/**CFile*********************************************************************** FileName [cuddExact.c] PackageName [cudd] Synopsis [Functions for exact variable reordering.] Description [External procedures included in this file: Internal procedures included in this module: Static procedures included in this module: ] Author [Cheng Hua, Fabio Somenzi] Copyright [This file was created at the University of Colorado at Boulder. The University of Colorado at Boulder makes no warranty about the suitability of this software for any purpose. It is presented on an AS IS basis.] ******************************************************************************/ #include "util_hack.h" #include "cuddInt.h" ABC_NAMESPACE_IMPL_START /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddExact.c,v 1.1.1.1 2003/02/24 22:23:52 wjiang Exp $"; #endif #ifdef DD_STATS static int ddTotalShuffles; #endif /*---------------------------------------------------------------------------*/ /* Macro declarations */ /*---------------------------------------------------------------------------*/ /**AutomaticStart*************************************************************/ /*---------------------------------------------------------------------------*/ /* Static function prototypes */ /*---------------------------------------------------------------------------*/ static int getMaxBinomial ARGS((int n)); static int gcd ARGS((int x, int y)); static DdHalfWord ** getMatrix ARGS((int rows, int cols)); static void freeMatrix ARGS((DdHalfWord **matrix)); static int getLevelKeys ARGS((DdManager *table, int l)); static int ddShuffle ARGS((DdManager *table, DdHalfWord *permutation, int lower, int upper)); static int ddSiftUp ARGS((DdManager *table, int x, int xLow)); static int updateUB ARGS((DdManager *table, int oldBound, DdHalfWord *bestOrder, int lower, int upper)); static int ddCountRoots ARGS((DdManager *table, int lower, int upper)); static void ddClearGlobal ARGS((DdManager *table, int lower, int maxlevel)); static int computeLB ARGS((DdManager *table, DdHalfWord *order, int roots, int cost, int lower, int upper, int level)); static int updateEntry ARGS((DdManager *table, DdHalfWord *order, int level, int cost, DdHalfWord **orders, int *costs, int subsets, char *mask, int lower, int upper)); static void pushDown ARGS((DdHalfWord *order, int j, int level)); static DdHalfWord * initSymmInfo ARGS((DdManager *table, int lower, int upper)); static int checkSymmInfo ARGS((DdManager *table, DdHalfWord *symmInfo, int index, int level)); /**AutomaticEnd***************************************************************/ /*---------------------------------------------------------------------------*/ /* Definition of exported functions */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Definition of internal functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Exact variable ordering algorithm.] Description [Exact variable ordering algorithm. Finds an optimum order for the variables between lower and upper. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddExact( DdManager * table, int lower, int upper) { int k, i, j; int maxBinomial, oldSubsets, newSubsets; int subsetCost; int size; /* number of variables to be reordered */ int unused, nvars, level, result; int upperBound, lowerBound, cost; int roots; char *mask = NULL; DdHalfWord *symmInfo = NULL; DdHalfWord **newOrder = NULL; DdHalfWord **oldOrder = NULL; int *newCost = NULL; int *oldCost = NULL; DdHalfWord **tmpOrder; int *tmpCost; DdHalfWord *bestOrder = NULL; DdHalfWord *order; #ifdef DD_STATS int ddTotalSubsets; #endif /* Restrict the range to be reordered by excluding unused variables ** at the two ends. */ while (table->subtables[lower].keys == 1 && table->vars[table->invperm[lower]]->ref == 1 && lower < upper) lower++; while (table->subtables[upper].keys == 1 && table->vars[table->invperm[upper]]->ref == 1 && lower < upper) upper--; if (lower == upper) return(1); /* trivial problem */ /* Apply symmetric sifting to get a good upper bound and to extract ** symmetry information. */ result = cuddSymmSiftingConv(table,lower,upper); if (result == 0) goto cuddExactOutOfMem; #ifdef DD_STATS (void) fprintf(table->out,"\n"); ddTotalShuffles = 0; ddTotalSubsets = 0; #endif /* Initialization. */ nvars = table->size; size = upper - lower + 1; /* Count unused variable among those to be reordered. This is only ** used to compute maxBinomial. */ unused = 0; for (i = lower + 1; i < upper; i++) { if (table->subtables[i].keys == 1 && table->vars[table->invperm[i]]->ref == 1) unused++; } /* Find the maximum number of subsets we may have to store. */ maxBinomial = getMaxBinomial(size - unused); if (maxBinomial == -1) goto cuddExactOutOfMem; newOrder = getMatrix(maxBinomial, size); if (newOrder == NULL) goto cuddExactOutOfMem; newCost = ABC_ALLOC(int, maxBinomial); if (newCost == NULL) goto cuddExactOutOfMem; oldOrder = getMatrix(maxBinomial, size); if (oldOrder == NULL) goto cuddExactOutOfMem; oldCost = ABC_ALLOC(int, maxBinomial); if (oldCost == NULL) goto cuddExactOutOfMem; bestOrder = ABC_ALLOC(DdHalfWord, size); if (bestOrder == NULL) goto cuddExactOutOfMem; mask = ABC_ALLOC(char, nvars); if (mask == NULL) goto cuddExactOutOfMem; symmInfo = initSymmInfo(table, lower, upper); if (symmInfo == NULL) goto cuddExactOutOfMem; roots = ddCountRoots(table, lower, upper); /* Initialize the old order matrix for the empty subset and the best ** order to the current order. The cost for the empty subset includes ** the cost of the levels between upper and the constants. These levels ** are not going to change. Hence, we count them only once. */ oldSubsets = 1; for (i = 0; i < size; i++) { oldOrder[0][i] = bestOrder[i] = (DdHalfWord) table->invperm[i+lower]; } subsetCost = table->constants.keys; for (i = upper + 1; i < nvars; i++) subsetCost += getLevelKeys(table,i); oldCost[0] = subsetCost; /* The upper bound is initialized to the current size of the BDDs. */ upperBound = table->keys - table->isolated; /* Now consider subsets of increasing size. */ for (k = 1; k <= size; k++) { #if DD_STATS (void) fprintf(table->out,"Processing subsets of size %d\n", k); fflush(table->out); #endif newSubsets = 0; level = size - k; /* offset of first bottom variable */ for (i = 0; i < oldSubsets; i++) { /* for each subset of size k-1 */ order = oldOrder[i]; cost = oldCost[i]; lowerBound = computeLB(table, order, roots, cost, lower, upper, level); if (lowerBound >= upperBound) continue; /* Impose new order. */ result = ddShuffle(table, order, lower, upper); if (result == 0) goto cuddExactOutOfMem; upperBound = updateUB(table,upperBound,bestOrder,lower,upper); /* For each top bottom variable. */ for (j = level; j >= 0; j--) { /* Skip unused variables. */ if (table->subtables[j+lower-1].keys == 1 && table->vars[table->invperm[j+lower-1]]->ref == 1) continue; /* Find cost under this order. */ subsetCost = cost + getLevelKeys(table, lower + level); newSubsets = updateEntry(table, order, level, subsetCost, newOrder, newCost, newSubsets, mask, lower, upper); if (j == 0) break; if (checkSymmInfo(table, symmInfo, order[j-1], level) == 0) continue; pushDown(order,j-1,level); /* Impose new order. */ result = ddShuffle(table, order, lower, upper); if (result == 0) goto cuddExactOutOfMem; upperBound = updateUB(table,upperBound,bestOrder,lower,upper); } /* for each bottom variable */ } /* for each subset of size k */ /* New orders become old orders in preparation for next iteration. */ tmpOrder = oldOrder; tmpCost = oldCost; oldOrder = newOrder; oldCost = newCost; newOrder = tmpOrder; newCost = tmpCost; #ifdef DD_STATS ddTotalSubsets += newSubsets; #endif oldSubsets = newSubsets; } result = ddShuffle(table, bestOrder, lower, upper); if (result == 0) goto cuddExactOutOfMem; #ifdef DD_STATS #ifdef DD_VERBOSE (void) fprintf(table->out,"\n"); #endif (void) fprintf(table->out,"#:S_EXACT %8d: total subsets\n", ddTotalSubsets); (void) fprintf(table->out,"#:H_EXACT %8d: total shuffles", ddTotalShuffles); #endif freeMatrix(newOrder); freeMatrix(oldOrder); ABC_FREE(bestOrder); ABC_FREE(oldCost); ABC_FREE(newCost); ABC_FREE(symmInfo); ABC_FREE(mask); return(1); cuddExactOutOfMem: if (newOrder != NULL) freeMatrix(newOrder); if (oldOrder != NULL) freeMatrix(oldOrder); if (bestOrder != NULL) ABC_FREE(bestOrder); if (oldCost != NULL) ABC_FREE(oldCost); if (newCost != NULL) ABC_FREE(newCost); if (symmInfo != NULL) ABC_FREE(symmInfo); if (mask != NULL) ABC_FREE(mask); table->errorCode = CUDD_MEMORY_OUT; return(0); } /* end of cuddExact */ /**Function******************************************************************** Synopsis [Returns the maximum value of (n choose k) for a given n.] Description [Computes the maximum value of (n choose k) for a given n. The maximum value occurs for k = n/2 when n is even, or k = (n-1)/2 when n is odd. The algorithm used in this procedure is quite inefficient, but it avoids intermediate overflow problems. Returns the computed value if successful; -1 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int getMaxBinomial( int n) { int *numerator; int i, j, k, y, g, result; k = (n & ~1) >> 1; numerator = ABC_ALLOC(int,k); if (numerator == NULL) return(-1); for (i = 0; i < k; i++) numerator[i] = n - i; for (i = k; i > 1; i--) { y = i; for (j = 0; j < k; j++) { if (numerator[j] == 1) continue; g = gcd(numerator[j], y); if (g != 1) { numerator[j] /= g; if (y == g) break; y /= g; } } } result = 1; for (i = 0; i < k; i++) result *= numerator[i]; ABC_FREE(numerator); return(result); } /* end of getMaxBinomial */ /**Function******************************************************************** Synopsis [Returns the gcd of two integers.] Description [Returns the gcd of two integers. Uses the binary GCD algorithm described in Cormen, Leiserson, and Rivest.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int gcd( int x, int y) { int a; int b; int lsbMask; /* GCD(n,0) = n. */ if (x == 0) return(y); if (y == 0) return(x); a = x; b = y; lsbMask = 1; /* Here both a and b are != 0. The iteration maintains this invariant. ** Hence, we only need to check for when they become equal. */ while (a != b) { if (a & lsbMask) { if (b & lsbMask) { /* both odd */ if (a < b) { b = (b - a) >> 1; } else { a = (a - b) >> 1; } } else { /* a odd, b even */ b >>= 1; } } else { if (b & lsbMask) { /* a even, b odd */ a >>= 1; } else { /* both even */ lsbMask <<= 1; } } } return(a); } /* end of gcd */ /**Function******************************************************************** Synopsis [Allocates a two-dimensional matrix of ints.] Description [Allocates a two-dimensional matrix of ints. Returns the pointer to the matrix if successful; NULL otherwise.] SideEffects [None] SeeAlso [freeMatrix] ******************************************************************************/ static DdHalfWord ** getMatrix( int rows /* number of rows */, int cols /* number of columns */) { DdHalfWord **matrix; int i; if (cols*rows == 0) return(NULL); matrix = ABC_ALLOC(DdHalfWord *, rows); if (matrix == NULL) return(NULL); matrix[0] = ABC_ALLOC(DdHalfWord, cols*rows); if (matrix[0] == NULL) return(NULL); for (i = 1; i < rows; i++) { matrix[i] = matrix[i-1] + cols; } return(matrix); } /* end of getMatrix */ /**Function******************************************************************** Synopsis [Frees a two-dimensional matrix allocated by getMatrix.] Description [] SideEffects [None] SeeAlso [getMatrix] ******************************************************************************/ static void freeMatrix( DdHalfWord ** matrix) { ABC_FREE(matrix[0]); ABC_FREE(matrix); return; } /* end of freeMatrix */ /**Function******************************************************************** Synopsis [Returns the number of nodes at one level of a unique table.] Description [Returns the number of nodes at one level of a unique table. The projection function, if isolated, is not counted.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int getLevelKeys( DdManager * table, int l) { int isolated; int x; /* x is an index */ x = table->invperm[l]; isolated = table->vars[x]->ref == 1; return(table->subtables[l].keys - isolated); } /* end of getLevelKeys */ /**Function******************************************************************** Synopsis [Reorders variables according to a given permutation.] Description [Reorders variables according to a given permutation. The i-th permutation array contains the index of the variable that should be brought to the i-th level. ddShuffle assumes that no dead nodes are present and that the interaction matrix is properly initialized. The reordering is achieved by a series of upward sifts. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int ddShuffle( DdManager * table, DdHalfWord * permutation, int lower, int upper) { DdHalfWord index; int level; int position; int numvars; int result; #ifdef DD_STATS long localTime; int initialSize; #ifdef DD_VERBOSE int finalSize; #endif int previousSize; #endif #ifdef DD_STATS localTime = util_cpu_time(); initialSize = table->keys - table->isolated; #endif numvars = table->size; #if 0 (void) fprintf(table->out,"%d:", ddTotalShuffles); for (level = 0; level < numvars; level++) { (void) fprintf(table->out," %d", table->invperm[level]); } (void) fprintf(table->out,"\n"); #endif for (level = 0; level <= upper - lower; level++) { index = permutation[level]; position = table->perm[index]; #ifdef DD_STATS previousSize = table->keys - table->isolated; #endif result = ddSiftUp(table,position,level+lower); if (!result) return(0); } #ifdef DD_STATS ddTotalShuffles++; #ifdef DD_VERBOSE finalSize = table->keys - table->isolated; if (finalSize < initialSize) { (void) fprintf(table->out,"-"); } else if (finalSize > initialSize) { (void) fprintf(table->out,"+"); } else { (void) fprintf(table->out,"="); } if ((ddTotalShuffles & 63) == 0) (void) fprintf(table->out,"\n"); fflush(table->out); #endif #endif return(1); } /* end of ddShuffle */ /**Function******************************************************************** Synopsis [Moves one variable up.] Description [Takes a variable from position x and sifts it up to position xLow; xLow should be less than or equal to x. Returns 1 if successful; 0 otherwise] SideEffects [None] SeeAlso [] ******************************************************************************/ static int ddSiftUp( DdManager * table, int x, int xLow) { int y; int size; y = cuddNextLow(table,x); while (y >= xLow) { size = cuddSwapInPlace(table,y,x); if (size == 0) { return(0); } x = y; y = cuddNextLow(table,x); } return(1); } /* end of ddSiftUp */ /**Function******************************************************************** Synopsis [Updates the upper bound and saves the best order seen so far.] Description [Updates the upper bound and saves the best order seen so far. Returns the current value of the upper bound.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int updateUB( DdManager * table, int oldBound, DdHalfWord * bestOrder, int lower, int upper) { int i; int newBound = table->keys - table->isolated; if (newBound < oldBound) { #ifdef DD_STATS (void) fprintf(table->out,"New upper bound = %d\n", newBound); fflush(table->out); #endif for (i = lower; i <= upper; i++) bestOrder[i-lower] = (DdHalfWord) table->invperm[i]; return(newBound); } else { return(oldBound); } } /* end of updateUB */ /**Function******************************************************************** Synopsis [Counts the number of roots.] Description [Counts the number of roots at the levels between lower and upper. The computation is based on breadth-first search. A node is a root if it is not reachable from any previously visited node. (All the nodes at level lower are therefore considered roots.) The visited flag uses the LSB of the next pointer. Returns the root count. The roots that are constant nodes are always ignored.] SideEffects [None] SeeAlso [ddClearGlobal] ******************************************************************************/ static int ddCountRoots( DdManager * table, int lower, int upper) { int i,j; DdNode *f; DdNodePtr *nodelist; DdNode *sentinel = &(table->sentinel); int slots; int roots = 0; int maxlevel = lower; for (i = lower; i <= upper; i++) { nodelist = table->subtables[i].nodelist; slots = table->subtables[i].slots; for (j = 0; j < slots; j++) { f = nodelist[j]; while (f != sentinel) { /* A node is a root of the DAG if it cannot be ** reached by nodes above it. If a node was never ** reached during the previous depth-first searches, ** then it is a root, and we start a new depth-first ** search from it. */ if (!Cudd_IsComplement(f->next)) { if (f != table->vars[f->index]) { roots++; } } if (!Cudd_IsConstant(cuddT(f))) { cuddT(f)->next = Cudd_Complement(cuddT(f)->next); if (table->perm[cuddT(f)->index] > maxlevel) maxlevel = table->perm[cuddT(f)->index]; } if (!Cudd_IsConstant(cuddE(f))) { Cudd_Regular(cuddE(f))->next = Cudd_Complement(Cudd_Regular(cuddE(f))->next); if (table->perm[Cudd_Regular(cuddE(f))->index] > maxlevel) maxlevel = table->perm[Cudd_Regular(cuddE(f))->index]; } f = Cudd_Regular(f->next); } } } ddClearGlobal(table, lower, maxlevel); return(roots); } /* end of ddCountRoots */ /**Function******************************************************************** Synopsis [Scans the DD and clears the LSB of the next pointers.] Description [Scans the DD and clears the LSB of the next pointers. The LSB of the next pointers are used as markers to tell whether a node was reached. Once the roots are counted, these flags are reset.] SideEffects [None] SeeAlso [ddCountRoots] ******************************************************************************/ static void ddClearGlobal( DdManager * table, int lower, int maxlevel) { int i,j; DdNode *f; DdNodePtr *nodelist; DdNode *sentinel = &(table->sentinel); int slots; for (i = lower; i <= maxlevel; i++) { nodelist = table->subtables[i].nodelist; slots = table->subtables[i].slots; for (j = 0; j < slots; j++) { f = nodelist[j]; while (f != sentinel) { f->next = Cudd_Regular(f->next); f = f->next; } } } } /* end of ddClearGlobal */ /**Function******************************************************************** Synopsis [Computes a lower bound on the size of a BDD.] Description [Computes a lower bound on the size of a BDD from the following factors: