R devel - Dec 2016 - Different results for cos,sin,tan and cospi,sinpi,tanpi

>>>>> Martin Maechler <maechler at stat.math.ethz.ch>
>>>>>     on Thu, 1 Dec 2016 09:36:10 +0100 writes:
>>>>> Ei-ji Nakama <nakama at ki.rim.or.jp>
>>>>>     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,
whereas

 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
necessity:
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.

Martin

    > Martin Maechler,
    > ETH Zurich


    >> -- 
    >> Best Regards,
    >> --
    >> Eiji NAKAMA <nakama (a) ki.rim.or.jp>
    >> "\u4e2d\u9593\u6804\u6cbb"  <nakama (a)
ki.rim.or.jp>

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

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

#ifdef HAVE_COSPI
#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 <maechler at stat.math.ethz.ch>
>>>>>>     on Thu, 1 Dec 2016 09:36:10 +0100 writes:
>
>>>>>> Ei-ji Nakama <nakama at ki.rim.or.jp>
>>>>>>     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,
> whereas
>
>  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
> necessity:
> 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.
>
> Martin

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Emeritus Professor of Applied Statistics, University of Oxford

hi,

my environment...
> sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 8 (jessie)

locale:
 [1] LC_CTYPE=ja_JP.UTF-8       LC_NUMERIC=C
 [3] LC_TIME=ja_JP.UTF-8        LC_COLLATE=ja_JP.UTF-8
 [5] LC_MONETARY=ja_JP.UTF-8    LC_MESSAGES=ja_JP.UTF-8
 [7] LC_PAPER=ja_JP.UTF-8       LC_NAME=C
 [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=ja_JP.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

It's not a very good example...

f0<-function(x,y)exp(complex(real=x,imag=y))
f1<-function(x,y)complex(real=exp(1)^x*cos(y),imag=exp(1)^x*sin(y))
f2<-function(x,y)complex(real=exp(1)^x*cospi(y/pi),imag=exp(1)^x*sinpi(y/pi))

f0(700,1.23)
f1(700,1.23)
f2(700,1.23)

f0(700,1.23e23)
f1(700,1.23e23)
f2(700,1.23e23)

Garbage number is required.

Thank you!

2016-12-01 18:31 GMT+09:00 Prof Brian Ripley <ripley at
stats.ox.ac.uk>:
> Please note that you need to report your platforms (as per the posting
> guide), as the C function starts
>
> #ifdef HAVE_COSPI
> #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 <maechler at
stat.math.ethz.ch>
>>>>>>>     on Thu, 1 Dec 2016 09:36:10 +0100 writes:
>>
>>
>>>>>>> Ei-ji Nakama <nakama at ki.rim.or.jp>
>>>>>>>     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,
>> whereas
>>
>>  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
>> necessity:
>> 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.
>>
>> Martin
>
>
>
> --
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Emeritus Professor of Applied Statistics, University of Oxford


-- 
Best Regards,
--
Eiji NAKAMA <nakama (a) ki.rim.or.jp>
"\u4e2d\u9593\u6804\u6cbb"  <nakama (a) ki.rim.or.jp>