Multi-Method Dispatch Using Multiple RowDisplacement

Candy Pang, Wade Holst, Yuri Leontiev, and Duane SzafronECOOP’99

Presented by: Irene ChengDate: 7 November 2002

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• Review of Terminology

• Review of Row Displacement Dispatchfor Single-Receiver

• Multiple Row Displacement (MRD)

• Optimizations

• Performance Results and Conclusion

Presentation Topics

Review of Terminology

• Single-receiver dispatch uses the dynamic type of a receiver object and the method name to determine which method to execute at run-time,

e.g. aPerson.id();

• Multi-method dispatch uses the dynamic types of the arguments and the method name to determine the method to execute,

e.g. shape.intersect( rectangle, circle );

Review of Terminology (cont)

What is a call-site ?• In single-receiver languages - viewed as a

message sent to the receiver object.e.g.

• In multi-method languages - viewed as the execution of a behavior on a set of arguments.

e.g.

The run-time determination of the method to invoke at a call-site is called method dispatch.

aPerson.id()

shape.intersect( rectangle, circle )

Review of Terminology (cont)

Dispatch strategy:• Cache-based (global or local)• Table-based -

Pre-determine the method for every possible call-site, and record these methods in a table.

When a method is defined, each argument has a specific static type. However, at a call-site, the dynamic type of each argument can either be the static type, or any of its subtypes, e.g.

Person (id1)

Student (id2)

Person aPerson;if (…) aPerson = new Person();else aPerson = new Student();aPerson.id( );

id1 id2

Product-Type Graph (for 2 arguments)

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The underlying Inheritance Hierarchy, H The 2-arity product-type graph, H2

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A product-type graph hierarchy contains all the possible call-sites

Inheritance Conflicts

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General DefinitionA conflict occurs when a product-type can see 2 different method definitions by looking up different paths in the induced product-type graph.

RelaxationLet = { P1 … Pn } and P < P1 … Pn, the methods in Pi and Pj do not conflict in P if :

i.e. 1 <= i, j, k <= n

• Pi < Pj or

• Pj < Pi or

• { Pk | Pk Pi Pk Pj }

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Review of single-receiver Row displacement Dispatch (RD)

Example: E anE = new E();anE.();

1 + 4 = 5 D::

A0 D3

B1 C2 , E4

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MRD Dispatch Table for method with 2 arguments

AA

AB BA

AC BB CA

AD BC CB DA

AE BD CC DB EA BE CD DC EB

CE DD EC

DE ED

EE

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AA

AB BA

AC BB CA

AD BC CB DA

AE BD CC DB EA BE CD DC EB

CE DD EC

DE ED

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MRD Dispatch Table for method with 2 arguments

Data Structure per Behavior - Array of pointers to arrays

A0 B1 C2 D3 E4 A0 B1 C2 D3 E4

• ( Level-0 array ) L0 - indexed by the 1st argument type• ( Level-1 array ) L1 - indexed by the 2nd argument type and

contains method addresses

Compressing the Data Structure for

M - Global Master Array I0 - Global Index Array B - Global Behavior Array

Compressing the Data Structure for and

M - Global Master Array I0 - Global Index Array B - Global Behavior Array

Example: Dispatch a call-site (anE, aD) M [ I0 [5 + 4 = 9 ] + 3 = 14 ]

MRD is designed for n-dimensional dispatch tables

1

BDBBDEBEBBEEEDBEDEEEBEEE

2

DBDDBEDEDDEEEBDEBEEEDEEE

Example: dispatch a call-site (anE, aD, aB)

M [I1 [I0 [ B [] +4] +3] +1]= M [I1 [I0 [ 7+4] +3] +1]= M [I1 [ 5+3] +1]= M[ 15+1]

BD DB EE

Optimizations

Single I - One Global Index Array, I, to store all L0 to Lk-2 arrays

I00 0 1 1 5 8 11 - - 11

- - 14 15 15 14 14 - 15 19

L0 - 8 - 9 13

0 5 17B

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

M [ I0 [ I0 [ B[] +4] +3] +1]= M [ I0 [ I0 [ 17+4] +3] +1]= M [ I0 [ 13+3] +1]= M [ 15+1]

Example: (anE, aD, aB)

I1

Optimizations (cont)

Row-matching instead of row-shifting (additional 10-14% )

Row-shifting

Row-matching

Row-matching cannot be used in single-receiver RD because different rows contain different behavior, and thus different method addresses.

Before displacement

Optimizations (cont)

Byte vs. Word Storage (MRD-B)

• M is the most memory consuming data structure (duplicate 4-byte method address)

• Use method-map per behavior (each method address is stored only once)

• Only 1 byte (max. 256 methods) is used in M to store the index of the corresponding method in the method-map.

• Size of M is reduced to 1/4 but extra redirection time at dispatch.

Timing results

Noop - dummy function to time the overhead incurredMRD - multiple row displacement MRD-B - MRD using byte instead of word for Master arrayCNT - Compressed N-Dimensional TablesSRP - Single Receiver ProjectionsLUA - Lookup Automata

Memory Utilization

LUA - Lookup AutomataMRD - multiple row displacementMRD-B - MRD using byte instead of word for Master arrayCNT - Compressed N-Dimensional TablesSRP - Single Receiver Projections

Conclusion

• A new multi-method dispatch technique is introduced to compress an n-dimensional table by row displacement.

• The first time a comparison of multi-method techniques has appeared in the literature.

• Experimental results shows that when comparing with other table-based multi-method techniques, MRD has the fastest dispatch time and the second smallest per-call-site code size.