/**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 [Converts a ZDD cover to a BDD graph.]
Description [Converts a ZDD cover to a BDD graph. If successful, it
returns a BDD node, otherwise it returns NULL. It is a recursive
algorithm as the following. First computes 3 cofactors of a ZDD cover;
f1, f0 and fd. Second, compute BDDs(b1, b0 and bd) of f1, f0 and fd.
Third, compute T=b1+bd and E=b0+bd. Fourth, compute ITE(v,T,E) where v
is the variable which has the index of the top node of the ZDD cover.
In this case, since the index of v can be larger than either one of T or
one of E, cuddUniqueInterIVO is called, here IVO stands for
independent variable ordering.]
SideEffects []
SeeAlso [Cudd_MakeBddFromZddCover]
******************************************************************************/
DdNode *
cuddMakeBddFromZddCover(
DdManager * dd,
DdNode * node)
{
DdNode *neW;
int v;
DdNode *f1, *f0, *fd;
DdNode *b1, *b0, *bd;
DdNode *T, *E;
statLine(dd);
if (node == dd->one)
return(dd->one);
if (node == dd->zero)
return(Cudd_Not(dd->one));
/* Check cache */
neW = cuddCacheLookup1(dd, cuddMakeBddFromZddCover, node);
if (neW)
return(neW);
v = Cudd_Regular(node)->index; /* either yi or zi */
cuddZddGetCofactors3(dd, node, v, &f1, &f0, &fd);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
b1 = cuddMakeBddFromZddCover(dd, f1);
if (!b1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(b1);
b0 = cuddMakeBddFromZddCover(dd, f0);
if (!b1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDeref(dd, b1);
return(NULL);
}
Cudd_Ref(b0);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
if (fd != dd->zero) {
bd = cuddMakeBddFromZddCover(dd, fd);
if (!bd) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDeref(dd, b1);
Cudd_RecursiveDeref(dd, b0);
return(NULL);
}
Cudd_Ref(bd);
Cudd_RecursiveDerefZdd(dd, fd);
T = cuddBddAndRecur(dd, Cudd_Not(b1), Cudd_Not(bd));
if (!T) {
Cudd_RecursiveDeref(dd, b1);
Cudd_RecursiveDeref(dd, b0);
Cudd_RecursiveDeref(dd, bd);
return(NULL);
}
T = Cudd_NotCond(T, T != NULL);
Cudd_Ref(T);
Cudd_RecursiveDeref(dd, b1);
E = cuddBddAndRecur(dd, Cudd_Not(b0), Cudd_Not(bd));
if (!E) {
Cudd_RecursiveDeref(dd, b0);
Cudd_RecursiveDeref(dd, bd);
Cudd_RecursiveDeref(dd, T);
return(NULL);
}
E = Cudd_NotCond(E, E != NULL);
Cudd_Ref(E);
Cudd_RecursiveDeref(dd, b0);
Cudd_RecursiveDeref(dd, bd);
}
else {
Cudd_RecursiveDerefZdd(dd, fd);
T = b1;
E = b0;
}
if (Cudd_IsComplement(T)) {
neW = cuddUniqueInterIVO(dd, v / 2, Cudd_Not(T), Cudd_Not(E));
if (!neW) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
neW = Cudd_Not(neW);
}
else {
neW = cuddUniqueInterIVO(dd, v / 2, T, E);
if (!neW) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
}
Cudd_Ref(neW);
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
cuddCacheInsert1(dd, cuddMakeBddFromZddCover, node, neW);
Cudd_Deref(neW);
return(neW);
} /* end of cuddMakeBddFromZddCover */
/**Function********************************************************************
Synopsis [Main function for testcudd.]
Description []
SideEffects [None]
SeeAlso []
******************************************************************************/
int
main(int argc, char **argv)
{
FILE *fp; /* pointer to input file */
char *file = (char *) ""; /* input file name */
FILE *dfp = NULL; /* pointer to dump file */
char *dfile; /* file for DD dump */
DdNode *dfunc[2]; /* addresses of the functions to be dumped */
DdManager *dd; /* pointer to DD manager */
DdNode *_true; /* fast access to constant function */
DdNode *M;
DdNode **x; /* pointers to variables */
DdNode **y; /* pointers to variables */
DdNode **xn; /* complements of row variables */
DdNode **yn_; /* complements of column variables */
DdNode **xvars;
DdNode **yvars;
DdNode *C; /* result of converting from ADD to BDD */
DdNode *ess; /* cube of essential variables */
DdNode *shortP; /* BDD cube of shortest path */
DdNode *largest; /* BDD of largest cube */
DdNode *shortA; /* ADD cube of shortest path */
DdNode *constN; /* value returned by evaluation of ADD */
DdNode *ycube; /* cube of the negated y vars for c-proj */
DdNode *CP; /* C-Projection of C */
DdNode *CPr; /* C-Selection of C */
int length; /* length of the shortest path */
int nx; /* number of variables */
int ny;
int maxnx;
int maxny;
int m;
int n;
int N;
int cmu; /* use CMU multiplication */
int pr; /* verbose printout level */
int harwell;
int multiple; /* read multiple matrices */
int ok;
int c; /* variable to read in options */
int approach; /* reordering approach */
int autodyn; /* automatic reordering */
int groupcheck; /* option for group sifting */
int profile; /* print heap profile if != 0 */
int keepperm; /* keep track of permutation */
int clearcache; /* clear the cache after each matrix */
int blifOrDot; /* dump format: 0 -> dot, 1 -> blif, ... */
int retval; /* return value */
int i; /* loop index */
long startTime; /* initial time */
long lapTime;
int size;
unsigned int cacheSize, maxMemory;
unsigned int nvars,nslots;
startTime = util_cpu_time();
approach = CUDD_REORDER_NONE;
autodyn = 0;
pr = 0;
harwell = 0;
multiple = 0;
profile = 0;
keepperm = 0;
cmu = 0;
N = 4;
nvars = 4;
cacheSize = 127;
maxMemory = 0;
nslots = CUDD_UNIQUE_SLOTS;
clearcache = 0;
groupcheck = CUDD_GROUP_CHECK7;
dfile = NULL;
blifOrDot = 0; /* dot format */
/* Parse command line. */
while ((c = util_getopt(argc, argv, (char *) "CDHMPS:a:bcd:g:hkmn:p:v:x:X:"))
!= EOF) {
switch(c) {
case 'C':
cmu = 1;
break;
case 'D':
autodyn = 1;
break;
case 'H':
harwell = 1;
break;
case 'M':
#ifdef MNEMOSYNE
(void) mnem_setrecording(0);
#endif
break;
case 'P':
profile = 1;
break;
case 'S':
nslots = atoi(util_optarg);
break;
case 'X':
maxMemory = atoi(util_optarg);
break;
case 'a':
approach = atoi(util_optarg);
break;
case 'b':
blifOrDot = 1; /* blif format */
break;
case 'c':
clearcache = 1;
break;
case 'd':
dfile = util_optarg;
break;
case 'g':
groupcheck = atoi(util_optarg);
break;
case 'k':
keepperm = 1;
break;
case 'm':
multiple = 1;
break;
case 'n':
N = atoi(util_optarg);
break;
case 'p':
pr = atoi(util_optarg);
break;
case 'v':
nvars = atoi(util_optarg);
break;
case 'x':
cacheSize = atoi(util_optarg);
break;
case 'h':
default:
usage(argv[0]);
break;
}
}
if (argc - util_optind == 0) {
file = (char *) "-";
} else if (argc - util_optind == 1) {
file = argv[util_optind];
} else {
usage(argv[0]);
}
if ((approach<0) || (approach>17)) {
(void) fprintf(stderr,"Invalid approach: %d \n",approach);
usage(argv[0]);
}
if (pr >= 0) {
(void) printf("# %s\n", TESTCUDD_VERSION);
/* Echo command line and arguments. */
(void) printf("#");
for (i = 0; i < argc; i++) {
(void) printf(" %s", argv[i]);
}
(void) printf("\n");
(void) fflush(stdout);
}
/* Initialize manager and provide easy reference to terminals. */
dd = Cudd_Init(nvars,0,nslots,cacheSize,maxMemory);
_true = DD_TRUE(dd);
dd->groupcheck = (Cudd_AggregationType) groupcheck;
if (autodyn) Cudd_AutodynEnable(dd,CUDD_REORDER_SAME);
/* Open input file. */
fp = open_file(file, "r");
/* Open dump file if requested */
if (dfile != NULL) {
dfp = open_file(dfile, "w");
}
x = y = xn = yn_ = NULL;
do {
/* We want to start anew for every matrix. */
maxnx = maxny = 0;
nx = maxnx; ny = maxny;
if (pr>0) lapTime = util_cpu_time();
if (harwell) {
if (pr >= 0) (void) printf(":name: ");
ok = Cudd_addHarwell(fp, dd, &M, &x, &y, &xn, &yn_, &nx, &ny,
&m, &n, 0, 2, 1, 2, pr);
} else {
ok = Cudd_addRead(fp, dd, &M, &x, &y, &xn, &yn_, &nx, &ny,
&m, &n, 0, 2, 1, 2);
if (pr >= 0)
(void) printf(":name: %s: %d rows %d columns\n", file, m, n);
}
if (!ok) {
(void) fprintf(stderr, "Error reading matrix\n");
exit(1);
}
if (nx > maxnx) maxnx = nx;
if (ny > maxny) maxny = ny;
/* Build cube of negated y's. */
ycube = DD_TRUE(dd);
Cudd_Ref(ycube);
for (i = maxny - 1; i >= 0; i--) {
DdNode *tmpp;
tmpp = Cudd_bddAnd(dd,Cudd_Not(dd->vars[y[i]->index]),ycube);
if (tmpp == NULL) exit(2);
Cudd_Ref(tmpp);
Cudd_RecursiveDeref(dd,ycube);
ycube = tmpp;
}
/* Initialize vectors of BDD variables used by priority func. */
xvars = ALLOC(DdNode *, nx);
if (xvars == NULL) exit(2);
for (i = 0; i < nx; i++) {
xvars[i] = dd->vars[x[i]->index];
}
yvars = ALLOC(DdNode *, ny);
if (yvars == NULL) exit(2);
for (i = 0; i < ny; i++) {
yvars[i] = dd->vars[y[i]->index];
}
/* Clean up */
for (i=0; i < maxnx; i++) {
Cudd_RecursiveDeref(dd, x[i]);
Cudd_RecursiveDeref(dd, xn[i]);
}
FREE(x);
FREE(xn);
for (i=0; i < maxny; i++) {
Cudd_RecursiveDeref(dd, y[i]);
Cudd_RecursiveDeref(dd, yn_[i]);
}
FREE(y);
FREE(yn_);
if (pr>0) {(void) printf(":1: M"); Cudd_PrintDebug(dd,M,nx+ny,pr);}
if (pr>0) (void) printf(":2: time to read the matrix = %s\n",
util_print_time(util_cpu_time() - lapTime));
C = Cudd_addBddPattern(dd, M);
if (C == 0) exit(2);
Cudd_Ref(C);
if (pr>0) {(void) printf(":3: C"); Cudd_PrintDebug(dd,C,nx+ny,pr);}
/* Test iterators. */
retval = testIterators(dd,M,C,pr);
if (retval == 0) exit(2);
cuddCacheProfile(dd,stdout);
/* Test XOR */
retval = testXor(dd,C,pr,nx+ny);
if (retval == 0) exit(2);
/* Test Hamming distance functions. */
retval = testHamming(dd,C,pr);
if (retval == 0) exit(2);
/* Test selection functions. */
CP = Cudd_CProjection(dd,C,ycube);
if (CP == NULL) exit(2);
Cudd_Ref(CP);
if (pr>0) {(void) printf("ycube"); Cudd_PrintDebug(dd,ycube,nx+ny,pr);}
if (pr>0) {(void) printf("CP"); Cudd_PrintDebug(dd,CP,nx+ny,pr);}
if (nx == ny) {
CPr = Cudd_PrioritySelect(dd,C,xvars,yvars,(DdNode **)NULL,
(DdNode *)NULL,ny,Cudd_Xgty);
if (CPr == NULL) exit(2);
Cudd_Ref(CPr);
if (pr>0) {(void) printf(":4: CPr"); Cudd_PrintDebug(dd,CPr,nx+ny,pr);}
if (CP != CPr) {
(void) printf("CP != CPr!\n");
}
Cudd_RecursiveDeref(dd, CPr);
}
FREE(xvars); FREE(yvars);
Cudd_RecursiveDeref(dd, CP);
Cudd_RecursiveDeref(dd, ycube);
/* Test functions for essential variables. */
ess = Cudd_FindEssential(dd,C);
if (ess == NULL) exit(2);
Cudd_Ref(ess);
if (pr>0) {(void) printf(":4: ess"); Cudd_PrintDebug(dd,ess,nx+ny,pr);}
Cudd_RecursiveDeref(dd, ess);
/* Test functions for shortest paths. */
shortP = Cudd_ShortestPath(dd, M, NULL, NULL, &length);
if (shortP == NULL) exit(2);
Cudd_Ref(shortP);
if (pr>0) {
(void) printf(":5: shortP"); Cudd_PrintDebug(dd,shortP,nx+ny,pr);
}
/* Test functions for largest cubes. */
largest = Cudd_LargestCube(dd, Cudd_Not(C), &length);
if (largest == NULL) exit(2);
Cudd_Ref(largest);
if (pr>0) {
(void) printf(":5b: largest");
Cudd_PrintDebug(dd,largest,nx+ny,pr);
}
Cudd_RecursiveDeref(dd, largest);
/* Test Cudd_addEvalConst and Cudd_addIteConstant. */
shortA = Cudd_BddToAdd(dd,shortP);
if (shortA == NULL) exit(2);
Cudd_Ref(shortA);
Cudd_RecursiveDeref(dd, shortP);
constN = Cudd_addEvalConst(dd,shortA,M);
if (constN == DD_NON_CONSTANT) exit(2);
if (Cudd_addIteConstant(dd,shortA,M,constN) != constN) exit(2);
if (pr>0) {(void) printf("The value of M along the chosen shortest path is %g\n", cuddV(constN));}
Cudd_RecursiveDeref(dd, shortA);
shortP = Cudd_ShortestPath(dd, C, NULL, NULL, &length);
if (shortP == NULL) exit(2);
Cudd_Ref(shortP);
if (pr>0) {
(void) printf(":6: shortP"); Cudd_PrintDebug(dd,shortP,nx+ny,pr);
}
/* Test Cudd_bddIteConstant and Cudd_bddLeq. */
if (!Cudd_bddLeq(dd,shortP,C)) exit(2);
if (Cudd_bddIteConstant(dd,Cudd_Not(shortP),_true,C) != _true) exit(2);
Cudd_RecursiveDeref(dd, shortP);
if (profile) {
retval = cuddHeapProfile(dd);
}
size = dd->size;
if (pr>0) {
(void) printf("Average distance: %g\n", Cudd_AverageDistance(dd));
}
/* Reorder if so requested. */
if (approach != CUDD_REORDER_NONE) {
#ifndef DD_STATS
retval = Cudd_EnableReorderingReporting(dd);
if (retval == 0) {
(void) fprintf(stderr,"Error reported by Cudd_EnableReorderingReporting\n");
exit(3);
}
#endif
#ifdef DD_DEBUG
retval = Cudd_DebugCheck(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_DebugCheck\n");
exit(3);
}
retval = Cudd_CheckKeys(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_CheckKeys\n");
exit(3);
}
#endif
retval = Cudd_ReduceHeap(dd,(Cudd_ReorderingType)approach,5);
if (retval == 0) {
(void) fprintf(stderr,"Error reported by Cudd_ReduceHeap\n");
exit(3);
}
#ifndef DD_STATS
retval = Cudd_DisableReorderingReporting(dd);
if (retval == 0) {
(void) fprintf(stderr,"Error reported by Cudd_DisableReorderingReporting\n");
exit(3);
}
#endif
#ifdef DD_DEBUG
retval = Cudd_DebugCheck(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_DebugCheck\n");
exit(3);
}
retval = Cudd_CheckKeys(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_CheckKeys\n");
exit(3);
}
#endif
if (approach == CUDD_REORDER_SYMM_SIFT ||
approach == CUDD_REORDER_SYMM_SIFT_CONV) {
Cudd_SymmProfile(dd,0,dd->size-1);
}
if (pr>0) {
(void) printf("Average distance: %g\n", Cudd_AverageDistance(dd));
}
if (keepperm) {
/* Print variable permutation. */
(void) printf("Variable Permutation:");
for (i=0; i<size; i++) {
if (i%20 == 0) (void) printf("\n");
(void) printf("%d ", dd->invperm[i]);
}
(void) printf("\n");
(void) printf("Inverse Permutation:");
for (i=0; i<size; i++) {
if (i%20 == 0) (void) printf("\n");
(void) printf("%d ", dd->perm[i]);
}
(void) printf("\n");
}
if (pr>0) {(void) printf("M"); Cudd_PrintDebug(dd,M,nx+ny,pr);}
if (profile) {
retval = cuddHeapProfile(dd);
}
}
/* Dump DDs of C and M if so requested. */
if (dfile != NULL) {
dfunc[0] = C;
dfunc[1] = M;
if (blifOrDot == 1) {
/* Only dump C because blif cannot handle ADDs */
retval = Cudd_DumpBlif(dd,1,dfunc,NULL,(char **)onames,
NULL,dfp);
} else {
retval = Cudd_DumpDot(dd,2,dfunc,NULL,(char **)onames,dfp);
}
if (retval != 1) {
(void) fprintf(stderr,"abnormal termination\n");
exit(2);
}
}
Cudd_RecursiveDeref(dd, C);
Cudd_RecursiveDeref(dd, M);
if (clearcache) {
if (pr>0) {(void) printf("Clearing the cache... ");}
for (i = dd->cacheSlots - 1; i>=0; i--) {
dd->cache[i].data = NIL(DdNode);
}
if (pr>0) {(void) printf("done\n");}
}
if (pr>0) {
(void) printf("Number of variables = %6d\t",dd->size);
(void) printf("Number of slots = %6d\n",dd->slots);
(void) printf("Number of keys = %6d\t",dd->keys);
(void) printf("Number of min dead = %6d\n",dd->minDead);
}
} while (multiple && !feof(fp));
fclose(fp);
if (dfile != NULL) {
fclose(dfp);
}
/* Second phase: experiment with Walsh matrices. */
if (!testWalsh(dd,N,cmu,approach,pr)) {
exit(2);
}
/* Check variable destruction. */
assert(cuddDestroySubtables(dd,3));
assert(Cudd_DebugCheck(dd) == 0);
assert(Cudd_CheckKeys(dd) == 0);
retval = Cudd_CheckZeroRef(dd);
ok = retval != 0; /* ok == 0 means O.K. */
if (retval != 0) {
(void) fprintf(stderr,
"%d non-zero DD reference counts after dereferencing\n", retval);
}
if (pr >= 0) {
(void) Cudd_PrintInfo(dd,stdout);
}
Cudd_Quit(dd);
#ifdef MNEMOSYNE
mnem_writestats();
#endif
if (pr>0) (void) printf("total time = %s\n",
util_print_time(util_cpu_time() - startTime));
if (pr >= 0) util_print_cpu_stats(stdout);
exit(ok);
/* NOTREACHED */
} /* end of main */
/**
@brief Implements the recursive step of Cudd_bddClippingAnd.
@details Takes the conjunction of two BDDs.
@return a pointer to the result is successful; NULL otherwise.
@sideeffect None
@see cuddBddClippingAnd
*/
static DdNode *
cuddBddClippingAndRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
int distance,
int direction)
{
DdNode *F, *ft, *fe, *G, *gt, *ge;
DdNode *one, *zero, *r, *t, *e;
int topf, topg;
unsigned int index;
DD_CTFP cacheOp;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
if (f == g || g == one) return(f);
if (f == one) return(g);
if (distance == 0) {
/* One last attempt at returning the right result. We sort of
** cheat by calling Cudd_bddLeq. */
if (Cudd_bddLeq(manager,f,g)) return(f);
if (Cudd_bddLeq(manager,g,f)) return(g);
if (direction == 1) {
if (Cudd_bddLeq(manager,f,Cudd_Not(g)) ||
Cudd_bddLeq(manager,g,Cudd_Not(f))) return(zero);
}
return(Cudd_NotCond(one,(direction == 0)));
}
/* At this point f and g are not constant. */
distance--;
/* Check cache. Try to increase cache efficiency by sorting the
** pointers. */
if (f > g) {
DdNode *tmp = f;
f = g; g = tmp;
}
F = Cudd_Regular(f);
G = Cudd_Regular(g);
cacheOp = (DD_CTFP)
(direction ? Cudd_bddClippingAnd : cuddBddClippingAnd);
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup2(manager, cacheOp, f, g);
if (r != NULL) return(r);
}
checkWhetherToGiveUp(manager);
/* Here we can skip the use of cuddI, because the operands are known
** to be non-constant.
*/
topf = manager->perm[F->index];
topg = manager->perm[G->index];
/* Compute cofactors. */
if (topf <= topg) {
index = F->index;
ft = cuddT(F);
fe = cuddE(F);
if (Cudd_IsComplement(f)) {
ft = Cudd_Not(ft);
fe = Cudd_Not(fe);
}
} else {
index = G->index;
ft = fe = f;
}
if (topg <= topf) {
gt = cuddT(G);
ge = cuddE(G);
if (Cudd_IsComplement(g)) {
gt = Cudd_Not(gt);
ge = Cudd_Not(ge);
}
} else {
gt = ge = g;
}
t = cuddBddClippingAndRecur(manager, ft, gt, distance, direction);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddClippingAndRecur(manager, fe, ge, distance, direction);
if (e == NULL) {
Cudd_RecursiveDeref(manager, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} else {
if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(manager,(int)index,Cudd_Not(t),Cudd_Not(e));
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(manager,(int)index,t,e);
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
}
}
cuddDeref(e);
cuddDeref(t);
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert2(manager, cacheOp, f, g, r);
return(r);
} /* end of cuddBddClippingAndRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddIsop.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddIsop]
******************************************************************************/
DdNode *
cuddZddIsop(
DdManager * dd,
DdNode * L,
DdNode * U,
DdNode ** zdd_I)
{
DdNode *one = DD_ONE(dd);
DdNode *zero = Cudd_Not(one);
DdNode *zdd_one = DD_ONE(dd);
DdNode *zdd_zero = DD_ZERO(dd);
int v, top_l, top_u;
DdNode *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
DdNode *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
DdNode *Isub0, *Isub1, *Id;
DdNode *zdd_Isub0, *zdd_Isub1, *zdd_Id;
DdNode *x;
DdNode *term0, *term1, *sum;
DdNode *Lv, *Uv, *Lnv, *Unv;
DdNode *r, *y, *z;
int index;
DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *);
statLine(dd);
if (L == zero) {
*zdd_I = zdd_zero;
return(zero);
}
if (U == one) {
*zdd_I = zdd_one;
return(one);
}
if (U == zero || L == one) {
printf("*** ERROR : illegal condition for ISOP (U < L).\n");
exit(1);
}
/* Check the cache. We store two results for each recursive call.
** One is the BDD, and the other is the ZDD. Both are needed.
** Hence we need a double hit in the cache to terminate the
** recursion. Clearly, collisions may evict only one of the two
** results. */
cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) cuddZddIsop;
r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
if (r) {
*zdd_I = cuddCacheLookup2Zdd(dd, cacheOp, L, U);
if (*zdd_I)
return(r);
else {
/* The BDD result may have been dead. In that case
** cuddCacheLookup2 would have called cuddReclaim,
** whose effects we now have to undo. */
cuddRef(r);
Cudd_RecursiveDeref(dd, r);
}
}
top_l = dd->perm[Cudd_Regular(L)->index];
top_u = dd->perm[Cudd_Regular(U)->index];
v = ddMin(top_l, top_u);
/* Compute cofactors. */
if (top_l == v) {
index = Cudd_Regular(L)->index;
Lv = Cudd_T(L);
Lnv = Cudd_E(L);
if (Cudd_IsComplement(L)) {
Lv = Cudd_Not(Lv);
Lnv = Cudd_Not(Lnv);
}
}
else {
index = Cudd_Regular(U)->index;
Lv = Lnv = L;
}
if (top_u == v) {
Uv = Cudd_T(U);
Unv = Cudd_E(U);
if (Cudd_IsComplement(U)) {
Uv = Cudd_Not(Uv);
Unv = Cudd_Not(Unv);
}
}
else {
Uv = Unv = U;
}
Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
if (Lsub0 == NULL)
return(NULL);
Cudd_Ref(Lsub0);
Usub0 = Unv;
Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
if (Lsub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
return(NULL);
}
Cudd_Ref(Lsub1);
Usub1 = Uv;
Isub0 = cuddZddIsop(dd, Lsub0, Usub0, &zdd_Isub0);
if (Isub0 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Isub0))) &&
(Cudd_Regular(Isub0)->index != zdd_Isub0->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Isub0->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Isub0);
Cudd_Ref(zdd_Isub0);
Isub1 = cuddZddIsop(dd, Lsub1, Usub1, &zdd_Isub1);
if (Isub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Isub1))) &&
(Cudd_Regular(Isub1)->index != zdd_Isub1->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Isub1->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Isub1);
Cudd_Ref(zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
if (Lsuper0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
return(NULL);
}
Cudd_Ref(Lsuper0);
Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
if (Lsuper1 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
return(NULL);
}
Cudd_Ref(Lsuper1);
Usuper0 = Unv;
Usuper1 = Uv;
/* Ld = Lsuper0 + Lsuper1 */
Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
if (Ld == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
return(NULL);
}
Ld = Cudd_Not(Ld);
Cudd_Ref(Ld);
/* Ud = Usuper0 * Usuper1 */
Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
if (Ud == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Cudd_RecursiveDeref(dd, Ld);
return(NULL);
}
Cudd_Ref(Ud);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Id = cuddZddIsop(dd, Ld, Ud, &zdd_Id);
if (Id == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Id))) &&
(Cudd_Regular(Id)->index != zdd_Id->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Id->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Id);
Cudd_Ref(zdd_Id);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
x = cuddUniqueInter(dd, index, one, zero);
if (x == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
return(NULL);
}
Cudd_Ref(x);
/* term0 = x * Isub0 */
term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
if (term0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, x);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDeref(dd, Isub0);
/* term1 = x * Isub1 */
term1 = cuddBddAndRecur(dd, x, Isub1);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, term0);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, Isub1);
/* sum = term0 + term1 */
sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
if (sum == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
return(NULL);
}
sum = Cudd_Not(sum);
Cudd_Ref(sum);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
/* r = sum + Id */
r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
r = Cudd_NotCond(r, r != NULL);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, sum);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDeref(dd, sum);
Cudd_RecursiveDeref(dd, Id);
if (zdd_Isub0 != zdd_zero) {
z = cuddZddGetNodeIVO(dd, index * 2 + 1, zdd_Isub0, zdd_Id);
if (z == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, r);
return(NULL);
}
}
else {
z = zdd_Id;
}
Cudd_Ref(z);
if (zdd_Isub1 != zdd_zero) {
y = cuddZddGetNodeIVO(dd, index * 2, zdd_Isub1, z);
if (y == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, r);
Cudd_RecursiveDerefZdd(dd, z);
return(NULL);
}
}
else
y = z;
Cudd_Ref(y);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDerefZdd(dd, z);
cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
cuddCacheInsert2(dd, cacheOp, L, U, y);
Cudd_Deref(r);
Cudd_Deref(y);
*zdd_I = y;
/*
if (Cudd_Regular(r)->index != y->index / 2) {
printf("*** ERROR : mismatch in indices between BDD and ZDD. ***\n");
}
*/
return(r);
} /* end of cuddZddIsop */
/**Function********************************************************************
Synopsis [Generates an ADD for the function x==y.]
Description [This function generates an ADD for the function x==y.
Both x and y are N-bit numbers, x\[0\] x\[1\] ... x\[N-1\] and
y\[0\] y\[1\] ... y\[N-1\], with 0 the most significant bit.
The ADD is built bottom-up.
It has 3*N-1 internal nodes, if the variables are ordered as follows:
x\[0\] y\[0\] x\[1\] y\[1\] ... x\[N-1\] y\[N-1\]. ]
SideEffects [None]
SeeAlso [Cudd_Xeqy]
******************************************************************************/
DdNode *
Cudd_addXeqy(
DdManager * dd /* DD manager */,
int N /* number of x and y variables */,
DdNode ** x /* array of x variables */,
DdNode ** y /* array of y variables */)
{
DdNode *one, *zero;
DdNode *u, *v, *w;
int i;
one = DD_ONE(dd);
zero = DD_ZERO(dd);
/* Build bottom part of ADD outside loop. */
v = Cudd_addIte(dd, y[N-1], one, zero);
if (v == NULL) return(NULL);
cuddRef(v);
w = Cudd_addIte(dd, y[N-1], zero, one);
if (w == NULL) {
Cudd_RecursiveDeref(dd, v);
return(NULL);
}
cuddRef(w);
u = Cudd_addIte(dd, x[N-1], v, w);
if (w == NULL) {
Cudd_RecursiveDeref(dd, v);
Cudd_RecursiveDeref(dd, w);
return(NULL);
}
cuddRef(u);
Cudd_RecursiveDeref(dd, v);
Cudd_RecursiveDeref(dd, w);
/* Loop to build the rest of the ADD. */
for (i = N-2; i >= 0; i--) {
v = Cudd_addIte(dd, y[i], u, zero);
if (v == NULL) {
Cudd_RecursiveDeref(dd, u);
return(NULL);
}
cuddRef(v);
w = Cudd_addIte(dd, y[i], zero, u);
if (w == NULL) {
Cudd_RecursiveDeref(dd, u);
Cudd_RecursiveDeref(dd, v);
return(NULL);
}
cuddRef(w);
Cudd_RecursiveDeref(dd, u);
u = Cudd_addIte(dd, x[i], v, w);
if (w == NULL) {
Cudd_RecursiveDeref(dd, v);
Cudd_RecursiveDeref(dd, w);
return(NULL);
}
cuddRef(u);
Cudd_RecursiveDeref(dd, v);
Cudd_RecursiveDeref(dd, w);
}
cuddDeref(u);
return(u);
} /* end of Cudd_addXeqy */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_CProjection.]
Description [Performs the recursive step of Cudd_CProjection. Returns
the projection if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_CProjection]
******************************************************************************/
DdNode *
cuddCProjectionRecur(
DdManager * dd,
DdNode * R,
DdNode * Y,
DdNode * Ysupp)
{
DdNode *res, *res1, *res2, *resA;
DdNode *r, *y, *RT, *RE, *YT, *YE, *Yrest, *Ra, *Ran, *Gamma, *Alpha;
unsigned int topR, topY, top, index;
DdNode *one = DD_ONE(dd);
statLine(dd);
if (Y == one) return(R);
#ifdef DD_DEBUG
assert(!Cudd_IsConstant(Y));
#endif
if (R == Cudd_Not(one)) return(R);
res = cuddCacheLookup2(dd, Cudd_CProjection, R, Y);
if (res != NULL) return(res);
r = Cudd_Regular(R);
topR = cuddI(dd,r->index);
y = Cudd_Regular(Y);
topY = cuddI(dd,y->index);
top = ddMin(topR, topY);
/* Compute the cofactors of R */
if (topR == top) {
index = r->index;
RT = cuddT(r);
RE = cuddE(r);
if (r != R) {
RT = Cudd_Not(RT); RE = Cudd_Not(RE);
}
} else {
RT = RE = R;
}
if (topY > top) {
/* Y does not depend on the current top variable.
** We just need to compute the results on the two cofactors of R
** and make them the children of a node labeled r->index.
*/
res1 = cuddCProjectionRecur(dd,RT,Y,Ysupp);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddCProjectionRecur(dd,RE,Y,Ysupp);
if (res2 == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddRef(res2);
res = cuddBddIteRecur(dd, dd->vars[index], res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
/* If we have reached this point, res1 and res2 are now
** incorporated in res. cuddDeref is therefore sufficient.
*/
cuddDeref(res1);
cuddDeref(res2);
} else {
/* Compute the cofactors of Y */
index = y->index;
YT = cuddT(y);
YE = cuddE(y);
if (y != Y) {
YT = Cudd_Not(YT); YE = Cudd_Not(YE);
}
if (YT == Cudd_Not(one)) {
Alpha = Cudd_Not(dd->vars[index]);
Yrest = YE;
Ra = RE;
Ran = RT;
} else {
Alpha = dd->vars[index];
Yrest = YT;
Ra = RT;
Ran = RE;
}
Gamma = cuddBddExistAbstractRecur(dd,Ra,cuddT(Ysupp));
if (Gamma == NULL) return(NULL);
if (Gamma == one) {
res1 = cuddCProjectionRecur(dd,Ra,Yrest,cuddT(Ysupp));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res = cuddBddAndRecur(dd, Alpha, res1);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddDeref(res1);
} else if (Gamma == Cudd_Not(one)) {
res1 = cuddCProjectionRecur(dd,Ran,Yrest,cuddT(Ysupp));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res = cuddBddAndRecur(dd, Cudd_Not(Alpha), res1);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddDeref(res1);
} else {
cuddRef(Gamma);
resA = cuddCProjectionRecur(dd,Ran,Yrest,cuddT(Ysupp));
if (resA == NULL) {
Cudd_RecursiveDeref(dd,Gamma);
return(NULL);
}
cuddRef(resA);
res2 = cuddBddAndRecur(dd, Cudd_Not(Gamma), resA);
if (res2 == NULL) {
Cudd_RecursiveDeref(dd,Gamma);
Cudd_RecursiveDeref(dd,resA);
return(NULL);
}
cuddRef(res2);
Cudd_RecursiveDeref(dd,Gamma);
Cudd_RecursiveDeref(dd,resA);
res1 = cuddCProjectionRecur(dd,Ra,Yrest,cuddT(Ysupp));
if (res1 == NULL) {
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
cuddRef(res1);
res = cuddBddIteRecur(dd, Alpha, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
}
}
cuddCacheInsert2(dd,Cudd_CProjection,R,Y,res);
return(res);
} /* end of cuddCProjectionRecur */
int main( int argc, char **argv )
{
FILE *fp;
FILE *stdin_backup = NULL;
bool help_flag = False;
bool ptdump_flag = False;
bool logging_flag = False;
unsigned char verbose = 0;
int input_index = -1;
int output_file_index = -1; /* For command-line flag "-o". */
char dumpfilename[64];
int i, j, var_index;
ptree_t *tmppt; /* General purpose temporary ptree pointer */
int horizon = -1;
DdNode *W, *etrans, *strans, **sgoals, **egoals;
DdManager *manager;
DdNode *T = NULL;
anode_t *strategy = NULL;
int num_env, num_sys;
int original_num_env, original_num_sys;
int max_sim_it; /* Number of simulation iterations */
anode_t *play;
vartype *init_state;
int *init_state_ints = NULL;
char *all_vars = NULL, *metric_vars = NULL;
int *offw, num_vars;
int init_state_acc; /* Accumulate components of initial state
before expanding into a (bool) bitvector. */
/* Look for flags in command-line arguments. */
for (i = 1; i < argc; i++) {
if (argv[i][0] == '-') {
if (argv[i][1] == 'h') {
help_flag = True;
} else if (argv[i][1] == 'V') {
printf( "grjit (experiment-related program, distributed with"
" gr1c v" GR1C_VERSION ")\n\n" GR1C_COPYRIGHT "\n" );
return 0;
} else if (argv[i][1] == 'v') {
verbose = 1;
j = 2;
/* Only support up to "level 2" of verbosity */
while (argv[i][j] == 'v' && j <= 2) {
verbose++;
j++;
}
} else if (argv[i][1] == 'l') {
logging_flag = True;
} else if (argv[i][1] == 'p') {
ptdump_flag = True;
} else if (argv[i][1] == 'm') {
if (i == argc-1) {
fprintf( stderr, "Invalid flag given. Try \"-h\".\n" );
return 1;
}
all_vars = strtok( argv[i+1], "," );
max_sim_it = strtol( all_vars, NULL, 10 );
all_vars = strtok( NULL, "," );
if (all_vars == NULL) {
fprintf( stderr, "Invalid use of -m flag.\n" );
return 1;
}
metric_vars = strdup( all_vars );
if (max_sim_it >= 0) {
all_vars = strtok( NULL, "," );
if (all_vars == NULL) {
fprintf( stderr, "Invalid use of -m flag.\n" );
return 1;
}
init_state_acc = read_state_str( all_vars,
&init_state_ints, -1 );
all_vars = strtok( NULL, "," );
if (all_vars == NULL) {
horizon = -1; /* The horizon was not given. */
} else {
horizon = strtol( all_vars, NULL, 10 );
if (horizon < 1) {
fprintf( stderr,
"Invalid use of -m flag. Horizon must"
" be positive.\n" );
return 1;
}
}
}
all_vars = NULL;
i++;
} else if (argv[i][1] == 'o') {
if (i == argc-1) {
fprintf( stderr, "Invalid flag given. Try \"-h\".\n" );
return 1;
}
output_file_index = i+1;
i++;
} else {
fprintf( stderr, "Invalid flag given. Try \"-h\".\n" );
return 1;
}
} else if (input_index < 0) {
/* Use first non-flag argument as filename whence to read
specification. */
input_index = i;
}
}
if (help_flag) {
/* Split among printf() calls to conform with ISO C90 string length */
printf( "Usage: %s [-hVvlp] [-m ARG1,ARG2,...] [-o FILE] [FILE]\n\n"
" -h this help message\n"
" -V print version and exit\n"
" -v be verbose; use -vv to be more verbose\n"
" -l enable logging\n"
" -p dump parse trees to DOT files, and echo formulas to screen\n"
" -o FILE output results to FILE, rather than stdout (default)\n", argv[0] );
printf( " -m ARG1,... run simulation using comma-separated list of arguments:\n"
" ARG1 is the max simulation duration; -1 to only compute horizon;\n"
" ARG2 is a space-separated list of metric variables;\n"
" ARG3 is a space-separated list of initial values;\n"
" ARG3 is ignored and may be omitted if ARG1 equals -1.\n"
" ARG4 is the horizon, if provided; otherwise compute it.\n" );
return 1;
}
if (logging_flag) {
openlogfile( NULL ); /* Use default filename prefix */
/* Only change verbosity level if user did not specify it */
if (verbose == 0)
verbose = 1;
} else {
setlogstream( stdout );
setlogopt( LOGOPT_NOTIME );
}
if (verbose > 0)
logprint( "Running with verbosity level %d.", verbose );
/* If filename for specification given at command-line, then use
it. Else, read from stdin. */
if (input_index > 0) {
fp = fopen( argv[input_index], "r" );
if (fp == NULL) {
perror( "grjit, fopen" );
return -1;
}
stdin_backup = stdin;
stdin = fp;
}
/* Parse the specification. */
if (verbose)
logprint( "Parsing input..." );
SPC_INIT( spc );
if (yyparse())
return -1;
if (verbose)
logprint( "Done." );
if (stdin_backup != NULL) {
stdin = stdin_backup;
}
/* Close input file, if opened. */
if (input_index > 0)
fclose( fp );
/* Treat deterministic problem in which ETRANS or EINIT is omitted. */
if (spc.evar_list == NULL) {
if (spc.et_array_len == 0) {
spc.et_array_len = 1;
spc.env_trans_array = malloc( sizeof(ptree_t *) );
if (spc.env_trans_array == NULL) {
perror( "gr1c, malloc" );
return -1;
}
*spc.env_trans_array = init_ptree( PT_CONSTANT, NULL, 1 );
}
if (spc.env_init == NULL)
spc.env_init = init_ptree( PT_CONSTANT, NULL, 1 );
}
/* Number of variables, before expansion of those that are nonboolean */
original_num_env = tree_size( spc.evar_list );
original_num_sys = tree_size( spc.svar_list );
/* Build list of variable names if needed for simulation, storing
the result as a string in all_vars */
if (max_sim_it >= 0) {
/* At this point, init_state_acc should contain the number of
integers read by read_state_str() during
command-line argument parsing. */
if (init_state_acc != original_num_env+original_num_sys) {
fprintf( stderr,
"Number of initial values given does not match number"
" of problem variables.\n" );
return 1;
}
num_vars = 0;
tmppt = spc.evar_list;
while (tmppt) {
num_vars += strlen( tmppt->name )+1;
tmppt = tmppt->left;
}
tmppt = spc.svar_list;
while (tmppt) {
num_vars += strlen( tmppt->name )+1;
tmppt = tmppt->left;
}
all_vars = malloc( num_vars*sizeof(char) );
if (all_vars == NULL) {
perror( "main, malloc" );
return -1;
}
i = 0;
tmppt = spc.evar_list;
while (tmppt) {
strncpy( all_vars+i, tmppt->name, num_vars-i );
i += strlen( tmppt->name )+1;
*(all_vars+i-1) = ' ';
tmppt = tmppt->left;
}
tmppt = spc.svar_list;
while (tmppt) {
strncpy( all_vars+i, tmppt->name, num_vars-i );
i += strlen( tmppt->name )+1;
*(all_vars+i-1) = ' ';
tmppt = tmppt->left;
}
*(all_vars+i-1) = '\0';
if (verbose)
logprint( "String of all variables found to be \"%s\"", all_vars );
}
if (ptdump_flag) {
tree_dot_dump( spc.env_init, "env_init_ptree.dot" );
tree_dot_dump( spc.sys_init, "sys_init_ptree.dot" );
for (i = 0; i < spc.et_array_len; i++) {
snprintf( dumpfilename, sizeof(dumpfilename),
"env_trans%05d_ptree.dot", i );
tree_dot_dump( *(spc.env_trans_array+i), dumpfilename );
}
for (i = 0; i < spc.st_array_len; i++) {
snprintf( dumpfilename, sizeof(dumpfilename),
"sys_trans%05d_ptree.dot", i );
tree_dot_dump( *(spc.sys_trans_array+i), dumpfilename );
}
if (spc.num_egoals > 0) {
for (i = 0; i < spc.num_egoals; i++) {
snprintf( dumpfilename, sizeof(dumpfilename),
"env_goal%05d_ptree.dot", i );
tree_dot_dump( *(spc.env_goals+i), dumpfilename );
}
}
if (spc.num_sgoals > 0) {
for (i = 0; i < spc.num_sgoals; i++) {
snprintf( dumpfilename, sizeof(dumpfilename),
"sys_goal%05d_ptree.dot", i );
tree_dot_dump( *(spc.sys_goals+i), dumpfilename );
}
}
var_index = 0;
printf( "Environment variables (indices; domains): " );
if (spc.evar_list == NULL) {
printf( "(none)" );
} else {
tmppt = spc.evar_list;
while (tmppt) {
if (tmppt->value == 0) { /* Boolean */
if (tmppt->left == NULL) {
printf( "%s (%d; bool)", tmppt->name, var_index );
} else {
printf( "%s (%d; bool), ", tmppt->name, var_index);
}
} else {
if (tmppt->left == NULL) {
printf( "%s (%d; {0..%d})",
tmppt->name, var_index, tmppt->value );
} else {
printf( "%s (%d; {0..%d}), ",
tmppt->name, var_index, tmppt->value );
}
}
tmppt = tmppt->left;
var_index++;
}
}
printf( "\n\n" );
printf( "System variables (indices; domains): " );
if (spc.svar_list == NULL) {
printf( "(none)" );
} else {
tmppt = spc.svar_list;
while (tmppt) {
if (tmppt->value == 0) { /* Boolean */
if (tmppt->left == NULL) {
printf( "%s (%d; bool)", tmppt->name, var_index );
} else {
printf( "%s (%d; bool), ", tmppt->name, var_index );
}
} else {
if (tmppt->left == NULL) {
printf( "%s (%d; {0..%d})",
tmppt->name, var_index, tmppt->value );
} else {
printf( "%s (%d; {0..%d}), ",
tmppt->name, var_index, tmppt->value );
}
}
tmppt = tmppt->left;
var_index++;
}
}
printf( "\n\n" );
print_GR1_spec( spc.evar_list, spc.svar_list, spc.env_init, spc.sys_init,
spc.env_trans_array, spc.et_array_len,
spc.sys_trans_array, spc.st_array_len,
spc.env_goals, spc.num_egoals, spc.sys_goals, spc.num_sgoals, stdout );
}
if (expand_nonbool_GR1( spc.evar_list, spc.svar_list, &spc.env_init, &spc.sys_init,
&spc.env_trans_array, &spc.et_array_len,
&spc.sys_trans_array, &spc.st_array_len,
&spc.env_goals, spc.num_egoals, &spc.sys_goals, spc.num_sgoals,
verbose ) < 0)
return -1;
spc.nonbool_var_list = expand_nonbool_variables( &spc.evar_list, &spc.svar_list,
verbose );
if (spc.et_array_len > 1) {
spc.env_trans = merge_ptrees( spc.env_trans_array, spc.et_array_len, PT_AND );
} else if (spc.et_array_len == 1) {
spc.env_trans = *spc.env_trans_array;
} else {
fprintf( stderr,
"Syntax error: GR(1) specification is missing environment"
" transition rules.\n" );
return -1;
}
if (spc.st_array_len > 1) {
spc.sys_trans = merge_ptrees( spc.sys_trans_array, spc.st_array_len, PT_AND );
} else if (spc.st_array_len == 1) {
spc.sys_trans = *spc.sys_trans_array;
} else {
fprintf( stderr,
"Syntax error: GR(1) specification is missing system"
" transition rules.\n" );
return -1;
}
if (verbose > 1)
/* Dump the spec to show results of conversion (if any). */
print_GR1_spec( spc.evar_list, spc.svar_list, spc.env_init, spc.sys_init,
spc.env_trans_array, spc.et_array_len,
spc.sys_trans_array, spc.st_array_len,
spc.env_goals, spc.num_egoals, spc.sys_goals, spc.num_sgoals, NULL );
num_env = tree_size( spc.evar_list );
num_sys = tree_size( spc.svar_list );
manager = Cudd_Init( 2*(num_env+num_sys),
0, CUDD_UNIQUE_SLOTS, CUDD_CACHE_SLOTS, 0 );
Cudd_SetMaxCacheHard( manager, (unsigned int)-1 );
Cudd_AutodynEnable( manager, CUDD_REORDER_SAME );
T = check_realizable( manager, EXIST_SYS_INIT, verbose );
if (verbose) {
if (T != NULL) {
logprint( "Realizable." );
} else {
logprint( "Not realizable." );
}
}
if (T != NULL) { /* Print measure data and simulate. */
if (horizon < 0) {
if (verbose)
logprint( "Computing horizon with metric variables: %s",
metric_vars );
horizon = compute_horizon( manager, &W, &etrans, &strans, &sgoals,
metric_vars, verbose );
logprint( "horizon: %d", horizon );
if (getlogstream() != stdout)
printf( "horizon: %d\n", horizon );
} else {
W = compute_winning_set_saveBDDs( manager, &etrans, &strans,
&egoals, &sgoals, verbose );
if (verbose)
logprint( "Using given horizon: %d", horizon );
}
if (max_sim_it >= 0 && horizon > -1) {
/* Compute variable offsets and use it to get the initial
state as a bitvector */
offw = get_offsets( all_vars, &num_vars );
if (num_vars != original_num_env+original_num_sys) {
fprintf( stderr,
"Error while computing bitwise variable offsets.\n" );
return -1;
}
free( all_vars );
init_state_acc = 0;
if (verbose) {
logprint_startline();
logprint_raw( "initial state for simulation:" );
}
for (i = 0; i < original_num_env+original_num_sys; i++) {
if (verbose)
logprint_raw( " %d", *(init_state_ints+i) );
init_state_acc += *(init_state_ints+i) << *(offw + 2*i);
}
if (verbose)
logprint_endline();
free( offw );
init_state = int_to_bitvec( init_state_acc, num_env+num_sys );
if (init_state == NULL)
return -1;
play = sim_rhc( manager, W, etrans, strans, sgoals, metric_vars,
horizon, init_state, max_sim_it, verbose );
if (play == NULL) {
fprintf( stderr,
"Error while attempting receding horizon"
" simulation.\n" );
return -1;
}
free( init_state );
logprint( "play length: %d", aut_size( play ) );
tmppt = spc.nonbool_var_list;
while (tmppt) {
aut_compact_nonbool( play, spc.evar_list, spc.svar_list,
tmppt->name, tmppt->value );
tmppt = tmppt->left;
}
num_env = tree_size( spc.evar_list );
num_sys = tree_size( spc.svar_list );
/* Open output file if specified; else point to stdout. */
if (output_file_index >= 0) {
fp = fopen( argv[output_file_index], "w" );
if (fp == NULL) {
perror( "grjit, fopen" );
return -1;
}
} else {
fp = stdout;
}
/* Print simulation trace */
dump_simtrace( play, spc.evar_list, spc.svar_list, fp );
if (fp != stdout)
fclose( fp );
}
Cudd_RecursiveDeref( manager, W );
Cudd_RecursiveDeref( manager, etrans );
Cudd_RecursiveDeref( manager, strans );
}
/* Clean-up */
free( metric_vars );
delete_tree( spc.evar_list );
delete_tree( spc.svar_list );
delete_tree( spc.env_init );
delete_tree( spc.sys_init );
delete_tree( spc.env_trans );
delete_tree( spc.sys_trans );
for (i = 0; i < spc.num_egoals; i++)
delete_tree( *(spc.env_goals+i) );
if (spc.num_egoals > 0)
free( spc.env_goals );
for (i = 0; i < spc.num_sgoals; i++)
delete_tree( *(spc.sys_goals+i) );
if (spc.num_sgoals > 0)
free( spc.sys_goals );
if (T != NULL)
Cudd_RecursiveDeref( manager, T );
if (strategy)
delete_aut( strategy );
if (verbose > 1)
logprint( "Cudd_CheckZeroRef -> %d", Cudd_CheckZeroRef( manager ) );
Cudd_Quit(manager);
if (logging_flag)
closelogfile();
/* Return 0 if realizable, -1 if not realizable. */
if (T != NULL) {
return 0;
} else {
return -1;
}
return 0;
}
/**Function********************************************************************
Synopsis [Builds an ADD for the residue modulo m of an n-bit
number.]
Description [Builds an ADD for the residue modulo m of an n-bit
number. The modulus must be at least 2, and the number of bits at
least 1. Parameter options specifies whether the MSB should be on top
or the LSB; and whther the number whose residue is computed is in
two's complement notation or not. The macro CUDD_RESIDUE_DEFAULT
specifies LSB on top and unsigned number. The macro CUDD_RESIDUE_MSB
specifies MSB on top, and the macro CUDD_RESIDUE_TC specifies two's
complement residue. To request MSB on top and two's complement residue
simultaneously, one can OR the two macros:
CUDD_RESIDUE_MSB | CUDD_RESIDUE_TC.
Cudd_addResidue returns a pointer to the resulting ADD if successful;
NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
Cudd_addResidue(
DdManager * dd /* manager */,
int n /* number of bits */,
int m /* modulus */,
int options /* options */,
int top /* index of top variable */)
{
int msbLsb; /* MSB on top (1) or LSB on top (0) */
int tc; /* two's complement (1) or unsigned (0) */
int i, j, k, t, residue, thisOne, previous, index;
DdNode **array[2], *var, *tmp, *res;
/* Sanity check. */
if (n < 1 && m < 2) return(NULL);
msbLsb = options & CUDD_RESIDUE_MSB;
tc = options & CUDD_RESIDUE_TC;
/* Allocate and initialize working arrays. */
array[0] = ALLOC(DdNode *,m);
if (array[0] == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
return(NULL);
}
array[1] = ALLOC(DdNode *,m);
if (array[1] == NULL) {
FREE(array[0]);
dd->errorCode = CUDD_MEMORY_OUT;
return(NULL);
}
for (i = 0; i < m; i++) {
array[0][i] = array[1][i] = NULL;
}
/* Initialize residues. */
for (i = 0; i < m; i++) {
tmp = cuddUniqueConst(dd,(CUDD_VALUE_TYPE) i);
if (tmp == NULL) {
for (j = 0; j < i; j++) {
Cudd_RecursiveDeref(dd,array[1][j]);
}
FREE(array[0]);
FREE(array[1]);
return(NULL);
}
cuddRef(tmp);
array[1][i] = tmp;
}
/* Main iteration. */
residue = 1; /* residue of 2**0 */
for (k = 0; k < n; k++) {
/* Choose current and previous arrays. */
thisOne = k & 1;
previous = thisOne ^ 1;
/* Build an ADD projection function. */
if (msbLsb) {
index = top+n-k-1;
} else {
index = top+k;
}
var = cuddUniqueInter(dd,index,DD_ONE(dd),DD_ZERO(dd));
if (var == NULL) {
for (j = 0; j < m; j++) {
Cudd_RecursiveDeref(dd,array[previous][j]);
}
FREE(array[0]);
FREE(array[1]);
return(NULL);
}
cuddRef(var);
for (i = 0; i < m; i ++) {
t = (i + residue) % m;
tmp = Cudd_addIte(dd,var,array[previous][t],array[previous][i]);
if (tmp == NULL) {
for (j = 0; j < i; j++) {
Cudd_RecursiveDeref(dd,array[thisOne][j]);
}
for (j = 0; j < m; j++) {
Cudd_RecursiveDeref(dd,array[previous][j]);
}
FREE(array[0]);
FREE(array[1]);
return(NULL);
}
cuddRef(tmp);
array[thisOne][i] = tmp;
}
/* One layer completed. Free the other array for the next iteration. */
for (i = 0; i < m; i++) {
Cudd_RecursiveDeref(dd,array[previous][i]);
}
Cudd_RecursiveDeref(dd,var);
/* Update residue of 2**k. */
residue = (2 * residue) % m;
/* Adjust residue for MSB, if this is a two's complement number. */
if (tc && (k == n - 1)) {
residue = (m - residue) % m;
}
}
/* We are only interested in the 0-residue node of the top layer. */
for (i = 1; i < m; i++) {
Cudd_RecursiveDeref(dd,array[(n - 1) & 1][i]);
}
res = array[(n - 1) & 1][0];
FREE(array[0]);
FREE(array[1]);
cuddDeref(res);
return(res);
} /* end of Cudd_addResidue */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addApply.]
Description [Performs the recursive step of Cudd_addApply. Returns a
pointer to the result if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [cuddAddMonadicApplyRecur]
******************************************************************************/
DdNode *
cuddAddApplyRecur(
DdManager * dd,
DdNode * (*op)(DdManager *, DdNode **, DdNode **),
DdNode * f,
DdNode * g)
{
DdNode *res,
*fv, *fvn, *gv, *gvn,
*T, *E;
unsigned int ford, gord;
unsigned int index;
DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *);
/* Check terminal cases. Op may swap f and g to increase the
* cache hit rate.
*/
statLine(dd);
res = (*op)(dd,&f,&g);
if (res != NULL) return(res);
/* Check cache. */
cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) op;
res = cuddCacheLookup2(dd,cacheOp,f,g);
if (res != NULL) return(res);
/* Recursive step. */
ford = cuddI(dd,f->index);
gord = cuddI(dd,g->index);
if (ford <= gord) {
index = f->index;
fv = cuddT(f);
fvn = cuddE(f);
} else {
index = g->index;
fv = fvn = f;
}
if (gord <= ford) {
gv = cuddT(g);
gvn = cuddE(g);
} else {
gv = gvn = g;
}
T = cuddAddApplyRecur(dd,op,fv,gv);
if (T == NULL) return(NULL);
cuddRef(T);
E = cuddAddApplyRecur(dd,op,fvn,gvn);
if (E == NULL) {
Cudd_RecursiveDeref(dd,T);
return(NULL);
}
cuddRef(E);
res = (T == E) ? T : cuddUniqueInter(dd,(int)index,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
cuddDeref(T);
cuddDeref(E);
/* Store result. */
cuddCacheInsert2(dd,cacheOp,f,g,res);
return(res);
} /* end of cuddAddApplyRecur */
/**Function********************************************************************
Synopsis [Writes a dot file representing the argument ZDDs.]
Description [Writes a file representing the argument ZDDs in a format
suitable for the graph drawing program dot.
It returns 1 in case of success; 0 otherwise (e.g., out-of-memory,
file system full).
Cudd_zddDumpDot does not close the file: This is the caller
responsibility. Cudd_zddDumpDot uses a minimal unique subset of the
hexadecimal address of a node as name for it.
If the argument inames is non-null, it is assumed to hold the pointers
to the names of the inputs. Similarly for onames.
Cudd_zddDumpDot uses the following convention to draw arcs:
<ul>
<li> solid line: THEN arcs;
<li> dashed line: ELSE arcs.
</ul>
The dot options are chosen so that the drawing fits on a letter-size
sheet.
]
SideEffects [None]
SeeAlso [Cudd_DumpDot Cudd_zddPrintDebug]
******************************************************************************/
int
Cudd_zddDumpDot(
DdManager * dd /* manager */,
int n /* number of output nodes to be dumped */,
DdNode ** f /* array of output nodes to be dumped */,
char ** inames /* array of input names (or NULL) */,
char ** onames /* array of output names (or NULL) */,
FILE * fp /* pointer to the dump file */)
{
DdNode *support = NULL;
DdNode *scan;
int *sorted = NULL;
int nvars = dd->sizeZ;
st_table *visited = NULL;
st_generator *gen;
int retval;
int i, j;
int slots;
DdNodePtr *nodelist;
long refAddr, diff, mask;
/* Build a bit array with the support of f. */
sorted = ALLOC(int,nvars);
if (sorted == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
goto failure;
}
for (i = 0; i < nvars; i++) sorted[i] = 0;
/* Take the union of the supports of each output function. */
for (i = 0; i < n; i++) {
support = Cudd_Support(dd,f[i]);
if (support == NULL) goto failure;
cuddRef(support);
scan = support;
while (!cuddIsConstant(scan)) {
sorted[scan->index] = 1;
scan = cuddT(scan);
}
Cudd_RecursiveDeref(dd,support);
}
support = NULL; /* so that we do not try to free it in case of failure */
/* Initialize symbol table for visited nodes. */
visited = st_init_table(st_ptrcmp, st_ptrhash);
if (visited == NULL) goto failure;
/* Collect all the nodes of this DD in the symbol table. */
for (i = 0; i < n; i++) {
retval = cuddCollectNodes(f[i],visited);
if (retval == 0) goto failure;
}
/* Find how many most significant hex digits are identical
** in the addresses of all the nodes. Build a mask based
** on this knowledge, so that digits that carry no information
** will not be printed. This is done in two steps.
** 1. We scan the symbol table to find the bits that differ
** in at least 2 addresses.
** 2. We choose one of the possible masks. There are 8 possible
** masks for 32-bit integer, and 16 possible masks for 64-bit
** integers.
*/
/* Find the bits that are different. */
refAddr = (long) f[0];
diff = 0;
gen = st_init_gen(visited);
while (st_gen(gen, (char **) &scan, NULL)) {
diff |= refAddr ^ (long) scan;
}
st_free_gen(gen);
/* Choose the mask. */
for (i = 0; (unsigned) i < 8 * sizeof(long); i += 4) {
mask = (1 << i) - 1;
if (diff <= mask) break;
}
/* Write the header and the global attributes. */
retval = fprintf(fp,"digraph \"ZDD\" {\n");
if (retval == EOF) return(0);
retval = fprintf(fp,
"size = \"7.5,10\"\ncenter = true;\nedge [dir = none];\n");
if (retval == EOF) return(0);
/* Write the input name subgraph by scanning the support array. */
retval = fprintf(fp,"{ node [shape = plaintext];\n");
if (retval == EOF) goto failure;
retval = fprintf(fp," edge [style = invis];\n");
if (retval == EOF) goto failure;
/* We use a name ("CONST NODES") with an embedded blank, because
** it is unlikely to appear as an input name.
*/
retval = fprintf(fp," \"CONST NODES\" [style = invis];\n");
if (retval == EOF) goto failure;
for (i = 0; i < nvars; i++) {
if (sorted[dd->invpermZ[i]]) {
if (inames == NULL) {
retval = fprintf(fp,"\" %d \" -> ", dd->invpermZ[i]);
} else {
retval = fprintf(fp,"\" %s \" -> ", inames[dd->invpermZ[i]]);
}
if (retval == EOF) goto failure;
}
}
retval = fprintf(fp,"\"CONST NODES\"; \n}\n");
if (retval == EOF) goto failure;
/* Write the output node subgraph. */
retval = fprintf(fp,"{ rank = same; node [shape = box]; edge [style = invis];\n");
if (retval == EOF) goto failure;
for (i = 0; i < n; i++) {
if (onames == NULL) {
retval = fprintf(fp,"\"F%d\"", i);
} else {
retval = fprintf(fp,"\" %s \"", onames[i]);
}
if (retval == EOF) goto failure;
if (i == n - 1) {
retval = fprintf(fp,"; }\n");
} else {
retval = fprintf(fp," -> ");
}
if (retval == EOF) goto failure;
}
/* Write rank info: All nodes with the same index have the same rank. */
for (i = 0; i < nvars; i++) {
if (sorted[dd->invpermZ[i]]) {
retval = fprintf(fp,"{ rank = same; ");
if (retval == EOF) goto failure;
if (inames == NULL) {
retval = fprintf(fp,"\" %d \";\n", dd->invpermZ[i]);
} else {
retval = fprintf(fp,"\" %s \";\n", inames[dd->invpermZ[i]]);
}
if (retval == EOF) goto failure;
nodelist = dd->subtableZ[i].nodelist;
slots = dd->subtableZ[i].slots;
for (j = 0; j < slots; j++) {
scan = nodelist[j];
while (scan != NULL) {
if (st_is_member(visited,(char *) scan)) {
retval = fprintf(fp,"\"%lx\";\n", (mask & (long) scan) / sizeof(DdNode));
if (retval == EOF) goto failure;
}
scan = scan->next;
}
}
retval = fprintf(fp,"}\n");
if (retval == EOF) goto failure;
}
}
/* All constants have the same rank. */
retval = fprintf(fp,
"{ rank = same; \"CONST NODES\";\n{ node [shape = box]; ");
if (retval == EOF) goto failure;
nodelist = dd->constants.nodelist;
slots = dd->constants.slots;
for (j = 0; j < slots; j++) {
scan = nodelist[j];
while (scan != NULL) {
if (st_is_member(visited,(char *) scan)) {
retval = fprintf(fp,"\"%lx\";\n", (mask & (long) scan) / sizeof(DdNode));
if (retval == EOF) goto failure;
}
scan = scan->next;
}
}
retval = fprintf(fp,"}\n}\n");
if (retval == EOF) goto failure;
/* Write edge info. */
/* Edges from the output nodes. */
for (i = 0; i < n; i++) {
if (onames == NULL) {
retval = fprintf(fp,"\"F%d\"", i);
} else {
retval = fprintf(fp,"\" %s \"", onames[i]);
}
if (retval == EOF) goto failure;
retval = fprintf(fp," -> \"%lx\" [style = solid];\n",
(mask & (long) f[i]) / sizeof(DdNode));
if (retval == EOF) goto failure;
}
/* Edges from internal nodes. */
for (i = 0; i < nvars; i++) {
if (sorted[dd->invpermZ[i]]) {
nodelist = dd->subtableZ[i].nodelist;
slots = dd->subtableZ[i].slots;
for (j = 0; j < slots; j++) {
scan = nodelist[j];
while (scan != NULL) {
if (st_is_member(visited,(char *) scan)) {
retval = fprintf(fp,
"\"%lx\" -> \"%lx\";\n",
(mask & (long) scan) / sizeof(DdNode),
(mask & (long) cuddT(scan)) / sizeof(DdNode));
if (retval == EOF) goto failure;
retval = fprintf(fp,
"\"%lx\" -> \"%lx\" [style = dashed];\n",
(mask & (long) scan) / sizeof(DdNode),
(mask & (long) cuddE(scan)) / sizeof(DdNode));
if (retval == EOF) goto failure;
}
scan = scan->next;
}
}
}
}
/* Write constant labels. */
nodelist = dd->constants.nodelist;
slots = dd->constants.slots;
for (j = 0; j < slots; j++) {
scan = nodelist[j];
while (scan != NULL) {
if (st_is_member(visited,(char *) scan)) {
retval = fprintf(fp,"\"%lx\" [label = \"%g\"];\n",
(mask & (long) scan) / sizeof(DdNode), cuddV(scan));
if (retval == EOF) goto failure;
}
scan = scan->next;
}
}
/* Write trailer and return. */
retval = fprintf(fp,"}\n");
if (retval == EOF) goto failure;
st_free_table(visited);
FREE(sorted);
return(1);
failure:
if (sorted != NULL) FREE(sorted);
if (support != NULL) Cudd_RecursiveDeref(dd,support);
if (visited != NULL) st_free_table(visited);
return(0);
} /* end of Cudd_zddDumpBlif */
int main(int argc, char** argv) {
unsigned int i;
Biddy_Boolean complete;
Biddy_Edge tmp;
Biddy_Edge r1,r2;
unsigned int n1,n2;
char *userinput;
#ifdef USA_YES
unsigned int usaSize = 0;
unsigned int **usaEdge;
unsigned int *usaOrder;
char *usaCodes;
Biddy_Edge *usaState;
Biddy_Edge *usaGraph;
#endif
#ifdef EUROPE_YES
unsigned int europeSize = 0;
unsigned int **europeEdge;
unsigned int *europeOrder;
char *europeCodes;
Biddy_Edge *europeState;
Biddy_Edge *europeGraph;
#endif
setbuf(stdout, NULL);
#ifdef USA_YES
setDataUSA(&usaSize,&usaEdge,&usaOrder,&usaCodes);
#endif
#ifdef EUROPE_YES
setDataEurope(&europeSize,&europeEdge,&europeOrder,&europeCodes);
#endif
#ifdef USE_BIDDY
/* There is only one unique table in Biddy */
/* There are three caches in Biddy */
/* Unique table grows over the time */
/* The max number of variables is hardcoded in biddyInt. h */
/* biddyVariableTable.usaSize = BIDDYVARMAX = 2048 */
/* The following constants are hardcoded in biddyMain.c */
/* biddyIteCache.usaSize = MEDIUM_TABLE = 262143 */
/* biddyEACache.usaSize = SMALL_TABLE = 65535 */
/* biddyRCCache.usaSize = SMALL_TABLE = 65535 */
/* DEFAULT INIT CALL: Biddy_Init() */
Biddy_Init();
#endif
#ifdef USE_CUDD
/* In CUDD each variable has its own subtable in the unique table */
/* There is only one cache in CUDD */
/* Subtables grow over the time, you can set limit for fast unique table growth */
/* Cudd_SetLooseUpTo(manager,1048576) */
/* Cache can grow over the time, you can set the max usaSize */
/* Cudd_SetMaxCacheHard(manager,262144) */
/* These two constants are hardcoded in v3.0.0 */
/* CUDD_UNIQUE_SLOTS = 256 (default initial usaSize of each subtable) */
/* CUDD_CACHE_SLOTS = 262144 (default initial usaSize of cache table) */
/* DEFAULT INIT CALL: Cudd_Init(0,0,CUDD_UNIQUE_SLOTS,CUDD_CACHE_SLOTS,0) */
manager = Cudd_Init(0,0,CUDD_UNIQUE_SLOTS,CUDD_CACHE_SLOTS,0);
Cudd_SetMaxCacheHard(manager,262144);
#endif
#ifdef USA_YES
usaGraph = (Biddy_Edge *) malloc(usaSize*sizeof(Biddy_Edge *));
usaState = (Biddy_Edge *) malloc(usaSize*sizeof(Biddy_Edge *));
#endif
#ifdef EUROPE_YES
europeGraph = (Biddy_Edge *) malloc(europeSize*sizeof(Biddy_Edge *));
europeState = (Biddy_Edge *) malloc(europeSize*sizeof(Biddy_Edge *));
#endif
i = 0;
complete = FALSE;
while (!complete) {
complete = TRUE;
tmp = Biddy_AddVariable();
#ifdef USA_YES
if (i < usaSize) {
usaState[usaOrder[i]] = tmp;
}
complete = complete && (i >= (usaSize-1));
#endif
#ifdef EUROPE_YES
if (i < europeSize) {
europeState[europeOrder[i]] = tmp;
}
complete = complete && (i >= (europeSize-1));
#endif
i++;
}
#ifdef USA_YES
createGraph(usaSize,usaEdge,usaState,usaGraph);
#endif
#ifdef EUROPE_YES
createGraph(europeSize,europeEdge,europeState,europeGraph);
#endif
#ifdef USE_BIDDY
Biddy_Clean();
#endif
r1 = Biddy_GetConstantZero();
r2 = Biddy_GetConstantZero();
#ifdef USE_CUDD
Cudd_Ref(r1);
Cudd_Ref(r2);
#endif
#ifdef USA_YES
if (!CALCULATE_KERNELS) {
/* CALCULATING INDEPENDENCE SETS FOR USA */
#ifdef USE_CUDD
Cudd_RecursiveDeref(manager,r1);
#endif
r1 = calculateIndependence(usaSize,usaState,usaGraph);
} else {
/* CALCULATING KERNELS (MAXIMUM INDEPENDENCE SETS) FOR USA */
#ifdef USE_CUDD
Cudd_RecursiveDeref(manager,r1);
#endif
r1 = calculateKernels(usaSize,usaState,usaGraph);
}
#ifdef USE_BIDDY
Biddy_AddPersistentFormula((Biddy_String)"usa",r1);
Biddy_Clean();
#endif
#ifdef USE_CUDD
for (i=0; i<usaSize; i++) {
Cudd_RecursiveDeref(manager,usaGraph[i]);
}
#endif
#endif
#ifdef EUROPE_YES
if (!CALCULATE_KERNELS) {
/* CALCULATING INDEPENDENCE SETS FOR EUROPE */
#ifdef USE_CUDD
Cudd_RecursiveDeref(manager,r2);
#endif
r2 = calculateIndependence(europeSize,europeState,europeGraph);
} else {
/* CALCULATING KERNELS (MAXIMUM INDEPENDENCE SETS) FOR EUROPE */
#ifdef USE_CUDD
Cudd_RecursiveDeref(manager,r2);
#endif
r2 = calculateKernels(europeSize,europeState,europeGraph);
}
#ifdef USE_BIDDY
Biddy_AddPersistentFormula((Biddy_String)"europe",r2);
Biddy_Clean();
#endif
#ifdef USE_CUDD
for (i=0; i<europeSize; i++) {
Cudd_RecursiveDeref(manager,europeGraph[i]);
}
#endif
#endif
userinput = strdup("...");
while (userinput[0] != 'x') {
/* We have problems with passing stdout in the case you compile this file */
/* with MINGW and use biddy.dll generated with Visual Studio. */
/* In such cases, please, use Biddy_PrintInfo(NULL) */
if (userinput[0] == 'r') Biddy_PrintInfo(stdout);
/* SIFTING */
#ifdef USE_BIDDY
#ifdef CONVERGE
if (userinput[0] == 's') Biddy_PurgeAndReorder(NULL,TRUE);
#ifdef USA_YES
if (userinput[0] == 'u') Biddy_PurgeAndReorder(r1,TRUE);
#endif
#ifdef EUROPE_YES
if (userinput[0] == 'e') Biddy_PurgeAndReorder(r2,TRUE);
#endif
#else
if (userinput[0] == 's') Biddy_PurgeAndReorder(NULL,FALSE);
#ifdef USA_YES
if (userinput[0] == 'u') Biddy_PurgeAndReorder(r1,FALSE);
#endif
#ifdef EUROPE_YES
if (userinput[0] == 'e') Biddy_PurgeAndReorder(r2,FALSE);
#endif
#endif
#endif
#ifdef USE_CUDD
#ifdef CONVERGE
if (userinput[0] == 's') Cudd_ReduceHeap(manager,CUDD_REORDER_SIFT_CONVERGE,0);
#else
if (userinput[0] == 's') Cudd_ReduceHeap(manager,CUDD_REORDER_SIFT,0);
#endif
#endif
n1 = Biddy_VariableNumber(r1);
n2 = Biddy_VariableNumber(r2);
if ((userinput[0] == 's')
#ifdef USA_YES
|| (userinput[0] == 'u')
#endif
#ifdef EUROPE_YES
|| (userinput[0] == 'e')
#endif
) {
#ifdef CONVERGE
printf("(CONVERGING SIFTING");
#ifdef USE_BIDDY
if (userinput[0] == 'u') {
printf(" ON FUNCTION FOR USA");
}
if (userinput[0] == 'e') {
printf(" ON FUNCTION FOR EUROPE");
}
#endif
printf(") ");
#else
printf("(SIFTING");
#ifdef USE_BIDDY
if (userinput[0] == 'u') {
printf(" ON FUNCTION FOR USA");
}
if (userinput[0] == 'e') {
printf(" ON FUNCTION FOR EUROPE");
}
#endif
printf(") ");
#endif
}
printf("Resulting function r1/r2 depends on %u/%u variables.\n",n1,n2);
printf("Resulting function r1/r2 has %.0f/%.0f minterms.\n",Biddy_CountMinterm(r1,n1),Biddy_CountMinterm(r2,n2));
#ifdef USE_BIDDY
printf("BDD for resulting function r1/r2 has %u/%u nodes (%u/%u nodes if using complement edges).\n",
Biddy_NodeNumberPlain(r1),Biddy_NodeNumberPlain(r2),Biddy_NodeNumber(r1),Biddy_NodeNumber(r2));
#endif
#ifdef USE_CUDD
printf("BDD for resulting function r1/r2 has %u/%u nodes (using complement edges).\n",Biddy_NodeNumber(r1),Biddy_NodeNumber(r2));
#endif
#ifdef USE_BIDDY
printf("Variable swaps performed so far: %u\n",Biddy_NodeTableSwapNumber());
#endif
#ifdef USE_CUDD
printf("Variable swaps performed so far: %.0f\n",Cudd_ReadSwapSteps(manager));
#endif
#ifdef USA_YES
printf("Order for USA: ");
writeOrder(r1,usaCodes,usaOrder,usaSize);
#endif
#ifdef EUROPE_YES
printf("Order for Europe: ");
writeOrder(r2,europeCodes,europeOrder,europeSize);
#endif
#ifdef USE_BIDDY
printf("E[x]it or [r]eport or ");
#ifdef CONVERGE
printf("Converging sifting ");
#else
printf("Sifting ");
#endif
#if (defined USA_YES) || (defined EUROPE_YES)
printf("on [s]ystem or Sifting on function for");
#ifdef USA_YES
printf(" [u]SA");
#endif
#ifdef EUROPE_YES
printf(" [e]urope");
#endif
#endif
printf(": ");
if (!scanf("%s",userinput)) printf("ERROR\n");
#endif
#ifdef USE_CUDD
printf("E[x]it or [r]eport or ");
#ifdef CONVERGE
printf("Converging sifting ");
#else
printf("Sifting ");
#endif
printf("on [s]ystem: ");
if (!scanf("%s",userinput)) printf("ERROR\n");
#endif
}
free(userinput);
/* EXIT */
#ifdef USE_BIDDY
Biddy_Exit();
#endif
#ifdef USE_CUDD
Cudd_RecursiveDeref(manager,r1);
Cudd_RecursiveDeref(manager,r2);
printf("CUDD: nodes with non-zero reference counts: %d\n",Cudd_CheckZeroRef(manager));
Cudd_Quit(manager);
#endif
return 0;
}
/**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 [Floyd-Warshall algorithm for all-pair shortest paths.]
Description []
SideEffects []
SeeAlso []
******************************************************************************/
static DdNode *
ntrWarshall(
DdManager *dd,
DdNode *D,
DdNode **x,
DdNode **y,
int vars,
int pr)
{
DdNode *one, *zero;
DdNode *xminterm, *w, *V, *V2;
DdNode *P, *R;
int i;
int nodes;
int k,u;
long start_time;
if (vars > 30)
nodes = 1000000000;
else
nodes = 1 << vars;
one = DD_ONE(dd);
zero = DD_ZERO(dd);
Cudd_Ref(R = D); /* make copy of original matrix */
/* Extract pivot row and column from D */
start_time = util_cpu_time();
for (k = 0; k < nodes; k++) {
if (k % 10000 == 0) {
(void) printf("Starting iteration %d at time %s\n",
k,util_print_time(util_cpu_time() - start_time));
}
Cudd_Ref(xminterm = one);
u = k;
for (i = vars-1; i >= 0; i--) {
if (u&1) {
Cudd_Ref(w = Cudd_addIte(dd,x[i],xminterm,zero));
} else {
Cudd_Ref(w = Cudd_addIte(dd,x[i],zero,xminterm));
}
Cudd_RecursiveDeref(dd,xminterm);
xminterm = w;
u >>= 1;
}
Cudd_Ref(V = Cudd_Cofactor(dd,R,xminterm));
Cudd_RecursiveDeref(dd,xminterm);
if (pr>2) {(void) printf("V"); Cudd_PrintDebug(dd,V,vars,pr);}
Cudd_Ref(xminterm = one);
u = k;
for (i = vars-1; i >= 0; i--) {
if (u&1) {
Cudd_Ref(w = Cudd_addIte(dd,y[i],xminterm,zero));
} else {
Cudd_Ref(w = Cudd_addIte(dd,y[i],zero,xminterm));
}
Cudd_RecursiveDeref(dd,xminterm);
xminterm = w;
u >>= 1;
}
Cudd_Ref(V2 = Cudd_Cofactor(dd,R,xminterm));
Cudd_RecursiveDeref(dd,xminterm);
if (pr>2) {(void) printf("V2"); Cudd_PrintDebug(dd,V2,vars,pr);}
Cudd_Ref(P = Cudd_addOuterSum(dd,R,V,V2));
Cudd_RecursiveDeref(dd,V);
Cudd_RecursiveDeref(dd,V2);
Cudd_RecursiveDeref(dd,R);
R = P;
if (pr>2) {(void) printf("R"); Cudd_PrintDebug(dd,R,vars,pr);}
}
Cudd_Deref(R);
return(R);
} /* end of ntrWarshall */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_MinHammingDist.]
Description [Performs the recursive step of Cudd_MinHammingDist.
It is based on the following identity. Let H(f) be the
minimum Hamming distance of the minterms of f from the reference
minterm. Then:
<xmp>
H(f) = min(H(f0)+h0,H(f1)+h1)
</xmp>
where f0 and f1 are the two cofactors of f with respect to its top
variable; h0 is 1 if the minterm assigns 1 to the top variable of f;
h1 is 1 if the minterm assigns 0 to the top variable of f.
The upper bound on the distance is used to bound the depth of the
recursion.
Returns the minimum distance unless it exceeds the upper bound or
computation fails.]
SideEffects [None]
SeeAlso [Cudd_MinHammingDist]
******************************************************************************/
static int
cuddMinHammingDistRecur(
DdNode * f,
int *minterm,
DdHashTable * table,
int upperBound)
{
DdNode *F, *Ft, *Fe;
double h, hT, hE;
DdNode *zero, *res;
DdManager *dd = table->manager;
statLine(dd);
if (upperBound == 0) return(0);
F = Cudd_Regular(f);
if (cuddIsConstant(F)) {
zero = Cudd_Not(DD_ONE(dd));
if (f == dd->background || f == zero) {
return(upperBound);
} else {
return(0);
}
}
if ((res = cuddHashTableLookup1(table,f)) != NULL) {
h = cuddV(res);
if (res->ref == 0) {
dd->dead++;
dd->constants.dead++;
}
return((int) h);
}
Ft = cuddT(F); Fe = cuddE(F);
if (Cudd_IsComplement(f)) {
Ft = Cudd_Not(Ft); Fe = Cudd_Not(Fe);
}
if (minterm[F->index] == 0) {
DdNode *temp = Ft;
Ft = Fe; Fe = temp;
}
hT = cuddMinHammingDistRecur(Ft,minterm,table,upperBound);
if (hT == CUDD_OUT_OF_MEM) return(CUDD_OUT_OF_MEM);
if (hT == 0) {
hE = upperBound;
} else {
hE = cuddMinHammingDistRecur(Fe,minterm,table,upperBound - 1);
if (hE == CUDD_OUT_OF_MEM) return(CUDD_OUT_OF_MEM);
}
h = ddMin(hT, hE + 1);
if (F->ref != 1) {
ptrint fanout = (ptrint) F->ref;
cuddSatDec(fanout);
res = cuddUniqueConst(dd, (CUDD_VALUE_TYPE) h);
if (!cuddHashTableInsert1(table,f,res,fanout)) {
cuddRef(res); Cudd_RecursiveDeref(dd, res);
return(CUDD_OUT_OF_MEM);
}
}
return((int) h);
} /* end of cuddMinHammingDistRecur */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_addWalsh.]
Description [Generates a Walsh matrix in ADD form. Returns a pointer
to the matrixi if successful; NULL otherwise.]
SideEffects [None]
******************************************************************************/
static DdNode *
addWalshInt(
DdManager * dd,
DdNode ** x,
DdNode ** y,
int n)
{
DdNode *one, *minusone;
DdNode *t, *u, *t1, *u1, *v, *w;
int i;
one = DD_ONE(dd);
if (n == 0) return(one);
/* Build bottom part of ADD outside loop */
minusone = cuddUniqueConst(dd,(CUDD_VALUE_TYPE) -1);
if (minusone == NULL) return(NULL);
cuddRef(minusone);
v = Cudd_addIte(dd, y[n-1], minusone, one);
if (v == NULL) {
Cudd_RecursiveDeref(dd, minusone);
return(NULL);
}
cuddRef(v);
u = Cudd_addIte(dd, x[n-1], v, one);
if (u == NULL) {
Cudd_RecursiveDeref(dd, minusone);
Cudd_RecursiveDeref(dd, v);
return(NULL);
}
cuddRef(u);
Cudd_RecursiveDeref(dd, v);
if (n>1) {
w = Cudd_addIte(dd, y[n-1], one, minusone);
if (w == NULL) {
Cudd_RecursiveDeref(dd, minusone);
Cudd_RecursiveDeref(dd, u);
return(NULL);
}
cuddRef(w);
t = Cudd_addIte(dd, x[n-1], w, minusone);
if (t == NULL) {
Cudd_RecursiveDeref(dd, minusone);
Cudd_RecursiveDeref(dd, u);
Cudd_RecursiveDeref(dd, w);
return(NULL);
}
cuddRef(t);
Cudd_RecursiveDeref(dd, w);
}
cuddDeref(minusone); /* minusone is in the result; it won't die */
/* Loop to build the rest of the ADD */
for (i=n-2; i>=0; i--) {
t1 = t; u1 = u;
v = Cudd_addIte(dd, y[i], t1, u1);
if (v == NULL) {
Cudd_RecursiveDeref(dd, u1);
Cudd_RecursiveDeref(dd, t1);
return(NULL);
}
cuddRef(v);
u = Cudd_addIte(dd, x[i], v, u1);
if (u == NULL) {
Cudd_RecursiveDeref(dd, u1);
Cudd_RecursiveDeref(dd, t1);
Cudd_RecursiveDeref(dd, v);
return(NULL);
}
cuddRef(u);
Cudd_RecursiveDeref(dd, v);
if (i>0) {
w = Cudd_addIte(dd, y[i], u1, t1);
if (w == NULL) {
Cudd_RecursiveDeref(dd, u1);
Cudd_RecursiveDeref(dd, t1);
Cudd_RecursiveDeref(dd, u);
return(NULL);
}
cuddRef(w);
t = Cudd_addIte(dd, x[i], w, t1);
if (u == NULL) {
Cudd_RecursiveDeref(dd, u1);
Cudd_RecursiveDeref(dd, t1);
Cudd_RecursiveDeref(dd, u);
Cudd_RecursiveDeref(dd, w);
return(NULL);
}
cuddRef(t);
Cudd_RecursiveDeref(dd, w);
}
Cudd_RecursiveDeref(dd, u1);
Cudd_RecursiveDeref(dd, t1);
}
cuddDeref(u);
return(u);
} /* end of addWalshInt */
/**Function********************************************************************
Synopsis [Selects pairs from R using a priority function.]
Description [Selects pairs from a relation R(x,y) (given as a BDD)
in such a way that a given x appears in one pair only. Uses a
priority function to determine which y should be paired to a given x.
Cudd_PrioritySelect returns a pointer to
the selected function if successful; NULL otherwise.
Three of the arguments--x, y, and z--are vectors of BDD variables.
The first two are the variables on which R depends. The third vectore
is a vector of auxiliary variables, used during the computation. This
vector is optional. If a NULL value is passed instead,
Cudd_PrioritySelect will create the working variables on the fly.
The sizes of x and y (and z if it is not NULL) should equal n.
The priority function Pi can be passed as a BDD, or can be built by
Cudd_PrioritySelect. If NULL is passed instead of a DdNode *,
parameter Pifunc is used by Cudd_PrioritySelect to build a BDD for the
priority function. (Pifunc is a pointer to a C function.) If Pi is not
NULL, then Pifunc is ignored. Pifunc should have the same interface as
the standard priority functions (e.g., Cudd_Dxygtdxz).
Cudd_PrioritySelect and Cudd_CProjection can sometimes be used
interchangeably. Specifically, calling Cudd_PrioritySelect with
Cudd_Xgty as Pifunc produces the same result as calling
Cudd_CProjection with the all-zero minterm as reference minterm.
However, depending on the application, one or the other may be
preferable:
<ul>
<li> When extracting representatives from an equivalence relation,
Cudd_CProjection has the advantage of nor requiring the auxiliary
variables.
<li> When computing matchings in general bipartite graphs,
Cudd_PrioritySelect normally obtains better results because it can use
more powerful matching schemes (e.g., Cudd_Dxygtdxz).
</ul>
]
SideEffects [If called with z == NULL, will create new variables in
the manager.]
SeeAlso [Cudd_Dxygtdxz Cudd_Dxygtdyz Cudd_Xgty
Cudd_bddAdjPermuteX Cudd_CProjection]
******************************************************************************/
DdNode *
Cudd_PrioritySelect(
DdManager * dd /* manager */,
DdNode * R /* BDD of the relation */,
DdNode ** x /* array of x variables */,
DdNode ** y /* array of y variables */,
DdNode ** z /* array of z variables (optional: may be NULL) */,
DdNode * Pi /* BDD of the priority function (optional: may be NULL) */,
int n /* size of x, y, and z */,
DdNode * (*Pifunc)(DdManager *, int, DdNode **, DdNode **, DdNode **) /* function used to build Pi if it is NULL */)
{
DdNode *res = NULL;
DdNode *zcube = NULL;
DdNode *Rxz, *Q;
int createdZ = 0;
int createdPi = 0;
int i;
/* Create z variables if needed. */
if (z == NULL) {
if (Pi != NULL) return(NULL);
z = ALLOC(DdNode *,n);
if (z == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
return(NULL);
}
createdZ = 1;
for (i = 0; i < n; i++) {
if (dd->size >= (int) CUDD_MAXINDEX - 1) goto endgame;
z[i] = cuddUniqueInter(dd,dd->size,dd->one,Cudd_Not(dd->one));
if (z[i] == NULL) goto endgame;
}
}
/* Create priority function BDD if needed. */
if (Pi == NULL) {
Pi = Pifunc(dd,n,x,y,z);
if (Pi == NULL) goto endgame;
createdPi = 1;
cuddRef(Pi);
}
/* Initialize abstraction cube. */
zcube = DD_ONE(dd);
cuddRef(zcube);
for (i = n - 1; i >= 0; i--) {
DdNode *tmpp;
tmpp = Cudd_bddAnd(dd,z[i],zcube);
if (tmpp == NULL) goto endgame;
cuddRef(tmpp);
Cudd_RecursiveDeref(dd,zcube);
zcube = tmpp;
}
/* Compute subset of (x,y) pairs. */
Rxz = Cudd_bddSwapVariables(dd,R,y,z,n);
if (Rxz == NULL) goto endgame;
cuddRef(Rxz);
Q = Cudd_bddAndAbstract(dd,Rxz,Pi,zcube);
if (Q == NULL) {
Cudd_RecursiveDeref(dd,Rxz);
goto endgame;
}
cuddRef(Q);
Cudd_RecursiveDeref(dd,Rxz);
res = Cudd_bddAnd(dd,R,Cudd_Not(Q));
if (res == NULL) {
Cudd_RecursiveDeref(dd,Q);
goto endgame;
}
cuddRef(res);
Cudd_RecursiveDeref(dd,Q);
endgame:
if (zcube != NULL) Cudd_RecursiveDeref(dd,zcube);
if (createdZ) {
FREE(z);
}
if (createdPi) {
Cudd_RecursiveDeref(dd,Pi);
}
if (res != NULL) cuddDeref(res);
return(res);
} /* Cudd_PrioritySelect */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_Cofactor.]
Description [Performs the recursive step of Cudd_Cofactor. Returns a
pointer to the cofactor if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_Cofactor]
******************************************************************************/
DdNode *
cuddCofactorRecur(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *one,*zero,*F,*G,*g1,*g0,*f1,*f0,*t,*e,*r;
unsigned int topf,topg;
int comple;
F = Cudd_Regular(f);
if (cuddIsConstant(F)) return(f);
one = DD_ONE(dd);
/* The invariant g != 0 is true on entry to this procedure and is
** recursively maintained by it. Therefore it suffices to test g
** against one to make sure it is not constant.
*/
if (g == one) return(f);
/* From now on, f and g are known not to be constants. */
comple = f != F;
r = cuddCacheLookup2(dd,Cudd_Cofactor,F,g);
if (r != NULL) {
return(Cudd_NotCond(r,comple));
}
topf = dd->perm[F->index];
G = Cudd_Regular(g);
topg = dd->perm[G->index];
/* We take the cofactors of F because we are going to rely on
** the fact that the cofactors of the complement are the complements
** of the cofactors to better utilize the cache. Variable comple
** remembers whether we have to complement the result or not.
*/
if (topf <= topg) {
f1 = cuddT(F); f0 = cuddE(F);
} else {
f1 = f0 = F;
}
if (topg <= topf) {
g1 = cuddT(G); g0 = cuddE(G);
if (g != G) { g1 = Cudd_Not(g1); g0 = Cudd_Not(g0); }
} else {
g1 = g0 = g;
}
zero = Cudd_Not(one);
if (topf >= topg) {
if (g0 == zero || g0 == DD_ZERO(dd)) {
r = cuddCofactorRecur(dd, f1, g1);
} else if (g1 == zero || g1 == DD_ZERO(dd)) {
r = cuddCofactorRecur(dd, f0, g0);
} else {
(void) fprintf(stdout,"Cudd_Cofactor: Invalid restriction 2\n");
return(NULL);
}
if (r == NULL) return(NULL);
} else /* if (topf < topg) */ {
t = cuddCofactorRecur(dd, f1, g);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddCofactorRecur(dd, f0, g);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} else if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(dd,(int)F->index,Cudd_Not(t),Cudd_Not(e));
if (r != NULL)
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(dd,(int)F->index,t,e);
}
if (r == NULL) {
Cudd_RecursiveDeref(dd ,e);
Cudd_RecursiveDeref(dd ,t);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
}
cuddCacheInsert2(dd,Cudd_Cofactor,F,g,r);
return(Cudd_NotCond(r,comple));
} /* end of cuddCofactorRecur */
/**Function********************************************************************
Synopsis [Generates a BDD for the function d(x,y) > d(y,z).]
Description [This function generates a BDD for the function d(x,y)
> d(y,z);
x, y, and z are N-bit numbers, x\[0\] x\[1\] ... x\[N-1\],
y\[0\] y\[1\] ... y\[N-1\], and z\[0\] z\[1\] ... z\[N-1\],
with 0 the most significant bit.
The distance d(x,y) is defined as:
\sum_{i=0}^{N-1}(|x_i - y_i| \cdot 2^{N-i-1}).
The BDD is built bottom-up.
It has 7*N-3 internal nodes, if the variables are ordered as follows:
x\[0\] y\[0\] z\[0\] x\[1\] y\[1\] z\[1\] ... x\[N-1\] y\[N-1\] z\[N-1\]. ]
SideEffects [None]
SeeAlso [Cudd_PrioritySelect Cudd_Dxygtdxz Cudd_Xgty Cudd_bddAdjPermuteX]
******************************************************************************/
DdNode *
Cudd_Dxygtdyz(
DdManager * dd /* DD manager */,
int N /* number of x, y, and z variables */,
DdNode ** x /* array of x variables */,
DdNode ** y /* array of y variables */,
DdNode ** z /* array of z variables */)
{
DdNode *one, *zero;
DdNode *z1, *z2, *z3, *z4, *y1_, *y2, *x1;
int i;
one = DD_ONE(dd);
zero = Cudd_Not(one);
/* Build bottom part of BDD outside loop. */
y1_ = Cudd_bddIte(dd, y[N-1], one, z[N-1]);
if (y1_ == NULL) return(NULL);
cuddRef(y1_);
y2 = Cudd_bddIte(dd, y[N-1], z[N-1], zero);
if (y2 == NULL) {
Cudd_RecursiveDeref(dd, y1_);
return(NULL);
}
cuddRef(y2);
x1 = Cudd_bddIte(dd, x[N-1], y1_, Cudd_Not(y2));
if (x1 == NULL) {
Cudd_RecursiveDeref(dd, y1_);
Cudd_RecursiveDeref(dd, y2);
return(NULL);
}
cuddRef(x1);
Cudd_RecursiveDeref(dd, y1_);
Cudd_RecursiveDeref(dd, y2);
/* Loop to build the rest of the BDD. */
for (i = N-2; i >= 0; i--) {
z1 = Cudd_bddIte(dd, z[i], x1, zero);
if (z1 == NULL) {
Cudd_RecursiveDeref(dd, x1);
return(NULL);
}
cuddRef(z1);
z2 = Cudd_bddIte(dd, z[i], x1, one);
if (z2 == NULL) {
Cudd_RecursiveDeref(dd, x1);
Cudd_RecursiveDeref(dd, z1);
return(NULL);
}
cuddRef(z2);
z3 = Cudd_bddIte(dd, z[i], one, x1);
if (z3 == NULL) {
Cudd_RecursiveDeref(dd, x1);
Cudd_RecursiveDeref(dd, z1);
Cudd_RecursiveDeref(dd, z2);
return(NULL);
}
cuddRef(z3);
z4 = Cudd_bddIte(dd, z[i], one, Cudd_Not(x1));
if (z4 == NULL) {
Cudd_RecursiveDeref(dd, x1);
Cudd_RecursiveDeref(dd, z1);
Cudd_RecursiveDeref(dd, z2);
Cudd_RecursiveDeref(dd, z3);
return(NULL);
}
cuddRef(z4);
Cudd_RecursiveDeref(dd, x1);
y1_ = Cudd_bddIte(dd, y[i], z2, z1);
if (y1_ == NULL) {
Cudd_RecursiveDeref(dd, z1);
Cudd_RecursiveDeref(dd, z2);
Cudd_RecursiveDeref(dd, z3);
Cudd_RecursiveDeref(dd, z4);
return(NULL);
}
cuddRef(y1_);
y2 = Cudd_bddIte(dd, y[i], z4, Cudd_Not(z3));
if (y2 == NULL) {
Cudd_RecursiveDeref(dd, z1);
Cudd_RecursiveDeref(dd, z2);
Cudd_RecursiveDeref(dd, z3);
Cudd_RecursiveDeref(dd, z4);
Cudd_RecursiveDeref(dd, y1_);
return(NULL);
}
cuddRef(y2);
Cudd_RecursiveDeref(dd, z1);
Cudd_RecursiveDeref(dd, z2);
Cudd_RecursiveDeref(dd, z3);
Cudd_RecursiveDeref(dd, z4);
x1 = Cudd_bddIte(dd, x[i], y1_, Cudd_Not(y2));
if (x1 == NULL) {
Cudd_RecursiveDeref(dd, y1_);
Cudd_RecursiveDeref(dd, y2);
return(NULL);
}
cuddRef(x1);
Cudd_RecursiveDeref(dd, y1_);
Cudd_RecursiveDeref(dd, y2);
}
cuddDeref(x1);
return(Cudd_Not(x1));
} /* end of Cudd_Dxygtdyz */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_SplitSet.]
Description [Implements the recursive step of Cudd_SplitSet. The
procedure recursively traverses the BDD and checks to see if any
node satisfies the minterm requirements as specified by 'n'. At any
node X, n is compared to the number of minterms in the onset of X's
children. If either of the child nodes have exactly n minterms, then
that node is returned; else, if n is greater than the onset of one
of the child nodes, that node is retained and the difference in the
number of minterms is extracted from the other child. In case n
minterms can be extracted from constant 1, the algorithm returns the
result with at most log(n) nodes.]
SideEffects [The array 'varSeen' is updated at every recursive call
to set the variables traversed by the procedure.]
SeeAlso []
******************************************************************************/
DdNode*
cuddSplitSetRecur(
DdManager * manager,
st_table * mtable,
int * varSeen,
DdNode * p,
double n,
double max,
int index)
{
DdNode *one, *zero, *N, *Nv;
DdNode *Nnv, *q, *r, *v;
DdNode *result;
double *dummy, numT, numE;
int variable, positive;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* If p is constant, extract n minterms from constant 1. The procedure by
** construction guarantees that minterms will not be extracted from
** constant 0.
*/
if (Cudd_IsConstant(p)) {
q = selectMintermsFromUniverse(manager,varSeen,n);
return(q);
}
N = Cudd_Regular(p);
/* Set variable as seen. */
variable = N->index;
varSeen[manager->invperm[variable]] = -1;
Nv = cuddT(N);
Nnv = cuddE(N);
if (Cudd_IsComplement(p)) {
Nv = Cudd_Not(Nv);
Nnv = Cudd_Not(Nnv);
}
/* If both the children of 'p' are constants, extract n minterms from a
** constant node.
*/
if (Cudd_IsConstant(Nv) && Cudd_IsConstant(Nnv)) {
q = selectMintermsFromUniverse(manager,varSeen,n);
if (q == NULL) {
return(NULL);
}
cuddRef(q);
r = cuddBddAndRecur(manager,p,q);
if (r == NULL) {
Cudd_RecursiveDeref(manager,q);
return(NULL);
}
cuddRef(r);
Cudd_RecursiveDeref(manager,q);
cuddDeref(r);
return(r);
}
/* Lookup the # of minterms in the onset of the node from the table. */
if (!Cudd_IsConstant(Nv)) {
if (!st_lookup(mtable, Nv, &dummy)) return(NULL);
numT = *dummy/(2*(1<<index));
} else if (Nv == one) {
numT = max/(2*(1<<index));
} else {
numT = 0;
}
if (!Cudd_IsConstant(Nnv)) {
if (!st_lookup(mtable, Nnv, &dummy)) return(NULL);
numE = *dummy/(2*(1<<index));
} else if (Nnv == one) {
numE = max/(2*(1<<index));
} else {
numE = 0;
}
v = cuddUniqueInter(manager,variable,one,zero);
cuddRef(v);
/* If perfect match. */
if (numT == n) {
q = cuddBddAndRecur(manager,v,Nv);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(q);
return(q);
}
if (numE == n) {
q = cuddBddAndRecur(manager,Cudd_Not(v),Nnv);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(q);
return(q);
}
/* If n is greater than numT, extract the difference from the ELSE child
** and retain the function represented by the THEN branch.
*/
if (numT < n) {
q = cuddSplitSetRecur(manager,mtable,varSeen,
Nnv,(n-numT),max,index+1);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
r = cuddBddIteRecur(manager,v,Nv,q);
if (r == NULL) {
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(r);
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(r);
return(r);
}
/* If n is greater than numE, extract the difference from the THEN child
** and retain the function represented by the ELSE branch.
*/
if (numE < n) {
q = cuddSplitSetRecur(manager,mtable,varSeen,
Nv, (n-numE),max,index+1);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
r = cuddBddIteRecur(manager,v,q,Nnv);
if (r == NULL) {
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(r);
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(r);
return(r);
}
/* None of the above cases; (n < numT and n < numE) and either of
** the Nv, Nnv or both are not constants. If possible extract the
** required minterms the constant branch.
*/
if (Cudd_IsConstant(Nv) && !Cudd_IsConstant(Nnv)) {
q = selectMintermsFromUniverse(manager,varSeen,n);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
result = cuddBddAndRecur(manager,v,q);
if (result == NULL) {
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(result);
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(result);
return(result);
} else if (!Cudd_IsConstant(Nv) && Cudd_IsConstant(Nnv)) {
q = selectMintermsFromUniverse(manager,varSeen,n);
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
result = cuddBddAndRecur(manager,Cudd_Not(v),q);
if (result == NULL) {
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(result);
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(result);
return(result);
}
/* Both Nv and Nnv are not constants. So choose the one which
** has fewer minterms in its onset.
*/
positive = 0;
if (numT < numE) {
q = cuddSplitSetRecur(manager,mtable,varSeen,
Nv,n,max,index+1);
positive = 1;
} else {
q = cuddSplitSetRecur(manager,mtable,varSeen,
Nnv,n,max,index+1);
}
if (q == NULL) {
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(q);
if (positive) {
result = cuddBddAndRecur(manager,v,q);
} else {
result = cuddBddAndRecur(manager,Cudd_Not(v),q);
}
if (result == NULL) {
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
return(NULL);
}
cuddRef(result);
Cudd_RecursiveDeref(manager,q);
Cudd_RecursiveDeref(manager,v);
cuddDeref(result);
return(result);
} /* end of cuddSplitSetRecur */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_SolveEqn.]
Description [Implements the recursive step of Cudd_SolveEqn.
Returns NULL if the intermediate solution blows up
or reordering occurs. The parametric solutions are
stored in the array G.]
SideEffects [none]
SeeAlso [Cudd_SolveEqn, Cudd_VerifySol]
******************************************************************************/
DdNode *
cuddSolveEqnRecur(
DdManager * bdd,
DdNode * F /* the left-hand side of the equation */,
DdNode * Y /* the cube of remaining y variables */,
DdNode ** G /* the array of solutions */,
int n /* number of unknowns */,
int * yIndex /* array holding the y variable indices */,
int i /* level of recursion */)
{
DdNode *Fn, *Fm1, *Fv, *Fvbar, *T, *w, *nextY, *one;
DdNodePtr *variables;
int j;
statLine(bdd);
variables = bdd->vars;
one = DD_ONE(bdd);
/* Base condition. */
if (Y == one) {
return F;
}
/* Cofactor of Y. */
yIndex[i] = Y->index;
nextY = Cudd_T(Y);
/* Universal abstraction of F with respect to the top variable index. */
Fm1 = cuddBddExistAbstractRecur(bdd, Cudd_Not(F), variables[yIndex[i]]);
if (Fm1) {
Fm1 = Cudd_Not(Fm1);
cuddRef(Fm1);
} else {
return(NULL);
}
Fn = cuddSolveEqnRecur(bdd, Fm1, nextY, G, n, yIndex, i+1);
if (Fn) {
cuddRef(Fn);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
return(NULL);
}
Fv = cuddCofactorRecur(bdd, F, variables[yIndex[i]]);
if (Fv) {
cuddRef(Fv);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
return(NULL);
}
Fvbar = cuddCofactorRecur(bdd, F, Cudd_Not(variables[yIndex[i]]));
if (Fvbar) {
cuddRef(Fvbar);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
return(NULL);
}
/* Build i-th component of the solution. */
w = cuddBddIteRecur(bdd, variables[yIndex[i]], Cudd_Not(Fv), Fvbar);
if (w) {
cuddRef(w);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
Cudd_RecursiveDeref(bdd, Fvbar);
return(NULL);
}
T = cuddBddRestrictRecur(bdd, w, Cudd_Not(Fm1));
if(T) {
cuddRef(T);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
Cudd_RecursiveDeref(bdd, Fvbar);
Cudd_RecursiveDeref(bdd, w);
return(NULL);
}
Cudd_RecursiveDeref(bdd,Fm1);
Cudd_RecursiveDeref(bdd,w);
Cudd_RecursiveDeref(bdd,Fv);
Cudd_RecursiveDeref(bdd,Fvbar);
/* Substitute components of solution already found into solution. */
for (j = n-1; j > i; j--) {
w = cuddBddComposeRecur(bdd,T, G[j], variables[yIndex[j]]);
if(w) {
cuddRef(w);
} else {
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, T);
return(NULL);
}
Cudd_RecursiveDeref(bdd,T);
T = w;
}
G[i] = T;
Cudd_Deref(Fn);
return(Fn);
} /* end of cuddSolveEqnRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addUnivAbstract.]
Description [Performs the recursive step of Cudd_addUnivAbstract.
Returns the ADD obtained by abstracting the variables of cube from f,
if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddAddUnivAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * cube)
{
DdNode *T, *E, *res, *res1, *res2, *one, *zero;
statLine(manager);
one = DD_ONE(manager);
zero = DD_ZERO(manager);
/* Cube is guaranteed to be a cube at this point.
** zero and one are the only constatnts c such that c*c=c.
*/
if (f == zero || f == one || cube == one) {
return(f);
}
/* Abstract a variable that does not appear in f. */
if (cuddI(manager,f->index) > cuddI(manager,cube->index)) {
res1 = cuddAddUnivAbstractRecur(manager, f, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
/* Use the "internal" procedure to be alerted in case of
** dynamic reordering. If dynamic reordering occurs, we
** have to abort the entire abstraction.
*/
res = cuddAddApplyRecur(manager, Cudd_addTimes, res1, res1);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
cuddDeref(res);
return(res);
}
if ((res = cuddCacheLookup2(manager, Cudd_addUnivAbstract, f, cube)) != NULL) {
return(res);
}
T = cuddT(f);
E = cuddE(f);
/* If the two indices are the same, so are their levels. */
if (f->index == cube->index) {
res1 = cuddAddUnivAbstractRecur(manager, T, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddUnivAbstractRecur(manager, E, cuddT(cube));
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = cuddAddApplyRecur(manager, Cudd_addTimes, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
cuddCacheInsert2(manager, Cudd_addUnivAbstract, f, cube, res);
cuddDeref(res);
return(res);
} else { /* if (cuddI(manager,f->index) < cuddI(manager,cube->index)) */
res1 = cuddAddUnivAbstractRecur(manager, T, cube);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddUnivAbstractRecur(manager, E, cube);
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = (res1 == res2) ? res1 :
cuddUniqueInter(manager, (int) f->index, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
cuddCacheInsert2(manager, Cudd_addUnivAbstract, f, cube, res);
return(res);
}
} /* end of cuddAddUnivAbstractRecur */
/**
@brief Approximates the AND of two BDDs and simultaneously abstracts the
variables in cube.
@details The variables are existentially abstracted.
@return a pointer to the result is successful; NULL otherwise.
@sideeffect None
@see Cudd_bddClippingAndAbstract
*/
static DdNode *
cuddBddClipAndAbsRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
DdNode * cube,
int distance,
int direction)
{
DdNode *F, *ft, *fe, *G, *gt, *ge;
DdNode *one, *zero, *r, *t, *e, *Cube;
int topf, topg, topcube, top;
unsigned int index;
ptruint cacheTag;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
if (f == one && g == one) return(one);
if (cube == one) {
return(cuddBddClippingAndRecur(manager, f, g, distance, direction));
}
if (f == one || f == g) {
return (cuddBddExistAbstractRecur(manager, g, cube));
}
if (g == one) {
return (cuddBddExistAbstractRecur(manager, f, cube));
}
if (distance == 0) return(Cudd_NotCond(one,(direction == 0)));
/* At this point f, g, and cube are not constant. */
distance--;
/* Check cache. */
if (f > g) { /* Try to increase cache efficiency. */
DdNode *tmp = f;
f = g; g = tmp;
}
F = Cudd_Regular(f);
G = Cudd_Regular(g);
cacheTag = direction ? DD_BDD_CLIPPING_AND_ABSTRACT_UP_TAG :
DD_BDD_CLIPPING_AND_ABSTRACT_DOWN_TAG;
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup(manager, cacheTag,
f, g, cube);
if (r != NULL) {
return(r);
}
}
checkWhetherToGiveUp(manager);
/* Here we can skip the use of cuddI, because the operands are known
** to be non-constant.
*/
topf = manager->perm[F->index];
topg = manager->perm[G->index];
top = ddMin(topf, topg);
topcube = manager->perm[cube->index];
if (topcube < top) {
return(cuddBddClipAndAbsRecur(manager, f, g, cuddT(cube),
distance, direction));
}
/* Now, topcube >= top. */
if (topf == top) {
index = F->index;
ft = cuddT(F);
fe = cuddE(F);
if (Cudd_IsComplement(f)) {
ft = Cudd_Not(ft);
fe = Cudd_Not(fe);
}
} else {
index = G->index;
ft = fe = f;
}
if (topg == top) {
gt = cuddT(G);
ge = cuddE(G);
if (Cudd_IsComplement(g)) {
gt = Cudd_Not(gt);
ge = Cudd_Not(ge);
}
} else {
gt = ge = g;
}
if (topcube == top) {
Cube = cuddT(cube);
} else {
Cube = cube;
}
t = cuddBddClipAndAbsRecur(manager, ft, gt, Cube, distance, direction);
if (t == NULL) return(NULL);
/* Special case: 1 OR anything = 1. Hence, no need to compute
** the else branch if t is 1.
*/
if (t == one && topcube == top) {
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, cacheTag, f, g, cube, one);
return(one);
}
cuddRef(t);
e = cuddBddClipAndAbsRecur(manager, fe, ge, Cube, distance, direction);
if (e == NULL) {
Cudd_RecursiveDeref(manager, t);
return(NULL);
}
cuddRef(e);
if (topcube == top) { /* abstract */
r = cuddBddClippingAndRecur(manager, Cudd_Not(t), Cudd_Not(e),
distance, (direction == 0));
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
r = Cudd_Not(r);
cuddRef(r);
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
cuddDeref(r);
} else if (t == e) {
r = t;
cuddDeref(t);
cuddDeref(e);
} else {
if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(manager,(int)index,Cudd_Not(t),Cudd_Not(e));
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(manager,(int)index,t,e);
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
}
cuddDeref(e);
cuddDeref(t);
}
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, cacheTag, f, g, cube, r);
return (r);
} /* end of cuddBddClipAndAbsRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addOrAbstract.]
Description [Performs the recursive step of Cudd_addOrAbstract.
Returns the ADD obtained by abstracting the variables of cube from f,
if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddAddOrAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * cube)
{
DdNode *T, *E, *res, *res1, *res2, *one;
statLine(manager);
one = DD_ONE(manager);
/* Cube is guaranteed to be a cube at this point. */
if (cuddIsConstant(f) || cube == one) {
return(f);
}
/* Abstract a variable that does not appear in f. */
if (cuddI(manager,f->index) > cuddI(manager,cube->index)) {
res = cuddAddOrAbstractRecur(manager, f, cuddT(cube));
return(res);
}
if ((res = cuddCacheLookup2(manager, Cudd_addOrAbstract, f, cube)) != NULL) {
return(res);
}
T = cuddT(f);
E = cuddE(f);
/* If the two indices are the same, so are their levels. */
if (f->index == cube->index) {
res1 = cuddAddOrAbstractRecur(manager, T, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
if (res1 != one) {
res2 = cuddAddOrAbstractRecur(manager, E, cuddT(cube));
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = cuddAddApplyRecur(manager, Cudd_addOr, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
} else {
res = res1;
}
cuddCacheInsert2(manager, Cudd_addOrAbstract, f, cube, res);
cuddDeref(res);
return(res);
} else { /* if (cuddI(manager,f->index) < cuddI(manager,cube->index)) */
res1 = cuddAddOrAbstractRecur(manager, T, cube);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddOrAbstractRecur(manager, E, cube);
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = (res1 == res2) ? res1 :
cuddUniqueInter(manager, (int) f->index, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
cuddCacheInsert2(manager, Cudd_addOrAbstract, f, cube, res);
return(res);
}
} /* end of cuddAddOrAbstractRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_bddIsop.]
Description []
SideEffects [None]
SeeAlso [Cudd_bddIsop]
******************************************************************************/
DdNode *
cuddBddIsop(
DdManager * dd,
DdNode * L,
DdNode * U)
{
DdNode *one = DD_ONE(dd);
DdNode *zero = Cudd_Not(one);
int v, top_l, top_u;
DdNode *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
DdNode *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
DdNode *Isub0, *Isub1, *Id;
DdNode *x;
DdNode *term0, *term1, *sum;
DdNode *Lv, *Uv, *Lnv, *Unv;
DdNode *r;
int index;
statLine(dd);
if (L == zero)
return(zero);
if (U == one)
return(one);
/* Check cache */
r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
if (r)
return(r);
top_l = dd->perm[Cudd_Regular(L)->index];
top_u = dd->perm[Cudd_Regular(U)->index];
v = ddMin(top_l, top_u);
/* Compute cofactors */
if (top_l == v) {
index = Cudd_Regular(L)->index;
Lv = Cudd_T(L);
Lnv = Cudd_E(L);
if (Cudd_IsComplement(L)) {
Lv = Cudd_Not(Lv);
Lnv = Cudd_Not(Lnv);
}
}
else {
index = Cudd_Regular(U)->index;
Lv = Lnv = L;
}
if (top_u == v) {
Uv = Cudd_T(U);
Unv = Cudd_E(U);
if (Cudd_IsComplement(U)) {
Uv = Cudd_Not(Uv);
Unv = Cudd_Not(Unv);
}
}
else {
Uv = Unv = U;
}
Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
if (Lsub0 == NULL)
return(NULL);
Cudd_Ref(Lsub0);
Usub0 = Unv;
Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
if (Lsub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
return(NULL);
}
Cudd_Ref(Lsub1);
Usub1 = Uv;
Isub0 = cuddBddIsop(dd, Lsub0, Usub0);
if (Isub0 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
return(NULL);
}
Cudd_Ref(Isub0);
Isub1 = cuddBddIsop(dd, Lsub1, Usub1);
if (Isub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Cudd_RecursiveDeref(dd, Isub0);
return(NULL);
}
Cudd_Ref(Isub1);
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
if (Lsuper0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
return(NULL);
}
Cudd_Ref(Lsuper0);
Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
if (Lsuper1 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
return(NULL);
}
Cudd_Ref(Lsuper1);
Usuper0 = Unv;
Usuper1 = Uv;
/* Ld = Lsuper0 + Lsuper1 */
Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
Ld = Cudd_NotCond(Ld, Ld != NULL);
if (Ld == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
return(NULL);
}
Cudd_Ref(Ld);
Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
if (Ud == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Cudd_RecursiveDeref(dd, Ld);
return(NULL);
}
Cudd_Ref(Ud);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Id = cuddBddIsop(dd, Ld, Ud);
if (Id == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
return(NULL);
}
Cudd_Ref(Id);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
x = cuddUniqueInter(dd, index, one, zero);
if (x == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
return(NULL);
}
Cudd_Ref(x);
term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
if (term0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, x);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDeref(dd, Isub0);
term1 = cuddBddAndRecur(dd, x, Isub1);
if (term1 == NULL) {
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, term0);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, Isub1);
/* sum = term0 + term1 */
sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
sum = Cudd_NotCond(sum, sum != NULL);
if (sum == NULL) {
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
return(NULL);
}
Cudd_Ref(sum);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
/* r = sum + Id */
r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
r = Cudd_NotCond(r, r != NULL);
if (r == NULL) {
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, sum);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDeref(dd, sum);
Cudd_RecursiveDeref(dd, Id);
cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
Cudd_Deref(r);
return(r);
} /* end of cuddBddIsop */
/**Function********************************************************************
Synopsis [Writes a blif file representing the argument BDDs.]
Description [Writes a blif file representing the argument BDDs as a
network of multiplexers. One multiplexer is written for each BDD
node. It returns 1 in case of success; 0 otherwise (e.g.,
out-of-memory, file system full, or an ADD with constants different
from 0 and 1). Cudd_DumpBlif does not close the file: This is the
caller responsibility. Cudd_DumpBlif uses a minimal unique subset of
the hexadecimal address of a node as name for it. If the argument
inames is non-null, it is assumed to hold the pointers to the names
of the inputs. Similarly for onames.]
SideEffects [None]
SeeAlso [Cudd_DumpBlifBody Cudd_DumpDot Cudd_PrintDebug Cudd_DumpDDcal
Cudd_DumpDaVinci Cudd_DumpFactoredForm]
******************************************************************************/
int
Cudd_DumpBlif(
DdManager * dd /* manager */,
int n /* number of output nodes to be dumped */,
DdNode ** f /* array of output nodes to be dumped */,
char ** inames /* array of input names (or NULL) */,
char ** onames /* array of output names (or NULL) */,
char * mname /* model name (or NULL) */,
FILE * fp /* pointer to the dump file */,
int mv /* 0: blif, 1: blif-MV */)
{
DdNode *support = NULL;
DdNode *scan;
int *sorted = NULL;
int nvars = dd->size;
int retval;
int i;
/* Build a bit array with the support of f. */
sorted = ALLOC(int,nvars);
if (sorted == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
goto failure;
}
for (i = 0; i < nvars; i++) sorted[i] = 0;
/* Take the union of the supports of each output function. */
support = Cudd_VectorSupport(dd,f,n);
if (support == NULL) goto failure;
cuddRef(support);
scan = support;
while (!cuddIsConstant(scan)) {
sorted[scan->index] = 1;
scan = cuddT(scan);
}
Cudd_RecursiveDeref(dd,support);
support = NULL; /* so that we do not try to free it in case of failure */
/* Write the header (.model .inputs .outputs). */
if (mname == NULL) {
retval = fprintf(fp,".model DD\n.inputs");
} else {
retval = fprintf(fp,".model %s\n.inputs",mname);
}
if (retval == EOF) {
FREE(sorted);
return(0);
}
/* Write the input list by scanning the support array. */
for (i = 0; i < nvars; i++) {
if (sorted[i]) {
if (inames == NULL) {
retval = fprintf(fp," %d", i);
} else {
retval = fprintf(fp," %s", inames[i]);
}
if (retval == EOF) goto failure;
}
}
FREE(sorted);
sorted = NULL;
/* Write the .output line. */
retval = fprintf(fp,"\n.outputs");
if (retval == EOF) goto failure;
for (i = 0; i < n; i++) {
if (onames == NULL) {
retval = fprintf(fp," f%d", i);
} else {
retval = fprintf(fp," %s", onames[i]);
}
if (retval == EOF) goto failure;
}
retval = fprintf(fp,"\n");
if (retval == EOF) goto failure;
retval = Cudd_DumpBlifBody(dd, n, f, inames, onames, fp, mv);
if (retval == 0) goto failure;
/* Write trailer and return. */
retval = fprintf(fp,".end\n");
if (retval == EOF) goto failure;
return(1);
failure:
if (sorted != NULL) FREE(sorted);
if (support != NULL) Cudd_RecursiveDeref(dd,support);
return(0);
} /* end of Cudd_DumpBlif */
/**Function********************************************************************
Synopsis [Tests Walsh matrix multiplication.]
Description [Tests Walsh matrix multiplication. Return 1 if successful;
0 otherwise.]
SideEffects [May create new variables in the manager.]
SeeAlso []
******************************************************************************/
static int
testWalsh(
DdManager *dd /* manager */,
int N /* number of variables */,
int cmu /* use CMU approach to matrix multiplication */,
int approach /* reordering approach */,
int pr /* verbosity level */)
{
DdNode *walsh1, *walsh2, *wtw;
DdNode **x, **v, **z;
int i, retval;
DdNode *_true = DD_TRUE(dd);
DdNode *_false = DD_FALSE(dd);
if (N > 3) {
x = ALLOC(DdNode *,N);
v = ALLOC(DdNode *,N);
z = ALLOC(DdNode *,N);
for (i = N-1; i >= 0; i--) {
Cudd_Ref(x[i]=cuddUniqueInter(dd,3*i,_true,_false));
Cudd_Ref(v[i]=cuddUniqueInter(dd,3*i+1,_true,_false));
Cudd_Ref(z[i]=cuddUniqueInter(dd,3*i+2,_true,_false));
}
Cudd_Ref(walsh1 = Cudd_addWalsh(dd,v,z,N));
if (pr>0) {(void) printf("walsh1"); Cudd_PrintDebug(dd,walsh1,2*N,pr);}
Cudd_Ref(walsh2 = Cudd_addWalsh(dd,x,v,N));
if (cmu) {
Cudd_Ref(wtw = Cudd_addTimesPlus(dd,walsh2,walsh1,v,N));
} else {
Cudd_Ref(wtw = Cudd_addMatrixMultiply(dd,walsh2,walsh1,v,N));
}
if (pr>0) {(void) printf("wtw"); Cudd_PrintDebug(dd,wtw,2*N,pr);}
if (approach != CUDD_REORDER_NONE) {
#ifdef DD_DEBUG
retval = Cudd_DebugCheck(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_DebugCheck\n");
return(0);
}
#endif
retval = Cudd_ReduceHeap(dd,(Cudd_ReorderingType)approach,5);
if (retval == 0) {
(void) fprintf(stderr,"Error reported by Cudd_ReduceHeap\n");
return(0);
}
#ifdef DD_DEBUG
retval = Cudd_DebugCheck(dd);
if (retval != 0) {
(void) fprintf(stderr,"Error reported by Cudd_DebugCheck\n");
return(0);
}
#endif
if (approach == CUDD_REORDER_SYMM_SIFT ||
approach == CUDD_REORDER_SYMM_SIFT_CONV) {
Cudd_SymmProfile(dd,0,dd->size-1);
}
}
/* Clean up. */
Cudd_RecursiveDeref(dd, wtw);
Cudd_RecursiveDeref(dd, walsh1);
Cudd_RecursiveDeref(dd, walsh2);
for (i=0; i < N; i++) {
Cudd_RecursiveDeref(dd, x[i]);
Cudd_RecursiveDeref(dd, v[i]);
Cudd_RecursiveDeref(dd, z[i]);
}
FREE(x);
FREE(v);
FREE(z);
}
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddPortToBdd.]
Description []
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
zddPortToBddStep(
DdManager * dd /* manager */,
DdNode * f /* ZDD to be converted */,
int depth /* recursion depth */)
{
DdNode *one, *zero, *T, *E, *res, *var;
unsigned int index;
unsigned int level;
statLine(dd);
one = DD_ONE(dd);
zero = DD_ZERO(dd);
if (f == zero) return(Cudd_Not(one));
if (depth == dd->sizeZ) return(one);
index = dd->invpermZ[depth];
level = cuddIZ(dd,f->index);
var = cuddUniqueInter(dd,index,one,Cudd_Not(one));
if (var == NULL) return(NULL);
cuddRef(var);
if (level > (unsigned) depth) {
E = zddPortToBddStep(dd,f,depth+1);
if (E == NULL) {
Cudd_RecursiveDeref(dd,var);
return(NULL);
}
cuddRef(E);
res = cuddBddIteRecur(dd,var,Cudd_Not(one),E);
if (res == NULL) {
Cudd_RecursiveDeref(dd,var);
Cudd_RecursiveDeref(dd,E);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(dd,var);
Cudd_RecursiveDeref(dd,E);
cuddDeref(res);
return(res);
}
res = cuddCacheLookup1(dd,Cudd_zddPortToBdd,f);
if (res != NULL) {
Cudd_RecursiveDeref(dd,var);
return(res);
}
T = zddPortToBddStep(dd,cuddT(f),depth+1);
if (T == NULL) {
Cudd_RecursiveDeref(dd,var);
return(NULL);
}
cuddRef(T);
E = zddPortToBddStep(dd,cuddE(f),depth+1);
if (E == NULL) {
Cudd_RecursiveDeref(dd,var);
Cudd_RecursiveDeref(dd,T);
return(NULL);
}
cuddRef(E);
res = cuddBddIteRecur(dd,var,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd,var);
Cudd_RecursiveDeref(dd,T);
Cudd_RecursiveDeref(dd,E);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(dd,var);
Cudd_RecursiveDeref(dd,T);
Cudd_RecursiveDeref(dd,E);
cuddDeref(res);
cuddCacheInsert1(dd,Cudd_zddPortToBdd,f,res);
return(res);
} /* end of zddPortToBddStep */
static inline void Aig_ObjCleanGlobalBdd( DdManager * dd, Aig_Obj_t * pObj ) { Cudd_RecursiveDeref( dd, (DdNode *)pObj->pData ); pObj->pData = NULL; }
/**Function********************************************************************
Synopsis [Computes shortest paths in a state graph.]
Description [Computes shortest paths in the state transition graph of
a network. Three methods are availabe:
<ul>
<li> Bellman-Ford algorithm for single-source shortest paths; the
algorithm computes the distance (number of transitions) from the initial
states to all states.
<li> Floyd-Warshall algorithm for all-pair shortest paths.
<li> Repeated squaring algorithm for all-pair shortest paths.
</ul>
The function returns 1 in case of success; 0 otherwise.
]
SideEffects [ADD variables are created in the manager.]
SeeAlso []
******************************************************************************/
int
Ntr_ShortestPaths(
DdManager * dd,
BnetNetwork * net,
NtrOptions * option)
{
NtrPartTR *TR;
DdNode *edges, *source, *res, *r, *q, *bddSource;
DdNode **xadd, **yadd, **zadd;
int i;
int pr = option->verb;
int algorithm = option->shortPath;
int selectiveTrace = option->selectiveTrace;
int nvars = net->nlatches;
/* Set background to infinity for shortest paths. */
Cudd_SetBackground(dd,Cudd_ReadPlusInfinity(dd));
/* Build the monolithic TR. */
TR = Ntr_buildTR(dd,net,option,NTR_IMAGE_MONO);
/* Build the ADD variable vectors for x and y. */
xadd = ALLOC(DdNode *, nvars);
yadd = ALLOC(DdNode *, nvars);
for(i = 0; i < nvars; i++) {
q = Cudd_addIthVar(dd,TR->x[i]->index);
Cudd_Ref(q);
xadd[i] = q;
q = Cudd_addIthVar(dd,TR->y[i]->index);
Cudd_Ref(q);
yadd[i] = q;
}
/* Convert the transition relation BDD into an ADD... */
q = Cudd_BddToAdd(dd,TR->part[0]);
Cudd_Ref(q);
/* ...replacing zeroes with infinities... */
r = Cudd_addIte(dd,q,Cudd_ReadOne(dd),Cudd_ReadPlusInfinity(dd));
Cudd_Ref(r);
Cudd_RecursiveDeref(dd,q);
/* ...and zeroing the diagonal. */
q = Cudd_addXeqy(dd,nvars,xadd,yadd);
Cudd_Ref(q);
edges = Cudd_addIte(dd,q,Cudd_ReadZero(dd),r);
Cudd_Ref(edges);
Cudd_RecursiveDeref(dd,r);
Cudd_RecursiveDeref(dd,q);
switch(algorithm) {
case NTR_SHORT_BELLMAN:
bddSource = Ntr_initState(dd,net,option);
source = Cudd_BddToAdd(dd,bddSource);
Cudd_Ref(source);
res = ntrBellman(dd,edges,source,xadd,yadd,nvars,pr);
if (res == NULL) return(0);
Cudd_Ref(res);
Cudd_RecursiveDeref(dd,source);
Cudd_RecursiveDeref(dd,bddSource);
if (pr >= 0) {
(void) fprintf(stdout,"Distance Matrix");
Cudd_PrintDebug(dd,res,nvars,pr);
}
break;
case NTR_SHORT_FLOYD:
res = ntrWarshall(dd,edges,xadd,yadd,nvars,pr);
if (res == NULL) return(0);
Cudd_Ref(res);
if (pr >= 0) {
(void) fprintf(stdout,"Distance Matrix");
Cudd_PrintDebug(dd,res,2*nvars,pr);
}
break;
case NTR_SHORT_SQUARE:
/* Create a third set of ADD variables. */
zadd = ALLOC(DdNode *, nvars);
for(i = 0; i < nvars; i++) {
int level;
level = Cudd_ReadIndex(dd,TR->x[i]->index);
q = Cudd_addNewVarAtLevel(dd,level);
Cudd_Ref(q);
zadd[i] = q;
}
/* Compute the shortest paths. */
res = ntrSquare(dd,edges,zadd,yadd,xadd,nvars,pr,selectiveTrace);
if (res == NULL) return(0);
Cudd_Ref(res);
/* Dispose of the extra variables. */
for(i = 0; i < nvars; i++) {
Cudd_RecursiveDeref(dd,zadd[i]);
}
FREE(zadd);
if (pr >= 0) {
(void) fprintf(stdout,"Distance Matrix");
Cudd_PrintDebug(dd,res,2*nvars,pr);
}
break;
default:
(void) printf("Unrecognized method. Try again.\n");
return(0);
}
/* Here we should compute the paths. */
/* Clean up. */
Ntr_freeTR(dd,TR);
Cudd_RecursiveDeref(dd,edges);
Cudd_RecursiveDeref(dd,res);
for(i = 0; i < nvars; i++) {
Cudd_RecursiveDeref(dd,xadd[i]);
Cudd_RecursiveDeref(dd,yadd[i]);
}
FREE(xadd);
FREE(yadd);
if (option->autoDyn & 1) {
(void) printf("Order after short path computation\n");
if (!Bnet_PrintOrder(net,dd)) return(0);
}
return(1);
} /* end of Ntr_ShortestPaths */
