One Seek File System

Sharath R. Cholleti

sharath@cs.wustl.edu

Center for Distributed Object ComputingDepartment of Computer Science and Engineering

Washington University

Fall 03 E71 CS 6785 Programming Languages Seminar

07 Nov 2003

Sharath R. Cholleti

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

Sharath R. Cholleti

Fixed size blocks

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

– O(S)

Sharath R. Cholleti

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

Sharath R. Cholleti

Knuth’s Buddy System

• Free lists segregated by size

128

64

32

16

8

4

2

1

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

Sharath R. Cholleti

Buddy System (1)

• Begin with one large block

• Suppose we want a block of size 8

128

64

32

16

8

4

2

1

Sharath R. Cholleti

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

Sharath R. Cholleti

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

Sharath R. Cholleti

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

Sharath R. Cholleti

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

Sharath R. Cholleti

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

2

1

Given to the program

Sharath R. Cholleti

Buddy System (7)

• Coalescing• Only buddies coalesce 128

64

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8

4

2

1

Deallocated

Sharath R. Cholleti

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%

Sharath R. Cholleti

Buddy System: Tree Notation

16

8

4

2

1

Allocate block of size 1

Free

Occupied

Sharath R. Cholleti

Buddy System: Tree Notation(2)

16

8

4

2

1

Allocate block of size 1

Free

Occupied

Sharath R. Cholleti

Buddy System: Tree Notation(3)

16

8

4

2

1

Allocate block of size 1

Free

Occupied

Sharath R. Cholleti

Buddy System: Tree Notation(4)

16

8

4

2

1

Allocate block of size 1

Free

Occupied

Sharath R. Cholleti

Buddy System: Tree Notation(6)

16

8

4

2

1

Allocate block of size 4

Free

Occupied

Sharath R. Cholleti

Sum of powers of 2 blocks

• Buddy blocks of different sizes• 13 = 8 + 4 + 1

1

2

4

8

16

32

Free

Occupied

Sharath R. Cholleti

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

Sharath R. Cholleti

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

Sharath R. Cholleti

Total number of blocks (segments)

Sharath R. Cholleti

Wasted space

Sharath R. Cholleti

Min/Avg/Max number of blocks

Sharath R. Cholleti

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

Sharath R. Cholleti

Heap Manager Algorithm

1 02

1 4

5

2 1

3

0 0

0

3

8

1

2

4

8

16

Sharath R. Cholleti

Defragmentation

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

1

2

4

8

16

32

Free

Occupied

Sharath R. Cholleti

Defragmentation (2)

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

1

2

4

8

16

32

Free

Occupied

Sharath R. Cholleti

Cost

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

Sharath R. Cholleti

Defragmentation Theory Assumptions

• All files are stored contiguously• Each file is stored big to small• File of size S, 2^n<S<=2^(n+1), lies entirely

within a buddy block of 2^(n+1)• Unit of the file is a block• There is a way to allocate or relocate a file

Sharath R. Cholleti

Bound on relocated file size

• For the relocation to be minimum, allocation of a file of size 2^n 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

Sharath R. Cholleti

Proof (cont)

a EDB

R = R(a) + R(B)

= |a| + R(D) + R(B)

> |E| + R(D) + R(B)

Sharath R. Cholleti

Proof (cont)

a EDB

Sharath R. Cholleti

Worst case relocation file size

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

Sharath R. Cholleti

Worst Case Defragmentation

• Worst-case relocation for a file of size S– SlogS blocks

• R(S) = S + 2*R(S/2)– 2(S-1) files

• R(S) = 1 + 2*R(S/2)