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

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. Outline. Introduction Different Levels of power estimation Gate-level Probabilistic Approach

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

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  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 Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  4. Simulation based Approach • Transistor Level Simulation • Circuit level • SPICE • Solving a large matrix of node current using the Krichoff’s 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 Fei Hu, ELEC6970 Fall 2004

  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, P=1/2CV2factive • 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 Fei Hu, ELEC6970 Fall 2004

  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. Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  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: c=a, Ps(c)=1-Ps(a) • AND: c=ab, Ps(c)=Ps(a)Ps(b) • OR: c=a+b, Ps(c)=1-[1-Ps(a)][(1-Ps(b)] Fei Hu, ELEC6970 Fall 2004

  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 132–138, 1989. • Ps(x1,x2)=Ps(x1)Ps(x2)Wx1,x2 • Approximate higher order correlation with pairwise correlations Ps(a)=0.5 Ps(c)=0.5x0.5=0.25 ? Ps(c)=0 Ps(b)=0.5 Fei Hu, ELEC6970 Fall 2004

  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 y=x1x2+x3 • Ps(y)=Ps(x1)Ps(fx1)+Ps(x1)Ps(fx1) • Traversal from bottom to top to derive signal probability x1 1 0 x2 0 1 x3 1 0 0 1 Fei Hu, ELEC6970 Fall 2004

  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)] Fei Hu, ELEC6970 Fall 2004

  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 294–299, 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->j ,ym->n)/P(xi->j)P(ym->n)i,j,m,n  {0,1} • Propagate transition probability from PI • OBDD based procedure • Global or local OBDD Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  15. Transition density • Example, c=ab • 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)=0.5*D(a)+0.5*D(b) =0.5*0.5+0.5*0.5 =0.5 Ps(a)=0.5 D(a)=Pt(a)=2*0.5*0.5 =0.5 d d Ps(b)=0.5 D(b)=Pt(b)=2*0.5*0.5 =0.5 Fei Hu, ELEC6970 Fall 2004

  16. Transition density Fei Hu, ELEC6970 Fall 2004

  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 204–207, 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 Fei Hu, ELEC6970 Fall 2004

  18. Probability waveform Pc01(t1)=Pa01(t1) Pb01(t1)+ Pa01(t1) Pb11(t1)+ Pa11(t1) Pb01(t1) =0.1*0.1+0.1*0.3+0.3*0.1 =0.07 • Example, c=ab 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) =0.2*0.2+0.2*0.3+0.3*0.2 =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) Fei Hu, ELEC6970 Fall 2004

  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,wz=Pa,bxy,wz /Paxy Pbwz • Transition correlation can be obtained from zero delay logic simulation • Bit-parallel simulation • Glitch filtering effect considered Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  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-t1<d Pc,uv01(t1)-= Pa,xy01(t1) Pb,wz10(t2)Wa,bxy,wzPc,uv10(t2)-= Pa,xy01(t1) Pb,wz10(t2)Wa,bxy,wz • Limitations • Rough filtering, Not exact description for pulse • Can’t filter glitch coming from one input Fei Hu, ELEC6970 Fall 2004

  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->1 at t1, b has 1->0 at t2) • Tagged waveform was correct ? a c t1 0 b t1 t2 t2 Fei Hu, ELEC6970 Fall 2004

  24. New glitch filtering scheme • In probability waveform (spatial independence) • P(c has 0->1 transition at t1 and 1->0 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 0.2 0.1 0.1 0.07 0.16 0.5 a t1 t1 t2 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 0.2 0.1 0.1 t1 t1 t2 t2 Fei Hu, ELEC6970 Fall 2004

  25. New glitch filtering and t1 t2 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) Fei Hu, ELEC6970 Fall 2004

  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-t1<d • Pc01,10(t1,t2) set to 0 • Pc01,11(t1,t2) set to Pc01(t1) • … • Otherwise • Pcij,kl(t1,t2) = wcij,kl(t1,t2)* P’cij(t1) P’ckl(t2) • P’cij(t1), P’ckl(t2) are probability of transition at t1,t2 after filtering Fei Hu, ELEC6970 Fall 2004

  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,uv01,10(t1,t2) is subtracted from Pc,uv01(t1), Pc,uv10(t2) if t2-t1<d • Similarly, Pc,uv10,01(t1,t2) is subtracted from Pc,uv10(t1), Pc,uv01(t2) Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  29. Preliminary results – tree circuit Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  31. Preliminary results – reconvergent fanout Fei Hu, ELEC6970 Fall 2004

  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 Fei Hu, ELEC6970 Fall 2004

  33. Fei Hu, ELEC6970 Fall 2004

  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” – 10~30 times speed up comparing to logic simulation • “Tag” – 200 times speed up • “Tag + new” – 1~5 speed up Fei Hu, ELEC6970 Fall 2004

  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 it’s propagation of Pcij,kl(t1,t2) • Only 1~5 times speed up than logic simulation • Software optimization has to be done Fei Hu, ELEC6970 Fall 2004

  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 ? Fei Hu, ELEC6970 Fall 2004

  37. Thank You ! For questions and comments, please contact me at hufei01@auburn.edu Fei Hu, ELEC6970 Fall 2004

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