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From: mitchalsup@aol.com (MitchAlsup1)
Newsgroups: comp.arch
Subject: Re: Short Vectors Versus Long Vectors
Date: Thu, 2 May 2024 20:10:35 +0000
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Thomas Koenig wrote:

> Terje Mathisen <terje.mathisen@tmsw.no> schrieb:
>> Thomas Koenig wrote:
>>> MitchAlsup1 <mitchalsup@aol.com> schrieb:
>>> 
>>>> Then contemplate for an instant that one would want SIMD instructions
for
>>>> Complex numbers and Hamiltonian Quaterions......
>>> 
>>> Quaternions would be a bit over the top, I tink.  Complex
>>> multiplication... implementing (e,f) = (a*c-b*d,a*d+b*c) is
>>> 
>>>          fmul    Rt1,Rc,Rb
>>>          fmac    Re,Rd,Ra,Rt1
>>> 
>>>          fmul    Rt2,Rd,Rb
>>>          fmac    Rf,Rc,Ra,-Rt2
>>> 
>>> So, you'd need both operands on both lanes.  Not very SIMD-friendly,
>>> I would assume, but (probably) not impossible, either.
>>> 
>> If you have the four operands spread across two SIMD registers, so 
>> (Re,Im) in each, then you need an initial pair of permutes to make 
>> flipped copies before you can start the fmul/fmac ops, right?
>>
>> This is exactly the kind of code where Mitch's transparent vector 
>> processing would be very nice to have.

> I'm actually not sure how that would help.  Could you elaborate?


VVM synthesizes SIMD (lanes) and strip-mining (Cray-like vectors) while
processing SCALAR code. So, as long as the compiler knows which operands
are participating, almost any amount of <strange> Complexity drops out
for free -- including things like Quaternions.

Physicists like quaternions because it means they don't have to worry
about
whether to add or subtract, the {i,j,k} does it for them. Complex is OK
for
flat spaces but when one is dealing with non Cartesian coordinates (like 
within the radius of the proton) other effects makes quaternions a better 
path.