/**CFile*********************************************************************** FileName [cuddZddReord.c] PackageName [cudd] Synopsis [Procedures for dynamic variable ordering of ZDDs.] Description [External procedures included in this module: Internal procedures included in this module: Static procedures included in this module: ] SeeAlso [] Author [Hyong-Kyoon Shin, In-Ho Moon] Copyright [Copyright (c) 1995-2004, Regents of the University of Colorado All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.] ******************************************************************************/ #include "util_hack.h" #include "cuddInt.h" ABC_NAMESPACE_IMPL_START /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ #define DD_MAX_SUBTABLE_SPARSITY 8 #define DD_SHRINK_FACTOR 2 /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddZddReord.c,v 1.47 2004/08/13 18:04:53 fabio Exp $"; #endif int *zdd_entry; int zddTotalNumberSwapping; static DdNode *empty; /*---------------------------------------------------------------------------*/ /* Macro declarations */ /*---------------------------------------------------------------------------*/ /**AutomaticStart*************************************************************/ /*---------------------------------------------------------------------------*/ /* Static function prototypes */ /*---------------------------------------------------------------------------*/ static Move * zddSwapAny (DdManager *table, int x, int y); static int cuddZddSiftingAux (DdManager *table, int x, int x_low, int x_high); static Move * cuddZddSiftingUp (DdManager *table, int x, int x_low, int initial_size); static Move * cuddZddSiftingDown (DdManager *table, int x, int x_high, int initial_size); static int cuddZddSiftingBackward (DdManager *table, Move *moves, int size); static void zddReorderPreprocess (DdManager *table); static int zddReorderPostprocess (DdManager *table); static int zddShuffle (DdManager *table, int *permutation); static int zddSiftUp (DdManager *table, int x, int xLow); static void zddFixTree (DdManager *table, MtrNode *treenode); /**AutomaticEnd***************************************************************/ /*---------------------------------------------------------------------------*/ /* Definition of exported functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Main dynamic reordering routine for ZDDs.] Description [Main dynamic reordering routine for ZDDs. Calls one of the possible reordering procedures: For sifting and symmetric sifting it is possible to request reordering to convergence.

The core of all methods is the reordering procedure cuddZddSwapInPlace() which swaps two adjacent variables. Returns 1 in case of success; 0 otherwise. In the case of symmetric sifting (with and without convergence) returns 1 plus the number of symmetric variables, in case of success.] SideEffects [Changes the variable order for all ZDDs and clears the cache.] ******************************************************************************/ int Cudd_zddReduceHeap( DdManager * table /* DD manager */, Cudd_ReorderingType heuristic /* method used for reordering */, int minsize /* bound below which no reordering occurs */) { DdHook *hook; int result; unsigned int nextDyn; #ifdef DD_STATS unsigned int initialSize; unsigned int finalSize; #endif long localTime; /* Don't reorder if there are too many dead nodes. */ if (table->keysZ - table->deadZ < (unsigned) minsize) return(1); if (heuristic == CUDD_REORDER_SAME) { heuristic = table->autoMethodZ; } if (heuristic == CUDD_REORDER_NONE) { return(1); } /* This call to Cudd_zddReduceHeap does initiate reordering. Therefore ** we count it. */ table->reorderings++; empty = table->zero; localTime = util_cpu_time(); /* Run the hook functions. */ hook = table->preReorderingHook; while (hook != NULL) { int res = (hook->f)(table, "ZDD", (void *)heuristic); if (res == 0) return(0); hook = hook->next; } /* Clear the cache and collect garbage. */ zddReorderPreprocess(table); zddTotalNumberSwapping = 0; #ifdef DD_STATS initialSize = table->keysZ; switch(heuristic) { case CUDD_REORDER_RANDOM: case CUDD_REORDER_RANDOM_PIVOT: (void) fprintf(table->out,"#:I_RANDOM "); break; case CUDD_REORDER_SIFT: case CUDD_REORDER_SIFT_CONVERGE: case CUDD_REORDER_SYMM_SIFT: case CUDD_REORDER_SYMM_SIFT_CONV: (void) fprintf(table->out,"#:I_SIFTING "); break; case CUDD_REORDER_LINEAR: case CUDD_REORDER_LINEAR_CONVERGE: (void) fprintf(table->out,"#:I_LINSIFT "); break; default: (void) fprintf(table->err,"Unsupported ZDD reordering method\n"); return(0); } (void) fprintf(table->out,"%8d: initial size",initialSize); #endif result = cuddZddTreeSifting(table,heuristic); #ifdef DD_STATS (void) fprintf(table->out,"\n"); finalSize = table->keysZ; (void) fprintf(table->out,"#:F_REORDER %8d: final size\n",finalSize); (void) fprintf(table->out,"#:T_REORDER %8g: total time (sec)\n", ((double)(util_cpu_time() - localTime)/1000.0)); (void) fprintf(table->out,"#:N_REORDER %8d: total swaps\n", zddTotalNumberSwapping); #endif if (result == 0) return(0); if (!zddReorderPostprocess(table)) return(0); if (table->realignZ) { if (!cuddBddAlignToZdd(table)) return(0); } nextDyn = table->keysZ * DD_DYN_RATIO; if (table->reorderings < 20 || nextDyn > table->nextDyn) table->nextDyn = nextDyn; else table->nextDyn += 20; table->reordered = 1; /* Run hook functions. */ hook = table->postReorderingHook; while (hook != NULL) { int res = (hook->f)(table, "ZDD", (void *)localTime); if (res == 0) return(0); hook = hook->next; } /* Update cumulative reordering time. */ table->reordTime += util_cpu_time() - localTime; return(result); } /* end of Cudd_zddReduceHeap */ /**Function******************************************************************** Synopsis [Reorders ZDD variables according to given permutation.] Description [Reorders ZDD variables according to given permutation. The i-th entry of the permutation array contains the index of the variable that should be brought to the i-th level. The size of the array should be equal or greater to the number of variables currently in use. Returns 1 in case of success; 0 otherwise.] SideEffects [Changes the ZDD variable order for all diagrams and clears the cache.] SeeAlso [Cudd_zddReduceHeap] ******************************************************************************/ int Cudd_zddShuffleHeap( DdManager * table /* DD manager */, int * permutation /* required variable permutation */) { int result; empty = table->zero; zddReorderPreprocess(table); result = zddShuffle(table,permutation); if (!zddReorderPostprocess(table)) return(0); return(result); } /* end of Cudd_zddShuffleHeap */ /*---------------------------------------------------------------------------*/ /* Definition of internal functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Reorders ZDD variables according to the order of the BDD variables.] Description [Reorders ZDD variables according to the order of the BDD variables. This function can be called at the end of BDD reordering to insure that the order of the ZDD variables is consistent with the order of the BDD variables. The number of ZDD variables must be a multiple of the number of BDD variables. Let M be the ratio of the two numbers. cuddZddAlignToBdd then considers the ZDD variables from M*i to (M+1)*i-1 as corresponding to BDD variable i. This function should be normally called from Cudd_ReduceHeap, which clears the cache. Returns 1 in case of success; 0 otherwise.] SideEffects [Changes the ZDD variable order for all diagrams and performs garbage collection of the ZDD unique table.] SeeAlso [Cudd_zddShuffleHeap Cudd_ReduceHeap] ******************************************************************************/ int cuddZddAlignToBdd( DdManager * table /* DD manager */) { int *invpermZ; /* permutation array */ int M; /* ratio of ZDD variables to BDD variables */ int i,j; /* loop indices */ int result; /* return value */ /* We assume that a ratio of 0 is OK. */ if (table->sizeZ == 0) return(1); empty = table->zero; M = table->sizeZ / table->size; /* Check whether the number of ZDD variables is a multiple of the ** number of BDD variables. */ if (M * table->size != table->sizeZ) return(0); /* Create and initialize the inverse permutation array. */ invpermZ = ABC_ALLOC(int,table->sizeZ); if (invpermZ == NULL) { table->errorCode = CUDD_MEMORY_OUT; return(0); } for (i = 0; i < table->size; i++) { int index = table->invperm[i]; int indexZ = index * M; int levelZ = table->permZ[indexZ]; levelZ = (levelZ / M) * M; for (j = 0; j < M; j++) { invpermZ[M * i + j] = table->invpermZ[levelZ + j]; } } /* Eliminate dead nodes. Do not scan the cache again, because we ** assume that Cudd_ReduceHeap has already cleared it. */ cuddGarbageCollect(table,0); result = zddShuffle(table, invpermZ); ABC_FREE(invpermZ); /* Fix the ZDD variable group tree. */ zddFixTree(table,table->treeZ); return(result); } /* end of cuddZddAlignToBdd */ /**Function******************************************************************** Synopsis [Finds the next subtable with a larger index.] Description [Finds the next subtable with a larger index. Returns the index.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddNextHigh( DdManager * table, int x) { return(x + 1); } /* end of cuddZddNextHigh */ /**Function******************************************************************** Synopsis [Finds the next subtable with a smaller index.] Description [Finds the next subtable with a smaller index. Returns the index.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddNextLow( DdManager * table, int x) { return(x - 1); } /* end of cuddZddNextLow */ /**Function******************************************************************** Synopsis [Comparison function used by qsort.] Description [Comparison function used by qsort to order the variables according to the number of keys in the subtables. Returns the difference in number of keys between the two variables being compared.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddUniqueCompare( int * ptr_x, int * ptr_y) { return(zdd_entry[*ptr_y] - zdd_entry[*ptr_x]); } /* end of cuddZddUniqueCompare */ /**Function******************************************************************** Synopsis [Swaps two adjacent variables.] Description [Swaps two adjacent variables. It assumes that no dead nodes are present on entry to this procedure. The procedure then guarantees that no dead nodes will be present when it terminates. cuddZddSwapInPlace assumes that x < y. Returns the number of keys in the table if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddSwapInPlace( DdManager * table, int x, int y) { DdNodePtr *xlist, *ylist; int xindex, yindex; int xslots, yslots; int xshift, yshift; int oldxkeys, oldykeys; int newxkeys, newykeys; int i; int posn; DdNode *f, *f1, *f0, *f11, *f10, *f01, *f00; DdNode *newf1, *newf0, *next; DdNodePtr g, *lastP, *previousP; #ifdef DD_DEBUG assert(x < y); assert(cuddZddNextHigh(table,x) == y); assert(table->subtableZ[x].keys != 0); assert(table->subtableZ[y].keys != 0); assert(table->subtableZ[x].dead == 0); assert(table->subtableZ[y].dead == 0); #endif zddTotalNumberSwapping++; /* Get parameters of x subtable. */ xindex = table->invpermZ[x]; xlist = table->subtableZ[x].nodelist; oldxkeys = table->subtableZ[x].keys; xslots = table->subtableZ[x].slots; xshift = table->subtableZ[x].shift; newxkeys = 0; yindex = table->invpermZ[y]; ylist = table->subtableZ[y].nodelist; oldykeys = table->subtableZ[y].keys; yslots = table->subtableZ[y].slots; yshift = table->subtableZ[y].shift; newykeys = oldykeys; /* The nodes in the x layer that don't depend on y directly ** will stay there; the others are put in a chain. ** The chain is handled as a FIFO; g points to the beginning and ** last points to the end. */ g = NULL; lastP = &g; for (i = 0; i < xslots; i++) { previousP = &(xlist[i]); f = *previousP; while (f != NULL) { next = f->next; f1 = cuddT(f); f0 = cuddE(f); if ((f1->index != (DdHalfWord) yindex) && (f0->index != (DdHalfWord) yindex)) { /* stays */ newxkeys++; *previousP = f; previousP = &(f->next); } else { f->index = yindex; *lastP = f; lastP = &(f->next); } f = next; } /* while there are elements in the collision chain */ *previousP = NULL; } /* for each slot of the x subtable */ *lastP = NULL; #ifdef DD_COUNT table->swapSteps += oldxkeys - newxkeys; #endif /* Take care of the x nodes that must be re-expressed. ** They form a linked list pointed by g. Their index has been ** changed to yindex already. */ f = g; while (f != NULL) { next = f->next; /* Find f1, f0, f11, f10, f01, f00. */ f1 = cuddT(f); if ((int) f1->index == yindex) { f11 = cuddT(f1); f10 = cuddE(f1); } else { f11 = empty; f10 = f1; } f0 = cuddE(f); if ((int) f0->index == yindex) { f01 = cuddT(f0); f00 = cuddE(f0); } else { f01 = empty; f00 = f0; } /* Decrease ref count of f1. */ cuddSatDec(f1->ref); /* Create the new T child. */ if (f11 == empty) { if (f01 != empty) { newf1 = f01; cuddSatInc(newf1->ref); } /* else case was already handled when finding nodes ** with both children below level y */ } else { /* Check xlist for triple (xindex, f11, f01). */ posn = ddHash(f11, f01, xshift); /* For each element newf1 in collision list xlist[posn]. */ newf1 = xlist[posn]; while (newf1 != NULL) { if (cuddT(newf1) == f11 && cuddE(newf1) == f01) { cuddSatInc(newf1->ref); break; /* match */ } newf1 = newf1->next; } /* while newf1 */ if (newf1 == NULL) { /* no match */ newf1 = cuddDynamicAllocNode(table); if (newf1 == NULL) goto zddSwapOutOfMem; newf1->index = xindex; newf1->ref = 1; cuddT(newf1) = f11; cuddE(newf1) = f01; /* Insert newf1 in the collision list xlist[pos]; ** increase the ref counts of f11 and f01 */ newxkeys++; newf1->next = xlist[posn]; xlist[posn] = newf1; cuddSatInc(f11->ref); cuddSatInc(f01->ref); } } cuddT(f) = newf1; /* Do the same for f0. */ /* Decrease ref count of f0. */ cuddSatDec(f0->ref); /* Create the new E child. */ if (f10 == empty) { newf0 = f00; cuddSatInc(newf0->ref); } else { /* Check xlist for triple (xindex, f10, f00). */ posn = ddHash(f10, f00, xshift); /* For each element newf0 in collision list xlist[posn]. */ newf0 = xlist[posn]; while (newf0 != NULL) { if (cuddT(newf0) == f10 && cuddE(newf0) == f00) { cuddSatInc(newf0->ref); break; /* match */ } newf0 = newf0->next; } /* while newf0 */ if (newf0 == NULL) { /* no match */ newf0 = cuddDynamicAllocNode(table); if (newf0 == NULL) goto zddSwapOutOfMem; newf0->index = xindex; newf0->ref = 1; cuddT(newf0) = f10; cuddE(newf0) = f00; /* Insert newf0 in the collision list xlist[posn]; ** increase the ref counts of f10 and f00. */ newxkeys++; newf0->next = xlist[posn]; xlist[posn] = newf0; cuddSatInc(f10->ref); cuddSatInc(f00->ref); } } cuddE(f) = newf0; /* Insert the modified f in ylist. ** The modified f does not already exists in ylist. ** (Because of the uniqueness of the cofactors.) */ posn = ddHash(newf1, newf0, yshift); newykeys++; f->next = ylist[posn]; ylist[posn] = f; f = next; } /* while f != NULL */ /* GC the y layer. */ /* For each node f in ylist. */ for (i = 0; i < yslots; i++) { previousP = &(ylist[i]); f = *previousP; while (f != NULL) { next = f->next; if (f->ref == 0) { cuddSatDec(cuddT(f)->ref); cuddSatDec(cuddE(f)->ref); cuddDeallocNode(table, f); newykeys--; } else { *previousP = f; previousP = &(f->next); } f = next; } /* while f */ *previousP = NULL; } /* for i */ /* Set the appropriate fields in table. */ table->subtableZ[x].nodelist = ylist; table->subtableZ[x].slots = yslots; table->subtableZ[x].shift = yshift; table->subtableZ[x].keys = newykeys; table->subtableZ[x].maxKeys = yslots * DD_MAX_SUBTABLE_DENSITY; table->subtableZ[y].nodelist = xlist; table->subtableZ[y].slots = xslots; table->subtableZ[y].shift = xshift; table->subtableZ[y].keys = newxkeys; table->subtableZ[y].maxKeys = xslots * DD_MAX_SUBTABLE_DENSITY; table->permZ[xindex] = y; table->permZ[yindex] = x; table->invpermZ[x] = yindex; table->invpermZ[y] = xindex; table->keysZ += newxkeys + newykeys - oldxkeys - oldykeys; /* Update univ section; univ[x] remains the same. */ table->univ[y] = cuddT(table->univ[x]); return (table->keysZ); zddSwapOutOfMem: (void) fprintf(table->err, "Error: cuddZddSwapInPlace out of memory\n"); return (0); } /* end of cuddZddSwapInPlace */ /**Function******************************************************************** Synopsis [Reorders variables by a sequence of (non-adjacent) swaps.] Description [Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.

  1. Select two variables (RANDOM or HEURISTIC).
  2. Permute these variables.
  3. If the nodes have decreased accept the permutation.
  4. Otherwise reconstruct the original heap.
  5. Loop.
Returns 1 in case of success; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddSwapping( DdManager * table, int lower, int upper, Cudd_ReorderingType heuristic) { int i, j; int max, keys; int nvars; int x, y; int iterate; int previousSize; Move *moves, *move; int pivot; int modulo; int result; #ifdef DD_DEBUG /* Sanity check */ assert(lower >= 0 && upper < table->sizeZ && lower <= upper); #endif nvars = upper - lower + 1; iterate = nvars; for (i = 0; i < iterate; i++) { if (heuristic == CUDD_REORDER_RANDOM_PIVOT) { /* Find pivot <= id with maximum keys. */ for (max = -1, j = lower; j <= upper; j++) { if ((keys = table->subtableZ[j].keys) > max) { max = keys; pivot = j; } } modulo = upper - pivot; if (modulo == 0) { y = pivot; /* y = nvars-1 */ } else { /* y = random # from {pivot+1 .. nvars-1} */ y = pivot + 1 + (int) (Cudd_Random() % modulo); } modulo = pivot - lower - 1; if (modulo < 1) { /* if pivot = 1 or 0 */ x = lower; } else { do { /* x = random # from {0 .. pivot-2} */ x = (int) Cudd_Random() % modulo; } while (x == y); /* Is this condition really needed, since x and y are in regions separated by pivot? */ } } else { x = (int) (Cudd_Random() % nvars) + lower; do { y = (int) (Cudd_Random() % nvars) + lower; } while (x == y); } previousSize = table->keysZ; moves = zddSwapAny(table, x, y); if (moves == NULL) goto cuddZddSwappingOutOfMem; result = cuddZddSiftingBackward(table, moves, previousSize); if (!result) goto cuddZddSwappingOutOfMem; while (moves != NULL) { move = moves->next; cuddDeallocMove(table, moves); moves = move; } #ifdef DD_STATS if (table->keysZ < (unsigned) previousSize) { (void) fprintf(table->out,"-"); } else if (table->keysZ > (unsigned) previousSize) { (void) fprintf(table->out,"+"); /* should never happen */ } else { (void) fprintf(table->out,"="); } fflush(table->out); #endif } return(1); cuddZddSwappingOutOfMem: while (moves != NULL) { move = moves->next; cuddDeallocMove(table, moves); moves = move; } return(0); } /* end of cuddZddSwapping */ /**Function******************************************************************** Synopsis [Implementation of Rudell's sifting algorithm.] Description [Implementation of Rudell's sifting algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique table.
  2. Sift the variable up and down, remembering each time the total size of the DD heap.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddZddSifting( DdManager * table, int lower, int upper) { int i; int *var; int size; int x; int result; #ifdef DD_STATS int previousSize; #endif size = table->sizeZ; /* Find order in which to sift variables. */ var = NULL; zdd_entry = ABC_ALLOC(int, size); if (zdd_entry == NULL) { table->errorCode = CUDD_MEMORY_OUT; goto cuddZddSiftingOutOfMem; } var = ABC_ALLOC(int, size); if (var == NULL) { table->errorCode = CUDD_MEMORY_OUT; goto cuddZddSiftingOutOfMem; } for (i = 0; i < size; i++) { x = table->permZ[i]; zdd_entry[i] = table->subtableZ[x].keys; var[i] = i; } qsort((void *)var, size, sizeof(int), (DD_QSFP)cuddZddUniqueCompare); /* Now sift. */ for (i = 0; i < ddMin(table->siftMaxVar, size); i++) { if (zddTotalNumberSwapping >= table->siftMaxSwap) break; x = table->permZ[var[i]]; if (x < lower || x > upper) continue; #ifdef DD_STATS previousSize = table->keysZ; #endif result = cuddZddSiftingAux(table, x, lower, upper); if (!result) goto cuddZddSiftingOutOfMem; #ifdef DD_STATS if (table->keysZ < (unsigned) previousSize) { (void) fprintf(table->out,"-"); } else if (table->keysZ > (unsigned) previousSize) { (void) fprintf(table->out,"+"); /* should never happen */ (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ , var[i]); } else { (void) fprintf(table->out,"="); } fflush(table->out); #endif } ABC_FREE(var); ABC_FREE(zdd_entry); return(1); cuddZddSiftingOutOfMem: if (zdd_entry != NULL) ABC_FREE(zdd_entry); if (var != NULL) ABC_FREE(var); return(0); } /* end of cuddZddSifting */ /*---------------------------------------------------------------------------*/ /* Definition of static functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Swaps any two variables.] Description [Swaps any two variables. Returns the set of moves.] SideEffects [None] SeeAlso [] ******************************************************************************/ static Move * zddSwapAny( DdManager * table, int x, int y) { Move *move, *moves; int tmp, size; int x_ref, y_ref; int x_next, y_next; int limit_size; if (x > y) { /* make x precede y */ tmp = x; x = y; y = tmp; } x_ref = x; y_ref = y; x_next = cuddZddNextHigh(table, x); y_next = cuddZddNextLow(table, y); moves = NULL; limit_size = table->keysZ; for (;;) { if (x_next == y_next) { /* x < x_next = y_next < y */ size = cuddZddSwapInPlace(table, x, x_next); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *) cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = x; move->y = x_next; move->size = size; move->next = moves; moves = move; size = cuddZddSwapInPlace(table, y_next, y); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = y_next; move->y = y; move->size = size; move->next = moves; moves = move; size = cuddZddSwapInPlace(table, x, x_next); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = x; move->y = x_next; move->size = size; move->next = moves; moves = move; tmp = x; x = y; y = tmp; } else if (x == y_next) { /* x = y_next < y = x_next */ size = cuddZddSwapInPlace(table, x, x_next); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = x; move->y = x_next; move->size = size; move->next = moves; moves = move; tmp = x; x = y; y = tmp; } else { size = cuddZddSwapInPlace(table, x, x_next); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = x; move->y = x_next; move->size = size; move->next = moves; moves = move; size = cuddZddSwapInPlace(table, y_next, y); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = y_next; move->y = y; move->size = size; move->next = moves; moves = move; x = x_next; y = y_next; } x_next = cuddZddNextHigh(table, x); y_next = cuddZddNextLow(table, y); if (x_next > y_ref) break; /* if x == y_ref */ if ((double) size > table->maxGrowth * (double) limit_size) break; if (size < limit_size) limit_size = size; } if (y_next >= x_ref) { size = cuddZddSwapInPlace(table, y_next, y); if (size == 0) goto zddSwapAnyOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto zddSwapAnyOutOfMem; move->x = y_next; move->y = y; move->size = size; move->next = moves; moves = move; } return(moves); zddSwapAnyOutOfMem: while (moves != NULL) { move = moves->next; cuddDeallocMove(table, moves); moves = move; } return(NULL); } /* end of zddSwapAny */ /**Function******************************************************************** Synopsis [Given xLow <= x <= xHigh moves x up and down between the boundaries.] Description [Given xLow <= x <= xHigh moves x up and down between the boundaries. Finds the best position and does the required changes. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int cuddZddSiftingAux( DdManager * table, int x, int x_low, int x_high) { Move *move; Move *moveUp; /* list of up move */ Move *moveDown; /* list of down move */ int initial_size; int result; initial_size = table->keysZ; #ifdef DD_DEBUG assert(table->subtableZ[x].keys > 0); #endif moveDown = NULL; moveUp = NULL; if (x == x_low) { moveDown = cuddZddSiftingDown(table, x, x_high, initial_size); /* after that point x --> x_high */ if (moveDown == NULL) goto cuddZddSiftingAuxOutOfMem; result = cuddZddSiftingBackward(table, moveDown, initial_size); /* move backward and stop at best position */ if (!result) goto cuddZddSiftingAuxOutOfMem; } else if (x == x_high) { moveUp = cuddZddSiftingUp(table, x, x_low, initial_size); /* after that point x --> x_low */ if (moveUp == NULL) goto cuddZddSiftingAuxOutOfMem; result = cuddZddSiftingBackward(table, moveUp, initial_size); /* move backward and stop at best position */ if (!result) goto cuddZddSiftingAuxOutOfMem; } else if ((x - x_low) > (x_high - x)) { /* must go down first:shorter */ moveDown = cuddZddSiftingDown(table, x, x_high, initial_size); /* after that point x --> x_high */ if (moveDown == NULL) goto cuddZddSiftingAuxOutOfMem; moveUp = cuddZddSiftingUp(table, moveDown->y, x_low, initial_size); if (moveUp == NULL) goto cuddZddSiftingAuxOutOfMem; result = cuddZddSiftingBackward(table, moveUp, initial_size); /* move backward and stop at best position */ if (!result) goto cuddZddSiftingAuxOutOfMem; } else { moveUp = cuddZddSiftingUp(table, x, x_low, initial_size); /* after that point x --> x_high */ if (moveUp == NULL) goto cuddZddSiftingAuxOutOfMem; moveDown = cuddZddSiftingDown(table, moveUp->x, x_high, initial_size); /* then move up */ if (moveDown == NULL) goto cuddZddSiftingAuxOutOfMem; result = cuddZddSiftingBackward(table, moveDown, initial_size); /* move backward and stop at best position */ if (!result) goto cuddZddSiftingAuxOutOfMem; } while (moveDown != NULL) { move = moveDown->next; cuddDeallocMove(table, moveDown); moveDown = move; } while (moveUp != NULL) { move = moveUp->next; cuddDeallocMove(table, moveUp); moveUp = move; } return(1); cuddZddSiftingAuxOutOfMem: while (moveDown != NULL) { move = moveDown->next; cuddDeallocMove(table, moveDown); moveDown = move; } while (moveUp != NULL) { move = moveUp->next; cuddDeallocMove(table, moveUp); moveUp = move; } return(0); } /* end of cuddZddSiftingAux */ /**Function******************************************************************** Synopsis [Sifts a variable up.] Description [Sifts a variable up. Moves y up until either it reaches the bound (x_low) or the size of the ZDD heap increases too much. Returns the set of moves in case of success; NULL if memory is full.] SideEffects [None] SeeAlso [] ******************************************************************************/ static Move * cuddZddSiftingUp( DdManager * table, int x, int x_low, int initial_size) { Move *moves; Move *move; int y; int size; int limit_size = initial_size; moves = NULL; y = cuddZddNextLow(table, x); while (y >= x_low) { size = cuddZddSwapInPlace(table, y, x); if (size == 0) goto cuddZddSiftingUpOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto cuddZddSiftingUpOutOfMem; move->x = y; move->y = x; move->size = size; move->next = moves; moves = move; if ((double)size > (double)limit_size * table->maxGrowth) break; if (size < limit_size) limit_size = size; x = y; y = cuddZddNextLow(table, x); } return(moves); cuddZddSiftingUpOutOfMem: while (moves != NULL) { move = moves->next; cuddDeallocMove(table, moves); moves = move; } return(NULL); } /* end of cuddZddSiftingUp */ /**Function******************************************************************** Synopsis [Sifts a variable down.] Description [Sifts a variable down. Moves x down until either it reaches the bound (x_high) or the size of the ZDD heap increases too much. Returns the set of moves in case of success; NULL if memory is full.] SideEffects [None] SeeAlso [] ******************************************************************************/ static Move * cuddZddSiftingDown( DdManager * table, int x, int x_high, int initial_size) { Move *moves; Move *move; int y; int size; int limit_size = initial_size; moves = NULL; y = cuddZddNextHigh(table, x); while (y <= x_high) { size = cuddZddSwapInPlace(table, x, y); if (size == 0) goto cuddZddSiftingDownOutOfMem; move = (Move *)cuddDynamicAllocNode(table); if (move == NULL) goto cuddZddSiftingDownOutOfMem; move->x = x; move->y = y; move->size = size; move->next = moves; moves = move; if ((double)size > (double)limit_size * table->maxGrowth) break; if (size < limit_size) limit_size = size; x = y; y = cuddZddNextHigh(table, x); } return(moves); cuddZddSiftingDownOutOfMem: while (moves != NULL) { move = moves->next; cuddDeallocMove(table, moves); moves = move; } return(NULL); } /* end of cuddZddSiftingDown */ /**Function******************************************************************** Synopsis [Given a set of moves, returns the ZDD heap to the position giving the minimum size.] Description [Given a set of moves, returns the ZDD heap to the position giving the minimum size. In case of ties, returns to the closest position giving the minimum size. Returns 1 in case of success; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int cuddZddSiftingBackward( DdManager * table, Move * moves, int size) { int i; int i_best; Move *move; int res; /* Find the minimum size among moves. */ i_best = -1; for (move = moves, i = 0; move != NULL; move = move->next, i++) { if (move->size < size) { i_best = i; size = move->size; } } for (move = moves, i = 0; move != NULL; move = move->next, i++) { if (i == i_best) break; res = cuddZddSwapInPlace(table, move->x, move->y); if (!res) return(0); if (i_best == -1 && res == size) break; } return(1); } /* end of cuddZddSiftingBackward */ /**Function******************************************************************** Synopsis [Prepares the ZDD heap for dynamic reordering.] Description [Prepares the ZDD heap for dynamic reordering. Does garbage collection, to guarantee that there are no dead nodes; and clears the cache, which is invalidated by dynamic reordering.] SideEffects [None] ******************************************************************************/ static void zddReorderPreprocess( DdManager * table) { /* Clear the cache. */ cuddCacheFlush(table); /* Eliminate dead nodes. Do not scan the cache again. */ cuddGarbageCollect(table,0); return; } /* end of ddReorderPreprocess */ /**Function******************************************************************** Synopsis [Shrinks almost empty ZDD subtables at the end of reordering to guarantee that they have a reasonable load factor.] Description [Shrinks almost empty subtables at the end of reordering to guarantee that they have a reasonable load factor. However, if there many nodes are being reclaimed, then no resizing occurs. Returns 1 in case of success; 0 otherwise.] SideEffects [None] ******************************************************************************/ static int zddReorderPostprocess( DdManager * table) { int i, j, posn; DdNodePtr *nodelist, *oldnodelist; DdNode *node, *next; unsigned int slots, oldslots; extern DD_OOMFP MMoutOfMemory; DD_OOMFP saveHandler; #ifdef DD_VERBOSE (void) fflush(table->out); #endif /* If we have very many reclaimed nodes, we do not want to shrink ** the subtables, because this will lead to more garbage ** collections. More garbage collections mean shorter mean life for ** nodes with zero reference count; hence lower probability of finding ** a result in the cache. */ if (table->reclaimed > table->allocated * 0.5) return(1); /* Resize subtables. */ for (i = 0; i < table->sizeZ; i++) { int shift; oldslots = table->subtableZ[i].slots; if (oldslots < table->subtableZ[i].keys * DD_MAX_SUBTABLE_SPARSITY || oldslots <= table->initSlots) continue; oldnodelist = table->subtableZ[i].nodelist; slots = oldslots >> 1; saveHandler = MMoutOfMemory; MMoutOfMemory = Cudd_OutOfMem; nodelist = ABC_ALLOC(DdNodePtr, slots); MMoutOfMemory = saveHandler; if (nodelist == NULL) { return(1); } table->subtableZ[i].nodelist = nodelist; table->subtableZ[i].slots = slots; table->subtableZ[i].shift++; table->subtableZ[i].maxKeys = slots * DD_MAX_SUBTABLE_DENSITY; #ifdef DD_VERBOSE (void) fprintf(table->err, "shrunk layer %d (%d keys) from %d to %d slots\n", i, table->subtableZ[i].keys, oldslots, slots); #endif for (j = 0; (unsigned) j < slots; j++) { nodelist[j] = NULL; } shift = table->subtableZ[i].shift; for (j = 0; (unsigned) j < oldslots; j++) { node = oldnodelist[j]; while (node != NULL) { next = node->next; posn = ddHash(cuddT(node), cuddE(node), shift); node->next = nodelist[posn]; nodelist[posn] = node; node = next; } } ABC_FREE(oldnodelist); table->memused += (slots - oldslots) * sizeof(DdNode *); table->slots += slots - oldslots; table->minDead = (unsigned) (table->gcFrac * (double) table->slots); table->cacheSlack = (int) ddMin(table->maxCacheHard, DD_MAX_CACHE_TO_SLOTS_RATIO*table->slots) - 2 * (int) table->cacheSlots; } /* We don't look at the constant subtable, because it is not ** affected by reordering. */ return(1); } /* end of zddReorderPostprocess */ /**Function******************************************************************** Synopsis [Reorders ZDD variables according to a given permutation.] Description [Reorders ZDD 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. zddShuffle assumes that no dead nodes are present. The reordering is achieved by a series of upward sifts. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static int zddShuffle( DdManager * table, int * permutation) { int index; int level; int position; int numvars; int result; #ifdef DD_STATS long localTime; int initialSize; int finalSize; int previousSize; #endif zddTotalNumberSwapping = 0; #ifdef DD_STATS localTime = util_cpu_time(); initialSize = table->keysZ; (void) fprintf(table->out,"#:I_SHUFFLE %8d: initial size\n", initialSize); #endif numvars = table->sizeZ; for (level = 0; level < numvars; level++) { index = permutation[level]; position = table->permZ[index]; #ifdef DD_STATS previousSize = table->keysZ; #endif result = zddSiftUp(table,position,level); if (!result) return(0); #ifdef DD_STATS if (table->keysZ < (unsigned) previousSize) { (void) fprintf(table->out,"-"); } else if (table->keysZ > (unsigned) previousSize) { (void) fprintf(table->out,"+"); /* should never happen */ } else { (void) fprintf(table->out,"="); } fflush(table->out); #endif } #ifdef DD_STATS (void) fprintf(table->out,"\n"); finalSize = table->keysZ; (void) fprintf(table->out,"#:F_SHUFFLE %8d: final size\n",finalSize); (void) fprintf(table->out,"#:T_SHUFFLE %8g: total time (sec)\n", ((double)(util_cpu_time() - localTime)/1000.0)); (void) fprintf(table->out,"#:N_SHUFFLE %8d: total swaps\n", zddTotalNumberSwapping); #endif return(1); } /* end of zddShuffle */ /**Function******************************************************************** Synopsis [Moves one ZDD variable up.] Description [Takes a ZDD 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 zddSiftUp( DdManager * table, int x, int xLow) { int y; int size; y = cuddZddNextLow(table,x); while (y >= xLow) { size = cuddZddSwapInPlace(table,y,x); if (size == 0) { return(0); } x = y; y = cuddZddNextLow(table,x); } return(1); } /* end of zddSiftUp */ /**Function******************************************************************** Synopsis [Fixes the ZDD variable group tree after a shuffle.] Description [Fixes the ZDD variable group tree after a shuffle. Assumes that the order of the variables in a terminal node has not been changed.] SideEffects [Changes the ZDD variable group tree.] SeeAlso [] ******************************************************************************/ static void zddFixTree( DdManager * table, MtrNode * treenode) { if (treenode == NULL) return; treenode->low = ((int) treenode->index < table->sizeZ) ? table->permZ[treenode->index] : treenode->index; if (treenode->child != NULL) { zddFixTree(table, treenode->child); } if (treenode->younger != NULL) zddFixTree(table, treenode->younger); if (treenode->parent != NULL && treenode->low < treenode->parent->low) { treenode->parent->low = treenode->low; treenode->parent->index = treenode->index; } return; } /* end of zddFixTree */ ABC_NAMESPACE_IMPL_END