Floorplanning Algorithm for multiple clock domains

Transcription

1 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( Floorlannng Algorthm for multle domans Changhong Zhao, Jan Chen, Dan Zhou, aofang Zhou, uan Zeng ASIC & System State Key Lab Fudan Unversty Rd Zhangheng No85 Shangha PRChna 0103 Abstract: Ths aer resents the roblem of floorlannng th multle domans and the corresondng algorthms based on smulated annealng algorthm and sequence ar reresentaton The man contrbuton of ths algorthm s to solve the floorlannng roblem th multle domans thout ncreasng the comlexty Exermental results sho that good results can be obtaned for the floorlannng th multle domans Key ord: floorlannng NOMENCLATURE * Parameter: N : number of blocks b : the th block n doman : The th doman N : number of blocks n doman node( : The th doman n the K : number of domans h : the heght of module : the dth of module a : the area of module b ( : the th block C ( : the doman of block b ( τ * : the asect rato of block Ths research s suorted by the H-Tech Research and Develoment (863 Program of Chna under Grant (003AA1Z110 and s also suorted by NSF grants CCR , artly by NSFC research roect , , artly by Cross-Century Outstandng Scholar s fund of Mnstry of Educaton of Chna, artly by Natonal 863 lan roects 004AA1Z1050, Shangha Scence and Technology commttee Key roect 04JC14015 and Shangha AM R&D fund 0418 constrant grah of domans V : node set n the constrant grah of domans : the frst sequence of the sequence ar : the second sequence of the sequence ar 1 Introducton Floorlannng s a key research ont n recent years and most of the ork s focused on the asects of area mnmzaton, total re length mnmzaton and mnmzaton of the tmng delay of the crtcal ath Wth the develoment of VLSI technology, more and more crcuts of dfferent s are ntegrated nto one ch So, a ch th several or even more s s becomng common Therefore, t s necessary to study the floorlannng th multle domans Prelmnares 1 Problem Formulaton of the Tradtonal

2 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( Floorlannng Let B = b, b,, b } be a set of n rectangular modules { 1 N b B s assocated th a three tule { h,, a}, here h, and a denote the dth, heght, and area of b resectvely The asect rato of vares from b B denoted by τ = h τ, mn to τ, max A floorlannng s an assgnment of rectangular modules th the coordnates of ther bottom-left corners beng assgned to x, y s so that there are no ( overlas beteen any to modules overla th τ τ τ The obect of, mn, max lacementfloorlannng s to mnmze a secfed cost metrc such as the area of the ch, the total re length and the combnaton of both area and total re length Sequence ar [1] In ths aer, sequence ar s adoted A sequence ar s a ar of combnatons of module names It reresents the relatonsh beteen any to modules a and b as follos: If a s ahead of b n both sequences, module b s on the rght of module a The corresondng sequence ar s ( a b, a b If a s ahead of b n the frst sequence hle behnd b n the second sequence, module a s above module b The corresondng sequence ar s ( a b, b a Wth the sequence ar, e aly the follong seven oeratons to erturb the soluton sace Rotaton: Rotate a module Sa blocks: Sa to blocks n Sa blocks: Sa to blocks n Sa blocks: Sa to blocks n both and Sa domans: Sa all blocks of to domans n Sa domans: Sa all blocks of to domans n Sa domans: Sa all blocks of to domans n and 3 Floorlannng th multle domans For a system th multle domans, ts floorlannng s more comlex than that of a system th only one Relatonshs of blocks thn the same doman and among dfferent domans must be consdered smultaneously Usually, blocks thn the same doman should be laced together and blocks of dfferent domans should be laced accordng to the number of nets connected beteen them In order to reresent the relatonsh of blocks of a system th multle domans, several cases are gven belo Gven a sequence ar (, and to domans D = b, b,, b } and clcok { 1 m D = b, B,, B } It s assumed that each { 0 1 n macro block has only one, e D D = φ and D D = m + n are true It s also assumed that the sequence ar of

3 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( D D s ( 1 m 1 n, = ( b b b, b b b, The subsequence ar that only ncludes the blocks of D D k < > l k l > < are true Case 1 and case are not admssble s, = b b b b b We ( m n defne the oston of b( n ( = and ( D = and as resectvely Wth the assumton above, the follong nadmssble cases can be obtaned Case 1: b If k, bl D ( 0 < k, l D b and b ( k are true, k ( l l b b bk 1 b 1 b 1 b k Fgure 1: examle of case 1 b 1 b 1 b b k 1 b D 0 < m D b k k l k are true Case f k > > l < < l b, b D ( < k, l b and ( k b are true, ( l k l 0 D b Fgure : examle of case Defnton 1: a floorlannng th multle domans s admssble ff there are no case 1 and case n t In order to dentfy the cases that are not admssble, e ntroduce the horzontal and vertcal constrant grahs of domans Defnton: Horzontal constrant grah of domans: If a block of of s to the left of a block k, there exsts a drected edge from b D 0 < m D node ( to node (k Defnton: Vertcal constrant grah of domans:

4 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( If a block of s above a block of, k node( to node ( n, fnally back to there exsts a drected edge from node ( node(1 thout loss of generalty to node (k node ( node( node(k node ( node( node(k Accordng to the defnton of constrant grah, the follong formula can be obtaned b1 1 b 1 1 < < b k b3 l (1 (a (b (a Horzontal constrant grah (b Vertcal constrant grah Fgure 3: the constrant grahs of fgure 1 node ( node( node(k node ( node( node(k (a (b (a Horzontal constrant grah (b Vertcal constrant grah Fgure 4: the constrant grahs of fgure Theorem 1: A floorlannng th multle domans s admssble ff there are no crcles n ts horzontal and vertcal constrant grah of domans Proof: Frst e rove that there are no crcles n the horzontal and vertcal constrant grah of an admssble floorlannng Proof: For a floorlannng th K domans, f t s assumed that there s a crcle n the horzontal constrant grah of an admssble floorlannng and the crcle s from node(1 to < < ( Because t s assumed that the floorlannng s admssble, the follong can be obtaned b1 1 b 1 1 < < b k Smlarly ( 1 < n k k < < < < b3 l (3 (4 bk b ( + 1 l + 1 ( + 1 l ( + 1 l Accordng to (5, (6 can be obtaned b1 1 b n 1 1 < < n n (5 (6 Accordng the assumton, there s a drected

5 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( edge from node (n to node (1 b1 1 b n 1 1 > > n n, so (7 Snce there s a contradcton ((6 and (7, therefore the assumton s reected and there are no crcles n the horzontal and vertcal constrant grahs of an admssble floorlannng The roof that a floorlannng s admssble f there s no crcle n ts horzontal and vertcal constrant grahs of domans can be obtaned from the defnton of the admssble floorlannng n ths aer The algorthm to convert an nadmssble floorlannng to an admssble one s gven belo Algorthm I Whle V s not emty{ For = 1 to N Calculate the n-degree and out-degree n both horzontal and vertcal constrant grah Fnd mn n-degree out-degree mn out If( mn n = 0 or mn out = 0 mn n and mn Remove the corresondng node Else Fnd the node v th max-degree Extract blocks of the corresondng doman and ut them to the last of sequences th the relatve oston n ths doman unchanged End for } From theorem 1, t s clear that the rocess to transform the constrant grahs th crcles to ones thout crcles s the rocess to transform nadmssble floorlannngs to admssble ones Another method s to avod nadmssble lacement from the begnnng Detals of the method are gven belo Algorthm II begn Let both of the ntal sequences of and be b ntal N =,,b,b K1 ntal K, b( = ( ntal = (b11,b1,,b1,b KNK N1,b 1,b,, Let Produce to random ntegers elem1and elem beteen [ 0, N e 0 elem1, elem < N If( rand ( 0,1 < change _ rato TENT-CHANGE( elem 1 h elem1 If ( rand ( 0,1 < rotate _ rato TENT-ROTATE b (elem1 Else f ( rand ( 0,1 < sa _ rato If ( elem1 = ( b( elem TENT-ECHGE b( elem1, b( elem n or or both and accordng to FAST-SP [4] Else TENT-ECHGE(C(b(elem1,C(b(elem cost = cost(ne_lace - cost(lace f ( cost > 0 lace = ne_ lace

6 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( cos t T else f( rand(0,1 > e lace = ne_ lace tmes = tmes +1 od od soft block adustment end In ths aer, algorthm II s adoted The constructon method [6] s adoted for the adustment of dth and heght of each soft block, e there are 11 canddate dths and heghts for each soft block Each canddate dth s calculate as follos: = 1 a τ = 09 a = 08 a = 07 a Exermental Results Based on the algorthm II, e mlement our algorthm n c++ language n a 38G Dell PC th 1G bytes memory We test our algorthm by am49 and a bg benchmark test196 hch s generated from four am49s The nformaton of the benchmark s shon n table 1 For each block, 033 τ 3 The number of teraton tmes n each temerature s 400 The cost functon s λ1 cost( area + (1 λ1 cost( re Exerment results are shon n table and fgure 5 and 6 Table 1: crcut Number of blocks Number of s Total area of all blocks am Test = 06 a = 05 a = 04 a = 03 a + 07 Fgure 5 Floorlannng result of am49 ( λ 1 = 1 9 = 0 a = 01 a + 09 τ 11 = a (8 The canddate heght corresondng to each canddate dth s calculate as h, = a ( 0 1 < (9

7 Proceedngs of the 4th WSEASIASME Int Conf on System Scence and Smulaton n Engneerng, Tenerfe, San, December 16-18, 005 ( Fgure 6: Floorlannng result of test196 ( λ = 1 1 In fgure 5 and 6, dfferent domans are reresented by dfferent colors Exerment results sho that blocks thn the same doman are laced together and blocks of dfferent domans are dvded clearly by the algorthm n ths aer 5 Concluson Ths aer resents the roblem of the floorlannng th multle domans and the corresondng algorthms The motvaton of ths ork as that more and more domans exst n an SOC Exermental results sho that e can get reasonable results by the algorthm In the exerment, ten domans ere acked effcently n a reasonable tme Wth the develoment of ne VLSI technologes, more and more s domans ll aear n a sngle ch Therefore, our algorthm ll be more sgnfcant than before References: [1] H Murata, K Fuyosh, S Nakatake, and Katan, VLSI module lacement based on rectangle-ackng by the sequence-ar, IEEE Trans Comuter-Aded Desgn, vol 15, , Dec 1996 [] Tang and D F Wong, FAST-SP: A fast algorthm for block lacement based sequence ar, Proc ASPDAC, 51 56, 001 [3] Hua ang, aong Tang, and Martn D F Wong Bus-Drven Floorlannng IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SSTEMS, VOL 3, NO 11, NOVEMBER 004 [4] DFWong and CLLu, A Ne Algorthm for Floorlan Desgns Proc 3 rd ACMIEEE Desgn Automaton Conf , 1986 [5] HMurata KFuyosh SNakatake and Katan VLSI module lacement based on rectangle-ackng by the sequence-ar IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SSTEMS, VOL 15, NO , Dec 1996 [6]Jae-Gon Km, eong-dae Km A Lnear Programmng-Based Algorthm for Floorlannng n VLSI Desgn IEEE Transactons on Comuter-aded Desgn of Integrated Crcuts and Systems, Vol, No 5, MA Table : crcuts area(mm total re length(mm λ = 1 λ = best average best (area average am Test