[R] : Ramanujan and the accuracy of floating point computations - using Rmpfr in R

[jim holtman]

This is the standard FAQ 7.31 and then read in detail the referenced paper.


Jim Holtman
Data Munger Guru

What is the problem that you are trying to solve?
Tell me what you want to do, not how you want to do it.

On Thu, Jul 2, 2015 at 2:02 PM, Aditya Singh via R-help <
r-help at r-project.org> wrote:

>
> Ravi
>
> I am a chemical engineer by training. Is there not something like law of
> corresponding states in numerical analysis?
>
> Aditya
>
>
>
> ------------------------------
> On Thu 2 Jul, 2015 7:28 AM PDT Ravi Varadhan wrote:
>
> >Hi,
> >
> >Ramanujan supposedly discovered that the number, 163, has this
> interesting property that exp(sqrt(163)*pi), which is obviously a
> transcendental number, is real close to an integer (close to 10^(-12)).
> >
> >If I compute this using the Wolfram alpha engine, I get:
> >262537412640768743.99999999999925007259719818568887935385...
> >
> >When I do this in R 3.1.1 (64-bit windows), I get:
> >262537412640768256.0000
> >
> >The absolute error between the exact and R's value is 488, with a
> relative error of about 1.9x10^(-15).
> >
> >In order to replicate Wolfram Alpha, I tried doing this in "Rmfpr" but I
> am unable to get accurate results:
> >
> >library(Rmpfr)
> >
> >
> >> exp(sqrt(163) * mpfr(pi, 120))
> >
> >1 'mpfr' number of precision  120   bits
> >
> >[1] 262537412640767837.08771354274620169031
> >
> >The above answer is not only inaccurate, but it is actually worse than
> the answer using the usual double precision.  Any thoughts as to what I am
> doing wrong?
> >
> >Thank you,
> >Ravi
> >
> >
> >
> >       [[alternative HTML version deleted]]
> >
> >______________________________________________
> >R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> >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.
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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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