REPETITION - `REVERSE' FOR LOOPS

2. EXAMPLE PROBLEM FACTORIAL

2.1 Requirements

Design and implement an Ada program that returns the value of N! (N Factorial) given a specific value for N. Note:

n! = n x (n-1) x (n-2) ... 3 x 2 x 1

For example:

10!= 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

Note also that N must be a positive integer and assume that the maximum permissible value for N is 12.

2.2 Design

A top down analysis of the problem is given below.

The operations identified above are trivial enough to be implemented as a single procedure incorporating a single fixed count loop.

1. FACTORIAL (top level procedure). Input number of terms and calculate product.

   NAME	DESCRIPTION	TYPE	RANGE
   NUMBER_OF_TERMS	Global input variable	POSITIVE	1..12
   PRODUCT	Global variable	POSITIVE	Default

So as to adhere to the generally accepted mathematical definition of factorial(N) we will process the loop in reverse. An appropriate Nassi-Shneiderman chart is given to the right.

2.3. Implementation

The encoding of the above design is as follows:

-- FACTORIAL
-- 15 September 1997
-- Frans Coenen
-- Dept Computer Science, University of Liverpool

with TEXT_IO;
use TEXT_IO;

procedure FACTORIAL is
    package INTEGER_INOUT is new INTEGER_IO(INTEGER);
    use INTEGER_INOUT;
    NUMBER_OF_TERMS : POSITIVE range 1..12;
    PRODUCT         : POSITIVE;
begin
-- Input N_VALUE
    PUT_LINE("Input number of terms (integer 1..12): ");
    GET(NUMBER_OF_TERMS);
    PRODUCT := NUMBER_OF_TERMS;
-- For loop
    for COUNTER in reverse 1..NUMBER_OF_TERMS-1  loop
        PRODUCT := PRODUCT*COUNTER;
    end loop;
-- Output result
    PUT(NUMBER_OF_TERMS);
    PUT("! = ");
    PUT(PRODUCT);
    NEW_LINE;
end FACTORIAL;

2.4. Testing

2.4.1 Black box testing

BVA, Limit and Arithmetic Testing. A suitable set of test cases is given in the table below.

2.4.2 White box testing

Loop testing. Test repetitions in fixed count loop using set of test cases of the form given below. Note that, except for the third test case ("two passes through loop") all these have been run as either BVA, limit or arithmetic test cases (see above).