Re: Short Vectors Versus Long Vectors

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.