Skip to main content

Chapter 17: Assumptions

This page is a generated reference surface for selective reading. It exists to keep the learner apps guide-first while still preserving source access.

Learning objectives​

  • Explain the main ideas and vocabulary in Assumptions.
  • Work through the source examples for Assumptions without depending on raw chunk order.
  • Use Assumptions as selective reference when learner modules point back to Ostep.

Prerequisites​

  • Earlier prerequisite concepts leading into Chapter 17: Assumptions.

Module targets​

  • module-02-memory-management-virtual-memory
  • module-04-file-systems-io

AI companion modes​

  • Explain simply
  • Socratic tutor
  • Quiz me
  • Challenge my understanding
  • Diagnose my confusion
  • Generate extra practice
  • Revision mode
  • Connect forward / backward

Source-of-truth note​

This unit is anchored to Ostep and the source chapter "Chapter 17: Assumptions". Use external resources only to clarify, extend, or modernize details without replacing the chapter's conceptual spine.

External enrichment​

No chapter-specific enrichment resources are curated yet. Add them in the unit manifest when a source clearly improves learning.

Source provenance​

  • Primary source: Ostep
  • Source chapter 17: Chapter 17: Assumptions
  • Raw source file: 075-17-1-assumptions.md
  • Raw source file: 076-17-2-low-level-mechanisms.md
  • Raw source file: 077-17-2-low-level-mechanisms-part-2.md
  • Raw source file: 078-17-3-basic-strategies.md
  • Raw source file: 079-17-4-other-approaches.md

Merged source​

Assumptions​

17.1 Assumptions

17 Free-Space Management​

In this chapter, we take a small detour from our discussion of virtualizing memory to discuss a fundamental aspect of any memory management system, whether it be a malloc library (managing pages of a process's heap) or the OS itself (managing portions of the address space of a process). Specifically, we will discuss the issues surroundingfree-space management.

Let us make the problem more specific. Managing free space can certainly be easy, as we will see when we discuss the concept ofpaging. It is easy when the space you are managing is divided into fixed-sized units; in such a case, you just keep a list of these fixed-sized units; when a client requests one of them, return the first entry.

Where free-space management becomes more difficult (and interesting) is when the free space you are managing consists of variable-sized units; this arises in a user-level memory-allocation library (as inmalloc() andfree()) and in an OS managing physical memory when usingsegmentationto implement virtual memory. In either case, the problem that exists is known asexternal fragmentation: the free space gets chopped into little pieces of different sizes and is thus fragmented; subsequent requests may fail because there is no single contiguous space that can satisfy the request, even though the total amount of free space exceeds the size of the request.

free used free 0 10 20 30

The figure shows an example of this problem. In this case, the total free space available is 20 bytes; unfortunately, it is fragmented into two chunks of size 10 each. As a result, a request for 15 bytes will fail even though there are 20 bytes free. And thus we arrive at the problem addressed in this chapter.

1

CRUX: HOWTOMANAGEFREESPACE

How should free space be managed, when satisfying variable-sized requests? What strategies can be used to minimize fragmentation? What are the time and space overheads of alternate approaches?

Most of this discussion will focus on the great history of allocators found in user-level memory-allocation libraries. We draw on Wilson's excellent survey [W+95] but encourage interested readers to go to the source document itself for more details1.

We assume a basic interface such as that provided bymalloc()and

free(). Specifically,void *malloc(sizet size)takes a single pa-
rameter, size, which is the number of bytes requested by the application; it hands back a pointer (of no particular type, or avoid pointerin
C lingo) to a region of that size (or greater). The complementary routine
void free(void *ptr)takes a pointer and frees the corresponding

chunk. Note the implication of the interface: the user, when freeing the space, does not inform the library of its size; thus, the library must be able to figure out how big a chunk of memory is when handed just a pointer to it. We'll discuss how to do this a bit later on in the chapter.

The space that this library manages is known historically as theheap, and the generic data structure used to manage free space in the heap is some kind offree list. This structure contains references to all of the free chunks of space in the managed region of memory. Of course, this data structure need not be a listper se, but just some kind of data structure to track free space.

We further assume that primarily we are concerned withexternal fragmentation, as described above. Allocators could of course also have the problem ofinternal fragmentation; if an allocator hands out chunks of memory bigger than that requested, any unasked for (and thus unused) space in such a chunk is consideredinternalfragmentation (because the waste occurs inside the allocated unit) and is another example of space waste. However, for the sake of simplicity, and because it is the more interesting of the two types of fragmentation, we'll mostly focus on external fragmentation.

We'll also assume that once memory is handed out to a client, it cannot be relocated to another location in memory. For example, if a program

calls malloc()and is given a pointer to some space within the heap,

that memory region is essentially "owned" by the program (and cannot be moved by the library) until the program returns it via a corresponding call tofree(). Thus, nocompactionof free space is possible, which 1It is nearly 80 pages long; thus, you really have to be interested!

would be useful to combat fragmentation2. Compaction could, however, be used in the OS to deal with fragmentation when implementingsegmentation(as discussed in said chapter on segmentation).

Finally, we'll assume that the allocator manages a contiguous region of bytes. In some cases, an allocator could ask for that region to grow; for example, a user-level memory-allocation library might call into the kernel to grow the heap (via a system call such assbrk) when it runs out of space. However, for simplicity, we'll just assume that the region is a single fixed size throughout its life.

Low Level Mechanisms​

17.2 Low-level Mechanisms

Before delving into some policy details, we'll first cover some common mechanisms used in most allocators. First, we'll discuss the basics of splitting and coalescing, common techniques in most any allocator. Second, we'll show how one can track the size of allocated regions quickly and with relative ease. Finally, we'll discuss how to build a simple list inside the free space to keep track of what is free and what isn't.

Splitting and Coalescing

A free list contains a set of elements that describe the free space still remaining in the heap. Thus, assume the following 30-byte heap:

free used free 0 10 20 30

The free list for this heap would have two elements on it. One entry describes the first 10-byte free segment (bytes 0-9), and one entry describes the other free segment (bytes 20-29):

addr:0 addr:20 head NULL len:10 len:10

As described above, a request for anything greater than 10 bytes will fail (returning NULL); there just isn't a single contiguous chunk of memory of that size available. A request for exactly that size (10 bytes) could be satisfied easily by either of the free chunks. But what happens if the request is for somethingsmallerthan 10 bytes?

Assume we have a request for just a single byte of memory. In this case, the allocator will perform an action known assplitting: it will find 2Once you hand a pointer to a chunk of memory to a C program, it is generally difficult to determine all references (pointers) to that region, which may be stored in other variables or even in registers at a given point in execution. This may not be the case in more stronglytyped, garbage-collected languages, which would thus enable compaction as a technique to combat fragmentation.

a free chunk of memory that can satisfy the request and split it into two.

The first chunk it will return to the caller; the second chunk will remain on the list. Thus, in our example above, if a request for 1 byte were made, and the allocator decided to use the second of the two elements on the list

to satisfy the request, the call to malloc() would return
(the address of
the 1-byte allocated region) and the list would end up looking like this:

addr:0 addr:21 head NULL len:10 len:9

In the picture, you can see the list basically stays intact; the only change is that the free region now starts at 21 instead of 20, and the length of that free region is now just 93. Thus, the split is commonly used in allocators when requests are smaller than the size of any particular free chunk.

A corollary mechanism found in many allocators is known ascoalescingof free space. Take our example from above once more (free 10 bytes, used 10 bytes, and another free 10 bytes).

Given this (tiny) heap, what happens when an application calls free(10),

thus returning the space in the middle of the heap? If we simply add this free space back into our list without too much thinking, we might end up with a list that looks like this:

addr:10 addr:0 addr:20 head NULL len:10 len:10 len:10

Note the problem: while the entire heap is now free, it is seemingly​

divided into three chunks of 10 bytes each. Thus, if a user requests 20 bytes, a simple list traversal will not find such a free chunk, and return failure.

What allocators do in order to avoid this problem is coalesce free space when a chunk of memory is freed. The idea is simple: when returning a free chunk in memory, look carefully at the addresses of the chunk you are returning as well as the nearby chunks of free space; if the newlyfreed space sits right next to one (or two, as in this example) existing free chunks, merge them into a single larger free chunk. Thus, with coalescing, our final list should look like this:

addr:0 head NULL len:30

Indeed, this is what the heap list looked like at first, before any allocations were made. With coalescing, an allocator can better ensure that large free extents are available for the application.

3This discussion assumes that there are no headers, an unrealistic but simplifying assumption we make for now.

The header used by malloc library ptr

The 20 bytes returned to caller

Figure 17.1:An Allocated Region Plus Header hptr size: 20 magic: 1234567 ptr

The 20 bytes returned to caller

Figure 17.2:Specific Contents Of The Header

Tracking The Size Of Allocated Regions

You might have noticed that the interface to free(void *ptr)does

not take a size parameter; thus it is assumed that given a pointer, the malloc library can quickly determine the size of the region of memory being freed and thus incorporate the space back into the free list.

To accomplish this task, most allocators store a little bit of extra information in aheaderblock which is kept in memory, usually just before the handed-out chunk of memory. Let's look at an example again (Figure 17.1). In this example, we are examining an allocated block of size 20 bytes, pointed to byptr; imagine the user calledmalloc()and stored

the results inptr, e.g.,ptr = malloc(20);.

The header minimally contains the size of the allocated region (in this case, 20); it may also contain additional pointers to speed up deallocation, a magic number to provide additional integrity checking, and other information. Let's assume a simple header which contains the size of the region and a magic number, like this:

typedef struct __header_t {
int size; int magic;
} header_t;
The example above would look like what you see in Figure 17.2. When the user callsfree(ptr), the library then uses simple pointer arithmetic to figure out where the header begins:
void free(void *ptr) {
header_t *hptr = (void *)ptr - sizeof(header_t);
...

After obtaining such a pointer to the header, the library can easily determine whether the magic number matches the expected value as a san-

ity check (assert(hptr->magic == 1234567)) and calculate the to-

tal size of the newly-freed region via simple math (i.e., adding the size of the header to size of the region). Note the small but critical detail in the last sentence: the size of the free region is the size of the header plus the size of the space allocated to the user. Thus, when a user requestsNbytes of memory, the library does not search for a free chunk of sizeN; rather, it searches for a free chunk of sizeNplus the size of the header.

Embedding A Free List

Thus far we have treated our simple free list as a conceptual entity; it is just a list describing the free chunks of memory in the heap. But how do we build such a list inside the free space itself?

In a more typical list, when allocating a new node, you would just call

malloc()when you need space for the node. Unfortunately, within the

memory-allocation library, you can't do this! Instead, you need to build the listinsidethe free space itself. Don't worry if this sounds a little weird; it is, but not so weird that you can't do it!

Assume we have a 4096-byte chunk of memory to manage (i.e., the heap is 4KB). To manage this as a free list, we first have to initialize said list; initially, the list should have one entry, of size 4096 (minus the header size). Here is the description of a node of the list:

typedef struct __node_t {
int size;
struct __node_t *next;
} node_t;

Now let's look at some code that initializes the heap and puts the first element of the free list inside that space. We are assuming that the heap is

built within some free space acquired via a call to the system callmmap();

this is not the only way to build such a heap but serves us well in this

Low Level Mechanisms Part 2​

17.2 Low-level Mechanisms (Part 2)

example. Here is the code:​

// mmap() returns a pointer to a chunk of free space
node_t *head = mmap(NULL, 4096, PROT_READ|PROT_WRITE,
MAP_ANON|MAP_PRIVATE, -1, 0);
head->size = 4096 - sizeof(node_t);
head->next = NULL;
After running this code, the status of the list is that it has a single entry, of size 4088. Yes, this is a tiny heap, but it serves as a fine example for us head [virtual address: 16KB] size:
header: size field next:
header: next field (NULL is 0)

... the rest of the 4KB chunk

Figure 17.3:A Heap With One Free Chunk

[virtual address: 16KB] size: 100 magic: 1234567 ptr

. . . The 100 bytes now allocated head size: 3980 next: 0

. . . The free 3980 byte chunk

Figure 17.4:A Heap: After One Allocation here. Theheadpointer contains the beginning address of this range; let's assume it is 16KB (though any virtual address would be fine). Visually, the heap thus looks like what you see in Figure 17.3.

Now, let's imagine that a chunk of memory is requested, say of size 100 bytes. To service this request, the library will first find a chunk that is large enough to accommodate the request; because there is only one free chunk (size: 4088), this chunk will be chosen. Then, the chunk will be splitinto two: one chunk big enough to service the request (and header, as described above), and the remaining free chunk. Assuming an 8-byte header (an integer size and an integer magic number), the space in the heap now looks like what you see in Figure 17.4.

Thus, upon the request for 100 bytes, the library allocated 108 bytes out of the existing one free chunk, returns a pointer (markedptrin the figure above) to it, stashes the header information immediately before the magic: 1234567

. . . 100 bytes still allocated size: 100 magic: 1234567 sptr

. . . 100 bytes still allocated

(but about to be freed)

size: 100 magic: 1234567

. . . 100-bytes still allocated head size: 3764 next: 0

. . . The free 3764-byte chunk

Figure 17.5:Free Space With Three Chunks Allocated allocated space for later use uponfree(), and shrinks the one free node in the list to 3980 bytes (4088 minus 108).

Now let's look at the heap when there are three allocated regions, each of 100 bytes (or 108 including the header). A visualization of this heap is shown in Figure 17.5.

As you can see therein, the first 324 bytes of the heap are now allocated, and thus we see three headers in that space as well as three 100byte regions being used by the calling program. The free list remains uninteresting: just a single node (pointed to byhead), but now only 3764 bytes in size after the three splits. But what happens when the calling program returns some memory viafree()?

magic: 1234567

. . . 100 bytes still allocated head size: 100 next: 16708 sptr

. . . (now a free chunk of memory) size: 100 magic: 1234567

. . . 100-bytes still allocated size: 3764 next: 0

. . . The free 3764-byte chunk

Figure 17.6:Free Space With Two Chunks Allocated

In this example, the application returns the middle chunk of allocated memory, by callingfree(16500)(the value 16500 is arrived upon by adding the start of the memory region, 16384, to the 108 of the previous chunk and the 8 bytes of the header for this chunk). This value is shown in the previous diagram by the pointersptr.

The library immediately figures out the size of the free region, and then adds the free chunk back onto the free list. Assuming we insert at the head of the free list, the space now looks like this (Figure 17.6).

And now we have a list that starts with a small free chunk (100 bytes, pointed to by the head of the list) and a large free chunk (3764 bytes).

next: 16492

. . . (now free) size: 100 next: 16708

. . . (now free) head size: 100 next: 16384

. . . (now free) size: 3764 next: 0

. . . The free 3764-byte chunk

Figure 17.7:A Non-Coalesced Free List

Our list finally has more than one element on it! And yes, the free space is fragmented, an unfortunate but common occurrence.

One last example: let's assume now that the last two in-use chunks are freed. Without coalescing, you might end up with a free list that is highly fragmented (see Figure 17.7).

As you can see from the figure, we now have a big mess! Why? Simple, we forgot tocoalescethe list. Although all of the memory is free, it is chopped up into pieces, thus appearing as a fragmented memory despite not being one. The solution is simple: go through the list and merge neighboring chunks; when finished, the heap will be whole again.

Basic Strategies​

17.3 Basic Strategies

Growing The Heap​

We should discuss one last mechanism found within many allocation libraries. Specifically, what should you do if the heap runs out of space?

The simplest approach is just to fail. In some cases this is the only option, and thus returning NULL is an honorable approach. Don't feel bad! You tried, and though you failed, you fought the good fight.

Most traditional allocators start with a small-sized heap and then request more memory from the OS when they run out. Typically, this means they make some kind of system call (e.g.,sbrkin most UNIX systems) to grow the heap, and then allocate the new chunks from there. To service thesbrkrequest, the OS finds free physical pages, maps them into the address space of the requesting process, and then returns the value of the end of the new heap; at that point, a larger heap is available, and the request can be successfully serviced.

Now that we have some machinery under our belt, let's go over some basic strategies for managing free space. These approaches are mostly based on pretty simple policies that you could think up yourself; try it before reading and see if you come up with all of the alternatives (or maybe some new ones!).

The ideal allocator is both fast and minimizes fragmentation. Unfortunately, because the stream of allocation and free requests can be arbitrary (after all, they are determined by the programmer), any particular strategy can do quite badly given the wrong set of inputs. Thus, we will not describe a "best" approach, but rather talk about some basics and discuss their pros and cons.

Best Fit

Thebest fitstrategy is quite simple: first, search through the free list and find chunks of free memory that are as big or bigger than the requested size. Then, return the one that is the smallest in that group of candidates; this is the so called best-fit chunk (it could be called smallest fit too). One pass through the free list is enough to find the correct block to return.

The intuition behind best fit is simple: by returning a block that is close to what the user asks, best fit tries to reduce wasted space. However, there is a cost; naive implementations pay a heavy performance penalty when performing an exhaustive search for the correct free block.

Worst Fit

Theworst fitapproach is the opposite of best fit; find the largest chunk and return the requested amount; keep the remaining (large) chunk on the free list. Worst fit tries to thus leave big chunks free instead of lots of small chunks that can arise from a best-fit approach. Once again, however, a full search of free space is required, and thus this approach can be costly. Worse, most studies show that it performs badly, leading to excess fragmentation while still having high overheads.

Other Approaches​

17.4 Other Approaches

First Fit​

Thefirst fit method simply finds the first block that is big enough and returns the requested amount to the user. As before, the remaining free space is kept free for subsequent requests.

First fit has the advantage of speed -- no exhaustive search of all the free spaces are necessary -- but sometimes pollutes the beginning of the free list with small objects. Thus, how the allocator manages the free list's order becomes an issue. One approach is to useaddress-based ordering; by keeping the list ordered by the address of the free space, coalescing becomes easier, and fragmentation tends to be reduced.

Next Fit

Instead of always beginning the first-fit search at the beginning of the list, thenext fit algorithm keeps an extra pointer to the location within the list where one was looking last. The idea is to spread the searches for free space throughout the list more uniformly, thus avoiding splintering of the beginning of the list. The performance of such an approach is quite similar to first fit, as an exhaustive search is once again avoided.

Examples​

Here are a few examples of the above strategies. Envision a free list with three elements on it, of sizes 10, 30, and 20 (we'll ignore headers and other details here, instead just focusing on how strategies operate):

head 10 30 20 NULL

Assume an allocation request of size 15. A best-fit approach would search the entire list and find that 20 was the best fit, as it is the smallest free space that can accommodate the request. The resulting free list:

head 10 30 5 NULL

As happens in this example, and often happens with a best-fit approach, a small free chunk is now left over. A worst-fit approach is similar but instead finds the largest chunk, in this example 30. The resulting list:

head 10 15 20 NULL

The first-fit strategy, in this example, does the same thing as worst-fit, also finding the first free block that can satisfy the request. The difference is in the search cost; both best-fit and worst-fit look through the entire list; first-fit only examines free chunks until it finds one that fits, thus reducing search cost.

These examples just scratch the surface of allocation policies. More detailed analysis with real workloads and more complex allocator behaviors (e.g., coalescing) are required for a deeper understanding. Perhaps something for a homework section, you say?

Beyond the basic approaches described above, there have been a host of suggested techniques and algorithms to improve memory allocation in some way. We list a few of them here for your consideration (i.e., to make you think about a little more than just best-fit allocation).

Segregated Lists

One interesting approach that has been around for some time is the use ofsegregated lists. The basic idea is simple: if a particular application has one (or a few) popular-sized request that it makes, keep a separate list just to manage objects of that size; all other requests are forwarded to a more general memory allocator.

The benefits of such an approach are obvious. By having a chunk of memory dedicated for one particular size of requests, fragmentation is much less of a concern; moreover, allocation and free requests can be served quite quickly when they are of the right size, as no complicated search of a list is required.

Just like any good idea, this approach introduces new complications into a system as well. For example, how much memory should one dedicate to the pool of memory that serves specialized requests of a given size, as opposed to the general pool? One particular allocator, theslab allocatorby uber-engineer Jeff Bonwick (which was designed for use in the Solaris kernel), handles this issue in a rather nice way [B94].

Specifically, when the kernel boots up, it allocates a number ofobject cachesfor kernel objects that are likely to be requested frequently (such as locks, file-system inodes, etc.); the object caches thus are each segregated free lists of a given size and serve memory allocation and free requests quickly. When a given cache is running low on free space, it requests someslabs of memory from a more general memory allocator (the total amount requested being a multiple of the page size and the object in question). Conversely, when the reference counts of the objects within a given slab all go to zero, the general allocator can reclaim them from the specialized allocator, which is often done when the VM system needs more memory.