/**CFile*********************************************************************** FileName [cuddZddFuncs.c] PackageName [cudd] Synopsis [Functions to manipulate covers represented as ZDDs.] Description [External procedures included in this module: Internal procedures included in this module: Static procedures included in this module: ] SeeAlso [] Author [In-Ho Moon] 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.] ******************************************************************************/ #include "util_hack.h" #include "cuddInt.h" ABC_NAMESPACE_IMPL_START /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddZddFuncs.c,v 1.16 2008/04/25 07:39:33 fabio 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. Returns 0 if successful; 1 otherwise.] 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, *f0); 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 */ ABC_NAMESPACE_IMPL_END