Memory Paging - Algorithmica

# Memory Paging

Consider yet again the strided incrementing loop:

const int N = (1 << 13);
int a[D * N];

for (int i = 0; i < D * N; i += D)
a[i] += 1;


We change the stride $D$ and increase the array size proportionally so that the total number of iterations $N$ remains constant. As the total number of memory accesses also remains constant, for all $D \geq 16$, we should be fetching exactly $N$ cache lines — or $64 \cdot N = 2^6 \cdot 2^{13} = 2^{19}$ bytes, to be exact. This precisely fits into the L2 cache, regardless of the step size, and the throughput graph should look flat.

This time, we consider a larger range of $D$ values, up to 1024. Starting from around 256, the graph is definitely not flat:

This anomaly is also due to the cache system, although the standard L1-L3 data caches have nothing to do with it. Virtual memory is at fault, in particular the translation lookaside buffer (TLB), which is a cache responsible for retrieving the physical addresses of the virtual memory pages.

On my CPU, there are two levels of TLB:

• The L1 TLB has 64 entries, and if the page size is 4K, then it can handle $64 \times 4K = 512K$ of active memory without going to the L2 TLB.
• The L2 TLB has 2048 entries, and it can handle $2048 \times 4K = 8M$ of memory without going to the page table.

How much memory is allocated when $D$ becomes equal to 256? You’ve guessed it: $8K \times 256 \times 4B = 8M$, exactly the limit of what the L2 TLB can handle. When $D$ gets larger than that, some requests start getting redirected to the main page table, which has a large latency and very limited throughput, which bottlenecks the whole computation.

### #Changing Page Size

That 8MB of slowdown-free memory seems like a very tight restriction. While we can’t change the characteristics of the hardware to lift it, we can increase the page size, which would in turn reduce the pressure on the TLB capacity.

Modern operating systems allow us to set the page size both globally and for individual allocations. CPUs only support a defined set of page sizes — mine, for example, can use either 4K or 2M pages. Another typical page size is 1G — it is usually only relevant for server-grade hardware with hundreds of gigabytes of RAM. Anything over the default 4K is called huge pages on Linux and large pages on Windows.

On Linux, there is a special system file that governs the allocation of huge pages. Here is how to make the kernel give you huge pages on every allocation:

$echo always > /sys/kernel/mm/transparent_hugepage/enabled  Enabling huge pages globally like this isn’t always a good idea because it decreases memory granularity and raises the minimum memory that a process consumes — and some environments have more processes than free megabytes of memory. So, in addition to always and never, there is a third option in that file: $ cat /sys/kernel/mm/transparent_hugepage/enabled


madvise is a special system call that lets the program advise the kernel on whether to use huge pages or not, which can be used for allocating huge pages on-demand. If it is enabled, you can use it in C++ like this:

#include <sys/mman.h>

void *ptr = std::aligned_alloc(page_size, array_size);


You can only request a memory region to be allocated using huge pages if it has the corresponding alignment.

Windows has similar functionality. Its memory API combines these two functions into one:

#include "memoryapi.h"

void *ptr = VirtualAlloc(NULL, array_size,
MEM_RESERVE | MEM_COMMIT | MEM_LARGE_PAGES, PAGE_READWRITE);


In both cases, array_size should be a multiple of page_size.

### #Impact of Huge Pages

Both variants of allocating huge pages immediately flatten the curve:

Enabling huge pages also improves latency by up to 10-15% for arrays that don’t fit into the L2 cache:

In general, enabling huge pages is a good idea when you have any sort of sparse reads, as they usually slightly improve and (almost) never hurt performance.

That said, you shouldn’t rely on huge pages if possible, as they aren’t always available due to either hardware or computing environment restrictions. There are many other reasons why grouping data accesses spatially may be beneficial, which automatically solves the paging problem.