Why calculation of complexity of various algorithms(Linear search,
bubble sort) confined to number of comparisons, whereas the arithmetic
operations and other operations are not considered, though these also
may eat significant processing power.
Your question isn't about the C programming language, nor about
any particular programming language, and probably belongs in a forum
like comp.programming.
... but for what it's worth, try the analysis yourself. Take
some simple algorithm, implement it, study the machine instructions
that it generates, and try to predict how much time it will take.
Don't forget to take account of pipeline parallelism, cache hits
and misses, translation look-aside buffer hits and misses, ... It
will be a difficult job, but perhaps you can get an answer after a
great deal of labor. And then you'll have an answer -- which will
go straight out the window as soon as you install a new compiler
version or change the compilation flags, or even add RAM. In other
words, all that enormous effort will produce, at best, an answer
that you can use only once and cannot transfer to the next machine.