1. CSE 237D: Spring 2008 Topic #6 Professor Ryan Kastner
9/19/2018
High Level Synthesis
CSE 237D: Spring 2008
Topic #6
Professor Ryan Kastner

2. Ant System Optimization: Overview
Ants work corporately on the graph
Each creates a feasible solution
Ants leave pheromones on their traces
Ant make decisions partially on amount of pheromones
Global Optimizations
Evaporation: Pheromones dissipate over time
Reinforcement: Update pheromones from good solutions
Quickly converges to good solutions
It is discovered that the ant is more biased to a path having more pheromone trails. Thus she is more likely to pick the “better” path. This will further enforce the better path, and leads future ants quickly converge to the optimal solution. ?

3. Solving Design Problems using AS
Problem model
Define the solution space: create decision variables
Pheromone model
Global heuristic: Provides history of search space traversal
Ant search strategy
Local heuristic: Deterministic strategy for individual ant decision making
Solution construction
Probabilistically derive solution from local and global heuristics
Feedback
Evaluate solution quality, Reinforce good solutions (pheromones), Slightly evaporate all decisions (weakens poor solutions)

4. Autocatalytic Effect

5. Max-Min Ant System (MMAS) Scheduling
Problem: Some pheromones can overpower others leading to local minimums (premature convergence)
Solution: Bound the strength of the pheromones
If , always a chance to make any decision
If , the decision is based solely on local heuristics, i.e. no past information is taken into account

6. MMAS RCS Formulation Idea: Combine ACO and List Scheduling
Ants determine priority list
List scheduling framework evaluates the “goodness” of the list
Global heuristics  permutation index
Local heuristic – can use different properties
Instruction mobility (IM)
Instruction depth (ID)
Latency weighted instruction depth (LWID)
Successor number (SN)

7. RCS: List Scheduling
A simple scheduling algorithm based on greedy strategies
List scheduling algorithm:
Construct a priority list based on some metrics (operation mobility, numbers of successors, etc)
While not all operations scheduled
For each available resource, select an operation in the ready list following the descending priority.
Assign these operations to the current clock cycle
Update the ready list
Clock cycle ++
Qualities depend on benchmarks and particular metrics

8. MMAS RCS: Global and Local Heuristics
Global heuristic:
Pheromones : the favorableness of selecting operation i to position j
Global pheromone matrix
Local heuristic:
Local metrics : Instruction mobility, number of successors, etc
Local decision making: a probabilistic decision
Evaporate pheromone and reinforce good solution
\tau should be very large at the very beginning, hence the ants just go everywhere to explore the search space

9. Pheromone Model For Instruction Scheduling
Each instruction opi  I associated with n pheromone trails where j = 1, …, n
each indicates the favorableness of assign instruction i to position j
op1
op2
op3
op4
op5
op6
Instructions 1 2 3 4 5 6
Priority List
Each instruction also has a dynamic local heuristic
Initially all  set to fixed value 0

10. Ant Search Strategy Each run has multiple iterations
Each iteration, multiple ants independently create their own priority list
Fill one instruction at a time
op1
op1 1 2 3 4 5 6
Priority List
op4
op2
op2
op1
op3
op3
op5
op4
op4
op6
op5
op5
op2
op6
op6
op3
Instructions

11. Ant Search Strategy
Each ant has memory about instructions already selected
At step j ant has already selected j-1 instructions
jth instruction selected probabilistically
op1
op1 1
op4
op2
op2
op1 2
op3
op3
op5 3
op4
op4 4
op5
op5 5
op6
op6 6
Instructions
Priority List

12. Ant Search Strategy
ij(k) : global heuristic (pheromone) for selecting instruction i at j position
j(k) : local heuristic – can use different properties
Instruction mobility (IM)
Instruction depth (ID)
Latency weighted instruction depth (LWID)
Successor number (SN)
,  control influence of global and local heuristics
ij(k) : global heuristic on the favorableness if we color tj with ck
j(k) : local heuristic on the favorableness if we color tj with ck . The local heuristic simply is the inverse of the local cost. In other words, it favors an assignment that yields smaller local cost.
The numerator is the production of the global heuristic tau and local heuristic local heuristic eta.

13. Pheromone Update Lists constructed are evaluated with List Scheduling
Latency Lh for the result from ant h
Evaporation – prevent stigmergy and punish “useless” trails
Reinforcement – award trails with better quality

14. Pheromone Update Evaporation happens on all trails to avoid stigmergy
Reward the used trails based on the solution’s quality
op1
op1 1 2 3 4 5 6
Priority List
op4
op2
op2
op1
op3
op3
op5
op4
op4
op6
op5
op5
op2
op6
op6
op3
Instructions

15. Max-Min Ant System (MMAS)
Risks of Ant System optimization
Positive feedback
Dynamic range of pheromone trails can increase rapidly
Unused trails can be repetitively punished which reduce their likelihood even more
Premature convergence
MMAS is designed to address this problem
Built upon original AS
Idea is to limit the pheromone trails within an evolving bound so that more broader exploration is possible
Better balance the exploration and exploitation
Prevent premature convergence
P_best is controlling parameter, when p_best is very small, we let t_max == t_min, which means all options approximately have the same chance. Thus more emphasis is given to exploration. When p_best is set to close to 1, t_min becomes close to 0, which gives a bigger dynamic range for difference choice. Thus more emphasis on exploitation.
We have implemented our system using both original AS and MMAS. The MMAS seems to consistently outperform the other one.

16. Max-Min Ant System (MMAS)
Limit (t) within min(t) and max(t)
Sgb is the best global solution found so far at t-1
f(.) is the quality evaluation function, i.e. latency in our case
avg is the average size of decision choices
Pbest  (0,1] is the controlling parameter
Conditional prob. of Sgb being selected when all trails in Sgb have max and others having min
Smaller Pbest  tighter range for   more emphasis on exploration
When Pbest  0, we set min  max
P_best is controlling parameter, when p_best is very small, we let t_max == t_min, which means all options approximately have the same chance. Thus more emphasis is given to exploration. When p_best is set to close to 1, t_min becomes close to 0, which gives a bigger dynamic range for difference choice. Thus more emphasis on exploitation.
We have implemented our system using both original AS and MMAS. The MMAS seems to consistently outperform the other one.
p is the evaporation factor [0,1]

17. Other Algorithmic Refinements
Dynamically evolving local heuristics
Example: dynamically adjust Instruction Mobility
Benefit: reduce search space progressively
Taking advantage of topological sorting of DFG when constructing priority list
Each step ants select from the ready instructions instead from all unscheduled instructions
Benefit: greatly reduce the search space
We can mention that for a 11 node example, constructing list under topological sorting saves the search space from 11! to
We can also mention GenLE, the tool we used to generate topologically ordered combinations.

18. MMAS RCS Algorithm

19. RCS Results: Pheromones (ARF)
The evolutionary effect on the global heuristics tau_ij is illustrated in Figure 3. It plots the pheromone values for the ARF testing sample after 100 iterations of the proposed algorithm. The x-axis is the index of instruction node in the DFG (shown in Figure 2), and the y-axis is the order index in the priority list passed to the list scheduler. There exist totally 30 nodes with node 1 and node 30 as the dummy source and sink of the DFG. Each dot in the diagram indicates the strength of the resultant pheromone trails for assigning corresponding order to a certain instruction – the bigger the size of the dot, the stronger the value of the pheromone.
It is clearly seen from Figure 3 that there are a few strong pheromone trails while the remaining pheromone trails are very weak. This might be explained by the strong symmetric structure of the ARF DFG and the special implementation in our algorithm of considering instruction list only with topologically sorted order. It is also interesting to notice that though a good amount of instructions have a limited few alternative “good” positions (such as instruction 6 and 26), for some of the instructions the pheromone heuristics are strong enough to lock their positions. For example, according to its pheromone distribution, instruction 10 shall be placed as the 28-th item in the list and there is no other competitive position for its
placement. After careful evaluation, this ordering preference cannot be trivially obtained by constructing priority lists with any of the popularly used heuristics mentioned above. This shows that the proposed algorithm has the possibility to discover better ordering which may be hard to achieve intuitively.

20. Benchmarks: ExpressDFG
A comprehensive benchmark for TCS/RCS
Classic samples and more modern cases
Comprehensive coverage
Problem sizes
Complexities
Applications
Downloadable from

21. Auto Regressive Filter

22. Cosine Transform

23. Matrix Inversion

24. RCS Experimental Results
Benchmark
(nodes/edges)
Resources
CPLEX
(latency
/runtime)
Force
Directed
List Scheduling
MMAS-IS
(average over 5 runs) IM ID
LWID SN
HAL(21/25)
la, lfm, lm, 3i, 3o
8/32 8 9
ARF(28/30)
2a, lfm, 2m
11/22 11 13
EWF(34/47)
la, lfm, lm
27 /24000 28 31
27.2 27
FIR1 (40/39)
2a, 2m, 3i, 3o
13/232 19 18
17.2 17
17.8
FIR2(44/43)
14/11560 21
16.2
16.4
COSINE 1(66/76)
2a,2m, lfm, 3i, 3o  20
17.4
18.2
17.6
COSINE2(82/91) 23
21.2
Average
19.3
20.5
18.5
16.8
17.0
16.9
17.1
Heterogeneous RCS = fast and slow multiplier
Real life DFG examples commonly used in instruction scheduling study.
Mention that we also examined MediaBench.
For each of the benchmark samples, we run the proposed algorithm with different choices of local heuristics. For each choice, we perform 5 runs where in each run we allow 100 iterations. The number of ants per iteration is set to 5. The evaporation rate is configured to be The scaling parameters for global and local heuristics are set to be = = 1 and delivery rate Q = 1.
The best schedule latency is reported at the end of each run and then the average value is reported as the performance for the corresponding setting.
The proposed algorithm generates better results consistently over all testing cases. For some of the testing samples, it provides significant improvement on the schedule latency. The biggest saving achieved is 23%. This is obtained for the FIR2 using LWID. Comparing with Force-directed, a 6.2% average improvements, maximum 14.7%.
For all the benchmarks with known optima, our algorithm improves the average schedule latency by 44% comparing with the list scheduling heuristics.
The proposed algorithm is more stable: it is easy to observe that the proposed algorithm is much less sensitive to the choice of different local heuristics and input applications. This is evidenced by the fact that the standard deviation of the results achieved by the new algorithm is much smaller than that of the traditional list scheduler. Based on the data shown in Table 1, the average standard deviation for list scheduler over all the benchmarks and different heuristic choices is , while that for the MMAS algorithm is only In other words, we can expect to achieve much more stable scheduling results on different application DFGs regardless the choice of local heuristic. This is a great attribute desired in practice.
Heterogeneous RCS – multiple types of resources (e.g. fast and normal multiplier)
ILP (optimal) using CPLEX
List scheduling
Instruction mobility (IM), instruction depth (ID), latency weighted instruction depth (LWID), successor number (SN)
Ant scheduling results using different local heuristics (Averaged over 5 runs, each run 100 iteration with 5 ants)

25. RCS Experimental Results
Homogenous RCS – all resources have unit delay
New benchmarks (compared to last slide) too large for ILP

26. MMAS RCS: Results
Consistently generates better results over all testing cases
Up to 23.8% better than list scheduler
Average 6.4%, and up to 15% better than force-directed scheduling
Quantitatively closer to known optimal solutions
Real life DFG examples commonly used in instruction scheduling study.
Mention that we also examined MediaBench.
For each of the benchmark samples, we run the proposed algorithm with different choices of local heuristics. For each choice, we perform 5 runs where in each run we allow 100 iterations. The number of ants per iteration is set to 5. The evaporation rate is configured to be The scaling parameters for global and local heuristics are set to be = = 1 and delivery rate Q = 1.
The best schedule latency is reported at the end of each run and then the average value is reported as the performance for the corresponding setting.
The proposed algorithm generates better results consistently over all testing cases. For some of the testing samples, it provides significant improvement on the schedule latency. The biggest saving achieved is 23%. This is obtained for the FIR2 using LWID. Comparing with Force-directed, a 6.2% average improvements, maximum 14.7%.
For all the benchmarks with known optima, our algorithm improves the average schedule latency by 44% comparing with the list scheduling heuristics.
The proposed algorithm is more stable: it is easy to observe that the proposed algorithm is much less sensitive to the choice of different local heuristics and input applications. This is evidenced by the fact that the standard deviation of the results achieved by the new algorithm is much smaller than that of the traditional list scheduler. Based on the data shown in Table 1, the average standard deviation for list scheduler over all the benchmarks and different heuristic choices is , while that for the MMAS algorithm is only In other words, we can expect to achieve much more stable scheduling results on different application DFGs regardless the choice of local heuristic. This is a great attribute desired in practice

27. MMAS TCS Formulation Idea: Combine ACO and Force Directed Scheduling
Quick FDS review
Uniformly distribute the operations onto the available resources.
Operation probability
Distribution graph
Self force: changes on DG of scheduling an operation
Predecessor/successor force: implicit effects on DG
Schedule an operation to a step with the minimum force

28. ACO Formulation for TCS
Initialize pheromone model
While (termination not satisfied)
Create ants
Each ant finds a solution
Evaluate solutions and update pheromone
Report the best result found
trails ij indicates the favorableness of assigning instruction i to position j 1 4 S S 1 1  v1  v2  v6  v8 +
v10  v1  v2 2  v3   v7 + v9
<
v11  v6 2 v3 3 - v4 3 - v4  v7  v8 +
v10 v9 - v5 - v5 +
<
v11 4 4 E vn E vn

29. ACO Formulation for TCS
Initialize pheromone model
While (termination not satisfied)
Create ants
Each ant finds a solution
Evaluate solutions and update pheromone
Report the best result found
Select operation oph probabilistically
Select its timestep as following:
Global Heuristics: tied with the searching experience
Local Heuristics: use the inverse of distribution graph, 1/qk(j)
Here and β are constants

30. ACO Formulation for TCS
Initialize pheromone model
While (termination not satisfied)
Create ants
Each ant finds a solution
Evaluate solutions and update pheromone
Report the best result found
Rewarding good partial solutions based on solution quality
Pheromone evaporation

31. Final Version of MMAS-TCS

32. Effectiveness of MMAS-TCS

33. MMAS TCS: Results
MMAS TCS is more stable than FDS, especially solution highly unconstrained
258 out of 263 test cases are equal to or better than FDS results
16.4% fewer resources

34. Design Space Exploration
DSE challenges to the designer
Ever increasing design options
Closely related w/ NP-hard problems
Resource allocation
scheduling
Conflict objectives (speed, cost, power, …)
Increasing time-to-market pressure

35. Our Focus: Timing/Cost
Timing/Cost Tradeoffs
Known application
Known resource types
Known operation/resource mapping
Question: find the optimal timing/cost tradeoffs
Most commonly faced problem
Fundamental to other design considerations

36. Common Strategies Usually done in an ad-hoc way
Experience dependent
Or Scanning the design space with Resource Constrained (RCS) or Time Constrained (TCS) scheduling
What’s the problem?
RCS and TCS are dual problems
Can we effectively use information from one to guide the other?

37. Design Space Model

38. Key Observations
A feasible configuration C covers a beam starting from (tmin, C)
tmin is the RCS result for C

39. Design Space Model

40. Key Observations
A feasible configuration C covers a beam starting from (tmin, C)
Optimal tradeoff curve L is monotonically non-increasing as deadline increases

41. Design Space Model

42. Theorem
If C is the optimal TCS result at time t1, then the RCS result t2 of C satisfies t2 <= t1.
More importantly, there is no configuration C′with a smaller cost can produce an execution time within [t2, t1].

43. Theorem (continued)

44. What does it give us? It implies that we can construct L:
Starting from the rightmost t
Find TCS solution C
Push it to leftwards using RCS solution of C
Do this iteratively (switch between TCS + RCS)

45. DSE Using Time/Resource Duality

46. Experiments Three DSE approaches FDS: Exhaustively scanning for TCS
MMAS-TCS: Exhaustively scanning for TCS
MMAS-D: Proposed method leveraging duality
* Scanning means that we perform TCS on each interested deadline

47. DSE: MMAS-D vs. FDS

48. Experimental Results

49. Algorithm Runtime

50. Real Design Complications
Heterogeneous mapping
One operation has many implementations
Different bit-width, e.g. 32-bit multiplier good for mul(24) and mul(32)
Different area and delay
Real technology library extremely sophisticated
Hard to estimate final timing and total area
Sharing depends on the cost of multiplexers
Downstream tools may not generate what we expect
Resource sharing, register sharing
Downstream tools break components’ boundaries
Logic synthesis, placement and routing

51. Resource Allocation and Scheduling
Scheduling Cost function?
Homogeneous TCS
Total number of component
Heterogeneous TCS
Total area of functional units
FPGA designs: LUTs, slicecs, BRAMs, …
ASIC design: Silicon Area
Total area comes from:
Functional units
Register
Multiplexers
Interconnect

52. Towards Real World: Constraint Graph
A hierarchical directed graph
Nodes V: operations
Edges E(vi,vj,Tij): timing constraints
Timing constraint Ti,j(c,o)
Start time dependencies
Finish time dependencies
Chained dependencies

53. Constraint Graph: Examples
Operation b must start after Operation a
Operation a starts at least two cycles after start of Operation b
Operations a and b scheduled at same cycle
Operation b scheduled exactly one cycle after start of Operation a

54. Pipelined Designs Start a new task before the prior one completed
Feedback constraints among nodes
Specific initial interval
Improve throughput
Requires more hardware

55. Operation Chaining
Two or more operations scheduled in the same clock cycle
Faster/larger component
Shorter latency
Saving registers
Chaining across clock edges

56. Speculative Execution

57. Problem Formulation Constraint graph Nodes V: operations
Edges E: data dependencies and timing constraints
Technology library Q
Area, timing
Resource constraints
Desired clock period: C
Determine start time and the allocation of each resource type
Resource constraint scheduling
Timing constraint scheduling

58. MMAS CRAAS: Overview Start with an initial results
Using fastest components
ASAP/ALAP
Resolving resource conflicts
Meet timing and resource constraints
MMAS iteratively searches optimal solutions

59. MMAS CRAAS: ASAP/ALAP Iteratively ASAP/ALAP
Handle loops/feedbacks in constraint graph
Check ill-posed timing constraint

60. MMAS CRAAS: Initial Schedule
Resource conflicts
More than available resources are used in the ASAP results
Pushing operations forward

61. MMAS CRAAS: Overview Individual ant constructs schedules
Load ASAP timing results
Update mobility range, operation probability
Update distribution graph
Probabilistically defer operations
Probabilistically select operations
Schedule operations using p(i,j,k)
Update ASAP/ALAP results

62. MMAS CRAAS: Global Heuristics
Local heuristics
Favor smaller functional units and less registers for this operation
Uniform probability among all compatible resources
Global heuristics
Favor solutions with smaller area

63. MMAS CRAAS: Scheduling
Defer operations from this iteration
Favor operations with many options
Schedule an operation
Update ASAP schedules
Update global heuristics

64. MMAS CRAAS: Results
Implemented in a leading high-level synthesis framework
Leverage the HDL back-ends to collect results
Front-end parses C and performs optimizations
Resource sharing and register sharing after scheduling
The existing algorithm
Based on FDS/FDLS
Refined for real designs
Force-directed operation deferring
Re-allocate resources and iterative until area increasing
Results overview
3 - 15% smaller (optimizing area)
1-4% faster (optimizing latency)

65. MMAS CRAAS: Results

66. MMAS CRAAS: Results
Hard to generate good results with control-dominant designs (158, 160, and 54)
Better resource allocation and sharing
Existing algorithm prematurely converges
Consistent with previous observations

67. Conclusions and Future Research
There is (was?) room for more work in fundamental algorithms; they make a difference on real designs
Ivory Tower: Most academics do not tackle real world problems
Constraint graph with pipelining, speculation, chaining
Actual delay and area (mux, interconnect, …)
Gripes:
Extremely hard to validate new algorithms against old ones (e.g. no open source code for FDS!)
Backend (hooks into commercial tools a la Quartus)
Benchmarks?!