A Vectorless Estimation of Maximum Instantaneous Current for Sequential Circuits

1
A Vectorless Estimation of Maximum Instantaneous
Current for Sequential Circuits

• Cheng-Tao Hsieh, Jian-Cheng Lin, and Shih-Chieh
  Chang
• National Tsing Hua University, Taiwan

2
Outline

• Maximum Instantaneous Current (MIC) problem
• Signal correlation problems
• MIC estimation considering signal correlation
• Experimental results conclusions

3
Power Noises

• Excessively large current through power bus may
  cause IR drop and EM.
• Severe IR drop and EM degrade the performance and
  reliability.
• Accurate estimation of Maximum Instantaneous
  Current (MIC) to analyze noises.

4
Maximum Instantaneous Current
t1
t2
t3
Maximum current4 at time t1.
Maximum current3 at time t3

• Maximum Instantaneous Current (MIC)
• Input vectors and time.

5
Previous Work

• Vector dependent
• Find a vector pair
• Lower bound estimation
• Vector Independent
• Not find the worst case vectors
• Upper bound estimation
• iMax and PIE H. Kriplani et al.

6
Outline

• Maximum instantaneous current (MIC) problem
• Signal correlation problems
• MIC estimation considering signal correlation
• Experimental results conclusion

7
Summary

• Identifying signal correlation is important for
  MIC estimation.
• Contribution Efficiently identify complex
  combinational and sequential correlations.

8
Combinational Correlation

• Signal correlation in a combinational circuit.

9
Combinational Correlation

• Can efficiently recognize complicated
  combinational correlations.

10
Sequential Correlation

• Correlation across sequential elements.

(0, 1)
(f1, f2) (0, 0)
(1, 0)
(1, 1)
f2
f1
11
Sequential Correlation

• Some (next) states are not reachable from a
  current state.
• Deriving state transition diagram is NOT
  practical.
• Implicitly obtain sequential correlation without
  the need of state transition diagram.
• None of the previous work can detect sequential
  correlation.

12
Outline

• Maximum instantaneous current (MIC) problem
• Signal correlation problems.
• MIC estimation considering signal correlation
• Experimental results conclusion

13
Before Exploring Signal Correlation

• Decide whether a set of gates can switch
  simultaneously at timet1.
• Goal Find necessary conditions for a gate to
  switch at timet1.

14
Necessary Conditions of a Switching

• A transition requires two vectors applied
  consecutively.

1st 2nd 0 1 0 0 1 0 1 0 1 1
15
Initial Value Stable Value

• We define
• 1st vector ? initial value.
• 2nd vector ? stable value.

initial value1
stable value1
initial value1
stable value0
1st 2nd 0 1 0 0 1 0 1 0 1 1
16
Stable Value Requirement

• Some requirements for initial and stable values
  for a gate to switch at timet1.

Stable value must be 0
17
Stable Value Requirement

• Stable value of gate u must be 0.

After time2, must hold stable value
18
Stable Value Requirement

• Stable value of gate u must be 0.

Stable value must be 0
19
Initial Value Requirement
g
switch at t4
Initial value must be 1
20
Transition Propagation
switch at t1
k
switch at t4
21
Initial Value Requirement

• Initial value of gate v must be 1.

switch at t1
k
Before time1, must hold initial value
22
Initial Value Requirement

• Initial value of gate v must be 1.

Initial value must be 1
k
23
A Summary of Necessary Conditions
switch at t4
1
0
Initial values
Stable values
24
Necessary Conditions in Sequential Circuits

• Combinational circuit The initial values and the
  stable values are treated independently.
• Sequential circuit Strong correlation between
  the initial values and the stable values.

25
Necessary Conditions in Sequential Circuits
switch at t2
Flip-flop
26
Necessary Conditions in Sequential Circuits

• To reveal sequential correlation, we link the two
  circuit copies through flip-flops.

switch at t2
Initial values
Stable values
27
MIC Estimation

• MIC estimation using mutually exclusive
  switching.
• Definition Two gates are Mutually Exclusive
  Switching (MES) at time t1 if they cannot switch
  simultaneously at t1.

28
An Example for MES Detection
Mutually Exclusive Switching at t4
?
29
Conflicts ? Mutually Exclusive Switching
Switch at t 4
Switch at t 4
30
Conflicts ? Mutually Exclusive Switching
Mutually Exclusive Switching at t4
31
MIC Estimation Based on MES

• Use an undirected graph to present the MES
  relation.
• Find a set of nodes that have no edge in between.
  
• ? Switch simultaneously.

Current contribution 1
Maximum current 3 at timet1
MES relation at timet1
32
Outline

• Maximum instantaneous current (MIC) problem
• Signal correlation problems
• MIC estimation considering signal correlation
• Experimental results conclusion

33
Experimental Flow

• Combinational and sequential MCNC ISCAS
  benchmarks.
• Upper bound estimations iMax, PIE (1000 s_nodes)
  , and MES.
• Lower bound estimations Random simulation for 3
  days.

34
Results for Combinational Circuits
iMax2.6 PIE2.3 Random0.95
35
Results for Sequential Circuits
36
Upper Bound Estimation

• Our method derives tighter upper bound especially
  for sequential circuits.

iMax3.1 PIE2.3
iMax2.3 PIE1.7
Avg. MIC
37
Lower Bound Estimation

• If an upper bound is close to the corresponding
  lower bound, both estimations are accurate.
• For small circuits, our upper bound results are
  close to the lower bound results.
• For large circuits, random simulation may only
  reach small portion of solution space.
• Ex. In s344, only 57 of 2625 reachable states.

38
Run Time Comparison

• The run time for iMax takes few seconds for the
  largest circuit.
• Our run time is in general faster than that of
  PIE.
• Ex. In s15850
• Ours 2502 sec
• PIE 15354 sec.

39
Conclusion

• A vectorless method to estimate the MIC for
  sequential circuits.
• Based on mutually exclusive switching.
• Experimental results on sequential circuits are
  encouraging.

40

• Thank you!