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C Library Functions  - greatest_common_divisor (3)

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NAME

greatest_common_divisor(3f) - [M_factor] calculate greatest common divisor of two integers or vector m(:), matrix m(:,:) or cuboid m(:,:,:) (LICENSE:MIT)

CONTENTS

Synopsis
Description
Examples
Author
License

SYNOPSIS

The function is generic and may take either two integers or an integer vector, matrix, or cuboid.

    integer function greatest_common_divisor(i,j)
    integer,intent(in)::  i,j
      or
    integer function greatest_common_divisor(m)
    integer,intent(in)::  m(:)
     or
    integer,intent(in)::  m(:,:)
     or
    integer,intent(in)::  m(:,:,:)

DESCRIPTION

The method used is the Euler algorithm; that for two integers ...

1.	Subtract the 2nd number (N) as many times as possible from the 1st one (M) and save remainder using FORTRAN function MOD.
2.	Test if remainder is equal to zero, if so GCD = N. If not replace M with N and N with remainder and proceed with step 1.
3.	Repeat both steps until remainder becomes zero.

EXAMPLES

Sample program:

   program demo_greatest_common_divisor
   use M_factor, only : gcd=>greatest_common_divisor
   implicit none
   integer, allocatable :: matrix(:,:)
      ! SCALAR:
         call writeit(26,130,26)
         call writeit(91,390,13)
         call writeit(-91,390,13)
         call writeit(91,-390,13)
         call writeit(-41,-43,1)
         call writeit(-20,-10,10)
         call writeit(20,10,10)
      ! VECTOR:
         call writeit_v([26,130,91,390],13)
         call writeit_v([5,7,11,13,17,19,23,29,31,37,41,43,47],1)
         call writeit_v([-20,-10,0],10)
         call writeit_v([20,10,0],10)
         call writeit_v([26,130],26)
         call writeit_v([91,390],13)
         call writeit_v([-91,390],13)
         call writeit_v([91,-390],13)
         call writeit_v([-41,-43],1)
         call writeit_v([-20,-10],10)
         call writeit_v([20,10],10)
      ! MATRIX:
         matrix=reshape([ 11,22,33,44,55,66],[2,3])
         call write_matrix(matrix,11)
         matrix=reshape([5,7,11,13,17,19,23,29,31,37,41,43,47],[13,1])
         call write_matrix(matrix,1)
         matrix=reshape([40,80,120,160],[2,2])
         call write_matrix(matrix,40)

      contains

      subroutine writeit(ii,jj,answer)
      integer,intent(in) :: ii,jj
      integer,intent(in) :: answer
         write(*,’("gcd([",i0,",",i0,"]) produces ",i0," which is ",l1)’) &
              & ii,jj,gcd(ii,jj),gcd(ii,jj).eq.answer
      end subroutine writeit

      subroutine writeit_v(vector,answer)
      integer,intent(in) :: vector(:)
      integer,intent(in) :: answer
         write(*,’("gcd([",*(i0:,","))’,advance=’no’)vector
         write(*,’("]) produces ",i0," which is ",l1)’) &
              & gcd(vector),gcd(vector).eq.answer
      end subroutine writeit_v

      subroutine write_matrix(matrix,answer)
      integer,intent(in) :: matrix(:,:)
      integer,intent(in) :: answer
         write(*,*)’MATRIX SHAPE:’,size(matrix,dim=1),size(matrix,dim=2)
         write(*,’("gcd([",*(i0:,","))’,advance=’no’)matrix
         write(*,’("]) produces ",i0," which is ",l1)’) &
              & gcd(matrix),gcd(matrix).eq.answer
      end subroutine write_matrix

   end program demo_greatest_common_divisor

Expected Output:

   >  SCALAR:
   > gcd([26,130]) produces 26 which is T
   > gcd([91,390]) produces 13 which is T
   > gcd([-91,390]) produces 13 which is T
   > gcd([91,-390]) produces 13 which is T
   > gcd([-41,-43]) produces 1 which is T
   > gcd([-20,-10]) produces 10 which is T
   > gcd([20,10]) produces 10 which is T
   >  VECTOR:
   > gcd([26,130,91,390]) produces 13 which is T
   > gcd([5,7,11,13,17,19,23,29,31,37,41,43,47]) produces 1 which is T
   > gcd([-20,-10,0]) produces 10 which is T
   > gcd([20,10,0]) produces 10 which is T
   > gcd([26,130]) produces 26 which is T
   > gcd([91,390]) produces 13 which is T
   > gcd([-91,390]) produces 13 which is T
   > gcd([91,-390]) produces 13 which is T
   > gcd([-41,-43]) produces 1 which is T
   > gcd([-20,-10]) produces 10 which is T
   > gcd([20,10]) produces 10 which is T
   >  MATRIX:
   >  MATRIX SHAPE:           2           3
   > gcd([11,22,33,44,55,66]) produces 11 which is T
   >  MATRIX SHAPE:          13           1
   > gcd([5,7,11,13,17,19,23,29,31,37,41,43,47]) produces 1 which is T
   >  MATRIX SHAPE:           2           2
   > gcd([40,80,120,160]) produces 40 which is T

AUTHOR

John S. Urban, 2015

LICENSE

MIT License

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Nemo Release 3.1

greatest_common_divisor (3)

February 23, 2025

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