The cudd package

The University of Colorado decision diagram package.



External functions and data strucures of the CUDD package. Modified by Abelardo Pardo to interface it to VIS.
DdApaDigit 
Cudd_ApaAdd(
  int  digits, 
  DdApaNumber  a, 
  DdApaNumber  b, 
  DdApaNumber  sum 
)
Adds two arbitrary precision integers. Returns the carry out of the most significant digit.

Side Effects The result of the sum is stored in parameter sum.

int 
Cudd_ApaCompareRatios(
  int  digitsFirst, 
  DdApaNumber  firstNum, 
  unsigned int  firstDen, 
  int  digitsSecond, 
  DdApaNumber  secondNum, 
  unsigned int  secondDen 
)
Compares the ratios of two arbitrary precision integers to two unsigned ints. Returns 1 if the first number is larger; 0 if they are equal; -1 if the second number is larger.

Side Effects None

int 
Cudd_ApaCompare(
  int  digitsFirst, 
  DdApaNumber  first, 
  int  digitsSecond, 
  DdApaNumber  second 
)
Compares two arbitrary precision integers. Returns 1 if the first number is larger; 0 if they are equal; -1 if the second number is larger.

Side Effects None

void 
Cudd_ApaCopy(
  int  digits, 
  DdApaNumber  source, 
  DdApaNumber  dest 
)
Makes a copy of an arbitrary precision integer.

Side Effects Changes parameter dest.

DdApaNumber 
Cudd_ApaCountMinterm(
  DdManager * manager, 
  DdNode * node, 
  int  nvars, 
  int * digits 
)
Counts the number of minterms of a DD. The function is assumed to depend on nvars variables. The minterm count is represented as an arbitrary precision unsigned integer, to allow for any number of variables CUDD supports. Returns a pointer to the array representing the number of minterms of the function rooted at node if successful; NULL otherwise.

Side Effects The number of digits of the result is returned in parameter digits.

See Also Cudd_CountMinterm
unsigned int 
Cudd_ApaIntDivision(
  int  digits, 
  DdApaNumber  dividend, 
  unsigned int  divisor, 
  DdApaNumber  quotient 
)
Divides an arbitrary precision integer by a 32-bit unsigned integer. Returns the remainder of the division. This procedure relies on the assumption that the number of bits of a DdApaDigit plus the number of bits of an unsigned int is less the number of bits of the mantissa of a double. This guarantees that the product of a DdApaDigit and an unsigned int can be represented without loss of precision by a double. On machines where this assumption is not satisfied, this procedure will malfunction.

Side Effects The quotient is returned in parameter quotient.

See Also Cudd_ApaShortDivision
int 
Cudd_ApaNumberOfDigits(
  int  binaryDigits 
)
Finds the number of digits for an arbitrary precision integer given the maximum number of binary digits. The number of binary digits should be positive. Returns the number of digits if successful; 0 otherwise.

Side Effects None

void 
Cudd_ApaPowerOfTwo(
  int  digits, 
  DdApaNumber  number, 
  int  power 
)
Sets an arbitrary precision integer to a power of two. If the power of two is too large to be represented, the number is set to 0.

Side Effects The result is returned in parameter number.

int 
Cudd_ApaPrintDecimal(
  FILE * fp, 
  int  digits, 
  DdApaNumber  number 
)
Prints an arbitrary precision integer in decimal format. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_ApaPrintHex Cudd_ApaPrintExponential
int 
Cudd_ApaPrintDensity(
  FILE * fp, 
  DdManager * dd, 
  DdNode * node, 
  int  nvars 
)
Prints the density of a BDD or ADD using arbitrary precision arithmetic. Returns 1 if successful; 0 otherwise.

Side Effects None

int 
Cudd_ApaPrintExponential(
  FILE * fp, 
  int  digits, 
  DdApaNumber  number, 
  int  precision 
)
Prints an arbitrary precision integer in exponential format. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_ApaPrintHex Cudd_ApaPrintDecimal
int 
Cudd_ApaPrintHex(
  FILE * fp, 
  int  digits, 
  DdApaNumber  number 
)
Prints an arbitrary precision integer in hexadecimal format. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_ApaPrintDecimal Cudd_ApaPrintExponential
int 
Cudd_ApaPrintMintermExp(
  FILE * fp, 
  DdManager * dd, 
  DdNode * node, 
  int  nvars, 
  int  precision 
)
Prints the number of minterms of a BDD or ADD in exponential format using arbitrary precision arithmetic. Parameter precision controls the number of signficant digits printed. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_ApaPrintMinterm
int 
Cudd_ApaPrintMinterm(
  FILE * fp, 
  DdManager * dd, 
  DdNode * node, 
  int  nvars 
)
Prints the number of minterms of a BDD or ADD using arbitrary precision arithmetic. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_ApaPrintMintermExp
void 
Cudd_ApaSetToLiteral(
  int  digits, 
  DdApaNumber  number, 
  DdApaDigit  literal 
)
Sets an arbitrary precision integer to a one-digit literal.

Side Effects The result is returned in parameter number.

void 
Cudd_ApaShiftRight(
  int  digits, 
  DdApaDigit  in, 
  DdApaNumber  a, 
  DdApaNumber  b 
)
Shifts right an arbitrary precision integer by one binary place. The most significant binary digit of the result is taken from parameter in.

Side Effects The result is returned in parameter b.

DdApaDigit 
Cudd_ApaShortDivision(
  int  digits, 
  DdApaNumber  dividend, 
  DdApaDigit  divisor, 
  DdApaNumber  quotient 
)
Divides an arbitrary precision integer by a digit.

Side Effects The quotient is returned in parameter quotient.

DdApaDigit 
Cudd_ApaSubtract(
  int  digits, 
  DdApaNumber  a, 
  DdApaNumber  b, 
  DdApaNumber  diff 
)
Subtracts two arbitrary precision integers. Returns the borrow out of the most significant digit.

Side Effects The result of the subtraction is stored in parameter diff.

void 
Cudd_AutodynDisableZdd(
  DdManager * unique 
)
Disables automatic dynamic reordering of ZDDs.

Side Effects None

See Also Cudd_AutodynEnableZdd Cudd_ReorderingStatusZdd Cudd_AutodynDisable
void 
Cudd_AutodynDisable(
  DdManager * unique 
)
Disables automatic dynamic reordering.

Side Effects None

See Also Cudd_AutodynEnable Cudd_ReorderingStatus Cudd_AutodynDisableZdd
void 
Cudd_AutodynEnableZdd(
  DdManager * unique, 
  Cudd_ReorderingType  method 
)
Enables automatic dynamic reordering of ZDDs. Parameter method is used to determine the method used for reordering ZDDs. If CUDD_REORDER_SAME is passed, the method is unchanged.

Side Effects None

See Also Cudd_AutodynDisableZdd Cudd_ReorderingStatusZdd Cudd_AutodynEnable
void 
Cudd_AutodynEnable(
  DdManager * unique, 
  Cudd_ReorderingType  method 
)
Enables automatic dynamic reordering of BDDs and ADDs. Parameter method is used to determine the method used for reordering. If CUDD_REORDER_SAME is passed, the method is unchanged.

Side Effects None

See Also Cudd_AutodynDisable Cudd_ReorderingStatus Cudd_AutodynEnableZdd
double 
Cudd_AverageDistance(
  DdManager * dd 
)
Computes the average distance between adjacent nodes in the manager. Adjacent nodes are node pairs such that the second node is the then child, else child, or next node in the collision list.

Side Effects None

DdNode * 
Cudd_BddToAdd(
  DdManager * dd, 
  DdNode * B 
)
Converts a BDD to a 0-1 ADD. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddPattern Cudd_addBddThreshold Cudd_addBddInterval Cudd_addBddStrictThreshold
DdNode * 
Cudd_CProjection(
  DdManager * dd, 
  DdNode * R, 
  DdNode * Y 
)
Computes the compatible projection of relation R with respect to cube Y. Returns a pointer to the c-projection if successful; NULL otherwise. For a comparison between Cudd_CProjection and Cudd_PrioritySelect, see the documentation of the latter.

Side Effects None

See Also Cudd_PrioritySelect
int 
Cudd_CheckKeys(
  DdManager * table 
)
Checks for the following conditions: Reports the average length of non-empty lists. Returns the number of subtables for which the number of keys is wrong.

Side Effects None

See Also Cudd_DebugCheck
int 
Cudd_CheckZeroRef(
  DdManager * manager 
)
Checks the unique table for nodes with non-zero reference counts. It is normally called before Cudd_Quit to make sure that there are no memory leaks due to missing Cudd_RecursiveDeref's. Takes into account that reference counts may saturate and that the basic constants and the projection functions are referenced by the manager. Returns the number of nodes with non-zero reference count. (Except for the cases mentioned above.)

Side Effects None

int 
Cudd_ClassifySupport(
  DdManager * dd, manager
  DdNode * f, first DD
  DdNode * g, second DD
  DdNode ** common, cube of shared variables
  DdNode ** onlyF, cube of variables only in f
  DdNode ** onlyG cube of variables only in g
)
Classifies the variables in the support of two DDs f and g, depending on whther they appear in both DDs, only in f, or only in g. Returns 1 successful; 0 otherwise.

Side Effects The cubes of the three classes of variables are returned as side effects.

See Also Cudd_Support Cudd_VectorSupport
void 
Cudd_ClearErrorCode(
  DdManager * dd 
)
Clear the error code of a manager.

Side Effects None

See Also Cudd_ReadErrorCode
double * 
Cudd_CofMinterm(
  DdManager * dd, 
  DdNode * node 
)
Computes the fraction of minterms in the on-set of all the positive cofactors of DD. Returns the pointer to an array of doubles if successful; NULL otherwise. The array hs as many positions as there are BDD variables in the manager plus one. The last position of the array contains the fraction of the minterms in the ON-set of the function represented by the BDD or ADD. The other positions of the array hold the variable signatures.

Side Effects None

DdNode * 
Cudd_Cofactor(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the cofactor of f with respect to g; g must be the BDD or the ADD of a cube. Returns a pointer to the cofactor if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddConstrain Cudd_bddRestrict
 
Cudd_Complement(
   node 
)
Returns the complemented version of a pointer.

Side Effects none

See Also Cudd_Regular Cudd_IsComplement
int 
Cudd_CountLeaves(
  DdNode * node 
)
Counts the number of leaves in a DD. Returns the number of leaves in the DD rooted at node if successful; CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_PrintDebug
double 
Cudd_CountMinterm(
  DdManager * manager, 
  DdNode * node, 
  int  nvars 
)
Counts the number of minterms of a DD. The function is assumed to depend on nvars variables. The minterm count is represented as a double, to allow for a larger number of variables. Returns the number of minterms of the function rooted at node if successful; (double) CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_PrintDebug Cudd_CountPath
double 
Cudd_CountPath(
  DdNode * node 
)
Counts the number of paths of a DD. Paths to all terminal nodes are counted. The path count is represented as a double, to allow for a larger number of variables. Returns the number of paths of the function rooted at node.

Side Effects None

See Also Cudd_CountMinterm
int 
Cudd_DagSize(
  DdNode * node 
)
Counts the number of nodes in a DD. Returns the number of nodes in the graph rooted at node.

Side Effects None

See Also Cudd_SharingSize Cudd_PrintDebug
int 
Cudd_DeadAreCounted(
  DdManager * dd 
)
Tells whether dead nodes are counted towards triggering reordering. Returns 1 if dead nodes are counted; 0 otherwise.

Side Effects None

See Also Cudd_TurnOnCountDead Cudd_TurnOffCountDead
int 
Cudd_DebugCheck(
  DdManager * table 
)
Checks for inconsistencies in the DD heap: Returns 0 if no inconsistencies are found; DD_OUT_OF_MEM if there is not enough memory; 1 otherwise.

Side Effects None

See Also Cudd_CheckKeys
DdNode * 
Cudd_Decreasing(
  DdManager * dd, 
  DdNode * f, 
  int  i 
)
Determines whether the function represented by BDD f is negative unate (monotonic decreasing) in variable i. Returns the constant one is f is unate and the (logical) constant zero if it is not. This function does not generate any new nodes.

Side Effects None

See Also Cudd_Increasing
double 
Cudd_Density(
  DdManager * dd, manager
  DdNode * f, function whose density is sought
  int  nvars size of the support of f
)
Computes the density of a BDD or ADD. The density is the ratio of the number of minterms to the number of nodes. If 0 is passed as number of variables, the number of variables existing in the manager is used. Returns the density if successful; (double) CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_CountMinterm Cudd_DagSize
void 
Cudd_Deref(
  DdNode * node 
)
Decreases the reference count of node. It is primarily used in recursive procedures to decrease the ref count of a result node before returning it. This accomplishes the goal of removing the protection applied by a previous Cudd_Ref.

Side Effects None

See Also Cudd_RecursiveDeref Cudd_RecursiveDerefZdd Cudd_Ref
void 
Cudd_DisableGarbageCollection(
  DdManager * dd 
)
Disables garbage collection. Garbage collection is initially enabled. This function may be called to disable it. However, garbage collection will still occur when a new node must be created and no memory is left, or when garbage collection is required for correctness. (E.g., before reordering.)

Side Effects None

See Also Cudd_EnableGarbageCollection Cudd_GarbageCollectionEnabled
int 
Cudd_DisableReorderingReporting(
  DdManager * dd 
)
Disables reporting of reordering stats. Returns 1 if successful; 0 otherwise.

Side Effects Removes functions from the pre-reordering and post-reordering hooks.

See Also Cudd_EnableReorderingReporting Cudd_ReorderingReporting
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
)
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.

Side Effects None

See Also Cudd_DumpDot Cudd_PrintDebug
int 
Cudd_DumpDDcal(
  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
)
Writes a DDcal file representing the argument BDDs. It returns 1 in case of success; 0 otherwise (e.g., out-of-memory or file system full). Cudd_DumpDDcal does not close the file: This is the caller responsibility. Cudd_DumpDDcal 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.

Side Effects None

See Also Cudd_DumpDot Cudd_PrintDebug Cudd_DumpBlif Cudd_DumpDaVinci
int 
Cudd_DumpDaVinci(
  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
)
Writes a daVinci file representing the argument BDDs. It returns 1 in case of success; 0 otherwise (e.g., out-of-memory or file system full). Cudd_DumpDaVinci does not close the file: This is the caller responsibility. Cudd_DumpDaVinci 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.

Side Effects None

See Also Cudd_DumpDot Cudd_PrintDebug Cudd_DumpBlif
int 
Cudd_DumpDot(
  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
)
Writes a file representing the argument DDs 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_DumpDot does not close the file: This is the caller responsibility. Cudd_DumpDot 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_DumpDot uses the following convention to draw arcs: The dot options are chosen so that the drawing fits on a letter-size sheet.

Side Effects None

See Also Cudd_DumpBlif Cudd_PrintDebug
int 
Cudd_DumpFactoredForm(
  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
)
Writes factored forms representing the argument BDDs. The format of the factored form is the one used in the genlib files for technology mapping in sis. It returns 1 in case of success; 0 otherwise (e.g., file system full). Cudd_DumpFactoredForm does not close the file: This is the caller responsibility. Caution must be exercised because a factored form may be exponentially larger than the argument BDD. If the argument inames is non-null, it is assumed to hold the pointers to the names of the inputs. Similarly for onames.

Side Effects None

See Also Cudd_DumpDot Cudd_PrintDebug Cudd_DumpBlif Cudd_DumpDaVinci Cudd_DumpDDcal
DdNode * 
Cudd_Dxygtdxz(
  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
)
This function generates a BDD for the function d(x,y) > d(x,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].

Side Effects None

See Also Cudd_PrioritySelect Cudd_Dxygtdyz 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
)
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].

Side Effects None

See Also Cudd_PrioritySelect Cudd_Dxygtdxz Cudd_Xgty Cudd_bddAdjPermuteX
void 
Cudd_EnableGarbageCollection(
  DdManager * dd 
)
Enables garbage collection. Garbage collection is initially enabled. Therefore it is necessary to call this function only if garbage collection has been explicitly disabled.

Side Effects None

See Also Cudd_DisableGarbageCollection Cudd_GarbageCollectionEnabled
int 
Cudd_EnableReorderingReporting(
  DdManager * dd 
)
Enables reporting of reordering stats. Returns 1 if successful; 0 otherwise.

Side Effects Installs functions in the pre-reordering and post-reordering hooks.

See Also Cudd_DisableReorderingReporting Cudd_ReorderingReporting
int 
Cudd_EqualSupNorm(
  DdManager * dd, manager
  DdNode * f, first ADD
  DdNode * g, second ADD
  CUDD_VALUE_TYPE  tolerance, maximum allowed difference
  int  pr verbosity level
)
Compares two ADDs for equality within tolerance. Two ADDs are reported to be equal if the maximum difference between them (the sup norm of their difference) is less than or equal to the tolerance parameter. Returns 1 if the two ADDs are equal (within tolerance); 0 otherwise. If parameter pr is positive the first failure is reported to the standard output.

Side Effects None

int 
Cudd_EquivDC(
  DdManager * dd, 
  DdNode * F, 
  DdNode * G, 
  DdNode * D 
)
Tells whether F and G are identical wherever D is 0. F and G are either two ADDs or two BDDs. D is either a 0-1 ADD or a BDD. The function returns 1 if F and G are equivalent, and 0 otherwise. No new nodes are created.

Side Effects None

int 
Cudd_EstimateCofactorSimple(
  DdNode * node, 
  int  i 
)
Estimates the number of nodes in a cofactor of a DD. Returns an estimate of the number of nodes in the positive cofactor of the graph rooted at node with respect to the variable whose index is i. This procedure implements with minor changes the algorithm of Cabodi et al. (ICCAD96). It does not allocate any memory, it does not change the state of the manager, and it is fast. However, it has been observed to overestimate the size of the cofactor by as much as a factor of 2.

Side Effects None

See Also Cudd_DagSize
int 
Cudd_EstimateCofactor(
  DdManager * dd, 
  DdNode * f, 
  int  i, 
  int  phase 1: positive; 0: negative
)
Estimates the number of nodes in a cofactor of a DD. Returns an estimate of the number of nodes in a cofactor of the graph rooted at node with respect to the variable whose index is i. In case of failure, returns CUDD_OUT_OF_MEM. This function uses a refinement of the algorithm of Cabodi et al. (ICCAD96). The refinement allows the procedure to account for part of the recombination that may occur in the part of the cofactor above the cofactoring variable. This procedure does no create any new node. It does keep a small table of results; therefore itmay run out of memory. If this is a concern, one should use Cudd_EstimateCofactorSimple, which is faster, does not allocate any memory, but is less accurate.

Side Effects None

See Also Cudd_DagSize Cudd_EstimateCofactorSimple
DdNode * 
Cudd_Eval(
  DdManager * dd, 
  DdNode * f, 
  int * inputs 
)
Finds the value of a DD for a given variable assignment. The variable assignment is passed in an array of int's, that should specify a zero or a one for each variable in the support of the function. Returns a pointer to a constant node. No new nodes are produced.

Side Effects None

See Also Cudd_bddLeq Cudd_addEvalConst
 
Cudd_E(
   node 
)
Returns the else child of an internal node. If node is a constant node, the result is unpredictable.

Side Effects none

See Also Cudd_T Cudd_V
DdNode * 
Cudd_FindEssential(
  DdManager * dd, 
  DdNode * f 
)
Returns the cube of the essential variables. A positive literal means that the variable must be set to 1 for the function to be 1. A negative literal means that the variable must be set to 0 for the function to be 1. Returns a pointer to the cube BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddIsVarEssential
DdGen * 
Cudd_FirstCube(
  DdManager * dd, 
  DdNode * f, 
  int ** cube, 
  CUDD_VALUE_TYPE * value 
)
Defines an iterator on the onset of a decision diagram and finds its first cube. Returns a generator that contains the information necessary to continue the enumeration if successful; NULL otherwise.

A cube is represented as an array of literals, which are integers in {0, 1, 2}; 0 represents a complemented literal, 1 represents an uncomplemented literal, and 2 stands for don't care. The enumeration produces a disjoint cover of the function associated with the diagram. The size of the array equals the number of variables in the manager at the time Cudd_FirstCube is called.

For each cube, a value is also returned. This value is always 1 for a BDD, while it may be different from 1 for an ADD. For BDDs, the offset is the set of cubes whose value is the logical zero. For ADDs, the offset is the set of cubes whose value is the background value. The cubes of the offset are not enumerated.

Side Effects The first cube and its value are returned as side effects.

See Also Cudd_ForeachCube Cudd_NextCube Cudd_GenFree Cudd_IsGenEmpty Cudd_FirstNode
DdGen * 
Cudd_FirstNode(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** node 
)
Defines an iterator on the nodes of a decision diagram and finds its first node. Returns a generator that contains the information necessary to continue the enumeration if successful; NULL otherwise.

Side Effects The first node is returned as a side effect.

See Also Cudd_ForeachNode Cudd_NextNode Cudd_GenFree Cudd_IsGenEmpty Cudd_FirstCube
 
Cudd_ForeachCube(
   manager, 
   f, 
   gen, 
   cube, 
   value 
)
Iterates over the cubes of a decision diagram f. Cudd_ForeachCube allocates and frees the generator. Therefore the application should not try to do that. Also, the cube is freed at the end of Cudd_ForeachCube and hence is not available outside of the loop.

CAUTION: It is assumed that dynamic reordering will not occur while there are open generators. It is the user's responsibility to make sure that dynamic reordering does not occur. As long as new nodes are not created during generation, and dynamic reordering is not called explicitly, dynamic reordering will not occur. Alternatively, it is sufficient to disable dynamic reordering. It is a mistake to dispose of a diagram on which generation is ongoing.

Side Effects none

See Also Cudd_ForeachNode Cudd_FirstCube Cudd_NextCube Cudd_GenFree Cudd_IsGenEmpty Cudd_AutodynDisable
 
Cudd_ForeachNode(
   manager, 
   f, 
   gen, 
   node 
)
Iterates over the nodes of a decision diagram f. The nodes are returned in a seemingly random order. Cudd_ForeachCube allocates and frees the generator. Therefore the application should not try to do that.

CAUTION: It is assumed that dynamic reordering will not occur while there are open generators. It is the user's responsibility to make sure that dynamic reordering does not occur. As long as new nodes are not created during generation, and dynamic reordering is not called explicitly, dynamic reordering will not occur. Alternatively, it is sufficient to disable dynamic reordering. It is a mistake to dispose of a diagram on which generation is ongoing.

Side Effects none

See Also Cudd_ForeachCube Cudd_FirstNode Cudd_NextNode Cudd_GenFree Cudd_IsGenEmpty Cudd_AutodynDisable
void 
Cudd_FreeTree(
  DdManager * dd 
)
Frees the variable group tree of the manager.

Side Effects None

See Also Cudd_SetTree Cudd_ReadTree Cudd_FreeZddTree
void 
Cudd_FreeZddTree(
  DdManager * dd 
)
Frees the variable group tree of the manager.

Side Effects None

See Also Cudd_SetZddTree Cudd_ReadZddTree Cudd_FreeTree
int 
Cudd_GarbageCollectionEnabled(
  DdManager * dd 
)
Returns 1 if garbage collection is enabled; 0 otherwise.

Side Effects None

See Also Cudd_EnableGarbageCollection Cudd_DisableGarbageCollection
int 
Cudd_GenFree(
  DdGen * gen 
)
Frees a CUDD generator. Always returns 0, so that it can be used in mis-like foreach constructs.

Side Effects None

See Also Cudd_ForeachCube Cudd_ForeachNode Cudd_FirstCube Cudd_NextCube Cudd_FirstNode Cudd_NextNode Cudd_IsGenEmpty
DdNode * 
Cudd_Increasing(
  DdManager * dd, 
  DdNode * f, 
  int  i 
)
Determines whether the function represented by BDD f is positive unate (monotonic decreasing) in variable i. It is based on Cudd_Decreasing and the fact that f is monotonic increasing in i if and only if its complement is monotonic decreasing in i.

Side Effects None

See Also Cudd_Decreasing
DdNode * 
Cudd_IndicesToCube(
  DdManager * dd, 
  int * array, 
  int  n 
)
Builds a cube of BDD variables from an array of indices. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddComputeCube
DdManager * 
Cudd_Init(
  unsigned int  numVars, initial number of BDD variables (i.e., subtables)
  unsigned int  numVarsZ, initial number of ZDD variables (i.e., subtables)
  unsigned int  numSlots, initial size of the unique tables
  unsigned int  cacheSize, initial size of the cache
  unsigned long  maxMemory target maximum memory occupation
)
Creates a new DD manager, initializes the table, the basic constants and the projection functions. If maxMemory is 0, Cudd_Init decides suitable values for the maximum size of the cache and for the limit for fast unique table growth based on the available memory. Returns a pointer to the manager if successful; NULL otherwise.

Side Effects None

See Also Cudd_Quit
 
Cudd_IsComplement(
   node 
)
Returns 1 if a pointer is complemented.

Side Effects none

See Also Cudd_Regular Cudd_Complement
 
Cudd_IsConstant(
   node 
)
Returns 1 if the node is a constant node (rather than an internal node). All constant nodes have the same index (CUDD_MAXINDEX). The pointer passed to Cudd_IsConstant may be either regular or complemented.

Side Effects none

int 
Cudd_IsGenEmpty(
  DdGen * gen 
)
Queries the status of a generator. Returns 1 if the generator is empty or NULL; 0 otherswise.

Side Effects None

See Also Cudd_ForeachCube Cudd_ForeachNode Cudd_FirstCube Cudd_NextCube Cudd_FirstNode Cudd_NextNode Cudd_GenFree
void 
Cudd_IterDerefBdd(
  DdManager * table, 
  DdNode * n 
)
Decreases the reference count of node n. If n dies, recursively decreases the reference counts of its children. It is used to dispose of a BDD that is no longer needed. It is more efficient than Cudd_RecursiveDeref, but it cannot be used on ADDs. The greater efficiency comes from being able to assume that no constant node will ever die as a result of a call to this procedure.

Side Effects None

See Also Cudd_RecursiveDeref
DdNode * 
Cudd_LargestCube(
  DdManager * manager, 
  DdNode * f, 
  int * length 
)
Finds a largest cube in a DD. f is the DD we want to get the largest cube for. The problem is translated into the one of finding a shortest path in f, when both THEN and ELSE arcs are assumed to have unit length. This yields a largest cube in the disjoint cover corresponding to the DD. Therefore, it is not necessarily the largest implicant of f. Returns the largest cube as a BDD.

Side Effects The number of literals of the cube is returned in length.

See Also Cudd_ShortestPath
MtrNode * 
Cudd_MakeTreeNode(
  DdManager * dd, manager
  unsigned int  low, index of the first group variable
  unsigned int  size, number of variables in the group
  unsigned int  type MTR_DEFAULT or MTR_FIXED
)
Creates a new variable group. The group starts at variable and contains size variables. The parameter low is the index of the first variable. If the variable already exists, its current position in the order is known to the manager. If the variable does not exist yet, the position is assumed to be the same as the index. The group tree is created if it does not exist yet. Returns a pointer to the group if successful; NULL otherwise.

Side Effects The variable tree is changed.

See Also Cudd_MakeZddTreeNode
MtrNode * 
Cudd_MakeZddTreeNode(
  DdManager * dd, manager
  unsigned int  low, index of the first group variable
  unsigned int  size, number of variables in the group
  unsigned int  type MTR_DEFAULT or MTR_FIXED
)
Creates a new ZDD variable group. The group starts at variable and contains size variables. The parameter low is the index of the first variable. If the variable already exists, its current position in the order is known to the manager. If the variable does not exist yet, the position is assumed to be the same as the index. The group tree is created if it does not exist yet. Returns a pointer to the group if successful; NULL otherwise.

Side Effects The ZDD variable tree is changed.

See Also Cudd_MakeTreeNode
DdApaNumber 
Cudd_NewApaNumber(
  int  digits 
)
Allocates memory for an arbitrary precision integer. Returns a pointer to the allocated memory if successful; NULL otherwise.

Side Effects None

int 
Cudd_NextCube(
  DdGen * gen, 
  int ** cube, 
  CUDD_VALUE_TYPE * value 
)
Generates the next cube of a decision diagram onset, using generator gen. Returns 0 if the enumeration is completed; 1 otherwise.

Side Effects The cube and its value are returned as side effects. The generator is modified.

See Also Cudd_ForeachCube Cudd_FirstCube Cudd_GenFree Cudd_IsGenEmpty Cudd_NextNode
int 
Cudd_NextNode(
  DdGen * gen, 
  DdNode ** node 
)
Finds the node of a decision diagram, using generator gen. Returns 0 if the enumeration is completed; 1 otherwise.

Side Effects The next node is returned as a side effect.

See Also Cudd_ForeachNode Cudd_FirstNode Cudd_GenFree Cudd_IsGenEmpty Cudd_NextCube
unsigned int 
Cudd_NodeReadIndex(
  DdNode * node 
)
Returns the index of the node. The node pointer can be either regular or complemented.

Side Effects None

See Also Cudd_ReadIndex
 
Cudd_NotCond(
   node, 
   c 
)
Complements a DD if condition c is true; c should be either 0 or 1, because it is used directly (for efficiency). If in doubt on the values c may take, use "(c) ? Cudd_Not(node) : node".

Side Effects none

See Also Cudd_Not
 
Cudd_Not(
   node 
)
Complements a DD by flipping the complement attribute of the pointer (the least significant bit).

Side Effects none

See Also Cudd_NotCond
void 
Cudd_OutOfMem(
  long  size size of the allocation that failed
)
Warns that a memory allocation failed. This function can be used as replacement of MMout_of_memory to prevent the safe_mem functions of the util package from exiting when malloc returns NULL. One possible use is in case of discretionary allocations; for instance, the allocation of memory to enlarge the computed table.

Side Effects None

DdNode * 
Cudd_OverApprox(
  DdManager * dd, manager
  DdNode * f, function to be superset
  int  numVars, number of variables in the support of f
  int  threshold, when to stop approximation
  int  safe, enforce safe approximation
  double  quality minimum improvement for accepted changes
)
Extracts a dense superset from a BDD. The procedure is identical to the underapproximation procedure except for the fact that it works on the complement of the given function. Extracting the subset of the complement function is equivalent to extracting the superset of the function. Returns a pointer to the BDD of the superset if successful. NULL if intermediate result causes the procedure to run out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SupersetHeavyBranch Cudd_SupersetShortPaths Cudd_ReadSize
unsigned int 
Cudd_Prime(
  unsigned int  p 
)
Returns the next prime >= p.

Side Effects None

int 
Cudd_PrintDebug(
  DdManager * dd, 
  DdNode * f, 
  int  n, 
  int  pr 
)
Prints to the standard output a DD and its statistics. The statistics include the number of nodes, the number of leaves, and the number of minterms. (The number of minterms is the number of assignments to the variables that cause the function to be different from the logical zero (for BDDs) and from the background value (for ADDs.) The statistics are printed if pr > 0. Specifically: Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_DagSize Cudd_CountLeaves Cudd_CountMinterm Cudd_PrintMinterm
int 
Cudd_PrintInfo(
  DdManager * dd, 
  FILE * fp 
)
Prints out statistics and settings for a CUDD manager. Returns 1 if successful; 0 otherwise.

Side Effects None

int 
Cudd_PrintLinear(
  DdManager * table 
)
Prints the linear transform matrix. Returns 1 in case of success; 0 otherwise.

Side Effects none

int 
Cudd_PrintMinterm(
  DdManager * manager, 
  DdNode * node 
)
Prints a disjoint sum of product cover for the function rooted at node. Each product corresponds to a path from node a leaf node different from the logical zero, and different from the background value. Uses the standard output. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_PrintDebug
void 
Cudd_PrintVersion(
  FILE * fp 
)
Prints the package version number.

Side Effects None

void 
Cudd_Quit(
  DdManager * unique 
)
Deletes resources associated with a DD manager and resets the global statistical counters. (Otherwise, another manaqger subsequently created would inherit the stats of this one.)

Side Effects None

See Also Cudd_Init
long 
Cudd_Random(
    
)
Portable number generator based on ran2 from "Numerical Recipes in C." It is a long period (> 2 * 10^18) random number generator of L'Ecuyer with Bays-Durham shuffle. Returns a long integer uniformly distributed between 0 and 2147483561 (inclusive of the endpoint values). The ranom generator can be explicitly initialized by calling Cudd_Srandom. If no explicit initialization is performed, then the seed 1 is assumed.

Side Effects None

See Also Cudd_Srandom
int 
Cudd_ReadArcviolation(
  DdManager * dd 
)
Returns the current value of the arcviolation parameter. This parameter is used in group sifting to decide how many arcs into y not coming from x are tolerable when checking for aggregation due to extended symmetry. The value should be between 0 and 100. A small value causes fewer variables to be aggregated. The default value is 0.

Side Effects None

See Also Cudd_SetArcviolation
DdNode * 
Cudd_ReadBackground(
  DdManager * dd 
)
Reads the background constant of the manager.

Side Effects None

double 
Cudd_ReadCacheHits(
  DdManager * dd 
)
Returns the number of cache hits.

Side Effects None

See Also Cudd_ReadCacheLookUps
double 
Cudd_ReadCacheLookUps(
  DdManager * dd 
)
Returns the number of cache look-ups.

Side Effects None

See Also Cudd_ReadCacheHits
unsigned int 
Cudd_ReadCacheSlots(
  DdManager * dd 
)
Reads the number of slots in the cache.

Side Effects None

See Also Cudd_ReadCacheUsedSlots
double 
Cudd_ReadCacheUsedSlots(
  DdManager * dd 
)
Reads the fraction of used slots in the cache. The unused slots are those in which no valid data is stored. Garbage collection, variable reordering, and cache resizing may cause used slots to become unused.

Side Effects None

See Also Cudd_ReadCacheSlots
unsigned int 
Cudd_ReadDead(
  DdManager * dd 
)
Returns the number of dead nodes in the unique table.

Side Effects None

See Also Cudd_ReadKeys
CUDD_VALUE_TYPE 
Cudd_ReadEpsilon(
  DdManager * dd 
)
Reads the epsilon parameter of the manager. The epsilon parameter control the comparison between floating point numbers.

Side Effects None

See Also Cudd_SetEpsilon
Cudd_ErrorType 
Cudd_ReadErrorCode(
  DdManager * dd 
)
Returns the code of the last error. The error codes are defined in cudd.h.

Side Effects None

See Also Cudd_ClearErrorCode
long 
Cudd_ReadGarbageCollectionTime(
  DdManager * dd 
)
Returns the number of milliseconds spent doing garbage collection since the manager was initialized.

Side Effects None

See Also Cudd_ReadGarbageCollections
int 
Cudd_ReadGarbageCollections(
  DdManager * dd 
)
Returns the number of times garbage collection has occurred in the manager. The number includes both the calls from reordering procedures and those caused by requests to create new nodes.

Side Effects None

See Also Cudd_ReadGarbageCollectionTime
Cudd_AggregationType 
Cudd_ReadGroupcheck(
  DdManager * dd 
)
Reads the groupcheck parameter of the manager. The groupcheck parameter determines the aggregation criterion in group sifting.

Side Effects None

See Also Cudd_SetGroupcheck
 
Cudd_ReadIndex(
   dd, 
   index 
)
Returns the current position in the order of variable index. This macro is obsolete and is kept for compatibility. New applications should use Cudd_ReadPerm instead.

Side Effects none

See Also Cudd_ReadPerm
int 
Cudd_ReadInvPermZdd(
  DdManager * dd, 
  int  i 
)
Returns the index of the ZDD variable currently in the i-th position of the order. If the index is CUDD_MAXINDEX, returns CUDD_MAXINDEX; otherwise, if the index is out of bounds returns -1.

Side Effects None

See Also Cudd_ReadPerm Cudd_ReadInvPermZdd
int 
Cudd_ReadInvPerm(
  DdManager * dd, 
  int  i 
)
Returns the index of the variable currently in the i-th position of the order. If the index is CUDD_MAXINDEX, returns CUDD_MAXINDEX; otherwise, if the index is out of bounds returns -1.

Side Effects None

See Also Cudd_ReadPerm Cudd_ReadInvPermZdd
unsigned int 
Cudd_ReadKeys(
  DdManager * dd 
)
Returns the total number of nodes currently in the unique table, including the dead nodes.

Side Effects None

See Also Cudd_ReadDead
int 
Cudd_ReadLinear(
  DdManager * table, CUDD manager
  int  x, row index
  int  y column index
)
Reads an entry of the linear transform matrix.

Side Effects none

DdNode * 
Cudd_ReadLogicZero(
  DdManager * dd 
)
Returns the zero constant of the manager. The logic zero constant is the complement of the one constant, and is distinct from the arithmetic zero.

Side Effects None

See Also Cudd_ReadOne Cudd_ReadZero
unsigned int 
Cudd_ReadLooseUpTo(
  DdManager * dd 
)
Reads the looseUpTo parameter of the manager.

Side Effects None

See Also Cudd_SetLooseUpTo Cudd_ReadMinHit Cudd_ReadMinDead
unsigned int 
Cudd_ReadMaxCacheHard(
  DdManager * dd 
)
Reads the maxCacheHard parameter of the manager.

Side Effects None

See Also Cudd_SetMaxCacheHard Cudd_ReadMaxCache
unsigned int 
Cudd_ReadMaxCache(
  DdManager * dd 
)
Reads the maxCache parameter of the manager.

Side Effects None

See Also Cudd_SetMaxCache Cudd_ReadMaxCache
double 
Cudd_ReadMaxGrowth(
  DdManager * dd 
)
Reads the maxGrowth parameter of the manager. This parameter determines how much the number of nodes can grow during sifting of a variable. Overall, sifting never increases the size of the decision diagrams. This parameter only refers to intermediate results. A lower value will speed up sifting, possibly at the expense of quality.

Side Effects None

See Also Cudd_SetMaxGrowth
long 
Cudd_ReadMemoryInUse(
  DdManager * dd 
)
Returns the memory in use by the manager measured in bytes.

Side Effects None

unsigned int 
Cudd_ReadMinDead(
  DdManager * dd 
)
Reads the minDead parameter of the manager. The minDead parameter is used by the package to decide whether to collect garbage or resize a subtable of the unique table when the subtable becomes too full. The application can indirectly control the value of minDead by setting the looseUpTo parameter.

Side Effects None

See Also Cudd_ReadDead Cudd_ReadLooseUpTo Cudd_SetLooseUpTo
unsigned int 
Cudd_ReadMinHit(
  DdManager * dd 
)
Reads the hit ratio that causes resizinig of the computed table.

Side Effects None

See Also Cudd_SetMinHit
DdNode * 
Cudd_ReadMinusInfinity(
  DdManager * dd 
)
Reads the minus-infinity constant from the manager.

Side Effects None

long 
Cudd_ReadNodeCount(
  DdManager * dd 
)
Reports the number of nodes in BDDs and ADDs. This number does not include the isolated projection functions and the unused constants. These nodes that are not counted are not part of the DDs manipulated by the application.

Side Effects None

See Also Cudd_ReadPeakNodeCount Cudd_zddReadNodeCount
double 
Cudd_ReadNodesDropped(
  DdManager * dd 
)
Returns the number of nodes killed by dereferencing if the keeping of this statistic is enabled; -1 otherwise. This statistic is enabled only if the package is compiled with DD_STATS defined.

Side Effects None

See Also Cudd_ReadNodesFreed
double 
Cudd_ReadNodesFreed(
  DdManager * dd 
)
Returns the number of nodes returned to the free list if the keeping of this statistic is enabled; -1 otherwise. This statistic is enabled only if the package is compiled with DD_STATS defined.

Side Effects None

See Also Cudd_ReadNodesDropped
int 
Cudd_ReadNumberXovers(
  DdManager * dd 
)
Reads the current number of crossovers used by the genetic algorithm for variable reordering. A larger number of crossovers will cause the genetic algorithm to take more time, but will generally produce better results. The default value is 0, in which case the package uses three times the number of variables as number of crossovers, with a maximum of 60.

Side Effects None

See Also Cudd_SetNumberXovers
DdNode * 
Cudd_ReadOne(
  DdManager * dd 
)
Returns the one constant of the manager. The one constant is common to ADDs and BDDs.

Side Effects None

See Also Cudd_ReadZero Cudd_ReadLogicZero Cudd_ReadZddOne
long 
Cudd_ReadPeakNodeCount(
  DdManager * dd 
)
Reports the peak number of nodes. This number includes node on the free list. At the peak, the number of nodes on the free list is guaranteed to be less than DD_MEM_CHUNK.

Side Effects None

See Also Cudd_ReadNodeCount Cudd_PrintInfo
int 
Cudd_ReadPermZdd(
  DdManager * dd, 
  int  i 
)
Returns the current position of the i-th ZDD variable in the order. If the index is CUDD_MAXINDEX, returns CUDD_MAXINDEX; otherwise, if the index is out of bounds returns -1.

Side Effects None

See Also Cudd_ReadInvPermZdd Cudd_ReadPerm
int 
Cudd_ReadPerm(
  DdManager * dd, 
  int  i 
)
Returns the current position of the i-th variable in the order. If the index is CUDD_MAXINDEX, returns CUDD_MAXINDEX; otherwise, if the index is out of bounds returns -1.

Side Effects None

See Also Cudd_ReadInvPerm Cudd_ReadPermZdd
DdNode * 
Cudd_ReadPlusInfinity(
  DdManager * dd 
)
Reads the plus-infinity constant from the manager.

Side Effects None

int 
Cudd_ReadPopulationSize(
  DdManager * dd 
)
Reads the current size of the population used by the genetic algorithm for variable reordering. A larger population size will cause the genetic algorithm to take more time, but will generally produce better results. The default value is 0, in which case the package uses three times the number of variables as population size, with a maximum of 120.

Side Effects None

See Also Cudd_SetPopulationSize
int 
Cudd_ReadRecomb(
  DdManager * dd 
)
Returns the current value of the recombination parameter used in group sifting. A larger (positive) value makes the aggregation of variables due to the second difference criterion more likely. A smaller (negative) value makes aggregation less likely.

Side Effects None

See Also Cudd_SetRecomb
long 
Cudd_ReadReorderingTime(
  DdManager * dd 
)
Returns the number of milliseconds spent reordering variables since the manager was initialized. The time spent in collecting garbage before reordering is included.

Side Effects None

See Also Cudd_ReadReorderings
int 
Cudd_ReadReorderings(
  DdManager * dd 
)
Returns the number of times reordering has occurred in the manager. The number includes both the calls to Cudd_ReduceHeap from the application program and those automatically performed by the package. However, calls that do not even initiate reordering are not counted. A call may not initiate reordering if there are fewer than minsize live nodes in the manager, or if CUDD_REORDER_NONE is specified as reordering method. The calls to Cudd_ShuffleHeap are not counted.

Side Effects None

See Also Cudd_ReduceHeap Cudd_ReadReorderingTime
int 
Cudd_ReadSiftMaxSwap(
  DdManager * dd 
)
Reads the siftMaxSwap parameter of the manager. This parameter gives the maximum number of swaps that will be attempted for each invocation of sifting. The real number of swaps may exceed the set limit because the package will always complete the sifting of the variable that causes the limit to be reached.

Side Effects None

See Also Cudd_ReadSiftMaxVar Cudd_SetSiftMaxSwap
int 
Cudd_ReadSiftMaxVar(
  DdManager * dd 
)
Reads the siftMaxVar parameter of the manager. This parameter gives the maximum number of variables that will be sifted for each invocation of sifting.

Side Effects None

See Also Cudd_ReadSiftMaxSwap Cudd_SetSiftMaxVar
int 
Cudd_ReadSize(
  DdManager * dd 
)
Returns the number of BDD variables in existance.

Side Effects None

See Also Cudd_ReadZddSize
unsigned int 
Cudd_ReadSlots(
  DdManager * dd 
)
Returns the total number of slots of the unique table. This number ismainly for diagnostic purposes.

Side Effects None

int 
Cudd_ReadSymmviolation(
  DdManager * dd 
)
Returns the current value of the symmviolation parameter. This parameter is used in group sifting to decide how many violations to the symmetry conditions f10 = f01 or f11 = f00 are tolerable when checking for aggregation due to extended symmetry. The value should be between 0 and 100. A small value causes fewer variables to be aggregated. The default value is 0.

Side Effects None

See Also Cudd_SetSymmviolation
MtrNode * 
Cudd_ReadTree(
  DdManager * dd 
)
Returns the variable group tree of the manager.

Side Effects None

See Also Cudd_SetTree Cudd_FreeTree Cudd_ReadZddTree
double 
Cudd_ReadUniqueLinks(
  DdManager * dd 
)
Returns the number of links followed during look-ups in the unique table if the keeping of this statistic is enabled; -1 otherwise. If an item is found in the first position of its collision list, the number of links followed is taken to be 0. If it is in second position, the number of links is 1, and so on. This statistic is enabled only if the package is compiled with DD_UNIQUE_PROFILE defined.

Side Effects None

See Also Cudd_ReadUniqueLookUps
double 
Cudd_ReadUniqueLookUps(
  DdManager * dd 
)
Returns the number of look-ups in the unique table if the keeping of this statistic is enabled; -1 otherwise. This statistic is enabled only if the package is compiled with DD_UNIQUE_PROFILE defined.

Side Effects None

See Also Cudd_ReadUniqueLinks
double 
Cudd_ReadUsedSlots(
  DdManager * dd 
)
Reads the fraction of used slots in the unique table. The unused slots are those in which no valid data is stored. Garbage collection, variable reordering, and subtable resizing may cause used slots to become unused.

Side Effects None

See Also Cudd_ReadSlots
DdNode * 
Cudd_ReadVars(
  DdManager * dd, 
  int  i 
)
Returns the i-th element of the vars array if it falls within the array bounds; NULL otherwise. If i is the index of an existing variable, this function produces the same result as Cudd_bddIthVar. However, if the i-th var does not exist yet, Cudd_bddIthVar will create it, whereas Cudd_ReadVars will not.

Side Effects None

See Also Cudd_bddIthVar
DdNode * 
Cudd_ReadZddOne(
  DdManager * dd, 
  int  i 
)
Returns the ZDD for the constant 1 function. The representation of the constant 1 function as a ZDD depends on how many variables it (nominally) depends on. The index of the topmost variable in the support is given as argument i.

Side Effects None

See Also Cudd_ReadOne
int 
Cudd_ReadZddSize(
  DdManager * dd 
)
Returns the number of ZDD variables in existance.

Side Effects None

See Also Cudd_ReadSize
MtrNode * 
Cudd_ReadZddTree(
  DdManager * dd 
)
Returns the variable group tree of the manager.

Side Effects None

See Also Cudd_SetZddTree Cudd_FreeZddTree Cudd_ReadTree
DdNode * 
Cudd_ReadZero(
  DdManager * dd 
)
Returns the zero constant of the manager. The zero constant is the arithmetic zero, rather than the logic zero. The latter is the complement of the one constant.

Side Effects None

See Also Cudd_ReadOne Cudd_ReadLogicZero
void 
Cudd_RecursiveDerefZdd(
  DdManager * table, 
  DdNode * n 
)
Decreases the reference count of ZDD node n. If n dies, recursively decreases the reference counts of its children. It is used to dispose of a ZDD that is no longer needed.

Side Effects None

See Also Cudd_Deref Cudd_Ref Cudd_RecursiveDeref
void 
Cudd_RecursiveDeref(
  DdManager * table, 
  DdNode * n 
)
Decreases the reference count of node n. If n dies, recursively decreases the reference counts of its children. It is used to dispose of a DD that is no longer needed.

Side Effects None

See Also Cudd_Deref Cudd_Ref Cudd_RecursiveDerefZdd
int 
Cudd_ReduceHeap(
  DdManager * table, DD manager
  Cudd_ReorderingType  heuristic, method used for reordering
  int  minsize bound below which no reordering occurs
)
Main dynamic reordering routine. Calls one of the possible reordering procedures: For sifting, symmetric sifting, group sifting, and window permutation it is possible to request reordering to convergence.

The core of all methods is the reordering procedure cuddSwapInPlace() which swaps two adjacent variables and is based on Rudell's paper. Returns 1 in case of success; 0 otherwise. In the case of symmetric sifting (with and without convergence) returns 1 plus the number of symmetric variables, in case of success.

Side Effects Changes the variable order for all diagrams and clears the cache.

void 
Cudd_Ref(
  DdNode * n 
)
Increases the reference count of a node, if it is not saturated.

Side Effects None

See Also Cudd_RecursiveDeref Cudd_Deref
 
Cudd_Regular(
   node 
)
Returns the regular version of a pointer.

Side Effects none

See Also Cudd_Complement Cudd_IsComplement
DdNode * 
Cudd_RemapOverApprox(
  DdManager * dd, manager
  DdNode * f, function to be superset
  int  numVars, number of variables in the support of f
  int  threshold, when to stop approximation
  double  quality minimum improvement for accepted changes
)
Extracts a dense superset from a BDD. The procedure is identical to the underapproximation procedure except for the fact that it works on the complement of the given function. Extracting the subset of the complement function is equivalent to extracting the superset of the function. Returns a pointer to the BDD of the superset if successful. NULL if intermediate result causes the procedure to run out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SupersetHeavyBranch Cudd_SupersetShortPaths Cudd_ReadSize
DdNode * 
Cudd_RemapUnderApprox(
  DdManager * dd, manager
  DdNode * f, function to be subset
  int  numVars, number of variables in the support of f
  int  threshold, when to stop approximation
  double  quality minimum improvement for accepted changes
)
Extracts a dense subset from a BDD. This procedure uses a remapping technique and density as the cost function. Returns a pointer to the BDD of the subset if successful. NULL if the procedure runs out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will cause overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SubsetShortPaths Cudd_SubsetHeavyBranch Cudd_UnderApprox Cudd_ReadSize
int 
Cudd_ReorderingReporting(
  DdManager * dd 
)
Returns 1 if reporting of reordering stats is enabled; 0 otherwise.

Side Effects none

See Also Cudd_EnableReorderingReporting Cudd_DisableReorderingReporting
int 
Cudd_ReorderingStatusZdd(
  DdManager * unique, 
  Cudd_ReorderingType * method 
)
Reports the status of automatic dynamic reordering of ZDDs. Parameter method is set to the ZDD reordering method currently selected. Returns 1 if automatic reordering is enabled; 0 otherwise.

Side Effects Parameter method is set to the ZDD reordering method currently selected.

See Also Cudd_AutodynEnableZdd Cudd_AutodynDisableZdd Cudd_ReorderingStatus
int 
Cudd_ReorderingStatus(
  DdManager * unique, 
  Cudd_ReorderingType * method 
)
Reports the status of automatic dynamic reordering of BDDs and ADDs. Parameter method is set to the reordering method currently selected. Returns 1 if automatic reordering is enabled; 0 otherwise.

Side Effects Parameter method is set to the reordering method currently selected.

See Also Cudd_AutodynEnable Cudd_AutodynDisable Cudd_ReorderingStatusZdd
void 
Cudd_SetArcviolation(
  DdManager * dd, 
  int  arcviolation 
)
Sets the value of the arcviolation parameter. This parameter is used in group sifting to decide how many arcs into y not coming from x are tolerable when checking for aggregation due to extended symmetry. The value should be between 0 and 100. A small value causes fewer variables to be aggregated. The default value is 0.

Side Effects None

See Also Cudd_ReadArcviolation
void 
Cudd_SetBackground(
  DdManager * dd, 
  DdNode * bck 
)
Sets the background constant of the manager. It assumes that the DdNode pointer bck is already referenced.

Side Effects None

void 
Cudd_SetEpsilon(
  DdManager * dd, 
  CUDD_VALUE_TYPE  ep 
)
Sets the epsilon parameter of the manager to ep. The epsilon parameter control the comparison between floating point numbers.

Side Effects None

See Also Cudd_ReadEpsilon
void 
Cudd_SetGroupcheck(
  DdManager * dd, 
  Cudd_AggregationType  gc 
)
Sets the parameter groupcheck of the manager to gc. The groupcheck parameter determines the aggregation criterion in group sifting.

Side Effects None

See Also Cudd_ReadGroupCheck
void 
Cudd_SetLooseUpTo(
  DdManager * dd, 
  unsigned int  lut 
)
Sets the looseUpTo parameter of the manager. This parameter of the manager controls the threshold beyond which no fast growth of the unique table is allowed. The threshold is given as a number of slots. If the value passed to this function is 0, the function determines a suitable value based on the available memory.

Side Effects None

See Also Cudd_ReadLooseUpTo Cudd_SetMinHit
void 
Cudd_SetMaxCacheHard(
  DdManager * dd, 
  unsigned int  mc 
)
Sets the maxCacheHard parameter of the manager. The cache cannot grow larger than maxCacheHard entries. This parameter allows an application to control the trade-off of memory versus speed. If the value passed to this function is 0, the function determines a suitable maximum cache size based on the available memory.

Side Effects None

See Also Cudd_ReadMaxCacheHard Cudd_SetMaxCache
void 
Cudd_SetMaxCache(
  DdManager * dd, 
  unsigned int  mc 
)
Sets the maxCache parameter of the manager. This parameter is normally automatically determined by the package based on the total number of nodes and the parameter maxCacheHard. Applications should normally change maxCacheHard rather than maxCache if they want to explicitly control the trade-off of memory versus speed.

Side Effects None

See Also Cudd_ReadMaxCache Cudd_SetMaxCacheHard
void 
Cudd_SetMaxGrowth(
  DdManager * dd, 
  double  mg 
)
Sets the maxGrowth parameter of the manager. This parameter determines how much the number of nodes can grow during sifting of a variable. Overall, sifting never increases the size of the decision diagrams. This parameter only refers to intermediate results. A lower value will speed up sifting, possibly at the expense of quality.

Side Effects None

See Also Cudd_ReadMaxGrowth
void 
Cudd_SetMinHit(
  DdManager * dd, 
  unsigned int  hr 
)
Sets the minHit parameter of the manager. This parameter controls the resizing of the computed table. If the hit ratio is larger than the specified value, and the cache is not already too large, then its size is doubled.

Side Effects None

See Also Cudd_ReadMinHit
void 
Cudd_SetNumberXovers(
  DdManager * dd, 
  int  numberXovers 
)
Sets the number of crossovers used by the genetic algorithm for variable reordering. A larger number of crossovers will cause the genetic algorithm to take more time, but will generally produce better results. The default value is 0, in which case the package uses three times the number of variables as number of crossovers, with a maximum of 60.

Side Effects None

See Also Cudd_ReadNumberXovers
void 
Cudd_SetPopulationSize(
  DdManager * dd, 
  int  populationSize 
)
Sets the size of the population used by the genetic algorithm for variable reordering. A larger population size will cause the genetic algorithm to take more time, but will generally produce better results. The default value is 0, in which case the package uses three times the number of variables as population size, with a maximum of 120.

Side Effects Changes the manager.

See Also Cudd_ReadPopulationSize
void 
Cudd_SetRecomb(
  DdManager * dd, 
  int  recomb 
)
Sets the value of the recombination parameter used in group sifting. A larger (positive) value makes the aggregation of variables due to the second difference criterion more likely. A smaller (negative) value makes aggregation less likely. The default value is 0.

Side Effects Changes the manager.

See Also Cudd_ReadRecomb
void 
Cudd_SetSiftMaxSwap(
  DdManager * dd, 
  int  sms 
)
Sets the siftMaxSwap parameter of the manager. This parameter gives the maximum number of swaps that will be attempted for each invocation of sifting. The real number of swaps may exceed the set limit because the package will always complete the sifting of the variable that causes the limit to be reached.

Side Effects None

See Also Cudd_SetSiftMaxVar Cudd_ReadSiftMaxSwap
void 
Cudd_SetSiftMaxVar(
  DdManager * dd, 
  int  smv 
)
Sets the siftMaxVar parameter of the manager. This parameter gives the maximum number of variables that will be sifted for each invocation of sifting.

Side Effects None

See Also Cudd_SetSiftMaxSwap Cudd_ReadSiftMaxVar
void 
Cudd_SetSymmviolation(
  DdManager * dd, 
  int  symmviolation 
)
Sets the value of the symmviolation parameter. This parameter is used in group sifting to decide how many violations to the symmetry conditions f10 = f01 or f11 = f00 are tolerable when checking for aggregation due to extended symmetry. The value should be between 0 and 100. A small value causes fewer variables to be aggregated. The default value is 0.

Side Effects Changes the manager.

See Also Cudd_ReadSymmviolation
void 
Cudd_SetTree(
  DdManager * dd, 
  MtrNode * tree 
)
Sets the variable group tree of the manager.

Side Effects None

See Also Cudd_FreeTree Cudd_ReadTree Cudd_SetZddTree
void 
Cudd_SetZddTree(
  DdManager * dd, 
  MtrNode * tree 
)
Sets the ZDD variable group tree of the manager.

Side Effects None

See Also Cudd_FreeZddTree Cudd_ReadZddTree Cudd_SetTree
int 
Cudd_SharingSize(
  DdNode ** nodeArray, 
  int  n 
)
Counts the number of nodes in an array of DDs. Shared nodes are counted only once. Returns the total number of nodes.

Side Effects None

See Also Cudd_DagSize
int 
Cudd_ShortestLength(
  DdManager * manager, 
  DdNode * f, 
  int * weight 
)
Find the length of the shortest path(s) in a DD. f is the DD we want to get the shortest path for; weight[i] is the weight of the THEN edge coming from the node whose index is i. All ELSE edges have 0 weight. Returns the length of the shortest path(s) if successful; CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_ShortestPath
DdNode * 
Cudd_ShortestPath(
  DdManager * manager, 
  DdNode * f, 
  int * weight, 
  int * support, 
  int * length 
)
Finds a shortest path in a DD. f is the DD we want to get the shortest path for; weight[i] is the weight of the THEN arc coming from the node whose index is i. If weight is NULL, then unit weights are assumed for all THEN arcs. All ELSE arcs have 0 weight. If non-NULL, both weight and support should point to arrays with at least as many entries as there are variables in the manager. Returns the shortest path as the BDD of a cube.

Side Effects support contains on return the true support of f. If support is NULL on entry, then Cudd_ShortestPath does not compute the true support info. length contains the length of the path.

See Also Cudd_ShortestLength Cudd_LargestCube
int 
Cudd_ShuffleHeap(
  DdManager * table, DD manager
  int * permutation required variable permutation
)
Reorders variables according to given permutation. The i-th entry of the permutation array contains the index of the variable that should be brought to the i-th level. The size of the array should be equal or greater to the number of variables currently in use. Returns 1 in case of success; 0 otherwise.

Side Effects Changes the variable order for all diagrams and clears the cache.

See Also Cudd_ReduceHeap
DdNode * 
Cudd_SolveEqn(
  DdManager * bdd, 
  DdNode * F, the left-hand side of the equation
  DdNode * Y, the cube of the y variables
  DdNode ** G, the array of solutions (return parameter)
  int ** yIndex, index of y variables
  int  n numbers of unknowns
)
Implements the solution for F(x,y) = 0. The return value is the consistency condition. The y variables are the unknowns and the remaining variables are the parameters. Returns the consistency condition if successful; NULL otherwise. Cudd_SolveEqn allocates an array and fills it with the indices of the unknowns. This array is used by Cudd_VerifySol.

Side Effects The solution is returned in G; the indices of the y variables are returned in yIndex.

See Also Cudd_VerifySol
DdNode * 
Cudd_SplitSet(
  DdManager * manager, 
  DdNode * S, 
  DdNode ** xVars, 
  int  n, 
  double  m 
)
Returns m minterms from a BDD whose support has n variables at most. The procedure tries to create as few extra nodes as possible. The function represented by S depends on at most n of the variables in xVars. Returns a BDD with m minterms of the on-set of S if successful; NULL otherwise.

Side Effects None

void 
Cudd_Srandom(
  long  seed 
)
Initializer for the portable number generator based on ran2 in "Numerical Recipes in C." The input is the seed for the generator. If it is negative, its absolute value is taken as seed. If it is 0, then 1 is taken as seed. The initialized sets up the two recurrences used to generate a long-period stream, and sets up the shuffle table.

Side Effects None

See Also Cudd_Random
int 
Cudd_StdPostReordHook(
  DdManager * dd, 
  void * data 
)
Sample hook function to call after reordering. Prints on stdout final size and reordering time. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_StdPreReordHook
int 
Cudd_StdPreReordHook(
  DdManager * dd, 
  void * data 
)
Sample hook function to call before reordering. Prints on stdout reordering method and initial size. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_StdPostReordHook
DdNode * 
Cudd_SubsetCompress(
  DdManager * dd, manager
  DdNode * f, BDD whose subset is sought
  int  nvars, number of variables in the support of f
  int  threshold maximum number of nodes in the subset
)
Finds a dense subset of BDD f. Density is the ratio of number of minterms to number of nodes. Uses several techniques in series. It is more expensive than other subsetting procedures, but often produces better results. See Cudd_SubsetShortPaths for a description of the threshold and nvars parameters. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_SubsetRemap Cudd_SubsetShortPaths Cudd_SubsetHeavyBranch Cudd_bddSqueeze
DdNode * 
Cudd_SubsetHeavyBranch(
  DdManager * dd, manager
  DdNode * f, function to be subset
  int  numVars, number of variables in the support of f
  int  threshold maximum number of nodes in the subset
)
Extracts a dense subset from a BDD. This procedure builds a subset by throwing away one of the children of each node, starting from the root, until the result is small enough. The child that is eliminated from the result is the one that contributes the fewer minterms. Returns a pointer to the BDD of the subset if successful. NULL if the procedure runs out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation and node count calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SubsetShortPaths Cudd_SupersetHeavyBranch Cudd_ReadSize
DdNode * 
Cudd_SubsetShortPaths(
  DdManager * dd, manager
  DdNode * f, function to be subset
  int  numVars, number of variables in the support of f
  int  threshold, maximum number of nodes in the subset
  int  hardlimit flag: 1 if threshold is a hard limit
)
Extracts a dense subset from a BDD. This procedure tries to preserve the shortest paths of the input BDD, because they give many minterms and contribute few nodes. This procedure may increase the number of nodes in trying to create the subset or reduce the number of nodes due to recombination as compared to the original BDD. Hence the threshold may not be strictly adhered to. In practice, recombination overshadows the increase in the number of nodes and results in small BDDs as compared to the threshold. The hardlimit specifies whether threshold needs to be strictly adhered to. If it is set to 1, the procedure ensures that result is never larger than the specified limit but may be considerably less than the threshold. Returns a pointer to the BDD for the subset if successful; NULL otherwise. The value for numVars should be as close as possible to the size of the support of f for better efficiency. However, it is safe to pass the value returned by Cudd_ReadSize for numVars. If 0 is passed, then the value returned by Cudd_ReadSize is used.

Side Effects None

See Also Cudd_SupersetShortPaths Cudd_SubsetHeavyBranch Cudd_ReadSize
DdNode * 
Cudd_SupersetCompress(
  DdManager * dd, manager
  DdNode * f, BDD whose superset is sought
  int  nvars, number of variables in the support of f
  int  threshold maximum number of nodes in the superset
)
Finds a dense superset of BDD f. Density is the ratio of number of minterms to number of nodes. Uses several techniques in series. It is more expensive than other supersetting procedures, but often produces better results. See Cudd_SupersetShortPaths for a description of the threshold and nvars parameters. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_SubsetCompress Cudd_SupersetRemap Cudd_SupersetShortPaths Cudd_SupersetHeavyBranch Cudd_bddSqueeze
DdNode * 
Cudd_SupersetHeavyBranch(
  DdManager * dd, manager
  DdNode * f, function to be superset
  int  numVars, number of variables in the support of f
  int  threshold maximum number of nodes in the superset
)
Extracts a dense superset from a BDD. The procedure is identical to the subset procedure except for the fact that it receives the complement of the given function. Extracting the subset of the complement function is equivalent to extracting the superset of the function. This procedure builds a superset by throwing away one of the children of each node starting from the root of the complement function, until the result is small enough. The child that is eliminated from the result is the one that contributes the fewer minterms. Returns a pointer to the BDD of the superset if successful. NULL if intermediate result causes the procedure to run out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation and node count calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SubsetHeavyBranch Cudd_SupersetShortPaths Cudd_ReadSize
DdNode * 
Cudd_SupersetShortPaths(
  DdManager * dd, manager
  DdNode * f, function to be superset
  int  numVars, number of variables in the support of f
  int  threshold, maximum number of nodes in the subset
  int  hardlimit flag: 1 if threshold is a hard limit
)
Extracts a dense superset from a BDD. The procedure is identical to the subset procedure except for the fact that it receives the complement of the given function. Extracting the subset of the complement function is equivalent to extracting the superset of the function. This procedure tries to preserve the shortest paths of the complement BDD, because they give many minterms and contribute few nodes. This procedure may increase the number of nodes in trying to create the superset or reduce the number of nodes due to recombination as compared to the original BDD. Hence the threshold may not be strictly adhered to. In practice, recombination overshadows the increase in the number of nodes and results in small BDDs as compared to the threshold. The hardlimit specifies whether threshold needs to be strictly adhered to. If it is set to 1, the procedure ensures that result is never larger than the specified limit but may be considerably less than the threshold. Returns a pointer to the BDD for the superset if successful; NULL otherwise. The value for numVars should be as close as possible to the size of the support of f for better efficiency. However, it is safe to pass the value returned by Cudd_ReadSize for numVar. If 0 is passed, then the value returned by Cudd_ReadSize is used.

Side Effects None

See Also Cudd_SubsetShortPaths Cudd_SupersetHeavyBranch Cudd_ReadSize
int 
Cudd_SupportSize(
  DdManager * dd, manager
  DdNode * f DD whose support size is sought
)
Counts the variables on which a DD depends. Returns the number of the variables if successful; CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_Support
DdNode * 
Cudd_Support(
  DdManager * dd, manager
  DdNode * f DD whose support is sought
)
Finds the variables on which a DD depends. Returns a BDD consisting of the product of the variables if successful; NULL otherwise.

Side Effects None

See Also Cudd_VectorSupport Cudd_ClassifySupport
void 
Cudd_SymmProfile(
  DdManager * table, 
  int  lower, 
  int  upper 
)
Prints statistics on symmetric variables.

Side Effects None

void 
Cudd_TurnOffCountDead(
  DdManager * dd 
)
Causes the dead nodes not to be counted towards triggering reordering. This causes less frequent reorderings. By default dead nodes are not counted. Therefore there is no need to call this function unless Cudd_TurnOnCountDead has been previously called.

Side Effects Changes the manager.

See Also Cudd_TurnOnCountDead Cudd_DeadAreCounted
void 
Cudd_TurnOnCountDead(
  DdManager * dd 
)
Causes the dead nodes to be counted towards triggering reordering. This causes more frequent reorderings. By default dead nodes are not counted.

Side Effects Changes the manager.

See Also Cudd_TurnOffCountDead Cudd_DeadAreCounted
 
Cudd_T(
   node 
)
Returns the then child of an internal node. If node is a constant node, the result is unpredictable.

Side Effects none

See Also Cudd_E Cudd_V
DdNode * 
Cudd_UnderApprox(
  DdManager * dd, manager
  DdNode * f, function to be subset
  int  numVars, number of variables in the support of f
  int  threshold, when to stop approximation
  int  safe, enforce safe approximation
  double  quality minimum improvement for accepted changes
)
Extracts a dense subset from a BDD. This procedure uses a variant of Tom Shiple's underapproximation method. The main difference from the original method is that density is used as cost function. Returns a pointer to the BDD of the subset if successful. NULL if the procedure runs out of memory. The parameter numVars is the maximum number of variables to be used in minterm calculation. The optimal number should be as close as possible to the size of the support of f. However, it is safe to pass the value returned by Cudd_ReadSize for numVars when the number of variables is under 1023. If numVars is larger than 1023, it will cause overflow. If a 0 parameter is passed then the procedure will compute a value which will avoid overflow but will cause underflow with 2046 variables or more.

Side Effects None

See Also Cudd_SubsetShortPaths Cudd_SubsetHeavyBranch Cudd_ReadSize
int 
Cudd_VectorSupportSize(
  DdManager * dd, manager
  DdNode ** F, array of DDs whose support is sought
  int  n size of the array
)
Counts the variables on which a set of DDs depends. The set must contain either BDDs and ADDs, or ZDDs. Returns the number of the variables if successful; CUDD_OUT_OF_MEM otherwise.

Side Effects None

See Also Cudd_VectorSupport Cudd_SupportSize
DdNode * 
Cudd_VectorSupport(
  DdManager * dd, manager
  DdNode ** F, array of DDs whose support is sought
  int  n size of the array
)
Finds the variables on which a set of DDs depends. The set must contain either BDDs and ADDs, or ZDDs. Returns a BDD consisting of the product of the variables if successful; NULL otherwise.

Side Effects None

See Also Cudd_Support Cudd_ClassifySupport
DdNode * 
Cudd_VerifySol(
  DdManager * bdd, 
  DdNode * F, the left-hand side of the equation
  DdNode ** G, the array of solutions
  int * yIndex, index of y variables
  int  n numbers of unknowns
)
Checks the solution of F(x,y) = 0. This procedure substitutes the solution components for the unknowns of F and returns the resulting BDD for F.

Side Effects Frees the memory pointed by yIndex.

See Also Cudd_SolveEqn
 
Cudd_V(
   node 
)
Returns the value of a constant node. If node is an internal node, the result is unpredictable.

Side Effects none

See Also Cudd_T Cudd_E
DdNode * 
Cudd_Xeqy(
  DdManager * dd, DD manager
  int  N, number of x and y variables
  DdNode ** x, array of x variables
  DdNode ** y array of y variables
)
This function generates a BDD 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 BDD 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].

Side Effects None

See Also Cudd_addXeqy
DdNode * 
Cudd_Xgty(
  DdManager * dd, DD manager
  int  N, number of x and y variables
  DdNode ** z, array of z variables: unused
  DdNode ** x, array of x variables
  DdNode ** y array of y variables
)
This function generates a BDD 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 BDD 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]. Argument z is not used by Cudd_Xgty: it is included to make it call-compatible to Cudd_Dxygtdxz and Cudd_Dxygtdyz.

Side Effects None

See Also Cudd_PrioritySelect Cudd_Dxygtdxz Cudd_Dxygtdyz
DdNode * 
Cudd_addAgreement(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Returns NULL if not a terminal case; f op g otherwise, where f op g is f if f==g; background if f!=g.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addBddInterval(
  DdManager * dd, 
  DdNode * f, 
  CUDD_VALUE_TYPE  lower, 
  CUDD_VALUE_TYPE  upper 
)
Converts an ADD to a BDD by replacing all discriminants greater than or equal to lower and less than or equal to upper with 1, and all other discriminants with 0. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddThreshold Cudd_addBddStrictThreshold Cudd_addBddPattern Cudd_BddToAdd
DdNode * 
Cudd_addBddIthBit(
  DdManager * dd, 
  DdNode * f, 
  int  bit 
)
Converts an ADD to a BDD by replacing all discriminants whose i-th bit is equal to 1 with 1, and all other discriminants with 0. The i-th bit refers to the integer representation of the leaf value. If the value is has a fractional part, it is ignored. Repeated calls to this procedure allow one to transform an integer-valued ADD into an array of BDDs, one for each bit of the leaf values. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddInterval Cudd_addBddPattern Cudd_BddToAdd
DdNode * 
Cudd_addBddPattern(
  DdManager * dd, 
  DdNode * f 
)
Converts an ADD to a BDD by replacing all discriminants different from 0 with 1. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_BddToAdd Cudd_addBddThreshold Cudd_addBddInterval Cudd_addBddStrictThreshold
DdNode * 
Cudd_addBddStrictThreshold(
  DdManager * dd, 
  DdNode * f, 
  CUDD_VALUE_TYPE  value 
)
Converts an ADD to a BDD by replacing all discriminants STRICTLY greater than value with 1, and all other discriminants with 0. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddInterval Cudd_addBddPattern Cudd_BddToAdd Cudd_addBddThreshold
DdNode * 
Cudd_addBddThreshold(
  DdManager * dd, 
  DdNode * f, 
  CUDD_VALUE_TYPE  value 
)
Converts an ADD to a BDD by replacing all discriminants greater than or equal to value with 1, and all other discriminants with 0. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddInterval Cudd_addBddPattern Cudd_BddToAdd Cudd_addBddStrictThreshold
DdNode * 
Cudd_addCmpl(
  DdManager * dd, 
  DdNode * f 
)
Computes the complement of an ADD a la C language: The complement of 0 is 1 and the complement of everything else is 0. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addNegate
DdNode * 
Cudd_addCompose(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  int  v 
)
Substitutes g for x_v in the ADD for f. v is the index of the variable to be substituted. g must be a 0-1 ADD. Cudd_bddCompose passes the corresponding projection function to the recursive procedure, so that the cache may be used. Returns the composed ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddCompose
DdNode * 
Cudd_addComputeCube(
  DdManager * dd, 
  DdNode ** vars, 
  int * phase, 
  int  n 
)
Computes the cube of an array of ADD variables. If non-null, the phase argument indicates which literal of each variable should appear in the cube. If phase[i] is nonzero, then the positive literal is used. If phase is NULL, the cube is positive unate. Returns a pointer to the result if successful; NULL otherwise.

Side Effects none

See Also Cudd_bddComputeCube
DdNode * 
Cudd_addConstrain(
  DdManager * dd, 
  DdNode * f, 
  DdNode * c 
)
Computes f constrain c (f @ c), for f an ADD and c a 0-1 ADD. List of special cases: Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddConstrain
DdNode * 
Cudd_addConst(
  DdManager * dd, 
  CUDD_VALUE_TYPE  c 
)
Retrieves the ADD for constant c if it already exists, or creates a new ADD. Returns a pointer to the ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addNewVar Cudd_addIthVar
DdNode * 
Cudd_addDiff(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Returns NULL if not a terminal case; f op g otherwise, where f op g is plusinfinity if f=g; min(f,g) if f!=g.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addDivide(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point division. Returns NULL if not a terminal case; f / g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addEvalConst(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Checks whether ADD g is constant whenever ADD f is 1. f must be a 0-1 ADD. Returns a pointer to the resulting ADD (which may or may not be constant) or DD_NON_CONSTANT. If f is identically 0, the check is assumed to be successful, and the background value is returned. No new nodes are created.

Side Effects None

See Also Cudd_addIteConstant Cudd_addLeq
DdNode * 
Cudd_addExistAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * cube 
)
Abstracts all the variables in cube from f by summing over all possible values taken by the variables. Returns the abstracted ADD.

Side Effects None

See Also Cudd_addUnivAbstract Cudd_bddExistAbstract Cudd_addOrAbstract
DdNode * 
Cudd_addFindMax(
  DdManager * dd, 
  DdNode * f 
)
Returns a pointer to a constant ADD.

Side Effects None

DdNode * 
Cudd_addFindMin(
  DdManager * dd, 
  DdNode * f 
)
Returns a pointer to a constant ADD.

Side Effects None

DdNode * 
Cudd_addHamming(
  DdManager * dd, 
  DdNode ** xVars, 
  DdNode ** yVars, 
  int  nVars 
)
Computes the Hamming distance ADD. Returns an ADD that gives the Hamming distance between its two arguments if successful; NULL otherwise. The two vectors xVars and yVars identify the variables that form the two arguments.

Side Effects None

int 
Cudd_addHarwell(
  FILE * fp, pointer to the input file
  DdManager * dd, DD manager
  DdNode ** E, characteristic function of the graph
  DdNode *** x, array of row variables
  DdNode *** y, array of column variables
  DdNode *** xn, array of complemented row variables
  DdNode *** yn_, array of complemented column variables
  int * nx, number or row variables
  int * ny, number or column variables
  int * m, number of rows
  int * n, number of columns
  int  bx, first index of row variables
  int  sx, step of row variables
  int  by, first index of column variables
  int  sy, step of column variables
  int  pr verbosity level
)
Reads in a matrix in the format of the Harwell-Boeing benchmark suite. The variables are ordered as follows:
x[0] y[0] x[1] y[1] ...
0 is the most significant bit. On input, nx and ny hold the numbers of row and column variables already in existence. On output, they hold the numbers of row and column variables actually used by the matrix. m and n are set to the numbers of rows and columns of the matrix. Their values on input are immaterial. Returns 1 on success; 0 otherwise. The ADD for the sparse matrix is returned in E, and its reference count is > 0.

Side Effects None

See Also Cudd_addRead Cudd_bddRead
DdNode * 
Cudd_addIteConstant(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode * h 
)
Implements ITEconstant for ADDs. f must be a 0-1 ADD. Returns a pointer to the resulting ADD (which may or may not be constant) or DD_NON_CONSTANT. No new nodes are created. This function can be used, for instance, to check that g has a constant value (specified by h) whenever f is 1. If the constant value is unknown, then one should use Cudd_addEvalConst.

Side Effects None

See Also Cudd_addIte Cudd_addEvalConst Cudd_bddIteConstant
DdNode * 
Cudd_addIte(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode * h 
)
Implements ITE(f,g,h). This procedure assumes that f is a 0-1 ADD. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddIte Cudd_addIteConstant Cudd_addApply
DdNode * 
Cudd_addIthBit(
  DdManager * dd, 
  DdNode * f, 
  int  bit 
)
Produces an ADD from another ADD by replacing all discriminants whose i-th bit is equal to 1 with 1, and all other discriminants with 0. The i-th bit refers to the integer representation of the leaf value. If the value is has a fractional part, it is ignored. Repeated calls to this procedure allow one to transform an integer-valued ADD into an array of ADDs, one for each bit of the leaf values. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addBddIthBit
DdNode * 
Cudd_addIthVar(
  DdManager * dd, 
  int  i 
)
Retrieves the ADD variable with index i if it already exists, or creates a new ADD variable. Returns a pointer to the variable if successful; NULL otherwise. An ADD variable differs from a BDD variable because it points to the arithmetic zero, instead of having a complement pointer to 1.

Side Effects None

See Also Cudd_addNewVar Cudd_bddIthVar Cudd_addConst Cudd_addNewVarAtLevel
int 
Cudd_addLeq(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Returns 1 if f is less than or equal to g; 0 otherwise. No new nodes are created. This procedure works for arbitrary ADDs. For 0-1 ADDs Cudd_addEvalConst is more efficient.

Side Effects None

See Also Cudd_addIteConstant Cudd_addEvalConst Cudd_bddLeq
DdNode * 
Cudd_addMatrixMultiply(
  DdManager * dd, 
  DdNode * A, 
  DdNode * B, 
  DdNode ** z, 
  int  nz 
)
Calculates the product of two matrices, A and B, represented as ADDs. This procedure implements the quasiring multiplication algorithm. A is assumed to depend on varibles x (rows) and z (columns). B is assumed to depend on varibles z (rows) and y (columns). The product of A and B then depends on x (rows) and y (columns). Only the z variables have to be explicitly identified; they are the "summation" variables. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_addTimesPlus Cudd_addTriangle Cudd_bddAndAbstract
DdNode * 
Cudd_addMaximum(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point max for Cudd_addApply. Returns NULL if not a terminal case; max(f,g) otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addMinimum(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point min for Cudd_addApply. Returns NULL if not a terminal case; min(f,g) otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addMinus(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point subtraction. Returns NULL if not a terminal case; f - g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addNand(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
NAND of two 0-1 ADDs. Returns NULL if not a terminal case; f NAND g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addNegate(
  DdManager * dd, 
  DdNode * f 
)
Computes the additive inverse of an ADD. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_addCmpl
DdNode * 
Cudd_addNewVarAtLevel(
  DdManager * dd, 
  int  level 
)
Creates a new ADD variable. The new variable has an index equal to the largest previous index plus 1 and is positioned at the specified level in the order. Returns a pointer to the new variable if successful; NULL otherwise.

Side Effects None

See Also Cudd_addNewVar Cudd_addIthVar Cudd_bddNewVarAtLevel
DdNode * 
Cudd_addNewVar(
  DdManager * dd 
)
Creates a new ADD variable. The new variable has an index equal to the largest previous index plus 1. Returns a pointer to the new variable if successful; NULL otherwise. An ADD variable differs from a BDD variable because it points to the arithmetic zero, instead of having a complement pointer to 1.

Side Effects None

See Also Cudd_bddNewVar Cudd_addIthVar Cudd_addConst Cudd_addNewVarAtLevel
DdNode * 
Cudd_addNonSimCompose(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** vector 
)
Given a vector of 0-1 ADDs, creates a new ADD by substituting the 0-1 ADDs for the variables of the ADD f. There should be an entry in vector for each variable in the manager. This function implements non-simultaneous composition. If any of the functions being composed depends on any of the variables being substituted, then the result depends on the order of composition, which in turn depends on the variable order: The variables farther from the roots in the order are substituted first. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addVectorCompose Cudd_addPermute Cudd_addCompose
DdNode * 
Cudd_addNor(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
NOR of two 0-1 ADDs. Returns NULL if not a terminal case; f NOR g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addOneZeroMaximum(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Returns 1 if f > g (both should be terminal cases) and 0 otherwise. Used in conjunction with Cudd_addApply. Returns NULL if not a terminal case.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addOrAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * cube 
)
Abstracts all the variables in cube from the 0-1 ADD f by taking the disjunction over all possible values taken by the variables. Returns the abstracted ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addUnivAbstract Cudd_addExistAbstract
DdNode * 
Cudd_addOr(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Disjunction of two 0-1 ADDs. Returns NULL if not a terminal case; f OR g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addPermute(
  DdManager * manager, 
  DdNode * node, 
  int * permut 
)
Given a permutation in array permut, creates a new ADD with permuted variables. There should be an entry in array permut for each variable in the manager. The i-th entry of permut holds the index of the variable that is to substitute the i-th variable. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddPermute Cudd_addSwapVariables
DdNode * 
Cudd_addPlus(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point addition. Returns NULL if not a terminal case; f+g otherwise.

Side Effects None

See Also Cudd_addApply
int 
Cudd_addRead(
  FILE * fp, input file pointer
  DdManager * dd, DD manager
  DdNode ** E, characteristic function of the graph
  DdNode *** x, array of row variables
  DdNode *** y, array of column variables
  DdNode *** xn, array of complemented row variables
  DdNode *** yn_, array of complemented column variables
  int * nx, number or row variables
  int * ny, number or column variables
  int * m, number of rows
  int * n, number of columns
  int  bx, first index of row variables
  int  sx, step of row variables
  int  by, first index of column variables
  int  sy step of column variables
)
Reads in a sparse matrix specified in a simple format. The first line of the input contains the numbers of rows and columns. The remaining lines contain the elements of the matrix, one per line. Given a background value (specified by the background field of the manager), only the values different from it are explicitly listed. Each foreground element is described by two integers, i.e., the row and column number, and a real number, i.e., the value.

Cudd_addRead produces an ADD that depends on two sets of variables: x and y. The x variables (x[0] ... x[nx-1]) encode the row index and the y variables (y[0] ... y[ny-1]) encode the column index. x[0] and y[0] are the most significant bits in the indices. The variables may already exist or may be created by the function. The index of x[i] is bx+i*sx, and the index of y[i] is by+i*sy.

On input, nx and ny hold the numbers of row and column variables already in existence. On output, they hold the numbers of row and column variables actually used by the matrix. When Cudd_addRead creates the variable arrays, the index of x[i] is bx+i*sx, and the index of y[i] is by+i*sy. When some variables already exist Cudd_addRead expects the indices of the existing x variables to be bx+i*sx, and the indices of the existing y variables to be by+i*sy.

m and n are set to the numbers of rows and columns of the matrix. Their values on input are immaterial. The ADD for the sparse matrix is returned in E, and its reference count is > 0. Cudd_addRead returns 1 in case of success; 0 otherwise.

Side Effects nx and ny are set to the numbers of row and column variables. m and n are set to the numbers of rows and columns. x and y are possibly extended to represent the array of row and column variables. Similarly for xn and yn_, which hold on return from Cudd_addRead the complements of the row and column variables.

See Also Cudd_addHarwell Cudd_bddRead
DdNode * 
Cudd_addResidue(
  DdManager * dd, manager
  int  n, number of bits
  int  m, modulus
  int  options, options
  int  top index of top variable
)
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.

Side Effects None

DdNode * 
Cudd_addRestrict(
  DdManager * dd, 
  DdNode * f, 
  DdNode * c 
)
ADD restrict according to Coudert and Madre's algorithm (ICCAD90). Returns the restricted ADD if successful; otherwise NULL. If application of restrict results in an ADD larger than the input ADD, the input ADD is returned.

Side Effects None

See Also Cudd_addConstrain Cudd_bddRestrict
DdNode * 
Cudd_addRoundOff(
  DdManager * dd, 
  DdNode * f, 
  int  N 
)
Rounds off the discriminants of an ADD. The discriminants are rounded off to N digits after the decimal. Returns a pointer to the result ADD if successful; NULL otherwise.

Side Effects None

DdNode * 
Cudd_addScalarInverse(
  DdManager * dd, 
  DdNode * f, 
  DdNode * epsilon 
)
Computes an n ADD where the discriminants are the multiplicative inverses of the corresponding discriminants of the argument ADD. Returns a pointer to the resulting ADD in case of success. Returns NULL if any discriminants smaller than epsilon is encountered.

Side Effects None

DdNode * 
Cudd_addSetNZ(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
This operator sets f to the value of g wherever g != 0. Returns NULL if not a terminal case; f op g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addSwapVariables(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** x, 
  DdNode ** y, 
  int  n 
)
Swaps two sets of variables of the same size (x and y) in the ADD f. The size is given by n. The two sets of variables are assumed to be disjoint. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addPermute Cudd_bddSwapVariables
DdNode * 
Cudd_addThreshold(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Threshold operator for Apply (f if f >=g; 0 if f<g). Returns NULL if not a terminal case; f op g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addTimesPlus(
  DdManager * dd, 
  DdNode * A, 
  DdNode * B, 
  DdNode ** z, 
  int  nz 
)
Calculates the product of two matrices, A and B, represented as ADDs, using the CMU matrix by matrix multiplication procedure by Clarke et al.. Matrix A has x's as row variables and z's as column variables, while matrix B has z's as row variables and y's as column variables. Returns the pointer to the result if successful; NULL otherwise. The resulting matrix has x's as row variables and y's as column variables.

Side Effects None

See Also Cudd_addMatrixMultiply
DdNode * 
Cudd_addTimes(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
Integer and floating point multiplication. Returns NULL if not a terminal case; f * g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addTriangle(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode ** z, 
  int  nz 
)
Implements the semiring multiplication algorithm used in the triangulation step for the shortest path computation. f is assumed to depend on varibles x (rows) and z (columns). g is assumed to depend on varibles z (rows) and y (columns). The product of f and g then depends on x (rows) and y (columns). Only the z variables have to be explicitly identified; they are the "abstraction" variables. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_addMatrixMultiply Cudd_bddAndAbstract
DdNode * 
Cudd_addUnivAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * cube 
)
Abstracts all the variables in cube from f by taking the product over all possible values taken by the variable. Returns the abstracted ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addExistAbstract Cudd_bddUnivAbstract Cudd_addOrAbstract
DdNode * 
Cudd_addVectorCompose(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** vector 
)
Given a vector of 0-1 ADDs, creates a new ADD by substituting the 0-1 ADDs for the variables of the ADD f. There should be an entry in vector for each variable in the manager. If no substitution is sought for a given variable, the corresponding projection function should be specified in the vector. This function implements simultaneous composition. Returns a pointer to the resulting ADD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addNonSimCompose Cudd_addPermute Cudd_addCompose Cudd_bddVectorCompose
DdNode * 
Cudd_addWalsh(
  DdManager * dd, 
  DdNode ** x, 
  DdNode ** y, 
  int  n 
)
Generates a Walsh matrix in ADD form. Returns a pointer to the matrixi if successful; NULL otherwise.

Side Effects None

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
)
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].

Side Effects None

See Also Cudd_Xeqy
DdNode * 
Cudd_addXnor(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
XNOR of two 0-1 ADDs. Returns NULL if not a terminal case; f XNOR g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_addXor(
  DdManager * dd, 
  DdNode ** f, 
  DdNode ** g 
)
XOR of two 0-1 ADDs. Returns NULL if not a terminal case; f XOR g otherwise.

Side Effects None

See Also Cudd_addApply
DdNode * 
Cudd_bddAdjPermuteX(
  DdManager * dd, 
  DdNode * B, 
  DdNode ** x, 
  int  n 
)
Rearranges a set of variables in the BDD B. The size of the set is given by n. This procedure is intended for the `randomization' of the priority functions. Returns a pointer to the BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddPermute Cudd_bddSwapVariables Cudd_Dxygtdxz Cudd_Dxygtdyz Cudd_PrioritySelect
DdNode * 
Cudd_bddAndAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * g, 
  DdNode * cube 
)
Takes the AND of two BDDs and simultaneously abstracts the variables in cube. The variables are existentially abstracted. Returns a pointer to the result is successful; NULL otherwise. Cudd_bddAndAbstract implements the semiring matrix multiplication algorithm for the boolean semiring.

Side Effects None

See Also Cudd_addMatrixMultiply Cudd_addTriangle Cudd_bddAnd
DdNode * 
Cudd_bddAnd(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the conjunction of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAndAbstract Cudd_bddIntersect Cudd_bddOr Cudd_bddNand Cudd_bddNor Cudd_bddXor Cudd_bddXnor
int 
Cudd_bddApproxConjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** conjuncts address of the first factor
)
Performs two-way conjunctive decomposition of a BDD. This procedure owes its name to the use of supersetting to obtain an initial factor of the given function. Returns the number of conjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The conjuncts produced by this procedure tend to be imbalanced.

Side Effects The factors are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the conjuncts are already referenced. If the function returns 0, the array for the conjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddApproxDisjDecomp Cudd_bddIterConjDecomp Cudd_bddGenConjDecomp Cudd_bddVarConjDecomp Cudd_RemapOverApprox Cudd_bddSqueeze Cudd_bddLICompaction
int 
Cudd_bddApproxDisjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** disjuncts address of the array of the disjuncts
)
Performs two-way disjunctive decomposition of a BDD. Returns the number of disjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The disjuncts produced by this procedure tend to be imbalanced.

Side Effects The two disjuncts are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the disjuncts are already referenced. If the function returns 0, the array for the disjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddApproxConjDecomp Cudd_bddIterDisjDecomp Cudd_bddGenDisjDecomp Cudd_bddVarDisjDecomp
DdNode * 
Cudd_bddBooleanDiff(
  DdManager * manager, 
  DdNode * f, 
  int  x 
)
Computes the boolean difference of f with respect to the variable with index x. Returns the BDD of the boolean difference if successful; NULL otherwise.

Side Effects None

DdNode ** 
Cudd_bddCharToVect(
  DdManager * dd, 
  DdNode * f 
)
Computes a vector of BDDs whose image equals a non-zero function. The result depends on the variable order. The i-th component of the vector depends only on the first i variables in the order. Each BDD in the vector is not larger than the BDD of the given characteristic function. This function is based on the description of char-to-vect in "Verification of Sequential Machines Using Boolean Functional Vectors" by O. Coudert, C. Berthet and J. C. Madre. Returns a pointer to an array containing the result if successful; NULL otherwise. The size of the array equals the number of variables in the manager. The components of the solution have their reference counts already incremented (unlike the results of most other functions in the package.

Side Effects None

See Also Cudd_bddConstrain
DdNode * 
Cudd_bddClippingAndAbstract(
  DdManager * dd, manager
  DdNode * f, first conjunct
  DdNode * g, second conjunct
  DdNode * cube, cube of variables to be abstracted
  int  maxDepth, maximum recursion depth
  int  direction under (0) or over (1) approximation
)
Approximates the conjunction of two BDDs f and g and simultaneously abstracts the variables in cube. The variables are existentially abstracted. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddAndAbstract Cudd_bddClippingAnd
DdNode * 
Cudd_bddClippingAnd(
  DdManager * dd, manager
  DdNode * f, first conjunct
  DdNode * g, second conjunct
  int  maxDepth, maximum recursion depth
  int  direction under (0) or over (1) approximation
)
Approximates the conjunction of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddAnd
DdNode * 
Cudd_bddCompose(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  int  v 
)
Substitutes g for x_v in the BDD for f. v is the index of the variable to be substituted. Cudd_bddCompose passes the corresponding projection function to the recursive procedure, so that the cache may be used. Returns the composed BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addCompose
DdNode * 
Cudd_bddComputeCube(
  DdManager * dd, 
  DdNode ** vars, 
  int * phase, 
  int  n 
)
Computes the cube of an array of BDD variables. If non-null, the phase argument indicates which literal of each variable should appear in the cube. If phase[i] is nonzero, then the positive literal is used. If phase is NULL, the cube is positive unate. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_addComputeCube Cudd_IndicesToCube
DdNode ** 
Cudd_bddConstrainDecomp(
  DdManager * dd, 
  DdNode * f 
)
BDD conjunctive decomposition as in McMillan's CAV96 paper. The decomposition is canonical only for a given variable order. If canonicity is required, variable ordering must be disabled after the decomposition has been computed. Returns an array with one entry for each BDD variable in the manager if successful; otherwise NULL. The components of the solution have their reference counts already incremented (unlike the results of most other functions in the package.

Side Effects None

See Also Cudd_bddConstrain Cudd_bddExistAbstract
DdNode * 
Cudd_bddConstrain(
  DdManager * dd, 
  DdNode * f, 
  DdNode * c 
)
Computes f constrain c (f @ c). Uses a canonical form: (f' @ c) = ( f @ c)'. (Note: this is not true for c.) List of special cases: Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddRestrict Cudd_addConstrain
double 
Cudd_bddCorrelationWeights(
  DdManager * manager, 
  DdNode * f, 
  DdNode * g, 
  double * prob 
)
Computes the correlation of f and g for given input probabilities. On input, prob[i] is supposed to contain the probability of the i-th input variable to be 1. If f == g, their correlation is 1. If f == g', their correlation is 0. Returns the probability that f and g have the same value. If it runs out of memory, returns (double)CUDD_OUT_OF_MEM. The correlation of f and the constant one gives the probability of f.

Side Effects None

See Also Cudd_bddCorrelation
double 
Cudd_bddCorrelation(
  DdManager * manager, 
  DdNode * f, 
  DdNode * g 
)
Computes the correlation of f and g. If f == g, their correlation is 1. If f == g', their correlation is 0. Returns the fraction of minterms in the ON-set of the EXNOR of f and g. If it runs out of memory, returns (double)CUDD_OUT_OF_MEM.

Side Effects None

See Also Cudd_bddCorrelationWeights
DdNode * 
Cudd_bddExistAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * cube 
)
Existentially abstracts all the variables in cube from f. Returns the abstracted BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddUnivAbstract Cudd_addExistAbstract
int 
Cudd_bddGenConjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** conjuncts address of the array of conjuncts
)
Performs two-way conjunctive decomposition of a BDD. This procedure owes its name to the fact tht it generalizes the decomposition based on the cofactors with respect to one variable. Returns the number of conjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The conjuncts produced by this procedure tend to be balanced.

Side Effects The two factors are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the conjuncts are already referenced. If the function returns 0, the array for the conjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddGenDisjDecomp Cudd_bddApproxConjDecomp Cudd_bddIterConjDecomp Cudd_bddVarConjDecomp
int 
Cudd_bddGenDisjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** disjuncts address of the array of the disjuncts
)
Performs two-way disjunctive decomposition of a BDD. Returns the number of disjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The disjuncts produced by this procedure tend to be balanced.

Side Effects The two disjuncts are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the disjuncts are already referenced. If the function returns 0, the array for the disjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddGenConjDecomp Cudd_bddApproxDisjDecomp Cudd_bddIterDisjDecomp Cudd_bddVarDisjDecomp
DdNode * 
Cudd_bddIntersect(
  DdManager * dd, manager
  DdNode * f, first operand
  DdNode * g second operand
)
Computes a function included in the intersection of f and g. (That is, a witness that the intersection is not empty.) Cudd_bddIntersect tries to build as few new nodes as possible. If the only result of interest is whether f and g intersect, Cudd_bddLeq should be used instead.

Side Effects None

See Also Cudd_bddLeq Cudd_bddIteConstant
int 
Cudd_bddIsVarEssential(
  DdManager * manager, 
  DdNode * f, 
  int  id, 
  int  phase 
)
Determines whether a given variable is essential with a given phase in a BDD. Uses Cudd_bddIteConstant. Returns 1 if phase == 1 and f-->x_id, or if phase == 0 and f-->x_id'.

Side Effects None

See Also Cudd_FindEssential
DdNode	* 
Cudd_bddIsop(
  DdManager * dd, 
  DdNode * L, 
  DdNode * U 
)
Computes a BDD in the interval between L and U with a simple sum-of-produuct cover. This procedure is similar to Cudd_zddIsop, but it does not return the ZDD for the cover. Returns a pointer to the BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddIsop
DdNode * 
Cudd_bddIteConstant(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode * h 
)
Implements ITEconstant(f,g,h). Returns a pointer to the resulting BDD (which may or may not be constant) or DD_NON_CONSTANT. No new nodes are created.

Side Effects None

See Also Cudd_bddIte Cudd_bddIntersect Cudd_bddLeq Cudd_addIteConstant
int 
Cudd_bddIterConjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** conjuncts address of the array of conjuncts
)
Performs two-way conjunctive decomposition of a BDD. This procedure owes its name to the iterated use of supersetting to obtain a factor of the given function. Returns the number of conjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The conjuncts produced by this procedure tend to be imbalanced.

Side Effects The factors are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the conjuncts are already referenced. If the function returns 0, the array for the conjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddIterDisjDecomp Cudd_bddApproxConjDecomp Cudd_bddGenConjDecomp Cudd_bddVarConjDecomp Cudd_RemapOverApprox Cudd_bddSqueeze Cudd_bddLICompaction
int 
Cudd_bddIterDisjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** disjuncts address of the array of the disjuncts
)
Performs two-way disjunctive decomposition of a BDD. Returns the number of disjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise. The disjuncts produced by this procedure tend to be imbalanced.

Side Effects The two disjuncts are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the disjuncts are already referenced. If the function returns 0, the array for the disjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddIterConjDecomp Cudd_bddApproxDisjDecomp Cudd_bddGenDisjDecomp Cudd_bddVarDisjDecomp
DdNode * 
Cudd_bddIte(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode * h 
)
Implements ITE(f,g,h). Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_addIte Cudd_bddIteConstant Cudd_bddIntersect
DdNode * 
Cudd_bddIthVar(
  DdManager * dd, 
  int  i 
)
Retrieves the BDD variable with index i if it already exists, or creates a new BDD variable. Returns a pointer to the variable if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddNewVar Cudd_addIthVar Cudd_bddNewVarAtLevel
DdNode * 
Cudd_bddLICompaction(
  DdManager * dd, manager
  DdNode * f, function to be minimized
  DdNode * c constraint (care set)
)
Performs safe minimization of a BDD. Given the BDD f of a function to be minimized and a BDD c representing the care set, Cudd_bddLICompaction produces the BDD of a function that agrees with f wherever c is 1. Safe minimization means that the size of the result is guaranteed not to exceed the size of f. This function is based on the DAC97 paper by Hong et al.. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddRestrict
int 
Cudd_bddLeq(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Returns 1 if f is less than or equal to g; 0 otherwise. No new nodes are created.

Side Effects None

See Also Cudd_bddIteConstant Cudd_addEvalConst
DdNode * 
Cudd_bddLiteralSetIntersection(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the intesection of two sets of literals represented as BDDs. Each set is represented as a cube of the literals in the set. The empty set is represented by the constant 1. No variable can be simultaneously present in both phases in a set. Returns a pointer to the BDD representing the intersected sets, if successful; NULL otherwise.

Side Effects None

DdNode * 
Cudd_bddMinimize(
  DdManager * dd, 
  DdNode * f, 
  DdNode * c 
)
Finds a small BDD that agrees with f over c. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddRestrict Cudd_bddLICompaction Cudd_bddSqueeze
DdNode * 
Cudd_bddNand(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the NAND of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAnd Cudd_bddOr Cudd_bddNor Cudd_bddXor Cudd_bddXnor
DdNode * 
Cudd_bddNewVarAtLevel(
  DdManager * dd, 
  int  level 
)
Creates a new BDD variable. The new variable has an index equal to the largest previous index plus 1 and is positioned at the specified level in the order. Returns a pointer to the new variable if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddNewVar Cudd_bddIthVar Cudd_addNewVarAtLevel
DdNode * 
Cudd_bddNewVar(
  DdManager * dd 
)
Creates a new BDD variable. The new variable has an index equal to the largest previous index plus 1. Returns a pointer to the new variable if successful; NULL otherwise.

Side Effects None

See Also Cudd_addNewVar Cudd_bddIthVar Cudd_bddNewVarAtLevel
DdNode * 
Cudd_bddNor(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the NOR of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAnd Cudd_bddOr Cudd_bddNand Cudd_bddXor Cudd_bddXnor
DdNode * 
Cudd_bddOr(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the disjunction of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAnd Cudd_bddNand Cudd_bddNor Cudd_bddXor Cudd_bddXnor
DdNode * 
Cudd_bddPermute(
  DdManager * manager, 
  DdNode * node, 
  int * permut 
)
Given a permutation in array permut, creates a new BDD with permuted variables. There should be an entry in array permut for each variable in the manager. The i-th entry of permut holds the index of the variable that is to substitute the i-th variable. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_addPermute Cudd_bddSwapVariables
DdNode ** 
Cudd_bddPickArbitraryMinterms(
  DdManager * dd, manager
  DdNode * f, function from which to pick one minterm
  DdNode ** vars, array of variables
  int  n, size of vars
  int  k number of minterms to find
)
Picks k on-set minterms evenly distributed from given DD. The minterms are in terms of vars. The array vars should contain at least all variables in the support of f; if this condition is not met the minterms built by this procedure may not be contained in f. Builds a BDD for the minterms and returns a pointer to it if successful; NULL otherwise. There are three reasons why the procedure may fail:

Side Effects None

See Also Cudd_bddPickOneMinterm Cudd_bddPickOneCube
int 
Cudd_bddPickOneCube(
  DdManager * ddm, 
  DdNode * node, 
  char * string 
)
Picks one on-set cube randomly from the given DD. The cube is written into an array of characters. The array must have at least as many entries as there are variables. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_bddPickOneMinterm
DdNode * 
Cudd_bddPickOneMinterm(
  DdManager * dd, manager
  DdNode * f, function from which to pick one minterm
  DdNode ** vars, array of variables
  int  n size of vars
)
Picks one on-set minterm randomly from the given DD. The minterm is in terms of vars. The array vars should contain at least all variables in the support of f; if this condition is not met the minterm built by this procedure may not be contained in f. Builds a BDD for the minterm and returns a pointer to it if successful; NULL otherwise. There are three reasons why the procedure may fail:

Side Effects None

See Also Cudd_bddPickOneCube
int 
Cudd_bddRead(
  FILE * fp, input file pointer
  DdManager * dd, DD manager
  DdNode ** E, characteristic function of the graph
  DdNode *** x, array of row variables
  DdNode *** y, array of column variables
  int * nx, number or row variables
  int * ny, number or column variables
  int * m, number of rows
  int * n, number of columns
  int  bx, first index of row variables
  int  sx, step of row variables
  int  by, first index of column variables
  int  sy step of column variables
)
Reads in a graph (without labels) given as an adjacency matrix. The first line of the input contains the numbers of rows and columns of the adjacency matrix. The remaining lines contain the arcs of the graph, one per line. Each arc is described by two integers, i.e., the row and column number, or the indices of the two endpoints. Cudd_bddRead produces a BDD that depends on two sets of variables: x and y. The x variables (x[0] ... x[nx-1]) encode the row index and the y variables (y[0] ... y[ny-1]) encode the column index. x[0] and y[0] are the most significant bits in the indices. The variables may already exist or may be created by the function. The index of x[i] is bx+i*sx, and the index of y[i] is by+i*sy.

On input, nx and ny hold the numbers of row and column variables already in existence. On output, they hold the numbers of row and column variables actually used by the matrix. When Cudd_bddRead creates the variable arrays, the index of x[i] is bx+i*sx, and the index of y[i] is by+i*sy. When some variables already exist, Cudd_bddRead expects the indices of the existing x variables to be bx+i*sx, and the indices of the existing y variables to be by+i*sy.

m and n are set to the numbers of rows and columns of the matrix. Their values on input are immaterial. The BDD for the graph is returned in E, and its reference count is > 0. Cudd_bddRead returns 1 in case of success; 0 otherwise.

Side Effects nx and ny are set to the numbers of row and column variables. m and n are set to the numbers of rows and columns. x and y are possibly extended to represent the array of row and column variables.

See Also Cudd_addHarwell Cudd_addRead
void 
Cudd_bddRealignDisable(
  DdManager * unique 
)
Disables realignment of ZDD order to BDD order.

Side Effects None

See Also Cudd_bddRealignEnable Cudd_bddRealignmentEnabled Cudd_zddRealignEnable Cudd_zddRealignmentEnabled
void 
Cudd_bddRealignEnable(
  DdManager * unique 
)
Enables realignment of the BDD variable order to the ZDD variable order after the ZDDs have been reordered. The number of ZDD variables must be a multiple of the number of BDD variables for realignment to make sense. If this condition is not met, Cudd_zddReduceHeap will return 0. Let M be the ratio of the two numbers. For the purpose of realignment, the ZDD variables from M*i to (M+1)*i-1 are reagarded as corresponding to BDD variable i. Realignment is initially disabled.

Side Effects None

See Also Cudd_zddReduceHeap Cudd_bddRealignDisable Cudd_bddRealignmentEnabled Cudd_zddRealignDisable Cudd_zddRealignmentEnabled
int 
Cudd_bddRealignmentEnabled(
  DdManager * unique 
)
Returns 1 if the realignment of BDD order to ZDD order is enabled; 0 otherwise.

Side Effects None

See Also Cudd_bddRealignEnable Cudd_bddRealignDisable Cudd_zddRealignEnable Cudd_zddRealignDisable
DdNode * 
Cudd_bddRestrict(
  DdManager * dd, 
  DdNode * f, 
  DdNode * c 
)
BDD restrict according to Coudert and Madre's algorithm (ICCAD90). Returns the restricted BDD if successful; otherwise NULL. If application of restrict results in a BDD larger than the input BDD, the input BDD is returned.

Side Effects None

See Also Cudd_bddConstrain Cudd_addRestrict
DdNode * 
Cudd_bddSqueeze(
  DdManager * dd, manager
  DdNode * l, lower bound
  DdNode * u upper bound
)
Finds a small BDD in a function interval. Given BDDs l and u, representing the lower bound and upper bound of a function interval, Cudd_bddSqueeze produces the BDD of a function within the interval with a small BDD. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddRestrict Cudd_bddLICompaction
DdNode * 
Cudd_bddSwapVariables(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** x, 
  DdNode ** y, 
  int  n 
)
Swaps two sets of variables of the same size (x and y) in the BDD f. The size is given by n. The two sets of variables are assumed to be disjoint. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddPermute Cudd_addSwapVariables
DdNode * 
Cudd_bddTransfer(
  DdManager * ddSource, 
  DdManager * ddDestination, 
  DdNode * f 
)
Convert a BDD from a manager to another one. Returns a pointer to the BDD in the destination manager if successful; NULL otherwise.

Side Effects None

DdNode * 
Cudd_bddUnivAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * cube 
)
Universally abstracts all the variables in cube from f. Returns the abstracted BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddExistAbstract Cudd_addUnivAbstract
int 
Cudd_bddVarConjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** conjuncts address of the array of conjuncts
)
Conjunctively decomposes one BDD according to a variable. If f is the function of the BDD and x is the variable, the decomposition is (f+x)(f+x'). The variable is chosen so as to balance the sizes of the two conjuncts and to keep them small. Returns the number of conjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise.

Side Effects The two factors are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the conjuncts are already referenced. If the function returns 0, the array for the conjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddVarDisjDecomp Cudd_bddGenConjDecomp Cudd_bddApproxConjDecomp Cudd_bddIterConjDecomp
int 
Cudd_bddVarDisjDecomp(
  DdManager * dd, manager
  DdNode * f, function to be decomposed
  DdNode *** disjuncts address of the array of the disjuncts
)
Performs two-way disjunctive decomposition of a BDD according to a variable. If f is the function of the BDD and x is the variable, the decomposition is f*x + f*x'. The variable is chosen so as to balance the sizes of the two disjuncts and to keep them small. Returns the number of disjuncts produced, that is, 2 if successful; 1 if no meaningful decomposition was found; 0 otherwise.

Side Effects The two disjuncts are returned in an array as side effects. The array is allocated by this function. It is the caller's responsibility to free it. On successful completion, the disjuncts are already referenced. If the function returns 0, the array for the disjuncts is not allocated. If the function returns 1, the only factor equals the function to be decomposed.

See Also Cudd_bddVarConjDecomp Cudd_bddApproxDisjDecomp Cudd_bddIterDisjDecomp Cudd_bddGenDisjDecomp
int 
Cudd_bddVarIsDependent(
  DdManager * dd, 
  DdNode * f, 
  DdNode * var variable
)
Checks whether a variable is dependent on others in a function. Returns 1 if the variable is dependent; 0 otherwise. No new nodes are created.

Side Effects None

DdNode * 
Cudd_bddVectorCompose(
  DdManager * dd, 
  DdNode * f, 
  DdNode ** vector 
)
Given a vector of BDDs, creates a new BDD by substituting the BDDs for the variables of the BDD f. There should be an entry in vector for each variable in the manager. If no substitution is sought for a given variable, the corresponding projection function should be specified in the vector. This function implements simultaneous composition. Returns a pointer to the resulting BDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddPermute Cudd_bddCompose Cudd_addVectorCompose
DdNode * 
Cudd_bddXnor(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the exclusive NOR of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAnd Cudd_bddOr Cudd_bddNand Cudd_bddNor Cudd_bddXor
DdNode * 
Cudd_bddXorExistAbstract(
  DdManager * manager, 
  DdNode * f, 
  DdNode * g, 
  DdNode * cube 
)
Takes the exclusive OR of two BDDs and simultaneously abstracts the variables in cube. The variables are existentially abstracted. Returns a pointer to the result is successful; NULL otherwise.

Side Effects None

See Also Cudd_bddUnivAbstract Cudd_bddExistAbstract Cudd_bddAndAbstract
DdNode * 
Cudd_bddXor(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the exclusive OR of two BDDs f and g. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

Side Effects None

See Also Cudd_bddIte Cudd_addApply Cudd_bddAnd Cudd_bddOr Cudd_bddNand Cudd_bddNor Cudd_bddXnor
DdNode * 
Cudd_zddChange(
  DdManager * dd, 
  DdNode * P, 
  int  var 
)
Substitutes a variable with its complement in a ZDD. returns a pointer to the result if successful; NULL otherwise.

Side Effects None

double 
Cudd_zddCountDouble(
  DdManager * zdd, 
  DdNode * P 
)
Counts the number of minterms of a ZDD. The result is returned as a double. If the procedure runs out of memory, it returns CUDD_OUT_OF_MEM. This procedure is used in Cudd_zddCountMinterm.

Side Effects None

See Also Cudd_zddCountMinterm Cudd_zddCount
double 
Cudd_zddCountMinterm(
  DdManager * zdd, 
  DdNode * node, 
  int  path 
)
Counts the number of minterms of the ZDD rooted at node. This procedure takes a parameter path that specifies how many variables are in the support of the function.

Side Effects None

See Also Cudd_zddCountDouble
int 
Cudd_zddCount(
  DdManager * zdd, 
  DdNode * P 
)
Returns an integer representing the number of minterms in a ZDD.

Side Effects None

See Also Cudd_zddCountDouble
int 
Cudd_zddDagSize(
  DdNode * p_node 
)
Counts the number of nodes in a ZDD. This function duplicates Cudd_DagSize and is only retained for compatibility.

Side Effects None

See Also Cudd_DagSize
DdNode * 
Cudd_zddDiffConst(
  DdManager * zdd, 
  DdNode * P, 
  DdNode * Q 
)
Inclusion test for ZDDs (P implies Q). No new nodes are generated by this procedure. Returns empty if true; a valid pointer different from empty or DD_NON_CONSTANT otherwise.

Side Effects None

See Also Cudd_zddDiff
DdNode * 
Cudd_zddDiff(
  DdManager * dd, 
  DdNode * P, 
  DdNode * Q 
)
Computes the difference of two ZDDs. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddDiffConst
DdNode	* 
Cudd_zddDivideF(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Modified version of Cudd_zddDivide. This function may disappear in future releases.

Side Effects None

DdNode	* 
Cudd_zddDivide(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the quotient of two unate covers represented by ZDDs. Unate covers use one ZDD variable for each BDD variable. Returns a pointer to the resulting ZDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddWeakDiv
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
)
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: The dot options are chosen so that the drawing fits on a letter-size sheet.

Side Effects None

See Also Cudd_DumpDot Cudd_zddPrintDebug
DdNode * 
Cudd_zddIntersect(
  DdManager * dd, 
  DdNode * P, 
  DdNode * Q 
)
Computes the intersection of two ZDDs. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

DdNode	* 
Cudd_zddIsop(
  DdManager * dd, 
  DdNode * L, 
  DdNode * U, 
  DdNode ** zdd_I 
)
Computes an irredundant sum of products (ISOP) in ZDD form from BDDs. The two BDDs L and U represent the lower bound and the upper bound, respectively, of the function. The ISOP uses two ZDD variables for each BDD variable: One for the positive literal, and one for the negative literal. These two variables should be adjacent in the ZDD order. The two ZDD variables corresponding to BDD variable i should have indices 2i and 2i+1. The result of this procedure depends on the variable order. If successful, Cudd_zddIsop returns the BDD for the function chosen from the interval. The ZDD representing the irredundant cover is returned as a side effect in zdd_I. In case of failure, NULL is returned.

Side Effects zdd_I holds the pointer to the ZDD for the ISOP on successful return.

See Also Cudd_bddIsop Cudd_zddVarsFromBddVars
DdNode * 
Cudd_zddIte(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g, 
  DdNode * h 
)
Computes the ITE of three ZDDs. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

DdNode * 
Cudd_zddIthVar(
  DdManager * dd, 
  int  i 
)
Retrieves the ZDD variable with index i if it already exists, or creates a new ZDD variable. Returns a pointer to the variable if successful; NULL otherwise.

Side Effects None

See Also Cudd_bddIthVar Cudd_addIthVar
DdNode * 
Cudd_zddPortFromBdd(
  DdManager * dd, 
  DdNode * B 
)
Converts a BDD into a ZDD. This function assumes that there is a one-to-one correspondence between the BDD variables and the ZDD variables, and that the variable order is the same for both types of variables. These conditions are established if the ZDD variables are created by one call to Cudd_zddVarsFromBddVars with multiplicity = 1. Returns a pointer to the resulting ZDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddVarsFromBddVars
DdNode * 
Cudd_zddPortToBdd(
  DdManager * dd, 
  DdNode * f 
)
Converts a ZDD into a BDD. Returns a pointer to the resulting ZDD if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddPortFromBdd
int 
Cudd_zddPrintDebug(
  DdManager * zdd, 
  DdNode * f, 
  int  n, 
  int  pr 
)
Prints to the standard output a DD and its statistics. The statistics include the number of nodes and the number of minterms. (The number of minterms is also the number of combinations in the set.) The statistics are printed if pr > 0. Specifically: Returns 1 if successful; 0 otherwise.

Side Effects None

int 
Cudd_zddPrintMinterm(
  DdManager * zdd, 
  DdNode * node 
)

Side Effects None

See Also Cudd_zddPrintDebug
void 
Cudd_zddPrintSubtable(
  DdManager * table 
)
Prints the ZDD table for debugging purposes.

Side Effects None

DdNode	* 
Cudd_zddProduct(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the product of two covers represented by ZDDs. The result is also a ZDD. Returns a pointer to the result if successful; NULL otherwise. The covers on which Cudd_zddProduct operates use two ZDD variables for each function variable (one ZDD variable for each literal of the variable). Those two ZDD variables should be adjacent in the order.

Side Effects None

See Also Cudd_zddUnateProduct
long 
Cudd_zddReadNodeCount(
  DdManager * dd 
)
Reports the number of nodes in ZDDs. This number always includes the two constants 1 and 0.

Side Effects None

See Also Cudd_ReadPeakNodeCount Cudd_ReadNodeCount
void 
Cudd_zddRealignDisable(
  DdManager * unique 
)
Disables realignment of ZDD order to BDD order.

Side Effects None

See Also Cudd_zddRealignEnable Cudd_zddRealignmentEnabled Cudd_bddRealignEnable Cudd_bddRealignmentEnabled
void 
Cudd_zddRealignEnable(
  DdManager * unique 
)
Enables realignment of the ZDD variable order to the BDD variable order after the BDDs and ADDs have been reordered. The number of ZDD variables must be a multiple of the number of BDD variables for realignment to make sense. If this condition is not met, Cudd_ReduceHeap will return 0. Let M be the ratio of the two numbers. For the purpose of realignment, the ZDD variables from M*i to (M+1)*i-1 are reagarded as corresponding to BDD variable i. Realignment is initially disabled.

Side Effects None

See Also Cudd_ReduceHeap Cudd_zddRealignDisable Cudd_zddRealignmentEnabled Cudd_bddRealignDisable Cudd_bddRealignmentEnabled
int 
Cudd_zddRealignmentEnabled(
  DdManager * unique 
)
Returns 1 if the realignment of ZDD order to BDD order is enabled; 0 otherwise.

Side Effects None

See Also Cudd_zddRealignEnable Cudd_zddRealignDisable Cudd_bddRealignEnable Cudd_bddRealignDisable
int 
Cudd_zddReduceHeap(
  DdManager * table, DD manager
  Cudd_ReorderingType  heuristic, method used for reordering
  int  minsize bound below which no reordering occurs
)
Main dynamic reordering routine for ZDDs. Calls one of the possible reordering procedures: For sifting and symmetric sifting it is possible to request reordering to convergence.

The core of all methods is the reordering procedure cuddZddSwapInPlace() which swaps two adjacent variables. Returns 1 in case of success; 0 otherwise. In the case of symmetric sifting (with and without convergence) returns 1 plus the number of symmetric variables, in case of success.

Side Effects Changes the variable order for all ZDDs and clears the cache.

int 
Cudd_zddShuffleHeap(
  DdManager * table, DD manager
  int * permutation required variable permutation
)
Reorders ZDD variables according to given permutation. The i-th entry of the permutation array contains the index of the variable that should be brought to the i-th level. The size of the array should be equal or greater to the number of variables currently in use. Returns 1 in case of success; 0 otherwise.

Side Effects Changes the ZDD variable order for all diagrams and clears the cache.

See Also Cudd_zddReduceHeap
DdNode * 
Cudd_zddSubset0(
  DdManager * dd, 
  DdNode * P, 
  int  var 
)
Computes the negative cofactor of a ZDD w.r.t. a variable. In terms of combinations, the result is the set of all combinations in which the variable is negated. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddSubset1
DdNode * 
Cudd_zddSubset1(
  DdManager * dd, 
  DdNode * P, 
  int  var 
)
Computes the positive cofactor of a ZDD w.r.t. a variable. In terms of combinations, the result is the set of all combinations in which the variable is asserted. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddSubset0
void 
Cudd_zddSymmProfile(
  DdManager * table, 
  int  lower, 
  int  upper 
)
Prints statistics on symmetric ZDD variables.

Side Effects None

DdNode	* 
Cudd_zddUnateProduct(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Computes the product of two unate covers represented as ZDDs. Unate covers use one ZDD variable for each BDD variable. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

See Also Cudd_zddProduct
DdNode * 
Cudd_zddUnion(
  DdManager * dd, 
  DdNode * P, 
  DdNode * Q 
)
Computes the union of two ZDDs. Returns a pointer to the result if successful; NULL otherwise.

Side Effects None

int 
Cudd_zddVarsFromBddVars(
  DdManager * dd, DD manager
  int  multiplicity how many ZDD variables are created for each BDD variable
)
Creates one or more ZDD variables for each BDD variable. If some ZDD variables already exist, only the missing variables are created. Parameter multiplicity allows the caller to control how many variables are created for each BDD variable in existence. For instance, if ZDDs are used to represent covers, two ZDD variables are required for each BDD variable. The order of the BDD variables is transferred to the ZDD variables. If a variable group tree exists for the BDD variables, a corresponding ZDD variable group tree is created by expanding the BDD variable tree. In any case, the ZDD variables derived from the same BDD variable are merged in a ZDD variable group. If a ZDD variable group tree exists, it is freed. Returns 1 if successful; 0 otherwise.

Side Effects None

See Also Cudd_bddNewVar Cudd_bddIthVar Cudd_bddNewVarAtLevel
DdNode	* 
Cudd_zddWeakDivF(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Modified version of Cudd_zddWeakDiv. This function may disappear in future releases.

Side Effects None

See Also Cudd_zddWeakDiv
DdNode	* 
Cudd_zddWeakDiv(
  DdManager * dd, 
  DdNode * f, 
  DdNode * g 
)
Applies weak division to two ZDDs representing two covers. Returns a pointer to the ZDD representing the result if successful; NULL otherwise. The result of weak division depends on the variable order. The covers on which Cudd_zddWeakDiv operates use two ZDD variables for each function variable (one ZDD variable for each literal of the variable). Those two ZDD variables should be adjacent in the order.

Side Effects None

See Also Cudd_zddDivide

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