On Fri, 31 May 2013 00:03:13 +0300, Carlos Nepomuceno wrote:
> ----------------------------------------
>> From: steve+comp.lang.pyt...@pearwood.info Subject: Re: Short-circuit
>> Logic
>> Date: Thu, 30 May 2013 05:42:17 +0000 To: python-list@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?
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.
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"?
--
Steven
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