> Bill Dunlap
> on Thu, 17 Aug 2023 07:31:12 -0700 writes:
> MKL's results can depend on the number of threads running and perhaps
other
> things. They blame it on the non-associativity of floating point
> arithmetic. This article gives a way to make results repeatable:
В Wed, 16 Aug 2023 16:08:57 -0500
"Therneau, Terry M., Ph.D. via R-help" пишет:
> I get the following error out of R, on a newer Ubuntu installation.
> ! X11 font -adobe-helvetica-%s-%s-*-*-%d-*-*-*-*-*-*-*, face 1 at
> size 12 could not be loaded
> Version:
> R Under development (unstable) (20
Dear Martin,
Thank you very much for your analysis.
I add only a small comment:
- the purpose of the modified formula was to apply l'Hospital;
- there are other ways to transform the formula; although applying
l'Hospital once is probably more robust than simple transformations (but
the computa
On Fri, 18 Aug 2023 12:17:51 +0200
Martin Maechler wrote:
> I think it would be nice to provide the average R user with a
> (possibly super small) R package that allows to turn on (and off)
> such CNR reproducibility.
Would it be possible to effect this on/off via options()?
cheers,
Rolf
I have added some clarifications below.
On 8/18/2023 10:20 PM, Leonard Mada wrote:
[...]
After more careful thinking, I believe that it is a limitation due to
floating points:
[...]
The problem really stems from the representation of 1 - x^2/2 as shown
below:
x = 1E-4
print(1 - x^2/2, digit
"The ugly thing is that the error only gets worse as x decreases. The
value neither drops to 0, nor does it blow up to infinity; but it gets
worse in a continuous manner."
If I understand you correctly, this is wrong:
> x <- 2^(-20) ## considerably less then 1e-4 !!
> y <- 1 - x^2/2;
> 1/(1 - y)
Dear Bert,
Values of type 2^(-n) (and its binary complement) are exactly
represented as floating point numbers and do not generate the error.
However, values away from such special x-values will generate errors:
# exactly represented:
x = 9.53674316406250e-07
y <- 1 - x^2/2;
1/(1 - y) - 2/x^2
"Values of type 2^(-n) (and its binary complement) are exactly represented
as floating point numbers and do not generate the error. However, values
away from such special x-values will generate errors:"
That was exactly my point: The size of errors depends on the accuracy of
binary representation
Dear Bert,
On 8/19/2023 2:47 AM, Bert Gunter wrote:
> "Values of type 2^(-n) (and its binary complement) are exactly
> represented as floating point numbers and do not generate the error.
> However, values away from such special x-values will generate errors:"
>
> That was exactly my point: The
This discussion is sooo familiar.
If you want indefinite precision arithmetic, feel free to use a language and
data type that supports it.
Otherwise, only do calculations that fit in a safe zone.
This is not just about this scenario. Floating point can work well when adding
(or subtracting) tw
"Are there any good indefinite (or much higher) precision packages"
A simple search on "arbitrary precision arithmetic in R" would have
immediately gotten you to the Rmpfr package.
See also:
https://cran.r-project.org/web/packages/Ryacas/vignettes/arbitrary-precision.html
-- Bert
On Fri, Aug 18
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