Exploiting the Commutativity Lattice Donald Nguyen, Dimitrios - - PowerPoint PPT Presentation

Exploiting the Commutativity Lattice

Milind Kulkarni Donald Nguyen, Dimitrios Prountzos, Xin Sui and Keshav Pingali

฀

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

Set S:

X Y Z

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

atomic { ... S.add(a) ... }

Set S:

atomic { ... S.contains(b) ... }

X Y Z

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

atomic { ... S.add(a) ... }

Set S:

atomic { ... S.contains(b) ... }

X Y Z X Y Z A

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

atomic { ... S.add(a) ... }

Set S:

atomic { ... S.contains(b) ... }

X Y Z X Y Z A

X

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

atomic { ... S.add(a) ... }

Set S:

atomic { ... S.contains(b) ... }

X Y Z X Y Z A

Wednesday, July 20, 2011

Exploiting semantics in transactional execution

2

atomic { ... S.add(a) ... }

Set S:

atomic { ... S.contains(b) ... }

X Y Z X Y Z A

Wednesday, July 20, 2011

X Y Z A

atomic { ... S.add(a) ... } atomic { ... S.contains(b) ... }

Exploiting semantics in transactional execution

3

Set S:

Wednesday, July 20, 2011

X Y Z A

atomic { ... S.add(a) ... } atomic { ... S.contains(b) ... }

Exploiting semantics in transactional execution

3

Set S:

Key insight: exploit commutativity properties to ensure transactional behavior

Wednesday, July 20, 2011

X Y Z A

atomic { ... S.add(a) ... } atomic { ... S.contains(b) ... }

Exploiting semantics in transactional execution

3

Set S:

Key insight: exploit commutativity properties to ensure transactional behavior

[Herlihy & Koskinen PPoPP 08] [Ni et al. PPoPP 07] [Kulkarni et al. PLDI 07] [Kulkarni et al. ASPLOS 08] [Koskinen et al. POPL 10] [Carlstrom et al. PPoPP 07] [Weihl et al. IEEE ToC 88]

Wednesday, July 20, 2011

How do we check commutativity?

• Can specify conditions for commutativity:
• How should a transactional run-time system

check these?

• Prior work: ad hoc combinations of logging

and locking

4

add(a)/r commutes with contains(b)/r if

a ≠ b

Wednesday, July 20, 2011

How do we check commutativity?

5

add(a)/r commutes with contains(b)/r if

a ≠ b

Wednesday, July 20, 2011

How do we check commutativity?

5

add(a)/r commutes with contains(b)/r if

a ≠ b or r = false

Wednesday, July 20, 2011

How do we check commutativity?

• Commutativity can be more complex:
• Prior work often did not fully check

commutativity to reduce overhead

• How do we know this is correct?

5

add(a)/r commutes with contains(b)/r if

a ≠ b or r = false

Wednesday, July 20, 2011

Contributions

• Define a commutativity lattice for reasoning

about commutativity specifications

• How do we check commutativity?
• Provide systematic approaches for

implementing commutativity checks

• How do we implement low overhead checks?
• Show how to use commutativity lattice to

correctly construct lower-overhead checkers

6

Wednesday, July 20, 2011

Commutativity

7

σ1

Wednesday, July 20, 2011

Commutativity

7

m1

r1 σ1

Wednesday, July 20, 2011

Commutativity

7

m1

r1 σ1 σ2

Wednesday, July 20, 2011

Commutativity

7

m1 m2

r1 r2 σ1 σ2

Wednesday, July 20, 2011

Commutativity

7

m1 m2

r1 r2 σ1 σ2 σ3

Wednesday, July 20, 2011

Commutativity

7

m1 m2

r1 r2 σ1 σ2 σ3 m1, m2 commute in σ1

Wednesday, July 20, 2011

Commutativity

8

m1 m2

r1 r2 σ1 σ’2 σ3 m1, m2 commute in σ1

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

9

B: A:

m1 m2 m3 m4 m1 m2 m3 m4

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

10

m1 m2 m3 m4 m1 m2 m3 m4

History :

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

10

m1 m2 m3 m4 m1 m2 m3 m4

History : σ1 σ2 σ3 σ4 σ5 σ6 σ7 σ8 σ9

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

11

m1 m2 m3 m4 m1 m2 m3 m4

History : σ1 σ2 σ3 σ’4 σ5 σ6 σ7 σ8 σ9

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

12

m1 m2 m3 m4 m1 m2 m3 m4

History : σ1 σ2 σ’3 σ’4 σ5 σ6 σ7 σ8 σ9

Wednesday, July 20, 2011

Using commutativity to guarantee serializability

13

m1 m2 m3 m4 m1 m2 m3 m4

History : σ1 σ2 σ’3 σ”4 σ’5 σ’6 σ’7 σ8 σ9

Wednesday, July 20, 2011

Runtime commutativity checks

• For each method invocation by transaction B
• Runtime checks commutativity with all

methods invoked by transaction A

• If all checks succeed, execution continues
• If any commutativity check fails, one

transaction rolled back

14

Wednesday, July 20, 2011

φ(ma, mb)

Commutativity conditions

15

Commutativity condition:

Wednesday, July 20, 2011

φ(ma, mb)

Commutativity conditions

15

Commutativity condition:

true only if ma and mb commute

Wednesday, July 20, 2011

φ(ma, mb)

Commutativity conditions

15

Commutativity condition: Precise condition:

φ(ma, mb)

*

Wednesday, July 20, 2011

φ(ma, mb)

Commutativity conditions

15

Commutativity condition: Precise condition:

φ(ma, mb)

*

true if and only if ma and mb commute

Wednesday, July 20, 2011

φ(ma, mb)

Commutativity conditions

15

Commutativity condition: Precise condition:

φ(ma, mb)

*

φ(add(a)/r1, contains(b)/r2)

* a ≠ b or r1 = false

Wednesday, July 20, 2011

Commutativity lattice

16

(add(a)/r1, contains(b)/r2) a ≠ b or r1 = false

Wednesday, July 20, 2011

Commutativity lattice

16

(add(a)/r1, contains(b)/r2) a ≠ b or r1 = false false a ≠ b r1 = false

Wednesday, July 20, 2011

Commutativity lattice

16

(add(a)/r1, contains(b)/r2) a ≠ b or r1 = false false a ≠ b r1 = false Allows most parallelism Allows no parallelism

Wednesday, July 20, 2011

Implementing Commutativity

Wednesday, July 20, 2011

Soundness and completeness

• A conflict detection implementation is sound

if it claims methods commute only if they actually do according to the conditions

• A conflict detection implementation is

complete if it claims methods commute if they do according to the conditions

18

Wednesday, July 20, 2011

Running example

• Set-like data structure
• Supports add and contains

19

(add(a)/r1, contains(b)/r2) a ≠ b or r1 = false (add(a)/r1, add(b)/r2) a ≠ b or (r1 = false and r2 = false) (contains(a)/r1, contains(b)/r2) true

Wednesday, July 20, 2011

Running example

• Set-like data structure
• Supports add and contains

20

(add(a)/r1, contains(b)/r2) a ≠ b (add(a)/r1, add(b)/r2) a ≠ b (contains(a)/r1, contains(b)/r2) true

Wednesday, July 20, 2011

Implementing commutativity

• Three schemes
• Abstract locking
• Forward gatekeeping
• General gatekeeping

21

Wednesday, July 20, 2011

Abstract locking

• Sound and complete implementation when

commutativity condition is simple

• Is either true, false, or a set of conjuncts
• f the form “x ≠ y”

22

(add(a)/r1, contains(b)/r2) a ≠ b a ≠ b or r1 = false Not simple: Simple:

Wednesday, July 20, 2011

Abstract locking

• Basic skeleton
• Associate an abstract lock with each object that

can be passed as an argument to a method

• When a method is called, acquire locks on each

argument in appropriate mode

• Object already locked → commutativity violation
• All locks released when transaction ends
• Key problem: building compatibility matrix

23

Wednesday, July 20, 2011

Building compatibility matrix

• One mode per argument of a method

24

add(a) → add:1 contains(b) → cont:1

Wednesday, July 20, 2011

Building compatibility matrix

• One mode per argument of a method

24

add(a) → add:1 contains(b) → cont:1

add:1 cont:1 add:1 cont:1

Wednesday, July 20, 2011

Building compatibility matrix

• Compatibility: If condition includes conjunct

“a ≠ b” then modes for a and b incompatible

25

add:1 cont:1 add:1 cont:1

φ(add(a)/r1, contains(b)/r2) :

a ≠ b

Wednesday, July 20, 2011

Building compatibility matrix

• Compatibility: If condition includes conjunct

“a ≠ b” then modes for a and b incompatible

25

add:1 cont:1 add:1 cont:1

φ(add(a)/r1, contains(b)/r2) :

a ≠ b

Wednesday, July 20, 2011

Building compatibility matrix

• Compatibility: modes for a and b

incompatible if condition includes conjunct “a ≠ b”

26

add:1 cont:1 add:1 cont:1

φ(add(a)/r1, add(b)/r2) :

a ≠ b

Wednesday, July 20, 2011

Building compatibility matrix

• Compatibility: modes for a and b

incompatible if condition includes conjunct “a ≠ b”

26

add:1 cont:1 add:1 cont:1

φ(add(a)/r1, add(b)/r2) :

a ≠ b

Wednesday, July 20, 2011

Building the compatibility matrix

• Compatibility: modes for a and b

incompatible if condition includes conjunct “a ≠ b”

27

add:1 cont:1 add:1 cont:1

φ(contains(a)/r1, contains(b)/r2) : true

Wednesday, July 20, 2011

Building the compatibility matrix

• Compatibility: modes for a and b

incompatible if condition includes conjunct “a ≠ b”

27

add:1 cont:1 add:1 cont:1

φ(contains(a)/r1, contains(b)/r2) : true

Wednesday, July 20, 2011

Other conflict detection techniques

• Forward gatekeeping: sound and complete

for more complex conditions

• General gatekeeping: allows most flexibility

in commutativity conditions

• Basic tradeoff: Increasing complexity = more

expressive, but more overhead

28

a ≠ b or r1 = false

Wednesday, July 20, 2011

Trading off parallelism for overhead

Wednesday, July 20, 2011

• No prior work fully implemented

commutativity for sets

• Used lower-overhead schemes instead

Set spec

Lowering overhead of conflict detection

30

Wednesday, July 20, 2011

• No prior work fully implemented

commutativity for sets

• Used lower-overhead schemes instead

Set spec

Lowering overhead of conflict detection

30

Forward gatekeeper

Wednesday, July 20, 2011

• No prior work fully implemented

commutativity for sets

• Used lower-overhead schemes instead

Set spec

Lowering overhead of conflict detection

30

Forward gatekeeper Abstract locks

Wednesday, July 20, 2011

• No prior work fully implemented

commutativity for sets

• Used lower-overhead schemes instead

Set spec

Lowering overhead of conflict detection

30

Forward gatekeeper Abstract locks

??

Wednesday, July 20, 2011

• To lower overhead, build sound and

complete implementation of a different specification

Set spec’

Disciplined approach

31

Forward gatekeeper Abstract locks

Set spec

Wednesday, July 20, 2011

• To lower overhead, build sound and

complete implementation of a different specification

Set spec’

Disciplined approach

31

Forward gatekeeper Abstract locks

Set spec

Wednesday, July 20, 2011

• To lower overhead, build sound and

complete implementation of a different specification

Set spec’

Disciplined approach

31

Forward gatekeeper Abstract locks

Set spec

Wednesday, July 20, 2011

• Find simpler specifications from lower in the lattice

Exploiting the commutativity lattice

32

a ≠ b ⋁ r1 = false

Forward gatekeeper

true

φ(contains(a)/r1, contains(b)/r2) : φ(add(a)/r1, contains(b)/r2) :

(add(a)/r1, add(b)/r2)

φ

a ≠ b ⋁ (...)

Wednesday, July 20, 2011

• Find simpler specifications from lower in the lattice

Exploiting the commutativity lattice

33

true a ≠ b

Forward gatekeeper R/W locks

φ(contains(a)/r1, contains(b)/r2) : φ(add(a)/r1, contains(b)/r2) :

a ≠ b (add(a)/r1, add(b)/r2)

φ

Wednesday, July 20, 2011

Exploiting the commutativity lattice

34

φ(contains(a)/r1, contains(b)/r2) : a ≠ b φ(add(a)/r1, contains(b)/r2) :

a ≠ b

Forward gatekeeper R/W locks Exclusive locks

(add(a)/r1, add(b)/r2)

φ

a ≠ b

• Find simpler specifications from lower in the lattice

Wednesday, July 20, 2011

• Speedup

0.0 1.0 2.0 3.0 Threads 1 2 4 8

• coarse

ex rw

Evaluation

• Moving through commutativity lattice

effectively trades off parallelism and

• verhead

35

Preflow push

Wednesday, July 20, 2011

Evaluation

• Showed that forward/general gatekeeping

can provide more parallelism and better performance than memory-level locking (e.g., STM)

• Tradeoffs vary for different applications

➡ Ability to generate and reason about different implementations critical

36

Wednesday, July 20, 2011

Conclusions

• Commutativity conditions are an attractive

way to perform conflict detection for transactional execution

• Commutativity checkers can be

systematically generated from specifications

• Commutativity lattice provides disciplined

approach to producing checkers, reasoning about behavior

37

Wednesday, July 20, 2011