FUNCTIONAL TESTING CONCEPTS OF HOWDEN

9.1 FUNCTIONAL TESTING CONCEPTS OF HOWDEN

William E. Howden developed the idea of functional testing of programs while vis- iting the International Mathematics and Statistics Libraries (IMSL) in Houston in 1977–1978. IMSL is presently known as Visual Numerics (http://www.vni.com/). The IMSL libraries are a comprehensive set of mathematical and statistical func- tions that programmers can embed into their software applications. IMSL uses proven technology that has been thoroughly tested, well documented, and continu- ously maintained. Howden applied the idea of functional testing to programs from edition 5 of the IMSL package. The errors he discovered can be considered to be of some subtlety to have survived to edition 5 status [1].

A function in mathematics is defined to be a set of ordered pairs (X i ,Y i ), where X i is a vector of input values and Y i is a vector of output values. In functional testing, a program P is viewed as a function that transforms the input vector X i into an output vector Y i such that Y i = P (X i ) .

Examples

1. Let Y

1 = X 1 . Here, P is a square-root computing function which calcu- lates the squareroot Y 1 of nonnegative integer X 1 . The result is assigned

to Y 1 .

2. Let Y 2 = C_compiler(X 2 ). The program P is viewed as a C_compiler function that produces object code from C program X 2 . The object code is held in Y 2 .

Software Testing and Quality Assurance: Theory and Practice , Edited by Kshirasagar Naik and Priyadarshi Tripathy Copyright © 2008 John Wiley & Sons, Inc.

9.1 FUNCTIONAL TESTING CONCEPTS OF HOWDEN

3. Let Y 3 = TelephoneSwitch(X 3 ). A telephone switch program P produces

a variety of tones and voice signals represented by the vector

Y 3 = {idle, dial, ring, fast busy, slow busy tone, voice} by processing input data represented by the vector

X 3 = {off hook, on hook, phone number, voice}.

4. Let Y 4 = sort(X 4 ). The program P in this example is an implementation of

a sorting algorithm which produces a sorted array Y 4 from the input vector

X 4 = {A, N}, where A is the array to be sorted and N is the number of elements in A.

The above four examples suggest that sometimes it is easy to view a program as a function in the mathematical sense and sometimes it is more difficult. It is easier to view a program as a function when the input values are algorithmically, or mathematically, transformed into output values, such as in the first and the

fourth examples above. In the fourth example, Y 4 is a certain permutation of the input array A. It is more difficult to view a program as a function when the input values are not directly transformed into the output values. For instance, in the third example above, an off-hook input is not mathematically transformed into a dial tone output. In functional testing we are not concerned with the details of the mechanism by which an input vector is transformed into an output vector. Instead,

a program is treated as a function in the general sense. Three key elements of a function are its input, output, and expected trans- formation of input to output. Ignoring the details of the actual transformation of input to output, we analyze the domains of the input and the output variables of programs to generate test data. The four key concepts in functional testing [2] are as follows:

• Precisely identify the domain of each input and each output variable. • Select values from the data domain of each variable having important