1. 1 Dynamic Memory Allocation

2. 2 Outline Implementation of a simple allocator Explicit Free List Segregated Free List Suggested reading: 10.9, 10.10, 10.11, 10.12, 10.13

3. 3 Dynamic Memory Allocation P731 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

4. 4 Dynamic Memory Allocation Allocation –In both cases the memory allocator provides an abstraction of memory as a set of blocks –Doles out free memory blocks to application Doles: 发放

5. 5 Malloc package P731 #include void *malloc(size_t size) –if successful: returns a pointer to a memory block of at least size bytes, aligned to 8-byte boundary. if size==0, returns NULL –if unsuccessful: returns NULL 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,calloc or realloc.

6. 6 sbrk() Function P732 #include void *sbrk(int incr) –If successful It returns the old value of brk –If unsuccessful It returns –1 It sets errno to ENOMEM –If incr is zero It returns the current value –incr can be a negative number

7. 7 10.9.2 Why Dynamic Memory Allocation

8. 8 1 #include "csapp.h" 2 #define MAXN 15213 3 4 int array[MAXN]; 5 6 int main() 7 { 8 int i, n; 9 10 scanf("%d", &n); 11 if (n > MAXN) 12 app_error("Input file too big"); 13 for (i = 0; i < n; i++) 14 scanf("%d", &array[i]); 15 exit(0); 16 } Why Dynamic Memory Allocation P734

9. 9 1 #include "csapp.h" 2 3 int main() 4 { 5 int *array, i, n; 6 7 scanf("%d", &n); 8 array = (int *)Malloc(n * sizeof(int)); 9 for (i = 0; i < n; i++) 10 scanf("%d", &array[i]); 11 exit(0); 12 } Why Dynamic Memory Allocation P734

10. 10 Assumptions made in this lecture –memory is word addressed (each word can hold a pointer) Allocated block (4 words) Free block (3 words) Free word Allocated word Assumptions

11. 11 p1 = malloc(4) p2 = malloc(5) p3 = malloc(6) free(p2) p4 = malloc(2) Allocation examples Figure 10.36 P733

12. 12 10.9.3 Allocator Requirements and Goals

13. 13 Constraints Applications: –Can issue arbitrary sequence of allocation and free requests –Free requests must correspond to an allocated block

14. 14 Constraints Allocators –Can’t control number or size of allocated blocks –Must respond immediately to all allocation requests i.e., can’t reorder or buffer requests –Must allocate blocks from free memory i.e., can only place allocated blocks in free memory

15. 15 Constraints Allocators –Must align blocks so they satisfy all alignment requirements usually 8 byte alignment –Can only manipulate and modify free memory –Can’t move the allocated blocks once they are allocated i.e., compaction is not allowed

16. 16 Goals P735 Given some sequence of malloc and free requests: – R 0, R 1,..., R k,..., R n-1 Want to maximize throughput and peak memory utilization. –These goals are often conflicting

17. 17 Performance goals: throughput Number of completed requests per unit time Example: –5,00 malloc calls and 5,00 free calls in 1 seconds –throughput is 1,000 operations/second.

18. 18 Performance goals: peak memory utilization Given some sequence of malloc and free requests: – R 0, R 1,..., R k,..., R n-1 Def: aggregate payload P k : – malloc(p) results in a block with a payload of p bytes. –After request R k has completed, the aggregate payload P k is the sum of currently allocated payloads. Aggregate: 合计，累计

19. 19 Performance goals: peak memory utilization Given some sequence of malloc and free requests: – R 0, R 1,..., R k,..., R n-1 Def: current heap size is denoted by H k –Note that H k is monotonically nondecreasing Def: peak memory utilization: –After k requests, peak memory utilization is: U k = ( max i<k P i ) / H k

20. 20 10.9.4 Fragmentation Fragmentation: 分裂

21. 21 Fragmentation Poor memory utilization caused by fragmentation –Comes in two forms: internal fragmentation external fragmentation

22. 22 Internal Fragmentation Internal fragmentation –For some block, internal fragmentation is the difference between the block size and the payload size payload Internal fragmentation block Internal fragmentation

23. 23 Internal Fragmentation Internal fragmentation –Is 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.

24. 24 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)

25. 25 External fragmentation External fragmentation depends on –the pattern of future requests –and thus is difficult to measure

26. 26 10.9.5 Implementation Issues

27. 27 Implementation issues How do we know how much memory to free just given a pointer? How do we keep track of the free blocks? p1 = malloc(1) p0 free(p0)

28. 28 Implementation issues What do we do with the extra space when allocating a structure that is smaller than the free block it is placed in? How do we pick a block to use for allocation –many might fit? How do we reinsert freed block? Reinsert ：重新插入

29. 29 Knowing how much to free Standard method –keep the length of a structure in the word preceding the structure This word is often called the header field or header –requires an extra word for every allocated structure

30. 30 Knowing how much to free free(p0) p0 = malloc(4)p0 Block sizedata 5

31. 31 10.9.6 Implicit Free Lists

32. 32 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 8 (mask out low order bit when reading size).

33. 33 Implicit list size 1 word Format of allocated and free blocks payload a = 1: allocated block a = 0: free block size: block size payload: application data (allocated blocks only) a optional padding 00 4426 p Figure 10.37 P738

34. 34 10.9.7 Placing Allocated Blocks

35. 35 Finding a free block 1 ） First fit: –Search list from beginning, choose first free block that fits –Can take linear time in total number of blocks (allocated and free) –In practice it can cause “splinters” at beginning of list p = start; while ((p < end) ||\\ not passed end (*p & 1) || \\ already allocated (*p <= len) );\\ too small

36. 36 Finding a free block 2 ） Next fit : –Like first-fit, but search list from location of end of previous search –Research suggests that fragmentation is worse 3 ） 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

37. 37 10.9.8 Splitting Free Blocks

38. 38 Allocating in a free block Allocating in a free block - splitting –Since allocated space might be smaller than free space, we might want to split the block 4426 p 424 2 4

39. 39 10.9.9 Getting Additional Heap Memory

40. 40 10.9.10 Coalescing Free Blocks Coalescing ：接合

41. 41 Freeing a block Simplest implementation: –Only need to clear allocated flag –But can lead to “false fragmentation” –There is enough free space, but the allocator won’t be able to find it 424 2 free(p) p 442 4 4 2 malloc(5)

42. 42 Coalescing Join with next and/or previous block if they are free –Coalescing with next block –But how do we coalesce with previous block? 424 2 free(p) p 442 4 6

43. 43 10.9.11 Coalescing with Boundary Tags

44. 44 Bidirectional 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!

45. 45 Bidirectional 44446464 size 1 word Format of allocated and free blocks payload and padding a = 1: allocated block a = 0: free block size: block size payload: application data (allocated blocks only) a sizea boundary tag (footer) header 00 00 Figure 10.41 P742

46. 46 allocated free allocated free block being freed Case 1Case 2Case 3Case 4 Constant time coalescing Figure 10.42 P743

47. 47 m11 1 n1 n1 m21 1 m11 1 n0 n0 m21 1 Constant time coalescing (case 1)

48. 48 m11 1 n+m20 0 m11 1 n1 n1 m20 0 Constant time coalescing (case 2)

49. 49 m10 0 n1 n1 m21 1 n+m10 0 m21 1 Constant time coalescing (case 3)

50. 50 m10 0 n1 n1 m20 0 n+m1+m20 0 Constant time coalescing (case 4)

51. 51 10.9.12 Putting it Together: Implementing a Simple Allocator

52. 52 1 int mm_init(void); 2 void *mm_malloc(size_t size); 3 void mm_free(void *bp); Implementing a Simple Allocator

53. 53 Data Structure Figure 10.44 P745

54. 54 1 #include "csapp.h" 2 3 /* private global variables */ 4 static void *mem_start_brk; /* points to first byte of the heap */ 5 static void *mem_brk; /* points to last byte of the heap */ 6 static void *mem_max_addr; /* max virtual address for the heap */ 7 8 /* 9 * mem_init - initializes the memory system model 10 */ 11 void mem_init(int size) 12 { 13 mem_start_brk = (void *)Malloc(size); /* models available VM */ 14 mem_brk = mem_start_brk; /* heap is initially empty */ 15 mem_max_addr = mem_start_brk + size; /* max VM address for heap */ 16 } 17 Initialize Figure 10.43 P745

55. 55 18 /* 19 * mem_sbrk - simple model of the the sbrk function. Extends the heap 20 * by incr bytes and returns the start address of the new area. In 21 * this model, the heap cannot be shrunk. 22 */ 23 void *mem_sbrk(int incr) 24 { 25 void *old_brk = mem_brk; 26 27 if ( (incr mem_max_addr)) { 28 errno = ENOMEM; 29 return (void *)-1; 30 } 31 mem_brk += incr; 32 return old_brk; 33 } Initialize

56. 56 1 /* Basic constants and macros */ 2 #define WSIZE 4 /* word size (bytes) */ 3 #define DSIZE 8 /* doubleword size (bytes) */ 4 #define CHUNKSIZE (1<<12) /* initial heap size (bytes) */ 5 #define OVERHEAD 8 /* overhead of header and footer (bytes) */ 6 7 #define MAX(x, y) ((x) > (y)? (x) : (y)) 8 9 /* Pack a size and allocated bit into a word */ 10 #define PACK(size, alloc) ((size) | (alloc)) 11 12 /* Read and write a word at address p */ 13 #define GET(p) (*(size_t *)(p)) 14 #define PUT(p, val) (*(size_t *)(p) = (val)) 15 Macros Figure 10.45 P746

57. 57 16 /* Read the size and allocated fields from address p */ 17 #define GET_SIZE(p) (GET(p) & ˜0x7) 18 #define GET_ALLOC(p) (GET(p) & 0x1) 19 20 /* Given block ptr bp, compute address of its header and footer */ 21 #define HDRP(bp) ((void *)(bp) - WSIZE) 22 #define FTRP(bp) ((void *)(bp) + GET_SIZE(HDRP(bp)) - DSIZE) 23 24 /* Given block ptr bp, compute address of next and previous blocks */ 25 #define NEXT_BLKP(bp) ((void *)(bp) + GET_SIZE(HDRP(bp))) 26#define PREV_BLKP(bp) ((void *)(bp) - GET_SIZE(((void *)(bp) - DSIZE))) size t size = GET SIZE(HDRP(NEXT_BLKP(bp))); Macros

58. 58 1 int mm_init(void) 2 { 3 /* create the initial empty heap */ 4 if ((heap_listp = mem_sbrk(4*WSIZE)) == NULL) 5 return -1; 6 PUT(heap_listp, 0); /* alignment padding */ 7 PUT(heap_listp+WSIZE, PACK(OVERHEAD, 1)); /* prologue header */ 8 PUT(heap_listp+DSIZE, PACK(OVERHEAD, 1)); /* prologue footer */ 9 PUT(heap_listp+WSIZE+DSIZE, PACK(0, 1)); /* epilogue header */ 10 heap_listp += DSIZE; 11 12 /* Extend the empty heap with a free block of CHUNKSIZE bytes */ 13 if (extend_heap(CHUNKSIZE/WSIZE) == NULL) 14 return -1; 15 return 0; 16 } mm_init() Figure 10.46 P747

59. 59 1 static void *extend_heap(size_t words) 2 { 3 char *bp; 4 size_t size; 5 6 /* Allocate an even number of words to maintain alignment */ 7 size = (words % 2) ? (words+1) * WSIZE : words * WSIZE; 8 if ((int)(bp = mem_sbrk(size)) < 0) 9 return NULL; 10 11 /* Initialize free block header/footer and the epilogue header */ 12 PUT(HDRP(bp), PACK(size, 0)); /* free block header */ 13 PUT(FTRP(bp), PACK(size, 0)); /* free block footer */ 14 PUT(HDRP(NEXT_BLKP(bp)), PACK(0, 1)); /* new epilogue header */ 15 16 /* Coalesce if the previous block was free */ 17 return coalesce(bp); 18 } mm_init() Figure 10.47 P748

60. 60 1 void mm_free(void *bp) 2 { 3 size_t size = GET_SIZE(HDRP(bp)); 4 5 PUT(HDRP(bp), PACK(size, 0)); 6 PUT(FTRP(bp), PACK(size, 0)); 7 coalesce(bp); 8 } 9 mm_free() Figure 10.48 P749

61. 61 10 static void *coalesce(void *bp) 11 { 12 size_t prev_alloc = GET_ALLOC(FTRP(PREV_BLKP(bp))); 13 size_t next_alloc = GET_ALLOC(HDRP(NEXT_BLKP(bp))); 14 size_t size = GET_SIZE(HDRP(bp)); 15 16 if (prev_alloc && next_alloc) { /* Case 1 */ 17 return bp; 18 } 19 20 else if (prev_alloc && !next_alloc) { /* Case 2 */ 21 size += GET_SIZE(HDRP(NEXT_BLKP(bp))); 22 PUT(HDRP(bp), PACK(size, 0)); 23 PUT(FTRP(bp), PACK(size,0)); 24 return(bp); 25 } 26 mm_free()

62. 62 27 else if (!prev_alloc && next_alloc) { /* Case 3 */ 28 size += GET_SIZE(HDRP(PREV_BLKP(bp))); 29 PUT(FTRP(bp), PACK(size, 0)); 30 PUT(HDRP(PREV_BLKP(bp)), PACK(size, 0)); 31 return(PREV_BLKP(bp)); 32 } 33 34 else { /* Case 4 */ 35 size += GET_SIZE(HDRP(PREV_BLKP(bp))) + 36 GET_SIZE(FTRP(NEXT_BLKP(bp))); 37 PUT(HDRP(PREV_BLKP(bp)), PACK(size, 0)); 38 PUT(FTRP(NEXT_BLKP(bp)), PACK(size, 0)); 39 return(PREV_BLKP(bp)); 40 } 41 } mm_free() Figure 10.48 P749

63. 63 1 void *mm_malloc (size_t size) 2 { 3 size_t asize; /* adjusted block size */ 4 size_t extendsize; /* amount to extend heap if no fit */ 5 char *bp; 6 7 /* Ignore spurious requests */ 8 if (size <= 0) 9 return NULL; 10 11 /* Adjust block size to include overhead and alignment reqs. */ 12 if (size <= DSIZE) 13 asize = DSIZE + OVERHEAD; 14 else 15 asize = DSIZE * ((size + (OVERHEAD) + (DSIZE-1)) / DSIZE); 16 mm_malloc() Figure 10.49 P750

64. 64 17 /* Search the free list for a fit */ 18 if ((bp = find_fit(asize)) != NULL) { 19 place (bp, asize); 20 return bp; 21 } 22 23 /* No fit found. Get more memory and place the block */ 24 extendsize = MAX (asize, CHUNKSIZE) ; 25 if ((bp = extend_heap (extendsize/WSIZE)) == NULL) 26 return NULL; 27 place (bp, asize); 28 return bp; 29 } mm_malloc()

65. 65 1.static void *find_fit(size_t asize) 2.{ 3. void *bp ; 4. 5. /* first fit search */ 6. for (bp = heap_listp; GET_SIZE(HDRP(bp)) > 0 ; bp = NEXT_BLKP(bp) ) { 7. if (!GET_ALLOC(HDRP(bp)) && (asize<=GET_SIZE(HDRP(bp)))) { 8. return bp; 9. } 10. } 11. return NULL; /*no fit */ 12. } mm_alloc()

66. 66 1. static void place(void *bp, size_t asize) 2. { 3. size_t csize = GET_SIZE(HDRP(bp)) ; 4. 5. if ( (csize –asize) >= (DSIZE + OVERHEAD) ) { 6. PUT(HDRP(bp), PACK(asize, 1)) ; 7. PUT(FTRP(bp), PACK(asize, 1)) ; 8. bp = NEXT_BLKP(bp) ; 9. PUT(HDRP(bp), PACK(csize-asize, 0) ; 10. PUT(FTRP(bp), PACK(csize-asize, 0) ; 11. } else { 12. PUT(HDRP(bp), PACK(csize, 1) ; 13. PUT(FTRP(bp), PACK(csize, 1) ; 14. } 15.} mm_alloc()

67. 67 10.9.13 Explicit Free Lists

68. 68 Explicit free lists Explicit list among the free blocks using pointers within the free blocks Use data space for link pointers –Typically doubly linked –Still need boundary tags for coalescing –It is important to realize that links are not necessarily in the same order as the blocks

69. 69 Explicit free lists ABC 4444664444 Forward links Back links A B C

70. 70 Freeing with explicit free lists Where to put the newly freed block in the free list –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.

71. 71 Freeing with explicit free lists Where to put the newly freed block in the free list –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

72. 72 10.9.14 Segregated Free Lists

73. 73 Segregated Storage Each size “class” has its own collection of blocks –Often have separate collection for every small size (2,3,4,…) –For larger sizes typically have a collection for each power of 2

74. 74 Segregated Storage 1-2 3 4 5-8 9-16

75. 75 Separate heap and free list for each size class 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 1) Simple segregated storage

76. 76 To free a block: –Add to free list –If page is empty, return the page for use by another size (optional) Tradeoffs: –fast, but can fragment badly Simple segregated storage

77. 77 Array of free lists, each one for some size class 2) Segregated fits

78. 78 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 –if no blocks is found in all classes, try more heap memory Segregated fits

79. 79 To free a block: –coalesce and place on appropriate list (optional) Tradeoffs –faster search than sequential fits (i.e., log time for power of two size classes) –controls fragmentation of simple segregated storage –coalescing can increase search times deferred coalescing can help Segregated fits

80. 80 A special case of segregated fits –Each size is power of 2 Initialize –A heap of size 2 m 3) Buddy Systems

81. 81 Allocate –Roundup to power of 2 such as 2 k –Find a free block of size 2 j (k  j  m) –Split the block in half until j=k Each remaining half block (buddy) is placed on the appreciate free list Free –Continue coalescing with the free buddies Buddy Systems

82. 82 10.10 Garbage Collection

83. 83 10.11 Common Memory-Related Bugs in C Programs

84. 84 10.12 Recapping Some Key Ideas About Virtual Memory

85. 85 10.13 Summary