Copy the pattern using exponentially increasing block sizes, using
the already-copied data as the source, yielding a logarithmic number
of memcpy()s, instead of linear.  The block size is not increased
indefinitely, as to not saturate the cache, so for large copies, the
number of memcpy()s is still linear, but using a big-enough block
size as to make it irrelevant.

I actually had a benchmark for this, but it died with the old hdd :P
IIRC, in some cases we care about, this about doubles performance.
In other cases, it's far less significant, but it never (in realistic
terms) seems to be a pessimization.