Machine_Routines Machine Routines

Machine_Routines Machine_Routines

User Manual: Machine_Routines

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ORCHARD
OREGON

THE RHMO-WOOLDRIDGE CORPORHTION
8820

BELLANCA

AVENUE

LOS ANGELES 45 , CALIFORKIA

October 10, 1955

Recipients of the Ramo-Wooldridge Utility Routine Library:
The enclosed "Table of Contents 11 should repla.c e the one currently in the
notebook.
The enclosed description for FRI-O is a revision and should replace the
present FRI-O description.
All thi rteen pages of the section currently in the notebook entitled
IIGeneral Description of ERA-l103 Operation Using the Service Routine
Library" should be replaced by the enclosed section liThe Utility Routine
Library Handling Package".
The routines currently included as appendices to this section (that is,
FRI-I, URT-O, and URT-l) should be replaced by the enclosed routines FRI-l,
UH.'l'-3, and UR'l'-l respectively. The three new routines should be placed in
their proper alphabetical position \,ri th the r est of the utility routines
r ather than as appendices to the II Utility Routine Library Handling Package".
The following enclosures are new additions to your library notebook:
CPO-I
DIE-O
EXP-3
WG-2

lI;DP-I
NUI-3
SIN-3
SNI-I
SNI-2
STT-O
TST-O

Card Punch Output for Floating Point Numbers
Definite Integral Evaluation Routine
Floating Point Exponential Routine
Floating Point Natural Logarithm
Hioctal Memory Dump
Numerical Integrat ion by the Gill V~thod
Floating Point Sine-Cosine Routine
Arcsine- il rco s ine Routine
Flouting Point jl rC8 :Lne-/~rco sine Routine
Storage to Nagnetic 'l'ape Transfer
~~ gnetic Tape to Storage Transfer

Walter F. Bauer, Head
Digital Computing Center
Computer Systems Division

I-S171
a-7IBI

.,

Page 1 of 2
Revised 10-3-55
THE RAMO""WOOLDRIDGE CORPORATION
:u,s Angeles 45, California
UTILITY ROUTINE LIBRARY
Table of Contents

A General Description of the Utility Routine Library Organization
Programming and Operating Conventions
Programming Reminders
The Utility Routine Library Handling Package
Octal-Decimal Conversion Tabl es
Pool of Flexowriter Codes
Service Routine Starting Addresses
Arithmetic Routines
Checking and Executive Routines
ALR- l
CMP=O
MDP=O
MDP-l
r-IDP=2
MII""O
SAM=O
STT-O
TST=O
URT-l
URT=3

Entrance Address Alarm Routine
The Ramo-Wooldridge One~Pass Assembly Program (RAWOOP)
The Flexowri ter Memory Dump
The Bioctal Memory Dump
The Oc tal Card Dump
Memory Inspection and Insertion
Automatic Sampler
Storage to Magnetic Tape Transfer
Magnetic Tape to St orage TranSfer
Utility Routine Transfer - Magnetic Tape to Drum
Utility Routine Transfer"" Drum to Magnetic Tape

Differential and Integral Equation Routines
DIE=O
NUI=3

Definite Integral Evaluation Routine
Numerical Integration by the Gill Method

Input and Output Routines
CPO=l
FRI=O
FRI=l
HTO-O

Card Punch Output for Floating Point Numbers
The Ferranti Input Routine
Simplified Ferranti Input Routine for Bootstrap Procedure
Decimal Output Routine for Flexowriter and Punch

Page 2 of 2
Revised 10-3<»55
Interpolation and Curve Fitting Routines
Logarithmie 9 Exponential t and Rooting Routines
EXP=l

EXP-3
LOG-2

SQR=O

~x

Approximation e - Routine
Floating Point Exponential Routine
Floating Point Natural Logarithm Routine
Square Root Routine

Matrix Routines
Statistical and Clerical Routines
Trigonometric Routines
SIN=O
SIN=l
SIN=2
SIN=3
SNI=l
SNI-2
TNI=O
TNI=l

Central Exchange Sine-Cosine Routine
Polynomial Multiply Sine-Cosine Routine
Small Angle Sine=Cosine Routine
Floating Point Sine-Gosine Routine
Arcsine-Arcosine Routine
Floating Point Arcsine-Arcosine Routine
Arctangent Routine
Floating Point Arctangent Routine

•

Pg o 1 of 2
THE

RAMO-\~OOLDRIDGE CORPORJ\.TION
Los Angeles 45, California

The Utility Routine Library Handling

Packa~or

Paper Tape Input

Norma l Oper a tion
During normal operation, the Service Routine Library i s stored on the drum .
In order to use one of the routines , control is tran sfe rred to one of the
low-numb ered drum addresses in the 40000b channel (see the list of "Service
Routine Starting Addresses") .
Details concerning the operation of these routines and their loc a tions can be
found in the write- ups .
MT Start
If, at any time , the library stored on MD i 8 destroyed by a program, or
because the drum interlace has been changed , Gr for some other r eason,
the entire library may be loaded onto ~ from magnetic tape. Selecting
ET Start and starting effects loa ding of the ser vic8 r outine library
from 1 0 , and starting effects
loading of the service routine library and the assembly pr ogram and subroutines from HT zero. PAK is set to the CI..:F- O starting address upon
completion of the transfer .
Bootstr~

Sinc e the Ferranti reade r requires a programmed r ead in, it i s necessary
to "bootstrap " into the machi ne when no input routine is s tored in memory.
The proc edure devised to load an input progr am involves the use of one
binary card ( since 'this method requi r es the fewest number of instructions
to be loaded manually) . It i s nece ssary to key in manually only f our
words which perform the r ead in of one binary card (24 words) and transfer
control to the se 24 words .
Thi s binary c ard contains a simplifi ed Ferranti Input Routine (FRI-O) which
then begi ns to r ea d in the s ervic e routine library paper tape. This tape
contains at its beginning the regul ar FRI-O input routine and instructions
transf erring it to it s proper loc ati on on ED. \-,ihen FRI-O has been loaded
on I0, i = 1, 2 , • • • , n.
n

Suppose I is to be approximated by a quadratur e forl;'u la of the form
n
n
r " = h L. c.l f(x.l ) = x n - Xo ~ c. y.
l=O l l
i=O
n
where the c. a re the appropria te coefficients, e . g ., for the trapezoidal rule
l

Co = c n = 1/2 and c.l

=1

otherwise.

Let

n

Jl}

= lin

I*

= (xn

Li=O

c. y .•
l
l

Then
- x ) J*.
0

Noti ce that J-:f does not involve x , and th er efore Jlf can be computed without r egard
to the scaling of x . For this reason Jlf rather than P is obtained by the subroutine.
If n is even Simpson ' s rule is us ed throughout the interva l (x O' xn ) . If n is odd
Simpson ' s rule is u s ed over th e interval (x ' x _ ) and Newton 's three - eighths rule
O n 3
is used over the interval (x 3 ' x ),
nn
therefore
Jlf

= 1/3n (yo + 4Yl + 2Y2 + 4Y3 + 2Y4 + •

J" = 1/3n (yo + 4Yl + 2Y2 + •

+ Ly
~ n -,~

. + 4y n - 1 + ".In ) for n even , and

DIE-O
Pg o 4 of 8

Let a be s ome value in the clos ed interval (xO,x ) and l et f::l and y be vdues in
n
th e clos ed interva ls (xO ,xn- 3 ) and ( x n- 3 ' xn ) respective ly.
If

~J
L

is continuous throughout the interval (xO, xn ) and if n is even

= y4(a)

(x - xO)5 , where y4(a)
n

18~

·

= d4~

J x=a

dx4

If d4 y is conti nuous throughout th e invertal (x , x _ ) and exists t hroughout the
O n 3
dx/+
interva l (x

~ , x) and if n is odd
n-J n ·

For the deri vation of these quadratur e formulas and their error t er ms , see
Numerical Calculus, pp . 120 thru 124 .

~Qlne ls

Machine Time
The time r equired f or t his subr outine is (2 . 25 + •62n ) ms , n
time r equired is 2. 73 ms .

f:.

3.

\-Ihen n = 3 the

,

l"Ia chine Checking

Two prelimina ry test ca se s ,,fer e run :
1.

n

= 99 ,

y.

1

= _( 235 _1 )

for all i .

The r esult obtained was _235 (it should ha ve

been -( 235 -1).
2.

n = 98 , ·y.1 = (235 _1) for all i.

The correc t result, (235 _1), was obtained .

In addition, the fo llowing computations were performed:
1.

SIN-O wes us ed to produce a tabl e of sines and cosines for the ar guments
y = TrX/ 2 = (rr/2 )' n- 2- 4 , n = 0, 1 , 2 ,
b

2.

Let S

, 99 .

b

=Jo cos ydy = sin band C =Jo sin ydy = I-cos b .

compute SJ< and GJ< for b

= (rr/2 ).n. 24 ,

DIE-O was us ed to

n = 2 , 3 , L" • • • 9 ,
n = 10,15 , 20 , 25
n = 30 , 40 , 50 , • • • 90 , and
n = 99 ·

DIEPO -"
Pg o

For 8BCh b (or n ) [. = S':- - sin band [.
fo llowing tabl es re~ulted :
c

3.

6

n

[. '10

2

.101
. 338 "
. 197
.422
. 287
·490
. 365
. 540
.429
. 560
·477
. 200
. 101
-. 365
-.506
.- .198
. 286
. 516
. 286
- . 338

[. ' 10

s

J

4
5
6
7
8
9
10
15
20
25
30
40
50
60
70
80
90
99

= c'* -

1

5 of 8

+ co s b 1.-!Ore computed.

The

6

c

. 010
.050
. 039
.125
. 087
. 215
.151
.316
. 229
. 650
. 71.3
1.056
1.022
. 881
.415
. 039
. 087
. 516
.945
. 981

It \.Jas to be ex-pected that , in general, the errors would be greater for n odd. The
overall behavier of [. and [. is easil y seen to be consi s t ent with the fact that
s.

[.

s

and [.

c

For exampl e , [.

s

ydy

.

Sl.11c e

c

represent t he errors in integrating the cosine and the sine r e spectively.

= 30

is sma ll for n

1

= WTi~
+
o

1

because it is the error obtained in

JWr

+
1T

16

7T

2

J ~Tr =
If
2

In fact , [.

s

equal to [. s f or n = 2 (b = (1/ 16) 71 ).
for n = 30 (b = (15/16 )1T ) is eX8ctly
.

Evidentl y, a ll the errors [.

s

and c:

c

are l e ss than their corresponding maximum estima t es

as c omputed by the formulas Ebove under Error.....estl mrits " In particular , for n = 10 and 15
t he f ollmJing maximum error estima "i:,c s ]'Jere hand computed :

DIE-O Pg o 6 of 8

n

10

15

Max(. S
.508
.740

Max

6

(.0

.421

.903

10

DIE-O
Pg o ? of 8

o
o
o
o
o
o
o
o
o
o
DO P 0 0
OOPOl
00P02
DO PO 3
00P04
DO P 0 5
00P06
00P07
00800
00801
00802
00803
0080 4
0080 5
00806
00807
00808
00809
00810
00811
00812
0081 3
00814
00815
00816
00817
00818
00819
00820
00821
00822
00823
00824

OOCOO
OOTOO
01COO
OOPOO
00800
OONOO
o 1 COO
DOPOO
00800
OONOO
M8 00000
MJ 00000
T P
A 0 000
T P QOOOO
o v 01COO
Z J
OONOO
T V 00822
T P OOTOl
MP 01 COl
T P AOOOO
T P 00 C 0 3
T P 01C02
T P 00 CO 3
T P 00 TO 3
o V 01COO
00 TO 8
R8
T V 00T02
8 P
OOCOO
R P 30003
MA 00T05
T P AOOOO
L A AOOOO
T P AOOOO
I J
00 TO 8
8 P 00 T 0 9
8 A OOTOO
o V 00T04
MJ 00000
T P 00T04
MJ 00000
o 0 00000
R A 00811
8 P
00 TO 9

00013
00023 .
01078
01024
01032
01059
49864
49810
49818
49845
OOPOO
00000
OOTOl
00T02
00T03
00P06
00819
00T03
OOTOl
00T04
00T05
00T06
00T07
AOOOO
00T08
00 C 0 3

00811
00000
00812
00000
00T09
00036
OOTOO
00823
00036
00036
00T04
00000
A 000 0
00 POl
00820
01COO
00036

o

o

I
R

R

E

Y

C

T
DR U M
8 TOR AGE
DIRECTOR Y
NO ALRM EXIT
NORMAL EX I T
ENTRY
8TORE
NAND AOR8
OF Y 0
IS N EVEN
Y E 8 E X ITT 0
820
N-BAR
EQUAL8 N
8TORE 3N
8TORE 1
4

AND
1
NOEX
18 ONE
HALF N-BAR
MIN U 8 0 N E
PRE 8 TOR E V
CLEAR A
FORM
8 UM

8 TOR E
PARTIAL
8 UM8

8
INDEX NEG
YE8
8TORE
INTEGRAL TO
X N-BAR
8TORE
INTEGRAL
IN A
GOT 0 E X I T
OU MMY-8 EE P6
MOFY V BY 2
RE8TORE PAR-

..

4

\

..

DIE-O
Pg. 8 of 8

00S2S
00S26
oONOO
oONOl
00N02
00N03
00N04
oONOS
00N06
~ONO?

00N08
00N09
00Ni0
00Ni1
00N12
DON 1 3
DON 1 4
DONiS
00N16
DONi?
00N18
o 1 COO
olCOi
o 1 CO2
o 1 C0 3

S A
MJ
TV
TP
S T
ZJ
TP
LA
TP
TP
TP
TP
RA
TV
SP
RP
MA
o V
RA
MJ
00
00
a 0
a 0
o 0

OOTOO
00000
00N18
OOTOl
01COl
OOSOO
AOOOO
OOTOl
01COl
01C03
01C03
01COl
00T02
00T02
OOCOO
30004
00T06
OOTOl
00T04
00000
00000
00000
00000
00000
00000

00036
00 S 1 0
00S19
AOOOO
00T03
00N04
00T04
00003
00T06
OOTO?
00T08
00T09
00T03
00N14
00000
OONiS
00000
00T06
00T06
00 pal
OONOS
00002
00003
00004
00009

T I A L SUM
Ga T a S I
N I S a 0 0
I T T0
NS
I S
N- BAR
N 3
I S
YES C LEA
S TOR E
STORE

S
0
EXN-3

R T4
8 N
3
9
9
AND 3
S TOR E A 0 R S
o F YN-BAR
C LEA R A
FOR M
SUM
S TOR E I NTEN A
GR AL
G0 T 0 E X I T
DUM MY -S E'E N 0
CON S TAN T S 2
3
4
AND 9

EXP-3
Pgo 1 of

4

THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45 , California
Floating Point Exponential Routine
Specifications
Identifica tion Ta g :

EXP-3

'I'yp
. e .•

Subroutine

Assembly Routine Spec :

SUB 50230 04715

Storage :

32 ins tructiocG , adur ess es
OOEOO thru 00E31
01EOO thru O1E31
15 constants in program, addresses
02EOO thru 02E14
O3EOO thru 03E14
47 words
OOEOO
01EOO
02EOO
03EOO
2

total program storage , addresses
thru 00E31
thru O1E31
thru 02E14
thru 03E14

words temporary s torage pool used, addresses
00027b thru 00030b

The constant pool is used by this routin e

Program Entrance:

1I.ddr ess 00E02 (01E02 )

Program Exit:

1I.ddres s 00E01 (OlEOl)

1I.larm Exit:

Th e al arm exit i s us ed by this routine

Drum 1I.ssignment:

Addresses 63766b thru 64045b

l1achine Time:

4.3 ms average , 5.46 ms maximum

Mode of Operation:

Floating point

Coded by: .

H. Perry

July 27, 1955

Code Checked by:

R. Bi ge1m-J

July 27, 19'55

lv;achine Check.ed by:

E. Perry

August 8, 195 5

Approved by :

H. Bauer

1I.ugust 10, 1955

EXP=3
Pg o 2 of 4
\,

De scription
\llien supplied with an argument X in SNAP form this routine will compute the
exponential (eX) using a Rand Polynomial Approximation producing the answer
in SNAP form.
Progra~ning

Instructions

This routine can be inserted into a program by ClI,P-O by the USe of a "SUB"
card in the input deck.
1.

Pl ace the double length extension of X in the accumulator.
X nrust be in SNAP form.

2.

Return JumIL.. to the subrouti~. Assuming that the subro,utine was assigned
to r egion 001mO for assembly, use the instruction RJ OOKOI 00K02.

3.

At the time of exit frq~~he sUQfoutine, the double length extension of eX
in SNAP form will be in the accumulator.

Error Analysis
.
-26
x
For X~2, the errcr in ex lS
less than 2
,for X >2; the error in e is less
than 2- (26-E) where E is the binary power of X.
1v1a th eE1~: ti~~;L Analysis

= (2-l29)'2~og2e+129)

1.

eX

2.

Divide (X.log e + 129) into an integra l part Rand
2
O~ S> l
By the necessary limit.s tions on X, R~O,

3.

eX = (2R-129 )(2S)
=
2

oc

.

lS

8

fractional part S.

(2R-128)(~S )
eva luat ed using the Rand Polynomial Approximation number 20. (2
S

S

= 10SloglO

5.

Since

6.

S
R-128 is the cha r acteristic of the answer in floating nota tion, and 2 is
the mantissa.
2

Ran~f

O~S > l

,

1~2

>2

l/2~2S/2>1

Variable

7
An a l arm 'vJill r esult if X is gr ea t er than . 693 x 27. If X is less than -.693 x 2 ,
the answer wi ll be zero, but no al a r m wi ll occur. Essentially, the exponential of
any nUJnber can be fo und, provided tha t exponential can be expressed in SNAP form.

EXP=:3
Pg o :3 of 4

Alarm Conditions

An alarm print will occur if the variable falls outside the permissible range
stated above . The fl exowriter ,.;ill print "aiarm" and the address of the cell
in the main program containing the RJ instruction ' l,.Thich was used to enter
EXP- 3.
Pushing the start button after an alarm halt will transfer control to the exit
of EXP- 3.

EXP-3
Pgo 4 of 4
'II.

0
0
0
0

EO 0
E0 1
E02
EO 3
E0 4
E05
E06
E07
E08
E0 9
E1 0
E 11
E12
E1 3
E1 4
E1 5
E1 6
E1 7
E 18
E1 9
E2 0
E 21
E2 2
E23
E2 4
E2 5
E 26
E 27
E28
E30
E 31
2 E0 0
2 E0 1
2E02
2E03
2 EO 4
2E05
2E06
2E07
2E08
2E09
2E10
2E11
2E12
2E13
2E14

37
MJ
TP
TM
TJ
SP
QJ
QT
Q T
Q J
AT
CC
RS
SJ
LA
TV
LA
MP
LA
AT
SS
MP
TP
SP
RP
PM
MP
SP
TP
RA
MJ
20
77
o0
1 3
27
11
00
00
00
00
o2
o5
11
10

OOEOO
01EOO
02EOO
03EOO
75701
00000
AOOOO
AOOOO
03EOO
00013
01E01
03E01
03E02
01E10
03E01
00024
00024
01E17
AOOOO
80000
00023
80000
AOOOO
03E05
00024
AOOOO
80000
03E07
20007.
03E08
80000
80000
80000
AOOOO
00000
75426
70000
07777
40000
05243
00000
50404
00750
01235
10726
45263
02177
23242
15354
00000

50230
01024
50262
01056
75702
00000
QOOOO
AOOOO
01E07
00000
01EOO
00024
00023
01 E 1 2
00023
03E01
03E03
01E14
00008
01E16
00000
03E04
00010
00024
00035
03E06
00023
00035
01E26
00023
QOOOO
00028
QOOOO
QOOOO
01E01
00000
00000
77777
00000
54511
00201
65025
76227
60322
65710
67026
57751
73144
37452
00000

8

EXP R 0 U T N 32
32
REL 2 0 0 0
EX P CON S T 15
R E L 2000
15
A L ARM E X I T
NORMAL E X I T

ZER0
E-128
M
NEG

A L ARM

E-36
ANS 1
M F I XED
LOG E 8 A S E
E

F I NAL

2

- .128

A R G OF POL Y
A-7
POLY
EVALUATI o N
FIN A L
PAC KED
OUT
RAN G E
MAS K
MAS K
92
LOG E 8 A S E 2
129
LG 2 8 AS E 1 0
34
A-7
33
A-6
33
A-5
33
A-4
A-3
33
33
A- 2
33
A-1
33
A-O
M

8
8
8
8
8
8
8
8
8
8
8
8
8
8
8

•
FRI..,O
Pg o 1 of 7

Revised 10-3=55
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
The Ferranti Input Routine
SDecifications
Identification Tag:

FRI-O

Type:

Service routine (with a subroutine entrance
provided)

Storage:

91 instructions, addresses 40001b and
75160b thru 75174b
75177b thru 75256b
75260b thru 75314b
16 constants in p~ogram, addresses 75175b,
75176b, 75257b, 75333b, and 75315b thru
75330b
2

words temporary storage used in program,
addresses 75331b thru 75332b

109 words total program storage, addresses
40001b and 75160b thru 75333b
The constant and temporary storage pools are
not used by this routine

Service Entrance:

Address 40001b

Program Entranc e :

Address 75161b

Program Exit:

Address 75173b

Mode of Operation:

Fixed point

Coded by:

R. Beach

l-Tay 18, 1955

Code ChGcked by :

R. Summe rs

May 19, 1955

Machine Checked by:

R. Beach

August 4., 1955

Approved by:

1
1.Vo

August 29, 1955

Bauer

FRI ...Q
Pgo 2 of 7
Revised 10-3""55

Description
I.

Genera l

This routine is designed to r ead , by mean s of the Ferranti r eader, seven- level
bioctal t.hpe prepared as descri bed belm,; . The routine r eads in paper tape at
th e f ull speed of the Ferranti \']i th only short he sitation when a check or ins~rt
addres s is ehcountered .
If desired , the to pe may contain a chec lr sum to b e t ested for agr eement with the
c omputed sum of the dElta r ead-in . The routine will r ea d data into any ES or 1',D
cell a l though the reading of informa tion into c ertain drum c ells (as described
in detail below) will r esult in abnorrral oper ation .
The r outine stores the contents of FS on }flJ) at addresses 76000b through 77777b
and th en transfers its elf to ES . It sums itse lf (in ES ) and checks the sum
against the correct sum (stored on I".D ) .
The Ferranti r eeder is star t ed in the free runni ng mode and the routine proc e eds
to read tape and process the info rmatiOJ~ contained on the tape in the same manner
as do e s t he El1.J\ photoel ec tric reader (for exceptions , see II. 3 and 4).
Each word to be transferred to me:r.ory is sumrted a s it is read in from tepe e Hords
which are to be r ead into ES are first stored in the Ivm i mage of ES (7 6000b thru
77777b) •
During operation all words are r ead into ES from t he tape and a block transfe r to
MD is ma de when (1) E,S has b een filled with data (that is , \.[hen 92LI- words have
been read i n) ; (2 ) an insert address appea rs on the tape ; or (3 ) the "end of tape "
seven - l evel c ombina tion has been r ea d in ( s ee II . 4).
The reader is stopped before maki ng the transfer and is started a-gain after the
transfer ha s been compl eted in the first two cas es; in the la st ces e , the reader
i s s topped , ES is restored from the I't:D image and control is t r ansferred to the
exit .
The r eader is also halted ",hen a check addres s appea r s on the tape . If no check
sum t est ( s ee II . 3 ) is to be made af t.er a succes sful check addre ss t est thp,
reader is started iw~e di 0 t e ly ; if the check sum t est is specifi ed the reader is
started after the tes t is made and the sum det ermined to be correct .
The r outine doe s not prev0n t read in to addre sse s 40001b , 75160b thru 75333b , or
76000b thru 77777b . 11 t ape specifying loael ing into the s e c el ls will ordinarily
hot be r 8£ d in cocrectly .
II.

Requi rements for Tape Preparatiog
1.
2.

The first "lOrd on a tape must be an insert address .
Chec k addresse s should be us ed , a lthough FrrI - O will operate without them.
J\ check addre ss irrJr.edia t ely fol l oHing an i ns ert addr e ss must be the same

as the ins ert addre s s .
3.

For a check Stun tes t the f ollO\.Jing four words mus t appear on the ta pe a t.
the point wher e the sum is to be tested :

FRI=O
Pg o 3 of 7
Revised 10",,3=55

1)

Ins ert address 75 202b

2)

High order 36 bits of check surri

3)

J~w

4)

Check address 75 204b

order 36 bits of check sum

Operating Instructions (to be folloHed when the routine is used as a service routine)
1.

Set PAK to 40001b and start.

2.

Computation vJill halt with the 1'1S instruction 56 00000 40001 at the completion
of the read in.

Progranuning Instructions (to be followed when the routine is us ed as a subroutine)
1.

Enter the routine with the RJ instruction 37 75173 75161.

2.

Control is r eturned to the cell immedia tely following the RJ instruction as
soon as an "end of block" punch is r eached on the tape.

Alarm Conditions
1.

No "end of t ape" punch. This condition is indic ated by the tape running completely out of the Ferranti reade r. vihen such a condition occurs the operGtor
should
a.

Master clear

b.

Set PfU( to 0007 L~b and start

c.

\t,lben computation ha lts (when a s ervice entry vIa s us ed) with the 1'1S
instruction 56 00000 40001 t he machine will r e returned to its original
state and th e data r ead from the tape will be properly stored.
If a program entry was used control will be transferred to the proper
c el l in the main pro gram .

2.

FfU-O not transferred tg ES c or rectly. If AL11.- l prints "FRI·O 75165" and (I\ )
and (Q), the sum of the program transferred to ES has failed to check. Starting at this point transfers FRI - O to ES aga in .
A second failure indic a t e s that
b e r estored .

3.

F~I -O

is not on the drum correctly and should

Check address failur e . If ALR-l prints "ALAH IC" and (A) and ( Q) , a check
address ha s fail ed. In the al arm print (An ) is the address of the next cell
to be loaded and ( ~~ ) is the check address that wa s r ead in from paper tape.
Starting at t his time will cause the mach ine to ignor the failure and operation
1-fi l l continue normally.

4.

Check sum fa ilure . If flLR-l prj.nts "AU\l"\ 11<" and (A) and ( Q), the check sum on
the tape has fail ed to agree with the computed sum.
Starting a t this poi nt will cause th e routine to ignor the f ailure and to begin
+,... .,..""" r'l 'in t.h p. t.ane aJ~_a.-",·,-,-,
n,-"
.______________

==-=====-________

~

FRI=O
Pg o 4 of ?
Revised 10",,3=55

If at any time (ES) need be r estored from its image, starting at 40040b
w5ll transfer the image to ES and transfer control to the FRI-O exit.

5.

And !lend of tape!l (or !lend of blocl{lI) punch nrust be present on the tape
to halt read in. This consists of seventh l evel punches in t"JO consecUtive frames on the tape at the point ",here the read in is to be stopped.
This seventh l evel combination HC ts as a signal to FRI-O to restore (ES)
and stop the Ferranti r ea der. It is compatible with the EnA photoelectric
reader in that it is an illegal combination which halts the ERA reader.

~

FRI=O
Pg o 5 of

"

Revised lO-J 55
eo

75161
75325
40000
75160
117
133
136
144
40001
75160
75161
75162
75163
75164
75165
75166
75167
75170
75171
75172
75173
75174
75175
75176
75177
75200
7520 1
75 20 2
7520 3
75204
7520 5
75206
75 207
75210
75211
75 2 1 2
7521 3
7 521 4
75215
75 2 16
75 217
75220
75 2 2 1
75222
75 2 2 3
7 5 2 2 4
7 5225
75 226

00
00
00
00
00
00
00
00
45
1 6
1 1
1 1
75
1 1
1 6
75
1 1
75
1 1
1 1
45
56
00
73
31
75
32
34
1 1
4 3
3 7
45
2 3
23
1 1
1 7
76
31
52
31
52
51
43
4 3
43
51
43
45

00000
00000
00000
00000
00000
00000
00000
00000
00000
7530 2
00000
75173
31777
00001
75306
30135
75177
31777
76001
76000
00000
00000
00000
53553
00000
2013 5
00001
75176
75257
75175
75701
00000
0013 6
00137
00120
00006
00000
00140
00121
00133
001 22
0012 2
00123
00124
0012 5
00126
00126
00000

00000
00000
00000
00000
00000
00000
00000
00000
75160
75173
76000
00000
75165
76001
40040
00001
00001
75172
00001
00000
00000
40001
00042
76415
00000
00004
00000
00044
75756
00011
75703
75166
00136
00137
00061
00014
10000
00006
00140
00001
10000
00133
00061
00074
00031
20000
00074
00015

FR I 0
D I RE C TOR Y
CAR D S
CAR D S

SET ENTRANCE
SET E X I T
S TOR E E S
A ND LOA 0
FR I 0
I NT 0
ES
SET RESTORE
RESTORE
E S FRO M
I MAG E
EX I T

COMPUTE
AND

T EST

C LEA R SUM
STORAGE
SET U P
S TAR T READER
REA D T 0 Q
ASS E MB L E
D AT A
oBT AI N
S EVE NTH
LEV E L COD E
S T HIS E D
S TH I S I A
CA
S T HIS
S T H I S END
o F TAP E
RET T 0 REA D

FRI=O
Pgo 6 of 7

Revised 10-3=55

75227
75230
75231
75232
75233
75234
75235
75236
75237
75240
75 241
75 2 42
75243
75244
75 2 45
75 2 46
75247
75250
75251
75 252
75 253
75 25 4
7 5 2 5 5
75 256
7 5 257
75260
75 2 61
75262
75263
75264
75265
75266
75 26 7
7 5270
75271
75 272
75 273
75274
75 2 75
75276
75277
75300
75301
75302
75303
7530 4
75305

1 7
1 1
36
2 1
43
4 3
1 6
1 1
37
43
45
23
45
31
32
34
34
34
43
54
32
1 6
37
45
2 6
2 1
31
32
32
1 1
54
1 1
1 1
43
45
1 7
31
34
35
1 1
42
1 6
00
1 1
1 1
4 3
43

00005
00061
00120
20000
00127
00140
0003 2
00140
75701
00135
00000
20000
00000
0013 6
00137
00144
00145
00145
00144
20000
00145
00071
75701
00000
12144
00061
00136
00137
00140
20000
20000
20000
00061
00117
00000
0000 5
00061
00120
00131
0013 4
00127
20000
00000
00144
00133
00123
00124

00031
25016
20000
00134
00044
00042
75756
10000
75703
00046
00014
20000
00036
00044
00000
00000
00000
00044
00011
00044
00000
75756
75703
0 0011
23704
00130
00044
00000
00000
00137
00044
00136
25007
00074
00015
00074
00000
00017
00103
20000
00111
00104
01634 75174
20000
00113
00115

S TOP

READER

ADDRESS
T EST
TAG T 0 A L ARM
TAPE C A T 0 Q
S P E C I FIE 0
MOO C A
T EST C H E C K
SU M

SET U P A L ARM
P R I NT
TAG T 0 A L AR M
")

"-

1'1

MOO A 0 R S
ADO
ASSEMBLED
WORD T 0
COMPUTED
SUM
WI TH

OAT --A

S TOP READER
SET U P N M B R
o F W0 R 0 S
T 0 TRNSFR
DOE S OAT A G 0
I N ES
SET U P T NSF R
TRANSFER
OAT A TOM 0
8
T HIS A
OAT A W0 R 0
S T HIS
- A "1'
1

FRI-O
Pg o 7 of 7
Revised 10-3~55

45
21
45
2 1
45
1 6
45
1 1
11
00
00
00
00
00
00
00
00
75
00
00
00
00

75306
75307
75310
75311
75312
75313
75314
75315
75316
75317
75320
7 5 321
75322
75323
75324
75 325
75326
75327
75330
75331
75332
75333
-

"

"lL

l

\

)

r ,"

00000
20000
00000
00134
00000
00140
00000
00140
00140
00000
00000
00000
00000
00000
00000
00000
00000
30000
00000
00000
00000
00000

75170
00132
00102
75301
00013
00134
00013
02000
00144
00077
17700
10100
11100
10500
00300
02000
00001
00105
76000
00000
00000
7 5204

M0
RET
T 0
MOD
S TOR AGE
ADDRESS
MOD
INSERT
ADDRESS
INS E R T
ADDRESS

o0

K0 0
1
2
3
4
5
6
7
8
9

•

I

1 0
11
00 S 0 0
1
Ci(

lfY'

COD E

I A

FRI-l
Pg o 1 of :3
Revised 10-3-55
THE RAHO-HOOLDRIDGE CORPORATION
Los Angeles 45, California
Simplified Ferranti Input Routine for Bootstrap

Procedur~

Specifications
Identification Tag:

FRI-l

Type:

Service routine, but not available as part of
service routine library

Storage:

17 instructions, addresses OOOOOb thru 00020b
6

constants in program, addresses 00021b thru
00025b and 00027b

1

word of temporary storage in program, address
00026b. Two wordb of temporary storage not
in program, addresse0 00030b and 00040b.

The temporary and constant storage pools are not
used by this routine.
Entrance:

OOOOOb (automatic entrance from keyed in binary
card read in routine).

Coded by:

R. Beach

April 1, 1955

Code Checked by:

R. Summers

April 2, 1955

R. Beach

April 12, 1955

1;[. Bauer

August 23 , 1955

~~chine

Checked by:

Approved by:

FRI-l
Pgo 2 of 3

Re.,,'! sed 10-3-55

This routine is a simplification of FRI- O which can be conta ined on one
bina ry card . It is used, as part of the bootstrap proc edure, to r ead
FRI-O into ES . The routine r e8 ,d~l tape into ES recognizing only ins ert
address e s , data 1.-lOrds , and the "end of tape" seven - level combination.
Hhen it f inds the "end of tap e " combination it tran sf ers control to the
transfer instructions a t 00050b t hru 00053b. The t ran sfer instructions
stop the reader , clear cells 40001b thru 40040b , 70000b thru 75777b, and
60000b thru 67777b , transfer FRI-O to its proper loc a tion on IifJD and then
transfer control to FRI-O.
Oper ating Instructions
See the "Bootstrap Proc edure " in the "Utility Routine Libra ry Handling
Package" description .

FRI...1
Pgo :3 of 3
Revi sed lo-.3~55

1
2
3
4
5
6
7
1 0
11
1 2
1 3
1 4
1 5
1 6
1 7
2 0
2 1
2 2
2 3
2 4
2 5
26
2 7

45
1 7
11
21
7 6
31
5 2
31
5 2
5 1
4 3
4 3
51
4 3
45
16
4 5
00
00
00
00
00
00
00

00000
00006
00030
00002
00000
00030
00022
00026
00023
00023
00024
00025
00027
00027
00000
00030
00000
00000
00000
00000
00000
00000
00000
00000

00001
00001
00040
00021
10000
00006
00030
00001
1 000 0
00026
00002
00017
2 0 000
00050
00004
00002
00004
00001
00077
17700
1 0 100
11100
00000
00300

ENTRANCE
S TAR T READER
E N T E R OAT A
MOD A 0 R S
REA 0 T 0 Q
ASS E M8 L E
OAT A
oBT AI N
SEVENTH
LEV E L COD E
S T HIS E 0
S T HIS
I A
S THI S END
o F 8 L0 CK
RET T 0 REA 0
INSERT
ADDRESS
A 0 R S MOOFIER
OAT A MAS K
7 L V L MAS K
E 0 COO E
I A COO E
7TH L V L COO E
END COO E

/

LOG-2

Page 1 of 3

THE RAMO-HOOLDRIDGE CORPORil.TION
Los Angeles 45, California
Floating Point Natural Logarithm__Routine
Spec ific a tions
Identification Tag:

LOG-2

Type:

Subroutine

Assembly Routine Spec:

"
SUB
50190 03810

Storage :

28 instructions, addresses
OLNOO thru OLN27
lLNOO thru lLN27
10 constants in program,
2INOO thru 2LN09
3 LNOO thru 3 LN09
38 \.JQrds
OLNOO
lLNOO
2INOO
3LNOO

addre~ses

total program storage, address es
thru OLN27
thru lLN27
thru 2LN09
thru 3LN09

3 words t emporary storage pool us ed, addresses
00027b thru 00031b
The constant pool is us ed by this routine

Program Entrance:

Address OIN02 (lLN02)

Program Exit:

Address OllJOl (lLN01 )

Alarm Exit:

The alarm exit is used by this routine

Drum Assignment:

Addres s 63716b thru 63763b

Machine Time:

3 . 37 ms average, 4.12 ms maximum

Mode of Opera tion:

Floeting point

Coded by:

M. Perry

July 27, 1955

Code Checked by:

R. BigelO1J

July 27, 1955

I<1achine Ch ecked by:

1-1. Perry

August 8 , 1955

/,pproved by:

H. Bauer

August 10, 1955

,

LOG-2

Page 2 of 3

When supplied with an argument X in SnAP form this routine will compute the
natural logarithm of X using a Rand Polynomial Approximation, producing an
answer in SNAP form.
PrograIT~ing

Instructions

Th is routine can be inserted into a program by
in the input deck.

Cl~-O

by the USe of a "SUB " card

1. ·

Place the double l engjJ1 extension of X in the accumulator.
SNAP form.

X must be in

2.

Return Jump to the subroutine. Assuming the,t the routine \-,as assigned
to r egion OOKOO for assembly, use the instruction RJ OOKOI 00K02.

3.

At the time of exit from this routine, the double length extension of In
X in SNAP form will be in the accumulator.

Error Analysis
The error i n the result of this routine is less than 2-26.
Mathematical Analysis
1.

Let X ::: M·2

e

Then In X

(In 2) (log2X)
e
(In 2) log2(M.2 )
(In 2) e-l + log2(2M)

2.

Log (2M) is found by evaluating the Rand Polynomial Approximation Number 42,
2
with argument 2M.

3.

Since 1/2 ~ M< 1,

1 ~ 2M< 2 and log2 (2M) is between 0 and 1.

Range of Variable
The logarithm of any number x, (X:>O) may be evaluated by this routine provided
X can be expressed in SNAP form.
Alarm Conditions
An alarm print will occur if the variable falls outside the permissible range
stated above. The flexowrit er will print "alarm" and the address of the cell
in the main program containing the RJ instruction which was used to enter LOG- 2.
Pushing the start button after an alarm halt will transfer control to the exit
of LOG-2.

,.
roQ..2

Page 3 of 3

D
0
D
D
LNOO
LNOl
L N0 2
LN03
LN04
LN05
LN06
LN07
LN08
L N0 9
LN10
L N 11
LN12
L N1 3
L N1 4
LN15
LN16
L N1 7
L N1 8
L N1 9
L N2 0
L N2 1
L N2 2
L N2 3
L N2 4
L N2 5
L N2 6
L N 27
2LNOO
2L N Ol
2LN02
2 L NO 3
2LN04
2LN05
2LN06
2LN07
2LN08
2LN09

37
MJ
S J
TP
QT
RS
S T
S P
AT
SS
DV
MP
TP
S P
RP
PM
PM
MP
TP
ZJ
S F
LA
TP
S P
AT
CC
TP
MJ
00
20
o0
o0
1 5
o2
00
00
1 3
1 0

OLNOO
lLNOO
2LNOO
3LNOO
75701
00000
lLNOO
AOOOO
3LNOO
QOOOO
3LNOl
00023
3LN02
3LN03
QOOOO
QOOOO
BOOOO
3LN04
20003
3LN05
00024
BOOOO
BOOOO
lLN20
AOOOO
AOOOO
BOOOO
00025
3 L NO 9
00023
AOOOO
00000
07777
04000
13240
26501
71272
23066
75434
56125
05620
00000

50190
01024
50218
01052
75702
00000
1 L N0 3
QOOOO
00023
00023
00024
00001
QOOOO
00034
00023
QOOOO
00025
00035
lLN16
00025
00023
3LN08
AOOOO
lLNOl
00025
00027
00023
00027
QOOOO
QOOOO
AOOOO
1LNOl
77777
00000
47463
17147
26456
04015
22311
07310
5774 0
00000

B

L N ROUTIN 28
TO B E ALTERD
L N CON S T
1 0
TO B E ALTERD
A L ARM E X I T
NORMAL
EXI T
NORMAL
E N TRY
M
E-128
E-ONE

HAL F

AR G

OF

POL Y

AR G
C-7

SQUARED

POLY
EVALUATI
LN 2
S CAL E
M

B
B
B
B
B
B
B
B
B
B

oN

M

FIN A L

E-128 F I N A L
PAC K
EXTEND
OUT
MAS K
SQ R T 2
2 X RT 2
C-7
C-5
C-3
C-l
LN 2
64

35
32
3 0
2 8
34

MDP-1
Page 1 of 7
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
The Biocta1 Memory I?t.mm
Specifications
Identification Tag:

MDP-l

Type:

Service routine (with a program entry available)

Storage:

157 instructions, addresses 40005b,
74703b thrq 74754b
74760b thru 75141b
,17 constants in program, addresses
74755b thru 74757b
75142b thru 75157b
174 words . total program storage, addresses
74703b thru 75157b
10 words temporary storage pool used, addresses
00027b thru 0OO40b

..

,

The constant pool is used by this routine

I

Service Entrance:

Address 40005b

Program Entrance:

Address 74705b

Program Exit:

Address 74704b

Alarm Exit:

The alarm exit is used by this routine

Drum

Addresses 74703b thru 75157b

Assignmen~:

Machine Time:

21 seconds per 100 words maximum

Mode of Operation:

Fixed point

Coded by:

w.

Dixon

August 15, 1955

Cod$ Checked by:

c.

Koos

August 20, 1955

Machine Checked by:

W. Dixon

September 15, 1955
1

Approved by:
(

w.

Bauer

September 19, 1955

MDP=l
hp2~ 7

Desoription
This routine will dump 9nto bioctal tape the contents of any specified number
of oonsecutive storage pells. It feeds leader and trailer, inserts insert
and oheck add~esses ang oheck sums, and may place a double seven-level punoh
(required to stop FRI-O) at the end of each dump.
The tape produced can /be read back into the 1103 with the Ferranti reader .
(using FRI-O) or with the ERA photoelectric reader. However, when using the
photoelectric reader 9ne should note that the check sum will be read into
oells 75702b and 75703b and that the double seven-level combination will stop
the reader by causing a fault.
I

i

This routine stores (ES) in cells 76oo0b thru' 77777b while operating and at
its conclusion restores (ES), (A), (Q), and (Fl) to their original state.
Operating Instructions (to be followed when the routine is used as a service
routine)
1.

Set PAK to 4oo05b and start.

2.

Computation will halt with the MS instruction 56 00000 74730 and Q will
be cleared.
Manually enter the parameter word in Q. Place the address of the first
cell to be dumped in ~ and the address of the last cell to be dumped in
Qv·
The range of the dump may extend from ES addresses to drum addresses.
For example, if the word 00 00200 4oo50b is placed in Q, the routine
will dump cells 00200b through 01777b and 40000b through 40050b.
If an FRI-O stop code is to be punched on the tape following the dump
place a 01 in the operation portion of Q. If no stop code is to be
punched place an 00 in the operation portion of Q.

4.

Start.

5.

Computation will halt at the conclusion of the dump with the MS instruction
56 00000 74706.

6.

For another dump one need only push the start button and return to step 2
above.

Programming Instructions (to be followed when the routine is used as a subroutine)
1.

Enter the routine with the RJ instruction 37 74704 74705 B.

2.

Enter the parameter word. If the RJ instruction is in cell n the parameter
word (as described in operating instruction 3 above) must be placed in cell
n + 1.

3.

At the conclusion of the routine control will be transferred to the instruction
in cell n + 2.

,.

MDP=l
Page 3 of 7
Alarm Conditions
An alarm print will oocur if an unacceptable parameter word has been supplied
to the routine. Anyone of the following three oonditions will produce an
alarm print:

'\t>

Qv

02000b ~Qu <: 40000b
~ Q <::40000b
02000b ~
v
If the service entrance was used the Flexowriter will print IIKl)P-l 74705".
The operator ~y push the start button at this time and return to operating
instruction 2 for another dump.
If the program entrance was '4-sed the Flexowriter will print "MDP-1II and the
address of the cell in the main program containing the unaccept.able parameter
word. Pushing the start button at this time will transfer control to the
exit of MDP-l .
.
Manual Restore
If' the oper a tor wishes to stop a dump before its normal completion he may
1.

Force stop while the punch is operating.

2.

Set PAR to 4OO40b and start.

3.

Computation will halt with an MS instruction in cell 74704b (the MDP-l
exit) •

If the service entrance has been used the operator may push the start button
and return t o operHting instruction 2 for another dump.
If the program entrance has been used pushing the start button will cause a
normal exit from the routine.

MDP-l
Page 4 of 7

75701
1 5
27
40000
74703
74767
41
75112
164
75142
214
1 5
1 6
1 7

20
2 1

22
23
24
2 5

26
27
30
31
32
33
34
3 5

36
37
40
40005
74703
74704
74705
74706
74707
74710
74711
74712
74713
74714
74715
74716
74717
74720
74721
74722
74723
74724
74725
74726
74727

00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
52
77
00
00
00
00
00
00
00
00
00
00
00
00
45
37
00
45
11
37
23
56
11
54
11
11
11
11
45
37
11
53
31
15
11
45

00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00001
00000
00001
00000
52525
00000
07777
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
75701
00000
00000
74755
74720
10000
00000
20000
20000
20000
10000
00000
74705
00000
74720
00024
74705
74704
20000
00000
00000

00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00077
00000
00001

o O· 0

0 1

00110
25252
00000
00000
07777
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
74706
75702
00000
74721
74704
74712
10000
74761
00030
00044
00027
00031
76000
00000
o 0000
74712
10000
74704
00017
74726
10000
74760

AL RiD
CON S T
P 0 0 L
TEMP
POOL
C
40000 ENTR A
ES

PROG

M

ES

PROG

P

Z E R0
SIX
BIT
EXTR
ADVANCE
U
A D V A NeE
V
ADV
U AND
V
DECIMAL
72
A L T ERN A TOR
OP
CODE
MASR
N MAS K
NR
MA SK
FIRST
ADORES
LAST
ADDRESS
INSERT
ADDRS
CHECK
ADORES
FA
INDEX
LA
INDEX
NBR
OF
WORDS
WORD
INDEX
SUM
H I
SUM
LOW
TOE N T RAN C E
ALARM
XT
EX IT
PRO G E N T R
SE R V E NT R
S TOR E
A Q
T0
CLEAR
Q
ENTER
PARAM
S TOR E

AR.

AL
Q

F I
SET

FI

TO

MJ

TO
STORE
A Q
OP
MASK
SET
XT
TO
MJ
PAR A M
W0 R 0
T 0
Q

MDP-l
Page 5 of 7

74730
74731
74732
74733
74734
74735
74736
74737
74740
74741
74742
74743
74744
74745
74746
74747
74750
74751
7 4 7 52
74753
74754
74755
7 4 7 56
74757
74760
74761
74762
74763
74764
74765
74766
74767
74770
74771
74772
74773
74774
74775
74776
74777
75000
75001
75002
75003
75004
75005
75006
7 5007
75010
75011

75
11
11
75
1 1
37
1 1
45
37
45
37
45
1 1
53
75
1 1
31
32
11
1 1
45
56
07
45
21
1 6
51
47
1 6
45
00
75
1 1
75
63
63
1 6
55
1 6
1 1
42
1 1
42
45
42
45
1 1
42
42
1 1

31777
00001
74757
30172
74767
74754
74756
00000
74754
00000
74754
00000
00024
74755
31777
76001
o 0027
00030
00031
76000
00000
00000
22155
00000
74704
74766
00024
74765
75103
00000
00000
10012
00015
0024 0
00000
10000
10000
10000
10000
00030
00027
0002 7
00214
00000
00215
00000
00030
00215
00214
00027

7473 2
76001
40040
00041
00041
74746
75756
74703
74746
7 4 704
74744
74704
10000
74704
74750
00001
00044
00000
10000
00000
00000
7 4 706
65204
74742
00020
75101
20000
74764
75101
74730
00155
00043
00027
00045
00015
00015
00030
00025
00027
20000
74735
20000
00056
00072
00060
74735
20000
00074
74735
00031

ES

T0

I MAG E

40040
G T0 ES
T T0 ES
RESTORE
T 0 ALR
A L ARM X T
RESTORE
EX I T
MS R S T R
EX I T
K T0 Q
T0 EXI T
R
0
U
T
T
0
I
R
N
E
E
CON S T
TAG
MAN RES T R
INC R I M E X I T
T EST FOR P U
o F S TOP
COD E
NO PUN C H

SET
PRO
EX I
TO
TAG
TO
TO
TO
TO
TO
MAS
MS
R
E
S

CON S T
C LEA R
T E MP S TOR E
PUN C H
LEADER
P U 7 LEV E L
LAS T ADRESS
FIR S T A DRS
T 0 S TOR E
LA T 0 A
AG N S T F A
FA T0 A
A G N S T 4 0 000
DR U M o N L Y
A G N S T 2000
TO A L R R S T R
LA T0 A
AGNS T 2 0 0 0
A G N S T 4 000 0
FA T0 I A

MDP-l
Page 6 of 7

75012
75013
75014
75015
7 5016
75017
75020
75021
75 022
75023
75024
75025
75026
75027
75030
75031
75032
75033
75034
7 5035
75036
75037
75040
75041
7 5 042
75043
75044
75045
75046
75047
75050
75051
75052
75053
7 5054
75055
75056
75057
75060
75061
75062
75063
75064
75065
75066
75067
75070
75071
75072
75073

1 1
1 1
1 1
1 1
1 6
45
75
1 1
37
2 1
2 1
1 6
11
36
35
1 1
42
23
45
1 1
45
1 6
1 1
37
1 1
31
35
53
53
31
1 5
21
75
11
3 1
32
75
32
1 1
54
11
37
1 1
47
11
37
45
1 1
37
1 1

00027
00 21 6
00216
00214
00226
00000
30004
00027
00072
00033
00034
00227
00034
00033
00020
00220
00035
00035
00000
00221
00000
00230
00031
00176
00025
00036
000 17
20000
20000
o 003 3
20000
0003 3
30000
00000
00037
00040
20000
00275
20000
20000
20000
00171
00035
00100
00032
00204
00000
00222
00176
00020

00033
00032
00034
00027
00142
0007 5
00077
00031
00072
00217
00217
00106
20000
00036
0 0035
20000
00107
00035
00114
00036
00106
0010 6
10 000
00172
10000
00017
20000
00124
00130
00017
00125
00220
00126
00275
00044
00000
00132
00000
00040
00044
00037
00164
20000
00140
10000
00177
00143
10000
00172
00036

FA T0 F A
017'77 T 0
017'77 T 0
40000 T 0
SET J U M P

NDX
CA
L AX
FA
1

F AL A
T0

AC A
LAX

T0
F AX

INC R F A X AND
L A X B Y 76000
SET J U M P 2
SET WR D I N D X
SET N B R WR D S
824 T 0 A
A G S T N B R WD S
CLER N B R WD S
J U MP 2
NDX
SET WR D
TO J U MP 2
SET J U M P 2
I A T0 Q
TO P U I A
MAS K T 0 Q
SET N U M B R o F
REPEATS
FOR SUM
AND TRNSFR
F A I N DE X T 0
T P INS TRCT
INC R F A I N D X
DAT A T 0
ES
SUM R 0 UT I N E
S TAR T S
HER E
AND
END S HER E
TO P U D A T A
Z J o N N U MB E R
o F ,W ORDS
CA T 0 Q
TO P U C A
J U MP 1
SUM
I A T0 Q
P
U
SUM I A
TO
SET W R D I N D X

· ....
MDP-l
Page? of ?

75074
75075
75076
75077
75100
75101
75102
75103
75104
75105
7510 6
75107
75110
75111
75112
75113
7 5114
75115
75116
75117
75120
75121
75122
75123
75124
75125
75126
75127
75130
75131
75132
75133
75134
75135
75136
75137
7 5 140
75141
75142
75143
75144
75145
75146
75147
75150
75151
75152
75153
75154
75155
75156
75157

1 1
11
37
1 1
37
75
63
75
63
75
63
45
1 6
45
1 5
1 1
21
37
41
45
1 1
37
1 1
37
45
21
11
37
23
37
45
1 1
55
63
41
55
63
45
00
00
00
00
00
00
00
00
00
00
00
00
00
00

00037
00040
00171
00223
00204
00022
00000
00002
10000
00240
00000
00000
00231
00000
00230
00000
00165
00213
00036
00000
00020
00 21 3
00020
00213
00000
10000
00224
00213
00041
00213
00000
00225
10000
00000
00041
10000
10000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
0027 5
00000

00275
00276
00164
10000
00177
00155
00015
00157
00015
00161
00015
74740
00142
00072
00165
10000
00017
00205
00165
00000
00041
00206
00041
00206
00000
00020
0004 1
00206
00041
00206
00000
00041
00006
10000
00206
00006
10000
00000
40000
02000
01777
76000
01470
01467
75202
75203
00002
00004
00162
00111
00114
00143

SUM T 0
ES
TP P U SUM
SUM C A T 0 Q
TO P U SUM C A
PUN C H
LEA D E R
PUN C H F R I 0
STOP COD E
PUN C H
LEADER
TO RESTORE
RESTORE
J U MP 1
WRD T 0 Q
P
U
I C R INS T
TO PUN C H
D
WRD
I N DX
A
T
SET I N D X
P
U
TO PUN C H
SET I N D X
TO PUN C H
r
A
INC R C A
P
SET I N D X
U
TO PUN C H
SET I N D X
C
TO PUN C H
A
SET

I NDX
P
U
N
C
H

R
0
U
T
I
N
E

40000
200 0
17778
76000
SUM
I A
SUM C A
28
48
DUM Y ADDRESS
DUM Y ADDRE SS
DUMY ADDRESS
DUMY ADDRESS

NUI-3
Pg. 1 of 8
THE RANO':"vJOOLDRIDGE CORPORATION
Los Angeles 1~5, California
Gill Method Subroutine
Specifications
Identification Tag:

NUI-3

Type:

Subroutine

Assembly Storage Spec:

SUB 49880 07414

Storage:

59 instructions, addresses
OGMOO thru OGM40
lGMOO thru lGMl 7
15 constants in program, addresses
OGCOO thru OGc14
74 words
OGMOO
lGMOO
OGCOO

total program storage, addresses
thru OGM1~0
thru lGMl 7
thru OGc14

10 vrords temporary storage pool used, addresses
00027b (OGTOO) thru 00040b (OGT09)
Drum Assignment:

Addresses 63230b thru 63354b

Program Entrances:

Addresses OGM02, OGM03, and OG!·104

Program Exit:

Address OGMOI

Machine Time:

(10.3 n + 1. 9 ) ms per point average) ",here n
equals the number of equations in the system

Mode of Operation:

Fixed point

Coded by:

J.
R.
M.
R.

Code Checked by:

M. Elmore

June 8, 1955

Machine Checked by:

M. Elmore

July 7, 1955

Approved by:

1,1. Bauer

July 22, 1955

Carlson
Douthitt
Elmore
Stunmers

NUl"'3
Pg. 2 of 8

Description
The Gill Method Subroutine integrates a system of first order, differential
equations using a ,s tep-by-step process. Using the values of the variables at a
point and, the coding for computing the derivative of each of the dependent variables
at that point, the Gill Method Subroutine produces the coordinates for the next
point of the solution each time it is entered.
A special entrance sets up the subroutine for a particular system of equations,
t hus allovnng the subroutine to solve concurrently several different systems in the
same program.
The independent variable is incremented within the subroutine itself.
Notation
The system of equations to be solved is

,y), (i

==

~
~

==

n

1,2, . . . ,n).

are intermediate values of the calculation (zero initially )

x is the increment of the independent variable x
h is the binary scaling power of x (i.e. x·2h is in the computer)
h-l is the binary scaling power cif

~x

m. is the binary scaling power of y.
~

~

f is the cornmon difference between the scaling power of Yi end the scaling
dy.
~
pO\-1'er of dx
for each i.
dy.
m - f is the binary scaling power of
i
L ==

73 +

f

~

ax

- h

Programming and Operating Instructions
Assign the Gill Method Subroutine to some arbitrary region, say OOMOO.
In order to solve a given system, the following array of variables, derivatives,
intermediate values, and parameters should be assigned a region, say OONOO.

NUI-3
Pg o :3 of 8
ooNOO

L

ooNOl

00 OGN05 OGN06

ooN02

n-l

ooN03

LlX

h
scaled 2 - l

ooN04

..

scaled 2h

OGN05

a.x-

scaled

~

OGN06

Y'1

scaled

~

OGN07

ql

initially zero

v

dYl

dY2

- f

OGN08

ax

scaled m - f
2

OGN09

Y2

scaled m
2

OGNlO

q2

initially zero

dy .
In addition, the coding for computing ,ax~

for all i, (i = 1, 2, • . • , n) shotud

be assigned a region, say ODEOO. This coding ivill use the values in region OGNOO
dyi
to compute all ~~ as specified by the equations in the system and should place the
results in the appropriate places in region ooNOO. It should then exit to the Gill
Method Subroutine With an HJ 00000 001'-104 (see belmv).
Assuming the Gill Hethod Subroutine is in region OGHOO, the three entrances are
OGM02, oot103, and ooM04. The exit is OGMOl.
The first entrance, OGM02, is used for setting up the Gill Hethod Subroutine only
for the particular system to be solved. It is entered by an RJ command followed
by a parameter word "'hich specifies the location of the variables, and the location
of the coding for calculating the derivatives:
RJ OGHOl OGM02
00 OGNOO ODEOO
second entrance, ooM03, is the entrance for producing a point of the solution.
It is entered by an RJ command: RJ ooMOl OGM03. Entering using this conunand
results in foUr passes through both the Gill Method Subroutine and the coding
for computing the derivatives, and leaves in region OGNOO the nei" values of the
variables, the derivatives at those values, and x advanced by ~x, ready for the
next step.
~le

The third entrance, OGM04, is the entrance from the coding for calculatinG the
derivatives and is used on each of the four passes necessary for computing one
pOint. As noted above, it is entered by an MJ command in the ODEOO region:
MJ 00000 ooM04

NUI-3
Pg. 4 of S

~hthematic al

Analysis

Theory. "A Process for the St~p-by-Step Integration of Differential Equations
in an Automatic Digital Computing Machine" by S. Gill, published in Cambridge
Philosophical Society Proceedings, Vol. In, Part I, January 1951, should be
consulted for a detailed analySis of the process on which the subroutine is
based.
Suppose ,,,e lcnow the point (X, Y , Y2' • . • , Y ) on the curve defined by the
l
n
system of equations
dYl
dx

dY2
"i - (1/3) <;1'1 ov er one step f rom all rounding off errors
is (':-There f is the quantity mentioned i n t h e section on notation)
1/6 l· 7/ 3 {2- 2f

.

-I-

(l/ 1 6 ) h

2

L. (O~i)
ay:
J

J

2}] 1 / 2
X

u, u == the va lue of
one unit in the
last digit of y.

Machine CheckinG
A driver routine solved tlva systems of equations bot h separately and conctU"rently,
us ing the Gill Hethod Subroutine . The tvlO systems solved are given belmT to
indic ate accuracy o,nd to serve as eX8.JJrples .

NUI-3
Pg. 7 of 8
1.

E(lUC1.·~ion::;

dYl
=

CL'(

Y2
equivalent to the second order

dY 2

==

dx

a2y

-Y1

e~lationf

+ Y = O.

-2-

ax

I nitial ConditionB

Solut i on
Y = sin x
l
Accuracy
In a spot check of the results , the greatest absolute error observed i -l aS
6
1. 5 x 10- • (For x = 3.1415925696, Y = . 0000015!~25. HOi-leVer, sin x =
l .
. 000000084 ).
2.

Equations
dYl
= Y
dx
2
dY2
= Y
dx
3
dY

3

Equivalent to the third order equ ation

Y + 4x2
3
x

dx

==

,6.x

= .1

= L~x 2

Initia l Conditions
At x

=

.1, Y == . 000025, Y
l
2

=

. 001, Y
3

=

.03

Sol ut ion
y=x
1

LI·

-3

3

- x+

bo

x

1

6000

! .ccuracy
In a spot check of the results, the greate st relative error observed was
6
3 · ~· x 10- .
(For x - . 1999999975, Yl = .OOO~.21j.99858 . Hm-rever, the solution
is a ctually . OOO~. 2500002) .

NUI-3
Pg. 8 of 8

D
0
0
0
0
,0
0

2Gt100
2G M01
2GM02
2 G Ivl 03
2 G M04
2GM0 5
2 G ~I 0 6·
2GM07
2GM08
,H 1.1 09
2 G ~"' 1 0
2 G 1111
2 G M1 2
2GM13
2GM14
2GM15
2 G M1 6
2GM17
2 G ~I 1 8
2GM19
2GM20
2GM2 1
2GM22
2 G ~I 2 3
2GM24
2 G /1 2 5
2GM 2 6 .
2GM 2 7
2GM 2 8
2 G 12 9
2GM30
2GM3 1
2GM32
2CM3 3
2GM34
2 G ~I 3 5
2GM36
2GM3 7
2 G'/,I 30
2GM39
2GM40
3 G ~I 0 0
3GMOl
3 G 1.102
3GM03
3 G M04
3 G M05
3 G ~I 0 6
3GM07
3GM08
3G h,1 09
3 G 1,110
3 G Ivl l l
3GM 1 2
3 G ~I l 3
3 G 1,11 4
3 G 1,11 5
3GM16
3G M17
1 G COO
1 G COl
1 G CO2
1 G C 03
lGC04lGC05lGC 06
lG C0 7l GCOO 1 GC0 9
lGC10l GCl l 1 Gel 2
l GC13 lG C14 -

FS
MJ
MJ
MJ
TP
QJ
QJ
TP
RA
.R P
TP
TU
TV
TP
RP
TP
MP
LA
TP
MP
MA
LA
TP
AT
AT
LA
MA
LA
AT
RA
RP
TP
RA
RA
IJ
MJ
T LJ
TP
R II
MJ
QJ
S P
TU
TP
TV
TU
TV
RA
RP
TU
RA
AT
TU
TU
LQ
TV
RA
RA
MJ

G IvI
1GM
2 G IvI
3 G 1,\
oGC
1 GC
oGT

OGT0 9
OGM06
OGM38
Q
OGM10
300 o· 3

1 G MOO
O G M36
Q
o G M40
OG M0 7
OG T09
OGCOl
OG Ml l
OGT0 5
OGM15
OGM31
OGT08
o G M1. 6
O GTOO
OGTOO

2000
2051
63230
6330:).
20 73
63323
. 27
63230
63231
63232

TO SE T UP
E NT E R
R E - ENTER
WHAT
PAS S
S'ff 0 R E C T R
UP PAS S
S TO R E
P AS S 'C 0 N S
RES ET
ADDRESSES
RES E T N- l

632~3

63234
63235
6323fi
63237

OGMi5
OGM31
OG T0 8

OG C02
OGM14

OGCOO
OGM21

OGM10

63240
63241
63242
63243
63244
6. 3245
63246
63247
6325 0
63251
63252
63253
63254
632 55
63256
63257
63260
63261
63262
63263
63264
63265
63266
63;:l 6 7
63270
63271
632 7 2
632 73
6:';2 7 4

Q

6.-3275

30003
A
A
OGT05
OGT06
A
A
A
OG T Q4
A

OG T07
A

OG T (l2

o G TO 1

30002

oGT0 1

CALC . K
S HI F T L
S T OR E K
AK
A K RQ

OGT03
OGT03
o GT 0 2
38
o G TO 4

S TO R E
2R
3R

A

A
34
OGT03
38
OGT02
OGT04
OGM32

R

3R C K
ADD O L D Q
EQUALS Q
NEW Y
S T OR E
y AND Q
ADVANCE
ADD RES S E S
CY C L E N

o G CO l

o G M0 7
OGMOl
OGMOl
A

OGM07
o Q0 1 5
:1.GM02
· OGTOO
OG T OO . OGM35
OG T OO lGM05
OGM17
OC T OO
15
10 O' 03 lGM09
OG T OO OGMll
OGM13
15
15 A
A
OG M1 6
A
OG M38
21
A
Q
OG M38
OGM38
15
OGM01
16
OGMOl
GC
3
3

5

8
8
1

o1

05
02
02
0 2
.1
0 1
01
1
o3
05

1 024
1065
49080
4992 1
1003
49939
23

92093
92893
92893
7 07 1 0
70710
70710
6 6606
33333

1
2 1 00 1 -0 1
2 1 88 1-0 1
2108 1-0 01
67012
6 78 1 2
67012
66667-0 1
3 3333 -0 1
1

3 4
34
3 4
3 4
3 4
34
3 4
34
3 4
34
34
34

A1
08 1
o C1
A2
o B2
oC2
A3
oB3
OC3
A4
084
o C4

S CAL E
S CA L E
S CAL E

34
34
34
34
34
34
34
34
34
34
34
34

63276
63277
63300
6330 1
63302
63303
6 3304
63305
63306
6330 7
633 10
633 11
63312
63313
63314
633 15
63316
63317
6332 0
6 3 .32 1
63322
6 33 2 3
63324
63325
63326
6332 7
63330
6333 1
03332
63333
63334
'63335
63336
63337
63:34 0
63341

00 00000 00000
00 00000 000' 00
60 00000 00000
00 00000 00000
00 00000 00 OD 0
00 00000 00000
00 00000 00000
57 00000 00000
4 5 00000 00000
45 00000 02051
45 00000 02044
11 00040 10000
4 4 02006 02050
4 4 02046 02007
11 10000 00040
21 02012 020 7 4
75 30003 0 20 13
11 00000 00034
1 5 00000 020 17
1 6 00000 02 ·037
11 00000 00037
75 30003 02020
11 00000 00027
71 000 0 0 00027
54 20000 00000
11 20000 0003<1
71 00034 00032
72 00035 00031
54 2aOOO 00046
11 20000 0003. 3
35 ;~ 0 0 00 200. 00
35 )0033 20000
54 20000 00042
72 00036 00032
54 20000 00046
35 00031 00031
21 00030 00033
75 30002 02040
11 00030 00000
21 020 17 02074
21 0203 7 020 75
41 00037 0201 6
4 5 00000 00000
15 020· 7 3 02012
11 0202:; 1 0000
21 00000 ' 00000
4 5 00000 02007
4 4 02001 02007
31 02001 00017
1 5 20000 02053
11 00 ,000 0002 7
16 00027 02043
1 5 00027 02056
1 6 00000 02021
2 1 0002 7 00017
75 10003 02062
15 00027 . 02013
21 02015 00017
35 00017 20000
1 5 200 00 02020
1 5 . 20000 0 .2 0 4 6
55 200 0 0 00025
1 6 10000 02046
2 1 020 4 6 00017
2 1 0200 1 00020
45 00000 02001
00 02073 00000
00 000 0 3 00000
00 00000 0000 3
10 00000 00000
5 7 77777 77 7 77
6 7 77777 7 7777
0 4 53730 3 14 60
73 24047 46317
73 2404 7 46317
33 2 4 047 46320
4 4 53730 3 14 5 7
4 4 5 373 0 3 14 57
02 52 5 25 25253
52525 2 5 25~
7 2
6 7 77777 77777

SIN-3
Pg o 1 of

4

THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Floating Point Sine-Cosine Routine
Specifications
Identification Tag:

clIN-3

Type:

Subroutine

Assembly Routine Spec:

sun 50075 05915

Storage:

44 instructions, addresses
OOSOO thru 00s43
OISOO thru 01s43
15 constants in program, addresses
02S00 thru 02Sl4
03S00 thtu 03Sl4
59 i-lOrds
OOSOO
OISOO
02S00
03S00

total program storage, addreuses
thru 00s43
thru 01s43
thru 02Sl4
thru 03S14

2 words temporary storage pool used, addresses
00027b thru 00030b
The constant pool is used by this routine
Program Entrances:

OOT02 (01T02) for sine, OOT04 · (01T04) for cosine

Program Exit:

OOTOI (OlTOl)

Drum Assignment:

Addresses 63533b thru 63625b

Machine Time:

3. 9

Mode of Operation:

Floating point

Coded by:

M. Perry

July 27, 1955

Code Checked by:

R. Bigelow

July 27, 1955

Machine Checked by:

M. Perry

August 8, 1955

Approved by:

W. Bauer

August 10, 1955

rns

average, 4.8

ms

maximum

SIN~3

Pg o 2 of

4

Description
When supplied with an argument X itiSNAP form, this routine will evaluate Sine X
or Cosine X (depending on which of the two entrances is used) using a Rand Poly~
nomial Approximation, producing the answer in SNAP form.
Pr0gramming Instructions
Thif? routine can be inserted into a program by CMP-O by the use of a "SUB" card
in the input deck.
1.

P~ace

the double length

e~~ension

of X in the accumulator.

X must be in radians and must be in SNAP form.
2.

Return jump to the subroutine. Assuming that the subroutine 'Ym.s assigned
to region OOKOO for assembly, use either the instruction RJ OOKOl 00K02
for the sine~ or the instruction RJ OOKOl OOK04 for the cosine.

3.

At the time of exit from the subroutine, the double length extension of
sine X (or cosine X) 'in SNAP form will be in the accumulator.

Error Analysis
The error in the result of this routine is less than 2-26 j however/ . the significance of the sine (or cosine) cannot exceed the significance of the fractional
part of X.
Mathematical Method
1.

Let y = (2/ n)X, then sine X
cosine X

= sin(n/2)(Y)
= sine

(n/2)(Y + 1)

2.

Divide y (or y + +) into an integral part R, and a fractional part S.

3.

R defines the quadrant into which X falls.

Let R' be the two low order
positions of R, since in binary notation, any other positions merely define
a number of complete revolutions.

4. R' is a number one less than the number of the quadrant into which X falls.
5.

S defines the displacement (in a position direction) within the quadrant
indicated by R' •

6.

Therefore, if R' = 00
R' - 01
R' = 10
R' = 11

7.

Sine (or cosine) X

8.

Sin(n/2)X is approximated by the Rand Polynomial Approximation Number 16,
using argument z.

z= S
first quadrant
Let Z = (l-S) second quadrant
Let Z = (-S) third quadrant
Let z = (l-S) fourth quadrant
Let

= sin(n/2)Z.

SIN~3

Pg o

3 of 4

Range of Variable
No alarm condition is recognized by this routine. However, as X approaches + 227
the number of significant digits in Sine X (or Cosine X) approaches zero, and
X merely defines a number of revolutions and does not significantly designate
an angle.

SIN-3
Pg. 4 of

0
0
0
0

800
S Ol
802
S03
804
S05
S06
S07
808
. 809
810
81 J
S12
8 13
814
S 15
S1 6
S17
S1 8
S 1'9
S2 0
821
82?
S2 3
824
S2 5
826
82 "(
828
829
S3 0
831
S3 2
833
834
835
S36
83 '7
838
839
840
84 1
842
843
2800
2801
2802
2 S0 3
2 S 04
2805
2S06
2807
2808
2809
2810
281 1
281 ;;
2813
2814

MJ
TP
MJ
TP
TP
QT
QT
QJ
CC
RA
LQ
RS
T 111
TJ
TP
LQ
AT
MP
TP
LA
AT
QT
r P
QJ
TP
QJ
SP
ST
MP
TP
8 P
RP
PM
MP
TP
ZJ
8 F
TP
8 P
8 A
8 A
TP
MJ
20
00
77
63
54
24
17
11
13
o0
7 .7
00
76
00
00

00800
0 1 800
02800
03800

50075
01024
50119
01068

00000
00013
00000
03800
AOOOO
03S01
03S02
01 SO 9
00024
OOO? :3
000?3
000?4
AOOOO
03S03
00013
000?4
03S0"4
03805
BOOOO
AOOOO
01S42
03806
03807
01825
03808
01S27
03S00
00023
00023
BOOOO
03809
20004
03810
80000
BOOOO
01837
AOOOO
AOOOO
00024
03814
00023
BOOOO
00000
00000
0 7777
70000
3 ·0000
20000
2 7 630
77777
30000
30000
02366
66333
50638
5524<:!
62207
00000

01 842
01805
01S42
QOOOO
00023
00024
01Sll
03S02
03S02
00008
03S00
ADOOO
01S16
00023
2 0 0 '09
01S20
00023
A 0000
00
QOOOO
00023
01S42
01826
01842
01 S29
00000
00023
00023
00024
00035
01334
00024
00023
AOOOO
01 SO l
00024
000.23
00000
00035
00027
110000
01S01
00000
77777
00000
00000
04107
15562
77777
20000
20000
5735}_
1 4 7 ::. 5
12,55
07 644
73244
00076

8 1 N R OUT N 44
TO A E ALTERD
8 I N CON 8 T 15
TO A E ALTERD
A L ARM E X I T
NORMA L E X I T
8 I N EN T RY
COS

E N TRY

M
[-1 28
N EG
M
E
E ABS

M

I N

35

QDRNTS

Z

1 MI NU8 Z
A R G OF POL Y
A R G SQUARED
33
C-9

//r/

POL Y
EVALUATI
8 CAL E

B
B
B

B
B
B
8
8
S
B

8
B
B

B
B

oN

M

E-12 8 F I N A L
PAC I( E 0
EXTEND
OU T
1 o I~ 128
MA 8 K
tv! A S I<
27
ADD R E 8 S MO D
2 PI
35
MAS I(
N TO A
PO S
NTO A
NEG
38
C-9
C-7
35
C-5
33
C- 3
31
2 9
C-l
62

63533
2000
6360 7
2054
63533
63534
63535
63536
63537
63540
63541
6 '3542
63543
6 354 rogram stora~e, addresses
OASOO (lASOO) thru OA S48 (lAS48)
2ASOO (3ASOO) thru 2ASll (3ASll)
3 words temporary storage pool u:!;ed, addresses
00027b thru 00031b
.
The constant pool is used by this routine

Program Entrances:

OAS02 for arcsine, OASO) for arcosine

Program Exit:

OASOl

Alarm Exit:

The alarm exit is used by this routine

Drum Assignment:

Address 04155b thru 64251b

Hachine Time:

7.17 ms average, 8.74 ms maximum

Hode of Operation:

F10nting point

Coded by:

1-1. Perry

August 25, 1955

Code Checked by:

R. Bigelow

August 28, 1955

M. Perry

September 7, 1955

H. Bauer

September 12, 1955

¥~chine

Checked by:

Approved by:

SI"1-2

Page 2 of 5
Description
When supplied with an argument X in SNAP form, this routine will compute the
arcsine or the arcosine of X (depending on which of two entrances was used)
using a Rand Polynomial Approximation producing the answer in SNAP form.
Programming Instructions
This routine can be inserted into a program by CMP-O by the use of a "SUB"
card in the input deck.
1.

Place the argument X in the accumulator.

2.

Return Jump to the subroutine. Assuming that the subroutine was assigned
to region OOKOO for assembly, use the instruction RJ OOKOI OOK02 for arcsine,
or RJ OOKOI 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.

Error

X must be in SNAP form.

Analys~
.

The error in the result produced by this subroutine is less than 2

-~
I ••

Mathematical Analysis
1.

The Rand Polynomial Number 39 is evaluated us:J.ng the absolute value of X
as the argument. Designate the result as p(X).

2.

The square root of 1 minus the absolute value of X is found using the square
root subroutine within SNAP. Designate this results as R(X).

3.

If X is positive, let Y = P(X)R(X)
If X is negative; let Y

4.

Arcsine

= X = (~/2)-Y

Arcosine X
5.

=~-P(X)R(X)

=Y

This procedure places arcsine X in the first or fourth quadrant, and
arcosine X in the first or second quadrant.

Range of Variable
An alarm will occur if the argument is outside the range -1 X 1. Any
within this range will give results with the above stated accuracy.

~rgument

Alarm Conditions
An alarm print will occur if the argument is outside the permissible . rang~. The
flexowriter will print "alarm" and the address of the cell in the main program
containing the RJ instruction which was used to enter SNI-2.

Special Note

SNI-2
Page 3 of 5

The SNAP floa ting point routine must be in electrostatic storage before this
subroutine can be used, since the square root subroutine is used within this
routine.

SNI-2
Page 4 of 5

D
D
D
D
D
D
D
D
D
AS 0 0
A S Ol
AS 0 2
AS 0 3
AS 0 4
AS 0 5
AS 0 6
AS 0 7
A S 08
A S 09
AS 1 0
AS 1 1
AS 1 2
AS 1 3
AS 1 4
AS 1 5
AS 1 6
AS 1 7
AS 1 8
AS 1 9
AS 2 0
AS 2 1
AS 2 2
AS 2 3
AS 2 4
AS 2 5
AS 2 6
AS 2 7
AS 2 8
AS 2 9
AS 3 0
AS 3 1
AS 3 2

37
MJ
TP
TP
TP
TM
TP
TP
ST
TJ
QT
SP
TV
LA
ST
SF
SJ
LA
TN
LA
TP
RJ
TP
SP
SS
TV
SN
RP
PM
MP
LA
SP
TP

OOKOO
OOTOO
OOCOO
SRTOO
OOPOO
OASOO
lASOO
2ASOO
3ASOO
75701

00906
00722
00754
00927
00877
50349
01024
50398
01073
75702

3 A S 11
0001 3
AOOOO
AOOOO
80000
80000
3 A SO 8
00K14
00K03
QOOOO
80000
00025
3 A SO 9
QOOOO
1 AS 1 7
AOOOO
80000
00T04
1 A SOl
OOCOO
00P02
00T04
S RT 2 6
80000
3 A S 00
20007
3 A SOl
80000
AOOOO
80000
80000

00013
00023
00024
A 000 0
00013
00025
QOOOO
1 AS 1 3
00025
00008
1 AS 1 3
00000
QOOOO
00T04
1 AS 0 0
00027
00T03
00027
OOCOO
S R TOO
00 COO
00000
00008
lAS31
00036
1 A S 29
00025
00T03
00010
00000
00025

8

S NAP CON S
S NAP T E MP
S NAP E X I T
S NAP S Q R a a T
S NAP CON S
ARC S N R T N 4 9
49
RE L 2 0 a 0
ARC S N eNS 11
REL 2 0 a 0
11
A L AR M E X I T
NORMAL E X I T
ARC SIN E N T R
ARC COS E N T R
X
X A8 S
C LEA R 1 3
C LEA R 2 5
X-50
X E QUA L Z ERa
M
M F I XED
X-l

i-X
SF

33

FLOATED
N Ta 4

FIN D ROO T
REPAIR S NAP

A-7
E V AL
POL Y

RAN D
2 9
56
66
31

SNI-2

Page 5 of

AS 3 3
AS 3 4
AS 3 5
AS 3 6
A S 37
A S 38
AS 3 9
A S 40
AS 4 1
AS 4 2
AS 4 3
AS 4 4
AS 4 5
AS 4 6
A S 47
A S 48
2ASOO
2 A SOl
2AS02
2AS03
2 AS 0 4
2AS05
2 AS 0 6
2AS07
2 A S 08
2 AS 0 9
2AS10
2 A S 11
S TAR T
S TAR T

TP
QJ
S P
S T
S P
ZJ
S T
S F
ZJ
LA
TP
S P
AT
CC
TP
MJ
o1
o6

o1
o3
o5
o8
o2
o1
o6
1 0
o7
o1

MEMO
ME MO

00024
1 AS 3 5
3 A S 11
00025
00023
1 AS 3 9
00025
00025
1AS42
AOOOO
BOOOO
00023
3 AS 1 0
00025
AOOOO
00000
26249
67009
70881
08918
01743
89789
14598
57079
20000
00000
40000
57079
00000
00000
SUM
Y
SU M
Y

QOOOO
1 A S 37
00001
00025
00000
1AS40
00025
00023
1 A SOl
00027
00025
00027
QOOOO
QOOOO
A 000 0
1 A SOl
11000
01000
25600
81000
04600
87400
80160
63 0 5 0
00000
00001
00000
63268
00000
00000

5

X
X NEG
P I

ARC

M

003
003
002
002
002
002
001

4 2
4 0
38
36
34
32
30
28

B
B
B
31

SIN

FIN A L

E FIN A L
PAC K
EXTEND
OUT
A-7
A-6
A-5
A-4
A-3
A-2
A-1
A 0
50
33
1
6 0
P I o VE R 2
TAP E OUTPUT
TAP E OUTPUT

STT=O
Pg o 1 of 6
THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
STOH.lI.GE TO MflGN.ETIC TAPE ·TRANSFER ROUTINE
Specifications
Identification Tag:

STT-O

Type:

Service routine (with a program entry available)

Storage:

97 instructions, addresses 40006b,
74667b

7L~530b

thru

11 constants in program, addresses 74670b thru
74702b
108 words total program storage, addresses 40006b,
74530b thru 74702b
':!be constant and temporary stora.ge pools are not
used by this routine

Service Entrance:

Address 40006b

Program Entrance:

Address 74532b

Program Exit:

Address 74544b

Alarm Exit:

The alarm exit is not used by this routine

Drum Assignment:

Addresses 74530b thru 74702b

. VJachine Time:
~~de

of Operation:

5.6 seconds for transfer of (ES)
Fixed point

Coded by:

R. Beach

~ray

Code Checked by:

C. Koos

August 14, 1955

VJachine Checked by:

c.

Koos

August 20, 1955

Approved by:

\~

. Bauer

August 30, 1955

11, 1955

STT-O
Pg o 2 of

6

Description
This routine transfers information from the internal computer memory to magnetic
tape where it will be stored until read back in 5.gain by TST-O.
A parameter word is used to specify
1.

The loc ation of data to be stored

2.

The HT unit to be used for stora ge

3.

Hhether or not IvlT is to be re,,,ound to its original position after storage

4.

The address to vlhich control is t o be transferred VJhen the data is read
back by T8T-0.

\'.Jhen using STT-O as a subroutine the parameter wo:cd follows the RJ instruction
used to enter the routine. ~.Jhen using STl'-C as a service routine the parameter
word is manually entered in Q when the computer halts (after being started at
the s ervice entrance) .
At the time of ent17 the routine stores (ES ) on the orura, bootstraps itself
into ES , stores (A) and (Q) and obt&ins the parameter word. At is conclusion
the routine restores (ES ), (A) and (Q) and transfers control to the exit
instruction.
The routine stores one block of informa tion i n addition to the number of blocks
necessa.ry for storing the data , as follows:
1.

The first half of the first block contains (Q), (J\ ), the parameter word
and tvJel ve zero words .

2.

The second half of the first block thru the first half of the l ast block
inclusive contain the information to be stored .

3.

The l ast half of the l ast block contains the Sum of the data (that is, the
double preciSion sum of the split 'extension of each word), the number of
blocks transferred to tape , the starting and stopping address es for the
transfer, and el even zero Hords.

Parameter Hard
This parameter word is of the form Be DEEFF GGGGG , ,,,here B, e, D, E, F, and G
are all octal digits.
If B

=0

B.

The octal digit B deter mine s whether (ES ) is to be stored on ET .
(ES ) '''ill be stored , if B f 0 (ES ) vTill no t be stored.

C.

;I'he octal digit e determines whether HT is to be rewound to its original
position after the data has been trc:.nsferred. If e = 0 the rewind Hill be
executed, if e f 0 it will not be .

Do

:'1'he octe.l digit D determine s the l~'l' unit un i.Jhich the data is to be stored.
HI' units are specified by the same digits u sed in the standa rd 1103 !-iT
cornrr..ands ..

STT-O
Pg. 3 of 6

E.

The two octal digit number EE specifies the address of the first word
to be transferred from interna l storage to tQP~. This number is the
integer part of the first address devided by 8. That is, (EE)(512)
is the address of the first cell to be transferred.

F.

The t\VO octal digit number FF specifies the address of the last word to
be transferred. As in E above this number must also be a multiple of
512. (F'F)(512) is the address of the l ast word t o be transferred.

G.

The V-address portion of the parameter "1Ord (GGGGG ) specifies the address
to which PAI<: is to be set when the transferred information is read back to
internal memory by '1'ST-O.

As an example consider the parameter 1.-lOrd 01 24246 00017B. This specifie·s a
transfer of (ES ) and the contents of cells 42000b thru 45777b with no re,.inding
after the transfer. PAI<: will be set to 00017b by TST- O when the routine is
read back to internal memory.
Operating Instructions (to be fo l lowed ",hen the routine is used as a service
routine) 1.

Set PAK to 40006b and start.

2.

ComputB:j:.ion

4.

Computation h§3.1.t£ ,.]hen the transfer is completed, setting PAK to the
address specified in the parameter word.

halt~

with the HS instruction 56 00000 00010.

Programming Instructions (to be followed when the routine is to be used as a
subroutine )
1.

Enter the routin~ l.]i th the ~ instruction 37 ?lr5.~)3?:.. If the ru
instruction is stored at addr;ess n the pa. rameter lITOI'd should be in
address n + 1 and B.t its c onclusion the routine will transfer control
to th e instruction i n address n + 2.

Res tore
To restore (ES ), (A), and ( Q) at any time before normal completion set. PAK to
40040b and start.
The magnetic tape will be reHound at this time if the parameter word specifies
a re"lind.

STT-O
Pgo 4 of 6
123
200
1200
137
7 4 5 3 0
74545
40000
40006
74530
74531
74532
74533
74534
74535
74536
74537
74540
74541
74542
74543
74544
74545
74546
74547
74550
74551
74552
74553
74554
74555
74556
74557
74 560
74561
74562
74563
74564
74565
74566
74567
74570
74571
74572
74573
74574
74575
74576
74577

00
00
00
00
00
00
00
45
1 6
45
1 6
1 1
11
75
1 1
75
1 1
75
1 1
1 1
45
56
1 6
11
11
54
1 1
45
2 3
56
1 1
1 6
1 6
45
31
1 5
11
42
2 1
1 1
21
1 1
11
53
53
53
75
23

00000
00000
00000
00000
00000
00000
00000
00000
74666
00000
74701
00000
7455 3
31777
00001
30135
74546
31777
76001
76000
00000
00000
00135
10000
20000
20000
20000
00000
10000
00000
10000
10000
00012
00000
74544
20000
00011
00022
00022
00000
74544
10000
00124
00142
00142
00142
30020
00143

00000
00000
00000
00000
00000
00000
00000
74530
74553
74533
74553
76000
00000
74537
76001
00001
00001
74543
00001
00000
00000
00000
40040
00137
00141
00044
00140
00000
10000
00011
00142
74545
74544
00025
00017
00022
20000
00.022
00133
00142
00123
10000
10000
00057
00112
00121
00033
00143

STT-O
Pgo 5 of 6
74600
74601
74602
74603
74604
74 6 0 5
74 6 06
74607
74610
7 4611
74 612
7 4613
74 6 14
74 615
7 4616
7 461 7
74 620
74621
74 622
7 4 623
7 4624
74625
74626
7 4627
74 630
74631
74 632
74633
74 6 34
74 635
74 636
74 6 37
74 64 0
74641
74 642
7 4643
74 64 4
7 4 6 45
74646
74647
74650
74651
74652
74653
7 4 654
74 655
74 656

75
1 1
55
51
47
1 6
55
51
47
1 1
2 1
75
11
31
32
75
32
1 1
54
1 1
65
75
1 1
21
43
45
1 6
55
51
4 2
55
51
1 1
1 5
1 1
1 5
45
2 1
31
32
75
32
11
54
1 1
75
11

30020
00137
10000
00142
00041
00030
10000
00142
00065
00127
00143
31000
76000
00144
00145
21000
00220
20000
20000
20000
00020
30020
01200
00047
00146
00000
00070
00142
00130
0013 2
10000
00130
00111
20000
00047
00147
00000
00143 ·
00144
00145
20005
00137
20000
20000
20000
30020
00143

00035
00200
00003
20000
00040
00120
00003
20000
00044
00146
00125
00050
00220
00044
00000
00054
00000
00145
00044
00144
00200
00062
00200
00126
00065
00045
00063
10003
00147
00100
00006
00146
00047
00047
00146
00047
00045
00131
00044
00000
00105
00000
00145
00044
00144
00112
00220

..

~

STT-O
Pg~ 6 of 6

.

74657
74660
74661
74662
74663
74664
74665
74666
74667
74670
74671
7 4 672
7 46 73
74674
74675
74 6 76
74 6 77
74700
74701
74702

65
1 1
53
1 1
31
32
45
67
45
00
00
00
00
1 2
00
00
00
00
00
00

00001

o 0 132
00143
00 1 3 7
00140
00141
00000
00000
00000
00000
70000
000 2 0
01000
00000
77000
00001
07777
76000
00000
00000

00200
10000
00121
10000
00044
00000
74541
00007
74541
00001
00000
00000
00000
00220
00000
00000
00000
00000
00015
00115

TST-O
Pg o 1 of 6

THE RAMO-HOOIDRIDGE CORPORATION
Los Angeles 45, California
Magnetic Tape to :3torage Transfer Routine
Specifications
Identification Tag:

TST-O

Type:

Service routine (with a program entry available)

Storage:

95 instructions, addresses 400071, 7434.0b thru
74L~75b

8

constants in program, addresses 74476b thru
74505b

103 words total program storage, addresses 400071,
74340b thru 74505b
The constant and temporary storage pools are not
us ed by this routine

Service Entrance:

Address 40007

Program Entrance:

Address 74342

Program Exit:

Address 74354

Alarm Exit:

The alarm exit is us ed by this routine

Drum Assignment :

Address es 74340b thru 74505b

l'lachine Time :

5. 6 s econds for transfer of (ES)

Mode of Oper ation:

Fixed point

Coded by:

R. Beach

May 11, 1955

Code Checked by:

C. 1\oos

August 13, 1955

lvfachine Checked by:

C. 1e then s et from values
stored on Iv1T, (E8) is restored , and control is transferl'~d to the exit instruction.
Parameter

\~ord

The form of the parameter word is OX YOo.o.o. ZZZZZ , where X, Y, and Z are octal digits .
X.

The octal digit X deterrr.ines the cell to which control will be transferred to
at the conclusion of the routine.
If X = 0 control ,,,ill be transferred to the address specified in the parameter
word used for 8TT-0 " hen the data va s transferred to magnetic tape. If X -j:; 0
control will he transferred to ZZZZZ.

Y.

The octal digit Y determines which NT unit will be selected. ET units are
spec ified by the same digits used in the st.andard 1103 11;T commands.

Z.

The V-address of the parameter word ( ZZZZZ ) specifies the address to which
control will he transferred at the conclusion of the routine (see X above).

~ting Instructions (to be followed when T8T-o. is us ed as a service routine)
th ELll.~ramet.e r

1.

}'IE-nually ent er

word in Q.

2.

8et PAt to 4o.o.07b and start.

3.

Computation will halt after a successful transfer ,nth PAK set as specified
(s ee "Par ameter Hord" above ).

Programming Instructions
1.

Use the R.J instruction 37 74354 74342B to e:G ter T8T-o.. The cell inunedia.t ely
following the RJ instruction must conta in the parameter \-lord.

TST-O
Pg. J of 6

20

Aft eE-~~~.£~~~fJful tra!~~fer

control "lill be transferred to the cell specified

by the parameter word .
Alarm Conditions
If the sum test fails Aill- l is entered and IITST-O 7577711 is printed on the fl exo writer .
Starting efter the alarm halt causes a rewind of the tape and another transfer of
the same d.ata from HT.
Re store
If, at any time during its oper a tion, T:3T- O is interrupted (or after en al erm
print), PAK s et to 40040b and the mechine started, the routine will
1.

.~ lewind H'~

2.

Restore (ES)~ (A) , end (Q)

3.

Transfer control to the TST- O exit instruction

(if this ha.0. been specified)

•

TST-O
Pg. 4 of 6
121
200
1220
132
74340
7 4 355
40000
40007
74340
74341
74342
74343
74344
74345
74346
74347
7 4 350
7 4 351
74352
74353
7 4 3 5 4
7 4 355
74356
74357
74360
74361
74362
74363
74364
74365
74366
74367
74370
74371
74372
74373
74374
7 4375
74376
74 377
74400
74401
74 4 02
74 4 0 3
74404

00

aa

00
00
00
00
00
45
1 6
45
1 6
1 1
11
75
1 1
75
1 1
75
1 1
1 1
45
56
11
45
42
2 1
11
1 6
11
53
53
53
64
23
2 3
55
51
47
1 6
11
1 6
64
31
32
75

00000
00000
00000
00000
00000
00000
00000
00000
74350
00000
74412
00000
74354
31777
00001
30130
74356
31777
76001
76000
00000
00000
10000
00000
00005
00005
00000
a a 066
00121
00132
0013 2
00132
00001
00133
00134
00121
00203
00043
00071
00122
00105
00020
00133
00134
21000

00000
00000
00000
00000
00000
00000
00000
74340
74347 .
7434 3
74347
76000
00000
74347
76001
00000
00001
74353
00001

oaaaa

00000
00000
00132
00006
00005
00130
00132
40040
10000
00013
00024
00071
00200
00133
00134
10006
20000
00021
00035
00135
00041
00240
00044
00000
00 0 31

TST-O
Pg o 5 of 6
7 440 5
74406
74407
74410
74411
74412
74413
74414
74415
74416
74417
7 4 420
74421
74422
74423
74424
74425
74426
74427
74430
74431
74432
74433
74434
74435
74436
74437
74440
74441
74442
74443
74444
74 445
74 446
74447
74450
74451
74452
74453
74454
74455
74456
74457
74460

32
1 1
54
11
75
11
75
11
21
43
45
1 6
1 5
55
51
42
55
51
1 6
11
1 6
45
1 1
53
31
32
75
32
32
34
43
11
37
67
45
55
5 1
47
1 6
11
4.3
1 6
51
47

00220
20000
20000
20000
31000
00220
30020
01220
00035
00135
00000
00047
00030
00203
00124
00125
10000
00124
20000
00035
00136
00000
00126
00220
0013 3
00134
20004
00200
00220
00222
00221
00127
75701
00000
00000
00121
00132
00077
00203
74362
00005
00132
00203
0010 6

00000
00134
00044
00133
00036
00115
00040
00220
00123
00106
00024
00041
00035
10030
00136
00056
00006
00135
00035
00135
00035
00024
10000
00071
00044
00000
00064
00000
00000
00044
00073
75756
75702
76000
00013
10003
20000
00076
00132
20000
00112
74354
20000
00104

TST-O
Pg o 6 of 6

74461
74462
7 4463
74464
74465
74466
74467
74470
74471
74472
74473
74474
74475
74476
74477
74500
74501
74502
74503
74504
74505

1 5
67
31
32
11
45
1 6
1 6
45
31
1 5
11
45
00
11
00
00
00
00
01
00

00071
00000
00201
00202
00200
00000
00132
00112
00000
74354
20000
00001
00000
70000
00221
00000
00000
00000
07777
24015
76000

00105
00043
00044
00000
10000
74351
74355
74354
00102
00017
00005
20000
00003
00000
00000
01000
77000
40000
00000
63704
00000

URT=l
Pgo 1 of 5
Revised 10<-3=55

THE MMO-v]OOLDRIDGE CORPORl\TION
los Angeles L.. 5, California
Utility Routine Transfer-Magnetic Tape to Drum

Identification Tag:

URT-l

Type:

Service routine (but not available as part
of servic e routine library)

Storage:

45 instructions, addresses OOOOOb thru 00054b
1

constant in program, address.00073b (remaining constants stored with instructions)

The remainder of ES is used as temporary storage
The constant and temporary storage pools are not
us ed by this routine

Entrance:

MT Start

Machine Time:

Approximately 15 seconds for successful transfer
of the service routine library only, or approxi mately 35 seconds for transfer if CHP-O and the
subroutine library are included.

Coded by:

R. Beach

April 1, 1955

Code Checked by:

R. Beach

April 2, 1955

Machine Checked by:

R. Beach

April 14, 1955

Approved by:

w.

August 23, 1955

Bauer

·-

URT=l
Pg o 2 of' 5
Revised lQo.3~55

This routine is located in the first two blocks of magnetic tape unit zero
and is specifically designed to transfer the library from magnetic tape to
magnetic drum .
It oper a tes in two different modec~ , the mode of operation having been selected
when it was activated. Mode No .1 loads addresses 40001b thru 40040b and
70000b thru 75777b only. Mode No. 2 loads these addresses and addresses 60000b
thru 67777b.
This routine does not save the contents of ES since it is assumed that it will
be us ed only when a complete reloading of the computer memory is necessary. An
NT Start r eads in the first 32 words of the routine and starts oper&tion. The
routin e first r eads in an additional 32 words from MT (remainder of the routine
its elf) and then checks its sum, which is stor~d at the end 9f the second block.
In doing this, it also checks the sum of the service routine library which is
stor ed in the second block.
After a succ essful sum check the routine reads in the 96 blocks needed to fill
70000b thru 75777b. Twenty-four blocks are r ead in at one time and transferred
to MD, then r ea d back into ES and sumrnE!d. vlhen all 96 blocks have been transf erred the routine ~e a ds in one more block and transfers this into 40001 thru
40041, r eads it back into ES, sums, and a dds the sum of the sum of the 96 blocks
previously transferred. This computed sum is then checked against .the correct
sum. If the sum checks, the mode of opera tion is determined.
If Mode No . 1 ha s been selected a reHind instruction is given and the computer
halts with the HS instruction 56 00000 L~OOO1, setting PAK to the FRI-O starting
a ddress.
If Mode No. 2 ha s been selected T8T-0 is activated to read in Rawoop and the
subroutine library. A r ewind instruction is given and the computer .then halts
wi th the l-(S instruction 56 00000 40010, setting PAK to the C~/iP-O starting
address .

1.

II.

To transfer the service routine library only
Star~

1.

Select MT

2.

Change PC R (if necessary) to select the proper MT unit

3.

Start . The routine loads 40001b thru 40041b and 70000b thru 75777b
and halts with the MS instruction 56 00000 40001, setting PAK to the
FRI - O starting address . Succ e ssful transfer takes about 15 ·seconds.

To transfer the s ervice routine librarY., CKP-O, and the subroutine library
1.

Sel ect 1<1T Stert

2.

Change PCR (if necessa ry) to sel ect the proper ET unit

3.

I.ft,ake (Art ) grea t er than zero

"-

URT-l
Pg o 3 of 5
Revised lO~3=55
L"..

Start. The routine loads4000lb thru 40040b, 70000b thru 75777b,
and 60000b thru 67777b and halts with the l·;S instruction 56 00000
40010 s etting PAK to .t he starting address of CMF- O. Successful
transfer takes about 35 seconds.

Alarm Conditions
1.

If the machine halts on a final~ almost immediately after an
IvIT start the transfer routine is not in ES correctly.

Sel ec t XT start and start for another transfer . If the second
transfer is not succe s sful r evert to the bootstrap procedure to
loa d the library .
2.

If the fl exO\'Jri ter prints an lie II and the machine halts with the
11S instructi on 56 00000 00051 the sum of the library transferred
to the drum is not correct.

Select ET start and start for another ·transfer .
3.

1:men orer a ting in Hode No.2 TST- O is activated after address 4000lb
thru 40040b and 70000b thru 75777b have been loaded successfully. If
the sum t est fails while loadin g addresses 60000b thru 67777b, the
a l a rm routine prints the tag \-Jord T8T-0 and the address 75777b . Starting cause s rewind and another 1'1T transfer to addresses 60000b thru
67777b .

VJarning
After a succ essful transfer the computer halts but MI' is still r ewinding to its
original position. If a Ha ster Clear is executed and the machine sta rted a
ref e r ence to the rewinding 111 (before r ewinding is compl et e ) will caUS e trouble .
If no Master Clear has been executed the machine will wait for the r ewinding to
be c ompleted .

URT-1
PgG 4 of 5
Revised 10-3-55
1700
1701
1702
1703
170 4
1705
1706
1707
1710
1711
1712
171 3
1714
1715
1716
1717
1720
1721
1722
1723
1724
1725
1726
1727
1730
1731
1732
1733
1734
1735
1736
1737
1740
1741
1742
1743
1744
1745
1746
1747
1750
1751
1752
1753
1754

45
1 1
64
3 1
75
32
34
43
67
57
75
2 3
1 6
6 4
75
11
31
1 5
75
1 1
2 1
31
75
32
11
54
1 1
4 1
6 4
75
1 1
75
1 1
31
75
32
34
43
61
34
67
56
4 1
1 6
45

00000
20000
00001
00000
20075
00001
00077
00076
00002
77777
30003
00175
00010
00030
31400
00200
00017
20000
31400
00000
00017
00176
21401
00177
20000
20000
20000
00175
00001
30040
00200
30040
40001
o 017 6
20041
00177
00075
00074
00000
00074
00143
00000
00172
00036
00000

o0

0 0 1
00172
o 004 0
00000
00006
00000
00044
00012
00003
77777
00014
00175
00175
00200
00020
70000
00017
00023
00024
00200
00073
00044
00030
00000
00177
00044
00176
00015
00200
00037
40001
00041
00200
00044
00044
00000
00044
00052
00016
00044
00000
00051
00055
00051
00050

URT-1

Page 5 o f 5
Revised 10 -3-55

17 S 5
1756
1757
1760
17 61
1762
1763
1764
1765
1766
1767
1770
1771
1772
1773
1774
1775
1776
1777

37
01
67
56
00
00
00
0 0
00
00
00
00
00
00
00
00
00
00
00

74354
00000
00344
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000

74342
00057
00000
40010
00000
00000
00000
0000 0
00000
00000
00000
00000
00000
00000
01400
00000
00000
00000
00000

LIB
LIB
UR T
UR T

SUM
HI
SUM
L0
1 SU M
1 SUM

HI
L0

URT=3
Pgo 1 of 5

THE RAMO-WOOLDRIDGE CORPORATION
Los Angeles 45, California
Utili ty Routine Transfer Drum to l1agnetic Tape
Specifications
Identification Tag:

URT-3

Type:

Service routine

Storage:

108 instructions, addresses 40000b and
00050b thru 00222b
8

constants in program, addreqses
00223b thru00232b

All of ES is used for temporary storage but
not included with the program
116 words total program storage, addresses
40000b and 00050b thru 00232b
The temporary and constant storage pools are
not used by this routine

l'1achine Time:

100 seconds approximately

Mode of Operation:

.Fixed point

Coded by:

R. Beach

August 1, 1955

R. Beach

August 15, 1955

H. Bauer

August 23, 1955

V~ chine

Checked by:

Approved by:

•

URT...3
Pgo 2 of

1l

5

Upon being entered the routine fir st s ets up all r eferences to magnetic tape
to correspond to the unit s el ected when URT-3 is activated.
The contents of cells 40001b thru 40040b and 70000b thru 75777b are then summed
and the sum pl aced in 01774b and 01775b. The contents of cells 01700b thru
01775b are then summed and the sum placed in 01776b and 01777b. The informa tion
in cells 01700b , 7000Gb thru 75777b , and 40001b thru 40040b are then transferred
to ET in that order .
The contents of cells 60002b thru 67777b are summed and the sum placed in 60000b
and 60001b.
STT-O is en t ered to dump the information in cells·60000b thru 67777b (the subroutine library consisting of Rawoop and the subroutines).
URT-3 computes the sum of all information pl aced on 1'(T , rewinds MT to its ori ginal
posi tion and reads back the data from IvIT , sUIIiIning 8S it reads.
If th e sum is correct, a BH instruction is given to return 1-1T to its original
position and computation halts with PAK set to 40001b, the FRI-O starting address.
Operating Instructions
1.

Select}ID Start.

2.

Set the number of the 11T to be loaded in the low order octal digit of Q.

3.

Start.
URT-3 transfers the complete library to MT and halts with the 118 instruction
56 00000 40001 after a succ essful transfer .

Alarm Conditions
-----If the sum of data r ead back from ~ is not correct the alarm routine is entered;
the tag \-lord URT-3 and the address 00067 are printed on the flexowri ter. The sum
of the da ta on ET appears in A.
Restarting at this time initiates another transfer of dota.
Harning
1.

It is advisable to position MT at the first block before loading so that the
1'(T can be repositioned, manually if nece ssary.

2.

lift er a successful transfer the machine halts but I,IT is still rewinding to
it.s original position. If a master clea r is executed and the machine started
a r ef er ence to the rewinding ET (b8fore the rewinding is complete) will cause
trouble. If no m~ster clear has been executed th e machine will wait for the
r eversing to be compl eted .

URT-3
Pg. 1 ,of $

60000
50
70
223
233
240
17 a a
40000
50
51
52
53
54
55
56
57
60
61
62
63
64
65
66
67
70
71
72
73
74
75
76
77
100
101
102
103
104
105
106
107
110
' 111
112
113
114
11 5
116
117

00
00
00
00
00
00
00
00
54
11
53
53
53
53
53
53
53
53
53
53
53
53
53
53
11
75
11
31
1 5
75
32
31
32
75
11
75
32
11
54
11
21
42
31
75
32
11
54
11

00000
00000
00000
00000
00000
00000
00000
00000
10000
00230
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
00214
30040
40001
00240
00226
20037
0024 1.
01774
01775
31400
00000
21400
00300
20000
20000
20000
00102
00224
01700
20075
01701
20000
20000
20000

00000
00000
00000
00000
00000
00000
00000
00000
00033
10000
00120
00124
00127
00175
00176
00202
00213
01.702
01710
01715
01734
01750
01756
01757
00000
00073
00240
00000
00102
00101
00000
00044
00000
00103
00300
00105
00000
01775
00044
01774
00223
00077
00000
00115
00000
01777
00044
01776

TRNSFR
FROM

4000 1

TRNSFR
AND S UM
FRO M 70000

SUM URT 1
AND S TOR E
o N MT

...

URT=3
Pg. 4 of 5
120
121
122
123
124
125
126
127
130
131
132
133
134
135
136
137
140
141
142
143
144
145
146
147
150
151
152
153
154
155
156
157
160
161
162
163
164
165
166
167
170
171
172
173
174
175
176

65
1 5
75
1 1
65
21
4 2
65
23
2 3
1 5
31
32
75
11
75
32
1 1
54
11
2 1
42
31
32
32
32
32
32
1 1
34
11
32
32
32
75
32
32
32
32
32
1 1
54
11
2 3
37
11
67

00002
00226
31400
00000
00030
0012 3
00224
00001
60000
60001
00130
60000
60001
31000
00000
21000
00300
20000
20000
20000
0013 6
00226
60000
00175
60000
60001
60001
002 27
20000
20000
20000
01774
01776
00233
2000 3
01775
00234
00234
00232
01777
20000
20000
20000
10000
74544
06070
00344

01700
00123
00124
00300
00300
00223
00122
00240
60000
60001
00136
00044
00000
00137
00300
00141
00000
60001
00044
60000
00225
00133
00044
00000
00000
00000
00000
00000
00234
00044
00233
00000
00044
00000
00164
00000
00000
00000
00000
00000
00234
00044
00233
10000
74532
00000
00215

S TOR E
SERV I CE
L I 8 RARY

·

.

URT-3
Pg. 5 of

177
200
201
202
203
204
205
206
207
210
211
212
213
214
215
216
217
220
221
222
223
224
225
226
227
230
231
232

23
55
11
64
75
32
11
44
1 6
34
43
1 6
67
45
56
54
32
1 1
37
45
00
1 1
00
11
00
00
34
1 2

10000
00230
10000
00014
20600
00300
00235
00207
00176
00234
00233
00213
00344
00000
00000
20000
00234
00231
75701
00000
01400
76000
01000
70000
00201
70000
12015
50000

10000
10030
00235
00300
00205
00000
10000
00201
00214
00044
00213
00214
00216
00000
4 0 001
00044
00000
75756
75702
00070
00000
00300
00000
00300
00000
00000
67004
00220

5

February 17, 1955

Nu o

33

(Re'lised)

RAMO-WOOLDRIDGE ONE-PASS ASSEMBLY PROGRAM
FOR THE ERA-1 103
By

Jules Marsel and Thomas Tack

The Ramo-\'looldridge one-pass a ssembly program (Rawoop ) is designed
t ranslat e an 1103 program or iginal l y coded in symbolic~ regiona.l 9 de ~imal rom
to its final octal form.
The program will accept instructions with symbolic addresses and
numer ical dat a in binary or decimal f orill. It will cause subroutines to be
appropriately assembl ed in the program. The result of assembli ng a program
will be output in a form to facilitate progrEml check=out and r apid program
read-in of the t ranslated datao
Input-Output
~ched cards afe used ~ s input for Rawoop.
The punched card has one
1103 word plus remarks on it or the c~d contains an instructi on to the assembly
program and remarks.

Rawoop' s output is both punched car ds and punched paper tape D
The output card contains an exact duplicate of t he corresponding i nput
card in addi 1(ion to the octal transl ation o~ the i nput card vs ini'oI"lll8 tionn The.
programmer can obtain a side );>y aide -.listing 'OlL hi;• .-unt.ranslated program1 remarkSl p
and translated program by running t he output deck of cards on associated equip=
ment such as the IBl-l 402.
The punched paper t ape is a seventh-level bioctal tape complete wit h
insert and check addresses, and is suff icient f or putting the translated program
into the 11 03 either by using the ERA photo-electric reader or by usi ng a Ferranti
tape reader wit h an appropriate read-in program.

The input and and output cards ar e standard

80-column~

12=row cards o

Columns 1-5 ar e used for the symholic addres s of the untr anslated ward o
Colurnns 7-10 are used for the 11 03 instruction or psuedo instruction o
Columns 12-16 are f or the u address.
Columns 18-22 are for the v address.
Columns 24-26 are for decimal scaling information.
Columns 28-30 are for binary scaling information.
Columns 32-43 are for alpha-numeric remarks.

rYE RAMO WOOLDRIDGE (Cf\"ORA liON

I

PAGE

. OF

(Figure 1)

PROBLEM

..ina

2

D

3

10

4

D

5

1""--

D

----1-

,r

6

;v

it
'I
i:

,

7

1

Ie

- ii

•

_x

.A • M.P L E

oF

:1

2

)C

8

:r
Jf E
Ii

:1 THE:

9

o

T Y P E

F

o
1

1 ;C

:2

1 ~c

'e

5

f

6

-

+

•

,f9

J

1 ·f:2

9 is

•

·1

3 4 5 6

3
4

- f -Q~~'LJL=-~-i

5

. -4I

6

..s

7

~.

j

e
9

o
1
:2

I
•

i

'r

C

:1

~

I
,
___ .___ -J.. _ _
~

1 CC'1

5

'jY

.~.

H
1L.... ___ .._. _Jl.
H

___

. __ .L. __ . .

7 --

'0

H

'!,I

I'

12 -

16

~

1

II ,

II

it

j

I'
: . !:

Ii:
i

• ___ ---...l...:

18 - 22

11

it

"

I
~

:i

it

iii
i

.

I[ . . .

t

'

j

I

I

I'

__ --'1-..L ___ .-"- . ___ . ____ .._____ ..

24 - 26 28-3 0

. CHECKED BY

F:tgun 1

i

."
32 - 43

2 In addition to the above columns, the output cards contain the translated
information in columns 47-67.
On

Speed of

~

input cards,

~ ~

not

~

punchedo

Ass~mbly

Due to the 1103 ' s ability to read and punch cardssimul taneously while 1.t
is punching paper tape, Rawoop takes only a few seconds more than the total lClard
readi ng time to execute its entire translation. Errors do not ne c~8sitate complete
re-assembly. Consequently, Rawoop is exceedingly e conow~cal in i s use of machine
time
0

Symbolic Addresses
A fi ve character form, in keeping with 1103 machine f orm p is used by Rawoop
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, 18JOO is the zeroth address in region 18J and OOG'! 9 is the
nineteenth :address i"1 region 01 C (01 COO is the first addres s in region 01 C)
In
keeping with the one-pass nature of Rawoop, the sequence numbers are consecutive
decJ,.mal nUl1lbers. The l:lbsolute' address assigned to 01 C19 is riineteen greater t han "the
address assigned to 01 COO o Thus, the address structure has a regional character
0

0

As indicated above, the first two characters of the relative address or
region are numeric and the ~hird character is alphabetic o
The absolute address for region 000 (all zeros ) has already been chosen in
Rawoop to be zero. Consequently, 00029 would have as its octal translation~ 00035
and absolute machine addresses up to 99 will be correctly translatedo The a ssembly
program recognizes the alphabetic letter "0" as different from the numerical uiO~ 8
to avoid confusion, the programmer will probably not want to use symbolic addresses
involving tho letter O.
A, B, and Q Addresses
The accumulator, the B register (accumulator bits A70 ~A35)p and the Q
register must be addressed by putting an A, B, or Q in the leftmost column of
ei ther the u or v fields. efhe remaining four columns may have no punches or zero
punches.
The octal translations of A, B, and Q are

20000~

30000~

and 10000 respectively o

Addresses Involving j, k, and n
The command structure of the 1103 is such that the u and v addresses at
times contain numbers rat-ber than machine addresses as is the case in the SPuk~
R.f>jn, loT and MJjv commands.
The representation of j,n ha.s j as the first character and n as the l ast
four characters. The quantities j and n are written as decimal numberso Thus a j9n
of 30199 is translated as 30307 (octal). No distinction is made by Rawoop betiol'een
j,n addresse~ and j addresses. If the programmer desires to use the last four
characters of a j address to store a number (not a relative address)9 he may do so
knowing that these four digits will be treated as the n in j9n addre sses o

3

In the 1103 i'" ddr~ss s truc ture , k 13ddresses indic.::.te left ci rcula r shift.s
of from 0 t o 127 pla ces a t . ost. H9,.re \Ter, since the 1103 inte rnal hard\l1ar9
occa sion,;; ly make s i t. j e s ir;;.ble t o ho va th~ 1'i s t octa.l bit of a k addresSl be a
number other theUl ze ro , k c. ddresses \-1i11 b~ treFlted in the same manner as lin
a ddresiil :; s ; f or exa.rnple, 20017 becomes 20021 (octa.l ) .
Void Address-es

~-

Certain of the 11\)3 COlIlD1Cillds such a s FS- -, BJj ,n c._ have ignored addresses
a ssocict ed with th.3n.,. All ~uc h addr e s ses re treated by Rawoop as if' they were
rel ative ad 'r es s.;;ls and i: j.re a va ilable f or the s torb.ge of pre=setting addresses o All
ze ros, of course , a.r e t~a..nsL; ted into a ll zeros .

In a 9ne-pass a s~embly program, it :i,s necessary that a.t the beginning of
the program sufficient inforlllatio:p is supplied tc enable all symbolic; addresses
to be assigned absolute addresses.
Rawoop doe s this by ffi~ans of d:i,.rectory cards. A di re ctory card has a. D
punched in column 1, the bese word of the region (e.g. 01GOO) in the u address
columns, and the a bsolute decii1'.al a.ddre s~ of the ba se word in the v address col'il.llIlillls o
For examples, see figure 1.
For purposes of a.ssigning decimq.l addresses to the drum.\) the convention
'vlc. S adopted that octal address 40,000 on the drum ha.s the decimal address 40 9 0000
Thus, the drum addres ses r~.nge f;rom 40,000 - 56,383.
Rawoop can handle up to 60 directory cards in anyone a ssembly

0

S;xmbolic Ad.dresses of Program_pata
With the exception of tpe D cards and tne START card D all the input cards
have a relative addre ss punched in colunms 1-5. This address is the address of the
word to the right and cow.pletely de termines the memory location into which this word
will be re,:td by the output bioctal tape.
Commands
The 1103 alphabetic representatio~ of the commands is used 8 These t wo
letter combin~tions, such as RA, are entered into columns 9 and 10
IJLl the stand=
ar d 1103 commands a re recognizeo. by ~woop and this recognition impl~es lmowing
whether the addresses associl-,ted with the cO!DIUe.nd ar e of the u ~ vi> the jn9 wl) Olr'
of the u,k types.
0

In addition to the s tanda.rd 1103 cOIIh'Tlands, the special commands 1P9 PN 9
and MM are r ecognized. The PM, MM cOlDIDa:pds and the availabilit y of the B register
for addre ssing are modifications on the Ramo-Wooldridge 1103 . PM is a ~polynomial
multiply" ca.'nmand for polynomial evaluc.tion whose octal equivalent is 241) MM is) 'it;h.e
"modified multiply-add" (fastar in opera tion tha.n HA) whose octa.l equivalent is 25 0
None of these mo dificat~ons are used in the operation of RawoOp1) the program will
oper ate on any 1103 with reproducer and high-speed punch.
IP comma..'lds are tree. t eq as if the cqrIlPlE.nd s tructure were IPuv
HoWeV9E'i>
for users of interpretive programs quch ~ s the Convair Flipp a psuedo ~ammand i~
avails.ble.. The command i"Pabuv ~ where a and b a.re octal digi t.s and Ul and VI are
0

4 .r':L ti v,~

a ssi gnf:d to th.:: al~ct.r·(,;.<::lt.tic :"t.or-.,;';, is '~t'-'n3 I;";cd :1:1, 'bo!',
l ' oit nu b~x' :'} ()c. cupyi n ,~ til' r' , '''' .~',\,
., . . :1.., ,~.f ,. l ,f;:,
tr rwl.'i:, .. G. \Jor, v/ith ;;-~ b to t ae 10ft. of them.
s is shr'm in .;, 5'-'
Y>
• ,I• •
iat.) colufnns 7 <:.nci E; the c~b oef:) int o col
s 9 . -:. n d 10 on the inp •. "':. ~ _ 0

2.

8

u 'v '.

i' t' ;:88 3,.,

U'

M ,e V I i ~)::;

It i s soma times (.e:;Jira bl e th,· t a r s l ""ti ve address be ph.ced in 11 word t s.t
To en~ble this ~ the co. mene 0 0 (zeros) .is recog=
rlized ~.nc.. transh t ed into 00. The U tald v addre sses must bi-.; symbo~iG add:resses o
As uSWil , hOvlcvcr , an a ddr ess of f i ve z eros is t ransla ted into. f"l.V6 zeros o
h e ::;

zeros for its cc;ulInC:i.nd Gode.

De cim&,l Numbe rs
De ci.rne.l n1lnl bers a re presented to Rawoop ' .s normali zed num,b~r~ times .-'< po~l6r
of ten. The progra ,mer a l,so st:::~ites the bin :ry s ca ling fbctor to . e ap,.' ed to the'
resulting r ounded bin2.ry nunlber. For eXfu.lple, -739. 1 is presen·ted as ~'':7 0 ~91 x 10"0

1

~nd

,11 decima.l numbers a re normalized so thf::i,t t heir absolu.te v"'"i.ue lias
9.99999 99999.

between

The sii:Sn of the nUlhOG r is in col UCi.n 9, the inte ~r:ll p<,rt in colu:v.rA 11 0 l) ~..nd
the fr 3.0tiuna.1 p t1rt in co,lumns 12-16 ' nd 18-22. The power of 10 allobled is ft"oJ:1l =4J0I
to +10. This eXFonent goes into columns 24- <'. 6. The desired binary sC5.le 'aGtol" goes
into colu;nns 28-30. For ex~n~ple s, f n li~e 13, Figure 1 p the nurr.ber- to be tran~lated
is 3.1 23 x 10- 6 with !:l. s c&.le f -;1.ctor of 2 2 ;,J 1
:Cn all ca ses a minus sign

r epre sent~

a nega tive nu.."Ilber and a

Z61'O

or

nt,

puni:<:,

a posi ti ve number.
FJ.o.::.. t ing de ci!il&l nuru bers .", r~ presented to Re.\voop in the S8J"~e IDb.nner a:s decd.1l..u
numbe rs. HO"'9ve r, :i,nste"ld of 3. binr:;ry s cale f ;':.ctor being pl""c&.rl .m cIJlumns 0;8=30" axA
F i s punch(: ' ;i.n column 28. The cOllve rted flo c:.. ting decimal num.bel' is in the for.n u~ed.
in the Conva ir l<'lip . Tha t is, the lei't,mo:?t 28 bits is a mantissa with the !nary
point just to the right of the sign bit a nc. t he rightmo st eight its is fa signed
ex ponent.
Oct, l Constants
Octa l const a nts ca n be insert8d i nto th~; progr am. usi ,ng !.awoopo ~~ha oJOOP

thl:l t all the crords have been r eceived is a card wit.h
a rplative ~ddress punched i n colun~s 1:=1~ o

colu.~ms 1~5, an~

This signa,l ca US,,1S Rr, woop to ips8rt into the tran slated program i n 1,:)ca.tioDSl
00000 a nd 40000 a manU'il jur,lP to the octa l transl:.:;.t.ton of the r eld.tive address, o
He;n:::8 , after the resulting punched paper t ape is re ad int ·:> the 1103 v a. .n!l.gnetl,~ I"'Lto,l'o,
sts,r t l"[i11. s t 'lrt the probl,em a t the rela tive address i ndi oated in the ~l 0.01· 'l~n;3o
-,:Subroutine
....
...... s
-'"''' ~ '' ''

..--~ -

R<3,woop is designed to tra nsla.t'3 subroutines coded in oct,ql

and stored on th~ arurll , and include thelli :i.nto the main progr alTl o
one psue' 0 cQ!mlV£l.nd, the "SUB" cO!Jll1land.

rel;'~tive

to 011000

This is erfs'Cited by

-

5 -

Columns 1-5 of the ::'UB co nand cont a i n the relative address 6ssigned to
the zeroth word of the 'subr out ine bJ one of the 0 cords o Columns 719 8 9 end 9
have the lett ,:;!r s SUB . GolulJl!ls 18 , 1 g , f:!n d 20 h:).v9 the nUlJ1ber of words in the
subroutine . Col umns 21 and 22 h,-,-ve t he nu;nber of constsnts at the end of the
subroutine T'[hich G.re not to be t r a.nsla ted . ColU1~'\.Tl s 12=15 have the location 0._
where the zeroth word of tho subroutine is stored on the drum. (this address iSl
t he decL-n.!tl 1rum addre ss) . I n operb.tion, t he inform.'1. t 1on i n these colUl.ms if;;
sirnply co pie d from a. subroutine specifica tion list .
A l i sting of t h" t ran sl at ed s ubroutine is ilSlutlly provided by he output
car ds . The :J nch.:tng of car ds f or this however p eM be sUP,)I'csscd by depressing
the j =3 jurr~ button .

Hawoop clllc'U.._ht e s the memory surn of al l t ranslated words including t..Jle
Thi s sum is the do uble precision sum. of the
spli t extension of t he tr!;l. nsh .t ad. words . The s um is both printed on the listing
and is re[\(1 by the output p.~ pe r t a pe i nto o(.}tal addr e sses 6'7 ~ 776 and 67 IJ 7I7I"?! of
the drum. The high or de r value of the sum :is in 67 ~ 77 5 .

0000 0 s.nd 40000 jUll P instructions.

_
_
UrderL'"lI'
l'
.

...._____
__
of___
Input
Ca._r.•ds

_E.
_ ~

Ra.woop makes the following requireme nts on the order i ng of the input
cards:
di recto~y

cards 9

howeve~9

1.

All dire ctory cards must come first. The
c:m hH.ve any orde r within tberase lve s.

2.

'l'he START card must come last.

3.

The SUB c'l rds, if any, :nust im.Tlledi dtely pre cede the ST]I;:!.T oorr'i o
However, the SUB cards can have any order wi t .hi n the:nselves o

The cards a ct ually giving the wor ds of the progrwn f oll ow the directory
cards. ~"or the s ake of minimizing the nUJ..lber of insert and che ck addresses on
the output bioctal tape; the cards should. be in order within their regions .
However, a correct output t ape will result no nett er what order these inc:olllll!ll":
c9.r ds a.re in. If the cF:\rds were out of ori er, a cornvenient listing s till can b~
obtained by re-orjering the output cards.

The following points are important in the oper'3.tion of

RaWOOpg

1.

The reproducer must be set for fields I end II onlyo

2.

The input cards are to be placed f a.ce down with a.t least six blank
car ds following the ST.J1T card.

3.

Two cards are to be fed into the punch channel o

4.

Both the typewri ter and tpe high-speed punch must be turned on.

5.

After reading the a sse:ubly program into the ma chine ll an i'1D start
is su.ffici·e nt to start or re-start Raw-oop . Rawoop c hecks its ow
me~ory swa a t the beginning of the proble
and gives a signal if
th~ check discloses an error .

6

6.

lLl l 0.9.r 1s ,:...rd el e '~re d out of the read snd write channels at the end
of the program.

If' it is desired to suppress the output subroutina
be depr essed .

~a.I'dS 9

jW:1P 3 should

Error Detection
Ra¥lOOP will s top and signal the reason i n case of €li ther of the followilllg
t¥lO occurrances8 More than sixty D CB,rris are e ntered or any a, I'd o·ther thl'lD ~i tnsxo
a SUB ca r or t he S'l'AH.'r c3.rd f oll ows 5. 3UB cr rd.
All other errors ~ including a D car d occurring in t he .l'.tdin jeck W'l..ll nc:: 2

62156

41

6 217~1

621 4·4

127

SP

N5

36

RESTORE AL

62157

31

62172

00044-

128

SA

N 6 00000

RESTORE AR

62160

32

62173

00000

129

TP

N7 Q

RESTORE Q

621 61

11

62174

10000

L30

TP

N 8 00000

RESTORE F1

62161

11

62175

00000

L31

PR 00000

Z10

PR CAR fu.-.orRN

62163

61

00000

62213

L32

MJ 00000

L

STOP

62164

45

00000

62124-

NOO

PR OQOOO OOZOO

PUMlvlY

6216 5

61

00000

62201

B

ADV U

62166

00

00001

00000

N02

,2 B

DEC 2

62167

00

00000

00002

N03

5 B

DEC 5

62170

00

00000

00005

DEC 11

62171

00

00000

00013

N01

N04

,

TAG TO Q

6

00000

N

1.24

1

11

IN Dl'~

·

..

Pg o 3l
N05

00 00000 00000 B

AL

6~1n

00

00000

00000

NOS

00 00000 00000 B

All.

62173

00

00000

00000

NO?

00 00000 00000 B

Q

6,,174

00

00000

00000

NOS

00 00000 00000 B

F1

62175

OOl

00000

00000

Nag

00 00000 00000 B

INDEX 1

62116

00

00000

00000

N1 0

00 00000 000 0 B

INDEX 2

62177

00

00000

00000

N11

00 00000 00000 B

TAG

62200

00

00000

00000

START

00101

00000

45

00000

62~25

START

OOL.Q1

40000

45

00000

62~

25

,,

REPORT ~"""90

DIV I 51 ON _-"'S""'
&no=....=D1~e.Q!:=o__

All

MODEL

DATE
8A,~c:;l1
r8Thed
14/~

12

TITLE
'LIP
A 'loa.tin, Point Subroutia. 'Syitem
for
The ERA 1103 Computer

,

'- ~--.

'.

,i

PREPARED BY_--",C=h!-rlet J .. Swtrt

~,,. ---.-'

CHECKED

-

.REFERENCE _ _ _-'---_ _--:,.~_

.; "mbere of D! g1..tal

ex

.'

qC!lPut1n.A...-r.,b~ratop"

. APPROV£D~: ey_
" ---.·;-.
· '_
' --:l~_ _-

".
.NO.'
•

Of: ~AGES
~..57.''-:-::~;
.....
.

• •

I

,-

NO ' OFOIAGR:.AMS·

.

··oAn:

,

CONS?LIOATED VULT£E AIRCRAFT CORPO~ATION

ANALYStS

/~HECK£O

1

PAGE

~EPORT NO

5" .... 011:00 01V 15 10'"

PR£'-AREO 8Y
BY

Z)'(..J..-}O

MODE~

REVISED BY

PA TE

12/07/';1.

liotl"s on FLTF

l~ro,

3.

t\l~}jOtl! ·~.

t~

exponent ptl.rt

,

In a?dition to cells,Oll,?';" to G1 T77 and th03e a~sj~ncd to . Dub-

• The

07

COMlTl8.nd . ca ~1

ct!

.,

ulerl to ten-dr.aLe a stories.

"

If
'..

An

~·xal1\ple of i t :

use lit tti61-

01 '1elO

11

00

11 100

11;01

~ +6X -u:,R

ClI.'01

11.

()7

lJ.;~ l

l1~oo

~ X-~+X~R

010 .. ,2

, L7

00500

01 0( ,3

I

l-~ ~ '2"Z"!
" )(

( add tar .... to series)

Lid tr.i ~ term
~l

tcr

U,e sum?

(l' .S 1)

./

,.

. ,

C0 NSO LlOAT~O

A N ALV_I S

P'RE,.ARtO."
CHECKED BY
"£YISE: O

VUL.TI:I A I .. CR ... "

C. J. '~

~AG.

CO .. P"O ..... noN

....N OlUO' O I VtetoH

ItIJllOfrr NO.
-..oDCL

ev

DATI[

A Fleat1n.,; P01.t Subl"outiDe Sy,tea U.1n,; A Paoked _.pre,.station tor

III 1103 Computer
(Flip)

t»

10/l5/~

R8T1a.d

The lyate& de.oribed her. U intended to be 1ndet1oi tely .xpud.d to includ.

card operationa, t l"anacendental funct1on. _to.
,10 oc taldl~lta lang (preoeded by oct.l

14,

rh. interpr.ted inltntetiOAI are

;the IP cOJllU.Jld).

The baa1o ' .,..tna

I

. ~coupi .. ES cen. 01477 to Qlm and 00001.

The whole .yttea 11 ,1eoated an the drUJll, 1..n locationl

more ,pac. 11 needed.
17m~,

7l:/:xx) to

It any ,ubrout1ne oper,a t1on. Ire Uled,

00014.

T>1e basic opera~ion. in P'LIP \1.Ie teapora.rl .. 00002 to

00031.

Subrout i ne ' operationa Ule celli 00002 to
Compo.ltiOll of In.truot1 Cln,

I

lnltruotion Code

' 6 bitl

Firat Addr .... z

12 bit,

29 ••• ~)
(123 ••• 112)

12 bite

(111 •••

SeoOlld Add!-

n

88' •

.,

(1

10)

Addr •• te. '

1M lut 10 bit. of each, addr... f,ol"1Dtl. ~ ..Uo· .. ddr ....

'tn.

firlt two bi ta, if one •• oaul. either or bo~ ' of the two 'pe()lal
oounter,1 bl and

~

to b e ad'4.d to this

-exeouti.- ..ddr~...
,

bali~

'1'b.a f1rat bit ·oa\1l ..

ht

adare .. to fora the
~o be ad(le.cl, ~he

"

..eOQ~' Qft ca~ea b
\W1n~

2

to be ~c1ditd.

The aatructio,n 18 .~cuted
"

th1. enout1oza addr... which _WIt ' not exceed Olm.

All

execvtion addreue', refer to E8. .
~I

Spec1al ' Regbtel"l
III a!' ui .~ .

pee 1a l1y-,refeITed to 1.n order.. In order to.', ref'er ~o ' l, Q"
and ..~. 1a the •• o.l"d.rt~.
' \aU ..ddr.e •••• ·:l774. 1775;lTr6
11711
. . . .

are •
bi

.'

. .~ :l"e.ptoti.,..ly.
...

,

'

'.
.

.. ~

•

'

J'LIP
&J'~ r~~~lrt1"~17 eq.~~" ~:, (:Rl· .u. ('Q) ''''.... b& . ~~
.,

.

!perat1oa

_'lluto~~:nt. A>r l~ .d 'iTr5 atter-~ ~T

U.

'

~

" ' .

,

.'.

.•

•

J

)

. ,

;'

. '

,.,.

,

-

...

;

-.,;.'

'

CONSOUOATItO VULT~E AIHCA"prT COAfOOf'''T'ION

ANALY .. S

~AE~A"ED.""

C. J. Swi rt

2
1.)(..u90

PAGE
.UPOOAT NO

eAN 01&00 Dlv,e,oM

CHECKEO BY

All

MOOt:L

10/20/~. (Rey )

DATE .

'UV.SI:O BY

If a reault 1s plaoed in both y and R. (j{) is not a

operation.

double extension of (R); otherwise it la.

IV

C~ntenta

of Reglatera

l-xeept for b 1 and b2' the contente of every re g1eter 11 interpreted ·aa a number of the ·fora q x 2 P •

bit••

!

the la.t 8.

looouplea the ftrat 28

Negative pt. and q"

Denta, the ftr.t d1 r1 t at both p and q

are "expre.8.d

bein~

by · e ~ mpl.­

The binary

a air-n bi t.

point of q follow. the sir,n bit • . Except tor the .peelal case
pc. q == 0, q is rutricteo to the valuea 1 ·/

q ~ .. and p h

re-

atricted to the range /P/<27 • · For p ~· 27 an alarm print oocura,

F'o~ p ~ -27 both p and q
V

Ilre . . t equal to Jero.

Loading
A lOader routine 11 included in the FLIP .y.teJl to. trand'er n.IP

and lueh of its Bubroutinee .. are Uled, into IS.

It u.ea ES .oell.

00000 to 00006, 0<><:l40 to. 00121 and 01477 to. Olm.

FLIP operaiiea

are o.f two ·type., buie' code o.peration. and .ubroutine operation••
I

The eoi:1er mUat .pecU'y whioh · of the latter he 11 Ul1.nl!; and the.
·.emory location. of the subroutine •• . rhea. are apecified by para-

.
oell.

l!)eter word. 1n consecuti ....

atart1i1~ in cell

Tlle 'tint

00122.

tWo oetal digi ta of each .uolv..ord for. the 'operation oode.
last five octal



.ep~" ~t1p17 .

.,.a .

'epth·. 1'81'1&. . .ulUpl.,
,

-

" 'pt1n

au1t1pl~' ~~

"
"

, . ' ''''r • .. s ~ a ·

'. J

.· ·t.·

x
'1

1

. - '- ,0 . " ,\
f.

'. ' 7

.,

1.~'1" IUltlp17

'~ ' ....

_,-~~~' ''''t_1Y.IIW.l'~ ,

• • Ii.

f :S - ~ ..)',

. "

, '

~ · DJ~l_ ·

:

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

C O N S O L I DA T ED VU L T EE A I RCRAFT CORPORATION

... "' A L YS IS
PREPARED BY

C. "\1. SWift

SA"

5

PAGE

Ol f GO DIV I S IO N

REPOR T N O

ZJl...490

C H( CK ED BY

MODEL

1.11

RE I, I SE D BY

DATE

8/11/9t

(rLIP)
~l

(reT1.ed

R:-:"-x......"y,R

Diyide and

32
33

12/9/sL)
tran8~it

Divid.
R

?(.v+ x) ...

Accumula te D~Tide

R

3L

..

He~ative

35

replaoe Divi de

Rep:ative Divide and tra.nlrui t

36

-y~

37

R -(y.:. x) .. R

40

Countei ~l

jUll'lp}

If (oounter b n )

1..4

Counter b

jump ,

counter b

x

~

R

2

legat1Te Divide
Aocumulate negative divide

n

counter b

n

The contents of the counters are

add on. to

e.nd jump to ~' .

to ,ero and continue pre.ent

~.

floe. ting nu..m,ber ••

continue pre.,e~t sequenc~.
unchan~d

It not,set

(R) 11 une~ nged.

sequence.
lote,

< (x).

by opera t ion.

( n ) 11

Irx.-R
r •

.. jump may oocur •

.45

IhtTltr'''' Ab.ol\lte Va.l ue Threaho ld

JUillp

l(Rl.

I(x)\~

It

contln~

ol"uent · sequence.

uncha.n~d

jUIap
'ixedto Floating

~Y .

Cail

by operation.

It x

~

-R a

not occut.

,t'h&.

last·S

"

bit. of (y) ....
P ': and let

.correctly ,n ormali.•• c; .al1dp... c~ed repr ...

1 ,

, ••
n~tlon .ot ':q . x 2P '. in ft. • .
'. .,
:

"

~

4'

.. '

(y) ' ~Y'.~ l;Ie , .!!!:!~:"

. .'

"

51

(R) i l

<'~' x) @)!I' q., . whe~e,' \ q \< ~ l. ~" ~~~. t.M ·

, .'

'6t.. ':;'.

jump to y, Qthenrhe

'loat:1~ .to · Fi-xea: ·

'.

Ta~

,.

q' a.nd

.~ "

..

pt·. fro. the· tlo&till« Jlwibn

.4NAL YB'S

,~.4()E

CONSOLIDATI[D VULTEE A1RCAAI"T CORf"O".4T10 N

c.

~RE"ARtD BY

tI. lwih

....N

R £POAT NO

01&00 DIV"ION

CJiICKItO lilY

- ' MODEL.

,REVISED BY

' DATI[

(PLYP)

8/l1/~

12/9/54)

(reY1I'e d

51 (ooat) Pl.. ting to Pixed

6 ,'
",-490
All

ill I.

fake p fro. the 1... t 8 bi t. of

(x).

Store q

q.::.,'

X

@

1n y and R where

2P'-P

B. Subroutine Oper.. ttou
(I.. uparate pa~e. tor detail.)

40 '

(bu1e ood.)

41

(bali q code)

42

(bade code)

4,

Ctm"ert neuwr1ter 1np"" data.

L4

(bade oode)

45

(bade code)

50

Sq,." Root

51

(b..·l0 : ~od.)

52

Print OIl 'leQW'tlt.r

t

'

",

.

,j

53
,~

56

'Loc¥, "
fla. CU.

,57

'll...dCa:r~

•

"

60 '

Cojl1¥
". ';1 ,',' ','
t'~ .•,S ""

'

~' 6Q

,

,C'etaii;'l ' ~.

63

.~

.

,. '

",

.

~

~:

'.

"

"<'!..

.'

"

... "
"

l< ' . ': . ,
,',

, ,

10
,

I,
~

)

TT

.

,
"

'.

',' :~
,~,-

i'

':tr:ae •

'

•

~ :

.. > .
,

~

,

','Sat

61

<

';

' .f

:~

.

.:

'

~

....
.'::'

~.

,

.

~.

,:"'.
;-

,f"

:
'"

.

,
),.

..
I

•

!

• ...

~"

'.'

'""

···.f,,,···

"

f.

ANA LV.9 15

CQNS OU QATEO liULT£e: A IAC.V.... T CORPORAT'JON

C. J. Swift

,.RI:PAR£O Sf
CHaCKn~

"AM

Oll~

7

,.ACiI:

1»0490

",a.-olri . NO,

0,11 . .10..

!!IY

111

MODEL.

REVISI!:O BY

8/n/54

DATa

(rni .. cl 12~/54)

FLIP

Subroutine Speelt1. . t1ona

to.tart 1n cen 01000 and a.r.aod1t1ed by tlW

P'LIP subroutiae. are ooded

.... embly routine under oontrol of tbe FLIP l ...d.r routine.

laob ••broutine 1._

.... t~ed a command eode number.

I

Co--.nd Code Par... tet-

~

placed in dr\B looat'-OD

It

• OPe

-,

hu the tora.-

D.1.

11 '

o :z:
DrUJI addre.tr ot the .u})routlne

where D.!: -

~"\' III

' ~lIt1IIber

. , number ot cell. modified

n

II

ot oe11. oecupp1ed

Inrut Intormatica
At ' the entty to the .ubroutine, the
SMoad. OG t& i. I>1~lt

. 1

0
00005

(x)

00006

(y)

(x)

(a)

0

00007

(01734)

(x)

.(y)

(y)

0

y

y

20000

Cod • .

4.

5_•

.(xl

-(x)
,

.

;

0

7

' ';'(x) "

-(x)

..
",

.: J

r

""~'

1

(R)

0

0

'1 .

(1)

,

"

.

,

20000

.

6_
. . (1)

(I)

(y)

.-

.(R)

0

ot Co • Qd

~

2
(-x)

GOAt.in thi. intor.at1aa.

t . .porar1e.

~

20000
. -'0- -

.,

, 36 'bit. exteAl10a
.,

00010

of .exp~••,", fro.

36 -b1~; ... rt.~lon · o~ ~xP-~Dt
.

00111

(00005)
..'

(00006) ·

fro

•

~.

000l~

.

.,

. ,' R

"

....

_...... .

11

ud \" ~~lt"GU,

.

,

.

,

,1 ~.

..

,

.'-.: ..... '

' . .,

',

'~

. :

.

.

..,.
t'

'"

..... "

'. '(~~r~.i~~: ~~".~~, . ;.n.7t'tt7~ .:( .. ~~~. , . .. :.
.....
"

.

:~

z

fr ~y Uplil!tllt' - - ~r~i i~ ' hal beG tran'.to~ · ~

'

.~

"\

.

..

".,

,',

. -C~nd , Oo# ;·ln , 1a-.·-t ~~ o~tai di~t.~

10000

';

the

-',

36 b1t~xtenaio.: ot 'e~"t ·' ~_ '(00005) ;' ~
.

.

1a

'lxeou&~oa addr~"~" , x ..cd y

".

'~

. . .'

"

..

·000000000Il00·

.~J

-

•

ANALYSIS

CONSOLI DATED V U LTE:E' AIRCRAFT CORPORATION

...

PREPARED BY

8

PA(iE

SAN O'I:G O 0 1"''' ' 0 101

REPORT NO

Z).!...J l 90

CHECKED BY

MODEL

All

REVISED BY

OATE

&/11/54

FLIP
tIl

{rev i e e d

12/9/ 54 >

Ext t Informa t 1 on

Subrou ti ne exits !l.re t o 01607, 01721,01731..., 017 35 or'
fl.

Exit at OL07.

1' .

EJ\:it a t

!S hou l d

01721.

Pl&C'~ zero 1n.fi&r.d

1':0

0173L

lo

q

e

o

@

1n

I n tr.i e c&se t.h e sub ro u tine

0dX~5

in 0(0 10

Where th e des i red result i s q

' . 2P • l_llnd.r. f':1.a y be

It :').'-'

The routi ·~ will nf" r ' al i le, test, na('~ int ' P. ', and

n u;:b e ra.

below)

(lI f' e

Nor:rAHt~, t<' € t. pack l1'"1 d r tor e .

leav~: '

7wL5.

pouible 3v 'bi t
'"0

t o 017 31 . •

:o.: x i t a t 91731. , 0173 tj or 01737

c.

[OO'

., .,-",::or:,

~. ·k

.x, . .

.JJ... ..., 1'11\..

... -ta."
~.'r~)(

\

Sex 4

\

" .

"k,'., .

Sc~. r~f.~ ~ ·t'

x,j·.. X: .

~

~~>~7,.

J.

"f h--+)C
l-t&)l .. ~~)(

•

~\,J

~~

~ ~

~ ~

>-

}~

Ilol

<)

~ 0 II
till 0
¥

.J L U •
eww~
Z I: :z: .
• LUI:

-

~~

f'

'.

'.'

I

"t-

u•

...

,.

s.)( +R~)(

:

. .'

~' l1-'t,~", t,~:., ~

J-. ~

~

t •• ';'~/~

.

,.tl~ )"_. ,,~~,,~

~

•

'"

tl~~

~- e

)(

.... )C

"

.

. III

...

')(

I

~ ~

,

) I

S".x-'~ ,...,~._ I

.,

0

..

I

-1

Ie •
-

)I . . l(. $c~

t---~W

1"-<'" ).) '><.Jl
..... ~

I

•

ANALYSI.
.. fltEP ... ,U;O 8Y

c.

CONSOUOAT..I[O VULl'&1l AJRCR ... "T COR~RAnON

J. Switt

10

PAQIl

ZM-490

RIlJllOJitT NO
MOOIlL

.AN DlhICS' DIYI.ION

CHECKED BY

fIt£VISED BY

All
8/l1/~

DATil

(r.,.ile4 12/9/~ )

FLIP

FLIP 8TOltAGI LOC.lTIOI8

Subroutine

l\aber

.r

Code
IuI1ber

DrUII
Addreu

Word.
Con.tant.l, ......bly
Routae

72

40

Buia Cod.

193

14T1

8wbroutiD. Part.lleter. /.

tIJ .

- 1704

J.oader

61

76~5

01537

17

76553

(01000)

26

76521

(Ol0(0)

31

7~62

(01000)

56

, 71262

(01000)

77260

(01000)

76000

(76000)

71'~

(01000)

me;..

(OlOOO)

2

17452

(01000)

18

,76,00 ,

(01000)

,S.,are Root
Trace

•

~'

PRln

~

. ,

'lexGWriter Iaput
COIrAr.101t

'. " 76414
,Pro.... !race

n~ '
,'

"

.
\

'

16414 '

~.

..

,

..

'~

,

OOU1

" 76~

(01001)

'16'56

(.1000)

...

.

"
'

.

J

"

.!

'"
"

............ _.
\ t ....

"

.

\

1

•

CO"'SOLIOAT~O VULT££ AI"C"A'-" COIlt"ORATlON

11

PAGE

....... 01£00 0""'5 ' ON

RE POR T N 0

ZIf.-49<

MODE L

All

DATE

1'::/1r:;/54

Loader

..

76575

01537

11 76655 OOOOQ

7~576

01540

75 30061 01615

76577

01541

11 76600 01542

-76600

D1542

75 30062 01544

76601

01?4~

11 77716 00040

76602

01544

11 0012 '

3

Requ1.1tion parnm9ter Pi

76603

01-545

11 0000

4

ft

76604

01546

31 00004 00017

76605

01547

11 20000 '00005

76606

01550

55 00003 00026

76607

01551

11 01621 10000

Ilui:

76610

01552

53 00Q.03 01554

Set order J

76611

0155~

75 ' 30002 01555 }

76612

01554 ' 11' 0~0~00006

76613

01555

76614

.01556 16 . 0900.4 01576

76615

01557 . 55 00006 00011

76616

01560 : 31 00005 00071

76617

01561
..

52

76620

01562

47 0156301601

76621

01563 . 55'· 00006 00'014 . (

.: 76622

... k

.J .

}

~

~

~

~d

Aaaembly to ES

th
,.

.....,e

(Pi)

.......

OP

~· e

~

( t

)
5
~

(t )

3

q

"requiai tion subroutine Fllrametera

Requhi tion S~.r.o'!.~~ ~ e Parametea Pi', P2

.

ot62~. .

Transfer Conltante

1.

15 00006 01576 }

""

Transfer loader to ES

Se t order, "ir~ns fer

!I

ubroutine t~ ES't

Place parametet'
f -; r &sserubly r.outioe ·
, .

00122
Ie this th,.

tflrmina~lort fla~?

\,

.01S€?4 : 11 .01577 ~Oooor'

Set repeat order t

·rr..n~ fer .lsbr~~t1ne

to U·

j

01565 ' . ,2 .Q1621-:01575
'/ ...
:
."..,:
.
76624 . .01566 . ,t6 Ol)'Oor 01571' .'

76623 ..

..

:

•

"

. .. o1.~i.' ·55 00007 00025 "
,
"' . '
..
.
'. ' . , 766~6. '. ',.:' 01570 ',1.0 '10000 01572

,'<

-

.

•

.

'.....,',':' '.:. : ~ ~ 766~_t~:< ·:· ~5'~i ~.·:~~'· ~~'4.[3QoO?J·
'; ... - ,

.

I

"

..

:',

. .

.

" Set

~

'

".

"

" .... ' .... -....-'::j.......::'~'.

-

•

166~5

'-:.

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.:"'.'

.ubrout!!'l~ r.~nenc..
"

' 111

sUle C.

.,

CON.Ol.I~AT£O VULT££

A I "CI'tAI"T tOA"OI't"TION

."Ioi Olf:QO

R

p O W', , '

M O Ot

D ATE

~ooog

01572. 15 00005

76631

01573

76632

0157'

76633

01575 [77 77177 777771}
01576 11 @OOOO 00000]

Transfer Subroutine t o ES

01577

75 30000 01544

Prototype order for

76636

01600

00 00000 00000

· Parameter for leTO subroutine"

76637

01601 '11 01620 01774

76640

n1602

11 01617 00001

76641

01603

11 01622 00002

76642

01604

37 00101 00100

76643

01605

75 10003 01607 } .

76644

01606

11 QP040 '01775

76645

01607

75 30275 01774 }

16646

01610 .11 i6755 0114 17

76647

016i1

75 30222
01776
•

76650

01612

11 77027 01551

76651

01613

75 30236 . 01776 '

76652

01614 . 11 77014 91536

76653

01615

75 30074 01542

76654

. 01616

1176661 01704

76655.

-01617 .45 OOQOO 01624

, 7,6656

01620 , 56 '00000 00010

21 01544 00073}
21 01561 00074

,

Step to next subroutine

-

.

01575

obsoleto order
Kod~ fy

subroutines

Clear FLIP temporaries

Tr~sf.r

in Ba.ic (LIP

"

Obsolete

-

Trans f er Subroutine parameters to ES

, (J.)
·2 ·
Exit' order tor· }oader
".

01621 ': 00 00177 ' 00000 ,

76660

' 01622 . 45 00000 76761 .

. E~traotor
",

obi olete

order

zw-.49C

111
1n 115/?lJ

ir e1-1" ..::, bI,1

. ~ 11~o '01m

.' ~.,

Oi'56~ ,4,' 00000 01605

~ 'b~

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TTO" ' ' oi~ ' i6
17IJio'
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jqp

to·~o 3"'. ,

01~ 0s.n6 "' }' '"

~(~, ~ O1m

~.

~ ~ .~~" 00000 017)~.. .

" '

co"-ud

J 40' coaau"

~ ,,' Ol~' 42 0001- 0160R
, ~

b-490

M O DEL

.:\

12/14/54

"<

.~'"

i

f

'

, .,.

t:"

CONSOLIDATED IIULTEE A I R C RAFT CO RPORATIO"l
SAN OI(GO D IVI S IO N

1..7

PI"'GE..

,

All
lo/15/~

MO DEL
D A TE

7704'r

01571

77050

01572

16 01734 00012}
16 01736 0173 4

77 051

01573

16 00012 01736

77052

01574 , 23 20000 00011

77053

01575

46 01602 01576

If

77054

01576

47 01603 01577

I f , 1S,eX

77055

01577

12 00005 00005'

77056

01600

12 00006 20000

77057

01601

42 00005 01603

,ty I ~R
If lx \ >\ T '1

1'7060

01602

16' ,01734

Chug_ ,xit

77061

01603

11 01774 20000 '

77062

01604

45 00090 01735

77063
77064

23 20000 00011
01606 " 42 00056 01611

77065

01607

77066

01610 ,45 00000 0173-

77067

01611

46 , 01r'37 01612

77070

01612

13 20000 .' 20000 .

77.071

01613

35 ' 01773

Interchanr. y ..nd Exit

.eX-.cY ~

41 c~d

jump to 1602

'7 ICY)

jump to

1603

~ I'

111

01736

\

\1 6 , command

R

~ .eX ,

!C!

, jUIllp to lW3

~~ ' R
Exit

01605

~

p .. pi

R

jump to 1611

11 00046 20000

Clea.r

a~wer

Exit

-

it

< o.
-> R

p - pt

' p' .. p,

o16l~

Set order I

jump t ~ ~

pf
2 P- -_ ,

0

q

'.

~

77072

,01'614 '54 00006 00110

7707l

01615 '45

77074

01616

q • 2 P- P '..., q

oooqo 0113'4 '

"

y..., B

11 00006, qooo7 .

..

,.

, Exit ,

t"pi'

o rd ~ r.

4

\

1707 5

01'617

77.076

01620

77077

01,621 ' 54 00011' 00054 '

,77100

01622 ,11 0177'4 00006

77101

01623 , 4-5, 00000 .oi7~~ "

31 01774 9003,4

.

I

\

I

"

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;

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20000 ,00011

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77103

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.

18

P,-.uf

, SA ... O'I:GO DIV I SION

RtP U Al

P\j L~

All

~ ODEL

10/15/:;....

D ATE

71105

01627

17106

.()163Q

35 01766 01631

71107

01631

11 [00000] 10000

77110

01632

75' 30004 01634

77111

01633

51 01761 00004

77112

01634

3~ 00007

31 00000.' 00017
,

72 00005 01777

77114

54 20000 00001

--.
b2

01637

77U6

01640 , 73 01765 10000

71117

01641

16 10000 01652

77120

01642

55 10000 00017'

77121

01643

11 10000 00013

77122

01644

S4 20000 00075

17123
.
7712-

01645 ' 16 ,20000 017 3~,
01646

16 20000 00013' :-

77125

01647

16 20000 01655

-17126

01650 75 10003 01652 . }

77127

.01651.', 11 00040 00005

'\ 71133

.-,

..,. ' t5 1
~

4ddressei

t6 J

Ba.i~

Address ••

Put Execution
Pr••• t

o

~OOO5 pOOog'

47 01655 0165,,
' 01654' 11 ' 01770 00005
01655 ~'1 00'0 ?6
" ,

•

I

Addre8 ~ ea

, PIckUp and Store

iato

~13

order.

1 .. T and B

(x) ~

1.

OtX
2" 1 55 , ~ ~

ooo,oq' "

.01656 ',: =1&7 01660 01957 , .'
<-

~

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' 01653

•

b 1. indicators

.

01652 r [21

•

q

72 00006 01776

'

-77132

~I

indic~tor.

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71115

77131

:>

Iutructlon

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77113 '

71130

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,

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,

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-19

P*OFf~TtON,

;- S"""'"

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O'£GO O h.~4): I~J "4

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77 235

01757

11 :00040 00007

o~

77236

017 60

45 00000 01701

Jump to ADD

77-Z37

01761

00 ' 77000 00000

77240

C' 1 762

00 002{)0 02000

77241

01763

00 00400 0400.0

77242

, 01764

77243

017~5

00 00400'00000

1'7244

01766

10 77777 ,1 0000

77245.-

01767 ' 54 ' OOOO~' OO107

7724()

01770

00 00000 00200

7724.7

017 71

71 77777 77600

77250

01772

77" 77777 77400-

7~251. ,

0177 3 ' 54 00006 00110

'00

2." - " ')(

ll'

M~C.' r:.

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l) 4, H

1" 'l :'. /;J-l

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00177 ' 717'77

01631

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22
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76000

76000

4, 00000 ~OOOO

76 02.~

7602~

76001

76001 . 45 00000 76024

7602~

76024' 16 76031 760 W .

76002

'7 760,0 76025

7602~

76025 11 20000

()()(){)4.

76003

31 76000 00017

76026

76026 .

~

20000

{)()()44

76oo~

76027

76027 11 20000

~

76030

760:~0

30000

760'1

.760'1 00

00000 76006

76032

760,2

U

~7

00006

760~n

760"

61 00000

~4

760~

760~

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7603'

7603"
..
.'

51 00067 20000 .

76036

'5 0004,2 760 37, .

76004

76004

76~

7600, U 30000 76000

76006

76006 11 7604} 00006

76007

76007

76010

76010 61 00000

760U

76011 41 00006 76007

76012

76012 l' ' oOo~ , 20000 •

•

l' 20000

,~

,

76042 00006
7~2

56

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4,

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10000 0000,
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7601.3

76013

'2 76000 0002,

,'.- 76036

7601~

7601- 11 20000 10000

760~1

760'7 00 OOOQO 00000

7601,

7601.5

U 00044 00006

76040

76040 41 00006

76016

76016

~7 7604t'· 760"

76~1

7604; . 4, 00000 30000 , .

76042

16042 -5 ~~ ' Oi207

16017 . - 76017 11

...

76020

.76021

76020

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37 76~1, 760,?

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.

~

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.

.
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76044 .

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"'s ..... D ' ''~<) O'''11HO ....

0" T

lliPl ' ! SW' CqfjCK for f'LIP

76414

•

51 00000 00000

Halt

oooooJ

76<.1'

7641, [00 00000

7f>416

76416

'U 40000 00000

7~11

16417

2, 10000 10000

76420

70.201'22000

76421

704 21

~2

76422

7b4~

~ 7641' 10000

7042~

7642~

2, 10000 7641'

76425

7642,

7' 10012 7~ 31

76426

76426

61 00000 764}4

16427

7tJ.+27

7' 100t2 7~141 '

BUll
76000

764~0

764 30 61 00000

764~6

76451

76431 " 16 7~"

40000,

764'2

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7~'3

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764,.

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764),

764 ~,

00 00000 0004 7

76436

764 }6

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7~40

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S

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76'7'

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'.

.

Print "N" 00"

•• t orrler
Halt
a.Jdreaa

FLE:XOWRITER

12/11./54

CONSOLl 'OATEO IIULTEE AIRCRAFT CORPORATION
,
SA'" OI~GO OrV1510 ..

.H E p~

M l 1rl.l

..
764-,

. 76445

76446

76446

00 00000

()()()4,

76447

76i447

00, 00000

00047

764,0

76450

00

764'1

761+'1 00 00000 00006'

764~

76452 ' 00 .00000 0000,

164" '

764,~

00 00000 00004

764~

76454

00 00000 0001'

76455

76455

00 00000 OOOO}

76456

76456

OQ 00000 00002

, 761+57

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OOOOO()()()()2

76457 00 00000 000'7

40000

45 00000

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MODE L

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FLIP
Flexowriter Input Conversi ': n RQut1ne
Command Codel

43

Numrer of Cella.

58

I

De;scription
-This cO!'IIM.nd

con~er t l! '

a twr-wor d inpv.t rl!tpreeentation of a .numberto tnt

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.

.

worde are (x) a r: d ~-r 1).

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character ' (' Od,tH.

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10

p' .
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the5e flexnwritercharactere arf.n .'

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3 4. 5 6

7

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9

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S. L. ?clhck

.....

. PAGE

OI[G() 01 111&10"-

c:,O-l '

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...

.H l

MODEl

REVISED BY

DATE

llils/ :;i.

FLIP
~in~ ~na

Sine ~ommand ~odel
Cosine Command

~ubrout\ne

60

Code.

61

Number of Cells,

I

Coeine

51

DelScript10n
'!'helle two eOmRlands cOl'!:pute the sine or cosine of (x) and store it in

A polYDoaial a pproximation i. U8~d(l) which rives a maxim~ .Tror

y and R.

of the order ot

FOor ar-~nt8 10 lar,a that the rO\mdoff error

... 5 • 10-9.

of the ar~nt obacur~. the result, an alar-m halt occUT.S.

If the cosine

\

au~:rout.i ntf] h

uaed, the aine sub routine mU15t also be .peeified tothe loader,

and i f the loop-ticn of the-f1rH cell of the cosine lubroutfne h .y,that of th •
• 1ne

lubrouti~e

must be y

~

2.

'-

"

",'

"

-

"
--....

.

.'

-

'

.. . -

(1) . Se• •he.t

<

-- ~ ...~

-.

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,~

..',

.

~,'

';:"

'14. · ·ipp.ri~_ti?~~·: in:: '.tiC:al b&lj.ia(/·"~ ~,~~b~~,~~~forl
.,: Rind, . c.<>.rp.oTCttioll

'.". ," : r -

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.

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.

ANAVI'SIS

CONSOLIDATED VULTE£ AIRCRAF"T CORPORATION

PRr,.,.,RED 8'1'

C. J. Swift

C HECK ED BY!:.

.... '1

c,\..-;,

PAGE.,

o,iGO DIVIS.O",

REPOI'H"'O

L. ! clltlck

... OOEL

RE vI SED BY

11/1"';/::.

DATF

Sine

60

~nd

Co.ine Subroutin&

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0 ... ,

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7671 7

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be SUre ' SliBR(tUTINR
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CONSOLIDATEO VULTEE AIRCRA FT CORPORATION

PREPAR~D BY

CH E C KED BY

P.e,Gf

C. J . :' IY,i t t
:; . I. ! o;bdc:

62-1

REPORT "10,

MODEL:

R£V1 S£ D HY

DAif

11

...

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Aro ran..-ent and A;c Coblln~ent Suhroutin,e

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These, two

~ompllte tan~1X

C

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i!Tl8tion is
$

1/2

10 -7' •

o reot-l X and ' t>tore the result in yt.nd

(l)
"

Tb e error h o f the order of

cotAne-ent!lubrouti'ne 'is u~e-d. ~e Ilf c hnp'l'tnt subroutine

If

.'Tlust flls o bf' f'lClec1fied t o t he loader, "nd if th~

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~

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20000 0Q006

76}16

11

Scx..;l

I

~12/14/54

•

Subroutine

76'00

()()()4

62-3.

RL' )\' ~Q 1 ''< ~ . ZII-L90

20000 00046 ,

76}22 .

01022 ,

76,2,

0102, }, [01044JOOO1"

7634'

; 01~'

76}46

0104-6

76 ~'76 110"

°11

76}l47 '

01041

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12/1.4/54

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27.

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00 ~61" ,~6,

76,~

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76"1

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13 .}U6

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010,2 6,

76,,}

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76}~

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10166

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':::ONS0LiOAT!O VULTEE A tRC RAJFT CO RPOIitATION

PIltr:PARtO 8 V

C. J. Swift

-

Cl lGe olv.ato...

. AN

70-1

"Avl:

tw-L90

REPO R l'" NO

CHECKEO BY

~1l

MOOEL

IItEVISI!:O BY

11/15/ 54
---,

OATI:

nIP
Exponential Subroutine

Co

ad Code.

70

JluJrber of Celli 1 25
I

De~arl,tiOil

'l"hh oGIf'.!lIlnd cOl!lP",te. the exponential

ot

(x) and . it~.

Full aoouraoy i . obtained by a power .eri...
alara halt ocour..
II

it 1n

For Talues nf (x )

~

it

&lid R.

64.

an

.-x 1. obtainec by c~~ut1ng .+x and reoip reoat1 n&'

'low ChArt

•

- --------....
'1-'/0

_

"' ~- r --- .
~--,
!

AI.-A R. .A.f

!

1'-·
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L.:Ii____

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01001

3~

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x -, A

01003

44 01004 01030

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01005

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BC'X

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0101~

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76"37'5

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76'76

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)

76400

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76401

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7640e

00022

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76403

dOO23 [U 00027 20000]

0000,

7

-7'

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0

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l e~porBry

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preset variable.

x,O

76370

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16410

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47 01607 1604,

+tr -, S.R

1'7'/81
s -"

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R

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ahift addrel.e •• EXIT

1-

•

1/. --.,. R
XtO

.
• .• -,,-"-..r

12/11./~

ANALYSIS

CONSOLJ DATI:O VUL..TI:I AIAC"AFT CO",.O'UT10N

"REPAAtO BY
CHECKI:D BY
fIt~I.I{D

C. J. Swift
S. 1-'o l1aok

PAQI:
MODEL

BY

77-1
l.-4~

ptl:l"'OfitT NO

....... DICGO PIYI.ION

DATI:

All

11/12/9..

Trace Subroutine

77

Comman d Codes
Numb~r

I

of Cells, 26

Delcr1ption
The trace rou ti'l e operates in

with the

runnin ~

Tape 2 (1.'12).

of ·the

r ~utin e

',WO

r-ei' r,

phases.
teet~d

Phase I

and

I

opera t~6

concurrently

tores information on

lla~.t1o

Phase II opf'ra tee eep!iTlltely f'rom t he routine b ei.n~ te.ted.

It

the information which was stored by Phase I on 1lT2, proceeses it and

r~&d.

p,. nchea a paper tape output. ' The con tent of 3S _111 t. autolll6tioll lly restored

after this phase.
II

Phase I

:-he traee subroutine mu.t be .pecified to the loade!'".
for this purpose · is 77. ' It requires· 2b cell ••
whenever MJl is on.

ce 11s 7L.000 to

When loaded, it will operate

'The MJ instruction is in cell 01735.

7L.oL,1 as

It. "c ~mt'\and cod."

This subroutine use.

tempora·des.

II I Phase 2
This operation ~es ·the ;;:S a nd cell

completed.
1.

Its operatint

in8tructi ~ n.

Set PAl to 77f::1Jo.

L.oooo

but will restore- ' oth when

ares . -

Preas Start.

The 1103 prints ·out ." Rewind

UT2- and hal ts.
2.

After rewindin.; MT2, .... rt.

(if PAl waS disturbed, set it to L.OOOO).

The routine will search t he tape for t he data, t hell process it one
block at a ti &". e. · The 'lutput is punched

011

paper1;npe.

The end of

data will be apparent ...men t he routi ne .earches Mr2 wi ttiout punchint. p.per.

' 3.
;

...... -.

",....

')

~

tape.

Halt,~

.

To continue the pro,; lem, set PAX toLlOOOO and I!Itart. The il03 wi H
. . .. .
rutore ES ..nd4 ~, 00 and halt with a 50 0()()90 40000 oomltland.

A ... A LYS..

,.",alr

CON$C UOATr:O \(UL Ti:E AIRCRAfI'T CO"P'O"ATION

&wi ft
S. r ollack

,.'UJI'AREO.... C. J.
CHECKEO.V

"II~," NO

.AN olaeJO O I V'.IOH

MOO!:1..

"("V'SI:O S':

IT

DAn:

77-2

Zll-L90
All
1l/12/~

Output

32

The tra ce routine output prints a

di t'"it 11ne for each FLIP ina t ruction.

If a jump occurs, either an erroneous line appear. or no line a.t a11 •
FLIP subroutine

include FLIp

OOMmAnds

ba. ~ ic

commands • . Theae will appear aa

extra lines before t he FLIP lubroutine oOnlJUnd line.
AAAA

OP

xxxx

yyyy

.... q.qqqqqq

The linea 'have the fonal _

. :t pp .

of the .addreu ot the

four ' di~its

where A.AAA is the lut

.;)ome

Inat~1on.

,op 18 the oOl!llDlU1d code.

xxxx is . t),Ut basic x .. 4)1relll.

YY'YY is the bade y. _ddr.sa.

tom,

The reeult of the operation, "In flo'a.tinr, decimal

1 ,

'q

1n R.

<. 10

0

1i

CI

•

lOP Where

Some of the FLIP ·.ub rout·l~e ecananda do not leave their reiult .

For .the.!ut. the r:esult. q. lOP

nil

beerroneoua·.

1.n order to avoid con1'ueioll when several probleM are traoed uai-ng the
aame ma~etle tape, ~ha!e II overwrite. the trace information •• it 1 •
. proceued.

.

.

.

,

.

>.

.~

. , .'.

.•: ' .

~

.......

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CON SOLIDATED VULTE! AIRCRAFT CORPOAATION

""I A ~,( Srs

PREPARED B Y

oJ • •1lIfi!'t

' .

C HE C KED 8'1'

PAG£

5"" OI FG O 01V 1510"

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DATE

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11/12/9:

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O"'i

~t(H~ 1 ... 0.,« g"",,'h-r,1ECfSED BY

S. L. Follack

CONSOLIDATED "tiL TEE: 'AIR C RAFT CoRPORATiON
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A MAGNETIC TAPE INTERPRETIVE ROUTINE
"TAPEWORM"

Dgscription
"Tapeworm" is a routine for controlling the operation of the
Uniservos on the Univac Scientific, Model 110)A. It is an
interpretive routine which permits a programmer to s~ ecify
with a single Interpret instruction a read, write, move, or
revind operation. This routine includes provision for rereading a block in case of a parity check failure and automa tic selection of the writing mode according to the
peripheral equipment for vhich the tape is intended.

Form of the Interpret Instruction
Use of the Inte~ret instruction provides a convenient means
of referencing magnetic tape subroutines. Because of the
availability of 10 octal digits in the instruction for the
storage of parameters, any of the Uniservo operations may be
specified with a single vord. The form of the Interpret
instruction for the operations of reading, vriting, moving and
rewinding is given belovo Here each character represents an
octal digit of the instruotion.

'-

a.

IP

OP -B UU SSSS for reading tape

b.

IP

OP LIB

un

c.

IP

OP

UU BBBB for moving tape

d.

IP

OP

~-

SSSS

for vri ting tape

for rewinding tape

UU

These Interpret instructions specify magnetic tape operations
as follovs,
a.

Reading Tape:

OP -B UU SSSS

IP

IP = .14

OP

= 01

For reading foreward

=0,

For reading backward

B=

UU=
SSSS

=

the number of blocks (not words)
to be read
the Uniservo involved
the address in Rapid Access
Storage of the first cell to be
read into

A MAGNETIC TAPE INTERPRETIVE ROUTINE "TAPEWORM"

b.

liri tipg Tape J IP OP Ll B UU SSSS

IP = 14
OP

=03
the code number as given below of
the peripheral equipment for which
the tape is intended

B

~

00=
SSSS

=

the number of blocks (not words)
to be ",ritten
the Unieervo involved
the address !p. Rapid Access Storage of the first cell to be read
from

The following code numbers are used for.4,
= 0 1103 A internal

6.

=1 High Speed Printer
= 2 Uniprinter
= 3 Magnetic Tape-to-Punohed-Card Converter
=4 Unitape-to-Teletape Converter
= 5 Unitape Transmission

Tgpes prepared for the Uni tape-to-Teletape
Converter may be used for Unitape Transmission
aDd oonversely. Any tapas may be read into
the ll03A.
o.

Hoving Tape: IP OP -

UU BBBB

IP=14

OP

=02

for moving foreward

= 06 for moving backward
00=

BBB&=

the Uniservo involved
the number of blocks to be moved

2

A MAGNETIC TAPE INTERPRETIVE ROUTINE "TAPEWORW'

d.

Rewinding:

IP OP

4_

UU

-

IP

::

14

OP

::

04

Ll

=

1

if interlock is desired

=

0

if interlock is not desired

UU

=

the Uniservo involved

Digits denoted by a dash may be filled with anything. A maximum of seven blocks may be written or ~ with a single
Interpret instruction but the tape may be ~ as many as
7777 blocks. Note that the block number for moving is in a
different position than the block number for reading or writing.
In reading baokward, the first word goes into SSSS and the

second into address~ - lJ in reading foreward the seoond
word goes into address SSSS + 1.

Reread
After a block is read from magnetic tape, the contents of lOA
are exrunined to see if a parity check failure has occurred. If
there is no failure, the next block is read in without stopping
the tape. If there is a failure, the reread subroutine is
entered. This subroutine performs successive rereads of the
block, reversing the direction of the read after each failure.
In case the direction of the original read is foreward, the
rereads are performed in the following sequenoea

1.

read backward, normal bias

2.

read foreward, high bias

.3.

read baokward, high bias

4. read foreward, low bias
5.

read baokward, low bias

After each reread, the parity check indicator is tested. If
the reread has been successful, the tape i6 positioned at the
end of the block, the bias returned to normal, and the next
blook read. If a reread fails, the next reread in the sequenoe
is performed. Should the entire sequence be executed without
asuocessfUl reading of the block, the oomputer is stopped. A
restart of the computer will oontinue with the reading of the
next block.

.3

A MAGNETIC TAPE INTERPRETIVE ROUTINE "TAPEWORM"

References to Tapeworm
When an Interpret instruction at address y is executed, y + 1
is inserted in the U-address of
and the next instruction is
obtained fram
must contain a manual Jump instruction
which provides the exit from Tapeworm to the next instruction
of the main program at address y + 1. '2 must contain a manual
Jump to the entrance of Tapeworm.

'1

'2. '1

The first eight instructions of Tapeworm detect whether an
Interpret instruction is referring to this magnetic tape interpretive routine or to some other interpretive routine used by
the same program. With the Interpret instruction of the form
IP

OP

XXXI XXXI,

if 00 < OP < 07 it is assumed the Interpret instruction refers to
Tapeworm. Two en ts are provided, one for OP
00 and the
other for OP? 07. If a program refers to interpretive routines
other than Tapeworm, these en ts may lead to the other interpretive routines • . If' no other interpretive routines are used,
the first eight instructions of Tapeworm may be omitted.

=

Location
Tapeworm occupies 14910 cells of Rapid Access Storage. Of
these, the parity check test and reread routine occupy 5010
cells; 8 cells are used to determine if an Interpret instruction refers to Tapeworm.

'Speed
For a reading or writing operation there is approximately one
millisecond between execution of the Interpret instruotion
which specifies the Uniservo operation and the External Function
instruction which initiates the. operation. This time is increased to 1.25 milliseconds if it is necessary to identify the
interpretive routine being referred to.

If absolute addresses are assigned to TapelolOrm, starting with
bl
01000, it is assembly modifiable.

=

In case Tapeworm is interrupted during operation, it must be
again transferred into Rapid Acoess Storage in order to operate

4 ·

A MAGNETIC TAPE INTERPRETIVE ROUTINE "TAPEWORM"

correctly the next time it is used. If Tapeworm stops after an
unsuccessful reread, it will reset itself if and only if it is
restarted wi thout any changes in the computer controls.

'-

5

f ~~~ ~~t ~~~-IA·
( "fi IOH

0)

..

'\

'--

I

~

I .... CIl' ..... RO

'

r---MO Y E

uu + stU
{ OR

TAPE:

F"OR1... RO

.ua l

REW : HQ

-.V,

V,

Cl.E .. R

OR
.. HO

a lTS

I"

10

sn

H IO

SET

1'1 11

FOR

JU MP ...... P9
FOIit

JUM,. ....... P I 3
5£T

I'll

PATTE""

FOIit

IN

Y!5

JUMP ...... PI

SET HIO FO,.
JU MP -+H3

SfT H II 'Oft
JU IIIP ___

,n

5£T MI FOft
.IUIII,. --.. PI

sn

1'110 FOR
JUIIIP ---.. 1'13

SET
1'1 11
FO"
JU MP --+ 113

'(1
H'
JUM"_

OP
01 02 03 04 05 06 -

CODES :
READ FDRWARD
MOVE FO RWARD
WRITE
REWIND
READ BACK
MOVE BACK

FOR

p,

KEY

VALUES OF 0 :

ABBREV IAT IONS ·

o

F I - ADDRESS 00000
F2 -ADDRESS
00001 (JU MP TO STA RT OF THIS PROGRAM )
PF - PREVIOUS FA ILURE
OP - DPERAT ION CODE
( H.)v - CO NTENTS OF V- ADDRESS AT ADDRESS H.

I
2
3
4
5

1I03 A INTERNAL
HIGH SPEED PRINTER
UNIPRINTER
TAPE TO CARD CONVERTER
UNITAPE - TELETYPE CONVERTER
UNITAPE TRANSMISSION

[-~

REMINDER FLAG

MAGNETIC TAPE INTERPRETIVE ROUTINE
"TAPEWORM"

I

I

( I

)

OPERATION

DEC.ISION ( JUMP )

8

@)

CON NECTOR

REFEREN CED CONNECTOR

I

Page 1

MAGBETIC TAPE IBTERPRETIVE ROtrrDfE
'l'apewona

REGION

REGIONAL

IHSTRtmION

ADDRESS

Resion B.
b1
Selects
Uniservo
Interpretive
Routine
b2

d1

left shift 15

0

17

36

c1

a

15

a

b2

address of IP

11[

yJ

vi

IP instruction

-?

vi

a

IP instruction

~

a

11

vi

42

c2 exit 1

42

c3

d1

exit 2

45

Resion D.
Set
Parameters,
Select
thiservo
Operation

IP instruction -7 AI

31

subtract 1 f'rom u-address

}

~

u of b2

Uniservo instruction? yes ~
too small

-7

exit 1

too large

~

exit 2

mask

q

d1

11

c4

q

53

vi

v2

11

c5

q

mask

53

v2

h4

ssss

55

vi

34

Right shift

IP by 8

53

c6

v2

OP code -7

v2

55

vi

21

2nd octal dig1t of OP code to left end

44

d2

vi

Back or rewind ? yes
no

~

uu + ssss ( or bbbb) '7

-7

v2

q

~

v address for EW or ER

d2

d1

d3

Read back or rewind
Move back
d1
~

d3

r1

d4

Read back ~ r1
Rewind ~ . d4

-7

d2

-7

vi

~

d3

Page 2

MAGlETlC TAPE Drl'ERPRETIVE ROUrINE
Tapeworm

RmlON

IBSTRUCTlOH

RmlONAL
ADDRESS

11

c8

vi

55

q

2

44

d5

d6

. d5

55

vi

1

d6

55

c6 q

40

53

v2

vi

31

c1

20

35

vi

v2

d4

d7

17

Rewind digit

}

lnterlock~

Set lOB i!~ --

vi

~

yes

~

d5

no -7

d6

lOB e3 for rewind
with interlock

}

Insert uu

}

Rewind lOB word -7

v2

v2

Oniservo selection for move and
rewind

15

c9

v2

Clear digits inv2

45

0

f1

Exit

r2

Move forevard or write
Read toreward - )
r2

d7

Write ~ v3
Move foreward

Region W.
Set up to
write

wi

44

v2

44

w3

v3

11

c10

a

44

w4

w?

~

Bit pattern -7
Separate b.

54

a

45
w5
w6

44

20

v2

d7

a

6 .. 4 or 5 ~
~ "O-

w4

~

3-1

Left shift 16 (4 groups)

w9
w6

w7

6 - 2 or 3 ~
t:::. ,. 0 or 1 ~

a

10

Lef't shif't 8 (2 groups)

v6
v7

w4
w5

MAGBETIC TAPE INTERPRETIVE ROUTINE

Tapeworm

REGION

RroIOlW.

INSTRreTIOII

RPJIARKS
I

ADDRESS

v7

v8

54

a

v9

55

c6

53

a

'5

vi

51
47

hi

h2

6 -1

~

v8

~ .

~

v9

0

.I

v8

Region H.
Read / Write

44

q

1..

4

Lef't shif't

2

Set mask for write bits

group

v2

Write bits

11

Number of blocks ~

v add. of q

c7

vi

lIumber of blocks ~

vi

h2

h5

Read (write) 0 blocks ~ yes -7
no ~ h2

v2

Start tape writing (reading)

q

17

~

v2

23

vi

c9

Set index for 2nd IJ

h3

11

c11

v3

Set index for 1st IJ

h4

'tTJ10000

h5

[ ssss]

21

h4

v4

41

v3

h4

41

vi [

h31

23

vi

c9

[

h6

45

h7

76

h8

43

c9

h9

21

vi

hl.O

41

vi

h5

r4]
a

[

pi]

Write (read) 1 block

n blocks done? no

yes -7

h3 if writing
h 7 if reading

r4 if writing
h7 if reading

Fezity check
Yes -7

~

h9

OK?
no

pi if 1st failure
~
p2 if previous failure

c9

[

h3J

All blocks readr
no ~ h3 no previous failure
p9 previous failure
yes ~ h11

MAGBETIC TAPE IJr1'ERPRETIVE ROU'l'IltE

Tapeworm.

RmIOB

REGIONAL

IBSTRUCTIOIf

ADDRESS

All. blocks are read •
no previous t'ailure ~ r ~
previous t'ailure ~ p13

btl

45

r1

13

v4

r2

23

h4

21

h5

ci4

Insert Parity check

23

h6

c15

Set exit t'or Parity check

Region R.
Set up to
read

v4

r3

r4

EW'

ci~

21

h4

ci3

23

h5

ci4

21

h6

ci5

11

c9

v4

11

c12

45

t'1

~

ER:.

Go to read

hi

45

direct ion ot' read

Change

ER~

}

w

Remove Parity check
Reset direction index
Stop tape
Exit

Region p,
Parity-Error pi

21

hiO

ci6

Reread

21

h11

ci8

21

h8

c11

11

c19

v5

p2

ci2

11
1~

v4

v4

21

h4

v4

55

v4

q

22

Set exits t'rom ER

Reset bit t'ol1D&tion
stop tape
Change direction index

Line up

direction bit with

IOBI~

5

Page

MAGltE'l'IC TAPE IN'rERPRE"I'IVE ROU'l'IlIE

Tapeworm

REGION

REGIOHAL

mSTRUCTIOB

ADDRESS

23

v2

q

Change tape direction

21

vi

c9

Reset b10ck counter to

11

v5

q

Set bit sequence

11

c20

a

Bias change instruction

"-

p3

p8

p3

1

change

bias -..,.

p3

o not change bias

~

p6

1 10v and stop -7
o high -7 p6
1 stop ~ p11
o 10v ~ p5

o~~set

~

h10

a

p8

p4

p4

44

p11

p5

p5

35

c9

p7

p6

35

c9

p7

p7

17

(c21-1)

p8

17

v2

Start tape

v5

store parity check bit pattern

11

p9

p10

Modity p7

q

45

h3

17

c23

bias change

~or

Change bias

Reread

Set bias to normal) stop

23

h10

c16

23

h11

c18

23

h8

c17

11

v5

q

"-

p10

h9

13

v4

v4

55

v4

q 22

23

v2

q

21

v2

c24

Change (v2 )\ 37;

round

sea Ie down

Store results
Jump to exit
Instruction for round and scale
down

CODE

Error code into AR
ERROR

264767031361

D=24 , 290, 062, 513

o

8

&

A

MJ
8

234

FILL

SP

Reset

K odd, jump

I

RIFT

8

}

srOREIl

LT

81

K6··· K l ~Q5 -;· ;QO

65324

A=27, 349

,

..

LOCATION

OPERATION

u ADDRESS

v

ADDRESS

EXPLANATION

B2

B

114534644516

8=10, 291. 988, 814

B3

B

330657140271

C-=29 , 104, 062, 651

B4

B

23

B5

B

265011714640

B6

B

77

B7

B

200000000000

B8

B

377777777777

CODE

B

243512001001

STORE

0

0

FIlL

STORE 1

FILL

FILL

FILL

STORE2

FILL

FILL

FILL

STORE3

FILL

FILL

FILL

TJ constant
24, 296, 004, 000
Mask for sca Ie factor
34
2
235 - 1

PROGRAM WRITE-UP
1.

IDENTIFICATION

SINE x, STATED POINT
A. E. ROBERTS, JR., M. D. BERNICK - MARCH, 1956
REMINGTON RAND UNIVAC

2.

PURPOSE
Given x, this program computes Sine x .

. 3.

METOOD

a.

Accuracy

b.

Range of argument~

c.

Derivation is obtained from
1T

sin 2" x

= 1-2

Ixl'

232 < 271

1T

sin 2 "4 (x-l)
1T

Polynomial approximation for sin 4 n as a funct ion of
n
(_n)2 for -1::5 n::51 is derived from the Chebyshev expansion :
1T

(]"

sin 4x = 2

k~l (_l)k J2k-l (;) T2k - l (xl.

x is entered and multiplied by ;. so that

;x = y.

The routine then computes

1T'

sin 2Y = sin x.
4.

USAGE
a.

Calling Sequence - Standard.

b.

Control and results
The argument is to be placed in the accumulatorj the function will
be found in the accumulator upon completion of the routine.

The

routine also stores the argument in t+3 and t+4 and the function in
t+5.
c.

Space required:

54 words including constants and working storage.

d.

Error codes - none.

5.

RESTRICT IONS

6.

CODING

lNFORMATI~

a.

Constants~

12 locations.

b.

Working Storage ~

c.

Timing

I loc,ation.

SINE x, STATED POINT
A. E. ROBERTS, JR. M. D. BERNICK - MARCH, 1956
REMINGTON RAND UNIVAC
LOCATION

OPERATION

ENTRY

MJ

ERROR

&J

EXIT

MJ

X

FILL

Xl

u ADDRESS

v ADDRESS

EXPLANATION

STARr

Jump to body of program

DlAG

Error exit to diagnostic routine

FILL

S ucces s exit

FILL

FILL

Most significant part of argument

FILL

FILL

FILL

Least significant part of argument

Y

FILL

FILL

FILL

Function

START

LT

~

x

Store M.S.P. of argument

LTI

~

Xl

Store L.S.P. of argument

DV

B

Q

R. 232 ~ Ai 0 ~ R < 2

MP

A

Bl

2
R· 7r
·2 67

LT

3

Q

Rl • 2 34-+ Q

DIAG+2

7r

= Rl ' 267-+

A

TP

PID

PROI

Set PROI for positive function

QJ

NEG

POS

Test for positive or negative functio

TP

PR02

PROI

Reset PROI for negative function

B2

A

Extract 235. (x mod 1)=235 x*-+AR

QJ

20R4

1OR3

Test for quadrant

1OR3

SS

B3

¢

7r I
7r
=cos /2
I sin 2x

20R4

MP

A

Q

.270 {x>l<_1)2 -+ A

SA

B3

o

NEG
POS

LT

(x*-l)' (x.-l)· 235 -+A

}ROURd & scale down [2 34 (x*-1l2+1/2 J

A

TN

A

STO~

-[2 34 {x*-1)2+1/2] =-N-+STORE

TU

PR02

PR03

Set u address of PR03 for i=O

LOCATION

PR04

OPERATION

uADDRESS

vADDRES5

TP

B4

Q

MP

Q

STORE

SA

B3

LT
PR03

A

EXPLANATI~

With Pi in Q, i =0, 1 , 2, 3; -N Pi

~

0

}ROUnd & scale down

A

[-NoP;o2- 36+1/2]->-AR

~Q

AT

FILL

Q

[ A3- r No Pi· 2- 36+1/2 J =Pi+l

RA

POO3

B5

i+l-+ i in POO3

TJ

PR05

PR04

Test end point

MP

Q

Q

P4 ::::::(2 35 sin4Y)+ Y in Q.P4 2

SA

B3

o

1T

LT

} Round & scale down

A

2-36P42+1/2

AR

A

-[2- 36P42+1/2]

.N:::;:-2 68 sin 2

MP

A

SIOlE

55

B6

37

Round

TN

A

A

: : : 2 32 2 sin24Y .... A

ST

B7

A

: : : 232 (2 sin 2 4y-l ) .... A

PROl

FILL

FILL

FILL

For + function complement A

PR06

TP

A

y

Store function

EXIT

Jump to exit

PRO

-+

&

~Y .... A
1T

scale down:::::: _2- 33 sin 2 "4Y .... AR
7T

MJ

1T

PR02

MJ

B8

PR06

.for - function, donVt complement A

PR05

AT

B6

Q

End point test threshold.

B2

B

377777777774

Mask for (Q34

B3

B

400000000000

235

B4

B

B8

B

462621024

B

12146566440

A2 = 1,369,107,744

B

122535716221

Al = 11,097,578,641

12265046

0

••

A4 = 2. 714, 150
A3 = 80,421,396

Q2)

,.

. ..
LOCATION

OPERATI~

uADDRESS

EXPLANATION

vADDRESS

= 26,986,075,408

B

311037552420

AO

B6

B

200000000000

234

B7

B

40000000000

232

B5

B

B

B

311037552421

21T x 2 32

Bl

B

242763015554

2/1T x 235

STORE

. FILL

100000

FILL

FILL

Advance of u

t
1.

IDENTIFICATION

2.

PURPOSE

RRF2, ARCTAN X STATED POINT
P. Johnson, M. Bernick - Revised 15 May 1957
Remington Rand Univac

=arctan

Given X, Compute I(X)

3.

METHOD

Iy(x) - arctan Xl! 2-25

a.

Accuracy.

b.

Range of Argument: Ix I~

c.

Scaling:

d.

Derivation:
7
y( X)--l:

1=1

4.

X

X· 233 , I(X) • 233
I(X) is computed using the polynomial approximation

C
2i+l

21 1
X +

given in Rand Sheet No. 13.

USAGE
a.

Calling Sequence

r

r+l
b.

RJ

U ADDR.

V ADDR.

+2

t

t

Normal Return

Control and Results
The argument, X, must be initially stored at t+4. the result,
Y(X), will be found at t+3, and in AR•

c.

Spaoe Required

54 oells of instruotions and constants
1 cell of working storage
d.

Error Codes
The following error codes are left in the accumulator on return
through the error exit.

EXPLANATION

~

RRF2 • 212 + 1
RRF2 • 212

-+

2

X < - 1

X >1

-2-

5.

REV.

5/15/57

RESTRICTIONS
The argument must be in radians, within the stated range, and
scaled 233.

6.

CODING INFORMATION
ao

Constants
CONSTANT

1.Q£

b.

B

677777777777

lower limit on X: -2 33

B1

100000000001

B2

040000000000

Upper limit on X: 233 + 1
232 for rounding

B3

573120142744

B4

263054507277

B5

432774360726

B6

305357575005

B7

561447164514

B8

314201226657

B9

525263620355

BIO

377777723167

37
C7 • 2
C • 237
5
C3 .236
C1 • 235

CODE

545431050001

Error code for X <-1

CODE 1

545431050002

Error code for X> 1

Working Spaoe
1 oel1 labeled STORE

o.

EXPLANATION

Timing
Average 3.19 mlB.
Maximum

3.2 mls.

C15 ~ ~2
C13 • 240
C11 • 239
38
C9 • 2

REMINGTON RAND UNIVAC

PAGE

J

PROBLEM

5

OF

RRF2

CODED BY Johnsop. Bernick PATE: REV 15 .May $57
0

ITEM NUMBER

OP

LOC

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

,
,
,
,
,
,
,
,

,

SUB

,
,

TEMPS,

1

INOUT,

1

MJ

,

0

RJ

,

ERROR

,
,

EXIT

,

Y

,
,
,
,

TJ

,

TJ

,

MJ

,

MP

ENTRY

X

START

OK

U

,
,

MJ

00
00

TP

SA
LTL

,

MP

,

LTL

,
,
,
,
,

MP

t

LTL

,

,
,
,
,

,
,
,
,
,
,

RRF2

1
START

FILL

FILL
FILL

B
B1
0

X
B2
0

MP

,

Q

BJ

B5
Q

2

FILL

,
,
,
,
,

ERROR 1

,
,
,

B4

2

FILL

A

X

AT ~

AT

0

,
,
,

1

,
,
,
,

54

DIAG

,
,
,

LTL

,
,
,
,

DIAG+2 ,
0

COMMENTS

V

OK
ERROR 2

&
$
.$

$

ERROR EXIT

$

SUCCESS EXIT

$

FUNCTION

$

ARGUMENT

$

ARGUMENT TO A

$

TEST FOR

$

ARGUMENT OUT

$

OF RANGE

$

FORM ROUND AND

,
,

STORE X SQRD

,

STORE

,

SCLD 33 IN TEMP

$

STORE

,

X
J

A
Q

,
,
,
,
,

,
,
,
,
,
,
,
,
,
,
,
,

STORE
A
Q

STORE
A

,
,
,
,
,
,
,

$

$

EVALUATE

$
$

POLYNOMIAL

$
$

EXPRESSION

$
$

FOR

$

PAGE 4

REMINGTON RAND UNIVAC

PROBLEM

OF

5

RRF2

CODED BY Johnson.Bernick DATE Rev.15May '57
ITEM NUMBER

OP

LOC

,
,
,
,

:- '.

,
,
,
,

,
,
,
,
,
,
,
,
,
,
,
,
,
,

ERROR 1

ERROR 2

B

,
,
,
,
,

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

AT
MP

LTL
AT
MP

,
,
,
,
,

LTL

,
,
,
,
,
,
,

AT

,

LTL
AT
MP

LTL
AT
MP

MP

LTL
TP
MJ

SP
MJ

SP
MJ

B67

B6
Q

2
B7
Q

3

B8
Q

2

2
BIO
Q

,
,
,
,
,
,
,
,

,
,
,

,
,
,
,
,
,

B9
Q

1
A
0

CODE
0

CODE 1
0

77777

COMMENTS

V

U

Q

STORE

,
,

ARCTAN X

A
Q

STORE
A
Q

STORE
A
Q

,
,
,
,

STORE

,
,
,
,
,
,
,
,

A

•
$

$

,
,
,
,

By

,
,
,

METHOD

$
$

NESTING

$
$
$

•
$
$

A

,
,

Q

,

$

,
,
,
,

$

X

y

EXIT
0

ERROR
0

ERROR
77777

,
,
,
,
,

$

$

STORE FUNCTION

$

TO SUCCESS EXIT

$

ERROR CODE TO A

$

TO ERROR EXIT

$

ERROR CODE TO A

$

TO ERROR EXIT

$

LOtIER LIMIT

$

#

PAGE.

REMINGTON RAND UNIVAC
PROBLEM

5

LOC

,

B1

,
,
,
,
,
,
,
,
,
,
,
,

B2
B3
' B4

B5
B6

B7
B8
B9
B10
CODE
CODE 1

OP

, B10
, B04
, B57
, B26
, B43
, B30
, B56
, B31
, B52
, B37
, B54
, B54
, ENDSUB

U

,
,
,

,
,

00000

DATE REV. 15 May ' 57

00000

31201
30545

,
,
,

00001
00000

42744
07277

,
,
,

14471

,
,
,

42012

,

26657

52636

20355

,
,
,

77777

,
,
,
,
,

27743

P 5'"'53575

,

54310
54310

eOlfl.ENTS

V

,

60726
75005
64514

23167
50001
50002

5

RRF2

CODED BY Johnson. Btrnick
ITEM NUMBER

OF

,
,
,
,
,
,

,
,
,
,
,
,
,

UPPER LIMIT

&

ROUND BIT

$

C15 SCLD 42

$

C13 SCLD 40

$

C1l SCLD 39

$

C9 SCLD 38

$

C7 SCLD 37

$

C5 SCLD 37

$

C3 SCLD 36

$

C1 SCLD 35

$

ERROR

•

CODES

$
$

THIS IS A USE PROGRAM
BATOOl

PRINT -

OF.F-Ln~

- STATED

DECJ}~

DATA

by D I Cook, Boeing Airplane Co , Dec 1956
A PURPOSE

The purpose of this program is to prepare a magnetic tape on
the l103A computer to print a block of consecutive words of
memory as stated dec imal data on the Univac High Spee d Printer .
The information is written on Uniservo number two in the fixed
block mode.
B J.1ETHOD

The data to be J..Tinted are scaled to proper bina.ry' fractions
(with the binary point between the sign and the most significant bits ) from the scaling information supplied by the
programmer as control information. Repeated multiplication
by ten is performed on the scaled word to obtain succes sive
decimal digits . The decimal point is inserted in t he appropriate position and a minus sign is inserted after the least
significant digit- i f the word is negative . Zeros praceeding
the most significant digit are not converted to XS) code and,
hence I are not printed by the high speed printer.
F.a.ch colunm to be printed may contain twelve characters
including the decimal point and sign. If' the word is too large
to be printed in the form indicated by the scaling information
the decimal point is shifted to the right and the low order
digit s are truncated . An eleven dieit integer is printed
without a decimal JX)int .
A "Fast Feed In symbol is inserted as the first character of

the first blockette and every sixtieth block9tte causing the
data to be printed at 60 lines per page. A "Printer stop"
symbol is inserted as the first character of the blockette
immediately foll~-ng t he last blockette to be printed in
order to stop the printer after completing the printing .

C USAGE
L.

The following instruction is written by the progra.'llIl1er to
ent er this program where "tl! is the locati on of the first
inst ruction of this program and "r" is a location in the
main program:

.

Lee

Op

U

v

r

RJ

t +2

t

r+l

Explanation
Jump to the first instruction of
this program.
Control is returned to this location
following the successful execution
of thi s program.

SA C 1546 l · R3

BOEING

I

NO.
PA GE

Tor:

+-

27000

C USAGE (cont'd)
2.

The following control data must be stored within this
prograI:l. prior to transferring control to location t.
Loe
t+3

Op

N

U

v

Explanation

L

M

Format Control . N is the number of
columns to be printed where OeN~8.
L is the location of the first data
word to be printed . It is assumed
that successive words are in consecutive locations .
M i s the number of lines to be
printed and must be chosen such that
L+M' N is a legal storage location.

t+4

t+5
t+6

•

•
•

•
t +ll

-

Scale Indices. Di is the number of
decimal places to be printed to the
right of the decimal point for all
data in the ith column where OeDi-lO .
B~ is the number of binary places to the
r~ght of the binary point for all data
to be printed in the ith column
rThere OI!!iBi j£ 3$

3. i'llhen using this program Uniservo number two must be ready
to receiva 'tn-itten information. The tape is not rewound
before or after printing so that additional information
rnsy be written on the tape.

4.

The following is the normal storage assignment for this
program . It should be noted that this assignment may be
altered by the compiler .
Item
Total Program

Starting Location Number of words
Dec
Oct
Dee
Oct
t

Without Erasable 8torage t
Subject to Address ':,10d.
t
Program Constants
t+143
t+168
Erasable storage

t
t

t
t +2l1
t +2$O

301
168
143

455

25

217
31

133

205

250

5. No error cheeks are made within this progr8lll and no error
oodes are used. Failure to comply with the restrictions
imposed on the Fbrmat Control Word in location t+3 may
result in an 11C':T fault.

SAC 1546 l -R3

27000

C USAGE (contld)

6.

The printed format produced by thie program consists of
N columns of 12 character s each with 3 blank spaces
between columns . The 12 characters within a column
consi st of 10 (or l ess) decimal digits , a decimal point
and a minus sign (if the number is negative) or a blank
space (iI§ the number i s positive ). Eleven digit integers
are printed without a decimal point and the 12 characters
then consist of 11 dec~l digits and a minus sign or a
blank Elpa.t:e .

D RESTRICTIONS
1.

This program will operate on the standard "minimum 1l0)AII
computer as establis hed by USE .

2.

This program is self- contained and no other programs
are used .

3.

This program will print data contained anywhere in the
addres s able IT'.emory of the computer other than that space
occupied by the program itself . The data are assumed to
be in s tated binary form in consecutive memory locations.

4.

The tape produced by tlrl.s program is in fixed block form
in blockettes of 120 characters each and a density of

128 lines per inch suitable for printing on the Univac High
Speed Printer .

5.

The standard USE 120- 120 printer board is used to print the
data from the tape .

E CODING
1.

INFOFU~TION

This program uses 133 words of erasable storage . In normal
usage this block of erasable storage begins with location

l O(t+168)
2.

= 8(t+2$0) .

This program will write a printer tape at approximately
blockettes per minute.

400

SAC 1546 l -R3

BOEI""G

I

NO.

'l'OO~

PAGE
2 · 7000

~------------~~
j:.l~ - TOQl

-:>qII\'T

IS

, ...... 1
,.tJ 71b~~LJC65 1 5

, 'If

, .. , 4". 0

, )I

'· ?5 . U

)(

, )<

F'lt'Tf

C'-RL
<:0

c,

S?
c:: •
c:: I)
c:o;
C:f.

)(

,j'JIJ
tRJ
,MJ
, FILL
,FILL
,F I L'_
,FILL
,J=ILL
. FILL
,F I LI_
, F I LI_

'+l 3~ · <'

, .. o. ('
H, 0 . <.'

'C

·2,0
-OTA G

, f'

·I=TLL
,J=ILL
.I=TLL
,FfLL
.J= LL
. FTLL
t FTLL
' FILL
· J="rLL
·FYLL

' ~TM~·2

' c Tli _
- "r LL
'C'?LL
· r::-rLL
, r::TLL
,cTLL
_cTLL
,cTLL

'LrN~<;

,F£I G~
.q,o

, M,-J

,C

,ExIT

LJA

,~Pl

, 12C

./.IlI2

U~l

,1

P
, TV

, ZFR<'

,TP
, '''P

I V';;'

' C\ l OCI(

·CTPL

'

41'l?
(::0

o1

,I T
, rJ
,j'JIJ
.TJ
• -r p

56?

,TU
. 'TV
, 'TV
. TV
.TV
,TV
, !.J A
, fJA

,RA
,RA
,TP

CALC

Cook

- ~TLL

,

q~

-6A

'c E4

·llNF.-C;
,L TNFC;

,r:

1

. F'TR~T

.

APR

•
•
•
•

~

0

l

•
•
•
•
•

Lor~TI ON

•

•
I

0

4

I

r II'E'"

10

WORD
PR I ~ I r

t-J~"E

C;ET LO(A I H' OJ= FfHCT I I E Or ...:.IX
10 op II'I -r cr'r( LT"'~')

~

' ~ TP"'T

·.t::1=2

,c:'lp "r

·~ P-4

,O::"P'-T
,r::'R"1

.~F 5

·1:1=6

·6 ~5

' DC

~Eq

Ot-= COl UM'\J'"

TO pP1Nr PFH

SAC 114 5 A ... ",

L'I\I~

PKT'\JT '\10 CUl[IMI\Ie:
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•
USE Subroutine

I.

Identification
R-W EXP-2, Stated point Exponential, Malcolm Perry,

22 March 1956 - Ramo-Wooldridge Corporation
II. Purpose
Given 2 35x this routine computes 2 35 eX.
III. Acoura.cy, Range, Method
a.

Truncation error of the polynomial is

b.

Range.

c.

Method.

-(ln2) (2 35 +2 -1)

< 34.5

X

ln2

The routine finds q, an integer such that
X

where

<

< 2- 35 •

=q

(1n2) + r

Ir I ~ ln2
2

This gives eX ~ (e ln2 )q 'e r

= Zq'e r = (2q+l).~
2

q l
Since the factor 2 + is easily applied by shifting, it
is only necessary to calculate the quantity e

r

/2.

This

is accomplished by a 7th order approximating polynomial
where the domain of r is

This polynomial was obt.e.ined with the aid of routine CVF -O.
The coefficients of the polynomial are listed in the
accompanying code listing.
between the function e

r

/2

interval stated above, is

The maximum discrepancy
and the polynOmial, in the

.75

X 2- 35 •

The error in the machine's approximation to e

in all case s by

.[(ll.3 + .7

Ix l

) eX + 1 J '2- 35

X

is bounded

That is
I( A)f -

eX'2 35 1 <

(l1.3 + .7

IxI ) eX + l

Most of the error is due to round-off within the routine.
The actual error is usually less than the bound stated

here.
IV.

Usa.&e

a.

Calling sequence

LOe

OP

r

RJ

r+l
b.

v

u

Normal return

Control and Results
2 35 X must be in A upon entry to the routine j 2 35 eX is

lett in A upon normal return.
c•

Space required

28 instructiona, l5 constants, 3 temporaries
d.

Alarm conditions

If X falls in the interval

34.5 (ln2)

 2,

the error in eX is less than 2-(26-E) where E is the
binary power of X.

b.

Range.

x

<

.693 x 27 •

If x < - .693 x 27 J the

answer will be zero.

c.

Method.

= (2-129 )

1.

eX

.2x(10g2e+1 29)

2.

Divide (X.lo32e + 129) into an integral part R and
a fractional part S.
on X,

R ~ O,

O ~S

By the necessary limitations

<1

3. eX = (2R - 129 ){2 S )

= (2R-128){~S)
2

4.

2

S

is evaluated using the Rand Polynomial Approximation

number 20.(2 S

5.

Since 0

~

= 10Slog102)

S <" 1

,1

~

2

S

<

8
1/2 :::; 2 /2

6.

2

<1

R-128 is the characteristic of the answer, in f'loating
notation, and 2

S

2"

1s the mantissa.

IV.

Usage

a.

Calling sequence
WC

OP

u

v

r

RJ

t+2

t

r+l
b.

Normal return

Control and Results
The arguIIltnt x in fioating point must be in A upon entry;

e
c.

x

in fioating point is left in A upon normal return .

Space required

43 instructions, 19 constants, 3 tempora.rie s
d.

Alarm conditions
The alarm exit is used if x falls outside tha

permissible range.
V.

No restrictions

VI. Coding Information
a.

Constants
WC

CON6'l'ANT

+44

2 35 ln2

+45

4
23 !ln2

+53

234

+54

40 07777 77777'0

+55

37 70000 ooOOOb

+56

00 00000 00170b

+57

00 00000 OOO44b

+58

6

+59

1
2 5

+60

227

+61

43

RW

EXP-3

3-26-56
E28

LT 00001 AOOOO

34

E29

AT 00000 02EOO

34

E30

IJ 02E02 00E26

E31

LA 02EOl 20027

E32

AT OlE09 QOOOO

E33

EJ AOOOO 00E36

E34

TP OlEla 00000

E35

MJ 00000 OOEOl

E36

SP 02EOO 00028

E37

LT 00000 02EOO

27

E38

LT 00001 AOOOO

28

E39

TJ 01E16 00E42

E40

RA QOOOO OlE16

E41

TP 02EOO AOOOO

E42

AT QOOOO AOOOO

PACK

E43

QJ 00E34 00E02

CHECK EXP

ALARM TAG

lEOO

06 93147 18056 -01

35 LN 2

lE01

06 93147 18056 -01

34 HLF LN 2

lE02

01 99243 65600 -04

34 C7

lE03

01 39485 76760 -03

34 C6

1E04

08 33324 84740 -03

34 C5

lE05

04 16662 18354 -02

34 C4

1E06

01 66666 66994 -01

34 (3

1E07

05 00000 01077 -01

34 C2

lE08

09 99999 99997 -01

34 C1

1E09

20 00000 00000 B

CO

.

RW
EXP-3
3-26-56

·'

lElO

40 01111 17111 B

MASK

lEI1

31 10000 00000 B

MASK

1El2

00 00000 00110 B

1El3

00 00000 00044 B

lEl4

00 00000 00006 B

lE15

00 00001 00000 B

lEl6

00 10000 00000 B

lEI1

00 00000 00053 B

lEIS

00 00000 00000

ALARM TAG

2EOO

00 00000 00000

MANTISSA

2EOl

00 00000 00000

EXPONENT

2E02

00 00000 00000

INDEX

\

PROGRAM WRITE-UP

1.

ARCSINE X, STATED POINT

IDENTIFICATION

A. FRANCK, M.D. r BERNICK - MARCH 1956
REMINGTON-RAND mIVAC
2.

PURPOSE
Given x, this program computes Arcsine x.

3.

METHOD

=I

"'-F (x) I ~ 2-24

·

B.

Accuracy

b.

Range of argument:

c.

F(x)

arcrln~-

=aresin x is

I (x) I ~

I

computed in radians from the polynomial

approximation
arcsin x ~ 1T/2

-.J1:X ~ a1 xi. The square root

is

1=0

computed by an approximation and one application of the NewtonRaphson Formula.
4.

USAGE
a.

Calling Sequence
u ADDR.

QE
r

r+l
b.

RJ

t+2

Normal

Return

v ADDR.
t

Control and Results
The argument is to be placed in the Accumulator and the
function will be found in the Accumulator.

The program also

places the argument in t+3 and the function in t+4.
c.

Space Required:
storage.

109 locations including constants and working

d.

Error Codes
£RLANATI I

301224060001
5.

RESTRICIIONS

6.

CODING INFORMATION

a.

Constants:

22 locations

b.

Working Storage:

c.

Timing

7 locations

ARCSINE x, STATED POINT

A. FRANCK, M.D. BERNICK - MARCH, 1956
REMINGTON-RAND UNIVAC
I.DCATION. OPERATION.
ENl'RY

MJ

ERROR

RJ

EXIT

MJ

uADDRESS.

DIAG+2

vADDRESS.

EXPLANATION

START

Jump to body of program

DIAG

Error exit to diagnositc routine

FILL

Success exit

X

FIlL

FHL

FILL

Argument

Y

FIlL

FilL

FIlL

Function

STAIn'

TP

A

x

1M

A

A

TJ

B2l

PROG

MJ
PROG

NOZERO

NEG

POS

ERRORl

Store argument

~x I > 1

TP

A

Y

ZJ

NOZERO

EXIT

x=O

TP

A

STORE

Store

TP

x

TP

Bl

SJ

NEG

TP

B2

TM

A

A

EJ

B

XONE

I x \::::1

MP

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B3

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LT

1

AT

B4

STORE 2

MP

STORE

STORE 2

LT

I

A

STORE 1

Ixl

x~A

Preset STOREI for sign determination

POS

STORE 1

A

A

Reset STOREI for negative argument
Ixl~ A

77

LOCATION.

OPERATION.

uADDRESS.

vADDRESS.

EXPLANATION
(a7x2+86x+a5) '2

AT

B5

STORE2

MP

STORE

STORE 2

LT

3

A

AT

86

STORE2

MP

STORE

STORE2

LT

2

A

AT

87

STORE 2

MP

STORE

STORE 2

LT

2

A

AT

88

STORE 2

MP

STORE

STORE2

LT

2

A

AT

B9

STORE2

MP

STORE

SfORE2

LT

fJ

AT

BID

TN

srORE

40

(a7x3+"'+84)'240

(87x4p"'+a3)'239

(87x5+ ••• +a2)·238

(a7x6+ ••• +al)·237

A

A

(a7 x7+ •• ·+ao ) .234
(A)=-x'2 33
(A) =(l-x) .233

STORE2

SA

8

fJ

SF

A

STORE3

SP

A

fJ

TP

A

SA

811

LT

fJ

STORES

Store F

MP

B12

STORE 5

A.F -+ AR

AT

813

STORE 6

Store A.f+B

SN

814

Scale factor
(Al):::(); (AR) =N; 234 ~ N~ 235

STORE 4

18

15

Store N
[ (N+D) ] ~ 218 =F-+A

-C.2 1S -+ A

lJ)CATION.

OPERATION.

uADDRESS.

vADDRESS.

DV

STORE 5

AT

STORE6

srORE5

SP

STORE4

32

SS

stORE 5

DV

STORE 5

A

AT

STORE 5

STORE 5

LQ

STORE 3

35

QT

B17

TV

A

A

A

EXPLANATION
(-C.215)~F=-G

AR

. Store AF+B-G=Yl
N.232

A

N.2 32

Yl

A

(N.232~Yl)-l

AR

Store (N·2 32 ~ Yl)-l+Yl=Y2
Ko

Q35,K6 ••• Kl ••• Q5 ••• Qo

(K-Ko)

~

2 ~ AR

RIFT

Set up V part of shift

PROGI

Set PROGl for storage of results

TP

DONE

TJ

B15

NOSCAR

(K-Ko)

TP

SCAR

PROGl

Reset PROGI for scale and round

NOSCAR

QJ

RIFT

I37, round & scale

I-x X(x)·2 67
I-x X(x)·2 33

(Q)=(c-arcsin X)·233
x neg, j wnp

LOCATIOO.

OPERATION.

EXPLANATION

EXIT

Jump

MJ

fJ

TN

B20

Q

MJ

fJ

PROG3

XONE

ERROR I

vADDRESS.

uADDRESS.

SP

CODE

MJ

fJ

A
ERROR

to exit

x=1;-

7T

2

"233-+ Q

Enter error code in A
Jump to error exit
233

100000000000

B

B

Bl

B

fJ

B2

B

1

B3

B

532413520070

87

44

B4

B

332441425535

86

42

B5

B

564007151545

85

40

B6

B

370417441233

84

40

B7

B

462370666522

83

39

sa

B

266165166073

82

38

B9

B

444200330653

81

37

BI0

B

311037551633

80

34

Bll

B

264767031361

0=24,290,062,513

B12

B

B13

B

114534644516

8--10,291,988,814

B14

B

330657140271

~29,104,062,651

B15

B

B16

B

265011714640

B17

B

77

B18

B

200000000000

234

B19

B

377777777777

235-1

B20

B

144417665210

1f

65324

23

A=27,349

1J constant
24,296,004,000
Masie for SF

2

"233

LOCATION.

OPERATION.

uADDRESS.

vADDRESS.

821

B

100000000001

CODE.

B

301224060001

STORE

FILL

FILL

FILL

srOREl

FILL

FILL

FILL

STORE 2

FILL

FILL

FlU.

sroRE3

FILL

FILL

FILL

srORE4

FILL

FILL

FILL

SImms

FILL

FILL

FILL

srORE6

FILL

FILL

Flu..

EXPLANATION

RW SIN-4
5/ 15 / 56

USE Subroutine

1.

Identification:

RW SIN-4, Floating Point Sine-Cosine
Routine
Malcolm Perry, April, 1956
Ramo-Wooldridge Corporation
Los Angeles 45, California

II.

Purpose:
Given x in floating point form, this program calculates sine x if
the parameter word is zero or cosine x if the paramete r word is
non-zero.

III.

Accur acy, Range, Method:
a.

Sine x or cosine x is computed to 26 binary places of accuracy,
or to as many correct bits as there are in the fractional portion
of the argument, whichever is less.
When

x ?;22 7 , this routine substitutes zero for the argument.

The alarm exit is not used.
b.

x may be any floating point number.

c.

The Rand Pplynomial Approximation Number 16 is used to calculate
sin x or cos x.
1.

Let Y = (2/n)x, then sine x
cosine x

2.

sin (n/2)Y
sin( n/2 )(y+l)

Divide y (or y+l) into an integral part R, and a
fractional part S.

RW SIN-4

5/15/56

3.

R defines the quadrant into which x falls.

Pg. 2

Let R'

be the two low order positions of R) since in binary
notation) other positions merely define a number of
complete revolutions.

4. R' is a number one less than the number of the
quadrant into which x falls.

5.

S defines the displacement (in a positive direction)
,vi thin the quadrant indicated by R I

6.

•

Therefore) i f R'

00) Let

S

first quadrant

R'

01) Let

(l-S)

second quadrant

R'

10 ) Let

( -s)

third quadrant

R'

11) Let

(l-S)

fourth quadrant

= sin(n/2)z

7.

Sine (or cosine) x

8.

(l/z) sin (n/2)z is approximated by the Rand Polynomial
Approximation Number 16) using argument z.
If x < 1/2) (2/ n )x) which is in float ing form, is

9.

substituted for z before doing step 10.
Multiply the approximat ion from item 8 by z giving the

10.

result) sin
TV.

(or cosine x).

Usage:
a.

b.

Calling Sequence
LOC

OP

r

RJ

r

Normal return

u

t + 2

v

t

Control and Results
The argument x must be placed in the Accumulator and the
parameter word (zero or non-zero) in t + 3.

At the time of

RW SIN -4
5/15/56
normal exit from the routine, sinx (or cos x) will be in the
Accumulator.
c.

Space Required
56 instructions, 12 constants, 4 temporaries.

d.

Error Codes
The alarm exit is not used by thi s routine.

V.

Restrictions:
The range of x as a floating point number is approximately

VI.

Coding
a.

Information:~ ,

Constants
2 35

+62
+63

17

77777

77777

+64

00

00001

00000

+65

00

00000

00200

+68

00

00000

00003

128

-

a/rc

..

~

~

10

38

Pg. 3

-

---

---

RW SIN-4

5/15/56

Pg . 4

oosoo
OOS Ol

0 0502
0 0503
00504
00505
') 0506
00 507
0 0508
00509
0 0 51 0
v OSll
(} 05 2
OOS13

J05_4
O OSI~

005 16
00S17
00518
00519
0 0520
0 0521
00522
00523
00524
00525
00526
0 05 7
(: 0528
00529
00530
00S31
00532
00533
0 0534
0 0535
00536
00537
00538
00539

MJ 0000 0
00 0000 0
MJ 0000 0
00 00000
TU 00537
I T 00009
LQ AOOO O
MP Q()OOO
LT 00000
TP QOOOO
TM 0250 0
ST 01508
S J 0051 3
S A 01510
SJ 00S17
TV Af)OO O
LA 00000
LT 00008
TP 00S03
ZJ 00S26
iJ 01510
CC QOOOO
TV AOOOO
LA QOOOO
iP 00503
ZJ 00526
TN 00000
AT 01 50 6
0;- 01506
CC 02500
QJ 00531
RS 00554
QJ 00533
TP 01506
5T 02501
TP 02501
MP QOOOO
LT 00002
TP 01500
TP 01511

00504
0000 0
0 000 0
0000 0
OC5S 4
02500
00035
0 1505
00000
02501
AOOO O
C2S0 0

ENTR Y
ALARM EX IT
NORMAL EX r . ~.
PARAM WD

SE T EX!: PC' S
C:X P PLU S 200
I"' ANT ;:, CI\ I_ :15
SC ALE) (0

OUADR ANTS
~) C AL ED 34
'. XPCf'E N T
I.)f\j (3 ! l .. _~ E X ~):JI !

0 05 2 0

00000
0051 5
0 0<)16
0000 0
0000 0
AOOOO

ANG~E

LESS

THAN HA L'·
t"1 AI\jj I

~5A

RS SC ALE D 34PARAMETER wD

00536

00522
Aaoo o
00523
00000
ADaOO
OOS28
AOOO O

AN GL ~

GR EATR

T HAN HAL. F

R5 SCALED 34
PARAM ETER Wf)
IF C05IN E

QOOOO

0 250 1

ARE Z FI XE!)

AOOOO
00532
01501
00535
AOOOO
02501
00000
QOOOO
02502
00000
02503

EXP

~INL

ZRO

QUADRN T 30R4
QUADRN T 2 0 R'+

Z SQUARE D
:.) CALE D 34
C9 SCAL ED j O
INDEX

RW SIN -4

5/15/56
5

Pg .

00S40
00541
00542
00543
00544
00S45
00546
00548
00549
00550
00S51
00552
00S53
00554
00555
00S41
0 1S00
0 1501
01502
01503
01504
01505
01506
01507
01 508
01509
01S10
. -; . 11

TU
RA
MP
LT
AT
IJ

MP
lJ
SF
LT
RA
SA
CC

RP
TN
LT
01
-4
07
~6

01
06
17
00
00
00
00
00

00S38 00544
00S44 01507
QOOOO 02502
00002 AOOOO
00000 00000
02503 00541
00000 02501
00S49 00S02
AOOOO 02503
00028 00000
02S00 02503
01509 00021
AOOOO 00000
00000 00502
AOOO O AOO OO
00006 AOOOO
5 }484 1900 0
61376 55700
96896 79280
4 5963 111 ,,) 6
51019 6318 5
36619 11225
77771 77777
00001 00000
00000 00200
00000 000 ? 3
00000 00034
00000 00003

BUMP CON5TNT
EVALUATE
RAND
I
POL YNOM I AL
5CALED '30
MULl By 1 64
EXI T TES T
FLOAT MNl5S A
PLUS 5CL Fc r
FINL EXPON' :
PACK
ONCE FOR NE.G
TW ! CE FR PCl5
FINL MANTS ..·iA
-0 '.,.

-0 1

-02
~01

-01
B
B
B

30 (- 9
30 C-'7

30 ( -5
30 (-3
30 C- 1
35 2 OVER P I
MASK
1 28

8
B

59

B

3

28

650 ... PC-Oooo 6s

11 April 1956

LOAD HUB TO AUTOMATIC PLOTTER CARD CONVERSION
This routine will retain the indicative information in the first
field of a load hub card and convert the other seven fields from floating
decimal form to fixed decimal form which can be read by the automatic plottero
Each output word will be of the form OOOXX.XXOOO and should not exceed 70.00.

The plotter does not distinguish between ~ X and Y punch on a load
hub card, so a constant must be added to fields having negative values, to make
all values positive. Each field is divided by a scaling factor so that the
final output will be u.'lits of centimeters. Use the following formula to
determine the scaling factors.

x M
+-

K •

)L~

~1J

Given X
K

= A Multiple

of M such that K bounds largest
negative number in the field o

M • Number of unit

of X desired per centimeter.

M s~ould be of the form 1 X lOP, 2 X loP, or 5 X loP where
p may equal any number. This facilitates easier

reading of the graph.

Xp • Plotter values in centimeters.
(

I.

Input (Use 533 Panel No.2, 7, or 12).
A.

wad Card.

B. FLAIR Deck (08 command is used) Decks 033.20 and 033.21.
C. Conversion Deck No. 079.00 - 16 cards.
D.

E.
F.

Load Hub Card containing K in floating point for each field (except
first rield -- first field may be used for indicative material and is
not used in the output).
Load Hub Card containing M in floating point for each field (except
first field -- not used in output).
Load Hub Cards to be converted.

NOTE~

II.

Input ~ be in this order for routine to work.

Console Setting -- Standard wad Setting.
OUtput.

III.

A.
B.

Load Hub form - fixed decimal in form OOOXX. XXOOO withy punch in un1 ts
position of each field o
A one (1) is added to the left position in the first field, which still
contains original indicative information, to identify it as a plotter
card. The last seven fields are converted at a rate of approximate~
25 cards per minute.

..

'

. '..

~

650-PC-OOoo6s

11 April 1956

-2-

EXAMPLE OF HOW TO DETERMINE SCALING FACTORS
2nd

/ l s t Field

4th

3rd

5th

6th

8th

7th

Indicative
Information

--

-------

-

-

.-

Suppose field number 4 is to be plotted against field number 6. In field 4
are the X values and in field 6' are the Y values. The highest X value is 1379 and the
largest negative X value is -17. The highest Y value is 120 and there are no negative
Y values. The graph is to be plotted on the regular size "centimeter paper", which is
70 X 70 centimeters (notebook size is 20 em. X 25 em.).

1379

M

1379

+ K

26

..,

120 + K

No more than 70 em.

K( ,

20 _ 69.95 em.

Therefore:

K· 20
M • 20

(f

120
~. Id

or . J.e

The X ax1 s i s moved up 1 em.

4)

+

2

0 • 60 em.

Therefore:

~~

T
~

Write-up

Approved

•

K •• 02 (for Field 6)
M

The Y axis does not move.

Coding

EWHrag

- No more than 10 em.

A

'IN.

?I~

'W.

W~

~ ~1---.
/

.

.

I

650-5D-OOOO7S

/

June 29, 1956
Revision of FLAIR
New 06 Command

Deck 033.24 consists of four cards and is now available 110 use in
conjunction with FLAIR.
This deck changes the 06 command from a NO-oP to a
repeat command of the fOrrll "repeat the set of commands starting at 0< the
number of times in ~ ". ' The 06 command MUst be sequential to the last
instruction of the set. At the completion of ~ loops, the next command is
sequential to the 06 command.
The form. of the instruetion is 06 oc::. N, where ae:- is the address
of the first instruction of the set to be repeated, and N is the number of timee
the loop is to be performed.
For example, if I is the address of the first instruction of the set,
and L is the last, the address of the 06 command MUst be L + 1.

-

-o

A

L+1

I

06

N

Thus, the set of conunands from address I to L will be performed N
times and the next instruction will be at L+2. The set of commands from I to L
may contain both "FLAIR and machine language comm.ands, providing L is a FLAIR
command, or a command to re-enter FLAIR at (1+1), where (1+1) is sequential to
the last FLAIR command used.
"
sequential.

If N is zero, the 06 command is a NO-oP, and the next instruction is
"

If the set of instructions I to L must be used again later in the
program, their addresses may be modified by use of the 08 and/or 8"1f command so
that the 06 command may be used again on the same set (even though it is not
sequential before the modification). "

This deck should be read into the machine following FLAIR so that the
proper modification of FLAIR will be made. Storages 1200 thru 1216 are required
for this command.
Coding of new 06 command:

-A
1678
1204
1205
1206 "
1203
1207
1208
1209
1210
1211

0
6$
16
69
22
6,
16
69
22
35
11

D'

161$
1793
1203
1203
0000
1202
1615

1890
0006
8003

I

1204
120,
1206
8001
1207
1208
1209
1210
1211
1212

650-SD-00007S

-2-

Coding of new 06 command I

t

!

.Q

1212
1213
1214
1215
1216
1200

65
15
20
60

1201
1202

4S

20
00
00

(continued)

-

-

I

D

1213
1202

1201
1202
1890
1202
0000
0000

1200
1214
1215
1216
8003
1612
0001
0000

Coding W.

o.

Write-up W.

Approved

ag

Wootan

o.

Wootan

..g.£ &«!::

650-sD-OOOO8S
June

29, 1956

ADDITION TO FLAIR
New 09 CoDlWld

DeCk 033.23 can be used in conjunction with FLAIR (Deck 033.20)
and the FLAIR index registers (Deck 0)3.21) to provide a "transfer and set
index" command.
'!he 09 ex ~
command, if' located in storage "n", sets the
index register tagged by "ex n
to "n + 1" and transfers the control sequence
to addresa .."..
This command makes an automatic return from subroutines possible.

Example.
sets index "D'"
to Olll

80
09
•

0008
8000

0250
0251

Hypothetical routine which

•
•

always uses number stored

•

in Position 0250

025
0260
Olll

00
OP

8000

0000
ex

~

'ntis Routine uses drum positions 1217 to 1227 inclusive.
Coding'

o
J.
6,
1681

1222
1218
1225

1219
1226
1220
1227
1221

122)
1224
1217

-

1217

)

122,

188,

19

1642

.30

69

69

I

1867

35
22

1,3,
23
6,22

-

D

1220

1222
1219
1226
1227

1209

1192

1867
1615

122)

2

4

1221
1224

1867

8003

IBB5

Coding

1218

e.D

WritA-up

ag

IM

2...

H 1iL~

CtAQ'4

HJ0:JJ7

Appro"~(LAcf£' #1rG--

·- .

5

YMB~L( c

i-I Bft4-f? '/

OP612 t1= ,IoNS .

0

LGT

45000

LOGIC TRACE

0

ODD

40000

DRUM STARTS

0

DAS

40172

TNT PR

0

ST

40;>03

START

0

RR

40203 00031

READ

0

BL

4')203 00053

LOAD

TIIPt

S
D
E
~
~AS

I-<;

Abb-I-NG

SEQUENCE
;.QN S-'J:.A-NT-S-F-O R

0

CN

40203 00104

OP PKG
-.Bt..

0

BS

40203 00123

STORE

D

MQ

4()203 001<=;5

ROUTINE

-C.l(S.lJfl4

READ
WITH BINARY
0

Olv

40441

PREPARE

0

MAF

5"'5500

MAFIA

C:;OO02

MISCRAP

4C:;~ 5 ?

nATA TAPE

D

MCR

Q

0

D

OTC

A-

CC>RREC+-I-O

nTC

Ll4632 RELOC

0

OUP

417 0 ?

TAPE

nup

Ll4230 RFLOC

0

CAM

46144

TAPE

CAM

44172 RELOC

~

s

0

pBT

4S516

PRINT BIN TAPE

PBT

Ll1325 RELOC

0

PBC

4 t 17~

PCH RIN CDS

PBC

46400 RFLOC

0

OCt

46600

DRUM CORE IMAGE

Q

FAp

41376

FAP

0

FF

01420

RUFFER

ER

ODDOO

MJ

onROO

RO SERVICE TPE

OD002

MS

ODDOO

STOP

DODOlJ.

MJ

O£,)Rl0

LOAD BINARY

ODQOfol

MJ

OOR21')

3

40000

00000 lJ.0026

40004

00000 40040

40006

4~'

00000 40052

40010

LtC:

00000

4001;>

4C,

00000 4007'"

40014

4C:;

00000 40110

~I GQ

OD010

MJ

Ol')R40

DOD!?

MJ

ODR<=;O

40061~

11

2

NOT USED

00013
DOOl5
DDDI7

MJ

40015
4001
40017

41:;
4f,

40023

4C,

40027

1 I 00001 00001

40031

00 00000 00000

LOAD FAP

40033

37 40224 40172

BINARY

40035

0(\ 00024 00000

40037

00 40415 00000

40041

1 1 00053 00053

40045

37 40224 4017?

A

40047

0(" 01500 00000

ARB

40051

0('1 53500 00000

40053

1 1 50000 50000

40055

or- 00000 00000

40057

37 40224 40172

40063
40065

00 50002 00000
3:'2 402211 UOl12
11 40557 40557

40067

00 00000 00000

40071

37 40224 4017?

REPL

00R6r:;

nATA TAPE CORR
E-----O-lJP-L.-LC-A--ll
TAPE COMPARE

DDR7r:;

ULAF0
READ B I J CDS

onR8r:;

I
READ PAPER TAPE

00R 5 5

MJ
MJ

DDDlc)

•
•

r

41:,

40115
4012~

40127
140
40141

USED

PREPARE LIBRARY
D -

DOROt

TP

STOt

DDR03

DDR07

SE VICE

STOt

e

A

00 01)024 00000

B

-1--0

I3R8
AD--A-SsEMB
BINARy TAPE

~

DDRI I

TP

~ Leo

RLoe
g

DDR13
DDRI5

RJ O\llPOO DASOO

DDR17

00 01500 00000

DDRIc)
DDR21

Ml\FOO
TP

~HPOO

OPTION
LOAD MAFIA

MHPOO

DDR23

A

MISCRAP
8

DOR29
DOR31

M~ROO

BRB

TP DUMOO ntJMOO

DOR"33

nUMP
B
LOGIC

ODR37

00 00516 00000

A

40073

0(\ 00516 00000

RFPL

DDR3C)

00 LGTOO 00000

BRB

40075

00 45000 00000

REPL

DDR41

TP FTROO FTROO

40077

I 1 44327 44327

RFPL

40101

00 00000 00000

5

DDR43
DDR45

TRACE
R

RJ DMPOO DASOO

NOT USED

DDR47

B

DDR49

B

37 40224 40172

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40107

00 00000 00000

,

z

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A 00

40 I 16

37 40224 40,72

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R

4() I 12

00 00000 00000

DDR54

B

40 I 14

00 00000 00000

40 I 16

11 45652 01774

40120

00 00000 00000

40122

37 40224 40172

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0 (' 41702 00000

40130

1 I 46144 00001

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00 00000 00000

40134

37 40224 40172

40140

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40142

1 I 45574 45574

40146

37

40 150

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40152

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4015u

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40156

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40166

37 40224 40172

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BRB

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TP ROQOO RPQ OO

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B
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40172

DDR92

B

40162

00 00000 00000

ODR94

B

40164

00 00000 00000

4016f:,

1 1 00236 00236

40170

00 00000 00000

SAVE F I CORE

40172

11 00000 46600

SAVE A LEFT
V
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RESET Fl CORE

4()t7u

2.;> 00000 40232

4017~

11 40203 00000

IMAGE

40200

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40202

11 40204 0000,

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3

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46601

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CHECKSUM ERROR
TP STOqE EXEC

40225

1 , 00031 00031

B

Q

40;>31

00 00000 (;0000

B

A RIGHT

40~33

00 00000 oooon

R

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02 on004 10001

A

40310

0;> 00004 10001

CNO'5

02 0 0 602 10000

R

40312

0;> 00602 10000

40314

0(1 00000 00003

4 0 316

0 (1 00000 00005

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40320

00 00000 00360

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40322

7(;: 30000 00000

SET STORE LaC

40326

I

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40330

1 c: 00170 00023

40334

3~

00 114 0015U

4033f,

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31000 00024

OV IN U V OF A

40342

3C:, 00024 32000

IF NEGATIVE

4034f-

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BS16

sJ

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BS18

TP

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A
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SET OVERLAP

A

'5

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40354

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9S24

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40356

00 00000 00000

MP 04

ZERO LOCATION

40360

1~

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MQ05

SET PPT

40362

3~

00122 00,62

CHECKSUM

40366

3:> 00031 00000

CORRECT SUM

40370

3L1 00025 00000

MOOO

TU

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AT

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5

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R-R-Q..R-.S+G-~
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CKSUM D1M+
L O-C---CALlOBTAIN CALL SEQ
R- C-6JRRE
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47 00167 00171
37

40401

1 t~ 32000 00017

40403

1f-. 0002, 00017

40405

31 32000 00017

EX LOC TO A Q

40407

55 32000 00017

OBTAIN ROUTINE
f; t
IF II\! CORE

40411

37 00 117 00130

TRANSFER

40415,

7r: 30022 01752
.

40417

1(- 0004c; 01771

40423

37 00103 00053

4f'1427

7r:: 21607

40431

3 L1 01772 00044

TEST FOR

40433

47 01767 01770

RCW

40435

11 01752 00055

4044,

37 00336 00320

40443

7~·

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•

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TV

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1 c:;

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75 31607

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36

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75 21607

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zy50

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0

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SET INDEX

LQ
TST END CKSUMS

4045,

41 00021 00320

OPERATIONS
R
ENO-LlOOOO OCT

40453

1~

40455

1 1 40231 31000

40461

7r; 30170 00260

TV

lY34

RROA

40463

1~

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lY1A

32000 40437

40445

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7y37

7Y47

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SET FIRST WORD

40u66

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40470

21 00302 00341

EXIT IF ZERO

40u7u

47 0027;? 00274

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4()476

37 00315 00301

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40')02

1"7 00000 00104

4050u

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40506

17

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T

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•

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40512

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40522

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40534

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ZY57

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3102C;

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ZY67
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167
02 00606 20001

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2

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4'5654
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45660

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37 01771 01760

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02

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4'5662
45664
45665
45666

5LI

w oe W-l OJ¥' 2
IF W IS
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4'5670
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45672
45674

11 02301 31000
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3" 00063 0230?
I ." 022~1 31000
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SET INDEX 4
SlIM
TIMES
lEN
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45676
4561'145700
45:Z01
45702

1 1 00065
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32 02300
I 1 32000
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l15f.63

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31 02302 00002

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45704
LI~+O§

4S706
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VC24
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BLOCK NUMBER

45712
4$713
45714
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45716

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21
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02045
02252
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45724

31000
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4'5726

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12

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•
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EF22
EF23

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EF25

SUBTRACT
SIX-O HS
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2

ARB

TP

TS07 A
R aG12
SA AF3(')0 00000
l J ----F';F-2 9
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RP 20120
A-~~152'

21

TP I
01 I
02
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03 CP04
T~ 1
0-6
G-1 I
TU EF12 HZ05

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SU M
TEST
B~6

RESTORE
6bO!;K
SET INDEX

-

RUMP ~LOCK CT
SE+ I~ggX +G ~
SET FIRST WD

03

HZ10

uc;

•
•
•
•
•
•
•
•
•
•
•

00000 02063

37 02075 02071
OOOGO GOO
75 10003 02067

61

oaai:4~

5f 00000 02000

45747

';lll
O-G-Q.
11 00066 00014

S

45755
457S6
45757
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5760

45761

11

oa~lo

H70S

TST BLOCK FILL

~r;:2t

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HZ10
11
HZ12
2;1
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l15
HZ16

TU

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RP

3000~1

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TP
TV

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HZ20

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HZ29

HZ22

sP ~F(')3
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1 1 00007 32000
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3;:> 01610 00000
7c:. 20170 00000

4577 1

21

L I§~:Z~

1 1 GOG 1(:) 000lS

45773

1 c::: 02066 02116
11 00000 32000
43 00012 02123

45775

--

45777

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2.

41 00015
4 C; 00000
1 r:, 02 116
1~ 3000/1
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-

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02.0-Z:Z
02125

•

02126

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02300

~

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TP

1Ll 61.+:"510 01610
r:, 20170 02103
23 01610 0,5-2-1

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1 I 00010 00011

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1.1-6001
46002
46003

WORDS

-Q.?-Q..2:.() 1-":l-

1 LI 74210 01610

45767

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~

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SET FIRST WORD

46005
1.+6006
46007

'"

0

31000 02130

1 1 OGOG
1(-. 02301

02147

>

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.
n

a

H719
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L15+6

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06

61 00000 31000
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4~ 00000 00000

41

Ll57614

45765

4~:Z:Zll

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IS THIS IN 66

IJ I

AT

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45745

45763

END FILE

81..0CI(

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SP

4574 1
4-!;-1-4-2415743

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M~J-O-Q-O~ 0

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37 02075 0207n
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2;2:3

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45737

45751
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45753

~

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R--.J- J::.F2Q
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210
FP6 l 1
310
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45735

I=l-I

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3

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4~~4

00000 02111
02107
III 74210 0161n

4~

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•
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45731
C;-7-3-245733

8 ~A-S---M

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•

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1
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46034

11

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02-,
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46030

1f

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M-J-O..Q.Q.nCI--CD 0 1

RP 3000S

23 0001 1 0006;>

46032

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sP

46026

IF LAST CORR
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R

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3S 02254 02
7r:.. 00000 02150

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46022
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46024

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46036
46037
46040

31

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BUMP STORE
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4f,042
46044

21 02212 00065
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4A046

7(- 00000 32000

ROW
SEl EOR ROW SUM
WD IND TO 3
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46050
lJ.605,
46052

7(-.

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46056
lleG57
46060
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46062

4~OLL;}

4~

t-

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46054

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1

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46074
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46076

51 00000 0161 1
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31 0161 1 OOOOLI

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04

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INDEX OF LIBRARY PROGRAMS

.z:a== •• ••••••• • •••••.• •

01 AUG 56
KEY TO CLASSIFICATION
B1
,B3
B4
El
FO
11

14
J4
KO
Ll
NO
Nl
N2
ZO

ELEMENTARY FUNCTIONS - TRIGONOMETRIC
ELEMENTARY FUNCTIONS - EXPONENTIAL AND LOGARITHMIC
ELEMENTARY FUNCTIONS - ROOTS AND POWERS
APPROXIMATIONS - TABLE LOOK-~P AND INTERPOLATION
MATRICES, VECTORS, AND SIMUt.c'TANEOUS LINEAR EQUAT·IONS
INPUT - BINARY
INPUT - COMPOSITE
OUTPUT - COMPOSITE
INFORMATION TRANSFER
EXECUTIVE ROUTINES - ASSEMBLY
DeBUGGING ROUTINES - TRAP MEMORY PRINT
DEBUGGING ROUTINES - TRACING
DEBUGGING ROUTINES - MEMORY DUMP
ALL OTHERS

INDEX OF TITLES
: ,: : = -

B1
B1
B3
B3
B4
B4
. E1
E1
FO
11
11

14
J4
KO
KO
KO
KO
KO
KO
KO
KO
KO
KO
Ll
NO
Nl
NZ
ZO

UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA

ATN1
S+C1
EXPl
LN 2
SQR3
'SQR4
BPEl
BPE3
INVI
CSBl
CSB2
DBCl
BDC1
CCBl
CSH2
CTH1
RWD2
5PHl
STHl
TCHI
TPHI
T5B3
T5M2
SAPl
SPMI
SP02
SPOl
OTMl

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

et_

;:.= .•

a::s

ARC TANGENT SUBROUTINE
SINE AND COSINE SUBROUTINE
EXPONENTIAL SUBROUTINE
NATURAL LOGARITHM SUBROUTINE
SQUARE ROOT SUBROUTINE
SQUARE ROOT SUBROUTINE
BIVARIATE POLYNOMIAL EVALUATION SUBROUTINE
BIVARIATE TABLE INTERPOLATION
MATRIX INVERSION
ABSOLUTE BINARY LOADER
ABSOLUTE BINARY LOADER
DECIMAL, OCTAL, BCD LOADER
GENERALIZED PRINT PROGRAM
BINARY CHECK SUM CORRECTOR
READ BCD TAPE OR ON-LINE CARD READER
OFF-LINE CARD READER SIMULATOR
READ-WRITE DRUM PROGRAM
BCD OUTPUT PROGRAM
BCD TAPE WRITING PROGRAM
OFF-LINE PUNCH SIMULATOR
OFF-LINE PRINTER SIMULATOR
LOAD BINARY CARD IMAGES FROM TAPE
READ TAPE WITH REDUNDANCV CHECKING
SHARE A5SEr-1BLER
TRAP DECIMAL MEMORY PRINT
FLOW TRACE
CONTROL PANEL PRINT AND OCTAL MEMORV PRINT ... '·SCOOP)
TAPE END-O~"'fILE ANDIOR REWIND

· ZO
ZO
ZO
ZO
ZO
lO
lO
lO
lO
,lO

ZO
ZO
ZO
ZO
ZO

UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA
UA

01'M2
OTM3
OTM4
OTM5
OTM6
OTM7
OTM8
OTM9
OTMA
PCSl
RWOl
VCSl
ZCSl
ZCS2
ZORl

0
0
0
0
0

0
0
0
0
0

0
0
0
0
0

TAPE REWIND CONTROL
WRITE END-oF-FILE AND/OR REWIND N TAPES
TAPE REWIND CONTROL
BEGINNING-OF-JOB PRINTER TAPE r-1A RK
PRINTER OUTPUT TAPE POSITIONER
BEGINNING-OF-JOB PRINTER TA PE MA RK
BEGINNING-OF-JOB PUNCH TAPE ' MARK
PUNCH OUTPUT TAPE POSITIONER
WRITE JOB TITLE AND BEGINNING-OF- JOB PRINTER TAPE MARK
PUNCH DRUM CHECK SUM VERIFIER
READ-WRITE DRUM
VERIFY DRUM CHECK SUM
CLEAR CORE STORAGE AND MAIN FRAME
SET CORE STORAGE TO ZERO
CLEAR N DRUMS

INDEX OF PROGRAMS
D:: . _ :

=_ ........ .

ELF.MENTARY FUNCTIONS - TRIGONOMETRIC

=:a;.::::'= _.= ==

B1
B1
81
B1

UA
UA
UA
UA

ATN1
ATNl
ATNl
ATNl

B1
B1
B1
B1

UA
UA
UA
UA

S+C1 0
S+C1 1
S+C1 2
S+C1 3

0
1

2
3

==a:.a.=s.::,: _

ARC TANGENT SUBROUTINE
COMPUTES PRI NCt,PAL VALUE OF THE ARC TANGENT. RESULT' IS GIVEN
IN RADIANS. USJ;S RAND POLYNOMIAL. ROU'TINE REQUIRES 39 CELLS
PLUS 3 COMMON. TIMING ABOUT 4.2 MS.
SINE AND COSINE SUBROU'rI NE
COMPUTES THE SINE OR COSINE OF AN ANGLE GIVEN IN RADIANS.
USES RAND POLYNOMIAL. ROUTINE REQUIRES 61 CELLS PLUS 2
COMMON. TIMING ABOUT 3 MS.

ELEMENTARY FUNCTIONS - EXPONENTIAL AND LOGARITHMIC
: : a : :'= .::..a.;:=

B3
B3
B3
B3

UA
UA
UA
UA

EXPl 0
EXPl 1
EXPl 2
EXPl 3

B3 UA LN 2 0
B3 UA LN 2 1
83 UA LN 2 2
B3 UA LN 2 3

======:lI::

EXPONENTIAL SUBROUTINE
COMPUTES E TO THE X FOR ALL. X LESS THAN 72. USES ECONOMIZED
POLYNOMIAL. ROUTINE REQUIRES 45 CELLS PLUS 2 COMMON. TIMING
ABOUT 3.1 MS.
NATURAL LOGARITHM SUBROUTINE
COMPUTES THE NATURAL LOGARITHM OF THE ABSOLUTE VALUE OF X.
USES A RAND POLYNOMlAL. ROUTINE REQUIRES 55 CELLS PLUS 3
COMMON. TIMING ABOUT 4 MS.

ELEMENTARY FUNCTIONS - ROOTS AND POWERS

B4 UA SQR3 0
B4 UA SQR3 1
B4 UA SQR3 2
B4
B4
B4
,B4

UA
UA
UA
UA

SQR4
SQR4
SQR4
SQR4

0
1
2
3

========== ====:=2:.

::t&:a:

.: ==

==-===.a

SQUARE ROOT SUBROUTINE
COMPUTES THE SQUARE ROOT OF THE ABSOLUTE VALUE OF
REQUIRES 22 CELLS PLUS 4 COMMON. TIMING 1.4 MS.
SQUARE ROOT SUBROUTINE
COMPUTES THE SQUARE RO(",T OF THE ABSOLUTE VALUE OF
ERROR RETURN RESULTS IF THE RADICAND IS NEGATIVe.
REQUIRES 25 CELLS PLUS 4 COMMON. TIMING 1.5 MS.

x.

ROUTINE

x.

AN
ROUTINE

APPROXIMATIONS - TABLE LOOf<'.-UP AND INTERPOLATION
==:= .=~= . =========

E1
El
E1
E1
E1

UA
UA
UA
UA
UA

BPEl
BPEl
BPEl
BPEl
BPEl

0

E1
El
El
El
El
E1
E1
El

UA
UA
UA
UA
UA
UA
UA
UA

BPE3
BPE3
BPE3
BPE3
BPE3
BPE3
BPE3
BPE3

0
1
2
3

1

2
3
4

4
5

6
7

==='== = ': .:=

==

=.== ======-==:: :....=-

BIVARIATE POLYNOMIAL EVALUATION SUBROUTINE
EVALUATES A BIVARIATE POLYNOMIAL OF TOTAL DEGREE N~ ROUTINE
REQUIRES 36 CELLS PLUS 4 COMMON. EACH POLYNOMIAL REQUIRES
«N+2)(N+l)/2)+5 CELLS FOR COEFFICIENT STORAGE. NO OUT-OF'"
RANGE TEST IS PERFORMED. TIMING 0.l8N*N+0.72N+1.056' MS.
BIVARIATE TABLE INTERPOLATION
SELECTS A SUITABLE 3 BY 3 ARRAY OF FUNCTION VALUES FROM AN
M BY N ARRAY IN CORE. PERFORMS BIVARIATE INTERPOLATION IN
THIS 3 BY 3 ARRAY BY FITTING AND EVALUATING 3 QUADRATICS , IN
V, FOLLOWED BY ONE IN X. AN OUT-OF-RANGE ERROR RETURN IS
PROVIDED. ROUTINE REQUIRES 161 CELLS PLUS 12 COMMON. VALUES
OF X, y, AND Z REQUIRE M+N+M*N CELLS. TIMING AVERAGES ABOUT
16 MS FOR A 10 BY 10 ARRAY.
{

MATRICES, VECTORS, AND SIMULTANEOUS LINEAR EQUATIONS
FO
FO
FO
FO
FO
FO
FO
FO

3

UA
UA
UA
UA
UA
UA
UA
UA

INVI 0
INVI 1
INVI 2
INV13
INVl 4
INVI 5
INVI 6
INVl 7

MATRIX INVERSION
INVERTS A MATRIX STORED IN CORE STORAGE. USES AN ELIMINATION
METHOD. THE STARRING ELEMENT IS THE LARGEST IN THE COLUMN,
BUT THE COLUMNS ARE USED IN ORDER FROM LEFT TO RIGHT. THE
ORIGINAL MATRIX IS DESTROYED, AND IS REPLACED IN STORAGE BY
THE INVERSE. THE ROUTINE REQUIRES 171 CELLS PLUS 2N+8
COMMON. A 61 BY 61 MATRIX CAN BE INVERTED IN A 4096 WORD
MACHINE IN ABOUT 100 SECONDS.

INJJUT .. BINARY
11 UA
Il . UA
11 UA
11 UA
11 UA

CSSl
CSSl
CSSl
CSSl
CSSl

0

UA
UA
UA
UA
UA

CSS2
CSS2
CSS2
CSS2
CSS2

0

11
.11
11
II
11

1

2
3
4

1
2
3

4

ASSOLUTE BINARY LOADER
LOADS SHARE STANDARD NON-RELOCATABLE BINARY INFORMATION CARDS
AND TRANSFER CARD~. ALSO LOADS PROGRAM CORRECTIONS PUNCHED
IN ROWS 8 TO 12 OF TRANSFER CARDS
PROGRAM IS SELF-LOADING
AND USES CELLS 0 TO 71.
:
ABSOLUTE BINARY LOADER
LOADS SHARE STANDARD NON-RELOCATABLE BINARY INFORMATION CARbS
AND TRANSFER CARDS. ALsO LOADS PROGRAM CORRECTIONS PUNCHED
IN ROWS 8 TO 12 OF TRANSFER CARDS. PROGRAM IS NOT SELFLOADING. PROGRAM REQU~RES 54 CELLS PLUS 3 COMMON.

INPUT - COMPOSITE
14 UA DSCl

0

14 UA DSCl 1
14 UA DSCl 2
14 UA DSCl 3

14
14
14
14
14
14

UA
UA
UA
UA
UA
UA

DSCl
DSC1
DSCl
DSC1
DSC1
DBCl

4
5
6

7
8

9

DECIMAL. OCTAL. BCD LOADER
USED WITH UA TSM 2 OR UA CSH 2. CONTROLS TAPE. PROGRAM UA TSM
2 OR TAPE OR CARD PROGRAM UA CSH 2 TO READ BCD INFORMATION
INTO CORE. CONVERTS THIS INFORMATION TO BINARY, .. FIXED OR
FLOATING DECIMAL NUMBERS BE .ING CONVERTED TO FIXE.D OR FLOATlNG
BINARY NUMBERS. AND DECIMAL OR OCTAL INTEGERS BEING CONVERTED
TO BINARY INTEGERS. ALSO READS AND STORES HOLLERITH LABELS.
COMMENTS. ETC.. INPUT CARD FORMAT IS VARIABLE. LOAOING MAY
BE CONTROLLED BY TRANSFER CARDS. ROUTINE REQUIRES 312 CELLS
PLUS 24 COMMON.
I

OUTPUT - COMPOSITE
J4
J4
J4
J4
J4
J4
J4
J4
J4

UA
UA
UA
UA
UA
UA
UA
UA
UA

SDCl
SDC1
SDC1
SDCl
SDCl
SOCl
SDC1
SDCl
eDCl

0
1

2
3
It

5
6
7
8

GENERALIZED PRINT PROGRAM
USED WITH UA STH 1 OR UA SPH 1. CONVERTS FLOATING BINARY
NUMBERS TO FIXED OR FLOATING BINARY CODED DE-A39-A36*A511 AS,6 ')
----- ,----- --.--'-'- Bl19=A32* (A58*A561 ASl) * (A3'7-A40-A31*A51/A5-6)
,
Cl19=A29*(ASS*A56/ASlt*(Dl-A51/A56J
-- --D119=A30*A5 8*A561 A5l
_.
-- 0 _
Ell'9= (A58ifA561 AS1)* « Al'9*A3) *(.A:3.6-A39-A36*AS,1,IN5-6):fo(A2G*A3:,2
- - ...-,-1,-- (A37-A40-A37*A51/A56)-(A23*A29)*("O'1 -ASltA56·;)i+A24*A30)
.
,--- - .--P120=A57*A59/A52
---- --.--- ,----- ,- ,A120=A3,1 *P120* (Dl-As'2/ AS1 J
B120=A32 ~~P 12 0
e12 O=A29 -l(- P120"~ (A42*{ DI-A52;,/ A5"71-+A25*A33*A38.
o 120=A30~(-P 120* C' A4:3-A46-A43*A521 A57+A41*A2-5*A33)
E120=A33';;'PI 20
F120=A44-A41+A24*A30*A41-A52*A44/A51+A38*A2:3*A29
- . .. --.. -.--___ .. --_ 0 _
H120=P120* (-AI9*A31* (DI-AS.21 A57 ,),+A20:*'A32+A23*A2:9*A42*(Ol"'A52/
A,57) +A30 -)<:- A24* (A43-A46-A43*A5ZI AS7lfoA2: 5*A313*( A44-A41+A2-4*A30*
-. --.-- - . 1 A41 +A38-l<-A,22*A29-As2*A441 A51)' .)
~ -- -- - - 2
A123=A67*A79*A80/A81
8123=(A13+A15'*A79*A67/A81

a*

1

C12~=A31*A64/A11

. __ 0
- - ----- 1 -

D123=A32*A65/A77
G123=A30 *A66/A77
P12'3=A34/A77
Q123=A35*A34/A71
R12'.3= (j -A 79*A 78*A6 7-A18,*A80*A.67*A7"9) I ASJ..+ tA94*A3S,*A'34+A19*A.31
*A64+A20~rA32*A65+A2"3*A29~A, 63+A30*A2'4*A6:6-A28*,A34l/'A17)

F124=A51*A77
A124=A3:1 * (A36-A39 )'IF1.24
B124=A32*(A37-A40)/F124
C124-=A29/F124
D124=A30/F124
-, - 0
E12-4= (A19*A31* (A,3'6 '-A39l-t:A20*A32* ',A37-A40 )'-A23*A29+A,2:1t*A30,ll
----------.----.1.-_____ .. F124
.
,
G!25<=A17*A82

A125,=A2'9/GI2's
B12'5:=A31 * A36;/ G'1'Z'5
- - --- - . -- ___ , __ E125=A53/ A82 _. _______ .
A 126=A 3 ,1 I R12.6
.'---.- ----- --...-.

~

_...... Bl,26=A3:2/R126 . _. __ .. _.
.
C12b= (A42+A3.3*A 3'8'*A25 )· *A2\9}R.l2~

F 12:6= A2'9* A38

o

G126=A30~~A41

P126= f A32*A20-A 1·9*A3.1+<'A2:3*A.29*'A4.2+A.2-4*A-30·* ,f A43-A46 it:+J:*:A6,..,A''*6&2o'1 -P12.6.1'I!A2*
_1
A126+A3*Bl.26+A,6*C126+A1*D126
. - -, - ------- ----- -- ----_____ _ _____________ ... Z 12 7:A 2*A 12 7 -A6,*B 12 7,...A 7*C12:7-A8,* .o127 +Z 126*E .121~F 1.21

Z128;=A8*A128-A6*B12:8-A2*C12,8-A3*0128-A7*.E,lZ,8+Z126.*F12B~G,128
Z129=AIO*A129+Z119-C12~
,
Z130=-AIO*A130+Z120~C130

X=COSF(Z129)

___________

Y=SINF(Z129)
Z131=Z127*X-Z 128*V
Z132=Z128*X+Z127*Y
ZI33=Z124*X-Z123*V
Z 134=Z 123*X+Z 124*V
Z141 =A9*A141+ (A13lf-A141*B14.1-(141
A135= ( (A5-A22 )*A 70+A,1 3:+At'5) ,. ",.t\9,·,,·A26 ,).*A71"+A13,.A14 '.

A139=D 1*A11*A79
Bl'39=D 1*A19

o

-

(139=D 1*A71*A79*A26
Z13~=A9*A137*Z136*Zl~6.Al:J9+
,tA13,4!~1,ift,.) *.Al~'l.Zl'6.Z)'{S;'''SlS9,

1· -.

A19-1*Z 196*Z136*C139
A143=( All*A73+Al3-+A.15-A27*A131t.(.A9.A7.l~13~A14~A26*A21~.
1----- - -- - -.- - -. Z136.=A135*SL+B
X136=Z136'*AL:P+BET
X143=A143*ALP+BET
A137=CO+X 13.6* ( C1 + X136* (:C2+ X.1 .36* t C3,+X136* t C4+X136* tC.5+X li:3O*
o
(6)
tll -l
1
o
Z14,3 =CO+){143* (CI:+X~43* tCZ'+ X1A3* t.C3+-X143* ,( C4+Xl.lf3* ·(eS+X143*

&---- -- -- 1.-.--.-- (6 .) ),:). .}..)

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

--

'c--- - ---------.--.---.......-_.-.-- "'-

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

r-.- - - - - - -- 1-- - -- - - -_ ....._--_.
1---- - - - - - -- - -

1-- - - - - - - -- - -

1-- - - - - - - ------_._-----

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

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

:- - - - - - - -- - _._----------1--- - -- - - - - - - - 1:-- - - - - -- - - - - - --

----- -----_._._-_.
1-- - _ . _- - - -

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

'1 .

1

/

REM
CODING BY ALGEBRAIC TRANSLATION SECTION OF FORTRAN
REM
Z • -A + (B-C*O)*(E*SINF(B-C*D))*(F~C*DJ/(RO • X*(Rl + X*(R2
1 REM
+ X*(R3 + X*R41l4, IZ3) Il2) IZ1'
·CL.A X
FOP l4
FMP R4
FAD R3
FOP Z3
FMP X
FAD R2
FOP Z2
FMP- X
FAD R1
FOP Z1
FMP 'X
FAD RO ·
DENOMINATOR
5TO 15+8
Loa C
FMP 0
C*O
STO 15+7
CHS
FAD F
C~D
F
STO 1S+6
CLA B
FSB lS+7
C*D
B
STO 15+5
5XO 15+4.4TSX SIN.4
LXD 1S+4.4
•
.4vn. (S-C*D)
5TO 15+4
Loa E
FMP 15+4
STO 15+3
E ~(B-C~O)
LOQ 15+3
FMP 15+5
FOP 15+8
FM·P 15+6
FSB A
STO Z

~

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-

".

I

Stacking Analysis

Reference:
T. C. Fry - "Probability and Its Engineering Uses" Chapter X-D. Van Nostrand Co.

Assumptions:
1.

Runs average 4 minutes each.

2.

Distribution of length of runs is approximately exponential.

3. System is in statistical

e~uilibriumj i.e., the probability
of its being in any specified condition is independent of the
time at which it is examined.

4.

Machine change-over time between one run and the next is
negligible.

5.

The number of job sources is large compared to the number of
machines.

6.

Any job can be handled on any machine.

7. All machines are in use whenever there is enough work available.
8.

Any run which cannot be handled immediately is held until a
machine becomes available. It is then handled at once. If
several runs are being held, they will be serviced in the
order in which they originate.

j f

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0 ."

0.7

LOAD

I.i--t-'

. . . -+.~

: Jh-'~'

_...l

.

~~

t ,-

::.I.~'i-:!'

- ;J+t . . .

~8

'FAcToR

+

.t4I~J::,,:r:rf:tp:··:·.··C·'-~I,fP~

~7 ·---d ~r-=r- r

Q9

~

---

"'r-

:~

1. 0

-"

0 ...

X;

-

I'"

..,

0 '"

I-'!l

0",

I- " •

:to>
'"
.,,1"I'I1:l
'" 0 0;: 4

() n :s:

~O ~

. ';'
W .g
rJ

=

....01:;:
, ~

I :

'r

1.7

L.oAD

," -,~-...

J.; >f8

FACTOR

'T-'-

r~

tE· . !?-::i ~l:
~9

4ili F~'

.:t'~
2 .0

-

'<:

0 '"

>< ~
_ rr

.

0 '"

1-0(1

0",

1-"
..... ".,
;;;:r. ~

,., c: .;

noS:
:EO.s:
'"

. '"

w g
R)~
QI~

1-, -x

4 "

(,) .

- :

o
2·55

. .. ,

2 .,",

"__.

'T'·:~i--, ·- r .....l~;.-.;:~;

2 .7

LOAD

. ......

~'."

2.8

FAC.TOR

"' 'l."::

~.

..- ~==t!-.~ ,, :~ . ~

,'"

±t:+C+-.n

.~.~;~.ti.;-

2.9

,:~l- ~'~tl~C:± P i· :tt:::tt
~ ~.
T
-~r=-_ .;:;-tl · i+t± ... -

'."

0.0

.

•

o~

..;>,$$

,

,

,

•

Tabulation of ryp1cal Results

Percentage of Idle Time

Delay in Minutes

One
704

Two
704's

Three
704'6

Four
704'6

Average

20.

10.

6.67

5·

11

19

10.

5.

3·33

2.5

25

41

89

5·

2·5

1.67

1.25

52

85

181

2·5

1.25

0.83

0.62

loB

173

365

1.25

0.62

0.42

0.]1

219

349

734

One out
of three

-

One out
of ten
43

Note that these results may easily be modified for cases where the
average length of run is greater than or less than 4 IDfnutes since, to a
close approximation, the delay is directly proportional to the average length

.

of run.

"

r----

~-

I
OR2
6 January 1958
DECIY.AL ClffiD READ ROUTINE
Compilable: 11inimum 1103A
Operations Research Office-Sumner
Revision of CVl31-Hauser and Gerkin
A.

PDRPOSE

This routine reads decimal numbers from cards and converts them into
the appropriate binary. numbers, sealed as de~ired by the programmer.
B.·

tTSAGE

l.

LEADING LINES
Sub
Temps
Inout

OR2

142

1

o

o

o

2 • . INPUT

The input consists of two basic parts. The actual input to the
routine is a control word having the following composition:
AB OPPPP ODDDD (octal)
,

A:

First· octal digit, controls picking o£ cards in ei ther channel
of the Bull reproducer.

=
0
=1

A
A
A
A•

=

B:

Do not pick
Pick a read card
2 Pick a punch card
3 Pick both read and punch cards

Second octal digit, controls the reading operation.
B
B

=0
=1

Do not read
Read a card

OPPPP:

Magnetic core address of the first. parameter word.

ODDDD:

Magnetic core address where the nUmber from the first
card field is to be stored.

This control vlOrd supplies the subroutine va th the location of
the parameter words which have the following composition:
FF SSBBL LRRZZ (octal)
FF:

flag for final parameter word
FF
FF

= 77

= 00

(octal) for final par~~eter word
otherwise

0R2

-2ri ~ht

SS:

Binary scaling factor (number of bits to the
the binary point) of converted number.

of

BB:

~~ber of blank or unused card columns to the left of
t he field. (See definition of field under D.)

LL:

~Umber of columns (digit positions) to the left of the
decimal point.

p~:

Number of remaining columns in the field, exclusive of
sign (number of decimal digits to the right of the decimal point plus one for the decimal point).

ZZ:

Not used.

Range of parameters:
DECI}llAL

OCTAL

00

S ss .5 35

00

S"

SS

S

00

S

BB $ 63

00

S

BB

5' 77

00

s:

LL S 10

00

~

LL

.s 12 _

00

s:

RR .$ 11

00

S

RR

~

01

oS

LL ;. RR

01 ~ LL

+ RR $

11

43

13
~

13

These parameter words should be stored as coristants by the
-programmer in consecutive order. To read a card containing ·
~ fieldS (numbers) ~ consecutive parameters must be stored
beginning at the aqdress specified by the u-address of the
control word. The ~th parameter should contain 77 (octal)
as the first two digits.

3.

RECOVERY PROCEDURE

In case of a card machine failure or an accidental stop in the
middle of a card cycle, the current card may be reread: reposition
the cards, set (Pft~)
00000, and Start.

=

4.

NUMBER OF TAGS USED

5.

RUNNI NG TIME -

= 23

(decimal)

The programmer has 14 ms. computing time available between
references to the card routine. If this time is regarded as a maximum, the Bull reader is virtually in a state of free run, and can
attain a reading speed of approximately 120 cards per minute.

-:$
o

T"""

C.

RESTRICTIONS
The only restrictions. are those caused by the parameter ranges.

OR2

-3D.

ADDITIONAL PROGRPl-J.ITN8-

A~TIJ

OP:sR.ATING

INFOPJ.~TION

This card routine operates on a two-cycle basis, making more efficient
use of the card cycle time than pre\Qous routines. As a result, as many as
forty fields may be read from each card without causing any timing qifficulties. Two basic operations are performed during the IB-point card cycle.
The first five points (about 140 ms.) are used to decode the control words and
to perform the final conversion of information read during the previous read
cycle. The remainder of the card cycle is used to read information from the
present card and convert this information into binary coded decimal form.
Trre--binary coded decimal information is then converted to binary and scaled
during the first part of the next read cycle. Thus , although it takes two
card cycles to complete the operation of reading and converting, the net
effect is conversion of one card each card cycle.
A field consists of a number of consecutive card columns. The last
column of a field is reserved for the sign of the decimal number stored in
that field. An II-punch signifies a negative number, no punch (blank column)
signifies a positive number. A combination 12, 3, and B punch in one column
may be used to represent a decimal point.
Fields need not be adjacent~there may be unused columns, punched or
unpunched, between them--nor need they be alike in size.
The read side of the Bull must be cycled once before reading. The
following coding is an example of a routine to read E cards, each of which
contains E decimal numbers.
TAG

Set

OPS
0R2
0R2
TP
0R2
RA

IJ

v.s
Cycle
Read ·

11
11

Cycle
Read
K

IJC

Read - 1
Read
1
IJC

Step
Set - 1

Pick a read card
Read (only) first card
Set counter for n -1
Read and conve~
Advance data storage
Check counter
Control word
II

Param

Data
n-l

X
B

Comments

V

10

K

IJC
Step
Param

U

p
1st. parameter word

"

"
"
cards,

No. of
minus one
Counter for n reads
Constant
Parameter words

•

Data

B
Reserv

pth. parameter word
pn
pn

Region at which data
is to be stored

Note that the above coding assumes the format on each of the n cards
to be the same. In other words, any particular field must have the same size
and location on all of the ~ cards, or else a new set of E parameter words
must be used for each card.

-4The information read from the card is stored witpin the card routine in
coded decimal form. Thus, if the subroutine is destroyed between card cycles,
this information ~~ not be converted on the following card cycle.

0R2
TAG

OPS
-

V ADD:tESS

U ADDRESS

-,

COHIICSNTS

,SUB

,OR2

~14.2

,

$

,TD~S

,0

,0

,

$

,INOUT

,1

,0

,

$

, MJ

,

,p·n

,ENTRANCE

~

,

,ALARM EXIT

$

,FILL

,NOID'lAL EXIT

$

,COI\TTROL

"lORD

$

,TEST CONTROL

~

,ALARH
,EXIT

, MJ

,P

,X

,

....

....

,TP

, BODY- 2

,Q

,

, QT

,P

,A

,
,
,

,ZJ

,BODY

,BODY-1

,07

,

,

,

SETTING

$

,RJ

,PICK+l

,PICK+l

,SET S\'lITCH

$

,BODY

,TP

,P

,PAR

,SET UP

$

,

,RJ

,GO

,GO

$

,PAR

,X

,

,
,

,

, V0

,

,EXIT

,

$

,GO

,M?

,K

,FILL

,

$

,

,TU

,A

, ROW+4

,STORE PARAMEI'ER WORD

$

,TV

,A

,NEG+2

,STORE DATA WORD

$

,

,LQ

,A

,3

$

,

,SP

,MASK+4

,30

,
,

,QA

, HASK-l

,A

, EXTRACT PICK CODES

$

,
,
,

,SA

,A

,1

,LQ

,Q

,2

,
,

,QJ

,OUT+l

,PICK

,READ?

$

,PICK

,EF

,A

,START CARD CYCLE

$

~'JORD

FOR

SWITCH

E~'1'RAN CE

$
$

$

$

.$

$

r-

~

0
......

,RJ

,PICK+l

,PICK+2

,CONVERSION SWITCH

$

,RJ

,PICK+2

,PICK+3

,READ SWITCH

$

-5-

0R2

TAG

to

-.:t

0

or-

V ADDRESS

U ADDRESS

oOPS

,

,SP

,GO

,

,AT

,K-l

,OUT

,X

,

,SA

,K

,
,

,RJ

,PICK+2

,RS

,

COHMENT3
....

,SET
,OUT

~

EXIT
,ROW WORD 3

~

,ADD READ CODE

$

,PICK

,SET TO READ

.,..'t

,A

,A

,

;;>

,RPI

,10

,OUTt6

,CLEAR

~

,

,TP

,A

,MASK+5

,
,

,TV

,K-2

,

,TV

,READ+6

,DIGIT

,READ

,ERa

,

,OUT

,READ

$

,

,ERI

,Q

, ONE

$

,

,ERI

,R WORD

,

$

,

,RJ

,READ+3

,REAOT4

,LAST ROW SWITCH

$

.,

,TP

, AWAY+2

,ADD

$

,

,TP

, MASK-l

,INDEX

,
,

,

,SP

,K-l

,9

,

$

,SA

,A

,3

,

oil>

,BIT

,QJ

,BIT+l

,BIT+2 ·

,BIT IN THIS COLUHN?

.;p

,
,
,

,SA

,DIGIT

,

,

$

,SJ

,BIT+3

,READ+7

,REACHED SENTINEL?

$

,SP

,A

,

$

,ADD

',X

,

,
,

,

$

,

,RA

,ADD

,MASK+2

,STEP MATRIX STORE

$

,
,
,

,IJ

,INDEX

,READ+6

,ROW WORD EXHAUSTED?

$

,RJ

,ADD+3

,ADD+4

,SWITCH

$

,LQ

,RWORD

,

$

,

,RJ

, ADD-+-3

, READ+ 5

,
,

..

MATRIX
,SET RERUN

-6-

'"

...

;;>

...

~

...

~

ROW

....

.;p

'"

...

$

OR2
PT"_ .-..:J
,.,r

U

OPS

V ADDR"2:SS

ADD:t~3 S

CGMHENTS

,LQ

, CUT

,28

$

,RJ

, A~D+3

,READ+6

$

, RJ

, ADD+8

, ADD~9

, S~..'ITCH FOR SIGN ROIy

$

,IJ

,DIGIT

,READ

,

$

, RJ

, ADD+8

, OUT+7

,RJ

, READ+3

,READ

,READ LAST ROW

$

,RJ

,PICK+l

,PICK+3

,SET CONVERSION SvJITCH

$

,TU

,A ,yAY+2

,STEP+l

,

;n>
"

,RJ

,NEG+5

,ROW+4

,SET CONVERSION REPEAT

$

,LQ

,FILL'

, LAST

, ~J

,LAST+1

,LAST+2

,LAST FIELD?

$

,

,TV

,PICK+1

, NEG+ 5

,SET CONVERSION EXIT

$

,

,LQ

,Q

,11

,

,QT

,MASK

,A

,TV

,A

,REMt3

,LQ

,Q

,6

,QT

,MASK

,INDEX

,

$

,LQ

,Q

,6

,

$

,QT

, Y~ SK

,RWORD

$

,LQ

,Q

,6

$

,

,QT

,MASK

,OUT

$

,

,SA

,A

,14

$

, SET

,AT

,A~>JAY+l

,SET+l

,SET NEXT INSTRUCTION

$

,

,X

,

,

,

$

,IJ

,INDEX

,NEG+6

$

$>

,
,RmJ

1

$

0'

~

$

$

,SET
SHIFI'

,
,

,RJ

,AWAY

,SET.J.4

,IJ

,RWORD

,STEP-2

,

,RJ

,STEP~3

,REM

,SHIFI' DECHLll.L POINT

-7-

$
$

,
,
,

0
,.-

$

$
~

O?.2

TAG

, RElI,

,

,NEG

,

OPS

U

ADD:t~S S

V ADDRESS

CCIY..2:1:TS
....

,RJ

, A:'!AY

, RErVi

, CCrJil:<:RT

.;.

,IJ

, OUT

,STEP-2

,

.

,TP

,SET+1

,A

,LT1

,71

,Q

,

·3

, SP

, INDEX

,FILL

,

$

,SA

,Q

,ADD ROUNDING TERM

$

,DV

,SET+1

,SET+1

,RJ

,ST EP~3

, STEP-2

, QT

,Y.ASK+4

,A

,ZJ

, NEG+1

, NEG+2

,SIGN NEGATIVE?

$

,TN

,SET+1

, SET+1

,

$

,TP

,SET+1

,FILL

,STORE RESULT

.;p

,RA

,RO'rJ+4

, MASKtl

,

$

,RA

, NEG+2

,K

,

'lP

,FILL

,

$

, MJ

REl·:AINI!{G T~FL·:S

$

$

,SHIFT SIGN

$
$

A

...

,TV

, Ai-1AY+3

,S TEP t3

,IJ

·,DIGIT

,STEP+2

, MATRIX HORD EXHAUSTED?

$

, TP

, HASK+4

,DIGIT

,

$

,STEP

,RA

, STEP+1

, t·1ASK+1

,

,TP

,FILL

, MASKt5

,

,LQ

, NASK+5

,4

,
,
,
,

,RJ

,ST EP~3

,STEPt4

, AWAY

, 11J

,

"

~

$

,TRANSFER NEH

~~TRIX

WORD

$
$

, SHITCH

$

,SP

. ,IHDEX

,2

$

,SA

,INDEX

,1

$

, QA

, MASK+3

,InDEX

ct

'If'

,FILL

,CONVERSION EXIT

$

,TP

,K

,SET+1

,PRESET

$

~ AT

, HASK+5

, HASK+5

,PRESET

$

-8-

.-.

0R2

OPS

TAG

U

,

$

,GO

,

$

,

,

$

,1

,

.jp

,1

,TABLE

$

,X

,10

,

$

,X

,100

,X

,1000

$

,X

,10000

;;p

,
,LA ·
,X
,X
,N

,..-

POiVERS

$

,>;.

,100000

,

,X

,1

,000000

,

,X

,10

,000000

,X

,100

,000000

,

,X

,1000

,000000

,
,
,

,

,X

,10000

,000000

,

,X

,3

,MASK

,

,
,

,
,

,77)B

"EXTRACTOR

$

,

,

,1

,0

,U ADVANCE

$

,

,1

,1

, U AND V ADVANCE

$

,

,
,

,17)B
,10)B

,

$

,RESERV

,9

,9

,11ATRIX WORD

$

,INDEX

.,X

,

,

.,INDEX

$

,DIGIT

,X

,

,

,DIGIT

$

,RWORD ·

,X

,

,ROW WORD 2

$

,

,ENDSUB

,

,

$

,

0

'"

,

,

,..-

,.
,

,X

,
,

tr\

CCl-iliENTS

,SET+2

,

,K

V ADDRESS

ADDRESS

,

-9-

$

OF

$
$
$
$

TEN

$
$

$

OR3
6 January 1958
DECIMAL CARD PUNCH ROUTINE
Compilable: lVlinimum 1103!!.
Operations Research Office-Sumner
Revision of CVl30-Hauser and Gerkin
A.

PURPOSE

This routine converts binary numbers into decimal, and punches them on
cards, complete with sign and decimal point.

B.

USAGE
l.

LEADING LIl\TES
Sub
Temps
Inout

2.

OR3
0
1

173
0
0

INPUT

The input to this routine consists of a control word and a series
of paramet er words. The progrannner must supply the routine with the
control word, which in turn supplies the routine with the location of
the parameter words and the location of the data which is to be punched.
The control word has the following composition:

AB OPPPP ODDDD (octal)
A:

First octal digit, controls picking of cards in either channel
of the Bull Reproducer.

=0
=1
A =2

A

A

B:

not pick
Pick a read card
Pick a punch card

Do

Second octal digit, controls the punching operation.
B
B

=0
=2

Do not punch
Punch a card

OPPPP:

Magnetic core address of the first parameter word.

ODDDD:

Magnetic core address of the first data word.

The parameter words (one for each data word) have the following
compositions:
FF

FF

= 77

= 00

(octal) for final parameter word.
otherwise

OR3
-2-

SS:

Binary scaling factor (number of bits to the right of the
binary po in t ) •

BB:

Number of blank or unused columns between previous field
(see definition of field under D), or edge of card, and
present field.

LL:

1Uffiber of digit positions to the left of the decimal point.

RR:

Number of remaining columns in the field exclusive of sign.
(RR
00 - no decimal point and no decinial fraction.)

ZZ:

Flag for zero suppression.

=

=

ZZ
77 (octal) for zero suppression
ZZ = 00 for no zero suppression. Only zeros in the integer
part are suppressed. A zero immediately preceding the decimal point is not suppressed.
The total size of a field is:

LL + RR

~

1

Range of Parameters:
OCTAL

DECI}fJ~

ss

00 S SS

~

35

ODS

00 ~ BB

i

63

00 ~ BB

~

43

S 77

s: LL S. 10

00

s: LL S 12

OO~RR5'll

00

~

00

01

S'.

LL - RR ~ 11

RR ,513

01 So LL - RR

~

13

The parameter words, one for each field, must be stored consecutively, starting at some w~gnetic core memory location 'OPPPP.
There must be an equal number of consecutive words starting with
some magnetic core memory location ODDDD, filled with data for
the punch routine.

3.

RECOVERY PROCEDURE

In the event of a card machine failure or an accidental stop in
the middle of a card cycle, the current card may be punched again. Set
(PAK)
00000, and Starto

=

OF TAGS USED = 18 (decimal)

4.

NmrnER

5.

RlJ111ITNG TIME

The programmer has 17 ros. computing time available between references to t.he card routine. If this time is regarded as a maximum, the
Bull punch is virtually in a state of free run, and can attain a punching
speed of approximately 120 cards per minute.

OR3
-3C.

?ESTRI CTImTS

The only restrictions are those caused by t he parameter ranges.
D.

ADDITIOJ~AL F?"OGR.t.l·}~If.TG

M.:D OPERATHTG Il;FOP..i':ATIGN

~:un:bers are rounded to the specified nu.n:ber of decimal digits after
the decimal point before punching takes place. A divide f ault occurs if
an insufficient number of card colurrns is allowed for the integer portion
of a field.

Punching takes place at the third card station in the punch channel.
Therefore, two punch cards must be advanced 'before punching can take place.
This may be done cy referencing the card routine twice, supplying the
appropriate control Hord. (See composition of control words.)
A field consists of a number of consecutive card columns. The last
colunn of the field is reserved for the sign of the decimal number stored
in that field. ~~ Il-punch signifies a negative number, no punch (blank
column) signifies a positive number. A combinat~on 12, 3, and 8 punch in
one column represents a decimal point. Fields need not be adjacent--there
may be unused columns, punched or unpunched, between them~-nor need they '
be alike in size.
I
It is possible to convert and punch as many as forty fields in a card
and have 17 IDS. computing time available between references to the punch
routine.

OR3
TAG

V ADDRESS

U ADDRESS

OPS

COMr·!E!\TTS

,SUB

,OR3 ·

,173

, TID:FS

,0

,0

,

-;;

,INOl1T

,1

,0

,

$

,BODY

,ENTRANCE

$

, HJ

$

,ALAP'}~

,ALAPcM

,.

l('\
l('\

0
~

,FlU

,X

,
,

,BODY

,TP

,P

,

,RJ

,PAR

,X

,

,EXIT

,MJ

,P

~,

EXIT

, NOPJ.fjI~

EXIT

ci!'

~

$

,CONTROL v.JORD

$

,PAR

,SET

$

,GO

,GO

,

$

,

,¥JJ

,
,

,EXIT

,.GO

,MP

,K+6

,
,
,

,TU

,

UP

ENTRA.NCE

"

$
$

,FILL

,
,

,A

, LAST-1

,SET PARAMETER PICKUP

$

,LQ

,A

,3

,

$

,SA

. ,A

,li

,

$

,TU

,A

,STORE4-7

,SET DATA PICKUP

$

,SP

,K+3

,32

,

$

,

,QA

,D1AGE-5

,A

,EXTRACT PICK CODES

$

,

,SA

,A

,1

$

,
,

,QJ

,BULL-1

,BULL-:),

,
,

$

,QJ

,PUNCH-1

,BUU

,PUNCH?

$

,BUil

,EF

,A

,START BUil

$

,

,SP

,GO

,SET

$

,

,AT

,K+5

,BULLl-3

,

$

,
,

,MB

,

,BtJLLt3

,EXIT

$

,SA

,K+3

,

,ADD PUNCH CODE

$

,PUNCH

,EF

,

,A

,START BUil

$

,

,CC

, DIAGE

,A

,

$

-4-

$

EXIT

OR3
TAG

OPS

..-

...

,35

,P1.JNCH+4

y

,TP

,A

,IHAGEt1

'"
.;;>

,

,TV

,K

,

,SET

,

,TP

,K+2

, BULL+3

,

$

,

,TP

, PRESET

,ALLt2

,

S

,

,RJ

, JI.LLt4

,LAST-1

,SET

,

,LQ

,FILL

,LAST

, QJ

.1NEG+4

,.LA.sT+1

,LQ

,Q

,il

,

,QT

,IHAGE-4

,A

,
,
,

,SN

,A

,AT

,PRESET+5

,STOREtS

.1SET UP SHIFT ORDER

$

,LQ

,Q

,6

,.

$

,

,QT

, D'lAGE-4

,sTEP+5

$

,
,

,LQ

,Q

,6

,
,

, F,AGE-4

,ALLt3

,

$

,SA

,A

,14

,

$

,AT

,PRESET+6

,SET+l

,SET NEXT I NSTRUCTION

$

,

,

$
$

. ,QT

,X

0

COElJEIITS

,RPV

,SET

-J)
Il"\

V ADDRESS

U ADDRESS

E1·~GENCY

RERUN

S~!ITCH

...

';(

...

y

,

y

,LAST FIELD?

$

....

$

,

$
~

ell-

<;j>

,LQ

,Q

,.6

,QT

, IJV.JAGE-4

,SET+1

,
,

,SA

,A

,14

,

$

,

,AT

,PRESET+7

,STORE

,SET NEXT I NSTRUCTION

$

,STORE

,X

,

,

$

,
,
,

,QJ

,NEGtl

,STORE+2

,ZERO SUPPRESSION?

$

,TV

, NOZERO

,PHESET-1

$

,RJ

,NOZEHotS

,STOREt4

,
,

,.

,IJ

,STEP+5

,NOZER0+3

,

$

,
,
,

-5-

$

$

OR3
TAG

I:'--

~

OPS

-U ltD:::lRESS

V ADDRESS

COl-:J.ZNTS
$

, STEPt5

,
,
,

,

,

,

$

,SA

,Q

,

,ADD ROUNDING TER}l

$.

,

,DV

,STEPt-6

,A

,

$

,

,AT

,A

,STORE

,

$

,

,RJ

, NOZEROt8

,DEC-l

,L TThES THROUGH

$;

,

,IJ

,AL1+3

, NOZERO+9

,

CONIlERSION LOOP

$

,DEC

,TV

,K-l

,NOZEROt-8

,STORE DECIMAL POINT

$

,

,IJ

, SET-r1

,STEP+2

$

,

,IJ

,SETt-l

, NOZERO~9

$

,.
,
,
,

,TU

,STORE+7

, NEG-I

,
,
,

,RA

,LAST-l

,D'JAGE-3

,STEP PAP.n~TER

$

,RA

,STORE+7

,D-1AGE-3

,

$

,TV

,ALL+4

, NOZEROt-8

,SET EXIT

$

,

,SN

,ll-1AGE-3

,

,

,LQ

,FILL

,

,
,

$

,NEG

,QJ

,NOZEROt-l

, NOZEROt3

,NEGATIVE?

$

,

,RJ

,PRESET-l

,STOREt3

,

$

,
,

,EJ

,ALL+3

; NOZERO

,

$

,HJ

,

,NOZERO+3

,

$

,
.,
,

,RJ

,AL1+4

,.LAST+l

,

$

,3

,ALL+l

,SET UP

$

,TP

,PRESET4-2 .

,ALL+2

,

,ALL

,EJ

,PRESETt-3

,BD1L+l

,
,

,TV

,K

,

,X

,

,

,SP

,DlA-GE-3

,19

,

,DV

,STORE

,Q

,

,'I'M

,FILL

,X

,

. ,RP3

$
....
;;p

$

....

'Il>

PUNCH

OR:;~"'RS

$

0
T"'"

$
,SET EMERGENC ;' RERUN
. ,PUNCH

-6-

$
$

OR3
TAG

OPS

,
,

,X

V ADDRESS

COKHENTS

.,

ONE

~
'ii'

,X

"
,

,

,STEP

, RP2

,3

,ALL

,STEP

w

,

,RS

,ALL+2

, K+-6

,

$

, SP

, I MAGE-2

,

, AT

, ALL+2

, STEP+5

, AT

, K+4

,STEP+6

,X

,

,
,
,
,

,X

,

,

,SN

,DiAGE-1

,

,PRESET-1

, NOZERO+1

,SET NO ZERO SUPPRESSION

$

, AT

,ALL+2

, NOZEROt2

$

,

,X

,

,

,
,

,
,

,LQ

,BtiLL+3

,35

,

$

,QJ

, NOZER0+5

, NOZER(}.f8

,ADVANCE TO 11EV1 CARD FIELD? $

,

,RA

,ALLt2

,Kt1

,

$

,
,

,TJ

,PRESET+1

, NOZER0+8

, THIRD CARD FIELD?

$

,LQ

,BULLt-3

,8

,

$

,.

,¥..J

,

,FILL

,

$

,
,
,
,
,

,SP

,STORE

,2

,

$

,SA

,STORE

,1

,

$

,.TP

,A

,STORE

,STORE FRACTIONAL PART

$

,SS

,A

,51

$

,ZJ

, NOZERO

,FILL

,
,

$

,.PRESET ,CC

,IMAGE+2

,BVL1+3

,P

$

,

,CC

,IMAGE+24

,BVL1+3

$

,

,EVJO

, DJ..AGE-+-35

,

,EWl

,
,

,
,

,
,

,

, NOZERO , RJ

to

U ADDRESS

Rml

PUNCH ORDERS

~

'or'

....

$

S
$
$

,

$
$

$

U"\

0
.-

, ITlAGE+ll
~7-

R

E
S

$
$

OR3
OPS

TJ"G

,
,
,
,
,K

,.

,

,
,
,

V

U ADD?..ESS

, K;,1J..

COMl'::ENTS

ADD?~SS

,D::AGE+23

$

E

,

,SP

,STEP+5

,35

,TP

,K+7

,STEP+6

, TP

,Kt6

,STORE

,

$

,DEC+2

,

$

,GO

,

$

T

$

S

'"

i,f

,
,
,

,12

,

,U ADVANCE

$

,B

,400000

,000000

,

$

,

,

,2

,

$

,5

,
,

,
,

$
$

,LA

,

,B

,1

,

$

,B

,
,

,1

,TABLE

$

,X

,

,10

$

,X

,

;100

,
,

,X

,

,1000

,X

,10000

$

,

,X

,
,

,

,X

,

,1000000

,

,X

,

,10000000

,
,
,
,
,

,
,
,

,X

,1

,00000000

,

$

,X

,10

,00000000

$

,x

,100

,00000000

,
,

,X

,

,3

,

$

,B

,

,77

,EXTRACTOR

$

,
,

,1

,

$

,3

,

,

,2

,

,
,
,

0'
~

,100000

POVJERS

$.

$
$
OF

$
$

TEN

$

0

,
,
,

-8-

$
$

OR3

TAG

U ADDRESS

OPS

,36

,mAGE

,RESERV

,

,:s::nS17B ,

V ADDRESS

,.36

,

."

8o

.....

-9-

COH1-:SNTS

,D-i.!;'GE R3GION

0R4
6 January 1958
COL~m

HEADING

ROUTI~~

Compilable: Minimum 1103A
Oper ations Research Office - Sumner
A.

PllRPOSE

This routine allows the programmer to i nc lude alpha-numeric information,
titles, and beadings in any punched card output.

B.

USAG:S
1.

LEP..DING LINES

Sub
Temps
Inout
2.

0R4

o

1

75

o

o

INPUT
The

inp~t

to this routine is a single parameter word having the

fO;rnl;

AO

00000

BBBBB (octal)

A =4 Read and store one card image
A ~ Q Punch one stored card image
~~BBB:

3.

The first storage address (drum or core) of a card image.
If a card is to be read and stored, BBBBB is the first
of 36 (decimal) storage locations which will be used by
the image. If a stored image is to be punched, BBBBB is
the first address at whicb the image is to be found.

RECOVERY PROCEDURE

There are only two ways in wbich a card fault can occur while this
routine is operating:
(a)

Erasure of tbe manual jump command at position 00000 before
entering t he column heading routine.

(b)

Failure of the external equipment in picking a read or punch
card. In either case, the routine may be restarted at the
normal entr~ce after tbe cards have been repositioned.

4.

NUMBER OF TAGS USED

5.

RUN~TING

=2

(decimal)

TIME

The time required for one use of the routine is approximately the
same as the time required for one complete read or punch cycle of the
Bull reproducer. Therefore, it is possible to achieve virtual free run
(120 cards per minute) if the programming between successive references
to the routine is kept to a minimum.

0R4
-2-

C.

RESTRICTIONS

The storage positions at vlhich a card image is to be stored should
not coincide with any address vii thin the column heading routine itself,
since this would result in writing over part of the routine. Similarly,
the programmer should not enter the read routine without specifying a
storage address, since the routine will then store the image beginning at
address 00000, erasing the manual jump at this posit~on.
D.

AnDITIOKAL

F~ OGRf1]-1·rr ~~G

ftJm

OPE...R.ATING I!l.1FOREATION

Since this routine does not attempt any conversion, but merely holds
a card image, it is possible to punch anything whatsoever on the input
cards. The output cards are limited by the Bull reproducer's inability
to perform depend?bly if more than 160 punches per card, or 60 punches in
any one row, are required. Since t here are no real limitations on the
input-output forrr;c.t, it is possible to include any number of special codes
to control t he t abul2.tiClg equipment when the output cards are printed.

OR4
TAG

,
,
,

$

, OR4

,76

,T2 ·P3

,C

,0

,

$

,I NOUT

,1

,0

,

$

,BODY

,NOID1AL ENTRANCE

$

,

$

, NOR.!.r.AL EXIT

$

,MJ
,ALARN
,HJ

,FILL

,X

,

$

,
,

,BODY

,RPO

,1

, BODY+2

,

,TP

,BODY-1

,A

,SJ

, BODY+17

, BODYf.3

,LA

,A

,15

,PUNCH ENTRANCE

$

,TU

,A

,BODYt6

,

$

,RP3

,36

,BODYf.7

,OBTAIN nl;.AGE

$

,TP

,FILL

,IJC"5

,

$

,TP

,IJC-1

,IJC

)SET IJC

$

,EF

,

,IJC+4

,PICK PUNCH

$

,IJC+5

,PUNCH

$

,IJc+6

,ONE

$

,IJC+7

, ROVJ

$

,
,
,

'"..-0

COHMENTS

,SUB

,EWO

C")

V ADDRESS

U ADDRESS

OF'S

,EVa

,

,EVa

$
$
$

,RP2

,3

,BODY+14

,ADVANCE

$

,RA

,BODY+-9

,IJC+1

,

$

,IJ

,IJC

,BODY+9

,CARD FINISHED?

$

,RP,LJ

,3

,BODY-2

, RESET, EXIT

$

,RS

,BODY+9

,IJ(;.f2

,

$

H'IAGE

,
,
,
,

,TV

,A

,BODY+29

$

,TP

,IJC-1

,IJC

$

,

,EF

,

IJC+3

,PICK READ

$

,

,ERO

,IJC1r5

,READ

$

-3-

OR4
TAG

V ADDRESS

U ADDRESS

OPS

,ER1

,
.,

,IJCt7

,RP2

,3

,RA

,

,

,ER1

,
,

COMMENTS

,IJC+6

ONE

$

ROW

$

,BODY+-25

,ADVANCE

.;p

,BODy... 20

,IJCt1

,

$

,IJ

,IJC

,BODY+20

,CARD FINISHED?

$

,

,RP2

,3

, BODY+28

,RESET

$

,
,
,

,RS

, BODY+-20

,IJC+-Z

,

$

,RP3

,36

,BODY-2

,STORE IMAGE, EXIT

$

,TP

,IJC+5

,FILL

,

$

,11

,N-1 ROWS

$

,ROW COUNTER

$

,X

D.fAGE

...

,IJC

,X

,

,x

,3

,ROW ADVANCE

$

,
,

,X

,36

,RESET CONSTANT

$

,B

,400000

,000005

,PICK READ CODE

$

,

,B

,400000

,000012

,PICK PUNCH CODE

$

,
,

,RE3ERV

,36

,36

,IMAGE REGION

$

,ENDSUB

,

,

,

$

-4-

OR5
6 January 1958
OCTAL TYPEi'ffiITER OUTPUT ROUTINE
Compilable: Jv1inirnum 1103A
Operations Res earch Offic e-Sumne r
A.

PPEPOSE

This routine types on the console flexovlri ter the octal contents of any
storage address, with the follovling options:

B.

(a)

Twelve digit octal type-out, no s pacing, no zero suppression.

(b)

Octal type-out with zero suppression, no spacing.

(c)

Tvlelve digit octal type-out, ·w ith spacing between the
and ~ portions of the word, no zero suppression.

~.,

B,

USAGE
1.

LEADING LINES

OR5
o

Sub
Temps
Inout
2.

1

55
o

o

TNPUT

The input t~ this routine consists of a single parameter word
which has the following composition:
AO
A

o

=0

=4

BBBBB CCCCC (octal)

no zero suppression
zero suppression (assumes that BBBBB = 0)

BBBBB:

Any bits at all within the u-portion of· the parameter will
cause the routine to space between the ~. ,E, and :y
portion of the word. BBBBB = 0 assumes no .spacing desired.

CCCCC:

The storage address at which the desired octal number is
to be found.

3 • RECOVERY PROCEDURE
No recovery procedure is necessary, since the only possible fault
which could occur would be one due to computer malfunction or typewriter
malfunction, either of which would be just cause for running maintenance
tests.

4.

NUMBER OF TAGS USED

5.

RUNNING TIME

= 3 (decimal)

The speed of the routine is limited only by the operating speed
of the console flexowriter.

-2C.

RESTRICTIONS

It is not possible to type out the contents of the Accumulator, but it
is possible to type out the contents of .the Q-register if so desired.
D.

P.DDITIONft~

PROGRAHMTNG AND OPERATING

INFOR.,.~TIO N

This routine is not intended to be used as a flexowriter dump of
consecutive storage addresses, and therefore, must be nsed one time for
each machine word to be typed out . For this same reason, the address of
the output word is not included in the type-out.

TAG

,
,

OPS
,SUB

,ORS -

,55

,

t

,TEHPS

,

,

,

$

,INOt~

,1

,0

,

.,;>

,Ptl

,ENTRANCE

$

,.

,ALARM

$

,FILL

,EXIT

$

, EJ

t'...0

0
..-

Cm,;}1ENTS

V ADDRESS

U ADD:lliSS

~

,

,ALARM

,

, MJ

,
,

,P

,X

,

,

,PARAKETER

$

,
,
,
,
,

,TP

,P

,A

,TEST FOR

$

,SJ

,IJCtl

,P+3

,ZERO SUPPRESSION

$

,TU

,A

,PRINT-2

,NO SUPPRESSION

$

,RS

,A

,A

,TEST FOR

$

,.EJ

,PRINT-2

,IJC+2

,SPACING

$

,

,SP

,.P

,.15

,. SHIFT PARAMETER

$

,

,TU

,A

,Pt9

,OBTAIN ADDRESS

$

,

,TP

,IJC-2

,.IJC

,SET IJC

$

,TP

,FILL

,PRINT-3

,OBTAIN NUMBER

$

,.SP

,PRINT-3

,

,NO. TO A

$

,LT

,39

,PRINT-3

,ISOLATE ONE DIGIT

$

, TP

,A

,A

,CLEAR A LEFT

$

,MJ

,

,P+14

,SWITCH

$

,AT

~PRINT

,P+15

,LOAD PRINT ORDER

$

,X

,

,

,PRINT

$

,IJ

,.IJC

,P+IO

"CHECK IJC

$

,IJC-l

,SPACE

$

,
,
,
,
,
,
,
,

,

. ,.PR

,

,.TP

,IJC-l

,IJC

,SET IJC

$

,

,.RJ

,IJC-9

,P+IO

,SWITCH

$

,

,TP

,IJC-l

,IJC

,SET IJC

$

,

. ,RJ

,IJC-9

,Pt1O

,.SWITCH

$

-3-

OPS

.TAG

,TV

,PRINT-l

,IJC-9

,RESET

$

,

,TV

, PRI NT-1

,IJC-7

,RESET

'II'

,
,

, MJ

,
,

,P-1

,GO TO EXIT

$

,13

, NO. OF DIGITS

..

,1

,

$

,.B

,
,

,4

,

$

,IJC

,x

,

,

,nJDEX JUNP COUNTER

$

,

,TP

,PRINT-5

,P+13

,SET S1tlITCH

$

,

,TP

,IJC-3

,IJC

,SET IJC

$

,SP

,P

,15

,SHIFT P.ARPJ.TrER

$

,

,TU

,A

,P+9

,OBI'AIN ADDRESS

$

,
,

,RJ

,IJC-9

,P+9

,RE-ENTER

$

,TP

,PRINT-4

,P+13

,RESET SWITCH

$

,B

T'""

/



$

1.

.-

IDEN'tIFICATION f"lL TOO), OCTAL TAPE WRITE

RooER SKINNER - 5 MARCH 1957
l.OChlIEED rUSSILES DIVISION
2.

PURPOSE
To write on a designated tape in octal format, n words from consecutive
core or drum locations.

).

METHOD
This program writes the necessary number of blocks as determined by
n in XS-) code with) blanks followin g each word, or

48 words per block.

No instructions are executed between external write commands during the
writing of each block.

4.

USAGE

a.

Calling Sequence

OPe

LOC.

b.

u

ADDR.

r

RJ

r+l

Normal Return

v ADDR.

t+2

t

Control and Results
A parameter word with the following form must be placed at

~).

aa bbbbb ccccc
a) Uniservo to be selected.

b) Number of words to be written.
c) Initial core or drum location.
c. Space Required

74 cells of instructions.
128 cells of erasable labeled COH!-10H t hrough CGr-1J;10H+ 127.

d. Error Codes
The parameter word is left in the Q-Register on return through the
error exit.

The followin g error code is left in the Accumulator on

return through the error exit.

EXPLANATION
Core overflow in attempting to fetch and write
n words.

e.

Tape Format
The tape is Hrittenat 128 lines densi ty and 1.0 inch block and blockette
spacin tY ,

5.

fl. Hords per blockett-e.

RESTRIC TIO!~ S

If the initial core address and n are such that this

routin(~

attempts

to fetch a Hord at a location one greater than th e last leeal core

address, the routine will H'ri te th e number of vlOrds up to and including
the last core address cl11d th en exit throu['; h the error exit.

6. CODING I NFOm1ATION
aL.

b.

Constants
LOCATION

CONSTANT

EXPLAlJATION

VHASK

000000077777

V address mask.

TI1ASK

000000170000

Tape indic;:ator mask.

BLANK

010101010101

XS-3 code for blank .,/ord.

XS3TS

3777 3777 3777

XS-3 conversion test.

ODDEV

525252:~;25252

Odd-even indicator.

LBKS

010101000000

Blanks in left half of vlOrd.

RBKS

000000010101

Blanks in ri ght half of Hord.

COD:!:!

660303060001

Error code for core overflQw..

Ul

000000100000

1 in U-address.

Nl

000000000001

One.

N3

000000000003

Three.

N5

000000000005

Five.

N7

000000000007

Seyen.

N47

000000000057

Forty-seven.

N48

000000000060

Forty-eight.

vlorking storage
128 cells labeled

c.

Timing
Unknom.

COl"r." ~ON

through COl·'[fv ON+127 •

T Dote

LOCKHEED AIRCRAFT CORPORATION

, March 19,7

Approved

MISSILE SYSTEMS DIVISION

Title

OCTAL TAPE WRITE

LOC

OP

ENTRY
MJ
ERROR
RJ
EX IT
MJ
Y FILL
START
SP
TU
LO
OT
LA
TP
OS
CYCLE
RS
TP
SJ
NTEST
SA
SJ
NZERO
ZJ
NPART
ST
RPV
TP
STBK
TV
TP
WORD
TN
CONV
SA
LO
QA
LQ
OJ
PTST
AT
LT
LQ
OJ
ODD
RPB
TP
EVEN
LA
LT
AT
LA
LT
AT
RA
RPB
STORE
TP
BUMP
RA
NEWV
RA
EJ
IJ
LQ
LASTW
QJ
ODDWD
LO
TV
RPB
FORM

MSO

#

8~20

 ••

U-ADDR
DIAG+
FILL
Y·
A
Y
VMASK
Y
TMASK
A
COMMON
N47
NTEST
N48
EXIT
NPART
Nl
120
BLANK
STBK
FILL
N3
N3
COMMON+
N7
XS3TS
CONV
N3
0
ODDEV
EVEN
2
COMMON+
COMMON+
0
LBKS
COMMON+
0
COMMON+
COMMON+
5
COMMON+
STORE
WORD
OVER
COMMON+
ODDEV
ODDWD
ODDEV
STORE
2

V-ADDR
2

ExpLANAT ION

START
DIAG
FILL
FILL
15
WORD
31025B
COMMON
32066B

SET INITIAL ADDR
NO. WORDS
POSITION T

0

WRITE
N48
COMMON+
STBK0
NZERO
EXIT
COMMON+
vJORDCOMMON +
STORE
COMMON+
A

SET WRITE
1

1

TEST FOR END
1
1

SET WORD INDEX

8

SET IMAGE TO BKS
1ST BUFFER ADDR
CURRENT WORD
-3 TO A
XS-3 POSITIONED
POSITION AND
ADD DIGIT
lOOP
TEST
STORE RIGHT
STORE LEFT
ODD-EVEN IND
EVEN OR ODD
FIRST AND
. SECOND
SPL IT WORD

2

6

2

3
A
1

PTST
CO ~1MON+

7

COMMON+

6

1

6
6

7

6
7
3

1

ODD
NEWV
COMMON+
18
A
COMMON+

3

5

BBBXXX THIRD
SPLIT WORD

6

FOURTH
XXX BBB FIFTH
STORE
IN BUFF ER
BUMP STORE
BUMP WORD FETCH
TEST FOR OVFL
NO. WORDS TEST

18

A
COMMON+
RBKS
BUMP
FILL
N5
Ul
BEXIT
WORD
31001B
WRBK
1
LSST
WRBK

SET WORD INDEX
TEST FOR FULL BLK

ODD NO. OF WORDS
RESET IND
STORE

Page

J

~

LOCKHEED AIRCRAFT CORPORATION

Dole

March

____~=-______M_I_ss_I_LE__SY_S_T_E_M_S_D_IV_IS_I_o_N________~~~____~__~~

195~1

Approved

Title

OCTAL TAPE WRITE

LOC
LSST .
WRBK
BE XlT
OVER
WRITE
VMASK
TMASK
BLANK
XS3TS
ODDEV
L8KS
R8KS

OP
TP
EF
RPV
EWB
TP
MJ
TP
B
B

B
B
8
B
B
B

Ul

B

Nl
N3

B

N5
N7
N47
N48

B
B
B
B

B

END

FOAM _
MSO 8~ 20

 ••

U-ADDR
COMMON+
120

ODDEV
100008

V"'ADDR
3

FILL
WRliE
CYCLE
COMMON+
COMMON
LASTW
COMMON+

620064600001
77777
170000
10101010101
377737773777
525252525252
10101000000
10101
100000
1
3
5
7
57
60

EXPLANATION

8
2

LAST WORD
START TAPE
COPY AND
RETURN
PREPARE EXIT
RETURN TO WRITE
OVERFLOW TEST
WRITE DUMMY
VMASK
TAPE IND MASK
ALL BLANKS
XS-3 CONV. TEST
ODD-EVEN TEST
LEFT 3 BLANKS
RT 3 BLANKS
1 IN U ADDR
ONE
THRE'E
FIVE
SEVEN
FORTY-SEVEN
FORTY-EIGHT

.

'.

1.

IDENTIFICATION

2.

PURPOSE

-r~;.1oL-

ML TOOl, OCTAL TAPE READ
Roger Skinner - Revised - 6 Harch 1957
Lockheed Missile Systems Division

To read and store into consecutive core or drum locations, n words from
a designated octal tape.

3.

METHOD
a.

This program reads the necessary number of blocks as determined by
n from the designated uniservo.
during reading of each block.

The blanks between words are removed
The conversion out of 15-3 and storing

of the converted information is accomplished between blocks.
b.

Four attempts will be made to read each block successfully in event
of parity check.

Two attempts will be made at normal bias, one at high

bias, and one at low bias..

4. USAGE
a.

Calling Sequence
lDC.

OPe

RJ

r

.

v ADDR.

t+2

t

Normal Return

r+ 1

b.

u ADDR.

Control and Results
A parameter word with

the fo]]&w.iing t&rm mUlS't.

be pla.eed. at t+ 3.

aa bbbbb cccee
a)

b'
~}

Uniservo to< be select.ed.
Number of octal ltlOrds to be read and stored.
Initial storage location.

86 cells of instructions.

101 cells of erasable labeled COMMON through

CO~10N+lOO.

-Pa~ e

d.

6 March 1957

2-

Error Codes
The parameter word is left in the Q-Register on return through
the error exit.

The diagnostic routine is entered immediately,

and no attempt is made to space the tape forward to correspond

to the number of blocks indicated by n.

The following error

codes are left in the Accumulator on return through the error
exit.

EXPLANATION

CODE

TOOl 212+1

Four unsuccessful attempts to read block.

TOOl. 212+2

Core overflow while storing information.

0

e.

Tape Format
The octal tape read by this routine consists of blocks containing

48

octal words in XS-3 code, each followed by 3 blanks.

5. RESTRICTIONS
a.

Information stored in such a way to overflow the last core address
will cause immediate

b.

e~t

to the diagnostic routine.

If other than 3 blanks separate the octal words on tape, then the
leading binary bit of the first of these 3 characters must not be
a binary one.

6 March 1957

-Page 3-

6.

CODING INFORl"IATION
a.

Constants
LOCATION

b.

CONSTANT

VHASK

000000077771

V address mask.

'!'MASK

000000170000

Tape indicator mask.

BIAS

020000150000

Normal bias.

'l}{REES

0)0)0)0)030)

Used in XS-) Conversion.

CODEl

660)0)040001

TOOl x 212+1

CODE2

660)0)040002

TOOl x 212+2

U2

000000200000

2 in U address

Nl

000000000001

One

N3

00000000000)

Three

N4

000000000004

Four

N.5

00000000000,5

Five

N7

00000()000001

Seven

N23

000000000027

Twenty-three

N48

000000000060

Forty-eight

Working Storage
101 cells labeled COMHON through COMMON+100.

c.

EXPLANATION

Timing

Unknown

""

...

.

T

LOCKHEED AIRCRAFT CORPORATION

Date
API" ;;:,ed

6 March 1921

Madel

MISSILE SYSTEMS DIVISION

Title

!leporl No.

OCTAL TAPE READ

LaC
FN TRY
FRROR
EX IT
Y
START

CYCLE
TEST
ZERO
PART
SBIAS
RDBK

STORE
COpy
POSIT

FAULT
RETRN
CHNGE

OK
FETCH
FORM It
MSO 852 0

® ••

OP
MJ
RJ
MJ
FILL
TV
LQ
QT
LA
TP
OS
OS
RS
TP
SJ
SA
SJ
ZJ
TP
EF
TP
EF
TV
TP
IJ
RPB
TP
RPV
ER B
LA
LA
LT
AT
ERB
LT
AT
RA
IJ
ERA
ZJ
IJ
SP
TP
MJ
SP
AT
EF
EF
RA
MJ
TU
RP B
TP

U-ADDR

V-A DDR

0

DIflG+

2

0

FILL
Y
Y
VMASK
Y
TMA SK
A
A
COMMON
N48
TEST
N48
EXIT
PART
A
N3
PART
N23
(OMMON+ 1
4
(OMMON+ 97
4

0
18

COMMON+IOO
STORE
(O MM ON+ 3
2

SHIFT
2

FILL

NO WORDS
POSIT ION T
SE T READ
SE T F3K SP ACE
1

SE T INDEX
TST FOR FULL BK

1

SE T INDEX
SE T NORMAL BIA S
SET BIA S IND EX
READ ONE BLOCK
SET FIRST STO RE
BLK INDEX TO 23

COM~10N+

2

3

COpy
COpy
FILL
PO S IT

STORE FOUR WORDS
97

RE AD FOU R \-JORDS
PO S ITION THI RD
SPLIT FOURTH

99
A
A
COMMON+IoO
N4
STORE 1
A
OK
CHNGE
0

THI RD STA ND ARD
FIFTH FRO~1 TAPE
POSITION
FOURTH STAND ARD
BUM P STO RE

18
18

A

C m~ t-10N+

0

ERROR

lOA TO A
CHEC K
TES T BIAS
TAPE ERROR CODE
PARAMETE R WORD
GO TO AL ARM EXIT
Er~ROR

12

0

0

ZERO
EX IT
COMr>lON+
BIAS
(OMMON+
READ
STORE

COMMO~I+

0

CO MM ON+ 99
COMMON+I00
0
(OM MO N+ 99

0
CO MMON +

SE T INITIAL ADD

0

0

FAULT
COMMON+
CODEI
Y
0
A
8 IA S

STAR T
Dr AG
FIl.L
F= ILL
FSTOR
31 0 25B
COMMON
32066B
Q
RE AD
BKSP
N48
(OMt-10N+
SB IA S

EXP LANATION

1

(OMMON+
COMMON+
8KS P
Nl
RD[1 K
OK +
SUBS TCOM MON+

4
4

2

CHANGE BIAS
BA CKSPA CE
REREAD
SE T FIR ST \."O RD

2

5

CU RR EN T \-.JORD

Ipage

4

...
to"

• Date
Approved

LOC

SUBST
SEC
SHIFT

FSTOR

OVER
OVERD
READ
BKSP
BIAS
VMASK
TMASK
N1
N3
N4
N5
N7
N23
N48
U2
THREES
CODEl
CODE2

FORM It
MSD 8520

 the diagnostic routine.
b.

tf other than 3 blanks separate the octal words on tape, then the
leading binary bit of the first of these 3 characters MUst not be
a binary one.

6.

CODING INFORMATION
a.

Constants
IDCATION

CONSTANT

OVDUM

353iooOl00oo

Overflow dullll1lY word

WMASK

OYl711111771

Conversion mask

TMASK

000000170000

Tape indicator mask.

MASK1

000000000077

XS-3 conversion mask

VMASK

000000071717

Normal Bias

NEl1AX

400000000000

Conversion constant

EXPI

035440262615

Conversion coefficient

EXP2

600000111150

Conversion coefficient

EXP3

210524354513

Conversion coefficient

WB2T

324464741134

Log to base 2 of 10, *33

U2

000000200000

2 in U address

ETAB

200000000000 .

2 to 0, *34

ETAB"'l

21345340"/440

2 to .125, *34

ETAB+2

230151101214

2 to .25, *34

ETAB+3

245775532516

2 to .315, *34

ETAB+4

265011114640

2 to .5, *34

ETAB+5

305316250212

2 to .625, *34

ETAB+6

327211763126

2 to .75, *34

ETAB+7

352601433417

2 to .815, *34

CODE1

660303050001

Tape error code

BIAS

020000150000

Normal Bias

•

EXPLANATION

-Page
6.

CODING
a.

b.

INFOR~TION

4-

(Continued)

Constants (Continued)
EXPLANATION

IDCATION

CONSTANT

CODE2

660303050002

Core overflow code

CODE3

66030 .305000 3

Power overflow code.

NZ

000000000000

Zero

Nl

000000000001

One.

N2

000000000002

Two

N3

000000000003

'!bree

N4

000000000004

Four

N5

00000000000,5

Five

N8

000000000010

Eight

N23

000000000027

Twenty-three.

N48

000000000060

Forty-etght

Nl29

,')00000000201

One hundred twenty-nine

N2,56

000000000400

One hundred fifty-six.

Wc'rking Storage
103 cells labeled COMMON through COMMON+102

c.

6 March 1957

Timing
Unknown

v

LOUS
FILL. 15. SE T UP lJ AUDRESSS
A"~TQL6,$

CN12.IDX).SET RT INDEX 3$
FILL.6.NUMBER TO Q LEFT 6$
CN27,A.MASK 6 LSD 10 AS
TM27.TM28.PREVIOUS XS3 DIGITS
A'T~27.CURRENT XS3 DIGITS
NOBLK,~LANK,ACC EQ ZEROS
.TSTDX4.BLANK NEXT CARDS
CN61,PLUS.A PLUS SlGN$
CN28.MINUS,A MINUS SIGN$
CNJO.ANO,A NU MBER$
CN8.ANL'ANLS
CN7,ANF'ANF$
CN6.AOEE.AD$
CN5.ABEE.ABS
CN20.APT.A POINT$
CN4.ACOM,A COMMAS
CN9.EXIT.AC-EXITS
.ERROR,ERRORS
L(O).SIGIND.CLEAR ~IGN INOS
.HTDX3.$
CN2Q.SIGIND.SETStGN I NO MINUS$
,RTDX3.$
CNIO,Q,NUMBER MINU~ 3$
TM7'2.SrO ACC$
TM7.1.MULT BY 10$
Q. n~7. ADD IN DIGITS
n16. TH8. M PLUS T TV M$
,H.TDX3.$
CN29.LINO.SET L INurCATOR$
L(O).TM7.CLEAR S~
.HTDX,.$
CN2Q.FIND,SET F INUICATOR$

.

I

2

LOCKHEED AIRCRAFT CORPORATION

T Dote

April 2, 1951

Model

Approved

Report No .

TItle

NUMERICAL CAPn DATA INPUT

CLEAT

,

,

,
SENSI G.
CLESIG.
ADEE
5TONS

•

ABE.E

STOD

NEGED

,
,

APT
RTDX3

ACOM
LSET

,
,
•
•

,

CLEAM

,

FINDQ

,

FSET

NEGF
DEE.a
DsET

•
•

FORM ::

MSD 8520
~t: ,.

Page

MISSILE SYSTEMS DIVISION

TP
TP
TP
TP
QJ
TP
TP
MJ
TP
TP
TP
MJ
TP
TP
TP
QJ
TP
Tp
TP
QJ
TN
MJ
TP
TP
IJ
RA
IJ
TU
IJ
MJ
EJ
TP
QJ
TP
A1
TV
TP
TP
TP
TP
MJ
TP
OJ
TP
TP
TP
QJ
TN
TP
MJ
TP
QJ
TP
Tp
QJ

NEGD

Tr-J

5TOD2

TP
MJ
TP

,
•

,
,
,
,
,
,•
•,
,•
•
•
•,
,

•
,•
,
•
•,
,
•,
•

•
•
•

•,

,

,
,
•
•
,•
,•

,
,•
,

,
•

•
•,
,
,
,
•,
,
,
,•

TM7,NFLOT,S TO N FlOAT$
LCO) ,TM A,C LEAR TS
LCO),N5IGN,$
SIGINO,Q,5lGN IND fO Q$
SENSIG.CLEARS.T£ST SIGN INOS
CN2Q,N5IGN,SET NO ~IGN IND!
L(O) .SIGINO.CLEAR SIGN INDS
,CLEARS.$
LCO).D5CF.CLEAR D ~CALE FACTORS
CN29.DIND.SET 0 INUICATOR$
TM7.NSTAT.S TO N SIATED$
.CLEAT,$
CN2Q, BINO ,SET B INUICATOR$
LCO).BSCF.CLEAR B SCALE FACTORS
OIND.Q,D INDICATOR TO Q$
STOD,STONS.$
TM7.0SCF,S TO 0 SCALE FACTOR$
L(O),OINO,CLEAR D lNDICATOR.S
S I GIN D, (J • 5 I GN IND 10 Q$
NEGED.CLEARS.TEST ~IGN INOS
DSCF,D5CF,NEG 0 SCA E FACTORS
.CLESIG.$
LCO),TM6,SET M Ea 10 ZEROS
CN29,pI~D,SET PT INDICATORS
IDX3,NTQL6,TEST RT INDEX 3$
NTQL6.CN3,MODIFY K~
IDX?,SEOXR3,TEST INDEX RT2$
CN25.SEUAD,CHANGE ~EUA O $
IDX1,sEDXR2.TEST INDEX RT1$
,TSTOX4,RETUR N TO MAIN ROUTINES
TM28.STORE,COMMA BY COMMAS
LIND,Q,l INO TO a$
LSET,FINDQ,TEST L .LNDS
TM7.A.S TO ACCS
TM5.A.AOD IN REt. LUCS
A.STORE.MODIFY STOKE I NS TRUCT lOt-.I S
L(O).TM~.CLEAR MS
L(O).TM7.CLEAR SS
L(O),LIND,CLEAR L lND$
L(Bl).TM8.SET E.O TO 1 $
,RTDX'.$
FIND,Q,FIND TO QS
FSET,DEEQ.TEST F INDICATORS
TM7.FLOAT.S TO F$
LCO) ,FIND,CLEAR F .lNDICATORS
SIGIND,Q,SIGN INDICATOR TO QS
NEGF.FLOP,TEST SIGN INDICATOR$
FLOAT.FLOAT.NEGATIVE F$
L(O),SIGINO,CLEAR ~IGNIND$
,FLOP.TO FLOATING ~T Co~v.s
DINO,Q.OINDICATOR TO QS
DSET.BEEQ,TEST 0 INDICATORS
L(O),DIND.CLEAR D INDICATORS
SIGlND,~,SIGN INDICATORS
NEGD.STOD2 ,TEST DS~ SIGNS
TM7,DSCF.MINUS OSF$
L(O),sIGINO.CLEAR ~IGN INDICATO~$
,STAP.TO 5P CONVE.R~IONS
TM7.DSCF,S TO DSF$

MLC 001

3

T

Mode l

Dote

Page

I

4

~~__~A~~~
:r=
i1~2~
, ~1~9~
5~
7 ____~~______________________________~~~____~____~
Approved

TItle

Re port N o.

Nm1ERICAL CARD DATA INPUT

BEEQ
BSET

••
•
•
•
•

STONS2 t
NEGN
STAP
DOK

•

•
,
•
•

•

•

T0081 (~.
PTOQ

•

,

PNSET •
t

PSET

,

•
STORE ,

•
•
COFLO ,
RETURN.
SPCON •
DENZO t
DELZO •

•
•
,•
DIVIG •

•
•
DIVRc.",.
SH 1FT ,

•

DEZO •
SHIFT2.

4

t

DEGRO.
•
•
FORM :;

MSD 852 0

t

MPVN •
SHIFT.,.
RESIGN,

MJ
TP
OJ
TP
TP
MJ
TP
TP
QJ
TP
TP
TM
SS
SJ
TP
MJ
TP
MJ
TP
QJ
TP
MJ
TP
ST
MJ
TP
RA
EJ
MJ
SP
TP
MJ
TP
ZJ
SJ
SN

SA
TU

Tv

SP
DV
SP
TU
OV
SP
SA
LA
MJ
TV
SP
MJ
TV
SP
SA
TU
MP
LA
TP
QJ

,
•
•
•
,
•
•
•
•
•
,
,
,
•
,
,
•
•
•
,
•
,
•
t

•
t

•
•
•
•
•
,
,
t

•
•
•
•
•
•
•
•
,
,
,
,
,
,
•
,
•
•
,
,
,
,
•
•
•

.STAP.TO SP CONVER~IONS
BIND.Q.S INDICATOR$
BSET.STONS2.TEST B INDICATO~S
TM7.BsCF,S TO BSF$
L(O) .eIND.CLEAR B iNDICATORS
.STAP.TO SP CONVER~IONS
TM7.NSTAT.S TO N STATED$
SIGI ND.Q,SIGN INDI~ATOR$
NEGN.STAP,TEST N SIGN~
CN29.NSIGN.SET NEG NUMBER INDS
L(O).SIGIND,CLEAR ~IGN INDICATOPS
DSCF,A,l) TO A$
CNI9 •• 0 MINUS
DOK.TOOBIG.TEST SI£E OF DSCF$
DSCF.A.$
,PTO(,),$
CN62,RESULT.DSF TOU LARGES
.STORE,$
PI ND.Q,PT INOICATOK TO QS
PSET.PNSET,S
OSCF.TEE,$
.SPCON,CONVERSION$
L(O),PIND.CLEAR PT INDICATOR$
TM6.TEE.D MINUS M$
,SPCON.CONVERSION$
RESULT,FILL,STORE NUMBE RS
STORE.LCBl), BUMB LOCATIONS
CN65.COFLO.TEST COKE OVE~FLOW$
• CLEAM, RE TURNS
CN63.0,CORE OVERFLUW TO AS
V.Q.PARAMETER TO Q~
.ERROR.TO ERROR EXiTS
TEE.A.D TO A$
DENZO,OEZO,D EQ ZEKOS
DELlO,DEGRO,D LESS THA N ZEROs
TEE.1 S .ABSOLUTE 0$
CN3I,.AOD TABLE OR!G$
A,DIVIG.SET UP DIV1DES
BSCF.SHIFT,SET UP ~HIFT$
NSTAT,.N TO ACCS
FILL,REG.DIVIDE BY 10DS
A.35.SHIFT RE~AIND~R$
DIVIG.~IVREM.SETUP REMAIN DIVIDES
FILL,TM~9,REMAINDEK 9 V 10$
REG.35,INTEGER TO A$
Q.37.FRACTION TO A~
A,FJLL,KESULT IN A$
,RE S I G:'-I. $
BSCF,SHIFT2,SET UP SHIFTS
NSTAT.FILL.SHIFT NS

"$

.~ESIGN.$

BSCF,SHIFT3,$
TE.E.15,a TO US
CN3t,.AOD TABLE OR1GS
A,MPYN.SET UP MPY$
FILL.NSTAT.MPY 10D NST$
A.FILL.SHIFT PRODU~TS
NSIGN,Q,N SIGN TO ~$
NNEG.NPOS.TEST IND1CATORS

MLC 001

T Dole

,

LOCKHEED AIRCRAFT CORPORATION

April 2, 1957

A pproved

NNEG
NPOS
FLOP

EXNEG

,
,

TN
MJ
TP
MJ
TP
ST
MP
LT
LQ
SJ
RS
SP

EXPOS

,

,
•

•
•
FPMY

AT
SP
LT
AT
QT
MP
LT
AT
MP
LT
AT
SP
DV
AT
MP
LT
~P

ZETOA

•

OFLO

,
SLEROW.
REGITA.

FORM r
M SO B52 0

®E'

rog e

Report No.

NUMERICAL CARD DATA INPUT

/ (J

M odel

MISSILE SYSTEMS DIVISION

CN2
eN3
CN4
CNS
CN6
eN1
CN8
CN9
eNIO
eN 11
CNI2
eNI3
CNI4
CNIS
CNI6

,
,
,

SF
TP
RA
AT
SJ
TP
MJ
TJ
SP
MJ
LQ
TP
LT
AT
MJ
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B

•
•,
,
•

•

•,
,•
,
,
,
,•
,
,
,
,
•
•
•

A.RESULT.NEGATIVE N$
.STORE.TO STORES
A.RESULT.POSITIVE N$
,STORE,TO STORES
FLOAT.A,F 10 AS
TM6,Q.F MINUS M TO OS
Q.CN43.E LOG lOS
3.LEROtJ.SAVE INTEGt.RS
A.35,F~ACTION TO AS
EXNEG,EXPOS.EXPONEf NEG S
L£ROW.L(BI),INTEGEK PLUS IS
CN2Q.,ISCALE035$
Q.Q.GET POS COMPs
Q.4,$
,A.$

CN46.FPMy.TLU SETU~$
CNLt5,Q.MASK ALL BUT 3$
Q.CN55.$
.A,$
CN56,RTKOw.S
Q.RTROW.S
.A.$
CN57.RTKOW.$

• Q.33,$
W.A.S
• RTRO
CN44.Q.$
•
•, Q.FILL,S
, A,NFLOT.$
, A.TM12,$
, A'REG,S
, LEROw.CN58,$

••

~.A.$

,

,•
,
,
,
,
•,
,
,
,
,
,

•
•
•,

,
•
,•
•
•,

,

•

TMI2.LEROW.$
ZETOA.OFLO.$
L(O).A.ZERO TO ACC~
.REGITA,$
CN59,SLEROW.OVERFLOWS
CN64,O,POWER OFLO 10 AS
.RETURN,TO ERROR Rt.TUR N$
LEROW,27.$
REG.A,S
28.A,$
Q,A,$
.RESIGN.s
20"TWENTYS
0000001.00000·$

24,.COMMAS
45 •• B$47 .. 0$
51 • ,F$
26. ,L$
46 .. Cs
3' .0$
4. ,ONE XS3S
5"TWO XS3S
6,.THREE XS3$
7 •• FOUR XS3$
lO"FIVt:: X~3S
1 1 , , S I X XS3s

l1LC 001

5

" Dote

-

LOCKHEED AIRCRAFT CORPORATION

April 2, 1957

Approved

CN22

•

CN2J •
CN24 •
CN25 ,
CN26 ,
CN27 •
CN28 •
CN29 •
CN30 •
,
CN31
CN32 •
CN33
CN34 ,
CN35 •
CN36 •
CN37 ,
CN38 •
CN39 •
CN40 •
CN41
•
CN42 •
CN43 •
CN44
CN45 •
CN46 •
CN47 •
CN48
•
CN49 •
CN50 •
CN51
•
CN52 •
CNS3
CN51.+ •
CN55 •
CN56 •
CN57 •
CN58 ,
CN59 ,
CN60 •
CN61
CN62
CN63
CN64 ,
CN65 •
10100 ,
ICIOO •
DIAG ,

,

,

•

•,
•

IJ

•
FORM :MSD 85 20

B
B
B
B
B

,•
,•
,
,
,

8

B
B

B

Page

HLC 001

NUMERICAL CARD DATA INPUT

,
,
,•
,

I

Report No .

Title

CN17
CN18
CNI9
CN20
CN21

Model

MISSILE SYSTEMS DIVISION

,•
•

•
•,
,•

12"SEVEN X53$
13 •• EIGHT X53$
1q,.NINE XS3~
61"PTi

.

5252525'25252..AlTE~NATOR$

CN 1Q •• i
CN24 .. S
IOIOO.I0IOO.$
CN26. ,$
tCIOO.ICIOO.$
77 •• MASK$
20.,NEGATIVE SIGNS
uOOOOOO.OOOOO,tNDI~ATORS

15. ,$
CN32,,$
B
• 1 , • TEtJ TO lEROS
12 •• TEN TO O~E$
B
144.,TEN
B
• 1750 •• TEN TOTO TWO$
B
• 23420.,TEN TO THREES
FOURS
B
, 303240 •• TEN TO FIV~$
B
B
TO SIXS
• 3641100.,TEN
B
461
1320.0,TfN
• 5753604.00,TEN TOTO StVENS
B
tIGHTS
B
73465,45000.TEN
TO
• 1124027,62000.TEN TONIN~$
8
• 3244647.41134.LOG 10 ELEVENS
B
BASE 25
• 2000000.00000., SCALEDTO 34$
B
• 0377777.77777.MASKS
B
~p
FOR T~US
• Q,CN47,OUMMY
1
B
2000000.00000.2 TO 0_8 534$
B
TO 1.. 8 S34S
• 2134534.07440.2
B
• 2301577.01214.2 TO 2-8 534$
B
2457755.32516'2 TO 3-8 S34$
• 2650117.,4640.2
B
U.. R $34S
• 3053162.50212.2 TO
B
TO
• 3272117.63126.2 TO 65 ..... 88 534$
B
•t 3526011.+.33477,2 TO 7-8 534S
B
531.+5
0354U02.62675.A~
StALED
36$
B
• 6000001 .7 I 150. A1 SCALED 35$
B
• 27052U3.54S13.LOG E BASE 2 S345
B
•
201 •• ,2.9$
B
400,
•$
B
• 4000000.00005.EF
RtAD CAROS5
8
B
40
••
POSITIVE
SIGNS
• 7777777.77777.$
B
• 31030.3040001.CORE OFlO CODES
B
•
B
31030.3040002.POWEK OFLO CODES
•
TP
RESULT.,0000)8.CORt OFLO IND$
RESERV' 6.6.$
RESERV. 6.6.$
RESERY, 3,3.$
, , ,$
END

,

•
•

,

•
•
•

r

6

A.

IDENTIFICATION.

ML DOOl OCTAL DUMP
T. H. DEWEY

16 APRIL 1951
LOCKHEED MISSILE SYSTEMS DIVISION

B.

PURPOSE.

To dump core or drum on any designated uniservo.

c.

METHOD.

The program prepares an XS-3 tape, suitable for listing on the off-line high
speed printer, which contains the contents of memory from A to B, where A and B
are specified in a parameter word. The program preserves core by making use
of a core image on drum. A 264 word buffer region is constructed, pulling out
6 words per blockette and replenishing the buf~er when necessary.

A sentinel block is appended to the end of each dump consisting of a printer
stop s.ymbol repeated 720 times.
other sentinel.

D.

Replace the constant at c+17 to substitute any

USAGE.
1.

The dump was programmed with the intention of being initiated by a drum
start. Modifications have been made in order to initiate it by a normal
USE entry, to wi tl

RJ

r
r+l
2.

t+2
normal return

t

to dump

There are five parameter words as followSI
(t+3)

•

(Q)

(t+4)

•

(AL)

(t+5)

•

(Aa)

-(t+6)

•

00 aaaaa bbbbb

where aaaaa is starting address
and bbbbb is last address to be dumped;

'.

ML DOOI OCTAL DUMP

D.

USAGE.

Page 2

(continued)

It (t+6) • 0

then entire core is dumped.

(t+7) • 00 00000 0000'1'
where T designates uniservo for dumping;
If (t+7) • 0

then uniservo 5 is used.

3. Space required

234 words
158 words
65 words
636 words

of
of
of
of

instructions and constants on drum
instructions in core
erasable and constants in core
image on drum

4. Tape format
Eaoh block of tape contains the contents of 36 consecutive locations. In
addition a heading block precedes each dump containing the contents of Q,
ALI
CORE F1' F2, ')' and the status of the manual jump switches.

Aa,

E.

RESTRICTIONS.
1.

When specifying dump lind ts A and B must be either both core or both drum
addresses. No continuous dumping from core to drum or drum to core is
allowed.

2.

The MJl switch is used to determine whether or not more than one dump is
to be put on a given uniservo. If the MJl switch is on, then after the
program has dumped from A to B the tape is left Positioned to receive
another du.rnp. If the MJl switch is off the tape is rewound. In either
case core is restored, if necessary, and control is returned to the
progrannner.

3.

That part of drum designated by the programmer to be the drum core image
cannot be dumped, since the lower part of core is immediately placed in
the image when entering the dump program. This restriction can be avoided
by a suitable modification.

>,

ML nCOl

F.

Page

OCTAL DUMP

CODING INFORMATION.

1.

NUmerical constants
22 cells labeled c thru c + 21

2.

.Alphabetic heading constants
31 cells labeled:
M thru M + 5
H thru H + 14
H2 thru H2 + 9

3.

Buffer storage
264 cells labeled z thru z + 263

4.

Tape wri te image
120 cells labeled IM thru IM + 119

5.

Working storage
49 cells labeled!
IND thru
thru
V thru
thru
L

w
6.

Timing

Unknown

INn
W
V
L

+7
+6
+13
+19

3

LULt\Ht.I:..U AIHLI'l

-2-

5.

RESTRICTIONS
The argument must be within the stated range and scaled 233.

6.

CODING I NFORMATION
a.

Constants

1QQ
C

CONSTANTS
10 00000 00000

EXPLANATIOn
33
1 • 2

Cl

00 00000 00000

Zero

C2

00 00000 00001

One

C3

53 24135 20070

~

C4

33 24414 25535

a6

C5

56 40071 51545

c6
C7

37 50417 41?34
4h 23706 66522

C8

26 61651 66073

C9

44 42003 30653

CI0

31 10375 51633

40
5 - 2
'a • 240
4
39
8
3 • 2
38
8
2 • 2
37
8
1 • 2
aO • 234

C11

37 77777 77777

Round Constant

C12

14 44176 65211

!l

C13

10 00000 00001'

1 - 233 + 1

C14

26 47670 31361

D = 24,291,062,513

C15

00 00000 65324

A = Z7,348

C16

11 45346 44516

B = 10,291,988,814

C17

33 06571 40273

C = 29,104,062,651

C18

00 00000 00077

Shift Count Mask

C19

26 50117 14640

$

C20

20 00000 00000

1

CODE

54 54311 10000

Error Code

• 244
-242

a

• 233

2

0

Q

234

~4

(Rounded)

-3b.

Work Space
7 cells labeled STORE thru ST0RE+6

c.

T1.m1ng

Approximate maximwn ot 6.75 m1s. for I

=-

(1_1.2-33 ).

REM1NGTON RAND UNIVAC

8

PAGE...-4.-0F
PROBLEM

IW6

CODED BYFraIjck. VapHi1st DATE 6-15-57
ITEr.f NUl1!3ER

OP

LOC

,
, SUB
,
TEMPS
,
, nmUT
, ENTRY MJ
, ERROR , ALARM
, EXIT , MJ
, y
, 00
,X
, 00
, START , TIt
,
, TJ
, SP
,
,MJ
, TP
, PROG
,
, ZJ
, NOZERO , TP
, TP
,
,
, TP
,
, EJ
J

J

J

TP

, MTImS

J

,

, TM

J

,

,
,

PLUS

,

EJ

, MP
, LTL
,

Arr>J.

RRF6

,
,

1

J

0

7

,
,

0

" FIlJ.

, FILL
, X
, C13
, CODE
, 0
, C12
, NOZERO
,
A
, X
,

C1

, MINUS
J

C2

,
A
,
C
, STOP..E
,
1
, C4

COMMENTS

V

U

, 98
, 0
, 1
, START
,
, FIlJ.
J

FILL

•
•
•
•
•

,
,
,
,
,
,
J

$

FtniCTION SCLD 33 $

, FILL

, ARGUMENT S6LD 33

,
,

, ABS X TO A

A

PROO

, 0
, ERROR
, y
, EXIT
, STORE

$

, CHCK FOR X GRTR 1 t

, ERROR CODE TO A
, GO
, Y

=PI ovr 2

, STORE+1
, PLUS

, TEST SIGN OF X

, STOP.E+l

, SET FOR NEG

,

, ABS

A

A

FOR X=O
STORE ABS X
X TO A

$

SET FOR POS X

X TO A

=1

, XONE

,

,

C3

, EVALUATE

,

A

, STORE-t-2

J

•
•
•
•

TO ERROR EXIT $

,
,
,
,

,

•

TES~

X

POLYNOMIAL

, EXPRESSION

I

$

•
•
•
•
•
$

$

REMINGTON RAlID UNIVAC

PAGE
PROBI»1

5

RRF6

CODED ByItanck. VanHiIst
10C

ITEM NUNBER

,
,
,
,
,
,
,

,
,
,
,
,
,

OP

,
,

STORE

, AT

,

C,

,MP

,
,
,
,

, 1TL
, AT

,

loW

, LTL
, AT

,

, MP
, LTL
, AT
, MP
, LTL
, AT

II

,

,
,

,
,
,
,
,
,

, TIl
, SA

,

J

1

STORE
:3
C6

COMMENTS

, STORE+2

,

IN

$

, A
, STORE+2

, APPROXIMATION

$

)

STORE+2

,

A

)

STORE+2

,

OF ARCSIN X

, ACCUMULATE
,

IN

•

,$' .

$

, STORE+2 SCLD 34

$

STORR

, STORE+2

,

$

, 2
, C7
, STORE
,
2
, CS, STORE
, 2

, A
, STORE+2

,

$

,
,
,
,
,
,
,
,
,

$

14P

,
,

STORE

,

LTL

,

0

I

AT

,
,
,

, SF

, SP
, TP
, SA
, LTL

DATE 6-15-57

V

U

• HP
, 1TL

8

OF

,
,
,
,

c9

, STORE+2
, A
, STORE+2
, STORE+2

,
,

A
STORE+2

, STORE+2

,

A

•
$

$
$

•
$

$

•
•

C

, STOF.E+2
, A
, 0

,

IN A

$

A

, STORE+3

, K TO STORE+3

$

A

,

, (R) = N SCLD 34

$

A

, STOilE+4

$

18

,
,

STORE+5

,

CIO
STORE

C14
0

,
I

0

, X(X) TO STORE+2
,

FOfu~

(I-X) SCLD 33$

STORE N

FORM AND STORE •
(N+D) SCLD -l8=F •

REM!~CTON

PAGE:-.....;6~OF_8_ _

RAND UNIVAC

PROBLEM

RRF6

COLED BY Frapck.YanHi1BtDATE 6-15-57
LOC

ITEM NUMBER
1

,
,
,
,
,
,
,
J

,
,

,

OP

COMMENTS

V

U

,SN

,
,
,

, r:v

, STORE+5

,

, AT

, STORE+6

, STORE+5

, Y(l) APPRX SQRT N SCLD 16'

,

SP

; STORE+4

, N SCLD 32 TO A

$

, ss

, STORE-t5

N - Y (1)

$

,
,

DV

, STORE+5

,
,
,

AT

, STORE+5

, STORE+5

, =Y(2):-aSQRT N SOLD 17 •

,LQ

, STORE+3

, K(O) IN Q(35)

, QT
, TV

,
,

,
,

, QJ

,MP
, AT

C15

, STORE+5

, A x F TO STORE

C16

,

STORFt+6

, A x F+B TO STORE $

C17

,

15

, -0 SCLD 15 TO A

$

A

, -0

$

C18

32

OVER F = -G

$

0

'.

A

, (Novr Y(l» -1+Y(1) •

35
A

$

, K-K(O) OVR 2 IN A •

, KODD

, SET SCALE FOR SQRT N •

, KODD

, KEVEN

, TEST PARITY OF K . $

,

, STORE+5

, (Y(2)+1) ovr 2

$

, SCLD 17 EQLS

$

A

, KEVEN

,MP

,

,

SA

, C20

,

,

,

LTL

,

, STORE+5

, SQRT (N SCLD K-1) $

, STORE+5

, FILL

,

,

C11

,

0

, RND SCL SQRT (1-X)'

0

,

A

, SCLD .3.3 IN A

$

A

, STORE+2

, FORM

$

:2

,

A

, SCLD .3.3

Q.

,

, KODD , Sp
,
, SA
,
, LTL
,
,MP
,
, LTL
,
, ST

,

.'

,
,
,
,

C19

0

C12

J

1

INA

- ARCSIN X

IN Q

$

•

$

PAGE 7 OF 8

-

IUl:MINGTON RAND UNIVAC

RRF6

PROBLEM

COLED BY Fre.pck, Va,p Hilst DATE 6-15-57

Lee

ITEM NUMBzn

,

TEST

,
, Nr::GX

,
,
,

, IJ
, TN
, I~
, '£N

,
,

, '1'1'

,

, } lJ

, XONE , ' '''! .
,
, 1'V
.. l 'i

,

, B10

I

)

,
,~
,
,

, C1
, C2
, C3

, B

,
,

, B5.3

,

, C4

I

, C5

,B56

j

~

, .237

, C7

,B46

I

,

,

, 0-

STORE+1
Q

COMMENTS

V
, .NEGX

,

,

Q

, Y IN 2ND QUAD .

$

"

FOR X NEG

$

C1.2

, - f.RCOS X EQUALS

A

,
,

A

, AROSINX - PI OVR 2$

A

,

Y

,

0

,

EXIT

C12

,

Q

,

TE[,T

,

e

,

00000

, 1 SOLD 33

$

1

0

,

ZERO

$

,

.4

ONE

$

Q

0

00000

2413:i

I

.,

, 20070

"

STORE FUNCTION

$

SOLD 33

$

FOR X

=1

$

, A(7) SOLD 44

$

•

, 24414

,

2553~

, A(6) SCLD 42 ,

40071

1

5154,

, A(5) SOLD 40

, 504rl

, 4J2 .34

, A(4) SOLD 40

$

237~

, 66,.G2

, A(3) SOUl 39

$

B26

, 61651

, 66073

, A(2) SOLD 38

$

, C9

,B44

, 4,2003

, 3a;S3

, A(l) SOLD 37

$

, C10

, B31

, 10375

, 51633

, A(O) SCLD 34

$$

Cl1

, D37

, 77777

, 77777

, ROUND

$

, C12

IB14

, 44176

,

, C13

, BI0
, B26

,

00000

, ()()()0l

, LIMIT

, 47(,70

, 31361

, D=24 291 062 513 $

I

,

0

u

OP

08

, C14

B'-'
'''
.,.)

65~1l

CONSTANT

$

, Plover 2 SCLD 33 $
ON X

$

' . PAGE.__8___ OF

I:?HI ?;CTOF HAND UlGVAC

PROBLEM

CODED BY
ITEM NUMBER

OP

toe

, C15

,

,

C16

Frnnc~.

RRF6

VanHilst DATE 6-15-57
COMMENTS

V

U

8

)

, 65324

, A = 27 348

, Bll

) 4534h

, 44516

, B = 10 291 988 814$

, C17

, B.33

, 06571

, 4027.3

, C = 29 104

,

, B

,

,

,

C18

B

77

, C19

,

B~6

, 50117

, 14640

, C20

, B20

00000

, 00000

,

, H54

, 54';11

, ENDSUB

,

1

CODE

,

l00cO .

$

~2

K MASK

651 •
$

, SQRT 2 RND SCLD 34$

,
,
,

1 SCLD 34
ERROR CODE

i
$

$

10

IDENTIFICATION

RRF1,

COS X

STATED POINT

A. E. Roberts, R. "Van Hl1et, 1 June 1957

Remington Rand Univac
2.

PURPOSE

Given X, computes Y(X) = sin (X + ~) = cos X

3.

METHOD

IY(x) - cos xl ! 2-30

a.

Accuracy:

b.

Range of lrgument:

o.

Scalin;J':

d.

X

IX + ~I

< 1f •

236 radians

• ~2 , Y(X) • 232

1f
2 n
obtained from the relation sin 2 ; = 1 - 2 sin
.
sin !L N
~
;}
and a polynomial expanslon for
4
• ~ee RRF3.. ~ Sin XJ
N
The argument X is incremented ~ ~ ; then ~/1f (X + n/2) :: i is

4 (i - 1)

Derivation:

formed and the routlnp. computes sin(1f/2)~ = cos X•
......)

4.

USAGE

a.

Calling Sequence

r
r

b.

+

1

Qf

U ADDR

RJ

t

Normal

Return

+ 2

V AnDR
t

Control and Hesults
The most signifi,c ant 36 hits of the argument, X, must be ini tislly stored
in cells t + 4, and the least significant 36 bits of X stored in t + 5.
The function Y(X) will be found in t +3, and in the accumulator at the
completion of the routine.

c.

Space Required
56 cella of instructions and constants
1 cell of working storage

d.

Error Codes
None

.

5. RESTRICTIONS
32
.
The argument, X, muet be scaled 2 and within the stated range.
CODING INFORMATION

6.

a.

Con8tants

.w.g

mLAtiATl2B

CQNSTANT

PIV2

06 22O'T1 32504

fJ/2 • ';2

2VPI

24 Z7630 15554

2/. • ~5

MASK

37 17m 77774

Modulus

m.

40 00000 00000

1 • ~5
":'

b.

12

20 00000 00000

1 ' ~4

N3,

04 00000 00000

1 • ~2

UAD

00 00001 00000

lJ-Addres8 Advance

A4

00 00122 65046

Coeffioients in

A4+l

00 04626 21024

Polynomial

A4+2

01 21465 66440

Expansion of

.4+3

' 12 25357 16221

A4+4

31 10375 52420

2PI

31 10375 5242l

Working Storage
1 cell labeled STORE

c.

Timing
Maximum 4.30 mls •

.

....

sin(Tf/4
2v • ~2

to'ls

PAGE

REMINGTON RAND UNIVAC
-.

PROBLEM

'j

3

OF 5

RRll

CODED BY Roberts. yap. Hillt DATE 611157
LOC

ITEM NUMBER

OP

U

, SUB

, REFl

,50

, TEMPS

1

,

0

2

,

1

0

, START

, FILL

FUNCTION Y

t

, FILL

, FILL

,

ARGUMENT X(MSP)

t

, FILL

, FILL

ARGUMENT X(LSP)

t

, SP

,IM

,36

X TO A

t

, SA

, XL

,

0

, AT

, PIV2

,

A

DV

, 21'1 '

I

Q

IMP

, A

I

2VPI

, LTL
, TP

,

,

Q

,
,
,
,
,
,
,

, NEGT

, NEGT + 2

, QJ

, MINUS

, PLUS

TP

, RELCl

ERROR , ALARM

,

EXIT

,MJ

,
,
,
,
,

,
,
,
,
,
,
,
,
,

Y

, 00

, FILL

XM

, 00

XL

,

START

, INOU'!'

,
,
,
,
,

,MJ

I

I

§OMMENTS

,
,
,
,
,
,
,

,
,
,
,
,

ENTRY

V

00

,
0

3

, FILL

t
t
t
t
NOT USED

,- t
t

$

ADD PI OVER 2

t

FCTR OUT 2 PI

$

FORM i SCLD 34

t

IN Q

$

FUNCTION PLUS
TEST SIGN OF Y

•

, NEGT + 2

,
,

FUNCTION MINUS

t

I

t

MINUS

I

PLUS

, QT

, MASK

,

A

,

W+i MOD 1 SCLD 35

t

, Qj

, EVEN

, ODD

TEST QUAD NUMBER

$

ODD

, SS

, Hl

,

0

FORM W-l INR

t

EVEN

IMP

I

A

,

Q

I

, SA

, N1

I

0

I

, LTL

,

,

A

,
,
,
,
,

I

0

W-l SQRD IN A
ROUND SCALE 34

IN A • N

•
•
•

REMINGTON RAND UNIVAC

~

.. "-. PAGE'

'" ... - PROBLEM

BBll

CODED BY Roberts. yan Hl18t
ITEM NUMBER

toe

OP

,
, TN
, ,
, TU
,
, TP
, NEST ,MP
, SA
,
,
, LTL
,
, AT
,
,RA
,
, TJ
,
,MP
,
, SA
,
, LTL
,
,MP
,
, 55
, NEaT , TN
,
, ST
,
,00
,
, TP
,
,MJ
, RELC 1 , MJ
, RELC 2 , AT
, RELC :3 , 00
, PIV2 ,B06
, 2VPI ,B24
tl

MASK

, B37

U

,

A

DATE 6/1/57

COMMENTS

V

, STORE

"

.. -,'v - N TO STORE

, RELC 3

, NEST + 3

,

FORM SINE OF

,
,
,
,

Ai.

,

PI(W-1) OVER

Q

, STORE

, NEST + 3 ,UAD

,
,
,
,
,
,

, RELC 2

, NEST

,

TEST END POINT

,
,

A

, STORE

,
,
,
,
,
,
,
,
,
,
,
,

SQUARE 5

0

,
,
,

N1
0

, FILL

,
,

Q
Nl

,.i". 52

,
,

A

N3

,
,
,

,
,
,

Q

0

A

Q

Q
0

A

37
A
A

, FILL

, FILL

,
,
,

A

,

0

, EXIT

0

, NEaT + 3

Y

, A4 + 5

,

, A4 + 1

, 00000

, 22077

, 32504

, 27630

, 15554

,77777

, 77774

Q

5

OF

,
,
,
,

4(W-1) SOLD
35 IN A
-,

illS

ROUND SCALE 34
IN A
ROUND AND SCL' 32
2S SQRD TIMES (-N)
MINUS 1
IN A
~

•
••
•••
•
•
•
•
•
•
•
•
•
•

...

$

TO A FOR Y POS •

STORE FUNCTION
TO EXIT
REUTIVE
CONSTANTS FOR
TEST ABD PRESET
PI OVER 2 SCLD 32
2 OVER PI SCLD 35
MODULUS

•
•
•
•
•
•
•
•

.-

REMINGTON RAND UNIVAC

PAGE
PROBLEM
CODED BY Bobert., Y'P

we

ITEM JfUJ:1BER

,
,

,
,
,
,
,

y

H1

, B40

, 00000

, 00000

12

,B2O

, ()()()(X)

, 00000

1.3

, B04

, 00000

, 00000

UAD

, B

A4

, B
, B

,
,
,

,
,

,
,

u

Of

2PI

1

, 00000

122

, 65046

462h

, 21024

, BOl

, 21465

, 66440

,B12

, 25.357

, 1622l

, B.31

, 10.375

, 52420

, 831

, 10.375

, 52421

, ENDSUB

,

,

,

or

,

RRF;L

lUlt~

DATI 6/1/57

Q9MMIITS

,
,
,
,
,
,
,
,
,
,
,

1 seLD 35
1 SCLD .34
1 seLD .32
U ADVAHCE
OCliST.AJlTS
FOR
POLDOMIAL

EXPANSION

2PI SOLD .32

•
•
•
•
•
•
•
•
•
•
•

1.

RftF5~

IDENTIFICATION

. S'tl'l'Efi POINT

. , ARCSI~ X '

A. Franck, M. D. Bernick,

REVISED 15 June 1957

Remington Rand Uni vec

.,

PURPOS.E

=erc~in X in radians •

Given X, compute Y(X)
.3 • METHOD

~ .~

IY(x) - arosin

a.

Accuracy I

b.

Range of Argument.

c.

Scaling:

d.

Derivationa

! 2-26

II

IXI! 1

X· ~) , y(X) • ~3

Y(X) i, computed in radiaM

~ -..1: - X

,
7
X (I), where X. -1:

trom, the polynomial approximation

air. (See Rand Sheet 1139.)
i=o
The square root i8 obtained as follows I tor ~N~, then tor sui table

Y(I) IS

A, B, C, D. yell

=J.(N+D)+B-C/(N+D)

1s an approximation to

S

with

relative error not in excess ot .0000172; one application ot the Newton
Raphson Formula gives Y(2).

4.

(See RRl9, SQUARE ROOT STATED POINT.)

USAGE

a.

Calling Sequence

-

OP

~

r
r+l
b.

, i .

YADDll

U ADRR ,

BJ

t+2

Normal

Return

t

Control and Results

.. ,
...' ./
The argument, X, must be initiallJ .tored at t+4J'
the reiult,
T(I), will
.
.
.
.

,

~

be found at t+3 upon sucoessful coapletiQnot the routine.
c.

Space Required

96 cells ot instructions and constants
7 cells ot working space
d.

Error Codes
The follOwing error oode is left in

the

AcicUlllUl:etor. on return through the
.

... '

error exits

•

.
I

~

I

:IqPLANATIOl!

Ixl>l

,

-25.

6-15-57

RESTRICTIONS
The argument must be

6.

REVISED.

wi thin the stated range and scaled

i33•

CODING INFORMATION
a.

Constants

Y&

CONSTAlft'

iIPLANATION

C

10 00000 00000

1 -·

Cl

00 00000 00000

Zero

C2

00 00000 00001

1 • 2

C3

53 24135 2CXY70

a., • 244

. C4

33 24414 25535

a6 • 242
40
a5 • 2
a .240
4
9
a
3

i33
0

C5 .

56 40071 51545

C6

37 50417 41234

C7

J.6 23706 66522

C8

26 61651 660?3

a2

C9

44 42003 30653

a

CI0

31 10375 51633

a O • ';4

Cll

37 77777 77777

1

f·~

.

)

• i3
• iJ8 .
• i37

'l

Round Constant
1f

C12

14 44176 65211

-2

C13

10 00000 00001

1 •

C14

26 47670 31361

1)::24,294062,513

C15

00 00000 65324

A='Z7,,48

C16

11 45346 44516

8=10,291,988,814

C17

33 06571 40273

C=29, 104, 062,651

C18

00 00000 C'IJOTI

Shirt Count Mask

C19

26 50117

l4640

~

C20

20 00000 00000

1 •

CODE

545431100000

Error Cod.

• i33
~3 + 1

• i34
i34

(rounded)

...

-3b.

6-15-57

Work Spice
7 cells labeled

c.

RIV.

STORE thru STORE + 6

Timing

• 2-33) •
Approximate maximum of 6 •66 mls. for X = - (1 - 1

PAGE

REMINGTON RAND UNIVAC

4 OF

7

PROBLEM RRF5
DATE REV. 6-15-57

CODED BY Franck, Bernick
ITEM NUMBER

LOG

,

OP
, SUB

,
, TEMPS
,
, IN OUT
, ENTRY ,MJ
, ERROR , ALARM
, EXIT ,MJ
, Y , 00
, X , 00
, START , TM
,
, TJ
, SP
,
, MJ
,
, PROG , TP
,
,ZJ
, NOZERO , TP
,.

, TP

,
, TP
,
,SJ
, MINUS , TP
, TJol
,
, PLUS ,EJ
, MP
,
,
, LTL
,
, AT
,
,MP

U

COM M EN T S

V

,
,
,
,
,
,

, FILL

, 96
, 0
, 1
, START
,
, FILL
, FILL
, FILL

,

,

, ABS X TO A

, RRF5

,
,

7
1

,
,

0

,

0

, FILL

X

, ARGUMENT SCLD 33

, PROG
, 0

, ERROR CODE TO A

0

, ERROR

, GO

A

,

, X=Y IF X=O

, C13

,
,
,

A

~

, FUNCTION SCLD 33

CODE

Y

, CHK FOR X GRTR 1

TO ERROR EXIT

, NOZERO

, EXrr

, TEST X = 0

,
,

A

, STORE

, ASS X TO STORE

X

,

, X TO A

,

C1

, STORE+1

, SET FOR POS Y

, PLUS
, STORE+1

, TEST SIGN OF X

A

,

A

, ABS X TO A

C

, XONE

, TEST X :: 1

,
,

C3

,

A

,
,
,

, MINUS

,

,
,

C2

, STORE

,
,

A

1

C4

, STORE

, STORE+2
, STORE+2

, SET FOR NEG Y

EVALUATE
POLYNCMIAL
EXPRESSION
IN

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•••
•
•
•
•
•
•
•
$

REMINGTON RAND UNIVAC

PAGE 5

or..t
' .~7

__

.. - PROBLEMl;..
' -.LRRl::.w;,.S"-_ _ __

CODED BY lranck.Berniok DATE REV.6-.5-57

ITEM NUMBER

,
,
,
,
,
,
,
,
,
,
,
,
,

Lob

OP
, LTL

U

, AT

, 1
, 05
, STORE
, 3
, C6

,MP
, LTL

, AT

,MP
, LTL

V
A

, STORE+2
,f

,

STORE+2
A

l

,
,
,

CQMMEl!TS
APPROIIMATION
O'IY

AOCUMUUTE
Dl

, STORE+2

, STORE+2S0LD 34

, STORE

, STORE+2

,

, AT

,
,

,MP

, STORE

, STORE+2

,

,
,

,

,
,
,
,
,
,
,
,
,
,
,

LTL

, AT

,MP
J

LTL

,
,

2

2

, STORE+2

STORE

, STORE+2

2

J

, LTL

,

a

, AT

,

CI0

, TN

, STORE

, SA

,
,
,
,
,
,
,

MP

,
,
,
,
,

, Sp

,

, TP

,SF

, SA
, LTL

,MP

J

A

08

J

, AT

A

, STORE+2

07

,
,

,
,
,

,

C9
STORE

,

A

J

STORE+2

, STORE+2
A

"

, STORE+.2

, X(X) TO STORE+2

0

,
,

A

, STORE+3

A

,

A

" STORE+4

,
,
,

,

, FORM AN» STORE

014

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
$

A

, FORM (l-X) SOLD 33.

0

,

0

18

INA
! TO STORE+3

(R)

=N SOLD 34 •

STORE N
"

0

, STORE+5

, (B+D) -SCLD -1&=1

C15

, STORE+5

,

A X F TO STORE •

, ,

REMINGTON RAND UNIVAC

6

PAGE
,

7

RRF2

PROBlEM

.
'.

or

CODED BY lIWl£k.I!!Gai12i DATE REVIR-'2-~:Z
-,.,

LOC

ITEM NUMBER
,

or

u

v

C9MHENTS

,

, AT

,

C16

,

STORE-+6

,

, SN

,

C17

,

15

, DV

, STORE+5

,

A

, AT

, STOREi6

,
,
,

, SF

, STORE+4

,ss

, STORE+5

, DV

, STORE+5

, STORE+5
, .32
, 0
, .A

,
,
,
,
,

, AT

, STORE+5

, STORE+5

,LQ

, STORE+3

,ctr

,

C18

,
,

,TV

,

A

, IODD ,

, SET SOALE FOR 'SQRT -N •

, QJ

, KODD

, KEVEN

, TES!' PARITl'{)F K

, KEVEN

,MP

,

C19

, STORE+5

, (Y(2)+1) OVR 2

, SA

C20

,

, SOLD 17 EQUALS

,
,

,
,

, LTL

,
,

, KODD

, SF

,

,
,
,
,

a

'.35

, AxF+B TO STORE

; -c sow

15 TO A

, -c ov.m F = . ..0
,

;

$

•
•
•
•

, Y(l)APRXfQRT~: atD'16 •
, N SCLD .32 TO·.• '
, li - 1(1)

,(N ovr I(l) )..l+I(l).

, =I(2)=SQRTI SOLD 17 •
, x{o)

in Q(35) .. ,

•
<

A

1

, I-X(O) OVER 2 IN A$

(Jl ~: sW X-l)

•
•
•

, STORE+5

, SQRTr

, STORE+5

, FILL

,

, SA

,

0

, miD SOL SQRT (I-X) •

, LTL

0

A

, SCLD .3.3 IN A

A

, STORE+2

, x(x) TIMES SQRT (l-I) •

2

,
,

A

, SCLD 3.3 IN A

, ST

,
,
,
,

,
,

Q

, -ARCSINX SOLD .3.3

, TEST

, IJ

, STORE+l

, NEOY

, TEST FOR NEG I

,

,TN

Q

,

Q

,

, NEGY

, TF

Q

,

I

, STORE FUNCTION

,

,MJ

,
,
,

0

, EXIT

,MP
, LTL

'r

Cll

C12

,

IN A

YPOS

•• •
t·

•
•
•
•
•
•

I.Y~Q •

- . ..

.

~.

7_.'_· _
PAGE___7_OF__

REMINGTON RAND UNIVAC

PROBLEM........RRF
...........
5 _ _ _ __
CODED BY Frapck.Bernick

IT'F:M NUMBIR
I

LOC
XONE

U

V

C

°FOR11 t1X E=N1 T S

Cl

I

C2

, B

, C12
,
°
, 00000
,
,

C3

, B53

, 24135

, 20070

, A(7) SCLD 44

,
,
,

OF

DATEREV.6-15-57

, TN
, MJ

C

, BI0
B

, Q
, TEST
, 00000

,
,

,

0

,

,

1

,

•
•
•
•
•
•
•
•
•
•

, 1 seLD 33
ZERO

,
,
,
,

C4

, B33

, 24414

, 25535

, A(6) SCLD 42-

C5

, B56

, 4ocrn.

, 51545

, A(5) SCLD 40

,

C6

, B37

, 50417

, 41234

, A(4) SCLD 40

,
,

C7

, B46

t

237~

, 66522

, A(3) SCLD 39

C8

,B2£>

t

61651

, 66073

, A(2) SCLD 38

C9

,B44

, ~"2003

,

3C65.'3

, A(l) SCLD 37

$

ONE

$

,

C10

J

B31

, 10375

, 51633

, A(O) SCLD 34

$

,

Cl1

, B37

, 77777

,77777

, ROUND

$

,

C12

,B14

, 44176

, 652ll

, Pl! OVER 2 SCLD 33 •

J

C13

, B10

, OOOX>

, ()(x)()1

,

C14

, B26

, 47670

, 31361

, 0=24 291

C15

, B

,

, 65324

, A

C16

,

, 453/..6

, 44516

, B=10 291 9S8 814 $

C17

, B33

06571

, 40273

, 0=29 104 C62 651

C1S

,

,
,
,
1

~2

$

513

= 273~'

•
$

•
•
•
•

,

,

B26

, 50117

, 14640

, SQRT 2 RND SCLD 34 •

C20

, B20

, 00000

, 00000

CODE

, B54

, 54311

, 00000

, ENDSUB

,

,

,
,
,

C19

,
,

,
,

I

LIMIT ON X

B

,
,
I

::2.1

CONSTANT

77

K MASK

1 SCLD '34
ERROR CODE

$

,
A.

Identifioat~on

CE 1002 Tape Handler*
Harold Dahl beck

Sperry Rand
Corps ot Engineers

Linnea Laure v
1 June 1957

B.

PURPOSE

This program provides the fa0111 ties to read, write, move or rewind
a tape am any or all uniservos in variations ot mode, spaoing and
direction.
It provides tor the preparation ot tapes to be read b.y several of
the peripheral equipments.
Provision is also made for the storage of data in the memory in
inverse or direot order ~ and may be read into memory in various
modes by indicating the number of blocks and/or amount of \lorking
storage to be tilleda
The routine can keep an account ot the relative position of all tapes
on the Uniservos in terms of blooks from the leader position, as veIl
as to establish conditions tor writing a full tape.

It will &180

varn the user of undesirable orders, suoh as reading or moving
back'Jard more blocks than it has moved forward.

When a tape

reading fault occurs the routine viII automatically attempt
rereads of that block in various directions and at different bias
levels.
C.

METHOD

The program takes as its oontrol the interpretation of two input
parameters whioh in! tiate all tape aotions a These parameters
function as pseudo tape commands.

* This routine follows the set of specifications set forth in
November 1956 by Capt. Roger Bate and George Toal of the Corps
of Engineers.

-2-

There are two counters kept for each servo:
1. Block counter R:-_ _ _ advances on all read, write,
and ,move orders in the forward direction; deoreases on
all read and move baokward.
2.

Tape length counter N_ _ _ _ increased each time a
blook is written bnto the tapeo

These two counters should be set to zero whenever a tape action 1.
initiated from the beginning of the tapeo
Do

USAGE

10

The routine was programmed to be used as a straight subroutine,
or as a USE aubroutineo
It is entered by means of the

2.

3.

r

RJ

r

-f 1

8eque~o.

(t is starting address of
routine)
normal return

There are two input parameters whioh must be pre-inserted
P1

at

P2

at

Before using this routine, one should insure the proper
setting of the following preset parameters for a given
installation.
1.

NOON

determines tape length

20

SERVV

number of servos plus one

3.

UL

upper address limit

40

LL

lower address limit

Manual control ot the routine is also possible Qy means of a small
add! tional routine known as Test 10

'.

-.3-

E.

CODING INFORMATION

1.

Tape Handler has 65.3 wordso

2.

The Tap

.3

There are three print routines which oan be used independent

0

Handler inserts a 45 oommand into 171770

or the tape handler.
&.

bo

Print Non-Negative deoimal integer
SP

K

RJ

PEXIT

SP

K

RJ
c.

0

PRINT

FLEX-CODE

PRINT

K

Word

42

W1

OCTAL

PRINT

K.

Word

K

.39

SP

I

RJ

PRElIT

PRWORD

These tags are internal to the Tape Handler.
Parameters
The two parameter vords have the octal form &

Ph

P2

M = 1st storage looation

OPERATION

B - Number or Blooks

c

D

W • Number of vords

OPERATION

L = lsngth of Blook

Not

Operation

Servo

Read Write

or Length of storage bin

Used

A

S

B

S

-4Every reference to the routine must be prefaced b.Y the insertion of these
two worde:
1.

Every pair must obey the following general restrictions.
1 -L SS< No. of servos plus one.

2.

LL ~ M ~ UL

3.

LL ~ M-fL ~ UL

Care should be taken to select the proper parameters to effect the
required action; thus, a brier discussion of how the routine translates
the parameters is in ordera

OP.A is first translated. This option permits the programmer to set
the servo counters to zero in order to begin a fresh tape with zero
readings and hence keep a meaningful block and tape length count.
Special heed should be given to this option in order to avoid
ambiguous interpretation of the counters which are automatically varied
with the tape action.

OP.A.

o

Has no effect on servo counters

1

Sets R

servo SS

2

Sets

all servos

3

Sets

4

Sets N - 0 for

5

Sets N = 0 & R = 0 for servo SS

6

Sets N

7

Sets switch to b.Jpass test for full output tape when

= 0 for
R = 0 for
N = 0 for

servo 55
aJ~

servos

=0 & R =0 for

vri ting.

all servos

Resets on next entry to this routine a

OP.B is neKt translated and selects the required action.

o

No action.

1

Sets Read s'Wi tch (after selecting tape oode and increment)

Exits from routine setting Q to aero.

Then it decodes OPe
READ.

-5Sets wri te switch (after selecting tape code and increment)

2

then decodes OPe
Write.
MOves B blocks forward or backward.

3

Exits from routine

setting Q to zero.
4

. Rewind servo S8.

5

Rewind servo 55 with interlock.

6

Re\lind all servos.

7

Rewind all servos \lith interlook.

After the selection of a rewind, both servs oounters are set to zero for
the appropriate servo.

Q is set to zero and normal exit is made.

OP.C initiates no tape action b,y itself; serves only to seleot the
necessary EF code word as well as to set the required switohes in the
routine;

e~t.,

tape direotiono

READ OPTION
0

Variable Forward

1

Variable Backward

2,6,7

Fixed Forward

3

Fixed Baokward

4

BSP Forward

5

HSP Baokward

WRITE OnION

o or

1

Variable

2 or 3

Fixed

4 or 5

HSP

6

Tape to Card

(Fixed Blook 128 - .1" - 2.4")

7

Uniprinter II

(Fixed Block 50 - O~ - 2 .4")

Options 6 and 7 should be read by using options 2 and 30

HSP

options reads a true machine variable n word block, whereas
writing with the HSP option writes a 20 word blocko
The direction of address inorementing in memory is determined from
OPe D.
OPt D.

0=3=4=5=6=7

Sets increment of plus one for forward
direction.

1

Sets increment of minus one for baokward direction.

2

Set. increment of sero (One looation
for all worda).

The WRITE options are translated only if the write switch was set
(OP. B)

o

Write W words from M. OP.C selects writing modeo

(0=2=3=5=7)

a - Fixed mode assumes 120 word blocks.
b - HSP mode assumes 20 word blocks.
c - Variable mode writes an (L

-I- 3)

word block.

The

BLI is automatioally generated from L and added during
the write.
If W is not an even multiple of 120, 20 or L, respectively,

the final block will be padded with tape sentinels to give
a full blocko
If W is equal to zero, a stopper block i B written onto tape.

1

Write B blocks, from M. Variable mode only.

Assumes that

block in memory has one BLI followed by n data words.
implies that M contains a BLI.)

L will be reduced by n

(This

Before writing each block, a

test is made to insure that the first word of
a BLI.

~

I-

!!fa

block contains

1 for each block to prevent

-7-

exceeding the initial L.

Failure to meet either of these conditions

causes an alarm printout.

4

Write B blocks from M. OPe C selects writing mode
a - Fixed mode assumes 120 word blocks
b - BSP mode assumes 20 word blocks
c - Variable mode writes an (L-I3) word block.

The BLI is auto-

matically generated from L and added during the write.
Before starting this option, a test is made to Bee whether the number
of words as given by blocks times size will satisfy

LL:: M..,tw~UL

If W is equal to zero, a stopper block is written onto tape.

6

Write all blocks contained within L words from M. Variable mode only.
Assumes that
words.

~

(This

b100k in memory has one BLI followed by n data

~mplies

that M contains a BLI).

following the last block must be a bin sentinel.

The first word
Starting at M,

blocks will be suocessively written on tape until one of the following oonditions occurl
1.

Bin Sentinel Found

normal exit

2.

Last block exceeds reduced L

Alarm print

3.

Proper location does not contain BLI

Alarm print

The READ Options are translated only if the read switoh was set

o

(oP .B.)

Read B blocks into Mo OP.C selects reading mode.

(0=2=.3=6) a - nxed mode reads in 120 word blocks.

b - BSP mode reads in N word blocks.
c - Variable mode does not insert BLI or sum check in memory.
1

Read B b100ks into

M.

Variable mode only.

Insert one BLI (but not Sum ~eok) into ~emory as first word of
b100k followed by n data words.
For options 1 and 00, L = maximum storage allowed and is reduoed
as eaoh variable block is read in.

Should the remaining space be

insuffioient to store the last blook; reading is stopped, the 1alt

-8block is not read in and the tape will be repositioned.

This latter action

will cause an alarm :.:>rint.
4

Read Blocks as needed to fill up

L

vorda.

On variable mode, no BLI or sum check is inserted.

5

Read Blocks as needed to fill up

L words. Variable mode only.

Inserts one BLI (but not sum check) into memory as first word
of block followed by n
For options

4 and 5,

(t - 1)

data words.

= maximum

storage allowed.

A special end

sentinel (07 77777 77777) is added as the next vord after the last valid
word stored.

W::: longest variable block expected.

8houU the re~ning

space be insufficient, (as determined by the incom1n; BLI) the last
block will not be read in and the tape is repositioned.

Also, if W

is larger than the reduced L, no further attempt viII be made to read.
7

Check Read Tape

OP. C selects mode.

At any desired time, this option may be invoked to
1.

Print out
CHRD

Servo No.
~ock

2.

NO • .

Read backward from tapes in the mode sele6ted that many blocks
without reading jhe vords into memory~

3. Revind the tape on that servo without interlock.
The
Fixed

n~ary

parameter words for check reading &reI
30,OOOO1,M
70,02oo0,001S8

HSP

50,00001, M
70,02000,00 1 SS

Variable

10,00001, M
70,02000,00 1 SS

-9ALARM EXIT AND ERROR PRINTOUT

Since the Tape Handler is normally referenced and controlled from
external routines

qy

means of the two parameter words, it was felt necessary

to incorporate into the routine itself a method which guards against the
insertion of improper parameter words as well as to monitor the dynamic
results of the initiated tape actions.

To facilitate this aim, it was

required that normal exit from the routine would always be accompanied

qy

the insertion of an appropriate bit pattern into the Q-Regiater, which

could then be interrogated further by an external diagnostic routine
which checks the bits in Q immediately following the exit from the Tape
Handler.
There are onl y three normal exits from the tape handlers
1•

When this routine exi ts wi th no unexpected resuJJfi "Q35=Oo

2.

Tape End Sentinel Found
a - Test is made for variable and fixed mode.
b - The block

~

c - The tape is

read into memory.

~

repositioned or rewound.

d - Exit is preoeded

3.

qy

a printouto

Output Tape Full
a -

~

each

bl~ok

is increased

qy

i8 written, the tape length oounter
an amount dependent on blook size and

spaeingo
b - Unless the b,ypass option was selected (1

1s made to aee it the last

~eaumulated

tape length oonstant NCON.

=7),

a test

sum exceeded the

It NCON was exoeeded, a

stopper block is automatioally written onto tape and
the block count increased
receive a stopper block.

qy

oneo

HSP option does not

-10-

c - Exit is preceded b.Y a printout.
Before each ex! t the accumulator will be filled with a 77 00000
%%XXX

where xxxxx will be the initial address of the current block entry

.bould the r ead order be interrupted b.Y an alarm conditiono
On an exit print out, the format will consist of the following

liz line.:
Example

!!xPlanation
1.

Normal Exi t Line

20

P1

30

P2

40

45 00000

01234

.... 30 00001

04000

00 02000 00103

Error (or ex! t) No.

Exit

34

50 Servo

Noo

Servo

3

6.

No.

Block

63

Block

This printout should enable the programmer to discover the cause
of the printout.
In the example given above, one can readily obtain the following

information:
1.

The tape handler was last referenced from address 012330

2.

No servo counters were set to zero.

3. The action called for was a read backward one fixed block from
servo 3 into the location 04000 and incrementing the address forward
in memory.

4. The exit number states that a tape sentinel was discovered in
block 6.30

-11-

SUMMARY OF FLEX0-WRITER PRINTOUTS
NO

EXPLANATION

34 End Sentinel round

ACTION TAKIN

TEST CONDITION

1. Variable mode: Found Print

stopper block
2. Fixed mode I

Exit

Firat

word was tape sentinel

33 End of Tape

NCON ...c:::::N ~

1 • Automatioally

writing last block

writes stopper blook
(except in HSP)
2.

Advances

~ock

counter
30

32 Mod 6

Print end Ex! t

Last failure to

Print and

read block due to

Cease

*

lokld6

31

Uhrockable Parity

30 Uhrockable Sum Cheok

29

Possible 720

Last failure to read

Print and

block due to parity

Cease

Last failure to read

Print and

block due to sum check

Cease

MACHINE HANGS UP

Set PAl to 17777

on 720 or sprocket

to print and exi t

*
*

trom routine.

*

Halts on easily identified

It)

00123, XXXIX.

to attempt another reread of blocko

Push start button

-12-

9

Illegal Servo No.

o~ sgc:::::: SERVV

Print and Cease

8

Insuffioient Spaoe

L~~UL

Print and

•

'i

LLe:::M

direction in memory.

U. "::::; Mrw ~UL

-/-=
7

6

5

7'L-===UL

Sign depends upon

Oease

,

forvard)
N '-::::::: 0

Move Back Neg

Print and

Read Back Neg

Cease

L reduted to point where (L - Block Size) ~ O

Print and

read or write not possible

Cease

lot Blook Length Indo

00

JIXXX

IIXU

Print and
Cease

Reoovery is poss! ble from errors 9, 8, 7, and 5

Note:

tt

1•

Correoting Parameters P1 and P2 manually 0

2.

Setting PAK to T. ito starting address and push START.

-13GWSSARX

FIXED BlPeK

The standard fixed block length is 120 words.

The blook

and blockette spacing depend on the option seleotedo

VARIABLE BLOCK

The block oontains n

~3

words where the first and last

words oontain the Block length Indicators, and immediately
preoeding the last word is the word containing the Sum Checko
BLOCK LENGTH

~TOR

L1

One octal word appearing as 00 XXXXX YYYYY where X

=Y =

the number of words in a variable block exoluding the

Bo 1010's and the Sum Check.
SUM CHECK

One word whioh equals the least 36 bits of the algebraio
summation of

the words within the blook excluding the

~

B. L. I. 'e and the Sum Cheok itself.
HSP BLOCK

The true machine variable blook consieting of n words.
However, since this option was intended for use with the
High Speed Printer, the writing of these blocks was restrioted to 20 wordso

This restriction can be removed

easily.
SENTINElS

Tape Sentinels:

74 74747 47474 whioh prints as

Basket Sentinel:

07 77777 7m7

eZzzaa

(used internally with

the tape handler routine).
STOPPER B100 K

1.

Fixed block length option,
This block contains 120 words of tape sentinelso

2.

Variable block length option.
This block consists of only one word, the tape sentinel.

Servo Number (Two octal digits)
Initial 3torage location from whioh words are written or
read into memory

0

-14Number ot blocks (Four octal digits)
.,

,,

Number of Words (Five octal digits)
Block Counter for servo
Tape Length

Coun~er

for Servo

Has various meanings depending on use.

In general, on

writing variable blocks, it is the number of words in the
block.

On reading, it determines the amount of space

available.
Preset constant equal to one more than the number of
servos existing at a particular installationo

\

Preset upper limit in memory beyond which reading and
wri ting is Prohi bi ted.
Preset lower limit in memory

~low

which reading and writing

is Prohi bi ted.
Preset constant used to limit writing on tapes beyond a
desired length.

Measured in tenths of frames

0

Currently

calculated from the formula:

(1500)' 90% X 12" X 1280
at 128/inch.

= 20,736,000

tenths ot frames

RWBFJN
10-15-57
P. 1 of 6
RWBFJN , Floating Point Bessel Function J

n

Subroutine

Pro grammed by : David G . Cantor, The Ramo- Wooldridge Corporation
Date : September 16, 1957

A.

Purpose :
This subroutine calculate s J

(x) for arbitrary x and integer n.

n

Floating point arithmetic is used.
B.

Usage :
1.

Specifications .

Standard USE subroutine using built-in

floating point.
SUB,

2.

3.

4.

RWBFJN, 171

TEMPS,

5

3

INOUT,

2

1

Input
First word

-

x in floating point .

Second word

-

n in fixed point scaled at 2

First word '

-

J

0

Output
n

(x) in floating point.

Space required
Length of subroutine - 171 words.
Temporary storage in compiled region - 8 words.
Other routine s used - R WSQF1, RWCNF4
Other temporary storage - None

•

RWBFJN
10-15-57
P. 2 of 6
5.
C.

Error codes -

The alarm exit is not used

Restrictions and Coding Information:
The routine u ses 11 03A built - in floating point arithmetic.

x

must be a standard floating point number and n must be an
integer .
D.

Timing :
If Ix l

..::> 3 and I n l

= 0

or 1,

t = 15 m. s .

= 25+lnl

If Ix l ?3 and Ixl ? ln l>1then t
If Ix l< \nl or Ixl

E.

<3

then t

= 15

m. s.

+ 1. 21n\ m. s.

Mathematical Method :
1.

Formu l as .
(a ) For J 0 and J 1 when I x l ~3 asympotic formulas are used.
See E . E . Allen ,

Analytical Approximations , Mathematical

Tables and Other Aids to Computation, Vol. 6, October, 1954,
pp . 240-1 .
(b)

For I n (x) when \ x l >Inl >1and \ x

I

?

3

the re cur sion formula
J

. 1 (x) =
nT

2n
x

is used for which the starting values J

o

(x) and

J 1 (x) are computed as in .(a) .
(c)

For J n (x ) when

I

x I E;

The test em-

which also serves to

prevent the product from becoming too small.

In the event this

test is violated an arbitrary change on z is imposed by adding
(previousl y defined) to the real part o~ z.

E

In this event the output

includes only z and F(z) while F (z) is replaced by zero.
r
b.

After each iteration a test is made to prevent undue growth in

the magnitude of the values of the function F r(zi) and F r(zi+1)'

*

these values do fluctuate a new iterant zi = (Zl' +zl'
2 +1)

If

is chosen.

One line skip indicates that z7 was formed.
Auxiliary program.

This program evaluates F(z) for a given z

determined by the subroutine.

This coding can include a control

option limiting the region of search for a root to a well defined
local portion of the complex plane by properly constraining successive iterants.

RWRTI 1
10-17-57
P. 10 of 20

The applicability of this method to general root finding problems
is noteworthy for a number of reasons.

The procedure is

completely general, requiring no knowledge of the location of
the roots nor any special starting process.

Furthermore,

complex roots are obtained with the same ease as are real
roots.

Since the iteration requires only the evaluation of the

function, and never the value of the derivative, the scheme is
useful in problems where the evaluation of the derivative is
very difficult.

While multiple roots do not present any

c:omputational difficulties, they are obtained with less accuracy
than simple roots.

Also, the rate of convergence is considerably

reduced in the case of multiple or clustered roots.

:D'Ct-e-~~i~e three starting values :
o

,_ _ _ _~ z l' z z ' and z3 according to

(\J

t"-

i option chosen.

Find the as soci , ated functional values.

- -.-. -r--

~ I

I- j If' G
I

I- I t"- rl

E-t rlrl
ff;1
~'- 0
•
P=:rlP-.

;~__

-....

i

\

\

I

-~

---~
i

parabola' and' d~ter~i~e new
l estimate zi+l' not equal to a
previously found root.
F(zi+l) and Fr(zi+l)'

- - --------1--·-

I
I
!

.~

--.

~

{

I
I

~--

\....

I
.....

--

!

, b)

Izi+l

- zi

I

out

VI

~ Option to accept conjugate Of'::]

L_____l_a_s_r_o.o_t_n_o_~

-

~--,./

Auxiliary Program

: Convergence test:

~: a)

I
I

.. I .

I
I

.-- -~

Option to output Zi+ I' F (Zi +l )
and F r (z.1 +1)'____ _ _ _ _ _ _ _ _ _ _

I

I

Find

I

Option to control search
for z in the canplex plane

I

IFit

r

'\

/

-- -

Flow Chart for Arbitrary Root Finding Substitute

/

RWRTl l

lO ..17..57
P. 12 0:' 20

,
,

,SUB
.RWRT Il
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• TEMPS
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,ALARM .ALARM •
,EXIT .MJ
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t
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• TII6

,A

,MS
,OPT1
,T1I6
.T'12
tT'7
.T'13
.T#6
.ARG
.T'7
,ARGI
tIN
,T
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,nU2

,ARG
.Tll3
.ARGl
, IN

,T'2

•

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,STARTtNG OPTioN

,•
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OF X.

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mlRT11
10-17-57
P. 13 of' 20

•

.TP
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t
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.OUT
.ANS
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.Cl
.C3
,OUT
,ANS
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.T#6
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.C4
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.Q
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.T#9
• T#8

,TH3

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.TH12
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tIN
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.T#10

• T#8
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to

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RvlRT~ ~

~0-~7-57

P. ~4 of 20

,
,
,
,
,
,
,
,
,
•,
,
,
,
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!
~
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5
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RvlRT1 1
10-17-57
P. 15 of 20

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RWRTll

lO-l7-57
P. l6 ot

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TO AUXLIARV

INDEX
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•••
,
,•
•
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•
•
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9
S
J

RWRT1 1
10-17-57
P. 17 of 20

,
,
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9
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~
~

RWRT1 1
10-17-57
P. 18 of 20

,

,RWPI
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RWRrl 1

\

10-11-51
P. 19 of 20

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RWRT1 1
10-11.. 51
P. 20 of 20

,TJ
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, ••• k..,.
RWBFFO
10-15-57
Page 1 of 5
RWBFFO, Floating Point Bessel Function Subroutine

Programmed by : David G . Cantor, The Ramo- Wooldridge Corporation
Date:

A.

August 25, 1957

Purpose:
This subroutine calculates J

o

(x ) or Y

(x) using floating point

0

arithmetic.
B.

Usage :
1.

Specifications.

Standard USE subroutine using built-in

floa tin g po i n t.
SUB,

2.

RWBFFO,

97

TEMPS ,

°

°

INOUT,

2

2

Input
First word: x, in floating point.
Second word:

a.

If a. is> 0, J
If a. is

=

0, J

o
o

If a.is0, J 1 (x) is calculated.

3.

4.

If a is

= 0,

If a is

=< 0,

,

J 1 (x) and Y 1 (x) are calculated.

Y1 (x) is calculated.

Output
First word :

J 1 (x), if calculated.

Second word:

Y 1 (x), if calculated.

Space required :
Length of subroutine - 97 words
Temporary storage in compiled region - none

·

-

RWBFFI
10-15-57
P. 2 of 5
Other routines used - RWLN F 2, RWCNF4 , RWSQF1
Other temporary storage - n one
5.

Error codes

If x

~-3

and Y 1 (x) i s to b e calculated the routine goes

to the alarm exit.

If - 3 0'0
<:

Th

e square root, x

.
. .
+ lY,
1S 1n

the right half-plane except when a :;: 0, in which case it is on
the non-negative imaginary axis.
.3.

•

L

0, the routine g'ves x

answe r if a :;: 0 and I b I

=y

< 2 -128

For the particular case
;:: 0 .

Zero is also given as an

/
whe re a and b are the real artd

imaginary parts of the given complex number.

«

•

1

..

RWCSQ1
10-15-57
Page 3 of 3

,

,SUB
, RWCS 01
,TEMPS d
,
,TNOUT ,2
,
,
,MJ
,ALARM ,ALARM ,
,EXIT ,MJ
,ANS 1 ,
,ANS2 ,
,ARGI ,
,
,ARG2 ,
,BODY , TM
,ARGI
,TM
,ARG2
,TJ
,TEMP
, ZJ
,N EX T1
,NEXTI ,TP
,A
,FD
,TEMP
,NEXT2 ,TP
,0
,FP
,ANS2
,RWSOFI,O
,TP
,A
,
,FP
,ANSI
,RS
,0
,SJ
,ZERO
,NEXT3 ,RWSOFI,A
,TP
,ARGI
,SJ
,NEXT4
,NEXT 4 ,TP
,ARG2
,SJ
,NEXT5
,NEXT5 ,TN
,SOtl3
,MJ
,NEXT6 ,TP
,SOtl3
,NEXT7 ,RA
,S Otl3
,FD
,ARG2
,TM
,0
,MJ
,NEXT8 ,TP
,SOtl3
,RA
,SOtl3
,FD
,ARG2
,TP
,0
,
,MJ
,CASE2 ,TP
,TE~~P
,NEXT9 ,FD
,ARG2
,MJ
,ZERO ,RS
,ANSI
,TP
,A
,
,
,MJ
,KI
,F
d.OOOO
,K2
,00
,100001'B
,ENDSUB,

,47
,2
,2
,BODY

,
,
,

,

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

,
,FILL
,
,

,TEMP
,A
,CASE2
,ZERO
,ANS I
,ANSI
,ANS2
,Kl
,SO
,0

, TEMP
,K2
,NEXT3
,SO
,A
,NEXT8
,A
,NEXT6
,ANS2
,NEXT7
,ANS2
,K2
,S Otl3
,ANS 1
,EX I T
,ANSI
,K2
,SOtl3

,ANS2
,EXIT
,ANSI
,ARG1
,NEXT2
,A
,ANS2
,EX IT

,

,

,
,

,
,
,
,
,
t
t
t

,
,
,
,
,
,
,
,
,
,
,
,

$
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RWMVM2
10-17-5 7
P. 1 of 5

_ R WMVM2, 'Complex, Floating Point Matrix- Vector Multiplication

Programmed by : F. W. Blackwell, The Ramo- Wooldridge Corporation
Date:

A.

August 20, 1957

Purpose:
This subroutine computes the product of the square matrix
A - a I and the vector x.

The computation is performed in

complex floating point arithmetic.

B.

Usage:
1.

Specifications.

Standard USE subroutine using built-in

floating point.
SUB

2.

R WMVM2,

86

TEMPS,

5

0

INOUT ,

4

0

Input.
First word:

o.

Second word:

0.

Third word:

00, A, x

Fourth word:

00, Y, N

where o.
0.

R
1

A

R

1

= floating point, real component of a

= floating point , imaginary component of a
= address of the first cell in the region of 2n2
cells where the matrix A is stored, row by
row.

A may be either in core storage or on

RWMVM2
10-17-57
P. 2 of 5

the magnetic drum.

It is as sumed

throughout this s ubroutine that each
element is stored in two consecutive cells,
the real part immediately preceding the
imaginary part.

x =

address of the first cell in a region of
4n cells, the fir st 2n of which contain
the vector X , and the second 2n of which
are successively used for temporary
storage of the rows of the matrix.

This

region should be in core storage for
efficient operation.
Y

= address of the first cell in the region of 2n
cells where the resultant vector Y is to be
stored.

N

3.

=

order of the matrix A

Output.
The vector Y which equals (A - a I) X is stored in a
region of 2n cells beginning at location Y, as indicated
above.

4.

Space requi red.
Length of subroutine:

86 cells

Temporary storage in compiled region:
Other routine s used:

5 cells

none

Other temporary storage :

data, re sults, and temporary

storage occupy an additional 2n2 t 6n cells, 2n2 of
which (the matrix) may be stored on the magnetic drum.

RWMVM2
10-17-57
P . 3 of 5

5.

Error Codes.
The alarm exit is not used by this subroutine • .

C.

Restrictions and Coding Information
Data must in standard USE floating point repres entation.

The pro-

gram is self- contained, performing its own complex arithmetic.
The 1103A built-in floating point is used.

The subroutine does

not destroy the input data, the matrix, or the vector.

If every-

thing (including the matrix) is in core storage of 4096 cells, the
limitation on the order of the matrix A is N ~ 43.

Since the

matrix may be stored on the drum, N may be as large as 90.

~ .

2
5ni'2 1. 5n

+ 1.8

milliseconds.

If the matrix is on the drum.

add 17n milliseconds to this time.
E.

Mathematical Method
The matrix is brought in a row at a time to temporary storage and
the complex inner product of this row and the given vector is computed to form an element of the resultant vector.

Representative

times obtained by trial on the 110 3'A for matrices having random
elements with a range of approximately 10

4

-

and stored on the drum

are as follows :
Orde r of Matrix

Time in Seconds

10

0.37

15

1. 01

20

1. 37

25

1. 74

30

3.08

50

6.88

80

19. 14

RWMVM2
10-17-57
P. 4 of 5

,
,
,
,EXIT
,ARG
,BODY

,
,

,

,
,
,
,

,
,

,
,
,
,

,
,
,
,R13
,R8
,R9
,RIO
,Rll
,R12

,

,
,R3
,Rl

,

,R2

,SUB
,RWMVM2
,TEMPS ,5
,INOUT ,4
,MJ
,ALARM ,
,
,MJ
,RESERV,4
,(3
,TP
,TV
,ARGtl3
,T3
tTP
,RS
,T3
,SP
,T4
,LO
,T4
,A
,RA
,TV
,A
,TV
,A
,TV
,A
,TV
,A
,RA
,A
,A
,TV
,A
,TV
,TV
,A
,A
,LA
,A
,TU
,RS
,A
,TU
,A
,A
,RS
,TU
,A
,TU
,A
,A
,RA
,A
,TU
,TU
,A
,TU
,ARGtl2
,SP
,ARGtl3
,TV
,A
,A
,RA
,TV
,A
, T4
,TP
,LO
,T5
,TU
,T4
,RA
,R13
,TP
, T3
,RP3
,0
,TP
,FILL
,FS
,FILL
,TP
,0
,FS
,F I LL
,TP
,0
,TP
, T3
,TP
,(3
,0
,TN
,FI
,FILL
,TN
,0
,FI
,FILL

,86
,0
,0
,BODY

,

,FILL
,4
,T3
,T3
, T4
,(4
,1
tl6
,ARGtl2
,R 8
,R 10
,R2
,R5
,(4
,R12
,R 1
,R4
,15
,R 11
,(6
,R9
, T4
,R2
,R4
,(6
,R 1
,R5
,R8
,57
,R6
,(4
,R7
,T5
,21
,T 5
,T4
,T2
,R9
,FILL
,ARG
,FILL
,ARGtll
,FILL
,T 1
,0
,0

,FILL

,

,
,

•
,
,
,

.N IN T3 %TEMPORARYt
,N IN T4 %TEMPORARYt
,N-l IN T3
,2N IN A
,2N IN U ADDRESS OF T4
,Xtl2N IN V ADDRESS OF A

,
,

,
,,Xtl2Ntll
,
,

IN V ADDRESS OF A

,Xtl2Ntl1 IN U ADDRESS OF A

•,Xtl2N
,
,x

,

IN U ADDRESS OF A

,
,,Xtl1
,
,
,y
,

IN U ADDRESS OF A

IN U ADDRESS OF A

IN V ADDRESS OF A

,,Ytl1
,
,

IN V ADDRESS OF A

,2N---2N IN T5
,SET REPEAT INSTRU(TION
,SET INDEX FOR LARGE ~OOP
,FILL 3--2N IN U
,FILL M IN U, Xtl2N IN V
,FILL Xtl2N IN U
,FILL Xtl2N IN V
,FILL Xtl2NtlI IN U
,FILL Xtl2Ntll IN V
,SET INDEX FOR SMALL LOOP 1
,(LEAR 0

,

,0

,,FILL

Xtll IN U, Xtl2NtlI IN V

,FILL

,FILL X IN U, Xtl2N IN V

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,.
RWMVM2
10-17-57
P. 5 of 5

,RA
,RA
tI J .

,R6

,
,R4
,R5

,TP
,RA
,RS
,RS
,TP
,TP
,FI
,FI
,RA
,RA
dJ

,R7

,
,

,TP
,RA
,RS
,RS
,RA
, RA
,RA
,RA
, RA
,JJ

,

,RS
,MJ

,C1
,C2
,C3
,C4
,C5
,C6

,0
,0
,0
,0
,0
,0

,R 1
,R2
,T1
,Q

,R6
,R 1
,R2
,T3
,C3
,FILL
,FILL
,R4
,R5
,T1
,Q

,R7
,R't
,R5
,R8
,R9
,RIO
,R 11
,R12
,T 2
,R13
,2
,0
,0
,0

,2
,1
,ENDSUB,

,C 1
,C 1
,R 3
,FILL
,C 2
,T 5
,T 5
,T1
,Q

,FILL
,FILL
,C 1
,Cl
,R4
,FILL
,C2
,T 5
,T5
,T4
,C5
,C2
,C5
,C2
,R 13
,T 4
,EXIT
,2
,2
,0
t1

,0
,0

,

,INCREAS[ U BY 2, V BY 2
,INCREASe U BY 2. V BY 2
,TEST END OF SMALL LOOP 1
,FILL Y IN V
,INCREASE V BY 2
,RESET U AND V
,RESET U AND V
,SET INDEX FOR SMALL LOOP 2
,CLEAR Q
.FILL X IN U, Xtif2 Ntif 1 IN V
.FILL Xtifl IN U, Xtif2N IN V
,INCREASE U BY 2. V BY 2
,INCREASE U BY 2. V BY 2
,TEST END OF SMALL LOOP 2
,FILL Ytifl IN V
,INCREASE V BY 2
,RESET U AND V
,RESET U AND V
,INCREASE U BY 2N
tI NCR EASE U BY 2
,INCREASE V BY 2
,INCREASE U BY 2
.INCREASE V BY 2
,TEST END OF LARGE LOOP
,RESET REPEAT INSTRUCTION

,

,CONSTANTS

,
,
,

$
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... ' •• ,filii

RWDETS
lO~lS-S7

Page 1 of 5
RWDET5, Complex, Floating Point Determinant
Evaluation for Tri-diagonal Matrices

Programmed by:

Werner L . Frank, The Ramo- Wooldridge Corporation

Date: August 15, 1957

A.

.Purpose :
Thi s subroutine evaluate s the determinant of the matrix A - A. I.
where A is a tri-diagonal matrix of order N.

A tri-diagonal

matrix, or Jacobi matrix is defined to be one for which a .. = 0
for

I

i - j

I > 1.

For the special case

determinant of A.

A=

lJ

0 one obtains the

The computation is performed in complex

floating point arithmetic .
B.

Usage:
1.

Specifications.

Standard USE subroutine using built-in

floating point.
SUB,

2.

RWDET 5, 59,

TEMPS,

7

, 0 ,

INOUT,

3

2

Input
First word
Second word
Third word
where A.R

AI

= floating
= floating

point, real component of
point, imaginary

A

compo~ent

of

A

RWDET5
10-15-57
Page 2 of 5

N

=

MATLOC =

order of the Matrix A
address of the first cell of a region of 4N-2
cells where the matrix A is stored.
elements a .. of A,
IJ

Ii

- j

I ~1
""-

Only the

are stored.

They

are arranged in the order of a . , (i = 1 •.• N) in the
11

first 2N cells and the products a,1, 1'+1· a 1
' +l, 1'
(i = 1. .. N-l) in the next 2(N-I) cells.
3.

Output

First word

- floating point, real component of

A

-A~

Second word - floating point , imaginary component of

I
4.

A

-Al l

Space required
Length of subroutine - 59 cells
Temporary storage in compiled region - 7 cells
Other temporary storage - (4N- 2) cells

5.
C.

Error codes - Alarm exit is not used

Restrictions and Coding Information:
Data must be in standard USE complex floating point representation.
The program is self contained performing its own complex arithmetic.

The 11 03A built-in floating point package is used.

subroutine does not destroy the input data.

The

For core storage of

4096 cells, the limitations on the order of the matrix A is N ~ 1 000.
D.

Timing:
(6 N + 1) milliseconds where N is the order of the
matrix

RWDET5
10-15-57
Page 3 of 5
E,

Mathematical Method :
Given the tri -diagonal matrix A

f;
I

c1

II

0

b
a
c

0

1

b

2

a

2

Z
3

0

0

0

0

b

0

3

I

I
II
I

!

c

ab
'
n-2 n-1 n-1

o
then the determinant P

n

( ~\ )

of (A -

j\

I) is obtained by application

of the recursion formula

whe re P

-

1 = 0 and P

0

= 1

T he routine assumes that the products b . . c. have been formed
1

1

prior to entry and are stored in order immediately following the

a .,
1

•
RWDET5
10-15-57
Pag e 4 of 5

,

.
RWDETS
10-17-57
Page 5 of 5

, ZER a
,ONE
, TWO
,ONEB

,MJ
,0 0
,F

,

,

,1

d

,2

, ENDSlJB ,

,E X IT

,
,

$
$
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$
$

RWCDV1
10-15-57
Page 1 of 3
R WCDV1, Complex Floating Point Division

Pro grammed by:
Date:

A.

David G. Cantor, The Ramo- Wooldridge Corporation

September 1, 1957

Purpos e:
Given the complex floating point numbers a

+ biand

c

+ di

this

subroutine calculates

p + qi =
B.

a+bi
c+d i

Usage:
1.

Specifications.

Standard USE subroutine using built-in

floating point.
SUB,

2.

RWCDV1,

41

TEMPS,

1

0

INOUT,

4

2

Input
Fir st word

-

a

Second word

-

b

Third word
Fourth word

c
-

d

a and b are the real and imaginary parts of
the numerator, respectively: c and dare
th e real and imaginary parts of the denominator,
respectively .

RWCDV1
10-15-57
Page 2 of 3
3.

Output
First word

-

p

Second word -

q

p and q are the real and imaginary parts of the denominator,
respectively.
4.

Space required
Length of subroutine - 41
Temporary storage in compiled region - 1
Other routines used - none
Other temporary storage - none

5.
C.

Error codes - Alarm exit is not used.

Restrictions and Coding Information:
Data must be in standard USE complex floating point repre sentation.

Built-in 11 03A floating point arithmetic is used.

.
rea 1 or .
ImagInary
par t

0

If the

f t h e answer IS
. 1arger t h an 2 12 7, a

division fault or characteri stic overflow fault will occur.
D.

Timing:
4 milliseconds

E.

Mathematical Method:
If

If

Icl~ldl then p+qi=

Ic

I ~ld I then p+qi

=

d
a+b (-)
c
d
c (1 +(-) 2)
c
c
a(cr) +b
d( 1 +(~) 2)
d

+i

d
b-a(-)
c
c(1 +(i) 2)
c

+i

c
b(cr) -a

d(1+(~)

2)

RWCDV1
10-15-57
Page 3 of 3

, Slit'

,';"!C8V 1

,41

,:E'-1P.c;

,1

,0

dNOU1

,4

,2
, BODY

, ~'J
, {,LA 0

~.I

,A L ;~p 'v1

,

,EXIT

, !v1J

, A~!S
, ARG

,~E S ~ q '/ , ?

,80DY

, t;;::-X71

,Q:::SER'J,4.

,FILL
,2
,4
,A

, H;~

,r~RGfi2

9TM

,A~Gf:/:3

,TE /"lP

, TJ

,Tc'W

,FD
,To

,Q

,FP

,r E ~1P

,t:"v
9 Tr

,0
~ 1

, CASE 2
,ARGIf2
,TEfvlP
,K
, ARG:lf2
,ANStil

,l\RGIf3

,T P
,T FMP
,F P
,A RG tll
, FD
,0
,TP
,0
,T N
, TEMP
,FP
,A RG
,Q
, FD
,T P
,0
,MJ
, ( ASf2 , FD
,A RG tI?
,Q
,TP
,FP
,TEMP
,Q
,FM
,NEXT 2 , TP
,0
tTP
,A RG
, FP
,T EMP
,FD
,0
,TP
,0
,TN
,A RG lfl
,FP
,TEMP
,Q
,FD
,Q
,TN
,MJ
,K
,F
tl.OOOO
,E NDSLJB ,

,0

,ARG
,ANStl1
,ANS
.0

,ARGtll
,ANStil
,ANS/fl
,E XI T
,ARGtl3
,TEMP
,K
,ARGtl3
,ANSlfl
,Q

.ARGtll
,ANStil
,ANS
,Q

,ARG
,AN Slfl
,ANSlfl
,EX I T
9000000

$
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RWDET4
10-15-5 7
P. 1 of 7
R WDET4, Complex, Floating Point Determinant Evaluation
for Nearly Triangular Matrices

Programmed by:

Werner L . Frank, The Ramo- Wooldridg-e Corporation

Date: August 1, 1957

A.

Purpose:
This subroutine evaluates the determinant of the matrix A

-A I,

where A is nearly triangular, square matrix of order N.

By a

nearly triangular matrix is meant a matrix for which a

>1 .

i - j

of A .

For the special case

A = a one

ij

= 0 if

obtains the determinant

The computation is performed in complex floating point

arithmetic.

B.

Usage:
1.

Specifications

Standard USE subroutine using built-in floating

point .
SUB,

RWDET4,

199,

1

a

TEMPS,

INOUT,
2.

42,

Input
Firat word

AR

Second word

A'1

Third word

0 0 , MATLOC, N

Fourth word

00, TEMLOC, 00000

'" iloa,Hng pOint, real component of

A

RWDET4
10-15-57
P . 2 of 7

AI
N

= floating point, llnaginary component of

= order

A

of the matrix A

MATLOC = address of the first cell in the region where the
matnx A is stored , row by row.

Zero elements,

>

a .. for i ,- J'
1 are not stored . This region of
1J
.
2
N + 3N- 2 cells should be in core storage for
efficient operation .
TEMLOC

= the

addre s s of the fir st c ell in a re gion of

temporary storage of length 2N.

'This region

should be in core storage for efficient operation .
3.

Output
First word

- floating point , real component of

I A - A. I I

Second word - floating point, imaginary component of

4.

Space required
Length of subroutine - 199 cells
Temporary storage in compiled region - 1 cell
Other temporary storage - (N

5.
C.

2

+ 5N - 2)

cells

Error codes - Alarm exit not used

Re strictions and Coding Information :
Data must be in standard USE complex floating point representation.
The program is self contained performing its own complex arithmetic ,

The 1103A built -in floating point package is used.

subroutine does not de stray the input data nor the matrix A .

The
For

RWDET4
10-15-57
P. 3 of 7

core storage of 4096 cells, the limitati on on the order of the
matrix A is N ~ 60.
D.

TIming :
(1 . 5n

E.

2

T

6n . 4) milh s econds

Mathernatlcal Method
Elementary row ope rations a re performe d on t he matrix A reducing it to an upper tnangular m atrix A.

AI

Before eliminating,

the rna gmtude of lea d.mg element s o f two rows whi c h are to be
linearly combined. are comp a re d and the e l ement of largest modulus
become s the p ivotal point.
ofAisthevalueof

The product of the diagonal elements

lA-Ali,

RWDET4

10-15-57
P.4 of 7

"S UB , RWDET4,198,$
,,TEMPS,l,O,$
, I NOUT ,4
,
,MJ
,nn
,ALARM ~ALARM ,
tMJ
,EX IT
t
,RI
,R2
,PARI
,
,PAR2
,
, PAR3
,
,
, PAR4
,PAR4
,$
~TU
,TU
,PAR4
,PAR4
,T U
,TU
,PAR4
, P4
• Rr-'\

,sp

.TV
,TV

.51

.r Ronl
, : ('l

,rp

\ C 01'13
t ," CI'J 4

,

,MATRIX LOC, N
, TEM LaC

,P 3
,p 14
,P 19
, P4
,CON7

,

,57

" /\
,/\
, f\

.P?Cr;l

,P 16
,PRODl
.PRO!)1l
,PROD12
I f ON5
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RWDET4
10-15-57
P. 5 of 7

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RWDET4
10-15-57
P . 6 of 7

,P22
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1#

......

RWDET4

10-15-57
P. 7 of 7

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to

A.

I$:i~nt'i{ibation

1.

Title: , High Speed Printer Edi.t Rou.t ine, . INFOOOl

2., AU,t hprs:

Date: ,
3.
B.

R. : Graharn, W., Bauer
1 Ju~y 1957

Installation: ,

Wriih~ Fi~ld

Purpose

Th,i s routihe edits alphanumeric information from core or drum memory and
prepares a magnetic tape on any designated servo. su). table for liating on the off-·
line hi~h speed printer. ,

c.

Hethod'

Any of a nUfTlber of conversion or translation rou,t ines may be uped to produce .
the alphanumeric characters for the Edit Routi~e from binary data.
This routine requ,ires that one ar~u~nt word be transferred into it by the
calling sequ~nce and that a paramet~r list be available . One entry into the Edit
Routine is sufficient to produpe any number of lines (blockettes) N, ' less than
1000, of identical format. ; Each column i~ the group of N lines requires two
descriptive \fOrds in the parameter list. , The edited information is recorded on
tape i~ blocks of 720 hexabit characters, each block thu~ containing s,ix blockettes of 120 characters.
D.

U§aQe
1.

Calling Sequence

~

Q1?

r-1

TP
Arg
Edit +, 2
RJ
Normal Return

r

r+l

U:"8dar'

V-e.ddr'.
Edit + 3
Ed,i t

2. ' Control Data

a. ; Argument
The argument word which is transferred into the Edit
calling sequence is made up as follows: (
Loc

Q1?

U-addr

V-actdr

Arg

xX

XX XXX

XXXXX

FE

T

N

Rou~ine

by the

P

P i p the address of the fi ,r st word of the parameter list. ·
N (decimal) is the number of Ilnes of identical format to be produped.
(1 ~ N ~ 009)

T (decimal) designates the servo unit on which output is to be recorded.
(1 ~ T ~ 10)
F and E (octal) are printer control digits •.
If F = 1,2,3, or 4, the corresponding Fast Feed Iv II, III, or IV is
placed in the first of the N blockettes.
If E32
If E31

N blockettes.

= 1,
= lv

a multiline symbol is placed in each of the N blockettes.
a printer breakpoint symbol is placed in the first of the

If E30 = 1, a printer stop symbol is placed in the last of the N

blockettes.
When the argument specifies printer control symbols , the total number of
characters available for blocKette construction is 120 minus the number of symbols
used.
b. : Parameters
The parameter list, whicn is stored beginning at address P9 contains
a pair of parameter words for each column and is followed by a pair of control
words Pi and PC) to signal the end of tne list. Pi is always zero. If}l2 is zero,
a partially firlea block is not written at the ena of N blockettes which permits
an accumulation of blockettes; nowever, a full block (six blockettes) is always
written on magnetic tape . , If P2 is not zero, a partially filled block is written
at the end of N blockettes wi th each unu,s ed blockette translated as a blank line
of output.
Each pair of words in the parameter list is made up as follows:
Loc

QQ

U-addr

V-addr

Param

XX
D

XXXXX

XXX XX
W

M

S

XXXXX

Param + 1

r<

v

I.V

(decimal)

IS

the nLlmber of ctlaracters allotted to tile column.
( 1 ~ W~ 120)

S (decimal) is the number of spaces to precede the column .
(0 ~ S ~ 98)
M is the address of the first word of data to appear in this column.
D (octal) is tne increment to be added to 1 to obtain the addresses of
data for succeeding lines of this column . . The original parameter list is never
altered.
2

C is the first address occupied by tne conversion routine which is
required for data in tnis colwnn.
The re~ainder of tne second word of the pair may contain additional
informa.tion required by tne partlcu~ar conversion routine, such as scaling, or
the first address of additional information requirea . "' he precise form of this
word will be specified by the particular conversion routine .
The Edit Routine generates a calling sequence which transfers this pair
of parameter words into the particular conversion routine witll the address C
replaced by the address (K) at wnich the conversion rOutine is to store W results.
The results from the conversion routine will be a series of six-bit excess
three characters . On exit fro~ the conversion routine Q35 will be zero if tr-.ese
characters are packed six to a word. Q3h will be one if these characte rs are
stored one to a word in the rigntmost SlX bi ts, wi th the leftmost trli rty bi ts
being zero. ,

3. ' Space Required
327 memory cells
4.

l!:rror Codes

If code = 1, Servo is greater than 10, or equal to zero .
= 2, N is zero.
= 3, P is zero.
= 4, C is zero .
= 5, the Blockette is to be greater than 120 characters . ,

(A R)

= Argument

(Q) =, WF'OOOl in Flex Code.

5.

Format Generated
The format is controlled entirely by the argument and

E.

par~neter

list.

Restrictions

1. A cban~e in servo designation causes a partially filled block (if it
exists ) to be recorded on the old servo.

2. If P2 is zero and N is not an even ~ultiple of 6, a "clean-up" pass must
be executed to.write the partiall) filled block.
3.

Other Program Required
One or more subsidiary rou,t ines are necessary to process data for editing .

3

F.

Coding Information
1.

Constants and their locations
a.

Alphanuneric
1K

b.

throu~h

iK6

Numeric
2K t hrough 2K27

c.

Internal temporary storage
3K

2.

throu~h

JK4

Erasable output storage
P t nrough Pi26

4

WFOOOl
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YlF00 91

Page 5 of 5 'pagtU,.

USE Letter No:
To:

PC-4

December 11, 1957

USE Policy Committee, Publications Committee, Installation Hpads.

Enclosed herewith is the coding only for USE routines WF 0001, WF 0002,
WFOOOJ, WF0004 and WF0005. The original routines, previously distributed,
were somewhat illegible. WF was kind enough to provide us with another master.
Please note that line C18(+2) in WF 0004 was incomplete in the original
copy which was distributed.

L' .( .tl
""; I

1

1.."

'-I..

~,

I /
(. l.l..

. -t ., i..

Dirk de Vries '
Executive Secretary, USE
Remington Rand Univac,
Uni vac Park,
st. Paul 16,
MINNESOTA.

DdV:diw

WFOOO1

,
,
,

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,B1
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,
,
,
,

,
,
,C1
,
,
,C2
,
,
,C3
,

,C4
,C5

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,C6
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,9 8

,

,C9
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,
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,
,

,C12
,e13

,
,
,C14
,
,
,
,C15
,
,C16
,

,

,C17

,SUB
,TEMPS
,IN OUT
,MJO
,ALARM
,MJO

,WFOOO1
,127
,1
,0

,

,
,0
,

,TP

,lKl

,RESERV ,120
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,lK2
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,F
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,0

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,
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,BIN
,PRESETS/SWITCH 1
,SlVITCH 2
,S~lITCH 3
,SET LOOP COUNT TO ZERO
,SET STORE DATA LOCATION

,ENTRY

, 0 ,EXIT ALARM
,EXIT NORMAL
,FILL
,
,
,P~126

,3K
,Cl
,P
,Q+3
,P+120
,C4
,lK6
,15
,C3
,P
,2Kl
,C6
,2K1
,F1
,2K1
,C9
;C$
,FILL
,2Kl
,C11
,2K1
,F4
,2K1
,9 ,
,P+120
,C12
,36
,0
,Q
,Bl
,6
,A
,P+l21
,C15
,36
,C13
,P+122
,A
,C18
,A

,

,STORE SPACES IN BLOCKETTE
, SHIFT AIDUMENT

,

,TEST FOR FAST FEED SYMBOL
,YES

,
,
, SET FF SYMBOL
,

,TEST FOR MULTILINE SYMBOL
,YES SET SWITCH 1
,SET ML LOCATION

,

,TEST FOR BREAKPOINT SYMBOL
,YES
,SET BP SYMBOL

,

,TEST FOR PRINTER STOP SYMBOL
, YES SET SWITCH 2
,SET PS LOCATION

,

,SHIFT ARGUMENT
,EXTRACT P
,DOES P EQUAL ZERO
,YES LOAD 3 CODE AND
,LOAD ARGUMENT INTO A

,

,GO TO ALARM EXIT TO PRINT A
, SHIFT AIDUMENT

,

,STORE SERVO NUMBER
, DOES NUMBER OF LINES EQUAL ZERO
, YES LOAD 2 CODE

,

,STORE N

,

; IS SERVO GREATER THAN 10
,NO

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WFOOOI

,
,CIS
,
,C19
,C20

,
,DO
,
,Dl
,
,
,D2
,
,D3
,
,
,D4
,05

,
,
,E
,
,

,ZJ
,SP
,MJO
,EJ

,TP

,ZJ
,TP
,ZJ
,EF
"RP1
,EW!

,RPI
,TP

,TV
,TV

,TP
,RJ

,TP

,54
,AT

,TP

,El
"E2
,E3

,IJ
,l-fJO
,TU
,RP3
,TP

,
,

,TP
,ZJ

,E4

,E5

,

,

,E6

,
,E7
,

,
,
,
,
,
,
,
,
,
,
,E8
,
,E9
,

,E10

,
,

,RA
,TP
,QT
,ZJ
,SP
,MJO
,TV

,LA
,TV
,RA
,TV
,RA
,QT
,DV
,RA
,TV
,RA
,TJ
,SP
,MJO
,TV
,IJ
,TV
,55
,QT

,C19
,2Kl
,0
,3Kl
,3K1
,DO
. ,3K2
,01
,0
,120
,0
,120
,2K20
,lK5
,lK5
,2K
,D4
,P+121
,P+12l
,2K19,
,3K
,P+122
,0
,P+120
,2
,FILL
,E3
,P+123
,E5
,2K17
,P+l24
,E7
,2K4
,0
,A
,A
,A
,El2
,El2
~El1

,P+123
,' 2K26

,A

,A
,A
,1K4
,2K5
,,0
,A
,A
,A
,P+123
,2K21

,C18
,36
,c13
,E
,A
,02
,A
,03
,3K3
,02
,B3
,D3
,B3
,F9
,FlO
,3K2
,05
,3Kl
,A+12
,3K3
,P+121
,El
,B2
,E)

,DOES SERVO EQUAL ZERO
,SERVO IN ERROR/LOAD 1, CODE

,

,DOES NEW SERVO EQUAL OLD
,NO
,TEST FOR INITIAL SEWP
,NO
"IS THERE ANY DATA IN BLOCK
"YES

,WRITE '

,BLOCK AND
,FILL BLOCK
,WITH CONDENSED SPACES

,
,
,SET BLOCKETTE COUNT TO
,
,STORE NEW SERVO NUMBER
,

ZERO

,PREPARE NEW MT COMMAND
,SET STORE DATA LOCATION
,DOES N EQUAL ZERO
, YES GO TO NORMAL EXIT
,SET E3

,
, OBTAIN
,
,

,E4

,P+123
,2K23

,A

,F
,Q
,A
,E6
,36
,c13 '
,El2
,15
,El2
,2K23
,Ell
,2K3
,A
,P+125
,P+12l
,P+l24
,P+125
,E9
,36
,C13
,P+121
,E10
,E22
,Q+6
,A

PAIR OF PARAt-lETER WORDS

,DOES PARAMETER EQUAL ZERO
,NO
,EXTRACT C
, DOES C EQUAL ZERO
,YES LOAD 4 CODE

,

,SET C IN RJ

,

,MODIFY RJ ORDER
,FORSUBRTN ENTRY
,SET UP RP TO
, STORE PARAMETERS
,EXTRACT WS
,STORE W
,MODIFY DATA
,STORAGE LOCATION BY S
,ADD W
, IS BLOCKETTE TOO LAroE
, YES LOAD 5 CODE

,

,STORE NEXT . DATA
,STORAGE LOCATION
,SETUP ORDER TO UNPACK

,

,EXTRACT 0

6

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WFOOO1

,

,
,
,

,Ell
,E12

,

,E13

,
,
,
,
,
,m
,
,
,
,E15
,
,
,E16
,
,
,

,El7
,E1a

,

,El9
,E20

,

,E2l

,
,
,
,

,E22

,F
,Fl
,F2

,

,MP
,LA
,AT
,RP3
,TP
,RJ
,QJ
,TV
,TP
,RS
,TP
,DV
,ZJ
,TP
,MP
,TV
,RA

,RA

,LA
,TU
,LQ
,TU
,TP
,ZJ
,TP
,SP

,TP
,RS

,IJ
,MJO
,IJ
,MJO
,QT
,RS
,LQ
,MJO
,MJO

,TP
,RA
,RA

,
,

,TP

,F3
,F4
,F5

,TP

I

,ZJ
,MJO
,TP
,ZJ

,F6

,RS

,17

,TU

,
,

,TP
,TP

,TP

,Fa
,F9
,FlO

,SP
,QA

,

IRA
,IJ
,RA

,
I

,A
,P+126
,A
,15
,P+123
,P+123
,2
,El2
,P+123
,FILL
,FILL
,FILL
,E2
, ,E13
,2K
,E16
,2K
,3K4
,P+l24 ' ,2Kl
,P+125
,A
,2K6
,P+123
,El4
,El5
,A
,3K4
,A
,2K6
,A
,El6
,P+123
,2Kl
,P+l24 " ,P+123
,15 '
,A
,A
,E16 ,
,FILL
,FILL
,El6
,Ela
,A
,3K4
;E19
,E17
,2K6
,3K4
,FILL
,0
,A
,Q
~E1a
;'2K24
,E2l
,3K4
,0
,E17
,P+125
,E22
,0
,E2
' ,2K21
,FILL
,E22
,2Kl
,Q
,30
,E20
,0
,0
,F2
,FILL '
,2Kl3
,2Kl
,3K2
,P+126
,2K!
,A
,P+122
,F7
,F3
,0
,F5
,FILL
,2K15
,A
,P+l24
,F6
,F7
,2Kl
,m
,FlO
,lK3
,2K2l
,Q
,P+123
,2K25
,P+124
12K5
,FILL
,6
,FILL
,FILL
,flO
,2K24
,P+l24
,F9
,2K24
,F9

,LOOP COUNT TIMES D

,
,MODIFY
,

M

,STORE PARAMETER PAIR
,GO TO SUBROUTINE
,IS DATA PACKED
,YES
,INDEX TO ZERO

,

,W TO A
,NUMBER OF LOCATIONS
, IS THERE A REMAINDER
,YES SET . INDEX

,

,SET LQ FOR SPECIAL SHIFT
,INCREASE LOCATION NO
,DETERMINE LAST LOCATION

,

,SET LQ
,SHIFT

,
,

,TEST FOR REMAINDER
,NO SET 6 INDEX '

,
, WORD
,

TO Q

,
,
,INDEX ON W
,
,EXTRACT '!'VIO CHARACTERS
,
,
,

,SWITCH 1
, SET ML SYMBOL
,INCREASE BLOCKETTE COUNT
,INCREASE LOOP COUNT

,

,DOES N EQUAL ZERO
,YES SWITCH 2
,SET PS SYMBOL

,

,DOES FINAL PARAMETER EQUAL ZERO
,NO SET SWITCH 3
, CONDENSE BLOCKETTE
, AND STORE IN BLOCK

"

,
,
,
,
,
,

7

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,$
$

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'$

1VFOOOI

,
,Fll
,F12

,
,

,F13
,F14
,F15
,F16

,

,1K
,1IU

,lK2
,lK3
,11\4,
,lK5
,lK6
,2K
,2Kl
,2K2
,2K3
,2K4
,2K5
,2K6
,2K7
,2K8
,2K9
,2KIO
,21ill

,2K12
,2K13
,2K14
,2Kl5
,2K16
,2K17
,21\18
,2K19
,2K20
,2K21
,2K22"
,21\23
,2K24
,21\25
,2K26
,2K27
,3K
,3Kl
,3K2
,3K3
,.3K4

,

,RA
,IJ
,TP
,EJ
,MJO
,RJ
,MJO
,RJ
,RP1
,TP
,MJO
,MJO
,MJO

,
,
,
,

,B
,B
,~

,B
,B
,B
,B,
,B
,B
,B
,B
,B
,B
,B
,B
,B
,B
,B
,B
,B02
,BOl
,B
,B
,B
,B
,13

,B
,B31
,B
,B
,B
,B

,

,ENDSUB

,FlO
,P+12.3
,.3K2
, 2K6
,0
,D4
,0
,D4
,120
,2K1
,0
,0
,0
,P

,
,B3
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,77777
,
,

,
,

,2Kl
,F8
,A
,Fl.3
,F14
,Dl
,F16
,DO
,E
,P
,F2
,F5
,F16

,

,IS BLOCK FULL
,NO
, YES WRITE BLOCK
,SWITCH 3
, WRITE BLOCK
,FILL BLOCKETTE
,WITH SPACES

,
,
,
,
,
,
,

,

,P+121
,B.3
,2K8
,0
,1
,2
,3
,4
,5
,6
,7
,12
,37
,42
,57
,76
,20
,61
,60
,00000
,77777
,01750
,00000
,00746
,01010
,10101
,
,77
,
,777
,
2 ,00000
,
1 ,00000
,23
,
,00144
,26373
,73752
,
,0
,
,0
,
,0 ·
,
,0
,
,0

,ZERO
,ONE
,TWO
,THREE
,FOUR
,FIVE
,SIX
,SEVEN
,INDEX
,FAST FEED - FF 1 .
,FF 2
,FF 3
,FF 4
,MULTILINE - ML
,BREAKPOINT BP
,PRINTER STOP
,MASK U
,MASK V
,DIVISOR
,OFF LINE WRITE BLOCK
,CONDENSED SPACES
,6 BIT MASK
,9 BIT MASK
,ADVANCE U
,ADVANCE U
,INDEX
,DIVISOR

,

,

,

,STORE DATA LOCATION
, SERVO NUMBER
,BLCCKETTE COUNT
, TAPE COMMAND
,INDEX

,

,

8

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v

WFOOO2 '

,
,

,

,B
,B1
,B2
,B3
,B4
,C

,
,
,
,Cl
,
,

,
,C2
,
,
,

,
,C3
,
,
,

,C4
,C5
,c6
,C7

,

,CS
,C9

,

,

,CI0
,GIl

,

,

,C12
,C13
,C14

,
,
,C15
,

,
,
,
,
,
,

,SUB
, TEMPS
,IN OUT
,MJO
,ALARM
,MJO
,B
,B
,TP
,QT
,DV
,TJ
,SP
,SA
,TP
,MJO
,LA
,AT
,TV
,RP1
,TN
,TV
,LQ
,QT
,EJ
,EJ
,TP
,TU
,SP
,TP
,LQ
,QT
,RA
,IJ
,RJ
,TP
,RP2
,RA
,RP3
,TP
,TP
,LQ
,MJO
,TP
,RJ

"

,RA

,K
,Kl

,TP
,RJ
,RA
,TP
,MJO
,RP3
,B

,WFOOO2
,15
,2
,0

,
,0
,
,

,KlO
,B3
,K9
,KS
,B3
,.B4
,Kl2
,0

,A
,K
,B4
,14
,K2
,C3-1
,B4
,K3
,Kl
,K2
,Kll
,B3
,FILL
,A
,Q

,K6
,C9
,P
,CI0
,C9
,14
,P+1

,

,P+1
,1\4
,B3
,0
,K1
,ClO
,C9

,K4

,C10
,C9

,K4
,0
,0

,

,
,
,

,61
,127
,0
,C

,ENTRY
,EXIT ALARM
,EXIT NORMAL

,

,FILL
,0
,0
,Q
,A
,A
,C2
,36
,0
,Q
,Bl
,15
,C12
:,C13
,C3
,P+1
,C9
,Q+21
,A
,C14
,C15
,P
,C7
,0

,
,
,

,EXTRACT WS
,W TO A
, IS \i TOO LAmE
,YES
, LOAD PARAMETERS
,AND CODE
,GO TO ALARH EXIT

,
,SET
,

,

,STORE - 2
,SET STORE DIGIT LOG

,

,EXTRACT CODE
,ADDRESS
,SPEX;IAL FORMAT
, SET 11 INDEX

,

,OBTAIN WORD
,\vORD TO Q

,Q

,

,3
,FILL
,Kl
,C8
,C11

,STORE DIGIT

,

,
,
,UNPACKED INDICATOR TO
,
,CONVERT TO XS~3
,

,Q

,C12
,K3
,B2
,FILL
,P
,Q+6
,C8
,P
,C6
,IG.

,P
,C8
,IG.
,P
,C8
,B2
,1

RP

,TRANSFER W RE,SULTS
,SET 4 INDEX

,
,

,SET 1 INDEX

"

. , SKIP FOR SPACE
,SET 4 INDEX

,

,SKIP FOR SPACE
,SET 4 INDEX

,
,
,

Q

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WFOOO2
,K2
,K3
,K4
,K5
,K6
,K7
,K8
,K9
,KlO
,Kll

,Kl2

,

,B'
,B

,B

,B~

,B
,B
,B

,B
,B
,B
,B31
,ENDSUB

,

,
,
,
,
,
,

,
,

,
,26373
,

,
,
,
,
,
,
,
,
,
,
,

,2
,3
,4
,5
,7
,16
,17
,144
,77777
,13
,73774

,

,

4

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$

\'lFOOO3

,
,
,

,B
,Bl
,B2
,B3
,B4

,e

,
,
,
,

,Cl

,
,
,
,
,
,

,
,
,
,C2
,
,C3
,
,
,C4
,
,
,"
,
,
,
,
,C5
,
,
,
,.
,
,C6
,
,C7
,
,CS
,
,
,C9
,C10
,Cll
,012

..

,SUB
,1»fPS
,IN OUT
,MJO
,ALARM
,MJO
,B
,B'
,TP
,QT

,DV
,TP
,TJ
,LA
,AT
,TP

,RPI
,TN

,TV
,LQ

,QT
,TP
,TJ
,ST
,ZJ
,MP
,SA
,TU

,TP

,ST
, A'11'

,TP
,RA
,LQ

,TP

,SA

,TV
,TP
,TV

,RA

,TV
,RA
,TU

,TP
,SJ

,TN
,TM

,LA
,TP

, ,ZJ
,SS
,RP3
,DV
,TU

,WFOOO3
,16
,2
,0

,
,0
,
,

,K7
,BS
,KlS
,K3
,P+13
,P+13
,J
,K
,13
,Kl
,B4
,B4
,K7
,K5
,P+13
,P+13
,C3
,A
,KS
"A
,K9
,P+14
,J2
,Jl
,CI0
,P+15
,J3
,P+14
,A

,K4

,A
,C19
,P+13
,ca
,B3
,FILL
,C7
,K20
,A
,A
,A
,C9
,A
,0
,KlO
,J3

,
,104
,
,127
,0
,
,C
,ENTRY
o ,
o ,EXIT ALARM
,FILL
,EXIT NORMAL
,0
,PARAMETER
,0
,CELLS
,Q
,MASK TO Q
,A
,EXTRACT WS
,P+13
,SAVE W
,A
,
,C23
, IS WTOO LAmE
,NO
,15
,C21
, SET TRANSFER
,
,P+14
,
,C1+5
,P
,
,C22
,SHIFT SS
,Q.+21
,SAVE SS
,P+~3
,A
,
, IS SS TOO LAFGE
,C23
,NO ·
,P-13
,IS S5 35
,C4
,K6
,NO
,0
,P...14
,SAVE I DIGITS
,A
,
,SAVE F DIGITS
,P+15
,ell
,SET DIVIDE
,CI0
,PLACE RP
,SET
N
,fof:14
,21 ',
,SHIFT F DIGITS
,
,A
,
,57
,
,C5
,SET POINT
,FILL
,SET F LOCATION
,C19
,
,K20
,SET LA
,ca
,K20
,SET K
,
,c6
,OBTAIN WOlID
,A
,IS WOlID . NEGATIVE
,CS
,YES SET SIGN
,P
,
,A
,SHIFT WOlID
,FILL
,SAVE F PART
,P+14
, IS WORD ZERO
,C15
,NO
,36
,
,C12
,EXTRACT INTEGRAL DIGITS
,P+l
,
,C13

,

,

3

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$

WFOO03

,
,C13

,

,C14

,
,
,
,C15
,

,C16
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,C21
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,END SUB

,C11
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,
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FOR ROUNDING

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,
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20114

,ADD OF FIRST POWER OF 10
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,OF TEN

.3

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WFOOO4
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,LOAD
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,
,
,
,
,
,
,

,WFOOO4

,
,
,

4

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WFOOO4
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WFOOO4

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,B33
,B34
,B34
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,B37
,B40
,END SUB

,74061
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WFOO05

,
,
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,END SUB

, 24

,WFOO05
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,PARAMETER
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IN EDIT ROUTINE

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1.

I DENTIFICATION

f!.

PUR pmE

APSD - SPECTRAL DENSITY
Harry Shaw - Octobe r 15, 1957
Appli ed Physics Laboratory

G).ven M + 1 lags (s ee APAC - AU.rcx:;ORltELATION) RH, H c:: O(l)M,
computo M + 1 values UJ, J

:=

O(l)M, of what is essentially the

speotral density function.

3.

METHOD

a.

The method of Tukey (see 1h£Sampling Theory of Power Spectra
Estimates, Symposium on Applications of Autocorrelation Analysis
to Physical Problems, Woods Hole, Mass., 1949) is used to compute

UJ ~ ~(J/2MA t)
where

2M

a( is

6(;

the spectral density function

~ (~

rr'

) ==

4~

R(t) cos

2nf't do

Since
M
!:

UJ rv RO

J:::O

furnishes a convenient check, the sum of the UJ is also computed.
b.

Inputs RH are integers scaled zero and can be computed by APAC (if
obtained in same .; other way care should be taken that IRHI
Outputs are integers scaled zero.

4.

USAGE
a.

Calling Sequence

r
r + 1

Q£
RJ
Normal

U

t + 2
Return

.L
t

<

2

29

).

Page 2
b.

Control and Results
Enter with the code word

00 OMMMM WWWWW

in the accumulator,

and lags RH in locations W + H.
Exit with UJ in locations W + M + 1 + J, LUJ in location
W + 2M + 2, and locations W-l thru W + M unchanged.
c.

Space Required
172 cells of instructions and constants

13 cells of temporary storage
Block of 3M + .3 locations beginning at core address W-l (inoludes
data mean and lag storage)
d.

EII'ror Codes
Nohe

5.

RESTRICTIONS
See .3.b.

6.

TIMING
"2

Approximately M

.,

mls •

APSD
PAGE 3
Oct. 15, 1957

APPLIED PHYSICS LAB

ITm1
NO.

LOC

,
,

OP

V

U
j

C011MENTS

,SUB

,APSD

,172

,LEADING LINE

$

,TEMPS

,13

,0

,TE}lPS

$

,T

,MJO

,PlOO

,ENTRANCE

$

,
,

,ALARM

,

,ALARM EXIT

$

,MJO

,
,
,

,

, NORMAL EXIT

$

,PlOO

,TV

,A

,UlOl

,GENERATE

$

,

,LT

,25)B

,UlOO

, V - ADDRESSES

$

,
,
,
,
,
,

,SP

,UlOl

,

,AT

,IG.

,U300

,AT

,UlOO

,U301

,AT

,IG.

. ,U302

,AT

,UlOO

,U303

,
,
,
,
,

,AT

,IG.

,U304

;

.

,AT

,Kl

,Ul03

,
,
,
,
,
,
,
,
,
,
,
,
,

,SP

,U302

,AT

$

$
~~

$
$
$

,

,
,

$

,IU

,U305

,

$

,TV

,U302'

,P205

,SET

$

,TV

.. U300

,P2l5

, V - ADDRESSES

$

,TV

,U303

,P226

,TV

,U300

,P228

,TV

,U304

,P264

,TV

,U304

,P302

,
,
,
,

,TV

,U305

,P307

,TV

,U301

,P320.,

,TV

,U304

,P.321

,TV

,U301

,P344

,TV

,U303

,P363

,
,
,

,
,

~~

$
$
$
$
$
$
$
$

$

,,
'.'

APPLIED

f3JiYP~CS

APSD PAGE 4
Oct. 15, 1957

UB

ITEI1
NO.

LOe

V

Q~

e01lMENTS

Y

,
,
,

,ST

,U210

,Ul02

,
,

,LQ

,U300

,17)B

,GENERATE

$

,LQ

,U301

,17)B

,V - ADDRESSES

$

,

.tLQ

,U302

,17)B

,LQ

1V305

,17)B

,SP

,Ul01

,17)B

,TP

,A

,v104

,SP

,UlOO

,17)B

,AT

,0104

,u304

,LQ

,V303

,17)B

,RS

,V303

,K2

,
,
,
,
,
,
,
,

,TV

,Ul04

,P200

,SET

~~

,TV

,Ul04

,P222

, V - ADDRESSES

~~

,TV

,Ul04

,P304

,

$

,

,TU

,V304

,P164

,

$

,P164

,TP

,FILL

,Ul04

,TU

,v304

,P201

,TU

,U300

,P204

,TV

,U300

,P215

,TU

,U304

,P219

,TU

"u304

,P221

,

,'lU

,V300

,P225

,

,TV

,U300

,P228

,TU

"V300

,P302

,TV

,U305

,P320

,TV

,V303

,P321

,

,
,
,
,
,
,
,
;

,
,

,
,
,
,
,

.,
,
,

,SP

,UlOO

J

,
,
,
,
,
,
,
,
,
,
,

$
$

$

$
$

$
$
$
$
~~

~~

$
~~

$
$
$
$

$

$
$

$

APSD PAGE 5
Oct. 1S, 19S7

APPLIED PHYSICS LAB

I TEM
NO.

LOC

,
,
,
,
,
,
,
,

,

OP

COl1MENTS

V

U

,

,TU

,U301

,P340

,TU

,u305

,P341

,TU

,U302

,P343

,TU

;U301

,P362

,
,
,

,SP

,UlOO

'~ 1~()B.

,SET

$

,AT

,U208

,A

,REPEATS

$

,TU

,A

,P203

,TU

,A

,P224

,TU

,A

, P36l

,AT

,U209

,A

,TU

,A

,P301

,RS

,P203

, K2

,RS

,P224

,K2

$
$
$
$

,
,

$
$

,
,

$

,
,
,
,
,
,

,RA

,P361

,K2

,RS

,P301

,K2

,
,
,
,
,

,P200

,TP

,FILL

,A

,to (SO)

$

,P20l

,AT

,FIIL

,A

,'10

$

,

\

,LT

,,43)B

,A

,W +M + 2

$

,P203

,RP

,FILL

,P205

,P204

,AT

,FI!L

"A

,P205

,DV

,U10O

,FILL

,
,
,

,
,

,SP

,UlOO

,43)B

,111

,TP

,A

,Q

,TO

$

,LT

,

,A

,w.'.+-,·2M + 2

$

,ST

,Kl

,UlOl

,TP

'UlOl

,u4oo

,
,

,
,
,

$
$
$
$
$
$

$
$
$

(SO)

~(

$
$

PH~ +CS

APPLIED

ITEM
NO.

LAB

LOG
,P215

APSD PAGE 6
Oct. 15, 1957

OP

COJl1HENTS

V

U

, TN

,FILL

,FILL

,

,
,

,RA

,P215

, U200

, IJ

, u400

, P215

,

"QJ

, P219

, P221

, P219

, TN

,FILL

,A

,

, MJ

,

, P222

,
,
,
,
,

, P221

, TP

, FILL

,A

,

, P222

,AT

, FILL

,A

,

, LT

,43):5

,A

;, P224

"RP

, FILL

, P226

, P225

, AT

, FILL

,A

,
,
,
,

, P226

, DV

, UlOO

, FILL

;

,

, TP

, U101

, u400

, P228

, TN

, FILL

, FILL

,
,
,
,

,RA

, P228

, U200

,
,
,

, IJ

/I

u400

, P228

,

SP

, u205

,

, COS pIIM

,DV

, UIOO

, Q

.)

,MP

,Q

,Q

,

, LT

,6

1 U300

.t

,MP

, U300

, U300

,

" LT

,6

, U301

,MP

, u300

, U301

,I.T

,6

, U302

, SP

, U201

,36)B

,MA

, lU300

, U202

, I1A

, U301

, u203

.t

.t

,
,
,
,

,
,
,
,
,
,
,
,
,
,

$
~i

$
$
$
$
~~

$

$
$
$
~~

$
~~

$

$
(S30)

$
~~
~~
~~

$
~p

$
$.
~~

$

$

APSD PAGE 7

APPLIE.D PHY'31 CS LAB

Oct. 15, 1957

ITEM
NO .

OP

IPC

,
,
,
,
,
,

U

COMMENTS

V

,MA

,U302

,u204

,

$

,LT

,6

,U302

, INITIALIZE

$

,LT

,1

,U300

,2 COS FIlM

$

,TP

,U201

,U301

,

$

,SP

,UlOO

,

,SET OUTSIDE LOOP

$

,ST

,Kl

,u400

,FOR M-l PASSES

$

,P260

,IJ

,u400

,P262

,M-l PASSES

$

,

,HJ

,

,P320

,TEST

$

,P262

,MP

~ U300

,U301

,no.

,

,LT

,6)B

,A

,P264

,ST

,U302

,FILL

,
,

,
,
,
,
,
,
,

,TP

,U301

",U302

,H + 1 TO H

$

,TP

,A

,U301

,

$

,TP

,A

,u304

,INITIALIZE

$

,TP

"U201

,u305

,

$

,LT

,10OOl)B ,U303

,2 YIn.

$

,TP

,UI02

,U401

,SET M-2 PASSES

$

,TV

,Ul03

,P282

, SET STORE 'YHP

$

,P280

,MP

,U303

,U304

,YHP TD W + 2M + 2 + P

$

,

,LT

,6)B

,A

,P282

,ST

,u305

,FILL

,
,

,

,TP

,U304

,u.305

,P + 1 TO P

J

,TP

,A

,u.304

(530)

$
$
$

~~

$
$

,
,
,

,RA

,P282

,Kl

,
,

,IJ

,U401

,P280

, M-2 PASSES TEST

$

,SP

,KO

,

, LH TO \-1 + M + 2 + H

$

,P.301

,RP

,FILL

,P.30.3

,

$

$
$

APSD

APPLIED PHYSI as LAB

Oct.
ITEM

NO.

IPC

v

Q

Or

15,

PAGE 8
1951

COt1MENIS

,P302

,M/\.

tFILL

,FILL

,

$

,P303

,LT

,1)B

,A

,

$

,P304

,AT

,FILL

,A

,

,TN

,Ul04

,Ul04

,

,AT

,Ul04

,A

,P301

,DV

,UlOO

,FILL

,
,
,
,

,

,RA

,P301

,IG.

,STEP LH STORE

$

,

,MJ

,

,P260

,JUr1P TO TEST

$

,.1'320

,TP

,FILL

,FILL

,IJ. 1OL,-1

$

,P32+

~TP

,FILL

,FILL

,

$

,

"TP

,UlOO

,u400

,SET .;. M + 1 PASSES

$'

,P340

,TP

,FILL

,A

,UJ TO t'T + 11 + 1 + J

$

,P341

,AT

,FILL

,A

,

IMP

,A

,u206

,P343

,M/\.

,FILL

,U207

,P344

,LT

,1)B

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,

,RA

,P340

,K2

j '~IJl~l

,RA

,P341

,K2

,RA

,P343

,K2

,RA

,P344

,IG.

,
,
,
,
,

$
$
$
$

,
,
,

$
~~
~~

$
$
$

,
,
,
,

,lJ

,u400

,P340

,M + 1 PASSES TEST

$

,TP

,KO

,A

,sm1

~~

,P361

,RP

,FILL

,P363

,TO

$

,P362

,AT

,FILL

,A

,W + 211 + 2

$

,P363

"TP

,A

,FILL

,

$

,

,ID

,

,T + 2

, JUNP TO EXIT

$

,U200

,00

,2

,2

,UUP2VUPP

$
$

UJ

$

9

APSD PAGE

APPLI:c:D PHYSICS LAB

Oct. 15, 1957

ITEl1

LOC

NO.

V

U

OP

,

COH~1ENTS

,U201

,01

,

,U202

,77

,37777)B ,77777)B ,~} (S30)

,U203

, 00

,2525)B

,u204

,77

,77722)B ,37223)B ,- 1/6 (S30)

$

,u205

,03

,1l037)B ,55242)B ,PI (S30)

$

,U206

,07

,27024)B ,36561)B ,.23 (s35)

$

,U207

,21

,21727)B ,2437)B ,.54 (S35)

$

,U208

,00

,20000)B

,U209

,00

,10000)B

,U210

,00

,

,KO

,00

,Kl.

,1 (S30)

,25252)B , ~ (S30)

~~
~~

$

,FOR

$

,PRF.BEI'S

~p

,

$

,.

,
,
,
,

,ZERO

$

,00

,

,1

,V - ADVANCE

$

,K2

,00

,1

,

,U - ADVANCE

$

,

"ENDSUB

,

,

,

$

<~

1.

IDENTI FICATWN

2.

PURPOOE

APAC - AUTOCORRELATION
Harry Shaw
October 15, 1957
Applied Physics Laboratory

Given N data XJ, J

= l(l)N, compute data mean

X

and M + 1 ,

lags RH, H = O(l)M.

/

J. METHOD
a.

R( 1:)

lIS

1m
T

L.r
T

T

y(t}
0

t:IO

is approximated by
1

N-H
L

R(H l:! t) ~ RH .. N:-H Ie"'l IT. Y K + H
where

YJ • XJ-X, J = l(l)N.
b.

Inputs XJ are integers scaled zero such that ILXJJ~9999.
Outputs are integers scaled zero.

4.

USAGE
a.

Calling Sequence

QL
r

r + 1

b.

RJ
Normal

t + 2

t

Retu,rn

Control and Results
Enter with the code word 00 OMMMM wwwwwrooooO-COreMOdeJ
in the aooumulator, the oode word 00 NNNNN L-VVVVV - Drum Mode
in the Q-register, and the data XJ in locations W + J-1 for the
Core Mode or V + J-1 for the Drum Mode.
Exit with the data mean X in location W-l and the lags RH in
locations W + H. The code word 00 OMMMM WWWWW is left in the
accumulator (See APSD -' Speotral Density).

Page 2

c.

SpRee Required
160 cel ls of instructi ons and constan ts

13 cells of t emporary storage
Core Mode - block of N + M + 2 locations beginning at core
address W-l
Drum Mode - block of N l ocations beginning at drum address V
and block of 3M + 2 locations beginning at core address W-l.
d.

Error Codes
None

5. RESTRICTIONS
See

6.

J.b.

TIMING
Approximately 1/2

MN/t s.

APPLIED PIITSICS LAB

TEM
NO.

LOC.

APAC
PAGE 3
Oct. 15, 1957

OP

,

,SUB

,

' , TEMPS

V

U
, APAC

,160

,,13

,,0

CONrOO1'l'S
, LEADING LINE

,
,

$

TEHPS

$

ENTRANCE

$

, ALARM EXIT

$

, NORMAL EXIT

$

,NJO

,
,
,

,
,

"PlOO

,TP

,A

,UlOO

, SAVE 1ST CD

,

"TV

,A

, UlO1

, H (SO)

$

,TV

, Q

, Ul03

, V (SO)

~~

, TU

,A

,Ul06

, M (S15)

$

"TU

,Q

, UlOB

, N (s15)

$

,LA

"A

,17)B

, W (s15)

$

,TU

,A

,Ul02

,

S

,LQ

,Q

,17)B

, V (S15)

$

"TU

,Q

, Ul04

,

~~

,LT

,6

,Ulo5

, M (so)

$

,LQ

,Q

,6

, N (so)

$

,TV

,Q

,UlO7

,

$

"TU

,UlO2

,P401

, PRESET INST

$

,TU

,UlO2

,p406

, CONHON TO

$

,TV

,UlOl

,P401

, BOTH HODES

$

,TV

,UlOl

,P501

,RS

,P401 -

,Kl

,TP

,Ul09

,Q

,Q':)

,Ul06

,p500

,RA

,p500

,K2

,SP

,UlO3

,

,
,
,
,
,
,

,ZJ

,P300

,P200

,

,T

,
,

,
,
,
,
,
,
,

,
,
,
,
,
,
,
,
,

,
,
,
,

,MJO
, ALARM

, PlOO

WI)

$

$
$
$
$
$
MODE TEST

$
$

· APPLIED PHYSI CS

ITEH
.NO.

IAP

.i\r.A C

Oct.

LOC.

OP

V

U

,QS

,Ul08

,P251

,QS

,Ul08

,P400

,Q')

,Ul08

,p405

,OS

,P500

,P254

, TP

, l-'too

,P414

,TU

., Ul02

,P408

,RA

,P408

,UI08

, TU

,U102

,P50l

,RA

,P501

,Ul08

, TV

,UlOl

,P252

,TV

,P40l

,P253

,TV

,UlOl

,P255

,RA

,P255

,Ul07

,TV

,11500

,PUO

,

,TP

,KO

,P251

,RP

,P252

,P200

,
,

,
,
,
,

PAGE 4
15, 1951

CONHENTS

,
,
,
,
,

COllE HODE PRESET

$
$
~~

$
$

,
,
,

$

$

,A

,
,
,
,
,
,
,

,10000)B

,P253

,

:~

,RA

,A

,FILL

,

$

,P253

,DV

, Ul07

,FILL

,P254

,RP

,10000)B

;P256

,P255

, TP

,KO

,FILL

,P256

,MJ

,

,p400

,P300

,TP

, U107

,A

,

,DV

, UlOS

, U300

,

,LT

,10017)B

, U301

, TP

, Ul09

,Q

,Q')

,A

,P3S6

,
,

,QS

,A

, P358

,

,
,
,
,
,
,
,

,
,
,

,
,
,
,
,
,
,

$
~~

$
$
$

$
$
CORE HODE

$

~~

$
$
JUMP TO E

.,$

DRUM MODE PRESET

~~

.

~~
¢!.

'l>

$
~~

~~

'PAGE 5
APAC
Oct. 15, 1957

,APPLIED PHYSU:;S LAB

ITEM
NO .

LOC

OP

U

V

\'"

, P60l

,

,QS

,.it"

,

,RA

, P601

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

,QS

"-

/

,

,
,
,
,
,
,

C01~mNTS

$

, ulo6

,
,

, Ulo6

, P35l

,

$

,QS

, Ulo6

, P353

$

,05

,Ulo6

, P361

,RA

,P36l

, K2

,SP

, Ulo6

,1

,QS

,A

,P369

,TV

, UlOl

,P350 .

,
,
,
,
,
,

,TV

,UlOl

,P352

$

,TV

,UlOl

,P354

,TV

,UlO1

,P357

,
,
,

,TV

,UlOl

,P359

,TV

,UlOl

,P360

,TV

~UlOl

,P370

,TV

,UlOl

,P602

,RS

,P350

,Kl

,RS

,P360

,Kl

,SP

,Ulo5

,1

,RA

,A

,UlOl

,TV '

,A

,P362

,TU

,Ulo4

,P352

,TU

,Ulo4

,P370

,
,
,
,
,
,
,
,
,
,
,

,TU

,UlO2

,P354

,

, ,TU

,UlO2

,P359

,RS

,P354

,K2

,RS

,P359

,K2

",,', ,.

,
,
,

$

$
~

$
$
$

$
$
~~

$.
$

$
$
$

$

$
$
$
$
$
$
$
~~

.f<.PAC -PAGE 6

APPLIED PHYSICS LAB

Oct. 15, 1957

ITFJ1

OP

LOO

NO.

,
,
,
,
,
,
,
,
,

OOl1l-1ENTS

V

U

,TP

,Ulo'8

,A

,

,RS

,A

,U3 01

. RA.

,

,A

,ulo4

,TU

,A

,P)57

,
,
,

,RS

,A

,Ulo6

,

,TU

,A

,P602

,RS

,U300

,Kl

,TP

,U)OO

,U)01

,RS

,U301

,IG.

,
,
,
,

,P350

,TP

,KO

,FILL

, DRU1'1 MODE

$

,P351

,RP

,30000)B

,P)53

,

$

,P352

,TP

,FILL

,FIUJ

,P)53
,P354'.
,P355

,RP
,IJ

,10000)B ,p)55
,F]1L
,FILL
,U300
,P3?5

,

,TU

,P)59

,P3552

IP3552

, 'l'P

,FILL

,A

;p)56

,RP

,30000)B

,P358

IP)57

,TP

,FILL

,FILL

,P358

,RP

,10000)B

,P360

,P359

,RA

,FILL

,FILL

,P360

,DV

,UI07

,FILL

,P361

,RP

,1OOOO)B

,p)6,3

,p)62

,TP '

,KO

,FILL

IP363

,TP

,U109

,Q

,
,

"QS

,Ulo6

,,P405

,SP

, Ulo6

,,1

,QS

,A

,p4oo

,

~RA

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

$
~~

$
~~

$
$

$
$

$

$
$
,,'

$
$
$
$

$
$

$
$
$
$

$
$
~~

$

}\PPLIED PHYSI CS

ITEI1
NO.

APAO - PAGE 7
Oct. 15, 1957

:L,AB

LOO

OP

U,

V

OONMENTS

,
,

,TP

,puS

,P41h

,TV

,r1600

,P410

,P369

,RP

,30000)B ,P371

,P370

,TP

,FILL

,FILL

,P371

,SP

,Ulo6

,1

,

,RA

,A

,UI02

,
,
,
,
,
,

,
,

,TU

,A

,P408

,

,MJ

,

,p400

,JU}1P

,P375

,RA

,P352

,UI06

,

$

,

,MJ

,

,P351

,LOOP

~~

,P400

,RP

,,20000)B ,P402

,El'

$

.P401

,RS

,FILL

,FILL

,

$

,P402

,TP

,UlO7

,U401

,

$

,

,TV

,UlOl

,P406

,

,TP

,ul05

,u400

,P4oU ,TP

,KO

,A

,p405

,RP

,30000)B

,P407

,P406

,MA

,FILL

,FILL

,P407

,DV

,U401

,Q

,p408

,RA

,FILL

,Q

,
,
,
,
,
,
,

,

,IJ

,u4oo

,P4l1

,

,PUO

,MJ

,

,FILL

, JUMP ,TO

,PW

,RS .

,U40l

,10.

,

,RA

,p406

,Kl

I

,RA

,P408

,K2

,P414
,PUS

,RS
,MJ

,P405

,K2
,P404 n.

'\

,!

,

$
$
$
$
$
$
$

TO E

~~

$
$
~~

$
$
$
~~

$

E

$

,
,
,

$

,

$

, LOOP

~~

$

$

--- PAGE 8
Oct. 15, 1957

' APPLIED PHYSICS LAB

ITEH
NO.

APAC

LOC

OP

U

V

Cmll·1ENTS

,p500

,RP

,30000)B ,P502

,E2

$

,P501

,TP

,FILL

,

$

,~502

,TP

,UIOO

,

$

,

,MJ

,

,T

, JUI'1P TO EXIT

$

,p600

,IJ

,U,301

,p613

,E3

$

,p601

,RP

,30000)B ,p603

$

,P602

,TP

,FILL

,FILL

,p603

,TP

,UI09

,Q

"QS

,P601

,P400

,TU

,p601

,P405

,TP

, M400

,P414

,
,
,
,

,SP

,Ul06

,1

,RA

,A

,UI02

,TU

,A

,P408

,TU

,A

,P501

,
,
,
,
,
,
,
,
,
,

,

,TV

,M500

,pUO

,

$

,

,NJ

,

,p400

,JID1P TO E

$

,p613

,RA

,P370

,Ul06

,

$

,

,MJ

,

,P369

,JUMP TO E

$

,1'ttoo

,RS

,pL~05

,K2

,PRESET

$

,,~OO

,00

,p500

,E

$

,:1'1600

,00

,
,

,P600

,E

$

,UI09

,00 .

,7777)B

,

,MASK

$

,KO

,00

,ZERO

$

,Kl

,
,
,

,FILL
"A
+

2

~~

$
$
$
~~

$
$
~~

$

,

,00

,
,

,1

,V - ADVANCE

$

,K2

,00

, 1

,U - ADv.aNCE

$

,

,ENDSUB

,

,
,

,

$

.

HOUSEl
1103-A Subroutine
1.

Identification:

HOUSEl
Use Compiler Tape Dump
Keipert, Tantzen, July 57
Holloman Air Development Center

2.

Purpose:

Punch USE compiler side-by-side output on cards for
listing on the IBM 407. Useful if the high speed
printer is down or for installations having none.

3.

Method:

The first 80 characters of each blockette are punched on
a first card, the next 36 characters are punched in
columns 37-72 on a second car d. The second card contains
also a control punch to facilit ate printing all 116
characters on one line. The last 4 characters of each
blockette are ignored. Tbe punching of the second card
is optionalo

4.

Usage:

The routine is a service routine. For purp oses of
distribution through USE it has been written as a standard
subroutine, with one exception, the control words are in
A and Q only. In the subroutine form the usage is:
Place Tape Unit number in AO_4
Set Q35 = 0 for punching 2 cards per blockette
Q35 = 1 for punching 1 card per blockette
Then RJ HOUSElt2 HOUSEl
No manual cycling of Bull necessary.

5.

Restrictions:
5.1.

Control Punch. The second card will have a punch in
row 12, column 7. The column may be change d easily by
taking a different constant C+7.

5.2.

Special Characters. There are 10 characters on the 407,
which will not be identical for different machines . The
compiler tape has 6 characte r s which have to be correlated
to 6 of the 10 hole combinations. This is done by 6 bioctal
special codes SC through sc+5. As coded now, the
correspondence is:

1

HOUSEl

Holes

Characters
plus

12

period

12-8-3

parenthe sis close

12-8-4

comma

0-3-3

space

none

parenthesis open

0-5-4

If your L07 is different, substitute other codes according
to the following correspondence t~ble.
Special octal code.

Holes wanted,

12

01

11

02

8-3

15

8-4

16

12-8-3

35

12-8-4

36

11-8-3

55

11-8-4

56

0-8-3

75

0-8-4

76

The end of line character is always punched as ll-8-3.

6.

5.3.

Wiring board. Use a standard 80-80 board. If wanted,
use control punch on second card to print columns 37-72 of
second card into paper columns 81-116.

5.4.

Parity erroro If a parity error is found, the routine
will automatically go to the parity error routine HOSPll
(see Useful Note #13). This is accomplished by the three
COlTunands PAR+2,3, and 4. If t his routine is not available
at your installation, replace those 3 commands by
something else.

Coding Information:
Space required in core to operate - 323 cells. Cards
are punched at a rate of 110 cards/min. Routine is
machine checked.
2

l
HOUSEl

FLG! CHART

EF, pick punch card
one card per blockette? JNO
.
set SWan I
jump - - - - - - :
set SW on 2 --- - form tape constants
EF, pick punch
read one block
parity checks? y e 3
go to tape reread routine
initialize PICK
rewind. Tu
last blockette? yes
~
OUT
clear
punch ch.
EF, pi9k punch, punch
jump to EXIT
clear image, set bit
set for field 1
mod. PICK --------------------------------------------~
set char index

BODY

I

READ

LAST

SET

Istore char in image I

PICK
i-JOR

field ready?
Trd ready?

r
i-

yes
yes

RJ

a

0

_ _ _ _---1......

-----~.~

set for field 2
set HJ to b
jump

b

no

'----~

F3

'-----,-+
. -

set for field 3
set, RJ to c
jump - - - - -

c
'"-----,"iif.

CARD

punch a card

sw
I

2
adv~nce

!
i

L

I"

PICK by 6

t

TVIO first card?

block ready?
/

nt
LAST

\

Yi

~es
READ

S

EF, pick punch, punch
set for field 2
set RJ to c
clear image

.____________._-___,___~:p
3

bit in field 1.

HOUSEl
FLO,.] CHART
rETAIL:

STOP..E CHAli.ACTER IN IMAGE

Set cmd for row 8
for row 4
for zone
for digits
PICK
shift for next character
mask character out
shift bit one rir,ht
blank? yes
TEST
test for special codes
change if necessary
REGION
code < 20B? yes
.
modify PUN
[_ _ _ _ ----.J
code - 20B

J

bit to zone ~
code < l5B? yes
. bit to row · 8
code = l6B? yes
set for bit to row~
SPECIL
bit to row 4 or 3··~
jump
set cmd to store bit 4 - NOHMAL
bit to raw 12 - 9

PUN

4

l;.:;...t

HOUSEl

'.

(_J

LOC

OP

U ADDR

8

20
126

V ADDR

REMARKS

"C''''''''-

X
X
X

31

166
y

START
BODY

READ
PAR

LAST

CL

SET

PICK

TEST

MJ

0
0
FILL
0

MJ
EF
wBODY+
OJ
TV
EST+
MJ
TV
EST+
LA
A
R+
AT
AT
R
EF
0
EF
0
RPV
120
ERB
0
0
ERA
PAR+
ZJ
TP
READ
TP
READ+
HOSP11+
RJ
TU
BODY
TU
PICK
~A
lAST+
TP
FILL
R+
EJ
EF
0
RPV
39
C+
TP
C+
TP
TP
CON
C+
TP
RA
PICK
TP
C1+
T+
TU
PUN+
RA
C+
AT
AT
C+
TP
A
lO
FIll
R+
OT
T+
LO
TEST
ZJ
EJ
CE
CE+
EJ

I

2
1

2
6

BODY
FILL
FIll
R+
BODY+

Sw

READSW
12
T+
T
R+
T
PAR

1
4

HOUSEl
PUNCH USE COMPILER
SIDE-BY-SIDEOUTPUT
ON CARDS
KEIPERT,TANTZEN
JULY1957
ENTRY
NOT USED
EXIT
PP
ONE OR TWO CARDS?
SET FOR 1 CARD

4

4

1

SET FOR 2 CARDS
FORM
TAPE
CONSTANTS
PP
READ
ONE BLOCK

W

2

1
2

2
4

1
2

2

2

2
:3
4
.5

3
1

A
PAR+
HOSP1l+
HOSPll+
HOSPll
PICK
LAST+
C+
A
OUT
R+
CL+
CR
T+
T+
I ND
C+
IND+
PUN+
C+
SPECll
PUN
NORMAL
6
T+

5
3
4

2

3

LAST BLOCKETTE?
2

pp,p

2

CLEAR
IMAGE
SET BIT
SET FIELD 1 ADDR
1ST CARD IND

1

2
3

1
:3
3

3

35

NORMAl+
CH
CHI
1

5

PARITY?
GO
TO
REREAD
INITIALIZE

1

CHAR IND
SET FOR RmoJ 8
FOR ROVI 4
ZONE
DIGIT
NEXT CHAR
MASK
SHIFT BIT 1 RIGHT
BLANK? NO, YES
CHECK

1
HOUSEl

---j
("{:)

LOC

CH
CHI
CH2
CH3
CH4
CH5
REGION

PUN

SPECIL

NORMAL

F3

WOR
CARD
WRITE

OP
EJ
EJ
EJ
EJ
MJ
TP
MJ
TP
MJ
TP
MJ
TP
NJ
TP
MJ
TP
TP
TJ
RS
RS
MJ
CC
TP
TJ
CC
TP
TJ
RA
CC
I'-1J
LTR
RS
CC
LQ
OJ
RJ
RA
TV
MJ
RA
LQ
TV
MJ
IJ
MJ
RP8
TV
TP
EWA
EWB

U ADDR
CE+
CE+
CE+
C+

2
3
4
2

0

CE+
0
CE+

5

6

0

CE+

7

0

CE+

8

0

CE+
0
CE+
T+
C1
PUN
T+
0
FILL
T+
C1+
FILL
C1+
T+
SPECIL
FILL
0

9

10
3
3
3

1
1
3

15

NORMAL
FILL
Q
NORMAL+
NORMAL+
T+
CON+
0
T+
T+
CON+
0
IND+
0

0
0

CH2
CH3
CH5
CH4
REGION
T+
REGION
T+
REGION
T+
REGION
T+
REGION
T+
NOR''''AL+
T+
A
PUN
C+
C1
REGION+
T+
A
NORMALT+
A
SPECIL
C+
T+
NORMAL+
T+
T+
T+

3
2
1
2
1
2

1
:3

WOR
NORMAL+
(1+
NORi"1AL+
SET
Cl+

REMARKS
FOR
SPECIAL
CODES

3

REPL 638 BY 018

3

REPL 22B BY 358

3

REPL 73B BY 368

3

REPL 21B BY 756

3
1

REPL 01 BY OOB

3

REPL 17B BY 768

3

LESS 208? YES
MODIFY ZONE
CODE-20B

1
1

2
1

3
1
1
3
3
1

35

3

3

CON+
C1+

V ADDR

4
4

BIT TO ZONE
NORMAL CODE? YES
nIT TO ROW 8
158 TO A
CODE 168? YES
SET FOR ROW 3
6IT TO ROW 4 OR 3
SET
FOR ROW
BIT TO RO'.~
TEST
FIELD DONE? YES,NO

3

SET FOR FIELD 2
SET RJ TO B

4

SET FOR FIELD 3

3

SET RJ TO C

2

WORD READY? NO

2

SET UP WRITE
0-1DS
ROW INDEX = 11
WRITE
NEXT

8

L+
SET
SET+
SET
CARD+
WRITE

NOR~1A

3

Q

FILL
FILL
6

· .
nOUSEl

:..l.)
-7

;'--=:J

LaC

OP

U ADDR

V ADDR

REMARKS

'P'"

SW

TWO

OUT

EWB
RPU
RA
IJ
MJ
RA
EJ
M..J
I..J
TP
M..J
EF
TP
RA
TV
RPV
TP
TP
MJ
EF

RP
EF
MJ

CON

EST

0

FILL

3

viR I TE+

WRITE

C+
WRITE
FILL
C+
READ
LAST
TWO+
A
SW+
R+
T+
C1+
NORMAL+
OUTCR
CR+
\vOR
T+
OUT+
R+
START+

Q

0
PICK
EST
0
IND
PICK
0
CON
T+
CON+
39
C+
C+
0

2
2

1

7

3

ROW
5
2

6
3

LQ

R

w+

119

FIRST CARD? YES
PICK CMD TO A

2
2
2

4
:3
2

11

PP.P
SET FOR
FIELD 2
SET RJ TO C
Cl.EAR
IMAGE
PLACE CONTROL BIT

4
:3

REWIND TAPE

5

CLEAR PUNCH
JUMP TO EXIT

2

CR
F3
CARD
CR+
CR
CR+
6
SW+
TWO

MODIFY
CARD READ? NO
JUMP IF 2 CARDS
ADVANCE PICK BY 6
BLOCK READY? YES

26
13
1

402B
40
40
61 61616B
40
0
2 00200B

C

lOB
12B
77B
161618
0
(\

PP

pp,p

MASK
END MARK
CYCl.E
DUMMY

120
1

ZERO
COMPJL CODE SPACE

1
4

(1

7
6
40000B

0
20B
158
5

7

CONTROL PUNCH

· ..
,- j

HOU GEl

'I.:..d

--'

~'

LOC

OP

U ADDR

V

ADDR

REMARKS

13B
15B
CE

63B
22B
438
21B
17B
1

35B
36B
758
76B
T RESERV
IND RESERV
W RESERV
CR RESERV
END

5

5

2
120

2

120

39

39

8

COMPILER CODE+
PERIOD
PAREN CLOSE
COMMA
PAREN OPEN
(PLUS)
6 SPECIAL
(PER I OD)
CODES
DETERMINED (PAR CL
BY LAYOUT OF (COMMA
INDIVIDUAL (SPACE)
(PAR OP
IBM 407
INDICES
BLOCK SPACE
CARD IMAGE SPACE

#

v ,- 1"";

2.

IDEwtIFICATIO:f

RRF010 - NATURAL LOG X FLOATI :~G POINT
L. M. Johnson - 15 August 1957
Remington Rand Univac

PURPOSE

= lnX

Given X, compute Y(X)
3.

in floating point, using stated point arithmetic.

METHOD
a.

Accuracy:

b.

Ra r ge of Argument:

c.

Scaling:

d.

Derivftionl

ly(X) -

In(X)I ~2-27 in a 27 bit mantissa.

1103AF, flo ating point binary number representEtion.

obtatfied from the relation InX = (1n2)(10j~) ; log2X is
1
4
_1.- 1
< <
X _ ./2
approxi~ted by the expreSS1.on 2 + ~
C2i - l X + J2
where 1_X_2.
i=l
.
(See Rend Sheet Number 42, and RRFOll - Natural Log X Stated Poi nt .)
I

4.

U

•

USAmE
a . . Calli ng Sequence

1QQ.

OP

U ADDR

r

RJ

t+2

Normal

Return

r+l
b.

V ADDR
t

Control &nd Results
The argument, X, in floating point form must be initiDlly stored et t+4; the
function Y(X) will be found in floeting point form at t+3 upon successful
completion of the routine.

c.

Y(X) is also left in

An.

•

Space Required
78 cells of instructions and constants
3 cells of working storege

d.

Error Codes
The followi ng error code in flex is left in the Q-register upon return through
the error exit .
EXPLANATIO!l
RRF010

5.

RESTRICTIONS
The argument must be within the stated range and must be in packed, normolized
floating binary form.

-2-

6.

CODrG r EFORJU '"' r m!

a.

Cons t ants
l£QQ.

00 00000 00000

Zero

01

55 20236 31500

J2 ·

02

00 00000 00002

03

20 00000 00000

04

00 00001 00000

05

15 71272 26456

06

22 34660 40144

07

36 61611 14432

08

34 25216 61765

09
010

26 13441 37677

Ln2 • 2

00 00000 00200

Characteristic Bia s

011

00 00000 00046

3810

C12

00 00000 00110

72

CODE

12 12263 75237

Working Space

3 cells labeled STORE thru STORE+2
c.

__ EXPLANATION

0

,

b.

CotlSTANTS

Timing
Maximum of 5.70 IDle.

35
2

D-Address Advance
o7 • 235
C .235
5
35
C • 2
3
35
(C - 2) • 2
1

35

10
Error Code (Flex)

PAGE....l-OF--LRRF010
CODED BY L ! JOMNSO~l
DATEB-15-57

REMINGTON RAlm UNIVAC

PROBLEt~

ITEM NUMBER

OP

LOG

,
,
,
,
,
,
,

, SUB
I NOUT
, TEMPS

ENTRY
ERROR
EXIT
Y

, ·,X

, START

,
,

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, t"'EST

,
,
,
,

, MJ
, ALARM
, MJ

, 00
,
,
,
,

00
TP
TJ
TP

U

,

RRF010
,1
, 3
, 0
I

,
,

, 0

, TP
, LTL
, LTR
, SP
, SA
, SA
, LTL
, SP
,SS
, DV
, MP
, SA
, LTL
, TU
, TP
, MP
, SA
) LTL
, AT

,

,

,
,

,

,RJ

, ROmID+4,

ROfiill

, LTL

, 1

,

A

, MP
,RJ

, A

,

C9

,
,

, ROUND+4,

ROUND

$
$
$
$
$
$
$
$
$

FUNCTION FP
ARGUMEliiT FP
TEST FOR X
LESS-EQUAL ZERO

,

, ERROR
,A
, STORE

,

FLOATING POINT

,
,
,
,

Q

, TJ
, MP

,

$
$
$

,

,
,
,
,

,RA

,

,
X
,
,
9
0
,
Q
Q
,
o
C1
, 0
,
C2
, 0
,
34
, STORE+1,
Q
0,
C1
, 3.3
,
STORE+1, STORE+2,
Q
, Q
,
C3
, 0
,
1
, STORE+1,
SET
, NEST+3,
C5
,.Q
,
Q
, STORE+l,
C.3
, 0
,
1
, A
,
, Q
FILL
,
NEST+3 , C4
,
TEST
, NEST
,
Q
STORE+2,

,M3

,
,
,
,
,
,
,
,
,
,
,
,

$

,

,
,
,

FILL
FILL
C
X
CODE

START

, LNX

FILL
,
FILL
,
FILL
,
A
START+4,

, 0

,

78
1
0

,
,
,
,
,
,

C 0 MMEN T S

V

•
,
,
,

STORE
CHARACTERISTIC
$
AND t1ANTISSA (=M)
$
FORM AND STORE
$
(2M+SQUARE ROOT 2)
$
ROmmED SCALED 3.3
$
IN T~~P
$
FORM (2M-SQUARE ROOT 2)
$
SCALED 68 IN A
$
FORt1 SQUARE OF Z=
$
«2M-SQUARE ROOT 2)/(2M+SQUARE ROOT 2)} $
ROUND SCALED
$
35 I~ TEMP
$

$
C(7) TO Q
PARTIAL EVALUATION
OF POLYNOMIAL (=P)
EXPRESSION
IN APPRX
OF !.h'X
SCALED 35 IN Q
FORM ROUND STORE
(P-2Z )
SCALED 35 IN A
FORM ROUND STORE
(P-2Z ) LN2 SCALD

$)

$

$

•

$
$
$
$
$
$
$
$

•

PAGE 4 OF . 5
PROBLEM R.1U'010
CODED BY L. J OIH7S0N DATE R-15- 57
OP

LOO

ITEM N:TMBER

-C

,

, LTL
LA

,

,
,
,
,
,
,
,
,
,
,
,
,
, NTZER

,
,
, YES

.

,
,
,

,MJ

, ROUND

,
,
,
,
,
,
,

, ST
, MP
,RJ
, LTL
,RS
, MP
, AT
, AT
, TP
, SF
, LTL
, LTL
, ZJ
, SP
, TJ
, ST
, AT
, LTR
, CC

SET
TEST
C
C1

, C2
, C3
, C4
, C5
, c6

, SJ
, ST
,MJ
, AT
,MJ
)00

., -AT
,f B
, B55
, B
, B20
,B
, B15
, B22

U
, 1

CO MM E NT S

V

,

, STORE+2 ,
,
, C3

STORE+1, 35 IN TEMP
, FORF (2Z-1/2) LN2
1
STORE+2, SCLD 35
, I N TE}l:P
C9
ROUND ,
STORE+2,
, ~m IA S CHAR (=C)
C10
, FORM C( LN2 ) SCLD 35
C9
A
, FOR~ (P+0-1/2) LN2
A
, SCLD 35 IN A
STORE , FORM
STORE , NOR!vf.ALIZED
, MANTISSA
Y
, I N Y AND A
A
,
EXIT
0
, TEST 38 GRTR K
YES
,
A
, ADD BIAS TO CHAR
A

, STORE+2 t
, ROUND+4 ,
,1
,
,
, STORE
,
, A
, STORE+2 ,
, STORE+1 ,
,
, C
,
, A
, 28
,
,
, 0
,
, NTZER
,
, STORE
,
, C11
,
, 012
,
, C10
, Q
,
, 27
, y
,
Q
, EXIT ,
, 0
, ROUND+1 , ROUND+3,
,
, A
, C3
, ROUND+4,
, 0
,
, A
, C3
, 0
, FILL ,
, FILL ,
, C6
, Q
,
, C6+3
,
,
0 ,
, 31500 ,
, 20236

,

,
, 00000
1
, 71272
, 34660

,
,
,
,
,

2
00000
00000
26456
40144

PACK UP Y(X) FP
EXIT

ZERO
SQUARE ROOT 2 SOLD 35

, ROUND BIT
, 1 SCLD 34
U ADD ADVA NCE
, C(7) SCALED 35
, C(5) SCALED 35

$
$
$
$
$
$
$
$
$
$
$
$

S
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$

•
$
$
$
$

•

•
REMINGTON RA!-ID U!HVAO
PROBI.IDfi

PAGE
5
RRFOIO

CODED BY L. JOm:SON
OF

LOO

NTMBER

,
,
,
,
,
,
,

,

C7
C8
C9
CI0
Cll
C12
CODE

, B36
, B34
, B26

, 61611
, 25216
, 13441

~

, B

,
,
,

, B

,

, B

,

, B12
, 12263
, ENDSUB ,

,

,

14432
61765
37677
200
/ 46
110
75237

5

DATE 8-15-57

CO Mt-1ENTS

V

U

OF

, C(3) SCALED 35
, C(I)-2 SCALED 35
, LN 2 SCALED 35
, DEC 128
38
, DEC 72
, ERROR CODE

, DEC

,

•

,

1.

Title:

2.

Autl1ors:
Date:

3.
B.

Single Precision Floating Point Conversion p WF0004.
W. Baue r and. H. Graham
1 July 1057

Installation:

Wr ight Field

Purpose

This routine converts a single length floating point binary word from core or
drwn memory to its floating decimal equivalent and then to excess-three characters.
wFOOO4 is to be used primarily as a subsidiary of the High Speed Printer Edit
Rout ine, WB~OOOl.

C.

Us~ge

1-

Calling Sequence
Loc

r
r+1
r+2
r+3
2.

QQ
RP3
TP

RJ

Normal

U-addr

'{ -aC1g.r

2
Parameter
C+2
Return

r+£
C+B
C

Contrvl Dena
Two parameters are required for each word to be converted.

They are as

follows:

Lbc

QQ

U:-add'r

V-ador

Param

XX

XXX XX

XXX XX

D
Param+1

11

S

VI

----_.

XXXXX
r~

\{ (decimal) is tl1e number of cnara.cters to be storea starting at address
'( 7 ~

K.

II{

~ 13)

S See WF0001, para D2(b).
M is the address of the first word to be converted.
D See WF'OOOl, para D2( b).
K is tne first address of the cells in whiCH tne converted word is stored.
This aata is a series of six-bit excess-tnree cnaracters stored one to a word in
tne ri ~n tmost six bits, tne leftmost t hirty oita bein, zero.
3.

Space Required
200 merlJory cells

·

(

4.

Error Codes
An alarm occurs if:
a..

W< 7

b.

W> 13
In either case the ala.rm is a.nnotatec.1 a.s .follows:
(AL)
(AR)
(Q)

R.

= first

parameter word
= second parameter word
= WF0004 in flex code

Format Generated
'II controls tne number of output cha.racters as follows:

Number of Ch~racter§
(-')X.XXXXXXX( - )XX
(--)X. XXXXXX(-)XX

W
18
12

(-)X.X(-)XX

7

D.

Res t-r::16t,iQh~ t

1. The word to be convertea must conform to the 1103A liefini tion of a
paCKea floating point number.

E.

2.

An unnormalized number is translatea as a series of space coaes.

3.

Rounding to n digits is accomplished by

Cooing Ihfor:mat'ion
1.

Constants ana their Locat ions
a.

Alphanumeric
J tttrougn J3

b.

Numeric
K1 througn K26
1K

2.

tlirOU~l1

lK115

Erasable Output Locations
P

t r. rou~ i1

P17

aCldin~

5 in the n+1 place.

.

(

\It'FOOO

or 5

Page

peges o

o

H
I

~

»

,2

'"
Q

.i

. 0

•-

-,
, <

,_

;

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a;

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f

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.... f

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~

r-

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lJ

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•

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~ (j

~ "'

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• 1 -;

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T

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lVIEANS

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t '" ;

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..,...,....
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(

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<-

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, ""

S'$

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~

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, ?

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; ,h,:'~

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$

M:!tl.NS +
..

WF0004
Page 2 of

5 pas-a .

,

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FOO04

Pllge 3 of 5 pages.

,,

,
,•

•.0
•

,

, 1.

o

,R

.. .1'

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, 0

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.0

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h k 72

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WF0004

5

Ps.ge4 (If

pages/>

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t 0

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WFOOOq.
Page 5 of

,
r

,

,

5

pag~ .

A.

I~ehtirication

1.

Title:

2.

Autl1ors:
Date:

3.

Single Precision Stated Point Conversion, WF0003
VI. Bauer and R. l:lrananJ

1 July 1957

Installation:

Wright Field

B. Purpose
This routine converts a single lengtn statea point binary word from core or
drum memory to its decimal equivalent and tnen to excess-tnree characters.
WF0003 is to be used prirr~rily as a subsidiary of the Hi~h Speed Printer Edit
Rou tine 9 \~F'0001.

c.

Usa.ge
1.

Calling SelJ.uence

Lac

QQ

LJ::;a.dar

r

RP3
TP

2

r+l
r+2
r+8

2.

RJ

Normal

Parameter
C+P,
Return

Y:'adar ·
r+£
C+3
C

Control Data
Two parameters are required for

eacil

word to be converteu.

They are as

follows:
Lac

Q£

U-actdr

Y-aadr

PararTJ

XX

XXXXX

D

M

XXX XX

Pararn+l

---XX
J

K.

VI

S

XXXXX
K

VI (decimal) is the numot!r of cnaracters to be stored starting at adaress
(1 ~ w ~: 13)
S See WF0001, para D2(b).
11 is the address of the first word to be converted .
D See 'ri'F00019 para D2(b).

K is the first address of tne cells in wnich the converted woro is
storeu. Tnis uata is a series of six-bit 9 excess-tnree cnaracters stored one to
a word in tne ri~rjtmost six bits, the leftmost tnirty oits oein~ zero.
J (<.tec irnal) is the binary scal int:; of tne woro to be convertea.
(0 ~ J ~ 35).

2.

Space Requ,ired
104 memory cells

4.

Error Codes
The alarm conditions are as follows:

a.

W > 18

b.

J > 35

Botn are annotated in the samE;! manner namely:
p

CAL) = first parameter word
CAR) = ~econd parameter word
CQ) = WFOOO3 in flex code

Output will be
E.

tru~cated

if W is less than 13; however p a word is never rounded o

CoCi,ih'g Informaqon"

1.

Constants and their Locations
a.

Alphanupler ic
J through

b.

J~

Numeric
K through K21

2.

Era.sable OU,t put Locations
P tnrougn P15

WF0003
Page 1 of 3 pageso

o

MEANS

#

MEANS +

/

MEANS

.."
"

,

,',

, f::'

.-

~

:..

- j'

"

.•,

; Tt)

.. "
•

.

1

,

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1

1"'~

' ; or

+

\18

/

j

L

J

L-

,.

r

, ~!')

•

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iii

,

.1

T~

,

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- (,

4 '--'";

j '.\

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~

y

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; Po. /, 'r

.,.
I,

. TI:'

,, ':':

•, ....

- T

iI

')

,. 0

, .~

, ':
f

ll,

T \~

•
•

C·

\

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r P' 1
,rq

• .--1
-

(-i

1

'r

r h

..

L ,'\
.I
~

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T

' I '" I -;- t'·().

$

WF0003

3 page-s •

Page 2 c,f

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, K (~

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WF0003

Page 3 of :3 pag«Bo

··
~

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f

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A.

Iil~h t iilca t ion

Title:

2.

Authors:
Date:

3.

B.

Octal Conversion, WFOO02

l.

W. Bauer anu R. Graham
1 ,J uly 1957

Ins talla t ion:

Wright Field.

PUI-pO£1e

'r nis routine converts binary data from core or arum memory to its octal equivalent and then to excess-three cnaracters. WF0002 is to be used primarily as a
subsidiary of the Hign Speed Printer Edit Routine, WFOOOl.
C.

Usage
1-

2.

Ca.lling Sequence
Loc

QQ

U-addr

V-addz:

r
r+1
r+2
r+3

RP3
TP
RJ
Normal

2

r+2
c+3
c

Parameter
c+2
Return

Control Data
Two parameters are required. for each wora to be converted.

They are as

follows:

Lac

Q£

U::~d~.r

V-addr

Param

XX

XXXXX

XXX XX

D

M

Param+l

W

--:--K
B

S

XXXXX
K

Vi (decima.l) is the number of ctlaracters, including spaces, to be stored. at

audress K.

S
~1

(1~w~14).

See

WFOOO1~

para D2(b)

is tne address of the first word to be converted.

K is the first adaress of the cells in which the converted word is stored.
This data is a series of six-bit, excess-tllree characters stored one to a worll in
the rightmost six bits~ the leftmost thirty bits being zero.
S is a format control word.
If B = 0) (M) is translated: XXXXXXXXXXXX__•
If B = 1, the address 1'1 is translateu: XXXXX_--,-__
If B = 2~ (M) is translated.: XX_XXxXX_XXXXX.

3.

Space Requ,ired
81 memory cells

4.

Error Codes
Wnen W is greater than 14, an alarm occurs.
(AL)

(AR)
(Q)

D.

= first parameter word
= second parameter word
= VlF0002 in flex COCle

Restrictioh§
Output will be truncated if:
1-

2.

3.

= O~
1:3 =
. 1,
E = 2~
B

and \'1 is less than 12
and. W is less than 5
and W is less tnan 14.

E. COdih~ Inforfuat1on
1-

Constants and their LOCiit ions
a.

Alphanumeric
K

b.

Numeric
K1 tnrougll K12

2.

Erasable Output
p

throu~n

P14

Stora~e

• K J ';
1

, :.

,

;<

'>

:tt 4:

,11)

,-12
~r

i '1

t -":1

~

r.>:tJ

1
') 1r; 1 T LOCb

.:p..
•

."

A.

Iaentification
1.

Title:

2.

Authors:
Date:

3.

B.

Alphanurner ic Conyers ion p WFOOOf)

W. Bauer ana R. Graham
1 July 1957

Installation:

Wright Field

Purpose

This routine assembles prestored p prepacKed excess~three characters from core
or urum memory for e~iting. WF0005 is to be used primarily as a subsidiary of
the High Speed Printer Edit Routine p ' ''FOOOL
C.

Usage
1-

2.

Calling Sequence
Loc

ill?

U.-ador

V':"6dd.r

r
r+l
r+£
r+8

RP3
TP
RJ
Normal

2

r+2
c+B
c

Parameter
c+2
Return

Control Data

Two parameters are required for each
They are as folloiNs:

~roup

Loc

QlL

U-e.di1r

V::... adc.i r

Param

XX

XXXXX

XXX XX

D

M

Vi

of cl1ara.cters to be assembledo

S

XXXXX

Param+1

K
W (aecimal) is tne nUf,lber of cnaracters, including spaces to' be · stored
starting at adaress K.
(1 ~ W~ 180 ).

S

See dF0001,

M is toe

~ ~r ~ D~ (b).

~aare8B

D See WF0001 9

of tne first six characters to be assembled.

pa.r~

D2(b).

K is the firs t a.daress of the cells in .inich the assembled data is storea.
This data is a series of six-bit, excess-tnree cnaracters pacKed six tea woru.

3.

Space i1equireJ
24 memory cells

7

D. Cooing Information
1.

Constants ana their Locat ions
K througn K4

. . .. Erasable Output Locations

9

p

I

.-

,

page.

~~.

10

•

RRFOO8 ~~COS X FLOATING POINT
L. I{rak, R. VDn Hi lst
15 July 1957
Remington Rend Univac

IDENTIFICATION

PURPOSE
Given X compute Y(X) = arcoosx in radians

3.

METHOD
a. Accuracy:

Iy(x) - arccoaxl ! 2-26 in a normalized 27 bit mantissa.

b.

Range of Argument:

c.

Sceling:

d.

Ixl ~

1; for O!IXI<2-32 , Y(X) is set equal to

tT

2•

1l03AF pecked, 8-27, floating point number representation.
33
Derivation: X is converted to stated point scaled 2 ; the function, arcsin X
1T

is computed; then arccos x

=2

-

arcsin x (See RRF6, Arccos x Stated Point),

and this stated point value is converted to floating point re?resentvtion for
y(x ) •

4.

USAGE
·a.

Calling Sequence
LOC

OP

U, ADDR
» J,

r

RJ

t+2

~

r+l
b.

v ADDR
,f!'

5)j

Normal

t

Return

Control and Results
The floating point representation of tqe argument, X, must be initially stored
at t+4, the floeting point representation of the function, Y(X), will be found
at t+3 upon successful completion of the routine.

c.

Space required
122 cells of instructions snd constants.

7 cells of working epace.
d.

Error Codes
The following error code is left in the Q-register on return through the error
exit:
EXPLANATION
I'XI>l

RRFQ()8

5.

RESTRICTIONS
The argument must be in 1103AF normalized, packed floating point number representation
and must be within the stated

•

--2-

6.

CO:JI;m I NfO-;tM;. TIOK

8.

Conste,nts

1QQ.

CONSTANT

I:;~~l.ll!:lA'T'IQN

2- 27 )

C

20 14000 00001

FP (1+1

C1

00 00000 00000

Zero

C2

14 14000 00000

FP 2-3'""-

C3

00 00000 00001

One

C4

20 14000 00000

FP 1

C5

37 70000 00000

Characteristic Mask

C6

00 00000 00126

Characteristic Unbias Constant

C7

53 24135 2 0Cfl0

~

C8

33 24414 25535

C9

56 40CJ71 51545

C10

37 50417 41234

C11

46 23706 66522

C12

26 61f51 66Cf73

0

'244

C13

44 42003 30653

C14

31 10375 51633

C15

10 00000 00000

4286 • 2
a • 240
5
40
8
4 • 2
39
6
3 • 2
38
6., • 2
37
8
1 • 2
• ,.,34
8
0 ..:
1 0 233

C16

26 47670 31361

Constant.s

C17

00 00000 65324

For

C18

11 453M) 44516

Square Root

C19

33 06571 40273

Routine

C20

00 00000 00077

Mask

C~l

26 50117 14640

$0 234

C22

20 00000 00000

34
1 • 2

C23

37 77777 77777

Round Factor

C24

' 14 44176 65211

C25

07 20000 00000

.!! , 233
2 •
Characteristic Bias I

c26

20 16220 77325

FP

IC.

TT

:2

-3(cant)

b.

EXPLAJ~A T IO N

LOC

CONSTANT

C27

11 00000 00000

Characteristic Bias II

CODE

12 12263 73760

Error Code

Work Space
7 cells labeled STORE thru STORE+6

c.

Timing

Approximate maximum of 7.22 mls. for X= _(1_1.2-

27

)

-

PAGE

REMI:NGTON RAND UNIVAC

IIIn08 '.' '.

PROBLEM
CODED BY Krak. Van Hi1st

I TEM NUMBER

OP

LOC

,

,
,

v

U

.....,--*

4 . OF 8

DATE. 70:-15=57

COMMENTS

,SUB

,. ~

,l22

,

$

, TEMPS

,

7

, o

,

1

,

,

•

o

, S'l'ART .

, INOm

,
,

1

$

,

ENTRY

,

,

ERROR

,A!..,ARM

,

EXIT

,MJ

o

, FILL

,
,
,

, Y

,00

, FILL

, FILL

, FUNCTION

$

,

X

,00

, FILL

, FILL

, ARGUMENT

$

,

START

t

x

,

,ABSXTOA

$

c

, PROG

, CHI{ FOR X GRTR 1

$

,

$

MJ

,

,

$

•

•
•

,

, TJ

,
,

,

,S'P

, CODE

,

,MJ

,

o

, ERROR

,

, TP

,

C26

,

, FOR SMALL X AND

$

, TJ

,

C2

, EXIT

,X~. O

$

, TP

,

A

, STORE

, STORE ABS X

$

, TP

,

x

,

,

$

C1

,
,

FROG

,
,
,

TM

,
,

, 'l'P

,

,SJ

, MINUS

, . MINUS

, TP

, C;

,

,'I'M

,

,EJ

, C4

, TP

,

C5

,

A

,

,
,
,
,
,

PLUS

, CC

,LQ
,RS

A

, STORE

,
,

A

Q

Y

A

, STORE+1

GO TO
ERROR

EXIT

Y=P!OVR2

. , SET FOR

ros

X

$

$

, TEST SIGN OF X

$

, STORE+l

, SET FOR TOO X

$

,

, ABS X TO A

A

, XONE

, TEST 1=1

•
•
$

,
,

Q

, MASK TO Q

Q

, CHAR TO Q

,

Q

, STORE MANTISSA

$

, FOF.M SHIFT COUNT

$

,

$

Q

,

Q

,

9
c6

IN Q

$

~

PAGE~OF S

REMINGTON RAND UNIVAC

PRODLEM RRFOOS
CODED BY KRAK' VAN HILST DATE 7-15-57
ITEM NUMBER

OP

LOC

,
,
,
,
,
,
,
,
,
,

SHIFT

V

U

, TV

,

,

COM ME NT S

, SHIFT

, K = CWiR -86

$

, STORE

, FILL

,

, LTL

,

, STORE

, ABS X SCLD 33 TO STORE

e
e

, MP

, STORE

,

C7

,

$

, LTL

,
,

,

A

, EVALuAT$

$

SP

, AT

Q

O·

1

CS

, STORE+2.

I

SHIFT MANT K LEFT

, MP

, STORE

, STORE+2

, EXPRESSION

, LTL

,

,

, AT

t

, MP

, STORE

,
,
,

1

C9

A

, STORE+2

, STORE+2
, A

J

, AT

, :3
, C10
, STORE
, 2
, C11

,

, MP

,

,

, LTL

,
,
,
,
,
,
,
,
,
,

, AT

,
,

, MP

, STORE

, LTL
, AT

,
,

, MP

, STORE

,

STORE+2

, LTL

,

,

A

t

, LTL

,

, AT

,
,

, MP
, LTL

, AT

~

STORE
.

2
C12

2
c13

0

C14

, STORE+2

,

STORE+2

•

A

, STORE+2

, STORE+2
,

A

$

APPROXIMATION

$

OF ARCSINX

$
$

J

IN

e

,
,
,
,
,

, STORE+2

,

,

,
,
,
,

, STORE+2

IN

ACCUMULATE

,

, STORE+2

$

J

, STORE+2

A

STORE+2

$

SCLD 34

$

•
•
•
•
•
$

$

.•

:. ;"

, X(I) TO

STO~+2

.,;

, TN

, STORE

,

A

, FORM (l-X)

, SA

,

C15

,

a

, SOLD 33 IN A

, SF

,

A

, STORE+3

e

roLYNOMIAL

, K TO STORE+3

$

I·
·t·

•
•
$

R»iINGTON RA~ UNI VAC

rAGI

ITEM NUMBER
.

...:......

~

.

OP

LOG

,
,

,
,
,
,
,
,

•

,
,

,
,
,
,
,
,
,
,
,
,
,
,
,

,
,
,
,
,
,
,
,
,
,
,

, OF , ".8 '

PROB:r.»i ~
a
which bits of word to be sorted. If no
extractor is desired set equal to zero.

t 7

SS

vvvvv

NNNNN

SSa - Code for last' parameter,' 77 - last

.~

RRRRR8 - First MD address for temporary
storage of relative locations of data .
while being sorted, must equal number of
data plus one.
WW

parameter, 00 - otherwise; VV~!a - First
MD address of data to be arranged in respe:C
to original sorted data. NNNn~8 - First ~/
address of final storage for data after
arrangement in respect to original sorted
data.
·Upon completion of the sort with the use of an extractor the oriqinal data will be
stored,sorted in respect to ' the extracted bits.

e. Space required
165 cells of instructions and constants
266 cells of working storage
2(n 1) cells of designated working storage.
sorted.
d.

N equals numbe:r of cells of data to be

Error codes
"ERROR" is printed.

5.

~.

RESTR ICf IONS

a.

This routine will operate on any 1l03A as established by USE but size of Me limits
the number of data to be sorted.

b.

This routine is self contained.

c.

This routine requires that the temporary storage beginning at Nm~~rna be in MG, there ~
by limiting the number of pieces of data to be sorted to the (number of locations
'in MC) minus 65;7?
If so desired, this temporary storage could be located in the MD.
but the timin~ Will be increased by a mUltiple of approximately 500.

d.

An extracto!" (t 6) must not be used when it is known that the data will contain
negatiVe numbers..:

e.

The octal numbers 40 00000 00000 and 37 17777 77777:. 'lJIust not be centained in the
data to be sorted as these numbers are used · by th~r.:~rp,tltine during·the sorting procedure.
'

f.

No internal check is made by the routine for over-lapping of regions.

CODING INFORMATION
a.

Working storage
266 cells labeled TEMPS through TEMPS 265

b.

Constants
20 cells labeled CON through CON 19

~.~IT~E~M~NO~.~______~T~AG~__~=O~P~E~R~AT~ro~N~~~U~AD~DR~ES~S~V~AD~D~R~E~S~S____~C~O~M~~lli~NT~S____~~__.
~
, SUB
t SORT
t
165
$

TEMPS
INOur
t
MJ
t
ALARM
t MJ
t
RESERV
, PR3
t
TP
PR2
t

, ENTRY
, ERROR
t
EXIT
, PAR
• START
t
1

2
3

l1J

4

, 5
, 6
7
8
, 9

,Sf

,-.1
, 2
, 3

,
,
,
,
,

4
5
6
7
8

, DA
, 1

,2
3

t

4
5

t
t

K
1

t
t

2,
, 3
EX
1

t
t

TV
, TV
• TU
, TP
t

qr

t

QT

, RS
, AT
• SA
t TU
• TV
t
RP
, TP
, SP
t SA
t

TV

, TP
t TP
, LT

l1J
, TP
t TP

• 14
, 3
t
PAR
3
TEMPS
PAR
t
PAR-ti
t

Q

• 25

Q
• A
t
PAR
,CON
t
PAR
, TEMPS
t TEMPSt-"4
, CONt4
, CON+5

t EX-t2

4

5

TV

6

, RP

2

, 3
4

t

, 5
, 6
7
8

,MA

t

t

qr

TP
, TJ
, TP
, TU
t TU

, TV
, RP
, 0
TP
, RPI

FILL
, 14
t STAR'1t-2
, TEMPS
STARTt4
17

t

t

$
$

PAR .TO
TEMP

$

SH 1FT TO U

$

$

Q
$
• A $
, 25
, SH 1FT TO V
$
• A
$
TEMPS
$
• TEMPS+-l
,.
$
t DA 1
$
t
Q
, EXT. TO Q $
, TEMPSt4
$
t

Q

$

$
, TEMPS+4
$
• 17
• SET UP RP
$
t A t DA
$
• TEMPSt-l
t
DA-tl
$
t
FilL
, DAt-2
$
, FILL
FILL
DATA TO Me
$
t DA 1
, 0
$
t TEMfSi-4
0
$
, A·
, DAi-5
$
t CONH'
t FilL
, .STORE SEN.
.$
, TEMPSt-4
, A·
, NO OF DATA TO A $
, 35
, TEMPS~, A/128 10 K
$
A
7
$
, Q
, TEMPS1-7
t
REM 10 K 1
$
t PARt-3
, A
tEXT. TO A
$
, A

7
WS
1
t

, LQ
. , LT

$
$
$
$
$

, 0
0
, START

to,

TP
t TU
TU

3

t

TP
TP

266 ~

14
., 0

t ZJ

, 2
t

t

t

t DA

t

Q

t WS
t Q
t EX~
EX -R
EX-fl

PARt-l
TEMPSi-l
, FlU.
,WS
·
, FilL
, FILL
PAR
t
A
CON}-8, WSt8
, A
, ~7
, DA
, WSt6
, PAR+l
t
WS..,..7
, DAf-l
, WS+7
, FILL
, WS+8
, FILL
, FILL
CON+9
A
, 128
, MA~ .

, SET RP

$
$
$

.$

$
, MASK our
, WITH EXT.

$

$
$
$
$

$
.$

$
$
$

$

$

C.

Timing
Depending on number of pieces of data and arrangement " the timing will vary
oonsiderably. For 77768 pieces of data it will be approximately 2 minutes.

ITEM NO,

OPERATION
TV

TAG

,
•
,
,

lB
1
2
3
4

• 5
t
6
7
t
8
9
t
RL
1

• SP
, AT
, 0
• SP
• SA
t
TU
TU
RS
t
MJ
• RP
t
TP
TP

2"
• 3
• 4
I
5
, 6,
7

•
,
,
"

, 8

,

,

9
10

t

11

,

12
13
I
, 14
t CON
1
, 2
, 3
, 4
5
t

6
I

,
,
,

7
8
9

10
11

12
, . 13
• 14
15
, 16
17
18
19
t
t
ER
, 1

t

'1

t
I
I

,

•,
,

RP3
TP
RA
RP3
TP
RA
RJ
MJ
TU ,
RJ
TU
MJ
B
B
B20

• B
B
, B
B40
B37
• TM
TP
, TP
, TJ
B
t B
• B
B
, TP
MJ
, MJ
"B·
, TP
, MJ

•
,
,
,
•

U ADDRESS
MA+33
CONt16
TEMP5t7
FILL
TEMPS+7
CONt-5

, A
t

, lBi3

TEMPSt3
0 '

• FILL
, FILL
CONti7
• 128
, FIll.
t
RLT4
, 128
, TEMPS i-l38
RL-r7
RLt9 .
• 0
I
TEMPStS
I
RLi"9
I
RL+5
0
0
0
t
12120
1

• FILL

,•

, SET RP

0

•

t
t

•
t

t

,
I

•
,

,
{

PARt4
FILL
, FILL

•

• BRING
• DATA

INDEX A ,$
$
IN
$

• BRING IN 128
, REL. LOG
, STORE TRUE
, VALUES ON MD

11
t
"

,FILL
RL+5
RL-ri 1 ,.
0

$

•

LOOP EXIT

$

$
$

$

..

'-

:~

.. .... ,.~

$
$
$
" ,$
~ " .$. . '

$
$,
" $
$

$

,
:;:

$
$
$
$
$
$
$
$

,Q
, ERROR

$
$
$
$
$
$
$
$
$
$
$
$

i'

<5

• 0

CLEAR

TEMPSi9
CONii9
RLT8
FILL
CON-jl4
RLTI0 ·
RL-r3
RL-H>
RLTo
RLf6
FILL
77777
2
31245
"0
1
30000
'.' 0 '
77777
0
TEMPSi137

$

•, A
MAt14
177
27777
• 200 .

• FILL'
0

$

$
$

MAt32

TEMPS~
I

$
$
$

17
MST32
TEMPS-f6

• RL1"2
, FILL
TEMPSt137

717"77': '.

0
,
0
, CONtl8
'0
0'
200
" CON+2

()

A

·0

;0,

$
,SET NI
• sroRE JUMP our

•

A
t

•

COMMENTS

V ADDRESS
CONfi6
0

, TO ALARM EX IT

$

EM NO.

OPERATION

TAG
1
2

,•

•
•
,
,

,3
4
5
, 6
, 7"
8
9
, 10

• 29
30
31
• 32
33
~; 34
35
36
t
37

,

38

t

,
,
,
,
,
,

39
40
41
BL
1
2
3
4
5

6
7
, 8
9
10

,11
, 12

rut

• CON-t4
PART 1
, PARtl
, CON-tll
, PARt2
t
TEMPSt6
, CONt12
, MA1"1
, CON+10
, CONfll
, FILL
, 4095
, FILL
• CONrl3
t
Q
• MAT11
• FILL
, CON+7
, MA+17
• MA-t"17
, MA-B3
, 0 "
t
MAiU
FILL
t CON+6 "
MATtI
t
MA'"t24
t
MA:tll
• CONt6 ~
, MAt27

IJ

• TEMPSi5

AT
TU
TU
RA

,

• TV

, TP
, TP

,TV
, TP
, TP
, TP
t
RP2

,11
, 12
, 13
, 14
15
, 16
, 17
, 18
, 19
, 20
t
21
, 22
, 23
24
t
25
26
t
27
, 28

U ADDRESS

• TJ
, TP

S5
t

'

,

,

AT
0
EJ

• TP
• TU
t

•

•
•
,
t

,

RA

MJ
TP
0

EJ
LQ
TU
TV
TP

RP3
• TP
, RA
• IJ
t TU
t TU
t TP
TU

,TV
t

t
t

RJ
TP
TP

,ZJ
• TU
• TU

,TV

• SJ

,RS
, RJ

,

•

RA
IJ

, TU
, MJ

'

, 128
t TEMPST9
• MA+33
TEMPSr3
RL-r3
t DA
t DAtI
, TEMPSi-2
, PARtI
. , RL-r14
, CON+15
t
PARt4
, BLt-3
• TEMPS1-2

• A
• A
, BLt-7
, TEMPSt-3
• RI::r14
, BL+l
, - TEMPSt3
, CON-rS
, 0

V ADDRESS

COMMENTS

i

TEMPS-+il.
CON-r10
CONii1
CON-j-3
MAt33
TEMPSi3
TEMPS t5
MAi27
, MA+l1 ,
, MAti3
, A
t

•
•
,
,
,
,

$
$
$
$
$
$
$
$
,1ST VALUE TO A $
$
• TEST FOR
$
• LARGEST VALUE
$
$
$
$
t
E ,UAL SENTINEL $
$
.,
$
, SET TJ
$
$
$
$
$
• 'EQUAL FILLER
SHIFT TO V
$
• STORE REL. LOC $
$
• WAD INDEX A
127 TO INDEX B

,

• ER
t
MA-r14
, A
17
t
MAt17
, FILL
, MA~23
t
MA't11 ·• MAt13
, CONt-3

• MAt 11 "
• MA/24
FILL

• ill '
25 ·
t
FILL
• MAt29
, FILL
CONi4

, SET EQUAL TO FIllER
INDE~ B;~EQUAL O( 127)

MAt 9
MA/34
• FILL , CONt14
MA;-7
MAt32
,RL
RL,1
RL'1"'4
ru:t-7
t
t ' RL "
, TEMPSi-3
t
A
• EXIT
t
RL't"4
t ' RLrl
, RLi'7
_. BL+a
,
, A '
, RL '
• CONi3
, BLTI

•

t

• BLi-1

, EXIT

$

$

srORE REL WC ON MD
INDEX k EQUAL 0

"

'"
t ·

t
9 TO INDEX A
, PAR TO A
• EQUAL 0

-

$

$

,
t

$

$
$
$
$
$
$
$
$
$
$
$
$
$
$

, CHECK FOR LAST PAR. , CLEAR INDX A
$

$
$

,
t
t

$

INDEX A EQUAL 0(9)

f TO

EXIT

$
$

$



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