PX71900 10_Centr Exch Newsl#10_Dec56 10 Centr Newsl#10 Dec56

PX71900-10_CentrExchNewsl#10_Dec56 PX71900-10_CentrExchNewsl%2310_Dec56

User Manual: PX71900-10_CentrExchNewsl#10_Dec56
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1103 CENTRAL EXCHANGE
NEWSLETTER NUMBER 10

December 1956

PX 71900-10

DIVISION Of SPERRY RAND CORPORATION
1 gO 2 WE S T MIN N E H A H A A V E.

ST. PAUL W4. MIN N E SOT A

4

CONTENTS 0F PUBLICATION
Titl~ ='

_U_ _-,-- Publi<;ation Date_.,....,..............---._ _...- Charge_93~~~
_ _'

TeXt pa:ges ___ :~_ _jO--,'_ _~ Photogl'aph$
Page No.

Contents

)

i thru i i i

10-1 thru 10-5

10-6 thru 10-15

...---___--......---.,....,......,.' Drawings -,._._._.-_:-

. Print
Number

itlePage,
71900-10
ont Hatter (Newsletter) ,71900-10
nere1 Card ~ed-In
Rouline
Eigenvalues of a Tr1-Diegor.al Me trix
. 71900-10-16

10-l6thru 10-17 Floo 1;.ing Point Cere Dump
10-018 thru 10-24 llD3 to l103A Conversion

719~lo.1

,
71900-10-1
~0-25 thru 10-48·· Floating ';Vector Arithmetio ,
.,
Pa'okage'
71900-10-1'
10-49 thru 10-73 Sierdficance Preservirg
F100ting Binary Point
Arithmetic for Digitol

Routine

Computers

10-74 thru 10-135 A Method for

. ',' j'

o

v

0"N

"1
IA-

rr'thro 10-3 TieClnite Ir.te£r81"' Eve:lui;-.
'.
~ ,_~,.;"
". "tio,~ Rcrutire. . . . . ~" 719O('~10-~(Rl~-B;9 REV)
10-372 ~~hru 10-38 ~NAP - Interpretl va floflt-"
~'
,I
·
,
inc Poitlt r8cl:arEl
·'7190C):.10-1'··· '(pt:roe KrVX
1Q-.382 thru 10-J8~Sr;AP Sempler Tr8c~'
'.
71906-10-1
(m,]-140 R"f.\1)
1
1~3~!
.lo-.~~S,~JI.~' - ~pterpri.tive Floc·t- , .
I
.
I

tr

.....

': ... , -jlong

P01:I;t

PfAc}.:Bce-C"rrplex1:71~lo-14p..

(R~:~l4l~)

10-390 ,thr.,U, ,:~,0-39,,)'1', l,ie, ",F.,e,rrar.ti .~r~l:t ',J~~ti'fel 71900-..' 10.:..6,~;', ", 
10-398 thru 10-40~F108.t1ne Point r.rcslr~e.
,,' I'
.
'
·
i Arcosine Routine'
71900-10-1
(P'·';-149
10-4.,.02:ttla:-U' l~~"'n08t~rie pOirt, Arcta,r.g~r,t, ... , ,"
, " '.' "",'"
·
.
Routlr;e
'..,
71900""110-7
'(f'Jt-74 P:F.V
19-406 tr.ru ~O-4 Ch8nged ,W6rd post-Mortem':
~
.1

r

'.' '
"Routi'1le
10-408 tl.oru 10-41 th Root, Routir.A.'.
lq-4l2 thru 10-42 i l l lltethod ~(;brou~ine,,'
j

PJ'1)

71(01)...;10-1.
(Rw-102 HEV.)
. 7190()....lo.ii ,- '. (F.1..\r~116 nB-a,),
71~0f\-10-9'
(pll-91 REV~

10-'~~ ",,~hru lO-J" . F;L~ tir.r. 'Poir:t elll Method! ?1900-10-U'
10-1.30 ~~."1O-4}· +~h'~ing'.Poh:t Sjre-...Cof:ir ',71900-10-. ..
lq-/+J5, . th,~:l0-:44! ~~lE
71900-10

(U\>!-.!43 P.E\l)
(RV-:l!+L.) (~V)

(~}.-86 ~f,V~.,
j

<.

I
,

I I !,' 1\,1

t

i" l\

(I

2

1··.:tl",i~ ...:~~"',"I·'~"'"

'.:"

~

of

I

•

I ~ ,'" _.

'-"

'

I

Newslet t\;r Number 10
Deoember 1956

EDITOR'S PAGE

Correction:

9-392 of Newsletter 9, line 2, paragraph 4,
35
of RR-162 should read " ••• will be p-l = 2 _32=34,
On page

359,738,336 ••• ".
Correction:

'The ootal equivalent given for the constant A4 in the
descriptions for the arsin-areos floating point (RR-75)
and the arosin-areos stated point (RR-25) routines is
in error and should read
37

50417 41233

instead of the listed value of

37 04174 41233.
This oorreotion 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

i

NEV1SLETTER 10

DECEJviBER 1956

ENCLOSURES

RW-168

General Card Read-In Routine

RW-169

Eigenvalues of a Tri-Diagonal Matrix

RW-170

Floating Point Card Dump

RR-171

l103 to l103A Conversion Routine

.~'\~

~172
(~173
.

\., ..-./

......
....

~

~

t:

Significance Preserving Floating Binary Point Arithmetic
for Digital Computers

W'8-174

A Method for

RV-l75

Evaluation of IA-iU for Matrix A(Complex Single
Precision Floating Point)
.

RW-176

Floating Point Linear Matrix Equation Solver (AX=B)

RW-177

Complex Single Precision Floating Point Linear Matrix
Equation Solver (~) .

RW-l78

Complex Gill Method Routine

RW~l79

AlgebraicEquat~on

.CV:~l80

Unpacked Floating Point Card' Olltput

OV-181

Continuous Matrix MUltiplier Using FLIP

CV-182

Continuous Matrix .Multiplier Using Single or MultiPrecision Arithmetic

CV-183

SPUR - Single Precision Unpacked Rounded Floating Point
Package r~ ERA-l103 Computers

.........

6

Floating Vector Atithmetic Package

Generati~g

Random Numbers on the ERA 1103

I

Solver

In

10.2:)

Computing Center Organization -.The Ramo-Wooldridge CorPoration

10:28

Mathematical Service Branch - Eglin Field

REVISIONS
CV-154

Unpacked Floating Point Card Read

RW-71

Utility Routine Library

1. Table of Contents

2.

Conventions

3. Reminders
4. Tape Bootstrap

5. Pool of Flex Codes
6. Cumulative Errata

,......
oM

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

RW-108

SNAP - Interpretive Floating Package

RW-140

SNAP Sampler Trace

RW-l4l

SNIP - Interpretive Floating Point Package, Complex

RW:-63

The Ferranti Input Routine

RW':148

Arcsine-Arcosine Routine, Stated Point

RW-149

Arcsine-Arcosine Routine, Floating Point

RR-74

Arctangent Routine, Floating Point

RW-I02

Changed Word Post-Mortem Routine

RW-116

~ Root Routine

RW-9l

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

I~tegral

Evaluation Routine

ori

oM
......,

I
0

'1
8

'"
f!

><
p..

iii

CRI-3

Pg. 1 of 5
11-5-56
THE RAlv.lO -\vGOLDRffiGE CORPORATION
Los ili1geles 45J California

General Card Read-In Routine
Specifications
Identification Tag:

CRI-3

Type:

Service Routine. (with subroutine entrance)

Special Storage:

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

Program Entrance:

400l7b

Program Exit:

40020b

Alarm Exit:

The alarm routine is used by this routine

Coded by:

M. Perry

November, 1956

Approved by:

w.

November, 1956

F. Bauer

-

CO'
-0

.....

,
,
o
'-'

o....

o

....

0"-

......
><
a..

10-1

Rtv-168

CRI-3
Pg. 2 of 5

11-5-56
Description
This routine reads cards produced by MDP-l (binary cards), CPO-O (fixed point
output), CPO-l (floating pOint output) and cards~key-punched on the 4 field
format (described below) for input in tloating 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 fieldo 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 !not be normalized to retain full significance. The
routine stores high speed memory on the drum, operates in high speed roomory,
and restores high speed memory from the drum prior to leaving the routine.
Qperating Instructions

1.

When routine is used as a service routine, set PAK to 40011b and start.
Routine will read ~ards until a stop code is recognized, at which time
the ma:chine will stop (MSO ) with PAK set to 40011b.

2.

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

37 40020 4OOl7b.. Routine vill 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.
not be restored.

A andQ will

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' subr'outine, initial card positioning should be programmed. This can only be
done by. one instruct ion, ~ 00000 VVVlf'iI where
vvvvv contains
00 00000 001l4b.

"
S
...
I

)
of

Stop Codes
1.

Read stoE, 12 col 80. When this code is detected on e~ther a binary card
ora four field input card, the' routine will stop reading, pos'ition a
card 'on the punch side of the bull, and then exit properly (see operating
instructions).

2.

Machine stop, 12 col 790 When this code i6 detected on
card, the routinewi1l stop reading, position a card on
of the bull, and stop MBO at 7243lb. If the machine is
from the routine will proceed as described in operating

10-2

a 4 field input
the punch side
started, the exit
instructions.

RW... 168
CRI-3
Pg. 3 of 5
11-5-56

Either of the above codes may be entered on a blank card and the routine
will sense them. The prograIDI!ler is cautioned not to place the machine
stop code on a binary card as this will result in improper loading (see
MOP -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 MOP -1 write -up) • If the sums
do not agree, the flexowriter will print
"ALARM 00211

000000000000

OOOOOOOvvvvv QQQQQQQQQQQQ"

a.nd the ma~hine will stop. vvvvv 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.

4 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 overflow. For fixed point numbers J 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 flexowriterwill print,
"ALARM 00164

000000000000

OOOOOOOvvvvv

and the machine will stop. vvvvv is
incorrect number. Any or all of the
vvvvv equal to 20,000 indicates, that
Starting the computer will cause the
incorrect numbers to be ignored, and
will proceed.

000000000000"

the storage address of the right-most
other numbers may have been incorrect.
the indicated address field was blank.
correct numbers to be stored, the
in the absence of a stop code', reading

4 Field Card Format

-....
-....
co

The format described below is one of the formats used'by this routine and
is the for.mat used by CPO-O, CPO-I, CRI-2, and SNAP Read.

...0

o•
I

o
o

The card columns are deSignated as follows:
Col 1 ...4

Identification

Col 5-23
Col 24-42

Field 1

Col 43-61

Field 3

Col 62-80

Field 4

This field is ignored by the
reading routines

....

0'

t-

:><

a..

Field 2

10-3

RW-168
CRI-3 .
Pg. 4 of 5

11-5-56
Each field (except identification) is divided as ·follows.

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

Location or address

(x digit 1 for octal location)

Value 'or Mantissa

(x digit

Decimal exponent
Binary exponent

15 for negative value)
(x digit 17 for negative exponent)
(x digit 19 for negative exponent)

Addressing Options
The following Addressing options are allowable on the
is used by CPO-O, CPO-I, CRI-2, and SNAP Input.

4 Field input card. Option

1.

Decimal - Stra.ight 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 1+0,000 decimal is designated as the first drum address
(40 ,OOOb). No indication is necessary.

3.

Octal -The octal. number appearing. on the card is the actual.. address.. This
mus-r-be indicated by an x(ll punch) ,over the first digit of the address.

4.

Blank'-' ,':A completely' blank a.ddress 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.

I

Input Numbers
The following varieties of input may be punched on'the 4 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 co:gsecutive, and on the same card.
For all input, thedecima.l point 1s presl.l1Iled to be at the extreme left end of the
value "field. It is 'recoIIl.Il.kended that the codes listed below be used for ea.ch field.
However, cards from CPO-o and CPO-l are differentiated by the fact that their
"B" (Binary Rxponent) fields are non-blank and blank respectively.
1.

Floating Point .., RS. An input n:umber is designated as floating po:Lnt by the
code RS (Read Snap) in the ''B" field. There is no restriction on the tiD"
field. The resulting floating binary number is rounded and is' in the form
used by SNAP and by the internal floating' painton the l103A computer. A
floating point number consisisof 3 parts; a sign bit., follo'W'ed by an 8
binary.bitcharacteristic 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
preciaion floating point by the code RT (Read Two) in the ''B''field. The
"value~1 portions of 2consecutlve fields are joined to allow 20 decimal digits
of in~ut. 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 ~he lower Gell

,...,

co
...0
.....
......,

•

0

.......
I

8
0......

t-

>It

c..

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 r~rr field is not blank and does not contain an R. Since the
tlB" 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 ne gat i ve
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 ntimber is rounded p r o p e r l y . "

4.

Octal- RU. An input number is designated as being octal by the code RU
(Read Unc.onverted) in the liB" field. Since 12 octal digit's are d.esirable,
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 1 /'

.,

Examples. The following ,list of, in,pu~.. w~d be. p~<
0..

LOCATION

4" 0.1 2 2
1 6.1 8.4
4·0 0 6. 4
4,0 06 5
o~o 1 2 3
,
99
1 0,0
o 0,1.2,2

l:d:z ,D

VALUE

d::- B :::b

o 1:..
1 2 O,·it 1 I
4 5 a 0 a b,b,0~0,4t 2 5:
3 1 4 1 5 ~ 9,2 ,6,5 3:- o 1:
5 8 9 79 3' 23,8 5:
,, o 4'
001 5
I
,, o 2:
1 5
,
,
, P,l:
1
, , ,I
1 5
,,- P Ii
1

j

I

j

1

I

I

r

,

I

I

I

I

I

I

,

I

I
I
I

I

R S:,
I

RIU'
I

R,TJ,

,
, ,
0 0:,
1 5:
I 2:
I

R s:+

COMMENTS

40122
40000
40100
40101
OQ123 ,
00143
00144
00122

20 14631 46315
45 00000 00425
57 51557·00452
75· 67513 47562
00 00000 .0001 7
00 0001 7 00000
77 77777 67777
57 61777'77777

mv-169

EGN-l
Pg. 1 of 10

10/1/56

THE RAlviO-}lOOLDRIDGE CORPORATION
J~s Angeles 45, California
Eigenvalues of a Tri-Diagonal

~~trix

Specifications
Identification Tag:

EGN-l

Type:

Subroutine available on cards for assembly.

Storage:

145 words of storage needed to assemble
this routine.
18 + 2n cells of temporary storage inunediately
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 rout ine •

Regional

Addresse~

Entrance and Exit:

Used:

OOR, OlM, 02M, OlR J OOK, OCT J FOO, COO
RJ

OOROI

OOR02

RJ

OOROl OOR03

No Punching }
.
See Instructions
Cards Punched

Machine Time:

See table in text.

Mbdeor Operation:

Floating Complex Arithmetic requiring SNIP
be activated.

Coded by:

w.

Approved by:

W. Bauer

Frank

10-6

September 1956
October 1956

HW-161.J

EGN-l

Pg. 2 of 10
10/1/56

Description
This subroutine

Co.il~utes

the n eigenvalues of any real or complex tri-

diagonal matrix D, having the form:

a

1

b

l

1

a

0

1

2

0

b
a

0
0

2

3

b

0

3

D =

I
a

U

n-l

b

J

n-1

I

1
I

1

anJ

Since complex arithmetic is employed, the elements of the matrix must be
presented according to the specification for number representation tor use
wi th SNIP.

The n elements of the main diagonal, ai' must be followed by the

n-1 elements of the upper adjacent diagonal, hi' in a region whose initial
address is specified by a parameter word.
The more general tri -diagonal matrix J, (also called a "Jacobi Matrix")
has all its non-zero elements on the main diagonal and on either of the two
immediately adjacent diagonals:

a
.-..

c

0"...0

--

l
l

b
a

l
2

o

0

b

2

o

0

r-I

0

I

0

I
"""'
0

J

=

c

2

a

3

b

o

3

0
0"r-!

t-

:><

c..

0

10-;

RW-lb'i
EGN-l

Pg. 3 of 10
10/1/56

This routine can also treat this case if in place of the n-l elements of the
upper adjacent diagonal, the n-1 products, c b , are supplied.
i i
The subroutine occupies 145 cells and uses the constant and temporary

In addition 18 + 2n cells of temporary storage must be provided

storage pools.

immediately following the

Ramo~ooldridge

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 (18+2n) cells of temporary storage.

In addition the eigen-

values tti and associa.ted residues in the characteristic polynomial p(;:\.. i) can be
punched on cards.
ti ve and six.
field.

pC (\ i)

appears in fields one and two while (\. i is in fields

The eigenvalues are also identified serially in the identification

At the option of the progra.xrmer thesl,1ccessive approximations to the

{\. i obtained during the iterative process can also be punched with their
associated residues in the reduced polynomial.
is desired then a third entrance is available.

In the event that no punching
~

or

PrOgrammdng Instructions
1.

Complex mode of SNIP must be activated.

2.

Entrance to the subroutine is made as follows:

a.

,RJ

OOROI

OOR03

xx

,OOAOO

vvvvv

where
OOROO is the location of the first word of the subroutine
OOAOO is the location of the real part of the first element of the
diagonal
vvvvv is the order n of the

tri~iagonal

10-8

matrix

RW-169
EGN- 1

Pg. 4 of 10
10/1/56

XX

gives the option selected

xx = 20,

only the eigenvalues 2l

i

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 tp.emselves 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 OOROI OOR02
20
3.

oOAdo

vvvvv

Control is returned to the cell following the parameter word.

Machine. Time
The time taken to find the n eigenvalues can be estimateqfrom the following
table of empirical times in se.conds.

Order of
Matrix
3
,.......
0"-

...0

I No Punching

5 Sec.

-Punching
Eigenvalues

8 Sec.

Punclling
Eigenvalues and
Iterations
13 Sec.

5

17

"

22

f!

36

n

8

50

"

58

fI

92

"

91 "

1 43

fI

~

'-"

0

I

10

81 "

r-t

0

I

0
0'
r-t

t-

27

776

"

803

39

2743

"

2782

"

><
~

•

RW-169
EGN-l
,Pg. 5 of 10
10/1/56

Given the

matrix J

tri~iagonal

a
c

b

l

a

l

c

0

l

2
2

0

0
b
a

2

3

b

3

J =

a

n-l

b

n-l

o
The following recursion formula evaluates the characteristic polynomial
p (it) of J for given A:
n

i

= 1, 2, •.• , n

where
P

-1

=0

P

= I

o

'l!he problem loses no generality by assuming all c i = 1 so that only the a

need be given.

i

and b i

Alternatively the general problem can be solved by this routine

if one supplies Cib

in place of b ,
i

i

Using P (-1), P (1) and P (0), the program enters a modified version of the

n

n

n

Algebraic' Equation Solver (POL-O) and finds, by iteration, the first root 1\1 of
"
":>

....
.
I
)

Pn(a).

, at

Having found r roots the (r+l),

root is fotind by considering the polynomial

I

)
)

..

"

10-10

•

RW-169

EGN-l
Pg. 6 of 10
10/1/56

where~l' ~2'

···,21r

are the eigenvalues already found.

This code prevents the

re-computation of a multiple eigenvalue by not allowing JLr+l 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- .Ai
:it i+l

L 10-k

is applied to determine the end of the iteration.

In this code k

gives an accuracy of 6 to 7 places in many low order cases.
(n~20)'accuracy

= 6. This

For large order

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.
acy deteriorates..

In the case eigenvalues are repeated the accur-

Furthermore, the residues of the characteristic polynomials

in 'the neighborhood of such a root are exceedingly small.

Rence, a second

convergence criterion was introduced in order to avoid exponent overflow.

If

the residue
P

n-r

(Ll)i 2 - 100

then Ai is accepted as a root..
find p estimates of

Ap

If Ap has multiplicity p then the code will

such that

a)

no two estimates are equal

b)

ail estimates have residues

L 2 -100

If Ak is an eigenvalue then det(D -AkI) should be zero.

Inspecting successive

iterations and associated residues can therefore give some, indication of the
convergence of the procedure..

The programmer is, however, cautioned in regards

10-11

RtV-169
EGN-l

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 .

...

,.
I'

I'"
)

..I
)

)

...
of

..

10-12

RW-169
EGN ..1

Pg. 8 of 10
10/1/56

OOROO 00100
OIMOO 00118

0
0
0
D
D
D
0
D

OOROO

00

OOROI

MJ
MJ
TP

OOR02
OOR03
OOR04
OOR05
OOR06
OOR07

OORoa
OOR09
OORIO
OORll

r-f

"-'

I

0

r-f

I

0
0
0'

...;

t-

><
P..

TU
TP

DORIS

QS

OOR16
OOR17

TP
TN
RA

LA

01M07

RP
TP
TP
TN
TP
TN
TP

OlM08

RJ

OlM09

TP

OlHIO
OlM!l
OlM12

TP
TP

OlMU6

":'"

TU

TP
TP
TP
TV
R5

OIMOO

-..0

TU

OOR1Z
OOR13
OOR14

OIMOI
01M02
01M03
01M04
OlMOS

0'

SP

01M13
01M14
01M15
01M16
01M17
OlM18
OlM19
OlM20
OlM21
01M22
01M23
OlM24

RJ
TP
TP
TP

RJ
TP
TP

MJ
LDMP
ADST

MPST
LDMP
STSU

02MOO 00151
OIROO 00204
OOKOO 00239
OOTOO 00033
FOOOO 00002
coooo 00003
00000 01R16
00000 00000
00000 02M37
01R34 02M50
OOROI 00015
ADOOO OOR07
AOOQO 02M32
00000 AOOOO
00013 00T15
00013 00T14
AOOQO 00T15
AOOOO OOROO
OOKOS QOOOO
00T15 00016
AOOOO 00016
AOOOO 01R06
00115 00T16
00016 00T17
OOROI 00016
10005 OlM03
00013 00T09
OOK01 00T12
OOKOO 00T08
aOKOO 00T10
00K01 00T06
00013 00T07
OlR30 OIRoa
00029 OOTOO
00030 OOTOI
OOKOl 00T06
OlR30 OlROC
00029 00T02
00030 00T03
00013 00T06
OlR30 01ROO
00029 00T04
00030 00T05
00000 02M31
OOTOO 00T08
00T04 00023
00T08 00025
OOT02 OOTlO
00027 00023

EXIT
ENTRANCE 1
ENTRANcE 2
S

E

T
A
0
0

R
N-1 [
2N-2" $
5

E
S

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
00116
00177
00200
00201
00202
;)0203
J0204
00205

ll\_l'l

45

11
31
15
15
11
11
11
16
15
11
23
54

53
11
13
21
75
11
11

13
11

00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00356
00145
20000
20000
00000
00015
00015
20000
20000
00364
000)60
20000
20000
000'60
00020
00145
10005
00015
00360
00357.
00357
00360

00000
00000
00000
00000
00000
00000
00000
00000
00334
00000
00274
00311

OOOl7
00153
00267
20000
00060
00057
00060
00144
10000
00020
00020
00322
00061
00062
00020
00171
00052
00055
,00051
00053
00047

13
11 00015 00050
37 00352 00314
11 00035 00041
11 00036·00042
11 00360- 00047
37 00352 00314
11 00035 00043
11 00036 00044 11 00015 00047

)0206

37 0035200314

0207
( 0210
r~ 0211
::>212
:J213
: ')214
0)215
(I 216

11
11
45
14
14

i

5

00
00
00
00
00
00
00
00
00
45

00035 00045
0003;6 000 46

0000000266

30041
04045
14 14051
14 30043
14 34033

14051
34027
34031
14053
11027

r~W-169

EGN-l
Pg. 9 of 10
10/1/56

01M25
01M26
01M27
01M28
01M29
OlM30
01M31
01M32
02MOO
02MOl
02M02
02M03
02M04
02MG5
02M06
02M07
02M08

02M09

02MIO
02Mll

lDMP
ADNO
TN
TN
ADMP
MPLD
SUMP
ADMP
ADRT
TN
LDMP
SJ

00T04 00T10
FOOOO 00000
FOOOO 00029
COOOO 00030
FOOOO 00T08
00023 00104
00027 00TI0
00025 FOOOO
00023 00023

S
S

COOOo COOOO

FOOOO
02M04
TN 00023
TN 00024
LOAD 00025
PMNO 00000
ZJ 02MIO
1P OOKOI
LODV 00029
STMP 00T08
ADNO 00T06
RJ 01R30
OVPM 00104
1J 00K02

02M12
02Ml3
02M14
02MlS
·TN
02Ml6
TP
02Ml7
02M18 LDMP
MJ
02Ml9
TP
02M20
02M21 ADNO
TP
02M22
TP
02M23
RP
02M24
02M25
TP
TP
02M26
TP
02M21
02M28 LDDV
02M29 PMNO
02M30
TJ
TP
02M31
TJ
02M32
RP
02M33
TP
02M34
02M35 PDNO
MJ
02M36
02M37
TP
02M38
MJ
MJ
02M39
Tp
02M40
LOST
02M41
02M42 5TST

5

00025
02M06
00023
00024
00023
00000
02M09
00023
00023
00T12
00000
OIROO
00000
02M20
OOKOO FOOOO
00013 cocoa
Fooeo 00T08
00000 02Mll
OOKOI FOOOO
00T08 00000
Fooao 00TI0
00T09 00T11
30004 02M26
00T02 OOTOO
00029 00T04
00030 00T05
00T12 OOT06
00000 00000
OOK03 02M40
02M29 Aoaoo
00000 0,lM20
30004 02M35
00T04 00006
00010 00000
00000 01M20
02~39 02M50
00000 OOR04
00000 02MS1
00114 00004
00T06 00008
00025 OOT18

F
I

5

N
0

ITERANT
S

AND

S

FUNCTIONAL
,j

VALUE

SET UP
FORNEXT
ITERATION
CONVERGED

B
10-14

00217
00220
00221
00222
00223
00224
00225
00226
00227
00230
00231
00232

14
14
13
13
14
14
14
14
14
13
14

00233
00234

00235
00236
00237
00240

13
13
14
14
47
11

00241

14 30035 20027

00242
00243
00244
00245
00246
00247
00250·
00251
00252
00253
00254
00255
00256
00251
00260 .
00261
00262
00263
00264
00265
00266
00267

14 34051 15055
14 05041 00000

46

30045
04002
00002
00003
04002
15021

14053
00000
00035
00036
14051
30045

10033 14053
05031
04021
00003
30002
00233
00027
00030
30031
24000
00241
00360

14002
51027
00003
14031
00235
00027
00030
05027
00000
00240
00027

37 00352 00314

00270
00271

14
42
13
11
14
45
11
14
11
11
75
11
11
11
14
14
ft2
'11
42
15
11

00272
00273
00274
00275
00216
00211
00300
00301

45
11
45
45
11
14
14

20045 24000
00361 00253
00357 00002
00015 00003
30002 14051
00000 00242
00360 00002
04051 .00000
00002 00053
00052 OOO~4
30004 00261
0·0043 00041
00035 00045
·00036 00046
30055 20047
24000' 00000
00362 00277
00264 20000
00000 00212
3.0004 00272
00045 00006

14 74012 00000
00000
00276
00000
00000
00057
30047
34031

00212
00311
00150
00312
00004
34010
36063

RW-169
EGN-l
Pg. 10 of 10

10/1/56

;:;-.
-D

.......
'-"

I

0

.......
I

0

.:::>
J"

,-i

t-

x

~

RA 00T14 00K04
02M43
RJ 01R1S OlROl
02M44
TP FOOOO 00006
02M45
TP COOoo 00007
02M46
02M47
RA 00T17 00016
SA 00016 00015
02M48
TU AOaeO 00005
02M49
02M50 PDPD 00010 00010
02M51
IJ 00T16 01MOI
MJ 00000 OOR01
02M52
OlROO
TV OOROO 01R15
RP 10003 01R03
01R01
TP 00013 00030
01R02
TP OOK01 00029
01R03
TU OOROO 00004
01R04
01ROS
TP 00T15 00023
S
01R06 LDMP 00000 00031 B
OlR07 LDSU 00000 00r06 B
OlRoa MPSU 00029 00031
01R09
TP 00029 00031
TP 00030 00032
OlRI0
TP Fooeo 0.0029
01Rll
TP coooo 00030
OlR12
01Rl)
RA 00004 QOK04
IJ 00023 OlR06
01R14
CJ1Ri5 MJ 00000 00000
TP 00T17 Aoaoo
OlR16
01R17
SJ a 1Ri8 01R18
TP 00T11 00023
01Rla
TP OOK01 00031
01R19
TP 00013 00032
01R20
TP 00013 00004
01R21
'8
01R22 LDSU oor06 OOT18
S
01R23 MPPM 00031 00000
Z,J 01R25 01R31
01R24
OlR25
RA 00004 OOK04
IJ 00023 01R22
01R26
01R27 LDDV 00029 00031
01R28 STPM 00029 00000
OlR29
ZJ OlR30 02M40
MJ 00000 00000
01R30
TP aOKOO FOOOO
01R31
S
01R32 ADNO 00T06 00000
OIROl
MJ 00000
01R33
01R34 PDPD 000.10 00010
OOKOO
05 0.0000 00000 -01 F
F
OOK01
01 00000 00000
1 F
OOK02
01 00000 00000
00000
-06 F
OOK03
01 00000
OOK04
00 00002 00000
OOKOS
00 00777 00000 B
START

PUNCH
ITERANT

E
V
L
U

T

E
S

C

00302
00303
00304
00305
00306
00301
00310
00311
00312
00313
00314
00315
00316
00317
00320
00321
00322
00323
00324
00325
00326

00327

H

A

R

A

c
T

E
R
ISTIC

EQUATION

CONVERGED

00330
00331
00332
00333
00334
00335
00336
00337
00340
00341
00342
00343
00344
00345
00346
00347
00350
00351
00352
00353
00354
00355

C
0
N

S

T
ANTS

00356
00351
00360
00361
00362
00363
00364
00000

21 00057
37 00333
11 00002
11 00003
21 00062
32 00020
15 20000
14 74012
41 00061
45 00000
16 00144
75 10003
11 00015
11 00360
15 00144
11 00060
14 32000
14 32000
14 14035
11 00035·
11 00036
11 00002
11 00003
21 00004
41 00027
45 00000
11 00062
46 00350
11 00062
11 00360
11 00015
11 00015
14 30047
14 15037
47 00345
21 00004
41 00027
14 30035·
14 34035
47 00352
45 00000
11 00351
14 05047
45 00000
14 74012
20 04000
20 14000
20 45000
15 54143
00 00002
00 00777

00363
00315
00006
00007
00020
00017
00005
74012
00167
00145
00333
00317
00036
00035
00004
00027
15037
10047
10037
00037
00040

00035
00036
00363
00322
00000
20000
00336
00027
00037
00040
00004
12063
24000
00-353
00363
00342
20037
24000
00277
00000
00002
00000
00315
74012
00000
00000
00000
36750
00000

00000·
45 00000 00000

mV-170
MDt.' -5
Pg. 1 of ).

10/15/56
THE RAMO -HOOLDRIDGE COHPORATION

Los Angeles

~'5,

California

P10ating Point Card Dump
Specifications
Identification Tag:

HDP-5

Type:

Service Routine (with subroutine entrance)

Service Entrance:

Address 40024 b

Program Entrance and Exit:

37

Other Routines ,Used:

This routine uses MDP-4 and SNAP Output

Coded and Checked by:

R. Beach

October, 1956

Approved:

w.

October, 1956

40020

F. Bauer

10-16

~,o024

b

RW-170

MDP-5
Pg. 2 of 2...

10/15/56

Description:
This routine operates exactly the same as MDP-4 (Octal Card Dump)
with the following exceptions:
1.

Entrance Address is.

40024 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 b.

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. instru.ctiOns 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 ..4, 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

IS December 1956
110) TO llO)A CONVERSION ROUTINE
I.

TYPEs

Service routine or subroutine.

II.

STATUS.

III.

PURPOSEs

IV.

Gode cheeked and machine checked by Bill Wallace.
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 i8
modified, (indicating also u or v portion) and punching the
converted program in bioctal or flex code.

USAGE:

A.

STORAGE REQUIRED: The program 1s coded in RECO form and it is
therefore possible to operate the program from 8 location
providing 320 ootal drum address and 2000 additional octal drum
addresses for a nss image regIon. Such a location of the program
Rnd image region is done b.y Rssigning the desired starting addresses
to regions BB end' IR respectively, of the reco tape (see coding)
'811 other regions being in HSS, and hence remaining the same.
The regional assignment can be ana separate tape from the main
program reeo tape, but this tape should have END. c .r. at the end.
(See RECO write-up.)
In addition to the REeO tapes, 8 bioetal tape of the program is
availBble where the program ie stored at 66000-66320, with the
image region 76OCJO-7?7n.

B.

INP11f-OUTPUT: Output is a punched tape in bioctal or nex code
of the changed program if desired. Also the following is printed
out as the conversion routine is operating: (This is also optional.)
u a88Ba or VSS8SS, where 8B6a8 is the sddress where an A or Q
reference has been modified 8nd u or v shows whether the u or
v.address of the instruction hes been modified. Also, TAPE 1s
printed out when an 1103 magnetic tape instruction is enco~tered,
snd EF and address when an externel function eommand occurSo

c.

OPERATING INSTRUCTIONS:

(1) Used

8S e. service routine proceed as follows: (the term
"program" here refers to a program to be converted.)

8)

b)
c)
d)
e)

Master cleer, MD stsrt
Set PAK to 66000, (or bb)
Insert in ~ the first addreB~ at the prosraInsert In ~ the last address ot" the program
Insert in v address of
the address ot the last
instruction ot the program, or the la8t address ot
the progrom wherein one wishes to have A and Q
addresses modified. .

Aa

10-18

RR-171

- 2 ...

r)

Insert in v address ot AL the following codes tor
thevarlous options:
00000

bioctal punoh 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 end
print out.

00003

same as above, but no print out.

00004

print out, but no punch of converted. progreme

00005

no print out and no puncb of converted progrmn.

A 56 0 66010 (bb10) stop occurs it a gross error is
made in the set-up, e.g. transposition ot ~ and ~.
(2)

Used as a subroutine, proceed as followsl
a)
b)
c)

(3)
a)
b)

Program the transfer of par8llleter as listed above to
the A and Q registers.
Execute the instruction}
RJ bb2 bb
The options are selected in the same manner a8
previously shown.
The use of this conversion routine assumes that tbe

program to be converted is stored either all in core
storage or all in drum storage.
The conversion routine is coded for operation on either
an 110)!, or on the 110,3 (Serial 9) at RRU, St. Paul.

BWapeo

10-19

RR-111

v.

COPINQ
A. Hegions
re
re
re
re
re
re
re
re
re

B.

bb66000
lr76000
rf30000
orO
ob33
od54
oMI
kk75
mm1l2

45

.3

0
0

0

0

0

7

13
14

IS

16
17
20

21
22
23

,....

......
•
0,.....
I

0

0

::t,....
to-

=-<
~

56

0
0
0

10
III
12

t-

45 0

1
2

4
S
6

,.....

un124
val37
up155
prI62
tp173
ef200
os205
dd212
tt.3l0

Program

bbO

-

r.
re
re
re
re
re
re
re
re

24
25

26
27
)0
31
32

33 obO
1
34
2
35
36
.3
37
4
40
5

0
4~

bblO
bblO
(rt)
0

0

0
0
0
0
tt
Q
bb6
10000 bb5
00000 A

tp
It
It
tp 0

tp bb

ir
0

rp
tp
rp
tp
rJ)
tp
tp

31m bbl7
1
irl
30400 cb
bbl
orl
)1777 bb23
irl
1
ir
0
tp bb6 Q
tp bb7
A
bb31
eJ bb2
rj 700)6 tTOOO6)
bb2
45 0
rj 70036 f10006)
56 00000 bb

ej

dd43
e.1 dd64
e.1 dd6S
e.1 dd66
e.1 dd60
tp or;

Entrance
Errer step
SubrCiJUtlne exit
storage first address
storage last address
storage initial A
stQrage initial Qr
Constant

Store HSS
To start ot core program
Conclusion ot program
Restore HSS
Restore Q tor dump
Test, subr. or BerY?
No, 8'Qbr.
To exit

od
od2
odS

No punch

cd13
od6

No print, punoh flex
No print, punch biootal
Laet address

A

10-20

Punch fiex

tJo print, no punoh

RR-171

-241

42

43

J.4
45

46

47
S<>
51
52
53

6
7
10
11
12.
13
14
15

16
17
20

iJ dd

.qt ddl

lq q
qt ddl
tv or3
la or3
tu A
ra or4
st or3
ij tt
45 0

14

,tv
45
ra
rs
45
rj
tv
tv
tv
tp
45
rj
45

71 efO
1
72
2
73
3
74

ra
ra
tp
45

75 kkO
76
1
2
77
100
3
101
4
102
5
6
103
7
104
105 10

tp
tp
qt
tp

54 odO
1
55

56

57
60
61
62
63
64
65
66

67

70

2

3

4

5
6
7

10
11
12
1J

ej

ej
ej
rp

ej

dd67
0
bb27
bbJl
0
cd1
up4
up4

va15
va15
0

cd4
0

or5
Q

cs
0
(ff)
Q

dd5
tt3
ddlO
ddll
ddl2
20014
dd13

ot
or4
25
or3
DUB

20017
kk

dd60
tt
kk
bbl

mm4
cb5

HSS?

Store first address
Store last address
Set up transfer
of Modified Contents
Set up first addres8
to be modified
No. of words
Error
No

punch

dd60

dd60
cb5
cd
'ualO
ua12
va7
vall
cb5
cd2
cd6
dd3
dd2
pr
cb7

Flex punch

No print

Add 76000 to V
Add 76000 to U and V
Arrange to print core address

Q

ttl
tt3
A
ef
mm
mm

kkll
tp

Mask

operation code

External function
Final stop
Interpret
Commands where
V only to be modified
and tape commsnda
Split instruction,
Modify U on~
Modify U
Modify V
Transfer modified
Content
Obtain current
(i

--~

t-

P""4

'-"

I

0

P""4

0
0

I

0--

P""4

l"-

><
p."

106 11
1(17 12
110 13
III 14
112 JIIIIlO
1
113
2
114
115
3
116
4
117
5

rp
ej
rj
rj
tp
tp
It
rs

20004
dd2'1
ua6
va5
ttl

kk13

kk

A

25

A
A

dd6

or5
ra kk

ej

mmlO

ua
va

(ttl)

blQl

dd7

10-21

AddreS8

Test, end ot
MOdifIable address

RR-171

... ;3 -

120
121
122
123

6

ra

7

45 0

10
11

124 uaO
125
1

l26

.127
130
131
132
133
134
135
136

2

J
4
5
6
7
10
II

12

137 vaO
1
140

141

2

142

J

143

4

144
1.45

l46

147
150
151
152
153
154

5
6
7
10
11

12
13
14
15

155 upO
1
156
2
157
160
J
161
4
162 prO
1
163
2
164
165
.3
166
4
167
5
6
170
171
7
172 10
173 tpO
1
174

JmJl

rj ua6
45 0

tp
lq
qt
tp
ej

dd60
ua

tU

Q

Q

dd33
tt4

25
tt4
1

.
st
Mask 1 octal digit

Q?
A1

dd34

\18?

dd35

45
ra;
45
ra
45

0

uall
if
ddJ6
up
dd3'Z
up

ttl
0
ttl
0

tp ttl
qt ddJ3
tp tt4
ej dd34
ej dd)5
45 0
ra ttl
0

ra ttl
pr 0
pr 0
pr 0
rj prl0
45 0
pr 0
pr

0

pr 0
rJ prl0
45 0
tp
1q
tp
1q
qt
at

Modify U only

IIDJl

ej

45

Add 1

obI?

Q

tt4
A
va6
va10

Add 21000
To Print
Add 12000

Carriage return
Space

"V-

pr

va5
dd42
dd45
dd43
pr
ua6
Q

Q

6

dd43

tt2
:3

dd46

Q?
A?

ff

dd40
vall
dd41
dd42
dd43
dd44

kk
Q

Add 21000
To print
Add 12000

Carriage return
"U.
Space

Index

A

(pr

dd47

pr6

0

rt)

i~

0

tt2

~3

rp 20004 kk14
ej dd20 tp2

10-22

Print digit

Teat for tape
Instructions

-4.175
176
177

2

'3
4

200 efO
201
1
202
2
203
3
204
4
205

206
207
210
211

.......
r-i

l'-

.....

'-"
I

0

r-i

I

0
0

0-

r-i

l'-

><
0...

osO
1
2

.3
4

212 ddO
1
213
2
214
215
.3
216
4
217
5
6
220
221
7
222 10
223 11
224 12
225 13
226 14
227 '15
230 16
231 17
232 20
2J3 21
234 22
235 23
236 24
237 25
240 26
241 27
242 30
24.3 31
244 32
245 33
246 34
247 35
250 36
251 37
252 40

pr 0
dd42
rp 10004 nun
pr 0
dd60

Carriage r.turn

pr
rp
pr
rj
45

Carriage return

dd42
0
10005 af3
dd70
0
prlO pr
kk14
0

rj cs4
tu kk
rs tt5
tp tt5
45 0

0

0
0
0 76000
0 0
76000
0
77 0
0 11
0 1
af 0
fa 0
ip 0
It 0
45 0
56 0
pr 0
pu 0
rm 0
WID
0
am 0
bm 0
rp 0
er' 0
ew 0
sp 0
sa 0
en 0
aa 0
0 0
0 0
0 0
0
21000
0 12000
0

0

0

cs1
tt5
dd4
Q

rr
02000
77777
76000
76000
0
()

0
0

0
0
0

0
0
0

0
0
0
0
()

0
0
0
0
0

0
0
0

70000
10000

20000
0

0
21000

10-23

Print ntapen

Print "EF"
.Print address
To V address mmdifioation

Subtract 76000 from V

RR-171

- 5-

·253
254
255
256
257
260
261
262
263
264
265
266
.267
2:70

271
272

Z73
274
275
276
277
300
301
302
303
304
305
306
307

41
42
43
44
4'5
46
47
50
51
52
53
54
55
56
57
60
61

62
63
64

65
66
67
70
71
72
7)
74
75

310 ttO
1
311
2
312
313
.3
4
314
315
5

0

0

0

0
0

0
0

0

0

0

0

0
0
0
0
0

61
0
0
0
0
0

0

0
0

0

0
0

0
0
0

0

0
0

0

0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0

0
0

0
0

0
0

0
0

0

0
0

0

0

0
0
0
0
0

0

12000
45
4

17
34

Carriage return
Space
V
U

7

dd50
37
52
74
70
64
62
66
72
1

30
15
20

...e

Flex code 0
1
2

.3
4
5
6
7

flex
flex
flex
flex

code t
code 8
code p
code 9

:2

5
.3
bb32
47

Shift up ..

20

n~n

26
'J7

4
0

"rtf

Shift down
Not used

0

0
0
0
0
0

BWzpac

10-24

Temporary storage

Remi ;igton Rnnc! Un i vac
Floating Vector Arithmetic Package

GENEHAL DESCHIPTION
This package contains four subroutines:

vectbr roll-off, vector

unpack, scalar product of two vectors, and vector sume

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 108
elements.

The arithmetic is floating point with one biased characteristic

serving for all of the elements of a vector.

The bias of the characteristic

PACKEO FOI!)1 OF A VECTOR

Associated with every vector. X

= (xl,.o~tXn)t

(bl, •• o,h n ), each element of which is either 0 or 1.
defined in the following t'my:

is a set of numbers,

This set of numbers is

if xi=O, then bi=O; if xi10, then bi=l.

The

three binary numbers,
blx235+b2x234+ ••• +b36.
b37x2 35+b 30x2 34+ ••• +b 72 ,
b73 x2 35+b 74 x2 34 +••• +b I08t
where bn+l=bn+2= ••• =bl08=O if n~I08. are called the Q-words of the vector X.
It is clear that u vector is well-defined if the Q-words, the number of elements, 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-

RR-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 sealed so that th-e numerically largest has 32 binary' digi ts.
There are no blank addresses between successive vectors.
Each vector hus 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

ke~vords

are$ored in the same order as the corresponding

vectors, and there are no hlank addresses between successive keywords.
lowing the last keYWQrd in the directory is a pseudo keyword.

Fol-

If the last

non-zero mantissa of the last stored vector is in location y. then y+l 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 storane.
as Ri" S. and T.

......

We shall refer to these blocks

By Ri we will mean the ith address in the block R.

We denote

by m the number of elements in the operand vectors •

N

r-

r-t

'-'

I

or-t

PROGRAM PAHAMETERS

I

o
o

:J'

......
r-

~

1.

Locations 00005 through 00017 are reserved for constants and

program parameters.

c...t

10-26

-3-

The following

RR-172

para~eters

must be provided by the programmer:

00005:

Rl=stdrting address of R

00006 :

Sl=starting address of S

00007:

T1=st3rting address of T

00010:

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+nurnber of non-zero elements of vector in S

00017:

(u-address) 3+number of non-zero elements of vector in T4

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 Qwords, from permanent storage to R.

It is coded in standard form \vith one

exit and one entrance, and is assembly mOdifiableo
UNPACK

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 o It is
coded in standard form with one exit and two entrances, and is assembly modifiable.
1f-27

RR-172
-1-

Defore cntcriag the unpack subroutine. X must be rolled-off in R.
The roll-off provides all program patameters.

If X=(xl •••• ,xn ) and Y=(Ylt ••• Yn ), then the scalar product,

X·V,

is defined by

The scalar product subroutine
in S and the vector in T.

for~s

the scalar product of the vector

It scales the mantiss2 of this product so that it

contains 32 binary digits.

If either xi=O or Yi=O then. of course, the term xiYi conttibutes
nothing to the scalar product; in this case the subroutine avoids formation
of the term xi Yi •
l~e

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

..-

m

Cl :

= ~ xiYi are three words
i=l
35
34
clx2 +c 2 x2 +••• +c 36 ,

C2 :

c 37 x235+c 36x234+ ••• +cI08.

Associated with the sum

X-V

analogous to the Q-words of a vector (i.e., if xiYi=O, then ci=O. and if

xi~i,Ot

C\I

t-

......

--o
t

......
I

o
o
0'
......

then ci=l; and if n( 108. then c n+l=-- •• =c 108=O).
A3

are the Q-words of

X,

and if

B • B2 , B3
l

It is clear that if AI' A2t

are the Q-words of

V, then

t-

><

c..

The subroutine forms Cl.

t 2,

C3 ; it then stores sequentially in S all those

Xi' and in T all those Yi' for whidh ci=l; finally. with a repeated multiply
add instruction, it forms the sum.
10-28

RR-172

!:-

X:y =~ (Si) (T i) t
i::::l
where k is the number of non-zero terms in the sum

Before entering this subroutine the vectors X and Y must be unpacked
in Sand T respectively.

The unpack subroutine provides all program parameters.

VECTOR SUM

by

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
in Sand T

respectively~

subro~tine.

the vectors X and Y must be unpacked

The unpack subroutine provides all

meters e

10-29

nec~ssary

para-

RR-172

-6;..

Roll-Off
Author:

P, Nikolai

Type:

subroutine

Code Check by:

Date:

R. C. Gunderson

Machine Check by:

p. Nikolai

Correction of Routine:

R. C. Gunderson

Revision of Routine:

C. D. Dixon

Form:

Standard 1103 Subroutine;
Assembly modifiable

Exit:

01001

Entrance:

27 August 1956

01002

Storage Required:
Instructions:

01000 through 01020

Constants:

01023 through 01023

Temporary Storage:

01021 through 01022

Number of commands for assembly modification: £1.Q

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
(OOOll)=Ke~vord

of vector

<00012)=Next keyword in directory
(00013)=3+number of non-zero elements of vector

Time:

3.64 milliseconds, maximum

10-30

RR-172 .

-7-

Unpack
Author:·

Po Nikolai

Type:

subroutine

Code Check by:

27 August 1956

R, C" Gunderson

Machine Check by:
Correction of

Date:

Po Nikolai

R~utine:

C. D. Dixon

Revision of Routine:
Form:

Standard 1103 Subroutine
Assembly modifiable

Exit:

01001

Entrance for unpock in T:

01002

Entrance for unpack in S:

01003

Storage Required:
Instructions:

01000

Constants:

01047

Temporary Storage:

through 01046
through

01054

01055 through

01056

Number of commands for assembly modification:
Preliminary Settings:

X.

~7(e)

Before entering the unpack subroutine. the vector.

must be rolled-off in R,

The roll-off subroutine provides all

program parameters,
Finul Results:
for unpack in S,
(S)=Q-words and mantissae of
(OO014)=Keyword of

X

x

(00016)=3+number of non-zero elements of

x

RR-172

-8~

for unpack in T,
(T)=Q-words and mantissae of
(OOOlS)=Keyword of

~

x

(000I7)=3+number of non-zero elements of

x

Operating instructions:

Time:

i

~ Au o

1.

Directory address of

2.

Enter Roll-off subroutine; roll-off i in R.

3.

Enter unpack subroutine at 01002 (01003); unpack
32.1 milliseconds.

maximum

10-32

x in T(S).

RR-112

Scalar Product
Author:

E. Feller

Type:

subroutine

Code Check by:

Date:

R, C. Gunderson

Machine Check by:

E, Feller

Correction of Routine:

Ro C, Gunderson

Revision of Routine:

Co D, Dixon

Form:

27 August 1956

Standard 1103 Subroutine;
Assembly modifiable !

Exit:

01001

Entrance:

01002

Stornge ,required:
Instructions:

01000

through

01124

Constants:

01125

through

01141

Temporary Storage:

01142

through 01152

Number of commands for assembly modification:
Preliminary settings:

125(8)

Before entering this subroutine the vectors

y must be unpacked in S ant T respectively.
provides all program parameters.
Final Results:
(A)=(01152)= mantissa of

x.y.

(Q)=(01151)= characteristic of
Accuracy:

32 bits

Other subroutines used:

Roll-off
Unpack

10-33

x.y.

x and

The unpack subroutine

RR-112

-10-

Operating Instructions:
1.

(

Enter Roll-off subroutine; vjfhll-0ff

x in

3.

Enter Unpack subroutine at 01003; unpack

4.

Directory address of

59

Enter Roll-off subroutine; roll-off

6.

Enter Unpack subroutine at 01002, unpack

7.

Enter Scalar product subrol!tine; for

R.

x in

So

y ----~Au.

Time:

10-34

y 'in R.

-X·Y.

y

in To

RR-172

-11-

Vector S!J!"r.
Author: ___r~,~N_i_!co_l~a~i___

Date :____2;;". 7"'--""A.. ;.u.....9'-"'u.;;;.s. _t_1;;,.9;...,;56;..;;...._

subroutine

Type:

Code check by:

Ro Gunderson

Machine Check by:

Po Nikolai

Correction of Routine:

R, Gunderson

Revision of Routine:

C, D. Dixon

Form:

Standard 1103 Subroutine
Assembly modifiable

Exit:

01001

Entrance:

01002

Storage Required:
Instructions:

01000

through

01132

Constants:

~

through

01142

Temporary Storage:

01143

through

01146

Number of Commands for assembly modification:
Preliminary settings:

133(8)

Before entering this subroutine, the vectors

and y must be unpacked in Sand T respectively.

x

The unpack sub-

routine provides all program parameters o
Final Results:
(S)=mantissae of

x+y, The routine does not provide Q-words for the
vector sum,

(OO014)=characteristic of i+Y.
Accuracy:

maximum 32 bits

Other Subroutines used:

Roll-off
Unpack

-12-

RR-172

Operating Instructions:

Time:

I.

Directory address of x

2.

Enter Roll-off subroutine; roll-off

3.

Enter Unpack subroutine at 01003; unpack

4.

Directory address of y ~ Au'

5,

Enter Roil-off subroutine; roll-off

6,

Enter unpack subroutine at 01002; unpack

7.

Enter Vector Sum subroutine; form

~

37,5 milliseconds, maximum

10-36

Au.

x

i

x+y.

in R.

x in

S.

in R.

y in

T.

Pa9'~ --I

of 2

RR-172"

UnpClck

..-..
N

r--

01000

00

00000 00000

Alarm exit (not used)

01001

45

00000

Normal exit

01002

1]5 00000 01040

01003

16

00006

01017

01004

16

00006

01024

01005

16

00006

01026

01006

11

00011

00014

Keyword of x ~

01007

11

00013

00016

3+ number of non-zero elements ofx~

01010

31

00005 00017

01011

15

20000 01023

01012

15

20000 01026

01013

21

01026

01051

01014

31

00010

00017

01015

35

010,16

01016

01016

00

00000

00000

01017

11

01047

00000

01020

11

00010

01055

01021

23

01055

01053

01022

11

01050 01056

01023

Il

00000

01024

11

30000

Entrance for unpack in T
Entrance for unpack in S
)

Set up

14

Set up

instruc~ions

10000

Q-LVord

-)

Q

10000 00000

Q-word

-/

S (or T)

/

."

and constants

r-1

'-"

I

0

r-1

I

0
0

0"

r-1

t-

:.><
a..

10-37

16(u)

Page 2 012

llnpack

01O~5

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

0,1036

21

01024

01053

01037

45 00000 01022

01040

16

01041

16 00007 01024

01042

16

00007

01026

01043

11

00011

00015

Keyword of

01044

11

00013

00017

3+ number of non-zero clements of x

01045

45

00000 01010

01046

15 10003 01020

01047

00

01050

00 00000 00043

01051

00 00003

00003

01052

00 00001

00001

01053

00

01054

00 00001

00000

01055

00

00000

00000

01056

00

00000

00000

00007 01017

i (unpacked)
I

)

I'

->S

(or T)

Set up for unpack in T

x~

15

00000 00000

Constants and temporary storage

00000 00001

10-38

~M(u)

Page 1

Vector Sum

of 4

Page 2 of 4

IUt-.1ll.

Vector Sum

01031

15

01074

01127

01032

11

01133

01144

01033

16 00014

01144

0103-1

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

If the difference of the characteristics

01044

75

00000

exceeds 31(10)' transmit

01045

11

00000 00000

to 00014; and transmit the corresponding mantissae

01046

11

01144

to S.

01001

20000

th~

larger

ch~racteristie

Then go to the,exit

01047 36 01145 01143
01050

42 01137 01056

01051

11

01144

00014

01052

45

00000

01001

01053

11

01145 00014

01054

15

01052

01064

If the characteristic& differ by less than

01055

45 00000 01060

32(10), shift the mantissae of the smaller

01056

II

01057

15 01055 01064

01060

11

01061

36 01143

01143

01062

16

01143

01064

. 01063

75

00000 01065

01144

00014

until the characteristics are equal; transmit
the larger characteristic to 00014.

01140 20000

10-40

Page 3 of '4

Vector Sum

01064

54 00000 00000

01065 75 00000 01067
21

00000 00000

01067 31

01074 00017

01066

01070

15 20000 01076

01071

15 20000 01100

01012

21

Add corres'ponding mantissae and transmit
to S.

01100 01141

01073 75 00000 :01075
01074

12 00000 00000

01075

11

01076

11 00000 20000

Ql133 01146

01077 75 00000 01110
01100 42 00000 01101
01101

55

10000 00017

01102

15 01071 01146

Find the numerically largest mantissae of
the

sum, ~nd transmit·to the aecu~ulator'

01103 23 01146 '10000
01104

21

01016 01146

01105 23 01077 01146
.-.,.
C"J

t-

......

"-'

I

a
......
0

01106 21

01100 01146

01107 45 00000 01076

Calculate the

01110 47 01113 01111

and transmit

I

0

0-

......

t-

><
c..

~haracteristic'of

.t
\

01111

11 01133 00014

01112

45 00000 01001

01113 74 20000 01143
01114

11 01140 20000

10-4i

to 00014

tbe sum

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
01124

16

10000

10000 01127

01125 23 00014 01143
01126 75 00000 01001

-

01127 54 00000 00000

Shift the mantissae of the sum so that the
numerically largest has 32(10) binary digits.

01145 00014

01130

11

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

Constants and temporary storage

01143 00 00000 00000
01144

00

00000

00000

01145 00 00000 00000
01146 00 00000 00000

10-42

RR-172
Page I of 1

Roll-Off

N

t-

......

01000

00

OOOGO

00000

Alarm exit (not used)

01001

45

00000

30000

Normal exi t

01002

16

00005

01017

Entrance

01003

15

20000

01023

01004

11

01023

01006

01005

75

30002

01007

Keyword of x

01006

11

00000

00011

Keyword of next vector

01007

15

00011

01017

Starting address of

01010

11

01022

00013

01011

15

00012

00013

01012

11

01022

01021

01013

15

00011

01021

Starting address of

01014

23

00013

01021

3+number of non-zero elements of ~ ----~ 13(u

01015

35

01020

01016

01016

00

00000

00000

01017

11

00000

00000

01020

75

30000

01001

01021

00

00000

00000

01022

00

00000

00000

I

......

01023

11

00000

00011

~

Set up instructions

11

x

~12

-/,1017(u)

Starting address of next vector

)x-

I

0
0
0-

......

t-

:><
c..

10-43

-> 13(u)

x ~ 1021(u)

R

Constants and tenporary storage

~

0

}

Page 1 of 5

Scalar Product

01000 00 00000 00000

Alarm exit (not used)

01001

45 00000 30000

Normal exit

01002

31 00007 00017

Entrance

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
01014

20000

00005

16 20000 01036

01015 15 20000 01040
"

01016 21

20000 01135

01017 35 01136 01056
O~029

16 20000 01075

~
,....

01021

31

I

01022

15 20000 01036

01023

31

01024

35 01124 01035

""'"

-

0
......

I
0
0

0"-

Set up instructions and constants

00006 00017

00010 00017

......

t-

><
0..

01025 11

01125 01142

01026

11

01125 01143

01027 11

01130 01145

10-44

Page 2 of 5

RR-172

Sc al ~~r Protinc t

,.....
C'J

t-

......
.....,
I

0

......

01030

II

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

010<15

47 01052

01046

01046

23

01147 01137

01047

46

01072

01050

01050

21

01044

01132

01051

45

00000

01044

01052

IS

01044

01053

01053

11

00000

10000

01054

44 01055 01067

Non-zero Xi ~R

01055

00

00000

00000

Non-zero Yi

01056

00

00000

00000

01057

21

01055 01134

01060

21

01056

01134

01061

21

01145

01132

01062

41

01147

01064

I

0
0

0'

......

t-

><
0..

) x->

)

R

1

)

Logical product of Q-words of -x and -y

~T

~TltT2tT3

Page 3 0 f 5

Scalar Product

01063

45 00000 01072

01004

41

01146 01054

01065

II

01127 01146

01066

45 00000 01050

01067 21

01055 01132

01070 21

01056 01132

01071

45 00000 01062

01072

15 01145 01074

01073

11

01074

75 30000 01076

01075 72

01125 20000

00000

00000

01076

47 01102 01077

01077

11 01125 01151

01100

11

01101

45 00000 01121

01102

43

20000 01107

01103

74

20000 01151

01104

11 ·20000 01152

01105

54 01152 00105

01106

45 00000 01113

01125 01152

01107 74

20000 01151

01110

11

20000 01152

01111

54 01152 00105

01112

23 01151

01126

01113

21

01151

01140

01114

16 00014

01142

i.y mantissa

----~ A

' i.y characteristic

10-46

----»

Q

RR-172

Pau e 4 of 5

Scall.tr Product

01115

16

00015

()1143

01116

21

011<'12

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

J'
"-

Constants

N

t....-1

'-"

I

I

0

....-1

I

0

0
0'

....-1

t-

><
0....

J
\

Temporary storage

(
10-47

nn-.1'c..

Page 5 of 5
Scalnr Product

01150

00

oonoo OOO()O

01151

00

00000

01152

00

00000 00000

)

00000

10-48

HR-173

SIG~IFICJ\NCE PHl~C·FRVILG

I.

FLOATING BINARY POINT

ARITm'~ETIC

FOR DIGITAL CONPUTERS

Introduction to the System
The motivution for this system wus a desire to be able to preserve in

some wayan indication of the sienificance of the result obtained from a series
of floating binary point arithmetic operations on a digital computer.
sake of abbreviation this system shall be referred to as "Spit.
and theory of SP are independent of any particular computer.

For the

Nov the ideas
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,"'.
Host floating point systems use a packed form of 28 bits for the mantissa
of a floating point number and 8 bits for the characteristic.
~etic

operation the mantissa is normalized so that 28 bits are always kept in

result.
~ake

After each aritb~he

Now sienificant bits can be easily lost by subtraction and this would
But when 28 bits

any computations depending on this 'result less accurate.

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 toal is to make SP a noti-normalizing

systeI1 and hence one Jnuct use

a

different reprecentation for floating point numbers.

C"J

r-

.......

.......

The rcprec(:ntation uced muct be capable of indicating how

J~lnny sicnific~nt

diGits

I

o.......

there arc •

I

o
o

0-

.......

!i 2E-8 rnc]ted forr:i W~\G cho[~on Lut in::'tc:1d

of the

terms ul1:Jnti[-5[.·nll nnd

t-

><

"ch8r~tctcri~.ticU,

tho tcn::f)

"~:i:.'nj nC:lnt p~:·rtn

0..

10-49

n.nll

nC:~l'onf'llt"

~

h:111 be

ll~'cd

respec-

RR-173

- 2 -

bits.

A number, N, in this syotcm, is then of tho form
N

= Na

• 2Mx

'Where Nand
Nx are the siGnificant part and exponent respectively.
s
this type shall be referred to as SF numbers.
Numerous exnDlples 'Will

l~¥

Numbers ot

given throughout the rest of this introduction.

Octal and binary representations will be used and it will be clear 1n each case
wldch of the two applies.
The number 5 written with 3, 10, and 2 significant bits

~ill

appear as

follows:
'0

101 x 10 ,
,
-111
1,010,{)()(),OOO x 10 "
11 x 101 •
Note that in the last case, 101 vas rounded to 11 and the exponent adjusted accordingly.

These numbers would appear in paoked fonn 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,

~~1

respectively (recall that the 1103 uses the one's complement system) where the
semi-colon marks the 28-8 split.
Con~idor

110
the SP number 1011 x 10 ' 0

This oan

ge thought of

IlS

being

1011,OXXIXX.XXX •••

the number

whtrc the X's denote uncertain bite nnd the comm:l marks the end of the significance.
!!ote tlHlt one }-)1 t after the
rr,rt \Jould h'!vo l.c'cn

r01:nch~d

COllUl~~

ie n zero.

off to 1100.

10-50

l'.n

If this were n one the siGnificant
nnalor:oHu

1nterprct~tion

C3n be civen

RR-173

- .3 to SP numbera with negntive exponents.
An SP number, N = N •
8

Nov suppose Ns

=O.

2~

satieties the folloving inequality.

This inequality irop11e!5

Note that the number 0 x 10111

SP can have many zeros instead of a unique zero.

could be interpreted

8S

the number

± oXXXXXX.XXX •••

where the X t s are uncertain

and there are no significant bits, 1.e., as a number with order of magnitude only.
Having these zeros in the system 1s an advantage.

Succ zeros cnn easily be generated

by subtraction and an SP zero for an answer does not give a false indication of

significance.

Let N

=3764521

X

217, M =754321062 x 225.

Note that M is a full sie;nlficance number.

Suppor;e Nand M are to be added.

do this they must bo adjusted so thllt their exponents Dre equal.
ia performed

nD

M& 754321062

00

x217

376/t 5

21

x217

NtH s 754360727

21

x217

Tho vertical lino indic:ltes whero tho
trllncnt.in~

Then the addition

follouo:

Ih

ond

To

here C1vc0

piGnlfic~nce

of tho nnC\lCl' DtopD.

RoundinG

RR-113

-4Note that
disc,nrded.

1-1

wus shifted left (25 - 17)

=6 binnry places and the 6 bits ·Yere

If the exponents 01'" two numbers to be added differ by more than

28 then the 1nreer number can be taken for the answor since there is no point

in left "shiftlng a nl.Unber morc than 28pla.ces.
eives 0 x 240 for the ansver.
the same method

65

Take·N

Thus adding 0 x 240 and 10 x 22

=0 x 227, M =1234 x 223 and follow

above.
Ns

00, 000, 000, 000

000, 0

M,

101, 001

110, 0

101, 001

110,

a

Rounding and truncating gives 110,010 x 1010111, 1.e., 52 x 227 tor N + M.
Nov subtraotion reduces immediately to addition.

Consider the

following two problems, however, which are examples of how an SP zero can be
generated and hov significance can be lost.
(a)

(54 x 2

57

- 1

00000

x 2 57

+1

01100

x 257

0

01100

x 2 57

.Anc\Jer,:

(b)

) - (1 x 264 )

o x 2 61...

-152
(-1073 x 2 , ) - (-43 x 2-~!+6)

+

100011

0000

100011

1011

-0

1011

10-52

x 2-152

RR-173

- 5 -

Answer,

-1 x 2-

146

(Notea round off mnkos nienificant part
different from zero).

Suppose that Nand M as eiven in the first example of addition are
to be multiplied (N

= 3764521

x 217, M = 754321062 x 225 ).

(3764521) (754321062)

I 46035172~.

=3646563

Only 7 ootal digits can be kept in the 'fi~l answer.

Therefore the

above product must be rounded and truncated where the vertical line is.
the significant part of the answer is 3646564.

Then

Now)3 bits were discarded.

This means the exponent of the answer is

17 + 25 + 33

=77,

i.e., N • M = 3646564 x 277.
Consider the problem of multiplying 2 SP zeros, say N = 0 x 2 10
and M = 0 x 223.

By the inequality given above,

<,

--

,,7

~

,

Hence the product should be such that

-

In view of this, 0 x 232 could be given as the product.

However, it turns

out that the algorithms and the coding for the 110) are simplified if the
answer 0 x 233 (obtained by simply adding

N.x and' ~~) is eiven. The decision

was made to elva thls answor rather than the first onc.

This does not differ

n:uch from tho other nncwcr and tj10 lldvllntDGcs out"Jeir,h the dif:ndvnnt:1Ccs.
One other

C11:30

turnn up,

a.e.,

'In

1"'''''

(0 x 227) (1231... x 223 ).

Sjncc tho

RR-173

-·6 .

,

number of bits which 111uSt be discarded.

27

e~~onent

Hence the

1s

+ 23 + 12 = 64,

and the nnSlier 1a 0 x 264.

The division is perhaps more difficult.
nnd H

= 754321062 x

Consider N

=3764521 x 217

Before dividing,. ahif't Ne and Me left until they

225.

hoth ha:ve .35 bits (and one leading zero, 1.e., sign bit).

One then has

(adjusting the exponents),

H, 011, 111, 110, 100, 101, 010, 001, 000, 000, 000, 000, 000

x 20

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

MI

all, 110, 110, 001, 101, 000, 100, 011, 001, 000, 000, 000

x 215

If the division 1e carried out to 43 places, the result is (discarding remainder

and not rounding)

01. 000, 010, 001, 011, 011, 000, 0

I 11, 111, 100, 110, 011, 0 •

The vertical line indicates where the quotient 18 to be rounded and truncated
(keepi~g

same. number of bits 8e there are in Ne ).

Rounding here and

~oving

the binary point to the line gives for the exponent

. a - 15 - 23

=- Jt).

Hence the answer 18 .

10, 000, 100, 010, 110, 001, x 10-100,000,
i.e.,

The next case to cons1der 1s N : M where Na
N

=0 x 227, M = 1234 x 22.3.

=0 llnd Me 'I O.

Take

Clearly an SP zero 10 required for the nnS\i/er.

Comparing this with the multiplication of the
one to take

27 - 23 - 12 ; -6

10-54

Stl1110

Nand H above would lead

RR-173

- 7 -

for tho exponent (subtracting 23 and 12 instead of adding).

This can be

justified by the above inequalities also as follows:

Hence [- N

l

i.e., N -;- M

Now suppose Ns

= 0,

Hs =

=0

x 2-6•

For example, N ::: 0 X 2-66, H ::: 0 X 2-42 •

o.

SP zero divisors can bo ullm-Ied providing the ans\tJer is interpreted correctly.

COI!'.paring aeain to multiplication, one 1:Iould be lead to give

=-

--66 - (-42)
for the e:A.-ponent.

24

This case differs sligp.tIy from ,-[hat the ineq1JD.li ties gives

as did the same case in multiplication.

I N I < 2-67 ,

approxirrlltely 2-24 or 0 x 2-23 for an ans\-Jer.

1 }1 I :S 2-~3

would give

But as in multiplication, it is

more convenient to take 0 x 2-24 for the answer.

l~ote that in multiplication

the exponent \-Jus given one higher than that given by the inequalities, and here
it is one 1m-lor.' One can not put this anSHer in an inequality very well since
- if the divisor is small compared to the dividend the result \.Jould be large,
and if the relative sizes orc the other '.tlay aro1L.l1d the anS'o{er is s111.311.
'-"

I

21
opproximately 2- "'+11 \-las used above.

IJ'

C'

,

Hence

A reliable ans\<
a..

exponen~s

are equal.

This is accomplished by

the exponents will be equel.

deter~ining

This adjusted significant part is

10-57

RR-113
- 2 -

then added to the other unndJuated significant part end the sum
i8 truncated ond rounded to give the aignitic8nt pert or the
.mawer. The exponent of thesnawer will be equal to the Max1..rnum
1:>£ tho two original exponents. This is the method in brief.

Hx =

Without loss of generolity, supPose
max (Nx,Nx ).
Then Ns is shifted left a number of binary plaoes equal to
(Nx - Mx ). After-adding Ms to this and rounding, the result
is truncated by dfscarding the right most (Nx - Mx> bits.
This number becomes Rs ' the lowest order bit i8 discarded

=

. (otter the round ott 88 sbove), and Rx Nx + 1. (A carry ot
on's bit can prOduce a 29 bit Bum). In this Cese it Nx = lZ1
then R.x: ,,"'·il == 128 and is out of range. When this h8.ppens

an

alarm is given and .computation stops.
Now there i8 one exception to the above outlined
·prooedure. Namely, when 28 < I Nx - Mxl. In this csse R is token
85 the number with the highest exponent.
The preceeding method
would give this result anyway. This exception is necessar,y
since the computer used imposes a limit of how much a number can
be shifted (the exponents could differ os much 8S 254 and the
shifting limit is much less than this).
Note that this algorithm oovers all possible SP
numbers,including zeros.

c.

Subtraction Algorithml

R = N - M.

To subtract M from N it is necessary only .to change the
sign of M and then add (change the sign ot M by replscing Me with
-1~8).

The nature of the 1103 puts one restriotion on this (see
part IV~ Bubtract control routine).

10-58

RR-173

- 3D.

Multiplication Algorithm:

R = N • M.

Briefly, multiplication is accomplished by adding the
exponents, multiplying the significant parts, rounding and
truncating ond 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 smeller

count gives the number to keep (this nmnber has been denoted by
C, see part A above).
Two distinct ceses arise in multiplication.
Cese 1.

0, Ms P O. In this case Ns and Ms are
multiplied and the product is rounded and
N~

t

truncated just to the right of the first
(high okder ) C bits.

This becomes Rs·

Rx

is given by the following:

Rx = Nx + Mx + (E -C r.
Note thot (E-C) is the number of bits that
are discarded.
Case 2.

Ns = 0 or Ms = O. If one of the two operands
is zero,'i. e. has. no Significance, then
the round off rules require that the>product
has no significance, i.e. Rs = O. Hence it
in only necessary to compute the exponent,

Rx.
Rx =

Now if both Ns

=0 and Ms = 0 then

Nx + Mx. Suppose one of the two is not
zero. Then the number of bits it hus, minus
one, (to aCCOU:lt for the sign bit) must be
added to Nx + Mx. Using the conventions

10-59

RR-173

-4",adopted, Rx 18 given by
R=
x Nx + M
-x + (D - 1).
'
Note that if Ns = 0 ond Me = 0 then D = 1, and
this formula agrees with the above statement.
~hus this equation i8 ueed tor both poseibi1itieo in
Cnse 2.

R = N + M.

E. Division Algorithm:

Consider first the cnse Ne

#0

ond Ms

# o.

Before

dividing Ne by Ms' they are both scaled up to full 36 bit word
length nnd He is shifted left 34 places in the accumulator. This
assures's 35 or 36 bit quotient., Bnd prevents a zero quotient
or a divide overflow. 'This quotient iathen rounded and truncated
the

80100

as, ia multiplication, to give Rs.

When computing Rx the

scaling up of Ns and Ms, shifting ofNs ' and the number of bits
discarded from the quotient must be taken into account. C bits
are kept as inmultiplicotion, hence (E - C) bits are discarded.
This must be &dded to Nx - 1-1.
x Subtracting 34 accounts for
shifting H ' and adding (A ~ B)8ccOun~S for the initisl shifting
s
of Nand M. Thus R is given by
x
Rx = Nx - J.1x - 34 + (A-B) + (E-C).
No,", suppose Ns
0 and M -I O.If the above algorithm
.

8

S

=

for

di~iding

N by M is followed, the; quotient will be zero.
S

8

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

8

count of 35 (see Part IV).

and this will cancel the

Now C s 1, hence (E - C)

= 34

-34 1n the above expression for'Rx •

Since A = 1 thetormUla reduces to

R=
Nx - M+'
(1 - B)
x
x
which is as it should be (B -I 1 since H ., 0). ThuB the
s
algorithm will give R correctly for ell casea except when Me

10-60

= O.

RR-173

- 5-

Suppose Ms
a zero by the

c

o.

Clearly the quotient must also be

off rules used.

ro~..:nd

necessary only to compute

Rx.

Hence in this case it is

If Ns = 0,

Rx = Nx

-

Mx.

But

if Ns t 0 then Rx must be adjusted to compensate for this. This
adjustment is token care of by adding (A - 1) to (Nx - MX). If
Ns = 0 then A = 1, hence one can say that for either case

Rx = Nx F.

Mx + (A - 1).

Comparison Algorithm
Two SP numbers are defined as equal if their difference
is an SP zero (see the two examples on sub:traction).

Hence to

compare Nand M it suffices to subtr6ct M from N bnd test the
difference.
N > M.

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

If N - M is a negative

SP number, N < M, and if M - N

is a zero then N = M.
;j:
Note that under this definition lif . equality all SP
'~

zeros are equal.

G.

Notes:
In multiplication and division it is possible for Rx

Rx

to get out of range in two ways, i.e.,
> 127 or Rx < - 127.
If
> 127 then an alarm is given as mentioned in part. B above.
If

Rx
Rx

< - 127, low order bits of Rs are discarded and the ex-

ponent is increased to - 127. If Rx + 127 + B(Rs) < 2, i.e.,
if all the bits of Rs are discarded and the exponent will still
be out of range, {hen 0 • 2 - 127 is given for the result.
,-

In all four arithmetic operations the truncating point
is deternincd before rounding.

Thus it is possible for the round

10-61

RR-173

- 6off to give a carry of one bit., If this extra bit makes
B(Rs) = 29 then ono low order bit ie discarded and Rx is increaaed
by one.

This necessitatos testing

Rx again

to Bee 1t it 18

still within range. (Rx 1s always tested before any truncating
or rounding is done).

10-62

RR-173

III.

now to use the SP Interpretative S,ystem
A.

Introduction.
There are 7 possible SP operations.
via the interpret instruction.

These are all performed

The general format of such an

IP order is IP X AAAA Y BBBB, where X and Yare operation codes
and AAAA, BBBB are

Me Addresses.

are single address

instl~ctions,

Four of the 7 SP operations
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-

missable psuedo operations, one corresponding to each of the
octal digits O' through 7 (1 and Y above are single octal
digitsJ.

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.

£QM

INSTRUCTION

~

single address

0

No-op.

1

Add

II

n

2

Subtract

II

II

3

Hultiply

II

II

1..

Divide

n

"

5

Compure

quadruple address

6

nepeot r·:ultiply Add

double address

Po 1:1' 1.(:· .. ."

;

'·\·Jtiply

10-63

rt

II

RR-173
- 2 -

These instruotions opernte on packed operands (see part I
for methodo! pocking) •. A psued~ acoumulator is used for the
arlthmeticoperotlons, e.g., operetion 1 adds the packed
operand to the pocked SP number contained in the psuedo
accumulator, leaving the result in the psuedo accumulator.
The other operDtlons ure of a similar nature.
accumulator shall heqceforth be denoted by fa.

This psuedo
The initial

loading ot fa and getting the answers out ot fa is lett up
to the

programe~.

rerister and

Furthermore the contents of the 1103 A-

Q~reglster

ere not saved.

This ·i5 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.

O. No -

See part V for address data.

Ope

The code for this is 0 ZZZZ where this 5 digit number can
be in either the u part or v part ot the IP order.

The

ZIS

can

be anything since they nre ignored.
All this order does is to jump to the next instruction,
which could be the v part ot 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 part or the v part otthe IP instruction.

!AAA must be the Me address or the packed opernnd to be added to
fn.

10-64

lUl-173

- 3-

This instruction adds the SP number in AAAA to the number
which is already in fa, leaving the sum ~.n f~ •.

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;
address of the operand which is
in fa.

~ubtracted

AAAA is the He

from the operand already

The difference is left in fa.

3. Kultiplication.
The code here is 3 AAM in u or v part of

IF

order.

This

"instruction multiplies fa by the SP number in AAAA leaving the
product in fa.

4.

Division
The number 4 AAAA in the u or v part of en IP order causes

the SP number in fa to be divided by the SP number in

AP~A.

The

quotient is left in fa.

5. Compare
This is a qundruple address instruction - a 3 way jump and requires 2 consecutive 1103 words.
t

The format of the code is

as follows:
1st word:

IP 5 AAAA

xxx XX

2nd word:

00 YYYYY

zzzzz

Thi3 opcrc.tion comperes the SP numbor in Me oddress A.AAA with the
SF nur::bc.:r in the psuedo accUlllulutor, fa.
jWT:p

It then C3uses a munusl

to one of tho addresses XXXXY, yyy.YY, or ZZZZZ

8S

fo110\.Js:

RR-173
- I .. -

AAAA

by N, than if

}-t> N

jtunp is to XXXXX, i f M

16 to YYYYY, ond if lot < N' jump 1a to ZZZZZ.

cun bo either Me 'or MD address.

= 1l

jllmp

llote that these

The 2 digits 00 can be any-

thing aince they ore lenored.

By choosing the jump addresses correctly one can use
ordor 5 for an equality jump, zero jump (if fa contains a zero),
l-Lroshold jump, or a three 'Woy dump.

The final contents of fa is N - M.
6.

Repeat lo1ultip1y 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

Me

address denoted by ws16 (work apace 16). The J has the same
function as the j in the, usual 1103 repeat instruction.
if J

= 3,

Thus

this operation multiplies the SP numbers in AAAA

ond BBBB and adds the product to fa, then multiplies the tvo
numbers in AAAA + 1 and BBBB + 1 and adds product to ta, 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

increased by 1 and if J

=1 then only the BBBB addresses are
=2 only the

AAAA. ,If J

= 0 the

numbers

in AAAA and BBBB are multiplied and added to fa n times.
The first bit of J 1s ignored, so that J = 4, 5, 6, 7
w1l1 cause the same

op~ration

J roppectively. Now if n

~O

to be performed

8S

J

=0;

1, 2,

the numbor in fa is left unchanged

and the next instruction ofter the IP is performed.

Further-

more tho index n stored in w816 18 preserved and can be used
acain.
", •

Polynomial

}~ul ti ply

10-66

llR-173

-5This SP IP instruction evaluates a polynomial of the
...n

n-1

form P (X) = An A + An- IX
+ ••• + AIX + A0 •
The format of the IP order is IP 'l XXXX 0 XAXX where
XXXX is the address of X and AAAA is the a ddress of A •

n.
An~l' A n- 2' ••• , A0 must be stored in consecutive addresses
following A.
n

The octul digit 0 is ignored.

The degree of the

polynomial, n, must be stored in the He address denoted by wsl7.
Note that n is the degree of the polynomial and hence n + I
coefficients are required.
amount of

sp~ce

The only restriction

~n

n is the

available in Me for the n + 1 coefficients.

This n is saved too as is the one for the multiply add operation
end hence can be used as many times as desired.
after the evaluation is completed.

If n

=0

P(X) is in fa

(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 leg:::.l.

Note that
t

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 interpretive system.

These are given if the exponent gets out of

ranee or if one has en SP zero for a divisor.
If at any time the exponent of the result of an

arit0~~etic

operLtion exceeds 127, the typewriter prints mx xp (maximum
and the eddress of the IP order being performed.

expone~t)

This can happen

also in the middle of the repent multiply add or the polynomiel
multiply operntion as well as during the simple

10-67

RR-173
- 6 -

nrithmetic oporotions.
on a mnnuol stop_

After the print out the computer ttopa

Starting will cause the alarm prir.t out to

be repeated.

When the SP zero divisor occurs the typewriter prints out
div :: 0 and the address of the IP inatruction being performed.
The computer stops on

8.

manual stop_

Starting the computer will

cause the division operntion to be completed and the program
continues in the normnl. manner.

10-68

v.

Mipcellaneous Notes

1. If an input SP number is supposed t9 be zero use 0x2-177
and not an 1103 zero.
2. It ia pos5ible to gain significance in all arithmetic
operations because of round orf and carrys.

3. If a programmer gete an mx-mp alarm he can reset PAK and
proceed only if further computationa do not depend on the one \-Jhich gave
the alarm. The exponent which gave the alarm is lost but some inforIf..e.tion
can be obtained by examining the contents of the working space (see coding,
part IV).
4. Every 1'103 number except all ones is a legal SP number.
5. When setting up od2 w1th the Me address of the operand,
00-07777-00000 is used for a mask. Thus an Me address must not exceed
1777 if an 1103 is ueed. This mask 1s used for two reasons:

(a)

SP can be used in an 110)A

(b)

If for the 1103 the proer,:l1nmer has
an illegal address he will get an
sec fault instead of the comFutation::
being done wrong with no warning.

6. ws and fa must be assigned equal regional values.
7. All regional assignments should be in MC except po., ea, da I
and po vhlch can be in MD to save space (po can be assigned'to any place
\there the fiex codee for 0 through 7 are stored in consecutive order).
'-"

I

o......
I

o
o

0'

......

t-

><
0..

10-69

RR-173

SP io codod usinc Roeo II.

Thore arc 1S reelons in the system

not countinG conctnnto and working apace. A brie! description of each ot
tho 18 partn of tho proGram will be given.

The coding for these follows •

.II! 2 Any intorprot instruotion causee oontrol to be turned
to IP.

ove19

This routine seta ,up the SP exit, locates and stores the

interpret order and drives ODe

.on:

OD decodec tho SP operation code in the u and/or v part

the interpret order.

or

It then causee a Jump to the control routine

correcponding to this operation code (or incase of no-op Jumps

back to IP).

Note that for

operat!ona~1 6~

and 7 aD decodes

o~

the u-op vince these are not single address instructions.

QAaAdd sleor!thm control.
Q§ z Subtract aleori thIn control •

.£Ml Multiply

algorithm control.-

Q121

Divide algorithm control.

~I

Comparison algor! thm control.

CC oomperes Nand M and aauses a Jump to the speoified deat1natlOD
for each of the three possible caeee l

M ') If, M 1& I, M< If..

lTote thn t this 18 the only oontrol routine that doee not exit
via tho SP EXIT.

E! J

eN oontrols the repeat mi1lt1pq add.

looate.- the Ii and

and does the preeoribed multiplJ add operation.

10-70

M1

RR-173

- 2 -

CP:

CP controls the polynomial multiply or polynomial eValuation:

locates coefficients and X value and computes

KU:

~ A
k :: 0 k

xk

KU clears working spaco and unpack3 the SP m.nnbcrs.

This

MD cOlU1ts the bits of Nand M and lines thom up.

s

S

routine is used only for multipl:I.cntion and division.

D..l: G1\. is tho basic add alcori tll..m routine.
G.1:

GM performs the main p3.rt of the multiply algorithm.

Q12:

GD performs the main part of the divide aleorithm.

to an nlarm ',Then

fiE:

D.

GD jumps

eli visor \.rhich is zero is encountered.

RP is the round and pack routine.

It is entered immediately

after the completion of the GA, CH, or GD routines.

vlhon RP is

entered the exponent determined in GA, GM, or GD,is in

th~

1103

accumulator and the significant bits of the ans\.;er are in w:314.

From

G1'-f and GD, WS14. contains 36 bits of the rOUGh uncuer, lined up.

(If the answer is a.n SP zero, ("18·14) ::; 0).
tr~ncates tr~s

at the proper place.

RP then rounds and

From GA, w614 contains the

oir.:nificant bi t~ of the o.nS\.,rer and one extra for round off, except
i:.:1 tho cuse whon the larcer m.unbcr is tol(cn for the

::;1.1'11,

then it

cant!) in;; only the ~'iLnific['-r:t p:-.rt of t1:..Q :J.n~;ucr (-'~hc ~e bi t3 ~~c

..

RR-173

- .3 -

~I

PA prints out the addres8 of the IP instruotion in 046e there

ia an alarm.
~I

Exponent eJ.o.n;l.

~I

Divide a1&nn.

EA prints out

"DDt

nA: prints out "div

xp"

= 0".

NQte a In the coding annQtations that follow,

used almost exclusively.

10-72

~

numbers are

RR-i73

-13 -

wsO

Packed answer (ws

1

N

2

M

3

4
5
6
7

c

fa

= psuedo

accumulator)

s

s
N
x
H
x

ga:

max (N , M ), md and gd:

ga:

I

gm:

bits of product (E)

x

Nx - Hx

1,

lined up N

x

rod and gd:

s

lined up. Hs

10

B(N )

11

B(M )

12

no. bits to keep in rp:

13

rod, gm, gd:

14
15

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

;.6

"n" for repeat

~.7

Un" for repeat polynor.lial

,:~~'

temporary stor,age for (C'"

21

various indexes

fx

s
s

B(max

B(min



(fNsJ,

IHs[> in rod, gm, gdj

.

IF order for decoding
mu1 tiply

add
lflU4.

tiply

: n multiply add

upsuedo x - register" -used

10-7;\

to

store SP operands.

43 or 44 in ga

WS-174

Prepared bJ pro. Riohard E. Adler
Flight Simulation Branch, EML
Whi te Sande Proving Ground
New Mexioo
.

A METHOD FOB GENERATINg RANDOM NUMBERS ON THE rnA 11Q]
DISCUSSIOH
The number )lS VIle taken as a starting point.

This number vae equared,

and from the equare the fourth digit through the eleventh were removed and
de8igna. ted

the first random number.

8.11

The first random number was mu1 ti-

plied by )15 and the fourth through the e1eV'enth digits ot the produot becftDle the

random number8

It

random munber.

8800nd

l8S8

8S

This process was oontinued for

8.8

many

needed.

than 8 dig!ta oome out in the result, sero. are placed be-

fore the number until 8 digits are reaohed.

When the random numbers are

u.ed in a problem on the 110), they are etored on the drum and used

88

Deeded or put on magnetio tape.

Listings at the end of this report are from IBM oarda oontaining 7
eats of 8 digits eaoh.
The table of random numbers attached can be used for as many digi ta
a8

needed.

The digits wi thin the 8 digit groups have been tested tor

randomness also.

1
10-74

One means

or

oheoklnu the rand.('IlllllefJ'

ot these d

diai t J:nnnber. *8 the

Chi Square teet which 18 a t08t -to detel.'lline the goodne •• of tl t

aotual data to the theoretlc.al distribution.
lat~lon of

rna,. be evaluated.

the

The teat In'Y'olYee tho ollltm-

" (t
i)2
X:2 (Chi Square).. X " ::: L-!.1L..=-r

t :: theoretioal frequenoios.

or

where fo ~ a.ctu81 trequencie.)

Dr reterenoe to a set

ot

-X" tA blea Ohi Sr,U8l"e

A program ws vrl tten and this test was applied to e.11

of the 16,000 8-digl t

eroup..

In order to oheck the

The reeu1 ts are found in Table ,.

rand~ne8B

of the individual dlglte within the
poker test, ev.,n-odd tellt, fre-

group.. , the following t.eta lIer:- applied'

quenolea or ordered pair., and the Chi Square te.t to Individualdlgite.·

TABLE I

tQUJ! AMI
SOO Groups ot S
~~

smeaL

to

(r,o ... t)2

(to .- t)

t

.t1

2,

l'

11

1)

20

1S,

15

17

15

23

:lJ

22

21

_27

1.91

25

25

'4_..- -

~6

l'

17

23

22

11

2.19

.:..----

191

;,,~

207
..._..........,.. ..

178

201

214

........

....

205

•

~

til·· ' ...

-:

6,~5 ~O.~5

,'8

l

.........

-

.76
I'

~._

... ,tI'_ ..

i

...

216

10.10 7.05 12.80
--_ .
.)5
.72 .24
• .I~

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

~

.

14)

l'-. ---196

l1!')

.

~1'

\

.04

••- _ • _ _ -_ • _ _ • • _ . _ -. . . . .

'16

21

. -'}.7

l).2,

18,

17

28

8

:22

25

~:1

;6,

--

19

20

'),6

7.85

,

. i'

16

22

l'
17

><

~

IA~)

22

l~

I

0
0

1'-""'---'-:

~, ~

....
"9

II

7

-

4

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

~

~

2.4

.~

--14 -

.1'"

1

6.2,

--

:-6-

.55

2

-- ..

...........

;

8.60

.........

t-

-·~Q.pd

~

-_._'""

-~h45
.....

"" l'

- ~.,

f

9 .. QS q.)O

.85

. -

,

A.75

().64.. "".................................

.58

.48 \
- ....- - ....- ...

~

.. _ _ ..... _ _ _. _.... _ _ .... _ _. - - - -...... -

189

\

.45

.50

~

WS-174

BESUl/fS <1.LIE~T{! (Cont'd)

Total - Top to Bottom

Total - Right to Lort

= 7.36

;t~

P =

.68

X)..:

7.S(.

p:-:

.65

The valuos for X2 indioAte, when oonverted to peroents, th0 amount

ot ohanoe, out ot 100 that the ti t obtained would be a iJ
than

tJ18

vorce

bad or

one sho\lll.
TADLE 4

QUQUP

FBF~UENCIES T~~

3000 - g-digi t numbers dona by MOO

GJY9R

fo

r

(ro - r)

(fo - t)2

(f _f)2
o

r

00,000,000 - 9,999,999

.31'

)00

15

225

.7

10,000,000 - 19,999,999

)04

300

4

16

0

20,000,000 - 29,999,999

.34~

)00

45

2025

6.7

30,000,000 - 39,999,999

)02

.300

2

4

0

40,000,000 - 49,999,999

294

)00

-6

36

.1

50,000,000 - 59,999,999

268

.300

-32

1024

3.4

60,000,000 - 69,999,999

.318

300

18

324

1.0

~

79,999,999

275

.300

-2'

62'

2.0

SO,OOO,COO - 89,999,999

284

.300

-16

2~6

.8

90,000,000 - 99,999,999

295

.300

-5

2'-

70,000,000

Q

)'1 = 12.7

P
The value of X2 indicates a value for

p

worse than the one show.

,

10-78

.28

ot .28. This Ihove that

there are 28 chances out ot a 100 that the tit obtained
or

=

~ould

be as bad

WS-114

ll.L.':l!.lrlL,

~F TESTS (Cant· d)

TABLE 5
~HQVP

rrmQQJ/NQI-f;S .'ttSI

16,000 8-diglt numbers tested b.r'the 1103.
~RQ.Uf

to

t

(to - t)

(to - t)2 (tg - t)2

t
9,999.999

16)3

1600

3)

1089

.67

lO,OOO,JOO - 19.999,999

1612

1600

12

1.44

.09

20,000,000 - 29,999,999

1628

1600

28

784

.49

30,000,000 - 39,999,999

1'98

1600

-2

4

.00

40,000,000 - 49,999,999

1514

1600

-86

7396

4.62

,0,000,000 - '9,999,999

1612

1600

12

144

.09

60,000,000 - 69,999,999

1627

1600

27

729

.4S

70,000,000 - 79,999,999

1609

1600

9

81

.05

80,000,000 - 89,999,999

1568

1600

-32

1024

.64

90,000)000 - 99,999,999

1~99

1600

-1

1

.20

00,000,000 -

Xl.·
P s=
The

Tuue ot X2 indicates a Talue tor

p

ot .72.

7.10

.72

Th1 • .mova that.

there aN 72 chanoe" out of 100 that the tf t obtained would be .8 bad or
~

vorse tht\n the one shown.

t-

..-4

,

0
..-4

I

0
0
0'-

..-4

t:><::
0...

1 {L7Q

WS-174

OAP TESTa

FPequenoy

or

Length ot Gaps between Suooessive Digits in Sample
(j:~)

Sample

(r0 _t)2

(I 0 -t)2

P

Juoo.,s81ve.

SiBe

Average Oap
between digit.

0

204

10.6

10.6

10

.36

.0)6

.8,

1

218

8.9

8.9

10

1.21

8121

.72

2

209

10.7

10.7

10

.49

.049

.82

3

207

9.2

9.2

10

.6.4

.064-

.80

4

,

205

9.6

9.6

10

.16

.016

.90

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

.00,

.88

8

209

10.2

10.2

10

.04

.004

.95

9

202

9.8

10

.04

.004

.95

~.tvfJon

9.8 .

The Chi Square" T&lues

or

to

t

-.p

all digits give a eatiataotory value tor P 1n

each o.a 8e •

10-80

PX 71900-10-(174)

J-I

0
I

co
J-I

25425018
5209165 LI41505940
9772606
54577061
84209253
14462379
50758033
33873158
35185855
89350406
69512902
27912823
40319279
43709917
59640776
50833670
69221130
14102943
45019601
36797697
15945567
59332898
8157247
7580823
51733249
6274564
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PX 71900-10-(174)

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72299373
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55076368
73625288
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20678087
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66113280
5489376
21942400
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9161852
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55459761
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21653627
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29836037
53339550
29257330
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66628357
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55684411
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21985866
33196834
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47748738
11227067
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7133532
46771733
92404982
69122726
95457957
1811657
94533656
13484947
89896842
1643679
54501573
87396129
10795333
39395326
34820520
61990482
54848675
49551436
22417805
84673501
963355
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83912465
15901777
92200704
226108
44122556

5241497
76575113
87496341
737256
52558873
98685932
46972847

93020846

5240396

51932412
1844386
61261956
50946334
91140709
87829556
71060552

16281311
77586333
44540222
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12042177
54353688
84046541

2842~66

71856~b8

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46123968
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12415367
85264714
6534427
2691127

7008735

607460;00
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14568326
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42593412
30290464
70700808
25553821
39037036
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499'+-3306
69324615
73833175
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33653231
63487648
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47853394
85038974

96152961
61483852
17427551
92395661
1107168
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69672898
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68255963
51380915
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9581701
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692287
54431212
39876746
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34696743
83424880
32088719
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50392402
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7795914
39902284
49067360
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38032144
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61200012
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33079214

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82581163
75871071
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33505100
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27578574
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22267840
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71912389
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31002841
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44457275
46783492
41131291
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61569027
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78647373
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43077151
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67389750
48430922
76890797
84870594
29657123
14408688
47033542

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PX 71900-10-(174)

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22945740
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98105117
72647302
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43008356
47405387

69237329
5.0243894

87598419
1193296
56027290

77312583
53863115
87503395
67323257
54043729
60371169
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99751623
69773368
86915648
46766959
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59742852
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48571313
22573290
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6737247
81-38241
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75257610
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52108503
57602676
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13558935
50954180
14958545
21573566
66793242
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30231132

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83943422
97740720
88134492
40213432
36611548
29753248
53914270
40128786

13799196

31354001
69725941
54915021
39919455
84153005
91088004
20243781

63422045
29290161
34647601

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79555102
54261774
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40621768
23769959
99188958
83355530
90784665
26335137
37278908
53510347
36542070

95226267
48190744
4337197
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76983675
72768368
97923609
2919556

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12725141
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39792198
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34828832
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32013886
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6190190
3122517
23260240
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6718847
66965777
10160021
91755059

36966861
91695070

20389921
41020082
37822454
59994280
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95798300
20586914
62372835
44506328
12951448
53815258
43260967
21153456
67203309
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96376281
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76066957
57140107
74526545
3246987
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2618771
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33720053
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80472609
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51797706
39651074
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56100235
54226082
74088520
75060750
35485441
70780294
65564584
80601587
39226515
71618325

~

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......
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45610841
15562331
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38323798
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29613229
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16164827
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27855673
435-38942
45252379
77353002
85601007
43827407
93061694
86807878
76544964
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~
I
......

-I

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PX 71900-10-(174)

....

~

...
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~

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63250009
71391298
31184834
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635448
17898866
64742580
16103405
2207054
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69576364
87552329
41051934
92825406
15282525
23282339
9394739
39361173
12850937
16180354
2868014
71425758
79169322
71835750
69427913
33004191
20058214
74610255
45096024
69023884
13634341
1371808
77679726
53240899
94667631
89369057
79703061
18282241
37296746

66553069
2967366
55451077
33899J85
22147355
25245635
74012890
34861130
30590462
79489806
8078067
64329565
1091857
96543514
49483794
14036572
23327299
35890672
14843325
5273968
69775570
47809481
17123838
85343788
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76372388
83483517
78466984
19413548
13070197
15532655
28171939
96518681
70740481
60368139
18938370
8909420
67153193
71812214
30437567
39185094

44841632
92344469
52093737
23195925
3041074
55477477
98238772
3878182
90447557
63175418
18774726
39457024
52079464
33034373
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54855108
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32577281
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63906604
80576132
49163431
5529642
503230
16517571
57515354
52225249
15888807
85354413
84225569
11317934

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27891666
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......
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A

RW-175
DET-2
Page 1 of 6

7-25-56
THE RAMO-WOOLDRIDGE CORPORATION
1.0 s Ange le s 45, California

Evaluation of IA -

AI I

for Matrix A

Complex Si.!!,gle Precision Floating Point

e.Eecifications
Identification Tag:

DET-2

Type:

Sub.routine ava.ilable on cards for

assembly
Regional Addresses Used:

OOR, OIR, 02R, 03R, CON, FOO, RvlT, COO

Storage:

132 words total program storage

1 emporary storage used but not stored
with program:
1

4n cells directly addressable by
SNIP

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

is the order of the ma.trix .

11

The constant and temporary storage pools
are used.

Entran.ce a.nd Ex! t :

RJ

Mode of

Floatlng Point..
in ES.

Qperation~

Machine Time:
Coded.

by~

Approved. by:

aOROI

aORO 2
SNIP must be ac:tivated

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

1956

W. L., Frank

July,

We F. Bauer

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
order

ne

For the special case

1\ = 0

A - /\ I, where

A

is a square matrix of

one obtains the determinant of

A if

Furthermore, one has obtained an eigenvalue

IA-

ILII

A.

the quantity

=0

The following options are provided:
Option No

0

1

-

A must be stored row by row in the memory (ES or MD)

0

The

location of the first element is supplied in the parameter
words.
Option No. 2

A must be supplied to this subroutine row by row by an
auxiliary routine to be prepared by the programmer to
fit his needso

This auxiliary must have the form which

allows for entry from this subroutine by an
OOXOl

RJ

OOXOO

instruction assuming i.t is stored starting at

location OOXOO.

The auxiliary w111 be entered

each time requ1ring the succeeding row of
up in a region

A

n

times,

to be set

preassigned by the programmer in

TEMOO

the parameter words.
In addi.tion to the 132 wcrds_,f storage needed by the subroutine, it is necessary
to provide

4n

cells of temporary storage addressable by SNIP and a block of

n(n+1) cells ei.ther all on ES or all on MD.

Qperatlng Instructions
1.

SNIP must be activated.

2.

Entrance to the subroutine is made by

1\ is
a.

' t l , ..

following instructions assuming

in the floating accumulator.
Option No. 1

OOR02

P

RJ 001<01

P+l

00

MA'l'OO

. ., '/ vv

P+2

00

TRIOO

TEMOO

RW-175
DET-2
Page 3 of 6

1-25-56
where

OOROO is the location of the first word of the subroutine.

MATOO is the :region in which the matrix

A

is stored row by row.

vvvvv is the order of the matrix A.
TRIOO

16

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

4n

cells of

temporary storage directly addressable by SNIP.
Option No. 2

b.

-

P

RJ

00001

00002

40 OOXOO vvvvv BRR

. P+1
P+2

00

TRIOO

TEMOO

OOROO, vvvvv, TRIOO and·TEMOO are as above.

where

OOXOO 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 TEMJO.

3.

Upon exit from the subroutine control is transferred to the word in
cell

P+3.

The value of I A -

1\ I I

is left in the floating accumulator and

also in the ninth 'and tenth words of the R-W temporary pool..

The input

A

can be found in the fif'th and sixth words of the R-W temporary pool.
Machine Time
Computing time for operation of this subroutine is given by

mere
oy

n

2

n (5n + 22) ms

1s the order of the matrix.

Incase the block of n(n+l) words is stored on MD the time must be increased
2
8.5(n +30) milliseconds. These times are approximate and will be conserva-

tive in most cases.
~thematlcal

Method

~lementary row operations are performed on the matrix

lPper triangular matrix

i..

A -"/\ I

reducing it to an

Before eliminating, leading elements of two rows

(hieh are to be linearly combined are compared and the element of largest magni~ude becomes the pivotal point.

~he value of

The product of the diagonal elements of

IA - /\. I I .

10-138

A is

RW-175
DET-2
Pg. 4 of 6

7/25/56

OOROO
DlRoa
02ROO
03ROO

D
D
0
D
D
D
D
0

OOROO
OOROl
OOR02
OOR03
OOR04
aOR05
OOR06
OORo7
OORoa
OOR09
OORIO
OORII
OOR12
00R13
OOR14
CORl5
OOR16
OORl7
OOR18
OOR19
OOR20
OOR21 .
OOR22
OOR23
00R24
00R25
OOR26
OOR27
,.-.,.

In
t~

'-"

I

0

,

~

0
0
0"-

~

r-

><
0..

OOR28
OOR29
OOR30
OOR31
OOR32
OOR33
OOR34
OOR35
OOR36
OOR37
OOR38
OOR39

CONOO

MJ
MJ
54
TU
AT
TU
TP
TV
TU

00500
00546
00562
00600
00625
00002
00003
00023
00000
00000
AOO15 BRR
OOR06

FOOOO
COOOO
RWTOO
00000
00000
OOR01
AoaaO
00015 AODDO
AOOOO OOR14
00000 AOOOO
Aoaoo CON06
AOOOO 03ROI

00764
01042
01062
01130
01161
00002
00003
00027
00764
00765
00766
00767
00170
00771
00772
00713
00774
00775
00776
00777
01000
01001

EXIT

N

TP CONOI aooeo
LA AOOOO 00016
TU AOODO CON04

as Aooao
TU
TP
TV
TV
TU

LA
TU
TU
LA
-TV

as
as
as
RA

TP

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62R04
CON02

01R04
03ROO
AOQOO
02R01
03ROl
02R29
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OIROS
02R27
00042
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02R06
02R12
02R04
CON04
aoooo

RA 02R01 CON06
RA 02ROl CON06
as 02R01 02R06
RS CoN06 00016
ST 00016 RWT02
TN FOOOO RWT04
TN coOOO RWTQ5
as 03ROl 03R04
TU 00R06 OOR37
TP 00000 AOOOO
SJ OOR39 00R45
TP OlR01 03R02

S

E

01002
01003
01004

T
A

D
0
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t
S

S
E

S

01005
01006
01007
01010
01011
01012
01013
01014
01015
01016
01011
01020
01021
01022
01023
01024
01025
01026
01027
01030
01031
01032
01033

00 00000 00000
00
00
00
00
00
00
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45
45
54
15
35
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16
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15
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16
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16
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20000
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01002
20000
20000
20000
20000
20000
01041
01047
01047
01066
01163

00000
00000
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00000
20017
00772
20000
01002
20000
01167
01131
10000
00020
01165
01046
01130
20000
01.063
01131
01117
00017
01047 .
01115
00052

01041
01070
01076
01066
01165
10000

21 01063 01167
21
53
23
36
13
13
53
15
11
46
11

01063
01063
01161
00020
00002
00003
01131
'00772
00000
01033
Oi051

01167
01070
00020
ooo~l
OOO~3

00034

01134
01031
20000
01041
01132

tlW-1/:J

DET-2

Pg. 5 of 6

7/25/56
OOR40

OOR41
OOR42
OOR43

OOR44
OOR45

OlROO
OIROI

TU 03ROI 03R02
SP 03R02 00051
TV AOOOO 03R02
RA 03R02 00016
MJ 00000 01ROa
TP 03R24 03R02

TP
TP
TU
RJ

CONOO J:<

0..

TU 00000 00004
02R29
S PRODUCT
02R30 LDMP 00000 RWT08 B
OF
02R31
RA 00004 CON04
DIAGONAlJ
RS CON04 CONOS
02R32
02R33
IJ CON06 02R30
ELEMENTS
RA aOROl CON03
02R34
02R35
TN RWT04 RWT04
02R36
TN RWT05 RWT05
MJ 00000 00R01
02R37
03ROO
RP 30000 03R02
NEXT
03R01
TP 00000 00000
ROW
03R02
RA 03R01 CON04
03R03
TU 03R06 00004
03R04 LDAD RWT04 00000
BS
03R05
RA 03R06 CaNaS
MJ 00000 00000
03R06
03R07
TU 02ROO 03R19
D
03R08
TU 02ROO 03R22
E
03R09
TP CONOI aoooo
T
QS 02R04 03R23
E
03RI0
R
03Rll
TP 02R02 AOOOO
M
03R12
AT RWTOO AOOOO
QS AODOO 03R20
03R13
I
N
03R14
TP CON02 QOOOO
03R15
E
LA AOOOO 00057
pIVOT
as AOODO 03R23
03R16
03R17
54 02ROI A0057 BRR
03R18
TV Aooao 03R20
03R19
RP 30000 03R21
03R20
TP 00000 00000
03R21
TN RWT08 RWT08
RP 30000 01RIS
03R22
03R23
TP 00000 00000
03R24
RA 03ROl CON04
CONOO
F
01 00000 00000
C
CaNol
00 00777 00000 B
0
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00 00000 00777 B
CON03
00 00000 00002
S
·00 00000 00000
CON04
T
CONOS
A
00 00002 00000
CON06
00 00000 00000
NTS
START
00000

01117
01120
01121
01122
01123
01124
01125
01126
01127
01130
01131
01132
01133
01134
01135
01136
01137
01140
01141
01142
01143
01144
01145
01146
01147
01150
01151
01152
01153
01154
01155
01156
01151
01160
01161
01162
01163
01164
01165
01166
01167
00000

15
14
21
23
41
21
13
13
45
75
11
21
15
14
21
45
15
15
11
53
11
35
53
11
54
53
54
16
15
11
13
75

11

21
20
00
00
00
00
00
00
45

00000
32000
00004
01165
01161
00765
00033
00034
00000
30000
00000
01131
01136
30033

01136
00000
01062
01062
01162
01066
01064
00021
20000
01163
20000
20000
01063
20POO
30000
00000
00037
30000
00000
01131
14000
00777
00000
00000
00000
00002
00000
00000

00004
15037
01165
01166
01120
01164
00033
00034
00765
01132
00000
01165
00004
07000
01166
00000
01153
01156
10000
01151
20000
20000
01154
10000

00071
01157
20071
01154
01155
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00037
01061

ooooc)

01165
00000
00000
00777
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RW-176
MrI-l
Pg. 1 of 8

7/26/56
THE RAMO-WOOLDRIDGE CORPORATION

Los Angeles 45, California
Floating Point Linear Matrix Equation Solver (AX=B)
Specifications
Identification Tag:

Ml'I-l

Type:

Subroutine available on cards for assembly

Regional Addresses Used:

OOM, OlM, 02M, 03M, CON, AUG, RWT

Storage:

171 words total program storage.
Temp9rary storage used but not stored with
program:
2(n + m) cells directly addressable
by SNAP and
nCn + 1) + nm cells all in ES or all in MD,
2

where x is an n by m matrix.
The constant and temporary storage pools are used.

Entrance and Exit:

RJ

.Alarm:

The alarm exit is used to print "SINGUL It

OOK>l

OOM02

if a singularity is detected.
MOde of Oper,tion:

Floating point.

Machine Time:

Approximately

SNAP must be in E.S.

2n2(n + 3m + 2) + 3000 milliseconds
where X is an n by m matrix.

Coded by:

W. L. Frank

June, 1956

Approved by:

W. F. Bauer

July, 1956

10-142

KW-I/O
MT1-l

Pg. 2 of 8

7/26/56
Description
This subroutine employs floating point arithmetic in· order to solve the
linear matrix eq~tion AX = B, where A is a non-singular matrix of size
men and B has the dimensions nxm. The solution X = A-~, 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

~,~ • (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 subrout lne sets up these two RJ

instructions from information gleaned from the

pH.

;I.m.eters of· the entry.

This

procedure allo'Ws storage of" A, B and X on ES, MD J magnet ic 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 171 words of storage needed by the subroutine, it is
,......

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

te

and a block of n{n + 1)

r-1

........

+ nm cells, either all on ES or all on MD.

2

I

o
r-1

Qperating Instructions

0'

o

1.

SNAP must be activated.

t-

2.

Entrance to the subroutine is

,
o
r-t

><
0...

~e

p

RJ OOMOl

OOM02

P + 1

00

OOXOO

OOYOI

P

+ 2

p +

3

uuuuu vvvvv
zzzzz

xxx.xx

by the following orders (B

!

I):

nn-.1'U

Ml'I-I
Pg. 3 of 8

7/26/56

where CONCO is the location of the first word of the subroutine

OOXOO is the location of the first word of the first auxiliary
OOYOI is the location of the second word of the second auxiliary

= m (number

uuuuu

of columns of B)

= n( number at rows of A)
zzzzz = is the location of the first

vvvvv

cell of the 2(n + m) cells at

temporary storage addressable directly by SNAP.

= is

xxxxx

the location of the first cell of the block of n{n + 1) + run
2

cells all in ES or all in MD.

3. For the case when B = I, the P + 1 word must be 40 OOXOO OOYOI BRR •
4. The auxiliary routines must be available and coded 60 that they can be
entered with
and

RJ

OOXOO COXOI

RJ

OOYOO

COYOI

respectively.

This implies that the first and second words of both auxiliaries are exit
and entrances respect1vely •

Alarm Conditions

I f a singular matrix. is detected in the process of inversion, the alarm routine

ALR-I is entered and "singnl-w-.;www" is printed where

cell from which the sub rout ine was entered.

'WWWWW

is the address of the

The rout ine cannot, however J detect

all singul.arities due to round··off errors (see below).
Starting after an alarm print-out will return control to P + 4 in the
main program.
Machine

T~

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.

the block otn(n +
8.5(n

2

1)

+ nmwords is stored on

2
2

+ 3n + nm + mn} milliseconds.

MD,

In case

the time must be increased by

These times are approximate and will be a

min1Jnum 1n most cases.
Matbematichl Method

(GaUss elimination method)

Elementary row operat10ns are
triangular matrix

i.

perto~d

on the matrix A reducing it to an upper

At the sane tiDe, these operations are performed on the

matrix B giv1ng a new matrix

B.

Before eliminating, leading elements of two rows

are compared and the eleD:tnt of largest magnitude becoDes the pivotal element.

Next, successive columns at if are taken and the equation AX
10-144

= B is

&&fI

....

v

MrI-l

Pg. 4 of 8

7/26/56

solved by the back substitution procedure.
Singularities in A are detected if a zero appears on the diagonal ot

K. Since round-ott errors can prevent this from occurring one must consider the
magnitudes ot the e~ements of X as compared to· those ot A.
difference ~ indicate poor conditioning of A.

A large order ot

Accuracy
The accuracy in the result is a tunctiQn of the condition ot 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
ot order 2 - 10 were inverted. Seven place accuracy was obtained tor the matrix
ot order 2. One more digit was lost for each succeeding higher order matrix •

.-

...0
l-

r-f

......,
I

o
.....
I

o

o

0'
r-f

t><

0..

OlM20
01M21
02MOO

02Mol
02M02
02M03
02M04
02M05
02M06
02M07
02M08
02M09
02M10
02M11
02M12
02M13

as

QS
RS
ST
RS
RJ
RJ
RP
TP
TN

RJ
RJ
TU
54
TU
RA
TP
TP
TP

ACOOO
AUG03
AUG03
lON07
0000
AODOO
CON06
AOOOO
AOODO
AOOOO
AOOOO
CON06
00016
CON07
00000
AUG06
30000
00000
00016
00000
AUG06
OlM02
01M03

Aoaoo

AUG03
AUGQ4
02M27

AOOOO
02Moi
02M05
AOaOO
03M16
03M20
03M25
03M28
00016
RWT02
00016
00000
AUGOO
01M04
00000
RWT03
00000
AUGOO
02MOO
20017 BRB
02MOI
00016
RWT01
RWTOO
00000
01M15

RwT03
RwT03
00013
CONOl
as 02M05
TM 00000 OOOO~
TU OlMl5. ()3M44
55 01M15 20025 B~B
Aoaoo 03M46
01M15 00015
TP 00002 Aoaao
ZJ 02MOO 02M14
RP 30000 02M02
TP 00000 00000
TP RwTOO 00004
TM 00000 AOOOO
TJ 00002 03M38
LDDV 00000 00000 B
TP 00002 RWT08
TP CON03 Qoooo
QS 02M01 02M09
LDMP RwT08 00000
SUNO 00000 00000 BS
RA 02M09 00016
RA 00004 00015
TJ CONOS 02M09

TO AUX 1
AUGMENT
SET INDEX
GET ITH ROW
AUGMENT

~X

SKlp IF ZERO
TRANSMIT ITH
ROW TO ES
B BOX

L

f
N

E
A
R

L

11l_lA7

00217
0.0220
00221
00222
00223
00224
002'25
0.02 ~:~ 6
00227
00230
00231
00232
00233
00234
00235
00236
00237
00240
00241
00242
00243
00244
00245
00246
00247
00250
00251
00252
0025300254
00255
00256
00257
00260
00261
00262
00263
00264
00265
00266
00261
00270
00271
00272
00273
00274
00275
00276
00271
oo~oo

53
16
16
35
53
53
35
53
53
53
53
23
36
23
31
37
75
11
13
37
37
15
54
15
21
11
11

11

53
12
15
55
16
21
11
47
75
11
11
12
42
14
11
11
53
14
14
21
21
42

20000 00402
00402 '00403
00402 00316
00415 20000
20000 00264
·20000 00270
00414 20000
20000 00340
20000 00344
20000 00351
20000 00354
00414 00020
00020 00031
00415 00020
00000 00000
00405 00377
30000 00241
00000 00000
00020 00032
00000 00000
00405 00377
00237 00263
0-0240 20017
20000 00264
00032 00020
00032 00030
00015 00027
OO407ioooo
00270 00254
00000 00002
00254 00374
00254 20025
20000 00376
00254 00011
00002 20000
00263 00301
30000 00265
00000 00000
00027 00004
00000 20000
OOO()2 00366
3200() 20000
00002 00037
00411 10000
00264 00274
30037 14000
13000 00000
00274 00020
00004 00017
00413 00274

RW-176
MrI-l
Pg. 7 of 8

7/26/56

0~M14

02M15
02M16
02M17
02M18
02M19
02M20
02M21
02M22
02M23
02M24
02M25
02M26
02M27
02M28
03MOO
03MOl
03M02
O~M03

63Mo4
03M05
03M06
03M07
03M08
03M09
03MIO
03M11
03M12
03M13
03M14
03M15
03M16
03M17
03M18
03M19
03M20
03M21
03M22
03M23
03M24
03M25.
03M26
03M27
03M26
03M29
03M30
03M31
03M32
03M33

TP 00021 QOOOO
TP 02MOI AOOOO
QA 02MOO 02MOI
RS 02MOO 00015
RA RWTOO 00015
IJ RWTOI 01M15
RA 02M25 00015
55 02M01 10025 BRB
TV aoooo 02M25
TU 02MOO 02M24
RP 30000 02M26
TP 00000 00000
IJ RwT02 OlMOS
TP CON02 00000
TP CON06 RWT05
TV 03M16 03M14
TU 02MOI 03M14
TP 00021 00000
Os 00013 03M13
tP 00016 Rwtol
TP 00013 RWT03
RA 03M14 00015
MJ 00000 03M09
RS 03M14 CON04
RA 03M13 00015
RA RwTOl 00015
TU 03M14 03M16
RS O:3M14 RWT01
RP 30000 03M15
TP 00000 00000
RA 03M16 RWT02
TN 00000 00000
TP 00013 00004
TP RWT03 RWTOO
TP 00013 RWT06
LOMP 00000 00000 B
S
ADNO RWT06 00000
Rs 00004 00015
1J RWTOO 03M20
RA RwT03 00016
NOLO 00000 00000
ZJ 03M27 03M36
TN RWT06 00002
NODV 00000 00000
STNO 00000 00000 B
IJ RWT05 03M08
RJ 00000 00000
RA RWT02 00015
IJ CON07 02M27

y

COMBINE
R
0
W
S

REPLACE
REDUCED ROW
N-2 TIMES

11
11
52
23
21
41
21
55
16
15
75
11
41
11
11
16
15

003L5

11

00326
00 ~12 7

21

00330

11
53

11
45

TRANSFER
ROWS OF

00331

UPPER

003:J3

23
2l
21
15

TRIANGULAR

00334

23

003~5

75
11
21

00332

MArRlx

00336
00337
00340

B

A

00341
OcJ342

~

K
B

00301
00302
00303
003'04
00305
00306
00307
00310
00311
00312
00313
00314
00315
00316
00311
00320
00321
00322
00323
00324

00343
00344
00:145

S
U

B

OO~46

S
T

B

1
T
U
T

B

t

TO

Aux

10-148

2

i3
11

11
11
14
14
23
4.1

00025
00264
00263
0026,3
00027
000'30
00314
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10000
00263
30000
00000
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0002'5
00015
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00335
00030
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30000
00000
00340
00000
00015
00032
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32000
05035
0'0004
00021
00032
00000
00353

10000
20000
00264
00017
00017
00254
00017
10025
00314
00313
00315
00000
00242
0000,0
00034
00336
003~6

10000
00335
000:30
00032

00011
00331
00412
00017
00017
00340
000:30
00331
00000
00031
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00004
00027
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00344
00020
32000
00364

00341
00350 21
0035i 14
00352· 47
00353 i3 '(l003!> 00002
00354 14 00000 22000
0035·5 14 36'000 00000
00356 41 00034 'OO3~O
00357 37 00000 00000
00360 21 00031 00011
00361 41 00415 003i6

.. ~ . . . . . . IV

Ml'I-l
Pg. 8 of 8

7/26/56

03M34
03M35
03M36
03M37
03M38
03M39
03M40
03M41
03M42
03M43
03M44
03M45
03M46
AUGOO
AUGOI
AUG02
AUG03
AUG04
AUG05
AUG06
CONOO
CONol
CON02
CON03
CON04
CON05
CON06

CONo7
CONOS

RA OOMOl
MJ 00000
11 CONOO
MJ 00000
TU 02M03
TU 02MOO
TU.02MOO
55 02MOI
TV AOOOO
RP 30000
TP 00000
RP 30000
TP 00000
TP 00000
SJ AUG02
RP 10000
TP 00013
TP CON02
RA AUG04
MJ 00000
24 14061
00 00171
01 00000.
00 00000
00 00000
00 00000
00 00000
00 00000
00 00000

START

OOMOO

CONoa
OOMOI
75756
OOMOO
03M46
03M43
03M45
20025
03M44
03M45
00000
02MOO
00000
AOOOO
AUG06
AUG04
00000
00000
00016
00000
33411
00000
00000
00771
00000
00000
00000
00000
00003

TO ALARM

BRB

INTERCHANGE
R

BRB

0

W
S

TEST TO SEE
IF INVERT
AUGMENT
IDENTITY
B
B

00406

CONSTANTS
F

B

00362
00363
00364
00365
00366
00367
00370
00371
00372
00373
00374
00375
00316
00317
00400
00401
00402
00403
00404
00405

ANO
TEMPORARY
STORAGE

,-.1...

""""'
-..0

r-

r-!

'-'

I

0
r-!

I

0

0

0r-!

t-

><
0..,

10-1dQ

00407
00410
00411
00412
00413
00414
00415
00416
00000

21
45
11
45
15
15
15
55
16
75
11
75
11
11
46

15
11
11
21
45
24
00
20
00
00
00
00
00
'00
4~

00145
00000
00406
00000
00266
00263
00263
00264
20000
30000
00000
30000
00000
00000
00401
10000
00015
00410
00403
00000
14061
00177
14000
00000
00000
00000
00000
00000
00000
00000

00416
00145
75756
00144
00376
00373
00375
20025
00374
00375
00000
00263
00000
20000
00405
00403
00000
00000
00020
00000
33411
00000
00000
00771
00000
00000
00000
00000
00003

00144

RW-177
Ml'I-2
P~.

THE RAMO -WOOLDRIDGE CORPORATION
Los Angeles 45, California

1 of 8

8/3/56

Complex Single Precision Floating Point Linear
Matrix Equation Solver (AX ::: B)
Specifications
Identification Tag:

MrI-2

Type:

Subroutine available on cards for assembly

Regional Addresses Used:

COM, OlM, 02M,

Storage:

185 words total program storage.

O~,

CON, AUG, RWT

Temporary storage used but not stored with
program:
4{n + m) cells directly addressable by
SNIP, and·
n(n + 1) + 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.

Entrance and Exit:

RJ

Alarm:

The

Mode of 01'·

OOMOI

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

!.Lion:

Floating pOint. Complex mode of SNIP must be
act i vated in ES.

Machine Time:

See Text.

Coded by:

w.
w.

Approved by:

ooM02

L. Frank

June, 1956

F. Bauer

June, 1956

10-150

Mr:t-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 ruen and B has the dimensions mon.

'solution, X

=

A-~, is a matrix of size

mon.

The

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

~, ~.

(When B

=

I, one only need supply rows of A).

consisting of 2(n + m} elements (or 2n elements when B

Each row, .

= I), must

be transferred to the first2(n + m} cells of the 4(n + m) cells
of temporary storage provided by the programmer.
The second auxiliary must take the successive columns of X, found

(b)

in the first 2n cells of the 4(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

ta~.

It is also possible to generate the elements of

successive rows when a functional relation exists.
In addition to the 185 words of storage needed by the
subroutine, it is necessary to provide 4{n + m) cells temporary
storage addressable by SNIP and a block of n(n + 1) + 2nm cells,
either all on ES or all on MD.
Operating Instructions

1. Entrance to the subroutine is made as follows (B
P

P

+ 1

P + 2
P +

3

RJ

OOMOI

OOM02

00

OOXOO

OOYOl

uuuuu vvvvv
zzzzz

xxxxx

~

I):

l{W-l"

Ml'I-2

Pg. 3 of 8

8/3/56
where OOMOO is the location of the first word of the subroutine
OOXOO is the location of the first word of the first auxiliary
OOYOI is the location of the second word of the second auxiliary
uuuuu = m (number of columns of B)
vvvvv

=n

xxxxx

= is

(number of rows of A)
the location of the first cell of the block of nCn + 1) + 2nm

cells all in ES or all in Me.

= is

zzzzz

the location of the first cell of the 4(n + m} cells

of temporary storage addressable directly by SNIP.
2.

For the case when B = I J the P + 1 word must be 40

OOXOO

OOYOl (BRR)

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

ooxao

OOXOl

OOYOO

OOYOI respectively.

and

RJ

This implies that the first and second words of both auxiliaries are exit
and entrances respectively.
Alarm Conditions
If a s1ngular' matrix is detected in the process of inversion, the alarm
routine ALR-lis entered and ttsingul_wwwwwtt is printed where
ad<:

a..

OOM41
TP CON03 QOOOO
OOM42
54 03M21 AC057 BRR
OOM43
as ADoeo AUG03
QOM44
TV AUG03 AUG04
OOM45
TV AUG03 02M29
OOM46
AT CON07 AOOOO
OOM47
AT CON07 AQODO
OOM48
as Aoaoo 02M01
OOM49
as AOaQO 02M06
OOMSO
AT CON06 Aoaeo
OOMSI
AT CoN06 Aoaoo
QOM52
as ACOOO 03fv116
as AOOOO 03M21
OOM53
as Aoaeo 03M26
OOM54
OOM55
as AOOOO 03M31
OOM56
RS CON06 00016
OOM57
5T 00016 RWT02
QOM58
RS CQN07 00016
OOM59
TV 02M29 02M30
OOM60
RA 02M30 00016
RJ 00000 00000
OlMOO
01Mal
RJ AUG06 AUGOO
RP 30000 OlM04
OlM02
01M03
TP 00000 00000
01M04
TN 00016 RWT03
0lM05
RJ 00000 00000
RJ AuG06 AUGOO
01M06
01M07
TU 01M02 02MOO
OlM08
54 OlM03 AeOI5 BRR
OlM09
TU Aoooo 02MOl
RA RwT03 00016
01M10
DIM!1
TP RWT03 RWTOI
TP 00013 RWTOO
01M12
OlM13
TU 02M06 02M02
01M14
TP RWTOO 00004
RP 30000 02M02
02MOO
02M01
TP 00000 00000
02M02 LDPM 00000 RWT08 8
02M03
ZJ 02M04 02M16
02M04 lDPM 00000 00000
02M05
TJ RWT08 03M41
02M06 LDDV 00000 00000 B
02~107
TP 00002 RWT08
02M08
TP 00003 RWT09
02tvl09
TP CON03 QOOOO
02MIO
as 02M01 02Ml1
02Ml1 LDMP RwT08 00000
02M12 SUNO 00000 00000 85
02M13
RA 02M11 CON09

SET INDEX
GET I TH ROvJ
AUGMENT

00215
00216
00217
00220
00221
00222
00223
00224
00225
00226
00227
00230
00231
00232
00233
00234
00235
00236
00237
00240
0024i
00242
00243
00244
00245
00246
00247
00250
00251
00252
,,)0253
00254

B BOX
tRANsM1T

tTH

ROW TO ES

00255
00256
00257
00260
00261

00262

S

SKIP IF ZERO

00263

00264
00265

t

N

s:

A

35

35
53
53
53
53
23
36
23
16
21

31
37
75
11
13
37
37
15
54
15
21
11
11
15

00425
00347
20000
00416
00416
00431
00431
20000
20000
00430
00430
20000
20000
20000
20000
00430
00020
00431
00315
00316
00000
00421
30000
00000
00020
00000
00421
00243

00244
20000
00032
00032
00015

10000
20071
00416
00417
00315
20000
20000
00261
00266
20000
20000
00342
00347
00354
00361
00020
00031
00020
00316
00020
00000
00413
00245
00000
00032
00000
00413
00260
20017
00261
00020
00030
00021

00266 0026~
11 00027 0000475 30000 00262
11 00000 00000
14 32000 25031
47 00264 00300

14 30000 24000

00266

42 OO()37 00373
14 32000 20000

00270

11

00271

11 00425

06261
L

11
54
53
16
16
35
35
53
53

11 00002 000a1

00272

00040
16000
53 00261 00273

00273

14 30637 14006

60274

14 1:;000 00000
21 00273 00433

00275

00003

RW-177
MrI-2
Pg. 7 of 8

8/3/56

)2M14
)2M15
)2M16
)2M17
)2M18
)2M19
)2M20
J2M21
)2M22
)2f\123
)2M24
)2M25
)2M26
)2M27
)2M28
)2M29
)2M30
)2M31
)2M32
)2M33
)3MOO
)3M01
)3M02
)3M03
)3M04
)3M05
)3M06
)3M07
)3f'.108
~3M09

RA
TJ
TP
TP
QA
RS
RA
IJ
RA
55
TV
TU
RP
TP
IJ
TP

TP
TP
TP
TV
TU
TP

as
TP
RA
MJ
RS
RS
RA
RA

~3~110

TU

13M11

RS

~3M12

RP
TP
RA
RP
TN
TP

00004
CON05
00021
02MOI
02MOO
02MOO
RWTOO
RWTOI
02M27
02M01
QOOOO
02MOO
30000
00000
RWT02
CON02
00013
CON06
00013
03M16
02M01
00021
00013
CoN09
03M13
00000
03M13
03M13
03M12
RWTOI
03M13
03M13
30000
00000
03MI6
30002
00000
00013
RWT03
00013
00013
00000

CONI0
02Mll
00000

L
y

AOOOO
02MOl
CONI0
CON10
01M14
CONIC
Q0021 'BRR
02M27
02M26
02M28
00000

COMBINE
R
0
W
S

REPLACE
REDUCED ROW
N-2 TIMES

OlMOS
00000
00000
R~JTO 5
RWT03
03M13
03M13
QOOOO
03M12
RWTOI
CONI0
03M08
CON04
CON04
CONIO
CONI0
03M16
RWTOI
03M14
00000

)3M13
13M14
R\lJT02
13M15
03M17
13M16
00000
13M17
00004
13r-118
TP
RWTOO
13M19
TP
RWT06
13M20
TP
RWT07
13M21 LDMP
00000
13M22 ADNO RWT06 00000
13M23
RS 00004 CON10
3M24
IJ RWTOO 03M21
31v125
RwT03 00016
3M26
00000 00000
3M27 PMNO 00000 00000
3M28
ZJ 03M29 03M39
3M29
TN RWT06 00002

NO~~

R

TRANSFER
ROWS OF
UPPER
TRIANGULAR

MATRIX

B
A

L
K

S
B

!l

U
B

S

i

1
T
lJ

I
E

10-156

00216
00271
00300
00301
00302
00303
00304
00305
00306
00307
00310
00311
00312
00313
00314
00315
00316
00317
00320
00321
00322
00323
00324
00325
00326
00327
00330
00331
00332
00333
00334
00335
00336
00337
00.340
00341
00342
00343
00344
003!+5
00346
00347
00350
00351
00352
00353
00354
00355
00356
00357

21 00004
42 00427
11 00025
11 00261
52 00260
23 00260
21 00027
41 00030
21 00313
55 OQ261
16 10000
15 00260
75 30000
11 00000
41 00031
11 00424
11 00015
11 00430
11 00015
16 00342
15 00261
11 00025
53 00015
11 00433
21 00337
45 00000
23 00337
23 00337
21 00336
21 00030
15 00337
23 00337
75 30000
11 00000
21 00342
75 30002
13 00000
11 00015
11 00032
11 00015
11 00015

00434
00273
10000
20000
00261
00434
00434
00257
00434
10025
00313
00312
00314
00000
00246
00000
00000
00034
00032
00337
00337
10000
00336
00030
00434
00332
00426
00426
00434
00434
00342
00030

00340
00000
00031
00343
00000
00004
00021
00035
00036

14 32000 16000
14 05035 00000

23 00004 O()434

41 06621 00341
21 00032
14 00000
i4 24000
41 00357
13 00035

00020
32000
00000
60371
00002

RW-177
Ml'I-2
Pg. 8 of 8

8/3/56

,-...

tt-

......

'-'

0

I

......
I

0

0

0"-

......

t-

><:

0-4

03M30
TN RWT07 00003
B
LDDV
03M31
00002 00000
03M32 STNO 00000 00000 B
tJ RWT05 03M06
03M33
RJ 00000 00000
03M34
03M35
RA RWT02 CON10
IJ COND7 02M29
03M36
RA COMOI CONoa
03M37
MJ 00000 OOM01
03M38
03M39
11 CONOO 75756 BRB
MJ 00000 OO~100
03M40
03M41
TU 02MOO 03M53
T0 o2M60 O3M55
03M4L
03M43
TP CaNOl QOOOO
03M44
as 02M04 03M56
03M45
TP 02M02 AQOOO
03M46
AT RWTOO AOOOO
03M47
as Aoooo 03M54
TP CON03 00000
03M48
03M49
LA AoOOO 00057
03M50
as Aoaao 03M56
54 02M01 AQ057 BRR
03M51
03MS2
TV AOOOO 03M54
RP 30000 03M54
03M53
03M54
TP 00000 00000
RP 30000 01M14
03M55
TP 00000 00000
03M56
AUGOO
TP 00000 AOOOO
SJ AUG02 AUG06
AUGOI
RP 10000 AUG04
AUG02
AUG03
TP 00013 00000
TP CON02 00000
AUG04
AUG05
RA AUG04 CON09
MJ 00000 00000
AUG06
24 14061 33411 B
CONoo
CONal
00 00777 00000 B
CON02
01 00000 00000
F
CON03
00 00000 00777 B
CON04
00 00000 00000
CON05
00 00000 00000
CON06
00 00000 00000
CON07
00 00000 00000
CON08
00 00000 00003
CON09
00 00000 00002
CONI0
00 00002 00000
START
ooMOO

TO AUX 2

TO ALARM

00360
00361
00362
00363
00364
00365
00366
00367
0,0370
00371
00372
00373
00374
00375
00376
00377
00400
O~)401

00402

TEST TO SEE
IF INVERT
AUGMENT
IDENTITY

CONSTANTS
AND

TEMPORARY
STOf112

01,\113
Oll'11L~

011'115
01 16

o li,a 7
OU118

Olr'il9
01[\'120

OlH21
01M2?
01 {,12:3
011',12 '+
011"125

01(·126

01H27
O'lj·~2(1

() 1 ;\1:29

TP OOKOO 00T10
TN OOKOI 00T12
Pfv1NO 00000 00000
ZJ 01H15 01 tvll it
TP OOl~() LiT ~J
() 2 ;\/It'i .:,}
TN
2 :v~O b LDf'[)
02 HO 7 Pf'.lNO
Z ,j
02 :v:08
021'-109
TP

o

021\(jLt

UL'f-.l06

COO2:~·

00(23

0002 Lt

00«24
OO()23

I)O(J;2:;,

00215
00216
00217
00220
00221
00222
00223
00224
00225
00226
00227
00230
00231
00232
00233
00234
00235
00236
00237
00240

INITIAL
VALUES
[

V

A
L

S

U

A
T
E

ROOT
.S
,

~;

00241

S

(ONJUGATL

s

DENOrAINATC)k

OOO(}O 00000

o 2 ~1l 0
001<,01

O?fv109
0(;023

02(·110 LDDV 00029 00023
02,,111 1
TP FOOOO COTOB
i? 1"'11 j~:~
TP COOOu C () T 09
.:~ j'i 1 :' j'~i t~"J ~) I cu I 1.~" 0;,",021
0:2/·114 ;\OS T (;OT06 00023
02;'~1~)
TP OCi6
[)VPH o() T(\II oooou

00267
1< 1\

TE UF

T,]

o ~~ f,1 ~~ ~

nOKO?

O?f'i 179

Ct'IAf'jGE

Til

OOf~:OO

FOOOO

FI 1

no:>

l' r>

J

\ j

.<

() 21

I

:': (Os

() 2 r-,/I ~~ f)
(',

\)

{: (~j () () (')
0]
! i)I·1P F: OOt) O('}T (i
r1 ,J 000(10 O?li 1.:3,
)\ t) rJ t) Oi,)TOl> OUOOD

"j I·'

f-

T f') C)

I)(i

i

0026 /"

J

U

IN

00270
00271
OO?7~

0027'i

0027 't

..:.::

,-I

00275

00276

Tl

00277
00300

CUTll

10- 1711

11
13
14
47
11
14
14,

14
14
14
14
If 7

14
1 it
13
13
14
14
14

]4
14
13
14

00367
00370
24000
00222
00]71
30041
04045
14051
30043
34033
30045
00231
30045
04002
00002
00003
04002
15027
10033
05031
0·4027
00003
30002
00245

46
13 00027
] 3 00030

14 30031
14 2'.000

47 00253
11 00370
14 30035
11 00002
11 00003
lit
I lt
11
11
1'+

00053
00055
00000
00221
00043
14051
34027
34031
14053
11027
24000
00315
14053
00000
00035
00036
14051
30045
14053
14002
51027
00003
14031
00247
00027
00030
05027
00000
00252
00027
20027
00051
0005~

1 L+O j 5 34033
OL.047 34027
00372 OOOO'i
00057 00037
00062 30060

) (I
1 Lj O? 7 0(;060
2J 0000 if OOj7t~
I. J 00037 0026~~
11 00002 00031
11 00003 00032
1 il 200l.t5 2L~OOO
00371 00360
1-.1 ] 00367 00002
1 ] OCl(J15 onOO'1
I/j
J 000;2 15051

,

')

1.1 I)

00000 OO?56

1 '+ o 40~) 1 00000
1 ] ()OOO? nOO~)3
} 1 OOOli;~ 0005'+

I~W-179
.POL~O

Pg. 10 of 11

9-4-56

o ;:~ 1'''137-

TP 00025

OOTOt~

TP 00026 00T05
o ~~ i·n 3
02,\134 LDDV 00T12 00r06
02 r·1J5 PrvlNO 00000 00000
o2 ('·i?)6
TJ 00K04 021v144
02 fv'13 7
TP 02M34 AOOOO
02,·'138
TU 00/Y106 02~"39
02/yi39
TJ 00000 01Ml5
O? rv1L~ 0 LDST 00T04 00008
02 i'i/t 1 LDST 00T06 00006
02HL~2 PDNO 00010 00000
02 [V1 l t 3
~-1J 00000 01 fv1l5
O;~H44
TP OOT06 00006
021\145
TP 00T07 00007
(i 2 Iv; Ii- 6
TLl 001\118 00004
TP OOKO'? 00031
02H47
o 2 i~ f~ H
TP 00013 00025
TP 00013 00026
CI 2 r'v~9
o?r,i~)O LDST 00000 00023
o;~ I.r·i66

(1 ?il(/"I
U ;:~ ;.\1) (~

TEr~ANT

I

003C]
00302
00303
00304
00305
00306
00307
00310
00311
00312
00313

00351
00352
00353
00 3 5L~

00355
00356
00357
00360
00361
00362

~

'l
oJ

00031
00032
30055
24000
00373
00303
00150
00000
30045
30047
74012
00000
00047
00050
00164

00045
00046
20047
00000
00315
20000
00310
00222
34010
3'+006
00000
00222
00006
00007
00004
00376 00037
00015 00031
00015 00032
~3 2000 34027
30031 l.{~O 47
OLtO 27 34031
30027 14047
06002 34027
00004 00372
00037 00324
3 000 L+ 00334
00027 00010
30031 24000
00336 00342
30027 00000
21031 10047
00002 00047
00003 00050
00 1 Lt 2 0000'1-

15
1/+ 300 I" 7 3600't
l't 74012 00000
14 34006 2 LtOOO

7 00350
4 c 00000
14 30031
14 25010
it

.)

00352
00353

20047
00000

l't 7 '+012 7 II-a 12

41 00057 00170
21 001 't3 00020
'+5 00000 00143
1 1 00347 00344
45 00000 00146
11 00033 00055
11 00034 00056
11 00027 000 1+ 7

I{W-179
:PO"['",O

Pe. 11 of 11
9"J+~56

02M82
02 (V18 3

02"'184
02M85
aOKOO
00K01
OOt(02
OOK03
OOK04
OOK05
OOK06

OOK07
S T Af< T

TP 00024 OOT07
TP OOKOI FOOOO
RP 30004 02M29
TP 00T02 OOTOO
05 00000 00000 -01 F
F
01 00000 00000
1 F
01 00000 00000
00 00002 00000
01 00000 00000 -04 F
PDNG 00010 00000
00 00004 00000
00 00000 00000
OOMOO

C
0

N
S

T

A
N

T5

lO-lW)

00363
00364
00365
00366
00367
00370
00371
00372
00373
00374
00375
00376
00000

11 00030 00050
11 00370 00002
75 30004 00276
11 00043 00041
20 04000 00000
20 14000 00000
20 45000 00000
00 00002 00000
16 36433 34212
14 74012 00000
00 00004 00000
00 00000 00000
itS 00000 00142

1
t.

J

- ..,

-.;'

\.l

PACE
f-(

••.. \ ' .

EPOHT NO.

MODEL

Ii

DAlE

IC-012-1
ZH 491
ALL

July 5, 1956

U1JPlI.Cl:ED FLOATIHG POINT CtlnD OU'ITUT

'l1liti routln,) \JritoiJ up to fivo duciInfil point nUlLlbors on cards fl..om.
() i thor r;S or f·1l)
VrUll\ t,Jdrotlu

/ ~/2013---72.357 inc.

HI..uuour of in:Jtruotiono

270 octal

55 ootl11

Conti V.lntu

E!3 bddri.H3tJ (incl u..1 l.ng tomporllr1.(Jtl) OlOOO-OlJ.42 ina ..

71760--'l2012 ino.

lJr1vor

of ·tho dl'lv(H", with gS utorod nturtlng tit 74001.

All constanta nuodod aro Includ0d in tho routlnu.

37

01001

01002

AB

llUOUlJ

vvvvv

To I1l'lO uf:l u

nu heuu tJ flU

~J~1 th

tho dr1.vor tho

HI.)qUtmcu

f.lhould 'btt!s

)'/

AU
I.

In

C/UW

UUUOiJ

vvvvv

of bull fttJ lurti n ntr\rt n t PAK

10·-I.OJ

~

7')007 \Jill rootore ES and

CV-IOO
IC-Ol?-2

I'AGE
'''/

(
.;"'

..

11

~. !\

ri

i

j

i

r'

l'

Z~·1

rU::rOHT NO.

)

DAYE

rio.

If)\ 10 oqunl to 4, 5, 6 or 7 tho cords viII not be numbered ot.herwiflo t.hey

\1')1 be numt\Hrt~d
j'ty

/,..91

ALL
July 5, 1956

MODeL

. ; . ,'t

bn not

lit

8

0)11 01270 (72303) corlUlins this cou.nter and

trtTting at one.

one leBO tlw.t1 tho noxt po::dtiVt'l

CH1~d

numhor desired.

Ut/UUll i:l tho otol'nge addrosa of tho first nnnt1ssa

6, 21,

J(l t

18--19,

51, 66

JJ--'31~,

dQc1n~.il

point punched in cArd.

4e·--4?, 63--61q 70-79, 6Xf\()nanta (po\.lor of ten)

r8.n~ft

99 to 99
20, 35, 50, 65, 80

sl~nB

of

oxr~nont.

!

No prjrno

COf[l;'hI1nds

nro includod.

17

00000

7231...2 will a(ivl.trlco

8

",neh ca.rd.

i

abov.,

I
I

~~f)ro.

In addition nn nlnr'lfl

\-1.111 occur on tho typ"\Jrl t·~~ r

li:3tjn(~
II

of tho f'irot f1uoh nddres8 f\nd mtlntis8t\

t the ond of tho lnnt

0((1:"<1

lind

II

56 tltop \1111 occur

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

FORM NO. E T .. 1 (i'· F

SAN DIEGO. CALIFORNIA

UNPACKED FLOATING POINT CARD OUTPUT
71760

007l~5

56 00000 30000

71761

00746

STORE

71762

00747

75 31777 71763
11 00001 74001

71763

00750

75 30400 00752

71764

00751

11 71760 00745

ROUTINE
TO E S

71765

00752

31 00145 00000

SET

71766

00753

36 01310 72011

71167

00754

16 00745 00772

71770

00755

21 00772 01310

71771

00756

55 00745 20025

71772

00757

l~4

71773

00760

32 00777 00000

71174

00761

55 20000 00017

REPEAT
SET
EXIT
f'10D I FY
E S
ADDRESSES
TO STORAGE

11775

00762

37 00762 00763

7177.6

00163

16 20000 00764

71777

00'164

71 01310 30000

72000

00765

55 20000 00006

72001

00766

37 00762 00757

72002

00767

55 20000 00017

72003

00770

37 01001 01006

72004

00771

11 01270 72303

00761 00760

72005

00772

75 31177 30000

.-,
f.I...

72006

00773

11 74001 00001

!

72007

00774

75 31777 72011

72010

00775

11 14001 00001

"'-;.

72011

00176

72012

00777

30 00000 00000
74 00000 OCOOO

72013

01000

72014

01001

30 00000 0000*
45 00000 30000

72015

01002

16 01001 01005

72016

01003

21 01001 01310

72017

0}004

36 01344 01000

-

E 5

. ACQUIRE
CONTROL ~JORD
EXAMINE
FOR E S
ADDRESSES
TO SUBROUT I NE
STORE CARD NU~-'BER
RESTORE
E S

,~

"'""
~~

-::J'

>

..

'W

~
fl..

RESTORE
E S
REPEAT
E S STORAGE
REPEAT LAST tNsr

EXIT

CV-IBO
1C-012-3
REPORT
ZM 491
PAGE

MODEL

All

DATE

7-5-56

lET, . i

rfr,

CONVAIR - DiviSION Of; GENERAL DYNAMICS CORP.

F

SAN DIEGO, CALIFORNIA

UNPACKED FLOATING POINT CARD OUTPUT
72020

01005

71 01310 30000

72021

01006

15 20000 01026

72022

01007

13 20000 01347

72023

01010

11 01310 01350

72024

01011

31 20000 00025

72025

01012

31: 20000 00063

72026

01013

36 01310 01351

72027

01014

46 01001 01015

72030

01015

17 00000 01327

720~1

01016

31 01351 00000

72032

01017

11

72033

01020

11 01325 10000

72034

01021

42 01342 01024

72035

01022

11 01306 01352

5 PER CARD

72036

01023

11 01324 10000

t~JR

72037

01024

17 00000 10000

72040

01025

75 30012 01027

72041

01026

11 30000 01353

72042

01027

75 10045 01031

12043
72044

01030

11 01307 Olj76

01031

15 01266 01050

72045

01032

72046

01033

11 01340 01374
11 01265 01375

CARD INSTRUCTION
5 HORDS TO
STORAGE
CLEAR FOR
CARD I ~1AGE
SET ACQUISITION
erT

72047

OID3 l •

41 013!J7

OlOI~7

72050

01035

11

01~32

01374

72051

C1036

21 01210 Oljl0

72052

01037

42 01315

72053

01040

31 01341 00000

72054

010'+1

32

72055

01042

32 01265 00000

72056

010'+3

73 01315 01365

72057

01044

54 01365 00001

~oooo

01352

010/~1

01301 00043

FIRST ADDRESS
FLAG
FLAG
EXTRACT
AND STORE
N-1

TEST FOR ZERO
PIC K \~ RI TEe ARD
N-1 PER CARD
~JR

I TE

I TE AND pICK CARD

BIT

INSTRUCTION

I DENT Nur,18 ER
BIT
COUNT'CARDS
5 I ZE OF \'!ORD
SET

999~9

INTEGER
TO
FRACTION
2 EXP 36

10-184

CV-100
1C-012-4
REPORT
ZM 491
PAGE

TE~)T

MODEL

All

DATE

7""5-56

FORM NO. E. T .. I

O~

'-Cit'ivAIR - DIVISION OF GEN~RAl DYNAMICS CORP.

f

UNPACKED FLOATING' POINT CARD OUTPUT
72060

01045

11

72061

01046

37 01200 01165

I DENT NUt,1BER

72062

01047

75 30002 01051

~1ANT

72063

01050

11 30000 01365

72064

01051

11 01365 01370

MANTISSA SIGN FLAG

72065

01052

54, 01366 00030

EXPONENT

72066

01053

54 01366 00060

72067

01054

12 20000 20000

72070

01055

42 01301 01067

72071

01056

41 01350 01062

FIRST T It·1E

72072

01057

11 01264 01370

~1ANT

72073

01060

75 10002 01156

SET EQUAL

72074

01061

11 01307 01365

TO ZEPO

72075

01062

13 01322 01350

72076

01063

11 01026 ("11345'

72077

01064

15 01050 01065

72100

01065

11 30000 01346

72101

010'66

45 00000 01057

',72102

01067

11 01365 20000

72103

01070

It 7 01071 01156

72104

01071

46 01072 01073

72105

'01072

13 01.365 01365

NEGATIVE MANTISSA

72106

01073

16 01323 0112'3

SET SHIFT TO 33

a
ro
r-i

72107

01074

32 01307 00001

EXP36

'-"
I

72110

01075

I}

~

72111.

01076

11 01307 01373

CLEAR FOR DEC H~AL EXP

0
C1'

72112

D1077

11 01366 20000

EXPONENT

t-

72113

01100

If

72114

01101

23 01373 013 l t2

10 EXP 5 ADJUSTMENT

72115

01102

11 01307 01.372

CLEAR FOR 74

72116

01103

71 01315 01365

X 10 EXP 5

72117

01104

7l~

a

I

0

01306 01376

3 20000 01056

N-1 DIGITS

r SSA

AND EXPONENT-

EXTENSION
EXPONENT
FLOATING TEST
I S SA FLAG

SET ALARr 1 FLAG
v

ACQUIRE
r~ANT

ZERO

I SS A

~1A~lTISSA

FLOATING TEST

r-i

~

Cl..i

6 01101

2nooO

01117

01372

CV-ltlU
PAGE

SAN OIE;GO. CALIFORNIA

SIGN

IC-012-5
491

REPORT

ZM

MODEL

All

DATE

7-5-56

) E. T .. 1

J~

CONVAIR - DIVISION Of GENERAL DYNAMiCS CORP.

,.

SAN DIE-:>O. CALIFORNIA

UNPACKED FLO/\TING POINT Cl\RD OUTPUT

01106

11 20000 01365
[,,6 01107 01114

TEST FOR ROUND

12122

01107

21 01365 01j10

ROUND

12123

01110

43 200(iO 01114

72124
72125

01111

31 01365 00107

01112

i1 20000 01365

72126

01113

21 01372 01310

72127

01114

21

72130

01115

12131

01116

46 01101 01116
31 01366 00000

72132

q1117

73

72133

01120

11 20000 01366

ADJUST RSF
SIGN OF 8SF
DIVIDE EXP
BY 33
EXPONENT REt·1 AI N[) ER

72134

01121

55 01365 00001

~1ANT

I ssA

72135

O~122

45 00000 01152

72136

01123

31 01365 30000

~;lANT

r SSA SHIFT

72137
721'40

01124

11 20000 01311

STORE AR

01125

34 20000 00044

ERASE'

72141

01126

11 2('1000 01365

STORE Al

72142

01127

75 20013 01426

72143

01130

l,,2 013'10 01131

TEST FOR l/l,RGER
PO\'JER OF rEtJ

72144

01131

51 01330 10000

72145

01132

31 01311 00000

72146

01133

36 10000 1('1000

72147

01134

"r;
.../_.,

72120

01105

12121

01~66

01~2~

01372

01367

01373 n137?

72150

01135

31 10000 00017

72151

01136

35

(l

72152

1"\11~~7

:~ t'\

r,"',rr·n

7"?)~"

r'1, : ' r'J

1

~

- .......,

i

~~

'1

{--

l

"\

MANT ISSA.
AND
ADJUST

10 EXP 1(1
INCRE/\~·F

f'J

exp

2 E:,,:r 15

v

/\

L! C, J 1\1.1:7

(""

....

'.

1"f".'1""

..

-"""\

,\CQ'! I RE [, I \1 I (' C' ~

-".....

r' r~') TO~E
t\
[)~

r 35

:~ f"

36

(;v ... UjU
PAGE

IC-012-6

REPORT

ZM

MODEL

All

DATE

7-5-56

491

\.VNVAIK -

UIVI!:IIUN VI'" (;;tNtKAL UYNAMI(,;)

(;ORP.

SAN DIEGO, CALIFORNIA

U~!PACKED

.0

co
r-I

-I

0

r-I

I

FLO;\TH!G

01145

31 20000 00001

D E TER~~ I

7'2161

01146

42 01372 01150

LAST

72162

J1147

27 10000 01310

BIT

72163

01150

11 10000 01365

72164

01151

37 01151 01152

72165

01152

41, 01367 01123

72166

J1153

16 01366 01123

72167

0115 l \-

37 01151 01123

72170 ' 01155

11 01373 01366

HIGHER ORDER DIGIT
LOI:!ER ORDER SHIFT
LOVIER ORDER DIGIT
DECH·1/\L EXPO~l[N T

72171

()1156

21 0101)0 01326

STEP

72172

01157

21 01026 01326

72173

01160

37 01200 01174

72174

01161

12 01366 20000

72175

01162

11 01333 01376

72176

01163

73 01311 01372

STEP
SHIFT FOR PERIOD
EXPONENT
TALLY
DIGITS

72177

01164

72200

01165

11 20000 01371
31 01365 00002

72201

01166

32 01365 00001

72202

01167

11 20000 01365

72203

01170

34 20000 00063

72204

01171

35 01375 01172

72205

01172

30 00000

72206

01173
01174

SHI FT 8IT

01175

37 01173 (i117'+
55 01374 000'+ 3
44 01176 01177

ADVANCE

7220"
72210

O()OOi~

0

72211

01176

21 01375 013 3 L~

72212

01177

41 01376 01165

72213

01200

37 01200 01201

72214
72215

01201
01202

11 01370 10000
44 0120.3 01205

72216

01203

13 01331 20000

72217

01204

37 01173 01171

r-I

l-

I><
0..

CARD OUTPUT

72160

0'

0

POI~lT

~,I E

ANSVJER X 2 EXP 36

OF EXP

EXTRACT
Af.lD

POSITION
DIGIT
ASSEn8LE INST
SET BIT

FIELD
TEST FOR END

SIGN

~V-ltjU

PAGE

IC-Ol2-7

REPORT

ZM 491

MODEL

All

DATE

7-5-56

10 E T. ' 1

.f~

"

PAG~!~

SAN DIEGO, C .... LIFO~NjA

: 1M"·

REeQ~T
MODEL

DATE

UNPACKED FLOATING

~OINT

CARD OUTPUT

SHIFT 8 I T

01206

55 0137 1• 00043
31 01206 01201

72222

01207

31 01312 00011

TENS DIGIT

7-2223

01210

37 01200 01171

72224

01211

31 01311 00017

12225

01212

37, 01200 01111

72226

01213

11 01266 01370

72227

01214

31 01206 01201

72230

01215

37 01215 01216

72231

01216

41 01352 01047

72232

01217

11 01335 01371

72233

01220

~2. 234

0.1221

'·72235

01222

21 01377 01336
21 01411 013:36
21 0140t~ 01336

72236

01223

21 0141:3 01337 .

72237
72!240

01224
01225

21 01425 01337
21 01420 01337

72241

01226

16 01267 01233

72242

01227

16 01127 01224

7.2243

01230

15 01267 01231

72244
72245

01231
01232

55 30000 (i'OO10
77 00000 10000

72246

01233

71 10000 30000

72247

01234

77 10000 30000

72250

01235

23 01231 01331

722~1

01236

2~

72252

01237

72253

012'+0

12254

012'11

72255

'012'+2

23 01234 01310
It 1 01371 01231
23 01351 01342
46 01243 01016

72256

01243

72257

01244

72220

01205

72Z21

0123~

UNITS DIGIT

\'/ORDS PER CARD
SIT FOR 12 ROt'JS

01210

41 01350 01001
75 10005 012 L.. 6

TEST FOR END OF CARD
TEST FOR
END

FLOATING FLAG

10-188

lti~12-8
~)j

491

'11

7-5-56

FORM NO. E. T .• 1

(I~

SAN DIEGO. CALIFORNIA

UNPACKED FLOATING PO H·lT CARD OUTPUT

0

0)
.-4

'-'
I

0

,
0

r-I

0

0'

;-I

t-

:><
c...

J

8

> Dl
6 >n

0 (mod 6) J let multiple of 6

~

0 (mod 6);' 1st multiple of

it n

I

0 '(mod 6)

.,0 (mod 6); 1st multiple of 6 > B if s

~

0 (mod 6)

lJl 11
:I

•

", 0

(iqpd 6)

PI

non-zero for A changed from cards to storage, otherwise zero

P2

non-zero for B changed ft'om cards to storage, otherwise zero

p)

non-zero for transpose of product wanted, otherwise zero

IO-Il I 5

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

CV-181

CONVAIR

ANALYSIS

W. J. stoner
J. P. Wilkinson

PREPARED BY
CHECKED BY

A DIVltlO.

(W • • • '!tAL

Dylt,..laI c:o...OllAnOIl

SAN DIEGO

PAGE
REPORT NO.
MODEL

DATE

REVISED BY

eN 015-6
ZM 491

All

8-9-56

non-zero for additional multiplication to do, otherwise zero
contents of a temporary storage cell in E.

s.

any _trix element on MD
any matrix eleD¥!tnt in ES after card read when

PJ.

or P2 ~ 0

one of a consecutive group ot elanents which Is forned In
ES be tore transfer to M.D.

The group Is a

rOll

or

A or a colUlQll

of .B on oard rea.d w1 th P or P2 ' 0, is a oollll'lln of C during
l
IIl1ltlp1icatlon, and Is a row

P4

a

0, p) .;

ot C it P4 .; 0, p)

o.

~

an element ot the Ith rov ot A

~

an al.mot or the kth column of B

1 (

)

location of quantIty in parenthesis

~J Bro, el-

indicated -.tr1:x: stored by rova

l

indica ted

0,·'

Ba, Co

DIB. trix

stored by

10-196

ool~s

::II

0, or if'

CV--181
ANALYSIS
PREPARED BY
CHECKED BY

W. J. Stor,er
J. P. Wilkinson

CONVAIR

PAGE
REPORT NO.

A .IYI.tO. 0' .1111( UL DYNAMIC. cO.l'OllAnON

SAN DIEGO

MODEL

REVISED BY

DATE

GENERAL

FLO

eN 015-7
ZM 491

All

8-9-56

CHART

\,AI

I/-DooD

Ac:t;"4te flip.
SLIm pYojYdm.

Print

Sum.

Ke4d 3 '«rJs
F,r

Pdrfltnet~".

~_""d fld.

j S.
CDm ute ~./~.

:uo

c.; ~A

C,..~A
0fr;D71~1 IJlltfCl.(

OfJ~io7l~1 Ol/tput.
"""~'7\"

~~?t

l1'\.o

o,k.
fie4d 1 Ccird (IJ7"
pdrf'/-mflte rs d nd

fIe".
Co -m p

1

\,f

t e Ie· 4'.

D./( .

Mt.lltiply
A,. A ~;:

C~~A
o~tpu.t

Orl.tput

170

Cc •
STOP

CONVAIR - DIVISION OF GENERAl DYNAMICS CORP.

CV-181
eN 015-8
REPORT ZM 491
P>\GE

(ONTINUOUS

MATRIX

MULTIPLIER

40000

45 00000 40001

40001 ..... (PAlO

40001

37 70160 70140

40002

00 00000 00000

4000'3

31 40000 00000

40004

75 20621 40006

ACTIVATE FLIP
FLAG
CHECK
SUM

40005

32 40001 00000

40006

40007

11 20000 10000
75 30231 00160

!~

00 10

11 40020 0014(')

i. 00 11

00 00000 00000

40012

00 00000 00000

4001~

40015

00 00000 00000
00 00000 00000
00 00000 00000

40016

00 00000 00000

401:)17

00 00000 00000

l.0014

PROGRAM

SUM ...... (a)
STARTER AND CARD READ
TO ESt 160 -+- (PAK)

00 4n6"3('J

4n6~(l

i ( (1", ) " Z IS+

~(\42n

I)n42<"

.e- Ct-,)

I (Il"

)

~~OO22

"()140
00141
00142

I.~OO23

00143

00 60210 60210
00 00377 01117

4')024

00144

00 00106 00100

~ 15 ... I( t,,)
.,e (",) JI.( IS of t (e,,)
R. (d, J) ... :J I 5 +- K ( ~ Ii )
.e (,.,-rl).( ). 15 1'" il ~,)

40025

00145

4

4· ('\1j20

4 0(' 21

"(l

.R.. ( -If, ~:<

·4-0026

00146

00 00000 00103
00 07717 00000

40027

00}47

00 00077 00000

2

0030

00150

00 00000 00006

6

4<"031

("l{ltll; 1

n0 OOO()O "~572

378

.~C032

00152

CO 00000 07571

3961

t)o~.,

nn15~

~o

('IO('lO()

n0301

034

0Ol!54

00

noooo

00000

4- ~')o

35

00155

00 00000 00000

t+

~16

00156

00 00000 00000

';.

37

00157

00 00000 00000

~+

II

lQS

10-1.98

15)

DIGIT U-EXTRACTOR
DIGIT U-EXTRACTOR

MODEL

All

DATE

8-9-56

GV-HH

CONVAiR - DIVISION OF GENERAL DYNAMICS CORP.
PAGE

CONTINUOUS

---.
..-4
co
..-4

,

MATRIX

PRINT

40042

61 00000 ('10042
00162 (55 10000 00003

OF

40043

00163

51 00067 20000

40044

00164

35 00042 00165

40045
40046

00165
00166

30 00000 00000

41 00121 00161.1

40047

00167

17 00000 73376

READY CARD REPRODUCER

40050

00170

1457 1010 ·0106

READ ?rt-....... (106)

40051
40052

00171
00172

1451 1010 0107

READ 11 ..... (107)

1457 1010 0110

READ ~ - P (110)

40053

00173

11 00106 20000

"Yt1

40054

00114

42 00153 00116

IS 193

40055

00175

37 76000 76001

40056

00176

40057

00177

11 00107 20000
42 00153 00201

NO. ALARM EXIT
YES. 'il ...... (A)

40060

00200

37 76000 76001

NO. ALARM EXIT

40061

00201

11 00110 20000

YES. A3,I --... (A)

40062

00202

IS 193

40063

00203

42 00153 00204
37 76000 76001

NO. ALARM EXIT

40064

00204'

11 00041 00121

YES. SET INDEX

40065

00205

15 00144 00210

i!. ( 7"11)

40066

00206

16 00144 (10215

~t

40067

00207

16 00145 00217

40070.

00210

40071

00211

73 00150 10000

00160

40041

(10161

"-'

1T1

30000 20000

> ""n1.?

r

IS 1.,3 ;> "1'1

>

r

~

--+-.((.111 J 7l J

dJ)

/(,) .-.,(( If;,)
~ (k . ~' J5) ~.f( Ir (; 2. '5)
J(

",)?I, ?'lJ OR .4/

(A)/6 .....,.

-+

to).

(A)

REM --,.{

47 00213 00214

40013

00213

21 10000 00074

IS (A)=O?
NO. (Q).,. 1 -+

......

40074

00214

71 10000 00150

YES.

><
0..

40075

00215

11 20000 30000

(R) ~Jr;.

40076

00216

54 20000 00017

( A)

4:"071

00217

11 20000 30000

(R)

t-

8-9-56

FOLLOWED BY FLAGS

-+ (A )

00212

0
0
0"-

DATE

SUM

40072

..-4

All

CHECK

I

0

ZM 491

MODEL

MULTIPLIER

11 00057 00121

40040

eN 015-9

REPORT

J(

(a)
2 15 - t

~ 6 --.( A)

(A)

-+ if. \'2'
{

(oJ

A)

CONVAIR - DIVISION OF (.. fNERAl DYNAMICS CORP.
SAN l>lf('O

PAGE

,L1FORNi ...

REPORT

CONTINUOUS

MATRIX

MODEL

All

DATE

8-9-56

MULTIPLIER
,£ (;,t., 'It, ,4,) + I -+.(1 ( "MI

00221
00222

21 00210 00073
21 00215 00074
21 00217 00074

40103

00223

41 00121 0021...2.J

TEST IND!X

40104

00224

71 00106 00101

-1n r

40105

00225

42 00152 00227

IS

40106

00226

37 .76000 76001

NO. ALARM EXIT

40101

00227

71 00101 00110

YES.

40110

00230

42

40111

00231

'37 76000 16001

J.;':I (4,... ..?
NO. ALARM EXIT

4°112

002~2

71 001 00 00110

YES. J?,

40113

tl023:3

4' 00152 00235

J 5 ~ q61

40114

00234

37 76000 76001

NO. ALARM EX t r'

4(\115

('10235

71 00106

40116

00236

42 00152 00240

40117

00237

37 76000 76001

40120

00240

56 30000 00241

40121

00241

11 00111 20000

40122

00242

47 00243 00250

IS f, ::: 0 rYES. 250

40123

00243

11 00100 00121

NO.1(.

40124

00244

11 00106 00122

40125

00245

11 00140 ·00123

40126

00246

37 00300 00301

CHANGE AC TO AA., ANO STORE

40127

00247

45 00000 00255

255 ..... (PAK)

401'30

00250

16 00140 00251

..f (Ci. II )

40131

00251

h457 0773 0000

40132

00252

21 00251 00151

40133
40134

00253
0'0254

11 00004 20000
47 00255 0025.!J

I S (A)

40135

00255

11 00112 20000

NO.

40136

00256

47 00257 OOZ64

r Sp<.- =0

40137

00257

11 00102

40100

00220

40101
40102

CV-181
eN 015-10
ZM 491

O~152

00232

nOlO~

~Ol~l

-t'l

4/)

£( i( ;1+/ ..... i( I(-i)
.R ( ~4' ~ 2 15) ..,. I -. .i' j, ~ ~ '9

"

If'). -.... (A)
3961 >- /IYt ~ 7
J(

n t4t-+
~

•

(A)

>

IS 3961

YES.

;;z

K

41 -.....

;> itI

?11.f

(A)

K  I?tt (.;;J
NO. ALARM EXIT
YES. MS-3

P, -..

?

.

~

(A)

....,. (PAt<)

....,.. I,

r~

",., -+

)(Q,,) ....... I)

-..-

if fli j)

6~ CARDS INTO f (~ )ETC.
P{f/i;) + 378 -.,.ftQi)d

READ

(00004) ___ (A)
,? YES.

251 ~ (PAK)

P:z .... (A)

NO. ~3

10-200

=0

I

.' YES.

-.....

I,

264

-+- (PAK)

CONVAiR - DiVISION
~A"'"

CONTINUOUS

MATRIX

0

CV-181

.. GENERAL DYNAMICS CORP.
)

CALIF-'OHNI'

PAGE

eN 015-11

REPORT

ZM 491

MODEL

All

DATE

8-9-56

MULTIPLtER

40140

00260

11 00110 00122

40141

00261

11 00141 00123

40142

00262

37 00300 00301

40143

00263

45 00000 00271-

40144

00264

16 00141 00265

40145

00265 (1457 0773 0000

40146

00266

4 0 147

-+

,.IV''''
5"

\
DII

\.7C"'CK~L

V I '''~'Vl'\'';)

\.Vl\r.

""'-101
PAGE

CALIFORNIA

-

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

CN 015-12
ZM 491

All
8-9-56

MULTIPLIER

40200

00320

47 00323 00321

IS (A)

=0 ?

40201

OO~21

11 00125 00126

YES.

15 -+

40202

00322

11 00132 00133

l,Z

40203

00323

71 00124 00132

NO.

40204

00324

Il 00141 10000

2 DIG IT U-EXTRACTOR

40205

00325

53 20000 00327

SET NO. OF CARDS TO READ

40206

00326

53 00132 00364

SET NO OF r!4., TO TRANSFER TO MD

40207

00321 11457 0000 0377

40210

00330

16 00123 00365

40211

00331

21 00365 001il

40212

00332

21 00131 00125

I II + 15 '-"'" 1/1

4021~

003'33

11 0(,004 2 00 00

(000"'4)

40214

00334

47

40215

00335

11 00064 00127

NO. 63 - + 17

40216

00336

16 00143 00350

~(Y;) ...... ((-,:

40217

00337

21 00350 00126

R( r,) T I, .......i( '1: .,.,)

40220

OO~40

31 00101 00000

1iJ, .... (It)

40221

00341

34 P0107 00011

(itJ-hl.) ~2'!---- (It)

4 0 222

00342

11 2 0 000 00124

4022:!

00343

11 00146 10000

(RJ ..... III
1+ DIGIT U-EXTRACTOR ....... (Q)

40224

00344

53 20000 00341

SET NO. OF

40225

00345

21 00124 00133

40226

00346

53 20000 00364

1,# Jr 1'3 ....... 11,4
SET NO. OF)-:.tr TO TRANSFER TO MD

40227

00:347

75 10000 00351

SET PROPER

402:30

00350

11 00040 30000

40231

00351

11

4 0 232
40233

00352
00353

11 00040 00130
00141 00360

'40234

00354

21 00360 00130

-f ( d,~ , + I,O ...... i ( '<
0...

A

I

37 73374 73374

0

262 ..... (PAt<)

(PAK)

......

<.

A

IF ON.

00264

I

~

c'c

. PUNCH

40364

.-i

NEW SETUP TO ES

MS-l

PUNCH

,
0

8-9-t"6

Plf .... lA)
IS R't = 0 .?

37 00350 00351

'-"

DATE

11 00114 20000

00263

.-i

All

00240

IS R~

11\

1)1\t:::

491

ZM

MODEL

40340

AND

eN 015-15

REPORT

MULTIPLIER

40363

co
r-I

CV-181

DIVISION OF GEt ERAL DYNAMICS CORP.

ALL CARDS PROCESSED

,-urn AIK

-

AL DYNAMICS CORP.

UIV')'UN Ot' utNt

GV-HH
PAGE

CONTINUOUS

MATRIX

ZM 491
All

DATE

8-9-56

MULTIPLfER
ALARM EXIT

EXIT

40402

00301
00302

37 76000 76002
45 00000 30000
16 00143 00312

40403

00303

21 00312 00110

flY,' ) I-- 41 --+ R ( r~ +1)

40404

00304

31 00102 00000

rt3

40405

00305

34 00110 00017

(¥?3

40406

00306

11 00146 10000

4 DIGIT U-EXTRACTOR ...... (a)

40407

00301

53 20000 00311

40410

00310

53 00105 00325

SET NO. OF Y6 TO BE ZERO
,
SET NO. OF ROWS OF Cc.

40411

00311

15 10000 00313

SET PROPER

40412

00312

11 00040 3.0000

40413

00313

11 00040 00122

a -.... 1:l.,

t.0414

~O'314

f( ~'I) ....,..

4041~

(\O~1-;

15 00142 00~?1
16 00140 00326

404()()

00300

40401

40416
4 0 417

00316

lli

00110 20000

R(r;) -+- R( Y

f

}

~ ({ (A)

40462

00362

73 00064 00122

NO.

40463

OO~63

11 20000 00121

40464

00364

23 00122 00074

40465

00365

11456 0173 0000

40466

00366

1"""'1

co
1"""'1

40467

00367

'-"

4047()

1'If)~70

I

40411

00371

0

40472

00372

11 ljf)l21 ,-'1(\00
16 0036t; OO!'7S
54 20000 00017

40473

00373

11 00147 10000

40414

00374

53 20000 00375

2 DIGIT U-EXTRACTOR - . (Q)
SET NO. CARDS TO PUNCH

40475

00375

1456 0003 0000

PUNCH ~ARDS

40416

00376

45 00000 00360

TO EX to.

I

0

.......
0

C1'

00150 20000

21 00365 00151
41 00122 0036~

~,t4J'" (A)
......... (A)

,f(c,,)

EXIT
1)''' lA3-+ fA)
( tJ/6

~(A)

R(a,,) --fIoo j' ( d "-f )

(A)

l•

........

(1J163
--+-

1..2. - 1

YES, 371 -+ (PArJ
I:l,

t

REM

...... (A)

I,
~

tz.

PUNCH 63 CARDS STARTING AT

J ( d.<'/) + 37 g -+ f( cJ"j)
TEST INDEX

lZ -+- (A)

~ ( d;. i) --- f (d i J')

(A) x 2'/S....... (A)

1"""'1

t~
~

40471

00 00000 00000

i(d"J)

CV-181

Cl ,""VAIR - DIVISION OF GENERAL l' "'4AMICS CORP.
SAN OIf,GO

CAl

PAGE

FO'" ',I"

CONTINUOUS

MATRIX

Zm 491
All

DATE

8-9-56

MULTIPLIER

40501

00160
00161

56 200no 00161
11 00113 20000

40502

00162

47 00163 00210

40503

00163

45' 10000 00167

MS-'
P3 -+- (A)
151)-'0[ VESt 210 -+-lPA~
NO, MJ-l. IF ON 167 ........... (PAK)

40504

00164

45 30000 00113

MJ-3. iF ON 173 ........ (PAK)

40505

00165

45 20000 00177

MJ- 2. I F ON 1 77

40506

00166

45 00000 00200

200 .-.. (PAK)

40507

00161

45 20000 00177

MJ-2. IF ON 177 ~ (PAKJ

,*0510

00170

37 00301 00302

cc

40511

00171

37 00350 00351

PUNCH c~

40.512

00172

45 COOOO 00200

200 ........ (PAK)

4051:3

00173

31 00301 00302

c <:

40514

00114

37

PUNCH Cf

40515

00175

MJ-2. IF ON 177 ....... (PAK)

40516

00176

45 20000 00177
45 00000 00200

40517

00171

37 00340 00341

40520

'00200

71 00}03 00110

PUNCH Cc.
.fp ~.(}II. 2 IS .... (

40521

,OOZOl

11 .00146 10000

4 DIGIT U-EXTRACTOR -...

40522

00202

53 20000 00203

SET NO. OF ELEMENTS OF C,

4052~

00203

75 30000 00205

SEND

405?4

()0204

11 60210 406'30

40525

00205

11 00106 00107

40526

n0206

11 00110 00106

40527

00207

45 00000 00225

225

405~O

00210

37 00301 00302

c'c: .......

405:31

00211

45 10000 00215

MJ-1. IF ON 215 ~(PAK)

40532

00212

45 20000 ('l0220

MJ-2. IF ON 220 -....... (PAK)

40533
40534

00213

45 3pOOO 00223

MJ-3. IF ON 223 ...... (PAK)

00214

45 00000 00224

224 ........ (PAK)

40535

00215

45 20000 00223

MJ .... 2. IF ON 223 ...... (PAK)

40536

00216

37 00340 00341

PUNCH Cc

40537

00217

45 00000 00224

224

40500

OO~50

00351

I

1

...... (P AK)

A

........

A

---

200 ..... (PAK)

,

cc ......
ml

--a...

A)

10 )

A

/)1..

~ .......... ")rTt

10-208

-+-(PAKJ
A

~(PAK)

eN 015-18

MODEL

REPORT

CV-181

ONVAIR - DIVISION Of GENERAL ( (NAMICS CORP.
~0R'" '""0

E

T

I

"

•

SA .... OneGO

CONTINUOUS

MATRIX

'AI.I~0A""A

PAGE

eN 015-19

REPORT

ZM 491

MODEL

All

DATE

8-9-56

MULTIPLIER

40540

00220

37 00'340 00341

PUNCH Cc

40541

00221

45 3,0000 00223

MJ-3. IF ON 22:3 -+-

40542

00222

45 00000 00224

224 ~ (PAK)

40543

00223

37 00350 00351

PUNCH Cc.

40544

00224

11 00110 00101

~""?t

40545

00225

40546

00226

56 ~OOOO 00226
1457 1010 0110

40541

00227

45 00000 00230

40550

00230

11 00041 00121

40551

00231

15 00144 00234

READ NEW pARAMETER AND FLAGS
230 -+ (PAK)
SET INDEX
"Y/f) 4ro R. ( ~t ~n, 4))

40552

00232

16 00144 00241

.,f ( ~, ) 4--

40553

00233

16 00145 00243

i( p?

40554

00234 fl1 30000 20000

40555

00235

73 001;0 1('1000

(tJ/6

40556

00236

40557

00237

47 00237 00240
21 10000 00074

IS REM
NO. t a) +1

40560

00240

71 10000 00150

YES'.

40561

00241

11 20000 30000

(RJ

40562

00242

54 20000 nOO17

( A) " 2 15 -+- (A )

4056~

00243

11 20000 30000

(R) ......

40564

00244

40565

00245

.-t

40566

00246

21 00234 00073
21 00241 00074
21 0024] 00074

r-I
'-'

40567

00247

41 00121

40570

00250

71 00101 00110

40571

00251

42 00152 00253

#:t,~A/-+(AJ
t S 3961 .,... Ir~ ~ ~

t-

40572

00252

37 76000 76001

NO. ALARM EXIT

><

40573

00253

71 00100 00110

YES.

40574
40575

00254

42 00152 00256

IS 3961 ;>~/~-d.I!

00255

37 76000 76001

NO. ALARM EXIT

40576

00256

71 00102 00106

YES.

40'571

00257

42 00152 00261

IS 3961 ;> m~1l

co

002~

I

0
.-l

I

0
0
0'

.-l

0..

(PAK)

,

MS-3

e(

A

I

.f ( #<)

~ 15) ~/( If.;. ~ 2 I~
:)
OR."v J -'tV, : ) -+ I ~ -m~,.,-" 4./)
.£ ( Ir· ) +1 ~.f ( Ir " )
i ( It," :;.15) -+- R ( It.( k 2 ' ;)
TEST INDEX

er

1(

~

n,

11:111

+,

A 41 ..... (

?

A)

J'l3...... fA}

(

1 •

11\

'){)Q

\.UNVAIK -

UIVI;)'UN UI" (.:itf
SAN

CONTINUOUS

MATRIX

t)l~GO

C...

ORN ....

00261

NO. ALARM EX IT"
YES. 4/ -+ (A)

40602

00262

42 00153 00210

IS 19~ ~-d;! YES. 27()

40603

00263

31 76000 76001

NO. ALARM EXIT

40604

00264

40605

00265

00 00000 00000
00 00000 00000

40606

00266

00 00000 00000

40607

00267

00 00000 00000

40610

00270

75 30120 00255

NE\tJ MATRIX

40611

C'0211

11 40135 00255

READ

40612

00272

40613

00273

00 00000 00000
00 00000 00000

40614

00274

40615

00275

00 00000 00000
00 00000 00000

40616

00276

00 00000 00000

40617

00277

00 00000 00000

n0260

40601

CARD

TO ES

40620

37 70563 70567

40621

00 00100 00377

E5 AND

40622

00 40000 40631

MD.

40623

56 00000 40623

40624

00 OOO()O 00000
00 00000 00000

40625
40626

40627

PAGE

eN 015-20

REPORT

ZM 491

MODEL

All

DATE

8-9-56

t4UL T IPL I ER

37 16000 76001
11 00110 20000

40600

""·-J.VJ.

tKAL DYNAMICS CORP.

BLOTTOS

STOP

00 00000 00000
00 00000 00000

10-210

-+

(PAr)

CONVAIR

ANALYSIS
PREPAR£D BY
CH ECKED BY

CV-182
PAGE eN 016- 1
REPORT NO. ZM 491

\1. J. Stonor
J. P. Wilkinson

SAN DIEGO

MODEL

REVISED BY

DATE

CONTINUOUS MATRIX l-ULTIHLlER
USING SINGLE OR MJLTI-PRECISION ARITHHETIC

This routine multiplies tvo matrices, take this product
or its transpose timos

8.

third matrIx, the resulting product or

its transpose tin¥9s a fourth, etc.
by meane

or

All input and output data 1s

cards with five floating deoimal numbers per card

(se9 IG-004 for card format).

The elements of anyone or the

matrices may be punched on cards w1th the elements of a rov or a

column in consecutive order vith or without eaoh row or oolumn
starting at the beginning of a ne\.! ca.rd. -

The input assumes i l l

matrices are punohed on the oards by oolumns in packed form (i.e.,
no .spaoes are left on the cards between the last element of one
column and the first element of the next).

Howver, the routine

will handle matrioes punohed by rovs and/or in unpaoked torm.
Flags punched ,as numbers-on oards are used to indicate the form

or

the matrioes on the oards.

Flags are also used to

1~d108.te·

the use of single or multi-preoision arithmetic, the use of the

transpose

or

anY' of

multiplioation.

th~

produots, and the continuation of the

Three parameters are necessary to furnish the

routine with the size ot the matrices.

The flags are denoted

b1 the symbols Po to P6 and the parameters by

* 'lbe

Ill,

n, and s.

stop read indicator (8. 12-punch in oolumn 1)

last card tor each matrix.

10-211

l!n!.!!

be on the

All

9-10-56

CV-182
COt~VA

ANALYSIS

CHECKED BY

R

It 01'11510" 01' .t:Nt:IIAL DYNAMICS COItPOaAnOM

J. Stoner
J. P. liilkinson

PREPARED BY ~.J.

SAN DIEGO

PAGE
REPORT NO.
MODEL
DATE

REVISED BY

eN 016-2
ZM 491

All
9-10-56

The nags and parruneters are .,.punohed as the mantissas on the
parsll\Gter oards and are read into the memory as fixed point integers
(see I C - 011).

Tvo parame tars _

III

and n, and three flags , Po t PI'

and P2' are on the first ot tva parameter cards while sand""; P3 to
~.

P6 are on the second oard.
a8

The parameters and flags are defined

tollows and appear on the cards in this order.

fIRST CARD
III

number of row of the first matrix

n

number, of columns of the first matrix (a.lso, number of

rows
Po

or

~e second)

=0 tor slngle-prtH',ision ari thrne tic

10

for multi-precision arithmetio

PloD tor first matrix punched packed

10
P2

~O

for first rna. trix punched unpacked

.tor t1rat matrix

pmched by eolWJU:ls

/0 tor tirstmatrix punched by ro\o.'S

8

number of columns of the second matrix

p3

:a0 for second ma trlx punched paoked

10
P4

P5

P6

for second matrix rmnchad unpacked

aO tor

second

rratrix punched by columns

10

for second matrix punched by rows

=0

tor product

10

tor transpose of product to be used

to be used

=0 for no turther multiplication

10

tor continued trIul tipllca tlon
10-212

FORM 18Ia·'\

CV-182

CON

ANALYSIS

PREPARED BY
CHECKED BY

'-t.'. J. Stoner
J. f. :,] 11' ir.~c.'n

V A

R

PAGE
REPORT NO.

it. DIVlIION 0' GENERAL DYNAMIC. COR .. OIIATlO ..

SAN DIEGO

MODEL

REVISED BY

DATE

eN 016-.3
Zt4 491
All

9-10-56

Examination of this card format reveals that before any

multirlication both puramewr oarda IIlus,t be used -while only the
seoond card is necessary Lafore each matrix in a oontinued produot.
To illus tra te the use of the parame ters and nags, surpose
the rroduct, ABC, of threo matfices is "Wanted using single-precision

arithmetio where the matrices have the following properties.
As

m by n, punched packed by roys

BI

n by s, punohed unpacked by columns

c:

8

by t, punohed unpacked by rows

The multiplication proceeds trom the left so AB is the first
product formed then this product multiplies C.

oarda contalns
card contains

8.5
a8

The first input

mantissa.s m,n,O,O, and non-zero.
mantissas a, non-zero, 0, 0, and

The seoond input
non~zero.

The

cards for A and B are the next input cards then one parameter oard
followed

~

the cards tor C.

mantissas t, non-zero,

The input card

non-zero~

0 and O.

~erore

C contains as

No blank cards appear

in the input. ,'!he last card of each matrix contains a l2-punoh
in column one to lndicate the and of that 'matrix.
Output of the intermediate produotJ! and the rinal product 1s

controlled by the MJ and MS swi tehea.

The interIll6diate output is

preoeded by the only 1-13-2 and followed by the only 1'£-3.

Setting

(PAK) * 00176 at MS-3 and starting viII give additional intermediate
output it the desired YJ

8\11 rohes

are set.

The final output is

preceded by the only 1£-1 and followed by MS-O.

Starting at MS-O

will give additional final output if' the deslred MJ svitehes are set.

It no MJ

BY! tches

are set ",heD the final product 18 formed, the

typevriter prints "SET MJ-S FOR OOTPUT" be tore stopping at MS-O.

10-213

CV-132

CON V A

I\NALYSIS

J. stoner

R

PAGE

A OIY1S10N 01' "CNERAl OYNAMIC' CORPORATION

PREPARED BY

\:.

CHECKED BY

J. F. 1Jilkinson

REPORT NO.

SAN DIEGO

MODEL

DATE

REVISED BY

Setting the IvlJ' s and starting yUl give the final output.

eN 016-4
ZM '491

All
9-10-56

All

output is by columns with the oolumn and roy indices of the first
element on each oard indica tad

a5

the card number (see IC-004).

'lbe form of the output as oontrolled by the MJ

8\1i tchas

Outwt for

is

65

follows.

rsiQ

nona

none

none

1

product

transpose packed

packed

product unpaoked

transpose unpnok6d

1 and 3

transposo packed

product packed

2 and 3

transpose unracked

product ullpacked

1 and 2

same as

1, 2, anc :3

88fOO

1

same as
SE~IIi8

as 1 and 3

none

1

as 1 and 3

none

This routine, the working

storage~

the

mat~1x

storage,

and the service routines use the entire E9 and most of MD storage.
The storage is

allott~d

as followss

00000 - 00070

temporaries

00071 - 00147

constanta

00150 - 00457

program

OO4bO - 01 Tl7

working storage

40000 - 41377

program

4l4OO - 41471

available

41500 - 54637

tirst rna trix

546.40 - 67?71

seoond matr1x and product

70000 - TnT!

service routines, Ie - 004) and Ie - 011.

Tests in the routine

ot

~ll

give an alarm exit it the size

a matrix is too large for tlw storlJ.ge space prov1d~d.
10-214

'lhe following

CON

ANALYSIS

PREPARED BY
CHECKED BY

r.

R

REPORT NO.

A OIVIIIOIil 0,. GEHIlRAoL DYNAMICS CORPORATION

I.;. J. storer

J.

V A

CV-182
PAGE eN 016-5

SIAN DIEGO

~~ill~inson

MODEL

ZH -491
All

DATE

REVISED BY

9-10-56

restrictions are imposed on the size of the lnatrices z

1.

No dimension greater ttan declrnal 120.

?

The nUIl:oor of elements in ar.y matrix not greater than

28GO (this includes the zeros in an unpacked form.)
Thus, the largest square matrix that ca.n be handled is

p5cked or a 52 by 52 unpacked siLca an unpacked form
on cards as a 52 by

(Note s

55

So

53 by 53

~ould

be' handled

containing 2860 ,elements inoluding the zeros.

oven though the rna trix is unpacked and the storage limitatIons

requIre consideration of this, the input dimensions on the pa.rameter
oards are the packed dimensions.)

A check Bum, equal to 0123456701?3, is printed at the beginning
of the program after reading the paper tape.
sum of this routine, IC-004, and
by paper tape.

A

pro~:rrammed

Ie-OIl,

This represents the

all of vhich sre loaded

motto is included in the code.

Setting

(PAR) ~41, 370 and starting gives a motto of 00000-00457 and 40000-

41311 which includes the temporaries, constants, and program in E.S.
and entire

pro~y,ram

on MD-

The program starts with (FAK) =40,000.

Severnl continuous

multtI,licatlons may be done by resettir>g (PAK) ::40,000 at 1£-0.
However, a blank oard

DlUB t

bo rlaced be t\.'6en the cards for the separate

continuous multiplications unlesB the rending hopper is loaded When
PAJ( is reset.

The check swn ohtained uhen 1)AJ( 1s reset 1s not the

same as that obtained after

re~l(l:1.ng

10-215

the paper tape.

II..)AM

~o

t.

1

1

I'

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

,

CV-182
P AGE

ZM 491

MODEL

All

DATE

CONTINUOUS

MATRIX

MULTIPLIER

40000

45 00000 40001

40001

31 40000 00000

40002

75 21371 41374

40003

32 40001 00000

40004

11 20000 10000

40005

40006

17 00000 72433
75 30370 00150

40007

11 40010 00070

CHECK
SUM

PROGRAM.
PRI~1E

BULL.

PROGRAM

TO ES.

40010

00070

00 00000 00000

40011

00071

00 00000 00110

DEC. 72.

40012

00012

40 00000 00000

SIGN

4001~

00073

00 00000 00003

40014

00074

00 00000 00001

40015

00075

71 77777 70000

40016

00076

71 77777 77777

MANTISSA AND EXPONENT MASK.
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 17711 74000

DEC.-2047.

40024

00104

00 00000 00012

DEC. 5a,

40025

00105

00 00000 00021

DEC. 17.

40026

00106

00 07717 00000

40027

00107

00 4J.500 41500

40030

00110

00 54640 54640

40031

00111

00 00460 00460

40032

00112

00 01040 01040

40033

00113

00 01420 01420

4-DIGIT U-EXTRACTOR.
START OF A.
START OF B.
START OF
ES WORKING
STORAGES.

40034

00114

40035

00115

00 00002 00000
00 00000 77177

V-EXTRACTOR.

40036

00116

40037

00117

00 00000 00002
41 45242 00145

FLEX CODE

10-216

eN 016-6

REPORT

MASK.

9-10-56

CONVAIR -

DIVL:C.J

Ci~ G:::J::~Al

SAN ()lfGO

DYNAMICS CORP.

C"Llf ()H'NIA

CV-182

eN 016-7

PAGE

REPORT
MODEL
DATE

CONTINUOUS

f'.1ATR r X

MULTIPLIER

40040

00120

07 32562 40404

FOR-

40041

00121

03 12040 33426

SET MJ-S

40042

00122

15 34010 45701

40043

00123

00 00000 00013

40044

00124

00 00000 00001

40045

00125

00 00000 00005

40046

00126

00 00000 00004

40047

00127

61 00000 00130

40050

00130

00 00000 00037

40051

00131

00 00000 00052

40052

00132

00 00000 00074

40053

00133

00 00000 00070

40054

00134

00 00000 00064

40055

00135

00 00000 00062

40056

00136

00 00000 00066

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

40066

00146

00 00000 00235

DEC. 36.
DEC. 157.

40067

00141

00 00000 00000

('I

40010

00150

11 00123 OOOOI

'-"

40011

00151

61 00000 00100

40072

00152

55 10000 00003

40073

00153

51 00124 20000

t-

40074

00154

35 00127 00155

><:

40075

00155

30 00000 00000

'40076

00156

41 00001 00152

40071

00157

31 12400 72401

co
......t

. FOR OUTPUT.

DEC. 11.

ZERO PRINT ORDER.
FLEX
CODES

FOR
0-7.

PRINT OF

I

0
....-I

CHECK

I

0
0
0-

....-I

~

SUM.

READ

ZM 491
All

9-10-56

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
5AN Olf.GO

CALIFORNIA

CV-182
PAGE

eN 016-8

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER

40100

00160

04 00021 00012

40101

00161

11 00023 00060

40102

00162

11 00026 00023

40103

00163

11 00032 00026

40104

00164

11 00021 20000

40105

00165

42 00140 00161

40106

00166

37 76000 16001

40107

00167

11 00022 20000

40110

00170

42 00140 00172

40111

00111

31 76000 76001

40112

00172

11 00023 20000

40113

00173

42 00140 00175

40114

00114

31 76000 76001

40115

00175

75 30003 00171

40116

00176

11 00021 00032

40111

00117

75 30003 00201

40120

00200

21 00032 00021

40121

00201

40122

00202

75 30003 0020'3
11 00021 0-0035

40123

00203

75 20003 00205

40124

00204

55 00035 00020

40125

00205

75 30003 00207

40126

00206

11 00021 00041

40127

00207

75 20003 00211

40130

00210

23 00041 00074

40131

00211

75 30003 00213

40132

00212

11 00021 00052

4013'3

00213

75 20003 00215

40134

00214

55 00052 00017

40135

00215

75 30003 00217

40136

00216

11 00021 00044

40137

00217

11 00021 20000

PARAMETER CARDS.
STORE

PARAMETERS
CONSECUTIVELY.
TEST

SIZE
OF

PARAMETERS.

DOUBLE
PARAMETERS.
SCALE
PARAMETERS.
DECREASE
PARAMETERS BY 1.
SCALE
PARAMETERS.

FIND

10-218

FIRST

z}1 491

All

9-10-56

,. 'I.)R M

~H.)

f.

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
Ttl'

,

SAN OlE60

CONTINUOUS

f'.1ATR I X

00220

73 00125 10000

40141

00221

47 00222 00224

40142

00222

71 10000 00125

40143

00223

3S 00125 00044

40144

00224

11 00022 20000

40145

00225

73 00125 10000

40146

00226

47 00227 00231

40141

00227

71 10000 00125

40150

00230

35 00125 00045

40151

00231

11 00023 20000

40152

00232

73 00125 10000

40153

00233

47 00234 00236

40154

00234

71 10000 00125

40155

00235

35 00125 00046

40156

00236

75 30003 00240

40157

00237

11 00044 00047

40160

00240

15 30003 00242

40161

00241

21 00047 00044

40162

00242

75 30003 00244

40163

00243

11 00044 00055

40164

00244

75 20003 00246

40165

00245

55 00055 00011

40166

00246

11 00021 00045

40167

00247

42 00141 00251

40170

00250

37 76000 76001

40111

00251

71 00045 00023

40172

00252

42 00141 00254

0
0

40113

00253

37 76000 76001

..-I

t-

40174

00254

71 00-044 00023

:><:

40115

00255

42 00141 00257

40176

00256

37 76000 76001

40177

00257

71 00046 00021

C\l

"--"'
I

0
..-I
I

0-

0...

10-21<)

MUTIPLE
OF 5

GREATER
THEN
OR

CV-182
eN 016-9
REPORT ZM 491
MODEL
All
DATE
9-10-56
PAGE

MULTIPLIER

40140

co
.-t

CAllFORNl.o.

EQUAL

TO

PARAMETERS.
DOUBLE
MULTIPLES.

SCALE
MULTIPLES.

TEST

SIZES

OF
MATRICES.

CV-IB2

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

eN 016-10
ZM 491
MODEL
All
P AGE

SAN DIEGO CALIFORNIA

REPORT

DATE

CONTINUOUS

MATRIX

MULTIPLIER

40200

00260

42 00141 00262

40201

00261

37 76000 16001

40202

00262

11 00070 20000

40203

00263

47 00'305 00264

40204

00264

11 00025 20000

40205

00265

47 00266 00276

40206

00266

31 72400 72401

40207

00267

00 41500 05544

40210

00270

11 00024 20000

4021-1

00271

47 00272 00305

40212

00272

11 00041 00001

40213

00273

40214

00274

11 00107 00002
37 00351 00.352

40215

00275

45 00000 00305

40216

00276

40217

00277

40220

00300

11 00021 00004
11 00035 00002 .
11 00107 0000:3

40221

00301

11 00024 20000

40222

00302

41 00303 00304

40223

00303

11 00044 00004

40224

00304

37 40400 40402

40225

00305

11 00030 20000

40226

00306

47 00317 00307

40227

00307

37 72400 72401

40230

00310

00 54640 05544

ONTO MD.

40231

00311

11 00027 20000

40232

00312

47 00313 00326

TEST FOR
UNPACKING B.

40233

00313

11 00043 00001

40234

00314

11 00110 00002

40235

00315

37 00351 00352

40236

00316

45 00000 00326

40237

00317

11 00023 00004

10-220

TEST FOR
READ OF A.
TEST FOR
CHANGE IN

FORM OF A.

READ A
ONTO MD.
TEST FOR
UNPACKING A.

PACK A.
CHANGE

A AND
STORE

ON MD.

TEST FOR
CHANG~

IN FORM OF B.

READ B

PACK

e.

CHANGE

9-10-56

CONVAIR - DIVISION OF

GENE~Al

CV-'182 .
eN 016-11

DYNAMICS CORP.

PAGE

SAN DIEGO CALIFORNIA

REPORT
MODEL /

ZM 491
,:All

DATE9-10-56

CONTINUOUS

MATRIX

MULTIPLIER

40240

00320

11 00037 00002

40241

00321

11 00110 00003

40242

00322

11 00021 20000

40243

00323

47 00324 00325

40244

00324

11 00046 00004

40245

00325

31 40400 40402

40246

00326

45 00000 00327

40247

00327

11' 00036 00040

40250

003:30

11 00022 20000

40251

OO~31

42 00021 00333

40252

00332

45 00000 00341

40253

00333

11 00110 00001

40254

00334

11 00033 00002

40255

00335

11 00032 00003

40256

00336

11 00023 00004

40257

00337

37 00371 00312

40260

00340

11 00035 00040

40261

00341

15 30060 00343

40262

00342

11 40540 00150

40263

00343

11 00060 20000

40264

00344

47 00347 00345

40265

00345

75 30100 00150

40266

00346

11 40620 00230

40267

00347

75 30150 00150

MULTI-PRECISION

40270

00350

11 40720 00230

40271

00351

45 00000 30000

TO ES.
EXIT-PACKING SUBROUTINE.

40272

00352

11 00106 10000

40213

00353

53 00036 00363

40274

00354

53 00036 00365

40275

OO~55

23 00001 00074-

40276

00356

15 00002 00364

40217

00357

16 00002 00366

BAND

STORE

ON MD.

TEST FOR

SPACING OF B.
SPACE
COLUMNS
OF B.

MULTIPLIER
TO ES.
TEST FOR
ARITHMETIC.
SINGLE PRECISION

TO ts.

SET

INITIAL
CONDITIONS.

.' '.\ ".. ,)

f

f

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP .

I

SAN l),fGO

CALIfORNIA

CV-182
PAGE eN 016-12
REPORT ZM 491
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER

40300

00360

40301

00361

31 00056 00001
35 00364 00364

40302

00362

21 00366 00033

40303

00363

75 30000 00365

UNPACKED

40304

00364

11 30000 01420

40305

00365

75 30000 00367

40306

00366

40307

00367

40310

00370

11 01420 30000
41 00001 00360
45 00000 00351

ROW TO ES.
PACKED
ROW TO MD.

40311

00311

45 00000 30000

40312

00372

11 00002 20000

40313

OO~73

43 00003 00375

40314

00374

45 00000 00403

40315

00315

13 00016 00005

40316

00316

1'3 00076 00006

40317

00377

15 00001 00005

40320

00400

16 00001 00006

40321

00401

54 00006 00017

40322

00402

43 00005 00371

40J23

00403

11 00003 00005

40324

00404

55 00005 00017

40325

00405

55 00002 00017

40326

00406

21 00004 00074

40321

00407

15 00001 00431

40330

00410

16 00001 00433

40331

601ft!

71 00002 00004

403:32

OO~12

35 00431 00431

40333

00413

71 00003 00004

403:34

00414

35 00433 00433

40335

00415

11 00106 10000

40:336

·00416

40337

00417

5~

00002 00430

ADVANCE

ADDRESSES.

EXIT-UNPACKING SUBROUTINE.
TEST

FOR
NEEDED

UNPACKING.

SET

LOCATIONS
OF LAST

COLUMN
OR ROW.
SET

53 00005 00432

10-222

All

9-6-56

... , '.\1

t

r

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP .
t

I-

,

S"'N DIEGO

C"LlFORNI"

CV-IB2
P AGE

eN 016-13

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER

40340

00420

23 00005 00002

40341

00421

53 20000 00426

40342

00422

11 00002 20000

40343

00423

52 00113 20000

40344

00424

55 20000 00025

40345

00425

16 20000 00427

40346

00426

15 10000 00430

40347

00427

13 00076 30000

40350

00430

15 30000 00432

40351

00431

11 30000 01420

40352

00432

75 30000 0.0434

40353

00433

11 01420 30000

40354

00434

23 00431 00002

40355

00435

23 00433 00003

40356

00436

41 00004 00430

40357

00431

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 00·000 00000

40~71

00457

00 00000 00000

10-??~

NUMBER

OF ELEMENTS IN
ROW OR COLUMN.

EXTRA
ELEMENTS TO ZERO.
PACKED ROW OR
COLUMN TO ES.
UNPACKED ROW OR
COLUMN TO MD.
RETARD
ADDRESSES.
SET

ZM

491

All

9-10-56

t;V-lt),

CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SA'" OtEGO ..... ,

I~OR"'t'"

P AGE

eN 016-14
ZM 491

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER
SUB ROUT r NE.

40400

00150

75 30160 30000

40401 -

O~151

11 40220 00300

EXIT-CHANGE
RELOAD ES.

40402

00152

15 30140 00154

LOAD

40403

00153

11 40400 00150

40404

00154

13 00076 00011

40405

00155

11 00143 20000

40406

00156

13 00004 00005

40407

00157

11 00004 00005

40410

00160

11 20000 00020

40411

00161

73 00125 00016

40412

00162

11 20000 00015

40413

00163

11 00132 00017

40414

00164

55 00004 00020

40415

00165

11 00022 20000

40416

00166

73 00005 10000

40417

00167

11 20000 00006

40420

00170

47 00172 00171

40421

00171

11 00005 00006

40422

00112

31 00001) 00020

40423

00173

11 00106 10000

40424

00174

53 20000 00233

40425

00115

11 00115 10000

40426

00116

53 00020 00205

40427

00177

13 00076 00001

40430

00200

11 00015 20000

40431

00201

47 00202 00204

TRANSFERS.
TEST FOR
CARD READ TYPE.

40432

00202

37 00242 00243

READ

40433

00203

45 00000 00206

40434

00204

37 72400 12401

40435

00205

00 00300 00000

40436

00206

16 00003 00234

40437

00207

21 0023/. 00011

PRESET
NUMBER
OF CARDS.
PRESET
ADDRESSES

10-224

FOR~-1

ES.
FIND
NUMBER
OF COLUMNS
OR

ROWS

PER READ.

PRESET
INDICES
AND

All

9-10-56

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

CV-182
PAGE

CN 016-15
ZM 491

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER
AND

40440

00210

31 00005 00001

40441

00211

35 00011 00011

40442

00212

11 00001 20000

40443

00213

47 00214 00220

40444

00214

11 00106 10000

40445

00215

31 00006 00020

40446

00216

53 20000 00233

CARD

40447

00211

11 00006 0"0005

40450

00220

13 00076 00010

READ.
SET COUNTER.

40451

00221

15 00142 00221

PRESET

40452

00222

21 002Z7 00010

ADDRESSES

40453

00223

16 00113 00221

AND

40454

00224

11 00005 20000

INDICES.

40455

00225

36 00074 00007

40456

00226

75 30002 00230

PUT ROW OR

40451

00227

11 30000 30000

COLUMN

40460

00230

21 00221 00116

40461

00231

35 00004 00227

ELEMENTS
IN ORDER.

40462

00232

41 00007 00226

40463

00233

15 30000 00235

40464

00234

11 01420 30000

40465

00235

21 00234 00033

40466

00236

21 00010 00114

40467

00237

42 00002 00221

40410

00240

11 00001 20000

40471

00241

41 00150 00200

'+0412

00242

45 00000 30000

40413

00243

11 00017 20000

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

INDICES.
TEST FOR
END OF MATRIX.
SET FOR
LAST

STORE
ROW OR
COLUMN
ON MD.
TEST FOR
LAST CARD READ

TEST FOR

All

9-10-56

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
1

I

t

CV-182

l

PAGE

ZM 491

MODEL

All

OAT E

CONTINUOUS

MATRIX

MULTIPLIER

PRESET

40500

00250

54 20000 00020

40501

00251

11 00106 10000

40502

00252

53 20000 00260

ADDRESSES,

40503

00253

40504

00254

15 00142 00261
31 00020 00020

TRANSFERS.

40505

00255

35 00261 00261

40506

00256

31 00014 00020

40501

00257

35 00273 00273

40510

00260

75 30000 00262

40511

00261

11 30000 00300

40512

00262

11 00014 20000

405}:3

00263

42 00015 00261

40514

00264

71 00125 00016

40515

00265

16 20000 00273

40516

00266

45 00000 00212

40511

00267

71 00125 00016

40520

00270

35 00125 20000

40521

00271

16 20000 00273

40522

00212

37 72400 12401

40523

00213.

00 30000 00000

40524

00274

23 00017 00015

40525

00275

45 00000 00242

40526

00216

00 00000 00000

40527

00277

00 00000 00000

40530

00300

00 00000 00000

405:31

00301

00 00000 00000

405"32

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

AND INDICES
PLACE ELEMENTS
FROM PREVIOUS READ.
TEST FOR NUMBER
OF CARDS TO READ.
PRESET NUMBER
OF NUMBERS.
PRESET NUMBER
OF NUMBERS.

10-226

READ
CARDS.

PREPARE FOR NEW READ.

eN 016-16

REPORT

9-10-56

,

." ... " .. ) t

r

CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
I

"

I

SAN DIEGO CALIF URNIA

CV-182
eN 016-17
REPORTZM 491
PAGE

MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER

40540

00150

45 00000 00151

40541

00151

11 00106 10000

40542

00152

53 00035 00211

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

40551

00161

11 30000 01040

ONE COLUMN
OF B TO ES.

40552

00162

15 00101 00166

PRESET

40553

00163

16 00113 00205

40554-

G0164

11 00041 00001

40555

00165

15

40556

00166

11 30000 00460

40557

00167

15 00111 00175

40560

00110

15 00112 00177

40561

00171

11 00042 00002

40562

00172

13 00076 00015

40563

00173

13 00076 00016

40564

00114

75 30002 00176

40565

00175

11 30000 00011

40566

00176

75 30002 00200

40567

00177

11 30000 00013

ADDRESSES
AND INDICES.
ONE ROW OF
A TO ES.
PRESET
ADDRESSES
AND INDICES.
ZERO
TO RESULT.
COMPUTE
ONE ELEMENT
OF A COLUMN
OF C.

40570 ' 00200

37 00231 00232

40571

00201

40512

00202

21 00175 00114
21 00177 00114

40573

00203

41 00002 00174

40514

00204

75 30002 00206

40575

00205

11 00015 30000

40576

00206

21 00166 00036

40511

00207

21 00205 00116

I

~OOOO

00167

PRESET
REPEATS.

ADVANCE

ADDRESSES.
STORE COMPUTED

ELEMENT.
ADVANCE
ADDRESSES.

All

9-10-56

CONVAIR -- DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO

CALlFOI'fNIA

CV-182
PAGE eN 016-18
REPORT

ZM 491

MODEL

All

DATE

CONTINUOUS

MATRIX

MULTIPLIER

40600

00210

41 00001 00165

40601

00211

75 30000 00213

40602

00212

11 01420 30000

40603

00213

21 00212 00032

40604

00214

21 00161 00040

40605

00215

41 00061 00160

40606

00216

15 30310 00150

40607

00211

11 41070 00150

40610

00220

00 00000 00000

.40611

00221

00 00000 00000

40612

00222

00 00000 00000

40613

00223

00 0,0000 OOQOO

40614

00224

00 00000 00000

40615

00225

00 00000 00000

1.. 0616

00226

00 00000 00000

40617

00227

00 00000 00000

40620

00230

37 76000 76002

40621

00231

45 00000 30000

40622

00232

16 00146 00320

40623

00233

75 30002 00265

40624

00234

11 00015 00017

40625

00235

11 00012 00016

40626

00236

23 10000 10000

SINGLE PRECISION
ARITHMEl1C-SEE ZM-521.
SET FOR ACC! ULATE MULTIPLY.
STORE
SUM,
ADD ENTRANCf ~
CLEAR A ANfl •

40627

00237

16 10000 00257

ERASE SH I F'j ..

40630

00240

43 00013 00257

40631

00241

43 00011 00255

40632

002·42

23 00012 00014

Y ZERO TEST.
x ZERO TEST,
EXPONENT DIFFERENCE.

40633

00243

12 20000 20000

40634

00244

42 00145 00247

40635

00245

40636

00246

41 00012 00257
'.5 00000 00255

0637

002 l .. 7

16 20000 00257

I

It

10-228

ONE COLUMN
OF C TO MD.
ADVANCE
ADD.RESSES.

OUTPUT

PROGRAM TO ES.

36 COMPARSION.
V.OR x.

SET SHIFT,

9-10-56

VII -- .LVSAN DIEGO CALIFORNIA

PAGE

eN 016-19

REPORT

DATE

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

40644

00254

75 00001 00257

40645

00255

11 00014 00016

40646

00256

11 00013 00011

y EXPONENT.
y TO X.

40641

00257

54 00011 30000

SHIfT X.

40650

00260

35 10000 00015

40651

00261

45 00000 00272

40652

00262

23 00016 00145

40653

00263

40654

00264

54 00015 00044
47 00273 00313

40655

00265

11 00014 20000

40656

00266

35 00012 20000

TO NORMALIZE.
A LEFT
NOT SIGNIFICANT.
ZERO TEST.
MULTIPLY ENTRANCE.
ADD EXPONENTS.

40657
40660

00267
00270

36 00144 00016
71 00013 00011

FORM PRODUCT.

40661

00271

11 20000 00015

TEST

40662

00272

43 20000 00262

40663

00213

13 00076 00005

40664

00274

11 00074 10000

40665

00275

46 00216 00277

40666

00276

13 10000 10000

40667

00277

11 10000 00006

40670

00300

74 20000 00005

EXTENT ION.
CLEAR FOR SF.
POSITIVE FLAG.
SIGN TEST.
NEGATIVE FLAG.
FOR ROUNDING.
SCALE FACTOR.

40671

00301

11 20000 00015

40672

00302

46 00303' 00304

40673

00303

13 10000 10000

40674

00304

21 00016 00005

40675

00305

44 00306 00313

40676

00306

21 00015 00006

40677

00301

43 20000 00313

Y TO Q.

AOJUST
FOR SIGN.
ADJUST FOR SF.
ROUND.
OVERFLOW TEST.

ZJ.1 491

All
9-10-56

MODEL

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN OI£GO

CALIFORNIA

CV-182
eN 016-20
ZH 491

PAGE

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPL!ER

ADJUST
FOR
OVERFLOW,
ZERO
TEST.
ERASE EXPONENT.
SET FOR
ADD.
TO ADD OR EXIT.

40700

00310

32 00147 00107

40701

00311

11 20000 00015

40702

00312

21 00016 00074

40703

00313

11 00015 20000

40704

00314

47 00316 00315

40705

00315

11 20000 00016

40706

00316

75 30004 00320

40707

00317

11 00015 00011

40710

00320

31 00320 00321

40711

00321

45 00000 00231

40712

00322

00 00000 00000

40713

00323

00 00000 00000

40714

00324

40715

00325

00 00000 00000
00 00000 00000

40716

00326

00 00000 00000

40711

00327

00 00000 00000

40720

00230

37 76000 16002

40721

00231

45 00000 30000

MULTI-PRECISION
ARITHMETIC--SEE CA-006.

40722

00232

75 30002 00246

STORE

40123

00233

11 00015 00017

40724

00234

75 10002 00301

ZERO TO

40725

00235

13 00076 00015

40726

00236

42 00102 00240

40127

00231

45 00000 00230

40730

00240

42 00103 00234

MULTIPLY RESULT.
TEST EXPONENT.
ALARM.
TEST EXPONENT.

40731

00241

13 00075 10000

STORE

40732

00242

53 20000 00016

40733

0024'3

11 00072 10000

40734

00244

53 00015 00016

40735

00245

45 00000 30000

40736

00246

71 00012 00013

40737

00247

72 00011 00014

EXPONENT.
STORE
SIGN.
TO .AOD OR EXIT.
MULTIPLV ENTRANCE.
FORM

SUM.

All

9-10-56

CONVAIR ~

" ..... ",,)

l:

r

DiViSiON OF Gt:hii.::

POSITION.

0021~

PRODUCT
TO POSITION.

~.

READ NEW
PARAMETER CARO.
,.. LOAD

10-234

ES.

O16-~4

ZM 491

All
9-10-56

~ORM

NO

f

Til'

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

,

SAN DIFGO

CALI~ORNIA

CV-IU2
PAGE

eN 016-;>5
ZM 491

REPORT
MODEL

All,

DATE9-10-56

CONTINUOUS

MATRIX

MULTIPLIER

EX I T-oUTPUT SUBROUTINE.
TEST FOR
TRANSPOSE.
TEST
MJ SWITCHES.

41140

00220

45 00000 30000

41141

00221

11 00031 20000

41142
41143
41144
41145

00222
00223

47 00263 00223
45 10000 00245

00224

45 20000 00226

00225

45 00000 00220

411~6

00226

45 30000 00236

41147

00227

41150

00230

37 00335 00336
15 00054 00234

41151
41152
41153
41154

00231

16 00044 00234

00232

~7

00233

FORM TRANSPOSE UNPACKED.

70440 70443

FORM PRODUCT UNPACKEO.
SET

PARAMETERS.
PVNCH.

41155

00235

41156

00236

00 41500 00000
00 00000 00000
45 00000 00220
37 00345' 00346

41157

00237

15 00052 00243

SET

41160
41161
41162

00240

16 00046 00243
37 70440 70443

PARAMETERS.
PUNCH.

00234

00241
00242

00 4'i500 00000

41163 ' 00243

00 00000 00000

45 00000 00220

41165

00244
00245

41166

0,0246

41167

00247

41170
41111
41112

00250

41173

00253

41174

00254

41175

00255

15 00054
16 00021
31 704ltO
00 54640
00 00000
45 00000
37 00272
15 00052

41176

00256

16 00023 00261

41177

00251

37 70440 70443

41164

00251
00252

45 30000 00254

00252

SET

00252

PARAMETERS.
PUNCH PRODUCT PACKED.

70443

00000
00000
00220
00213

FJRM TRANSPOSE PACKED.

00261

S:ET

PARAMETERS.
PUNCH.
t

.'"

nn'"

CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.
SAN OI£G;)

CALIFORNIA

CV-182
PAGECN

016-26

ZM 491
All
9-10-56

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER

412,00

00260

00, .,},500 00000

41201

00261

00 00000 00000

41202

00262

45 00000 00220

41203

00263

45 10000 00270

41204

00264

45 20000 00266

41205

00265

45 00000 00220

41206

00266

45 30000 00221

41201

00267

45 00000 00236

41210

00210

45 30000 00246

41211

00271

45 00000 00254

41212

00212

45 00000 30000

41213

00273

11 00106 10000

41214

00274

53 00037 00310

41215

00275

13 00076 00002

41216

00276

16 00107 00311

41217

00271

15 00110 00304

41220

00300

21 00304 00002

41221

00301

11 00043 00001

41222

00302

16 00113 00304

41223

00303

15 30002 00305

41224

00304

11 30000 30000

ONE ELEMENT
OF PRODUCT TO E$.

41225

00305

21 00304 00116

ADVANCE

41226

00306

35 00035 00304

41227

00307

41 00001 00303

41230

00310

75 30000 00312

41231

00311

11 01420 30000

41232

00312

21 00311 00034

41233

00313

21 00002 00114

41234

00314

42 00035 00277

41235

00315

45 00000 00212

41236

00316

45 00000 !OOOO

41237

00317

11 00106 10000

TEST
MJ SWITCHES.
PUNCH PRODUCT UNPACKEO&
PUNCH TRANSPOSE UNPACKED.
PUNCH PRODUCT PACKED.
PU~CH TRANSPOSE PACKED.
EXIT-FORM TRANSPOSE SUBROUTINE.
PRESET

INDICES
AND

ADDRESSES.

ADDRESSES.
ONE COLUMN
OF TRAN SP{'; S£ TO MD.
}\CIVANCE
ADDRESSES.

EXIT-STORE PRODUCT SUBROUTINE.
PRESET

~

ORM NO

E

Til'

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

•

CV~ltl2

eN 016-27
'ZM 491
MODEL All
DATE
9-10-56

SAN DIEGO CALIFORNIA

PAGE

REPORT

CONTINUOUS

MATRIX

MULTIPLIER

41240

00320

53·00035 00325

41241

00321

53 00035 00321

REPEATS.
INDICES.

41242

00322

11 00043 00001

AND

41243

00323

ADDRESSES.

41244

00324

15 00110 00326
16 00107 00330

41245

00325

15 30000 00327

ONE COLUMN

41246

0'0326

11 30000 01420

41247

00327

75 30000 00331

41250

00330

41251

00331

11 01420 30000
21 00326 00035

TO ES.
ONE COLUMN
TO MD.

41252

00332

41253

00333

21 00330 000'2
41 00001 00325

41254

00334

45 00000 00316

41255

003:35

45 00000 30000

41256

00336

15 00110 00001

41251

00337

16 00107 00001

41260

00340

41261

00341

11 00032 00002
11 00041 00003

41262

00342

11 00023 00004

41263

00343

31 00371 00312

41264

00344

45 00000 00335

41265

00345

45 00000 30000

41266

00346

37 00212 00273

41267

00347

11 00101 00001

4'1270

00350

11 00034 00002

41271

00351

11 00051 00003

AND

41272

00352

11 00021 00004

INDICES. '

41273

00353

37 00371 00372

41274

00354

45 09000 00345

41275

00355

00 00000 00000

41276

00356

00 00000 00000

41217

003'57

00 00000 00000

ADVANCE

ADDRESSES.

EXIT-UNPACKING PRODUCT SUBROUTINE.
PRESET
ADORESSES
AND

INDICES.
UNPACK PRODUCT.
EXIT-UNPACKING TRANSPOSE SUBROUTINE.
STORE TRANSPOSE
PRESET
ADDRESSES

UNPACK PRODUCT.

CON" AIR - DIVISION OF GENERAL DYNAMICS CORP.
SAN DIEGO

CALIFORNIA

CV-I02
REPORT

ZM 491

MODEL

All

DATE

CONTINUOUS

MATRIX

MULTIPLIER

41300

00360

00 00000 00000

41301

00361

00 00000 00000

41302

00362

00 00000 00000

4130'

OO~63

00 00000 00000

41304

00364

00 00000 00000

41305

00365

00 00000 00000

41306

00366

00 00000 00000

41307

OO~67

00 00000 00000

41310

00370

00 00000 00000

41311

00371

45 00000 30000

41312

00372

11 00002 20000

41313

00373

1t3 00003 00375

41~14

00374

45 00000 00403

41315

00375

13 00076 00005

41316

00376

13 00076 00006

41311

00377

15 00001 00005

41320

00400

16 00001 00006

41321

00401

54 00006 00017

41322

00402

43 00005 00371

41323

00403

11 00003 00005

41324

00404

55 00005 00017

41325

004Q5

'5

41326

00406

21 00004 00014

41327

00407

15 00001 00431

41'330

00410

16 00001 00433

41331

00411

71 00002 00004

41"2

00412

35 00411 00.'1

413'3'

00413

71 00003 00004

41334

0041 ..

35

413'35

00415

11 00106 10000

41336

00416

53 00002 00430

41331

00417

53 OOOOS 004'2

EXIT-tJNPACKING SUBROUTINE.

TEST
FOR
NEEDED

UNPACKING.

SET

00002 00017

004~3

LOCATIONS
OF LAST
COLUMN
OR ROW.

004]3
SET

eN 016-28

PAGE

9-10-56

~

dRM NO

E

TIP

CONVAIR - DIViSION OF GENERAL DYNAMICS CORP.

,

SAN DIEGO

CALIFORNIA

CV-182
P AGE

eN 016-29
ZM 491

REPORT
MODEL
DATE

CONTINUOUS

MATRIX

MULTIPLIER
NUMBER

41340

00420

23 00005 00002

41341

00421

53 20000 00426

41342

00422

11 00002 20000

41343

00423

52 00113 20000

41344

00424

55 20000 00025

41345

00425

16 20000 00427

41346

00426

15 10000 00430

41341

00421

13 00016 30000

41350

00430

75 30000 00432

41351

00431

11 30000 01420

41352

00432

75 30000 00434

41353

00433

11 01420 30000

EXTRA
ELEMENTS TO ZERO.
PACKED ROW OR
COLUMN TO ES.
UNPACKED ROW OR
COLUMN TO MD.

41354

00434

23 00431 00002

RETARD

41355

00435

23 00433 00003

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

413'65

00445

00 00000 00000

41366

00446

41367

00447

41370

00450

41371

00451

00 00000 00000
27 64146 061:30
37 71163 77767
00 00000 00457

41372

00452

00 40000 41317

AND

41373

0045'3

56 00000 4131!

MD.

41314

00454

75 20550 41376

41375

00455

32 70440 00000

1(-004

41:376

'00456

75 20352 40001t-

AND

41377

00457

32 72400 00000

le-Ol1.

OF ELEMENTS IN
ROW OR COLUMN.
SET

ADDRESSES.

FOR CONVENIENT CHECK SUM.
BlOTTOS
ES

SUMS

All

9-10-56

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP,
5~N

OIEGO

C~,LIFORNIA

CV-182

PAGE

ZM

MODEL

All

DATE

CONTINUOUS

MATRIX

eN 016-30

REPORT

9-10-56

MULTIPLIER

SEE IC·004 FOR CODE OF 70440-71207.

SEE Ie-OIl 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 14001

10-240

491

CV-183

-

; lG ·

""

"'-

.

)

DIVISION

SaD Die a

MODEL

ALL

~'"
....

~

~-

~./~.'

.

-.

.'

,

(~

. \".'

"",~

.

REPORT ZM,:5 27

.,,-

n-

-:'-""'-'

..

8/291.56

DATE

V

r

TITlE
SPUR
~

Single preoision unpaoked rounded tloating
point package tor,BRA-llO) Computers

,-

-,

Part I

"

PREPARED BY

..

Operation Speoifica tione'

GROUP O1g1+a' Camp) +1ng Lab.

If ftJrt-N»

REFERENCE
CHECKED BY

C• ..1.

APPROVED

~ui:tt

BY~ ~~..

DonJl Parker

,..

Diok Bielelcer
NO. OF

PAGES

NO. OF

DIAGRA~S

22

;~

0

REVISIONS
NO.

DATE

BY

CHANG.

taAGES AF....CTEO

"

,

..

GO ~.f.A

10-241

vV-~UoJ

ANALYSIS'

PREPARED BY
CHECKED BY

L &rton

CON V A I R

PAGE

REPORT NO.

'DIYUlOII 0' ol:u£aAl. DV_AIIIlea (;O.I'OIAT'O.

SAN DlltGO

C.J. Swift, D.Parker,D. bielakor

MODEL
DATE

REVISED BY

1
ZM-527
ALL
8/29/56

SINGLE PRECISION UNPACKED ROONDED FLOATING FOINT PACKAGE

Briet Speoifioations

I

Occuplea
00000, CXlOOl
01500 to 01771 inolu8ive

76000 to 71771

SODl8

part.

OpeD

7JJ;lCIJ .tq 7577/ ( I. S. image )
Regis tara

:

p

01764, 01765

8

01766, 01767

C

.01770, 01771.

s

01'n2, 01773

R

OlTl4, 01775

~

01'716,

b2

01Tn

;

'. 'ColJ8taaU UNe! .ud anilable

017'0 00 00000 00000
017S1 00 00000 00001
01752 00 00000 00002
01153 00 00002 00000
01754 00 OCXXJO 00041
Ol.?~'

00 00000 OOQ44.

017S6 '00 00000 00177
017'7 00 QQQOO Ol7/?

Aotl.atlOil

37 76000 76001 (.to"d paoltage to I.S.)
17 00000 77413 (ini t1allJ pr$._oard.)

......,.-A

lO~42

I

LV-10")
ANALYSIS
PREPARED BY
CHECKED BY

C 0 t~ V A I It
L. Inrton
A .lYbloa op C:C1!1W. DTIIAt:IQ CORL"OaAno.
C.S~....alit
......J. I D• n.l""ark or, D. D1e 1ak erGAM DIt::GO

PAGE
REPORT NO.
MODEL

REYISED BY

DATE

Two addre ••

2
ZM-527

ALL
8 29

56

001'lllnalld8

14 CO IXII

Add1tion

(CO)
00

04

SUbtraotion

Y+ItoR
ft,+

! + I to R, I

,24

R + I + I to R, I

(00)

05

'I-XtoR

..

R+Y-XtoR
Y - X to ft,

21

25

"

Il • Y - X to a,I

02

Y,· X to R

06

ft-. Y • I to R

26

I • I to R, I
R + Y • I to

0)

1/1 to R

-...;

07

R + 1/1 to R

I

a,

Y

(ce)

"""
C")
ro
;-t
0

t

(00) ·

22

Di1l'.ia1oll

Y + I to R

20

01

IttltiplIcat10n

nn

,...;

I

0

0

2)

, 1/1

~ ft, !

27

R +1/1

to ft, t

17

It- I 18 grea tar than R

0"-

,...;

t-

><:

0...

1breehold jump

continue with the next 1netru.ct1on,
v1ll be Ullobanpd in R, S, and B.

Jump to I J

otherVia.

In eIther oa.. R original
(OAtl~IORJ due

to roundinl a

jUllp _Y occur '.1 tiler ~ when X approache8 ft, it I aDd R WN
.'

oalculated

b7 ditterent operation.)

\..V-.LOv

ANALYSIS

PREPARED 8Y
CHECKED BY
REVISED BY

L.

COt-,~'VAIR
A OIWail..,. 0' tl:::~II!l'lAL DrRA.ne.

'r\.o-tO""
DIU'

lI-l

C.Swtft, D.Farkor, D. Bielskor

tlJU.t DIEGO'

P,AGE

eoa,ounoa

RItPORT NO.
MODEL

'. DATE'

,

ZM-527
ALL

8/29/56

One address oommande

14 CO K N!l YllYY (The rightmost bit ot K i8 used with NIl, the lett1108 t two 'bi ta of I &1'. used al tags tor the Y addre8..

Betel"

to

dl.fta1led cOmJDal1d explanation. tor detall••
Index jUlllp8 with IJlOdlflcat1on

ot index counter regiatera b (1 or 2)

(ce)
76 with 'b 1
71 with b 2
Add 2 to the content.

ot b (lor 2).

It I 1. greater than one halt

ot b (1 or 2) Jump to t,. nd lea",. b (1 or 21 adYanced" Ottlend"
aet b (lor 2) equal to ..ro and ~ooDt1Due w.rt.I' ~ next ibatruotloD.
'!he .ttect la,togo ~ugh the loop 11'.

le_a,with

end of the loop or I t.imes ~-t~ ~ teet a1;

-a.

the "-at attbe

.ntr&noe to the- loop.

, • ''PolpOlllial (cq)

h,r .,. ,.. + .&nl'l J

75 Collplte the po~oJda.l .Ao + 'll'•.
\IMIna,

I, •• a fioatin, point nuu.ber, mat be preatored in register P.
, "I i8 the addr,e•• ot
tloa tiDg po1tat

~

nuJAbel'l

l •• t con.tant,
.tored

.~ch

Art.

vile" the· oon.~t.....

in tw, o.Ua-autl.88., exponeQt-

oOln••cutl...1)" I

, Ao, '11 " ~1 ~

f

Ara-

• 1. the deare. ot the equation.
'the

&D8WS-

'appears 1rl R.

It R I, 1.81 than OM DO opera \10n will be ptrtor..d.
Card

inetrootionl (00)
'7, lead N Carda into oella oonaecut1_lJ starting at I.

56 Punoh H carda trom colla
1'0.... '8,a••

con8.ctutl~17 .~

10-244

at !.

I

\.IV-~Uv

ANALYSIS
PREPARED BY
CHECKED BY

CO N V A ,I R

L. Parton

A IIlvasa08 0 .. U.u:UL OYUIClet

~rt , D• f ark ar,. D• Bie 1 s kor .
C• S.."'....

4

PAGE

REPORT NO. ZM-527

cOlrol"no.

SAN DIE.GO

ALL

MODEL

REVISED BY

8/29/56

DATE

Mbre detailed,instructions and options available are given in the
detailed instruotions.

'!he contents

or

register C cannot be pmohed

by a 14 instruotion.

In caee ot EW.l tailure eet PAl equal, to
77430 tor read, or
77007 tor, write.
IS vUl be restored followed

b7

a

56

stop vith V addres8 that

ot

the interrupted oard ins tructlon.

" A BUll i8 stored at 77lT1.

Entranoe at 77371 vill calculate a' new

sum over the area 7600CJ to Trn6 inclusive; place the nev awa 1D the
l~"

Q registerJ place the ditterence between t.be new su. and the

sua in the aocwnulator, and

001118

oomputer will replace the stored

to a 56 00000 ?7m stop.
IJUIQ

.tored
Re8tart1D,

with the oalculated awa ad

't'.dm1nate witb a 56 00000 )0000 stop'.' In general vhen

,DO

changes

"

have been made in the tape a aero dirterenee in the accumulator
indicates the routine la oorreotl7 stored on the Mlgnetio Drum.

ANALYSIS
PREPARED BY
CHECKKD BY

t~

C 0

V A I R

PAGE

L. Barton
""VI.IOM O'.U:;H:.·At. DYeJAUla cOlU'oltAno.
C. Swift, 0.. Parker, D. Bielakor SAN DIt:GO

REPORT NO.
MODEL

~ATE

REVISED BY

II

;

ZM-527
ALL

8/29/56

Detailed Speoifications
This i8 an unpacked tloa ting point package including oard input and

output, addition, subtraotion, mu.lt1p11cation, division, two index

register" and normalization, all with rounding.
l~UDlber

The tloating point

represerrta tion 1& defined in the· 1103 storage as follow J

If • M ... 28 where 1/2~ ,.,( I and O~le'<23S
M 1s scaled

35, • 1. 8caled 0,· where M 18 :in the firet ot t'WO oon-

seout1" oella and e in the second.
Examples.

or Yl'Y17rrtrrn OOOOOOOOOOOO
-1

a

')',"rrrrrn7 000000000001

- to a 3l46,lI.63l1.6 _Tm7'mm6
The oard inplt and output will on1,. bpdle a -xirtwa deoiJJal exponent

ot 99.

aooura"" beca\l88 .35 bite

a~e,~,u8ed

in a bormall_d

IQJUlU,aa, , Bo:..ver,

.the add! t1oll, nbtraot10n, ed nW. ti plioa tion opera tiona 'WIn handle

noating J1U.JDbera not nor.l1aed and give normalized anewer. which an.
,

oorreot to' a l.aeer DUlQber ot places.

The division operation require.

a normaliled d1.1sor or will go to the alarm exit, where 1t· vUl alarm

print the divisor and halt with a 56 stop.
the· ourrent 1natt"uot1on ueing

8.l1

";restart will then tinish

-incorrect &nswr .end No taul t v1ll

be oauaed by • Don-normalized dividend which will give a nOb-normalized
quotient correot to..a lesser number ot places •.
11» number whose unti8sa 18 in the aooWJUlator Icaled 35 and who..

exponenti. in 0177' \,"i11 be norlnalized by the re'turn jump 3i 01741 Olu2
10-246

VW-J..V,",

c

ANALYSIS
PREPARED BY

CHECKED

0 ·t,~ V A I

L. Barton
A DIV:!:lO• •,
BVO.Swift, D.Parker" D.B1elsker

n

SAN DIEGO

MODEL

DATE

REVISED BY

The mantissa

or

6

PAGE

RCFO:lT NO. ZJ+.52?

U;U::!AL DTflAt7 the interpret1...

From 76760 to 77.357 i8 a sim1lar 'card output. :' 'lhe paekage

requires

00000 45 00000 (

)

00001 45 00000 01547

01500 - 01771 inolueive, package operation

76000 -'77771 inclusive tor paokage alld' 8ubroutiDe
storage.
74000 - 75771 inclusive, ES1mage during so_

operations as tor example oard

c

~NALYSIS

0

t~

V A ·1

CV-183
PAGE 7
RIZPORT NO. ZM-B27

n

L. B9.rton
A DIVI:~O. ~ g;;a\t::AL DYrlASIICI c'Ca::POJlAnOIil
:HECJ$;~D Bye.swift, D.Parkar, D. Biolsker DAN DIEGO

f'lREPARED BY
~EVlSED

MOO:5:LALL

BY

DATE

8/29/56

input and outPJ,t. '

To attempt greater oonvenience

or

programing subroutines and

sj.lIlPler explJ,tla tion of operation; a core package, to operate trom
01500 to 01777 inclusive, 'i8 !ndependent

ot any 8Ubr~1ne8 used.

The intention 1s that 8117 subroutine may be eas11,.. ~8seDtbJ.ed',to uS.

vith it.

It includes rounded' operations for'aoouracy and the tundamen-4

J

_

•

tal arithmatie ope1:"at1ons.

'!bese last arltlurwJ,tio operations can be

Wted with interpretive instruotions tor pormal prograu or with return
jump instructions

,tor greater speed in loops and eapeoial17 tor

construction ot subroutines.
The package starts vith' a aeltconta1ned arlthme~io unit from

to 01775' incluai...e which

'vlll.~r!orDl

01633

addition, SUQi:ractiob, DIllt1-

plication, division, and nonal1Ation operating on speoitied re-

gisters by return jump instructions.

ho. 01500

to 01632 Inolual.,.

18 an interpretive aysteIQ whioh uae.the smaller arltbDlat1c paokage.
Fr01ll 7I4OCJ to Tn51 on the drum is a card input, selt contained and

operated .1ther by roturn jump instructions ot b7 the ,1nteJpret1ft
system.

76760 to 71357 lsa ebdlar card output.

PrOIl

..

.'

The package "quires

00000 45 00000 (

)

00001 4S 00000 01547

01500 - Ol7TI 1oCllual_,

paeka'~,:opetation'

76000 - '7f17"! 1Dolu81ve tor'package and subroutine storage.
74000 - 7577/ inclu8ive, ES image during some operations a8 tor

example oard input and output.
'l'he tape reada into cells 76000 - 77TI7 inolusive YI 76000 76001

transfers

frOIll

dt'UlIl storago to B.S. oells 00000, 00001, and 01500

CO~~YAI
L. Barton
A DI'fUl01f 0' GltIlESlAL Oy,.AtQIC" COR,oUnOtt
SAN OJ EGO '
C.S\/1ft, D.Farker, D.Bielsker

ANALYSIS
PREPARED BY

CHECKED BY

PAGE

8

Ra;:PORT NO. Z~527

REVISED BY

MODEL ALL
DATE

8/29/56

.

..

to,01757 inclusive and clears cells 01760 to 01771

tOll

register••

,17 0000077413 vill prime read and. punoh cards initially and succeeding'
card lItovemnts vUl be automatic •
. "OJ002 - 01471 inclusive remain available for anT prograIll or ad,ied

subroutines.
Register.

tor

01764 p

storage

operand tor 1terat10n

.01765

.oi766

or an

'8 ,tor storage ~t the

01767

(X) operand

01770 O. tor storage

or

the

·01771,

. (I) operand '

01773

operand tor

orn4

1ter.tl~

Jt .'Jhe ans-wer t~r storage of result

01775'

q1776 b 1

lQd~x

Bbgisters for

address mod1t1cat

01'771 )\ 2
.seoondary, ~g1ste~D

01160

I· adnta1ns the Current or

01761

I

in,

s.-f9i'V'f,lve (14) 1natnct1:Qtl

1. used as aoounter .. reeo1vea, J trODl 81ngle address in.tNc~on.

01762
0176)

l1sed as temporar1e&

in.·normalizat1on and ar1thtnet10 cperationtJ (elC«,1ept
division)

C

ANALYSIS
PREPAR~D

BY

CHECKED BY
f~r::V!SEO

~J

.\/

r~

,.

9

PACt:

L. Barton
"L"·' ::c, ('~ ('1:':,11. U1(n:.mc:I C~Jl",.o~,.nOJI
C.Stv'lI4'T, D.farker, D.Bjelsk~~r t;iU·J r:m•. ~.:o

Rt:C;'Oi,T t,:o.
MOD::~L.
DATg

BY

ZN-527

ALL

8/29/56

.-,

,..--------.......;.-..;.:....;.------------'-----------~------~.

Two Ilddrees COfilI'\.ands

14 CC IIXX YIlt
14 i8 the interpretiv. code
CO 18 ths peeudo command ood.

XXIX (excluding the leftlnost two bite) 1. the
address ot the operand plaoed

1D register B. .

yyyy (exo~uding the leftmost two bits)

i.the

address of the oper8lld placed :lD register C.
'Ib8 first (lettmost) bit

ot XXII or

nn

t. oalled a tar. U.

0_,

it will oau.e a temporary addItion of the cOl.ltenta ot· index register
b l;'·to· thati .addx-e •• ~du.r1ns'.operat1ori.

Af'tt!r the operation the instruction r8SWQeS ita original unalteredtora.

The 'second (next) bit, it 'one, will add the contents
b '2 but othervi•• operate a8 desoribed tor b 1.

or

index register

Ibth -7 be used in

the same operation.

One address commands

14 CO KNN l1lYt
~

1a the interpretive (1103) code.

CO 11 the p.8udo command coda
I 18 divided into two' parts.
The leftmost 2 bits are used a8 taga on tbe Y addre~ ••
The first (leftmost) bit

or

addS.t1on of the contents

ot inc1ax register b 1 to the

operation.

K it .• on. vill oaus8 a temporar,
t' address durin,

After the operation the instruction reaum.ee its original

ur.alt0rod torm.

The 3econd (next) bit it a one will add the

10-250·

content~

J

c

ANAL-YOl.:)

0

~. ~

V

t,

I

n.

Barton, L.
C.Swlft, n".Farker,

PREPARED BY
CHECKED DY

PAGE: 10
n;O::POnT NO. ZM-527
MODEL

DATE

REVISED BY

ALL
8/29/56

of index register b 2 but otherwise orera te as above tor b 1.

Both

tags may be" used in the same operation.
The third (rightmost) bit of K will be used with :NN as a number N.
/

NN vith the third bit

or

Jt is the number N placed in register B

'Uld usually used as a oounter.

Its maxiIll.Ull size 1s 177 ootal or.l27

decimal.
lYIYY 1a the address

or

the number plaeed in register C•.

Commands and Registers

14 00 IXXX

nn

I+ItoR

or 37 01741 01656
C + B to R
14 01

un nn

y-XtoR

or 37 01741 01655
C - B to R

·14 '02 XUX !YYY
Y.ItoR

or 3.7 01741 01706
CeStoR

14 03 IXIX

nn

1/1 to R

or 37 01741

01b3~

C/B to R
Registers
R tinal vi1l bedupllca ted in C and the double extension

tinnl mantissa will aieo be in the accumulator

or

the R '

CV-183

CON V A I R

ANALYSIS

PREPARED flY
CHECKED BY

PAGE
REPORT NO.

L. .Parton
A DIVI$lO. 0" elUIIUIAL DYNAM.CS CO_POeATlON
·1
C. S'W1ft ,D.l'ark er, D• E e 1 s k·er SAN
. ou.tGO

MODEL
DATE

REVISED BY

11
ZV1-527

ALL

8/29/56

P will be unchanged

For 14 type instructions
R in1 t1al vUl be in S and B

For 37 type instructions
S \iiIl be. !unchanged and dupl1ca ted in B.
Commands and ~g1ster8

14 04 XXXI mY

R in! tial + Y + I to R
/

14 05 XXIX YIn
R in!t1a1 + Y - X to R

14 06 XXXI YIn
R in! tlal + I • X to R

or YI 01741 01617
S + Y • Xc/'to R

14

nn
R in! tial ... III
07 XXXI

to R

Reg1a'btra

R .final will be duplicated in C and the double extension
t;1nal mantissa vill a1ao be in the accww.lator

P will be unohanged

For 14' type instrUction.

R initial Yill be in S and B
For

)7 ~.

instructions

S will be unchanged and duplicated in B

,.0".....'.·1.

10-252

or

the

a

ANALYSIS

L. f}1rton
A 1J1i"~lO:l 0' ~r..';::P.L DY;lM,lca CCEPOaAiiON
C,,'\N OIt::CO
BY C. Swj ft, D. F::trker, D. Bi e 1 s k er

PREPARED BY
CHECKED

PA!.it! 12
NO. ZM-527

~m~:~~T

~l9D;ZL

QATE

REVISED BY

ALL

8/29/56

Commands and Registers

14 20 XXXI

nyy

y .. X to R, Y

or 37 01746 01656

c+

B to R, S98 footnote.

14 21 XXXI InY
y - X to R, Y

or 37 01746 01655
C - B to R,' se" footnote.

14 22 XXXI lIll
Y. • X to R, Y

or

')7

01746 01706

c • B to R, see footnote •
.l4~'23 XXIX ,mY

I/x to Rt I

or 37 01746 01633

c/B

toR, see footnote.

Registers
P,v1l1 be unchanged

For 14 type instructions
R tinal will be dup11ca ted in 0 and I and the double extension' of

theR tinal mantissa will' also be in the accumulator.
R in! t1al w1ll' be in S and B

For 37 type instructions
• R thlal will be dup1ioa ted in C and also 8: t the "Y" address takell

frolll the last 14 instruotion, used and located in the V portion ot cell

, 01744 (where it is subject to ,modifioation by the ~grammar)

AN~LYSIS

C 0

PREPARED BY
CHECKED BY
REVISED BY

~4

V A I R

PAGE

L. Barton
ADlnao. 0' .."tKA.. 011lAata ~o.I'O."no.
SAN DIEGO
C.S\o,'ift, D.f'arker, D. Blelsker

13

REPORT NO. ,ZM-527
MODEL AU,
DATE

8/29/56

The double extension or the final mantissa will also be in the
8ccumla tor •.

S

~11

be unohanged Rnd duplioated in B.

Commands and Registers
14 24 XXXX 'tYY¥

R ... Y ... I to R, Y
14 25 XXIX

nn

R + Y - X to R, Y
14 '6 XXXI

nn

R + Y • I to R, Y

or

)7

01746 01617

s ...

C· B to R, •

14 ")7 IXXX IYlY
R .. T/I to R, T
IsgiatAillre

P vill be unchanged

For 14 type instructions
R tinal will be duplicated in CandY and the double .mosloD ot the R

tinal mantissa will also be in the accumul.ator.
R in1 t1al will be in S and B
for

37 type instruotions
~

tlnu viII be duplic. ted in

from the last

a and also at· the

"f~

address tOeD

14 inptruot101}<' used and loea ted in, the V portion of Cell

01744 (Were it is subject to IIlOdltioation b,. the progr8.IllDler)
r

double extension

or

•

,

'!be

the R final mantissa will a180 be in the acoumalator

S will be unohanged and dupl1ca ted' in B.

,.0" . . . . . . . 4

•

10-254

CON V A I It

ANALYSIS
PREPARED BY

CHECKED BY
REVlSEJ:) BY

. PAO.

L. Barton
A INWIIOIIW ........ mIA""- ~110.
C.Svift, D.farker, D.Bielsker SAN DIEGO.

REPORT NO.
MODEL
DATE

14·
ZM-527

ALL

8/29/56
\.

Co--.nda 8lld

Regl~ tars

Threshold jump
14 17 IXXI ~

It X 1s greater tban R Jump to Y; otherwise continue with the next
instruction (caution - due to rounding .. jump .7 occur e1·tber way
\lhen X approaches R i t X and R b.s:ve be~n,ealculated by 41rterent operat /

tiona)
R ini t1a1 will be unchanged in R, S, and B

R - I will be in C and the manti8sa of R - X will be in the acauaulator
P will be unchanged.
~dex

jumps vi th modifioa tion of b indexregieters

14 76 KNJ !lYYY

'With b

1

1.4 77 KNN YfYIY with b 2·
Add 2 to the contents of b 1 or b 2.

I t . (last bito! K with II

from instruction is-greater than hl or b2· jUDlp to y and l~ave bl or b2

advanced.
Otherwise set bl or b2 equal to zero and continue with the next
instructior..
The oontents of Y (2 cells) will be placed in register C'.

N (from the last hit of K and D) vill be placed in register N and
remain unchanged
R initial Yill be duplicated in S

R, P, and B will be unchanged.

Polynomial
14 75 101M YmY
ComputA the polynomial

Ao ..

All + Ai'2 + ••• +

X must be pre8tore~ in register

P

A"xnJ

Where I

ANAL.YSIS
PREPAREO BY

CHECKED BY
REVISED

CONVAI R

PAGa:
REPORT NO.

L. Barton
,...-o.U."DM..QAJdaco~no.
SAN DlaGO
C.Swift, D.I'arker, D. Eielsker

MODEL

av

DATE

Y 18 the addres. o,t the last constant,

'Nt

15
ZM-527
ALL
8/29/56

where the constanta

.are .floating point nwnber8 stored each in. t'WO cella .... JI'BIlt1... ,
.~onent

- consecutively,

I is, the "degr..

. 1ha

8lUJ'WW

or

10,

'1.

+ ••• +

'B.

the equation •

appears iD R.

It N 18 ,1••• thaD one, no operation will bepertormed."
'B. and C will oontain the an.wer.
B aD4 B

v1ll oontain

.Ao

P will COlltaln I
• vill be aero
~

double extension of the "I1B.Dtl...

&be aoOUlllla tor.

P'OIIIM tata-4

10-256

ot

the aD....,. wUl ..:leo be" ill

PREPARED BY

L. Barton

CHECKED BY

8.3wllt,

N V A I R
COIII'O""'••

C 0

ANALYSIS

A ........ . , .aDA&. DTIIA.acs

'

~.Parker,

D+Eielsker

SAN DIEGO .

PAGE

REPORT NO.
MODEL

Commands and Regis tars

ALL

I
l.
;~

Card Instructions

14 57 KNll

ZM-5"

DAn: 8/?9/56

f

REVISED BY

16

r

-rnn/

.

~a~. N cardll <, is .~ with the rightmost hit or r.)
seeutive~y

I

into cells con-

'

starting at Y in normalized floating point tor••

14 56 KNN YYYYY

Punch N oards (N is NN with the rightmost bit of K) trom cells consecutively

8tarti~g

at Y where numbers are stored in normalized

floating point form.
Re~isters

Register N will contain the number N unchanged.
Register C will contain the first word stored at Y.

In the case

or

read or punch this will be the contents of Y betore read or punch

- R, S, P, and B \Jill be unchanged.' Register C cannot be punched
by a

14 inetruction since Y is placed

in C at the start

ot all 14

in terrre ta tiona.
Re turn jump

card ortlons

Card read
37 77400 77401

.t;'Ij

AB utt)UU \rvvYV

OJ

--S
r-I

I

A. If a is equal to 4,5,6 or 7 do not print sum, otherwise print a

I

li;h8

sum which is characteristic of those cards.

'"t-

,.....

B. If B is equal to 4,5,6 or 7 read in mantissas as integers to

:><

0..

the zero. scale factor, and store them in single consecutive oe11s.
Ignore all exponents.

Otherwise read in and store normsl !losting

point numbers in normalized form.
lJUUUU

Address for storage of the first data word.

C ,0 N V A I R

ANALYSIS
PREPARED BY
CHECKED BY

PAGIE

L. Eerton
& . . . . OF ••aDA&. DYIWIIa COINUIIOII
N
it
e.s", t, D.Parker, D• .w.elsker MN~~

MODEL
DATE

REVISED' BY

" " ' Nwnber
nWllOer

ot noatina

17

REPORT NO. ZM-5'7

ALL '

8/29/56

point nwabera to b. read, or with optlol1

ot JllaDtiaau stored &8 integer••

Card outplt

37 76760' 76761 '

',a tM1UU vvvv,-.
It

,_

;

4,',6

It ~'1. tlqual'to
~,

'

or 7 the carda will not be m:uabered,
~'

,

Cell 77303

, otherv1ee tbe1vW. be numbered swt1ng'at one.

taiDe this oounter and ay-, be

At

at

OM

GOD-,

1••• thaD, tM Dext po.lti...

oardnumber d••ired.
B Ie DOt uaed.

'1IUUUlT Ie theatonp .ddree. of the tirat 1BD14a.. :;

ot

" " " I. the JlWIber

Co4J.DI

tloating poiDt IlWIber. to be p:dlohed.

1o~,8

..;-

~'·-lD 0 •••

ot .11 tailure

let PJI[equal to.

71430 tor nat, or'

7700? tor w1 tie'.
IS will be reatored

ot

the $.Ilterrupted

~oard" 'are

toll~wed by .. ~.top'v.1tb -they

~rd

addreu ,that'

ae tnictlon.

POt priMd at .tart of

Progr... '

1700Q00 77433 will adn.noe em.' re_~ card.

;1.700000 77342 wUl .dYanoe

punob' cud.

0D8
,

1700000 '17413 v1ll .~o. one,
,

"_<:

17154

01141

31 01365 00044

RESTORE

77155

01142

32 01371 00000

A

77156

01143

13 10000 10000

2 EXP 35

77157

01144

55 10000 00001

2 EXP 36

,--..
C"J

0

r-l

'-"
I

0
r-l

I

0

0
0"r-l

0...

10-277

TEST FOR ROUND
ROUND
MANTISSA
AND
ADJUST
ADJUST BSF
SIGN OF BSF
DIVIDE EXP
BY 33

10 EXP 10

ACQUIRE DIVISOR

9-6-56

!

\'

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

CV-ltlJ

f

SAN DIEGO, CALIFORNIA

PAGE

ZM 5?7-1I

MODEL

All

DATE

77160

01145

31 20000 00001

77161

01146

42 01372 01150

77162

01147

71163

01150

77164

01151

27 10000 01310
11 10000 01365
37 01151 01152

71165

01152

41 01367 01123

77166

01153

16 01366 01123

77161

01154

31 01151 01123

17110

01155

11 01373 01366

11171

01156

21 01050 01326

11172

01151

21 01026 01326

11173

01160

37 01200 01174

17174

01161

12 01366 20000

77175

01162

11 01333 01316

71176

01163

73

Ol'-~ll

.-,

01~12

01311

77117

01164

11

L

77200

01165

31

,:.

77201

01166

32 01365 00001

77202

01161

11 2aOQO 01365

17203

01170

34 20000 00063

77204

01171

35 01375 01172

71205

01172

30 00000 00000

77206

01113

31 01173 01114-

71201

01174

55

77210

01115

44 01176 01171

77211

01116

21 013'1'5 01334

11212

01117

41 01376 01165

17213

01200

37 01200 01201

77214

01201

11 01370 10000

77215

01202

44 01203 01205

77216

01203

13 01331 20000

77217

01204

37 01173 01171

'.)
i

~j

,j

":;

Ol~74

00002

00043

DETERMINE
LAST
BIT
ANSWER X 2 EXP 36
HIGHER ORDER DIGIT
LOWER ORDER SHIFT
LOWER ORDER DIGIT
DECIMAL EXPONENT
STEP
STEP
SHIFT FOR PERIOD
EXPONENT
TALLY
DIGITS
OF EXP
EXTi,' (T
ANL'

IrION
DIGIT
ASSEt-1BLE INST
SET BIT
po-

SHIFT BIT
ADVANCE FIELD
TEST FOR END

SIGN

10-278

1/...

REPORT

9-6-56

-~

REPORT
MODEL

2M 527-11
All

DATE9-6-56

...,
J

)

SHIFT BIT

11220

01205

55 01374 00043

77221

01206

37 01206 01207

77222

01207

31 01312 00017

77223

01210

37 01200 01171

77224

01211

31 01371 00017

77225

01212

37 01200 01171

77226

01213

11 01366 01370

77227

01214

37 01206 01201

77230

01215

37 01215 01216

77231

01216

41 01352 01047

WORDS PER CARD

77232

01217

11 01335 01311

SIT FOR 12 ROWS

77233

01220

21 01377 01336

77234

01221

21 01411 01336

77235

01222

21 01404 01336

77236

01223

21 01413 01337

77237

01224

21 01425 01337

71240

01225

21 01420 01337

77241

01226

16 01267 01233

77242

01221

16 01127 01234

77243

01230

15 01267 01231

71244

01231

55 300-00 00010

77245

01232

11 00000 10000

77246

01233

11 10000 30000

77247

01234

77 10000 30000

77250

01~35

23 01231 01331

77251

01236

23 01233 01310

77252

01237

23 01234 01310

71253

01240

41 01371 01231

TEST FOR END OF CARD

77254

01241

23 01351 01342

TEST FOR

71255

01242

46 01243 01016

77256

01243

77251

01244

41 01350 01001
75 10004 01246

END
FLOATING FLAG

TENS DIGIT
UNITS DIGIT

-!

--'
!
)
-!

,
)
)

"-!
~

.

10- 27 9

CONVAIR .... DIVISION OF GENERAL DYNAMICS CORP.
51\N DIEGO. CAl.IFORNIA

77260

01245

61 00000 01302

77261

01246

11 01305 01371

77262

01247

55 01345 10011

77263

01250

31 01264 00000

77264

01251

52 01343 01252

77265

01252

30 00000 00000

77266

01253

55 10000 00003

77267

01254

41 01311 01250

77270

01255

37 01255 01256

77271

01256

55

17272

01251

61 00000 01305

77273

01260

11 01335 01311

11214

01261

31 01255 01250

77275

01262

77276

01263

45 00000 01001
55 01310 10001

71277

01264

61 00000 01271

77300

01265

21 01401 01374

77301

01266

00 01353 00000

77302

01267

00 01442 01412

77303

01270

00 00000 00000

77304

01211

00 00000 00031

17305

01212

00 00000 00052

77306

01273

00 00000 00014

77307

01214

00 00000 00070

71310

01215

00 00000 00064

17311

01276

00 00000 00062

17312

01217

00 00000 00066

77313

01300

00 00000 OQ072

77314

01301

00 00000 00513

77315

01302

00 00000 00045

77316

01303

00 00000 00006

77317

01304

00 00000 00026

01346 10003

10-280

CARD COUNTER

CV-183

PAGE 16
REPORT ZM 5?7-I1
MODEL All
DATE
9-6-56

REPORT
MODEL
DATE

...-..
('j
co
......
~

77320

01305

00 00000 00004

77321

01306

00 00000 00143

77322

01301

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 24021 62000

71336

01323

00 00000 00041

77337

01324

00 00000 00112

77340

01325

00 00000 00102

77341

01326

00 00002 00000

77342

01F21

00 00000 00110

77343

01330

00 00000 00077

17344

01331

00 00001 00000

77345

01332

40 00000 00000

17346

01333

00 00000 00011

77347

01334

00 00014 00000

77350

01335

00 00000 00013

71351

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

00 00000 000.07
01344 ·00 00000 '00002

I

0

......
I

0

0

0"

......

t-

x

0....

77357

01343

10-281

EXCESS

21-.1 527-11
All

9-6-56

CV.,.,183

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

PAGE ... '18
REPORT ZM 527-11
MODEL All
DATE
9-6-56

SAN DIEGO. CALIFORNIA

Revjsed 10-?Q-56

SPUR SUM AND MT IKS1'RUCTION

SROK FROfvl MT 3
FLIP FROM r.1T 3
SPUR FROM '''IT 3
sur.., SPUR
CHANGE SUPUR SUf\1
ERA f'.1A I NT. FROf\1 ~1T 3
START SUM

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

77375

32 76000 00000

77376

75 00001 77371

77377

11 10000 77771

71400

34 77303 00000

71401

34 77400 00000

71402

75 20013

71l~26

FROr4

71403

34 76110 00000

SUM

11404

11 71423 00000

SET

71405

75 31777 71407

STORE

71'+- 06

11 00001 74001

71 L.07

75 30015 00411

71l+-10

11 11411 00411

111~OO

CHANGE
SUr-.1

REtv10VE
VARIABLE

F

r:S
THIS
TO ES
READ ONE BLOCK
TEST FOR
ZERO DLOCK

71411

00411

6 L• 30001 00000

71412

00412

11 00000 20000

71'1-13

00413

43 00 1.. 25 00421

71414

00414

31 71 f t 2 4 00052

71415

00415

61 00000 20000

71/+ 16

00 1+16

34 20000 00006

71417

00417
00 /.. 20

it 7

56 00000 00411

TRY AGAIN

COl~21

66 30 /100 00.'")00

ADVANCE TO

71 /t20
71 /f 21

71',22

OO'~

22

PRINT
TAPE
AL!"R ~~

00415 '00'+20

6 L+ 30001 00000

10-282

t-\ ,.. •

,.....

to< t./-\u

SPUR

i i"! FIR 5 T 8 L 0 C K

REPORT
DATE

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

71330

01315

00 00003 03240

77331

01316

00 00036 41100

77332

01317

00 00461 13200

77333

01320

00 05753 60400

71334

01321

00 73465 45000

11335

01322

11 24027 62000

17336

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

71351

01336

01 00001 00001

t-

77352

01337

00 00100 00100

:x:

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

,.-...

co
......
I

0

......
I

0

0

0"-

......
0...

lO-28l

EXCESS

Zlv1 527-11

All
9-6:"'56

MODEL

CV.,.183

CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.

PAGE ~_

SAN DIEGO. CALIFORNIA

'18

REPORT ZM 527-11
MODEL All
DATE
9-6-56

Revjsed lO-?Q-56

SPUR SUM AN D MT It\SfRU eTlON

70000

45 00000 70006

SROK FROr"1 !\1T 3

70001

45 00000 70100

70002

45 00000 71404

70003

45 00000 77371

70004

45 00000 77376

70005

45 00000 70071

77371

31 70000 00000

FLIP FROM MT 3
SPUR FROM MT 3
sur~ SPUR
CHANGE SUPUR SUM
ERA r-.1A I NT. FRorv1 ~1T 3
START SU~4

77372

75 23777 77374

77373

32 70001 00000

77374

75 21777 71 '.00

77375

32 76000 00000

77376

75 00001 77371

77377

11 10000 71777

CHANGE
SUf-.1

71400

34 77303 00000

RE~10VE

71401

34 77400 00000

71/+02

75 20013 71'.. 26

71403

34 76110 00000

71404

11 71423 00000

71405

75 31777 71407

VARIABLE
FROM
SUM
SET F
STORE

71 1.. 06

11 00001 74001

71407

75 30015 00411

71'.. 10

11 71411 00411

E's

THIS
TO ES
READ ONE BLOCK
TEST FOR
ZERO ULOCK

71411

00411

64 30001 00000

71412

00412

11 00000 20000

71'1-13

00413

43 OOL+?5 00421

71414

00414

31 71 /,? 'f- 00052

71'+15

00415

61 00000 20000

71/+16

00416

34 20000 00006

71417

00417

47 00415 '00420

71420

00420

56 00000 00411

TRY AGAIN

7 ).t.~ 2 1

00421

66 304-00 001)00

ADVANCE TO

71 Lj-2 2

00 /+22

6 f t 30001

1"\,../1,",

1"\1"11"11'\'"
UI,,/VUI.,j

PRINT
TAPE
ALAR~·1

1"\

c,-,

LJ

,J.I-l""

SPUR
FIRST L.. v\.. "
1"')1

'~i

ArU'

h,J

E.

T.

I

,'"

F

PAGE

SAN DIEGO. CALIFORNIA

18A

REPORT

21',1 527-11

MODEL

All

9-6-56
Revised 10-28-56
DATE

71423

00423

45 00000 00002

71424

OOll- 2 4

45 01301 52056

71l~25

00425

45 07777 00002

JUMP TO FIRST BLOCK
FLEX TAPE
LOCATOR ON ZERO BLOCK

71426

34 77432 00000

FURTI-IER

71427

34 76760 00000

71430

34 77011 00000

71431

11 20000 20000

71432

11 20000 10000

sut~

71433
71434

36 77777 20000
i~ 7 71435 71445

71435

31 71466 00052

71436

61 00000 20000

SUBTRACT STORED
SUt,1. TES T
SPUR FOR PRINT
PRINT

71437

34 20000 00006

71440

47 71436 71441

71441

37 71't41 71442

71442

31 71470 00052

71443

37 71441 71'+36

71444

56

71'~4 5

37 71441 71435

71446

31 71467 00052

71447
71450

37 7144,1 71436'
56 00000 7~451

71L~51

75 17000 71453

71452

11 20000 40000

71453

75 17000 71455

-;

71454

11 20000 47000



"'i

-'

I

)
-I

I
)
)

i'

l....

___

~rt.n

SUM

ADJUSTMENTS
TO

Q

\fJORD

S\~ITCH

' PR I NT
NO SUM
TO RgAD FROM
PRINT SPUR
PRINT
SUM OK
TO CLEAR
START CLEAR

t-1T

C()NVAtR

-~

DIVISION OF GENERAL DYNAMICS CORP.

CV-183

18B
ZM 527-11
MODEL All

SAN DIEGO. CAL.IFORNIA

PAGE

REPORT

DATE9-6-56

Hevised 10-/0-56

31 71471 00052
37 71441 71436
57 00000 00000

PRINT
CLEAR

45 24153 41204

FLEX

SPUR

. : 67

24 34070 40336

F:"'EX

SU~~

,

M

06 03042 43407

:I

04 16112 03012

'-'53
~'.

c.' !~

:', E~

:~

:;.

.I

i

75 12000 71461
11 20000 74000

OK

FLEX NO SUM
FLEX CLEAR
CLEAR 74000
75777

~ORM

NO. E. T. - I

,I')· F

PAGE

SAN OIEGO. CAL,IFORNIA

19

REPORT
MODEL
DATE

SPUR CARD INPUT
EXIT
STORE

77400

00742

56 00000 30000.

77401

00743

75 31777 77403

77402

00744

11 00001 74001

ES

71403

00745

75 30352 00741

17404

00746

11 77400 00742

77405

00747

11 00742 20000

17406

00750

36 01264 77432

ROUTINE
TO ES
SET
REPEAT

77407

00151

35 01305 20000

SET

77410

00752

71411

00753

EXIT
TEST FOR

77412

00754

16 20000 00770
55 00742 20025
44 00757 00756

77413

00755

00 00000 00114

71414

00156

32 00716 00000

ADDRESSES
ADDRESS MODIFICATION

77415

00757 . 55 20000 00017

77416

00760

37 00760 00761

17417

00761

17420

00762

16 20000 00763
II' 00177 01024

17421

00763

7l 01264 30000

77422

00764

55 20000 00006

71423

00765

37 00760 00754

77424

00766

55 20000 00017

77425

00761

37 01001 01004

TP SIBRPITOME

71426

00770

75 31711 30000

77427

00771

11 74001 0000_1

71430

00772

75 31777 71432

0

77431

00773

11 74001 00001

t- .

......

77432

00774

30 00000 00000

RESTORE E S
AND EXIT
RESTORE E S
AND
REPEAT

><:

77433

00775

02 00000 00104

77434

00716

74 00000 00000

'7743 ~ I. 00717

11 00000 00000

71436

30 00000 000.00
45 00000 30000

.--C"J

co
......

,
0

'--'
....-4

I

0
0"

0...

77437

I

01000
01001

ES

SET ACQUISITION
ERASE INSTRUCTION
ACQUIRE CONTROL WORD
X

REPEAT
EXIT

ZM 527-11
All

9-6-56

PAGE

SAN DIEGO. CALIFORNIA

ZM 527-1I

MODEL

All

DATE

77440

01002

16 01001 01003.

77441

01003

71 01264 30000

77442

01004

13 20000 01352

77443

01005

11 01263 01314

71444

01006

11 01263 01315

17445

"01007

16 20000 01314

77446

01010

55 20000 00003

77447

01011

13 20000 01351

READ AS INTEGER FLAG

77450

01012

31 01255 00000

77451

01013

35 012.17 01227

77452

01014

;11 01305 01356

11453' '01015

11 01265 01351

SET FINAL
TRANSFER
SET TRANSFER
STEPS

77454

01016

77455

01017

44 01017 01022
23 01227 01313

17456

01020

77451

01021

11 01264 01356
23 01357 01261

17460

·01022

55 10000 00021

71461

01023

16 10000 01230

77462

01024

21 0100101264

17463

01025

36 01305 01000

77464

01026

23 01314 01264

77465

01027

46 01001 01030

77466

010.30

41 01352 01032

77467

01031

61 OiOOOO 0130,3

77470

·01032

17 0'0000 01300

77471

01033

11 01260 01350

77472

01034

16 01256 01224

77473

01035

75 10011 01037

17474

01036

11415

01037

11 01263 01316
76 00000 01361

71476

01040

.76 10000 10000

77477

01041

76 10000 01360

I

ACQUIRE CONTROL WORD
PRINT SUM FLAG
CLEAR
CELLS
N
NUMBER OF WORDS

MODIFICATINNS
FOR INTEGER
STORAGE
SET DATA
STORAGE

EXIT
SET REPEAT
N-l
EXIT IF N 0
SUM TEST
(:ARRIAGE RETURN
READ AND PICK CARC
9
LINE DIGIT
SET TEMPORARY STORAGE
CLEAR
MATRIX
SET

10-286

20

REPORT

9-6-56

FORM NO. E. T .. 1 \i~, I'

~XG~Hil

SAN DIEGO. CAL,IFORNIA

REPORT
MODEL
DATE

9-6-56

77500

01042

31 01042 01043

77501

01043

54 01361 00034

77502

01044

11 01257 01054

SET 1ST STORAGE

77503

01045

11 01304 01327

SET INDEX

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 01041

TEST DIGITS

77511

01053

31 20000 00000

CLEAR A LEFT

77512

01054

30 00000 00000

STORE MATRIX WORD

77513

01055

21 01054 01301

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

71524

01066

46 01067 01037

TEST FOR 11 ROW

77525

01067

11 01264 01350

77526

01070

37 01064 01031

11 ROW

C'J

77527

01071

37 01042 01031

12 ROW. DUMMY

--

77530

01072

44 01073 01075

TEST EXIT FLAG

71531

01073

11 01302 01314

OVERRIDE INDEX

77532

01074

11 01255 01350

SET FLAG

r-

775.33

01075

31 01314 00000

N-l REMAINDER

><
Cl.!

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

,-..,

co
.-t
I

0

.-t

I

0
0
0"-

.-t

ZM 527-11
All

3

0
9

PAGE;!;J.
REPORT

ZM 5??-II

MODEL

All

DATE

77540

01102

55 01316 00024

SHIFT FOR IDENT NUMBER

77541

01103

11 01302 01341

SET FOR 5 DATA WORDS

71542

01104

31 01304 00000

TEST FOR

17543

01105

42 01314 01115

LESS THAN

11544

01106

11 01314 01347

5 WORDS

71545

01101

31 01314 00011

N-1

11546

01110

35 01306 10000

TEST FOR

77547

01111

41 01351 01113

71550

01112

55 10000 00001

11551

01113

31 01255 00000

SET SMALLER

77552

01114

35 10000 01227

STORAGE

77553

01115

37 01124 01120

SPACE FOR PERIOD

71554

01116

11 01260 01331

SET TALLY

77555

01117

11 01263 01321

CLEAR

71556

01120

41 01332 01123

TEST TO

71557

01121

21 01123 01306

17560

01122

11 01262 01332

77561

01123

55 30000 00004

71562

01124

37 01124 01125

77563

01125

31 01321 00002

71564

01126

32 01321 00001

77565

01127

52 01301 01327

77566

01130

41 01331 01120

TEST N COMPLETE

17567

01131

11 01327 01334

SET EXPONENT FOR N

775jO

01132

31 01124 01120

ACQUIRE

71571

01133

51 01301 20000

SZePN

11572

01134

,11 01265 01330

FLAG

. 11573

01135

47 01136 01140

TEST SIGN

77514

,01136

13 01327 01334

SET EXPONENT FOR N

71515

01131

13 01265 01330

-FLAG

77516

01140

37 01140 01141

77577

01141

11 0132.1 01354

10-288

INTEGER
OPTION

9

CHANGE MATRIX
WORD
PSSITION DIGIT
N X 10
ADD
DIGIT

MANTISSA X 10 EXP 10

3

0

9-6-~6

""-.LV,",

FOR'" NO. E. T .. 1 \f~," ..

SAN OIEGO. CAl.IFORNIA

PAGE

23

REPORT
MODEL
DATE

C')

co
.-f
'-"
I

0
.-f

I

0

0

0'
.-f

t~

0...

77600

01142

11 01330 01355

MANTISSA FLAG

77·601

01143

11 01264 01331

SET TALLY

77602

01144

37 01140 01117

EXPONENT INFORMATION

71603

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

77607

01151

23 01327 01330

77610

01152

12 20000 20000

77611

01153

73 01265 01353

TENS DIGIT

77612

01154

31 20000 00017

UNITS DIGIT

77013

01155

35 01254 01215

UNITS POWER

77614

01156

11 20000 01251

77615

01157

23 01334 01265

ADJUST EXPONENT

11616

01160

11 01216 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

71622

01164

31 01354 00000

N

17623

01165

13 01327 01333

N ADJUSTMENT

77624

01166

77625

01167

31 20000 00043
13 0132.7 10000

77626

01170

55 10000 00001

77627

01171

~2

01263 00001

LAST

71630

01172

42 01327 01174

BIT

77631

011.73

27 10000 01264

77632

01174

31 10000 00044

77633

01175

32 01333 00044

17634

01176

11 01263 01331

CLEAR

77635

01177

74 20000 01331

SCALE FACTOR N

17636

01200

11 20000 01354

STORE N

17631,

01201

46 01202 01207

TEST FOR ROUNDING

FOR

a

EXPONENT
ADJUSTMENT,

OF 10

FOR NEGATIVE
EXPONENT
DETERMINE

OF N
ASSEMBLE
M

ZM 527-11
All

9-6-56

,.Aul:.

;(4

REPORT

All

DATE

9-6-56

77640

01202

21 01354 01264

ROUND

11641

01203

43 20000 01207

77642

01204

32 01263 00101

11643

01205

11 20000 01354

11644

01206

21 01334 01264

77645

01207

31 01331 00000

ADJUST FOR
OVERFLOW
IF
NECESSARY
ADJUST

77646

01210

42 01303 01212

77647

01211

23 01334 01312

77650

01212

21 01334 01331

77651

01213

37 01213 01214

71652

01214

41 01353 01163

77653

01215

30 00000 00000

77654

01216

37 01213 01163

TEST TENS DIGIT
POWER FOR UNITS DIGIT
ADJUST FOR UNITS DIGIT

77655

01217

11 01354 01333

N

77656

01220

41 01355 01222

77657

01221

13 01333 01333

77660

01222

21 01315 01333

77661

01223

75 30002 01225

77662

01224

11 01333 30000

71663

01225

21 01224 01356

77664

01226

41 01347 01115

17665

01227

30 00000 00000

17666

01230

11 01335 30000

77667

01231

21 01230 01351

77670

01232

23 01314 01261

17671

012.33

46 01234 01033

77672

01234

41 01352 01001

71673

01235

31 01263 00000

11614

01236

15 00006 01240

SIGN OF N
NEGATIVE
SUM
STORE
TEMPORARY
STEP STORAGE
TEST END OF CARD
FINAL
STORAGE
STEP
TEST FOR
END
TEST PRINT SUM
CLEAR
SUM

71675

01231

32 01315 00014

77676

01240

31 '20000 00030

77677

01241

32 0126,4 00004

SCALE
FACTOR

10-290

ZM 527-11

MODEl..

FORM NO. E. T .. I

\,U .... VAIK -

(I' "

U'YI~IU'"

Vt' vtNI:KAL UINAMI\.:' "'UKt'.

SAN DIEGO. CALIFORNIA

\.III-LV")

PAGE25
REPORT
MODEL
DATE

-C")

OJ

77700

01242

61 00000 20000

77701

01243

34 20000 00000

17702

01244

41 01241 01001

71103

01245

71 01354 01327

77704

01246

37 01213 01176

71705

01247

37 01247 01250

77706

01250

41 01353 01245

71707

01251

30 00000 00000

77710

01252

31 01247 01245

17711

01253

45 00000 01217

77712

01254

11 01264 01327

77713

01255

75 30000 01231

77714

01256

00 00000 01335

77715

01251

35 01316 01316

71716 . 01260

00 00000 00011

71717

01261

00 00000 00005

17120

01262

00 00000 00010

17721

01263

00 00000 00000

77722

01264

00 00000 OOuOl

77723

01265

00 00000 00012

77724

01266

00 00000 00144

77125

01267

00 00000 01750

77726

01210

00 00000 23420

77127

01211

00 00003 03240

77130

01272

00 00036 41100

77731

01273

00 00461 13200

77732

01274

00 05753 60400

77733

01275

00 73465 45000

71734

01276

11 24027 62000

. 77735 ! 01217

00 00012 00000

..-I

'--'

0

I

..-I

I

0
0

0"..-I

t-

><
~

11736 ' 01300 ' 00'00000 00105
11737

01301

0000000 00017

PRINTING
ADJUSTMENT
OF N
AND
EXPONENT
FOR
POSITIVE
SCALE FACTOR
CONSTANTS

ZM 527-11
All

9-6-56

SAN DIEGO. CALIFORNIA

'"'v-.&.vu
PAGE 26

REPORTZM
MODEL All
DATE

77740

01302

00 00000 00004

77741

01303

00 00000 00045

77142

01304

00 00000 00003

71143

01305

00 00000 00002

77744

01306

00 00001 00000

77745

01307

00 00001 00001

77746

01310

00 00000 00043

71147

01311

00 00000 00044

77750

01312

77151

01313

00 00000 00110
00 00005' 00000

527-1I

9-6-56

FORM NO E. T .• i

,1>,

"'"" .... " ~I~ -

..,." 1.;tIV''''

vr ,",101'1"11\",,, .., I

"'.-.&.vo

1'1 ",ml"' .. "'VKr.

F

SAN DIEGO. CALIFORNIA

PAGE

27

REPORT

ZM 527-11

MODEL

All

9-6-56
Revised 10-20-56
DATE

SPUR DIVIS I Of,· AND

--..
J

../

75 30700 77754

STORE PART

77753

11 01100. 75100

77754

75 30021 01100

OF E.S.
THIS TO

77755

11 77756 01100

77756

01100

75 30200 01102

77757

01101

11 77213 01200

77760

01102

31 01746 00000

77761

01103

36 01310 10000

77762

01104

55 10000 00030

E.S.
PART OF
CARD ROUTINE
ADDRESS
OF
INST.

77763
7776 /t

01105

11 01305 01371

5 DIGITS

01106

61 00000 01302

77765

01107

37 01255 01250

77766

01110

61 00000 01305

CAR. RET.
ADDRESS
SPACE

77767

01111

31 01355 00052

PRINT

77770

01112

61 00000 2000'0

77771

01113

77772

0111 Lt

34 20000 00006
It 7 01112 01115

77773

01115

61 00000 01311

7777,4

01116

77775

01117

11 01766 10000
37 01351 a 13/~6

DI VISO R

77776

01120

77360

0134'5

45 00000 01345
55 01760 10003

TO CONTINUE
INSTRUCTION

77361

01346

12 DIGITS

77362

01347

11 01335 01371
61 00000 01305

SPACE

77363

01350

37 01255 01250

a OCTAL

77364

01351

37 01351 01352

77365

01352

75 30700 76061

77366

01353

11 75100 01100

77'367 . 01354

·56 00000 01741

77370

.22 14171 42403

I
:)
'-1

I
.)
)

l'
-I

-<....

ALARMS

77752

:)

.....

GEt;I~RAL

01355

76014

75 30021 76016

76015

11 77736 01100

LABEL
DIVISOR
~.'J 1\

RESTORE
ES
EXCESS
FLEX CODE
PART

OF

NTIS S!\

SAN DIEGO. CALIFORNIA

PAGE

28

REPORT

DATE

.;76016
76017

75 30200 76022
11 77213 01200

76020

75 30700 76014

76021

11 01100 75100

76022

75 30035 01137

76023

11 76024 01115

76024

01115

61 00000 01142

76025

01116

76026

01117

21 01115 01751
55 01760 10003

76027

01120

37 01351 01346

76030

01121

76031

01122

21 01117 01151
37 01122 01123

76032

01123

76033

01124

61 00000 01302
37 01124 01125

76034

01125

37 01124 01115

76035

01126

21 01117 01150

76036

01127

37 01122 01115

76037

01130

37 01124 01117

76040

'01131

37 01131 01132

DIVISION
ALARt·1
STORE
ES
THIS
TO ES
PRINT LETTER
STEP
PRINt
REGISTER
STEP
S\'J ITCH
CAR. RET.··
S\~J ITCH
PRINT N
STEP
PRINT
B

76041

01132,

37 01131 01127

76042

01133

21 01117 01753

76043

01134

37 01131 01127

7604~

01135

37 01131 01127

SWITCH
PRINT C
STEP
PRINT R
PRINT BOXES

76045

01136

76046

0113-7

45 00000 01352
11 01141 01355

SET,FLEX ALARM

76047

01140

45 00000 01102

76050

01141

30 11301 20745

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

FLEX ALARM

ZM 527-11

All
.. 9_6_56

MODE...,

FORM NO. E. T .• i

(I,.

F

SAN DIEGO. CALIFORNIA

ZM 527-11

MODEL

All

DATE

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

29

PAGE

REPORT

SET NO ACCUrvtULATE
SET STORE IN Y
RETURN TO N. I •

9-6-56

I,

E, T,· I (1-',

,",VI... '''''''' -

"

UIY';)I~

vr \:rI:Nr:KAL UY'NAMIC5 CORP.

CV-183

/1).30
2M 5?7-11
MODEL All

SAN DIEGO. CALIFORNIA

PAGE

REPORT
DATE

SF1JR 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
72012

11 20000 72012
00 01000 10001

PRINT

72013

44 72014 72007

LOOP

72014

11 10000 72012

RESTORE FLAG

72015

61 00000 72021

SPACE

72016

37 72016 72017

SvJITCH

72017

31 00000 00044

72020

11 72000 00000

SET

72021

37 72016 72004

PRINT

72022

37 72022 72023

'S\'JITCH

72023

31 72000 00017

FOR

72024

15 20000 72025

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

72032

41 00000 72033

ADJUST ADDRESS

72033

31 20000 00071

72034

37 72016 72'005 -.

72035

56 00000 00000

72036

00 00000

72037

61 00000 72037

JUf~P

(1.1 AI

ROUTINE AD

ALARM

PRINT 5 DIGITS
EXCESS

10-296

N

9-6-:-56

Wi<#- 10 •

iIo~. _ . .

......

...., . . . . . . ." , . . . . .

...,.

. . . . . . . . . . . . ""...

,.--,,,,,..

SAN DIEGO. CALIFORNIA

V i r ' J.VV

PAGE
REPORT
MODEL
DATE

-/2 a [I- 0

00 00000

72041

00 00000 00 74

72042

43 01130 12070

72043

00 00000 00 64

72044

00 00000 00062

72045

00 00000 00 66

72 0 L~6

00 00000 00 72

72047

61 00000 20045

72050

34 20000 00006

72051

47 72047 72015

52

FLEX
PRINT
LOOP

31
ZM 5;J7-11
All

9-6-56

PAG E 38

SAN DIEGO. CALIFORNIA

REPORT 2M 527-11
MODEL All
DATE 11-14-56

SPUR PAPERTAPE ruMP

73234

37 73234 73235

73235
73236

45 00000 73265
45 00000 73270

73237

45 00000 73273

73240

45 00000 73277

73241

11 00000 74000

73242
73243

11 73235 00000
75 30152 73245

732"44

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

7326'0

11 00010 13300

73261

75 30152 73263

73262

11 74001 00001

73263

11 7.4000 00000

73264

45 00000 73'234

73265

37 73253 73241

73266

75 3005.7 00041

'73267

11 73366 00072

73270

37 73253 73241'

73271

75 30040 00.120

73272

11 73445 00072

73273

11 10000 73275

10-298

EXIT
AUTiJ FLEX
AUTO BIOCTAL
MANUAL FLEX
MANUALBIOCTAL

RESTORE
ES

TO EXIT
STORE IMAGE
FLEX
PROGRA~~

STORE IMAGE
6IOCTAL
PROGRAM
PARAtv1ETER \.AID.

;"Vi'<

0..

onooo

00007

FLEX 0

CAR. RET.
STOP CODE

~V-J.O"

10.1£. T .• ' (i., "

SA" DIEGO. CALIFORNIA

PAGE

ZM 527-11

MODEL

All

DATE

73334

00040

45 00000 00072

JUMP TO PUNCH

7'3335

00041

75 00010 00043

LENDER

73336

00042

63 00000 00010

73337

00043

31 73234 00017

73340

00044

11 20000 00001

73341

00045

31 00014 00000

PARAMETER

73342

'00046

42 00001 00050

ADDRESS

73343

00047

21 00001 00015

73344

00050

15 00001 00051

73345

"00051

11 30051 10000

PARAMETER

73346

00052

11 00010 00001

CLEAR

73341

00053

11 00010 00003

73350

00054

15 10000 00003

73351

00055

11 00003 00004

73352

00056

16 10000 00001

73353

00057

44 73254 00060

73354

00060

44 73254 00061

13355

00061

44 73254 00062

73356

00062

21 73234 00011

733~7

00063,

31 00001 00011

73360'"
13361

00064
00065

34 00-003 00071
11 20000 00002

73362

00066

46 00043 00067

PAR. END

73363

00067

21 00001 00ql1

STEP

7336~

000.70

43 00033 00035

2000 TO ZERO

73365

00071

43 00006 00037

10000 TO 40000

73366

00072

55 10000 06002

73367

00073

44 00074 00075

73370

00074

16 00042 00135-

73371

00075

31 00014 00000

73372

00076

.42 00004 001"02

IN IMAGE·

73373

00077

21 00003 00015

ADJUST FOR

10-300

PARAMETER ADDRESS

IN IMAGE
..

TEMPORARIES
AD. OF FIRST WD.
AD. ·OF LAST WD.
PAR. INST.
STEP
LAST '),0.
FIRST AD.
NO. OF vIDS.

NO STOP PUNCH
CURRENT WORD
H~AGE

4D

REPORT

Il-P14-56

_ _ . . . . . . . .......

_

.... _

. . . . . <¥

.......

..., . . . . . . . . . , . . . ...

W' • . . . . . . . . . . ~_

~Ar"

FORM NO. E. T .• I (i'J."

PAGE

4l

REPORT
DATE'

73374

00100

16 00031 00127

73375

00101

45 00000 00103

73376

00102

16 00101 00127

73377

00103

11 00004 10000

73400

00104

56 10000 00105

73401

00105

55 10000 00006

73402

00106

37 00150 00142

5 DIGITS

73403

00107

15 00003 00110

73404

00110

31 30110 00000

73405

00111

43 00010 00121

73406

00112

75 00002 00114

CURRENT
v/ORD
ot~ I T PUNCH I NG
2 SPACES

73407

00113

63 00000 00013

73410

00114

11 2,0000 10000

CURRENT WD.

73411

00115

73412

00116

11 00011 00005
37 00150 00143

2 DIGITS

73413

00117

37 00150 00141

73414

00120

37 00150 00141

73415

00121

41 00140 00124

73416

00122

11 00017 00140

73417

00123

63 0.0000 00027

73420

00124

63 00'000 00027

' 73421

00125

21 00004 00006

73422·

00126

11 00004 00003

0
.....

73423

00127

41 00002

0
0
0"-

73424

00130

16 00032 00127

r-

.....

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

7343.3

00137

45 00000 00041

..-..
C>J

CD

.....

'-"

I

I

a..

30~27

CURRENT ·AD.

DLG ITS
5 DIGITS
32 HDS.
RESTORE TALLY
CAR.
RET.
STEP
5

END

TO NEXT PAR.

ZM 527-1J

All
11-14-56

MODEL

•. T .• '

......,..... "'.ft. - "." •••...,."

~. ~

vr VI;I'U;;tt"~ ""NAM't.~ ~UK"•

SAN DIEGO. CAl.IFORNIA

,",V-lUi)

PAGE

TALLY
SPfi:CE
SET TALLY

00140

00 00000 00037

73435

00141

63 00000 00013

73436

00142

11 00013 00005

73437

00143

55 10000 00003

73440

00144

51 00007 20000

73441

0014.5

35 00016 00146

73442
73443

00146

PUNCH DIGIT

00147

00 .00000 00000
41 00005 00143

73444

00150

45 00000 30150

73445

00072

63 10000 00010

73446

00073

73447

00074

11 00004 10000
55 10000 00025

73450

00075

37 00130 00122

EXIT
7TH LEVEL
PUNCH
INSERT
ADDRESS

73451

00076

37 00130 00122

73452

00077

31 00014 00000

IN

73453

00100

42 00004 00104

73454

00101

21 00003 00015

IHAGE
ADJUST

13455

00102

16 00131 00113

73456

00}03

45 00000 00105

73457

00104

16 00103 00113

73460

00105

73461

00106

15. 00003 00106
11 30000 10000

7.3462

,00107

11 00013 00005

734(>3

00110

37 00130 00123

73464

00111

21 00004 00006

73465 . 00112

11 00004 00003

73466

00113

41 00002 30113

73467

00114

11·00012 00005

73470

00115

11 00001 10000

73471
73472

00116
00117'

37 00130 00123
37 00130 00123

73473

00120

75 00310 00041

EXTRACT DIGIT

I

CURRENT ADDRESS
PUNCH
CURRENT
~JORD

STEP

>

10-302

END
CHECK
ADDRESS
PUNCH

42
ZM 527-11

MODEL

All

DATE

73434

I·'

REPORT

11-14-56

FORM NO. E. T. - 1

.I'

... _ .... .-. .." F

... ," ....... ," .... r

....

1ii."..

K~ ..

"I

n"'m."'~

,",UKr.

7'3, if 7 L~

0::. 1:2 1

63 00000 00010

731.1-75

O~)122

11 00011 00005

73L~76

OC123

55 10000 00006

7 3 L~ 77

00124

63 00000 10000

73500

00125

41 00005 00123

73501

00126

55 10000 00006

73502

00127

63 10000 10000

73503

00130

56 10000 30130

73504

00131

00 00000 00077

"'"

... ,,""

PAGE 4.3
REPORT ZM 527-11
MODEL All
DATE 11-14-:56

SAN DIEGO. CALIFORNIA

LEADER
PUNCH
2

DIGITS

___ ......._

t.T.·'

' _ a . . . _~_ . . .

~,JI'

_.,.

_ . , . ..... _ . . . . " . . .

SAN OIEGO. C;AJ.,IP:ORNIA

".~

..... _

..

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

"v-~q->

PAGE 44
REPORT
MODEL
DATE

SUPER OTTO SPUR

72052

01000

45 00000 01013

72053

01001

47 01002 01004

72054

01002

72055

01003

35 01304 01172
45 00000 01171

72056

01004

55 00022, 00043

72057

01005

72060

01006

53 10000 00004
53 10000 00013

72061

01007

45,00000 01173

72062

01010

56 0000.0 01010

72063

01011

11 01316 10000

72064
72065

01012
01013

37 01273 01266
45 30000 01016

72066

01014

75 00002 01020

72067

01015

17 00000 01332

72070

01016

72011

01017

12074

01022

75 00276 01020
63 00000 01314
45 10000 01042
11 01317 10000
37 01273 01266

72075

01023

11 01320 10000

72016

01024

37 01273·01267

1207'7

01025

11 40000 00003

72100

01026

11 01275 40000

72101

01027

57 00000 00000

-'72102

01030

11 00003 40000

74 1 03

01031

72104

01032

15 01332 01033
.i:'
15 01383 01034

'72105

01033

11 30000
,.4! 10000

72106

01034

72107

01035

31 30000 00000
56 10000,01036
..

72110

01036

11 10000 00017

72072 01020
72073 ' 01021

"

~

.i.

Y··~r

!

10"':304

ZM 527-11
All

11-14~56

FOAM NO, E, T, • 1

\.,VAVAIK ..... UIWI:'IUN Ufo .~fNfKAL

~.,.

gTNAMICS CORP.
PAGE ~:;45

SAN DIEGO. CALIFORNIA

·REPORT
MODEL

QATE

.-

72111

01037

11 20000 00020

72112

01040

37 01261 01262

72113

01041

44 72441 01044

72114

01042

23 10000 10000

72115

01043

72116

01044

56 00000 01036
61 00000 01340

72117 . 01045

11 01334 00023

72120

01046

11 00020 10000

.72121

01047

61 00000 01340

72122

01050

37 01261 01264

72123

01051

11 00017 10000

72124

01052

51 01355 20000

72125

01053

73 01345 00003

72126

QI054, 36 10000 OQ025

72127

010.55

11 00003 20000

72130

01056

42 01335 01070

72131

01057

11 00017 00026

72.132 .,' 010·60

11 01276 01110

72133

010-61

11 01312 01202

7"2134

01062

55 00017 10005 .

72135

01063

44 01064 01075

72136

01064

11 01277 01114

72137

01065

11 01300 01210

72140

('I')

co
......
'-"
I

0
......
I

0
0
0'

......

t-

><

0..

...
. 72141

01066

75 20002 011.01

01067

55 00026 000,06

74'142

01070

11 00017 00027

72143

01071

21 00017 01336

72144

01072

11 01301 01110

72145

Oi073

11 .01302 01202

'72146

45 oqooo 0107,6
'01075 . 11 00020'00027

"'t·

.72147

01074

\

ZM 5/7-1:
All

11-14-56

t.

T .• I

(1',.,.

,",V-lOU
SAN OIEGO. CAL.'FO~N'A

PAGE

46

ZM 5/7-11
All
11-14-56

REPORT
MODEL
DATE

72150

01076.

11 01303 01114

72151

01077

72152

01100

11 01313 01210
45 00000 01066

72153

01101

45 30000 01175

72154

01102

15 00017 01107

72155

01103

75 30014 01105

72156

Oi104

23 00003 00003

72157

01105

11 01311 00000

72160

01106

17 00000 01333

72161

01107

11 30000 00030

72162

01110

11 00026 30000

72163

01111

11 01337 00022

72164

01112

72165

01113

11 01340 00023
37 01174 01166

72166

01114

11 00027 30000

72167

01115

11 013LJl 00022

72170

0111'6

11 01340 00023

7'2171

01117

37

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 . Ol126

55 00022 00043

72201

01127

11 01340 00023

72202

01130

37'01174 01166

72'203

01131

41 0002 11- 01126

72204

01i32

11 01343 00024.

72205

01133

16 01305 01135

72.206

01134

77 00000 01314

0117L~

01166

10-306

\.UNVAIR .... DIVI~ION

FORM NO. E. T .• 1 (\'",.

OF GENERAL DYNAMICS CORP.

SAN DIEGO. CALIFORNIA

CV-183
PAGE'47
REPORT
-MODEL
DATE

.M

0:>

.....

'-'

0

I

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

72216

01144

17 00000 01332
45 10000 01043

72217

01145

75 20002 01033

72220

01146

21 01033 01344

72221

01147

72222

01150

21 01107 01345
75 20002 01103

72223

01151

21 00026 01346

72224

01152

11 00030 10000

72225

01153

72226

01154

51 01347 20000
43 01350 01156

72227

01155

45 00000 01121

72230

0,115'6

11 00030, 00021

72231 ' 01157

11 01342 00022

72232

01160

11 01351 00024

722_33

01161

72234

01162

11 01352 00023
37 01174 01166

7223·5

01163

55 00022 ' 00043

72236

01164

4J: 00024 01161

......

72237

01165

0
0
0'

72240

01166

45 00000 01132
55 00021 00003

t-

72241

01167

51 01353 20000

><
~

72242

01170

45 00000 01001

72243

01171

55 00022 00043

,72244

01172

53 01321 30000

722L~,5

. 01173

41 00023 01166

I

.....

Z1'-1 527-11
All

11-14-56

.. _ .... "".11\ -

). E. T .. , 0-,.,

.,lv ••tVf.. vr vCNCKAI. UTNAMIC5 CORP.
SAN DIEGO. CALIFORNIA

CV-183
48

PAGE

ZN 527-11
All

REPORT
MODEL
DATE

72246

01174

LI-S

72247

01175

15 00017 01200

72250

01176

72251

01177

75 00036 01200
63 00000 0131 Lt

72252

01200

72253

01201

72254

01202

72255

01203

72256

01204

72257

01205

75 00002 01210
63 00000 01340

72260

01206

75 00007 01210

72261

01207

63 00000 01340

12262

01210

11 00027 30000

72263

01211

37 01261 01250

12264

01212

75 00002 01216

12265

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

01'225

37 01261 01250

72300

01226

56 20000 01227

72301

01227

41 00025 01232

72302

01230

75 00003 01144

72303

01231

63 00000 01301

72304

01232

21 01200 01345

00000 01174

11 30000 00030
63 00000 01307
11 00026 30000
37 01261 01250

10-306

11-14-56

....... i·H·~II\ -

IoJ'YI;;lIVN

vt ut:Nt:KAL UYNAMIt;)

S"N DIEGO. C"LIFORN'A

CORP.

CV-183
49

PAGE

527-11
All
DATE 11-14-56

REPORTZM
MODEL

72305

01233

75 20002 01200

72306

01234

21 00026 01346

72307

01235

11 00030 10000

72310

01236

72311

01237

51 01347 20000
43 01350 01241

72312

01240

45 00000 01217

72313

01241

11 01351 00024

72314

012L+2

11 00030 10000

72315'

012!j. 3

72316

012L:-4

11 01352 00023
37 01261 01253

72317

012 LI5

63 00000 01340

72320

o12 Ll-6

72321

012LJ·7

41 00024 d1243
L~ 5 00000 01226

72322

01250

72323

012:51

11 013{;.0 00023
Lf- 5 00000 01253

7232 Ll-

01252

11 01343 00023

72325

01253

15 01305 01256

72326

01254

55 10000 00003

72327

01255

51 01353 20000

72330

01256

35 30000 01257

72331

01257

63 00000 30000

72332

01260

41 00023 01254

72333

01261

Ll·

72334

01262

61 00000 01307

:f')

:0
r-i

5 00000 01261

~

I

72335

01263

11 01343 00023

I

72336

01264

15 01307 01256

::J'

r-i

72337

01265

45 00000 01254

;><.

72340

01266

61 00000 01307

72341

01267 . 11 01354 00023

72342-

o 1~270

55 10000 00006

72343

01271

61 00000 10000

0

r-i

::>
::>

r-

~

t"AUt:.

:JV.

REPORTZM
MODEL
DATE

72344

01272

72345

01273

41 00023 01270
45 00000 01273

72346

01274

45 00000 01013

72347

01215

L~5

72350

01276

11 00026 00.021

72351

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

72351

01305

00 01306 00016

72360

01306

63 00000 01322

72361

01307

00 01310 00045

72362

01310

61 00000 01322

72363

01311

45 00000 01103

72364

01312

11 00026 10000

723'65

01313

11 00027 10000

72366

01314

00 00000 00000

72361

01315

24 34070 40613

72370

01316

03

.72371

01317

15 30123 00720

72372

01320

01 12240 41406

72373

01321

77 71777 77777

72374

01322

00 00000 00037

72375

01323

00 00000 00052

.72376

01324

00 00000 00074

72377

013.25

00 .OOQOO 00070,

12400

01326

00 00000 00064

72401 , 01327

00 00 000 00062

01330

00 00000 00066

72402

00000 01030

010~0,

40336

1

10-310

5='7-11

All

11-14-56

REPORT

ZM 5?7-11

MODEL

All

DATEII-14-56

,.-...
CVJ

co
.....-t

'-"

0

I

.....-t

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 40'000 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

7 2l~21

01347

77 00000 00000

72422

01350

14 00000 00000

72423

01351

00 00000 00002

72424

01352

00 0'0000 00003

72425

01353

00 00000 00007

72426

01354

00 00000 00005

72427

01355

00 77.777 77777

72430

01356

00 00000 00000

72431

11 00000 7l+0Q.Q., .

72432

11 72540 00000

72433

75 31777 72435

72434

11 00001 74001

0
0
0'

72435

75 30260 72 37--

t-

72436

11 72445 00020

72437

75 30073 00020

72440

11 7272.5 00700

72441

75 31777 72443

I

.....-t

><
0...

'f

10-311

. 1. T.·1

~.

CONVAIR - DIVISION Of GENERAL DYNAMICS CORP.

F

SAN DIEGO.

CA~IFORNIA

CV-l83
PAGE

52

REPORT
MODEL

DATE

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

00.025

55 10000 00001

72453

00026

11 10000 00016

72454

00021

11 10000 00017

72455

00030

21 00017 00015

72459

00031

11 00703 00011

72457

00032

75 30010 00250

72460

00033

72461

00034

23 00001 00001
45 10000 00216

72462

00035

11 00714 10000

12463

00036

31 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

001L~7

'+0000

72473

00046

57 00300 .00000

72474

00047

17 . 0030·1 00702

7i475

00050

11 00010 40000

72476

00051

15 00046 00053

72477

00052

15 00047 00054

72500

00053

11 30300. 10000

10-312

Z14 5/7-11

All

11-14-56

FORM NO .... T •• ;

\.IV-.!Vu

(f~, i'

SAN DIEGO. CALIFORNIA

PAGE

53

REPORT

ZM 5?7-IJ

MODEL

All

DATEll~14-56

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

31" 00237 00230

'72523

00076

61 00000 -00712

72524

00077

75 00005 00101

72525

00100

61 00000 00727

72526'

00101

15 00001 0'0131

72527

00102

72530

00103

11 0,0001 10000
55' 10000 00003

72531

00104

51 00731 00003

~

,......
C"')

OJ

-....-f

I

0

72532· '00105

55 10000 00017

0
0
0'

72533

00106

51 00731 0000.4

t- '

72534

00107

11 00732 20000

:><
a..

72535

00110

42 00003 00114

72536

00111

21 00131 00733

72537 ·00112

11 00124 00136

....-f

I

....-f

I.

E. T.· 1 (i'!

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

,.

SAN DIEGO. CALIFORNIA

LV-l0')
PAGE

ZM 527-11

MODEL

All

DATE

725 ItO

00113

45 00000 00130

725 Ii-I

00114

11 0073 Lt 10000

72542

00115

725 /+3

00116

51 00001 20000
Lt 7 00127 00117

725 LIA

00117

11 00002 10000

72545

00120

55 10000 00003

725 Lt6

00121

51 00731 00005

72547

00122

11 00125 Q0136

72550

00123

72551

00124

45 00000 00130
Lt 5 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

4'5 00000 30136

725,64

00137

11 00003 00010

72565

001 LIO

15 00703 00011

72566

001 L.l

37 00247 00240

72567

001 Lt 2

21 00011

72570

00143

11 00005 00010

72571

00144

37, 00247 00240

72512

00145

11-5

72573

0014·6

11 00003 00010

72574

OOlLt 7

15 00703 00011

72575

00150

37 00247'00240

72576

00151

21 00011 00017

0001L~

00000 0015.7

10-:314

54

REPORT

11-14-56

FORM NO. E. T .• ,

.... \"UNVAIK ... ·UrVI:»IUN·Vr

(i'·,.

·\:rCI"ICK~U-·V'"1"I"Mm'''';;J

SAN DIEGO. CALIFORNIA

"''''IU.

-'--'-'--'- --v-w··-·-:a."V'o.J""-·--·----···· .

PAGE55
REP,?RTZl'1
MODEL
DATE

72577

00152

45 00000 00160

72600

00153

15 00703 00011

72601

00154

21 00011 00016

72602

00155

72603

00156

11 00003 00010
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

72614

00167

11 00006 00010
55 booia 00003

72615

00170

37 00247 00240
21 00011 00704

72616 00171
72617 . 00172

37 00247 00240

72620

.00173

11 00740 10000

72621

00174

51 00011 20000

72622

00175

43 00013 00206

72623

00176

21 0001] 00705

72624

00177

11 00003 20000

72625

00200

43 00004 00213

co
r-1

72626

00201

21 00003 00741

0

72627

00202

21 00005 00741

72630

00203

11 00134 20000

72631

00204

72632

00205

43 00742 00130
45 00000 00134

72633

00206

16 00703 00011

72634

00207

17 OCOOO 00701

72635

00210

17

.-,.
C"')

,-,.
I
r-1

I

0
0
0'

r-1

t-

~

0..

ocooo

00700

527-11

All

11-14-56

T .• i

CONVAIR - I?fYISK>N Of GENERAL DYNAMICS CORP.

(T~,,.

SAN DIEGO. CAI-IFORNIA

CV-183
PAGE

56

REPORT
MODEL
DATE

72636

00211

17 00000 00702

72637

00212

45 00000 00177

72640

00213

Lf.5

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

7'2653

00:226

41 00007 00224

72654

00227

ltS

12655

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 30.237

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

002,,·5

54 00010 00003

72673

002'+6

41 00007 00242

72674

C02L~ 7

45 00000 30247

10000 00216

00000 30227

10-316

ZM 527-11
All

11-14-56

FORM NO. E. T .• I

O·~

V~-.l.V'"

"

SAN DIEGO. CALIFORNIA

PAGE

2M 527-11

MODEL

All

DATE

72675

00250'

11 00740 10000

72676

00251

51 00703 20000

72677

00252

72 00705 00706

72700

00253

11 20000 00013

72701

00254

72702

00255

17 00000 00702
45 00000 00034

72703

00256

72704

00257

11 00006 10000
51 00745 20000

72705

00260'

43 00746 00262

72706

00261

45 00000 00161

72707

00262

72710

00263

11 00006 00010
55 ·00010 00041

72711

00264

72712

00265

11 00711 00007
37 . 00247 00241

72713

00266

21 00011 00704

72714

00267

72715

00270

11 00006 00010
55 00010 00011

72716

00271

11 00711 00007

72717

00272

37 00247 00241

72720

00273

21 00011 00704

72721

00274

11 00711 00007

72722

00275

72723

00276

37 00247 00241
45 00000 00173

72724

00277

00 00000 00000

72725

00700

00 00000 06000

I

"72726

00701

00 obooo 04400

a-

7272·7

00702

00 00000 05000

t-

72730

00703

00 00200 00020

72731

00704

00 00024 00000

72732

00705

00 00000 00040

72733

00706

00 00000 00037

.......1
C'j

co.
r-i

........
0

I

r-i

0
0

~

><:

0...

57

REPORT

11-14-56

CONYAIR - DIVISION OF GENERAL DYNAMICS CORP.

E. T .. ' ~.,.

SAN DIEGO. CAI-IFORN.A

CV-183
58

PAGE

Z}1 5'7-11
All
11-14-56

REPORT
MODEL
DATE

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

0071.4

45 47150 10411

72742

007.15

72743

00716

03 30220 40407
22 04240 15745

72744

00717·

00 00000 00037

12745

00720

00 00000 00052

72146

00721

00 00000 00074

12141

00722

00 00000 00070

72750

00723

00 00000 00064

72751

00724

00 00000 00062

72752

00125

00 00000 00066

72153

00726

00 00000 00072

72754

00721

00 00000 00042

72755

00730

61 00000 00717

72756

00731

01 17770 00000

72751

00732

00 17770 00000

7'2760

00733

00 74000 00000

72761

00734

01 00000 0'0000

72762

007'35

00 01000 00000

72763

00736

00 00001 00000

72764

00737

07 00000 00000

72765

00740

00 00000 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

· ·--··-SAN~IE~O. CAL.IFOR;;;"'- ..'. - . - - - - . - - - - - . - - - - - - - ----.-. PAGE--59--~--:-----·'

REPORT

ZH 5?7-1l

MODEL.

All

DATEll-14-56

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

00763

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

7'3017

00772

00 00000 00220

73020

11 00000 74000

73021

11 72152 00000

73022

75 31777 73024

73023

11 00001 74001

I

73024

75 30357 01013

0
0

73025

11 72052 01000

r--C"j

0:>

.......

'-'

I

0

.......

'"r-.......
><
0....

O. It. T.·'

CONVAIR - DIVISION OF GENERAl DYNAMICS CORP.

0', "

CV-183
PAGE

SAN DIEGO. CALIFORNIA

60

REPORT
MODEL
DATE

SPUR SUBROUTn~E ASSElvffiLY

y

76151

15 01601 76153

76152

75 30052 76154

ADDRESS
Pt-} FOR

76153

11 30000 00002

EXAt'1 INA T ION

7~154

75 30304 00056

76155

11 76156 00056

76156

00056

15 01753 00121

76157

00057

11 00347 00372

76160

00060

11 01752 00373

76161

00061

15 01753 00064

76162

00062

31 01761 00000

76163

00063

36 01751 00374

76164

00064

11 30000 20000

76165

00065

42 00357 00067

76166

00066

76167

00067

42 00360 00115
21 0006 /t 01753

76170

00070

41 00374

76171

00071

41 01761 00120

76172

00072

75 312 Lj·O 00074

76173

00073

11 aOLrOO 74400

16174

00074

75 30200 00076

76175

00075

11 77213 01200

76176

000.76

61 acaoo 01302

76177

00077

31 00361 00052

76200

00100

61 00000 2JOOO

76201

00101

?,4 20000 00006

76202

00102

L~ 7

76203

00103

55 00373- 10030

76204

0010 Lt

61 00000 01305

76205

00105

11 01305 01371

76206

OC'll 06

:;,7 0125.5 01250

76207

00107

37 00107 00110

THIS TO

ES
P\-I ACQUISITION
INITIAL INST. LI·ivj I T
INITIAL TEMP. LII·; I T
SET TREE TEST
SET TALLY
I FFL ETREE
TEST
STEP
~'JH

0OO6t~

TEST FOR Ei'!D
STORE
r·;ODIFIED ES

OF
C/\RD ROUT Ii",iE
CAf~ • HET.
PR I {-~ T
PART

/\ V;\ I L 0
(\[\10

ES

00100 00103

FF{c E
SPACE

L Itlj ITS

10-320

ZM 5::>7-11

All
11-14-56

. "OltM NO. I. ,. .• ,

~.,

SAN DIEGO. CALIFORNIA

. --_...,.

...---- _. - PAGE

~----.--

-~.,.

.
ZM 527-11

·bI·~·--~:···

REPORT
MODEL.. All
DATE 11-14-56

"'C'?""'
co,

.....

--

76210

00110

23 00372 01751

76211

00111

55 20000 00030

76212

00112

31 00107 00104

76213

00113

75 31777 01746

EX!T

76214

00114

11· 74001 00001

76215
76216

00115

76217

00117

23 00372 00322
75 30007 00071
11 00350 01472

76220

00120

75 30002 00122

76221

00121

11 30000 00362

RESTORE E.S.
ADJUST INST. LIMITS
WHIFFLETREE
ADDITION
CURRENT
P W

76222

00122

76223

00123

76224

00124

21 00121 01753
15 00362 00165
31 00363 00060

76225

00125 . II' 20000 00364

76226

00126

34 20000 00014

76227

00127

11 20000 00365

76230

00130

34 20000 00014

76231

00131

11 20000 00366

76232

0013~

31 00364 00000

76233

00133

35 ,00365 00374

7'6234

00134

35 00317 00164 '

76235

00135

55 0016.4 00017

76236

,00136

23 00372 00374

76237

00137

42 00343 00151

76240

00140

00116

76'241

16 20000 00165
00141 ' 16 20000 0'0312

0
0

76242

00142

36 003146 00367

'M

l-

76243

00143

11 00340 10000

I><:

16244

00144

52

OO~62

76245

00145

13

00841 20000

76246

00146

36 00374 00370

I

0

M

I

STEP

SET SUB. R. EXTRACT.
NUMBER OF INST.
NUMBER OF CONST'.
NUMBER OF TEMP.
NUMBER
INST. AND CaNST.
SUB. R.
TRANSFER
NEW INST. LIMIT
ALARM
SUB. R. LANDING
INST. RETURN
INST. MODIFICATION

0-

,Cl..

00363

MODIFIED ENTRANCE

TEMP. MOD.

CONVAIR - DIVISION OF GENERAl. DYNAMICS CORP.

t:.T.·l ~.I"

SAN DIEGO. CALIFORNIA

CV-l83
PAGE

62

REPORT
MODEL

ZM 527-11

All

DATEl1-14-56

76247

00147

76250

00150

55 00362 10006
51 00336 00362

76251

00151

31 00366 00000

76252

00152

35 01752 20000

76253

00153

42 00373 00155

76254

00154

11 20000 00373

76255

00155

11 00373 20000

76256

00156

42 00372 00161

76257

00157

15 31777 76020

76260

00160

11 74001 00001

76261

00161

31 00346 00000

76262

00162

35 00374 00365

76263

00163

35 00366 00366

76264

00164'

30 30000 30000

76265

00165

11 30000 30000

76266

00166

37 00260 00251

76261

00167

45 00000 00312

76270

00170

31 00165 00017

76271
76272

00111

15 20000 00233

00172

41 00364 00233

76273

00173

11 00315 00231

76274

00174

31 00363 00017

76275

00175

35 00363.00363

76276

00176

55 00362 10043

76277

00117

44 00201 00200

76'300

00200

11 00316 00231

76'301

00201

·5.5 00362 10041

76302.

00202

76303

00203

51 00334 20000
55 10000 00003

76304

.00204

43 00322 00222

76305

00205

16 00344 00231

o

P

TEST
TEMP

LIMIT
CHANGE LIMIT

ALARM

UPPER LIMIT INST. MOD.
UPPER LIMIT TEMP.
sue. R. FOR
MODIFICATION
MODIFY
U ONLY
SET INITIAL
INST ACQUIS·ITION
TAL LYIN ST. tv10 D•

TEST 6Q TO 67
SET FOR 10,·30

10.-322

FORM NO. lit. T .• I

-_ ...,...... ·-.--.

(P.I. F

'-;~~~OI;GO.~AL.;~O;~'-~---'--'

--_.

--~~"-'-"---'-PAGE

REPORT
MODEL.
DATE

76306

00206

43 00320 00220

TEST FOR

76307

00207

10,30

76310

00210

43 01751 00220
43 00334 00212

76311

00211

45 00000 00157

76312

00212

16 00345 00231

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

16320

00220

51 00324 20000

TEST FOR

76321

00221

43 00324 00157

17, 37

7632.2

00222

51 00322 10000

76323

00223

47 00224 00231

76324

00224

43 01752 00230

75325

00.225

43 0.0321 00227

76326

00226

23 00231 01751

76327

00227

23 00231 01752

76330

00230

23 00231 01751

76331

00231

30 00000 00000

763'32

00232

45 00000 00011

76333

00233

76334

OO~34

II 30000 00375
21 0023:3 00337

76335

00235

55 00375 10006

I

76336

0023'6

51 00336 20000

0"-

76-337

00237

43 00323 00271

14 SPECIAL

76340

00240

43 00324 00261

V ONLY

76341

00241

43 00327 00261

V ONLY

76342
7"6343

00242

42 00325 002.51

U, V

00243

42 00326 00166

U ONLY

76344 . 00244

42 0.0.330 00251

U, V

.-..
M
co
.....
~

I

0

.....

0
0

.....

f'..

~

c..

TEST FOR

70 TO 77

SET FOR 74

CURRENT INST.
STEP

-_.-:--;-.
5?7-11

6J~~'

ZM
All

11-14-56

CONVAIR - DIVISION OF GENERJtt DYNAMICS CORP.

T.·' ~. F

CV-183
PAGE

SAN DIEGO. CALIFORNIA

64

REPORT
MODEL
DATE

16345

00245

42 00331 00166

76346

00246

42 00333 00261

U ONLY
V ONLY

76341

00247

42 00335 00251

u.

76350

00250

45 00000 00261

V ONLY

76351

00251

55 00375 00025

16352

00252

51 00340 10000

76353

0025:3

42 00346 00256

76354

00254

42 00365 00265

76355

00255

42 00366 00'267

76356

00256

37 00256 00257

76357

00257

55 00375 00011

76360

00260

37 00260 00261

76361

00261

11 00315 10000

76362

-00262

37 00256 00252

76:363

00263

31 00263 00264

76364

00264

45 00000 00312

76365

00265

21 00315 00367

76366

0,0.266

45 00000 00256

76361

00267

21 00375 00370

76370

00270

45 00000 00256

763'71

00271

11 00375 00371

76372

00272

11 00375 10000

7637'3

00273

51 01757 00375

76314

00274

51 00342 20000

76375

0021'5

31 20000 00003

76-376

00276

35 00375 00375

76377

00277

55 00371 10006

76400

00300

44 00301 00303

76401

00301

37 00263 00261

76402

00302

45 00000 b0304

76403

00303

37 00263 00251

V

NO ,.100.
MOD INST
MOD TEMP

TO RESTOR

DUPLICATE
SYNTHETIC

INSTRUCTION
ONE, TWO ADDRESS

10-324

ZM 527-11
All

11-14-56

FOR .... NO, E. T .• I

(f'

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP. '

"

SAN OIEGO. CALIFORNIA

76404

00304

55 00375 20041

76405

00305

11 00342 10000

76406

00306

53 20000 00371

76407

00307

11 01751 10000

76410

00310

53 00375 00311

" 76411

00311

11 00371 00315

16412

00312

11 00375 30000

76413

00313

21 00312 01751

764'14

00314

45 00000 00172

76415'

00315

15 00363 01477

76416

00316

76417

00317

16 00363 01471
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

16425 ' 0032'5

00 00000 00031

76426

00326

00 00000 00035

76427

00327

QO 00000 00045

764,30

00330

00 00000 00054

76431

00331

00 ,00000 00056

76432

00332

00 00000' 01505

764~3

00333

00 00000 00071

76434

00334

00 00000 00007

0

76435

00335

a-

76436

00336

OQ 00000 00075
00 00000 00077

76437

00337

00 00001 00000

76440

00340

00 00000 77777

76441

00341

76442

00342

00 00000 00776
00 00177 70000

REPLACE
\oJ I TH
~

"'"'
C't)
co
r-I
-.....;

0

I

r-I

I

0

r-I

t-

><
0..

SYNTHETIC
PARTS
RETURN INST.
STEP

CV-183
PAGE
65
REPORT ZM 5'7-11
MODEL All
DATE 11-14-56

CONYAIR - DIVISION OFGlJ8At DYNAMICS CORP;

.1£. T .• ' 7-11

MODEL

All

DATE

SPUR SQU ARE ROOT

70252

01000

70253

01001

11 01766 0177..4
11 01766 20000

70254

01002

46 76020 01003

70255

01003

47 01004 01742

70256

01004

12 01767 10000

70257

01005

55 10000 00043

CASE ZERO
N TO A'
NEGATIVE
ZERO
P EVEN
OR

70260

01006

44 01007 01011

ODD

70261

01001

21 01767 01751

70262

01010

54 01766 00107

70263

01011

5:1 01767 00043

70264

01012

11 01767 01775

70265

01013

43 01025 01742

1 TO P
N/2 TO N
N /2 TO P
P TO R
N EQUAL .9

70266

01014

11 01025 01762

.9

70267

01015

31 01766 00042

70270

01016

70271

01017

13 01762 01763
54 01762 00107

70272

01020

23 10000 01762

70273

01021

21 011'62 01763

70274

01022

44 01015 01023

70275

01023

11 20000 01774

N

70276

01024

45 00000 01742

EXT

70277

01025

37 77777 77777

.9

P

2

TO X

COf\1PUTE

. SQUARE

ROOif

TO R

11-14-56

CQNVAIR - DIVISION OF GENERAl

). II. T,. I (PJ.,.

DY~C$,

CORP.

SAN OIEGO. CALIFORNIA

SPUR CU BE ROOT

7030.0

01000

11 01766 01774

70301

01001

11 01766 20000

70302

01002

47 01003 01742

70303

01003

11 01767 20000

P/3

70304' 01004

13 '01036 10000

TO

70305

01005

47 01006 01013

R Et·1. ZERO

70306

01006

43 01752 01011

REt 1. 2

10301

01007

21 01.767 01751

P

70310

01010

54 01766 00107

70311

01011

21 01767 01751

70312
70313
10314

54 01766 00107
11 01767 20000
01014 . 73 01036 01775

N / 2 TO N
P
1 TO P
N I 2 TO N

10315

01015

11 01037 01762

70316

01016

11 01766 20000

70311

01017

46 01020 01021

NEG.

70320

01020

13 01037 01762

-.9 TO X

70321

01021

43 01162 01742

7·0322

01022

71 01762 01762

X

70323

01023

54 20000 00045

EXP 35

70324

01024

11 20000 01763

70325

01025

54 01766

70326

01026

13 01763 20000

70327

01021

36 01762 20000

-X

70330

01030

73 01036 10000

70331

01031

21 01762 10000

X
X EXP &5

70332

01032

71 10000 01766

N

70333

01033

46 01022 01034

70334

01034

11 01762 01714

70335

01035

70336

01036

45 00000 01142
00 00000 00003

NEG.
'x EQUAL
EXIT

10337

01037

37 77777 71777

01012
0'1013

200L~3

CASE ZERO
N TO A
N ZERO
Q

v

1 TO &

P

3

/

TP P
TO X

.9 X 2
N

N

EXP 10
X

.9

10-328

EXP 35

X
N

CV-ltlJ
PAGE 68
REPORT ZM 577-11
MODEL All
DATE 11-14-56

FORM NO. E. T .. I

(f~

CV 183

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP.

~

SAN DIEGO. CALIFORNIA

69

PAGE

REPORT

ZN 527-11

MODEL

All

DATE

11-14-56

SPUR nth ROOT SUBRaJTU:E

70200

01000

11 01761 20000

70201

01001

42 01752 76020 ~

70202

01002

75 30004 01004

7020~

01003

11 01770 01772

70204

01004

11 01770 20000

70205

01005

47 01006 01736

N ::: O? -t EX IT

70206

01006

11 01051 01764

.9 --t

70207

01007

46 01010 01013

N NEG.

70210

01010

13 01764 01764

-.9 -7 P

70211

01011

55 01761 10043

70212

01012

44 01013 76020

70213

01013

11 01771 20000

EXP

70214

01014

73 01761 01775

EXP / N

--t

70215

01015

11 10000 01765

EXP/N

---t P

70216

01016

47 01017 01022

R E~~. -.::

70217

01017

21 01765 01751

EXP/N + 1

70220

01020

70221

01021

75 3 0002 0 1
11 01772 01770

70222

'01022

11 01770 20000

N

70223

01023·

43 01764 01742

N

70224

01024

11 01761 20000

\'\ --t

70225

01025

36 01752 01052.

~ -2

=

70226

01026

11 01764 01766

}

X i-I

70227

01027

11 01765 01767

70230

01030

37 01030 01031

70231

01031

37 01741 01633

70232

01032

41 01052 01026

70233

01033

37 01030 01026

XJ.-, --t- 8

70234

01034

37 01741 01655

NIX i-I

70235

01035

73 01761 20000

70236

01036

37 01741 01712

NORMALIZE A X

70237

01037

47 01040 01047

A X

"- ~

f

<

A

2·---1 ALA Rt,1
N ~ S.

N ---;. A

I"

p

?

EVEN - t ALAR~'1

-+

024'J

]

R

S

-+

A

1 775 f

0 '?

-t

P

= N --7

C

A

=::t:..9 -'r

EXIT

A

-t

J

1052

-t

B

N/X~-'
1-1

n.- l

~Xi_t

A=A"¥-

= 0 r-t EX IT

REt 1.

-7

A

1:. T .• 1 (Ill

CONVAIR - OIVISION OF GENERAL DYNAMICS

,.

COR,:

tV -183'''"';'
70 '

SAN DIEGO, CALIFORNIA

.PAGE

REPORT
MODEL
DATE

70241

01040
01041

11 01775 01052.
37 0103'0 01026

10242
70243
70.244
70245

0,10\2
01043
01044
~~
01045

3~,

70246

010~6

70240

.,

01741 01656

11 01774 01764
11 01775 01765
23 01771 01052
42 01754- 01020'

',A'X EXP.

10250

70251

01041
01050
01051

. Xi-l

+Ax :: Xi

]

X

i. ~

P

(X l'EXP)- fiX. EXP) ~ A
A
3l5'---t EXIT

>

75 30002 01142

EXIT

11 011'64 01714
37 77777 71777

X'I

10-330

105.2.

Xf-I ~ B

~.~"'lI

70241

~

.9

---+

R

Zl1 527-11
All

11-14-56

10:27

THE RRMO-WOOLDRIDGE CORPORATION
Los

.SU8&JECT:

ANGELES

45,

CALIFORNIA

Computing Center
OrGanization

-===================:a....... . ----,._. _____ .--.
~.-~'

DATE:

J anllary 9, ·1956

FROM:

W. F ~ Bauer

=_==:::;.::;==~================

The following delineates the areas of interest, cognizance, and responsibility
of the five groups cOT',prising the organization of the Digital. Computing Center.
SYSTEI~JS AND TRAINING

1.

Develop, lTiaintain ~nd improve a cor.prehensive CC)lnpll ta tion system for the
1103 and· 1103A including component parts such a~ cOInpiler, algebraic
coding sehenle, service routines, and the routines MGessary for e.ffecting
an auton.latic system, implementing, insofar as is pos:;>ible, the suggestions
for such prog!'CJl.s and routines made by all other grQUps ..

2.

Develop sUch adnJinistrative procedures concomitant to the con;putatiOri
systeJi~ to 'ensure the proper 1"'101-1 of information to a:nq frorrl the personnel
of the Operations Group uhich. operates thE! various equipments, and'
cooperate with that croup in effectinG the plc-.n.

3.

Ke.ep subroutine and service routine library recoro.s, dissefi,inate appropriate
system operation inforrr:nt;ion to Cornputin:3 Center personnel
and other interested parties, and participate in 'cooperative prograr..n.ing
~fforts and in the exchange of progrrun information petlofeen 1103 or 1103A
userso
pr0EraIl:Il.~nGcmd

4-

Aid in the :genera.l recruitinG pro~rC:Uli and asmme major ;responsibility iIi
the initia.l instruction and trainin.G of personnel in pro{;rmmning techniques,

5.

Recruit and train computer operators, operate ~le 1103 (or 1103A) computer,
and. develop operating techn:i,ques necessary to. insure the highest standards
ofcon;puter US~.

6.

Carry out specific projects in pro~3Ilillling and computer studies as may be
assiened •

OPEH.ATlONS,
1.

Aid the Syste:rns Group in developing RJethods and proc'edures for operation
of the 1103 (or il03Ab computation system, and· appropriately execute such
procedures.

10:27
Page 1/2
2.

Schedule' 1103 (or 110JA) computer time and develop and initiate nlethods
and procedures as necessary to generate and maintain adequate records
concerning problem assignments, records necessary for budget arid fisc'a!
, requirements, and records of computer operating data.

3. Operate all auxiliary and off-line equipment, including hand computer equipment, recruit and train operators 9f such equipment, and design procedures
as are necessary in the operation of such equipment.

4.

Determine the need and specifications for any equipment to be modified,
purchased or especially built, and transmit informa,tion as needed to prograJnJO.ing groups on the operation and characteristics of such equipment.

5.

Perform computer progrannning as necessary, especially on those problems
involving special equipment such as analog-digital converters used in '
simulation and data reduction activitieso
'
PROGRANl-lING

1.

Make contacts as necessary Witll customers and problem originators in the
programming and running of assigned problems.

2.

Assume majqr
respon~ibility for the central GJiliD progranmdng effort as
"
assigned" such as aerodynamics, struotur~s, and air fran:e and trajectory
analysis.
~,

,

,.l

J.

Cooperate with and advise the Numerical Analysis and Systems Groups on
the development of routines necessary for production .computation.
Cooperate with and advise the Operations Group in the 'development of a
computations,ystenl and its subsequent adoption.

.

,

Assume major responsibility for the general recruiting program' and the
evaluation of prospective programmers.

NUfffiRICAL 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 respons~bility ,for ,certain problelus as assigned.
,

,

'

't;

2.

,'!;:'t

Conduct basic and applied research in numerical analysis and machine
techniques and publish the results whenever ,appropriate.

3. Ascertain the need for, deterrrine specifications,

and develop techniques
of standard numerical operations (e.g., matrix inversion, differential
equation solving) as are needed and, when appropriate, perforre the
computer programming necessary.

4.

Aid in the general recruiting program, and assume major 'responsibility
in the r,ecruitment of numerical analysts in cooperation with the
Progratnliiing Group.

10-332

10:27

5.

I'l'ovide technical support and coordinpticn to the: aetJv:i.t:i.cB
to the Computing Center in numcricnl [',rwl;,{[.:;is.

()f

conmtitc:rlts

l":A T: IEl,Ne I GhL AHAl
,'~L :;:~.
.

1e

Consult \>1i th customers or problem oriGinators on rrc lilC'li' [j, per :~'c~_'Tin~,:
such mathematical research and analysis as is as~:;i~':ncd. (,1' necessary;
advise the ComputinG Center on the formulation of problenm when appropriate;
and consult l-dththe Nunlerical Analysis Group to d.eterr.inc ,the Gon.binc::tion
of mach me and analyticCll techniques likely to ei va rr.ost .Fruitful resu1 ts.

2.

Conduct basic research. in Applied J.'j·athematics as is apP:l."opriate and
publish such results.

3. Aid in the general recruiting proeram, and assume n.ajor responsibility
in the recruitment of applied mathematicianD 1.n coopcrution '.lith the
Programn.ing Group.

4.

Provide technical support and coordination to theactivitios of consultDnts
to the Computing Center ·in applied JI·athematics,

5.

Provide and maintain sources of infornwtion in [l.ppliod Ii nthcn:utics in
the form of appropriate senJinars, lectures, covTBes, rind tho. COJ{'p1.lting
~t.er Library.

~v~

1rJalter F. B~

:njs

/

Digital
Computing Center
-

Numerical

!':a therr.a tical

Analysis

Analysis

.

f

Systerr.s
and
Training

Operations

Pro gr arrlting

10:28
MATHEMNfICAL 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 sui table for analysis and/or inclusion in the final report. ,This Branch is
divided into three Sections; Te.st Data, Computation and Equipment Maintenance ."
The Tes~ Data ~ction establishes mathematical and assessment procedures
for processing test data; receives, stores, edits, and reviews raw and proc~ssed
data; assists other agencies in programming problemB; spot lchecks processed data,
accomplishes assessment on selected po~tions of test data; prepares data for submission to project an~ analysis personnel.
~e Computatio~'Section accomplishes computation on 'the, electronic digital
computer; assists mathematicians in working out computation and reduction techniques and in selecting instrumentation methods compatible with computing and
analyzing equipment; operates analog-to-digital converts, plotters, electronic
analyzers I recorders, and computer output deVices, develops techniques and procedures applicable thereto.

The EqUipment Maintenance Section maintains data reduction andco~puting
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 organizationch8rt.
, Within the Directorate of Ballistics the 'Ballistics~ Computa.tions Officer
performs neces~ary data programming and computationsuti~izing existing facilities
to ,greatest extent possIble; provides consultant services to develop new data
reduction and computation techniq~es.

-.
0::>

.

N

~

o
.....

--.....,
o

'

I

o

o
0".....

t-

~

A third organization, the Analysis Divlsion,also initiates computing requirement,s at the Air Force Armament Center • Within this Division the Test Analysis '
Branch recommends priorities for all the Center's computing facilities arid
laSsociated functions; 'applies numerical analysis techniques and p~rforms coding
and computations of analysis problems on the Center's computers as required.
The Research Branch originates improved anq/or new computing tecbn1quesand procedures where existing ones ~e inadequate or non-existent, except in the ,balliStics area; 'invest~~ates I on a continuing basis, computing methods and techniques
employed elsewhere I for" possible use at the, Center.
In addition the Applied Mathematics Division of the Directorate of Statistical Services I Air Proving GroWld Conmand, assists in progranming and operating
Air Force Armament Center projects on the computers available, in that Command •

. E. T .• ,

CV-l54 (REV)

CONVAIR - DIVISION OF GENERAL DYNAMICS CORP•

(r~·,

SAN DIEGO. CALIFORNIA

PAGE
REPORT

ZM 491

MOOEL

All

OATE

5-1-56

REVISED

UNPACKED FLOATING POINT CARD READ
EXtT
STORE

7 400

(')07l~2

56 Ot')()OO 30(\00

7 401

0'0743

75 31777 72403

7 402

00744

11 00001 74001

ES

72403

00745

75 30352 00747

72404

00746

11 72400 00742

ROUTINE
TO' ES

72405

00747

11 00742 20000

SET

72406

00750

36 01264 72432

72407

00751

35 01205 20000

SET

72410

00752

16 20000 00770

72411

00753

55

7'2412

00754

44 00757 00756

72413

·00755

EXIT
TEST FOR
ES
ADDRESSES
ADDRESS MODIFICATION

.

007l~2

20025

00 00000 00114
\':

32 00776 00000

REPEAT

7241.4

00756

72415

C07S7

12416

00760

55 .20000 C0017
37 00760 0(1761

72'417

00761

16 20000 00763

12420

00762

11 p0777 01024

72421

00763

71

72422

00764

55 20000 00006

72423

00765

37 00760 00754

X

72424

00766

72425

00767

55 20000 0001t
37 01001 0100.4

TP S t BRPr TOME

72426

00770

75 ·31 777 30000

,72427

00771

11 74001 00001

RESTORE E S
AND EXIT

72430

00772

75 21771 72432

RESTORE E S

724pl

00773

124:32 . 00774

11 74001 00001
30 00000 0000

72433

00775

02 00000 00104

72434

00776

74 00000 00000

72435

00777

11 00000 00000

7243.6

01000

30 00000 0000*

72437

01001

1+

~-r

':

~.

*

01264 30000

5 00000 3(1000

SET ACQUISITION
ERASE INSTRUCTION
ACQUIRE CON TROL \vORD

AND
REPEAT

REPEAT
EXIT
10-336

Ie 011-3

RW-71
(REV)

PAGE'10F 2
REVIS'ED '09-05-56 ,

THE RAMO-WOOLDRIDGE CORPORATION
L.OS ANGELES 45. CALIFORNIA

UTILITY ROUTINE LIBRARY
TABlEOF'CONTENTS
A DESCRIPTION OF THE LIBRARY ORGANIZATION

04-01-55

PROGRAMMJ NG AND OPERA! I N'G CONVENT IONS 06-20-:56

PROGRAMMING REMINDERS 06-15-56
LIBRARY HANDLING PACKAGE FOR PAPER TAPE INPUT 06-15-56
BOOTSTRAP PROCEDURE USING CARDS
OS-01-50
OCTAL-DECIMAL CONYERS I ON ,TABLES
40000 GROUP'" SERVICE ROUTINE - ENTRANCES 06-01-56
"~~

ALR-l

08-16~:S5

ENTRANCE ADDRESS ALARM RoutINE

ATM-l

05-01-56

STANDARD ATMOSPHERE ,CAL,CULATION

CMP-O

07-10-56
03-26-56

RAWOOP. ONE PASS ASSEMBL.Y, PROGRAM
FIXED POINT CARD OUTPUT
CARD PUNCH OUTPUT FOR FLOATING POINT 'NUMBERS
STAlED POINT CARO OUTPUT
BINARY CARD READ-IN ROUTINE

CPO-O
CPo-l

04-16-,56
12-0'9-55
12-09-55
11-14-55

DEM-O
DEM-1

10-, -55
10-, ' -55

DET~2
OlE~O

07-25·56

OlE-2

06-15-56
11-25-55
11-25-55

EGN-O

05-01~56

EXP-2

ll-15-55
' 08-10-55

DIE·1

EXP~3

..-

.....

,r-,o

,
.....,
o

.......
o

09~23-55

CPG-2
CRI-l
CRI-2
CVF-O

Fl.X-O
FPP-O
FRI-O
FRI-l

06-15-56,

07'-20-56
'01-10-56
10-03-55

FIXED POINT, DECIMAL' CARD READ-IN ROUlINf>
CURVE FITlING BY MINI-MAX PROCEDURE'
, -NIM. A DEMONSTRATION RO'UlINE
DATE TO DAY CONVERSION, DEMONSTRATION
'DETERMINANT EVALUATI.ON. COMPLEX
DEFINITE INTEGRAL EVALtjATIONROU11NE

ROUTINE

FIXEO POINT DEFINITE INTEGRAL EVALUATION
FL.OATING POINT DEFINITE' .JMTEGRAL EVALUAtION
EIGENVECTORS, VALUES OF'REAL SYMMETRIC MAfRlCES
FJ XED POINT EXPONENIJAL., ROUl'lNE
FLOATING POINT EXPO~ENTIAL ROUTINE
i
.~,
FLEXOWR ~ TER CONST ANT POOL,.:
FLOATING POINT PACKAGE.~SNAPt SN1P~ AND TRACE
I

FERRANTI INPUT ROUTINE'
.
SIMPLIFIED FERRANTI INPUT FOR BOOTSTRAP
~

#"" ,

,"""',

"

o
c.....

HTo-O

07-25-55

DECIMAL OUTPUT ROUTINE FOR FLEXOWRITER ANt> PUNCH

><
c..

INT-l

1'0·10-55

INTERPOLATION WITH UNEQUAL INcREMENTS I'M ARGUMENT

LOG-1

11-'Z2-55
08-10-55

FJ~ED POINT NATURA~ LOGARITHM
FLOATINGPQINT
NATURAL LOGARITHM, ROUTINE
.

......

L..O~2

'1!'

,

.

.
~~

.

\

RW-11
(REV)

PAGE 2 OF 2
REVISED 09-05-56

12-09-55
12-09-55
12-09-55
12-09-55
05-01-56
05-01-56
11-30-55
07-26-56
08-03-56

THE FLEXOWRITER MEMORY DUMP, REVISED
THE BIOCTAL MEMORY DUMP, REVISED
THE OCTAL CARD DUMP
CHANGED WORD POST MORTEM
OCTAL CARD DUMP
MANUAL INSPECTION AND INSERTION
LINEAR MATRIX EQUATION SOLVER
LINEAR MATRIX EQUATION SOlVER, FLOATING POINT
LINEAR MATRIX EQUATION SOLVER, COMPLEX

NRT-O

NUI-3
NUI-4
NUI-5

12-01-55
05-01-56
05-10-56
06-20-56

NTH ROOT. ROUT I NE
NUMERICAL INTEGRATION BY THE GILL METHOD
FLOATING POINT GILL METHOti
GILL METHOD. COMPLEX

POL-O

09-04-56

ALGEBRAIC EQUATION SOLVER,

RAN-O

05-20-56
05-23-56

NORMALLY DISTRIBUTED PSEUDO RANDOM NUMBERS
COLUMN HEADING ~OUTJNE

08-09-55
05-01-5'6
05-01-56
05-01-56
08-10-55
05-15-56
06-15-56
08-01-56
05-01-56
12-09-55

AUTOMATIC SAMPLER
CENTRAL EXCHANGE 5~NE-COSINE ROUTINE
POLYNOMIAL MULTIPLY SINE-COSINE ROUTINE
SMALL ANGLE SINE-COSINE ROUTINE
FLOATING POINT SINE-COSINE ROUTINE
FLOATING POINT SINE-COSINE
ARCSINE-ARCOSINE ROUTINE
ARCSINE-ARCOSINE. FLOATING POINT
SQUARE ROOT ROUTINE
STORAGE TO MAGNETIC TAPE TRANSFER

MDP-O
MDP-l
MDP-2

MDP-3
MDP-4
MII-0

MTI-O
MTI-1
MTI-2

RPH-O

SAM-O
SlN-O
5IN-l
SIN-2
SIN-3

SIN-4
SNI-l
SNI-2
SQR-O
51'1'-0

TNI-O 05-01-56
TNI-l' 06-15-56
T51-0 12-09-55
URT-l
URT-a

ARCTANGENT ROUTINE
Fl,OATING POINT ARCTANGENT ROUTINE
MAGNETIC TAPE TO STORAGE TRANSFER

WRITE UP NOT.AVAILABLE
WRITE UP NOT AVAILABLE

CUMULATIVE ERRATA 08-15-56
BULLETINS

N12 AND _l4

10-338

RW-71
(REV)

CONVENTlONS
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 (16000b to 11171b) have been r-e~erved
tor the drum image of electrostatic storage. These 1024 cells will
be used by those service routines which operate in electrost~tic
storage and which must restore electrostatic storage after pe~torming
their functions. This part of the drum should I).ot be used by the
programmer to store part of his production program. (Note: D~l,llU
addresses start at 40000 in decimal notation).

2.

Drum cells 52287 to 55358 (70000b to 75177b) are reserved for the

storage of service routines and are not, in general,
general program use.
3.

availab~

for

Drum cells 48191 to 52286 (60000b to 61177b) 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 ~paee
is required for subroutines, cells 57771b and lower may be used.

4-. Electrostatic stor :ge cells 13 through 22 (15b

~

26b) ~ve. been set

aside for a ten-word constant pool as follows:
13
14
15
16
11
18
19
20
21
22

Zero
. Six Bit Extractor
Advance u
Advance v
.Advance u and v
. Dec1IDaJ.12
Alternator
Operation Code Extractor
"n" Extractor
(not yet assigned)

00015
00016
00011
00020
ooo21
00022

00023
00024
00025
00026

00 00000 00000
00 00000 00017

00 00001 00000
00 00000 00001

00 00001 00001
00 00000 00110
52 52525 25252
11 00000 00000
00 01717 00000

5. Cells 23 through 32 (27b through 40b) have been set aside for temporary
storage. These temporary cells should be used in the etrictest sense
of the word and the programmer should not assttIJe information will
remain in these cells unchanged in passage from one portion of a
program to another.

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
by transferring control to cell 40001.

in

RW-71
(REV)

CONVENTIONS
Pg. 2 of 2
Revised 6/20/56

7.

b.

If the service routines are not on the dru.nf, an Mr start is
performed which reads the service routines onto the drum
from magnetic tape Unit ::: o. During this transfer J check
sums are completed and checked against sums previously obtained
upon storage at the rout ines on tape.

c.

In the event the service library data bas been l:"emoved from
the magnetic tape, Unit::: 0 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-i~
routine into appropriate positions in the computer from
either paper tape or binary cards.

Certain Jump instructions will be:read into cells 40001 through 40040
along with the service library datao The jump instruction will cause
control to revert to the routines as indicated in the list of 40000
group entrances.
The jump word in 40000 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 t'ransfer control
to ,the appropriate service routines vill 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 litthout changing the entrance
address, and the programmer need not concern himself with the knowledge
of the new location. ,

8.

In prograJl1Dling 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 J therefore, that the
, programmer supply the, computer operator with the following data:

a.

Bow to set up the stop order ( s) • That is J for example J
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

RW-71 (REV)

Page 1 of 2
Revised 6/15/56
RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California

THE

PROGRA.M;~1ING

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, eMF-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 ia performed after
the operation.

3.

Clear the accumulator before using anMA instruction.

4. 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

6.

n

j

w

The B'register occupies A70 i A69 ••
A and i6 different from AL. Not
35
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
o.pera.tion SF B k will result in the scale"factoring at A. + B. (This i.s
applicable only to the Ramo.-Wooldridge 1103.)
t

•••

7. Wb.enthe. computer isha!ted in the middle .of a repeat instruction sequence J
the PAK register contains the complement o.f j(n-r)~

8. When using an RP instruction follo.wed by a TJ o.r EJ instruction, t h e .
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 pro.duct (contents of B register) is too.
small i f a x b > 0
the truncated

produc~

is too large ifaxb <. 0

the absolute value o.f the pro.duct is always too small

RW-71
Page 2 of 2
Revised 6/15/56
Division (a/b)
the actual quotient is too sntal1 if b)O
too large if b< 0 .
Hence, one can predict, for example, that

,-_.-

4--

ailbi will be too small if

b /> O. This bias precludes the possibility of employing theusua.l formulas for
i
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 35bits plus
a sign bit.'

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.
D O3Ml5 00515.

5.

For example, D O3MOO 00500 must be used and not

Since SNAP addresses are limited to 9 bits the A, Q and B registers cannot
be address'ed directly.

10-342

R\\T-11 (REV)
Papef,:-Tape Bootstra.p
Pg o 1 of 2

Rev~

6/15/56

THE RAMO-WOOIDRIDGE CORPORATION

Los, Angeles 45, California

The Utility Routine Library Handling Package for Paper Tape Input

Normal Operation
During normal operation, the Service Routine Library is stored on the drume
In order to use one of the routines, control is' transferred to one of the
low-numbered drum addresses in the 40000b channel (see the list of "Service
Routine Starting Addresses").'
,
Details conoerning the operation of these routines and their locations can be
found in the write-ups.
MT Start
If" at any t~me, the library stored on MD 1~ destroyed by a program, or
because the drum interlace has been changed, ct' for some other reason,
the entire library may be loaded onto MD from ma~~~tic tape. Selecting
MT Start and starting effects loading of the se,rvice, routine library
from lv~~,:z,ero. PAK is set to the FRI-O stflrting .address upon comPletion
of the, -transfer. Sele,cting MT Start, setting AR=, ~,and starting effects
loading of the service routine library and the assembly program and subroutines from HT zero. PAK is set to' the CEP-O starting address upon
oompletion of the transfer~
Bootstrap
Since the Ferranti r~ader requires a programmed read in, it is necessary
to ,I~ootstrap 11 into the machine when no input routine is stored in memory.
The procedure devised to load an input program involves the uSe of one
pinary card (sinc~ '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.
'
,-...

,.....

tI

o
.....
I

o
o

'".....

r-

><
0..

This binary card oontainsa simplified Ferranti Input Routine (FRI-O) which
then begins to read in the service routine library paper tape. ,This tape
contains at its beginning the regularFRI~O input routine and instructions
transferring it to its proper location on l~. vJben FRI-O has been loaded
on MD control is transferred to it and FRI-O reads in the remainder of the
tape •
FollowingFRI-O on the tape are the library, 'a Magnetic Tape to MD transfer
routine (URT-l), and an MD to l".I8gnetic Tape transfer routine (URT-3). lilien
, :the complete paper tape has been read In the computer halts wi ththe library
loaded on MD. PAK is set to 40000 by an I-f.D Start, the, machine is, started
and URT-3transfers the library and UR.T-I to magnetic tape unit zero'. The
computer then halts with PAK set to 40001, the FRI-O starting address.
Detailed Descriptions of Routines
Detailed descriptions, operating instructions, and codes for the routine
mFmtioned above are included in the notebook.

RW-71 (REV)
Paper Tape Bootstrap
Pg. 2 or 2
Revised 6/15/56

Operating Instructions for the Bootstrap Procedure (wads MD and MT zero with
Service Routine Libraq)
.Put the bina!y card deck in reade~ 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 bot operate without them.

2.

Put the library: paper tape in the Ferranti Reader.~
Position NT Zero at the dead space immediately preceeding the first
block. (¥~intenance people will perform this function if requested).
Key in the following program:
00104
00105
00106
00107

17
17
75·
76

00000
00000
30030
10000

00104
0010;
00000
00000

pick
read
read
then

card
and pick card
one binary card
jump to 00000

5.

START at 00104. The computer reads in one card containing the'
simplified Ferranti routine, then switches control to this routine
which reads in F:lI-O and the necessary orders to transfer it "to lID.
Aft~r FRI-O has been placed on I·ll, control is transferred to it and
it' reads in the library tape and the H'1' to ND and MT t:~"ansrer routines.
The computer then halts with the ¥S tnstruction ;6 00000 40001.

6.

Select MD 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 ND to MT· routine loads the IvfIto MDroutine. 40001b thru
40040b, 70000b thru 7;777b, and 60000 th-ril"67777 onto MT zero. The
computer then halts with the JvfB instruction 56 00000 40001, setting
PAK to the FRI-O starting address.

10-344

RW-71
(REV)
FLX-O

Pg. 1 of 2
Revised 6/15/56

THE RAMO-WOOLDRIDGE CORPORATION

Los Angeles 45, Calitornia
Pool ot F1exowriterCodes
Specifications

Identification Tag:

FLX-O

Type:

Constant Pool

Storage:

17 cells, addresses 75757b thru
15771b

,....
r-!

r..I

o
......
I

o
o

0"-

r-!

r-

><
0..

Note:

This .pool of certain flexowriter codes
has. been established in ord~r to prevent·
duplication ot storage in the Service
Routine Library. See the listing tor
details.

Approved by:

w.

F. Bauer

June, 1956·

RW-71
(REV)

FLX-O

Pg. 2 of 2

Revised 6/15/56

D

FLXOO
FLXoI
FLX02
FLX03
FLX04
FLX05
FLX06
FLX07
FLX08
FLX09
FLXIO
FLXll
FLX12
FLX13
FLX14
FLX15
FLX16
START

FLXOO 55343
37
52
74
70
64
62
. 66
72
60
33
45
04
57
47
51

B
B

B
B
B
B

B
B
B
B

B

F
L
E
X
0

B

B
42 B
56 B

1

2
3

4
W 5
R 6
1 7

T 8
E 9
R CAR RETURN
SPACE

B

B

a

C SHIFT DOWN

0 SHIFT UP
D

TAB

E PERIOD
S ~11 NUS

10-346

75757 00
75757 00
75760 00
75761 00
75762 00
75763 00
75764 00
75765 00
75766 00
75767 00
75770 00
75771 00
75772 00
75773 00
75774 00
75775 00
75776 . 00
75777 00

00000
00000
00000
00000\
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000

00000
00037
00052
00074
00070
00064
00062
00066
00072
00060
00033
00045
00004
00057
00047
00051
00042
00056

RW-71
(REV)

Eratta
Pg. 1 of J
Revised 8/15/56 '
THE RAMO-WOOLDRIDGE CORPORATION

Los Ange~~S 45 J California
CUMULATIVE ERRATA

11/14/55
Page 5J line 12 from the bottom should read "n = (50000b) and not '
+ 1 = (50000b)" .

CVF-O

U

Itn

"'~ 7/25/56
.".
Page
4,
Line
CORlO
should
read
"SP AOOOO 00016
...
EGN-O 5/1/56
~

-

00776 31 20000 00020"

Page 8, line 14 should start "or the ERA paper ta.pe reader) ...... ..
~

Page 16, line 7 should start "if n~ 38, .......

8/10/55

Pa~ l'~

-

HTO-O

to

~.
drum assignment shoulCi re~' 1'63766 b through 64044 b. It

'-

t

7/25/55
Page 1, drum assignment should read "62504 bthrough 63037 b U ..

MDP~3

12/9/55
~
"'t,''' .;"V,(

'~

:'-,...

~\ '"

Page 2, line 12, reference to MOP -2 ,should read MOP -4 .
~~.~

Page, 2, line 14 J should start "each card contains six words It ..

"

NRT-O
'~.,

"

,.,
'~\

NUI:~J

.

... ~.~
.~~

,12/1/55'
12 '
Page 2, line 5 should read tf2 ~ n ~ 2. rr

.

q,

.

5/.J./56

,~~.
~~

NUI~ t},,5/~0/56

....

.\

:","'<""
,.

,:::-

NUI-5 6/20/56
l:-

•

In each ,of these Gill Method rout:inea it should be noted under

1'",

,," ,:>,f

uOperating inat,ructions" that the cells
.......

to

......

zero'~'~

t-

'-',
I

programmer

init~ally

for ,the

~

must be set

and whenever adiscont1nuity occurs'•

. .It baa been pointed out that the ,error ana.lysis ·1n Gill's, ,paper is

.'

o......

not l\l.pp1icab1e ,to these routines •

o
o

NUI-5 6/20/56

,

0"-

......
t-

Page 1 "type" should read "subi";;;rLlne, available on cards for assembly".

><

Cl..

rese~d

"Assembly Routine Spec tf line sL,',; <1 La replaced by "Regions used:

,

" ~,

"

GIL, GIN J GIM, GeN"

'

SIN -4

5/15/56
Page l, "Storage fI should read "65 words total program storage. ., words
'.

temporary storage pool used, addresses 27 b through 33b 1f ..

'"

URT-3
Pg. 1 of .l.
Revised 10/15/56

THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Utility Routine Transfer Drum to Magentic Tape
Specifications

Identification Tag: ,
Type: .

Service rout1ne(part of library load1ng package)

storage: .

110 instructions, addresses 00a45b
8

thru 00222b·

.constants 1nprogram, .addresses
00223b tbru 00232b

.

All of ES i.s used tor te~ary storage but
not incluQ,ed' with the program

liB words total program storage, .addresses
.ooo45b :thru 00232b

The temporary and constant storage pools are
not used by this routine
Entranee:

Machine Time:
~"Ot

. Operation,:

ioo seconds approximately
FiXed po1nt

Coded and Checked by:

R. Beach

August, 1955

Approved. by:

W. F. Bauer

August, 1955

10... 348

RW-71
(REV)

tm'l'-a
PS. 2

ot

~

Revised 10/15/;6

Desoription
Upon being entered the routine first bootstraps itself and URT-l into ES , then
sets up all referenoes to magnetic tape to oorrespond to the unit selected when
URT-3 is aotivated. URT-l is transferred to ES.beginning at oell l700b8
contents of cells 40001b thru 4004Ob and 70000b thru 75777'0
the sum pla.ced in 01774b and 01775b. The contents of cells
01775'0 are then summed and the sum placed in 01776b and 01777b.
in cells 01700b , 70000b thru 75777'0, and 40001b thru 4oo4Ob are
to ~ in that order,

The
and

The contents otcells 60002b
60000b and 60001b.

are then summed
01700b thru
The information
then t~anlferre4

thru' 67777'0 are summed and thesUlrl placed in

STT-O is entered to dump the information in cells 60000b thru 67777b(the lubroutine library consisting ot RAWOOP and the subroutines)o
computes the sum of all intormation plaoed onM'!', rewind. Mr to ita
'original position and reads back the data trom Ml', summing as it reads.

URT-3

It the sum is correct, a BM instruotion is given to return ~ to ita original
position·andoomputation halta with PAl( set to 4000lb, the 'RI-O Itartins addrel.,
Op!ratins Instruct'ions
~

1.

Select MD Start,'

2. Set the number' 0'1 the Mr toea loaded. in the low order ootal. d1S:1t ot Q.

3.

~.

3 transfers the oOtr;)lete library to Ml' and halta with the Me 1natruct:Lon
56 00000. 40001 atter' a IUOCCUJ8tul transfer.
'

lm'r

1lli

Alarm Conditions
It the Dum of data reM baok trom MI' 10 nab correct tho Alum routine 11 enterfldJ
the tag word ijRT-3 ~nd tho addr@oo 00070 aropr1nted on tho tlexowr1ter. ~
oum or tho data on MI' ~:Pl)ear6 1n A.

ReBtart1ns at th1l time initiate. Another trAnotor to data.
Warning
lj
2il

It 11 adv10able

to.polition~

at tho t1%'nt

Ml'. CM bo ropoo1t1oMd, mnUAlly it

bl~~k.

MC006~)".

bfttoro

19~inl 00

that tbG

<
c..

starting address.
II.

Successful transfer taltes· about, 15 ... conds.

To transfer the service routine libra", CMP-O, and the subroutine libl'&O:
1.

Select Mr Start

2.

Change PCR (it necess&%7') to select the pro~x-- m' unit.

RW-71
URT-l
(REV)
Pg. 3 of 3
Revised 10/15/56

3.
4.

III.

Make A

=1

Start. The
60000b thru
setting PAK
takes about

routine loads 40001b thru 4oo4ob, 70000b thru 15777b I and
61111b and halts with the MS instruction 56 00000 40010.
to the starting address of CMP-O. Successful transfer
35 seconds.

To load ERA Maintenance Routines
1.

Select MT Start.

2.

Change

3.

Make A~ 2

4.

peR

(if necessary) to select the properMr unit.

Start. The routine advances the Mr unit and loads the 229th 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 Mr
start the tranafer routi.tte is not in ES correctly·.
Select Mr 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 flexowri ter prints an tie II and the machine halts on a final stop
the sum of the library transferred to the drum is not correct.
Select MT start and start for another transfer •
to be completed before executing start).

(Wait for rewinding

~rating in Mode No, 2 TST-O is activated after address 4000lb
tbru 040b and 70000b. thru 75117b have been .loaded successfully. It
the sum test fails while loading addresses 6oo00b thru 61771b, the
alar.m routine prints the tag word TST-O and the address 75777'0.
'Starting causes rewind and another MT transfer to addresses 60000b
thru.61177b.

3. When

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, ~ reference
to the rewinding Mr (before rewinding is complete) will cause trouble. If
no Master Clear has been executed the machine will wait for· the rewinding to
pe completed.

RW-72
(REV)

CMP-O

Pg. 1 of 11
Rev. 7/10/56

THE RAMO -WOOLDRIDGE CORPORATION
Los

Angeles 45, California

THE RAMO -WOOLDRIDGE ONE -PASS ASSEMBLY ROUTINE

Specifications

Identification Tag:

CMP-O

Type:

Service Routine

Entrances:

40000b

Coded by:

Jules Mersel

Code Revised by:

Thomas Tack

October 1955

Approved by:

Walter F. Bauer

October 1955

and

40010b

RW-72
(REV)

CMP-O

Pg. 2 of 11
Rev. 7/10/56
Description
The Ramo -Wooldridge one -pass assembly program (RAWOOP) is designed to
translate an llq3 program originally coded in symbolIc, reglonaJ., 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 progr~
with remarks. RAWOOF's output is via both punched cards and punched paper
tape
The output card conta.ins an exact duplicate of the corresponding
input card plus an octal translat·ion of the.. input data.... The programmer
can obtain a side by side listing of his untransla.ted program, remarks, and
translated program by listing the output deck on associated eqUipment such
as the IBM 407.
0

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 ERAphoto~lectric reader or by the Ferranti tape
.reader with an appropriate read in. program. A leader and trailer is
automatically included on each tape prepared
0

Input and Output C8.rds
The input and output cards are sta.nda.rd Bq -column, 12 -row cards. The
alloca.tion of the information ~ith respect to the card columns is· as
follows:
1 ...5

7-10
12-16
18.-22

24-26
28-30

3243

symbolic address of the untranslated word
1103 operation characters or pseudO-instruction symbols ot the
untranslated word
uaddress of the untranslated word
v address of the untranslated word
decimal scaling information for the untranslated word
binar.y scaling information tor the untranslated word
alpha-numeric remarks·

It is noted. that symbolic coding for SNAP (Interpretive tlo~t1ng point
In addition to.the
. above columns, the output cards contain the translated information in
columns\,41;..61.
pac~) deviates from these conventions (see pg. 6).

On· the input catds, ~ need not be punched •

. 10-354

THE RAMO-WOOLDRIDGE CORPORATION

CODED BY_____________ ~ ____________________ ~_CHECKEO BY_--,---_ _ _ _ _ _ _....,--_ _ _ I_
FORM 64

.....

LOCATION

SOCAL ::iTA"'.

REMARKS

SYMBOLIC
[Jr""F6IIII0A''''

OPN.

.11.
U

_f D

V

• B

ABSOLUTE
CAT~

DIDiO

DOO

.. . . . . . Ullet

8801

11111 1111I 11111 _11M

til

111111111111

11111

fa

ZZZ2Z 2 Zt2 Z Z22Z 2 ZZZ 2 2 2'2'2 222

222U222Z222

UZ22

22

11111

• III 0
I

11 . . 0

,
I

_08
THE

II
II

33333 3313

33333 313'3 333 333333333333

44444

44444 ""'14 444 444444444444

33333

33

44444

44

ONE PASS

, I

I

55555 5515

.....

.1&66

.....
11111

J.,

II

nUl

&'1.'

In)}

NI}

II

.. IIM2Ia
lIMe696e~

I" ",,,&8 ..

U.

111 111JJl1)111}

I,

"'.," "'

119 81 9,9"

91999
12

1-'

55555 5,5,5 555 555555555555

Hn

919

~2t

-----

.. 111188 ....

55555

RW-72
(REV)

CMP-O

Pg. 4 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 excee.Q.inglyeconomical
in its use of machine time (see below).
Symbolic Addresses
A five 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 OIC (OICOO is the zeroth address in region
Ole) • In keeping with the one -pass nature of RAWOOP, tiW sequence numbers
are consecutive decimal numbers. The absolute address assigned to 01019
is nineteen greater than the address assigned to 01000. Thus, the address
structure bas a regional charac~er.
As 1ndicate~ above, the first three characters ot the relative address or
region are alpha-numeric.·
The. absolute address for region 000 (all zeros) has already been chosen
i'll- BAWOOP 00 be zero.
Consequently, 00029 would have 00035 as its .

octal: translation; absolute machine addresses up to 99 will be correctly
translated. Furthermore, the regions AOO, BOO, and QOO are best aVOided,
as in aomecases reference to them will be interpreted as addressing the
A, B, orQ registers respectively.
The a·ssemb1y program recognizes the alphabetic letter "0" as different
from the numeric zero but in order to avoid confusion the programmer will
pro'tlably not want to use· symbolic addresses involving the. letter "0".

AzB, and Q Addresses
The accumulator, the B register ( accumulator bits A
- A ), and the Q
10
35
register must be addressed by putting an A, B, or Q, respectively, in the
leit"most column of either the u 'or v fields. The remaining ·four columns
of the field "fI1/3.Y have no punches or zero punches
The octal translations
of A, B" or Q are 20000, 30000, and. 10000 respectively.
0

Adare saing Involving. jl.l k I and n

The command structt~e of the 1103 is such that the u and v addresses at times
contain numbers rather than machine addresses (as in the case intbe SPuk,
RPjn, w and MJjv commands) . The representation of j, n t~ 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-O
Pg. 5 of 11
Rev •. 7/10/56

is translated to 30307b. No distinction is made bet'ween j, n addresses and
addresses,. If the programmer desires to use the last four characters of
a j,
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.
j

In the ·1103 the k address .structure is used to represent":left circular shifts
from 0 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 will be treated in exactly the same manner as j, n addresses;
for example, 20017 becomes 2002lb.
Octal-8ymbolic 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 BRRfI) have
been included in RAWOOP. The first letter of the triad ,refers to the operation, 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 RAWOOP 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. RAWOOP does this by means of directory
c.ards. A directory card has a D p1nched in column l, the base word of the
region (e .g. OlCOO) in the u address columns, and the absolute decimal
address of the base word in the v address columns. For examples, see figure
lo RAWOOP can handle up to 73 directory cards in any one assembly. The
programmer is cautioned not to follow his directory cards With-program cards
destined for a region DOO. Suchan ordering would prevent RAWOOP from
differentiating between the two types of cards.
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 addre sse s range dec lmally from 40,000 - 56,383.

1{L-:t~7

RW-72
(REV)
CMP-Q

Pg. 6 of 11
Rev. 7/10/56

Sl~olic

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 be rea.d by the bioctal tape punched by RAWOOP.
Commands
The 1103 alphabetic representation of the commands is used. These two letter
combina.tions, such a.s RA for the nreplace add" or "21 conunand", are entered
into colwnns 9 aild 10. All the standard 1103 commands are recognized by
RAWOOP and this recognition implies knowing whether the addresses associat~d
with the command are of the u, v, the jn, v, or of the u, k types.
In addi tionto the standard 1103 cOJllllV3.nds, the special commands IP, PM, and
MM are recognizedo The PM and MM commands and the ava.ilability of the B
register for addressing are modifications on the RamO -Wooldridge 1103. The
PM command is a "polynomial multiply" command for polynomial evaluation whose
octal equivalent 1s 24; the MM co:mmand is the "modified multiply~" (faster
1n opera.tion than MAl whose octal equivalent is 25. None of these modifications
are Used in the operation of RAWOOPj 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 thef'orm 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 14A'u'e 'v t where A' and
C' a.re the octal representations of the SNAP commands. AB and CD respectively,
while u t and v I are 9 bit numbers. A I and u' are packed into the u address
of the translated command and occupy the left 6 bits and right 9 bits
respectively.. C a.nd v' ~re similarly placed in the va.ddress. On the input
card AB occupies columns 7 and 8, while CD appears in columns 9 and 10.
I

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 ''Btl is placed in column 25 of the D
field to modify the u address, or in column 29 of the Bfield to modify the
v address of the SNAP command.. Upon finding a "B u in column 25" a:(Jii/or29, "
RAWOOP adds two (2) to the corresponding SNAP operatioQ,.
.
It 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 (1) 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-O
Pgo 7 of 11
Rev. 7/10/56

For example, if symbolic address K9POO bas its octal address equal to 00500,
the translation of lines 26-31, of figure 1, are ~espectively:
14
14
14
14
14
14

04500
16500
24500
31500
46500

70000

10501
20501
31501
40501
51501
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 recpgnized and translated into OO~ The u and v addresses must be
symbolic addresses.. As usual, however, an address. of five zeros is translated into five zeroso
0

Decimal Numbers
Decimal numbers are presented to RAWOOP as normalized numbers times a
power of teno The programmer also states the binary scaling factor to be
applied to the resulting rounded binary numbero For example, -739.1 is
presented as -70391 x 102 ..
All de~imal numbers are normalized
1 and 9.99999 99999.

80

that their absolute value lies between

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 +100 This exponent goes into columns 24-26.. The desired binary
scale ~actorgoes into columns 28-300 For examp1es, in line 13, fi~e 1,
the number to be translated is 30123 x 10-6 with a scale factor of 222.
In all cases a minus sign represents a negative number and
punch a positive number.

a zero

or no

Floating de.cimal numbers are presented to RAWOOP in the same manner as decimal
numbers" However, instead of a binary scale factor being placed in columns
28 -30 9 an F is punched in column 280 The converted floating pOint decimal
number is in the form used by SNAP" That is, thelef't most bit is a sign
bitJ the next eight bits represent the exponent (increased by 128) and the
twenty-seven bits on the right comprise the mantissa. In this form a negative
number appear~ as the complement of the corresponding positive nUmber.
Octal Constants
Octal constants can be inserted into the program usingRAWOOP. . The octB.l
conet~t is. entered into colunms 9 -10, 12 -16, and 18 -220 A ''B'' is punched

into column 24 to signify that the number is in octal (binary) form. This
feature implies that progranl': ':'.. ! 0, 1 j II the usual machine language will be
correctly assembled.

RW- 72
(REV)

CMP-O
Pg. 8 of 11
Revo 7/10/56'

Start Card,
Tbe 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

12-1"60
The signal causes RAWOOP to insert into the translated program (in locations
00000b and 40000b) a manual jump to the octal translation of the relative
address. For this reason, it is not possible to program anything in cells
OQOOOb and 40000b
0

After the result~ng punched paper tape is read into the 1l03J a magnetic
drum start will start the probl-am at the relative address indicated in
the u columns of the untranslated word ..
Subroutines
RAWOOP.isdesigned to translate subroutines coded in octal relative to
OlOOOb (or 02000b) and stored on the drum, and include them into the main
program.. This is accom:.plished by one pseudo command,the "SUB u 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 udec1:ma),.
drum

address")"

Columns 18 ,19, and 20 contain the number· of wQrds (in de.ci:mal) in the
subroutine
Columns 21 arid 22 contain the number of constants (1n decimal)'
which 'arepl'9.ced at the end of the subroutine and are not to be modified
durir..g translation., In practice the inf"ormation in these columns is
•
simply copied by theprogra.mrte~ from a subroutine specification given on
the title page of' the subroutine write -up" Columns 25, 26, 28, 29, and 30
(!ontain the relative address-at vhich the subroutine 'is to be executed if
this 'differs from the storage addresse If these columns are blank or zero
the storage address will be used El.S the execution address ~ The subroutine
will be transla:ted relative to the execution address but loa.ded (via the
bioctal output tape) at the storage address.
Q

•

The progr~~r is cautioned not to place a SUB card immediately after
directory cards ..

t~e

The programmer bas the options of including in the output cards the translated
subroutine cards.. With jump switch No. 3 off, the punching of tbesecards
is sUPJtlressed. On th~ other hand, with this switch on, prior to starting
the as~e~ly, these cards are provided.

10-360

HW-t~

(REV) .

CMP-O
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 RAWOJP assumes that subroutines stored on the drum are coded relative
to address OlOOOb. The Ramo -Wooldridge version of RA.WOOP assumes that subroutines
are coded relative to address 02000b.
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 ll~
and st~rt.s in memory location OOOI5b. The sum of this pool is included in the·
memory sum recorded on the output tape" These constants are- PmlC~ by RAWOQP
bef::rre D cards are re.ad ahd, of course, can 'be> Wiltittet.\. o~ aft,er t-.hey enter the~
high ·~speed stora.ge.. If constant pool .cards: ~ also; desired. they may be obtained
by putting MJ 1 on before begil:tmding the asse.mbly-

Memory Sums
HAWO)f' cal.culates the me.mory ~um of all translated words includinSi the OOOOOb
and 40000b jump inst.ructions
This sum is the double precision sum. of the·
SI.li t extension of the translated words" The sum. is both printed: on the li.~ting
and rea-i by the output paper tape into addresses 15202b and 75203b of the c:ir\lm.
The high order va·lue of the sum is in 75202b. This placimg of the sum is QQ~-iste;J'3t
with the R3._:no~WooJ.dridge Ferranti read in routine
RAWOOP checks its own II1.E}lIOi"Y
sm!.a.t .the. beginning of every assembly. Upon a memory sum disagrae-ment, the
routine prints "CMP-O"0
0

p

9rdering of II2£ut CardE
RAWO)P places. the following requirements on the ordering of the input cards:
1

<>

All directory cards must come first
i3.i0;y order witl;lin themselves

0

The directory cards however, can bave

0

Tte ~ard2, ;:j.ct.u.a.lly giving the words of the program, subject to the restrictions
9lready ma,de j follow the d.ireet·ory cards _ In the interest of minimizing the
n~ber of insert ~~d check addresses on the output bioctal tape the cards should
be :in ')r.d.er within their regions
However, a correct outpu"G tape will be
pr.)duced. regardless of' t,he order of the incoming program cards.
0

Suppression of" Punched Paper Tape
If for ~'1.y reason an input paper tape is not desired, the high-speed punching
can be suppressed by turnin.g on t,he j = 2 ma..'I'}ually selective jump.
~torage

Used by RAWOOP

RAWOOP uses all of high speed storage, c~lls 40000b and 400l0b and stores
itself in 6000Gb through 62117b ~ If subroutines are compiled, it also uses
43000b through 47777b
0

10-361

RW-72
(REV)
CMP-O

Pg. 10 of 11
Rev. 1/10/56

OPerating Instructions
The foliowing points are important in the operation of RAWOOP:

1.

The reproducer BruSt 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.

30

Both the typewriter and the high-speed punch must be turned on.

4..' When RAWOOP :is first read into the ll03, an MD start will store RAWOOP
on the drum and start RAWOOP. All subsequent starts are made' from
address 40010bo When a run is completed, it atQPs with a manually selective 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-O" 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 (allay from the card
hoppers on the Ramo-Wooldridge 1103).

7.

All)s and MJ sntches should be turned off' except

as noted above.

Error Detection
If more than 13 direc.tory cards are entered the flexowriter prints "tooma.ny
d carda II and the computer halts. It is not possible to continue the assembly
after this error bas occurred.

All other errors, including a D card occurring 1n the main deck will not stop
the machine. For each card with an error on it, "ERROR tf 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 tterror"
pUnched on the.m 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 OOOOOb by the paper tape.
0

The detected errors can be corrected by a seoond assembly of only the new
corrEtcted input cards, their associated D cards, and the START card. This
will gi-ve a secondary input tape with its own memory-sum •..
Programming Reminders
1.

If' it .1s desirable to refer to the constant and tem,porary storage pools
with symbolic addresses, directory cards should be ineluded for them.

2..

RAWOOP converts decimal numbers to binary numbers occupying 35 bits pl.us
a sign.. Decimal numbers not in the correct range will be translated incorrectly or can cause an error card to be punched.

10-362

RW-72
(REV)

CMP-O

Pg. 11 of 11
Rev. 1/1Q/56

].

When converting d.rrum 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..
D 03MI5 00515.

For example, D 03M00 00500 must be used, and not

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.
b.

SUB cards
program cards directed to region 000.

7. Attention is called to the use of Aoo, BOO and QOO as regions.

If these
regions are addressed, reference may be made to the A, B, or Q registers.

8. Since the last

t.wo words of the translated program are start addresses
inserted in 00000 and 40000, it is impossible to program for these cells
using RAWOOP.

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
has the following options for correcting or altering a program:
a.
b.
c ..

re-assemble
the corrected words with proper insert and check addresses
after. the sum check
re -assemble the incorrect cards ,only and enter into the
machine the old and new assemblies in that order •
8~d

. 10-363

RW-89
(REV)

Pg. 1 of 8
Revised 6/15/56

THERAM}-WOOLDRIDGE CORPORATION
Los Arigeles 45, California

Definite Integral Evaluation Routine
Specifications
Identification Tag:

D!E-O

'Type:

Subroutine

Assembly Routine Spec:

SUB 49810 05804

Storage:

54 instructions, addresses
OOPOO thru OOP07
OOSOO thru 00S26
OONOO thru 00Ul8

4 constants in program, addresses
OIGOO thru 01C03

58 words total program storage, addresses
OOPOO thru OOPO?
OOSOO·thru 00S29
OONOO thru OONl8
OICOO thru 01C03
10 words temporary storage pool

UBed

t
. 0OO27b (OOTOO) thru00040b (OO'.rQ~J)

The

Drum Assignment:

.addresses

constant paolis used by this routine

. Addresses 63l22b thru 632IJb

Program· Entrance:

Address OOP02

Program Exit:

Address OOPOI

Mode of Operation:

Fixed point

Coded by:

F. Heek

June 7, 1955

Code Checked by:

R. Bige1:ow

June 10, 1955

Machine Checked by:

F.Meek

July 7, 1955

Approved by:

tl. Bauer

July 26, 1955

10-364

RW-UCJ
(REV)

DIF..-O

Pg. 2 of 8
Revised 6/15/56
Description
Assuming that

y = rex) is a tabulated function with equal increments in-the

argum~nt beO' Xl' x2 , • • • , x), this routine will approximate the definite
integral
, n
' -

fxn

1

ydx

xo
using either Simpson's rule or a modific6tion 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 ,yO = r(xO).
The routine gives'as a result an approximation to
i

1

and the programmer must then multiply :this' result by Cxn - x ) to obtain 'the
O
approximation to the integral itself.
Notation

rex)

<
0..

Th~ only restriction on the, Yi~s is that they must ,be single precision fixed
pOlnt numbers. The number of lntervals n must be greater than one but can be
arbitrarily large. The result J* will be given scaled by, the same amount that
the Yi's were scaied.

In order to obtain th~ maximum significance for J~. the Yi's should be scaled as
far to the'left as'posjible.
Programming Instructions
Before en~ering the routine the function values Yi must be stored in ascending
order of the a'rguments in consecutive storage .c·e1Is.

RW-89
(REV)

DIE-O

Pg. 3 of 8
Revised 6/15/56

o

1.

Place n-2

in A.

2.

Place the address of YO ::: f(x O) in Q
v

3.

Enter the routine with the instruction RJ OOKOI OOK02 (assuming OOKOO is the
region that was assibmed 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. IS were scaled. The numbers Yi have been left in their
original state.
1
¥~thematical

Analysis

Let the equal increment of x be denoted by
h ::::: x. - x. 1 :::
1

1-

X ,- Xo
.....n:o.::-_..;;;.

>0, i ::: 1, 2, •• - , n.

n

Suppose I is to be approximated by a quadrature
n

L

1* ::: h

where the c
c

o :::: C n

::::

i=O
1

c i f(x i ) :::: xn~

fon~~la

of the form

n

Xo

n

f==o

c 1 Yi

oJ.

are the appropriate coefficients, e.g., for the trapezoidal rule

1/2 and c. :::: 1 otherwise.
1

let

n

J* ::: lin

2:
c.
i=O

Yi.

1

Then

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 t.han I* 1s obtained by the subroutine.
If n 1s even, Simpson's rule is used throughout the interval (xO' xn ). If n is odd
Simpson's ,rule is used Over the interval (xO' x _ ) and Newton's three-eighths rule
n 3
is used over the interval(xn~3' xn ),
therefore
J* ::: 1/3n (Yo + 4Yl + 2:y2 + 4Y3. + 2Y4' + • • • + 4Yn-l + Yn ) for n even, and
J* ::: 1/3n (YO

+ 4Yl + 2y2 + • • • + LI-Yn_4 + Yn-3) +

+ J/8n (Yn-3 + 3Yn-2 + 3Yn- 1 + Yn ) for,n odd.

10-366

RW-89
. (REV)

DIE-O
Pg. 4 of 8
Revised 6/15/56
Error Analysis
Let a be some value in.· the closed interval (xO'xn ) and let .~ and y be values in
the closed intervals (xO,xn-·3) and (xn-3'x)
n respectively.

If ~ is continuous throughout the interval (xO,xn ) and if n is even

;l

L'= y4(a) (x - xo)5, where y4(a) = d4

n

dx4J x=o.

l80n4

If

6

dx4

is continuous throughout the invertsl (xO,x _ ) and exists throughout the
n J

interval (xn-J'x)
n and if n is odd
£

=

I/n 5 [n-3
.

y4(p)

180

+.1... y4(y~[xn
80]

-

xJ

1

5.

For the derivation of these quadrature formulas and their error terms, see Nilne's
Numerical Calculus, pp. 120 thru 124.
lv1achine Time
The time required for this subroutine is (2.25 + .62n) ms, n
time required is 2.73 ms.

f:.

3.

\-lhen n

=3

the

l/.achine Checking
Two preliminary test cases ,.rere run:

--I

.

( 35 -~) for all i.

1.

n = 99, Yi =,- 2
35 .
been - ( 2 -1).

2.

n

= 98,

y.= (235 _1). for all i.
~

The result obtained was _235 (it should have

1he cor.rect result, (235 _1), was obtained.

0"-

co

--.....
I

o

I

o
o

In additi?n, the following computations were performed:
1.

C1'

.....

t-

SIN-O was used to produce a table of sines and cosines for the arguments
y =

11

Let

s

><
0..
2.

x/2

= (11/2) ·'n • 2-4 , n

= 0,

1, 2, • • • , 99 •

=J: cos ydy = sin band G =I: sin.ydy =

compute S* and C* for b = (~/2).n.24, n
n
n
n

=2,

1-006

b •. DIE-O was used to

3, 4, • • • 9 ,

= 10,15,20,25
= 30,40~50, • • •
= 99'

90, and

RW-89

DIE-O

(REV)

Pg •. 5 ot 8
Revised 6/15/56

3.

For cnch b (or n) c ::: S* -sin b an.d c ::: C* - 1
following tDbles re~u1ted:
c
n

·6
c's -10

6
c ·10
c

.101
.338.
.197

.010
.050

2

3
4
5
6

.422
.287

7
8

.365

9
10
15

.540

.215
.151
.316

.42:1
.560

.221
.650

20

.477

25
30

~200

40
50
60
70
80

-.365
- .. 506

.713'
1.056
1.022
.881

+ cos b were computed.

The

.039

.125

.087

.490

.101

.415
.039

90

-.198
.286
.516
.286 .

.945

99

-.338

.981

.087

.516

It westo be expected that, in general, the errors would be greater for n odd. 'The
overall behavier of c and C is easily seen to be consistent yith the fact ·that
.
a
c
. .
C and Co represent the errors in integrating. the cosine and the sine respectively.
s
For example, c s is small for . n = 30 because
it is the error obtained in
.

.J~r

1i6n·i~

J~

cos ydy =:
+
001

.

since

f

~1T
1T

"2

+

~

1T

. 2

fi
=) 1

Rn

In fact, c:: lor n
s

=:

30 (b :: (lS/16)1T) is· exactly equal to
.

Evidently, all the errol's c

£,

s

for n ::: 2 (b.::
(l/16)7T).
.

are IGsa th1.Hl their corresponding maximum estimates
c
as computed by the formulas above under l~~rrOL~it.fi. In partioular. for n ::: 10 and 15.
the follo"Jing maximum error estimtt"l..<:;s were h~nd computed:

s

and

£-

10-368

nIE-O

R\V-89
(REV)

Pg. 6 of 8
Revised 6/15/56
n

........

0-

co
......,.
I

or-4
I

o
o

0-

r-4

t-

><
c..

Max

(;.8

6
10

10

.508

.421

15

~740

.903

RW':'89

DIE-O

(REV)

Pg. 7 of 8
Revised 6/15/5 6

o
D
'0

'0

o

o
o
o
o
o

oOPOO
DOP.o1
00P02
DOP03

00P04
DOPOS
DOP06
OOP07

ooseo

OOSOl
00s02
00503
0.0504
D.o505
0.0506
00S07
DOSo8
I)Os09

00510
00S11

OOS12

DOCOO 0.0013
OOTOO '.00.023
.o1C.o001078
OOPO.o .01.024
.oOSOO .01032
OONOO 01059
01CDO 49864
oaP0049810
OOSO.o 49818
DONO.o 49845
MS 00000 DOPOO
MJ OOO~o 000.00

TP AODeo OCTC1

TP aoa.oo .oOT02
. oV D1CCO O.oTD3
ZJ CONOO O.oP06
TV .0.0522 0.0519
TP OOT01 00103
MP 01C01 OOTOI

TP AoaO.o O.oT.o4
TP 00(.03 OCTD5
TP .o1C.o2 .o.oTC6
TP .0.0(.03 O.oT07

TP CcT03 AOOOO
OV CICOO OCTC8
RS 00T08 00C03
TV 00TC2 00S11
sP DOCOO 00000
~p

30003 00512
.oOT05 0.0.000
f~ ACODO .0.0109

MA

o

00015

I

0

R
E

R
Y

C
j

DRUM
STORAGE
DIRECI
TORY

NO ALRM EXIT
NORMAL EXIT
ENTRY STORE
NAND AoRS

OF YO

IS N EVEN
YES EXIT TO

$20

N/BAR

EQUALS N
STORE 3N
'STORE 1

4

AND 1
INDEX IS ONE
HALF N/BAR
MINUS ONE
PRESTORE V
CLEAR A

FORM

S1ok~

suM

.00.036

DOS14

Abooa

TP AcOCO COTCO

00S15
0.0516
0.0517
DDS18
0.0519

IJ .00108
SP'ooT09
SA ooTOO
ov 00T04
M.J 00000
TP 00T04
M,J 00000
00 00000

.00523
0.0.036
00036
OOT04
00000

tNTEGRAL TO
X N/sAR
STORE INtEl

OoPOl

GO'TO EXIT

00513

0.0520

00S21
00S2.2
0.0523

00524
00525
00S26

O.oNOO'

LA

AoooO

00$20

RA 00S11 OICOa
sP 00109 00036

SA OOTOO 00036
MJ 00000 OOS10
TV OON18 00S19

PARTIAL
SUMS
IS INDEX NEG

YES

00 00000
00 00000
02066 0000000
02000 00 00000
02010 00 00000
02043 00 00000
63210 00 00000
631.22 00 00000
63132 00 00000
63165 00 00000
63122' 56 00000
63123 45 00000
63124 11 20000
63125 11 10000
63126 73 02066
63127 47 02043
63130 16 02036
63131 11 00.030
63132 71 02067
63133 11·20000
63134 11 00020
63135 11 0207.0
63136 ,11 00020
63137 11 00032
63140 73 02066
63141 23 00037
63142 16 00031
63143 31 00015
63}44 75 30003
00027

STaRt:

GRAl IN A

00000
00000
00000
00000
00000
00000
00·000
00000
00'000

00000
0200000000
00030
00031

0-0032

02006
02033
00032
00030
00033
00034
00035
00036
20000
00037
00020
02023
000·00

02024

63145
63146

12 00034 00000

6·3147
63150
63151
63152
63153
63154

54 20000 00044
11 20000 00027
41 00037 02037

63155
63156

11

20000 06040

3i 00040 00044
32 .00027 00044
73 00033 00033
45 00000 00000
11 00033 20000

P6
MDFY V BY 2

63151
63160
63161

4.5 0·0000 02001
00 00000 02034

TIAL SliMs

63162
63i63
63164

31 00040 OOO~4

OUM~v/$EE'

RESTORt: PARI
GO TO SJO

N IS

~ODD

10-370

EX!

63165

21 02023 02066
~~

00027 00044

45 00006 02622
16 02065 ~2633

DIE-O

HW-09
(REV)

Pg. 8 of 8
Revised 6/15/56

DONOl
DON02
DON03
,D:ON04
DONOS
DON06

DoNO?

DONoB

DON09
DONI0 ,
DONll
DON12
DON13
DON14
DONIS
DON16
DON17
DONIS
DlCOO
OltOl
01C02
01(03

START

TP OOTOl
5T OleOl
ZJ 00500
TP AOOOO
LA OOTOl
TP 01(01
f~

AOOOO
OOT03
OON04
OOT04
00003
00T06

01e03 06107

TP 01C03 OOT08
TP 01COI OOT09
RA
TV
SP
RP
MA
DV
RA
MJ
00
00

00T02
00T02
OOCOO
30004
00106
OOTOl
OoT0400000
00000
00000

OOT03
OONI4
00000
00NI5
00000

00T06
OOT06
OOP01
OON05

00002
00 00000 00003

00 00000 00004
00 00000 00009

IT TO N5
N/BAR 'IS N/3

is N 3

YES

,CLEAR .14

stORE aN
STORE 3
l)
9

63167
63170
63171

FORM
SUM

STORE INTEl
GRAL IN A
GO TO EXIT
DUMMY/SEE NO

2
3

4

AND 9

11 ,20000 00033

54

63173

11 02067
11 02071
11 02071
11 02067
21 00031
16 00031
31 00015
75 30004
72 00035

63116
63177
63200
63201

CLEAR A

11 00030 20000
36 02067 0:0032
47 02010 02041

63112

63174
63175

AND 3
STORE ADRS
OF YN/BAR

~oNstA~TS

63166

63202
63203
63204

ooo~o ooOO~

00035

00036
00037
00040
00032
0206,1

00000
02062
00000

73 00030 00035

63205

21 00033 00035

63206

45 00000 0'20'01

63201

63210

00 00000 O(O5~
6() 00006 6606'

63211
63212
63213

00 00000 00004
00 00000 oooil

oo-oonoo

O()OO~

RW-I08
(REV)

SMP
Pg. 1 of 10
Revised 7/20/56

THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles

45,

Ca1irornia

Interpretive Floating Point Package
Specifications
Identification Tag:

SNAP

Type:

Service Routine (with
program available)

Storage:

Cells (00000-00012)
(00724-01023)
. ( 10000b-117.50b)

entrance~ro~

.

The constant pool is used by this routine.

Servioe Entrance:

Address 40012b

Program Entrance:

See Description

Coded by:

R. Beach
D. Gantner
M. Perry
Mo Speer
Ro Summers

Approved by:

w.

Bauer

October 10.

10-372

1955

RW-I08

SlAP

(REV)

Pg. 2 ot 10
Revised 7/20/56

Description

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-£ixed conversion, square root, load and store operations o Additional :features include an address modifier, ortlB-boxf ' ,
and optional replacement of the result o:f an operation in the
address o:f the operand. Experience has shown that representative
programs using SNAP operate at about 1,000 programmed operations per
secondo, 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) instruct10~.
The u and v portions of this instruction each contain a complete
.
SNAP command. Of these :fi:fteen bits, fourconta,in the operation
part, one the B-box option, one the replace option, and the remaining
nine the address parto 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 executiono' Each :floating point number occupies one 36
'bit cello One bit contains the sign, eight the characteristic and
twenty-seven the m~gtissao Hence the range of the numbers is
approximately .:t 10
and approximately eight signi:ficant decima:l
digits are contained-in the mantissa o The representation is such
that all 1103 logical commands may be validly applied. Therefore,
floating poirit number comparisons may be made at regular machine
speed and no need exists for inclusion of comparison commands in the
SNAP,repertoire o
SNAP occupies approximately 900 cells on the magnetic drum and 300
cells in electrostatico 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.

..co'
o......
'-'
I

o......
I
o
o

0"-

......

t-

><
~

SNAP commands may be written with alphabetic operations and symbolic
addresses, and then assembled by RAWOOPo Floating point numbers may
also be included in the program and will be converted and assembled
by RAWOOP o
.
Storage
SNAP uses cells (00000 - 00012), (00724 - 01023) and (10000b
111$Ob).
In addition~ it makes use of the Ramo-Wooldridge.constantpool (00013
- (0022)0 When executing SNAP commands, c'el1 00000 must contain the
word (45 00001 VVVVV)o
The following assignments are of interest to the programmer:
00002 F
00003

c

00004 B-box

RW-IOB
(REV)

SNAP
Pg. 3 of 10
Revised

00005 Po

7/20/56

00006 P .
1

00001 P2
00008 P3

output hopper

00009 P

4

s

00010 P

00011 P6

Instruction Structure
An instruction occupies a 36 bit cell and contains two SNAP commands,
as schematically shown below.
" IP

"1

Lei't Command

35-30

29-15

Right Command
14-0

The left and right SNAP commands are identical in .form and have the
format shown below o
Operation

IB I S I
25

29-26
14-11

10

24
9

Address

23-15

8 .... 0

Replace option (result replaced
if' blot is one)
B-box option (address modified
it' bIt 1s one)
Number Representation
Floa:'ting binary point numbers are each packed into a single 36 bit
cel~4.. wi th assigrunents as follows:

Is I

Char

3$

34-21

,I

0

26-0

"Sign" (zero when positive)
The characteristic has a bias of 128 (200b)o The binary point lIes
between bits 26 and 270 To negate a number, the full )6 bits are
complemented 0
This representation allows use ot the Transmit ~~gnitude Lid Transmit
Negative instructions as well as all comparison jumps. In addition,
fixed point declmal output routines give useful 'conversions when
supplied with 27 as a seale factor.
10-374

RW-I08
(REV)

SNAP'

SNAP

Pg. 4 of 10
Revised 1/20/56

Comman~

The list of commands follows o Parentheses indicate "contents of'''.· F
and C are specific electrostatic cells reserved f'or the package o a is
the address part of a SNAP command and may be any address in the lower
half of' electrostatic (00000-00511)0 Double length extensions of' the
results are stored in A~ the machine accumulatoro The time col~~
below gives average execution times in milliseconds o The, operations
are further clarified on succeeding pages~
, CODE

OPERATION

TIME

RESULT

\.

NO 00

No operation

AD 04

Add

2018

(F) + (a )

SU 10

Subtract

2021

(F) - (a )

II

MP 14

Multiply

1.94

(F) x (a )

.... A,F

DV 20

Divide

2.20

(F) f (a )

.. A,F

Polyo Mpyo

3045

Load

1 0 06

(a)

lit"

A,F

.98

(F)

pr

a ,A,F

PM

24

LD 30
ST

34

8.....
I

o.....
o•
o

0"-

.....

t-

><
0..

... A,F
... A,F

[(F) x (C)]+ (a)

A,F

I

:II

A,F

1.39

(F) floa ting---[A, FJ f'ixed 'at
scalo a

Float

1 087

(F) fixed at scale a ...... [A,FJ f'loating

RT 50

Square Root

3.25

RD 70

Read Data

500

Floating decimal numbers (f'our
per card)~ are read, converted,
and stored.

Punch Data

583

Floating binary numbers are converted and punched as f'loatin~
decimal numbers (six per card •

FL

'-'

(F)

Fix

FI 40

......

Store

043

PD

44

74

{(F)

_.•

...... A,F

nW-lOO
(REV)

SNAP

Pg. 5 of 10
Revised 1/20/56
NO (oo}

The No Operation command is included to complete the right half of a partial
instruct'ion. 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 dtl1l1DlY addresses. When used as a left command,
execution time is extendedo The B-box option must not be exercised.

AD (04), SU (10), MP (14), DV (20), PM (24).
Results are normalized after each execution. Alarms are provided for "division
by zero", and "exponent overflow". When the result is less than 2-129 , it is
made exactly zero.

LD (30), ST (34)
The Load and Store commands perform functions normally ~eft to standard
machine instructions. However, their inclusion in the repertoire extends the
use of the B-box 1 permitting address modification of more complete loops.
Note especially that the reserved cells F, C, B-box, and Pi' are simply
electrostatic cells
They may be operated on by machine instructions, as
well a.s 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.
0

FI (40).1 FL

(44)

When Fixing or Floating, tqe s.-:a,le a 1s in the standard 1103 notation;
1 oe when ex is zero, the point is at the extreme right and when ex is 35, the
pOint lies between bits a35 and a34- The scale a may not be negative but
th~r,e is no restriction on the upper limit, other than that imposed by overflow.
An alarm is provided for this condition.
0

Since ex 1s. 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
argwnent is in F, the address part may be used (in connection with the re»lace
option) to store the resuit. An alarm is provided for negative arguments.
RD

70

Upon,e4ecution of the Read Data command, floating decimal numbers, each with
an aasociat~d address (four I per card), are- read, converted to floating binary
numbers, and· stored at address ex (or ex plus B-box) 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 lett blank.

10-376

SNAP

HW-I08
(HEV)

Pg. 6'of' 10
reYised

7/20/56

EACh floating decimal number consists of a ten digit signed mantissa and a two digit
signed exponent
Upon conversion, the mantissa. is truncated to 27 bits. The dectHl
point is at the left of the mantissa field and the leading digit must be non-zero.
An alarm is provided ,if the absolute value of the exponent is greater than 37.
b

A single RD com.~a.nd initiates the reading of any number of cards. Reading lstermiDated either by the detection of a blank card, or after loading a card vhfch contain.
a 12 punch in either column 79 or 80. A blank card or a. 12 punch in column 80 returns
control to the cO:mn.l8.nd following the RD connnand. 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. Readini is accomplished at tbe rate
of 480 numbers per minute.
'
The following card column assignments are made:
( 1-4 )( 22-23) (41-42)( 60-61)

( 5-9 ) (24-28) (43-47) (62-66)
(10-19)(29-38)(48-57)(67-76)

(20-21)( 39-40) (58-59) (77-78)

( 79-80)

Not used
Associated 'address

Mantissa (decimal point at lett)
Exponent of 10
12 punch Will terminate read.

It the exponent or the mantissa isnegat1ve, an eleven punch is included over its
rightmost digit.

P1> (74)
Output ie in :f'loatiq deciM.l, eight significant digits with sign and a signed
exponent whose range i8 + 38. Results may be puncbed in any of six punch positions,
up to six numbers per
In addition, a four digit identif1cation, number..,. be
punched" Punching ltJay occur at ra.tes up to 100 cards per minute.

card.

"'co""'
o..-t
'-"

I

o..-t

Dependent on the value of a,. execution of' the command (PD 0) stores the' number for
future punching or punches a ce.~d. Specifically, when 06a:-6, (F), is stored in
cell Pa for future plIDching in card field a. When ex is 10, 20, BO, or 50, contents
ot the output bop~r 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 Po ~re converted to a decimal integer and punChed in, the identification field, It (Pi) 10 zero, ita field 1n the output card will be blank. A1l
SNAP output cards have a 12 punch in column 75 and also have a 12 punch in eolUlm
18, 79, or 80 when a is 50, 30, or 20 respectively. The SNAP output board is
11ired to give single spe.cing before printing except when 78, 79, or 80 contain
12 punches. In these cases, page ejection, triple spacing, or double spacing
occUr respectively, before print in« . .

I

o
o

0"..-t

t-

><
0..

Because ot the characteristics ot the Bull Reproducer, a blank card 1s pwshed throup
the punch side on the first read cycle following & punch cycle. SNAP keep. track ot
these sequences and positions an extra. card vhen required. Slnee a card cycle of
one half second is wasted each time this occurs, interspersed r.ead1ns and punch1nc
should be avoided when convenient. The blank cards may be removed from tbe output
deck by a single sort, selectIng 12 pWlcbee in colWllIl 15, since only leg1t1.-.te
output cards contain thie punch. Upon completion ot a program using the PD co_nd,
the Bull should be cleared manually to punch and feed the tinal card.

ll~E~cr
SNAP

Pg. 7

-

or 10

Revised 7/20/56

The output hopper (cells 00005-00011) need not be loaded by a PD
command g but may be loaded by any appropriate 1103 or SNAP command.
It is also possible tous,e the hopper as temporary storage. Note,
however, that if fixed point 'numbers remain in the hopper when
punching is initated, the punch routine may fail.
The following card column assignments are made:

( 25 )
( 37 )
(49)
( 61 )
( 2-9 )(14-21)(26-33)(38-45)(50-57)(62-69)
(10)
(22)
(34)
(46)
(58)
(70)
(11-12)(23-24)(35-36)(47-48)(59-60)(71-72)
(77-80)
,
(1)

..

( 13 )

Sign of mantissa
Mantissa (point at left)
Sign of exponent
Exponent
Identification

Replace Option
When a
result
of the
result

bit is present in the replace position of a SNAP command, the
of the execution is stored (replaced) at the effective address
operation. This is in addition to the normal storage of the
in A and F.
'

B-box Option
The B-box, or address modifier, is contained in cell 00004. When a
SNAP command has a bit present in its B-box' 'position, the U-portion
of cell 00004 is added to the address part (IQ) 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 ad.dress must not exceed 77177b. Use
o£ 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
destroyad o Note that, although the nine bit address part ot a SNAP
command compels the actual address to be less than 512, the effeotive
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 RAWOOP. The advantages ot
llsing alphabetiC operations and symbolic addresses are magnified
by the peculiar command structure of SNAP instructions. Regu1a.r
machine instructions may be interspersed arbitrarily with SNAP
inatructions o
At the end of this section 1s a facsimile of a standard RAWOOP
coding sheet. It contai~ 80me sample floating point numbers and
SNAP Instructions (not a program), and their assembled equivalents
(1n the Comments column). There are two alphabetic operations,
two s~~bolic addresses, and two optional B-box and store columns
in each 1nstructiono The left hand items in each pair are comb1ned
10-378

RW-I08
(REV)

SNAP

Pgo 8 of 10
Revi8~d

7/20/56

to form the left SNAP command D the right hand items to form the rlgnt
commando The numbers in rows (l)~ (2)g and (3) are respectively 0125
-4096 g and 101250
9 9
c:>

z0

1

2. ;

4

0 9 6

1

v

u

OP

ADDRESS
D

2 5 6

0

5
z'
9 9 0 2 9 9 z0 4

+

+

D

<::>

0 1

F

.3

F
F

-""'"

""'"

1 2

LD S U
A DF I 9 9 Z 0 3
R D LD 9 9 Z 0 0
A D N 0 9 9 Z 0 '7

9 9 z·

2 1
0

5.
,~

. 17

64000

00000

56 23771 7fI"J.71[
20 1«00· t¥lOOO
B S

B
B S.

COMMENTS

B

14 32402 13404

: 14

(J7403

40025,

L4 7Q400JQ4OS,

.

11..

05~07.

QOOOO.

Consult the RAWOOP writeaoup for more complete details on symbo11e
codingo
Alarms
An alarm routine is sel.f=contained in SNAPo When an alarm conditioD:
is reached, the flexowri ter types out a word having the f·orDt-;

where'TT lis the alarm type~ P is an L or an"Ri (1eft or right command),
and XXXXX is the location of' the instruction which caused th$ alarm.
Upon completion of the typfng9 a Manual stop zero occurS o If the
computer is now startedS' F and A are set to zero and eX;.6cutiQn of the.
next command is initiated o See below for the exception whe. reading
data o
The following types of" alarm may occur:

co
o..-I

---o,

10

EO

Exponent Overflow "'" Tp,e absolute value

20

RT'

Square Root of .a negative number

30

DV

Division by zero

40

FI

Fixing causes the :n.:wnber to overflow the F register·

50

RD

Ab.qglute value of input number is equal to or greater than
1~ •
Starting the computer after alarm causes normal
reading except that a zero replaces the erroneous numb.er •

..-I

I

o
o

0"-

..-I

{)f the reflul'\i, ,is greater

than (1 "" 2",,27)2126. ~

Operating Instructions (Activation of SNAP)

t-

><
Cl.!

10

Insure that SNAP is intact on the magnetic drum
(This can be
of the Service Routine Library trom
magnetic tape)o-

20

Load the problem Qrogram - Program should include the R-W
constant poolo

0

aceomplished~a-rransrer

t~~
SlAP

Pg. 9 of 10
Revised 7/20/56

30

Set PAl( to 400l2b' and start - This causes SNAP to be read into
its electrostatic locatlons p sets the B-box g F, 0, ~nd output
hopper to zero" supplies an appropriate jump in cell zero,
positions cards on each side of the reproducer, and gives control to cell 40000 which normally initiates execution ot the
problem programo

Programmed Activation of

SNAP

It 1s ocoasionally desira.ble to activate SNAP from the program o This
may be accomplished by execution of o~e of the two oommands given
belowo
It Is assumed that cell 40000b contains (MJ OOOOOVVVVV) which RAWOOP
supplies 0
For initial activation

(37 40000 40012) - execution ot
this instruction has the same
effect as (3) in Operating Instructions above except that control is
given to cell (n + 1) when the
instruction is in cell no

For reactivation

(a)

(37 40000 71050) - same as (1),
above except that card positioning is omitted.

(b)

(31 40000 71047) - BamEt as (2',a)
above except that one blank is
fed on the punch side to insure
that a RD has .not cleaFed the
punch atation o

Subrout1.ne!

Many'ot the,oommon subroutines ha.ve been coded
representation. for argument and resulto
use Is extremely simplso

u~lng the SNAP number
Others are In procesBoTheir

It ls~ however, posslble t.o employany1'l:x:sd point
:.elQ~tl.p.g point program by the expedient of the Fix

suproutine in a
and Float commands
contained in SNAPo Note that conversion is rapld·and that scaling is
easily: supplied In the address p.art ot the commando
Desl.gn Crt tar..±.!

The ph·11o~opb.Y which leads to this .package states that" in order of
Imports.noe~ 'tb.e fo'llowlng three items are virtues:
(~)

Simplicity - To produce faster ooding with fewer errors o

(2)

Ex~out1on

(3 )

Minimum storage u8ag~ - Both in the problem program and 1n
theVpaokage~ to conserve high speed storage.

speed ... To conserve machine tlme o

10-380

RW-I08
(REV)

SNAP

Pg o 10 of 10
Revised 7/20/56

With these in mind$) a single address system was choseno While logical
operations are generally best served by multiple addresses, use of a
single address Is indicated for arithmetic operations o Since the four
basic arithmetic operations may occur in a great variety of sequences g
a multiple address system must either waste many of the addresses or
contain contain a very large number of' ari.thmetic command types o
Wasting addresses wastes storage in the main program; inclusion of; Qi,
large number of command types expends storage in the package o T.hua
(3) is satisfied by the single address o With only one kind ~$ each
of the al"ithmetic operations, jumping and sorting in the ari,tbmetlc
section is minimized o

Furthermore; use of only one operand sav;-es' the unpaekinB:"of multipl~
packed numbers
So the requirements of' t,2) are met
Ftnally, the
consideration of (1) ~ ul timate simplictty' is achieved wi th a system;
which always operates on baa sama register with but a singlElr operanqo.
0

co
o
~

'-"
I

o......

,

o
o

0-

......

t-

><
0..

Q

RW-140
(REV)

SNAP Sampler
Pg. 1 of 4
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 bas the following specifications:
a.

The list is made up of sublists of four words each.
These sublists have the form:
00

00
00
00

FA
Np

LA

00000

00000

00000

00000

Ns

FA is the address -where the trace is to start and IA the
Np is the number ot times

address at which it is to stop.

FA iato be passed before starting the trace, while Bs 15
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 lis t must not be placed in cells 15b thru 107b, but may
be put on the drum.

In any case, a parameter word 00 Lo

Lf will specify its location.

Lo is the address of the

first word of the list and Lf is the address of the last
word.

This parameter word must be loaded into cell 71777b

Restoring the library from magnetic tape loads an all zero
word into cell 11171b.

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
1s not possible.

d.

The storage addresses FA and IA must be the addresses in which
the instructions to be blocked are actually stored at the
time the blocking rout j

:~t(~ti

10-382

vated.

RW-140
(REV)

SNAP Sampler
Page 2 of 4
Revised 1/20/56
The operation of the trace is as follows:
a.

When a blocked FA is reached in the program, Np and
N are examined.
s

If N =0, N

s

p

I ° then tracing

is

initiated and a start indicator placed in the word
containing Nand N. On the other hand, if N = 0
P
s
P
and'N
does not occur, then no action is taken.
s
At each SNAP execution, after a trace start, the F

10

b.

register is transferred to the next available position
,

irithe trace output hopper (last seven cells in ES).
When this hopper contains the results of six SNAP
commands (three IPinstructions) then the

SNA~

output

routine is used to punch a card containing the information in the trace hopper.

The identification field of

the output card contains .the address' of the instruction
which

the numbers in fields one and two.

~oduced

This

address is in octal and will be 1125 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 anytime, start at 72l25b.
One card will be punched and the machine1will 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
address 7177 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
start indicator was set up in the word containing the
associated Nand N then tracing is stopped and the trace
p

hopper emptied.
f.

s

Otherwise, no action is taken.

The execution of the instruction at FA will be traced,
but that at LA will not.

RW-140
(REV)

SNAP Sampler
Page 3 or 4
Revised 7/20/5 6

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 71117b with the parameter word 00

Lo

1£

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 7200Ob.

The routine will block the proper instructions as

per the list supplied, modiry SNAP in order to perform the trace,
and then stop with

4.

PAl(

set at 40012b.

In the event no parameter word is loaded (and no list is supplied)

a start at 12000b will initiate the blockiDS. routine to modify SNAP
on NO so that all SNAP commands will be tra~ed.

Astop will

follow

with PAX set at 4001Gb.
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.

4.

The instruct ions 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 eopy of SNAP on MD and destroys
the complex arithmetic portion of SNAP'.
USing SNAP or

it~

To start another program

complex ver'sion, it is necessary-to restore the

library from magnetic tape.

10-384

RW-140
(REV)·

SNAP Sampler
Page

4 of 4

Revised 7/20/56

8. An abnormality exists for the following type of a list:
00

FAl

LAI

00

Npl

Nsl

00

00000

00000

00

00000

00000

00

F42

LA2

00

Np2

NaG

00

00000

00000

00

00000

00000

1

~'

Assume that N ' N ' Np2' N· are such that tracing in both sublists
sI
s2
pl

is concurrent.

Further, suppose that FAl , FA2' LA ' LAI are executed

1n the order given.

Z

ffence, the trace will be initiated at FAland

once again at FA " When LA2 is reached, the trace will stop since it
2
was started at FA •
2
The instructions·from LA2 to LAl will not be traced and the trace will
be stopped once again when LAI is reached.
be punched.
fashion.

At this· time the hopper will

Other unusual combinations can be analyzed ina. similar

RW-141
(REV)

SNIP
Pg. 1 of 4
Revised 1/20/56
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Interpretive Floating Point Package - Complex

Identification:

SNIP

Type:

Service Routine (with entrance from
program available)

Storage:

Cells

634
70000b

thru
thru

1023
71662b

This includes
SNAP

The constant pool is used by this routine.
Service Entrance:

Address ·40013b

Program Entrance:

See description

Coded by:

C. Koos

M.. Perry

January, 1956

Code Checked by:

c.

J~uary,

Machine Checked by:

C. Koos

January, 1956

Approved by:

W. F. Bauer

April, 1956

Koos

10-386

1956

RW-141
(REV)
SNIP
Pg. 2 of 4

5/1/56
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.
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.

·The

SNIP performs its operations in either real or complex arithmetic depending 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
'; the real and imag~nary parts of the number stored in consecutive cells
(For example, the complex number x + iy would be stored in the machine
with x in cello( and y in cell c<.. + I).
.

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, Fc.

3.

The Polynomial Multiply command of SNAP is changed so that its
execution will result in computing the absolute value of the number
stored in Fc.

4.

The Fix., Float ,. Read, Punch and No Operation 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'forthe floating
accumulator and cells 0( and 0<. + 1 for the argument as explained
above. .

5. The machine accumulator A contains the real part of the result after
the ex·ecution of any one of these operations.

6.

The Replace and B-box options may be used in all cases· that are
permitted by SNAP, with two consecutive cells being operated on as
described. Keep in mind that the B -box must be indexed by two when
used in referencing a list of complex numbers.

1. It is not permissible to load Fc with TP instructions; a Load command
must be executed for this purpose.
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 (Fc) just as it does in the complex mode.

RW-141

SNIP
Pg. 3 of 4

5/1/56
Revised

(REV)

7/20/56

SNIP commands
The Complex Accumulator, Fc ' 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\.C
represents the address of a complex number x +iy, where x is stored
at <.< and y at C( + I, that is, (0<.) = x, (D( + 1) = y.
The following definitions apply when in the complex mode:
Code

Result

AD 04

(F c ) +

;

(F) ->A

SU lO

(F ) - (ex. c ) ~ 'F c ;
c

(F) ~A

MP 14

(F ) x (0( )
c
·c

(F)

DV 20

(F )
c

PM 24

' '{Fc)1

LD 30

(C( )
c

~

ST 34

(F )

RT50

i(i]
c

c

(~

c

)

~F

--=;.

c

F ;

c

~A

~ ) ~F ;

c

c

(F) -~A

~

F .

(F) ~ A

c"
F .
,c'

(F) ~A

-,->

eK c ;

(F) -> A

--------7

F .

(F) -7 A

c'

file NO (no operation), FI (fix), FL (float); RD (read data) and
PD (pmIch~ta) instructions of SNAP are unaltered. The PM (poly'nomia! multiply) instruction ot SNAP' is :replaced, 'by the" absolute value
instruction whether o~erating in the real or complex'arithmetic mode
i t SNIP has been act~vated.

Manual' Activation of SNIP
1.

Insure that both ~his routine and SNAP are intact on the 'magnetic
drum. (This can be accomplished by a trans'ter of the Service
Routine Library from magnetic' tape}.
'

2,.

LOad the problem program ... The program. shoUld include the, RamoWooldridge conat$nt pool, and a jump to start in 40000b, as
supplied byRAWOOP.

3.

Set PAK to 40013 and start --this changes SNAP into SNIP and causes,
it to be read into its e,lectrostatic locations, sets the B-box, F,
C, and output hopper to zero, supplies an appropriate jump in
cells zero and 9ne, positions cards on both sides of the reproducer,
and gives control to cell 40000b which normally initiates execution
of th~ problem program. At this time the rou~i,ne is in ,the real
arithmetic mode.

. 10-388,

RW-141
(REV)

SNIP
Pg. ~ of

5/1/56
Revised ,7/20/56

Programmed Activation of SNIP

Depending on the card positioning desired any one or 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' ,40000b
(such as that supplied by RAWOOP), and in each case control -is :returned
to the instruction inunediately followlng the return jump.
a.

Exe,cut,io.h of 37 - 40000
the reproducer.

40013b positions cards on both sides of'

b.

Execution of 31 40000
of the reproducer.

1l644b feeds one -caraon the punch side

c • Execution! of -31

40000

11646b omits all carQ, ',positioning.

Otherwise the effect of programmed activation is the same as that described
iri .step 3 under manual activation.

Switching Modes
Activation of SNIP by any one of' the methods describe~ above leaves it
in the real arithmetic mode. At any time arter SNIP bas been activated the mode may be switched as follows:
To switch from the real mode to the complex mode execute
31 01541

th~

return jump

01113b

To switch from the complex mode to the real mode execute the return jump
31' 01541

011l5b

In either case the desired mode change is accomplished~ cell-OOOO3, 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
The -SNAP alarm routine is used, with the possibility of the' same type
of alarm occurring (EW, RT, DV, FI, RD). It is not advisable ,to continue
the problem after an alarm, since either the real ,or iniaginarypart of
a number may have caused the alarm.
-

"A DV alarm will occur if the real and the imaginary parts ot the denominatorare both less than about
2·2 -b5 in absolute value.

RW-63
FRI-O
(REV)
Pg. 1 of 4
Revised 1/10/56

THE RAMO-WooIDRIDGE CORPORATION

los Angeles 45, Cali:fornia
The Ferranti Input

Routine

(reyised)

Specifications

Identification Tag:

FRI-O

Type:

Service routine (with subroutine ,entrance)

Special'Storage:

The constant and temporary storage pools
are not used by this routine

Service,Entrance:

Address 40001b

Program Entrance:

Address 40001b

Program Ex1 t:

Address 4oo20b

Alarm Exit:

The alarm exit is used by this routine

Coded by:

R. Beach

lIay 18, 1955

Code Checked by:

R. Summers

May 19, . 1955

Machine Checked br:

R. Beach

August

Revised by:

c.
w.

Koos

December 1, 1955

Bauer

December 9, 1955

Approved by:

10-390 '

4, 1955

RW-63
FRI-O ·(REV)

Pg. 2 of 4·
Revised 7/10/$6

·Description
I. aeneral
This routine is designed to read, by means of the Ferranti reader, seven-level
biootal tape prepared as described below. The routine. reads in paper tape at
the full speed of the Ferranti with only short hesitation when ·a.chacko1>insert address is enoountered.
.
If' desired, the tape'may contain a.oheck sum to·be tested for agreement with the
computed Sum' of' the data read-in. The routine 'Will read data irito any ES or MD
cell although the reading of information into certain drum cells (as described
in detail below) will result in abnormal operation.

The routine stores'the contents of ESon MD at addresses 76000b~through'77777b
andtben transfers itself to ES. It sums itself (in ES) and checks the sum
against-·the·correot 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 thesa~e manner
as does·the ERA photoelectric reader (for exoeptions,.see II. 3 and 4).
Each 'Word to be transferre'd to memory is summed as it is l;'ead in from tape.
Words. ·whioh are to be read into ES are first stored in. the MD image .of ES
(76000b. tbru 77777b) ~
.
.
.
DUring operation all words are read into ES from the tape and .a ·black transfer
to MD 'ismade when (1) ES has been filled with data (that is, when 924 words have
been read in);. (2) an insert addresi3 appears on the .tape; or (3) the nend 6f ~j)e"
seven-l~vel combination. has been read in (see II·•. ·4) ~.
.
, : , ' . '

.

, "

The reader is stopp.ed before' making the transfer 'and is' started again after the'
transfer has been completed in the first .two ca'ses; in the·lastc8se, the reader
is stopped, . ES is restored. from 'the MD. image and control is transferred to . the
exit. !;it' , , '
.
.., '1"

~

(Ij

--o

....0
I

.

~

.' .'. ",

.

.

'

"

.

The'. reader is also halted when a .cheokaddress appears '~n the tape. . If no. check
sum tes·t (see ·II. 3) is to be made after a successful oheck address test' the
reader is started 1mnlediately; if the ohec.k sumtest.1sspeciti~d the reader is
sterted after the test is made and' the' sUm determined to be correct.

;-t

I

0"

o

0"-

The routine does not prevent read into addresses 76000b· 'thru 77777b' nor to
those·calls:usedby thero~tine for its own operations.
.

...-t

['-'

><

II.

Reguireme~t§for

Tape Preparation.

~

1.

The first word on a tape must :beit an insert address.·
~'\

.

2. kheck addresse'a- should be use~, although'''FRI-O ·will operate' wi th9Ut
them. A oheck address immediately following an insert .address must
be the same as the insert address.

RW-63

FRI-O

(REV)

Pg~.3 of 4
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 75204b

Operatin~ Instructions (to be followed when the routine is used as

8

service

routine)

1.

Set PAK to 4QQOlb and start.

2.

Computation will halt with the 113 instruction 56 00000 40001b at the completion of the read in.

Prouamm1ni Instructions
routine)

(to be followed when the routine is used as a sub-

I.

Enter. thO routine with the ·RJ instruction 27 40020 400Qlb

2.

Control is returned to the cell immediatelY following the RJ instruction
as soon as an "end of block u punch is reached on the tape.

Alarm Conditions
1.

No "end of tape" punch. This oondition is indioated bby the tape running
completely out of the Ferranti reader. When such a condition OCOUl"S the
operator.should.
8.

Master clear

b,

Set FAK to OOQ74b and start

o.

When oomputation halts (when a service entry was. used) 'With the MS
instruction 56 00000 4000lb the maohine will be returned to· its
originsl state and the data read from the tape will be properly.
stored.
.

If a program entry vas used control will be traner-erred to the proper
oell in the main program.
·2.

FRI-O not transferred toES cgrregtlx. It ALR-l printe "FRI-O xxxxx and·
(A) and (Q), the sum of the program ·transferred to ES has failed tooheck.
Starting et this point transfers FRI-O to ES again.

A second failure indicates that FRI-O is not ·on the drum correctly. and
should be restored •

.3.

Check eddrgee f'ai1ltrs. If ALR-l prints "ALAR ott e.nd (A) and .(Q), 8 check
address hae failed. In the alarm print (A ) is the address or the next
R

10-392

RW-63
FRI-O (REV)
Pg. 4 of 4

revised

T(I~O/5.6.

cell to b~ 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.
Check sum. failure. If ALR-I prints "ALAR Mit 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 end
to begin to read in the tape again.
If a.t any time (ES) need to be restored from its Image, starting at
40040b Will t~ansfer the image to ES and transfer control to the FRI~O
exit.

5.

And '''end of tape n (or "end of block n) punch must be present on the tape
to halt read in. This consists of seventh level punches in two consecutive fra~es on the tape at the point where the read in is to be stopped.
This seventh level combination acts as a signal to FRI-O 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 baving seventh level punches the stop is bypasSed. The C~ck SUlD
is cleared and the readingcon:tinues •. This will still 'be an illegal
combination which will halt an ERA photo-electric reader.

RW-148
(REV)

SllI-l

Pg. 1 of 4
Revised 6/15/56
THE RAMO -WOOIDRIDGE CORPORATION

Los Angeles 45, California
Arcsine-Arcosine Routine
S~eitications

Ident1fication Tag:

SNI-l·

Type.:

Subroutine

Assembly Routine Spec:

SUB 50410 08014

Storage:

80 words total program storage
7 words· tempor&.r7 storage pool used,
addresses 00027b thru 000351>
The constant pool is used by this routine
'.

OOKOl OOK03 tor the ar.esine
RJ OQKOl OOK02 tor the arcosine

Entrance and Exit:

RJ

Alarm:

The aJ..arm exit is used to print uAlarm"
if the absolute value of the argument exceeds
one.

Drum As signnent :

Addresses 64252bthru 64371b

Machine
Mode

T~:

ot Operation:

6.0

Dl8

average, 6.6

Dl8

ma.ximtun time

Fixed point

Coded· by:

A • Franck (ERA)

... 1:14., 1955

'b-anslated by":

D. Gantner

August 16,1955·

Machine Checked by:

T. Tack

August 25, 1955

Approved by:

w.

September 12, 1955

;.

Bauer

10-394

RW-148
(REV)

SNI-l·
Pg. 2 of 4
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:
- lC/2£arcsine x ~lC/2

OLarcosine X~lC
Programming
1.
2.

Ins~ructi~ns

Place the argument scaled by 233 (ioeo x.2 33 ) in A.
Enter -the routine with an RJ instruetion.. If the routine was assigned to
region·OOKOO for assembly use the instruction

3 •. At

RJ

OOKOI

OOK03

for the arcsine, or

RJ

OOKOI

OOK02

for the arcosine.

the time of exit

~rom the routine the result F(x) "2 33 is lett in

A ..

Alarm Conditions

......
co

If the·txt is grea.ter ·than one an alarm exit will oeC1lr.

The word "alarm"

'-'
I

and·. the address of the· cell in the main program conta.ining the RJ instruction
which was used to enter SNI-I will be printed on the flexowriter.

o

Pushing the start button atter the alarm halt will transfer control
exit ot SNI-l •

~

......

o......
I
o
. 0'

......

l-

I><

0..

to

the

RW-148
(REV)

SNI-l
Pg. 3 of 4
Revised 6/15/56

0
0

DSCOO

DSCOO 50410
ASCOO 01024
37 75101 1570.2 B

osee1

M.J 00000 00.000

DSC02
DSC03
Dsce4
Dsce5
Dsce6
osee7

TP 000.13 0.0.024
TM AOOOo. 00.0.25

DSCOS

DSco9
DSC10
OSCll
DSCl2
DSC13
DSC14
D5C15
05(16
OSCl7

05C18
DSC19
DSC20
DSC21
DSC22

DSC23
DSC24
DSC25
DSC26

05(27
DSC28
DSC29

DSC30
DSC31
DSC32
DSC33
bSC~4

DSC35

DSC36
05C37
DSC38

0$C39
DSC40

DSC41
DSC42

DsC43
DSC44

MJ 00000 ASC57
MJ 00000. ASC60

ALARM EXIT
ROUTINE EXIf
ARCCOS ENTRY
ARCSIN ENTRY

TJ ASC66 ASCOO

TJ ASC67 ASC09

MJ

000.0.0
TP AOOOO

Ascoo
QOooe

64252

00 00000 00000

020.00.
64252
64253
642·54
64255
64256

00. 0000.0. 00000
37 75701 75702

64257
64260.
64261
64262

20000.
42 .02102
42 0.210.3
45 00000
11 200.0.0
41 02013
46 020.14
11 00020
12 20000
4.3 02104

64263

ZJ ASCII ASC52

64264

SJ ASC12 ASC13
TP 0.0.0.16 00024
1M AOOOO AcceO
EJ ASC68 ASC55
MP 00025 ASC69
LA AOOOO 00037
AT AsC70 000.26
MP 00025 00026
LA AoOOO 00.037
AT AsC.11 00026

64265

64266
64267

64270
64211
64272
64273
64214
""64215

MP 00025 00026

64276
64277
64300

MP 0·0025 00026
LA AooOO 00038

64301
64302
64303

LA AOOOO 00039
AT A5C72 00026
AT AsC:73 00026
00025 00026
LA Aoooo 00038

MP

64310
64311
64312
64313
6431'4
64315
64.316
64311
64320
64321
64322
64323

AODOO 00028
00028 00034

DV 00027 00029

LA

RS

00027 00071
acoool 00027

10-396

0.2011
02000.
10.00.0.

02064
0.2015
ooo~o

20000

02067'

71 00031 02105
54 20000 00045
35 02106 00032
71 00031 000:32
54 20000 00045
35 02107 00032
71 000.31 00032
54 20000 00041
35 0.2110 00032

71 00031 000302
71 00031 00032

00025 000.26

TP
SP

00031
02000

64305

64307

TP ASC78 00027
EJ A$C7B ASt47

0OO15000~O

54' 20000 0004'6
35 02111 000·32

64~O6

LA Aoaoo 00038
AT ASC15 00026
MP 00025 00026
LA Acaoo 000:;6
AT ASC16 00026
TN 000.25 Aoaoo
SA· ASC68 ,00002

000.00 00000.
0.0000 02071
00000 02614

64304

Ai AsC74 00026

MP

45
45
45
11
12

S4 20000 OO() 46

35 02112 00032
7.1 00031 00032
54 20000 00046
35 02113 00032
71 00031 00032
54 20000 00044
35 02114 00032
13 00031 20000
32 02104 00002
11 0,2116 00033

43·
11
31
73

·02057
2000000034
00034 00042
00033 0OO3S

,02'11·6

64324
64325

54 00033 00107

64326

23 10000 00633

SNI-l
.
Pg. 4 of 4

Revised 6/15/56

DSC45
D5C46
OSC47
DSC48
05C49
DSC50
OSCS!
D5C52
05C53

05C54
DSC55
05C56'
05C57

DSC58
D5C59
DSC60

00027

00029

6·4327

21 00033 00035

QJ ASC41 ASC41

64330
6·4331

44 02051 02057

RA

MP Aoaoo 00026

64332
64'333

LA AOOOO 0'0037

5T ASC17 QOOOO
IJ 00024 ASC52
TN QOOOO QOOOO
RS QOOOO 00023
DV ASC19 Aoaoo
MJ 00000 ASC01
TN ASC77 QOOOO
MJ 00000 ASC50
TP Ase77 00023
TV ASC65 ASC54
MJ 00000 AsC04

64334
64335
64336
6·433'7

1.1 00015 00021

'64341

05C62
05C63
DSC64
D5C65
D5C66

MJ 00000 ASC04

643·50

TN AOOOO AOOOO

16 02100 ().2066
4500000 0'2004
64351 . 13 20000 20000

M.JOOOOO A5eo 1
00 000.00 ASC63

64352
64353

45 O()OOO .02001
00 00000 02071

643"54

67 117"71 77777

67 77777'71717 B
10.00000 00001 B

00000
05(69
20070
05(70
2:5535
05(71
51545
50417 41233
DSC12
D5C13 . . 46 ·23106 66522

05C74
DSC75
05C76

10
53
33
56
37

00000
24135
2441.4
40071

10 00000 00001
1Q 00000 ·00000
6435753.24135 20Q70

64355
64356

8
B
B

B

64360
'64361

B

6436237 50411

26. ~1651 6607"'3

B

4442003 30653
31 10375 51633

e

33 ',,24414 2553S
56 40071 S154~

4123~

64363 4623106 66§2~'
64364. 26·61651 66073'
64365 44 42003' 3665·~
6,43.6,6 Sl: 1031.S .S1033
6436131 10315 52421
64370 '. '31,7771'117771
.64371' 60:. (lol106 :06602

~

a

31 10375 52421 a
OSC'78
31 77177 777'17 ·9
DS.C19· . 00 00000.00002

05C7'1-

STARr

loono'

100'00 00021

643:46

TV AsC64 ASC54

DSC68

02064

64345

DSC61

D5C67

23

00032
00045
10000

73 02117200no
45 00000 02001
1'3 02.11 S lO()Q:O
45':00000 0.2,062
It 0'2115 0002·1
16'02101 02066
45 0.0006 020:04

64340
. 64341
6.43'42
6·43·43
64344

TP 00013 0002~

71 20000
54 .20000
36'02115
41 00030
13 10000

a

10-397'

RW-149
'(REV)

00-2 ..
Page

f ot'4
8/1/56

RevitUKi

THE RAMO-WOOLDRIIGE CORPORA1'ION
Los Angeles 45, Calffomia
Floating Point Arcsine-Ar<:osine Rout,ine
Specificationf ~
Identification Tag:

SNI-2

Type:

Assembly Routine Spec:

SUB 50349 06112

Storage:

61 words t~otal PrQgram storage.

3 we rda temporary storage pool

us~d.)

ad.tember 1.2,

25, 1955

1, 1955
1955

SltI-2

Page 2 of 4
Revised 8/1/56
Description
'it,1}1en 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 Pqlynomial Approximation producing the ansver in SNAP fonn.

The SNAP floating point routine must be in LS. when this subroutine is entered.
X must be in SNAP form.

1.

Place the argument X in the accumulator.

2.

Return Jump to the subroutine.

Assuming that the subroutine was assigned
to region OOKOO for assf?mbly, use the instruction RJ OOKOl 001r0.2 for arcsine,
or RJ OOKOl OOK03 .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:

-1f./2 .s arcsine X S: n/2

o~

arcosine X S

n/

Error Analysis

. -26 •

The error in the result produced by this subroutine is less than 2
Mathematical Analysis
I.

The Ra~d 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 usingtbe square.
root subroutine wi thin SNAP. Designate this resul.t. as R(~).

34 If X is positive, let Y = P(X)R(X)
If X is negative, let Y =
0'

~

4 •. Arcsine X

n-P(X)R(X)

= (rc/2}-Y

......

"'(
o......

6

~

.-t

Arcosine X

=

Y

5. This procedure places arcsine X in the first or fourth quadrant, and
arcosine X in the first or second quadrant.

.

t-

:><

0..

Alarm Cond!tions
Analann print will occur i f the argument is outside the range -l~ X~l. The
flexowriter \nll p=int "ala.::m" and the address of the cell in tbe·-ll'Jain program.
containing the RJinstruction which was used to enter SNI-2.

10-399

RW-149
SNI-2
(REV)
3 of 4

Pa.

Revised

D
D
D
D

aOKoe
OOTOO
00(60
SRTOO

D

DOPOO 00877

b
D
D
D

OASOO
OAsal
OASQ2
OASQ3
OAS04
OAsa5
OAS06
OAS07

oAsaa

.......
c::J'

"'C:2I

......

-I

0

I""'t

I

8

""

.....
r--

OAS09
OASIO
OAS1I
OAS12
OAS13
OAS14
OASI5
OAS16
OAS11
OAS18
OAS19
OAS20
OAS21
OAS22 '
oAS23
OAS24
OAS25
OAS26
OAS21
OAS28
OAS29
OAS30
OAS:?1
OAS32
OAS33

00906
00722
00754
·00927

OAsao 50349
lAsoo 01024
2Asoo 50398
3ASOO 01073
31 75701 15702 8

MJ
RP 20002 lAS04
TP 00018 00023
TP Acaoo 00024
TM AOOOO AOQeO
TP BOOOO 00025
ST 3AS08 Qooqo,
TJ OOK14 lAS12
QT OOK03 00025
SP QOOOO Ooooa
TV 80000 lAS12
LA 00025 00000
5T 3AS09 'QOOOO
SF QOOOO 00T04
SJ lAS17 lAS16
ZJ lASOO lAS32
LA ADOOO 00027
TN 80000 00T03
LA 00T04 00027
TP lASOl oocoo
RJ OOCOO SRTOO
TP OOP02 OOCOO
SP 00T04 00000
SS SRT26 coooa
TV BOO.OO lAS31
SN 3ASOO 00036
RP 20007 lAS29
PM 3ASOI 00025
MP BOOOO 00T03
LA AOOOO 00010
SP BOOOO 00000
TP BOOOO 00025
TP 00024 aoooo

SNAP CONS
SNAP. TEMP
SNAp EXIT
SNAP SQ ROOT
SNAP CONS
ARCSN RTN 49
REL 2000 49
ARCSN eNS 11
REL 2000 11
ALARM EXIT
NORMAL' EXIT
COS ENTRY

x

X ASS
CLEAR 25
X-50
X ZERO
M
M

FIXED

33

1/X FLOATED
SF IN T04
FIND ROoT,!
REPAIR SNAP

AJ7

EVAL

RAND.
29
56

66
31

x

~

10-400

OiS5!1
64155
02000
64236
02061
64155
64156
64151
64160
64161
64162
64163
64164
64165
64166

X LESS 1

POLY

01612
:0132'2
01362
0163'1

64167
64170
64171
64172
64113
64174
64175
64176
64177
64200
64201
6,4202
64203
64204
64205
64206
64207
64210
64211
64212
64213
64214
642.15
64216

8/1/56

00 00000 00000
OOO.oQ:O'O 00000
00 POtlOO '00000
00 00'000 00000
00 00000 00000
00 00000 00000
00 00000 00000
00 00000 00000
00 00000 00000
37 75701 75702
45 00000 00000
75 2000'2 02004
11 00022 00027
11 20000 00030
12 20000 20000
11 30000 00031
36 02071 10000
42 01630 02014
51 01615 00031
31 10000 00010
16 30000 02014
54 00031 00000
36 02072 10000
14 10000 01326
46 02021 02020
47 02000 02040
54 20000 00033
13 30000 013'25
54 01326 00033
11 '02001 01362
37 01362 01637
11 01557 01362
31 01326 00000
34 01671 00010
16 ;30000 02031
33 '02061 00044
75 20007 02035
24 02062 06031
71 30000 01325
54 20000 00012
31 30000 00000
11 30000 00031
11 000:30 10000

RW-149
SNI=2

(REV)

4 of 4
Revised 8/1/56

Pgo

OAS34
OAS35
OAS36
OAS37
OAS38
OAS39
QAS40
OAS41
OAS42
OAS43
OAS44
OAS45
OAS46
OAS47
.OAS48
2ASOO
2AS01
2AS02
2AS03
2ASQ4
2AS05
2AS06
2ASQ7
2AS08
2AS09
2AS10
2AS11
START

QJ
SP
ST
IJ
SP
5T
SF

1AS35
3ASll
00025
00023
3ASll
00025
00025
ZJ lAS42
LA AOOOO
TP BOOOO
SP 00023
AT 3A510
CC 00025
TP AOOOO
MJ 00000
01 26249
06 67009
-1 70881
03 08918
-5 01743
08 89789
-2 14598
01 57079
06 20000
10 00000
07 40000
01 57079

1AS37
00001
00025
1AS40
00000
00025
00023
lASOI
00027
00025
00021,
QOOOO
QOOOO
AOQOO
lASOl
11000 -03
01000 -03
25600 -02
81000 -02
04600 -02
87400 -02
80160 -01
63050
00000 8
00000 B
00000 B
63268

X NEG
PI

A)7
A/6
A/5

642·17
64220
64221
64222
64223
64224
64225
64226
64227
64230
64231
64232
64233
64234
64235
64236
64231
64240

AJ4

64241

A)3
A/2

64242
64243

M FINAL
E FINAL
PACK
EXTEND

OUT
42
40
38
36
34
32
30
28

All
A0

64244

50
1
60

31

33

PI OVER 2

,

10-401

64245
64246
64247
64250
64251
00000

,44 02i043 .0.2045

31 02074
36 00031
41 00027
31 02074
36 00031
74 00031
47 02052
54 20000
11 30000
31 00027
.35 02073
27 00031
11 20000
45 00000
05 12750
06 65103
73 5001'6
01 '76420
77 14476
06 26616
77 62210
00 3'1103
06 20000
10 00000
07 40000
,03 11037
45 00000

OO,O() 1
00031
02050
00000
00031
00027
020() 1

00933
00031
00033
10000
lQOOO
20000
02001
53762
05327
32330

76052
15552
51661
01542
15516
00000
00000
00000
55242
00000

RR-74
(REV)

'mI-l

PS. 1 of 4

Revised 6/15/56
THE RAMO-WOOLDRlOOE CORPORATION

Los Angeles 45, California

Floating Point

~ctangent

Routine

Specif1cations

Identification Tag:

TNI-l

Type:

Subroutine .

Assembly Routine Spec:

SUB

storage:

51 words

50131 05114
total program storage e

3 words WIQ?O;ra.ry storage pool used, addresses
00021b tllru 00031b

The constant pool is used.
~trance

and Exit:

RJ

OOK01

OOK02

Drum Assignment:

Address 63631b thru 63113b

Machine Time:

4.27 me ave rage, 5.8 ms maximum

·Mode ot Operation:

Floating pOint

Coded by:

M. Perry

July, 1955

Code Cbecked by:

R. Bigelow

July., 1955

Machine Checked by:

M. Perry

August, 1955

Approv~d

w.

August, 1955

by:

Bauer

10-402

RR-7t!
(REV)

TNI-1
Pg. 2 of 4
Revised 6/15/56

Description
When supplied with an argument X in SNAP fonn, this routine will evaluate
Arctan X (in radians) using a Rand Polynomial Approximation producing an
answer in SNAP fom.
Programming Instructions

1.

Place the double length extension of X in,the accumulator.
X must be in SNAP fonn.

2.

Return Jump to the subroutine. Assuming that the subroutine was assigned
to region OOKOO for assembly, use the instruction RJ OOKOl OOK02.

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 valus, defined as follows:

-rc/2 :S Arctan X:; rc/2
Error Analysis
The error in the result produced by the routine is less than

2:2~.

Mathematical Analysis
1.

If x2: 1, the identity Arctan X = (rc/2) - Arctan (l/x) is used.

2.

Rand Polynomial Number 13 is evaluated usi~ X (or

l/x)

as the ,argument.

Range of Variable
No alarm. cond1 tions exist. Any number which can be expressed in SNAP form can
be entered and the result will have the accuracy stated above. '
-.
~

t-

'-'

I

0

r-i

I

0
0

ar-i

t-

><
~

RR-74
(REV)
TNI-1

Pg. 3 of 4
Revised 6/15/56

D
0

D
D

OOTOO
OOTOI
00T02

00T03
60T04
00T05

oor06
OOT07

00T08
00T09
OOTID

OOT.l1
OOT12
OOT13
00T14
00T15
00T16
00117

00T18
00T19
00T20

OOT21
00122
00123
00124

OOT25
00T26
00T27
00T28

OOTOO 50137
01TOO 01024

ARCTN RTN 37

50174
01061
00000

ARCTN eNS 14
TO, BE AL 1ERD

00000

NORMAL EXIT

02100
03TOO
00 00000
MJ 00000
TP 00013
TP'091oo
sJ 01T05
TP 03TOI
TM Aoaeo
QT 03T02
SS QOOOO
SA 03T03

00025
01135
01T06
01T35
00000·
00023
00000

OOOOB
TM BOOOO 00024

SJ 01T12 01T15
SN 00015 00039
DV 00023 00023.
TP '03T04 00025
SP 03TQ5 00000
5S 00024 00000
sJ 01T20 01T18
TV Aoaoo 01-T 19
LA 00023 00000
TP BOOOO 00023
MP BOOOO aoaao
LA Aoaoo 00001
TP 8'0000 00024
sN 03106 00035
RP 20007 01.27
PM 03T07 00024
PM 00025 00023

TP BOOOO

AoooO

00T29

ZJ 01130 01T01

00T30
00T31
00T32
00133
OOT34
00T35
00T36

SF AoOOO 00024
TP
SP
SA
SA

AOOOO
00024
00014
00023

00023
00000
00035
00027

TP BOOOO AOODO
MJ 00000 01T01

TO at: ALtERO

63631
o~ooo

63676

ALARM ExiT

02045
63631

NORMAL f;NtRY

63633

63632
63634

63635
63636
63637
63640
63641
63642

NEG ARG

M
MINUS E

63643
63644

E ASS

1
1

OV~R

M

63645

28

OVE~ ~

PI

42/E ASS

63646
63647
63650
63651
63652
63653
63654

ARG OF POLY
ARG SQUARED
e)15

poLy
EvALUATioN

SCALE:

M FINAL

63655
63656
63657
63660
63661
63662
63663
63664
63665

63666
63667
63610
63671

E/12B FINAL
PACK

EXTEND

our

10-404

63612
63673
63674
63675

00 00000 00·000
00000 00000
00000 00000
00000 00000
00000 00000
45 00000 00000
11 00015 00031
11 02045 02043
46 02005 02006
11 02046 02043

00
00
00
00

12 20000
51 02047
34 10000
32 02050
12 30000
46

10000
00021
00·000

00010
00030

02014 02017

33 00017
13 00027
11 02051
31 02052
34 000:50
46 02024
16 20000
54 00027
11 30000
71 30000
54 20000
11 30000
33 02053
75 20007
24 02054
24 00031
11 30000
47 02036
74 20000
11 20000
31 00030
32 00016
32 00027
11 30000
45 00000,

00047
00027
00031
00'000

00000
02022
02023
00000
00027
10000
00001
00030
00043
02033

ooojO

00021
20000
02001
00030

00021
00000
00043

00033
20000

02001

RR-74
(REV)

TNI-l
Pg. 4 of 4

Revised 6/15/56

02TOO
02TOI
02T02
02T03
02T04
02T05
02T06
02T07
02T08
02i09
02TI0
02T11
02T12
02T13
sTART

POS CONDITN
NEG CONDITN

TP BOOOO AOOOO

TN BOOOO AQaOO

07177
00000
57079
00000
05/+05
18612
-5 59098
09 64200
~1 39085
01 99465
-3 33298
09 99999
00
20
01
00
04
02

71777
00000
63268
00052
80000
28800
86100
44100
33510
35990

B

B
B
-03
;~O2

-02
-Q2
...,;01
~Ol

56050 -01

33290 "01

MASK

128
27 PI OVER 2'
42
36 e/15
34 C/13
33 Cill
32 C/9
31 C.17
30 Cl5
29 C/3
28 ell

63676
63677
63100
63701
63702
63703
63704
63705
63706
63707

63710
63711
6371?
63713

11 30000 20000
13' 30000 20000
00 07-177 77777
20 000.00 00000
00 14441 76652
00 00000 00:052
0.0 20465 76350
DO 26305 45073
77 43277 43606
00 30535 75750
77 56144 71644

00 14610 OSi33
77 65253 17101
00 17777 71515

RW .. I02
(REV)

1mP-3

Pg. 1 ot 2
revised 9i-14-5'6
THE RAMO-WOOLDRIDGE CORPORATION
1A:>s Angeles 45, California
CHANGED HORDPOST-MORTEM Rt?UTINE (revised)

Spee1figat1ons

Identifioation· Tag:

MDP-3

Type:

Service Toutine (with subroutine entrance)

Special Storage:

'1)1e constant pool and temporary storage pool
are not used by this routine.
Address 40037b

Program Entrance:

40037b

Program Exit:

40020b

Alarm Exit:

The alarm exit is not used by this routine.

Machine Time:

(14.1

+ .5n) seconds where n=number of cards

punched.

.......
C\I

0

r-!

Coded by:

R. .f5each

00 tobel" 26,

Code Checked by:

R. Beach

October 26, 1955

Nechine Checked by:

R. Beach

October 26, 1955

Revised by:

C. Koos

Deoember 1, 1955

Approved by:

w.

Deoember 9, 195;

1955

'-'

I

0

,

r-!

F. Bauer

0
0
0"r-!

r-

><
0..

10-406

RW-I02
(REV)

MDP-3
Pgo 2 of 2
revised 9-l4~56

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 compares 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 45:40037
40020b. The changed words and zeros are then read into ES. ES is then
dumped on the line printer. (~: Until the line printer is in use,
this dump will be made onto cards by employing MDP-It:). ES and the 76000b
image are then restored from the 66000b imageo
If anyone word is, zero, it should be igEach card contains six. words
nored as it is not a changed word. A word which has been changed to zero
has been given the arbitrary tag 45 40037 40020b and will be punched as
such. Also, a yOrd that was changed to this tag will be identified in the
same manner. The programmer must therefore distinguish between these
two cases.
0

Qp~rating

Instructions

1.

When 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 subrQutine enter routine with 37 40020
40037b. Operation of routine is the same except that routine
exits to address y+l if y is the address of the RJ instruction
used to enter the routine.

3.

MOst service routines use all or parts ofES and their activation
will destroy the old 76000b image. Hence, if a changed word ,comparison is desired, the execution of MDP-3 mUst precede the use ofotber
post-mortem routines.
.

Alarm Conditions
There are no alarm conditions in this routine. However, if the routine
hangs up during punching, or if the machine is halted during punohing,
a start at 40040b will clear the punch, restore ES, and up-date the
76000b image.

RW-116
(REV)

NRT-o

Pg. 1 of 4
Revia.d 9-14.56

'!'HE RAl-10-WOOLDRmGE' CORPORATION
Loa .Angeles ,4$, California
Nth Root Routine
Specifications'

Identification Tag:

NRT-O

Type:

Subroutine

Assembly Routine Spec:

SUB 51316 03701

Storage:

.36 instructions, addresses
10FOO thru lOF35
1 constant' jn program, address

10F.36

37 words total program storage, addresses
10FOO ,thru 101)6,

4 words

temporary storage pool used,
00027b thru 0OO33b

addresses

b.1 this routine.

The constant pool' is used

10F02

Program Entrance:'

Addre~s

Program Exit: ,"

Address lOFOl

Al8l'J1l Ex;!t :

The alarm exit is used by this routine.

DrwIi AS6igmnent:

Address

66OS4b tbru 66130b

l'lSCh:1ne Time:

Aver~e

execution time

2(n-2) +

5 milliseconds

MOde of Operation:

Fixed point

Ooded by:

w.
w.

cOde

Ohecked bY': ,

lor n

'= 50
25, 1955

Frank

November

Frank

November 28,

Nach1ne Checked by:

W. Frank

November

Approved by:

w.

December

F. Bauer

10-408

1955
30~ 1955
1, 1955

mV-116
(REV)

NRT-o
Pg. 2 of 4
Revised. 9-14.56
Desoription
This subroutine extracts the nth root of ~ number M, scaled at 235, and

suoh that

n must be

Q..Tl

integer in the range

2,

n L 212

The routine must be entered with M_235 in A and n.2° in Q_

The result will

be left in AJ 'scaled a.t 235 , at the conclusion of the routine.

PrOgramming Instructions
1e

Place }'ie235 in ARe

(At) is ignored by this routine.

2. Plaoe n-2° in Q.

3.

Ente~

the subroutine with RJ OOrOl

OOF02, where OOFOO is the looation

of the first word of NRT-Q.

4-

The

eubroutineret~ns

oontrol to the oell following the RJ instruotion

with ( nfM) _2 35 in A•.

Alarm Conditions
11

The' subroutine enters the alarm routine ALR-l if n is negative or M is

negative for

n even.

In 61 ther oase I the word ualarm u is .printed on the

......,
~

fiexowr1ter, followed by the ootal address of the RJ instruoti9n used to

....-4

'-"

6

enter NRT-O •

....-4

I

o

o

~
t-

Exeou t10n Time

~

The time taken to find the nth root of a number is inversely proportional to
the 'magn1tu~e ot: the number and direotly ~roportional to the size of n.
avera.B9 estilriate, tor n --' 50, is approximately 3(n-2) + $ milliseconds.

An

RW-116
(REV)
NR'l'-O
P~. j

MathematioAl Method
An iterat:LvG prooedur@, employinB th@ Ntn"ton-RAphoon m@thod·~, in

'HUlet

to

Dolvo tho oquation

Tho iterAtion is t@rmiMt@d when

A leoendArY telt ia mAdo to inaurG

1M

I

L

(~1)n-l

'!'hill tali 11 nooerunAl'Y, Gv@n thou~h tM prooall 11 monotonio J tor, it i.
pODoibltt

thAt

trunoation ot the rowlt of multiplioation

And

div1110n

OAn

violAto thin proporty.

A. IpaoiAl

CAOO

In that want, x1_ 10 tUGn AI thG aolution.
1
1n M • 0, whorl tho Dolut:Lon il x • 0 tor all p.

ACQUrAOl

Tho Irror in tho %'Iwlt ot thil %lOU tin;

WAI

found. to 'bI 11.. thAn 10-10 J

that ii, tor an inputuSUmlnt, whioh il oorroot to )$ bitl, Onl OM Ixpeot

an anlWOr whioh

*Soa.rboroush.

m~

of L

Rov1.ld 9~4.'6

be

inaerrlot It mOlt in tbe right oatil dilit.

.

J.D. ,NwTtGrioal MAthlmatiaal4n!lY111, .Ioond Iclition, 'l'hI
John Hopkin. PrO.D, BAlttmOZ'I, Md., 19$0, p. 192.

10-410

RW-116
(REV. )
NRr-o
Pg. 1.,
0
0
0

10fOO
10fOl
10f02
10 F 03
10F04
10 F 05
10 F 0 6
lOF07
10Foe
10 F,O 9
1 OF 1 0
lOFll
10F12
10F13
10F14
lOF15
10F16
10Ft7
10F1S
lOF19
10F20
lOF21
10F22
1,0 F 23
10F24
10F25
10F26
10F27
lOF2S
10F29
10f30
lOF31
10F32
1'0 F 3 3
10F34
lOF35
10F36

"""'
...0
......
......

'-'

I

o......
I

o
o

0-

......

t-

><
p..

OOFOO
lOFOO
OCPOO
37 75701
MJ 00000
00F03
ZJ
T P AOOOO
T P 00000
o T 00016
Z J 00F09
TP OCPl1
OOFOO
S J
TM OCP11
TP 00F36
54 OCPI0
S J OOFOO
TU AOOOO
RS
00F17
RS
00F17
SP OCP12
RP 00000
MP BOOOO
TP BOOOO
T P OCP14
T J OCP13
MJ 00000
L A AOOOO
ov OCP13
S T OCP12
S J 00F27
ov OCP10
A T OCP12
MJ 00000
T P OCP11
S J 00F32
TN OCP12
MJ 00000
T P OCP12
MJ 00000
37 77777

01024
51316
00013
75702
0
OOFOl
oepll
OCPI0
AOOOO
OOF07
AOOOO
00F09
OCP14
OCP12
20017
00F13
OOF17
00015
00015
00035
00F19
OCP12
oeP13
AOOOO
00r23
00F30
00035
AOOOO
AOOOO
00F30
AOOOO
oeP12
00F16
AOOOO
00F34
AOOOO
OOFOl
AOOOO
OOFOl
77777

B

ALARM
EXIT
A R G ZERO
N EVEN

OR

00

ALARM
SET

X0

V Al UE

BRB
N NEGAT I VE

SET
XI TH

UP
TO

B
N-l

CONVFRGENCE
x I TH

B

P l US

1

2000
66064
15
66064
66065
66066
66067
66070
66071
66072
66073
66074
66075
66076
66077
66100
66101
66102
66103
66104
66105
66106
66107
66110
66111
66112
66113
66114
66115
66116
66117
66120
66121
66122
66123
66124
66125
66-126
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
46
73
35
45
11
46
13
45
11
4,5
37

00000
00000
00000
75701
00000
02003
20000
10000
00020
02011
00030
02000
00030
02044
00027
02000
20000
02021
02021
00031
00000
30000
30000
00033
00032
00000
20000
00032
00031
02033
00027
00031
00000
00030
02040
00031
00000
00031
000.00
77777

or 4

00000
00000
00000
75702
00000
02001
00030
00027
20000
02007
20000
02011
60033
00031
20017
02015
02021
00017
00017
00043
02023
00031
00032
20000
02027
02036
00043
20000
20000
02036
20000
00031
02020
20000
02042
20000
02001
20000
02001
77777

RW-91
(REV)

HDI-.3

Pg. 1 of 9
revised 9/ilt/56
THE RAMO;..WOOLDRIOOE CORPORATION
Loa Angeles la.5, California
Q111 Method Subroutine

Specifications
Identification Tag:
!ne~

SUbroutine

AaseJDbly storage Spec:

SUB

storage:

59 instructions, addresaea

49860 07414

OOM)() thru ()(H.M
lGK>O thru l.GMl.7

15

74

constants in px"ogram, ac:1iIressea'

OGCOO thru OOC14' "
'WOrds total program storage , atIdre••ee
(0)1)() tbru ooMlK>
1(M)() thrtt IGl-U7

00000 thru OOC14

10 'WOrds temporary storage pool used, ad4re....
00021b' (00l'00) thru ()()()4()b ( 00'.009 )

Drum b81gnment:

~88e8

Prosraa Entrances:

Addresses CXJM)2, (XM)3, u4

Proarem 'B:Id:':

Address OGMOl

:f.Bchine 'rime:

(10.'3 n + 1.9) lDB per point average, 'Where D
equals the' number of equationa in the qat.

Mode .of operation:

Fixed po:J.nt

Coded by:

632300 thru 6334Ib
00M:>lI.

J. Carlson
R.. Douthitt
M. Elmore
. R. Stunmers

Cole Checked by:

N. Elmore

. JUne 8, 1955

M!.ch1ne Checked b,.:

M.' E.l.more

J\1l7 7, 1955

AiP',prove4 by:

ll. Bauer

~ 22,' 1955

10-412

RW-91
(REV)

NUI-3

Pg.' 2 of 9
revised 9/J.4/56
~scription

The Gi;L1 Method Subroutine integrates a system of first order,dlrrereritlal

eqnatlons us1nga~tep-by-step process. Using the values of the variables at a
'point and the coding for computing the derivative of each of the dependent variables
at that po~t, 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,
tll.u. allQllillg the' subroutine to ,solve concurrently several different systems, in the
same program.
The· independent variable is inc,rementedw1thin the, subroutine ,i-eself.
Notation
The system of equations to be solved is

, ~' are int~diate values of the calcUlation (zeroinitiaJ.ly)
~x

'is the increment of 'the independent ,variable x

h,1s the billaryscaling' power of x (i.e. x·

'if

Is In the comlluter)

h-l is the binary scaling Power of ~x
m '~sthe binary s~aling power ,of y 1

1

f 1s the connnondifterence between the sca.lingpower of y 1

.

...-,
,

......

--.....•

power of

ely

axi

for each 1 •

'0'

o

t

arid the'- 8cal~ ,

dy
m - f 1s, the binary scaling pover of
i

iJ:X1

a

.0
0"

......

'r-

>< "
,c..

Pro~

arid Operating In.tructiona

,Assign the G111 J.1ethod Subroutine to sane arbitrary region, say OO}.l)().
In order to solve a given system, the following array ot varia.bles; derivatives,
intermediate values, and parameters should be usigneda ~g1on, aayOOt«>O. '

(REV)

NUl"",)
Pg o

.3

o~

9

revised 9/14/56
OGNOO

L

OGOOl

00 OON05 OON06

. n-~

00002

OON03

,6x·

scaled ~-l

OON04·

J~

.
h
scaled 2

dy

1

roN05

(bC

acaJ.ed ~ - f

001«>6

Y1

scaled ~

OON01

ql

ii::u.t la.lly zero

ooNOS

·q2
dX

OO~

Y2

scaled ~

OONlO

~

1n1tia.l.ly zero

The q1 must be set to

.

scaled ~ - f

~ero l.niti*i~ly

b:J the

.

progbs.rnmer~

dy

In addition, the coding tor canput.ing

.ax1

for oJ.l 1, (1 ;:; 1, 2, • .. .. , n) sb.oul4

This coding 'Will use the·values in region OONO, the three entrance. are
cx:ap.~ .. . OGMO),
and
ooz«>4.. The exit 1s OOml..
.
.

.Aa~tmd.ngthe

The first entrance,.OGMD2, ieused for setting up theG1ll Method SUbroutine onlJ
fQr ·the particular sya~em to be solved. It is entered by an RJ caxmand tollowed·
by a parameter, 'WOrd which specifies the location ot the var18.bles I and the location .
ot the coding tor calculating the derivatives:
RJ' OO!.r>l OOK>2
00 OONOO ODEOO

!1'he second entrance, OOm), is the entrance. 'tor producing a point of the solutiOD'.
It 1s entered by an RJ command: RJ OGl~l ·00K>3. Entering using this come:od ..
results in four passes through both .the Gill Method Subroutine and ~he coding
tor ccaputing the deriva.tives, and leaves in region OONOO the lle" value. ot the·
.....1abl.•• , the 4eriYat1ves at those values, 8Jl4 x ad:ftnced by ~X, r~ tor the
DOS·

.tep.

.

. .

The third eI!ft'ance, Qt"~ 1 1s the entrance from the cocl1ng tor calculat1il.g the
der1vatives and 1s used on ea.ch of the four passes necessary for computing one
point. Aa noted above, it 1s entered by an MaT command in the ODlOOO region:
.
10-414

RW-91
(REV)

NUI-3
Pgo 4 of 9

"

revised 9/14/56

Mathematical Analysis

Theoq. "A Process for the St~:p-by-Step Integration of Differential Equa.tions
in an Automatic Digital Conwuting Machine u by S. Gill, published in Cambr1~e
Philosophical Society Proceedings, Vol .. 47, Part I, January 1951, 'should be . .
consulted for a detailed. analysis .of the process on which the subroutine 18
based.
'
Suppose we know the point
system of equations

(x,Y1 )

Y ' • . • , Y ) on the curve defined
Z
n

by

the'

dyl

a:.x- :;: fl
dyZ

ax

::

(x, Y1 , Y2' • • • , Yn )

f2 (x, Yl , Y2' • • ,"

1

Yn )

The Gill Method is a. process by 'Which we can find the next point on the curve:
i.e. the value of '"I' Y2' • · ., J Yn for x :: X + h.

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

~ ~,f (x,y),and

We have the point '(X, Y) on the curve

X + h;

we want to find

y~' at

;: 'r (X + h, Y +
X + h, Y + k ' , -

i.e. we ,\1ant k ;; Sy such. t h a t : ] '
"

,

k).'

We derive k by malting four approximations and averaging them ina. particular Way.
First approxinlate the curve by a straight line through

(X, Y)

= f ~, y), and. find a first approximation to k:

,.....

w1ththe, slope

,

.

"~J

'

Xy
,I

r-f

--o

0-

ko :: h·f (X,Y)

I

r-f

Then we travel ,a traction m of the 'JaY along this, line· to thepo1nt (X + 'mh, Y + mko:
andf'1nd r(x ... mh, Y + mk ).

o•
o

o

0"-

r-f

t-

This gives us a new straight line through (X + mh, Y +
Y+ mko ) ,and we .find
'~
.

><:'
0..

mkol

with slop,e t (X+ 1Ih,

""~

It1 == lr't (X + mh, Y +mk )
o
,

:

,

We 'now use ko and ~ to find
y + [ n.. r ] ko +

#

8.

r~).
k2

:=

'

,

third point at 'Which t 18 calcUlated: ,(X + 00,

" ,
h f (X + nh, Y + [

n-r]

ko

+'r~)

'

\n.C.1I J

UVJ,..-""

Pg. 5 of 9
revised 9/1.,4/56
Similarly,

~

= h·:r (X + ph,

r

+

[P-B-t]

kQ + ski +tk2

The weighted average. of ko' ~, k2~ and k3 is the desired k.= 67:

= coko

6y .= y(X + h) -y (X)

+ clkl + c 2k2 + c k 3
3

lntere Co + c + c +c = 1.
2
1
3
For a system of equations,the same four steps given above are made for each
equation and.

.

6Yi

= cokio· +

cl~ll + c 2k i2 + ~3k13 where Co + c1 + 02 + c -1.
3

l'he above process is, for certain values of m, n, p,·.8, t, Co' Cl ' c 2 , an:lc , the
3
Rurige-Kutta process.· The Gill process wae derived, 'With application to machine use
in Ilind, by minimizing thenuniber of storage cella required. For the G111 Method
the above constanta are
m == 1/2 ,

= 1- 'fl/2,
=
-tr:J2

n = ~l2

,

B

=1

,

t=l+

p

"The Gill

r

proc~ss

and simplify the

Co ==

1/6

c1· -(1/3) (1 -

1

Yffi '.

02

.(1/3) (1 +

c

~

3

i.i72)
Yr72) .

lIe

:f\.t.rther systematizes the calculation so as to increase the accuracy
codi~.

The Subroutine A8 used in the Gill Me't?hod. f?ubrout1ne, the process i.

as

tollow:

1st pass:

= h-ti (x, Y10' Y20' •
r ll ::a(l/i)kio - ~o
~l = ~o·+ 3r1l ·"(1/2}k10

k10

Yu = Y1(')" + ·rU

Calculate t1 (~'Yll'Y21' • ••.,

'¥ni.

in progranmer's ow c()d1ng.·

..-

2nd pIL•• :

r 12

a

(1 - "'1/2) (kil

-.03 02013

, (; 3:i <1 3
632 ft l~

1 J \)DGCO ~JO(; )·:t·
1:, f){)C"(:';} 02 C' 1 7
1 (, 00f:~,HJ () ~~ C} 7

00000 OCOOG

TP :,)G0100 QDCUO

Rt,. CGfv!lG OG:.=Ol
RP 3GOC 3 oGf"q 1
TP
0(11 (!S
TII
C :,? j·i 1 :~
TV
C0I\;:'::

I'

~_-

63240

o'j 2 l t:'

21 02012 02074

1 ~_ O{i()GC OO{: 3'/

62020
11 C00BO 00021

'I S 300(}.'3
~3;~7

:Vi i·~'

63?:jO

L~)' l~

2G}~n9

C)G T '~,~" 3
;.
;-'iP OG lO ~I (lG i C ~"

2 G;-l2 0

MA (\ (:j 1 ~) (

Tr-~

S"I 1FT L
STOi~r~ ;;:
,", !(

~11

j

t.'32 :: ~~
6:'j I~i) '3

Q(~i (:;'

-:t,

0i.){).CO \!Ct;;~Cl
~~t)GO(:

OU()(H)

20\.':10{. f,)!)f)32
7 1 O'O(i 34 0<)0 '~2
72 {JOO.3:;, 00031
l.l.

&3255 ~4 20000 ~6046
(. :.:: :~ (.~i. 1 ~~ ;:;C:~;0 00033

2S i ";2)
2 (; f\·~ ~' ~!
;~ 0; i~i 2 :,~
2 Gr-i2 t~
2GV.?~

,~,,:;.,

?i:;: (1<.
;\DD Oll) 0

CGr~):'

L.I\ /\'
f~

-:.

~~ ,~',

:)

f~~'

/".

'.~ t"'",
~ _",~

RA 06M1S QC,C",)}
RAOGf431 OG( :);::

2Gt-1:~4

IJ OG10f'

2Gr·135

j"~J

2G~36

Tt) :JGCOO

\j

_'"\

.

63:~62

1:.J3~66

'II

£.' Gt·~31
2G~1~32
2 Gl'>13 3 '

f:,f',

35

3~ 0b033 20000
5A· 2tiijOD OOOh2
72 QiJe , 3f, ;)()(~ j~'
':':'4 20000 (jOCA,G
:3 5 U C C: 3 1 'Clj (. ~I .
2 i ~Y}t) 3 0 IJ 00 -j :3
!~) 3:;002 020~O
11 llOO 30 O(IQ()C
21 02 C 1:/ C 2 ~) .., I, .

6 :~ '/. 6 ~-'
._

2 Gf,,'i3 ~I

S32~7

63260
f, :?;: 6 i
T \'~. :~

' ": ';- () 1
l,/ ,,": ",

2 Gt439

.

!J (j ~. i)

t\~ J

(.I()

MJ

~ Gi"n ~)

~: (.i ':~'; 2· t)
2i.:;H'2 "(

~~

00 00\'.-00 GGOC{)
00 00000 J(,OOv
63230
63?31' '+5 OOOOe, OG,OOO
?")
O:J ... ;j L
lt5· ffUO(lO ~)2CSi
63235 . l'i'S {.}O'OOO l)Z{)i+,u
6323 1+ i. 1 0 ;.: (~() G i,0 ,; l~ I)
i)323:::
,~ fl' 0 :: ('tt 6 '0 :;:i SG
!.,,4 'C~: (,; ~t' 6 0 .i qa -,'
,) 323 '7
11 lOO('O 020(.(;

2'G~'<~ it

ZGr-1,l,e

~j'()

, ·::602-;

2;5

2Gt.; 13

2: G:-11 C

L'O V\Y)OC, ;.}(rl~·00
l1 i~~: (':~) {: () {; ~:.'~ =~)~)
():.1:~ t~ t) t.; ~,; (} <:~ \) (: (f
:, j{)

()l~

f)

D

9/14/56

Ai;u ""

p. ~)'\/ A~~ .: t.

t::

3;~' 6i'

03210
63271

- " " ) ,.,.,

t>::JI-:L

c{~r.n i)
r.
,.;..£

63?f3
63:~-;4

632'; S
63'1.'/6

·6;2'17

~u000

~0UOO

020;) 7 6~Ot5
OOO?·1 02026
(>U{}(h) OO(iOO
0 2 \} ·i~ 3 J ~~ oJ 1" ;:~
11 02 G25 }. 0 Gf~ ~i
')1. OOOOt· iJOO'jC
if~ (;O{)OO '.:5200 {

,21
-41
'.5
1 t.:..

.• ~ and the Yi ~e available.

1st .pass:
Advance xby -(1/2)h
k io == h.ri

(x, Y10' Y20' • •• , Yno )

r i1 =(1/2)k iO - %0

~1 == ~o + 3r i1 -(1/2)kiO
Yi1 == Yio + r i1 .
Calculate f'i (x'Yll'YZ1 '
~nd

., Y ) in progra.nuner's own coding.
nl

pass:
ki). == h fi (x,Yll ,Y 21 , • • ., Ynl )
r i2 == (1 -

;~2

=

Yi2

= "il

{liz) (ki1 - ~l)

~ + 3ri2 - (1 - Y1/2)ki
+ r i2

Calculate f'i (x,. Y12' Y22 ,'··· -, ~n2) in progra.mme rr f3 own codi~.

(REV)

NUI-4
Pg. 6 of 9

Revised 9/1~/56

3rd pass:
Advance x by (1/2)h

k12=

h et 1

(x')"12'Y22'

e

•• ,

1'n2)

r13 = (1 + Y1/2) (k12 - ~2)

~3 = ~2

+ 3r13 - (1 +

Y 1/2)k12

)"13 • 1"12 + r13
23 , • • ., Yn3)

Calculate t1 (x,':I13 ,':I

4th ~ss:

k13

= h t 1 (x')"13,Y'23' • • -:Yn3)
e

r i 4 - (1/6)(k13 ~ 2~3)
~4 = ~3 - 3r 14 - (1/2)k13

1'14 = 1'13 + r 14
s own coding.
,Calculate f'i (x,1'14,1'24' • • ., yn4) in programmer'
.

10-426

R~R~~~
IroI-4

Pg . . 7 of 9'
R,oV!;od"9!14/56
Machine Checking

two

The following system. o'f

equationsw.s solved using this routine:

dyl

-dx = cos. x
dy2

ax

= -sin x

The initial c.onditions,

at,

and

= 0,

x
y

2

were

=1

The interval, !:::.x, used was 2./360 radianS.
were accurate· to 8 decimal digits.

At

x

= 360-

the results

RW-143
(RI!\l )

NUI-4

Pg.
,

~

of 9

R~vised

\

9/14/56

D

GILOO·OI024

02000

D

GIMOO. ~1921

67221 00 00000' 00000
6722'1 : '56 ~'OO!O() ,0·2000
'6;72,22' 45 00000 00000
672'2'3 45 0000002061

GIMOO

MS

GIM01

MJ 00000 00000

GiM02

MJ 00000 GtL.49

61M03

t-U 0'0000 GILOS
RA GIL 71 OOQ16

. GlM04

GIM05·

00000' GILOO

67224
61225
67226

EJGIL69 GIL13

GtMO.

EJ GIL68 Glt.Ol

GIM07

M;J 000.00 GlL18

GIN08

67221
61230
61'231
67232
67233
612.,.
61:2·35

TP 00016 GIL71

to Gtl.a72 G1L20

SlM09

TP 0<)000 GIL8:.

GJMIO

GtMll

TP .08000'00024
00002
GIM13 AnNO 00024 00000

GI .. 12

tP G·IL.a8

61M14

·tP 00. . 2 Gt·LS?

"61236

1P 6tt.1S·,06031
6JN1' ADMP 00024 60031

G.tM1B

62'241
67242

fP 00002 00000

.

tv

OOOOO;GtL 10

67243

GJM19

RP 30;id3 GIL21

.612·44

stM20

TP 00000

61M21

RA GIL20 GIL61

61246

GtM22

GJL66 GIL2:;

67247

tu

tv·
tIP
fP
TP
6·tM21 .MPitO
81 M2flJ
TP

61M2:!
.1.1'424
at "2'
&IM26

6tl66
30"3
00000
00024

45 0000002010
21 02107 00020'
43 02105 02111
43 02104 02001
45 00000 02022
1.1 0002002107·
15 02110 02024
11 00000 02130
11 00000 08030
11- 02130 00002
14'·040'30 OGOOO .

6123? .1'1 00002 02'121
~6t240 11 0211~ 0(l037

GtM15

.G:IM17

00 00000 00000

0002~

61245

GtL44,
6t1&26'
00.0

61zSQ
67251

2"" '.

672S~

0.8002
00028 00.000
00002 00029
6tM29
.1P Gtb.88 00002
~I M3.0 MP.NO 00026 00·000

1404030: 14637
11 ()ooo2 00000
.16 00000 02106

1S ~660l C2c).~5
11 0000000621
21 0·202'•., ,o·2i03

15 02102 02031
16 ,02102 020;4'
7530003 Q2tJ:a2'

11 00000 oOC):!2

61253

11 00030 00042
14 14634 6OOo~

61255

11 00002 00035
11 02130 00002

612;4
'72S6
6l2'57
61260

14' 14032 OQOOO

.TP 00002 00'030

&1M32 tlPSU 00023 00(J2'9

612:61

tP 00802 0OO2i

6,1262

14 14027 10035
11 00002 ~ 00035

61,..:31

.INM

G~IH34

61263 . 14 ,0,40·3; 00000·
'7264 11 60002 OOO3~

AONO 00021 00·000
61M35
iP 00002 OG027'

atM36

TN OO()25 00002

6726,5

It"!? "AD OOO!O 00028
,61".
TP eOOO2 00030
81M:19
'1P CilL.SS Moal
61"'.0
iP 00029 00002

6~

6?2h1

6;'2'10
.612'1'1
61Z72
'1273

aiM.! DYAD 00031 00030
&t'M42

11 00002000,)0

,TP 00'002 000 2:8

10-428

13 000 31 .0000 2
14 .14036 04034
11 00002· oOo~'

11 0212$ OOC)'31 .
11 00035

000() 2

14 '200:37 040~
11 00002 000 M

RW-143
(REV)

NUI-4

Pg. 9 of 9
R~vi~eci 9/14/56

GIM43
GIM44

GIM45
GIM46
GIM47
GIM48
GIM49
GIM50

GINS1
GIMS2
GIM53
GIM54

GIM5S

Gtr.t64

~1t1&~
. Gi 6b

clM67

GtM68
GtM69

GIM10

GfM7i

GIM72
GIM73

GIM14
GIM15
GIM76

0

.....,

0
0

0-

.....

r-

><
c..

GIM77
GIM78

GtM79

GtMao
alMSl
GtM82

GIM83
GIM84

GIM8S
GIM86

Gttj61

ci as

stA~t

67304

67305

75 30003 02055
11 00032 00,000
21 0202i 02iO~·

21 020'54 02105
23 02106 00020
41 02030- 00006
11 02001 20:006
54 20000 00017
,20000 02064
000,00 20000

15
11
16
15

TV AOCOO GIL48

67"3,06

AOOOO GILlS
AT 00015 AOOOO

67307
67310
67311
67,)'12

20000 ;020Z2
,35 ,00017 20:000,:

61313

15 20000'02013

61'31'4
61.3.15

15 -20000 02.102
54 20000 OtlO71
.16; 20000 02021
16- :20000.02102.
21 ·02102 OO:O~ll

tu

GIM60
GIM63

.....

00016
00000
AOOOO
00015
GtL52
AOOOO

tv
LA

Glt,,161
Glf.¢62

'-'
I

GIL69

'tU AOCOO GIL10
AT 00015 AOOOO

GIMSa
GIMS9

C"j
~

ZJ GIL24
TP GtLOl
LA AOOOO
TU AOOOO
TP 00000

67274
67275
67276
61277
61300
'61301
67302
67303

GIL45
O~
"0
GtL67

GIM57

GIM.56

,......

RP 30003
TP 00026
RA G1L25
RA G: Li:A
RS G!L70

TU AOOOO GILll

AOOOO GIL66

AOOOO 0.0057

TV AOOOO GIL17
iV AOOOO GIL66
RA GI,",,66 00017
t2S01' .QOOOO

61163

67:1,60

44 02041 02043

11 02015 20000
~6

OoO!6 00010

11 00030 10000
I

RW-144

sm-4

(REV)

5 of 5
ReviSed 9-14-56
P~.

DOS36
00531
00538

. 00539
. OOS40

00S41
DOS42'

00543
DOS44
OOS45

00$46
00547

MP QOOOO QOOOO

61164

71 1 o·~;oo

SA 01506 00001

6n65

32 02015 CUCOl

TP.B,O~qo ,02502
PM' O1.S'Oll 01;500

69
68

·FINAL MANT33

ZJ'OOS~5

00501
SF AOOO:O 00554
LA AocoO 00027'
TP 80000 00000
RA02S0,O 00S54
SA 01S09 00021
CC AOQOO QOOOO

00S51

ItP 00000 00S01

TN AOOOO AOOOO
LA QOOOO 00001
.00 000.010 00000
DOS54.
DISOO
01 51484 19000 -04
01501 . -4 67376 55700 -03
07 96896 79,Z80 -02
01502
.01503. -6 45963 71106 -01
D1504
01 51079 6·3185
06 36619 .17225 -01
01$05
Dl$06
1777771 17777 8
01S07
00 00000 00034 8

stAAT

67172
, 67173."
67174'}li'"
6711:; ..
611.1·6'
6nn
61'2 CO
61201 .

67202

DOSS2

00 00000 00200 8

6n66 . 11 3000'0 0'0031
61167 24 02010 02067
61110 75' 20003 02052
671'71 24 02071 00031

. 67203

00553

OlS08
D1SOc)

3'4

RP 20003 00542

PM 01S02 02S02
t4P 80000 02S01
TP BOOUOAOOOO

00549
00550

DOS48

SQ\J'ARED

71 30000 00030
11 30000
47. .oios's'
74 20000
SIt 20000
11'30000
21 00027
32 02100

<:9
'(1
CS.
C3

33 tl

34 2·0VeR PI
MASK

28
'128

00 00000 00012 B

10-434

20000
02eOl:
02066

00033.
101000·
02066
00033

27 20000 100(1)
75 00&00' 02E).Ol .

67204
6720$

13 20000 20000
541000000001

6·7201

00:Q2366 57351
77 $4666 .3163:1

'720(, . . 00
31
36
35
34

lC~~O

"12:10
'61211

. 6121.2
672:1'3

OOOO()t

024.3~50

OOOOb

5-3.66J..

6S'52.tA20. 76491

14 441~6 6!):t02
6721.4 12 13714 06667
67215 . 17 77777 77177
61'216 00 00000 00034
67211' 0000000 0020G
61220 . 00 0.0000.000:72·
.5 00000 00000

1llI...flb.
(~)

FLlIIE (BB-86 RaY.
~:

8/56)

Service Routwe

I. Description:
This routine 18 a revised version or the original FLEXIE (RJl,-86). 1t18
designed to 1oa~, b7 means of a Ferranti Reader, a Plexeode tape prepared o~
a nexowriter in the cOIlventional fashion for translatiDg to bioctal. rLUlE
reads at the full speedot the Ferrenti, hesitating only on insert ad'Ciref>f,3Eu;l~ ,
check addresses, or when the temporaq storage is tull ot data. FLEXIE provitl~
a check 8.9-dress test and a cheek BUIll test on the data read in.
"
i:'
,I", "

n.

'lape PreparatiOll:

The tape should be prepared in the manner described in the original
PLKlIE write up. 1 rew reJl8rks are appropriate here hOllever. A check e.dcires8
should be given following the last information' on the tape and before the
'
?th level punch stop code. If' there is DO cheek address prior to the 7th level
punch, the 7th 18Ye1 punch will ill general be ignored.
'
For a check sum test of data on the tape, the follm.'ine four words
should be on the tape after the data to which the SUBl apP1.ies:

(1)
(2)

(3)
·(4)

insert address 75202,
high order 36 bits of ~heck sum,
low order 36 bits of check sum,
check address 752040
.'

,',"

must be the sum of all the data on the t.a.~ff)llowing the
preceding cheek SUIl. The check SUIIl vUl lOt be loaded '¥1to 75202 aDd.
'15203. These two words vill not be disturbed at all. Bote that a check
SUII test is performed whenever a check address ot 75204 l&ej)countered.
!bus 75204 should not be used tor any other check addreas.
The check

III.

SUlIl

Operati

pr

Instrp.cti 9D8:

Since the coding is in Reco n form, all operating dataw;p. be given
relative to the regions used in the code.

To load a tape, place it in the reader, turn the reader:9n ~ STAR! at
bbO. At the completion of the loading (if a 7th level punch -,"8 preseJ,lt
on the end ot the tape) a stop-re-enter bbO is given. It the:re i8 no ,7th
level punch present, let the tape pass through the reader, ~hen FORCE STOP,
KASTER CLEAR, START at '880 (eeO will be 000221n absQlute f9"'). FLEXU
can also be used as a subroutine to load data. To do, tbis,,' place a 7th level
punch after each section or the tape and perform the instrUction 37 1)bll bbO

whenever it is desired to load a section ,of

th~~pe.

~\\."L.~j' 0'1

t~\Sd.LxX

$'t

RR-86
(REV)

-2Three 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)

"til: FLEXIE has not been t~ansferred to HSS correctly.
START causes another transfer. If "t" occurs again, reload
FLEXIE onto l-m.

(2)

"c": a check address has failed. to check. START causes
FLEXIE to ignore error and proceed to read the rest of the tape.

(3)

"m"s

the check sum given on the tape does not agree with the
START causes FLEXIE to ignore the

Bum as computed by FLEXIE.

error.
IV.

Coding:

FLEXIErequires 166 (octal) words of storage on Y.D, i.e., relative
addresses bbO through bb165. 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 oralIo! FLEXIEwill be in the image region and consequently be destroyed when FLEXIE is used. The rest of the regions used in
the coding must. be assigned the following values:

co

00001

dd

00010

ee

00022

gg
hh
i1

00045
OCX)61

jj
kp

CYJO?4
00116

00052

YB

00147

ts
xx

00154
01624

Tbus one can place FLEXIE on any part of the drum by assigning a value to only
on~ of the relative addresses, i.e., bb.

re bb 74520
re eel
1'e ddlO

re
re
re
re
re
re'
re

ee22
gg45
1161
hh52
jj74
'kpl16'
wa147

re ts154
re xxl624
10-436

RR-86
(REV)

-3bbO

tp 00000 760CXJ
00000
rp 31777 ' bb4
tp 00001 76001
rp 30151 cc
tp bb15 cc
rp 31777 bb10
tp 76001 00001
tp 76000 00000
rj bb11 bb12
bb
me 0

.3
4
5

6
7

10
11
12

13

00
00

1-'.

15 ' co\"·
16

17
20

21
22
23

1
2

.3
4
5
6

24 ddO
25

1

26

2

27

.3
4

)0

a

rp
ej

20010 ddl0

Digit

kp6

ej
tj

kp5
kp16

test
Period test
Ignore or 7th level

a...-t
I-

50

12

8

VB

Clear check
SUlIl cells
Set up
Start read~r
One shot switch
Read to A

\oIs3
ws4
1i
kp3

7
10
11

7
10
11

I

rs v83
re w84
tp kp26
af 0
rj dd4

6~

Error, print t
Stop - reload routine

6

4
5

~

che ck
sum of
routine
'test check
Comput,~

3.3
34

4243'
44
45
46
47

0

sp 00000 0
rp 20151 c03
sa co
0
Sb bb13
44
ej hb14
dd
pr 0
jj2
,bb4
Jn5 0

32

1

I

0

5

)6 eeO

..0

0

0

er 0

37
40
41

Q)

0

31

35

--

Entrance - store 00000
Set up 00000
Store HSS
on MD
Load routine
into HSS
Restore
HSS from
I'ill ,image
Subroutine exit
Eervice routine exit - re-enter
F1exie check sum, 10 or-der
Hi order

tp bb52

1
2

2

.3

6

gg
hh

dd5

et 0

kp4

tp ii
ss kp26
at kp27
tp waI

a

tj

kp
a
30000

tv
rp
tp ts
tp w52
ej kp22

Stop reader
Set up DUmber of
words to transfer
Eat up transfer
Is 'de. te. destined
for HSS or 1-1>?
Set up. transfer
Transfer
data
Test period~ coda
is this ED?

17
se7
6.

ee15
aelO
eell

b
a
ee17

>C
0..

10-437

RR-86
(REV)

-451
52
53
54
55
56

1.3

57
60

21

14
15

16
17
20
22

ej
mj
at
mj
ra
mj

·kp2.3
0

kpl
0

vsl
0
tp ws
mj 0

61 .ggO
62
1
6.3
2
.3
6465
4

sp 'Ws2
tp a
sp ws
qa .kp17
mj 0

66 hhO
1
67
2
70

sp
at
tp
ej
ej
ej
mj

ws2
kp21
ws2
kp22
kp23
kp24

tp
ra
sp
sa.
sa
tp

ws

71

.3

?2

4
5

7.3
74

6

75 iiO
76
77
100
101
102
10.3
104
105
106
107

1
2
3
4
')

6
7
10
11
12

110 jjO
111
1
112
2
11.3 ' 3
114
4
')
115
116
6
117
?
120 10
121 11
122 12
12.3 1.3

124

14

la

0
ii

we3
ws4

ws
a
a
a
ii

tp
tp
ej kp25
mj 0
ef
tp
at
at
ej
pr

Modify IA

Return to read
Store IA
Return to read
Assemble period code
Store period code
Assemble
data digit
Return to :read

1
ws2
3
WB

dd5

1

Assemble peviod code
and store
Period cOde to A
Is this ED code?
Is thIs'IA code?
Is this CA code?
Return to read

ws2
a
ii
ee
jj
dd5

te
kp20
44

Store data word temporarily
Set up for next word
Add assembleCl
word to computed
cheek SllIn
Store computed
check
sum.
Is'HSS fill~d
with data7
Retwn to read

0
0

ws4
44
wa.3
a
ee
dd5

Stop reader
Compute number
of. words read in
Add to IA
Does this equal CA?
Error - print c
Stop - Ign,Qre error
Is sum check'test
specified1
No, return ·to read
Yes, computed check
sum to A
Correct computed

kp4
a7

kp26

al

ws1

a16

'Ws

jj7
jj.3
jj7

0

is this IA?
Return to MD
Modify IA to }tID image
Jump to set up and transfer

a
eOO
kp2
dd2
wsl
dd2

0
i1

0
tp ws
ej kp.30
mj 0
ep wa.3
sa wa4
ss ts

IDS

ee21

bb6

a'

jj12'
dd3

44
0
0

10-438

RR-86
(REV)

-5check sum
Subtract 10 - order part of
given sum and test difference
Error - print M
Stop - ignore error

02000
76000
xx
00000
00000
42
72
66
62
64
70
74
52
37
100
7

Constant for test
Constant
Max~um block size
Reader start code
Reader stop code
Flex codes - period

er 0
mj 0

q
dd5

000

0

Clear lOA
Return to regular read
Period code space

tsl
tsl
ts
0
0

15
16
17

132
133
134
135
136
137

kpO.

140

6
7
10
11

000

12

000
000

141
142

14.3
144

20
2l

000

1

000

2
.3
4

000

5

006

005
000
000
000
000

145

.13

146

14
15

00 0

147

000

150
151

16

000

17

152

20

153

21

154

22
23
24
25

000
000
1
00100 00000
20 00100 .00000
40 20100 00000
40 04100 00000
02000
tp ws
ts
tp ws
rp 30000 ee11
00 00000 75204

155
156
157
160
16b
162

26

27
3.0

:163 ws

0

164

1
2

165
.......

0
44
dd
jjl
dd

sa
ss
ej
pr
ms

125
126
127
130
131

7

6
5
4
3
2

1
0

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

Working Space Uses:

...0

--

.CO
I

o

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

w~O

~

'1

o
o

0'

.......

l'-

><
a...

~:

(1)

Three of the "Working spaces are stored on MD and transterred
to HSS with the rest of the program. Two of these are used
initially for a one-shot clear. lOA. Then they are used as
indicated above throughout the rest of the program.

(2)

The FLEXIE check sum cells, bb13 and.bb14, are blank since
the check sum depends on the value assigned to bb. The check

·

Rn~8{J

(REV)

samey be obtained trom the tape assembled by Reco II
as follows-: load the tape and ~ART at bbO; theeomputer
v1ll stop with a "t" ~rtIl as mentioned above; at this
point A-left contains the Lo-order part of the check sum
and A-right the Hi-order part.

10-440
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