This thread is about multiple precision floating point arithmetic. What have machine floats got to do with it?
I'm using mpfr, which is what Sage uses. It has guaranteed rounding for *arbitrary precision* floats with essentially arbitrary precision exponents (there is a limit of course). There's no need to even think about what happens when you switch from machine doubles to multiple precision, because the writers of the mpfr library already thought it through already. Their mpfr_t type just works. Bill. On May 3, 12:06 am, rjf <fate...@gmail.com> wrote: > On May 2, 9:02 am, Bill Hart <goodwillh...@googlemail.com> wrote: > > > On May 2, 4:14 pm, rjf <fate...@gmail.com> wrote: > > > > I repeat, > > > > The interesting cases are obvious those which are not covered. > > > Sorry, I don't know what you mean. Are you saying that by definition > > they are interesting because they are not covered by Joris' algorithm, > > whatever they may be? > > I haven't looked at Joris' algorithm, and if all you are doing is > copying > what he has done, that might be better than making up something to do > something that you haven't defined. I assumed Joris defined what > he is doing. > > > > > > > > > > > > I don't know what your fix is, nor do I especially care, but I gather > > > that, now, at least your "stable" word is meant to indicate something > > > like a small bound in the maximum over all coefficients of the > > > difference in relative error between the true result and the computed > > > result. > > > That sounds reasonable as a definition to me. However it isn't > > precisely the measure Joris defines. > > > > I have no reason to believe this is an especially relevant measure, > > > since some coefficients (especially the first and the last) are > > > probably far more important and, incidentally, far easier to compute. > > > > Here are some more cases. > ... snip.. > > > Here is another > > > > p=1.7976931348623157E308; > > > q= 10*x > > > > What do you do when the coefficients overflow? > > > I actually don't understand what you mean. Why would there be an > > overflow? > > there would be an overflow if you are using machine floating point > numbers, > since p is approximately the largest double-float, and 10*p cannot be > represented > in a machine double-float. > > I'm missing something important here. I'm using floating > > > point and the exponents can be 64 bits or something like that. There > > should be no overflow. > > Really? So you are not using IEEE double-floats? > > What, then, do you do if the number exceeds whatever bounds you have > for your floats? > > ... snip... > > In fact, what does Sage do? Probably you can't say, because it > doesn't do the same thing > in various circumstances. For example, you could cause a floating > point overflow in the > midst of some computation with Maxima. > In that case it might depend on which Lisp that Maxima was running in. > Or in what operating system, or what hardware. > > And if the overflow occurred somewhere else, perhaps in Python or C, > maybe something > yet different. > > RJF > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
