The computation of the interaction matrix is done with a series of depth-first searches. The searches start from those nodes that have only external references. The matrix is stored as a packed array of bits; since it is symmetric, only the upper triangle is kept in memory. As a final remark, we note that there may be variables that do intercat, but that for a given variable order have no arc connecting their layers when they are adjacent.] SeeAlso [] Author [Fabio Somenzi] 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.h" #include "cuddInt.h" /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ #if SIZEOF_LONG == 8 #define BPL 64 #define LOGBPL 6 #else #define BPL 32 #define LOGBPL 5 #endif /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddInteract.c,v 1.12 2004/08/13 18:04:49 fabio Exp $"; #endif /*---------------------------------------------------------------------------*/ /* Macro declarations */ /*---------------------------------------------------------------------------*/ /**AutomaticStart*************************************************************/ /*---------------------------------------------------------------------------*/ /* Static function prototypes */ /*---------------------------------------------------------------------------*/ static void ddSuppInteract (DdNode *f, int *support); static void ddClearLocal (DdNode *f); static void ddUpdateInteract (DdManager *table, int *support); static void ddClearGlobal (DdManager *table); /**AutomaticEnd***************************************************************/ /*---------------------------------------------------------------------------*/ /* Definition of exported functions */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Definition of internal functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Set interaction matrix entries.] Description [Given a pair of variables 0 <= x < y < table->size, sets the corresponding bit of the interaction matrix to 1.] SideEffects [None] SeeAlso [] ******************************************************************************/ void cuddSetInteract( DdManager * table, int x, int y) { int posn, word, bit; #ifdef DD_DEBUG assert(x < y); assert(y < table->size); assert(x >= 0); #endif posn = ((((table->size << 1) - x - 3) * x) >> 1) + y - 1; word = posn >> LOGBPL; bit = posn & (BPL-1); table->interact[word] |= 1L << bit; } /* end of cuddSetInteract */ /**Function******************************************************************** Synopsis [Test interaction matrix entries.] Description [Given a pair of variables 0 <= x < y < table->size, tests whether the corresponding bit of the interaction matrix is 1. Returns the value of the bit.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddTestInteract( DdManager * table, int x, int y) { int posn, word, bit, result; if (x > y) { int tmp = x; x = y; y = tmp; } #ifdef DD_DEBUG assert(x < y); assert(y < table->size); assert(x >= 0); #endif posn = ((((table->size << 1) - x - 3) * x) >> 1) + y - 1; word = posn >> LOGBPL; bit = posn & (BPL-1); result = (table->interact[word] >> bit) & 1L; return(result); } /* end of cuddTestInteract */ /**Function******************************************************************** Synopsis [Initializes the interaction matrix.] Description [Initializes the interaction matrix. The interaction matrix is implemented as a bit vector storing the upper triangle of the symmetric interaction matrix. The bit vector is kept in an array of long integers. The computation is based on a series of depth-first searches, one for each root of the DAG. Two flags are needed: The local visited flag uses the LSB of the then pointer. The global visited flag uses the LSB of the next pointer. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int cuddInitInteract( DdManager * table) { int i,j,k; int words; long *interact; int *support; DdNode *f; DdNode *sentinel = &(table->sentinel); DdNodePtr *nodelist; int slots; int n = table->size; words = ((n * (n-1)) >> (1 + LOGBPL)) + 1; table->interact = interact = ALLOC(long,words); if (interact == NULL) { table->errorCode = CUDD_MEMORY_OUT; return(0); } for (i = 0; i < words; i++) { interact[i] = 0; } support = ALLOC(int,n); if (support == NULL) { table->errorCode = CUDD_MEMORY_OUT; FREE(interact); return(0); } for (i = 0; i < n; 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)) { for (k = 0; k < n; k++) { support[k] = 0; } ddSuppInteract(f,support); ddClearLocal(f); ddUpdateInteract(table,support); } f = Cudd_Regular(f->next); } } } ddClearGlobal(table); FREE(support); return(1); } /* end of cuddInitInteract */ /*---------------------------------------------------------------------------*/ /* Definition of static functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Find the support of f.] Description [Performs a DFS from f. Uses the LSB of the then pointer as visited flag.] SideEffects [Accumulates in support the variables on which f depends.] SeeAlso [] ******************************************************************************/ static void ddSuppInteract( DdNode * f, int * support) { if (cuddIsConstant(f) || Cudd_IsComplement(cuddT(f))) { return; } support[f->index] = 1; ddSuppInteract(cuddT(f),support); ddSuppInteract(Cudd_Regular(cuddE(f)),support); /* mark as visited */ cuddT(f) = Cudd_Complement(cuddT(f)); f->next = Cudd_Complement(f->next); return; } /* end of ddSuppInteract */ /**Function******************************************************************** Synopsis [Performs a DFS from f, clearing the LSB of the then pointers.] Description [] SideEffects [None] SeeAlso [] ******************************************************************************/ static void ddClearLocal( DdNode * f) { if (cuddIsConstant(f) || !Cudd_IsComplement(cuddT(f))) { return; } /* clear visited flag */ cuddT(f) = Cudd_Regular(cuddT(f)); ddClearLocal(cuddT(f)); ddClearLocal(Cudd_Regular(cuddE(f))); return; } /* end of ddClearLocal */ /**Function******************************************************************** Synopsis [Marks as interacting all pairs of variables that appear in support.] Description [If support[i] == support[j] == 1, sets the (i,j) entry of the interaction matrix to 1.] SideEffects [None] SeeAlso [] ******************************************************************************/ static void ddUpdateInteract( DdManager * table, int * support) { int i,j; int n = table->size; for (i = 0; i < n-1; i++) { if (support[i] == 1) { for (j = i+1; j < n; j++) { if (support[j] == 1) { cuddSetInteract(table,i,j); } } } } } /* end of ddUpdateInteract */ /**Function******************************************************************** Synopsis [Scans the DD and clears the LSB of the next pointers.] Description [The LSB of the next pointers are used as markers to tell whether a node was reached by at least one DFS. Once the interaction matrix is built, these flags are reset.] SideEffects [None] SeeAlso [] ******************************************************************************/ static void ddClearGlobal( DdManager * table) { int i,j; DdNode *f; DdNode *sentinel = &(table->sentinel); DdNodePtr *nodelist; int slots; for (i = 0; i < table->size; 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 */