An apparatus and method are provided for executing a plurality of threads. The apparatus has processing circuitry arranged to execute the plurality of threads, with each thread executing a program to perform processing operations on thread data. Each thread has a thread identifier, and the thread data includes a value which is dependent on the thread identifier. Value generator circuitry is provided to perform a computation using the thread identifier of a chosen thread in order to generate the above mentioned value for that chosen thread, and to make that value available to the processing circuitry for use by the processing circuitry when executing the chosen thread. Such an arrangement can give rise to significant performance benefits when executing the plurality of threads on the apparatus.