Halstead complexity measures

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

Calculation

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

• ${\displaystyle n1}$  = the number of distinct operators
• ${\displaystyle n2}$  = the number of distinct operands
• ${\displaystyle N1}$  = the total number of operators
• ${\displaystyle N2}$  = the total number of operands

From these numbers, five measures are derived:

• Program length: ${\displaystyle N=N1+N2\,}$ 
• Program vocabulary: ${\displaystyle n=n1+n2\,}$ 
• Volume: ${\displaystyle V=N\times \log _{2}n\,}$ 
• Difficulty : ${\displaystyle D={n_{1} \over 2}\times {N_{2} \over n_{2}}\,}$ 
• Effort: ${\displaystyle E=D*V\,}$ 

• Number of the used different operators ((${\displaystyle n_{1}}$ ) and operand (${\displaystyle n_{2}}$ ), ), together the vocabulary size ${\displaystyle n}$ .
• Number of the altogether used operators (${\displaystyle N_{1}}$ ) and operand (${\displaystyle N_{2}}$ ), together the implementation length ${\displaystyle N}$ .

From this then the sizes of Halstead length become (${\displaystyle HL}$ ) and Healstead volume (${\displaystyle HV=V}$ ) are calculated:

• ${\displaystyle HL=n_{1}\times \log _{2}n_{1}+n_{2}\times \log _{2}n_{2}}$ 
• ${\displaystyle HV=N\times \log _{2}n}$ 

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

• ${\displaystyle D={n_{1} \over 2}\times {N_{2} \over n_{2}}}$ 

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

From http://www.sei.cmu.edu/str/descriptions/halstead.html [1] and the German wikipedia entry.

See also

• Function point
• Cyclomatic complexity