A data processing apparatus and method are provided for performing a reciprocal operation on an input value d to produce a result value X. The reciprocal operation involves iterative execution of a refinement step to converge on the result value, the refinement step performing the computation: Xi=Xi−1*M, where Xi is an estimate of the result value for the i-th iteration of the refinement step, and M is a value determined by a portion of the refinement step. The data processing apparatus comprises a register data store having a plurality of registers operable to store data, and processing logic operable to execute instructions to perform data processing operations on data held in the register data store. The processing logic is responsive to a single refinement instruction to implement the portion of the refinement step by performing at least a multiply-accumulate operation in which the input value, a value derived from the previous estimate of the result value, and a constant are used as inputs of the multiply-accumulate operation. The constant is determined from the single refinement instruction without reference to the register data store. Such an approach improves code density, and improves efficiency of use of registers of the register data store.