[R] Strange behaviour of as.integer()

[Martin Maechler]

>>>>> "MT" == Magnus Torfason <zulutime.net at gmail.com>
>>>>>     on Thu, 07 Jan 2010 10:01:28 -0500 writes:

    MT> There have been some really great responses to this question. I would 
    MT> like to make a minor contribution by throwing the 'gmp' package into the 
    MT> mix.

    MT> On 1/7/2010 8:12 AM, Duncan Murdoch wrote:
    >> On 07/01/2010 7:31 AM, Ulrich Keller wrote:
    >>>> as.integer(.57 * 100)
    >>> [1] 56
    >> 
    >> Yes, as the man page states, non-integer values are truncated towards
    >> zero.
    >> 
    >> > .57*100 < 57
    >> [1] TRUE

    MT> gmp provides the bigz and bigq classes which provide arbitrary precision 
    MT> integers and rationals, and would solve Ulrich's original
    MT> problem quite effectively:

    >> library(gmp)
    >> 
    >> # bigq will not parse "0.57" but writing such a parser
    >> # would be a trivial extension.
    >> x = as.bigq("57")/100
    >> x
    MT> [1] "57/100"
    >> 
    >> # as.integer(x*100) does not seem to be overloaded correctly, so
    >> # we need to use as.numeric first, but the end result is 57
    >> as.integer(as.numeric(x*100))
    MT> [1] 57
    >> 
    >> # And we conclude by making some comparisons, and finding the that
    >> # the results are what a fifth-grader would expect, rather than
    >> # what a CS grad would expect :-)
    >> x*100<57
    MT> [1] FALSE
    >> x*100==57
    MT> [1] TRUE

    MT> Of course there is still the problem that:
    >> 1+1 == sqrt(2)*sqrt(2)
    MT> [1] FALSE
    MT> and gmp will not solve this . I don't know if there is an R-package for 
    MT> arbitrary-precision reals floating around, but probably not.

Yes, there's package  'Rmpfr' for arbitrary precision
floating-point, written and maintained by me.
As it is based on the (GNU) library MPFR which itself is based
on the GNU MP (=: GMP) library, for Windows the Rmpfr package is
currently not available from CRAN, but thanks to Brian Ripley
from his CRANextras collection.

However, that does *still* not allow the equivalent
of
    1+1 == sqrt(2)*sqrt(2)

because that would need *infinite* precision not just arbitrary
precision, or then *symbolic* computation, as I assume the following does

    MT> However, Wolfram Alpha will return the correct answer:
    MT> http://tr.im/1plus1equals2

BTW: I see that I seem to have forgotten to upload the
somewhat newer and better R-forge version of  Rmpfr  to CRAN,
something to be done "Real Soon Now".

In the mean time, you can use
   install.packages("Rmpfr", repos="http://R-Forge.R-project.org")

which -- thanks to Stefan Theussl as R-forge maintainer -- may
even on Windows give a working version of Rmpfr.

Martin Maechler, ETH Zurich