Please note that you need to report your platforms (as per the posting guide), as the C function starts

#elif defined HAVE___COSPI
double cospi(double x) {
    return __cospi(x);

And AFAICS the system versions on Solaris and OS X behave the same way as R's substitute.

On 01/12/2016 09:12, Martin Maechler wrote:
Martin Maechler <>
    on Thu, 1 Dec 2016 09:36:10 +0100 writes:

Ei-ji Nakama <>
    on Thu, 1 Dec 2016 14:39:55 +0900 writes:

    >> Hi,
    >> i try sin, cos, and tan.

    >>> sapply(c(cos,sin,tan),function(x,y)x(y),1.23e45*pi)
    >> [1] 0.5444181 0.8388140 1.5407532

    >> However, *pi results the following

    >>> sapply(c(cospi,sinpi,tanpi),function(x,y)x(y),1.23e45)
    >> [1] 1 0 0

    >> Please try whether the following becomes all right.

    > [..............................]

    > Yes, it does  -- the fix will be in all future versions of R.

oops.... not so quickly, Martin!

Of course, the results then coincide,  by sheer implementation.

*BUT* it is not at all clear which of the two results is better;
e.g., if you replace '1.23' by '1' in the above examples, the
result of the unchnaged  *pi() functions is 100% accurate,

 R> sapply(c(cos,sin,tan), function(Fn) Fn(1e45*pi))
 [1] -0.8847035 -0.4661541  0.5269043

is "garbage".  After all,  1e45 is an even integer and so, the
(2pi)-periodic functions should give the same as for 0  which
*is*  (1, 0, 0).

For such very large arguments, the results of all of sin() ,
cos() and tan()  are in some sense "random garbage" by
Such large numbers have zero information about the resolution modulo
[0, 2pi)  or (-pi, pi]  and hence any (non-trivial) periodic
function with such a "small" period can only return "random noise".

    > Thank you very much Ei-ji Nakama, for this valuable contribution
    > to make R better!

That is still true!  It raises the issue to all of us and will
improve the documentation at least!

At the moment, I'm not sure where we should go.
Of course, I could start experiments using my own 'Rmpfr'
package where I can (with increasing computational effort!) get
correct values (for increasingly larger arguments) but at the
moment, I don't see how this would help.


Brian D. Ripley,        
Emeritus Professor of Applied Statistics, University of Oxford

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