# Re: [Rd] Computing means, variances and sums

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Sun 19 Feb 2006 - 21:58:23 GMT

```>>> p.s.  If my computations are correct, 0.2 = 0*/2 + 0/4 + 1/8 + 1/16 +
>>> 0/32 + 0/64 + 1/128 + 1/256 + 0/512 + 0/1024 + 1/2048 + 1/4096 + ... =
>>> 0.3333333333333h.  Perhaps someone can extend this to an FAQ to help
>>> explain finite precision arithmetic and rounding issues.
>> This is drifting a bit off topic, but the other day I discovered this
>> rather nice illustration of the perils of finite precision arithmetic
>> while creating a contrast matrix:
>>
>>> n <- 13
>>> a <- matrix(-1/n, ncol=n, nrow=n) + diag(n)
>>> rowSums(a)
>> [1]  2.775558e-16  2.775558e-16  5.551115e-17  5.551115e-17  5.551115e-17
>> [6]  5.551115e-17  0.000000e+00 -5.551115e-17  0.000000e+00  5.551115e-17
>> [11]  1.110223e-16  1.665335e-16  2.220446e-16
>>
>> Not only do most of the rows not sum to 0, they do not even sum to the
>> same number!  It is hard to remember the familiar rules of arithmetic
>> do not always apply.
```

>
> I think you will find this example does give all 0's in R-devel, even
> on platforms like Sparc.

Only until the fpu precision gets changed:

``` > n <- 13
> a <- matrix(-1/n, ncol=n, nrow=n) + diag(n)
> rowSums(a)
```

[1] 0 0 0 0 0 0 0 0 0 0 0 0 0
> RSiteSearch('junk')
A search query has been submitted to http://search.r-project.org The results page should open in your browser shortly
``` > n <- 13
> a <- matrix(-1/n, ncol=n, nrow=n) + diag(n)
> rowSums(a)
```

[1] 2.775558e-16 2.775558e-16 5.551115e-17 5.551115e-17 5.551115e-17   [6] 5.551115e-17 0.000000e+00 -5.551115e-17 0.000000e+00 5.551115e-17 [11] 1.110223e-16 1.665335e-16 2.220446e-16

We still need to protect against these changes. I'll put something together, unless you're already working on it.

The approach I'm thinking of is to define a macro to be called in risky situations. On platforms where this isn't an issue, the macro would be null; on Windows, it would reset the fpu to full precision.

For example, RSiteSearch causes damage in the ShellExecute call in do_shellexec called from browseURL, so I'd add protection there. I think we should also add detection code somewhere in the evaluation loop to help in diagnosing these problems.

> But users do need to remember that computer
> arithmetic is inexact except in rather narrowly delimited cases.

Yes, that too.

Duncan Murdoch

R-devel@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel Received on Mon Feb 20 09:59:37 2006

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