[r-t] Delta-based transposition representation

[Alan Burlison]

On 09/06/2016 19:31, Don Morrison wrote:

> I'm sorry, but unless I am misconstruing what "reversing the signs" means,
> I don't think this is true at all.

You are right, when I actually went and looked at the code I'd written 
it didn't do that at all to generate the inverse. Oops ;-) The other 
points are I believe valid, though.

>> I haven't seen changes described this way anywhere else which
>> puzzles me a bit, because to me it's the blindingly obvious way of
>> doing it, rather than the position-based notation I've seen used
>> elsewhere.
>
> I can see it may be a slightly more convenient representation when drawing
> bluelines, but I'm not seeing any particular reason for generally
> preferring it over the representation that keeps changes and rows
> represented in the same way.

I'm not sure why having a representation that looks identical for two 
different semantics is considered to be a bonus, but that's just me.

> It's a trivially easy, linear time (that is, proportional to the
> stage) transformation from one representation to the other, so it
> seems unlikely it offers any big performance improvement for any
> operations you might want to perform. In fact, I suspect that on
> many underlying hardware architectures it might be slightly slower at
> the permute-a-row operation since you need to do some explicit
> arithmetic before dereferencing the element of the row -- I'm not
> sure about that, though, and such minuscule performance issues are
> rarely worth worrying about anyway.

Yes, I didn't mention performance at all, I wasn't concerned with that 
aspect.

> Like so many things in ringing and in life I suspect it all just
> comes down to your personal taste and what you find the most
> congenial representation for the code you're writing.

Agreed, purely personally I believe the code is simpler and easier to 
reason about if you use deltas. Of course both approaches are equally 
valid but I hadn't seen the 'delta' approach anywhere else and was 
wondering if there was any particular reason why, other than common 
practice and convention. The question was "Am I missing something 
obvious?" not "The conventional way is deficient".

-- 
Alan Burlison
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