Halstead complexity measures: Difference between revisions

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{{short description|Software maintainability index}}

* <math>n1</math> = 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.

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

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.

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

These metrics are therefore computed statically from the code.

*<math>N2</math> = 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.

== Calculation ==

*Program length: <math>N= N1 + N2 \,</math>

For a given problem, let:

*Program vocabulary: <math>n= n1 + n2 \,</math>

*Volume: <math>V= N * (LOG2 n) \,\eta_1</math> = the number of distinct operators

* <math>n1\,\eta_2</math> = the number of distinct operatorsoperands

*Difficulty : <math>D= (n1/2) * (N2/n2) \,</math>

*Effort: <math>E= D * V \,N_1</math> = the total number of operators

* <math>n2\,N_2</math> = the total number of distinct operands

From these numbers, fiveseveral measures arecan derivedbe calculated:

* Program vocabulary: <math>n\eta = n1\eta_1 + n2 \eta_2 \,</math>

* Program length: <math>N = N1N_1 + N2 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>HVV = N \times \log_2 n\eta </math>

* Difficulty : <math>D = (n1/{ \eta_1 \over 2) * (N2/n2)} \,times { N_2 \over \eta_2 } </math>

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

WhereThe Ddifficulty =measure is related to the difficulty of the program to write or understand, e.g. withwhen onedoing [[Codecode review]] (?).

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

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

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

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

* Time required to program: <math>HLT = n_1{E \timesover \log_2 n_1 + n_2 \times \log_2 n_218}</math> seconds

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

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

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

*Number of delivered bugs : <math>DB = { n_1E^{2 \over 23} \over 3000}</math> \timesor, {more N_2recently, <math>B = {V \over n_2 3000}</math> is accepted.<ref name="Elements of Software Science" />

Where D = difficulty of the program to write or understand, e.g. with one [[Code review]] (?).

== Example ==

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

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]]