That should say arbitrary exponents, not arbitrary precision. On May 3, 2:36 am, Bill Hart <goodwillh...@googlemail.com> wrote: > 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 athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org
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