Power estimation techniques and a new glitch filtering effect modeling based on probability waveform

1
Power estimation techniques and a new glitch
filtering effect modeling based on probability
waveform

• Fei Hu
• Department of Electrical and Computer
  Engineering,
• Auburn University, AL 36849

2
Outline

• Introduction
• Different Levels of power estimation
• Gate-level Probabilistic Approach
• Signal Probability
• Transition probability
• Transition density
• Probability waveform
• A new glitch filtering method
• Based on Probability waveform
• The idea and examples
• Preliminary experimental results
• Summary

3
Introduction

• Power estimation is critical to IC (low power)
  design
• Total power consumption must be estimated during
  the design phase.
• Helps to find the hot-spot which may lead to the
  failure
• Levels of power estimation
• Transistor Level
• Gate Level
• RTL Level
• Behavior Level
• Software Level
• Two approaches
• Simulation based
• Non-simulative

4
Simulation based Approach

• Transistor Level Simulation
• Circuit level
• SPICE
• Solving a large matrix of node current using the
  Krichoffs Current Law (KCL)
• Basic components include resistor, capacitor,
  inductors, current sources and voltage sources.
• Diodes and transistors are modeled by basic
  components
• PowerMill
• Table based device model
• Even driven timing simulation
• 2-3 orders of magnitude faster than Spice

5
Simulation based Approach

• Transistor Level Simulation -continued
• Switch level
• Model transistor as a on-off switch with a
  resistor
• Short circuit power can be accounted by observing
  the time in which the switches form a
  power-ground path
• Gate Level Simulation
• Basic components, logic gates
• Logic simulation to find switching activity,
  P1/2CV2factive
• Monte Carlo simulation, statistical method
• Each sample has N Random input vector
• Energy consumption has a normal distribution
• Stopping criterion derived from sample average
  and sample standard deviation

6
Simulation based Approach

• RTL level simulation
• Basic components, register, adder, multiplier,
  etc.
• RT-level simulation collect input statistics of
  each module
• Macro-modeling of each component based on
  simulation
• Simulating the component with random input
• Fitting a multi-variable regression curve (power
  macro model equation) using a least mean square
  error fit.

7
High level estimation

• Most of the high level power prediction use
  profiling and simulation techniques to address
  data dependencies
• Behavior level estimation
• No much RT (or lower) level circuit structure
  information available
• Information theoretic models
• Total capacitance estimated based on output
  entropy
• Average switching activity for each line,
  approximated by ½ its entropy
• Complexity based models, equivalent gate
• Software level estimation
• Energy consumption by a application program
• Instruction level power macromodel
• Profile-driven program synthesis, RT level
  simulation

8
Non-simulative Approach

• Gate level probabilistic approach
• Concepts
• Signal Probability
• Transition probability
• Transition density
• Probability waveform
• Factors
• Spatial, temporal correlation
• Zero delay or real delay (glitch power)
• With or w/o glitch filtering

9
Gate level probabilistic approach - concepts

• Signal Probability
• Ps(x), the fraction of clock cycles in which the
  steady-state value of signal x is high
• Spatial independence, the logic value of an input
  node is independent of the logic value of any
  other input node
• Under spatial independence assumption, signal
  probability for simple gate is
• NOT ca, Ps(c)1-Ps(a)
• AND cab, Ps(c)Ps(a)Ps(b)
• OR cab, Ps(c)1-1-Ps(a)(1-Ps(b)

10
Signal probability w/ spatial correlation

• Example
• Signal correlation
• S. Ercolani, M. Favalli, M. Damiani, P. Olivo,
  and B. Ricco. Estimate of signal probability in
  combinational logic networks. In Proceedings of
  the First European Test Conference, pages
  132138, 1989.
• Ps(x1,x2)Ps(x1)Ps(x2)Wx1,x2
• Approximate higher order correlation with
  pairwise correlations

Ps(a)0.5
Ps(c)0.5x0.50.25 ?
Ps(c)0
Ps(b)0.5
11
Signal probability w/ spatial correlation

• Global OBDD
• Ordered binary decision diagram corresponding to
  the global function of a node (function of node
  in terms of circuit input)
• Give exact signal correlation
• Example, function yx1x2x3
• Ps(y)Ps(x1)Ps(fx1)Ps(x1)Ps(fx1)
• Traversal from bottom to top to derive signal
  probability

x1
1
x2
0
0
1
x3
1
0
0
1
12
Gate level probabilistic approach - concepts

• Transition probability
• Pt(x), average fraction of clock cycles in which
  the steady state value of x is different from its
  initial value
• Temporal independence, the signal value of a node
  at clock cycle i is independent to its signal
  value at clock cycle i-1
• Under temporal independence assumption,
  transition probability Pt(x)2Ps(x)1-Ps(x)

13
Transition probability w/ spatial temporal
correlations

• R. Marculescu, D. Marculescu, and M. Pedram.
  Logic level power estimation considering
  spatiotemporal correlations. In Proceedings of
  the IEEE International Conference on Computer
  Aided Design, pages 294299, Nov. 1994.
• Zero delay assumption, lag one markov chain
• Pt(x) ?2Ps(x)1-Ps(x)
• Transition correlations
• Used to describe the spatial temporal correlation
  between two signals in consecutive clock periods
• TCxy(ij,mn)P(xi-gtj ,ym-gtn)/P(xi-gtj)P(ym-gtn)i,j,m
  ,n ? 0,1
• Propagate transition probability from PI
• OBDD based procedure
• Global or local OBDD

14
Gate level probabilistic approach - concepts

• Transition density
• D(x), average number of transitions a logic
  signal x makes in a unit time (one clock cycle)
• Boolean difference, if y is a function depending
  on x then
• and
• Under differential delay assumption, no two
  signal has transition happened at the same time.
• Under spatial independence assumption
• Considers glitch power
• No glitch filtering effect

15
Transition density

• Example, cab
• Depending on delay model above result can be true
  or false

P(?c/?a)P(b)0.5 P(?c/?b)P(a)0.5 D(c)0.5D(a)
0.5D(b) 0.50.50.50.5 0.5
Ps(a)0.5 D(a)Pt(a)20.50.5 0.5
d
d
Ps(b)0.5 D(b)Pt(b)20.50.5 0.5
16
Transition density
Inputs Inputs Number transition on c Number transition on c
a b Zero delay Unit delay
00 00 0 0
00 01 0 0
00 10 0 0
00 11 0 0
01 00 1 1
01 01 0 0
01 10 1 1
01 11 0 0
10 00 1 1
10 01 1 1
10 10 0 2
10 11 0 0
11 00 0 0
11 01 1 1
11 10 1 1
11 11 0 0
Total 6 8
17
Gate level probabilistic approach - concepts

• Probability waveform
• F. N. Najm, R. Burch, P. Yang, and I. N. Hajj.
  CREST - a current estimator for cmos circuits. In
  Proceedings of IEEE International Conference on
  Computer-Aided Design, pages 204207, Nov. 1988
• A sequence of value indicating the probability
  that a signal is high for certain time
  interverals, and the probability that it makes
  low-to-high at specific time point
• Real delay model
• Propagation of probability waveform deals with
  probability of making transitions
• Transition density is the sum of all probability
  of transitions
• CREST assumes spatial independence

18
Probability waveform
Pc01(t1)Pa01(t1) Pb01(t1) Pa01(t1)
Pb11(t1) Pa11(t1) Pb01(t1) 0.10.10.10.30.30
.1 0.07

• Example, cab

P
0.1
0.2
0.5
P
0.2
0.1
0.07
0.16
0.5
a
t1
t2
0.07
0
0.16
c
b
t1
t2
P
Pc10(t1)Pa10(t1) Pb10(t1) Pa10(t1)
Pb11(t1) Pa11(t1) Pb10(t1) 0.20.20.20.30.30
.2 0.16
0.1
0.2
0.5
0.2
0.1
t1
t2
Pc11(t1)Pc1(t1-)- Pc10(t1) Pc1(t1)Pc01(t1)Pc11
(t1)
19
Probability waveform

• Tagged Probability waveform
• Divide probability waveform into 4 tagged
  waveform depending the steady state signal values
• Probability waveforms are for one clock period
• Use transition correlation of steady state signal
  to approximate spatial temporal correlation
  between two inputs Wa,bxy,wzPa,bxy,wz /Paxy
  Pbwz
• Transition correlation can be obtained from zero
  delay logic simulation
• Bit-parallel simulation
• Glitch filtering effect considered

20
Tagged probability waveform

• Example of decomposition

11
0.35
0.15
0.15
t1
t2
01
0.15
P
11
0.1
0.05
0.2
0.1
0.5
0.2
0.1
t1
t2
10
t1
t2
0.1
0.15
0.05
t1
t2
00
0.35
t1
t2
21
Tagged probability waveform

• Propagation of waveform
• Similar to untagged waveform
• Two input gates, 16 combinations of tagssum up
  waveform with same resulting tags, 4 output
  waveform
• Example for an AND gate

Pc,uv01(t1)Pa,xy01(t1) Pb,wz01(t1)Pa,xy01(t1)
Pb,wz11(t1)Pa,xy11(t1) Pb,wz01(t1) Wa,bxy,wz
Pc,uv10(t1)Pa,xy10(t1) Pb,wz10(t1)Pa,xy10(t1)
Pb,wz11(t1)Pa,xy11(t1) Pb,wz10(t1) Wa,bxy,wz
uv, xy, wz are tags, (00,01,10,11) uv xy and wz
here
22
Tagged probability waveform

• Glitch filtering scheme
• If pulse width less than gate inertial delay, it
  is subject to glitch filtering
• For time t1 for at time point t2, t2-t1ltd
  Pc,uv01(t1)- Pa,xy01(t1) Pb,wz10(t2)Wa,bxy,wz
  Pc,uv10(t2)- Pa,xy01(t1) Pb,wz10(t2)Wa,bxy,wz
• Limitations
• Rough filtering, Not exact description for pulse
• Cant filter glitch coming from one input

23
A new glitch filtering scheme

• Why important
• Glitch power can be a significant portion of
  total switching power
• Bad filtering scheme gave errors
• Basic idea look at the exact condition for a
  pulse
• P(c has transition at t1 and t2)P(a has 0-gt1 at
  t1, b has 1-gt0 at t2)
• Tagged waveform was correct ?

a
c
0
t1
b
t1
t2
t2
24
New glitch filtering scheme

• In probability waveform (spatial independence)
• P(c has 0-gt1 transition at t1 and 1-gt0 at t2)
• P(a,b) at t1 is (01,11) or (11,01) or (01,01)
  and (a,b) at t2 is (10,11) or (11,10) or (10,10)

P
P
0.1
0.1
0.2
0.2
0.5
0.5
P
0.2
0.1
0.2
0.1
0.07
0.16
0.5
a
t1
t2
t1
t2
0.07
0
0.16
c
b
t1
t2
P
P
0.1
0.1
0.2
0.2
0.5
0.5
0.2
0.1
0.2
0.1
t1
t2
t1
t2
25
New glitch filtering
a 01 11 01
b 11 01 01
a 10 11 10
b 11 10 10
and
t1
t2
a 01,10 01,11 01,10 11,10 11,11 11,10 01,10 01,11 01,10
b 11,11 11,10 11,10 01,11 01,10 01,10 01,11 01,10 01,10
t1,t2
Pc01,10(t1,t2) is a sum of 9 terms Example term
Pa01,10(t1,t2)Pb11,11(t1,t2) This sum
Pc01,10(t1,t2) is subtracted from Pc01(t1),
Pc10(t2) Similarly, Pc10,01(t1,t2) is subtracted
from Pc10(t1), Pc01(t2)
26
New glitch filtering

• Keep track of Pcij,kl(t1,t2) for every signal
  during the waveform propagation in the form of
  correlation coefficient
• wcij,kl(t1,t2) Pcij,kl(t1,t2)/Pcij(t1) Pckl(t2)
• After the filtering
• If t2-t1ltd
• Pc01,10(t1,t2) set to 0
• Pc01,11(t1,t2) set to Pc01(t1)
• Otherwise
• Pcij,kl(t1,t2) wcij,kl(t1,t2) Pcij(t1)
  Pckl(t2)
• Pcij(t1), Pckl(t2) are probability of
  transition at t1,t2 after filtering

27
New glitch filtering scheme

• In tagged probability waveform
• Consider spatial correlation
• Approximate spatial correlation with steady state
  signal transition correlations, Wabxy,wz

Pc,uv01,10(t1,t2) is a sum of sub-sum of 9
terms Each sub-sum is corresponding to a pair of
input waveform Example term in sub-sum
Pa,xy01,10(t1,t2)Pb,wz11,11(t1,t2)Wabxy,wz Pc,uv0
1,10(t1,t2) is subtracted from Pc,uv01(t1),
Pc,uv10(t2) if t2-t1ltd Similarly,
Pc,uv10,01(t1,t2) is subtracted from Pc,uv10(t1),
Pc,uv01(t2)
28
Preliminary experimental results

• Small circuit with tree structure
• No spatial correlations
• Randomly specified delay
• Input signal probability 0.5
• Results by probability waveform compared to logic
  simulation under random input vectors

29
Preliminary results tree circuit
Node time interval Logic Simulator Prob Wave new Errors Tag Tag Tag new Tag new
17 (2,2) 0.45701 0.4608 0.83 0.460576 0.78 0.460576 0.78
18 (4,4) 0.45991 0.4608 0.19 0.460277 0.08 0.460277 0.08
19 (2,2) 0.46043 0.4608 0.08 0.46039 0.01 0.46039 0.01
20 (5,5) 0.46193 0.4608 0.24 0.460373 0.34 0.460373 0.34
21 (2,2) 0.46222 0.4608 0.31 0.460688 0.33 0.460688 0.33
22 (6,6) 0.46184 0.4608 0.23 0.460396 0.31 0.460396 0.31
23 (2,2) 0.46104 0.4608 0.05 0.461046 0.00 0.461046 0.00
24 (3,3) 0.45848 0.4608 0.51 0.460052 0.34 0.460052 0.34
25 (3,5) 0.58581 0.589824 0.69 0.589791 0.68 0.589791 0.68
26 (5,8) 0.48563 0.483656 0.41 0.483775 0.38 0.483775 0.38
27 (4,8) 0.59225 0.589824 0.41 0.589889 0.40 0.589889 0.40
28 (4,5) 0.48332 0.483656 0.07 0.483814 0.10 0.483814 0.10
29 (4,9) 0.60493 0.605951 0.17 0.605226 0.05 0.605226 0.05
30 (7,11) 0.32617 0.324893 0.39 0.324305 0.57 0.324305 0.57
31 (7,12) 0.49869 0.481971 3.35 0.605226 21.36 0.481551 3.44
32 (8,12) 0.32617 0.324893 0.39 0.324305 0.57 0.324305 0.57
33 (10,15) 0.46703 0.457838 1.97 0.546224 16.96 0.456386 2.28
total 8.05286 8.0289 0.30 8.23635 2.28 8.02284 0.37
Standard Deviation Standard Deviation 0.84 6.31 0.89
Average 0.60 2.55 0.63
30
Preliminary results reconvergent fanout

• Small circuit with reconvergent fanout
• Introduce spatial correlations
• Randomly specified delay
• Input signal probability 0.5
• Results by probability waveform compared to logic
  simulation under random input vectors

31
Preliminary results reconvergent fanout
Node time interval Logic Simulator Prob Wave new Errors Tag Tag Tag new Tag new
25 (3,5) 0.58581 0.589824 0.69 0.589791 0.7 0.589791 0.7
26 (5,8) 0.48563 0.483656 0.41 0.483775 0.4 0.483775 0.4
27 (4,8) 0.59225 0.589824 0.41 0.589889 0.4 0.589889 0.4
28 (4,5) 0.48332 0.483656 0.07 0.483814 0.1 0.483814 0.1
29 (4,9) 0.60493 0.605951 0.17 0.605226 0.0 0.605226 0.0
30 (5,9) 0.49029 0.490675 0.08 0.49081 0.1 0.49081 0.1
31 (7,11) 0.32617 0.324893 0.39 0.324305 0.6 0.324305 0.6
32 (7,12) 0.49869 0.481971 3.35 0.605226 21.4 0.481551 3.4
33 (8,12) 0.32617 0.324893 0.39 0.324305 0.6 0.324305 0.6
34 (8,15) 0.29495 0.196084 33.52 0.284186 3.6 0.27001 8.5
35 (6,13) 0.47879 0.464104 3.07 0.451358 5.7 0.451358 5.7
36 (8,17) 0.47557 0.549163 15.47 0.535572 12.6 0.506832 6.6
Total (2,18) 9.32543 9.27109 0.58 9.45205 1.4 9.28546 0.4
Std Dev 7.96 5.37 2.50
Avg 3.02 2.42 1.46
32
Preliminary results benchmark circuits

• ISCAS 85 benchmark
• Input signal probability 0.5
• Logic simulation 40,000 random vectors
• Error statistics
• Large percentage error for low activity node
  exclude error for node activity less than 0.1
• Total energy estimated from transition density
  and load capacitance. CL is proportional to
  fanout of a gate

33
 Circuit Errors Prob wave new Tag Tag new
  Avg node error 8.16 6.10 5.32
c880 Std Dev 9.31 9.64 8.11
  Totoal energy 7.26 1.64 5.93
  Avg node error 15.16 22.99 4.65
c1355 Std Dev 15.95 25.71 6.47
  Totoal energy 18.33 32.85 5.43
  Avg node error 14.34 10.66 11.49
c1908 Std Dev 20.01 19.42 19.29
  Totoal energy 19.66 4.09 11.19
  Avg node error 15.22 12.65 11.98
c2670 Std Dev 16.42 15.98 14.15
  Totoal energy 15.03 7.24 9.93
  Avg node error 14.08 16.29 6.60
c3540 Std Dev 19.24 26.08 11.31
  Totoal energy 10.08 9.78 2.42
  Avg node error 13.06 8.14 7.72
c5315 Std Dev 14.87 10.26 10.62
  Totoal energy 17.24 2.29 10.07
  Avg node error 23.67 28.62 12.76
c6288 Std Dev 13.52 22.94 11.11
  Totoal energy 26.37 32.12 4.05
  Avg node error 17.62 12.40 11.42
c7552 Std Dev 25.76 20.25 18.61
  Totoal energy 16.39 3.17 7.78
34
Preliminary results benchmark circuits

• Observations
• Single probability waveform does not perform
  better than Tag new for benchmark circuits
• New glitch filtering improves node error std dev.
  error more even distributed
• New glitch filtering improves overall and node
  estimation accuracy in some cases
• In some other case, it tends to give worse total
  energy estimation
• Filtering is based on tagged probability waveform
  
• Waveform before filtering is underestimated, a
  correct amount of subtraction by filtering effect
  will lead to overall underestimated value
• Tag tends to underestimate the amount of
  subtraction by filtering effect
• Estimation speed
• Prob new 1030 times speed up comparing to
  logic simulation
• Tag 200 times speed up
• Tag new 15 speed up

35
Future work

• Improve the estimation accuracy by improving the
  estimation of waveform before filtering
• Need to consider more on spatial correlations
• Take care of special case that spatial
  correlation between two signal is poorly
  approximated by steady state transition
  correlation
• Improving the estimation speed
• The new method of glitch filtering take too much
  time because of its propagation of
  Pcij,kl(t1,t2)
• Only 15 times speed up than logic simulation
• Software optimization has to be done

36
Summary

• Introductions to different Levels of power
  estimation
• Gate-level Probabilistic Approach
• Signal Probability
• Transition probability
• Transition density
• Probability waveform
• A new glitch filtering method
• Based on Probability waveform
• A more accurate glitch filtering
• Preliminary experimental results shows the
  potential of the new method
• Problems are to be tackled
• Questions ?

37
Thank You !

• For questions and comments, please contact me at
  hufei01_at_auburn.edu