On Thu, Nov 5, 2009 at 9:14 PM, <josef.p...@gmail.com> wrote: > On Thu, Nov 5, 2009 at 10:42 PM, David Goldsmith > <d.l.goldsm...@gmail.com> wrote: > > 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"? > > Since according to my calculations there are only about > > >>> 4* 10**17 * 308 > 123200000000000000000L > > double-precision floats, there are huge gaps in the floating point > representation of the real line. >
2**64 minus some flags for nans and such. Chuck
_______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
