float - 7th decimal place not visible toString

Unity Engine
1

I’ve almost gone crazy with this.

Using: Unity 2017.4.1f1 on Windows 10 64bit.

I have a position.z(of Vector3) of a gameObject which prints -5.5.
I do the operation position.z - (-4.5) and I expect -1…
But the result is -0.9999995 !

So after a lot of research I wrote this code to
test a theory :

And the console output is this:

Without “F7” the output is -3.5 instead of -3.5000005.
Even with “F7” I can’t print the real value of j.
But the result of j - k is printable…

Based on my theory the position.z is 5.5000005 and not 5.5, so this is why i get this result.
This 0.0000005 may not be significant but it lead to a bug which because of toString() method, Debug.Log didn’t print the real value and it was very difficult to find.

Any idea what’s going on ?

2

There’s no bug; that’s how floating point works. You are printing the real value. If you don’t want to deal with floating point limitations, use integers instead.

–Eric

3

The value just can’t be represented as a float, I imagine.

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4

Floats have tons of errors involved with them.

For starters… floats are stored in binary in a format like so:

It’s effectively the scientific notation, but base 2 instead of base 10.

So instead of being like 1.3 * 10^-8 = 1.3e-8 = 0.000000013. Where you have the sig value range and the number of digits to move the decimal point by (hence the name ‘float’).

Instead it’s a binary sig value range, and the amount of binary digits to move the binary point.

Now in decimal there are values that are weird… like say 1/3 = 0.333333333333333… Well in binary super common values are repeating… like 0.1dec = 0.0001100110011001100110011001100110011… It’s a repeating value.

But here in lies an issue. A computer has a finite amount of memory. It can’t hold all those 1’s and 0’s. Instead you get 24 binary digits of sig value (23 stored, and 1 implied, because all non-zero binary digits have a leading 1). So a maximum of 24 of those 1’s and 0’s get stored. Meaning you have a value just shy of 0.1… more like 0.09999998.

This is the sort of thing happening to you in your example code.

Floats just work this way.

When you convert a float to string, you should be using format strings to make them look good.

Here is a long article going into all the math and what nots about floating point error:
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

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5

Thanks everyone for your time and your answers!
I knew that numbers are stored in binnary and I’ve done binary operations in my University, but I didn’t know that sometimes can’t be stored exact like 0.1.I have to read more about it.

For future reference If I want to check if an object is in a exact position (such as pos.z == 5.5) How would I do it ? Do I have to round always the transform values ?

6

To compare two float and take this error into account I believe you need to do something like this: (sorry for the lack of code tags, on mobile)

If(Mathf.abs(Mathf.abs(value1) - Mathf.abs(value2)) < mathf.epsilon) return true

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7
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