/**
* @brief Basic ADD test.
* @return 0 if successful; -1 otherwise.
*/
static int
testAdd(int verbosity)
{
DdManager *manager;
DdNode *f, *var, *tmp, *bg;
int i, ret;
CUDD_VALUE_TYPE pinf;
manager = Cudd_Init(0, 0, CUDD_UNIQUE_SLOTS, CUDD_CACHE_SLOTS, 0);
if (!manager) {
if (verbosity) {
printf("initialization failed\n");
}
return -1;
}
pinf = Cudd_V(Cudd_ReadPlusInfinity(manager));
if (verbosity) {
printf("Plus infinity is %g\n", pinf);
}
f = Cudd_addConst(manager,5);
Cudd_Ref(f);
for (i = 3; i >= 0; i--) {
var = Cudd_addIthVar(manager,i);
Cudd_Ref(var);
tmp = Cudd_addApply(manager,Cudd_addTimes,var,f);
Cudd_Ref(tmp);
Cudd_RecursiveDeref(manager,f);
Cudd_RecursiveDeref(manager,var);
f = tmp;
}
if (verbosity) {
Cudd_PrintMinterm(manager, f);
printf("\n");
}
Cudd_RecursiveDeref(manager, f);
bg = Cudd_ReadBackground(manager);
if (verbosity) {
printf("background (%g) minterms : ", Cudd_V(bg));
Cudd_ApaPrintMinterm(Cudd_ReadStdout(manager), manager, bg, 0);
}
ret = Cudd_CheckZeroRef(manager);
if (ret != 0 && verbosity) {
printf("%d non-zero ADD reference counts after dereferencing\n", ret);
}
Cudd_Quit(manager);
return ret != 0;
}
/**Function********************************************************************
Synopsis [Computes the Hamming distance ADD.]
Description [Computes the Hamming distance ADD. Returns an ADD that
gives the Hamming distance between its two arguments if successful;
NULL otherwise. The two vectors xVars and yVars identify the variables
that form the two arguments.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
Cudd_addHamming(
DdManager * dd,
DdNode ** xVars,
DdNode ** yVars,
int nVars)
{
DdNode *result,*tempBdd;
DdNode *tempAdd,*temp;
int i;
result = DD_ZERO(dd);
cuddRef(result);
for (i = 0; i < nVars; i++) {
tempBdd = Cudd_bddIte(dd,xVars[i],Cudd_Not(yVars[i]),yVars[i]);
if (tempBdd == NULL) {
Cudd_RecursiveDeref(dd,result);
return(NULL);
}
cuddRef(tempBdd);
tempAdd = Cudd_BddToAdd(dd,tempBdd);
if (tempAdd == NULL) {
Cudd_RecursiveDeref(dd,tempBdd);
Cudd_RecursiveDeref(dd,result);
return(NULL);
}
cuddRef(tempAdd);
Cudd_RecursiveDeref(dd,tempBdd);
temp = Cudd_addApply(dd,Cudd_addPlus,tempAdd,result);
if (temp == NULL) {
Cudd_RecursiveDeref(dd,tempAdd);
Cudd_RecursiveDeref(dd,result);
return(NULL);
}
cuddRef(temp);
Cudd_RecursiveDeref(dd,tempAdd);
Cudd_RecursiveDeref(dd,result);
result = temp;
}
cuddDeref(result);
return(result);
} /* end of Cudd_addHamming */
/**Function********************************************************************
Synopsis [Calculates the product of two matrices represented as
ADDs.]
Description [Calculates the product of two matrices, A and B,
represented as ADDs, using the CMU matrix by matrix multiplication
procedure by Clarke et al.. Matrix A has x's as row variables and z's
as column variables, while matrix B has z's as row variables and y's
as column variables. Returns the pointer to the result if successful;
NULL otherwise. The resulting matrix has x's as row variables and y's
as column variables.]
SideEffects [None]
SeeAlso [Cudd_addMatrixMultiply]
******************************************************************************/
DdNode *
Cudd_addTimesPlus(
DdManager * dd,
DdNode * A,
DdNode * B,
DdNode ** z,
int nz)
{
DdNode *w, *cube, *tmp, *res;
int i;
tmp = Cudd_addApply(dd,Cudd_addTimes,A,B);
if (tmp == NULL) return(NULL);
Cudd_Ref(tmp);
Cudd_Ref(cube = DD_ONE(dd));
for (i = nz-1; i >= 0; i--) {
w = Cudd_addIte(dd,z[i],cube,DD_ZERO(dd));
if (w == NULL) {
Cudd_RecursiveDeref(dd,tmp);
return(NULL);
}
Cudd_Ref(w);
Cudd_RecursiveDeref(dd,cube);
cube = w;
}
res = Cudd_addExistAbstract(dd,tmp,cube);
if (res == NULL) {
Cudd_RecursiveDeref(dd,tmp);
Cudd_RecursiveDeref(dd,cube);
return(NULL);
}
Cudd_Ref(res);
Cudd_RecursiveDeref(dd,cube);
Cudd_RecursiveDeref(dd,tmp);
Cudd_Deref(res);
return(res);
} /* end of Cudd_addTimesPlus */
/**Function********************************************************************
Synopsis [Repeated squaring algorithm for all-pairs shortest paths.]
Description []
SideEffects []
SeeAlso []
******************************************************************************/
static DdNode *
ntrSquare(
DdManager *dd /* manager */,
DdNode *D /* D(z,y): distance matrix */,
DdNode **x /* array of x variables */,
DdNode **y /* array of y variables */,
DdNode **z /* array of z variables */,
int vars /* number of variables in each of the three arrays */,
int pr /* verbosity level */,
int st /* use the selective trace algorithm */)
{
DdNode *zero;
DdNode *I; /* identity matirix */
DdNode *w, *V, *P, *M, *R, *RT;
DdNode *diff, *min, *minDiag;
int n;
int neg;
long start_time;
zero = Cudd_ReadZero(dd);
/* Make a working copy of the original matrix. */
R = D;
Cudd_Ref(R);
I = Cudd_addXeqy(dd,vars,z,y); /* identity matrix */
Cudd_Ref(I);
/* Make a copy of the matrix for the selective trace algorithm. */
diff = R;
Cudd_Ref(diff);
start_time = util_cpu_time();
for (n = vars; n >= 0; n--) {
printf("Starting iteration %d at time %s\n",vars-n,
util_print_time(util_cpu_time() - start_time));
/* Check for negative cycles: They are identified by negative
** elements on the diagonal.
*/
/* Extract values from the diagonal. */
Cudd_Ref(w = Cudd_addIte(dd,I,R,zero));
minDiag = Cudd_addFindMin(dd,w); /* no need to ref */
neg = Cudd_V(minDiag) < 0;
Cudd_RecursiveDeref(dd,w);
if (neg) {
Cudd_RecursiveDeref(dd,diff);
(void) printf("Negative cycle after %d iterations!\n",vars-n);
break;
}
/* Prepare the first operand of matrix multiplication:
** diff(z,y) -> RT(x,y) -> V(x,z)
*/
/* RT(x,y) */
Cudd_Ref(RT = Cudd_addSwapVariables(dd,diff,x,z,vars));
Cudd_RecursiveDeref(dd,diff);
/* V(x,z) */
Cudd_Ref(V = Cudd_addSwapVariables(dd,RT,y,z,vars));
Cudd_RecursiveDeref(dd,RT);
if (pr > 0) {
double pathcount;
(void) printf("V"); Cudd_PrintDebug(dd,V,2*vars,pr);
pathcount = Cudd_CountPath(V);
(void) printf("Path count = %g\n", pathcount);
}
/* V(x,z) * R(z,y) -> P(x,y) */
Cudd_Ref(P = Cudd_addTriangle(dd,V,R,z,vars));
Cudd_RecursiveDeref(dd,V);
/* P(x,y) => M(z,y) */
Cudd_Ref(M = Cudd_addSwapVariables(dd,P,x,z,vars));
Cudd_RecursiveDeref(dd,P);
if (pr>0) {(void) printf("M"); Cudd_PrintDebug(dd,M,2*vars,pr);}
/* min(z,y) */
Cudd_Ref(min = Cudd_addApply(dd,Cudd_addMinimum,R,M));
Cudd_RecursiveDeref(dd,M);
if (R == min) {
Cudd_RecursiveDeref(dd,min);
if (pr>0) {printf("Done after %d iterations\n",vars-n+1); }
break;
}
/* diff(z,y) */
if (st) {
Cudd_Ref(diff = Cudd_addApply(dd,Cudd_addDiff,min,R));
} else {
Cudd_Ref(diff = min);
}
Cudd_RecursiveDeref(dd,R);
R = min; /* keep a copy of matrix at current iter. */
if (pr > 0) {
double pathcount;
(void) printf("R"); Cudd_PrintDebug(dd,R,2*vars,pr);
pathcount = Cudd_CountPath(R);
(void) printf("Path count = %g\n", pathcount);
}
if (n == 0) {
(void) printf("Negative cycle!\n");
break;
}
}
Cudd_RecursiveDeref(dd,I);
Cudd_Deref(R);
return(R);
} /* end of ntrSquare */
/**Function********************************************************************
Synopsis [Bellman-Ford algorithm for single-source shortest paths.]
Description [Bellman-Ford algorithm for single-source shortest
paths. Returns the vector of the distances of all states from the
initial states. In case of multiple initial states the distance for
each state is from the nearest initial state. Negative-weight
cycles are detected, though only in the naive way. (Lack of
convergence after nodes-1 iterations.) In such a case, a constant
ADD with value minus infinity is returned. Bellman-Ford is based on
matrix-vector multiplication. The matrix is the distance matrix
D(x,y), such that D(a,b) is the length of the arc connecting state a
to state b. The vector V(x) stores the distances of all states from
the initial states. The actual vector used in the matrix-vector
multiplication is diff(x), that holds those distances that have
changed during the last update.]
SideEffects []
SeeAlso [ntrWarshall ntrSquare]
******************************************************************************/
static DdNode *
ntrBellman(
DdManager *dd,
DdNode *D,
DdNode *source,
DdNode **x,
DdNode **y,
int vars,
int pr)
{
DdNode *u, *w, *V, *min, *diff;
DdApaNumber i, nodes, one;
int digits = vars + 1;
/* To avoid overflow when there are many variables, use APA. */
nodes = Cudd_NewApaNumber(digits);
Cudd_ApaPowerOfTwo(digits,nodes,vars);
i = Cudd_NewApaNumber(digits);
one = Cudd_NewApaNumber(digits);
Cudd_ApaSetToLiteral(digits,one,1);
#if 0
/* Find the distances from the initial state along paths using one
** arc. */
w = Cudd_Cofactor(dd,D,source); /* works only if source is a cube */
Cudd_Ref(w);
V = Cudd_addSwapVariables(dd,w,x,y,vars);
Cudd_Ref(V);
Cudd_RecursiveDeref(dd,w);
#endif
/* The initial states are at distance 0. The other states are
** initially at infinite distance. */
V = Cudd_addIte(dd,source,Cudd_ReadZero(dd),Cudd_ReadPlusInfinity(dd));
Cudd_Ref(V);
/* Selective trace algorithm. For the next update, only consider the
** nodes whose distance has changed in the last update. */
diff = V;
Cudd_Ref(diff);
for (Cudd_ApaSetToLiteral(digits,i,1);
Cudd_ApaCompare(digits,i,digits,nodes) < 0;
Cudd_ApaAdd(digits,i,one,i)) {
if (pr>2) {(void) printf("V"); Cudd_PrintDebug(dd,V,vars,pr);}
/* Compute the distances via triangulation as a function of x. */
w = Cudd_addTriangle(dd,diff,D,x,vars);
Cudd_Ref(w);
Cudd_RecursiveDeref(dd,diff);
u = Cudd_addSwapVariables(dd,w,x,y,vars);
Cudd_Ref(u);
Cudd_RecursiveDeref(dd,w);
if (pr>2) {(void) printf("u"); Cudd_PrintDebug(dd,u,vars,pr);}
/* Take the minimum of the previous distances and those just
** computed. */
min = Cudd_addApply(dd,Cudd_addMinimum,V,u);
Cudd_Ref(min);
Cudd_RecursiveDeref(dd,u);
if (pr>2) {(void) printf("min"); Cudd_PrintDebug(dd,min,vars,pr);}
if (V == min) { /* convergence */
Cudd_RecursiveDeref(dd,min);
if (pr>0) {
(void) printf("Terminating after ");
Cudd_ApaPrintDecimal(stdout,digits,i);
(void) printf(" iterations\n");
}
break;
}
/* Find the distances that decreased. */
diff = Cudd_addApply(dd,Cudd_addDiff,V,min);
Cudd_Ref(diff);
if (pr>2) {(void) printf("diff"); Cudd_PrintDebug(dd,diff,vars,pr);}
Cudd_RecursiveDeref(dd,V);
V = min;
}
/* Negative cycle detection. */
if (Cudd_ApaCompare(digits,i,digits,nodes) == 0 &&
diff != Cudd_ReadPlusInfinity(dd)) {
(void) printf("Negative cycle\n");
Cudd_RecursiveDeref(dd,diff);
Cudd_RecursiveDeref(dd,V);
V = Cudd_ReadMinusInfinity(dd);
Cudd_Ref(V);
}
Cudd_Deref(V);
FREE(i);
FREE(nodes);
FREE(one);
return(V);
} /* end of ntrBellman */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addOuterSum.]
Description [Performs the recursive step of Cudd_addOuterSum.
Returns a pointer to the result if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
cuddAddOuterSumRecur(
DdManager *dd,
DdNode *M,
DdNode *r,
DdNode *c)
{
DdNode *P, *R, *Mt, *Me, *rt, *re, *ct, *ce, *Rt, *Re;
int topM, topc, topr;
int v, index;
statLine(dd);
/* Check special cases. */
if (r == DD_PLUS_INFINITY(dd) || c == DD_PLUS_INFINITY(dd)) return(M);
if (cuddIsConstant(c) && cuddIsConstant(r)) {
R = cuddUniqueConst(dd,Cudd_V(c)+Cudd_V(r));
cuddRef(R);
if (cuddIsConstant(M)) {
if (cuddV(R) <= cuddV(M)) {
cuddDeref(R);
return(R);
} else {
Cudd_RecursiveDeref(dd,R);
return(M);
}
} else {
P = Cudd_addApply(dd,Cudd_addMinimum,R,M);
cuddRef(P);
Cudd_RecursiveDeref(dd,R);
cuddDeref(P);
return(P);
}
}
/* Check the cache. */
R = cuddCacheLookup(dd,DD_ADD_OUT_SUM_TAG,M,r,c);
if (R != NULL) return(R);
topM = cuddI(dd,M->index); topr = cuddI(dd,r->index);
topc = cuddI(dd,c->index);
v = ddMin(topM,ddMin(topr,topc));
/* Compute cofactors. */
if (topM == v) { Mt = cuddT(M); Me = cuddE(M); } else { Mt = Me = M; }
if (topr == v) { rt = cuddT(r); re = cuddE(r); } else { rt = re = r; }
if (topc == v) { ct = cuddT(c); ce = cuddE(c); } else { ct = ce = c; }
/* Recursively solve. */
Rt = cuddAddOuterSumRecur(dd,Mt,rt,ct);
if (Rt == NULL) return(NULL);
cuddRef(Rt);
Re = cuddAddOuterSumRecur(dd,Me,re,ce);
if (Re == NULL) {
Cudd_RecursiveDeref(dd, Rt);
return(NULL);
}
cuddRef(Re);
index = dd->invperm[v];
R = (Rt == Re) ? Rt : cuddUniqueInter(dd,index,Rt,Re);
if (R == NULL) {
Cudd_RecursiveDeref(dd, Rt);
Cudd_RecursiveDeref(dd, Re);
return(NULL);
}
cuddDeref(Rt);
cuddDeref(Re);
/* Store the result in the cache. */
cuddCacheInsert(dd,DD_ADD_OUT_SUM_TAG,M,r,c,R);
return(R);
} /* end of cuddAddOuterSumRecur */
/**Function********************************************************************
Synopsis [Composes an ADD with a vector of 0-1 ADDs.]
Description [Given a vector of 0-1 ADDs, creates a new ADD by
substituting the 0-1 ADDs for the variables of the ADD f. There
should be an entry in vector for each variable in the manager.
This function implements non-simultaneous composition. If any of the
functions being composed depends on any of the variables being
substituted, then the result depends on the order of composition,
which in turn depends on the variable order: The variables farther from
the roots in the order are substituted first.
Returns a pointer to the resulting ADD if successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_addVectorCompose Cudd_addPermute Cudd_addCompose]
******************************************************************************/
DdNode *
Cudd_addNonSimCompose(
DdManager * dd,
DdNode * f,
DdNode ** vector)
{
DdNode *cube, *key, *var, *tmp, *piece;
DdNode *res;
int i, lastsub;
/* The cache entry for this function is composed of three parts:
** f itself, the replacement relation, and the cube of the
** variables being substituted.
** The replacement relation is the product of the terms (yi EXNOR gi).
** This apporach allows us to use the global cache for this function,
** with great savings in memory with respect to using arrays for the
** cache entries.
** First we build replacement relation and cube of substituted
** variables from the vector specifying the desired composition.
*/
key = DD_ONE(dd);
cuddRef(key);
cube = DD_ONE(dd);
cuddRef(cube);
for (i = (int) dd->size - 1; i >= 0; i--) {
if (ddIsIthAddVar(dd,vector[i],(unsigned int)i)) {
continue;
}
var = Cudd_addIthVar(dd,i);
if (var == NULL) {
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,cube);
return(NULL);
}
cuddRef(var);
/* Update cube. */
tmp = Cudd_addApply(dd,Cudd_addTimes,var,cube);
if (tmp == NULL) {
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,cube);
Cudd_RecursiveDeref(dd,var);
return(NULL);
}
cuddRef(tmp);
Cudd_RecursiveDeref(dd,cube);
cube = tmp;
/* Update replacement relation. */
piece = Cudd_addApply(dd,Cudd_addXnor,var,vector[i]);
if (piece == NULL) {
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,var);
return(NULL);
}
cuddRef(piece);
Cudd_RecursiveDeref(dd,var);
tmp = Cudd_addApply(dd,Cudd_addTimes,key,piece);
if (tmp == NULL) {
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,piece);
return(NULL);
}
cuddRef(tmp);
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,piece);
key = tmp;
}
/* Now try composition, until no reordering occurs. */
do {
/* Find real substitution with largest index. */
for (lastsub = dd->size - 1; lastsub >= 0; lastsub--) {
if (!ddIsIthAddVar(dd,vector[lastsub],(unsigned int)lastsub)) {
break;
}
}
/* Recursively solve the problem. */
dd->reordered = 0;
res = cuddAddNonSimComposeRecur(dd,f,vector,key,cube,lastsub+1);
if (res != NULL) cuddRef(res);
} while (dd->reordered == 1);
Cudd_RecursiveDeref(dd,key);
Cudd_RecursiveDeref(dd,cube);
if (res != NULL) cuddDeref(res);
return(res);
} /* end of Cudd_addNonSimCompose */
ref_t shadow_xor(shadow_mgr mgr, ref_t aref, ref_t bref) {
ref_t r = REF_ZERO;
dd_type_t dtype = IS_BDD;
bool za = is_zdd(mgr, aref);
bool zb = is_zdd(mgr, bref);
bool aa = is_add(mgr, aref);
bool ab = is_add(mgr, bref);
if (mgr->do_cudd && mgr->nzvars > 0) {
/* Check whether arguments are ZDDs */
DdNode *an = get_ddnode(mgr, aref);
DdNode *bn = get_ddnode(mgr, bref);
DdNode *rn;
if (za || zb) {
if (aa || ab) {
err(false, "Can't mix ADDs and ZDDs");
}
dtype = IS_ZDD;
/* Make sure they're both ZDDs */
if (!za) {
an = zconvert(mgr, an);
}
if (!zb) {
bn = zconvert(mgr, bn);
}
rn = Cudd_zddSymmetricDiff(mgr->bdd_manager, an, bn);
reference_dd(mgr, rn);
r = dd2ref(rn, IS_ZDD);
add_ref(mgr, r, rn);
if (!za)
unreference_dd(mgr, an, IS_ZDD);
if (!zb)
unreference_dd(mgr, bn, IS_ZDD);
}
}
if (mgr->do_cudd) {
/* Check whether arguments are ADDs */
DdNode *an = get_ddnode(mgr, aref);
DdNode *bn = get_ddnode(mgr, bref);
DdNode *rn;
if (aa || ab) {
dtype = IS_ADD;
/* Make sure they're both ADDs */
if (!aa) {
an = aconvert(mgr, an);
}
if (!ab) {
bn = aconvert(mgr, bn);
}
rn = Cudd_addApply(mgr->bdd_manager, Cudd_addXor, an, bn);
reference_dd(mgr, rn);
r = dd2ref(rn, IS_ADD);
add_ref(mgr, r, rn);
if (!aa)
unreference_dd(mgr, an, IS_ADD);
if (!ab)
unreference_dd(mgr, bn, IS_ADD);
}
}
if (dtype == IS_BDD)
r = shadow_ite(mgr, aref, shadow_negate(mgr, bref), bref);
#if RPT >= 4
char buf1[24], buf2[24], buf3[24];
shadow_show(mgr, aref, buf1);
shadow_show(mgr, bref, buf2);
shadow_show(mgr, r, buf3);
report(4, "%s %sXOR %s --> %s", buf1, dtype == IS_ZDD ? "Z" : dtype == IS_ADD ? "A" : "" , buf2, buf3);
#endif
return r;
}
