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General-purpose GPU applications increasingly use synchronization to enforce ordering between many threads accessing shared data. Accordingly, recently there has been a push to establish a common set of GPU synchronization primitives. However, the expressiveness of existing GPU synchronization primitives is limited. In particular the expensive GPU atomics often used to implement fine-grained synchronization make it challenging to implement efficient algorithms. Consequently, as GPU algorithms scale to millions or billions of threads, existing GPU synchronization primitives either scale poorly or suffer from livelock or deadlock issues because of heavy contention between threads accessing shared synchronization objects. We seek to overcome these inefficiencies by designing more efficient, scalable GPU barriers and semaphores. In particular, we show how multi-level sense reversing barriers and priority mechanisms for semaphores can be designed with the GPUs unique processing model in mind to improve performance and scalability of GPU synchronization primitives. Our results show that the proposed designs significantly improve performance compared to state-of-the-art solutions like CUDA Cooperative Groups and optimized CPU-style synchronization algorithms at medium and high contention levels, scale to an order of magnitude more threads, and avoid livelock in these situations unlike prior open source algorithms. Overall, across three modern GPUs the proposed barrier algorithm improves performance by an average of 33% over a GPU tree barrier algorithm and improves performance by an average of 34% over CUDA Cooperative Groups for five full-sized benchmarks at high contention levels; the new semaphore algorithm improves performance by an average of 83% compared to prior GPU semaphores. [ABSTRACT FROM AUTHOR]