# Part 1: How to translate address

## How to translate address

a RISC-V page table is logically an array of 2^27 (134,217,728) page table entries (PTEs). The paging hardware *translates a virtual address by using the top 27 bits of the 39 bits to index into the page table to find a PTE*, and making a 56-bit physical address whose top 44 bits come from the PPN in the PTE and whose bottom 12 bits are copied from the original virtual address. Thus a page table gives the operating system control over virtual-to-physical address translations at the granularity of *aligned chunks of 4096 (2^12) bytes*. Such a chunk is called a page.

![](/files/-M4bud-m8TZ1GnujEIqb)

* The total supported number of pages are: 2^27
* Each size is 2^12.
* GB size is 2^30.
* MAXVA is actually one bit less than the max allowed by Sv39, to avoid having to sign-extend virtual addresses that have the high bit set.

  `#define MAXVA (1L << (9 + 9 + 9 + 12 - 1))`
* So the total virtual memory can support up to 2^(27+12-30 - 1) => 2^8.&#x20;
* The available virtual memory is 256 GB.

the actual translation happens in three steps.

![](/files/-M4bufr5-ZZ8anm7y3Ry)

kernel must write the physical address of the root page-table page into the `satp` register. Each CPU has its own `satp`.

### Open questions:

#### Why kernel maps stacks via high-memory mappings?

Read: Reference: “Understanding the Linux Kernel”, third edition - sections “8.1.3. Memory Zones” and “8.1.6. Kernel Mappings of High-Memory Page Frames”.

For 32 bit machines: Page frames above the 896 MB boundary are not generally mapped in the fourth gigabyte of the kernel linear address spaces, so the kernel is unable to directly access them.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://xiayingp.gitbook.io/build_a_os/virtual-memory/page-table/part-1-how-to-translate-address.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.