On Thu, Nov 5, 2009 at 6:36 PM, Charles R Harris <charlesr.har...@gmail.com> wrote: > > > On Thu, Nov 5, 2009 at 4:26 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 believe that was the argument for the extended precision formats. The > givien number of decimal digits is sufficient to recover the same float that > produced them if a slightly higher precision is used in the conversion. > > Chuck
>From the discussion for the floating point representation, it seems that a uniform random number generator would have a very coarse grid in the range for example -1e30 to +1e30 compared to interval -0.5,0.5. How many points can be represented by a float in [-0.5,0.5] compared to [1e30, 1e30+1.]? If I interpret this correctly, then there are as many floating point numbers in [0,1] as in [1,inf), or am I misinterpreting this. So how does a PRNG handle a huge interval of uniform numbers? Josef > > > _______________________________________________ > 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