B Is there a way to find the integer representation of a real number?

You want an algorithm for a function without allowing the use of functions, right ?

How about IF statements ? Range of your function ?

(by the way, in many computer languages a = b does tthe trick if a is an integer and b a real )

 

You can get pretty close by starting with arctan(tan(x)). This gives you a sawtooth which you can shift, scale and subtract from f(x)=x. It's just those pesky points where tan x is undefined that get you.

Will you allow arctan2 as part of an algebraic formula?