/**CFile***********************************************************************
FileName [cuddSolve.c]
PackageName [cudd]
Synopsis [Boolean equation solver and related functions.]
Description [External functions included in this modoule:
- Cudd_SolveEqn()
- Cudd_VerifySol()
Internal functions included in this module:
- cuddSolveEqnRecur()
- cuddVerifySol()
]
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.h"
#include "cuddInt.h"
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/* Constant declarations */
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/* Type declarations */
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/* Structure declarations */
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/* Variable declarations */
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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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/* Macro declarations */
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/**AutomaticStart*************************************************************/
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/* Static function prototypes */
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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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/* Definition of internal functions */
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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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