Section 1.16: Factorial Recursion

Adapted from: “Guide to Fortran 2008 Programming” by Walter S. Brainerd (Springer 2015)

Program to calculate factorials using recursion in Fortran.¶

section_1_16_factorial_recursion.f90

module factorial_module

    implicit none
    public :: factorial

contains

    recursive function factorial(n) result (factorial_result)

        integer, intent(in) :: n
        integer :: factorial_result

        if (n <= 0) then
            factorial_result = 1
        else
            factorial_result = n * factorial(n - 1)
        end if

    end function factorial

end module factorial_module

program test_factorial
    
    use factorial_module
    implicit none

    integer :: n

    read *, n ! Will be piped in from command line
    print *
    write (unit = *, fmt = "(i10, a, i10)") n, "! = ", factorial(n)

end program test_factorial

The following explanation is given by “Code Copilot” within ChatGPT 4.

The provided Fortran program consists of two main components: a module named factorial_module and a program named test_factorial. Here is an explanation of each part and their interactions:

Module: factorial_module¶

Purpose:¶

The module defines and makes publicly available a recursive function factorial that computes the factorial of a given integer n. The factorial of a number is the product of all positive integers less than or equal to that number. It’s defined as:

$n! = n \times (n-1) \times ... \times 2 \times 1$
$0! = 1$ (by definition)

Structure:¶

Function Declaration: The function factorial is declared as recursive, allowing it to call itself within its definition.
Parameters:
Input: n (integer) - the number for which the factorial is to be computed.
Output: factorial_result (integer) - the computed factorial value.
Logic:
If n is less than or equal to zero, the factorial is defined as 1. This also correctly handles the base case for the recursion.
Otherwise, the function computes the factorial by calling itself with n - 1 and multiplying the result by n.

Program: test_factorial¶

Purpose:¶

This program uses the factorial function defined in the factorial_module to compute the factorial of an integer read from the command line.

Structure:¶

Module Usage: It includes the factorial_module using the use statement to access the factorial function.
Input Handling: Reads an integer n from the standard input. In the given context, this input is expected to be piped in from the command line.
Output: Prints the result of the factorial computation in a formatted string showing n and n!.

Execution Flow:¶

Compilation and Linking:

The factorial_module is compiled first to ensure that the definition of the factorial function is available.
The test_factorial program is compiled and linked with the factorial_module.

Running:

The program expects an integer input from the command line.
It computes the factorial of the input integer using the factorial function.
It outputs the result in the format “n! = result”.

Conclusion:¶

This Fortran setup efficiently demonstrates modular programming by separating the mathematical logic (factorial computation) into a module for reuse. The recursive function is a straightforward and classic implementation for calculating factorials, suitable for small to moderately large values of n due to potential stack overflow issues with very large recursion depths. The program is well-structured for educational purposes and basic computational tasks involving factorials.

Program Compilation and Execution¶

The above program is compiled and run using Fortran Package Manager (fpm):

import os
root_dir = os.getcwd()

code_dir = root_dir + "/" + "Fortran_Code/Section_1_16_Factorial_Recursion"

os.chdir(code_dir)

build_status = os.system("fpm build 2>/dev/null")

Calculate:¶

\Large 3!

(1)

exec_status = os.system("echo 3 | fpm run 2>/dev/null")


         3! =          6

Calculate:¶

\Large 6!

(2)

exec_status = os.system("echo 6 | fpm run 2>/dev/null")


         6! =        720

Calculate:¶

\Large 15!

(3)

exec_status = os.system("echo 15 | fpm run 2>/dev/null")


        15! = 2004310016