Re: [Rd] Different results for cos,sin,tan and cospi,sinpi,tanpi
hello, i read this pdf (http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1950.pdf) i think ... x to be integer only(more accurate value). following test code and patch. ### F.10.1.12 The cospi functions ## cospi(+-0) : 1, 1 cospi(c(+0,-0)) ## cospi(n + 1/2) : all 0 cospi((-4:4)+.5) ## cospi(+-Inf): NaN cospi(c(+Inf,-Inf)) ## cospi(n) cospi((-4:4)) ### F.10.1.13 The sinpi functions ## sinpi(+-0) :+0,-0 sprintf("%a",sinpi(c(+0,-0))) ## sinpi(n + 1/2) : all 0 sinpi((-4:4)) ## sinpi(+-Inf): NaN sinpi(c(+Inf,-Inf)) ## sinpi(n):1 -1 1 -1 1 -1 1 -1 1 sinpi((-4:4+.5)) ### F.10.1.14 The tanpi functions ## tanpi(+-0) :+0,-0 sprintf("%a",tanpi(c(+0,-0))) ## tanpi(pos even and neg odd) :+0 sprintf("%a",tanpi(c(-3,-1,2,4))) ## tanpi(pos odd and ned even) :-0 sprintf("%a",tanpi(c(-4,-2,1,3))) ## tanpi(n+1/2) n = even:+Inf tanpi(c(1:3*2)+.5) tanpi(c(1:3*2)*-1+.5) ## tanpi(n+1/2) n = odd :-Inf tanpi(c(1:3*2+1)+.5) tanpi(c(1:3*2+1)*-1+.5) ## tanpi(+-Inf) :NaN NaN tanpi(c(+Inf,-Inf)) ## no integer sinpi(1.23e23) # 0.4652223 cospi(1.23e23) # 0.8851939 tanpi(1.23e23) # 0.5255597 --- R-3.3.2.orig/src/nmath/cospi.c2016-09-15 07:15:31.0 +0900 +++ R-3.3.2/src/nmath/cospi.c2016-12-05 21:29:20.764593514 +0900 @@ -21,13 +21,10 @@ The __cospi etc variants are from macOS (and perhaps other BSD-based systems). */ -#ifdef HAVE_COSPI -#elif defined HAVE___COSPI -double cospi(double x) { -return __cospi(x); -} + +#if defined(__STDC_WANT_IEC_60559_FUNCS_EXT__) && __STDC_WANT_IEC_60559_FUNCS_EXT__ >= 201506L +/* use standard cospi */ #else -// cos(pi * x) -- exact when x = k/2 for all integer k double cospi(double x) { #ifdef IEEE_754 /* NaNs propagated correctly */ @@ -35,7 +32,11 @@ #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.; @@ -44,11 +45,8 @@ } #endif -#ifdef HAVE_SINPI -#elif defined HAVE___SINPI -double sinpi(double x) { -return __sinpi(x); -} +#if defined(__STDC_WANT_IEC_60559_FUNCS_EXT__) && __STDC_WANT_IEC_60559_FUNCS_EXT__ >= 201506L +/* use standard cospi */ #else // sin(pi * x) -- exact when x = k/2 for all integer k double sinpi(double x) { @@ -57,6 +55,12 @@ #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); + +if( x == 0 || x == -0 ) +return(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.; @@ -69,26 +73,50 @@ #endif // tan(pi * x) -- exact when x = k/2 for all integer k -#if defined(HAVE_TANPI) || defined(HAVE___TANPI) +#if defined(__STDC_WANT_IEC_60559_FUNCS_EXT__) && __STDC_WANT_IEC_60559_FUNCS_EXT__ >= 201506L +/* use standard cospi */ // for use in arithmetic.c, half-values documented to give NaN -double Rtanpi(double x) #else double tanpi(double x) -#endif { + int _sig=0; + int _even=0; + int _odd=0; + int _int=0; #ifdef IEEE_754 if (ISNAN(x)) return x; #endif if(!R_FINITE(x)) ML_ERR_return_NAN; -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--; -return (x == 0.) ? 0. : ((x == 0.5) ? ML_NAN : tan(M_PI * x)); +if (( x > 9007199254740991 )|| /* 2^53-1 */ +( x < -9007199254740991 ) ) /* -2^53-1 */ +return tan(M_PI * x); + +if( x == 0. || x == -0. ) +return(x); +if(x>0) _sig = 1; +if(x<0) _sig =-1; + +x = fmod(x, 2.); +if(( x == 0.0 )||( x == -0.0)){ _even = 1; _int=1;} +if(( x == 0.5 )||( x == -0.5)) _even = 1; +if(( x == 1.0 )||( x == -1.0)){ _odd = 1; _int=1;} +if(( x == 1.5 )||( x == -1.5)) _odd = 1; +if(_int){ + if( _sig == 1 && _even ) return( 0.); + if( _sig == -1 && _odd ) return( 0.); + if( _sig == 1 && _odd ) return( -0.); + if( _sig == -1 && _even ) return( -0.); +} +if(_even){ +if ( x == 0.5 ) return(R_PosInf); +if ( x == -0.5 ) return(R_NegInf); +}else if (_odd){ +if ( x == 1.5 ) return(R_NegInf); +if ( x == -1.5 ) return(R_PosInf); +} +// otherwise +return tan(M_PI * x); } -#if !defined(HAVE_TANPI) && defined(HAVE___TANPI) -double tanpi(double x) { -return __tanpi(x); -} #endif 2016-12-01 18:45 GMT+09:00 Ei-ji Nakama
Re: [Rd] Different results for cos,sin,tan and cospi,sinpi,tanpi
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-8LC_COLLATE=ja_JP.UTF-8 [5] LC_MONETARY=ja_JP.UTF-8LC_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: > 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 >>> 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, >> 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, rip...@stats.ox.ac.uk > Emeritus Professor of Applied Statistics, University of Oxford -- Best Regards, -- Eiji NAKAMA "\u4e2d\u9593\u6804\u6cbb" __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
Re: [Rd] 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 Maechleron 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, 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, rip...@stats.ox.ac.uk Emeritus Professor of Applied Statistics, University of Oxford __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
Re: [Rd] Different results for cos,sin,tan and cospi,sinpi,tanpi
> 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, 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" > __ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
Re: [Rd] Different results for cos,sin,tan and cospi,sinpi,tanpi
> 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. 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" __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
[Rd] 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 07:15:31.0 +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" __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel