Static Analysis of Static Analysis of Communication Structures in Communication Structures in

Parallel ProgramsParallel Programs

So-Yan Ho and Nai-Wei Lin

Department of Computer Science and Information Engineering

National Chung Cheng University

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MotivationsMotivations

• Communication structures in message passing programs is the key to understand the behaviors of the programs

• Static analysis of communication structures allows programmers to identify potential communication bugs at compile time

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Message Passing SchemesMessage Passing Schemes

• Direct-Addressing: CSP, Occam, Ada, MPI

send(task-id, message);message = receive(task-id);

• Indirect-Addressing: Fortran M, CCCsend(channel-id, message);message = receive(channel-id);

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Channels in CCCChannels in CCC

• Pipes: one-to-one communication

• Spliters: one-to-many communication

• Mergers: many-to-one communication

• Multiplexers: many-to-many communication

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Merits of Abundant ChannelsMerits of Abundant Channels

• Communication structures are more comprehensive

• The specification of communication structures is easier

• The implementation of communication structures is more efficient

• The static analysis of communication structures is more effective

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Higher-Order ChannelsHigher-Order Channels

• A channel is first-order if it is used to transfer data

• A channel is higher-order if it is used to transfer channels

• The static analysis of higher-order channels is much more difficult than the static analysis of first-order channels

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A Simple CCC ProgramA Simple CCC Program

task::main(){ spliter int ch; /* one-to-many channel */  int i;

ch = channel(); par { producer(ch, many); /* one sender */ parfor (i = 0; i < many; i++) consumer(ch); /* many receivers */ }}  

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A Simple CCC ProgramA Simple CCC Program

task::producer(ch, many)spliter int ch;int many;{ int i;  for (i = 0; i < num_data; i++) send(ch, i); for (i = 0; i < many; i++) send(ch, end_data); /* signal end of data */}

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A Simple CCC ProgramA Simple CCC Program

task::consumer(ch)spliter int ch;{ int data;  while (1) { data = receive(ch); if (data == end_data) break; process(data); }}

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Overview of the AnalysisOverview of the Analysis

• For each channel ch, infer the number of senders of ch, ch.s and the number of receivers of ch, ch.r

• Intraprocedural analysis: within a function– infer them once and for all, and use them as the

initial values of the interprocedural analysis

• Interprocedural analysis: among functions– propagate the values among functions until they

reach a fixed point

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First-Order ChannelsFirst-Order Channels

• Use aliasing induced by parameter passing

• For each channel ch, inferch.s = ch.self.s + ch.others.sch.r = ch.self.r + ch.others.r

where,ch.self.s, ch.self.r: {0, 1}ch.others.s, ch.others.r: {0, 1, 2}

• We call the four tuple {ch.self.s, ch.self.r, ch.others.s, ch.others.r} the mode of ch

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Intraprocedural AnalysisIntraprocedural Analysis

• For each channel ch,if ch is sent by current function then ch.self.s = 1else ch.self.s = 0if ch is received by current function then ch.self.r = 1else ch.self.r = 0

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Interprocedural AnalysisInterprocedural Analysis

• Compact control flow trees– call nodes, spawn nodes, block nodes, alternativ

e nodes, repetition nodes– depth-first order (once)

• The call graph and the strongly connected component graph– topological sort order (once)

• Strongly connected components– worklist (iterations)

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Compact Control Flow TreesCompact Control Flow Treestask::main(){ spliter int ch;  int i;

ch = channel(); par { producer(ch, many); parfor (i = 0; i < many; i++) consumer(ch); }}  

B

B

S

S

B

R

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The Call Graph and Strongly The Call Graph and Strongly Connected Component GraphConnected Component Graph

main

producer consumer

process

task :: main() { . . . par { producer(ch,…); parfor ( . . . ) consumer(ch); } . . .}

task :: consumer(ch){ . . . process(data); . . .}

task ::producer(ch, …){ . . .}

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Call NodesCall Nodes

• Let L be the set of channel parameters aliased with ch at the call node n

• Then chn.self.s = x L x.self.s,

chn.self.r = x L x.self.r,

chn.others.s = x L x.others.s,

chn.others.r = x L x.others.r

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Spawn NodesSpawn Nodes

• Let L be the set of channel parameters aliased with ch at the spawn node n

• Then chn.self.s = 0,

chn.self.r = 0,

chn.others.s = x L x.self.s + x L x.others.s,

chn.others.r = x L x.self.r + x L x.others.r

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Block NodesBlock Nodes

• If the block node n is the initial node chn.self.s = value from intraprocedural analysis, chn.self.r = value from intraprocedural analysis, chn.others.s = 0, chn.others.r = 0

• Otherwise chn.self.s = 0, chn.self.r = 0, chn.others.s = 0, chn.others.r = 0

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Bolck NodesBolck Nodes

• Let L be the sequence of nodes inside the block node n

• Then chn.self.s = chn.self.s || x L chx.self.s,

chn.self.r = chn.self.r || x L chx.self.r,

chn.others.s = chn.others.s + x L chx.others.s,

chn.others.r = chn.other.r + x L chx.others.r

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Alternative NodesAlternative Nodes

• Let L be the sequence of nodes inside the alternative node n

• Then chn.self.s = maxx L chx.self.s,

chn.self.r = maxx L chx.self.r,

chn.others.s = maxx L chx.others.s,

chn.others.r = maxx L chx.others.r

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Repetition NodesRepetition Nodes

• Let m be the node inside the repetition node n

• Then chn.self.s = chm.self.s,

chn.self.r = chm.self.r,

chn.others.s = if chm.others.s == 0 then 0 else 2,

chn.others.r = if chm.others.r == 0 then 0 else 2

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Second-Order ChannelsSecond-Order Channels

• Use aliasing induced by both parameter passing and message passing

• For each second-order channel ch, inferch.sS = the set of channels sent to chch.rS = the set of channels received from

ch

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Intraprocedural AnalysisIntraprocedural Analysis

• For each second-order channel ch, ch.sS = ch.rS = For each first-order channel x, if x is sent to ch ch.sS = ch.sS ∪ { x } if x is received from ch ch.rS = ch.rS ∪ { x }

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Parameter Passing AliasingParameter Passing Aliasing

task :: main(){ merger pipe int ch; pipe int m; . . . par { parfor ( . . . ) client(ch, m); server(ch); }}

task :: client(ch, c) { . . . send(ch, c); . . .}

task :: server(ch){ . . . s = receive(ch); . . .}

ch.sS : { c }

ch.sS : { m }ch.sS ::

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Call and Spawn NodesCall and Spawn Nodes

• Let S be the set of second-order channel parameters aliased with ch at the call node n

• Let F be the set of first-order channel parameters at n, and for each p F, let (p) represent the corresponding channel argument of p at n

• Then chn.sS = x S x.sS{pF ,p/(p)} ,

chn.rS = x S x.rS {pF ,p/(p)}

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Message Passing AliasingMessage Passing Aliasing

task :: main(){ merger pipe int ch; pipe int m, n; . . . par { parfor ( . . . ) client(ch, m); server(ch, n); }}

task :: client(ch, c) { . . . send(ch, c); . . .}

task :: server(ch, s){ . . . s = receive(ch); . . .}

ch.sS : { c }ch.rS:

ch.sS : { m }ch.rS: { n }

ch.sS :: ch.rS: { s }

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Call and Spawn NodesCall and Spawn Nodes

• For each x in ch.sS, x is aliased with every y in ch.rS

• Then, for each c in {x} ch.rS c.self.s = d {x} ch.rS d.self.s,

c.self.r = d {x} ch.rS d.self.r,

c.others.s = d {x} ch.rS d.others.s,

c.others.r = d {x} ch.rS d.others.r

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Block NodesBlock Nodes

• If the block node n is the initial node chn.sS = value from intraprocedural analysis,

chn.rS = value from intraprocedural analysis

• Otherwise chn.sS = ,

chn.rS =

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Block NodesBlock Nodes

• Let L be the sequence of nodes inside the block node n

• Then chn.sS = chn.sS x L chx.sS,

chn.rS = chn.rS x L chx.rS

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Alternative NodesAlternative Nodes

• Let L be the sequence of nodes inside the alternative node n

• Then chn.sS = x L chx.sS,

chn.rS = x L chx.rS

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Repetition NodesRepetition Nodes

• Let m be the node inside the repetition node n

• Then chn.sS = chm.sS,

chn.rS = chm.rS

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Time ComplexityTime Complexityintraprocedural analysis;for each SCC in SCCG begin while changed begin for each CCFT in the SCC begin for each node in the CCFT begin … endfor endfor endwhileendfor

The time complexity: O(V+E)

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ConclusionsConclusions

• Design a linear algorithm to infer the number of senders and receivers for each channel

• Handle both first-order and higher-order channels

• Use the information about aliasing induced by both parameter passing and message passing