Ehsan hessami

Islamic Azad University OF Qazvin

Software Metrics

Software measurement is the mapping of symbols to objects

What?

Software measurement is the mapping of symbols to objects

What?

quantify some attribute of the objects

Why!!!!!? !

Criteria

Criteria

A metric must allow different entities to be distinguished.

A metric must obey a representation condition

Criteria…

Each unit of the attribute must contribute an equivalent amount to the metric

Different entities can have the same attribute value

Many timesthe attribute of interest is not directly measurable .

An indirect measure involves a measure and a prediction formula

Example

density

mass volume

Software Measurement Theory

2 Kinds :

numerical relation system

empirical relation system

The empirical relation system

two parts:

A set of entities, E

A set of relationships, R

The numerical relation system

two parts:A set of entities, N

A set of relationships, P

EXP : Integers , Real

EXP : Less , Equal

MappingM, maps (E, R) to (N, P)

related in the empirical system

related in the numberical system

MappingM, maps (E, R) to (N, P)

related in the empirical system

related in the numberical system

x rel y if M(x) rel M(y)EXP :

EXP . Mapping

X height=< Y height and X weight =< Y weight

measure, BIG

MONOTONICITY

IF increase the value of attribute , the object Will not Reverse .

MONOTONICITY

IF increase the value of attribute , The object will not Reverse . Exp :

y = 5x - x 2X>0 And X<5

X>=5 And X<10

Increaes

DecreaseNot Monotonicity

y = X2

Monotonicity

MEASUREMENT SCALES

There are five different scale types :nominalordinal

intervalratio

absolute

NormalThis type basically assigns numbers or symbols without regard to any quantity

NormalThis type basically assigns numbers or symbols without regard to any quantity

EXP:

Ordinalthere is an implied ordering of the entities by the numbers assigned to the entity

Ordinalthere is an implied ordering of the entities by the numbers assigned to the entity

EXP:

Not Equal1

3 2

First – Second

Second - third

Intervalthe amount of the difference is constant

Intervalthe amount of the difference is constant

EXP: converting from a Celsius to a Fahrenheit

Formule : 9.5 x +32

Ratio

the amount of the difference is constant and Well Zero

absolute

The absolute is a counting scale measure

EXP:

Product Metrics

The most basic metric for size is the lines of code metric .

Product metrics are metrics that can be calculated from the document independent of how it was produced .

McCABE’S CYCLOMATIC NUMBER

introduced in 1976 .

Use the Gragh Theory : C = E – N + 2

C = Cyclomatic number .

N = number of Eodes .E = number of Edges .

McCABE’S CYCLOMATIC NUMBEREXP :

E = 11 N = 8 C = 11 – 8 + 2

C = 5

2 3 4 51

McCABE’S CYCLOMATIC NUMBER

Calculating the cyclomatic number from control flow graphs is time-consuming .

McCabe found a more directMethod of calculating his measure .

McCABE’S CYCLOMATIC NUMBER

IN source Code :

IF , For , While

Case or multiple Branch

1 decision

1 less decision

Restriction :

McCABE’S CYCLOMATIC NUMBER

Control flow graphs are required to have a distinct starting node and a distinct stopping node

C = D + 1D = Sum of Decisions

Formula :

Restriction … :

Example

E = 3D = 2

E = 2D = 1

E = 2D = 1

D = 4

Complexity C = 5

Threshold Value

If the Complexity is greater than 10, efforts should be made to reduce the value or to split the module

HALSTEAD’S SOFTWARE SCIENCE

He did his work in the late 1960s and 1970s.

He empirically looked for measures of intrinsic size

HALSTEAD’S SOFTWARE SCIENCE

variablesconstants

Operands

commasparenthesesarithmetic operatorsbrackets

Operator

Basic Measures—η1 and η2

η2 = Count of unique Operands Count of unique Operatorη1 =

η = η1 + η2 total count of unique tokensη =

Basic Measures—η1 and η2

Exp :z = 0;While x> 0 z = z + y ; x = x + 1;End –while ;Print(z) ;

Operator = ; > + - Print () While-endwhileOperand z x y 0 1

η1 =8 η2 = 5 η = 13

Length(N)

N2 = Count of OperandsCount of OperatorN1 =

N = N1 + N2

N = total count of tokens

LengthEXP :

z = 0;While x> 0 z = z + y ; x = x + 1;End –while ;Print(z) ;

Operators= 3; 5While 1> 1+ 1- 1Print 1() 1

OperandsZ 4X 3Y 20 21 1

N = N1 + N2 = 14+12 = 26

Estimate of the Length(est N)

est N = η1*log + η2*logη12 2

η2

Estimate of the Length(est N)

est N = η1*log + η2*log

Exp :η1=8 , η2=5

est N = 8*3 +5*2.32 = 35.6

η12 2

η2

Volume ( V )

V = N * Log 2(η1+ η2)

Volume = number of bits

Volume ( V )

V = N * Log 2(η1+ η2)

Volume = number of bits

Exp: N = 26 , η1=8 , η2=5

V = 26 * Log = 96.2213

Potential Volume, V*

V* = (2 + η2*)log2(2+ η2*)

Potential Volume = Min number of bits

η2* = The Minimal number of Operands

Implementation Level : L = V* / V

Other Parameter

Implementation Level : L = V* / V

Effort : E = V / L unit of Effors is emd

Other Parameter

Implementation Level : L = V* / V

Effort : E = V / L

Time: T = E / S

18 emd / sec

unit of Effors is emd

Other Parameter

HENRY–KAFURA INFORMATION FLOW

measure the intermodule complexity of source code .

In = into the moduleOut = out the module

i

i

Weight = weight the module

HK = Weight *(out * in )i i i i

i

HENRY–KAFURA INFORMATION FLOWExp : Weight = 1

HK = 1110