Maxima has bigfloats in which the exponent is an arbitrary size integer, so overflow requires you to fill up RAM with the exponent. The IEEE machine floats do something very specific that is death to "real number" representation, which is there are not enough bits. e.g. 64 bits can hardly be enough for all the reals. And then some of the configurations are not real numbers at all -- infinities, NaNs. Sage numbers presumably are not limited to 64 bits, and so some of the compromises forced on the IEEE 754 designers need not be part of the design. MPFR does some of this, but it too has limits e.g. cannot represent certain real numbers. Like pi, e, or (at least in binary) 1/3.
Much of the detailed description of operations in the IEEE754 standard is lost in some programming languages. I don't know about Python 3 or whatever Sage is using now. But NaNs are unordered, and in particular if x is a NaN, it is not equal to x. There is a partial calculus that allows for rational number-like objects including 1/0, -1/0, 0/0, 0/1, 0/(-1). Which I've written about. And implemented. It can be read into the Maxima part of Sage. RJF On Thursday, March 10, 2016 at 5:13:05 PM UTC-8, Thierry (sage-googlesucks@xxx) wrote: > > On Thu, Mar 10, 2016 at 11:34:00AM -0800, Fredrik Johansson wrote: > [...] > > The fact that Sage provides multiple implementations of real numbers > > with different pros and cons is a good thing. I think the case can be > > made for having an abstract RR (perhaps with another name) really > > representing the real numbers, and making the conceptual separation > > between real numbers (as a mathematical concept) and > > floating-point/interval/lazy/other approximations even stronger. My own > > biased opinion is also that interval arithmetic should be used and > > encouraged more in Sage... I would also like lazy real numbers to be > > more useful than they are currently, and overall it would be nice to > > have numerical functionality much better integrated with symbolic > > expressions (which is something that Mathematica does *extremely* well). > > I think we agree on that, see > http://trac.sagemath.org/ticket/17713#comment:3 > > Ciao, > Thierry > > > > > > > Fredrik > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sage-devel+...@googlegroups.com <javascript:>. > > To post to this group, send email to sage-...@googlegroups.com > <javascript:>. > > Visit this group at https://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/d/optout. > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
