Trade-off Analysis between Timing Error Rate and Power Dissipation - PowerPoint PPT Presentation

Trade-off Analysis between Timing Error Rate and Power Dissipation for Adaptive Speed Control with Timing Error Prediction Hiroshi Fuketa * † , Masanori Hashimoto * † , Yukio Mitsuyama * † , and Takao Onoye * † *Dept. Information Systems Engineering, *Osaka University † JST, CREST

Table of Contents � Background � Systematic evaluation of power dissipation and timing error rate � Experimental results � Conclusion

Table of Contents � Background � Systematic evaluation of power dissipation and timing error rate � Experimental results � Conclusion

Background � Circuit speed is becoming more sensitive to: � manufacturing variability � operating environment (supply voltage, temperature, etc) � aging (NBTI, HCI, etc) Timing margin of a chip varies chip by chip. � “Worst case design” is inefficient for large variation. � Run-time adaptive speed control is promising. Target Speed Speed up Slow down Chip A Chip B Chip C Speed

Adaptive speed control � Adaptive speed control with timing error prediction � Canary FF [1] Timing error occurs at canary FF due to delay buffer before main FF captures a wrong value. Comparator During a monitoring period, Delay buffer warning signal is: detected speed up not detected slow down Canary FF Speed control unit Warning signal [1] T.Sato, et al., “A Simple Flip-Flop Circuit for Typical-Case Designs for DFM,” in Proc. ISQED , 2007

Problem of adaptive speed control � A timing error can not be completely eliminated � If path activation probability is extremely low, a warning signal may not occur during the monitoring period. � Circuit is slowed down excessively Timing errors could occur before a warning signal emerges. � When the occurrence of timing errors is extremely rare, some systems could accept the errors. � Need to estimate the occurrence of timing errors systematically and quantitatively

Timing error rate and power dissipation � How to improve timing error rate? ex) 32b Ripple carry adder � Insert larger buffer delay FA � Timing margin of canary FF is much severer than main FF FA speeded up more than required increase in power dissipation � Change inserted location FA � Lengthen the monitoring periods Path activation probability trade-off relations between 32 ⎛ ⎞ 1 1 timing error rate and power ⎜ ⎟ ≈ ⎝ ⎠ 9 2 10 * FA = Full Adder

Contributions � Propose a framework that systematically evaluates power dissipation and occurrence of timing errors. � Explore the design space of the adaptive speed control with canary FF � Examine the relationship between the timing error rate and the power dissipation

Table of Contents � Background � Systematic evaluation of power dissipation and timing error rate � Experimental results � Conclusion

Assumed system � Only one canary FF is inserted. � Circuit speed is controlled digitally. (“speed level”) Goal Goal � Reveal the relationship between power dissipation and timing error rate of this system � Find the optimum design parameters satisfying the required power dissipation and timing error rate � Where should canary FF be inserted? � How large should buffer delay be set? Canary FF � How long should monitoring period be set? Focus on a path activation probability

Path activation probability Probability that at least one of paths terminating at ( ) P i t t i the th FF whose delays are larger than is activated. Probability that at least one path in a circuit whose ( ) P t t all delay is larger than is activated. � Path activation probability depends on: � circuit structure � speed level � operating condition (ex. temperature) ( ) P i t , l , X Functions of speed level and condition : l X ( ) P t , l , X all

Framework overview - Path activation probability at each speed level given parameter and operation condition P P P , , - Power dissipation at each speed level i all ow and operation condition warning probability P w P error probability Design parameters err - Inserted location of canary FF transition probability P - Delay time of the delay buffer d - Monitoring period π state probability - Expected power dissipation of the system expected power P ow, avg timing error rate - Timing error rate of the system N err

Warning and error probability ( ) � Let be the occurrence probability P w , l X given parameter of a warning signal at speed level and l P P P , , condition in a cycle X i all ow i � Canary FF is inserted at the th FF warning probability P is the buffer delay in the canary FF w D � d P error probability err is the clock cycle T � c ( ) ( ) ( ) P l , X P T D , l , X P T , l , X = − − transition probability P w c d c i i d π ( ) state probability � Let be the occurrence probability P err , l X of a timing error at speed level and l X condition in a cycle expected power P ow, avg timing error rate N ( ) ( ) P l , X = P T , l , X err err all c

Speed level transition � Speed level : How fast or slow the circuit is controlled � Higher speed level means the circuit is controlled faster. � Once a warning signal is detected during the monitoring period, speed level is incremented by 1. No warnings No warnings speed level speed level speed level 1 0 -1 Warning Warning � Speed level transition satisfies Markov property. � The next speed level is determined by the present speed level and by the detection of the warning signal.

Speed level transition probability � Probability that speed level transits given parameter ( ) � Let be the probability that at P d , l X P P P , , i all ow least one warning signal is detected during the monitoring period at N mon warning probability P w speed level and condition : l X P error probability err N ( ) ( ( ) ) P l , X 1 1 P l , X = − − mon d w transition probability P d P : warning probability w π state probability Probability that warning is not detected in a cycle expected power P ow, avg timing error rate N err

Transition Matrix � Transition matrix of the Markov chain: P No warnings No warnings ( ) ( ) 1 1 1 0 − P − P d d speed level speed level speed level 1 0 -1 ( ) ( ) P 0 P − 1 d d Warning Warning L ( ) ( ) 0 0 0 0 P l 1 P l − d max d max ( ) ( ) M 1 − P l max − 1 P l max − 1 0 P = d d O M ( ) ( ) P l min + 1 1 − P l min + 1 0 d d ( ) ( ) 0 0 0 L 0 P l 1 P l − d min d min * and are maximum and minimum speed level l l max min

State probability ( ) � Let be a state probability vector in π n given parameter n-th time step P P P , , i all ow ( ) ( ) P π n + 1 = π n ⋅ P : transition matrix warning probability P w P error probability ( ) err π X � Let be a steady state probability of l being at speed level when condition l X transition probability P d ( ) = π n → ∞ π state probability ( ) ( ) ( ) L π X π X π X l l − 1 l max max min expected power P ow, avg timing error rate N err * and are maximum and minimum speed level l l max min

Average cycle of a single stay ( ) X π � State probability is not suitable to evaluate l the power dissipation and the timing error rate. ( ) π X is not directly related to actual time. � l � Speed level is changed immediately once a warning signal is observed. � Periods (# cycles) of being at a certain speed level are not always the same. � Need “Time”-based state probability ( ) : the average cycle of a single stay at speed level l N rem l � ( ) ( ) ( ) N − 1 ( ) N L N l = 1 ⋅ P + 2 ⋅ 1 − P P + + N 1 − P P + N 1 − P mon mon rem w w w mon w w mon w P : warning probability w

Conversion to time based state probability State Probability l l l l l l l l l − 1 − 1 − 1 min max max max max max max min min π π π l l l min max − 1 max Time Based Probability ( ) ( ) ( ) N rem l N rem l N rem l max − 1 min Time based max Probability l l l l l l − 1 − 1 max max max max min min P time l ( ) = π π π ( ) l l l N l ⋅ π min max max − 1 rem l ∑ ( ) N j ⋅ π rem j l l l − 1 j max max min P time l ( max ) P ( max l 1 ) P time l ( min ) − time