[Numpy-discussion] Random int64 and float64 numbers

David Goldsmith d.l.goldsmith at gmail.com
Thu Nov 5 22:42:51 EST 2009

On Thu, Nov 5, 2009 at 3:26 PM, David Warde-Farley <dwf at 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"?

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