On Thu, Nov 5, 2009 at 8:07 PM, Anne Archibald <peridot.face...@gmail.com>wrote:
> 2009/11/5 David Goldsmith <d.l.goldsm...@gmail.com>: > > On Thu, Nov 5, 2009 at 3:26 PM, David Warde-Farley <d...@cs.toronto.edu> > > wrote: > >> > >> On 5-Nov-09, at 4:54 PM, David Goldsmith wrote: > >> > >> > Interesting thread, which leaves me wondering two things: is it > >> > documented > >> > somewhere (e.g., at the IEEE site) precisely how many *decimal* > >> > mantissae > >> > are representable using the 64-bit IEEE standard for float > >> > representation > >> > (if that makes sense); > >> > >> IEEE-754 says nothing about decimal representations aside from how to > >> round when converting to and from strings. You have to provide/accept > >> *at least* 9 decimal digits in the significand for single-precision > >> and 17 for double-precision (section 5.6). AFAIK implementations will > >> vary in how they handle cases where a binary significand would yield > >> more digits than that. > > > > I was actually more interested in the opposite situation, where the > decimal > > representation (which is what a user would most likely provide) doesn't > have > > a finite binary expansion: what happens then, something analogous to the > > decimal "rule of fives"? > > If you interpret "0.1" as 1/10, then this is a very general > floating-point issue: how you you round off numbers you can't > represent exactly? The usual answer (leaving aside internal > extended-precision shenanigans) is to round, with the rule that when > you're exactly between two floating-point numbers you round to the one > that's even, rather than always up or always down (the numerical > analysis wizards tell us that this is more numerically stable). > More numerically stable, or simply unbiased, since half the time your rounding up, and the other half rounding down (that's the rationale as it was explained to me). DG > > Anne > > > DG > > > > _______________________________________________ > > NumPy-Discussion mailing list > > NumPy-Discussion@scipy.org > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion >
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