cuddBddAbs.c File Reference

#include "misc/util/util_hack.h"
#include "cuddInt.h"

Go to the source code of this file.

Functions
static int	bddCheckPositiveCube (DdManager *manager, DdNode *cube)
DdNode *	Cudd_bddExistAbstract (DdManager *manager, DdNode *f, DdNode *cube)
DdNode *	Cudd_bddXorExistAbstract (DdManager *manager, DdNode *f, DdNode *g, DdNode *cube)
DdNode *	Cudd_bddUnivAbstract (DdManager *manager, DdNode *f, DdNode *cube)
DdNode *	Cudd_bddBooleanDiff (DdManager *manager, DdNode *f, int x)
int	Cudd_bddVarIsDependent (DdManager *dd, DdNode *f, DdNode *var)
DdNode *	cuddBddExistAbstractRecur (DdManager *manager, DdNode *f, DdNode *cube)
DdNode *	cuddBddXorExistAbstractRecur (DdManager *manager, DdNode *f, DdNode *g, DdNode *cube)
DdNode *	cuddBddBooleanDiffRecur (DdManager *manager, DdNode *f, DdNode *var)

Variables
static ABC_NAMESPACE_IMPL_START char rcsid[]	DD_UNUSED = "$Id: cuddBddAbs.c,v 1.26 2004/08/13 18:04:46 fabio Exp $"

Function Documentation

static int bddCheckPositiveCube ( DdManager *  manager, DdNode *  cube  )

static

AutomaticStart

Function********************************************************************

Synopsis [Checks whether cube is an BDD representing the product of positive literals.]

Description [Returns 1 in case of success; 0 otherwise.]

SideEffects [None]

Definition at line 708 of file cuddBddAbs.c.

{
    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 */

DdNode* Cudd_bddBooleanDiff	(	DdManager *	manager,
		DdNode *	f,
		int	x
	)

Function********************************************************************

Synopsis [Computes the boolean difference of f with respect to x.]

Description [Computes the boolean difference of f with respect to the variable with index x. Returns the BDD of the boolean difference if successful; NULL otherwise.]

SideEffects [None]

SeeAlso []

Definition at line 246 of file cuddBddAbs.c.

{
    DdNode *res, *var;

    /* If the variable is not currently in the manager, f cannot
    ** depend on it.
    */
    if (x >= manager->size) return(Cudd_Not(DD_ONE(manager)));
    var = manager->vars[x];

    do {
        manager->reordered = 0;
        res = cuddBddBooleanDiffRecur(manager, Cudd_Regular(f), var);
    } while (manager->reordered == 1);

    return(res);

} /* end of Cudd_bddBooleanDiff */

DdNode* Cudd_bddExistAbstract	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	cube
	)

AutomaticEnd Function********************************************************************

Synopsis [Existentially abstracts all the variables in cube from f.]

Description [Existentially abstracts all the variables in cube from f. Returns the abstracted BDD if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [Cudd_bddUnivAbstract Cudd_addExistAbstract]

Definition at line 130 of file cuddBddAbs.c.

{
    DdNode *res;

    if (bddCheckPositiveCube(manager, cube) == 0) {
        (void) fprintf(manager->err,
                       "Error: Can only abstract positive cubes\n");
        manager->errorCode = CUDD_INVALID_ARG;
        return(NULL);
    }

    do {
        manager->reordered = 0;
        res = cuddBddExistAbstractRecur(manager, f, cube);
    } while (manager->reordered == 1);

    return(res);

} /* end of Cudd_bddExistAbstract */

DdNode* Cudd_bddUnivAbstract	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	cube
	)

Function********************************************************************

Synopsis [Universally abstracts all the variables in cube from f.]

Description [Universally abstracts all the variables in cube from f. Returns the abstracted BDD if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [Cudd_bddExistAbstract Cudd_addUnivAbstract]

Definition at line 207 of file cuddBddAbs.c.

{
    DdNode      *res;

    if (bddCheckPositiveCube(manager, cube) == 0) {
        (void) fprintf(manager->err,
                       "Error: Can only abstract positive cubes\n");
        manager->errorCode = CUDD_INVALID_ARG;
        return(NULL);
    }

    do {
        manager->reordered = 0;
        res = cuddBddExistAbstractRecur(manager, Cudd_Not(f), cube);
    } while (manager->reordered == 1);
    if (res != NULL) res = Cudd_Not(res);

    return(res);

} /* end of Cudd_bddUnivAbstract */

int Cudd_bddVarIsDependent	(	DdManager *	dd,
		DdNode *	f,
		DdNode *	var
	)

Function********************************************************************

Synopsis [Checks whether a variable is dependent on others in a function.]

Description [Checks whether a variable is dependent on others in a function. Returns 1 if the variable is dependent; 0 otherwise. No new nodes are created.]

SideEffects [None]

SeeAlso []

Definition at line 284 of file cuddBddAbs.c.

{
    DdNode *F, *res, *zero, *ft, *fe;
    unsigned topf, level;
    DD_CTFP cacheOp;
    int retval;

    zero = Cudd_Not(DD_ONE(dd));
    if (Cudd_IsConstant(f)) return(f == zero);

    /* From now on f is not constant. */
    F = Cudd_Regular(f);
    topf = (unsigned) dd->perm[F->index];
    level = (unsigned) dd->perm[var->index];

    /* Check terminal case. If topf > index of var, f does not depend on var.
    ** Therefore, var is not dependent in f. */
    if (topf > level) {
        return(0);
    }

    cacheOp = (DD_CTFP) Cudd_bddVarIsDependent;
    res = cuddCacheLookup2(dd,cacheOp,f,var);
    if (res != NULL) {
        return(res != zero);
    }

    /* Compute cofactors. */
    ft = Cudd_NotCond(cuddT(F), f != F);
    fe = Cudd_NotCond(cuddE(F), f != F);

    if (topf == level) {
        retval = Cudd_bddLeq(dd,ft,Cudd_Not(fe));
    } else {
        retval = Cudd_bddVarIsDependent(dd,ft,var) &&
            Cudd_bddVarIsDependent(dd,fe,var);
    }

    cuddCacheInsert2(dd,cacheOp,f,var,Cudd_NotCond(zero,retval));

    return(retval);

} /* Cudd_bddVarIsDependent */

DdNode* Cudd_bddXorExistAbstract	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	g,
		DdNode *	cube
	)

Function********************************************************************

Synopsis [Takes the exclusive OR of two BDDs and simultaneously abstracts the variables in cube.]

Description [Takes the exclusive OR 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_bddUnivAbstract Cudd_bddExistAbstract Cudd_bddAndAbstract]

Definition at line 169 of file cuddBddAbs.c.

{
    DdNode *res;

    if (bddCheckPositiveCube(manager, cube) == 0) {
        (void) fprintf(manager->err,
                       "Error: Can only abstract positive cubes\n");
        manager->errorCode = CUDD_INVALID_ARG;
        return(NULL);
    }

    do {
        manager->reordered = 0;
        res = cuddBddXorExistAbstractRecur(manager, f, g, cube);
    } while (manager->reordered == 1);

    return(res);

} /* end of Cudd_bddXorExistAbstract */

DdNode* cuddBddBooleanDiffRecur	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	var
	)

Function********************************************************************

Synopsis [Performs the recursive steps of Cudd_bddBoleanDiff.]

Description [Performs the recursive steps of Cudd_bddBoleanDiff. Returns the BDD obtained by XORing the cofactors of f with respect to var if successful; NULL otherwise. Exploits the fact that dF/dx = dF'/dx.]

SideEffects [None]

SeeAlso []

Definition at line 636 of file cuddBddAbs.c.

{
    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 */

DdNode* cuddBddExistAbstractRecur	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	cube
	)

Function********************************************************************

Synopsis [Performs the recursive steps of Cudd_bddExistAbstract.]

Description [Performs the recursive steps of Cudd_bddExistAbstract. Returns the BDD obtained by abstracting the variables of cube from f if successful; NULL otherwise. It is also used by Cudd_bddUnivAbstract.]

SideEffects [None]

SeeAlso [Cudd_bddExistAbstract Cudd_bddUnivAbstract]

Definition at line 352 of file cuddBddAbs.c.

{
    DdNode      *F, *T, *E, *res, *res1, *res2, *one;

    statLine(manager);
    one = DD_ONE(manager);
    F = Cudd_Regular(f);

    /* Cube is guaranteed to be a cube at this point. */        
    if (cube == one || F == one) {  
        return(f);
    }
    /* From now on, f and cube are non-constant. */

    /* Abstract a variable that does not appear in f. */
    while (manager->perm[F->index] > manager->perm[cube->index]) {
        cube = cuddT(cube);
        if (cube == one) return(f);
    }

    /* Check the cache. */
    if (F->ref != 1 && (res = cuddCacheLookup2(manager, Cudd_bddExistAbstract, 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) {
        if (T == one || E == one || T == Cudd_Not(E)) {
            return(one);
        }
        res1 = cuddBddExistAbstractRecur(manager, T, cuddT(cube));
        if (res1 == NULL) return(NULL);
        if (res1 == one) {
            if (F->ref != 1)
                cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, one);
            return(one);
        }
        cuddRef(res1);
        res2 = cuddBddExistAbstractRecur(manager, E, cuddT(cube));
        if (res2 == NULL) {
            Cudd_IterDerefBdd(manager,res1);
            return(NULL);
        }
        cuddRef(res2);
        res = cuddBddAndRecur(manager, Cudd_Not(res1), Cudd_Not(res2));
        if (res == NULL) {
            Cudd_IterDerefBdd(manager, res1);
            Cudd_IterDerefBdd(manager, res2);
            return(NULL);
        }
        res = Cudd_Not(res);
        cuddRef(res);
        Cudd_IterDerefBdd(manager, res1);
        Cudd_IterDerefBdd(manager, res2);
        if (F->ref != 1)
            cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
        cuddDeref(res);
        return(res);
    } else { /* if (cuddI(manager,F->index) < cuddI(manager,cube->index)) */
        res1 = cuddBddExistAbstractRecur(manager, T, cube);
        if (res1 == NULL) return(NULL);
        cuddRef(res1);
        res2 = cuddBddExistAbstractRecur(manager, E, 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. */
        res = cuddBddIteRecur(manager, manager->vars[F->index], res1, res2);
        if (res == NULL) {
            Cudd_IterDerefBdd(manager, res1);
            Cudd_IterDerefBdd(manager, res2);
            return(NULL);
        }
        cuddRef(res); //Added
        Cudd_IterDerefBdd(manager, res1); //cuddDeref(res1);
        Cudd_IterDerefBdd(manager, res2); //cuddDeref(res2);
        cuddDeref(res); //Added
        if (F->ref != 1)
            cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
        return(res);
    }       

} /* end of cuddBddExistAbstractRecur */

DdNode* cuddBddXorExistAbstractRecur	(	DdManager *	manager,
		DdNode *	f,
		DdNode *	g,
		DdNode *	cube
	)

Function********************************************************************

Synopsis [Takes the exclusive OR of two BDDs and simultaneously abstracts the variables in cube.]

Description [Takes the exclusive OR 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]

Definition at line 464 of file cuddBddAbs.c.

{
    DdNode *F, *fv, *fnv, *G, *gv, *gnv;
    DdNode *one, *zero, *r, *t, *e, *Cube;
    unsigned int topf, topg, topcube, top, 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 (cuddF2L(f) > cuddF2L(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);
    }

    /* 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 */

Variable Documentation

ABC_NAMESPACE_IMPL_START char rcsid [] DD_UNUSED = "$Id: cuddBddAbs.c,v 1.26 2004/08/13 18:04:46 fabio Exp $"

static

CFile***********************************************************************

FileName [cuddBddAbs.c]

PackageName [cudd]

Synopsis [Quantification functions for BDDs.]

Description [External procedures included in this module:

• Cudd_bddExistAbstract()
• Cudd_bddXorExistAbstract()
• Cudd_bddUnivAbstract()
• Cudd_bddBooleanDiff()
• Cudd_bddVarIsDependent()

Internal procedures included in this module:

• cuddBddExistAbstractRecur()
• cuddBddXorExistAbstractRecur()
• cuddBddBooleanDiffRecur()

Static procedures included in this module:

• bddCheckPositiveCube()

]

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.]

Definition at line 93 of file cuddBddAbs.c.