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author | Alan Mishchenko <alanmi@berkeley.edu> | 2007-09-30 08:01:00 -0700 |
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committer | Alan Mishchenko <alanmi@berkeley.edu> | 2007-09-30 08:01:00 -0700 |
commit | e54d9691616b9a0326e2fdb3156bb4eeb8abfcd7 (patch) | |
tree | de3ffe87c3e17950351e3b7d97fa18318bd5ea9a /abc70930/src/bdd/cudd/cuddSat.c | |
parent | 7d7e60f2dc84393cd4c5db22d2eaf7b1fb1a79b2 (diff) | |
download | abc-e54d9691616b9a0326e2fdb3156bb4eeb8abfcd7.tar.gz abc-e54d9691616b9a0326e2fdb3156bb4eeb8abfcd7.tar.bz2 abc-e54d9691616b9a0326e2fdb3156bb4eeb8abfcd7.zip |
Version abc70930
Diffstat (limited to 'abc70930/src/bdd/cudd/cuddSat.c')
-rw-r--r-- | abc70930/src/bdd/cudd/cuddSat.c | 1305 |
1 files changed, 1305 insertions, 0 deletions
diff --git a/abc70930/src/bdd/cudd/cuddSat.c b/abc70930/src/bdd/cudd/cuddSat.c new file mode 100644 index 00000000..1755a1c1 --- /dev/null +++ b/abc70930/src/bdd/cudd/cuddSat.c @@ -0,0 +1,1305 @@ +/**CFile*********************************************************************** + + FileName [cuddSat.c] + + PackageName [cudd] + + Synopsis [Functions for the solution of satisfiability related + problems.] + + Description [External procedures included in this file: + <ul> + <li> Cudd_Eval() + <li> Cudd_ShortestPath() + <li> Cudd_LargestCube() + <li> Cudd_ShortestLength() + <li> Cudd_Decreasing() + <li> Cudd_Increasing() + <li> Cudd_EquivDC() + <li> Cudd_bddLeqUnless() + <li> Cudd_EqualSupNorm() + <li> Cudd_bddMakePrime() + </ul> + Internal procedures included in this module: + <ul> + <li> cuddBddMakePrime() + </ul> + Static procedures included in this module: + <ul> + <li> freePathPair() + <li> getShortest() + <li> getPath() + <li> getLargest() + <li> getCube() + </ul>] + + Author [Seh-Woong Jeong, Fabio Somenzi] + + 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 */ +/*---------------------------------------------------------------------------*/ + +#define DD_BIGGY 1000000 + +/*---------------------------------------------------------------------------*/ +/* Stucture declarations */ +/*---------------------------------------------------------------------------*/ + +/*---------------------------------------------------------------------------*/ +/* Type declarations */ +/*---------------------------------------------------------------------------*/ + +typedef struct cuddPathPair { + int pos; + int neg; +} cuddPathPair; + +/*---------------------------------------------------------------------------*/ +/* Variable declarations */ +/*---------------------------------------------------------------------------*/ + +#ifndef lint +static char rcsid[] DD_UNUSED = "$Id: cuddSat.c,v 1.1.1.1 2003/02/24 22:23:53 wjiang Exp $"; +#endif + +static DdNode *one, *zero; + +/*---------------------------------------------------------------------------*/ +/* Macro declarations */ +/*---------------------------------------------------------------------------*/ + +#define WEIGHT(weight, col) ((weight) == NULL ? 1 : weight[col]) + +/**AutomaticStart*************************************************************/ + +/*---------------------------------------------------------------------------*/ +/* Static function prototypes */ +/*---------------------------------------------------------------------------*/ + +static enum st_retval freePathPair ARGS((char *key, char *value, char *arg)); +static cuddPathPair getShortest ARGS((DdNode *root, int *cost, int *support, st_table *visited)); +static DdNode * getPath ARGS((DdManager *manager, st_table *visited, DdNode *f, int *weight, int cost)); +static cuddPathPair getLargest ARGS((DdNode *root, st_table *visited)); +static DdNode * getCube ARGS((DdManager *manager, st_table *visited, DdNode *f, int cost)); + +/**AutomaticEnd***************************************************************/ + + +/*---------------------------------------------------------------------------*/ +/* Definition of exported functions */ +/*---------------------------------------------------------------------------*/ + + +/**Function******************************************************************** + + Synopsis [Returns the value of a DD for a given variable assignment.] + + Description [Finds the value of a DD for a given variable + assignment. The variable assignment is passed in an array of int's, + that should specify a zero or a one for each variable in the support + of the function. Returns a pointer to a constant node. No new nodes + are produced.] + + SideEffects [None] + + SeeAlso [Cudd_bddLeq Cudd_addEvalConst] + +******************************************************************************/ +DdNode * +Cudd_Eval( + DdManager * dd, + DdNode * f, + int * inputs) +{ + int comple; + DdNode *ptr; + + comple = Cudd_IsComplement(f); + ptr = Cudd_Regular(f); + + while (!cuddIsConstant(ptr)) { + if (inputs[ptr->index] == 1) { + ptr = cuddT(ptr); + } else { + comple ^= Cudd_IsComplement(cuddE(ptr)); + ptr = Cudd_Regular(cuddE(ptr)); + } + } + return(Cudd_NotCond(ptr,comple)); + +} /* end of Cudd_Eval */ + + +/**Function******************************************************************** + + Synopsis [Finds a shortest path in a DD.] + + Description [Finds a shortest path in a DD. f is the DD we want to + get the shortest path for; weight\[i\] is the weight of the THEN arc + coming from the node whose index is i. If weight is NULL, then unit + weights are assumed for all THEN arcs. All ELSE arcs have 0 weight. + If non-NULL, both weight and support should point to arrays with at + least as many entries as there are variables in the manager. + Returns the shortest path as the BDD of a cube.] + + SideEffects [support contains on return the true support of f. + If support is NULL on entry, then Cudd_ShortestPath does not compute + the true support info. length contains the length of the path.] + + SeeAlso [Cudd_ShortestLength Cudd_LargestCube] + +******************************************************************************/ +DdNode * +Cudd_ShortestPath( + DdManager * manager, + DdNode * f, + int * weight, + int * support, + int * length) +{ + register DdNode *F; + st_table *visited; + DdNode *sol; + cuddPathPair *rootPair; + int complement, cost; + int i; + + one = DD_ONE(manager); + zero = DD_ZERO(manager); + + /* Initialize support. */ + if (support) { + for (i = 0; i < manager->size; i++) { + support[i] = 0; + } + } + + if (f == Cudd_Not(one) || f == zero) { + *length = DD_BIGGY; + return(Cudd_Not(one)); + } + /* From this point on, a path exists. */ + + /* Initialize visited table. */ + visited = st_init_table(st_ptrcmp, st_ptrhash); + + /* Now get the length of the shortest path(s) from f to 1. */ + (void) getShortest(f, weight, support, visited); + + complement = Cudd_IsComplement(f); + + F = Cudd_Regular(f); + + st_lookup(visited, (char *)F, (char **)&rootPair); + + if (complement) { + cost = rootPair->neg; + } else { + cost = rootPair->pos; + } + + /* Recover an actual shortest path. */ + do { + manager->reordered = 0; + sol = getPath(manager,visited,f,weight,cost); + } while (manager->reordered == 1); + + st_foreach(visited, freePathPair, NULL); + st_free_table(visited); + + *length = cost; + return(sol); + +} /* end of Cudd_ShortestPath */ + + +/**Function******************************************************************** + + Synopsis [Finds a largest cube in a DD.] + + Description [Finds a largest cube in a DD. f is the DD we want to + get the largest cube for. The problem is translated into the one of + finding a shortest path in f, when both THEN and ELSE arcs are assumed to + have unit length. This yields a largest cube in the disjoint cover + corresponding to the DD. Therefore, it is not necessarily the largest + implicant of f. Returns the largest cube as a BDD.] + + SideEffects [The number of literals of the cube is returned in length.] + + SeeAlso [Cudd_ShortestPath] + +******************************************************************************/ +DdNode * +Cudd_LargestCube( + DdManager * manager, + DdNode * f, + int * length) +{ + register DdNode *F; + st_table *visited; + DdNode *sol; + cuddPathPair *rootPair; + int complement, cost; + + one = DD_ONE(manager); + zero = DD_ZERO(manager); + + if (f == Cudd_Not(one) || f == zero) { + *length = DD_BIGGY; + return(Cudd_Not(one)); + } + /* From this point on, a path exists. */ + + /* Initialize visited table. */ + visited = st_init_table(st_ptrcmp, st_ptrhash); + + /* Now get the length of the shortest path(s) from f to 1. */ + (void) getLargest(f, visited); + + complement = Cudd_IsComplement(f); + + F = Cudd_Regular(f); + + st_lookup(visited, (char *)F, (char **)&rootPair); + + if (complement) { + cost = rootPair->neg; + } else { + cost = rootPair->pos; + } + + /* Recover an actual shortest path. */ + do { + manager->reordered = 0; + sol = getCube(manager,visited,f,cost); + } while (manager->reordered == 1); + + st_foreach(visited, freePathPair, NULL); + st_free_table(visited); + + *length = cost; + return(sol); + +} /* end of Cudd_LargestCube */ + + +/**Function******************************************************************** + + Synopsis [Find the length of the shortest path(s) in a DD.] + + Description [Find the length of the shortest path(s) in a DD. f is + the DD we want to get the shortest path for; weight\[i\] is the + weight of the THEN edge coming from the node whose index is i. All + ELSE edges have 0 weight. Returns the length of the shortest + path(s) if successful; CUDD_OUT_OF_MEM otherwise.] + + SideEffects [None] + + SeeAlso [Cudd_ShortestPath] + +******************************************************************************/ +int +Cudd_ShortestLength( + DdManager * manager, + DdNode * f, + int * weight) +{ + register DdNode *F; + st_table *visited; + cuddPathPair *my_pair; + int complement, cost; + + one = DD_ONE(manager); + zero = DD_ZERO(manager); + + if (f == Cudd_Not(one) || f == zero) { + return(DD_BIGGY); + } + + /* From this point on, a path exists. */ + /* Initialize visited table and support. */ + visited = st_init_table(st_ptrcmp, st_ptrhash); + + /* Now get the length of the shortest path(s) from f to 1. */ + (void) getShortest(f, weight, NULL, visited); + + complement = Cudd_IsComplement(f); + + F = Cudd_Regular(f); + + st_lookup(visited, (char *)F, (char **)&my_pair); + + if (complement) { + cost = my_pair->neg; + } else { + cost = my_pair->pos; + } + + st_foreach(visited, freePathPair, NULL); + st_free_table(visited); + + return(cost); + +} /* end of Cudd_ShortestLength */ + + +/**Function******************************************************************** + + Synopsis [Determines whether a BDD is negative unate in a + variable.] + + Description [Determines whether the function represented by BDD f is + negative unate (monotonic decreasing) in variable i. Returns the + constant one is f is unate and the (logical) constant zero if it is not. + This function does not generate any new nodes.] + + SideEffects [None] + + SeeAlso [Cudd_Increasing] + +******************************************************************************/ +DdNode * +Cudd_Decreasing( + DdManager * dd, + DdNode * f, + int i) +{ + unsigned int topf, level; + DdNode *F, *fv, *fvn, *res; + DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *); + + statLine(dd); +#ifdef DD_DEBUG + assert(0 <= i && i < dd->size); +#endif + + F = Cudd_Regular(f); + topf = cuddI(dd,F->index); + + /* Check terminal case. If topf > i, f does not depend on var. + ** Therefore, f is unate in i. + */ + level = (unsigned) dd->perm[i]; + if (topf > level) { + return(DD_ONE(dd)); + } + + /* From now on, f is not constant. */ + + /* Check cache. */ + cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) Cudd_Decreasing; + res = cuddCacheLookup2(dd,cacheOp,f,dd->vars[i]); + if (res != NULL) { + return(res); + } + + /* Compute cofactors. */ + fv = cuddT(F); fvn = cuddE(F); + if (F != f) { + fv = Cudd_Not(fv); + fvn = Cudd_Not(fvn); + } + + if (topf == (unsigned) level) { + /* Special case: if fv is regular, fv(1,...,1) = 1; + ** If in addition fvn is complemented, fvn(1,...,1) = 0. + ** But then f(1,1,...,1) > f(0,1,...,1). Hence f is not + ** monotonic decreasing in i. + */ + if (!Cudd_IsComplement(fv) && Cudd_IsComplement(fvn)) { + return(Cudd_Not(DD_ONE(dd))); + } + res = Cudd_bddLeq(dd,fv,fvn) ? DD_ONE(dd) : Cudd_Not(DD_ONE(dd)); + } else { + res = Cudd_Decreasing(dd,fv,i); + if (res == DD_ONE(dd)) { + res = Cudd_Decreasing(dd,fvn,i); + } + } + + cuddCacheInsert2(dd,cacheOp,f,dd->vars[i],res); + return(res); + +} /* end of Cudd_Decreasing */ + + +/**Function******************************************************************** + + Synopsis [Determines whether a BDD is positive unate in a + variable.] + + Description [Determines whether the function represented by BDD f is + positive unate (monotonic decreasing) in variable i. It is based on + Cudd_Decreasing and the fact that f is monotonic increasing in i if + and only if its complement is monotonic decreasing in i.] + + SideEffects [None] + + SeeAlso [Cudd_Decreasing] + +******************************************************************************/ +DdNode * +Cudd_Increasing( + DdManager * dd, + DdNode * f, + int i) +{ + return(Cudd_Decreasing(dd,Cudd_Not(f),i)); + +} /* end of Cudd_Increasing */ + + +/**Function******************************************************************** + + Synopsis [Tells whether F and G are identical wherever D is 0.] + + Description [Tells whether F and G are identical wherever D is 0. F + and G are either two ADDs or two BDDs. D is either a 0-1 ADD or a + BDD. The function returns 1 if F and G are equivalent, and 0 + otherwise. No new nodes are created.] + + SideEffects [None] + + SeeAlso [Cudd_bddLeqUnless] + +******************************************************************************/ +int +Cudd_EquivDC( + DdManager * dd, + DdNode * F, + DdNode * G, + DdNode * D) +{ + DdNode *tmp, *One, *Gr, *Dr; + DdNode *Fv, *Fvn, *Gv, *Gvn, *Dv, *Dvn; + int res; + unsigned int flevel, glevel, dlevel, top; + + One = DD_ONE(dd); + + statLine(dd); + /* Check terminal cases. */ + if (D == One || F == G) return(1); + if (D == Cudd_Not(One) || D == DD_ZERO(dd) || F == Cudd_Not(G)) return(0); + + /* From now on, D is non-constant. */ + + /* Normalize call to increase cache efficiency. */ + if (F > G) { + tmp = F; + F = G; + G = tmp; + } + if (Cudd_IsComplement(F)) { + F = Cudd_Not(F); + G = Cudd_Not(G); + } + + /* From now on, F is regular. */ + + /* Check cache. */ + tmp = cuddCacheLookup(dd,DD_EQUIV_DC_TAG,F,G,D); + if (tmp != NULL) return(tmp == One); + + /* Find splitting variable. */ + flevel = cuddI(dd,F->index); + Gr = Cudd_Regular(G); + glevel = cuddI(dd,Gr->index); + top = ddMin(flevel,glevel); + Dr = Cudd_Regular(D); + dlevel = dd->perm[Dr->index]; + top = ddMin(top,dlevel); + + /* Compute cofactors. */ + if (top == flevel) { + Fv = cuddT(F); + Fvn = cuddE(F); + } else { + Fv = Fvn = F; + } + if (top == glevel) { + Gv = cuddT(Gr); + Gvn = cuddE(Gr); + if (G != Gr) { + Gv = Cudd_Not(Gv); + Gvn = Cudd_Not(Gvn); + } + } else { + Gv = Gvn = G; + } + if (top == dlevel) { + Dv = cuddT(Dr); + Dvn = cuddE(Dr); + if (D != Dr) { + Dv = Cudd_Not(Dv); + Dvn = Cudd_Not(Dvn); + } + } else { + Dv = Dvn = D; + } + + /* Solve recursively. */ + res = Cudd_EquivDC(dd,Fv,Gv,Dv); + if (res != 0) { + res = Cudd_EquivDC(dd,Fvn,Gvn,Dvn); + } + cuddCacheInsert(dd,DD_EQUIV_DC_TAG,F,G,D,(res) ? One : Cudd_Not(One)); + + return(res); + +} /* end of Cudd_EquivDC */ + + +/**Function******************************************************************** + + Synopsis [Tells whether f is less than of equal to G unless D is 1.] + + Description [Tells whether f is less than of equal to G unless D is + 1. f, g, and D are BDDs. The function returns 1 if f is less than + of equal to G, and 0 otherwise. No new nodes are created.] + + SideEffects [None] + + SeeAlso [Cudd_EquivDC Cudd_bddLeq Cudd_bddIteConstant] + +******************************************************************************/ +int +Cudd_bddLeqUnless( + DdManager *dd, + DdNode *f, + DdNode *g, + DdNode *D) +{ + DdNode *tmp, *One, *F, *G; + DdNode *Ft, *Fe, *Gt, *Ge, *Dt, *De; + int res; + unsigned int flevel, glevel, dlevel, top; + + statLine(dd); + + One = DD_ONE(dd); + + /* Check terminal cases. */ + if (f == g || g == One || f == Cudd_Not(One) || D == One || + D == f || D == Cudd_Not(g)) return(1); + /* Check for two-operand cases. */ + if (D == Cudd_Not(One) || D == g || D == Cudd_Not(f)) + return(Cudd_bddLeq(dd,f,g)); + if (g == Cudd_Not(One) || g == Cudd_Not(f)) return(Cudd_bddLeq(dd,f,D)); + if (f == One) return(Cudd_bddLeq(dd,Cudd_Not(g),D)); + + /* From now on, f, g, and D are non-constant, distinct, and + ** non-complementary. */ + + /* Normalize call to increase cache efficiency. We rely on the + ** fact that f <= g unless D is equivalent to not(g) <= not(f) + ** unless D and to f <= D unless g. We make sure that D is + ** regular, and that at most one of f and g is complemented. We also + ** ensure that when two operands can be swapped, the one with the + ** lowest address comes first. */ + + if (Cudd_IsComplement(D)) { + if (Cudd_IsComplement(g)) { + /* Special case: if f is regular and g is complemented, + ** f(1,...,1) = 1 > 0 = g(1,...,1). If D(1,...,1) = 0, return 0. + */ + if (!Cudd_IsComplement(f)) return(0); + /* !g <= D unless !f or !D <= g unless !f */ + tmp = D; + D = Cudd_Not(f); + if (g < tmp) { + f = Cudd_Not(g); + g = tmp; + } else { + f = Cudd_Not(tmp); + } + } else { + if (Cudd_IsComplement(f)) { + /* !D <= !f unless g or !D <= g unless !f */ + tmp = f; + f = Cudd_Not(D); + if (tmp < g) { + D = g; + g = Cudd_Not(tmp); + } else { + D = Cudd_Not(tmp); + } + } else { + /* f <= D unless g or !D <= !f unless g */ + tmp = D; + D = g; + if (tmp < f) { + g = Cudd_Not(f); + f = Cudd_Not(tmp); + } else { + g = tmp; + } + } + } + } else { + if (Cudd_IsComplement(g)) { + if (Cudd_IsComplement(f)) { + /* !g <= !f unless D or !g <= D unless !f */ + tmp = f; + f = Cudd_Not(g); + if (D < tmp) { + g = D; + D = Cudd_Not(tmp); + } else { + g = Cudd_Not(tmp); + } + } else { + /* f <= g unless D or !g <= !f unless D */ + if (g < f) { + tmp = g; + g = Cudd_Not(f); + f = Cudd_Not(tmp); + } + } + } else { + /* f <= g unless D or f <= D unless g */ + if (D < g) { + tmp = D; + D = g; + g = tmp; + } + } + } + + /* From now on, D is regular. */ + + /* Check cache. */ + tmp = cuddCacheLookup(dd,DD_BDD_LEQ_UNLESS_TAG,f,g,D); + if (tmp != NULL) return(tmp == One); + + /* Find splitting variable. */ + F = Cudd_Regular(f); + flevel = dd->perm[F->index]; + G = Cudd_Regular(g); + glevel = dd->perm[G->index]; + top = ddMin(flevel,glevel); + dlevel = dd->perm[D->index]; + top = ddMin(top,dlevel); + + /* Compute cofactors. */ + if (top == flevel) { + Ft = cuddT(F); + Fe = cuddE(F); + if (F != f) { + Ft = Cudd_Not(Ft); + Fe = Cudd_Not(Fe); + } + } else { + Ft = Fe = f; + } + if (top == glevel) { + Gt = cuddT(G); + Ge = cuddE(G); + if (G != g) { + Gt = Cudd_Not(Gt); + Ge = Cudd_Not(Ge); + } + } else { + Gt = Ge = g; + } + if (top == dlevel) { + Dt = cuddT(D); + De = cuddE(D); + } else { + Dt = De = D; + } + + /* Solve recursively. */ + res = Cudd_bddLeqUnless(dd,Ft,Gt,Dt); + if (res != 0) { + res = Cudd_bddLeqUnless(dd,Fe,Ge,De); + } + cuddCacheInsert(dd,DD_BDD_LEQ_UNLESS_TAG,f,g,D,Cudd_NotCond(One,!res)); + + return(res); + +} /* end of Cudd_bddLeqUnless */ + + +/**Function******************************************************************** + + Synopsis [Compares two ADDs for equality within tolerance.] + + Description [Compares two ADDs for equality within tolerance. Two + ADDs are reported to be equal if the maximum difference between them + (the sup norm of their difference) is less than or equal to the + tolerance parameter. Returns 1 if the two ADDs are equal (within + tolerance); 0 otherwise. If parameter <code>pr</code> is positive + the first failure is reported to the standard output.] + + SideEffects [None] + + SeeAlso [] + +******************************************************************************/ +int +Cudd_EqualSupNorm( + DdManager * dd /* manager */, + DdNode * f /* first ADD */, + DdNode * g /* second ADD */, + CUDD_VALUE_TYPE tolerance /* maximum allowed difference */, + int pr /* verbosity level */) +{ + DdNode *fv, *fvn, *gv, *gvn, *r; + unsigned int topf, topg; + + statLine(dd); + /* Check terminal cases. */ + if (f == g) return(1); + if (Cudd_IsConstant(f) && Cudd_IsConstant(g)) { + if (ddEqualVal(cuddV(f),cuddV(g),tolerance)) { + return(1); + } else { + if (pr>0) { + (void) fprintf(dd->out,"Offending nodes:\n"); +#if SIZEOF_VOID_P == 8 + (void) fprintf(dd->out, + "f: address = %lx\t value = %40.30f\n", + (unsigned long) f, cuddV(f)); + (void) fprintf(dd->out, + "g: address = %lx\t value = %40.30f\n", + (unsigned long) g, cuddV(g)); +#else + (void) fprintf(dd->out, + "f: address = %x\t value = %40.30f\n", + (unsigned) f, cuddV(f)); + (void) fprintf(dd->out, + "g: address = %x\t value = %40.30f\n", + (unsigned) g, cuddV(g)); +#endif + } + return(0); + } + } + + /* We only insert the result in the cache if the comparison is + ** successful. Therefore, if we hit we return 1. */ + r = cuddCacheLookup2(dd,(DdNode * (*)(DdManager *, DdNode *, DdNode *))Cudd_EqualSupNorm,f,g); + if (r != NULL) { + return(1); + } + + /* Compute the cofactors and solve the recursive subproblems. */ + topf = cuddI(dd,f->index); + topg = cuddI(dd,g->index); + + if (topf <= topg) {fv = cuddT(f); fvn = cuddE(f);} else {fv = fvn = f;} + if (topg <= topf) {gv = cuddT(g); gvn = cuddE(g);} else {gv = gvn = g;} + + if (!Cudd_EqualSupNorm(dd,fv,gv,tolerance,pr)) return(0); + if (!Cudd_EqualSupNorm(dd,fvn,gvn,tolerance,pr)) return(0); + + cuddCacheInsert2(dd,(DdNode * (*)(DdManager *, DdNode *, DdNode *))Cudd_EqualSupNorm,f,g,DD_ONE(dd)); + + return(1); + +} /* end of Cudd_EqualSupNorm */ + + +/**Function******************************************************************** + + Synopsis [Expands cube to a prime implicant of f.] + + Description [Expands cube to a prime implicant of f. Returns the prime + if successful; NULL otherwise. In particular, NULL is returned if cube + is not a real cube or is not an implicant of f.] + + SideEffects [None] + + SeeAlso [] + +******************************************************************************/ +DdNode * +Cudd_bddMakePrime( + DdManager *dd /* manager */, + DdNode *cube /* cube to be expanded */, + DdNode *f /* function of which the cube is to be made a prime */) +{ + DdNode *res; + + if (!Cudd_bddLeq(dd,cube,f)) return(NULL); + + do { + dd->reordered = 0; + res = cuddBddMakePrime(dd,cube,f); + } while (dd->reordered == 1); + return(res); + +} /* end of Cudd_bddMakePrime */ + + +/*---------------------------------------------------------------------------*/ +/* Definition of internal functions */ +/*---------------------------------------------------------------------------*/ + + +/**Function******************************************************************** + + Synopsis [Performs the recursive step of Cudd_bddMakePrime.] + + Description [Performs the recursive step of Cudd_bddMakePrime. + Returns the prime if successful; NULL otherwise.] + + SideEffects [None] + + SeeAlso [] + +******************************************************************************/ +DdNode * +cuddBddMakePrime( + DdManager *dd /* manager */, + DdNode *cube /* cube to be expanded */, + DdNode *f /* function of which the cube is to be made a prime */) +{ + DdNode *scan; + DdNode *t, *e; + DdNode *res = cube; + DdNode *zero = Cudd_Not(DD_ONE(dd)); + + Cudd_Ref(res); + scan = cube; + while (!Cudd_IsConstant(scan)) { + DdNode *reg = Cudd_Regular(scan); + DdNode *var = dd->vars[reg->index]; + DdNode *expanded = Cudd_bddExistAbstract(dd,res,var); + if (expanded == NULL) { + return(NULL); + } + Cudd_Ref(expanded); + if (Cudd_bddLeq(dd,expanded,f)) { + Cudd_RecursiveDeref(dd,res); + res = expanded; + } else { + Cudd_RecursiveDeref(dd,expanded); + } + cuddGetBranches(scan,&t,&e); + if (t == zero) { + scan = e; + } else if (e == zero) { + scan = t; + } else { + Cudd_RecursiveDeref(dd,res); + return(NULL); /* cube is not a cube */ + } + } + + if (scan == DD_ONE(dd)) { + Cudd_Deref(res); + return(res); + } else { + Cudd_RecursiveDeref(dd,res); + return(NULL); + } + +} /* end of cuddBddMakePrime */ + + +/*---------------------------------------------------------------------------*/ +/* Definition of static functions */ +/*---------------------------------------------------------------------------*/ + + +/**Function******************************************************************** + + Synopsis [Frees the entries of the visited symbol table.] + + Description [Frees the entries of the visited symbol table. Returns + ST_CONTINUE.] + + SideEffects [None] + +******************************************************************************/ +static enum st_retval +freePathPair( + char * key, + char * value, + char * arg) +{ + cuddPathPair *pair; + + pair = (cuddPathPair *) value; + FREE(pair); + return(ST_CONTINUE); + +} /* end of freePathPair */ + + +/**Function******************************************************************** + + Synopsis [Finds the length of the shortest path(s) in a DD.] + + Description [Finds the length of the shortest path(s) in a DD. + Uses a local symbol table to store the lengths for each + node. Only the lengths for the regular nodes are entered in the table, + because those for the complement nodes are simply obtained by swapping + the two lenghts. + Returns a pair of lengths: the length of the shortest path to 1; + and the length of the shortest path to 0. This is done so as to take + complement arcs into account.] + + SideEffects [Accumulates the support of the DD in support.] + + SeeAlso [] + +******************************************************************************/ +static cuddPathPair +getShortest( + DdNode * root, + int * cost, + int * support, + st_table * visited) +{ + cuddPathPair *my_pair, res_pair, pair_T, pair_E; + DdNode *my_root, *T, *E; + int weight; + + my_root = Cudd_Regular(root); + + if (st_lookup(visited, (char *)my_root, (char **)&my_pair)) { + if (Cudd_IsComplement(root)) { + res_pair.pos = my_pair->neg; + res_pair.neg = my_pair->pos; + } else { + res_pair.pos = my_pair->pos; + res_pair.neg = my_pair->neg; + } + return(res_pair); + } + + /* In the case of a BDD the following test is equivalent to + ** testing whether the BDD is the constant 1. This formulation, + ** however, works for ADDs as well, by assuming the usual + ** dichotomy of 0 and != 0. + */ + if (cuddIsConstant(my_root)) { + if (my_root != zero) { + res_pair.pos = 0; + res_pair.neg = DD_BIGGY; + } else { + res_pair.pos = DD_BIGGY; + res_pair.neg = 0; + } + } else { + T = cuddT(my_root); + E = cuddE(my_root); + + pair_T = getShortest(T, cost, support, visited); + pair_E = getShortest(E, cost, support, visited); + weight = WEIGHT(cost, my_root->index); + res_pair.pos = ddMin(pair_T.pos+weight, pair_E.pos); + res_pair.neg = ddMin(pair_T.neg+weight, pair_E.neg); + + /* Update support. */ + if (support != NULL) { + support[my_root->index] = 1; + } + } + + my_pair = ALLOC(cuddPathPair, 1); + if (my_pair == NULL) { + if (Cudd_IsComplement(root)) { + int tmp = res_pair.pos; + res_pair.pos = res_pair.neg; + res_pair.neg = tmp; + } + return(res_pair); + } + my_pair->pos = res_pair.pos; + my_pair->neg = res_pair.neg; + + st_insert(visited, (char *)my_root, (char *)my_pair); + if (Cudd_IsComplement(root)) { + res_pair.pos = my_pair->neg; + res_pair.neg = my_pair->pos; + } else { + res_pair.pos = my_pair->pos; + res_pair.neg = my_pair->neg; + } + return(res_pair); + +} /* end of getShortest */ + + +/**Function******************************************************************** + + Synopsis [Build a BDD for a shortest path of f.] + + Description [Build a BDD for a shortest path of f. + Given the minimum length from the root, and the minimum + lengths for each node (in visited), apply triangulation at each node. + Of the two children of each node on a shortest path, at least one is + on a shortest path. In case of ties the procedure chooses the THEN + children. + Returns a pointer to the cube BDD representing the path if + successful; NULL otherwise.] + + SideEffects [None] + + SeeAlso [] + +******************************************************************************/ +static DdNode * +getPath( + DdManager * manager, + st_table * visited, + DdNode * f, + int * weight, + int cost) +{ + DdNode *sol, *tmp; + DdNode *my_dd, *T, *E; + cuddPathPair *T_pair, *E_pair; + int Tcost, Ecost; + int complement; + + my_dd = Cudd_Regular(f); + complement = Cudd_IsComplement(f); + + sol = one; + cuddRef(sol); + + while (!cuddIsConstant(my_dd)) { + Tcost = cost - WEIGHT(weight, my_dd->index); + Ecost = cost; + + T = cuddT(my_dd); + E = cuddE(my_dd); + + if (complement) {T = Cudd_Not(T); E = Cudd_Not(E);} + + st_lookup(visited, (char *)Cudd_Regular(T), (char **)&T_pair); + if ((Cudd_IsComplement(T) && T_pair->neg == Tcost) || + (!Cudd_IsComplement(T) && T_pair->pos == Tcost)) { + tmp = cuddBddAndRecur(manager,manager->vars[my_dd->index],sol); + if (tmp == NULL) { + Cudd_RecursiveDeref(manager,sol); + return(NULL); + } + cuddRef(tmp); + Cudd_RecursiveDeref(manager,sol); + sol = tmp; + + complement = Cudd_IsComplement(T); + my_dd = Cudd_Regular(T); + cost = Tcost; + continue; + } + st_lookup(visited, (char *)Cudd_Regular(E), (char **)&E_pair); + if ((Cudd_IsComplement(E) && E_pair->neg == Ecost) || + (!Cudd_IsComplement(E) && E_pair->pos == Ecost)) { + tmp = cuddBddAndRecur(manager,Cudd_Not(manager->vars[my_dd->index]),sol); + if (tmp == NULL) { + Cudd_RecursiveDeref(manager,sol); + return(NULL); + } + cuddRef(tmp); + Cudd_RecursiveDeref(manager,sol); + sol = tmp; + complement = Cudd_IsComplement(E); + my_dd = Cudd_Regular(E); + cost = Ecost; + continue; + } + (void) fprintf(manager->err,"We shouldn't be here!!\n"); + manager->errorCode = CUDD_INTERNAL_ERROR; + return(NULL); + } + + cuddDeref(sol); + return(sol); + +} /* end of getPath */ + + +/**Function******************************************************************** + + Synopsis [Finds the size of the largest cube(s) in a DD.] + + Description [Finds the size of the largest cube(s) in a DD. + This problem is translated into finding the shortest paths from a node + when both THEN and ELSE arcs have unit lengths. + Uses a local symbol table to store the lengths for each + node. Only the lengths for the regular nodes are entered in the table, + because those for the complement nodes are simply obtained by swapping + the two lenghts. + Returns a pair of lengths: the length of the shortest path to 1; + and the length of the shortest path to 0. This is done so as to take + complement arcs into account.] + + SideEffects [none] + + SeeAlso [] + +******************************************************************************/ +static cuddPathPair +getLargest( + DdNode * root, + st_table * visited) +{ + cuddPathPair *my_pair, res_pair, pair_T, pair_E; + DdNode *my_root, *T, *E; + + my_root = Cudd_Regular(root); + + if (st_lookup(visited, (char *)my_root, (char **)&my_pair)) { + if (Cudd_IsComplement(root)) { + res_pair.pos = my_pair->neg; + res_pair.neg = my_pair->pos; + } else { + res_pair.pos = my_pair->pos; + res_pair.neg = my_pair->neg; + } + return(res_pair); + } + + /* In the case of a BDD the following test is equivalent to + ** testing whether the BDD is the constant 1. This formulation, + ** however, works for ADDs as well, by assuming the usual + ** dichotomy of 0 and != 0. + */ + if (cuddIsConstant(my_root)) { + if (my_root != zero) { + res_pair.pos = 0; + res_pair.neg = DD_BIGGY; + } else { + res_pair.pos = DD_BIGGY; + res_pair.neg = 0; + } + } else { + T = cuddT(my_root); + E = cuddE(my_root); + + pair_T = getLargest(T, visited); + pair_E = getLargest(E, visited); + res_pair.pos = ddMin(pair_T.pos, pair_E.pos) + 1; + res_pair.neg = ddMin(pair_T.neg, pair_E.neg) + 1; + } + + my_pair = ALLOC(cuddPathPair, 1); + if (my_pair == NULL) { /* simlpy do not cache this result */ + if (Cudd_IsComplement(root)) { + int tmp = res_pair.pos; + res_pair.pos = res_pair.neg; + res_pair.neg = tmp; + } + return(res_pair); + } + my_pair->pos = res_pair.pos; + my_pair->neg = res_pair.neg; + + st_insert(visited, (char *)my_root, (char *)my_pair); + if (Cudd_IsComplement(root)) { + res_pair.pos = my_pair->neg; + res_pair.neg = my_pair->pos; + } else { + res_pair.pos = my_pair->pos; + res_pair.neg = my_pair->neg; + } + return(res_pair); + +} /* end of getLargest */ + + +/**Function******************************************************************** + + Synopsis [Build a BDD for a largest cube of f.] + + Description [Build a BDD for a largest cube of f. + Given the minimum length from the root, and the minimum + lengths for each node (in visited), apply triangulation at each node. + Of the two children of each node on a shortest path, at least one is + on a shortest path. In case of ties the procedure chooses the THEN + children. + Returns a pointer to the cube BDD representing the path if + successful; NULL otherwise.] + + SideEffects [None] + + SeeAlso [] + +******************************************************************************/ +static DdNode * +getCube( + DdManager * manager, + st_table * visited, + DdNode * f, + int cost) +{ + DdNode *sol, *tmp; + DdNode *my_dd, *T, *E; + cuddPathPair *T_pair, *E_pair; + int Tcost, Ecost; + int complement; + + my_dd = Cudd_Regular(f); + complement = Cudd_IsComplement(f); + + sol = one; + cuddRef(sol); + + while (!cuddIsConstant(my_dd)) { + Tcost = cost - 1; + Ecost = cost - 1; + + T = cuddT(my_dd); + E = cuddE(my_dd); + + if (complement) {T = Cudd_Not(T); E = Cudd_Not(E);} + + st_lookup(visited, (char *)Cudd_Regular(T), (char **)&T_pair); + if ((Cudd_IsComplement(T) && T_pair->neg == Tcost) || + (!Cudd_IsComplement(T) && T_pair->pos == Tcost)) { + tmp = cuddBddAndRecur(manager,manager->vars[my_dd->index],sol); + if (tmp == NULL) { + Cudd_RecursiveDeref(manager,sol); + return(NULL); + } + cuddRef(tmp); + Cudd_RecursiveDeref(manager,sol); + sol = tmp; + + complement = Cudd_IsComplement(T); + my_dd = Cudd_Regular(T); + cost = Tcost; + continue; + } + st_lookup(visited, (char *)Cudd_Regular(E), (char **)&E_pair); + if ((Cudd_IsComplement(E) && E_pair->neg == Ecost) || + (!Cudd_IsComplement(E) && E_pair->pos == Ecost)) { + tmp = cuddBddAndRecur(manager,Cudd_Not(manager->vars[my_dd->index]),sol); + if (tmp == NULL) { + Cudd_RecursiveDeref(manager,sol); + return(NULL); + } + cuddRef(tmp); + Cudd_RecursiveDeref(manager,sol); + sol = tmp; + complement = Cudd_IsComplement(E); + my_dd = Cudd_Regular(E); + cost = Ecost; + continue; + } + (void) fprintf(manager->err,"We shouldn't be here!\n"); + manager->errorCode = CUDD_INTERNAL_ERROR; + return(NULL); + } + + cuddDeref(sol); + return(sol); + +} /* end of getCube */ |