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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.
The rem function produces a result that is either zero or has the same sign as the dividend. Another difference is the convention when the divisor is zero. The mod function follows the convention that mod(a,0) returns a, whereas the rem function follows the convention that rem(a,0) returns NaN. Both variants have their uses. For example, in signal processing, the mod function is useful in the context of periodic signals because its output is periodic (with period equal to the divisor).