Dynamic Memory Allocation

Harsh Reality
 Memory Matters
 Memory is not unbounded (Statically reserving the
maximum amount of global memory is NOT good!)
– It must be allocated and managed
– Many applications are memory dominated
• Especially those based on complex, graph algorithms
 Memory referencing bugs especially pernicious
– Effects are distant in both time and space
 Memory performance is not uniform
– Cache and virtual memory effects can greatly affect program
performance
– Adapting program to characteristics of memory system can
lead to major speed improvements

2
 Dynamic Memory Allocation
Application

Dynamic Memory Allocator

Heap Memory

 Dynamic Memory Allocator allocates a memory block only

when necessary
 Explicit vs. Implicit Memory Allocator
– Explicit: application allocates and frees space
• E.g., malloc and free in C
– Implicit: application allocates, but does not free space
• E.g. garbage collection in Java, ML or Lisp
 Allocation
– In both cases the memory allocator provides an abstraction of
memory as a set of blocks
– Doles out free memory blocks to application
 Will discuss simple explicit memory allocation today
3
 Process Memory Image
memory invisible to
kernel virtual memory
user code
stack
%esp

Memory mapped region for

Allocators request shared libraries
additional heap memory
from the operating
system using the sbrk the “brk” ptr
function.
run-time heap (via malloc)

uninitialized data (.bss)

initialized data (.data)
program text (.text)

0
4
 Malloc Package
 #include <stdlib.h>
 void *malloc(size_t size)
– If successful:
• Returns a pointer to a memory block of at least size bytes, (typically)
aligned to 8-byte boundary.
• If size == 0, returns NULL
– If unsuccessful: returns NULL (0) and sets errno.

 void free(void *p)

– Returns the block pointed at by p to pool of available memory
– p must come from a previous call to malloc or realloc.

 void *realloc(void *p, size_t size)

– Changes size of block p and returns pointer to new block.
– Contents of new block unchanged up to min of old and new size.

5
 Malloc Example
void foo(int n, int m) {
int i, *p;

/* allocate a block of n ints */

if ((p = (int *) malloc(n * sizeof(int))) == NULL) {
perror("malloc");
exit(0);
}
for (i=0; i<n; i++)
p[i] = i;

/* add m bytes to end of p block */

if ((p = (int *) realloc(p, (n+m) * sizeof(int))) == NULL) {
perror("realloc");
exit(0);
}
for (i=n; i < n+m; i++)
p[i] = i;

/* print new array */

for (i=0; i<n+m; i++)
printf("%d\n", p[i]);

free(p); /* return p to available memory pool */

}
6
 Assumptions
 Assumptions made in this lecture
– Memory is word addressed (each word can hold a pointer)

Free word
Allocated block Free block
(4 words) (3 words) Allocated word

7
 Allocation Examples
p1 = malloc(4)

p2 = malloc(5)

p3 = malloc(6)

free(p2)

p4 = malloc(2)

8
 Goals of Good malloc/free
 Primary goals
– Good time performance for malloc and free
• Ideally should take constant time (not always possible)
• Should certainly not take linear time in the number of blocks
– Good space utilization
• User allocated structures should be large fraction of the heap.
• Want to minimize “fragmentation”.

9
 Performance Goals: Throughput
 Given some sequence of malloc and free requests:
– R0, R1, ..., Rk, ... , Rn-1

 Want to maximize throughput and peak memory

utilization.
– These goals are often conflicting

 Throughput:
– Number of completed requests per unit time
– Example:
• 5,000 malloc calls and 5,000 free calls in 10 seconds
• Throughput is 1,000 operations/second.

10
 Performance Goals:
Peak Memory Utilization

 Given some sequence of malloc and free requests:

– R0, R1, ..., Rk, ... , Rn-1

 Def: Aggregate payload Pk:

– malloc(p) results in a block with a payload of p bytes..
– After request Rk has completed, the aggregate payload Pk is
the sum of currently allocated payloads.
 Def: Current heap size is denoted by Hk
– Assume that Hk is monotonically nondecreasing
 Def: Peak memory utilization:
– After k requests, peak memory utilization is:
• Uk = ( maxi<k Pi ) / Hk

11
 Internal Fragmentation
 Poor memory utilization caused by fragmentation.
– Comes in two forms: internal and external fragmentation
 Internal fragmentation
– For some block, internal fragmentation is the difference between
the block size and the payload size.

block

Internal Internal
payload fragmentation
fragmentation

– Caused by overhead of maintaining heap data structures, padding

for alignment purposes, or explicit policy decisions (e.g., not to
split the block).
– Depends only on the pattern of previous requests, and thus is easy
to measure.

12
 External Fragmentation
Occurs when there is enough aggregate heap memory, but no single
free block is large enough
p1 = malloc(4)

p2 = malloc(5)

p3 = malloc(6)

free(p2)

p4 = malloc(6)
oops!
External fragmentation depends on the pattern of future requests, and
thus is difficult to measure.
13
 Implementation Issues

 How do we know how much memory to free just

given a pointer? (free(p)?)
 How do we keep track of the free blocks?
 What do we do with the extra space when allocating
a structure that is smaller than the free block it is
placed in? (Splitting or not?)
 How do we pick a block to use for allocation --
many might fit? (Placement issue)
 How do we reinsert freed block? (Merge or not?)
p0

free(p0)
p1 = malloc(1)
14
 Knowing How Much to Free
 Standard method
– Keep the length of a block in the word preceding the block.
• This word is often called the header field or header
– Requires an extra word for every allocated block

p0 = malloc(4) p0

free(p0) Block size data

15
 Keeping Track of Free Blocks

 Method 1: Implicit list using lengths -- links all blocks

5 4 6 2

 Method 2: Explicit list among the free blocks using

pointers within the free blocks (Fast search for a
fitting free block)

5 4 6 2

 Method 3: Segregated free list

– Different free lists for different size classes (Faster search for
fitting free block)
 Method 4: Blocks sorted by size
– Can use a balanced tree (e.g. Red-Black tree) with pointers
within each free block, and the length used as a key
16
 Method 1: Implicit List

 Need to identify whether each block is free or

allocated
– Can use extra bit
– Bit can be put in the same word as the size if block sizes are
always multiples of two (mask out low order bit when reading
size).
1 word

size a a = 1: allocated block

a = 0: free block
Format of
size: block size
allocated and payload
free blocks
payload: application data
(allocated blocks only)
optional
padding

17
 Implicit List: Finding a Free Block
 First fit:
– Search list from beginning, choose first free block that fits
p = start;
while ((*p & 1) || \\ already allocated
(*p <= len)); \\ too small

– Can take linear time in total number of blocks (allocated and free)
– In practice it can cause “splinters” (small free blocks) at beginning
of list (Very likely search many small blocks from the beginning until
find a large enough block later of the list)
 Next fit:
– Like first-fit, but search list from location of end of previous search
(Likely to find a fit in the remainder of the previous block)
– Research suggests that fragmentation is worse
 Best fit:
– Search the list, choose the free block with the closest size that fits
– Keeps fragments small --- usually helps fragmentation
– Will typically run slower than first-fit because of exhaustive search

18
 Implicit List: Allocating in Free Block
 Allocating in a free block - splitting
– Since allocated space might be smaller than free space, we
might want to split the block

4 4 6 2

p
void addblock(ptr p, int len) {
int newsize = ((len + 1) >> 1) << 1; // add 1 and round up
int oldsize = *p & -2; // mask out low bit
*p = newsize | 1; // set new length
if (newsize < oldsize)
*(p+newsize) = oldsize - newsize; // set length in remaining
} // part of block

addblock(p, 2)

4 4 4 2 2
19
 Implicit List: Freeing a Block
 Simplest implementation:
– Only need to clear allocated flag
void free_block(ptr p) { *p = *p & -2}
– But can lead to “false fragmentation”

4 4 4 2 2

free(p) p

4 4 4 2 2

malloc(5)
Oops!

There is enough free space, but the allocator won’t be able to

find it

20
 Implicit List: Coalescing
 Join (coelesce) with next and/or previous
block if they are free
– Coalescing with next block
void free_block(ptr p) {
*p = *p & -2; // clear allocated flag
next = p + *p; // find next block
if ((*next & 1) == 0)
*p = *p + *next; // add to this block if
} // not allocated

4 4 4 2 2

free(p) p

4 4 6 2

– But how do we coalesce with previous block?

21
 Implicit List: Bidirectional Coalescing
 Boundary tags [Knuth73]
– Replicate size/allocated word at bottom of free blocks
– Allows us to traverse the “list” backwards, but requires extra space
– Important and general technique!

1 word
Header size a
a = 1: allocated block
a = 0: free block
Format of
allocated and payload and
padding size: total block size
free blocks
payload: application data
Boundary tag size a (allocated blocks only)
(footer)

4 4 4 4 6 6 4 4

22
 Constant Time Coalescing

Case 1 Case 2 Case 3 Case 4

allocated allocated free free

block being
freed
allocated free allocated free

23
Constant Time Coalescing (Case 1)

m1 1 m1 1

m1 1 m1 1
n 1 n 0

n 1 n 0
m2 1 m2 1

m2 1 m2 1

24
Constant Time Coalescing (Case 2)

m1 1 m1 1

m1 1 m1 1
n 1 n+m2 0

n 1
m2 0

m2 0 n+m2 0

25
Constant Time Coalescing (Case 3)

m1 0 n+m1 0

m1 0
n 1

n 1 n+m1 0
m2 1 m2 1

m2 1 m2 1

26
Constant Time Coalescing (Case 4)

m1 0 n+m1+m2 0

m1 0
n 1

n 1
m2 0

m2 0 n+m1+m2 0

27
 Summary of Key Allocator Policies
 Placement policy:
– First fit, next fit, best fit, etc.
– Trades off lower throughput for less fragmentation
• Interesting observation: segregated free lists (next lecture) approximate
a best fit placement policy without having the search entire free list.
 Splitting policy:
– When do we go ahead and split free blocks?
– How much internal fragmentation are we willing to tolerate?
 Coalescing policy:
– Immediate coalescing: coalesce adjacent blocks each time free is
called
– Deferred coalescing: try to improve performance of free by deferring
coalescing until needed. e.g.,
• Coalesce as you scan the free list for malloc.
• Coalesce when the amount of external fragmentation reaches some
threshold.

28
 Implicit Lists: Summary
 Implementation: very simple
 Allocate: linear time worst case (in number of TOTAL blocks)
 Free: constant time worst case -- even with coalescing
 Memory usage: will depend on placement policy
– First fit, next fit or best fit

 Not used in practice for malloc/free because of linear

time allocate. Used in many special purpose
applications.

 However, the concepts of splitting and boundary tag

coalescing are general to all allocators.

29
 Keeping Track of Free Blocks
 Method 1: Implicit list using lengths -- links all
blocks

5 4 6 2

 Method 2: Explicit list among the free blocks using

pointers within the free blocks

5 4 6 2

 Method 3: Segregated free lists

– Different free lists for different size classes
 Method 4: Blocks sorted by size (not discussed)
– Can use a balanced tree (e.g. Red-Black tree) with pointers
within each free block, and the length used as a key
30
 Explicit Free Lists
A B C

 Use data space for link pointers

– Typically doubly linked
– Still need boundary tags for coalescing
Forward links
A B
4 4 4 4 6 6 4 4 4 4
C
Back links

– It is important to realize that links are not necessarily in the

same order as the blocks

31
Allocating From Explicit Free Lists

pred succ

Before: free block

pred succ

After:
(with splitting) free block

32
 Freeing With Explicit Free Lists
 Insertion policy: Where in the free list do you put a
newly freed block?
– LIFO (last-in-first-out) policy
• Insert freed block at the beginning of the free list
• Pro: simple and constant time
• Con: studies suggest fragmentation is worse than address
ordered.
– Address-ordered policy
• Insert freed blocks so that free list blocks are always in address
order
– i.e. addr(pred) < addr(curr) < addr(succ)
• Con: requires search
• Pro: studies suggest fragmentation is better than LIFO

33
 Freeing With a LIFO Policy
 Case 1: a-a-a pred (p) succ (s)
– Insert self at beginning of
free list
a self a

 Case 2: a-a-f p s
– Splice out next, coalesce
before:
self and next, and add to
beginning of free list a self f

p s
after:
a f

34
 Freeing With a LIFO Policy (cont)
p s

 Case 3: f-a-a before:

– Splice out prev, coalesce f self a
with self, and add to
beginning of free list p s
after:
f a

p1 s1 p2 s2
 Case 4: f-a-f
before:
– Splice out prev and next,
coalesce with self, and f self f
add to beginning of list

p1 s1 p2 s2
after:
f
35
 Explicit List Summary
 Comparison to implicit list:
– Allocate is linear time in number of FREE blocks instead of
total blocks -- much faster allocates when most of the
memory is full
– Slightly more complicated allocate and free since needs to
splice blocks in and out of the list
– Some extra space for the links (2 extra words needed for
each “free” block)
 Main use of linked lists is in conjunction with
segregated free lists
– Keep multiple linked lists of different size classes, or
possibly for different types of objects

36
 Keeping Track of Free Blocks
 Method 1: Implicit list using lengths -- links all
blocks

5 4 6 2

 Method 2: Explicit list among the free blocks using

pointers within the free blocks

5 4 6 2

 Method 3: Segregated free list

– Different free lists for different size classes

 Method 4: Blocks sorted by size

– Can use a balanced tree (e.g. Red-Black tree) with pointers
within each free block, and the length used as a key

37
 Segregated Storage
 Each size class has its own collection of blocks

1-2

5-8

9-16

– Often have separate size class for every small size (2,3,4,…)
– For larger sizes typically have a size class for each power of 2

38
 Simple Segregated Storage
 Separate heap and free list for each size class (each block in the
same list has the same size)
 No splitting
 To allocate a block of size n:
– If free list for size n is not empty,
• allocate first block on list (note, list can be implicit or explicit)
– If free list is empty,
• get a new page
• create new free list from all blocks in page
• allocate first block on list
– Constant time
 To free a block:
– Add to free list

 Tradeoffs:
– Fast, but can fragment badly
39
Segregated Fits
(Improved Segregated Storage)
 Array of free lists, each one for some size class
 To allocate a block of size n:
– Search appropriate free list for block of size m > n
– If an appropriate block is found:
• Split block and place fragment on appropriate list (optional)
– If no block is found, try next larger class
– Repeat until block is found
 To free a block:
– Coalesce and place on appropriate list (optional)
 Performance
– Faster search than sequential fits (i.e., log time for power of
two size classes)
– Controls fragmentation of simple segregated storage
(Utilization performance is similar to Best Fit)
– Coalescing can increase search times for free (free to which
size class?)
• Deferred coalescing can help 40
 For More Info on Allocators

 Donald. Knuth, “The Art of Computer Programming,

Second Edition”, Addison Wesley, 1973
– The classic reference on dynamic storage allocation

 Wilson et al, “Dynamic Storage Allocation: A Survey

and Critical Review”, Proc. 1995 Int’l Workshop on
Memory Management, Kinross, Scotland, Sept, 1995.
– Comprehensive survey

41
 Implicit Memory Management:
Garbage Collection
 Garbage collection: automatic reclamation of heap-
allocated storage -- application never has to free

void foo() {
int *p = malloc(128);
return; /* p block is now garbage */
}

 Common in functional languages, scripting

languages, and modern object oriented languages:
– Lisp, ML, Java, Perl, Mathematica,
 Variants (conservative garbage collectors) exist for C
and C++
– Cannot collect all garbage
42
 Garbage Collection
 How does the memory manager know when memory
can be freed?
– In general we cannot know what is going to be used in the
future since it depends on conditionals
– But we can tell that certain blocks cannot be used if there
are no pointers to them

43
 Classical GC algorithms

 Mark and sweep collection (McCarthy, 1960)

– Does not move blocks (unless you also “compact”)
 Reference counting (Collins, 1960)
– Does not move blocks (not discussed)
 Copying collection (Minsky, 1963)
– Moves blocks (not discussed)

 For more information, see Jones and Lin, “Garbage

Collection: Algorithms for Automatic Dynamic
Memory”, John Wiley & Sons, 1996.

44
 Memory as a Graph
 We view memory as a directed graph
– Each block is a node in the graph
– Each pointer is an edge in the graph
– Locations not in the heap that contain pointers into the heap are
called root nodes (e.g. registers, locations on the stack, global
variables)

Root nodes

Heap nodes reachable

Not-reachable
(garbage)

 A node (block) is reachable if there is a path from any root to that node.
 Non-reachable nodes are garbage (never needed by the application)
45
 Assumptions For This Lecture
 Application
– new(n): returns pointer to new block with all locations cleared
– read(b,i): read location i of block b into register
– write(b,i,v): write v into location i of block b

 Each block will have a header word

– addressed as b[-1], for a block b
– Used for different purposes in different collectors

 Instructions used by the Garbage Collector

– is_ptr(p): determines whether p is a pointer
– length(b): returns the length of block b, not including the header
– get_roots(): returns all the roots

46
 Mark and Sweep Collecting
 Can build on top of malloc/free package
– Allocate using malloc until you “run out of space”
 When out of space:
– Use extra mark bit in the head of each block
– Mark: Start at roots and set mark bit on all reachable memory
– Sweep: Scan all blocks and free blocks that are “allocated”
but “not marked”
Mark bit set
root

Before mark

After mark

After sweep free free

47
 Mark and Sweep (cont.)
Mark using depth-first traversal of the memory graph
ptr mark(ptr p) {
if (!is_ptr(p)) return; // do nothing if not pointer
if (markBitSet(p)) return // check if already marked
setMarkBit(p); // set the mark bit
for (i=0; i < length(p); i++) // mark all children
mark(p[i]);
return;
}

Sweep using lengths to find next block

ptr sweep(ptr p, ptr end) {
while (p < end) {
if markBitSet(p)
clearMarkBit();
else if (allocateBitSet(p))
free(p);
p += length(p);
}

48
 Conservative Mark and Sweep in C
 A conservative collector for C programs
– Is_ptr() determines if a word is a pointer by checking if it
points to an allocated block of memory.
– But, in C pointers can point to the middle of a block.
ptr
header

 So how do we find the beginning of the block?

– Can use balanced tree to keep track of all allocated blocks
where the key is the location
– Balanced tree pointers can be stored in header (use two
additional words)
head data So, we can traverse the tree to
see if the pointer is pointing a
size
valid location of a allocated
block
left right
all blocks located at all blocks located at
smaller addresses larger addresses 49
 Memory-Related Bugs

 Dereferencing bad pointers

 Reading uninitialized memory
 Overwriting memory
 Referencing nonexistent variables
 Freeing blocks multiple times
 Referencing freed blocks
 Failing to free blocks

50
 Dereferencing Bad Pointers
 The classic scanf bug

scanf(“%d”, val);

51
 Reading Uninitialized Memory
 Assuming that heap data is initialized to zero

/* return y = Ax */
int *matvec(int **A, int *x) {
int *y = malloc(N*sizeof(int));
int i, j;

for (i=0; i<N; i++)

for (j=0; j<N; j++)
y[i] += A[i][j]*x[j];
return y;
}

52
 Overwriting Memory
 Allocating the (possibly) wrong sized object

int **p;
should be
sizeof(int *)
p = malloc(N*sizeof(int));

for (i=0; i<N; i++) {

p[i] = malloc(M*sizeof(int));
}

This is a problem if
sizeof(int) != sizeof(int *)

53
 Overwriting Memory
 Off-by-one error

int **p;

p = malloc(N*sizeof(int *));

for (i=0; i<=N; i++) {

p[i] = malloc(M*sizeof(int));
}

54
 Overwriting Memory
 Not checking the max string size
char s[8];
int i;

gets(s); /* reads “123456789” from stdin */

55
 Overwriting Memory
 Referencing a pointer instead of the object it points
to

int *BinheapDelete(int **binheap, int *size) {

int *packet;
packet = binheap[0];
binheap[0] = binheap[*size - 1];
*size--;
Heapify(binheap, *size, 0);
return(packet);
}

Intent is to decrement the integer value

pointed by the pointer “size”

So, should be (*size)--

56
 Overwriting Memory
 Misunderstanding pointer arithmetic

int *search(int *p, int val) {

while (*p && *p != val) should be

p += sizeof(int); p++
return p;
}

57
 Referencing Nonexistent Variables
 Forgetting that local variables disappear when a
function returns

int *foo () {
int val;
return &val;
}

58
 Freeing Blocks Multiple Times
 Nasty!

x = malloc(N*sizeof(int));
<manipulate x>
free(x);

y = malloc(M*sizeof(int));
<manipulate y>
free(x);

59
 Referencing Freed Blocks
 Evil!

x = malloc(N*sizeof(int));
<manipulate x>
free(x);
...
y = malloc(M*sizeof(int));
for (i=0; i<M; i++)
y[i] = x[i]++;

60
 Failing to Free Blocks
(Memory Leaks)
 Slow, long-term killer!

foo() {
int *x = malloc(N*sizeof(int));
...
return;
}

61
 Failing to Free Blocks
(Memory Leaks)

 Freeing only part of a data structure

struct list {
int val;
struct list *next;
};

foo() {
struct list *head =
malloc(sizeof(struct list));
head->val = 0;
head->next = NULL;
<create and manipulate the rest of the list>
...
free(head);
return;
}

62
 Don’t make memory related bugs

 Deep understanding on the memory management

mechanism will help!

63