text: /**CFile***********************************************************************
  
    FileName    [cuddAndAbs.c]
  
    PackageName [cudd]
  
    Synopsis    [Combined AND and existential abstraction for BDDs]
  
    Description [External procedures included in this module:
  		<ul>
  		<li> Cudd_bddAndAbstract()
  		<li> Cudd_bddAndAbstractLimit()
  		</ul>
  	    Internal procedures included in this module:
  		<ul>
  		<li> cuddBddAndAbstractRecur()
  		</ul>]
  
    Author      [Fabio Somenzi]
  
    Copyright   [Copyright (c) 1995-2012, 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                                                     */
  /*---------------------------------------------------------------------------*/
  
  
  /*---------------------------------------------------------------------------*/
  /* Stucture declarations                                                     */
  /*---------------------------------------------------------------------------*/
  
  
  /*---------------------------------------------------------------------------*/
  /* Type declarations                                                         */
  /*---------------------------------------------------------------------------*/
  
  
  /*---------------------------------------------------------------------------*/
  /* Variable declarations                                                     */
  /*---------------------------------------------------------------------------*/
  
  #ifndef lint
  static char rcsid[] DD_UNUSED = "$Id: cuddAndAbs.c,v 1.20 2012/02/05 01:07:18 fabio Exp $";
  #endif
  
  
  /*---------------------------------------------------------------------------*/
  /* Macro declarations                                                        */
  /*---------------------------------------------------------------------------*/
  
  
  /**AutomaticStart*************************************************************/
  
  /*---------------------------------------------------------------------------*/
  /* Static function prototypes                                                */
  /*---------------------------------------------------------------------------*/
  
  
  /**AutomaticEnd***************************************************************/
  
  
  /*---------------------------------------------------------------------------*/
  /* Definition of exported functions                                          */
  /*---------------------------------------------------------------------------*/
  
  
  /**Function********************************************************************
  
    Synopsis [Takes the AND of two BDDs and simultaneously abstracts the
    variables in cube.]
  
    Description [Takes the AND of two BDDs and simultaneously abstracts
    the variables in cube. The variables are existentially abstracted.
    Returns a pointer to the result is successful; NULL otherwise.
    Cudd_bddAndAbstract implements the semiring matrix multiplication
    algorithm for the boolean semiring.]
  
    SideEffects [None]
  
    SeeAlso     [Cudd_addMatrixMultiply Cudd_addTriangle Cudd_bddAnd]
  
  ******************************************************************************/
  DdNode *
  Cudd_bddAndAbstract(
    DdManager * manager,
    DdNode * f,
    DdNode * g,
    DdNode * cube)
  {
      DdNode *res;
  
      do {
  	manager->reordered = 0;
  	res = cuddBddAndAbstractRecur(manager, f, g, cube);
      } while (manager->reordered == 1);
      return(res);
  
  } /* end of Cudd_bddAndAbstract */
  
  
  /**Function********************************************************************
  
    Synopsis [Takes the AND of two BDDs and simultaneously abstracts the
    variables in cube.  Returns NULL if too many nodes are required.]
  
    Description [Takes the AND of two BDDs and simultaneously abstracts
    the variables in cube. The variables are existentially abstracted.
    Returns a pointer to the result is successful; NULL otherwise.
    In particular, if the number of new nodes created exceeds
    <code>limit</code>, this function returns NULL.]
  
    SideEffects [None]
  
    SeeAlso     [Cudd_bddAndAbstract]
  
  ******************************************************************************/
  DdNode *
  Cudd_bddAndAbstractLimit(
    DdManager * manager,
    DdNode * f,
    DdNode * g,
    DdNode * cube,
    unsigned int limit)
  {
      DdNode *res;
      unsigned int saveLimit = manager->maxLive;
  
      manager->maxLive = (manager->keys - manager->dead) +
        (manager->keysZ - manager->deadZ) + limit;
      do {
  	manager->reordered = 0;
  	res = cuddBddAndAbstractRecur(manager, f, g, cube);
      } while (manager->reordered == 1);
      manager->maxLive = saveLimit;
      return(res);
  
  } /* end of Cudd_bddAndAbstractLimit */
  
  
  /*---------------------------------------------------------------------------*/
  /* Definition of internal functions                                          */
  /*---------------------------------------------------------------------------*/
  
  
  /**Function********************************************************************
  
    Synopsis [Takes the AND of two BDDs and simultaneously abstracts the
    variables in cube.]
  
    Description [Takes the AND of two BDDs and simultaneously abstracts
    the variables in cube. The variables are existentially abstracted.
    Returns a pointer to the result is successful; NULL otherwise.]
  
    SideEffects [None]
  
    SeeAlso     [Cudd_bddAndAbstract]
  
  ******************************************************************************/
  DdNode *
  cuddBddAndAbstractRecur(
    DdManager * manager,
    DdNode * f,
    DdNode * g,
    DdNode * cube)
  {
      DdNode *F, *ft, *fe, *G, *gt, *ge;
      DdNode *one, *zero, *r, *t, *e;
      unsigned int topf, topg, topcube, top, index;
  
      statLine(manager);
      one = DD_ONE(manager);
      zero = Cudd_Not(one);
  
      /* Terminal cases. */
      if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
      if (f == one && g == one)	return(one);
  
      if (cube == one) {
  	return(cuddBddAndRecur(manager, f, g));
      }
      if (f == one || f == g) {
  	return(cuddBddExistAbstractRecur(manager, g, cube));
      }
      if (g == one) {
  	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;
      }
  
      /* Here we can skip the use of cuddI, because the operands are known
      ** to be non-constant.
      */
      F = Cudd_Regular(f);
      G = Cudd_Regular(g);
      topf = manager->perm[F->index];
      topg = manager->perm[G->index];
      top = ddMin(topf, topg);
      topcube = manager->perm[cube->index];
  
      while (topcube < top) {
  	cube = cuddT(cube);
  	if (cube == one) {
  	    return(cuddBddAndRecur(manager, f, g));
  	}
  	topcube = manager->perm[cube->index];
      }
      /* Now, topcube >= top. */
  
      /* Check cache. */
      if (F->ref != 1 || G->ref != 1) {
  	r = cuddCacheLookup(manager, DD_BDD_AND_ABSTRACT_TAG, f, g, cube);
  	if (r != NULL) {
  	    return(r);
  	}
      }
  
      if (topf == top) {
  	index = F->index;
  	ft = cuddT(F);
  	fe = cuddE(F);
  	if (Cudd_IsComplement(f)) {
  	    ft = Cudd_Not(ft);
  	    fe = Cudd_Not(fe);
  	}
      } else {
  	index = G->index;
  	ft = fe = f;
      }
  
      if (topg == top) {
  	gt = cuddT(G);
  	ge = cuddE(G);
  	if (Cudd_IsComplement(g)) {
  	    gt = Cudd_Not(gt);
  	    ge = Cudd_Not(ge);
  	}
      } else {
  	gt = ge = g;
      }
  
      if (topcube == top) {	/* quantify */
  	DdNode *Cube = cuddT(cube);
  	t = cuddBddAndAbstractRecur(manager, ft, gt, Cube);
  	if (t == NULL) return(NULL);
  	/* Special case: 1 OR anything = 1. Hence, no need to compute
  	** the else branch if t is 1. Likewise t + t * anything == t.
  	** Notice that t == fe implies that fe does not depend on the
  	** variables in Cube. Likewise for t == ge.
  	*/
  	if (t == one || t == fe || t == ge) {
  	    if (F->ref != 1 || G->ref != 1)
  		cuddCacheInsert(manager, DD_BDD_AND_ABSTRACT_TAG,
  				f, g, cube, t);
  	    return(t);
  	}
  	cuddRef(t);
  	/* Special case: t + !t * anything == t + anything. */
  	if (t == Cudd_Not(fe)) {
  	    e = cuddBddExistAbstractRecur(manager, ge, Cube);
  	} else if (t == Cudd_Not(ge)) {
  	    e = cuddBddExistAbstractRecur(manager, fe, Cube);
  	} else {
  	    e = cuddBddAndAbstractRecur(manager, fe, ge, Cube);
  	}
  	if (e == NULL) {
  	    Cudd_IterDerefBdd(manager, t);
  	    return(NULL);
  	}
  	if (t == e) {
  	    r = t;
  	    cuddDeref(t);
  	} else {
  	    cuddRef(e);
  	    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_DelayedDerefBdd(manager, t);
  	    Cudd_DelayedDerefBdd(manager, e);
  	    cuddDeref(r);
  	}
      } else {
  	t = cuddBddAndAbstractRecur(manager, ft, gt, cube);
  	if (t == NULL) return(NULL);
  	cuddRef(t);
  	e = cuddBddAndAbstractRecur(manager, fe, ge, cube);
  	if (e == NULL) {
  	    Cudd_IterDerefBdd(manager, t);
  	    return(NULL);
  	}
  	if (t == e) {
  	    r = t;
  	    cuddDeref(t);
  	} else {
  	    cuddRef(e);
  	    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);
  	}
      }
  
      if (F->ref != 1 || G->ref != 1)
  	cuddCacheInsert(manager, DD_BDD_AND_ABSTRACT_TAG, f, g, cube, r);
      return (r);
  
  } /* end of cuddBddAndAbstractRecur */
  
  
  /*---------------------------------------------------------------------------*/
  /* Definition of static functions                                            */
  /*---------------------------------------------------------------------------*/
  
  