🚀 go-pugleaf

"Nick Maclaren" <nmm1@cus.cam.ac.uk> wrote in message
news:blbcjf$lrn$1@pegasus.csx.cam.ac.uk...
>
> In article <Zs2eb.157980$0v4.11847973@bgtnsc04-news.ops.worldnet.att.net>,
> "James Giles" <jamesgiles@worldnet.att.net> writes:
> |> Glen Herrmannsfeldt wrote:
> |> > "James Giles" <jamesgiles@worldnet.att.net> wrote in message
> |> > news:r%0eb.163529$3o3.11771639@bgtnsc05-news.ops.worldnet.att.net...

(snip)

> |> > Well, since truncating is systematic at puting in zeros, random bits
would,
> |> > on the average, be closer.
> |> >
> |> > The process of digitizing analog data, such as converting analog
audio into
> |> > digital form, works best with a process called dithering.  Random
noise of
> |> > approximately 1 LSB in amplitude is added before sampling.   The left
over
> |> > bits in registers might not be very random, though.   Using true
random
> |> > bits, one might even be able to sum into a single precision register
and get
> |> > good results!
> |>
> |> Or not.  The problem is that using "garbage bits" doesn't permit any
> |> useful or reliable analysis of the algorithms.  Clearing the bits does.
> |> Further, clearing the bits allows algorithmic work-arounds (like
> |> Kahan's summation).  Keeping "garbage bits" simply makes that
> |> inoperable.
>
> Yes, definitely.  Despite Kahan's analysis, there are very good
> reasons to want true probabilistic rounding.  Several of us have
> analysed that it has BETTER properties than nearest rounding (of
> any type) in some important operations, like vector summation.
> My limited experiments indicated that these benefits mean that it
> delivers comparable accuracy to nearest rounding on at least one
> of the analyses where the latter does well.
>
> But note that means TRUE probabilistic rounding - accept no
> imitations!

Not so long ago, someone came up with this statement from the standard:

>> Item (6) listed in Section 1.4 of the Fortran standard explicitly
>> states that the standard does not specify
>>
>>    (6)  The physical properties of the representation of quantities and
>>         the method of rounding, approximating, or computing numeric
>>         values on a particular processor.

I had tried to argue that at least the rounding would be expected to be
consistent (repeatable), but the discussion seems to say that it doesn't
need to be.   But yes, I agree that only true probabilistic rounding should
be used, if any is.

It seems that some processors now have a hardware random number generator
using an electronic noise source.  I don't know how fast it is, though.   It
would be interesting to see that work.

-- glen