[Rd] Computing means, variances and sums
Duncan Murdoch
murdoch at stats.uwo.ca
Sun Feb 19 22:58:23 CET 2006
On 2/19/2006 3:18 PM, Prof Brian Ripley wrote:
> On Sun, 19 Feb 2006, hadley wickham wrote:
>
>>> 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
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