Halstead complexity measures: Difference between revisions

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{{short description|Software maintainability index}}

'''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 makesmade 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.

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== Calculation ==

For a given problem, Letlet:

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

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

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

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

* 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>

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

*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 {{Citation needed||reasonname='By"Elements whom?'|date=Augustof 2013}}.Software Science" />

== Example ==

Let us considerConsider the following [[C (programming language)|C]] program:

<syntaxhighlight lang="c">

<pre>

main( )

{

int a, b, c, avg;

scanf(“"%d %d %d”d", &a, &b, &c);

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

printf(“avg"avg = %d”d", avg);

}

</syntaxhighlight>

</pre>

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

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

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

The uniquedistinct 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>

a, b, c, &a, &b, &c, a+b+c, avg, 3, “%d %d %d”, “avg = %d”

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

Therefore,

* <math>\,\eta_1N_1 = 27</math>, <math>N_2 = 12, 15</math>\,\eta_2 </math>N = 11 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>

Calculated Program Length (or Estimated Length) = (12*log₂12 + 11*log₂11) = (12*3.58 + 11*3.45) = (43+38) = 81

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

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

Volume = Length*log₂(23) = 81*4.52 = 366

* 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>

==References==

<references />

== See also ==

* [[Function point]]

* [[Cyclomatic complexity]]

==References==

{{Reflist}}

==External links==

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* [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)

* [httphttps://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]]