[Numpy-discussion] Random int64 and float64 numbers
Charles R Harris
Thu Nov 5 17:36:40 CST 2009
On Thu, Nov 5, 2009 at 4:26 PM, David Warde-Farley <firstname.lastname@example.org>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.
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