Studies of Timing Structural Studies of Timing Structural Properties for Early Evaluation of Properties for Early Evaluation of Circuit Design Circuit Design Andrew B. Kahng*, Ryan Kastner, Andrew B. Kahng*, Ryan Kastner, Stefanus Mantik, Majid Sarrafzadeh Stefanus Mantik, Majid Sarrafzadeh and Xiaojian Yang and Xiaojian Yang UCLA CS Dept., Los Angeles, CA, USA UCLA CS Dept., Los Angeles, CA, USA *UCSD CSE and ECE Depts., La Jolla, *UCSD CSE and ECE Depts., La Jolla, CA, USA CA, USA
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Studies of Timing Structural Properties for Studies of Timing Structural Properties for Early Evaluation of Circuit DesignEarly Evaluation of Circuit Design
Andrew B. Kahng*, Ryan Kastner,Andrew B. Kahng*, Ryan Kastner,
UCLA CS Dept., Los Angeles, CA, USAUCLA CS Dept., Los Angeles, CA, USA
*UCSD CSE and ECE Depts., La Jolla, CA, USA*UCSD CSE and ECE Depts., La Jolla, CA, USA
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AbstractAbstract
The Rent parameter has been widely used to characterize interconnect complexity of designs. The Rent power-law relationship is often used for a priori wire estimation, which is an enabling component of timing closure methodologies. However, the Rent parameter does not explicitly address timing information. In this work, we propose studies of circuit timing structure that can potentially help identify useful characterizations of the timing behavior of the design. We believe that such characterizations can allow us early identification of designs for which timing closure will prove difficult. One characterization of the timing structure is analogous to the Rent parameter: we propose a temporal Rent characterization based on the analysis of the number of active signals intersecting a specified timing boundary within the clock period.
Motivation:Motivation:Early “a priori” Early “a priori” timing timing prediction à la Rent’s Ruleprediction à la Rent’s Rule
A step towards timing closure through identification of critical A step towards timing closure through identification of critical temporal areas of a designtemporal areas of a design
Innovations:Innovations:Active IntervalActive Interval of a timing edge of a timing edge
Timing Structure Analysis Timing Structure Analysis for crosstalk, peak power and other for crosstalk, peak power and other timing propertiestiming properties
Temporal Analysis of Temporal Analysis of Special TopologiesSpecial Topologies
Traditional Timing ParametersTraditional Timing Parameters
RAT: RAT: AATAAT::
New Timing Parameter: Active IntervalNew Timing Parameter: Active Interval
Edge Edge eeijij is is activeactive at time at time tt iff start iff startijij tt end endijij, where, where
ijiEeij daataatij
:maxijjEeji dratratij
:min
kikEekij dtstartki
:min
kjkEekij dtendkj
:max
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Active Interval Distribution GraphActive Interval Distribution Graph
x-axis: size of the active interval; y-x-axis: size of the active interval; y-axis: the number of edges with active axis: the number of edges with active interval less than or equal to xinterval less than or equal to x
A large initial slope corresponds to a A large initial slope corresponds to a large number of nets with small large number of nets with small active intervalsactive intervals small active duration for nets small active duration for nets
less chance for crosstalkless chance for crosstalk
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x-axis: clock cycle offset from zero; x-axis: clock cycle offset from zero; y-axis: the number of edges that are y-axis: the number of edges that are currently active at time xcurrently active at time x
A “flatter” plot corresponds to a A “flatter” plot corresponds to a more well-distributed signal activitymore well-distributed signal activity long tail long tail critical paths critical paths
{For single-source Rentian circuit: For a symmetrical Rentian circuit
with two latches at opposite ends of the netlist
A rentian circuit example: A=3, p=0.5
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ConclusionsConclusions
Pessimist model of active interval Pessimist model of active interval (worst case, overestimate)(worst case, overestimate)
Studies of circuit timing structure that help identify useful Studies of circuit timing structure that help identify useful
characterizations of the timing behavior of the designcharacterizations of the timing behavior of the designsize of active intervals: possibility of having crosstalk problemssize of active intervals: possibility of having crosstalk problems
nets activity: distribution of slacks among timing pathsnets activity: distribution of slacks among timing paths
On going worksOn going works translate the analyses into estimators for optimizationtranslate the analyses into estimators for optimization
Studies of Timing Structural Properties for Studies of Timing Structural Properties for Early Evaluation of Circuit DesignEarly Evaluation of Circuit Design
Andrew B. Kahng*, Ryan Kastner,Andrew B. Kahng*, Ryan Kastner,
used for used for a prioria priori estimation of wirelength and congestion estimation of wirelength and congestion
lack of timing informationlack of timing information
Temporal Rent’s RuleTemporal Rent’s Ruleadd timing domain to traditional Rent’s ruleadd timing domain to traditional Rent’s rule
used for used for a prioria priori estimation of timing related behavior, e.g., estimation of timing related behavior, e.g., crosstalks, slacks, cycle time, etc.crosstalks, slacks, cycle time, etc.
need to find (power) lawsneed to find (power) laws
