/**CFile***********************************************************************

  FileName    [cuddSolve.c]

  PackageName [cudd]

  Synopsis    [Boolean equation solver and related functions.]

  Description [External functions included in this modoule:
		<ul>
		<li> Cudd_SolveEqn()
		<li> Cudd_VerifySol()
		</ul>
	Internal functions included in this module:
		<ul>
		<li> cuddSolveEqnRecur()
		<li> cuddVerifySol()
		</ul> ]

  SeeAlso     []

  Author      [Balakrishna Kumthekar]

  Copyright [This file was created at the University of Colorado at
  Boulder.  The University of Colorado at Boulder makes no warranty
  about the suitability of this software for any purpose.  It is
  presented on an AS IS basis.]

******************************************************************************/

#include "util_hack.h"
#include "cuddInt.h"

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#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddSolve.c,v 1.1.1.1 2003/02/24 22:23:53 wjiang Exp $";
#endif

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/* Definition of exported functions                                          */
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/**Function********************************************************************

  Synopsis    [Implements the solution of F(x,y) = 0.]

  Description [Implements the solution for F(x,y) = 0. The return
  value is the consistency condition. The y variables are the unknowns
  and the remaining variables are the parameters.  Returns the
  consistency condition if successful; NULL otherwise. Cudd_SolveEqn
  allocates an array and fills it with the indices of the
  unknowns. This array is used by Cudd_VerifySol.]

  SideEffects [The solution is returned in G; the indices of the y
  variables are returned in yIndex.]

  SeeAlso     [Cudd_VerifySol]

******************************************************************************/
DdNode *
Cudd_SolveEqn(
  DdManager *  bdd,
  DdNode * F /* the left-hand side of the equation */,
  DdNode * Y /* the cube of the y variables */,
  DdNode ** G /* the array of solutions (return parameter) */,
  int ** yIndex /* index of y variables */,
  int  n /* numbers of unknowns */)
{
    DdNode *res;
    int *temp;

    *yIndex = temp = ALLOC(int, n);
    if (temp == NULL) {
	bdd->errorCode = CUDD_MEMORY_OUT;
	(void) fprintf(bdd->out,
		       "Cudd_SolveEqn: Out of memory for yIndex\n");
	return(NULL);
    }

    do {
	bdd->reordered = 0;
	res = cuddSolveEqnRecur(bdd, F, Y, G, n, temp, 0);
    } while (bdd->reordered == 1);

    return(res);

} /* end of Cudd_SolveEqn */


/**Function********************************************************************

  Synopsis    [Checks the solution of F(x,y) = 0.]

  Description [Checks the solution of F(x,y) = 0. This procedure 
  substitutes the solution components for the unknowns of F and returns 
  the resulting BDD for F.] 

  SideEffects [Frees the memory pointed by yIndex.]

  SeeAlso     [Cudd_SolveEqn]

******************************************************************************/
DdNode *
Cudd_VerifySol(
  DdManager *  bdd,
  DdNode * F /* the left-hand side of the equation */,
  DdNode ** G /* the array of solutions */,
  int * yIndex /* index of y variables */,
  int  n /* numbers of unknowns */)
{
    DdNode *res;

    do {
	bdd->reordered = 0;
	res = cuddVerifySol(bdd, F, G, yIndex, n);
    } while (bdd->reordered == 1);

    FREE(yIndex);

    return(res);

} /* end of Cudd_VerifySol */


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/**Function********************************************************************

  Synopsis    [Implements the recursive step of Cudd_SolveEqn.]

  Description [Implements the recursive step of Cudd_SolveEqn. 
  Returns NULL if the intermediate solution blows up
  or reordering occurs. The parametric solutions are
  stored in the array G.]

  SideEffects [none]

  SeeAlso     [Cudd_SolveEqn, Cudd_VerifySol]

******************************************************************************/
DdNode *
cuddSolveEqnRecur(
  DdManager * bdd,
  DdNode * F /* the left-hand side of the equation */,
  DdNode * Y /* the cube of remaining y variables */,
  DdNode ** G /* the array of solutions */,
  int  n /* number of unknowns */,
  int * yIndex /* array holding the y variable indices */,
  int  i /* level of recursion */)
{
    DdNode *Fn, *Fm1, *Fv, *Fvbar, *T, *w, *nextY, *one;
    DdNodePtr *variables;

    int j;

    statLine(bdd);
    variables = bdd->vars;
    one = DD_ONE(bdd);

    /* Base condition. */
    if (Y == one) {
	return F;
    }

    /* Cofactor of Y. */
    yIndex[i] = Y->index;
    nextY = Cudd_T(Y);

    /* Universal abstraction of F with respect to the top variable index. */
    Fm1 = cuddBddExistAbstractRecur(bdd, Cudd_Not(F), variables[yIndex[i]]);
    if (Fm1) {
	Fm1 = Cudd_Not(Fm1);
	cuddRef(Fm1);
    } else {
	return(NULL);
    }

    Fn = cuddSolveEqnRecur(bdd, Fm1, nextY, G, n, yIndex, i+1);
    if (Fn) {
	cuddRef(Fn);
    } else {
	Cudd_RecursiveDeref(bdd, Fm1);
	return(NULL);
    }

    Fv = cuddCofactorRecur(bdd, F, variables[yIndex[i]]);
    if (Fv) {
	cuddRef(Fv);
    } else {
	Cudd_RecursiveDeref(bdd, Fm1);
	Cudd_RecursiveDeref(bdd, Fn);
	return(NULL);
    }

    Fvbar = cuddCofactorRecur(bdd, F, Cudd_Not(variables[yIndex[i]]));
    if (Fvbar) {
	cuddRef(Fvbar);
    } else {
	Cudd_RecursiveDeref(bdd, Fm1);
	Cudd_RecursiveDeref(bdd, Fn);
	Cudd_RecursiveDeref(bdd, Fv);
	return(NULL);
    }

    /* Build i-th component of the solution. */
    w = cuddBddIteRecur(bdd, variables[yIndex[i]], Cudd_Not(Fv), Fvbar);
    if (w) {
	cuddRef(w);
    } else {
	Cudd_RecursiveDeref(bdd, Fm1);
	Cudd_RecursiveDeref(bdd, Fn);
	Cudd_RecursiveDeref(bdd, Fv);
	Cudd_RecursiveDeref(bdd, Fvbar);
	return(NULL);
    }

    T = cuddBddRestrictRecur(bdd, w, Cudd_Not(Fm1));
    if(T) {
	cuddRef(T);
    } else {
	Cudd_RecursiveDeref(bdd, Fm1);
	Cudd_RecursiveDeref(bdd, Fn);
	Cudd_RecursiveDeref(bdd, Fv);
	Cudd_RecursiveDeref(bdd, Fvbar);
	Cudd_RecursiveDeref(bdd, w);
	return(NULL);
    }

    Cudd_RecursiveDeref(bdd,Fm1);
    Cudd_RecursiveDeref(bdd,w);
    Cudd_RecursiveDeref(bdd,Fv);
    Cudd_RecursiveDeref(bdd,Fvbar);

    /* Substitute components of solution already found into solution. */
    for (j = n-1; j > i; j--) {
	w = cuddBddComposeRecur(bdd,T, G[j], variables[yIndex[j]]);
	if(w) {
	    cuddRef(w);
	} else {
	    Cudd_RecursiveDeref(bdd, Fn);
	    Cudd_RecursiveDeref(bdd, T);
	    return(NULL);
	}
	Cudd_RecursiveDeref(bdd,T);
	T = w;
    }
    G[i] = T;

    Cudd_Deref(Fn);

    return(Fn);

} /* end of cuddSolveEqnRecur */


/**Function********************************************************************

  Synopsis    [Implements the recursive step of Cudd_VerifySol. ]

  Description []

  SideEffects [none]

  SeeAlso     [Cudd_VerifySol]

******************************************************************************/
DdNode *
cuddVerifySol(
  DdManager * bdd,
  DdNode * F /* the left-hand side of the equation */,
  DdNode ** G /* the array of solutions */,
  int * yIndex /* array holding the y variable indices */,
  int  n /* number of unknowns */)
{
    DdNode *w, *R;

    int j;

    R = F;
    cuddRef(R);
    for(j = n - 1; j >= 0; j--) {
	 w = Cudd_bddCompose(bdd, R, G[j], yIndex[j]);
	if (w) {
	    cuddRef(w);
	} else {
	    return(NULL); 
	}
	Cudd_RecursiveDeref(bdd,R);
	R = w;
    }

    cuddDeref(R);

    return(R);

} /* end of cuddVerifySol */


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/* Definition of static functions                                            */
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