Nested IF-THEN-ELSE-END IF

The THEN part and the ELSE part, if any, can contain one or more IF-THEN-ELSE-END IF statement in one of the three forms. That is, when you feel it is necessary, you can use as many IF-THEN-ELSE-END IF statements in the THEN part and the ELSE part as you want. However, please note that any such IF-THEN-ELSE-END IF must be fully contained in the THEN part or the ELSE part. If you follow the box trick, this requirement is automatically satisfied. The following is an example:

IF (logical-expression) THEN
   statements
   IF (logical-expression) THEN
      statements
   ELSE
      statements
   END IF
   statements
ELSE
   statements
   IF (logical-expression) THEN
      statements
   END IF
   statements
END IF

Examples

• Suppose we need a program segment to read a number x and display its sign. More precisely, if x is positive, a + is displayed; if x is negative, a - is displayed; otherwise, a 0 is displayed. With an IF-THEN-ELSE-END IF statement, we have a two-way decision (i.e., true or false). What we need is a tree-way decision and some trick is required. In this case, the box trick can be very helpful.

  Let us start testing if x is positive. What we get is the following:

  x > 0	display +
  	one down (i.e., +) two to go (i.e., - and 0)

  In the lower part, no decision can been reached. What we want to know is finding out is x is zero or negative (x cannot be positive here since it has been ruled out in the upper part). To determine whether a - or a 0 should be displayed, one more decision is required:

  x < 0	display -
  	display 0)

  Since this is the work for the lower rectangle, let us put it there yielding the following:

  x > 0	display +
  	x < 0	display -
  		display 0

  Converting to a IF-THEN-ELSE-END IF construct is easy since the above box is almost identical to that. So, here is our answer:

  IF (x > 0) THEN
     WRITE(*,*)  '+'
  ELSE
     IF (x < 0) THEN
        WRITE(*,*)  '-'
     ELSE
        WRITE(*,*)  '0'
     END IF
  END IF
  

• Given a x, we want to display the value of -x if x < 0, the value of x*x if x is in the range of 0 and 1 inclusive, and the value of 2*x if x is greater than 1.

  Obviously, this problem cannot be solved with a two-way IF and the box trick becomes useful. Let us start with x<0.

  x < 0	display -x
  	here we have x >= 0

  For the x >= 0 part, x may be in the range of 0 and 1; if not, x must be greater than 1 since x cannot be less than 0. Therefore, we have the following box for the case of x >= 0:

  x <= 1	x is in the range of 0 and 1. display x*x
  	here we have x > 1. display 2*x

  Inserting this box into the previous one yields the following final result:

  x < 0	display -x
  	x <= 1	display x*x
  		display 2*x

  Converting to using IF, we have the following:

  IF (x < 0) THEN
     WRITE(*,*)  -x
  ELSE
     IF (x <= 1) THEN
        WRITE(*,*)  x*x
     ELSE
        WRITE(*,*)  2*x
     END IF
  END IF
  

• Given three numbers a, b and c, we want to find out the smallest one.

  There are many solutions to this problem; but, we shall use the box trick again. Let us pick two numbers, say a and b. Thus, we get the following:

  a < b	a has the potential to be the smallest
  	since b <= a, b has the potential to be the smallest

  Now we know a possible smallest number. To find the real smallest one, this "possible" number must be compared against c. If the possible one is a (the upper part), we need to do the following:

  a < c	a is the smallest
  	since c <= a and b <= a, c is the smallest

  Let us turn to the lower part, where b has the potential to be the smallest. Comparing with c yields:

  b < c	b is the smallest
  	since c <= b and b <= a, c is the smallest

  Inserting the above two boxes into the first one yields the following complete solution:

  a < b	a < c	the smallest is a
  		the smallest is c
  	b < c	the smallest is b
  		the smallest is c

  Converting to the IF version, we have

  IF (a < b) THEN
     IF (a < c) THEN
        Result = a
     ELSE
        Result = c
     END IF
  ELSE
     IF (b < c) THEN
        Result = b
     ELSE
        Result = c
     END IF
  END IF
  WRITE(*,*)  'The smallest is ', Result
  

  The above code segment uses variable Result to hold the smallest value.