A Metric for Memory Fragmentation

Wed

06

Apr 2022

Listed right here, I would bag to discuss the sphere of reminiscence fragmentation and propose a intention for calculating a metric telling how badly the reminiscence is fragmented.

The topic may presumably even be acknowledged admire this:

• We shield under consideration a linear, addressable reminiscence with a restricted capability.
• We fabricate some code that allocates and frees parts of this reminiscence by search info from from the person (a program that is the usage of our library).
• Allocations may presumably even be of arbitrary dimension, masses of from single bytes to megabytes and even gigabytes.
• “Allocate” and “free” requests can happen in random remark.
• Allocations can’t overlap. Every must contain its contain reminiscence assign.
• Every allocation must be placed in a continuous assign of reminiscence. It can’t be fabricated from a pair of disjoint areas.
• As soon as created, an allocation can’t be moved to a diversified negate. Its assign must be conception to be occupied till the allocation is freed.

So it’s a ways a frail reminiscence allocation field. Now, I will account for what make I mean by fragmentation. Fragmentation, for this article, is an undesirable field the place free reminiscence is spread all over many tiny areas in between allocations, as against a single broad one. We desire to measure it and ideally steer sure of it due to:

• It increases a gamble that some future allocation couldn’t be made, even with passable complete quantity of free reminiscence, due to no broad passable free assign would be found to fulfill the search info from.
• When talking in regards to the full reminiscence readily within the market to a program, this can also simply consequence in program failure, wreck, or some undefined conduct, reckoning on how wisely the program handles reminiscence allocation screw ups.
• When talking about acquiring broad blocks of reminiscence from the running machine (e.g. with WinAPI draw VirtualAlloc) and sub-allocating them for the person’s allocation requests, high fragmentation my require allocating any other block to fulfill the search info from, making the program the usage of more machine reminiscence than undoubtedly wanted.
• Equally, when most allocations are freed, our code can also simply no longer release reminiscence blocks to the machine, as there are few tiny allocations spread all over them.

A intention to this field is to kind defragmentation – an operation that moves the allocations to organize them subsequent to each diversified. This can also simply require person involvement, as tips to the allocations will alternate then. It will even be a time-ingesting operation to calculate greater places for the allocations after which to reproduction all their data. It’s thus perfect to measure the fragmentation to decide when to kind the defragmentation operation.

What may presumably presumably be a fanciful metric for reminiscence fragmentation? Right here are some properties I would admire it to contain: First, it needs to be normalized to range 0..1, or 0%..100%, with a greater number that intention greater fragmentation – more unpleasant field. It will also simply quiet no longer count on the size of the conception to be reminiscence – same structure of allocations and free areas between them can also simply quiet give the the same consequence in spite of whether or no longer their sizes are bytes or megabytes.

A single empty range is the finest doable case, intention no fragmentation, so it would also simply quiet give F=0.

|###############|.......................

An reverse field, the worst doable fragmentation, happens when the free location is spread evenly all over free ranges in between allocations. Then, the fragmentation needs to be 1 or as high as doable.

........|######|........|######|........

It will also simply quiet no longer count on the full quantity of free versus allocated reminiscence. The amount of reminiscence purchased from the machine however no longer aged by the allocations is a crucial quantity, however an fully diversified one. Right here we ideal ought to measure how badly is that this location fragmented. Following case can also simply quiet give the the same consequence because the outdated one:

....|############|....|############|....

The metric can also simply quiet no longer count on the sort of allocations. One broad allocation can also simply quiet give the the same consequence as many tiny ones, as lengthy as they lie subsequent to each diversified.

....|#####|.......|####################|
....|##|##|.......|###|#######|##|##|##|

Present, nonetheless, that more allocations give a possibility for greater fragmentation if empty spaces occur between them.

Memory totally empty or totally beefy are two special conditions that don’t can contain to be handled. Fragmentation is undefined then. We can address these conditions one at a time, so the designed intention is free to realize again 0, 1, and even draw division by 0.

........................................
|####|#########|#######|###|###########|

How can also the intention search for admire? First conception is to ideal measure the largest free assign, admire this:

Fragmentation_Try1=1 - LargestFreeRegionSize / TotalFreeSize

This can precisely return 0 when total free reminiscence is contained within one assign. The smaller the largest free assign is comparing to the full quantity of free reminiscence, the greater the fragmentation. This intention would give a no longer-so-immoral estimate of the fragmentation. In the end, it’s all about being ready to search out a broad passable continuous assign for a new allocation. However there could be a venture with this easy metric: it totally ignores the entire lot besides the one largest free assign. Following two scenarios would give the the same consequence, while we’d bag the second field to legend greater fragmentation.

|##|##|##|........|##|..................
|##|..|##|..|##|..|##|..................

One other conception would be to shield under consideration the sort of free areas between allocations. The more of them, the greater fragmentation. It sounds less dear, because the title “fragmentation” itself intention empty location divided into many fragments.

Fragmentation_Try2=(FreeRegionCount - 1) / AllocationCount

There are problems with this intention, though. First, it considers the sort of allocations, which we bag no longer to make, as described above. 2d and more importantly, tiny holes between allocations would elevate the fragmentation estimate vastly, while they can even simply quiet contain entirely a tiny affect on the final consequence when there are also some broad free areas.

|##|##|##|........|##|..................
|##|.|##|.|##|....|##|..................

I propose the following intention. Given ideal a list of sizes of free areas:

Quality=0
TotalFreeSize=0
for(int i=0; i {
    Quality +=FreeRegionSize[i] FreeRegionSize[i]
    TotalFreeSize +=FreeRegionSize[i]
}
QualityPercent=sqrt(Quality) / TotalFreeSize
Fragmentation=1 - (QualityPercent QualityPercent)

If you prefer a more scientific form over a code snippet, here it is:

Where:

F – result fragmentation metric
n – number of free regions
f_i – size of a free region number i=1..n

The whole secret here is the usage of square and square root. Final calculations are optional and only transform the result to a desired range. (1-x) is there to return higher number for higher fragmentation, as natively it does the opposite (therefore I called the intermediate variable “quality”). The last square is also just to change the shape of the characteristics, so it can be omitted or changed to something else if desired.

This metric fulfills most of the requirements described above. Given the array of sizes of free regions on input and observing the output, we can see that: For just one free region, fragmentation is 0:

[1000] -> F=0

When the free location is spread evenly all over two areas, it’s 1/2=50%:

[500,500] -> F=0.5

When there are 3 free areas of equal dimension, the final consequence is 2/3=0.6666, for 4 areas it’s 3/4=0.75, etc. This can also simply be conception to be a flaw, because the final consequence is rarely any longer 1, in spite of we’re talking in regards to the worst doable fragmentation field right here. It also depends on the sort of free areas and it approaches 1, as we contain now got more of them. Let’s deliver, 20 equal free ranges give fragmentation=95%:

[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] -> F=0.95

The entire lot else works as desired. Having one free assign greater and one smaller gives fragmentation estimate lower than 50%:

[200,800] -> F=0.32

Including some shrimp holes between allocations doesn’t alternate the final consequence critical:

[200,800,1,1,1,1] -> F=0.3254

I am fairly glad with this intention. I mediate it would even be aged to estimate reminiscence fragmentation, let’s deliver, to benchmark masses of allocation algorithms or to decide whether or no longer it’s time to defragment.

I came up with this intention about a months ago, after discussions with my buddy Łukasz Izdebski. The general topic of reminiscence allocation is my location of pastime due to I fabricate Vulkan Memory Allocator and D3D12 Memory Allocator libraries as fraction of my work at AMD.

I did now not study prior work that has been performed on this field too completely. Now I’m able to witness my conception is rarely any longer new. I googled for “intention reminiscence fragmentation metric” and the very first consequence mentions the the same intention, the usage of square root of sum of squares of free assign sizes.

The entire lot I described above used to be about a single block of reminiscence. If an allocator manages a complete place of such blocks, we can discuss totally distinct problems. Let’s deliver, a defragmentation operation can also switch some allocations out of an nearly-empty block to realize again it to the machine. This may occasionally presumably presumably be the most perfect final consequence, so discovering such alternatives is critical more most predominant than measuring how immoral is the fragmentation in a single block.

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