An efficient wear-leveling-aware multi-grained allocator for persistent memory file systems

Persistent memory(PM)file systems have been developed to achieve high performance by exploiting the advanced features of PMs,including nonvolatility,byte addressability,and dynamic random access memory(DRAM)like performance.Unfortunately,these PMs suffer from limited write endurance.Existing space management strategies of PM file systems can induce a severely unbalanced wear problem,which can damage the underlying PMs quickly.In this paper,we propose a Wear-leveling-aware Multi-grained Allocator,called WMAlloc,to achieve the wear leveling of PMs while improving the performance of file systems.WMAlloc adopts multiple min-heaps to manage the unused space of PMs.Each heap represents an allocation granularity.Then,WMAlloc allocates less-worn blocks from the corresponding min-heap for allocation requests.Moreover,to avoid recursive split and inefficient heap locations in WMAlloc,we further propose a bitmap-based multi-heap tree(BMT)to enhance WMAlloc,namely,WMAlloc-BMT.We implement WMAlloc and WMAlloc-BMT in the Linux kernel based on NOVA,a typical PM file system.Experimental results show that,compared with the original NOVA and dynamic wear-aware range management(DWARM),which is the state-of-the-art wear-leveling-aware allocator of PM file systems,WMAlloc can,respectively,achieve 4.11×and 1.81×maximum write number reduction and 1.02×and 1.64×performance with four workloads on average.Furthermore,WMAlloc-BMT outperforms WMAlloc with 1.08×performance and achieves 1.17×maximum write number reduction with four workloads on average.

Elliptic genera of level N for complete intersections

We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<0.In particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.