[Rd] Speeding up squaring of vectors

[Radford Neal]

I see that some of the speed patches that I posted have been
incorporated into the current development version (eg, my patch-for,
patch-evalList, and patch-vec-arith).

My patch for speeding up x^2 has been addressed in an inadvisable way,
however.  This was a simple addition of four lines of code that speeds
up squaring of real vectors by a factor of about six (for vectors of
length 10000), by just converting x^2 to x*x.  Modifications in the
current development version (r52936 and r52937) attempt to address
this issue in a different way, but they produce a smaller speedup. My
modification is about 2.6 faster than the current development version
(on an Intel/Linux system).  Similarly, in the current development
version, x*x is still about 2.6 times faster than x^2.  Furthermore,
the modification in the current development version slows down
exponentiation by 0.5 (square roots) by about 4%.

I think there's no reason not to just use my patch.  One could also
put in a similar modification to speed up squaring of integer vectors,
but I think that is a much less common operation than squaring of real
vectors, which arises all the time when computing squared residuals,
squared Euclidean distances, etc.