Exercise 1. Running a Fortran program

Try to run the following program. Make sure to use file extension (拡張子) .f90. If you use .f, you will have to enter 6 spaces at the beginning of each line.

print *, "Hello"
end

For example, save it in a file hello.f90, and then compile and run it as

$ gfortran hello.f90
$ ./a.exe                   # use ./a.out on macOS or Linux
Hello

Text following $ are commands to be typed on the terminal command line (端末) (cygwin on Windows). Lines without $ show the output of the commands. Replace ./a.exe with ./a.out if you are on macOS or Linux.

Exercise 2. Fun with numbers

1. What does the following program print? Why?

   i = 2.5
   if (i == 2.5) then
       print *, "Equal"
   else
       print *, "Math is wrong!"
   endif
   end

2. What about this one?

   x = 1
   y = x / 2
   z = 1 / 2
   
   print *, y
   print *, z
   end

3. And this one?

   x = 2
   S = x**2
   x = 3
   
   print *, S
   end

Explanation…

Exercise 3.

Solving the quadratic equation

Write a program that finds the solutions x of the quadratic equation ax^2 + bx + c = 0 given a, b and c from the user. Print the solutions, if any, from smaller to larger.

Example. Suppose that the user enters 1 -3 2, the program should output something like:

x1 = 1
x2 = 2

Exercise 4.

Write a program that reads 3 numbers a, b and c and prints them out from the smallest to the largest.

Example: If the user enters 3 1 2, the program should print 1 2 3.

Exercise 5.

Write a program that prints the factorial (階乗) n! = 1 \cdot 2 \cdot \cdots \cdot n where n is a number entered by the user.

Example. If the user enters 4, the program outputs 24.

Exercise 6.

Write a program that prints the Fibonacci number F_n. The Fibonacci numbers are defined by the iterative formula \begin{aligned} F_0 &= 0\\ F_1 &= 1\\ F_k &= F_{k-1} + F_{k-2}, \qquad k = 2, 3, \ldots \end{aligned} where n is he number entered by the user.

Example. If the user enters 6, the program should print 8.

Exercise 7.

1. Write a program that reads a number n and tests whether it is a prime number (素数).

   Example. For n = 5, print yes, for n = 6, print no.

   Hint. mod(k, m) returns the remainder (剰余) of the division (除法) k / m. For example mod(5, 3) returns 2.

   Hint. Recall that you can use the exit command to exit a do loop early:

   do i = 1, 100 
       print *, i
       if (i > 20) then
           exit
       end if
   end do
   print *, "stopped looping"
   end

2. Modify the program to print all the prime numbers between 2 and n.

   Example. If the user enters 10, the program should print

   2
   3
   5
   7

3. Modify the program to print the first n prime numbers.

   Hint. You might want to use the do while loop like:

   k = 2   ! lowest possible prime
   do while (n > 0) 
       ... ! check that k is prime
   
       if (k is prime) then
           print *, k
           n = n - 1
       end if
   
       k = k + 1   ! consider next number
   end do

   Example. If the user enters 5, the program should print

   2
   3
   5
   7
   11

4. Find all the prime numbers less than 1000 using the Sieve of Eratosthenes (エラトステネスの篩).