Complexity Metrics and Models

Software Quality Management Unit – IV G. Roy Antony Arnold Asst. Prof. /CSEh li f d ( OC) i ll f • The lines of code LOC) count is usually for executable statements. • LOC count represents the program size and complexity, it is not a surprise that . • More recent studies point to a curvilinear relationship between lines of code and defect rate:Maximum Source Lines of Modules Average Defect per 1,000 Source Lines 63 1.5 100 1.4 158 0.9 251 0.5 398 1.1 630 1.9 1000 1.3 >1000 1.4Wh d l i b l h • When module size becomes very large, the complexity increases to a level beyond a programmer's immediate span of control and total programmer s comprehension. • The curvilinear model between size and defect density sheds new light on software quality engineering. It implies that there may be an g g p y optimal program size that can lead to the lowest defect rate. • Such an optimum may depend on language, project, product, and environment; apparently i i li ti ti d d many more empirical investigations are needed.• Halstead (1977) distinguishes software science from computer science. • The premise of software science is that any programming task consists of selecting and arranging a finite number of program “tokens” which are tokens , . di f • A computer program, according to software science, .Th i iti f H l t d' ft i • The primitive measures of Halstead's software science are • Based on these primitive measures, Halstead developed a system of equations expressingand other features such as development effort and the projected number of faults in the software.Vocabulary, Length, Volume, Level, Difficulty Difficulty, Effort, Faults, h f l i l i b • The measurement of cyclomatic complexity by McCabe (1976) was designed (maintainability). • It is the classical graph theory cyclomatic number,. • To determine the paths, the program procedure is represented .• The general formula to compute cyclomatic complexity is: p y Wh • Where, V(G) – Cyclomatic Number of G ( ) y e – Number of edges n Number nodes – of p – Number of unconnected parts of the graph• If we count the edges, nodes, and disconnected parts of the graph, • The iteration test in a looping statement is counted as one binary decision. In the preceding simple example, since there are two binary decisions, M = 2 + 1 = 3 • The cyclomatic complexity metric is additive The of several additive. complexity graphs considered as a group is equal to the sum of the individual graphs' complexities. g p pneeding detailed inspections. g p likely to have a defect and therefore low rate candidates for development without l detailed inspections. , identify troublesome code, and estimate effort testing effort.• McCabe's cyclomatic complexity index is a . • It does not distinguish different kinds of control flow complexity such as p y . • In studying the quality and syntactic indicators among a sample of twenty modules of a COBOL compiler product found that product, at the module level can be estimated through the following equations: • Lo found that most developers were having difficulty p g y mastering the DO WHILE construct. • As a result, minimizing the use of DO WHILE was one of the actions the team took to reduce defects in the compiler product.St t t i t t t k i t t th • Structure metrics try to take into account the . • The most common design structure metrics are the which are , based on the proposed by (1979) and (1978): A count of the modules that call a given module : A count of modules that are called by a given module I l d l ith l f i • In general, modules with a large fan‐in are . • In contrast, modules that are large and complex are likely to have a small fan‐in. structure complexity is defined as: • Henry and Selig's work (1990) defines a hybrid form of their information‐flow metric as information where, Cip – internal complexity of procedure p C d d Gl (1990) d l d t l it d l • Card and Glass developed a system complexity model C – System Complexity S – Structural (intermodule) Ct Complexity, St complexity, Dt – Data (intermodule) complexity • They defined relative system complexity as n – no. Of modules in the system S l i i f h d fi d • Structure complexity is further defined as i f S ∑ = ) ( 2 Where S – Structural Complexity, f(i) – Fan‐out of Module i, n n – no. Of modules in the systemD t C l it i f th d fi d • Data Complexity is further defined as Di – Data Complexity of Module i, V(i) – I/O Variables in module i, f(i) – fan‐out of module i D – Data (intramodule) Complexity, D(i) – Data Complexity of module i, n = Number of new modules in the system