Uncertainty-aware circuit tuning.

Uncertainty-Aware Circuit Optimization
Xiaoliang Bai
University of California at San Diego
La Jolla, CA 92037
Chandu Visweswariah
IBM Thomas J. Watson Research Center
Yorktown Heights, NY 10598
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Philip N. Strenski
IBM Thomas J. Watson Research Center
Yorktown Heights, NY 10598
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David J. Hathaway
IBM Microelectronics
Essex Junction, VT 05452
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ABSTRACT
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1.
INTRODUCTION AND MOTIVATION
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39th Design Automation Conference New Orleans, Louisiana. June 10-14,
2002.
Copyright 2002 ACM ??? ... — 5.00.
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2.
UNCERTAINTY-AWARE TUNING
2.1 Background
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2.2 Penalty function
¸ ›¡—”˜*¦˜*œŸ³Ÿ” ?XššYtŸ”®4™ZŸ”X›œ¹²4¤s˜!¡—”›¡^›šY˜!™§U§žŸ”ž›œ$›¯™¡^˜*œ4™¥tŸg¬
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2.3 Choice of penalty function
¸ ?˜—”˜™—”˜:šY˜*¦˜—I™¥—”˜+¶®Ut—”˜*¢˜œCŸ”šu›œ7Ÿ” U˜ ¡^˜*œ4™¥tŸg¬¯®Uœ?©Ÿ”ž›œ¹·ÃðÝt—”šjŸ+²
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4. RESULTS
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ß O2KjFL? ßzà
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ÚÛpäQÛ
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MP`dC²BxD!O?{åæ ×Iç åtuPè4YdâRwBRGH}BcWFPGIF:?QBC8haI`d?!aOJFbGdO)GIC@GIFPBR?pO)a4D!@8h
E@]2BRD!@OGaBMQ€BW)F äRépê’ç’×ä\ëpÛ t ì&Yv&Yèxwl Ž XdF3ad?!O)UdCFPE¸@SJpi*OR?h
E^`dCSBRD!F2HBRJb@G1•ux—:Y@GIMPC`IHd@GIW#BR??!@ABC7D!@EFcad?!`dGI@GIWt8uxv2wl Ž XIF
HdFLC²BPZ4JpBGIH#JCFLKpJ{Oi7@GHd@A&@SHd`IBCCO)W)@M[UdCSOTMQ€&JpBR?!F|MLO)EaI`4D!F2H}U&Z
?!`IGdGI@GIW#B}D!@SEF:hgH4O)E}BR@SGJ@EV`ICSBRD!@O)G`IGIHdFL?sD!XIFcMPOxA\FL?!JPíW?QBHd@8h
FPGTD!JjKp@8D!X ?!FPJaFPM:DoD!O^D?QBGdJ@SJD!OR?pKp@²H&D!XIJPYd@GIaI`4DoJCFLKpJsBGH#O)`4Dh
aI`4DCO\BHdJzBR?!FjOUdDQB@GdF2HVUTZ3D!XIF>B)HRfgO)@GTD’EFLD!XIO&Hl Ž XIFz?!FPJ`IC8D!@GIW
O)a4D!@E@S]PBRD!@O)G©a4?!O)UdCSFLEJ[M2BG©UFA)FL?ZC²Bx?!W)F#BGIHD!XdFr?!FPJ`IC8D!@GIW
?!`IG‘D!@SEF#±T`I@8D!FCO)GdWdlî{FPMPFPGTD!C8ZTYnB/MP@8?!MP`d@8D^Kp@8D!XšïTìTY ¨¨)¨D?QBG4h
J@JD!O?!JcKoBJcD!`IGdF2Hl Ž XIF}O)a4D!@SE@]2BxD!@O)Gšad?!OUICFPEðXBH%uPï)¨4Y ¨)¨¨
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@GIWBCWO?!@8D!XIEòD!OCSFPBxA)F#D!XdF#a4?!@E}BR?Z©O`dD!ad`dD!J3`IGdad?!`IGdF2H©BRGH
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MP@C@8DgZrORi äépê’ç’×ä)ë{Û t ì2wKoBRJ>FL~4adCSO@8D!F2H^D!O[FL~4ad?!FPJJnD!XIFoaFLGBC8D‰Z
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MPOGIJD?QB@GTD!J}KjFL?!F`dJF2H¥BJ}JFPaIBR?QBxD!@SOG´A)Bx?!@SBUICFPJ}D!O.ikO?!EõD!XIF
aFPGIBC8DgZVi*`IGdMLD!@O)GY4BW\BR@GFL~4a4?!FPJJF2H}BJ>B3WR?!O)`da}ik`IGdMLD!@O)Glzö @G4h
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@8DgZ3MPOGIJD?QBR@SGTD!J’BGIH3D!XdF>JCSBMQ€3A)Bx?!@SBUICFPJ’BRGH[D!XIFP@8?nUO)`dGH4J7KjFL?!F
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BPKoBx?!FrD!`IGI@GdW@J[MPOEaBR?!FPH@G‘D!XdFVi*BMPFORijABR?!@SBRD!@O)GdJPl Ž Xd@?QHY
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4.1 Slack histograms
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BR?!F#JXIO2KpG™@G Š @SW4lzµ&l Ž XIF#JCSBMQ€šXI@JD!O)WR?QBEJ^@GšD!XI@JVJFPMLD!@O)G
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4.2 Degradation due to variations
140
120
# s ig nals
100
80
P re-tuning
60
Normal-tuning
S igma=5
S igma=10
40
S igma=20
20
0
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-40
-20
0
20
40
60
80
100
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120
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100
80
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40
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0
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-40
-20
0
20
40
60
80
100
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6. CONCLUSIONS AND FUTURE WORK
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7.
ACKNOWLEDGMENTS
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8.Z [,\5] REFERENCES
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