1. Apparatus for processing data comprising: processing circuitry to perform processing operations under control of program instructions; and decoding circuitry to decode program instructions to generate control signals to control said processing circuitry to perform said processing operations; wherein said decoding circuitry is responsive to a given program instruction and a rounding position input operand to generate control signals to: control said processing circuitry to process a floating point input operand having a significand value, and to control said processing circuitry to generate an output result dependent upon a value from rounding said floating point input operand using a variable rounding point within said significand of said floating point input operand specified by said rounding position input operand.