Computing Factorial

Problem Statement

The factorial of a non-negative integer n, written as n!, is defined as follows:

Write a program that reads in an integer and computes its factorial. This program should detect if the input is negative and display an error message.

Solution

! ----------------------------------------------------------
! Given a non-negative integer N, this program computes
! the factorial of N.  The factorial of N, N!, is defined as
!         N! = 1 x 2 x 3 x .... x (N-1) x N
! and 0! = 1.
! ----------------------------------------------------------

PROGRAM  Factorial
   IMPLICIT  NONE

   INTEGER :: N, i, Answer

   WRITE(*,*)  'This program computes the factorial of'
   WRITE(*,*)  'a non-negative integer'
   WRITE(*,*)
   WRITE(*,*)  'What is N in N! --> '
   READ(*,*)   N
   WRITE(*,*)

   IF (N < 0) THEN                 ! input error if N < 0
      WRITE(*,*)  'ERROR: N must be non-negative'
      WRITE(*,*)  'Your input N = ', N
   ELSE IF (N == 0) THEN           ! 0! = 1
      WRITE(*,*)  '0! = 1'
   ELSE                            ! N > 0 here
      Answer = 1                   ! initially N! = 1
      DO i = 1, N                  ! for each i = 1, 2, ..., N
         Answer = Answer * i       ! multiply i to Answer
      END DO
      WRITE(*,*)  N, '! = ', Answer
   END IF

END PROGRAM  Factorial

Program Input and Output

• If the input is -5, a negative number, the program generates the following output indicating the input is wrong.

  This program computes the factorial of
  a non-negative integer
  
  What is N in N! -->
  -5
  
  ERROR: N must be non-negative
  Your input N = -5
  

• If the input is a zero, the output is 0! = 1.

  This program computes the factorial of
  a non-negative integer
  
  What is N in N! -->
  0
  
  0! = 1
  

• If the input is 5, the factorial of 5 is 5!=1*2*3*4*5=120.

  This program computes the factorial of
  a non-negative integer
  
  What is N in N! -->
  5
  
  5! = 120
  

• If the input is 13, the factorial of 15 is 13! = 1*2*3*...*13=1932053504

  This program computes the factorial of
  a non-negative integer
  
  What is N in N! -->
  13
  
  13! = 1932053504
  

Discussion

It is worthwhile to note that most CPU's do not report integer overflow. As a result, on a typical computer today, the maximum factorial is around 13!. If you try this program on a PC, you should get 13! = 1932053504 and 14! = 1278945280. But, 13! > 14! is obviously incorrect. Then, we have 15! = 2004310016, 16! = 2004189184, and 17! = -288522240. These results are obviously wrong. This shows that a typical PC can only handle up to 13!