Is there a package or technique availabe for calculating large factorials in R?

Question

If I calculate factorial(100) then I get an answer of [1] 9.332622e+157 but when I try to calculate a larger factorial, say factorial(1000) I get an answer of [1] Inf

Is there a way to use arbitrary precision when calculating factorials such that I can calculate say factorial(1000000)?

Answer 1

For arbitrary precision you can use either gmp or Rmpfr. For specifically factorial gmp offers factorialZ and Rmpfr has factorialMpfr. So you can run something like below

> Rmpfr::factorialMpfr(200)
1 'mpfr' number of precision  1246   bits 
[1] 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000
> gmp::factorialZ(200)
Big Integer ('bigz') :
[1] 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000

HTH

Answer 2

I wrote a web scraper; @Khashaa's answer is probably faster, but I went through for proof of concept and to hone my nascent rvest skills:

library(rvest)
Factorial<-function(n){
  x<-strsplit(strsplit((html(paste0(
    #%21 is URL speak for !
    "http://www.wolframalpha.com/input/?i=",n,"%21")) %>%
      #to understand this part, I recommend going to the site
      #  and doing "Inspect Element" on the decimal representation
      html_nodes("area") %>% html_attr("href")),
    split="[=&]")[[1]][2],split="\\+")[[1]]
  cat(paste0(substr(x[1],1,8), #8 here can be changed to the precision you'd like;
                               #  could also make it match printing options...
             "e+",gsub(".*E","",x[3])))
}

> Factorial(10000)
2.846259e+35659

Another possible advantage is using Wolfram's computing power instead of your own (I don't know how efficient the package options are, I imagine they just use asymptotic approximations so this probably isn't a concern, just thought I'd mention it)