Halstead complexity measures: Difference between revisions

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{{short description|Software maintainability index}}

n1 = the number of distinct operators

'''Halstead complexity measures''' are [[software metric]]s introduced by [[Maurice Halstead|Maurice Howard Halstead]] in 1977<ref name="Elements of Software Science">{{cite book |author=Halstead, Maurice H. |title=Elements of Software Science |publisher=Elsevier North-Holland, Inc. |___location=Amsterdam |year=1977 |isbn=0-444-00205-7}}</ref> as part of his treatise on establishing an empirical science of software development.

Halstead made the observation that metrics of the software should reflect the implementation or expression of algorithms in different languages, but be independent of their execution on a specific platform.

n2 = the number of distinct operands

These metrics are therefore computed statically from the code.

N1 = the total number of operators

N2 = the total number of operands

Halstead's goal was to identify measurable properties of software, and the relations between them.

From these numbers, five measures are derived:

This is similar to the identification of measurable properties of matter (like the volume, mass, and pressure of a gas) and the relationships between them (analogous to the [[ideal gas law|gas equation]]).

Thus his metrics are actually not just complexity metrics.

Program length

== Calculation ==

N= N1 + N2

For a given problem, let:

n1* <math>\,\eta_1</math> = the number of distinct operators

Program vocabulary

n2* <math>\,\eta_2</math> = the number of distinct operands

N1* <math>\,N_1</math> = the total number of operators

N2* <math>\,N_2</math> = the total number of operands

From these numbers, fiveseveral measures arecan derivedbe calculated:

n= n1 + n2

* Program vocabulary: <math>\eta = \eta_1 + \eta_2 \,</math>

* Program length: <math>N = N_1 + N_2 \,</math>

Volume

* Calculated estimated program length: <math>\hat{N} = \eta_1 \log_2 \eta_1 + \eta_2 \log_2 \eta_2 </math>

* Volume: <math>V = N \times \log_2 \eta </math>

* Difficulty : <math>D = { \eta_1 \over 2 } \times { N_2 \over \eta_2 } </math>

* Effort: <math>E = D \times V </math>

The difficulty measure is related to the difficulty of the program to write or understand, e.g. when doing [[code review]].

V= N * (LOG2 n)

Difficulty

The effort measure translates into actual coding time using the following relation,

D= (n1/2) * (N2/n2)

* Time required to program: <math>T = {E \over 18}</math> seconds

Effort

Halstead's delivered bugs (B) is an estimate for the number of errors in the implementation.

E= D * V

*Number of delivered bugs : <math>B = {E^{2 \over 3} \over 3000}</math> or, more recently, <math>B = {V \over 3000}</math> is accepted.<ref name="Elements of Software Science" />

== Example ==

From http://www.sei.cmu.edu/str/descriptions/halstead.html [http://www.sei.cmu.edu/str/descriptions/halstead.html]

Consider the following [[C (programming language)|C]] program:

==see also==

<syntaxhighlight lang="c">

main()

{

int a, b, c, avg;

scanf("%d %d %d", &a, &b, &c);

avg = (a+b+c)/3;

printf("avg = %d", avg);

}

</syntaxhighlight>

The distinct operators (<math>\,\eta_1</math>) are:

<code>main</code>, <code>()</code>, <code>{}</code>, <code>int</code>, <code>scanf</code>,

<code>&</code>, <code>=</code>, <code>+</code>, <code>/</code>, <code>printf</code>, <code>,</code>, <code>;</code>

The distinct operands (<math>\,\eta_2</math>) are:

<code>a</code>, <code>b</code>, <code>c</code>, <code>avg</code>, <code>"%d %d %d"</code>, <code>3</code>, <code>"avg = %d"</code>

* <math>\eta_1 = 12</math>, <math>\eta_2 = 7</math>, <math>\eta = 19</math>

* <math>N_1 = 27</math>, <math>N_2 = 15</math>, <math>N = 42</math>

* Calculated Estimated Program Length: <math>\hat{N} = 12 \times log_2 12 + 7 \times log_2 7 = 62.67</math>

* Volume: <math>V = 42 \times log_2 19 = 178.4</math>

* Difficulty: <math>D = { 12 \over 2 } \times { 15 \over 7 } = 12.85</math>

* Effort: <math>E = 12.85 \times 178.4 = 2292.44</math>

* Time required to program: <math>T = { 2292.44 \over 18 } = 127.357</math> seconds

* Number of delivered bugs: <math>B = { 2292.44 ^ { 2 \over 3 } \over 3000 } = 0.05</math>

==see See also ==

* [[Function point]]

* http://de.wikipedia.org/wiki/Halstead-Metrik [http://de.wikipedia.org/wiki/Halstead-Metrik]

* [[Cyclomatic complexity]]

==References==

{{Reflist}}

==External links==

* [http://www.virtualmachinery.com/sidebar2.htm The Halstead metrics] - Extensive discussion on the calculation and use of Halstead Metrics in an object-oriented environment (with specific reference to Java).

* [http://www.verifysoft.com/en_halstead_metrics.html Calculation of Halstead metrics] - Measurement of Halstead Metrics.

* [http://www.win.tue.nl/~aserebre/2IS55/2010-2011/10.pdf Explanation with a Sample Program] - Example (on Page 6 of the PDF)

* [https://github.com/dborowiec/commentedCodeDetector Script computing Halstead Metrics and using them for commented code detection]

* [http://pic.dhe.ibm.com/infocenter/rtrthelp/v8r0m0/index.jsp?topic=%2Fcom.ibm.rational.testrt.studio.doc%2Ftopics%2Fcsmhalstead.htm IBM]

* [https://www.vcalc.com/wiki/halstead%20software%20complexity Calculator for computing Halstead metrics]

[[Category:Software metrics]]

[[de:Halstead-Metrik]]