[Rd] Different results for tan(pi/2) and tanpi(1/2)

[William Dunlap]

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 <hwborchers at 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
>
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