Where in each claim do you see their proposed "hardware implementation" - the novel device you suppose they've invented - that we might distinguish from, for example, every modern microcomputer ? What I see is a description of the algorithm because of course the intent is to patent the algorithm and not some special hardware implementation nobody will manufacture because it's patented.

If you have some novel arrangement of gears and levers to propose, or some recipe of doping material A with chemical B and then doing so-and-such - that's a classical hardware patent, but the whole point of these "an apparatus" patents is that they aren't trying to describe a novel device anybody invented, they're describing the algorithm the patent is for the algorithm and phrases like "an apparatus" are just a wafer thin excuse for this to be waved through by people whose salary is paid for by the endless flood of such software patents.

As a parallel comment is explaining there hasn't for many years been any substantial difference between what seems to be very much "hardware" and what common folk think of as "software".

The patent application even spells it out, explaining that "A general purpose computer [...] can execute the invention in a single instruction cycle [...]". What "invention" do you suppose is being "executed" here? Is the general purpose computer... making a special circuit? Maybe your laptop is now selling DVD players to Best Buy? No. Their "invention" is just the algorithm, they successfully patented the algorithm.

Nobody would "stop you writing that algorithm", but if they wanted to, and if you've got enough money for it to be worth taking your money, while that patent was valid they could sue you for infringing on their invention and unless you've got deep pockets and proof you invented it first, you are screwed.