12.2.1. Introduction to Hashed Page Tables

The next approach that is used to reduce page table sizes is by using hierarchical page tables. So firstly, what did we use? We used a page table length register. The which was without segmentation and then we said that typically the virtual address space has a stack part and a heap part to address and the page table length register only allows the page table to grow in one direction.

This chunk introduces the reader to the concept of hierarchical page tables and how they help reduce the size of page tables. The discussion begins with the use of a Page Table Length Register (PTLR), which is critical in managing the memory of a virtual address space. The virtual address space is typically divided into sections such as the stack and heap, but a challenge arises because the PTLR allows the page table to grow in only one direction, leading to inefficiencies in memory usage.

Consider your digital wardrobe. If you have a wardrobe with limited shelves, and you can only add clothes from the top, it can become cluttered and disorganized over time. Similarly, without being able to efficiently manage how memory areas (like stack and heap) grow, your program can run into memory allocation issues.

So, we addressed that by having two segments; one containing possibly the stack, the other containing the heap and each of these two segments has two page tables. And so, by directions two possible directions of increase for the process becomes available.

To solve the limitation of the PTLR, we introduce segmentation, wherein the virtual address space is divided into multiple segments. This allows for separate handling of different data types, such as stack and heap, and provides multiple page tables for each segment. This strategic division means that when one segment grows, the other's size can remain manageable, improving memory efficiency.

Think of this segmentation like having different compartments in a toolbox. If one compartment (the stack) gets full, you can still utilize space in the other compartments (the heap) without compromising the entire toolbox's organization.

We come to hierarchical page tables. So, here we do not go into segmentation, we don’t have segmentation here and but we have multiple page table levels; hierarchical page tables or multiple page tables multiple multi-level page tables.

Hierarchical page tables are a further refinement of the segmented approach, allowing the logical address space to be broken into multiple levels of page tables. Instead of a single table, a two-level page table system, for example, manages memory more effectively by allowing certain parts of the page tables to occupy physical memory only when needed. This helps to further alleviate memory issues.

Consider a library system where instead of storing all books on a single shelf, books are organized into multiple levels based on genre. This library system ensures efficient organization and access instead of having all books crammed together, making it easy to find a specific one.

The simplest scheme in this is a two level page table. So, what happens in a two level page table? The page number is split into two parts.

In a two-level page table scheme, the logical address space is divided into two components: one that indexes the outer page table and the other indexes the inner page table. This improved structure means that rather than finding a page in a single table, the system seeks it through two sequential lookups, reducing the memory overhead of maintaining a single large structure.

This is like looking for a book in a multi-sectioned library. Instead of scanning every single book (like a single large page table), you first go to the right section (the outer page table) and then find the specific shelf (the inner page table) in that section.

Now, two-level paging is not always sufficient. So, even two-levels paging is not sufficient for 64 bit computers. So, what do we do?

While two-level page tables improve memory handling, they can still be inadequate for large address spaces such as those used in 64-bit computing. A two-level scheme can lead to exceedingly large outer page tables, prompting the need for further segmentation to avoid excessive memory usage.

Consider trying to organize a much larger library without additional shelving for new genres. If the library keeps growing but remains with the original two-shelving system, it quickly becomes unmanageable, necessitating more levels to maintain order.

In order to control in order to control size of another technique that is used to control the size of a page table is by using a hashed page table. It is commonly used for address spaces greater than 32 bits.

Hashed page tables offer a sophisticated solution by allowing pages to be indexed through a hash function, creating a flexible structure that can cater to large virtual address spaces associated with 64-bit systems. This approach limits the search space by linking colliding entries, making data retrieval efficient and minimizing memory usage.

Think of this approach as an online search engine that uses keywords to quickly find relevant documents. Instead of searching through a vast number of records, a quick hash retrieves related documents, making the process faster and requiring less storage for indexing.

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