Hello everyone
On 1 Sep 2007, at 01:39, Duncan Murdoch wrote: > The IEEE floating point standard allows for negative zero, but it's > hard > to know that you have one in R. One reliable test is to take the > reciprocal. For example, > >> y <- 0 >> 1/y > [1] Inf >> y <- -y >> 1/y > [1] -Inf > > The other day I came across one in complex numbers, and it took me a > while to figure out that negative zero was what was happening: > >> x <- complex(real = -1) >> x > [1] -1+0i >> 1/x > [1] -1+0i >> x^(1/3) > [1] 0.5+0.8660254i >> (1/x)^(1/3) > [1] 0.5-0.8660254i > > (The imaginary part of 1/x is negative zero.) > > As a Friday question: are there other ways to create and detect > negative zero in R? > > And another somewhat more serious question: is the behaviour of > negative zero consistent across platforms? (The calculations above > were > done in Windows in R-devel.) > I have been pondering branch cuts and branch points for some functions which I am implementing. In this area, it is very important to know whether one has +0 or -0. Take the log() function, where it is sometimes very important to know whether one is just above the imaginary axis or just below it: (i). Small y > y <- 1e-100 > log(-1 + 1i*y) [1] 0+3.141593i > y <- -y > log(-1 + 1i*y) [1] 0-3.141593i (ii) Zero y. > y <- 0 > log(-1 + 1i*y) [1] 0+3.141593i > y <- -y > log(-1 + 1i*y) [1] 0+3.141593i > [ie small imaginary jumps have a discontinuity, infinitesimal jumps don't]. This behaviour is undesirable (IMO): one would like log (-1+0i) to be different from log(-1-0i). Tony Plate's example shows that even though y<- 0 ; identical(y, -y) is TRUE, one has identical(1/ y, 1/(-y)) is FALSE, so the sign is not discarded. My complex function does have a branch cut that follows a portion of the negative real axis but the other cuts follow absurdly complicated implicit equations. At this point one needs the IEEE requirement that x=x == +0 [ie not -0] for any real x; one then finds that (s-t) and -(t-s) are numerically equal but not necessarily indistinguishable. One of my earlier questions involved branch cuts for the inverse trig functions but (IIRC) the patch I supplied only tested for the imaginary part being >0; would it be possible to include information about signed zero in these or other functions? > Duncan Murdoch > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel -- Robin Hankin Uncertainty Analyst and Neutral Theorist, National Oceanography Centre, Southampton European Way, Southampton SO14 3ZH, UK tel 023-8059-7743 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
