Other examples of functions like this are log1p(x), which is log(1+x) accurate for small x, and expm1(x), which is exp(x)-1 accurate for small x. E.g., > log1p( 1e-20 ) [1] 1e-20 > log( 1 + 1e-20 ) [1] 0 log itself cannot be accurate here because the problem is that 1 == 1 + 1e-20 in double precision arithmetic (52 binary digits of precision).
Bill Dunlap TIBCO Software wdunlap tibco.com On Fri, Sep 9, 2016 at 12:58 PM, Greg Snow <538...@gmail.com> wrote: > If pi were stored and computed to infinite precision then yes we would > expect tan(pi/2) to be NaN, but computers in general and R > specifically don't store to infinite precision (some packages allow > arbitrary (but still finite) precision) and irrational numbers cannot > be stored exactly. So you take the value of the built in variable pi, > which is close to the theoretical value, but not exactly equal, divide > it by 2 which could reduce the precision, then pass that number (which > is not equal to the actual irrational value where tan has a > discontinuity) to tan and tan returns its best estimate. > > Using finite precision approximations to irrational and other numbers > that cannot be stored exactly can have all types of problems at and > near certain values, that is why there are many specific functions for > calculating in those regions. > > > > > > On Fri, Sep 9, 2016 at 12:55 PM, Hans W Borchers <hwborch...@gmail.com> > wrote: > > The same argument would hold for tan(pi/2). > > I don't say the result 'NaN' is wrong, > > but I thought, > > tan(pi*x) and tanpi(x) should give the same result. > > > > Hans Werner > > > > > > On Fri, Sep 9, 2016 at 8:44 PM, William Dunlap <wdun...@tibco.com> > wrote: > >> It should be the case that tan(pi*x) != tanpi(x) in many cases - that > is why > >> it was added. The limits from below and below of the real function > >> tan(pi*x) as x approaches 1/2 are different, +Inf and -Inf, so the > limit is > >> not well defined. Hence the computer function tanpi(1/2) ought to > return > >> Not-a-Number. > >> > >> Bill Dunlap > >> TIBCO Software > >> wdunlap tibco.com > >> > >> On Fri, Sep 9, 2016 at 10:24 AM, Hans W Borchers <hwborch...@gmail.com> > >> wrote: > >>> > >>> As the subject line says, we get different results for tan(pi/2) and > >>> tanpi(1/2), though this should not be the case: > >>> > >>> > tan(pi/2) > >>> [1] 1.633124e+16 > >>> > >>> > tanpi(1/2) > >>> [1] NaN > >>> Warning message: > >>> In tanpi(1/2) : NaNs produced > >>> > >>> By redefining tanpi with sinpi and cospi, we can get closer: > >>> > >>> > tanpi <- function(x) sinpi(x) / cospi(x) > >>> > >>> > tanpi(c(0, 1/2, 1, 3/2, 2)) > >>> [1] 0 Inf 0 -Inf 0 > >>> > >>> Hans Werner > >>> > >>> ______________________________________________ > >>> R-devel@r-project.org mailing list > >>> https://stat.ethz.ch/mailman/listinfo/r-devel > >> > >> > > > > ______________________________________________ > > R-devel@r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-devel > > > > -- > Gregory (Greg) L. Snow Ph.D. > 538...@gmail.com > [[alternative HTML version deleted]] ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
