1. Software metrics are used to quantify attributes of software objects by mapping symbols to those objects. There are different types of metrics that can be calculated. 2. Important metrics include McCabe's cyclomatic complexity metric, which measures the number of linearly independent paths through a program, and Halstead's software science metrics which measure properties like program volume and difficulty. 3. Product metrics measure attributes of the software independent of how it was produced, like lines of code. Process metrics measure attributes relating to the development process.

1. Software Metrics Ehsan hessamiIslamic Azad University OF Qazvin

2. What ? Software measurement is the mapping of symbols to objects

3. What ? Software measurement is the mapping of symbols to objects Why ?!!!!!! quantify some attribute of the objects

4. Criteria

5. Criteria A metric must allow differententities to be distinguished. A metric must obey a representation condition

6. Criteria… Each unit of the attribute must contribute an equivalent amount to the metric Different entities can have the sameattributevalue

7. Many times the attribute of interest is not directly measurable . An indirect measure involves a measure and a prediction formula

8. Example density mass volume

9. Software Measurement Theory 2 Kinds : numerical relation system empirical relation system

10. The empirical relation system two parts: A set of entities, E A set of relationships, R

11. The numerical relation system two parts: A set of entities, N EXP : Integers , Real A set of relationships, P EXP : Less , Equal

12. Mapping M, maps (E, R) to (N, P) related in the empirical system related in the numberical system

13. Mapping M, maps (E, R) to (N, P) related in the empirical system related in the numberical system EXP : x rel y if M(x) rel M(y)

14. EXP . Mapping measure, BIG X height=< Y height and X weight =< Y weight

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

16. MONOTONICITY IF increase the value of attribute , The object will not Reverse. Exp : 2 y = X Monotonicity X>0 And X<5 2 y = 5x - x Increaes X>=5 And X<10 Decrease Not Monotonicity

17. MEASUREMENT SCALES There are five different scale types : nominal ordinal interval ratio absolute

18. Normal This type basically assigns numbers or symbols without regard to any quantity

19. Normal This type basically assigns numbers or symbols without regard to any quantity EXP:

20. Ordinal there is an implied ordering of the entities by the numbers assigned to the entity

21. Ordinal there is an implied ordering of the entities by the numbers assigned to the entity EXP: First – Second Not Equal 1 Second - third 2 3

22. Interval the amount of the difference is constant

23. Interval the amount of the difference is constant EXP: converting from a Celsius to a Fahrenheit Formule : 9.5 x +32

24. Ratio the amount of the difference is constant and Well Zero

25. absolute The absolute is a counting scale measure EXP:

26. Product Metrics Product metrics are metrics that can be calculated from the document independent of how it was produced . The most basic metric for size is thelinesof code metric .

27. McCABE’S CYCLOMATIC NUMBER introduced in 1976 . Use the Gragh Theory : C = E – N + 2 C = Cyclomatic number . E = number of Edges . N = number of Eodes .

28. McCABE’S CYCLOMATIC NUMBER EXP : 5 1 4 3 2 E = 11 N = 8 C = 11 – 8 + 2 C = 5

29. McCABE’S CYCLOMATIC NUMBER Calculating the cyclomatic number from control flow graphs is time-consuming . McCabe found a more direct Method of calculating his measure .

30. McCABE’S CYCLOMATIC NUMBER Restriction : IN source Code : 1 decision IF , For , While Case or multiple Branch 1 less decision

31. McCABE’S CYCLOMATIC NUMBER Restriction … : Control flow graphs are required to have a distinct starting node and a distinct stoppingnode Formula : C = D + 1 D = Sum of Decisions

32. Example E = 2 D = 1 E = 2 D = 1 E = 3 D = 2 D = 4 C = 5 Complexity

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

34. HALSTEAD’S SOFTWARE SCIENCE He did his work in the late 1960s and 1970s. He empirically looked for measures of intrinsic size

35. HALSTEAD’S SOFTWARE SCIENCE variables Operands constants commas parentheses Operator arithmetic operators brackets

36. Basic Measures—η1 and η2 η = η1 + η2 η = total count of unique tokens Count of unique Operator η1 = Count of unique Operands η2 =

37. Basic Measures—η1 and η2 Exp : z = 0; While x> 0 z = z + y ; x = x + 1; End –while ; Print(z) ; Operator = ; > + - Print () While-endwhile Operand z x y 0 1 η1 =8 η2 = 5 η = 13

38. Length(N) N = N1 + N2 N = total count of tokens Count of Operator N1 = Count of Operands N2 =

39. Length EXP : Operators = 3 ; 5 While 1 > 1 + 1 - 1 Print 1 () 1 Operands Z 4 X 3 Y 2 0 2 1 1 z = 0; While x> 0 z = z + y ; x = x + 1; End –while ; Print(z) ; N = N1 + N2 = 14+12 = 26

40. Estimate of the Length(est N) η1 η2 est N = η1*log + η2*log 2 2

41. Estimate of the Length(est N) η1 η2 est N = η1*log + η2*log 2 2 Exp : η1=8 , η2=5 est N = 8*3 +5*2.32 = 35.6

42. Volume ( V ) Volume = number of bits (η1+ η2) V = N * Log 2

43. Volume ( V ) Volume = number of bits (η1+ η2) V = N * Log 2 Exp: N = 26 , η1=8 , η2=5 13 V = 26 * Log = 96.2 2

44. Potential Volume, V* Potential Volume = Min number of bits V* = (2 + η2*)log (2+ η2*) 2 η2* = The Minimal number of Operands

45. Other Parameter Implementation Level : L = V* / V

46. Other Parameter Implementation Level : L = V* / V Effort : E = V / L unit of Effors is emd

47. Other Parameter Implementation Level : L = V* / V Effort : E = V / L unit of Effors is emd Time : T = E / S 18 emd / sec

48. HENRY–KAFURA INFORMATION FLOW measure the intermodule complexity of source code . HK = Weight *(out * in ) i i i i In = into the module i Out = out the module i Weight = weight the module i

49. HENRY–KAFURA INFORMATION FLOW Exp : Weight = 1 HK = 1110