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

Greg Snow 538280 at gmail.com
Fri Sep 9 21:58:31 CEST 2016

```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 <hwborchers at 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 <wdunlap at 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 <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
>>>
>>> ______________________________________________
>>> R-devel at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>>
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

--
Gregory (Greg) L. Snow Ph.D.
538280 at gmail.com

```