Digital PDFs

XX-5F5D8-4E

June 1973

13 pages

Original

2.1MB

Document:	DECUS FOCAL8-284 8-E EAE Routine For FOCAL 1973
Order Number:	XX-5F5D8-4E
Revision:
Pages:	13
Original Filename:	http://bitsavers.org/pdf/dec/pdp8/focal/DECUS_FOCAL8-284__8-E_EAE_Routine_For_FOCAL__1973.pdf

OCR Text

PROGRAM

DECUSNo.

TITLE

AUTHOR

COMPANY

DATE

SOURCE LANGUAGE

LIBRARY

FOCAL8-r284

8/E EAE ROUTINE FOR FOCAL

James Van Zee

University of Washington
Seattle, Waf.hington
.

June 1973

PAL8

ATTENTION
This is a USER program. Other than requiring that it conform to submittal and review standards,
no quality control has been imposed upon this program by DECUS.
The DECUS Program Library is a clearing house only; it does not generat~ or test programs. No
warranty, express or implied, is made by the contributor, Digital Equipment Computer Users
Society or Digital Equipment Corporation as to the accuracy or functioning of the program or
related mqterial, and no responsibility is assumed by these parties in connection therewith.

8/E EAE ROUT! NE FOR FOCAL
DECUS Program library Write-up

DECUS NO. FOCAl8-284

THIS FOCAL EAE PATCH WAS DESIGNED SPECIFICALLY FOR THE 8/E
COMPUTER SERIES.
IT USES MODE B EAE INSTRUCTIONS AND A NEW
MULTIPLY ALGORITHM TO PROVIDE A SUBSTANTIAL IMPROVEMENT OVER
THE REGULAR PATCH SHOWN ON PAGE 89 OF THE LISTING.
THE TIME
REQUIRED TO MULTIPLY TWO 36 BIT NUMBERS IS NOW ONLY 155 MICROSECONDS COMPARED TO TYPICALLY 700 MICROSECONDS WITH THE OLDER
EAE ROUTINE AND OVER 2800 MICROSECONDS WITH SOFTWARE.
THE
RESULT IS ALSO ROUNDED OFF - NOT JUST TRUNCATED - WHiCH iMPROVES
THE ACCURACY.
THIS is DEMONSTRATED BY THE COMMAND liT %, 1E99"
WHICH NOW GIVES 1I¢.1¢¢¢¢¢¢¢¢7E+1¢¢" INSTEAD OF "¢.9999999954E-+99~'
THE THREE-WORD NORMALIZE ROUTINE HAS ALSO BEEN REWRITTEN~
THE ENTIRE NORMALIZATION NOW TAKES ONLY 60 MICROSECONDS.
PREVIOUSLY IT TOOK THAT LONG JUST TO DEAL WITH NEGATIVE NUMBERS
SINCE THE SOfTWARE (UNLIKE THE HARDWARE) COULD ONLY HANDLE
POSITiVE NUMBERS.
ADDITIONALLY A SHORTCUT USED BY THE SOFTWARE HAS BEEN ELIMINATED WHICH IMPROVES THE ACCURACY Of CERTAIN NEGATIVE NUMBERS BY A fACTOR Of TWO.
ANOTHER ADVANTAGE
OF THE HARDWARI ROuTINE IS THAT MULTIPLE SHifTS ADD ONLY A
fRACTION OF A MICROSECOND PER SHifT.
THIS MEANS THAT EVEN THE
LONGEST NORMALIZATION (34 SHifTS) TAKES ONLY 67 MICROSECONDS
IN CONTRAST TO THE SOFTWARE WHICH IS 23.5 TiMES SLOWER (1.573
MILLISECONDS).
WHILE SUCH DRAMATIC IMPROVEMENTS ARE NOT AS
COMMON AS fACTORS OF 2~4J SiNCE THE NORMALIZE ROUTINE IS USED
AT THE END OF EVERY ARITHMETIC OPERATION THESE IMPROVEMENTS
SPEED UP ALL FLOATING POINT CALCULATIONS AND NOT JUST THOSE
INVOLVING MULTIPL1CATION.
BECAUSE THE HARDWARE DIVIDE INSTRUCTION USES ONLY A SINGLEWORD DIVISOR (AND BECAUSE DIVISION IS NOT ASSOCIATIVE) THIS
INSTRUCTION CANNOT BE USED IN THE FLOATiNG DIVIDE ROUTINE, BUT
IT IS USED IN TWO OTHER P LA CE ST 0 CREA T E 8 W0 R D II H0 LE S II •
FOR
FLOATING DIVISION TWO DISTINCT APPROACHES HAVE BEEN USED: ONE
FOR THE STANDARD VERSION OF FOCAL AND THE OTHER FOR THE 10DIGIT VERSION.
THE LATTER OFFERS ONLY MINOR iMPROVEMENTS UPON
THE ROUTINE SHOWN IN THE FOCAL LISTING, BUT THE REGULAR VERSION NOW TAKES ADVANTAGE OF THE DAD INSTRUCTION TO REDUCE THE
DIVIDE TIME BY A FACTOR OF 1.7 (TYPICALLY).
IN BOTH CASES
THE " Z E ROD I V I SO R" ERR 0 ReO DE HAS BEE N CHAN GEDT 0 28. 1 AS A
RESULT OF MOVING THINGS AROUND TO CONSOLIDATE EMPTY AREAS~

THERE ARE SEVERAL OTHER PLACES WHERE EAE INSTRUCTIONS (OR
EVEN JUST THE BSW INSTRUCTION) COULD BE USED.
HOWEVER, SINCE
GENERALLY ONLY A FEW MICROSECONDS WOULD BE SAVED, THESE CHANGES
WE REF E L T TO BEl NS I GN I F I CAN T •
ON E EXC E P T ION 1ST HE ALI GN/F I X
ROUTINE WHICH COULD GREATLY BENEfiT FROM THE ASR INSTRUCTION.
UNFORTUNATELY THE MODIF ICATION WOULD REQUIRE ADDITiONAL CORE
SPACE IN A TIGHTLY-CODED AREA AND SO WAS NOT INCLUDED.
LASTLY IT SHOULD BE NOTED THAT BEFORE EXITING FROM THE
FLOATING-POINT INTERPRETER THE MQ REGISTER IS CLEARED AND THE
EAE RETURNED TO MODE A.
THUS OTHER ROUTINES, ESPECIALLy THOSE
WRITTEN FOR PREVIOUS EAE's, MAY BE USED WITHOUT CONCERN AS TO
WHICH MODE IS SET.

THE BINARY TAPE CONTAINS TWO SECTIONS: THE FIRST LOADS THE
la-DIGIT VERSION OF AL~ ROUTINES AND THE SECOND MODIFIES THE
MULTIPLY AND DIVIDE ROUTINES FOR THE NORMAL (3 WORO) VERSION.
THUS FOR STANDARD FOCAL THE ENTIRE TAPE SHOULD BE READ !N AFTER
LOADING FOCAL.
WHEN THE 4-WORD (10 DIGIT) OVERLAY IS USED, IT
SHOULD BE LOAOED FIRST, FOLLOWED BY THE fiRST SECTION (ONLY)
OF THE EAE TAPE.
THERE IS NO KNOWN CONFLICT WITH OTHER FOCAL·
OVERLAYS.
THE TOTAL FREE SPACE AVAILABLE DEPENDS ON WHETHER THE 6- OR
la-DIGIT VERSION IS USED.
WITH THE lO-DIGIT VERSION THE LARGEST
FREE BLOCK IS 46 WORDS LONG.
IF ONLY THE 6-DIGIT VERSION IS
REQUIRED, THIS PARTICULAR AREA BECOMES 49 WORDS LONG AND ANOTHER
WORD BLOCK is ALSO AVAILABLE.
(THIS COULD BE
WORDS
IF "MINUS" WERE SIMPLIFIED.)
THE LOCATION OF STILL OTHER fREE
AREAS CAN BE DETERMINED FROM THE LISTING.
SINCE THE REGULAR
EAE PATCH SAVED ONLY 12 WORDS THIS fEATURE MAY BE CONSIDERED
A BIG IMPROVEMENT TOO.
THE AUTHOR, fOR INSTANCE, HAS IMPLE~ENTED HIS FCOM FUNCTION IN PART Of THIS SPACE.

THE FOLLOWING COMPARATIVE EXECUTION TIMES (IN MICROSECONDS)
MAY BE OF INTEREST.
THE MEASUREMENTS DO NOT INCLUDE THE TIME
REQUIRED FOR SIGN-CHECKING OR NORMALIZATION, NOR DO THEY INCLUDE THE ARGUMENT FETCH - ALL OF WHICH NATURALLY REDUCE THE'
NET IMP R0 VEMEN TIN PRO GRAM S PEE. D•
ASAN 0 VERA L L F IG URE, I T
WAS OBSERVED THAT A PROGRAM PERfORMING A LEAST-SQUARES fiT ON
1022 DATA POINTS (DATA WAS STORED ON DECTAPE IN ASCII FORMAT)
RAN 14% SLOWER WITH THE REGULAR EAE PATCH AND 25% SLOWER WITH
JUST THE SOfTWARE ROUTINES (10 DIGIT VERSIONS).
THIS RESULT
IS PROBABLY TYPICAL fOR CALCULATION-BOUND PROGRAMS.

4 WORD VERSION

3 WORD VERSION

tFOCAl. PATCHES FOR 8/E EAE

JVZ

PAL8-V7

IFOCAl. PATCHES FOR a/EEAE

6/7113
JVZ

ITHESE PATCHES SUBSTANTIALl.Y REW!!!TE FOCAL'S MULTIPLY AND
INORMALIZE RtlUTINES IN ORDER TO USEEAE INSTRUCTIONS.
'niE
IHARDWARE ASStt-IED' IS A 'PDP-S/E EXTl:NDED ARITHMETIC EtEMmT
ITYPE KE8-E.
MODE 13 INSTRUCTIONS ARE USED EXTENSIVELY. THE
IMEASURED EXECUTION TIME FOR A 36 BIT BY 36 BIT MULTIPLY
115 ONLY 155 MICROSECONDS - ABOUT HALF THE TIME NEEDED FOR
lONE 12 SIT PRODUCT (OF WHICH mERE ARE 9) USING THE STAI'JIDARD SOFTWARE ROUTINES AND FASTER BY A FACTOR OF 4.5 'THAN
ITHE PATCH SHOWN O~ P. 89 or THE FOCAL L 1 5TIN G.
SUUl.ARl. Y
ITHE TIME FOR A 1 Bl T "NOAMAl.12:.E HAS BEEN DECREASED BY A
IFACTOR OF 2.
FOR NEGATIVE NUMBERS A FACTOR OF 3 IS OBITAINED SINCE NO INVERSION IS REQUIRED.
DIVIDE AND SOME
IOTHER ROUTINES HAVE ALSO BEEN· REWRl TTiN IN ORDER TO CONI SOL! DATE EMPTY AREAS.
nU:SE MODI FI CATION S MAKE AVAIl.ABLE
178 WORDS AND CHANGE THE ZERO-DIVI SOR ERROR CODE TO 28.< 1.
I SYSTEM SYMBOLSs

74i5
1487
74U
1413
7421
1431
7441
7445
7447
7451
7521
7575
7621
77fH

HUY-1415
DVI-1411
NNl111117411
SHL- 7413
MQL-7421
SWAB-7431
seA-744l
OST·7445
SWSAIIIII7447
DPSZllll7451
SWP-7521
DQ4-7575
CAM-7621
. ACLIIII771U
FIXTAS
IFOCAL SYMBOLS.

1033
e01i8

."44
IIJIi!lS0
1113
8124
2442
611"
6136
6154
64'S
6520

T3 1111 33
n.OP-4i
PLAC-44
S1GNFW58
C260 111 1 ! 3
P40QUI. 124

IOPERAND
IACCUMULATOR
lSI caN OF RESUL. T

PRNT-2442
FLOUTP&6000
SlUN1II613~

o UTPG- 61 54
FPN T- 6408
ZERO-6520

,/FOCAL PATCHES FOR 8/E EAi:

JVZ

6/7113

PALS-V7

IFOCAL IN STRUCTI ON 511
4451

4527
4551
4566

82444
82445
82446
112441
(12451
02451
82452
02453
S2454

2444
7427
"812

1I13
455i
1521
5642

61114
7181
'1144

16116
86117
16tll
86111
16112
16113
06114
86115
16116

1336

06 i ! 1

16120

4551
UJ33
7SH}
7141
7427
0144
7521

4737

86122

5618

IPRINT TWO DECIMAL DJ GJ TS
IDIVIDE BY TEN

I
I

IS!
166

IGET QUOTI!NT

IFOR4 ASCII
I GET R91AIN DER

Zm.OCK 10

IEIGHT LEFT OVER

*6104
SMA CLA
CMA CLL RAL.
TAD SUN
PRINTC
TAD T3
SPA

IEXPONENT OUTPUT ROUTINE
ITEST SIGN OF EXPONENT
ICREATE It."
lOR "-"

CIA

ITAKE ABSOLUTE VALUE
IDIVJDE BY ONE HUNDRED

IGET DECIMAL EXPONENT

MQL DVI

144

SWP

7448
4354
7521

16121

1 127

TAD C261
PRINTC
JMP I PRNT

1113
4551

16185

*2444
MQl. DVI

SWP

82455

16114

IJMS
ltoIMS
ltoIMS
IJMS

12
SWP
TAD C261
PRINTC

1521

NEGATE=445!
SHIFTL-4521
PRIN TC- 4SS 1
ERROR2-4566

16123

IPRINT QUOTIENT
IUN1.ESS J T' S ZERO

SZA
JMS OUTDS
SliP
dillS 1 PANTI
dMP 1 FLOUTP

INOW PRINT REMAINDER

ZBL.OCK 11

IEIGHT FREE

IPOINTERS REQUIRING CHANGES:
86131

6131
2442

*6131

16384

716g

RESOL 5, RESOt. V

IFOR FLOATING INPUT

16565

6565
1123

*6565
OPMINS, MINUS

IFOR SUBTRACTION

6516

*6576

06576

7165

FLDV

,86152

7160

PRNT!,

6314

PRNT

*6314

6752

IFOR Dl VI SION

*6752
RESOL,

RESOLV

IFOR FIX

'IFOCAL PATCHES FOR S/E EAE

PALS-V?

J'UZ

6/7/73

ITHREE WORD BY THREE WORD UNSIGNED MULTIPLY ROUTINE
I

(A+B+C)$( D+E+F>

CONE+ TWO+THREE+ FOUR+FI VE+SIX)

lrII

IruE METHOD GENERATES ALL 6 WORDS" Bur IS MODIFIED
IHERE TO. PRESERVE OMLY THE :3 MOST SIGNIFICANT ONES ..
IADDITIONALLY THE RESULT I S RO~DED OFF RATHER THAN
ISIMPLY TRUNCATED WHICH IMPROVES THE ACCURACY ..

7103

07113

7135

fJ7ee4
17015
87886
87017
I?IUI
07811
17012
17113

;0013
U'41

S71!4
17tU5

*7003
-43

MUL T"

4323
7431

SWAB

ISET MODE B

TAD C

Ie TAD P4180> FOR 2X2
ICJMP BE-I>
FOR 2X2

4341
7451

5757
7710

11347

CF,

7425

07128
87821
.7S22
17123
87124
17825
17126

1046
7525
001&3
1124
3360
7084
3349

BF"

07027

1047
7525

CE"

87032

8842

17034
87035

1360
7421
7430
2340

87136
07137

7525

17133

07048

07041
87042
07143

17844
87045
07046
07147

H'4S

ITEST FOn ZERO OPERAND

IPOSITIVE OPERAND REQUIRED

ISAVE HIGH ORDER" ERASE SIX

TAD B
SWP HOY
F
TAD P4881
DCA FOUR
RAL
DCA THREE

IUSE PREVIOUS HIGH ORDER AS
lRDtAINDER IN THIS POSITION
lROUND OFF
ISAVE INTERMEDIATE RESULT
ISAVE CARRY ANDIOR CLEAR THREE

TAD C
SWP HOY

IADD IN PREVIOUS
lPARTIAL PRODUCT
lSUM HIGH ORDER PARTS
IDISCARD FIVE lIND SAVE CARRY

E
TAO FOUR
MQL
SZL
ISZ THREE

AT"

0943
1340
3340
1047
7525
094'
1340
3340

IADD EXPONENTS CPLUSD

HQL MUY
F
MQl.

1843
7421

87030
07031

13
TAD EXI
JMS SI GN
SNA
JMP I NULL
SPA CLA
JMS MINUS

071U7

87016

1l.0 0 P CO U>J TTEf4\Ii IN ATES LIST

IACCUMULATE CARRIES

TAD A
SliP HUY

F
TAD mBEE

IBUILD UP l.EAST SIGNIFICANT
IPART OF FINAL RtSUL T

DCA THREE
CD#

TAD C
SliP HOY

D
TAD THREE
DCA THREE

liNTRY POINT FOR 2X2

JVZ

/Fo-CAl. PATCHES FOR 8/E EAE

,01950

1046

07851
071!1J52
81053
011554
11855
07156

7525
01412

11151
011'1
01861
11062
11063

BE"

SWP M'UY

1340

TAD THREE
MQI..

?fH1I4

RAJ..

3323

DCA TWO
A~

101 SCARI) FOUR

0142
1323
3323

TAl) TWO
DCA TWO
SO ..

/SAVE CARRY

TAD A

SWP MUY
E

81e64 ·1846
11165 1525
81066 8e41
01161
1323
.,11flJ 1521

6/7/73

TAD B

142J

U'45
1525

PALS-V1

/SlM CARRY BITS
/WITH CARRY WORD

TAD B

SWP HOY
D
TAD

TWO
/UIQL) FOR 2X2
ISAVEnU:tEE

sWP

.'871

3841

81012
17113
07174
01015
01816

UJ45
1525
0141
7565

ee45

SWP DST
HORD

/SAVE
ONE & TWO
.

07177
\ 01UUJ

4102

JMS I

JHS RESOLV
JHlP I HOLT
mORM

/NORMALIZE IF REQUIRED
IRESTORE PROPER SIGN
lAND RETtmN

17112

4360
5604
7335

07103

eeee

~e1HH

DCA OVER2
AD"

TAD A
SliP MUY

NOAH ..

NORM

ZBl.O CK 29

/SIXTEEN FREE WORDS

/ STAN DARD DEFIN I TI ON S.
0e49
0041
""'42
9143

£Xl-FLOP
AC lH·1LOP+ 1
AC1L-FLOP+2
OVERl-fLOP+3

9944
1045
9046
9047

EXPIIIIFLAC
HO RDa f'LAC+ 1
LO RD* f1.AC+ 2
OVER211111 fLAC+3
/LETTER ASSIGNMENTS:

0045
.046
0047

A-HORD
B-LORD
C-OVER2

/FLAC

9041
0042
9943

DaAC 1M
EaACIL
Fill 0 VERI

/OPERAND

".IFOCAL. PATCHES FOR 8.1E EAE

JVZ

PALS-V7

6/7.173

.I TH ESE SUBRO UT IN E5 PREPARE MUL TI PI.. Y AN D Dl VI DE FO R
.IANY COMBINATION OF 51 GN ED ARGttiDJTS" OR FOR ZERO •
.ITHE RESULT OF EITHER IS ZERO IF FLAC 15 ZERO; IF'·
ITHE OPERAND 15 ZERO THE PRODUCT 1 S ALSO ZERO" BUT
) A TTEMPTED DIVISION BY ZERO RETURI S WITH AN ERROR.
.

.ITHE SIGN ROUTINE IS PNTERED WITH THE' OPERAND EXPOlNDlT 1{\J THE AC AND EXITS WITH THE SIGN OF THE OPIERAND THERETO FACILITATE FURTHER TESTING, THE
ISIGN OF THE RESULT 15 STORED IN SIGNr.
-.
87123
87124
87125
87126
87127
87130
87131
87132
87133
87134
87135
87136
87137

8.88
1431
18"2
7575
1565
"842
71&47
7224
1841
781&1

811116

1845
3858
1845

87168
87161
17162
87163
87164

5WP DST
ACll.

SWBA
CLA CMLRAL
TAD ACIH
CIA
'DCA ACtH
JMPI"MINt1S

3illl

8'"''
7881
1844

/NEGATE5 OPERAND

8
TAD OVER1
SWAB
TAD AC1L

DeM

5723

8114.
87141
87142
871113
87144
• 7145
.7147
.7158
87151
87152
.7153
87154
81155
87156
.7157

M 1{\J US"

U,43

SIGN"

3.411
7138

.8111

8
lAC
TADEXP
DCA EXP
S1'1. RAR
AND ACIH
TAD HORD
DCA SIGN'
TAD HORD

.IADD I TO EXPONDITOFOP.
'COMPUTE EXPONDIT OF RESULT

.ISET BIT •
IEXTRACT 51 ON
IFORM XOIlO' 51 ON S
ISIaI OF REStiLT

SMA

71158
5151

ITEST IF RESULT •

JMP I NULL
SPA CLA
NEGATE
TA~ ACIH
"HPI SIGN
ZERO

7718
4451
1'41
5748
6528

NULL"

1888
1158
7711
4451
5760

RESOLV" 8
TAD SIGNF
SPA OLA
NEGATE
tlMP I RESOLV

IABSOLUTEVALUE REQUIRED

ICHECK THE OPERAND
IFOR VARIOUS THINGS
.I SET PROPER SIGN

INtl\fBER ASSIGNMENTS.
7123
7i41
716"

ZERO

'. TWO-MINUS
THREE-SIGN
YO URa RESOL V

/FOCAL PATCHES FOR 8/E £AI:

J'VZ

PALS-V7

6/1/73

ITHIS IS THE FLOAtING DIVIDE ROUTINE (THREE VOROS)

07165
11166
01161
81110
61111
17.172
07173
17114
11115
07116
81117
87210
07211
01202
07213
07204
.,285
87286
81207
07210
87211
17212
81213
17214
87215
11216
81211
01220

81221
81222
07223
07224
07225

81226
07227
07230
81231
"7232
17233
17234
07235
07236
11237
01241
87241
87242
07243
012"4

81245
\ 07246
/ .7247

181/U}

n.DV#

TAD EXI

/ GET 0 PERM D EXPON iN T

CIA
JMS SIGN

IMD NEGATE
ICHECK SIGNS" ZERO
lCHECK FOR ZERO Dl VI SOft
'THAT'S A NO-NOI

7041
4340
7450
4566
7700
4323
1203
3040
1431

SNA
ERROR2
SMA CLA
JMS MINUS
TAD HUl.T-l
DCA £Xl
SWAB

14H1J

SKP

/NEGATIVE OPERAND REQUIRED
lSET UP LOOP COUNT
I CLEAR RESUL T

1 If"

CLL

I SHIFT FLAt LEFT
ITHREE WORD SUBTRACTION

1043
1047
3335
10e4
1042

TAD OVERI
TAD OVERa
DCA mORN

/TEMPORARY STORAGE

4527

DLOOP.,

SHirTL

HAL
TAD AC!!..
TAD LORD
DCA SCNT

1.46
3364
1104
11141
1045
1420
5223
3.45
1364
3046
1335
3847
1701
""04

HAL
TAD ACtH

TAD HORD
SIIIL
DCA HORD
TAD SCNT
DCA LORD
TAD moJl.t
DCA OVER2
ACt.
JW..

1421

MQJ..

1311
1004
3377
1316
7004
3316

TAD QLO
HAL
DCA QLO
TAD

5210
1316
3.45
1317
1565

/ SAVE RES'UL T

/SAVE LINK BI TS IN QHI# QLO.,MQ

RAL.
DCA QHI
ISZ EXl
.IMP OLOOP

2040

TAD mil
DCA HORD

/INCREMENT STEP COUNTER
ISAVE RESULT AT THE END

TAD QLO

SWP DST

001&6
1&335

4641
5646
6411
7160

/LINK-l IF SUCCESSFUL CEG >0)

J'MP .+6

LORD
JMS DNOli4

.IMS 1 RSLV
JMP I .+ 1
RSLV.,

FAiT+
RE$OLV

INOfiHALIZE IF NECESSARY
'SET PROPER SIGN

•
/FOCAL PATCHES FOR 8/E £AE

JVZ

ZSLOCK 56

PALS-V1

.IFREE SPACE

.lEA!: SIGNED NORMALIZE ROUTINEa

17326
11321
0133e
81331
11332

7411

GT13"

6/7/"3

(THREE WORDS)

INORMALIZE LOWER PART

NMl

1565

SWP DST

8145
7661

CAM SCA

1334

TAD 1314

tlMP ALLI-2

HORD

IGET NEW SHIFT COUNT
IPLUS twELVE

01333

5367

11334

8014

P1I4"

81335

888"
7311

IH 0 RN"

81336
11331
11341

18146
1421

17341
07342
11343

1845
1447

TAD HORD

14U

UN!

7431
7441
7451

SWAB
SCA

I SET MODE A TO
IPROTECT 4110 111I
ISAVE RESULT IN MQ
IGET SHI"T COUNT

DPSZ

ICHECK FOR ZERO

11344
11345

11346
11347
11351

1141

11351
81352
11353
11354

1641

tI..l+. CLL
TAD LORD

.ICLEAR LINK FOR LATER

MQL

ILOAD At" MQ

SWaA

11355
11356

1411

5371

CLL CIA
TAD 13·14
CLA SCA
DCA SCNT
TAD OVERS
SWP DPSZ
SKP
JMP ALI..I

11357
17361

3845
!846

DCA HORD
TAD LORD

01361

1420

SNL

17362

JMP GT13

11363

5326
7413

11364

81118

11365

11366

3146
1364

117367

71141

11310
81311
07312

UI44

17313

07374
87375

"1334
3364
1147
7511

3144

SRI..
SCN T"

ALL0"

DCA LORD
TAD SCNT
CIA
TAD EXP
DCA EXP

ISET LINK IF c TWELVE
/SAVE SHIFT COWT

.ICHECK FOR ZERO
lAC-RESULT

I. GE. twD.. VE .,
/YESi IGNORE SIGN BITS
IMODE B

I CO RRECT EXPON OJ T

1521

SWP

3047
7447
5735

DCA OVER2

ICLEAR MQ
ISAVE ORCLtAR LAST WORD

SWBA

IRESTORE MODE A

07316

0100

07371

1010

JMP 1 Il\lOllM

,nu"
QLO"

0
I

PAGE 8
ITHESE OVER.AYS MODIFY THE £AE MUL TI PI. Y &01 VIDE ROUTINES
24 SI T MAN TI SSAS. nlE MUI,. TI PI..Y
/1'IME IS LESS nlM 70 MICROSECONDS AND THE DIVIDE TIME IS
IABoUT 958 MICROSECONDS CAJI'ACTOROJl' •• 1IMPROVDtDlT)~ JtN
IADDITIONAL 35 WORDS ARE AVAILA81.E (TOTAl. 0 ' 1 1 3 , . "
I FOR MAX IMUC SPEED WITH

lADDITIONALEAEINSTRUCTIONSI

DA1)a1.443
1t.1)I1663

7443
1663

11WO WORD BY TWO WORD WSIGNED MuLTIPLY ROUTINE
I

CA+S).CD+E) • (ONE+TWO+THREE+FOUR)

ITH~RESULT

70.3
'7."3

IS ROtJNDEDTO

• '883
-21

7751

07015
87016
878"

811128
87821
81022
81823

1"42
7525
fU'45
3323

81824
'''825
,7.26
81821
"8a,
87031
01832
01833
87834

184.
7525
8846
7521
7118
2323
7581
.1323
7421

TAD D
. SWP HUY
D
SWP
SPA CL.A
ISZ TWO

81035
87836
8"'31
8.,848
818"1

104.
1525
8045
1565
0045

TAD J)
SWP MUY

81.1&2
81843

4645
4368

8'8~4

5684

818.5

1335

81846

8888

ED"

INEW LOOP COW T

.,014
TAD E
MQt. MUY

78.4
1042
7425
0046
1421

070.4

nu; two MOSTSIGNIFICANTWOilJ)S•

IDISCARD FOUR

MQI..
~

TAD E
SWP MUY

IUSE PREVIOUS HI GK ORDER AS
IREMAINDER IN nil S POSITION
I SAVE IN TEFIIEDI ATE RESUl.T '

DCA TWO

IADD IN PREVIOUS
lPARTIAL PRODUCT

0,.,

ICHECK AND 01 SCARD THREE
IROWD

MQA

TAD TWO

I SUM HIGH ORDER PARTS AND
I
ADD INTO LAST PRODUCT

HQL

N8RM ..

SWP DST
HORD

I SAVE 'INAl.. RESUt. T

JMS 1 N811t
JMS RESOLV
JMP I NULT

INOHMA1.1ZE
IRESTORE PROPER SIGN
I AN D RETUflN

ZBL.OCK 35

IEXTRA FREE SPACE

mofIC

'FOCAl. PATCJiES PO'. 8/E EAI . ,tvz

81116
81171
.,2.e
,na81

"282

1116.
1842,
1431
1841
1445

••••

.,2.3
.,284
87285
"'21'

.,a.,

1663
"46
3'46
1845
52."

• ,21.
e121 I·
.,212
.,213
81214·
87215
.7216
17211
81228
87221
11222
81223
81224

1663 . DLI1P~
1316
7413
" •• 1
1445
1316
1443
1841
1428
5a24
""45
131.6
76al

.,225

III~6

.'226

.7221

'".4
3146

l'U
",a3'
8'231 "'4

.,232

3.45
:.,233 - 2""8
17234 5218
87235
".236
.•,231
"24.
17a41

5641
1161.
641"

e7242

e8 ••

4335
4641

PALS-V?

.,116
TAD' AClJ,..

PAGE 9

l~iTDlvtsoa .

SWAB
. TAD ACIH.

/REVERSI WORD oaOSR

DST

DLD

611113

ACl"

IGEf J)I VI DEN D

.LORD
,DCA LORD
fAD HORD

1C1..~aQUOTIENT,

J)l..D

IGET OPERMD

-INP ...+5
QIU

I SillY,. LIFT

$It.
I

DST

1SAVE
FOR N&XTTIlCt
,'.

QJll

ISUBTRACT FLOP

DAD

SlfL

ACtH

. ITEST
tOR OVERFl..OV
.
,

J"P ...+3

DS?

QJU

TAJ)·L.ORO
.RAL.
DCAI-0RD'
TAD-HORD

RAJ.
DCA'HORD.
is& ~l

I TEST J..OOPCOt.llt

"liP D1.OP
"liS ~Oltl
tlHS I. _+2
tlMP I _+2

,NOlll4!ZE ., . .
I SET PBOPER SIGN
IUfU.,.
. '.

RESOl.V·

FAfT+ 1
ZBJ.,OCK 6
$

I EXTRA

'FOCAl. PATCHES FOR 8/E EAE
A

AClH
ACU..
AD

1145
1141
..42
7'.12'

1.S7 .

1136

ALt..
B

1311
·•••6

1864

Bl£
SF

,.18

C
CD
CE
CF
C268

1858

'.41
7.43
7127
7814
8113 .

811&1

7.35

DAD
DB'

1443
7"24

11.0
a.OOP

7663
72"

a.. UP

JlIZ

PAL.8-V7

QHI
7376
&0
7377 .
RESOL 6152 . ·
BESOLV '16'
R£SOLS6314
RSLV
1241
'SGN t .' .7364
$UFn. 4527
SIGN
11laiJ
SIGN,. •• 58
aUN
6136THREE 7.4.·

TWO
T3
Z£RO

1123
,.33
6Sa.

121.

1110111

7335

.842

182e
1814
ERRORa IiS66
EXP
,.44

EXI
F
Ft.AC

.84.
8.43
8."4
PLDV
1165
PLOP
•• 48
F1.0UTP 68 ••
FOUR
116.
FPNT
648.
GT13
7326
HORD
'845
MINUS

881&' .
1123

KUl.T

7884

LORD

NEGATE 4451
NORM
71'2
NUl.L
1151
NIlII
1845
OPNINS 6565
OUTOS 6154
OVERI '"43.
oVERa 1847
PRINTC 4551
PSNT
2442
PSNTI 6137
PI47334
'. P4888 8124

611/13"

PAGE I.