTA
PRESET
COMPUTE
\AJ MINUS WN
OR WO MINUS WN
GIVING
FACTORS
CONTROL WORD TO Q
9-484
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
B I VAR I ATE
-..0
-..0
~
I~!T ~ p
01201
PAGE
REPORT
MODEL
DATE
eN 012-9
ZM 491-11
July 10, 1956
DOL AT I () M
"'1~12
TEST FOR PARTIAL
STORE DELTA FOR P,l\RT TAL
COr-1PUTE
SU~J1 OF
PRODUCTS
FOR
PARTIAL f!/\CTOR
AND
NORf-1AL I ZE
JUMP TO STORE
COMPUTE
T-R !PLE
PRODUCT
AND
NORMALIZE
STORE OJ
ROTAT E
°1200
If l~
01201
11 00010 00001
01202
54 00021 00041
01203
73 00010 00,021
01204
54 0'0022 20041
01205
73 00010 1(,,000
01206
71 100('0 00023
01207
7~
01210
72 10000 00023
01211
45 00000 01217
01212
54 00021.. 00041
01213
73 00010 20000
012-14
71 20000 00022
01215
73 00010· 20000
01216
71 20000 00023
01217
73 00010 30015
01220
11 00002 00006
01221
75 30004 01223
01222
11
01223
?1 01217 01235
01224
42 01245 01173
01225
45 00000 3()OOO
\1N
J PLUS ONE
TEST FOR LAST J
EXIT INNER LOOP
01226
0122.7
00 00000 01212
00 00000 01177
C
0
01230
00 00004 4000C
N
01231
00 nOOOl 00001
00 00020 00000
S
00021 00022
()OOO~
CV-166
00002
TH~
~
I
0'
I
(l)
0
0'
~
t-
01232
><: ('11233
0..
1"1('
"""'02
("t~OCHJ
01234
00 00001 0000('
:"1235
00 00000 00001
01236
ao 00000 00*-
"1237
1"1('1
T
A
N
T
S
(,(')"15 00011
9-485
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
S"N OIEGO. C"I.-IFORNI"
CV-166
PAGE
REPORT
eN 012-10
ZM 491-1I
MODEL
DATE
8IVA~tATE
July 10, 1956
TNTEpPOL/\T!I"'\'"
01240
00 1)0054 00054
01241
11 20000 00074
01242
71 00021"00000
0124~
71 00021 (lOO15
~1244
,'"'0 ('\f:\(\on 01132
01245
73 00010 00021
0124t1
35 00002 00002
\...OtJST,!J.NT~.
--
9-486
CV-167
CONVAIR
A .....~
PRaPARaD 8V
D. SlIlJllAI
C. J. SWIFT
CHECKED BY
RIEVISD) r f
& . . - . . . ' _ . . . . . .IL
CN 813-1
PAGK
.,.wacs ' ......11. .
ZM 491
RIEIIO..,. NO.
MODIEL
aAN DIEGO
JUDe 28, 195
DATE
POOR POD! UGIWI1I. DI'1'1WOl..l!lm J(Il 1IlVARUB
!DCt'IOI$ OR mu: z:aam'Tl'fII~ 2(rtDl) :pom)
z'o
SPECIFICATIONS.
SlORAGla ". sub-routine i8 stored in cells 01000 - 01)05 and . , be
BS verking storage 00002 - 00363 is u8ed.
relocated.
Tables ot an,- aize
are DOrall;y on MD.
ntS.
Approx. 0.3 sec. Ilinilml + 0.15 sec. tor each change in 64 poiDt
grid.
IItJI)J). Tbird order interpolation i. ettected b;y the use ot the
4 pOint interpolation torzmla tor 3 'Yarables.
through a
the
II.
~ange
This passes a tunotion
64 pt. cubio array or &a4 ot pointe chosen from the XJS apace ot
table.
IBSCRIPTIOR I
It two quantit1es, '1 and '2, are tunctions ot three variable., x, 1, s
and their 'Y&lues are given in tabular tora (not necessarily at equal
intervals),
d.~i~tift8
tid. subroutine can evaluate '1 ana '2 or one or their partial
as specified by a control word.
The 64 pt. grid i. first
selected so that the interpolated poini (x, y, .) is as close to the center
ot the grid .a possible. 'fbi. grid is then used tor interpolating '1 and
'2 (or apecified partial derivative or same) in parallel.
All tacton in the Lagrangian coetticients are norualised to 'Values
to obviate o'ftrfiov difriculti.s.
~1
It extrapolation is attempted too tar
outside ot the outermost grid, a divide fault vU1 occur.
III.
LOCATION AND STORAGE,
The _in sub-routine i8 coded to operate in cells 01000 - 01265.
oe118 01266 - 01305 tor constant. and eella 00002 - 00363 in IS tor
teaaporar1ee.
It usee
CV-167
CON
ANALYSIS
PREPAR£D BY
CI-!ECKEDBY
V
A
R
PAGE
D. SHUMWAY
C. J. SWIFT
REPORT NO,
CN 013-2
ZM 491
MODEL
REVISED BY
DATE
June 28. 1956
A starter programtollowed by cmrrent grid intor_tioD tor escheat of
two functions lsstored 'in (.333)8 callaot MD.
nov referred to as cells d thru d + 332.
!hiB optional MD location is
Initial set up of d thru d + 16 is
as followss
75
30326
(30000)
1
11
00036
d +
d + 2
75
30327
01002
d + 3
11
d + 4
45
d + 5
00
00000
•
II •
d + 6
00
00000
n
n • no. of values in y tabl_
d+7
00
2J
d + 10
77
77776
d
d
+
d
4
+
5
00035
d
00004 J,
no. ot value. in x table
no. of values in Z table
a
index ot current loea tioD in x table •
"r'f7'n U".
iDttlal1y • 1
--------.-----0
d' + 11
0
d + 12
0 --------0
fJ.
index ot current location in '1 tabl••
initially • 0
"f'. index
or current location in • table
initial1,.
=0
+
13
00
00000
Ax-
d +
14
00
00000
'Y- location ot 1st y
d+ 15
00
00000
d + 16
11
00164
d
AsAt-
location ot 1st x table value
table value
location of 1st z table value
looation
or 1st Fl
table value
Infonationin d + 17 - d + 332 1s generated by the sub-routine.
In order
to II1nW.. acces8 tbe, the tables should be stOred in the following sequence J
1.
All
l[
2.
All
1 values
).
All. values in ascending order
4.
All'l and '2 values alternate, Fl (X1,
'1(X1.
"J'
'Yalue"s :lit a8cending order
in ascending order
z k.l), F2(xi.
yJ,
xk+l), etc.
13' at),
F2(Xi, 1j, Zt), -
with i the major, J the
9-488
GV-167
CON
ANALYSIS
PREPARtD BY
CHECKED BY
D. SHUMWAY
C. J. S'-1FT
~"'N
V'A
R
DllvO
PAGE
ON
REPORT NO.
ZM
013~3
491
MODEL
REVISED BY
DATE
June 28, 19~
intermediate and k the minor ordering subscript.
Coordinates of the point to be interpolated
ANl>
a control word are
entered:
(000)1) • X
(OOO32)
:II
(000)3) •
Y
z
(00034)- Control ,word.
For eomputing '1 and '2' the control word • 00 OOOOOOOOOO
, dF'
dF
For computing A· ~ and d' ~ the control ward - 0""0---0
a())yF,
and
A '. ~
For computing ~. )~,
and
A.
For
C01'lmt1 ting
-r-
~.
d~
Entl7
d Fa,
Y
the control word- ()()()()()444.4
~
the control word •
dZ
to the subroutine isprogr..-ds 37 d+2
4OOOOOOOO444
d.
RESULTS.
(00002)
-'"
~
(in case or partial differentiation)
(00003)
'1
or
(00004)
'2
or
A. ;If,
~,)(
A . ~~~
d)(
.) F,
or
~.~
or
6..
~
or
A .
or
D.. •
)F"
SF;
y
~l
WHERE (00002) bas the scaling of the independent variable
(00003) has the sealing of the '1
t-
....
(00004) bas the scaling of the '2
I
0-
o•
'!be main subroutine is coded in standard torm fro. 01000 and can be
o
....
t-
0-
assembly modified.
~
Subroutine length (including constanta)
()06)8 • (198 }10
ES Temporaries required
()62)8 • (242)10
Total IS working space
(670)8· (440)10
No.
ru .. •a •• -"
ot words tor assembly mod.
(J01)a- (193)10
9-489
CONVAIR -"DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-167
P AGE
REPORT
eN 013-4
ZM 491-11
MODEL
DATE
Ju~e
28, 1956
3 VARIABLE INTERPOLATION
01000
37 16000 76002
0100l
01002
45 00000 30000
01003
11 00041 20000
01004
01005
46 Ol041 01005
11 00031 20000
01006
42 00051 01032
01001
42 00052 01014
01010
33 00036 00017
01011
35 00041 20000
01012
35 01266 20000
01013
01014
46 01041 01014
11 00032 20000
01015
42 00055 01034
01016
01011
42 00056 0102'
3~ 00037 00017
01020
35 00042 20000
01021
35 01266 20000
01022
01023
46 -01044 0102'
11 00033 200CO
01024
42 00061 01036
01025
42 00062 01077
01026
01027
11 0004~ 20000
32 01266 00001
...0
-
01030
36 00040 20000
I
01031
46 01047 01017
0
0
01032
11 00041 20000
01033
47 01040 01014
01034
><
c..
01035
11 00042 20000
47 01043 01023
01036
01037
11 00043 20000
47 01046 01077
t-
.....
a-I
a.....
t--
16 00035 01001
ALARM EXIT
EXIT
SET UP EXIT
COMPARE SIGMA
WITH ZERO
TEST FOR X
AT CENTER
OF· GRID
TEST FOR
UPPER
LIMIT OF
X TABLE
TEST FOR Y
AT CENTER
OF GRIO
TEST FOR
UPPER
LIMIT OF
Y TABLE
TEST FOR l
AT CENTER
OF GRID
TEST FOR
UPPER
LIMIT OF
Z TA6lE
TEST FOR
ZERO SIGMA
TEST FOR
ZERO RHO
TEST FOR
ZERO TAU
9-490
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-167
PAGE
REPORT
eN 013-5
2M 491-11
MODEL
DATE
June 28, 1956
3 VARIABLE INTERPOLATION
01040
01041
01042
01043
01044
01045
01046
01047
01050
01051
01052
01053
01054
01055
01056
01057
01060
01061
01062
01063
01064
01065
01066
01067
t-
...0
P""'I
01070
'-'
01071
0
01072
0
aP""'I
t- 01073
><
01074
0..
01075
I
aI
01076
01077
23
21
45
23
21
45
23
21
37
16
15
37
16
16
16
15
71
54
11
16
71
54
11
21
43
21
42
21
42
21
45
37
00041
00041
00000
00042
00042
00000
00043
00043
01077
01267
01231
01~03
01304
01050
01303
01304
01050
01303
01304
01137
01235
01234
01227 01210
01275
01270
01271
01270
30000
20000
20000
01272
10000
20000
20000
01066
01235
01060
01066
01060
30000
00047
10000
01064
30000
00047
30000
01305
01273 01077
01064 01305
01274 01064
01060 01304
01275 01060
01060 01305
00000 01057
01077 30000
SIGMA MINUS TWO
SIGMA PLUS ONE
JUMP TO NEW VALUES
RHO MINUS TWO
RHO PLUS ONE
JUMP TO NEW VALUES
TAU MINUS TWO
TAU PLUS ONE
SET SWITCH AND JUMP
SET UP FOR
DENOMINATOR
JUMP TO PQS SUBR
PARTIAL SWITCH TO NUM
PI SET TO PO
RIJK SET TO ROOO
QJ SET TO QO
QJ
TIMES
PI
SK SET TO SO
QJPI TIMES
SK EQUALS
RIJK
IJK
PLUS ONE
JUMP TO NUM AFTER I.AST I JK
K PLUS ONE
TEST FOR LAST K
J PLUS ONE
TEST FOR LAST J
I PLUS ONE
INTO lOOP AGAIN
HUM-DEN SWITCH
9-491
CONVAiR - DIVISION OF GENERAL DYNAMiCS CORP.
SAN DIEGO. CALIFORNIA
CV-167
PAGE
eN 013-6
REPORT
MODEL..
ZM 491-11
DATE
June 28, 1956
3 VARIABLE INtERPOLATION
01100
01101
01102
01103
01104
01105
01106
01107
01110
01111
01112
01113
()1114
01115
01116
01117
01120
01121
01122
01123
0:124
.t...0
.....
I
0"I
80-
.....
t-
><
a..
01125
01126
01121
01130
01131
01132
01133
01134
01135
01136
01137
15
37
16
23
11
16
15
15
71
01272 01234
012'27 01207
01270 01110
00003 20000
20000 00004
01273 01116
01271 01115
01270 01110
30000 30000
54 20000 0004"6
11 20000 00005
16 01272 01114
71 00005 30000
l ' JOO()O 10000
71 10000 30000
54 20000 00050
35 00003 00003
21 Oll16 01305
11 20000. 01123
30 30000 30000 .
54 20000 00050
35 00004 00004
21 01116 01305
43 01276 01001
21 01115 01304
21 01114 01305
42 01217 01114
21 01110 01304
42 01275 01110
21 01110 01305
45 00000 01107
16 01300 01162
SET UP FOR HUM
JUMP TO PQS SUBR
SET PI TO PO
ZERO TO
SUM CELLS'
SET FI-IJK TO FI-oOO
SET RIJK TO RooO
SET QJ TO QO
QJ
TIMES
PI
SET SK TO SO
QJPI TIMES SK
DIVIDE BY Rt'JK
TIMES F1-t JK
PLUS
Fl SUM
l-IJK PLUS ONE
TO GIVE 2-tJK
TIMES F2-IJK
PLUS
F2 SUM
NEXT Fl
EXIT AFTER LAST F
I JK PLUS ONE
K PLUS ONE
TEST FOR LAST K
J PLUS ONE
TEST FOR LAST J
I PLUS ONE
INTO LOOP AGAIN
SET COORD SWITCH
9-492
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OIEGO, CAl.IFORNIA
CV-167
PAGE
REPORT
MODEL
DATE
eN 013-7
ZM 491-11
June 28,
3 VARIABLE INTERPOLATION
01140
15 00044 01164
01141
01142
01143
21
15
21
15
01144
01145
01146
01147
01150
01151
01152
01153
01154
01155
01156
01157
01160
...0
f"""'!
-.;...
,
,
0-
8
0-
f"""'!
r-
:><:
0..
0004'1
01166
00042
01170
01170 00043'
01266 00006
00047 01173
00040 20Q70
20000 00042
21
11
11
54
7135 00043
71 10000
71 20000
32 00010
35 01173
35 00040
35 00040
00010
00037
00041
00001
0117~
01175
01177
X ADDRESS
SET FIRST
y ADDRESS
SET FIRST
Z ADDRESS
SET LAVER INDEX
COMPUTE
ADDRESS OF
' FIRST FUNCTION
ON
FIRST
YZ
LAYER
FOR FIRST
SECOND
THIRD
FOURTH ROW
COORD SWITCH
01163
01164
01165
35 00040 01201
45 00000 30000
75 30004 01165
11 30000 00050
75 30004 01167
PICK UP
X COORD
PICK UP
01166
01167
11 30000 00054
75 30004 01171
V COORD
PICK UP
01170
01111
01172
01173
01174
11 30000 00060
37 01162 01172
75 30010 01174
30 30000 30000
75 30010 01176
30 30000 30000
75 30010 01200
30 30000 30000
Z COORD
SET COORD SWITCH
PICK UP
01161
01162
r-
01164
00045,
01166
00046
SET FIRST
01175
01176
01177
FIRST ROW
PICK UP
SECOND RO\oJ
PICK UP
THIRD ROW
9--493
1956
CV-167
CONVAIR - D!V!SION OF GENERAL DYNAMICS COlP.
SAN DIEGO. CALIFORNIA
'
PAGE
eN 013-8
REPORT
ZM 491-II
MODEL
DATE
June 28, 1956
3 VARIABLE INTERPOLATION
01200
01201
012,02
75 ~OO10 01202
30 30000 30000
23 00006 01304
01203
42 01304 01003
012Q4
31 10000 00013
01205
01206
32 01305 00005
45 00000 01156
01207
11 00031 00010
0121P
75 30004 01212
01'211
11
01212
37 01265 01230
75 30004 01215
01213
ooo~o
("\0003
PICK UP
,FOU,R TH ROW
TEST FOR
' LAST LAVER
SPACING TO
NEXT LAYER
INTO LOOP· AGAIN
W SET,TO X
WN SeT TO
XI
JUMP TO INN£R, "LOOP
PI IN
PLACE
W $ET 10 y
WN- SET
01215
11 00022 00012
11 00032 00010
01216
75 30004 01220
01217
01220
11 00054 00003
37 01265 01230
JUMP TO
01221
75 30004 01223
QJ
01222
11 00022 00016
0122~
W SET TO Z
WN SET
01225
11 00033 00010
75 30004 01226
11 00060 00003
01226
01227
37 01265 01230
45 00000 30000
01230
01232
01233
11 00006 20000
36 00003 00011
16 01272 01257
75 10003 01235
~ 01234
11 30000 00026
01235
75 30003 30000
01236
01237
23 00026 00004
55 00034 00003
JUMP TO INNER LOOP
EXIT PQS SUB
W3 MINUS WO
EQUALS f>ELTA
SET SK TO S~
COMPUTE
W MINUS WN
OR WO MINUS WN
GIVING ~ACTORS
CONTROL WORD TO Q
01214
01224
........
t-
-'"
r-4
I
0"I
0
0
0"-
r-4
t-
01231
TO
y~
INNER LOOP
IN
PLACE
TO ZK
9-494
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-167
P AGE
REPORT
eN 013-9
ZM 491-1I
MODEL
DATE
June 28, 1956
3 VARIABLE INTERPOLATION
t-
TEST WHETHER PARTIAL
STORE DELTA FOR PARTIAL
COMPUTE
SUM OF
PRODUCTS
FOR
PARTIAL FACTOR
AND
NORMALIZE
JUMP TO STORE
COMPUTE
TRIPLE
PRODUCT
AND
NORMALIZE
STORE SK
ROTAT E
THE
01240
44 01241 01252
01241
11 00011 00002
01242
01243
01244
54 00026 00041
73 00011 00026
54 00027 20041
01245
73 00011 10000
01246
71 10000 00030
01247
72 00026 00027
01250
72 10000 00030
01251
45 00000 01257
01252
54 00026 00041
01253
73 00011 10000
01254
01255
71 10000 00027
73 00011 10000
01256
71 10000 00030
01257
01260
73 00011 30000
11 00003 00007
01261
75 30004 01263
01262
11 00004 00003
01263
21 01257 01305
01264
42 01302 01233
01265
45 00000 30000
K PLUS ONE
TEST FOR LAST K
EXIT INNER LOOP
01266
00 00004 40000
C
01267
00 00000 01252
01270
00 00016 00012
01271
00 00064 00064
01272
00 00010 00022
01273
11 20000 00164
01274
71 10000 00026
01275
71 00021 01237
01276
71 10000 00364
01277
71 00005 90026
vJN
0
-.0
.-I
'-'
I
CJ'
I
0
0
CJ'
N
S
T
.-I
t-
><
0...
A
N
T
S
9-495
CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO. CALIFORNIA
CV-167
PAGE
CK 013-10
REPORT
MODEL
ZI~I
DATE
June 78, 1956
491-I1
3 VARIABLE INTERPOLATION
01300
01301
01302
00 00000 01163
11 00164 00164
73 00011 00026
01303
00 00002 00000
01304
00 00001 00000
01305
00 00000 00 *1
t-
-.0
--ar-!
I·
t
oo
ar-!
t-
><
0..
9-496
9:23
ORGAN12..ATIOI~ OF Dlr-PARDm:If.l'
66r_...],0
..
__ ~ .. """"'~J':I;~~Il""""'~"I""'I!':.'W'';~''rUP3rTJ.~..
I.
~
GENERAL OBJECTIVES
A.
The ultimate a..'tm is to estabJ.1.sh ])apQrt-ment (56.,..10 o.s Ol\() of the lea(JJng
computing and da.ta. reduotion centers in th:ts coUntry 0 An a CO~lB9qucnc:e,
the Missile Syntems Division "rill beNe at its d:Lopooal an important and
prot!to.ble asset in mectiT18 :i.ts oblisatiOllG, in, L'1creasing its reputetioo
and. in attrac.tl.tl8 bl.ls1.ltess. Furthormore I the rnaltheed Ai.rcx-a.f·t, Corrorat1on
will be in an even bet'~or po::d.tlon t, :meet ita eo.mm:ttments, to increase
its prod,,,at:f.y1:ty, to enhance its roputat1on and to better ita c(YJIlletltive
positiooo
B.
1.
Department
of it.s
66.. ,10
ohaJ~ perr·)l~m all Mtt.;j) volek faLling ~1.tb1Jl the E;Copft
I t l.,:,LU utlflertake the troiru..ng of 1m pr.!7.'3cIlnel
in tJ,e appliC3'.t:t.OD of e.nQ1y t.:tca1. und numericaJ. lr.ethoda to the:lr
individueJ. probJ~erruJ.
20
n.c;:t:tvit.i~s~
Depa."t't;mOtt.t 66,,·1() 'tv:i~\ coai~i',~ue
to absorb the tP..lCCeGB (J:£ OOZ.!?11ti:nC end
data. redu.a..?;lo~> loads g~.1(31~9,tc~d by oth.'Sr l...,ockheed divloiona. Ito
Appllod. ~!athentt6ti(;fJ S'i;at':4? 'W'.1.1l b~ avtdlable .~ li.elp solve dif'fi(n.u.t
cOltpt.\tational pl"O\'lemn ~ -;;:0· ~l(-+vt'''flop ne".( simu.lo.t10P- l'ile"l'thods, to e!';~ltta.t(~
eomp1.\'i;ing i?l"O{".e(lUl~CS 'Used. i!l :ll'!UOunt:ttlg Qn.d to j. dvp.at:tgn,i.e 'l~be' faaG1 ...
bi11t.y ,of :r:u~ther nroc:ooydzQ.t:;.on of I..ocltbeed lluH.il1eas prol')l~av The
A:ppl:l~..d ri.~theni.e3~ieG Sta.f~:r or DepartU}~nt 66-..10 ,dJ~ be a. nOUXl!C (Jf
aatb€:mntiCf.'tl c~nsuJ..tant f;!,(l"!Ji(,~e j.'"ead:tly ave,ilo,ble to the (:'ntixe (!orpora."'"
t1oo.
3v The
E"~xtra. c·a!w:.eity of Dc:&artri£lli::: 66-10 requi:t'ed tel" pealt loods ,,1.11 be
appl:J.ed to outs!.de bUS:f.lV~OG.. '£hia pol'.<:y ~,!1J. avoi d l~G'~-:Y r: ~'Innoicn
and nu.nimi:;&e ovcrt;me follotdng the a1·ro.rd or lm"ge CC'll'l1;I'tlC:(j~
outs1do
bua1b.eSt3 Si.~rv€·s to GlUootb. Oll1:; j;'"l.uct"UE~t1ons in :urtemal d(~:T'~
DepaJ;..tment 66 u lO, to (1.ivQ:;7·sify If£D fle;·tiviiliea trott tc ua.1n~ p" ,!~.'l1; for
the eomp~.n;.y 0
;; c.
C\J
-
~he reput,at1ctl or DepalJtmen:li 66....)"O,{,ylll be based on '-to l>ertOl'ill:'1lJCe and
not on its alz·e; Ol~ jurisQ.!et:i.on. 'lb bavo satisfied. clwtonta"u iz (l1.n of
tile moat ~rtallt goals tOl-- De.pti.l..tli'!en~ G6....10.~
I
~ D.
o
o
0"-
r-f
t-
><
0..
For 1ts 6~rivol,l, Depal'tmant 66 ....10 rau">t be able 'i;o recrui to the sl)le:rt $
best prepared and most decU~J.tE:d young men aud 'WOIOOn into 1tb Bel:-vice ~
To attrat."t and hold 81.\ch pEllll.ll.e, the pr'1Diae of e career or 11vellhcod
or of eeono.m:I.c 3uncess 13 not (.lnougho The DeptIr·tment must 0.100 give t.hem.
esprit. de
COl"ps.
9-497
9:23
Page i\:o
II.
(JDrnIAL ft'IIr!IPL'lS
ANI)
OPwnm PROCKDtlft'!,q
A.
l~od;T ~ld bMre ouJ~ ODe supervisor (e.xeept tecba1¢sJ. eupervtn1<:
0...
..
9-500
PX
IV.
71900-9-(9:~3)
Pa.ge Five
OltG.\..lIJ!ZJ:m:Ol'J Clm1t1'
----_.>,
I
I
I
~t101lS
'I
I
Section
Ane.lys1s &
Applied
Jf&th
S'bff
ProgrGmriling
j
,._---
Data.
0
'Section
Seotion
t
"
I
{
I Sys~'-',I
;~t
~
,
Trajectories
I
----
I
Linear
I
..0
I
CJ1
o
.....
Problems
'
Na.ch1ne
Data
Operation
Dandling
Pa.lo Alto
/1
. ,. --
--.~---
"I, ::!:on.
---,
t
!
•
Van Buys
Desk
Computers
,....------Automatic t
Reports
and
Ana.lysis
Data
!leduct1on
Data
I
Conversion ,
I
Data
Systems
Development
..
[\,j
~
9:23
rage Sis
v.
A. 'Ihe bM4 of the
~t
aercd.aes scmaNl ...,nt ltrat1'ft!1 8D4 techrd.oa1
~.
, B.
1. 'lbt AD&'Ip18 aa4 P".tOQt8IDilDa BecttOll 18 NQ0D8lble tor 'the JiIrOII"'W"OC
aDd eoa1nS ot·all. probl.e. solved em. the Cblj;art.at'. general. plI'lM)B8
41&1ta1 8114 aualOS
COJI,paters. Ia eW:t1aD., l ' 18 ft8JCD81ble ~ the
8Ol.ut1ca of aU COl!I~utat1crUU. problea _eDt to ~t 66-10 with
the ezaept1cG ,of date. Nduot1on prob1ema.
a.
&0
t'b.e B1&tems Developa!ct G~ 1s respcmalb1e tor eettiDs up IID4
1mproviDg cod11Je; procedures aud tor 1m.Proving the OJ.ler8t1on or ....
ADalye 1.8 and h-cgamadns Sect1oa. It does DOt tak.e part 18 tbI
solution or oui;s1de pl'Oblems sent to De,partment 66-10.
b.
Through the Syat.ems Developaent Group, the .Aaal.;ys18 aDd P.roglaadtns
Sectloa 1s also responsible tor keep1Dg up to
0
0"r.-f
r-
~
a..
e. CoOgerate 1B tlv~ acquisition,. operat11)D.' 8rl4 -.1nten3DCO ot tm¥
8Daloa-to-d1g1"UYo and 'd:lg1:tal-to-analog conversion equ1pment when
such equ1pnent ta intended tor use With the aDalog OOJIWuter.
9~502
9:23
Pag(!
c.
Seven
,.
Promising members at the prog:rsQrnj ng groups should have an opporturdty
to contribute both to the m>rk of' the Bystema Developnent Group aDd to
the DIl:theDatical and numerical. ana.\yai8 ot problems which voul4
usually be C&tTled out by m.e!ljl)~9 of the AppUed tethematlcs Stan'.
Each group leader should mo.1nta1n close lUdson with the Applied
M!\theDi.tles Sta:rt and the Sys-t<:IDa Devel.opnent Group and, wenever
possible, contribute to either one ot theso two aci~lv1tles.
~
Data Section 1a respon81ble
tor the
tol.l.ow1Dg functions:
1. '!he processing ot data as requested.
2.
Participation in instrumentation checkout operatl00s and
of tre t1Dal laborato.l7 caUbrat1cms.
eve~U&tlon
3. Production
of a ~17 z,r,;;port deacrlbiDg.the resuts of systerra
c.beckaut nma eoDthlct.ed prlar to shipuent of a veh1cl.e to the test
4. fite publication of
fA,
alte.
poet fllp.l1t conference ft quick look" night elata
CD
'rexJOrt and condu.ct:l.ng the post..rught conference, os well as ed.tt1Dg
minutes of the post-flight 6'01.d"erence I 1Dclud1ng S1JIID1\l'Y and ccucluslou
drawn.
5.
~
6.
~s
publie.atlon or the f1ritll night test datA report (when require/,
covering a.ll date. reducedc
at telemeter performmee to keep iDstrurJJeD.tation personnel
informed of the per.romsn~e ot their equipment I incl\Xd.1ng a.cc.'\J.l"8C1'
determinations 0
f(.~ tuture da.ta aequisition requirements to ,all
cnstaners reEFINITE INTEGRAL EVALUATION
CPo-1
CPo-2
CRI-1
CRl-2
CVF-o
OEM-O
D£M-l
01E-0
01E-1
01E-2
11-25-55
11-25-5'5
EGN-O
05-01-56
___ EXP-2
~ EXP-3
..
0"
-55
-55
07-26-55
FPP-O
11-15 ..... 55
08-10-55
EIGENVECTORS. VALUES OF REAL S-YMMETRIC MATRICES
FIXED POINT EXPONENTIAL. ROUttNE
FLOATING POINt EXPONENTIAL ROUTINE
FLOATING POINT PACKAGE SNAP. SNIP AND TRACE
THE FERRANTI INPUT ROUTINE
05-25-56
12-09-55
10-03-5.5
SIMPLIFIED FERRANTI INPUT FOR BOOTstRAP
r- HTo-O
:><
01-25-55
DECIMAL OUTPUT ROUTINE FOR FLEXOWRITER AND PUNCH
INT-l
10-10-55
INTERPOLAtION WITH UNEQUAL INCREMENTS IN ARGUMENT
LOG-1
LOG-2
11-22-55
08-10-55
FIXED POINt NATURAL LOGARITHM
FLOATING POINT NATURAL LOGARITHM ROUTINE
'j'
Cf FRI-O
8
FRI-l
0'
,.....j
a..
9-506
9:24
PAGE 2 OF 2
REVISED 06-01-56
MDP-O
MDP-l
MDP-2
MDP-3
MOP-4
MII-O
MTI-O
12-09-55
12-09-55
12-09-55
12-09-55
05-01-56
05-01-56
11-30-55
THE FLEXOWRITER MEMORY DUMP, REVISED
THE BIOCTAL MEMORY DUMP, REVISED
THE OCTAL CARD DUMP
CHANGED WORD POST MORTEM
OCTAL CARD DUMP
MANUAL INSPECTION AND INSERTION
LINEAR MATRIX EQUATION SOLVER
NRT-O
NUI-3
NUI-4
12-01-55
05-01-56
05-10-56
NTH ROOT ROUTINE
NUMERICAL INTEGRATION BY THE GILL METHOD
FLOATING POINT GILL METHOD
RAN-O
RPH-O
05-20-56
05-23-56
NORMALLY DISTRIBUTED PSEUDO RANDOM
COLUMN HEADING ROUTINE
SAM-O
SIN-O
SIN-l
SIN-2
SIN-3
SIN-4
SNI-l
SNI-2
SQR-O
5TT-0
08-09-55
05-01-56
05-01-56
05-01-56
08-10-55
05-15-56
09-12-55
09-12-55
05-01-56
12-09-55
AUTOMATIC SAMPLER
CENTRAL EXCHANGE SINE-COSINE RoutINE
POLY NOM tAL MUL TI PL Y SINE-COS I NE ROUleI NE
SMALL ANGLE SINE-COSINE ROUTINE
FLOATING POINT SINE-COSINE ROUTINE
FLOATING POINT SINE-COSINE
ARCSINE-ARCOSINE ROUTINE
FLOATING POINT ARCSINE-ARCOSINE ROUTINE
SQUARE ROOT ROUTINE
STORAGE TO MAGNETIC TAPE TRANSFER
TNI-O
05-01-56
08-10-55
12-09-55'
ARCTANGENT ROUTtNE
FLOATING POINT ARCTANGENt ROUTINE
MAGNETiC TAPE TO STORAGE TRANSFER
10-03-55
08-23-55
UTILITY ROUTINE TRANSFER - MAGNETIC TAPE TO DRUM
UTILITY ROUTINE TRANSFER - DRUM TO MAGNETIC TAPE
TNI-l
T5T-0
URT-l
URT-3
NUMB~RS
9-507
9:25
Pg. 1 of 3
06/01/56
CUMULATIVE ERRATA
Programming and Operating Conven-ciolls
Paragraphs 6, 8, and 9 should be deleted.
CMP-O 10/
/55
Pages 8A and 10 dated '4/18/56 should be included.
Page 8 - delete from "Subroutines" to end of page.
Page
9 - delete first three lines.
Page 9, paragraph two i and page 10, paragraph numbered 4 - should
read "prints 'CMP-O,1t and not fTprints 'check sum fails
CVF-O
I II.
11/14/55
Page 5, line 12 from the bottom should read lin
(50000b ) n and not
"n + 1 = (50000b)".
DIE -07/26/55
Page 4, last line should read:
EGN-O
b =
(~).n'2-4
and not b =
(~).n'24
5/1/56
Page 8, line 14 should start "~ the ERA paper tape reader) ...•..
11
Page 16 line 7 should start "if n ~38 , .•••.
EXP-3
8/10/55
Page 1, drum assignment should read 1163766 b through 64044 b."
l()
C"J
~ YPF-O
I
5/25/56
0'
I
o
o
Should include SNAP page 6 dated 5/10/56.
0'
......
t-
><
0..
SNAP, page 5,/last sentence should read: "If it is desired to read
in less than four numbers per card, then the associated address field of the
decimal number to be ignored must be left blank".
SNAP, page 6, first line below table "should start "If the exponent or
the mantissa ..•.. "
9-508
9:25
Pg. 2 of 3
06/01/56
SNAP Smapler trace, page 1, the last sentence of paragraph b should be
replaced by:
"Restoring the library from magnetic tape loads an all zero word
into cell 71777b.
If this word is not changed, a complete trace of all SNAP
commands is automatically performed.
1I
FRI-O 12/9/55
Page 4, following paragraph numbered 5, add "Note:
s~th
level punch in the second of two consecutive frames having seventh
level punches the stop is bypassed.
continues.
The check sum is cleared and the reading
This will still be an illegal combination which will halt an ERA
photo -electric reader
HTO-O
If there is a
II •
7/25/55
Page 1, drum assignment should read "62504 b through 63037 b
MDP-2
ll
•
12/9/55
Page .. 1, opposite TYPE add Itobsolete.
available on symbolic cards"
Page 2, first sentence below the list of card column assignments
should read:
tlADy
card is omitted if each of the four words to be punched
consists of 36 zeros or 36 ones, and in this event the next card produced carries
a punch in the l2 row of column 9".
Page 2, line 12, reference to MDP-2 should read MDP-4.
Page 2, line 14, should start !leach card contains s.ix cards!!.
9/12/55
Page 2, under programming instructions add:
tiThe ranges of the
reaults are the principal values, defined as follows:
- 1(/2 ~arcsine &£ '1(/2
o'=arcosine
&b rc "
9-509
9:25
Pg. 3 of 3
06/01/56
$1 ..2
9/12/55
Page 2, under programming instructions add:
"The ranges of the results
are the principal values, defined as follows:
- 1(/2 ~arcsine g.Ln /2
O~arcosine g.~lt "
TNI-l 8/10/55
Page 2, under programming instructiQns add:
tiThe range of the result
is the principal value, defined as follows:
_ 3(/2~rctangent x.L'1(/2
UBT-l
11
10/3/55
Page 2 following paragraph six add liES is cleared".
I.()
C"Il
-0'
I
0'
o•
o
0"-
.....
r-
><
c..
9-510
9:25
PSEUDO-RANDOM NUMBER GENERATOR SUBROUTINE
by - Harold Dahlbeck
The basic method used- in this subroutine was described by D. H~- Lehmer in
The Annals of the Computation Laboratory of Harvard University, Volume XXVI,
Proceedings of a Second Symposium of Large-Scale Digital Calculating Machinery
Harvard University Press, Cambridge, Yassachusetts, 1951.
The method itself requires the following simple form to be used as the iteration
formula:
Xi + 1 =
eXi
(mod p)
i
= 1, 2, 3, - - -
Although this method is considered to be quite optimal in guaranteeing both
randomness and greatest periodicity of the Xi, there are considerable problems
involved in the obtaining of c and p subject to the following conditions:
maximum
1.
2.
P should be the largest prime number which can be contained in a register.
c must be of the form Rl when R is required to be a primi ti ve root of p
and l has to be relatively prime to p-1. In addition c should be as large
as possible.
The following twdnumbers satisfy the above conditions:
p
= 235
- 31 = 34, 359, 738, 337
c = 513 = 1, 220, 703, 125
A subroutine for generating the Xi is given below. The periodicity of the Xi
will be p - 1 = 232 - 32 34, 359, 738, 336. Any positive number may be used
as a starting-point for this series.
=
-
I..(')
(\J
1l0J Subroutine for Pseudo-Random Numbers
0"'-'
~01000
601001
~ 01002
....
01777
01775
20000
01776
10000
01777
A mod p
37
01
00
77777
10604
00000
77741
71625
00001
35 - 31
213
5
Ri
t-
><:
~
01775
01776
01777
513 Rl
71
73
11
1
A
)
Rl
(51~.R1) mod p---) A
9-511
9:26
A Linear Pro,ramming Routine for the 1103 Computer
General Remarks,
A working draft ot a linear progr8.DJDJ1ng routine for the llO) is now in
operation. The routine finds a basic set of values of the variables in a
linear form, which will max1 mj ze or minimize the value of that llne~ form,
(hereafter called "profit function"), subject to a set of linear reetrainte.
bee restraints fDa:y be equations or inequalities, and are acceptable with
or without slack variables. Rovner, it slack varlablee are included, they
ehould be clearly labelled aesuchJ if they are omitted, the sense ot the
inequali ties must be indicated.
The method followed is the Alternate Algorithm of' the Revised Simplex
Method ot Imltzig, as deecribed ,in Rand Corporation manual RM-1268, with
certain modifications. Since zero suppression is ueed throughout, the size
of the problem which can be handled by this program will depend upon the
number ot zeros in the original matrix of coefficients and in the columns
etored tor the inverse matrix in product form. In an:y case, the number of
restraint. cannot exceed 106, the number of variables, including slack
variables, must be le68 than 258, and the product of the two dimensions should
not exceed about 15,000.
The time required tor solving a partiCular system depends upon the size
ot the matrix, the number of non-zero elements, and the number of iterativa
cycle. performed in reaching a solution. In general, the time will range from
a rew minutes tor a emall aystem to about 2t hours for the largest system
ao1yable by thia program. High speed has been achieved by confining the CYClic
program and vector storage to the rapid-access memory and the magnetic drum
(helloe the limitation on size ot the systea). Magnetio tape units supply
progra.me tor input, computation, and output, and receive intermittent dumps
ot the entire oontents of rapid-aoce6s storage and drum as protection against
l1Jlt.....n interruption, and to prO'Yide tor output ot re8Ults ot previous cycles.
The program mal ot course be moditied to handle larger systeme by using magnetic
tape ...torage during cyclic computationaJ however, th18 will considerably increase
production time on the 110.3. Some actual computation times are as tollows.
lumber ot Variables
Including Slack
Bumber ot
Computation
lteratlone
Time
24
49
21
33
27
37
59
88
lumber of
"'''-1nt.
26
63
31
59
2
minutes
.3.3
"
4
1l.7
ft
•
Total Time, Incl.
Input and Output
4.5 Minutes
n
6.2
6.5
15.6
"
"
The present program calls tor input data on punched paper tape in Flexowr1ter
oode. The matrix is read in by rowe just ae they appear on the matrix sheet, with
the profit function as the tirst row. A detailed description of input format
18 attached. While the paper tape is being read into the computer, the input program
convert. the decimal numbers to binary, as~1gns a slack variable ot appropriate sign
to eaoh inequat10n and ecales the elements of each row according to the numerically
largest coefficient in that row. The ll'I8trix is then transposed, and each column is
9-512
9:26
-2a88igned a scaling based on the numerically largest element in that column.
The program then packs each oolumn vector by retaining only its non-zero
elements, in sequence, preceded b,y three code-words displaying the pattern ot
zero and 'non-zero element. in the column. Packed oolumna are then stored in
sequence on the drum, and a directory is prepared which records the starting
addres8 and ecal1ng or each column vector.
Artificial variables are assumed where needed, but their oolumns are not
storea, and should not be included in the matrix. The input program prepares
the redundant equation which serves to eliminate the artificial variables during
the first phase ot computation.
Cgmwktigpa
Ploating vector arithmetic is used for addition and soalar multiplication
ot two vectors and for multiplying a vector b.Y a constant. This greatly reduces
computation time as oompared with tloating point arithmetic, yet avoids the
overflow problems and 10S8 of significance which arise in fixed point arithmetic.
Significance retained in final answers will depend, of course, upon the amount
of computation necessary to reach the anevere ; results to date have been
exoellent, with all answers correct to at least ri~ significant digits.
The computation proceeds through two phases I Phase I eliminates artificial
variables b7 maxi m:i zing the artificial variable in the redundant equation. When
feasible solutions exist, ccmputation then proceeds into phase II, which maximizes
(or minimizes) the profit !unction itself. Detaileof the method may be found in
the Rand Corporation literature.
OutPUts
The type or output will vary with the nature ot the conolusions reached.
In most oases, an optimum feasible solution will result; the values and identifying
indicee ot the basic variables will be printed, as will the shadow prices, the
baok solution, and the quantities labelled delta-sub-J in the',notation otRM-1268.
.,0
C\l
~
'-'
d-
The inverse matrix i tselt is stored in the convenient product form. Thus, at
the end of the computational program, the inverse matrix as it lNould appear at the
end ot AD.'t apecitied cycle is still available. Except for the inverse matrix, re5Ults
ot previoua cycles are not retained. If these are desired, the program provides for
output after specified cycles. It is recommended that output be kept to a reasonable
minimum, to r;ave computer time.
I
o
o
~
~
t-
In caee an infinite solution is indicated, the output program will identify at
least one varia.ble which is unbounded.
><:
It the original Bystem contains inoompatible restraints, computation will halt
0...
when this is recognized through an unfeasible maximum or minimum. At lesGt one
restraint will be identified b.1 the presence or a non-zero artificial variable as
being inconsistent with others in the system.
In case of linear dependence among restraints, the program will proceed exactly
,
a8
in the case of an optimum feasible solution, except that one or more artificial
variables will be listed in the final basic solution, with assigned va1uP!l of zero.
Theee serve to identity redundant restraints which may then be deleted by the anal~E,t,
9-513
9:26
-3though they do no harm other than to increase computation time.
ProgrQPP&"
Comment••
The linear program described above i . presented as a working draft, rather
than as a compl.ted product. It will be expanded and adapted to the needs of
customere ae we become more f'smiliar with these needs. As the result of' experience
gained in cheoking out and using the program, certain possibilities for improvement
have become evident and will be incorporated in the program as soon as possible.
One .pecific. change contemplated in the present 1103 version is the add! tion of
th.·tacil1ty tor finding alternate solutions b~ imposing increments upon specified
quantities and continuing the computational cyole. This is recognized 85 highly
desirable and will be added as .oon a. possible.
Suggestione a8 to other service' which milht be inoorporated in the linear
program rill be 8J.:preciated. ·We will of course be happy to ansver any questions·
which .aight sri se concerning the program.
PM
or
the Program on the llOlA I
The 110) program ia available in a slightly altered form for use on the llO)A.
The only changes are in the addressing ot the accumulator and quotient regi:::ter, and in
the referencea to magnetic tap.; only lO24 vords of core memory are ueed. Thus, running
time on the nOlA with this program will be approximately the same as on the nO).
Thi8 time is governed to a large extent b.y the number of' references to the I~et1e
drum. At present, the entire c~cl1c program, the floating vector subroutines, and the
directory which Uete vector 8torage locations, are kept on the drum beec;.u~e of llmi'ted
epace in the 1024 word rapid-access storage ot the 1103. Portions of the program are
then transterred from the drum to the core storage as needed.
A complete rewriting ot the Linear Programming Routine tor the 1103A has been
initiated. Since the 4096-vord core memory provides space for everything except the
vectors themselves, at least halt ot the drum references will be eliminated, which in
turn will reduce computation time. by an estimated 40 or 45 percent.
9-514
CV-39
CONVAIR - DIVI310N OF GENERAL DYNAMICS CORP.
SAN OiEGO. CALIi'"ORINiA
REPORT
Ie 004-7
ZM 491
MODEL
All
PAGE
2/22/55
Revised: 6/22/56
DATE
1(004
EXPLANATION
01033
73 01247 10000
R=
70766
01034
11 20000 01266
STORE R
70767
01035
36 01212 01267
STORE R-1
70770
01036
35 01242 20000
R+4-+(A)
70771
01037
73 01242 01270
STORE R+4 DIVIDED BY 5
70772
01040,
23 01270 01213
STORE
70773
01041
STORE
70774
01042
31 01266 00020
11 20000 01271
70775
01043
31 01266 00001
STORE
70776
01044
36 01213
70777
01045
45 00000 01047
71000
01046
00 00000 00140
71001
01047
37 00540 00540
71002
01050
20 00000 0000
71003
01051
37 00540 00540
71004
01052
20 00000 0000
71005
01053
15 010'00 01077
71006
01054
15 01000 01107
71007
01055
11 00777 01264
SET COLUMN INDEX
71010
01056
11 01250 10000
MASK ----+- (Q )
71011
71012
01057
01060
53 01251 01076
11 00537 01207
SET BLOCK TRANSFER
STORE 310 OCTAL
0"-
71013
01061
11 01260 20000
'-'
I
71014
01062
47 01072 0'1063
INDEX
71015
01063
11 01271 20000
YES:
71016
01064
47 01065 01072
>< 71017
01065
11 01250 10000
R=
NO:
71020
01066
53 01271 01076
71021
01067
11 01270 01254
SET BLOCK TRANSFER
SET CARD INDEX
71022
01070
75 10002 01075
SET
71023
71 0 24
01071
01 0 72
11 01267 01252
RE~/1A
6
0
~
t-
c..
0127~
11 01246 01252
)
R+ 4 DIVIDED BY 5
t"1INUS 1
2R X 2's
2R-l
POSITION
CARD
TO
PUNCH
SET INITIAL
DATA ADDRESS
CIj
0"-
I NDER
(A)
70765
=M
= o?
O?
MASK~ (Q)
NUMBER INDICES
NO:
SET BLOCK BY COL. TRANSFE~ INDEX
9-515
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