Testing Scientific Code

Tolerance Check

Compare Reals Safely

Scientific tests usually compare real values with a tolerance instead of exact equality.

Program

Play the program to tighten or loosen the tolerance around the same measured value.

tolerance
tolerance_check.f90
Replay: real traced execution (multi-file project)
program tolerance_check_demo
    implicit none
    real :: expected
    real :: measured
    real :: tolerance
    real :: error
    logical :: passed
    character(len=5) :: status

    expected = 10.0
    measured = 9.98
    tolerance = 0.05
    error = abs(measured - expected)
    passed = error <= tolerance
    if (passed) then
        status = 'pass'
    else
        status = 'fail'
    end if
    print '(A, 1X, F0.3)', trim(status), error
end program tolerance_check_demo

program tolerance_check_demo
    implicit none
    real :: expected
    real :: measured
    real :: tolerance
    real :: error
    logical :: passed
    character(len=5) :: status

    expected = 10.0
    measured = 9.98
    tolerance = 0.01
    error = abs(measured - expected)
    passed = error <= tolerance
    if (passed) then
        status = 'pass'
    else
        status = 'fail'
    end if
    print '(A, 1X, F0.3)', trim(status), error
end program tolerance_check_demo

program tolerance_check_demo
    implicit none
    real :: expected
    real :: measured
    real :: tolerance
    real :: error
    logical :: passed
    character(len=5) :: status

    expected = 10.0
    measured = 9.98
    tolerance = 0.10
    error = abs(measured - expected)
    passed = error <= tolerance
    if (passed) then
        status = 'pass'
    else
        status = 'fail'
    end if
    print '(A, 1X, F0.3)', trim(status), error
end program tolerance_check_demo

  1. expected ← 10.000

    10expected = 10.011measured = 9.98
    values this step10.000expected

  2. measured ← 9.980

    10expected = 10.011measured = 9.9812tolerance = 0.05
    values this step9.980measured

  3. tolerance ← 0.050

    11measured = 9.9812tolerance = 0.0513error = abs(measured - expected)
    values this step0.050tolerance

  4. error ← 0.020

    12tolerance = 0.0513error = abs(measured - expected)14passed = error <= tolerance
    values this step0.020error9.980measured10.000expected

  5. passed ← .true.

    13error = abs(measured - expected)14passed = error <= tolerance15if (passed) then
    values this step.true.passed0.020error0.050tolerance

  6. status ← pass

    15if (passed) then16    status = 'pass'17else
    values this steppassstatus

  7. print '(A, 1X, F0.3)', trim(status), error

    19    end if20    print '(A, 1X, F0.3)', trim(status), error21end program tolerance_check_demo
    outputpass 0.020
    values this steppassstatus0.020error

  1. expected ← 10.000

    10expected = 10.011measured = 9.98
    values this step10.000expected

  2. measured ← 9.980

    10expected = 10.011measured = 9.9812tolerance = 0.01
    values this step9.980measured

  3. tolerance ← 0.010

    11measured = 9.9812tolerance = 0.0113error = abs(measured - expected)
    values this step0.010tolerance

  4. error ← 0.020

    12tolerance = 0.0113error = abs(measured - expected)14passed = error <= tolerance
    values this step0.020error9.980measured10.000expected

  5. passed ← .false.

    13error = abs(measured - expected)14passed = error <= tolerance15if (passed) then
    values this step.false.passed0.020error0.010tolerance

  6. status ← fail

    17else18    status = 'fail'19end if
    values this stepfailstatus

  7. print '(A, 1X, F0.3)', trim(status), error

    19    end if20    print '(A, 1X, F0.3)', trim(status), error21end program tolerance_check_demo
    outputfail 0.020
    values this stepfailstatus0.020error

  1. expected ← 10.000

    10expected = 10.011measured = 9.98
    values this step10.000expected

  2. measured ← 9.980

    10expected = 10.011measured = 9.9812tolerance = 0.10
    values this step9.980measured

  3. tolerance ← 0.100

    11measured = 9.9812tolerance = 0.1013error = abs(measured - expected)
    values this step0.100tolerance

  4. error ← 0.020

    12tolerance = 0.1013error = abs(measured - expected)14passed = error <= tolerance
    values this step0.020error9.980measured10.000expected

  5. passed ← .true.

    13error = abs(measured - expected)14passed = error <= tolerance15if (passed) then
    values this step.true.passed0.020error0.100tolerance

  6. status ← pass

    15if (passed) then16    status = 'pass'17else
    values this steppassstatus

  7. print '(A, 1X, F0.3)', trim(status), error

    19    end if20    print '(A, 1X, F0.3)', trim(status), error21end program tolerance_check_demo
    outputpass 0.020
    values this steppassstatus0.020error
tolerance A tolerance defines how close a computed real value must be.
abs `abs(measured - expected)` turns signed difference into magnitude.
status label The trace carries a small pass/fail label instead of raising a runtime error.