/* "NETGEN", a netlist-specification tool for VLSI Copyright (C) 1989, 1990 Massimo A. Sivilotti Author's address: mass@csvax.cs.caltech.edu; Caltech 256-80, Pasadena CA 91125. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation (any version). This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; see the file copying. If not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ /* greedy.c -- a greedy graph-partitioning algorithm for the PROTOCHIP */ #include "config.h" #include #ifdef IBMPC #include /* memset */ #endif #include "timing.h" #include "hash.h" #include "objlist.h" #include "netfile.h" #include "embed.h" #include "print.h" #include "dbug.h" /**************************************************************************/ /***** *****/ /***** Recursive top-down placement *****/ /***** *****/ /**************************************************************************/ static struct nlist *curcell; int permutation[MAX_LEAVES+1]; int TopDownStartLevel; int leftnodes[MAX_NODES + 1]; int rightnodes[MAX_NODES + 1]; int PartitionFanout(int left, int right, int side) /* returns number of pins for partition (left,right) */ /* has side-effect of setting up the leftnodes and rightnodes arrays; these represent the integrated node usages for the left and right partitions */ { int i, E; int ports; int sum; ports = 0; for (i = 1; i <= Nodes; i++) { sum = 0; for (E = left; E <= right; E++) sum += CSTAR[permutation[E]][i]; /* save total node usage in 'leftnodes' and 'rightnodes' */ if (side == LEFT) leftnodes[i] = sum; else rightnodes[i] = sum; if (sum && (sum < CSTAR[0][i] || C[0][i])) ports ++; } return(ports); } #ifndef DBUG_OFF void Dbug_print_cells(int left, int right) { int i; Fprintf(DBUG_FILE,"("); for (i = left; i <= right; i++) { Fprintf(DBUG_FILE,"%s", (InstanceNumber(curcell, permutation[i]))->instance); if (i != right) Fprintf(DBUG_FILE," "); } Fprintf(DBUG_FILE,") "); } #endif int FindOptimum(int left, int right, int *mynodes, int *othernodes) { int E, max, choice, i; int gain[MAX_LEAVES + 1]; /* find the left optimum */ for (E = left; E <= right; E++) { gain[E] = 0; for (i = 1; i <= Nodes; i++) { #ifdef BAD if (C[permutation[E]][i] && mynodes[i] == 1) gain[E]++; #else /* remember: left,rightnodes built up from CSTAR */ if (C[permutation[E]][i] && mynodes[i] == CSTAR[permutation[E]][i]) gain[E]++; #endif else if (C[permutation[E]][i] && othernodes[i] == 0) gain[E]--; } } max = 0; choice = 0; for (E = left; E <= right; E++) { DBUG_PRINT("place",("gain for %d is %d", E, gain[E])); if (gain[E] >= max) { max = gain[E]; choice = E; } } DBUG_EXECUTE("place", {Fprintf(DBUG_FILE, "\n");} ); return(choice); } int GradientDescent(int left, int right, int partition) /* try to exchange pairs in the (left..partition) (partition+1..right) sets in order to reduce the number of cut nodes */ /* returns 1 if a swap was possible */ { int leftchoice, rightchoice; int tmp; #if 1 int E, leftmax, rightmax, i; int gain[MAX_LEAVES + 1]; /* find the left optimum */ for (E = left; E <= partition; E++) { gain[E] = 0; for (i = 1; i <= Nodes; i++) { #ifdef BAD if (C[permutation[E]][i] && leftnodes[i] == 1) gain[E]++; #else if (C[permutation[E]][i] && leftnodes[i] == CSTAR[permutation[E]][i]) gain[E]++; #endif else if (C[permutation[E]][i] && rightnodes[i] == 0) gain[E]--; } } leftmax = 0; leftchoice = 0; for (E = left; E <= partition; E++) { DBUG_PRINT("place",("gain for %d is %d", E, gain[E])); if (gain[E] >= leftmax) { leftmax = gain[E]; leftchoice = E; } } DBUG_EXECUTE("place", Fprintf(DBUG_FILE, "\n"); ); /* find the right optimum */ for (E = partition+1; E <= right; E++) { gain[E] = 0; for (i = 1; i <= Nodes; i++) { #ifdef BAD if (C[permutation[E]][i] && rightnodes[i] == 1) gain[E]++; #else if (C[permutation[E]][i] && rightnodes[i] == CSTAR[permutation[E]][i]) gain[E]++; #endif else if (C[permutation[E]][i] && leftnodes[i] == 0) gain[E]--; } } rightmax = 0; rightchoice = 0; for (E = partition+1; E <= right; E++) { DBUG_PRINT("place",("gain for %d is %d", E, gain[E])); if (gain[E] >= rightmax) { rightmax = gain[E]; rightchoice = E; } } DBUG_EXECUTE("place", Fprintf(DBUG_FILE, "\n"); ); if (leftmax == 0 && rightmax == 0) return(0); #else leftchoice = FindOptimum(left, partition, leftnodes, rightnodes); if (leftchoice == 0) return(0); rightchoice = FindOptimum(partition+1, right, rightnodes, leftnodes); if (rightchoice == 0) return(0); #endif DBUG_PRINT("place",("Swapping %s and %s", (InstanceNumber(curcell,permutation[leftchoice]))->instance, (InstanceNumber(curcell,permutation[rightchoice]))->instance)); #ifdef BAD tmp = permutation[leftchoice]; permutation[leftchoice] = permutation[rightchoice]; permutation[rightchoice] = tmp; /* update node usage lists */ for (tmp = 1; tmp <= Nodes; tmp++) { if (C[permutation[leftchoice]][tmp]) { leftnodes[tmp] -= C[permutation[leftchoice]][tmp]; rightnodes[tmp] += C[permutation[leftchoice]][tmp]; } if (C[permutation[rightchoice]][tmp]) { leftnodes[tmp] += C[permutation[rightchoice]][tmp]; rightnodes[tmp] -= C[permutation[rightchoice]][tmp]; } } #else /* update node usage lists, remembering that CSTAR goes into leftnodes */ for (tmp = 1; tmp <= Nodes; tmp++) { if (CSTAR[permutation[leftchoice]][tmp]) { leftnodes[tmp] -= CSTAR[permutation[leftchoice]][tmp]; rightnodes[tmp] += CSTAR[permutation[leftchoice]][tmp]; } if (CSTAR[permutation[rightchoice]][tmp]) { leftnodes[tmp] += CSTAR[permutation[rightchoice]][tmp]; rightnodes[tmp] -= CSTAR[permutation[rightchoice]][tmp]; } } /* THEN swap the elements */ tmp = permutation[leftchoice]; permutation[leftchoice] = permutation[rightchoice]; permutation[rightchoice] = tmp; #endif return(1); } int GenerateGreedyPartition(int left, int right, int level) /* tries to find a balanced partition, as far as leaf cell usage */ { int i; int head, tail; int queue[MAX_LEAVES + 1]; char status[MAX_LEAVES + 1]; int IncludedElements; #define QUEUED 1 #define INSIDE 2 #define OUTSIDE 3 #if 0 Printf("before GreedyPermutation\n"); for (i = left; i <= right; i++) Printf(" %d",permutation[i]); Printf("\n"); #endif memzero(status, sizeof(status)); for (i = left; i <= right; i++) status[permutation[i]] = OUTSIDE; head = 0; tail = 0; IncludedElements = 0; while (IncludedElements <= (right - left) / 2) { int element; element = level; /* keep the compiler from bitching */ if (head != tail) element = queue[head++]; else { /* start from some random element */ for (i = left; i <= right; i++) { if (status[permutation[i]] == OUTSIDE) { element = permutation[i]; break; } } } status[element] = INSIDE; IncludedElements++; for (i = left; i <= right; i++) { /* check to see if an element should be added to the queue */ if (status[permutation[i]] == QUEUED) continue; if (status[permutation[i]] == INSIDE) continue; /* otherwise, add it to the queue, if it has common nodes with element */ if (AnyCommonNodes(element, permutation[i])) { status[permutation[i]] = QUEUED; queue[tail++] = permutation[i]; } } } /* at this point, status contains the list of elements, classified as either INSIDE, OUTSIDE, or QUEUED. It is now easy to generate a permutation. */ head = left; tail = right; for (i = 1; i <= Leaves; i++) { if (status[i] == INSIDE) permutation[head++] = i; else if (status[i] != 0) permutation[tail--] = i; } return (left + IncludedElements - 1); #if 0 { int leftsum, rightsum; leftsum = rightsum = 0; while (left < right) { if (leftsum < rightsum) leftsum += POW2(LEVEL(permutation[left++])); else rightsum += POW2(LEVEL(permutation[right--])); } if (leftsum > POW2(level) || rightsum > POW2(level)) { Fprintf(stdout,"No valid partition found at level %d\n",level); return(0); } return(left); } #endif } int GreedyPartition(int left, int right, int level) /* return index of new element, if successful partition has been found */ { int partition; int iterations; int found; int OriginalNewN; int leftelement, rightelement; #define MAX_PARTITION_ITERATIONS 10 DBUG_ENTER("GreedyPartition"); OriginalNewN = NewN; #if 0 if (level < 0) DBUG_RETURN(0); #else if (level < LEVEL(permutation[left])) { Fprintf(stdout,"Failed at level %d; subtree too deep\n",level); DBUG_RETURN(0); } #endif if (left == right) DBUG_RETURN(permutation[left]); /* use a greedy algorithm to gather elements, starting at 'left', until about 1/2 have been collected. Then check to see if it is valid */ /* DBUG_PRINT("place",("trying to partition %d, %d",left,right)); */ iterations = 0; do { int i; int leftfanout, rightfanout; iterations++; partition = GenerateGreedyPartition(left, right, level); if (partition == 0) DBUG_RETURN(0); /* no valid partition */ found = 0; leftfanout = PartitionFanout(left,partition,LEFT); rightfanout = PartitionFanout(partition+1, right, RIGHT); if (leftfanout <= TreeFanout[level] && rightfanout <= TreeFanout[level]) found = 1; if (!found || level > TopDownStartLevel - 2) { for (i = MAX_TREE_DEPTH; i > level; i--) Fprintf(stdout, " "); Fprintf(stdout, "Level: %d; L (%d leaves) fanout %d; R (%d leaves) fanout %d (<= %d) %s\n", level, (partition - left + 1), leftfanout, (right - partition), rightfanout, TreeFanout[level], found ? "SUCCESSFUL" : "UNSUCCESSFUL"); } if (!found) { int IterationLimit; for (IterationLimit = 0; IterationLimit < 20 && GradientDescent(left, right, partition); IterationLimit++); found = 0; leftfanout = PartitionFanout(left,partition,LEFT); rightfanout = PartitionFanout(partition+1, right, RIGHT); if (leftfanout <= TreeFanout[level] && rightfanout <= TreeFanout[level]) found = 1; for (i = MAX_TREE_DEPTH; i > level; i--) Fprintf(stdout, " "); Fprintf(stdout, " Iteration %2d: L fanout %d; R fanout %d (<= %d) %s\n", iterations, leftfanout, rightfanout, TreeFanout[level], found ? "SUCCESSFUL" : "UNSUCCESSFUL"); } DBUG_EXECUTE("place", Fprintf(DBUG_FILE,"Level %d: ",level); Dbug_print_cells(left,partition); Dbug_print_cells(partition+1,right); Fprintf(DBUG_FILE,"\n"); { int i; Fprintf(DBUG_FILE,"L "); for (i = 1; i <= Nodes; i++) Fprintf(DBUG_FILE,"%2d ",leftnodes[i]); Fprintf(DBUG_FILE,"\nR "); for (i = 1; i <= Nodes; i++) Fprintf(DBUG_FILE,"%2d ",rightnodes[i]); Fprintf(DBUG_FILE,"\n"); } Fprintf(DBUG_FILE, "%s\n", found?"SUCCESSFUL":"UNSUCCESSFUL"); ); } while (iterations < MAX_PARTITION_ITERATIONS && !found); if (!found) { Fprintf(stdout,"Failed embedding at level %d; no partition\n",level); goto fail; } leftelement = GreedyPartition(left, partition, level-1); if (leftelement == 0) goto fail; rightelement = GreedyPartition(partition+1, right, level-1); if (rightelement == 0) goto fail; /* add it to the list */ AddNewElement(leftelement, rightelement); DBUG_RETURN(NewN); fail: NewN = OriginalNewN; DBUG_RETURN(0); } void TopDownEmbedCell(char *cellname, char *filename, enum EmbeddingStrategy strategy) { struct nlist *tp; int i; int Found; float StartTime; tp = LookupCell(cellname); curcell = tp; if (!OpenEmbeddingFile(cellname, filename)) return; StartTime = CPUTime(); if (!InitializeMatrices(cellname)) return; NewN = Elements; for (i = 1; i <= Leaves; i++) permutation[i] = i; RandomSeed(1); Found = 0; TopDownStartLevel = MAX_TREE_DEPTH; switch (strategy) { case random_embedding: Found = RandomPartition(1, Leaves, TopDownStartLevel); break; case greedy: Found = GreedyPartition(1, Leaves, TopDownStartLevel); break; case anneal: Found = AnnealPartition(1, Leaves, TopDownStartLevel); break; case bottomup: Fprintf(stderr,"ERROR: called TopDownEmbedCell with bottomup strategy\n"); break; } if (Found) { Printf ("successful embedding (Element %d) (time = %.2f s):\n", NewN, ElapsedCPUTime(StartTime)); #if 0 for (i = 1; i <= Leaves; i++) Printf("%d ",permutation[i]); Printf("\n"); #endif #if 1 PrintE(stdout,NewN); Printf("\n"); #endif FreeEmbeddingTree((struct embed *)(tp->embedding)); tp->embedding = EmbeddingTree(tp, Found); PrintEmbeddingTree(stdout,cellname,1); PrintEmbeddingTree(outfile,cellname,1); if (logging) PrintEmbeddingTree(logfile,cellname,1); } else { Fprintf(stdout,"No embedding found. Sorry.\n"); Fprintf(outfile,"No embedding found. Sorry.\n"); if (logging) Fprintf(logfile,"No embedding found. Sorry.\n"); } CloseEmbeddingFile(); }