protential rounding error concern

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protential rounding error concern

jimmycloud
Dear All,

I am running a r code on 32bit win, involving absolutely small numbers.
Although I tried sth like the ratio of numers like 10^(-100) and did not
have issue to get the correct answer,
but still a little concerned about it.
Could anyone give some suggestion or have any experience?

Best wishes,
Jie

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Re: protential rounding error concern

Michael Weylandt
On Tue, Jul 31, 2012 at 2:45 PM, Jie <[hidden email]> wrote:
> Dear All,
>
> I am running a r code on 32bit win, involving absolutely small numbers.
> Although I tried sth like the ratio of numers like 10^(-100) and did not
> have issue to get the correct answer,
> but still a little concerned about it.
> Could anyone give some suggestion or have any experience?

This would be a canonical reference:

http://www.validlab.com/goldberg/paper.pdf.

Hope this helps,
M

>
> Best wishes,
> Jie
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [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.

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Re: protential rounding error concern

Petr Savicky
In reply to this post by jimmycloud
On Tue, Jul 31, 2012 at 03:45:14PM -0400, Jie wrote:
> Dear All,
>
> I am running a r code on 32bit win, involving absolutely small numbers.
> Although I tried sth like the ratio of numers like 10^(-100) and did not
> have issue to get the correct answer,
> but still a little concerned about it.
> Could anyone give some suggestion or have any experience?

Hi.

Numbers of the order 10^(-100) are still relatively far from the lower
limit and are represented with full precision, which is 53 bits.

The smallest number representable in full precision is 2^-1022 = 2.225074e-308
and the smallest representable number (in limited precision) is 2^-1074 =
4.940656e-324.

See

  http://en.wikipedia.org/wiki/Double_precision_floating-point_format

for more detail.

Hope this helps.

Petr Savicky.

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