Data processing apparatus and method perform data processing operations on floating point data elements. The data processing apparatus has processing logic for performing data processing operations on the floating point data elements, and decode logic operable to decode a data processing instruction in order to determine a corresponding data processing operation to be performed by the processing logic. The data processing instruction has an m-bit immediate value encoded therein. Further, constant generation logic is provided to perform a logical operation on the m-bit immediate value in order to generate an n-bit floating point constant for use as at least one input floating point data element for the processing logic when performing the corresponding data processing operation. The values “n” and “m” are integers, and n is greater than m. This approach provides a particularly efficient technique for generating floating point constants.