A processing element is configured to approximate a transcendental function. The processing element comprises an input storage and a look-up storage. The processing element obtains floating-point input data from the input storage representing having an input exponent value and an input mantissa value. The processing element looks up approximation parameters and an output exponent value from the look-up storage, wherein each group of approximation parameters and output exponent value are stored in the look-up storage in association with a respective range of a plurality of ranges that are defined by the input exponent value and the input mantissa value. The ranges cover values of the input exponent value and input mantissa value such that the output exponent value associated with each range does not change by more than a predetermined number. An approximation function is evaluated that approximates the transcendental function based on the looked-up approximation parameters and output exponent.