I can see ?. is biased and buggy, but many codes depend on this 'bug'. It
is ok to implement a better ?. but only as another new primitive if there
are enough user demand.

On Mon, Jul 20, 2020 at 12:22 AM Skip Cave <[email protected]> wrote:

> It's clear that the statistical properties of ?. are repeatable, but they
> are are
> significantly different than ?
>
> mean"1(?."0,:?)2^i.50
>
> 3.98766e12 1.46478e13
>
> mean"1(?."0,:?)2^i.50
>
> 3.98766e12 1.29535e13
>
> mean"1(?."0,:?)2^i.50
>
> 3.98766e12 1.67325e13
>
> mean"1(?."0,:?)2^i.50
>
> 3.98766e12 1.50923e13
>
> mean"1(?."0,:?)100#1e3
>
> 194 494.96
>
> mean"1(?."0,:?)100#1e3
>
> 194 538.78
>
> mean"1(?."0,:?)100#1e3
>
> 194 527.15
>
> mean"1(?."0,:?)100#1e3
>
> 194 513.06
>
> The issue is whether that is a problem that needs to be fixed or not:
>
>
> Skip Cave
> Cave Consulting LLC
>
>
> On Sun, Jul 19, 2020 at 11:02 AM Raul Miller <[email protected]>
> wrote:
>
> > Well... I think we can agree that if ?. were replaced with 0: that
> > that would not be random enough.
> >
> > So there has to be a better way of talking about this issue.
> >
> > If the current test suite is looking for hard coded results from ?. --
> > and I think it does -- then of course changing the ?. implementation
> > would require careful update of the test suite, and this would become
> > an ongoing future issue if the underlying implementation changed. So I
> > think that that level of effort is what you are talking about??
> >
> > Thanks,
> >
> > --
> > Raul
> >
> > On Sun, Jul 19, 2020 at 11:58 AM bill lam <[email protected]> wrote:
> > >
> > > Even ?. is not good, it won't change. Its purpose is to provide
> > repeatable
> > > random data for testing, it doesn't matter if it is not random enough.
> > >
> > > On Sun, Jul 19, 2020 at 11:41 PM Julian Fondren <
> > [email protected]>
> > > wrote:
> > >
> > > > On 2020-07-19 10:31, Brian Schott wrote:
> > > > > Yes, I see the problem you are describing better now.
> > > > > This behavior for powers of 2 is dissimilar with other power bases.
> > > > > It suggests a flaw in the algorithm for ?. .
> > > > >
> > > > >
> > > > >    ?.2^11
> > > > > 1826
> > > > >    ?.2^12
> > > > > 1826
> > > > >    ?.2^13
> > > > > 1826
> > > > > NB. compared to the following
> > > > >    ?.3^11
> > > > > 35532
> > > > >    ?.3^12
> > > > > 212679
> > > > >    ?.3^13
> > > > > 1275561
> > > >
> > > >     #@~."1 (?."0 ,: ?.) 2^i.20
> > > > 7 18
> > > >     #@~."1 (?."0 ,: ?.) 3^i.20
> > > > 13 20
> > > >
> > > > It's only not as obvious with powers of 3.
> > > >
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