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McCabe

The McCabe metrics are a collection of four software metrics:

• Cyclomatic complexity;
• Essential complexity;
• Design complexity;
• Lines of Code (LOC).

Cyclomatic Complexity: a.k.a “v(G)”, measures the number of “linearly independent paths”. A set of paths is said to be linearly independent if no path in the set is a linear combination of any other paths in the set through a program’s “flowgraph”. A flowgraph is a directed graph where each node corresponds to a program statement, and each arc indicates the flow of control from one statement to another. “v(G)” is calculated by “v(G) = e - n + 2” where “G” is a program’s flowgraph, “e” is the number of arcs in the flowgraph, and “n” is the number of nodes in the flowgraph. The standard McCabes rules (“v(G)” over 10), are used to identify fault-prone module.

Essential Complexity: a.k.a “ev(G)” is the extent to which a flowgraph can be “reduced” by decomposing all the subflowgraphs of “G” that are “D-structured primes”. Such “D-structured primes” are also sometimes referred to as “proper one-entry one-exit subflowgraphs” (for a more thorough discussion of D-primes, see the Fenton text referenced above). “ev(G)” is calculated using “ev(G)= v(G) - m” where “m” is the number of subflowgraphs of “G” that are D-structured primes.

Design Complexity: a.k.a. “iv(G)”, is the cyclomatic complexity of a module’s reduced flowgraph. The flowgraph, “G”, of a module is reduced to eliminate any complexity which does not influence the interrelationship between design modules. According to McCabe, this complexity measurement reflects the modules calling patterns to its immediate subordinate modules.

Lines of code (LOC): LOC is measured according to McCabe’s line counting conventions.

Halstead

The Halstead metrics falls into three groups:

Вузов.

• the base measures,
• the derived measures,
• and lines of code measures.

Base measures:

• mu1 = number of unique operators
• mu2 = number of unique operands
• N1 = total occurrences of operators
• N2 = total occurrences of operands
• length = N = N1 + N2
• vocabulary = mu = mu1 + mu2

Constants set for each function:

• mu1’ = potential operator count (just the function name and the “return” operator)
• mu2’ = potential operand count (the number of arguments to the module)

For example, the expression “return max(w+x,x+y)” has “N1=4” operators “return, max, +,+)”, “N2=4” operands (w,x,x,y), “mu1=3” unique operators (return, max,+), and “mu2=3” unique operands (w,x,y).

Derived measures:

• P = volume = V = N x log2(mu) (the number of mental comparisons needed to write a program of length N)
• V* = volume on minimal implementation = (2 + mu2’) x log2(2 + mu2’)
• L = program length = V*/N
• D = difficulty = 1/L
• L’ = 1/D
• I = intelligence = L’ x V’
• E = effort to write program = V/L
• T = time to write program = E/18 seconds

For notes on defect prediction and the relation of Halstead measures to defect predictors, please refer to our short tutorial on defect prediction here.