Short-circuit Logic

[Carlos Nepomuceno]

----------------------------------------
> From: steve+comp.lang.python at pearwood.info
> Subject: Re: Short-circuit Logic
> Date: Fri, 31 May 2013 05:13:51 +0000
> To: python-list at python.org
>
> On Fri, 31 May 2013 00:03:13 +0300, Carlos Nepomuceno wrote:
>
>> ----------------------------------------
>>> From: steve+comp.lang.python at pearwood.info Subject: Re: Short-circuit
>>> Logic
>>> Date: Thu, 30 May 2013 05:42:17 +0000 To: python-list at python.org
>> [...]
>>> Here's another way, mathematically equivalent (although not necessarily
>>> equivalent using floating point computations!) which avoids the
>>> divide-by- zero problem:
>>>
>>> abs(a - b) < epsilon*a
>>
>> That's wrong! If abs(a) < abs(a-b)/epsilon you will break the
>> commutative law. For example:
>
> What makes you think that the commutative law is relevant here?

How can't you see?

I'll requote a previous message:

}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:
 
Since we are considering Chris's supposition ("to compare floating point numbers") it's totally relevant to understand how that operation can be correctly implemented.


> Many things break the commutative law, starting with division and
> subtraction:
>
> 20 - 10 != 10 - 20
>
> 1/2 != 2/1
>
> Most comparison operators other than equality and inequality:
>
> (23 < 42) != (42 < 23)
>
> String concatenation:
>
> "Hello" + "World" != "World" + "Hello"
>
> Many operations in the real world:
>
> put on socks, then shoes != put on shoes, then socks.
>

That's is totally irrelevant in this case. The commutative law is essential to the equality operation.

> But you are correct that approximately-equal using *relative* error is
> not commutative. (Absolute error, on the other hand, is commutative.) As
> I said, any form of "approximate equality" has gotchas. But this gotcha
> is simple to overcome:
>
> abs(a -b) < eps*max(abs(a), abs(b))
>
> (Knuth's "approximately equal to" which you give.)
>
>
>> This discussion reminded me of TAOCP and I paid a visit and bring the
>> following functions:
>
> "TAOCP"?

The Art of Computer Programming[1]! An old book full of excellent stuff! A MUST READ!!!! ;)

http://www-cs-faculty.stanford.edu/~uno/taocp.html

[1] Knuth, Donald (1981). The Art of Computer Programming. 2nd ed. Vol. 2. p. 218. Addison-Wesley. ISBN 0-201-03822-6.

>
>
> --
> Steven
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