It is effectively the design plan of a computing machine."
erm... for instance Babbage would disagree there, this is a patentable "computing machine".
"The analytical engine, an important step in the history of computers, was the design of a mechanical general-purpose computer by English mathematician Charles Babbage. First described in 1837, in its logical design the machine was essentially modern"
and just like Babbage's son You too can run an algorithm on that patentable "computing machine" such as a Pi algorithm.
"pi is a mathematical constant whose value is the ratio of any circle's circumference to its diameter"
"In 1910, Babbage's son Henry Prevost Babbage reported that a part of the mill and the printing apparatus had been constructed and had been used to calculate a (faulty) list of multiples of pi."
Now the only so called "abstract" thing about any given algorithm is that you can get many, they all take that same input and provide the same output as per al these for instance.
and this is the important bit about any given algorithm in case anyone missed it.
Leibniz formula for pi
Liu Hui's π algorithm
and that's just 10 separate Pi algorithm as listed , each taking the same input and providing the same output given the same data.
each and everyone of these given algorithm are automatic copyright of the given person weather they submitted and got a patten or not OC, in these cases they all did....
now here's the important thing people here seem to be missing, Anyone even today can write another new Pi algorithm and so get's automatic copyright and a potential patent If there's no Prior art on that explicit algorithm, so if there's a patent an a given algorithm, then write and use another one that provides the same functionality and is your copyright+patent if you can be bothered
for instance this S3TC algorithm everyone keep's bringing up and given the above, its clear that for instance the FFmpeg version that does so called DXT1 and DXT3 but not DXT5 as yet (as no one bothered to write that code yet and the S3TC entry is old too not touched since 2007, so get to it and make it better ) see:
is fine to use as your base today and its not even an algorithm as such but using different parts of the code base to simply provide the encode/decode bit exact input/output as required by the standard, with no algorithm patent problems to date.