One Seek File System

1
One Seek File System
Sharath R. Cholleti sharath_at_cs.wustl.edu
Center for Distributed Object Computing Department
of Computer Science and Engineering Washington
University
Fall 03 E71 CS 6785 Programming Languages
Seminar 07 Nov 2003
2
Outline

• Fixed size blocks file system
• Extent based file system
• Buddy system
• Buddy file system
• Sum of powers of 2 blocks
• Experiments
• Heap manager algorithm
• Defragmentation
• Bounds

3
Fixed size blocks

• Blocks could be non-contiguous
• Could be spread all over the disk
• Number of seeks proportional to file size
• O(S)

4
Extent based File System

• Limited number of extents per file
• An extent can be of arbitrarily large
• Number of seeks is limited
• O(1)
• Problems
• Difficult to predict the size of the extents
• Cross the limit of number of extents per file
• Variable size gives rise to fragmentation
• DTSS shown to be practical without too much
  internal or external fragmentation

5
Knuths Buddy System

• Free lists segregated by size

128
64
32

• All the requests are rounded up to a power of 2

16
8
4
2
1
6
Buddy System (1)

• Begin with one large block
• Suppose we want a block of size 8

128
64
32
16
8
4
2
1
7
Buddy System (2)

• Begin with one large block
• Suppose we want a block of size 8
• Subdivide recursively

128
64
32
16
8
4
2
1
8
Buddy System (3)

• Begin with one large block
• Suppose we want a block of size 8
• Subdivide recursively

128
64
32
16
8
4
2
1
9
Buddy System (4)

• Begin with one large block
• Suppose we want a block of size 8
• Subdivide recursively

128
64
32
16
8
4
2
1
10
Buddy System (5)

• Begin with one large block
• Suppose we want a block of size 8
• Subdivide recursively
• 2 blocks of size 8

128
64
32
16
8
4
2
1
11
Buddy System (6)

• Begin with one large block
• Suppose we want a block of size 8
• Subdivide recursively
• 2 blocks of size 8
• One of those given to the program

128
64
32
16
8
4
Given to the program
2
1
12
Buddy System (7)

• Coalescing
• Only buddies coalesce

128
64
32
16
8
4
Deallocated
2
1
13
Buddy File System

• Round the file size to a power of 2
• Only one large block
• Mostly only 1 seek
• Fast allocation
• Deallocation coalescing with its buddy
• High internal fragmentation
• Worse case almost 50
• Average 25

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Buddy System Tree Notation
Free
Allocate block of size 1
Occupied
16
8
4
2
1
15
Buddy System Tree Notation(2)
Free
Allocate block of size 1
Occupied
16
8
4
2
1
16
Buddy System Tree Notation(3)
Free
Allocate block of size 1
Occupied
16
8
4
2
1
17
Buddy System Tree Notation(4)
Free
Allocate block of size 1
Occupied
16
8
4
2
1
18
Buddy System Tree Notation(6)
Free
Allocate block of size 4
Occupied
16
8
4
2
1
19
Sum of powers of 2 blocks
Free

• Buddy blocks of different sizes
• 13 8 4 1

Occupied
32
16
8
4
2
1
20
Allocation as Sum of powers of 2 blocks

• Internal fragmentation same as file system with
  blocks of equal size
• Buddy type coalescing helps control the external
  fragmentation
• Number of seeks is O(log S)
• What if allocate the blocks contiguously?
• Or make it contiguous after allocation
• Only one seek necessary

21
Experiments

• CEC data
• user file sizes
• Usual (blocks of same size) vs Buddy vs Sum of
  powers of 2
• Total blocks (segments)
• Wasted space
• Min/avg/max number of segments

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Total number of blocks (segments)
23
Wasted space
24
Min/Avg/Max number of blocks
25
Results

• Sum of powers of 2
• Much lesser internal fragmentation compared to
  buddy
• Very few blocks compared to fixed block size file
  system
• Experiments to limit the number of segments to a
  constant

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Heap Manager Algorithm
16
8
8
5
3
4
1
4
3
0
1
02
2
1
0
0
2
1
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Defragmentation

• Need to allocate a block of size 8
• No free block of size 8 -- relocate

Free
Occupied
32
16
8
4
2
1
28
Defragmentation (2)

• Need to allocate a block of size 8
• No free block of size 8 -- relocate

Free
Occupied
32
16
8
4
2
1
29
Cost

• M disk size
• Allocation O(logM)
• Deallocation O(logM)
• Relocation O(slogM) file of size s

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Defragmentation Theory Assumptions

• All files are stored contiguously
• Each file is stored big to small
• File of size S, 2nltSlt2(n1), lies entirely
  within a buddy block of 2(n1)
• Unit of the file is a block
• There is a way to allocate or relocate a file

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Bound on relocated file size

• For the relocation to be minimum, allocation of a
  file of size 2n does not relocate file of size
  greater than 2(n-1)
• Proof
• X a file or a set of files
• R(X) number of blocks moved to relocate X

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Proof (cont)
B
a
D
E
R R(a) R(B) a R(D) R(B) gt E
R(D) R(B)
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Proof (cont)
B
a
D
E
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Worst case relocation file size

• In worst case, to allocate a file of size 2n,
  two files of size 2(n-1) are relocated

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Worst Case Defragmentation

• Worst-case relocation for a file of size S
• SlogS blocks
• R(S) S 2R(S/2)
• 2(S-1) files
• R(S) 1 2R(S/2)