Funami, Yasao

Halstead, M. H.

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Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1975 A Software Physics Analysis of Akiyama's Debugging Data Yasao Funami M. H. Halstead Report Number: 75-144 Funami, Yasao and Halstead, M. H., "A Software Physics Analysis of Akiyama's Debugging Data" (1975). Department of Computer Science Technical Reports. Paper 93. https://docs.lib.purdue.edu/cstech/93 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. A SOFTWARE PHYSICS ANALYSIS OFAKIYAMAlS DEBUGGING DATAYasao FunamiandM. H. HalsteadMay 1975CSO-TR 144A SOFTWARE PHYSICS ANALYSIS OFAKIYAMA'S DEBUGGING DATAYasao FunamiM. H. HalsteadF. Akiyama [1] has published a careful study of the number of bugswhich occurred in the programming of each of the nine modules of a 100 man-month software system called SAMPLE. All of his observed data are reproducedin Table 1. In the case of Module Me, 53 bugs were reported before machineruns were obtained, and these have been included.Table 1. Akiyama's ObservationsProgram Module MA MB MC MD ME MF MG MH MXProgram Steps (S) 4032 1329 5453 1674 2051 2513 699 3792 3412Decisions (D) 372 215 552 1II 315 217 104 233 416Ca 11 5 (J) 283 44 362 130 197 186 32 110 230Number of Bugs (B) 102 18 146 26 71 37 16 50 80In presenting his data, Akiyama reported that the coefficient of correlationbetween number of bugs and number of program steps was 0.83. while the corre-lation between bugs and the sum of decisions plus calls was much higher, at 0.92.An interesting and quantitative explanation of this result is providedby the theory of software physics [2]. According to that theory, the numberof effective mental discriminations, E, require for the implementation of aprogram is given by:( I)2where:V • Program volume.L = Program level.* = 2 = Unique operators requ ired by ca 11."I a"I = Unique operators used ;n the program."2 = Un i que operands used in the program.N2 = Total usage of operands.N = Total usage of operands and operators."="I + "2While Akiyama's data do not include these parameters directly. they dosupply observations from which they may be estimated. If we assume that eachof the S machine language steps includes one operator and one operand, then:and N "" 2S.(2)(3)The number of unique operators, D1, is composed of three classes ofoperators. The first is the number of distinct operators used from the machine'srepertoire of instructions. For large programs, this component may be roughlyapproximated as an octal hundred. Second is the number of distinct operationsprovided by functions or subroutines. This component should correspond toitem J in Table 1. Finally, each transfer to ~ unique location has been shownby Bulut [3] to contribute directly to nl . Since the number of transfers impliedby item D in Table 1 do not each involve transfer to a unique location. only afraction, perhaps one third, should contribute to n1. We then have, roughly:"I=D/3+J+64 (4)At this point. we need only an estimate of n2 to be able to calculate E.From the length equation as presented by Halstead and Bayer [4] and independentlyvalidated by Bohrer [5].3(5)It is possible to findUsing equationsin Table 2.nzwhenth roughnl and N are known.5, the data of Table I yield the results shownTable 2. Software Physics Parameters derived from Table I.Module MA MB Me MD ME MF MG MM MXN 8064 2658 10906 3348 4102 5026 1398 7584 6824N2 4032 1329 5453 1674 2051 2513 699 3792 3412"1 471 180 610 231 366 322 131 252 433"2 442 176 574 201 138 287 76 603 357E(Millions) 170.3 15.3 322.6 28.2 100.2 65.5 6.5 58.5 135.9The carre 1aU on coefficient between number of effective mental discrim-inations, E, and the reported number of bugs, S, is 0.982, indicating thatmos.t of the var i.at i on has been exp 1a i ned.Further, by using the usual figure of 18 mental discriminations per secondfor fluent, concentrating programmers [6], (Stroud [7J gives the range as 5 to20 per secorid), and summing the values of E, one obtains the total effort ofthe task as 903 x 106 effective discriminations, or a~ man-months. This figurecompares reasonably well with the lOa man-months reported by Akiyama.4REFERENCES,[T] Akiyama, F~, lIAn Example of Software System Debugging" Proe. IFIPCongress, 1971.[2] Halstead, M. H., "Software Physics Comparison of a Sample Program inDSL ALPHA and COBOL,II IBM Research Report RJ1460, October 1974.[3] Bulut, Necdet, lIAn Invariant Property of Algorithms," Ph.D. Thesis,Purdue University, August 1973.[4] Halstead, M. H. and Rudolf Bayer, "Algorithm Dynamics," Proe. ACM NationalConference, 1973 (Atlanta).Is] Bohrer, Robert, "Halstead ' s Criterion and Statistical Algorithms,"Proe. Eighth Annual Computer Science/Statistics Interface Symposium,February 1975 (Los Angeles).[6] Halstead, M. H. IlToward a Theoretical Basis for Estimating ProgrammingEffort,1I Technical Report CSD-TR 11J3. Purdue University. May 1975.[7] Stroud, John M.New York AcademyliThe Fine Structureof Sciences, 1966.of Psychologicalpp. 623-631.Time,l' Annuals of

A Software Physics Analysis of Akiyama\u27s Debugging Data

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A Software Physics Analysis of Akiyama\u27s Debugging Data

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