In a data processor that executes programs to perform data processing operations for groups of execution threads, when the threads of a thread group are all to process a same, common input data value, different portions of the common input data value are loaded into respective registers of different threads of the group of threads, such that the common input data value is stored in a distributed fashion across registers of plural different threads of the thread group. Then, when the threads of the thread group are to process a portion the common input data value, the portion is provided from the thread that stores it to all the threads in the thread group.