Post-Floorplanning Power/Ground Ring Synthesis for Multiple-Supply-Voltage Designs International Symposium on Physical Design March 30, 2009 Wan-Ping Lee Diana Marculescu Yao-Wen Chang
Outline • Introduction • Problem Formulation • Algorithm • Experiment Results • Conclusion 2
Voltage Island & Power Ring • Multiple-supply voltage (MSV) design – Power rings enclose the voltage islands – Each voltage island has its individual power ring • MSV complicates the power-ring synthesis power ring voltage islands power rings traditional design MSV design 3
Outline • Introduction • Problem Formulation • Algorithm • Experiment Results • Conclusion 4
Problem Formulation • Inputs: – An MSV floorplan • Objective: – Identify the voltage islands – Find the power ring of each voltage island – Minimize the number of corners in the power rings 5
IR Drop and Corners in Power Rings • The fewer corners in power rings, the less IR drop in power rings # of corners = 4 # of corners = 8 IR drop = 4.49 e-02 IR drop =11.94 e-02 6
Outline • Introduction • Problem Formulation • Algorithm – Voltage-Island Identification – Voltage-Island Boundary Search – Power-Ring Corner Patching • Experiment Results • Conclusion 7
Voltage-Island Identification • A voltage island consists of several circuit blocks – Operate at the same supply voltage – Are adjacent to at least one circuit block in the island • Check the adjacencies block by block b 1 five voltage islands b 2 b 3 8
Outline • Introduction • Problem Formulation • Algorithm – Voltage-Island Identification – Voltage-Island Boundary Search – Power-Ring Corner Patching • Experiment Results • Conclusion 9
Straightforward Approaches, but …… • Straightforward, but incorrect approaches – Edge-overlap approach • If the edges overlap no other edges, they are assumed to be the contour edges • Cannot distinguish these lightly shaded segments – Line-sweeping approach • Determine if an edge is a contour segment when the scanning line sweeps the edge • Hardly indicates which parts are outer boundaries non-outer boundary segment w outer boundary segment 10
Properties of Contour Sequence • Counterclockwise trace vertical and horizontal contour segments – From the segment with the smallest x and y coordinates y 4 x 1 x 5 y 5 y 3 increasing x 4 y 2 x 2 x 3 y 1 decreasing * =<x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 1 > * =<y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 1 > S x S y vertical segments horizontal segments 11
Properties of Contour Sequence • If tracing does NOT start the segment with the smallest x and y coordinates – The sequences are still composed of alternate increasing and decreasing subsequences – BUT, may NOT start and end in increasing and decreasing subsequences, respectively x 1 x 5 Both of <x 2 ,x 3 > and <x 1 ,x 2 > are x 4 x 2 increasing subsequences x 3 S x =<x 2 ,x 3 ,x 4 ,x 5 ,x 1 ,x 2 > * =<x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 1 > S x vertical segments 12
Vertical and Horizontal Inversions • Occur when sequences change from increasing to decreasing, and vice versa horizontal inversions y 4 x 1 x 5 y 5 y 3 x 4 y 2 x 2 vertical inversion x 3 y 1 S x =<x 2 ,x 3 ,x 4 ,x 5 ,x 1 ,x 2 > S y =<y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 1 > vertical segments horizontal segments 13
Voltage-Island Boundary Search d σ ' d σ no inv. vertical inv. horizontal inv. RU/(RD) RU/(RD) DR/(UR) UL/(DL) LD/(LU) LD/(LU) UL/(DL) DR/(UR) UL/(UR) UL/(UR) LD/(RD) RU/(LU) DR(DL) DR/(DL) RU/(LU) LD/(RD) p 5 p 3 P 3 d p3 : UL p 1 p 2 p 2 d p1 : RU d p2 : RU (a) (b) (c) point σ point σ ' inversion searched contour 14
Correctness of Voltage-Island Boundary Search 1. Start at the correct beginning • Start at the point with the smallest y coordinate • Set the beginning direction pair to RU 2. Prove that the succeeding point must exist • It must exist in the directions indicated by the direction pair 3. Make a correct inversion detection • Correctly detect inversions if they exist • Correctly change the direction pair 15
Summary p 1 p 2 d p1 : RU p 3 p 2 d p2 : RU p 5 P 3 d p3 : UL 16
Outline • Introduction • Problem Formulation • Algorithm – Voltage-Island Identification – Voltage-Island Boundary Search – Power-Ring Corner Patching • Experiment Results • Conclusion 17
Power-Ring Refinement • Make power rings more regular for IR-drop reduction • Use whitespace for power-ring refinement power rings voltage islands corners power rings whitespaces 18
Power-Ring Corner Classification • Double joints – Individually extend vertical and horizontal contour segments – A double joint is enclosed by one extended and three original segments Here is a double joint Here is no double joint while extending vertical segments while extending horizontal segments 19
Power-Ring Corner Classification • Single joints – Simultaneously extend vertical and horizontal contour segments – A single joint is enclosed by two extended and two original segments NOTE: This is a double joint Here is a single joints 20
Complete Whitespace for a Corner • The whitespace can fill the corner Complete whitespaces for the double/single joints w 3 w 2 w 1 No complete whitespace for this single joint 21
Power-Ring Corner-Patching Flow Patch double joints Patch single joints Update contours Update contours Any adjustable Any adjustable double joints ? single joints ? YES YES NO NO Done 22
Optimality of Power-Ring Corner Patching • Filling single joints will not induce double joints – The corner-patching flow is correct • Power-ring corner patching optimizes (minimizes) the # of corners in power rings – There is no complete whitespace left 23
Outline • Introduction • Problem Formulation • Algorithm • Experiment Results • Conclusion 24
IR Drop & # of Corners • Corners in a power ring induce IR drop p 3 s 2 d 3 s 1 s 3 p 4 p 2 d 2 d 1 p 1 25
Experimental Results – Corner Patching • All running times are less than 0.06 second – 2.2 GHz CPU and 8 GB memory 200 160 corner # original 120 double-joint patching 80 single-joint patching 40 0 n10 n10b n10c n30 n30b n30c n50 n50b n50c 1000 800 600 400 200 0 26 n100 n100b n100c n200 n200b n200c n300
Experimental Results -- Layouts double joint single joint n30 n50 27
Outline • Introduction • Problem Formulation • Algorithm • Experiment Results • Conclusion 28
Conclusion • Proposed an algorithm for power-ring synthesis for multiple-supply-voltage design – Voltage-Island Identification – Voltage-Island Boundary Search – Power-Ring Corner Patching 29
Thank You! Wan-Ping Lee planet@eda.ee.ntu.edu.tw 30
Correctness of Direction-Pair Switch • Assume the current direction pair is RU σ σ ' σ ' island σ island vertical horizontal RU DR RU UL inversion inversion 31
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