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With the evolvement of hardware, 64-bit Central Processing Units (CPUs) and 64-bit Operating Systems (OSs) have dominated the market. This article investigates the performance of virtual memory management of Virtual Machines (VMs) with a large virtual address space in 64-bit OSs, which imposes different pressure on memory virtualization than 32-bit systems. Each of the two conventional memory virtualization approaches, Shadowing Paging (SP) and Hardware-Assisted Paging (HAP), causes different overhead for different applications. Our experiments show that 64-bit applications prefer to run in a VM using SP, while 32-bit applications do not have a uniform preference between SP and HAP. In this article, we trace this inconsistency between 32-bit applications and 64-bit applications to its root cause through a systematic empirical study in Linux systems and discover that the major overhead of SP results from memory management in the 32-bit GNU C library (glibc). We propose enhancements to the existing memory management algorithms, which substantially reduce the overhead of SP. Based on the evaluations using SPEC CPU2006, Parsec 2.1, and cloud benchmarks, our results show that SP, with the improved memory allocators, can compete with HAP in almost all cases, in both 64-bit and 32-bit systems. We conclude that without a significant breakthrough in HAP, researchers should pay more attention to SP, which is more flexible and cost effective.