[Python-ideas] Python-ideas Digest, Vol 103, Issue 2

[u8y7541 The Awesome Person]

Floats internally use numerator and denominator (float.as_integer_ratio().)
It makes no sense to have sign and mantissa while displaying numerator and
denominator. Perhaps a redo of the class? I believe fractions should be the
standard, and just keep the ieee754 floats as a side option.

On Sun, May 31, 2015 at 7:37 PM, <python-ideas-request at python.org> wrote:

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>    1. Python Float Update (u8y7541 The Awesome Person)
>    2. Re: Python Float Update (Nathaniel Smith)
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> ----------------------------------------------------------------------
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> Message: 1
> Date: Sun, 31 May 2015 19:25:46 -0700
> From: u8y7541 The Awesome Person <surya.subbarao1 at gmail.com>
> To: python-ideas at python.org
> Subject: [Python-ideas] Python Float Update
> Message-ID:
>         <
> CA+o1fZONRG_dZzct_VZwcUvtwD-5rJ6zOFxNR34jWFrpUXiw9Q at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Dear Python Developers:
>
> I will be presenting a modification to the float class, which will improve
> its speed and accuracy (reduce floating point errors). This is applicable
> because Python uses a numerator and denominator rather than a sign and
> mantissa to represent floats.
>
> First, I propose that a float's integer ratio should be accurate. For
> example, (1 / 3).as_integer_ratio() should return (1, 3). Instead, it
> returns(6004799503160661, 18014398509481984).
>
> Second of all, even though 1 * 3 = 3 (last example), 6004799503160661 * 3
> does not equal 18014398509481984. Instead, it equals 1801439850948198**3**,
> one less than the value in the ratio. This means the ratio is inaccurate,
> as well as completely not simplified.
>
>
> [image: Inline image 1]
>
>
> Even if the value displayed for a float is a rounded value, the internal
> numerator and denominator should divide to equal to completely accurate
> value.
>
> Thanks for considering this improvement!
>
> Sincerely,
> u8y7541
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> ------------------------------
>
> Message: 2
> Date: Sun, 31 May 2015 19:37:14 -0700
> From: Nathaniel Smith <njs at pobox.com>
> To: u8y7541 The Awesome Person <surya.subbarao1 at gmail.com>
> Cc: python-ideas at python.org
> Subject: Re: [Python-ideas] Python Float Update
> Message-ID:
>         <CAPJVwBnJqygpOktfD+qRy0J_UZE9MD0hkR+R2=
> wE1PWDSrquzg at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> On May 31, 2015 7:26 PM, "u8y7541 The Awesome Person" <
> surya.subbarao1 at gmail.com> wrote:
> >
> > Dear Python Developers:
> >
> > I will be presenting a modification to the float class, which will
> improve its speed and accuracy (reduce floating point errors). This is
> applicable because Python uses a numerator and denominator rather than a
> sign and mantissa to represent floats.
>
> Python's floats are in fact ieee754 floats, using sign/mantissa/exponent,
> as provided by all popular CPU floating point hardware. This is why you're
> getting the results you see -- 1/3 cannot be exactly represented as a
> float, so it gets rounded to the closest representable float, and then
> as_integer_ratio shows you an exact representation of this rounded value.
> It sounds like you're instead looking for an exact fraction representation,
> which in python is available in the standard "fractions" module:
>
> https://docs.python.org/3.5/library/fractions.html
>
> -n
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> End of Python-ideas Digest, Vol 103, Issue 2
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>



-- 
-Surya Subbarao
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