Question

Fortran has a three-way IF statement of the form IF(expression) \(n 1, n 2, n 3\) where expression is a numeric expression and n1, n2, n3 are statement numbers. Control transfers to statement \(\mathrm{n} 1\) if expression is negative, to statement \(n 2\) if expression equals 0 , and to \(n 3\) if expression is positive. What is the output of the following section of Fortran code if \(/\) has the value 3 and \(M A X\) has the value 4 ? IF (I - MAX) \(10,20,30\) 10 WRITE \((*, *) \quad 2 * I\) 20 WRITE \((*, *)\) I*I 30 WRITE \((*, *) \quad I * \star \mathrm{MAX}\)

Short answer

The output is 6.

Step-by-step solution

Evaluate the Expression

We need to evaluate the expression inside the IF statement: \( I - MAX \). Given \( I = 3 \) and \( MAX = 4 \), calculate:\[ I - MAX = 3 - 4 = -1 \] Since \( I - MAX \) is negative, control will transfer to statement \( n_1 \), which is statement 10.

Execute Statement 10

Since control transfers to statement 10, we execute the code associated with it:\[\text{WRITE (*, *) } 2 * I \]Here, \( 2 * I = 2 \times 3 = 6 \), so the output will be 6.

Key concepts

Numeric Expressions

In programming, especially within Fortran, a **numeric expression** refers to a combination of numbers and operators that yield a numerical result. In this context, it involves operations such as addition, subtraction, multiplication, and division.
For example, in the expression \( I - MAX \), both \( I \) and \( MAX \) are numeric variables or constants, and the subtraction operator \(-\) combines them to yield a new numeric value.
Numeric expressions serve as the logical foundation for many programming functions, providing the data upon which decisions are made and actions are carried out. Make sure to always pay attention to the order of operations, which follows standard mathematical principles. Even though Fortran is known for its numeric computation strengths, it is your responsibility to carefully craft these expressions based on logic specific to your task.

Control Flow

**Control flow** is a fundamental concept that governs the execution order of statements in a program. In Fortran, the control flow is especially significant when using conditional statements like the three-way IF statement. This type of IF statement diverts the program's execution to different parts of code based on the outcome of a numeric expression.
When you write an IF statement such as \( \text{IF}( \text{expression})\ n1, n2, n3\), the evaluated result controls which subsequent statement number your code will jump to.

• If the expression is negative, control will go to the first statement, \( n1 \).
• If it's zero, the program moves to the second statement, \( n2 \).
• If it's positive, then the execution shifts to the third statement, \( n3 \).

Using this mechanism, you can direct how the program responds to different computed values, enabling basic decision-making processes within your code.

Expression Evaluation

**Expression evaluation** refers to the process of interpreting a numeric expression to determine its value. This step occurs before any control flow redirection and informs the decision about which execution path to take.
For example, in the exercise, the expression \( I - MAX \) must be evaluated to decide which statement will be executed. Subtraction yields \( -1 \) when \( I = 3 \) and \( MAX = 4 \). The result, \( -1 \), is negative, directing the flow to the first statement number, \( n1 \), which corresponds to a specific block of code that will execute next.
Understanding how to evaluate expressions is crucial in Fortran, as it directly impacts the code's control flow. During evaluation, ensure you handle all variables correctly and account for their signs, which can critically influence the chosen path.

Fortran Programming

**Fortran programming** has a storied history, being one of the oldest high-level programming languages focused primarily on numeric and scientific computation. Its syntax and features, like the three-way IF statement, make it particularly effective for operations that require precise calculations and data manipulation.
The three-way IF statement from the exercise showcases a unique feature of Fortran that allows decision-making based on numeric conditions, showing its capability to handle complex computation routes efficiently.
While modern programming languages have evolved with new paradigms, Fortran remains relevant due to its efficiency and reliability in engineering and scientific applications where computation speed and numerical accuracy are paramount. As you get acquainted with Fortran, pay attention to its approach to variables, control structures, and distinctly designed functions, which might differ significantly from newer languages. Continuing to learn and apply Fortran will enhance your capability to tackle challenging numeric problems effectively.