# Introduction to Code Metrics

This section contains a brief explanations of the metrics that Radon can compute.

## Cyclomatic Complexity

Cyclomatic Complexity corresponds to the number of decisions a block of code contains plus 1. This number (also called McCabe number) is equal to the number of linearly independent paths through the code. This number can be used as a guide when testing conditional logic in blocks.

Radon analyzes the AST tree of a Python program to compute Cyclomatic Complexity. Statements have the following effects on Cyclomatic Complexity:

Construct | Effect on CC | Reasoning
--- | --- | ---
if | +1 | An if statement is a single decision.
elif | +1 | The elif statement adds another decision.
else | +0 | The else statement does not cause a new decision. The decision is at the if.
case pattern | +1 | The case pattern statement is a single decision.
case _ | +0 | The case _ statement does not cause a new decision. The decision is at the case pattern.
for | +1 | There is a decision at the start of the loop.
while | +1 | There is a decision at the while statement.
except | +1 | Each except branch adds a new conditional path of execution.
finally | +0 | The finally block is unconditionally executed.
with | +1 | The with statement roughly corresponds to a try/except block (see PEP 343 for details).
assert | +1 | The assert statement internally roughly equals a conditional statement.
Comprehension | +1 | A list/set/dict comprehension of generator expression is equivalent to a for loop.
Boolean Operator | +1 | Every boolean operator (and, or) adds a decision point.

## Maintainability Index

Maintainability Index is a software metric which measures how maintainable (easy to support and change) the source code is. The maintainability index is calculated as a factored formula consisting of SLOC (Source Lines Of Code), Cyclomatic Complexity and Halstead volume. It is used in several automated software metric tools, including the Microsoft Visual Studio 2010 development environment, which uses a shifted scale (0 to 100) derivative.

Common formulas are:

- the original formula:

  \[MI = 171 - 5.2 \ln V - 0.23 G - 16.2 \ln L\]

- the derivative used by SEI:

  \[MI = 171 - 5.2\log_2 V - 0.23 G - 16.2 \log_2 L + 50 \sin(\sqrt{2.4 C})\]

- the derivative used by Visual Studio:

  \[MI = \max \left [ 0, 100\dfrac{171 - 5.2\ln V - 0.23 G - 16.2 \ln L}{171} \right ].\]

Radon uses another derivative, computed from both SEI derivative and Visual Studio one:

\[MI = \max \left [ 0, 100\dfrac{171 - 5.2\ln V - 0.23 G - 16.2 \ln L + 50 \sin(\sqrt{2.4 C}))}{171} \right ]\]

Where:

  - `V` is the Halstead Volume (see below);

  - `G` is the total Cyclomatic Complexity;

  - `L` is the number of Source Lines of Code (SLOC);

  - `C` is the percent of comment lines (important: converted to radians).

Note

Maintainability Index is still a very experimental metric, and should not be taken into account as seriously as the other metrics.

## Raw Metrics

The following are the definitions employed by Radon:

> - LOC: The total number of lines of code. It does not necessarily correspond to the number of lines in the file.

> - LLOC: The number of logical lines of code. Every logical line of code contains exactly one statement.

> - SLOC: The number of source lines of code - not necessarily corresponding to the LLOC.

> - Comments: The number of comment lines. Multi-line strings are not counted as comment since, to the Python interpreter, they are just strings.

> - Multi: The number of lines which represent multi-line strings.

> - Blanks: The number of blank lines (or whitespace-only ones).

The equation `SLOC + Multi + Single comments + Blank = LOC` should always hold. Additionally, comment stats are calculated:

> - C % L: the ratio between number of comment lines and LOC, expressed as a percentage;

> - C % S: the ratio between number of comment lines and SLOC, expressed as a percentage;

> - C + M % L: the ratio between number of comment and multiline strings lines and LOC, expressed as a percentage.

## Halstead Metrics

Halstead’s goal was to identify measurable properties of software, and the relations between them. These numbers are statically computed from the source code:

> - \(\eta_1\) = the number of distinct operators

> - \(\eta_2\) = the number of distinct operands

> - \(N_1\) = the total number of operators

> - \(N_2\) = the total number of operands

From these numbers several measures can be calculated:

> - Program vocabulary: \(\eta = \eta_1 + \eta_2\)

> - Program length: \(N = N_1 + N_2\)

> - Calculated program length: \(\widehat{N} = \eta_1 \log_2 \eta_1 + \eta_2 \log_2 \eta_2\)

> - Volume: \(V = N \log_2 \eta\)

> - Difficulty: \(D = \dfrac{\eta_1}{2} \cdot \dfrac{N_2}{\eta_2}\)

> - Effort: \(E = D \cdot V\)

> - Time required to program: \(T = \dfrac{E}{18}\) seconds

> - Number of delivered bugs: \(B = \dfrac{V}{3000}\).

## Further Reading

1. Paul Omand and Jack Hagemeister. “Metrics for assessing a software system’s maintainability”. Proceedings International Conference on Software Mainatenance (ICSM), 1992. (doi)

2. Don M. Coleman, Dan Ash, Bruce Lowther, Paul W. Oman. Using Metrics to Evaluate Software System Maintainability. IEEE Computer 27(8), 1994. (doi, postprint)

3. Maintainability Index Range and Meaning. Code Analysis Team Blog, blogs.msdn, 20 November 2007.

4. Arie van Deursen, Think Twice Before Using the “Maintainability Index”.