On 23-nov-10, at 10:20, tn wrote:
bearophile Wrote:
Don:
Since the probability of actually generating a
zero is 1e-4000, it shouldn't affect the speed at all <g>.
If bits in double have the same probability then I think there is a
much higher probability to hit a zero, about 1 in 2^^63, and I'm
not counting NaNs (but it's low enough to not change the substance
of what you have said).
For uniform distribution different bit combinations should have
different probabilities because floating point numbers have more
representable values close to zero. So for doubles the probability
should be about 1e-300 and for reals about 1e-4900.
But because uniform by default seems to use a 32 bit integer random
number generator, the probability is actually 2^^-32. And that is
actually verified: I generated 10 * 2^^32 samples of
uniform!"[]"(0.0, 1.0) and got 16 zeros which is close enough to
expected 10.
Of course 2^^-32 is still small enough to have no performance
penalty in practise.
-- tn
that is the reason I used a better generation algorithm in blip (and
tango) that guarantees the correct distribution, at the cost of being
slightly more costly, but then the basic generator is cheaper, and if
one needs maximum speed one can even use a cheaper source (from the
CMWC family) that still seems to pass all statistical tests.
The way I use to generate uniform numbers was shown to be better (and
detectably so) in the case of floats, when looking at the tails of
normal and other distributions generated from uniform numbers.
This is very relevant in some cases (for example is you are interested
in the probability of catastrophic events).
Fawzi
