Analysis and construction
of software measures
Jean-Marc Desharnais
Analysis of software measures
 Scale and units
 McCabe
 Albrecht Function Point
 Halstead Measure
The following presentation is inspire from Dr. Alain Abran documents that I
am using with his permission. A book should be published in a near future.
Scale and units
Scale numbering
 Nominal
 Ordinal
 Interval
 Ratio
 Absolute
Exercise Scale
 Function Point Analysis (FPA) is using Adjusted and
Unadjusted point;
 Unadjusted FPA is the total number of point based on total
components based on their type, their complexity and the
points giving by the 5 tables;
 Adjusted FPA is: Unadjusted FPA * by an adjustment factor
between 0.65 and 1.35
 This adjustment factor is coming from 14 questions quote
between 0 and 5 (14 * (0) 5 = 70)/100 = (0) 0.7;
 1.35 - 0.65 = 0.7
 What is inappropriate in this approach?
Analysis of software measures
 Scale and units
 McCabe
 Albrecht Function Point
 Halstead Measure
McCabe Cyclomatic
Complexity Number
 This short presentation will show that McCabe:
 measure software design has some ambiguity
 as much the measure interpretation
 Measurement concepts and measurement instruments
are based on imprecise empirical representations
Mc Cabe and complexity
 Prior to investigating the explicit and implicit definitions
behind the McCabe ‘cyclomatic complexity number’ , it
is interesting to survey how complexity has been
defined (characteristics of the measure);
Complexity definition: IEEE
 Degree to which a system or component has a design
or implementation that is difficult to understand and
verify;
 complexity is a property of the design implementation;
 also a relationship to on the effort needed to understand
and verify the design implementation.
 Two different entities are involved in the definition,
process (effort) and product (design or source code)
Complexity and McCabe
 By adding the label ‘complexity’ to the expression
‘Cyclomatic Number’, McCabe leads the reader to
believe that the attribute he considered is the
complexity of a source code program, but does not
explicitly document this claim by association.
 What some authors say about complexity?
Complexity: Evans et al.
 Degree of complication of a system or system
component;
 Determined by such factors as the number and
intricacy of interfaces, the number and intricacy of
conditional branches, the degree of nesting, and the
types of data structures.
Note: many concepts to be measured.
Complexity: Whitmire
 Also include computational, psychological and
representational complexity;
 Computational: hardware resources to execute the
software
 Psychological: complexity of the problem solved by the
software, characteristics of the software (size,
cohesion, coupling, etc.)
 Representational: complexity that includes knowledge
and experience of the problem.
Cyclomatic complexity
number
 McCabe analysis is based on measurement concepts
in the graph theory and transpose on software
measurement;
 Cyclomatic number is: v(G) = e − n + p (1)
 e = edges; n = nodes (vertices); p = separates
components
Simple example
E (edge or arrow) = 4
N (nodes or square) = 5
P = 1 (connected component)
+ 1 (virtual edge)
v(G) = E – N + P
v(G)= 4 – 5 +2 =1
Exercise
What is the
complexity ?
Edge =
Node =
V(G) = E – N + P
Answer
Edge = 16
Node = 13
V(G) = 16 - 13 + 2 =5
Definition of units
 Left side of the equation:
 Units of v(G) derived from the definition: maximum
number of linearly independent cycles in a strongly
connected graph;
 Strongly connected graph explain indirectly the metamodel.
 Right side of the equation:
 Three distinct types of units: edges, nodes and 'separate
components';
 Numerical assignment rule: add and subtract.
Definition of unit not clear
 Different types of units are involved;
 At the level of each unit different types of units cannot
be added (edge and node);
 Needed to be transposed into a higher level of
abstraction (ex: apple and orange have a higher
abstraction of fruit);
 Graph theory has not documented clearly how the
units are manipulated in their measurement procedure;
 There is a lack of clarity.
In Zuse, a proof of the scale type associated with the cyclomatic number is suggested
Analysis: Definition of the
measured Entity
 The entity measured by the Cyclomatic Complexity
Number is a control flow graph.
 According to McCabe, the measured entity is the
source code of a given module, which corresponds to
a function or a subroutine.
Analysis: Definition of the
measured Entity
 But, do graphs correctly represent the source code
entity in order to measure its Cyclomatic Number?
 In other words, is the assumption concerning the oneto-one relation of a given module source code and its
corresponding graph verified?
Analysis: Definition of the
measured Entity
 One source code of one module is related to one and
only one graph. But the contrary is not necessarily true;
that is, one graph can be related to one or many
source codes.
 So, it is not obvious that the final source code
corresponds to the measured graph.
 Moreover, McCabe suggests to use this Cyclomatic
Number in order to plan the testing effort (ex: test the
more complex modules).
Source code and graph
Source code 1
Graph 1
Source code 2
Graph 2
Source code 3
Interpretation in measurement
 We should explore:
 whether or not there is a relationship across multiple
variables?
 what are the strengths of such relationships?
 how much these relationships vary (or not) under various
conditions?
McCabe complexity
 McCabe by adding the term ‘complexity’ to the
‘cyclomatic number’ has explicitly made an association
between this number and a concept of complexity:
 but has neither described explicitly such association;
 nor associated quantitative numbers to this association;
 nor described under which conditions it would hold for
particular quantities.
Interpretation in industry
 Ratio scale or exponential scale ?
 Program A Cyclomatic number = 10
 Program B Cyclomatic number = 5
 Testing program A versus program B: is A more than
twice the testing time than B?
 Practitioners build their own interpretation scale without
clear rules and non measurement-related convention.
Conclusion McCabe
 Artificially labeling the Cyclomatic Number as a
‘complexity’ concept has led to considerable
ambiguity on the use of this Number as a
measurement number rather than as a
qualitative empirical model which varies
according to the empirical contexts.
 The key problem of measurement units:
 Related concepts have not been either adequately
explored or adequately explained. Without such
knowledge and insights, it is difficult to improve such
a design.
Analysis of software measures
 Scale and units
 McCabe
 Albrecht Function Point
 Halstead Measure
The following presentation is inspire from Dr. Alain Abran documents that I
am using with his permission. A book should be published in a near future.
Albrecht Function Point
 Alan Albrecht was the first to propose in 1979 a new
way of quantifying software size
 Size was based on the users view of the software
 functional size of software was proposed as a generic
measure of the “output” of the development process
 It allows a comparison of projects in which software
was developed using different programming languages
Albrecht Function Point (continued)
 Approach proposed by Albrecht is characterized by its
empirical nature
 It was a quite useful method to solve 60’s and 70’s
problems, but more difficult to apply in modern software
development (Alain Abran)
Note: Dr. Abran article will publish in December 2009
Albrecht (global vision)
Unadjusted count
 There are two main parts:
 The measurement process for the logical data files ;
 The measurement process for the transactions.
Ret = Record Element Type
Validity of the model
It must be noted that, neither in the original Albrecth’s paper nor in the
IFPUG’s documentation:
• none of the relations of these models is based on any experimentally
justified theories in any precise framework
• they are only described in a set of rules established by a consensus
within the normative committee of IFPUG, the Counting Practices
Committee.
Unadjusted FPA
 The final results, (unadjusted) function points, are most
difficult to interpret:
 Many implicit dimensions;
 Use of different types of measurement;
 Mix of measurement scale types;
 No mathematical significance unless the validity of each
transformation can be demonstrated theoretically or
empirically.
Value Adjustment factors
 14 general questions with 6 characteristics for each
(counting 0 as one);
 Classify as 0 to 5 (ordinal);
 Each 14 general questions result (characteristic
number) is add (interval);
 Classification in the previous step of a system
characteristic is next multiplied by an ‘impact’ of each
answer. Ex: question 1 answer is 2 then 0.02 (ratio).
Analysis of software measures
 Scale and units
 McCabe
 Albrecht Function Point
 Halstead Measure
The following presentation is inspire from Dr. Alain Abran documents that I
am using with his permission. A book should be published in a near future.
Halstead Measures
 According to Halstead, a computer program is:
 an implementation of an algorithm
 considered to be a collection of tokens
 that can be classified as either operators or operands.
Halstead operators and operands
 By counting the tokens and determining which are
operators and which are operands
 The following base measures can be collected:




n1: Number of distinct operators.
n2: Number of distinct operands.
N1: Total number of occurrences of operators.
N2: Total number of occurrences of operands.
 Number of potential operators
 Number of potential operands
Operator or operand
 Unfortunately, there is a problem in distinguishing
between operators and operands
 Halstead has not explicitly described the generic
measurable concepts of operators and operands
 He assume that the example he gave was explicit
enough
Example of algorithms use
 10 equations are based on the results of 6 based
measures: n1, n2, N1, N2, n1* and n2*
 Example: length (N) of a program P is:
 N = N1 + N2.
 Example: vocabulary (n) of a program P is:
 n = n1 + n2
 There are also volume, level, difficulty, estimator,
intelligent content, programming effort, programming
“time”.
Halstead measures
 In summary, the Halstead measures, as designed
almost thirty years ago, do not meet a key design
criterion of measures in engineering and the physical
sciences.
 The implementation of the measurement functions of
Halstead’s measures has been interpreted in different
ways than the goals specified by Halstead in their
designs.
 For example, the program length (N) has been interpreted
as a measure of program complexity, which is a different
characteristic of a program.