Aditya Singh
2015-Jul-02 17:38 UTC
[R] Ramanujan and the accuracy of floating point computations - using Rmpfr in R
Ravi 1. You may want to check the sqrt too. 2. Why not take log and try? Aditya ------------------------------ On Thu 2 Jul, 2015 10:18 AM PDT Boris Steipe wrote:>Just a wild guess, but did you check exactly which operations are actually done to high precision? Obviously you will need high-resolution representations of pi and e to get an improved result. > >B. > > > >On Jul 2, 2015, at 10:28 AM, Ravi Varadhan <ravi.varadhan at jhu.edu> 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.