Two Elementary Instructions make Compare-and-Swap

Abstract

Herlihy showed that multiprocessors must support advanced atomic objects, such as compare-and-swap, to be able to solve any arbitrary synchronization task among any number of processes (Herlihy, 1991). Elementary objects such as read-write registers and fetch-and-add are fundamentally limited to at most two processes with respect to solving an arbitrary synchronization task. Later, it was also shown that simulating an advanced atomic object using elementary objects is impossible. However, Ellen et al. observed that the above impossibility assumes computation by synchronization objects instead of synchronization instructions applied on memory locations, which is how the actual multiprocessors compute (Ellen et al., 2016). Building on that observation, we show that two elementary instructions, such as max-write and half-max, can be much better than the advanced compare-and-swap instruction. Concretely, we show the following. •[1.] Half-max and max-write instructions are elementary, i.e., have consensus number one.•[2.] Half-max and max-write instructions can simulate compare-and-swap instruction in O(1) steps.•[3.] For a pipelined butterfly interconnect, concurrent throughput of half-max and max-write instructions exceeds the concurrent throughput of compare-and-swap by a factor n — the number of processes.•[4.] The family of instructions max-write-or-⊙ are also elementary, where ⊙ is a commutative and an associative operation.•[5.] It takes Ω(logn) steps to simulate max-write-or-add using compare-and-swap but O(1) steps to simulate compare-and-swap using max-write-or-add and half-max.