How deterministic is floating point inaccuracy?

Question

I understand that floating point calculations have accuracy issues and there are plenty of questions explaining why. My question is if I run the same calculation twice, can

Answer 1

I think your confusion lies in the type of inaccuracy around floating point. Most languages implement the IEEE floating point standard This standard lays out how individual bits within a float/double are used to produce a number. Typically a float consists of a four bytes, and a double eight bytes.

A mathmatical operation between two floating point numbers will have the same value every single time (as specified within the standard).

The inaccuracy comes in the precision. Consider an int vs a float. Both typically take up the same number of bytes (4). Yet the maximum value each number can store is wildly different.

• int: roughly 2 billion
• float: 3.40282347E38 (quite a bit larger)

The difference is in the middle. int, can represent every number between 0 and roughly 2 billion. Float however cannot. It can represent 2 billion values between 0 and 3.40282347E38. But that leaves a whole range of values that cannot be represented. If a math equation hits one of these values it will have to be rounded out to a representable value and is hence considered "inaccurate". Your definition of inaccurate may vary :).