R devel - Sep 2016 - Different results for tan(pi/2) and tanpi(1/2)

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

On Fri, Sep 9, 2016 at 12:24 PM, 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
>
>
>
?When I do a ?tanpi, I see the following:

     ?tanpi(0.5)? is ?NaN?.  Similarly for other inputs with fractional
     part ?0.5?.
?


?I don't know why this is, but apparently the function is working as
documented. Whether that is correct or not is not for me to say.?



-- 
Unix: Some say the learning curve is steep, but you only have to climb it
once. -- Karl Lehenbauer
Unicode: http://xkcd.com/1726/

Maranatha! <><
John McKown

	[[alternative HTML version deleted]]

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
>
	[[alternative HTML version deleted]]

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
>
>