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EXAMPLE 5.10
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Identify the unique operators and operands in the following code that does multiplication by repeated addition. Z = 0; while X > 0 Z=Z+Y; X = X-1 ; end-while ; print(Z) ; operators = ; while-endwhile > +-print () operands Z0XY1 thus, 1 = 8 and 2 = 5
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Potential Operands, g2*
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Halstead wanted to consider and compare di erent implementations of algorithms. He developed the concept of potential operands that represents the minimal set of values needed for any implementation of the given algorithm. This is usually calculated by counting all the values that are not initially set within the algorithm. It will include values read in, parameters passed in, and global values accessed within the algorithm.
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Length, N
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The next basic measure is total count of operators, N1, and the total count of operands, N2. These are summed to get the length of the program in tokens: N N1 N2
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EXAMPLE 5.11
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Software Metrics
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Calculate Halstead s length for the code of Example 5.10. operators = ; while-endwhile > + print () operands Z 0 X Y 1
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3 5 1 1 1 1 1 1
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4 2 3 2 1
There are 14 occurrences of operators, so N1 is 14. Similarly, N2 is 12. N N1 N2 14 12 26.
Estimate of the Length (est N or N_hat)
The estimate of length is the most basic of Halstead s prediction formulas. Based on just an estimate of the number of operators and operands that will be used in a program, this formula allows an estimate of the actual size of the program in terms of tokens: est N 1 log2 1 2 log2 2
EXAMPLE 5.12
Calculate the estimated length for the code of Example 5.10. The log2 of x is the exponent to which 2 must be raised to give a result equal to x . So, log2 of 2 is 1, log2 of 4 is 2, of 8 is 3, of 16 is 4: log2 of 1 log2 8 3 log2 of 2 log2 5 2:32 est N 8 3 5 2:32 24 11:6 35:6 while the actual N is 26. This would be considered borderline. It is probably not a bad approximation for such a small program.
From experience, I have found that if N and est N are not within about 30 percent of each other, it may not be reasonable to apply any of the other software science measures.
CHAPTER 5 Software Metrics
Volume, V
Halstead thought of volume as a 3D measure, when it is really related to the number of bits it would take to encode the program being measured.4 In other words: V N log2 1 2
EXAMPLE 5.13
Calculate V for the code of Example 5.10. V 26 log2 13 26 3:7 96:2
The volume gives the number of bits necessary to encode that many di erent values. This number is hard to interpret.
Potential Volume, V*
The potential volume is the minimal size of a solution to the problem, solved in any language. Halstead assumes that in the minimal implementation, there would only be two operators: the name of the function and a grouping operator. The minimal number of operands is 2 : V 2  log2 2  2 2
Implementation Level, L
Since we have the actual volume and the minimal volume, it is natural to take a ratio. Halstead divides the potential volume by the actual. This relates to how close the current implementation is to the minimal implementation as measured by the potential volume. The implementation level is unitless. L V =V The basic measures described so far are reasonable. Many of the ideas of operands and operators have been used in many other metric e orts. The remaining measures are given for historical interest and are not recommended as being useful or valid.
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