In this paper, we revisit the design of synchronization primitives---specifically barriers, mutexes, and semaphores---and how they apply to the GPU. Previous implementations are insufficient due to the discrepancies in hardware and programming model of the GPU and CPU. We create new implementations in CUDA and analyze the performance of spinning on the GPU, as well as a method of sleeping on the GPU, by running a set of memory-system benchmarks on two of the most common GPUs in use, the Tesla- and Fermi-class GPUs from NVIDIA. From our results we define higher-level principles that are valid for generic many-core processors, the most important of which is to limit the number of atomic accesses required for a synchronization operation because atomic accesses are slower than regular memory accesses. We use the results of the benchmarks to critique existing synchronization algorithms and guide our new implementations, and then define an abstraction of GPUs to classify any GPU based on the behavior of the memory system. We use this abstraction to create suitable implementations of the primitives specifically targeting the GPU, and analyze the performance of these algorithms on Tesla and Fermi. We then predict performance on future GPUs based on characteristics of the abstraction. We also examine the roles of spin waiting and sleep waiting in each primitive and how their performance varies based on the machine abstraction, then give a set of guidelines for when each strategy is useful based on the characteristics of the GPU and expected contention.