### [Rd] 1/tan(-0) != 1/tan(0)

Testing the code that Morten Welinder suggested for improving extreme tail behavior of qcauchy(), I found what you can read in the subject. namely that the tan() + floating-point implementation on all four different versions of Redhat linux, I have access to on i686 and amd64 architectures, 1/tan(c(-0,0)) gives -Inf Inf and of course, that can well be considered a feature, since after all, the tan() function does jump from -Inf to +Inf at 0. I was still surprised that this even happens on the R level, and I wonder if this distinction of -0 and 0 shouldn't be mentioned in some place(s) of the R documentation. For the real problem, the R source (in C), It's simple to work around the fact that qcauchy(0, log=TRUE) for Morten's code proposal gives -Inf instead of +Inf. Martin MM == Martin Maechler [EMAIL PROTECTED] on Wed, 1 Jun 2005 08:57:18 +0200 (CEST) writes: Morten == Morten Welinder [EMAIL PROTECTED] on Fri, 27 May 2005 20:24:36 +0200 (CEST) writes: . Morten Now that pcauchy has been fixed, it is becoming Morten clear that qcauchy suffers from the same problems. Morten Morten qcauchy(pcauchy(1e100,0,1,FALSE,TRUE),0,1,FALSE,TRUE) Morten should yield 1e100 back, but I get 1.633178e+16. Morten The code below does much better. Notes: Morten 1. p need not be finite. -Inf is ok in the log_p Morten case and R_Q_P01_check already checks things. MM yes Morten 2. No need to disallow scale=0 and infinite Morten location. MM yes Morten 3. The code below uses isnan and finite directly. Morten It needs to be adapted to the R way of doing that. MM I've done this, and started testing the new code; a version will MM be put into the next version of R. MM Thank you for the suggestions. double qcauchy (double p, double location, double scale, int lower_tail, int log_p) { if (isnan(p) || isnan(location) || isnan(scale)) return p + location + scale; R_Q_P01_check(p); if (scale 0 || !finite(scale)) ML_ERR_return_NAN; if (log_p) { if (p -1) lower_tail = !lower_tail, p = -expm1 (p); else p = exp (p); } if (lower_tail) scale = -scale; return location + scale / tan(M_PI * p); } __ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-devel

### RE: [Rd] 1/tan(-0) != 1/tan(0)

On 01-Jun-05 Martin Maechler wrote: Testing the code that Morten Welinder suggested for improving extreme tail behavior of qcauchy(), I found what you can read in the subject. namely that the tan() + floating-point implementation on all four different versions of Redhat linux, I have access to on i686 and amd64 architectures, 1/tan(c(-0,0)) gives -Inf Inf and of course, that can well be considered a feature, since after all, the tan() function does jump from -Inf to +Inf at 0. I was still surprised that this even happens on the R level, and I wonder if this distinction of -0 and 0 shouldn't be mentioned in some place(s) of the R documentation. Indeed I would myself consider this a very useful feature! However, a query: Clearly from the above (ahich I can reproduce too), tan() can distinguish between -0 and +0, and return different results (otherwise 1/tan() would not return different results). But how can the user tell the difference between +0 amnd -0? I've tried the following: sign(c(-0,0)) [1] 0 0 sign(tan(c(-0,0))) [1] 0 0 sign(1/tan(c(-0,0))) [1] -1 1 so sign() is not going to tell us. Is there a function which can? Short of wrting one's own: sign0 - function(x){ if(abs(x)0) stop(For this test x must be +0 or -0) return(sign(1/tan(x))) } ;) Best wishes, Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 094 0861 Date: 01-Jun-05 Time: 10:50:06 -- XFMail -- __ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-devel

### Re: [Rd] 1/tan(-0) != 1/tan(0)

On Jun 1, 2005, at 5:50 AM, (Ted Harding) wrote: However, a query: Clearly from the above (ahich I can reproduce too), tan() can distinguish between -0 and +0, and return different results (otherwise 1/tan() would not return different results). But how can the user tell the difference between +0 amnd -0? That's indeed a good question - by definition (-0)==(+0) is true, -00 is false and signum of both -0 and 0 is 0. I don't see an obvious way of distinguishing them at R level. Besides computational ways (like the 1/tan trick) the only (very ugly) way coming to my mind is something like: a==0 substr(sprintf(%f,a),1,1)==- Note that print doesn't display the sign, only printf does. At C level it's better - you can use the signbit() function/macro there. Any other ideas? Cheers, Simon __ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-devel

### Re: [Rd] 1/tan(-0) != 1/tan(0)

On 6/1/05, Simon Urbanek [EMAIL PROTECTED] wrote: On Jun 1, 2005, at 5:50 AM, (Ted Harding) wrote: However, a query: Clearly from the above (ahich I can reproduce too), tan() can distinguish between -0 and +0, and return different results (otherwise 1/tan() would not return different results). But how can the user tell the difference between +0 amnd -0? That's indeed a good question - by definition (-0)==(+0) is true, -00 is false and signum of both -0 and 0 is 0. I don't see an obvious way of distinguishing them at R level. Besides computational ways (like the 1/tan trick) the only (very ugly) way coming to my mind is something like: a==0 substr(sprintf(%f,a),1,1)==- Note that print doesn't display the sign, only printf does. On my XP machine running R 2.1.0 patched 2005-05-14 sprintf(%f,-0) [1] 0.00 does not print the sign. however, the tan trick can be done without tan using just division: R sign0 - function(x) if (x != 0) stop(x not zero) else sign(1/x) R sign0(0) [1] 1 R sign0(-0) [1] -1 __ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-devel