A digital signal processor is provided having an instruction set with an exponential function that uses a reduced look-up table. The disclosed digital signal processor evaluates an exponential function for an input value, x, by decomposing the input value, x, to an integer part, N, a first fractional part, q1, larger than a specified value, x0, and a second fractional part, q2, smaller than the specified value, x0; computing 2q2 using a polynomial approximation, such as a cubic approximation; obtaining 2q1 from a look-up table; and evaluating the exponential function for the input value, x, by multiplying 2q2, 2q1 and 2N together. Look-up table entries have a fewer number of bits than a number of bits in the input value, x.