Arrays 是连续的吗？ （虚拟与物理）

Question

I read that arrays are contiguous in Virtual Memory but probably not in Physical memory, and I don't get that.

Let's suppose I have an array of size 4KB (one page = one frame size), In virtual memory that array is one page.

In virtual memory every page in translated into one frame so our array is still contiguous...

(In Page Table we translate pages into frames not every byte into its own frame...)

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Side Question: (When Answering this please mention clearly it's for the side note):

When allocating array in virtual memory of size one page does it have to be one page or could be split into two contiguous pages in virtual memory (for example bottom half of first one and top half of the second)? In this case at worst the answer above is 2, am I wrong?

Answer 1

Unless the start of the array happens to be aligned to the beginning of a memory page, it can still occupy two pages; it can start near the end of one page and end on the next page. Arrays allocated on the stack will probably not be forced to occupy a single page, because stack frames are simply allocated sequentially in the stack memory, and the array will usually be at the same offset within each stack frame.

The heap memory allocator ( malloc() ) could try to ensure that arrays that are smaller than a page will be allocated entirely on the same page, but I'm not sure if this is actually how most allocators are implemented. Doing this might increase memory fragmentation.

Answer 2

I read that arrays are contiguous in Virtual Memory but probably not in Physical memory, and I don't get that.

This statement is missing something very important. The array size

For small arrays the statement is wrong. For "large/huge" arrays the statement is correct.

In other words: The probability of an array being split over multiple non-contiguous physical pages is a function of the array size.

For small arrays the probability is close to zero but the probability increases as the array size increase. When the array size increases above the systems page size, the probability gets closer and closer to 1. But an array requiring multiple page may still be contiguous in physical memory.

For you side question:

With an array size equal to your systems page size, the array can at maximum span two physical pages.

Answer 3

Anything (array, structure, ...) that is larger than the page size must be split across multiple pages; and therefore may be "virtually contiguous, physical non-contiguous".

Without further knowledge or restriction; anything (array, structure, ...) that is between its minimum alignment (eg 4 bytes for an array of uint32_t ) and the page size has a probability of being split across multiple pages; where the probability depends on its size and alignment. For example, if page size is 4096 bytes and an array has a minimum alignment of 4 bytes and a size of 4092 bytes, then there's 2 chances in 1024 that it will end up on a single page (and a 99.8% chance that it will be split across multiple pages).

Anything (variable, tiny array, tiny structure, ...) that has a size equal to its minimum alignment won't (shouldn't - see note 3) be split across multiple pages.

Note 1: For anything using memory allocated from the heap, the minimum alignment can be assumed to be the (implementation defined) minimum alignment provided by the heap and not the minimum alignment of the object itself. Eg for an array of uint16_t the minimum alignment would be 2 bytes; but malloc() will return memory with much larger alignment (maybe 16 bytes)

Note 2: When things are nested (eg array inside a structure inside another structure) all of the above applies to the outer structure only. Eg if you have an array of uint16_t inside a structure where the array happens to begin at offset 4094 within the structure; then it will be significantly more likely that the array will be split across pages.

Note 3: It's possible to explicitly break minimum alignment using pointers (eg use malloc() to allocate 1024 bytes, then create a pointer to an array that begins at any offset you want within the allocated area).

Note 4: If something (array, structure, ...) is split across multiple pages; then there's a chance that it will still be physically contiguous. For worst case this depends on the amount of physical memory (eg if the computer has 1 GiB of usable physical memory and 4096 byte pages, then there's approximately 1 chance in 262000 that 2 virtually contiguous pages will be "physically contiguous by accident"). If the OS implements page/cache coloring (see https://en.wikipedia.org/wiki/Cache_coloring ) it improves the probability of "physically contiguous by accident" by the number of page/cache "colors" (eg if the computer has 1 GiB of usable physical memory and 4096 byte pages, and the OS uses 256 page/cache colors, then there's approximately 1 chance in 1024 that 2 virtually contiguous pages will be "physically contiguous by accident").

Note 5: Most modern operating systems using multiple page sizes (eg 4 KiB pages and 2 MiB pages, and maybe also 1 GiB pages). This can either make it hard to guess what the page size actually is, or improve the probability of "physically contiguous by accident" if you assume the smallest page size is used.

Note 6: For some CPUs (eg recent AMD/Zen) the TLBs behave as if pages are larger (eg as if you're using 16 KiB pages and not 4 KiB pages) if and only if page table entries are compatible (eg if 4 page table entries describe four physically contiguous 4 KiB pages with the same permissions/attributes). If an OS is optimized for these CPUs the result is similar to having an extra page size (4 KiB, "16 KiB", 2 MiB and maybe 1 GiB).

When allocating array in virtual memory of size one page does it have to be one page or could be split into two contiguous pages in virtual memory (for example bottom half of first one and top half of the second)?

When allocating an array in heap memory of size one page; the minimum alignment would be the implementation defined minimum alignment provided by the heap manager/ malloc() (eg maybe 16 bytes). However; most modern heap managers switch to using an alternative (eg mmap() or VirtualAlloc() or similar) when the amount of memory being allocated is "large enough"; so (depending on the implementation and their definition of "large enough") it might be page aligned.

When allocating an array in raw virtual memory (eg using mmap() or VirtualAlloc() or similar yourself, and NOT using the heap and not using something like malloc() ); page alignment is guaranteed (mostly because the virtual memory manager doesn't deal with anything smaller).