Repetitive Instructions and DO Loops

When doing numerical calculations it is often necessary to do the same calculation many times. An example might be computing the solar elevation angle for each hour of the day.

Fortran provides a standardized set of instructions - called a "DO loop" - for performing these repetitive calculations. An example of a repeated calculation using a DO loop could be a simple program to compute the number of elapsed seconds at each hour of the day, beginning at midnight:

      PROGRAM MAIN
      INTEGER I, SECOND
      DO 10 I = 0, 24
      SECOND = 3600 * I
      PRINT *, 'HOUR = ', I, '  SECONDS =', SECOND
10    CONTINUE
      STOP
      END

The statement beginning with DO controls the instructions that are to be repeated and the number of times they are repeated. We need to look closely at each part of the DO statement, from left to right:

      DO 10 I = 0, 24

• The word DO means that this line is the first of the statements that will be repeated.

• The number 10 is the statement number of the last instruction to be repeated. Essentially, this tells the system "we will repeat all statements from here up to and including the statement that is numbered 10." This final statement is sometimes referred to as the terminal statement of the loop.

• The letter I is called the index of the DO loop. By default, the index increases by 1 each time the loop is repeated.

• The number following the equals sign is the initial value of the DO loop index. This is the value that is assigned to the index the first time the loop is executed.

• The number following the comma is the limit of the DO loop. Once the index exceeds the limit, the loop is no longer repeated.

A verbal description what happens in a DO loop might be as follows:

Set the index to its initial value. Then, repeat all the instructions from the DO line down to the statement with the given statement number. After these instructions are completed, add 1 to the index. Keep doing this until the index exceeds the limit.

Some details:

• The index does not have to be called I. It is a variable that is treated the same as any other variable in Fortran. Your DO loop indices should always be integer variables. Some systems allow you to use real variables for DO look indices but this is poor programming and can produce unreliable results.

• The amount that the index is increased with each repetition of the loop is called the increment or stride of the loop. The default increment is 1, as in the example above, but you can specify the increment to be some other value. You do this by adding a comma and the desired increment after the limit. That is, the DO statement above is equivalent to:

      DO 10 I = 0, 24, 1

For example, if we wanted to do some calculations every three hours, we would construct a DO statement like:

DO 10 I = 0, 24, 3

This would perform the calculations in the loop for values of I equal to 0, 3, 6 ... up to and including 24.

• The CONTINUE statement is essentially a "do-nothing" statement. It is recommended that the terminal statement of your DO loop always be a CONTINUE statement.

• Recall from our very first lesson that all statements had to begin from the seventh (or later) position of a line. The first five spaces are reserved for the statement number of a numbered statement such as the terminal statement of our DO loop. The statement number must appear completely within these first five spaces; that is, the number cannot spill over into the sixth or following spaces. (It follows that the largest possible number for a statement number is 99999.)

• Statement numbers must be unique; that is, a program cannot include two statements with the same number.

Update. Fortran 90 and later now allows DO loops to be terminated with the END DO statement instead of using a numbered statement. Using this approach the loop in the short program at the top of this page would be written as follows:

      DO I = 0, 24
      SECOND = 3600 * I
      PRINT *, 'HOUR = ', I, '  SECONDS =', SECOND
      END DO

Notice that since there is no numbered termination statement, the DO at the start of the loop is not followed by a statement number.

Assignment: Construct a DO loop around the solar elevation computations in the previous exercise, so that you compute the solar elevation angle at each hour of the day.