Loop Order Shape - Modern Fortran Programming

Fortran arrays are column-major, so loop order is part of performance-aware design even when no elapsed-time measurement is run.

Program

Play the program to choose a traversal shape and see the same grid summarized with different visit patterns.

loop_order_shape.f90

program loop_order_shape_demo
    implicit none
    integer :: grid(2, 3)
    integer :: order_mode
    integer :: row
    integer :: col
    integer :: visits
    integer :: total
    character(len=12) :: order_name

    grid = reshape([1, 2, 3, 4, 5, 6], [2, 3])
    order_mode = 
    visits = 0
    total = 0
    if (order_mode == 1) then
        order_name = 'column'
        do col = 1, 3
            do row = 1, 2
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else if (order_mode == 2) then
        order_name = 'row'
        do row = 1, 2
            do col = 1, 3
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else
        order_name = 'sample'
        do col = 1, 3
            row = 1 + mod(col + 1, 2)
            visits = visits + 1
            total = total + grid(row, col)
        end do
    end if
    print '(A, 1X, I0, 1X, I0)', trim(order_name), visits, total
end program loop_order_shape_demo

program loop_order_shape_demo
    implicit none
    integer :: grid(2, 3)
    integer :: order_mode
    integer :: row
    integer :: col
    integer :: visits
    integer :: total
    character(len=12) :: order_name

    grid = reshape([1, 2, 3, 4, 5, 6], [2, 3])
    order_mode = 
    visits = 0
    total = 0
    if (order_mode == 1) then
        order_name = 'column'
        do col = 1, 3
            do row = 1, 2
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else if (order_mode == 2) then
        order_name = 'row'
        do row = 1, 2
            do col = 1, 3
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else
        order_name = 'sample'
        do col = 1, 3
            row = 1 + mod(col + 1, 2)
            visits = visits + 1
            total = total + grid(row, col)
        end do
    end if
    print '(A, 1X, I0, 1X, I0)', trim(order_name), visits, total
end program loop_order_shape_demo

program loop_order_shape_demo
    implicit none
    integer :: grid(2, 3)
    integer :: order_mode
    integer :: row
    integer :: col
    integer :: visits
    integer :: total
    character(len=12) :: order_name

    grid = reshape([1, 2, 3, 4, 5, 6], [2, 3])
    order_mode = 
    visits = 0
    total = 0
    if (order_mode == 1) then
        order_name = 'column'
        do col = 1, 3
            do row = 1, 2
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else if (order_mode == 2) then
        order_name = 'row'
        do row = 1, 2
            do col = 1, 3
                visits = visits + 1
                total = total + grid(row, col)
            end do
        end do
    else
        order_name = 'sample'
        do col = 1, 3
            row = 1 + mod(col + 1, 2)
            visits = visits + 1
            total = total + grid(row, col)
        end do
    end if
    print '(A, 1X, I0, 1X, I0)', trim(order_name), visits, total
end program loop_order_shape_demo

column-major Fortran stores the leftmost subscript contiguously.

loop order Changing traversal order changes the access pattern, not the mathematical total.

shape summary A small visit count and total can explain the loop shape without timing.