1 UCSD VLSI CAD Laboratory ISQED-2009 Revisiting the Linear Programming Framework for Leakage Power vs. Performance Optimization Kwangok Jeong, Andrew B. Kahng, Hailong Yao University of California, San Diego

Outline Background Main Contributions LP-Problem Formulation Experimental Results Conclusion 2 UCSD VLSI CAD Laboratory ISQED-2009

3 Background Sizing problem –Knobs to optimize power, timing and area Vdd, Vth, L gate, W gate, etc. –Find optimal sizing for tradeoff of power, timing and area Basic idea of leakage optimization –High speed (high leakage) gates  critical paths –Low speed (low leakage) gates  non-critical paths Previous works on leakage optimization –Iterative optimization  local optimum –Simplified timing model  timing violations

Contributions Key difference from previous work –Detailed delay modeling with signoff timing analysis –on per-timing-arc / per-instance –to capture local delay sensitivity accurately –High-speed and high-quality linear programming (LP) Key applications of LP-framework  Leakage power minimization under timing constraints  Simultaneous timing legalization with leakage minimization 4 UCSD VLSI CAD Laboratory ISQED-2009

5 Cell Delay Model SPICE simulations –65GP technology –All timing arcs –Rise and fall –7 input slew x 7 load –More than 50 cell masters –Gate length from 50nm to 75nm  Cell delay is approximately linear in gate length Delay vs. gate length (A1 to Y in 2-input AND) d: cell delay L g : gate length ,  : calibrated coefficients for each timing entry

Circuit Delay Model Directed acyclic graph (DAG) representation –Cell  vertex –Wire  edge –Super source S and super sink T 6 UCSD VLSI CAD Laboratory ISQED-2009 Delay variables d v u : cell delay w u,v : wire delay a v : arrival time to node v Delay constraint Flip-flop A Flip-flop B Q u v D S CK T

7 UCSD VLSI CAD Laboratory ISQED-2009 LP for Leakage Power Optimization Objective: −Maximize weighted sum of gate lengths (  Minimize leakage power) without degrading circuit performance D: max. delay minL v : min. gate length maxL v : max. gate length v :  Power /  Delay

8 UCSD VLSI CAD Laboratory ISQED-2009 LP for Timing Legalization Objective: −Given a design with timing violations, −Improve the worst negative slacks of the design with minimum leakage increase D: min. delay bound  : scaling parameter minL v : min. gate length maxL v : max. gate length v :  Power /  Delay

9 UCSD VLSI CAD Laboratory ISQED-2009 Timing and Leakage Optimization Flow Cell libraries Coefficients calibration LP-Solver Netlist + Parasitic + Timing const. Slew / Load / DelayTiming Graph LP-Generator Cell Swapping New Netlist Timing / leakage analysis Timing and leakage report

10 UCSD VLSI CAD Laboratory ISQED-2009 Experimental Setup Test case: 65nm technology Library preparation –65GP from TSMC (L gate = 60nm) –Multi-L gate libraries: 50nm, 60nm, 70nm –L gate biasing: 55nm, 56nm, …, 65nm –Naming convention: e.g., L60  L gate 60nm Delay and leakage evaluation –RC extraction:Synopsys STAR-RCXT (v ) –Delay: Synopsys PrimeTime (v ) –Leakage power: Cadence SOC Encounter (v5.2) Comparison –Synopsys Astro (v SP5) / Cadence SOC Encounter (v5.2)

11 UCSD VLSI CAD Laboratory ISQED-2009 Leakage Optimization with L gate -Biasing Inputs –Initial design with L60 –L gate biased libraries: from L55 to L65 Outputs –Meet timing –Better leakage –8X  16X faster runtime than SOCE SOCE AstroLP SOCEAstroLP SOCE AstroLP

12 UCSD VLSI CAD Laboratory ISQED-2009 Leakage Optimization with Multi-L gate Inputs: –Initial design with L60 –Multi-L gate libraries: L50, L60 and L70 Outputs –Meet timing –Better leakage –5X  14X faster than SOCE SOCE AstroLP SOCEAstroLP SOCE AstroLP

13 UCSD VLSI CAD Laboratory ISQED-2009 Timing Legalization with L gate Biasing Inputs –Initial design with L60 –SOCE leakage optimization  worsen timing slack –L gate biased libraries: from L55 to L65 Outputs –Turn timing slacks back or even better –Still obtains smaller leakage power than original

14 UCSD VLSI CAD Laboratory ISQED-2009 Timing Legalization with Multi-L gate Inputs –Initial design with L60 –SOCE leakage optimization  worsen timing slack –Multi-L gate libraries: L50, L60 and L70 Outputs –Turn timing slacks back or even better –Still obtains smaller leakage power than original

15 UCSD VLSI CAD Laboratory ISQED-2009 Conclusion and Ongoing Work We revisited and implemented LP-based frameworks –Leakage power minimization and timing legalization Compared with commercial tools, our work shows –Always meet timing –Better leakage power –~10X faster runtime Our methods enable very fast, high-quality power-delay tradeoff estimation and optimization Ongoing work –Larger industrial testcases –Multi-V th, multi-L gate and L gate -biasing –Timing margin and don't-touch methodologies, –Hold time –Multi-mode/multi-corner analysis –dynamic/total power constraints

THANK YOU 16 UCSD VLSI CAD Laboratory ISQED-2009