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 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
