# [Numpy-discussion] Random int64 and float64 numbers

Charles R Harris charlesr.harris at gmail.com
Thu Nov 5 23:49:12 EST 2009

```On Thu, Nov 5, 2009 at 9:14 PM, <josef.pktd at gmail.com> wrote:

> On Thu, Nov 5, 2009 at 10:42 PM, David Goldsmith
> <d.l.goldsmith at gmail.com> wrote:
> > 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"?
>
> 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
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