Supporting atomic durability of updates for persistent memories is typically achieved with Write-Ahead Logging (WAL). WAL flushes log entries to persistent memory before making the actual data persistent to ensure that a consistent state can be recovered if a crash occurs. Performing WAL in hardware is attractive because it makes most aspects of log management transparent to software, and it completes log persist operations (LPOs) and data persist operations (DPOs) in the background, overlapping them with the execution of other instructions.Prior hardware logging solutions commit atomic regions synchronously. That is, once the end of a region is reached, all outstanding persist operations required for the region to commit must complete before instruction execution may proceed. For undo logging, LPOs and DPOs are both performed synchronously to ensure that the region commits synchronously. For redo logging, DPOs can be performed asynchronously, but LPOs are performed synchronously to ensure that the region commits synchronously. In both cases, waiting for synchronous persist operations (LPO or DPO) at the end of an atomic region causes atomic regions to incur high latency.To tackle this limitation, we propose ASAP, a hardware logging solution that allows atomic regions to commit asynchronously. That is, once the end of an atomic region is reached, instruction execution may proceed without waiting for outstanding persist operations to complete. As such, both LPOs and DPOs can be performed asynchronously. The challenge with allowing atomic regions to commit asynchronously is that it can lead to control and data dependence violations in the commit order of the atomic regions, leaving data in an unrecoverable state in case of a crash. To address this issue, ASAP tracks and enforces control and data dependencies between atomic regions in hardware to ensure that the regions commit in the proper order.Our evaluation shows that ASAP outperforms the state-of-theart hardware undo and redo logging techniques by 1.41× and 1.53×, respectively, while achieving 0.96× the ideal performance when no persistence is enforced, at a small hardware cost (< 3%). ASAP also reduces memory traffic to persistent memory by 38% and 48%, * Ahmed Abulila is currently affiliated with Microsoft Corporation.