Halstead complexity measures: Difference between revisions

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{{short description|Software maintainability index}}

'''Halstead complexity metric''' is a [[software metric]] indroduced by Maurice Howard Halstead in 1977. This metric is computed statically, without program execution.

'''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.

These metrics are therefore computed statically from the code.

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

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.

== Calculation ==

For a given problem, let:

First we need to compute the following numbers, given the program:

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

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

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

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

From these numbers, fiveseveral measures arecan derivedbe calculated:

* Program lengthvocabulary: <math>N\eta = N1\eta_1 + N2 \eta_2 \,</math>

* Program vocabularylength: <math>nN = n1N_1 + n2 N_2 \,</math>

* VolumeCalculated estimated program length: <math>V= \hat{N} = \timeseta_1 \log_2 n\eta_1 + \eta_2 \,log_2 \eta_2 </math>

* Difficulty Volume: <math>DV = { n_1N \over 2 }times \times { N_2log_2 \overeta n_2 } \,</math>

* EffortDifficulty : <math>ED = D{ *\eta_1 V\over 2 } \,times { N_2 \over \eta_2 } </math>

* Effort: <math>HVE = N D \times \log_2V n</math>

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

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

* Number of the used different operators ((<math>n_1</math>) and operand (<math>n_2</math>), ), together the vocabulary size <math>n</math>.

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

* Number of the altogether used operators (<math>N_1</math>) and operand (<math>N_2</math>), together the implementation length <math>N</math>.

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

From this then the sizes of Halstead length become (<math>HL</math>) and Healstead volume (<math>HV=V</math>) are calculated:

*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" />

* <math>HL = n_1 \times \log_2 n_1 + n_2 \times \log_2 n_2</math>

* <math>HV = N \times \log_2 n</math>

== Example ==

From the base quantities one can compute different characteristic numbers, e.g.:

* <math>D = { n_1 \over 2 } \times { N_2 \over n_2 }</math>

Where D = difficulty of the program to write or understand, e.g. when doing [[code review]].

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

From http://www.sei.cmu.edu/str/descriptions/halstead.html [http://www.sei.cmu.edu/str/descriptions/halstead.html] and the German wikipedia entry.

<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>HLV = n_142 \times \log_2 n_119 + n_2 \times \log_2= n_2178.4</math>

* Difficulty: <math>D = { n_112 \over 2 } \times { N_215 \over n_27 } = 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 also ==

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* [[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]]