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Date: Thu, 30 May 2013 18:29:23 +1000
Subject: Re: Short-circuit Logic
From: Chris Angelico <rosuav@gmail.com>
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Xref: csiph.com comp.lang.python:46442

On Thu, May 30, 2013 at 3:42 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On Thu, 30 May 2013 13:45:13 +1000, Chris Angelico wrote:
>
>> Let's suppose someone is told to compare floating point numbers by
>> seeing if the absolute value of the difference is less than some
>> epsilon.
>
> Which is usually the wrong way to do it! Normally one would prefer
> *relative* error, not absolute:
>
> # absolute error:
> abs(a - b) < epsilon
>
>
> # relative error:
> abs(a - b)/a < epsilon

I was picking an epsilon based on a, though, which comes to pretty
much the same thing as the relative error calculation you're using.

> But using relative error also raises questions:
>
> - what if a is negative?
>
> - why relative to a instead of relative to b?
>
> - what if a is zero?
>
> The first, at least, is easy to solve: take the absolute value of a.

One technique I saw somewhere is to use the average of a and b. But
probably better is to take the lower absolute value (ie the larger
epsilon). However, there's still the question of what epsilon should
be - what percentage of a or b you take to mean equal - and that one
is best answered by looking at the original inputs.

Take these guys, for instance. Doing the same thing I was, only with
more accuracy.

http://www.youtube.com/watch?v=ZNiRzZ66YN0

ChrisA