Www.ischool.drexel.edu INFO 631 Prof. Glenn Booker Week 3 – Complexity Metrics and Models 1INFO631...

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INFO 631 Prof. Glenn Booker

Week 3 – Complexity Metrics and Models

1INFO631 Week 3

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Origin

• Complexity metrics were developed by computer scientists and software engineers

• Strongly based on empirical (real world) measurement, with little theory

• Primarily broken into internal and external measures


Internal versus External

• Internal measures describe the complexity within a module (number of decisions, loops, calculations, etc.)

• External measures describe relationships among modules (program or function calls, external file activities, input/output, etc.)


Internal Measures


Internal Product Attributes

• Size measures– Input to prediction models– Normalizing factor for cost, productivity, etc.– Progress during development

• Typically use lines of code (LOC) or function point counts; – LOC is a better measure for predicting cost

and schedule


Lines of Code

• Simple complexity metric, often based on number of executable statements or instruction statements– Highest defect rates often occurs in small

modules– Larger modules have a smaller defect rate

(if they exist at all) - until too cumbersome– Optimum module size ~ 250 lines


Function Points

• Function points help avoid biases due to the programming language(s) used

• Provide a more “fair” basis for comparing different environments

• Focuses on how much work the program accomplishes, not how concisely it is expressed


Halstead Metrics

• Also known as Software Science, 1977• Examine program as compilable “tokens”• Tokens are either operators (+, -) or operands

(variables)• Derive metrics such as Vocabulary, Length, Volume,

Difficulty, etc.• Not widely used


Data Structure (Halstead)

• Halstead’s 2 - number of distinct operands in a module– Operands include: number of variables,

number unique constants, and number of labels

• Operand usage (OU)– OU = 2/N2 where N2 is the total number of

operand references


Software Complexity

• Is a characteristic that influences the resources needed to build and maintain it

• Many different characteristics of software relate to complexity

• These complexity characteristics revolve around the structure of the software


Types of Structural Measures

• Control flow– Addresses sequence in which instructions are

executed– Iteration and looping

• Data flow– Follows trail of data as it is created and

handled– Depicts behavior of data as it interacts with

the program


Types of Structural Measures

• Data structure– Concerned with organization of data itself– Provides information about difficulties in

handling data and in defining test cases


Control Flow

• Modeled by directed graphs (control flow graphs)– Each node corresponds to a single program

statement– Arcs (directed edges) indicate flow of control

from one statement to another


Control Flow

• Control flow graphs are useful for:– Analysis (estimating number of defects)– Expressing complexity by a single value– Assessing testability and test coverage


Basic Control Constructs

If A then X else Y

A

YX

t f

Repeat X until A

X

A

f

t

Case A of a1 : X1

. . an : Xn

...

a1

a2an

A

X1 X2Xn

Note: t=true f=false

If A then X

A

X

t

f

While A do X

A

X

ft


Cyclomatic Complexity

• McCabe, 1976• Based on a program’s control flow chart• Related to number of separate graphable

areas, or number of linearly independent paths in the program

• Complexity MC = edges - nodes + 2*(# of unconnected paths)



• Complexity under 10 generally desired• Can also find M as number of binary

decisions (yes/no) minus one– Multiple choice decisions with ‘n’ choices

count as (n-1) binary decisions• Ignores differences among specific types

of control structures



• Uses of complexity metric:– Identify complex modules needing detailed

inspection or redesign– Identify simple modules needing minimal

inspection and/or testing– Estimate programming, testing and

maintenance effort– Identify potentially troublesome code


Control Flow Representation of Programs

• Software programs can be represented by linear directed segments combined with the basic control flow constructs

• Control flow constructs may be nested, e.g. an IF statement can be inside of a WHILE loop


Control Flow Representation of Programs

• Example:

1 2

3

4

5

6

7

89

10

111213

14

McCabe cyclomatic complexity (MC) - counts the number of linearly independent paths through a program

MC = # of edges - # of nodes +2

Linearly independent paths for example <2, 11> <2, 10, 12, 14> <2, 10, 12, 13, 12, 14> <1, 3, 5, 6, 9> <1, 4, 6,9> <1, 4, 6, 7, 8, 9>


Control Flow--Linearly Independent Paths

b

c

e

g

f

d

a1 2

3 4

5 6

7

8

910

MC = edges - nodes + 2 = 10 - 7 + 2 = 5

Set of linearly independent paths:

b1: abcg

b2: abcbcg

b3: abefg

b4: adefg

b5: adfg

Any arbitrary path is equal to a linear combination of the linearly independent paths listed above

For example, path abcbefg is equal to:

b2 + b3 - b1


Knots - Control Flow Crossovers

• Knot measure -- total number of points at which control flow lines cross

IF (TIME) 30,30,1010 CALL TEMP1 IF (X1) 20,20,4020 Y1=Y+1 Y2=0 CALL TEMP2 GO TO 5030 Z1=140 CALL TEMP3 Z2=Z2+150 CALL TEMP4

How many are here?


Syntactic Constructs

• Examine effect of using specific control structures on defect rate

• Is, by definition, language-specific• Can result in statistically significant

relationships– e.g. Lo used to show that DO WHILE should

be avoided in COBOL


External Measures


Computational Complexity

• Examines algorithmic efficiency and use of machine resources (memory, I/O, storage)

• Studies quantitative aspects of solutions to computational problems

• Examples may include sorting efficiency for a database, managing I/O constraints across a large scale network, etc.


Psychological Complexity

• Concerned with characteristics of software that affect human performance- Injection of defects (when and why does a

programmer make errors?)- Ease of building the software (effort required)- Ease of maintenance (effort required)


Data Structure (Database)

• Database size per program size (DBSPPS)– DBSPPS = DBS/PS

• Where DBS is database size in bytes or characters• PS is program size in source instructions

– Used in COCOMO model as a cost driver• Ordinal scale measure derived from DBSPPS


Fan-in and Fan-out

• Focus is the interaction among code modules– Fan-in = # of modules which call a given

module– Fan-out = # of modules which are called by a

given module• Or, more formally...


Fan-in and Fan-out

• Fan-in of a module is the number of local flows terminating at the module, plus the number of data structures from which info is retrieved by the module

• Fan-out of a module is the number of local flows that emanate from the module, plus the number of data structures (tables, arrays) that are updated by the module


Fan-in and Fan-out

• Do fan-in and fan-out affect software quality?– Large fan-in modules may be interpolation or

look-up routines - no defect correlation– Large fan-out often relates to high defect rate

- has a high defect correlation• Is large fan-in and fan-out bad?


Fan-in and Fan-out

• Information flow complexity– Henry and Kafura: Size*(fan-in * fan-out)2

– Shepperd: (fan-in * fan-out)2

• Henry and Kafura measure helps predict the number of software maintenance problems

Henry, S. and D. Kafura, IEEE Transactions on Software Engineering, 1981. SE-7(5): p. 510-518 Shepperd, M. 1990. Software Engineering Journal 5, 1 (January), pp. 3-10.


Structure Metrics

• Shepperd measure correlates with software development time

• Information flow metric (Henry & Selig) HC = C * (fan-in * fan-out)^2– where C is the cyclometric complexity


Structure Metrics

• System complexity (Card & Glass)– Based on structural complexity (average fan-

out squared) and data complexity (based on number of I/O variables and fan-out)

– Quantified effect of complexity on error rate


Module Call Graph

• Module - a contiguous sequence of program statements, bounded by boundary elements, having an aggregate identifier– Or, a distinct, named group of LOC

• The module call graph shows which modules call each other, and what key information is passed among them


Module Call Graph example

Find_Ave

Main

AverageRead_Scores

Print_Ave

scores

average

average

scores

eof

scores


Module Coupling Measures

• Average number of calls per module (ANCPM)

• Fraction of modules that make calls (FMC)

ANCPM = Number of Interconnections

Number of Modules

FMC = Number of Modules that call

Number of Modules


Information Flow Measures

• Types of information flows– Local direct flow

• Module invokes a 2nd module & passes info to it• Invoked module returns result to the caller

– Local indirect flow• Invoked module returns info that is subsequently passed

to a second invoked module

– Global flow• Info flows from one module to another via a global

data structure


IEEE-STD-982

• Number of Entries and Exits per Module, ‘m’– Like fan-in and fan-out

m = entries + exits• Software Science measures


IEEE-STD-982

• Graph-Theoretic Complexity– Static Complexity

C = Edges - Nodes + 1– Generalized Static Complexity

Based on summing resources needed for each module (e.g. storage, access time, etc.)

– Dynamic complexityComplexity as it changes over time across a network


IEEE-STD-982

• Cyclomatic complexity• Minimal Unit Test Case Determination

– Determine number of independent paths through a module, to get minimum number of test cases for unit testing

• Data or information flow complexity– Fan-in and fan-out of variables


IEEE-STD-982

• Design Structure adds weighted (%) average of six parameters:

1. Whether designed top down (Y/N)

2. Module inter-dependence

3. Module dependence on prior processing

4. Database size (# of elements)

5. Database compartmentalization

6. Module single entrance and exit (Y/N)

– Weighting is chosen to meet project needs


Other Measures

• Compiler measures– Size (bytes of compiled code)– Number of symbols and variables– Cross-reference of all labels– Statement count


Other Measures

• Configuration Management Library Measures– Number of code modules– Number of versions of each module– History of change dates of each module– Module size– Number of related documents for each

module


Availability Metrics

• Most information systems are critical to day-to-day operations– Witness Google or Blackberry being offline

for mere minutes is news• Availability depends on 1) how often the

system goes down, and 2) how long it takes to restore it after a crash



• Perfect availability (100%) is nice to dream of, but realistically, higher reliability is more expensive

• Often measure availability by the number of 9’s in the desired level of availability – Two nines is 99%, three nines is 99.9%, four

nines is 99.99%, etc.– How many nines can you afford?



No. of 9’s AvailabilityDown time

per year

2 99% 87.6 hours

3 99.9% 8.8 hours

4 99.99% 53 minutes

5 99.999% 5.3 minutes


Achieving High Availability

• Many techniques are used to help ensure that high levels of availability are possible– Duplicate systems (clustering)– RAID data duplication– Duplicate power supplies– Independent power supplies– Uninterruptible power supplies (UPS’)


Availability and Code Quality

• Capers Jones demonstrated a clear connection between code quality (defect rate) and the corresponding mean time to failure (MTTF), which is a key aspect of availability– Consistent methods for measurement and

definitions of terms are needed for further refinement


Customer Outage Data

• In order to determine availability, the actual customer-visible system outage time needs to be collected– In order to get this data, the customer must

place a very high priority on availability– This data could be used to identify software

components which most reduce availability


Availability

• We also expect that availability for a new system should increase over the first couple years of its use

• Defect causal analysis can help reduce the root cause of defects, thereby improving availability

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