[Python-Dev] Expert floats (original) (raw)

Tim Peters tim.one at comcast.net
Tue Apr 6 12:23:09 EDT 2004

[Tim]

I believe Ping would have

>>> 2.20 - 1.20 1.0000000000000002

[Andrew Koenig]

As would I.

Only sometimes, right? You earlier gave a list of 4 behaviors you sometimes want, and that particular output isn't suitable for all of them.

OTOH, he'd have

>>> 2.20 - 1.10 1.1

Believe it or not, this apparent anomaly doesn't bother me, but

>>> 1.1 1.1000000000000001 does. The reason is that the first example does arithmetic, and it is easy to explain that floating-point arithmetic is not completely accurate.

Wouldn't it bother you to give a wrong explanation? It's simply impossible to explain why 2.2-1.2 is inaccurate without explaining that "2.2" and/or "1.2" are already inaccurate on their own. The arithmetic in both examples is exactly correct (if you watched the hardware's inexact flag across the subtractions, you'd see that it doesn't get set; x-y is always exact in 754 binary floating point when x and y are within a factor of 2 of each other). The only cause of "funny results" in these examples is representation error.

So trying to "explain" this by telling a newbie that arithmetic is inaccurate may pacify them, but at the cost of increasing their confusion (the explanation they're given then doesn't actually explain anything about what they're seeing, and the true cause has been left untold).

OTOH,

2.2 2.2000000000000002 1.1 1.1000000000000001

points to the true cause, and the Tutorial Appendix on binary fp issues has been successful in bringing newbies to a correct understanding of that.

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