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September 1969

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Document:	PDP-8 Floating-Point System Programmers Reference Manual
Order Number:	DEC-08-YQYB-D
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Pages:	74
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PDP-8
FLOATING-POINT SYSTEM
PROGRAMMER'S REFERENCE MANUAL

For additional copies of this document, order No. DEC-08-YQYB-D from Program
Library, Digital Equipment Corporation, Maynard, Mass. 01754

DIGITAL

EQUIPMENT

Price $2.00

CORPORATION • MAYNARD, MASSACHUSETTS

1st Printing August 1965
2nd Printing January 1967
3rd Printing June 1967
4th Printing November 1967
5th Printing Revised February 1968
6th Printing Revised July 1968
7th Printing January 1969
8th Printing May 1969
9th Printing September 1969

The following are registered trademarks of Digital
Equipment Corporation, Maynard, Massachusetts:
DEC
FLIP CHIP
DIGITAL

PDP
FOCAL
COMPUTER LAB

PREFACE

This manual supplies a detailed description of fl_oating-point software for the PDP-8
family of computers.
The software consists of individual routines which perform basic arithmetic and
trigonometric functions on data stored in floating-point format and foci Iitate data
readin, decimal-binary conversion, conversion to floating-point format, and
writeout.

Four programs obtainable from Digital Equipment Corporation provide

various combinations of these functions; I istings, entry points, and order numbers
for the programs are supplied in this manual.
Automatic calling of user subroutines can be incorporated in the existing routines
with minor coding modifications.

iii

CONTENTS
Chapter

Page
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-1

FLOATING-POINT REPRESENTATION ................................... .

2-1

Arithmetic ..•...................................................•..

2-4

Basic Floating-Point Commands ...................................... .

2-4

Interpreter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-4

Floating-Point Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-4

FLOATING-POI NT INPUT/OUTPUT ..................................... .

3-1

Floating-Point Input

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

3-1

Flags .. . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-1

Rubout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . • . • . . . . . . • . . . . . •

3-3

Floating-Point Output . . . . • . . . . . . . • • . • • . . . • • • • . . . . . . . . . . . . . . . . . . . • . . .

3-4

Entry . . . . . . . . • . • . . . . . . • . . • • . . . • . . • . . . . • • . . . . . . . . . . . . . . . . . . . . . . .

3-4

Program Example

. . . . . . . . . . . . . . . . . •. . . . . . •. •. . . . . . . . . . . . . . . . . . . .

3-4

The Basic Package . . . . • . . . . . . . . . . . . . . . • . • . . • . . . . . . . . . . . • . . . . . • . . . . . .

3-6

Subroutines . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . .

3-6

Description of Basic Function . . . . . . • • . . • . . . • . . . . . . . . • . . . . • . . . . . . . . . . . .

3-7

Addition

. . . . •. •. . . . . . . •. . •. . . . ••••. . •. . . . . . . . . . . . . . . . . . . . . . . . .

3-7

Subtraction . . . . . . • . • . . . . . • . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-7

Multiplication

. . . .•. . . . . . . . . . . . . . . .•. . •. . . . . .. . . . . . .. . .. . .. . . . .

3-7

. .. . . . . .. .. . . . . . . . . . . .. . .•. . . . . . . . . . . . . .. . . . . . .. .. . . . .

3-7

Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . • . . . . . . . . . . . . . . . . . . . . .

3-8

Square Root . . . . . . • . . . . . . . . . . . . . . • . . . . . . . . . . . . • . . . . . . . . . . . . . . . . .

3-8

Error Flag

3-8

Division

. . . . •••. •. . •. . . . . . .•. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .

Summary of Basic Package

. .. . . .. . . . . . . .. . . . .. . .•. . . . . . .. . . . . . .. . . . . .

3-9

Entry Points . . . . . . • • . . • . • . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . .

3-9

Flags . . . . . . . . . . . . . . . . . . . . . . . • • . • . . . . . . . • . . . . . . . . . • . . . . • . . . . . . .

3-9

Commands . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-9

Storage

. . . . . . •. •. . . . •. . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . .

3-10

Fixed to Floating/Floating to Fixed Point . • . . . . . . . . • . • . . • . . . . . . . . . . . . . .

3-10

Extended Floating-Point Package

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

3-11

Sine . . . . . . • . • • • • • . . •. . . . . • • • . . . . • • . . . • . . . . . . . . . . . . . . . . . • . . . . • .

3-12

CONTENTS (continued)
Chapter
3 (cont)

Cosine ........•.•.............................................

3-12

Arc Tangent .................................................. .

3-12

Logarithm .................................................... .

3-13

..............................................
Output Controller ..............................................

3-14

Floating Point Package Versions ................................. , . . . .

3-16

Floating Exponent

3-15

PROGRAM LISTINGS •...........••.•.•..••.............•..••....•......

4-1

Floating Point Arithmetic Interpreter . . . . • . . • . . . . . • . . . . . . . . . • . . . • . • . • . .

4-1

Floating Point 1/0 Routines..........................................

4-14

Double Precision Decimal-Binary . . • • . • • • • • • . • . • • . • • • . • • • . • • . • • • • . • • . •

4-15

Input and Conversion............................................

4-15

Floating Output 11 E11 Format......................................

4-17

F looting Point Input.............................................

4-19

Floating Point Package • • . . • • • • . • • • . . • • . . • . • • • • . • • • . • • • • • . • • . • • • • • • . .

4-23

Floating Point Exponential . . . • . . • . • . . . • • . • • . • . • • . . • . . • . . . • • . • • • • •

4-23

Negation Subroutine • • . • . • . . • • . • . • • • • . • • • • • • • • . . . • • • • • • • • • . • • • . .

4-24

Floating Point Arc Tangent.......................................

4-25

Floating Logarithm..............................................

4-26

tJ..........................

4-27

F looting Point Cosine . . • • . • . • • • . . . • • • • • • . . • • • • • . . • . . . . • • • • . . • • • .

4-28

Floating Output Program . . . • . . . . • . . . . • • • . • • . • . • • . • • . • • • • • • • • . . • • . • . • •

4-31

Floating Point Sine ..................

CHAPTER 1
INTRODUCTION

The Floating-Point System enables the programmer to concentrate on the logic of his computation
rather than on decimal points. The system maintains a constant number of significant digits throughout
the computation, thereby enhancing the accuracy of the res~lt.
Floating-point notation is particularly useful for computations involving numerous multiplications and
divisions where magnitudes are Iikely to vary widely and where only crude predictions can be made as to
the amount of variation involved. The main advantage of the Floating-Point System is derived
from the ability to store very large or very small numbers by storing only the significant digits together
with the exponent for that number.

In an integral or fractional fixed-point machine, the programmer

must either include all of the O's between the significant digits and the decimal point (and in so doing
loose considerable accuracy), or account for the point in each step of his programming.
The Floating-Point System is constructed as a self-contained package which includes its own input,
arithmetic, and output routines.

It al lows the programmer to use floating-point arithmetic without having

to construct his own arithmetic subroutines.

For example, the polynomial:

y = AX + BX + ex + D
may be programmed as follows (the variables X and Y, and the parameters A, B, C, and D are stored in
registers of the same name):

JMS
FGET
FMPY
FADD
FMPY
FADD
FMPY
FADD
FPUT
FEXT

I 7
A
X
B
X
C
X
D
Y

/ENTER FLOATING PACKAGE
/LOAD PSEUDO AC
/MULTIPLY
/ADD
/MULTIPLY
/ADD
/MULTIPLY
/ADD
/STORE
/EXIT FLOATING PACKAGE

1-1

CHAPTER

FLOATING- PO I NT. REP RESE NTATI 0 N

A floating-point number consists of a mantissa and an exponent.

For example, the decimal number 12 may

be represented as:
2

l 200 . 0 . l 0 -

l 20 . 00 . l 0 - l
0
12.000· l o
l . 2000. l 0 l
2
. 12000· l o
etc.
where the exponents are the numbers - 2, -1, 0, etc.
Since the PDP-8 is a binary machine, floating-point numbers are stored as floating-point binary internally.
For example, the binary number 110 (6 decimal) may be represented as:

l l 000 . 0 . 2 -

(24· l/4 = 6)

l l 00 . 00 . 2 - l

( 12. l /2 = 6)

110.000.2°
1
11 . 0000. 2

(6·1 =6)

l. lOOOO·l
3
.110000·2

(3·2=6)
(3/2·4 = 6)
(3/4·8=6)

etc.
Notice that the binary exponent is always a signed integer.

The PDP-8 Floating-Point System uses the

convention:
1/2 <

I MANTISSA I < l.

When this is true, the word is said to be normalized.
The value of the number is then:
MANTISSA·lXPONENT
where the MANTISSA is a signed quantity.
retained.

The result of this convention is that more significant bits are

For example, the number . l 0 (decimal) is equal to:
2-1

Io.oo o11 oo 1 1oo I 11o o11 oo 1 1oo I 11 o o11 oo 1 1oo 11 o . . . .
in binary.
When this word is stored in two 12-bit words (24 bits), the leading O's are nonsignificant and only 20 bits
of significance are maintained.
3
2- . I

If the number is rewritten as:

o. 11 oo 1 1oo 11 o I o11 oo 1 1oo 11 o I o11 oo 1 1oo 11 o . . ..

and the mantissa stored in two 12-bit words, 23 bits of significance are maintained.
The exponent is stored in a third word making a total of three words for storage.
sign of exponent

binary exponent 2's complement
signed quantity

sign of mantissa

+>I

high order mantissa word
low order mantissa word

The number .1 (decimal) would be stored as:
111

1 11

o I o11 oo 11 oo 11 o I ol 1oo 11 oo 11 o

11 1 1 1

or written in octal:
7775 3146 3146
The address of this number would be considered 2146 if it were stored as follows:
2146/7775
2147/3146
2150/3146

Thenumber-.1 (decimal)would be -.063146314(octal)which is0.000 110 011 001100110 011 011 100
(binary).
3
Normalized, this becomes: (2- ) ·(0. ll 001100110 011 001100110)

Complemented and incremented to become thEi, negative 2's complement
3
this becomes:
(2- ) • (l.00 110 011 001 100 110 011 010)
2
8
3
which is:
(2- ) ·(4
6
3
l 4 6 3 2 )

2-2

This number would be stored (within octal) as:
7775

exponent of -3

463 l

high order mantissa word

4632

low order mantissa word

Since the mantissa is greater (in magnitude) than 1/2 and less than l, its binary point is considered to
be between bit 0 and bit 1 of the high order mantissa word.
Further examples:
12 (decimal)
4
1100. = (2 ) (0.11000000000000000000000)
would be stored as (written in octal):
0004
3000
0000
Octal

Decimal

-1

0001

6000

0000

-10

-8

0004

6000

0000

2000

0000

0002

3000

0000

0004

3000

0000

.25

7777

2000

0000

14.26074475

12.3456

0004

3054

1711

-14.26074475

12.3456

0004

4723

6067

Floating Binary

Convert the decimal number l . 6 to floating-binary form for storage.
An easy method to convert a decimal fraction to an octal fraction is i Ilustrated below:

.6
x

1 .610 = l .463146318

4).8
x 8

= 1 . l 00 l l 001 l 0011 00 l 10011 00 l

6'):4

= (2 1) (0 . l 100 l l 0011 0011 00 l 100 l l 0)

x 8
3~

= 0001

2-3

x 8

lJ-:6

3146

8
4}:'8

3146

6,--:-:4
8

3"'):2
8
1).6

ARITHMETIC
Since floating-point numbers are stored in a three-register format, the floating-point system uses a 11 psuedo 11
floating accumulator (FAC) which consists of three registers in the floating-point package: 44, 45, and 46.
Register 44 contains the exponent; 45 and 46 contain the high and low order parts of the mantissa, respectively.

BASIC FLOATING-POINT COMMANDS
The basic floating-point commands include the fol lowing:
load floating accumulator
store floating accumulator
add to floating accumulator
subtract from floating accumulator
multiply by floating accumulator
divide into floating accumulator
normalize floating accumulator
Al I arithmetic operations are cal led through an interpreter. The command codes have a format that is
almost identical to the format of the memory reference instruction, namely:

I l Iz I
OP

ADDRESS

where the op code is from 000 to 111 or 0

- 7 .
8
INTERPRETER

The interpreter contains, at al I times, the address of the memory location containing the next pseudo instruction to be executed.

This is initially stored when the program enters the interpreter using a JMS

2-4

instruction.

When the interpreter encounters an instruction with an op code of 0 and with bits 8-11 of

the pseudo instruction equal to 0, it exits to the next memory location.

FLOATING-POI NT INSTRUCTIONS
The floating-point instructions are:
Mnemonic

Effect

FADD

Floating Addition
Add the contents of the effective address
to the floating accumulator.

FSUB

Floating Subtract
Subtract the contents of the effective address
from the floating accumu later.

FMPY

Floating Multiply
Multiply the floating accumulator by the
contents of the effective address.

FDIV

Floating Divide
Divide the floating accumulator by the
contents of the effecitve address.

FGET

Floating Get
Load the floating accumulator with the
contents of the effective address.

FPUT

Floating Put
Store the contents of the floating accumulator
at the locations specified by the effective
address. The contents of the floating accumulator are unchanged.

FNOR

Floating Normalize
Normalize the contents of the floating
accumu later.

is decoded as fol lows:

Op Code

Bits 8-11 = 0000

Floating Exit
Return control to fol lowing instruction

= 0001

Floating Square
Square the contents of the floating accumulator

2-5

= 0010

Floating Square Root
Take the root of the absolute value of the
floating accumulator

= 0011-1111

Expandable commands

This may be summarized:
FADD

Y; 1000; C(FAC) + C(Y) ~ C(FAC)

FSUB

Y; 2000; C(FAC) - C(Y) ~ C(FAC)

FMPY

Y; 3000; C(FAC) x C(Y) ~ C(FAC)

FDIV

Y; 4000; C(FAC) -=:- C(Y) ~

FGET

Y; 5000; C(Y) ~ C(F AC)

FPUT

Y; 6000; C(FAC) ~ C(Y)

FNOR

; 7000; C(FAC) normalized ~ C(FAC)

FEXT

; 0000; exit from interpreter to instruction following this command

Result is

C(FAC)

C(Y)
unchanged

SQUARE ; 0001; C(FAC) 2 ~ C(FAC)
2
SQROOT; 0002; C(FAC) l / ~ C(FAC)
The assembler recognizes all of these mnemonics except for SQUARE and SQROOT which may be defined
as:
SQUARE=OOOl
SQROOT=0002
The floating-point interpreter is entered with an effective JMS 5600.
For example:
SQROOT=0002
*7
5600
*200
JMSl7
FGET A
SQROOT
FPUT I B
FEXT
HLT
0003
A,
2000
0000
300
B,

200/
201/
202/
203/
204/
205/
206/
207/
210/
211/

4407
5206
0002
6611
0000
7402
0003
2000
0000
0300

2-6

When this program is started at 0200, it wi 11 halt at location 205. The state of the machine wi 11 be:

46/

0002
2000
0000

206/
207/
210/

0003
2000
0000

300/
301/
302/

0002
2000
0000

answer stored here

44/

45/

floating accumulator contains
2 •0 I i. e • I ( 4 •0) 1/2

2-7

CHAPTER 3
FLOATING-POINT INPUT/OUTPUT

FLOA Tl NG-POI NT INPUT
The basic floating-point package contains an input routine to read characters from the 33 ASR keyboard.
Numbers are read in in decimal and converted to the internal floating-point binary format.

Input format

is floating decimal. The number 726.7 may be read in in any of the fol lowing forms:

726.7
.7267E3
.7267E+03
+7267E-l
etc.
Input is terminated when a character is typed that is not a part of this format.

The conversion of 11 12.0. 11

wou Id be terminated on the second 11 • 11 and the binary number:
000000000100

(octal 0004)

011000000000

(octal 3000)

000000000000

(octal 0000)

would be in the floating-point accumulator upon completion of the conversion.

There are several flags associated with the input routine that are useful to the programmer.
0056

This register is a switch that has th~ fol lowing meaning:
If C(56) = 0, do not type a line-feed after a carriage-return was read.
If C(56) = 7777, type a line-feed when a carriage-return is inputted.
This switch is initially set to 7777.

0057

This register contains the character that terminated the input conversion.

0060

This register contains 0000 if no input conversion was made; i.e., a
space or other terminator was initially typed.

3-1

The input routine is entered with an effective JMS 7400.

It returns control to the instruction following

the cal Ii ng J MS upon receipt of a terminator. The floating accumulator contains the input number in
norm a Iized floating-bi nary.

di cates whether or not there was a valid input.
For example:
*5
7400
*7
5600
*200
JMS 15
JMS I 7
FPUT A
FEXT
JMSl5
JMS 17
FPUT B
FEXT
HLT
A, 0
0
0
B, 0
0
0
$

/INPUT ROUT! NE
/CALL FLOATING POI NT

When this program is started at 0200 and the following is typed:
X2.0Y
The program will halt at location 0210, and A and B will contain

A, 0
B,

0
0
0002
2000
0000

and C(57) = 0331, the second TERMINATOR

The first input was considered a 0 because a terminator 11 X 11 wa~ inputted.

3-2

Th is program cou Id be written to ignore the non-numeric information as fol lows:

*5
7400

*7
5600
*200

JMSl5
TAD 60
SNA CLA
JMP .-3
JMSl7
FPUT A
FEXT
JMSl5
TAD 60
SNA CLA
JMP .-3
JMSl7
FPUT B
FEXT
HLT
/HALT

/CALL INPUT ROUTINE
/ANY VALID INPUT?
/NO - IGNORE

/YES
/STORE IT
/GET NEXT
/VALID?
/NO - IGNORE
/YES
/STORE IT

0
0
0

$
Register 57 may be used for integrating control characters into the input.

Rubout
There is one special input character, the rubout.

If it is struck before an input delimiter, the input rou-

tine is restarted and previous numbers deleted.
For example, assume the input routine has been entered.

::>

276 _g l T
a:::

The input routine would exit with l (decimal) in the floating accumulator or:
44/

0001

2000
0000

3-3

FLOATING-POI NT OUTPUT
The basic floating-point package contains an output routine.

Upon entry the contents of the floating ac-

cumulator are converted to floating-point decimal and typed out on the ASR 33 in the following format:
±0. XXXXXXXE±XX
For example, if the floating accumulator contained:

44/

0002
2000
0000

and the output routine were entered,
+0.2000000E+Ol
would be typed.

The output routine is entered by an effective JMS 7200. After outputting the contents of the floating accumulator, it returns control to the instruction fol lowing the calling JMS instruction. The contents of the
floating accumulator are lost. The floating-output routine has a flag or program switch in location 0055
on page 0.

If C(0055) does not equal 0, type a carriage-return/line-feed following each output. This location initially contains 7777.

Program Example
/SOLVE THE QUADRATIC EQUATION
/ AX2+BX+C=O FOR VALUES
/OF A, B, C.

TYPE OUT ROOTS

SQROOT=0002
S QUARE=OOOl
*5

7400
7200
5600

/POINTER TO INPUT ROUTINE
/POINTER TO OUTPUT ROUTINE
/POINTER TO INTERPRETER

*200
KCC
TLS
BEGIN,

JMSl5
JMSl7

/INPUT A
/ENTER INTERPRETER

3-4

TWO,

MINl,

TEMP,
A,

FMPY TWO
FPUT A
FEXT
JMSl5
JMSl7
FPUT B
FEXT
JMSl5
JMSl7
FMPY TWO
FMPY A
FPUT TEMP
FGET B
SQUARE
FSUB TEMP
SQROOT
FPUT TEMP
FGET B
FMPY MINl
FPUT B
FSUB TEMP
FDIV A
FEXT
JMSl6
JMSl7
FGET B
FADD TEMP
FDIV A
FEXT
JMSl6
JMP BEGIN
0002
2000
0000
0001
6000
0000
0
0
0
0
0
0
0
0
0
0
0
0

/2.0
/STORE 2.0·A
/INPUT B
/ENTER INTERPRETER
/STORE B
/INPUT C
/ENTER INTERPRETER
/MULTI PLY BY 2.
/MULTIPLY BY 2A
/4AC
/B SQUARED
/B SQUARED -4AC
/TAKE SQUARE ROOT
/STORE IT
/-1 • B = - B
/STORE
/-B-SQUARE ROOT
/ANSWER IN FAC
/OUTPUT IT
/ENTER INTERPRETER
/-B
/-B +SQUARE ROOT
/ANSWER IN FAC
/OUTPUT IT
/CONTINUE
/CONSTANT 2.0
/CONST ANT -1 . 0

$
Both the input-conversion routine and the output-conversion routine use a typeout subroutine that contains
the instructions:

3-5

TSF

JMP .-1
TLS
CLA
This means that the teleprinter flag must be set when these routines are entered or it must be in the process
of typing.

A TLS instruction can be put into the initialization section of a program.

THE BASIC PACKAGE

Subroutines
When the floating-point interpreter encounters a 0 op code, it further decodes bits 8-11.
equal 0, the interpreter exits.

If these bits

If the bits are nonzero, they are used in a table look-up to specify the

address of a subroutine. The called subroutine may use the floating-point interpreter, the input, or the
output, but it may not U:>e bits 8-11 to cal I another subroutine. The look-up table is on page 16 of the
interpreter listing.

For example, if the user wished to define a routine that negated the contents of the

floating accumulator, the fol lowing ~teps wou Id be taken:
On page 6 of the interpreter Iisting, there is a routine to negate the floating accumulator.
routine and has, as entry point, the address 6000.

It is a sub-

If the negate subroutine were to be cal led by 0010 in

the interpreter mode, the word 6000 wou Id be placed in address 6554 of the cal Iing table.

Input and out-

put could be called in the interpreter mode if 7400 were placed in 6555 (0011) and 7200 were placed in
6556 (0012).
NEGATE= 0010
INPUT
= 0011
OUTPUT = 0012
SQUARE = 0001
*7
5600
*200
KCC

TLS
JMS17
INPUT
SQUARE
NEGATE
OUTPUT
FEXT
HLT

/ENTER INTERPRETER
/CALL INPUT ROUTINE
/SQUARE IT
/CALL OUTPUT ROUTINE
/CALL OUTPUT ROUT! NE
/EXIT
/HALT

3-6

DESCRIPTION OF BASIC FUNCTION

Addition
Floating-point addition is carried out by first aligning the binary points of the two numbers.

This is ac-

complished by scaling the smaller number to the right. Then the mantissas are both scaled right once so
that overflow wi 11 not occur into the sign bit. A 2 1s complement addition of the mantissas is then made.
The result is normalized and control returns to the interpreter. This may be represented as:

Can operands be aligned?

•

Yes

Align Exponents
Add Mantissas
Normalize
Return to Interpreter

No
Put larger number in FAC

....
~,___ _ _ _ __,

Subtraction
Floating-point subtraction is accomplished by negating the operand, and then cal ling the addition subprogram.
Negate Operand
Cal I Addition

Multiplication
Floating-point multiplication is accomplished by adding the exponents together and then performing a
double-precision multiplication. The resu It is normalized and control returns to the interpreter.
Add Exponents
Multiply Mantissas carrying result to 35 bits
Normalize
Return to Interpreter

Division
Floating-point division is accomplished by subtracting the exponent of the divisor from the exponent of
the dividend.

The mantissa is divided and the result is normalized. Control returns to the interpreter.

3-7

Is divisor = O?

Yes

Subtract Exponents
Divide Mantissas
Normalize
Return to interpreter ._

+ 1 to error flag
Set resf It to highest possible

The square routine cal Is the multiplication routine internally.

Square Root
The square root is calculated using Newton's method in which an initial approximation is made and then
each succeeding approximation is calculated. The routine exits when two successive approximations are
equal to within the least significant bit of the mantissas.
Form first approximation, x , of ~
1
then:

N
X.+l = 1/2 (X. + -X )
I

•
I

I xi - xi+l I < 1east significant bit?

--~o Yesl
Return to interpreter

Error Flag
Division by 0 causes C(61) to be incremented by 1. The quotient is set to the highest positive number.
Attempting to extract the square root of a negative number causes C{6 l) to be incremented by 1.

The root of the absolute value is taken •
The contents of 61 are set to 0 at the beginning of each divide and square root operation.

3-8

SUMMARY OF BASIC PACKAGE

Entry Points
5600

Arithmetic Interpreter

7400

Floating Input

7200

Floating Output

NOTE: Both the input and the output routines require that register 7 contains
the interpreter entry point: 5600.

If I 0, type carriage-return/line-feed after output.

If I 0, follow each input carriage-return by a line-feed.

Contains the input terminating character.

Equals 0 if no valid input.

Is nonzero if (a) divide by 0 or (b} square root of a negative number.

Commands
FADD

1000

Floating Add

FSUB

2000

Floating Subtract

FMPY

3000

Floating Multiply

FDIV

4000

Floating Divide

FGET

5000

Floating Get

FPUT

6000

Floating Put

FNOR

7000

Floating Normalize

FEXT

0000

Floating Exit

SQUARE

0001

Square

SQROOT

0002

Square Root

0003
Expandable
0017

3-9

Storage
The floating accumu later is in registers:
44 - Exponent
45 - High Order Mantissa

46 - Low Order Mantissa
The basic floating-point package ( DEC-08-YQ lA-PB) uses memory locations:
5-7; 40-61; 5600-7577

FIXED TO FLOATING/FLOATING TO FIXED
Since the floating-point package stores numbers in the following format:

II
Signed Exponent

2 1s Complement Signed Mantisa

l1mpl ied Binary Point
and since the exponent indicates where the real exponent is, this information may be used to either convert a floating-point number to fixed point or to convert ·a fixed-point number to floating point.
For example, assume that there is an integer in the accumulator that is less in magnitude than 2047. To
float this number, the following sequence of steps may be employed:

DCA45
DCA 46
TAD Cl3
DCA44
JMSl7
FNOR
FEXT

/PUT INTO HIGH-ORDER MANTISSA
/PUT 0 INTO LOW-ORDER MANTISSA
/11 (10} INTO
/EXPONENT
/CALL INTERPRETER
/NORMALIZE
/LEAVE INTERPRETER

Cl3,

0013

/11 (DECIMAL)

At point C, we have set the binary point of the integer to the right end of the high order mantissa word,
or eleven (decimal) locations to the right of the implicit binary point.

To float this number, the floating accumulator is scaled right until the exponent contains the location of
the desired binary point. To fix the floating accumu later as an 11-bit signed integer, the fol lowing sequence of coding may be employed:

3-lO

DONE,

CLA
TAD 44
SZA SMA
JMP .+3
CLA
JMP DONE+l
TAD Ml 3
SNA
JMP DONE
SMA
JMP ERROR
DCA44
CLL
TAD 45
SPA
CML
RAR
DCA 45
ISZ 44
JMP 00
TAD 45

/NO: SET Bl NARY POI NT AT
/11 ( l 0) PLACES TO RIG HT OF CUR RE NT POI NT
/IT IS ALREADY THERE: ALL DONE
/TEST TO SEE IF IT IS TOO LARGE
/YES: NUMBER >2** l l
/NO: SET SCALE COUNT
/0 TO C(L)
/FETCH MANTISSA
/IS IT <0?
/YES: PUT A I IN LEFT BIT
/SCALE RIGHT
/RESTORE IT
/TEST IF SHIFTED ENOUGH
/NO: CONTINUE
/ANSWER IN C(AC)

Ml3,

-13

/-11 (DECIMAL)

GO,

/FETCH EXPONENT
/IS THE NUMBER <l?
/NO:
/YES: FIX IT TO 0

This may be coded as a subroutine.

EXTENDED FLOATING-POI NT PACKAGE
The extended floating-point package contains the following additional commands:
0003

Floating Sine
Take the sine of the angle in the floating accumulator (considered to be in
radians) and leave the result in the floating accumulator.

0004

Floating Cosine
Take the cosine of the angle in the floating accumulator (considered to be
in radians) and leave the result in the floating accumulator.

0005

Floating Arc Tangent
Take the arc tangent of the number in the floating accumulator and leave
the result (in radians) in the floating accumulator.

0006

Floating Exponent
Raise e to the C(FAC) power. Leave the result in the floating accumulator.

,0007

Floating Logarithm
Take the natural logarithm of the absolute value of the number in the floating
accumu Iator.
3-11

Sine
The sine routine uses the fol lowing identities:
SI N(-X)=-SI N(X)
SI N(X)=SI N(21T N+F)=SI N(F)
where O<F<2 1T and N is an integer:
SIN( 1T-F)=-SI N(F)
Using these identities, F is reduced to the range -1T/2<F<'o/2.
If Y = 2F/1T so that -1 <F<l, then:

SIN(X)=(C/+Cl +C F
5

+Cl 7+C9 F9)

where:

c 1 = i .57079631847
c3 = -o. 64596371106
c

= +o. 07968967928

c7 = -o. 0046737 6557
c9 = +o .00015148419
The sine subroutine is val id over the range:
-21T .2047<X<21T .2047

Cosine
The cosine routine uses the identity:
COS(X)=SI N(1T /2-X)
It then uses the SINE routine.

Arc Tangent
The arc tangent routine uses the fol lowing identities:
ARCTAN(-X)=-ARCTAN(X)
IF X>, l; then ARCTAN(X)=lT/2-ARCTAN(l/X)
FOR O<X<l,

3-12

where:

AO = +O. 6402481953
A = +O . 42299081 44
1
A = +O. 0264694361
2
B = +0.6402487022
0

B =+0.6363779373
1

= +O . 11 08328778

The result is in the range:

-n /2<ARCTAN(X)<n/2

-c.o<X<

Logarithm
The logarithm routine uses the identities:
For X<l;

LOG(X)=LOG(2N · F) (l <F<2)
=NLOG(2)+LOG(F)

LOG(l +Y)=

C=l
where:

A = +0.9999964239
1
A
A

2
3

= -0.4998741238
= +0. 331 7990258

A = +0.2407338084
4
~ = +O. 1676540711

A = -0. 0953293897
6

3-13

~ = +O. 0360884937

= -0. 006455 3442

for:
O<X<l, the identity:
LOG(X)=-LOG(l/X) is used.

Floating Exponent
The exponent routine uses the identity for X)(),

where N is an integer and <F<l

i =l +--2_F_ __
A-F+BF 2-

_c__
D+F

where:
A = +9. 95459578
B = +O. 03465735903

c = +617. 97226053
D = +87 . 417 497202
Log e=l .4426950409
2

If X<O
e

-x

Example, input A, B, and output:

Y = LOG(COS(A/B)+/'A-B)
SQR OOT =0002
COS==0004
LOG=0007

/DEFINITIONS TO ASSEMBLER

*5
7400
7200
5000
/USES EXTENDED INTERPRETER
3-14

*200
KCC
TLS
BEGIN,

JMS I 5
JMSl7
FPUT A
FEXT
JMSl5
JMSl7
FPUT B
FMPY A
SQROOT
FPUT TEMP
FGET A
FDIV B

cos

FADD TEMP
LOG
FEXT
JMSl6
JMP BEGIN
0

/INPUT A
/ENTER INTERPRETER
/STORE A
/EXIT
/INPUT B
/ENTER INTERPRETER
/STORE B
/A-B
/EXTRACT ROOT
/STORE IT
/LOAD FAC WITH A
/DIVIDE BY B
/TAKE COSINE
/ADD
/TAKE LOG.
/OUTPUT ANSWER

0
0

TEMP,

0
0
0
0
0

$
Output Controller
There is an additional routine avai Iable that formats floating-point output. It is avai Iable with both the
basic floating-point package and the extended package.
The control Ier routine requires two parameters for output formatting.

It is cal led by an effective JMS 7200.

At this point:
C(62) ==total number of digits to be outputted. If C(62)==0, output in E format.
C(AC) ==number of digits to the right of the decimal point. If it equals 0, do
not type a 11 • 11 •
If the number in the floating accumulator is larger than the field width allows,
sign is typed and leading O's are suppressed.
Example: If the contents of the floating accumulator are 678.234 (decimal).

3-15

X's 11 will be typed. The

C(62)

C(AC)

3
4
4
5
6
3
2
0

0
0
1
2
2
2
0
1

Output
+ 678
+ 678
+ 678 .2
+ 678 .23
+ 678.23
+ 678.
+XX
+ 0. 678234E +0.3

FLOAT! NG POI NT PACKAGE VERSIONS
Four versions of the floating-point package are avai Iable:
DEC-08-YQlA-PB
This is the basic floating-point package.
instructions.

It consists of the input/output package and the basic arithmetic

lh core limits are:

5-7; 40·-6 l; 5600-7577

DEC-08-YQ2A-PB
This is the basic floating-point package with the output controller.

Its limits are:

7; 40-62; 5400-7577
The output control !er does not type a carriage-return/I ine-feed after output and, hence, the programmer
must provide his own routine to do so.

Because of the way in which the typeout routine in the floating-

point packages are constructed, the user must construct similar typeout routines in order to avoid timing
errors in the teleprinter.

In other words, the floating-point package uses a routine sim i Iar to:

TSF

JMP . -1
TLS
to do its typing.

The user must use a similar routine, i.e., one that waits for the teleprinter flag to be

set before executing the TLS instruction.

DEC-08-YQ3A-PB
This is the basic floating-point package with the extended functions.
mands are provided for input and output.

In addition, two interpretive com-

The additional interpretive commands are:

3-16

SINE
COSINE
ARCTANGENT
EXPONENTIAL
LOG
INPUT
OUTPUT

3
4
5
6
7
13
14

Its core limits are:
7; 40-61; 4757-7577
Using this package, the routine on page 3-14 and 3-15 for calculating:
Y=LOG(COS(A/B)+ fA':B) may be rewritten as:
SQROOT=2
COS=4
LOG=7
INPUT=l3
OUTPUT=l 4
*7
5600
*200
KCC

TLS
BEGIN,

A,
B,
TEMP,

JMS 17
/CALL INTERPRETER
INPUT
/READ A
FPUT A
/STORE IT
INPUT
/READ B
FPUT B
FMPY A
/A·B
SQROOT
FPUT TEMP /(A· B)** .5
FGET A
FDIV B
FCOS
FADD TEMP
FLOG
OUTPUT
FEXT
JMP BEGIN
0
0

0
0
0
0
0
0
0

$
3-17

DEC-08-YQ4A-PB
This is the basic package, the output controller, and the extended functions. This package does not
have the interpretive 1/0 commands of input and output. Its core limits are:

7; 40-62; 4557-7577

3-18

CHAPTER 4
PROGRAM

0040
0041
0042
0043
0044
0045
0046
0047
0050
0051
0052
0053
0054

0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000

0061

0000

5600
5601
5602
5603
5604
5605
5606
5607
5610
5611
5612
5613
5614
5615
5616
5617
5620
5621
5622
5623
5624
5625
5626
5627
5630
5631
5632

0000
7300
3043
3047
1600
3253
1253
0263
7650
5214
1261
0200
3256
1262
0253
1256
3256
1264
0253
7650
5227
1656
3256
2200
1656
3040
1256

LISTINGS

/FLOATING POINT ARITHMETIC INTERPRETER
*40
/OPERAND STORAGE
EXl I
0
AClH,
0
AClL,
0
OVERl I
0
EXP,
/F.A.
0
HORD,
0
LORD,
0
OVER2,
0
EXPl I
0
QUOL,
0
0
FPACl I
0
0
*61
/ARITHMETIC ERROR FLAG
FLAG,
0
*5600
FPNT I

LOOPOl,

0
CLA CLL
DCA OVERl
DCA OVER2
TAD I FPNT
DCA JUMP
TAD JUMP
AND PAGENO
SNA CLA
JMP .+3
TAD MASK5
AND FPNT
DCA ADDR
TAD MASK7
AND JUMP
TAD ADDR
DCA ADDR
TAD INDRCT
AND JUMP
SNA CLA
JMP LOOPOl
TAD I ADDR
DCA ADDR
ISZ FPNT
TAD I ADDR
DAC EXl
TAD ADDR

/GET NEXT INSTRUCTION

/GET PAGE BIT
/PAGE ZERO?
/YES
/NO
/C(FPNT)0-4 CONTAINS PAGE BITS
/GET 7 BIT ADDRESS

/INDIRECT BIT=l?

/NO-GO ON
/YES DEFER

/EXPONENT

4-l

5633
5634
5635
5636
5637
5640
5641
5642
5643
5644
5645
5646
5647
5650
5651
5652
5653
5654
5655
5656
5657
5660
5661
5662
5663
5664
5665
5666
5667
5670
5671
5672
5673
5674
5675
5676
5677
5700
5701
5702
5703
5704
5705
5706
5707
5710
5711
5712
5713
5714
5715
5716
5717
5720

3257
2257
1657
3041
2257
1657
3042
1253
7106
7006
0260
1265
3254
1654
3254
5654
0000
0000
0000
0000
0000
0017
7600
0177
0200
0400
5666
5742
5716
5737
5761
6305
5676
5705
5773
1040
3044
l 041
3045
1042
3046
5201
l 044
3656
2256
1045
3656
2256
1046
3656
5201
4771
5201
4772

JUMP,
JUMP2,
G02,
ADDR,
SAVE,
MASK3,
MASK5,
MASK7,
PAGENO,
INDRCT I
TABLE,

FLGT,

FLPT I

FLAD,

DCA SAVE
ISZ SAVE
TAD I SAVE
DCA AClH
ISZ SAVE
TAD I SAVE
DAC AClL
TAD JUMP
CLL RTL
RTL
AND MASK3
TAD TABLE
DCA JUMP2
TAD I JUMP2
DCA JUMP2
JMP I JUMP2
0
0
0
0
0
0017
7600
0177
0200
0400
.+1
EXIT
FLAD
FLSU
FLMY
FLDV
FLGT
FLPT
NORF
TAD EXl
DCA EXP
TAD AClH
DCA HORD
TADAClL
DCA LORD
JMP FPNT+l
TAD EXP
DCA I ADDR
ISZ ADDR
TAD HORD
DCA I ADDR
ISZ ADDR
TAD LORD
DCA I ADDR
JMP FPNT+l
JMS I ALGN
JMP FPNT+l
JMS I UNORM

/HIGH ORDER MANTISSA

/LOW ORDER MANTISSA

/GET BITS 0-2, IE OPCODE
/LOOKUP IN TABLE

/GO THERE

/TABLE USED IN INTERPRETING
/BITS 0-2 OF PSEUDO
/INSTRUCTION
/IF OPCODE=O, GO TO EXIT
/AND INTERPRET BITS 8-11

/FGET=5

/FPUT=6

/FLAD=l - FIRST ALIGN EXPONENTS
/RETURN IF NO ALIGNMENT IS POSSIBLE
/LARGER OF THE TWO IS IN F.A.
4-2

5721
5722
5723
5724
5725
5726
5727
5730
5731
5732
5733
5734
5735
5736

7100
1043
1047
3047
7004
1042
1046
3046
7004
1041
1045
3045
4770
5201

5737
5740
5741
5742
5743
5744
5745
5746
5747
5750
5751
5752
5753
5754
5755
5756
5757
5760
5761
5762
5763
5764
5765
5766
5767
5770
5771
5772
5773
5774

4741
5316
6400
1253
0260
7450
5600
1360
3254
1654
3254
1200
3255
4654
1255
3200
5201
6544
7201
1040
1044
3044
4767
5201
6221
6600
6020
6564
4770
5201

6000
6001
6002
6003
6004
6005
6006
6007

0000
7300
1047
7041
3047
1046
7040
7430

CLL
TAD OVERl
TAD OVER2
DCA OVER2
RAL
TAD ACl L
TAD LORD
DCA LORD
RAL
TADAClH
TAD HORD
DCA HORD
JMS I NORM
JMP FPNT+l
FLSU,
OPMINS,
EXIT I

ACON6,
FLMY,

MULT,
NORM,
ALGN,
UN ORM,
NORF,
*6000
ACMINS,

/TRIPLE PRECISION ADDITION
/SINCE BITS ARE SHIFTED
/RIGHT

/NORMALIZE THE RESULT

JMS I OPMINS
JMP FLAD
MINUS2
TAD JUMP
AND MASK3
SNA
JMP I FPNT
TAD ACON6
DCA JUMP2
TAD I JUMP2
DCA JUMP2
TAD FPNT
DCA G02
JMS I JUMP2
TAD G02
DCA FPNT
JMP FPNT+l
TABLE6-1
CLA IAC
TAD EXl
TAD EXP
DCA EXP
JMS I MULT
JMP FPNT+l
DMULT
DNORM
ALIGN
DUN ORM
JMS I NORM
JMP FPNT+l

/FSUB=2 - NEGATE THE OPERAND
/ADD
/OPCODE=O

I ARE BITS 8-11=0?
/YES=FEXT
/LOOKUP ON TABLE

/CALL AS A SUBROUTINE
/RESTORE F. P. POINTER
/GET NEXT PSEUDO INSTRUCTION
/CALLING CAN BE TO A DEPTH ONE
/FMPY=3
/ADD EXPONENTS TOGETHER
/MULTIPLY

/ROUTINE TO PERFORM

0
CLL CLA
TAD OVER2
CMA IAC
DCA OVER2
TAD LORD
CMA
SZL

/TRIPLE PRECISION NEGATION
/OF FLOATING AC

4-3

6010
6011
6012
6013
6014
601S
6016
6017
6020
6021
6022
6023
6024
602S
6026
6027
6030
6031
6032
6033
6034
603S
6036
6037
6040
6041
6042
6043
6044
604S
6046
6047
60SO
60Sl
60S2
60S3
60S4
60SS
60S6
60S7
6060
6061
6062
6063
6064
6065
6066
6067
6070
6071
6072
6073
6074
607S

7101
3046
104S
7040
7430
7101
304S
S600
0000
104S
7640
S227
1046
76SO
S337
1041
7640
S23S
1042
76SO
S620
1040
7041
1044
74SO
S314
7SOO
7041
3342
1342
1343
7700
S256
4316
7430
13SO
1347
S32S
4316
7420
13SO
1347
3344
1342
7041
1744
3744
2344
1344
334S
234S
134S
3346
2346

ALIGN,

CLL IAC
DCA LORD
TAD HORD
CMA
SZL
CLL IAC
DCA HORD
JMP I ACMINS
0
TAD HORD
SZA CLA
JMP .+4
TAD LORD
SNA CLA
JMP NOHERE
TAD AClH
SZA CLA
JMP .+4
TADAClL
SNA CLA
JMP I ALIGN
TAD EXl
CMA IAC
TAD EXP
SNA
JMP DONE
SMA
CMA IAC
DCA AMOUNT
TAD AMOUNT
TAD TEST2
SMA CLA
JMP .+6
JMS OUTGO
SZL
TAD TAG2
TAD TAGl
JMP NOGO
JMS OUTGO
SNL
TAD TAG2
TAD TAGl
DCA TEST3
TAD AMOUNT
CMA IAC
TAD I TEST3
DCA I TEST3
ISZ TEST3
TAD TEST3
DCA TEST4
ISZ TEST4
TAD TEST4
DCA TESTS
ISZ TESTS

4-4

/SUBROUTINE TO ALIGN
/BINARY POINTS FOR
I ADD-SUBTRACT
/IS MANTISSA ZERO?
/YES
/IS OPERAND ZERO?

/BOTH ARE ZERO-EXIT

/ARE EXPONENTS EQUAL?
/YES

/CAN EXPONENTS BE ALIGNED?
/YES
/NO

/SET UP ADDRESSES

6076
6077
6100
6101
6102
6103
6104
6105
6106
6107
6110
6111
6112
6113
6114
6115
6116
6117
6120
6121
6122
6123
6124
6125
6126
6127
6130
6131
6132
6133
6134
6135
6136
6137
6140
6141
6142
6143
6144
6145
6146
6147
6150
6151
6152
6153
6154
6155
6156
6157
6160
6161
6162

7100
1744
7510
7020
7010
3744
1745
7010
3745
1746
7010
3746
2342
5276
2220
5620
0000
1040
7041
1044
7004
7200
5716
3344
1744
3044
2344
1744
3045
2344
1744
3046
5620
1040
3044
5314
0000
0030
0000
0000
0000
0044
7774
5601
1362
3044
1362
3045
7040
3046
2061
5751
3777

SHIFT I

DONE,
OUTGO,

NOGO,

NOH ERE,

AMOUNT,
TEST2,
TEST3,
TEST4,
TEST5,
TAGl I
TAG2,
RETN2,
ERRORl I

GOOF,

CLL
TAD I TEST3
SPA
CML
RAR
DCA I TEST3
TAD I TEST4
RAR
DCA I TEST4
TAD I TEST5
RAR
DCA I TEST5
ISZ AMOUNT
JMP SHIFT
ISZ ALIGN
JMP I ALIGN
0
TAD EXl
CMA IAC
TAD EXP
RAL
CLA
JMP I OUTGO
DCA TEST3
TAD I TEST3
DCA EXP
ISZ TEST3
TAD I TEST3
DCA HORD
ISZ TEST3
TAD I TEST3
DCA LORD
JMP I ALIGN
TAD EXl
DCA EXP
JMP DONE
0
0030
0
0
0
EXP
EXl-EXP
FPNT+l
TAD GOOF
DCA EXP
TAD GOOF
DCA HORD
CMA
DCA LORD
ISZ FLAG
JMP I RETN2
3777

/THIS ROUTINE DOES
/THE ACUTAL SHIFTING

/DETERMINE WHICH TO SHIFT

/CAN'T BE ALIGNED
/LARGEST GOES INTO FAC

/MANTISSA=O

/DIVISION BY ZERO
/SET TO LARGEST+ VALUE

/SET FLAG

4-5

6163
6164
6165
6166
6167
6170
6171
6172

0000
4407
6052
3052
0000
5763
0000
5771

6200
6201
6202
6203
6204
6205
6206
6207
6210
6211
6212
6213
6214
6215
6216
6217
6220
6221
6222
6223
6224
6225
6226
6227
6230
6231
6232
6233
6234
6235
6236
6237
6240
6241
6242
6243
6244
6245
6246
6247
6250
6251
6252
6253

0000
7300
1045
7510
7120
7010
3045
1046
7010
3046
1047
7010
3047
7100
2044
7000
5600
0000
7300
1363
3347
4336
l 042
3756
1046
4755
7200
1757
3047
l 045
3756
l 042
4755
1047
3047
7004
1757
3367
7004
3370
l 041
3756
l 046
4755

SQUARE,

EXIT6,
*6200
DIVl I

DMULT,

0
JMS I 0007
FPUT FPACl
FMPY FPACl
FEXT
JMP I SQUARE
0
JMP I EXIT6

/DUMMY SUBROUTINE

0
CLA CLL
TAD HORD
SPA
CLL CML
RAR
DCA HORD
TAD LORD
RAR
DCA LORD
TAD OVER2
RAR
DCA OVER2
CLL
ISZ EXP
NOP
JMP I DIVJ
0
CLA CLL
TAD SMACLA
DCA SNSWIT
JMS SIGN
TADAClL
DCA I MP2PT
TAD LORD
JMS I MP4PT
CLA
TAD I MP5PT
DCA OVER2
TAD HORD
DCA I MP2PT
TADAClL
JMS I MP4PT
TAD OVER2
DCA OVER2
RAL
TAD I MP5PT
DCA D
RAL
DCA KEEP
TAD AClH
DCA I MP2PT
TAD LORD
JMS I MP4PT

/SHIFT FAC RIGHT

/DOUBLE PRECISION MULTIPLY
/SAVE PRODUCT TRIPLE PRECISION
/CALLS A SINGLE PRECISION
/MULTIPLY 3 TIMES

4-6

6254
6255
6256
6257
6260
6261
6262
6263
6264
6265
6266
6267
6270
6271
6272
6273
6274
6275
6276
6277
6300
6301
6302
6303
6304
6305
6306
6307
6310
6311
6312
6313
6314
6315
6316
6317
6320
6321
6322
6323
6324
6325
6326
6327
6330
6331
6332
6333
6334
6335
6336
6337
6340

l 047
3047
7004
1757
1367
3367
7004
1370
3370
l 045
3756
l 041
4755
1367
3046
7004
1757
1370
3045
4760
3047
2365
5621
4773
5621
l 041
7640
5313
1042
7650
5774
l 040
7041
1044
7001
3044
1362
3347
4336
4761
1757
l 041
7630
7001
3042
3041
2365
4773
5735
5720
0000
1366
3365

FLDV,

SIGN,

TAD OVER2
DCA OVER2
RAL
TAD I MP5PT
TADD
DCA D
RAL
TAD KEEP
DCA KEEP
TAD HORD
DCA I MP2PT
TADAClH
JMS I MP4PT
TADD
DCA LORD
RAL
TAD I MP5PT
TAD KEEP
DCA HORD
JMS I NORMF
DCA OVER2
ISZ SGN
JMP I DMULT
JMS I MINS
JMP I DMULT
TAD AClH
SZA CLA
JMP .+4
TAD ACl L
SNA CLA
JMP I ERROR
TAD EXl
CMA IAC
TAD EXP
IAC
DCA EXP
TAD SPACLA
DCA SNSWIT
JMS SIGN
JMS I DIVIDE
TAD I MP5PT
TADAClH
SZL CLA
IAC
DCA AClL
DCA AClH
ISZ SGN
JMS I MINS
JMP I .+l
FLAD+2
0
TAD REST
DCA SGN

/DIVISION BY ZERO

/SUBTRACT EXPONENTS

/SET UP SIGNS
/DIVIDE
/ROUND OFF IN 23RD BIT

/TEST SIGN
/NEGATE
/ADD ROUNDING
/TEST SIGN OF RESULT
/SET UP BY MULTIPLY AND
/DIVIDE

4-7

6341
6342
6343
6344
6345
6346
6347
6350
6351
6352
6353
6354
6355
6356
6357
6360
6361
6362
6363
6364
6365
6366
6367
6370
6371
6372
6373
6374

1045
7700
5346
4773
2365
l 041
7700
5736
4771
2365
7000
5736
6437
6471
6465
6600
6472
7710
7700
5601
0000
7776
0000
0000
6400
6420
6000
6152

6400
6401
6402
6403
6404
6405
6406
6407
6410
6411
6412
6413
6414
6415
6416
6417
6420
6421
6422
6423
6424
6425
6426
6427

0000
7300
1043
7041
3043
l 042
7040
7430
7101
3042
1041
7040
7430
7101
3041
5600
0000
7300
1041
7510
7120
7010
3041
1042

SNSWIT I

MP4PT I
MP2PT I
MP5PT I
NORMF,
DIVIDE,
SPACLA,
SMACLA,
RETURN,
SGN,
REST,
D,
KEEP I
MINS2,
RAR2,
MINS,
ERROR,
*6400
MINUS2,

DIV2,

TAD HORD
SMA CLA
JMP .+3
JMS I MINS
ISZ SGN
TAD AClH
SMA CLA
JMP I SIGN
JMS I MINS2
ISZ SGN
NOP
JMP I SIGN
MP4
MP2
MP5
DNORM
DUB DIV
SPA CLA
SMA CLA
FPNT+l
0
7776
0
0
MINUS2
DIV2
ACM INS
ERRORl

/OR SPA CLA

/-ACl H,ACl L

I ACl H, ACl L/2

0
CLA CLL
TAD OVERl
CMA IAC
DCA OVERl
TAD AClL
CMA
SZL
CLL IAC
DCA ACl L
TAD AClH
CMA
SZL
CLL IAC
DCA AClH
JMP I MINUS2
0
CLA CLL
TAD AClH
SPA
CLL CML
RAR
DCA AClH
TADAClL

/NEGATE OPERAND
/TRIPLE PRECISION

/SHIF-T OPERAND RIGHT
/TRIPLE PRECISION

4-8

6430
6431
6432
6433
6434
6435
6436
6437
6440
6441
6442
6443
6444
6445
6446
6447
6450
6451
6452
6453
6454
6455
6456
6457
6460
6461
6462
6463
6464
6465
6466
6467
6470
6471
6472
6473
6474
6475
6476
6477
6500
6501
6502
6503
6504
6505
6506
6507
6510
6511
6512
6513
6514

7010
3042
l 043
7010
3043
7100
5620
0000
3266
3265
1270
3267
7100
1266
7010
3266
1265
7420
5255
7100
1271
7010
3265
2267
5245
1266
7010
7100
5637
0000
0000
0000
7764
0000
0000
7300
3051
1344
3267
5306
1046
7004
3046
l 045
7004
3045
1042
1046
3271
7004
1045
1041
7420

MP4,

MP5,
MPl I
MP3,
THIR,
MP2,
DUBDIV,

DV3,

DVX,

RAR
DCA ACl L
TAD OVERl
RAR
DCA OVERl
CLL
JMP I DIV2
0
DCA MPl
DCA MP5
TAD THIR
DCA MP3
CLL
TAD MPl
RAR
DCA MPl
TAD MP5
SNL
JMP .+3
CLL
TAD MP2
RAR
DCA MP5
ISZ MP3
JMP MP4+6
TAD MPl
RAR
CLL
JMP I MP4
0
0
0
7764
0
0
CLA CLL
DCA QUOL
TAD MIF
DCA MP3
JMP DVX
TAD LORD
RAL
DCA LORD
TAD HORD
RAL
DCA HORD
TAD ACl L
TAD LORD
DCA MP2
RAL
TAD HORD
TADAClH
SNL

/SINGLE PRECISION MULTIPLY
/12 BITS BY 12 BITS

/DOUBLE PRECISION DIVIDE

4-9

6515
6516
6517
6520
6521
6522
6523
6524
6525
6526
6527
6530
6531
6532
6533
6534
6535
6536
6537
6540
6541
6542
6543
6544
6545
6546
6547
6550
6551
6552
6553
6554
6555
6556
6557
6560
6561
6562
6563

5321
3045
1271
3046
7200
1051
7004
3051
1047
7004
3047
2267
5300
1051
3046
1045
7106
3265
1047
3045
3047
1265
5672
7751
6163
6656
6171
6171
6171
6171
6171
6171
6171
6171
6171
6171
6171
6171
6171

6564
6565
6566
6567
6570
6571
6572

0000
4220
4772
2040
7000
5764
6200

6600
6601
6602
6603
6604
6605

0000
7300
3255
3254
1045
7510

DV2.1

MIF,
TABLE6,

DU NORM,

RARl I
*6600
DNORM,

JMP DV2-·1
DCA HORD
TAD MP2
DCA LORD
CLA
TAD QUOL
RAL
DCA QUOL
TAD OVER2
RAL
DCA OVER2
ISZ MP3
JMP DV3
TAD QUOL
DCA LORD
TAD HORD
CLL RTL
DCA MP5
TAD OVER2
DCA HORD
DCA OVER2
TAD MP5
JMP I DUBDIV
7751
SQUARE
SQROOT
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6

/TABLE FOR INTERPRET A Tl ON
/OF BITS 8-11
/CONTAINS ABSOLUTE ADDRESSES
/OF PROGRAMS CALLED AS
/SUBROUTINES
/EXIT6=A DUMMY OR NOP

0
JMS DIV2
JMS I RARl
ISZ EXl
NOP
JMP I DUNORM
DIVl

/SHIFT OPERAND RIGHT

/SUBROUTINE TO NORMALIZE
/FLOATING ACCUMULATOR

0
CLA CLL
DCA AMTl
DCA SIGNl
TAD HORD
SPA

/IS MANTISSA NEGATIVE?
4-10

6606
6607
6610
6611
6612
6613
6614
6615
6616
6617
6620
6621
6622
6623
6624
6625
6626
6627
6630
6631
6632
6633
6634
6635
6636
6637
6640
6641
6642
6643
6644
6645
6646
6647
6650
6651
6652
6653
6654
6655
6656
6657
6660
6661
6662
6663
6664
6665
6666
6667
6670
6671
6672
6673

2254
7640
5217
1046
7640
5217
'1047
7650
5251
1254
7640
4653
1045
7104
7710
5241
1047
7104
3047
1046
7004
3046
1045
7004
3045
2255
5222
1255
7041
l 044
3044
1254
7640
4653
5600
3044
5600
6000
0000
0000
0000
3362
4407
6052
0000
1045
7710
5351
1044
7100
7510
7020
7010
3356

G06,

LOP,

EXITl I

EXIT2,
NEG,
SIGNl I
AMTl,
SQROOT,

ISZ SIGNl
SZA CLA
JMP G06
TAD LORD
SZA CLA
JMP G06
TAD OVER2
SNA CLA
JMP EXIT2
TAD SIGNl
SZA CLA
JMS I NEG
TAD HORD
RAL CLL
SPA CLA
JMP EXITl
TAD OVER2
CLL RAL
DCA OVER2
TAD LORD
RAL
DCA LORD
TAD HORD
RAL
DCA HORD
ISZ AMTl
JMP LOP
TAD AMTl
CMA IAC
TAD EXP
DCA EXP
TAD SIGNl
SZA CLA
JMS I NEG
JMP I DNORM
DCA EXP
JMP I DNORM
ACM INS
0
0
0
DCA FLAGl
JMS I 007
FPUT FPACl
FEXT
TAD HORD
SPA CLA
JMP SQENDl
TAD EXP
CLL
SPA
CML
RAR
DCA ITERl

/YES
/IS MANTISSA=O?
./NO

/YES
/NO
/NEGATIVE?
/YES
/WI LL SH I FT BE TOO FAR?

/YES

/NO SHIFT MANTISSA LEFT

/COUNT NO. OF TIMES SHIFTED
/CORRECT EXPONENT

/NEGATIVE?
/YES
/SET TO ZERO

/FLOATING SQUARE ROOT
/TAKES ROOT OF ABSOLUTE
/VALUE
/NEWTON 1 S METHOD IS USED

/NUMBER IS NEGATIVE

/MAKE FIRST APPROXIMATION
4-11

6674
6675
6676
6677
6700
6701
6702
6703
6704
6705
6706
6707
6710
6711
6712
6713
6714
6715
6716
6717
6720
6721
6722
6723
6724
6725
6726
6727
6730
6731
6732
6733
6734
6735
6736
6737
6740
6741
6742
6743
6744
6745
6746
6747
6750
6751
6752
6753
6754
6755
6756
6757
6760
6761
6762

7430
2356
7000
1361
3357
3360
l 053
7640
5310
1054
7650
5354
4407
5052
4356
1356
0000
7240
l 044
3044
1044
7041
1356
7640
5345
1045
7041
1357
7640
5345
l 046
7041
1360
7500
7041
7001
7710
5345
1362
3061
5656
4407
6356
0000
5310
4653
2362
5260
3044
5656
0000
0000
0000
3015
0000

CLCU,

ROOTGO,

SQENDl I

SQEND,
ITER 1 ,

SQCONl I
FLAGl I

SZL
ISZ ITERl
NOP
TAD SQCONl
DCA ITERl+l
DCA ITER1+2
TAD FPACl+l
SZA CLA
JMP CLCU
TAD FPAC1+2
SNA CLA
JMPSQEND
JMS I 0007
FGET FPACl
FDIV ITERl
FADD ITERl
FEXT
CLA CMA
TAD EXP
DCA EXP
TAD EXP
CMA IAC
TAD ITERl
SZA CLA
JMP ROOTGO
TAD HORD
CMA IAC
TAD ITERl+l
SZA CLA
JMP ROOTGO
TAD LORD
CMA IAC
TAD ITERl +2
SMA
CMA IAC
IAC
SPA CLA
JMP ROOTGO
TAD FLAGl
DCA FLAG
JMP I SQROOT
JMS I 0007
FPUT ITERl
FEXT
JMP CLCU
JMS I NEG
ISZ FLAGl
JMP SQROOT+2
DCA EXP
JMP I SQROOT
0
0
0
3015
0
4-12

/NUMBER=O

/ARE EXPONENTS EQUAL?
/NO
/ARE HIGH-ORDER MANTISSAS EQUAL?

/NO

/DO LOW-ORDER MANTISSAS AGREE?
/WITHIN ONE BIT?

/NO

/NEGATE FAC

ACM INS
ACON6
AClH
ACl L
ADDR
ALGN
ALIGN
AMOUNT
AMTl
CLCU
D
DIVIDE
DIVl
DIV2
DMULT
DNORM
DONE
DUB DIV
DU NORM
DVX
DV2
DV3
ERROR
ERRORl
EXIT
EXITl
EXIT2
EXIT6
EXP
EX Pl
EXl
FLAD
FLAG
FLAGl
FLDV
FLGT
FLMY

6000
5760
0041
0042
5656
5771
6020
6142
6655
6710
6367
6361
6200
6420
6221
6600
6114
6472
6j64
6506
6522
6500
6374
6152
5742
6641
6651
6171
0044

ooso

0040
S716
0061
6762
630S
S676
S761

FLPT
FLSU
FPACl
FPNT
GOOF
G02
G06
HORD
INDRCT
ITERl
JUMP
JUMP2
KEEP
LOOPOl
LOP
LORD
MASK3
MASKS
MASK7
MIF
MINS
MINS2
MINUS2
MPl
MP2
MP2PT
MP3
MP4
MP4PT
MPS
MPSPT
MULT
NEQ
NOGO
NOH ERE
NORF
NORM

4-13

5705
5737
0052
5600
6162
5655
6617
0045
5664
6756
5653
5654
6370
5627
6622
0046
5660
5661
5662
6544
6373
6371
6400
6466
6471
6356
6467
6437
63SS
646S
63S7
S767
66S3
612S
6137

S773
S770

NORMF
OPMINS
OUTGO
OVERl
OVER2
PAGE NO
QUOL
RARl
RAR2
REST
RETN2
RETURN
ROOT GO
SAVE
SGN
SHIFT
SIGN
SIGNl
SMACLA
SNSWIT
SPACLA
SQCONl
SQEND
SQENDl
SQROOT
SQUARE
TABLE
TABLE6
TAGl
TAG2
TEST2
TEST3
TEST4
TESTS
THIR
UN ORM

6360
5741
6116
0043
0047
5663
0051
6572
6372
6366
6151
6364
6745
5657
6365
6076
6336
6654
6363
6347
6362
6761
6754
6751
6656
6163
5665
6545
6147
61SO
6143
6144
614S
6146
6470

S772

/FLOATING POINT l/O ROUTINES
/REQUIRES FLOATING POINT INTERPRETER
/ENTRY AT 0007
*1

FPNT,

5600

*44
EXPO NT,
HORDER,
LORD ER,

0
0
0

0007

5600

0044

0000

0045

0000

0046

0000

0052
0053
0054
0055
0056
0057
0060

0000
0000
0000
1171
0000
0000

SW! Tl,
SWIT2,
CHAR,
DSWIT,

6767

0000

*6767
PR CHAR,

677~

6771
6772
6773
6774
6775
6776
6777

7177

Hl56
7650
5767
1377
4776
5767
7344
0212

*52
FPACl,

OPUT,
LFED,

0
0

0
7777
1111

"'0

/IF : 0, NO CH-LF AFTER OUTPUT
/IF : 0, NO LF AFTER CR IN INPUT
/CONTAINS LAST CHARACTER READ
/: 0 IF NO CONVERSION TOOK PLACE

TAD SWIT2
SNA CLA
JMP I PRCHAR
TAD LFED
JMS I OPUT
JMP I PRCHAR
OUT
0212

4-14

/DOUBLE PRECISION DECIMAL-BINARY
/INPUT AND CONVERSION
*7000
7000
7001
7002
7003
7004
70!05
7006
7007
7010

1011
7012
7013
7014
7015
7016
701 7
7020
7021
7022
7023
7'124
7025
7026
7'/J2 7
7030

7031
7062
7033

7004
W.35

7036
70S7
7040
7041
7!042
7043
7044
7045
7046
7047
7050
7051
7052
7053
7054
7055
7056
7057
7060
7061
7062
7063
7064
7065
7066
7067

0000

7200
3045
3046
3265
3266
4342
1336
7450
5217
1335
7440
5220
7240
3265
4342
7200
1057
1337
7500
5600
1340
7510
5600
3263
1045
0341
7440
5217
2060
2266
4241
5217
0000

DECONV,

DECON,

MULT10,

1046
3261
1045
3262
3264
4267
4267
4303
4267
1263
3261
3262
4303
1264
5641
0000
0000
0000

0000

0000
0000
0000

LTEMP,
HTEMP,
DIGIT,
REMAIN,
SIGN,
DNUMBR,
MULT2,

CLA
DCA HORD ER
DCA LORD ER
DCA SIGN
DCA DNUMBR
JMS INPUT
TAD PLUS
SNA
JMP DEGON
TAD MINUS
SZA
JMP .+4
CLA CMA
DCA SIGN
JMS INPUT
CLA
TAD CHAR
TAD MIN9
SMA
JMP I DECONV
TAD PLUS12
SPA
JMP I DECONV
DCA DIGIT
TAD HORD ER
AND MASK
SZA
JMP DECON
ISZ DSWIT
ISZ DNUMBR
JMS MULTI 0
JMP DEC ON

/INITIALIZE MANTISSA

/TEST FOR SIGN

/IF-, SET SWITCH
/IS IT A DIGIT
/NO
/NO
/YES
/OVERFLOW?
/YES-IGNORE
/INDEX NUMBER OF DIGITS
/CONTINUE
/ROUTINE TO MULTIPLY
/DOUBLE PRECISION WORD
/BY TEN <DECIMAL)
/REMAIN=REMAINDER

TAD LOR DER
DCA LTEMP
TAD HORD ER
DCA HTEMP
DCA REMAIN
JMS MULT2
JMS MULT2
JMS DUBLAD
JMS MULT2
TAD DIGIT
DCA LTEMP
DCA HTEMP
JMS DUBLAD
TAD REMAIN
JMP I MULT10

/CALL SUBROUTINE TO
/MULTIPLY BY TWO
/CALL DOUBLE ADD
/ADD LAST DIGIT RECEIVED

/EXIT WITH REMAINDER
/IN AC

/DOUBLE PRECISION WORD

0
0

/STORAGE FOR DIGIT

0
0

/:0 IF PLUS: :7777 IF MINUS
/:NUMBER OF DIGITS
/MULTIPLY LORDER, HORDER BY 2

0
0

4-15

7070
:7071
7072
11/J 73
7074
7075
7076
7100
7101
7102
7103
7104
7105
7106
7107
7110
7111
7112
7113
7114
7115
7116
7117
7120
7121
7122
7123
7124
7125
7126
7127
7130
7131
7132
7133
7134

7300
1046
7004
3046
1045
7004
3045
1264
7004
3264
5667
0000
7300
1046
1261
3046
7004
1045
1262
3045
71cH14
1264
3264
5703
0000
7300
2265
5720
1046
7041
3046
1045
7040
7430
7001
3045
5720

7135
7136
7137
7140
7141

7776
7525
7506
0012
7600

7142
7143
7144
7145
7146
7147
7150
7151
7152
7153
7154
7155
7156
7157
7160

0000
7200
6031
5344
6036
3057
1057
4766
1057
7450
5343
1.370
7450
5767

W17

1371

DU BLAD,

CLA CLL
TAD LORD ER
RAL
DCA LORD ER
TAD HORD ER
RAL
DCA HORD ER
TAD REMAIN
RAL
DCA REMAIN
JMP I MULT2
0
CLA CLL
TAD LORD ER
TAD LTEMP
DCA LORD ER
RAL
TAD HORD ER
TAD HTEMP
DCA HOR DER
RAL
TAD REMAIN
DCA REMAIN
JMP I DUBLAD

MSIGN,

/DOUBLE PRECISION ADDITION

/ROUTINE TO FORM
/2'S COMPLEMENT IF
/MINUS
/SIGN=0000: EXIT

CLA CLL
ISZ SIGN
JMP I MSIGN
TAD LORD ER
CMA IAC
DCA LORD ER
TAD HORD ER
CMA
SZL
!AC
DCA HORDER
JMP I MSIGN

/TEST FOR SIGN
253-255
MI NUS,
-253
PLUS,
/TEST FOR DIGIT
-272
MIN9,
272-260
PLUS12,
/TEST FOR OVE:RFLOW
7600
MASK,
/INPUT A CHARACTER, IF CR, TEST
/INPUT SWITCH TO SEE IF LF SHOULD
/BE TYPED. IF RUBOUT, RESTART INPUT
/INPUT A CHARACTER
IO
INPUT,
CLA
KSF
JMP .-1
KRB
DCA CHAR
TAD CHAR
JMS I OUTPUT
TAD CHAR
SNA
/IGNORE BLANKS
JMP INPUT+l
TAD MRBOUT
SNA
JMP I RESTRT
/RUBOUT-RESTART INPUT
TAD MI NCR
4-16

7161
7162
7163
7164

7650
4765
1057
5742

7165
7166
7167
7170
71 71

6767
7344
7401
7401
0162

7200
7201
7202
7203
7204
7205
7206
7207
7210
7211
7212
7213
7214
7215
7216
721 7
7220
7221
7222
7223
7224
7225
7226
7227
7230
7231
7232
7233
7234
7235
7236
7237
7240
7241
7242
"/243
7244
7245
7246
7247
7250
7251

0000

4217
1324
3044
1343
4344
4737
1055
7650
5600
1341
4344
1342
4344
5600
!0000

7300
1045
7710
7220
1327
7430
1330
4344
4352
1331
4344
7300
1045
7700
5242
7040
3733
4732
7240
1044
3044
3324
1044
7500
5263
13:26

SNA CLA
JMS 1 PRINT
TAD CHAR
JMP I INPUT
PRINT,
OUTPUT,
RESTRT,
MRBOUT,
Ml NCR,

/CR - SEE IF TO BE FOLLOWED
/BY LF
/EXIT ROUTINE

PR CHAR
OUT
FLINTP+l
-377
377-215

/FLOATING OUTPUT "£" FORMAT
/USES:
TSF
JMP .-1
I
I
TLS
*7200
FLOUTP,
JMS FOUTCN
/CONVERT MANTISSA AND OUTPUT
TAD BEXP
DCA EXPONT
TAD CHE
JMS OUT
JMS I FEXPPT
/CONVERT EXPONENT AND OUTPUT
TAD SWITl
/PRINT CR-LF?
SNA CLA
JMP I FLOUTP
/NO-EXIT
TAD CARRIN /YES
JMS OUT
TAD LNFEED
JMS OUT
JMP 1 FLOUTP
/EXIT
/THIS WHOLE SUBROUTINE MAY BE ALTERED TO BUFFER
/THE OUTPUT DIGITS : CHANGE JMS OUTDG TO DCA I 10, ETC.
F'OUTCN,
0
CLA CLL
TAD HORD ER
/NUMBER>0??
SPA CLA
CLA CML
/NO SET LINK
TAD SPLUS
/YES
SZL
TAD SM I NUS /NO
JMS OUT
JMS OUTDG
/OUTPUT "0"
TAD PERIOD
JMS OUT
/OUTPUT " • "
CLA CLL
TAD HOR DER
SMA CLA
JMP FGOl
CMA
/NUMBER IS NEGATIVE
DCA 1 SNPT
/NEGATE
JMS I MSNPT
FGOl,
CLA CMA
/SUBTRACT 1 FROM BINARY EXPONENT
TAD EXPONT
/COMPENSATE AT FG04
DCA EXPONT
DCA BEXP
/INITIALIZE DECIMAL EXPONENT
TAD EXPONT
FG02,
/IS -4<EXPONENT<-1
SMA
JMP FG03
/TOO LARGE: MULTIPLY BY 1/10
TAD FOUR

4-17

7252
7253
7254
7255
7256
7257
7260
7261
7262
7263
7264
7265
7266
7267
7270
7271
7272
7273
7274
7275
7276
7277
7300
7301
7302
7303
7304
7305
7306
7307
7310

7700
5270
4407
3740
0000
7240
1324
3324
5246
4407
3372
0000
2324
5246
3734
4736
4735
7410
4357
2044
5274
7450
5311
4352
1325
3044
4735
4352
2044
5304
5617

7311
7312
7313
7314
7315
7316
7317
7320
7321
7322
7323

7240
1324
3324
1045
7640
5322
1046
7650
3324
7240
5302

FG07,

7324
7325
7326
7327
7330
7331
7332
7333
7334
7335
7336
7337
7340
7341
7342
7343

0000
7772
0004
0253
0002
0256
7120
7065
7063
7041
7067
7522
7504
0215
0212
0305

BEXP,
MINUS7,
FOUR,
SPLUS,
SMINUS,
PERIOD,
MSNPI,
SNPI,
DPT,
Ml0PI,
t-t2 PI,
FEXPPT,
TENPT,
CARRIN,
LNFEED,
CHE,

FG03,

FG04,

FG05A,

FG06,
FG06A,

SMA CLA
JMP FG04
JMS I FPNI
FMPY I TENPT
FEXT
CLA CMA
TAD BEXP
DCA BEXP
JMP FG02
JMS I FPNT
FMPY C.llO
FEXT
ISZ BEXP
JMP FG02
DCA I DPT
JMS I M2PT
JMS I Ml0PT
SKP
JMS DIVTWO
ISZ EXPONT
JMP FG05A
SNA
JMP FG07
JMS OUTDG
TAD MINUS7
DCA EXPONT
JMS I M10PT
JMS OUTDG
ISZ EXPONT
JMP FG06A
JMP I FOUTCN

/TOO SMALL-TIMES TEN
/TEN

/ONE TENTH

/MULTIPLY BY TWO
/IE.SHIFT LEFT
/MULTIPLY BY TEN
/COMPENSATE FOR
/BINARY EXPONENT
/IS FIRST DIGIT A ZERO
/YES, IGNORE
/MULTIPLICATIONS YIELD
/DECIMAL DIBITS AS HIGH
/ORDER REMAINDERS
/IE •• 672Xl0:6+.72 •• ETC
11 DIGITS OUTPUT??

/NO: CONTINUE
/YES: EXIT

CLA CMA
TAD BEXP
DCA BEXP
TAD HORDER
SZA CLA
JMP .+4
TAD LORDER
SNA CLA
DCA BEXP
CLA CMA
JMP FG06+1

/IGNORE FIRST DIGIT
/SUBTRACT 1 FROM
/DECIMAL EXPONENT

/CONTAINS DECIMAL EXPONENT
/NUMBER OF DIGTS OUTPUT

/IS MANTISSA ZERO?
/YES:EXP=0

7772
0004
253
255-253
256
MSIGN
SIGN
DIGIT
MUL Tl 0
MULT2
FEXC
TEN
0215
0212
305

/POINTERS

4-18

7.344
7.345
7346
7347
7350
7351

00Ql0

OUT,

604.1
53~,5

6046

12e0
5744

OUTDG,

TSF
JMP .-1
TLS
CLA
JMP I OUT

7.352
7.3 5.3
7354
7355

4344

7356

0260

C260,

0260

7357

0000
7110

DIVTWO,

7360
7.361
7362

7363
7364
7365
7366
7367

00f2l0

5752

3344
1045
7010
3045
1046
7010

3046

1344

7.3 71
7.372
7.373

5757
7775

7374

3146
3147

7400

0000

7401

7240

7402

3313

7403

3060

7404

4716

7405
7406

7410

1312
7640

7411

5220

7412

1313
7650

7413

7414

5222

7415

3721
3313
5717

7416
7417

c.10,

/FLOATING POINT INPUT
FLINTP,

7420

1313

FIGOl ,

7650
1721

FIG02,

7427

7430
7431
7432
7433
7434
7435

7041
3314

4720
1311

3044
4407
7000
6052
0000
1057
1310

/CONSTANT .10 USED IN
/FLOATING OUTPUT-PROVIDES

1115

*7400

7421

7422
7423
7424
7425
7426

/DIVIDE BY TWO IE.
/ROTATE RIGHT
/TEMPORARY STORAGE

CLL RAR
DCA OUT
TAD HORDER
RAR
DCA HORDER
TAD LORDER
RAR
DCA LORDER
TAD OUT
JMP I DIVTWO
3146
3147

7200
1057

7407

/OUTPUT ONE DIGIT

TAD C260
JMS OUT
JMP I OUTDG

1356

7370

/OUTPUT ONE ASCII CHARACTER

FIG03,

CLA CMA
DCA PRSW
DCA DSWIT
JMS I DPCVPT
CLA
TAD CHAR
TAD PER
SZA CLA
JMP FIGOl
TAD PRSW
SNA CLA
JMP FIG02
DCA I DPN
DCA PRSW
JMP I DPCSPT

/INITIALIZE "PERIOD SWITCri"
/7777

= NO PERIOD

/PERIOD FOUND
/SECOND PERIOD
/YES, TERMINATE
/NO - SET NUMBER OF DIGITS TO 0
/SET PERIOD SWITCH TO 0
/CONVERT REST OF STRING

TAD PRSW
SNA CLA
TAD I DPN
CMA !AC
DCA SEXP
JMS I MSGNPT
TAD C27
DCA EXPONT
JMS I FPNT
FNOR
FPUT FPACl
FEXT
TAD CHAR
TAD MINUSE

/PERIOD READ IN PREVIOUSLY?
/YES:-NUMBER OF DIGITS IN SEXP
/NO
/TEST SIGN
/NORMALIZE F.P. NUMBER
/SAVE NUMBER

4-19

7436
7437
7440
7441
7442
7443
7444
7445
7446
7447
7450
7451

7640
5252
4716
4720
1045
7510
7001
7640
5277
1046
1314
3314

I" E" READ I N7
SZA CLA
/NO
JMP END FI
JMS I DPCVPT
/YES - CONVERT DECIMAL EXPONENT
/TEST SIGN
JMS I MSGNPT
/EXPONENT TOO LARGE??
TAD HORDER
SPA
!AC
SZA CLA
/YES
JMP EXCESS
TAD LORD EH
/NO:DECIMAL POINT IS
/CCSEXP>PLACES TO RIGHT
TAD SEXP
DCA SEXP
/OF LAST DIGIT
/END OF FLOATING POINT INPUT
/COMPENSATE FOR DECIMAL EXPONENTS

7452
7453
7454
7455
7456
7457
7460
7461
7462
7463
7464
7465
7466
7467

4407
5052

ENDFI,

7470
7471
7472
7473
7474
7475
7476
7477
7500
7501
7502
7503
75i04
7505
7506
7507
7510
7511
7512
7513
7514
7515

0000

1314
7450
5600
7700
5270
4407
3707
0000

2314
5255
5600
44~J7

FIG04,

3304
0000

7240
1314
3314
5255
1315
3044
1315
3045
5600

EXCESS,

!0004

TI'~N,

JMS I FPNT
FGET FPACl
FEXT
TAD S£XP
SNA
JL'1P I FLINTP
SMA CLA
JMP FIG04
JMS I FPNT
FMPY I PC.10
FEXT
ISZ SEXP
JMP ENDFI+3
JMP I FLINTP

/RESTORE MANTISSA

JMS I FPNT
FMPY TEN
FEXT
CLA CMA
TAD SEXP
DCA SEXP
JMP ENDF1+3
TAD C3 777
DCA EXPONT
TAD C3777
DCA HORDEH
Jr1P I FLINTP

1. IS TO THE RIGHT:
/MULTIPLY BY 10

0004

2400

0000

ltH1~0

PC. 10,
MI NUSE,
C27,
P£R,

c.10
-305
0027
-256

~0L10

PRS~v,

0000

0
0

3777

SEXP,
C3777,

7516
7517
7520
7521

7000
7017
7120
7066

DECO NV
DPCVPT,
DEC ON
DPCSPT,
MSIGN
MSGNPT,
DNUMBR
DPN,
/OUTPUT THE EXPONENT

7522
7523

0000

FEXC,

7372
747.3
0027
7522

7300

1. IS TO THE LEFT:
/TIMES .1000

I .10

/CONTAINS DECIMAL EXPONENT

3777

CLA CLL
4-20

TAD EXPO NT
SPA
CMA !AC CML
DCA EXPO NT
TAD C253
SZL
TAD C255
JMS I DGPT
DCA HORD ER
TAD EXPO NT
ISZ HORDER
TAD Ml44
SMA
JMP .-3
TAD Cl44
DCA EXPO NT
CMA
TAD HORD ER
SZA
JMS I DGPT
DCA HORD ER
TAD EXPO NT
ISZ HORD ER
TAD Ml2
Si'1A
JMP .-3
TAD C12
DCA LORD ER
CLA CMA
TAD HORDER
Jl1S I DGPT
TAD LORD ER
JMS I DGPT
JMP I FEXC

1044
7510
7061
3044
1366
7430
1367
4774
3045
1044
2045
1370

7524
7525
7526
7527
7530
7531
7532
7533
7534
7535
7536
7537
7540
7541
7542
7543
7544
7545
7546
7547
7550
7551
7552
7553
7554
7555
7556
7557
7560
7561
7562
7563
7564
7565

5336
1371
3044
7040
1"145
7440
4774
3045
1044
2045
1372
7500
5352
1373
3046
7240
1045
4774
1046
4774
5722

7566
7567
757'/J
7571
7572
7573
7574

7773
0002
7634
0144
7766
0012
7352

75~0

C253,
C255,
M144,
Cl44,
M12,
Cl 2,
DGPT,

0253-260
255-253
7634
0144
7766
0012
OUTDG

4-21

BEXP
CARR TN
CrlAH
CHE
c. 10
Cl2

Cl44
C253
C255

C260
C27
C3777
DEGON
DECO NV
DGPT
DIGIT

DI VTWO
DNUMBH
DPCSPT
DPCVPT
DPN
DPT
DSWI T
J.)U.6LAD
END FI
£XC£S~

EXPO{H
FEXC
F£XPPI
FGOl
FG02
FG03
FG04
FG05A
FG06
FG06A
FG07
FIGOl
FIG02
FIG03
FIG04
FLINTP
FLOUTP
FOUR
FOUTCN
FPACl
FPNT

7.524
7341
lcH157
734-3
7372
7?73
7571
7566
7567
7356
7511
7515
7017
7000
7574
7063
7357
7066
7517
7516
7521
7334
0060
7103
7452
7477
0044
7522
7337
7242
7246
7263
7270
7274
7301
7304
7311
7420
7422
7426
747lJ
7400
7200
7326
7217
0052
'1007

HORD ER
HTEMP
INPUT
LFED
LNFEED
LORDEH
LTEMP
MASK

MI NCR
.Ml NUS

rvu NUSE

Ml NUS7
MI N9

MRBOUI
~lSGNPT

MSIGN
MS NP I
MUL Tl kj
MULT2
Ml 0PT
Ml2
Ml 44
M2PI
OPUT
OUT
OLJTDG
OUTPUT
PC.10
PER
PERI OD
PLUS
PLUS12
PR CHAR
PRINT
PRSW

REMAIN
RESTRT
SEXP
SIGN
SMINUS
SNPT
SPLUS
SW! Tl
SWI T2
TEN
TENPT

4-22

0045
7062
7142
6777
7342
0046
7061
7141
7171
7135
7510
7325
7137
7170
7520
7120
7332
7041
7C/J67
7335
7572
7570
7336
6776
7344
7352
7166
7507
7512
7331
7136
7140
6767
7165
7513
7064
7167
7514
7065
7330
7333
7327
0055
0'156
7504
7340

EXTENDED FUNCTIONS
/FLOATING POINT PACKAGE
GETSGN=TAD 45
CLFPNT=JMS I 7
/FLOATING POINT EXPONENTIAL
*5000

5000
5001
5002
5003
5004
5005
5006
5007
5010
5011
5012
5013
5014
5015
5016
5017
5020
5~21

5'122
5023
51£l24
5025
5026
5027
5030
5031
5032
5033
5034
5035
5036
5037
5040
5041
5042
5043

0000

1045
7710
4310
3304
4407
3273
6315
0000

4706
1045
3305
4707
4407
6320
5315
2320
6315
3315
6320
1270
6323
5265
4323
2315
1257
6323
5262
3320
1323
6323
5315
4323
3301
1276
0000

5045
5046
5047
5050
5!051
5052
5053
5054
5055
5!056

1305
1044
3044
2304
5600
4407
6315
5276
4315
0000
5600

5057
5060
5061

0004
2372
1402

5~44

FEXP,

0
GETSGl~

SPA CLA
JMS FNEG
DCA SIGN
CLFPNT
FMPY LG2E
FPUT X
FEXT
JMS I FIXIT
GETSGN
DCA FLAG2
JMS I FLOAT
CLFPNT
FPUT XSQR
FGET X
FSUB XSQR
FPUT X
FMPY X
FPUT XSQR
FADD D
FPUT TEMP
FGET C
FDIV TEMP
FSUB X
FADD A
FPUT TEMP
FGET B
FMPY XSQR
FADD TEMP
FPUT TEMP
FGET X
FDIV TEMP
FMPY TWO
FADD ONE
FEXT
TAD FLAG2
TAD 44
DCA 44
ISZ SIGN
JMP I FEXP
CLFPNT
FPUT X
FGET ONE
FDIV X
FEXT
JMP I FEXP
/CONSTANTS FOR FEXP
A,

/CCSIGN>=-1 IF X<0

0004

2372
1402
4-23

5062
5063
5064
5065
5066
5067
5070
5071
5072
5073
5074
5075
5076
5077
5100
5101
5102
5103
5104
5105
5106
5rn7

7774
2157
5157
0012
5454
0343
0007
2566
5341
0001
2705
2435
0001
2000

c,
D,
LG2E,
ONE,

0000

0002
2000

7774
2157
5157
0012
5454
0343
0007
2566
5341
0001
2705
2435
"0"' 1
2000
000"

TWO,

!0000

0002
2000
01dldl0

4714
7240
5710
6000

SIGN,
0
FLAG2,
0
FIXIT,
FIX
FLOAT,
FLOA
/NEGATION SUBROUTINE
FNEG,
0
JMS I ACMINS
CLA CMA
JMP I FNEG
ACMINS,
6000

5115
5116
511 7
5120
5121
5122
5123
5124
5125
5126
5127
5130

0000

/TEMPORARY STORAGE
x,
0

5131
5132
5133
5134
5135
5136
5137
5140
5141
5142
5143
5144
5145
5146
5147
515ft:)
5151
5152
5153

4407
5315
3315
632rtJ
3373
1370
3320
1365
6323
5362
3320
1357
3320
1354
3315
4323

5110
5111
5112
5113
5114

0000
0000

4757
5563
0000

0000

0000
001J0
0000
0000

XSQR,

0000
0000
0000

TEMP,

00i01d

ZER,

0000

5753
5226

/CALL SUBROUTINE IN
/INTERPRETER
/POINTER TO INTERPRETER

0
0
0
0
0
0
0
0
0

/MAIN ALGORITHM FOR ARCTANGENT
ARCA LG,
CLFPNT
FGET X
FMPY X
FPUT XSQR
FMPY BET2
FADD BETl
FMPY XSQR
FADD BETZ
FPUT TEMP
FGET ALF2
FMPY XSQR
FADD ALFl
FMPY XSQR
FADD ALFZ
FMPY X
FDIV TEMP
FEXT
JMP I .+1
ARCRTN

4-24

5154
5155
5156
5157
5160
5161
5162
5163
5164
5165
5166
5167
5170
5171
5172
5173
5174
5175

0000
2437
1643
7777
3304
4434
7773
3306
5454
0000
2437
1646
0000
2427
2323
7775
3427
7052

5200
5201
5202
5203
5204
5205
5206
5207
5210
5211
5212
5213
5214
5215
5216
5217
5220
5221
5222
5223
5224
5225
5226
5227
5230
5231
5232
5233
5234
5235
5236
5237
5240
5241

0000
1045
7710
4642
3243
4407
6644
5644
2645
0000
1045
7710
5223
4407
5645
4644
6644
7240
3251
5625
5131
2251
5235
4407
6644
5246
2644
0000
2243
5600
4642
7200
5600

5242
5243
5244
5245

5110
0000
5115
5076

0fiH?.10

/CONSTANTS - FLOATING ARC TANGENT
0000
ALFZ,
2437
1643
1111
ALFl,
3304
4434
7773
ALF2,
3306
5454
0000
BETZ,
2437
1646
0000
BETl,
2427
2323
7775
BET2,
3427
7052
/FLOATING POINT ARC TANGEN,T
*5200
0
ARTN,
GETSGN
SPA CLA
JMS I NEGIT
DCA FLAG!
CLFPNT
FPUT I Xl
FGET I Xl
FSUB I CONl
FEXT
GETSGN
SPA CLA
JMP GO
CLFPNT
FGET I CONl
FDIV I Xl
FPUT I Xl
FEXT
CLA CMA
DCA .FLOG
/FLAG
GO,
JMP I .+1
/CALL ALGORITHM
ARCA LG
ISZ FLOG
/RETURN HERE
ARCRTN,
JMP EXIT
CLFPNT
FPUT I Xl
FGET PIOT
FSUB I Xl
FEXT
ISZ FLAG!
EXIT,
JMP I ARTN
JMS I NEGIT
CLA
JMP I ARTN
/CONSTANTS FOR ARCTANGENT
NEGIT,
FLAG!,
Xl,
CONl t

FNEG
0

ONE
4-25

5246
5247
5250

0001
3110
3755

0001
3110
3755
/FLOATING LOGARITHM

5251
5252
5253
5254
5255
5256
5257
5260
5261
5262
5263
5264
5265
5266
5267
5270
5271
5272
5273
5274
5275
5276
5277
5300
5S0 l
5.502
5303
5304
531.15
5306
5307
5310
5311
5312
5313
5314
5315
5316
5317
5320
5321
5322
5323
5324
5325
5326
5327
53.50
53..51
5332
5..5..5..5
5334
5335
5336
5337
5341.1

0000

FLOG,

PIOT,

1045
7440
5261
4407
4775
0000

5651
7710
4642
4407
6774
2645

OK,

0000

1045
7450
5350
7710
5341
3243
7040
1774
3045
4777
4407
3776
6644
0000

7001
3774
4407
5774
2645
6774
3773
1772
3774
1 771
3774
1770
3774
1365
3774
1362
3774
1357
3774
1354
3774
1644
0000

2243
5651
4642
7200
5651

START,

GETSGN
SZA
JMP OK
CLFPNT
FDIV I ZERO
FEXT
JMP I FLOG
SPA CLA
JMS I NEGIT
CLFPNT
FPUT I TEM
FSUB I CONl
FEXT
GETSGN
SNA
JMP ZERGO
SPA CLA
JMP INVERT
DCA FLAGl
CMA
TAD I TEM
DCA 45
JMS I FLOATP
CLFPNT
FMPY I LOG2
FPUT I Xl
FEXT
IAC
DCA I TEM
CLFPNT
FGET I TEM
FSUB I CONl
FPUT I TEM
FMPY I L8
FADD I L7
FMPY I TEM
FADD I L6
FMPY I TEM
FADD I L5
FMPY I TEM
FADD L4
FMPY I TEM
FADD L3
FMPY I TEM
FADD L2
FMPY I TEM
FADD L1
FMPY I TEM
FADD I Xl
FEXT
lSZ FLAGl
JMP I FLOG
JMS I NEGIT
CLA
JMP I FLOG

/INDICATE ERROR
/DIVIDE BY ZERO

4-26

5341
5342
5343
5344
5345
5346
5347
5350
5351
5352
5353
5354
5355
5356
5357
5360
5361
5362
5363
5364
5365
5366
5367
5370
5371
5372
5373
5374
5375
5376
5377
5400
5401
5402
5403
5404
5405
5406
5407
5410
5411
5412
5413
5414
5415
5416
5417
5420
5421
5422
5423
5424
5425
5426
5427
5430
5431
5432
5433
5434

4407
5645
4774
6774
0000
7240
5274
4407
5775
0000
5651
0000
3777
7742
1111

4000
4100
7777
2517
0307
7776
4113
7211
5547
5552
5555
5560
5123
5126
5544
5563
0000
1045
7740
5210
1045
7700
5600
4741
3343
4407
4315
6724
0000
4742
4363
4407
6723
5724
2723
3315
6723
2320
0000
1045
7710

5241
4407
6723
0000

INVERT,

CLFPNT
FGET I CON!
FDIV I TEM
FPUT I TEM
FEXT
CLA CMA
JMP START
CLFPNT
ZERGO,
FGET I ZERO
FEXT
JMP I FLOG
0000
Ll,
3777
7742
7777
L2,
4000
410'21
7777
L3,
2517
0307
7776
L4,
4113
7211
LOG5
L5,
LOG6
L6,
LOG7
L7,
LOG8
L8,
TEMP
TEM,
ZER
ZERO,
LOGE2
LOG2,
FLOA
FLOATP,
/FLOATING POINT SINE
*5400
0
FSIN,
GETSGN
SMA SZA CLA
JMP MOD
GETSGN
SMA CLA
JMP I FSIN
JMS I NEGT
DCA PNTR
MOD,
CLFPNT
FDIV TWOPI
FPUT I XSQ2
FEXT
JMS I FI XR
JMS FLOA
CLFPNT
FPUT I X2
FGET I XSQ2
FSUB I X2
FMPY TWOPI
FPUT I X2
FSUB Pl
FEXT
GETSGN
SPA CLA
JMP PCHECK
CLFPNT
FPUT I X2
FEXT

/X>07
/YES
/NO X=07
/YES SINC0) =IO
/NO:SINC-X>=-SIN<X>
/REDUCE X MODULO 2 Pl

/X<PI?

/YES
/NO SINCX-PI>:-SINCX>
4-27

5435
5436
5437
5440
5441
5442
5443
5444
5445
5446
5447
5450
5451
5452
5453
5454

1343
7650
7040
3343
4407
5723
2714
0000
1045
77U?J
5255
4407
5320
2723
6723
0000

5455
5456
5457
5460
5461
5462
5463
5464
5465
5466
5467
5470
5471
5472
5473
5474
5475
5476
5477
5500
5501
5502

4407
5723
4714
6723
3723
6724
5325
3724
1330
3724
1333
3724
1336
3724
1714
3723

55·03
5504
5505
5506
5507
5510
5511
5512
5513

0000
4407
6723
5714
2723
0000
1303
3200
5201

0000

2343
5600
4741
7200
5600

PCHECK,

TAD PNTR
SNA CLA
CMA
DCA PNTR
CLFPNT
FGET I X2
FSUB I PI2
FEXT
GETSGN
SPA CLA
JMP PALG
CLFPNT
FGET Pl
FSUB I X2
FPUT I X2
FEXT

/X<PI/27

/YES
/NO
/SINCX>=SINCPI-X>

CLFPNT
FGET I X2
FDIV I PI2
FPUT I X2
FMPY I X2
FPUT I XSQ2
FGET C9
FMPY I XSQ2
FADD C7
FMPY I XSQ2
FADD C5
FMPY I XSQ2
FADD C3
FMPY I XSQ2
FADD I PI2
FMPY I X2
FEXT
ISZ PNTR
JMP I FSIN
JMS I NEGT
CLA
JMP I FSIN
/FLOATING POINT COSINE

PALG,

FCOS,

CLFPNT
FPUT I X2
FGET I PI2
FSUB I X2
FEXT
TAD FCOS
DCA FSIN
JMP FSIN+l

/COSCX>=SINCPI/2-X)

/CONSTANTS AND POINTERS
5514
5515
5516
5517
5520
5521
5522
5523
5524

5246
0003
3110
3755
0002
3110
3755
5115
5120

PI2,
TWOPI,
PI,
X2 t

XSQ2,

/PI/2

PIOT
0003
3110
3755
0'102
3110
3755

XSQR
4-28

5525
5526
5527
5530
5531
5532
5533
5534
5535
5536
5537
5540
5541
5542
5543

7764
2366
5735
7771
5466
6317
7775
2431
5053
0000

5325
0420
5110
4757
0000

/SINE CONSTANTS
7764
C9,
2366
5735
C7,
7771
5466
6317
7775
C5,
2431
5053
C3,
0000
5325
0420
FNEG
NEGT,
FIXR,
FIX
PNTR,
IJ
/LOGARITHM CONSTANTS

5544
5545
5546
5547
5550
5551
5552
5553
5554
5555
5556
5557
5560
5561
5562
5563
5564
5565
5566
5567
5570
5571
5572
5573
5574
4757
4760
4761
4762
4763
4764
4765
4766
4767
4770
4771
4772
4773
4774

0000

LOGE2,

2613
4414
7776
2535
.3301
7775
4746
0771
7774
2236
4304
7771
4544
1 735

2613
4414
7776
LOG5,
2535
3301
7775
LOG6,
4746
0771
LOG7,
7774
2236
4304
7771
LOG8,
4544
1 735
/FLOAT C(45)
FLOA,
0
CLA CLL
DCA 46
TAD Cl3
DCA 44
CLFPNT
FNOR
FEXT
JMP I FLOA
C13,
0013
*4757
/FIX CCFAC)
0
FIX,
TAD 44
SMA SZA
JMP .+3
CLA
JMP FIXEND
TAD Ml3
DCA 44
TAD 44
LOOP,
SMA CLA
JMP l FIX
JMS l .+2
JMP LOOP
6200

0000

7300
3046
1374
3044
4407
7000
0000

5763
0013
0000

1044
7540
5365
7200
5375
1377
3044
1044

7700
5757
4774
5367
6200

0000

/DIVl IN INTERPRETER
4-29

4775
4776
4777

3045

5757
7765

FIXEND,

DCA 45
JMP I

A
AClvJ1 NS
ALFZ
ALFl
ALF2
AH CA LG
AR CR TN
ARTN
B

BETZ
BETl
BET2

CLFPNT
CONl
C13
C3

C5
C7
C9
D

EXIT
FCOS
FEXP
FIX
FIXEND
FI XI T
FIXR
FLAG!
FLAG2
FLOA
FLOAT
FLOATP
FLOG
FNt:G
FSI l~

GET3GN
GO

INVERT
LG2E
LOGE2

FIX

-13

Ml 3,

LOG2
LOG5
LOG6
LOG7
LOG8
LOOP

5057
5114
5154
5157
5162
5131
5226

5200

L3
L4
LS
L6
L7
L8
MOD
M13
NEGI T
NEGT
OK
ONE
PALG
PC KECK
PI
PIOT

5062
5165
5170
5173
5065
4407
5245

5574
5536
5533
5530
5525
5070
5235
5503
5000

Pl2

4757
4775
5 UJ6
5542
5243
5105
5563
5107
5.577
5251
511 IO

PNTR
SIGN
STA HT

TEM
TEMP

TWO
TWOPI

XSQH
XSQ2

5400

X2
ZEH
ZEH GO

1045
5223
5341

ZERO

5073

5544

4-30

5376
5547

5552
5555
5560
4767
5354
5357
5362
5365
5370
5371
5372
5373
5410
4777
5242
5541
5261
5076
5455
5441
5520
5246
5514
5543
5U14
5274
5374
5123
5101
5515
5115
5120
5524
5244
5523
5126
5350
5375

/FLOATING OUTPUT PROGRAM
/IFC62):0, THEN OUTPUT IN E FORMAT
/ELSE, CC62):NUMiER OF DIGITS
/CCAC):NUMBER OF PLACES TO RIGHT OF •
/IF CCAC>:i·, THEN DON'T OUTPUT POINT
/SIGN AND • NOT CQUNTED IN OUTPUT
/CONTENTS OF 15 LOST DURING OPERATION
7201
7202
7203
7204

4777
421 7
1324
4776

72(()7

7200

7227
7231()
7231
7232

3415
7000
701d0
7000

7301

3415

73~5

3415

7376
7377

5412
5400

5400
5401
5402
5403
5404
5405
5406
5407
5410
5411
5412
5413
5414
5415
5416
5417
5420
5421
5422
5423
5424
5425
5426
5427
5430
5431
5432

0000
3352
1062
7041
3347
1357
3350
1363
3!015

*7201

*7207

*7227

00"IO

3044
1363
3015
1415
47i1
1062
7650
5327
2212
2212
1044
7510
5300
1352
7041
10'2

CLA

DCA I 15
NOP
NOP

NOP

*7301
*7305
*737,

5600

JMS I 7377 /ALTERATIONS FLOATING OUTPlJI
JMS 7217
TAD 7324
JMS I 7376

DCA I 15
DCA I 15
TGO
EDIT

*54"'"'
EDIT,

TGO,

TRYAGN,

DCA SAC
TAD &2
CMA IAC
DCA COUNTl
TAD MB
DCA COUNT2
TAD SADl
DCA 15
JMP I EDIT
DCA 44
TAD SADl
OCA 15
TAD I 15
JMS I OUil
TAD ~2
SNA CLA
JMP EJi'OHM
ISZ TGO
ISZ TGO
TAD 44
SPA
JMP MINS
TAD SAC
CMA IAC
TAD &2
4-31

SPA

5433
54.34
5435
5436
5437
5440
5441
5442
5443
5444

7510
5266
7450
5245
7041
3351
1353
4321
2351
5241

5445
5446
5447
545rcl
5451
5452
5453
5454
5455

1044
7041
7450
5256
3351
4337
4321
2351
5252

GOl,

TAD 44
CMA IAC
SNA
JMP G02
DCA CNTR
JMS GET
JMS OUT
ISZ CNTR
JMP .-3

5456
5457
5460
5461
5462
5463
5464
5465
5466
5467
5470
5471
5472
5473

1352
7650
5263
1354
4761
4337
4321
52ti3
1352
7700
5274
1356
4321
5271

G02,

TAD SAC
SNA CLA
JMP .+.3
TAD PERIOD
JMS I OUTl
JMS GET
JMS OUT
JMP .-2
TAD SAC
SMA CLA
JMJll ERGO
TAD CHX
JMS OUT
JMP .-2

5474
5475
5476
5477

7240
1352
3352
5225

ERGO,

CLA CMA
TAD SAC
DCA SAC
JMP TRYAGN

5500
5501
5502
5503
5504

720'6
1062
76041
1352
7450
5313
.3351
135.3
4321
2351
5307

MINS,

CLA
TAD 62
CMA IAC
TAD SAC
SNA
JMP G03
DCA CNTR
TAD SPCE
JMS OUT
ISZ CNTR
JMP .-3

1354
4761
4321
2044
5315
5263

G03,

TAD ptERIOD

55~5

5506
55~7

5510
5511
5512
5513
5514
5515
5516
5517
552ta
5521
5522

0000

4762

JMP ERR
SNA
JMP GOl
CMA !AC
DCA CNTR
TAD SJ-CE
JMS OUT
ISZ CNTR
JMP .-3

ERR,

OUT,

JMS I OUTl
JMS OUT
ISZ 44
JMP .-2
JMJ8 G02+5
0

JMS I OUT2
4-32

5523
5524
5525
5526

2347
5721
1355
5612

5527

4762
1354
4761

55.30

5531
5532
5533
55..34
5535

ld01it0

5540

235(d
5..345
724id
3350
5737
1415
5737

5544

JMS I OUT2
TAD J9ERIOD
JMS I OUTl
TAD M7
DCA COUNTl
JMS GET
JMS our
JMP .-2

GET,

ISZ COUNT2
"'JMP
.+4

136~

5537

5545
5546
5547
5550
5551
5552
5553
5554
5555
555,
5557
5560
5561
5562
5563

EFORM,

3..347
4..3..37
4321
5334

5536

5541
5542
5543

ISZ COUNTl
JMJ9 I OUT
TAD CrlE
JMP I IGO

CL.A CMA
DCA COUNT2
JMP I GET
TAD I 15
JL'lP l GET
COUNTl,
COUNT2,
CNTR,
SAC,
SPCE,
PERIOD,
CHE,
CHX,

00CditJ

0000
ld001tt
0000

7760
025&

0305
0050
777'id
7771
7344

MS,
M7,

oun,

7~52

5563

bUFFER
CHE:

CKX
CNTH
COUNT!
COUNT2
EDIT
EFOHM
EkGO

ERR
GET
GOl
G02
G03

SUFFER,

Ml NS

5500
5561d

5557
5521
55'1
5562
5554
5552
55i3
5553
5412

OUTl
Ol.JT2
PEHIOD
SAC

SADl
~PCE

I\30
T,-(YAGN

240·2i0
25&
305
330-260
-10
-7
7.344
7352
auFFER-1

5564
5555
5556
5551
5547
5550
5400
5527
5474
5466
5537
5445
545,
5513

M7
OUT

OUT2,
SADl,

0
0
0
0

5425

4-33

INDEX

Accumulator, 2-4

FGET I 2-5

Addition, 2-5, 2-6, 3-7

Fixed to Floating, 3-10

After Output, 3-4

Flags
Input, 3-1
Listed, 3-9
Operational, 3-8

Arithmetic, 2-4
Basic Commands, 2-4
Basic Function, 3-7
Basic Package, 3-6
Summary, 3-9

Floating Point Package Versions, 3-16
Floating to Fixed, 3-10
FMPY, 2-5
FNOR, 2-5

Cal I Subroutine, 3-6
Commands, 2-4
Conversion
Fixed-to-Floating, 3-10
Floating-to-Fixed, 3-10
Cosine, 3-11
Decimal to Octal Conversion, 2-3
Division, 2-5, 2-6, 3-7
Double Precision, 4-15
e, raising to power
Entry Points
Input Routine, 3-2
Interpreter, 2-4, 2-6
Listed, 3-9
Negate Subroutine, 3-6
Output Subroutine, 3-6
Error flag, 3-8
Exponent
Floating, 3-11
In floating point format, 2-1
Storage, 2-2

Format
Commands, 2-4
11
E11 Format, 4- 17
FPUT I 2-5
FSUB, ?-5
Functions
Addition, 3-7
Division, 3-7
Multiplication, 2-5, 2-6, 3-7
Square, 3-8
Square Root, 3-8
Subtraction, 3-7
GET (FGET), 1-1
High Order (Register), 2-4
Identities
Arc Tangent, 3- 12
Cosine, 3-12
Floating Exponent, 3-14
Logarithm, 3-13
Sine, 3-12
Input routines, 1-1, 3-1
Instructions, 2-5

FAC (floating accumulator), 2-4

Interpreter, 2-4

FADD, 2-5
FDIV, 2-5

JMS (Jump to Subroutine),
Interpreter, 2-4

INDEX (Cont)

1-7, 1-1
5600, 2-6
7400, 15, 3-2

Square, 2-5, 3-8
Square Root, 2-6, 3-8
Storage, 3-10

Listings, Program, 4-1

Subroutines, 3-6

Logarithm, 3-11

Subtraction, 2-5, 2-6, 3-7

Lookup Table, 3-6

Summary
Basic Package, 3-9
Extended Floating Point, 3-11

Low Order (Register), 2-4
Mantissa
Binary point relative position, 2-3
Storage, 2-1, 2-2

Tangent, Arc, 3-11
Teleprinter flag, 3-6

Mnemonics, 2-5

Terminator, 3-1

Multiplication, 3-7

TLS, 3-6
Typeout subroutine, 3-5

Negate, 3-6
Negative Root, 3-8
Normalize, 2-1, 2-2, 2-5, 2-6
Octal, Conversion to, 2-3
OP Code, 2-5, 3-6
Output Controller, 3-15
Output, Floating Point, 3-4
Package Summaries
Basic, 3-9
Extended, 3- 11
Output Controller, 3-15
Package Versions, 3-16
Program Listings, 4-1
Pseudo Floating Accumulator, 2-4
Register, 2-4, 3-1 to 3-3
Rubout, 3-3
Sine, 3-\ 1
Specia I Input Character, 3-3

Variables, 1-1

READER'S COMMENTS

FLOATING-POINT SYSTEM
PROGRAMMER 1 S REFERENCE
DEC-08-YQYB-D

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