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DOCUMENTATION FEATURES FOR COMPUTER PROGRAMS

Abrom Hisler Information Processing Division

GODDARD SPACE FLIGHT CENTER Greenbelt, Maryland

DOCUMENTATION FEATURES FOR COMPUTER PROGRAMS

Abrom Hisler Information Processing Division

SUMMARY

Computer programs may best be prepared by means of docu- mentation features. These features, as demonstrated, may also be used in the computer program gamut of planning, development, and operation. By automating these features, the documentation (and development) effort should be further eased.

iii

CONTENTS

Page

SUMMARY ......................................... iii INTRODUCTION ..................................... 1

DOCUMENTATION FEATURES ........................... 1

Engineering Analysis ............................... 2 Decision Circle Flow Pattern. 2 Program Listing with Running Commentary Decoding Sheet.. .................................. 3 Additional Documentation Features 3

......................... ................ 2

...................... .................. DOCUMENTATION FEATURE AUTOMATION 3

APPENDIXES ....................................... A-1

V

DOCUMENTATION FEATURES FOR COMPUTER PROGRAMS

INTRODUCTION

How can one possibly compare the present day burgeoning technology with biblical t imes? Impossible? And yet both are similar in these two ways - there is a flood of information* and to the extent that this information remains "undigested," it reminds one of the Tower of Babel.

This is true in many technical areas and especially in the all-encompassing area of computer programs. These programs, for the most part, represent the state-of-the-art in particular fields of interest.

Translation of technical computational techniques into neat packages - computer programs - is the effort to prepare such techniques for immediate use. Obviously, there is no difficulty where the originating team of engineer (scientist) and programmer is concerned. However, transmit the same pro- gram to another engineer-programmer team and the immediate-use advantage vanishes and may return only after much head scratching if the documentation of the program is not adequate.

How then to best document a computer program? How can computer auto- mation aid in this effort? Answers to these questions have become the concern of many people who realize that the generation of computer programs has pro- LlltxaLeu io the point where a vast number of these programs are now avaiiabie after considerable expense.

1 1 1 - -- L - ̂1

DOCUMENTATION FEATURES

The obvious approach to the documentation problem may be to develop and refine those documentation features which a r e most effective.

What may those documentation features be? And how readily may they be automated?

The nature of documentation features developed thus far can be readily grasped by thumbing through Appendices A through G. Having done so, one can then notice how these features cover the various facets of computer program

*Coughlen, William J.: The Flood. Technology Week. Vol; 50, No. 1, p. 30, 1366.

1

planning, development, and operation. The appendixes appear in the order they would in a typical documentation presentation. They are referenced in the text in the order they would be developed.

The appendixes contain not only the documentation features but also some points of information relating to a particular feature. The documentation fea- tures themselves were taken from a preliminary report on PUTT (Propellant Utilization Time Trace), a computer program to simulate the vertical ascent of a boost-sustain sounding rocket.

Engineering Analysis

The planning effort is first noted in the engineering analysis documentation feature (Appendix C). It tends to unify and integrate the scope of the intended sequence of computations as initially envisaged by the engineer (scientist).

Decision Circle Flow Pattern

A s the engineering analysis is translated into the computer program itself by the programmer, the decision circle flow pattern (Appendix E) emerges to follow the ramifications of the program's logic as developed by the programmer, Where the program operates in a simple calculation sequence, no major prob- lems are anticipated. Straightforward computation flow occurs between decision circles.

The programmer's greatest debugging efforts usually concern the manner in which the program pivots about each decision circle as conditions change during the course of the computation.

Program Listing with Running Commentary

With the program finally debugged and operational, one may then begin to go into the innards of the program by preparing a running commentary of the com- puter program's listing (Appendix B). The documentation feature developed for this purpose allows for simple comments where these are adequate. Where this is not possible, a complete discussion may be appropriately appended onto the listing.

Likewise, as appropriate references to the literature become known, they too may be appended in the proper place for later discussion o r for suggesting new follow-on efforts.

* The running commentary effort need not await that point in time when the computer program is all checked out and operational. During the development

2

of a computer program, it may be wise to "freeze" it at some point in time to append the information known then. This w a s done with the PUTT computer pro- gram about which the documentation features were developed.

Decoding Sheet

By sorting the parameters in the listing, alphabetically, the decoding sheet (Appendix D) may be next prepared. Here it is possible, in one swoop, to indi- cate which parameter must be inputted initially, which is outputted as a result of computer computations or important initial conditions, and which remains in the program, merely awaiting an appropriate writeout statement.

At this point, the program is no longer the black box* it was before the start of the documentation effort.

Additional Documentation Features

However, the problem of operating the computer program remains. The correlating input format (Appendix F) helps to feed the necessary data into the program as for a test run. It is a t this point that the decoding sheet proves worthwhile in refreshing one's memory about unfamiliar parameters.

The data display sheet(s) (Appendix G) of the input and output data com- pletes the test run picture.

A computer program brief sheet (Appendix A) then gathers together all tid';its of kiiormatiorL which atill reniaiii after the a'mve documentation efforts.

DOCUMENTATION FEATURE AUTOMATION

How readily can these documentation features be automated?

The engineering analyses sheet may require the use of computer-aided tech- niques whereby the engineer reacts directly with the computer to order the se- quential arrangement of the various engineering equations. A photograph taken of the final sequence or engineering analysis pattern records the engineer's thinking at that particular point in time. Without computer-aided techniques, the engineer must resort to simple pencil (with eraser) and paper trial and error. A t any rate the programmer should more readily appreciate the nature of the problem to be programmed with the engineering analysis before him than

*Hisler, Abrom: Avoiding "Black Box" Computer Programs. X-671-64-34. GSFC, October 1964.

3

receiving a helter-skelter list of engineering equations without apparent relationship.

Again, with computer-aided techniques, the decision circle flow pattern can be generated. And yet present-day automation techniques prepare flow charts in the more traditional fashion. It should be a simpler matter to do so with the less sophisticated decision circle concept.

To aid in the preparation of a running commentary of the computer program listing, present-day automation techniques should again be adequate to print out the listing with appropriate columns for card numbers, references, discussion, and comments, and to consecutively number the statements of the program. Thereafter, the programmer-engineer team need only complete this listing format with appropriate information, which would be typed on duplicate listing.

The self-same automation techniques would prepare the decoding sheet with parameters listed in alphabetical order, as input, output, and internal. Again, a typewritten decoding sheet would follow rough-draft efforts.

Similarly, correlated input formats, data output sheets, and computer pro- gram brief sheets would be prepared. To be sure, the data display sheets a r e the sole present-day example of an automated documentation feature.

Once these documentation features have been developed and compiled, the documentation report body will require only broad stroke discussion of the program's objectives and general flow to present the big picture since the program details would be imbedded in the documentation features, auto- mated o r not.

And yet it would be a mistake to "freeze" any set of documentation features a s the only acceptable set and so t f strait-jacket" the documenting programmer. The important thing is to expand our rfpool" of documentation features so that from this pool, documentation features mutually acceptable to programmer and user, may appear in the final computer program documentation report.

A growing set of documentation features, then, is one way to cope with the rising flood of computer programs and so reduce Tower of Babel complaints.

4

APPENDIX A

COMPUTER PROGRAM DOCUMENTATION BRIEF

The computer program documentation brief as presented on the following page may still be too brief, even fo r a brief. It may be advisable to expand it by extracting items of information from the two GSFC short forms (p. A-3 to A-6) for programs and subprogram documentation.

A- 1

PUTT COMPUTER PROGRAM DOCUMENTATION BRIEF

1. FORTRAN IV

2.

3.

4.

5.

Running Time - 2.22 seconds/4 flights

Computer - IBM 7094 and 7040

Lines of Output - 4000 lined2.22 second run

Information Retrieval - Key Concepts and Areas

Sounding Vehicle

Computer Program

Vertical Ascent

Documentation

A- 2

GODDARD SPACE FLIGHT CENTER

SUBPROGRAM DOCUMENTATION - SHORT FORM

Form ini t iated / / DISPOSITION Access No.

Est. completion :sed exis!ing routine Program No.

Actual completion- 0 Task discontinued

outine written

Parent Prog. No. (IWOICATE REASON FOR CHANGE I N ABSTRACT1

Subject codes: (primary) - (secondary) __ - ___ ___

Title:-

Phone: Author: REGISTERED ID, F U L L NAME

Author Location: GSFC CODE. BLDG. 6 ROOM NO. OR COMPANY, CONTRACT NO. & ADDRESS OR USER'S GROUP I D

Tosk Sponsor: GSFC Code: Ext.

Sponsor No. Proiect: Field of Application:

Purpose ICONCISE STATEMENT OF FUNCTION OF ROUTINE):

NOTE: USE ADDENDUM SHEETS. I F NECESSARY. TO EXTEND ANY OF THE FOLLOWING I T E M S FOR WHICH MORE SPACE I S NEEOEO. DATE AND LABEL EACH SHEET WITH THE ACCESS NO.. AN0 INDICATE I T E M NO. O F EACH CONTINUED I T E M

E.G., OS/asO. FMS, EXEC 11, . . _ 2. System or Monitor: E.G.. 380. 7094. 1108. . . 1. Computer Type:

3. Source Longuage(s):

4. Memory Required, other than Monitor:

( w PRIMARY ( '); SECONDARY. I F M I X E D

INDICATE BASE I O C T A L . DECIMAL, . . . I AND U N I T S (WORDS. BYTES. . . . 1

Above figure 0 includes 0 does not include system Iibrory routines

5. L i s t Program Numbers of any required subprograms that are documented separately

E.G.. 2250. 65K. 1004. ETC. 6 . Special Configuration Requirements:

7. I/O Configuration

A-3

9. KNOWN RESTRICTIONS (c.a., LIMITS. PWYSICAL CONOITIOIIS NOT WAYOLIO. AIRAT IIZLS. ETC.):

10. FILE DESCRIPTION IEXPLAIY FORMAT AIID COYTINT OF LACW CXTLRYAL I/O FILC. IF A Y V , IIICLUOIWS LaacLs. ILOCKIYC, ~COROI IS uooc. IYC~ICAL

ILCRLILYTATIO*. U I I lT l . CTC.1:

A-4

11. USAGE IDITAILID OC~INITIOII or cALun8 SCOUUCI. bmuyInTr. COYYOII rrourc, LTC.):

12. OPERATING INSTRUCTIONS fcowsoLc COUMUIIICATIOIIS, SWITCII SCTTIIISS, LTC.I:

13. TERMINATING CONDITIONS IIOIYAL ANO ALTLRIIATC RLTUWS. CRROR CXITS. CTC.I:

A-5

15. SOURCE MATERIAL FOR DERIVATION, T E X T REFERENCES, etc.:

P R O G R A M M E R , LOC.. E X T . REV. NO. __ ) A T E R E A S O N

7. LIBRARY MATERlAL AVAILABLE:

0 Source program Form E.G., HOLLERITH CARDS. 7-TRACK BCO TAPE, ETC. co%:CkTE STATEMENTS. CARDS. RECORDS, . . . 0 Reloc. object program Form Count

0 Abs. object program Form ~ Count

(specify): E.G., WRITEUP, FLOWCHART. L IST ING. T E S T CASE, ETC.

NUMBER ASSIGNED D A T E 0 Submitted to other libraries: NAME OF ORblNllATION

18. ESTIMATED TIME AND COST FOR DEVELOPMENT:

Manmonths Machine hours Total cost $

A- 6

APPENDIX B

COMPUTER PROGRAM LISTING WITH RUNNING COMMENTARY

The format of the computer program listing with running commentary ac- complishes a number of things:

0 Consecutively numbers the program statements via the C (card number) column

0 Notes references of interest pertinent to a particular statement via the R (reference) column

0 Comments on particular statements with the opportunity to go into dis- cussion of greater depth through the use of the D (discussion) column

0 Prepares a computer program deck of cards from the listing.

The exact manner in which the above is done is illustrated below:

0 Card number 4 (p. B-2) is used to identify the Card 4 discussion which appears on page B-10.

0 Card numher 158 (p. B-6) has associated with it referecse (1) appearkg at the end of this appendix which refers to the particular Runge Kutta method that was selected to program the KRPAR integration subroutine.

0 F o r those who would wish to prepare a program deck of cards from the listing as given, it might be difficult to punch cards 584 and 585 (p. B-4) since exact spacing is necessary in the location of the output headings. To assist in this problem of proper column collation, it would be advis- able to incorporate the technique shown in the reference below. Whereas this reference calls for placing the numbered columns at the top of the listing, it would be less obvious to set it at the bottom. Here then is an example of assimilating other valuable documentation techniques into the present group of documentation features,

REFERENCE: A Study of Performance Trade-offs for Solid Propellant Propulsion Systems. Final Report No . AFRPL-TR-6565, Vol. 1. Lockheed Propulsion Company, Redlands, Cal. 1 March 1965. pp. 2-64.

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B- 8

Appendix B2

PUTT CARD DISCUSSIONS

B- 9

Card 1 Discussion

The listing format provisions permit the future incorporation of critiques into follow-on versions of this documentation report.

Card 4 Discussion

The program documentation effort consisted in first setting up the decoding sheet from the alphabetical ordering of the Symbol Reference Data. Thereafter emphasis was shifted to the listing to complete the detailed information input into the decoding sheet. All information indicated by the decoding sheet was not inserted for this would have prolonged the documentation effort. However, s i n e the decoding sheet is also a worksheet, appropriate information of interest to the reader may be inserted in the appropriate place by him.

The ordering in the Symbol Reference Data is not strictly alphabetical. P appears for instance between PPTY and P V and not above PAX. The subroutine should also be altered so that PC1 would follow PCX or after P C Z if such did exist. The R numbers also do not appear in numerical order so that R1 occurs between R19 and R20.

There is a need for a subroutine to aid somewhat in the automatic documen- tation of computer programs. The subroutine would start with the alphabetically listed parameters in the Symbol Reference Data and set up a FORTRAN decoding form to be employed by the programmer to personally input that information he has acquired in the course of the computer program development.

A subroutine is also required to sequentially number the cards in the source deck for later reference by the adequately documented report in discussing the more interesting cards.

In preparing the PUTT Fortran Decoding and Worksheet, the IBFTC PROPE card requested REF, the Symbol Reference Data. This data arranges the PUTT parameters in alphabetical order which is then helpful in readily preparing the decoding sheet.

B-10

REFERENCES

1. Singer, James, "Elements of Numerical Analysis," Academic Press, New York and London, 1964, p. 315.

2. Nielsen, K. L., "Methods in Numerical Analysis," MacMillan, New York, 1956.

3. Scarborough, J. B., "Numerical Mathematical Analysis," 5th ed. Johns Hopkins Press, Baltimore, 1962.

4. Wooldridge, R., "An Introduction to Computing," Oxford University Press, London, New York and Toronto, 1962, p. 67.

5. Ralston, A. and H. S. Wilf, "Mathematical Methods for Digital Computers," John Wiley & Sons, Inc., New York and London, 1960, p. 110.

Booth, A. D., "Numerical Methods," Academic Press, Inc., New York, 1957, p. 61.

6.

7. Mickley, H. S., T. K. Sherwood, and C. E. Reed, "Applied Mathematics in Chemical Engineering," McGraw-Hill Book Co., Inc ., New York, 1957, p. 198.

8. McCracken, D. D., and W. S. Dorn, "Numerical Methods and Fortran Pro- gramming," John Wiley and Sons, Inc., New York, 1964, p. 317.

9. Levy, H., and E. A. Baggett, "Numerical Solutions of Differential Equations," Diver Publications, Inc., New York, 1950, p. 91.

10. McCormick, J. M., and M. G. Salvadori, "Numerical Methods of Fortran", Prentice-Hall, Englewood Cliffs, N. J., 1964, p. 245.

Jenson, V. G., and G. V. Jeffreys, "Mathematical Methods in Chemical Engineering", Academic Press, London and New York, 1963, p. 382.

Aerobee 350 Performance Re-evaluation, R. M. Kramer, August 1964, Final Report No. 265 FR- 18, Space-General Corp., Contract No. NAS5-2252,

11.

12.

p. 35.

13. Aerobee 350, Propulsion Final Acceptance Test Results, R. Fleming and J. Ryan, July 1964, Report No. 265 FR-13, Space-General Corp. Contract NO. NAS5-2252.

14. Aerobee 350 Flight Performance and Propulsion Analysis - C. P. Chalfant and R. M. Kramer, February 1963, Final Report 265 FR-1, Vol 1, Figure 2, after page A-8.

B-11

APPENDIX C

ENGINE ERIN G ANALYSIS

The engineering analysis outlines the basic nature of the computations. It shows the necessary input information at a glance together with the calculation flow to provide the desired output.

In the case of the PUTT program, the computation input is into the f = ma equation so that this acceleration equation may be integrated twice employing the Range Kutta technique.

The parameters themselves are defined in another documentation feature, the decoding work sheet.

F o r purposes of developing composite computer programs, the underlying engineering analyses of comparable computer programs must be known to ex- pedite the effort. Why develop composite computer programs? One must realize that computer programs are developed after much preliminary thought and effort. A particular computer program represents the very best thinking of those people who have decided that the computer program development would be worthwhile. By consolidating the efforts of such people, one is, as it were, paraphasing the words of Newton, "standing on the shoulders of many giants" in a particular technical area,

c-1

Q g = 0 7 x Pa x M2

c ITS =

RUNGE ' KUTTA I I .INTEGRATION

AFTER 1 I 0.6 SECONDS

V v = A v . n t (52.21 I H v = V V A t 1 LAW= ( A t ) x 7 5 0 / 3 . 2

D = C ~ X QBX Sg 1 1 tSg=2.64

PUTT ENGINEERING ANALYSIS

c- 2

APPENDIX D

DECODING WORKSHEET

The FORTRAN decoding worksheet provides for the following:

0 Input parameters

0 Internal parameters

0 Output parameters

0 Notation for the engineering analysis documentation feature

0 Parameter definition

0 Applicable card numbers as assigned in the listing documentation feature

0 Reference and comment column to refer to appropriate comments o r discussions in the discussion appendix.

Numbers in parenthesis in the Reference/Comment column would be references, although none is shown on page D-2.

rnl 2 . -1- - - I ills uocaiieiiAatioli feiiti-ii-e is regarded 2s a workshe& since it p r ~ t i d ~ s the framework of reference for appropriate follow-on annotations and inser- tions by those working with the program during its development and by those studying the computer program documentation to learn the ramifications of the program.

D- 1

u i 1 3 *. i V !2

0 ID

W m

3 m 0 (D

(D

(D W

m m m 3

3

P. r-. m a l m a l Y Y

- 3

$ $ n e 0 0

6.

3 4 v1 n 0

y’ J F 0

V B V m E m

D- 2

APPENDIX E

DECISION CIRCLE FLOW

The decision circle flow pattern reveals the decision-making nature of the program.

A s an example, statement number 46 provides the "46" decision circle whereby the circle radius pivots about to statements 7, 41, 42, 43, 65, 66 de- pending upon the value of the appropriate (MPV) pivot control number at the time before decision.

It may be said of this pattern that it reflects the skeletal logic of the com- puter program. Traditional computer program flow charts "flesh out" this skeleton. Both serve a purpose from the points of view of simplicity and com- prehensiveness. One gives a fast bird's eyeview without the appended details which otherwise may hamper debugging efforts. With the decision circle ap- proach, logic decisions stand out to facilitate these efforts.

The traditional flow charts present a more complete picture which is de- sirable in the final computer program documentation report.

The one emphasizes the pivoting decisions and the other encompasses these decisions with details of additional information.

E-1

READ STATEMENTS

4

DECISION CIRCLE FLOW OF PUTT COMPUTER PROGRAM

7- 34

I

3p I

33 'py 29

64

31 - .31

Note: Numbers are those o f Program's FORTRAN Statements

503

E-2

503 9014 35

IO t 39639 36 I

1

66

t 20

i9 18

dl01

9 7 22 , , & - - A 33

+ 17 32 58 49

1 5 2

15 602 702 703 601

1' 701

t

97 610 61 1 613 DECISION CIRCLE FLOW OF 2;; PUTT COMPUTER P R O G R A M 620 621 622 630 63 1 632

STOP END

Note: Numbers are those o f Program's FORTRAN Statements

E-3

APPENDIX F

DATA READ-INPUT CORRESPONDENCE

The data read-input correspondence proves of value in setting up for a run. Here the data are inserted, sandwich-like, between the read and format statements.

For example, the READ (5, 88) card on the following page readily shows the correspondence of JAL to 78, JVS to 54, etc. The 88 statement shows its present form and the manner in which it would have to be changed if additional values were to be read in.

The columns below, 1 to 0, enable one to readily place new data in proper columns.

Without the above correspondence, one would have to cope with the problem of locating the data as they appear in the program listing (Appendix B) to modify the read-input in one way o r another. This would make the task more formidable, time consuming, and less palatable.

F- 1

S D A T A

R E A C ( 5 45 K n t X I’ILi Z.UY029ULE+07 1 4 0 . 5 7 8 4 9 t + 1 4

45 F n K k A T ( E 14.-/, E 14.5 1

R t A D ( 5 7 7 4 ) FY (2 I tH: l l l t d I C t A T , S d IG 47 300 L 6 500‘3 1636.5 36.46 2.64

7 4 F O K i i A T ( 5 F l u . Z )

K E h U ( 5 9 UU TI12 7 h*rG 1, k L 2 t F h i 9 D T 0 1 t UT02 9 W ~ 3 t >.is3 7 F 6 3 F I BFX 0.6 6bUY.4 6 0 4 d . 1 51057. 2.6 0.8 627.7 231.5 4 7 3 0 0 . 8 0 1 0 . t i0 1 U K I / IT ( F7.L 7 L F 7.17 F 7.0 t 2 F 7 3 t 2 F 7.2 t F 7 0 t F 7.1 1

KI’biU ( 598 1 ) ~ Y O L 7 A F L ~ S P G F Y t SPGOtUFX ,L!OtVFTCl, V i l T U t A K F X ~ i?r(ci 4.3 6U.Y 1.064 1.541 6.Y286 6.66 17.002 33.348 1.65 4 . 1

8 1 ~ C J K I L I L ~ ( ~ F 7 . 3 7 4 F 1 . 4 t 3 F 7 . 3 t F 7.4)

h E AC) ( 5 t d 3 1 ( T P A ( L I t L = l t JAL 0.21162~ U 4 i i . l Y 6 6 7 t 0 4 0 . 1 R L 7 7 t U4 U.16460E 0 4 0.15721E 0 4 0.14556E 0 4 0 . 1 5 4 6 Z t d 4 U . l L 4 3 6 E 0 L U . 1 1 4 7 5 t U4 (1.10575E 0 4 0 . 9 7 3 L 7 t 0 3 O.69459E 0 5 U.b2116c U 3 U.75L71E 02 0.68b96E 0 3 O.6L966E 0 3 0.5745dE 03 0.52347F 0 3

U.Lbb07t d 5 u . L 4 3 6 1 t U3 D.191HOE 0 3 0 . 1 5 1 d 3 t 0 3 O . l l b 9 3 E U 5 0.9367LE O L

0 . 1 4 ~ 4 7 E O L u.V’cl37LF 0 1 0 . 6 5 7 3 5 t 0 1 U.44552E 0 1 0.30597E 0 1 0.L1247E 0 1

0.23U>OE-u1 U . i l h 7 0 t - d l 0 . 2 0 3 n u t - 0 1 u . 1 3 L 7 U t - 0 1 0 . 7 1 9 4 0 t - O L 0.390LOE-OL

0 . 4 7 6 1 2 t U3 u . 4 5 ~ 6 3 E 0 3 0 . 3 9 3 1 1 ~ 0 3 0.35723C 0 3 0.32462E 0 3 0.2949YE 0 3

0 . 7 3 7 F 4 t O L ~ - 5 d l d 5 E O L ( -45HL71- 02 0.3h292F 0 2 0.28878E 02 0.23085E 0 2

0 . 1 4 7 X 4 ~ U l U . l O L I L t 0 1 U . 4 7 1 5 1 t 00 0.19835E 00 0 .7L774E-01 0 .24460E-01

0 . L l l b O F - U I L . 1 1 7 I U t - O L 0.67Y2UE-U3 0.40550E-03 0 .24940E-03 0 .15760E-02 0.10570E-U3 U . 7 5 5 6 0 t - U 4 0 . 5 8 3 7 U t - 0 4 0 .46L00E-04 0 .37620E-04 0 .31320E-04 0.L6550E-04 U.LL840E-04 0.198YOE-UL 0 .17510E-04 0.15550E-04 0 .13910E-04 U.1254UE-04 U . 1 1 3 7 U t - 0 4 0.10560E-U4 0 . 1 0 5 6 0 t - 0 4 0.10560F-04 0 . 1 0 5 h O t - 0 4

8 3 F U i < l ~ i u T ( b E l L . 5 1

K E A U ( 5 1 8 3 ) ( V S ( Y ) t k = l t J V S ) 0 .11164t b 4 U . l l U 8 7 E 0 4 0 . 1 1 0 1 0 t 0 4 0.1093LE 0 4 0.10b53E 0 4 0.10774E 0 4 0.10694E 0 4 U. lU614E 0 4 0 . 1 0 5 3 3 t 0 4 0.10451E 0 4 0.10369E 0 4 0.10286E 0 4 0.10L03E 0 4 U.10119E 0 4 0.10034E 0 4 0.99485E 0 3 0.9862LE 0 3 0.97752E 0 5 ( ’ - 9 6 8 7 5 t 0 3 U.Y6808E 0 3 0 . 9 6 8 0 8 t 0 3 U . 9 6 8 0 8 t 0 3 0.96808E 0 3 0.96808E 0 3 0 .96808t U 3 U.96aOkiE 0 3 U.96808E 0 3 0.9h808E 0 3 0.96808E 03 0.9680RE 0 3 0.96808E d 3 U.96bU8t 0 3 0.97344E 0 3 0.98346E 0 3 0.99338E 0 3 0.10032E 0 4 0 . 1 0 2 2 5 t 0 4 iJ.10415E 0 4 0.10601E 0 4 0.10783E 0 4 0.10963E 0 4 0.11057E G 4 0.11057E 0 4 O.lO934E 0 4 0 . 1 0 3 8 7 t 04 U.98116E 03 0.92011E 0 3 0-+8548OE 0 3 0.85140E 0 3 U.84800E 0 3 0.84650E 0 3 0.84650E 0 3 0.84650E 0 3 0 - 8 4 6 5 0 E 0 3

8 3 FOfiIv1AT(6El2.5)

1 2 3 4 5 6 7 8 9 0 1 - 12 345 6 7 8 9 0

2 - 1 2 3 4 5 6 7 8 9 0 3 - 1 2 3 4 5 6 7 8 9 0

4 - 1 2 3 4 5 6 7 8 9 0 5 - 1 2 3 4 5 6 7 8 9 0

6 - 1 2 3 4 5 6 7 8 9 0

F-2

D A T A READ-INPUT C O R R E S P O N D E N C E

R E A D ( 5 7 8 2 ( T H ( L 7 L = l , JAM 0.0 E 00 0.2 E 0 4 0.4 E 0 4 0.6 E 0 4 0.8 E 04 0.1 E 05 0.12 E 05 0.14 E 05 0.16 E 0 5 0.18 E 05 0.20 E 0 5 0.22 E 05 0.24 E 05 0.26 E 05 0.28 E 05 0.30 E 05 0.32 E 05 0.34 E 05 0.36 E 05 0.38 E 05 0.40 E 05 0.42 E 05 O i 4 4 E 05 0.46 E 05 0.48 E 05 0.50 E 05 0.55 E 05 0.60 E 0 5 0.65 E 05 0.70 E 05 0.75 E 05 0.80 E 05 0.85 E 05 0.90 E 05 0.95 E 05 0.10 E 06 0.11 E 06 0.12 E 06 0.13 E 0 6 0.14 E 06 0.15 E 06 0.16 E 06 0.17 E 06 0.18 E 06 0.20 E 06 0.22 E 06 0.24 E 06 0.26 E 06 0 . 2 6 1 ~ 06 0 . 2 6 2 ~ 06 0 . 2 6 3 ~ 06 0.27 E 06 0.28 E 06 0.29 E 06 0.30 E 06 0.31 E 06 0.32 E 06 0.33 E 06 0.34 E 0 6 0.35 E 06 0.36 E 06 0.37 E 06 0.38 E 06 0.39 E 06 0.40 E 06 0.41 E 06 0.42 E 0 6 0.43 E 06 0.44 E 06 0.45 E 06 0.46 E 06 0.47 E 06 0.48 E 06 0.49 E 06 0.50 E 06 0.999E 06 0.999E 08

82 FORHAT (7E 10.3 1

R E A D ( 5 9 8 4 ) ( XMCH ( M 7 M = l , JMC 0.70 0.80 0.91 1 - 0 1 1.11 1.21 1.51 2.00 3.00 3.50 4.00 5.0 7.00 9.00 11.0

8 4 F O R M A T ( 14F5 - 3 I

R E A D ( 5 9 8 5 1 ( C D ( M ) 7 M = l , JMC 1 e95 -98 008 e15 e 1 5 - 1 4 e03 ,865 -595 a503 e44 -366 e242 e133 - 0 3

85 FORMAT ( 14F5.3

R E A D (5 ,86) (TVO(N) ,N= l ,JVO) 35. 34. 33. 32. 31. 30. 29. 28. 27.. 26. 25. 24. 23. 22. 21. 20 . 19. 18. 17. 16. 15, 14, 13. 12. 11. 10. 9. 8 . 7. 6. 5. 4. 3. 2. 1.65 1.75

.a5 .45 .05 .oz5 86 F O R M A T ( 12F6.3)

READ (5,87)(TVFX(N),N=17JVFXl 20. 19. 18. 17. 16. 15. 14. 13. l i e 11. 10. 9.

a. 7. 6. 5. 4. 3. 2.59 2.19 1 - 7 9 1.39 099 ,5

87 FORMAT(12F6.21

1234567890 1-1234567890

2-1234567890 3-1234567890

4- it 3 45 6 7 a 40 5-1234567890

6-1 2745 678 9 o

F-3

R €AD ( 5 , 8 7 ) ( T H F X ( N ) , N = l , J V F X ) 258.97254.38249.8 2 4 4 ~ 7 6 2 4 0 ~ 6 3 2 3 6 ~ 0 4 2 3 1 ~ 4 6 2 2 6 ~ 8 7 2 2 2 ~ 2 9 2 1 7 ~ 7 0 2 1 3 ~ 1 2 2 0 8 o 5 2 2 0 3 .Y!ZYP .26-E4 7 8 19 0 19 18 5 6 1 1 8 1 0 2 1 7 9 1 3 1 7 7 2 3 1 7 5 1 3 1 7 3 0 3 16 8 1 3 0.0

87 FORMAT ( 12F6.2 )

RE4D (5923) ( R T ( L H 1, LH=1, K H ) 0 .o 2.0290 3.0650 4.0640 5.0620 6.0610 7.0590 8.0580 9.0560 10.0540 11.0530 12.0510 13.0500 14.0480 15.0460 16.0450 17.0430 18.0420 19.0400 20.0380 21.0370 22.0350 23.0340 24.0320 25.0300 26.0290 27.0270 28.0260 29.0240 30.0220 31.0210 32.0190 33.0180 34.0160 35.0140 36.0130 37.0110 38.0100 39.0080 40.0070 41.0050 42.0030 43.0020 44.0000 45.0750 46.0740 47.0720 48.0710 49.0690 50.0030 51.0020 52.0000 52.5120 53.0110

23 FORMATf9F8.4)

R E A D ( 5 , 2 4 ) ( P H R G ( L H ) , L H = l , K H I 461.17 461.17 465.57 467.07 467.87 468.47 469.67 472.07 472.87 473.37 475.27 475.77 476.27 477.57 478.97 480.67 481.27 483.17 483.67 485.27 487.07 488.46 488.86 490.26 491.36 492.96 492.26 492.06 492.86 492.86 492.26 491.26 491.36 492.06 491.16 489.36 488.86 487.67 486.47 484.87 483.67 483.77 486.27 487.47 488.36 488.16 485.47 478.67 470.57 463.02 455.32 448.82 444.69 441.78 24 FORMAT(9F8.2)

READ ( 5 , 3 ) ( T I P C ( J P ) , J P = l , K P ) 0 .o 1 504 1 645 1.811 2 029 3.065 4 064 3 FORMAT (7F 10 -4

1 2 3 4 5 6-1 8 9 0 1-12 34567890

2- 12 3 4 5 6 7 8 90 3-1234567890

4-1234567890 5-1234567890

6-1234567890

F-4

APPENDIX G

DATA DISPLAY FORMAT

A typical data display format is shown on page E 2 of this appendix as called for by card numbers 709, 710, 715, and 716 on the program listing (Appendix B, page B-5.)

G-1

ABBREVIATED DATA DISPLAY FORMAT

J I Y i n

1 -0.000E-19 0. 0.739E 0 4 -0.0OOE-19

0.725E 0 4 -0 -000E-19

0.725E 0 4 0.112E 0 4

0.717E 0 4 O.11ZE 0 4

0.707E 04 0.11ZE 0 4

0.698E 0 4 O.1l'ZE 04

WG V S Y

2 -0.000E-19 0.600E

3 0.68bE 01 0.610E

4 0.389E 01 0.868E

5 0 . 5 9 6 ~ a i 0.113E

6 0.634E 01 0.138E

7 0.655E 0 1 0.164E

8 0.670E 01 0.190E

9 0.68ZE 0 1 0.216E

0.6896 04 O.11ZE 04

6.681E 04 O.11ZE 0 4

D.672E 0 4 0 . l l l E 04 10 0.693E 01 O.24ZE

0.664E 0 4 O . l l l E 04

0.655E 0 4 O.1 l lE 04

0.6471 04 O . l l l E 04

11 O.7OZE 0 1 0.267E

12 0.712E 0 1 0.293E

1 3 0.721E 0 1 0.319E

14 0.822E 0 1 0.320E

15 0.192E 01 0 . 3 2 l E

16 0.183E 01 0.371E

17 0.179E 01 0.4ZlE

18 0.176E 01 0.471E

19 0.175E 01 0.521E

20 0.175E 01 0.571E

2 1 0 . 1 7 4 ~ a i 0.621E

2 2 0.175E 01 0.671E

0.639E 0 4 0 . l l l E 0 4

0.568E 0 4 O . l l l E 04

0.568E 0 4 0.111E 04

0.564E 0 4 O . l l l E 0 4

0.561E 0 4 0 - l l l E 0 4

0.557E 04 0 . l l l E 04

0.552E 0 4 0 - l l l E 04

0.548E 0 4 O . l l l E 04

0.544E 0 4 O.l lOE 04

0.540E 04 0 - l l O E 04

0.536E O+ O.llOE 0 4

0.531E 0 4 O.l lOE 04

0.527E 04 O.11OE 04

0.523E 0 4 OellOE 0 4

23 0.175E 01 0.72lE

24 0.184E 01 0.771E

25 0.196E 01 0.821E

26 O-ZlOE 0 1 0.871E

27 0.225E 01 0.921E 0.519E 0 4 0.109E 04

0.514E 0 4 O.lO9E 04

0.510E 0 4 0.109E 04

0.506E 0 4 0.109E 0 4

0.501E 04 0.1OIE 04

28 O.ZZ8E 01 0.971E

29 0.231E 01 O.IO2E

30 0.234E 01 0.107E

3 1 0.238E 01 0 . l l Z E

G S T l R R PFT POT

Y m c n C O Y c e 0 -0.000E-19 -0.0OOE-19 -0.000E-19 -0.000E-19

00 -0.000E-19 -0.000E-19 -0.000E-19 -0.000E-19 -0.OOOE-19 -0.000E-19 -0 .OOO E-19 -0.000E-19

-0.OOOE- 19

0.106E-00

0.136E-00

0.172E-00

0.214E-00

O.Zb6E-00

0.316E-00

0.367E-00

0.419E-00

0.471E-00

0.524E 00

00 0.322E

00 0.322E

01 0.322E

01 0.322E

01 0.322E

0 1 0.322E

01 0.322E

0 1 0.322E

01 0.322E

01 0.32ZE

01 0.322E

01 0.322E

01 0.322E

0.577E 00

0.580E 00 ~~

0.581E 00

0.609E 00

0.636E 00

0.663E 00

0.689E GO

0.715E 00

0.742E 00

0.768E 00

0.795E 00

O.BZ2E 00

01 0.322E

01 0.322E

0 1 ~ 0.3228

01 0.322E

01 0.322E

01 0.322E

01 0.322E

0 1 0.322E

0 1 0.322E

0 1 0.322E

01 0.322E

01 0.322f

0.850E 00

O.881E 00

-0.000E-19 0.428E 03 02 0.209E 08

0.950E 00 0.167E 02 0.419E 02 O.4ZBE 03 02 0.209E 08

0.950E 00 0.273E 02 0.685E 02 02 0.209E 08 0.438E 03 0.428E 03

0.109E 03 0.436E 0 2 0.950E 00 02 0.209E 08 0.438E 03 0.428E 03

0.950E 00 0.673E 0 2 0.169E 03 02 O.209E 0 8 0.438E 03 0.428E 0 3

0.950E 00 0.104E 03 0.260E 03 02 0.209E 08 0.438E 0 3 0.428E 03

0.950E 00 0.146E 03 0.367E 03 02 0.209E 08 0.438E 03 0.428E 03

0.950E 00 G.196E 03 0.493E 03 0.438E 0 3 0.428E 03 02

0.950E 00 0.254E 0 3 0.638E 03 02 O.ZO9E 08 0.438E 03 0.428E 03

0.950E 00 0.320E 03 0.803E 0 3 0 2 0.209E 08 0.439E 0 3 0.429E 03

0.950E 00 0.3946 03 0.989E 03 0.440E 03 0.430E 03 02

0.119E 04 0.950E 00 0.476E 03 02 0.209E 08 O.44OE 03 0.430E 03

0.950E 00 0.481E 03 O.lZ1E 0 4 0.430E 03 02 0.209E 08 0.440E 03

0.950E 00 0.482E 03 0.121E 0 4 0.432E 0 3 0.442E 03 02 0.209E 08

0.950E 00 0.523E 03 0.131E 0 4 02 0.209E 08 0.443E 03 0.433E 03

0.950E 00 0.564E 03 0.14lE 04 0.434E 0 3 0.209E 08 0.444E 03 02

0.950E 00 0.604E 03 0.151E 0 4

-0.OOOE-19 -0 .OOO E-19 0.438E 03

0.438E 0 3

0.209E 08

0.209E 0 8

02 0.209E

02 0.209E

02 0.209E

02 0.209E

a 2 0.209E

a2 0.209E

c2 0.209E

az 0.209E

a2 0.209E

0.950E 00

0.955E 00

0.962E 00

0.970E 00

0.978E 00

0.800E 00

0.571E 00

0.320E-00

0 2 0.322E 02 0.209E

02 0.321E 02 0.209E O.1OZE 01 0.150E-00

0.106E 0 1 0.150E-00

0.434E 0 3 0.444E 0 3 08 0.644E 03 O . l b l E 0 4

0.435E 03 0.445E 03 08 0.684E 0 3 0.172E 0 4

08 0.445E 0 3 0.435E 03 0.724E 0 3 O.184E 0 4

0.435E 03 0.445E 03 08 0.765E 03 0.196E 0 4

0.436E 03 08 0.446E 0 3 O.ZO8E 0 4 0.806E 03

0.436E 03 08 0.446E 0 3 0.849E 03 0.179E 04

0.438E 03 08 0.448E 0 3 0.134E 0 4 0.892E 03

0.439E 0 3 0.449E 03 08 0.941E 03 0.795E 0 3

0.439E 03 08 0.449E 03 0.217E 03 0.994E 03

08 0.450E 0 3 0.440E 03 0.298E 03 0.105E 0 4

0.440E 03 08 0.390E 03 O . l l l E 0 4

08 O.45OE 03 0.440E 03 O.l l7E 0 4 0.464E 03

08 O.451E 03 0.441E 03 0.123E 0 4 0.487E 03

0.450E 03

G-2