precedence does matter in this example. the square root was taken of a doubleprecision (53 bit) number. my revision takes the square root of a 120 bit number.
> sqrt(mpfr(pi, 120)) 1 'mpfr' number of precision 120 bits [1] 1.7724538509055159927515191031392484397 > mpfr(sqrt(pi), 120) 1 'mpfr' number of precision 120 bits [1] 1.772453850905515881919427556567825377 > print(sqrt(pi), digits=20) [1] 1.7724538509055158819 > Sent from my iPhone > On Jul 3, 2015, at 00:38, Ravi Varadhan <ravi.varad...@jhu.edu> wrote: > > Hi Rich, > > The Wolfram answer is correct. > http://mathworld.wolfram.com/RamanujanConstant.html > > There is no code for Wolfram alpha. You just go to their web engine and plug > in the expression and it will give you the answer. > http://www.wolframalpha.com/ > > I am not sure that the precedence matters in Rmpfr. Even if it does, the > answer you get is still wrong as you showed. > > Thanks, > Ravi > > -----Original Message----- > From: Richard M. Heiberger [mailto:r...@temple.edu] > Sent: Thursday, July 02, 2015 6:30 PM > To: Aditya Singh > Cc: Ravi Varadhan; r-help > Subject: Re: [R] : Ramanujan and the accuracy of floating point computations > - using Rmpfr in R > > There is a precedence error in your R attempt. You need to convert > 163 to 120 bits first, before taking > its square root. > >> exp(sqrt(mpfr(163, 120)) * mpfr(pi, 120)) > 1 'mpfr' number of precision 120 bits > [1] 262537412640768333.51635812597335712954 > > ## just the last four characters to the left of the decimal point. >> tmp <- c(baseR=8256, Wolfram=8744, Rmpfr=8333, wrongRmpfr=7837) >> tmp-tmp[2] > baseR Wolfram Rmpfr wrongRmpfr > -488 0 -411 -907 > > You didn't give the Wolfram alpha code you used. There is no way of > verifying the correct value from your email. > Please check that you didn't have a similar precedence error in that code. > > Rich > > >> On Thu, Jul 2, 2015 at 2:02 PM, Aditya Singh via R-help >> <r-help@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@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@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@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.
