Approximate property checking of mixed-signal circuits Parijat - PowerPoint PPT Presentation

Approximate property checking of mixed-signal circuits Parijat Mukherjee, Texas A&M University Chirayu Amin, Intel Corporation Peng Li, Texas A&M University TAU 2014 Thursday, March 6 th 2014

Outline • Mixed-signal design • Property checking • Why approximate? • Interpreting “failure probability” • Approximate property checking • Implementation details • Conclusion : Challenges and future work Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 2

Mixed-signal design • Significant analog components – Inherently complex : Continuous variables – Extremely large state space – Simulation computationally expensive • Why talk of it now? – Circuit complexity – Process variability INCREASING ! – Frequency band of interest – Effect of Jitter / Noise etc Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 3

Does a circuit “always” perform its intended function? Violations are observed here May not always capture the intended function (specification) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 4

Does a circuit “always” perform its intended function? Violations are observed here May not always capture the intended function (specification) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 5

Detection and Diagnosis • Outputs PVT Circuit – Probability of failure – Debug information Input Output • Counterexamples Specs Specs • Important parameters Property • Failure patterns checking Does circuit meet Why doesn’t it meet specifications over its entire target specifications? range of operation? Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 6

Statistical property checking • What is the statistical quantity varied? – Any parameter that can change circuit behavior • What is the statistical quantity checked? – Output signals vs. specifications Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 7

Addressing circuit complexity Can be simulated Cannot be simulated via SPICE via SPICE Failure Probability Circuit level System level techniques techniques Hierarchical decomposition via models Circuit Size Warning : Figure may not be drawn to scale Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 8

Addressing circuit complexity Can be simulated Cannot be simulated via SPICE via SPICE Failure Probability Circuit level System level techniques techniques Hierarchical decomposition via models Circuit Size Warning : Figure may not be drawn to scale Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 9

Existing work - Detection Standard Failure Probability Monte Carlo System level techniques Yield Estimation Circuit Size Warning : Figure may not be drawn to scale Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 10

Existing work - Detection M. H. Kalos and P. A. Whitlock, “Monte carlo methods”, Wiley -VCH, 2008. R. Kanj, R. Joshi, and S. Nassif , “Mixture Standard importance sampling and its application Failure Probability to the analysis of sram designs in the Monte Carlo System level presence of rare failure events” DAC ’06 techniques S. Sun, Y. Feng, C. Dong, and X. Li, “Efficient sram failure rate prediction via gibbs sampling,” TCAD ’12 Yield Proposed P. Mukherjee, C. Amin and P. Li, Estimation "Approximate property checking of mixed-signal circuits", DAC 2014 Circuit Size Warning : Figure may not be drawn to scale Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 11

Outline • Mixed-signal design • Property checking • Why approximate? • Interpreting “failure probability” • Approximate property checking • Implementation details • Conclusion : Challenges and future work Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 12

An example Unknown Circuit Uniform Input Parameter Time domain property distribution Gaussian Process Parameter Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 13

Parameter and property spaces Parameter space Property space There exists a mapping between Parameters and Properties ! Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 14

Parameter and property spaces Parameter space Property space 𝑄 𝐺 𝑍1 = 0 𝑄 𝐺 𝑍1 = 1 Failure can be observed directly in the property space ! Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 15

Parameter and property spaces Parameter space Property space 𝑄 𝐺 𝑌1 ∈ 𝑠𝑓𝑒, 𝑌2 ∈ 𝑠𝑓𝑒 = 1 𝑄 𝐺 𝑍1 = 0 𝑄 𝐺 𝑍1 = 1 Interactions between parameters give rise to failures ! Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 16

The real picture Parameter space Property space Property 1 Property 2 Multiple violations over multiple parameter combinations Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 17

Failure probability estimation Statistical framework Approximate failure probability Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 18

Requirements • A statistical framework that : – Requires low number of SPICE simulations – Can bound the failure probability uncertainty – Can deal with varying input distributions – Does not need to assume an output distribution – Does not assume an input-output relationship – Can exit early with an approximate bounded estimate • By assuming that : – Failure regions are more or less contiguous (Few probable failure regions vs. many unlikely ones) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 19

What is Failure probability? P (Y1) vs Y1 𝐵𝑠𝑓𝑏 𝑠𝑓𝑒 𝑄 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 = 𝐵𝑠𝑓𝑏 𝑠𝑓𝑒 + 𝐵𝑠𝑓𝑏 𝑕𝑠𝑓𝑓𝑜 Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 20

Where does uncertainty arise? Part 1 P (Y1) vs Y1 Have we followed the output distribution exactly? Have the relative areas been estimated correctly? Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 21

Adaptive sampling Few Strategic Samples Failure SPICE is Expensive ! (Arbitrary distribution) Estimate Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 22

Model driven sampling Few Strategic Samples SPICE is Expensive ! (Arbitrary distribution) TRAINING SET TRAINING SET Extensive Resampling Failure Inexpensive ! (Parameter distribution) Estimate Accuracy ∝ How well model has captured failure boundaries Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 23

Where does uncertainty arise? Part 2 P (Y1) vs Y1 Have we covered all the failure regions? Do we have at least one sample in the “likely” regions? Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 24

The N initial samples Target parameter space Initial samples Following parameter distribution can cause redundant effort Warning : Artificial test case designed to excite complex interactions Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 25

The N initial samples Target parameter space Initial samples Spread out samples using prior information (only if it exists) Warning : Artificial test case designed to excite complex interactions Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 26

Where does uncertainty arise? Part 3 P ( misclassification(Y1) ) vs Y1 How accurate are our boundaries? Are inaccurate boundaries for unlikely events really a problem? Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 27

Reducing uncertainty P ( misclassification(Y1) ) vs Y1 Observation: Highest uncertainty around failure boundaries ( Warning : Chosen model may introduce additional spurs ) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 28

Reducing uncertainty P ( misclassification(Y1) ) vs Y1 Can be reduced by Active learning !!! ( Run SPICE simulations for low confidence regions ) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 29

Adaptive Sampling Target parameter space Training samples Model accuracy ∝ How well failure boundaries have been captured ( Discussed previously ) Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 30

Adaptive Sampling Target parameter space Training samples Model accuracy ∝ How well failure boundaries have been captured Adaptive sampling produces new samples close to boundary Approximate property checking of mixed-signal circuits - Parijat Mukherjee, TAU '14 31