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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Float conversion
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Date: Fri, 30 Jul 2010 10:43:20 +0200
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Date: 2010-07-30T10:43:20+02:00
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On Thu, 29 Jul 2010 18:30:06 -0700 (PDT), Phil Clayton wrote:

> On Jul 29, 8:15�pm, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
> wrote:
>> You should never use equality or inequality for floating-point types.
> 
> Inequalities (<, <=, >, >=) are ok - I think you meant don't use 'not
> equals' (which is still an equality operator).

Yes I did, thanks for correction.

> However, just because equality between floating point numbers is a
> dubious concept and should be avoided, it does not mean e.g. "<" and
> "<=" are simply interchangeable.  Far from it.

They are almost same. According to the extension principle:

I1<=I2

  T (true) if forall x in I1, forall y in I2  x<=y
  F (false) if forall x in I1, forall y in I2  not x<=y
  _|_ (undefined) otherwise

I1<I2

  T if forall x in I1, forall y in I2  x<y
  F if forall x in I1, forall y in I2  not x<y
  _|_ otherwise

The difference comes from _|_ being rendered T for "<=" and F for "<" when
I1 and I2 are equal as sets. It would be ill-advised to exploit this
difference without care.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de