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Date: Sat, 09 Aug 2014 16:55:00 -0000
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To: libstdc++@gcc.gnu.org, Ulrich Drepper <drepper@gmail.com>
Cc: Jonathan Wakely <jwakely@redhat.com>, GCC Patches <gcc-patches@gcc.gnu.org>
Subject: Re: [PATCH] libstdc++: add uniform on sphere distribution
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On 08/09/2014 11:33 AM, Marc Glisse wrote:
> On Sat, 9 Aug 2014, Ulrich Drepper wrote:
>
>>> If you are going to specialize for dim 2, I imagine you won't be 
>>> computing
>>> normal distributions, you will only generate a point uniformy in a 
>>> square
>>> and reject it if it is not in the ball? (interestingly enough this 
>>> is used
>>> as a subroutine by the implementation of normal_distribution)
>>
>> We need to be *on* the circle, not inside.
>
> Yes, you still need the normalization step (divide by the norm). It 
> works whether you start from a uniform distribution in the disk or 
> from a Gaussian in the plane, but the first one is easier to generate 
> (generate points in a square until you get one in the disk). When the 
> dimension becomes higher, the probability that a point in the cube 
> actually belongs to the ball decreases, and it becomes cheaper to use 
> a Gaussian.
>
If we pull in the implementation of normal you will just be able to use 
the two values that normal computes on the first, (and third, ...) calls 
without doing two calls.  That and hypot would be a real win.