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Re: 1-0.95

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Steven D'Aprano <steve+comp.lang.python@pearwood.info>:

> On Wed, 02 Jul 2014 23:00:15 +0300, Marko Rauhamaa wrote:
>> Steven D'Aprano <steve+comp.lang.python@pearwood.info>:
>>>>    >>> Rational(2).sqrt() * Rational(2).sqrt() == Rational(2)
>>>>    False
>>> Square root of 2 is not a rational number.
>> Nobody said it was. 
>
> Your comment can be read as implying it. You stated:
>
>     [quote]
>     Even "arbitrary-precision" RATIONALS [emphasis added] would 
>     suffer from the same problem 
>     [end quote]
>
> and then showed an invented example where you squared a NON-RATIONAL.

While √2 is irrational, the hypothetical Rational(2).sqrt() probably
would be another "arbitrary-precision" Rational number and thus,
necessarily an approximation.

That's completely analogous to Decimal(1) / Decimal(3) being an
approximation.

And the point: when dealing with real numbers on a computer, there's no
way to avoid approximations. If an aspiring programmer is dismayed at
the imprecision of 0.1, that probably wouldn't be the right moment to
talk about Decimal().

> By the way, there's no need to use an invented example. Here is an
> actual example:
>
> py> import math
> py> from fractions import Fraction
> py> math.sqrt(Fraction(2))**2
> 2.0000000000000004

Sure, although you were invoking "arbitrary-precision" rational numbers,
which Fraction() is not.

> I'm sorry Marko, have you not being paying attention? Have you ever
> done any numeric programming?

Your style is consistent and impeccable.

> Floating-point is *hard*, not "perfect".

It can be both. The point is, regular floating point numbers will likely
the optimal choice for your numeric calculation needs. They are compact,
fast and readily supported by hardware and numeric software. Switching to
Decimal might give you a false sense of security.


Marko

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1-0.95 Pedro Izecksohn <izecksohn@yahoo.com> - 2014-07-01 14:17 -0700
  Re: 1-0.95 pecore@pascolo.net - 2014-07-02 01:13 +0200
  Re: 1-0.95 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-07-02 15:27 +0000
    Re: 1-0.95 Marko Rauhamaa <marko@pacujo.net> - 2014-07-02 19:59 +0300
      Re: 1-0.95 Skip Montanaro <skip@pobox.com> - 2014-07-02 12:34 -0500
      Re: 1-0.95 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-07-02 18:34 +0000
        Re: 1-0.95 Marko Rauhamaa <marko@pacujo.net> - 2014-07-02 23:00 +0300
          Re: 1-0.95 Chris Angelico <rosuav@gmail.com> - 2014-07-03 10:16 +1000
          Re: 1-0.95 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-07-03 02:19 +0000
            Re: 1-0.95 Rustom Mody <rustompmody@gmail.com> - 2014-07-02 21:06 -0700
              Re: 1-0.95 Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-07-03 16:55 +1200
                Re: 1-0.95 Rustom Mody <rustompmody@gmail.com> - 2014-07-02 22:21 -0700
                Re: 1-0.95 Ian Kelly <ian.g.kelly@gmail.com> - 2014-07-02 23:50 -0600
              OT: speeds (physical, not computing) [was Re: 1-0.95] Steven D'Aprano <steve@pearwood.info> - 2014-07-03 09:15 +0000
            Re: 1-0.95 Marko Rauhamaa <marko@pacujo.net> - 2014-07-03 09:51 +0300
              Re: 1-0.95 Steven D'Aprano <steve@pearwood.info> - 2014-07-03 09:36 +0000
                Re: 1-0.95 Marko Rauhamaa <marko@pacujo.net> - 2014-07-03 14:17 +0300

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