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Date: Thu, 30 May 2013 20:11:38 -0700 (PDT)
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Subject: Re: Short-circuit Logic
From: 88888 Dihedral <dihedral88888@gmail.com>
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Xref: csiph.com comp.lang.python:46570

Steven D'Aprano=E6=96=BC 2013=E5=B9=B45=E6=9C=8830=E6=97=A5=E6=98=9F=E6=9C=
=9F=E5=9B=9BUTC+8=E4=B8=8A=E5=8D=8810=E6=99=8228=E5=88=8657=E7=A7=92=E5=AF=
=AB=E9=81=93=EF=BC=9A
> On Wed, 29 May 2013 10:50:47 -0600, Ian Kelly wrote:
>=20
>=20
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> > On Wed, May 29, 2013 at 8:33 AM, rusi <rustompmody@gmail.com> wrote:
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> >> 0.0 =3D=3D 0.0 implies 5.4 =3D=3D 5.4
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> >> is not a true statement is what (I think) Steven is saying. 0 (or if
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> >> you prefer 0.0) is special and is treated specially.
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> >=20
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> > It has nothing to do with 0 being special.  A floating point number wil=
l
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> > always equal itself (except for nan, which is even more special), and i=
n
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> > particular 5.4 =3D=3D 5.4.  But if you have two different calculations =
that
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> > produce 0, or two different calculations that produce 5.4, you might
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> > actually get two different numbers that approximate 0 or 5.4 thanks to
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> > rounding error.  If you then compare those two ever-so-slightly
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> > different numbers, you will find them unequal.
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> EXACTLY!
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> The problem does not lie with the *equality operator*, it lies with the=
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> calculations. And that is an intractable problem -- in general, floating=
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> point is *hard*. So the problem occurs when we start with a perfectly=20
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> good statement of the facts:
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>=20
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> "If you naively test the results of a calculation for equality without=20
>=20
> understanding what you are doing, you will often get surprising results"
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> which then turns into a general heuristic that is often, but not always,=
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> reasonable:
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> "In general, you should test for floating point *approximate* equality,=
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> in some appropriate sense, rather than exact equality"
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> which then gets mangled to:
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> "Never test floating point numbers for equality"
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> and then implemented badly by people who have no clue what they are doing=
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> and have misunderstood the nature of the problem, leading to either:
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>=20
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> * de facto exact equality testing, only slower and with the *illusion* of=
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> avoiding equality, e.g. "abs(x-y) < sys.float_info.epsilon" is just a=20
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> long and slow way of saying "x =3D=3D y" when both numbers are sufficient=
ly=20
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> large;
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> * incorrectly accepting non-equal numbers as "equal" just because they=20
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> happen to be "close".
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> The problem is that there is *no one right answer*, except "have everyone=
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> become an expert in floating point, then judge every case on its merits",=
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> which will never happen.
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> But if nothing else, I wish that we can get past the rank superstition=20
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> that you should "never" test floats for equality. That would be a step=20
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> forward.
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> --=20
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> Steven

The string used to represent a floating number
in a computer language is normally in the decimal base of very=20
some limited digits.

Anyway with the advances of A/D-converters in the past 10 years
which are reflected in the anttena- transmitter parts in phones,=20
the long integer part in Python can really beat the low cost=20
32- 64 bit floating computations in scientific calculations.