problem with sum function

[Mark A. Albins]

Hi!

I'm running R version 2.13.0 (2011-04-13)
Platform: i386-pc-mingw32/i386 (32-bit)

When i type in the command:

sum(c(-0.2, 0.8, 0.8, -3.2, 1.8))

R returns the value:

-5.551115e-17

Why doesn't R return zero in this case?  There shouldn't be any rounding
error in a simple sum.

Thanks,

Mark

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[Sarah Goslee]

Of course there's rounding error: your computer can't
store those decimal numbers precisely. See R FAQ 7.31 for
details.

See also:
sum(10*c(-0.2, 0.8, 0.8, -3.2, 1.8)) / 10

Sarah

On Thu, Mar 1, 2012 at 4:49 PM, Mark A. Albins <[hidden email]> wrote:

> Hi!
>
> I'm running R version 2.13.0 (2011-04-13)
> Platform: i386-pc-mingw32/i386 (32-bit)
>
> When i type in the command:
>
> sum(c(-0.2, 0.8, 0.8, -3.2, 1.8))
>
> R returns the value:
>
> -5.551115e-17
>
> Why doesn't R return zero in this case?  There shouldn't be any rounding
> error in a simple sum.
>
> Thanks,
>
> Mark

--
Sarah Goslee
http://www.functionaldiversity.org

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[William Dunlap]

In base ten, using any fixed number of digits, compute
   1/3 + 1/3 + 1/3
(doing the divisions before the additions).
Why isn't it 1?

1/5 has the same sort of problem in base two.

Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com

> -----Original Message-----
> From: [hidden email] [mailto:[hidden email]] On Behalf Of Mark A. Albins
> Sent: Thursday, March 01, 2012 1:50 PM
> To: [hidden email]
> Subject: [R] problem with sum function
>
> Hi!
>
> I'm running R version 2.13.0 (2011-04-13)
> Platform: i386-pc-mingw32/i386 (32-bit)
>
> When i type in the command:
>
> sum(c(-0.2, 0.8, 0.8, -3.2, 1.8))
>
> R returns the value:
>
> -5.551115e-17
>
> Why doesn't R return zero in this case?  There shouldn't be any rounding
> error in a simple sum.
>
> Thanks,
>
> Mark
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[MRD]

sum(-0.2, 0.8, 0.8, -3.2, 1.8) =0

[Petr Savicky]

On Thu, Mar 01, 2012 at 01:49:44PM -0800, Mark A. Albins wrote:

> Hi!
>
> I'm running R version 2.13.0 (2011-04-13)
> Platform: i386-pc-mingw32/i386 (32-bit)
>
> When i type in the command:
>
> sum(c(-0.2, 0.8, 0.8, -3.2, 1.8))
>
> R returns the value:
>
> -5.551115e-17
>
> Why doesn't R return zero in this case?  There shouldn't be any rounding
> error in a simple sum.

Hi.

There is a rounding error, since numerical values are represented
in binary system and, for example, 0.2 = 1/5 cannot be represented
in binary exactly. A simpler version is

  0.1 + 0.2 - 0.3

  [1] 5.551115e-17

Use round(), for example

  round(sum(c(-0.2, 0.8, 0.8, -3.2, 1.8)), digits=7)

  [1] 0

See FAQ 7.31 and/or

  http://rwiki.sciviews.org/doku.php?id=misc:r_accuracy

for further hints.

Hope this helps.

Petr Savicky.

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[Petr Savicky]

On Thu, Mar 01, 2012 at 04:55:55PM -0500, Sarah Goslee wrote:
> Of course there's rounding error: your computer can't
> store those decimal numbers precisely. See R FAQ 7.31 for
> details.
>
> See also:
> sum(10*c(-0.2, 0.8, 0.8, -3.2, 1.8)) / 10

Hi.

This is 0. This works without rounding for one digit precision,
since we always have i == 10*(i/10). Already for two digits, we
may have i != 100*(i/100). So, for example

  sum(100*c(0.28, -0.21, 0.66, -0.73))/100
  [1] 3.552714e-17

Rounding the multiples to be integers yields the expected result

  sum(round(100*c(0.28, -0.21, 0.66, -0.73)))/100
  [1] 0

Petr Savicky.

______________________________________________
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[glsnow]

Others explained why it happens, but you might want to look at the
zapsmall function for one way to deal with it.

On Thu, Mar 1, 2012 at 2:49 PM, Mark A. Albins <[hidden email]> wrote:

> Hi!
>
> I'm running R version 2.13.0 (2011-04-13)
> Platform: i386-pc-mingw32/i386 (32-bit)
>
> When i type in the command:
>
> sum(c(-0.2, 0.8, 0.8, -3.2, 1.8))
>
> R returns the value:
>
> -5.551115e-17
>
> Why doesn't R return zero in this case?  There shouldn't be any rounding
> error in a simple sum.
>
> Thanks,
>
> Mark
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.