Halstead's software science - ananalytical technique

HALSTEAD’S SOFTWARE SCIENCE
- AN ANALYTICAL TECHNIQUE

PROJECT ESTIMATION TECHNIQUES
● Empirical Estimation Techniques
● Heuristic Techniques
● Analytical Estimation Techniques
○ HALSTEAD’S SOFTWARE SCIENCE

INTRODUCTION
Halstead’s Technique measure
● Size
● Development effort
● Development cost of s/w products

INTRO (cont’d)
Halstead used few primitive program parameters to develop expressions for:
● Overall program length
● Potential minimum volume and Program level
● Actual volume
● Effort
● Development time

INTRO (cont’d)
For any giving programs lets define the following parameters:
● η1
be the number of unique operators used in the program
● η2
be the number of unique operands used in the program
● N1
be the number of the total operators used in the program
● N2
be the number of the total operands used in the program

INTRO (cont’d)
Operator in general: a symbol or function representing a mathematical
operation.
● assignments arithmetic and logical operators
● Parentheses pair, block begin/end pair
● If…then… else… endif
● Do…. While
● Statement terminator “;”
● Bitwise operator
● Pointers operator

INTRO (cont’d)
Operands in general: A quantity to which an operator is applied
● Subroutine declarations
● Variable declarations
● Variables and constants used with operators in an expression

Operators and Operands for the ANSI C Language
● List of operators
( [ . , -> * + - ~ ! ++ -- * / % + - << >> < > <= >= != == & ^ | && ||
= *= /= %= += -= <<= >>= &= ^= |= : ? { ; CASE DEFAULT IF ELSE SWITCH
WHILE DO FOR GOTO CONTINUE BREAK RETURN and a function name in
function call
● Operands are those variables and constants which are used with
operators in expressions
Eg : a=&b;
a,b are operands and = & are operators

Length and Vocabulary
● Length : total usage of all operators and operands ie., total number of
tokens used in the program
Program Length (N)= N1
+ N2
● Vocabulary : is the number unique operands and operators used in the
program
Program Vocabulary (η)= η1
+ η2

Program Volume
● Program vocabulary and length depends on the programming style
● Different lengths of programs, corresponding to the same problem when
different languages are used
● We need to express the program length by taking the programming
language into consideration
Program volume (V) is the minimum number of bits needed to encode the
program

Program Volume (cont’d)
Program volume V = N log2
(η)
● To represent η different tokens we need log2
(η) bits
○ Example: to represent 8 operands we need 3 bits
● For a program of N length, we need N log2
(η) bits
Program volume represents the size of the program by approximately
compensating the effect of the programming language used

Potential Minimum Volume (V*)
● V* is the volume of the most concise program in which the problem can
be coded
● A program require at least 2 operators (η1
=2) and the required number of
operands is η2
=n
V* = (2+η2
) log2
(2+η2
)

Potential Minimum Volume (V*) (cont’d)
Program Level (L) = V*/V
● Program level measures the level of abstraction provided by
programming language
● Higher L, less effort it takes to develop a program using that language
○ Example: Assembly vs. C#

Effort and Time
● To obtain the needed effort , we divide the program volume (size) on the
program level (complexity)
Effort (E) = V / L
= V2
/ V* (as L = V*/V)
● The programmer’s time needed to finish the program
T = E / S
where S is the speed of mental discriminations, recommended value of S
is 18

Length Estimation
● Although the program length can be estimated easily using the previous
discussed equation N = N1
+N2
, this can be done before starting the
programming activities.
● Instead, we can calculate the length depending on the unique numbers of
operands and operators

Length Estimation (cont’d)
Halstead assumptions are based on:
● Program are unlikely to have several identical parts that are greater than
(η)
● Identical parts are usually made into procedures and functions
N = η1
log2
(η1
) + η2
log2
(η2
)
● Experimental evidence showed that the actual and the computed values
are very close
● Results may be inaccurate when dealing with small programs or
subsystems individually

Recap
● Unique operators : η1
● Unique Operands : η2
● Total Operators : N1
● Total Operands : N2
● Program Vocabulary: η=η1
+η2
● Program Length : N=N1
+N2
● Program Volume : Nlog2
η
● Effort : E=V/L
● Time : T=E/S
● Estimated Length : N=η1
log2
η1
+η2
log2
η2

Example
Main()
{
int a, b, c, avg;
scanf(“%d %d %d”, &a, &b, &c);
avg = (a +b +c )/3;
printf(“avg = %d”, avg);
}

Example (cont’d)
● The unique operators are: main, (), {}, int, scanf, &, “, “, “ ; ”, =, +, /, printf
● The unique operands are : a, b, c, &a, &b, &c, a +b +c, avg, 3, “%d %d %d”,
“avg = %d”
therefore η1 = 12, η2 = 11
N = 12 log2(12)+ 11log2(11) = 81
V = Nlog2(η) = 81log2(23) = 366

Halstead's software science - ananalytical technique

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