[Numpy-discussion] Random int64 and float64 numbers

[David Cournapeau]

On Fri, Nov 6, 2009 at 6:54 AM, David Goldsmith <d.l.goldsmith at gmail.com> 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); and are such decimal mantissae uniformly distributed

They are definitely not uniformly distributed: that's why two numbers
are close around 1 when they have only a few EPS difference, but
around 1e100, you have to add quite a few EPS to even get a different
number at all.

That may be my audio processing background, but I like to think about
float as numbers which have the same relative precision at any "level"
- a kind of dB scale. If you want numbers with a fixed number of
decimals, you need a fixed point representation.

David