1. Region-based Hierarchical Operation Partitioning for Multicluster Processors
Michael Chu, Kevin Fan, Scott Mahlke
Advanced Computer Architecture Lab
University of Michigan
November 14, 2018

2. Clustered Architectures
Conventional Architecture
Increasing width from 4 to 8 increases total delay 29% [Palacharla ‘98]
Clustered Approach:
Decentralized architecture
Communication through interconnection network
Used in Alpha 21264, TI C6x, Analog Tigersharc and others.
Register File FU RF FU
Register
File FU
Cluster 1
Cluster 2
Clustered Architecture

3. Basics of Multicluster Compilation
Objectives:
Balance workload per cluster
Minimize critical intercluster communication
Interconnection Network +
>>
&
Register
File
Register
File * LW I
MEM I
MEM +
Intercluster move
Cluster 1
Cluster 2

4. Problem #1: Local vs Global Scope
Local scope clustering
Global scope clustering 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 3 1 4 1 2 7 1 2 8 2 3 4 5 6
move 4 2 3 4 5 6 5 10 8 3 9 6 7 8 9
cycle 6 7 8 9
cycle 5 7 11 10 11
move 10 11 9
move 10 12 12 11 12 12

5. Problem #2: Scheduler-centric
Cluster assignment during scheduling adds complexity
Detailed resource model/reservation tables is slow
Forces local decisions
Reservation Tables
cycle
Cluster 1
cycle
Cluster 2 1 X X 1 X X 1 2 X X 2 X X 2 3 4 5 1 X X 1 X X 6 7 8 9 2 X X 2 X X 10 11 1 X X 1 X X 12 2 X X 2 X X

6. Our Approach Opposite approach to conventional clustering Global view
Graph partitioning strategy [Aletà ‘01, ‘02]
Identify tightly coupled operations - treat uniformly
Non scheduler-centric mindset
Prescheduling technique
Doesn’t complicate scheduler
Enable global view of code
Estimate-based approach [Lapinskii ‘01]

7. Region-based Hierarchical Operation Partitioning (RHOP)
Program
Region 1 10 8
int main {
int x;
printf(…); . }
Weight
Calculation
Graph
Partitioning
Code is considered region at a time
Weight calculation creates guides for good partitions
Partitioning clusters based on given weights

8. Node Weights Create a metric to determine resource usage 1 2
Dedicated Resources
Shared Resources 3 8 5 9 6 10 7 11 13 14 12 1 2 4 1 2 I F M B
Register File I F M B
Register File 3
Accounts for FU’s
Accounts for buses, ports

9. Edge Weights
Slack distribution allocates slack to certain edges
Edge slack = lstartdest - latencyedge - estartsrc
First come, first serve method used
(0,0) 1
(0,0) 2 10
(1,1) 3
(0,1) 4
(0,1) 5
(0,1) 6
(0,1) 7 1 1 2 8 1
(2,2) 8
(1,2) 9
(0,2) 10
(1,2) 11 1 1
(3,3) 12
(2,3) 13
(estart, lstart) 1 14
(4,4)

10. RHOP - Partitioning Phase
Modified Multilevel-KL algorithm [Kernighan ‘69]
Multilevel graph partitioning consists of two stages
Coarsening stage
Refinement stage

11. Cluster Refinement 3 questions to answer:
Which cluster should operations move from?
How good is the current partition?
How profitable is it to move X from cluster A to B? ?

12. Where Should Operations Move From?
Cluster 1
2.5
2.0
0.5
0.0 1 2
Cluster_wgt1= 5.0
0.33
Cluster_wgt2= 0.67 1 2 3 4 1 2 4 5 6 3 9
cycle 8 12 14
Cluster 2 1 2 3 4 7 10 11
cycle 13

13. How Good is this Partition?
Cluster 1
Cluster 2
Max 1 2 1 2
2.5
0.0
2.5
2.0
0.33
2.0
0.5
0.33
0.5
0.0
0.0
0.0
0.0
0.0
0.0
Cluster_wgt1= 5.0
Cluster_wgt1= 0.67
SL= 5.0

14. How Good is This Proposed Move?
Cluster 1 1 2 3 4 1 2
1.0
SL(before)= 5.0 3
0.0
cycle 8
0.0
SL(after)= 4.5 12
0.0 14
0.0
Cluster 2
Lgain= 0.5 1 2 3 4 7 4 5 6
1.33 10 11 9
2.33
Egain= -1.0
cycle 13
0.83
0.0
Mgain= 4.0
0.0

15. Experimental Evaluation
Trimaran toolset: a retargetable VLIW compiler
Evaluated DSP kernels and SPECint2000
Name
Configuration
2-1111
2 Homogenous clusters
1 I, 1 F, 1 M, 1 B per cluster
2-2111
2 I, 1 F, 1 M, 1 B per cluster
4-1111
4 Homogenous clusters
4-2111
4-H
4 Heterogeneous clusters
IM, IF, IB and IMF clusters
64 registers per cluster
Latencies similar to Itanium
Perfect caches
For more detailed results, see paper

16. 2 Cluster Results vs 1 Cluster

17. 4 Cluster Results vs 1 Cluster

18. Conclusions A new, region-scoped method for clustering operations
Prescheduling technique
Estimates on schedule length used instead of scheduler
Combines slack distribution with multilevel-KL partitioning
Performs better as number of resources increases
Average Improvement
Machine
RHOP vs BUG
2-1111
-1.8%
2-2111
3.7%
4-1111
14.3%
4-2111
15.3%
4-H
8.0%

19. Questions?

20. Backup Slides

21. Previous Work X X X X Algorithm UAS CARS Convergent Leupers Capitanio
GP(B)
B-ITER
BUG
RHOP
When (rel. to sched)
During
Iterative
Before X
Scope
Local
Region X
Desirability Metric
Sched
Pseudo
Est
Count X
Grouping
Hier.
Flat X

22. Bottom-Up Greedy (BUG)
Typical clustering strategy, falls into trouble because of its limited view
Places operations without knowing the rest of the graph
Uses the scheduler to determine where to best place each operation
First used in Multiflow trace [Ellis ‘85]

23. Graph Partitioning Algorithms
Local improvement methods:
Kernighan-Lin
Swaps pairs of operations between partitions
Fiduccia and Matheyses
KL-inspired, efficent O(|E|) algorithm
Simulated annealing
Genetic algorithms

24. Graph Partitioning Algorithms
Global methods:
Geometric methods
Coordinate based, not suitable for clustering
Coordinate-free methods
Recursive spectral bisection (RSB)
Multilevel-RSB
Multilevel-KL

25. RHOP - Example

26. Improvement at Increasing CPLs

27. Resource Manager Overhead