/**CFile***********************************************************************
FileName [cuddZddFuncs.c]
PackageName [cudd]
Synopsis [Functions to manipulate covers represented as ZDDs.]
Description [External procedures included in this module:
<ul>
<li> Cudd_zddProduct();
<li> Cudd_zddUnateProduct();
<li> Cudd_zddWeakDiv();
<li> Cudd_zddWeakDivF();
<li> Cudd_zddDivide();
<li> Cudd_zddDivideF();
<li> Cudd_zddComplement();
</ul>
Internal procedures included in this module:
<ul>
<li> cuddZddProduct();
<li> cuddZddUnateProduct();
<li> cuddZddWeakDiv();
<li> cuddZddWeakDivF();
<li> cuddZddDivide();
<li> cuddZddDivideF();
<li> cuddZddGetCofactors3()
<li> cuddZddGetCofactors2()
<li> cuddZddComplement();
<li> cuddZddGetPosVarIndex();
<li> cuddZddGetNegVarIndex();
<li> cuddZddGetPosVarLevel();
<li> cuddZddGetNegVarLevel();
</ul>
Static procedures included in this module:
<ul>
</ul>
]
SeeAlso []
Author [In-Ho Moon]
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"
/*---------------------------------------------------------------------------*/
/* Constant declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Stucture declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Type declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Variable declarations */
/*---------------------------------------------------------------------------*/
#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddZddFuncs.c,v 1.1.1.1 2003/02/24 22:23:53 wjiang Exp $";
#endif
/*---------------------------------------------------------------------------*/
/* Macro declarations */
/*---------------------------------------------------------------------------*/
/**AutomaticStart*************************************************************/
/*---------------------------------------------------------------------------*/
/* Static function prototypes */
/*---------------------------------------------------------------------------*/
/**AutomaticEnd***************************************************************/
/*---------------------------------------------------------------------------*/
/* Definition of exported functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Computes the product of two covers represented by ZDDs.]
Description [Computes the product of two covers represented by
ZDDs. The result is also a ZDD. Returns a pointer to the result if
successful; NULL otherwise. The covers on which Cudd_zddProduct
operates use two ZDD variables for each function variable (one ZDD
variable for each literal of the variable). Those two ZDD variables
should be adjacent in the order.]
SideEffects [None]
SeeAlso [Cudd_zddUnateProduct]
******************************************************************************/
DdNode *
Cudd_zddProduct(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddProduct(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddProduct */
/**Function********************************************************************
Synopsis [Computes the product of two unate covers.]
Description [Computes the product of two unate covers represented as
ZDDs. Unate covers use one ZDD variable for each BDD
variable. Returns a pointer to the result if successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_zddProduct]
******************************************************************************/
DdNode *
Cudd_zddUnateProduct(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddUnateProduct(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddUnateProduct */
/**Function********************************************************************
Synopsis [Applies weak division to two covers.]
Description [Applies weak division to two ZDDs representing two
covers. Returns a pointer to the ZDD representing the result if
successful; NULL otherwise. The result of weak division depends on
the variable order. The covers on which Cudd_zddWeakDiv operates use
two ZDD variables for each function variable (one ZDD variable for
each literal of the variable). Those two ZDD variables should be
adjacent in the order.]
SideEffects [None]
SeeAlso [Cudd_zddDivide]
******************************************************************************/
DdNode *
Cudd_zddWeakDiv(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddWeakDiv(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddWeakDiv */
/**Function********************************************************************
Synopsis [Computes the quotient of two unate covers.]
Description [Computes the quotient of two unate covers represented
by ZDDs. Unate covers use one ZDD variable for each BDD
variable. Returns a pointer to the resulting ZDD if successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_zddWeakDiv]
******************************************************************************/
DdNode *
Cudd_zddDivide(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddDivide(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddDivide */
/**Function********************************************************************
Synopsis [Modified version of Cudd_zddWeakDiv.]
Description [Modified version of Cudd_zddWeakDiv. This function may
disappear in future releases.]
SideEffects [None]
SeeAlso [Cudd_zddWeakDiv]
******************************************************************************/
DdNode *
Cudd_zddWeakDivF(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddWeakDivF(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddWeakDivF */
/**Function********************************************************************
Synopsis [Modified version of Cudd_zddDivide.]
Description [Modified version of Cudd_zddDivide. This function may
disappear in future releases.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
Cudd_zddDivideF(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
do {
dd->reordered = 0;
res = cuddZddDivideF(dd, f, g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_zddDivideF */
/**Function********************************************************************
Synopsis [Computes a complement cover for a ZDD node.]
Description [Computes a complement cover for a ZDD node. For lack of a
better method, we first extract the function BDD from the ZDD cover,
then make the complement of the ZDD cover from the complement of the
BDD node by using ISOP. Returns a pointer to the resulting cover if
successful; NULL otherwise. The result depends on current variable
order.]
SideEffects [The result depends on current variable order.]
SeeAlso []
******************************************************************************/
DdNode *
Cudd_zddComplement(
DdManager *dd,
DdNode *node)
{
DdNode *b, *isop, *zdd_I;
/* Check cache */
zdd_I = cuddCacheLookup1Zdd(dd, cuddZddComplement, node);
if (zdd_I)
return(zdd_I);
b = Cudd_MakeBddFromZddCover(dd, node);
if (!b)
return(NULL);
Cudd_Ref(b);
isop = Cudd_zddIsop(dd, Cudd_Not(b), Cudd_Not(b), &zdd_I);
if (!isop) {
Cudd_RecursiveDeref(dd, b);
return(NULL);
}
Cudd_Ref(isop);
Cudd_Ref(zdd_I);
Cudd_RecursiveDeref(dd, b);
Cudd_RecursiveDeref(dd, isop);
cuddCacheInsert1(dd, cuddZddComplement, node, zdd_I);
Cudd_Deref(zdd_I);
return(zdd_I);
} /* end of Cudd_zddComplement */
/*---------------------------------------------------------------------------*/
/* Definition of internal functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddProduct.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddProduct]
******************************************************************************/
DdNode *
cuddZddProduct(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v, top_f, top_g;
DdNode *tmp, *term1, *term2, *term3;
DdNode *f0, *f1, *fd, *g0, *g1, *gd;
DdNode *R0, *R1, *Rd, *N0, *N1;
DdNode *r;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
int flag;
int pv, nv;
statLine(dd);
if (f == zero || g == zero)
return(zero);
if (f == one)
return(g);
if (g == one)
return(f);
top_f = dd->permZ[f->index];
top_g = dd->permZ[g->index];
if (top_f > top_g)
return(cuddZddProduct(dd, g, f));
/* Check cache */
r = cuddCacheLookup2Zdd(dd, cuddZddProduct, f, g);
if (r)
return(r);
v = f->index; /* either yi or zi */
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
Cudd_Ref(gd);
pv = cuddZddGetPosVarIndex(dd, v);
nv = cuddZddGetNegVarIndex(dd, v);
Rd = cuddZddProduct(dd, fd, gd);
if (Rd == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(Rd);
term1 = cuddZddProduct(dd, f0, g0);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
return(NULL);
}
Cudd_Ref(term1);
term2 = cuddZddProduct(dd, f0, gd);
if (term2 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
Cudd_RecursiveDerefZdd(dd, term1);
return(NULL);
}
Cudd_Ref(term2);
term3 = cuddZddProduct(dd, fd, g0);
if (term3 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
return(NULL);
}
Cudd_Ref(term3);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g0);
tmp = cuddZddUnion(dd, term1, term2);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
Cudd_RecursiveDerefZdd(dd, term3);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
R0 = cuddZddUnion(dd, tmp, term3);
if (R0 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
Cudd_RecursiveDerefZdd(dd, term3);
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(R0);
Cudd_RecursiveDerefZdd(dd, tmp);
Cudd_RecursiveDerefZdd(dd, term3);
N0 = cuddZddGetNode(dd, nv, R0, Rd); /* nv = zi */
if (N0 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, Rd);
Cudd_RecursiveDerefZdd(dd, R0);
return(NULL);
}
Cudd_Ref(N0);
Cudd_RecursiveDerefZdd(dd, R0);
Cudd_RecursiveDerefZdd(dd, Rd);
term1 = cuddZddProduct(dd, f1, g1);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, N0);
return(NULL);
}
Cudd_Ref(term1);
term2 = cuddZddProduct(dd, f1, gd);
if (term2 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, N0);
Cudd_RecursiveDerefZdd(dd, term1);
return(NULL);
}
Cudd_Ref(term2);
term3 = cuddZddProduct(dd, fd, g1);
if (term3 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, gd);
Cudd_RecursiveDerefZdd(dd, N0);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
return(NULL);
}
Cudd_Ref(term3);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
tmp = cuddZddUnion(dd, term1, term2);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, N0);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
Cudd_RecursiveDerefZdd(dd, term3);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
R1 = cuddZddUnion(dd, tmp, term3);
if (R1 == NULL) {
Cudd_RecursiveDerefZdd(dd, N0);
Cudd_RecursiveDerefZdd(dd, term3);
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(R1);
Cudd_RecursiveDerefZdd(dd, tmp);
Cudd_RecursiveDerefZdd(dd, term3);
N1 = cuddZddGetNode(dd, pv, R1, N0); /* pv = yi */
if (N1 == NULL) {
Cudd_RecursiveDerefZdd(dd, N0);
Cudd_RecursiveDerefZdd(dd, R1);
return(NULL);
}
Cudd_Ref(N1);
Cudd_RecursiveDerefZdd(dd, R1);
Cudd_RecursiveDerefZdd(dd, N0);
cuddCacheInsert2(dd, cuddZddProduct, f, g, N1);
Cudd_Deref(N1);
return(N1);
} /* end of cuddZddProduct */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddUnateProduct.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddUnateProduct]
******************************************************************************/
DdNode *
cuddZddUnateProduct(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v, top_f, top_g;
DdNode *term1, *term2, *term3, *term4;
DdNode *sum1, *sum2;
DdNode *f0, *f1, *g0, *g1;
DdNode *r;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
int flag;
statLine(dd);
if (f == zero || g == zero)
return(zero);
if (f == one)
return(g);
if (g == one)
return(f);
top_f = dd->permZ[f->index];
top_g = dd->permZ[g->index];
if (top_f > top_g)
return(cuddZddUnateProduct(dd, g, f));
/* Check cache */
r = cuddCacheLookup2Zdd(dd, cuddZddUnateProduct, f, g);
if (r)
return(r);
v = f->index; /* either yi or zi */
flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0);
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
term1 = cuddZddUnateProduct(dd, f1, g1);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
return(NULL);
}
Cudd_Ref(term1);
term2 = cuddZddUnateProduct(dd, f1, g0);
if (term2 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, term1);
return(NULL);
}
Cudd_Ref(term2);
term3 = cuddZddUnateProduct(dd, f0, g1);
if (term3 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
return(NULL);
}
Cudd_Ref(term3);
term4 = cuddZddUnateProduct(dd, f0, g0);
if (term4 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
Cudd_RecursiveDerefZdd(dd, term3);
return(NULL);
}
Cudd_Ref(term4);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
sum1 = cuddZddUnion(dd, term1, term2);
if (sum1 == NULL) {
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
Cudd_RecursiveDerefZdd(dd, term3);
Cudd_RecursiveDerefZdd(dd, term4);
return(NULL);
}
Cudd_Ref(sum1);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term2);
sum2 = cuddZddUnion(dd, sum1, term3);
if (sum2 == NULL) {
Cudd_RecursiveDerefZdd(dd, term3);
Cudd_RecursiveDerefZdd(dd, term4);
Cudd_RecursiveDerefZdd(dd, sum1);
return(NULL);
}
Cudd_Ref(sum2);
Cudd_RecursiveDerefZdd(dd, sum1);
Cudd_RecursiveDerefZdd(dd, term3);
r = cuddZddGetNode(dd, v, sum2, term4);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, term4);
Cudd_RecursiveDerefZdd(dd, sum2);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDerefZdd(dd, sum2);
Cudd_RecursiveDerefZdd(dd, term4);
cuddCacheInsert2(dd, cuddZddUnateProduct, f, g, r);
Cudd_Deref(r);
return(r);
} /* end of cuddZddUnateProduct */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddWeakDiv.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddWeakDiv]
******************************************************************************/
DdNode *
cuddZddWeakDiv(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
DdNode *f0, *f1, *fd, *g0, *g1, *gd;
DdNode *q, *tmp;
DdNode *r;
int flag;
statLine(dd);
if (g == one)
return(f);
if (f == zero || f == one)
return(zero);
if (f == g)
return(one);
/* Check cache. */
r = cuddCacheLookup2Zdd(dd, cuddZddWeakDiv, f, g);
if (r)
return(r);
v = g->index;
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
Cudd_Ref(gd);
q = g;
if (g0 != zero) {
q = cuddZddWeakDiv(dd, f0, g0);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
}
else
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g0);
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (g1 != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDiv(dd, f1, g1);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
}
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (gd != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDiv(dd, fd, gd);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
}
cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, q);
Cudd_Deref(q);
return(q);
} /* end of cuddZddWeakDiv */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddWeakDivF.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddWeakDivF]
******************************************************************************/
DdNode *
cuddZddWeakDivF(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v, top_f, top_g, vf, vg;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
DdNode *f0, *f1, *fd, *g0, *g1, *gd;
DdNode *q, *tmp;
DdNode *r;
DdNode *term1, *term0, *termd;
int flag;
int pv, nv;
statLine(dd);
if (g == one)
return(f);
if (f == zero || f == one)
return(zero);
if (f == g)
return(one);
/* Check cache. */
r = cuddCacheLookup2Zdd(dd, cuddZddWeakDivF, f, g);
if (r)
return(r);
top_f = dd->permZ[f->index];
top_g = dd->permZ[g->index];
vf = top_f >> 1;
vg = top_g >> 1;
v = ddMin(top_f, top_g);
if (v == top_f && vf < vg) {
v = f->index;
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
pv = cuddZddGetPosVarIndex(dd, v);
nv = cuddZddGetNegVarIndex(dd, v);
term1 = cuddZddWeakDivF(dd, f1, g);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDerefZdd(dd, f1);
term0 = cuddZddWeakDivF(dd, f0, g);
if (term0 == NULL) {
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, term1);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDerefZdd(dd, f0);
termd = cuddZddWeakDivF(dd, fd, g);
if (termd == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term0);
return(NULL);
}
Cudd_Ref(termd);
Cudd_RecursiveDerefZdd(dd, fd);
tmp = cuddZddGetNode(dd, nv, term0, termd); /* nv = zi */
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term0);
Cudd_RecursiveDerefZdd(dd, termd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, term0);
Cudd_RecursiveDerefZdd(dd, termd);
q = cuddZddGetNode(dd, pv, term1, tmp); /* pv = yi */
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, tmp);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
Cudd_Deref(q);
return(q);
}
if (v == top_f)
v = f->index;
else
v = g->index;
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
Cudd_Ref(gd);
q = g;
if (g0 != zero) {
q = cuddZddWeakDivF(dd, f0, g0);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
}
else
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g0);
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (g1 != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDivF(dd, f1, g1);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
}
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (gd != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDivF(dd, fd, gd);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
}
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
Cudd_Deref(q);
return(q);
} /* end of cuddZddWeakDivF */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddDivide.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddDivide]
******************************************************************************/
DdNode *
cuddZddDivide(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
DdNode *f0, *f1, *g0, *g1;
DdNode *q, *r, *tmp;
int flag;
statLine(dd);
if (g == one)
return(f);
if (f == zero || f == one)
return(zero);
if (f == g)
return(one);
/* Check cache. */
r = cuddCacheLookup2Zdd(dd, cuddZddDivide, f, g);
if (r)
return(r);
v = g->index;
flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0); /* g1 != zero */
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
r = cuddZddDivide(dd, f1, g1);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
return(NULL);
}
Cudd_Ref(r);
if (r != zero && g0 != zero) {
tmp = r;
q = cuddZddDivide(dd, f0, g0);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
return(NULL);
}
Cudd_Ref(q);
r = cuddZddIntersect(dd, r, q);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, q);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDerefZdd(dd, q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
cuddCacheInsert2(dd, cuddZddDivide, f, g, r);
Cudd_Deref(r);
return(r);
} /* end of cuddZddDivide */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddDivideF.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddDivideF]
******************************************************************************/
DdNode *
cuddZddDivideF(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
DdNode *f0, *f1, *g0, *g1;
DdNode *q, *r, *tmp;
int flag;
statLine(dd);
if (g == one)
return(f);
if (f == zero || f == one)
return(zero);
if (f == g)
return(one);
/* Check cache. */
r = cuddCacheLookup2Zdd(dd, cuddZddDivideF, f, g);
if (r)
return(r);
v = g->index;
flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0); /* g1 != zero */
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
r = cuddZddDivideF(dd, f1, g1);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
return(NULL);
}
Cudd_Ref(r);
if (r != zero && g0 != zero) {
tmp = r;
q = cuddZddDivideF(dd, f0, g0);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
return(NULL);
}
Cudd_Ref(q);
r = cuddZddIntersect(dd, r, q);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, q);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDerefZdd(dd, q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
cuddCacheInsert2(dd, cuddZddDivideF, f, g, r);
Cudd_Deref(r);
return(r);
} /* end of cuddZddDivideF */
/**Function********************************************************************
Synopsis [Computes the three-way decomposition of f w.r.t. v.]
Description [Computes the three-way decomposition of function f (represented
by a ZDD) wit respect to variable v.]
SideEffects [The results are returned in f1, f0, and fd.]
SeeAlso [cuddZddGetCofactors2]
******************************************************************************/
int
cuddZddGetCofactors3(
DdManager * dd,
DdNode * f,
int v,
DdNode ** f1,
DdNode ** f0,
DdNode ** fd)
{
DdNode *pc, *nc;
DdNode *zero = DD_ZERO(dd);
int top, hv, ht, pv, nv;
int level;
top = dd->permZ[f->index];
level = dd->permZ[v];
hv = level >> 1;
ht = top >> 1;
if (hv < ht) {
*f1 = zero;
*f0 = zero;
*fd = f;
}
else {
pv = cuddZddGetPosVarIndex(dd, v);
nv = cuddZddGetNegVarIndex(dd, v);
/* not to create intermediate ZDD node */
if (cuddZddGetPosVarLevel(dd, v) < cuddZddGetNegVarLevel(dd, v)) {
pc = cuddZddSubset1(dd, f, pv);
if (pc == NULL)
return(1);
Cudd_Ref(pc);
nc = cuddZddSubset0(dd, f, pv);
if (nc == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
return(1);
}
Cudd_Ref(nc);
*f1 = cuddZddSubset0(dd, pc, nv);
if (*f1 == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
return(1);
}
Cudd_Ref(*f1);
*f0 = cuddZddSubset1(dd, nc, nv);
if (*f0 == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
Cudd_RecursiveDerefZdd(dd, *f1);
return(1);
}
Cudd_Ref(*f0);
*fd = cuddZddSubset0(dd, nc, nv);
if (*fd == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
Cudd_RecursiveDerefZdd(dd, *f1);
Cudd_RecursiveDerefZdd(dd, *f0);
return(1);
}
Cudd_Ref(*fd);
} else {
pc = cuddZddSubset1(dd, f, nv);
if (pc == NULL)
return(1);
Cudd_Ref(pc);
nc = cuddZddSubset0(dd, f, nv);
if (nc == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
return(1);
}
Cudd_Ref(nc);
*f0 = cuddZddSubset0(dd, pc, pv);
if (*f0 == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
return(1);
}
Cudd_Ref(*f0);
*f1 = cuddZddSubset1(dd, nc, pv);
if (*f1 == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
Cudd_RecursiveDerefZdd(dd, *f1);
return(1);
}
Cudd_Ref(*f1);
*fd = cuddZddSubset0(dd, nc, pv);
if (*fd == NULL) {
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
Cudd_RecursiveDerefZdd(dd, *f1);
Cudd_RecursiveDerefZdd(dd, *f0);
return(1);
}
Cudd_Ref(*fd);
}
Cudd_RecursiveDerefZdd(dd, pc);
Cudd_RecursiveDerefZdd(dd, nc);
Cudd_Deref(*f1);
Cudd_Deref(*f0);
Cudd_Deref(*fd);
}
return(0);
} /* end of cuddZddGetCofactors3 */
/**Function********************************************************************
Synopsis [Computes the two-way decomposition of f w.r.t. v.]
Description []
SideEffects [The results are returned in f1 and f0.]
SeeAlso [cuddZddGetCofactors3]
******************************************************************************/
int
cuddZddGetCofactors2(
DdManager * dd,
DdNode * f,
int v,
DdNode ** f1,
DdNode ** f0)
{
*f1 = cuddZddSubset1(dd, f, v);
if (*f1 == NULL)
return(1);
*f0 = cuddZddSubset0(dd, f, v);
if (*f0 == NULL) {
Cudd_RecursiveDerefZdd(dd, *f1);
return(1);
}
return(0);
} /* end of cuddZddGetCofactors2 */
/**Function********************************************************************
Synopsis [Computes a complement of a ZDD node.]
Description [Computes the complement of a ZDD node. So far, since we
couldn't find a direct way to get the complement of a ZDD cover, we first
convert a ZDD cover to a BDD, then make the complement of the ZDD cover
from the complement of the BDD node by using ISOP.]
SideEffects [The result depends on current variable order.]
SeeAlso []
******************************************************************************/
DdNode *
cuddZddComplement(
DdManager * dd,
DdNode *node)
{
DdNode *b, *isop, *zdd_I;
/* Check cache */
zdd_I = cuddCacheLookup1Zdd(dd, cuddZddComplement, node);
if (zdd_I)
return(zdd_I);
b = cuddMakeBddFromZddCover(dd, node);
if (!b)
return(NULL);
cuddRef(b);
isop = cuddZddIsop(dd, Cudd_Not(b), Cudd_Not(b), &zdd_I);
if (!isop) {
Cudd_RecursiveDeref(dd, b);
return(NULL);
}
cuddRef(isop);
cuddRef(zdd_I);
Cudd_RecursiveDeref(dd, b);
Cudd_RecursiveDeref(dd, isop);
cuddCacheInsert1(dd, cuddZddComplement, node, zdd_I);
cuddDeref(zdd_I);
return(zdd_I);
} /* end of cuddZddComplement */
/**Function********************************************************************
Synopsis [Returns the index of positive ZDD variable.]
Description [Returns the index of positive ZDD variable.]
SideEffects []
SeeAlso []
******************************************************************************/
int
cuddZddGetPosVarIndex(
DdManager * dd,
int index)
{
int pv = (index >> 1) << 1;
return(pv);
} /* end of cuddZddGetPosVarIndex */
/**Function********************************************************************
Synopsis [Returns the index of negative ZDD variable.]
Description [Returns the index of negative ZDD variable.]
SideEffects []
SeeAlso []
******************************************************************************/
int
cuddZddGetNegVarIndex(
DdManager * dd,
int index)
{
int nv = index | 0x1;
return(nv);
} /* end of cuddZddGetPosVarIndex */
/**Function********************************************************************
Synopsis [Returns the level of positive ZDD variable.]
Description [Returns the level of positive ZDD variable.]
SideEffects []
SeeAlso []
******************************************************************************/
int
cuddZddGetPosVarLevel(
DdManager * dd,
int index)
{
int pv = cuddZddGetPosVarIndex(dd, index);
return(dd->permZ[pv]);
} /* end of cuddZddGetPosVarLevel */
/**Function********************************************************************
Synopsis [Returns the level of negative ZDD variable.]
Description [Returns the level of negative ZDD variable.]
SideEffects []
SeeAlso []
******************************************************************************/
int
cuddZddGetNegVarLevel(
DdManager * dd,
int index)
{
int nv = cuddZddGetNegVarIndex(dd, index);
return(dd->permZ[nv]);
} /* end of cuddZddGetNegVarLevel */