When an OpenCL kernel is to be executed, a bitfield index representation to be used for the indices of the kernel invocations is determined based on the number of bits needed to represent the maximum value that will be needed for each index dimension for the kernel. A bitfield placement data structure 33 describing how the bitfield index representation is partitioned is then prepared together with a maximum value data structure 32 indicating the maximum index dimension values to be used for the kernel. A processor then executes the kernel invocations 36 across the index space indicated by the maximum value data structure 32. A bitfield index representation 35, 37, 38 configured in accordance with the bitfield placement data structure 33 is associated with each kernel invocation to indicate its index.