Re: sum accuracy

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From	Jussi Piitulainen <jussi.piitulainen@helsinki.fi>
Newsgroups	comp.lang.python
Subject	Re: sum accuracy
Date	Fri, 15 Apr 2016 14:31:12 +0300
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Tony van der Hoff writes:
> On 15/04/16 11:10, Ben Bacarisse wrote:
>> Oscar Benjamin <oscar.j.benjamin@gmail.com> writes:
>>
>>> On 15 April 2016 at 10:24, Robin Becker <robin@reportlab.com> wrote:
>> <snip>
>>>> yes indeed summation is hard :(
>>>
>>> Not with Fraction it isn't:
>>>
>>> from fractions import Fraction
>>>
>>> def exact_sum(nums):
>>>      return sum(map(Fraction, nums))
>>>
>>> This will give you the exact result with precisely zero rounding
>>> error. You can convert it to float at the end.
>>
>> Just a word of warning for people new to numerical work: there's no
>> rounding error, but unless you start with Fraction objects you still
>> have input or conversion errors.  The uninitiated might expect
>>
>>    exact_sum([0.3, 0.7])
>>
>> to be 1.
>>
>
> So I'm uninitiated:
> NameError: name 'exact_sum' is not defined
>
> I appreciate the word of warning, but, in my case, it's not helpful.

There's a reason Ben included some context.

His point is that Fraction(0.3) is not equal to Fraction(3, 10). That in
turn is because the floating point number differs a little from the
mathematical ideal, and the representation of that floating point number
as a Fraction in Python preserves that difference.

Try Fraction(0.3), Fraction("0.3"), Fraction(3, 10), Fraction(3)/10 and
see for yourself.

Also, Fraction(0.3).limit_denominator() gives Fraction(3, 10). See the
documentation.

Thread

Re: sum accuracy Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2016-04-15 10:36 +0100
  Re: sum accuracy Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-04-15 11:10 +0100
    Re: sum accuracy Tony van der Hoff <tony@vanderhoff.org> - 2016-04-15 11:39 +0100
      Re: sum accuracy Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-04-15 14:31 +0300
    Re: sum accuracy Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2016-04-15 08:11 -0400
    Re: sum accuracy Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2016-04-15 14:49 +0100
      Re: sum accuracy Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-04-15 17:54 +0100
    Re: sum accuracy Matt Wheeler <m@funkyhat.org> - 2016-04-15 18:04 +0100

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