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1103 CENTRAL EXCHANGE 
NEWSLETTER NUMBER 10 

December 1956 



PX 71900-10 



DIVISION OF SPERRY RAND CORPORATION 
1902 WEST MINNEHAHA AVE. ST. PAUL W4. MINNESOTA 



py 719Q0-»lQ 



■— — ■»■— p—i i i.j . — »»— i— i i .i... ,. immmm^r^^m wmm^Hrrmp^mm 

CONTENTS OF PUBLICATION 



Page 1 of 2 



Title : 1103 CENTRAL EXCHANGE NEWSLETTER LUMBER 10, December 1956 



o 
o 

X 



Classification 



Text pages — 



U 







Publication Date 
Photographs __._ , 



Charge V*®t± 



pr a wings 



Page No, 
(of ) 



i thru iii 
10-1 thru 10-5 

10-6 thru 10-15 

10-16 thru 10-17 
10-a8 thru 10-24 

10-25 thru 10-48 

10-49 thru 10-73 



10-74 thru 10-135 



Contents 



Title Page 

Front Matter (Newsletter) 

General Card Read-In 

Routine 
Eigenvalues of a Tri~r&s- 

gonal Matrix 
Floating Point Card Dump 
1103 to 1103A Conversion 

Routine 
Floating Rector Arithm'etic 

Package " 
Significance Preserving 

Floating Binary Point 

Arithmetic for Digitel 

Computers 
A Method for Generating 

Random Numbers on the 

ERA- 1103-' , | 

10-136 thru 10-143jEvaluatibn of |A-^j|for 

Matrix A ^Complex Single 

Precision Floating Point) 
10-142 thru 10-14^Floating Point Linear 

Matrix Equation £olv@r 

(AX=B) | 

10-150 thru 10-157Complex Single Precision 

Floating Point Linear 

Matrix Eauation Solver 

(AX = B) *■ 



Print 
Number 



71900-10 
71900-10 

71900-10-16^ (RW-168) 



71900-10-16? 
71900^10-173 

71900-10-17 L 
71900-a0-172 



10-158 thru 10-16* Complex Gill Method Routin ?7190CW10-17? 



10-170 thru 10-13C Algebraic Equation Solver 

10-181 thru 10-19C)Uhpa eked Floating Point 

Card Output 

10-191 thru lO-210Contihiious Matrix Multi- 
plier Using FLIP III 

10-211 thru lO-240Continuous Matrix Multi- 
plier Using Single or 
Multi-precision Arith- 
Metic 

10-241 thru 10-33<JSFUR - Single Precision 

Unpacked Rounded Floating 
Point Package for ERA- 
1103 Computers 



71900*10-47? 



71900-10-177 



71900-10-17? 
71900-10-18 D 
7190O-10-13L 



71900-10-182 (CV-182) 



71900-10-183 (CV-183) 



Drawing 
Number 



(RWf-169) 
(I&V170) 

(RIU171) 

(RJU172) 



71900-lO^XTt? >(RR*173) 

71900,10*1714 (WS-174) 

71900-10^1715 (RW*175) 

(RW-176) 



(RVU177) 
(KW-178) 
(RW»179) 

(CV-1SQ) 
(GVa8l) 



Number 



0RM fRA 9 Q 





Px 71900-10 


CONTENTS OF PUBLICATION 


Page 2 f 2 



:" T Title: 1103 CENTRAL EXCHANGE REWSLETtl^ 10, receive* 1956 



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Classification 
Text pages, -.,, 



Publication Date 

^Photographs __ 



Charge 93S88-4 
Drawings 



,Page 
Jpf_ 



No, 



) 



10-331/;vthjFu: 

10-335 thru 

1^3% thru 

1G-337 thru 
10-353 thru 

10-364 'thru 

10-372 -thru 10-3831 



10-382 thru 
10-3S6 thru 

10-390 thru 
10-394 thru 

10-39B thru 

10-4.02 thru 

10-406 thru 

10-408 thru 
1Q-412 thru 
10-421 thru 
10-430 thru 
10-435 thru 



Contents 



lQ-33/\QaK$)\i%lTig Cer:t< r Organiza- 
tion «-' The Ramo-Wdbldridg $ 
Gorporetion 

10-33 3Mathemi,ti eel Services 
Branch 

10-3 36|Urm eked Flo* tire . Point 
Card Read '" 

10-3 ^Utility Routire Library l 

10-^6 ^The Rsmo^Wooldridge" Corp 
One-Pass Assembly Routine 

10-373|r;e f ini te Ir. t eg re l" Eve lue - 
tion Routire 
SNA? - Interpretive Float- 
ing Point Package 

10-38^i?K A P Sampler Trace 

1G-389SNIP - Interpretive Floct-j 

ing Point Peckere-C-orplex] 71900-10-14(1 

71900-10-63 



Print 

Number 



71900-10t27 

71900-10; 28 

71900-10-1 5 U 
71900-10-71 

71900-10-72 

71900^10-89 

71900-10-IC3 
71900-10-140 



10-393The Ferranti I£m:t Routire 
lC-39'jArcsine-Arcosine Routire, 

Stated Point 
10-40]|Floatinp Point Arcsire- 

Arcoeir.e Routine 
10-4'0^?ioatinf Poirt Arctangent 

Routine 
10-407Changed Word Post-MorteiE 

Routine 
10-4liK th Root Routire 
10-42CG111 Method Subroutine 
10-42< Floating Point Gill Method 71900-10-14B 
10-& Floating' Point Sire- Coeirb71900-10-l4C 

lo-iacFiiaciE " 71900-10-^6 



71900-10-14 S (PW-148 REV) 



71900-10-140 

71900-10-74 

719OO-10-1C2 
71900-10-11 E. 
71900-10-91 



Drawing 
Number 



(I0s27) 

(10*28') 

(CV-154 PEvf) 
.(PK-71 REV) 

(PU-72 REV) 

'(KW-&9 REV) 



(T>r:i"08 K£V) 
(RW-H0 RHV 



Number 



) 



(P.W-141 P-EVJ^ 
(py-63 ?rv) 



(P.s-149 P-H) 
{^Jw74 REV) 

(Rv-102 ywi) 

(RW-116 R 
(HV r -91 REV) 
(RW-143 PS 
(1W-144) (* 
(RI.-36 ft£V) 



"EV) 



Newsletter Number 10 
December 1956 

EDITOR »S PAGE 

Correction s On page 9-392 of Newsletter 9, line 2, paragraph 4, 

35 
of RR-162 should read ". . .will be p-1 = 2 -32=34, 

359,738,336. . .\ 

Correction ? The octal equivalent given for the constant A^ in the 

descriptions for the arsin-arcos floating point (BR-75) 

and the arcsin-arcos stated point (RR-25) routines is 

in error and should read 

37 50417 41233 
instead of the listed value of 

37 04174 -41233. 
This correction should be entered in Newsletter 3 
(pg. 3-108) for RR~25 and in Newsletter 6 (pg. 6-73) 
for RR-75. 



Editor, 

Central Exchange 



3 



p. 



NEWSLETTER 10 
DECEMBER 1956 



ENCLOSURES 



RW-168 
RW-169 
RW-170 
RR-171 

AR/172 

4£ 



173 

WS-174 
RW-175 

RW-176 
RW-177 

RW-178 
RW^-179 

cv~iao 
cv-iai 

CV-182 
CV-183 



A 


10t27 




10*28 








REVISIONS 




CV-154 




RW-71 



G e neral Card Read-In Routine 

Eigenvalues of a Tri-Diagonal Matrix 

Floating Point Card Dump 

1103 to U03A Conversion Routine 

Floating Vector Arithmetic Package 

Significance Preserving Floating Binary Point Arithmetic 
for Digital Computers 

A Method for Generating Random Numbers on the ERA 1103 

Evaluation of lA— Tvll for Matrix A (Complex Single 
Precision Floating Point) 

Floating Point Linear Matrix Equation Solver (AX=B) 

Complex Single Precision Floating Point Linear Matrix 
Equation Solver (AX=S) 

Complex Gill Method Routine 

Algebraic Equation Solver 

Unpacked Floating Point Card' Output 

Continuous Matrix Multiplier Using FLIP IH 

Continuous Matrix Multiplier Using Single or Multi- 
Precision Arithmetic 

SPUR - Single Precision Unpacked Rounded Floating Point 
Package for ERA-1103 Computers 

Computing Center Organization -» The Ramo-Wooldridge Corporation 

Mathematical Service Branch - Eglin Field 



Unpacked Floating Point Card R e ad 
Utility Routine Library 

1. Table of Contents 



■M 



I 

o 

1 

8 

0^ 



2. Conventions 

3# Reminders 

4.. Tape Bootstrap 

5. Pool of Flex Codes 

6, Cumulative Errata 

7. Utility Routine Transfer Drum to Magnetic Tape 

8, Utility Routine Transfer - Magnetic Tape to Drum 
RW-72 The Ramo-Wooldridge One-Pass Assembly Routine 

RW-89 Definite Integral Evaluation Routine 

RW-108 SNAP - Interpretive Floating Package 

RW-140 SNAP Sampler Trace 

RW-141 SNIP - Interpretive Floating Point Package, Complex 

RW-63 The Ferranti Input Routine 

RW-14.8 Arcsine-Arcosine Routine, Stated Point 

RW-149 Arcsine-Arcosine Routine, Floating Point 

RR-74- Arctangent Routine, Floating Point 

RV-102 Changed Word Post-Mortem Routine 

RW-116 N^ Root Routine 

RW-91 Gill Method Subroutine 

RW-143 Floating Point Gill Method Subroutine 

RW-144. Floating Point Sine-Cosine Routine 

RR-86 FLEXIE - Flex Code Paper Tape Input Routine 



iii 



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THE RMO~WGOLDRIDGS CORPORATION 
Los Angeles k^ , California 

General Card Read -In Routine 
Specifications 



CRI-3 

Pg. 1 of 5 

11-5-56 



Identification Tag: 

Type: 

Special Storage: 

Program Entrance: 
Program Exit: 
Alarm Exit: 



CRI-3 

Service Routine (-with subroutine entrance) 

The constant pool and temporary pool are not 
used by this routine 

Ji0017b 

l*0020b 

The alarm routine is used by this routine 



Coded by: 
Approved by: 



M. Perry 
W. F. Bauer 



November, 1956 
November, 1956 



10-1 



R1V-168 



CRI-3 

Pg. 2 of 5 

11-5-56 



Description 



This routine reads cards produced by MDP-1 ("binary cards), CPO-0 (fixed point 
output), CPO-1 (floating point output) and cards key -punched on the 4 field 
format (described below) for input in floating point, double precision floating 
point, fixed point, or octal. These input forms may be intermixed on a card, 
and the cards may be in any sequence desired. The routine automatically 
differentiates the 2 card forms, and for 4 field cards, recognizes the type of 
input in each field. All input is rounded properly. This routine reads 
cards at full card reader speed and loads the memory as directed by the address 
or addresses appearing on the cards. Once activated, it continues to read 
cards until it has read and stored a card containing a stop code as described 
below. The input need pot be normalized to retain full significance. The 
routine stores high speed memory on the drum, operates in high speed memory, 
and restores high speed memory from the drum prior to leaving the routine. 

Operating Instructions 

1. When routine is used as a service routine , set PAK to 40017b and start. 
Routine will read cards until a stop code is recognized, at which time 
the machine will stop (MSO) with PAK set to 4001 7b. 

2. When routine is used as a subroutine , enter the routine with 

37 40020 40017b. Routine will read cards until a stop code -is recognized, 
at which time control is transferred to cell 40020b and hence to the cell 
following the return jump mentioned above. 

To restore high speed memory at any time, start at 40040b. A and Q will 
not be restored. 

Card Positioning 

Card positioning is required before the initial read only. Card reading 
automatically positions the next card to be read, and a card will be positioned 
for punching before leaving the routine. If the routine is used as a service 
routine, the initial positioning must be manual. If the routine is used as 
a subroutine, initial card positioning should be programmed. This can only be 
done by one instruction, [EF 00000 vwvv] where vww contains 
00 00000 00114b. 

Stop Codes 

1. Read stop, 12 col 80 . When this code is detected on either a binary card 
or a four field input card, the routine will stop reading, position a 
card on the punch side of the bull, and then exit properly (see operating 
instructions). 

2. Machine stop, 12 col 79 ° When this code is detected on a 4 field input 
card, the routine will stop reading, position a card on the punch side 

of the bull, and stop MSO at 72431b. If the machine is started, the exit 
from the routine will proceed as described in operating instructions. 



10-2 



RW-168 



CRI-3 
Pg. 3 of 
11-5-56 



Either of the above codes may be entered on a blank card and the routine 
will sense them. The programmer is cautioned not to place the machine 
stop code on a binary card as this -will result in improper loading (see 
MDP-1 write-up). 

Alarm Conditions 

1, Binary Cards - As a binary card is read, the words are summed and the result 
is compared with a sum punched in the card (see MDP-1 write-up). If the sums 
do not agree, the flexowriter will print 

,. "ALARM 00271 000000000000 OOOOOOOwwv QQQQQQQQQQQQ" 

and the machine will stop, wwv is the storage address appearing on the 
card. The contents of Q are not important. Starting the computer will bypass 
the alarm, the words will be stored as read, and in the absence of a stop code, 
reading will proceed. 

2. h Field Cards - An alarm on a four field card indicates that a number was 
too large to be entered appropriately into the computer. For floating point 
numbers (single and double precision) this is equivalent to exponent over- 
flow. For fixed point numbers, this indicates that the input properly 
scaled and rounded was too large to be- entered into a single cell. If an 
alarm condition is detected, the flexowriter will print 

"ALARM 00164 000000000000 OOOOOOOvww 000000000000" 

and the machine will stop, wwv is the storage address of the right -most 
incorrect number. Any or all of the other numbers may have been incorrect, 
wwv equal to 20,000 indicates that the indicated address field was blank. 
Starting the computer will cause the correct numbers to be stored, the 
incorrect numbers to be ignored, and in the absence of a stop code, reading 
will proceed. 

k Field Card Format 

The format described below is one of the formats used by this routine and 
o is the format used by CPO-0, CPO-1, CRI-2, and SNAP Read. 

vO 

Y The card columns are designated as follows: 
o 

o Col 1-4 Identification This field is ignored by the 

§ reading routines 



a. 



Col 5-23 Field 1 

Col 24-42 Field 2 

Col 43-61 Field 3 

Col 62-80 Field 4 



10-3 



RW-168 



CRI-3 

Pg. h of 5 
11-5-56 

Each field (except identification) is divided as follows. 

(x digit 1 for octal location) 
(x digit 15 for negative value) 
(x digit 17 for negative exponent) 



digit 1-5 
digit 6 -15 
digit 16-17 
digit 18-19 



Location or address 
Value or Mantissa 
Decimal exponent 
Binary exponent 



(x digit 19 for negative exponent) 



Addressing Options 



The following Addressing options are allowable on the k Field input card. Option 1 
is used by CPO-0, CPO-1, CRI-2, and SNAP Input. 

1. Decimal - Straight conversion to the octal equivalent of the decimal address 
in the card. No indication is necessary. 

2. RAWOOP Decimal - Straight conversion to the octal equivalent of the decimal 
address except that U0,000 decimal is designated as the first drum address 
(*K),000b). No indication is necessary. 

3. Octal » The octal number appearing on the card is the actual address. This 
must be indicated by an x(ll punch) over the first digit of the address. 

h. Blank - "A completely blank ^ address field indicates that the number in that 
field is not to be stored. This is differentiated from an address containing 
1 or more zeros which will load cell zero. 

Input Numbers 

The following varieties of input may be punched on the k field input card. They 
may be in any combination on a card with the exception that for a double precision 
floating point number the two fields must be consecutive and on the same card. 
For all input, the decimal point is presumed to be at the extreme left end of the 
value field. It is recommended that the codes listed below be used for each field. 
However, cards from CPO-0 and CPO-1 are differentiated by the fact that their 
"B" (Binary Exponent) fields are non -blank and blank respectively. 

1 Floating Point - RS. An input number is designated as floating point by the 
code RS (Read Snap) in the "B" field. There is no restriction on the n D" 
field. The resulting floating binary number is rounded and is in the form 
used by SNAP and by the internal floating point on the 1103A computer. A 
floating point number consists of 3 parts; a sign bit, followed by an 8 
binary bit characteristic biased by 200b, and a 27 bit normalized mantissa. 
To negate a floating point number, the complete cell is complemented. 

2. Double Precision Floating Point - RT. An input number is designated as double 
precision floating point by the code RT (Read Two) in the **B" field. The 
"value" portions of 2 consecutive fields are joined to allow 20 decimal digits 
of input. Both fields must contain addresses but the control information 
(RT code, algebraic sign, and decimal exponent) is taken from the first field 
only and ignored on the second field. The resulting floating binary number 
is rounded and is in the form used by double precision SNAP. The upper cell 
is identical to a single precision floating point number and the lower cell 



10-4 



RW-168 



CRI-3 
Pg. 5 of 5 
11-5-56 



consists of a sign "bit and 35 "binary digits which are an extension of the 
27 binary digit mantissa in the upper cell. - ■** 

The programmer is again cautioned that the two fields concerned must be 
consecutive and on the same card. 

3o Fixed Point - No code . An input number is designated as fixed point by the 
fact that the "B" field is not blank and does not contain an R. Since the 
"B" field is used to express the binary scale factor desired, the only caution 
is that it must not be left blank. 00 (zero zero) must be punched if a scale 
factor of zero is desired* The binary scale factor is allowed to be negative 
and the only restriction is that the combination of the B and D fields result 
in a number which is not too large for a single cell. Normalization is not 
important since the conversion is done in double precision. The resulting 
binary number is rounded properly. v, :*... 

^' Octal - RU . An input number is designated as being octal by the code RU 
(Read Unconverted) in the "B" field. Since 12 octal digits are desirable, 
the "value" and "D" fields are joined giving 12 digits. Each digit is 
- loaded modulo 8, such that an 8 becomes a zero, and a 9 becomes a if 

Examples . The following list of ihjnat would be punched on two cards. The second 
card would have 7 a "Stop Restd" code in col 80 because of the "+" sign on the 
last line. The octal address and translation are listed in the comments. 









\ 








, s Ny 


QUANTITY 


LOCATION 


VALUE |i 


D LL 


B jdr 


COMMENTS 




IT. 0.1,2,2 


1,2,0 


\ 1 1 1 1 




0,'1{ 


R.S, 1 


40122 20 14631 46315 




1,6,3,8,4 


^,0 


0,0,0,0,0,0 


4; 


z.^i- 


R.U! 


40000 45 00000 00425 




4/0,0,6.4 


3,1.4 


1.5,9.2,6,5 


3|- 


1 

0,l| 


r,t| 


40100 57 51557 00452 




4,0,0,6,5 


5 8,9 


7,9.3,2,3,8 


5! 


1 
1 

, 1 


1 

1 [ 


40101 75 67513 ^7562 




0,0,1,2,3 


0,0,1 


5 „ , , , 1 


1 
1 


o,4; 


0,0; 


00123 00 00000 00017 




, . ,9,9 


1.5, 


. , , 1 1 


1 
1 


°,2i 


1 ' 5 I 


00143 00 00017 00000 




100 

, 1 , 1 


!. , 


, . . 1 \ 


1 
1— 

i 


o,i: 


1 2! 

< 1 


00144 77 77777 67777 




00122 

!._,-. 1 1 1- 


l ,5, 


, , .I 


1 
1— 


1! 
1 ■ . 


r s:+ 
« < 


00122 57 61777 77777 



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10-5 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 45 , California 



Eigenvalues of a Tri -Diagonal Matrix 
Specifications 



RW-169 



EGN-1 

Pg. 1 of 10 

10/1/56 



Identification Tag: 

Type: 

Storage : 



Regional Addresses Used: 
Entrance and Exit: 

Machine Time: 
Mode of Operation: 



EGN-1 

Subroutine available on cards for assembly. 

1^5 words of storage needed to assemble 
this routine. 

18 + 2n cells of temporary storage immediately 
following the temporary pool used, but not stored 
with subroutine, (n =* order of matrix). 

The constant pool and temporary storage pools 
are used by this routine, 

00R, 01M, 02M, 01R, OOK, OOT, F00, COO 

RJ 00R01 00R02 No Punching -, 

RJ 00R01 0OR03 Cards Punched 

See table in text. 



J 



See Instructions 



Floating Complex Arithmetic requiring SNIP 
be activated. 



Coded by: 
Approved by: 



W. Frank 
W. Bauer 



September 195& 
October 1956 



10-6 



EGN-1 

Pg. 2 of 10 

10/1/56 






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Description 

This subroutine computes the n eigenvalues of any real or complex tri- 
diagonal matrix D, having the form: 



D = 



a. 



a 



n-1 







n-1 



n 



Since complex arithmetic is employed, the elements of the matrix must be 
presented according to the specification for number representation for use 
with SNIP. The n elements of the main diagonal, a , must be followed by the 
n-1 elements of the upper adjacent diagonal, b , in a region whose initial 
address is specified by a parameter word. 

The more general tri -diagonal matrix J, (also called a "Jacob i Matrix") 
has all its non-zero elements on the main diagonal and on either of the two 
immediately adjacent diagonals: 



a., 



a. 







c _ a t b , 
n-1 n-1 n-1 



10- i 



RW-I6V 

EGN-1 

Pg. 3 of 10 

IO/I/56 



This routine can also treat this case if in place of the n-1 elements of the 
upper adjacent diagonal, the n-1 products, c b . , are supplied. 

The subroutine occupies 1^5 cells and uses the constant and temporary 
storage pools. In addition 18 + 2n cells of temporary storage must he provided 
immediately following the Ramo-Wooldridge Temporary Pool . Practical limitations 
are imposed on n by the available 1024 words of ES storage and the use of SNIP, 
hence n must be less than 157. In all cases the eigenvalues can be found in the 
last 2n cells of the (l8+2n) cells of temporary storage. In addition the eigen- 
values 7U and associated residues in the characteristic polynomial P(rt .) can be 
punched on cards. P(7\ ± ) appears in fields one and two while ^\ is in fields 
five and six. The eigenvalues are also identified serially in the identification 
field. At the option of the programmer the successive approximations to the 
~^ obtained during the iterative process can also be punched with their 
associated residues in the reduced polynomial. In the event that no punching 
is desired then a third entrance is available. " r 
Programming Instructions 

1. Complex mode of SNIP must be activated. 

2. Entrance to the subroutine is made as follows: 

a. RJ 00R01 00R03 

XX 0QA00 vww 

where 

00R00 is the location of the first word of the subroutine 

00A00 is the location of the real part of the first element of the 
diagonal 

vww is the order n of the tri -diagonal matrix 



10-8 



RW-169 

EGN- 1 

Pg. h of 10 
IO/1/56 



XX gives the option selected 

XX = 20, only the eigenvalues 2L . and their respective 

residues in the characteristic equation are punched. 

XX = 00, in addition to the above, the successive approximation 
to the eigenvalues are punched. 

In either case the eigenvalues themselves are stored 
in the machine starting at the location 51 = 63b. 
b. Should no punching of cards be desired then one must use the entrance: 

RJ 00R01 00R02 

20 00A0O wwv 
3. Control is returned to the cell following the parameter word. 

Machine . Time 

The time taken to find the n eigenvalues can be estimated from the following 

table of empirical times in seconds . 






1 

o 

I 

o 
o 



X 

Oh 



Order of 
Matrix 


No Punching 


Punching 
Eigenvalues 


Punching 
Eigenvalues and 
Iterations 


3 


5 Sec. 


8 Sec . 


13 Sec. 


5 


17 " 


22 " 


36 " 


8 


50 " 


58 " 


92 " 


10 


81 " 


91 " 


1^3 " 


27 


776 " 


803 " 


- 


39 


27^3 " 


2782 * 





in_Q 



Given the tri -diagonal matrix J 



RW-169 

EGN-1 

Pg. 5 of 10 

10/1/56 



J = 



a. 









a. 



a n b 1 
n-1 n-1 



c . a 

n-l n 



The following recursion formula evaluates the characteristic polynomial 
P (71) of J for given A: 



p ± (a> - (a t -a) p^cpu - ^ c ^ p (R> 



X *** ■ -L * &* * # • • • XI 



where 



P _ = P = 1 
-1 o 



1!he problem loses no generality by assuming all c. = 1 so that only the a. and b 
need be given. Alternatively the general problem can be solved by this routine 
if one supplies c b in place of b., 

Using P (-1), P (l) and P (0), the program enters a modified version of the 
Algebraic Equation Solver (POL-0) and finds, by iteration, the first root 71 of 

Having found r roots the (r+l) root is found by considering the polynomial 



P (7\) ■ P n^ ) 



n-r 



i=l 



10-10 



o 

I 

o 
o 



X 

a* 



RW-169 

EGN-1 

Pg. 6 of 10 

10/1/56 



where ~X -. > ~X 9 t • • • ) ~X are ^e eigenvalues already found. This code prevents the 

re -computation of a multiple eigenvalue by not allowing ^- r+ i to approach the 

value of any of the r roots already found. This, however, did not prohibit the 

determination of multiple roots in any of the matrices tested, for the reason statec 

below. 

Convergence 

A convergence criterion 

^i+l"-^i 



Z10 



-k 



^ i+1 

is applied to determine the end of the iteration. In this code k = 6. This 
gives an accuracy of 6 to 7 places in many low order cases . For large order 
(n^20) accuracy is reduced since not enough figures are carried in the 27 bit 
word of SNIP to accurately define the roots after a large number of arithmetic 
operations have been performed. In the case eigenvalues are repeated the accur- 
acy deteriorates. Furthermore, the residues of the characteristic polynomials 
in the neighborhood of such a root are exceedingly small. Hence, a second 
convergence criterion was introduced in order to avoid exponent overflow. If 
the residue 

P (2L)Z 2 - 100 



n-r 

then ^_. is accepted as a root. If 2l has multiplicity p then the code will 
&■ find p estimates of ~X such that 

1 a) no two estimates are equal 



b) all estimates have residues 42 

If ~\ is an eigenvalue then det(D -.A.l) should be zero. Inspecting successive 
k k 

iterations and associated residues can therefore give some indication of the 
convergence of the procedure . The programmer is, however, cautioned in regards 



10-11 



RW-169 

EGN-1 

Pg. 7 of 10 

10/1/56 



to using this quantity as a measure of accuracy of the root. It is possible, for 
example, to have a root accurate to 6 places and yet obtain a residue of high 
order . 



10-12 



RW-169 

EGHM 

Pg. 8 of 10 

J.O/l/56 






I 

Q 

1— I 
I 

o 
o 



X 



D 

D 

D 

D 

D 

D 

D 

D 

00R00 

00R01 

00R02 

00R03 

00R04 

00R05 

00R06 

00R07 

00R08 

0ORO9 

00R10 

OORll 

00RI2 

00R13 

O0R14 

00R15 

00R16 

00R17 

01 MOO 

01M01 

01M02 

01M03 

01M04 

01M05 

01M06 

01M07 

01M08 

01M09 

01M10 

01M11 

01M12 

01M13 

01M14 

01M15 

01M16 

01M17 

01M18 

01M19 

01M20 

01M21 

01M22 

01M23 

01M24 



00 
MJ 
MJ 
TP 
SP 
TU 
TU 
TP 
TP 
TP 
TV 
TU 
TP 
R5 
LA 
QS 
TP 
TN 
RA 
RP 
TP 
TP 
TN 
TP 
TN 
TP 
RJ 
TP 
TP 
TP 
RJ 
TP 
TP 
TP 
RJ 
TP 
TP 
MJ 
LDMP 
ADST 
MPST 
LDMP 
STSU 



OOROO 
01M00 
02M00 
01R00 
OOKOO 
OOTOO 
FOOOO 
COOOO 
00000 

00000 

00000 
01R34 
00R01 
AOOOO 
AOOOO 
00000 
00013 
00013 
AOOOO 
AOOOO 
00K05 
00T15 
AOOOO 
AOOOO 
00T15 
00016 
00R01 
10005 
00013 
00K01 
OOKOO 
OOKOO 
00 KOI 
00013 
01R30 
00029 
00030 
00K01 
01R30 
00029 
00030 
00013 
01R30 
00029 
00030 
00000 
OOTOO 
00T04 
00T08 
00T02 
00027 



00100 
00118 
00151 
00204 
00239 
00033 
00002 
00003 
01R16 
00000 
02M37 
02M50 
00015 
00RO7 
02M32 
AOOOO 
00T15 
00T14 
00T1.5 
OOROO 
QOOOO 
00016 
00016 
01R06 
00T16 
00T17 
00016 
01M03 
00T09 
00T12 
00T08 
00T10 
00T06 
0OT07 
01R00 
OOTOO 
00T01 
00T06 
01R00 
OOT02 
00T03 
00T06 
01R00 
00 TO 4 
00T05 
02M31 
OOT08 
00023 
00025 
00T10 
00023 



EXIT 

ENTRANCE 1 
ENTRANCE 2 



A 
D 

R 
N-l 
2N-2 



SET 
UP 

STARTING 
VALUES 



00144 
00166 
00227 
00314 
00357 
00041 
00002 
00003 
00144 
00145 
00146 
00147 
00150 
00151 
00152 
00153 
00154 
00155 
00156 
00157 
00160 
00161 
00162 
00163 
00164 
00165 
00166 
00167 
00170 
00171 
00172 
00173 
00174 
00175 
00176 
00177 
00200 
00201 
00202 
D0203 
00204 
00205 
)0206 
t 0207 
1 0210 

;02ii 

:D212 
*D213 

;o2i4 

0)215 
216 



00 00000 
00 00000 
00 00000 

00 00000 
00 00000 

00 00000 
00 00000 
00 00000 
00 00000 
45 00000 
45 00000 
11 00356 
31 00145 
15 20000 

15 20000 
11 00000 
11 00015 
11 00015 

16 20000 
15 20000 
11 00364 
23 00060 
54 20000 
53 20000 
11 00060 
13 00020 
21 00145 
75 10005 
11 00015 
11 00360 
13 00357. 
11 00357 

13 00360 
11 00015 
37 00352 
11 00035 
11 00036 
11 00360 
37 00352 
11 00035 
11 00036 
11 00015 
37 00352 
11 00035 
11 00036 
45 00000 

14 30041 
14 04045 
14 14051 
14 30043 
14 34033 



00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00334 
00000 
00274 
00311 
00017 
00153 
00267 
20000 
00060 
00057 
00060 
00144 
10000 
00020 
00020 
00322 
00061 
00062 
00020 
00171 
00052 
00055 
.00051 
00053 
00047 
00050 
00314 
00041 
00042 
00047 
00314 
00043 
00044 
00047 
00314 
00045 
00046 
00266 
14051 
34027 
34031 
14053 
11027 



RVJ-169 

EGN-1 

Pg. 9 of 10 

IO/1/56 



01M25 


LDMP 


00T04 


00T10 


01M26 


ADNO 


FOOOO 


00000 


01M27 


TN 


FOOOO 


00029 


01M28 


TN 


COOOO 


00030 


01M29 


ADMP 


FOOOO 


O0T08 


01M30 


MPLD 


00023 


00T04 S 


01M31 


SUMP 


00027 


00T10 


01M32 


ADMP 


00025 


FOOOO S 


02M00 


AORT 


00023 


00023 


02M01 


TN 


GOOOO 


COOOO 


02M02 


LDMP 


FOOOO 


00025 


02M03 


SJ 


02M04 


02M06 


02M04 


TN 


00023 


00023 


O2M05 


TN 


00024 


00024 


02M06 


LOAD 


00025 


00023 


02M07 


PMNO 


00000 


00000 


02M08 


ZJ 


02M10 


02M09 


02M09 


TP 


00K01 


00023 


02M10 


LDDV 


00029 


00023 


02M11 


ST MP 


00T08 


00T12 


02M12 


ADNO 


00T06 


00000 S 


02M13 


RJ 


01R30 


01R00 


02M14 


DVPM 


00T04 


00000 


02M15 


TJ 


00K02 


02M20 


02M16 


TN 


OOKOO 


FOOOO 


02M17 


TP 


00013 


COOOO 


02M18 


LDMP 


FOOOO 


00T08 


02M19 


MJ 


00000 


02M11 


02M20 


TP 


00K01 


FOOOO 


02M21 


ADNO 


00T08 


00000 


02M22 


TP 


FOOOO 


00T10 


02M23 


TP 


00T09 


00T11 


02M24 


RP 


30004 


02M26 


02M25 


TP 


00T02 


OOTOO 


02M26 


TP 


00029 


00T04 


02M27 


TP 


00030 


00T05 


02M28 


LDDV 


00T12 


00T06 


02M29 


PMNO 


00000 


00000 


02M30 


TJ 


00K03 


02M40 


02M31 


TP 


02M29 


AOOOO 


02M32 


TJ 


00000 


01M20 


02M33 


RP 


30004 


02M35 


02M34 


TP 


00T04 


00006 


02M35 


PDNO 


00010 


00000 


02M36 


MJ 


00000 


01M20 


02M37 


TP 


02M39 


02M50 


02M38 


MJ 


00000 


00R04 


02M39 


MJ 


00000 


02M51 


02M40 


TP 


00T14 


00004 


02M41 


LDST 


00T06 


00008 


02M42 


STST 


00025 


00T18 



I 

S N 
D 



ITERANT 
AND 

FUNCTIONAL 
VALUE 



SET UP 
FORNEXT 
ITERATION 

CONVERGED 



B 



00217 
00220 
00221 
00222 
00223 
00224 
00225 
00226 
00227 
00230 
00231 
00232 
00233 
00234 
00235 
00236 
00237 
00240 
00241 
00242 
00243 
00244 
00245 
00246 
00247 
00250 
00251 
00252 
00253 
00254 
00255 
00256 
00257 
00260 
00261 
00262 
00263 
00264 
00265 
00266 
00267 
00270 
00271 
00272 
00273 
00274 
00275 
00276 
00277 
00300 
00301 



14 30045 
14 04002 
13 00002 

13 00003 

14 04002 
14 15027 
14 10033 
14 05031 
14 04027 

13 00003 

14 30002 

46 00233 
13 00027 

13 00030 

14 30031 
14 24000 

47 00241 
11 00360 
14 30035 
14 34051 
14 05047 
37 00352 
14 20045 
42 00361 

13 00357 
11 00015 

14 30002 
45 00000 
11 00360 
14 04051 
11 00002 
11 00052 
75 30004 
11 00043 
11 00035 
11 00036 
14 30055 
14 24000 
42 00362 
11 00264 
42 00000 
75 30004 
11 00045 
14 74012 
45 00000 
11 00276 
45 00000 
45 00000 
11 00057 
14 30047 
14 34031 



14053 
00000 
00035 
00036 
14051 
30045 
14053 
14002 
51027 
00003 
14031 
00235 
00027 
00030 
05027 
00000 
00240 
00027 
20027 
15055 
00000 
00314 
24000 
00253 
00002 
00003 
14051 
00242 
00002 
00000 
00053 
00054 
00261 
00041 
00045 
00046 
20047 
00000 
00277 
20000 
00212 
00£72 
00006 
00000 
00212 
00311 
00150 
00312 
00004 
34010 
36063 



10-14 



RW-169 

EGN-1 

Pg. 10 of 10 

10/1/56 



a- 

o 



1 

o 

1— t 

1 

o 
o 

.—i 

t~ 



02M43 
02M44 
02M45 
02M46 
02M47 
02M48 
02M49 
02M50 
02M51 
02M52 
01R00 
01R01 
01R02 
01R03 
01R04 
01R05 
01R06 
01R07 
01R08 
01R09 
01R10 
01R11 
01R12 
01R13 
01R14 
01R15 
01R16 
01R1? 
01R18 
01R19 
01R20 
01R21 
01R22 
01R23 
01R24 
01R25 
01R26 
01R27 
01R28 
01R29 
01R30 
01R31 
01R32 
01R33 
01R34 
00K00 
00K01 
00K02 
00K03 
00K04 
00K05 
START 



RA 
RJ 
TP 
TP 
RA 
SA 
TU 
PDPD 
IJ 
MJ 
TV 
RP 
TP 
TP 
TU 
TP 
LDMP 
LDSU 
MPSU 
TP 
TP 
TP 
TP 
RA 
IJ 
MJ 
TP 
SJ 
TP 
TP 
TP 
TP 
LDSU 
MPPM 
ZJ 
RA 
IJ 
LDDV 
STPM 
ZJ 
MJ 
TP 
ADNO 
MJ 
PDPD 
05 
01 
01 
01 
00 
00 



00T14 
01R15 
FOOOO 
COOOO 
00T17 
00016 
AOOOO 
00010 
00T16 
00000 
OOROO 
10003 
00013 
00K01 
OOROO 
00T15 
00000 
00000 
00029 
00029 
00030 
FOOOO 
COOOO 
00004 
00023 
00000 
00T17 
01R28 
00T17 
00K01 
00013 
00013 
00T06 
00031 
01R25 
00004 
00023 
00029 
00029 
01R30 
00000 
OOKOO 
00T06 
00000 
00010 
0.0000 

00000 
00000 

00000 
00002 
00777 



00K04 
01R01 
00006 
00007 
00016 
00015 
00005 
00010 
01M01 
00R01 
01R15 
01R03 
00030 
00029 
00004 
00023 
00031 
00T06 
00031 
00031 
00032 
00029 
00030 
00K04 
01R06 
00000 
AOOOO 
01R18 
00023 
00031 
00032 
00004 
00T18 
00000 
01R31 
00K04 
01R22 
00031 
00000 
02M40 
00000 
FOOOO 
00000 
01R01 
00010 
00000 
00000 
00000 
00000 

00000 

00000 



PUNCH 
ITERANT 



•01 

1 

»06 



H 



ISTIC 



EQUATION 



CONVERGED 



F C 
F 
F N 
F S 



B 



ANTS 



00302 


21 


00057 


00363 


00303 


37 


00333 


00315 


00304 


11 


00002 


00006 


00305 


11 


00003 


00007 


00306 


21 


00062 


00020 


00307 


32 


00020 


00017 


00310 


15 


20000 


00005 


00311 


14 


74012 


74012 


00312 


41 


00061 


00167 


00313 


45 


00000 


00145 


00314 


16 


00144 


00333 


00315 


75 


100Q3 


00317 


00316 


11 


00015 


00036 


00317 


11 


00360 


00035 


00320 


15 


00144 


00004 


00321 


11 


00060 


00027 


00322 


14 


32000 


15037 


00323 


14 


32000 


10047 


00324 


14 


14035 


10037 


00325 


11 


00035 


00037 


00326 


11 


00036 


00040 


00327 


11 


00002 


000 35 


00330 


11 


00003 


00036 


00331 


21 


00004 


00363 


00332 


41 


00027 


00322 


00333 


45 


00000 


00000 


00334 


11 


00062 


20000 


00335 


46 


00350 


00336 


00336 


11 


00062 


00027 


00337 


11 


00360 


00037 


00340 


11 


00015 


00040 


00341 


11 


00015 


00004 


00342 


14 


30047 


12063 


00343 


14 


15037 


24000 


00344 


47 


00345 


00353 


00345 


21 


00004 


00363 


00346 


41 


00027 


00342 


00347 


14 


30035 


20037 


00350 


14 


34035 


24000 


00351 


47 


00352 


00277 


00352 


45 


00000 


00000 


Q0353 


11 


00357 


00002 


00354 


14 


05047 


00000 


00355 


45 


00000 


00315 


00356 


14 


74012 


74012 


00357 


20 


04000 


00000 


00360 


20 


14000 


00000 


00361 


20 


45000 


00000 


00362 


15 


54143 


36750 


00363 


00 


00002 


00000 


00364 


00 


00777 


00000 


00000 


45 


00000 


00000 



THE RAM04700LDRIDGE CORPORATION 
Los Angeles h^> , California 

Floating Point Card Dump 

Specifications 



RW-170 

MDP ~5 

Pg. 1 of 1, 

10/15/56 



Identification Tag: 

Type: 

Service Entrance: 

Program Entrance and Exit: 

Other Routines Used: 



MDP -5 

Service Routine (with subroutine entrance) 

Address U0024 b 

37 ^0020 1+002^ b 

This routine uses MDP -4 and SNAP Output 



Coded and Checked by: 
Approved: 



R. Beach 
W. F. Bauer 



October, 1956 
October, 1956 



o 






10-16 



RW-170 



o 



i 

o 



o 

o 



a* 



MDP-5 

Pg. 2 of O. 

10/15/56 



Description: 

This routine operates exactly the same as MDP-4 (Octal Card Dump) 
with the following exceptions: 

1. Entrance Address is kOQ2h b 

2. Output is floating decimal on SNAP output cards. Addresses are 
five digit octal numbers with leading zeros suppressed. 

3 . A parameter word of zero will dump cells 00000 - 00777 h . 

The routine treats each word to be dumped as a floating point (SNAP 
form) number and converts it to a floating decimal number. Non SNAP numbers 
(i.e. instructions and fixed point numbers) may be included among the words 
to be dumped but their converted values will be meaningless. 

The listing will be double -spaced; however, if a card was omitted 
because it would have contained all zeros, no additional spacing is provided 
on the listing. 

The routine is essentially a driver for the SNAP output routine and 
MDP^, modifying each so that MDP-4 uses the SNAP output routine instead of its 
octal output section. 



10-17 



RR-171 



REMINGTON RAND UNIVAC 
ST. PAUL DEPARTMENT— INFORMATION SCIENCE 

1103 TO 1103A CONVERSION ROUTINE 



18 December 1956 



I* TYPE i Service routine or subroutine, 
II • STATUS: Code checked and machine checked by Bill Wallace. 



III. PURPOSEt 



IV. USAGE* 



A. 



This routine changes A and Q machine addresses from 20000 and 
10000 to 32000 and 31000 respectively, and detects magnetic tape 
and external function instructions. Various options are provided 
for print out of those addresses where an A or Q reference is 
modified, (indicating also u or v portion) and punching the 
converted program in bioctal or flex code. 



STORAGE REQUIRED: The program is coded in RECO form and it is 
therefore possible to operate the program from a location 
providing 320 octal drum address and 2000 additional octal drum 
addresses for a HSS image region. Such a location of the program 
and image region is done by assigning the desired starting addresses 
to regions BB end IR respectively, of the reco tape (see coding) 
all other regions being in HSS, and hence remaining the same. 
The regional assignment can be on a separate tape from the main 
program reco tape, but this tape should have END. c.r. at the end* 
(See RECO write-up.) 

In addition to the RECO tapes, a bioctal tape of the program is 
available where the program is stored at 66000-66320, with the 
image region 76000-77777. 

INPUT-OUTPUT: Output is a punched tape in bioctal or flex code 
of the changed program if desired. Also the following is printed 
out as the conversion routine is operating: (This is also optional.) 
u aaaaa or vaaaaa, where aaaaa is the address where an A or Q 
reference has been modified and u or v shows whether the u or 
v address of the instruction hss been modified. Also, TAPE is 
printed out when an 1103 magnetic tape instruction is encountered, 
and EF and address when an external function command occurso 



C. OPERATING INSTRUCTIONS: 

(1) Used as a service routine proceed as follows: (the term 
"program" here refers to a program to be converted.) 



B. 



a) 
b) 
c) 
d) 
e) 



Master clear, MD start 
Set PAK to 66000, (or bb) 

Insert in Q the first address of the program 
Insert In Q^ the last address of the program 
Insert in v address of A„ the address of the last 
Instruction of the program, or the last address of 
the program wherein one wishes to have A and Q 
addresses modified. 



10-18 



BWtpao 



o 
o 



X 



RR-171 



- 2 - 

f ) Insert in v address of Aj. the following codes for 
the various options: 

00000 bioctal punch of converted program and print 
out of addresses where modification occurs* 

00001 same as above but no print out. 

00002 flex code punch of converted program and 
print out. 

00003 same as above, but no print out. 

0Q004 print out , but no punch of converted program. 

00005 no print out and no punch of converted program « 

A $6 66010 (bblO) stop occurs if a gross error is 
made in the set-up, e.g. transposition of Q and Q • 

(2) Used as a subroutine, proceed as follows t 

a) Program the transfer of parameter as listed above to 
the A and Q registers. 

b) Execute the instruction! 

RJ bb2 bb 

c) The options are selected in the same manner as 
previously shown. 



(3) 



a) The use of this conversion routine assumes that the 
program to be converted is stored either all in core 
storage or all in drum storage. 

b) The conversion routine is coded for operation on either 
an 1103A, or on the 1103 (Serial 9) at RRU, St. Paul. 



10-19 



RR-171 



v. S9PTO 












A. Regions 










re 


bb66000 




re ual24 


■ 


re 


lr76000 




re val37 




re 


ff30000 




re upl55 




re 


erO 




re prl62 




re 


ob33 




re tpl73 




re 


od54 




re ef200 




re 


cf71 




re cs205 




re 


kk75 




re dd212 




re 


mmH2 




re tt310 




B. Program 










bbO 




45 





bblO 


Entrance 


1 




56 





bblO 


Errer step 


2 




45 





(ff) 


Subroutine exit 


3 













Storage first address 


4 













Storage last address 


5 













Storage Initial A 


6 













Storage initial Q r 


7 




45 





ff 


Constant 


10 




tp 


Q 


bb6 




111 




It 


10000 


bb5 




12 




It 


00000 


A 




13 




tp 





ir 




14- 




tp 


bb 







15 




rp 


31777 


bbl7 




16 




tp 


1 


irl 


Store HSS 


17 




rp 


30400 


cb 


To start of core program 


20 




tp 


bbl 


crl 


Conclusion of program 


21 




rp 


31777 


bb23 




22 




tp 


irl 


1 


Restore HSS 


23 




tp 


ir 







24 




tp 


bb6 


Q 


Restore Q for dump 


25 




tp 


bb7 


A 




26 




©J 


bb2 


bb31 


Test, subr. or serv? 


27 




rj 


70036 


fr0006) 


No, subr* 


30 




45 





bb2 


To exit 


31 




rj 


70036 


(70006) 




32 




56 


00000 


bb 




33 


obO 


ej 


dd43 


ed 


No punch 


34 


1 


•J 


dd64 


od2 


Punch flex 


35 


2 


ej 


dd65 


od5 


No print, no punch 


36 


3 


•J 


dd66 


odl3 


No print, punch flex 


37 


U 


•J 


dd60 


od6 


No print, punch bi octal 


40 


5 


tp 


or5 


A 


Last address 



10-20 



RR-171 



- 2 - 



i 

o 

I 

o 
o 
o 



X 



41 


6 


ij 


dd 


of 


42 


7 


qt 


ddl 


cr4 


43 


10 


lq 


q 


25 


u 


11 


qt 


ddl 


cr3 


45 


12 


tv 


cr3 


mm 


46 


13 


la 


cr3 


20017 


47 


14 


tu 


A 


kk 


50 


15 


ra 


cr4 


dd60 


51 


16 


at 


cr3 


tt 


52 


17 


ij 


tt 


kk 


53 


20 


45 





bbl 


54 


odO 


tv 


dd67 


mm4 


55 


1 


45 





cb5 


56 


2 


rs 


bb27 


dd60 


57 


3 


rs 


bb31 


dd60 


60 


4 


45 





cb5 


61 


5 


rj 


cdl 


cd 


62 


6 


tv 


up4 


ualO 


63 


7 


tv 


up4 


ual2 


64 


10 


tv 


val5 


va7 


65 


11 


tp 


val5 


vail 


66 


12 


45 





cb5 


67 


13 


rj 


cd4 


cd2 


70 


14 


45 





cd6 


71 


cfO 


ra 


0*5 


dd3 


72 


1 


ra 


Q 


dd2 


73 


2 


tp 


cs 


pr 


74 


3 


45 





cb7 


75 


kkO 


tp 


(ff) 


Q 


76 


1 


tp 


Q 


ttl 


77 


2 


qt 


dd5 


tt3 


100 


3 


tp 


tt3 


A 


101 


4 


ej 


ddlO 


ef 


102 


5 


ej 


ddll 


mm 


103 


6 


ej 


ddl2 


mm 


104 


7 


rp 


20014 


kkll 


105 


10 


ej 


ddl3 


tp 


106 


11 


rp 


20004 


kkl3 


107 


12 


ej 


dd27 


ramlO 


110 


13 


rj 


ua6 


ua 


111 


14 


rj 


va5 


va 


112 


hbbO 


tp 


ttl 


(ttl) 


113 


1 


tp 


kk 


A 


114 


2 


It 


25 


A 


115 


3 


rs 


dd6 


A 


116 


4 


ej 


or5 


bb21 


117 


5 


ra 


kk 


dd7 



HSS? 

Store first address 

Store last address 
Set up transfer 
of Modified Contents 
Set up first address 
to be modified 
No* of words 

Error 



No punch 



Flex punch 



No print 



Add 76000 to V 

Add 76000 to U and V 

Arrange to print core address 



Mask operation code 

External function 
Final stop 
Interpret 
Commands where 
V only to be modified 
and tape commands ' 
Split instruction, 
Modify U only 
Modify U 
Modify V 
Transfer modified 

Content 
Obtain current 
Address 
Test, end of 
Modifiable address 



10-21 



RR-171 



-* 3 - 



120 


6 


ra 


mm 


dd60 


Add 1 


121 


7 


45 





ebl7 




122 


10 


rj 


ua6 


ua 


Modify D only 


123 


11 


45 





mm 




124 


uaO 


tp 


01/-L 


Q 




125 


1 


lq 


Q 


25 


Mask 1 octal digit 


126 


2 


qt 


dd33 


tt4 


127 


3 


tp 


tt4 


A 




130 


4 


ej 


dd34 


ua7 


Q? 


131 


5 


ej 


dd35 


uall 


A? 


132 


6 


45 





ff 




133 


7 


ra 


ttl 


dd36 


Add 21000 


134 


10 


45 





up 


To print 


135 


11 


ra 


ttl 


dd37 


Add 12000 


136 


12 


45 





up 




137 


vaO 


tp 


ttl 


Q 




140 


1 


qt 


dd33 


tt4 




141 


2 


tp 


tu 


A 




142 


3 


ej 


dd34 


va6 


Q? 


143 


4 


ej 


dd35 


valO 


A? 


144 


5 


45 





ff 




145 


6 


ra 


ttl 


dd40 


Add 21000 


146 


7 


45 





vail 


To print 


147 


10 


ra 


tu 


dd41 


Add 12000 


150 


11 


pr 





dd42 


Carriage return 


151 


12 


pr 





dd43 


Space 


152 


13 


pr 





dd44 


ny*t 


153 


14 


rj 


prlO 


pr 




154 


15 


45 





va5 




155 


upO 


pr 





dd42 


Carriage return 


156 


1 


pr 





dd45 


«u w 


157 


2 


pr 





dd43 


Space 


160 


3 


rj 


prlO 


pr 




161 


4 


45 





ua6 




162 


prO 


tp 


kk 


Q 




163 


1 


iq 


Q 


6 




164 


2 


t P 


dd43 


tt2 


Index 


165 


3 


lq 


Q 


3 




166 


4 


qt 


dcLifC 


A 




167 


5 


at 


dd47 


pr6 


Print digit 


170 


6 


(pr 





ff) 




171 


7 


8 


tt2 


B? 




172 


10 







173 


tpO 


rp 


20004 


kkl4 


Test for tape 


174 


1 


ej 


dd20 


tp2 


Instructions 



10-22 



-4- 



I 

o 

r-H 

a 

o 
o 
a- 



x 
a. 



175 


2 


pr 





dd42 


Carriage return 


176 


3 


rp 


10004 


mm 




177 


4 


pr 





dd60 


Print "tape* 


200 


efO 


pr 





dd42 


Carriage return 


201 


1 


rp 


10005 


ef3 




202 


2 


pr 





dd70 


Print "EF" 


203 


3 


rj 


prlO 


pr 


Print address 


204 


4 


45 





kkl4 


To V address modification 


205 


csO 


rj 


cs4 


csl 




206 


1 


tu 


kk 


tt5 




207 


2 


rs 


U5 


dd4 


Subtract 76000 from V 


210 


3 


tp 


tt5 


Q 




211 


4 


45 





ff 




212 


ddO 








02000 




213 


1 








77777 




214 


2 





76000 


76000 




215 


3 








76000 




216 


4 





76000 







217 


5 


77 










220 


6 





11 







221 


7 





1 







222 


10 


ef 










223 


11 


f8 










224 


12 


ip 










225 


13 


It 










226 


14 


45 










227 


15 


56 










230 


16 


pr 










231 


17 


pu 










232 


20 


rm 










233 


21 


wm 










234 


22 


em 










235 


23 


bm 










236 


24 


rp 










237 


25 


er 










240 


26 


ew 










2a 


27 


sp 










242 


30 


sa 










243 


31 


sn 










244 


32 


88 










245 


33 








70000 




246 


34 








10000 




247 


35 








20000 




250 


36 





21000 







251 


37 





12000 







252 


40 








21000 





10-23 



RR-171 



i 

o 



r-t 
I- 

X 



BWipac 



- 5 - 



253 


41 








12000 


254 


42 








45 


255 


43 








4 


256 


44 








17 


257 


45 








34 


260 


46 








7 


261 


47 


61 





dd50 


262 


50 








37 


263 


51 








52 


264 


52 








74 


265 


53 








70 


266 


54 








64 


267 


55 








62 


270 


56 








66 


271 


57 








72 


272 


60 








1 


273 


61 








30 


274 


62 








15 


275 


63 








20 


276 


64 








2 


277 


65 








5 


300 


66 








3 


301 


67 








bb32 


302 


70 








47 


303 


71 








20 


304 


72 








26 


305 


73 








57 


306 


74 








4 


307 


75 











310 


tto 











311 


1 











312 


2 











313 


3 











314 


4 











315 


5 












Carriage return 

Space 

V 

U 



Flex code 

1 

2 

3 

4 

5 

6 

7 

flex code t 

flex code a 

flex code p 

flex code e 



Shift up 

Shift down 
Not used 



Temporary storage 



10-24 



liii-172 



x 
a. 



Remington Rand Univac 
Floating Vector Arithmetic Package 



GENERAL DESCRIPTION 

This package contains four subroutines: vect'or roll-off, vector 
unpack, scalar product of two vectors, and vector sura. Each of the subrou- 
tines is self-contained and can be used independently of the others. These 
operations are performed on arbitrarily located vectors of not more than 106 
elements* The arithmetic is floating point with one biased characteristic 
serving for all of the elements of a vector. The bias of the characteristic 
is 40,000 (8) . 

PACKED FORM OF A VECTOR 

Associated with every vector, X = (x, , ••• ( x n ) t is a set of numbers, 
(b| t ««« ( b n ) r each element of which is either or 1, This set of numbers is 
defined in the following way: if X|=0, then bj-O; if Xj^O, then bi=l. The 
three binary numbers, 

b 1 x2 35 +b 2 x2 34 +. . ,+b 36 , 
£ b 37 x2 35 +b 38 x2 34 +. a .+b 72 , 

i b 73 x2 35 +b 74 x2 34 +... + b 1()89 

o where b n+ i =b n -|.2 SSo «* ,sI:> i08 sl0 ** nJ *- 1 ®®* are ca l led tne Q-words of the vector X, 



It is clear that a vector is well-defined if the Q-words, the number of ele- 
ments, and an ordered list of the non-zero elements are given. 

The operand vectors of the floating vector subroutines must be 
packed (or stored) in the manner which we now describe. The first three 
addresses of a vector storage location are occupied by the three Q-words, 



" 2 " RS-172 



The mantissae of the non-zero elements of the vector are stored sequentially 
in the addresses immediately following the address of the last Q-word. These 
mantissae are scaled so that the numerically largest has 32 binary digits. 
There are no blank addresses between successive vectors* 

Each vector has a keyword. The v-address of the keyword contains 
the biased characteristic of the vector; the u-address contains the starting 
address (address of the first Q-word) of the vector. The address of the key- 
word of a vector is called the directory address of that vector; the aggregate 
of all the directory addresses of a system of vectors is called the directory 
of that system. The keywords are stored in the same order as the corresponding 
vectors, and there are no blank addresses between successive keywords. Fol- 
lowing the last keyword in the directory is a pseudo keyword. If the last 
non-zero mantissa of the last stored vector is in location y t then y+1 is 
entered in the v-address of the pseudo-keyword. 

NOTATION 

1. Throughout the subroutines three blocks of addresses are utilized 
for vector work spaces and temporary storage. We shall refer to these blocks 
as R, S t and T, By Rj we will mean the i address in the block R. We denote 
by m the number of elements in the operand vectors. 

PROGRAM PARAMETERS 

1. Locations 00005 through 00017 are reserved for constants and 



^ program parameters. 

Q-. 



10-26 



" 3 " RR-172 






I 

O 



00006 
00007 
00010 



The following parameters must be provided by the programmer: 
00005: Restarting address of R 
Sj=starting address of S 
Tjpstarting address of T 
m=number of elements in operand vectors. 
The following parameters are provided by the various subroutines: 
00011: Keyword of vector in R 
00012: Keyword of next vector in the directory 
00013: (u-address) 3+number of non-zero elements of vector in R 
00014: Keyword of vector in S 
00015: Keyword of vector in T 

00016: (u-address) 3+number of non-zero elements of vector in S 
00017: (u-address) 3+number of non-zero elements of vector in T, 

In the event that the programmer wishes to use some of the routines 
without using the whole package^ it will be necessary for him to provide some 
of the parameters in this last group. 

ROLL-OFF 

The roll-off subroutine transfers a packed vector, X, including Q- 
words, from permanent storage to R. It is coded in standard form with one 
exit and one entrance, and is assembly modifiable. 



o UNPACK 

o ■ 

Ch 
«— I 
f- 

x The unpack subroutine unpacks (i.e., provides all zero elements that 

were omitted in the packed vector) the vector, X, contained in R and leaves 
the result in either S or T, depending on which entrance is selected. It is 
coded in standard form with one exit and two entrances, and is assembly modi- 
fiable. 

If -27 



RR-172 

-4- 






t 
O 

i-H 
I 

o 
o 



X 



Before entering t!ie unpack subroutine, X must be rolled-off in R. 
The roll-off provides all program parameters. 

SCALA R PRODUCT 

If X=(Xj,.. .,x n ) and Y=(yj f , „y ), then the scalar product, X*Y, 
is defined by 

m 

X'Y»X x iy .. 
i=l 

The scalar product subroutine forms the scalar product of the vector 
in S and the vector in T„ It scales the mantissa of this product so that it 
contains 32 binary digits. 

If either Xj=0 or yj-0 then, of course, the term xjy^ contributes 

nothing to the scalar product; in this case the subroutine avoids formation 

of the term x^y.. 

We give a brief explanation of how the Scalar product is formed. 

m 

Associated with the sum X«Y = 2T Xfy* are three words 

i=l 

vi • G| Xfc. TCnX^ ' • • • * Cq/ f 

C 9 : c~-x2 +c«~x2 +..«+Cjqq, 
analogous to the Q-words of a vector (i.e., if x.yj=O t then c^O, and if x^yj^O, 
then c.=l; and if n/108, then c n+ j=,..=c,QQ=0), It is clear that if A,, A2, 
Ag are the Q-words of X, and if EL, B2, B„ are the Q-words of Y, then 

Cj = UA-HB.), i=l, 2, 3. 

The subroutine forms Cj, C^, C 3 ; it then stores sequentially in S all those 
Xj, and in T all those y^, for whidh c.=l; finally, with a repeated multiply 
add instruction, it forms the sum. 



10-28 



RR-172 



X-Y =51 (Si) (Ti), 
i=l 

where k is the number of non-zero terms in the sum 

m 

i=l 

Before entering this subroutine the vectors X and Y must be unpacked 

in S and T respectively. The unpack subroutine provides all program parameters. 

VECTOR SUM 

The sum of two vectors X=Cxj t ... t x p ) and Y=(y l9 .,. ,y n ) is defined 
by 

X+Y = (x 1 +y 1 ,.., f x n +y n ). 

The vector sum subroutine forms the sum of the vector in S and the vector in 
T and leaves the result in S, 

The subroutine compares the characteristics of X and Y; it then 
shifts right the mantissae of the vector with the smaller characteristic a 
number of bits equal to the absolute value of the difference of the characteristics; 
next it adds corresponding mantissae of the two vectors; finally it shifts the 
mantissae of the sum until the largest has 32 binary digits. 

Before entering this subroutine, the vectors X and Y must be unpacked 

'—\ 

CM 

£ m S and T respectively. The unpack subroutine provides all necessary para- 

I 

2 meters, 

o 
o 
o 

I— I 

x: 



10-29 



-6- 



RR-172 



Roll-Off 



Author: P» Nikolai 



Type : subroutine 

Code Check by: R. C« Gunderson 

Machine Check by: P. Nikolai 

Correction of Routine: R» C. Gunderson 

Revision of Routine: C. D. Dixon 



Date: 27 August 1956 



Form: Standard 1103 Subroutine ; 
Assembly modifiable 



Exit: 01001 
Entrance: 01002 
Storage Required: 

Instructions: 01000 through 01020 

Constants: 01023 through 01023 

Temporary Storage: 01021 through 01022 

Number of commands for assembly modification: 240 

Preliminary settings: The directory address of the vector to be rolled- 
off must be placed in the u-address of the accumulator. 

Final Results: 

(R)=Q-words and non-zero mantissae of vector 

(00011 )=Keyword of vector 

(00012 )=Next keyword in directory 

(00013 )=3+number of non-zero elements of vector 

Time: 3>64 milliseconds , maximum 



10-30 



-7- 



RR-172 



Unpack 



Author: P« Nikolai 



Type: subroutine 
Code Check by: R« C 9 Gunderson 
Machine Check by: P, Nikolai 
Correction of Routine: 



Revision of Routine: C # P. Dixon 



Form: Standard 1103 Subroutine 
Assembly modifiable 



Date: 27 August 1956 



Exit: 01001 



CM 



i 

o 

I 

o 
o 



X 

Oh 



Entrance for unpack in T: 01002 

Entrance for unpack in S: 01003 

Storage Required: 

Instructions: 01000 through 01046 
Constants: 01047 through 01054 



Temporary Storage: 01055 throug h 01056 
Number of commands for assembly modification: 47, ^ 

Preliminary Settings: Before entering the unpack subroutine, the vector, 
x, must be rolled-off in R, The roll-off subroutine provides all 
program parameters. 

Final Results: 

for unpack in S, 

(S)=Q-words and mantissae of x 

(00014 )=Keyword of x 

(00016 )=3+n umber of non-zero elements of x 



RR-172 
-8- 



for unpack in T, 

(T)=Q-words and mantissae of "X 

(00015 )=Keyword of x 

(00017)-3+number of non-zero elements of x 

Operating instructions: 

1 # Directory address of x — ^> A « 

2. Enter Roll-off subroutine; roll-off x in R. 

3, Enter unpack subroutine at 01002 (01003); unpack x in T(S). 

Time : 32.1 milliseconds. maximum 



10-32 



I 

o 



o 
o 



,9- 



RR-172 



Scalar Product 



Author: E. Feller Date: 27 August 1956 

Type : subroutine 

Code Check by: R» C. Gunderson 

Machine Check by: E« Feller 

Correction of Routine: R„ C 9 Gunderson 

Revision of Routine: C a Do Dixon 



Form: Standard 1103 Subroutine ; 
Assembly modifiable ' 



Exit: 01001 



Entrance: 01002 
Storage required: 

Instructions: 01000 through 01124 

Constants: 01125 through 01141 

Temporary Storage: 01142 through 01152 
Number of commands for assembly modification: 125 ^ 
Preliminary settings: Before entering this subroutine the vectors x and 

y must be unpacked in S ant T respectively. The unpack subroutine 

provides all program parameters. 



£l Final Results: 



(A)=(01152)= mantissa of x.y. 



§ (Q)=(01151)= characteristic of x.y. 



x 

** Accuracy: 32 bits 



Other subroutines used: Roll-off 

Unpack 



10-33 



-10- RR-172 



Operating Instructions: 

1* Directory of x — j>A u . 

2. Enter Roll-off subroutine; ffbll-off x in R. 

3. Enter Unpack subroutine at 01003; unpack x in S« 

4. Directory address of y — ^ A u . 

5. Enter Roll-off subroutine; roll-off y in R» 

6. Enter Unpack subroutine at 01002, unpack y in T« 

7. Enter Scalar product subroutine; for x»y. 

Time: 



10-34 






-11- 



RR-172 



Vector Sum 



Author: P. Nikolai Date: 27 August 1956 

Type : subroutine 

Code check by: R» Gunrierson 

Machine Check by: P« Nikolai 

Correction of Routine: R« Gunderson 

Revision of Routine: C, P. Dixon 



Form: Standard 1103 Subroutine 
Assembly modifiable 



Exit: 01001 



Entrance: 01002 



Storage Required: 

Instructions: 01000 through 01132 

Constants: 01133 through 01142 

Temporary Storage: 01143 through 01146 

Number of Commands for assembly modification: 133 

(8) 

Preliminary settings: Before entering this subroutine, the vectors x 
and y must be unpacked in S and T respectively. The unpack sub- 
routine provides all program parameters. 



i 

2 Final Results: 

i 

o 

§? (S)=mantissae of x-fy. The routine does not provide Q-words for the 

£ vector sum, 

x . _ - 

^ (00014)=characteristic of x+y. 



Accuracy: maximum 32 bits 

Other Subroutines used: Roll -off 

Unpack 



10-35 



~ l2 ~ RR-172 



x 



Operating Instructions: 

lo Directory address of H ^ A u « 

2. Enter Roll-off subroutine; roll-off x in R. 

3, Enter Unpack subroutine at 01003; unpack x in S, 
4* Directory address of y — ^ A u . 

5, Enter Roll-off subroutine; roll-off y in R. 

6, Enter unpack subroutine at 01002; unpack y in T e 
7„ Enter Vector Sum subroutine; form x+y. 

Time: 37+5 milliseconds , maximum 



10-36 



Page 1 of 2 RR - i72 



Unpack 






i 

o 

r~t 

i 

o 
o 
o 



X 
cu 



01000 


00 


00000 


00000 


01001 


45 


00000 


30000 


01002 


45 


00000 


01040 


01003 


16 


00006 


01017 


01004 


16 


00006 


01024 


01005 


16 


00006 


01026 


01006 


11 


00011 


00014 


01007 


11 


00013 


00016 


01010 


31 


00005 


00017 


01011 


15 


20000 


01023 


01012 


15 


20000 


01026 


01013 


21 


01026 


01051 


01014 


31 


00010 


00017 


01015 


35 


01046 


01016 


01016 


00 


00000 


00000 


01017 


11 


01047 


00000 


01020 


11 


00010 


01055 


01021 


23 


01055 


01053 


01022 


11 


01050 


01056 


01023 


11 


00000 


10000 


01024 


11 


10000 


00000 



Alarm exit (not used) 
Normal exit 

Entrance for unpack in T 
Entrance for unpack in S 

Set up 

Keyword of x — ^ 14 

3+ number of non-zero elements of x 



16(u) 



Set up instructions and constants 



Q-word ^ Q 

Q-word >? S (or T) 



10-37 



Unpuck 



Page 2 of 2 



01025 


44 


01026 


01031 


01026 


11 


00000 


00000 


01027 


21 


01026 


01052 


01030 


45 


00000 


01032 


01031 


21 


01026 


01053 


01032 


41 


01055 


01034 


01033 


45 


00000 


01001 


01034 


41 


01056 


01025 


01035 


21 


01023 


01054 


01036 


21 


01024 


01053 


01037 


45 


00000 


01022 


01040 


16 


00007 


01017 


01041 


16 


00007 


01024 


01042 


16 


00007 


01026 


01043 


11 


00011 


00015 


01044 


11 


00013 


00017 


01045 


45 


00000 


01010 


01046 


75 


10003 


01020 


01047 


00 


00000 


00000 


01050 


00 


00000 


00043 


01051 


00 


00003 


00003 


01052 


00 


00001 


00001 


01053 


00 


00000 


00001 


01054 


00 


00001 


00000 


01055 


00 


00000 


00000 


01056 


00 


00000 


00000 



x (unpacked) >* s (°r T ) 



Set up for unpack in T 

Keyword of x •— -^r 15 

3+ number of non-zero elements of x > >M(u) 



Constants and temporary storage 



10-38 



RR* , 172 



Page 1 of 4 



Vector Sum 



CM 



I 

O 

r- 1 
I 

o 
o 



X 

0* 



01000 


00 


00000 


00000 


01001 


45 


00000 


30000 


01002 


31 


00010 


00017 


01003 


35 


01134 


20000 


01004 


15 


20000 


01063 


01005 


15 


20000 


01077 


01006 


15 


20000 


01126 


01007 


11 


01133 


01143 


01010 


35 


01135 


20000 


01011 


15 


20000 


01044 


01012 


15 


20000 


01065 


01013 


15 


20000 


01073 


01014 


16 


00006 


01045 


01015 


31 


00007 


00017 


01016 


15 


20000 


01045 


01017 


21 


01045 


01136 


01020 


15 


01045 


01055 


01021 


16 


00007 


01066 


01022 


31 


00006 


00017 


01023 


15 


20000 


01066 


01024 


15 


20000 


01074 


01025 


16 


00005 


01074 


01026 


21 


01066 


01136 


01027 


15 


01066 


01052 


01030 


21 


0107.1 


01136 



Alarm exit (not used) 
Normal exit 
Entrance 



Set up constants and instructions 



in_^Q 



Page 2 of 4 



KK-lfZ 



Vector 


Sum 






01031 


15 


01074 


01127 


01032 


11 


01133 


01144 


01033 


16 


00014 


01144 


01034 


11 


01133 


01145 


01035 


16 


00015 


01145 


01036 


11 


01145 


20000 


01037 


42 


01144 


01046 


01040 


43 


01144 


01130 


01041 


36 


01144 


01143 


01042 


42 


01137 


01053 


01043 


11 


01145 


00014 


01044 


75 


00000 


01001 


Q1045 


11 


00000 


00000 


01046 


11 


01144 


20000 


01047 


36 


01145 


01143 


01050 


42 


01137 


01056 


01051 


11 


01144 


00014 


01052 


45 


00000 


01001 


01053 


11 


01145 


00014 


01054 


15 


01052 


01064 


01055 


45 


00000 


01060 


01056 


11 


01144 


00014 


01057 


15 


01055 


01064 


01060 


11 


01140 


20000 


01061 


36 


01143 


01143 


01062 


16 


01143 


01064 


01063 


75 


00000 


01065 



If the difference of the characteristics 
exceeds 31,, {) w transmit the larger characteristic 
to 00014; and transmit the corresponding mantissae 
to S, Then go to the. exit 



If the characteristics- differ by less than 
32(10) » shift the mantissae of the smaller 
until the characteristics are equal; transmit 
the larger characteristic to 00014. 



10-40 



Page 3 of 4 






I 

o 

r-i 
I 

o 
o 
o 



X 

a. 



Vector 


Sum 






01064 


54 


00000 


00000 


01065 


75 


00000 


01067 


01066 


21 


00000 


00000 


01067 


31 


01074 


00017 


01070 


15 


20000 


01076 


01071 


15 


20000 


01100 


01072 


21 


01100 


01141 


01073 


75 


00000 


01075 


01074 


12 


00000 


00000 


01075 


11 


01133 


01146 


01076 


11 


00000 


20000 


01077 


75 


00000 


01110 


01100 


42 


00000 


01101 


01101 


55 


10000 


00017 


01102 


15 


01077 


01146 


01103 


23 


01146 


10000 


01104 


21 


01076 


01146 


01105 


23 


01077 


01146 


01106 


21 


01100 


01146 


01107 


45 


00000 


01076 


01110 


47 


01113 


onu 


01111 


11 


01133 


00014 


01112 


45 


00000 


01001 


01113 


74 


20000 


01143 


01114 


11 


01140 


20000 



Add corresponding mantissae and transmit 

toS, 



Find the numerically largest mantissae of 
the sum, and transmit to the accumulator 



Calculate the characteristic of the sum 
and transmit ft to 00014 



10-41 



Page 4 of 4 



Vector 


Sum 






01115 


36 


01143 


01143 


01116 


36 


01142 


01143 


01117 


46 


01122 


01120 


01120 


16 


01143 


01127 


01121 


45 


00000 


01125 


01122 


11 


01140 


20000 


01123 


35 


01143 


10000 


01124 


16 


10000 


01127 


01125 


23 


00014 


01143 


01126 


75 


00000 


01001 


01127 


54 


00000 


00000 


01130 


11 


01145 


00014 


01131 


45 


00000 


01065 


01132 


11 


00014 


10000 


01133 


00 


00000 


00000 ~\ 


01134 


00 


20000 


00000 \ 


01135 


00 


10000 


00000 


01136 


00 


00003 


00003 / 


01137 


00 


00000 


00040 


01140 


00 


00000 


00110 } 


01141 


00 


00001 


00000 / 


01142 


00 


00000 


00003 / 


01143 


00 


00000 


00000 / 


01144 


00 


00000 


00000 / 


01145 


00 


00000 


00000 / 


01146 


00 


00000 


00000 / 



Shift the mantissae of the sum so that the 
numerically largest has 32(io) binary digits, 



Constants and temporary storage 



10-42 



RR-172 



Page 1 of 1 



CM 



i 

o 
o 



X 

a, 



01000 


00 


00000 


00000 


01001 


45 


00000 


30000 


01002 


16 


00005 


01017 


01003 


15 


20000 


01023 


01004 


11 


01023 


01006 


01005 


75 


30002 


01007 


01006 


11 


00000 


00011 


01007 


15 


00011 


01017 


01010 


11 


01022 


00013 


01011 


15 


00012 


00013 


01012 


11 


01022 


01021 


01013 


15 


00011 


01021 


01014 


23 


00013 


01021 


01015 


35 


01020 


01016 


01016 


00 


00000 


00000 


01017 


11 


00000 


00000 


01020 


75 


30000 


01001 


01021 


00 


00000 


00000 


01022 


00 


00000 


00000 


01023 


11 


00000 


00011 



Roll-Off 



Alarm exit (not used) 
Normal exit 
Entrance \ 

/ Set up instructions 

; 

Keyword of x ■*■ >^> 11 

Keyword of next vector < ^I > 12 

Starting address of x ^rl017(u) 

Starting address of next vector p> 13(u) 

Starting address of x . — -~> 1021 (u) 
3+number of non-zero elements of -x ~? 130 



Constants and temporary storage 



10-43 



Page 1 of 5 



Scalar Product 



fs» 



I 

o 



01000 


00 


00000 


00000 


01001 


45 


00000 


30000 


01002 


31 


00007 


00017 


01003 


21 


20000 


00007 


01004 


15 


20000 


01037 


01005 


16 


20000 


01040 


01006 


15 


20000 


01044 


01007 


21 


20000 


01135 


01010 


35 


01136 


01055 


01011 


15 


20000 


01075 


01012 


31 


00005 


00017 


01013 


21 


20000 


00005 


01014 


16 


20000 


01036 


01015 


15 


20000 


01040 


01016 


21 


20000 


01135 


01017 


35 


01136 


01056 


0}02p 


16 


20000 


01075 


01021 


31 


00006 


00017 


01022 


15 


20000 


01036 


01023 


31 


00010 


00017 


01024 


35 


01124 


01035 


01025 


11 


01125 


01142 


01026 


11 


01125 


01143 


01027 


11 


01130 


01145 



Alarm exit (not used) 
Normal exit 
Entrance 



Set up instructions and constants 



10-44 



Page 2 of 5 



RR-172 



Scaler Product 



CM 



1 
o 

r-l 
I 

o 
o 
a- 



x 



01030 


11 


01125 


01151 


01031 


11 


01127 


01146 


01032 


11 


00010 


20000 


01033 


36 


01133 


01147 


01034 


11 


01131 


01150 


01035 


00 


00000 


00000 


01036 


11 


00000 


00000 


01037 


11 


00000 


10000 


01040 


51 


00000 


00000 


01041 


21 


01037 


01132 


01042 


21 


01040 


01134 


01043 


41 


01150 


01037 


01044 


31 


00000 


00000 


01045 


47 


01052 


01046 


01046 


23 


01147 


01137 


01047 


46 


01072 


01050 


01050 


21 


01044 


01132 


01051 


45 


00000 


01044 


01052 


15 


01044 


01053 


01053 


11 


00000 


10000 


01054 


44 


01055 


01067 


01055 


00 


00000 


00000 


01056 


00 


00000 


00000 


01057 


21 


01055 


01134 


01060 


21 


01056 


01134 


01061 


21 


01145 


01132 


01062 


41 


01147 


01064 



x £> R 



Logical product of Q-words of x and y ^^^1^2*^3 



Non-zero x* > ^y R 



Non-zero yj 



Page 3 of 5 



Rfi-172 



Scalar 


Pro 


duct 




01063 


45 


00000 


01072 


01044 


41 


01146 


01054 


01065 


11 


01127 


01146 


01066 


45 


00000 


01050 


01067 


21 


01055 


01132 


01070 


21 


01056 


01132 


01071 


45 


00000 


01062 


01072 


15 


01145 


01074 


01073 


11 


01125 


20000 


01074 


75 


30000 


01076 


01075 


72 


00000 


00000 


01076 


47 


01102 


01077 


01077 


11 


01125 


01151 


01100 


11 


01125 


01152 


01101 


45 


00000 


01121 


01102 


43 


20000 


01107 


01103 


74 


20000 


01151 


01104 


11 


20000 


01152 


01105 


54 


01152 


00105 


01106 


45 


00000 


01113 


01107 


74 


20000 


01151 


01110 


11 


20000 


01152 


01111 


54 


01152 


00105 


01112 


23 


01151 


01126 


01*13 


21 


01151 


01140 


01114 


16 


00014 


01142 



x«y mantissa -~-J> A 
? x*y characteristic — — ■£> Q 



10-46 



Page 4 of 5 



tut -n£ 



Scalar Product 



CM 



O 

r-K 
I 

o 
o 
o 



X 
cu 



01115 


16 


00015 


01143 


01116 


21 


01142 


01143 


01117 


21 


01151 


01142 


01120 


23 


01151 


01141 


01121 


11 


01152 


20000 


01122 


11 


01151 


10000 


01123 


45 


00000 


01001 


01124 


75 


30003 


01037 


01125 


00 


00000 


00000 


01126 


00 


00000 


00110 


01127 


00 


00000 


00043 


01130 


00 


30000 


00000 


01131 


00 


00000 


00002 


01132 


00 


00001 


00000 


01133 


00 


00000 


00001 


01134 


00 


00001 


00001 


01135 


00 


00003 


00003 


01136 


11 


00000 


00000 


01137 


00 


00000 


00044 


01140 


00 


00000 


00003 


01141 


00 


00000 


40000 


01142 


00 


00000 


00000 


01143 


00 


00000 


00000 


01144 


00 


00000 


00000 


01145 


00 


00000 


00000 


01146 


00 


00000 


00000 


01147 


00 


00000 


00000 



Constants 



J 



Temporary storage 



10-47 



tttt-1 16 



Page 5 of 5 



Scalar Product 

01150 00 00000 00000 

01151 00 00000 00000 

01152 00 00000 00000 



10-48 



RR-173 



SIGNIFICANCE PRESERVING FLOATING BINARY POINT ARITHMETIC FOR DIGITAL COMPUTERS 

I, Introduction to the System 

The motivation for this system was a desire to be able to preserve in 
some way an indication of the significance of the result obtained from a series 
of floating binary point arithmetic operations on a digital computer* For the 
sake of abbreviation this system shall be referred to as M SP W . Now the ideas 
and theory of SP are independent of any particular computer. However, since it 
was designed for the ERA 1103, it will be convenient here to make frequent refer** 
ences to the 1103 and to use "1103 language"* 

Most floating point systems use a packed form of 28 bits for the mantissa 
of a floating point number and 8 bits for the characteristic • After each arith- 
metic operation the mantissa is normalized so that 28 bits are always kept in the 
result. Now significant bits can be easily lost by subtraction and this would 
make any computations depending on this result less accurate • But when 28 bits 
are always kept the programmer has no indications of any significance being lost* 
It is the aim of SP to overcome this difficulty by preserving only the significant 
bits in the result of each arithmetic operation* 

A desirable way to accomplish this goal is to make SP a non-normalizing 

system and hence one must use a different representation for floating point numbers « 

The representation used must be capable of indicating how nany significant digits 

2 there are, 
i 

§. A 28-8 packed form was chosen but instead of the terms "mantissa 11 and 

r-i 

r- ■- 

x "characteristic", the terms "si;nJ fjcant p::-rt" and "exponent". t hall be used respec- 






Q* 



tively* In ST, loth the .* i; ul fj.crnt ]"rt r'lul the opponent are into; org* Thus 
lr'tVjv.r y.'--t)i .•••.'' r.:><\ i>i V. < :i tr! "-icnt j:rl. .if th. iv r.w. Lets th-n 2S si;nifionni 



10-49 



_ 2 _ RR-173 



bits. A number, N, in this system, is then of the form 

N = N .2^ 



where N and N are the significant part and exponent respectively. Number© of 

S X 

this type shall be referred to as SP numbers. 

Numerous examples will b# given throughout the rest of this introduction* 
Octal and binary representations will be used and it will be clear in each case 
wliich of the two applies. 

The number 5 written with 3, 10, and 2 significant bits Will appear as 
follows * 

101 x 10°, 
1,010,000,000 x io~ 111 , 
11 x 10 1 » 
Note that in the last case, 101 was rounded to 11 and the exponent adjusted accord- 
ingly. These numbers would appear in packed form in the 1103 as 

0, 000, 000, 000, 000, 000, 000, 000, 000, 101; 00, 000, 000 
0, 000, 000, 000, 000, 000, 001, 010, 000, 000; 11, 111, 000 
0, 000, 000, 000, 000, 000, 000, 000, 000, 011; 00, 000, r ^1 

respectively (recall that the 1103 uses the one's complement system) where the 

semi-colon marks the 28-8 split. 

110 

Consider the SP number 1011 x 10 * This can be thought of as being 

the number 1011,0XXXXX.XXX... 

where the X*s denote uncertain bite and the comma marks the end of the significance. 
Ilote that one bit after the comma it a zero. If this were a one the significant 
P'irt would h'jvo l.cc.n rounded off to 1100. An analogous interpretation can be given 



10-50 



RR-173 



t- 



o 



x 

CL. 



•> 3 ■* 



to SP numbers with negative exponents. 

An SP number, N = N • 2 * eatisfies the following inequality! 



(■ -lA).2^N<(N ♦ 1 /0.2* 



Now suppose N = 0. This inequality implies 
s 

^2fc1 £ k < 2^~ 1 

SP can have many zeros instead of a unique zero. Note that the number x 10' ' 
could be interpreted as the number ± 0XXX300C.XXX..* where the X's are uncertain 
and there are no significant bits, i.e., as a number with order of magnitude only. 
Having these zeros in the system is an advantage* Such zeros can easily be generated 
by subtraction and an SP zero for an answer does not give a false indication of 
significance. 

Let N = 376^521 x 2 17 , M = 754321062 x 2 25 . 

Note that M is a full significance number. Suppose N and M are to be added. To 
do this they must be adjusted so that their exponents are equal. Then the addition 
is performed as follows? 



£ Mi 754321062 



' Nt 37645 



o 

S N-fMt 754360727 



00 x2 17 

21 x2 17 



21 x2 17 



Tho vertical lino indies tes wjicro the significance of the answer stops. Rounding 
ond truncating here gives 

II + J! = 76/.360727 x 2 25 . 



RR-173 



- 4 - 



Note that M was shifted left (25 - 17) = 6 binary places and the 6 bits were 
discarded. If the exponents of two numbers to be added differ by more than 
28 then the larger number can be taken for the answer since there is no point 
in left shifting a number more than 28 places. Thus adding x 2* and 10 x 2 
gives x 2^° for the answer. Take N = x 2 27 , M = 1234 x 2 2 3 and follow 
the same method as above t 



Nt 

Ml 



00, 000, 000, 000 
101, 001 



101, 001 J 110, 



000, 
110, 



x2*3 
x 2 23 



223 



Rounding and truncating gives 110,010 x 10 1 111 , i.e., 52 x 2 ' for N + M. 

Now subtraction reduces immediately to addition. Consider the 
following two problems, however, which are examples of how an SP zero can be 
generated and how significance can be lost* 



>57 



(a) (54 X2?') _ (1 x2 ^) 



64, 



- 1 
+ 1 



00000 
01100 



01100 
Answers x 2 6j/f . 



x2* 7 
x257 



x 2 



57 



(b) (-1073 x 2~ 152 ) - (-43 x 2~ U6 ) 



100011 
100011 



0000 
1011 



-0 1011 



x 2"" 1 * 
x 2152 

,, -->-l f ;2 



10-52 



RR-173 



CO 



- 5 - 



—1 / ( 

Answer i -1 x 2~ (Notei round off makes significant part 

different from zero)* 
Suppose that N and M as given in the first example of addition are 

to be multiplied (N = 3764521 x 2 17 , M = 754321062 x 2 25 ) # 
(3764521) (754321062) =3646563 | 460351722. 
Only 7 octal digits can be kept in the final answer* Therefore the 

above product must be rounded and truncated where the vertical line is* Then 

the significant part of the answer is 3646564* Now 33 bits were discarded* 

This means the exponent of the answer is 

17 + 25 + 33 = 77, 

i.e., N . M = 3646564 x 2 77 . 

Consider the problem of multiplying 2 SP zeros, say N = x 2 ' 

23 
and M = x 2 . By the inequality given above, 



|h| < 2?, | m|| 2 22. 



Hence the product should be such that 

) N . M | < 231. 
In view of this, 0x2^ could be given as the product. However, it turns 



o out that the algorithms and the coding for the 1103 are simplified if the 



gj answer x 2r* (obtained by simply adding ^ and li^) is given. The decision 

was made to give this answer rather than the first one. This does not differ 

cu 

much from the other answer and the advantages outweigh the disadvantages. 

One other case turns up, e.g., (0 x 2 27 ) (1234 x 2'^). Since the 
operand with the least signif jemee is an f<P zero, the answer riven iiuot also 
Le an CP zero. The answer here is obtained by adding the exponents and the 



i i\ rrrt 



RR-173 



- 6- 



number of bits which must be discarded . Hence the exponent iB 

27 + 23 + 12 = 64, 

and the answer is x 2 % 

17 

The division is perhaps more difficult. Consider N = 3764521 x 2 

and M = 754321062 x 2 25 # Before dividing, shift N s and M s left until they 
both have 35 bits (and one leading zero, i.e., sign bit). One then has 
(adjusting the exponents) I 
Nj 011, 111, 110, 100, 101, 010, 001, 000, 000, 000, 000, 000 x 2° 

. 

M; 011, 110, 110, 001, 101, 000, 100, 011, 001, 000, 000, 000 x 2 1 5 

If the division is carried out to 43 places, the result is (discarding remainder 

and not rounding) 

01. 000, 010, 001, 011, 011, 000, I 11, 111, 100, 110, 011, . 

The vertical line indicates where the quotient is to be rounded and truncated 

(keeping same, number of bits as there are in N ). Rounding here and moving 

the binary point to the line gives for the exponent 

- 15 - 23 = - 40, 
Hence the answer is . 

10, 000, 100, 010, 110, 001, x to" 100 ' 000 , 

i.e., 2042661 x 2""^°. 

The next case to consider is N -f M where N = and M s ^ 0. Take 

27 23 

N = x 2 ,M= 1234 x2 ; , Clearly an SP zero is required for the answer. 

Comparing this with the multiplication of the same N and M above would lead 

one to take 

27 - 23 - 12 = -6 



10-54 



RR-173 



>< 



- 7 - 



for the exponent (subtracting 23 and 12 instead of adding). This can be 
justified by the above inequalities also as follows: 

[ N ( < 2 26 and J M [< 1234 x 2 23 < 2 3 > : . 

M 
Now suppose N = 0, M = 0. For example, N = x 2~"° , M = x 2"^, 



Hence 



N 



< 2~ 7 , i.e., N -r M = x 2~ 6 . 



SP zero divisors can be allowed providing the answer is interpreted correctly. 
Comparing again to multiplication, one would be lead to give 

—66 - (-42) = - 24 

for the exponent. This case differs slightly from what the inequalities gives 
as did the same case in multiplication. | N | < 2 , J M ] < 2 . would give 
approximately 2~~* or x 2"^ for an answer. But as in multiplication, it is 
more convenient to take x 2"^ for the answer. Note that in multiplication 
the exponent was given one higher than that given by the inequalities, and here 
it is one lower. One can not put this answer in an inequality very well since 
• if the divisor is small compared to the dividend the result would be large, 
t2 and if the relative sizes are the other way around the answer is small. Hence 



,-2Z 



o • "approximately 2 *"* n was used above. A reliable answer can not be given in 



i 

6 this case. 



If II / and M o = the result is not quite so unpredictable. Take 
s ^> 

IT = 621 x 2~", M = x 2'~ { - # Since the numerator is not zero, the number of 
cite in II should bo added to the difference of the exponents. Hence the exponc: 



•i -■ - ::i:."i 



RR-173 



- l\ - 



(it turns out th.-:t this 3c out of ivin^e - cee [-.art II). Thus the answer is 

-212 
0x2^ . One can argue this case on the basis of the inequalities similarly 

to the previous one. Mote tint here, since the divisor is not bounded away from 

sero, the result is not bounded above, i.e., 

-212 



|N ~ M (>2 . 



This is the interpretation for answers resulting from zero divisors which was 
referred to above. 



10-56 



RR-173 



II. SP Arithmetic Algorithms 
A. General Remarks 

It is intended that the discussion and examples given in 
Part I should serve as motivation and illustrations for the follow- 
ing algorithms. 

A list of the notation used throughout the rest of this 
paper is given here for convenience. 

1. Operands shall be denoted by N and M, where N = N s »2* x and 

M = Ms-2*^ the subscript s denoting the significant 
part and the subscript x denoting the exponent of en SP 
number. 

2. The result of an operation shall be denoted by R = R s »2 x» 

3. B(X) shall denote the number of binary digits in an integer 
X, including one and only one sign bit. This convention is 
used on all bit counts. 

4. Let A = B(N S )> 

B = B(M S )> 

C = B(min(|NsU|M s |)), 

D ~ B(max(|N s J,|M s ))), 

and let J2 be the number of bits of the raw product, quotient, 
or sum of N a and Ms» Observe that C = min(A,B) and D = max(A,B) 

^ B. Addition Algorithm: R = N + M. 

CO 

£; To add N and M it is necessary to adjust them so that 

^ their exponents are equal. This is accomplished by determining 

e-i 

^ - which number has the larger exponent and then shifting the binary 

o 

£ point of the significant part of this number to the right so that 

r- 

x the exponents will be equal. This adjusted significant part is 

a. 



10-57 



RR-173 



- 2 - 



then added to the other unadjusted significant part and the sum 
is truncated rmd rounded to give the significant part of the 
tmswer. The exponent of the answer will be equal to the maximum 
of tho two original exponents. This is the method in brief . 

Without loss of generality, suppose R^ » max (N X ,H X )« 
Then N 3 is shifted left a number of binary places equal to 
(N x - M x ), After adding M fl to this and rounding, the result 
is truncated by discarding the right most (N x - M x ) bits* 
This number becomes R„, the lowest order bit is discarded 
(after the round off as above ) f and R x *= N x + 1« (A carry of 
one bit can produce a 29 bit sum)* In this case if N x = 127 
then Rx H- 1 *= 128 and is out of range. When this happens an 
alarm is given and computation stops. 

Now there is one exception to the above outlined 
procedure. Namely, when 28 < I Nx - M x [ • In this case R is taken 
as the number with the highest exponent. The proceeding method 
would give this result anyway. This exception is necessary 
since the computer used imposes a limit of how much a number can 
be shifted (the exponents could differ as much as 2% and the 
shifting limit is much less than this). 

Note that this algorithm covers all possible SP 
numbers, including zeros, 

C, Subtraction Algorithm! R = N - M, 

To subtract M from N it is necessary only to change the 
sign of M and then add (change the sign of M by replacing M 8 with 
-M s ). The nature of the 1103 puts one restriction on this (see 
part IV, subtract control routine). 



10-58 



RR-173 



- 3 - 



D. Multiplication Algorithm: R = N * M. 

Briefly, multiplication is accomplished by adding the 

exponents, multiplying the significant parts, rounding and 
truncating and then compensating for the truncation by adjusting 
the sum of the exponents. 

In order to determine the number of bits to keep it 
is necessary to count the bits of the operands* The smaller 
count gives the number to keep (this number has been denoted by 
C, see part A above). 

Two distinct cases arise in multiplication. 

Case 1. N s / 0, M s £ 0. In this case N s and M s are 
multiplied and the product is rounded and 
truncated just to the right of the first 
(high order ) C bits. This becomes R s . R^. 

is given by the following: 

Rx = N x + M x + (E -C). 
Note that (E-C) is the number of bits that 
are discarded. 

Case 2. N s = or M 8 = 0. If one of the two operands 
is zero,'i. e. has.no significance, then 
the round off rules require that the; product 



CO 



£ has no significance, i.e. R s = 0. Hence it 

■ is only necessary to compute the exponent, 

V R x# Now if both N s ~ and M s = then 

o- R x = N x + M x . Suppose one of the two is not 

., zero. Then the number of bits it has, minus 

one, (to account for the sign bit) must be 
added to R x + M x . Using the conventions 



10-59 



RR-173 



-4- 



adopted, R is given by 

\ = N x + H^ + (D - 1). 
Note that if N fl = and M fl = then D = 1, and 
this formula agrees with the above statement. 
Thus this equation is used for both possibilities in 
Case 2, 

E. Division Algorithm i R = N -f M, 

Consider first the case N ^ and M_ J, 0. Before 
dividing N Q by M a , they are both scaled up to full 36 bit word 

length and N is shifted left 34 places in the accumulator. This 
s 

assures a 35 or 36 bit quotient, end prevents a zero quotient 

or a divide overflow. This quotient is then rounded and truncated 

the same as in multiplication to give R fl , When computing R the 

scaling up of N s and M 3 , shifting of N , and the number of bits 

s 

discarded from the quotient must be taken into account, C bits 

are kept as in multiplication, hence (E - C) bits are discarded. 

This must be added to N - M • Subtracting 34- accounts for 

shifting K and adding (A - B) accounts for the initial shifting 
s 

of N and M • Thus R is given by 

s S X 

R x = N x - M x - 34 + (A-B) + (E-C). 

Now suppose N = and M / 0. If the above algorithm 
s 

for dividing N by M is followed, the quotient will be zero, 

8 S 

However, the method used for counting the bits of the quotient will 

give a count of 35 (see Part IV), Now C * 1, hence (E - C) = 34 

and this will cancel the -34 in the above expression f or R , 

Since A = 1 the formula reduces to 

R = N - M +' (1 - B) 
x x x 

which is es it should be (B / 1 since M £ 0), Thus the 

8 

algorithm will give R correctly for all cases except when M = 0, 

s 



10-60 



RR-173 



- 5 - 



Suppose M s = 0. Clearly the quotient must also be 
a zero by the ro-;nd off rules used. Hence in this case it is 
necessary only to compute R^. If Ng = 0, R x = N x - M^ But 

if N s 4 then B^ must be adjusted to compensate for this. This 
adjustment is taken care of by adding (A - 1) to (N x - Mx). If 
Ns = then A = 1, hence one can say that for either case 
**= N x -M x+ (A-l). 

F. Comparison Algorithm 

Two SP numbers are defined as equal if their difference 

is an SP zero (see the two examples on subtraction). Hence to 

compare H and M it suffices to subtract M from N and test the 

difference. If N - M is a positive SP number (not a zero) then 

N > M. If N - M is a negative SP number, N < M, and if M - N 

is a zero then N = M. 

"is * 
Note that under this definition ©f equality all SP 

zeros are equal, 

G. Notes: 

In multiplication and division it is possible for R 
to get out of range in two ways, i.e., R > 127 or B^ < - 127, 
If B^ > 127 then an alarm is given as mentioned in part B above. 
If R^ < - 127, low order bits of R s are discarded and the ex- 
ponent is increased to - 127. If R^ + 127 + B(R S ) < 2, i.e., 
^ if all the bits of R s &re discarded and the exponent will still 

£; be out of range, then • 2 x ' c ' is given for the result. 

i 

o . 

£ In all four arithmetic operations the truncating point 

o 

°2; is determined before rounding. Thus it is possible for the round 

h- 

x 
a, 



10-61 



RR-173 



- 6 - 



off to give a carry of one bit., If this extra bit makes 
B(R S ) = 29 then one low order bit is discorded and R^ is increased 
by one. This necessitates testing R^ again to see if it is 
still within range. (R x is always tested before any truncating 
or rounding is done)* 



10-62 



CO 



I 

o 

I— I 
I 

o 
o 



X 
(X. 



RR-173 



III* How to use the SP Interpretative J^rstem 
A. Introduction • 

There are 7 possible SP operations. These are all performed 
via the interpret instruction. The general format of such an 
IP order is IP X MM X BBBB, where X and I are operation codes 
and AAM, BBBB are MC Addresses. Four of the 7 SP operations 
are single address instructions, i.e., the u and v part of 
the IP order are each a complete instruction. This necessitates 
a no-op code to fill in space if the programer happens to have 
an odd number of instructions to perform in a given group of 
IP orders. This no-op instruction makes a total of 8 per- 
mis sable psuedo operations, one corresponding to each of the 
octal digits 0" through 7 (X and I above are single octal 
digits). Two of the SP operations are of such a nature as to 
require both the u and v part of an IP order and hence are 
double address instructions. There is one quadruple address 
instruction, i.e., one which uses two 1103 words. 

The 8 possible instructions and their codes are as follows s 

TTPE 
single address 



CODE 


INSTRUCTION 





No-op. 


1 


Add 


2 


Subtract 


3 


Multiply 


U 


Divide 


5 ■ 


Compare 


C 


Repeat Kultiply Add 



quadruple address 
double address 



Polype-...'' ; 'Vltiply 



10-63 



RR-173 



- 2 - 



These instructions operate on packed operands (see part I 
for method of packing). A psuedo accumulator is used for the 
arithmetic operations, e.g., operation 1 adds the packed 
operand to the packed SP number contained In the psuedo 
accumulator, leaving the result in the psuedo accumulator. 
The other operations are of a similar nature. This psuedo 
accumulator shall henceforth be denoted by fa. The initial 
loading of fa and getting the answers out of fa is left up 
to the programer. Furthermore the contents of the 1103 A- 
register and Q-reglster are not saved. This is not incon- 
venient since the 1103 arithmetic operations use these registers, 
B. Each of the 8 SP operations will now be described individually. 
Part C describes the alarms. See part V for address data. 

0. No - op. 

The code for this is ZZZZ where this 5 digit number can 
be in either the u part or v part of the IP order. The Z's can 
be anything since they are ignored. 

All this order does is to jump to the next instruction, 
which could be the v part of the same IP order or the 1103 
instruction immediately following the IP order (this could be 
another IP order). 

1. Add 

The code for this is 1 AAAA where this 5 digit number 
can be in either the u port or the v part of the IP instruction. 
AAAA must be the KC address of the packed operand to be added to 
fa. 



10-64 



IiR-173 



CO 



o 



- 3 - 



This instruction adds the SP number in MA A to the number 
which is already in fa, leaving the sum in fa. - 

2. Subtract 

The 5 digit code for subtraction is 2 AAAA and this too can be 
either in the u part or v part of the IP order; AAAA is the MC 
address of the operand which is subtracted from the operand already 
in fa. The difference is left in fa. 

3. Multiplication. 

The code here is 3 AAAA in u or v part of IP order. This 
instruction multiplies fa by the SP number in AAAA leaving the 
product in fa. 
4.. Division 

The number U AAAA in the u or v part of an IP order causes 
the SP number in fa to be divided by the SP number in AAAA. The 
quotient is left in fa. 
5. Compare 

This is a quadruple address instruction - a 3 way jump - 
and requires 2 consecutive 1103 words. The format of the code is 
as follows: 

1st word: IP 5 AAAA XXXXX 

2nd word: 00 TTTfl ZZZZ2 



» 

o* This operation compares the SP number in KG address AAAA with the 

h- 

x: SP number in the pcuedo accumulator, fa. It then causes a manual 

jump to one of the addresses XXXX7, YYYYY, or ZZZZZ as follows: 

let the SP number in fa bo denolod by H and the SP number in 



lfWif; 



RR-173 

- 4 - 

AAAA by M, thon if M >N jump is to XXXXX, if M = 2! jump 
is to XYYYY, and if M < N jump ie to ZZZZZ, N te that these 
can bo either MC or MD address. The 2 digits 00 can be any- 
thing since thoy are ignored. 

By choosing the jump addresses correctly one can use 
order 5 for an equality jump, zero jump (if fa contains a zero), 
threshold jump, or a three way jump* 

The final contents of fa is N - M, 

6, Repeat Multiply Add 

Format of code is IP 6 AAAA J BBBB. The number, n, of 
times the operation is to be done must be stored in the MC 
address denoted by wsl6 (work space 16), The J has the same 
function as the j in the usual 1103 repeat instruction. Thus 
if J = 3, this operation multiplies the SP numbers in AAAA 
and BBBB and adds the product to fa, then multiplies the two 
numbers in AAAA + 1 and BBBB + 1 and adds product to fa, etc. 
This is done a total of n times. Hence n operands must be 
stored in consecutive addresses starting at AAAA and n more 
starting at BBBB, If J = 1 then only the BBBB addresses are 
increased by 1 and if J = 2 only the AAAA, .If J s the numbers 
in AAAA and BBBB are multiplied and added to fa n times. 

The first bit of J is ignored, so that J = 4, 5, 6, 7 
will cause the same operation to be performed es J = 0, 1, 2, 
3 respectively. Now if n a the numbor in fa is left unchanged 
and the next instruction after the I* 1 is performed. Further- 
more the index n stored in wsl6 is preserved and can be used 
a£ain, 

7, Polynomial Multiply 

10-66 



RR-173 



-5- 

This SP IP instruction evaluates a polynomial of the 

form P (X) = A f 1 + A ^X*" 1 + .., + A,X + A . 

' n n-1 1 o 

The format of the IP order is IP 7 XXXX XXXX where 

XXXX is the address of X and MAA is the address of A . 

n. 

A , , A ~, .... A must be stored in consecutive addresses 
n-1 n-2 ' o 

following A . The octal digit is ignored. The degree of the 
polynomial, n, must be stored in the MC address denoted by wsl7. 
Note that n is the degree of the polynomial and hence n + 1 
coefficients are required. The only restriction on n is the 
amount of space available in KC for the n + 1 coefficients. 
This n is saved too as is the one for the multiply add operation 
and hence can be used as many times as desired. P(X) is in fa 
after the evaluation is completed. If n = (or if a negative 
integer is given for n) then the first coefficient is left in fa. 
Thus evaluation of a zero degree polynomial is legal. Note that 
the contents of fa prior to the start of evaluating P(X) is lost. 

C. Alarms 

As mentioned previously, there are two alarms in the SP inter- 
pretive system. These are given if the exponent gets out of 
range or if one has an SP zero for a divisor. 

If at any time the exponent of the result of an arithmetic 
operation exceeds 127, the typewriter prints mx xp (maximum exponent) 
and the address of the IP order being performed. This can happen 
co also in the middle of the repeat multiply add or the polynomial 

multiply operation as well as during the simple 



h- 



I 

O 

i— i 

l 

o 
o 



X 



10-67 



RR-173 
- 6 - 



arithmetic operations. After the print out the computer etope 
on a manual stop. Starting will cause the alarm print out to 
be repeated. 

When the SP zero divisor occurs the typewriter prints out 
div = and the address of the IP instruction being performed. 
The computer stops on a manual stop. Starting the computer will 
cause the division operation to be completed and the program 
continues in the normal, manner. 



10-68 



V» Miscellaneous Notes 

-177 
!• If an Input SP number is supposed to be zero use 0x2 

and not an 1103 zero. 

2. It is possible to gain significance in all arithmetic 
operations because of round off and earrys. 

3« If a programmer gets an mx-mp alarm he can reset PAK and 
proceed only if further computations do not depend on the one which gave 
the alarm* The exponent which gave the alarm is lost but some information 
can be obtained by examining the contents of the working space (see coding, 
part IV). 

4-« Every 1103 number except all ones is a legal SP number. 

5. When setting up od2 with the MG address of the operand, 
00-07777-00000 is used for a mask. Thus an MC address must not exceed 
1777 if an 1103 is used. This mask is used for two reasons i 

(a) SP can be used in an 1103A 

(b) If for the 1103 the programmer has 
an illegal address he will get an 
SCO fault instead of the computations 
being done wrong with no warning, 

6. ws and fa must be assigned equal regional values. 

?• All regional assignments should be in MC except pa, ea, da, 
^ and pc which can be in MD to save space (pc can be assigned to any place 

co where the flex codes for through 7 are stored in consecutive order). 

rH 
I 

o 

r— I 
I 

o 
o 
o 

r— I 

X 

a. 



10-69 



RR-173 

•^« Pcrcr:*] tlo n oC In I. <*r pre t .System 

SP io codod using Roco II* There aro 18 regions in the system 
not counting constants and working space, A brief description of each of 
the 18 parts of the program will be given. The coding for these follows. 

I£j Any interpret instruction causes control to be turned over 
to IP. This routine sets up the SP exit, locates and stores the 
interpret order and drives OD* 

£D j OD decodes the SP operation code in the u and/or v part of 
the interpret order. It then causes a jump to the control routine 
corresponding to this operation code (or in case of no-op Jumps 
back to IP). Note that for operations 5 # 6> and 7 OD decodes only 
the u-op since these are not single address instructions* 

CA t Add algorithm control. 

CS i Subtract algorithm control* 

CM* Multiply algorithm control* 

CDs Divide algorithm control* 

CC t Comparison algorithm control* 

CC compares N and M and causes a jump to the speolfled destination 
for each of the three possible cases s M > If, M « If, M < If* 
Note that this is the only control routine that does not eadt 

via the SP EXIT. 

CNj CN controls the repeat multiply addt locates the H^ and M^ 
and does the prescribed multiply add operation* 



10-70 



RR-173 



CO 



i 

o 



~ 2 - 



CP: CP controls the polynomial multiply or polynomial evaluation: 

locates coefficients and X value and computes X A & 

k = k 

EH: KU clears working space and unpacks the SP numbers* 



HQs MD counts the bits of N and M and lines them up. This 

s s 

routine is used only for multiplication and division. 

£A: GA is the basic add algorithm routine. 

CMs GM performs the main part of the multiply algorithm. 

DP : GD performs the main part of the divide algorithm. GD jumps 
to an alarm when a divisor which is zero is encountered. 

HP : RP is the round and pack routine. It is entered immediately 
after the completion of the GA, GM, or GD routines. When RP is 
entered the exponent determined in GA, GM, or GD^is in the 1103 
accumulator and the significant bits of the answer are in ws14-» From 
GM and GD, ws14- contains 36 bits of the rough answer, lined up. 
(if the answer is an SP zero, (ws14-) =0). RP then rounds and 
truncates this at the proper place. From GA, ws14 contains the 



i significant bits of the answer and one extra for round off, except 

o 
-• in the case when the larger number is token for the cum, then it 

cu contains only the significant part of the answer (these bits are 

in the low order part of wa1/,, the higher order bits being sign 

Vits). RP puts the significant part of the answer in A left and 

r -"!: -t ' . T,a Ma .m;;'..\r :* .: * scl . C v.. ::' ra J ; in. fa., E? 



RR-173 



- 3 



£Ai PA prints out the address of the IP instruction in caee there 
is an alarm* 

£A| Exponent alartu EA prints out "bdc xp* 

DA j Divide al&rau DA prints out w div «= O"* 

Note i In the coding annotations that follow, pcta^ numbers are 
used almost exclusively* 



10-72 



RR-I73 



CO 



« 

o 



o 
o 



Cu 



-13 - 



wsO Packed answer (ws = f a = psuedo accumulator) 

1 N 

s 

2 M 

s 

3 N 

x 

4 M 

x 

5 ga: max (N , M ), md and gd: lined up N 

XX 3 

6 ga: IN - M 1, md and gd: lined up M 

'XXI 3 

7 gm: bits of product (E) 

10 B(N s ) 

11 E(K ) 

s 

12 no. bits to keep in rp: B(min (|N , |m () in md, gm, gd; 43 or 44. in ga 

13 md, gm, gd: B(max (|n1, JM g |) 

14- significant part of answer (+ some bits to be discarded) 

15 IP order for decoding 

16 "31" for repeat multiply add 

17 "ai" for repeat polynomial multiply 

20 temporary storage for (CY,, n multiply add 

21 various indexes 



fx "psuedo x - register" —used to store SP operands, 



1 n-73 



WS-174 



Prepared by Pfo. Riohard E. Adler 
Flight Simulation Branch, EML 
White Sands Proving Ground 
New Mexico 



a reiTM to opera tor uw)tt wmms W TO m h 11Q3 

The number 3 " was taken aa a starting point, This number was squared, 
and from the aquare the fourth digit through the eleventh were removed and 
designated aa the first random number. The first random number was multi- 
plied by 3 ^ and the fourth through the eleventh digits of the product be- 
came the second random number. This process was continued for as many 
random numbers as needed. 

If less than 8 digits come out in the result, seros are placed be- 
fore the number until 8 digits are reaohed. When the random numbers are 
used in a problem on the 1103, they are stored on the drum and used as 
needed or put on magnetic tape. 

Listings at the end of this report are from IBM cards containing 7 
sets of 8 digits eaoh. 

The table of random numbers attached can be used for as many digits 
as needed. The digits within the 8 digit groups have been tested for 
randomness also. 



1 

10-74 






I 

O 

r-( 
I 

o 

o 



WSrl^ 



Rr.sni.T3 OF TESTS 

One moans of checking the randomness of theae 8 digit numbers was the 
Chi Square test which ia a teat to determine the goodnesd of fit of the 
actual data to the theoretical distribution* The teat involves the calcu- 
lation of *Y (Chi Square),^ gj? '£ft. h ~..£r. where f » actual frequencies ; 
f s theoretical frequencies* By reference to a set of ~X* tables Chi Square 
may he evaluated, A program was written and this teat was applied to all 
of the 16,000 6-digit groups. The results are found in Table 5* 

In order to check the randomness of the individual digits within the 
groups, the following tests were applied! poker test, even-odd test, fre- 
quencies of ordered pairs and the Chi Square test to individual digits »■ 









TABLE 


I 
















^SffiSLJSESX 
















500 Group i 


$ of 5 










W.vAjSmj,^ 


&222&QL 


*0 


f 


(^o ■- *> 


(*, 


»-*>* 


(f 


o-f> 2 
f 


Busts 


abode 


175 


151 


24 




576 




3.8" 


Pairs 


aabod 


230 


252 


-22 




484 




1.9 


2 Pairs 


aabbc 


61 


54 


7 




49 




-9 


Vn 


amabo 


28 


36 


- 8 




64 




1.3 


Full House 


aaabb 


4 


4 















4 f a 


aaaab 


2 


Z 















5'a 


aaaaa. 






















S ' ' p ' .30 

The value of X a indicates a value for jp of .30. It shows that there 
are 30 chances out of 100 that the fit obtained would be as bad or worse 
than the one shown* 



WS-174 



pESPLTfl OF TESTS (Cont'd) 

Statistically, when a value for p is between ,05 and .95, the data 
is considered satisfactory* The nearer to .95 the higher is the level of 
randomness for the numbers generated* 

TABUS 2(a) 

mmrnxmrn M m mm 

(f - f) (f - f )* ( f c - f )2 

f 

144 .36 

144 .36 

441 1*10 
121 ,30 

400 1.00 
36 .09 

1024 2.56 
9 .02 

49 .12 

256 ,,, , ,64 , 
X^6.55 

P * .75 

The value of X indicates a value for J> of .75. This shows that 
there are 75 chances out of 100 that the fit obtained would be as bad or 
worse than the one shown. 






*o 

38a 


1 


412 


2 


421 


3 


411 


4 


420 


5 


406 


6 


368 


7 


397 


8 


393 


9 


384 



400 


-12 


400 


12 


400 


21 


400 


11 


400 


20 


400 


6 


400 


-32 


400 


-3 


400 


-7 


400 


-16 



3 

10-76 



RFSM/TS OF TESTS' (Cont'd) 







TABLE 


2(b) 










HfflrQPR.TRffl 








hmik 


msmis.& 


('•- 


f) 


100 .05 


Ky«a 


1990 


2000 


-10 




Odd 


2010 


2000 


10 




100 .05 




X % - .w 












P * .95 






i 

o 

I 

o 
o 



X 

CU 



Ths ralna of 1% indicates a valua for p of .95. Thi* shows that tlw»M nr* 
95 chanees out of 100 that the fit obtained would bo us bad or worse tb&n 
the on* ehovn. 

TABUS 3 

ws&mm wMmw m® q? sighs 



F" 


E 

i 


>i*si 


5.45 


.65 





8,60 


♦55 


1 


3.25 


.97 


2 


6,25 


.70 


3 


9,9$ 


.45 


4 


10.06 


.42 


5 


W5 


.60 


6 


10,95 


.35 


7 


7,85 


;65 


8 


19.25 


.04 


9 






Total . 


~~- — 


l_ 









geSoM-ftiWJf 















~T 


$ 


.3 


4 


5 


6 


7 


;•: """8"" 


;*' 


15 


20 


21 


18 


22 


15 


17 


14 


19 


22 


183 


24, 


22 


13 


24 


20 


25 


17 


16 


26 


21 


208 


20 


17 


14 


21 


20 


3L ?'.. 


20 


21 


24 


19 


195 


15 


22 


* 6 


22 


16 


20 


25 


17 


21 


15 


189 


tt 


28 


27 , 


19 


17 


2? 


14 


22 


23 


23 


2X9 


18 


28 


22 


18 


115 


18 


n 


15 


23 


29 


21<> 


19 


17 


19 


h 


23 


20 




iT 


15 


21 


195 


15 


22 


21 


15 ! 23 


X* 


25 


11 


13 


20 


m 


19 


15 


17 


15 


23 


23 


22 


21 


15 


27 


197 


15 


14 


25 


25 


34 


26 


17 


23 


22 


17 


219 


1*3 


205 


196 


191 


216 


209 


207 


178 


201 


214 




6.55 


10.95 


10.10 


7.05 


12.80 


5.45 


9.05 


9.30 


8.75 


» 
9.64 


_._ 


.76 


.35 


. .41 


.72 


.24 


.85 


.45 


.50 


.58 


.48 



WS-174 



nF.sm.T3 o r tr.™ (c nt»d) 

Total - Right to toft Total - Top to Bottom 

X 2 = 7.36 % X = 7.86 

p = .68 p - .65 

2 
The valuea for X indicate, when converted to porcente, tho amount 

of ohancea out of 100 that the fit obtained would be a a bad or voree 

than the one ehoun. 

TABLE 4 



Croup 

00,000,000 - 9,999,999 
10,000,000 - 19,999,999 
20,000,000 - 29,999,999 
30,000,000 - 39,999,999 
40,000,000 - 49,999,999 
50,000,000 - 59,999,999 
60,000,000 - 69,999,999 
70,000,000 - 79,999,999 
80,000,000 - 89,999,999 
90,000,000 - 99,999,999 



- 8~digit numbers done by hand 






f o 


f 


(f - f ) 


(*o - f > 2 


<r 9 -r] 

f 


315 


300 


15 


225 


.7 


304 


300 


K 


16 





345 


300 


45 


2025 


6.7 


302 


300 


2 


4 





294 


300 


-6 


36 


• 1 


268 


300 


-32 


1024 


3.4 


318 


300 


18 


324 


1.0 


275 


300 


-25 


625 


2.0 


284 


300 


-16 


256 


.8 


295 


300 


- 5 


25 

p 



s 12.7 
— *2o 



The value of X^ indicate a a value for p of .28. This shows that 
there are 28 chancee out of a 100 that the fit obtained would be os bad 
or woroe than the one ahown. 



lO-76 



WS-174 






O 

r-t 
i 

o 
o 
o 

I— I 

x 



UL1LCL 2LIES12 (Cont'd) 

TABLE 5 

Qmw mmwm .tesi 

16,000 8-digit numbers tested by th* 1103, 



A iillfclfl i 



00 
10 
20 
30 

40 
50 
60 
70 
SO 
90 



000,000 - 9 
000, J00 - 19 
000,000 - 29 
000,000 - 39 
000,000 - 49 
000,000 - 59 
000,000 ~ 69 
000,000 - 79 
000,000 - 89 



999 
999 
999 
999 
999 
999 
999 
999 
999 



000,000 - 99,999 



,999 
,999 
,999 
,999 
,999 
,999 
,999 
,999 
,999 
,999 



1633 
1612 
1620 
1598 
15U 
1612 
1627 
1609 
1568 
1599 



f 

1600 
1600 
1600 
1600 
1600 
1600 
1600 
1600 
1600 
1600 



(f Q -f) (f -f)2 (f^f)* 



33 

12 

26 

-2 

-86 

12 

27 

9 

-32 

- 1 



1069 

144 

784 

4 

7396 

144 

729 

81 

1024 
1 



f 

•67 

.09 
.49 
00 
62 
09 
45 
05 
64 



X « 7.10 

P * ,72 

Tha ralu* of X^ indicates a Talus for Z> of ,72# This shows that 

thsrs ara 72 obanoes out of 100 that the fit obtained would bs as bad or 
worse than tha one shown. 



1H-7Q 



WS-174 



GAP TEST I Frequency of Length of Gaps between Successive Digits in Sample 

letween Sample Average Gap f Q f (f Q -f) 2 ( f Q -f) 2 P 

raocessivei Siae between digite ■ £■■ 

204 10.6 10.6 10 .36 .036 .85 

1 218 8.9 8.9 10 1.21 .121 .72 

2 209 10.7 10.7 10 .49 .049 .82 

3 207 9.2 9.2 10 .64 .064 .80 

4 205 9.6 9.6 10 .16 .016 .90 

5 216 8.9 8.9 10 1.21 .121 .72 

6 205 10.2 10.2 10 .04 .004 .95 

7 204 9.5 9.5 10 .25 .005 .88 

8 209 10.2 10.2 10 .04 .004 .95 

9 202 9.8 9.8 10 .04 .004 .95 



The Chi Square values of all digits give a aatlafaotory value for P in 
each case. 



10-80 



PX 71900-10-(174) 



o 
t 

CO 



25425013 
52091654 
41505940 

9772606 
54577061 
84209253 
14462379 
50758033 
3 3 873158 
35185855 
89350406 
69512902 
27912823 
40319279 
43709917 
59640776 
50833670 
69221130 
14102943 
45019601 
36797697 
15945567 
59332898 

8157247 

7580823 
51733249 

6274564 
27383443 
49104373 
56535823 
16572943 
77716255 
67125128 
54320653 

6311923 
95020039 
45329916 
94023920 
48778011 
30891640 
34963756 



1544355 
35247776 
70739474 
41666627 
26421999 

2694794 
36712770 
9 9246631 
96319727 
17394992 
79340621 
9 43 49004 
60173235 
90067398 
6 36 68181 
72092429 
79556969 
74101375 

2840746 
69 793315 
929 72 5 89 
19531435 
909559 
98755466 
91731621 
19051813 
17552991 
38976650 
13389124 

6343999 
86133313 
14247515 
31630297 
60998096 

7195700 
16734921 

2892490 
19647381 
98309397 
83659401 
40785928 



92934327 
44974009 
7 259 3 573 
27727856 
54417258 
89987106 
32510446 
15613509 
45769069 
99243589 
76322759 
10958290 
26506534 
146 31337 
89395170 
49419970 
67145092 
58730855 
55336257 
70925172 
16067295 
98416637 
86031030 
32700878 
92211535 
27769798 

7 6 5 3 3 7 6 
53023418 
41355478 
91826215 
54007003 
32030761 
13449306 

3696959 
26611000 
79440161 
34585569 

4726.226 
49685098 
32319012 
82487729 



95996944 
56969404 
54568290 
91241977 
94301999 
5589360 
13029317 

73431533 
8961893 
29817344 
4476355 
4790313 
93172056 
94226739 
547953 
38284777 
56429731 
93543697 
43242663 
95 8929 30 
88498249 
34620792 
25077660 
1437388 
36995748 
63180270 
16 8 92124 
74853550 
55804649 
66942682 
95874774 
74637253 
18840584 
76574637 
79133433 
57975340 
4960496 
31005240 
72409322 
40179798 
25976570 



92154304 
8 3 906 50 7 
43114715 

7924055 
57341452 
63983772 
24549336 

5449197 
51982537 
84631187 
31042506 

4830377 
80277137 
88136797 
57804581 
51061924 
63615501 
66170487 
72377528 
66238920 
69661847 
56317660 
27683326 
48733049 
27330278 
54359847 
72635587 
12256901 
66547138 
25526723 
10753799 
31667667 

4739498 
24462366 
83639966 
62609695 
94739221 
62821931 
15959161 
76699566 
82575826 



51671604 
75683574 
94959820 
65641900 
54215149 
89731175 
63223009 
18280823 
52613798 
61236154 
56508932 
58155151 
39562859 
29814693 
90714747 
53268645 
82407170 
19595307 
16662798 
89405394 
54149717 

2880616 
46493963 
41413508 
^6786549 
3 9 8483 31 
23532062 

1558451 
12210518 
44101968 
19180257 
60799696 
51715372 
32532139 
24024781 
50836254 

9538631 
40020578 
58497433 

1480104 
88371814 



29706453 
9915732 
41387949 
47736366 
45786057 
53584256 
48719068 
81676930 
94289925 
96069017 
14969277 
20716922 
35271808 
10054171 
74239768 
68309031 
41420007 
16193469 
63766778 
156 31291 
84123845 
21228542 
6775191 
20611236 
43981443 
7939262 
32091121 
86825442 
38905209 
86857683 
17092689 
59521323 
53013146 
86418381 
70573170 
18031436 
28506238 
26762593 
22649306 
30278371 
64563019 



i 



•si 



30235574 
81153239 
105 48 20 5 
73681902 
86799209 
3 3 2 56-97 7 
78439042 
50337936 
92845075 
33493094 

9686705 
99241297 
82242238 
53898898 
82803249 
77324974 
77234724 
6 4005183 
27439464 
51133359 
985247-53 
66239168 
31846367 

6044463 
24378609 
14668037 
515447 
17541506 
82412964 
51566297 
33928345 
44336257 
40393830 
50730232 
97260693 
45079606 
8393966.7 
14866526 
29071949 
21219942 
76605374 
62157518 



38972399 
73376193 
506 02431 
69421496 

4939745 
76215763 
80592733 
93 789 7 52 

85 66187 
96993618 
41043495 
93116777 
99230481 

5584842 
501466 2 9 
39043437 
23974 415 
4 08 60 2 44 
3 13 61611 
54587450 
632 07 830 
72657264 

1718482 
25531193 
92 2 2 82 74 
50850225 

4862188 
37214510 
70197084 
200-36349 
38208597 
82290366 
57976033 
40375683 
75806870 
74797687 
53032604 
70011250 
53402300 
85836127 
36057882 

5247943 



81719311 

8 V c. Z> O I O 4 

163723C5 
73383343 
61280389 
31509616 

1042220 

3782829 
60189 566 
78738067 
86956733 

15 8 24 2 7 
57280260 
76102686 
79309901 
54210604 

42 4 8 506 
256361C1 
40572701 
502462 99 
23860994 

5016687 
25359459 
3 5632734 
87751186 

3405594 
13527110 
72233635 
.14667672 
75403567 
5 5476148 
96849164 
82245590 
84341320 
82370130 
51351033 
70644411 
21341220 
21445062 

1106498 
84500605 
52334371 



1816124 6 
2 2 351243 
3196524 3 

f 4 7 7 7 7 '"f J 

-0235921 
24674031 
59908037 
73194638 
75^24270 
36 91566 4 
56957542 
9022 1346 
7921630 
403 26302 
17424707 
52145416 
63724150 
34073307 

4 344-950 3 
64 b 195 9 7 
26376659 
64372271 
3630942 3 
6 97618 3 6 

5 3 5 7531 6 
15183553 
32723275 
45025417 
40582171 
50106283 
86293802 
41539917 
59310058 
41785869 
73165356 

4101679 
34207296 

7 9 259 6 9 
85890509 
49651483 
11627128 
18174384 



7-3 221304 
3538266 / ; 
60661784 

8 4 9 3 '- 1 5 
30 8 71647 

31433714 

74393720 
52087352 
95645010 
561 36231 
18644279 
18479390 
47128147 
37 3 4987 9 

2 26 90 892 
71266766 

5 3 78 2 994 
96138170 
11685696 
11255575 

6 3 4 5 2110 
5853609 

4 7 225 475 

3 7 84 3 614 

3140 0845 
57653498 
94681137 
26766430 
67637166 
18052001 



84283379 
87044596 
29471215 
26759378 
33642619 
93987312 
49449184 
34973667 
54567114 
66873439 
1742225 
40161794 



29461346 
23977231 
72142727 
23 297'?- 2 
P i >- 0^319 
4 3 3 4 93 9 8 
9 5 5 9 7 9 2 2 
4 8 4 9 312 7 
21056267 
96431266 
68^62415 
20 550553 
35840062 
57509274 
9 5 5 52779 
41 8208 8 2 
34114065 
38343974 

33744213 
18324460 
51253255 
13545351 
43664961 
49141596 

7 848201 
1 249589 

95020891 
23903024 
74 8 59404 

8 6 93 64 74 
74715880 
40 253451 
11126232 
92552471 
53327221 
63545604 
54816558 
51163298 
15031390 
64791943 
22200687 
50585291 



■;> /■. u 



7 27 
4479 

65^0 

/, i ' ■'• 

■ x . *•*■ c 

5 loo 

1215 

7980 

7080 

2 8 3 2 

9494 

9099 

^327 

7845 

900 

694 

616 

7605 

4286 

723 

4272 
1579 
3168 
119 
357 
9863 
3139 
2779 
5298 
9151 

8 608 
2779 
2696 
7156 



•0674 
■7267 
94 3 3 
0362 
7913 
3 i 7 8 
3190 

2 2 97 
9 9 97 
7277 
2311 
8041 
5011 
3416 
2411 
7617 
1369 
1082 
3214 
5015 

3 1 95 
9 7 &. =■ 

1031 

"i O "7 O 
-l (_' .' U 

8176 
6166 
6652 
0554 
0749 
9929 
4393 
2408 
4679 
9708 
5458 
3453 
6662 



I 



-1 



PX 71900-10-U74) 



o 
i 

00 
CO 



2 2 67 456 5 
73352331 
94659123 
17703331 
2 5 415 9 

7 410 3 409 
73201615 
33214293 

8 4^-24 8 3 1 
9689323C 
61935511 
90996335 
53674185 
80095769 
61316019 
79278983 
86873582 
66179507 
33185172 
80526018 
95560836 
66518645 
95079140 
49512882 

8080843 
16536122 
96098816 
36868126 
73059370 
16079292 
1059766 
5158619 
14599627 
49170550 
27972279 
554071 
62339674 
64203799 
88033080 
91158471 

m 1 A Q G, f) A 



70 3 80 4 56 
3 20 32 998 
3 3141 4 1 g 
32657253 
36373540 
89096890 
395 745 61 
3 3 4 3 7 8 3 
28869336 
7 3 2 2 9 3 4 3 
630 569 34 
76930036 
2 5 2427 51 
36463 914 
89026840 
87174315 
61184931 

4907373 
69483246 

3287095 
37528560 
15961660 
42613740 
46671028 
97008857 
57737650 

5192675 
60990949 

4871123 
23340522 
16635131 
31122389 

54-11947 

1009419 
85573467 
17677379 
29323899 
88991261 
78564694 
74681235 

A97R4736 



72951720 
3400036 
44696068 
9748 7311 
6 90040 9 S ; 
610557 34 
96032970 
26 287239 
2 6 7 1 
72355633 
73874183 
43938108 
31062189 
98345582 
9724529 
65584858 
25183198 
76696357 
72323576 
91080222 
57659263 
69600964 
96473208 
15410079 
33947181 
86883185 
49649912 
71075482 
21749834 
14370636. 
90754667 
22048496 
44118525 
76685740 
69687478 
17232662 
27633016 
42327238 
66311331 
99205987 
67968153 



3 5615012 
2 265 7501 

8 4 95159 
8453071 
1 4 5 3 6 513 
5 i. 6 3 !>'i '"jo 
98056415 
75139643 
447 7 4 57 5 
91107404 
40607562 
'54278775 
5 7101313 
31358363 
53 6 63277 
43351341 

4 5 4 2 3 3 5 3 
47130056 
20891066 
29210848 
22041913 
68476206 

8533705 
31225525 
62897751 
64482686 
29394591 
9440687 8 

5967242 
12903592 
4 0546150 
15762572 
15185036 
39904749 
54459 
87409855 
89761669 
89455913 
39312160 
95601708 



98811223 
89003974 

5 9 7 6 A 5 7 4 
7532034^ 

8 615 5 9 3 6 

6 413 4 3 4 6 

2 6 3 54 06 9 
46422514 

7 6 3 2 5 2 

3 3 70 5 6 37 
8714289 

3 813 014 

•; U O 5 U i. £ V 

3 6 684 77 2 
8 3 718 815 
89 970185 
29693245 
31293040 
13 343621 
95033421 
6 8546 838 
30336502 
56122497 
8 5 941267 
62503966 
25478958 
52036765 

3050002 
55471207 
96229049 
74652819 
48022325 
17112932 
99372741 
63885487 
55626753 

4 3322108 
54341634 
94637055 
96233791 
2 0897173 



74019207 

3 7 5 2 3 1 9 

65 074040 

94952517 

5 2 74951 
50606715 
99046679 

3 6 2 1 9 9 9 
83 216092 
62222751 
65794263 
42 970263 

6 139530 
3213271 

30 2 88508 
66444549 
83181948 
53305751 
42978511 
93639917 
29851533 
59672216 
15549417 

-6078615 
87726395 
42570780 
20812761 
36473676 
81513026 
44983753 

2506379 
46013112 
54343379 
32757560 
29056951 
28094301 
25595427 
48932499 
88280054 
44166329 
54058228 



28910460 
63806711 
44304789 
4 2 72 54 
82558524 
3170584 
8195829 
2 1 5 ' 



4267 
96 84 
2313 
6052 
2661 
7990 
8880 
2251 



Q' 

9191 
9552 
3 8 99 
6 9 86 

826 
6609 
5169 
7900 
93934924 
96594491 
2 3 319 8 2 2 
86736244 
3036,2324 
17027544 
15248009 

8110311 
41317942 
95896892 
39667879 
63204790 

5387095 
62648788 
44280364 
29191075 
29229452 
63012345 
34136933 

65180980 
97810952 
15127382 
33339253 
18390894 
60523757 



l 








A Q '"> Q 7 C C C 


8 30 7021° 


3 7821065 


25195863 


99241761 


49054460 


90643871 




97264750 


55719263 


804-16 80 6 


18036874 


64092124 


70735296 


5 26325 21 




34127977 


964 071 13 


8316270? 


37617216 


4 2873974 


35311093 


14056192 




13 307336 


1 2 8 1 7 9 7 -°. 


321084 7/ 


94267996 


40804907 


79527484 


98596634 




78479 936 


2 4/i 2 75 3 


3804 413 3 


593713 26 


3 267210 


-■-. -7 o r- r- o -i r 

J / 3 D 5 3 1 D 


76215218 




66177864 


92904 793 


7 791958 2 


9 7 2 7 8 1 3 


2 3 992558 


75780024 


37263952 




5 6 2 5 9 7 1 9 


2 17 7 7 7 5 3 


74 508166 


93927758 


47428678 


56664272 


79159443 




6 7 2 2 3 9 


13 2 3 8603 


71009797 


6 0615071 


34161114 


9716964 


86977855 




7 9 7 5 9 5 6 1 


50637946 


7644391 1 


5 7 2 3 9 3 5 7 


27157850 


27939870 


15748771 




41 766 90 3 


30065335 


14757794 


2 5 72628 3 


21050981 


30304166 


39531139 




63335233 


48945302 


3111794' 


29954395 


47788428 


42772239 


25631638 




42744462 


15802937 


33645423 


67198429 


80492769 


7461818 


13487307 




77425993 


359 786 84 


40134 96 


29172745 


70388233 


23436798 


38419225 




75210197 


7 66 83 808 


95052407 


95876593 


61925278 


43621221 


56973326 




60021127 


34577032 


33236019 


23503464 


34795899 


16 311312 


88089218 




33515994 


5488244 


42995704 


19525887 


76 5 59 947 


37734374 


16419552 




65958525 


96551359 


39106492 


81815019 


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I 



2? 



PX 71900- 16-( 174). 



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60564009 
60690317 
93446 3 39 
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94354925 
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86491620 

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94982745 
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57845508 

8198242 
12125251 
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42536403 
20160375 
94001181 
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CO 

I 



-si 



PX 71900- 10-( 174) 



38792823 


2 9247946 


38433125 


63587008 


88065772 


45029867 


1773&614 


16735160 


86163626 


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6 5 3633.18 


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533 50942 


2 762 2 260 


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26572859 


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54970582 


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4863 3 721 


6 5 72483 8 


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21508691 


15101222 


23247644 


85913408 


27665226 


74186932 


49671697 


6242135 


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6054244 


98832484 


1037669 


66098606 


10729785 


4419830 


51513482 


10658036 


21232174 


27289339 


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774 609 2 7 


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41653247 


53979506 


5155605 


80551311 


43 732388 


24725944 


65442275 


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6569275 


27009461 


14261388 


19648017 


22617-959 


8 8 57276 8 


80586901 


60010240 


4236809 


3103645 


69145000 


79922181 


62004816 


4455365 


6065409 


39256869 


17201501 


51770079 


4702463 


8 36013 79 


82062754 


16104577 


63560761 


20782882 


4428548 


28329789 


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94981925 


29188297 


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51484.123 


76285354 


259 5 36 5 


5 304642 5 


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84 99112 


52 30704 6 


5478 3298 


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7 77 5796 3 


6 72 808 7 8 


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9522572 


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2 01 71 481 


9 56 02 2 64 


2 3 3 317 8 4 


369916 97 


47586674 


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in 
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At 



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93319757 
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en 
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-4 



PX 71900-10-U74) 



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70736631 
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CO 

i 



-4 



PX 71900- 10-( 174) 



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7838195 
82901192 
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60482761 
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32329063 

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PX 71900-10-U74) 



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t— » 



PX 71900-10-(174) 



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PX 71900-10-Q74) 



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38152134 77691283 1873924.2 92859873 22205223 20350909 65126695 

33114642 98628588 36468188 84362545 20035048 62271021 43186962 

46451600 16552928 59949665 37498673 82581075 78268456 99679657 

76877779 43850675 50036751 75267734 51987387 54834593 23465881 

51265759 21122094 17564578 65179398 55909606 66371162 27770457 

81719_030 10256251 91410041 38221923 27705389 63664909 91889919 

69936791 74170020 25262054 73927591 1737652 27772360 1035340 

14645810 96656585 9456998 21461526 36889571 51401522 82263493 

26080153 43746957 31922832 27878879 44801508 36069114 24916477 

56741644 42551537 91430380 73520727 • 93704866 34810867 34732730 

88106777 38286979 16016597 4456920 21174716 21513482 22102794 

91643707 34964384 58452607 67147147 58812637 21061980 71288775 

915996 59904823 31984473 95631923 24057549 52867122 35984198 

24913710 58852315 37305270 10543859 44089734 11130481 71187823 

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13494632 58587503 76502491 94578909 63149619 40952132 60460719 

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7960344 62475188 83460516 11667646 67838770 64823267 11754825 

o 66725L34 53476520 70678215 93908680 10348023 60854150 30591312 

g 56156260 25834365 36759634 95939255 * 79880535 98393493 29519591 

o* 29845861 81555204 9918Q335 50468754 14413538 4911922 70449525 

2711031 30117376 693108'25 47233275 87618884 89797573 42421646 

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41316797 40007381 58162335 88596999 91156376 15745419 26181667 

80931423 66945929 90789643 33704500 49311657 78268650 4557289 

26148438 85663779 11830670 90570828 52092053 46472306 62176050 

66664176 83457602 63909734 40076533 61698785 33879112 46302655 

13079564 58980353 15347367 90295501 91316295 85346419 49236320 

92424783 24581414 26106120 76806219 49015414 65962122 63523192 

37646586 82868889 11219682 82336816 75511521 23147 51143169 

62123522 9545072 83209742 70519756 99377051 19787262 47496049 

4948695 31193024 45184039 59880724 79508980 95243606 2556995 

48914855 55643385 93326791 4043640 71866965 14977881 43122199 

38969125 13083802 43984576 5651994 86151344 10312123 52569094 

44652003 51013112 27283615 76256445 18002024 23228068 72079056 

75868541 98874871 47350276 64862621 '2813601 94317102 80060643 * 

64855821 79953808 18641094 16148827 26213814 45755618 33216195 i 

2692461 44583467 76230568 95345574 21650153 80508500 47347687 ^ 

15612710 50954341 50071671 85251721 69579481 88778223 89013630 ^ 

515573 8406776 4879447 96398147 80954182 61119076 51621296 



PX 71900-10-ei74) 



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PX 71900-10-C174) 



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C/5 
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-4 



PX 71900-10-(174) 



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69644920 
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21061645 
21018620 
64732716 
56404459 
11971540 
44134391 
34781955 
43392945 
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21940933 
76155988 
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90881827 

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96077823 
89217332 
30395573 
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91375929 
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22538017 
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23894457 
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83543996 
39486907 
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8927764 
50694510 
91281851 
41058516 
93326676 
36275523 
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26033880 
43747068 
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39843883 
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76122804 
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36556618 
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66725016 
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46100048 
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31401404 
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61646467 
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55541366 


41935S40 


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63327477 


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35122310 
99702062 
76797937 
85706342 
57798796 

9680372 
57350255 
64434956 
53556409 

1605472 
28971799 
77888958 
91025006 
74544650 
27985130 
13240532 
22974980 
95122240 
60761539 
26753689 
93740010 
20356479 
53879349 
25558621 
80682522 
57109955 
56471336 
21600613 
31426164 
93984815 
47312591 
22838141 
62813778 
69068864 

5149893 
99074425 
86749428 



CO 






PX 7L900-10-U74) 



87816668 
92966770 
94776443 
79647661 
21356832 

2392548 
95031142 
38857524 
93813148 

1152627 
31515722 
58638152 
93770979 
84265488 
25686216 
29182522 
74465173 
65013611 
19978071 
12070244 
93418859 
56452115 
18241453 
45854364 
88262058 
84605559 
46597966 

5903014 
61706340 
91421832 
58030800 
75883252 
10184025 
15018677 
63315710 
73528596 
26460455 
17669417 
54643128 
73219760 
36204516 



16644111 
76604657 
98151939 
87059625 
44464172 
63251496 
34527877 
57255168 
56296042 
78831849 
81302780 
52343551 
17528195 
42744331 
65548522 
76995966 
92423096 
89667515 
46559754 
52412981 
43931956 
27225811 
47875524 
58204262 
63952914 
11366757 
89947277 
34219621 
63548581 
46337271 
12178507 
61800842 
72839098 
15278973 
29937958 
51637398 

4853110 
61683887 

5947811 
87722132 
48808033 



74941466 
15887486 
49316099 
60390899 
75708068 
44799136 

2620165 
69856885 
65819154 
24070938 
31085687 

7987514 
7663-3958 
12117691 
55154625 
18203301 
82976630 

7553607 
10870277 
82120080 

1759353 
60747036 
77007697 
60113316 
46841813 
59050304 
93093253 
45002926 
80792516 
21514496 
77906920 
37691615 
90745500 
57621391 
28151180 

6959182 
26583408 
32689047 
86473787 
41544600 

3353826 



69560317 
51052469 
69011730 
80517012 
26288556 
77766898 
24043308 
2628463 
68128680 
26868657 
63302344 
21505867 
34866721 
39604074 
33907693 
48338473 
89362231 
28797394 
50890291 
18167055 
42629473 
54503415 
79780282 
77869278 
17209572 
96589649 
10902031 
65146083 
10198989 
50628291 
9260262 
7431870 
31363165 
37550661 
54668609 
83854789 
57948290 
71314970 
88579353 
84567405 
67124899 



86534113 
60719309 
88912997 
18368873 
888076 
96741604 
54897417 
50319380 
77535350 
79743777 

5696592 
76315702 
60395009 
33534190 
89029814 
81409306 

9344249 
28817108 
61786631 

2080978 

2197613 
59908270 
96683043 
24070355 
10385205 
67704591 

4658745 
58227639 
91147989 
73268245 
49728996 
93795123 
84589291 
68694511 
51681855 
97365685 
57072390 
55701816 
48830601 
11773443 
25238148 



40819066 
79803405 
82139876 

8532259 
18549613 
10677339 
45978467 
72621993 
25364259 

9261099 

4656409 
74386727 
83513420 
90047821 
53145083 
21360076 
70871107 
73437159 
40565860 
22424287 
82334314 
80948395 
65901853 
10467903 
95220734 
92588003 
61701269 
46658359 
48240691 
79000168 

7545058 
25660216 
90591917 
23387800 
49648585 
76615502 
28283040 
51540880 
49278176 
91293383 
69962789 



75190393 

76082645 

38190372 

45262895 

8273098 

14125707 

73385010 

48763538 

37123636 

13425429 

36702803 

33090992 

23549677 

55593270 

7830342 

1505530 

51350048 

29500156 

65626319 

8968137 

5126122 

74290778 

1256418 

5733177 

72365630 

24462866 

55110690 

61663335 

14994446 

28275347 

56735337 

41384511 

14976882 

2201708 

27151981 

52539821 

6012160 

39262971 

75916828 

36790908 

230401 



w 
1 



o 
i 

I— ' 
CO 



7619424 
54873787 
43868230 
23548429 
41277020 
29567924 
36814798 
85983757 
91529307 
70452701 
36545407 

7605132 
72243055 
97272319 
32084527 
61152829 
37439042 

1552953 
38326932 
40669609 

2445586 
46308403 
32787660 
28018816 
28764174 
67688161 
26379730 
92093653 
48712689 
19827488 
13438682 
86851990 
74836728 
11094471 
65334153 
45448030 
51727448 
46122072 
46081864 
83382084 
84985319 
11878949 



1290293 
52316116 
88089743 
91776182 
73292117 
47355828 
37181097 
32357309 
37928604 
92057165 
28445827 

1885874 
41905257 
212299 
40158988 
61624927 
15675134 
66375335 
28992259 
31467305 
78903169 
147Io26R 
26889507 
89146703 
29247786 
33038107 
15626692 
76223276 

5523939 
71803313 
95234181 
30906854 
75897125 
49605178 
66317303 
97798362 
78011101 

7408383 
84250379 
86947112 
91443281 

3556964 



59290057 
41501947 
48285112 

3608903 
19286526 
86831838 

7012878 
72880331 
97655819 
91622382 
22077016 
36752855 
29898121 
66742043 
28150752 
54967586 
62214265 
10946123 
93292145 
61429754 
71803185 
65490764 
82540966 
93097390 
33932060 
93056075 
41637947 
24427279 
20610859 
33965837 
43120919 
25957652 

9731548 
14000814 

7512046 
34722040 
20736121 
96273780 
85895384 
53543375 
33794015 
71074234 



3680910 
92627507 
56671109 
55809218 
53825443 
94816706 

6257195 
68481533 
51283482 
3488 
37554562 
39452499 
75320450 
47035079 
42628261 

6682597 
83392570 
37080095 

6425636 
67355070 
99789162 
90997958 
47226442 
11944814 

8499964 
38765212 
26218379 
67256405 
88920426 
19178756 

2960607 
87252102 
94596717 
71245370 
67577262 
86019106 
31141542 
95381229 
57491201 
72371771 

7379859 
10239788 



68219329 
62033913 
13873824 
60862938 
88565284 
41886216 
65805200 
71762092 
74494499 
98123210 
44218366 
17670183 

7430534 
56219630 
29658051 
87689409 
42379396 
92392497 
82956174 
57878205 
70426838 

6210247 
70868271 
80404904 
76275215 
10502729 
39958892 
96955538 
62887426 

2464165 
71781272 
76368030 
27247207 
33260388 
273521 
48334806 
23983159 
85160191 
81976031 
93879183 
75714741 
30931801 



77504848 
17695742 
64298138 
93792940 

4267328 
31114204 
78232760 
17516916 

2648024 
46428171 

5882780 
83232734 
56211233 
63706834 
32640603 
60516573 
80657486 
27482509 
50772023 
14396015 
35576830 
87257574 
71109553 
85810845 

9162263 
45922073 
36263830 
81226495 

3455084 
64690262 
20211133 
70064925 
45617719 
37955107 
44187718 

3651283 
55098662 
44825995 
47805914 
54485879 
79793357 
29201887 



62154511 
80565629 
94887620 
98466543 
56347235 
60226362 
48872994 
66545771 

2456697 
28545040 

1874640 
46234111 
95920789 
56512739 
50682389 
13648915 
77820767 
34329118 
90155340 
48831856 
20474252 
73699684 
48344089 
95188382 
51577533 
18250231 
25280334 
43928854 
23593582 

8106005 
26310696 
54912756 
46203311 
37922684 
83227935 
40069176 
70188660 
53840293 
96736146 
11458329 
61851239 
84894540 



5f 



PX 71900-10-C174) 



78009640 
77940365 
99225429 
61082714 

7721098 
44708748 
51664545 
76022956 
86194876 
20945968 
38466141 
62140416 
51512557 
89738287 
59942983 
67258294 
74916109 
86831841 
49885620 
73028669 
43095246 
72209237 
24147306 
46616592 
48937986 
13505563 
92753235 
64549244 
20031715 
51147816 
92232821 
75115893 
90213607 
45892664 
76499431 
58484938 
13129480 

3819894 
96945130 
54504010 
56249050 



80371503 
10599344 
49376871 
15183908 
42975824 
50013174 
99560561 
26238866 
26979746 
28904769 
52857610 
61011304 
61367486 

5919459 
97488189 
19763789 
27314599 
94901101 
50644110 
80725300 
86043014 
42820174 
27743184 
94648082 
35268041 
97659160 
78516987 
45375220 
79259209 
58633592 
98935229 
10424445 
69203974 

7418668 

8496047 
37147566 

2685844 
85755058 
56867693 
67551597 
86033735 



85709556 
79507293 
33798161 
67640235 
81947795 
83096361 
81953478 
79421182 
98360155 
47972815 
40440609 
11964429 
60483684 
94191492 
33194752 
58250368 

8363525 
138076 
88108771 
72728650 
49817757 
29676535 
36659202 
80920872 
10891764 
11053611 
90887219 
69409404 
67769895 
58280936' 
72852202 
20495159 
23945508 
851085 
28157213 

3254474 
86648035 

2202792 
41180104 
83580981 
57219592 



64333538 
67461364 
64870563 
26977723 

3343203 
50643324 
28997666 
60935585 

1196599 
81095654 
31769415 
95336391 
27951033 
36104474 
70554038 
14974089 
70246427 
32110702 
46703313 
96411374 
88619721 
15755189 
89193239 
68044119 
89512868 
76658975 
943242^0 

1851? 36 
5Co49363 
69596130 
82472V-- 
97585987 
66742153 
51673413 
90169151 
17246990 
24407915 
93810423 
31239269 
45104181 

8569248 



17006358 
95314251 
92022471 
60943040 
97421440 
93518220 
65524261 
66964909 
81521167 
56180490 
46833954 
31752627 
61346972 
53033362 

4127660 
70664694 
60590610 
41858453 
75642894 
73813958 
59275185 
32592473 
87157934 
92895512 
86262689 
67547676 
12428935 

4665875 
46231267 
20^71224 

2^69693 
31232334 
52433298 
80596615 
26542702 
58484898 
34804570 
73421343 
88850779 
95044451 
12082832 



65001512 
80006441 
87021780 
65493336 
34483151 
20548971 
93799886 
87857529 
81187313 
36375709 
35385235 
34945941 
20261840 
86159265 
19569455 
15973194 
83166284 
55401453 
71884311 
26278852 
17713496 
38883148 

7413413 
85265155 
55623426 
72504053 

9321258 
64514388 
98794941 
33147260 
58950027 
27975484 
50182001 
18748166 
36895904 
36022299 
12874996 
14101350 
27489640 

6278880 
70765455 



17738086 
16458903 
69490266 
29134845 
76562742 
793832 
25433558 
92389813 
84562960 
32912119 
86527385 
76491418 
72160657 
98925228 
94240310 

6853901 
55933875 
23051148 
84030453 
35207162 
93739525 
56237308 
70641928 
44846941 
68718015 
86359430 
95184883 

4342374 
18632796 
76702792 
94297842 
78105411 
640953 
75471300 
37125674 
23016046 
75506401 
80917079 
33823961 

4751483 
31974525 



i 



-4 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles h^ 7 California 



E valuation of | A - A I I for Matrix A 
Complex Single Precis ion Floating Point 



RW-175 



DET-2 

Page 1 of 6 

7-25-56 



Identification Tag: 
Type; 

Regional Addresses Used 
Storage : 



Entrance and Exit; 
Mode of Operation; 

Machine Time: 



Specifications 

DET-2 

Subroutine available on cards for 
assembly 

00R, 01 R, 02R, 03R, CON, F00, RWT, COO 

132 words total, program storage 

Temporary storage used but not stored 
with program: 

4n cells directly addressable by 
SNIP 

n(n+l) cells all in ES or all in MD 

where 11 is the order of the matrix.. 

The constant and temporary storage pools 
are used* 

RJ OOR01 00R02 

Floating Point. SNIP must be activated 

In ES. 

2 
Approximately n (5n+22)ms (see text) 



Coded by: 
Approved by: 



W. L .. Frank 
W. F. Bauer 



July, 1956 
July, 1956 



10-136 



RW-175 

DET-2 

Page 2 of 6 

7-25-56 

Description 

This subroutine employs complex floating point arithmetic (SNIP) in order to 
evaluate the determinant of the matrix A - A I, where A is a square matrix of 
order n. For the special case A = one obtains the determinant of A. 
Furthermore , one has obtained an eigenvalue A if the quantity 

|a - All = 

The following options are provided: 

Option No. 1 - A must be stored row by row in the memory (ES or MD). The 
location of the first element is supplied in the parameter 
words . 
Option Wo. 2 - A must be supplied to this subroutine row by row by an 
auxiliary routine to be prepared by the programmer to 
fit his needs. This auxiliary must have the form which 
allows for entry from this subroutine by an RJ 00X00 
00X01 instruction assuming it is stored starting at 
location 00X00. The auxiliary will be entered n times, 
each time requiring the succeeding row of A to be set 
up in a region TEMOO preasdigned by the programmer in 
the parameter words. 

In addition to the 132 words .,f storage needed by the subroutine, it is necessary 

to provide kn cells of temporary storage addressable by SNIP and a block of 

n(n+l) cells either all on ES or all on MD. 



r~ Operating Instructions 

r-i 

Y 1* SNIP must be activated. 

o 

7* 2. Entrance to the subroutine is made by *.?io following instructions assuming 

a- A is in the floating accumulator . 

^ a. Option No. 1 - P RJ 00R01 00R02 

** P+l 00 MATOO wv 

P+2 00 TRIOO TEMOO 



RW-175 



DET-2 

Page 3 of 6 

7-25-56 



where 00R00 is the location of the first word of the subroutine. 

MATOO is the region in which the matrix A is stored row by row, 

vww is the order of the matrix A. 

TRIOO is the location of the first cell of the block of n(n+l) cells 
either all in ES or all in MD. 

TEMOO is the location of the first cell of the block of kn cells of 
temporary storage directly addressable by SNIP. 

b. Option No. 2 - P RJ OOR01 OOR02 

. P+l kO 00X00 vww BRR 

P+2 00 TRIOO TEMOO 

where 00R00, wvw, TRIOO and TEMOO are as above. 

00X00 is the location of the first word of the auxiliary which 
supplies the successive rows of A. The auxiliary must 
provide successive rows of the matrix A and place each 
row in the first 2n cells of TEMOO. 

3. Upon exit from the subroutine control Is transferred to the word in 

cell P+3. The value of | A - A 1 1 is left in the floating accumulator and 

also In the ninth and tenth words of the R-W temporary pool. The input X 

can be found in the fifth and sixth words of the R-VT temporary pool. 

Machine Time 

2 
Computing time for operation of this subroutine is given by n (5n + 22) ms 

where n is the order of the matrix. 

In case the block of n(n+l) words is stored on MD the time must be increased 

2 
by 8.5(n + 3b.) milliseconds. These times are approximate and will be conserva- 
tive in most cases. 



Mathematical Method 

Slementary row operations are performed on the matrix A - *A I reducing it to an 
lpper triangular matrix A. Before eliminating, leading elements of two rows 
fhlch are to be linearly combined are compared and the element of largest magni- 
tude becomes the pivotal point. The product of the diagonal elements of A is 
.he value of lA - A 1 1 . 



10-138 



RW-175 



DET-2 
Pg. k of 
7/25/56 



10 



1 

o 



o 

o 



X 



D 




00R00 


00500 


D 




01ROO 


00546 


D 




02R00 


00562 


D 




03R00 


00600 


D 




cokoo 


00625 


D 




FOOOO 


00002 


D 




coooo 


00003 


D 




RWTOO 


00023 


00R00 


MJ 


00000 


00000 


00R01 


MJ 


00000 


00000 


00R02 


54 


00R01 


A0015 BRR 


00R03 


TU 


AOOOO 


00R06 


00R04 


AT 


00015 


AOOOO 


00R05 


TU 


AOOOO 


00R14 


00R06 


TP 


00000 


AOOOO 


00R07 


TV 


AOOOO 


C0N06 


00R08 


TU 


AOOOO 


03R01 


00R09 


TP 


C0N01 


QOOOO 


00R10 


LA 


AOOOO 


00016 


OORH 


TU 


AOOOO 


C0N04 


00R12 


QS 


AOOOO 


01R04 


00R13 


TU 


01R04 


03R00 


00R14 


TP 


00000 


AOOOO 


00R15 


TV 


AOOOO 


02R01 


00R16 


TV 


AOOOO 


03R01 


00R17 


TU 


00R14 


02R29 


00R18 


LA 


AOOOO 


00015 


00R19 


TU 


AOOOO 


01R05 


00R20 


TU 


AOOOO 


02R27 


00R21 


LA 


AOOOO 


00042 


00R22 


•TV 


AOOOO 


01R05 


00R23 


QS 


01R05 


02R06 


00R24 


QS 


01R05 


02R12 


00R25 


QS 


01R05 


02R04 


00R26 


RA 


02R04 


C0N04 


00R27 


TP 


C0N02 


QOOOO 


00R28 


RA 


02R01 


C0N06 


00R29 


RA 


02R01 


C0N06 


00R30 


QS 


02R01 


02R06 


00R31 


RS 


C0N06 


00016 


00R32 


ST 


00016 


RWT02 


00R33 


TN 


FOOOO 


RWT04 


00R34 


TN 


COOOO 


RWTQ5 


00R35 


QS 


03R01 


03R04 


00R36 


TU 


00R06 


00R37 


00R37 


TP 


00000 


AOOOO 


00R38 


SJ 


00R39 


00R45 


00R39 


TP 


01R07 


03R02 



EXIT 



D 



D 



R 



00764 
01042 
01062 
01130 
01161 
00002 
00003 
00027 
00764 
00765 
00766 
00767 
00770 
00771 
00772 
00773 
00774 
00775 
00776 
00777 
01000 
01001 
01002 
01003 
01004 
01005 
01006 
01007 
01010 
01011 
01012 
01013 
01014 
01015 
01016 
01017 

01020 
01021 
01022 
01023 
01024 
01025 
01026 
01027 
01030 
01031 
01032 
01033 



00 
00 
00 
00 
00 
00 
00 
00 
45 
45 
54 
15 
35 
15 
11 
16 
15 
11 
54 
15 
53 
15 
11 
16 
16 
15 
54 
15 
15 
54 
16 
53 
53 
53 
21 
11 

21 
21 
53 
23 
36 
13 
13 
53 
15 
11 
46 
11 



00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00765 
20000 
00017 
20000 
00000 
20000 
20000 
01162 
20000 
20000 
20000 
01046 
00000 
20000 
20000 
01002 
20000 
20000 
20000 
20000 
20000 
01047 
01047 
01047 
01066 
01163 

01063 
01063 
01063 
01167 
00020 
00002 
00003 
01131 
00772 
00000 
01033 
01051 



00000 
OQOOO 
00000 
00000 
00000 
00000 

00000 

00000 
00000 
00000 
20017 
00772 
20000 
01002 
20000 
01167 
01131 
10000 
00020 
01165 
01046 
01130 
20000 
01063 
01131 
01117 
00017 
01047 
01115 
00052 
01047 
01070 
01076 
01066 
01165 
10000 

01167 
01167 
01070 
00020 
00031 
000 33 
00034 
01134 
01031 
20000 
01041 
61132 



TU 


03R01 


SP 


03R02 


TV 


AOOOO 


RA 


03R02 


MJ 


ooooo 


TP 


03R24 


TP 


CONGO 


TP 


00013 


TU 


00013 


RJ 


03R06 


RP 


30000 


TP 


ooooo 


TN 


00016 


RJ 


03R06 


TU 


01R04 


54 


01R05 


TU 


AOOOO 


RA 


RWT03 


TP 


RWT03 


1*p 


00013 


TU 


02R06 


fp 


RWTOO. 


RP 


30000 


TP 


ooooo 


LDPM 


ooooo 


ZJ 


02R04 


LDPM 


ooooo 


TJ 


RWT06 


LDDV 


ooooo 


TN 


F0000 


TN 


coooo 


TP 


CON02 


QS 


02R01 


LDMP 


RWT06 


ADNO 


ooooo 


RA 


02RH 


RA 


00004 


TJ 


C0N04 


TP 


00021 


TP 


02R01 


QA 


02R00 


RS 


02R00 


RA 


RWTOO 


IJ 


RWT01 


RA 


02R27 


55 


02R01 


TV 


QOOOO 


TU 


02R00 


RP 


30000 


TP 


OOOOO 


IJ 


RWT02 



03R02 
00057 

03R02 
00016 
01R00 
03R02 
ftwTOS 
RWT09 
03R06 
O3RO0 
01R06 
OOOOO 
RWT03 
03R00 
02R00 
A0015 
02R01 
00016 
RWT01 
RWTOO 
02R02 
00004 
02R02 
OOOOO 
RWT06 
02R16 
OOOOO 
03R07 
OOOOO 
RWT06 
RWT07 
QOOOO 
02R11 
OOOOO 
OOOOO 
C0N03 
C0N05 
02R11 
QOOOO 
AOOOO 
02R01 
C0N05 
C0N05 
01R15 
C0N05 
Q0021 
02R27 
02R26 
02R28 
OOOOO 
01R07 



BRR 



B 



BS 



BRR 









KW-l/D 






DET-2 








Pg. 5 


of 6 






7/25/56 


01034 


15 


01131 


01132 


01035 


31 


01132 


00071 


01036 


16 


20000 


01132 


01037 


21 


01132 


00020 


01040 


45 


OOOOO 


01042 


01041 


11 


01160 


01132 


61042 


11 


61161 


0063? 


01043 


11 


00015 


00040 


01044 


15 


00015 


01136 


01045 


37 


01136 


01130 


01046 


75 


30000 


01050 


01047 


11 


OOOOO 


OOOOO 


01050 


13 


00020 


00032 


GET ITH ROW 01051 


37 


01136 


01130 


01052 


15 


01046 


01062 


01053 


54 


01047 


20017 


01054 


15 


20000 


01063 


01055 


21 


00032 


00020 


01056 


11 


00032 


00030 


01057 


11 


00015 


00027 


01060 


15 


01070 


01064 


01061 


11 


00027 


00004 


01062 


75 


30000 


01064 


01063 


11 


OOOOO 


OOOOO 


01064 


14 


32000 


25035 


SKIP IF ZEKO 01065 


47 


01066 


01102 


01066 


14 


30000 


24000 


INTERCHANGL 01067 


42 


00035 


01137 


01070 


14 


32000 


20000 


01071 


13 


00002 


00035 


01072 


13 


00003 


00036 


L 01073 


11 


01163 


10000 


I 01074 


53 


01063 


01075 


N 01075 


14 


30035 


14006 


£ 01076 


14 


07000 


OOOOO 


A 01077 


21 


01075 


01164 


R 01100 


21 


00004 


01166 


L 01101 


42 


01165 


01075 


Y 01102 


11 


00025 


loooo 


01103 


11 


01063 


20000 


COMBINE 01104 


52 


01062 


01063 


01105 


23 


01062 


01166 


01106 


21 


00027 


01166 


R 01107 


41 


00030 


0l06l 


OHIO 


21 


01115 


61166 


01111 


55 


01063 


10625 


S 01112 


16 


loooo 


0111$ 


01113 


15 


01662 


61114 


01114 


75 


36000 


61lU 


01115 


ii 


OOOOO 


00006 


01116 


41 


00031 


0105i 



10-140 



RW-175 



















DET-2 

Pg. 6 of 6 


















7/25/5^ 






02R29 


TU 


ooooo 


00004 




01117 


15 


OOOOO 


00004 




02R30 


LDMP 


00000 


RWT08 B 


S PRODUCT 


01120 


14 


32000 


15037 




02R31 


RA 


00004 


C0N04 


OF 


01121 


21 


00004 


01165 




02R32 


RS 


C0N04 


C0N05 


DIAGONAL 


61122 


23 


61165 


61166 




02R33 


IJ 


C0N06 


02R30 




01123 


41 


01167 


01120 




02R34 


RA 


O0R01 


C0N03 


ELEMENTS 


01124 


21 


00765 


01164 




02R35 


TN 


RWT04 


RWT04 




01125 


13 


00033 


00033 




02R36 


TN 


RWT05 


RWT05 




01126 


13 


00034 


00034 




02R37 


MJ 


OOOOO 


00R01 




01127 


45 


OOOOO 


00765 




03R00 


RP 


30000 


03R02 




01130 


75 


30000 


01132 




03R01 


TP 


OOOOO 


OOOOO 


NEXT 


01131 


11 


OOOOO 


OOOOO 




03R02 


RA 


03R01 


C0N04 


ROW 


01132 


21 


01131 


01165 




03R03 


TU 


03R06 


00004 




01133 


15 


01136 


00004 




03R04 


LDAD 


RWT04 


OOOOO 


BS 


01134 


14 


30033 


07000 




03R05 


RA 


03R06 


C0N05 




01135 


21 


01136 


01166 




03R06 


MJ 


OOOOO 


OOOOO 




01136 


45 


OOOOO 


OOOOO 




03R07 


TU 


02R00 


03R19 


D 


01137 


15 


01062 


01153 




03R08 


TU 


O2R0O 


03R22 


E 


01140 


15 


01062 


01156 




03R09 


TP 


CONOl 


QOOOO 


T 


01141 


11 


01162 


10000 




03R10 


QS 


02R04 


03R23 


E 


01142 


53 


01066 


01157 




03RH 


TP 


02R02 


AOOOO 


R 


01143 


11 


01064 


20000 




03R12 


AT 


RWTOO 


AOOOO 


M 


01144 


35 


00027 


20000 




03R13 


QS 


AOOOO 


03R20 


I 


01145 


53 


20000 


01154 




03R14 


TP 


C0N02 


QOOOO 


N 


01146 


11 


01163 


10000 




03R15 


LA 


AOOOO 


00057 


E 


01147 


54 


20000 


00071 




03R16 


QS 


AOOOO 


03R23 


PIVOT 


01150 


53 


20000 


01157 




03R17 


54 


02R01 


A0057 BRR 




01151 


54 


01063 


20071 




03R18 


TV 


AOOOO 


03R20 




01152 


16 


20p00 


01154 




03R19 


RP 


30000 


03R21 




01153 


75 


30000 


01155 




03R20 


TP 


OOOOO 


OOOOO 




01154 


11 


OOOOO 


OOOOO 




03R21 


TN 


RWT08 


RWT08 




01155 


13 


00037 


00037 




03R22 


RP 


30000 


01R15 




01156 


75 


30000 


01061 




03R23 


TP 


OOOOO 


OOOOO 




61157 


11 


OOOOO 


00006 




03R24 


RA 


03R01 


C0N04 




01160 


21 


01131 


61165 




CONOO 


01 


OOOOO 


OOOOO 


F C 


01161 


20 


14000 


OOOOO 




CONOl 


00 


00777 


OOOOO B 





01162 


00 


00777 


OOOOO 




CON02 


00 


OOOOO 


00777 B 


N 


01163 


00 


OOOOO 


00777 




CON03 


00 


OOOOO 


00002 


S 


01164 


00 


OOOOO 


00002 


lO 


CONCH 


00 


OOOOO 


OOOOO 


T 


01165 


00 


OOOOO 


OOOOO 


t— 1 


C0N05 


00 


00002 


OOOOO 


A 


01166 


00 


00002 


OOOOO 


1 


C0N06 


00 


ooooo 


OOOOO 


NTS 


01167 


00 


OOOOO 


OOOOO 


o 

1 

o 
o 
o 

r-\ 

r» 

X 


START 




ooooo 






OOOOO 


45 


OOOOO 


OOOOO 



RW-176 



MTI-1 

Pg. 1 of 8 

7/26/56 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles k$, California 



Floating Point Linear Matrix Equation Solver (AX=B) 
Specifications 



Identification Tag: 

Type: 

Regional Addresses Used; 

Storage: 



Entrance and Exit: 
Alarm: 

Mode of Operation: 
Machine Time: 



MTI-1 

Subroutine available on cards for assembly 

00M, 01M, 02M, 03M, CON, AUG, RWT 

171 words total program storage. 

Temporary storage used but not stored with 
program: 

2(n + m) cells directly addressable 
by SNAP and 

' *■ + nm cells all in ES or all in MD, 

where x is an n by m matrix. 

The constant and temporary storage pools are used. 

RJ OOM01 00M02 

The alarm exit is used to print "SINGUL" 
if a singularity is detected. 

Floating point. SNAP must be in E.S. 

Approximately 

2n (n+ 3m+ 2) + 3000 milliseconds 

where X is an n by m matrix. 



Coded by: 
Approved by: 



W. L. Frank 
w • if > jjauer 



June, 1956 
July, 1956 



10-142 



KW-I/O 



js 



i 
O 



MTI-1 

Pg. 2 of 8 

7/26/56 



Description 

This subroutine employs floating point arithmetic in order to solve the 
linear matrix equation AX = B, where A is a non -singular matrix of size 
nxn and B has the dimensions nxm. The solution X = A B, is a matrix of 
size nxm. For the special case, when B is the identity matrix (i), one 
obtains the inverse of the matrix A. Otherwise , one can solve m sets of n 
simultaneous linear equations in n unknowns. 

Considerable flexibility is afforded the programmer with respect to the 
storage of the matrices A, B and the answer X. The programmer must code 
two auxiliary routines as follows: 

(a) The first must provide successive rows of the augmented matrix 

|A, B . (When B = I, one only need supply rows of A). Each 
row, consisting of (n + m) elements (or n elements when B = I), 
must be transferred to the first (n + m) cells of the 2(n + m) 
cells of temporary storage provided by the programmer. 

(b) The second auxiliary must take the successive columns of X, found 
in the first n cells of the 2(n + m) cells of temporary storage 
and either store them internally or punch them out. 

These auxiliary routines are automatically entered n and m times respectively 

by RJ instructions in the subroutine. The subroutine sets up these two RJ 

instructions from information gleaned from the pa: .meters 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 17! words of storage needed by the subroutine, it is 

necessary to provide 2(n + m) cells temporary storage addressable by SNAP 

and a block of n(n + l) +■ nm cells, either all on ES or all on MP. 

2 
Operating Instructions 



i 

o 

§ 1. SNAP must be activated. 

^" 2. Entrance to the subroutine is made by the following orders (B £ I): 

°* P RJ 00M01 00M02 

P + 1 00 00X00 00Y01 

P + 2 — uuuuu vww 

P + 3 — zzzzz xxxxx 



un-iiu 



MPI-1 

Pg. 3 of 8 
7/26/56 

where 00M00 is the location of the first word of the subroutine 

00X00 is the location of the first word of the first auxiliary 

00Y01 is the location of the second word of the second auxiliary 

uuuuu » m (number of columns of B) 

vww = n (number of rows of A) 

zzzzz = is the location of the first cell of the 2(n + m) cells of 

temporary storage addressable directly by SNAP. 

xxxxx - is the location of the first cell of the block of n(n + l) + nm 

2 
cells all in ES or all in MP , 

3. For the case when B = I, the P + 1 word must be kO 00X00 00Y01 BRR. 

h. The auxiliary routines must be available and coded so that they can be 

entered with 

RJ 00X00 00X01 

and RJ 00Y00 00Y01 respectively. 

This implies that the first and second words of both auxiliaries are exit 

and entrances respectively. 

Alarm Conditions 

If a singular matrix is detected in the process of inversion, the alarm routine 
ALR-1 is entered and "sinful -w„ www" is printed where wwwww is the address of the 
cell from which the subroutine was entered. The routine cannot, however, detect 
all singularities due to round -off errors (see below). 

Starting after an alarm print -out will return control to P + k in the 
main program. 

Machine Time 

The machine time is as indicated on the first page when all operations are carried 

on in ES. This time is exclusive of the times taken by the auxiliaries. In case 

the block of n(n + l) + nm words is stored on MD, the time must be increased by 
2 

- • ■ o ■ ■ o 

8.5(n + 3& + nm + mn) milliseconds. These times are approximate and will be a 
minimum in most cases. 

Mathematical Mathod (Gauss elimination method) 

Elementary row operations are performed on the matrix A reducing it to an upper 

triangular matrix A. At the same time, these operations are performed on the 

matrix B giving a new matrix B. Before eliminating, leading elements of two rows 

are compared and the element of largest magnitude becomes the pivotal element. 

Next, successive columns of B are taken and the equation AX = B is 

10-144 



llfl X * \J 






I 

o 

H 
I 

o 
o 



(X, 



Pg. 4 of 8 
7/36/56 



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 consider the 
magnitudes of the elements of X as compared to those of A. A large order of 
difference may indicate poor conditioning of A. 

Accuracy 

The accuracy in the result is a function of the condition of the matrix A. 
Six to seven decimal place accuracy was obtained for matrices of order 10 to 
16. A test was performed in which the highly ill conditioned Hilbert matrices 
of order 2-10 were inverted. Seven place accuracy was obtained for the matrix 
of order 2. One more digit was lost for each succeeding higher order matrix. 



Jf\ 1 AC 



RW-176 















Pg. 


-i. 
5 of 8 














7/26/56 


D 




OOMOO 


00100 




00144 


00 


OOOOO ooooo 


D 




OlMOO 


00157 




00235 


00 


ooooo ooooo 


D 




02MOO 


00179 




00263 


00 


ooooo ooooo 


D 




03M00 


00208 




00320 


00 


ooooo ooooo 


D 




AUGOO 


00255 




00377 


00 


ooooo ooooo 


D 




CONOO 


00262 




00406' 


00 


ooooo ooooo 


D 




RWTOO 


00023 




00027 


00 


ooooo ooooo 


OOMOO 


37 


75701 


75702 B 


ALARM 


00144 


37 


75701 75702 


OOMOl 


MJ 


ooooo 


OOOOO 


EXIT 


00145 


45 


ooooo ooooo 


OOM02 


54 


OOMOl 


20017 BRB 


ENTRY 


00146 


54 


00145 20017 


00M03 


TU 


AOOOO 


00M09 




00147 


15 


20000 00155 


OOM04 


TU 


AOOOO 


AUGOO 




00150 


15 


20000 00377 


OOM05 


AT 


00015 


AOOOO 




00151 


35 


00017 20000 


00M06 


TU 


AOOOO 


00M26 




00152 


15 


20000 00176 


00M07 


AT 


00015 


AOOOO 




00153 


35 


00017 20000 


00M08 


TU 


AOOOO 


00M19 




00154 


15 


20000 00167 


00M09 


TP 


00000 


AOOOO 




00155 


11 


OOOOO 20000 


OOMlO 


TU 


AOOOO 


OlMOO 


SET 


00X56 


15 


20000 00235 


OOMll 


TV 


AOOOO 


03M31 




00157 


16 


20000 00357 


00M12 


AT 


00015 


AOOOO 


A 


00160 


35 


00017 20000 


0OM13 


SS 


00016 


00015 


U 


00161 


34 


00020 00017 


OOM14 


TU 


AOOOO 


03M31 


X 


00162 


15 


20000 00357 


00M15 


LA 


AOOOO 


00042 


I 


00163 


54 


20000 00052 


00M16 


TV 


AOOOO 


OlMOO 


L 


00164 


16 


20000 00235 


00M17 


TP 


OlMOO 


01M05 




00165 


11 


00235 00242 


00M18 


TP 


C0N01 


QOOOO 




00166 


11 


00407 10000 


00M19 


TP 


ooooo 


AOOOO 


S 


00167 


11 


OOOOO 20000 


OOM20 


TV 


AOOOO 


01M03 


E 


00170 


16 


20000 00240 


00M21 


TU 


AOOOO 


01M03 


T 


00171 


15 


20000 00240 


00M22 


TU 


AOOOO 


02M25 




00172 


15 


20000 00314 


00M23 


QS 


01M03 


02M05 




00173 


53 


00240 00270 


00M24 


QS 


01M03 


02M10 


A 


00174 


53 


00240 00275 


00M25 


TU 


02M25 


02M03 


D 


00175 


15 


00314 00266 


00M26 


TP 


ooooo 


AOOOO 


D 


00176 


11 


OOOOO 20000 


00M27 


TU 


AOOOO 


C0N04 


M R 


00177 


15 


20000 00412 


00M28 


TV 


AOOOO 


C0N06 


N E 


00200 


16 


20000 00414 


00M29 


54 


C0N06 


20017 BRB 


S 


00201 


54 


00414 20017 


OOM30 


QS 


AOOOO 


AUG02 


S 


00202 


53 


20000 00401 


00M31 


AT 


02M25 


AOOOO 


E 


00203 


35 


00314 20000 


00M32 


QS 


AOOOO 


03M20 


S 


00204 


53 


20000 00344 


00M33 


QS 


AOOOO 


03M29 




00205 


53 


20000 00355 


0OM34 


TP 


AUG02 


AOOOO 




00206 


11 


00401 20000 


00M35 


AT 


C0N04 


AOOOO 




00207 


35 


00412 20000 


00M36 


QS 


AOOOO 


C0N05 




00210 


53 


20000 00413 


00M37 


QS 


AOOOO 


01M02 




00211 


53 


20000 00237 


0OM38 


RA 


02M03 


C0N05 




00212 


21 


00266 00413 


00M39 


55 


C0N04 


10025 BRB 




00213 


55 


00412 10025 


00M40 


TV 


QOOOO 


C0N07 




00214 


16 


10000 00415 


00M41 


TP 


C0N03 


QOOOO 




00215 


11 


00411 10000 


00M42 


54 


03M20 


20071 BRB 




00216 


54 


00344 20071 



10-146 



RW-176 



MTI-1 

Pg. 6 of 8 

7/26/56 



00M43 


QS 


AOOOO 


AUG03 






00217 


53 


20000 


00402 


Q0M44 


TV 


AUG03 


AUG04 






00220 


16 


00402 


00403 


00M45 


TV 


AUG03 


02M27 






00221 


16 


00402 


00316 


00M46 


AT 


C0N07 
AOOOO 


AOOOO 






00222 


35 


00415 


20000 


00M4V 


QS 


O2H0i 






00223 


53 


20000 


00264 


O0M48 


OS 


AOOOO 


02M05 






00224 


53 


20000 


00270 


00M49 


AT 


C0N06 


AOOOO 






002 2 5 


35 


00414 


20000 


00M50 


QS 


AOOOO 


03M16 






002 26 


53 


20000 


00340 


00M51 


QS 


AOOOO 


03M20 






00227 


53 


20000 


00344 


00M52 


QS 


AOOOO 


03M25 






00230 


53 


20000 


00351 


00M53 


QS 


AOOOO 


03M28 






00231 


53 


20000 


00354 


00M54 


RS 


C0N06 


00016 






00232 


23 


00414 


00020 


00M55 


ST 


00016 


RWT02 






00233 


36 


00020 


00031 


00M56 


RS 


C0N07 


00016 






00234 


23 


00415 


00020 


01 MOO 


RJ 


00000 


OOOOO 


TO AUX 1 


00235 


37 


OOOOO 


OOOOO 


01M01 


RJ 


AU606 


AUGOO 


AUGMENT 


00236 


37 


00405 


00377 


01M02 


RP 


30000 


01M04 






00237 


75 


30000 


00241 


01M03 


TP 


ooooo 


OOOOO 






00240 


11 


OOOOO 


OOOOO 


01M04 


TN 


00016 


RWT03 


SET 


INDEX 


00241 


13 


00020 


00032 


01M05 


RJ 


ooooo 


OOOOO 


GET 


ITH ROW 


00242 


37 


OOOOO 


OOOOO 


01M06 


RJ 


AUG06 


AUGOO 


AUGMENT 


00243 


37 


00405 


00377 


01M07 


TU 


01M02 


02M00 






00244 


15 


00237 


00263 


01M08 


54 


01M03 


20017 BRB 






00245 


54 


Q0240 


20017 


01M09 


TU 


AOOOO 


02M01 






00246 


15 


20000 


00264 


01M10 


RA 


RWT03 


00016 






00247 


21 


00032 


00020 


01M11 


TP 


RWT03 


RWT01 






00250 


11 


00032 


00030 


01M12 


TP 


00013 


RWTOO 






002 51 


11 


0OO15 


00027 


01M13 


TP 


CONOl 


QOOOO 






00252 


11 


00407 


ioooo 


01M14 


QS 


02M05 


01M15 






00253- 


53 


00270 


00254 


oiMi5 


tM 


ooooo 


00002 






00254 


12 


OOOOO 


00O02 


0lMl6 


TU 


0lMl5 


03M44 






00255 


15 


002^4 


00374 


6iMi7 


55 


6lHl5 


20025 feftB 






00256 


55 


00254 


20025 


01M18 


RA 


AOOOO 


03M46 






00257 


16 


20000 


00376 


6iMi9 


6lMl5 


00015 






60266 


21 


00254 


0001? 


01M20 


TP 


00002 


Aoooo 






00261 


11 


00002 


20000 


01M21 


ZJ 


02M00 


02M14 


SKIP IF ZERO 


00262 


47 


00263 


00301 


02MO0 


RP 


30000 


02M02 


TRANSMIT ITH 


00263 


75 


30000 


00265 


£ 02M01 


TP 


ooooo 


OOOOO 


ROW 


TO ES 


00264 


11 


OOOOO 


OOOOO 


^ 02M02 


TP 


RWT00 


00004 


B BOX 


00265 


11 


00027 


00004 


Y 02M03 


TM 


ooooo 


Aoooo 






00266 


12 


OOOOO 


20000 


2 02M04 


TJ 


00002 


03M38 






00267 


42 


06002 


00366 


o 02M05 


LDDV 


ooooo 


00000 B 






00270 


14 


32000 


20000 


§. 02M06 


TP 


00002 


RWT08 






00271 


11 


00002 


00037 


£ 02M07 


TP 


C0N03 


QOOOO 


L 




00272 


11 


00411 


10000 


x 02M08 


QS 


02M01 


02M09 


I 




00273 


53 


00264 


00274 


^ 02M09 


LDMP 


RWT08 


OOOOO 


N 




00274 


14 


30037 


14000 


02M10 


SUNO 


OOOOO 


OOOOO BS 


E 


00275 


14 


13000 


ooood 


02M11 


RA 


02M09 


00016 




A 


00276 


21 


00274 


00020 


02M12 


RA 


00004 


00015 




R 


00277 


21 


00004 


000 it 


02M13 


TJ 


C0N05 


02M09 




L 


00300 


42 


00413 


00274 



1H-1A7 



RW-176 



MTI-1 

Pg. 7 of 8 

7/26/56 



TP 
TP 
QA 
RS 
RA 
IJ 
RA 
55 
TV 
TU 
RP 
TP 
IJ 
TP 
TP 
TV 
TU 
TP 
OS 
TP 
TP 
RA 
MJ 
RS 
RA 
RA 
TU 
RS 
RP 
TP 
RA 
TN 
TP 
TP 
TP 
LOMP 
AD NO 
RS 
lJ 
RA 
NOLD 
ZJ 
TN 
NODV 
STNO 
IJ 
RJ 
RA 
I J 



00021 
02M01 
02M00 
02M00 
RWTOO 
RWT01 
02M25 
02M01 
QOOOO 
02M00 
30000 

00000 

RWT02 
C0N02 
C0N06 
03M16 
02M01 
00021 
00013 
00016 
00013 
03M14 
00000 
03M14 
03M13 
RWT01 
03M14 
03M14 
30000 
00000 
03M16 
00000 
00013 
RWT03 
00013 
00000 
RWT06 
00004 
RWTOO 
RWT03 
00000 
03M27 
RWT06 
00000 
00000 
RWT05 
00000 
RWT02 
C0N07 



QOOOO 
AOOOO 
02M01 
00015 
00015 
01M15 
00015 
10025 
02M25 
02M24 
02M26 
00000 
01M05 
00000 
RWT05 
03M14 
03M14 

Ooooo 

03M13 
RWTOl 
RWT03 
00015 
03M09 
C0N04 
00015 
00015 
03M16 
RWTOl 
03M15 
OOOOO 
RWT02 
OOOOO 
00004 
RWTOO 
RWT06 
OOOOO 
OOOOO 
00015 
03M20 
00016 
OOOOO 
03M36 
00002 
OOOOO 
OOOOO 
03M08 
OOOOO 
00015 
02M27 



COMBINE 
R 







BRB 



W 



REPLACE 

REDUCED ROW 
N-2 TIMES 



B 



B 



TRANSFER 
ROWS OF 
UPPER 

TRIANGULAR 
MATRIX 



B 



B S 



U 



U 



TO AUX 2 



00301 

00302 

00303 

00304 

00305 

00306 

00307 

00310 

00311 

00312 

00313 

00314 

00315 

00316 

00317 

00320 

00321 

00322 

00323 

00324 

00325 

00326 

00 3 27 

00 3 30 

00 331 

00332 

00333 

00334 

00335 

00336 

00337 

00340 

00341 

00542 

00343 

00344 

00345 

00346 

00347 

00350 

00351 

00352 

00353 

00354 

00355 

00356 

00357 

00360 

00361 



11 00025 
11 00264 

52 00263 
23 00263 
21 00027 
41 00030 
21 00314 
55 00264 
16 10000 

15 00263 
75 30000 
11 OOOOO 
41 00031 
11 00410 
11 00414 

16 00340 
15 00264 
11 00025 

53 00015 
11 00020 
11 00015 
21 00336 
45 OOOOO 
23 00336 
21 00335 
21 00030 
15 00336 
23 00336 
75 30000 
11 OOOOO 
21 00340 
i3 OOOOO 
11 00015 
11 00032 
11 60015 
14 32000 
14 05035 
23 00004 
41 00627 
21 00032 
H OOOOO 
47 00353 
i3 0003£ 
14 OOOOO 
i4 3600O 
41 00034 
37 OOOOO 
21 00031 
41 60415 



10000 
20000 
00264 
00017 
00017 
00254 
00017 
10025 
00314 
00313 
00315 
OOOOO 
00242 
OOOOO 
00034 
00336 
00336 

ioooo 

00335 
00030 
00032 
0001? 
00331 
00412 
00017 
00017 
00340 
00030 
00337 
OOOOO 
00031 
OOOOO 
00004 
0002"/ 
0003$ 
16000 
OOOOO 
00017 
00344 
00020 
32000 
00364 
00002 
22000 
OOOOO 
00336 
OOOOO 
00017 
06316 



10-148 



'Ill J. 1 \J 



SO 



o 
o 



X 



MTI-1 

Pg. 8 of 8 

7/26/56 



03M34 


RA 


00M01 


C0N08 




00362 


21 


00145 


00416 


03M35 


MJ 


ooooo 


00M01 




00363 


45 


OOOOO 


00145 


03M36 


11 


CONOO 


75756 BRB 


TO ALARM 


00364 


11 


00406 


75756 


03M37 


MJ 


OOOOO 


OOMOO 




00365 


45 


OOOOO 


00144 


03M38 


TU 


02M03 


03M46 


INTERCHANGE 


00366 


15 


00266 


00376 


03M39 


TU 


02M00 


03M43 




00367 


15 


00263 


00373 


03M40 


TU 


02M00 


03M45 


R 


00370 


15 


00263 


00375 


03M41 


55 


02M01 


20025 BRB 





00371 


55 


00264 


20025 


03M42 


TV 


AOOOO 


03M44 


W 


00372 


16 


20000 


00374 


03M43 


RP 


30000 


03M45 


S 


00373 


75 


30000 


00375 


03M44 


TP 


ooooo 


ooooo 




00374 


11 


OOOOO 


OOOOO 


03M45 


RP 


30000 


02M00 




00375 


75 


30000 


00263 


03M46 


TP 


ooooo 


ooooo 




00376 


11 


OOOOO 


OOOOO 


AUGOO 


TP 


00000 


AOOOO 


TEST TO SEE 


00377 


11 


OOOOO 


20000 


AUGOl 


SJ 


AUG02 


AUG06 


IF INVERT 


00400 


46 


00401 


00405 


AUG02 


RP 


10000 


AUG04 




00401 


75 


10000 


00403 


AUG03 


TP 


00013 


ooooo 


AUGMENT 


00402 


11 


00015 


OOOOO 


AUG04 


TP 


C0N02 


ooooo 


IDENTITY 


00403 


11 


00410 


OOOOO 


AUG05 


RA 


AUG04 


00016 




00404 


21 


00403 


00020 


AUG06 


MJ 


ooooo 


OOOOO 




00405 


45 


OOOOO 


OOOOO 


CONGO 


24 


14061 


33411 B 




00406 


24 


14061 


33411 


CONOl 


00 


00777 


OOOOO B 


CONSTANTS 


00407 


00 


00777 


OOOOO 


C0N02 


01 


ooooo 


OOOOO F 




00410 


20 


14000 


OOOOO 


C0N03 


00 


ooooo 


00777 B 


AND 


00411 


00 


OOOOO 


00777 


C0N04 


00 


ooooo 


OOOOO 




00412 


00 


OOOOO 


OOOOO 


C0N05 


00 


ooooo 


OOOOO 


TEMPORARY 


00413 


00 


OOOOO 


OOOOO 


C0N06 


00 


ooooo 


OOOOO 


STORAGE 


00414 


00 


OOOOO 


OOOOO 


C0N07 


00 


ooooo 


OOOOO 




00415 


00 


ooooo 


OOOOO 


C0N08 


00 


ooooo 


00003 




00416 


00 


ooooo 


00003 


START 




00M00 






OOOOO 


45 


ooooo 


00144 



10-149 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles k-5, California 

Complex Single Precision Floating Point Linear 
Matrix Equation Solver (AX - B) 

Specifications 



RW-177 

MTI-2 

Pg. 1 of 8 

e/3/56 



Identification Tag: 

Type: 

Regional Addresses Used; 

Storage : 



Entrance and Exit : 
Alarm: 

Mode of 0|. it ion: 

Machine Time : 



MTI-2 

Subroutine available on cards for assembly 

OGM, 01M, 02M, 03M, CON, AUG, RWT 

185 words total program storage. 

Temporary storage used but not stored with 
program: 

k(n + m) cells directly addressable by 
SNIP, and- 

n(n + l) + 2nm cells all in ES or all in 
MD, where X is an n by m matrix. 

The constant and temporary storage pools are 
used. 

RJ 00M01 00M02 

The alarm exit is used to print "SINGUL" 
if a singularity is detected. 

Floating point. Complex mode of SNIP must be 
activated In ES. 

See Text. 



Coded by: 
Approved by: 



W. L. Frank 
W. F. Bauer 



June, 1956 
June, 1956 



10-150 



mt-2 

Pg. 2 of 8 
8/3/56 



Description 



This subroutine employs single precision complex floating point 
arithmetic (SNIP) in order to solve the linear matrix equation AX ~ B, where 
A is a non -singular matrix of size nxn and B has the dimensions nxm. The 
solution, X = A HB, is a matrix of size nxm. For the special case, when B 
is the identity matrix (I), one obtains the inverse of the matrix A. Otherwise 
one can solve m sets of n simultaneous linear equations in n unknowns. 

Considerable flexibility is afforded the programmer with respect to the 
storage of the matrices A, B and the answer X. The programmer must code two 
auxiliary routines as follows: 

(a) The first must provide successive rows of the augmented matrix 

[A, Bj . (When B = I, one only need supply rows of A). Each row, 
consisting of 2(n + m) elements (or 2n elements when B = l), must 
be transferred to the first 2(n + m) cells of the ^(n + m) cells 
of temporary storage provided by the programmer. 

(b) The second auxiliary must take the successive columns of X, found 
in the first 2n cells of the k(n + m) cells of temporary storage 
and either store them internally or punch them out. 

These auxiliary routines are automatically entered n and m 

times respectively by RJ instructions in the subroutine. The 

subroutine sets up these two RJ instructions from information 

gleaned from the parameters 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. 

p In addition to the 185 words of storage needed by the 

^ subroutine, it is necessary to provide k(n + m) cells temporary 

o storage addressable by SNIP and a block of n(n + 1) + 2nm cells, 

1 

o either all on ES or all on MP . 

o 
I"- Operating Instructions 

cu 1. Entrance to the subroutine is made as follows (B ■f I): 

P RJ 00M01 00M02 

P + 1 00 00X00 00Y01 

P + 2 — uuuuu wwv 

P + 3 — zzzzz xxxxx 



KW-H t 

MTI-2 

Pg. 3 of 8 

8/3/56 

where OOMOO is the location of the first word of the subroutine 
00X00 is the location of the first word of the first auxiliary 
00Y01 is the location of the second word of the second auxiliary 
uuuuu = m (number of columns of B) 
vww - n (number of rows of A) 
xxxxx - is the location of the first cell of the block of n(n + l) + 2nm 

cells oil ifl ES or all in MP , 
zzzzz = is the location of the first cell of the K(n + m) cells 

of temporary storage addressable directly by SNIP. 

2. For the case when B = I, the P + 1 word must be kO 00X00 00Y01 (BRR) 

3. The auxiliary routines must be available and coded so that they can be 
entered with 

RJ 00X00 00X01 

RJ 00Y00 00Y01 respectively. 
This implies that the first and second words of both auxiliaries are exit 
and entrances respectively. 

Alarm Conditions 

If a singular matrix is detected in the process of inversion, the alarm 
routine ALR-1 is entered and "singul-wwwww" is printed where wwwww is the 
address of the cell from which the subroutine was entered. The routine cannot , 
however, detect all singularities due to round -off errors (see below). 

Machine Time 

Computing time for operation of this subroutine can be estimated from 
the following table: 

Order (n « m) Time in seconds 

3 : 1.7 

5 '4.7 

8 15.6 

10 27.7 

This time is exclusive of the times taken by the auxiliaries. In 

case the block of n(n + l) + 2nm words is stored on MD, the time must be 

2 2 

increased 3Mn + nm + 2nm ) milliseconds. These times are approximate and 

are conservative in most cases. 



10-152 






i 

o 

r— I 
I 

o 
o 
o 






KW-lff 

MTI-2 

Pg. k of 8 

8/3/56 

Mathematical Method (Gauss elimination method) 

Elementary row operations are performed on the matrix A reducing it to 
an upper triangular matrix A. At the same time, these operations are performed 
on the matrix B giving a new matrix B. 

Before eliminating, leading elements of two rows are compared and the 
element of largest magnitude becomes the pivotal point. 

Next, successive columns of B 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 consider 
the magnitudes of the elements of X as compared to those of A. A large 
order of difference may indicate poor conditioning of A. 

Accuracy 

The accuracy in the result is a function of the condition of the matrix 
A. Six to seven decimal place accuracy was obtained for matrices of order 

jJjjV/ ^»%j JLO * 



ikn ~ x i i 



MTI-2 

Pg. 5 of 8 

8/3/56 



00M00 
01M00 
02M00 
03M00 
AUGOO 
CONOO 
RWTOO 
37 75701 
MJ 00000 

54 00M01 
TU AOOOO 
TU AOOOO 
AT 00015 
TU AOOOO 
AT 00015 
TU AOOOO 
TP 00000 
TU AOOOO 
TV AOOOO 
AT 00015 

55 00016 
TU AOOOO 
LA AOOOO 
TV AOOOO 
TP 01M00 
TP C0N01 
TP 00000 
TV AOOOO 
TU AOOOO 
TU AOOOO 
QS 01M03 
QS 01M03 
QS 02M27 
TP 00000 
TU AOOOO 
TV AOOOO 
54 C0N06 
QS AOOOO 
AT 02M27 
QS AOOOO 
QS AOOOO 

54 C0N04 
AT AUG02 
QS AOOOO 
QS AOOOO 
RA 02M04 

55 C0N04 
TV QOOOO 



00100 

00161 

00176 

00210 

00267 

00274 

00023 

75702 B 

00000 

A0015 BRR 

00M09 

AUGOO 

AOOOO 

O0M26 

AOOOO 

00M19 

AOOOO 

01M00 

03M34 

AOOOO 

00015 

03M34 

00042 

OlMOO 

01M05 

QOOOO 

AOOOO 

01M03 

01M03 

02M27 

02M06 

02M12 

02M04 

AOOOO 

C0N04 

C0N06 

A0016 BRR 

AUG02 

AOOOO 

03M21 

03M32 

A0001 BRR 

AOOOO 

01M02 

C0N05 

C0N05 

Q0021 BRR 

C0N07 



ALARM 

EXIT 

ENTRANCE 



SET 

A 



U 



A 
D 
D 
M R 
N E 

S 



00144 
00241 
00260 
00322 
00413 
00422 
00027 
00144 
00145 
00146 
00147 
00150 
00151 
00152 
00153 
00154 
00155 
00156 
00157 
00160 
00161 
00162 
00163 
00164 
00165 
00166 
00167 
00170 
00171 
00172 
00173 
00174 
00175 
00176 
00177 
00200 
00201 
00202 
00203 
00264 
00205 
00206 
00207 
00210 
00211 
00212 
00213 
00214 



00000 
00000 
00000 
00000 
00000 
00000 
00000 
75701 
00000 
00145 
20000 
20000 
00017 
20000 
00017 
20000 
00000 
20000 
20000 
00017 
00020 
20000 
20000 
20000 
00241 
00423 
00000 
20000 
20000 
20000 
00244 
00244 
00313 
00000 
20000 
20000 
54 00430 
53 20000 
00313 
20000 
20000 
00426 
35 00415 
53 20000 
20000 
00264 
00426 
10000 



00 
00 
00 
00 
00 
00 
00 
37 
45 
54 
15 
15 
35 
15 
35 
15 
11 
15 
16 
35 
34 
15 
54 
16 
11 
11 
11 
16 
15 
15 
53 
53 
53 
Ik 
15 
16 



35 
53 
53 
54 



21 
55 
16 



00000 
00000 
00000 
00000 
00000 
00000 
00000 
75702 
00000 
20017 
00155 
00413 
20000 
00176 
20000 
00167 
20000 
00241 
00364 
20000 
00017 
00364 
00052 
00241 
00246 
10000 
20000 
00244 
00244 
00313 
00266 
00274 
00264 
20O00 
00426 
00430 
20020 
00415 
2000d 
0634-/ 
00362 
20O0 i 
20006 
00243 
00427 
00427 
10025 
00431 



10-154 



MTI-2 

Pg. 6 of 8 

8/3/56 






i 

o 

r-H 
i 

o 

o 
o 



cu 



00M41 
00M42 
00M43 
Q0M44 
00M45 
00M46 
00M47 
00M48 
00M49 
00M50 
00M51 
00M52 
00M53 
00M54 
00M55 
00M56 
00M57 
00M58 
00M59 
00M60 
01 MOO 
01M01 
01M02 
01M03 
01M04 
01M05 
01M06 
01M07 
01M08 
01M09 
01M10 
01M11 
01M12 
01M13 
01M14 
02MOO 
02M01 
02M02 
02M03 
02M04 
02M05 
02M06 
02M07 
02M08 
02M09 
02M10 

02M11 
02M12 
02M13 



TP 
54 
QS 
TV 
TV 
AT 
AT 
QS 
QS 
AT 
AT 
QS 
QS 
QS 
QS 
RS 
ST 
RS 
TV 
RA 
RJ 
RJ 
RP 
TP 
TN 
RJ 
RJ 
TU 
54 
TU 
RA 
TP 
TP 
TU 
TP 
RP 
TP 

LDPM 
ZJ 

LDPM 
TJ 

LDDV 
TP 
TP 
TP 
QS 

LDMP 

SUNO 
RA 



C0N03 
03M21 
A0000 
AUG03 
AUG03 
C0N07 
C0N07 
A0000 
A0000 
C0N06 
C0N06 
A0000 
A0000 
AOOOO 
AOOOO 
C0N06 
00016 
C0N07 
02M29 
02M30 
00000 
AUG06 
30000 
00000 
00016 
00000 
AUG06 
01M02 
01M03 

Aoooo 

RWT03 
RWT03 
00013 
02M06 
RWTOO 
30000 
00000 
00000 
02M04 
00000 
RWT08 
00000 
00002 
00003 
C0N03 
02M01 
RWT08 
00000 
02M11 



QOOOO 

A0057 BRR 

AUG03 

AU604 

02M29 

AOOOO 

AOOOO 

02M01 

02M06 

AOOOO 

AOOOO 

03M16 

03M21 

03M26 

03M31 

00016 

RWT02 

00016 

02M30 

00016 

00000 

AUGOO 

01M04 

00000 

RWT03 

00000 

AUGOO 

02M00 

A0015 BRR 

02M01 

00016 

RWT01 

RWTOO 

02M02 

00004 

02M02 

00000 

RWT08 

02M16 

00000 

03M41 

00000 

RWT08 

RWT09 

QOOOO 

02M11 

00000 

00000 

C0N09 



SET INDEX 
GET ITH ROW 
AUGMENT 



8 



B BOX 

TRANSMIT ITH 
ROW TO ES 

SKIP IF ZERO 



N 



BS 



00215 
00216 
00217 
00220 
00221 
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13 00020 
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11 00425 
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RW-177 

MPI-2 

Pg. 7 of 8 

8/3/56 



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10-156 



RW-177 



MIT -2 

Pg. 8 of 8 

8/3/56 






! 

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f— ( 
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X 

a* 



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TO AUX 2 



BRB 



BRR 



TO ALARM 



TEST TO SEE 
IF INVERT 

AUGMENT 
IDENTITY 



CONSTANTS 
AND 

TEMPORARY 
STORAGE 



00360 
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00144 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles h^ f California 



RW-178 

NUI-5 

Page 1 of 12 

6/20/56 



Identification Tag: 

Ttype: 

Assembly Routine Spec 

Storage : 



Entrance and Exit: 



Complex Gill Method Routine 

Specifications 

NUI-5 

Subroutine 

SUB 51071 12^+31 

124 words total program storage 

The temporary pool is used. In addition, 
cells 33 through 38 (4lb - 46b) are 
used as temporary storage . 

The constant pool is used. 

RJ GIM01 GIM02 set up 

RJ GIM01 GD403 to get next point 

MJ 00000 GIM04 from derivative calculation 



Coded by: 
Approved by: 



W. Mancina 
W. F. Bauer 



May, 1956 
June, 1956 



10-158 



RW-178 



NUI-5 

Page 2 of. 12 

6/20/56 



Description 



The Gill Method Subroutine (NUI-5) integrates a system of first order, differential 
equations using a step-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, this 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 t 
thus allowing 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 

dx™ = f i (x ' y i> V ' • • ' 7 n h U *1, 2, . . . , n). 



CO 



I 

o 

1 

o 

o 
o^ 



X 

ex, 



n is the number of equations in the system 

q. are intermediate values of the calculation (zero initially) 

Ax is the increment of the independent variable x 
Programming and Operating Instructions : 

1. Assign NUI-5 to some arbitrary region, say GIMOO. (The Complex Arithmetic 
Interpretive Routine, SNIP, must be in ES during the execution of NUI-5. 

SNIP begins in register 63^ decimal and extends through register 1023 decimal). 
SNIP complex must be activated from the program with a 37 015^1 01 713 command 
before entering NUI-5r 

2. In order to solve a given system, the following array of variables, derivatives 
intermediate values, and parameters should be assigned a region, say 00N00: 



Floating point form 



00N00 


n 


Fixed p 


00N01 


Ax 


( real ) 


00N02 


Ax 


(imag. ) 


00N03 


X 


( real ) 


00N01+ 


X 


( imag . ) 


0ON05 


dy-L 


1 ( real ) 


00N06 


dx 


J ( imag . ) 



RW-178 

NUI-5 

Page 3 of 12 

6/20/56 





00N07 
00N08 


y l 




initially 


"00N09 


H 


3 


zero 


_00N10 




00N11 


d I2 


1 




00N12 


dx 


J 




00N13 
00N14 


y 2 


] 


initially 


"00N15 


1 2 


] 


zero 


00N16 


J 



(real) 
( imag . ) 
(real) 
( imag . ) 
(reed.) 
(imag. ) 
( real ) 
(imag. ) 
( real ) 
( imag . ) 



Floating point form 



3. In addition, the coding for computing y i for all values of i, 

dx 

(i = 1, 2, 3, ... n) should be assigned a region, say DEVOO. This coding 

will use the values in region 00N00 to compute all y i as specified by 

dx 

the equations in the system and should store the results in the appropriate 

cells in region 00N00. It should then exit to NUI-5 with a MJ 0000 GIMO^ 

(see below). 

Entrances 

Assuming NUI-5 is in region GIMOO; the three entrances are GIM02, GIMO3, 

and GIMOif. The exit is GIM01. 

1. The first entrance, GIM02, is used for setting up NUI-5 only for the particular 
system to be solved. It is entered by an RJ command followed by a parameter 
word which specifies the locations of the variables, and the location of the 
coding for calculating the derivatives: 

RJ GIM01 GIM02 
00 00N00 DEVOO 

2. The second entrance, GIM03, is the entrance for producing a point of the 
solution. It is entered by an RJ command: RJ GIM01 GIMO3. The use of this 
entrance command results in four passes through both NUI-5 and the coding for 
computing the derivatives, and leaves in region 00N00 the new values of q_, the 
variables, the derivatives at those values, and "x" advanced by "Ax", ready for 
the next step. 



10-160 



I 
o 



RW-178 

NUI-5 

Page k of 12 

6/20/56 

3. The third entrance , GIMO^, is the entrance from the coding for 

calculating the derivatives and is used on each of the four passes 

necessary for computing one point. As noted above, it is entered by 

an MJ command in the DEVOO region; 

MJ 00000 GIM04 

Mathematical Analysis 

Theory . "A Process for the Step-by -Step Integration of Differential Equations 
in an Automatic Digital Computing Machine" by S. Gill, published in Cambridge 
Philosophical Society Proceedings, Vol. k^ , 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 , Y , . . . , Y ) on the curve defined by the 
system of equations 

dy i 

dx~ " f 1 ( x > 7 1> y 2' ' * * > Y r? 



ax 



h (X ' y i' V • • • ' y n } 



dy 
dx 



f (x, y n , y„, . . . , y) 



The Gill Method is a process by which we can find the next point on the curve: 
i. e. the value of y, , y , . . . , y for x = X + h. 

The process can be better understood if the case where n=l is first considered. 



00 

<-< X + h; i.e. we want k = oy such that ■— - 



= f (X + h, Y + k). 



We have the point (X,Y) on the curve -—- = f (x,y), and we want to find y at 



-•X + h, Y + k 



o We derive k by making four approximations and averaging them in a particular way. 



x First approximate the curve by a straight line through (X,Y) with the slope -£- 



dy 

uuiuu^yi \A,±J WXU1 l»i«3 oxujjc; 

f (X,Y), and find a first approximation to k: 
k = h-f (X,Y) 



• J X,Y 



Then we travel a fraction m of the way along this line to the point (X + mh, Y +* , inik ) 



and find f (X + mh, Y + mk ). 
7 o 



o 



m-iAi 



RW-178 



NUI-5 

Page 5 of 12 

6/20/56 

This gives us a new straight line through (X + mh, Y + mk ) with slope f (X + irih, 
Y + mk ), and we find 

k n = h«f (X + mh, Y + mk ) 
1 ' o 

We now use k and k 1 to find a third point at which f is calculated: (X + nh ; 



Y + fn-rj k + rk ). 



k = h f (X + nh, Y + 



n-r 



-» o 



k + rk ) 



Similarly j, 



k = h.f (X + ph, Y + 



p-s-t 



k -1- sk n + tk„ 
o 1 2 



The weighted average of k . k- , k , and k_ is the desired k - 'by, 

o 1 2 3 

Sy = y (X + h) -y (X) = C Q k Q + c^ + c g k 2 + c k 

where c +c,+c rt + c_=l. 
o 1 2 3 

For a system of equations , the same four steps given above are made for each 

equation and 

Sy, = c k, + c_k._ + c„k._ + cjk. „ where c + c_ + c. = 1. 
1 1 o 10 1 ll 2 i2 3^3 o 1 3 

n'he above process is, for certain values of 1, n, p, s ; t, c , c , c , and c„, 

the 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 constants are 



m = 1/2 , 

n = 1/2 , 

P = 1 > 



r = 1 - Vl/i" , 



c = 1/6 

o ' 



s = - VT/2 , 
t = 1 + Vl/2 , 



c x =(1/3) (1 - yT/2) 

c 2 =(1/3) (1 + /T72) 
c = 1/6 



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; 



1st pass 



Advance x by (l/2)h 

k io = h * f i (X > y 10> y 2G> 

r il = (l/2)k io " ho 



* y no' 



*il " ^io + 3r il " (l / 2)k io 

10-162 



00 



i 

o 

I 

o 
o 
o 






2nd pass: 



3rd pass: 



4th pass : 



y il " y io + r il 



Calculate f ± (x,y llt y 21 , 
coding. 



RW-178 



NUI-5 

Page 6 of 12 

6/20/56 



, y . ) in programmer ' s own 



k il " h,f i (x ' y ll> y 21> • ' • ' y nl } 
r i2 = (1 - YI72) (k u - q,.,) 



11 



12 



= c. + 3r. 9 - (1 - VI72) k 



11 



12 



y i2 ~ y il + r i2 
Calculate t ± (x,y 12 , y 22 , 

coding . 

Advance x by (l/2)h 



k i2 - h.f. (x,y 12 ,y 22 , . 



il 



, y ) in programmer's own 



> y n2> 



r ±3 = (1 + VT/2) (k,,, - q, 9 ) 



12 



13 



= q i2 + 3r n - (1 +71/2) k 



12 



y i3 y i2 + r i3 

Calculate f ± ( x >y 1 3>y 2 3> • - 

coding . 

k i3 = h.t ± (x,y 13 ,y 23 , . • . 

r i4 - (1/6) (k. 3 - 2q i3 ) 

Hk = *i 3 " 3r ±k ' ( 1 /2)k i3 

y i4 " y i 3 + r i4 

Calculate f ± (x^^y^, . , 

coding. 



. , y ) in programmer's own 



^ 



y . ) in programmer's own 



Errors The paper by S. Gill mentioned previously includes a detailed analysis 
of errors, both truncation error and round -off error. 



10-163 



RW-178 

NUI-5 

Page 7 of 12 

6/20/56 

The expression for the truncation error in<§y. is too complicated to give here, but 
its dominating term, the author states, is 



n 



h> 


\ 




if. 


\ 


f 

m 


f. ! 

1 ; 


. 


-120 


> 

/ 





,i J 


y j 


*1 


' y .J 


x=X 



where y = x, f = l,j, k, 1, m 



and the truncation error in &y, will be approximately this when the second partial 
derivatives are all close to zero. It is probably more useful to say merely that 
the truncation error is of the order of h^. 

The standard deviation in y. - (l/3) q. over one step from all rounding off errors 
is (where f is the quantity mentioned in the section on notation) 



1/6 



7/3 1 2" 2f +(1/I6)h 2 }^ j_5i 



\ 2 J j 1/2 

r ; u, u = the value 
. _. \ y / } \ of one unit in 

J x J ' ' -> the last digit 

of y. 
Machine Checking 

A driver routine was used to solve the following system of equations using the 
NUI-5 method: 



dx 


= y 2 


*2 

dx 


2 

* - a y 1 


Lival 


ent to the 


A 2 

d y 

dx 


2 A 

+ a y = 





The initial conditions used were: 



AT x=0 ( y 2 - -31 



a was taken as 3> and Ax as 0.0872664626 which -is equivalent to five degrees. 



*o 



The correct solution, y^ = cos ox * i sin ax,- when evaluated at ax = 90 and 
at ax = 135° yields y = - li and y = O.707IO678 - O.707IO678 i. 



The routine gave 



y ± = 0.000000044704 - li and 

y =0.70710672 - 0.70710684 i at these values of ox. 



10-164 



KW-lYtJ 



NUI-5 

Page 8 of 12 

6/20/56 

Another driver routine using NUI-5 was utilized to solve the following systems 
of equations: 



(1) 



sr = y i a u + y 2 a i2 + y 3 a i3 + '^ a ih 



(2) 



^2 

ST = y l a 21 + y 2 a 22 + y 3 S 23 + yj * a 2^ 



(3) 



dT " y l a 3 l + y 2 a 32 + y 3 a 33 + y * *& 



W 



dyj 

±r - y i %i + y 2 a i+2 + y 3 a ^3 + y * a H 



where the a's were the elements of the following matrix: 



CD 



\ 

o 

r— i 
I 

o 
o 



cu 



. 38942862 

-.056561159 i 



31354398 
xlO" 1 



-.10142552 

_2 
xlO c 



-.91876338 



xlO 



-3 



64293399 



. 51067378 
.23430743 i 



.63584648 
xlO" 1 



-.57287441 

_2 
xlO c 



- . 38130278 



.353^3118 



. 52424601 
-.53041144 i 



.86142025 
xlO -1 



.31636930 



•.15651804 



. 28190968 



. 52841129 
.94494028 i 



10-165 



RW-170 

NUI-5 

Page 9 of 12 

6/20/56 



At x = 0, the initial conditions were: 



y l 1 



y 2 =0 



y 3 = o 



y k 



consequently } at x = the four derivatives were equivalent to the first column 
of the matrix, respectively. 

Two cases were calculated. Case 1, with ax = .1 and case 2 with £x = .025. 
The former case was checked by hand calculations. 

The following table of the calculated results indicate that at x = ,1, the 
results of all calculations agree to six decimal places. 



A SUMMARY OF THE VALUES OF 

y i ' y 2 > y 3 AMD y 4 F0R THE 
HAND CALCULATION, CASE 1, AND CASE 2 AT x = .1 



■■ - - 


Hand Calculation 
&x = .1 


Case 1 
Ax = .1 


Case 2 
Ax = .025 


X 


.1 


.1 


.1 


y l 


I.O3980O8 
-.0058823261 


I.O398OOO 
-.00588189961 


1.0397999 
-.00588190071 


y 2 


.0032784372 

-.0000477404901 


.0032785024 
-.0000477392191 


.0032785024 
-.0000477400411 


y 3 

\ \ 
1 

1 
( 

( 


-.000097036022 
+.00000290489771 


-.OOOO97O3835I 
+.0O00029O475541 


-.000097038244 
+.00000290455801 


-. 00009 7^127 1 +3 

+ .00000^8946661 


-. 00009741 4832 
+.00000488444l4i 


-.000097414673 
+.00000468434841 



10-166 



Rto-178 



NUI-5 

Pg. 10 of 12 

6/20/56 



D .. 
D 
D 
D 

GIMOO 
GIMOl 
GIM02 
GIM03 
GIM04 
6IM05 
GIM06 
GIM07 
GIM08 
GIM09 
GIM10 
G I M 1 1 
GIM12 
GIM13 
GIM14 
G I M 1 5 
GIM16 
G1M17 
GIM18 
GIM19 
GIM20 
GIM21 
GIM22 
-G.1M.23 
-<HM24 
X3IM25 
GIM26 
GIM27 
GIM28 
GIM29 
GIM30 
GIM31 
GIM32 
GIM33 
GIM34 
GIM35 
GIM36 
GIM37 
GIM38 
GIM39 
GIM40 
GIM41 
GIM42 
GIM43 
GIM44 



MS 
MJ 
MJ 
MJ 
RA 
EJ 
EJ 
TP 
TP 
MJ 
TP 
TU 
RP 
TP 
TP 
TP 

LDAD 
TP 
TP 
TP 
TP 

ADMP 
TP 
TP 
TV 
RP 
TP 
RA 
TU 
TV 
RP 
TP 

LDMP 
TP 
TP 

LDMP 
TP 
TP 

MPSU 
TP 
TP 

ADNO 
TP 
TP 

LDMP 



GILOO 
GINOO 
GIMOO 
GCNOO 
00000 
00000 
00000 

00000 

GIN01 
GIN27 
GIN28 
GIN32 
GIN33 
00000 
00016 
GIN02 
30004 
00000 
00023 
00024 
00023 
00002 
00003 
GIN03 
GIN04 
00025 
00002 
00003 
00000 
30006 
00000 
GIL26 
G1L78 
GIL78 
30006 
00000 
00033 
00002 
00003 
00025 
00002 
00003 
00031 
00002 
00003 
00027 
00002 
00003 
00023 



01024 
01114 
51071 
51161 
GILOO 
00000 
GIL59 
GIL10 
00016 
GIL79 
GIL01 
00023 
00024 
GIL24 
GIN01 
GIL26 
GIL14 
00023 
GIN32 
GIN33 
000 2 5 
00037 
00038 
00027 
00028 
00027 
00000 
00000 
GINOO 
GIL27 
00031 
GIN29 
GIL31 
GIL54 
GIL32 
00025 
00029 
00033 
00034 
00023 
00023 
00024 
00033 
00031 
00032 
00000 
00027 
00028 
00035 



SET UP ENTRA 
1ST PASS 

EQLTY AGNST3 
EQLTY AGNST5 
BRING IN DEL 
BRING IN DEL 

SET PASS CNT 
SET LOC A 
DELTA T IN23 
24 IN 25 26 
STORE DELTAT 
REAL / IMAG 
T PLUS DELTA 
STOR T PLUS 
DELTA T 
BRG ONE HALF 
TO 27 28 
GET T PLUS 
STORE T PLUS 
ONE HALF DEL 
SET EQ COUNT 
A31 32 B33 
C 35 36 
SETABC FOR 
SET UP Y ADD 
REVERSE PREV 
Y25 26Y27 28 
Q 29 30 
BQ 

STORE BQ IN 
33 AND 34 
COMP Y DEL T 
STORE K IN 
23 AND 24 
AK BQ EQS R 
STORE R IN 
31 AND 32 
R PLUS 4 
NEW Y STORED 
IN 27 AND 28 



2'000 

02132 

65477 

65631 

65477 

65500 

65501 

65502 

65503 

65504 

65505 

65506 

65507 

65510 

65511 

65512 

65513 

65514 

65515 

65516 

65517 

65520^ 

65521 

65522 

65523 

65524 

65525 

65526 

65527 

65530 

65531 

65532 

65533 

65534 

65535 

65536 

65537 

65540 

65541 

65542 

65543 

65544 

65545 

65546 

65547 

65550 

65551 

65552 

65553 



00 
00 
00 
00 
56 
45 
45 
45 
21 
43 
43 
11 
11 
45 
11 
15 
75 
11 
11 
11 
14 
11 
11 
11 
11 
14 
11 
11 
16 
75 
11 
21 
15 
16 
75 
11 
14 
11 
11 
14 
11 
11 
14 
11 
11 
14 
11 
11 
14 



OOOOO 
00000 
OOOOO 
OOOOO 
OOOOO 
OOOOO 
OOOOO 
OOOOO 
02133 
02165 
02166 
02172 
02173 
OOOOO 
00020 
02134 
30004 
OOOOO 
00027 
00030 
30027 
00002 
00003 
02135 
02136 
04031 
00002 
00003 
OOOOO 
30006 
OOOOO 
02032 
02116 
02116 
30006 
OOOOO 
30041 
00002 
00003 
30031 
00002 
00003 
14037 
00002 
00003 
04033 
00002 
00003 
30027 



OOOOO 
OOOOO 
OOOOC 
OOOOO 
02000 
OOOOC 
02073 
02012 
00020 
02117 
02001 
00027 
00030 
02030 
02133 
02032 
02016 
00027 
02172 
02173 
04031 
00045 
00046 
00033 
00034 
14033 
OOOOO 
OOOOO 
02132 
02033 
00037 
02167 
02037 
02066 
02040 
00031 
14035 
00041 
00042 
14027 
00027 
00030 
10041 
00037 
00040 
OOOOO 
00033 
00034 
14043 



10-167 



R-W-178 



NUI-5 

Pg. 11 of 12 

6/20/56 



GIM45 


TP 


00002 


00035 


STORE CK IN 


65554 


11 


00002 


00043 


GIM46 


TP 


00003 


00036 


35 AND 36 


65555 


11 


00003 


00044 


GIM47 


TP 


GIN23 


00033 


BRING IN 


65556 


11 


02161 


00041 


GIM48 


TP 


00013 


00034 


ONE 


THIRD 


65557 


11 


00015 


00042 


G I M49 


LDDV 


00031 


00033 


COMPUTE 3R 


65560 


14 


30037 


20041 


GIM50 


ADSU 


00029 


00035 






65561 


14 


04035 


10043 


GIM51 


TP 


00002 


00029 


NEW 


Q STORED 


65562 


11 


00002 


00035 


GIM52 


TP 


00003 


00030 


IN 29 AND 30 


65563 


11 


00003 


00036 


GIM53 


RP 


30006 


GIL55 


YDAT IN25 26 


65564 


75 


30006 


02067 


GIM54 


TP 


00025 


00000 


YIN27 28 QIN 


65565 


11 


00031 


00000 


GIM55 


RA 


GIL31 


GIN29 






65566 


21 


02037 


02167 


GIM56 


RA 


GIL54 


GIN30 






65567 


21 


02066 


02170 


GIM57 


R5 


GINOO 


00016 


SUB1 FMEQ CN 


65570 


23 


02132 


00020 


GIM58 


ZJ 


GIL83 


00000 






65571 


47 


02123 


00000 


GIM59 


TP 


GIL01 


AOOOO 


SET 


UP 


65572 


11 


02001 


20000 


GIM6C 


LA 


AOOOO 


00015 






65573 


54 


20000 


00017 


GIM61 


TU 


AOOOO 


GIL62 


SET 


PARAMETE 


65574 


15 


20000 


02076 


GIM62 


TP 


00000 


AOOOO 


PARA WORK A 


65575 


11 


00000 


20000 


GIM63 


TV 


AOOOO 


GIL58 


SET 


DER ENTR 


65576 


16 


20000 


02072 


GIM64 


TU 


AOOOO 


GIL24 


SET 


EQ C ADD 


65577 


15 


20000 


02030 


GiM65 


AT 


00015 


AOOOO 


SET 


DEL T AD 


65600 


35 


00017 


20000 


GIM66 


TU 


AOOOO 


GIL13 






65601 


15 


20000 


02015 


GIM67 


LA 


AOOOO 


00057 






65602 


54 


20000 


00071 


GIM63 


AT 


GIN31 


AOOOO 






65603 


35 


02171 


20000 


GIM69 


TV 


AOOOO 


GIL22 


SET 


T REL AD 


65604 


16 


20000 


02026 


GIM70 


AT 


00016 


AOOOO 






65605 


35 


00020 


20000 


GIM71 


TV 


AOOOO 


GIL23 


SET 


T IM ADD 


65606 


16 


20000 


02027 


GIM72 


AT 


00016 


AOOOO 






65607 


35 


00020 


20000 


GIM73 


TV 


AOOOO 


GIL78 


SET 


LOC Y 


65610 


16 


20000 


02116 


GIM74 


LA 


AOOOO 


00015 






65611 


54 


20000 


00017 


GIM75 


TU 


AOOOO 


GIL78 


SET 


LOC Y 


65612 


15 


20000 


02116 


GIM76 


RA 


GIL01 


00016 , 


SET 


BY PAR W 


65613 


21 


02001 


00020 


GIM77 


MJ 


00000 


GIL01 






65614 


45 


00000 


02001 


GIM78 


00 


00000 


00000 B 


LOC 


OF Y 


65615 


00 


00000 


00000 


GIM79 


LDNO 


00037 


00000 






65616 


14 


30045 


00000 


GIM80 


TP 


GIN32 


00023 


RESTORE DEL 


65617 


11 


02172 


00027 


GIN181 


TP 


GIN33 


00024 


IN 23 24 


65620 


11 


02173 


00030 


7T GIM82 


MJ 


00000 


6IL22 






65621 


45 


00000 


02026 


t- J GIM83 


TP 


GIN32 


00023 






65622 


11 


02172 


00027 


- GIM84 


TP 


GIN33 


00024 






65623 


11 


UZi 1 j 


00030 


■i GIM85 


TU 


G I L26 


GIL88 






65624 


15 


02032 


02130 


J GIM86 


RS 


GIL88 


GIN29 






65625 


23 


02130 


02167 


G I M 8 7 


RP 


30006 


GIL89 






65626 


75 


30006 


02131 


-f GIM88 


TP 


00000 


00031 






65627 


11 


00000 


00637 


^ GIV'89 


MJ 


00000 


GIL30 






65636 


45 


00000 


02036 


cu GCNOO 


00 


00000 


00000 B 


EQ COUNTER 


65631 


00 


00000 


00000 


GCNOI 


00 


00000 


00000 B 


PASS COUNTER 


65632 


00 


00000 


00000 


GCN02 


00 


GIN03 


00000 BR8 


LOCATION A 


65633 


00 


02135 


00000 


r~ r r. v ; ^ '5 


05 


00000 


00000 -01 F 




Al 


65634 


20 


04000 


00000 



10-168 



RW-178 



r- 



i 

o 
o 

o- 

r— I 

t- 

X! 



NUI-5 

Pg. 12 of 12 

6/20/56 



GCN04 


00 


00000 


00000 


B 




Al 


65635 


00 


00000 


00000 


GCN05 


01 


00000 


00000 


00 


F 


Bl 


65636 


20 


14000 


00000 


GCN06 


00 


00000 


00000 


B 




Bl 


65637 


00 


00000 


00000 


GCN07 


05 


00000 


00000 


-01 


F 


CI 


65640 


20 


04000 


00000 


GCN08 


00 


00000 


00000 


B 




CI 


65641 


00 


00000 


00000 


GCN09 


02 


92893 


21881 


-01 


F 


A2 


65642 


17 


74537 


30314 


GCN10 


00 


00000 


00000 


B 




A2 


65643 


00 


000.00 


00000 


GCNH 


02 


92893 


21881 


-01 


F 


B2 


65644 


17 


74537 


30314 


GCN12 


00 


00000 


00000 


B 




B2 


65645 


00 


00000 


00000 


GCN13 


02 


92893 


21881 


-01 


F 


C2 


65646 


17 


74537 


30314 


GCN14 


00 


00000 


00000 


B 




C2 


65647 


00 


00000 


00000 


GCN15 


01 


70710 


67812 


00 


F 


A3 


65650 


20 


16650 


11714 


GCN16 


00 


00000 


00000 


B 




A3 


65651 


00 


00000 


00000 


GCN17 


01 


70710 


67812 


00 


F 


B3 


65652 


20 


16650 


11714 


GCN1.8 


00 


00000 


00000 


B 




B3 


65653 


00 


00000 


00000 


GCN19 


01 


70710 


67812 


00 


F 


C3 


65654 


20 


16650 


11714 


6CN20 


00 


00000 


00000 


B 




C3 


65655 


00 


00000 


00000 


GCN21 


01 


66666 


66667 


-01 


F 


A4 


6 56 56 


17 


65252 


52525 


GCN22 


00 


00000 


00000 


B 




A4 


65657 


00 


00000 


00000 


GCN23 


03 


33333 


33333 


-01 


F 


B4 


65660 


17 


75252 


52525 


GCN24 


00 


00000 


00000 


B 




B4 


65661 


00 


00000 


00000 


GCN25 


05 


00000 


00000 


-01 


F 


C4 


65662 


2C 


04000 


00000 


GCN26 


00 


00000 


00000 


B 




C4 


65663 


00 


00000 


00000 


6CN27 


00 


00000 


00003 


B 






65664 


00 


00000 


00003 


GCN28 


00 


00000 


00005 


B 






65665 


00 


00000 


0000 5 


GCN29 


00 


00006 


00000 


B 






65666 


00 


00006 


00000 


GCN30 


00 


00000 


00006 


B 






65667 


00 


00000 


00006 


GCN31 


00 


00000 


00002 


B 






65670 


00 


00000 


00002 


GCN32 


00 


00000 


00000 


B 




FOR STORING 


65671 


00 


00000 


00000 


GCN33 


00 


00000 


00000 


B 




DELTA T 


65672 


00 


00000 


00000 


START 




00000 












45 


00000 


00000 



in 1 /. n 



THE RAMO-WOOLDRIDGE COLORATION 
Los Angeles U5 , California 



RW-179 



POL-0 

Pg. 1 of 11 

9-U-56 



Identification Tag; 
Type ; 

Regions Used: 
Storage : 



Entrance and Exit: 

Alarm Exit: 

Machine Time: 
Mode of Operation: 



Algebraic Equation Solver 
S pecifications 

POL-0 

Subroutine available on cards for 
assembly 

00M, 01M 02M, 00K, F00 ? COO. 00T 

157 words total program storage 

2n + 1'/' cells temporary storage used 
immediately following the RVJ temporary 

pool i/hore n is the order of the 
po I yi loin i a .1 ( Se e text ) 

The constant poof and temporary storage 
pool are used by this routine 

RJ SUB01 SUB02 results not punched) 

I See 
RJ SUB01 SUB03 results punched ) text 

A SNIP exponent overflow alarm may 
occur. (See text). 

See enclosed table . 

Floating Complex Arithmetic. SNIP must 
have been activated. 



Coded by: 
Approved by : 



Werner L . Frank 
W. F. Bauer 



May, 1956 
July, 19'n.) 



10-170 



RW-179 



o 

■ — i 

i 

o 
o 
o- 

r-H 
I- 

X 



POL-G 

Pg. 2 of 11 
9-4-56 



Description 



This subroutine employs .5. new iterative procedure due to D, Mailer for 
finding the n roots of the polynomial equation 

P(x) = X a x n ~ J = 

; ■.:.■.•" j~o J ■■- 
where the coefficients a, can be real or complex and the roots need not be 
distinct. The routine operates using the complex arithmetic version of SNIP, 
finding the real and complex roots in an approximately ascending order of 
magnitude. As each root is obtained , the intermediate and final iterants 
can be punched out on cards , depending on the option chosen by the programmer. 
The polynomial is reduced one order after finding each root so that the k 
root is obtained from the polynomial P (x) where 

-T-f(X-X, ) 

i=l 
In addition to the 157 words of storage needed by the subroutine t it is 
necessary to provide 2n 4- 17 cells of temporary storage immediately following 
the Ramo -Wooldridge Temporary Pool. 

The polynomial coefficients must appear in succession beginning with the 
coefficient of the highest power of x, in a block of cells all of which must 
be in ES or all on the drum. Each coefficient occupies two cells, one for the 
real component and one for the complex. This code can theoretically solve 
polynomials of extremely large order. However , practical limitations are imposed 
by the available 102^ words of ES storage when using SNIP so that n must be 
less than 211. 



1 

A paper "A Method for Solving Algebraic Equations using an Automatic 

Computer" by D. Muller is forthcoming in MTAC. 



RW-179 






i 

o 

o 



X 



POL-0 

Pg. 3 of 11 

9-4-56 



A serious deterioration in accuracy can result for polynomials with multiple 
roots and arbitrary polynomials of high-degree. This fs probably due to the low 

precision of the coefficients (27 binary bits) which necessarily define the roots. 

128 
Also, for large degree , the range of numbers in SNIP (+2 ) is often exceeded 

(see Alarm section). Hence, for problems of degree larger than 20, special 

care must be taken. 

Operating Instructions 

SNIP must have been activated, and be in ES. 

The code provides for three options for output depending upon the entrance 
selected. In every case, the n roots of the polynomial P(x) can be found in the 
2n cells starting at cell 50 = 62b when the subroutine is exited. The programmer 
is cautioned to note that the output hopper of SNIP is used regardless of the 
option selected. Assuming that the subroutine is assigned to region SUBOO; 
that 00X00 is the location of the real part of the coefficient of the highest 
power of x in P(x) and that vww is the degree, n, of the polynomial, then 
the options available to the programmer are: 
Entrance No. la : RJ SUB01 SUB03 

20 00X00 vww 
n sets of 3 cards each are punched each set containing the follow- 
ing information 



Card No. 1 


X. 

1 


P(x.) 






P'(x.) 
1 


Card No. 2 


i+1 


X. ..P 

1+1 


(x 


i> 




Card No. 3 


blank 











where x. _ and x. are the last two successive iterations for the 

l+l 1 

root, real part in field one and imaginary part in field two. 



10-172 



RW-179 



POL-0 

Pg. 6 of 11 

9.4-56 



P(x ) rj a + a _ + a , 
2 n n-1 n-< 



P(xJ = a 
3 n 

At each step of the iteration violent jumps in the function P(x, .. ) are 
prevented in order to provide a smooth convergence. This is accomplished 
by testing to see if 






< 10 



If this inequality does not hold then d . is continually multiplied by l/2 

J~*~X 

until anx*. , is found sufficiently close to x . so that the test is passed* 
0+1 J 

In case the denominator of d. is zero, unity is used in place of the denomina- 

i+3 

tor and the computation is resumed. The iteration continues until the conver- 
gence criterion 



"V 1 " x j 



x, 
J+l 



<icr m 



is met 



In this code m = k. After an iterant x. , meets the above criterion 

J+l 

one cycle of the second order Newton procedure is performed obtaining 
thereby the finally accepted approximation x 

P(x. +1 ) 
X j + 2 = X j + l" ^x"^") 

This is approximately equivalent to a convergence criterion of 10 

After one root is obtained the polynomial is depressed one degree and 
another root is sought. Possible errors in successive roots > due to errors 
in the deflated polynomial, are eliminated by the final cycle of the Newton 
process which always refers back to the original polynomial. The code provides 
;* ..he punching of successive iterants, their associated residues in the 



RW-179 

POL-0 

Pg. k of 11 
9J+-56 

x ? [x 4 ) - residue of polynomial at. x , components in field three 

and four respectively. 

P'(x.) = derivative of polynomial at x . , components in field 

five end six respectively 

'Fix, ) 
i 



«*t* f "ft ^ \ *** A / I 

1 .A. ( * "1 I 



i'j'j 



measure of -accuracy of root (see Mathematical Method) 

in field three . 

^ItliJ^l^'lIlb.JI 1 - RJ SUB01 SIIB03 
00 00X00 vvwv 
Each set of three cards is preceded hy cards containing the values of 
tJl the «.utc«.-6:-1w it, e rants and their corresponding residues in the 
associated polynomjal. These cards contain: 

x, P, (x •) 

.1 ** J 

ill", field... oii«-^ two, three and four in addition to the results indicated 

for entrance Ho* la. 
rn'ihf»;<; So. ?i RJ SITB01 81X002 
KO 00X00 vvwv 
^c cards are; punched, 
r fa o nd 1. 1 1 o n s 

i'i'^ "* ", r. 1 '.r-ij' m i-KT"' .tUtria fox* exponent overflow vhen the 

dot range of + 2"' ( '' ' ia violated. It is advised in such instances that the 

k 
aiciii be rescaied. This can be done by making the transformation x = 10 y 

.;v .;1vit T *ln,; >.',-.. - i K"7i'i'jLC <<t'tii,ti u«* lh*s x'^lyf 1010 ^^! °J some factor. The latter 

- - - * 1 "• ' 1 .~;i*^ t t^i wi-^'" rooto are equal to those of the 



uft to D. Muller"*" of the University of Illinois 



RW-179 



o 

I 

o 

o 

1- 

X 



POL-0 

Pg. 5 of 11 

9 ~k -56 



is employed in which quadratic fits are made to the polynomial 

n 
P(x) = ^_4 a x n-J = 
0=0 J 

Given three arbitrary points, x , x. lf and x. , we find the parabola passing 

through the points P(x.) > P(x. 1 )and P(x. ? ). Locating the root of this 

quadratic closest to x. f say x , the process is repeated using now the 

i+<d i+j 

points x 1+1 , x 1+2 , and x. +3 . 

The explicit formulas used are: 

X i+3 = X i+2 + (x i+2 " X i+1 ) d i+3 
where 



d = -2P(x 1+2 ) ^ d 1+2 > 

i+3 ~ b i +2 i{ b i + 2 2 - k ^\,zKJ u \^\K,z- p W + i)( 1+d i +2 ) + p K +2 | i/2 

and 

b 1+2 = p ( x i) d i! 2 - p < x i + i)( 1+d i +z ) 2 + p K +2 ) ( 1+2d i +2 ) 

The sign in the denominator is chosen in such a way so as to give d. the 

i+3 

smallest magnitude. Coupled with the starting procedure this finds the roots 
in an approximately ascending order of magnitude . 

To start the process off, the following choice of values is made: 



x l 


= -1 


x 2 


= 1 


x 3 


= 


% 





1/2 

with the associated functional values approximating the polynomial P(x) in 

the neighborhood of the origin: 

P(x, )r~<a -a ., + a n 
1 n n-1 n-2 



10-175 



RW-179 



POL-0 

?g. 7 of 11 
9-4-56 



i -uuoed. polynomials and finally the five values x _, p(x.), P'(x,), x, ,, and 

m vbere 

M = x . -.P'lx, ) i 

! o+i ' j i 

This latter information givey an indication of the relative accuracy of the 

-7 
approximation x. , Thus one should expect a value of M = 10 ar smaller 

..for roots which are accurate to 6 places or more,, Larger values of M indicate 

the oosslbilxty of U-bp significance. In the event either x. . or P'(x.) 

j+1 j 

tire equal to >',t:;/u m> v^lue for M :1s ounched and x. . = k. . 

'*- * 14-1 "1 

J+-»- «J 

Local convergence >.'f the Muiier process hay been shown to be somewhat 
juss than .second order J'or s l.mpie roots. Tn the case of multiple roots the 
order of convergence approaches a first order process. In this case the 
.•a: curacy in the calculated roots deteriorates rapidly, 
Mae i 1 1 1 ie 1 ime 

The time, in seconds _, taken to find the n roots of a polynomial and punch 
the results according to the format described can be estimated from the 
loi lowing table of repr <-eentHt..Lv^ problems. 
.Degree n 



ill. 



uaauice 


no. 


la 


h'ntr 


ance 


Wo. 


lb 


Eni 


trance 


No.. JJ 


Ik 








20 








8 




T_S 








'U 








■13 




ct> 








106 








35 




»3 








iSa 








59 




2170 








- 








H22 




PJi'- 








_ 








7tO 





10- [7i 



RW-179 

















POL-O 


















P 


g. 8 of 


11 
















9 


-4-56 






D 




OOMOO 


00098 




00142 


00 


OOOOO 


OOOOO 




D 




OlMOO 


00131 




00203 


00 


OOOOO 


OOOOO 




D 




02M00 


00161 




00241 


00 


OOOOO 


OOOOO 




D 




OOKOO 


00247 




00367 


00 


OOOOO 


OOOOO 




D 




FOOOO 


00002 




00002 


00 


OOOOO 


OOOOO 




D 




COOOO 


00003 




00003 


00 


OOOOO 


OOOOO 




D 




OOTOO 


00033 




00041 


00 


ooooo 


OOOOO 




OOMOO 


MJ 


00000 


OOOOO 




00142 


45 


ooooo 


OOOOO 




OOM01 


MJ 


ooooo 


OOOOO 


EXIT 


00143 


45 


ooooo 


OOOOO 




OOM02 


MJ 


00000 


02M77 


ENTRANCE 1 


00144 . 


45 


ooooo 


00356 




OOM03 


TP 


00K05 


02M67 


ENTRANCE 2 


00145 


11 


00374 


00344 




00M04 


SP 


00M01 


00015 




00146 


31 


00143 


00017 




00M05 


TU 


AOOOO 


00M06 




00147 


15 


20000 


00150 




00M06 


TP 


OOOOO 


AOOOO 




00150 


11 


OOOOO 


20000 




OOM07 


TU 


AOOOO 


00M18 




00151 


15 


20000 


00164 




00M08 


TV 


AOOOO 


00K07 




00152 


16 


20000 


00376 




00M09 


LA 


AOOOO 


00016 




00153 


54 


20000 


00020 




OOMIO 


TP 


00021 


QOOOO 




00154 


11 


00025 


10000 




OOM11 


QS 


AOOOO 


00M17 




00155 


53 


20000 


00163 




OOM12 


AT 


02M17 


AOOOO 




00156 


35 


00262 


20000 




00M13 


QS 


AOOOO 


01 MO 5 




00157 


53 


20000 


00210 




00M14 


ST 


00K06 


AOOOO 




00160 


36 


00375 


20000 




00M15 


TU 


AOOOO 


OOMOO 




00161 


15 


20000 


00142 




00M16 


RA 


00M17 


0OKO3 




00162 


21 


00163 


00372 




OOM17 


RP 


30000 


00M19 


TRANSFER 


00163 


75 


30000 


00165 




00M18 


TP 


ooooo 


00T15 




00164 


11 


OOOOO 


00060 




00M19 


RS 


00K07 


00016 




00165 


23 


00376 


00020 




OOM20 


TP 


00K07 


00T14 




00166 


11 


00376 


00057 




00M21 


MJ 


ooooo 


00M28 




00167 


45 


OOOOO 


00176 




OOM22 


TP 


00013 


00004 




00170 


11 


00015 


00004 




00M23 


TP 


00T14 


00031 




00171 


11 


00057 


00037 




0QM24 


LDMP 


00T15 


00T06 B 




00172 


14 


32060 


14047 




00M.25 


ADNO 


00T17 


OOOOO BS 




00173 


14 


07062 


OOOOO 




00M26 


RA 


00004 


00K03 




00174 


21 


00004 


00372 




00M27 


IJ 


00031 


00M24 




00175 


41 


00037 


00172 




00M28 


RS 


OOMOO 


00K03 




00176 


23 


00142 


00372 




00M29 


TU 


OOMOO 


00004 




00177 


15 


00142 


00004 




00M30 


R5 


01M05 


00015 




00200 


23 


00210 


00017 


.-— . 


00M31 


TU 


01M05 


1 MO 6 




00201 


15 


00210 


00211 




00M32 


RS 


01M05 


00015 




00202 


23 


00210 


00017 


f~i 


OlMOO 


LDAO 


OOOOO 


00004 B [ 


3 


00203 


14 


32000 


06004 


1 

o 


OlMOl 


SUST 


00002 


OOTOO B 


FO 


00204 


14 


12002 


34041 


1 


01M02 


ADAD 


00002 


00002 B 1 


3 


00205 


14 


06002 


06002 


o 


01M03 


TP 


FOOOO 


00T02 


Fl 


00206 


11 


00002 


00043 


o- 


01 MO 4 


TP 


COOOO 


00T03 




00207 


11 


00003 


00044 


1- 


01M05 


TP 


ooooo 


00T04 




00210 


11 


OOOOO 


00045 


Cl, 


01 MO 6 


TP 


ooooo 


00T05 


F2 


00211 


11 


OOOOO 


00046 




01M07 


RP 


10008 


1 MO 9 




00212 


75 


10010 


00214 




01M08 


TP 


00013 


00T06 


S 


00213 


11 


00015 


00047 




01 MO 9 


TN 


OOKOO 


00T08 


E 


00214 


13 


00367 


00051 



i n _ i 77 



RW-179 















POI 


',-0 
















Pg, 


9 of 11 














9-c 


?4-56 




1M10 


j p 


OOKOO 


00T10 


T 


00215 


n 


00367 


00053 


1 M 1 1 


TN 


00K01 


00T12 




00216 


13 


00370 


00055 


1M12 


PMNO 


ooooo 


OOOOO 


INITIAL 


00217 


14 


24000 


OOOOO 


01 Ml 3 


Z J 


01 Ml 5 


01 Ml 4 




00220 


47 


00222 


00221 


01 Ml 4 


TP 


OOP 02 


00 TO 2 


VALUES 


00221 


11 


00371 


00043 


01M15 


LDMP 


OOTOO 


00T08 




00222 


14 


30041 


14051 


1 M 1 6 


AD ST 


00T04 


0002 3 


L 


00223 


14 


4045 


340 2 7 


1 M 1 7 


MP ST 


OOTOB 


00025 


V 


00224 


14 


14051 


34031 




LDMP 


00T02 


00T10 


A 


00225 


14 


30043 


14053 


1 M 1 9 


STSU 


00027 


00023 


S L 


00226 


14 


34033 


11027 


01M20 


LDPM 


00T04 


OOOOO 


U 


00227 


14 


30045 


24000 


01M21 


Z J 


0iM22 


02M44 


A 


00230 


4 7 


00231 


00315 


01M22 


LDMP 


00T04 


00T10 


T 


00231 


14 


30045 


14053 


01M23 


AD NO 


FOOOO 


ooooo 


E 


00232 


14 


04002 


OOOOO 


DIM? 4 


TM 


FOOOO 


0002 9 




00233 


13 


00002 


00035 


01M25 


TN 


coooo 


00030 




00234 


13 


00003 


00036 


1 M 2 6 


AD MP 


FOOOO 


00 TO 8 


ROOT 


00235 


14 


04002 


14051 


01M27 


MPLD 


00023 


00T04 


s 


00236 


14 


15027 


30045 


U I ' ■ i L. O 


SUMP 


000 2 7 


00T10 




00237 


14 


10033 


14053 


01M29 


AD MP 


0002 b 


FOOOO 


5 


00240 


14 


05031 


14002 


1 • ■ ''0 


AORT 


0002 3 


00023 


s 


00241 


14 


040 2 7 


51027 


2M01 


TN 


coooo 


COOOO 


CONJUGATE; 


00242 


13 


00003 


00003 




LDMP 


FOOOO 


0002 5 




00243 


14 


30002 


14031 


2 MO 3 


S J 


2 MO 4 


02 MO 6 




00244 


46 


00243 


00247 


2 MO 4 


TN 


0002 3 


00C2 3 




00245 


13 


00027 


00027 


2 Ml) 5 


TN 


00024 


00 02 4 




00246 


13 


000 30 


000 3 


2 MO 6 


L DAD 


0002 3 


00023 


S DENOMINATOR 


002 4 7 


14 


30031 


05027 


2 MO / 


P M N 


ooooo 


OOOOO 




00250 


14 


24000 


OOOOO 


2M08 


Zj 


2M10 


2M0 9 




002 51 


47 


00253 


00252 


2 MO 9 


TP 


00 KOI 


000 2 3 




00252 


11 


00370 


00027 


2M10 


LDDV 


00029 


00023 




00253 


14 


30035 


20027 


2 M 1 1 


TP 


FOOOO 


00T08 




00254 


11 


00002 


00051 


G2M12 


TP 


cooou 


T 9 




00255 


11 


00003 


00052 


C 2 M 1 3 


MPS i 


00 1 12 


u U 2 7 




00256 


14 


14055 


34033 


2 Ml 4 


ADST 


TOO 


00023 




00257 


14 


04047 


34027 


2- Ml 3 


TP 


G K 3 


0000 4 




00260 


11 


003 7 2 


00004 


A ■;> m t r. 


TP 


T 1 A 


00031 




00261 


11 


00057 


000 3 7 


2 M 1 7 


liUL D 


GOT 17 


GOT 15 




00262 


14 


0062 


30060 


° M 1 H 


MP AD 


002 3 


00T1 3 


D FORM 


00 2 6 3 


J4 


14027 


6 6 


02M 19 


RA 


4 


K 3 


F I J. 


002 64 


21 


0004 


00 372 


2M20 


I J 


000 3 1 


2 M l 8 




02 6 5 


4 ]. 


0037 


2 6 3 


2M21 


T P 


FOOOO 


000 2 3 




002 6 6 


l'l 


0002 


000 31 


2M22 


T P 


coooo 


2 6 




002 6 7 


11 


00003 


000 3 2 


I M 2 3 


DVPM 


OOTO'i 





RAIL OF 


00270 


14 


2 0045 


24000 


G2M24 


TJ 


O0K02 


2M79 


CM A NO E IN 


00271 


42 


003 71 


00360 


2M2 5 


Tl» 


OOKOO 


FOOOO 


FI 1 


00272 


11 


367 


00002 


n m ;;■ a 


T ["') 


]. 3 


COOOO 




002 7 3 


1 1 


000 15 


000 3 




!, DI-1P 


F OOOU 


00 TOO 


c 


002 74 


14 


30002 


15051 


2M28 


MJ 


OOOOO 


','. M 1. 3 




002 7 5 


4 5 


ooooo 


00 2 56 


2M29 


A I.) NO 


1 s 


u 




002 7 6 


14 


4051 


OOOOO 


? M '5 


T P 


F 0(iO 


T 1 




002 7 7 


1 "I 


00002 


000 5 3 


n *> f,i ^ i 




si ii i u v -' 


T 1. 1 




00 3 00 


1 1 


5 2 


000 5 4 



1 - J li I 



RW-179 















POL-0 
















Pg. 


. 10 of 


11 














9-4-56 




2M32 


TP 


00025 


00 TO 4 




0030J 


11 


00031 


00045 


2M33 


TP 


00026 


00T05 




00302 


11 


00032 


00046 


2M34 


LDDV 


00T12 


00T06 




00303 


14 


30055 


20047 


2M35 


PMiMO 


00000 


00000 




00304 


14 


24000 


00000 


02M36 


TJ 


00K04 


02M44 


CONVERGED 


00305 


42 


00373 


00315 


2M37 


TP 


02M34 


AOOOO 




00306 


11 


00303 


20000 


2M38 


TU 


00 MO 6 


02M39 




00307 


15 


00150 


00310 


2M39 


TJ 


00000 


01M15 




00310 


42 


00000 


00222 


2M40 


LOST 


00T04 


00008 




00311 


14 


30045 


34010 


2M41 


LDST 


00T06 


00006 




00312 


14 


30047 


34006 


2M42 


PDNO 


00010 


00000 


ITERANT 


00313 


14 


74012 


00000 


02M43 


MJ 


00000 


01M15 




00314 


45 


00000 


00222 


2M44 


TP 


00T06 


00006 


LOAD 


00315 


11 


00047 


00006 


2M45 


TP 


00T07 


00007 


ROOT 


00316 


11 


00050 


00007 


2M46 


TU 


00M18 


00004 


SET B BOX 


00317 


15 


00164 


00004 


2M47 


TP 


00K07 


00031 


SET INDEX 


00320 


11 


00376 


00037 


2i14B 


TP 


00013 


00025 




00321 


11 


00015 


000 31 


2M49 


TP 


00013 


00026 




0032 2 


11 


00015 


000 32 


2M50 


LDST 


00000 


00023 13 


FORM 


003 23 


14 


3 2000 


34027 


2M51 


LDMP 


00025 


00T06 


RESIDUAL 


003 24 


14 


300 31 


14047 


2M52 


ADST 


00023 


000 2 5 


AND 


00325 


14 


04027 


340 31 


2M53 


LDMP 


00023 


00T06 


DERIVATIVE 


00326 


14 


30027 


14047 


2M54 


ADST 


FOOOO 


00023 (3 




00327 


14 


06002 


34027 


Q2M55 


RA 


00004 


00K03 




00330 


21 


00004 


00372 


2M56 


U 


00031 


02M51 




00331 


41 


00037 


00324 


2M57 


RP 


30004 


02M59 




00332 


75 


3 0004 


00334 


2M58 


TP 


00023 


00008 




0033 3 


11 


00027 


00010 


2M59 


LDPM 


00025 


00000 


N 


00 3 34 


14 


30031 


24000 


2M60 


ZJ 


02M61 


02M65 


E 


00335 


47 


00336 


00342 


2M61 


LDNO 


00023 


00000 


W 


00336 


14 


30027 


00000 


02M62 


DVSU 


00025 


00 TO 6 S 


T 


00337 


14 


21031 


10047 


2M63 


TN 


FOOOO 


00T06 





00340 


13 


00002 


00047 


2M64 


TN 


COOOO 


00 TO 7 


N 


00341 


13 


00003 


00050 


2M65 


T U 


OOMOO 


00004 


C 


00342 


15 


00142 


00004 


2M66 


LDST 


00T06 


00004 


B Y 


00 34 3 


14 


30047 


36004 


2 Mo 7 


PDNO 


OOOJO 


00000 


C 


00344 


14 


74012 


00000 


2 Mo 8 


STPM 


00006 


0000 


L 


00 3 45 


14 


3 4006 


24000 


2M69 


ZJ 


2M71 


02M7 3 


E 


00 3 46 


47 


003 50 


00352 


02M70 


M J 


00 000 


2 M 7 4 




00347 


45 


00000 


003 53 


2 M 7 i 


LDDV 


00025 


00T06 




00350 


14 


30031 


20047 


U2M72 


PMNO 


00000 


00000 S 




00351 


14 


2 5010 


00000 


2M73 


PDPD 


000 10 


00010 




00352 


14 


74012 


74012 


2M74 


I J 


00T14 


00M2 2 




00353 


41 


00057 


00170 


2M75 


ra 


00M01 


00016 




00354 


21 


00143 


00020 


G2M76 


MJ 


00000 


00M01 




00355 


45 


00000 


00143 


02M77 


TP 


02M70 


2M67 




00356 


.11 


00347 


00344 


2M78 


MJ 


00000 


00 MO 4 




00357 


45 


00000 


00146 


2M79 


TP 


00027 


00T12 




00360 


11 


00033 


00055 


2M80 


TP 


00028 


00T13 




00361 


11 


00034 


00056 


02M81 


TP 


00023 


00106 




00362 


11 


00027 


00047 



RW-179 



02M82 


TP 


00024 


00T07 








2M33 


TP 


OOKOl 


FOOOO 








02M84 


RP 


30004 


02M29 








02M85 


TP 


00T02 


OOTOO 








OOKOO 


05 


00000 


OOOOO 


-01 


F 


c 


OOKOl 


01 


ooooo 


OOOOO 




F 





OOK02 


01 


00000 


OOOOO 


1 


F 


N 


OOK03 


00 


00002 


OOOOO 






S 


00K04 


01 


OOOOO 


OOOOO 


-04 


F 


T 


OOK05 


PDNO 


00010 


OOOOO 






A 


00K06 


00 


00004 


OOOOO 






N 


OOK07 


00 


ooooo 


OOOOO 








START 




OOMOO 











PC 


)L-0 






Pg. 11 of 11 




9- 


4-5< 


5 




00363 


11 


00030 


00050 


00364 


11 


00370 


00002 


00365 


75 


30004 


00276 


00366 


11 


00043 


00041 


00367 


20 


04000 


OOOOO 


00370 


20 


14000 


OOOOO 


00371 


20 


45000 


OOOOO 


00372 


00 


00002 


OOOOO 


00373 


16 


36433 


34272 


00374 


14 


7 4012 


OOOOO 


00375 


00 


00004 


OOOOO 


00376 


00 


OOOOO 


OOOOO 


OOOOO 


45 


OOOOO 


00142 



10-lliO 



L. 1-. l",«.iOJ s,AM i>.k.C. REPOHT NO. ZM £91 

C. SV'.VT model ALL 

date July 5, I956 



UNPACKED FLOATING POINT CARD OUTPUT 

Thi« rout In o wrltoa up to fivo docimal point numbers on cards from. 
oithor LS or Ml) 

Drum addroms ,,72013 72357 inc. 

Number of Instructions 270 octal 

Con s tan to 55 octal 

Temporaries 76 octal 
&3 addroao (including temporaries) 01000— -01^42 inc. 
Driver 71760—72012 Inc. 

Tho routino iwty bo ruodii'ied or luay bo uuod as a Bubroutl.no by the us© 
of tho driver, with KS utorod starting at 7-4001. 

All conatanta nuodod aro included in tho routine, 

Tho tmbroutlno ia coded to wtart in coll 01000 and ie onterod by the 
write £tuquenc6 

37 01001 01002 

AD UUUUU VVVVV 

In caoo of bull failuro a start at PAK * 01000 v/ill romilt in repeat 
of th«:) Intorruptod Instruction. 

To uho n& « aulxroutJno with tho drivor tho aoquonco nhould ba 
37 71760 71761 

AB UUUUU WVVV 

In caoo of bull fnllury a otftrt at PAK - 72007 v/Ill rowtore ES and 
coi;.» to a 56 halt, Rolonuo of 56 atop will ropoat intorruptod Instruction. 



Old] 



C O H V Z\ I i 



L. h\ PM 



CV-100 

I'AGE IC-012-2 
REPORT NO. ZM A91 
MODEL ALL 

date July 5> 1956 



A. If A lo equal to A, 5, 6 or 7 the cards will not bo numbered otherwise they 
w.1 XI be numbered starting at one. Call 01270 (72303) contains this counter and 
1 1)' bo 00 1 nt one loon than tho next positive card numbor desired, 
h, T« not unod. 

UUUUU la tho storage addross of tho first mantissa 
W'VVV is the number of floating point numboro to be punched. 
C.^'V vp^M COTTU '■'?»« 

6, 21, 36, 51> 66 decimal point punched in card. 

7— 16, 2?—?l, 37— /*6, 52—61, 67—76 ton docimal digit nwntinoaa 

17, 3?» 4.7, 62, 77 oign of tho idantlseas 

18 — 19, 33 — 34., ££ — 49, 63 — 64, 70 — 79, exponents (powor of tan) ranga — 

99 to 99 

i 

20, 35# f>0, 65, 80 algns of oxjonont. j 

i 

conj t-o nnwt \ 

No prim* conwwdo aro included. 17 00000 7234.2 will advance a punch card. I 

In caoo of an unnornalissod imntlaiui or an oxponont with absolute value abova I 
513 octal in any fujrioo to bo punohad, that numbor will be punched an nogfitiv© 
ssoro. In addition an alnrm listing of tho first *mch addreas and mantissa 
will occur on tho typ^writor at tho ond of tho Inst card and a 56 stop will occur I 

which may be rolottsod to continuo. \ 

Tho r.vixlm.Hfi absolute value of axpononta is 90 or 99 do ponding on tha j 

imntinoa vo.luoo 

Th- coMbinud orror of rouA U) with 10011 and road out with XC012 will not ok« 
0- • a om in tho t*»nth digit. ; 



JO-U'VJ 



FORM NO. E T. • 1 (f»y F 



CONVA1R - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-180 
page IC-012-3 

REPORT ZM 4.91 
MODEL All 

DATE 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 



33 



1 

Q 
3' 






71760 


00745 


56 


00000 


30000 




71761 


00746 


75 


31777 


71763 


STORE 


71762 


00747 


11 


00001 


74001 


E S 


71763 


00750 


75 


30400 


00752 


ROUTINE 


71764 


00751 


11 


71760 


00745 


TO E S 


71765 


00752 


31 


00745 


00000 


SET 


71766 


00753 


36 


01310 


72011 


REPEAT 


71767 


00754 


16 


00745 


00772 


SET 


71770 


00755 


21 


00772 


01310 


EXIT 


71771 


00756 


55 


00745 


20025 


MODIFY 


71772 


00757 


44 


00761 


00760 


E S 


71773 


00760 


32 


00777 


00000 


ADDRESSES 


71774 


00761 


55 


20000 


00017 


TO STORAGE 


71775 


00762 


37 


00762 


00763 




71776 


00763 


16 


20000 


00764 


ACQUIRE 


71777 


00764 


71 


01310 


30000 


CONTROL WORD 


72000 


00765 


55 


20000 


00006 


EXAMINE 


72001 


00766 


37 


00762 


00757 


FOR E S 


72002 


00767 


55 


20000 


00017 


ADDRESSES 


72003 


00770 


37 


01001 


01006 


TO SUBROUTINE 


72004 


00771 


11 


01270 


72303 


STORE CARD NUMBER 


72005 


00772 


75 


31777 


30000 


RESTORE 


72006 


00773 


11 


74001 


00001 


E S 


72007 


00774 


75 


31777 


72011 


RESTORE 


72010 


00775 


11 


74001 


00001 


E S 


72011 


00776 


30 


00000 


00000 


REPEAT 


72012 


00777 


74 


00000 


00000 


E S STORAGE 


72013 


01000 


30 


00000 


0000* 


REPEAT LAST INST 


72014 


01001 


45 


00000 


30000 


EXIT 


72015 


01002 


16 


01001 


01005 




72016 


01003 


21 


01001 


01310 




72017 


01004 


36 


01344 


01000 





:ONVASfe - OH/iSiON Of GENERAL DYNAMICS CORP. 



SAN DIEGO, CALIFORNIA 



CV-180 

PAGE IC-012-4 

REPORT ZM 491 

MODEL All 

DATE 7**5-$6 



UNPACKED FLOATING POINT CARD OUTPUT 



72020 


01005 


71 


01310 


30000 




72021 


01006 


15 


20000 


01026 


FIRST ADDRESS 


72022 


01007 


13 


20000 


01347 


FLAG 


72023 


01010 


11 


01310 


01350 


FLAG 


72024 


01011 


31 


20000 


00025 


EXTRACT 


72025 


01012 


31 


20000 


00063 


AND STORE 


72026 


01013 


36 


01310 


01351 


N-l 


72027 


01014 


46 


01001 


01015 


TEST FOR ZERO 


72030 


01015 


17 


00000 


01327 


PICK WRITE CARD 


72031 


01016 


31 


01351 


00000 




72032 


01017 


11 


20000 


01352 


N-l PER CARD 


72033 


01020 


11 


01325 


10000 


WRITE 


72034 


01021 


42 


01342 


01024 




72035 


01022 


11 


01306 


01352 


5 PER CARD 


72036 


01023 


11 


01324 


10000 


WRITE AND PICK CARD 


72037 


01024 


17 


00000 


10000 


CARD INSTRUCTION 


72040 


01025 


75 


30012 


01027 


5 WORDS TO 


72041 


01026 


11 


30000 


01353 


STORAGE 


72042 


01027 


75 


10045 


01031 


CLEAR FOR 


72043 


01030 


11 


01307 


01376 


CARD IMAGE 


72044 


01031 


15 


01266 


01050 


SET ACQUISITION 


72045 


01032 


11 


01340 


01374 


BIT 


72046 


01033 


11 


01265 


01375 


BIT INSTRUCTION 


72047 


01034 


41 


01347 


01047 


I DENT NUMBER TEST 


72050 


01035 


11 


01332 


01374 


BIT 


72051 


C1036 


21 


01270 


01310 


COUNT -CARDS 


72052 


01037 


42 


01315 


01041 


SIZE OF WORD 


72053 


01040 


31 


01341 


00000 


SET 99999 


72054 


01041 


32 


01307 


00043 


INTEGER 


72055 


01042 


32 


01265 


00000 


TO 


72056 


01043 


73 


01315 


01365 


FRACTION 


72057 


01044 


54 


01365 


00001 


2 EXP 36 



10-184 



FORM NO. E. T. ■ 1 (f»> r 



CCiftVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



cv-iou 

page IC-012-5 

REPORT ZM 4.91 
MODEL All 

date 7-5-56 



UNPACKED FLOATING' POINT CARD OUTPUT 



o 



1 

o 

«— I 

I 

o 
o 
o 



X 



72060 


01045 


11 


01306 


01376 


N-l DIGITS 


72061 


01046 


37 


01200 


01165 


IDENT NUMBER 


72062 


01047 


75 


30002 


01051 


MANTISSA 


72063 


01050 


11 


30000 


01365 


AND EXPONENT- 


72064 


01051 


11 


01365 


01370 


MANTISSA SIGN FLAG 


72065 


01052 


54, 


01366 


00030 


EXPONENT 


72066 


01053 


54 


01366 


00060 


EXTENSION 


72067 


01054 


12 


20000 


20000 


EXPONENT 


72070 


01055 


42 


01301 


01067 


FLOATING TEST 


72071 


01056 


41 


01350 


01062 


FIRST TIME 


72072 


01057 


11 


01264 


01370 


MANTISSA FLAG 


72073 


01060 


75 


10002 


01156 


SET EQUAL 


72074 


01061 


11 


01307 


01365 


TO ZERO 


72075 


01062 


13 


01322 


01350 


SET ALARM FLAG 


72076 


01063 


11 


01026 


01345 




72077 


01064 


15 


01050 


01065 


ACQUIRE 


72100 


01065 


11 


30000 


01346 


MANTISSA 


72101 


01066 


45 


00000 


01057 




72102 


01067 


11 


01365 


20000 




72103 


01070 


47 


01071 


01156 


ZERO MANTISSA 


72104 


01071 


46 


01072 


01073 




72105 


01072 


13 


01365 


01365 


NEGATIVE MANTISSA 


72106 


01073 


16 


01323 


1 1 2'3 


SET SHIFT TO 33 


72107 


01074 


32 


01307 


00001 


EXP 36 


72110 


01075 


43 


20000 


01056 


FLOATING TEST 


72111. 


01076 


11 


01307 


01373 


CLEAR FOR DECIMAL EXP 


72112 


01077 


11 


01366 


20000 


EXPONENT 


72113 


01100 


?\6 


01101 


01117 


SIGN 


72114 


01101 


23 


01373 


01342 


10 EXP 5 ADJUSTMENT. 


72115 


01102 


11 


01307 


01372 


CLEAR FOR 74 


72116 


01103 


71 


01315 


01365 


X 10 EXP 5 


72117 


01104 


74 


20000 


01372 





CONVAIR - DIVISION Or GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-lbU 
page IC— 022— 6 

REPORT ZM 491 
MODEL All 

DATE 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 



72120 


01105 


11 


20000 


01365 




72121 


01106 


4 6 


01107 


01114 


TEST FOR ROUND 


72122 


01107 


21 


01365 


01310 


ROUND 


72123 


OHIO 


43 


20000 


01114 


MANT ISSA 


72124 


01111 


31 


01365 


00107 


AND 


72125 


01112 


ii 


20000 


01365 


ADJUST 


72126 


01113 


21 


01372 


01310 




72127 


01114 


21 


01366 


01372 


ADJUST RSF 


72130 


01115 


46 


01101 


01116 


SIGN OF BSF 


72131 


01116 


31 


01366 


00000 


DIVIDE EXP 


72132 


91117 


73 


01323 


01367 


BY 33 


72133 


01120 


11 


20000 


01366 


EXPONENT REMAINDER 


72134 


01121 


55 


01365 


00001 


MANTISSA 


72135 


01122 


45 


00000 


01152 




72136 


01123 


31 


01365 


3C000 


MANTISSA SHIFT 


72137 


01124 


11 


20000 


01371 


STORE AR 


72140 


01125 


34 


20000 


00044 


ERASE 


72141 


01126 


11 


20000 


01365 


5T0RE AL 


72142 


01127 


75 


20013 


01426 


TEST FOR LARGER 


72143 


01130 


42 


01310 


01131 


POWER OF TEN 


72144 


01131 


51 


01330 


10000 




72145 


01132 


31 


01311 


00000 


10 EXP 10 


72146 


01133 


36 


10000 


10000 




72147 


01134 


3 5 


01373 


01373 


INCREASE EXP 


72150 


01135 


31 


10000 


00017 


N X 2 EXP 15 


72151 


01136 


q c. 


oi;/^3 


e*» ] 1 *> 7 




72152 


^1137 


3 •"* 


r ; ^ p r- n 


/*■ r- r\ r\ 


ACQ!! I RE DI\M r 0R 


7il r. r> 


oil '.r, 


T •* 


■5 ,-, - - '• 


• -* - -. 






■> 








P r STORF 
A 

'"■ EXP 3 5 
' XP 36 



CUINVAIK — UIVIXUN Uf- OtlMfcKAL DYNAMICS CORP. 

SAN DIEGO, CALIFORNIA 



UV-lbU 
PAGE IC-012-7 

REPORT ZM 491 
MODEL All 

date 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 





72160 


01145 


31 


20000 


ooool 


DETERMINE 




72161 


01146 


42 


01372 


01150 


LAST 




72162 


J1147 


27 


10000 


01310 


BIT 




72163 


01150 


11 


10000 


01365 


ANSWER X 2 EXP 36 




72164 


01151 


37 


01151 


01152 






72165 


01152 


41, 


01367 


01123 


HIGHER ORDER DIGIT 




72166 


01153 


16 


01366 


01123 


LOWER ORDER SHIFT 




72167 


01154 


37 


01151 


01123 


LOWER ORDER DIGIT 




72170 


01155 


11 


01373 


01366 


DECIMAL EXPONENT 




72171 


01156 


21 


010 r >0 


01326 


STEP 




72172 


01157 


21 


01026 


01326 


STEP 




72173 


01160 


37 


01200 


01174 


SHIFT FOR PERIOD 




72174 


01161 


12 


01366 


20000 


EXPONENT 




72175 


01162 


11 


01333 


01376 


TALLY 




72176 


01163 


73 


01311 


01372 


DIGITS 




72177 


01164 


11 


20000 


01371 


OF EXP 




72200 


01165 


31 


01365 


00002 


EXTRACT 




72201 


01166 


32 


01365 


00001 


AND 




72202 


01167 


11 


20000 


01365 


POSITION 




72203 


01170 


34 


20000 


00063 


DIGIT 




72204 


01171 


35 


01375 


01172 


ASSEMBLE INST 




72205 


01172 


30 


00000 


0000* 


SET BIT 


o 


72206 


01173 


37 


01173 


01174 




CO 
1— 1 


72207 


01174 


5 5 


01374 


00043 


SHIFT BIT 


1 

o 

r-4 


72210 


01175 


44 


01176 


01177 




I 

o 
o 


72211 


01176 


21 


01375 


01334 


ADVANCE FIELD 


r-i 


72212 


01177 


41 


01376 


0U65 


TEST FOR END 


X 


72213 


01200 


37 


01200 


01201 






72214 


01201 


11 


01370 


10000 






72215 


01202 


44 


012 03 


01205 






72216 


01203 


13 


01331 


20000 






72217 


01204 


37 


01173 


01171 


SIGN 



lO C T - 1 Xi r 



C0NVA1R — Divisor- ~r -jzhit*. '- , 

SAN DIEGO, CALIFORNIA 



'.'..'Hi'. 



CV-18G 
page I-*'" IC-012-8 

RER0HT ZM 4-91 
MODEL AJ1 

date 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 



72220 


01205 


55 


01374 


00043 


SHIFT BIT 


72Z21 


01206 


37 


01206 


01207 




72222 


01207 


31 


01372 


00017 


TENS DIGIT 


72223 


01210 


37 


01200 


01171 




72224 


01211 


31 


01371 


00017 


UNITS DIGIT 


72225 


01212 


37, 


01200 


01171 




72226 


01213 


11 


01366 


01370 




72227 


01214 


37 


01206 


01201 




72230 


01215 


37 


01215 


01216 




72231 


01216 


41 


01352 


01047 


WORDS PER CARD 


72232 


01217 


11 


01335 


01371 


SIT FOR 12 ROWS 


72233 


01220 


21 


01377 


01336 




72,234 


01221 


21 


01411 


01336 




72235 


01222 


21 


01404 


01336 




72236 


01223 


21 


01413 


01337 




72237 


01224 


21 


01425 


01337 




72 240 


01225 


21 


01420 


01337 




72241 


01226 


16 


01267 


01233 




72242 


01227 


16 


01127 


01234 




72243 


01230 


15 


01267 


01231 




72244 


01231 


55 


30000 


00010 




72245 


KJ jJL tmr •*' •"■ 


77 


00000 


10000 




72246 


01233 


77 


10000 


30000 




72247 


01234 


77 


10000 


30000 




72250 


01235 


23 


01231 


01331 




72251 


01236 


23 


01233 


01310 




72252 


01237 


23 


01234 


01310 




72253 


01240 


41 


01371 


01231 


TEST FOR END OF CARD 


72254 


01241 


23 


01351 


01342 


TEST FOR 


72255 


01242 


46 


01243 


01016 


END 


72256 


01243 


41 


01350 


01001 


FLOATING FLAG 


72257 


01244 


75 


10005 


01246 





10-188 



FORM NO. E. T. - 1 (n F 



CONVAIR- DIVISION OF GENERAL DYNAMICS CORP. CV-180 

SAN OIEGO. CALIFORNIA PAGE IC""012«»9 

REPORTZM4.91 

MODEL AH 
DATE 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 





72260 


01245 


61 00000 


01302 






72261 


01246 


11 01306 


01371 






72262 


01247 


55 01345 


10011 






72263 


01250 


31 01264 


00000 






72264 


01251 


52 01343 


01252 






72265 


01252 


30-- 00000 


00000 






72266 


01253 


55 10000 


00003 






72267 


01254 


41 01371 


01250 






72270 


01255 


37 01255 


01256 






72271 


01256 


55 01346 


10003 






72272 


01257 


61 00000 


01306 






72273 


01260 


11 01335 


01371 






72274 


01261 


37 01255 


01250 


- 




72275 


01262 


56 00000 


01001 






72276 


01263 


55 01310 


10001 






72277 


01264 


61 00000 


01271 






72 300 


01265 


21 01401 


01374 






72301 


01266 


00 01353 


00000 






72302 


01267 


00 01442 


01412 






72303 


01270 


00 00000 




CARD COUNTER 




72304 


01271 


00 00000 


00037 


* 




72305 


01272 


00 00000 


00052 







72306 


01273 


00 00000 


00074 




CO 

r-4 


72307 


01274 


00 00000 


00*70 




1 

O 
r-i 


72310 


01275 


00 00000 


00064 




1 

O 
O 


72311 


01276 


00 00000 


00062 




a- 


72312 


01277 


00 00000 


00066 




X 


72313 


01300 


00 00000 


72 






72314 


01301 


00 00000 


00513 






72315 


01302 


00 00000 


00*45 






72316 


01303 


00 00000 


00031 






72317 


01304 


00 00000 


00020 





i n_ i RQ 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. CV-180 

SAN PIEGO. CALIFORNIA PAGE IC~012-*10 

REPORT ZM 491 
MODEL, All 
DATE 7-5-56 



UNPACKED FLOATING POINT CARD OUTPUT 



72320 01305 00 00000 0***1 

72321 01306 00 C0000 00*04 

72322 01307 00 00000 00 * 

72323 01310 00 00000 1 

72324 01311 00 00000 00012 

72325 01312 00- 00000 00144 

72326 01313 00 00000 01750 

72327 01314 00 00000 23420 

72330 01315 00 00003 03240 

72331 01316 00 00036 41100 

72332 01317 00 00461 13200 

72333 01320 00 05753 60400 

72334 01321 00 73465 45000 

72335 01322 11 24027 62000 

72336 01323 00 00000 00041 

72337 01324 00 00000 00112 

72340 01325 00 00000 00102 

72341 01326 00 00002 00000 
'72342 01327 00 00000 00110 

72343 01330 00 00000 00 77, 

72344 01331 00 00001 00000 

72345 01332 40 00000 00000 

72346 01333 00 00000 00011 

72347 01334 00 00014 00000 

72350 01335 00 00000 ^0013 

72351 01336 01 00001 000O1 

72352 01337 00 00100 00100 

72353 01340 01 00000 00000 

72354 01341 00 00003 03237 

72355 01342 00 00000 00*05 

72356 01343 00 00000 00 *7 

72357 fU344 ^0 n^oo no #? 



10- 190 



ANALYSIS 

PREPARED BY W* J* Stotier 

checked by J. P. Wilkinson 

REVISED BY 



C O N V A I R 

A OIVKIOM OF • INEaAL DYNAMICS CORPORATION 

SAN DIEGO 



CV-181 
page CN 015-1 

REPORT NO. ZW 491 
MODEL *H 
DATE 8-9-56 



CONTINUOUS MATRIX MJLTIPLBR USING FLIP III 

This routine multiplies two matrices, takes this product times a 
third matrix, the resulting product times a fourth, etc* All input and out* 
put data is by means of six-field flip cards. The elements of any one of 
the matrices may be punched on cards with the elements of a row or a column 
in consecutive order with each row or column starting at the beginning of a 
flip card** The multiplier assumes the matrix on the left is stored by rows 
and the one on the right is stored by columns. Even though one or both of 
the matrices may not be of this form on the cards, the multiplication may 
still be performsd by using flags to indicate storage form different from 
the card form* A third flag is used to indicate a change in the form of the 
product if it is desired, and a fourth flag is used to indicate further 
multiplication* These flags are denoted by the symbols p^, p^, p*, and p,* 
Three parameters, m, n, and s, are necessary to furnish the routine with the 
sise of the matrices* 

To illustrate the use of the parameters and flags, suppose the pro- 
duct, ABC, of three matrices is wanted where the matrices have the following 
properties! 

As a m x n matrix, punched by columns on flip cards 
fit a n x s matrix, punched by columns on flip cards 
t a 8 X tn matrix, punched by rows on flip cards. 



* The 8 top read indicator (a 12 - punch in column 1) must be on the last 
card for each matrix* 



10-191 



ANALYSIS 

prepared by W. J. Stoner 

CHECKED BY J. P. WllkiHSOll 

REVISED BY 



C O N V A I R 

A Bl VISION Of •CMCKAL DYNAMIC* CORPOMTIIM 
SAN DIEGO 



CV-181 
page CN 015-2 

REPORT NO. 2M 4-91 
MODEL All 

DATE 8-9-56 



The multiplication proceeds from the left, so AB is the first product formed, 
then this multiplies C. 

Before reading matrix A, the routine reads three parameter cards. 
The first of these parameter cards contains *m* as the card number, the sec- 
ond contains "n* as the card number, and the third contains n s" as the card 
number. The third card also contains any of the four flags that need to be 
indicated. If flag p^ is necessary, it appears as any number different from 
aero in field 1 and so on for the other three flags in the next three fields. 
Thus, for this multiplication p, pd since A needs to be changed in form be- 
fore storage, p 2 » since B does not need to be changed, p* 3 since AB is 
multiplying C instead of the transpose of AB times C, and p, j*£ since the 
multiplication will not terminate with the product AB. After the product AB 
has been computed by columns, it is stored by rows in the position of the first 
matrix in the multiplier, and the routine Is ready to receive C. However, a 
new parameter card must be read before reading C. This card contains the sec- 
ond dimension c of C, i. e. "t*, as the card number, nothing in field 1 since 
the first matrix in the multiplier has been properly 3tored, p« ^ in field 2 
since the form of C must be changed from cards to storage, p^ ■ since the product 
of ABC is wanted not its transpose, and p^ « since the multiplication is to 
terminate when ABC is formed. 

To summarise, 
p. ( - for first matrix pinched by rows 

( ^0 for first matrix punched by columns 
p ( » for second matrix punched by columns 



( r* 



for second matrix punched by rows 



p.( • for the product to be used as formed 

( f£ for the transpose of the product to be used 



•ORM iaifi.A 



10-192 



ANALYSIS 

prepared by W. J. Stoner 

CHECKEP BY J. P. VllkiliSOn 

REVISED BY 



C O N V A I R 

A OIVtSIOH Of «MCI«L DYNAMICS CORPORATION 

SAN DIEGO 



page CN 015 -3 

REPORT NO. ZM 491 

MODEL All 

DATE 8-9-56 



CO 



I 

o 

I— i 
I 

o 
o 



a. 



p ( * for no further multiplication 



^ for continued multiplication 
NOTSt If p, a 0, then p, controls the form of the output. 

The final output is the product by columns for p^ a 0, or is the 
transpose (of the product) by columns f or p^ ^ 0. In the routine, just prior 
to the final output, the only MS - 1 appears in the program. If a stop is 
made here and HT - 1 is set, then the output is that specified by p, and also 
its transpose. 

In a continuous multiplication, output of the intermediate products 
may be obtained. The only MS - 2 in the routine is just prior to the inter- 
mediate output. A stop at this point allows the operator to set the MJ *s 
which control the intermediate output as follows* 



none 
1 

2 

3 

1 & 2 

1 & 3 

2 & 3 

1, 2, & 3 



Output 
none 

( product by columns for p^ * 0, 

( ' 

( transpose (of product) by columns for p^^ 0, 

Product regardless of p^ 

Transpose (of Product) regardless of p~ 
( transpose (of product) for po *■ 
( Product for p^ ^ 0, 

Sama as 1* 
( Product followed by transpose for po » 
( Transpose followed by product for p^ ^ 0. 

Same as 1 & 2, 
This routine, the working storage, the matrix storage and flip use 

10-193 



ANALYSIS 

prepared by W» J« Stoner 
checked 8Y J» P« Wilkinson 

REVISED BY 



C O N V A I R 

A OIVWON Or •IMHAL OTHAMICS CO Ml* OK ATI ON 
SAN DIEGO 



CV-181 
page CN 015-4 

REPORT NO. ZM 491 
MODEL All 
DATE 8-9-56 



the entire ES storage and all of MD. The storage is allotted as follows 1 


00000 - 


00077 ) 
01777 ) Flip 
77777 ) 




0H77 - 




70000 - 




00100 - 


00137 - Temporaries 




00140 - 


00157 - Constants 




00160 - 


00376 - Program 




00377 - 


014.76 - Working storage 




40000 - 


40627 • Program 




^0630 - 


50417 - 1st matrix 




50420 - 


60207 - 2nd matrix 




60210 - 


67777 - Product 




Testa are built into the routine that give an alarm exit if the size 


of a matrix is too large for the multiplier. 


The following restrictions are 


imposed on ra, n, s, k lf k 2f & ky (see next page for definition of k ± •sji 


1 <: m, 


n, s "S 192 1Q 




lin 


' k 2 £ 3960 - 60(66) + 1 




1< k 2 


* s < 3960 - 60(66) ♦ 1 




1 :£. m » 


< k < 3960 » 60(66) + 1 




1 S k x * s < 3960 » 60(66) ♦ 1 




thus, the largest 


square matrix that can be 


handled is a 60*60 matrix, and the 


largest rectangular matrix is a 60 * 66. The 


largest square matrix is a 60 x 60 


since a 61 * 61 would be handled on cards and 


in the memory as a 61 * 66 or 66 * 61 


and the product 61 


*66 » 4026 which is greater than the 3960 number of elements 


allowed .for each matrix. 






10-194 





ANALYSIS 

prepared by W. J. Stoner 
checked by J. P» Wilkinson 

REVISED BY 



C O N V A I R 

A 0IVIMOM Or 0gNCML DYNAHIICS COHfOMHOH 

SAN PIEOO 



CV-1«1 

page CN 015-5 

REPORT NO. ZM 491 
MODEL. AU- 

date 8-9-56 



CO 



I 

o 

I 

o 
o 
o> 



X 

cu 



A check sum is printed at the beginning of the program. This ©heck 
sum is equal to 22420523 56Q r . A programmed KLotto is included in the routine. 
Setting (PAK) » 40620 and starting gives a KLotto of 00100 - 00377 and 40000 
to 40637> which includes the temporaries, constants, and program in E.S. and 
entire program on M.D. 

The program starts with (PAK) » 40000. Several continuous multiplication 
may be done by resetting (PAK) * 40000 at MS-0. However, either the cards 
should be loaded in the reading hopper when PAK is resetj or, all cards may be 
loaded beforehand if a blank card is placed between the cards for the separate 
continuous multiplications. 

List of Symbols In Flow Chart and Code. 



A 

6 
C 

a ij 

b jk 

°ik 
m 

n 

a 

k l 
*2 

k 3 

Pi 
P2 
P3 



Matrix on left in product 

Matrix on right in product 

Product of A and B 

Element of A in ith row, jth column (refers to M.D. storage) 

Element of B in jth row, kth column (refers to M.D. storage) 

Element of C in 1th row, kth column (refers to M.D* storage) 

Number of rows of A, number of rows of C 

Number of columns of A and number of rows of B 

Number of columns of B, number of columns of C 

m, if m a (mod 6)j 1st multiple of 6 > m if & / (fod 6) 

n, if n a (mod 6); 1st multiple of6>nifn^0 (mod 6) 

s, if s 3 (mod 6); 1st multiple of 6 > s if s £ (mod 6) 

non-zero for A changed from cards to storage, otherwise zero 

non-zero for B changed from cards to storage, otherwise zero 

non-zero for transpose of product wanted, otherwise zero 

10-1V5 



ANALYSIS 

prepared by W. J» Stoner 
checked by J. p. Wilkinson 

REVISED BY 



C O N V A I R 

A DlVlSlOa Or OIMMAL DYNAMIC* COHrOMTIOM 

SAN DIEGO 



CV-181 

page CN 015-6 

REPORT NO. ZM J+91 
MODEL All 

DATE 8-9-56 



p 4 



1 ( ) 

V V s 



non-zero for additional multiplication to do, otherwise zero 

contents of a temporary storage cell in E. S. 

any matrix element on MD 

any matrix element in ES after card read when p^ or p« / 

one of a consecutive group of elements which is formed in 

ES before transfer to M»D, The group is a row of A or a column 

of B on card read with p or p / 0, is a column of C during 

multiplication, and is a row of C if p, / f p^ ■ # or if 

PA * °» P3 t °* 

an element of the ith row of A 

an element of the kth column of B 

location of quantity in parenthesis 
Indicated matrix stored by rows 
Indicated matrix stored by columns 



10-196 



ANALYSIS 

prepared by W» J. Stor,er 

CHECKED BY J. P. Wilkinson 
REVISED BY 



C O N V A I R 

A •IVMION OP «IN(**L DYNAMICS COIIFOMT10N 
SAN DIEGO 



CV-181 
page CN 015-7 

REPORT NO. ZM 491 
MODEL All 

date 8-9-56 



CO 



I 

o 

i— i 

I 

o 
o 
a* 



x 

a* 



GENERAL FLOW CHART 



$0000 



i 



Activate flip. 

St/ 7* projrdm. 



U± 




Jto 



Print Sum. 
Re4<J 3 arJs 
f#r p*r4n\ct<rs 
And fldQS- 

Compute $1* 



2M 



tpf-°y 



fU 



210 



Sue of wt r»'ce$ , 



Ml 



\ Too h 



r<?€ 



<HE> £ 



Option*! output. 

<4" -* n 



O.H. 



i 



Of>tio7uf Output. 



^r 



di<trm 
^ 



i. 



250 



<jllD 



tie id d -nd 
Store A r . 



m >/ 



store dS Ar< 



22(* 



Ht*d 1 cdrd far 
fir* meters A nd 



-^** 



250 w 
r *°J* r r fe *e of rn*tr,ctsh 



ok 



355 

.I. . f O * Q \ • *■■ ■ 

H4 sf & 7 ^ 



/f e a d <3 t\ d 
Store fi c - 



ft cad & r and 
Store <j$ 8c 



*& 



no 



Multiply 
Ay*8 c 



c c > 





CONVA1R 



DIVISION OF GENERAi DYNAMICS CORP. 

S»N Olt.O i!AHfOR» 



CV-181 
page CN 015-8 

REPORT ZM 4-91 
MODEL All 

DATE 8-9-56 



:0NT 1 MUOUS MATRIX MUL T I PL I ER 



4 0000 




45 


00000 


40001 


40001-^ (PAK) 


40001 




37 


70160 


70140 


ACTIVATE FLIP 


40002 




00 


00000 


00000 


FLAG 


40003 




31 


40000 


00000 


CHECK 


40004 




75 


20627 


40006 


SUM 


40005 




32 


40001 


00000 


PROGRAM 


4^006 




11 


20000 


10000 


SUM— •*- (Q) 


40007 




75 


30237 


00160 


STARTER AND CARD READ 


40010 




11 


40020 


00140 


TO ES# 160 -*■ (PAK) 


40011 




00 


00000 


00000 




40012 




00 


00000 


00000 




40013 




00 


00000 


00000 




40014 




00 


00000 


00000 




40015 




00 


OOQOO 


00000 




40016 




00 


00000 


00000 




40017 




00 


00000 


00000 




40020 


00140 


00 


40 630 


40630 


e«L h \*z a +U* l% } 


40021 


00141 


^0 


50420 


50420 


&(K>*i t5 +t(V 


40022 


00142 


00 


60210 


60210 


*U„xi' 3 + t(c„> 


40023 


00143 


00 


00377 


01177 


tU tl X2 t§ 1-Jt($ u ) 


40024 


00144 


00 


00106 


00100 


i(^)4U ,5 titV 


4 0025 


00145 


00 


00000 


00103 


M*m*) 


40026 


00146 


00 


07777 


00000 


4 DIGIT U-EXTRACTOR 


4 0027 


00147 


00 


00077 


00000 


2 DIGIT U-EXTRACTOR 


40030 


00150 


00 


00000 


00006 


6 


4 0031 


00151 


00 


00000 


O0572 


378 


4 0032 


00152 


CO 


00000 


07571 


3961 


40033 


00153 


00 


00000 


00301 


193 


4 u 3 4 


00154 


00 


00000 


00000 




4 DO 3 5 


00155 


00 


00000 


00000 




4 0036 


00156 


00 


00000 


00000 




4 3 7 


00157 


00 


00000 


00000 





10-198 



CONVAiR - DiVISiON OF GENERAL DYNAMICS CORP. 



SAN "EGO CALIKDRNIA 



CV-Ibl 
PAGE CN 015-9 

REPORT ZM 491 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



o 

r-H 
I 

o 
o 
o 



X 

a, 



40040 


00160 


40041 


00161 


40042 


00162 


40043 


00163 


40044 


00164 


40045 


00165 


40046 


00166 


40047 


00167 


40050 


00170 


4 0051 


00171 


40052 


00172 


40053 


00173 


40054 


00174 


40055 


00175 


40056 


00176 


40057 


00177 


40060 


00200 


40061 


00201 


40062 


00202 


40063 


00203 


40064 


00204 


40065 


00205 


40066 


00206 


40067 


00207 


40070. 


00210 


40071 


00211 


40072 


00212 


40073 


00213 


40074 


00214 


40075 


00215 


40076 


00216 


4^077 


00217 



11 00057 00121 

61 00000 00042 

|T5 10000 00003 

51 00067 20000 
35 00042 00165 
30 00000 00000 

41 00121 00162] 
17 00000 73376 
1457 1010 0106 
1457 1010 0107 
1457 1010 0110 
11 00106 20000 

42 00153 00176 
37 76000 76001 
11 OO1O7 20000 
42 00153 00201 
37 76000 76001 
11 00110 20000 
42 00153 00204 
37 76000 76001 
11 00041 00121 

15 00144 00210 

16 00144 00215 
16 00145 00217 

FTl 30000 20000 
73 00150 10000 
47 00213 00214 
21 10000 00074 
71 10000 00150 
11 20000 30000 
54 20000 00017 
11 20000 30000 



PRINT 
OF 

CHECK 

SUM 
READY CARD REPRODUCER 
READ ?*— V (106) 
READ -n — * (107) 

READ 4^-^ Y 110 ) F0 ^ L °WED BY FLAGS 
W\ — > (A ) 
IS 193 > nnf 
N0t ALARM EXIT 

yes # n ~+ ( A ; 

IS 193 ><7\ ? 
N0» ALARM EXIT 
Y£S. 4, -+> (A) 
IS 193 > 4, ? 
NO* ALARM EXIT 
YES. SET INDEX 
l(^) -***{<* ,71,4s) 

*y*\ t -ri y 0R ,4/— ► (k) 
(A^/6 — *lQ)t Rem 

IS (A)zO? 

NO, (Q) t 1 -+(q) 

YES. (o) * 6 -^(a) 

(R) — *4; 

(A)x2 ,5 -t (A) 
(R) ~+%M { 



'(A) 






CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN [)IKiO 



CV-181 
page CN 015-10 

REPORT ZM 4.91 
MODEL All 
DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40100 


00220 


40101 


00221 


40102 


00222 


40103 


00223 


40104 


00224 


40105 


00225 


40106 


00226 


4O1O7 


00227 


40110 


00230 


40111 


00231 


40112 


00232 


40113 


00233 


40114 


00234 


4011S 


00235 


40116 


00236 


40117 


00237 


40120 


00240 


40121 


00241 


40122 


00242 


40123 


00243 


40124 


00244 


40123 


00245 


40126 


00246 


40127 


00247 


40130 


00250 


40131 


00251 


40132 


00252 


40133 


00253 


40134 


00254 


40135 


00255 


40136 


00236 


40137 


00257 



21 00210 00073 
21 00215 00074 
21 00217 00074 

41 00121 00210J 
71 00106 00101 

42 00152 00227 
37 76000 76001 
71 00101 OOHO 
42 00152 00232 
37 76000 76001 
71 00i00 OOnO 
4? 00152 00235 
37 76000 76001 
71 00106 O0l0? 
42 00152 00240 
37 76000 76001 
56 30000 00241 
11 00111 20000 
47 00243 00250 
11 00100 00121 
11 00106 00122 
11 00140 00123 
37 00300 00301 
45 00000 00255 
16 00140 00251 

Il457 0773 0000 
21 00251 00151 
U 00004 20000 
47 00255 0025jy 
11 00112 20000 
47 00257 00264 
11 00102 00121 



TEST INDEX 



*k 



(A) 



YES. % t ** 



IS 3961 > ^i *% ? 
NO* ALARM EXIT 

- M 

IS 3961 > 4j<4s? 
NO. ALARM EXIT 
Y E S # % t *v -► fa) 
IS 3061 >Jjj> ** ? 
NO. ALARM Ex'lT 
YES. <w 4 k —♦• (a) 
IS 3961 >/»,<# f 
NO. ALARM EXIT 
YES. MS*3 

p, ~+ (a) 
IS ft s ? YES. 250 
NO. % % <-*. I, 

nn — *■ 1^ 

CHANGE A c TO A^ AND STORE 

255 «•#» (PAK) 

AU h ) ~+f(<L<j) 

READ 63 CARDS INTO /^ )ETC. 

X<**j) + 378 ^tl^' 

(00004J -** (A ) 

IS (Aj r ? YES* 251 — V (PAK^ 

NO. p a ~+ fa) 

IS O rO f YES. 264 — *»(pak) 
I, 



(pakJ 



Pz 
no. 4 t 



10-200 



OHM NO t T I I' 



coNVAiR — division 



GENERAL DYNAMICS CORP. 



) CALIFORNIA 



CV-181 
page CN 015-11 

REPORT ZM ^91 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



I 

O 

r-i 
I 

o 
o 
a* 



x 



40140 


00260 


40141 


00261 


40142 


00262 


40143 


00263 


40144 


00264 


40145 


00265 


40146 


00266 


40147 


00267 


40150 


00270 


40151 


00271 


40152 


00272 


40153 


00273 


40154 


00274 


40155 


00275 


40156 


00276 


40157 


00277 


40160 


00300 


40161 


00301 


40162 


00302 


40163 


00303 


40164 


00304 


40165 


00305 


40166 


OO3O6 


40167 


00307 


40170 


00310 


40171 


00311 


40172 


00312 


40173 


00313 


40174 


00314 


40175 


00315 


40176 


00316 


40177 


00317 



11 00110 00122 

11 00141 00123 

37 00300 00301 

45 00000 Q027t 

16 00141 00265 
|T457 0773 0000 

21 00265 00151 

11 00004 20000 

47 00274 00265) 

00 00000 00000 

00 00000 00000 

00 00000 00000 

75 30217 00170 

11 40260 00160 

00 00000 00000 

00 00000 00000 

45 00000 30000 

11 00040 00127 

11 00040 00131 

55 00122 00017 

11 00121 20000 

73 00150 00124 

55 00121 00017 

11 00064 20000 

73 00124 00125 

55 10000 OOO17 

11 10000 00132 

11 00107 20000 

73 00125 10000 

11 20000 00126 

54 20000 00017 

11 20000 00133 



CHANGE B A TO B c AND STORE 

READ 63 CARDS INTO K^'JEJC. 
ttir.j) + 378 -*■ Khjf 
(00004) — ►• ^A^ 
IS (A) = Of YES* 265 -*■ (?kK) 



NO* MULTIPLIER AND 

FINAL OUTPUT TO ES 



EXIT 

— #* I 

-4 



h* 2 
I, ~ 

(A>/6 - 

I, * 2 
63 — * 

(Q)*?. 

<r\ — 

REM 



7 

hi 

/5 



t5 



(A) 



(a; 



>5 



I 5 AND (0) 



(0) 
I 



tZ 



M 



«5 






REM 



/a; 



REM * 2 
I, * 2 ,5r — * I 



if A) 



73 



10-201 



S* OK CALIFORNIA 



""-lOJL 

page CK 015-12 

REPORT ZM 4-91 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40200 


00320 


40201 


00321 


40202 


00322 


40203 


00323 


40204 


00324 


40205 


00325 


40206 


00326 


40207 


00327 


40210 


00330 


40211 


00331 


40212 


00332 


40213 


00333 


40214 


00334 


40215 


00335 


40216 


00336 


40217 


00337 


40220 


00340 


40221 


00341 


4O222 


OO342 


40223 


00343 


40224 


00344 


40225 


00345 


40226 


00346 


40227 


00347 


40230 


00350 


40231 


00351 


40232 


00352 


40233 


00353 


40234 


00354 


40235 


00355 


40236 


00356 


40237 


00357 



47 00323 00321 

11 00125 00126 

11 00132 00133 

71 00124 00132 

11 00147 10000 

53 20000 00327 

53 00132 00364 
fl457 0000 0377 

16 00123 00365 

21 00365 00131 

21 00131 00125 

11 00004 2^00 

47 00335 00352 

11 00064 00127 

16 00143 00350 

21 00350 00126 

31 00101 00000 

34 00107 00017 

11 20000 OO124 

11 00146 10000 

53 20000 00347 

21 00124 00133 

53 20000 00364 

75 10000 00351 

11 00040 30000 

11 00126 00125 

11 OOO4O 00130 

(Ts 00143 00360 

21 00360 00130 

16 00143 00360 

11 00125 20000 

36 00074 00124 



IS (a) =of 

Y£S # I 5 -► 
l tZ ~~ *<* 



NO, I^M l2 — * (A) 

2 DIGIT U-EXTRACTOR —*• (Q) 

SET NO* OF CARDS TO READ 

SET NO OF r'A, TO TRANSFER TO MD 

READ PRESET NO. OF CARDS INTO ES 

h, + I 5 -*- hi 

(OOOO4) -+• (A) 

IS (a) » f YES, 352 — +> (*>**) 

NO. 63 — * I7 

) 






<#,-,«) *z tS -*l ft) 

4 DIGIT U-EXTRACTOR — ► (Oj 
SET NO. OF >-i,T0 BE ZERO 

SET NO. OF y% TO TRANSFER TO MD 
SET PROPER 



4 



»5 

ho 







10-202 



CONVAIR - DIVISION >F GENERAL DYNAMICS CORP. 



SAN D iO CALIFORNIA 



CV-181 

page CN 015-13 

REPORT ZM 491 

MODEL All 

date 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



i 

o 



o 
o 



x 
a, 



40240 
40241 
40242 
40243 
40244 
40245 
40246 
4^247 
40250 
40251 
40252 
40253 
40254 
40255 
40256 
40257 
40260 
40261 
40262 
40263 
40264 
40265 
40266 
40267 
40270 
40271 
40272 
40273 
40274 
40275 
40276 
40277 



00360 
00361 
00362 
00363 
00364 
00365 
00366 

00367 
00370 
00371 
00372 
00373 
00374 
00375 
00376 

00160 
00161 
00162 
00163 
00164 
00165 
00166 
00167 
00170 
00171 
00172 
00173 
00174 
00175 
00176 
00177 



fTT 30000 
21 00360 
35 00121 

41 00124 
75 30000 
11 01177 
21 00365 
21 OO13O 

42 00122 
11 00127 
47 00300 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
56 30000 
16 00143 
21 00203 
31 00100 
34 00106 
11 00146 
53 20000 
53 00104 



30000 
00074 

00360 

00360J 

00366 

30000 
00101 
OOO73 
00353J 

20000 

00327J 

00000 

00000 

00000 

00000 

00000 

00000 

0000a 

00000 
00000 
00000 
00000 
00000 
00000 
00171 
00203 
00106 
00000 
00017 
10000 
00202 
00210 



cf< 



J 



r". 



JH-r f )+l 



SiTj) 



TEST INDEX 
SEND ALL 

TEST INDEX 
l 7 ~- (A) 

TEST E0R MORE CARD READS 



MS-3 

(fir™)** 15 -** 1 *) 

4 DIGIT U-EXTRACT0R — *• (q) 
SET NO* OF ri-TO BE ZERO 
SET NO. OF ROWS OF B, 



CONVAIR - DIVISION OF GENERA DYNAMICS CORP. 



S*N OlEGO CALIFOR * 



page CN 015-14 

REPORT ZM 491 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40300 


00200 


40301 


00201 


40302 


00202 


40303 


00203 


40304 


00204 


40305 


00205 


4O3O6 


00206 


4O3O7 


OO2O7 


40310 


00210 


40311 


00211 


40312 


00212 


40313 


00213 


40314 


00214 


40315 


00215 


40316 


00216 


40317 


00217 


40320 


00220 


40321 


00221 


40322 


00222 


40323 


00223 


40324 


00224 


40325 


00225 


40326 


00226 


40327 


00227 


40330 


00230 


40331 


00231 


40332 


00232 


40333 


00233 


40334 


00234 


40335 


00235 


40336 


00236 


40337 


00237 



53 00104 00216 

53 00103 00231 

75 10000 00204 

11 00040 30000 

15 00141 00211 

16 00142 00232 
11 00110 20000 
36 00074 00121 

|7i 30000 00212 

11 30000 00677 

15 00140 00217 

16 00143 00225 
11 00106 20000 
36 00074 00122 

[75 30000 00220 

11 30000 00377 

11 00101 20000 

36 00074 00123 

11 00040 20000 
17423 4377 4677 
1440 0123 0223J 

11 20000 30000 

21 00217 00104 

21 00225 00074 

41 00122 00216J 

75 30000 00233, 

11 01177 30000 

21 00232 00100 

21 00211 00104 

41 00121 002101 

56 30000 00237 

45 00000 00240 



SET NO* OF COLUMNS OF A^ 

SET NO* OF ROWS OF C c 

SET PROPER 

7- Us - 

4* - 1 -*• \\ 
SEND-ft^ COLUMN OF 
B c TO ES 

Hi J -*»*(**}) 

sm — *• (a) 



m - 1 — *■ i x 

SENDx ^ ROW OF 






k/^ TO ES 




-WaJ 
( r; + <X-fy — ► ( R ) 

i si- <i-^YES. : 

1 * 


>23 


NO 

Ha, 




■v ; 



(p*k) 



TEST INOEX 
SEND 9s ^ COLUMN OF 
C c TO MD 

TEST INOEX 
MS-3 
240 -*- fPAK) 



10-204 



IRM NO t T 



CONVAIR - DIVISIONS OF GEf ERAL DYNAMICS CORP. 



SAN OIEGO C* OflNlA 



CV-181 
page cn 015-15 

REPORT ZM 491 
MODEL All 
DATE 8-9- r 6 



CONTINUOUS MATRIX MULTIPLIER 



CO 



I 

o 

i-H 

I 

o 
o 



Q-i 



40340 


00240 


11 


00114 


20000 


/° ¥ — (a; 




40341 


00241 


47 


00244 


00246 


iSftr ? 




40342 


00242 


00 


00000 


00000 






40343 


00243 


00 


00000 


00000 






40344 


00244 


75 


30120 


00160 


N0« INTERMEDIATE OUTPUT 


40345 


00245 


n 


40500 


00160 


AND NEW 


f SETUP TO ES 


40346 


00246 


56 


10000 


00247 


YES* MS-1 




40347 


00247 


11 


00113 


20000 


ft «•+• (a; 




40350 


00250 


47 


00251 


00257 


isp^-of 




40351 


00251 


37 


00301 


00302 


N0 # C c ' -> A 




40352 


00252 


37 


00350 


00351 


• PUNCH C c ' 




40353 


00253 


45 


10000 


00255 


MJ-1* IF ON* 


255 — MPAK) 


40354 


00254 


45 


00000 


00264 


264 -+• (PAK) 




40355 


00255 


37 


00340 


00341 


PUNCH C c 




40356 


00256 


45 


00000 


00264 


264 — ► ^PAK) 




40357 


00257 


37 


00340 


00341 


PUNCH C c 




40360 


00260 


45 


10000 


00262 


MJ-1 § IF ONt 


262 — ►• (PAKJ 


40361 


00261 


45 


00000 


00264 


264 -#• (PAK) 




40362 


00262 


37 


00301 


00302 


C c ' -*" A 




40363 


00263 


37 


00350 


00351 


PUNCH C^ 




40364 


00264 


37 


73374 


73374 


ADVANCE ALL CARDS PROCESSED 


40365 


00265 


56 


00000 


40365 


STOP 




40366 


00266 


00 


00000 


00000 






40367 


00267 


00 


00000 


00000 






40370 


00270 


00 


00000 


00000 






40371 


00271 


00 


00000 


00000 






40372 


00272 


00 


00000 


00000 






40373 


00273 


00 


00000 


00000 






40374 


00274 


00 


00000 


00000 






40375 


00275 


00 


00000 


00000 






40376 


00276 


00 


00000 


00000 






40377 


00277 


00 


00000 


00000 







i a nnr 



iuinvmik - UIVISION Vt UtNt AL DYNAMICS CORP. 



SAN OIEGO l M_l> "*N|* 



CV-ltfl 

page CN 015-16 

REPORT ZM 4-91 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40400 


00300 


37 


76000 


76002 


ALARM EXIT 


40401 


00301 


45 


00000 


30000 


EXIT 


40402 


00302 


16 


00143 


00312 


ecn) ^e(r f ) 


40403 


00303 


21 


00312 


00110 


e(r;)^4/ ~> ^ r <n-J 


40404 


00304 


31 


00102 


00000 


* s -+(fi) 


40405 


00305 


34 


00110 


00017 


i£- 4 ,)*2 l5 -+lR) 


40406 


00306 


11 


00146 


10000 


4 DIGIT U-EXTRACT0R -*~ fa ) 


40407 


00307 


53 


20000 


00311 


SET NO. OF ri TO BE ZERO 


40410 


00310 


53 


00105 


00325 


SET NO* OF ROWS OF C c ' 


40411 


00311 


75 


10000 


00313 


SET PROPER 


40412 


00312 


11 


00040 


30000 


rrlv = 


40413 


00313 


11 


00040 


00122 


-*■ I* 


40414 


00314 


15 


00142 


00321 


4, -*"( A) J 


40415 


00315 


16 


00140 


00326 


40416 


00316 


rn 


00110 


20000 


40417 


00317 


36 


OOO74 


00121 


A*~ 1 -+• I, 


40420 


00320 


16 


00143 


00321 


TEST INDEX 


40421 


00321 


rn 


30000 


30000 


40422 


00322 


21 


00321 


00074 


40423 


00323 


35 


00103 


00321 


40424 


00324 


41 


00121 


0032JJ 


40425 


00325 


75 


30000 


00327 


SEND /^COLUMN OF 


40426 


00326 


11 


01177 


30000 


C c ' TO MD 


40427 


00327 


21 


00326 


00102 


*(<l<j)+fi 5 -*-{U<jJ 


40430 


00330 


21 


00122 


00074 


1^1 -~ u 


40431 


00331 


54 


20000 


00017 


(a) - 2 ~* (a) 


40432 


00332 


15 


00142 


00321 




40433 


00333 


35 


00321 


00321 


40434 


00334 


11 


00122 


20000 


40435 


00335 


42 


00106 


00316J 


TEST INDEX 


40436 


00336 


45 


00000 


00301 


TO EXIT 


40437 


00337 


00 


00000 


00000 





10-206 



CONVAIR - DIVISION OF GENEt 4L DYNAMICS CORP. 



b»N OIEGO < *l IF <NlA 



CV-181 
page CN 015-17 

REPORT ZM 491 
MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



1 

o 



o 
o 






40440 


00340 


40441 


00341 


40442 


00342 


40443 


00343 


40444 


00344 


40445 


00345 


40446 


00346 


40447 


00347 


40450 


00350 


40451 


00351 


40452 


00352 


40453 


00353 


40454 


00354 


40455 


00355 


40456 


00356 


40457 


00357 


40460 


00360 


40461 


00361 


40462 


00362 


40463 


00363 


40464 


00364 


40465 


00365 


40466 


00366 


40467 


00367 


40470 


^0370 


40471 


00371 


40472 


00372 


40473 


00373 


40474 


00374 


40475 


00375 


40476 


00376 


40477 





45 00000 30000 
71 00100 00110 
73 00150 20000 

16 00142 00365 
37 00360 00361 

17 00000 00077 
45 00000 00340 
00 00000 00000 
45 00000 30000 
71 00102 00106 
73 00150 20000 

16 00140 00365 
37 00360 00361 

17 00000 00077 
45 00000 00350 
00 00000 00000 
45 00000 30000 
42 00064 00371 
73 00064 00122 
11 20000 00121 
23 00122 00074 

(T456 0773 0000 
21 00365 00151 
41 00122 00365] 
11 00121 ?0000 
16 00365 00375 
54 20000 00017 
11 00147 10000 
53 20000 00375 
1456 0003 0000 
45 00000 00360 
00 00000 00000 



EXIT 

PUNCH C c 

BLANK CARD IN OUTPUT 

TO EXIT 



EXIT 




/yn ** 3 «— *- (aJ 




<Al/6 ~*~(A) 




PUNCH C c ' 




BLANK CARD IN OUTPUT 




TO EXIT 




EXIT 




IS 63 >(k)1. YESt 371 — • 


*(pmO 


NO. (AV63 -** 1^ t REM 


-*<%/ 


(A) — I, 




l* - 1 ~+ lz 





PUNCH 63 CARDS STARTING AT i(ciit) 

TEST INDEX 
\ z -+- (A) 



(0) 



( A) x 2 '*—** (a) 
2 DIGIT U-EXTRACTOR 
SET N0» CARDS TO PUNCH 
PUNCH TARDS 

to exr 



- --. Oz~*l- 



a NVAIR - DIVISION OF GENERAL V "4AMICS CORP. 



SAN OifcGO CAi FO* 



CV-181 

page CN 015-18 
report 2m 491 

MODEL AH 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40500 


00160 


56 


20000 


00161 


MS~2 




40501 


00161 


11 


00113 


20000 


p 3 —+- (a) 




40502 


00162 


47 


00163 


00210 


l$p 3 -*0f YES« 210 — *-(PAi< 


40503 


00163 


45' 


10000 


00167 


N0# MJ-1# IF ON 


167 — ^PAKj 


40504 


00164 


45 


30000 


00173 


MJ-3» IF ON 173 


~*~(PAK) 


4O5O5 


00165 


45 


20000 


00177 


MJ-2* IF ON 177 


-*• IPaK) 


40506 


00166 


45 


00000 


00200 


200 -** (PAK) 




40507 


00167 


45 


20000 


00177 


MJ-2» IF ON 177 


— *-(pakJ 


40510 


00170 


37 


00301 


00302 


C c ' — ** A 




40511 


00171 


37 


00350 


00351 


PUNCH C* c 




40512 


00172 


45 


00000 


00200 


200 — *• (PAK) 




40513 


00173 


37 


00301 


00302 


C c ' •"*■" A 




40514 


00174 


37 


00350 


00351 


PUNCH C c ' 




40515 


00175 


45 


20000 


00177 


MJ-2t IF ON 177 


-WpakJ 


40516 


00176 


45 


00000 


00200 


200 -*■> (PAK) 




40517 


00177 


37 


00340 


00341 


PUNCH C c 




40520 


00200 


71 


00103 


00110 


$ t >t4>x2 ,S ~+*( A) 




40521 


00201 


11 


00146 


10000 


4 DIGIT U-EXTRACTOR -*■ (Q ) 


40522 


00202 


53 


20000 


00203 


SET NO. OF ELEMENTS OF C^ 


40523 


00203 


75 


30000 


00205 


SEND 




40524 


^0204 


11 


60210 


40630 


C c < -"*- A 




40525 


00205 


11 


00106 


00107 


/rA -*- sn* 




40526 


00206 


11 


00110 


00106 


^ — *- W- 




40527 


00207 


45 


00000 


00 22 5 


225 — MPAKJ 




40530 


00210 


37 


00301 


00302 


C^ ""•*** A 




40531 


00211 


45 


10000 


00215 


MJ-li IF ON 215 


*-*>(pakj 


40532 


00212 


45 


20000 


00220 


MJ~2* IF ON 220 


~Wp A kj 


40533 


00213 


45 


30000 


00223 


MJ-3# IF ON 223 


-*-(pak; 


40534 


00214 


45 


00000 


00224 


224 ~#* (PAK) 




40535 


00215 


45 


20000 


00223 


MJ~2# IF ON 223 


~*» (PAKy) 


40536 


00216 


37 


00340 


00341 


PUNCH C c 




40537 


00217 


45 


00000 


00224 


224 — MPak) 





10-208 



'ONM NO E T I 



ONVAIR - DIVISION OF GENERAL I /NAMICS CORP. 

SAN OltGO CAI. If-ORNlA 



CV-181 

PAGE CN 015-19 

REPORT ZM 491 

MODEL All 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



I 

o 

r— I 
I 

O 

o 
o 

X 



40540 


00220 


37 


00340 


00341 


40541 


00221 


45 


3,0000 


00223 


40542 


00222 


45 


00000 


00224 


40543 


00223 


37 


00350 


00351 


40544 


00224 


11 


00110 


00107 


40545 


00225 


56 


30000 


00226 


40546 


00226 


1457 1010 0110 


40547 


00227 


45 


00000 


00230 


40550 


00230 


11 


00041 


00121 


40551 


00231 


15 


00144 


00234 


40552 


00232 


16 


00144 


00241 


40553 


00233 


16 


00145 


00243 


40554 


00234 


Hi 


30000 


20000 


40555 


00235 


73 


00150 


10000 


40556 


00236 


47 


00237 


00240 


40557 


00237 


21 


10000 


00074 


40560 


00240 


71 


10000 


00150 


40561 


00241 


11 


20000 


30000 


40562 


00242 


54 


20000 


^0017 


40563 


00243 


11 


20000 


30000 


40564 


00244 


21 


00234 


00073 


40565 


00245 


21 


00241 


00074 


40566 


00246 


21 


00243 


00074 


40567 


00247 


41 


00121 


00234J 


40570 


00250 


71 


00101 


00110 


40571 


00251 


42 


00152 


00253 


40572 


00252 


37 


76000 


76001 


40573 


00253 


71 


00100 


00110 


40574 


00254 


42 


00152 


00256 


40575 


00255 


37 


76000 


76001 


40576 


00256 


71 


00102 


00106 


40577 


00257 


42 


00152 


00261 



Oak) 



£(<**, w>m) 



PUNCH C c 
MJ-3» IF ON 223 
224 -»► (PAK) 
PUNCH C^ 
4s -*► n\ 
MS-3 

READ NEW PARAMETER AND FLAGS 
230 — *■ (PAK) 
SET INDEX 

stti, <p, t OR 4/ — ** (A ) 

(A^6 -"*• (0) * REM -*■ (a) 

IS REM ~ of 

NO. (Q)+l — **(Q) 

yes- # (q)*6 -** (a; 

(A) * 2 15 — *• (A) 

(r) -► %.*2 iS 

< j 

TEST INDEX 

IS 3961 y \ *4, ? 
NO* ALARM EXIT 
YES. #,*<f-*fAj 
IS 3961 > -ft, * & f 
NO* ALARM EXIT 

yes. w* &—+*/*) 

IS 3961 > ft* A ? 
i • 



i n OAO 



IUNVHIK - DIVISION Uh Otr cKAL DYNAMICS CORP. 



SAN OlfcGO C* OMNIA 



page CN 015-20 

REPORT Z M 491 
MODEL AH 

DATE 8-9-56 



CONTINUOUS MATRIX MULTIPLIER 



40600 


00260 


37 


76000 


76001 


N0» ALARM EXIT. 


40601 


00261 


11 


oono 


20000 


YES, 4/—*- (A) 


40602 


00262 


42 


00153 


00270 


IS 193 **/ YES* 270 


40603 


00263 


37 


76000 


76001 


NO* ALARM EXIT 


40604 


00264 


00 


00000 


00000 




40605 


00265 


00 


00000 


00000 




40606 


00266 


00 


00000 


00000 




40607 


00267 


00 


00000 


00000 




40610 


00270 


75 


30120 


00255 


NEW MATRIX CARD 


40611 


00271 


11 


40135 


00255 


READ TO ES 


40612 


00272 


00 


00000 


00000 




40613 


00273 


00 


00000 


00000 




40614 


00274 


00 


00000 


00000 




40615 


00275 


00 


00000 


00000 




40616 


00276 


00 


00000 


00000 




40617 


00277 


00 


00000 


00000 




40620 




37 


70563 


70567 


BL0TT0S 


40621 




00 


00100 


00377 


ES AND 


40622 




00 


40000 


40637 


MD« 


40623 




56 


00000 


40623 


STOP 


40624 




00 


00000 


00000 




40625 




00 


00000 


00000 




40626 




00 


00000 


00000 




40627 




00 


00000 


00000 





(pak) 



10-210 



ANALYSIS 

PREPARED BY V, J, Stonor 

checked by J, p. Wilkinson 

REVISED BY 



C O N V A I R 



San DIEGO 



CV-182 
page CN 016- 1 

REPORT NO. ZM 4>91 
MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MJLTIPLBR 
USING SINGLE OR MJLTI-PRECISION ARITHMETIC 



This routine multiplies two matrices, take this product 
or its transpose times a third matrix, the resulting product or 
its transpose times a fourth, etc. All input and output data is 
by means of cards with five floating decimal numbers per card 
(see IC-004 for card format). The elements of any one of the 
matrices may be punched on cards with the elements of a row or a 
column in consecutive order with or without each row or column 
starting at the beginning of a new card.* The input assumes all 
matrices are punched on the cards by columns in packed form (i.e., 
no spaces are left on the cards between the last element of one 
column and the first element of the next). However, the routine 
will handle matrices punohed by rows and/or in unpacked form. 
Flags punched. as numbers • on cards are used to indicate the form 
of the matrices on the cards. Flags are also used to indicate 
the use of single or multi-precision arithmetic, the use of the 
transpose of any of the products, and the continuation of the 
multiplication. Three parameters are necessary to furnish the 
routine with the size of the matrices. "Hie flags are denoted 
by the symbols P to P& and the parameters by m, n, and s. 

* The stop read indicator (a 12-punch in column 1) must be on the 
last card for each matrix. 



10-211 



CV-182 



ANALYSIS 

PREPARED BY t^ J # Stoner 

checked by j. p. Uilkinson 

REVISED BY 



C O N V A I R 

A DIVISION Or «CMC*AL DYNAMIC* CORPONATION 
SAN DIEOO 



PAGE CH 016-2 

REPORT NO. ZM 491 

MODEL All 

DATE 9-10-56 



The 


flags and parameters are punched as the mantissas on the 

* 


parameter cards and are read Into the memory as fixed point integers 


(see I C- 


Oil), Two parameters, m and n, and three flags, P Q , P^, 


and p£, an 


t on the first of two parameter cards while s and P to 


r 
*£ are on the second card. The parameters and flags are defined 


as follows 


and appear on the cards in this order t 


f> JR,ST QAHg 




■ 


number of rows of the first matrix 


n 


number of columns of the first matrix (also, number of 




rows of the second) 


P 



=»0 for single-precision arithmetic 




/0 for multi-precision arithmetic 


p i 


=0 for first matrix punched packed 




/0 for first matrix punched unpacked 


*? 


*0 f or first matrix punched by columns 




/0 for first matrix punched by rows 


SEfMl>,mi 


) 


B 


number of columns of the second matrix 


h 


=»0 for second matrix punched packed 




/0 for second matrix punched unpacked 


\ 


*0 for second matrix pinched by columns 




/0 for second matrix punched by rows 


P 5 


»0 for product to be used 




/0 for transpose of product to be used 


P 6 


=»0 for no further multiplication 




/0 for continued multiplication 




10-212 



form eaiz-A 



ANALYSIS 

PREPARED BY V,'. J. Stpner 

checked by J. f , v'ilVir.son 

REVISED BY 



C O N V A I R 

AOIVMION Of 4EHEKAL DTNAMICS COAroHATIOH 
SAN DIEGO 



CV-182 

PAGE CN 016-3 
REPORT NO. ZM 4-91 
MODEL All 

date 9-10-56 



Examination of this card format reveals that before any 
multiplication both parameter cards must be used while only the 
second card is necessary before each matrix in a continued product. 

To illustrate the use of the parameters and flags, suppose 
the product, ABC, of three matrices is wanted using single-precision 
arithmetic where the matrices have the following properties t 

As m by n, punched packed by rows 

Bt n by s, punched unpacked by columns 

Ct s by t, punched unpacked by rows 

The multiplication proceeds from the left so AB is the first 
product formed then this product multiplies C, The first input 
cards contains as mantissas m,n,0,0, and non-zero. The second input 
card contains as mantissas s, non-zero, 0, 0, and non-zero. The 
cards for A and B are the next input cards then one parameter card 
followed by the cards for C. The input card before G contains as 
mantissas t, non-zero, non-zero r and 0. No blank cards appear 
in the input, Ihe last card of each matrix contains a 12-punch 
in column one to indicate the end of that matrix. 

Output of the intermediate products and the final product is 
controlled by the MJ and MS switches. The intermedia t© output is 
preceded by the only HS-2 and followed by the only M3-3. Setting 
(PAK) * 00176 at MB-3 and starting will give additional intermediate 
output if the desired MJ switches are set. The final output is 
preceded by the only MS-1 and followed by MS-0. Starting at MS-0 
will give additional final output if the desired MJ switches are set. 
If no MJ switches are set when the final product is formed, the 
typewriter prints "SET MJ-S FOR OUTPUT" before stopping at MS-0. 

10-213 



ANALYSIS 

PREPARED BY r. J. Stoner 
CHECKED BY J. p. Wilkinson 
REVISED BY 



C O N V A I R 

A DIVISION Or CtNEItAL OVHAMICf COAfOHATION 
SAN DIEGO 



CV-182 

pageCK 016-4- 
report no. zm 491 

MODEL All 

date 9-10*56 



Setting the MJ's and starting will give the final output. All 


output is by columns with the column and row indices of the first 


element on each card indicated as the card number (see 10-004). 


The form of the output as controlled by the MJ switches is as follows i 


W J'a 


Output fox,JP^,Q Output for ?$& 


none 


none none 


1 


product packed transpose packed 


?. 


product unpacked transpose unpacked 


1 and 3 


transposo packed product packed 


2 and 3 


transpose unpacked product unpacked 


1 and 2 


same as 1 same as 1 


1, 2 f and 3 


some as 1 and 3 s«»«e a3 1 and 3 


3 


none none 


This routine, the 


working storage, the matrix storage, 


and the service routines 


use the entire E3 and most of MD storage. 


The storage is allotted 


as followst 


00000 - 00070 


temporaries 


00071 - 00147 


constants 


00150 - 00457 


program 


00^60 - 01777 


working storage 


40000 - 41377 


program 


O400 - 41477 


available 


41500 - 54637 


first matrix 


54640 - 67777 


second matrix and product 


70000 - 77777 


sorvice routines, IC - 004, end IC - 011. 


Tests in the routine will give an alarm exit If the size 


of a matrix la too large 


for the storage space provided. 'Ihe following 




10-214 



ANALYSIS 

prepared by V. J. 3 toner 

CHECKED BY J. I. Vt'ilkinSOH 
REVISED BY 



C O N V A I R 

* DIVISION OF GENERAL DYNAMICS CORPORATION 
SAN DIEGO 



CV-182 
page CN 016-5 

REPORT NO. ZH 491 
MODEL All 

date 9-10-56 



restrictions are imposed on the siae of the ma trices* 

1. No dimension greater than decimal 120. 

2. The number of elements in ar.y matrix not greater than 
2860 (this includes the aeros in an unpacked form.) 

Thus, the largest square matrix that can be handled is a 5 3 by 53 
packed or a 52 by 52 unpacked since an unpacked form would be handled 
on cards as a 52 by 55 containing 2860 elements including the zeros. 
(Notes even though the matrix is unpacked and the storage limitations 
require consideration of this, the input dimensions on the parameter 
cards are the packed dimensions.) 

A check sum, equal to 012345670123, is printed at the beginning 
of the program after reading the paper tape. This represents the 
sure of this routine, IC-004, and IC-011, all of which &r® loaded 
by paper tape. A programmed Blotto is included in the code. Setting 
(PAK) -a, 370 and starting gives a Blotto of 0000O-00457 and 40000- 
41377 which includes the temporaries, constants, and program in S.S. 
and entire program on MD» 

The program starts with (FAK) =40,000. Several continuous 
multiplications may be done by resetting (PAK) =40,000 at KS-0. 
However, a blank card must be placed between the cards for the separate 
continuous multiplications unless the reading hopper is loaded when 
PAK is reset. The check sura obtained when PAK is reset is not the 
same a3 that obtained after reading the paper tape. 



10-215 



NO {. 1 IV 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN OitGO CALIFORNIA 



CV-182 

PAGE CN 016-6 
report ZM ^91 

MODEL yi]jL 

date 9.10-56 



CONTINUOUS MATRIX MULTIPLIER 



40000 




45 


00000 


40001 






40001 




31 


40000 


00000 


CHECK 




40002 




75 


21377 


41374 


SUM 




40003 




32 


40001 


00000 


PROGRAM. 




40004 




11 


20000 


10000 






40005 




17 


00000 


72433 


PRIME BULL. 




40006 




75 


30370 


00150 


PROGRAM 




40007 




11 


40010 


00070 


TO ES. 




40010 


00070 


00 


00000 


00000 






40011 


00071 


00 


00000 


00110 


DEC. 72. 




40012 


00072 


40 


00000 


00000 


SIGN MASK. 




40013 


00073 


00 


00000 


00003 






40014 


00074 


00 


00000 


00001 






40015 


00075 


77 


77777 


70000 


MANTISSA AND EXPONENT 


MASK. 


40016 


00076 


77 


77777 


77777 


NEGATIVE ZERO. 




40017 


00077 


00 


00000 


00152 


DEC. 106. 




40020 


00100 


00 


00000 


00045 


DEC* 37* 




40021 


00101 


00 


00000 


00042 


DEC. 34. 




40022 


00102 


00 


00000 


04000 


DEC. 2048. 




40023 


00103 


77 


77777 


74000 


DEC. -2047. 




40024 


00104 


00 


00000 


00072 


DEC. 58. 




40025 


00105 


00 


00000 


00021 


DEC* 17* 




40026 


00106 


00 


07777 


00000 


4-DIGIT U-EXTRACT0R. 




40027 


00107 


00 


41500 


41500 


START OF A. 




40030 


00110 


00 


54640 


54640 


START OF B. 




40031 


00111 


00 


00460 


00460 


START OF 




40032 


00112 


00 


01040 


01040 


ES WORKING 




40033 


00113 


00 


01420 


01420 


STORAGES. 




40034 


00114 


00 


00002 


00000 






40035 


00115 


00 


00000 


77777 


V-eXTRACTOR. 




40036 


00116 


00 


00000 


00002 






40037 


00117 


47 


45242 


00145 


FLEX CODE 





10-216 



iHM NO i. T t 



CONVAIB - DIVIiiO.J Of GCII^Al DYNAMICS CORP. 

SAN DISCO CALIfORNIA 



CV-182 
page CN 016-7 

REPORT Z M ^91 
MODEL ^11 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



CO 



I 

o 

t 

o 
o 

o 



X 



40040 


00120 


07 


32562 


40404 


FOR — 


40041 


00121 


03 


12040 


33426 


SET MJ-S 


40042 


00122 


15 


34010 


45701 


FOR OUTPUT. 


40043 


00123 


00 


00000 


00013 


DEC. 11* 


40044 


00124 


00 


00000 


00007 




40045 


00125 


00 


00000 


00005 




40046 


00126 


00 


00000 


00004 




40047 


00127 


61 


00000 


00130 


ZERO PRINT ORDER. 


40050 


00130 


00 


00000 


00037 


FLEX 


40051 


00131 


00 


00000 


00052 




40052 


00132 


00 


00000 


00074 


CODES 


40053 


00133 


00 


00000 


00070 




40054 


00134 


00 


00000 


00064 


FOR 


40055 


00135 


00 


00000 


00062 




40056 


00136 


00 


00000 


00066 


0-7. 


40057 


00137 


00 


00000 


00072 




40060 


00140 


00 


00000 


00171 


DEC* 121. 


40061 


00141 


00 


00000 


05455 


DEC. 2861. 


40062 


00142 


00 


00300 


00300 


START OF ES STORAGE 


40063 


00143 


00 


00000 


00442 


DEC. 290. 


40064 


00144 


00 


00000 


00043 


DEC. 35. 


40065 


00145 


00 


00000 


00044 


DEC. 36. 


40066 


00146 


00 


00000 


00235 


DEC. 157. 


40067 


00147 


00 


00000 


ooooo 




40070 


00150 


11 


00123 


00001 


PRINT OF 


40071 


00151 


61 


ooooo 


00100 




40072 


00152 


55 


10000 


00003 


CHECK 


40073 


00153 


51 


00124 


20000 




40074 


00154 


35 


00127 


00155 


SUM. 


40075 


00155 


30 


ooooo 


ooooo 




40076 


00156 


41 


00001 


00152 




40077 


00157 


37 


72400 


72401 


READ 



NO £ T I 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN OIF.GO CAUIFORNM 



CV-182 
page CN 016-8 

REPORT ZM 491 
MODEL All 

DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40100 


00160 


04 


00021 


00012 


PARAMETER CARC 


>S 


40101 


00161 


11 


00023 


00060 


STORE 




40102 


00162 


11 


00026 


00023 


PARAMETERS 




40103 


00163 


11 


00032 


00026 


CONSECUTIVELY. 




40104 


00164 


11 


00021 


20000 






40105 


00165 


42 


00140 


00167 


TEST 




40106 


00166 


37 


76000 


76001 






40107 


00167 


11 


00022 


20000 


SIZE 




40110 


00170 


42 


00140 


00172 






40111 


00171 


37 


76000 


76001 


OF 




40112 


00172 


11 


00023 


20000 






40113 


00173 


42 


00140 


00175 


PARAMETERS* 




40114 


00174 


37 


76000 


76001 






40115 


00175 


75 


30003 


00177 


DOUBLE 




40116 


00176 


11 


00021 


00032 






40117 


00177 


75 


30003 


00201 


PARAMETERS* 




40120 


00200 


21 


00032 


00021 






40121 


00201 


75 


30003 


00203 


SCALE 




40122 


00202 


11 


00021 


00035 






40123 


00203 


75 


20003 


00205 


PARAMETERS* 




40124 


00204 


55 


00035 


00020 






40125 


00205 


75 


30003 


00207 


DECREASE 




40126 


00206 


11 


00021 


00041 






40127 


00207 


75 


20003 


00211 


PARAMETERS BY 


1 


40130 


00210 


23 


00041 


00074 






40131 


00211 


75 


30003 


00213 


SCALE 




40132 


00212 


11 


00021 


00052 






40133 


00213 


75 


20003 


00215 


PARAMETERS* 




40134 


00214 


55 


00052 


00017 






40135 


00215 


75 


30003 


00217 


FIND 




40136 


00216 


11 


00021 


00044 






40137 


00217 


11 


00021 


20000 


FIRST 





10-218 



1HM NO I. T 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEC>0 CAt IFORNIt 



CV-182 

PAGE CN 016-9 

REPORT ZM ^ 91 
MODEL All 

date 9..10-.56 



CONTINUOUS MATRIX MULTIPLIER 



CM 
CO 



i 

o 

I 

o 
o 
a- 



x 
a. 



40140 


00220 


73 


00125 


10000 




40141 


00221 


47 


00222 


00224 


MUTIPLE 


40142 


00222 


71 


10000 


00125 




40143 


00223 


35 


00125 


00044 


OF 5 


40144 


00224 


11 


00022 


20000 




40145 


00225 


73 


00125 


10000 


GREATER 


40146 


00226 


47 


00227 


00231 




40147 


00227 


71 


10000 


00125 


THEN 


40150 


00230 


35 


00125 


00045 




40151 


00231 


11 


00023 


20000 


OR EQUAL 


40152 


00232 


73 


00125 


10000 




40153 


00233 


47 


00234 


00236 


TO 


40154 


00234 


71 


10000 


00125 




40155 


00235 


35 


00125 


00046 


PARAMETERS 


40156 


00236 


75 


30003 


00240 




40157 


00237 


11 


00044 


00047 


DOUBLE 


40160 


00240 


75 


30003 


00242 




40161 


00241 


21 


00047 


00044 


MULTIPLES* 


40162 


00242 


75 


30003 


00244 




40163 


00243 


11 


00044 


00055 


SCALE 


40164 


00244 


75 


20003 


00246 




40165 


00245 


55 


00055 


00017 


MULTIPLES* 


40166 


00246 


71 


00021 


00045 




40167 


00247 


42 


00141 


00251 




40170 


00250 


37 


76000 


76001 


TEST 


40171 


00251 


71 


00045 


00023 




40172 


00252 


42 


00141 


00254 


SIZES 


40173 


00253 


37 


76000 


76001 




40174 


00254 


71 


00044 


00023 


OF 


40175 


00255 


42 


00141 


00257 




40176 


00256 


37 


76000 


76001 


MATRICES* 


40177 


00257 


71 


00046 


00021 





10-21*) 



MM NO t 1 I 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIFORNIA 



CV-182 

page CN 016-10 

REPORT ZM 491 
MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40200 


00260 


42 


00141 


00262 




40201 


00261 


37 


76000 


76001 




40202 


00262 


11 


00070 


20000 


TEST FOR 


40203 


00263 


47 


00305 


00264 


READ OF A. 


40204 


00264 


11 


00025 


20000 


TEST FOR 


40205 


00265 


47 


00266 


00276 


CHANGE IN FORM OF A 


40206 


00266 


37 


72400 


72401 


READ A 


40207 


00267 


00 


41500 


05544 


ONTO MD« 


40210 


00270 


11 


00024 


20000 


TEST FOR 


40211 


00271 


47 


00272 


.00305 


UNPACKING A. 


40212 


00272 


11 


00041 


00001 




40213 


00273 


11 


00107 


00002 




40214 


00274 


37 


00351 


00352 


PACK A* 


40215 


00275 


45 


00000 


00305 




40216 


00276 


11 


00021 


00004 


CHANGE 


40217 


00277 


11 


00035 


00002 




40220 


00300 


11 


00107 


00003 


A AND 


40221 


00301 


11 


00024 


20000 




40222 


00302 


47 


00303 


00304 


STORE 


40223 


00303 


11 


00044 


00004 




40224 


00304 


37 


40400 


40402 


ON MD« 


40225 


00305 


11 


00030 


20000 


TEST FOR 


40226 


00306 


47 


00317 


00307 


CHANGE IN FORM OF B 


40227 


00307 


37 


72400 


72401 


READ B 


40230 


00310 


00 


54640 


05544 


ONTO MD» 


40231 


00311 


11 


00027 


20000 


TEST FOR 


40232 


00312 


47 


00313 


00326 


UNPACKING B. 


40233 


00313 


11 


00043 


00001 




40234 


00314 


11 


00110 


00002 




40235 


00315 


37 


00351 


00352 


PACK B« 


40236 


00316 


45 


00000 


00326 




40237 


00317 


11 


00023 


00004 


CHANGE 



10-220 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIFORNIA 



CV-182 

page CN 016-11 
REPORT ZM 491 

MODEL '//JQI 
DATE9-10-$6 



CONTINUOUS MATRIX MULTIPLIER 



40240 


00320 


11 


00037 


00002 


B AND 


40241 


00321 


11 


00110 


00003 




40242 


00322 


11 


00027 


20000 


STORE 


40243 


00323 


47 


00324 


00325 




40244 


00324 


11 


00046 


00004 


ON MD. 


40245 


00325 


37 


40400 


40402 




40246 


00326 


45 


00000 


00327 




40247 


00327 


11 


00036 


00040 


TEST FOR 


40250 


00330 


11 


00022 


20000 




40251 


00331 


42 


00021 


00333 


SPACING OF B. 


40252 


00332 


45 


00000 


00341 




40253 


00333 


11 


00110 


00001 


SPACE 


40254 


00334 


11 


00033 


00002 




40255 


00335 


11 


00032 


00003 


COLUMNS 


40256 


00336 


11 


00023 


00004 




40257 


00337 


37 


00371 


00372 


OF B« 


40260 


00340 


11 


00035 


00040 




40261 


00341 


75 


30060 


00343 


MULTIPLIER 


40262 


00342 


11 


40540 


00150 


TO ES. 


40263 


00343 


11 


00060 


20000 


TEST FOR 


40264 


00344 


47 


00347 


00345 


ARITHMETIC. 


40265 


00345 


75 


30100 


00150 


SINGLE PRECISION 


40266 


00346 


11 


40620 


00230 


TO £S. 


40267 


00347 


75 


30150 


00150 


MULTI-PRECISION 


40270 


00350 


11 


40720 


00230 


TO ES. 


40271 


00351 


45 


00000 


30000 


EXIT-PACKING SUBROUTINE 


40272 


00352 


11 


00106 


10000 




40273 


00353 


53 


00036 


00363 


SET 


40274 


00354 


53 


00036 


00365 




40275 


00355 


23 


00001 


00074 


INITIAL 


40276 


00356 


15 


00002 


00364 




40277 


00357 


16 


00002 


00366 


CONDITIONS. 



1A_0)1 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN filTGO CALIFORNIA 



CV-182 

page CN 016-12 

REPORT 2M 491 
MODEL All 
DATE 9-6-56 



CONTINUOUS MATRIX MULTIPLIER 



40300 


00360 


31 


00056 


00001 


ADVANCE 


40301 


00361 


35 


00364 


00364 




ADDRESSES. 


40302 


00362 


21 


00366 


00033 






40303 


00363 


75 


30000 


00365 


UNPACKED 


40304 


00364 


11 


30000 


01420 




ROW TO ES. 


40305 


00365 


75 


30000 


00367 


PACKED 


40306 


00366 


11 


01420 


30000 




ROW TO MD. 


40307 


00367 


41 


00001 


00360 






40310 


00370 


45 


00000 


00351 






40311 


00371 


45 


obooo 


30000 


EXIT-UNPACKING 


40312 


00372 


11 


00002 


20000 






40313 


00373 


43 


00003 


00375 


TEST 


40314 


00374 


45 


00000 


00403 






40315 


00375 


13 


00076 


00005 




FOR 


40316 


00376 


13 


00076 


00006 






40317 


00377 


15 


00001 


00005 




NEEDED 


40320 


00400 


16 


00001 


00006 






40321 


00401 


54 


00006 


00017 




UNPACKING. 


40322 


00402 


43 


00005 


00371 






40323 


00403 


11 


00003 


00005 






40324 


00404 


55 


00005 


00017 


SET 




40325 


00405 


55 


00002 


00017 






40326 


00406 


21 


00004 


00074 




LOCATIONS 


40327 


00407 


15 


00001 


00431 






40330 


00410 


16 


00001 


00433 




OF LAST 


40331 


00411 


71 


00002 


00004 






40332 


00412 


35 


00431 


00431 




COLUMN 


40333 


00413 


71 


00003 


00004 






40334 


00414 


35 


00433 


00433 




OR ROW. 


40335 


00415 


11 


00106 


10000 






40336 


00416 


53 


00002 


00430 


SET 




40337 


00417 


53 


00005 


00432 







10-222 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN OieGO CALIFORNIA 



CV-182 

page CN 016-13 

report ZM 491 

MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40340 


00420 


23 


00005 


00002 


NUMBER 


40341 


00421 


53 


20000 


00426 




40342 


00422 


11 


00002 


20000 


OF ELEMENTS IN 


40343 


00423 


52 


00113 


20000 




40344 


00424 


55 


20000 


00025 


ROW OR COLUMN* 


40345 


00425 


16 


20000 


00427 




40346 


00426 


75 


10000 


00430 


SET EXTRA 


40347 


00427 


13 


00076 


30000 


ELEMENTS TO ZERO. 


40350 


00430 


75 


30000 


00432 


PACKED ROW OR 


40351 


00431 


11 


30000 


01420 


COLUMN TO ES« 


40352 


00432 


75 


30000 


00434 


UNPACKED ROW OR 


40353 


00433 


11 


01420 


30000 


COLUMN TO MD. 


40354 


00434 


23 


00431 


00002 


RETARD 


40355 


00435 


23 


00433 


00003 


ADDRESSES* 


40356 


00436 


41 


00004 


00430 




40357 


00437 


45 


00000 


00371 




40360 


00440 


00 


00000 


00000 




40361 


00441 


00 


00000 


00000 




40362 


00442 


00 


00000 


00000 




40363 


00443 


00 


00000 


00000 




40364 


00444 


00 


00000 


00000 




40365 


00445 


00 


00000 


00000 




40366 


00446 


00 


00000 


00000 




40367 


00447 


00 


00000 


00000 




40370 


00450 


00 


00000 


00000 




40371 


00451 


00 


00000 


00000 




40372 


00452 


00 


00000 


00000 




40373 


00453 


00 


00000 


00000 




40374 


00454 


00 


00000 


00000 




40375 


00455 


00 


00000 


00000 




40376 


00456 


00 


00000 


00000 




40377 


00457 


00 


00000 


00000 





1 0-993 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN (JltGO i»l.iK)»Nl» 



PAGE cN 016-H 

REPORT ZM ^91 
MODEL All 

date 9-IO-56 



CONTINUOUS MATRIX MULTIPLIER 



40400 


00150 


75 


30160 


30000 


EXIT-CHANGE FORM SUBROUTINE. 


40401 


00151 


11 


40220 


00300 


RELOAD ES» 


40402 


00152 


75 


30140 


00154 


LOAD 


40403 


0015 3 


11 


40400 


00150 


ES. 


40404 


00154 


I 3 


00076 


00011 




40405 


00155 


11 


00143 


20000 


FIND 


40406 


00156 


73 


00004 


00005 




40407 


00157 


71 


00004 


00005 


NUMBER 


40410 


00160 


11 


20000 


00020 




40411 


00161 


73 


00125 


00016 


OF COLUMNS 


40412 


00162 


11 


20000 


00015 




40413 


00163 


11 


00132 


00017 


OR ROWS 


40414 


00164 


55 


00004 


00020 




40415 


00165 


11 


00022 


20000 


PER READ. 


40416 


00166 


73 


00005 


10000 




40417 


00167 


11 


20000 


00006 




40420 


00170 


47 


00172 


00171 




40421 


00171 


11 


00005 


00006 


PRESET 


40422 


00172 


31 


00005 


00020 




40423 


00173 


11 


00106 


10000 


INDICES 


40424 


00174 


53 


20000 


00233 




40425 


00175 


11 


00115 


10000 


AND 


40426 


00176 


53 


00020 


00205 




40427 


00177 


13 


00076 


00001 


TRANSFERS. 


40430 


00200 


11 


00015 


20000 


TEST FOR 


40431 


00201 


47 


00202 


00204 


CARD READ TYPE. 


40432 


00202 


37 


00242 


00243 


READ 


40433 


00203 


45 


00000 


00206 


PRESET 


40434 


00204 


37 


72400 


72401 


NUMBER 


40435 


00205 


00 


00300 


00000 


OF CARDS. 


40436 


00206 


16 


00003 


00234 


PRESET 


40437 


00207 


21 


00234 


00011 


ADDRESSES 



10-224 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 

SAN OlEGO CALIFORNIA 



CV-182 
page CN 016-15 

REPORT ZM A91 
MODEL All 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40440 


00210 


31 


00005 


00001 




AND 


40441 


00211 


35 


00011 


00011 




INDICES* 


40442 


00212 


11 


00001 


20000 


TEST FOR 


40443 


00213 


47 


00214 


00220 




END OF MATRIX. 


40444 


00214 


11 


00106 


10000 


SET 


FOR 


40445 


00215 


31 


00006 


00020 




LAST 


40446 


00216 


53 


20000 


00233 




CARD 


40447 


00217 


11 


00006 


00005 




READ. 


40450 


00220 


13 


00076 


00010 


SET 


COUNTER. 


40451 


00221 


15 


00142 


00227 


PRESET 


40452 


00222 


21 


00227 


00010 




ADDRESSES 


40453 


00223 


16 


00113 


00227 




AND 


40454 


00224 


11 


00005 


20000 




INDICES. 


40455 


00225 


36 


00074 


00007 






40456 


00226 


75 


30002 


00230 


PUT 


ROW OR 


40457 


00227 


11 


30000 


30000 




COLUMN 


40460 


00230 


21 


00227 


00116 




ELEMENTS 


40461 


00231 


35 


00004 


00227 




IN ORDER. 


40462 


00232 


41 


00007 


00226 






40463 


00233 


75 


30000 


00235 


STORE 


40464 


00234 


11 


01420 


30000 




ROW OR 


40465 


00235 


21 


00234 


00033 




COLUMN 


40466 


00236 


21 


00010 


00114 




ON MD. 


40467 


00237 


42 


00002 


00221 






40470 


00240 


11 


00001 


20000 


TEST FOR 


40471 


00241 


47 


00150 


00200 




LAST CARD READ 


40472 


00242 


45 


00000 


30000 






40473 


00243 


11 


00017 


20000 


TEST FOR 


40474 


00244 


73 


00125 


10000 




NEED OF 


40475 


00245 


15 


00142 


00273 




ENTIRE 


40476 


00246 


47 


00247 


00267 




LAST CARD. 


40477 


00247 


11 


20000 


00014 







CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



b»N Olff.O CALIFORNIA 



CV-182 
page CN 016-16 

REPORT ZM 491 
MODEL All 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40500 


00250 


54 


20000 


00020 


PRESET 


40501 


00251 


11 


00106 


10000 




40502 


00252 


53 


20000 


00260 


ADDRESSES* 


40503 


00253 


15 


00142 


00261 




40504 


00254 


31 


00020 


00020 


TRANSFERSt 


40505 


00255 


35 


00261 


00261 




40506 


00256 


31 


00014 


00020 


AND INDICES 


40507 


00257 


35 


00273 


00273 




40510 


00260 


75 


30000 


00262 


PLACE ELEMENTS 


40511 


00261 


11 


30000 


00300 


FROM PREVIOUS READ* 


40512 


00262 


11 


00014 


20000 


TEST FOR NUMBER 


40513 


00263 


42 


00015 


00267 


OF CARDS TO READ* 


40514 


00264 


71 


00125 


00016 


PRESET NUMBER 


40515 


00265 


16 


20000 


00273 


OF NUMBERS. 


40516 


00266 


45 


00000 


00272 




40517 


00267 


71 


00125 


00016 


PRESET NUMBER 


40520 


00270 


35 


00125 


20000 


OF NUMBERS. 


40521 


00271 


16 


20000 


00273 




40522 


00272 


37 


72400 


72401 


READ 


40523 


00273 


00 


30000 


00000 


CARDS. 


40524 


00274 


23 


00017 


00015 


PREPARE FOR NEW READ. 


40525 


00275 


45 


00000 


00242 




40526 


00276 


00 


00000 


00000 




40527 


00277 


00 


00000 


00000 




40530 


00300 


00 


00000 


00000 




40531 


00301 


00 


00000 


00000 




40532 


00302 


00 


00000 


00000 




40533 


00303 


00 


00000 


00000' 




40534 


00304 


00 


00000 


00000 




40535 


00305 


00 


00000 


00000 




40536 


00306 


00 


00000 


00000 




40537 


00307 


00 


00000 


00000 





10-226 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN Oifc'GO C*LlfOHNIA 



CV-182 

page CN 016-17 

REPORT^ 491 
MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40540 


00150 


45 


00000 


00151 




40541 


00151 


11 


00106 


10000 


PRESET 


40542 


00152 


53 


00035 


00211 


REPEATS* 


40543 


00153 


53 


00036 


00160 


ADDRESSES* 


40544 


00154 


53 


00036 


00165 


AND 


40545 


00155 


15 


00110 


00161 


INDICES. 


40546 


00156 


16 


00110 


00212 




40547 


00157 


11 


00043 


00061 




40550 


00160 


75 


30000 


00162 


ONE COLUMN 


40551 


00161 


11 


30000 


01040 


OF B TO ES. 


40552 


00162 


15 


00107 


00166 


PRESET 


40553 


00163 


16 


00113 


00205 


ADDRESSES 


40554 


00164 


11 


00041 


00001 


AND INDICES* 


40555 


00165 


75 


30000 


00167 


ONE ROW OF 


40556 


00166 


11 


30000 


00460 


A TO ES. 


40557 


00167 


15 


00111 


00175 


PRESET 


40560 


00170 


15 


00112 


00177 


ADDRESSES 


40561 


00171 


11 


00042 


00002 


AND INDICES* 


40562 


00172 


13 


00076 


00015 


ZERO 


40563 


00173 


13 


00076 


00016 


TO RESULT* 


40564 


00174 


75 


30002 


00176 


COMPUTE 


40565 


00175 


11 


30000 


00011 


ONE ELEMENT 


40566 


00176 


75 


30002 


00200 


OF A COLUMN 


40567 


00177 


11 


30000 


00013 


OF C. 


40570 


' 00200 


37 


00231 


00232 




40571 


00201 


21 


00175 


00114 


ADVANCE 


40572 


00202 


21 


00177 


00114 


ADDRESSES, 


40573 


00203 


41 


00002 


00174 




40574 


00204 


75 


30002 


00206 


STORE COMPUTED 


40575 


00205 


11 


00015 


30000 


ELEMENT* 


40576 


00206 


21 


00166 


00036 


ADVANCE 


40577 


00207 


21 


00205 


00116 


ADDRESSES* 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



san Diego California 



CV-182 

pag e CN 016-18 

REPORT 2M 4-91 
MODEL All 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40600 


00210 


41 


00001 


00165 




40601 


00211 


75 


30000 


00213 


ONE COLUMN 


40602 


00212 


11 


01420 


30000 


OF C TO MD. 


40603 


00213 


21 


00212 


00032 


ADVANCE 


40604 


00214 


21 


00161 


00040 


ADDRESSES. 


40605 


00215 


41 


00061 


00160 




40606 


00216 


75 


30310 


00150 


OUTPUT 


40607 


00217 


11 


41070 


00150 


PROGRAM TO ES. 


40610 


00220 


00 


00000 


00000 




40611 


00221 


00 


00000 


00000 




40612 


00222 


00 


00000 


00000 




40613 


00223 


00 


opoop 


oopoo 




40614 


00224 


00 


00000 


00000 




40615 


00225 


00 


00000 


00000 




40616 


00226 


00 


00000 


00000 




40617 


00227 


00 


00000 


00000 




40620 


00230 


37 


76000 


76002 


SINGLE PRECISION 


40621 


00231 


45 


00000 


30000 


ARITHMETIC— SEE 


40622 


00232 


16 


00146 


00320 


SET FOR ACCl ULATE M 


40623 


00233 


75 


30002 


00265 


STORE 


40624 


00234 


11 


00015 


00017 


SUM. 


40625 


00235 


11 


00012 


00016 


ADD ENTRANCE . 


40626 


00236 


23 


10000 


10000 


CLEAR A ANf> •. 


40627 


00237 


16 


10000 


00257 


ERASE SHIF1 * 


40630 


00240 


43 


00013 


00257 


Y ZERO TEST. 


40631 


00241 


43 


00011 


00255 


X ZERO TEST* 


40632 


00242 


23 


00012 


00014 


EXPONENT DIFFERENCE. 


40633 


00243 


12 


20000 


20000 




40634 


00244 


42 


00145 


00247 


36 COMPARSION. 


40635 


00245 


41 


00012 


00257 


Y. OR X. 


40636 


00246 


4 5 


oodoo 


00255 




4063? 


00247 


16 


20000 


00257 


SET SHIFT. 



10-228 



SAN DIEGO CALIFORNIA 



page CN 016-19 

REPORT ZM 491 
MODEL AH 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40640 


00250 


41 


00012 


00253 


Y OR X, 


40641 


00251 


11 


00011 


10000 


X TO Q. 


40642 


00252 


45 


00000 


00256 




40643 


00253 


11 


00013 


10000 


Y TO Q. 


40644 


00254 


75 


00001 


00257 




40645 


00255 


11 


00014 


00016 


Y EXPONENT* 


40646 


00256 


11 


00013 


00011 


Y TO X* 


40647 


00257 


54 


00011 


30000 


SHIFT X* 


40650 


00260 


35 


10000 


00015 




40651 


00261 


45 


00000 


00272 


TO NORMALIZE* 


40652 


00262 


23 


00016 


00145 


A LEFT 


40653 


00263 


54 


00015 


00044 


NOT SIGNIFICANT* 


40654 


00264 


47 


00273 


00313 


ZERO TEST* 


40655 


00265 


11 


00014 


20000 


MULTIPLY ENTRANCE* 


40656 


00266 


35 


00012 


20000 


ADD EXPONENTS. 


40657 


00267 


36 


00144 


00016 




40660 


00270 


71 


00013 


00011 


FORM PRODUCT* 


40661 


00271 


11 


20000 


00015 


TEST 


40662 


00272 


43 


20000 


00262 


EXTENTION* 


40663 


00273 


13 


00076 


00005 


CLEAR FOR SF. 


40664 


00274 


11 


00074 


10000 


POSITIVE FLAG* 


40665 


00275 


46 


00276 


00277 


SIGN TEST. 


40666 


00276 


13 


10000 


10000 


NEGATIVE FLAG* 


40667 


00277 


11 


10000 


00006 


FOR ROUNDING* 


40670 


00300 


74 


20000 


00005 


SCALE FACTOR* 


40671 


00301 


11 


20000 


00015 




40672 


00302 


46 


00303 


00304 


ADJUST 


40673 


00303 


13 


10000 


10000 


FOR SIGN* 


40674 


00304 


21 


00016 


00005 


ADJUST FOR SF* 


40675 


00305 


44 


00306 


00313 




40676 


00306 


21 


00015 


00006 


ROUND* 


40677 


00307 


43 


20000 


00313 


OVERFLOW TEST* 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN Ulfc'GO CALIFORNIA 



CV-182 

page CN 016-20 

REPORT ZM ^91 
MODEL ^22. 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



40700 


00310 


32 


00147 


00107 


ADJUST 


40701 


00311 


11 


20000 


00015 


FOR 


40702 


00312 


21 


00016 


00074 


OVERFLOW. 


40703 


00313 


11 


00015 


20000 


ZERO 


40704 


00314 


47 


00316 


00315 


TEST. 


40705 


00315 


11 


20000 


00016 


ERASE EXPONENT. 


40706 


00316 


75 


30004 


00320 


SET FOR 


40707 


00317 


11 


00015 


00011 


ADO. 


40710 


00320 


37 


00320 


00321 


TO ADD OR EXIT* 


40711 


00321 


45 


00000 


00231 




40712 


00322 


00 


00000 


00000 




40713 


00323 


00 


00000 


00000 




40714 


00324 


00 


00000 


00000 




40715 


00325 


00 


00000 


00000 




40716 


00326 


00 


00000 


00000 




40717 


00327 


00 


00000 


00000 




40720 


00230 


37 


76000 


76002 


MULTI-PRECISION 


40721 


00231 


45 


00000 


30000 


ARITHMETIC— SEE CA-006. 


40722 


00232 


75 


30002 


00246 


STORE 


40723 


00233 


11 


00015 


00017 


SUM. 


40724 


00234 


75 


10002 


00301 


ZERO TO 


40725 


00235 


13 


00076 


00015 


MULTIPLY RESULT. 


40726 


00236 


42 


00102 


00240 


TEST EXPONENT. 


40727 


00237 


45 


00000 


00230 


ALARM. 


40730 


00240 


42 


00103 


00234 


TEST EXPONENT. 


40731 


00241 


13 


00075 


10000 


STORE 


40732 


00242 


53 


20000 


00016 


EXPONENT. 


40733 


00243 


11 


00072 


10000 


STORE 


40734 


00244 


53 


00015 


00016 


SIGN. 


40735 


00245 


45 


00000 


30000 


TO ADD OR EXIT. 


40736 


00246 


71 


00012 


00013 


MULTIPLY ENTRANCE, 


40737 


00247 


72 


00011 


00014 


FORM 



0-9 "2.0 



CONVAIR — PiviSiON OF GtNi-RAL DYNAMICS CORP. 



SAN DifcCO CALIFORNIA 



CV-itfZ 

page CN 016-21 
REPORT ZM 491 

MODEL j^H 
DATE 9-.1Q-56 



CONTINUOUS MATRIX MULTIPLIER 



40740 


00250 


54 


20000 


00044 


LOW 




40741 


00251 


11 


20000 


20000 


ORDER 




40742 


00252 


54 


20000 


00001 


PRODUCT. 




40743 


00253 


72 


00011 


00013 


ADD HIGHER ORDER, 


► 


40744 


00254 


37 


00300 


00271 


NORMALIZE* 




40745 


00255 


23 


00005 


00074 






40746 


00256 


31 


00012 


00030 


STORE 




40747 


00257 


11 


20000 


00003 






40750 


00260 


54 


00003 


00060 


EXPONENTS. 




40751 


00261 


31 


00014 


00030 






40752 


00262 


11 


20000 


00010 






40753 


00263 


54 


00010 


00060 






40754 


00264 


37 


00264 


00265 






40755 


00265 


21 


00005 


00003 


CORRECT 




40756 


00266 


35 


00010 


20000 


EXPONENT . 




40757 


00267 


37 


00245 


00236 


TESTt STORE EXPt 


SIGN. 


40760 


00270 


45 


00000 


00301 


TO ADD. 




40761 


00271 


47 


00272 


00234 


ZERO TEST. 




40762 


00272 


13 


00076 


00005 


STORE ZERO. 




40763 


00273 


74 


20000 


00005 


NORMALIZE 




40764 


00274 


11 


20000 


00015 


AND 




40765 


00275 


54 


20000 


0004 3 


STORE 




40766 


00276 


11 


20000 


00016 


RESULT. 




40767 


00277 


23 


00005 


1 1 






40770 


00300 


45 


00000 


30000 






40771 


00301 


75 


30004 


00303 


ADD EXTRANCE. 




40772 


00302 


11 


00015 


00011 






40773 


00303 


11 


00013 


20000 






40774 


00304 


47 


00305 


00231 


ZERO TEST. 




40775 


00305 


11 


00011 


20000 






40776 


00306 


47 


00311 


00307 


ZERO TEST. 




40777 


00307 


75 


30002 


00231 


ZERO TO 





CO:4VAIR 



DIVISIO.N Of : GLNEKAl DYNAMICS CORP. 

t.AN Pit i,l) (' M l> UMMIA 



CV-1132 

PAGE CN 016-22 
REPORT ZM A91 

MODEL All 
DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



41000 


00310 


11 


00013 


00015 


RESULT. 


41001 


00311 


37 


00264 


00256 


STORE EXPONENTS. 


41002 


00312 


11 


00003 


20000 


SUBTRACT 


41003 


00313 


36 


00010 


20000 


EXPONENTS. 


41004 


00314 


46 


00315 


00322 


NEGATIVE TEST. 


41005 


00315 


11 


00013 


00005 




41006 


00316 


11 


00014 


00006 


STORE 


41007 


00317 


11 


00010 


00003 




41010 


00320 


75 


30002 


00326 


LARGER NUMBER. 


41011 


00321 


11 


00011 


00007 




41012 


00322 


11 


00011 


00005 


STORE 


41013 


00323 


11 


00012 


00006 




41014 


00324 


11 


00013 


00007 


LARGER NUMBER. 


41015 


00325 


11 


00014 


00010 




41016 


00326 


12 


20000 


20000 


STORE 


41017 


00327 


13 


20000 


00015 


EXPONENT DIFFERENCE. 


41020 


00330 


42 


00101 


00341 


34 COMPARISON. 


41021 


00331 


42 


00104 


00334 


58 COMPARISON. 


41022 


00332 


75 


30002 


00231 


LARGER 


41023 


00333 


11 


00005 


00015 


TO RESULT. 


41024 


00334 


21 


00015 


00077 




41025 


00335 


16 


20000 


00347 


SET 


41026 


00336 


13 


00076 


00004 




41027 


00337 


11 


00007 


00010 


SHIFT. 


41030 


00340 


45 


00000 


00347 




41031 


00341 


21 


00015 


00101 


SET 


41032 


00342 


16 


20000 


00344 




41033 


00343 


11 


00074 


00004 


SHIFT. 


41034 


00344 


55 


00004 


30000 


SHIFT CORRECTION. 


41035 


00345 


35 


00100 


20000 


SET 


41036 


00346 


16 


20000 


00347 


SHIFT. 


41037 


00347 


54 


00010 


30000 


SHIFT MANTISSA. 



10-232 



CC.--VAI3 - DIVISION Oi : GENERAL DYNAMICS CORP. 



5»N IllfOO CAL.lfOfiNIt, 



CV-iBZ 

PAGE CN 016-23 
report ZM ^91 

MODEL jQ3_ 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



41040 
41041 
41042 
41043 
41044 
41045 
41046 
41047 
41050 
41051 
41052 
41053 
41054 
41055 
41056 
41057 
41060 
41061 
41062 
41063 
41064 
41065 
41066 
41067 
41070 
41071 
41072 
41073 
41074 
41075 
41076 
41077 



00350 
00351 
00352 
00353 
00354 
00355 
00356 
00357 
00360 
00361 
00362 
00363 
00364 
00365 
00366 
00367 
00370 
00371 
00372 
00373 
00374 
00375 
00376 
00377 
00150 
00151 
00152 
00153 
00154 
00155 
00156 
00157 



54 00006 
54 00005 
35 00006 
72 00004 

35 00010 
47 00360 
75 10002 
13 00076 
37 00300 
42 00073 
42 00105 

36 00071 
35 00003 
42 00102 
45 00000 
42 00103 

37 00245 
45 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
45 00000 
11 00026 
47 00175 
56 10000 
45 10000 
45 20000 
11 00073 
11 00071 



00107 
20042 
20000 
00007 
20000 
00356 
00231 
00015 
00272 
00364 
00356 
20000 
00003 
00367 
00230 
00356 
00241 
00231 
00000 
00000 
00000 
00000 
00000 
00000 
00151 
20000 
00153 
00154 
00173 
00173 
00001 
20000 



SHIFT 

MANTISSA 

AND 

ADD* 

ZERO TO 

RESULT* 
NORMALIZE* 
EXPONENT 

TESTS* 
CORRECT 

EXPONENT* 
EXPONENT TEST* 

EXPONENT TEST* 

STORE EXPONENT* SIGN. 



TEST 



CONTINUOUS FLAG. 



TEST 



MJ SWITCHES. 



TYPES- 



Ct'NVAIIi -- DIVIblON Or GLNLUAL DYNAMICS CORP. 

SAN I'll <.,-.) C Al if i >iiNi« 



CV-182 

page CN 016-24 

report 2M 491 

MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



'+11 00 


00160 


32 


00124 


00017 




41101 


00161 


15 


20000 


00162 


SET 


41102 


00162 


11 


30000 


10000 




41103 


00163 


11 


00125 


00002 


' MJ-S 


41104 


00164 


61 


00000 


10000 




41105 


00165 


55 


10000 


00006 


FOR 


41106 


00166 


41 


00002 


00164 




41107 


00167 


31 


00074 


00017 


OUTPUT. 


41110 


00170 


35 


00162 


00162 




41111 


00171 


41 


00001 


00162 




41112 


00172 


56 


00000 


00154 




41113 


00173 


37 


00220 


00221 


OUTPUT • 


41114 


00174 


56 


00000 


00154 




41115 


00175 


56 


20000 


00176 




41116 


00176 


45 


10000 


00201 


TEST 


41117 


00177 


45 


20000 


00201 


HJ SWITCHES. 


41120 


00200 


45 


00000 


00202 




41121 


00201 


37 


00220 


00221 


OUTPUT* 


41122 


00202 


56 


30000 


00203 




41123 


00203 


11 


00031 


20000 


TEST F0- 


41124 


00204 


47 


00210 


00205 




41125 


00205 


37 


00272 


00273 


AND SEND 


41126 


00206 


11 


00023 


00022 


TO POSITION. 


41127 


00207 


45 


00000 


00213 




41130 


00210 


37 


00316 


00317 


PRODUCT 


41131 


00211 


11 


00021 


00022 


TO POSITION. 


41132 


00212 


11 


00023 


00021 




41133 


00213 


11 


00115 


00070 




41134 


00214 


37 


72400 


72401 


READ NEW 


41135 


00215 


04 


00026 


00005 s 


PARAMETER CARD. 


41136 


00216 


75 


30310 


00162 


, LOAD 


41137 


00217 


11 


40070 


00150 


ES. 



10-234 



fORM NO E T II- 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIf-ORMA 



CV-102 

PAGE CN Ol6-?5 
report 2M 491 

MODEL ^11 

DATE 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



41140 


00220 


45 


00000 30000 


EXIT-OUTPUT SUBROUTINE* 


41141 


00221 


11 


00031 20000 


TEST FOR 


41142 


00222 


47 


00263 00223 


TRANSPOSE. 


41143 


00223 


45 


10000 00245 


TEST 


41144 


00224 


45 


20000 00226 


MJ SWITCHES* 


41145 


00225 


45 


00000 00220 




41146 


00226 


45 


30000 00236 




41147 


00227 


37 


00335 00336 


FORM PRODUCT UNPACKED* 


41150 


00230 


15 


00054 00234 


SET 


41151 


00231 


16 


00044 00234 


PARAMETERS* 


41152 


00232 


37 


70440 70443 


PUNCH* 


41153 


00233 


00 


41500 00000 




41154 


00234 


00 


00000 00000 




41155 


00235 


45 


00000 00220 




41156 


00236 


37 


00345 00346 


FORM TRANSPOSE UNPACKED 


41157 


00237 


15 


00052 00243 


SET 


41160 


00240 


16 


00046 00243 


PARAMETERS* 


41161 


00241 


37 


70440 70443 


PUNCH* 


41162 


00242 


00 


41500 00000 




41163 


00243 


00 


00000 00000 




41164 


00244 


45 


00000 00220 




41165 


00245 


45 


30000 00254 




41166 


00246 


15 


00054 00252 


SET 


41167 


00247 


16 


00021 00252 


PARAMETERS* 


41170 


00250 


37 


70440 70443 


PUNCH PRODUCT PACKED. 


41171 


00251 


00 


54640 00000 




41172 


00252 


00 


00000 00000 




41173 


00253 


45 


00000 00220 




41174 


00254 


37 


00272 00273 


FORM TRANSPOSE PACKED. 


41175 


00255 


15 


00052 00261 


S;ET 


41176 


00256 


16 


00023 00261 


PARAMETERS* 


41177 


00257 


37 


70440 70443 


PUNCH* 



i *\ r\nf 



CONVAiR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIFORNIA 



CV-182 

pagecn 016-26 
report ZM 491 

MODEL A H 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



41200 
41201 
41202 
41203 
41204 
41205 
41206 
41207 
41210 
41211 
41212 
41213 
41214 
41215 
41216 
41217 
41220 
41221 
41222 
41223 
41224 
41225 
41226 
41227 
41230 
41231 
41232 
41233 
41234 
41235 
41236 
41237 



00260 
00261 
00262 
00263 
00264 
00265 
00266 
00267 
00270 
00271 
00272 
00273 
00274 
00275 
00276 
00277 
00300 
00301 
00302 
00303 
00304 
00305 
00306 
00307 
00310 
00311 
00312 
00313 
00314 
00315 
00316 
00317 



00 41500 
00 00000 
45 00000 
45 10000 
45 20000 
45 00000 
45 30000 
45 00000 
45 30000 
45 00000 
45 00000 
11 00106 
53 00037 
13 00076 
16 00107 

15 00110 
21 00304 
11 00043 

16 00113 
75 30002 
11 30000 
21 00304 
35 00035 

41 00001 
75 30000 
11 01420 
21 00311 
21 00002 

42 00035 
45 00000 
45 00000 
11 00106 



00000 
00000 
00220 
00270 
00266 
00220 
00227 
00236 
00246 
00254 
30000 
10000 
00310 
00002 
00311 
00304 
00002 
00001 
00304 
00305 
30000 
00116 
00304 
00303 
00312 
30000 
00034 
00U4 
00277 
00272 
30000 
10000 



TEST 

MJ SWITCHES. 

PUNCH PRODUCT UNPACKED* 
PUNCH TRANSPOSE UNPACKED. 
PUNCH PRODUCT PACKED, 
PUNCH TRANSPOSE PACKED. 
EXIT-FORM TRANSPOSE SUBROUTINE. 
PRESET 

INDICES 

AND 

ADDRESSES. 

ONE ELEMENT 

OF PRODUCT TO ES. 
ADVANCE 

ADDRESSES. 

ONE COLUMN 

OF TRANSPOSE TO MD. 
ADVANCE 

ADDRESSES* 



EXIT~STORE PRODUCT SUBROUTINE. 
PRESET 



10-236 



I- ORM NO E T I !■ 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 

SAN DIEGO CALIFORNIA 



CV-152 

PAGE CN 016-27 

REPORT 2M U91 
MODEL All 
DATE 9 ^ 10-56 



CONTINUOUS MATRIX MULTIPLIER 



41240 


00320 


53 00035 


00325 


REPEATS* 


41241 


00321 


53 00035 


00327 


INDICES* 


41242 


00322 


11 00043 


00001 


AND 


41243 


00323 


15 00110 


00326 


ADDRESSES* 


41244 


00324 


16 00107 


00330 




41245 


00325 


75 30000 


00327 


ONE COLUMN 


41246 


00326 


11 30000 


01420 


TO ES« 


41247 


00327 


75 30000 


00331 


ONE COLUMN 


41250 


00330 


11 01420 


30000 


TO MD* 


41251 


00331 


21 00326 


00035 


ADVANCE 


41252 


00332 


21 00330 


00032 


ADDRESSES* 


41253 


00333 


41 00001 


00325 




41254 


00334 


45 00000 


00316 




41255 


00335 


45 00000 


30000 


EXIT-UNPACKING PRODUCT SUBROUTINE. 


41256 


00336 


15 00110 


00001 


PRESET 


41257 


00337 


16 00107 


00001 


ADDRESSES 


41260 


00340 


11 00032 


00002 


AND 


41261 


00341 


11 00047 


00003 


INDICES. 


41262 


00342 


11 00023 


00004 




41263 


00343 


37 00371 


00372 


UNPACK PRODUCT* 


41264 


00344 


45 00000 


00335 




41265 


00345 


45 00000 


30000 


EXIT-UNPACKING TRANSPOSE SUBROUTINE. 


41266 


00346 


37 00272 


00273 


STORE TRANSPOSE 


41267 


00347 


11 00107 


00001 


PRESET 


41270 


00350 


11 00034 


00002 


ADDRESSES 


41271 


00351 


11 00051 


00003 


AND 


41272 


00352 


11 00021 


00004 


INDICES. 


41273 


00353 


37 00371 


00372 


UNPACK PRODUCT. 


41274 


00354 


45 00000 


00345 




41275 


00355 


00 00000 


00000 




41276 


00356 


00 00000 


00000 




41277 


00357 


00 00000 


00000 





CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIFORNIA 



CV-102 

page CN 016-28 

REPORT ZM 491 

MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



41300 
41301 
41302 
41303 
41304 
41305 
41306 
41307 
41310 
41311 
41312 
41313 
41314 
41315 
41316 
41317 
41320 
41321 
41322 
41323 
41324 
41325 
41326 
41327 
41330 
41331 
41332 
41333 
41334 
41335 
41336 
41337 



00360 
00361 
00362 
00363 
00364 
00365 
00366 
00367 
00370 
00371 
00372 
00373 
00374 
00375 
00376 
00377 
00400 
00401 
00402 
00403 
00404 
004Q5 
00406 
00407 
00410 
00411 
00412 
00413 
00414 
00415 
00416 
00417 



00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
45 00000 
11 00002 
43 00003 
45 00000 
13 00076 
13 00076 
13 00001 
16 00001 

54 00006 
43 00005 
11 00003 

55 00005 
55 00002 
21 00004 

15 00001 

16 00001 
71 00002 
35 00431 
71 00003 
35 00433 
11 00106 
53 00002 
53 00005 



00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
00000 
30000 
20000 
00375 
00403 
00005 
00006 
00005 
00006 
00017 
00371 
00005 
00017 
00017 
00074 
00431 
00433 
00004 
00431 
00004 
00433 
10000 
00430 
00432 



EXIT-UNPACKING SUBROUTINE. 



TEST 



FOR 



NEEDED 



UNPACKING, 



SET 



LOCATIONS 
OF LAST 
COLUMN 
OR ROW. 



SET 



10-230 



)SM NO E T I 



CONVAiR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO CALIFORNIA 



CV-182 

page CN 016-29 

REPORT ZM 4.91 
MODEL All 
DATE 9«10-56 



CONTINUOUS MATRIX MULTIPLIER 



41340 


00420 


23 


00005 


00002 




NUMBER 


41341 


00421 


53 


20000 


00426 






41342 


00422 


11 


00002 


20000 




OF ELEMENTS IN 


41343 


00423 


52 


00113 


20000 






41344 


00424 


55 


20000 


00025 




ROW OR COLUMN. 


41345 


00425 


16 


20000 


00427 






41346 


00426 


75 


10000 


00430 


SET 


EXTRA 


41347 


00427 


13 


00076 


30000 




ELEMENTS TO ZERO. 


41350 


00430 


75 


30000 


00432 


PACKED ROW On 


41351 


00431 


11 


30000 


01420 




COLUMN TO ES» 


41352 


00432 


75 


30000 


00434 


UNPACKED ROW OR 


41353 


00433 


11 


01420 


30000 




COLUMN TO MD« 


41354 


00434 


23 


00431 


00002 


RETARD 


41355 


00435 


23 


00433 


00003 




ADDRESSES. 


41356 


00436 


41 


00004 


00430 






41357 


00437 


45 


00000 


00371 






41360 


00440 


00 


00000 


00000 






41361 


00441 


00 


00000 


00000 






41362 


00442 


00 


00000 


00000 






41363 


00443 


00 


00000 


00000 






41364 


00444 


00 


00000 


00000 






41365 


00445 


00 


00000 


00000 






41366 


00446 


00 


00000 


00000 






41367 


00447 


27 


64146 


06130 


FOR 


CONVENIENT CHECK SUM* 


41370 


00450 


37 


77763 


77767 


BLOTTOS 


41371 


00451 


00 


00000 


00457 




E5 


41372 


00452 


00 


40000 


41377 




AND 


41373 


00453 


56 


00000 


41373 




MD# 


41374 


00454 


75 


20550 


41376 


SUMS 


41375 


0045$ 


32 


70440 


00000 




IC-004 


41376 


00456 


75 


20352 


40004 




AND 


41377 


00457 


32 


72400 


00000 




IC-011* 



CONVAIR -DIVISION OF GENERAL DYNAMICS CORP ri/-lfl2 

CV L % 016- 



SAN OttfGO CALIFORNIA 



page m 016-30 

REPORT ZM 491 
MODEL All 

date 9-10-56 



CONTINUOUS MATRIX MULTIPLIER 



SEE IC-004 FOR CODE OF 70440-71207* 



SEE IC~Q11 FOR CODE OF 72400*72751 EXCEPT FOR THE FOLLOWING 
CHANGE WHICH STORES THE FLAG FOR THE STOP READ INDICATOR IN 
CELL 00001 AFTER ES HAS BEEN RESTORED* 

72532 01074 11 01255 74001 



10-240 



CV-183 



nivigioN San Diego 
MODEL ALL 




REPORTjaH=52SL 



DATE ft/?9/f>6 



TITLE 
SPUR 

Single precision unpacked rounded floating 
point package for. ERA-HOI Computers 



Part I Operation Specifications 



PREPARED BY T- ****** 



GROUP Mg1t,al Computing Lab*. 



REFERENCE 



CHECKED BY C. J. Svlft 

Donn Parker 
"*;> D i° k Bieleker 

NO. OF PAGES J22 



APPROVED BY. 



rtJW. ^AH*W 



NO. OF DIAGRAMS_0. 



i 

o 

r-t 
I 

o 
o 
a* 



x 
a* 



REVISIONS 



NO. 



DATE 



BY 



CHANGE 



QO?4«A 



PAGES AFFECTED 



10-241 



ANALYSIS 

prepared by L Barton 



C O H V A I R 

A DIVISION Or CEHCSAl DYNAMIC* COBPOIATIOM 



checked by C»J. Swift, D. Parker, D. Bielskor 

REVISED BY 



SAN DICGO 



PAGE 1 
REPORT NO. ZM-527 
MODEL ALL 

date 8/29/56 





SINGLE PRECISION UNPACKED ROUNDED FLOATING POINT PACKAGE 


I 


Brief Specification* 
Occupies 






Kfi 


00000, 00001 

01500 to 01777 inclusive 




MD 


76000 to 77777 some parte open 
74000 to 75777 ( B. S, image) 




Regis tora 






P 


01764, 01765 




B 


01766, 01767 




C 


01770, 01771 




S 


01772, 01773 




R 


01774, 01775 




h 


01776, 




h 2 


01777 




Constants used and available 


01750 00 00000 00000 

01751 00 00000 00001 

01752 00 00000 00002 ' 

01753 00 00002 00000 

01754 00 00000 00045 

01755 00 00000 O0Q44 

01756 00 00000 00177 

01757 00 QQQOO 01777 




Activation 


37 76000 76001 (stored package to k\fl.) 






17 00000 77413 (initially prina oards) 



MM t«t«»A 



10-242 



C O N V A I R 



ANALYSIS 

PREPARED BY L. Barton * •nrtww or taatML dtnakics corpobatioii 

checked by C.Swift, D. Parker, D* Blelsker *" DIE °° 

REVISED BY 



CO 
CO 



I 

o 
o 



X 

a* 



PAGE 2 
REPORT NO. ZM-527 
MODEL ALL 
pate e/29/56 



Two address commands 




j 




u cc mi xm 


Addition 


(cc) 






00 


T ♦ X to R 




04 


R ♦ I'+XtoR 




20 


I ♦ X to R, I 




24 


R ♦ X ♦ X to R, X 


Subtraction 


(cc) 


..„ . 









01 I-XtoR 








05 R + T-XtoR 








21 I - X to R, I 








25 R ♦ X - X to R,I 


Hiltiplioatlon 




(cc) • 








02 X ■ • X to R 








06 R ■♦ X : • X to R 








22 X • X to R, X 








26 R ♦ X • X to R, X 


Division 






(cc) 

03 I/XtoR 
07 R ♦ I A to R 
23 J/X to R, X 
27 R ♦ XA to R, X 


threshold 


Jump 




17 If X is greater than R jump to Xj otherwise 


continue with the next instruction, In either case R original 


will be unchanged in R, 3 P and 8* (CAUTION f due to rounding a 


jump 


may occur 


» either way uhen X approaches R, if X and R were 


calculated 


by 


different operations) 



ANALYSIS C O II V A I R PAGE 3 

PREPARED BY L. Barton Aww«j»w«MHuiprMM«eo«oiMKM REPORT NO. ZM-527 

checked by C.Swift, D.Farkor, D. Biolskor model ALL 

REVISED BY DATE 8/29/56 



On© address commands 

U CC K HN XYTTT (Ins rightmost bit of K is used with NN, ths left- 
most two hits of K are used aa tags for the I address. Refer to 
detailed command explanations for details. 

Index jumps with modification of index counter registers b (1 or 2) 
(CC) 

76 with b 1 

77 with b 2 

Add 2 to the contents of b (1 or 2). If H is greater than one half 
of b (1 or 2) jump to T a nd leave b (1 or 2 J advanced. Otherwise 
set b (1 or 2) equal to sero and continue wTOS the next instruction. 
Ine effect is to go through the loop N'+ 1 tima with the teat at the 
end of the loop or K times w£th the test at the entrance to the loop. 

Polynomial (CC) 

75 Compute the polynomial Aq ♦ A l*" .'♦ Aja* 2 ♦**••♦ *o&l 
Vkaret 

X, as a floating point number » must be prestored in register P. 
,7 is the address of t^e last constant, Ag, where the constants are 
floating point numbers stored each in two cells-mantissa, exponent- 
consecutively* 

«0# AxfU*! i *«• 
H if the degree of the equation. 
The answer appears in R. 

If N is less than one no operation will be performed. 
Card instructions (CC) 

57 Read K cards into cells consecutively starting at I. 
56 Punch N cards from cells conaectutivcly starting at X. 

rc H Mi.ia.A 10-244 



t/ v -iuo 



C O N V A I R 



ANALYSIS 

PREPARED BY L. J&rtoil »»miio«or«wMM.O¥«»ni«co»POMno« 

BAN DIUlGO 

checked by C.Swift, D.Farker, D.Bielsker 

REVISED BY 



PAGE £ 

REPORT no.zm-527 

MODEL ALL 

date 8/29/56 



Sua 



Mar* detailed instructions and options available are given In the 

detailed instructions* The contents of register C cannot be punohed 

by a 14- instruction. 

In case of Bull failure set PAK equal, to 

77430 for read, or 

77007 for write • 

S3 will be restored followed by a $6 stop with V address that of 

the interrupted card instruction, 

A sum is stored at 77777. Entrance at 77371 will calculate a new 
sum over the area 76000 to 77776 inclusive; place the new sum in the 
Q register | place the difference between the new sum and the stored 
sum in the accumulator, and come to a 56 00000 77377 stop* Restarting 
computer will replace the stored sum with the calculated sum and 
terminate with a 56 00000 30000 stop. In general when no changes 
have been made in the tape a sero difference in the accumulator 
indicates the routine is correctly stored on the Magnetic Drum. 



ANALYSIS C O N V A I R PAGE 5 

PREPARED BY L. Barton **««»■ or «u*.*LM«Aiii«eow««Mio« REPORT NO. ZM-527 

checked by C.Swift, D.Parker, D.Blelokor SAN D, ^ GO model ALL 

REVISED BY DATE 8/29/56 



POMM »«I«.A 



II Do tailed Specifications 

This is an unpacked floating point package including card input and 
output, addition, subtraction, multiplication, division, two index 
registers and normalisation; all with rounding. The floating point 
Lumber representation is defined in the 1103 storage as follows j 
N • M ♦ 2» where V 2 ^H^ ,and ^1 <» 

M Is scaled 35# o is scaled 0, where M is in the first of two con* 
seoutive cells and e in the second • 
Examples i 

1 * 200000000000 000000000001 

or 377777777777 000000000000 

-1 » 577777777777 000000000001 

- 16 - 3M63U63U6 777777777776 

The card input and output will only handle a maximum decimal exponent 

of 99. 

The nuaber ;ph6uld. b€-nprmali«ed at all times to gain the maximum 
accuracy because 35 bits are used in a normalised mantissa. However, 
the addition, subtraction, and multiplication operations will handle 
floating numbers not normalised and give normalised answers which are 
correct to a lesser number of places* The division operation requires 
a normalised divisor or will go to the alarm exit, where it will alarm 
print the divisor and halt with a 56 stop* A restart will then finish 
the current instruction using an incorrect answer # end Mo fault will 
be caused by a non-normalised dividend which will give a non~normallsed 
quotient correct to ji lesser number of places. 

The number whose mantissa is in the accumulator scaled 35 and whose 
exponent is in 01775 will be normalized by the return jump 37 01741 01712 

'■ ' "" ■ " i ii« i n ii m—n i i , .i . i n ii ii— — mm m ii i i n mm — — — n i wmiiinn ■ i i i i i i 11 ii i i i i— ■— >— — ■ umi i m iii m— — ■ — ■ — mm* i «n 

10-246 



V V ~ J-KJ\J 



ANALYSIS C O -M V A I El PAGE 6 

PREPARED BY L. Barton ktiKCuniwxittuu. mama towmxnom REFOftT NO. Z&-527 

checked byC. Swift, D.Parker, D.Bielsker SAN DIEGO model ALL 

REVISED BY DATE 8/29/56 



The mantissa of the answer vill bo duplicated in 01774, and the 
accumulator, with the exponent in 01775, I.e. the normalized number 
vill be left in R as for arithmetic operation answers. 
To attempt greater convenience of programming subroutines and simpler 
explanation of operation; encore package, to operate from 01500 to 
01777 inclusive, is independent of any subroutines used. Ihe intention 
is that any subroutine may be easily assembled to use with it. It 
includes rounded operations for accuracy and the fundamental arithmetic 
operations. Thesa last arithmetic operations can be used with inter- 
pretive instaructlons for normal programs or with return Jump instructions 
for greater speed in loops and especially for construction of suh*» 
routines. 

She package starts with a self contained arithmetic unit from 0163^ 
to 01775 inclusive which will perform addition, subtraction, multi- 
plication, division, and normalization operation on specified registers 
by return jump instructions. From 01500 to 01632 inclusive Is an 
interpretive system which uses the smaller arithmetic package. From 
77400 to 77751 on the drum is a card input, self contained and 
operated either by return Jump instructions of by the interpretive 
system. From 76760 to 77357 is a similar card output. The package 
requires 

00000 45 00000 ( ) 

00001 45 00000 01547 

01500 - 01777 inclusive, package operation 

76000 -77777 inclusive for package and subroutine 

storage. 
74000 - 75777 Inclusive, ES image during some 

operations as for example card 



CV-183 

\NALYSIS C O N V A I R PAGE J 

PREPARED BY L. Barton *Biifi5So«o»63a»JitDTB*aic»eoBPOBAiio« REPORT NO. 2M^S27 

checked by C. Swift, D.Parker, D. Biolsker CANOIEGO model ^ 

REVISED BY DATE 8/29/56 



input and output. 
To attempt greater convenience of programming subroutines and 
simpler explanation of operation; a core package, to operate from 
01500 to 01777 inclusive, is independent of any subroutines used. 
The intention is that any subroutine may be easily assembled to us* 
with it. It includes rounded operations for accuracy and the fundamen- 
tal arithmetic operations. These last arithmetic operations can be 
used with interpretive instructions for normal programs or with return 
Jump instructions for greater speed in loops and especially for 
construction of subroutines. 

The package starts with a self contained arithmetic unit from 01633 
to 01775 Inclusive which will. perform addition, subtraction, multi- 
plication, division, and normalisation operating on specified re- 
gisters by return jump instructions. Prom 01500 to 01632 inclusive 
is an interpretive system which uses the smaller arithmetic package. 
From 77-400 to 77751 on the drum is a card input, self contained and 
operated either by return Jump instructions of by the interpretive 
system. Prom 76760 to 77357 is a similar card output. 
The package requires 

00000 45 00000 ( ) 

00001 45 00000 01547 

01500 - 01777 Inolusiup, package operation 

76000 - 77777 inclusive for package and subroutine storage. 

74000 - 75777 inclusive, E3 image during some operations as for 

example card input and output. 
The tape reads into cells 76000 - 77777 inclusive 37 76000 76001 
transfers from drum storage to E.S. cells 00000, 00001, and 01500 
, wym 



>»M taia-A 



N V A I R 



ANALYSIS C i 

PREPARED BY L» Barton * oi««o» «f «a«wi oyiuhic* cowomtim 

checked by C.Swift, D.Farker, D.Bielsker SAN Dlcco 

REVISED BY 



pages 8 
REPORT no. 2M-527 

MODEL J&J, 
DATE 8/29/56 



to, 01757 inclusive and clears cells 01760 to 01777 for registers* 
rH7 00000 77413 will prims read and punch cards initially and succeeding 
card movements will be automatic. 

00002 - 01477 inclusive remain available for any program or added 
subroutines. 
Registers 

01764 F for storage of an 

0176$ operand for iteration 

01766 B for storage of the 

01767 (X) operand 
01770 C for storage of the 
01771, (¥) operand 

01772 3 for storage of an 

01773 operand for Iteration 

01774 R thai answer for storage of result 
01775 

01776 b 1 Index Registers for 

01777 > 2 address modificat 
Secondary registers 

01760 I contains the current or isa? in^BT^rtrtive (14) Ins true tloa 

01761 V la used as a counter * receives ll from single address instruc- 

tions 

01762 Used as temporaries 

01763 in normalisation and arithmetic operations (except 
division) 



At. 



ANALYSIS 

prepared by L. Barton 

checked by C. SWIFT, D. barker, D.Biclsker 

REVISED BY 

r— ■ " ' ' "" '"' --""- ij """- ' ' ' ' ' r 



.C-, fFf.: ■', - !. OVt.'.'.MSUJ CfJl.PORSTtOJI 



pa&cz 9 

RCi-oirr r<:o. ZM-527 

MOD2L ALL 

DATE 8/29/56 



Corcisands 

Two address commands 

U cc xra mi 

14 is the Interpretive code 
CC is tba pseudo command oode 
XXXX (excluding the leftmost two bite) le the 
address of the operand placed in register B* 
YYH (excluding the leftmost two bits) Is the 
address of the operand placed in register C* 
Tfce first (leftmost) bit of XXXX or YH1 Is called a tag* If a one, 
it will cause a temporary addition of the contents of index register 
b lto that » address daring. operation* 

After the operation the instruction resumes its original unaltered form* 
The second (next) bit, if one, will add the contents of index register 
b 7 but otherwise operate as described for b 1« Both may be used in 
the same operation. 

One address commands 

u cc kkn ran 

M is the interpretive (1103) code* 

CC is the pseudo command code 

t le divided into two parts* 

The leftmost 2 bits are used as tags on the I address* 

The first (leftmost) bit of K if a one will cause a temporary 

addition of the contents of ind&ac register b 1 to the f address during 

operation. After the operation the instruction resumes its original 

«,*..» 1 4-^v.m.A *•«*.« m*m. aanwi) fw*v+ \ V. -f ♦ 4f « fWtOk %H1 1 *d^ th«* ^Ont^Ht-S 



FORM IStt-A 



iO-SKT 



ANALYSIS 

PREPARED BY Barton, L, 

checked oy C.Swift, D'.Farker, 

REY1SED BY 



C O N V A I El 

A onru;o» or •Eucn.u dthakio cobmkatioii 
^, „ ■ CAN DILGO 

Bielsker 



CO 

co 



i 

o 

H 
I 

o 
o 
o 



X! 



PAGE 10 

nszpomr no. ZM-527 
model AIL 
date 8/29/56 



of Index register b 2 but otherwise operate as above for b 1. Both 
tags may be used In the same operation. 

Ihe third (rightmost) bit of K will be used with NS as a number N. 
NN with the third bit of K is the number W placed In register H 
«md usually used as a counter. Its maximum size is 177 octal or 127 
decimal* 

TYTTT is the address of the number placed in register C* 
Commands and Registers 

U 00 mXTHT 
T + XtoR 
or 37 017U 01656 
C ♦ B to R 
H 01 XXXI OTX 
I-XtoR 
or 37 01741 01655 
C- BtoR 
U«£ XXX* XXIX 
I ,XtoR 
or 37 01741 01706 
C ♦ BtoR 
14 03 XXXX xTxT 
Y/X to R 
or 37 017U 01633 
C/B to R 
Registers 

R final will be duplicated in C and the double extension of the R 
final mantissa will also be in the accumulator 
r "" ' ■ ' " ' ■""" "•■ i r i n Mg ' i" ' , " ' —"""■--"-- '■ 



C O N V A I I* 



ANALYSIS 

PREPARED BY L» Barton * Mvisie» Of «khe«al ov»a«ic« corporation 

SAN DICGO 

checked by C« Swift, D.Jarker, B.fiielsker 

REVISED BY 



CV-183 

PAGE »•*■» 
REPORT NO. ZM-527 
MODEL AIX 

DATE 8/29/56 



P will be unchanged 

For H type instructions 
R initial will be in S and B 
For 37 type instructions 
S will be unchanged and duplicated in B. 
Commands and Registers 

u 04. mx rm 

R initial + Y ♦ X to R 

u 05 xxxx nn 

R initial + ! - X to R 

14 06 mr xnr 

R initial + I • X to R 
or 37 017U 01617 
I"to R 
U 07 XXXX YTCT 

R initial + Y/X to R 
Registers 

R final will be duplicated in C and the double extension of the R 
final mantissa will also be in the accumulator 
P will be unchanged 
For H type instructions 

R initial will be in S and B 
For 37 type instructions 

S will be unchanged and duplicated in B 



FORM IBIB-A 



10-1*52 



o 



ANALYSIS 

prepared by L. Barton 

checked by C.Swift, D.Farker, D.Biolsker 

REVISED BY 



%j il V A I kl 

A Bivi.icri or cr.;..;:;fiL oy.;;.: ,:cs ccr.PoafiTio* 
CAN DIEGO 



PA<?£ 12 

REFC^T KO. ZH-527 

tylQDSL ALL 

DATE 8/29/56 



Commnds and Regis tera 

14 20 xxxx xra 

X + X to R, X 
or 3? 01746 OI656 

C ♦ B to R, see footnote* 

u 21 xxxx mx 

Y - X to R, Y 
or 37 01746 01655 

C - B to R, 300 footnote* 

14 22 xxxx xxxx 

X • X to R, I 
or 37 01746 01706 

• B to R, see footnote* 

14323 xxxx rrax 

X/X to R, I 
or 37 01746 01633 

C/B to R, see footnote* 

Registers 

P will be unchanged 

For 14 type instructions 

R final will be duplicated in G and T and the double extension of 
the R final mantissa will also be in the accumulator, 
R initial will be in S and B 

For 37 type instructions 

• R final will be duplicated in C and also at the "X" address taken 
from the last 14 instruction used and located in the V portion of cell 
017-44 (where it is subject to modification by the programmer) 



ANALYSIS C O N V A I R PAGE 13 

prepared by L, Barton * vm ' tto * or " KSML on * me * w« M »» T ">« report no. ZM-527 

checked by c.Svift, D.Parker, D.Blelsker 8AN D,EQO model A£L 

REVISED BY DATE 8/29/56 



The double extension of the final mantissa will also be in the 
accumulator* 

S will be unchanged and duplicated in B. 
Commands and Registers 

14 24 XXXX YYYY 

R + Y + X to R, I 

14 25 xxxx rm 

R * Y - X to R, I 
H ?6 XXXX YYYX 
R + Y • X to R, X 
or 37 01746 01617 

S ♦ C '• B to R, • 
14 ?7 XXXX YYTY 
R v Y/X to R, T 
Registers 

P will be unchanged 
For 14 type instructions 

R final will be duplicated in C and I and the double extension of the R 
final mantissa will also be in the accumulator. 
R initial will be in S and B 
For 37 type instructions 

*R final will be duplicated in C and also at' the "t* address taken 
from the last 14 instruction- used and located in the V portion of Cell 
01744 (where it is subject to modification by the programmer) l!he 
double extension of the R final mantissa will also be In the accumulator 
S will be unchanged and duplicated in B. 

ro«M lata-A 10-254 



C O N V A I R 



ANALYSIS 

prepared by L. Barton * *"**" " **"* vnAUKt C9mmxnm 

checked by c. Swift, D. Parker, D.Bielsker 

REVISED BY 



PAGE H 

REPORT MO. ZM-527 

MODEL ALL 

DATE 8/29/56 



v o5 



1 

o 



x 
a. 



Commands and Registers 
Threshold jump 

H 17 xra m% 

If X is greater than R jump to Y; otherwise continue with the next 

instruction (caution - due to rounding a jump ©ay occur either way 

when X approaches R if X wad R have been calculated by different opers>: 

tions) 

R initial will be unchanged in R, S, and B 

R - X will be in C and the mantissa of R - X will be in the accumulator 

P will be unchanged* 
Index jumps with modification of b index registers 

U 76 KNH Tim with b 1 

U 77 KKK YTTTT with b? 

Add 2 to the contents of b 1 or b 2. If H (last bit of K with NH 

from instruction is greater than bl or b2 jump to y and leave bl or b2 

advanced. 

Otherwise set bl or b2 equal to zero and continue with the next 

instruction . 

The contents of I (2 cells) will be placed in register C. 

N (from ths last bit of K and m) will be placed in register K and 

remain unchanged 

R initial will be duplicated in S 

R, P, and B will be unchanged. 
Polynomial 

u 75 km iiirr 

Compute the polynomial A© ♦ A3X ♦ AjX 2 ♦ ••• ♦ A^} Wherei 
X must be prestored in register P 



ANALYSIS C O N V A I R PAGE 15 

PREPARED BY L. Barton * •»««« •«<«*. orwiuc. co*m*muw report no. ZH-527 

checked by CSvift, D.Farker, D. Bielsker **" DIBG ° model ALL 

REVISED BY DATE 8/29/56 



Y ie the address of the last constant, A$, where the constants 

are floating point numbers stored each in- two cells - mantissa, 

exponent - consecutively, Aq, Ajl, + ••• ♦ Ajj. 

8 is the degree of the equation. 

Tba ansver appears in R. 

If N is less than one, no operation will be performed* 

R and G will contain the ansver* 

s and B will contain Mq 

P will contain X 

N will be aero 

The double extension of the mantissa of the ansver vill also be In 

the accumulator • 



rOMM IBU-A 



"IS35o~ 



CO 
CO 



I 

p 
I 



X 



C O N V A I R 

: a mvuw* tr «oupuul onuuncs cotfounoii 
. „, j SAN D1EOO 

checked by G.Swift, i^.Parker, BfBielsker 

REVISED BY ; 



ANALYSIS 

PREPARED BY L. Barton 



PAGE 16 

REPORT NO. ZM~5?7 

MODEL ALL 

DATE 8/?9/56 



Commands and Registers 



Card Instructions 



U 57 KUK YYYY3 

■ ■■ i 

Reafy N cards (M is NN with the rightmost bit of K) into cells con- 

f ' 

secutively starting at Y in normalized floating point form. 

14 56 KM Yim 

Punch S cards (N is NK with the rightmost bit of K) from cells con- 
secutively starting at I where numbers are stored in normalized 
floating point form. 

Registers 

Register N will contain the number N unchanged. 

Register G will contain the first word stored at Y. In the case of 

read or punch this will be the contents of Y before read or punch 

- R, S, P, and B will be unchanged.* Register C cannot be punched 

by a 14 instruction since Y is placed in C at the start of all 14 

interpretations* 

Return jump card options 

Card read 

37 77400 77401 
AB UU1JUU WWV 

A. If a is equal to 4,5,6 or 7 do not print sum, otherwise print a 
sum which is characteristic of those cards. 

B. If B is equal to 4,5,6 or 7 read in mantissas as integers to 
the zero, scale factor, and store them in single consecutive cells. 
Ignore all exponents. Otherwise read in and store normal flosting 
point numbers in normalized form. 

UUUUU Address for storage of the first data word. 



ANALYSIS C O N V A I R PACK 17 

PREPARED BY L. Barton *«*««■ o»mm«aidwiaiuc»co«w*mi©ii REPORT NO. ZM- 5 ^7 

checked by C. Swift, D.Parker, D.ftLelsker 0AHOlwao model ALL 

REVISED BY DATE 8/29/56 



WWV Rumber of floating point numbers to bs read or with option 

number of mantissas stored as integers* 
Card output 

37 76760 76761 

AB UtJWJUVvWf^ 

A* If A is equal to 4. 5*6 or 7 the cards will not be numbered. 

otherwise they will be numbered starting at one. Oell 77303 con- 

tains this oounter and may be set at one less than the next positive 

card number desired* 

8 Is not used* 

OTJUff Is the storage address of the first mantissa 

VWV? Is the number of floating point numbers to be punched* 
Coding Rotes 

In oase of Bull failure set PAK equal tot 

77430 for read, or 

77007 for write. 

BS will be restored followed by a 56 stop with the V address that 

of the interrupted card instruction* 

If cards are not primed at start of programi 

17 00Q00 77433 will advance one read card. 

17 00000 77342 will advance one punch card 

17 00000 77413 will advance one read oard and one punch oard 

If the mantissa is sero after any arithmetic operation the exponent 

will be set equal to ssro* During card read the exponent of a sero 

mantissa will be retained* 



v^m 



Q*MfSt*-A "" """" 



ANALYSIS C O N V A I R PAOE 18 

PREPARED BY *>• Barton *9tnu9* wcncx*. bynmhcs cmpomhm REPORT IRQ, ZM-527 

checked by C.Swift, D.Parker, D.Blelaker**" "" 50 model AI4k 

REVISED BY DATE 8/29/56 



In punching or waiting cards if an un-normalized mantissa or an 
exponent with abaoluts value above 513 octal in any series is to be 
Jiinohed, that number will be punched as negative zero. In this 
last case an alarm lining («f ) f the address of the first such 
number in any card instruction and its mantissa will be made on the 
typewriter but the program will continue, the ^maximum absolute value 
of exponents punched on cards is 98 or 99 depending on the mantissa 
value. 

In reading cards a punch in column number one and row number twelve 
df any card will act as a flag and terminate the read instruction 
at the end of that card with a normal return to the program. If N 
Is exhausted first an exit will occur. If it is desired to read a 
large number of cards with only a flag termination without regard 
to N, change the Instruction at address 77445 to 11 01006 01314 
Card Form Columns $ 

6, 21, 36, §1, 66 decimal point punched in card 

7 - 16, 22-31, 37-46, $2-61,-67-76, ten decimal digit mantissas. 

17, 32, 47, 62 77 sign of the mantissas. 

18 -'IV 33 - 34, 48 - 49, 63-64, 78-79, exponents (power of ten) 

range - 99 to 99 

20, 35, 50, 65, 80 signs of exponent. 



t rv f\c!(\ 



CO N V A I R 



ANALYSIS 

prepared by L. Barton ■Ammm»mu^wmum^m^mm 

checked by C. Swift, tUFarker, D.Eielsker 

REVISED SY 



Ctf-183 
page 19 
REPORT NO. ZH-527 
MODEL ALL 
DATE 8/29/56 



Codas end Exits Available For Subroutines 
Two address references froa K, S« Uhlffletree 



Oode 


tf Address of 


V Address of 


10, 30* 




01632 


U, 31* 


01632 




12, 32* 




01631 


13, 33* 


01631 




14, 34* 




01627 


15, 35* 


01627 




16, 36* 




01626 



Note that the 10 to 17 series will set to prevent storage of the 
result, in !♦ 

One address reference* froa S. S, tfeiffletree 





Code 






tf address of 


V Address of 




60, 61, 


62, 


63 




01527 




64, 65, 


66, 


67 


01527 






70 








01505 




71 






01505 






72 








01504 




73 






01504 






U 








01531 






One address references from drum WhiffLetree 




Code 






address of 


V address of 




40 








76122 




u 






76122 






42 








76121 










/oAia 




KM »•»■•* 








10-260 





C O N V A I R 



ANALYSIS 

PREPARED BY L. Barton *»in«oii <m.«««al oyj.«i« co«pomtioi. 

checked by C.Swift, D.Farker, D.Eielsker 

REVISED BY 



PAGE 20 

REPORT NO. ZM-527 

MODEL ALL 

DATE 8/29/56 



Code 
44 
45 
46 

50 
51 
52 
53 
54 
55 



D Address of 



7613# 



76116 



76113 



76112 



76110 



V Address of 
76117 

76116 

76113 

76112 



76U0 



The drun whiffle tree stores £, S. f transfers Itself to S» S,, sod 

Jumps to the chosen address* 



V * 4.<L*0 



-C O N V A I R 

a Mvtnoa or •mn *l dynamics cokpomtioh 
SAN DIEGO 

checked by c.Sv/ift, D.rarker , D. Fielder 

REVISED BY 



ANALYSIS 

prepared BY L. Barter 



PAGE 21 
REPORT NO. 2-14-5^7 
MODEL ALL 

DATE 8/P9/56 



'■ 


SPUR ACCURACY T5STS: 
20,000 Operations 






07,21 i 


Octal 




Number in 


2^6033531747 / r/7777777774 




Number out 


246033536705 / 777777777774 
Decimal 




Number in 


.8108108108 01- 




Number out 


.8108109027 01- 




04,01: 


Octal 




Number in 


400000000012 / 000000000005 




Number out 


400000077460 / 000000000005 
Decimal 




Number in 


.3199999998 - 02 




Number out 


.3199996967 - 02 




03,22 


Octal 




Number in 


207002533507 / 000000000000 




Number out 


207002543105 / 000000000000 
Decimal 




Number in 


.5273641890 00 




Number out 


.5273643007 00 




8th degree palynoraial: 


Exact Computed 
1330157 1330156.999 
231285 231284.9999 
24835 24834.99999 




. . . 


in-269 



C O N V A I R 



ANALYSIS 

PREPARED BY L . J3ar ton * *****•• w «mn«. orMNic* cowouitOR 

checked by c. Swift, D.Parker, D.Eielsker 

REVISED BY 



CO 
CO 



I 

o 

I 

o 
o 
o 



X 
Q-, 



PAGE 22 
REPORT NO. ZM-527 
MODEL. ALL 
DATE 8/29/56 



SPUR time toetaj 




Command 


Tlaa (Millieecounda) 


U/ 00 


3.84 


04 


5.69 


20 


3.95 


24 


5.73 


01 


3.80 


05 


5.74 


21 


3.90 


2$ 


5.80 


02 


3.49 


06 


5.33 


22 


3.48 


26 


5.28 


03 


3.65 


07 


5.45 


23 


3.71 


27 


5.60 


17 


3.81 


76 


1.47 


77 


1.47 


75 
17 017A6 01706 (ComDaraKU to Hi 


27.0 (For 8th dagrea poly.) 
22) 1.73 bub. 



37 017U 01633 (Comparable to 1403) *M bub. 



U\-VL'A 



CV-103' 



C O N V A 1 R 

A DIVISION OF GENERAL DYNAMICS CORPORATION 

SAN DIEGO 




PFPnPT 2M 527-11 
DATE 9-6^ 6 



MODEL All 



TITLE 

SPUR 



Single Precision Unpacked Rounded 
Floating Point Package for 



ERA 1103 Computer 



Part II Codes 



PREPARED BY 



L. W-i 3arton 



CHECKED BY 



C. J.-Svlft, D. Parker 
D. Bielsker 



GROUP Digital finmpHting T.nh, 



REFERENCE. 



APPROVED BY 



NO. OF PAGES, 



27 



NO. OF DIAGRAMS. 



REVISIONS 



NO. 



DATE 



BY 



CHANGE 



PAGES AFFECTED 



FORM IAI2A-4 



10-264 



00 
CO 



I 

o 

I 

O 

o 






SPUR ACTIVATION 



76000 


01760 


45 


00000 


30000 


EXIT 


76001 


01761 


11 


76012 


00000 


SET F 


76002 


01762 


11 


76013 


00001 


SET F 1 


76003 


01763 


75 


30020 


01765 


THIS TO 


76004 


01764 


11 


76000 


01760 


ES 


76005 


01765 


75 


30260 


01767 


SPUR TO 


76006 


01766 


11 


76500 


01500 


ES 


76007 


01767 


16 


01760 


01770 


SET EXIT 


76010 


01770 


75 


10020 


30000 


CLEAR 


76011 


01771 


11 


01750 


01760 


EXIT 


76012 


01772 


45 


00000 


00700 


F 


76013 


01773 


45 


00000 


01547 


F 1 



reportzm 527-H 

MODEL All 

date 9-6-56 



10-265 



CONVAiR - DIVISION Of GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



: f ; . "'CV-183 ■ 

PAGE 2 

REPORT ZM 527-11 

MODEL All 

9-6-56 



DATE 



SPUR DRUM WHIFFLE TREE 



76100 




75 


31777 


76102 




STORE 


76101 




11 


00001 


74001 




ES 


76102 




75 


30045 


00004 




THIS TO 


76103 




11 


76104 


00004 




ES 


76104 


00004 


44 


00005 


00014 


WHIFFLETREE 


76105 


00005 


44 


00006 


00011 






76106 


00006 


44 


00007 


00010 






76107 


00007 


44 


00023 


00036 


CARD READ WRITE 


76110 


00010 


44 


30000 


30000 


55 


54 


76111 


00011 


44 


00012 


00013 






76112 


00012 


44 


30000 


30000 


53 


52 


76113 


00013 


44 


30000 


30000 


55 


50 


76114 


00014 


44 


00015 


00020 






76115 


00015 


44 


00016 


00017 






76116 


00016 


44 


30000 


30000 


47 


46 


76117 


00017 


44 


30000 


30000 


45 


44 


76120 


00020 


44 


00021 


00022 






76121 


00021 


44 


30000 


30000 


43 


42 


76122 


00022 


44 


30000 


30000 


41 


40 


76123 


00023 


"75 


30352 


00025 




CARD READ 


76124 


00024 


11 


77400 


00742 




TO ES 


76125 


00025 


16 


01746 


00770 


SET EXIT 


76126 


00026 


16 


01746 


00742 




SET 


76127 


00027 


31 


00742 


00000 




FAULT 


76130 


00030 


36 


01264 


77432 




REPEAT 


76131 


00031 


31 


01761 


00002 




ASSEMBLE 


76132 


00032 


35 


01761 


00742 




PARAMETER 


76133 


00033 


15 


01601 


00742 




WORD 


76134 


00034 


16 


00032 


00763 


SET ACQUISITION 


76135 


00035 


45 


00000 


00762 






76136 


00036 


75 


30400 


00040 




CARD WRITE 


76137 


00037 


11 


76760 


00745 




TO ES 



10-266 



CO 
CO 



I 

o 

r— I 
I 

o 
o 

c> 



X 

a, 



report ZM 5?7-II 

MODEL All 
DATE 9-6-^6 



76140 


00040 


16 


01746 


00772 


SET EXIT 


76141 


00041 


16 


01746 


00745 


SET 


76142 


00042 


31 


00745 


00000 


FAULT 


76143 


00043 


36 


01310 


77011 


REPEAT 


76144 


00044 


31 


01761 


00002 


ASSEMBLE 


76145 


00045 


35 


01761 


00745 


PARAMETER 


76146 


00046 


15 


01601 


00745 


WORD 


76147 


00047 


16 


00045 


00764 


SET ACQUISITION 


76150 


00050 


45 


00000 


00764 





10-267 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-18b 

PAGE 4 

REPORT ZM 527-11 

MODEL All 

date 9-6-56 
Revised 10-20-56 



SPUR ES PACKAGE 



76500 


01500 


44 


30064 


30060 




76501 


01501 


44 


01516 


01530 




76502 


01502 


44 


01501 


01503 




76503 


01503 


44 


01504 


01505 




76504 


01504 


44 


30073 


30072 




76505 


01505 


44 


30071 


30070 




76506 


01506 


44 


01502 


01500 




76507 


01507 


11 


01750 


01770 


ONf /pORf^S //vST, 


76510 


01510 


16 


01760 


01770 


APDK?5 3 


76511 


01511 


55 


10000 


00016 




76512 


01512 


51 


01756 


01761 


jx/t'M^G'R M 


76513 


01513 


55 


01760 


10014 




76514 


01514 


37 


01603 


01570 


SrT AfORt^S TA&S 


76515 


01515 


44 


01506 


76100 


E S" OR MP 


76516 


01516 


15 


01527 


01524 


SET 


76517 


01517 


16 


01564 


01526 


b 1 


76520 


O1520 


44 


01521 


01523 




76521 


01521 


15 


01541 


01524 


SET 


76522 


01522 


16 


01566 


01526 


fc> £— - 


76523 


01523 


55 


01761 


10001 


2 N 


76524 


01524 


21 


30000 


01752 


bji + 2 


76525 


01525 


42 


10000 


01747 


JUMP TO Y 


76526 


01526 


11 


01750 


30000 


CLEAR 


76527 


01527 


45 


01776 


01746 


JUMP TO HI 


76530 


01530 


15 


01601 


01537 


ste-t Y ACPf^SS 


76531 
76532 
76533 

76534 


01531 
01532 
01533 
01534 


44 
37 
11 
11 


01533 
01742 
01764 
01765 


30074 
01617 
01766 
01767 


A (2-C.v M ouAT £ MO«*T 


76535 


01535 


23 


01537 


01753 


55 T G f° 


76536 
76537 


U X -' -j 

015 3 7 


75 
11 


'3 0002 
3 0000 


01340 
01772 








CO 



I 

o 

r— ( 
I 

o 

o 



a, 



REPORT 2ft $27^H 
MODEL Q\ 

date 9^6-56 
Revised 10-20-56 



76540 


01540 


41 


01761 


01532 


TEST DEGREE 


7 6 5 41 


01541 


45 


01777 


01745 






76542 


01542 


11 


01774 


01770 






76543 


01543 


11 


01775 


01771 






76544 


01544 


37 


01741 


01655 


R 


SUB X TO R 


76545 


01545 


75 


30002 


01616 




REPLACE 


76546 


01546 


11 


01772 


01774 




R 


76547 


01547 


16 


00000 


01746 


INTERPRET ENTRANCE 


76550' 


01550 


31 


00000 


00000 






76551 


01551 


34 


01751 


00017 






76552 


01552 


15 


20000 


01553 






76553 


01553 


11 


30000 


01760 


STORE INST. 


76554 


01554 


55 


01760 


10006 






76555 


01555 


44 


01507 


015 56 


ONE OR TWO ADDRESS 


76556 


01556 


11 


01760 


10000 






76557 


01557 


51 


01757 


01770 


Y 


ADDRESS 


76560 


01560 


5 5 


10000 


00030 






76561 


01561 


51 


01757 


01766 


X 


ADDRESS 


76562 


01562 


55 


01760 


10014 






76563 


01563 


44 


01564 


01565 






76564 


01564 


21 


01766 


01776 


X 


Bl 


76565 


01565 


44 


01566 


01567 






76566 


01566 


21 


01766 


01777 


X 


132 


76567 


01567 


55 


10000 


00012 






76570 


01570 


44 


01571 


01572 


ENT FROM ONE AD 


76571 


01571 


21 


01770 


01776 


Y 


Bl 


76572 


01572 


44 


01573 


01574 






76573 


01573 


21 


01770 


01777 


Y 


B2 


76574 


01574 


16 


01770 


01747 




SET 


76575 


01575 


16 


01770 


01744 




Y JUMP 


76576 


01576 


31 


01770 


00017 




AND 


76577 


01577 


15 


20000 


01601 




TRANSFERS 



10-269 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE £ 

REPORT ZH 527-11 
MODEL A11 
DATE 9.6-56 



76600 


01600 


75 


30002 


01602 


Y TO 


76601 


01601 


11 


30000 


01770 


OP C 


76602 


01602 


55 


01760 


10007 




76603 


01603 


37 


01603 


01604 


EXIT FOR ONE AD 


76604 


01604 


11 


01774 


01772 


R TO 


76605 


C1605 


11 


01775 


01773 


S 


76606 


01606 


44 


01610 


01607 




76607 


01607 


21 


01742 


01752 


NO TRANSMIT 


76610 


01610 


31 


01766 


00017 




76611 


01611 


15 


20000 


01613 




76612 


01612 


75 


30002 


01614 


X TO 


76613 


01613 


11 


30000 


01766 


OP B 


76614 


01614 


44 


01624 


01615 




76615 


01615 


44 


01620 


01621 




76616 


01616 


46 


01747 


01746 


Y OR Nl JUMP 


76617 


01617 


75 


00001 


01706 


JUMP TO MULT 


76620 


01620 


16 


01623 


01741 


SET FOR ACCUMULATE 


76621 


01621 


44 


01622 


01623 




76622 


01622 


44 


01633 


01706 


DIVIDE MULT* 


76623 


01623 


44 


01655 


01656 


SUB.t ADDt 


76624 


01624 


44 


01625 


01630 




76625 


01625 


44 


01626 


01627 




76626 


01626 


44 


01542 


30016 


TJt 16 


76627 


01627 


44 


30015 


30014 


15» 14 


76630 


01630 


44 


01631 


01632 




76631 


01631 


44 


30013 


30012 


13# 12 


76632 


01632 


44 


30011 


30010 


lit 10 


76633 


01633 


54 


01766 


20001 


TEST FOR DIVISOR DIVISION 


76634 


01634 


43 


20000 


77752 


ZERO OR UNNORMALIZED 


76635 


01635 


11 


01771 


20000 


EXPONENT 


76636 


01636 


36 


01767 


01775 


DIFFERENCE 


76637 


01637 


12 


01770 


20000 


COMPARE 



10-270 



report 2M 527-11 

MODEL A H 
DATE 9.6-56 





76640 


01640 


12 


01766 


10000 


MANTISSA 




76641 


01641 


36 


10000 


20000 


SIZE 




76642 


01642 


46 


01643 


01645 






76643 


01643 


54 


01770 


20043 


SHIFT 




76644 


01644 


45 


00000 


01647 


OR ADJUST 




76645 


01645 


21 


01775 


01751 


EXPONENT 




76646 


01646 


54 


01770 


20042 


AND SHIFT 




76647 


01647 


73 


01766 


01774 


DIVIDE 




76650 


01650 


32 


01750 


00001 


TEST 




76651 


01651 


12 


01767 


10000 


FOR 




76652 


01652 


42 


10000 


01734 


ROUND 




76653 


01653 


21 


01774 


01751 


ROUND 




76654 


01654 


45 


00000 


01730 






76655 


01655 


13 


01766 


01766 


SUBTRACTION 




76656 


01656 


11 


01767 


01775 


ADDITION 




76657 


01657 


23 


10000 


10000 


CLEAR At Q 




76660 


01660 


16 


10000 


01700 


ERASE SHIFT 




76661 


01661 


43 


01770 


01700 


Y ZERO TEST 




76662 


01662 


43 


01766 


01676 


X ZERO TEST 




76663 


01663 


23 


01767 


01771 


EXPONENT DIFFERENCE 




76664 


01664 


12 


20000 


20000 






76665 


01665 


42 


01755 


01670 


36 COMPARISON 




76666 


01666 


41 


01767 


01700 


Y OR X 


CO 


76667 


01667 


45 


00000 


01676 




CO 

r-H 


76670 


01670 


16 


20000 


01700 


SET SHIFT 


1 

O 

r-H 


76671 


01671 


41 


01767 


01674 


Y OR X 


1 

O 
O 


76672 


01672 


11 


01766 


10000 


X TO Q 


r— 1 


76673 


01673 


45 


00000 


01677 




0. 


76674 


01674 


11 


01770 


10000 


Y TO Q 




76675 


01675 


75 


00001 


01700 






76676 


01676 


11 


01771 


01775 


Y EXP 




76677 


01677 


11 


01770 


01766 


Y TO X 



10-271 



CONVAiR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO, CALIFORNIA 



CV-183 

PAGE 8 

report zm 5?7 II 

MODEL All 

date 9-6-56 



76700 


01700 


54 


01766 


30000 


SHIFT X 


76701 


01701 


35 


10000 


01774 




76702 


01702 


45 


00000 


01713 


TO NORMALIZE 


76703 


01703 


23 


01775 


01755 


A LEFT 


76704 


01704 


54 


01774 


00044 


NOT SIGNIFICANT 


76705 


01705 


47 


01714 


01734 


ZERO TEST 


76706 


01706 


11 


01771 


20000 


MULTIPLICATION 


76707 


01707 


35 


01767 


20000 


ADD EXPONENTS 


76710 


01710 


36 


01754 


01775 




76711 


01711 


71 


01770 


01766 


PRODUCT 


76712 


01712 


11 


20000 


01774 


TEST 


76713 


01713 


43 


20000 


01703 


EXTENTION 


76714 


01714 


11 


01750 


01762 


CLEAR FOR SF 


76715 


01715 


11 


01751 


10000 


POS« FLAG 


76716 


01716 


46 


01717 


01720 


SIGN 


76717 


01717 


13 


10000 


10000 


NEG# FLAG 


76720 


01720 


11 


10000 


01763 


FOR ROUNDING 


76721 


01721 


74 


20000 


01762 


SCALE FACTOR 


76722 


01722 


11 


20000 


01774 




76723 


01723 


46 


01724 


01725 


ADJUST 


76724 


01724 


13 


10000 


10000 


FOR SIGN 


76725 


01725 


21 


01775 


01762 


ADJUST FOR SF 


76726 


01726 


44 


01727 


01734 




76727 


01727 


21 


01774 


01763 


ROUND 


76730 


01730 


43 


20000 


01734 


OVERFLOW TEST 


76731 


01731 


32 


01750 


00107 


ADJUST 


76732 


01732 


11 


20000 


01774 


FOR 


76733 


01733 


21 


01775 


01751 


OVERFLOW 


76734 


01734 


11 


01774 


20000 


ZERO 


76735 


01735 


47 


01737 


01736 


TEST 


76736 


01736 


11 


20000 


01775 


ERASE EXPONENT 


76737 


01737 


75 


30004 


01741 


SET FOR 



10-272 



FORM MO. ■e.»T.^ ■*..■■$ ■ F 



LUNVAiK — UlVi^iMN Uf UMMfeKAL DYNAMICS CORP. 

SAN DIEGO. CALIFORNIA 



PAGE 9 

report zm '527-II 

MODEL £T_^ 
DATE 996-56 

Reviad 10-20-56 



3. 



t 

o 



t 



76740 


01740 


11 01772 01764 


ITERATION 


7&741 


01741 


S? 01741 01742 


FOR ITERATION 


76742 


01742 


'37 01742 _ 01743 


for bypass 


7*743 


0174$ 


75 3mm 01749 


STORE \ 

R 'TO 4. 


76744 . 


: 01744 


11 01774 01774 


74745 


01745 


45 00000 0174$ 


for trace ' 


76746 


01746 


45 00000 30000 


T0 NEXT !N$T# 


7674? 


61747 


45 00000 30000 


to y 


76750 


01750 


00 00000 00000 


CONSTANTS 


76751 


01751 


00 00000 00001 




76752 


01752 


00 00000 00002 




76753 


01753 


00 00002 00000 




767S4 


; 01754 


00 00000 00043 




76755 


. 01755 


00 00000 00044 




76756 


. 01T56 


00 00000 00177 




76757 


01757 


00 00000 01777 


CONSTANTS 




01760 


00 00000 00000 


I FOR INSTRUCTION 




0*7*1 


00 00000 00000 


H COUNTER 




01761 


oo ooooo 00000 


TEMPORARY 




0***S ' 


00 00000 00000 


TEMPORARY 




017&4 


00 00000 00000 


P FOR OPERAND 




01765 


00 00000 00000 


STORAGE FOR ITERATION 




017&6 


.00 00000 00000 


8 FO 




01767 


00 00000 00000 


X OPERAND 




01770 


00 00000 00000 


C FOR 




01771 


00 00000 00000 


Y OPERAND 




01772 


00 0G000 00000 


S FOR OPERAND 




01773 


00 00000 00000 


STORAGE FOR ITERATION 




01774 


00 00000 00000 


R FOR 




01775 


00 00000 0OGO0 


THE RESULT 




01776 


00 00000 00000 


1 INDEX 




01777 


00 00000 00000 


2 REGISTERS 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 10 

REPORT ZM 5?7-]l 

MODEL All 
DATE 9-6-56 



SPUR CARD OUTPUT 



76760 


00745 


56 


00000 


30000 




76761 


00746 


75 


31777 


76763 


STORE 


76762 


00747 


11 


00001 


74001 


E S 


76763 


00750 


75 


30400 


00752 


ROUTINE 


76764 


00751 


11 


76760 


00745 


TO E S 


76765 


00752 


31 


00745 


00000 


SET 


76766 


00753 


36 


01310 


77011 


REPEAT 


76767 


00754 


16 


00745 


00772 


SET 


76770 


00755 


21 


00772 


01310 


EXIT 


76771 


00756 


55 


00745 


20025 


MODIFY 


76772 


00757 


44 


00761 


00760 


E S 


76773 


00760 


32 


00777 


00000 


ADDRESSES 


76774 


00761 


55 


20000 


00017 


TO STORAGE 


76775 


00762 


37 


00762 


00763 




76776 


00763 


16 


20000 


00764 


ACQUIRE 


76777 


00764 


71 


01310 


30000 


CONTROL WORD 


77000 


00765 


55 


20000 


00006 


EXAMINE 


77001 


00766 


37 


00762 


00757 


FOR E S 


77002 


00767 


55 


20000 


00017 


ADDRESSES 


77003 


00770 


37 


01001 


01006 


TO SUBROUTINE 


77004 


00771 


11 


01270 


77303 


STORE CARD NUMBER 


77005 


00772 


75 


31777 


30000 


RESTORE 


77006 


00773 


11 


74001 


00001 


E S 


77007 


00774 


75 


31777 


77011 


RESTORE 


77010 


00775 


11 


74001 


00001 


E S 


77011 


00776 


30 


00000 


00000 


REPEAT 


77012 


00777 


74 


00000 


00000 


E S STORAGE 


77013 


01000 


30 


00000 


00000 


REPEAT LAST INST 


77014 


01001 


45 


00000 


30000 


EXIT 


77015 


01002 


16 


01001 


01005 




77016 


01003 


21 


01001 


01310 




77017 


01004 


36 


01344 


01000 





10-274 



' "~ t - XX 

report 2M 527-11 

MODEL ^21 

date 9-6-56 



CO 
CO 



I 

o 

I— I 

I 

o 
o 
a- 



x 



77020 


01005 


71 


01310 


30000 




77021 


01006 


15 


20000 


01026 


FIRST ADDRESS 


77022 


01007 


13 


20000 


01347 


FLAG 


77023 


01010 


11 


01310 


01350 


FLAG 


77024 


01011 


31 


20000 


00025 


EXTRACT 


77025 


01012 


31 


20000 


00063 


AND STORE 


77026 


01013 


36 


01310 


01351 


N-l 


77027 


01014 


46 


01001 


01015 


TEST FOR ZERO 


77030 


01015 


17 


00000 


01327 


PICK WRITE CARD 


77031 


01016 


31 


01351 


00000 




77032 


01017 


11 


20000 


01352 


N-l PER CARD 


77033 


01020 


11 


01325 


10000 


WRITE 


77034 


01021 


42 


01342 


01024 




77035 


01022 


11 


01305 


01352 


5 PER CARD 


77036 


01023 


11 


01324 


10000 


WRITE AND PICK CARD 


77037 


01024 


17 


00000 


10000 


CARD INSTRUCTION 


77040 


01025 


75 


30012 


01027 


5 WORDS TO 


77041 


01026 


11 


30000 


01353 


STORAGE 


77042 


01027 


75 


10045 


01031 


CLEAR FOR 


77043 


01030 


11 


01307 


01376 


CARD IMAGE 


77044 


01031 


15 


01266 


01050 


SET ACQUISITION 


77045 


01032 


11 


01340 


01374 


BIT 


77046 


01033 


11 


01265 


01375 


BIT INSTRUCTION 


77047 


01034 


41 


01347 


01047 


IDENT NUMBER TEST 


77050 


01035 


11 


01332 


01374 


BIT 


77051 


01036 


21 


01270 


01310 


COUNT CARDS 


77052 


01037 


42 


01315 


01041 


SIZE OF WORD 


77053 


01040 


31 


01341 


00000 


SET 99999 


77054 


01041 


32 


01307 


00043 


INTEGER 


77055 


01042 


32 


01265 


00000 


TO 


77056 


01043 


73 


01315 


01365 


FRACTION 


77057 


01044 


54 


01365 


00001 


i.2 EXP 36 



10-275 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 12 

REPORT 2M 5"7-H 

MODEL A ll 

date 9-6-56 



77060 


01045 


11 


01305 


01376 


N-l DIGITS 


77061 


01046 


37 


01200 


01165 


IOENT NUMBER 


77062 


01047 


75 


30002 


01053 


MANTISSA 


77063 


01050 


11 


30000 


01365 


AND EXPONENT 


77064 


01051 


11 


01307 


01366 


ZERO EXPONENT 


77065 


01052 


45 


00000 


01156 




77066 


01053 


li 


01365 


01370 


MANTISSA SIGN FLAG 


77067 


01054 


12 


01366 


20000 


EXPONENT 


77070 


01055 


42 


01301 


01067 


FLOATING TEST 


77071 


01056 


41 


01350 


01062 


FIRST TIME 


77072 


01057 


11 


01264 


01370 


MANTISSA FLAG 


77073 


01060 


75 


10002 


01156 


SET EQUAL 


77074 


01061 


11 


01307 


01365 


TO ZERO 


77075 


01062 


13 


01322 


01350 


SET ALARM FLAG 


77076 


01063 


11 


01026 


01345 




77077 


01064 


15 


01050 


01065 


ACQUIRE 


77100 


01065 


11 


30000 


01346 


MANTISSA 


77101 


01066 


45 


OOOro 


01057 




77102 


01067 


21 


1 ? 6 5 


01307 




77103 


01070 


47 


01071 


01051 


ZERO MANTISSA 


77104 


01071 


46 


01072 


01073 




77105 


01072 


13 


01365 


01365 


NEGATIVE MANTISSA 


77106 


01073 


16 


01323 


01123 


SET SHIFT TO 33 


77107 


01074 


32 


01307 


00001 


EXP 36 


77110 


01075 


43 


20000 


01056 


FLOATING TEST 


77111 


01076 


11 


01307 


01373 


CLEAR FOR DECIMAL EXP 


77112 


01077 


11 


01366 


20000 


EXPONENT 


77113 


01100 


46 


01101 


01117 


SIGN 


77114 


01101 


23 


01373 


01342 


10 EXP 5 ADJUSTMENT 


77115 


01102 


11 


01307 


01372 


CLEAR FOR 74 


77116 


01103 


71 


01315 


01365 


X 10 EXP 5 


77117 


01104 


74 


20000 


01372 





10-276 



REPORT ZM 527 II 
MODEL All 

date 9-6-56 



CO 
CD 



I 

O 
i— i 

o 
o 
o 






77120 
77121 
77122 
77123 
77124 
77125 
77126 
77127 
77130 
77131 
77132 
77133 
77134 
77135 
77136 
77137 
77140 
77141 
77142 
77143 
77144 
77145 
77146 
77147 
77150 
77151 
77152 
77153 
77154 
77155 
77156 
77157 



01105 
01106 
01107 
OHIO 
01111 
01112 
01113 
01114 
01115 
01116 
01117 
01120 
01121 
01122 
01123 
01124 
01125 
01126 
01127 
01130 
01131 
01132 
01133 
01134 
01135 
01136 
01137 
01140 
01141 
01142 
01143 
01144 



11 20000 
46 01107 
21 01365 
43 20000 
31 01365 
11 20000 
21 01372 
21 01366 
46 01101 
31 01366 
73 01323 
11 20000 
55 01365 
45 00000 
31 01365 
11 20000 

34 20000 
11 20000 
75 20013 
42 01310 
51 01330 
31 01311 
36 10000 

35 01373 
31 10000 
35 01263 

30 00000 
11 10000 

31 01365 

32 01371 
73 10000 
55 10000 



01365 
01114 
01310 
01114 
00107 
01365 
01310 
01372 
01116 
00000 
01367 
01366 
00001 
01152 
30000 
01371 
00044 
01365 
01426 
01131 
10000 
00000 
10000 
01373 
00017 
01137 
00000 
01372 
00044 
00000 
10000 
00001 



TEST FOR ROUND 
ROUND 
MANTISSA 
AND 
ADJUST 

ADJUST BSF 
SIGN OF BSF 
DIVIDE EXP 

BY 33 
EXPONENT REMAINDER 
MANTISSA 

MANTISSA SHIFT 
STORE AR 
ERASE 
STORE AL 
TEST FOR LARGER 
POWER OF TEN 

10 EXP 10 

INCREASE EXP 
N X 2 EXP 15 

ACQUIRE DIVISOR 

RESTORE 

A 
2 EXP 35 
2 EXP 36 



10-277 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO, CALIFORNIA 



CV-H53 
page i/ + 

REPORT Z M ??7-II 
MODEL A]l 

date 9-6-56 



77160 


01145 


31 


20000 


00001 


DETERMINE 


77161 


01146 


42 


01372 


01150 


LAST 


77162 


01147 


27 


10000 


01310 


BIT 


77163 


01150 


11 


10000 


01365 


ANSWER X 2 EXP 36 


77164 


01151 


37 


01151 


01152 




77165 


01152 


41 


01367 


01123 


HIGHER ORDER DIGIT 


77166 


01153 


16 


01366 


01123 


LOWER ORDER SHIFT 


77167 


01154 


37 


01151 


01123 


LOWER ORDER DIGIT 


77170 


01155 


11 


01373 


01366 


DECIMAL EXPONENT 


77171 


01156 


21 


01050 


01326 


STEP 


77172 


01157 


21 


01026 


01326 


STEP 


77173 


01160 


37 


01200 


01174 


SHIFT FOR PERIOD 


77174 


01161 


12, 


01366 


20000 


EXPONENT 


77175 


01162 


11 


01333 


01376 


TALLY 


77176 


01163 


73 


1 U 1 


01372 


DIGITS 


77177 


01164 


11 


O f- ''• '". :■"■• 

C > 1 'J U -J 


01371 


OF FXP 


77200 


01165 


31 


;'. i :5 6 b 


00002 


EXTi CT 


77201 


01166 


32 


01365 


00001 


ANt 


77202 


01167 


11 


20000 


01365 


PO ITION 


77203 


01170 


34 


20000 


00063 


DIGIT 


77204 


01171 


35 


01375 


01172 


ASSEMBLE INST 


77205 


01172 


30 


00000 


00000 


SET BIT 


77206 


01173 


37 


01173 


01174 




77207 


01174 


55 


01374 


00043 


SHIFT BIT 


77210 


01175 


44 


01176 


01177 




77211 


01176 


21 


01375 


01334 


ADVANCE FIELD 


77212 


01177 


41 


01376 


01165 


TEST FOR END 


77213 


01200 


37 


01200 


01201 




77214 


01201 


11 


01370 


10000 




77215 


01202 


44 


01203 


01205 




77216 


01203 


13 


01331 


20000 




77217 


01204 


37 


01173 


01171 


SIGN 



10-278 



report zm 527-H 

MODEL All 
DATE9_6_56 



77220 
77221 
77222 
77223 
77224 
77225 
77226 
77227 
77230 
77231 
77232 
77233 
77234 
77235 
77236 
77237 
77240 
77241 
77242 
77243 
77244 
77245 
77246 
77247 
77250 
77251 
77252 
77253 
77254 
77255 
77256 
77257 



01205 
01206 
01207 
01210 
01211 
01212 
01213 
01214 
01215 
01216 
01217 
01220 
01221 
01222 
01223 
01224 
01225 
01226 
01227 
01230 
01231 
01232 
01233 
01234 
01235 
01236 
01237 
01240 
01241 
01242 
01243 
01244 



55 01374 
37 01206 
31 01372 
37 01200 
31 01371 
37 01200 
11 01366 
37 01206 
37 01215 
41 01352 
11 01335 
21 01377 
21 01411 
21 01404 
21 01413 
21 01425 
21 01420 
16 01267 
16 01127 
15 01267 
55 30000 
77 00000 
77 10000 
77 10000 
23 01231 
23 01233 
23 01234 
41 01371 
23 01351 
46 01243 
41 01350 
75 10004 



00043 
01207 
00017 
01171 
00017 
01171 
01370 
01201 
01216 
01047 
01371 
01336 
01336 
01336 
01337 
01337 
01337 
01233 
01234 
01231 
00010 
10000 
30000 
30000 
01331 
01310 
01310 
01231 
01342 
01016 
01001 
01246 



SHIFT BIT 
TENS DIGIT 
UNITS DIGIT 



WORDS PER CARD 
SIT FOR 12 ROWS 



TEST FOR END OF CARD 
TEST FOR 

END 
FLOATING FLAG 



10-27 9 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 16 

REPORT 2M 527-11 

MODEL ^}2 

date 9_6„56 



77260 
77261 
77262 
77263 
77264 
77265 
77266 
77267 
77270 
77271 
77272 
77273 
77274 
77275 
77276 
77277 
77300 
77301 
77302 
77303 
77304 
77305 
77306 
77307 
77310 
77311 
77312 
77313 
77314 
77315 
77316 
77317 



01245 
01246 
01247 
01250 
01251 
01252 
01253 
01254 
01255 
01256 
01257 
01260 
01261 
01262 
01263 
01264 
01265 
01266 
01267 
01270 
01271 
01272 
01273 
01274 
01275 
01276 
01277 
01300 
01301 
01302 
01303 
01304 



61 00000 
11 01305 
55 01345 
31 01264 
52 01343 
30 00000 
55 10000 
41 01371 
37 01255 
55 01346 
61 00000 
11 01335 
37 01255 
45 00000 
55 01310 
61 00000 
21 01401 
00 01353 
00 01442 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 
00 00000 

00 ooooo 
00 ooooo 
00 ooooo 
00 ooooo 
00 ooooo 



01302 
01371 
10011 

ooooo 

01252 

ooooo 

00003 
01250 
01256 
10003 
01305 
01371 
01250 
01001 
10001 
01271 
01374 
00000 
01412 
00000 
00037 
00052 
00074 
00070 
00064 
00062 
00066 
00072 
00513 
00045 
00006 
00026 



CARD COUNTER 



10-280 



REPORT ZM 527-11 

MODEL All 

date 9-6-56 



CO 

co 



i 

o 

r— I 
I 

o 
o 
o 



X 

a, 



77320 


01305 


00 


00000 


00004 


77321 


01306 


00 


00000 


00143 


77322 


01307 


00 


00000 


00000 


77323 


01310 


00 


00000 


00001 


77324 


01311 


00 


00000 


00012 


77325 


01312 


00 


00000 


00144 


77326 


01313 


00 


00000 


01750 


77327 


01314 


00 


00000 


23420 


77330 


01315 


00 


00003 


03240 


77331 


01316 


00 


00036 


41100 


77332 


01317 


00 


00461 


13200 


77333 


01320 


00 


05753 


60400 


77334 


01321 


00 


73465 


45000 


77335 


01322 


11 


24027 


62000 


77336 


01323 


00 


00000 


00041 


77337 


01324 


00 


00000 


00112 


77340 


01325 


00 


00000 


00102 


77341 


01326 


00 


00002 


00000 


77342 


01F27 


00 


00000 


00110 


77343 


01330 


00 


00000 


00077 


77344 


01331 


00 


00001 


00000 


77345 


01332 


40 


00000 


00000 


77346 


01333 


00 


00000 


00011 


77347 


01334 


00 


00014 


00000 


77350 


01335 


00 


00000 


00013 


77351 


01336 


01 


00001 


00001 


77352 


01337 


00 


00100 


00100 


77353 


01340 


01 


00000 


00000 


77354 


01341 


00 


00003 


03237 


77355 


01342 


00 


00000 


00005 


77356 


01343 


00 


00000 


00007 


77357 


01344 


00 


00000 


00002 



EXCESS 



10-281 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE ,. '18 

REPORT z,M 527-11 

MODEL All 

DATE 9-6-56 
Revised 10-PO-56 



SPUR SUM AND MT INSTRUCTION 



70000 




45 


00000 


70006 


SROK FROM MT 3 


70001 




45 


00000 


70100 


FLIP FROM MT 3 


70002 




45 


00000 


71404 


SPUR FROM MT 3 


70003 




45 


00000 


77371 


SUM SPUR 


70004 




45 


00000 


77376 


CHANGE SUPUR SUM 


70005 




45 


00000 


70071 


ERA MA I NT. FROM MT 


77371 




31 


70000 


00000 


START SUM 


77372 




75 


23777 


77374 




77373 




32 


70001 


00000 




77374 




75 


21777 


71400 




77375 




32 


76000 


00000 




77376 




75 


00001 


77371 


CHANGE 


77377 




11 


10000 


77777 


SUM 


71400 




34 


77303 


00000 


REMOVE 


71401 




34 


77400 


00000 


VARIABLE 


71402 




75 


20013 


71426 


FROM 


71403 




34 


76110 


00000 


SUM 


71404 




11 


71423 


00000 


SET F 


71405 




75 


31777 


71407 


STORE 


71406 




11 


00001 


74001 


ES 


71407 




75 


30015 


00411 


THIS 


71410 




11 


71411 


00411 


TO ES 


71411 


00411 


64 


30001 


00000 


READ ONE BLOCK 


71412 


00412 


11 


00000 


20000 


TEST FOR 


71413 


00413 


43 


00425 


00421 


ZERO 13L0CK 


71414 


00414 


31 


71424 


00052 


PRINT 


71415 


00415 


61 


00000 


20000 


TAPE 


71416 


00416 


34 


20000 


00006 


ALARM 


71417 


00417 


47 


00415 


-00420 




71420 


00420 


56 


00000 


00411 


TRY AGAIN 


714 21 


00421 


66 


30400 


ooooo 


ADVANCE TO SPUR 


7 1 4 2 2 


004 2 2 


64 


3 0001 





READ IN FIRST BLOC 



10-282 



REPORT ZM 527-11 

MODEL All 

date 9-6-56 



CO 

co 



I 

o 



o 

o 



X 

a, 



77320 


01305 


00 


00000 


00004 


77321 


01306 


00 


00000 


00143 


77322 


01307 


00 


00000 


00000 


77323 


01310 


00 


00000 


00001 


77324 


01311 


00 


00000 


00012 


77325 


01312 


00 


00000 


00144 


77326 


01313 


00 


00000 


01750 


77327 


01314 


00 


00000 


23420 


77330 


01315 


00 


00003 


03240 


77331 


01316 


00 


00036 


41100 


77332 


01317 


00 


00461 


13200 


77333 


01320 


00 


05753 


60400 


77334 


01321 


00 


73465 


45000 


77335 


01322 


11 


24027 


62000 


77336 


01323 


00 


00000 


00041 


77337 


01324 


00 


00000 


00112 


77340 


01325 


00 


00000 


00102 


77341 


01326 


00 


00002 


00000 


77342 


01F27 


00 


00000 


00110 


77343 


01330 


00 


00000 


00077 


77344 


01331 


00 


00001 


00000 


77345 


01332 


40 


00000 


00000 


77346 


01333 


00 


00000 


00011 


77347 


01334 


00 


00014 


00000 


77350 


01335 


00 


00000 


00013 


77351 


01336 


01 


00001 


00001 


77352 


01337 


00 


00100 


00100 


77353 


01340 


01 


00000 


00000 


77354 


01341 


00 


00003 


03237 


77355 


01342 


00 


00000 


00005 


77356 


01343 


00 


00000 


00007 


77357 


01344 


00 


00000 


00002 



EXCESS 



10-281 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 1 '18 
REPORT ZM 5?7-ll 
MODEL All 
DATE 9-6-56 

Revised 10-PO-56 



SFUR SUM AND MT INSTRUCTION 



70000 




45 


00000 


70006 


70001 




45 


00000 


70100 


70002 




45 


00000 


71404 


70003 




45 


00000 


77371 


70004 




45 


00000 


77376 


70005 




45 


00000 


70071 


77371 




31 


70000 


00000 


77372 




75 


23777 


77374 


77373 




32 


70001 


00000 


77374 




75 


21777 


71400 


77375 




32 


76000 


00000 


77376 




75 


00001 


77371 


77377 




11 


10000 


77777 


71400 




34 


77303 


00000 


71401 




34 


77400 


00000 


71402 




75 


20013 


71426 


71403 




34 


76110 


00000 


71404 




11 


71423 


00000 


71405 




75 


31777 


71407 


71406 




11 


00001 


74001 


71407 




75 


30015 


00411' 


71410 




11 


71411 


00411 


71411 


00411 


64 


30001 


00000 


71412 


00412 


11 


00000 


20000 


71413 


00413 


43 


0042 5 


00421 


71414 


00414 


31 


7 1 h 2 4 


00052 


71415 


00415 


61 


00000 


20000 


71416 


00416 


34 


20000 


00006 


71417 


00417 


47 


00415 


-00420 


71420 


00420 


56 


00000 


00411 


71421 


00421 


66 


30400 


00000 


"7 1 /, <) 1 

/ x-\-c. C 


a rs 1. <-i <i 


64 


1 A A A "( 

'J \j u i 


A a A A A 

u u u u ^ 



SROK FROM MT 3 

FLIP FROM MT 3 

SPUR FROM MT 3 
SUM SPUR 

CHANGE SUPUR SUM 
ERA MA I NT. FROM MT 
START SUM 



CHANGE 

SUM 
REMOVE 

VARIABLE 
FROM 
SUM 
SET F 
STORE 

£S 
THIS 

TO ES 
READ ONE BLOCK 
TEST FOR 

ZERO BLOCK 

PRINT 
TAPE 

ALARM 

TRY AGAIN 
ADVANCE TO SPUR 



.0-28: 



SAN DIEGO. CALIFORNIA 



PAGE 18A 

REPORT ZM 5?7-ll 

MODEL All 

date 9-6-56 
Revised 10-20-56 



71423 00423 45 


00000 


00002 


JUMP TO FIRST BLOCK 


71424 00424 45 


01301 


52056 


FLEX TAPE 


71425 00425 45 


07777 


00002 


LOCATOR ON ZERO BLOCK 


71426 


34 


77432 


00000 


FURTHER 


71427 


34 


76760 


00000 


SUM 


71430 


34 


77011 


00000 


ADJUSTMENTS 


71431 


11 


20000 


20000 




71432 


11 


20000 


10000 


SUM TO Q 


71433 


36 


77777 


20000 


SUBTRACT STORED 


71434 


47 


71435 


71445 


SUM* TEST 


71435 


31 


71466 


00052 


SPUR FOR PRINT 


71436 


61 


00000 


20000 


PRINT 


71437 


34 


20000 


00006 


WORD 


71440 


47 


71436 


71441 




71441 


37 


71441 


71442 


SWITCH 


71442 


31 


71470 


00052 


- PRINT 


71443 


37 


71441 


71436 


NO SUM 


71444 


56 


10000 


71404 


TO R£AD FROM MT 


71445 


37 


71441 


71435 


PRINT SPUR 


71446 


31 


71467 


00052 


PRINT 


71447 


37 


71441 


71436' 


SUM OK 


71450 


56 


00000 


71451 


TO CLEAR 


71451 


75 


17000 


71453 


START CLEAR 


71452 


11 


20000 


40000 




71453 


75 


17000 


71455 




71454 


11 


20000 


47000 




71455 


75 


17000 


71457 




71456 


11 


20000 


56000 




71457 


75 


13000 


71472 




71460 


11 


20000 


65000 




71461 


75 


11777 


71463 




71462 


11 


20000 


00001 





CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 

SAN lilESO. CALIFORNIA 



CV-183 

PAGE 18 g 
REPORT 2jvj 527-11 
MODEL £-- 
DATE9. 6-56 

Revised 10-PO-56 



;, c -5, 


31 


71471 


00052 


PRINT 


l 5 4 


37 


71441 


71436 


CLEAR 


6, >, ^ 


57 


00000 


00000 




L 6 6 


45 


24153 


41204 


FLEX SPUR 


'-6 7 


24 


34070 


40336 


FLEX SUM OK 


^7": 


06 


03042 


43407 


FLEX NO SUM 


-:■ v I 


04 


16112 


03012 


FLEX CLEAR 


-', "/ '> 


75 


12000 


71461 


CLEAR 74000 




1 i. 


20000 


74000 


75777 



• /\-"9fl4 



KORM NO. E. T. - I \}>) 



SAN DIEGO. CALIFORNIA 



PAGE 19 

report ZM 527-IJ 

MODEL All 

DATE 9-6-56 



SPUR CARD INPUT 



CO 
CO 



I 

o 
o 



X 

a, 



77400 


00742 


56 


00000 30000 


EXIT 


77401 


00743 


75 


31777 77403 


STORE 


77402 


00744 


11 


00001 74001 


ES 


77403 


00745 


75 


30352 00747 


ROUTINE 


77404 


00746 


11 


77400 00742 


TO ES 


77405 


00747 


11 


00742 20000 


SET 


77406 


00750 


36 


01264 77432 


REPEAT 


77407 


00751 


35 


01305 20000 


SET 


77410 


00752 


16 


20000 00770 


EXIT 


77411 


00753 


55 


00742 20025 


TEST FOR 


77412 


00754 


44 


00757 00756 


ES 


77413 


00755 


00 


00000 00114 


ADDRESSES 


77414 


00756 


32 


00776 00000 


ADDRESS MODIFICATION 


77415 


00757 


55 


20000 00017 




77416 


00760 


37 


00760 00761 




77417 


00761 


16 


20000 00763 


SET ACQUISITION 


77420 


00762 


11 


00777 01024 


ERASE INSTRUCTION 


77421 


00763 


71 


01264 30000 


ACQUIRE CONTROL WORD 


77422 


00764 


55 


20000 00006 




77423 


00765 


37 


00760 00754 


X 


77424 


00766 


55 


20000 00017 




77425 


00767 


37 


01001 01004 


TP SIBRPITOME 


77426 


00770 


75 


31777 30000 


RESTORE E S 


77427 


00771 


11 


74001 00001 


AND EXIT 


77430 


00772 


75 


31777 77432 


RESTORE E S 


77431 


00773 


11 


74001 00001 


AND 


77432 


00774 


30 


00000 00000 


REPEAT 


77433 


00775 


02 


00000 00104 




77434 


00776 


74 


00000 00000 




77435 


00777 


11 


00000 00000 




77436 


' 01000 


30 


00000 00000 


REPEAT 


77437 


01001 


45 


00000 30000 


EXIT 



SAN DIEGO. CALIFORNIA 



PAGE 20 

REPORT ZM 527-11 
MODEL A H 
DATE 9-6-56 



77440 


01002 


16 


01001 


01003 




77441 


01003 


71 


01264 


30000 


ACQUIRE CONTROL WORD 


77442 


01004 


13 


20000 


01352 


PRINT SUM FLAG 


77443 


01005 


11 


01263 


01314 


CLEAR 


77444 


01006 


11 


01263 


01315 


CELLS 


77445 


01007 


16 


20000 


01314 


NUMBER OF WORDS N 


77446 


01010 


55 


20000 


00003 




77447 


01011 


13 


20000 


01351 


READ AS INTEGER FLAG 


77450 


01012 


31 


01255 


00000 


SET FINAL 


77451 


01013 


35 


01277 


01227 


TRANSFER 


77452 


01014 


11 


01305 


01356 


SET TRANSFER 


77453 


01015 


11 


01265 


01357 


STEPS 


77454 


01016 


44 


01017 


01022 




77455 


01017 


23 


01227 


01313 


MODIFICATINNS 


77456 


01020 


11 


01264 


01356 


FOR INTEGER 


77457 


01021 


23 


01357 


01261 


STORAGE 


77460 


01022 


55 


10000 


00021 


SET DATA 


77461 


01023 


16 


10000 


01230 


STORAGE 


77462 


01024 


21 


01001 


01264 


SET EXIT 


77463 


01025 


36 


01305 


01000 


SET REPEAT 


77464 


01026 


23 


01314 


01264 


N~l 


77465 


01027 


46 


01001 


01030 


EXIT IF N 


77466 


01030 


41 


01352 


01032 


SUM TEST 


77467 


01031 


61 


00000 


0130,3 


CARRIAGE RETURN 


77470 

1 


01032 


17 


00000 


01300 


READ AND PICK CARC 


77471 


01033 


11 


01260 


01350 


LINE DIGIT 9 


77472 


01034 


16 


01256 


01224 


SET TEMPORARY STORAGE 


77473 


01035 


75 


10011 


01037 


CLEAR 


77474 


01036 


11 


01263 


01316 


MATRIX 


77475 


01037 


76 


00000 


01361 




77476 


01040 


76 


10000 


10000 




77477 


01041 


76 


10000 


01360 





10-286 



FORM NO. E. T. - i Jl. r 



i^«* %vm 



SAN DIEGO. CALIFORNIA 



REPORT ZM 527-11 
MODEL All 

date 9-6-56 



CO 

co 



I 

o 

I— I 
I 

o 
o 
o 



a, 



77500 


01042 


37 


01042 


01043 




77501 


01043 


54 


01361 


00034 




77502 


01044 


11 


01257 


01054 


SET 1ST STORAGE 


77503 


01045 


11 


01304 


01327 


SET INDEX 3 


77504 


01046 


31 


01306 


00024 


2 EXP 35 


77505 


01047 


32 


01263 


00004 


SHIFT 4 


77506 


01050 


44 


01051 


01052 


TEST BIT 


77507 


01051 


32 


01350 


00000 


ADD LINE DIGIT 


77510 


01052 


46 


01053 


01047 


TEST DIGITS 9 


77511 


01053 


31 


20000 


00000 


CLEAR A LEFT 


77512 


01054 


30 


00000 


00000 


STORE MATRIX WORD 


77513 


01055 


21 


01054 


01307 


STEP STORAGE 


77514 


01056 


41 


01327 


01046 


4 TIMES 


77515 


01057 


37 


01057 


01060 




77516 


01060 


11 


01360 


10000 




77517 


01061 


37 


01057 


01045 




77520 


01062 


11 


01361 


10000 




77521 


01063 


37 


01057 


01046 




77522 


01064 


37 


01064 


01065 




77523 


01065 


23 


01350 


01264 


REDUCE LINE DIGIT 


77524 


01066 


46 


01067 


01037 


TEST FOR 11 ROW 


77525 


01067 


11 


01264 


01350 




77526 


01070 


37 


01064 


01037 


11 ROW 


77527 


01071 


37 


01042 


01037 


12 ROW* DUMMY 


77530 


01072 


44 


01073 


01075 


TEST EXIT FLAG 


77531 


01073 


11 


01302 


01314 


OVERRIDE INDEX 


77532 


01074 


11 


01255 


01350 


SET FLAG 


775.33 


01075 


31 


01314 


00000 


N-l REMAINDER 


77534 


01076 


42 


01261 


01100 


TEST LAST CARD 


77535 


01077 


17 


00000 


01300 


READ AND PICK CARD 


77536 


01100 


11 


01302 


01332 


SET INDEX FOR WORD CHANGE 


77537 


01101 


15 


01257 


01123 


SET FOR 1ST EXTRACTION 



page;^ 

report ZM 5?7-II 

MODEL All 
DATE 9_6-^6 



77540 


01102 


55 


01316 


00024 


SHIFT FOR IDENT NUMBER 


77541 


01103 


11 


01302 


01347 


SET FOR 5 DATA WORDS 


77542 


01104 


31 


01304 


00000 


TEST FOR 


77543 


01105 


42 


01314 


01115 


LESS THAN 


77544 


01106 


11 


01314 


01347 


5 WORDS 


77545 


01107 


31 


01314 


00017 


N-l 


77546 


OHIO 


35 


01306 


10000 


TEST FOR 


77547 


01111 


41 


01351 


01113 


INTEGER 


77550 


01112 


55 


10000 


00001 


OPTION 


77551 


01113 


31 


01255 


00000 


SET SMALLER 


77552 


01114 


35 


10000 


01227 


STORAGE 


77553 


01115 


37 


01124 


01120 


SPACE FOR PERIOD 


77554 


01116 


11 


01260 


01331 


SET TALLY 9 


77555 


01117 


11 


01263 


01327 


CLEAR 


77556 


01120 


41 


01332 


01123 


TEST TO 


77557 


01121 


21 


01123 


01306 


CHANGE MATRIX 


77560 


01122 


11 


01262 


01332 


WORD 


77561 


01123 


55 


30000 


00004 


PSSITION DIGIT 


77562 


01124 


37 


01124 


01125 




77563 


01125 


31 


01327 


00002 


N X 10 


77564 


01126 


32 


01327 


00001 


ADD 


77565 


01127 


52 


01301 


01327 


DIGIT 


77566 


01130 


41 


01331 


01120 


TEST N COMPLETE 


77567 


01131 


11 


01327 


01334 


SET EXPONENT FOR N 3 


77570 


01132 


37 


01124 


01120 


ACQUIRE 


77571 


01133 


51 


01301 


20000 


SZnPN 


77572 


01134 


11 


01265 


01330 


FLAG 


77573 


01135 


47 


01136 


01140 


TEST SIGN 


77574 


01136 


13 


01327 


01334 


SET EXPONENT FOR N 


77575 


01137 


13 


01265 


01330 


-FLAG 


77576 


01140 


37 


01140 


01141 




77577 


01141 


11 


01327 


01354 


MANTISSA X 10 EXP 10 



10-288 



FORM NO. E. T. - t W- r 



ni>/Mn — wK^ivn V"~ VEi^Eiuni, u I Mftnuvj <>vi\r, 
SAN DIEGO. CALIFORNIA 



V/W — 1W 



PAGE 23 

REPORT 2M 527-H 
MODEL m 
DATE 9 ^ -$6 



CO 



I 

O 

1— 1 

I 

o 
o 



X 

Dl, 



77600 


01142 


11 


01330 


01355 


MANTISSA FLAG 


77601 


01143 


11 


01264 


01331 


SET TALLY 


77602 


01144 


37 


01140 


01117 


EXPONENT INFORMATION 


77603 


01145 


41 


01351 


01217 


TEST INTEGER OPTION 


77604 


01146 


11 


01263 


01333 


CLEAR 


77605 


01147 


11 


01354 


20000 


TEST N 


77606 


01150 


47 


01151 


01223 


FOR 


77607 


01151 


23 


01327 


01330 


EXPONENT 


77610 


01152 


12 


20000 


20000 


ADJUSTMENT^ 


77611 


01153 


73 


01265 


01353 


TENS DIGIT 


77612 


01154 


31 


20000 


00017 


UNITS DIGIT 


77613 


01155 


35 


01254 


01215 


UNITS POWER 


77614 


01156 


11 


20000 


01251 


OF 10 


77615 


01157 


23 


01334 


01265 


ADJUST EXPONENT 


77616 


01160 


11 


01276 


01327 


10 EXP 10 


77617 


01161 


11 


01310 


01334 


ADJUST AXPONENT 


77620 


01162 


46 


01214 


01250 


SIGN OF EXPONENT 


77621 


01163 


23 


01334 


01311 


ADJUST EXPONENT 


77622 


01164 


31 


01354 


00000 


N 


77623 


01165 


73 


01327 


01333 


N ADJUSTMENT 


77624 


01166 


31 


20000 


00043 


FOR NEGATIVE 


77625 


01167 


73 


01327 


10000 


EXPONENT 


77626 


01170 


55 


10000 


00001 


DETERMINE 


77627 


01171 


32 


01263 


00001 


LAST 


77630 


01172 


42 


01327 


01174 


BIT 


77631 


01173 


27 


10000 


01264 


OF N 


77632 


01174 


31 


10000 


00044 


ASSEMBLE 


77633 


01175 


32 


01333 


00044 


M 


77634 


01176 


11 


01263 


01331 


CLEAR 


77635 


01177 


74 


20000 


01331 


SCALE FACTOR N 


77636 


01200 


11 


20000 


01354 


STORE N 


77637 


01201 


46 


01202 


01207 


TEST FOR ROUNDING 



report Z M 527-11 

MODEL ^22 
DATE 9^.56 



77640 


01202 


21 


01354 


01264 


ROUND 


77641 


01203 


43 


20000 


01207 


ADJUST FOR 


77642 


01204 


32 


01263 


00107 


OVERFLOW 


77643 


01205 


11 


20000 


01354 


IF 


77644 


01206 


21 


01334 


01264 


NECESSARY 


77645 


01207 


31 


01331 


00000 


ADJUST 


77646 


01210 


42 


01303 


01212 




77647 


01211 


23 


01334 


01312 


SCALE 


77650 


01212 


21 


01334 


01331 


FACTOR 


77651 


01213 


37 


01213 


01214 




77652 


01214 


41 


01353 


01163 


TEST TENS DIGIT 


77653 


01215 


30 


00000 


00000 


POWER FOR UNITS DIGIT 


77654 


01216 


37 


01213 


01163 


ADJUST FOR UNITS DIGIT 


77655 


01217 


11 


01354 


01333 


N 


77656 


01220 


41 


01355 


01222 


SIGN OF N 


77657 


01221 


13 


01333 


01333 


NEGATIVE 


77660 


01222 


21 


01315 


01333 


SUM 


77661 


01223 


75 


30002 


01225 


STORE 


77662 


01224 


11 


01333 


30000 


TEMPORARY 


77663 


01225 


21 


01224 


01356 


STEP STORAGE 


77664 


01226 


41 


01347 


01115 


TEST END OF CARD 


77665 


01227 


30 


00000 


00000 


FINAL 


77666 


01230 


11 


01335 


30000 


STORAGE 


77667 


01231 


21 


01230 


01357 


STEP 


77670 


01232 


23 


01314 


01261 


TEST FOR 


77671 


01233 


46 


01234 


01033 


END 


77672 


01234 


41 


01352 


01001 


TEST PRINT SUM 


77673 


01235 


31 


01263 


00000 


CLEAR 


77674 


01236 


75 


00006 


01240 


SUM 


77675 


01237 


32 


01315 


00014 




77676 


01240 


31 


20000 


00030 




77677 


01241 


32 


01264 


00004 





10-290 



FORM NO. E. T. - I (11 F 



MJNVAIK «~ UJVI3H-MM %jr IjfclMtKAL UTNAMKLb CUKf. 

SAN DIEGO. CALIFORNIA 



PAGE 25 

REPORT ZM 527-n 
MODEL £21 
DATE 9 ^„ 56 



CO 

CO 



I 

o 

1—1 

I 

o 

o 



X 

a, 



77700 


01242 


61 


00000 


20O00 




77701 


01243 


34 


20000 


00000 




77702 


01244 


47 


01241 


01001 


PRINTING 


77703 


01245 


71 


01354 


01327 


ADJUSTMENT 


77704 


01246 


37 


01213 


01176 


OF N 


77705 


01247 


37 


01247 


01250 


AND 


77706 


01250 


41 


01353 


01245 


EXPONENT 


77707 


01251 


30 


00000 


00000 


FOR 


77710 


01252 


37 


01247 


01245 


POSITIVE 


77711 


01253 


45 


00000 


01217 


SCALE FACTOR 


77712 


01254 


11 


01264 


01327 


CONSTANTS 


77713 


01255 


75 


30000 


01231 




77714 


01256 


00 


00000 


01335 




77715 


01257 


35 


01316 


01316 




77716 


01260 


00 


00000 


00011 




77717 


01261 


00 


00000 


00005 




77720 


01262 


00 


00000 


00010 




77721 


01263 


00 


00000 


00000 




77722 


01264 


00 


00000 


00001 




77723 


01265 


00 


00000 


00012 




77724 


01266 


00 


00000 


00144 




77725 


01267 


00 


00000 


01750 




77726 


01270 


00 


00000 


23420 




77727 


01271 


00 


00003 


03240 




77730 


01272 


00 


00036 


41100 




77731 


01273 


00 


00461 


13200 




77732 


01274 


00 


05753 


60400 




77733 


01275 


00 


73465 


45000 




77734 


01276 


11 


24027 


62000 




77735 , 


01277 


00 


00012 


00000 




77736 


01300 


00 


00000 


00105 




77737 


01301 


00 


000Q0 


00017 





SAN DIEGO. CALIFORNIA 



PAGE *>£ 

REPORT 2M 527.JT 
MODEL AU 
DATE 9 ^. 56 



77740 


01302 


00 


00000 


00004 


77741 


01303 


00 


00000 


00045 


77742 


01304 


00 


00000 


00003 


77743 


01305 


00 


00000 


00002 


77744 


01306 


00 


00001 


00000 


77745 


01307 


00 


00001 


00001 


77746 


01310 


00 


00000 


00043 


77747 


01311 


00 


00000 


00044 


77750 


01312 


00 


00000 


00110 


77751 


01313 


00 


00005 


00000 



10-292 



FORM NO E. 



SAN DIEGO. CALIFORNIA 



PAGE 27 

REPORT ZM 527-11 

MODEL All 

date 9-6-56 
Revised 10-20-56 



SPUR DIVISION AND GENERAL ALARMS 



77752 




75 


30700 


77754 


STORE PART 


77753 




11 


01100 


75100 


OF E#S. 


77754 




75 


30021 


01100 


THIS TO 


77755 




11 


77756 


01100 


E.S« 


77756 


01100 


75 


30200 


01102 


PART OF 


77757 


01101 


11 


77213 


01200 


CARD ROUTINE 


77760 


01102 


31 


01746 


00000 


ADDRESS 


77761 


01103 


36 


01310 


10000 


OF 


77762 


01104 


55 


10000 


00030 


INST, 


77763 


01105 


11 


01305 


01371 


5 DIGITS 


77764 


01106 


61 


00000 


01302 


CAR* RET. 


77765 


01107 


37 


01255 


01250 


ADDRESS 


77766 


onio 


61 


00000 


01305 


SPACE 


77767 


01111 


31 


013 5 5 


00052 


PRINT 


77770 


01112 


61 


00000 


2000O 




77771 


01113 


34 


20000 


00006 


LABEL 


77772 


01114 


47 


01112 


01115 




77773 


01115 


61 


00000 


01311 


DIVISOR 


77774 


01116 


11 


01766 


10000 




77775 


01117 


37 


01351" 


01346 


DIVISOR MANTISSA 


77776 


01120 


45 


00000 


01345 


TO CONTINUE 


77360 


01345 


55 


01760 


10003 


INSTRUCTION 


77361 


01346 


11 


01335 


01371 


12 DIGITS 


77362 


01347 


61 


00000 


01305 


SPACE 


77363 


01350 


37 


01255 


01250 


Q OCTAL 


77364 


01351 


37 


01351 


013 5 2 




77365 


01352 


75 


30700 


76061 


RESTORE 


77366 


01353 


11 


75100 


01100 


ES 


77367 


01354 


56 


00000 


01741 


EXCESS 


77370 


01355 


.22 


14171 


42403 


FLEX CODE 


76014 




75 


30021 


76016 


PART 


76015 




11 


77756 


01100 


OF 



SAN DIEGO. CALIFORNIA 



PAGE 28 

REPORT ZM 5?7_11 

MODEL £Q 

DATE 9-6-56 



76016 




75 


30200 


76022 


DIVISION 


76017 




11 


77213 


01200 


ALARM 


76020 




75 


30700 


76014 


STORE 


76021 




11 


01100 


75100 


ES 


76022 




75 


30035 


01137 


THIS 


76023 




11 


76024 


01115 


TO ES 


76024 


01115 


61 


00000 


01142 


PRINT LETTER 


76025 


01116 


21 


01115 


01751 


STEP 


76026 


01117 


55 


01760 


10003 


PRINT 


76027 


01120 


37 


01351 


01346 


REGISTER 


76030 


01121 


21 


01117 


01151 


STEP 


76031 


01122 


37 


01122 


01123 


SWITCH 


76032 


01123 


61 


00000 


01302 


CAR. RET* 


76033 


01124 


37 


01124 


01125 


SWITCH 


76034 


01125 


37 


01124 


01115 


PRINT M 


76035 


01126 


21 


01117 


01150 


STEP 


76036 


01127 


37 


01122 


01115 


PRINT 


76037 


01130 


37 


01124 


01117 


B 


76040 


01131 


37 


01131 


01132 


SWITCH 


76041 


01132 


37 


01131 


01127 


PRINT C 


76042 


01133 


21 


01117 


01753 


STEP 


76043 


01134 


37 


01131 


01127 


PRINT R 


.76044 


01135 


37 


01131 


01127 


PRINT BOXES 


76045 


01136 


45 


00000 


01352 




76046 


01137 


11 


01141 


01355 


SET FLEX ALA 


76047 


01140 


45 


00000 


01102 




76050 


01141 


30 


11301 


20745 


FLEX ALARM 


76051 


01142 


00 


00000 


00014 




76052 


01143 


00 


00000 


00006 




76053 


01144 


00 


00000 


00023 




76054 


01145 


00 


00000 


00016 




76055 


01146 


00 


00000 


00012 





10-294 



FORM NO. E. T. . i «.F SAN DIEGO. CALIFORNIA PAGE ?9 



REPORT ZM 527-11 
MODEL All 

DATE 9-6-56 



76056 


01147 


00 


00000 


00001 


76057 


01150 


00 


00004 


00000 


76060 


01151 


00 


00001 


00000 


76061 




37 


01741 


01741 


76062 




37 


01742 


01742 


76063 




56 


00000 


01746 



SET NO ACCUMULATE 
SET STORE IN Y 
RETURN TO N# I. 



co 

CO 



I 

o 

<—» 
I 

o 
o 

o 



X 

a* 



VAsnvMiK — ui vision wr VCNEKAL DYNAMICS CORP. 

SAN DIEGO. CALIFORNIA 



CV-183 

PAGE »')30 

REPORT ZM 5?7-ll 
MODEL AH 

DATE 9-6-56 



SPUR SROK ALARM 



72000 


45 


00000 


72000 




72001 


16 


72026 


72022 




72002 


11 


20000 


00000 




72003 


61 


00000 


72047 




72004 


55 


72012 


00005 




72005 


55 


72012 


00011 


SET FOR 5 DIGITS 


72006 


55 


72012 


00012 


SET FOR 2 DIGITS 


72007 


34 


20000 


00003 


OCTAL 


72010 


32 


72037 


00000 




72011 


11 


20000 


72012 


PRINT 


72012 


00 


01000 


10001 




72013 


44 


72014 


72007 


LOOP 


72014 


11 


10000 


72012 


RESTORE FLAG 


72015 


61 


00000 


72021 


SPACE 


72016 


37 


72016 


72017 


SWITCH 


72017 


31 


00000 


00044 




72020 


11 


72000 


00000 


SET JUMP 


72021 


37 


72016 


72004 


PRINT 


72022 


37 


72022 


72023 


SWITCH 


72023 


31 


72000 


00017 


FOR MAIN 


72024 


15 


20000 


72025 


ROUTINE AD 


72025 


16 


72000 


00000 


SET JUMP 


72026 


15 


72023 


72025 


RESTORE 


72027 


16 


72027 


72000 


RESTORE 


72030 


31 


72042 


00047 




72031 


37 


72016 


72047 


PRINT ALARM 


72032 


41 


00000 


72033 


ADJUST ADDRESS 


72033 


31 


20000 


00071 




72034 


37 


72016 


72005 , 


PRINT 5 DIGITS 


72035 


56 


00000 


00000 




72036 


00 


00000 




EXCESS 


72037 


61 


00000 


72037 





10-296 



SAN DIEGO. CALIFORNIA PAGE ^T 



15 



I 

3 
—i 
I 
3 



report Z M 5?7-ll 

MODEL £Q 

DATE 9-6-56 



72 40 


00 


00000 


52 . 




72041 


00 


00000 


00 74 




72042 


43 


01130 


12070 




72043 


00 


00000 


00 64 




72044 


00 


00000 


00062 




72045 


00 


00000 


00 66 




72046 


00 


00000 


00 72 




72047 


61 


00000 


20045 


FLEX 


72050 


34 


20000 


00006 


PRINT 


72051 


47 


72047 


72015 


LOOP 



SAN DIEGO. CALIFORNIA 



PAGE38 

REPORT ZM 527-11 
MODEL m 
DATE 11-1^-56 



SPUR PAPERTAPE DUMP 



73234 


37 


73234 


73235 


EXIT 


73235 


45 


00000 


73265 


AUTti FLEX 


73236 


45 


00000 


73270 


AUTO BIOCTAL 


73237 


45 


00000 


73273 


MANUAL FLEX 


73240 


45 


00000 


73277 


MANUAL BIOCTAL 


73241 


11 


00000 


74000 




73242 


11 


73235 


00000 




73243 


75 


30152 


73245 




73244 


11 


00001 


74001 




73245 


75 


30064 


73247 




73246 


11 


73302 


00006 




73247 


11 


10000 


73300 




73250 


11 


20000 


00151 




73251 


54 


20000 


00044 




73252 


11 


20000 


00152 




73253 


37 


73253 


73254 




73254 


11 


73300 


10000 




73255 


31 


00152 


00044 




73256 


32 


00151 


00000 




73257 


11 


00010 


73275 




73260 


11 


00010 


73300 




73261 


75 


30152 


73263 


RESTORE 


73262 


11 


74001 


00001 


ES 


73263 


11 


74000 


00000 




73264 


45 


00000 


73234 


TO EXIT 


73265 


37 


73253 


73241 


STORE IMAGE 


73266 


75 


30057 


00041 


FLEX 


73267 


11 


73366 


00072 


PROGRAM 


73270 


37 


73253 


73241 


STORE IMAGE 


73271 


75 


30040 


00120 


BIOCTAL 


73272 


11 


73445 


00072 


PROGRAM 


73273 


11 


10000 


73275 


PARAMETER WD. 



10-298 



'i<M NO E T .1 



Lur<VAiK 



LHVI3IWSN Ur tjtNtKAL UTINM«VMt,S V.UKC. 
SAN DIEGO. CALIFORNIA 



V/K ~XUO 

PAGE 39 

REPORT ZM 5P7-11 
MODEL All 
DATE 11-14-56 



CO 

co 



I 

o 

I— « 
1 

o 
o 
o 



04 



7 3 2 7 4 




37 


73234 


73265 


SET EXIT 


7 3 2 7 3 




00 


00000 




P. If* STORAGE 


7 3 276 




56 


00000 


73237 


MANUAL FLEX. 


73277 




37 


73234 


73270 


SET EXIT 


73300 




00 


0000 




Q 


7 3 3 01 




56 


00000 


73240 


MANUAL BIOCT. 


73302 


00006 


00 


00001 


00000 




73303 


00007 


00 


00000 


00007 




73304 


0010 


00 


00000 


00000 




73305 


00011 


00 


00000 


00001 




733 06 


00012 


00 


00000 


00002 




73307 


00013 


00 


00000 


00004 




73310 


00014 


00 


00152 


00000 




73311 


00015 


00 


74000 


00000 




73312 


00016 


63 


00000 


00017 




73313 


00017 


00 


00000 


00037 


FLEX 


73314 


00020 


00 


00000 


00052 




73315 


00021 


00 


00000 


00074 




73316 


00022 


00 


00000 


00070 




73317 


00023 


00 


00000 


00064 




73320 


00024 


00 


00000 


00062 




73321 


00025 


00 


00000 


00066 




73322 


00026 


00' 


00000 


00072 




73323 


00027 


00 


00000 


00045 


CAR. RET. 


7332 4 


00030 


00 


00000 


00043 


STOP CODE 


73325 


00031 


00 


00000 


00075 




73326 


00032 


00 


00000 


00132 




73327 


00033 


00 


00000 


02000 




73330 


00034 


00 


00000 


40000 




73331 


00035 


11 


00010 


00001 


CHECK ADDRESS 


73332 


00036 


45 


00000 


00072 


JUMP TO PUNCH 


73333 


00037 


11 


00034 


00001 


40000 



SAN DIEGO. CALIFORNIA 



UV-iOO 
PAGE 4£) 

REPORT ZM 527-11 

MODEL All 

DATE 11^14-56 



73334 


00040 


45 


00000 


00072 


JUMP TO PUNCH 


7333 5 


00041 


75 


00010 


00043 


LEADER 


73336 


00042 


63 


00000 


00010 




73337 


00043 


31 


73234 


00017 


PARAMETER ADORES. 


73340 


00044 


11 


20000 


00001 




73341 


00045 


31 


00014 


00000 


PARAMETER 


73342 


00046 


42 


00001 


00050 


ADDRESS 


73343 


00047 


21 


00001 


00015 


IN IMAGE 


73344 


00050 


15 


00001 


00051 




73345 


00051 


11 


30051 


10000 


PARAMETER 


73346 


00052 


11 


00010 


00001 


CLEAR 


73347 


00053 


11 


00010 


00003 


TEMPORARIES 


73350 


00054 


15 


10000 


00003 


AD. OF FIRST WD. 


73351 


00055 


11 


00003 


00004 




73352 


00056 


16 


10000 


00001 


AD. OF LAST WD. 


73353 


00057 


44 


73254 


00060 




73354 


00060 


44 


73254 


00061 


PAR. INST. 


73355 


00061 


44 


73254 


00062 




73356 


00062 


21 


73234 


00011 


STEP 


73357 


00063 


31 


00001 


00017 


LAST AD. 


73360* 


00064 


34 


00003 


00071 


FIRST AD. 


73361 


00065 


11 


20000 


00002 


NO. OF V/DS. 


73362 


00066 


46 


00043 


00067 


PAR. END 


73363 


00067 


21 


00001 


ooqii 


STEP 


73364 


00070 


43 


00033 


00035 


2000 TO ZERO 


73365 


00071 


43 


00006 


00037 


10000 TO 40000 


73366 


00072 


55 


10000 


00002 




73367 


00073 


44 


00074 


00075 


NO STOP PUNCH 


73370 


00074 


16 


00042 


00135 




73371 


00075 


31 


00014 


00000 


CURRENT WORD 


73372 


00076 


.42 


00004 


00102 


IN IMAGE 


73373 


00077 


21 


00003 


00015 


ADJUST FOR IMAGE 



10-300 



FORM NO. E. T. - I (ft ■ r 



W * 4WU 



PAGE £L 

REPORT ZM 5^7-1] 
MODEL AH 
DATE 11-14-56 



CO 

co 



i 

o 

I 

o 

o 
o 






73374 


00100 


16 


00031 


00127 




73375 


00101 


45 


00000 


00103 




73376 


00102 


16 


00101 


00127 




73377 


00103 


11 


00004 


10000 


CURRENT AD. 


73400 


00104 


56 


10000 


00105 




73401 


00105 


55 


10000 


00006 




73402 


00106 


37 


00150 


00142 


5 DIGITS 


73403 


00107 


15 


00003 


00110 


CURRENT 


73404 


00110 


31 


30110 


00000 


WORD 


73405 


00111 


43 


00010 


00121 


OMIT PUNCHING 


73406 


00112 


75 


00002 


00114 


2 SPACES 


73407 


00113 


63 


00000 


00013 




73410 


00114 


11 


20000 


10000 


CURRENT WD. 


73411 


00115 


11 


00011 


00005 




73412 


00116 


37 


00150 


00143 


2 DIGITS 


73413 


00117 


37 


00150 


00141 


5 DIGITS 


73414 


00120 


37 


00150 


00141 


5 DIGITS 


73415 


00121 


41 


00140 


00124 


32 WDS. 


73416 


00122 


11 


00017 


00140 


RESTORE TALLY 


73417 


00123 


63 


00000 


00027 


CAR. 


73420 


00124 


63 


00000 


00027 


RET. 


73421 


00125 


21 


00004 


00006 


STEP 


73422 


00126 


11 


00004 


00003 




73423 


00127 


41 


00002 


30*27 


END 


73424 


00130 


16 


00032 


00127 




73425 


00131 


11 


00017 


00002 




73426 


00132 


31 


00140 


00000 




73427 


00133 


43 


00017 


00135 




73430 


00134 


45 


00000 


00121' 




73431 


00135 


63 


00000 


00030 




73432 


00136 


11. 


73431 


00135 




73433 


00137 


45 


00000 


00041 


TO NEXT PAR. 



bWM«nin 



w«vi#i\sm vr uciicnHl UINAMIO COKK. 

SAN DIEGO. CALIFORNIA 



uv-ioo 

PAGE]- 4,2 
REPORT zM 5?7-ll 

MODEL All 
DATE 11-14-56 



73434 


00140 


00 


00000 


00037 


TALLY 


73435 


00141 


63 


00000 


00013 


SPACE 


73436 


00142 


11 


00013 


00005 


SET TALLY 


73437 


00143 


55 


10000 


00003 




73440 


00144 


51 


00007 


20000 


EXTRACT DIGIT 


73441 


00145 


35 


00016 


00146 




73442 


00146 


00 


.00000 


00000 


PUNCH DIGIT 


73443 


00147 


41 


00005 


00143 




73444 


00150 


45 


00000 


30150 


EXIT 


73445 


0007 2 


63 


10000 


00010 


7TH LEVEL 


73446 


00073 


11 


00004 


10000 


PUNCH 


73447 


00074 


55 


10000 


0002 5 


INSERT 


73450 


00075 


37 


00130 


00122 


ADDRESS 


73451 


00076 


37 


00130 


00122 




73452 


00077 


31 


00014 


00000 


IN 


73453 


00100 


42 


00004 


00 104 


IMAGE 


73454 


00101 


21 


00003 


00015 


ADJUST 


73455 


00102 


16 


00131 


00113 




73456 


00103 


45 


00000 


00105 




73457 


00104 


16 


00103 


00113 




73460 


00105 


15 


00003 


00106 


CURRENT ADDRESS 


73461 


00106 


11 


30000 


10000 


PUNCH 


73462 


.00107 


11 


00013 


00005 


CURRENT 


73463 


00110 


37 


00130 


001.23 


WORD 


73464 


00111 


21 


00004 


00006 


STEP 


73465 


00112 


11 


00004 


00003 




73466 


00113 


41 


00002 


30113 


END 


73467 


00114 


11 


00012 


00005 




73470 


00115 


11 


00001 


10000 


CHECK 


73471 


00116 


37 


00,130 


00123 


ADDRESS 


73472 


00117 


37 


00130 


00123 




73473 


00120 


75 


00310 


00041 


PUNCH 



10-302 



FORM NO. E T. - 1 ,1' f 



SAN DIEGO. CALIFORNIA 



PAGE 43 

REPORT ZM 527-11 
MODEL All 
DATE H-14-, 56 



73474 


0012 1 


63 


00000 


00010 


LEADER 


7 3 4 7 5 


00122 


11 


00011 


00005 




73476 


00123 


55 


10000 


00006 


PUNCH 


73477 


00124 


63 


00000 


10000 


2 


73500 


00125 


41 


00005 


00123 


DIGITS 


73501 , 


00126 


55 


10000 


00006 




73502 


0012 7 


63 


10000 


10000 




73503 


00130 


56 


10000 


30130 




73504 


00131 


00 


00000 


00077 





co 

CO 



I 

o 

I 

o 
o 



X 

a, 



K.T. ■ I <R r 



SAN OIEOO. CALIFORNIA 



PAGE 4A 

REPORT ZM 527-11 
MODEL All 
DATE 11-14-56 



SUPER OTTO SPUR 



72052 


01000 


45 


00000 


01013 


72053 


01001 


47 


01002 


01004 


72054 


01002 


35 


01304 


01172 


72055 


01003 


45 


00000 


01171 


72056 


01004 


55 


00022. 


00043 


72057 


01005 


53 


10000 


00004 


72060 


01006 


53 


10000 


00013 


72061 


01007 


45. 


00000 


01173 


72062 


01010 


56 


00000 


01010 


72063 


01011 


11 


01316 


10000 


72064 


01012 


37 


01273 


01266 


72065 


01013 


45 


30000 


01016 


72066 


01014 


75 


00002 


01020 


72067 


01015 


17 


00000 


01332 


72070 


01016 


75 


00276 


01020 


72071 


01017 


63 


00000 


01314 


72072 


01020 


45 


10000 


01042 


72073 


01021 


11 


01317 


10000 


72074 


01022 


37 


01273 


01266 


72075 


01023 


11 


01320 


10000 


72076 


01024 


37 


01273 


-01267 


72077 


01025 


11 


40000 


00003 


72100 


01026 


11 


01275 


40000 


72101 


01027 


57 


00000 


00000 


72102 


01030 


11 


00003 


40000 


72103 


01031 


15 


01352 


01033 


72104 


01032 


15 


01333 


01034 


72105 


01033 


11 


30000 


10000 


72106 


01034 


31 


30000 


00000 


72107 


01035 


56 


10000^ 


,0103.6 


72110 


01036 


11 


10000 


00017 



10-304 



FORM NO. E. T. - 1 (ft r 



X 



UuWiVAlK * uiVidlUN Of GENERAL DYNAMICS CORP. v> »-■*««* 

SAN DIEGO. CALIFORNIA PAGE • ''4-5 

REPORT ZM 5?7-I 
MODEL All 
DATE 11-14-56 



72111 01037 11 20000 00020 

72112 01040 37 01261 01262 

72113 010^1 44 72441 01044 

72114 01042 23 10000 10000 

72115 01043 56 00000 01036 

72116 01044 61 00000 01340 

72117 01045 11 01334 00023 

72120 01046 11 00020 10000 

72121 01047 61 000Q0 01340 

72122 01050 37 01261 01264 

72123 01051 11 00017 10000 

72124 01052 51 01355 20000 

72125 01053 73 01345 00003 

72126 01054, 36 10000 00025 

72127 010.55 11 00003 20000 

72130 01056 42 01335 01070 

72131 01057 11 00017 00026 

72132 - 01060 11 01276 OHIO 

72133 01061 11 01312 01202 

72134 01062 55 00017 10005 

72135 01063 44 01064 01075 

72136 01064 11 01277 01114 
^ 72137 01065 11 01300 01210 
§ 72140 01066 75 20002 01101 



wfc* 



^ . 72141 01067 55 00026 000.06 

2 7|l42 01070 11 00017 00027 

o ■*■ ■ 

£ 72143 01071 21 00017 01336 



72144 01072 11 01301 OHIO 

72145 01073 11 01302 01202 

72146 01074 45 00000 01076 

72147 01075 11 00020 00027 



E. T. . I Mr 



SAN DIEGO. CALIFORNIA PAGE /,£. 

REPORT 2M 5?7-ll 
MODEL £Q 



72150 


01076. 


11 


01303 


01114 


72151 


01077 


11 


01313 


01210 


72152 


01100 


45 


00000 


01066 


72153 


01101 


45 


30000 


01175 


72154 


01102 


15 


00017 


01107 


72155 


01103 


75 


30014 


01105 


72156 


01104 


23 


00003 


00003 


72157 


01105 


11 


01311 


00000 


72160 


01106 


17 


00000 


01333 


72161 


01107 


11 


30000 


00030 


72162 


OHIO 


11 


00026 


30000 


72163 


01111 


11 


01337 


00022 


72164 


01112 


11 


01340 


00023 


72165 


01113 


37 


01174 


01166 


72166 


01114 


11 


00027 


30000 


72167 


01115 


11 


01341 


00022 


72170 


0111'6 


11 


01340 


00023 


72171 


01117 


37 


01174 


01166 


72172 


01120 


45 


20000 


01152 


72173 


01121 


11 


00030 


00021 


72174 


01122 ' 


11 


01342 


00022 


.72175 


01123 


11 


01337 


00023 


72176 


01124 


37 


01174 


01166 


72177 


01125 


11 


01337 


0~0024 


72200 ■ 


01126 


55 


00022 


00043 


72201 


01127 


11 


01340 


00023 


72202 


01130 


37 


01174 


01166 


72203 


01131 


41 


00024 


01126 


72204 


01132 


11 


01343 


00024. 


72205 


01133 


16 


01305 


01135 


72206 


01134 


77 


00000 


01314 



10-306 



FORM NO. E. T. ■ 1 (ft ■ r 



uuNvAiK - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 4,7 

REPORT ZM 527-11 

MODEL All 
DATE 11-14-56 



CO 

CO 



I 

o 

I 

o 
o 



X 



72207 


01135 


77 


10000 


30000 


72210 


01136 


77 


10000 


01314 


72211 


01137 


23 


01135 


01337 


72212 


01140 


41 


00024 


01134 


72213 


01141 


56 


20000 


01142 


72214 


01142 


41 


00025 


01147 


72215 


01143 


17 


00000 


01332 


72216 


01144 


45 


10000 


01043 


72217 


01145 


75 


20002 


01033 


72220 


01146 


21 


01033 


01344 


72221 


01147 


21 


01107 


01345 


72222 


01150 


75 


20002 


01103 


72223 


01151 


21 


00026 


01346 


72224 


01152 


11 


00030 


10000 


72225 


01153 


51 


01347 


20000 


72226 


01154 


43 


01350 


01156 


72227 


01155 


45 


00000 


01121 


72230 


01156 


11 


00030. 


00021 


72231 


01157 


11 


01342 


00022 


72232 


01160 


11 


01351 


00024 


72233 


01161 


11 


01352 


00023 


72234 


01162 


37 


01174 


01166 


72235 


01163 


55 


00022 


00043 


72236 


01164 


41 


00024 


01161 


72237 


01165 


45 


00000 


01132 


72240 


01166 


55 


00021 


00003 


72241 


01167 


51 


01353 


20000 


72242 


01170 


45 


00000 


01001 


72243 


01171 


55 


00022 


00043 


72244 


01172 


53 


01321 


30000 


722^5 


■ 01173 


41 


00023 


01166 



e. T. • t (ft ■ r 



wt.nm •< mviMwn wr vcraeKAL OT NAMICS CORP. CV-183 

SAN DIEGO, CALIFORNIA PAGE LQ 

REPORT ZM 527-11 
MODEL All 
DATE 11-14-56 



72246 


01174 


45 


00000 


01174 


72247 


01175 


15 


00017 


01200 


72250 


01176 


75 


00036 


01200 


72251 


01177 


63 


00000 


01314 


72252 


01200 


11 


30000 


00030 


72253 


01201 


63 


00000 


01307 


72254 


01202 


11 


00026 


30000 


72255 


01203 


37 


01261 


01250 


72256 


01204 


75 


00002 


01210 


72257 


01205 


63 


00000 


01340 


72260 


01206 


75 


00007 


01210 


72261 


01207 


63 


00000 


01340 


72262 


01210 


11 


00027 


30000 


72263 


01211 


37 


01261 


01250 


72264 


01212 


75 


00002 


01216 


72265 


01213 


63 


00000 


01340 


72266 


01214 


75 


00007 


01216 


72267 


01215 


63 


00000 


01340 


72270 


01216 


45 


20000 


01235 


72271 


01217 


11 


00030 


10000 


722,72 


01220 


11 


01337 


00023 


72273 


01221 


37 


01261 


01253 


72274 


01222 


63 


00000 


01340 


72275 


01223 


37 


01261 


01250 


72276 


01224 


63 


00000 


01340 


72277 


01225 


37 


01261 


01250 


72300 


01226 


56 


20000 


01227 


72301 


01227 


41 


00025 


01232 


72302 


01230 


75 


00003 


01144 


72303 


01231 


63 


ooooo' 


01307 


72304 


01232 


21 


01200 


01345 



10-308 



wt^vHin — U(vs?iun wr ly&NEKAL UTNAMICS CORP. CV-183 

SAN DiEGO. CALIFORNIA PAGE /Q 





72305 


01233 


75 


20002 


01200 




72306 


01234 


21 


00026 


01346 




72307 


01235 


11 


00030 


10000 




72310 


01236 


51 


01347 


20000 




72311 


01237 


43 


01350 


01241 




72312 


01240 


45 


00000 


01217 




72313 


01241 


11 


01351 


00024 




72314 


01242 


11 


00030 


10000 




72315' 


012 4 3 


11 


01352 


00023 




72316 


01244 


37 


01261 


01253 




72317 


01245 


63 


00000 


01340 




72320 


01246 


41 


00024 


01243 




72321 


01247 


45 


00000 


01226 




72322 


012 5 


11 


01340 


00023 




72323 


01251 


45 


00000 


01253 




72 32 4 


01252 


11 


01343 


00023 




72325 


012 53 


15 


01305 


01256 




72326 


01254 


55 


10000 


00003 




72327 


01255 


51 


01353 


20000 




72330 


02256 


35 


30000 


01257 




72331 


01257 


63 


.00000 


30000 




72332 


01260 


41 


00023 


01254 


-s 


72333 


01261 


45 


00000 


01261 


r-i 


72334 


01262 


61 


00000 


01307 


1 

o 


72335 


01263 


11 


01343 


00023 


1 

o 

r— 1 


72336 


01264 


15 


01307 


01256 


72337 


01265 


45 


00000 


01254 




72340 


01266 


61 


00000 


01307 


3-i 


72341 


01267, 


11 


01354 


00023 



report zm 5?7-ll 

MODEL £Q 
DATE II-I4-56 



72342' 011270 55 10000 00006 
72343 01271 61 00000 10000 



»AN uiimWi viAkifOHNIA 



reportZM 5?7-ll 

MODEL All 
DATE 11-14-56 



72344 


01272 


41 


00023 


01270 


72345 


01273 


45 


00000 


01273 


72346 


01274 


45 


00000 


01013 


72347 


01275 


45 


00000 


01030 


72350 


01276 


11 


00026 


00.021 


72 351 


01277 


45 


00000 


01120 


72352 


01300 


45 


00000 


01214 


72353 


01301 


45 


00000 


01114 


72354 


01302 


45 


00000 


01206 


72355 


01303 


11 


00027 


00021 


72356 


01304 


53 


01321 


00005 


72357 


01305 


00 


01306 


00016 


72360 


01306 


63 


00000 


01322 


72361 


01307 


00 


01310 


00045 


72362 


01310 


6.1 


00000 


01322 


72363 


01311 


45 


00000 


01103 


72364 


01312 


11 


00026 


10000 


72365 


01313 


11 


00027 


10000 


72366 


01314 


00 


00000 


00000 


72367 


01315 


24 


34070 


40613 


72370 


01316 


03 


01030. 


40336 


72 371 


01317 


15 


30123 


00720 


72372 


01320 


01 


12240 


41406 


72373 


01321 


77 


77777 


77777 


72374 


01322 


00 


00000 


00037 


72375 


01323 


00 


00000 


00052 


72376 


01324 


00 


00000 


00074 


72377 


01325 


00 


ooooo 


00070 


72400 


01326 


00 


00000 


00064 


72401 


. 01327 


00 


00000 


00062 


72402* 


01330 


00 


00000 


00066 



10-310 



REPORT ZM 5?7-ll 

MODEL All 
DATE 11-14-56 





72403 


01331 


00 


00000 


00072 




72404 


01332 


00 


00300 


00110 




72405 


01333 


00 


00301 


00112 




72406 


01334 


00 


00000 


00006 




72407 


01335 


00 


00000 


20000 




72410 


01336 


00 


74000 


00000 




72411 


01337 


00 


00000 


00001 




72412 


01340 


00 


00000 


00004 




72413 


01341 


00 


40000 


00000 




72414 


01342 


00 


00200 


00000 




72415 


01343 


00 


00000 


00013 




72416 


01344 


00 


00002 


00000 




72417 


01345 


00 


00001 


00000 




72420 


01346 


00 


00100 


00000 




72421 


01347 


77 


00000 


00000 




72422 


01350 


14 


00000 


00000 




72423 


01351 


00 


00000 


00002 




72424 


01352 


00 


00000 


00003 




72425 


01353 


00 


00000 


00007 




72426 


01354 


00 


00000 


00005 




72427 


01355 


00 


7 7777 


77777 




72430 


01356 


00 


00000 


00000 




72431 




11 


00000 


740 0Q 


CO 

co 


72432 




11 


72540 


00000 


- > 


72433 




75 


31777 


72435 


<— > 

C— 1 

1 

o 

o 


72434 




11 


00001 


74001 


72435 




75 


30260 


72437 


h- 


72436 




11 


72445 


00020 




72437 




75 


30073 


00020 




72440 




11 


72725 


00700 




72441 




75 


31777 


72443 



10-311 



f . T. • I fir 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO, CALIFORNIA 



CV-183 

PAGE 5? 

REPORT ZM 5p7.ll 
MODEL AH 
DATE H-l^-56 



72442 




11 


74001 


00001 


72443 




11 


74000 


00000 


72444 




57 


00000 


00000 


72445 


00020 


17 


00000 


00700 


72446 


00021 


71 


00704 


00711 


72447 


00022 


11 


20000 


00014 


72450 


00023 


55 


10000 


00002 


72451 


00024 


11 


10000 


00015 


72452 


00025 


55 


10000 


00001 


72453 


00026 


11 


10000 


00016 


72454 


00027 


11 


10000 


00017 


72455 


00030 


21 


00017 


00015 


72456 


00031 


11 


00703 


00011 


72457 


00032 


75 


30010 


00250 


72460 


00033 


23 


00001 


00001 


72461 


00034 


45 


10000 


00216 


72462 


00035 


11 


00714 


10000 


72463 


00036 


37 


00227 


00223 


72464 


00037 


11 


00715 


10000 


72465 


00040 


37 


00227 


00223 


72466 


00041 


11 


00716 


10000 


72467 


00042 


37 


00227 


00223 


72470 


00043 


11 


40000 


00010 


72471 


00044 


11 


00747 


00000 


72472 


• 00045 


11 


00747 


40000 


72473 


00046 


57 


0030Q 


00000 


72474 


00047 


17 


00301 


00702 


72475 


00050 


11 


00010 


40000 


72476 


00051 


15 


00046 


00053 


72477 


00052 


15 


00047 


00054 


72500 


00053 


11 


30300. 


10000 



10-312 



FORM NO- E. T, - ■ & 



CO 
CO 



I 

o 

I 

o 
o 



x: 

a, 



SAN DIEGO. CALIFORNIA PAGE 53 

REPORT ZM 527-1] 
MODEL All 
DATEll-.l4.-56 



72501 


00054 


31 


30301 


00000 


72502 


00055 


56 


10000 


00056 


72503 


00056 


11 


10000 


00001 


72504 


00057 


11 


20000 


00002 


72505 


00060 


61 


00000 


00716 


72506 


00061 


61 


00000 


00716 


72507 


00062 


11 


0:0001 


10000 


72510 


00063 


11 


00707 


00007 


72511 


00064 


37 


00237 


00232 


72512 


00065 


37 


00237 


00230 


72513 


00066 


37 


00237 


00230 


72514 


00067 


44 


00220 


00070 


72515 


00070 


11 


00002 


10000 


72516 


00071 


61 


00000 


00716 


72517 


00072 


61 


00000 


00727 


72520 


00073 


61 


00000 


00727 


72521 


00074 


55 


10000 


00005 


72522 


00075 


37 


00237 


00230 


72523 


00076 


61 


00000 


-00712 


72524 


00077 


' 75 


00005 


00101 


72525 


00100 


61 


00000 


00727 


72526 


00101 


15 


00001 


00131 


72527 


00102 


11 


0,0001 


10000 


72530 


00103 


55 


10000 


00003 


72531 


00104 


51 


00731 


00003 


72532- 


00105 


55 


10000 


00017 


72533 


00106 


51 


00731 


0000.4 


72534 


00107 


11 


00732 


20000 


72535 


00110 


42 


00003 


00114 


.72536 


00111 


21 


00131 


00733 


72537 


•00112 


11 


00124 


00136 



E. T. • 1 <pi r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. LV-lOO 

SAN DIEGO. CALIFORNIA PAGE *}£, 



72 5 40 


00113 


45 


00000 


00130 


72541 


001.14 


11 


00734 


10000 


72542 


00115 


51 


00001 


20000 


72543 


00116 


47 


00127 


00117 


72 5 44 


00117 


11 


00002 


10000 


72545 


00120 


55 


10000 


00003 


72546 


00121 


51 


00731 


00005 


72547 


00122 


11 


00125 


00136 


72550 


00123 


45 


00000 


00130 


72551 


00124 


45 


00000 


00153 


72552 


00125 


45 


00000 


00137 


72553 


00126 


45 


00000 


00146 


72554 


00127 


11 


00126 


00136 


72555 


00130 


75 


31000 


00132 


72556 


00131 


11 


30000 


01000 


72557 


00132 


21 


00131 


00735 


72560 


00133 


15 


00735 


00134 


72561 


00134 


11 


31000 


00006 


72562 


00135 


21 


00134 


00736 


72563 


00136 


45 


00000 


30136 


72 5 64 


00137 


11 


00003 


00010 


72565 


00140 


15 


00703 


00011 


72566 


00141 


37 


00247 


00240 


72567 


00142 


21 


00011 


00014 


72570 


00143 


11 


00005 


00010 


72571 


00144 


37 


00247 


00240 


72572 


00145 


45 


00000 


0015.7 


72573 


00146 


11 


00003 


00010 


72574 


00147 


15 


00703 


00011 


72575 


00150 


37 


00247' 


00240 


72576 


00151 


21 


00011 


00017 



REPORT ZM 527-11 

MODEL All 
DATE ll-H-56 



10-314 



FORM NO. E. T. - I [}") r 



CUWVAIK ~ UrViaWJW Ur WI1CKHl.-yri Wl tl lW VW lv r. ■ — : vr— -x-ww 

SAN DIEGO. CALIFORNIA PAGE55 

reportZM 527-11 

MODEL All 
DATE 11-14-56 





72577 


00152 


45 


00000 


00160 




72600 


00153 


15 


00703 


00011 




72601 


00154 


21 


00011 


00016 




72602 


00155 


11 


00003 


00010 




72603 


00156 


37 


00247 


00240 




72604 


00157 


21 


00011 


00015 




72605 


00160 


45 


20000 


00256 




72606 


00161 


11 


00006 


00010 




72607 


00162 


55 


00010 


00041 




72610 


00163 


11 


00707 


00007 




72611 


00164 


37 


00247 


00241 




72612 


00165 


21 


00011 


00704 




72613 


00166 


11 


00006 


00010 




72614 


00167 


55 


00010 


00003 




72615 


00170 


37 


00247 


00240 




72616 


00171 


21 


00011 


00704 




72617 


00172 


37 


00247 


00240 




72620 


00173 


11 


00740 


10000 




72621 


00174 


51 


00011 


20000 




72622 


00175 


43 


00013 


00206 




7262 3 


00176 


21 


00011 


00705 




72624 


00177 


11 


00003 


20000 


•—\ 


72625 


00200 


43 


00004 


00213 


CO 
CO 

1— 1 


72626 


00201 


21 


00003 


00741 





72627 


00202 


21 


00005 


00741 


1 


O 

1— 1 


72630 


00203 


11 


00134 


20000 


72631 


00204 


43 


00742 


00130 


X 


72632 


00205 


45 


00000 


00134 


cu 


72633 


00206 


16 


00703 


00011 




72634 


00207 


17 


ocooo 


00701 




72635 


00210 


17 


00000 


00700 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. CV-183 

3AN DIEGO. CALIFORNIA PAGE &£> 

REPORT ZM 5 p7. n 
MODEL ni 

DATE 11-14-56 



72636 


00211 


17 


00000 


00702 


72637 


00212 


45 


00000 


00177 


72640 


00213 


45 


10000 


00216 


72641 


00214 


75 


20002 


00053 


72642 


00215 


21 


00053 


00743 


72643 


00216 


23 


10000 


10000 


72644 


00217 


56 


00000 


00056 


72645 


00220 


17 


00000 


00701 


72646 


00221 • 


75 


00003 


72441 


72647 


00222 


17 


00000 


00700 


72650 


00223 


11 


00713 


00007 


72651 


00224 


55 


10000 


00006 


72652 


00225 


61 


00000 


10000 


72653 


00226 


41 


00007 


00224 


72654 


00227 


45 


00000 


30227 


72655 


00230 


61. 


00000 


00712 


72656 


00231 


11 


00712 


00007 


72657 


00232 


55 


10000 


00003 


72660 


00233 


51 


00744 


20000 


72661 


00234 


35 


00730 


00235 


72662 


00235 


61 


00000 


30235 


72663 


00236 


41 


00007 


00232 


72664 


00237 


45 


00000 


30237 


72665 


00240 


11 


00712 


00007 


72666 


00241 


11 


00737 


10000 


72667 


00242 


53 


00010 


00011 


72670 


00243 


45 


00000 


00762 


72671 


00244 


21 


00011 


00704 


72672 


00245 


54 


00010 


00003 


72673 


00246 


41 


00007 


00242 


72674 


00247 


45 


00000 


30247 



10-316 



FORM NO. E. T. - I 01 r 



SAN DIEGO. CALIFORNIA 



\SV ~ 1UO 



PAGE 57 

REPORT ZM 527-11 

MODEL All 
DATE ll-H-56 



CO 

CO. 



o 

r-H 

I 

O 
O 



a. 



72675 


00250" 


11 


00740 


10000 


72676 


00251 


51 


00703 


20000 


72677 


00252 


72 


00705 


00706 


72700 


00253 


11 


20000 


00013 


72701 


00254 


17 


00000 


00702 


72702 


00255 


45 


00000 


00034 


72703 


00256 


11 


00006 


10000 


72704 


00257 


51 


00745 


20000 


72705 


00260 


43 


00746 


00262 


72706 


00261 


45 


00000 


00161 


72707 


00262 


11 


00006 


00010 


72710 


00263 


55 


00010 


00041 


72711 


00264 


11 


00711 


00007 


72712 


00265 


37 


00247 


00241 


72713 


00266 


21 


00011 


00704 


72714 


00267 


11 


00006 


00010 


72715 


00270 


55 


00010 


00011 


72716 


00271 


11 


00711 


00007 


72717 


00272 


37 


00247 


00241 


72720 


00273 


21 


00011 


00704 


72 721 


00274 


11 


00711 


00007 


72722 


00275 


37 


00247 


00241 


72723 


00276 


45 


00000 


00173 


72724 


00277 


00 


00000 


00000 


72725 


00700 


00 


00000 


06000 


72726 


00701 


00 


00000 


04400 


72727 


00702 


00 


00000 


05000 


72730 


00703 


00 


00200 


00020 


72731 


00704 


00 


00024 


00000 


72732 


00705 


00 


00000 


00040 


72733 


00706 


00 


00000 


00037 



in-317 



E. T. . I <p) ■ r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN OIEGO. CALIFORNIA 



CV-183 

PAGE 58 

REPORT 2M 5?7-ll 
MODEL ^22 
DATE H-14-56 



72734 


00707 


00 


00000 


00001 


72735 


00710 


00 


00000 


00002 


72736 


00711 


00-' 


00000 


00003 


72737 


00712 


00 


00000 


00004 


72740 


00713 


00 


00000 


00005 


72741 


00714 


45 


47150 


10411 


72742 


00715 


03 


30220 


40407 


72743 


00716 


22 


04240 


15745 


72744 


00717 


00 


00000 


00037 


72745 


00720 


00 


00000 


00052 


72746 


00721 


00 


00000 


00074 


72747 


00722 


00 


00000 


00070 


72750 


00723 


00 


00000 


00064 


72751 


00724 


00 


00000 


00062 


72752 


00725 


00 


00000 


00066 


72753 


00726 


00 


00000 


00072 


72754 


00727 


00 


00000 


00042 


72755 


00730 


61 


00000 


00717 


72756 


00731 


07 


77770 


00000 


72757 


00732 


00 


17770 


00000 


72760 


00733 


00 


74000 


00000 


72 761 


00734 


01 


00000 


obooo 


72762 


0073 5 


00 


01000 


00000 


72763 


00736 


00 


00001 


ooooo 


72764 


00737 


07 


00000 


00000 


72765 


00740 


00 


Q0000 


77777 


72766 


00741 


00 


00010 


00000 


72767 


00742 


11 


02000 


00006 


72770 


00743 


00 


00002 


00000 


72771 


00744 


00 


00000 


00007 


72772 


00745 


77 


00000 


00000 



10-318 



ruRM ww. t. i. . I yi f 



CO 

CO 



o 

r-H 
I 

o 
o 

a* 



X! 
cu 



SAN DlfeGO. CALIFORNIA PAGE 59 

REPORT ZM 5P7-11 

MODEL All 
DATEll-H-56 



72773 


00746 


14 


00000 


00000 


72774 


00747 


45 


00000 


00047 


72775 


00750 


00 


00000 


01777 


72776 


00751 


11 


73015 


72461 


72777 


00752 


45 


00000 


72431 


73000 


00753 


45 


00000 


72776 


73001 


00754 


45 


00000 


72431 


73002 


00755 


45 


00000 


73020 


73003 


00756 


11 


00771 


76461 


73004 


00757 


11 


00750 


00001 


73005 


00760 


16 


00772 


00200 


73006 


00761 


45 


00000 


00101 


73007 


00762 


42 


00766 


00764 


73010 


Q0763 


35 


00767 


20000 


73011 


00764 


77 


10000 


20000 


73012 


00765 


45 


00000 


00244 


73013 


00766 


06 


00000 


00000 


73014 


00767 


02 


00000 


00000 


73015 


00770 


45 


00000 


00756 


73016 


00771 


45 


10000 


00216 


73017 


00772 


00 


00000 


00220 


73020 




11 


00000 


74000 


73021 




11 


72152 


00000 


73022 




75 


31777 


73024 


73023 




11 


00001 


74001 


73024 




75 


30357 


01013 


73025 




11 


72052 


01000 



O. E. T. • I (B r 



CONVAIR - DIVISION OF GENERAL DYNAMICS COUP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 60 

REPORT ZM 5?7-ll 
MODEL All 
DATE ll-K-56 



SPUR SUBROUTINE ASSEMBLY 



76151 




15 


01601 


76153 


Y ADDRESS 




76152 




75 


30052 


76154 


PW FOR 




76153 




11 


30000 


00002 


EXAMINATION 




76154 




75 


30304 


00056 


THIS TO. 




76155 




11 


76156 


00056 


ES 




76156 


00056 


15 


01753 


00121 


PW ACQUISITION 




76157 


00057 


11 


00347 


00372 


INITIAL INST* L I i 


11 T 


76160 


00060 


11 


01752 


00373 


INITIAL TEMP* Lli 


■SIT 


76161 


00061 


15 


01753 


00064 


SET TREE TEST 




76162 


00062 


31 


01761 


00000 






76163 


00063 


36 


01751 


00374 


SET TALLY 




76164 


00064 


11 


30000 


20000 






76165 


00065 


42 


00357 


00067 


WHIFFLETREE 




76166 


00066 


42 


00360 


00115 


TEST 




76167 


00067 


21 


00064 


01753 


STEP 




76170 


00070 


41 


00374 


00064 






76171 


00071 


41 


01761 


00120 


TEST FOR END 




76172 


00072 


75 


3 1240 


00074 


STORE 




76173 


00073 


11 


00400 


74400 


MODIFIED ES 




76174 


00074 


75 


30200 


00076 


PART OF 




76175 


00075 


11 


77213 


01200 


CARD ROUTINE 




76176 


00076 


61 


ocooo 


01302 


CAR* RET. 




76177 


0007 7 


31 


003 61 


00052 


PRINT 




76200 


00100 


61 


COOOO 


c. \) O \J \J 


AVAIL* 




76201 


00101 


34 


20000 


00006 


AMD 




76202 


00102 


47 


00100 


00103 


ES 




76203 


00103 


55 


003 73 


10030 


FREE 




76204 


00104 


61 


00000 


01305 


SPACE 




76205 


00105 


11 


01305 


01371 


LIMITS 




76206 


00106 


37 


0125.5 


01250 






76207 


CC107 


37 


00107 


00110 







10-320 



FOBM NO- C. T. . 1 <B • r 



SAN DIEGO. CALIFORNIA 



PAGE~6T 

REPORT ZM 5?7-ll 
MODEL. All 
DATE 11-14-56 





76210 


00110 


23 


00372 01751 






76211 


00111 


55 


20000 00030 






76212 


00112 


37 


00107 00104 






76213 


00113 


75 


31777 01746 


EXIT 




76214 


00114 


11 


74001 00001 


RESTORE E.S. 




76215 


00115 


23 


00372 00322 


ADJUST INST* LIMITS 




76216 


00116 


75 


30007 00071 


WHIFFLETREE 




76217 


00117 


11 


00350 01472 


ADDITION 




76220 


00120 


75 


30002 00122 


CURRENT 




76221 


00121 


11 


30000 00362 


P W 




76222 


00122 


21 


00121 01753 


STEP 




76223 


00123 


15 


00362 00165 


SET SUB. R. EXTRACT. 




76224 


00124 


31 


00363 00060 






76225 


00125 : 


11 


20000 00364 


NUMBER OF INST. 




76226 


00126 


34 


20000 00014 






76227 


00127 


11 


20000 00365 


.NUMBER OF CONST. 




76230 


00130 


34 


20000 00014 






76231 


00131 


11 


20000 00366 


NUMBER OF TEMP. 




76232 


00132 


31 


00364 00000 


NUMBER 




76233 


00133 


35 


00365 00374 


INST. AND CONST. 




76234 


00134 


35 


00317 00164 


SUB. R. 




76235 


00135 


55 


00164 00017 


TRANSFER 




76236 


00136 


23 


00372 00374 


NEW INST. LIMIT 


CO 


76237 


00137 


42 


Q0343 00157 


ALARM 


cu. 
1—1 


76240 


00140 


16 


20000 00165 


SUB. R. LANDING 


O 
r-1 


76241 


00141 


16 


200P0 00312 


INST* RETURN 


1 

O 

O 


76242 


00142 


36 


00346 00367 


INST. MODIFICATION 


s 


76243 


00143 


11 


00340 10000 




(X. 


76244 


00144 


52 


00362 00363 


MODIFIED ENTRANCE 




76245 


00145 


13 


00641 20000 






76246 


00146 


36 


00374 00370 


TEMP. MOD. 



C. T. - « (ftp 



CONVAIR 



DIVISION OF GENERAL DYNAMICS CORP. 

SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 6? 

REPORT ZM 527-11 

MODEL All 
DATEll-H-56 



76247 


00147 


55 


00362 


10006 




76250 


00150 


51 


00336 


00362 


P 


76251 


00151 


31 


00366 


00000 


TEST 


76252 


00152 


35 


01752 


20000 


TEMP 


76253 


00153 


42 


00373 


00155 


LIMIT 


76254 


00154 


11 


20000 


00373 


CHANGE LIMIT 


76255 


00155 


11 


00373 


20000 




76256 


00156 


42 


00372 


00161 




76257 


00157 


75 


31777 


76020 


ALARM 


76260 


00160 


11 


74001 


00001 




76261 


00161 


31 


00346 


00000 




76262 


00162 


35 


00374 


00365 


UPPER LIMIT INST. MOD. 


76263 


00163 


35 


00366 


00366 


UPPER LIMIT TEMP. 


76264 


00164 


30 


30000 


30000 


SUB. R. FOR 


76265 


00165 


11 


30000 


30000 


MODIFICATION 


76266 


00166 


37 


00260 


00251 


MODIFY 


76267 


00167 


45 


00000 


00312 


U ONLY 


76270 


00170 


31 


00165 


00017 


SET INITIAL 


76271 


Q0171 


15 


20000 


00233 


INST ACQUISITION 


76272 


00172 


41 


00364 


00233 


TALLY INST. MOD. 


76273 


00173 


11 


00315 


00231 




76274 


00174 


31 


00363 


00017 




76275 


00175 


35 


00363, 


00363 




76276 


00176 


55 


00362 


10043 




76277 


00177 


44 


00201 


00200 




76300 


00200 


11 


00316 


00231 




76301 


00201 


55 


00362 


10041 




76302 


00202 


51 


00334 


20000 




76303 


00203 


55 


1000O 


00003 




76304 


00204 


43 


00322 


00222 


TEST 60 TO 67 


76305 


00205 


16 


00344 


00231 


SET FOR 10»30 



10-322 



FORM NO. E. T. • I 



SAN PIEGO. CALIFORNIA 



PAGE 63 

REPORT ZM 5?7-ll 
MODEL All 
DATE 11 -14- 56 



CO 

CO 



o 

r-H 
I 

o 

o 
o 



X 

a. 



76306 


00206 


43 00320 


00220 


TEST FOR 


76307 


00207 


43 01751 


00220 . 


10,30 


76310 


00210 


43 00334 


00212 


TEST FOR 70 TO 77 


76311 


00211 


45 00000 


00157 




76312 


00212 


16 00345 


00231 


SET FOR 74 


76313 


00213 


51 00334 


20000 




76314 


00214 


43 00321 


00231 


TEST FOR 74 


76315 


00215 


16 00332 


00231 


SET FOR 70, 71, 72, 73 


76316 


00216 


42 00321 


00222 


TEST FOR 75, 76, 77 


76317 


00217 


45 00000 


00157 


ALARM 


76320 


00220 


51 00324 


20000 


TEST FOR 


76321 


00221 


43 00324 


00157 


17, 37 


76322 


00222 


51 00322 


10000 




76323 


00223 


47 00224 


00231 




76324 


00224 


43 01752 


00230 




7632 5 


0022 5 


43 00321 


00227 




76326 


00226 


23 00231 


01751 




76327 


00227 


23 00231 


01752 




76330 


00230 


23 00231 


01751 




76331 


00231 


30 00000 


00000 




76332 


00232 


45 00000 


00071 




76333 


00233 


11 30000 


00375 


CURRENT INST* 


76334 


00234 


21 00233. 


00337 


STEP 


76335 


00235 


55 00375 


10006 




76336 


00236 


51 00336 


20000 




76337 


00237 


43 00323 


00271 


14 SPECIAL 


76340 


00240 


43 00324 


00261 


V ONLY 


76341 


00241 


43 00327 


00261 


V ONLY 


76342 


00242 


42 00325 


00251 


U, V 


76343 


00243 


42 00326 


00166 


U ONLY 


76344 


00244 


42 00330 


00251 


U, V 



T. - I (ft r 



CONVAIR - DIVISION OF GENERAt DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 
page 6A 
report ZM 527-11 

MODEL All 
DATE ll-H-56 



76345 


00245 


42 00331 


00166 


U ONLY 


76346 


00246 


42 00333 


00261 


V ONLY 


76347 


00247 


42 00335 


00251 


U# V 


76350 


00250 


45 00000 


00261 


V ONLY 


76351 


00251 


55 00375 


00025 




76352 


00252 


51 00340 


10000 




76353 


002 53 


42 00346 


00256 


NO MOD. 


76354 


00254 


42 00365 


00265 


MOD INST 


76355 


002 55 


42 00366 


00267 


MOD TEMP 


76356 


00256 


37 00256 


00257 




76357 


00257 


55 00375 


00017 




76360 


00260 


37 00260 


00261 




76361 


00261 


11 003 75 


10000 




76362 


00262 


37 00256 


00252 




76363 


00263 


37 00263 


00264 




76364 


00264 


45 00000 


00312 


TO RESTOR 


76365 


00265 


21 00375 


00367 




76366 


00266 


45 00000 


00256 




76367 


00267 


21 00375 


00370 




76370 


00270 


45 00000 


00256 




76371 


00271 


11 00375 


00371 


DUPLICATE 


76372 


00272 


11 00375 


10000 


SYNTHETIC 


76373 


00273 


51 01757 


00375 




76374 


00274 


51 00342 


20000 




76375 


00275 


31 20000 


00003 




76376 


00276 


35 00375 


00375 


INSTRUCTION 


76377 


00277 


55 00371 


10006 




76400 


00300 


44 00301 


00303 


ONE, TWO ADDRESS 


76401 


00301 


37 00263 


00261 




76402 


00302 


45 00000 


00304 




76403 


00303 


37 00263 


002 51 





10-324 



FORM NO. E. T. - I (R r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN PIEGO, CALIFORNIA 



CV-183 

PAGE 65 
REPORT ZM 5?7-ll 
MODEL All 
DATE II-I4-56 





76404 


00304 


55 00375 


20041 


REPLACE 




76405 


00305 


11 00342 


10000 






76406 


00306 


53 20000 


00371 


WITH 




76407 


00307 


11 01757 


10000 


SYNTHETIC 




76410 


00310 


53 00375 


00371 






- 76411 


00311 


11 00371 


00375 


PARTS 




76412 


00312 


11 00375 


30000 


RETURN INST* 




76413 


00313 


21 00312 


01751 


STEP 




76414 


00314 


45 00000 


00172 






76415 


00315 


15 00363 


01477 






76416 


00316 


16 00363 


01477 






76417 


00317 


00 17075 


30000 






76420 


00320 


00 00000 


00003 






76421 


00321 


00 00000 


00004 






76422 


00322 


00 00000 


00006 






76423 


00323 


00 00000 


00014 






76424 


00324 


00 00000 


00017 






76425 


00325 


00 00000 


00031 






76426 


00326 


00 00000 


00035 






76427 


00327 


00 00000 


00045 






76430 


00330 


00 00000 


00054 






76431 


00331 


00 .00000 


00056 




/~\ 


76432 


00332 


00 00000 


01505 




CO 

co 

r-i 


76433 


00333 


00 00000 


00071 




1 

O 


76434 


00334 


00 00000 


00007 




1— I 

O 


76435 


00335 


00 00000 


00075 




O 


76436 


00336 


00 00000 


00077 






76437 


00337 


00 00001 


00000 




cl, 


76440 


00340 


00 00000 


77777 






76441 


00341 


00 00000 


00776 






76442 


00342 


00 00177 


70000 





K. T. - » (JV w 



CONVAIR - DIVISION OF GENfflAt DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 

PAGE 66 

REPORT ZM 527-11 

MODEL ALL 
DATE 11-14-56 



76443 


00343 


00 


00000 


00400 


LOWE LIMIT INST 


76444 


00344 


00 


00000 


01632 




76445 


00345 


00 


00000 


01531 




76446 


00346 


00 


00000 


01000 




76447 


00347 


00 


00000 


01500 




76450 


00350 


44 


01473 


01474 


01472 


76451 


00351 


44 


30067 


30066 


01473 


76452 


00352 


44 


30065 


30064 


01474 


76453 


00353 


44 


01476 


01477 


01475 


76454 


00354 


44 


30063 


30062 


01476 


76455 


003 55 


44 


30061 


30060 


01477 


76456 


00356 


44 


01472 


01475 


01500 


76457 


00357 


60 


00000 


00000 


WHIFFLETREE 


76460 


00360 


67 


77777 


77777 


EXTENSION TESTS 


76461 


00361 


30 


17301 


41142 





10-326 



FORM NO. E. T. • t (ft -r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV-183 
page67 
report Z M 5?7-ll 

MODEL £Q 
DATE H-I4.-56 



SPUR SQUARE ROOT 



CO 



I 

o 

r-H 
I 

o 
o 



70252 


01000 


11 


01766 


01774 


CASE ZERO 


70253 


01001 


11 


01766 


20000 


N TO A 


70254 


01002 


46 


76020 


01003 


NEGATIVE 


70255 


01003 


47 


01004 


01742 


ZERO 


70256 


01004 


12 


01767 


10000 


P EVEN 


70257 


01005 


55 


10000 


00043 


OR 


70260 


01006 


44 


01007 


01011 


ODD 


70261 


01007 


21 


01767 


01751 


P 1 TO P 


70262 


01010 


54 


01766 


00107 


N/2 TO N 


70263 


01011 


55 


01767 


00043 


N /2 TO P 


70264 


01012 


11 


01767 


01775 


P TO R 


70265 


01013 


43 


01025 


01742 


N EQUAL .9 . 


70266 


01014 


11 


01025 


01762 


•9 2 TO X 


70267 


01015 


31 


01766 


00042 


COMPUTE 


70270 


01016 


73 


01762 


01763 




70271 


01017 


54 


01762 


00107 


SQUARE 


70272 


01020 


23 


10000 


01762 




70273 


01021 


21 


01762 


01763 




70274 


01022 


44 


01015 


01023 


ROOT 


70275 


01023 


11 


20000 


01774 


N TO R 


70276 


U1024 


45 


00000 


01742 


EXT 


70277 


01025 


37 


77777 


77777 


.9 



X 

0- 



J. t. T. . I (TV r 



CONVAIR - DIVISION OF GB&RAL DYNAMICS CORP. 

SAN DIEGO. CALIFORNIA 



CV-ltW 

PAGE 68 

REPORT ZM 5?7-ll 
MODEL All 
DATE ll-H-56 



SPUR CU1E ROOT 



70300 


01000 


11 


01766 


01774 


CASE ZERO 


70301 


01001 


11 


01766 


20000 


N TO A 


70302 


01002 


47 


01003 


01742 


N ZERO 


70303 


01003 


11 


01767 


20000 


P/3 


70304 


01004 


73 


01036 


10000 


TO Q 


70305 


01005 


47 


01006 


01013 


REM. ZERO 


70306 


01006 


43 


,01752 


01011 


REM. 2 


70307 


01007 


21 


01767 


01751 


P 1 TO & 


70310 


01010 


54 


01766 


00107 


N / 2 TO N 


70311 


01011 


21 


01767 


01751 


P 1 TO P 


70312 


01012 


54 


01766 


00107 


N / 2 TO N 


70313 


01013 


11 


01767 


20000 


P/3 


70314 


01014 


73 


01036 


01775 


TP P 


70315 


01015 


11 


01037 


01762 


.9X2 TO 


70316 


01016 


11 


01766 


20000 


N 


70317 


01017 


46 


01020 


01021 


NEG. 


70320 


01020 


13 


01037 


01762 


-.9 TO X 


70321 


01021 


43 


01762 


01742 




70322 


01022 


71 


01762 


01762 


X 


70323 


01023 


54 


20000 


00045 


EXP 35 


70324 


0102^ 


11 


20000 


01763 




70325 


01025 


54 


01766 


20043 


N EXP 70 


70326 


01026 


73 


01763 


20000 


X 


70327 


01027 


36 


01762 


20000 


-X EXP 35 


70330 


01030 


73 


01036 


10000 


X 


70331 


01031 


21 


01762 


10000 


X EXP &5 


70332 


01032 


71 


10000 


01766 


N X 


70333 


01033 


46 


01022 


01034 


NEG. 


70334 


01034 


11 


01762 


01774 


■■X EQUAL N 


70335 


01035 


45 


00000 


01742 


EXIT 


70336 


01036 


00 


00000 


00003 




70337 


01037 


37 


77777 


77777 


.9 



10-328 



FORM NO. E. T. ■ » <f5 r 



CONVAiR - DiViSiON OF GENERAL DYNAMICS CORP. 



SAN DIEGO. CALIFORNIA 



CV 183 

PAGE 69 

REPORT zm 527-11 

MODEL All 
DATE H-I4.-56 



SPUR nth ROOT SUBROUTINE 



CO 
CO 



I 

o 



o 
o 
o 



X 

a, 



70200 


01000 


11 


01761 


20000 


\ -* A 




70201 


01001 


42 


01752 


76020 


*\ <^ 2 — > ALARM 




70202 


01002 


75 


30004 


01004 


1 N -^ S » R 




7020S 


01003 


11 


01770 


01772 


J 




70204 


01004 


11 


01770 


20000 


N —* A 




70205 


01005 


47 


01006 


01736 


N = ?-f EXIT 




70206 


01006 


11 


01051 


01764 


■ .9 —► P 




70207 


01007 


46 


01010 


01013 


N NEG. ? 




70210 


01010 


13 


01764 


01764 


-.9 — > P 




70211 


01011 


55 


01761 


10043 


1 \ EVEN — > ALARM 




70212 


01012 


44 


01013 


76020 


J 




70213 


01013 


11 


01771 


20000 


EXP — }> A 




70214 


01014 


73 


01761 


01775 


EXP/N — f 1775", REM. -> A 


70215 


01015 


11 


10000 


01765 


EXP/N — y P 




70216 


01016 


47 


01017 


01022 


REM. - ? 




70217 


01017 


21 


01765 


01751 


EXP/N. + 1 — > P 




70220 


01020 


75 


30002 


01024 


1 s = h -jr c 




70221 


01021 


11 


01772 


01770 


J 




70222 


01022 


11 


01770 


20000 


n — y a 




70223 


01023 


43 


01764 


01742 


N = it. 9 -V EXIT 




70224 


01024 


11 


01761 


20000 


A-t A 




70225 


01025 


36 


01752 


01052, 


V^ ~2 - J -f 1052 




70226 


01026 


11 


01764 


01766 


7 X £_, -^ B 




70227 


01027 


11 


01765 


01767 


J 




70230 


01030 


37 


01030 


01031 






70231 


01031 


37 


01741 


01633 


1 N/X?"' 
1 1 — 1 




70232 


01032 


41 


01052 


01026 


J 




70233 


01033 


37 


01030 


01026 


Xi-l-~* B 




70234 


01034 


37 


01741 


01655 


"'*T-I rX £-| 




70235 


01035 


73 


01761 


20000 


A « &y- 




70236 


01036 


37 


01741 


01712 


NORMALIZE A X 




70237 


01037 


47 


01040 


01047 


A X = 0?-VEXIT 





K. T. - I CP> r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEOO. CALIFORNIA 



CV-183 j 

PAGE 70 

REPORT ZM 5?7-ll 
MODEL All 
DATE 11-14-56 



70240 


01040 


70241 


01041 


70242* 


01042 


70243 


01043 


70244 


01044 


70245 


01045 


70246 


01046 


70247 


01047 


70250 


01050 


70251 


01051 



11 01775 01052 
37 01030 01026 
37, 01741 01656 
11 01774 01764 
11 01775 01765 
23 01771 01052 
42 01754 01020 

75 30002 01742 
11 01764 01774 
37 77777 77777 



A'X EXP* — >► 105^2 



} 



(x yEXP)- fax EXP) 
A y 35 -^ EXIT 
EXIT 



.9 



10-330 



10:27 

The Ramq-Wooldridge Corporation 



Los Angeles 45, California 



i 

o 
o 



Date: January 9, 1956 



Subject: Computing Center From: W. F. Bauer 

Organization 



The following delineates the areas of interest, cognizance, and responsibility 
of the five groups comprising the organization of the Digital Computing Center, 

SYSTEMS AMD TRAINING 

1. Develop, maintain &nd improve a cor, prehensive computation system for the 
1103 and 1103A including component parts such as compiler, algebraic 
coding scheme, service routines, and the routines necessary for effecting 
an automatic system, implementing, insofar as is possible, the suggestions 
for such programs and routines made by all other groups. 

2. Develop such administrative procedures concomitant to the computation 
system to ensure the proper flow of information to and from the personnel 
of the Operations Group which, operates the various equipments, and 
cooperate with that group in effecting the plan. 

3. Keep subroutine and service routine library records, disseminate appropriate 
programming and system operation information to Computing Center personnel 
and other interested parties, and participate in cooperative programming 
efforts and in the exchange of program information between 1103 or 1103A 
users. 

h* Aid in the general recruiting program and assume major responsibility in 

the initial instruction and training of personnel in programming techniques. 

5># Recruit and train computer operators, operate the 110J (or 1103A) computer, 

—v and develop operating techniques necessary to. insure the highest standards 

c\i of computer use. 
© 

C 6 f Carry out specific projects in programming and computer studies as may be 

© assigned. 



OPERATIONS 



cu 1. Aid the Systems Group in developing methods and procedures for operation 
of the 1103 (or 1103AJ computation system, and appropriately execute such 
procedures. 



10:27 

Page #2 

2. Schedule 1103 (or 1103A) computer time and develop and initiate methods 
and procedures as necessary to generate and maintain adequate records 
concerning problem assignments, records necessary for budget and fiscal 
requirements, and records of computer operating data* 

3, Operate all auxiliary and off-line equipment, including hand computer equip- 
ment, recruit and train operators of such equipment, and design procedures 
as are necessary in the operation of such equipment© 

k* Determine the need and specifications for any equipment to be modified, 
purchased or especially built, and transmit information as needed to pro- 
gramming groups on the operation and characteristics of such equipment. 

£• Perform computer programming as necessary, especially on those problems 
involving special equipment such as analog-digital converters used in 
simulation and data reduction activities » 



PROGRAMING 

1, Make contacts as necessary with customers and problem originators in the 
programming and running of assigned problems, 

2, Assume major responsibility for the central GHRD programming effort as 
assigned^ such as aerodynamics, structures, and air frame and trajectory 
analysis. ** 

3, Cooperate with and advise the Numerical Analysis and Systems Groups on 
the development of routines necessary for production computation, 

k* Cooperate with and advise the Operations Group in the development of a 
computation system and its subsequent adoption ° 

5?. Assume major responsibility for the general recruiting program and the 
evaluation of prospective programmers* 



NUMERICAL ANALYSIS 

1. Consult with customers or problem originators on problems requiring 
special attention in regards formulation for numerical handling, advise 
on the formulation and machine plan of all problems in the Computing 
Center, and assume major responsibility for certain problems as assigned, 

2. Conduct basic and applied research in numerical analysis and machine 
techniques and publish the results whenever appropriate* 

3. Ascertain the need for, determine specifications, and develop techniques 
of standard numerical operations (e«g. matrix inversion, differential 
equation solving) as are needed and, when appropriate, perform the 
computer programming necessary,, 

h* Aid in the general recruiting program, and assume major responsibility 
in the recruitment of numerical analysts in cooperation with the 
Programming Group. 



10-332 



O 



I 

o 



a 






10:27 

£, Provide technical support unci coordination to the activities of consul tents 
to the Computing Center in numerical analysis. 

KATlIEi-ATIC AL AIM ,TS1X 

1, Consult with customers or problem originators on prc.bleivs, pori'orr. inj_; 
such mathematical research and analysis as is assigned cr necessary; 
advise the Computing Center on the formulation of problems when appropriate; 
and consult with the Numerical Analysis Group to deterr.inc the combination 
of machine and analytical techniques likely to (jive most fruitful results. 

2, Conduct basic research in Applied Mathematics as is appropriate and 
publish such results, 

3, Aid in the general recruiting program, and assume major responsibility 
in the recruitment of applied mathematicians in cooperation with the 
Programming Group. 

2|* Provide technical support and coordination to the activities of consultants 
to the Computing Center in applied mathematics. 

5. Provide and maintain sources of information in applied n athematics in 
the form of appropriate seminars, lectures, courses, Mid the Computing 
"^tiier Library. 




Walter F . W ' 



:njs 



Digital 
Computing Center 



? 



Numerical 
Analysis 



Systems 

and 
Training 




Operations 




Ti 




?J 




TO 


• *«* 


CO 


xs 




■ •• 


■P* 


'tj 



10:28 

MATHEMATICAL SERVICES BRANCH 

At the Air Force Armament Center the bulk of the machine computations are 
performed by two Directorates, the Directorate of Ballistics and the Directorate 
of Technical Support. 

Within the Directorate of Technical Support the Mathematical Services Branch 
is responsible for the reduction of data on each test project to insure that data 
are suitable for analysis and/or inclusion in the final report* This Branch is 
divided into three Sections; Test Data, Computation and Equipment Maintenance* 

The Test Data Section establishes mathematical and assessment procedures 
for processing test data; receives, stores, edits, and reviews raw and processed 
data; assists other agencies in programming problems; spot lcnecks processed data, 
accomplishes assessment on selected portions of test data; prepares data for sub- 
mission to project and analysis personnel. 

The Computation Section accomplishes computation on the electronic digital 
computer; assists mathematicians in working out computation and reduction techni- 
ques and in selecting instrumentation methods compatible with computing and 
analyzing equipment; operates analog-to -digital converts, plotters, electronic 
analyzers, recorders, and computer output devices, develops techniques and proce- 
dures applicable thereto. 

The Equipment Maintenance Section maintains data reduction and computing 
equipment of the Center; provides service assistance in the electronic, computer 
and associated equipment; accomplishes minor modification of existing equipment 
as required by Project Mathematicians. 

Each of these Sections are divided into operating groups with defined 
responsibilities in specialized fields as indicated on the organization chart. 

Within the Directorate of Ballistics the Ballistic s r Computations Officer 
performs necessary data programming and computations utilizing existing facilities 
to greatest extent possible; provides consultant services to develop new data 
reduction and computation techniques. 

A third organization, the Analysis Division, also initiates computing require- 
ments at the Air Force Armament Center. Within this Division the Test Analysis 
Branch recommends priorities for all the Center's computing facilities and 
associated functions; applies numerical analysis techniques and performs coding 
and computations of analysis problems on the Center's computers as required. 
^ The Research Branch originates improved and/or new computing techniques and pro- 
oi cedures where existing ones are inadequate or non-existent, except in the ballis- 
o tics area; investigates, on a continuing basis, computing methods and techniques 
w employed elsewhere, for possible use at the Center, 
o 

7 In addition the Applied Mathematics Division of the Directorate of Statis- 

o tical Services, Air Proving Ground Comnand, assists in programming and operating 
r* Air Force Armament Center projects on the computers available in that Command. 

x 



E. T. • 1 (ft ■ r 



CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. 



SAN DIEOO, CALIFORNIA 





CV-154 (f 


PAGE 


IC 011-3 


REPORT 


ZM 491 


MODEL 


All 


DATE 


5-1-56 


REVISED 





UNPACKED FLOATING POINT CARD READ 



7 400 


00742 


56 


ooooo 


30000 


EXIT 


7 401 


00743 


75 


31777 


72403 


STORE 


7 40? 


00744 


11 


00001 


74001 


ES 


72403 


00745 


75 


30352 


00747 


ROUTINE 


72404 


00746 


11 


72400 


00742 


TO ES 


72405 


00747 


11 


00742 


20000 


SET 


72406 


00750 


36 


01264 


72432 


REPEAT 


72407 


00751 


35 


013 05 


20000 


SET 


72410 


00752 


16 


20000 


00770 


EXIT 


72411 


00753 


55 


00742 


200 2 5 


TEST FOR 


72412 


00754 


44 


00757 


00756 


ES 


72413 


00755 


00 


00000 


00114 


ADDRESSES 


72414 


00756" 


32 
. 55 


00776 


00000 


ADDRESS MODIFICATION 


72415 


00757, 


20000 


00017 




72416 


00760 


37 


00760 


00761 




72417 


00761 


16 


20000 


00763 


SET ACQUISITION 


72420 


00762 


11 


00777 


01024 


ERASE INSTRUCTION 


72421 


00763 


71 


01264 


30000 


ACQUIRE CONTROL WORD 


72422 


00764 


55 


20000 


00006 




72423 


00765 


37 


00760 


00754 


X 


72424 


00766 


"55 


20000 


00017 




72425 


00767 


37 


01001 


01004 


TP SIBRPITOME 


72426 


00770 


75 


31777 


30000 


RESTORE E S 


72427 


00771 


11 


74001 


00001 


AND EXIT 


72430 


00772 


75 


31777 


72432 


RESTORE E S 


72431 


00773 


11 


74001 


00001 


AND 


72432 


00774 


30 


00000 


0000 


REPEAT 


72433 


00775 


02 


00000 


00104 




72434 


00776 


74 


00000 


00000 




72435 


00777 


11 


00000 


00000 




72436 


01000 


30 


00000 


0000* 


REPEAT 


72437 


01001 


45 


00000 


30000 


EXIT 



10-336 



RW-71 
(REV) 

PAGE 1 OF 2 
REVISED 09-05-56 



THE RAMO-WOOLDRIDGE CORPORATION 
LOS ANGELES 45 # CALIFORNIA 



UTILITY ROUTINE LIBRARY 
TABLE OF CONTENTS 



■t* 



i 

o 
© 






A DESCRIPTION OF THE LIBRARY ORGANIZATION 04-01-55 

PROGRAMMING AND OPERATING CONVENTIONS 06-20-56 

PROGRAMMING REMINDERS 06-15-56 

LIBRARY HANDLING PACKAGE FOR PAPER TAPE INPUT 06~15-« 

BOOTSTRAP PROCEDURE USING CARDS 05-01-56 

OCTAL-DECIMAL CONVERSION TABLES 

40000 GROUP * SERVICE ROUTINE - ENTRANCES 06*01-56 



ENTRANCE ADDRESS ALARM ROUTINE 
STANDARD ATMOSPHERE CALCULATION 

RAWOOP* ONE PASS ASSEMBLY PROGRAM 

FIXED POINT CARD OUTPUT 

CARD PUNCH OUTPUT FOR FLOATING POI&T NUMBERS 

STATED POINT CARD OUTPUT 

BINARY CARD READ-IN ROUTINE 

FIXED POINT DECIMAL CARD READ-IN ROUTINE 

CURVE FITTING BY MINI -MAX PROCEDURE 

NIM# A DEMONSTRATION ROUTINE 

DATE TO DAY CONVERSION DEMONSTRATION ROUTINE 

DETERMINANT EVALUATION* COMPLEX 

DEFINITE INTEGRAL EVALUATION ROUflNE 

FIXED POINT DEFINITE INTEGRAL EVALUATION 

FLOATING POINT DEFINITE INTEGRAL EVALUATION 

EIGENVECTORSt VALUES OF REAL SYMMETRIC MATRICES 
FIXED POINT EXPONENpAL. ROUTINE 
FLOATING POINT EXPONENTIAL ROUTINE 

FLEXOWRITER CONSTANT POOL , 

FLOATING POINT PACKA6E*-SNAP» SNIP* AND TRACE 

FERRANTI INPUT ROUTINE 

SIMPLIFIED FERRANTI INPUT FOR BOOTSTRAP 

DECIMAL OUTPUT* ROUTINE FOR FLEXOWRITER AND PUNCH 

INTERPOLATION WITH UNEQUAL INCREMENTS IN ARGUMENT 

FIXED POINT NATURAL LOGARITHM 

FLOATING POINT NATURAL LOGARITHM ROUTINE 



ALR-1 


08-16-55 


ATM-1 


05-01-56 


CMP-0 


07-10-56 


CPO-0 


03-26-56 


CPO-1 


09-23-55 


CPO-2 


04-16-56 


CRI-1 


12-09-55 


CRI-2 


12-09-55 


CVF-0 


11-14-55 


DEM-0 


10- -55 


DEM-1 


10- -55 


DET-2 


07-25-56 


DIE^O 


06-15-56 


DIE-1 


11-25-55 


DIE-2 


11-25-55 


EGN-0 


05-01-56 


EXP-2 


11-15-55 


EXP-3 


08-10-55 


FLX-0 


06-15-56 


FPP-0 


07-20-56 


FRI-0 


07-10-56 


FRI-1 


10-03-55 


HTO-0 


07-25*55 


INT-1 


10-10-55 


LOG-1 


11-22-55 


LOG-2 


08-10-55 



1 A_^Q7 



RW-71 
(REV) 

PAGE 2 OF 2 
REVISED 09-05-56 



THE FLEXOWRITER MEMORY DUMPf 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 

LINEAR MATRIX EQUATION SOLVER ♦ FLOATING POINT 

LINEAR MATRIX EQUATION SOLVER i COMPLEX 

NTH ROOT ROUTINE 

NUMERICAL INTEGRATION BY THE GILL METHOD 

FLOATING POINT GILL METHOD 

GILL METHOD* COMPLEX 

ALGEBRAIC EQUATION SOLVER 

NORMALLY DISTRIBUTED PSEUDO RANDOM NUMBERS 
COLUMN HEADING ROUTINE 

AUTOMATIC SAMPLER 

CENTRAL EXCHANGE SlNE-COSINE ROUTINE 

POLYNOMIAL MULTIPLY SINE-COSINE ROUTINE 

SMALL ANGLE SINE-COSINE ROUTINE 

FLOATING POINT SINE-COSlNE ROUTINE 

FLOATING POINT SINE-COSINE 

ARCSINE-ARCOSINE ROUTINE 

ARCSINE-ARCOSINEi FLOATING POINT 

SQUARE ROOT ROUTINE 

STORAGE TO MAGNETIC TAPE TRANSFER 

TNI-0 05-01-56 ARCTANGENT ROUTINE 

TNI-1 06-15-56 FLOATING POINT ARCTANGENT ROUTINE 

TST-0 12-09-55 MAGNETIC TAPE TO STORAGE TRANSFER 

URT-1 WRITE UP NOT AVAILABLE 
URT-3 WRITE UP NOT AVAILABLE 

CUMULATIVE ERRATA 08-15-56 

BULLETINS #12 AND #14 



MDP-0 


12-09-55 


MDP-1 


12-09-55 


MDP-2 


12-09-55 


MDP-3 


12-09-55 


MDP-4 


05-01-56 


MII-0 


05-01-56 


MTI-0 


11-30-55 


MTI-1 


07-26-56 


MTI-2 


08-03-56 


NRT-0 


12-01-55 


NUI-3 


05-01-56 


NUI-4 


05-10-56 


NUI-5 


06-20-56 


POL-0 


09-04-56 


RAN-0 


05-20-56 


RPH-0 


05-23-56 


SAM-0 


08-09-55 


SIN-0 


05-01-56 


SIN-1 


05-01-56 


SIN-2 


05-01-56 


SIN-3 


08-10-55 


SIN-4 


05-15-56 


SNI-1 


06-15-56 


SNI-2 


08-01-56 


SQft-0 


05-01-56 


STT-0 


12-09-55 



10-338 



RW-71 
(REV) 
CONVENTIONS 
Pg. 1 of 2 
Revised 6/20/56 

THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 45 > California 

RAMO-WOOLDRIDGE PROGRAMMING AND OPERATING CONVENTIONS 

1. Drum addresses 55359 to 56383 ( 76000b to 77777b) have been reserved 
for the drum image of electrostatic storage. These 1024 cells will 
be used by those service routines which operate in electrostatic 
storage and which must restore electrostatic storage after performing 
their functions. This part of the drum should not be used by the 
programmer to store part of his production program (Note: Drum 
addresses start at 40000 in decimal notation). 

2. Drum cells 52287 to 55358 (70000b to 75777b) are reserved for the 
storage of service routines and are not, in general, available for 
general program use. 

3. Drum cells 48191 to 52286 (60000b to 67777b) will be used for the 
assembly data, assembly program, and subroutines. These cells are 
available for general program use, since the information will be 
stored in these cells only during program assembly. If more space 
is required for subroutines, cells 57777b and lower may be used. 

4. Electrostatic stor ge cells 13 through 22 (15d - 26b) have been set 
aside for a ten -word constant pool as follows: 

00 00000 00000 
00 00000 00077 
00 00001 00000 

00 00000 00001 

00 00001 00001 

00 00000 00110 

52 52525 25252 

77 00000 00000 
00 07777 00000 

T 5« Cells 23 through 32 (27b through 40b) have been set aside for temporary 

r-i storage. These temporary cells should be used in the strictest sense 

o of the word and the programmer should not assume information will 

o remain in these cells unchanged in passage from one portion of a 

^ program to another. 

x 

04 6, There will be three methods of starting the computer depending upon 

the amount of information stored on the drum and magnetic tape as 

follows: 

a. If the Ferranti read -in program is stored on the drum in 
its normal place along with the other utility routines, a 
tape can be read in by transferring control to cell 40001. 



1 0-339 



13 


Zero 


00015 


14 


Six Bit Extractor 


00016 


15 


Advance u 


OOOI7 


16 


Advance v 


00020 


17 


Advance u and v 


00021 


18 


Decimal 72 


00022 


19 


Alternator 


00023 


20 


Operation Code Extractor 


00024 


21 


"n" Extractor 


00025 


22 


(not yet assigned) 


00026 



RW-71 
(REV) 

CONVENTIONS 
Pg. 2 of 2 
Revised 6/20/56 



b. If the service routines are not on the drum, an MP start is 
performed which reads the service routines onto the drum 
from magnetic tape Unit = 0. During this transfer, check 

sums are completed and checked against sums previously obtained 
upon storage of the routines on tape. 

c. In the event the service library data has been removed from 
the magnetic tape Unit = and the drum due to engineering 
maintenance or another reason, a bootstrap procedure will be 
used to read the service routine library and Ferranti read -in 
routine into appropriate positions in the computer from 
either paper tape or binary cards . 

7. Certain jump instructions will be read into cells 1+0001 through 1*00^0 
along with the service library data. The jump instruction will cause 
control to revert to the routines as indicated in the list of ^0000 
group entrances. 

The jump word in ^0000 is placed there during read -in of the program 
tape prepared by the assembly routine. The remaining jump words will 
be assigned as necessary. The usage of these cells to transfer control 
to the appropriate service routines will result in the following 
advantages: the cells are easily remembered; the PAK is easily set 
to addresses in the indicated range by means of the MD start; and the 
cells serve as "symbolic entrances" since the position of the service 
routines on the drum can be changed without changing the entrance 
address, and the programmer need not concern himself with the knowledge 
of the new location. 

8. In programming production problems it is desirable that conditional 
stop orders be included so that the computer operator can halt the 
progress of a production run when it becomes necessary. Such stops should 
be strategically placed in short loops and at a point where the contents 
of A and Q are not relevant. It will be necessary, therefore, that the 
programmer supply the computer operator with the following data: 

a. Bow to set up the stop order (s). That is, for example, 
which MS selecting switches must be set to "stop". 

b. What are the areas of ES and the drum used by the program. 



10-340 



o 



RW-71 (REV) 
Page 1 of 2 
Revised 6/15/56 

THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles kj, California 

PROGRAMMING REMINDERS 

The following list of Programming Reminders has been compiled using the 
experience of the members of the programming staff. The list has "been divided 
into two groups: general, and those reminders pertaining to the One Pass Assembly 
Routine (RAWOOP, CMP-O). 

General Reminders 

1. An index junp changes the contents of the accumulator. 

2. Use (n-l) with an index junp, assuming the index jump is performed after 
the operation. 

3* Clear the accumulator before using an MA instruction. 

k. A magnetic tape command changes the contents of the Q-register, 

5, The order of the j and n in a repeat instruction is as follows: 

RP j n w 

6, The B- register occupies A Q , A^ Q A_,- and is different from AL. Not 

only can one perform such operations as TP B A but the fault circuitry will 
not prevent one from jumping to B, as it will for the A register. The 
operation SF B k will result in the scale factoring af A + B. (This is 
applicable only to the Ramo -Wooldridge 1103 . ) 

7, When the computer is halted in the middle of a repeat instruction sequence , 
the PAK register contains the complement of j(n-r). 

8, When using an RP instruction followed by a TJ or EJ instruction, the 
rightmost fifteen bits of the Q-register contain j(n-r) upon jumping out of 
the sequence. Since j is present n-r must be obtained by an extraction 
rather than with a TV instruction, 

9, It is interesting to note that much can be said concerning error growth for 
unrounded multiplication and division. The following; rules hold: 

Multiplication ( axb ) 

^ the truncated product (contents of B register) is too 

small if axb>0 



i 

o 
o 
£ the truncated product is too large if axb<0 

h- 

g the absolute value of the product Is always too small 



RW-71 
Page 2 of 2 
Revised 6/15/56 

Division (a/b ) 

the actual quotient is too small if b yo 
too large if b<0 
Hence, one can predict, for example, that / & j,A>4 will be too small if 

A. 11 

b.>0. This bias precludes the possibility of employing the usual formulas for 
probable error which assume a normal distribution of error about a mean zero. 

Reminders for the One Pass Assembly Routine 

1. If it is desirable to refer to the constant and temporary storage pools 
with symbolic addresses, directory cards should be included for them. 

2. Rawoop converts decimal numbers to binary numbers occupying 35 bits plus 
a sign bit. 

3. When converting drum addresses, 40000 in decimal is equivalent to 1*0000 in 
octal . 

k. When specifying the beginning of a region, one must use the first symbolic 
address of a block. 5br example, D 03M00 00500 must be used and not 
D 03ML5 00515. 

5, Since SNAP addresses are limited to 9 bits the A, Q and B registers cannot 
be addressed directly. 



10-342 



RW-71 (REV) 
Paper' Tape Bootstrap 

Pgo 1 of 2 

Rev. 6/15/56 



THE RAMO-WOOIDRIDGE CORPORATION 
los Angeles 4-5, California 



The Utility Routine Library Handling Package for Paper Tape Input 



Normal Operation 

During normal operation, the Service Routine Library is stored on the drum. 
In order to use one of the routines, control is transferred to one of the 
low-numbered drum addresses in the 4.0000b channel (see the list of " Service 
Routine Starting Addresses "). 

Details concerning the operation of these routines and their locations can be 
found in the write-ups. 

MT Start 

If, at any time, the library stored on MD is destroyed by a program, or 
because the drum interlace has been changed, or for some other reason, 
the entire library may be loaded onto MD f rom magnetic tape. Selecting 
MT Start and starting effects loading of the service, routine library 
from KT .zero. PAK is set to the FRI-0 starting address upon completion 
of the 'transfer. Selecting MT Start, setting A R « 1 : , and starting effects 
loading of the service routine library and the assembly program and sub- 
routines from MT zero. PAK is set to the CKP-0 starting address upon 
completion of the transfer. 

Bootstrap 

Since the Ferranti reader requires a programmed read in, it is necessary 
to "bootstrap" into the machine when no input routine is stored in memory. 
The procedure devised to load an input program involves the use of one 
binary card (since this method requires the fewest number of instructions 
to be loaded manually). It is necessary to key in manually only four 
words which perform the read in of one binary card (24- words) and transfer 
control to these 24 words. " 

^ This binary card contains a simplified Ferranti Input Routine ( FRI-0 ) which 

w then begins to read in the service routine library paper tape. This tape 

o contains at its beginning the regular FRI-0 input routine and instructions 

1 transferring it to its proper location on MD. When FRI-0 has been loaded 

o on MD control is transferred to it and FRI-0 reads in the remainder of the 

«-• tape. 

a, Following FRI-0 on the tape are the library, a Magnetic Tape to MD transfer 

routine (URT-l), and an MD to Magnetic Tape transfer routine (URT-3). When 
the complete paper tape has been read in the computer halts with the library 
loaded on MD. PAK is set to 4-0000 by an MD Start, the machine is started 
and URT-3 transfers the library and URT-l to magnetic tape unit zero. The 
computer then halts with PAK set to 4-0001, the FRI-0 starting address. 

Detailed Descriptions of Houtines 

Detailed descriptions, operating instructions, and codes for the routine 
mentioned above are included in the notebook. 



RW-71 (REV) 

Paper fape Bootstrap 
Pg. 2 of 2 
Revised 6/15/56 

Operating Instructions for the Bootstrap Procedure (Loads MD and W£ zero with 
Service Routine Library ) 

1. Put the binary card deck in reader making sure that card reader is 
set for two fields and that all three switches on the reproducer 
are away from the card hoppers . Also be sure that there are cards 
in the punch hopper as the reader will tiot operate without them. 

2» Put the library paper tape in the Ferranti Reader &■ 

3* Position MT zero at the dead space immediately proceeding the first 
block* (Maintenance people will perform this function if requested). 

•4« Key in the following program : 

00104 17 00000 00104- pick card 

00105 17 00000 00105 read and pick card 

00106 75 30030 00000 read one binary card 

00107 76 10000 00000 then jump to 00000 

5. START at 001 04 . The computer reads in one card containing the 
simplified Ferranti routine, then switches control to this routine 
which reads in FRI-0 and the necessary orders to transfer it to MD* 
After FRI-0 has been placed on KD, control is transferred to it and 

it reads in the library tape and the MT to MD and MT transfer routines. 
The computer then halts with the MS instruction 56 00000 40001. 

6. Select KD Start 

7. Set low order octal digit of Q to the address of the MT unit desired* 
To load tape zero, omit this step of the procedure. 

8. START . The MD to KT routine loads the Ml to MD routine, 40001b thru 
40040b, 70000b thru 75777b, and 60000 thru '67777 onto MT zero. The 
computer then halts with the MS instruction 56 00000 40001, setting 
PAK to the FRI-0 starting address. 



10-344 



RW-71 
(REV) 



FLX-0 

Pg. 1 of 2 

Revised 6/15/56 



THE RAMO-WOOLDRUXSE CORPORATION 
Los Angeles k5, California 



Pool of Flexowr iter Codes 



Spec if icat ions 



Identification Tag! 



FLX-0 



Type; 



Constant Pool 



Storage : 



17 cells , addresses 75757b thru 
75777b 



Note: 



This pool of certain flexowriter codes 
has been established in order to prevent 
duplication of storage in the Service 
Routine Library. See the listing for 
details. 



Approved by: 



W. F. Bauer 



June, 1956 



1 

o 

J 

o 
o 

o 



X 



FLX-0 

Pg. 2 of 2 

Revised 6/15/56 



RW-71 
(REV) 



D 


FLXOO 55343 










75757 


00 


00000 


00000 


FLXOO 


37 


B 


F 







75757 


00 


00000 


00037 


FLXOl 


52 


B 


L 


1 




75760 


00 


00000 


00052 


FLX02 


74 


B 


E 


2 




75761 


00 


00000 


00074 


FLX03 


70 


B 


X 


3 




75762 


00 


00000 


00070 


FLX04 


64 


B 





4 




75763 


00 


00000 


00064 


FLX05 


62 


B 


w 


5 




75764 


00 


00000 


00062 


FLX06 


66 


B 


R 


6 




75765 


00 


00000 


00066 


FLX07 


72 


B 


1 


7 




75766 


00 


00000 


00072 


FLX08 


60 


B 


T 


8 




75767 


00 


00000 


00060 


FLX09 


33 


B 


E 


9 




75770 


00 


00000 


00033 


FLX10 


45 


B 


R 


CAR RETURN 


75771 


00 


00000 


00045 


FLXH 


04 


B 




SPACE 




75772 


00 


00000 


00004 


FLX12 


57 


B 


C 


SHIFT 


DOWN 


75773 


00 


00000 


00057 


FLX13 


47 


B 





SHIFT 


UP 


75774 


00 


00000 


00047 


FLX14 


51 


B 


D 


TAB 




75775 


00 


00000 


00051 


FLX15 


42 


B 


E 


PERIOC 


> 


75776 


00 


00000 


00042 


FLX16 


56 


B 


S 


MINUS 




75777 


00 


00000 


00056 


START 





















10-346 



RW-71 
(REV) 



Eratta 
Pg. 1 of 4 
Revised 8/15/56 

THE RAM04TO0LDRIDGE CORPORATION 
Los Angeles U5, California 

CUMULATIVE ERRATA 

CVF-0 11/1V55 

Page 5, line 12 from the bottom should read "n = (50000b)" and not 
"n + 1 = (50000b)". 

DET-2 7/25/56 'V ^ 

* Page k, Line 00R10 should read "SP A0000 00016 OO776 31 20000 00020" 
EGN-0 5/1/56 J 

Page 8, line' lit should start "or the ERA paper tape reader). ... ." 

Page 16, line 7 should start "if n^ 38, ..... 
EXT-3 8/10/55 v. ^ 

Page 1, drum assignment should read "63766 b through 6h0kk b." 
HTO-Q 7/25/55 

Page 1, drum assignment should read "6250^ b through 63037 b". 

MDP*3 12/9/55 . ^ 

;- 0\ Page 2, line 12, reference to MDP -2 should read MDP-4. 

'>*-« '''%' ■ ■ ■ ■ ■ . 

* v st, * Page 2, line 1^. should start "each card contains six words". 

nrt-o 12/1/55 

12 

Page 2, line 5 should read "2^n^2 " 

' uui4i 5/10/56 > .*'*■'. 

,^6/30/56 
, ^ In each of these Gill Method routines it should be noted under 
"Operating instructions" that the cells reserved for the q. must be set 

^ to zero by the programmer initially and whenever a discontinuity occurs. 

h- 

Y^ It has been pointed out that the error analysis in Gill's paper is 

o -■ r 

Y not applicable to these routines. 

o 
o 
a* 



MJI-5 6/20/56 

P Page 1 "type" should read "subr; ^ilne, available on cards for assembly"* 

a. "Assembly Routine Spec" line sh; ! be replaced by "Regions used: 

% * GIL, GIN, GIM, GCN" 

SIN -4 5/15/56 

Page 1, "Storage" should read "65 words total program storage. 5 words 
temporary storage pool used, addresses 27 b through 33b ". 



RW-71 

tREV) 
URT-3 

Pg. 1 of x 
Revised 10/15/56 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 45, California 



Utility Routine Transfer Drum to Magentic Tape 



Specifications 



Identification Tag: 

Type: 

Storage; 



Entrance: 
Machine Time: 
«cia» x>f Operation: 



URT-3 

Service routine (part of library loading package) 

110 instructions, addresses 00045b thru 00222b 

8 constants in program, addresses 
00223b thru 00232b 

All of ES is used for temporary storage but 
not included with the program 

118 words total program storage, addresses 
000^5b thru 00232b 

The temporary and constant storage pools are 
not used by this routine 

40036b 

lOO seconds approximately 

Fixed point 



Coded and Checked by: 
Approved by: 



R. Beach 
W. F. Bauer 



August, 1955 
August, 1955 



10-348 



X 

a. 



RW-71 
(REV) 
•3 



Revised 10/15/56 



Description 

Upon being entered the routine first bootstraps itself and URT-1 into DS, than 
sets up all references to magnetic tape to correspond to the unit selected when 
URT-3 is activated. URT-1 is transferred to ES beginning at cell 1700b. 

The contents of cells ^OOOlb thru ^OO^Ob and 70000b thru 75777b are then summed 
and the sum placed in 0177^+b and 01775b . The contents of cells 01700b thru 
01775b are then summed and the sum placed in 01776b and 01777b. The information 
in cells 01700b, 70000b thru 75777b, and IfOOOlb thru l+00l+0b are then transferred 
to MP in that order. 

The contents of cells 60002b thru 67777b are summed and the sum placed in 
60000b and 60001b. 

STT-0 is ente'red to dump the information in cells 60000b thru 67777b (the sub- 
routine library consisting of RAWOOP and the subroutines). 

URT-3 computes the sum of all information placed on MT, rewinds MI to its 
original position and reads back the data from MP, summing as it reads. 

If the sum is correct, a BM instruction is given to return MT to its original 
position and computation halts with PAK set to ItOOOlb, the FRI-0 starting address 

Operating Instructions 

^1* Select MP Start . 

2. Set the number of the MP to be loaded in the low order octal digit of Q. 

3» si 



URT-3 transfers the complete library to ME and halts with the Ml instruction 
56 00000 ^0001 after a successful transfer. 

Alarm Conditions 

If the sum of data read back from MC is not correct the alarm routine is entered) 
the tag word URT-3 &&& the address 00070 are printed on the flexowriter. The 



<=> sum of the data on MP appears in A. 



1 

o 

g Restarting at this time initiates another transfer to data. 



1. It is advisable to position MS at the first block before loading so that the 



2. After a successful transfer the machine halts but MT is still rewinding to 
its original position. If a master clear is executed and the machine 
started a reference to the rewinding MP (before the rewinding is complete) 
will cause trouble. If no master clear has been executed the maqhine will 
wait for the reversing to be completed. 



RW-71 
(REV) 

URT-1 

Pg. 1 of 3 

Revised 10/15/56 



the ramo-wqoldrjdge CORPORATION 
Los Angeles k^ f California 



Utility Routine Transfer -Magnetic Tape to Brum 

■ i n 1 » 1 1 1 n i l 1 ■ ii • ' 1 .,. 1 ' i n i i , Wn i .". I 1 11 1 i t ,. ■ i n i |,] 111 Mumi i j ii . .« urn 1 



Specifications 



Identification Tag: 
Type: 

Storage : 



URT-1 

Service routine (part of Library Loading 
Package) 

57 Instructions, addresses 00000b thru 00070b, 

1 constant in program, address QQ073b (remain 
lng constants stored with instructions) 

The remainder of ES is used as temporary storage 

The constant and temporary storage pools are 
not used by this routine 



Entrance: 
Machine Time: 



MT Start 

Approximately 15 seconds for successful transfer 
of the service routine library only, or approxi^ 
mately 35 seconds for transfer if CMP-0 and 
the subroutine library are included. 



Coded and Checked By: 
Approved by: 



R. Beach 
W. F. Bauer 



April, 1955 
August, 1955 



10-350 



a* 



RW-71 

(REV) 
URT-1 

Pg. 2 of 3 

Revised 10/15/56 



Description 

This routine is located in the first two blocks of the magnetic tape unit used 
for the library (normally MT$0) and is specifically designed to transfer the 
library from magnetic tape to magnetic -drum. 

It operates in three different modes, the mode of operation having been selected 
when it was activated, Mode No. 1 loads addresses If 0001b thru kOOlfOb and 70000b 
thru 75777b only. Mode No, 2 loads these addresses and addresses 6QOO0b thru 
67777b. Mode No. 3 advances past the library and reads in the first block of 
the ERA. maintenance routine loader, then transfers control to that loader. 

This routine does not save the contents of ES since it is assumed that it will be 
used only when a complete reloading of the computer memory is necessary, An MT 
Start reads in the first 32 words of the routine and starts operation. The routine 
first reads in an additional 32 words from MT (remainder of the routine itself) and 
then checks its sum, which is stored at the end of the second block, In doing this* 
it also checks the sum of the service routine library which is stored in the second 
block. 

After a successful sum check the routine reads in the 96 blocks needed to f IH 
70000b thru 75777b. Twenty -four blocks are read in at one time and transferred to 
MD, then read back into E3 and summed. When all 96 blocks have been transferred, the 
routine reads in one more block and transfers this into IjOOOI thru ^OOkl, reads 
it back into ES, sums, and adds the sum to' the sum of the 96 blocks previously 
transferred. This computed sum is then checked against the correct sum. 

If Mode No. 1 has been selected a rewind instruction is given and the computer 
halts with the MS instruction 56 00000 kOQQl-, setting PAK to the FRI-0 starting 



If Mode No. 2 has been selected, TST-0 is activated to read in RAWOOP and the 
subroutine library. A rewind instruction is given and the computer then halts 
with the MS instruction 56 00000 kOOlO, setting PAK to the CMP^O starting 



Operating Instructions 

!'• To transfer the service routine library only 



1 1. Se3.ect MP Start 



o 2. Change PCR (if necessary) to select the proper MT unit 



3* Start * The routine loads k 0001b thru MX&lb and 70000b thru 75777b and 
>< halts with the MS instruction 56 00000 40001, setting PAK to the FRI-0 

starting address. Successful transfer takes about 15 seconds. 

11 • To transfer the service routine library, CMP-0, and the subroutine library 

!• Select MT Start 

2. Change PCR (if necessary) to select the proper MT unit, 



RW-71 

URT-1 ( R E^) 
Pg. 3 of 3 
Revised IO/15/56 

3. Make A = 1 

k. Start. The routine loads 40001b thru *K)040b, 70000b thru 75777b, and 
60000b thru 67777b and halts with the MS instruction % 00000 toOlO 
setting PAK to the starting address of CMP-0. Successful transfer 
takes about 35 seconds. 

III. To load ERA Maintenance Routines 

1. Select MT Start. 

2. Change PCR (if necessary) to select the proper MT unit. 

3. Make A^2 

k. Start . The routine advances the MT unit and loads the 229 block into 
ES placing the first word in cell zero. The number in the accumulator 
is reduced by 2 and left in A for the ERA loader to use in selecting its 
mode of operation. Control is then transferred to cell zero. 

Alarm Conditions 

1. If the machine halts on a final stop almost immediately after an MT 
start the transfer routine is not in ES correctly. 

Select MT start and start for another transfer. If the second transfer 
is not successful revert to the bootstrap procedure to load the library. 

2. If the flexowriter prints an "e" and the machine halts on a final stop 
the sum of the library transferred to the drum is nbt correct. 

Select MT start and start for another transfer. (Wait for rewinding 
to be completed before executing start). 

3. When operating in Mode No. 2 TST-0 is activated after address liOOOlb 
thru W)0iU)b and 70000b thru 75777b have been loaded successfully. If 
the sum test falls while loading addresses 60000b thru 67777b, the 
alarm routine prints the tag word TST-0 and the address 75777b. 
Starting causes rewind and another MT transfer to addresses 60000b 
thru 67777b. 

Warning. 

After a transfer the computer halts but MT is still rewinding to its original 
position. If a Master Clear is executed and the machine started, a reference 
to the rewinding MT (before rewinding is complete ) will cause trouble . If 
no Master Clear has been executed the machine will wait for the rewinding to 
be completed. 



1f>-*^9 



RW-72 
(REV) 
CMP-0 

Pg. 1 of 11 
Rev. 7/10/56 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles k^, California 



THE RAMO-WOOLDRIDGE ONE -PASS ASSEMBLY ROUTINE 



Specifications 



Identification Tag; 
Type: 



CMP-0 

Service Routine 



Entrances : 



UOOOOb and UOOlOb 



Coded by: 

Code Revised by: 

Approved by: 



Jules Mersel 
Thomas Tack 
Walter P. Bauer 



October 1955 
October 1955 



I 

O 

r-l 
I 

o 
o 
o^ 






tr\ qco 



RW-72 
(REV) 



CMP-0 

Pg. 2 of 11 

Rev. 7/10/56 



Description 



The Ramo -Wooldrldge one -pass assembly program (RAWOOP) is designed to 
translate an 11Q3 program originally coded in symbolic, regional, octal, 
and decimal form into its final octal form. 

The program will accept instructions with symbolic addresses and numerical 
data in binary or decimal form. It will cause subroutines to be appropriately 
assembled into the program* The result of assembling a program will be output 
in a form which facilitates program check out and rapid read in of the 
translated data. 

Input -Output 

Punched cards are used as input for RAWOOP. The punched card contains one 
1103 word with remarks or contains an instruction to the assembly program 
with remarks. RAWOOP's output is via both punched cards and punched paper 
tape. The output card contains an exact duplicate of the corresponding 
input card plus an octal translation of the input data* The programmer 
can obtain a side by side listing of his untranslated program, remarks, and 
translated program by listing the output deck on associated equipment such 
as the IBM 407- 

The punched paper tape is a seventh -level bioctal tape complete with insert 
and check addresses, and is used to read the translated program into the 
1103 by either the ERA photo-electric reader or by the Ferranti tape 
reader with an appropriate read in. program. A leader and trailer is 
automatically included on each tape prepared. 

Input and Output Cards 

The input and output cards are standard 80 -column, 12 -row cards. The 
allocation of the information with respect to the card columns is as 
follows : 

1-5 symbolic address of the untranslated word 

7-10 1103 operation characters or pseudo -instruction symbols of the 

untranslated word 

12-16 u address of the untranslated word 

18-22 v address of the untranslated word 

24-26 decimal scaling information for the untranslated word 

28-30 binary scaling information for the untranslated word 

32-43 alpha -numeric remarks 

It is noted that symbolic coding for SNAP (interpretive floating point 
package) deviates from these conventions (see pg. 6). In addition to the 
above columns, the output cards contain the translated information in 
columnsl 47-67. 

On the input cards, zeros need not be punched . 



10-354 



CM 

I 

o 

r— 1 
I 

o 
o 
o 



x 

CL. 





































*• 


1UU1UI JL 




































THE RAMO-WOOLDRIDGE CORPORATION 

pac;f of 




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THE 
RAMO-WOOLDRIDGE 

ONE PASS 
ASSEMBLY PROGRAM 



MM069ee» 



RW-72 

(REV) 

CMP-0 

Pg. 1+ of 11 

7/10/56 



Speed of Assembly 

Due to the 1103' s ability to read and punch cards while simultaneously 
punching paper tape, RAWOOP takes only a few seconds more than the total 
card reading time to execute its entire translation. Errors do not 
necessitate complete re -assembly and consequently the routine is exceed- 
ingly economical in its use of machine time (see below). 

Symbolic Addresses 

A f±we character form, in keeping with 1103 machine form, is used for 
symbolic addresses. The first three characters designate the region 
of the address while the last two characters are the sequence number of 
the address within its region . 

For example, DRJOO is the zeroth address in region DRJ and 01C19 is the 
nineteenth address in region 01C (01C00 is the zeroth address in region 
01C). In keeping with the one -pass nature of RAWOOP, the sequence numbers 
are consecutive decimal numbers. The absolute address assigned to 01C19 
is nineteen greater than the address assigned to 01C00. Thus, the address 
structure has a regional character* 

As indicated above, the first three characters of the relative address or 
region are alpha -numeric . 

The absolute address for region 000 (all zeros) has already been chosen 
i*i RAWOOP tto be zero. Consequently, 00029 would have 00035 as its 
octal translation; absolute machine addresses up to 99 will be correctly 
translated. Furthermore, the regions A00, BOO, and Q00 are best avoided, 
as in some cases reference to them will be interpreted as addressing the 
A, B, or Q registers respectively. 

The assembly program recognizes the alphabetic letter "0" as different 
from the numeric zero but in order to avoid confusion the programmer will 
probably not want to use symbolic addresses involving the letter "0". 

A, B, and Q Addresses 

The accumulator, the B register (accumulator bits A 70 - A.-), an< ^ ^^ e Q 

register must be addressed by putting an A, B, or Q, respectively, in the 
leftmost column of either the u or v fields. The remaining four columns 
of the field may have no punches or zero punches. The octal translations 
of A, B, or Q are 20000-, 30000, and 10000 respectively. 

Addressing Involving J>, k, and n 

The command structure of the 1103 is such that the u and v addresses at times 
contain numbers rather than machine addresses (as in the ease in the SPuk, 
RPjn, w and MJjv commands). The representation of J, n type instructions 
uses j as the first character and n as the last four characters with the 
quantities j and n written as decimal numbers. Thus the j, n number 30199 



10-356 



RW-72 
(REV) 

CMP-0 

Pg. 5 of 11 

Rev.. 7/10/56 



is translated to 30307b. No distinction is made between j, n addresses and 
j addresses.. If the programmer desires to use the last four characters of 
a <3> type address to store a number (this cannot be used to store a relative 
address) he may do so accounting for the fact that these four digits will be 
treated as the n portion of a j, n type address. 

In the 1103 the k address structure is used to represent left circular shifts 
from to 127 places. However, since the internal hardware occasionally makes 
it desirable to have the first octal bit of a k address be a number other than 
zero, k addresses ^ill be treated in exactly the same manner as j, n addresses; 
for example, 20017 becomes 20021b. 

Octal -Symbolic Words 

In order to allow the programmer to mix octal and symbolic addresses in the 
same instruction three special types of words ("BBR","BRB", and BRR") have 
been included in RAW00P. The first letter of the triad refers to the opera- 
tion, the second, to the u address and the third, to the v address. R means 
symbolic (regional) and B means octal (binary). Thus, a BBR word has its 
operation and u address octal and its v address regional. The flag BBR 
goes into the D card field (columns 24-26). These flags cannot be attached 
to SNAP commands . Examples can be found on lines 23-25 of figure 1. 

Void Addresses 

Certain of the 1103 commands such as FS — , RJj,n — have ignored addresses 
associated with them. All such addresses are treated by RAW00P as if they 
were relative addresses and are available for the storage of pre -setting 
addresses. An all -zero address, of course, is translated into all zeros. 

Directory Cards 

In a one -pass assembly program, it is necessary that at the beginning of the 
program sufficient information is supplied to enable all symbolic addresses 
to be assigned absolute addresses. RAW00P does this by means of directory 
cards. A directory card has a D punched in column 1, the base word of the 
^J region (e.g. 01C00) in the u address columns, and the absolute decimal 

t address of the base word in the v address columns. For examples, see figure 

o 1. RAW00P can handle up to 73 directory cards in any one assembly. The 

V programmer is cautioned not to follow his directory cards with program cards 

§ destined for a region D00. Such an ordering would prevent RAW00P from 

differentiating between the two types of cards. 



o 



£ For purposes of assigning decimal addresses to the drum, the convention 

was adopted that octal address 40,000 on the drum has the decimal address 
40,000. Thus the drum addresses range decimal ly from 40,000 - 56,383' 



in_ , }c;7 



RW-72 
(REV) 
CMP-0 

Pg. 6 of 11 
Rev. 7/10/56 



SsTribolic Addresses of Program Data 

With the exception of the D cards and the START card, all the input cards have 
a relative address punched in columns 1-5. This address is the address of 
the word to the right and, in conjunction with the decimal address of the 
corresponding directory card, completely determines the memory location 
into which this card will he read by the bioctal tape punched toy RAWOOP. 

Commands 



The 1103 alphabetic representation of the commands is used. These two letter 
combinations, such as RA for the "replace add" or "21 command", are entered 
into columns 9 and 10. All the standard 1103 commands are recognized by 
RAWOOP and this recognition implies knowing whether the addresses associated 
with the command are of the u, v, the jn, v, or of the u, k types. 

In addition to the standard 1103 commands, the special commands IP, PM, and 
MM are recognized . The PM and MM commands and the availability of the B 
register for addressing are modifications on the Ramo -Wooldridge IIO3. The 
PM command is a "polynomial multiply" command for polynomial evaluation whose 
octal equivalent is 2k; the MM command is the "modified multiply -add" (faster 
in operation than MA) whose octal equivalent is 25- None of these modifications 
are used in the operation of RAWOOP ; the program will operate on any 1103 
with reproducer and high-speed punch. 

The IP commands are treated as if the command structure were IPuv. However, 
for use in SNAP, a pseudo command is available. This has the form ABCDuv, 
where AB and CD are alphabetic SNAP commands, while u and v are .symbolic 
addresses restricted in their assignment to the lower half of electrostatic 
storage. This form is translated by RAWOOP into llfA'u'C'v' where A 1 and 
C are the octal representations of the SNAP commands AB and CD respectively, 
while u 1 and v 1 are 9 bit numbers. A' and u' are packed into the u address 
of the translated command and occupy the left 6 bits and right 9 bits 
respectively. C and v' are similarly placed in the v address. On the input 
card AB occupies columns 7 and 8, while CD appears in columns 9 and 10. 

SNAP provides for a B-box whose contents can be added to the address of a 
SNAP command before its execution. To cause RAWOOP to translate SNAP commands 
so that this signal will be given, a "B" is placed in column 25 of the D 
field to modify the u address, or in column 29 of the B field to modify the 
v address of the SNAP command. IJpon finding a "B" in column 25 and/or 29, 
RAWOOP adds two (2) to the corresponding SNAP operation. 

If the programmer places the letter "S" in column 26 of the D field and/or 
column 30 of the B field of a SNAP pseudo command, RAWOOP adds one (l) to 
the corresponding SNAP operation. On execution of this command, the contents 
of the F register will be stored in the address associated with this command. 



10-358 



(REV) 



CMP-0 

Pg. 7 of 11 

Rev. 7/10/56 



For example , if symbolic address K9P00 has its octal address equal to 00500, 
the translation of lines 26-31, of figure 1, are respectively: 

Ik 04500 10501 

14 16500 20501 

14 24500 31501 

Ik 37500 1+0501 

Ik 1+6500 51501 

14 70000 74010 

It is sometimes desirable to place a relative address in a word that has 
zeros for its command code. To allow for this, the command 00 (zeros) 
is recognised and translated into 00. The u and v addresses must be 
symbolic addresses. As usual, however, an address of five zeros is trans- 
lated into five zeros. 

Decimal Numbers 

Decimal numbers are presented to RAWOOP as normalized numbers times a 
power of ten. The programmer also states the binary scaling factor to be 
applied to the resulting rounded binary number. For example, -739 -1 is 
presented as -7«391 x 10^. 

AH decimal numbers are normalized so that their absolute value lies between 
1 and 9.99999 99999- 

The sign of the number is in column 9, the integral part in column 10, and the 
fractional part in columns 12-16 and 18-22. The power of 10 allowed is from 
-10 to +10 . This exponent goes into columns 24-26. The desired binary 
scale factor goes into columns 28-3O. For examples, in line 13, figure 1, 
the number to be translated is 3°123 x 10-" with a scale factor of 2". 

In all cases a minus sign represents a negative number and a zero or no 
punch a positive number. 

Floating decimal numbers are presented to RAWOOP in the same manner as decimal 
numbers. However, instead of a binary scale factor being placed in columns 
£J 28 -30 , an F is punched in column 28. The converted floating point decimal 

t> number is in the form used by SNAP. That is, the left most bit is a sign 

o bit , the next eight bits represent the exponent (increased by 128) and the 

V twenty -seven bits on the right comprise the mantissa. In this form a negative 

§ number appears as the complement of the corresponding positive number. 

o 



X 

a, 



Octal Constants 

Octal constants can be inserted into the program using RAWOOP. The octal 
constpit is. entered into columns 9-10, 12-16, and 18-22. A "B" is punched 
into column 24 to signify that the number is in octal (binary) form. This 
feature implies that program* ^ ; i in the usual machine language will be 
correctly assembled. 



i0--3;?> 



RW- 72 
(REV) 



CMP-0 

Pg. 8 of 11 

Rev, 1/10/56 



Start Card . 

The signal to RAWOOP that all the cards have been received is a card with 
START punched in columns 1-5, and a relative address punched in columns 
12-16. 

The signal causes RAWOOP to insert into the translated program (in locations 
00000b and ta)00b) a manual jump to the octal translation of the relative 
address. For this reason, it is not possible to program anything in cells 
00000b and 40000b. 

After the resulting punched paper tape is read into the H03> a magnetic 
drum start will start the problem at the relative address indicated in 
the u columns of the untranslated word. 

Subroutines 

RAWOOP is designed to translate subroutines coded in octal relative to 
0100Gb (or 02000b) and stored on the drum, and include them into the main 
program. This is accomplished by one pseudo command, the "SUB" command. 

Columns 1-5 of the SUB command contain the relative address at which the 
subroutine is to be stored. Columns 7, 8, and 9 contain the letters SUB . 

Columns 12-16 contain the drum address of the cell in which the first word 
of the subroutine is stored for use by RAWOOP (this address is a "decimal 
drum address") » 

Columns 18, 19, and 20 contain the number of words (in decimal) in the 
subroutine. * Columns 21 and 22 contain the number of constants (in decimal) 
which are placed at the end of the subroutine and are not to be modified 
during translation. In practice the information in these columns is 
simply copied by the programmer from a subroutine specification given on 
the title page of the subroutine write-up. Columns 25, 26, 28, 29 > and 30 
contain the relative address at which the subroutine is to be executed if 
this differs from the storage address. If these columns are blank or zero 
the storage address will be used as the execution address. The subroutine 
will be translated relative to the execution address but loaded (via the 
bioctal output tape) at the storage address. 

The programmer is cautioned not to place a SUB card immediately after the 
directory cards. 

The programmer has the options of including in the output cards the translated 
subroutine cards. With jump switch No. 3 oft, the punching of these cards 
is suppressed. On the other hand, with this switch on, prior to starting 
the assembly, these cards are provided. 



10-360 



KW-fZ 
(REV) 

CMP-0 

Pg. 9-of 11 

Rev. 7/10/56 



Subroutine Compiling and Constant Pools 

There are two versions of RAWOOP (only four words differ). The non Ramo-Wooldridge 
version of RAWOOP assumes that subroutines stored on the drum are coded relative 
to address 01000b. The Ramo-Wooldridge version of RAWOOP assumes that subroutines 
are coded relative to address 03000b. 

The Ramo-Wooldridge version of RAWOOP punches out on the bioctal tape a constant' 
pool which is used in Ramo-Wooldridge subroutines. The pool is ten= words Jio®g 
and starts in memory location 00015b. The sum of this pool is included in the 
memory sum recorded on the output tape. These constants are- punched by RAWOOP 
before D cards are read and,, of course, cam be writ tern ovoar al^er* %hey enter t he- 
high -speed storage. If constant pool cards. «re also- desired 8 they may be obtained 
by putting MJ 1 on before beginning the assembly. 

Memory Sums 



RAWOOP calculates the memory sum of all translated words including, the 00000b 
and 40000b jump instructions. This sum is the double precision sum of the 
split extension of the translated words . The sum. is both printed ©& the lifting 
and read by the output paper tape into addresses 75202b and 75203b of the dsrum. 
The high order value of the sum is in 75202b. This placing of the sum is QQ«^-iste^t. 
with the Ramo-Wooldridge Ferranti read in routine, RAWOOP checks its own mejpory 
sum. at the beginning of every assembly* Upon a memory sum disagreement, the 
routine prints "CMP-0". 

O rdering of In put Cards 

RAWOOP places the following requirements on the ordering of the input cards: 

1. All directory cards must come first. The directory cards however, can have 
aa>y order within themselves. 

2, The START card must come last. 

£J The cards actually giving the words of the program, subject to the restrictions 

Y already made, follow the directory cards. In the interest of minimizing the 

2' number of insert and check addresses on the output bioctal tape the cards should 

^ be in order within their regions. However, a correct out pu'c tape will be 

§J produced regardless of the order of the incoming program cards. 

X Suppression of Punched Paper Tape 

If for any reason an input paper tape is not desired, the high-speed punching 
can be suppressed by turning on the j = 2 manually selective jump. 

Storage Used by RAWOOP 

RAWOOP uses all of high speed storage, cells 40000b and 40010b and stores 
itself in 60000b through 62117b. If subroutines are compiled, it also uses 
43000b through 47777b . 

10-361 



RW-72 
(REV) 

CMP-0 

Pg. 10 of 11 

Rev. 7/10/56 



Operating Instructions 

The following points are important in the operation of RAWOOP: 

1. The reproducer must be set for three fields. 

2. The input cards must be placed face down with at least four blank cards 
following the START card at the back of the deck. 

3. Both the typewriter and the high-speed punch must be turned on. 

4. When RAWOOP is first read into the 1103, an MD start will store RAWOOP 
on the drum and start RAWOOP. All subsequent starts are made from 
address 40010b. When a run is completed, it stops with a manually selec- 
tive stop to 40010. Pressing the START button causes another program to 
be assembled. The program checks its own memory sum at the beginning of 
an assembly and prints out "CMP-0" when the check sum fails. 

5. All cards should be cleared from the read and write channels of the. 
reproducer at the end of the program. 

6. All reproducer switches must be on normal setting (away from the card 
hoppers on the Ramo-Wooldridge 1103). 

7. All MS and MJ switches should be turned off except as noted above. 

Error Detection 

If more than 73 directory cards are entered the flexowriter prints "too many 
d cards" and the computer halts. It is not possible to continue the assembly 
after this error has occurred. 

All other errors , including a D card occurring in the main deck will not stop 
the machine. For each card with an error on it, "ERROR" will be printed on 
the Flexowriter. The contents of the erroneous card will be ignored and will 
not effect the memory sum. The corresponding output cards will have "error" 
punched on them in the place ordinarily used for the translated information. 
If the error appears with respect to the START card, addresses 00000 and 
40000 will be loaded with the word 45 00000 00000b by the paper tape. 

The detected errors can be corrected by a second assembly of only the new 
corrected input cardLs, their associated D cards, and the START card. This 
will give a secondary input tape with its own memory sum. 

Programming Reminders 

1. If it Is desirable to refer to the constant and temporary storage pools 
with symbolic addresses, directory cards should be included for them. 

2. RAWOOP converts decimal numbers to binary numbers occupying 35 bits plus 
a sign. Decimal numbers not in the correct range will be translated in- 
correctly or can cause an error card to be punched. 

10-362 



CM 
1^ 
w 

I 
O 
i— l 

I 

o 
o 
o 



X 



RW-72 
(REV) 

CMP-0 

Pg. 11 of 11 

Revo 7/10/56 



3. When converting drum addresses, 40000 in decimal is equivalent to 40000 
in octal » 

4. When specifying the beginning of a region, one must use the first symbolic 
address of a block. For example, D 03M00 00500 must be used, and not 

D 03M15 00515. 

5. To assemble a number of programs consecutively, it is necessary to have 
two cards between programs. 

6. Directory cards must not be followed immediately by 

a. SUB cards 

b. program cards directed to region D00. 

7. Attention is called to the use of A00, BOO and Q00 as regions. If these 
regions are addressed, reference may be made to the A, B, or Q registers. 

8. Since the last two words of the translated program are start addresses 
inserted in 00000 and 40000, it is impossible to program for these cells 
using RAW00P. 

9. Correcting or replacing words on an assembled program tape will in most 
cases invalidate the sum checks at the end of the tape. The programmer 

the following options for correcting or altering a program: 

a. re -assemble 

b. add the corrected words with proper insert and check addresses 
after. the sum check 

c. re -assemble the incorrect cards only and enter into the 
machine the old and new assemblies in that order. 



10-363 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 4-5 $ California 



RW-89 
(REV) 

DIE-0 

Pg. 1 of 8 

Revised 6/15/56 



Definite Integral Evaluation Routine 
Specifications 



Identification Tag! 
Type i 

Assembly Routine Specs 
Storage : 



DIE-0 

Subroutine 

SUB 49810 05804 

54- instructions, addresses 
00P00 thru 00P07 
00S00 thru 00S26 
00N00 thru 00N18 

U constants in program, addresses 
01C00 thru 01C03 

58 words total program storage, addresses 
00P00 thru 00P07 
OOSOOthru 00S26 
OONOO thru 00N18 
01C00 thru 01C03 

10 words temporary storage pool used, addresses 
00027b (00T00) thru 0004.0b (00TQ9) 

The constant pool is used by this routine 



Drum Assignment: 
Program Entrance : 
Program Exits 
Mode of Operation: 



Addresses 63122b thru 63213b 
Address 00P02 
Address 00P01 
Fixed point 



Coded by: 
Code Checked bys 
Machine Checked bys 
Approved bys 



F. Meek 
R. Bigelow 
F. Meek 
W. Bauer 



June 7, 1955 
June 10, 1955 
July 7, 1955 
July 26, 1955 



10-364 



CO 



RW-89 
(REV) 

DIE-0 
Pg. 2 of 8 
Revised 6/15/56 
Description 

Assuming that y = f(x) is a tabulated function with equal increments in the 
argument Gcq> x,, x 2 » • • • , x ), this routine will approximate the definite 
integral 



(x n _x ) x 



/x 



ydx 



using either Simpson's rule or a modifies tion of Simpson's rule. 

The function values may be stored in ascending order of the argument in any 
block of consecutive storage cells. 

At the time of entry into the subroutine the programmer must supply the value 
of n (that is, the number of intervals, one less than the number of points) 
and the address of the cell containing the first function value y~ = f(x Q ). 

The routine gives as a result an approximation to 

*x 



/" 



1 / ydx 

^ X n " x cr x o 

and the programmer must then multiply .this result by (x - x Q ) to obtain the 
approximation to the integral itself. 

Notation 

1= I n f(x) dx, J = _L_ I. 

(x n " X ) 

I tf and -J* are approximations to I and J, respectively. 

e = I* - I. 

Range of y. , J*, and n 



^ The only restriction on the y.'s is that they must be single precision fixed 

V point numbers. The number of intervals n must be greater than one but can be 

g arbitrarily large. The result. J* will be given scaled by. the same amount that 

2i the y. f s were scaled. 

£J In order to obtain the maximum significance for J*' the y^s should be scaled as 
far to the left as posjible. 

Programming Instructions 

Before entering the routine the function values y. must be stored in ascending 
order of the arguments in consecutive storage cells. 



1. Place n*2 in A. 



RW-89 
(REV) 

DIE-0 

Pg. 3 of 8 

Revised 6/15/56 



2. Place the address of y~ = f (x~) in Q 
MJ __\r 

3. Enter the routine with the instruction RJ OOKOl 00K02 (assuming 00K00 is the 
region that was assigned to the routine during assembly) 

At the time of exit from the routine the result J* is left in A, scaled by the 
same amount that the y. 's were scaled. The numbers y, have been left in their 
original state. 

Mathematical Analysis 

Let the equal increment of x be denoted by 

h = x i " x i-l = x n "~ x >0 * i = lf 2f " * ' 9 n ' 

n 

Suppose I is to be approximated by a quadrature forrcula of the form 

I* = h 21 c i f(x i) = x n ~ x n X- °i y i 
i=0 — " 13) 

n 

where the c, are the appropriate coefficients, e.g., for the trapezoidal rule 

c_= c = l/2 and c. = 1 otherwise. Let 
On 1 

J* = 1/n £ c y . 

i=0 



Then 



I* = (x n - x Q ) J*. 



Notice that J* does not involve x, and therefore J* can be computed without regard 

to the scaling of x. For this reason J* rather than I* is obtained by the subroutine. 

If n is even Simpson's rule is used throughout the interval (x n » x ). If n is odd 

Simpson's rule is used over the interval (x~, x ~) and Newton's three-eighths rule 

is used over the interval (x a , x ), 

n-3 n 

therefore 

J* = l/3n (y Q + ^ + 2y 2 + Uy^ + 2y^ + . . . + Ay n _ 1 + y n ) for n even, and 

J* = l/3n (y Q + AV 1 + 2y 2 + . . . -f 4y n ^ + y n _ 3 ) + 

+ 3/Bn (y n _ 3 + 3y R _ 2 + 3y n-1 + y n ) for n odd. 



10-366 



RW-89 

DIE-0 <SEV) 

Pg. U of 8 
Revised 6/15/56 



Error Analysis 



Let a be some value in; the closed interval (x~,x ) and let JB and y be values in 
the closed intervals (x ,x ~) and (x _3> x n ) respectively. 



A.. , 



If d y is continuous throughout the interval (x ,x ) and if n is even 



£ = y (a) (x n - x Q ) , where y 4 (a) = d 4 yl 

dx4] 



l80n 4 ""-» x=a 



A„ , 



If d v is continuous throughout the invertal (x n ,x ~) and exists throughout the 
dx4 ° n ~> 

interval (x Q >x ) and if n is odd 
n-3 n 



£ = l/n' 



n-3 y 4 (p) + 3 y 4 (y) 



180 80 JL 



r> 



x - x n 
n 



For the derivation of these quadrature formulas and their error terms, see Mine's 
Numerical Calculus, pp. 120 thru 124. 

Machine Time 

The time required for this subroutine is (2.25 + .62n) ms, n / 3. Mien n = 3 the 
time required is 2.73 ms. 

Machine Checking 

Two preliminary test cases Were run: 

1. n = 99, y. = ,-(2 35 -l) for all i. The result obtained was -2 35 (it should have 
been -(2 35 -l). 

2. n =98, y. = (2 35 -l) for all i. The correct result, (2 35 -l), was obtained. 
£' 1 

CO 

Y In addition, the following computations were performed: 
o 

^ 1. SIN-0 was used to produce a table of sines and cosines for the arguments 
o 



y = ttX/2 = (7r/2)'n«2~ 4 , n = 0, 1, 2, . . . , 99. 

2. Let S =1 cos ydy = sin b and C =1 sin ydy = 1-cos b. DIE-0 was used to 
} J 



compute S* and C* for b = (Tr/2)-n'2 , n = 2, 3, /,., • . . 9 , 

n = 10,15,20,25 
n = 30,^0,50, . . .90, and 

n = 99 



RW-89 

(REV) 
DIE-0 

Pg. 5 of 8 

Revised 6/15/56 



3. For each b (or n) e = S* -sin b and £ = c* - 1 + cos b were computed. The 
following tables resulted: 





n„6 


6 


n 


c -10 


c -10 




s 


c 


2 


.101 


.010 


3 


.333 


.050 


U 


.197 


.039 


5 


• £(.<,<C 


.125 


6 


.287 


.087 


7 


.490 


.215 


8 


.365 


.151 


9 


.540 


.316 


10 


.429 


.229 


15 


.560 


.650 


20 


.477 


.713 


25 


.200 


1.056 


30 


.101 


x. \JK.*L 


40 


-.365 


.881 


50 


-.506 


• l\.X.j 


60 


-.198 


.039 


70 


.286 


.087 


BO 


.516 


.516 


90 


.286 


.945 


99 


-.338 


.981 



It wes to be expected that, in general, the errors would be greater for n odd. The 

overall behavier of e and £ is easily seen to be consistent with the fact that 

s. c •'•.,. 

£ and £ represent the errors in integrating the cosine and the sine respectively. 

For example, £ is small for n = 30 because it is the error obtained In 
s 



I cos ydy =1 +J + I 

J J J 1 J TL 

W 2 



fi6 J2 (2 J: 

1 1 A A 



jLtt 'Ur '0 
16 16 



Ijir jr 



a fl6 (2 

since I = -J 

Jar Jl 



16" 

In fact, £ for n = 30 (b = (15/i6)it) is exactly equal to £ for n = 2 (b = {1/i6)tt); 
s s 

Evidently, all the errors £ arid £ are less than their corresponding maximum estimates 

s c 

as computed by the formulas above under Error e 3 tima t e . in particular, for n = 10 and 15» 

the following maximum error estimates were hand computed: 

10-368 









RW-89 

(REV) 
DIE-0 

Pg. 6 of 8 

Revised 6/15/56 


n 


Max e s 10 6 


Max c Q 10 




10 


.508 


.4.21 




15 


,740 


.903 





CO 

I 

o 

I 

o 

o 
o 



X 
Oi 



RW-89 

(REV) 
DEE-0 

Pg. 7 of 8 

Revised 6/15/56 



D 

t> 

D 



D 

D 

D 

D 

D 

D 

DOPOO 

DOPOl 

D0P02 

D0P03 

D0P04 

D0P05 

O0P06 

DOP07 

DOSOO 

DOSOl 

DOS02 

DOS03 

D0S04 

D0S05 

D0S06 

D0S07 

D0S08 

D6S09 

D6S10 

OOS11 

DOS12 

DOS13 

D0$l4 

DOS15 

00S16 

OOS17 

D0S18 

D0S19 

DOS20 

D0S21 

DOS22 

DOS23 

D0S24 

DOS25 

D0S26 

DONOO 



OOCOO 

OOTOO 

OlCOO 

OOPOO 

OOSOO 

OONOO 

DlCOO 

DOPOO 

DOSOO 

DONOO 

MS OOOOO 

MJ 00 000 

TP AOOOO 

TP QOOOO 

DV OlCOO 

ZJ OONOO 

TV 00S22 

TP 00T01 

MP 01C01 

TP AOOOO 

TP 00C03 

TP 01C02 

TP 00C03 

TP 00T03 

DV OlCOO 

RS 00T08 

TV 00T02 

SP OOCOO 

kP 30O03 

MA 00T05 

TP Aoooo 

LA AOOOO 
TP AOOOO 
IJ 0QT08 
SP 00T09 
SA OOTOO 
DV 00T04 
MJ OOOOO 
TP 00T04 
MJ OOOOO 
60 OOOOO 
ftA OOSll 
SP 00T09 
SA OOTOO 
MJ OOOOO 
TV 00N18 



00013 
00023 
01078 
01024 
01032 
01059 
49864 
49810 
49818 
49845 
OOPOO 
OOOOO 
0OT01 
0OTO2 
00T03 
00P06 
00S19 
00 TO 3 
00T01 
00T04 
0OT05 
00T06 
00T07 
AOOOO 
O0T08 
0OC03 
OOSll 
OOOOO 
00S12 
OOOOO 
00T09 
00036 
OOTOO 
O0S23 
00036 
00036 
00T04 
OOOOO 
AOOOO 
OOP01 
00520 
OlCOO 
00036 
00036 
00S10 
OOS 19 



D 


00015 


00 


OOOOO 


OOOOO 


I 


00027 


00 


OOOOO 


OOOOO 


R R 


02066 


00 


OOOOO 


OOOOO 


E Y 


02000 


00 


OOOOO 


OOOOO 


C 


02010 


00 


OOOOO 


OOOOO 


T 


02043 


00 


OOOOO 


OOOOO 


DRUM 


6 32 1 


00 


OOOOO 


OOOOO 


STORAGE 


63122 


00 


OOOOO 


OOOOO 


DIREC/ 


63132 


00 


OOOOO 


OOOOO 


TORY 


63165 


00 


OOOOO 


OOOOO 


NO ALRM EXIT 


63122 


56 


OOOOO 


02000 


NORMAL EXIT 


63123 


45 


OOOOO 


OOOOO 


ENTRY STORE 


63124 


11 


20000 


00030 


N AND ADRS 


63125 


11 


10000 


00031 


OF YO 


63126 


73 


02066 


00032 


IS N EVEN 


63127 


47 


02043 


62066 


YES EXIT TO 


63130 


16 


02036 


02033 


$20 N/BAR 


63131 


11 


00030 


00032 


EQUALS N 


63132 


71 


02067 


00030 


STORE 3N 


63133 


11 


•20000 


00033 


STORE 1 


63134 


11 


00020 


00034 


4 


63135 


11 


02070 


00035 


AND 1 


63136 


11 


00020 


00036 


INDEX IS ONE 


63137 


11 


00032 


20000 


HALF N/BAR 


63140 


73 


02066 


00037 


MINUS ONE 


63141 


23 


00037 


00020 


PRESTORE V 


63142 


16 


00031 


02023 


CLEAR A 


63143 


31 


00015 


OOOOO 


FORM 


63144 


75 


30003 


02024 


SUM 


63145 


72 


00034 


00006 


SfORfc 


63146 


11 


20000 


00046 


PARTIAL 


63147 


54 


20000 


00044 


SUMS 


63150 


11 


20000 


00027 


IS INDEX NE6 


63151 


41 


00037 


02037 


YES STOfcE 


63152 


31 


00040 


00044 


INTEGRAL TO 


63153 


32 


00027 


00044 


X N/BAR 


63154 


73 


00033 


00033 


STORE INTE/ 


63155 


45 


OOOOO 


00006 


GRAL IN A 


63156 


11 


00033 


20000 


GO TO EXIT 


63157 


45 


OOOOO 


02001 


DUMMY/SEE P6 


63160 


00 


OOOOO 


02034 


MDFY V BY 2 


63161 


21 


02O23 


02066 


RESTORE PAR/ 


63162 


31 


00040 


00044 


TtAL SUMS 


63i63 


32 


66627 


60044 


GO TO $10 


63164 


45 


60060 


62652 


N IS "ODD £X/ 


63165 


16 


02065 


62633 



10-370 



o 

CO 

I 

o 

r-i 
I 

o 
o 



UW-89 
(REV) 
DIE-0 

Pg. 8 of 8 
Revised 6/15/56 



D0N01 


TP 


00T01 


AOOOO 


D0N02 


ST 


01C01 


00T03 


D0N03 


2J 


OOSOO 


O0N04 


D0N04 


TP 


AOOOO 


O0T04 


D0N05 


LA 


00T01 


00003 


D0N06 


TP 


01C01 


00T06 


DONO? 


TP 


61C03 


06T07 


D0N08 


TP 


01C03 


00T08 


D0N09 


TP 


01C01 


OOT09 


D0N10 


RA 


00T02 


00 TO 3 


DONU 


TV 


00T02 


00N14 


D0N12 


SP 


oocoo 


00000 


D0N13 


RP 


30004 


00N15 


D0N14 


MA 


00T06 


00000 


D0N15 


DV 


00T01 


00T06 


D0N16 


RA 


00T04 


00T06 


D0N17 


MJ 


00000 


00P01 


D0N18 


00 


00000 


00N05 


D1C00 


00 


00000 


00002 


D1C01 


00 


00000 


00003 


D1C02 


00 


00000 


00004 


D1C03 


00 


00000 


00009 


START 









IT TO N5 
N/BAR IS N/3 
IS H 3 
YES CLEAR T4 

StORe 8H 

STORE 3 

9 

AND 3 

STORE APRS 

OF YN/BAR 

CLEAR A 

FORM 

SUM 
STORE INTE/ 
6RAL IN A 

go to exit 
dummy/see no 
comstAnts 1 

3 

4 

AN6 9 



63166 
63167 
63170 
63171 
63172 
63173 
63174 
63175 
63176 
63177 
63200 
63201 
63202 
63203 
63204 
63205 
63206 
63207 
63216 
63211 
63212 
63213 



11 00030 
36 02067 
47 02010 
11 20000 
54 00030 
11 02067 
11 02071 
11 02071 
11 02067 
21 00031 
16 00031 
31 00015 
75 30004 

72 00035 

73 00030 
21 00033 
45 00000 
00 00000 
60 60000 
00 "00000 
00 OOOOO 
00 OOOOO 



20000 
00032 
02647 
00033 
0060 3 
00035 
00036 
00037 
00040 
00032 
02061 
OOOOO 
02062 
OOOOO 
00035 
06635 
02001 
02056 



00003 
00004 
006 ll 



x 
a, 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles l\% 9 California 



RW-108 
(REV) 
SHAP 

Pg» 1 of 10 

Revised 7/20/56 



Interpretive Floating Point Package 
Specifications 



Identification Tags 
Type % 



Storage : 



SNAP 

Service Routine (with entrance from 
program available) 

Cells (00000-00012) 
(0072ij.-01023) 
(70000b-71750b) 

The constant pool is used by this routine. 



Service Entrance: 
Program Entrance; 



Address lj.0012b 
See Description 



Coded by: 



Approved by: 



R. Beach 
D , Gantner 
M. Perry 
Mo Speer 
R. Summers 

W, Bauer 



October 10, 1955 



10-372 



RW-108 

(REV) 
SNAP 

Pg. 2 of 10 

Description Revised 7/20/56 

SNAP is an interpretive floating point package for the ERA 1103» It 
contains a single address floating binary point arithmetic section, 
floating decimal data input and output on cards, fixed-to-floating 
and floating-to-f ixed conversion, square root, load and store opera- 
tions o Additional features include an address modifier, or "B-box 11 , 
and optional replacement of the result of an operation in the 
address of the operand. Experience has shown that representative 
programs using SNAP operate at about 1,000 programmed operations per 
second. The speed is obtained by fast floating point operations and 
the fact that many operations are performed at machine speed. 

The package is entered by execution of an Interpret (IP) instruction. 
The u and v portions of this instruction each contain a complete 
SNAP command. Of these fifteen bits, four contain the operation 
part, one the B-box option, one the replace option, and the remaining 
nine the address part. Accordingly, only the lower half (512 cells) 
of electrostatic may be addressed directly. However, use of the 
B-box makes any electrostatic or magnetic drum cell indirectly 
addressable, 

A packed number representation is used and results are normalized 
after each execution* Each floating point number occupies one 36 
bit cello One bit contains the sign, eight the characteristic and 
twenty-seven the mantis sa Hence the range of the numbers is 
approximately + 10^ and approximately eight significant decimal 
digits are contained in the mantissa. The representation is such 
that all 1103 logical commands may be validly applied. Therefore, 
floating point number comparisons may be made at regular machine 
speed and no need exists for inclusion of comparison commands in the 
SNAP repertoire. 

SNAP occupies approximately 900 cells oh the magnetic drum and 300 
cells in electrostatic „ When a card is to be punched or read, 
appropriate coding is brought in automatically from the drum. These 
are the only occasions on which drum references are made. 

SNAP commands may be written with alphabetic operations and symbolic 

addresses, and then assembled by RAW00P. Floating point numbers may 

^ also be included in the program and will be converted and assembled 

8 by RAWOOPo 
1— • 

o Storage 

8 SNAP uses cells (00000 - 00012), (0072l|. - 01023) and (70000b - 71750b). 

£ In addition, it makes use of the Ramo-Wooldridge constant pool (00013 

^ - 00022)o When executing SNAP commands, cell 00000 must contain the 

g word (li£ 00001 WWV). 

The following assignments are of interest to the programmer: 

00002 P 

00003 C 

OOOOij. B-box 



00005 p 



o 



00006 P, 



00007 P, 



RW-106 
(REV) 

SNAP 

Pgo 3 of 10 

Revised 7/20/56 



00008 P- 



00009 P, 



00010 P r 



00011 P, 



> output hopper 



Instruction Structure 

An instruction occupies a 36 bit cell and contains two SNAP commands, 
as schematically shown below,, 



IP 



Left Command 



Right Command 



35-30 



29-15 



34-0 



The left and right SNAP commands are identical in form and have the 
format shown below*, 



Operation B S Address 



29-26 
li-ll 



2$ 
10 



2k 
9 



23-15 
8-0 

Replace option (result replaced 
if bit is one) 

B-box option (address modified 
if bit is one) 



Number Representation 



Floating binary point numbers are each packed into a single 36 bit 
cel?L with assignments as follows : 



S 


Char* 


Mantissa 



35 34-27 26-0 

"Sign" (zero when positive) 

The characteristic has a bias of 128 (200b)« The binary point lies 
between bits 26 and 27 * To negate a number „ the full 36 bits are 
complemented o 

This representation allows use of the Transmit Magnitude and Transmit 

Negative Instructions as well as all comparison jumps* In addition, 

fixed point decimal output routines give useful conversions when 

supplied with 27 as a scale factor* 

10-374 



SNAP Commands 



RW-108 
(REV) 
SNAP 
Pg. A. of 10 

Revised 7/20/56 



The list of commands follows© Parentheses indicate "contents of 1 ',- P 
and G are specific electrostatic cells reserved for the package* a is 
the address part of a SNAP command and may be any address in the lower 
half of electrostatic (00000-005>ll)© Double length extensions of the 
results are stored in A s the machine accumulator© The time column 
below gives average execution times in milliseconds© The operations 
are further clarified on succeeding pages© 



CO 

o 



1 

o 

I— I 

I 

o 

o 
o 



CODE 


0PERATI0N 


TIME 


RESULT 


NO 00 
AD Ok 
SU 10 
MP Ik 
DV 20 
PM 2k 
LD 30 
ST 3k 

pi ko 

FL kk 
RT 50 
RD 70 

PD 7J4- 


No operation 

Add 

Subtract f 

Multiply 

Divide 

Poly c Mpy„ 

Load 

Store 

Fix 

Float 

Square Root 
Read Data 

Punch Data 


•1*3 
2©18 

2©21 

1.9k 
2© 20 

3.W 
1©06 

.98 

lo39 

1©87 
3-25 
500 

583 


(T?\ k» AT? 


(P) + (a) *-A,F 

(p) - ( a ) *-A,F 

(F) x (a) — A,F 

(P) * (a) -A,F 

[(F) x (C)]+ (a) -A,F 

(a) ■- A,F 

i 

( "P \ »— n A T? ' 


(F) floating-*-[A,F] fixed at j 

scale a 

(P) fixed at scale a-— |A,F] floating 

\J(F) *~A,F 

Floating decimal numbers (four 
per card), are read, converted, 
and stored© 

Floating binary numbers are con- 
verted and punched as floating 
decimal numbers (six per card)© 



X 

a. 



Mtf-108 
(REV) 

SNAP 

Pg. 5 of 10 

Revised 7/20/56 



NO (00) 



The No Operation command is included to complete the right half of a partial 
instruction. To gain speed, it short-circuits the normal interpretive loop, 
disabling the replace feature. For this reason the address part (3 octal digits) 
is available for storage of dummy addresses. When used as a left command, 
execution time is extended. The B-box option must not be exercised. 

AD (0*Q, SU (10), MP (1*Q, DV (20), PM (2*Q . 

Results are normalized after each execution. Alarms are provided for "division 
by zero", and "exponent overflow". When the result is less than 2~^9, it is 
made exactly zero. 

LP (30), ST (3*0 

The Load and Store commands perform functions normally left to standard 
machine instructions. However, their inclusion in the repertoire extends the 
use of the B-box y permitting address modification of more complete loops. 

Note especially that the reserved cells F, C, B-box, and P^, are simply 
electrostatic cells. They may be operated on by machine instructions, as 
well as SNAP commands. Since the use of machine instructions invariably saves 
execution time (by a factor of ten to twenty), such use is recommended when 
storage is not extremely critical or the B--box is not being used. 

FI (40), PL (kk) 

When Fixing or Floating, the scale a is in the standard 1103 notation; 

i.e. when a is zero, the point is at the extreme right and when a is 35, the 

point lies between bits aoc and a^. The scale a may not be negative but 

there is no restriction on the upper limit, other than that imposed by overflow. 

An alarm is provided for this condition. 

Since a is not an address, the B-box and store options lose their usual meaning. 
SNAP does not handle them in the normal manner and they should therefore 
not be programmed. 

RT 50 

The square root is accurate to one in the last place. Note that since the 
argument is in F, the address part may be used (in connection with the replace 
option) to store the result. An alarm is provided for negative arguments. 

RD 70 

Upon execution of the Read Data command, floating decimal numbers, each with 
an associated address (four ( per card), are- read, converted to floating binary 
numbers, and stored at address a (or a plus B-*ox) plus the associated address. 
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. 



10-376 



RW-108 
SHAP (REV) 
Pg. 6 of 10 

revised 7/20/56 

Each floating decimal number consists of a ten digit signed mantissa and a tvo digit 
signed exponent » Upon conversion, the mantissa is truncated to 27 hits. The decimal 
point is at the left of the mantissa field and the leading digit must he non-zero. 
An alarm is provided if the ahsolute value of the exponent is greater than 37* 

A single RD command initiates the reading of any number of cards. Reading is termina- 
ted either by the detection of a blank card, or after loading a card which contains 
a 12 punch in either column 79 or 80. A blank card or a 12 punch in column 80 returns 
control to the command following the RD command. A 12 punch in column 79 halts the 
computer with PAK «= 71336 after the card has been loaded. Starting will then return 
control to the command following the RD command. Reading is accomplished at the rate 
of 480 numbers per minute . 

The following card column assignments are made: 

( 1-k )(22-23)(kL J +2)(60-6l) Not used 

( 5-9 )(2i* -28) (1*3-1*7) (62 -66) Associated address 

(lO-19)(29-38)(^-57)(67-76) Mantissa (decimal point at left) 

(20-21) (39 -to) (56-59) (77-78) Exponent of 10 

(79-80) 12 punch will terminate read. 

If the exponent or the mantissa is negative, an eleven punch is included over its 
rightmost digit. 

H> Cft) 

Output is in floating decimal, eight significant digits with sign and a signed 
exponent whose range is +38. Results may be punched in any of six punch positions, 
up to six numbers per card. In addition, a four digit identification number may be 
punched. Punching May occur at rates up to 100 cards per minute. 

Dependent on the value of <2,. execution of the command (PD a) stores the number for 
future punching or punches a card. Specifically, when 0^oe~6, (p) is stored in 
cell P a for future punching in card field a* When a is 10, 20, 30, or 50, contents 
of the output hopper are converted to decimal and punched, after which the output 
hopper is set to zero. Only the four least significant octal digits of the 
U -address part of P are converted to a decimal integer and punched in the identi- 
fication field. If (V ± ) is zero, its field in the output card will be blank. All 
SWAP output cards have a 12 punch in column 75 end also have a 12 punch in column 
~ 78, 79, or 80 when a is 50, 30, or 20 respectively. The SNAP output board is 
o wired to give single spacing before printing except when 78, 79 > or 80 contain 
C 12 punches. In these cases, page ejection, triple spacing, or double spacing 
© occur respectively, before printing. 



o Because of the characteristics of the Bull Reproducer, a blank card is pushed through 
S the punch side on the first read cycle following a punch cycle. SNAP keeps track of 
*"" these sequences and positions an extra card when required. Since a card cycle of 
2 one half second is wasted each time this occurs, interspersed reading and punching 
should be avoided when convenient . The blank cards may be removed from the output 
deck by a single sort, selecting 12 punches in column 75* since only legitimate 
output cards contain this punch. Upon completion of a program using the PD command, 
the Bull should be cleared manually to punch and feed the final card. 



P-10B 
(REV) 



SNAP 

Pg. 7 of 10 

Revised 7/20/56 

The output hopper (cells 00005-00011) need not be loaded by a PD 
command, but may be loaded by any appropriate 1103 or SNAP command. 
It Is also possible to use the hopper as temporary storage. Note, 
however, that If fixed point numbers remain in the hopper when 
punching Is inltated, the punch routine may fail, - 

The following card column assignments are made: 

(1) (13) (25) (37) (k9) (61) Sign of mantissa 

( 2-9 )( 1^-21 )( 26-33 )(38-l4-5)( 50-57) (62-69) Mantissa (point at left) 

(10) (22) (3k) (¥>) (58) (70) Sign of exponent 

(11-12) (23-2ij.) (35-36) (47-i|8) (59-60) (71-72) Exponent 

(77-80) Identification 

Replace Option 

When a bit is present In the replace position of a SNAP command, the 
result of the execution Is stored (replaced) at the effective address 
of the operation o This is in addition to the normal storage of the 
result in A and P. 

B-box Option 

The B-box, or address modifier, is contained in cell 0000l|. When a 
SNAP command has a bit present in its B-box' position, the U-portion 
of cell OOOOij. Is added to the address part {a ) of. the command to 
form the effective address for this execution. The operation part 
and the V-portion of the B-box must be zero (either positive or 
negative), and the effective address must not exceed 77777b* Use 
of this option does not alter the actual address which remains 
constant. 

The B-box is loaded by standard 1103 Transmit Instructions and may 
be incremented or decremented by the Replace Instructions. 

If the effective address exceeds77777b, a portion of SNAP will be 
destroyedo Note that, although the nine bit address part of a SNAP 
command compels the actual address to be less than 512, the effective 
address using the B-box may be as large as 77777b. Note also that 
it is possible to decrement an actual address by loading the B-box 
with a negative number© 

Symbolic Coding 

Although it Is possible to code for SNAP in octal, It is much easier 
to code symbolically for assembly on RAW00P* The advantages of 
using alphabetic operations and symbolic addresses are magnified 
by the peculiar command structure of SNAP instructions. Regular 
machine instructions may be Interspersed arbitrarily with SNAP 
instructions. 

At the end of this section is a facsimile of a standard RAW00P 
coding sheet. It contain* some sampLo floating point numbers and 
SNAP instructions (not a program), and their assembled equivalents 
(In the Comments column). There are two alphabetic operations, 
two symbolic addresses, and two optional B-box and store columns 
in each ins true tion The left hand items in each pair are combined 

10-378 



RW-108 
(REV) 
SNAP 

Pgo 8 of 10 



■!& 7 /fA 6 



to form the left SNAP command^ the right hand items to form w 

command^ The numbers in rows (l) p (2) p and (3) are respectively 125 
~lj.096p and l«125o 



(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 



ADDRESS 



OP 



U 



D + B 



COMMENTS 



D 


















9 


9 


z 





G> 






2 


P 


6 














; 


















1 


2 


5 


















<=> 





1 


F 






17 64000 00000 
















~ 


4 





9 


6 




















3 


F 






56 23777 WTTT' 


















1 


1 


2 


5 






















F 






20 14400 00000 












L 


D 


S 


U 


9 


9 


z 





2 


9 


9 


Z 





4 




B 






B 


s 


14 32402 13404 












A 


D 


F 


I 


9 


9 


z 





3 








2 


1 




B 


s. 






T 14 07403 40025, 












R 


D 


L 


D 


9 


9 


z 





Q 


9 


9 


Z 





5- 














14 70400 3040^ 










, 


A 


D 


N 





9 


9 


z 





7 
















*s 


. 






14 05407 00000 



03 
O 



I 

o 

■—I 
I 

o 
o 



0-. 



Consult the RAW00P write-up for more complete details on symbolic 
coding o 

Alarms 

An alarm routine is self-contained in SNAPo When an alarm condition; 
is reached, the flexowriter types out a word having the form; 

TT P-XXXXX 

where TT is the alarm type, P is an L or an R- (left or right command), 
and XXXXX is the location of the instruction which caused the alarm. 
Upon completion of the typing p a Manual Stop zero occurs a If the 
computer is now started, P and A are set to zero and execution of the 
next command is initiated* See below for the exception when? reading 
data 

The following types of' alarm may occurs 



lo 


E0 


2„ 


RT 


3o 


DV 


U* 


PI 


5o 


RD 



The absolute value Jbf the result is greater 
than (1 - Z°°^)Z 1Z K 



Exponent Overflow 

Square Root of a negative number 

Division by zero 

Fixing causes the naamber to overflow the P register 

Absolute value of input number is equal to or greater than 
10^ . Starting the computer after alarm causes normal 
reading except that a zero replaces the erroneous number. 

Operating Instructions (Activation of SNAP) 

!•> Insure that SNAP is intact on the magne tic drum . (This can be 
accomplished by a transfer of the Service Routine Library from 
magnetic tape)* 



2o Load the problem program 
constant poolo 



Program should include the R-W 



«" 



SRAP 

Pgo 9 of 10 

Revised 7/20/56 

3© Set PAK to J4.0012b and start - This causes SNAP to be read into 
its electrostatic locations, sets the B«box, F, G, and output 
hopper to zero, supplies an appropriate jump in cell zero p 
positions cards on each side of the reproducer, and gives con- 
trol to cell lj.0000 which normally initiates execution of the 
problem program*. 

Programmed Activation of SNAP 

It is occasionally desirable to activate SNAP from the program*, This 
may be accomplished by execution of one of the two commands given 
below,, 

It is assumed that cell UOOOOb contains (MJ 00000 VVVW) which RAW00P 
supplieso 

1 For initial activation (37 I4.OOOO [{.0012 ) - execution of 

this instruction has the same 
effect as (3) in Operating Instruc- 
tions above except that control Is 
given to cell (n + 1) when the 
Instruction Is In cell n D 

2o For reactivation (a) (37 U0000 71050) - same as (1) 

above except that card position- 
ing is omitted, 

(b) (37 Ij-0000 7101^7) - same as (2,a) 
above except that one blank Is 
fed on the punch side to Insure 
that a RD has not cleared the 
punch s tat ion o 

Subroutine s 

Many of the common subroutines have been coded using the SNAP number 
representation for argument and result,. Others are In process,. Their 
use Is extremely simple e 

It Is, however, possible to employ any fixed point subroutine in a 
floating point program by the expedient of the Fix and Float commands 
contained In SNAP C Note that conversion Is rapid 'and that scaling Is 
easily supplied In the address part of the commando 

Design Criteria 

The philosophy which leads to this package states that, In order of 
importance 1, tne following three items are virtue ss 

(1) Simplicity - To produce faster coding with fewer errors* 

(2) Execution speed - To conserve machine tlme 

(3) Minimum storage usage - Both in the problem program and in 
the package, to conserve high speed storage. 

10-380 



CO 

o 



I 

o 



© 
o 






RW-108 
(REV) 

SNAP 

Pgo 10 of 10 

Revised T/20/56 



With these in mind p a single address system was chosen c While logical 
operations are generally best served by multiple addresses, use of a 
single address Is indicated for arithmetic operations Since the four 
basic arithmetic operations may occur in a great variety of sequences^ 
a multiple address system must either waste many of the addresses or 
contain contain a verj large number of arithmetic command types 
Wasting addresses wastes storage in the main program; inclusion of % 
large number of command types expends storage in the package Thvm 
(3) is satisfied by the single address With only one kind ®f e>ach 
of the arithmetic operations 9 jumping and sorting In the arithmetic 
section is "minimiz,ed 

Furthermore , use of only one operand sases- the unpacking: of multiply 
packed numbers „ So the requirements of 42 ) are met* Finally, the 
consideration of (l), ultimate simplicity Is achieved with a system 
which always operates on the same register with but a single^ operand© 



RW-140 
(REV) 

SNAP Sampler 
Pg. 1 of if 
Revised 7/20/56 



SNAP Sampler 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 Ns 

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 Ns 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 10Tb, but may 
be put on the drum. In any case, a parameter word 00 Lo 

Lf wiH specify its location. Lo is the address of the 
first word of the list and Lf is the address of the last 
word. This parameter word must be loaded into cell 71777b 

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 

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 in which 
the instructions to be blocked are actually stored at the 
time the blocking routine ; : Motivated. 



10-382 



RW-140 
(REV) 

SNAP Sampler 
Page 2 of *J- 

Revised 7/20/56 

The operation of the trace is as follows: 

a. When a blocked FA is reached in the program, N and 

N are examined. If N = 0, N £ then tracing is 
s p s ' 

initiated and a start indicator placed in the word 

containing N and N . On the other hand, if N =0 
p s P 

and N £ does not occur, then no action is taken, 
s 

b. At each SNAP execution, after a trace start, the F 
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 IP instructions) then the SNAP output 
routine is used to punch a card containing the informa- 
tion 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 trace hopper at any time, start at 72125b. 
One card will be punched and the machine will stop on 
MS with PAK = 77777b. SNAP must be in ES to exercise 
this option. 

d. In the event the trace hopper is emptied when it contains 
no information, a card will be punched containing the 

o address 7777 in the identification field, while the rest 

of the card will be blank. 

e . When a blocked LA is reached in the program and if a 

o 

o start indicator was set up in the word containing the 

1- associated N and N then tracing is stopped and the trace 

p s 

a. hopper emptied. Otherwise, no action is taken. 

f. The execution of the instruction at FA will be traced, 
but that at LA will not. 



1 

o 



RW-140 
(REV) 
SNAP Sampler 
Page 3 of ^ 
Revised 7/20/56 



g. The seven cells of ES, 1771b - 1777b, cannot be used 
by the programmer if the trace is to be employed. 
Normal SNAP operation will not destroy the contents of 
these cells. 

Programming Instructions 

1. Load cell 71777b 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 at 72000b. The routine will block the proper instructions as 
per the list supplied, modify SNAP in order to perform the trace, 
and then stop with PAK set at ItOOlZb. 

h. In the event no parameter word is loaded (and no list is supplied) 
a start at 72000b will initiate the blocking routine to modify SNAP 
on MD so that all SNAP commands will be traced. A stop will follow 
with PAK set at ^OOlZb. 

Warnings and Restrictions 

1. The list can not occupy cells 15b - 107b. 

2. Cells 1771b - 1777b 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. 

h. The instructions in FA and LA must not be read into or out of by the 
program. 

5. Only SNAP commands are traced. 

6 . The trace can only be used with SNAP and not with the complex 
version. 

7- Activating the trace modifies the copy of SNAP on MD and destroys 
the complex arithmetic portion of SNAP. To start another program 
using SNAP or its complex version, it is necessary to restore the 
library from magnetic tape. 



10-384 



RW-140 
(REV) 

SNAP Sampler 
Page k of h 

Revised T/20/56 



8. An abnormality exists for the following type of a list: 



00 



FA, 



LA, 



N 



N 



pi 

00000 


si 

00000 


00000 


00000 


Ao 


m z 


V 

00000 


\z 

00000 


00000 


00000 

■ k 



00 
00 
00 
00 
00 
00 
00 



Assume that N 1 , N ., N , N ' are such that tracing in both sublists 

is concurrent. Further, suppose that FA- , FA , LA , LA, are executed 

in the order given. Hence, the trace will be initiated at FA n and 
once again at FA_. When LA_ is reached, the trace will stop since it 

was started at FA p . 

, /•>. 

The instructions from LA to LA., will not be traced and the trace will 
be stopped once again when LA, is reached. At this time the hopper will 
be punched. Other unusual combinations can be analyzed in a similar 
fashion. 



o 



o 

l—l 
I 

o 
o 



X 



RW-141 
(REV) 

SNIP 

Pg. 1 of k 

Revised 7/20/56 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles h5 f California 



Interpretive Floating Point Package - Complex 



Identification: 
Type: 

Storage : 



Service Entrance: 
Program Entrance: 



SNIP 

Service Routine (with entrance from 
program available) 



Cells 

634 
70000b 



thru 
thru 



1023 

71662b This includes 
SNAP 



The constant pool is used by this routine. 
Address 40013b 
See description 



Coded by: 

Code Checked by: 
Machine Checked by; 
Approved by: 



C. Koos 
M. Perry 
C. Koos 
C. Koos 
W. F. Bauer 



January, 1956 
January, 1956 
January, 1956 
April, 1956 



10-386 



HW-I41 
(REV) 

SNIP 

Pg. 2 of k 

5A/56 

Revised 7/20/56 

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 in either real or complex arithmetic depend- 
ing on a mode which is selected by the programmer, 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 
p 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 cell c< and y in cell o{ + l). 

2. The floating Complex Accumulator requires two cells: Cell 00002, F, 
is used for the real part; Cell 00003, C, is used for the imaginary 
part, that is, the two cells 00002 and 00003 constitute the Complex 
Floating Accumulator, F c . 

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 F c . 

h. The Fix, Float,. Read, Punch and No Operation commands 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 £<and «K + 1 for the argument as explained 
above . 

5. The machine accumulator A contains the real part of the result after 

the execution of any one of these operations . 
/— \ 

r— I 

3 6. The Replace and B-box options may be used in all cases that are 

Y permitted by SNAP, with two consecutive cells being operated on as 

2 described. Keep in mind that the B-box must be indexed by two when 

^ used in referencing a list of complex numbers, 

o 

p 7» It is not permissible to load F c with TP instructions; a Load command 

^ must be executed for this purpose. 

cu 

In the real mode 

1. All SNAP commands except Polynomial Multiply operate, as in SNAP 
itself. 

2. The execution of the Polynomial Multiply command will give the absolute 
value of (F c ) just as it does in the complex mode. 



RW-141 

(REV) 

SNIP 

Pg. 3 of it 
5/1/56 
Revised l/ZQ/56 



SNIP commands 



AD 


04 


SU 


10 


MP 


14 


DV 


20 


PM 


24 


ID 


30 


ST 


3^ 


RT 


50 




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 y are stored as SNAP 
numbers; that is, each has its own binary exponent. The notation <\. c 
represents the address of a complex number x + iy, where x is stored 
at <and y at <* + 1, that is, ( <X) = x, (a< + l) = y. 

The following definitions apply when in the complex mode: 

Cocte Result 

<F ) + e* c ) 

(F c ) - («g 

(F o ) x (<xj 
(F c ) 

l<V 
(«) 
(F c ) 

I— — — — « 

fhe NO (no operation), FI (fix), FL (float), RD (read data) and 
PD (punch data) instructions of SNAP are unaltered. The PM (poly- 
nomial 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. 

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). v 

2. Load the problem program •*. The program should include the Ramo- 
Wooldrldge constant pool, and a Jump to start in 40000b, as 
supplied by RAWOOP. 

3. Set PAK 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. 



10-380 



RW-141 
(REV) 
SNIP 
Pg. h of 
5/1/56 

Revised 1/20/56 

Programmed Activation of SNIP 

Depending on the card positioning desired any one of three different ' 
return jump instructions may be used to activate SNIP from the program. 
Each assumes that there is a manual jump instruction in cell ^OOOOb 
(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 ^0000 4001 3b positions cards on both sides of 
the reproducer. 

b. Execution of 37 ^0000 7l6kkb feeds one card on the punch side 
of the reproducer. 

c. Execution of 37 ^0000 Jl6k6b 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 activa- 
ted the mode may be switched as follows : 

To switch from the real mode to the complex mode execute the return jump 

37 015^1 01713b 
To switch from the complex mode to the real mode execute the return jump 

37 01541 01715b 

In either case the desired mode change is accomplished, cell 00003, C, 
is set to zero, and control is returned to the cell immediately following 
the return jump. The real mode should ordinarily be used wherever possible 
because it is considerably faster than the complex mode. 

Alarms 



Y The SNAP alarm routine is used, with the possibility of the same type 

2 of alarm occurring (EW, RT, DV, FI, RD). It is not advisable to continue 

© the problem after an alarm, since either the real Or imaginary part of 

§. a number may have caused the alarm. 



x 

Oh 



"A DV alarm will occur if the real and the imaginary parts of the denomina- 
tor are both less than about 2*2 5 ± n absolute value. 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 45 » California 



The Ferranti Input R outine (revised) 



RW-63 

PRI-0 (RE * } 
Pg* 1 of U 
Revised 7/IO/56 



Identification Tag: 

Type: 

Special Storage : 

Service Entrance : 
Program Entrance: 
Program Exit: 
Alarm Exit: 



FRI-0 

Service routine (with subroutine entrance) 

The constant and temporary storage pools 
are not used by this routine 

Address 4-OOOlb 
Address 40001b 
Address 40020b 
The alarm exit is used by this routine 



Coded by: 
Code Checked by: 
Machine Checked by: 
Revised by: 
Approved by: 



R. Beach 
R. Summers 
R. Beach 
C. Koos 
W. Bauer 



May 18, 1955 
May 19, 1955 
August U* 1955 
December 1, 1955 
December 9» 1955 



10-390 



RW-63 
FRI-0 ^ R EV) 
Pg. 2 of U 
Revised t/lO/56 

Description 

I. General 

this routine is designed to read, by means of the Ferranti reader, seven-level 
bioctal tape prepared as described below. The routine reads in paper tape at 
the full speed of the Ferranti with only short hesitation when a check o^ 
insert address is encountered. 

If desired, the tape may contain a. check sum to be tested for agreement with the 
computed sum of the data read-in. The routine will read data into any ES or MD 
cell although the reading of information into certain drum cells (as described 
in detail below) will result in abnormal operation* f 

The routine stores the contents of ES on MD at addresses 76000b through 77777b 
and then transfers itself to ES* It sums itself (in ES) and checks the sum 
against the correct sum (stored on MD). 

The Ferranti reader is started in the free running mode and the routine proceeds 
to read tape and process the information contained on the tape in the same manner 
as does the ERA photoelectric reader (for exceptions, see II. 3 and 4). 

Each word to be transferred to memory is summed as it is read in from tape. 
Words which are to be read into ES are first stored in the MD image of ES 
(76000b thru 77777b). 

During operation all words are read into ES from the tape and a block transfer 
to MD is made when (l) ES has been filled with data (that is, when 924 words have 
been read in);.. '('2) an insert address appears on the tape? or (3) the M end of tape" 
seven-level combination, has been read in (see II. 4.). 

The reader is stopped before making the transfer and is started again after the 
transfer has been completed in the first two cases; in the last case, the reader 
is stopped, ES is restored from the MD image and control is transferred to the 
exit, m •■ 

'?■ . - % ■ .■( ■ '■ • ■' 
The reader is also halted when a check address appears on the tape. If no check 

^ sum test (see II. 3) is to be made after a successful check address test the 

eg reader is started immediately; if the check sum test is specified the reader is 

Y started after the test is made and the sura determined to be correct. 

o 

^ - The routine does not prevent read in to addresses 76000b- thru 77777b nor to 
§ those calls used by the routine for its own operations. 



x 

a* 



II. Requirements for Tape Preparation 

!• The first word on a tape must be* an insert address, 

2. feheck addresses- should be used, although FRI-0 will operate without 
them, A check address immediately following an insert address must 
be the same as the insert address. 



RW-63 

FRI-0 (REV) 
Pg. 3 of U 
Revised 7/10/56 



3* For a check sum test the following four words must appear on the tape 
at the point where the sum is to be tested: ! 

a. Insert address 75202b 

b. High order 36 bits of check sum 

c. Low order 36 bits of check sum 

d. Check address 7520£b 

Operating Instructions (to be followed when the routine is used as a service 
routine ) 

1. Set PAK to AOOOlb and start* 

2« Computation will halt with the MS instruction 56 00000 4-OOOlb at the com- 
pletion of the read in. 

Programming Instructions (to be followed when the routine is used as a sub- 
routine ) 

1. Enter the routine with the RJ instruction 37 A0020 AOOOlb 

2. Control is returned to the cell immediately following the RJ instruction 
as soon as an "end of block" punch is reached on the tape. 

Alarm Conditions 

1* No "end of tape" punch . This condition is indicated bby the tape running 
completely out of the Ferranti reader. When such a condition occurs the 
operator should. 

a. Master clear 

b< Set PAK to 00Q7Ab and start 

c. When computation halts (when a service entry was used) with the MS 
instruction 56 00000 40003b the machine will be returned to its 
original state and the data read from the tape will be properly 
stored. 

If a program entry was used control will be transferred to the proper 
cell in the main program. 

2. FRI-Q not transferred to ES gprrwtly. If ALR-l prints "FRI-0 xxxxx and 
(A) and (Q) t the sum of the program transferred to ES has failed to check. 
Starting at this point transfers FRI-0 to ES again. 

A second failure indicates that FRI-0 is not on the drum correctly and 
should be restored. 

3* Check address failure . If ALR-l prints "ALAR C" and (A) and (Q), a check 
address has failed. In the alarm print (A R ) is the address of the next 

10-392 



RW-63 

FRI-0 (REV) 
Pg. 4 of U 
revised ^/XO/jS 

cell to be loaded and (Q) is the check address that was read in from 
paper tape. 

Starting at this time will cause the machine to ignore the failure and 
operation will continue normally, 

4« Check sum failure . If ALR-1 prints "ALAR M" and (A) and (Q), the check 
sum on the tape has failed to agree with the computed sum. The computed 
sum is in A at the time the alarm print occurs* 

Starting at this point will cause the routine to ignore the failure and 
to begin to read in the tape again. 

If at any time (ES) need to be restored from its image, starting at 
4.004.0b will transfer the image to ES and transfer control to the FRI-0 
exit* 

5. And "end of tape" (or "end of block") punch must be present on the tape 
to halt read in. This consists of seventh level punches in two consecu- 
tive frames on the tape at the point where the read in is to be stopped. 
This seventh level combination acts as a signal to FRI-0 to restore (ES) 
and stop the Ferranti reader. It is compatible with the ERA photoelectric 
reader in that it is an illegal combination which halts the ERA reader • 

Note: If there is a sixth level punch in the second of two consecutive 
frames having seventh level punches the stop is bypassed. The check sum 
is cleared and the reading continues. This will still be an illegal 
combination which will halt an ERA photo-electric reader. 



CO 

nO 

I 

o 

r-i 
I 

o 
© 
o^ 



X 



in ono 



THE RAH)-WOOIDRIDGE CORPORATION 
Los Angeles 45, California 

Arcsine -Arcosine Routine 
Specifications 



RW-148 
(REV) 



SNI-1 

Pg. 1 of 4 

Revised 6/15/56 



Identification Tag: 

Type: 

Assembly Routine Spec: 

Storage : 



Entrance and Exit: 
Alarm: 

Drum Assignment: 
Machine Time: 
Mode of Operation: 



SNI-1 

Subroutine 

SEB 50410 08014 

80 words total program storage 

7 words temporary storage pool used, 
addresses 00027b thru 00035b 

The constant pool is used by this routine 

RJ 00K01 00K03 for the arcsine 
RJ 0QK01 00K02 for the arcosine 

The alarm exit is used to print "Alarm" 

if the absolute value of the argument exceeds 

one. 

Addresses 64252b thru 64371b 

6.0 ms average, 6.6 ms maximum time 

Fixed point 



Coded by: 
Translated by: 
Machine Checked by: 
Approved by: 



A. Franck (ERA) 
D. Gantner 
T. Tack 
W. Bauer 



*fr ifc, 1955 
August 16, 1955 
August 25, 1955 
September 12, 1955 



10-394 



I 

o 



RW-148 

OT(rr . (REV) 
SNI-1 

Pg. 2 of k 

Revised 6/15/56 



Description 

This subroutine computes F(x) = arcsin x or F(x) » arcos x (depending on which 
of two entrances is used) by use of a polynomial approximation. (See Rand 
Sheet No. 39). 

The routine was originally coded by Dr. A. Franck of ERA. and has been adopted 
for use at The Ramo -Wooldridge Corporation. 

Notation 

x = sine or cosine of an angle F(x). 

F(x) » the computed angle in radians whose sine or cosine is x. 

The ranges of the results are the principal values, defined as follows: 

- 3t/2^arcsine x^jt/2 

O^arcosine x^it 

Programming Instructions 

1. Place the argument scaled by 2 ~* (i.e. x*2~* 3 ) in A . 

2. Enter the routine with an RJ instruction . If the routine was assigned to 
region OOKQO for assembly use the instruction 

RJ 00K01 00K03 for the arc sine, or 
RJ 00K01 G0K02 for the arcos ine. 

3. At the time of exit from the routine the result -F(x). # 2 is left in A. 
Alarm Conditions 



.» 



2 If the |x| is greater than one an alarm exit will occur. The word "alarm" 

3 and the address of the cell in the main program containing the RJ instruction 
Y which was used to enter SNI-1 will be printed on the flexowriter. 



Pushing the start button after the alarm halt will transfer control to the 



g exit of SNI-1. 



a. 



RW-148 

(REV) 
SNI-1 

Pg. 3 of k 
Revised 6/15/56 



D 




DSCOO 


50410 


64252 


00 OOOOO 00000 


D 




ASCOO 


01024 


02000 


00 OOOOO OOOOO 


DSCOO 


37 


75701 


75702 B ALARM EXIT 64252 


37 75701 75702 


DSCOl 


MJ 


00000 


00000 ROUTINE EXIT 64253 


45 OOOOO OOOOO 


DSC02 


MJ 


00000 


ASC57 ARCCOS ENTRY 64254 


45 OOOOO 020T1 


DSC03 


MJ 


00000 


ASC60 ARCSIN ENTRY 64255 


45 OOOOO 026?4 


DSC04 


TP 


00013 


00024 


64256 


11 0O015 00030 


DSC05 


TM 


AOOOO 


00025 


64257 


12 20000 00031 


OSC06 


TJ 


ASC66 


ASCOO 


64260 


42 02102 0^000 


DSC07 


TJ 


ASC67 


ASC09 


64261 


42 02103 02011 


DSC08 


MJ 


00000 


ASCOO 


64262 


45 OOOOO 02000 


DSC09 


TP 


AOOOO 


QOOOO 


64263 


11 20000 10000 


DSC10 


ZJ 


ASCII 


ASC52 


64264 


47 02013 02564 


DSCH 


SJ 


ASC12 


ASC13 


64265 


46 02014 02015 


DSC12 


TP 


00016 


00024 


64266 


11 00020 00030 


OSC13 


TM 


AOOOO 


AOOOO 


64267 


12 20000 20000 


DSC14 


EJ 


ASC68 


ASC55 


64270 


43 02104 02067 


DSC15 


MP 


00025 


ASC69 


64271 


71 00031 02105 


0SC16 


LA 


AOOOO 


00037 


64272 


54 20000 OOO 45 


DSC17 


AT 


ASC70 


00026 


64273 


35 02106 00032 


OSC18 


MP 


00025 


00026 


64274 


71 00031 00032 


DSC19 


LA 


AOOOO 


00037 


"64275 


54 20000 00045 


DSC20 


AT 


ASC71 


00026 


64276 


35 02107 00032 


DSC21 


MP 


00025 


00026 


64277 


71 00031 00032 


OSC22 


La 


AOOOO 


00039 


64300 


54 20000 0004? 


DSC23 


AT 


ASC72 


00026 


64301 


35 02110 00032 


DSC24 


MP 


00025 


00026 


64302 


71 00031 00032 


DSC25 


LA 


AOOOO 


00038 


64303 


54 20000 00046 


DSC26 


AT 


ASC73 


00026 


64304 


35 02111 00032 


DSC27 


MP 


00025 


00026 


64305 


71 00031 00032 


DSC28 


LA 


A0000 


00038 


64306 


$4 20000 000 U 


DSC29 


At 


AS<t74 


00026 


64307 


35 02112 00032 


DSC 30 


MP 


00025 


00026 


64310 


71 00031 00032 


DSC31 


LA 


AOOOO 


00038 


64311 


54 20000 00046 


DSC32 


AT 


ASC75 


00026 


64312 


35 02113 00032 


DSC33 


MP 


00025 


00026 


64313 


71 00031 00032 


DSC34 


LA 


Aoooo 


00036 


64314 


54 20000 00044 


DSC35 


AT 


ASC76 


00026 


64315 


35 02114 00032 


DSC36 


TN 


00025 


AOOOO 


64316 


13 00031 20000 


DSC37 


SA 


ASC68 


00002 


64317 


32 02104 00002 


DSC38 


TP 


ASC78 


00027 


64320 


11 02116 00033 


D5C39 


EJ 


A$C78 


ASC47 


64321 


43 ,02116 0205? 


DSC40 


TP 


AOOOO 


00028 


64322 


11 20000 00034 


DSC41 


SP 


00028 


00034 


64323 


31 00034 00042 


DSC42 


DV 


00027 


00029 


64324 


73 00033 00036 


DSC43 


LA 


00027 


00071 


64325 


54 00033 0010? 


DSC44 


RS 


QOOOO' 


00027 


64326 


23 10000 00033 



10-396 



SNI-I 

Pg. k Of 4 

Revised 6/15/56 



DSC45 
DSC46 
DSC47 
DSC48 
DSC49 
DSC50 
DSC51 
DSC52 
DSC53 
DSC54 
DSC55 
DSC56 
DSC57 
DSC58 
DSC59 
DSC60 
DSC61 
DSC62 
DSC63 
DSC64 
DSG65 
DSC66 
DSC67 
DSG68 
DSC69 
0SC70 

DSG71 
DSC72 
DSC73 
DSC74 
DSC75 
DSC76 
DSC77 
DSC'78 
DSt?9 
STARt 



RA 00027 
QJ ASC41 
MP AOOOO 
LA AOOOO 
ST ASC77 
IJ 00024 
TN QOOOO 
R5 00000 
OV ASC79 
MJ 00000 
TN ASC77 
MJ 00000 
TP ASG77 
TV ASC65 
MJ 00000 
TP 00013 
TV ASC64 
MJ 00000 
TN AOOOO 
MJ 00000 
00 00000 
67 77777 
10 00000 
10 00000 
53 24135 
33 24414 
56 40071 
37 50417 
46 23706 
26 61651 
44 42003 
31 10375 
31 10375 
37 77777 
00 OOOOO 



00029 
ASC47 
00026 
00037 
QOOOO 
ASC52 
QOOOO 
00023 
AOOOO 
ASG01 
QOOOO 
ASG50 
00023 
ASG54 
ASC04 
0002S 
ASCI54 
ASG04 
AOOOO 
ASC01 
ASC63 
77777 B 

00001 B 
00000 B 
20070 B 
25535 B 
51545 B 
41233 B 
66522 6 
66073 § 
30653 & 
51633 B 
52421 6 
77777 8 

00002 § 



64327 
64330 
64331 
64332 
64333 
64334 
64335 
64336 
64337 
64340 
64341 
64342 
64343 
64344 
64345 
64346 
64347 
64350 
64351 
64352 
64353 
64354 
64355 
64356 
64357 
64360 
64361 
643^2 
6434* 
64364 
64365 
64366 



64376 
643?L 



21 00033 

44 02051 
71 20000 
54 20000 

36 02115 
41 00030 
13 10000 
23 16000 
73 02117 

45 00000 
13 02115 
45 OOOOO 
11 02115 
16 02101 
45 60006 

li 600 is 

16 02100 
45 OOOOO 
13 20000 

45 OOOOO 
00 OOOOO 
67 77777 
10 OOOOO 
io OOOOO 
53 24135 
33 ,.24414 
56 46071 

37 5641? 

46 23?66 
26 6i6$i 
44 42663 
31 16375 
31 16375 
37 77777 
60 60666 



00035 
02057 
00032 
00045 
10000 
02064 
10000 
0662? 
200O0 
02001 
10000 
02062 
6002? 
02066 
02664 



62666 
02004 
20000 
02001 
02077 
77777 
0000 1 
00000 
20070 
2553$ 
5154$ 



66671 



5242 
7777 



CO 



I 

o 
o 
o- 



x 



10-397 



THE BAMO-WOOLDRUXJE CORPORATION 
Los Angeles k5> California 



SNI-2,., 
Page i of k 
ttevissa 8/l/5<5 



RW-149 
(REV) 



Identification Tag: 

Type: 

Assembly Routine Spec: 

Storage : 



Floating Point Arc sine -Arco sine Routine 
Specifications 
SNI-2 
Subroutine 
SUB 503^9 06112 
6l words total program storage. 



Entrance and Exit: 

Alarm Exit: 

Drum Assignment: 
Machine Time: 
Mode of Operation: 



3 wcrds temporary storage pool use-d^ addresses 
00027b thru 00031b 

The constant pool is used by this routine. 

RJ 00K01 00K02 for the arcsine 
RJ 00K01 00K03 for the arcosine 

The alarm exit is used to print "alarm" if the 
absolute value of the argument exceeds one. 

Address 64l55b thru 64251b 

7.17 ms average, 8.7^ ms maximum 

Floating £oint 



Coded by: 
Code Checked by: 
Machine Checked by: 
Approved by: 



M. Perry 
R. Bigelow 
M. Perry 
W . Bauer 



August 25, 1955 
August 28, 1955 
September 7> 1955 
September 12, 1955 



10-^ 



o 



SHI- 2 

Page 2 of h 

Revised 8/1/56 



Description 



When supplied with an argument X in SNAP form, this routine will compute the 
arcsine or the arcosine of X (depending on which of two entrances was used) 
using a Rand Polynomial Approximation producing the answer in SNAP form. 

Programming Instructions 

The SHAP floating point routine must be in E~S. when this subroutine is entered. 

1. Place the argument X in the accumulator * X must he in SHAP form. 

2 . Return Jump to the subroutine . Assuming that the subroutine was assigned 

to region 00K00 for assembly, use the instruction RJ 00KQ1 Q0KQ2 for arcsine, 
or RJ 00K01 00K03 for arcosine. 

3. At the time of exit from the subroutine, the double length extension of 
arcsine X, or arcosine X, in SNAP form will be in the accumulator. 

The ranges of the results are the principal values, defined as follows: 

-jt/2 < arcsine X S n/2 
^ arcosine XS «/ 

Error Analysis 

■ -26 

The error in the result produced by this subroutine is less than 2 . 

Mathematical Analysis 

1. The Rand Polynomial Number 39 is evaluated using the absolute value of X 
as the argument. Designate the result as P(X). 

2. The square root of 1 minus the absolute value of X is found using the square 
root subroutine within SNAP. Designate this result as R(x). 

3. If X is positive, let Y = P(X)R(X) 
If X is negative, let Y = *-P(X)R(X) 

<? k. Arcsine X = (n/2)-Y 



Arcosine X = Y 



o 5* This procedure places arcsine X in the first or fourth quadrant, and 
a- arcosine X in the first or second quadrant. 

r— H 

x Alarm Conditions 

a, ■■ — ■ — 

An alarm print will occur if the argument is outside the range -1^ X< 1 . The 
flexowriter will print "alarm" and the address of the cell in the maaH program 
containing the RJ instruction which was used to enter SNI-2. 



10-399 



RW-149 

SHI-2 (REV > 
Pg. 3 of k 
Revised 8/I/56 



D 




OOKOO 


00906 


SNAP CONS 




01612 


00 


00000 


00000 


D 




OOTOO 


00722 


SNAP. TEMP 




01322 


00 


OOOOO 


00000 


D 




oocoo 


00754 


SNAP EXIT 




01362 


00 


100000 


00000 


D 




SRTO-0 


00927 


SNAP SQ ROOT 


01637 


00 


00000 


00000 


D 




oopoo 


00877 


SNAP CONS 




oi553 


00 


00000 


00000 


D 




OASOO 


50349 


ARCSN RTH 


49 


64155 


00 


00000 


OOOOQ 


D 




1ASOO 


01024 


REL 2000 


49 


02000 


00 


00000 


00000 


D 




2AS00 


56398 


ARCSN CNS 


11 


64236 


00 


00000 


00000 


D 




3AS00 


01073 


REL 2000 


11 


02061 


00 


00000 


00000 


0ASO0 


37 


75701 


75702 B 


ALARM EXIT 




64155 


37 


75701 


75702 


0AS01 


MJ 






NORMAL EXIT 


64156 


45 


00000 


00000 


0AS02 


RP 


20002 


1AS04 






64157 


75 


20002 


02004 


0AS03 


TP 


00018 


00023 


COS ENTRY 




64160 


11 


00022 


00027 


0AS04 


TP 


AOOOO 


00024 


X 




64161 


11 


20000 


00030 


OAS05 


TM 


AOOOO 


AOOOO 


X ABS 




64162 


12 


20000 


20000 


0AS06 


. TP 


BOOOO 


00025 


CLEAR 25 




64163 


11 


30000 


00031 


0AS07 


ST 


3AS08 


QOOOO 


X-50 




64164 


36 


02071 


10000 


0AS08 


TJ 


00K14 


1AS12 


X ZERO 




64165 


42 


01630 


02014 


0AS09 


QT 


O0KO3 


00025 


M 




64166 


51 


01615 


00031 


OAS10 


SP 


QOOOO 


00008 






64167 


31 


10000 


00010 


OASll 


TV 


BOOOO 


1AS12 






64170 


16 


30000 


02014 


OAS12 


LA 


00025 


00000 


M FIXED 


33 


64171 


54 


00031 


00000 


0AS13 


ST 


3AS09 


QOOOO 


A L. EL 00 X 




64172 


36 


02072 


10000 


0AS14 


SF 


QOOOO 


00T04 






64173 


74 


10000 


01326 


OAS15 


SJ 


1AS17 


1AS16 






64174 


46 


02021 


02020 


0AS16 


ZJ 


1AS00 


1AS32 






64175 


47 


02000 


02040 


OAS17 


LA 


AOOOO 


00027 






64176 


54 


20000 


00033 


0AS18 


TN 


BOOOO 


00T03 


l/X FLOATED 


64177 


13 


30000 


01325 


0AS19 


LA 


00T04 


00027 


SF IN T04 




64200 


54 


01326 


00033 


OAS20 


TP 


1AS01 


OOCOO 






64201 


11 


02001 


01362 


0AS21 


RJ 


oocoo 


SRTOO 


FIND ROOT 




64202 


37 


01362 


01637 


OAS22 


TP 


00P02 


OOCOO 


REPAIR SNAP 


64203 


11 


01557 


01362 


OAS23 


SP 


00T04 


00000 






64204 


31 


01326 


00000 


0AS24 


SS 


SRT26 


C0008 






64205 


34 


01671 


00010 


0AS25 


TV 


BOOOO 


1AS31 






64206 


16 


30000 


02037 


0AS26 


SIN! 


3AS00 


00036 


A/7 




64207 


33 


02061 


00044 


0AS27 


RP 


20007 


1AS29 


EVAL rand. 




64210 


75 


20007 


02035 


0AS28 


PM 


3AS01 


00025 


POLY 


29 


64211 


24 


02062 


00031 


0AS29 


MP 


BOOOO 


00T03 




56 


64212 


71 


30000 


0132* 


OAS30 


LA 


AOOOO 


00010 




66 


64213 


54 


20000 


00012 


0AS31 


SP 


BOOOO 


00000 






64214 


31 


30000 


00000 


0AS32 


TP 


BOOOO 


00025 




31 


64215 


11 


30000 


00031 


0AS33 


TP 


00024 


QOOOO 


X 




64216 


11 


00030 


ioooo 



10-400 






i 

o 

r— I 
I 

o 
o 



X 

Oh 





RW-14' 


SNI-2 


(REV) 


Pg. ** 


of k 


Revised 8/1/56 



0AS34 


GJ 


1AS35 


1AS37 






X NEG 


64217 


,44 


02043 


02045 


0AS35 


SP 


3AS11 


00001 






PI 


64220 


31 


02074 


0000 1 


0AS36 


ST 


00025 


00025 








64221 


36 


00031 


00031 


0AS37 


IJ 


00023 


1AS40 








64222 


41 


00027 


02050 


0AS38 


SP 


3AS11 


00000 








64223 


31 


02074 


00000 


0AS39 


ST 


00025 


00025 








64224 


36 


00031 


00031 


QAS40 


SF 


00025 


00023 








64225 


74 


00031 


00027 


0AS41 


ZJ 


1AS42 


1AS01 








64226 


47 


02052 


02001 


0AS42 


LA 


A0000 


00027 








64227 


54 


20000 


00033 


0AS43 


TP 


B0000 


00025 






M FINAL 


64230 


11 


30000 


00031 


0AS44 


SP 


00023 


00027 








64231 


31 


00027 


00033 


0AS45 


AT 


3AS10 


Q0000 






E FINAL 


64232 


35 


02073 


10000 


0AS46 


CC 


00025 


Q0000 






PACK 


64233 


27 


00031 


10000 


0AS47 


TP 


A0000 


A0000 






EXTEND 


64234 


11 


20000 


20000 


0AS48 


MJ 


00000 


1AS01 






OUT 


64235 


45 


00000 


02001 


2AS00 


01 


26249 


11000 


-03 


42 


A/7 


64236 


05 


12750 


53762 


2AS01 


06 


67009 


01000 


-03 


40 


A/6 


64237 


06 


65103 


05327 


2AS02 


-1 


70881 


25600 


-02 


38 


A/5 


64240 


73 


50016 


32330 


2AS03 


03 


08918 


81000 


^02 


36 


A/4 


64241 


01 


76420 


76052 


2AS04 


-5 


01743 


04600 


-62 


34 


A/^3 


64242 


77 


14476 


15552 


2AS05 


08 


89789 


87400 


-02 


32 


A/2 


64243 


06 


26616 


51661 


2AS06 


-2 


14598 


80160 


-01 


30 


A/1 


64244 


77 


62210 


01542 


2AS07 


01 


57079 


63050 




28 


A 


64245 


00 


31103 


75516 


2AS08 


06 


20000 


00000 


B 




50 


64246 


06 


20000 


00000 


2AS09 


10 


00000 


00000 


B 




1 33 


64247 


10 


00000 


00000 


2AS10 


07 


40000 


00000 


B 




60 


64250 


07 


40000 


00000 


2ASH 


01 


57079 


63268 




31 


PI OVER 2 


64251 


03 


11037 


55242 


START 














00000 


45 


00000 


00000 



10-401 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles 45, California 



Floating Point Arctangent Routine 
Specifications 



RR-74 
(REV) 



WII-1 

Pg. 1 of h 
Revised 6/15/56 



Identification Tag: 

Type: 

Assembly Routine Spec; 

Storage : 



I&itrance and Exit: 
Drum Assignment: 
Machine Time: 
Mode of Operation: 



TNI-1 
Subroutine 
SUB 50137 05114 
51 words total program storage. 
3 words temporary storage pool used, addresses 
00027b thru 00031b 
The constant pool is used. 
RJ 00K01 00K02 
Address 63631b thru 63713b 
4.27 ms average, 5*8 ms maximum 
Floating point 



Coded by: 
Code Checked by: 
Machine Checked by: 
Approved by: 



M. Perry 
R. Bigelow 
M. Perry 
W. Bauer 



July, 1955 
July, 1955 
August, 1955 
August, 1955 



10-402 



I 

o 

I 

o 
o 
o 






RR-74 
(REV) 

TRfI-1 

Pg. 2 of k 
Revised 6/15/56 



Description 

When supplied with an argument X in SNAP form, this routine -will evaluate 
Arctan X (in radians) using a Band Polynomial Approximation producing an 
answer in SNAP form. 

Programming Instructions 

1. Place the double length extension of X in the accumulator . 
X must he in SNAP form. 

2. Return Jump to the subroutine . Assuming that the subroutine was assigned 
to region 00K00 for assembly, use the instruction RJ 00K01 O0KO2. 

3. At the time of exit from the subroutine, the double length extension of 
Arctan X will be in the accumulator in SNAP form. The range of the result 
will be the principal value, defined as follows: 

-%/Z < Arctan X < it/ 2 

Error Analysis 

-25 

The error in the result produced by the routine is less than 2- . 

Mathematical Analysis 

1. If x>l, the identity Arctan X = (n/Z) - Arctan (l/x) is used. 

2. Rand Polynomial Number 13 is evaluated using X (or l/x) as the argument. 

Range of Variable 

No alarm conditions exist. Any number which can be expressed in SNAP form can 
be entered and the result will have the accuracy stated above. 



in_,irtt 



RR-74 
(REV) 

TNX-1 

Pg. 3 Of k 

Revised 6/15/56 



D 

D 

D 

D 

00T00 

OOT01 

OOT02 

OOT03 

OOT04 

00T05 

00T06 

OOT07 

00T08 

00T09 

OOTIO 

OOTH 
00T12 
OOT13 
00T14 
00T15 
OOT16 
OOT17 
00T18 
00T19 
OOT20 
00T21 
OOT22 
OOT23 
0OT2A 
OOT25 
00T26 
00T27 
OOT28 
00T29 
00T30 
OOT31 
00T32 
00T33 
00T34 
OOT35 
00T36 



OOTOO 
OiTOO 
02T00 
03TOO 
00 00000 
MJ 00000 
TP 00013 
TJV03T00 
SJ 0iT05 
TP 03T01 
TM AOOOO 
QT 03T02 
SS QOOOO 
SA 03T03 
TM BOOOO 
SJ 01T12 
SIM 00015 
DV 00023 
TP 03T04 
SP 03TQ5 
SS 00024 
SJ 01T20 
TV AOOOO 
LA 00023 
TP BOOOO 
MP BOOOO 
LA AOOOO 
TP BOOOO 
SH 03T06 
RP 20007 
PM 03T07 
PM 00025 
TP BOOOO 
ZJ 01T30 
SF AOOOO 
TP AOOOO 
SP 00024 
SA 00014 
SA 00023 
TP BOOOO 
MJ 00000 



50137 


ARCTN RTN 37 


63631 


00 


OOOOO 


OOOOO 


01024 


TO BE aLTeRD 


o£ooo 


00 


OOOOO 


OOOOO 


50174 


ARCTN CMS 14 


63676 


00 


OOOOO 


OOOOO 


01061 


TO BE ALTERD 


02045 


00 


OOOOO 


OOOOO 


00000 


ALARM EXIT 


63631 


00 


OOOOO 


OOOOO 


00000 


NORMAL EXIT 


63632 


45 


OOOOO 


OOOOO 


00025 


NORMAL ENTRY 


63633 


11 


00015 


00031 


01T35 




63634 


11 


02045 


02043 


01T06 




63635 


46 


02005 


02006 


01T35 


NE6 ARG 


63636 


11 


02046 


02043 


QOOOO 




63637 


12 


20000 


10000 


00023 


M 


63640 


51 


02047 


00027 


00000 




63641 


34 


10000 


OOOOO 


00008 


MINUS E 


63642 


32 


02050 


00010 


00024 


E ABS 


63643 


12 


30000 


00030 


01T15 




63644 


46 


02014 


02017 


00039 


1 


63645 


33 


00017 


00047 


00023 


1 OVER M 28 


63646 


73 


00027 


00027 


00025 


PI OVER 2 


63647 


11 


02051 


00031 


00000 




63650 


31 


02052 


OOOOO 


00000 




63651 


34 


0O030 


OOOOO 


01T18 




63652 


46 


02024 


02022 


01T19 


42/E ABS 


63653 


16 


20000 


02023 


OOOOO 




63654 


54 


00027 


OOOOO 


00023 


ARG OF POLY 


63655 


11 


30000 


00027 


QOOOO 




63656 


71 


30000 


10OO0 


00001 




63657 


54 


20000 


0000 1 


00024 


ARG SQUARED 


63660 


11 


30000 


00030 


00035 


CJ15 


63661 


33 


02053 


00043 


01T27 




63662 


75 


20007 


02033 


00024 


POLY 


6 366 3 


24 


02054 


00030 


00023 


EVALUATION 


63664 


24 


00031 


00027 


AOOOO 




63665 


11 


30000 


20000 


01T01 




63666 


47 


02036 


02001 


00024 


SCALE 


63667 


74 


20000 


00030 


00023 


M FINAL 


63670 


11 


20000 


00027 


00000 




63671 


31 


00030 


OOOOO 


00035 


E/128 FINAL 


63672 


32 


00016 


00043 


00027 


PACK 


63673 


32 


00027 


00033 


AOOOO 


EXTEND 


63674 


11 


30000 


20000 


01T01 


OUT 


63675 


45 


OOOOO 


02001 



10-404 



I 

o 
r-t 

i 

o 
o 



04 



RR-74 
(REV) 



TNI-1 

Pg. k of k 

Revised 6/15/56 



02T00 


TP 


B0000 


AOOOO 






POS CO&DITN 


63676 


11 


30000 


20000 


02T01 


TN 


BOOOO 


AOOOO 






NEG CONDITN 


63677 


13 


30000 


20000 


02T02 


00 


07777 


77777 


B 




MASK 


63700 


00 


07777 


77777 


02T03 


20 


00000 


00000 


B 




128 


63701 


20 


00000 


00000 


02T04 


01 


57079 


63268 




27 


PI OVER 2 * 


63702 


00 


14441 


76652 


02T05 


00 


00000 


00052 


B 




42 


63703 


00 


00000 


00052 


02T06 


04 


05405 


80000 


-03 


36 


C/15 


63704 


00 


20465 


76350 


02T07 


02 


18612 


28800 


-02 


34 


C/13 


63705 


00 


26305 


45073 


02T08 


-5 


59098 


86100 


-02 


33 


C/ll 


63706 


77 


43277 


43606 


02T09 


09 


64200 


44100 


^02 


32 


C/9 


63707 


00 


30535 


75750 


02T10 


-1 


39085 


33510 


-01 


31 


t/1 


63710 


77 


56144 


71644 


02TH 


01 


99465 


35990 


^01 


30 


C/5 


63711 


00 


14610 


05133 


02T12 


-3 


33298 


56050 


-01 


29 


C/3 


63712 


77 


65253 


17101 


02T13 


09 


99999 


33290 


-01 


28 


t/1 


63713 


00 


17777 


77515 


START 























1 0-405 



THE RAMD-WOOLDRIDGE CORPORATION 
Los Angeles 45 » California 

CHANGED WORD POST-MORTEM ROUTINE (revised) 

SpesijrigetJtQUB 



RW-102 
(REV) 



MDP-3 

Pg, 1 of 2 

revised 9*1^-53 



Identification Tagi 

Types 

Special Storage: 

Service Entrance: 
Program Entrance: 
Program Exit: 
Alarm Exit: 
Machine Time: 



MDP-3 

Service Toutine (with subroutine entrance) 

The constant pool and temporary storage pool 
are not used by this routine. 

Address 4.0037b 

4.0037b 

4.0020b 

The alarm exit is not used by this routine. 

(14 »1 + «5n) seconds where n=number of cards 
punched* 





Coded by: 


R« £*each 


October 26, 1955 




Code Checked by: 


R. Beach 


October 26, 1955 


/— s 


Machine Checked by: 


R. Beach 


October 26, 1955 


O 
■— t 


Revised by: 


C. Koos 


December 1, 1955 


1 

O 

r-4 


Approved by: 


W. F. Bauer 


Deo ember 9 > 1955 


I 





i— 1 

















10-406 



o 



RW-102 
(REV) 

MDP-3 

Pg« 2 of 2 

revised 9~lk<»56 



Description 

This routine compares ES with the MD image of ES and prints out those 
words of ES which are not the same as their correspondent in the image. 
ES is not altered by the routine, and the MD image is up-dated to be 
identical with ES when exit is made from the routine * 

The routine stores ES at addresses 66000b to 67777b and reads portions 
of this image and the regular image (76000b - 77777b) into ES and com- 
pares wbrds. 

If the corresponding words are the same, they are replaced by zero, unless 
the new value is zero. In the latter case the word is replaced by 4-5 4-0037 
40020b. The changed words and zeros are then read into ES. ES is then 
dumped on the line printer. ( Note % Until the line printer is in use, 
this dump will be made onto cards by employing MDP^**). ES and the 76000b 
image are then restored from the 66000b image. 

Each card contains six. words. If any one word is zero, it should be ig- 
nored as it is not a changed word. A word which has been changed to zero 
has been given the arbitrary tag 45 4-0037 4.0020b and will be punched as 
such. Also, a word that was changed to this tag will be identified in the 
same manner. The programmer must therefore distinguish between these 
two cases. 



Operating Instructions 

!• Mien routine is used as a service routine set PAK to 40037b. 
Routine will find changed words, print them out, and stop 
on 56 00000 40037b. 

2. When routine is used as a subroutine enter routine with 37 4.0020 
4.0037b. Operation of routine is the same except that routine 
exits to address y+1 if y is the address of the RJ instruction 
used to enter the routine. 



3. Most service routines use all or parts of ES and their activation 
f will destroy the old 76000b image. Hence, if a changed word compari- 

son is desired, the execution of MDP-3 must precede the use of otiber 



o post-mortem routines. 

o 



>< AXa,rm Condi t^Qfls 



There are no alarm conditions in this routine. However, if the routine 
hangs up during punching, or if the machine is halted during punching, 
a start at 40040b will clear the punch, restore ES, and up-date the 
76000b image. 



Identification Tag: 

Type: 

Assembly Routine Spec: 

Storage : 



Program Entrances 
Program Exit: - 
Alarm Exit: 



THE M404flD0LDRIDGE CORPORATION 
Los Angeles h£ p California 

Nth Root Routine 
Specifications 
NRT-0 
Subroutine 
SUB £1316 03701 

36 instructions, addresses 
10FOO thru 10F35 

1 constant in program, address 
10F36 

37 words total program storage, addresses 
10F00 thru 10*36 

U words temporary storage pool used, 
addresses 00027b thru 00033b 

The constant pool is used by this routine. 

Address 10F02 

Address 10F01 

The alarm exit is used by this routine. 



RW-116 

(REV) 
NRT-0 
Pg. 1 of h 

Revised 9-H1.-56 



Drum Assignment: 
Machine Time: 

Mode of Operation: 



Address 66061;b thru 66130b 

Average execution time 

2(n-2) + 5 milliseconds for n 4s $0 

Fixed point 



Coded by: 
Code Checked by: 
Machine Checked by: 
Approved by: 



¥• Frank 
W. Frank 
W, Frank 
Wo F. Bauer 



November 25, 1955 
November 28, 1955 
November 30, 1955 
December 1, 1955 



10-408 



RW-116 . 

(REV) 
NRT-0 

Pg. 2 of k 
Revised 9-14-56 



Description 

This subroutine extracts the n tn root of any number K, scaled at 2^, and 

such that 

|m«2 3 ^| L 2& -1. 
n must be an integer in the range 

2 ^ n Z. 2 12 
The routine must be entered with M«2^ in A and n»2° in Q. The result will 
be left in A, scaled at 2^ f at the conclusion of the routine • 

Programming Instructions 

1* Place M»2^ in A^« (Ay) is ignored by this routine. 

2. Place n*2° in Q. 

3. Enter the subroutine with RJ 00F01 00F02, where 00F00 is the location 
of the first word of NRT~Q. 

k* The subroutine returns control to the cell following the RJ instruction 
with ( VTO *2& in A. 

Alarm Conditions 

The subroutine enters the alarm routine ALR-1 if n is negative or M is 
negative for n even. In either case, the word "alarm" is .printed on the 
^ flexowriter, followed by the octal address of the RJ instruction used to 

r-H 

J enter NRT-0. 

rH 
I 

o 

o 

£ Execution Time 

h- . 

g The time taken to find the n^ root of a number is inversely proportional to 

the magnitude of the number and directly proportional to the size of n. An 
average estimate, for n ^ $0 $ is approximately 3(n-2) + 5> milliseconds* 



RW-116 
(REV) 
HRT-0 

Mathematioal Method Hevifled AM6 

An iterative proo©dur©, employing the Newton-Bapheen method** 1 , ie used t© 
solve th© equation 

x n ■ M 
Th© prooesi ii of second order and is defined fey 

x i+l " x i ~ (x^p^ " x l 

where x e «2^ - 2^ - 1 

The iteration is terminated when 



|M| - Xi £h 

fir 

A secondary test is mad© to insure 
n-1 



This test is necessary | evenfoeugh the presses is monotonia j for, it ie 
possible that truncation of the result of multiplication and division oan 
violate this property. In that event, x. , is taken as the solution^ 
A speoial oase ie M * 0, where the solution is x ■ for aH p. 

Aeouraey 

The error in the result of this routine wai found to be less than ICT^j 
that is, for an input argument, whioh is oorreot to 1% bits, one oan expeot 
an answer whioh may be incorrect at most in the right ootel digit* 



^Scarborough, J.B., Numerical Mathematical Analysis . seoond edition. The 
John Hopkins Press, Baltimore, Kd«, 1?J0, p. 1?2« 



10-410 



sO 



I 

o 
o 
o 



RW-116 
(REV. ) 



NRT-0 

p S. h of k 








00 F 00 


10 24 







10 F 00 


5 13 16 







CP 00 


000 13 


10F 


37 


75701 


7 5702 


10F 1 


M J 


00 000 





10F 2 


Z J 


OOF 3 


00F01 


10F0 3 


T P 


A 000 


CP 11 


10F 4 


T P 


00 


0CP10 


10F 5 


Q T 


00016 


AOOOO 


10F 6 


Z J 


00 F 9 


OOF 07 


10F 07 


T P 


CP 1 1 


AOOOO 


1OF08 


S J 


00 F 00 


OOF 09 


10F09 


T M 


CP 1 1 


CP 14 


lOf 10 


T P 


OOF 3 6 


CP 12 


10F11 


54 


CP 10 


200 17 


10F 1 2 


S J 


00 F 00 


OOF 1 3 


10F 1 3 


T U 


A 000 


OOF 17 


10F 1 4 


RS 


00 F 1 7 


00015 


10F 1 5 


R S 


00 F 1 7 


000 15 


10F 1 6 


S P 


CP 1 2 


000 35 


10F 1 7 


RP 


00 000 


OOF 19 


10F 1 8 


MP 


BOOOO 


CP 12 


10F 1 9 


T P 


B 00 


CP 1 3 


10F 20 


T P 


CP 1 4 


AOOOO 


10F 2 1 


T J 


C P 1 3 


OF 2 3 


10F 22 


MJ 


00 000 


OOF 30 


10F 2 3 


L A 


AOOOO 


000 35 


10F 2 4 


D V 


0CP1 3 


AOOOO 


10F 2 5 


S T 


C P 1 2 


AOOOO 


10F 26 


S J 


00 F 27 


OOF 30 


10F 2 7 


D V 


OCP 10 


AOOOO 


10F 28 


A T 


CP 1 2 


OCP 12 


10F 29 


MJ 


00 000 


OOF 16 


10F 30 


T P 


0CP11 


AOOOO 


10F 31 


S J 


F 3 2 


OOF 34 


1 F 3 2 


T N 


CP 1 2 


AOOOO 


10F 3 3 


M J 


00000 


OOF 01 


10F 34 


T P 


CP 1 2 


AOOOO 


1 F 3 5 


MJ 


00 000 


OOFO 1 


10F 36 


37 


77777 


7 7777 



AL 
EX 
A R 



ARM 

I T 

G ZERO 



B R B 



N EVEN OR 
00 

ALARM 

SET XO VALUE 

N NEGATIVE 



SET UP B 
XITH TO N-l 



CONVFRGENCE 
XITHPLUS 1 



2000 
6 6 064 
15 
6 606 4 
6 606 5 
6 6066 
6 6067 
6 6070 
66071 
6 6 072 
6073 
6 074 
6075 
6 076 
6077 
6100 
6 610 1 
6 6102 
6 610 3 
6 610 4 
6610 5 
6 6 10 6 
66107 
6 6110 
6 6 111 
6 6112 
6 6113 
6 6114 
6 6115 
6 6116 
6 6117 
6 6120 
6 612 1 
6 6122 
6 612 3 
6 6124 
6 6125 
6 612 6 
66127 
66130 



00 
00 
00 
37 
45 
47 
11 
11 
51 
47 
11 
46 
12 
11 
54 
46 
15 
23 
23 
31 
75 
71 
11 
11 
42 
45 
54 
73 
36 
4 6 
73 
35 
45 
11 
46 
13 
45 
11 
4 5 
37 



00000 
00000 
00000 
75701 
00000 
02003 
20000 
10000 
00020 
02011 
000 30 
02000 
00030 
02044 
00027 
02000 
20000 
02021 
02021 
00031 
00000 
3 00 00 
30000 
00033 
000 32 
00000 
20000 
00032 
00031 
02033 
00027 
00031 
00000 
00030 
2 4 
00031 
00000 
00031 

77777 



X 



THE RAMO-WOOLDRIDGE CORPORATION 
Los Angeles ^5> California 



RW-91 
(REV) 



N0I-3 

Pg« 1 of 9 

revised 9/1^/56 



Identification Tag: 

Assembly Storage Spec; 
Storage: 



Drum Assignment: 



Gill Method Subroutine 

Spec ificat iona 

SWI-3 

Subroutine 

SUB 1*9800 07^1^ 

59 instructions, addresses 
0GM30 thru OGJ&O 
1GM0O thru 1GM17 

15 constants in program, addresses 
0GC00 thru OGClV 

7^ words total program storage, addresses 
OGMDO thru (XMhO 
1GMD0 thru 1GML7 
OGCOO thru OGClU 

10 words temporary storage pool used, addresses 
00027b (0GT00) thru OOOtob (0GT09) 

Addresses 63230b thru 633*ab 



Program Entrances: 
Program Sadt: 
tfechine Time: 

Mode of Operation: 



Addresses 00MD2, OOM03, and (XMh 

Address 0GMD1 

(10.3 n + 1.9) ms per point average, ^ihere n 
equals the number of equations in the system 

Fixed point 



Coded by: 

Code Checked by: 
fefechine Checked by: 
Approved by: 



J. Carlson 
R. Douthitt 
M. Elmore 
R. Summers 

M. Elmore 

M. Elmore 

W. Bauer 



June 8, 1955 

July 7> 1$55 
July 22, 1955 



10-412 



o 



a, 



RW-91 
(REV) 



NUI-3 

Pg. 2 of 9 

revised ^/lk/^6 



Description 



The Gill Method Subroutine integrates a system of first order, differential 
equations using a step-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 allowing the subroutine to solve concurrently several different systems in the 
same program. 

The independent variable is incremented "within the subroutine it self • 

Notation 

The system of equations to be solved is 

^- . « t ± (x, y x , y 2 , . . . , y n ), (i » 1> 2, . . . , n). 

q. are intermediate values of the calculation (zero initially) 
Ax is the increment of the independent variable x 
h is the binary scaling power of x (i.e. x*2T is in the computer) 
h-1 is the binary scaling power of Ax 
m* is the binary scaling power of y. 
f is the common difference between the scaling power of y. and the- scaling 



power of -x — for each i. 



T '*?± 

o m. - f is the binary scaling power of -=—- 

1 

o 

§■ L ■ 73 + f - b 



Progranming and Operating Instructions 

Assign the Gill Method Subroutine to some arbitrary region, say OGMDO. 

In order to solve a given system, the following array of variables, derivatives, 
intermediate values, and parameters should be assigned a region, say OGIfOO. 



OGNOO 


L 




OGHOl 


00 0GN05 0GHO6 




OGN02 


n-1 




OGN03 


Ax 


scaled 2 11 - 1 


OGNOV 


X 


h 
scaled 2 


OGN05 


dx 


scaled hl. - f 


OGH06 


y i 


scaled el 


OGNOT 


h 


initially zero 


OGK08 


'5s 

dx 


scaled nu - f 


OGHOO 


y 2 


scaled m~ 


OGNIO 


%. 


initially zero 



(REV) 

NUI-3 

Pgo 3 of 9 

revised 9/14/56 



The q. must be set to zero . initially by the programmer. 

ay t 

In addition, the coding for computing 3—- for all i, (i « 1, 2, . . . , n) should 
be assigned a region, say 0DE00. This coding vill use the values in region 0GH00 

to compute all -=r-~ as specified by the equations in the system and should place the 

results in the appropriate places in region OGNOO* It should then exit to the Gill 
Method Subroutine with an MJ 00000 0GMC& (see below). 

Assuming the Gill Method Subroutine is in region 0GM0O, the three entrances are 
<XM)2, 0GMD3, and 0GMC&. The exit is 0GMD1. 

The first entrance, 0GM02, is used for setting up the Gill Method Subroutine only 
for the particular system to be solved. It is entered by an RJ comnand followed 
by a parameter word which specifies the location of the variables, and the location 
of the coding for calculating the derivatives: 

RJ 0GMD1 0GMD2 
00 0GH00 0BE00 

The second entrance, 0GMD3, is the entrance for producing a point of the solution* 
It is entered by an RJ command: R J 0GMD1 OGMO3. Entering using this command 
results in four passes through both the Gill Method Subroutine and the coding 
for computing the derivatives, and leaves in region OGNOO the new values of the 
variables, the derivatives at those values, and x advanced by ax, ready for the 
next step. 

!£he third entrance, 0GMD*f, is the entrance from the coding for calculating the 
derivatives and is used on each of the four passes necessary for computing one 

point. As noted above, it is entered by an MJ command in the ODBOO region: 

10-414 



o 



o 



RW-91 
(REV) 
NUI-3 

Pgo U of 9 " 
revised 9/1A./56 

Mathematical Analysis 

. • i 
Theory . "A Process for the Step~by-Step Integration of Differential Equations 
in an Automatic Digital Computing Machine" "by S. Gill/ published in Cambridge 
Philosophical Society Proceedings, Vol. kj, 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.,, Y„, , . . , Y ) on the curve defined by the 
system of equations 

dy ■ " 

if = f i (x * vi> v • * • > yj 



^2 

dx 



- f z <*, yi , r 2 , -.,, y n ) 



dy 

2 =f n U, r x , r z , , .... , y n ) 



dx 



The Gill ^fethod is a process by -which we can find the next point on the curve: 

i.e. the value of y ', y„, . . . , y for x = X + h. 

x o n 

The process can be better understood if the case where n=l is first considered. 
We have the point (X,Y) on the curve j& ~ £ (x,y), and we want to find y at 

UX .a ' "I 

X + h; i.e. we -want k = 5y such that ~U = f (X + h, Y + k). 

CDCJ X + h, Y + k 

We derive k by malting four approximations and averaging them in a particular way. 

First approximate the curve by a straight line through (X,Y) with the. slope ^Z I 

*^J X Y 
- f (X,Y), and find a first approximation to k: . ■'■ 

k - h*f (X,Y) 



^ Then we travel a fraction m of the way along this line* to the point (X + mh, Y + mk ] 
o and find f (X + mh . Y + mk ) . 

«— H 

^ This gives us a new straight line through (X + mh, Y + mk ) with slope f (X + «h, 
ou Y + mk ), and we find 

k. = h f (X + mh, Y + mk ) 
1 o 

We now use k and k.^ to find a third point at which f is calculated: (X + nh, 
Y + [n-r J k o + rJ^). 



k 2 * h f (X + nh, Y + [n-r J \ + *\) 



Pg. 5 of 9 
revised $/lk/$6 

Similarly, 

k- « h*f (X + ph, ¥ + I p-s-t J k + sk. + tk 

The weighted average of k , k , k„, and k 1b the desired k = 6y: 

6y » y fX + h) -y (X) « c Q k o + c^ + c g k 2 + c^ 

inhere c + c, + c rt + c~ « 1. 
12 3 

For a system of equations , the same four steps given above are made for each 
equation and 

6y i " C o k io + c l k il + c 2 k i2 * C 3 k i3 ^^ C o + c l + c 2 + c 3 "" 1 ' 
9!he above process is, for certain values of m, n, p, s, t, c , c 1 , c , and c , the 

O A. fa ,3 

Burige-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 constants are 

m * 1/2 , r « 1 - Vl/2 , c ■" l/6V 

n *= 1/2 , s * - -/TfZ , c^ -(1/3) (l - -/Tfz) 

p*l , -t-"l+ VTfl , c 2 »(l/3) (1+ Vl72) 

c~ *■ l/6 

!Ehe 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: 

1st pass: 

Advance x by(l/2)h 

k io =W i (X ' y 10' y 20' ' •"• ' *«>> 

y il " y 16 + r ll 

Calculate t. (x^-,,/-., . . . , y_) In prOgranmer'B ovn coding. 

k n - h f ± (x, yil ,y 2i ; .. :'. , y^) 

r 12 - (1 - VI72) (k u - q^) 

*12 "hi + ^±2 ' {1 " V3[ 7 §) k il 
y i2 * y il + r i2 

Calculate t ± (x,y 12 ,y 22 , . . . , y^g) in prograntaer's ova. co&infc, 

10-416 



End pass: 



I 

o 

I— \ 
I 

o 
o 
o 



X 

a* 



RW-91 

(REV) 

NUI-3 

Pg. 6 of 9 

revised 9-IU-56 



3rd pass: 



Advance x by (l/2)h 

k i2 = h * f l ^ x ' y l2' y 22' * ' *' y n2^ 

r. 3 « (1 + Yl/i) (k i2 . q i2 ) 



%3 = q i2 + 3r i3 * (1 + ^ k i2 

y i 3 = y i2 + r i 3 

Calculate f (x,y ,y.,, . . . , y ) in programmer^ own coding. 



^th pass: 



k 13 - h.f t (x,y 13 ,y 23 , . . . y n3 ) 
r ±k - (l/6)(k i3 - 2 %3 ) 

%4 ■ ^3 * 3r i^ " (l/2)k i3 

y i4 = y i 3 + r ±k 

Calculate f.(x,y . ,y . , . . ., y . ) in programmer's own coding. 

Machine Checking 

A driver routine solved two systems of equations both separately and concurrently, 
using the Gill Method Subroutine. The two systems solved are given below to 
indicate accuracy and to serve as examples . ( 



1 r\ a 1 < 



(REV) 



1. Equations 

dx B " y J 



mn-3 

Pg. 7 of 9 
revised SfXkf-%6 



► equivalent to the second order equation. 



sLz + 



0. 



dx 



Ax * .0872664626 * rt/36 « 5* 
Initial Conditions 



Ax-O, y -0aaajr 8 -l. 



Solution 



r x - sin x 

Accuracy 

In a spot check of the results, the greatest . absolute error observed "was 

1.5 x 1Q" . (For x - 3.1415925696, y, - .0000015425. However, sin x » 
.000000084). A 

2. Equations 
dy 1 
dx" = y 2 



* Equivalent to the third order equation 



*3 *2 
x dry - d y 

dx dx 



w 



dy 2 

dx J 3 

^3 „ y 3 * W* 

dx "" x 

Ax » .1 

Initial Conditions 

At x ■ .l*.y, * .000025, y 2 » .001, 'y» » .03 

Solution 

" * 3 • 1 
y, » x - x + x - 1 

3 So Soocf 



120,000 



Accuracy 

In a spot-^check of the results, the greatest relative error observed vas 
3-4 x 10"°. (For x - 4999999975, y-, * .00042499858. However, the solution 

is actually ,00042500002). 



10-418 



RW-91 
KUI-3 .(REV) 

Pg. 8 of 9 
revised Sl/lfr/S'6 



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10-420 



THE BAMO-WOOIDRIDGE CORPORATION 
Los Angeles k*?, California 

Floating , Point Gill .Method 



RW-143 
(REV) 
Wl-k 

Pg. 1 of 9 
Revised 9/lh/36 



Identification Tags 



HUI-U 



Type: 

Assembly Routine Spec: 

Storage : 



Entrance and Exit; 



Machine Time: 



Subroutine 

SUB 51921 0891^ 

89 words total program storage 

9 words temporary pool used, 
addresses 27 b thru 37 b 

The constant pool is used. 

RJ GIL01 GIL02 set up 

R*T G3X01 GIL03 to get next point 

MJ GIL04 From derivative calcu- 
lation 

Approximately (9,7 + 8**-.6n) m.s. per time 
interval, where n equals the number pf 
equations in the system. 



CO 



© 
I 

o 
o 



Coded by; 
Approved by; 



J. Carlson 
W. F. Bauer 



May, 1956 
May 10, 1956 






RW-143 

, (REV) 
HUI-4 

Pg. 2 of 9 

Eevised 9/lk/% 



Description 

The Gill Method Subroutine integrates a system of first order, differential 
equations using a step-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 allowing the subroutine to solve concurrently several differ- 
ent systems in the same program. 

The independent variable is incremented within the subroutine .itself. 

Notation 

The system of equations to be solved is 



dy d 
dx" 



*i ^ X ' ?!> y 2' ' • ' ' y n^' U = 1> 2, . . . , n). 



n Is the number of equations in the system. 

q^ are intermediate values of the calculation (zero initially) 

x is the increment of the independent variable x 

Programming and Operating Instructions 

SNAP must be in E.S. 

.Assign the Gill Method Subroutine to some arbitrary region, say GILOO. 
This region need not be located in the l^w.&umbefced half of E.S. 

In order to solve a given system, the following array of 
variables, derivatives, intermediate values, and parameters should be 
assigned a region, say DEQOO. Although the programmer will undoubtedly 
desire to have this region located in the low numbered half of E*S., it 
is not necessary for the operation of this subroutine. 

Fixed point form scaled 2 . 
Floating point form 



DEQOO 


n 


DEQ01 


Ax 


DEQ02 


X 


DEQOf 


dy. 



dx. 



DEQplt 



DEQQ** 



£ The q^. must be set to zero initially by the programmer ."} 



m_/!99 



"S3 1 



O 



RW-143 
(REV) 

Pg. 3 of 9 
Revised 9flhJ% 



DEQ06 ^2 
dx 

DEQ07 y 2 

DEQ08 g^ 



*y ± 



In addition, the coding for computing -^- for all i, (i = 1, 2, ... .» ., n) 

should be assigned a region, say DFQOO. This coding will use the values in 

region DEQOO to compute all j^j. as specified by the equations in the system 

dx 
and should place the results in the appropriate places in region DEQOO. It 
should then exit to the Gill Method Subroutine with an MJ 00000 GIL04 (see below) 

Assuming the Gill Method Subroutine is in region GIIXX), the three entrances are 
GIL02, GIL03, and GILO**-. The exit is GIL01. 

The first entrance, GIL02, is used for setting up the Gill Method Subroutine 
only for the particular system to be solved. It is entered by an RJ command 
followed by a parameter word which specifies the location of the variables^ 
and the location of the coding for calculating the derivatives: 

RJ GIL01 GIL02 
00 DEQOO DFQOO 

The second entrance, GIL03/ is the entrance for producing a point of the 
solution. It is entered by an RJ command: RJ GIL01 GIL03. Entering using 
this command results in four passes through both the Gill Method Subroutine 
and the coding for computing the derivatives, and leaves in region DEQOO 
the new values of the variables, the derivatives at those values, and x 
advanced by ipc, ready for the next step. 

The third entrance, GU&h, is the entrance from the coding for calculating 
the derivatives and is used on each of the four passes necessary for computing 
one point. As noted above, it is entered by an MJ command in the DFQOO region: 

MJ 00000 GIL04 ' 

Mathematical Analysis 

2 Theory . "A Process for the Step -by -Step Integration of Differential Equations 

In an Automatic Digital Computing Machine" by S. Gill, published in Cambridge 

f Philosophical Society Proceedings, Vol. 47, Part I, January 1951 , should be 

consulted for a detailed analysis of the process on which the subroutine is 

o based. 

o 

o ' 

£ Suppose we know the point (X, Y, , Y ? , . . . , Y ) on the curve defined by the 

xj system of equations 

a. 



dy-L 
- - f x (x, j v y 2 , . - .,y n ) 



dx 



liM"- Afi«J 

(REV) 
NUI-4 

Pg. k of 9 
Revised 9/lV56 



^2 



— = f 2 (x> y v y 2 , . . ., y n ) 



dy 

ST" f n (x ' V V * # " y n } 

The Gill Method is a process by which we can find the next point on the curve: 

i„e. the value of y ', y , . . ♦ , y for x = X + h. 

x u n* 

33ms process can be better understood if the case where n = 1 is first considered. 

We have the point (X?,Y) on the curve * « f(x,y), and we want to find y at 

X + h; i.e. we want k « 5y such that 2*L s f(x + h, Y + k). 

^X + h, Y + k 

Ve 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 



d£ 

dx 



« f(X,Y), and find a first approximation to k: 



—J A. jX 

k Q « h-f (X,Y) 

Then we travel a fraction m of the way along this line to the point (x+mh, Y+mk ) 

and find f(X + mh, Y + mk ). ° 

o 

This gives us a new straight line through (X + mh, Y + mk ) with slope 
f(X + mh,, Y + ink ), and we find 

k = h f (X + mh, Y + ink. ) 

We now use k and k, to find a third point at which f is calculated: (X V nh. 
o 1 

Y + [n-r] k + rk ) . 

k« - h f (X + nh, Y + (n-r] * + rk, ) 

c • *- -» O X 

Similarly, 



k ■ h*f(x + ph, Y + [p-s-t] k + sk + 



tk. 



The weighted average of k Q> V kg , and ^ is the desired k -^: 
&y * y(X + h)-y(X) - c Q k o + c^ + c 2 k 2 + c k 



where c + c n + c« + c„ - 1, 
o 1 2 3 



tO-424 



CO 



I 

o 



RW-143 
(REV) 

Fg, 5 of 9 
invited 9AV56 

For a system of equations, the same four steps given above are made for each 
equation and 

iy i = c o k lo +C Al + c 2 k 12 + °3 k i3 WhSre C o + C l + °2 + c 3 = X - 

The above process is, for certain values of m, n, p, s, t, c , c , c„, and c , 

the 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 constants are 



m 



= 1/2, r = 1 -lf±/Z, c =1/6 

n « 1/2, s = -4T/Z, c x =(1/3) (1 /-.Jt/Z) 

P - 1 , t = 1 + /l/i", c 2 =(1/3) (1 + Ti/i) 

c = 1/6 ""■■■ ■.. 

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 f (x, y^, y ?0 > -*•• • > 7 ) ■ *b& the y 1 oxe available. 

1st pass: 

Advance x by (l/2)h 

k io =h - f i < x ' y 10' y 20' • ■ - y no ) 
r u =(l/2)k lo - ^ 

111 " «io + 3r il "<Va)k i0 

y il = y io + r il 

Calculate f. (x,y in ,y„, . . ., y _) in programmer's own coding. 
1 jll c±. nx 



gnd pass: 



k u = hf i ( x ' y u' y 2i' • • •• y»i) 



I r ±2 = (1-/172) (k^-q^) 

2 *i2 " "in + 3r i2 - (1 - ^Ti")^ 



y !2 " y U + r l2 



Calculate f (x, y , y 2 , -. . ., y ) in programmer's own coding. 



3rd pass: 



kth pass: 



Advance x by (l/2)h 

k i2 ssh ' f ± < x ' y i2' y 22' * • •' y n2 J 
r i3 - (1 + /I75) (k i2 - q^) 

q i3 aq i2 + ^13 - (1 + ^ 2) k i2 



y i3 * ^12 + r i3 



Calculal 



,te t ± ( x ^y 13 ^y 23 > • • •* y n3 ) 



n3' 



(REV) 



Pg. 6 of 9 
Revised 9/\k/$6 



\ 3 - *f ± (^y 13 ,y 23 , • . .: y n3 ) 
r ±k - (l/6)(k i3 - 2qi3 ) 
0^ - ^3 - 3r i4 - (l/2)k i3 

y iU = y i 3 + r i* 

Calculate f (x,y llf ,y ^, , . ., y. ) in programmer's own coding, 



10-426 



CO 



I 

o 

r-i 
I 

o 
o 
o 



X 

a. 



Pg- T of 9 
Kavifcod 9/l V56 



Machine Checking 

The following system of two equations was solved using this routine: 



cbc 


= 


COS X 


<3y« 






dx 


ES 


-sin x 



The initial conditions, at x » 0, were 
y x - and y = 1 

The interval, Ax, used was 2*/360 radians* At x * 36O the results 
were accurate to 8 decimal digits. 



RW-143 
(REV) 

KUI-4 

Pg. 8 of 9 

Revised 9AV56 



D 


61 LOO 01024 


D 


GfMOO 51S21 


61 MOO 


MS 00000 6 I LOO 


GIM01 


MJ 00000 00000 


6IM02 


MJ 00006 G1L49 


GIM03 


MJ 00000 GILO 8 


GIM04 


RA GIL71 0OQ16 


GIM05 


EJ GIL69 G1LT3 


GIM06 


EJ GIL68 GIL01 


GIM07 


MJ 00000 GIL18 


GIM08 


TP 00016 GIL 71 


GIM09 


TU 6!i*72 GiL26 


GIMIO 


TP 00000 GIL88 


6IM11 


TP 0®0®O 00024 


GIM12 


TP GIL88 00002 


GIM13 


ADJ*0 00024 00000 


GIM14 


TP 00002 S1L87 


GfMlS 


TP StlTS 00031 


01 Ml* 


ADMP 00024 00031 


Gl M17 


TP 00002 00000 


GIM18 


TV 00000 Gtk70 


GIM19 


UP 30003 G1L21 


G1M20 


TP 00000 00023 


GIM21 


RA 6IL20 GIL67 


GIM22 


TU GJL66 SIL25 


SIM 23 


TV GIL66 GiL44 


GIM24 


ftp 30003 GiL2* 


GIM25 


TP 00000 00026 


6IM26 


TP 00024 ©0002 


61M27 


MN*0 O0O28 00OOO 


GIM28 


TP 00002 00029 


GIM29 


TP 6tk88 00002 


GIM30 


MPJiO 00026 00000 


GIM31 


TP 00002 00030 


GIM32 


MPSU 00023 0002^ 


fclM33 


TP 00002 00023 


GIM34 


ADUO 00027 00000 


&IM35 


TP 00002 00027 


GIM36 


TN 00025 00002 


&1M37 t«>AD 00036 00018 


GIM36 


TP 00002 00030 


GIM39 


TP S1L85 0©031 


GIM40 


TP 00029 00002 


6tM41 


0VAO 00031 00030 


G1M42 


TP 0O0O2 00028 



02000 


00 


O000O 00000 


67221 


00 


00000 00000 


67^21 


56 00000 02000 


67222 


45 


00000 00000 


67223 


45 


00000 02061 


67224 


45 


OOOOO 02010 


67225 


21 


02107 00020 


67226 


43 


02105 02111 


67227 


43 


02104 02001 


67230 


45 


00000 02022 


67231 


11 


00020 02107 


67232 


15 


02110 02024 


67233 


11 


00000 02130 


67234 


11 


OOOOO 00030 


67235 


11 


02130 00002 


67236 


14 


04030 OOOOO 


67237 


11 


00002 02127 


6*240 


11 


02113 00037 


67241 


14 


04030 14637 


67242 


11 


00002 00000 


67243 


16 


OOOOO 02106 


67244 


75 


36663 62625 


67245 


11 


OOOOO 006^ 


67246 


21 


02024 02103 


67247 


15 


02102 02031 


6t250 


16 


02102 02054 


67251 


75 


36663 6£632 


67252 


11 


00000 O0032 


67253 


11 


60036 O$062 
14634 60006 


6*254 


14 


67255 


11 


00002 0O035 


67256 


11 


02130 00602 


67257 


14 


14032 OOOOO 


67260 


11 


OO0O2 00036 


672*1 


14 


14027 10035 


67262 


11 


OO002 00035 


67343 


14 64633 0$©o6 


67244 


11 


66d62 60633 


672*5 


13 


00031 00002 


67266 


14 


14036 04034 


67267 


11 


06002 00634 


67270 


11 


02125 00037 


672T1 


11 


00035 00002 


67272 


14 


20037 04034 


67273 


11 


00OO2 000 M 



10-428 



RW-143 
(REV) 

NUI-4 

Pg. 9 of 9 

Revised 9/1U/56 



CO 



I 

o 

r-l 
I 

o 

o 



cu 



Qtm3 


RP 


-2 A A f\ "5 

5Vw v J 


GIL45 






GIM44 


TP 


00026 


j , : 






GIM45 


RA 


Oil*, si, .J 


6iL67 






G1M46 


RA 


g:l^4 


G1L69 






G1M47 


RS 


GIL70 


00016 






GIM48 


ZJ 


G1L24 


00000 






GIM49 


TP 


GIL01 


AOOOO 






GIM50 


LA 


A0000 


00015 






G1M51 


TU 


A0C00 


GIL52 






GIM52 


TP 


00000 


AOOOO 






GIM53 


TV 


A0C00 


GIL48 






GIM54 


TU 


A0C00 


GIL18 






GIM55 


AT 


00015 


AOOOO 






G1N56 


TU 


A0000 


G1L16 






GIM57 


AT 


00015 


AOOOO 






GIM53 


TU ACOOO 


GlLll 






G1M59 


TU 


A0O00 


GIL66 






GIM60 


LA 


AOOOO 


00057 






G-IW61 


TV 


AOOOO 


G1L17 






61 1462 


TV 


AOOOO 


GIL66 






GIM63 


RA 


GIL 66 


00017 






G1M64 


RA, 


GfLOl 00016 






6iM&6 


MJ 


66000 


GiLOi 






00 00006 


00000 


6 




61M6? 


60 


06C03 


66600 


R 




&M66 


00 


00000 


00005 


S 




6iM69 


00 


00000 


00005 


B 




GiM?6 


00 


00000 


00000 


B 




GlM7i 


00 


00000 


00000 


B 




GIM72 


00 


GIL75 


00000 


BRB 




GIM73 


TP 


GIL87 


00002 






GIM74 


MJ 


00000 


GIL17 






GIM75 


05 


00000 


00000 


-01 


F 


GIM76 


01 


00000 


00000 


00 


F 


6IM77 


05 


00000 


00000 


-01 


F 


GIM78 


02 


92893 


21881 


**01 


F 


G1M79 


02 


92893 


21881 


-01 


F 


GtM8C 


02 


92893 


21881 


^61 


F 


G1M81 


01 


70710 


67812 


00 


F 


G1M82 


01 


70710 


67812 


00 


F 


6IM83 


01 


70710 


67812 


00 


F 


6TM84 


01 


66666 


66667 


-01 


F 


GIM85 


03 


33333 


33333 


"-01 


f 


G1M86 


05 


00000 


00000 


-01 


F 


GiMs? 


00 


00000 


00000 


B 




00 00000 00006 & 




SfA&t 













67274 
67275 
67276 
67277 
67300 
67301 
67302 
67303 
67304 
67305 
67306 
67307 
67310 
67311 
67312 



6733:4 

67;3- : I ; 5 
6T316 



6732.1 



47323 
6*324 
67325 
67326 
67327 
6t3^6 
67331 
67332 
67333 
67334 
67335 
67336 
67337 
67340 
67341 
67342 
67343 
67344 
67345' 
67346 
67347 
67350 
6?35i 



75 30003 
11 00032 
21 62d3i 
21 02054 
23 02106 
47 02030 
11 02661 
54 20000 

15 20000 
11 00000 

16 20000 
15 20000 
35 00017 
15 20000 
35 00017 
15 20OO0 

15 20000 
54 20000 

16 20000 

16 20000 
21 02102 
21 62661 
4£ 60666 
66 66660 
66 60663 
00 00000 
00 60000 
00 00006 
00 00000 
00 62113 
11 02127 
45 00000 
20 04000 
20 14000 
20 04000 

17 74537 
17 74537 
17 74537 
20 16650 
20 16650 
20 16656 
17 65252 
17 75252 
20 04000 

00 00000 

00 00000 
45 00000 



02055 
00000 
62163 
02105 
00020 
00006 
20606 
00017 
02064 
20000 
02060 
02022 
20000 
02012 
20000 
02013 
02102 
00071 
02021 
02l02 
00621 
000^6 

6£d6I 
00606 
OO60O 

00005 
00003 
00000 
00006 
00000 
00002 
02021 
00000 
00000 
00000 
30314 
30314 
30314 
11714 
11714 
11714 
52525 
52525 

00000 
00000 
00000 

00000 



THE RAMO-WOOIDRUXJE CORPORATION 
Los Angeles k5, California 

FLOATING POINT SINE -COSINE 

Specifications 



SIN 


-1* 
1 of 


RW-14 
(REV) 

5 


Revised 9 


-lU-56 



Identification Tag: 

Type: 

Assembly Routine Spec: 

Storage : 



Entrance and Exit: 



Machine Time: 



SIN -4 

Subroutine 

SUB 51856 06510 

65 words total program storage 

5 words temporary storage pool used, 
addresses 27 b through 33 b. 

The constant pool is used by this routine 

RJ SUBOl SUB02 for the sine 
RJ SUBOl SUB03 for the cosine 
3.9 ms average, k.& ma maximum 



Coded by: 
Approved by: 



M. Perry 
W. Bauer 



May, 1956 
May 15, 1956 



10-430 



RW-144 

SIN-4 (REV > 
Pg. 2 of 5 

Revised 9-1^-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. 

Programming Instructions 

This routine can be inserted into a program by CMP-0 by the use of a "SUB" 
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. Return jump to the subroutine . Assuming that the subroutine was assigned 
to region SUBOO for assembly, use either the instruction RJ STJB01 SUB02 
for the sine, or the instruction RJ SUB01 SUB03 for the cosine. 

3* At the time of exit from the subroutine, the double length extension of 
. sift'. X (or "cos x) "in SNAP form will be in the accumulator. 

Error Analysis 

Sin . X or cos X is computed to 26 bits of accuracy or to as many correct bits 
as there are in the Fractional portion of X, whichever is less . For 
X^2^7, this routine substitutes zero for the argument. The alarm exit is 
not used. 

Mathematical Method 

1. Let y = (2/tOx, then sin X = sin(jt/2)(y) 

cos X = sin(jt/2)(y + l) 

2. Divide y (or y+ l) into an integral part R, and a fractional part S. 

3. R defines the quadrant into which X falls. Let R' be the two low order 
2; positions of R, since in binary notation, any other positions merely 

^ define a number of complete revolutions . 

o 4. R 1 is a number one less than the number of the quadrant into which X falls. 

o , . 

o 5. s defines the displacement (in a position direction) within the quadrant 

£ indicated by R • . 

x 

a* 6. Therefore, if R* = 00 Let Z = S first quadrant 

,R* = 01 Let Z « (l-S) second quadrant 

R' = 10 Let Z = (-S) third quadrant 

R* = 11 Let Z = (l-S) fourth quadrant 



RW-144 
Sft^ (REV > 

Pg, 3 of 5 

Itevxsed 9-1^-56 

7. Sin (or cos) X « ein(x/Z)Z. 

8. (l/z)si»(ic/2)z is approximated by the Baud Polynomial Approximation 
Number 1.6, using argument z. 

9. If x^l/Z, (2/n)x, which Is In floating forni, is substituted for % 
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 
+ 2^7 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. 



10-432 



RW-144 

(REV) 

SIN-if 

Pg. ^ of 5 
Revised 9-14..56 






I 

O 

1—1 

I 

o 

o 



a. 



D 

D 

D 

D 



DOSGO 

D0S01 

00S02 

00S03 

D0S04 

D0S05 

D0S06 

00S07 

D0S08 

D0SO9 

D0S10 

D0S11 

D0S12 

00S13 

D0S14 

D0S15 

D0S16 

D0S17 

00S18 

D0S19 

D0S20 

D0S21 

D0S22 

D0S23 

D0S24 

D0S25 

DGS26 

00S27 

D0S28 

D0S29 

D0S30 

D0S31 

D0532 

D0S33 

D0S34 

D0S35" 



02S00 
00S00 

oisoo 

DOSOO 
D1S00 
RJ 00000 
MJ 00000 
RP 20002 
TP 00013 
TU 00S02 
LA A0000 
TM BOOOO 
LA AOOOO 
LQ AOOOO 
HP QOOOO 
TP BOOOO 
TP QOOOO 
RS 02S00 
SJ 00S14 
SA 01507 
SJ 00S18 
AT 00S53 
LA QOOOO 
TP BOOOO 
TP 02S04 
2J 00S36 
TJ 01S07 
CC QOOOO 
TV AOOOO 
LA QOOOO 
IJ 02S04 
TN QOO&O 
AT 01 
GT oisfl 

cc ozmo 

QJ O&SSlj 
RS 00SS1 
QJ 00S33 
TP 01S06 
ST 02S01 
TP 02S01 



00023 
01024 
01079 
51856 
51911 
00000 
00000 
0OS04 
02S04 
00S51 
00008 
02S00 
00001 
00035 
01S05 
QOOOO 
02S01 
01S08 
00S21 
00000 

00S16: 

00S1? 
00007 
QOOOO 
AOOOO 
00526 
00S21 
AOOOO 
00S24 
00000 
00S28 
AOOOO 
QOOOO 

#$01 

#0000 
b ( 0S32 
00015 
00S35 
AOOOO 
02S01 
QOOOO 







00027 


00 


00000 00000 






02000 


00 


00000 00000 






02067 


00 


00000 00000 






67120 


00 


00000 00000 






67207 


00 


00000 00000 


ALARM 


* 7 \ 2 T 


37 


00000 00000 


NORMAL EXIT 


*T&t 


45 


00000 00000 


SIN 


ENTRY 


■ ei&zffs 


20002 02004 


COS 


ENTRY 


67123 


11 


00015 00033 


SET 


FOR POS 


67124 


15 


02002 02063 






6712S 


54 


20000 00O10 


EXP 


PLUS 200 


671'26 


12 


30000 00027 






67127 


•54 


20000 00001 






67130 


55 


2O000 00043 




69 


67131 


:71 


10000 02074 




34 


67132 


11 


30000 10000 






67133 


11 


100,fflS£ 00030 


EXP 




67134 


23 


000^,02077 






67135 


46 


020l6 02025 






67X36 


32 


02076 00000 






67q$jk 


46 


02022 02020 






67140 


3=5 


02065 02021 






67141 


54 


1000,O,:O0007 






67142 


nir^ooo^ ioooo 






6714% 


'.%:«"'( 


mOO 35 20000' 






67r^k 


m& 


%2044 02032' 






67J3p§ 


4^' 02076 02027 






69fefc& 


'2? 


IOOOO 20O00 






6?l#ff 


16 


20000 02030 






6#0 


54 


10000 00000 


SIN 




6fS!31 


41 


00033 02034 


COS 




6^152 


13 


10000 20000 






67153 


35 


02075 IOOOO 






67154 


51 


02075 0003d 






67155 


27 


06027 26000 






671» 


44 02037 02046 






67137 


23 


02063 00617 






67160 


44 


02041 02043 






67161 


11 


02075 26606 






67162 


% 606S6 000^0 






67163 


11 


00030 10000 



RW-144 
(REV) 



SBJ-4 

Pg. 5 of 5 

Revised 9-14-56 



00S36 


MP 


QOOOO QOOOO 








67liS4 


71 


1G30Q 


1 (*#>i-0>*-£\ 


D0S37 


SA 


01S06 00001 








67165 


32 


02075 


6>£**l«isjl 


D0S38 


TP 


BOOOO |02S02 






SQUARED 34 


67166 


11 


30000 


: i3031 


0OS39 


PH Ol^O'li 0150 








67167 


24 


02070 


02067 


D0S40 


RP 


2Q0O3 00S42 








67170 


75 


20003 


02052 


D0S41 


PM 


01S02 02S02 






69 


67171 


24 


02071 


00031 


D0S42 


HP 


BOOOO 02501 






68 


67172 


71 


30000 


00030 


D0S43 


TP 


BOOUO AOOOO 






PINAL MANT33 


67173 


11 


30000 


20000 


D0S44 


2J 


00S45 00S01 








67174 


47 


02055 


02091: 


00S45 


SF 


AOOOO 00S54 








67175 


74 


20000 


02066 


D0S46 


LA AOOOO 00027 








67176 


54 


20000 


00$ 33. 


D0S4T 


TP 


BOOOO QOOOO 








67177 


11 


30000 


10000'. 


D0S48 


RA 


02S00 00S54 








67200 


21 


00027 


02066 


D0S49 


SA 


01S09 00027 








67201 


32 


02100 


00033 


D0S50 


CC 


AOOOO QOOOO 








67202 


27 


20000 


1COCSO 


D0S51 


fcp 


00000 0QS01 








67203 


75 


OOOOO 


02001 


D0S52 


TN 


AOOOO AOOOO 








67204 


13 


20000 


20000 


D0S53 


LA 


QOOOO 00007 








67205 


54 


10000 


00007 


00S54 


00 


00000 00000 








6*206 


00 


ooooo* ooood 


D1S00 


01 


51484 19000 


-04 


36 


C9 


67207 


00 


02366 


573S1 


0X501 


-4 


67376 55700 


-03 


36 


C7 


67210 


77 


54666 


31633 


01S02 


07 


96096 79280 


-02 


35 


C5 


672X1 


02 


43150 


53&5J» 


01S03 


~6 


45963 71106 


-01 


34 


C3 


67212 


65 


52420 


764*91 


D1S04 


01 


57079 63105 




33 


CI 


67213 


14 


44176 


65102 


O1S0S 


06 


36619 77225 


-01 


34 


2 OVIR PI 


67214 


12 


13714 


06667 


D1S06 


17 


7777*7 77777 


8 




MASK 


67215 


17 


77777 


77777 


D1S07 


00 


00000 00034 


8 




28 


67216 


00 


OOOOO 


00034 


D1S08 


00 


OOOOO 00200 


8 




128 


67217 


00 


OOOOO 


00200 


D1S09 


00 


00000 00072 


B 






67220 


00 


OOOOO 


00072 


STAftT 














45 


OOOOO 


00000 



10-434 



88-86 
(MM) 



smwwxm rakd uhhtac 

FLEXIE (BB-86 Rev* 8/56) 

Types Service Routine 

I. peserfrptfions ^g 

This routine is a revised version of the original FLEXIE (RJU86). It is 
designed to loa$, by means of a Ferranti Reader, a Flexcode tape prepared on 
a Flexowriter in the conventional fashion for translating to bioctal. FLEXIE 
reads at the full speed of the Ferranti, hesitating only on insert addresses , 
check addresses, or when the temporary storage is full of data. FLEXIE provides 
a check address test and a check sua test on the data read in* 

II. fane Preparation s 

The tape should be prepared in the Banner described in the original 
FLEXIE write up. A few remarks are appropriate here however. A check address 
should be given following the last information on the tape and before the 
7th level punch stop code. If there is no check address prior to the 7th level 
punch, the 7th level punch will in general be ignored. 

For a check sum test of data on the tape, the following four words 
should be on the tape after the data to which the sum applies i 

(1) insert address 75202, 

(2) high order 36 bits of check sum, 

(3) low order 36 bits of check sum, 
(4.) check address 75204? 

The check sum must be the sum of all the data on the tape following the 
preceding cheek sum. The check sum will HOT be loaded into 75202 and 
75203. These two words will not be disturbed at all. Bote that a check 
sum test is performed whenever a check address of 75204 is encountered. 
Thus 75204 should not be used for any other check address. 

III. Operating Instructions s 

§ Since the coding is in Reco II form, all operating data will be given 

Y relative to the regions used in the code. 

o 



£ To load a tape, place it in the reader, turn the reader on and STABT at 

§ bbO. At the completion of the loading (if a 7th level punch is present 
£ on the end of the tape) a stop-re-enter bbO is given. If there is no 7th 
^ level punch present, let the tape i>ass through the reader, then FORCE STOP, 
o- MASTER CLEAR, START at'eeO (eeO will be 00022 in absolute form). FLEXIE 

can also be used as a subroutine to load data* To do this, place a 7th level 
punch after each section of the tape and perform the instruction 37 bbll bbO 
whenever it is desired to load a section of the tape. 

,}\v lew 0*1 



RR-86 
(REV) 



-2- 



Three different alarm conditions can occur when using FLEXIE. 
If one of these does occur, a tag letter is typed on the typewriter and 
the computer stops on a manual stop. These three conditions are now listed 
according to their tags. 

(1) "t": FLEXIE has not been transferred to HSS correctly. 
START causes another transfer. If "t" occurs again, reload 
FLEXIE onto MA» 

(2) n e M : a check address has failed. to check. START causes 
FLEXIE to ignore error and proceed to read the rest of the tape. 

(3) w m M : the check sum given on the tape does not agree with the 
sum as computed by FLEXIE. START causes FLEXIE to ignore the 
error. 

IV. Coding : 

FLEXIE requires 166 (octal) words of storage on KD, i.e., relative 
addresses bbO through bbl65. The region bb can be assigned any drum 
address except 75612 through 77777. The reason for this exception is that 
76000-77777 is used for an image region of HSS and if bb has a value greater 
than 75612, part or all of FLEXIE will be in the image region and conseq- 
uently be destroyed when FLEXIE is used. The rest of the regions used in 
the coding must be assigned the following values : 

cc 00001 

dd 00010 

ee 00022 

gg 00045 

hh 00052 

ii 00061 

jj 00074. 

kp 00116 

ws 00147 

ts 00154 

xx 01624 

Thus one can place FLEXIE on any part of the drum by assigning a value to only 
one of the relative addresses, i.e., bb. 

re bb 74520 
re ccl 
re ddlO 
re ee22 
re gg45 
re ii6l 
re hh52 
re j j74 
re &pli6 
re wsl47 
re tsl54 
re xxl624 

10-436 



-3- 



RR-06 
(REV) 



CO 



I 

o 



x 



bbO 




tp 


00000 


76000 


1 




tp 


bb52 


00000 


2 




rp 


31777 


bb4 


3 




tp 


00001 


76001 


A 




rp 


30151 


cc 


5 




tp 


bbl5 


cc 


6 




rp 


31777 


bblO 


7 




tp 


76001 


00001 


10 




tp 


76000 


00000 


11 




rj 


bbll 


bbl2 


12 




ms 





bb 


13 




00 








U 




00 








15 


ccC- 


sp 


00000 





16 


1 


rp 


20151 


cc3 


17 


2 


sa 


cc 





20 


3 


ss 


bbl3 


44 


21 


4 


ej 


bbl4 


dd 


22 


5 


pr 





Jj2 


23 


6 


ms 





bb4 


24 


ddO 


rs 


ws3 


ws3 


25 


1 


rs 


vs4 


w&4 


26 


2 


tp 


kp26 


ii 


27 


3 


ef 





k P 3 


30 


4 


rj 


dd4 


ws 


31 


5 


er 





a 


32 


6 


rp 


20010 


ddlO 


33 


7 


ej 


kp6 


gg 


34 


10 


ej 


kp5 


hh 


35 


11 


tj 


kpl6 


dd5 


36 


eeO 


ef 





k P 4 


37 


1 


tp 


ii 


a 


40 


2 


38 


kp26 


17 


u 


3 


at 


k P 27 


ee7 


42 


4 


tp 


wsl 


a 


43 


5 


tj 


kp 


eel5 


UU 


6 


tv 


a 


eelO 


45 


7 


rp 


30000 


eel! 


46 


10 


tp 


ts 





47 


11 


tp 


ws2 


a 


50 


12 


ej 


kp22 


eel7 



Entrance - store 00000 
Set up 00000 
Store HSS 

on MD 
Load routine 

into HSS 
Restore 

HSS from 

KD image 
Subroutine exit 

Service routine exit - re-enter 
Flexie check sum, Lo order 
Hi order 

Compute check 

sum of 

routine 
'fest check 

sum 
Error, print t 
Stop - reload routine 

Clear check 

sum cells 
Set up 
Start reader 
One shot switch 
Read to A 

Digit 

test 
Period test 
Ignore or 7th level 

Stop reader 

Set up number of 

words to transfer 
Set up transfer 
Is data destined 

for HSS or KD? 
Set up. transfer 
Transfer 

data 
Test period. code 

is this ED? 



10-437 



RR-86 
(REV) 



51 


13 


ej 


kp23 


ee21 


52 


14 


mj 





bb6 


53 


15 


at 


kpl 


a 


54 


16 


mj 





ee6 


55 


17 


ra 


wsl 


kp2 


56 


20 


mj 





dd2 


57 


21 


tp 


ws 


wsl 


60 


22 


mj 





dd2 


61 


ggO 


sp 


ws2 


1 


62 


1 


tp 


a 


ws2 


63 


2 


sp 


ws 


3 


64. 


3 


qa 


kpl7 


ws 


65 


A 


mj 





dd5 


66 


hhO 


sp 


ws2 


1 


67 


1 


at 


kp21 


ws2 


70 


2 


tp 


ws2 


a 


71 


3 


ej 


kp22 


ii 


72 


A 


ej 


kp23 


ee 


73 


5 


ej 


kp2A 


jj 


IA 


6 


mj 





dd5 


75 


iiO 


tp 


ws 


ts 


76 


1 


ra 


ii 


kp20 


77 


2 


sp 


ws3 


44 


100 


3 


sa 


ws4 





101 


A 


sa 


ws 





102 


5 


tp 


a 


ws4 


103 


6 


la 


a 


44- 


104 


7 


tp 


a 


ws3 


105 


10 


tp 


li 


a 


106 


11 


ej 


kp&5 


ee 


107 


12 


mj 





dd5 


110 


JJO 


ef 





kp4 


111 


1 


tp 


ii 


a7 


112 


2 


st 


kp26 


ax 


113 


3 


at 


wsl 


al6 


1H 


4 


ej 


ws 


jj7 


115 


5 


pr 





jj3 


116 


6 


ms 





jj7 


117 


7 


tp 


ws 


a 


120 


10 


ej 


kp30 


JJ12 


121 


11 


mj 





dd3 


122 


12 


sp 


ws3 


AA 


123 


13 


sa 


ws4 





124 


14 


ss 


ts 






is this IA? 
Return to MD 
Modify IA to MD image 
Jump to set up and transfer 
Modify IA 
Return to read 
Store IA 
Return to read 

Assemble period code 
Store period code 
Assemble 

data digit 
Return to read 

Assemble period code 

and store 
Period code to A 
Is this ED code? 
Is this IA code? 
Is this CA code? 
Return to read 

Store data word temporarily 
Set up for next word 
Add assembled 

word to computed 

check sum 
Store computed 

check 

sum 
Is HSS filled 

with data? 
RetT&ra to read 

Stop reader 
Compute number 

of. words read in 
Add to IA 

Does this equal CA? 
Error - print c 
Stop - ignore error 
Is sum check test 

specified? 
No, return to read 
Yes, computed check 

sum to A 
Correct computed 



10-438 



-5- 



RR-86 
(REV) 



125 
126 
127 
130 
131 

132 
133 
134 
135 
136 
137 
HO 
HI 
H2 
H3 
1/,/, 

H5 
146 

H7 
150 
151 
152 
153 
154 
155 
156 
157 
160 
161- 
162 

163 ws 

164 

165 



15 
16 
17 
20 
21 

kpO 

1 

2 

3 

4 

5 

6 

7 

10 

11 

12 

13 

H 

15 

16 

17 

20 

21 

22 

23 

24 

25 

26 

27 

30 


1 
2 



ss tsl 





ss tsl 


44 


ej ts 


dd 


pr 


m 


ms 


dd 


00 


02000 


00 


76000 


00 


XX 


00 6 


00000 


00 5 


00000 


00 


42 


00 


72 


00 


66 


00 


62 


00 


64 


00 


70 


00 


74 


00 


52 


00 


37 


00 


100 


00 


7 


00 


1 


00 100 


00000 


20 00100 00000 


40 20100 00000 


40 04100 00000 


tp ws 


02000 


tp ws 


ts 


rp 30000 eell 


00 00000 75204 


er 


q 


mj 


dd5 


00 






vO 

00 

I 

o 

«— ) 
I 

O 

o 

0^ 



X 



check sum 
Subtract lo - order part of 

given sum and test difference 
Error - print M 
Stop - ignore error 

Constant for test 

Constant 

Maximum block size 

Reader start code 

Reader stop code 

Flex codes - period 

7 

6 

5 

4 

3 

2 

1 

Constant for test 

Mask 

Constant 

Constant to set up period code 

ED code 

IA code 

CA code 

Constant for test 

Constants for 

set up 
Sum check CA 

Clear I0A 

Return to regular read 

Period code space 



Working Space Uses : 

ws Assembly space for data 

1 Storage for IA 

2 Period code space 

3 Hi-order part of computed check sum 

4 Lo-order part of computed check sum 

Notes i (l) Three of the working spaces are stored on MD and transferred 
to HSS with the rest of the program. Two of these are used 
initially for a one-shot clear I0A. Then they are used as 
indicated above throughout the rest of the program, 

(2) The FLEXIE check sum cells, bbl3 and bbH, are blank since 

the check sum depends on the value assigned to bb. The check 



i n-dZQ 



W -06 
(REV) 



•aQaa* 



sum may be obtained from the tape assembled by Reco II 
as follows: load the tape and START at bbO; the computer 
will stop with a "t" alarm as mentioned above; at this 
point A-l eft contains the Lo-order part of the check sum 
and A-right the Hi-order part. 



10-440