On Wed, Apr 29, 2009 at 10:18 AM, John H Palmieri <jhpalmier...@gmail.com> wrote: > > On Apr 29, 9:51 am, mark mcclure <mcmcc...@unca.edu> wrote: >> >> On the other hand, I'll happily go on record as saying that I find >> Wolfram's explanation of "Why You Do Not Usually Need to Know >> about Internals" personally offensive. You can read that >> here:http://reference.wolfram.com/mathematica/tutorial/WhyYouDoNotUsuallyN... >> >> The funny thing about that statement is that no one who believes >> it could possibly be inquisitive enough to be employed in a >> technical position at Wolfram in the first place. I honestly >> assume that virtually nobody there believes it. > > One interesting thing from this page, though: > > In[7]:= N[Sin[10^50], 20] > Out[7]= -0.78967... (I can't copy and paste from that page, but this > is how the number starts) > In[8] := Sin[10.^50] > Out[8] := 0.669369 > > Sage doesn't get the right answer here (assuming that -0.78967... is > the right answer): > > sage: sin(10^50).n > (10) > 0.74 > sage: sin(10^50).n > (20) > 0.82842 > sage: sin(10^50).n > (40) > -0.052373001636 > sage: sin(10^50).n > (80) > 0.90620599081868764998830 > sage: sin > (10.^50) > -0.480500143493759 >
The Sage implementation of numerical_approx currently (and correctly) simply does all the arithmetic in the expression tree using the given bits of precision for the leaf nodes, and by that definition the above output by Sage is correct. I thought that I had clearly documented this in the numerical_approx docstring, but I haven't. I would not be opposed to somebody rewriting numerical_approx to instead use interval arithmetic, and hence given a proven number of correct digits of precision of output, which would fix the above problem. This should be easy given how good Cwitty's RIF and CIF is now. william --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
