Where the exponential functions are used?
The exponential functions are used mainly where non-linear behavior are present. An example of exp(x) is given in Figure 1. Since we are dealing with an exponential behavior, in the normal use of the function, the value of the exponent is range limited. For example, your algorithm could use 0<x<1, or -1<x<1 and so on. It is very unlikely you should deal with x in the entire real range when you implement a signal processing algorithm in FPGA.