Saving and restoring branch prediction state

A branch predictor is provided with a branch state buffer, branch prediction save circuitry responsive to a branch prediction save event associated with a given execution context to save at least a portion of the active branch prediction state associated with the given execution context to a branch state buffer; and branch prediction restore circuitry responsive to a branch prediction restore event associated with the given execution context to restore active branch prediction state based on previously saved branch prediction state stored in the branch state buffer for the given execution context. This is useful for reducing the performance impact of mitigating against speculative side-channel attacks.