Counted Work - Modern Fortran Programming

Performance-aware code starts by making the amount of loop work explicit, before any timing or tuning claims.
Program

Play the program to choose how many values are included and watch the operation count stay visible.
                            limit
                            limit = 3 (default)limit = 2limit = 5
                        

                            counted_work.f90
                        
Replay: real traced execution (multi-file project)

                            program counted_work_demo
    implicit none
    integer :: values(5)
    integer :: limit
    integer :: i
    integer :: total
    integer :: operations

    values = [2, 4, 6, 8, 10]
    limit = 3
    total = 0
    operations = 0
    do i = 1, limit
        total = total + values(i)
        operations = operations + 1
    end do
    print '(I0, 1X, I0)', total, operations
end program counted_work_demo
program counted_work_demo
    implicit none
    integer :: values(5)
    integer :: limit
    integer :: i
    integer :: total
    integer :: operations

    values = [2, 4, 6, 8, 10]
    limit = 2
    total = 0
    operations = 0
    do i = 1, limit
        total = total + values(i)
        operations = operations + 1
    end do
    print '(I0, 1X, I0)', total, operations
end program counted_work_demo
program counted_work_demo
    implicit none
    integer :: values(5)
    integer :: limit
    integer :: i
    integer :: total
    integer :: operations

    values = [2, 4, 6, 8, 10]
    limit = 5
    total = 0
    operations = 0
    do i = 1, limit
        total = total + values(i)
        operations = operations + 1
    end do
    print '(I0, 1X, I0)', total, operations
end program counted_work_demo

                        
1values ← [2, 4, 6, 8, 10]⋯9values = [2, 4, 6, 8, 10]10limit = 3⋯values this step[2, 4, 6, 8, 10]values
2limit ← 3⋯9values = [2, 4, 6, 8, 10]10limit = 311total = 0⋯values this step3limit
3total ← 0⋯10limit = 311total = 012operations = 0⋯values this step0total
4operations ← 0⋯11total = 012operations = 013do i = 1, limit⋯values this step0operations
5total ← 2⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step0 → 2total1i2values(i)
6operations ← 1⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step0 → 1operations
7total ← 6⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step2 → 6total2i4values(i)
8operations ← 2⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step1 → 2operations
9total ← 12⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step6 → 12total3i6values(i)
10operations ← 3⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step2 → 3operations
11print '(I0, 1X, I0)', total, operations⋯16    end do17    print '(I0, 1X, I0)', total, operations18end program counted_work_demooutput12 3values this step12total3operations
1values ← [2, 4, 6, 8, 10]⋯9values = [2, 4, 6, 8, 10]10limit = 2⋯values this step[2, 4, 6, 8, 10]values
2limit ← 2⋯9values = [2, 4, 6, 8, 10]10limit = 211total = 0⋯values this step2limit
3total ← 0⋯10limit = 211total = 012operations = 0⋯values this step0total
4operations ← 0⋯11total = 012operations = 013do i = 1, limit⋯values this step0operations
5total ← 2⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step0 → 2total1i2values(i)
6operations ← 1⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step0 → 1operations
7total ← 6⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step2 → 6total2i4values(i)
8operations ← 2⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step1 → 2operations
9print '(I0, 1X, I0)', total, operations⋯16    end do17    print '(I0, 1X, I0)', total, operations18end program counted_work_demooutput6 2values this step6total2operations
1values ← [2, 4, 6, 8, 10]⋯9values = [2, 4, 6, 8, 10]10limit = 5⋯values this step[2, 4, 6, 8, 10]values
2limit ← 5⋯9values = [2, 4, 6, 8, 10]10limit = 511total = 0⋯values this step5limit
3total ← 0⋯10limit = 511total = 012operations = 0⋯values this step0total
4operations ← 0⋯11total = 012operations = 013do i = 1, limit⋯values this step0operations
5total ← 2⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step0 → 2total1i2values(i)
6operations ← 1⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step0 → 1operations
7total ← 6⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step2 → 6total2i4values(i)
8operations ← 2⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step1 → 2operations
9total ← 12⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step6 → 12total3i6values(i)
10operations ← 3⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step2 → 3operations
11total ← 20⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step12 → 20total4i8values(i)
12operations ← 4⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step3 → 4operations
13total ← 30⋯13do i = 1, limit14    total = total + values(i)15    operations = operations + 1⋯values this step20 → 30total5i10values(i)
14operations ← 5⋯14    total = total + values(i)15    operations = operations + 116end do⋯values this step4 → 5operations
15print '(I0, 1X, I0)', total, operations⋯16    end do17    print '(I0, 1X, I0)', total, operations18end program counted_work_demooutput30 5values this step30total5operations
work bound `limit` makes the loop bound visible and easy to reason about.
operation count `operations` records how many iterations actually ran.
work shape Counting work shows the performance shape without measuring elapsed time.