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A function of real numbers is also called a step function if it is piecewise constant function involving a finite number of inputs. There are two types of step functions. Greatest Integer function (floor function) - A function f(x) is said to be a floor function which possesses biggest integer that is less than or equal to the input value x Smallest Integer function (ceiling function) - A function f(x) is said to be a ceiling function which is composed of the lowest integer that is either bigger or equal to the input value x A step function is also known as staircase function, since it looks like a staircase.
Ceiling function. In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, floor(x) = is the largest integer not greater than x and ceiling(x) = is the smallest integer not less than x.loor and ceiling may be defined by the set equations. Since there is exactly one integer in a half-open interval of length one, for any real x there are unique integers m and n satisfying. Then and may also be taken as the definition of floor and ceiling.