From: Rick DeNatale <rick.denatale@...>
Date: 2009-05-06T12:30:15+09:00
Subject: Re: Unexpected BigDecimal rounding issue

On Tue, May 5, 2009 at 9:01 PM, Samuel Lown <me@samlown.com> wrote:
> Hi,
>
> Some more not so fun rounding issues.
>
> Using Floats:
>
>>> ((30 / 1.16) * 1.16) == 30
> => true
>
> Cool, so you'd think it would work with BigDecimal:
>
>>> ((30 / BigDecimal("1.16")) * BigDecimal("1.16")) == 30
> => false
>>> ((30 / BigDecimal("1.16")) * BigDecimal("1.16")).to_s
> => "30.0000000000000000000000002"
>
> I'm clearly missing something here as I thought BigDecimal was supposed
> to fix this type of thing.
>
> Tested in:
> ruby 1.8.6 (2008-03-03 patchlevel 114) [universal-darwin9.0]
> ruby 1.9.1p0 (2009-01-30 revision 21907) [i386-darwin9.6.0]
>
> Can anyone offer an explanation?

BigDecimal is still a kind of float, albeit a decimal float rather
than a binary float.

So it helps with problems when the fractional part of a number can be
expressed exactly as a finite string of decimal digits, but just as
certain fractional parts can't be expressed exactly as a finite string
of binary digits, there are some which have the same problem when the
base is 10.

For example 1/3 cannot be expressed as a decimal float, no matter how
many digits 0.33333.....

Similarly 3000/116 (which is the same as 30/1.16) can't be expressed
by a finite sequence of decimal digits.

It comes out as

25.862068965517241379310344827[5862068965517241379310344827]...

where the digits in the brackets repeat infinitely.


-- 
Rick DeNatale

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