RaceConditionAware Clock Skew Scheduling

1
Race-Condition-Aware Clock Skew Scheduling

• Shih-Hsu Huang, Yow-Tyng Nieh,
• and Feng-Pin Lu

Department of Electronic Engineering Chung Yuan
Christian University, Taiwan
2
Outline

• Introduction
• Motivation
• RCA algorithm
• Overview
• Experimental results
• Conclusions

3
Introduction

• Optimal clock skew scheduling (OCSS)
• Does NOT achieve the low bound of
  sequentialtiming optimization
• Due to the limitation of hold constraints
• The race condition can be resolved by delay
  insertion
• Padding method 4 in ICCAD 1993
• The combination of OCSS and delay insertion
• Huang and Nieh 5 in ICCAD 2003
• The time complexity is O(E2TOCSS)
• Our RCA algorithm achieves the same results,but
  the time complexity is only O(ETOCSS)
• A fresh viewpoint to look at the interactions
  between clock skew scheduling and delay insertion

4
Motivations

• The limitation of OCSS
• The limitation of only applying the padding method

5
Optimal Clock Skew Scheduling
If we relax this hold edge, the clock period can
be further reduced
6
The limitation of padding
Lower bound P is achieved without any delay
insertion under OCSS (0,-3,0,0)
Both hold constraints and setup constraint are
considered (P6)
7
The limitation of padding cont.
Only setup constraints are considered (P6)
8
Relaxed constraint graph

• The constraint graphs under OCSS (0,-3,0,0)and
  (0,-3,3,0) are both relaxed constraint graph

R1
R1
-3
-3
-3
3
3
0
-3
3
3
0
Host
Host
0
3
0
3
0
0
2
00
2
03
0
0
0
3
R2
R3
0
R2
R3
0
3
3
9
Irredundant-relaxed constraint graph

• Only the constraint graphs under OCSS
  (0,-3,0,0) is irredundant-relaxed constraint graph

R1
-3
No extra delay insertion is needed
-3
3
3
0
Host
0
3
0
2
00
0
0
R2
R3
0
3
10
RCA algorithm

• Procedure Relax_Hold
• Procedure Parameter_Assign
• Procedure Parameter_Minimization

P10
11
Procedure Relax_Hold
12
Procedure Parameter_Assign
2
-3
5
R1
R3
-5
-1
7
5
0
5
4
-2
Host
-4
1
0
2
7
4
1
R2
R4
1
5
3
13
Procedure Parameter_Minimization
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Our approach overview
15
Our approach overview cont.
16
Our approach overview cont.
Sequential circuit (constraint graph)
The race conditions can be resolved by applying
the padding method.
RCA algorithm
Padding method
17
Experimental results (clock period)
Clock period
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Experimental results (CPU time)
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Conclusions

• This paper proposes an irredundant-relaxed
  constraint graph to model the interaction between
  clock skew scheduling and delay insertion.
• Compared with previous work 5, our RCA clock
  skew scheduling has significant improvement in
  the time complexity.
• Experimental data consistently show that our RCA
  clock skew scheduling can solve large circuits
  within only few minutes.

20
Thank you !