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DEC-08-FFAD-D

December 1968

96 pages

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Document:	dec-08-ffad-d
Order Number:	DEC-08-FFAD-D
Revision:
Pages:	96
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OCR Text

_U_nw_._->F NBC—BENZ... 003.003.94.07.

7>><Z>DU. EDWWPUICWmAIfim

POP-8
PROGRAM

LIBRARY

MATH ROUTINES
January, I968

Order No. DEC-08-FFAA-D from Program Library, Maynard, Mass.‘
Direct comments concerning this manual to Software Quality Control,
DIGITAL EQUIPMENT

CORPORATION

Price

$ I.5O

Maynard, Mass.

MAYNARD. MASSACHUSETTS

Reprinted
September, 1967

CONTENTS
Part

3393
Single-Precision Square Root
1-1

DEC-OB-FMAA-D

Single-Precision Signed Multiply Subroutine
2-1

DEC-O8-FMBA-D

Single-Precision Signed Divide Subroutine
DEC-08-FMCA-D

3-1

Double-Precision Signed Multiply
DEC-OB-FMDA-D

4-1

Double-Precision Signed Divide Subroutine
DEC-O8-FMEA-D

5-1

Double-Precision Sine Subroutine
DEC-08-FMFB-D

6-]

Double-Precision Cosine Subroutine
DEC-O8—FMGB-D

7-1

Four-Word Floating-Point Package
DEC-08-FMHA-D

8-1

DEC-OB-FMlA-D

9-1

Logical Subroutines

l0.

Arithmetic Shift Subroutines
DEC-08-FMJA-D

ll.

Logical Shift Subroutines
DEC-OB-FMKA-D

000000000000

10-1

Single Precision Square Root, DEC-OB-FMAA-D

ABSTRACT
will extract the square root of a single-precision integer. Given
an integer K and a remainder R, such that N: K2 + R.

This

subroutine
input N (O_ N 212), it will produce
<

REQUIREMENTS

3 I

Storage

This subroutine uses 23 (decimal) memory locations.
3.3

Equipment
Standard PDP-8

USAGE

4.l

library tape that is supplied is a symbolic tape. It does not begin with an
origin setting, although it does end with a dollar sign. The binary tape produced by assembling this tape, or the binary tape produced by assembling this tape with other tapes, is loaded
with the Binary Loader.
The

4.2

Calling Sequence
This subroutine is called with an effective JMS SQRT with the argument in the

accumulator.
swer

The subroutine returns control to the location following the JMS with the an-

in the accumulator and with the remainder in the

DESCRIPTION

6.2

Examples and/or Applications

The following program will illustrate the use of this subroutine:
400
CLA
TAD

JMS

SQRTPT

HLT

X,
SQRTPT,

0145

(I IOI

DEC IMAL)

SQRT

This sample program will halt at location 403 with OOI2 (octal) or ID (decimal)

in the accumulator.

METHODS

7.2

Algorithm
The algorithm makes use of the fact that the sum of the odd

Z(2K-1)=2
K==T

E
K=i

EXECUTION TIME

9.4

Timing Equation

N
K—

21=2(—I;—l-)(N+1)-N=N2

K=l

If the answer is N, the time for the subroutine is

(30 + N (25.5)) usec
TO.

PROGRAM

10.4

Program Listing

integers is a square:

/DEU 08*FMAA-LA
/SGUAHE R00!
[00,000

tNIER

w1[H

SQUARt

tXLTb

WIIH

HUU]

0000
6222
5226

0205

1223
6225
1222

0226

/100

0207

1225
i420
5217
2226
6222
1225
1224
3204

@2z4

0210
0211
0212

0213
0214
0215
0216

{6217

f300

0220

1226
b600
0000
///7
//76

0221
0222
0223
0224
0225
0226

SQR‘P

SQX,

lNlLbLH

ODD

0220
0201
0252
mzzs

IN AU
AC

MEIHUU

BOA
DCA

SURl
ROOF

/5AVE
/0 10

TAD
DCA
TAD
CLL
TAD

SUR2
SURU
SQRl

/~1:

INPUT
ANSWER

FIRST

AIIEMPL

/COMPARE

lNPU]
THIS IRY

INIIH

SURU

SNL
JMP

50?},

ISZ
DCA
TAD
TAD
JMP
CLA
TAD
JMp

3991:

000b

5092:
$9969
SQRUu

“Z
0

0000

RUOIo

SURF
R001

/1tST)INPUT3

SURl
SURU
SQR6
SUX

/1NPUT=INPU|-1EST

R001
I SUR;

IFE1CH
IEXIT

PAUS E

THERE ARE

LHHUHS

SYMBOL

iABLt

RUOi

0226

SURU
SUR+
SuRi

022b
021/
0200

SURl
SURZ
SURé

0222
0220

SQX

0204

0224

/AUU

ALL

ANSWLR

/ILST=TEST-2
/CUNT1NUE
ANSNtR

DONE

Signed Multiply Subroutine

ABSTRACT

Single Precision, DEC-O8-FMBA-D.

This subroutine forms a 22-bit signed product from 11-bit signed multiplier and multiplicand.
3.

REQUIREMENTS

3 1

Storage

This subroutine uses 44 (decimal) memory locations.
4.

USAGE

4.1

Loading
It does not begin with an origin set-

The library tape that is supplied is a symbolic tape.

The binary tape produced by assembling this tape, or the
binary tape produced by assembling this tape with other tapes, is loaded with the Binary Loader.

ting, although it does end with a dollar sign.

4.2

Calling Sequence
The subroutine is called by an effective JMS MULT.

the subroutine, the multiplier must be in the accumulator (AC).
contain the multiplicand.

When the JMS is executed to enter

The location following the JMS must

The subroutine returns to the instruction immediately following the latter

location with the most significant part of the product in the AC.

The least significant part of the product

is stored in location MP1.

DESCRIPTION

6 .1

Discussion
Reference to the flow chart (11.1) will illustrate the following discussion.
On entry, the sign of the multiplier is tested, and if negative, the multiplier is made

6.1.1

positive.
6.1.2

The multiplicand is obtained and tested for 0.

If it equals 0,

iump to the exit is executed.

Next the sign of the multiplicand is tested, and if it is negative, the multiplicand is made positive.

6.1.3

At this point, the content of the link is as follows:

Sign of Multiplier

Sign of Multiplicand

Link

and represents,

therefore, the sign of the product.

6.1 .4
cant

The multiplication loop proper (tagged MP4) is entered. During this loop, the least signifihalf of the product shifts into the most significant end of MP1, while the multiplier shifts out the

least significant end of MP1 and is lost.
6.1 .5

Note that the sign of the product is retained in MP1.

The sign of the product is tested.

If positive, the subroutine exits.

mentation of the product is performed before the exit.

If negative,

comple-

6.2

Examples or Applications

Example (See 11.1 Flow Chart)
The C(Y) are tested. If C(Y)
0, C(MPl) C(MP5) 0. If C(Y) 75 0,
cleared and mulitplication is carried out as described below.
=

C(MP5)

are

If C(MPl)” contains a
are

then shifted right one bit.

right one bit.

C(Y)” C(MP2),

l, C(MP2) are added to C(MP5). The contents of MP5 and the MP1
0, the contents of MP5 and those of the MP1 are shifted

C(MPl)1 1:

For this example, assume that the registers MP1, MP5, and MP2 are five bits in length inThe following sequential steps occur in a multiply operation. The multiplicand is 9 and the
multiplier is 4.

stead of 11.

MP5

MP1

00000

01001

00100

01001

C(MP2) + C(MP5)» C(MP5) since C(MPl) is a 1.

00010

00100

C(MP5, MP1) rotated right one place.

Comments

Initial contents of the register MP1

ready to be tested.

tested.

00001

00010

C(MPl)“ is

No addition, because

C(MPl)” is 0. C(MP5, MP2)
AC” is tested.
No addition, C(MPl)”
0, C(MP5, MP1) rotated
is tested.
bit.
right
C(MPl)“
+
C(MP2) C(MP5)
C(MP5) since C(MPl)“ is 1.
rotated right one bit and

00000

10001

one

00100

10001

00010

01000

C(MP5, MP1) rotated right.

00001

00100

No addition,

—’

C(MPl)“

0, C(MP5, MP1) rotated

right one bit. Rotation counter indicates that the
multiplication is complete since it has been reduced
to

Scaling
Upon entry the binary point is assumed to be located between bit positions 0 and l in both
multiplier and multiplicand. Since there are 11 magnitude bits in each of the two factors, the product
contains 22 magnitude bits.
The product is double signed; i.e. , bit positions 0 and 1 of the most significant word of the

product both contain the sign.

The remaining ten bits of the most significant word of the product are

magnitude bits.
The least significant word of the product is devoted entirely to magnitude.
If the binary points of the factors are as stated above, the binary point of the product will

be located between bit positions 1 and 2 in the most significant position of the product.
On entry,

multiplier and multiplicand must be 25 complement binary.

product is contained in two words in 25 complement form

For more information on binary scaling for fixed-point computers,

2-2

After return, the

see

Application Note 501

METHOD

7.l

Algorithm
The conventional algorithm is used.

The least significant bit of the multiplier is tested.
l, the multiplicand is added to the developing product and this quantity is shifted right.
If the least significant bit of the multiplier is 0, no addition is made before the shift. The process is
repeated until all bits of the multiplier in order from least significant to most significant have been
processed.
If it is equal

EXECUTION TIME

9.]

Minimum

When the subroutine discovers that the multiplicand is 0, it bypasses the multiplication
In this case, execution time is 25.5 psec if the multiplier is positive and 27.0 usec if the multi-

loop.
plier is negative.
9.2

Maximum
Maximum execution time occurs when the sign of the product is negative and the multipl

«consists (in binary) of all Is.

IO.

PROGRAM

l0.4

Program Listing

This time is approximately 350 psec.

2-3

/DEc-¢8~FMBA
/TMU'b

lfiifUHN

COMPLEMENT SleLt PRtCISION MULTIPLY ROUTINE
HIGH ORDER PRUUUCT 1N AC. LON IN MP1
0

Mzrfl

DDDD

2201
M222

/1MM

CLL

751D
lwbl
3252
5251
1689

SPA

2227

/4bD

SNA

M210

5254

2211
2212
2213

/b10
/Db1
6252

JMP
SPA
CMA

CML

DCA

MP2

M214
M215
2216
2217

1247

M223
M204
M2M5
Mazé

2220

MULI,

CMA
DUA
DCA
TAD

6255

12b6
/M12
52:2

2221
M222

12:1

2223
2224

12:2

M225
2226
@227
D260
M251
w2é2

6231
22b6

M263

3240

b264

5252
12:1

MP4.

/11D

5216
12:2
/le

MP1

ISTDRE

/JMP

MPSNéZ
IAC

MULTIPLIER

MULTIPLILR

JMP

MP4

TAD

MP1

/TES1 FOR ZERU MULTIPLICAND
IF MULllPLICANU=w
/TESI FDR NEGAT£VE MULTIPLICAND

ISTORE

TAD THIR
DCA MP3
TAD MP1
RAR
DCA MP1
TAD MP9

/MULIIPLY

MULTIPLICAND

PROPER

LOOP

MULTIPLICAND

/TE81

ITLSI

FDR

/EX1T

END OF

SHOULD

LOOP

RAR
MPSN.

StL
JMP

2242

/141

CMA

M241
M242
M243

5252

DCA

MP;

1251
/M42

TAD

MP5

CMA

M244

/452

2245
D246

/221
b2¢6

M247
DZDB

1/64
M222

TMIP.

JMP MP2
7/54

MP1.

2251

Mwwv

MP5,

D252

wwww

MP2.

w2b3

MMMU

MP3.

2267

22mm

NEGATIVE

MP5
I MUL.

COMP
MP1
M99
MUL‘
1 NHL!
CLL 1A0

D265
2256

FDR

JAG

52L
TAD MP2
CLL RAR
DCA MP5
152 MP3

/4sD

745D

/TEST
CML

DCA
M92.

:OMM

COMP.

TAD
182
JMP

CALLING PROGRAM

/COMPLEMENT PRODUCT

SiL
IAC
/EL£VEN

PAUSE

2-4

DECIMAL

ADDED

IABLL

SYMBOL

@24W
@232
@256
025%
0252
@256
0216
@251
DZZO
924/

CUMP
MPSN
MP2
MP1

MP2
MP3
MP4

MP5
MULI
THIR

I I

DIAG RAMS

Flow Chart

11.]

CLEAR

IS
MULT| PLI CAND

NEGATIVE

YES

COMPLEMENT MULTIPLIER

MULTIPLIER
NEGATIVE

LINK

‘

SET

LINK

SAVE MULTIPLIER

CIACI*C(MPI)

MULTIPLICAND
ZERO?

LOAD MULTIPLICANO

C((MULTII-‘CIACI

IT WILL BE
SIGN STATUS IS IN LINK
SHIFTED ALONG WITH MULTIPLIER
ANDEND UP IN LINK AT END OF LOOP.

SAVE MULTIPLICAND C(ACI—‘UMPZI
CLEAR MOST SIGNIFICANT HALF
OF PRODUCT O —-’ C (M P5)

COMPLEMENT MULTIPLICAND
COMPLEMENT LINK

I
LOAD LEAST SIGNIFICANT HALF OF
PRODUCT AND MULTIPLIER

C(MPI) —O C(AC)

IS LINK I I 7’
WAS LEAST SIGNIFICANT 8|
1 BEFORE
OF MULTIPLIER I
ROTATE ?

IS LOOP coum REDUCED
T0 ZERO

ROTATE RIGHT
CILI —- C(MPII

C(MPI)“—-’C(L?

ADD MULTI PLICAND

C(MPSI +C(MP2)—OC(AC)

SHOULD
PRODUCT 8E POSITIVE
I. IS LINK -O ?

STORE LEAST HALF OF PRODUCT
AND MULTIPLIER
C(AC)” C(MPI)

CLEAR LINK AND ROTATE MOST
SIGNIFICANT HALF OF PRODUCT
RIGHT
C(ACIH—.CIL)

COM PLEMENT BOTH HALVES
OF

PRODUCT

2-5

LOAD MOST SIGNIFICANT HALF
OF PRODUCT

C(MPS)

—-.

C(AC)

SAVE MOST SIGNIFICANT HALF OF PRODUCT

C(AC) ——OC(MP5I

RETURN TO
CALLING PROGRAM

Single Precision Signed Divide Subroutine, DEC-08-FMCA-D
ABSTRACT

Single-Precision Divide Subroutine will divide a 12-bit signed divisor into
a 24-bit
signed dividend to produce a l2-bit signed quotient and a I2-bit signed remainder.
The

REQUIREMENTS

3.I

Storage
This subroutine requires 62 (decimal) memory locations.

It is provided in two

binary tape assembled with an origin of 0200, and a symbolic tape with no origin setand
ting
ending with a dollar sign.

forms:

USAGE

4.I

Loading
It is provided as a

This subroutine requires 62 (decimal) memory locations.
symbolic tape with no origin setting and ending with a dollar sign.
4.2

Calling Sequence
The subroutine is called with an effective JMS DIVIDE

The accumulator contains

the high-order bits of the dividend; the location following the JMS contains the low-order bits
of the dividend; the location following this contains the divisor; and the subroutine returns to
the following location with the quotient in the accumulator and the remainder in C(HDIVND).
If a divide error has occurred,
TAD

HIGH D

JMS

C(L)

I and the accumulator contains 0, otherwise C(L)

/C(AC) HIGH DIVIDEND
/CALL DIVIDE
2

DIVDP

DIVSOR

/LOW DIVIDEND
/DIVISOR

HLT

/C(AC)=QUOTIENT IF L=0

DIVDP,
HIGHD,

DIVI DE

/(0200)
/H|GH DIVIDEND

4.5

Errors in Usage

LOWD

There are two types of errors that may be encountered in using the divide subroutine, the first of which is tested by the routine. The divide may be represented as:

(High-Order Dividend)

212 + Low-Order Dividend

Divisor
=

Quotient, Remainder

Ol'

(High-Dividend)

212+ Low-Dividend

3-l

(Quotient) (Divisor) + Remainder.

Since (Quotient) < 3777(8), it is possible that a divisor and dividend are so

specified that no quotient may be Found that satisities this identity.

Z Quotient, then the divide will not take place and C(L) will be 1
that are not detected by this test.
1 777

It High-Order Dividend
.

There are cases,

however,

For example:

7777

2000

Since (3777) (2000) + 3777

1000

1777, there is no possible quotient that when multiplied

by the divisor will yield the dividend.
RESTRICTIONS

See Section 4.5
6.

DESCRIPTION

6.1

Discussion

The algorithm works by shifting the dividend left and comparing it with the

Dividend-Divisor, and a bit is set in the quotient. This is repeated the proper number of times. The remainder will have the same sign as
the dividend, and the quotient will be signed properly: (Dividend Sign) XOR (Divisor Sign)

divisor.

If Dividend Z Divisor then Dividend

(Quotient Sign).

Scaling

6.3

Single-Precision Divide Subroutine is scaled analogous to the scaling of the
Single-Precision Multiply Subroutine (DEC-08-FMBA, previously Digital-8-l l-F). It may be
thought of as either an integer divide or a fractional divide
The

2-22

2.1 2"2
0

Dividend (2's

1:— Binary Point
Dividend Sign

2
0

-1

L- Binary Point
Sign

-ll

Diwsor (2 s

Complement)

2—] 2—2

2-H

i LBinary

Quotient (2's

Complement)

Point

Sign

High-Order Dividend

I_I

Low-Order Dividend

Quotient

Divisor
HD

212

D
so

thotQ

DUO
70

Remainder

D+R=(HD)

:QIR

212+(LD)

(HD

+ED1)

—22

—Q-2-H,R 2-H

Examples:
(0)

000

-3—— 2,
_

(b)

000

000 000

000

0]]

2000

000

010

Remoinder=000

000

00]

000_
—010

000

Remainder: 000

000

100

000

000 000

010

000

fl—J.
T

2
7.

METHODS (See Above)

EXECUTION TIME

9.]

Minimum

58.5 psec

(Divide Check)
3-3

9.2

Maximum

478 .5 psec

9.3

Average

5:5 460 psec

10.

PROGRAM

10.4

Program Listing

3-4

/QEU~08~FMCA-LA
/SIUNLU bINGLt PRECISION
/CALLINU SLQULNCt:
L(AC) CONTAINS
/
JMb UIVIUE
/
ORDER

LOW

UIVISUR

RETURN:

UIVIUE
HIGH

SUBROUTINE

ORDER

DIVIDEND

C(AU)=OUOTIENT:

REMAINDER

HUIVND

HIGH DHDLR DIVIDEND IS EQUAL TO OR GREATER
NO UIVISIDN TAKES PLACE AND
/THAN THL UIVISOR;

/1F

/PAGE

620%

C(L)=1

DIVIDL.

@221

mafia
Vlflw

UZDZ

Iblw

:PA

6203

UMA

UML

wZDd

7D6v
3207

UCA

HDIVNU

lDIVIDEND<D7
/YES COMPLEMENT AND SET
/HIGH ORDER DIVIDEND

@205

7420

bNL

dZDé
@207

7w4u

6272

UMA
UCA

021D

160%

TAU

SUVNU
I DIVIDE

/SLT DIVIDEND SIGN SWITCH
/FETCH LON ORDER DIVIDEND

2211

7439

5tL

$212

7141
527w

UMA

CLL

UCA

LUIVNU

6214

743M

D215

226/

ISt

HUIVNU

/YES

@216

2200

ISt

£217

lbflm

IAU

UIVIUE
I DIVIDL

IFETCH

@220

71mm

ULL

4221
ozzz

7bwn
7&61

UMA

CML

£223

3271

UCA

UIVSDH

6224

7420

aNL

D225

764$

UMA

D226
0227

1272
3275

UCA

UZJD

71WM

ULL

@213

DLL

IAC

/YES:

lLON

/CARRY?

DIVISOR

DMA

IAU

IAC

SDVNU
SNSWER

INEGATE IT
/SAVE DIVISOR
wa3 IT <u?
/YES: Ac=—1
/ANSWER

0261

1271

TAU

UIVSOR

6262

1267

IAU

/WITH

M253

22mm

ISt

HDIVNU
UIVIDE

v2é4

70$n
5630

ULA
I DIVIUL

/DVER

@255

COMPLEMENT
ORDER DIVIDEND

JMP

3—5

SIGN

SWITCH

/COMPARE DIVISOR
DIVIDEND

/YES:

FLOW?
DIVISOR<DIVIDEND

C(L)

/PAGE

£256

1279

IAU

M15

Z237
624%

3274
5251

UcA

UIVCNT

JMP

/01v1ut
@241
$242
0243

1267

0V3;

/13

SHIFTS

UV2

LDUP
IAU

HUIVNU

7264
3207

HAL

UCA

HUIVNU

lDIVIDEND

@244
$245
8246
w247

1267
1271
7430
3267

[AU
TAU

HDIVNU
UIVSOR

/COMPARE

5iL
UCA

HDIVND

IREMAINDER

@293

7200

LLA

U2bl
@292
6253

127m

LDIVNU

/0UOTIENT BITS
IENTER HERE

2294

$255
@256

0V2:

[AU

LEFT

DIVISORzDIVIDEND
AFTER

7ww4

HAL

327M

UCA

2274

15¢

5241

JMP

1267
2272

TAU

BPD7

mZbS

7241

UMA

SUVNU
LAC

2261

5267

UCA

HDIVND

£262
@263
@204

127w
2273

[AU

LDIVNU

/QUOTIENT

15t

SNSwEH

7241

UMA

LAC

/ANSNER<@?
/YES: NEGATE

$205

71%”

@266

Dbfifl

ULL
JMP

/EXIT

£267

wwaw

227%

wwwv

$271

Evan

@272
£273

amew
@vww

@274

wawv
7766

2275

SYMbOL

TABLh

DIVCNT

$274

DiVIDh
DIVSOR

@266

UVZ
0V3

W291
@241

HUIVND

@267

LUIVND

627%

M13
SUVND

@275
@272

SNSWEH

@273

0271

[St

HUIVNU:
LDIVNU:

DIVbOH:
SUVND:

SNSNEHv
DIVCNT:
M13:

ISGESE

LDIVNU
UIVCNT
UVS
HUIVNU

DIVlUt

/DONE

12?

CONTINUE
/REMAINDER
/DIVIDEND<0?
/N03

/YES

/*13(1@)

SHIFT

SUBTRACT

Signed Double Precision MultipIy, DEC-O8-FMDA-D

ABSTRACT

This subroutine forms a 46-bit signed product from the 23-bit signed multiplier
and multiplicand.

REQUIREMENTS

3 I

Storage

This subroutine uses I25 (decimal) memory locations.
4.

USAGE

4.2

Calling Sequence
The signed double precision multiply routine is called by an effective JMS DMUL

The two locations following the JMS must contain the address of the high-order multiplicand and

the address of the high-order multiplier respectively.
The subroutine will return to the instruction immediately following the latter loca-

tion, with the most significant portion of the answer in the accumulator.
of the answer will be in registers (from high to low) B, C, and D.

DESCRIPTION

6.I

Discussion

The low order portions

The double precision multiply routine calls a single precision multiply routine
four times after the absolute values of the multiplier and multiplicand have been taken.

Sign

(4)

®
®

Multiplicand (2's Complement)

G)
Multiplier (2's Complement)

The results are added:
Result of Multiply l

Result of Multiply 2

Result of Multiply 3

Result of Multiply 4

Accumulator

Answer

Sign
6.2

Examples
To multiply two double precision numbers which are located in registers tagged

X and Y:

0400
JMS

DMULTP

X
Y

HLT

0
O

0
0

DMULTP,

DMUL

If X and Y contained:
X

0000

00l2

6000

0000

00l 2

3000

0000

0144

7200

0000

The answers would be:

For Further examples see the Double Precision Sine Routine, DEC—08—FMFA

Formerly Digital-B-lo-F.

Scaling

6.3

Since there are 23 magnitude bits in both the multiplier and the multiplicand,
the product will contain 46 magnitude bits.
D registers.

These are right

iustitied in the AC and B, C, and

Since the answer is in 2's complement form, the two sign bits are equal (redundant).

The multiply routine may be thought of as

integer multiplication, as a fraction
multiplication, or as any combination of these. When the double precision multiply routine is
given two 23-bit numbers, it produces a 46-bit product that is right justified. If the scaling is

(xxxx

XXX.X)

(xxxx

xxxx.)

the scaling of the answer will be
XXXX

XXXX

XXX.X

The operands and the answer are in 2's complement form.

product may be produced and since the answer is right-iustified, the two
are

Since only 46 bits of

”sign" bits (0 and l)

redundant.

METHODS

See the Single Precision Multiply Routine write-up, DEC-O8—FMBA
Formerly Digital-8-l l-F.

7.l

EXECUTION TIME

The execution time is a function of the number of 1's in the operands.
The maximum execution time is l .605 msec
i .4 msec

lO.

any page.

Average time will be around

PROGRAM
The subroutine occupies approximately one memory page and may be located on
The symbolic library tape does not start with an origin setting, but does end with a

dollar sign.
lO.4

Program Listing

4-3

/DEU~D8-FMDA-LA
/SIUNEO DOUBLE PRECISION MULTIPLY ROUIlNE
/CALL1NU SEQUENCE:
JMS DMDL
ADDRESS 0» MULIIPLIOAND(HIOH ORDER)
ADDRESS Or MULIIPLIER(HIUH ORDER)
RETURN. HIGH UNDER PRODUCI 1N AC
NEXT HIGH TU LDw 1N 8,C.U

/RAOE
025%

MODE

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C(L)

Double Precision Signed Divide Subroutine, DEC-08-FMEA-D.

ABSTRACT

The Double-Precision Divide Subroutine will divide a 24-bit signed divisor into
a 48-bit signed dividend to Produce a 24—bit signed quotient and an unsigned remainder.
3.

REQUIREMENTS

3 1

Storage

This subroutine requires l05 (decimal) memory locations.
forms:

It is provided in two

binary tape assembled with an origin of 0200 and, a symbolic tape with no origin

setting.
4.

USAGE

4.l

Binary Loader (Digital-8-2-U). The symbolic
is either assembled with the user program or separately with the proper origin setting.
The subroutine is loaded with the

4.2

Calling Sequence
The subroutine is called with an effective JMS DUBDIV with the address of the

high-order word of the dividend (address of the dividend) in the accumulator, followed by the
address of the high-order word of the divisor (address of the divisor).

calling program

Control returns to the

the address of the JMS plus 2.

TAD

HIGH

JMS

DDIVP

Low
HLT

DDIVP,
HIGH,

DUBDIV
-

/ADDRESS OF DIVIDEND
/DIV|DEND

o
o
0

Low,

/DIVISOR

The high-order quotient is returned in the accumulator and the remaining bits of
the answer are found as follows:

C(DIVN D4)
C(DlVNDl)
C(DlVND2)

Low-order quotient

High-order remainder
H

Low-order remainder

The quotient is signed, while the remainder is left unsigned.
5-l

Errors in Usage

4.5

Since the division process may be represented as:

W
DIVIsor

Dividend

Quotient, Remainder

such that:

(Quotient) (Divisor) + Remainder

It is possible to specify a dividend and a divisor such that the quotient cannot

be contained within the word size

nonvalid.
more

(in this case, 23 bits). If this is true, the results will be
This condition is not tested by the Double-Precision Divide Subroutine. (For a

complete description, see DEC—08-FMCA, Formerly Digital-8—l2-F, Section 4.5.)
RESTRICTIONS

See Section 4.5
6.

DESCRIPTION

6.1

Discussion

See DEC-O8-FMCA, Section 6. l

6.3

Scaling

The Dobule-Precision Divide Subroutine is scaled analogous to the scaling of the
Double-Precision Multiply Subroutine (DEC-08-FMDA, Formerly Digital-8-l3-F). It may be
considered either an integer divide or a fractional divide.

2-.46

2—]
O

i i

Sign

2-23

2-1
O

Complement)

L Binary Point
Dividend

Dividend (2's

L Binary Point
Divisor Sign

Divisor (2's

Complement)

2—23

2-]

Quotient (2's

L Binary Point
Quotient Sign

245
0

21 2O
47

LSign
222

2] 2O
23

LSign
222

21 2O

LSign
9.

EXECUTION TIME

9.]

Minimum

1 .424 msec

9.2

Maximum

1 .705 msec

9.3

Average

1 .65 msec

10.

PROGRAM

10.4

Program Listing

5—3

Complement)

.,L__r

/oEc—w8~FMEA-LA
/UOUBLE PRECISION DIVLUL SUURUUIINt
/CALL1N0 SEQUENCE:
C(AC)=AUDHESS 0+ HIGH ORDER
/
/

DUBUIV
ADDRESS 0r

RETURN;

JMS

6661
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DIVISOR<DIVIDLNUI HLSULIS UNSPhCIFIED
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C(DLVND4):LUN

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C(AU)=HlGH ORDER QUOTIENT

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12.

REFERENCES
See

DEC—DS-FMDA, formerly Digital—8—13-F.

5-7

Double—Precision Sine Subroutine, DEC-08-FMFB-D.

ABSTRACT

The Double-Precision Sine Subroutine will evaluate the function Sin(X) for
4 < X < 4 (X is in radians). The argument is a double-precision word, 2 bits representing

—

integer part and 2I bits representing the fractional part.

the

fraction

—

Sin(X)

I <

REQUIREMENTS

3 I

Storage

The result is a 23-bit signed

< I.

This subroutine uses 248 (decimal) memory locations.
3 2
.

Subprograms and/or Subroutines

Double-Precision Multiply Subroutine (DEC-08—FMDA, formerly Digital-8-I3-F)
(Digital-8-23-F).

The
or

EAE Version

USAGE

4.2

Calling Sequence

The Double-Precision Sine Subroutine is called by an effective JMS DSIN followed by the address of the high-order word of the argument. Control returns to the calling
program at the address of argument address + I with
answer in registers ARG, ARG + I.
For example:

JMS
ARGMNT

C(AC)

0, C(L)

0 and with the

DSINP

HLT

bsuN

DSINP,
ARGMNT,

I000

0000

DESCRIPTION

6.I

Discussion

input to the sine subroutine is considered to be in radians within the range
The subroutine is able to call itself recursively and does so when reducing the
the
of
range
argument to the first quadrant. The following identities are used:
The

—

4 < X < 4.

X < 0,

Sin(O) 0
Sin(—X) —Sin(X) (recursive call)

X <1T,

Sin(X)

-Sin(X

6—I

1T) (recursive call)

X > 1r/2

for

O<X<1T/2,

Sin(X)

Tr/Z

F=—2;)r—<
6.3

—

1T) (recursive call)

Sin(1r/2) :1

sothat

O<F<l,

I=(c1

then:
4

—Sin(X

C3F

C5F

c7|=

c9F )

Scaling
The scaling for the argument is:

t— Implied
Binary Point

(word is 2'5 complement)

Sign
The binary weightings of the argument may be represented as:

22O 2

1222324i..{

220221

L Binary Point
Sign

and

Thus,

1.5 radians would be:

001

100

000

-l .5 radians would be:

100

000

The answer is a 23-bit signed fraction (2's complement) with the following binary

weightings:

2-I 2-2 2-3 2-4

fi— Implied

E 2-2] 2-22 2-23

Binary Point
Sign
Thus if the answer were 0.75(IO), it would appear as follows:
ARG

000

ARG+I

000

If the answer were

-0.75(I 0), it would appear as:

ARG

IOI

000

AR (3+1

000

METHODS
7.2

Algorithm
See Section 6.1

EXECUTION TIME
9.I

Minimum

When the argument is a multiple of 1r:

9.2

Maximum

Without EAE:
With EAE:

I0.6 msec
2.78 msec

9.3

Average

Without EAE:
With EAE:

I0.4 msec

I0.

PROGRAM

I0.I

Core Map

70 psec

2.6 msec.

The Double—Precision Sine Subroutine,

listed, was assembled starting at
0400(8). It assumes that the Double-Precision Multiply Subroutine ( DEC-08-FMDA,
formerly Digital-8—I3-F) is in core starting at 0200. If the multiply subroutine is placed
elsewhere, the pointers on page I of the program should be changed.

6-3

10.4

Program Lis’ring
/DEC’UBHFMFB-PA
IDOUBLE PRECISION Sth
/P01NIERS T0 DEC-DU'FMUA
U341
@342

DMUL‘ZUU
8:341
5:542

040%

uaaw

@4UU

@229

DSIN,

U401
U402

1600

TAD

0404
D405

3347
2351

DCA
TAD
DCA

ThMP

U403

3351
1751

U4E6
@407

1751

TAD

3350

DOA

0410

2200
1296
3763

TAD

0299

@411
@412

0413
0414
@415
0416
0417
042%

$421
U422
U423

U424

7640

StA

5233

JMP

NtG

1350

TAD
SiA

XZ¢1
CLA
NtG INO

BOA

7640
5233
72mm

JMP

PNTJ

DCA

3755

DCA
CLA

I PNT6*1
CMA ILXIT
PUSH

XITl;

TAD
'DCA
TAD
DCA

3365

770%
5261

1350
7141
3350

0441

1347

U442
U443

7040
7430

0444

7091
3347

IHIGH

ARGUMENT

ORDER

/LON

ORDER

/t1x EXIT
/$AVE 0N PUSHDOWN

FOR

ZERO

CLA

3754

1763
3351
5751
1347

@445

152 031

ISZ

0436

@435
0436
@437
U44@

I ThMP
X2¢1

TAD

7240

@434

TLMP

1347

1363

@453

lADURhSS

X2
TtMP

2363

0426
0427

@432

152

DSIN

08!
I PUSH
PUSH
X2
ICHLCK
CLA

0425

@431

NEG;

pUsH
I

TAD
SMA

TAD
CLL
DCA
TAD
CMA

ThMP
/CHhCK

CLA
P05
XZ+1
CMA

XZ¢1
x2

StL
IAC
DCA

PUSH

ThMP

JMP

ISIN<U)=U

FOR

NEGATIVE

/SIN<°X)=«SIN(X)

IAC

LIST

/PAGE

0446

4200

JMS

@447

0547
1755

x2
TAD

045%

0451
0452
0453
0454
@455
0456

XLTZ,

7141
3755

CLL
DCA

1754

TAD
CMA

7040
7430

7001
3754
5225
7100

DSIN

IRECURSIVh CALL FOR SINE

I PNT3‘1
CMA 140
I PNT3‘1
I PNT3

INEGATE

sgL
1Ac

0462
0463
0464
0465
0466
0467
@479

1350
1360
3351

TAD

I PNT3
XITl
/IS
XZ*1

TAD
DCA

MPI*l
TEMP

7004

RAL

1347

TAD
TAD

@471

5300
3347

@457
0460

0461

$472
0473
0474
0475
0476
0477
wszv

1350

1362

0504
$505
0506
$507

JMP
CLL

ICARRY
X2
MPI

JMP

PCHK

DCA
TAD

DCA
J s

X2*l

JMP

PCHK,

CLA
TAD

/SIN(X):-31N( x .pl ’

TEMP

DSIN
XITZ
CLL IIS
XZ*1

TAD
DUA
RAL

MPIO*1

1347
1361
7510

TAD

M910

5337

JMP

3351
7004

X<PI?

SPA

3350
4200
0547

8583

PCS:

1351

w501
2

DCA

1357
7510

5250
7300

SPA

ALG

7440

StA

5324
1351

JMP

@514

7440

StA

5324
7140
7010

JMP

PZNG

CMA
RAR

CLL

3754

DCA

PNT3

7040
3755
5225

CMA
DCA

PNTJ*1

JMP

x:71

0522
0523

X<PI/Z?

TtMP

0510
0511
0512
0513
0515
0516
@517
0520
$521

THE

7A0

6-5

PZNG
TLMP

/SIN(Pl/2)=1

ANSWER

0524
@525
@526
0527
0530
0531
@532
@533
@534
0535
0536
@537
0540

7300
135%
1360
3359
7004
1347
1357
3347
4203
@547
5250
72mm

IDECPvBHFMFB-PA
IPAUE 3
CLL CLA
PZNBI
TAD
TAD
DCA

X2‘l

MPI*1
X2*l

RAL
XZ

TAD
TAD
DCA

MPI

JMS

DSIN

JMP

XITZ

1350

XZ*1

0541

7104

CLL

RAL

0542
@543

3753
1347

DCA
TAD

0544
0545
0546

7904

RAL

3752
5756

DCA

@551
0552
@553
0554

9900
game
game
0743
0744

0741

0555

@742

@556
0557
0560

060m
4667

@561
0562
@563

4023
6333

ALG;

JMP

IALIGN

CALL

FOR

SCALING

ALGORITHM

PNTZ*1

PNTZ
PNTA

I
;

ISYMBQLS AND
D
X2,

CONSTANTS

FOR

THIS

PAGE

TEMP:
PNTZ:

0
X

X‘l

PNTS:
PNTQt
M910

ARG
ARG* 1

DALG
4667

/e(PI)

4025

MPIUt

6912
0564

IRECURSIVL

CLA
TAD

0547
0550

/SIN(X)=~SIN(X'PI)

PUSH.

6533
6W12
PUSH t1

I'IPI/Z)
/

POINTER

FOR

PUSHUOWN

LIST

SINE

/UECHW8-FMFB-PA
lPAbE

Dbbfl
0600

$601
$602

0603
0604

B605

0606
0607

061%
9611
@612
0613
0614
@615
@616

4736
@743
@755

ROUND

4736
0743
@743
4277

JMS

DMTG

SCAL

XSQR

TAD
DCA
TAD

FYX
PNT

DCA
DCA
DCA

CHK
AHG

3345

7100

LOOP:

CLL

FOUR
/
/

AHG‘;

7924
1341

RAL

@641

4312
9741

ISE
TAD
TAD
DCA

15%
JMS
XSQR

4277

JMS
JMS

@645
@646

1541

@647

7510

7U2E
7910

BIT

/UET

x«x

IUET

RID

EXTRA

SIGN

BIT

\r'3>\—4

lit

ARG
I PNT
ARG

PNT

/1NCRtMtNT

POINTER

FOR

DMTG

ARG

0737

2346
5223
7100

SIGN

PNT

ARG*1
ARG‘l
PNT

4736
0741

EXTRA
NOW

/IN1

TAD
DCA

0635
@656
0657
064%

TAD

2345

ROUND

1745
1342
3342
2345

1745
3341

1353

3342

0652
@653
@654
@655

0737

@623
0624
@625
@626
@627

RID

/SCALING

JMS
JMS

@622

(Z/PI)*ARG

4312

3341

IkORM

/GET

JMS

0621

@651

7091
JMS sgAL

4312
@743

3346

065%

DMTG

SUAL

1354

@642
@643
0644

JMS

B620

0633
@634

“USIN‘ZMfl
JMS
DALE,

4277
4277

0617

@650
@631
0632

SCAL

/GET

RID

ROUND

ARG

ISZ
JMP
CLL
TAD

CHK

LOOP
ARG

/SHIFT

SPA

CML
RAR

3341
1342
701%

DCA

ARC

TAD
RAR

ARG‘1

3342

DCA

ARG*1

6-7

ARE

PLACE

SIGN

BIT

$656
0657
@666

@661
$662
$663
@664

@665
@666

@667
@670

@671
@672
0673
@674
0675
@676

CLL

136%
1342

TAD

Cl*l

TAD

AHG*1
ARG*1

1341
1357
3341
4736
0741

5676
@425

@715
@716

JMS

JMS
JMS

/UET

ALING
0 OF S

“f

ACK
6N

TO
BIT

iERd

OUT:
SCAL:

OUT

JMP I
XlTl

lRDUTINt

CLL

RAL

1751

DCA
TAD

1
1

7w04

RAL

3751
1350
7E04

DCA
TAD

I BTG
TtMZ

RAL
JMP

5677

ROUND;

ADJUST

SCALING

are
are

SCAL

3347
1712
2312

BOA
TAD

335a

:82

@717
@720

1347

@721

1350

0722

7%01
3347

DCA

@724

1751

TAD

0725

3747

DOA

0726
@727

1752
7710
5712

TAD

TtMl
I ROUND
ROUND
TLMZ

IADDRESS

HIGH

TfiMl

TtMZ

TLMZ

IAC

SPA

@731

2747

$732

5712

0753
@734
@735

2750

JMP
132
JMP
ISZ

7090

NOP

5712

JMP

073%

S~AL
5 AL
ROUND

ARC

BOA
TAD
DCA
TAD

@723

/PUT

ARC
I DMTG

7104
3752

3750

CONSTANT

TtMZ
I CTG

0090

LAST

ARC

9
BOA
TAD

1752

ARG

4312
@741

0701
0702

@710
@711
0712
@713
0714

JMS

@743
4277
4277

0@@@
3350

@704
0705
0706
0707

DCA
RAL
TAD
TAD
DCA

3342
7@@4

@677
@7@@

0703

/Auu

7100

TLMl
1 ETC
1 ThMl
1 CTG
LA

1811

Y ROUND

“1-.“
1

ThMl
ROUND

m=1??
/N03 EXIT
/YES: ROUND

TEN?
[RETURN
ROUND

/~ARRY

sk 1? 0R N072!

ORDER

/DEC-W8mFMFB-PA
lPAUE

AND

/SYMBULS
@200

DMTG,

0090
0000
0990
0090
0000
000%

XSQHa

@747
@750

0090
000%
0900
EEEQ

PNT:
CHKI
.EMI.

@751

0341

@752
0753
0754
0755

@342

8T5;
CTGa
FYXa
FOUR:
7091:

B756
0757
@760

6303

@736
@737
@740

0741
D742
0743
0744
0745
@746

@761
@762
0763
69764
0765
@766
@767
0770

0761
7774

2427

3110
3755
2367

ARG:
X0

$EM20

OWQQGQGGSG

ICS~C9

C9:
C7:

7766

1505

C5:

0243

042%

/2/PI

El:

@000

3331

CONSTANTS

DMUL

93:

5325

6-9

STORED

BACKNARDS

ORDER

SYMBOL

TABLE

0537

@741
0341
@751

BTG

C
CHK

0.6
6
Cs
6:
C7
09

DALG
DMTG
DMUL
DSIN
FOUR
FYX
LOOP
MP!
MPIO

@342
@746
@752
‘fl757
0767
$765
@763

@761
@600
@736
@290
@409
0754

@753
0623
0557
@561

NEG
our
PCHK
PNT
PNTZ
PNTS

@433
@676
0500
@745
@552

pNTa
POS

@556

PUSH

SUAL

@563
@524
0712
0677

TEMP

@551

TEMl
TLMZ
TUPI

@747
0750
@755

0743
0425
045%
@737
@547

PZNG

ROUND

X171
XITZ
XSQR
X2

@554
@461

6-10

Double—Precision Cosine Subroutine, DEC-OB-FMGB-D

ABSTRACT

This subroutine will form the cosine of a double-precision argument (in radians).
The

input range is

4 < X < 4.

REQUIREMENTS

3 I

Storage

This subroutine requires 64 (decimal) memory locations.
3.2

Subprograms and/or Subroutines
This subroutine requires the Double-Precision Sine Subroutine

(DEC-O8-FMFB-D).

The symbolic tape contains definitions that are used as intercommunication registers to the
sine subroutine.

3.3

If the sine subroutine is moved, these

"pointers" must be changed.

Equipment
Standard PDP-8.

USAGE

4.]

library tape that is supplied is a symbolic tape. It begins with an absolute
The binary tape produced by assembling this tape,
or the
binary tape produced by assembling this tape with other tapes, is loaded with the Binary
The

origin setting and ends with a dollar sign.
Loader.
4.2

Calling Sequence
The Double-Precision Cosine Subroutine is called in a

to the way in which the

Double-Precision Sine Subroutine is called.

manner

that is identical

For more complete in-

formation, see DEC-08-FMF B-D
5.

RESTRICTIONS
See DEC-O8-FMFB-D

DESCRIPTION

6.]

Discussion

The Double-Precision Cosine Subroutine uses the following identities:
If

X<O; COS(—X)

Then

SIN(1T/2

—

COS(X)
COS(X)

This insures that the argument presented to the sine subroutine is in the proper
range.

6.3

Scaling
See DEC-OS-FMFB—D

METHODS
See DEC-O8—FMFB-D

FORMAT
See DEC-08-FMFB-D

EXECUTION TIME

9.]

Minimum
The minimum time occurs when the argument is O.

9.3

In this case, time

55.5 psec.

Average
In general, the Double—Precision Cosine Subroutine takes from 75 psec to 93 psec

longer than the Double-Precision Sine Subroutine (see DEC-08—FMFB—D).
TO.

PROGRAM

10.4

Program Listing

/OEC-OB-FMGB~PA

@741
$420

1222

/DOUBLE PRECISION COSINE
/CALLS OEC-OB-FMFA
/POINTERS TO DEC-OB-FMFB
ARG=741
OSIN=4OO

§1000
DCQS:

2222

1622
3262

TAD

1003
1024
1225

1662
3256

TAD

I DCOS
ADDRSS
I ADDRSS

DCA

2262

1206
1207
121“
1211
1012

1662
3257

ISZ
TAD

ADDRSS
I ADDRSS
EX+1

1213
1214
1915
1216

1257

TAD

7642

SZA

5224
7242

CMA

1217
1020
1021
1922
1223

DCA

DCA
TAD

SZA
JMP

JMP

7212

RAR

3662

OCA

7242

CMA
DCA

3661
5254

1024

1256

1025

7722

JMP
TAD
SMA

1026

5237
1257

TAO

1927
103m

7141

TSIGNN:

122M
lflfll
lag?

1256
7642
5224

SUBROUTINE

JMP
CLL
DCA

1031

3257

1032
1033
1934

TAD

1935

1256
7242
7432
7221

1936

3256

DCA

CLA
TSIGNN
FX+1
CLA
TSIGNN

/FETCH ADDRESS OF
/ARGUMENT
/FETCH HIGH ORDER
/ARGUMENT
/INCREMENT ADDRESS POINTER
/EETCH LON ORDER
/ARGUMENT
/IS ARGUMENT EQUAL
/TO ZERO
/NO: TEST THE SIGN
/TEST LON ORDER BITS
/FOR ZERO
/NOT EQUAL TO ZERO

ARGPNT

I ARGPNT+1
EXIT

/SET

ANSWER

/SEE

X>g

CLA

ARGPOS
EX+1
CMA IAC

Ex+1
EX

CMA

SZL
IAC
EX

/ARGUMENT IS
/ARGUMENT IS
/NEGATE IT

>2
(O

ARGPOS:

1%37

73G®

CLL

CLA

1949

1257
7M41
1265
3257

TAD
CMA

TAD

EX+1
IAC
PIOT¢1

DCA

EX+1

1256
794w
743G
7091
1264
3256
4663

TAD

1041
1G42

1Q43
l$44

1M45
1@46
1047
195$
1351
1952
1953
1054
1055
1956
1057
1W60
1961
1962
1fl63
1Q64
1965

/SUBTRACT
/PI/2

FROM

CMA
32L
IAC
TAD

PIOT

DCA

JMS
EX

DCOS
I DCUS

1056
2209
5690

EXIT;

13?
JMP

@@@9

EX;

DSINPT

/CALL SINE SUBROUTINE
/ARGUMENT ADDRESS
/RETURN TO CALL*1
/ANSNER IN ARG:ARG*1

@@@®

@741
@742
BWQQ

ARGPNT;

ARG

ADDRSS:

@400

DSINPT:
PIOTn

DSIN
1444

ARG*1

1444

1767

PAUSE

SYMBOL

TABLE

ADDRSS

1@62

ARG

@741
1G6®

ARGPNT

ARGPOS
DCOS
DSIN
DSINPT
EX
EXIT
PIOT
TSIGNN

1G37
1Mfi®
@4Wfi
1963

1®56
1654
1®64
1W24

12.

REFERENCES

12 1

Other Library Programs

‘

See Digital-8-1I6-F For Further expianation of the calling sequence, timing,

and algorithm.

scaling,

Four-Word Floating-Point Package, DEC-08—FMHA-D.

ABSTRACT

This program is almost identical to the 3-word Floating-Point Package

(Digital-8-5-S) except that accuracy is carried to 35 bits, and 4 I2-bit words are used for
storage.
3.

REQUIREMENTS

3.I

Storage
This program occupies registers 7;

USAGE

4.I

40-6l; 5600-7577 (octal).

Binary Loader (Digital-8-2-U) or DECtape System.
4.2

Calling Sequence
Identical to Digital—8-5-S.
RESTRICTIONS

See Digital-8-5-S.

DESCRIPTION

The floating accumulator resides in memory locations 44,

45, 46, and 47.

The

instructions FGET, FPUT use 4—word arguments

(II-bit exponent + sign; 35—bit mantissa + sign).
The 4-word package contains all operations except for square root (0002) and square (000i).
METHODS

See

Digital-8-5—S.

FORMAT

EXECUTION TIME

9.3

Average

(Not Applicable)

Execution times are very difficult to estimate as they greatly depend upon the data
on

which the floating-point package is operating.

FADD

FSUB

FDIV

Generally speaking:

382 usec + 42(N) where N is the number of shifts to align

binary points.
FADD time + 42 psec
3.4 msec

(approximately)

8—I

FMPY

FGET

FPUT

FNOR

FEXT

10.

PROGRAM

10.4

Program Listing

3.3 msec

(approximately)

156 psec

1721mec
168 + N(42) psec where N is number of shifts;
+84 psec if argument <0.
140.5 psec

WORD FLOATING POINT
/ARITHMETIC INTERPRETER
/PAGE 1
/4

*AE

@640

0366

0041
DDAZ

fivbfl

0646

Duflfl

DDAA
0645

DEED

flflflfl

wnmw

0046
ADA?
aDSD

fldflfl

0651

DWDD

DEED

flflbfl

EXI,
HIGHI,
MIDI,
LOWI,
EXP,
HORDER,
MIDDL,
LORDER,
OVERZ,
OVERI,

w
0

fl
6

D
v

*61

/ARITHMETIC

ouél

Uflflfl

FLAG,

5606

mama

FPNT,

5661

7566

CLA

CLL

5692
5605
56v4

SD51
3653
16DD

DCA
DCA

5605
56U6

5257
1257

56%?
5616
5611

6265
7655
5214

AND

5612
5616
5614
5615
5616
5617

1267
DZDD
6262
127m
0257
1262

OVERI
0V£R2
I FPNT
JUMP
JUMP
PAGENO
CLA
.+5
MASKS
FPNT
ADDRS
MASK7
JUMP
ADDRS

562d

6262

TAD
AND
DCA
TAD
AND
TAD
DCA ADDRS

ERROR

FLAG

*5600
m

TAD
DCA
TAD
SNA
JMP

/GET

INSTKUCTION

/PAGE 0??
/YES
/N0

/GET

GET

PAGE BITS

BIT ADDRESS

5621
5622

1266
0257

5626
5624
5625

765%
5227
1662

5626

6262

5627
566M
5661
5662

2200

5666
5664

6266
2266
1666
6641
2266

564m

1666
6U42
2266
1666
6046
1257
71W6
7066
U264

5644
5645
5646

5647
5656
5651
5652
5656

6260
1666

6269
466m
5261

5657
566d

0900

10131010

5661

$666

5662
5666

@200
dfiUB

5664
5665
5666
5667

@017
UZMB

5676
5674
5675
5676
5677
57b0

5761

MASK6
TABLE
JUMP2
I JUMPZ
JUMP2
I JUMPZ
FPNT+1

1271

5654
5655
5656

5670
5671
5672

FPNT
I ADDRS
3X1
ADDRS
SAVE
SAVE
I SAVE
HIGHI
SAVE
I SAVE
MIDI
SAVE
I SAVi
LOVl
JUMP
RTL

1262

5666
5667

0463

7696
@177
5672
5714
660%
6626

6667

666%
5702
5766
62am

/BIT6=1??

/YES

DEFER

ADDRS

LOOPDI,

1662
604%

5665

5641
5642
5646

INDRCT
JUMP
CLA
LOOPal
1 ADDRS

JUMP,
JUMPZ,
602,
ADDRS,
SAVE,
mam,
PAGENO,
INORCT,
MASK5,
mam,
TABLE,

flfl17
$260
2460

7600

M177
0+1
EXIT
FLAD
FLSU
FLMY
FLDV
FLGT
FLPT
FNOR M

8-3

/EXPONENT

/HIGH ORDER

IMIDDLE BITS

/LOWER BITS

/LOOK-UP ON

/EXECUTE
/GET NEXT

TABLE

5702
57fi3
5724
5725
57fl6
5767
571m
5711
5712
5716

Dflfiv
1D4fl

FLGT,

TAD
DCA
TAD
DCA

/FLOATING

EXl
EXP
HIGHI
HORDER
TAD MlDl
DCA MIDDL
TAD LOdl
DCA LORDER
JMP FPNT+1
EXIT OR SUBROUTINEZEDXK

EXIT,

1241
5645
1242
5046
1W45

5847
5231
flbflfi

5726
5724
5725

166B
526%
1236
5261
466%

5765
5754
5755

GET:5fiflw

5m44

5714
5715
5716
5717
5726
5721
5722

5726
5727
5750
5751
5752

/FLOATING

fl264

TAD
AND

745D

SNA

1257

56Dfl
155D

626D

1261
5260
52D1
9006

JUMP
MASK5

/BITS 8-11:D??

JMP I FPNT
TAD TABLE6
DCA JUMPZ
TAD I JUMPZ
DCA JUMP2
TAD FPNT
DCA 602
JMS I JUMPZ
TAD 602
DCA FPNT
JMP FPNT+1
/FLOATING Pur:smwm

FLPT,

5766
5767
5740

1945
2262

TAD HORDER
ISZ ADDRS
DCA I ADDRS

5741
5742

1246
2262
5662

575a
5751
5752
5756
5754
5755
5756

/RESTORE PSEUDU

/RETURN

ADDRS

TAD MIDDL
ISZ ADDRS
DCA I ADDRS
TAD LORDER
ISZ ADDRS
DCA I ADDRS
JMP FPNT+1

1047
2262
5662

5201

575m
577m
577m
577w
577w
577m
5770

EXP

TAD
DCA

5745
5744
5745
5746
5747

/SAVE PSEUDO

1644
5662

5662

/YES:FEXT
/NO:LOOKUP BITS 8-11
/ON SUBROUTINE TABLE

TABLE6,
EXIT6
EXIT6
EXIT6
EXIT6
EXIT6
EX1T6

/SUBROUTINE TABLE
/ABSOLUTE ADDRESSES
/OF SUBROUTTNES

/EXIT6=DUMMY

NOP

5762
'5766
5764

577D
577D
577D
577D
577m
577D

5765
5766
5767

577D
577d
577$

5776
5771

660$

5757
5769

5761

EXITS
EXITS
EXITS

EXITS
EXITG
EXIT6
EXIT6
EXITS
EXITG

EXITS,

JMP

577D

/FLOAT1NG

EXIT6

ADD=1won

*6DDD

FLAD,

6dflfl

dflflfl

6wfl1

4261

JMS ALIGN

66v2
6w06

5660
4612

JMP

6004

76mm

60b5
6&36

1051
Ins»
6056
7064
1m46

6Dv7
6&10
6v11
6w12
6616
6014
6015

6616
6u17
6020
6021
6w22
6v26
6624

6025

JMS

CLL
OVERI
OVERZ
OVLRZ

1041
1m45
6045

CLA
TAD
TAD
DOA
HAL
TAD
TAD
DCA
RAL
TAD
TAD
DCA
HAL
TAD
TAD
DCA

4705
56%”

JMS
JMP

I
I

1v47
6047
7mn4
1043
1w46
6v46
7604

6D26

JDDD

6627
Svév

47m6
52U1

6n61
SD62

UDJW

/ALIGN WOKDS
/NO ALIGNMENT

I FLAD
SCALE

/TRIPLE ADDITION

/CARRY
LOdl
LORDfiR
LORDER
MIDI
MIDDL
MIDDL
HIGHI
HORDER
HORDER
NORMAL

FLAD

/FLOATING

SUBTRACTZZDDD

FLSU,

Jms
JMP

/ALIGN BINARY

ALIEN,

I OPMINS
FLSUX

POINTS

TAD

6066

1045
764D

SZA

HORDER
CLA

6v64

524D

JMP

.+4

8-5

/NEGAT£

/ADD

OPhRAND

6655

6056
6057

1046
5644
5272

6D41

1641
765a

6642
6645
6544

5651
1640
7641

6645
6a46

6552

104
745%
5272
75ww
7fl4l
5564

6655
6w54
6655

1554
1557
771%

6656
6657
6666

5274
1m4w
7041
1644
7004
7620
151M
1511
5555
4765
2564
5267
2251
5651
104%
7541
1044
77mm
5651
5702
5765

6046

6547
6656
6651

6661
6562
6w65
6664
6D65
6666

6567
667D
6571
6372
-6575

6674
6675
6076
6077
6160
6141

6132
6165
6164
6155

6655

MODE

6250

6116

6566
0645
0525

6111

6116

6156

6167

TAD EXT
DCA EXP
JMP DONE
TAD HIGHI
SNA CLA
JMP I ALIGN
TAD 8X1
CMA IAC
TAD EXP
SNA
JMP
SMA
CMA

DCA

TAD
TAD
SPA
JMP
TAD
CMA
TAD
RAL
SNL
TAD
TAD
DCA
JMS
ISZ
JMP

DONE,
NOGO,

POINT,
AMOUNT,
NORMAL,
OPNINS,
TESTI,
TCONI,
TCONZ,

/C(FAC):H

/OPERAND=@

DONE

/EXPONENTS

EQUAL

IAC
AMOUNT

/NUMBER

PLACES

EXIT‘

AMOUNT
TESTI
CLA

NOGO
EXI
IAC
dXP
CLA
TCONI
TCONZ
POINT

I POINT
AMOUNT
0-2
ISZ ALIGN
JMP I ALIGN

TAD EXT
CMA IAC
TAD EXP
SMA CLA
JMP I ALIGN
5MP I .+l
FLGT+1
d

FNORM
OPNEG
£645

SHFTOP-SHFTAC
SHFTAC

/NO

SHIFTING

/SHIFT
/SHIFT

POSSIBLE

OPERAND RIGHT
FAC RIGHT

6112

6666

6116
6114

4641
4616

6115

5712

6116
6117

6666

/SCALL

BOTH

SCALE,

SHFTAC,

6126
6124
6125

6645
1646

6126

7616

6127
6166
6161
6162
6166
6164
6165
6166
6167
6146

6646
1647

CLA

CLL
TAD HORDER
SPA
CML
RAR
DCA HORDER
TAD MIDDL
RAR

7666
1645

7516
7626
7616

6121
6122

SHFTOP
SHFTAC
JMP I SCALE
FLOATING AC RIGHT
JMS
JMS

/SCALE

6126

RIGHT

7616
6647
1656

7616
6656
2644

7666

5716

DCA
TAD
RAR

MIDDL
LORDER

DCA
TAD
RAR

LORDER
OVERZ

DCA

OVERZ

ISZ
NOP
JMP

EXP

/SCALE OPERAND
6141
6142
6146
6144

6145
6146

6147
6156

6666

7666
1641
7516
7626
7616
6641

7616

6152
6156

6642
1646

6154

7616

6155
6156

6646
1651

6157

7616

6166
6161

6651
2646

6162

6164

7666
5741
4200

6165

5626

SHFTAC
RIGHT

CLA
TAD
SPA
CML

CLL
HIGHI

RAR

DCA HIGHI
TAD MIDI
RAR

1642

6151

6166

SHFTOP,

DCA MIDI
TAD L061
RAR
DCA L061
TAD OVERI
RAR
DCA OVdfil
ISZ EXl

NOP
JMP

FLSUX,

I SHFTDP
JMS FLAD

JMP I FLUX

8-7

/NORMALIZE

FLOATING ACCUMULATOR

*6200

6220
6201

6202
6205
6204
6205
6206
6207
6210
6211
6212
6215
6214
6215
6216
6217
622a
6221
6222
6225

0600
7500
5561
5565
1045
7510
2565
7640
5224
1046
764a

5600

6252
6255

5251
1656

6254

7104
5050
1547

6255
6256

6257

7004

6246
6241

6242

5047
1046
7004

6245
6244

5046
1045

6245

7024

6246

5045
2561

6247
6250

6251
6252

JMP

1047
7640
5224
1050
7640
5224
5044

6227
6250
6251

6225
6226

5227
1561
7041

0
CLA
DCA
DCA
TAD
SPA

ISZ
SZA

5224

1565
7640
4261
1545
7104
7710

6224

FNORM,

606,

SHIFT,

NOREXT,

LORDER
CLA
006
OVER2
CLA
606
EXP
I FNOKM
MP5
CLA
ACNEG
HOKDER

JMP
TAD
CLL
DCA
TAD
RAL
DCA
TAD
RAL
DCA
TAD
RAL
DCA
TSZ
JMP
TAD
CMA

1644

TAD
DCA
TAD

4261

/NO

TAD
SZA
JMP
TAD
SZA
JMP
DCA
JMP
TAD
SZA
JMS
TAD
CLL
SPA

5044
1565
7642
5603

/INPUT<0
/YES‘5LT SWITCH
/FAC:0?

MP5
CLA
806

MIDDL
CLA

6254
6255
6256

6257

# OF SHIFTS
/R£SET SWITCn

TAD
SZA
JMP

6255

6260

CLL
MP1
MP5
HOKDER

606

/NO

/NO
/YES
/EXIT
/NA5

INPUT

/YES

RAL
CLA

/TOO

NOREXT
OVER2

/YiS:LXIT ROUTINE

FAK?

/NO

RAL

/SHIFT

OVLRZ
LORDER

LEFT

LORDER
MIDDL
MIDDL
HOKDER

HORDER
MP1
SHIFT

MP1
IAC
EXP
LAP
MP5

/ADD 1 TO
/CONTINUE

COUNT

/SUBTRACT
/EXPONLNT

COUNT

/NAS

SZA CLA
JMS ACNEG
JMP I FNORM

8—8

/YES
/EXIT

INPUT<077

FROM

/NEGATE

FLOATING

6261

0000

6262

7500

CLA

CLL

6265

1050

6264
6265

5050

TAD
CMA
DCA
TAD
CMA
SZL
CLL
DCA
TAD
CMA

OVERZ
IAC
OVERZ
LORDER

6266
6267
6270
6271
6272
6275
6274
6275
6276
6277

7041
1047
7040
7450
7101
5047
1046
7040

ACNEG,

IAC
LORDER
MIDDL

6500
6501
6502
6505
6504
6505

745a
7101
5046
1045
7040
7450
7101
5045
5661

SZL
CLL IAC
DCA MIDDL
TAD HORDER
CMA
SZL
CLL IAC
DCA HORDER
JMP I ACNEG
/NEGATE OPERAND

6506

0000

6507

6512

7500
1051
7041
5051

6515
6514
6515

1045
7040
7450

CLA CLL
TAD OVERI
CMA IAC
DCA OVERI
TAD L001
CMA

6516
6517
6520

7101
5045

6510
6511

6521
6522
6525
6524
6525
6526
6527
6550
6551
6552

1042
7040
7450

7101
5042
1041
7040
7450
7101
5041
5706

SZL
CLL IAC
DCA LOW!
TAD MIDI
CMA
SZL
CLL IAC
DCA MIDI
TAD HIGHI
CMA

SZL
CLL IAC
DCA HIGHl
JMP I OPNEG

8-9

6555
6554
6555
6556
6557
6540
6541
6542
6545
6544
6545
6546
6547
6553
6551
6552
6555
6554
6555
6556
6557
656M
6561
6562
6565
6564
6565
6566
6567
6570
6571
6572
6575
6574
6575
6576

6577

M003

MULTIP,

D666

JEDM
DEED
DDDD

7764
6490
DDMD

4766
4259
5D5D
2777
5767
4261
5767
675W

DCA

5561
5564
1565
5565
71mm
1561
7D1D
5561
1564
742%
5551
715%
1562
791%
5564
2565
5541
1561
731%
7106
5755

DCA
TAD
DCA

MP1
MPSCON
THIR
MP5

CLL
TAD MP1
RAR
DCA MP1
TAD MPSCON
SNL
JMP .+5
CLL
TAD MP2CON

MPSCON
MP5
MULTIP+6
MP1

MP1,
MP2 cow,
MP5,
MPSCON,
THIR,
FMULTI,
FLMY,

MULTIP

~14

EMULT

JMS I FMULTl
JMS FNORM
DCA OVERZ
ISZ I SIGNI
JMP I FLMY
JMS ACNEG

SIGNl,

JMP I FLMY
SGNTST

*64DD

/FLOATING MULTIPLY
/(A*2?24+B*2T12+C)*(D*2124+E*2T12+F)
640%
64v1
6402

6435
6464
6465
6406
6467

@206

7261
164%
1344
5M44
1577

5772
4775

FMULT,

CLA IAC
TAD EXI
TAD EXP
DCA EXP
TAD SMACLA
DCA I SGNSW
JMS I SIGNP

/ADD

EXPONENTS

/SET UP SIGN ROUTINd
/GO THERE

6414
6411

1040
6775

6412
6416

1447
4774
7244
1776
6671
1446
6775
1446
4774
1671
6671
7444
1776
6674
7444
6667
1442
6775
1447
4774

TAD L041
DCA I MP2
TAD LORDER
JMS I DMULT
CLA
TAD I MP5
DCA MUL5
TAD MIDDL
DCA I MP2
TAD LOWI
JMS I DMULT
TAD MUL5
DCA MULS
RAL
TAD I MP5
DCA MUL4
RAL
DCA MUL5
TAD MIDI
DCA I MP2
TAD LORDER
JMS I DMULT

1671
6671
7444
1674
1776
6674

TAD
DCA
RAL
TAD
TAD
DCA

7444
1667

RAL

6414

6415
6416
6417
6424

6421
6422
6426
6424
6425

6426
6427
6464

6461
6462
6466
6464
6465
6466
6467
6444
6441
6442
6446
6444

6445

6667
1445
6775
1446
6452
4774
6456- 1674
6454
6674
6455
7444
6456
1667
6457
1776
6464
6667
6461
7444
6462
6666
6466
1441
6464
6775
6446
6447
6454
6451

6465
6466
6467
6474
6471

1447
4774
1674
6674
7444

TAD
DCA
TAD
DCA
TAD
JMS
TAD
DCA
RAL
TAD
TAD
DCA
RAL
DCA
TAD

/C*F

/B*F

/C*E

MUL5
MUL5

MUL4
I MP5
MUL4

MULS
MUL5
HORDER
I MP2
LOWI
I DMULT
MUL4
MUL4

/A*F

MUL5
I MP5

MUL5

MUL2
HIGHI
DCA I MP2
TAD LORDER
JMS I DMULT
TAD MUL4
DCA MUL4
RAL

/D*C

6472

6475
6474
6475
6476
6477
6542
6541
6542

1567
1776
5567
7DM4

1566
5566
1D46
5775
1542

6545
6544
6565
6546
6547
6514
6511
6512
6515
6514
6515

4774
157m
557%
7594
1567
1776
5567
7Mfl4

6516

5775
1942
4774
1567
5567
7084

6517
6522
6521
6522
6525

6524
6525
6526

6527
6552
6551
6552
6555
6554

6555
6556
6557
654a
6541
6542

6545
6544
6545
6546
6547
6556
6551
6552

1566
5566
1M45

1566
1776
5566
7054
5565
1841
5775
1046
4774
1567
5567
7364
1566
1776
5566
7224
1565
5565
1645
5775
1fl4l
4774
1566

TAD MUL5
TAD I MP5
DCA MUL5
RAL
TAD MULZ
DCA MULZ
TAD MIDDL
DCA I MP2
TAD MID1
JMS I DMULT
TAD MUL4
DCA MUL4
RAL
TAD MUL5
TAD I MP5
DCA MUL5
RAL
TAD MULZ
DCA MULZ
TAD HORDER
DCA I MP2
TAD MIDl
JMS I DMULT
TAD MUL5
DCA MUL5
RAL
TAD MULZ
TAD I MP5
DCA MULZ
RAL
DCA MUL1
TAD HIGHl
DCA I MP2
TAD MIDDL
JMS I DMULT
TAD MUL5
DCA MUL5
RAL
TAD MULZ
TAD I’MPS
DCA MULZ
RAL
TAD MUL1
DCA MUL1
TAD HORDER
DCA I MP2
TAD HIGHl
JMS I DMULT
TAD MULZ

/B*D

/A*E

/B*D

/A*D

6555

5D46

6554
6555

7DD4
1565
1776
5645
1567
5047
157D
535%

6556
6557
656d
6561
6562
6565
6564
6565
6566
6567
657%
6571
6572
6575
6574
6575

6576
6577

DCA
RAL
TAD
TAD
DCA
TAD
DCA
TAD
DCA
JMP

5680
WEED

DEED

DEED
0060
@090

674%
6727
6555
6562
6564
77flfi

MIDDL
MULI
I MP5
HORDER
MUL5
LORDER
MUL4
OVERZ
I FMULT

MULl,
MUL2,
MULs,
MUL4,
MULS,
SGNsw,
SIGNP,
DMULT,
MP2,
MP5,
SMACLA,

SGNSWT
SIGNCL
MULTIP
MPZCON
MPSCON
SMA CLA

/FLOATING

DIVIDEz4flflfl

*66DD
6600

DDDD

‘6601

1D4D
7fl41
1944
7b01

66fl2
66D5

6664

6605
66D6

6667
6616
6611

6612

6615
6614
6615
6616
6617
6626

6621
6622
6625

6624
6625
6626

FLDV,

5fi44
1526
554M

5047
1346
7DD4

TAD EXl
CMA IAC
TAD EXP
IAC
DCA EXP
TAD SPACLA
DCA SGNSWT

/SUBTRACT

SIGNCL
HIGHI
SNA CLA
JMP DVER
CLA CLL
DCA QUOL
DCA QUOH
TAD MIF
DCA DIVCNT
JMP DVX
TAD LORDER
RAL

/SET

JMS
TAD

4527
1D41
765%
5595
759%
552%
5521
1525
5524
5255
1647
7E®4

DV5,

DCA LORDER
TAD MIDDL
RAL

EXPONfiNTS

UP SIGNS

/DIVISOR=D?
ERROR
/YES
-

6627

5046

6656
6651

1D45
7934

6652
6655
6654

5045
1345
1547

6655
6656

5522
7DD4
1042
1646
5525
7694
1W4l
1045
7428
5254
5645
1525
5846
1522
5D47
720%
1523
7064
5520
1521
7Dfl4
5521
1D5D
7DD4
565%
2524
5222
1529
5D47

6657
6640

6641
6642
6645
6644
6645
6646
6647
665%
6651
6652
6655
6654
6655
6656
6657
6668
6661
6662
6665
6664
6665
6666
6667
667M
6671
6672
6675
6674
6675
6676
6677
676%
6761
67D2

DVX,

SNL
JMP
DCA
TAD
DCA
TAD

sz,

DCA
CLA
TAD
RAL
DC
TAD
RAL
DC
TAD
RAL
DCA

ISZ
JMP
TAD
DCA
TAD

1521

HORDER
LOWI
LORDER
DTEMI

/PARTIAL SUBTRACT

/DIVISOK<DIVIDEND7
DV2-1
HORDER
DTEMZ
MIDDL
DTEMI

/NO

/YES:C(L)=QUOTIENT BIT

LORDER
/SHIFT BIT

QUOL

/QUOTIENT
QUOL
QUOH
QUOH
OVERZ
OVERZ
DIVCNT
DV5
QUOL
LORDER

/DONE?
/N0

QUOH

DCA MIDDL
TAD OViRZ
DCA HDRDER

5w45

DCA
JMS

5D59

4717
4746
5690

MIDDL
HORDER

RAL
TAD MIDI
TAD MIDDL
DCA DTEMZ
RAL
TAD HIGHI
TAD HORDER

5646
155%

2550

DCA
TAD
RAL
DCA
TAD
TAD
DCA

DEXIT,

ISZ
JMS
JMP

OVERZ
I NORMIT
SGNTST
l
I

FACNEG
FLDV

8-14

INTO

6706
6704

67d5

7240
6347
724%

6706
67a7
6719
6711
6712
6716
6714
6715
6716

6%46
7&43

6717
672%
6721
6722
6726
6724
6725
6726

6260
U960

7119
6345
1045
6244

2661
70d0

5696

@flflfl
@039
EMQD
006%

7765
771%

6746
6747
675%
6751

mama

1651
665%
1245
7730
5667
4746
2658
1041
7760
5727
4747
265M
766%
5727
6261
66%6
@992

7776

CMA
LORDER
CMA
MIDDL

/DIVIDE

ERROR

CLA
DCA
CMA
CLL RAR
DCA HORDER
TAD HORDER
DCA EXP
ISZ FLAG
NOP
JMP DEXIT

NORMIT,
QUOL,
QUOH,
DTEMI,
DTEMZ,
DIVCNT,
MIF,
SPACLA,
/TEST

6727
676%
6761
6762
6766
6764
6765
6766
6767
6740
6741
6742
6746
6744
6745

CLA
DCA

DViR,

FNORM

0
U

3
2
~46

SPA

SUBROUTINE

SIGN

SIGNCL,

SGNSWT,

FACNEG,
OPNEGS,
SGNTST,
RESTOR,

/ST£P COUNT
CLA

TAD RESTOR
DCA SGNTST
TAD HORDER
SMA CLA
JMP .+6
JMS I FACNEG
ISZ SGNTST
TAD HIGHI
SMA CLA
JMP I SIGNCL
JMS I OPNEGS
ISZ SGNTST
NOP
JMP I SIGNCL
ACNEG
OPNEG
U

‘2

/OR

SPA

CLA

ACNEG

6261

MPSCON

6564

ADDRS

5662
6m51

MP1
MP2
MPZCON
MP5
MP5
MULTIP
MULI

NORfiIT

6561
6575
6562
6565
6576
6555
6565
6566
6567
6576
6571
6374
6251
6105
6717

OPMINS
OPNEG
OPNEGS
OVERI
OVERZ
PAGENO
POINT
QUOH
QUOL
RESTOR
SAVE
SCALE
sGNSW
SGNSWT
SGNTST
SHFTAC
SHFTOP
SHIFT
SIGNCL
SI GNP
31 GM
SMACLA
SPACLA
TABLE
IABLE6
TCONI
TCONZ
TESTI
THIR

6136
6556
6747
0251
@055
5665
6155
6721
6720
6751
5665
6112
6572
6749
675%
6116
6141
6227
6727
6575
6577
6577
6726
5671
575$
611%
6111
6137
6565

ALIGN
AMOUNT

DEXIT
DIVCNT
DMULT
DONE
UTEMl
DTEMZ
DVER
DVX
DV2
5V5
EXIT
EXIT6
LXP
EXl
FACNEG

FLAD
FLAG
FLDV
FLGT
FLMY
FLPT
FLSU
FMULT
FMULTI
FNORM

FPNT
602
606
HIGHI
HORDEK

INDKCT
JUMP
JUMPZ
LOOPfll
LORDEK
LOW1
MASK5
MASK5
MASK7
MIDDL
MIDI
MIF

6104
672%

6724
6574
6972
6722
6725
6725
6655
6655

MULZ

MUL5
MUL4
MULS
NOGO

6622

NOREXT

5714
5770
@244
mm4a
6746
6505
flm61

NORMAL

66mw
5702

6567
5755
6026
64mm

6566
seam
566%
5661
6224
@541
(M45
5666
5657
566%

5627
@047
@645
5664

5667
567m
@246
6042
6725

8—16

/4/17/65-HB-OEC
/4 WORD
/FLOATING POINT I/O ROUTINES
/REQUIRES FLOATING POINT INTERPRETER
/ENTRY AT 0007
*7

0007

5600

0044

0000

0045
0046
0047

0000

0052

0000

0055
0054

0000
0000

0055

0000

0056
0057

7777
7777

FPNT,

5600

*44

0000
0000

EXPONT,
HORDER,
MIDDL,
LORDER,

5.9616.

*52

0060

0000

0061

0000

6767
6770
6771

0000

FPACl,

SWITI,
SWITZ,
CHAR,
OSWIT,

6.35.6»

7777
7777

/IF 2 0, NO CR-LF AFTER OUTPUT
/IF : 0, NO LF AFTER CR IN INPUT
/CONTAINS LAST CHAKACTER HEAD
/= 0 IF NO CONVERSION TOOK PLACi

0
0

*6767

6770
6776
6774

6775
6776
6777

1057
7650
5767
1677
4776
5767
7645
0212

PRCHAR,

TAD
SNA

JMP
TAD
005

JMP
OUT

LPED,

50172
CLA
I PKCHAR
LFED
I OPUT
I

PKCHAR

0212

/DOU6L£ PKLCISION DiCIMAL-BINAKY
/INPUT AND CONVERSION
*7000
7000
7001
7002

6045

DCA

HORDER

7006
7004

6046
6047

DCA
DCA

7005

6266

DCA

MIDDL
LORDER
SIGN

7006

6267
4650

DCA
JMS

DNUMBR
INPUT

7007

0000
7200

DECONV,

CLA

/INITIALIZE

MANTISSA

7u1v

1546

TAD

PLUS

7U11
7612
7616
7614
7u15
7U16
7017
7fl2v
7021

7456

SNA
JMP
TAD

DECUN
MINUS

7&22
7626
7024
7035
7026
7u27
7u6u

7u61
7v52
7066

7a54
7065

5220
1557
744a
5221
7246
5266
4356

72au
1969
1641
7594

7513

1645
D646
7440

5220

764v

4242

7U46
7047
7U5U
7951
7652
7056
7054
7w55
7456
7U57
766w
7U61
7662
7v65
7664

/IF-,

SET

.+4

SIGN

SNITCH

INPUT
CdAR

/IS

DIGIT

MIN9

SmA

5600
6265

2U61

FOR SIGN

CMA

JMP I DECONV
TAD PLUfilZ
SPA
JMP I DECONV
DC
DIGIT
TAD HOKDER

5650
1642

7066
7u67

7U41
7042
7u4s
7644
7645

DECON,

SZA
JMP
CLA
DCA
JMS
CLA
TAD
TAD

/TEST

5220

/NO

/YES

AND

MASK

/OV¢RFLUw?

SZA
JMP

DECUN

/YzS-IGNOKL

ISZ DSWIT
ISZ DNUMBR
JMS MULTlu
JMP macaw

2267

/NO

/INDEX

NUMDLR

016115

/CONTINUL
/ROUTIN£ TO MULIIPLY
/DOUBLE PRECISION NOKD
lfiY TEN (DECIMAL)
4

MULTlu,
TAD
DCA

1647
6046

LORDER
46

1U46

TAD

MIDDL

5w42
1445

DCA
TAD
DCA

DCA
JMS
JHS

5441
5646
427%

4667
4270
1265
6245
6&42

5641
45n7
1646
5642
Uwvfl

7u7w

aaéu

0291010

DUDE

/REMAIN=REMAINDER

MULTZ
MULTZ
JMS DUBLAD
JMS MULTZ
TAD DIGIT
DCA 46
DCA 42
DCA 41
JMS DUBLAD
TAD 4D
JMP I MULTlU

4274

7w65
7066
7w67

HORDER
41

DIGIT,
SIGN,
DNUMBR,
MULTZ,

/CALL SUBROUTINE
/MULTIPLY BY TdO

/CALL DOUBLE ADD
/ADD

LAST

DIGIT

RECEIVED

/EXIT WITH REMAINDER
/IN AC
/STOKAGE FOR DIGIT
/=D IF PLUS: 27777 IF MINU:
/:NUM5£R OF DIGITS
/MULTIPLY LOKDEH, HOflan DY 2

6;:
E}...
E“
E;

8-18

7071
7072
7076
7074
7075
7076
7077

1047
7004
6047

6046

1045
7004
6045

7111
7112

7117
7120
7121
7122
7126
7124
7125
7126
7127
7160
7161
7162
7166
7164

7165
7166

TAD
RAL
DCA

1046
7004

7100
7101
7102
7106
7104
7105
7106
7107
7110

7116
7114
7115
7116

CLA CLL
TAD LORDER
RAL
DCA LORDER

7600

TAD
RAL
DCA
TAD
RAL
DCA

1040
7004

6040
5670

MIDDL
MIDDL
HORDER

HORDER
40

MULTZ

jMP

7600

CLA

CLL

1047
1046
6047

TAD
TAD

LORDER

0000

DUBLAD,

/DOUBLE PRECISION ADDITION

DCA LORDER
RAL
TAD MIDDL
TAD 42
DCA MIDDL
RAL
TAD HORDER

7004
1046

1042
6046
7004

1045

5707

TAD
DCA
RAL
TAD
DCA
JMP

0000

1041
6045
7004
1040
6040

MSIGN,

CLA

7600
2266

41
HORDER
40

DUBLAD

/ROUTINE TO FORM
/2'S COMPLEMENT
/IF C(SIGN)=7777

CLL
SIGN

5760
4766
5760

lSZ
JmP
JMS
JMP

6261

/"ACNEG"

MINUS,
PLUS,
WINS,
PLUSI2,
MASK,

256-255
-256
-272
272-260
7600

/TEST

FOR

/TESI

FUR D1611

/TEST

FOR

0.10,

7775

7167
7140
7141
7142

7776

7146

7600

7144

7775

7145

6146

7147

6147

7525
7506
0012

I
1
1

MSIGN
.+2
MSIGN

7146

6146

INTERPADTEA

519“

OVERFLOJ

/INPUT A CHARACTER, 1F Cm, TEST
/INPUT SWITCH TO SEE IF LF SHOULD
/BE

715d
7151
7152
7155
7154
7155
7156
7157
7166
7161
7162
7165
7164
7165
7166
7167
7170
7171
7172

7175
7174
7175
7176
7177

QUUU

6651
5552
6056
5U6U

RUBOUT, KESTAKT INPUT
/INPUT A

CLA
KSF
JMP

72v%

1U6U

v-1

DCA

CHAR

TAD
JMS
TAD

CHAR
I OUTPUT
CHAR

SNA
JMP
TAD
SNA
JMP
TAD
SNA
JMS
TAD
JMP

745D
5551
1576
7456
5775
1577
7656
4775
1U6U
5756

PRINT,
OUTPUT,
RESTRT,
MRBOUT,
MINOR,

INPUT+1
MRBOUT

/IGNORE BLANKS

I RESTRT
MINOR
CLA
I PRINT
CHAR
I INPUT

/RUBOUT-RESTART

UUUO

7201
7202

4217
1524

72w3

5U44

72U4
72%5

1545
4545

72%6
7207
721m
7211

4757
1056
7659
569$
1541
4545
1542
4545

7212
7215
7214

7215
7216

56UU

FLOUTP,

/CR

INPUT

SEE IF TO BE
/BY LF
/EKIT ROUTINE
-

FOLLOWED

PRCHAR

OUT
FLINTP+1
-577
577-215

/FLOATING OUTPUT "E"
TSF
/USES:
JMP 0-1
/
TLS
/
*72au
72ww

CHARACTbfi

KRB

1U66
4774

6767
7545
7481
74U1
U162

TYPED.

INPUT,

FORMAT

JMS
TAD
DCA
TAD
JMS
JMS
TAD
SNA

JMP
TAD
JMS

TAD
JMS
JMP

/CONV£RT

FOUTCN

MANTISSA

AND OUTPUT

BEXP
LXPONT
CHE
OUT
I FEXPPT
SWITI
CLA
I FLOUTP
CARRTN
OUT
LNFEED
OUT
I FLOUTP

8-20

/CONV£RT EXPONENT AND OUTPUT
/PRINT CR-LF?

/NO-EXIT
/YES

/EXIT

/THIS WHOLE SUBROUIINE MAY BE ALIEKED
/THE OUTPUT DIGITS : CHANGE JMS OUTDG

7217
7226
7221
7222
7226
7224
7225
7226

7227
7260
7261
7262
7266
7264

7265
7266
7267
7240
7241
7242
7246
7244
7245
7246
7247
725a
7251
7252
7256
7254
7255
7256
7257
7260
7261
7262
7266
7264
7265
7266
7267

160010

FOUICN,

T0 BUFFER
TO DCA I 10,

76v”

CLA

CLL

1045
7712

TAD
SPA

HORDER
OLA

/NUMBER>6??

CLA

CML
SPLUS

/NO

SMINUS
OUT
OUTDG
PERIOD
OUT
CLL
HORDER
OLA
FGOI

/NO

7220
1627
7466
1660
4645

TAD
SZL
TAD
JMS
JMS
TAD
JMS
CLA
TAD

4656

1661
4645
76m6
1045
7700
5242
7040

SMA

6766
4762
7246

DCA
Jms
CLA

JMP
CMA

F601,

6624
1w44
7526
5266
1626
7700
527m

F002,

2624
5246

/OUTPUT

”0"

/OUTPUT "."

/NUMBER
I SNPT
I MSNPT
CMA

EXPONI
EXPONT
BEXP
TAD EXPONI

JMP
TAD
SMA
JMP

NEGATIVE

/NEGATE

/SUBTHACT 1 FSOM BINARY
/COMPENSATE AT F004

LXPON

/INITIALIZE DECIMAL EXPONLNI
/IS -4<EXPONENI<-l

F006
FOUR
CLA
F004

/TOO

I FPNT
FMPY I IENPT
FEXI
CLA CMA
TAD BEXP
DCA BEXP
JMP F802
JMS I FPNT
FMPY I PRC.10
FEXT
ISZ BEXP
JMP FGOZ
Jms

Baum

260%

LINK

SMA

4467
674a
7240
1624
6624
5246
4407
6744

SET

/YES

TAD
DCA
DCA

1044
6m44

LTC.

F606,

8-21

LARGE:

MULTIPLY BY

/IOO SMALL‘TIMdS
/TEN

/ONE

TENTH

ILN

l/lu

7276

6764

7271
7272
7276
7274
7275
7276
7277
76mm
7621
7622
7626
7664
7665
7666
7627

4766
4765
7410
4666

F604,

F005A,

2644

5274
745%
5611
4656
1625

F006,

FGO6A,

4656
2644

5664

5617

7611
7612
7616
7614
7615
7616
7617
7626
7621
7622
7626

7246
1624
6624
1045
7640
5622
1647
7650
6624
7246
5662

F607,

7624

163101610

BEXP,
MINUS7,
FOUR,
SPLUS,
SMINUS,
PERIOD,
MSNPT,
SNPT,
DPT,
MIWPI,
MZPT,
FEXPPT,
TENPT,
CARRTN,
LNFEED,
CHE,
PRC.10,

7641
7642
7646
7644

7767
0664

6256
@662
@256

7166
7366
7665
7042

7670
7526
7564
2215
6212
M665
7144

DPT

I
I

MZPT
MlflPT

DIVTNO

/MULTIPLY BY TNO
/IE.SHIFT LEFT
/MULTIPLY BY TEN
/COMPENSATE F02
/BINARY EXPONENT

EXPONT
FGO5A

FIRST DIGIT A ZERO
/YES, IGNORE
/MULTIPLICATIONS YIELD
/DECIMAL DIGITS AS HIGH
/OHDER REMAINDERS
/1£. .672x1w:6+.72.. ETC
/IS

JMP

7610

7625
7626
7627
7662
7661
7662
7666
7664
7665
7666
7667
7640

JMS
JMS
SKP
6M3
ISZ
JMP
SNA

6044

4765

DCA

F807
JMS OUTDG
TAD MINUS7
DCA EXPONT
JMS I MIEPT
JMS OUTDG
ISZ EXPONT
JMP F3064
JMP I FOJTCN

TAD

LORDER
CLA

DIGITS OdTPdT??

/NO:

CONTINUE

/Y£S:£XIT
/IGNORE FIRST DIGLT
/SUBTRACT 1 FdOM
/DECIMAL EXPONdNT

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

/IS

MARTISSA

ZLHU?

DCA BEXP
CLA CMA
6MP F806+1

/YiS:iXP:w

/CONTAINS DECIMAL LKPONENI
/NUMBER OF DIGITS OUTPUT

‘11
0664
256

255-256
256
MSIGN

/P01NTERS

SIGN
DIGIT
MULTIQ
MULTZ
FEXC
TEN
0215
0212
665
0.10

8—22

OUT,

0060

7646
7647
7650

6641
5646
6646

7651
7652

726%
5745

7656
7654
7655

DUDE

7656

5756

7657

U260

0260,

0263

7666
7661

wwnw

DIVTWO,

7662

7666
7664
7665
7666
7667
767w
7671
7672
7676
7674
7675

7406

7461
7402

7406
7464
7465

7466
7467
7416

TSF
JHP
TLS
CLA
JMP

OUTDG,

6645

1v46
7610
6w46
1647
761%
6047
1645
576m

5226

7415
7416
7417

6722

1614
7650
5222

6614

5726

.-1

OUT

/OUTPUT ONE DIGIT

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

CLL RAB
DCA OUT
TAD HORDER
RAR
DCA HORDER
TAD MIDDL

7116
6645
1645
701%

7411
7412
7416
7414

CHARACTEH

TAD C26fi
JMS OUT
JMP I OUTDG

1657
4645

6066
7240
6614
6661
4717
7266
1666
1616
764a

/OUTPUT ONE ASCII

7645

RAR

DCA
TAD

MIDDL
LORDER

RAR

DOA
TAD
JHP

LORDEH
OUT
I DIVTUO

/FLOATING
*7400

POINT

FLINTP,

INPUT

CLA
DCA

CNA
PRSN

DCA

DSNIT

JMS
CLA

/INITIALIZE "PERIOD SWITCH"

DPCVPT

TAD CHAR
TAD PER
SZA CLA
JMP FIGOI
TAD PRSN
SNA CLA
JMP F1802

/7777

PERIOD

/PERIOD FOUND
/SECOND PERIOD

/YES,T£RMINATE

DCA I DPN
DCA PRSN
JMP I DPCSPT

8-23

/NO
SET NUMBER OF DIGITS
/SET PERIOD SNITCH TO 6
CONVERT REST OF STRING
-

7422

7421
7422
7425
7424
7425
7426
7427
7455
7451
7452
7455
7454
7455
7456

7457
744d

7441
7442
7445
7444
7445
7445

7447
7450
7451

1514
765%
1722
7w41
5515
4721
1512

F1601,

F1605,

5&44

44fl7
703%
6052

TAD PRSN
SNA CLA
TAD I DPN
CMA IAC
DOA SEX?
JMS I MSGNPT
TAD C45
DCA EXPONT
JMS I FPNT

-FNOR
FPUT FPACl
FEXT
TAD CHAR
TAD MINUSE
SZA CLA
JMP ENDFI
JMS I DPCVPT
JNS I MSGNPT
TAD HORDER
SPA
IAC
SZA CLA
JMP EXCESS
TAD LORDER
TAD SEX?
DOA SEXP

BOQD

1D6O
1511
764$

5252
4717
4721

1545
7510
7OD1
764M
5277
1047
1515
5515

/PERIOD READ

/Y£S:'NUMBER OF

PREVIOOSLY?
DIGITS

/TE5T

7466

7467

44m?
5652

ENDFI,

JMS

FGET

FPNT
FPACI

0096
1515

FEXT
TAD SEXP

745D

SNA

5663
77UO

SMA

5276
4407
571M
DOOM

2515
5255
5606

JMP

/NOHMALIZ£ F.P.
/SAVE

/"E"

NUMBER

NUMBifi

READ

IN?

/NO

/YES
CONVERT DECINAL
/TEST SIGN
/EXPONENT TOO LARGE77
-

/YES
/NO:DECIMAL POINT IS
/C(SEXP)PLACES TO NIGHT
/OF LAST DIGIT

JMP

/RESTORE

I FPNT
FMPY I PC.1v
FEXT
ISZ SEXP

JMP
JMP

MANTISSA

I FLINTP
CLA
FIGO4

JMS

ENDFI+6
I FLINT?

8-24

éflR

SIGN

/END OF FLOATING POINT INPUT
/COMPENSAT£ FOR DECIMAL EXPONENTS
7452
7455
7454
7455
7456
7457
746%
7461
7462
7465
7464
7465

/NO

/TIMES

TO THE LEFT:
.luva

bXPONE

747a

4407

7471

5504

7472

ovum

7475
7474
7475
7476
7477

724m
1515
5515
5255
1516
5044
1516
5u45
5695

75uu
7501
7502
7505
75m4
7555
7566
7507
7510

7511
7512
7515
7514
7515
7516

5554

TEN,

www@
umwm

DUDD
$066

7144
7475
0545

7522
5505
BEEU

5777
7DDD

7029
7158
7567

Pc.1a,
MINUSE,
C45,
PER,
Pst,
SEXP,
cs777,
DPCVPT,
DPCSPT,
NSGNPT,
DPN,
/0UTPUT

7526
7527
755a
7551
7552
7555
7554
7555
7556
7557
7540

7541
7542

2666

7555
1544
7512
7561
5544
1567
7456
1579
4775
5045
1544
2545
1571
755b

5557

FEXC,

/. IS TO THE RIGHT:
/MULTIPLY BY lb

@504

24nd

7520

7525
7524
7525

I FPNT
FMPY TEN
FEXT
CLA CMA
TAD SEXP
DOA SEXP
JMP ENDF1+5
TAD 05777
DCA EXPONT
TAD 05777
DCA HORDEH
JMP I FLINTP

JMS

2405

7517
7521
7522

F1604,

0.1%

'505
@545
'256
D

/00NTAINS

5777
DECO NV
DECON

MSIG N
DNUMBR
THE

EXPONENT

CLA

CLL

TAD
SPA

EXPONT

CMA

1A0

DCA

EXPONT

CML

TAD 0255
SZL
TAD 0255
JMS I DGPT
DCA HORDER
TAD EXPONT
ISZ HORDER
TAD M144
SMA
JMP .-5

8—25

DECIMAL

EXPONENT

7545
7544
7545
7546
7547
755m
7551
7552
7555
7554
7555
7556
7557
756%

7561
7562
7565
7564
7565
7566

TAD 0144
DCA EXPONT

1572
5044

CMA
TAD

7042
1fl45
744m

HORDER
SZA
JMS I DGPT
DCA HORDER
TAD EXPONT
ISZ HORDER
TAD M12

4775
5545
1944
2945
1575
756d

SMA

JMP
TAD
DCA
CLA
TAD
JMS
TAD
JMS

5555
1574
5547
7249
1545
4775
1047
4775
5725

7567
757%
7571
7572
7575
7574
7575

7775
WQBZ
7654
@144
7766

0212
7555

BEXP
CARRTN

7524
7541

CHAR
CHE

2669
7545

Cglfl
C12
C144
C255
C255
026%
C5777
C45
DECON
DECONV
DEPT
01617
DIVTWO
UNUMBK
DPCSPT

7144
7574
7572
7567
7576
7557
7516
7512
7323
756%
7575
7565
756w
7567
7520

0’6
C12
LORDER
CMA
HORDER
I DGPT

LORDER
I DGPT
JMP I FEXC

0255,
0255,
M144,
0144,
M12,
012,
DGPT,

@255 -260

255‘255
'7654
2144
7766

4412
OUTDG

8-26

UPUVPI
1)? N
0P1

05411
UUBLAU
"ya-w

7517
7522
7554

MINUdi
filNUS7
MlN9
MKBUUI
NSGNPT
6516N
MSNPT
MULTIU
MULTZ
UIJPT
M12
m144
MZPT
OPUT
OUT
OUTDG
OUTPUT
PC.1U
PER
PERIOD
PLUS

0661
7107
7452
7477

dAPONT

0044

FLAU

FEXPPT
F601
F602
F605
F604
F6054
F606
F606A
F607
F1601
F1602
F1605
F1604
FLINTP
FLOUTP
FOUR
FOUTCN
FPACl
FPNT

7525
7557
7242
7246
7265
727m
7274
7501
7504
7511
7420
7422
7426
747g
7422
720m
7526
7217
0052
0607

fiORUdn

$045

SiGN

INPUT
LFEU
LNFEdD
LOKDEH

7150
6777
7542

SMLNUS

6047

swlTl

PESK

7145

64112

MIDDL
M1NCR
MINUS

ggqs

PLUSIZ
PRCHAR
Pn0.16
PRINT
Pnsw
R¢STKT
six?

SNPT
SPLUd

{LN
TdNPT

7177
7157

11.

DIAGRAMS (Not Applicable)

REFERENCES
See

Digital-8—5-S.

8-27

7511
7525
7141
7176
7521
7156
7552
7642
7670
7555
7575
7571
7556
6776
7545
7555
7174
7516
7515
7551
7140
7142
6767
7544
7175
7514
7175
7515
7666
755a

7555
7527
mw56
@057
7504
7540

Logical Subroutines, DEC-O8-FMIA-D.

ABSTRACT

Subroutines for performing the logical operations of inclusive and exclusive OR
are

presented as a package

REQUIREMENTS

3 I

Storage

Inclusive OR requires I2 (decimal) core locations.
I4 (decimal) locations.
3.3

Exclusive OR requires

Equipment
Basic PDP-8

USAGE

4.I

The subroutines may be placed in memory by means of the Binary Loader.
Digital-8—2-U-Rim for a complete description of this loader and its use.
4.2

See

Calling Sequence

Both subroutines are called by a JMS instruction with one argument in the accumulator. The location following the calling JMS contains the address of the second argument.
Both subroutines return to the location following that containing the latter address with the
result in the AC.
6.

DESCRIPTION

6 I

Discussion

These subroutines
in the performance of logical

supplement the AND and CMA hardware instructions

operations.

Note that the result of the exclusive OR is the com-

plement of the logical operation termed the "biconditional ."
6.2

Examples

Truth tables for these functions are as follows. Depending on the values of
corresponding bits in A and B, the associated bit of the result conforms to the following truth
tables:

—-—ao>

Exclusive OR

Inclusive OR

AND

Biconditional

Result

Or for complete data words

Exclusive OR

Inclusive OR
A

011010111001

010110101 100

010110101 101

Result 001 100 010 100

Result 011 110111 101
9.

EXECUTION TIME

9.2

Maximum
Execution time is actually fixed for these subroutines.

precisely 32.0 microseconds.
10.

PROGRAM

10.4

Program Listing

Inclusive OR requires

Exclusive OR requires exactly 46.0 microseconds.

A listing of both subroutines with INCOR stored in 0200 is as follows:

/LOGICAL SUBROUTINES
/ENTER WITH A IN AC
/ADDRESS OF B FOLLOWS CALLING JMS
/RETURN WITH RESULT IN AC TO
/LOCAT|ON FOLLOWING THAT HOLDING ADDRESS
INCOR,

/|NCLUSIVE OR

0200

0000

0201

3226

DCA

0202

1600

TAD

0203

3227

DCA

0204

1627

TAD

0205

7040

CMA

0206

0226

AND

TEMPYI
I

INCOR

TEMPY2
I

TEMPY2
TEMPYI

TEMPY2

0207

1627

TAD

0210

2200

ISZ

0211

5600

JMP

0212

0000

0213

3226

DCA

0214

1612

TAD

0215

3227

DCA

TEMPY2

0216

1226

TAD

TEMPY1

0217

0627

ANDI

TEMPY2

0220

7041

CLA

0221

7104

CLL

0222

1226

TAD

0223

1627

TAD

0224

2212

ISZ

0225

5612

JMP

0226

0000

0227

0000

EXCOR,

TEMPY1,
TEMPY2,

9-3

INCOR
I

INCOR

/EXCLUS|VE OR
|

TEMPY1
EXCOR

RAL

TEMPY1
I

TEMPY2
EXCOR

EXCOR

Arithmetic Shift Subroutines, DEC-OB-FMJA-D

ABSTRACT

Four basic subroutines, shift right and shift left each at both single and double

precision,

are

presented as a package.

REQUIREMENTS

3 l

Storage

These are arithmetic shifts.

Core storage required for these subroutines is as follows in decimal:
Shift Left

3.3

Shift Right

Single Precision

Double Precision

Equipment
Basic PDP-8

USAGE

4.l

Loading
These subroutines may be loaded using the Binary Loader.

See

Digital-8-2-U-Rim

for a complete description of this loader.

4.2

Calling Sequence
All four subroutines are called with -N

accumulator.

(the 2's complement form of N) in the

N is a binary integer specifying the number of bit positions the data words are to

be shifted.
.

case

In the location following the calling JMS instruction is an address which in the
of the single-precision subroutines is the address of the data to be shifted.

In the case of

the double-precision subroutines, this address is that of the most significant portion of the data.
The least significant portion of the data must be located in the address following that of the
most significant

portion.

These subroutines will

return to

the address following that of the calling JMS plus

Upon exit, the AC will hold the shifted data in the case of single-precision shifts. In
the case of double—precision shifts, the AC will hold the most significant portion of the result
two.

while the least significant portion of the result will be stored in location LSH.

4.5

Errors
It is possible by specifying too large an N to shift data completely out of a com-

puter word or words in the case of single-precision shifts or double-precision shifts, respectively.
These subroutines do not test for this eventuallity.

lO-l

DESCRIPTION

6.
6

Discussion

These subroutines are arithmetic shift subroutines.
case

of any shift, bits shifted "out" of the register are lost.

By this is meant that in the

In the case of left shifts, bits

moving into the least significant bit position are always 0. In the case of right shifts, bits
moving into the most significant bit position (the sign) bits are 0 if the original data was positive but are I if the original data was negative.
6 .2

Examples
The following examples illustrate the nature of the single-precision shift process.

In each example,

Positive

Ne 9 afive

6.3

shift of four bits is shown:

Right

5ft

Data

000 010 100 100

000 000 111 101

Result

000 000 001 010

001 111 010 000

Data

111111010100

111110000101

Result

111111111101

100001010000

Scaling
Shift right and shift left operations are the fundamental means by which numerical

data is scaled in fixed-point computers.

Application

For more information on numerical
Note 801.

EXECUTION TIMES

9.3

Timing Equations

binary scaling for fixed-point computers, see

Time needed for a given shift may be calculated from the following equations.

9.3.I

Single-Precision Shift Left

9.3.2

Single-Precision Shift Right

Time in microseconds

—

For negative data, time in microseconds

Double-Precision Shift Left

9.3.4

Double-Precision Shift Right

22.4

I 0—2

22.4 + 9.6N.

40.0 + 20.8N

For positive data, time in microseconds

For negative data, time in microseconds

II.2N.

Time in microseconds
-

“

22.4 + 6.4N

For positive data, time in microseconds

9.3.3

40.0 + 25.6N.

40.0 + 24.0N.

10.

PROGRAM

10.4

Progrom Listing
A

listing of all four subroutines with SPSL located at 0600 is as follows:

/SHIFT RIGHT SHIFT LEFT SUBROUTINES
/SINGLE AND DOUBLE PRECISION
/SHIFTS ARE ARITHMETIC RATHER THAN LOGICAL
/BITS SHIFTED OUT OF REGISTER ARE LOST
/DURING LEFT SHIFTS ZEROS ENTER LEAST SIG. BIT
/DURING POSITIVE RIGHT SHIFTS ZEROS ENTER MOST SIG. BIT
/DURING NEGATIVE RIGHT SHIFTS SIGN IS PROPAGATED
/ENTER WITH -N IN AC
/CALL|NG SEQUENCE. JMS SPSL OR SPSR OR DPSL OR DPSR
ADDRESS OF DATA
/
RETURN, RESULT IN AC FOR SINGLE
/
RESULT (MSB) IN AC FOR DOUBLE
/
RESULT (LSB) IN LSH FOR DOUBLE
/
0600

0000

0601

3302

DCA CNTR

0602

1600

TAD I SPSL

0603

3303

DCA ADDR

0604

1703

TAD IADDR

0605

2200

ISZ SPSL

0606

7104

CLLRAL

0607

2302

ISZ CNTR

0610

5206

JMP .-2

SPSL,

0611

5600

JMP I SPSL

0612

0000

0613

3302

DCA CNTR

0614

1612

TAD I SPSR

0615

3303

DCA ADDR

SPSR,

0616

1703

TAD IADDR

0617

2212

ISZ SPSR

0620

7100

CLL

0621

7510

SPA

0622

7020

CML

0623

7010

RAR

0624

2302

ISZ CNTR

0625

5220

JMP .-5

0626

5612

JMP I SPSR

10-3

/SINGLE PRECISION SHIFT LEFT

/SINGLE PRECISION SHIFT RIGHT

0627

0000

0630

3302

DCA CNTR

0631

1627

TAD I DPSL

0632

3303

DCA ADDR

DPSL,

0633

1703

TAD | ADDR

0634

3304

DCA MSH

2303

ISZ ADDR

0635

/MOST SIGNIFICANT HALF

0636

1703

TAD I ADDR

0637

3305

DCA LSH

0640

2227

ISZ DPSL

0641

1305

TAD LSH

/LEAST SIGNIFICANT HALF
/SH|FT LEFT

0642

7104

CLL RAL

0643

3305

DCA LSH

0644

1304

TAD MSH

0645

7004

RAL

0646

3304

DCA MSH

0647

2302

ISZ CNTR

0650

5241

JMP .-7

0651

1304

TAD MSH

0652

5627

JMP I DPSL

0653

0000

0654

3302

DCA CNTR

0655

1653

0656

3303

TAD I DPSR
DCA ADDR

0657

1703

TAD I ADDR

0660

3304

DCA MSH

0661

2303

ISZ ADDR

0662

1703

TAD I ADDR

0663

3305

DCA LSH

0664

2253

ISZ DPSR.

DPSR,

0665

1304

TAD MSH

0666

7100

CLL

/DOUBLE PRECISION SHIFT LEFT

/DOUBLE PRECISION SHIFTRIGHT

/MOST SIGNIFICANT HALF

/LEAST SIGNIFICANT HALF
/SH|FT RIGHT

0667

7510

SPA

0670

7020

CML

0671

7010

RAR

0672

3304

DCA MSH

0673

1305

0674

7010

TAD LSH
RAR

0675

3305

DCA LSH

0676

2302

ISZ CNTR

0677

5265

JMP .-12

10-4

0700

1304

TAD MSH

070]

5653

JMP l DPSR

0702

0000

0703

0000

0704

0000

0705

0000

ADDR

0703

CNTR

0702

DPSL

0627

DPSR

0653

LSH

0705

AASH

0704

SPSL

0600

SPSR

0612

CNTR,
ADDR,
MSH,
LSH,

0
0

10-5

Logical Shift Subroutines, DEC—O8-FMKA-D

ABSTRACT

Two basic subroutines, shift right at both single and double precision are presented
as a

package.

The shifts are

logical in nature.

REQUIREMENTS

3 .l

Storage
Core storage required for these subroutines is 12 (decimal) locations for single pre—

cision and 24 (decimal) locations for double precision.

3.3

Equipment
Basic PDP-8

USAGE

4.l

These subroutines may be loaded using the Binary Loader.
for a complete description of this loader.
4.2

See

Digital-8-2-U-Rim

Calling Sequence
Call with -N

(the 2's complement form of N) in the accumulator.

N is. a binary

integer specifying the number of bit positions the data word is to be shifted
In the location following the calling JMS is the address of the data in the case

of single precision.

For double precision this location contains the address of the most signi-

ficant portion of the data which mustbe stored in two consecutive words.

The subroutines return to the location following that containing the data address.
For single precision the result is in the accumulator upon return.

For double precision the most significant part of the result is in the accumulator on return while the balance
of the result is in location LESTSG.

4.5

Errors
It is quite possible by specifying too

pletely out of a computer word or words.
6.

DESCRIPTION

6 I

Discussion

large an N effectively to shift data com-

These subroutines are logical shift subroutines.
is no difference between arithmetic and

It is important to note that there

IOgicaI shifts in the case of left shifts.

Consequently
only two new subroutines in addition to those described in Digital-8-8-U-Sym are required to
supply all logical shifts.
Logical right shifts are defined as those in which bits shifted ”out“ of the least
significant bit position are lost. Bits moving into the most significant bit position are always 0.
6.3

Examples
The following examples illustrate the nature of the single-precision logical right

shift.

In each example,

shift of four bits is shown.
Result

Data
000
111

010
010

111

000

001

011

000

011

101

000

EXECUTION TIMES

9.3

Timing Equations
Time needed for a given shift may be calculated from the following equations.

9.3.1

Single-Precision Logical Right Shift

9.3.2

Double-Precision Logical Right Shift

10.

PROGRAM

10.4

Program Listing

Time in microseconds

22.4

36.8 + 24.0N.

A listing of both subroutines with LSRSP located in 0200 is as follows;

0200

/LOGICAL SHIFT RIGHT SUBROUTINES
/SINGLE AND DOUBLE PRECISION
/ENTER WITH -N IN AC
/DATA ADDRESS FOLLOWS CALLING JMS
/RETURN WITH DATA IN AC
/MOST SIGNIFICANT PART FOR DOUBLE
/LEAST SIG. PART FOR DOUBLE IN LESTSG
0
0000
/SINGLE PRECISION
LSRSP,

0201

3236

DCA TIMES

0202

1600

TAD I LSRSP

0203

3237

DCA COMMUN

6.4N.

0204

1637

TAD I COMMUN

0205

7110

CLL RAR

/SHIFT LOOP

0206

2236

ISZ TIMES

0207

5205

0210

2200

/EXIT

0211

5600

JMP .-2
ISZ LSRSP
JMP I LSRSP

0212

0000

/DOUBLE PRECISION

0213

3236

DCA TIMES

0214

1612

TAD I LSRDP

0215

3237

DCA COMMUN

0216

1637

TAD I COMMUN

0217

3240

DCA MOSTSG

0220

2237

ISZ COMMUN

0221

1637

TAD I COMMUN

0222

3241

DCA LESTSG

0223

1240

0224

7110

0225

3240

DCA MOSTSG

0226

1241

TAD LESTSG

0227

7010

RAR

0230

3241

DCA LESTSG

LSRDP,

SHIFT,

TAD MOSTSG

CLL RAR

0231

2236

ISZ TIMES

0232

5223

0233

1240

JMP SHIFT
TAD MOSTSG

0234

2212

ISZ LSRDP

0235

5612

JMP I LSRDP

0236

0237

0240
0241

/SHIFT LOOP

0
TIMES,
COMMUN, 0
MOSTSG, 0
0
LESTSG,

/EXIT

DIGITAL EQUIPMENT CORPORATION

MAYNARD. MASSACHUSETTS