Data Representation, Arithmetic Instructions,
j·.nd Computer .efficiency
An
Honors Thesis (IU 499)
By
Carol A. Nichols
'rhes~s
Director
,:
/
5"
/
Ball state University
Muncie. IndiCtna
t~ote1
.spring, 19tH
'"
TABL~
OF
GONT~NTS
Preface
page 1
Thesis
page 2
1
In order that those wlth limited knowledge of data processing
can comprehEmd the follow lng research and understand its impact.
it is necessary to begin with explanations of the terms unfaml.llar
to the red.dOr8
The purpose of thlS research is to determine
which representatlon of numeric data 1n the computer causes the
arithmetic operations of addition, subtraction, multiplication,
and division to be executed the most efficiently.
Numerlc data,
or numbers, can be represented inside the computer in several
different wa.ys.
In the GOBOL language, there is a
USAGE
clause
in which one can specify the type of representation to be used.
One possibill.ty is to have a
U$AGt~
I;;:; DISPLAY clause for a
numerlc data item WhlCh causes the internal representation to
be the stantiar(! character form of the number.
USAGL IS COMPUTATIONAL
representat~Lon.
A alal-lSe of
(or COMP) defines another type of
In COBOL. t.he C01,u') data type causes the number
to be in its equivalent binary integer form.
'rhe binary number
system is based on powers of two and uses only the digl.ts 0 and 1.
A number represented in COM?, or binary integer, does not have to'
be an
irlttegE~r
however;
1
t is p05slble to have a declmal represented
as COMP data by using an implied decimal PU..I.ot.
'jUlvl.PUTATIONAL-J
(or COfiiP-)} data is the last of the data types to be consldered
In this study.
data item.
A packed declmal number lS the same as a COlvIP- J
When a decimal number is "packed" into a oacked decimal
number, two digits are stored into one byte (a unit of computer
storage) exeept for the last byte whl.ch contal.ns one dlgl.t in
the left half of the byte and a letter code in the r.lght half
indicating 1;he slgn of the number
8
Data Representation. iU'i thmetic Instructions,
~nd Computer ~fficiency
In data processJ.ng, emphasJ.s
.l.S
placed upon wrJ.tJ.ng programs
that are effJ.cient J.n the use of varlOUS computer rt:sources.
especlally -rame.
The desirab1lity of reducing the amount of time
taken tel eXE'!cute a program cannot be argued against; 'the old
adage that "tlme 15 money" certainly appll13s to the computer
world.
It
a progralli
often d1ff1cult. however. to find a way to caUSE;
J.8
t;)
run faster.
In DJ.gl tal- s
rrO?S-lO/TOP;:)-~O;OBO.i."-74
Lang'.lAgE! kE'.l1ual, it in recommended that .. programming standard::.:
shouLd inRist on using the correct data types for certa:ln
operatl.ons.
1
It
Before €lstablJ.shlng these programnung standards
t mJ.st be }rnown what data type to use fr):r what operatl.on.
Ine resf.;arch under consideration is desl.gned to match up
approprlate data types and the normal ar1thmetlC operatlons
of alidltioll, subtraction, multiplJ.cation. and dJ.vlslon; the
data types \'lsed are
represeni:attons.
character~
blnary 1ntegcr, and pacKed decimal
A Djj,,;-lO computer wJ.th TO.PS-IO operatlng
syst~?m and t'ORTHAN and GOBOL
languages were used in thls
inve:3tlga tHIn.
'1'0 beg1ll this research ~ t was decided to use FORTrlAN programs
to generate 200 random numbers to be used as 1nput data.
one hundred paJ.rs of numbers were added. subtracted,
'rhese
multlpl~ed.
and divided in a COBOL program, referred to as the test program.
3
It was determined that
th~?'
test program should be executed
twenty-five times for each of the three data representations
in order to get statistically accurate
results~
(See Appendix
A for copie's of the programs mentioned.)
In ()rder to obtain the time elapsed during each of the four
operations for each of the dat;::, types, the ,test program was
exec1 .. ted under the control of COBDD'f . a dynamic debugging utili ty
program..
';,O,duDT
has a histogram feature which sets up a table in
'.vhich variolJs statistics about program behavior are recorded.
'rhe
only statistic interesting to this study was the CPU {Central
i?rocessing Jni t} time taken for each of the GOBOl, paragraphs
in which addition.
(~ee
perf0rmed.
9ubtraction~
Append~x
multipllcation, or division was
C for a sample
h~stogram
table. )
,-Tior to obtalnlng aby histogram results, the translation
of COBOL statements into machine language statements for each
of the three data types was examined.
(';;;ee Appendix
machlne laJlguage code for each case.)
It was found that for
I)
for
perform:lng arithmetic on two numbers in character form ~ it
1S
necessary to generate five statements 1n machine langu.age code.
The first
t~o
instructions in thlS case cause the numbers to
become packed decimal numbers.
In the next instruction, the
packed decimal equivalents of the
subtracted, multiplied. and
specified.
lJISt~LAY
divided~
numbers are added.
depending on the operation
The last two instructions cause the result of the
appropriate operation to be unpacked so that it is once again
in
characte~
'W hen
form and then it is stored in the proper memory cell.
dealing with two binary integer
(C01~i?)
numbers, the
numbers do not have to be packed since the computer is capable
4
of bl.nary al"'i thmetl.c; this results in fewer machine language
instruct;ions being generated.
For arithmetic to take place with
two binary numbers, only three machine language instructions
are needed.
The first l.nstraction
one of the registers of the
is performed on the two
m~ves
computer~
numbers~
the first; operand to
Next, the correct operation
Finally the result of the
arithmetlc, which loS located in the register. is stored in the
appropriate location lon memorys
Perform:Lng packed decimal arithmetic requires only two
machine
la~~uage
statements8
since both numbers are already
in packed eQimal form. it is not necessary to change their form,
as with DISPLAY numbers. or to move one of the numbers to a
register, as lon binary arithmetlc.
The
(!OI~iP-3
numbers have
ari thmetic :performed on them in the first instruction.
In the
second machine language instruction, the result of the operation
must be stoJr;'ed in the specified memory
cell~
Because packed decimal arithmetic requires fewer machine
language instructions, one can suppose that arithmetic
USl.ng
packed decimal numbers would be the fastest and most efficient
to perform.
However, research findings l.ndl.cate that this is
true in only one case.
For addition of two numbers, the lowest average time, in
seconds. for onE::: hundred additions was assocl.ated wi til
(packed decimal) uata. the average time was 0 .. 33252.
COlVIP-3
An
average
time of 0.3:3)04- seconds for binary integer data was extremely
close to
thE~
time for
can be cons:Ldered
COMP-3
data and, therefore. the dl.ff'erence
insl.gnifl.cant~
FOr DISPLAY data, an average
tl.me of 0.)5764 was slower than for the other types of data.
5
when subtracting two numbers, a binary
~nteger
representation
provided thE' fastest average time of o. 41~7.2 seconds for one
hundred subt.ractions.
An average time of O~47lJ6 seconds was
recorded for the use of pacKed decimal data, the second fastest
time.
Once again, data in character form was the slowest of
the three wi.th an average time. in seconds, of 0.4924.
In the case of multiplication of one hundred pairs of
numbers, COlV.[y (binary integer) data again proved to have the
quickest average time, in seconds, of 0.4JJtl.
UISPLAY data
representation yielded the next fastest average time of
0.47656 seco'nds. bettering the average time of O. 4tl70tl seconds
when using COMt>-J data.
Divl.slon of two numbers produced the same ranking of
data types as did
subtraction~
F'or COMe data, an average
time of .o.J956 seconds for one hundred divisions was calculated,
the lowest average time of the three representations.
i>acked
decimal data was ranked next in terms of efficiency, with
an average time of
O~4~6~~
~s
expected, data in character
form gave the slowest average time of 0.4)076 seconds.
Overall, when comparlng average tlmes for each of the
operatlons and data types, lt can be observed that numbers
represented in blnarYlnteger
form allow
(CO!'Iu..})
operations to be performed the most
eff~clently
arl thmetic
and qUlckly.
Because GOlvlP data was shown to be faster than packed declmal
data, as was orlginally expected to be the fastest, one may
hypothesize as to why the results came out as they did.
Appendix B fl:>r a summary of results.)
(See
6
'ro justlfy the results of
in a
D~C··IOcomputer,
th~s
study, one m.lght assume that,
the loading to a register and storing from
a register of a bl.nary integer 1.S performed faster than when
slmply movlng a packed d.ecimal number from one location 1n
memory t<) another.
arithmet:ic in a
1".1:30 ~
u~~-lO
1t
might be that b.lnary integer
computer takes place in less time than
packed decimal arl.thmet1.c.
l'hese explanatlons are probably
the most feaslble ones as to why arlthmetlc carrled out w1th
COi'il~
(binary integer) data representation is performed more
qUlckly, for the most part, than e1 ther packed decimal (\;OlYiP-;)
or character (DISPLAY) arl thmetlc"
'I'o prove these assumptions.
however. requlres more research Into the operation of a Uc;C-IO
computer. wiuch is beyond the scope of th.ls research.
In con c:lus10n. thls research has found that for GOBOL
programs with numerous arithmetic calculatlon. b.lnary lnteger
or GOM£' representatlon should be used to reduce the amount
of tlme tak€tn for execution of the program.
'rhe reader should
keep in mincl that this research and its flndings are very much
machine and language dependent.
Similar results mayor may not
be obtained when execut.lng the same or
sim~lar
on other computers and/or 1n other languages.
research programs
00100
00200
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00700
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IDENTIFICATION DIVISION.
)PROGRAM-ID.
DATAREP.
AUTHOR.
CAROL A NICHOLS.
ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
SOURCE-COMPUTER.
OBJECT-COMPUTER.
DECSYSTEM-l0.
DECSYSTEM-l0.
p.
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SELECT INPUT-FILE ASSIGN TO DSK.
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DATA DIVISION.
FILE SECTION.
FD
INPUT-FILE
RECORDING MODE IS ASCII
LABEL RECORDS ARE STANDARD
VALUE OF ID IS 'DATREPDAT'
RECORD CONTAINS 20 CHARACTERS
DATA RECORD IS INPUT-REC.
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Appendix A
00100
00200
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00400
00500
00600
SUBROUTINE RANDOM (X)
INTEGER MOD
REAL FLOAT
INTEGER Av MULT, BASE
DATA A/l~7271¥ MULT/25211/, nnSE/327581
A = MODCMULT*A, 32768)
X = FLOATCA) I FLOAT(BASE)
RETURN
END
OO?OO
00800
00900
INTEGER I,N,IN1,IN2
REAL RANDOM,Nl,N2
0'0300
DO 100 I
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00900
01000
01100
01200
01300
01400
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01600
10
. .,,::J.'_",J
CD
= 1,100
CALL RANDOM(Nl)
CALL RANDOMCN2)
INl = 10**9
Nl
IN2 = 10**9
N2
WRITE (1,5) IN1,IN2
FORMAT (Il0yll0)
CONTINUE
READ (5,10,END
FORMATCI2)
END FILE1
STOP
END
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UATA F'Url uISPLAY
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Additl.on
1
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3
4
5
6
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ts
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10
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22
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24
25
subtraction
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0.47656
0.43076
Appendix B
11
uATA FOB COMPUTATIONAL
(Binary Integer)
Additi4)n
subtraction
1
2
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Sum
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i..J
.
')
• •. ' -' j
"
.
-"'--8.)26
0.)3)04
---10.468
0.4its72
Division
.415
.486
.473
.440
.516
.470
.484
.471
.J69
.)85
.J37
.4)4
.)60
.449
·397
"
lVlul tiplication
-10.845
O.4)Jts
~409
.)98
.)04
.449
.. 420
.. 427
9.89
0.3956
Appendix
B
12
FOR COMPUTATIONAL-oJ
-DATA (Packed
Decimal)
Add1t1. I::>n
.253
.476
.44ti
8465
,271
~472
~J09
.471
.4)1
~441
~497
.453
::;
.5..:...2
.417
• )i)()
,1+66
' ::5{~
• ,,+'/1
" ,:!~{}
.ll-51
.jJ.~1
,497
' )}.1
.50~
~ ~;.
If-.~
').5'··
.50)
.501
·557
.505
.4CSCS
.502
·55CS
.414.45CS
• ;,; ~',1 :.::
.~H3
.. 462
· ", ',:,9
.551
"
,t..;.
• LH56
.460
.4B9
.5)0
.4ti1
.4Bl
.445
e4Bt:i
.455
·513
.470
.516
2
.321
3
4
5
23
24
25
Sum
-x
Dlvl.sl.on
.)5)
.J))
22
Multl.pll.catl.on
.54)
1
6
7
CS
9
10
11
12
13
14
15
16
17
1CS
19
20
21
subtraction
'-.
,-'"
:,\j
, .':::;::~.,
.'
"
,
)
iLl
·;
,.,
•
~1
·
'"
.46)
_!:
./~30
(is
.«540
·517
.4-CS9
.4J7
l~'
~
~ -,iI.
., J'.'
)
;
;
'f
,l...,
:~,.) ~"J
'1
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'
,,)72
~~o
J(,)~)
·
&.~
.~ c,.1
..
",I
....
tie ;.13
0.))252
·533
.527
.432
_a.,_.-
11_7CS4
0.47136
.421
12.177
0.4B70B
~477
8477
~441
.)76
.. 406
.)t:i4
,,42ti
.. 421
.506
~3B6
.490
.3B4
.. 4)7
.. 424
.401
.466
.466
.4,36
.41B
.4t:i3
10.67
0.426B
Appendl.x
B
COBDDT
ALiD-R iN-EX I T
SUBTRACT-RTN
SUBTRACT-RTN-EXIT
MULTIPLY-RTN
MULTIPLY-RTN-[XIT
DIVIDE-RTN
DIVIDE-RTN-EXIT
READ-RTN
READ-RTN-EXIT
*
OVERHEAD:
ELAPSED:
.-
~
_
~
~
.
~
"
,
_
~
,
__
CPU
ENTRIES
-GENERATED-SECTION-NAMEMAIN-RTN
CONTROL-RTN
CONTROL-RTN-EXIT
ADD-RTN
• ___
REPORT:
iSTOGRAM FOR tiATARE
- PROCEDURE- --
u
•
o
1
100
100
10{}100
100
100100
100
-100
100
101
101
28.549
5.562
0.031
0.636
0.519
-{}-r3-21--
0.342
0.448
0 .. 541
0.472
0.570
Qf 3(}9
0.525
0.385
0.463
CPU:
1
•
ELAPSED
2t05.964
0.485
28.863
16.549
2-.-3535.563
,18.236
5.984
11.379
3.650
-- 2.238 12.445
5.554
12.665
0.231
~CIl
s:::
CIl
<It
~
•••
p, ~
.....,
o
ti_
n;:T
~.
til
ti
CD
CIl
CD
.
:.::
~
CD
0
0
~-
'V
I
I"..)
t-3
::r
~.
CIl
c+
I»
0'
~ ~
n- CD
I»
•
~
I»
CIl
~ 1-3
::r .....,
::r
CD
0
•
ti
o
§p,
CD
~
c+
::r
CD
:x:
~.
CIl
c+
o
1-3
CD
CIl
~
~
~. ~
1-3
CD
~
~_
:J
CD
p,
c+
S
c+
0
Otl
ti
CIl
~
~
CIl-
CD
c+
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CD
~.
c+
CD
~
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CD
CIl
CD
0
0
:J
Pti
§
>
"0
"0
CD
a
~.
><
o
.....
I"..)
iv!ach~ne
Language Gode
--,----
racks IN-ONl\- into temporary gi;orage
--'---
racks IN-TWO into temporsry ~'t?rage
Adds IN-ON'~ and IN-TwO, result. .l.S
in temporary storage
Unpacks result ~nto IN-T~O
i-\.? _ ... . - _ , _ _
---- ---
,~loves
result from IN-TWO to
1'1;:- iU~SU
[,I'
For ":;Oil1 f) d8 t a:
LR _ _
L1.
ft
J _ _ __
_____ • _ _ _ _
• ~1
c~·!).
_ _ .... ~'_,....,. .. f _ _ __
Moves Ii~-ONc into a register
Adds Il'i-ON~ and IN-twO, result
in the reg~ster
0tores result from register to
1 ':
'i.s-RI1~ULT
I~i
___ , _ __
--- ---
Adds I.N-ON£. and IN-'rINa. resul t
~n
L~
IN-'fwO
I.vloves result from IN-'rwO to WS-tLSULT
Note: For each case the addition statement can be replaced by
th" appropriate statement. ':;;ubst~ tute the f~rst letter of
the OperEitlon in place of the letter A in each of the addit~O;1
~nstruct.\..ons.
Append~x
D