MATLAB: Machine eps related query

machine eps

1 + eps > 1
ans =
logical
1
% as expcted
1 + eps
ans =
1.000000000000000
% unexpected, and indeed
1+2.5*eps
ans =
1.000000000000000
any help appreciated

Best Answer

It happens because of finite precision of double() precision datatype: https://en.wikipedia.org/wiki/Double-precision_floating-point_format. Also, because of the fact that MATLAB only prints 16 digits by default, the remaining digits after conversion are not shown (double datatype cannot store more than 16 digits accurately). Try the following
>> fprintf('%0.20f\n', 1+eps)
1.00000000000000022204
>> fprintf('%0.20f\n', 1+2.5*eps)
1.00000000000000044409