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978 lines
26 KiB
978 lines
26 KiB
/**
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@file
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@ingroup cudd
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@brief Quantification functions for BDDs.
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@author Fabio Somenzi
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@copyright@parblock
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Copyright (c) 1995-2015, Regents of the University of Colorado
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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Neither the name of the University of Colorado nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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@endparblock
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*/
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#include "util.h"
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#include "cuddInt.h"
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/*---------------------------------------------------------------------------*/
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/* Constant declarations */
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/*---------------------------------------------------------------------------*/
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/*---------------------------------------------------------------------------*/
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/* Stucture declarations */
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/*---------------------------------------------------------------------------*/
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/*---------------------------------------------------------------------------*/
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/* Type declarations */
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/*---------------------------------------------------------------------------*/
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/*---------------------------------------------------------------------------*/
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/* Variable declarations */
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/*---------------------------------------------------------------------------*/
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/*---------------------------------------------------------------------------*/
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/* Macro declarations */
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/*---------------------------------------------------------------------------*/
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/** \cond */
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/*---------------------------------------------------------------------------*/
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/* Static function prototypes */
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/*---------------------------------------------------------------------------*/
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static int bddCheckPositiveCube (DdManager *manager, DdNode *cube);
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/** \endcond */
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/*---------------------------------------------------------------------------*/
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/* Definition of exported functions */
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/*---------------------------------------------------------------------------*/
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/**
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@brief Existentially abstracts all the variables in cube from f.
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@return the abstracted %BDD if successful; NULL otherwise.
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@sideeffect None
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@see Cudd_bddUnivAbstract Cudd_addExistAbstract
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*/
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DdNode *
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Cudd_bddExistAbstract(
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DdManager * manager,
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DdNode * f,
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DdNode * cube)
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{
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DdNode *res;
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if (bddCheckPositiveCube(manager, cube) == 0) {
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(void) fprintf(manager->err,
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"Error: Can only abstract positive cubes\n");
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manager->errorCode = CUDD_INVALID_ARG;
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return(NULL);
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}
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do {
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manager->reordered = 0;
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res = cuddBddExistAbstractRecur(manager, f, cube);
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} while (manager->reordered == 1);
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if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
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manager->timeoutHandler(manager, manager->tohArg);
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}
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return(res);
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} /* end of Cudd_bddExistAbstract */
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/**Function********************************************************************
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Synopsis [Just like Cudd_bddExistAbstract, but instead of abstracting the
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variables in the given cube, picks a unique representative that realizes the
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existential truth value.]
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Description [Returns the resulting BDD if successful; NULL otherwise.]
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SideEffects [None]
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SeeAlso []
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Note: Added by Christian Dehnert 9/21/15
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******************************************************************************/
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DdNode *
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Cudd_bddExistAbstractRepresentative(
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DdManager * manager,
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DdNode * f,
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DdNode * cube)
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{
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DdNode *res;
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if (bddCheckPositiveCube(manager, cube) == 0) {
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(void) fprintf(manager->err,"Error: Can only abstract positive cubes\n");
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manager->errorCode = CUDD_INVALID_ARG;
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return(NULL);
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}
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do {
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manager->reordered = 0;
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res = cuddBddExistAbstractRepresentativeRecur(manager, f, cube);
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} while (manager->reordered == 1);
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return(res);
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} /* end of Cudd_bddExistAbstractRepresentative */
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/**
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@brief Existentially abstracts all the variables in cube from f.
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@return the abstracted %BDD if successful; NULL if the intermediate
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result blows up or more new nodes than <code>limit</code> are
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required.
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@sideeffect None
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@see Cudd_bddExistAbstract
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*/
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DdNode *
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Cudd_bddExistAbstractLimit(
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DdManager * manager,
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DdNode * f,
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DdNode * cube,
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unsigned int limit)
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{
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DdNode *res;
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unsigned int saveLimit = manager->maxLive;
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if (bddCheckPositiveCube(manager, cube) == 0) {
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(void) fprintf(manager->err,
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"Error: Can only abstract positive cubes\n");
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manager->errorCode = CUDD_INVALID_ARG;
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return(NULL);
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}
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manager->maxLive = (manager->keys - manager->dead) +
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(manager->keysZ - manager->deadZ) + limit;
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do {
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manager->reordered = 0;
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res = cuddBddExistAbstractRecur(manager, f, cube);
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} while (manager->reordered == 1);
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manager->maxLive = saveLimit;
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if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
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manager->timeoutHandler(manager, manager->tohArg);
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}
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return(res);
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} /* end of Cudd_bddExistAbstractLimit */
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/**
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@brief Takes the exclusive OR of two BDDs and simultaneously abstracts the
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variables in cube.
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@details The variables are existentially abstracted.
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@return a pointer to the result is successful; NULL otherwise.
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@sideeffect None
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@see Cudd_bddUnivAbstract Cudd_bddExistAbstract Cudd_bddAndAbstract
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*/
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DdNode *
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Cudd_bddXorExistAbstract(
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DdManager * manager,
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DdNode * f,
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DdNode * g,
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DdNode * cube)
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{
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DdNode *res;
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if (bddCheckPositiveCube(manager, cube) == 0) {
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(void) fprintf(manager->err,
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"Error: Can only abstract positive cubes\n");
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manager->errorCode = CUDD_INVALID_ARG;
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return(NULL);
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}
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do {
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manager->reordered = 0;
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res = cuddBddXorExistAbstractRecur(manager, f, g, cube);
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} while (manager->reordered == 1);
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if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
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manager->timeoutHandler(manager, manager->tohArg);
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}
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return(res);
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} /* end of Cudd_bddXorExistAbstract */
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/**
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@brief Universally abstracts all the variables in cube from f.
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@return the abstracted %BDD if successful; NULL otherwise.
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@sideeffect None
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@see Cudd_bddExistAbstract Cudd_addUnivAbstract
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*/
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DdNode *
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Cudd_bddUnivAbstract(
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DdManager * manager,
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DdNode * f,
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DdNode * cube)
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{
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DdNode *res;
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if (bddCheckPositiveCube(manager, cube) == 0) {
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(void) fprintf(manager->err,
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"Error: Can only abstract positive cubes\n");
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manager->errorCode = CUDD_INVALID_ARG;
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return(NULL);
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}
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do {
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manager->reordered = 0;
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res = cuddBddExistAbstractRecur(manager, Cudd_Not(f), cube);
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} while (manager->reordered == 1);
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if (res != NULL) res = Cudd_Not(res);
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if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
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manager->timeoutHandler(manager, manager->tohArg);
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}
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return(res);
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} /* end of Cudd_bddUnivAbstract */
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/**
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@brief Computes the boolean difference of f with respect to x.
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@details Computes the boolean difference of f with respect to the
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variable with index x.
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@return the %BDD of the boolean difference if successful; NULL
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otherwise.
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@sideeffect None
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*/
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DdNode *
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Cudd_bddBooleanDiff(
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DdManager * manager,
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DdNode * f,
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int x)
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{
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DdNode *res, *var;
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/* If the variable is not currently in the manager, f cannot
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** depend on it.
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*/
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if (x >= manager->size) return(Cudd_Not(DD_ONE(manager)));
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var = manager->vars[x];
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do {
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manager->reordered = 0;
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res = cuddBddBooleanDiffRecur(manager, Cudd_Regular(f), var);
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} while (manager->reordered == 1);
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if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
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manager->timeoutHandler(manager, manager->tohArg);
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}
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return(res);
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} /* end of Cudd_bddBooleanDiff */
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/**
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@brief Checks whether a variable is dependent on others in a
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function.
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@details No new nodes are created.
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@return 1 if the variable is dependent; 0 otherwise.
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@sideeffect None
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*/
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int
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Cudd_bddVarIsDependent(
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DdManager *dd, /**< manager */
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DdNode *f, /**< function */
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DdNode *var /**< variable */)
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{
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DdNode *F, *res, *zero, *ft, *fe;
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unsigned topf, level;
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DD_CTFP cacheOp;
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int retval;
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zero = Cudd_Not(DD_ONE(dd));
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F = Cudd_Regular(f);
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if (cuddIsConstant(F)) return(f == zero);
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/* From now on f is not constant. */
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topf = (unsigned) dd->perm[F->index];
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level = (unsigned) dd->perm[var->index];
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/* Check terminal case. If topf > index of var, f does not depend on var.
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** Therefore, var is not dependent in f. */
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if (topf > level) {
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return(0);
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}
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cacheOp = (DD_CTFP) Cudd_bddVarIsDependent;
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res = cuddCacheLookup2(dd,cacheOp,f,var);
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if (res != NULL) {
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return(res != zero);
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}
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/* Compute cofactors. */
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ft = Cudd_NotCond(cuddT(F), f != F);
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fe = Cudd_NotCond(cuddE(F), f != F);
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if (topf == level) {
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retval = Cudd_bddLeq(dd,ft,Cudd_Not(fe));
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} else {
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retval = Cudd_bddVarIsDependent(dd,ft,var) &&
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Cudd_bddVarIsDependent(dd,fe,var);
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}
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cuddCacheInsert2(dd,cacheOp,f,var,Cudd_NotCond(zero,retval));
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return(retval);
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} /* Cudd_bddVarIsDependent */
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/*---------------------------------------------------------------------------*/
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/* Definition of internal functions */
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/*---------------------------------------------------------------------------*/
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/**
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@brief Performs the recursive steps of Cudd_bddExistAbstract.
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@details It is also used by Cudd_bddUnivAbstract.
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@return the %BDD obtained by abstracting the variables of cube from f
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if successful; NULL otherwise.
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@sideeffect None
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@see Cudd_bddExistAbstract Cudd_bddUnivAbstract
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*/
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DdNode *
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cuddBddExistAbstractRecur(
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DdManager * manager,
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DdNode * f,
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DdNode * cube)
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{
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DdNode *F, *T, *E, *res, *res1, *res2, *one;
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statLine(manager);
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one = DD_ONE(manager);
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F = Cudd_Regular(f);
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/* Cube is guaranteed to be a cube at this point. */
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if (cube == one || F == one) {
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return(f);
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}
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/* From now on, f and cube are non-constant. */
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/* Abstract a variable that does not appear in f. */
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while (manager->perm[F->index] > manager->perm[cube->index]) {
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cube = cuddT(cube);
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if (cube == one) return(f);
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}
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/* Check the cache. */
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if (F->ref != 1 && (res = cuddCacheLookup2(manager, Cudd_bddExistAbstract, f, cube)) != NULL) {
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return(res);
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}
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checkWhetherToGiveUp(manager);
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/* Compute the cofactors of f. */
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T = cuddT(F); E = cuddE(F);
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if (f != F) {
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T = Cudd_Not(T); E = Cudd_Not(E);
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}
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/* If the two indices are the same, so are their levels. */
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if (F->index == cube->index) {
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if (T == one || E == one || T == Cudd_Not(E)) {
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return(one);
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}
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res1 = cuddBddExistAbstractRecur(manager, T, cuddT(cube));
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if (res1 == NULL) return(NULL);
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if (res1 == one) {
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if (F->ref != 1)
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cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, one);
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return(one);
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}
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cuddRef(res1);
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res2 = cuddBddExistAbstractRecur(manager, E, cuddT(cube));
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if (res2 == NULL) {
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Cudd_IterDerefBdd(manager,res1);
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return(NULL);
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}
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cuddRef(res2);
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res = cuddBddAndRecur(manager, Cudd_Not(res1), Cudd_Not(res2));
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if (res == NULL) {
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Cudd_IterDerefBdd(manager, res1);
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Cudd_IterDerefBdd(manager, res2);
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return(NULL);
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}
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res = Cudd_Not(res);
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cuddRef(res);
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Cudd_IterDerefBdd(manager, res1);
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Cudd_IterDerefBdd(manager, res2);
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if (F->ref != 1)
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cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
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cuddDeref(res);
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return(res);
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} else { /* if (cuddI(manager,F->index) < cuddI(manager,cube->index)) */
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res1 = cuddBddExistAbstractRecur(manager, T, cube);
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if (res1 == NULL) return(NULL);
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cuddRef(res1);
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res2 = cuddBddExistAbstractRecur(manager, E, cube);
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if (res2 == NULL) {
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Cudd_IterDerefBdd(manager, res1);
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return(NULL);
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}
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cuddRef(res2);
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/* ITE takes care of possible complementation of res1 and of the
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** case in which res1 == res2. */
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res = cuddBddIteRecur(manager, manager->vars[F->index], res1, res2);
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if (res == NULL) {
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Cudd_IterDerefBdd(manager, res1);
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Cudd_IterDerefBdd(manager, res2);
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return(NULL);
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}
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cuddDeref(res1);
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cuddDeref(res2);
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if (F->ref != 1)
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cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
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return(res);
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}
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} /* end of cuddBddExistAbstractRecur */
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/**Function********************************************************************
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Synopsis [Performs the recursive steps of Cudd_bddExistAbstractRepresentative.]
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Description [Performs the recursive steps of Cudd_bddExistAbstractRepresentative.
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Returns the BDD obtained by picking a representative over the variables in
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the given cube for all other valuations. Returns the resulting BDD if successful;
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NULL otherwise.]
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SideEffects [None]
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SeeAlso []
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******************************************************************************/
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DdNode *
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cuddBddExistAbstractRepresentativeRecur(
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DdManager * manager,
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DdNode * f,
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DdNode * cube)
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{
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DdNode *F, *T, *E, *res, *res1, *res2, *one, *zero, *left, *right, *tmp, *res1Inf, *res2Inf;
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statLine(manager);
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one = DD_ONE(manager);
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zero = Cudd_Not(one);
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F = Cudd_Regular(f);
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// Store whether f is negated.
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int fIsNegated = f != F;
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/* Cube is guaranteed to be a cube at this point. */
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if (F == one) {
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if (fIsNegated) {
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return f;
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}
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if (cube == one) {
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return one;
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} else {
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res = cuddBddExistAbstractRepresentativeRecur(manager, f, cuddT(cube));
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if (res == NULL) {
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return(NULL);
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}
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cuddRef(res);
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// res1 = cuddUniqueInter(manager, (int) cube->index, zero, res);
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// We now build in the necessary negation ourselves.
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res1 = cuddUniqueInter(manager, (int) cube->index, one, Cudd_Not(res));
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if (res1 == NULL) {
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Cudd_IterDerefBdd(manager,res);
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return(NULL);
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}
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res1 = Cudd_Not(res1);
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cuddDeref(res);
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return(res1);
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}
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} else if (cube == one) {
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return f;
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}
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/* From now on, cube and f are non-constant. */
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|
|
|
|
|
/* Abstract a variable that does not appear in f. */
|
|
if (manager->perm[F->index] > manager->perm[cube->index]) {
|
|
res = cuddBddExistAbstractRepresentativeRecur(manager, f, cuddT(cube));
|
|
if (res == NULL) {
|
|
return(NULL);
|
|
}
|
|
cuddRef(res);
|
|
|
|
// res1 = cuddUniqueInter(manager, (int) cube->index, zero, res);
|
|
|
|
// We now build in the necessary negation ourselves.
|
|
res1 = cuddUniqueInter(manager, (int) cube->index, one, Cudd_Not(res));
|
|
if (res1 == NULL) {
|
|
Cudd_IterDerefBdd(manager,res);
|
|
return(NULL);
|
|
}
|
|
res1 = Cudd_Not(res1);
|
|
cuddDeref(res);
|
|
|
|
return(res1);
|
|
}
|
|
|
|
/* Check the cache. */
|
|
if (F->ref != 1 && (res = cuddCacheLookup2(manager, Cudd_bddExistAbstractRepresentative, f, cube)) != NULL) {
|
|
return(res);
|
|
}
|
|
|
|
/* Compute the cofactors of f. */
|
|
T = cuddT(F); E = cuddE(F);
|
|
if (f != F) {
|
|
T = Cudd_Not(T); E = Cudd_Not(E);
|
|
}
|
|
|
|
/* If the two indices are the same, so are their levels. */
|
|
if (F->index == cube->index) {
|
|
res1 = cuddBddExistAbstractRepresentativeRecur(manager, E, cuddT(cube));
|
|
if (res1 == NULL) {
|
|
return(NULL);
|
|
}
|
|
if (res1 == one) {
|
|
if (F->ref != 1) {
|
|
cuddCacheInsert2(manager, Cudd_bddExistAbstractRepresentative, f, cube, Cudd_Not(cube));
|
|
}
|
|
return(Cudd_Not(cube));
|
|
}
|
|
cuddRef(res1);
|
|
|
|
res2 = cuddBddExistAbstractRepresentativeRecur(manager, T, cuddT(cube));
|
|
if (res2 == NULL) {
|
|
Cudd_IterDerefBdd(manager,res1);
|
|
return(NULL);
|
|
}
|
|
cuddRef(res2);
|
|
|
|
left = cuddBddExistAbstractRecur(manager, E, cuddT(cube));
|
|
if (left == NULL) {
|
|
Cudd_IterDerefBdd(manager, res1);
|
|
Cudd_IterDerefBdd(manager, res2);
|
|
return(NULL);
|
|
}
|
|
cuddRef(left);
|
|
|
|
res1Inf = cuddBddIteRecur(manager, left, res1, zero);
|
|
if (res1Inf == NULL) {
|
|
Cudd_IterDerefBdd(manager,res1);
|
|
Cudd_IterDerefBdd(manager,res2);
|
|
Cudd_IterDerefBdd(manager,left);
|
|
return(NULL);
|
|
}
|
|
cuddRef(res1Inf);
|
|
|
|
Cudd_IterDerefBdd(manager,res1);
|
|
|
|
res2Inf = cuddBddIteRecur(manager, left, zero, res2);
|
|
if (res2Inf == NULL) {
|
|
Cudd_IterDerefBdd(manager,res1);
|
|
Cudd_IterDerefBdd(manager,res2);
|
|
Cudd_IterDerefBdd(manager,left);
|
|
Cudd_IterDerefBdd(manager,res1Inf);
|
|
return(NULL);
|
|
}
|
|
cuddRef(res2Inf);
|
|
|
|
Cudd_IterDerefBdd(manager,res2);
|
|
Cudd_IterDerefBdd(manager,left);
|
|
|
|
assert(res1Inf != res2Inf);
|
|
int compl = Cudd_IsComplement(res2Inf);
|
|
res = cuddUniqueInter(manager, (int) F->index, Cudd_Regular(res2Inf), compl ? Cudd_Not(res1Inf) : res1Inf);
|
|
if (res == NULL) {
|
|
Cudd_IterDerefBdd(manager,res1Inf);
|
|
Cudd_IterDerefBdd(manager,res2Inf);
|
|
return(NULL);
|
|
}
|
|
if (compl) {
|
|
res = Cudd_Not(res);
|
|
}
|
|
cuddRef(res);
|
|
|
|
cuddDeref(res1Inf);
|
|
cuddDeref(res2Inf);
|
|
|
|
cuddCacheInsert2(manager, Cudd_bddExistAbstractRepresentative, f, cube, res);
|
|
cuddDeref(res);
|
|
return(res);
|
|
} else { /* if (cuddI(manager,F->index) < cuddI(manager,cube->index)) */
|
|
res1 = cuddBddExistAbstractRepresentativeRecur(manager, E, cube);
|
|
if (res1 == NULL){
|
|
return(NULL);
|
|
}
|
|
cuddRef(res1);
|
|
|
|
res2 = cuddBddExistAbstractRepresentativeRecur(manager, T, cube);
|
|
if (res2 == NULL) {
|
|
Cudd_IterDerefBdd(manager, res1);
|
|
return(NULL);
|
|
}
|
|
cuddRef(res2);
|
|
|
|
/* ITE takes care of possible complementation of res1 and of the
|
|
** case in which res1 == res2. */
|
|
int compl = Cudd_IsComplement(res2);
|
|
res = cuddUniqueInter(manager, (int)F->index, Cudd_Regular(res2), compl ? Cudd_Not(res1) : res1);
|
|
if (res == NULL) {
|
|
Cudd_IterDerefBdd(manager, res1);
|
|
Cudd_IterDerefBdd(manager, res2);
|
|
return(NULL);
|
|
}
|
|
if (compl) {
|
|
res = Cudd_Not(res);
|
|
}
|
|
cuddDeref(res1);
|
|
cuddDeref(res2);
|
|
if (F->ref != 1) {
|
|
cuddCacheInsert2(manager, Cudd_bddExistAbstractRepresentative, f, cube, res);
|
|
}
|
|
return(res);
|
|
}
|
|
|
|
} /* end of cuddBddExistAbstractRepresentativeRecur */
|
|
|
|
/**
|
|
@brief Takes the exclusive OR of two BDDs and simultaneously abstracts the
|
|
variables in cube.
|
|
|
|
@details The variables are existentially abstracted.
|
|
|
|
@return a pointer to the result is successful; NULL otherwise.
|
|
|
|
@sideeffect None
|
|
|
|
@see Cudd_bddAndAbstract
|
|
|
|
*/
|
|
DdNode *
|
|
cuddBddXorExistAbstractRecur(
|
|
DdManager * manager,
|
|
DdNode * f,
|
|
DdNode * g,
|
|
DdNode * cube)
|
|
{
|
|
DdNode *F, *fv, *fnv, *G, *gv, *gnv;
|
|
DdNode *one, *zero, *r, *t, *e, *Cube;
|
|
int topf, topg, topcube, top;
|
|
unsigned int index;
|
|
|
|
statLine(manager);
|
|
one = DD_ONE(manager);
|
|
zero = Cudd_Not(one);
|
|
|
|
/* Terminal cases. */
|
|
if (f == g) {
|
|
return(zero);
|
|
}
|
|
if (f == Cudd_Not(g)) {
|
|
return(one);
|
|
}
|
|
if (cube == one) {
|
|
return(cuddBddXorRecur(manager, f, g));
|
|
}
|
|
if (f == one) {
|
|
return(cuddBddExistAbstractRecur(manager, Cudd_Not(g), cube));
|
|
}
|
|
if (g == one) {
|
|
return(cuddBddExistAbstractRecur(manager, Cudd_Not(f), cube));
|
|
}
|
|
if (f == zero) {
|
|
return(cuddBddExistAbstractRecur(manager, g, cube));
|
|
}
|
|
if (g == zero) {
|
|
return(cuddBddExistAbstractRecur(manager, f, cube));
|
|
}
|
|
|
|
/* At this point f, g, and cube are not constant. */
|
|
|
|
if (f > g) { /* Try to increase cache efficiency. */
|
|
DdNode *tmp = f;
|
|
f = g;
|
|
g = tmp;
|
|
}
|
|
|
|
/* Check cache. */
|
|
r = cuddCacheLookup(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube);
|
|
if (r != NULL) {
|
|
return(r);
|
|
}
|
|
|
|
checkWhetherToGiveUp(manager);
|
|
|
|
/* Here we can skip the use of cuddI, because the operands are known
|
|
** to be non-constant.
|
|
*/
|
|
F = Cudd_Regular(f);
|
|
topf = manager->perm[F->index];
|
|
G = Cudd_Regular(g);
|
|
topg = manager->perm[G->index];
|
|
top = ddMin(topf, topg);
|
|
topcube = manager->perm[cube->index];
|
|
|
|
if (topcube < top) {
|
|
return(cuddBddXorExistAbstractRecur(manager, f, g, cuddT(cube)));
|
|
}
|
|
/* Now, topcube >= top. */
|
|
|
|
if (topf == top) {
|
|
index = F->index;
|
|
fv = cuddT(F);
|
|
fnv = cuddE(F);
|
|
if (Cudd_IsComplement(f)) {
|
|
fv = Cudd_Not(fv);
|
|
fnv = Cudd_Not(fnv);
|
|
}
|
|
} else {
|
|
index = G->index;
|
|
fv = fnv = f;
|
|
}
|
|
|
|
if (topg == top) {
|
|
gv = cuddT(G);
|
|
gnv = cuddE(G);
|
|
if (Cudd_IsComplement(g)) {
|
|
gv = Cudd_Not(gv);
|
|
gnv = Cudd_Not(gnv);
|
|
}
|
|
} else {
|
|
gv = gnv = g;
|
|
}
|
|
|
|
if (topcube == top) {
|
|
Cube = cuddT(cube);
|
|
} else {
|
|
Cube = cube;
|
|
}
|
|
|
|
t = cuddBddXorExistAbstractRecur(manager, fv, gv, Cube);
|
|
if (t == NULL) return(NULL);
|
|
|
|
/* Special case: 1 OR anything = 1. Hence, no need to compute
|
|
** the else branch if t is 1.
|
|
*/
|
|
if (t == one && topcube == top) {
|
|
cuddCacheInsert(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube, one);
|
|
return(one);
|
|
}
|
|
cuddRef(t);
|
|
|
|
e = cuddBddXorExistAbstractRecur(manager, fnv, gnv, Cube);
|
|
if (e == NULL) {
|
|
Cudd_IterDerefBdd(manager, t);
|
|
return(NULL);
|
|
}
|
|
cuddRef(e);
|
|
|
|
if (topcube == top) { /* abstract */
|
|
r = cuddBddAndRecur(manager, Cudd_Not(t), Cudd_Not(e));
|
|
if (r == NULL) {
|
|
Cudd_IterDerefBdd(manager, t);
|
|
Cudd_IterDerefBdd(manager, e);
|
|
return(NULL);
|
|
}
|
|
r = Cudd_Not(r);
|
|
cuddRef(r);
|
|
Cudd_IterDerefBdd(manager, t);
|
|
Cudd_IterDerefBdd(manager, e);
|
|
cuddDeref(r);
|
|
} else if (t == e) {
|
|
r = t;
|
|
cuddDeref(t);
|
|
cuddDeref(e);
|
|
} else {
|
|
if (Cudd_IsComplement(t)) {
|
|
r = cuddUniqueInter(manager,(int)index,Cudd_Not(t),Cudd_Not(e));
|
|
if (r == NULL) {
|
|
Cudd_IterDerefBdd(manager, t);
|
|
Cudd_IterDerefBdd(manager, e);
|
|
return(NULL);
|
|
}
|
|
r = Cudd_Not(r);
|
|
} else {
|
|
r = cuddUniqueInter(manager,(int)index,t,e);
|
|
if (r == NULL) {
|
|
Cudd_IterDerefBdd(manager, t);
|
|
Cudd_IterDerefBdd(manager, e);
|
|
return(NULL);
|
|
}
|
|
}
|
|
cuddDeref(e);
|
|
cuddDeref(t);
|
|
}
|
|
cuddCacheInsert(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube, r);
|
|
return (r);
|
|
|
|
} /* end of cuddBddXorExistAbstractRecur */
|
|
|
|
|
|
/**
|
|
@brief Performs the recursive steps of Cudd_bddBoleanDiff.
|
|
|
|
@details Exploits the fact that dF/dx = dF'/dx.
|
|
|
|
@return the %BDD obtained by XORing the cofactors of f with respect
|
|
to var if successful; NULL otherwise.
|
|
|
|
@sideeffect None
|
|
|
|
*/
|
|
DdNode *
|
|
cuddBddBooleanDiffRecur(
|
|
DdManager * manager,
|
|
DdNode * f,
|
|
DdNode * var)
|
|
{
|
|
DdNode *T, *E, *res, *res1, *res2;
|
|
|
|
statLine(manager);
|
|
if (cuddI(manager,f->index) > manager->perm[var->index]) {
|
|
/* f does not depend on var. */
|
|
return(Cudd_Not(DD_ONE(manager)));
|
|
}
|
|
|
|
/* From now on, f is non-constant. */
|
|
|
|
/* If the two indices are the same, so are their levels. */
|
|
if (f->index == var->index) {
|
|
res = cuddBddXorRecur(manager, cuddT(f), cuddE(f));
|
|
return(res);
|
|
}
|
|
|
|
/* From now on, cuddI(manager,f->index) < cuddI(manager,cube->index). */
|
|
|
|
/* Check the cache. */
|
|
res = cuddCacheLookup2(manager, cuddBddBooleanDiffRecur, f, var);
|
|
if (res != NULL) {
|
|
return(res);
|
|
}
|
|
|
|
/* Compute the cofactors of f. */
|
|
T = cuddT(f); E = cuddE(f);
|
|
|
|
res1 = cuddBddBooleanDiffRecur(manager, T, var);
|
|
if (res1 == NULL) return(NULL);
|
|
cuddRef(res1);
|
|
res2 = cuddBddBooleanDiffRecur(manager, Cudd_Regular(E), var);
|
|
if (res2 == NULL) {
|
|
Cudd_IterDerefBdd(manager, res1);
|
|
return(NULL);
|
|
}
|
|
cuddRef(res2);
|
|
/* ITE takes care of possible complementation of res1 and of the
|
|
** case in which res1 == res2. */
|
|
res = cuddBddIteRecur(manager, manager->vars[f->index], res1, res2);
|
|
if (res == NULL) {
|
|
Cudd_IterDerefBdd(manager, res1);
|
|
Cudd_IterDerefBdd(manager, res2);
|
|
return(NULL);
|
|
}
|
|
cuddDeref(res1);
|
|
cuddDeref(res2);
|
|
cuddCacheInsert2(manager, cuddBddBooleanDiffRecur, f, var, res);
|
|
return(res);
|
|
|
|
} /* end of cuddBddBooleanDiffRecur */
|
|
|
|
|
|
/*---------------------------------------------------------------------------*/
|
|
/* Definition of static functions */
|
|
/*---------------------------------------------------------------------------*/
|
|
|
|
/**
|
|
@brief Checks whether cube is a %BDD representing the product of
|
|
positive literals.
|
|
|
|
@return 1 in case of success; 0 otherwise.
|
|
|
|
@sideeffect None
|
|
|
|
*/
|
|
static int
|
|
bddCheckPositiveCube(
|
|
DdManager * manager,
|
|
DdNode * cube)
|
|
{
|
|
if (Cudd_IsComplement(cube)) return(0);
|
|
if (cube == DD_ONE(manager)) return(1);
|
|
if (cuddIsConstant(cube)) return(0);
|
|
if (cuddE(cube) == Cudd_Not(DD_ONE(manager))) {
|
|
return(bddCheckPositiveCube(manager, cuddT(cube)));
|
|
}
|
|
return(0);
|
|
|
|
} /* end of bddCheckPositiveCube */
|
|
|