Question

The reason I’m asking this is because there is a validation in OpenERP that it’s driving me crazy:

>>> round(1.2 / 0.01) * 0.01
1.2
>>> round(12.2 / 0.01) * 0.01
12.200000000000001
>>> round(122.2 / 0.01) * 0.01
122.2
>>> round(1222.2 / 0.01) * 0.01
1222.2

As you can see, the second round is returning an odd value.

Can someone explain to me why is this happening?

Answer 1

This has in fact nothing to with round, you can witness the exact same problem if you just do 1220 * 0.01:

>>> 1220*0.01
12.200000000000001

What you see here is a standard floating point issue.

You might want to read what Wikipedia has to say about floating point accuracy problems:

The fact that floating-point numbers cannot precisely represent all real numbers, and that floating-point operations cannot precisely represent true arithmetic operations, leads to many surprising situations. This is related to the finite precision with which computers generally represent numbers.

Also see:

• Numerical analysis

• Numerical stability

A simple example for numerical instability with floating-point:
the numbers are finite. lets say we save 4 digits after the dot in a given computer or language.
0.0001 multiplied with 0.0001 would result something lower than 0.0001, and therefore it is impossible to save this result!
In this case if you calculate (0.0001 x 0.0001) / 0.0001 = 0.0001, this simple computer will fail in being accurate because it tries to multiply first and only afterwards to divide. In javascript, dividing with fractions leads to similar inaccuracies.