A data processing apparatus, comprising: processing circuitry responsive to data processing instructions to execute integer data processing operations and floating point data processing operations; a first set of integer registers useable by said processing circuitry in executing said integer data processing operations, and a second set of floating point registers useable by said processing circuitry in executing said floating point data processing operations; wherein said processing circuitry is responsive to an interrupt request to perform one of an integer state preservation function in which at least a subset of only said integer registers are copied to a stack memory, and a floating point state preservation function in which at least a subset of both said integer registers and said floating point registers are copied to said stack memory, said one of said integer state preservation function and said floating point state preservation function being selected by said processing circuitry in dependence on state information; said state information comprises first state information which is indicative of whether a current data processing context being executed by said processing circuitry when the interrupt request is received is a floating point data processing context which includes one or more floating point data processing operations or an integer data processing context which does not include any floating point data processing operations; said processing circuitry is responsive to said interrupt request to perform said integer state preservation function if said first state information indicates that the current data processing context is an integer data processing context, and to perform said floating point state preservation function if said first state information indicates that the current data processing context is a floating point data processing context; when said integer state preservation function is performed, said processing circuitry sets second state information to indicate that the floating point registers have not been copied into the stack memory, and when said floating point state preservation function is performed, said processing circuitry sets said second state information to indicate that the floating point registers have been copied to the stack memory. processing circuitry responsive to data processing instructions to execute integer data processing operations and floating point data processing operations; a first set of integer registers useable by said processing circuitry in executing said integer data processing operations, and a second set of floating point registers useable by said processing circuitry in executing said floating point data processing operations; wherein said processing circuitry is responsive to an interrupt request to perform one of an integer state preservation function in which at least a subset of only said integer registers are copied to a stack memory, and a floating point state preservation function in which at least a subset of both said integer registers and said floating point registers are copied to said stack memory, said one of said integer state preservation function and said floating point state preservation function being selected by said processing circuitry in dependence on state information; said state information comprises first state information which is indicative of whether a current data processing context being executed by said processing circuitry when the interrupt request is received is a floating point data processing context which includes one or more floating point data processing operations or an integer data processing context which does not include any floating point data processing operations; said processing circuitry is responsive to said interrupt request to perform said integer state preservation function if said first state information indicates that the current data processing context is an integer data processing context, and to perform said floating point state preservation function if said first state information indicates that the current data processing context is a floating point data processing context; when said integer state preservation function is performed, said processing circuitry sets second state information to indicate that the floating point registers have not been copied into the stack memory, and when said floating point state preservation function is performed, said processing circuitry sets said second state information to indicate that the floating point registers have been copied to the stack memory.