Re: [PATCH] libstdc++: add uniform on sphere distribution

[Paolo Carlini <paolo dot carlini at oracle dot com>]

Hi,

On 07/13/2014 06:18 PM, Ulrich Drepper wrote:
> On Sun, Jul 13, 2014 at 12:07 PM, Paolo Carlini
> <paolo.carlini@oracle.com> wrote:
> > Sorry, I still don't get it. When operator() of x and y, two
> > uniform_on_sphere_distribution, call _M_n(__urng) and those _M_n have a
> > different state, the numbers produced are in general different.
> Correct.  But in the case of this distribution once you have the
> random numbers the remainder of the work is done by a fixed formula:
>
>     v = (N(0,1), ..., N(0,1))
>
>     result = v / ||v||_2
>
> That's it, nothing else to be done.
>
> If you have two calls of operator() of two different uniform_on_sphere
> objects and you pass to each an RNG object in exactly the same state
> you will get the same result.
I don't think so. It depends on the past of the two different 
uniform_on_sphere: each time each uniform_on_sphere calls _M_n(__urng) 
the state of *its own* _M_n changes, evolves from the initial state. For 
instance, you call it 4 times on one and 7 times on another. The states 
of the two _M_n are different, and from that point the next numbers will 
be different. This is exactly what happens when you call os << x and is 
>> y, no object is destroyed, no object is constructed, and x has 
called _M_n(__urng) 4 times, and y has called it 7 times. Your inserters 
and extractors are trivial. The next numbers will be different. Note 
that, if I understand the standard correctly, we are comparing the 
numbers *from that point on*, not the whole story, whatever that may 
mean. In other terms, I'm saying the sequence of numbers produced after 
the 4th number isn't in general the same sequence of numbers produced 
after the 7th number.

Paolo.