src/cuBdd/cuddEssent.c File Reference

#include "util.h"
#include "cuddInt.h"

Include dependency graph for cuddEssent.c:

Go to the source code of this file.

Data Structures
struct	DdTlcInfo
struct	TlClause
Defines
#define	BPL   32
#define	LOGBPL   5
Typedefs
typedef long	BitVector
typedef struct TlClause	TlClause
Functions
static DdNode *	ddFindEssentialRecur (DdManager *dd, DdNode *f)
static DdTlcInfo *	ddFindTwoLiteralClausesRecur (DdManager *dd, DdNode *f, st_table *table)
static DdTlcInfo *	computeClauses (DdTlcInfo *Tres, DdTlcInfo *Eres, DdHalfWord label, int size)
static DdTlcInfo *	computeClausesWithUniverse (DdTlcInfo *Cres, DdHalfWord label, short phase)
static DdTlcInfo *	emptyClauseSet (void)
static int	sentinelp (DdHalfWord var1, DdHalfWord var2)
static int	equalp (DdHalfWord var1a, short phase1a, DdHalfWord var1b, short phase1b, DdHalfWord var2a, short phase2a, DdHalfWord var2b, short phase2b)
static int	beforep (DdHalfWord var1a, short phase1a, DdHalfWord var1b, short phase1b, DdHalfWord var2a, short phase2a, DdHalfWord var2b, short phase2b)
static int	oneliteralp (DdHalfWord var)
static int	impliedp (DdHalfWord var1, short phase1, DdHalfWord var2, short phase2, BitVector *olv, BitVector *olp)
static BitVector *	bitVectorAlloc (int size)
static DD_INLINE void	bitVectorClear (BitVector *vector, int size)
static void	bitVectorFree (BitVector *vector)
static DD_INLINE short	bitVectorRead (BitVector *vector, int i)
static DD_INLINE void	bitVectorSet (BitVector *vector, int i, short val)
static DdTlcInfo *	tlcInfoAlloc (void)
DdNode *	Cudd_FindEssential (DdManager *dd, DdNode *f)
int	Cudd_bddIsVarEssential (DdManager *manager, DdNode *f, int id, int phase)
DdTlcInfo *	Cudd_FindTwoLiteralClauses (DdManager *dd, DdNode *f)
int	Cudd_ReadIthClause (DdTlcInfo *tlc, int i, DdHalfWord *var1, DdHalfWord *var2, int *phase1, int *phase2)
int	Cudd_PrintTwoLiteralClauses (DdManager *dd, DdNode *f, char **names, FILE *fp)
void	Cudd_tlcInfoFree (DdTlcInfo *t)
Variables
static char rcsid[]	DD_UNUSED = "$Id: cuddEssent.c,v 1.24 2009/02/21 18:24:10 fabio Exp $"
static BitVector *	Tolv
static BitVector *	Tolp
static BitVector *	Eolv
static BitVector *	Eolp

---

Define Documentation

#define BPL   32

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

FileName [cuddEssent.c]

PackageName [cudd]

Synopsis [Functions for the detection of essential variables.]

Description [External procedures included in this file:

• Cudd_FindEssential()
• Cudd_bddIsVarEssential()
• Cudd_FindTwoLiteralClauses()
• Cudd_ReadIthClause()
• Cudd_PrintTwoLiteralClauses()
• Cudd_tlcInfoFree()

Static procedures included in this module:

• ddFindEssentialRecur()
• ddFindTwoLiteralClausesRecur()
• computeClauses()
• computeClausesWithUniverse()
• emptyClauseSet()
• sentinelp()
• equalp()
• beforep()
• oneliteralp()
• impliedp()
• bitVectorAlloc()
• bitVectorClear()
• bitVectorFree()
• bitVectorRead()
• bitVectorSet()
• tlcInfoAlloc()

]

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 86 of file cuddEssent.c.

#define LOGBPL   5

Definition at line 87 of file cuddEssent.c.

---

Typedef Documentation

typedef long BitVector

Definition at line 138 of file cuddEssent.c.

typedef struct TlClause TlClause

Definition at line 139 of file cuddEssent.c.

---

Function Documentation

static int beforep	(	DdHalfWord	var1a,
		short	phase1a,
		DdHalfWord	var1b,
		short	phase1b,
		DdHalfWord	var2a,
		short	phase2a,
		DdHalfWord	var2b,
		short	phase2b
	)			[static]

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

Synopsis [Returns true iff the first argument precedes the second in the clause order.]

Description [Returns true iff the first argument precedes the second in the clause order. A clause precedes another if its first lieral precedes the first literal of the other, or if the first literals are the same, and its second literal precedes the second literal of the other clause. A literal precedes another if it has a higher index, of if it has the same index, but it has lower phase. Phase 0 is the positive phase, and it is lower than Phase 1 (negative phase).]

SideEffects [None]

SeeAlso [equalp]

Definition at line 1229 of file cuddEssent.c.

{
    return(var1a > var2a || (var1a == var2a &&
           (phase1a < phase2a || (phase1a == phase2a &&
            (var1b > var2b || (var1b == var2b && phase1b < phase2b))))));

} /* end of beforep */

static BitVector * bitVectorAlloc

(

int

size

)

[static]

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

Synopsis [Allocates a bit vector.]

Description [Allocates a bit vector. The parameter size gives the number of bits. This procedure allocates enough long's to hold the specified number of bits. Returns a pointer to the allocated vector if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [bitVectorClear bitVectorFree]

Definition at line 1315 of file cuddEssent.c.

{
    int allocSize;
    BitVector *vector;

    /* Find out how many long's we need.
    ** There are sizeof(long) * 8 bits in a long.
    ** The ceiling of the ratio of two integers m and n is given
    ** by ((n-1)/m)+1.  Putting all this together, we get... */
    allocSize = ((size - 1) / (sizeof(BitVector) * 8)) + 1;
    vector = ALLOC(BitVector, allocSize);
    if (vector == NULL) return(NULL);
    /* Clear the whole array. */
    (void) memset(vector, 0, allocSize * sizeof(BitVector));
    return(vector);

} /* end of bitVectorAlloc */

static DD_INLINE void bitVectorClear	(	BitVector *	vector,
		int	size
	)			[static]

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

Synopsis [Clears a bit vector.]

Description [Clears a bit vector. The parameter size gives the number of bits.]

SideEffects [None]

SeeAlso [bitVectorAlloc]

Definition at line 1349 of file cuddEssent.c.

{
    int allocSize;

    /* Find out how many long's we need.
    ** There are sizeof(long) * 8 bits in a long.
    ** The ceiling of the ratio of two integers m and n is given
    ** by ((n-1)/m)+1.  Putting all this together, we get... */
    allocSize = ((size - 1) / (sizeof(BitVector) * 8)) + 1;
    /* Clear the whole array. */
    (void) memset(vector, 0, allocSize * sizeof(BitVector));
    return;

} /* end of bitVectorClear */

static void bitVectorFree

(

BitVector *

vector

)

[static]

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

Synopsis [Frees a bit vector.]

Description [Frees a bit vector.]

SideEffects [None]

SeeAlso [bitVectorAlloc]

Definition at line 1379 of file cuddEssent.c.

{
    FREE(vector);

} /* end of bitVectorFree */

static DD_INLINE short bitVectorRead	(	BitVector *	vector,
		int	i
	)			[static]

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

Synopsis [Returns the i-th entry of a bit vector.]

Description [Returns the i-th entry of a bit vector.]

SideEffects [None]

SeeAlso [bitVectorSet]

Definition at line 1400 of file cuddEssent.c.

{
    int word, bit;
    short result;

    if (vector == NULL) return((short) 0);

    word = i >> LOGBPL;
    bit = i & (BPL - 1);
    result = (short) ((vector[word] >> bit) & 1L);
    return(result);

} /* end of bitVectorRead */

static DD_INLINE void bitVectorSet	(	BitVector *	vector,
		int	i,
		short	val
	)			[static]

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

Synopsis [Sets the i-th entry of a bit vector to a value.]

Description [Sets the i-th entry of a bit vector to a value.]

SideEffects [None]

SeeAlso [bitVectorRead]

Definition at line 1430 of file cuddEssent.c.

{
    int word, bit;

    word = i >> LOGBPL;
    bit = i & (BPL - 1);
    vector[word] &= ~(1L << bit);
    vector[word] |= (((long) val) << bit);

} /* end of bitVectorSet */

static DdTlcInfo * computeClauses	(	DdTlcInfo *	Tres,
		DdTlcInfo *	Eres,
		DdHalfWord	label,
		int	size
	)			[static]

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

Synopsis [Computes the two-literal clauses for a node.]

Description [Computes the two-literal clauses for a node given the clauses for its children and the label of the node. Returns a pointer to a TclInfo structure if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [computeClausesWithUniverse]

Definition at line 764 of file cuddEssent.c.

{
    DdHalfWord *Tcv = Tres->vars; /* variables of clauses for the T child */
    BitVector *Tcp = Tres->phases; /* phases of clauses for the T child */
    DdHalfWord *Ecv = Eres->vars; /* variables of clauses for the E child */
    BitVector *Ecp = Eres->phases; /* phases of clauses for the E child */
    DdHalfWord *Vcv = NULL; /* pointer to variables of the clauses for v */
    BitVector *Vcp = NULL; /* pointer to phases of the clauses for v */
    DdTlcInfo *res = NULL; /* the set of clauses to be returned */
    int pt = 0; /* index in the list of clauses of T */
    int pe = 0; /* index in the list of clauses of E */
    int cv = 0; /* counter of the clauses for this node */
    TlClause *iclauses = NULL; /* list of inherited clauses */
    TlClause *tclauses = NULL; /* list of 1-literal clauses of T */
    TlClause *eclauses = NULL; /* list of 1-literal clauses of E */
    TlClause *nclauses = NULL; /* list of new (non-inherited) clauses */
    TlClause *lnclause = NULL; /* pointer to last new clause */
    TlClause *newclause; /* temporary pointer to new clauses */

    /* Initialize sets of one-literal clauses.  The one-literal clauses
    ** are stored redundantly.  These sets allow constant-time lookup, which
    ** we need when we check for implication of a two-literal clause by a
    ** one-literal clause.  The linked lists allow fast sequential
    ** processing. */
    bitVectorClear(Tolv, size);
    bitVectorClear(Tolp, size);
    bitVectorClear(Eolv, size);
    bitVectorClear(Eolp, size);

    /* Initialize result structure. */
    res = tlcInfoAlloc();
    if (res == NULL) goto cleanup;

    /* Scan the two input list.  Extract inherited two-literal clauses
    ** and set aside one-literal clauses from each list.  The incoming lists
    ** are sorted in the order defined by beforep.  The three linked list
    ** produced by this loop are sorted in the reverse order because we
    ** always append to the front of the lists.
    ** The inherited clauses are those clauses (both one- and two-literal)
    ** that are common to both children; and the two-literal clauses of
    ** one child that are implied by a one-literal clause of the other
    ** child. */
    while (!sentinelp(Tcv[pt], Tcv[pt+1]) || !sentinelp(Ecv[pe], Ecv[pe+1])) {
        if (equalp(Tcv[pt], bitVectorRead(Tcp, pt),
                   Tcv[pt+1], bitVectorRead(Tcp, pt+1),
                   Ecv[pe], bitVectorRead(Ecp, pe),
                   Ecv[pe+1], bitVectorRead(Ecp, pe+1))) {
            /* Add clause to inherited list. */
            newclause = ALLOC(TlClause,1);
            if (newclause == NULL) goto cleanup;
            newclause->v1 = Tcv[pt];
            newclause->v2 = Tcv[pt+1];
            newclause->p1 = bitVectorRead(Tcp, pt);
            newclause->p2 = bitVectorRead(Tcp, pt+1);
            newclause->next = iclauses;
            iclauses = newclause;
            pt += 2; pe += 2; cv++;
        } else if (beforep(Tcv[pt], bitVectorRead(Tcp, pt),
                   Tcv[pt+1], bitVectorRead(Tcp, pt+1),
                   Ecv[pe], bitVectorRead(Ecp, pe),
                   Ecv[pe+1], bitVectorRead(Ecp, pe+1))) {
            if (oneliteralp(Tcv[pt+1])) {
                /* Add this one-literal clause to the T set. */
                newclause = ALLOC(TlClause,1);
                if (newclause == NULL) goto cleanup;
                newclause->v1 = Tcv[pt];
                newclause->v2 = CUDD_MAXINDEX;
                newclause->p1 = bitVectorRead(Tcp, pt);
                newclause->p2 = 1;
                newclause->next = tclauses;
                tclauses = newclause;
                bitVectorSet(Tolv, Tcv[pt], 1);
                bitVectorSet(Tolp, Tcv[pt], bitVectorRead(Tcp, pt));
            } else {
                if (impliedp(Tcv[pt], bitVectorRead(Tcp, pt),
                             Tcv[pt+1], bitVectorRead(Tcp, pt+1),
                             Eolv, Eolp)) {
                    /* Add clause to inherited list. */
                    newclause = ALLOC(TlClause,1);
                    if (newclause == NULL) goto cleanup;
                    newclause->v1 = Tcv[pt];
                    newclause->v2 = Tcv[pt+1];
                    newclause->p1 = bitVectorRead(Tcp, pt);
                    newclause->p2 = bitVectorRead(Tcp, pt+1);
                    newclause->next = iclauses;
                    iclauses = newclause;
                    cv++;
                }
            }
            pt += 2;
        } else { /* !beforep() */
            if (oneliteralp(Ecv[pe+1])) {
                /* Add this one-literal clause to the E set. */
                newclause = ALLOC(TlClause,1);
                if (newclause == NULL) goto cleanup;
                newclause->v1 = Ecv[pe];
                newclause->v2 = CUDD_MAXINDEX;
                newclause->p1 = bitVectorRead(Ecp, pe);
                newclause->p2 = 1;
                newclause->next = eclauses;
                eclauses = newclause;
                bitVectorSet(Eolv, Ecv[pe], 1);
                bitVectorSet(Eolp, Ecv[pe], bitVectorRead(Ecp, pe));
            } else {
                if (impliedp(Ecv[pe], bitVectorRead(Ecp, pe),
                             Ecv[pe+1], bitVectorRead(Ecp, pe+1),
                             Tolv, Tolp)) {
                    /* Add clause to inherited list. */
                    newclause = ALLOC(TlClause,1);
                    if (newclause == NULL) goto cleanup;
                    newclause->v1 = Ecv[pe];
                    newclause->v2 = Ecv[pe+1];
                    newclause->p1 = bitVectorRead(Ecp, pe);
                    newclause->p2 = bitVectorRead(Ecp, pe+1);
                    newclause->next = iclauses;
                    iclauses = newclause;
                    cv++;
                }
            }
            pe += 2;
        }
    }

    /* Add one-literal clauses for the label variable to the front of
    ** the two lists. */
    newclause = ALLOC(TlClause,1);
    if (newclause == NULL) goto cleanup;
    newclause->v1 = label;
    newclause->v2 = CUDD_MAXINDEX;
    newclause->p1 = 0;
    newclause->p2 = 1;
    newclause->next = tclauses;
    tclauses = newclause;
    newclause = ALLOC(TlClause,1);
    if (newclause == NULL) goto cleanup;
    newclause->v1 = label;
    newclause->v2 = CUDD_MAXINDEX;
    newclause->p1 = 1;
    newclause->p2 = 1;
    newclause->next = eclauses;
    eclauses = newclause;

    /* Produce the non-inherited clauses.  We preserve the "reverse"
    ** order of the two input lists by appending to the end of the
    ** list.  In this way, iclauses and nclauses are consistent. */
    while (tclauses != NULL && eclauses != NULL) {
        if (beforep(eclauses->v1, eclauses->p1, eclauses->v2, eclauses->p2,
                    tclauses->v1, tclauses->p1, tclauses->v2, tclauses->p2)) {
            TlClause *nextclause = tclauses->next;
            TlClause *otherclauses = eclauses;
            while (otherclauses != NULL) {
                if (tclauses->v1 != otherclauses->v1) {
                    newclause = ALLOC(TlClause,1);
                    if (newclause == NULL) goto cleanup;
                    newclause->v1 = tclauses->v1;
                    newclause->v2 = otherclauses->v1;
                    newclause->p1 = tclauses->p1;
                    newclause->p2 = otherclauses->p1;
                    newclause->next = NULL;
                    if (nclauses == NULL) {
                        nclauses = newclause;
                        lnclause = newclause;
                    } else {
                        lnclause->next = newclause;
                        lnclause = newclause;
                    }
                    cv++;
                }
                otherclauses = otherclauses->next;
            }
            FREE(tclauses);
            tclauses = nextclause;
        } else {
            TlClause *nextclause = eclauses->next;
            TlClause *otherclauses = tclauses;
            while (otherclauses != NULL) {
                if (eclauses->v1 != otherclauses->v1) {
                    newclause = ALLOC(TlClause,1);
                    if (newclause == NULL) goto cleanup;
                    newclause->v1 = eclauses->v1;
                    newclause->v2 = otherclauses->v1;
                    newclause->p1 = eclauses->p1;
                    newclause->p2 = otherclauses->p1;
                    newclause->next = NULL;
                    if (nclauses == NULL) {
                        nclauses = newclause;
                        lnclause = newclause;
                    } else {
                        lnclause->next = newclause;
                        lnclause = newclause;
                    }
                    cv++;
                }
                otherclauses = otherclauses->next;
            }
            FREE(eclauses);
            eclauses = nextclause;
        }
    }
    while (tclauses != NULL) {
        TlClause *nextclause = tclauses->next;
        FREE(tclauses);
        tclauses = nextclause;
    }
    while (eclauses != NULL) {
        TlClause *nextclause = eclauses->next;
        FREE(eclauses);
        eclauses = nextclause;
    }

    /* Merge inherited and non-inherited clauses.  Now that we know the
    ** total number, we allocate the arrays, and we fill them bottom-up
    ** to restore the proper ordering. */
    Vcv = ALLOC(DdHalfWord, 2*(cv+1));
    if (Vcv == NULL) goto cleanup;
    if (cv > 0) {
        Vcp = bitVectorAlloc(2*cv);
        if (Vcp == NULL) goto cleanup;
    } else {
        Vcp = NULL;
    }
    res->vars = Vcv;
    res->phases = Vcp;
    /* Add sentinel. */
    Vcv[2*cv] = 0;
    Vcv[2*cv+1] = 0;
    while (iclauses != NULL || nclauses != NULL) {
        TlClause *nextclause;
        cv--;
        if (nclauses == NULL || (iclauses != NULL &&
            beforep(nclauses->v1, nclauses->p1, nclauses->v2, nclauses->p2,
                    iclauses->v1, iclauses->p1, iclauses->v2, iclauses->p2))) {
            Vcv[2*cv] = iclauses->v1;
            Vcv[2*cv+1] = iclauses->v2;
            bitVectorSet(Vcp, 2*cv, iclauses->p1);
            bitVectorSet(Vcp, 2*cv+1, iclauses->p2);
            nextclause = iclauses->next;
            FREE(iclauses);
            iclauses = nextclause;
        } else {
            Vcv[2*cv] = nclauses->v1;
            Vcv[2*cv+1] = nclauses->v2;
            bitVectorSet(Vcp, 2*cv, nclauses->p1);
            bitVectorSet(Vcp, 2*cv+1, nclauses->p2);
            nextclause = nclauses->next;
            FREE(nclauses);
            nclauses = nextclause;
        }
    }
    assert(cv == 0);

    return(res);

 cleanup:
    if (res != NULL) Cudd_tlcInfoFree(res);
    while (iclauses != NULL) {
        TlClause *nextclause = iclauses->next;
        FREE(iclauses);
        iclauses = nextclause;
    }
    while (nclauses != NULL) {
        TlClause *nextclause = nclauses->next;
        FREE(nclauses);
        nclauses = nextclause;
    }
    while (tclauses != NULL) {
        TlClause *nextclause = tclauses->next;
        FREE(tclauses);
        tclauses = nextclause;
    }
    while (eclauses != NULL) {
        TlClause *nextclause = eclauses->next;
        FREE(eclauses);
        eclauses = nextclause;
    }

    return(NULL);

} /* end of computeClauses */

static DdTlcInfo * computeClausesWithUniverse	(	DdTlcInfo *	Cres,
		DdHalfWord	label,
		short	phase
	)			[static]

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

Synopsis [Computes the two-literal clauses for a node.]

Description [Computes the two-literal clauses for a node with a zero child, given the clauses for its other child and the label of the node. Returns a pointer to a TclInfo structure if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [computeClauses]

Definition at line 1064 of file cuddEssent.c.

{
    DdHalfWord *Ccv = Cres->vars; /* variables of clauses for child */
    BitVector *Ccp = Cres->phases; /* phases of clauses for child */
    DdHalfWord *Vcv = NULL; /* pointer to the variables of the clauses for v */
    BitVector *Vcp = NULL; /* pointer to the phases of the clauses for v */
    DdTlcInfo *res = NULL; /* the set of clauses to be returned */
    int i;

    /* Initialize result. */
    res = tlcInfoAlloc();
    if (res == NULL) goto cleanup;
    /* Count entries for new list and allocate accordingly. */
    for (i = 0; !sentinelp(Ccv[i], Ccv[i+1]); i += 2);
    /* At this point, i is twice the number of clauses in the child's
    ** list.  We need four more entries for this node: 2 for the one-literal
    ** clause for the label, and 2 for the sentinel. */
    Vcv = ALLOC(DdHalfWord,i+4);
    if (Vcv == NULL) goto cleanup;
    Vcp = bitVectorAlloc(i+4);
    if (Vcp == NULL) goto cleanup;
    res->vars = Vcv;
    res->phases = Vcp;
    /* Copy old list into new. */
    for (i = 0; !sentinelp(Ccv[i], Ccv[i+1]); i += 2) {
        Vcv[i] = Ccv[i];
        Vcv[i+1] = Ccv[i+1];
        bitVectorSet(Vcp, i, bitVectorRead(Ccp, i));
        bitVectorSet(Vcp, i+1, bitVectorRead(Ccp, i+1));
    }
    /* Add clause corresponding to label. */
    Vcv[i] = label;
    bitVectorSet(Vcp, i, phase);
    i++;
    Vcv[i] = CUDD_MAXINDEX;
    bitVectorSet(Vcp, i, 1);
    i++;
    /* Add sentinel. */
    Vcv[i] = 0;
    Vcv[i+1] = 0;
    bitVectorSet(Vcp, i, 0);
    bitVectorSet(Vcp, i+1, 0);

    return(res);

 cleanup:
    /* Vcp is guaranteed to be NULL here.  Hence, we do not try to free it. */
    if (Vcv != NULL) FREE(Vcv);
    if (res != NULL) Cudd_tlcInfoFree(res);

    return(NULL);

} /* end of computeClausesWithUniverse */

int Cudd_bddIsVarEssential	(	DdManager *	manager,
		DdNode *	f,
		int	id,
		int	phase
	)

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

Synopsis [Determines whether a given variable is essential with a given phase in a BDD.]

Description [Determines whether a given variable is essential with a given phase in a BDD. Uses Cudd_bddIteConstant. Returns 1 if phase == 1 and f-->x_id, or if phase == 0 and f-->x_id'.]

SideEffects [None]

SeeAlso [Cudd_FindEssential]

Definition at line 235 of file cuddEssent.c.

{
    DdNode      *var;
    int         res;

    var = Cudd_bddIthVar(manager, id);

    var = Cudd_NotCond(var,phase == 0);

    res = Cudd_bddLeq(manager, f, var);

    return(res);

} /* end of Cudd_bddIsVarEssential */

DdNode* Cudd_FindEssential	(	DdManager *	dd,
		DdNode *	f
	)

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

Synopsis [Finds the essential variables of a DD.]

Description [Returns the cube of the essential variables. A positive literal means that the variable must be set to 1 for the function to be 1. A negative literal means that the variable must be set to 0 for the function to be 1. Returns a pointer to the cube BDD if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [Cudd_bddIsVarEssential]

Definition at line 205 of file cuddEssent.c.

{
    DdNode *res;

    do {
        dd->reordered = 0;
        res = ddFindEssentialRecur(dd,f);
    } while (dd->reordered == 1);
    return(res);

} /* end of Cudd_FindEssential */

DdTlcInfo* Cudd_FindTwoLiteralClauses	(	DdManager *	dd,
		DdNode *	f
	)

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

Synopsis [Finds the two literal clauses of a DD.]

Description [Returns the one- and two-literal clauses of a DD. Returns a pointer to the structure holding the clauses if successful; NULL otherwise. For a constant DD, the empty set of clauses is returned. This is obviously correct for a non-zero constant. For the constant zero, it is based on the assumption that only those clauses containing variables in the support of the function are considered. Since the support of a constant function is empty, no clauses are returned.]

SideEffects [None]

SeeAlso [Cudd_FindEssential]

Definition at line 273 of file cuddEssent.c.

{
    DdTlcInfo *res;
    st_table *table;
    st_generator *gen;
    DdTlcInfo *tlc;
    DdNode *node;
    int size = dd->size;

    if (Cudd_IsConstant(f)) {
        res = emptyClauseSet();
        return(res);
    }
    table = st_init_table(st_ptrcmp,st_ptrhash);
    if (table == NULL) return(NULL);
    Tolv = bitVectorAlloc(size);
    if (Tolv == NULL) {
        st_free_table(table);
        return(NULL);
    }
    Tolp = bitVectorAlloc(size);
    if (Tolp == NULL) {
        st_free_table(table);
        bitVectorFree(Tolv);
        return(NULL);
    }
    Eolv = bitVectorAlloc(size);
    if (Eolv == NULL) {
        st_free_table(table);
        bitVectorFree(Tolv);
        bitVectorFree(Tolp);
        return(NULL);
    }
    Eolp = bitVectorAlloc(size);
    if (Eolp == NULL) {
        st_free_table(table);
        bitVectorFree(Tolv);
        bitVectorFree(Tolp);
        bitVectorFree(Eolv);
        return(NULL);
    }

    res = ddFindTwoLiteralClausesRecur(dd,f,table);
    /* Dispose of table contents and free table. */
    st_foreach_item(table, gen, &node, &tlc) {
        if (node != f) {
            Cudd_tlcInfoFree(tlc);
        }
    }
    st_free_table(table);
    bitVectorFree(Tolv);
    bitVectorFree(Tolp);
    bitVectorFree(Eolv);
    bitVectorFree(Eolp);

    if (res != NULL) {
        int i;
        for (i = 0; !sentinelp(res->vars[i], res->vars[i+1]); i += 2);
        res->cnt = i >> 1;
    }

    return(res);

} /* end of Cudd_FindTwoLiteralClauses */

int Cudd_PrintTwoLiteralClauses	(	DdManager *	dd,
		DdNode *	f,
		char **	names,
		FILE *	fp
	)

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

Synopsis [Prints the two literal clauses of a DD.]

Description [Prints the one- and two-literal clauses. Returns 1 if successful; 0 otherwise. The argument "names" can be NULL, in which case the variable indices are printed.]

SideEffects [None]

SeeAlso [Cudd_FindTwoLiteralClauses]

Definition at line 389 of file cuddEssent.c.

{
    DdHalfWord *vars;
    BitVector *phases;
    int i;
    DdTlcInfo *res = Cudd_FindTwoLiteralClauses(dd, f);
    FILE *ifp = fp == NULL ? dd->out : fp;

    if (res == NULL) return(0);
    vars = res->vars;
    phases = res->phases;
    for (i = 0; !sentinelp(vars[i], vars[i+1]); i += 2) {
        if (names != NULL) {
            if (vars[i+1] == CUDD_MAXINDEX) {
                (void) fprintf(ifp, "%s%s\n",
                               bitVectorRead(phases, i) ? "~" : " ",
                               names[vars[i]]);
            } else {
                (void) fprintf(ifp, "%s%s | %s%s\n",
                               bitVectorRead(phases, i) ? "~" : " ",
                               names[vars[i]],
                               bitVectorRead(phases, i+1) ? "~" : " ",
                               names[vars[i+1]]);
            }
        } else {
            if (vars[i+1] == CUDD_MAXINDEX) {
                (void) fprintf(ifp, "%s%d\n",
                               bitVectorRead(phases, i) ? "~" : " ",
                               (int) vars[i]);
            } else {
                (void) fprintf(ifp, "%s%d | %s%d\n",
                               bitVectorRead(phases, i) ? "~" : " ",
                               (int) vars[i],
                               bitVectorRead(phases, i+1) ? "~" : " ",
                               (int) vars[i+1]);
            }
        }
    }
    Cudd_tlcInfoFree(res);

    return(1);

} /* end of Cudd_PrintTwoLiteralClauses */

int Cudd_ReadIthClause	(	DdTlcInfo *	tlc,
		int	i,
		DdHalfWord *	var1,
		DdHalfWord *	var2,
		int *	phase1,
		int *	phase2
	)

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

Synopsis [Accesses the i-th clause of a DD.]

Description [Accesses the i-th clause of a DD given the clause set which must be already computed. Returns 1 if successful; 0 if i is out of range, or in case of error.]

SideEffects [the four components of a clause are returned as side effects.]

SeeAlso [Cudd_FindTwoLiteralClauses]

Definition at line 355 of file cuddEssent.c.

{
    if (tlc == NULL) return(0);
    if (tlc->vars == NULL || tlc->phases == NULL) return(0);
    if (i < 0 || (unsigned) i >= tlc->cnt) return(0);
    *var1 = tlc->vars[2*i];
    *var2 = tlc->vars[2*i+1];
    *phase1 = (int) bitVectorRead(tlc->phases, 2*i);
    *phase2 = (int) bitVectorRead(tlc->phases, 2*i+1);
    return(1);

} /* end of Cudd_ReadIthClause */

void Cudd_tlcInfoFree

(

DdTlcInfo *

t

)

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

Synopsis [Frees a DdTlcInfo Structure.]

Description [Frees a DdTlcInfo Structure as well as the memory pointed by it.]

SideEffects [None]

SeeAlso []

Definition at line 451 of file cuddEssent.c.

{
    if (t->vars != NULL) FREE(t->vars);
    if (t->phases != NULL) FREE(t->phases);
    FREE(t);

} /* end of Cudd_tlcInfoFree */

static DdNode * ddFindEssentialRecur	(	DdManager *	dd,
		DdNode *	f
	)			[static]

AutomaticStart

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

Synopsis [Implements the recursive step of Cudd_FindEssential.]

Description [Implements the recursive step of Cudd_FindEssential. Returns a pointer to the cube BDD if successful; NULL otherwise.]

SideEffects [None]

Definition at line 482 of file cuddEssent.c.

{
    DdNode      *T, *E, *F;
    DdNode      *essT, *essE, *res;
    int         index;
    DdNode      *one, *lzero, *azero;

    one = DD_ONE(dd);
    F = Cudd_Regular(f);
    /* If f is constant the set of essential variables is empty. */
    if (cuddIsConstant(F)) return(one);

    res = cuddCacheLookup1(dd,Cudd_FindEssential,f);
    if (res != NULL) {
        return(res);
    }

    lzero = Cudd_Not(one);
    azero = DD_ZERO(dd);
    /* Find cofactors: here f is non-constant. */
    T = cuddT(F);
    E = cuddE(F);
    if (Cudd_IsComplement(f)) {
        T = Cudd_Not(T); E = Cudd_Not(E);
    }

    index = F->index;
    if (Cudd_IsConstant(T) && T != lzero && T != azero) {
        /* if E is zero, index is essential, otherwise there are no
        ** essentials, because index is not essential and no other variable
        ** can be, since setting index = 1 makes the function constant and
        ** different from 0.
        */
        if (E == lzero || E == azero) {
            res = dd->vars[index];
        } else {
            res = one;
        }
    } else if (T == lzero || T == azero) {
        if (Cudd_IsConstant(E)) { /* E cannot be zero here */
            res = Cudd_Not(dd->vars[index]);
        } else { /* E == non-constant */
            /* find essentials in the else branch */
            essE = ddFindEssentialRecur(dd,E);
            if (essE == NULL) {
                return(NULL);
            }
            cuddRef(essE);

            /* add index to the set with negative phase */
            res = cuddUniqueInter(dd,index,one,Cudd_Not(essE));
            if (res == NULL) {
                Cudd_RecursiveDeref(dd,essE);
                return(NULL);
            }
            res = Cudd_Not(res);
            cuddDeref(essE);
        }
    } else { /* T == non-const */
        if (E == lzero || E == azero) {
            /* find essentials in the then branch */
            essT = ddFindEssentialRecur(dd,T);
            if (essT == NULL) {
                return(NULL);
            }
            cuddRef(essT);

            /* add index to the set with positive phase */
            /* use And because essT may be complemented */
            res = cuddBddAndRecur(dd,dd->vars[index],essT);
            if (res == NULL) {
                Cudd_RecursiveDeref(dd,essT);
                return(NULL);
            }
            cuddDeref(essT);
        } else if (!Cudd_IsConstant(E)) {
            /* if E is a non-zero constant there are no essentials
            ** because T is non-constant.
            */
            essT = ddFindEssentialRecur(dd,T);
            if (essT == NULL) {
                return(NULL);
            }
            if (essT == one) {
                res = one;
            } else {
                cuddRef(essT);
                essE = ddFindEssentialRecur(dd,E);
                if (essE == NULL) {
                    Cudd_RecursiveDeref(dd,essT);
                    return(NULL);
                }
                cuddRef(essE);

                /* res = intersection(essT, essE) */
                res = cuddBddLiteralSetIntersectionRecur(dd,essT,essE);
                if (res == NULL) {
                    Cudd_RecursiveDeref(dd,essT);
                    Cudd_RecursiveDeref(dd,essE);
                    return(NULL);
                }
                cuddRef(res);
                Cudd_RecursiveDeref(dd,essT);
                Cudd_RecursiveDeref(dd,essE);
                cuddDeref(res);
            }
        } else {        /* E is a non-zero constant */
            res = one;
        }
    }

    cuddCacheInsert1(dd,Cudd_FindEssential, f, res);
    return(res);

} /* end of ddFindEssentialRecur */

static DdTlcInfo * ddFindTwoLiteralClausesRecur	(	DdManager *	dd,
		DdNode *	f,
		st_table *	table
	)			[static]

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

Synopsis [Implements the recursive step of Cudd_FindTwoLiteralClauses.]

Description [Implements the recursive step of Cudd_FindTwoLiteralClauses. The DD node is assumed to be not constant. Returns a pointer to a set of clauses if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [Cudd_FindTwoLiteralClauses]

Definition at line 616 of file cuddEssent.c.

{
    DdNode *T, *E, *F;
    DdNode *one, *lzero, *azero;
    DdTlcInfo *res, *Tres, *Eres;
    DdHalfWord index;

    F = Cudd_Regular(f);

    assert(!cuddIsConstant(F));

    /* Check computed table.  Separate entries are necessary for
    ** a node and its complement.  We should update the counter here. */
    if (st_lookup(table, f, &res)) {
        return(res);
    }

    /* Easy access to the constants for BDDs and ADDs. */
    one = DD_ONE(dd);
    lzero = Cudd_Not(one);
    azero = DD_ZERO(dd);

    /* Find cofactors and variable labeling the top node. */
    T = cuddT(F); E = cuddE(F);
    if (Cudd_IsComplement(f)) {
        T = Cudd_Not(T); E = Cudd_Not(E);
    }
    index = F->index;

    if (Cudd_IsConstant(T) && T != lzero && T != azero) {
        /* T is a non-zero constant.  If E is zero, then this node's index
        ** is a one-literal clause.  Otherwise, if E is a non-zero
        ** constant, there are no clauses for this node.  Finally,
        ** if E is not constant, we recursively compute its clauses, and then
        ** merge using the empty set for T. */
        if (E == lzero || E == azero) {
            /* Create the clause (index + 0). */
            res = tlcInfoAlloc();
            if (res == NULL) return(NULL);
            res->vars = ALLOC(DdHalfWord,4);
            if (res->vars == NULL) {
                FREE(res);
                return(NULL);
            }
            res->phases = bitVectorAlloc(2);
            if (res->phases == NULL) {
                FREE(res->vars);
                FREE(res);
                return(NULL);
            }
            res->vars[0] = index;
            res->vars[1] = CUDD_MAXINDEX;
            res->vars[2] = 0;
            res->vars[3] = 0;
            bitVectorSet(res->phases, 0, 0); /* positive phase */
            bitVectorSet(res->phases, 1, 1); /* negative phase */
        } else if (Cudd_IsConstant(E)) {
            /* If E is a non-zero constant, no clauses. */
            res = emptyClauseSet();
        } else {
            /* E is non-constant */
            Tres = emptyClauseSet();
            if (Tres == NULL) return(NULL);
            Eres = ddFindTwoLiteralClausesRecur(dd, E, table);
            if (Eres == NULL) {
                Cudd_tlcInfoFree(Tres);
                return(NULL);
            }
            res = computeClauses(Tres, Eres, index, dd->size);
            Cudd_tlcInfoFree(Tres);
        }
    } else if (T == lzero || T == azero) {
        /* T is zero.  If E is a non-zero constant, then the
        ** complement of this node's index is a one-literal clause.
        ** Otherwise, if E is not constant, we recursively compute its
        ** clauses, and then merge using the universal set for T. */
        if (Cudd_IsConstant(E)) { /* E cannot be zero here */
            /* Create the clause (!index + 0). */
            res = tlcInfoAlloc();
            if (res == NULL) return(NULL);
            res->vars = ALLOC(DdHalfWord,4);
            if (res->vars == NULL) {
                FREE(res);
                return(NULL);
            }
            res->phases = bitVectorAlloc(2);
            if (res->phases == NULL) {
                FREE(res->vars);
                FREE(res);
                return(NULL);
            }
            res->vars[0] = index;
            res->vars[1] = CUDD_MAXINDEX;
            res->vars[2] = 0;
            res->vars[3] = 0;
            bitVectorSet(res->phases, 0, 1); /* negative phase */
            bitVectorSet(res->phases, 1, 1); /* negative phase */
        } else { /* E == non-constant */
            Eres = ddFindTwoLiteralClausesRecur(dd, E, table);
            if (Eres == NULL) return(NULL);
            res = computeClausesWithUniverse(Eres, index, 1);
        }
    } else { /* T == non-const */
        Tres = ddFindTwoLiteralClausesRecur(dd, T, table);
        if (Tres == NULL) return(NULL);
        if (Cudd_IsConstant(E)) {
            if (E == lzero || E == azero) {
                res = computeClausesWithUniverse(Tres, index, 0);
            } else {
                Eres = emptyClauseSet();
                if (Eres == NULL) return(NULL);
                res = computeClauses(Tres, Eres, index, dd->size);
                Cudd_tlcInfoFree(Eres);
            }
        } else {
            Eres = ddFindTwoLiteralClausesRecur(dd, E, table);
            if (Eres == NULL) return(NULL);
            res = computeClauses(Tres, Eres, index, dd->size);
        }
    }

    /* Cache results. */
    if (st_add_direct(table, (char *)f, (char *)res) == ST_OUT_OF_MEM) {
        FREE(res);
        return(NULL);
    }
    return(res);

} /* end of ddFindTwoLiteralClausesRecur */

static DdTlcInfo * emptyClauseSet

(

void

)

[static]

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

Synopsis [Returns an enpty set of clauses.]

Description [Returns a pointer to an empty set of clauses if successful; NULL otherwise. No bit vector for the phases is allocated.]

SideEffects [None]

SeeAlso []

Definition at line 1136 of file cuddEssent.c.

{
    DdTlcInfo *eset;

    eset = ALLOC(DdTlcInfo,1);
    if (eset == NULL) return(NULL);
    eset->vars = ALLOC(DdHalfWord,2);
    if (eset->vars == NULL) {
        FREE(eset);
        return(NULL);
    }
    /* Sentinel */
    eset->vars[0] = 0;
    eset->vars[1] = 0;
    eset->phases = NULL; /* does not matter */
    eset->cnt = 0;
    return(eset);

} /* end of emptyClauseSet */

static int equalp	(	DdHalfWord	var1a,
		short	phase1a,
		DdHalfWord	var1b,
		short	phase1b,
		DdHalfWord	var2a,
		short	phase2a,
		DdHalfWord	var2b,
		short	phase2b
	)			[static]

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

Synopsis [Returns true iff the two arguments are identical clauses.]

Description [Returns true iff the two arguments are identical clauses. Since literals are sorted, we only need to compare literals in the same position.]

SideEffects [None]

SeeAlso [beforep]

Definition at line 1193 of file cuddEssent.c.

{
    return(var1a == var2a && phase1a == phase2a &&
           var1b == var2b && phase1b == phase2b);

} /* end of equalp */

static int impliedp	(	DdHalfWord	var1,
		short	phase1,
		DdHalfWord	var2,
		short	phase2,
		BitVector *	olv,
		BitVector *	olp
	)			[static]

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

Synopsis [Returns true iff either literal of a clause is in a set of literals.]

Description [Returns true iff either literal of a clause is in a set of literals. The first four arguments specify the clause. The remaining two arguments specify the literal set.]

SideEffects [None]

SeeAlso []

Definition at line 1284 of file cuddEssent.c.

{
    return((bitVectorRead(olv, var1) &&
            bitVectorRead(olp, var1) == phase1) ||
           (bitVectorRead(olv, var2) &&
            bitVectorRead(olp, var2) == phase2));

} /* end of impliedp */

static int oneliteralp

(

DdHalfWord

var

)

[static]

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

Synopsis [Returns true iff the argument is a one-literal clause.]

Description [Returns true iff the argument is a one-literal clause. A one-litaral clause has the constant FALSE as second literal. Since the constant TRUE is never used, it is sufficient to test for a constant.]

SideEffects [None]

SeeAlso []

Definition at line 1261 of file cuddEssent.c.

{
    return(var == CUDD_MAXINDEX);

} /* end of oneliteralp */

static int sentinelp	(	DdHalfWord	var1,
		DdHalfWord	var2
	)			[static]

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

Synopsis [Returns true iff the argument is the sentinel clause.]

Description [Returns true iff the argument is the sentinel clause. A sentinel clause has both variables equal to 0.]

SideEffects [None]

SeeAlso []

Definition at line 1170 of file cuddEssent.c.

{
    return(var1 == 0 && var2 == 0);

} /* end of sentinelp */

static DdTlcInfo * tlcInfoAlloc

(

void

)

[static]

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

Synopsis [Allocates a DdTlcInfo Structure.]

Description [Returns a pointer to a DdTlcInfo Structure if successful; NULL otherwise.]

SideEffects [None]

SeeAlso [Cudd_tlcInfoFree]

Definition at line 1458 of file cuddEssent.c.

{
    DdTlcInfo *res = ALLOC(DdTlcInfo,1);
    if (res == NULL) return(NULL);
    res->vars = NULL;
    res->phases = NULL;
    res->cnt = 0;
    return(res);

} /* end of tlcInfoAlloc */

---

Variable Documentation

char rcsid [] DD_UNUSED = "$Id: cuddEssent.c,v 1.24 2009/02/21 18:24:10 fabio Exp $" [static]

Definition at line 146 of file cuddEssent.c.

BitVector* Eolp [static]

Definition at line 152 of file cuddEssent.c.

BitVector* Eolv [static]

Definition at line 151 of file cuddEssent.c.

BitVector* Tolp [static]

Definition at line 150 of file cuddEssent.c.

BitVector* Tolv [static]

Definition at line 149 of file cuddEssent.c.