Different results for cos,sin,tan and cospi,sinpi,tanpi

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Different results for cos,sin,tan and cospi,sinpi,tanpi

 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. diff -ruN R-3.3.2.orig/src/nmath/cospi.c R-3.3.2/src/nmath/cospi.c --- R-3.3.2.orig/src/nmath/cospi.c      2016-09-15 07:15:31.000000000 +0900 +++ R-3.3.2/src/nmath/cospi.c   2016-12-01 13:54:38.863357149 +0900 @@ -35,7 +35,11 @@  #endif      if(!R_FINITE(x)) ML_ERR_return_NAN; -    x = fmod(fabs(x), 2.);// cos() symmetric; cos(pi(x + 2k)) == cos(pi x) for all integer k +    x = fabs(x); +    if ( x > 9007199254740991 ) /* 2^53-1 */ +        return cos(M_PI * x); + +    x = fmod(x, 2.);// cos() symmetric; cos(pi(x + 2k)) == cos(pi x) for all integer k      if(fmod(x, 1.) == 0.5) return 0.;      if( x == 1.)       return -1.;      if( x == 0.)       return  1.; @@ -57,6 +61,9 @@  #endif      if(!R_FINITE(x)) ML_ERR_return_NAN; +    if (( x >  9007199254740991 )||  /*  2^53-1 */ +        ( x < -9007199254740991 )  ) /* -2^53-1 */ +        return sin(M_PI * x);      x = fmod(x, 2.); // sin(pi(x + 2k)) == sin(pi x)  for all integer k      // map (-2,2) --> (-1,1] :      if(x <= -1) x += 2.; else if (x > 1.) x -= 2.; @@ -81,6 +88,10 @@  #endif      if(!R_FINITE(x)) ML_ERR_return_NAN; +    if (( x >  9007199254740991 )||  /*  2^53-1 */ +        ( x < -9007199254740991 )  ) /* -2^53-1 */ +        return tan(M_PI * x); +      x = fmod(x, 1.); // tan(pi(x + k)) == tan(pi x)  for all integer k      // map (-1,1) --> (-1/2, 1/2] :      if(x <= -0.5) x++; else if(x > 0.5) x--; -- Best Regards, -- Eiji NAKAMA "\u4e2d\u9593\u6804\u6cbb"   ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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Re: Different results for cos,sin,tan and cospi,sinpi,tanpi

 >>>>> Ei-ji Nakama <[hidden email]> >>>>>     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. Thank you very much Ei-ji Nakama, for this valuable contribution to make R better! Martin Maechler, ETH Zurich     > --     > Best Regards,     > --     > Eiji NAKAMA     > "\u4e2d\u9593\u6804\u6cbb"   ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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Re: Different results for cos,sin,tan and cospi,sinpi,tanpi

 >>>>> Martin Maechler <[hidden email]> >>>>>     on Thu, 1 Dec 2016 09:36:10 +0100 writes: >>>>> Ei-ji Nakama <[hidden email]> >>>>>     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     >> "\u4e2d\u9593\u6804\u6cbb"       > ______________________________________________     > [hidden email] mailing list     > https://stat.ethz.ch/mailman/listinfo/r-devel______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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Re: Different results for cos,sin,tan and cospi,sinpi,tanpi

 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 <[hidden email]> >>>>>>     on Thu, 1 Dec 2016 09:36:10 +0100 writes: > >>>>>> Ei-ji Nakama <[hidden email]> >>>>>>     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,                  [hidden email] Emeritus Professor of Applied Statistics, University of Oxford ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel