scope-based method cache analysis - ulm...scope-based method cache analysis benedikt huber1, stefan...

Scope-based Method Cache Analysis

Benedikt Huber1, Stefan Hepp1, Martin Schoeberl2

1 Vienna University of Technology 2 Technical University of Denmark

14th International Workshop on Worst-Case Execution Time Analysis (WCET 2014)July 8, 2014

Outline

Motivation The method cache

Scope-based Cache Analysis Basic principle Conflict detection

Evaluation

2

Motivation: The T-CREST Project

3

.c

Compiler WCET Analysis

RTOS

MemoryFPGA

Memory controller

M$

S$D$

LM

Patmos

ALU M$

S$D$

LM

Patmos

ALU M$

S$D$

LM

Patmos

ALU

NOC

T-CREST: The quest for a time-predictable multicore platform

Motivation: The T-CREST Project

4

.c

Compiler WCET Analysis

RTOS

MemoryFPGA

Memory controller

M$

S$D$

LM

Patmos

ALU M$

S$D$

LM

Patmos

ALU M$

S$D$

LM

Patmos

ALU

NOC

MethodCacheSplit

Caches

Time-composablememoryhierarchy

T-CREST: The quest for a time-predictable multicore platform

Motivation: The Method Cache Instruction cache that holds blocks of code of variable size

Functions or parts of functions (compiler defined) Cache updates only at call, return and special branches Fully associative tag memory

More dynamic than I-SPM Address translation, replacement done in hardware

Less hardware costs than n-way LRU instruction cache Instructions only stall in memory stage Smaller tag memory

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main: 2

main() g() f()

Tag memory g: 10 f: 14 -

Cache

Motivation: Analysis of the M$

But: Only FIFO replacement (fragmentation)

But: Variable sized cache blocks

Path-sensitive analysis techniques based on abstract interpretation do not work well for the method cache

Instead: Generalized persistence analysis

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main: 2

main() g() f()

Tag memory g: 10 f: 14 -

Cache

Cache Analysis Techniques

Always-miss/always-hit classification [Grund10]: Shown to work for FIFO [Reineke08]: bound FIFO caches based on smaller LRU

cache performance

Persistence Analyses ([Cullmann13], [Huynh11])

Deal with LRU caches (first-miss) Use functions and loops as scopes

Scope-based Cache Analysis Find at-most-one-miss scopes Find fine-grained persistence scopes

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Scope-based cache analysis

1) Build scope graph Scope graph: Functions, loops, callsites

Access graph (per scope graph node): control flow, memory accesses, subscopes and backedge nodes

2) For each memory block B: Find set of single-entry scopes S(B) (regions) on the access

graphs s.t.:• every access to B is within a scope• B is conflict-free / missed at most once within each scope

3) Maximum number of misses of B ≤ sum of maximum number of executions of all scopes S(B)

Extend IPET by cache miss frequency variables and bound sum of variables by ∑ f(S(B))

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Example: Building the Scope Graph

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g() { for (;;) { access(X); } }

f() { for (;;) { access(Y); }c3: g(); }

main() { access(Y);c2: if (?) f(); access(Z);c1: g(); access(Y); }

Scope graph

Example: Building the Scope Graph

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g() { for (;;) { access(X); } }

f() { for (;;) { access(Y); }c3: g(); }

main() { access(Y);c2: if (?) f(); access(Z);c1: g(); access(Y); }

Scope graphAccess graph

for main()

Example: Finding conflict-free scopes

11

Scope graph

Assuming a 2-way set-associative cache:

OK

OK


12

Scope graph


OK

OK

OK

OK


13

Scope graph


OK

OK

OK

OK

OK OK


14

Scope graph


OK

OK

OK

OK

OK OK

Conflict!


15

Scope graph


OK

OK

OK

OK

OK OK

Conflict!

Access graphfor main()


16

Scope graph


OK

OK

OK

OK

OK OK

Conflict!



17

Scope graph


OK

OK

OK

OK

OK OK

Conflict!



18

Scope graph


OK

OK

OK

OK

OK OK

Conflict!


Conflict!


19

Scope graph


OK

OK

OK

OK

OK OK

Conflict!



20

Scope graph


OK

OK

OK

OK

OK OK

Conflict!



21

Scope graph


OK

OK

OK

OK

OK OK

Conflict!



22


OK

OK

OK

OK

OK OK

Conflict!

S1:{Y,X}

S2:{Z,X}

S3:{Y}

Cache misses of X ≤ f(S1) + f(S2)Cache misses of Y ≤ f(S1) + f(S3) Cache misses of Z ≤ f(S2)


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OK

OK

OK

OK

OK OK

Conflict!

S1:{Y,X}

S2:{Z,X}

S3:{Y}

Cache misses of X ≤ f(S1) + f(S2)Cache misses of Y ≤ f(S1) + f(S3) => Total cache misses ≤ 5 f(main)Cache misses of Z ≤ f(S2)

Conflict Detection For FIFO and LRU n-way set-associative caches:

conflict-free if at most n distinct cache lines are accessed path-insensitive, one analysis per cache set

For method cache: conflict-free if size and number of accessed functions does

not exceed capacity of cache path-insensitive, one single analysis

For LRU n-way set-associative caches:

conflict-free if at most n-1 distinct cache lines accessed between two accesses of a block B

path sensitive, per block, abstract interpretation

• similar to [Cullmann13] or [Huynh11], but more fine-grained scopes

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Implementation

Implemented in the platin analysis tool Persistence analysis based on [Huynh11] Scope-based analysis for set-associative FIFO/LRU

caches Scope-based analysis for method cache 'Simple' scope-based analysis: only functions and

loops as scopes, no construction of fine-grained scopes

Evaluated on Mälardalen and PapaBench benchmarks

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Evaluation

Results for a 1 kB 8-way LRU set-associative cache

Evaluation

Results for a 1 kB method cache

Conclusion

Scope-based cache analysis framework M$ or set-associative caches, FIFO or LRU Generalization of Persistence Analysis Improved concept of scopes Evaluation promises good analysis precision

Implemented in platin, available at:

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http://github.com/t-crest/

Thanks! Questions?

http://patmos.compute.dtu.dk/

http://github.com/t-crest/

http://patmos.compute.dtu.dk/

scope-based method cache analysis - ulm...scope-based method cache analysis benedikt huber1, stefan...

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