Get Machine epsilon in Microsoft Excel

Question

This seems like a question better directed at those with some programming experience rather than just general Excel users, hence my asking on here as opposed to Superuser.

Is there any way, preferably through a function, to return epsilon (i.e. the smallest non-zero number representable in Excel's calculations)? If it's not retrievable through a function, is there a quick way to calculate it through a compact function?

To be clear, I'm not looking for a VBA-based solution, I'd like an Excel formula/ spreadsheet based solution that does not require running macros.

My searches online have mostly turned up discussions on how to display the symbol Epsilon.

Thanks.

Answer 1

Excel always operates on IEEE doubles.

A non-VBA expression that will get you the smallest non-denormalized floating point number greater than 0 is

=2^-1022

Machine epsilon, on the other hand, is the smallest number that can be added to 1 and result in a number that is greater than 1. For double precision it is given by

=2^-52

Answer 2

Microsoft defines its floating point number precision limits for XL. The smallest floating point number is listed as 2.2250738585072E-308 in the Microsoft support article ID: 78113. When I enter this number in my spreadsheet it actually stores a floating point 0, but if I store 2.2250738585073E-308, (I added 1 to the least significant digit) I can see all the digits. I see you asked for a machine epsilon, but since you are using XL, what you will really see is the C/C++ floating point library epsilon. See the Microsoft Developer Network xlfRegister (Form 1) topic.

Answer 3

You may write a VBA subroutine like:

 Public Sub ComputeMachineEpsilon()
     Dim g, ex, eps As Double
     Dim i As Long
     g = 1
     i = 0
     Do
        i = i + 1
        g = g / 2
        ex = g * 0.98 + 1
        ex = ex - 1
        If ex > 0 Then eps = ex
     Loop While ex > 0

     MsgBox ("No. of Iterations " & i)
     MsgBox ("Machine Epsilon is " & eps)

    End Sub

But on my machine it gives 2,22E-16, and it's strange because I can write =2^-113 in a cell and get 9,62965E-35.

EDIT:

=1*(0,5-0,4-0,1)

I get: -2,78E-17