strange fluctuations in system.time with kernapply

Hello expeRts,

here is something which strikes me as kind of odd and I would like to
ask for some enlightenment:

First let's do this:

tkern <- kernel("modified.daniell", c(5,5))
test <- rep(1,1000000)
system.time(kernapply(test,tkern))
User System verstrichen
1.100 0.040 1.136

That was easy. Now this:

test <- rep(1,1100000)
system.time(kernapply(test,tkern))
User System verstrichen
1.40 0.02 1.43

Still fine. Now this:

test <- rep(1,1110000)
system.time(kernapply(test,tkern))
User System verstrichen
1.390 0.020 1.409

Ok, by now it seems boring. But wait:

test <- rep(1,1110300)
system.time(kernapply(test,tkern))
User System verstrichen
12.270 0.030 12.319

There is a sudden - and repeatable! - jump in the time needed to execute
kernapply. At least from a naive point of view there should not be much
difference between applying a kernel to a vector 1110000 or 1110300
entries long. But maybe there is some limit here?

So I tried this:

test <- rep(1,1110400)
system.time(kernapply(test,tkern))
User System verstrichen
1.96 0.01 1.97

which doesn't fit into the pattern. But the best thing is still to come.
When I try this

test <- rep(1,1110308)
system.time(kernapply(test,tkern))

then the computer starts to run and does so for longer than 15 minutes
until when I normally kill the process. As noted above this behaviour is
repeatable and occurs every time I issue these commands.

I really would like to know if there is some magic to the number 1110308
I'm not aware of.