PLACEMENT USING DON’T CARE WIRES Fan Mo Don’t Care Wire Group: P.Chong, Y-J.Jiang, S.Singha and R.K.Brayton

OUTLINE Design flow overview What is don’t care wire? What is our macro-cell placer? How to use don’t care wires in placement? Experiment, results and conclusion

DESIGN FLOW OVERVIEW PLA-based Decomposition SPFD-based Don’t Care Wire Generation Placement based on Wire Choices Resynthesis Netlist Layout Final Placement pins with wire choices Cell area and net connection determined wire choice made

SPFD Yamashita and etc., “A new method to express functional permissibility for LUT based FPGAs and its applications”, ICCAD96 Brayton, “Understanding SPFDs: A new method for specifying flexibility”, IWLS97 Sinha and Brayton, “Implementation and use of SPFD”, ICCAD98 y1y1y1y1 y2y2y2y2 y5y5y5y5 y4y4y4y4 YAYA y2y2y2y2 y3y3y3y3 y5y5y5y5 y4y4y4y4 YBYB y1y1y1y1 y3y3y3y3 y4y4y4y4 y5y5y5y5 YCYC Y-space Z-space Primary Inputs YAYA YBYB YCYC

SPFD 11 Y-space 00 22 55 33 77 99 44 66 88  10 need SPFD Y A provide at least SPFD Y A need SPFD Y B provide at least SPFD Y B need SPFD Y C provide at least SPFD Y C Each input pin of a node needs information described by its SPFD, and some other non-TFO nodes provide the required information.

DON’T CARE WIRES Denition 1 Given a set of sets of nodes R={R k }, a selection is an ordered set of nodes {  1, …,  |R| } such that  k  R k. Denition 2 A set of sets R={R k } is compatible if for each selection, there exist logic functions at each node such that the implied netlist for that selection can implement the specications at the primary outputs. Theorem Any set of sets of nodes {R k } satisfying 1. For any selection, the resulting netlist is acyclic, and 2.  ’  R k  SPFD k  SPFD  ’ is compatible.

DON’T CARE WIRES Procedure (Constructing a compatible set, but still acyclic network) 1. Starting from the outputs and proceeding in a backward topological order, for each node  in the network, and each of its input pins, , assign SPFDs, SPFD  and SPFD  so that the required information is supplied. Once this is done, each SPFD represents the set of minterms which must be distinguished by that node or pin. 2. Initialize for each node , ex(  )={  }  TFO  and for each input pin,  of , let R  ={  ’ }, where  ’ is the initial choice of source for pin . R  will eventually represent the set of alternate wires for . 3. Starting from the inputs and proceeding in some topological order, at each node , do the following: (a) Let C =~ex(  ) (b) For each fanin wire  of  : # Find an  ’  C such that SPFD   SPFD  ’. # Include  ’ in R , R  = R   {  ’ }. # Update ex(  ’ ) = ex(  )  ex(  ’ ). (to avoid cycles.) # This continues until no more nodes can be added to R .   RR ’’ ex(  ) ex(  ’ )

USE DON’T CARE WIRES IN PLACEMENT Based on current placement, determine which wire among the choice set is chosen in terms of wire length reduction. Based on current netlist, determine the movement of the cells. Wire choice interleaves cell placement

AWC PHASE I For each pin with alternate wires, temporarily disconnect it from the current net. For each net form the bounding boxes of the currently connected pins. These partial bounding boxes form a lower bound on the total wire length. For each pin with alternate wires, if its pin position is inside one of the partial bounding boxes for its candidate wires (the original wire plus its alternates), assign it to that net. No increase has been caused by this, and hence the partial assignment seen so far must be part of an optimum assignment. For each remaining pin with alternate wires, compute the “delta” costs if it is assigned to each of the candidate nets. There is a net assignment which increase the total net length by the least amount. Choose this assignment and update the chosen net. Continue last step until all pins have been assigned.

AWC PHASE I

AWC PHASE II For each pin which is an extreme of the bounding box of its currently assigned net, temporarily release it from its assignment, and compute the best net to put it in and its delta decrease cost in doing this. Note that the delta decrease is nonnegative. Choose the pin with the maximum delta decrease and reassign the pin to the new net. Repeat the above steps until the best delta is 0.

AWC PHASE II

AWC After PHASE I, there may be pins that can be moved to different nets to improve the total cost. During PHASE II, a pin may be reassigned more than once. To speed up the process, one may want to “lock” a pin once it is reassigned once. After PHASE II (with no locking), the solution is locally optimal, in that there is no pin which can be moved to a new net such that the total cost is decreased. However, there might be a set of pins that can be reassigned all at once which decreases the cost. Chong and etc., “Don’t care wires in logic/physical design”, IWLS00

FORCE-DIRECTED MACRO-CELL PLACER Iterative so that wire choice can be merged into the placement. Incremental so that final placement can start from the layout done after wire choice instead of starting from scratch. Need to handle maro-cell, not only standard cell. Standard cell design Macro-cell design Iterative and Incremental Quinn and Breuer, “A Forced Directed Component Placement Procedure for Printed Circuit Boards”, IE 3 Trans.-CAS79 Eisenmann and Johannes, “Generic global placement and floorplanning”, DAC98

FORCE-DIRECTED MACRO-CELL PLACER Short Total Wire Length Attractive forces applied on connected cells. Small Area Cells are dragged by attractive forces. Cell Orientation and Aspect Ratio (for soft cell) Gain function describing the relation between force reduction and cell orientation and shape. Eliminate Overlapping Density field method. Make an evenly distributed layout. Also use pads to pull cells apart. Iterative It should be. AWC can be easily merged in the placer. Run Time We seek more speed up by using a new wire model. Other Interesting Features Wire congestion estimation. Pad positioning.

PLACER ATTRACTIVE FORCE Cell[1] Star[s] Chip Pad[1]Pad[2] Cell[2] Using star wire model instead of clique wire model. About 30% saving. k: net weight; Pc: cell location; O T : terminal offset; Ps: star location

PLACER DENSITY FIELD MLBX [ c ] BLBY [ c ] BLBX [ c ] BRTX [ c ] BRTY [ c ] MLBY [ c ] MRTX [ c ] MRTY [ c ] BinSize

PLACER FORCE EQUATIONS

PLACER CELL ORIENTATION EWTN S HVR Gain of taking an orientation:

PLACER CELL ASPECT RATIO new width/height ratio:

PLACER ORIENTATION vs ASPECT RATION ORIENTATION ASPECT RATIO discrete continuous find a better one find the best easy to compute more run time for both hard/soft cell only for soft cell better in earlier stage better in later stage

PLACER PAD POSITIONING A B C D A B C D Attract force one dimensional density field and filling force

PLACER WIRE CONGESTION ESTIMATION 1 Area paid for connections to star in terms of contribution to density field. w BinSize L

PLACER WIRE CONGESTION ESTIMATION 2 Area paid for the connections to the terminals in terms of keepout distance of cell edges. #W-,#W+ : the no. of wires go two opposite directions. w : wire pitch e=left,bottom,right,top cell edge; KO C : the constant keepout distance

PLACER WIRE CONGESTION ESTIMATION 3 1/4 1/3 1/2 1/31/4 1/21/41/3 1/21/31/4 1/31/41/2 T S 1/40 1/3 1/2 1/31/41/31/21/41/3 1/21/31/41/31/4 1/31/41/31/41/2 T S 1/4 1/3 1/2 1/31/4 1/21/41/3 1/21/31/4 1/31/41/2 T S No obstruction Obstruction, not fully blocked Obstruction, fully blocked Area paid for the wiring between star and terminal in terms of contribution to density field.

PLACEMENT FLOW Initialize_and_ZeroSize_Cells(); SetCellsSizeZero(); loop Stage1IterationNumber { ComputeAttractiveForces_and_Move_Stars(); ComputeAttractiveForces_and_Move_Cells(); AWC( ); DetermineChipBoundary(); ComputeAttractiveAndFillingForce_and_Slide_Pads(); } explode(); loop Stage2IterationNumber { IncreaseCellSize(); ComputeAttractiveForces_and_Move_Stars(); ComputeAttractiveForces_Cells(); ComputeKeepOutDistance_for_Cells(); ComputeBinDensity(); ComputeFillingForces_Cells(); MoveWithLimit_Cells(); ComputeOrientationGain_and_ChooseOrientation_for_Cells(); AWC( ); DetermineChipBoundary(); ComputeAttractiveAndFillingForce_and_Slide_Pads(); } while (exist bin, density > densityThreshold) { ComputeAttractiveForces_and_Move_Stars(); ComputeAttractiveForces_Cells(); ComputeKeepOutDistance_for_Cells(); ComputeBinDensity(); ComputeFillingForces_Cells(); MoveWithLimit_Cells(); ComputeSoftCellAspectRatio(); DetermineChipBoundary(); ComputeAttractiveAndFillingForce_and_Slide_Pads(); } CleanUp(); Resynthesis( ); UpdateCellInformation( ); resynthesis

EXPERIMENT Characterization of Examples number of pins with alternates the percentage of such pins among all pins average alternate number of these pins break the acyclic constrain

EXPERIMENTAL RESULTS Average improvement: regular 5.1%, re-synthesis 3.9% max 5.4%

EXPERIMENTAL RESULTS Average improvement: 4i2o 7.0%, 1i1o 8.2%

CONCLUSION Synthesis-interactive placer. AWC. Improvement in terms of total wire length and area. Macro-cell placement algorithm, handling cell orientation, cell aspect ratio and pin(pad) position. Also with wiring estimation.