1. Apparatus for processing data in response to program instructions having a program execution order, said apparatus comprising: processing circuitry configured to perform processing operation in response to said program instructions; sticky bit storage circuitry configured to store one or more sticky bits, each sticky bit having either an initial value or a sticky value and being subject to: (i) a first outcome of an event that leaves said sticky bit unchanged independent of whether said sticky bit has said initial value or said sticky value; and (ii) a second outcome of said event that leaves said sticky bit with said sticky value independent of whether said sticky bit has said initial value or said sticky value; and speculative execution control circuitry configured to control speculative execution of program instructions by said processing circuitry to follow a speculative sequence of program instructions including a plurality of segments of program instructions, each of said plurality of segments separated from one or more adjacent segments by a respective speculation node corresponding to a program instruction following which a plurality of alternative instructions may serve as a next program instruction to be executed, said speculative execution control circuitry controlling said speculative sequence of program instructions to use one of said alternative instructions as said next program instruction; wherein said sticky bit storage circuitry is configured to store separate versions of said sticky bit, each version corresponding to a value of said sticky bit associated one of said plurality of segments.