1. Chapter 20 Smaller Tables Chien-Chung Shen CIS, UD cshen@cis.udel.edu

2. Problem Big page table 32-bit address space (2 32 bytes) with 4KB (2 12 byte) pages and 4-byte page table entry 2 32 /2 12 pages and 4MB page table per process Problem: how to make page table smaller? The simplest way –bigger pages –e.g., 16KB pages -> 1MB page table –internal fragmentation

3. Hybrid Approach Paging + segmentation PFN valid prot present dirty 10 1 r-x 1 0 - 0 — - - 23 1 rw- 1 1 - 0 — - - 28 1 rw- 1 1 4 1 rw- 1 1 Any thing bad? –too many invalid PTEs

4. Paging + Segmentation One page table per segment –base (physical address of page table) + bounds –3 page tables for code, heap, and stack –on TLB miss, use Seg to decide which base/bounds SN = (VirtualAddress & SEG_MASK) >> SN_SHIFT // Seg VPN = (VirtualAddress & VPN_MASK) >> VPN_SHIFT AddressOfPTE = Base[SN] + (VPN * sizeof(PTE)) Issues: –segmentation is not quite flexible (e.g., sparsely- used heap) –external fragmentation caused by page tables

5. Multi-level Page Tables How to get rid of those invalid regions in page table (instead of keeping them in memory) ? –turns linear page table into something like a tree –chop up page table into page-sized units –if an entire page of PTEs is invalid, don’t allocate that page of page table at all –page directory PFN valid prot present dirty 10 1 r-x 1 0 - 0 — - - 23 1 rw- 1 1 - 0 — - - 28 1 rw- 1 1 4 1 rw- 1 1

6. Multi-level Page Tables Page directory entry (PDE)

7. Multi-level Page Tables Pros page-table space allocated is proportional to amount of address space used growing page table by getting more page frames (which could be anywhere in physical memory Cons on TLB miss, need two memory accesses to get translation info (one for page directory and one for PTE itself) time-space trade-off complexity: perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away -- Antoine de Saint-Exupery

8. Detailed Example 16 KB address space + 64-byte pages –14-bit virtual address space –Assume 1 KB page table

9. Inverted Page Table Instead of having many page tables (one per process), a single page table that has an entry for each physical page of the system –which process is using this page (frame) –which virtual page of that process maps to this physical page