Process Page Tables: why don't we use simple linear array?

I would like to know why we need hierachical page tables in OS that handle per-process page tables, using PTBR and PTLR registers in CPU (tipically stored in PCB).
Thanks to PTLR I can check the limit of page table size for the current process, so its page table will contain just entries for its address memory space (that will be not so large as system address memory space).
If virtual address space of a process isn't sparse (its virtual page numbers are 0, 1, 2, ...) I will have a process page table of at most some K entries: totally its size will be at most some MBs, and I think it would be better to use a simple contiguous array.
So, why a lot of real solutions (ie x86 and x64) are based on multi-level page tables (or Hashed Page Tables)?

Thanks.


Because sparse virtual address space is good. Sparse address space allows the OS to crash a program that chases (some) wild pointers, and it makes prelinked shared libraries practical, and perhaps most useful of all, it allows your stack to grow from the "top" end of memory and your heap from the "bottom" end. You could of course define the page table index as a signed integer, which would allow you to implement the latter feature with just a simple array.

Also, think of "memory overcommit" allocation - when you malloc a few gigabytes the OS might say, "sure, fine!", knowing that most programs that ask for a few gigabytes turn out to use only a small fraction thereof. You could have problems supporting things like that with a simple array that isn't unnecessarily large.

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