# The cudd package (Internal)

## Internal data structures of the CUDD package.

###

- ### External abstracts

- ### All abstracts

- ### External functions

- ### All functions

    int
    Cudd_AddHook(
      DdManager * dd,
      int  (*f)(DdManager *, char *, void *),
      Cudd_HookType  where
    )

  Adds a function to a hook. A hook is a list of application-provided functions called on certain occasions by the package. Returns 1 if the function is successfully added; 2 if the function was already in the list; 0 otherwise.

  Side Effects None

  See Also `Cudd_RemoveHook`

    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`

    int
    Cudd_BddToCubeArray(
      DdManager * dd,
      DdNode * cube,
      int * array
    )

  Builds a positional array from the BDD of a cube. Array must have one entry for each BDD variable. The positional array has 1 in i-th position if the variable of index i appears in true form in the cube; it has 0 in i-th position if the variable of index i appears in complemented form in the cube; finally, it has 2 in i-th position if the variable of index i does not appear in the cube. Returns 1 if successful (the BDD is indeed a cube); 0 otherwise.

  Side Effects The result is in the array passed by reference.

  See Also `Cudd_CubeArrayToBdd`

    DdNode *
    Cudd_BiasedOverApprox(
      DdManager * dd, manager
      DdNode * f, function to be superset
      DdNode * b, bias function
      int  numVars, number of variables in the support of f
      int  threshold, when to stop approximation
      double  quality1, minimum improvement for accepted changes when b=1
      double  quality0 minimum improvement for accepted changes when b=0
    )

  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_RemapOverApprox Cudd_BiasedUnderApprox Cudd_ReadSize`

    DdNode *
    Cudd_BiasedUnderApprox(
      DdManager * dd, manager
      DdNode * f, function to be subset
      DdNode * b, bias function
      int  numVars, number of variables in the support of f
      int  threshold, when to stop approximation
      double  quality1, minimum improvement for accepted changes when b=1
      double  quality0 minimum improvement for accepted changes when b=0
    )

  Extracts a dense subset from a BDD. This procedure uses a biased remapping technique and density as the cost function. The bias is a function. This procedure tries to approximate where the bias is 0 and preserve the given function where the bias is 1. 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_RemapUnderApprox Cudd_ReadSize`

    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:
  - Wrong sizes of subtables.
  - Wrong number of keys found in unique subtable.
  - Wrong number of dead found in unique subtable.
  - Wrong number of keys found in the constant table
  - Wrong number of dead found in the constant table
  - Wrong number of total slots found
  - Wrong number of maximum keys found
  - Wrong number of total dead found
  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 if 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_CountPathsToNonZero(
      DdNode * node
    )

  Counts the number of paths to a non-zero terminal of a DD. 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 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 if successful; (double) CUDD_OUT_OF_MEM otherwise.

  Side Effects None

  See Also `Cudd_CountMinterm`

    DdNode *
    Cudd_CubeArrayToBdd(
      DdManager * dd,
      int * array
    )

  Builds a cube from a positional array. The array must have one integer entry for each BDD variable. If the i-th entry is 1, the variable of index i appears in true form in the cube; If the i-th entry is 0, the variable of index i appears complemented in the cube; otherwise the variable does not appear in the cube. Returns a pointer to the BDD for the cube if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddComputeCube Cudd_IndicesToCube Cudd_BddToCubeArray`

    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:
  - node has illegal index
  - live node has dead children
  - node has illegal Then or Else pointers
  - BDD/ADD node has identical children
  - ZDD node has zero then child
  - wrong number of total nodes
  - wrong number of dead nodes
  - ref count error at node
  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`

    void
    Cudd_DelayedDerefBdd(
      DdManager * table,
      DdNode * n
    )

  Enqueues node n for later dereferencing. If the queue is full decreases the reference count of the oldest node N to make room for n. If N dies, recursively decreases the reference counts of its children. It is used to dispose of a BDD that is currently not needed, but may be useful again in the near future. The dereferencing proper is done as in Cudd_IterDerefBdd.

  Side Effects None

  See Also `Cudd_RecursiveDeref Cudd_IterDerefBdd`

    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_DumpBlifBody(
      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 blif body 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. This function prints out only .names part.

  Side Effects None

  See Also `Cudd_DumpDot Cudd_PrintDebug Cudd_DumpDDcal Cudd_DumpDaVinci Cudd_DumpFactoredForm`

    int
    Cudd_DumpBlif(
      DdManager * dd, manager
      int  n, number of output nodes to be dumped
      DdNode ** f, array of output nodes to be dumped
      char ** inames, array of input names (or NULL)
      char ** onames, array of output names (or NULL)
      char * mname, model name (or NULL)
      FILE * fp pointer to the dump file
    )

  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_DumpBlifBody Cudd_DumpDot Cudd_PrintDebug Cudd_DumpDDcal Cudd_DumpDaVinci Cudd_DumpFactoredForm`

    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 Cudd_DumpFactoredForm`

    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 Cudd_DumpDDcal Cudd_DumpFactoredForm`

    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:
  - solid line: THEN arcs;
  - dotted line: complement arcs;
  - dashed line: regular ELSE 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 Cudd_DumpDDcal Cudd_DumpDaVinci Cudd_DumpFactoredForm`

    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_EpdCountMinterm(
      DdManager * manager,
      DdNode * node,
      int  nvars,
      EpDouble * epd
    )

  Counts the number of minterms of a DD with extended precision. The function is assumed to depend on nvars variables. The minterm count is represented as an EpDouble, to allow any number of variables. Returns 0 if successful; CUDD_OUT_OF_MEM otherwise.

  Side Effects None

  See Also `Cudd_PrintDebug Cudd_CountPath`

    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

  See Also `Cudd_bddLeqUnless`

    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, manager
      DdNode * f, function
      int  i, index of variable
      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`

    double
    Cudd_ExpectedUsedSlots(
      DdManager * dd
    )

  Computes the fraction of slots in the unique table that should be in use. This expected value is based on the assumption that the hash function distributes the keys randomly; it can be compared with the result of Cudd_ReadUsedSlots to monitor the performance of the unique table hash function.

  Side Effects None

  See Also `Cudd_ReadSlots Cudd_ReadUsedSlots`

    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.
  - DdManager *manager;
  - DdNode *f;
  - DdGen *gen;
  - int *cube;
  - CUDD_VALUE_TYPE value;
  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.
  - DdManager *manager;
  - DdNode *f;
  - DdGen *gen;
  - DdNode *node;
  The nodes are returned in a seemingly random order. Cudd_ForeachNode 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 Cudd_CubeArrayToBdd`

    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_CONST_INDEX). 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`

    int
    Cudd_IsInHook(
      DdManager * dd,
      int  (*f)(DdManager *, char *, void *),
      Cudd_HookType  where
    )

  Checks whether a function is in a hook. A hook is a list of application-provided functions called on certain occasions by the package. Returns 1 if the function is found; 0 otherwise.

  Side Effects None

  See Also `Cudd_AddHook Cudd_RemoveHook`

    int
    Cudd_IsNonConstant(
      DdNode * f
    )

  Returns 1 if a DD node is not constant. This function is useful to test the results of Cudd_bddIteConstant, Cudd_addIteConstant, Cudd_addEvalConst. These results may be a special value signifying non-constant. In the other cases the macro Cudd_IsConstant can be used.

  Side Effects None

  See Also `Cudd_IsConstant Cudd_bddIteConstant Cudd_addIteConstant Cudd_addEvalConst`

    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 Cudd_DelayedDerefBdd`

    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`

    DdNode	*
    Cudd_MakeBddFromZddCover(
      DdManager * dd,
      DdNode * node
    )

  Converts a ZDD cover to a BDD graph. If successful, it returns a BDD node, otherwise it returns NULL.

  See Also `cuddMakeBddFromZddCover`

    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`

    int
    Cudd_MinHammingDist(
      DdManager * dd, DD manager
      DdNode * f, function to examine
      int * minterm, reference minterm
      int  upperBound distance above which an approximate answer is OK
    )

  Returns the minimum Hamming distance between the minterms of a function f and a reference minterm. The function is given as a BDD; the minterm is given as an array of integers, one for each variable in the manager. Returns the minimum distance if it is less than the upper bound; the upper bound if the minimum distance is at least as large; CUDD_OUT_OF_MEM in case of failure.

  Side Effects None

  See Also `Cudd_addHamming Cudd_bddClosestCube`

    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:
  - pr = 0 : prints nothing
  - pr = 1 : prints counts of nodes and minterms
  - pr = 2 : prints counts + disjoint sum of product
  - pr = 3 : prints counts + list of nodes
  - pr > 3 : prints counts + disjoint sum of product + list of nodes
  For the purpose of counting the number of minterms, the function is supposed to depend on n variables. 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 to a leaf node different from the logical zero, and different from the background value. Uses the package default output file. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_PrintDebug Cudd_bddPrintCover`

    void
    Cudd_PrintVersion(
      FILE * fp
    )

  Prints the package version number.

  Side Effects None

    DdNode *
    Cudd_PrioritySelect(
      DdManager * dd, manager
      DdNode * R, BDD of the relation
      DdNode ** x, array of x variables
      DdNode ** y, array of y variables
      DdNode ** z, array of z variables (optional: may be NULL)
      DdNode * Pi, BDD of the priority function (optional: may be NULL)
      int  n, size of x, y, and z
      DdNode * (*Pifunc)(DdManager *, int, DdNode **, DdNode **, DdNode **) function used to build Pi if it is NULL
    )

  Selects pairs from a relation R(x,y) (given as a BDD) in such a way that a given x appears in one pair only. Uses a priority function to determine which y should be paired to a given x. Cudd_PrioritySelect returns a pointer to the selected function if successful; NULL otherwise. Three of the arguments--x, y, and z--are vectors of BDD variables. The first two are the variables on which R depends. The third vectore is a vector of auxiliary variables, used during the computation. This vector is optional. If a NULL value is passed instead, Cudd_PrioritySelect will create the working variables on the fly. The sizes of x and y (and z if it is not NULL) should equal n. The priority function Pi can be passed as a BDD, or can be built by Cudd_PrioritySelect. If NULL is passed instead of a DdNode *, parameter Pifunc is used by Cudd_PrioritySelect to build a BDD for the priority function. (Pifunc is a pointer to a C function.) If Pi is not NULL, then Pifunc is ignored. Pifunc should have the same interface as the standard priority functions (e.g., Cudd_Dxygtdxz). Cudd_PrioritySelect and Cudd_CProjection can sometimes be used interchangeably. Specifically, calling Cudd_PrioritySelect with Cudd_Xgty as Pifunc produces the same result as calling Cudd_CProjection with the all-zero minterm as reference minterm. However, depending on the application, one or the other may be preferable:
  - When extracting representatives from an equivalence relation, Cudd_CProjection has the advantage of nor requiring the auxiliary variables.
  - When computing matchings in general bipartite graphs, Cudd_PrioritySelect normally obtains better results because it can use more powerful matching schemes (e.g., Cudd_Dxygtdxz).

  Side Effects If called with z == NULL, will create new variables in the manager.

  See Also `Cudd_Dxygtdxz Cudd_Dxygtdyz Cudd_Xgty Cudd_bddAdjPermuteX Cudd_CProjection`

    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 random 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_CONST_INDEX, returns CUDD_CONST_INDEX; 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_CONST_INDEX, returns CUDD_CONST_INDEX; 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
    )

  Returns the soft limit for the cache size. The soft limit

  Side Effects None

  See Also `Cudd_ReadMaxCache`

    double
    Cudd_ReadMaxGrowthAlternate(
      DdManager * dd
    )

  Reads the maxGrowthAlt parameter of the manager. This parameter is analogous to the maxGrowth paramter, and is used every given number of reorderings instead of maxGrowth. The number of reorderings is set with Cudd_SetReorderingCycle. If the number of reorderings is 0 (default) maxGrowthAlt is never used.

  Side Effects None

  See Also `Cudd_ReadMaxGrowth Cudd_SetMaxGrowthAlternate Cudd_SetReorderingCycle Cudd_ReadReorderingCycle`

    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 Cudd_ReadMaxGrowthAlternate`

    unsigned int
    Cudd_ReadMaxLive(
      DdManager * dd
    )

  Reads the maximum allowed number of live nodes. When this number is exceeded, the package returns NULL.

  Side Effects none

  See Also `Cudd_SetMaxLive`

    long
    Cudd_ReadMaxMemory(
      DdManager * dd
    )

  Reads the maximum allowed memory. When this number is exceeded, the package returns NULL.

  Side Effects none

  See Also `Cudd_SetMaxMemory`

    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 rate 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

    unsigned int
    Cudd_ReadNextReordering(
      DdManager * dd
    )

  Returns the threshold for the next dynamic reordering. The threshold is in terms of number of nodes and is in effect only if reordering is enabled. The count does not include the dead nodes, unless the countDead parameter of the manager has been changed from its default setting.

  Side Effects None

  See Also `Cudd_SetNextReordering`

    long
    Cudd_ReadNodeCount(
      DdManager * dd
    )

  Reports the number of live 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`

    int
    Cudd_ReadPeakLiveNodeCount(
      DdManager * dd
    )

  Reports the peak number of live nodes. This count is kept only if CUDD is compiled with DD_STATS defined. If DD_STATS is not defined, this function returns -1.

  Side Effects None

  See Also `Cudd_ReadNodeCount Cudd_PrintInfo Cudd_ReadPeakNodeCount`

    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_CONST_INDEX, returns CUDD_CONST_INDEX; 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_CONST_INDEX, returns CUDD_CONST_INDEX; 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`

    double
    Cudd_ReadRecursiveCalls(
      DdManager * dd
    )

  Returns the number of recursive calls if the package is compiled with DD_COUNT defined.

  Side Effects None

    int
    Cudd_ReadReorderingCycle(
      DdManager * dd
    )

  Reads the reordCycle parameter of the manager. This parameter determines how often the alternate threshold on maximum growth is used in reordering.

  Side Effects None

  See Also `Cudd_ReadMaxGrowthAlternate Cudd_SetMaxGrowthAlternate Cudd_SetReorderingCycle`

    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

    FILE *
    Cudd_ReadStderr(
      DdManager * dd
    )

  Reads the stderr of a manager. This is the file pointer to which messages normally going to stderr are written. It is initialized to stderr. Cudd_SetStderr allows the application to redirect it.

  Side Effects None

  See Also `Cudd_SetStderr Cudd_ReadStdout`

    FILE *
    Cudd_ReadStdout(
      DdManager * dd
    )

  Reads the stdout of a manager. This is the file pointer to which messages normally going to stdout are written. It is initialized to stdout. Cudd_SetStdout allows the application to redirect it.

  Side Effects None

  See Also `Cudd_SetStdout Cudd_ReadStderr`

    double
    Cudd_ReadSwapSteps(
      DdManager * dd
    )

  Reads the number of elementary reordering steps.

  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:
  - Swapping
  - Sifting
  - Symmetric Sifting
  - Group Sifting
  - Window Permutation
  - Simulated Annealing
  - Genetic Algorithm
  - Dynamic Programming (exact)
  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_RemoveHook(
      DdManager * dd,
      int  (*f)(DdManager *, char *, void *),
      Cudd_HookType  where
    )

  Removes a function from a hook. A hook is a list of application-provided functions called on certain occasions by the package. Returns 1 if successful; 0 the function was not in the list.

  Side Effects None

  See Also `Cudd_AddHook`

    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_SetMaxGrowthAlternate(
      DdManager * dd,
      double  mg
    )

  Sets the maxGrowthAlt parameter of the manager. This parameter is analogous to the maxGrowth paramter, and is used every given number of reorderings instead of maxGrowth. The number of reorderings is set with Cudd_SetReorderingCycle. If the number of reorderings is 0 (default) maxGrowthAlt is never used.

  Side Effects None

  See Also `Cudd_ReadMaxGrowthAlternate Cudd_SetMaxGrowth Cudd_SetReorderingCycle Cudd_ReadReorderingCycle`

    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 Cudd_SetMaxGrowthAlternate`

    void
    Cudd_SetMaxLive(
      DdManager * dd,
      unsigned int  maxLive
    )

  Sets the maximum allowed number of live nodes. When this number is exceeded, the package returns NULL.

  Side Effects none

  See Also `Cudd_ReadMaxLive`

    void
    Cudd_SetMaxMemory(
      DdManager * dd,
      long  maxMemory
    )

  Sets the maximum allowed memory. When this number is exceeded, the package returns NULL.

  Side Effects none

  See Also `Cudd_ReadMaxMemory`

    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 rate 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_SetNextReordering(
      DdManager * dd,
      unsigned int  next
    )

  Sets the threshold for the next dynamic reordering. The threshold is in terms of number of nodes and is in effect only if reordering is enabled. The count does not include the dead nodes, unless the countDead parameter of the manager has been changed from its default setting.

  Side Effects None

  See Also `Cudd_ReadNextReordering`

    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_SetReorderingCycle(
      DdManager * dd,
      int  cycle
    )

  Sets the reordCycle parameter of the manager. This parameter determines how often the alternate threshold on maximum growth is used in reordering.

  Side Effects None

  See Also `Cudd_ReadMaxGrowthAlternate Cudd_SetMaxGrowthAlternate Cudd_ReadReorderingCycle`

    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_SetStderr(
      DdManager * dd,
      FILE * fp
    )

  Sets the stderr of a manager.

  Side Effects None

  See Also `Cudd_ReadStderr Cudd_SetStdout`

    void
    Cudd_SetStdout(
      DdManager * dd,
      FILE * fp
    )

  Sets the stdout of a manager.

  Side Effects None

  See Also `Cudd_ReadStdout Cudd_SetStderr`

    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`

    int
    Cudd_SetVarMap(
      DdManager * manager, DD manager
      DdNode ** x, first array of variables
      DdNode ** y, second array of variables
      int  n length of both arrays
    )

  Registers with the manager a variable mapping described by two sets of variables. This variable mapping is then used by functions like Cudd_bddVarMap. This function is convenient for those applications that perform the same mapping several times. However, if several different permutations are used, it may be more efficient not to rely on the registered mapping, because changing mapping causes the cache to be cleared. (The initial setting, however, does not clear the cache.) The two sets of variables (x and y) must have the same size (x and y). The size is given by n. The two sets of variables are normally disjoint, but this restriction is not imposeded by the function. When new variables are created, the map is automatically extended (each new variable maps to itself). The typical use, however, is to wait until all variables are created, and then create the map. Returns 1 if the mapping is successfully registered with the manager; 0 otherwise.

  Side Effects Modifies the manager. May clear the cache.

  See Also `Cudd_bddVarMap Cudd_bddPermute Cudd_bddSwapVariables`

    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,
      char * str,
      void * data
    )

  Sample hook function to call after reordering. Prints on the manager's stdout final size and reordering time. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_StdPreReordHook`

    int
    Cudd_StdPreReordHook(
      DdManager * dd,
      char * str,
      void * data
    )

  Sample hook function to call before reordering. Prints on the manager's 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_SubsetWithMaskVars(
      DdManager * dd, manager
      DdNode * f, function from which to pick a cube
      DdNode ** vars, array of variables
      int  nvars, size of vars
      DdNode ** maskVars, array of variables
      int  mvars size of maskVars
    )

  Extracts a subset from a BDD in the following procedure. 1. Compute the weight for each mask variable by counting the number of minterms for both positive and negative cofactors of the BDD with respect to each mask variable. (weight = #positive - #negative) 2. Find a representative cube of the BDD by using the weight. From the top variable of the BDD, for each variable, if the weight is greater than 0.0, choose THEN branch, othereise ELSE branch, until meeting the constant 1. 3. Quantify out the variables not in maskVars from the representative cube and if a variable in maskVars is don't care, replace the variable with a constant(1 or 0) depending on the weight. 4. Make a subset of the BDD by multiplying with the modified cube.

  Side Effects None

    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_SupportIndex(
      DdManager * dd, manager
      DdNode * f DD whose support is sought
    )

  Finds the variables on which a DD depends. Returns an index array of the variables if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_Support Cudd_VectorSupport Cudd_ClassifySupport`

    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_VectorSupportIndex(
      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 an index array of the variables if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_SupportIndex Cudd_VectorSupport Cudd_ClassifySupport`

    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_addApply(
      DdManager * dd,
      DdNode * (*op)(DdManager *, DdNode **, DdNode **),
      DdNode * f,
      DdNode * g
    )

  Applies op to the corresponding discriminants of f and g. Returns a pointer to the result if succssful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addMonadicApply Cudd_addPlus Cudd_addTimes Cudd_addThreshold Cudd_addSetNZ Cudd_addDivide Cudd_addMinus Cudd_addMinimum Cudd_addMaximum Cudd_addOneZeroMaximum Cudd_addDiff Cudd_addAgreement Cudd_addOr Cudd_addNand Cudd_addNor Cudd_addXor Cudd_addXnor`

    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:
  - F @ 0 = 0
  - F @ 1 = F
  - 0 @ c = 0
  - 1 @ c = 1
  - F @ F = 1
  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_addGeneralVectorCompose(
      DdManager * dd,
      DdNode * f,
      DdNode ** vectorOn,
      DdNode ** vectorOff
    )

  Given a vector of ADDs, creates a new ADD by substituting the ADDs for the variables of the ADD f. vectorOn contains ADDs to be substituted for the x_v and vectorOff the ADDs to be substituted for x_v'. 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_addVectorCompose Cudd_addNonSimCompose Cudd_addPermute Cudd_addCompose Cudd_bddVectorCompose`

    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_addLog(
      DdManager * dd,
      DdNode * f
    )

  Natural logarithm of an ADDs. Returns NULL if not a terminal case; log(f) otherwise. The discriminants of f must be positive double's.

  Side Effects None

  See Also `Cudd_addMonadicApply`

    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 variables x (rows) and z (columns). B is assumed to depend on variables 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_addMonadicApply(
      DdManager * dd,
      DdNode * (*op)(DdManager *, DdNode *),
      DdNode * f
    )

  Applies op to the discriminants of f. Returns a pointer to the result if succssful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addApply Cudd_addLog`

    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 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_addOuterSum(
      DdManager * dd,
      DdNode * M,
      DdNode * r,
      DdNode * c
    )

  Takes the pointwise minimum of a matrix and the outer sum of two vectors. This procedure is used in the Floyd-Warshall all-pair shortest path algorithm. Returns a pointer to the result if successful; NULL otherwise.

  Side Effects None

    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. This function can be used also to take the AND of two 0-1 ADDs.

  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 variables x (rows) and z (columns). g is assumed to depend on variables 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`

    int
    Cudd_bddBindVar(
      DdManager * dd, manager
      int  index variable index
    )

  This function sets a flag to prevent sifting of a variable. Returns 1 if successful; 0 otherwise (i.e., invalid variable index).

  Side Effects Changes the "bindVar" flag in DdSubtable.

  See Also `Cudd_bddUnbindVar`

    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_bddClosestCube(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      int * distance
    )

  Finds a cube of f at minimum Hamming distance from the minterms of g. All the minterms of the cube are at the minimum distance. If the distance is 0, the cube belongs to the intersection of f and g. Returns the cube if successful; NULL otherwise.

  Side Effects The distance is returned as a side effect.

  See Also `Cudd_MinHammingDist`

    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 Cudd_CubeArrayToBdd`

    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:
  - f @ 0 = 0
  - f @ 1 = f
  - 0 @ c = 0
  - 1 @ c = 1
  - f @ f = 1
  - f @ f'= 0
  Returns a pointer to the result if successful; NULL otherwise. Note that if F=(f1,...,fn) and reordering takes place while computing F @ c, then the image restriction property (Img(F,c) = Img(F @ c)) is lost.

  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_bddIsNsVar(
      DdManager * dd,
      int  index
    )

  Checks whether a variable is next state. Returns 1 if the variable's type is present state; 0 if the variable exists but is not a present state; -1 if the variable does not exist.

  Side Effects none

  See Also `Cudd_bddSetNsVar Cudd_bddIsPiVar Cudd_bddIsPsVar`

    int
    Cudd_bddIsPiVar(
      DdManager * dd, manager
      int  index variable index
    )

  Checks whether a variable is primary input. Returns 1 if the variable's type is primary input; 0 if the variable exists but is not a primary input; -1 if the variable does not exist.

  Side Effects none

  See Also `Cudd_bddSetPiVar Cudd_bddIsPsVar Cudd_bddIsNsVar`

    int
    Cudd_bddIsPsVar(
      DdManager * dd,
      int  index
    )

  Checks whether a variable is present state. Returns 1 if the variable's type is present state; 0 if the variable exists but is not a present state; -1 if the variable does not exist.

  Side Effects none

  See Also `Cudd_bddSetPsVar Cudd_bddIsPiVar Cudd_bddIsNsVar`

    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`

    int
    Cudd_bddIsVarHardGroup(
      DdManager * dd,
      int  index
    )

  Checks whether a variable is set to be in a hard group. This function is used for lazy sifting. Returns 1 if the variable is marked to be in a hard group; 0 if the variable exists, but it is not marked to be in a hard group; -1 if the variable does not exist.

  Side Effects none

  See Also `Cudd_bddSetVarHardGroup`

    int
    Cudd_bddIsVarToBeGrouped(
      DdManager * dd,
      int  index
    )

  Checks whether a variable is set to be grouped. This function is used for lazy sifting.

  Side Effects none

    int
    Cudd_bddIsVarToBeUngrouped(
      DdManager * dd,
      int  index
    )

  Checks whether a variable is set to be ungrouped. This function is used for lazy sifting. Returns 1 if the variable is marked to be ungrouped; 0 if the variable exists, but it is not marked to be ungrouped; -1 if the variable does not exist.

  Side Effects none

  See Also `Cudd_bddSetVarToBeUngrouped`

    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 Cudd_ReadVars`

    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_bddLeqUnless(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * D
    )

  Tells whether f is less than of equal to G unless D is 1. f, g, and D are BDDs. The function returns 1 if f is less than of equal to G, and 0 otherwise. No new nodes are created.

  Side Effects None

  See Also `Cudd_EquivDC Cudd_bddLeq Cudd_bddIteConstant`

    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_bddMakePrime(
      DdManager * dd, manager
      DdNode * cube, cube to be expanded
      DdNode * f function of which the cube is to be made a prime
    )

  Expands cube to a prime implicant of f. Returns the prime if successful; NULL otherwise. In particular, NULL is returned if cube is not a real cube or is not an implicant of f.

  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 k minterms
      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 an array of BDDs for the minterms and returns a pointer to it if successful; NULL otherwise. There are three reasons why the procedure may fail:
  - It may run out of memory;
  - the function `f` may be the constant 0;
  - the minterms may not be contained in `f`.

  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:
  - It may run out of memory;
  - the function `f` may be the constant 0;
  - the minterm may not be contained in `f`.

  Side Effects None

  See Also `Cudd_bddPickOneCube`

    int
    Cudd_bddPrintCover(
      DdManager * dd,
      DdNode * l,
      DdNode * u
    )

  Prints a sum of product cover for an incompletely specified function given by a lower bound and an upper bound. Each product is a prime implicant obtained by expanding the product corresponding to a path from node to the constant one. Uses the package default output file. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_PrintMinterm`

    int
    Cudd_bddReadPairIndex(
      DdManager * dd,
      int  index
    )

  Reads a corresponding pair index for a given index. These pair indices are present and next state variable. Returns the corresponding variable index if the variable exists; -1 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetPairIndex`

    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`

    int
    Cudd_bddResetVarToBeGrouped(
      DdManager * dd,
      int  index
    )

  Resets a variable not to be grouped. This function is used for lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetVarToBeGrouped Cudd_bddSetVarHardGroup`

    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`

    int
    Cudd_bddSetNsVar(
      DdManager * dd, manager
      int  index variable index
    )

  Sets a variable type to next state. The variable type is used by lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetPiVar Cudd_bddSetPsVar Cudd_bddIsNsVar`

    int
    Cudd_bddSetPairIndex(
      DdManager * dd, manager
      int  index, variable index
      int  pairIndex corresponding variable index
    )

  Sets a corresponding pair index for a given index. These pair indices are present and next state variable. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddReadPairIndex`

    int
    Cudd_bddSetPiVar(
      DdManager * dd, manager
      int  index variable index
    )

  Sets a variable type to primary input. The variable type is used by lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetPsVar Cudd_bddSetNsVar Cudd_bddIsPiVar`

    int
    Cudd_bddSetPsVar(
      DdManager * dd, manager
      int  index variable index
    )

  Sets a variable type to present state. The variable type is used by lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetPiVar Cudd_bddSetNsVar Cudd_bddIsPsVar`

    int
    Cudd_bddSetVarHardGroup(
      DdManager * dd,
      int  index
    )

  Sets a variable to be a hard group. This function is used for lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetVarToBeGrouped Cudd_bddResetVarToBeGrouped Cudd_bddIsVarHardGroup`

    int
    Cudd_bddSetVarToBeGrouped(
      DdManager * dd,
      int  index
    )

  Sets a variable to be grouped. This function is used for lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddSetVarHardGroup Cudd_bddResetVarToBeGrouped`

    int
    Cudd_bddSetVarToBeUngrouped(
      DdManager * dd,
      int  index
    )

  Sets a variable to be ungrouped. This function is used for lazy sifting. Returns 1 if successful; 0 otherwise.

  Side Effects modifies the manager

  See Also `Cudd_bddIsVarToBeUngrouped`

    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. The orders of the variables in the two managers may be different. Returns a pointer to the BDD in the destination manager if successful; NULL otherwise.

  Side Effects None

    int
    Cudd_bddUnbindVar(
      DdManager * dd, manager
      int  index variable index
    )

  This function resets the flag that prevents the sifting of a variable. In successive variable reorderings, the variable will NOT be skipped, that is, sifted. Initially all variables can be sifted. It is necessary to call this function only to re-enable sifting after a call to Cudd_bddBindVar. Returns 1 if successful; 0 otherwise (i.e., invalid variable index).

  Side Effects Changes the "bindVar" flag in DdSubtable.

  See Also `Cudd_bddBindVar`

    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_bddVarIsBound(
      DdManager * dd, manager
      int  index variable index
    )

  This function returns 1 if a variable is enabled for sifting. Initially all variables can be sifted. This function returns 0 only if there has been a previous call to Cudd_bddBindVar for that variable not followed by a call to Cudd_bddUnbindVar. The function returns 0 also in the case in which the index of the variable is out of bounds.

  Side Effects none

  See Also `Cudd_bddBindVar Cudd_bddUnbindVar`

    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_bddVarMap(
      DdManager * manager, DD manager
      DdNode * f function in which to remap variables
    )

  Remaps the variables of a BDD using the default variable map. A typical use of this function is to swap two sets of variables. The variable map must be registered with Cudd_SetVarMap. Returns a pointer to the resulting BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddPermute Cudd_bddSwapVariables Cudd_SetVarMap`

    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

    DdNode	*
    Cudd_zddComplement(
      DdManager * dd,
      DdNode * node
    )

  Computes a complement cover for a ZDD node. For lack of a better method, we first extract the function BDD from the ZDD cover, then make the complement of the ZDD cover from the complement of the BDD node by using ISOP. Returns a pointer to the resulting cover if successful; NULL otherwise. The result depends on current variable order.

  Side Effects The result depends on current variable order.

    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 (double) 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. If the procedure runs out of memory, it returns (double) CUDD_OUT_OF_MEM.

  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`

    char *
    Cudd_zddCoverPathToString(
      DdManager * zdd, DD manager
      int * path, path of ZDD representing a cover
      char * str pointer to string to use if != NULL
    )

  Converts a path of a ZDD representing a cover to a string. The string represents an implicant of the cover. The path is typically produced by Cudd_zddForeachPath. Returns a pointer to the string if successful; NULL otherwise. If the str input is NULL, it allocates a new string. The string passed to this function must have enough room for all variables and for the terminator.

  Side Effects None

  See Also `Cudd_zddForeachPath`

    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:
  - solid line: THEN arcs;
  - dashed line: ELSE 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`

    DdGen *
    Cudd_zddFirstPath(
      DdManager * zdd,
      DdNode * f,
      int ** path
    )

  Defines an iterator on the paths of a ZDD and finds its first path. Returns a generator that contains the information necessary to continue the enumeration if successful; NULL otherwise.

  A path is represented as an array of literals, which are integers in {0, 1, 2}; 0 represents an else arc out of a node, 1 represents a then arc out of a node, and 2 stands for the absence of a node. The size of the array equals the number of variables in the manager at the time Cudd_zddFirstCube is called.

  The paths that end in the empty terminal are not enumerated.

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

  See Also `Cudd_zddForeachPath Cudd_zddNextPath Cudd_GenFree Cudd_IsGenEmpty`

    Cudd_zddForeachPath(
       manager,
       f,
       gen,
       path
    )

  Iterates over the paths of a ZDD f.
  - DdManager *manager;
  - DdNode *f;
  - DdGen *gen;
  - int *path;
  Cudd_zddForeachPath allocates and frees the generator. Therefore the application should not try to do that. Also, the path is freed at the end of Cudd_zddForeachPath 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_zddFirstPath Cudd_zddNextPath Cudd_GenFree Cudd_IsGenEmpty Cudd_AutodynDisable`

    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`

    int
    Cudd_zddNextPath(
      DdGen * gen,
      int ** path
    )

  Generates the next path of a ZDD onset, using generator gen. Returns 0 if the enumeration is completed; 1 otherwise.

  Side Effects The path is returned as a side effect. The generator is modified.

  See Also `Cudd_zddForeachPath Cudd_zddFirstPath Cudd_GenFree Cudd_IsGenEmpty`

    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_zddPrintCover(
      DdManager * zdd,
      DdNode * node
    )

  Prints a sum of products from a ZDD representing a cover. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_zddPrintMinterm`

    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:
  - pr = 0 : prints nothing
  - pr = 1 : prints counts of nodes and minterms
  - pr = 2 : prints counts + disjoint sum of products
  - pr = 3 : prints counts + list of nodes
  - pr > 3 : prints counts + disjoint sum of products + list of nodes
  Returns 1 if successful; 0 otherwise.

  Side Effects None

    int
    Cudd_zddPrintMinterm(
      DdManager * zdd,
      DdNode * node
    )

  Prints a disjoint sum of product form for a ZDD. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_zddPrintDebug Cudd_zddPrintCover`

    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:
  - Swapping
  - Sifting
  - Symmetric Sifting
  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`

    DD_LSDIGIT(
       x
    )

  Extract the least significant digit of a double digit. Used in the manipulation of arbitrary precision integers.

  Side Effects None

  See Also `DD_MSDIGIT`

    DD_MINUS_INFINITY(
       dd
    )

  Returns the minus infinity constant node.

  Side Effects none

  See Also `DD_ONE DD_ZERO DD_PLUS_INFINITY`

    DD_MSDIGIT(
       x
    )

  Extract the most significant digit of a double digit. Used in the manipulation of arbitrary precision integers.

  Side Effects None

  See Also `DD_LSDIGIT`

    DD_ONE(
       dd
    )

  Returns the constant 1 node.

  Side Effects none

  See Also `DD_ZERO DD_PLUS_INFINITY DD_MINUS_INFINITY`

    DD_PLUS_INFINITY(
       dd
    )

  Returns the plus infinity constant node.

  Side Effects none

  See Also `DD_ONE DD_ZERO DD_MINUS_INFINITY`

    DD_ZERO(
       dd
    )

  Returns the arithmetic 0 constant node. This is different from the logical zero. The latter is obtained by Cudd_Not(DD_ONE(dd)).

  Side Effects none

  See Also `DD_ONE Cudd_Not DD_PLUS_INFINITY DD_MINUS_INFINITY`

    DdNode *
    cuddAddApplyRecur(
      DdManager * dd,
      DdNode * (*op)(DdManager *, DdNode **, DdNode **),
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_addApply. Returns a pointer to the result if successful; NULL otherwise.

  Side Effects None

  See Also `cuddAddMonadicApplyRecur`

    DdNode *
    cuddAddBddDoPattern(
      DdManager * dd,
      DdNode * f
    )

  Performs the recursive step for Cudd_addBddPattern. Returns a pointer to the resulting BDD if successful; NULL otherwise.

  Side Effects None

    DdNode *
    cuddAddCmplRecur(
      DdManager * dd,
      DdNode * f
    )

  Performs the recursive step of Cudd_addCmpl. Returns a pointer to the resulting ADD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addCmpl`

    DdNode *
    cuddAddComposeRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * proj
    )

  Performs the recursive step of Cudd_addCompose. Returns the composed BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addCompose`

    DdNode *
    cuddAddConstrainRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * c
    )

  Performs the recursive step of Cudd_addConstrain. Returns a pointer to the result if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addConstrain`

    DdNode *
    cuddAddExistAbstractRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * cube
    )

  Performs the recursive step of Cudd_addExistAbstract. Returns the ADD obtained by abstracting the variables of cube from f, if successful; NULL otherwise.

  Side Effects None

    DdNode *
    cuddAddIteRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Implements the recursive step of Cudd_addIte(f,g,h). Returns a pointer to the resulting ADD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_addIte`

    DdNode *
    cuddAddMonadicApplyRecur(
      DdManager * dd,
      DdNode * (*op)(DdManager *, DdNode *),
      DdNode * f
    )

  Performs the recursive step of Cudd_addMonadicApply. Returns a pointer to the result if successful; NULL otherwise.

  Side Effects None

  See Also `cuddAddApplyRecur`

    DdNode *
    cuddAddNegateRecur(
      DdManager * dd,
      DdNode * f
    )

  Implements the recursive step of Cudd_addNegate. Returns a pointer to the result.

  Side Effects None

    DdNode *
    cuddAddOrAbstractRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * cube
    )

  Performs the recursive step of Cudd_addOrAbstract. Returns the ADD obtained by abstracting the variables of cube from f, if successful; NULL otherwise.

  Side Effects None

    DdNode *
    cuddAddRestrictRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * c
    )

  Performs the recursive step of Cudd_addRestrict. Returns the restricted ADD if successful; otherwise NULL.

  Side Effects None

  See Also `Cudd_addRestrict`

    DdNode *
    cuddAddRoundOffRecur(
      DdManager * dd,
      DdNode * f,
      double  trunc
    )

  Implements the recursive step of Cudd_addRoundOff. Returns a pointer to the result.

  Side Effects None

    DdNode *
    cuddAddScalarInverseRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * epsilon
    )

  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 *
    cuddAddUnivAbstractRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * cube
    )

  Performs the recursive step of Cudd_addUnivAbstract. Returns the ADD obtained by abstracting the variables of cube from f, if successful; NULL otherwise.

  Side Effects None

    cuddAdjust(
       x
    )

  Enforces DD_MINUS_INF_VAL <= x <= DD_PLUS_INF_VAL. Furthermore, if x <= DD_MINUS_INF_VAL/2, x is set to DD_MINUS_INF_VAL. Similarly, if DD_PLUS_INF_VAL/2 <= x, x is set to DD_PLUS_INF_VAL. Normally this macro is a NOOP. However, if HAVE_IEEE_754 is not defined, it makes sure that a value does not get larger than infinity in absolute value, and once it gets to infinity, stays there. If the value overflows before this macro is applied, no recovery is possible.

  Side Effects none

    DdNode *
    cuddAllocNode(
      DdManager * unique
    )

  Fast storage allocation for DdNodes in the table. The first 4 bytes of a chunk contain a pointer to the next block; the rest contains DD_MEM_CHUNK spaces for DdNodes. Returns a pointer to a new node if successful; NULL is memory is full.

  Side Effects None

  See Also `cuddDynamicAllocNode`

    int
    cuddAnnealing(
      DdManager * table,
      int  lower,
      int  upper
    )

  Get x, y by random selection. Choose either exchange or jump randomly. In case of jump, choose between jump_up and jump_down randomly. Do exchange or jump and get optimal case. Loop until there is no improvement or temperature reaches minimum. Returns 1 in case of success; 0 otherwise.

  Side Effects None

    int
    cuddBddAlignToZdd(
      DdManager * table DD manager
    )

  Reorders BDD variables according to the order of the ZDD variables. This function can be called at the end of ZDD reordering to insure that the order of the BDD variables is consistent with the order of the ZDD variables. The number of ZDD variables must be a multiple of the number of BDD variables. Let `M` be the ratio of the two numbers. cuddBddAlignToZdd then considers the ZDD variables from `M*i` to `(M+1)*i-1` as corresponding to BDD variable `i`. This function should be normally called from Cudd_zddReduceHeap, which clears the cache. Returns 1 in case of success; 0 otherwise.

  Side Effects Changes the BDD variable order for all diagrams and performs garbage collection of the BDD unique table.

  See Also `Cudd_ShuffleHeap Cudd_zddReduceHeap`

    DdNode *
    cuddBddAndAbstractRecur(
      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.

  Side Effects None

  See Also `Cudd_bddAndAbstract`

    DdNode *
    cuddBddAndRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * g
    )

  Implements the recursive step of Cudd_bddAnd by taking the conjunction of two BDDs. Returns a pointer to the result is successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddAnd`

    DdNode *
    cuddBddBooleanDiffRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * var
    )

  Performs the recursive steps of Cudd_bddBoleanDiff. Returns the BDD obtained by XORing the cofactors of f with respect to var if successful; NULL otherwise. Exploits the fact that dF/dx = dF'/dx.

  Side Effects None

    DdNode *
    cuddBddClippingAndAbstract(
      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. Returns a pointer to the resulting BDD if successful; NULL if the intermediate result blows up.

  Side Effects None

  See Also `Cudd_bddClippingAndAbstract`

    DdNode *
    cuddBddClippingAnd(
      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_bddClippingAnd`

    DdNode *
    cuddBddClosestCube(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      CUDD_VALUE_TYPE  bound
    )

  Performs the recursive step of Cudd_bddClosestCube. Returns the cube if succesful; NULL otherwise. The procedure uses a four-way recursion to examine all four combinations of cofactors of f and g. The most interesting feature of this function is the scheme used for caching the results in the global computed table. Since we have a cube and a distance, we combine them to form an ADD. The combination replaces the zero child of the top node of the cube with the negative of the distance. (The use of the negative is to avoid ambiguity with 1.) The degenerate cases (zero and one) are treated specially because the distance is known (0 for one, and infinity for zero).

  Side Effects None

  See Also `Cudd_bddClosestCube`

    DdNode *
    cuddBddComposeRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * proj
    )

  Performs the recursive step of Cudd_bddCompose. Exploits the fact that the composition of f' with g produces the complement of the composition of f with g to better utilize the cache. Returns the composed BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddCompose`

    DdNode *
    cuddBddConstrainRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * c
    )

  Performs the recursive step of Cudd_bddConstrain. Returns a pointer to the result if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddConstrain`

    DdNode *
    cuddBddExistAbstractRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * cube
    )

  Performs the recursive steps of Cudd_bddExistAbstract. Returns the BDD obtained by abstracting the variables of cube from f if successful; NULL otherwise. It is also used by Cudd_bddUnivAbstract.

  Side Effects None

  See Also `Cudd_bddExistAbstract Cudd_bddUnivAbstract`

    DdNode *
    cuddBddIntersectRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Implements the recursive step of Cudd_bddIntersect.

  Side Effects None

  See Also `Cudd_bddIntersect`

    DdNode	*
    cuddBddIsop(
      DdManager * dd,
      DdNode * L,
      DdNode * U
    )

  Performs the recursive step of Cudd_bddIsop.

  Side Effects None

  See Also `Cudd_bddIsop`

    DdNode *
    cuddBddIteRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Implements the recursive step of Cudd_bddIte. Returns a pointer to the resulting BDD. NULL if the intermediate result blows up or if reordering occurs.

  Side Effects None

    DdNode *
    cuddBddLICompaction(
      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_bddLICompaction`

    DdNode *
    cuddBddLiteralSetIntersectionRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_bddLiteralSetIntersection. Scans the cubes for common variables, and checks whether they agree in phase. Returns a pointer to the resulting cube if successful; NULL otherwise.

  Side Effects None

    DdNode *
    cuddBddMakePrime(
      DdManager * dd, manager
      DdNode * cube, cube to be expanded
      DdNode * f function of which the cube is to be made a prime
    )

  Performs the recursive step of Cudd_bddMakePrime. Returns the prime if successful; NULL otherwise.

  Side Effects None

    DdNode *
    cuddBddRestrictRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * c
    )

  Performs the recursive step of Cudd_bddRestrict. Returns the restricted BDD if successful; otherwise NULL.

  Side Effects None

  See Also `Cudd_bddRestrict`

    DdNode *
    cuddBddTransfer(
      DdManager * ddS,
      DdManager * ddD,
      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

  See Also `Cudd_bddTransfer`

    DdNode *
    cuddBddXorExistAbstractRecur(
      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_bddAndAbstract`

    DdNode *
    cuddBddXorRecur(
      DdManager * manager,
      DdNode * f,
      DdNode * g
    )

  Implements the recursive step of Cudd_bddXor by taking the exclusive OR of two BDDs. Returns a pointer to the result is successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_bddXor`

    DdNode *
    cuddBiasedUnderApprox(
      DdManager * dd, DD manager
      DdNode * f, current DD
      DdNode * b, bias function
      int  numVars, maximum number of variables
      int  threshold, threshold under which approximation stops
      double  quality1, minimum improvement for accepted changes when b=1
      double  quality0 minimum improvement for accepted changes when b=1
    )

  Applies the biased remapping underappoximation algorithm. Proceeds in three phases:
  - collect information on each node in the BDD; this is done via DFS.
  - traverse the BDD in top-down fashion and compute for each node whether remapping increases density.
  - traverse the BDD via DFS and actually perform the elimination.
  Returns the approximated BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_BiasedUnderApprox`

    DdNode *
    cuddCProjectionRecur(
      DdManager * dd,
      DdNode * R,
      DdNode * Y,
      DdNode * Ysupp
    )

  Performs the recursive step of Cudd_CProjection. Returns the projection if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_CProjection`

    void
    cuddCacheFlush(
      DdManager * table
    )

  Flushes the cache.

  Side Effects None

    void
    cuddCacheInsert1(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *),
      DdNode * f,
      DdNode * data
    )

  Inserts a result in the cache for a function with two operands.

  Side Effects None

  See Also `cuddCacheInsert cuddCacheInsert2`

    void
    cuddCacheInsert2(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *, DdNode *),
      DdNode * f,
      DdNode * g,
      DdNode * data
    )

  Inserts a result in the cache for a function with two operands.

  Side Effects None

  See Also `cuddCacheInsert cuddCacheInsert1`

    void
    cuddCacheInsert(
      DdManager * table,
      ptruint  op,
      DdNode * f,
      DdNode * g,
      DdNode * h,
      DdNode * data
    )

  Inserts a result in the cache.

  Side Effects None

  See Also `cuddCacheInsert2 cuddCacheInsert1`

    DdNode *
    cuddCacheLookup1Zdd(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *),
      DdNode * f
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookupZdd cuddCacheLookup2Zdd`

    DdNode *
    cuddCacheLookup1(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *),
      DdNode * f
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookup cuddCacheLookup2`

    DdNode *
    cuddCacheLookup2Zdd(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *, DdNode *),
      DdNode * f,
      DdNode * g
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookupZdd cuddCacheLookup1Zdd`

    DdNode *
    cuddCacheLookup2(
      DdManager * table,
      DdNode * (*op)(DdManager *, DdNode *, DdNode *),
      DdNode * f,
      DdNode * g
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookup cuddCacheLookup1`

    DdNode *
    cuddCacheLookupZdd(
      DdManager * table,
      ptruint  op,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookup2Zdd cuddCacheLookup1Zdd`

    DdNode *
    cuddCacheLookup(
      DdManager * table,
      ptruint  op,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Returns the result if found; it returns NULL if no result is found.

  Side Effects None

  See Also `cuddCacheLookup2 cuddCacheLookup1`

    int
    cuddCacheProfile(
      DdManager * table,
      FILE * fp
    )

  Computes and prints a profile of the cache usage. Returns 1 if successful; 0 otherwise.

  Side Effects None

    void
    cuddCacheResize(
      DdManager * table
    )

  Resizes the cache.

  Side Effects None

    int
    cuddCheckCube(
      DdManager * dd,
      DdNode * g
    )

  Checks whether g is the BDD of a cube. Returns 1 in case of success; 0 otherwise. The constant 1 is a valid cube, but all other constant functions cause cuddCheckCube to return 0.

  Side Effects None

    cuddClean(
       p
    )

  Clears the 4 least significant bits of a pointer.

  Side Effects none

    void
    cuddClearDeathRow(
      DdManager * table
    )

  Clears the death row.

  Side Effects None

  See Also `Cudd_DelayedDerefBdd Cudd_IterDerefBdd Cudd_CheckZeroRef cuddGarbageCollect`

    DdNode *
    cuddCofactorRecur(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_Cofactor. Returns a pointer to the cofactor if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_Cofactor`

    int
    cuddCollectNodes(
      DdNode * f,
      st_table * visited
    )

  Traverses the BDD f and collects all its nodes in a symbol table. f is assumed to be a regular pointer and cuddCollectNodes guarantees this assumption in the recursive calls. Returns 1 in case of success; 0 otherwise.

  Side Effects None

    int
    cuddComputeFloorLog2(
      unsigned int  value
    )

  Returns the floor of the logarithm to the base 2. The input value is assumed to be greater than 0.

  Side Effects None

    DdNode *
    cuddConstantLookup(
      DdManager * table,
      ptruint  op,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Looks up in the cache for the result of op applied to f, g, and h. Assumes that the calling procedure (e.g., Cudd_bddIteConstant) is only interested in whether the result is constant or not. Returns the result if found (possibly DD_NON_CONSTANT); otherwise it returns NULL.

  Side Effects None

  See Also `cuddCacheLookup`

    cuddDeallocNode(
       unique,
       node
    )

  Adds node to the head of the free list. Does not deallocate memory chunks that become free. This function is also used by the dynamic reordering functions.

  Side Effects None

  See Also `cuddAllocNode cuddDynamicAllocNode`

    cuddDeref(
       n
    )

  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 cuddRef. This being a macro, it is faster than Cudd_Deref, but it cannot be used in constructs like cuddDeref(a = b()).

  Side Effects none

  See Also `Cudd_Deref`

    int
    cuddDestroySubtables(
      DdManager * unique,
      int  n
    )

  Destroys the n most recently created subtables in a unique table. n should be positive. The subtables should not contain any live nodes, except the (isolated) projection function. The projection functions are freed. Returns 1 if successful; 0 otherwise.

  Side Effects The variable map used for fast variable substitution is destroyed if it exists. In this case the cache is also cleared.

  See Also `cuddInsertSubtables Cudd_SetVarMap`

    DdNode *
    cuddDynamicAllocNode(
      DdManager * table
    )

  Dynamically allocates a Node. This procedure is similar to cuddAllocNode in Cudd_Table.c, but it does not attempt garbage collection, because during reordering there are no dead nodes. Returns a pointer to a new node if successful; NULL is memory is full.

  Side Effects None

  See Also `cuddAllocNode`

    int
    cuddExact(
      DdManager * table,
      int  lower,
      int  upper
    )

  Exact variable ordering algorithm. Finds an optimum order for the variables between lower and upper. Returns 1 if successful; 0 otherwise.

  Side Effects None

    cuddE(
       node
    )

  Returns the else child of an internal node. If `node` is a constant node, the result is unpredictable. The pointer passed to cuddE must be regular.

  Side Effects none

  See Also `Cudd_E`

    void
    cuddFreeTable(
      DdManager * unique
    )

  Frees the resources associated to a unique table.

  Side Effects None

  See Also `cuddInitTable`

    int
    cuddGarbageCollectZdd(
      DdManager * unique,
      int  clearCache
    )

  Performs garbage collection on a ZDD unique table. If clearCache is 0, the cache is not cleared. This should only be specified if the cache has been cleared right before calling cuddGarbageCollectZdd. (As in the case of dynamic reordering.) Returns the total number of deleted nodes.

  Side Effects None

  See Also `cuddGarbageCollect`

    int
    cuddGarbageCollect(
      DdManager * unique,
      int  clearCache
    )

  Performs garbage collection on a unique table. If clearCache is 0, the cache is not cleared. This should only be specified if the cache has been cleared right before calling cuddGarbageCollect. (As in the case of dynamic reordering.) Returns the total number of deleted nodes.

  Side Effects None

  See Also `cuddGarbageCollectZdd`

    int
    cuddGa(
      DdManager * table, manager
      int  lower, lowest level to be reordered
      int  upper highest level to be reorderded
    )

  Genetic algorithm for DD reordering. The two children of a crossover will be stored in storedd[popsize

  Side Effects None

    void
    cuddGetBranches(
      DdNode * g,
      DdNode ** g1,
      DdNode ** g0
    )

  Computes the children of g.

  Side Effects None

    DdHashTable *
    cuddHashTableInit(
      DdManager * manager,
      unsigned int  keySize,
      unsigned int  initSize
    )

  Initializes a hash table. Returns a pointer to the new table if successful; NULL otherwise.

  Side Effects None

  See Also `cuddHashTableQuit`

    int
    cuddHashTableInsert1(
      DdHashTable * hash,
      DdNode * f,
      DdNode * value,
      ptrint  count
    )

  Inserts an item in a hash table when the key is one pointer. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `cuddHashTableInsert cuddHashTableInsert2 cuddHashTableInsert3 cuddHashTableLookup1`

    int
    cuddHashTableInsert2(
      DdHashTable * hash,
      DdNode * f,
      DdNode * g,
      DdNode * value,
      ptrint  count
    )

  Inserts an item in a hash table when the key is composed of two pointers. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `cuddHashTableInsert cuddHashTableInsert1 cuddHashTableInsert3 cuddHashTableLookup2`

    int
    cuddHashTableInsert3(
      DdHashTable * hash,
      DdNode * f,
      DdNode * g,
      DdNode * h,
      DdNode * value,
      ptrint  count
    )

  Inserts an item in a hash table when the key is composed of three pointers. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `cuddHashTableInsert cuddHashTableInsert1 cuddHashTableInsert2 cuddHashTableLookup3`

    int
    cuddHashTableInsert(
      DdHashTable * hash,
      DdNodePtr * key,
      DdNode * value,
      ptrint  count
    )

  Inserts an item in a hash table when the key has more than three pointers. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `[cuddHashTableInsert1 cuddHashTableInsert2 cuddHashTableInsert3 cuddHashTableLookup`

    DdNode *
    cuddHashTableLookup1(
      DdHashTable * hash,
      DdNode * f
    )

  Looks up a key consisting of one pointer in a hash table. Returns the value associated to the key if there is an entry for the given key in the table; NULL otherwise. If the entry is present, its reference counter is decremented if not saturated. If the counter reaches 0, the value of the entry is dereferenced, and the entry is returned to the free list.

  Side Effects None

  See Also `cuddHashTableLookup cuddHashTableLookup2 cuddHashTableLookup3 cuddHashTableInsert1`

    DdNode *
    cuddHashTableLookup2(
      DdHashTable * hash,
      DdNode * f,
      DdNode * g
    )

  Looks up a key consisting of two pointer in a hash table. Returns the value associated to the key if there is an entry for the given key in the table; NULL otherwise. If the entry is present, its reference counter is decremented if not saturated. If the counter reaches 0, the value of the entry is dereferenced, and the entry is returned to the free list.

  Side Effects None

  See Also `cuddHashTableLookup cuddHashTableLookup1 cuddHashTableLookup3 cuddHashTableInsert2`

    DdNode *
    cuddHashTableLookup3(
      DdHashTable * hash,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Looks up a key consisting of three pointers in a hash table. Returns the value associated to the key if there is an entry for the given key in the table; NULL otherwise. If the entry is present, its reference counter is decremented if not saturated. If the counter reaches 0, the value of the entry is dereferenced, and the entry is returned to the free list.

  Side Effects None

  See Also `cuddHashTableLookup cuddHashTableLookup1 cuddHashTableLookup2 cuddHashTableInsert3`

    DdNode *
    cuddHashTableLookup(
      DdHashTable * hash,
      DdNodePtr * key
    )

  Looks up a key consisting of more than three pointers in a hash table. Returns the value associated to the key if there is an entry for the given key in the table; NULL otherwise. If the entry is present, its reference counter is decremented if not saturated. If the counter reaches 0, the value of the entry is dereferenced, and the entry is returned to the free list.

  Side Effects None

  See Also `cuddHashTableLookup1 cuddHashTableLookup2 cuddHashTableLookup3 cuddHashTableInsert`

    void
    cuddHashTableQuit(
      DdHashTable * hash
    )

  Shuts down a hash table, dereferencing all the values.

  Side Effects None

  See Also `cuddHashTableInit`

    int
    cuddHeapProfile(
      DdManager * dd
    )

  Prints to the manager's stdout the number of live nodes for each level of the DD heap that contains at least one live node. It also prints a summary containing:
  - total number of tables;
  - number of tables with live nodes;
  - table with the largest number of live nodes;
  - number of nodes in that table.
  If more than one table contains the maximum number of live nodes, only the one of lowest index is reported. Returns 1 in case of success and 0 otherwise.

  Side Effects None

    cuddIZ(
       dd,
       index
    )

  Finds the current position of ZDD variable index in the order. This macro duplicates the functionality of Cudd_ReadPermZdd, but it does not check for out-of-bounds indices and it is more efficient.

  Side Effects none

  See Also `Cudd_ReadPermZdd`

    int
    cuddInitCache(
      DdManager * unique, unique table
      unsigned int  cacheSize, initial size of the cache
      unsigned int  maxCacheSize cache size beyond which no resizing occurs
    )

  Initializes the computed table. It is called by Cudd_Init. Returns 1 in case of success; 0 otherwise.

  Side Effects None

  See Also `Cudd_Init`

    int
    cuddInitInteract(
      DdManager * table
    )

  Initializes the interaction matrix. The interaction matrix is implemented as a bit vector storing the upper triangle of the symmetric interaction matrix. The bit vector is kept in an array of long integers. The computation is based on a series of depth-first searches, one for each root of the DAG. Two flags are needed: The local visited flag uses the LSB of the then pointer. The global visited flag uses the LSB of the next pointer. Returns 1 if successful; 0 otherwise.

  Side Effects None

    DdManager *
    cuddInitTable(
      unsigned int  numVars, Initial number of BDD variables (and subtables)
      unsigned int  numVarsZ, Initial number of ZDD variables (and subtables)
      unsigned int  numSlots, Initial size of the BDD subtables
      unsigned int  looseUpTo Limit for fast table growth
    )

  Creates and initializes the unique table. Returns a pointer to the table if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_Init cuddFreeTable`

    int
    cuddInsertSubtables(
      DdManager * unique,
      int  n,
      int  level
    )

  Inserts n new subtables in a unique table at level. The number n should be positive, and level should be an existing level. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `cuddDestroySubtables`

    cuddIsConstant(
       node
    )

  Returns 1 if the node is a constant node (rather than an internal node). All constant nodes have the same index (CUDD_CONST_INDEX). The pointer passed to cuddIsConstant must be regular.

  Side Effects none

  See Also `Cudd_IsConstant`

    int
    cuddIsInDeathRow(
      DdManager * dd,
      DdNode * f
    )

  Checks whether a node is in the death row. Returns the position of the first occurrence if the node is present; -1 otherwise.

  Side Effects None

  See Also `Cudd_DelayedDerefBdd cuddClearDeathRow`

    cuddI(
       dd,
       index
    )

  Finds the current position of variable index in the order. This macro duplicates the functionality of Cudd_ReadPerm, but it does not check for out-of-bounds indices and it is more efficient.

  Side Effects none

  See Also `Cudd_ReadPerm`

    void
    cuddLevelQueueDequeue(
      DdLevelQueue * queue,
      int  level
    )

  Remove an item from the front of a level queue.

  Side Effects None

  See Also `cuddLevelQueueEnqueue`

    void *
    cuddLevelQueueEnqueue(
      DdLevelQueue * queue, level queue
      void * key, key to be enqueued
      int  level level at which to insert
    )

  Inserts a new key in a level queue. A new entry is created in the queue only if the node is not already enqueued. Returns a pointer to the queue item if successful; NULL otherwise.

  Side Effects None

  See Also `cuddLevelQueueInit cuddLevelQueueDequeue`

    DdLevelQueue *
    cuddLevelQueueInit(
      int  levels, number of levels
      int  itemSize, size of the item
      int  numBuckets initial number of hash buckets
    )

  Initializes a level queue. A level queue is a queue where inserts are based on the levels of the nodes. Within each level the policy is FIFO. Level queues are useful in traversing a BDD top-down. Queue items are kept in a free list when dequeued for efficiency. Returns a pointer to the new queue if successful; NULL otherwise.

  Side Effects None

  See Also `cuddLevelQueueQuit cuddLevelQueueEnqueue cuddLevelQueueDequeue`

    void
    cuddLevelQueueQuit(
      DdLevelQueue * queue
    )

  Shuts down a level queue and releases all the associated memory.

  Side Effects None

  See Also `cuddLevelQueueInit`

    int
    cuddLinearAndSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  BDD reduction based on combination of sifting and linear transformations. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique table.
  2. Sift the variable up and down, remembering each time the total size of the DD heap. At each position, linear transformation of the two adjacent variables is tried and is accepted if it reduces the size of the DD.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 if successful; 0 otherwise.

  Side Effects None

    void
    cuddLocalCacheClearAll(
      DdManager * manager
    )

  Clears the local caches of a manager. Used before reordering.

  Side Effects None

    void
    cuddLocalCacheClearDead(
      DdManager * manager
    )

  Clears the dead entries of the local caches of a manager. Used during garbage collection.

  Side Effects None

    DdLocalCache *
    cuddLocalCacheInit(
      DdManager * manager, manager
      unsigned int  keySize, size of the key (number of operands)
      unsigned int  cacheSize, Initial size of the cache
      unsigned int  maxCacheSize Size of the cache beyond which no resizing occurs
    )

  Initializes a computed table. Returns a pointer the the new local cache in case of success; NULL otherwise.

  Side Effects None

  See Also `cuddInitCache`

    void
    cuddLocalCacheInsert(
      DdLocalCache * cache,
      DdNodePtr * key,
      DdNode * value
    )

  Inserts a result in a local cache.

  Side Effects None

    DdNode *
    cuddLocalCacheLookup(
      DdLocalCache * cache,
      DdNodePtr * key
    )

  Looks up in a local cache. Returns the result if found; it returns NULL if no result is found.

  Side Effects None

    int
    cuddLocalCacheProfile(
      DdLocalCache * cache
    )

  Computes and prints a profile of a local cache usage. Returns 1 if successful; 0 otherwise.

  Side Effects None

    void
    cuddLocalCacheQuit(
      DdLocalCache * cache cache to be shut down
    )

  Initializes the computed table. It is called by Cudd_Init. Returns a pointer the the new local cache in case of success; NULL otherwise.

  Side Effects None

  See Also `cuddLocalCacheInit`

    DdNode	*
    cuddMakeBddFromZddCover(
      DdManager * dd,
      DdNode * node
    )

  Converts a ZDD cover to a BDD graph. If successful, it returns a BDD node, otherwise it returns NULL. It is a recursive algorithm as the following. First computes 3 cofactors of a ZDD cover; f1, f0 and fd. Second, compute BDDs(b1, b0 and bd) of f1, f0 and fd. Third, compute T=b1+bd and E=b0+bd. Fourth, compute ITE(v,T,E) where v is the variable which has the index of the top node of the ZDD cover. In this case, since the index of v can be larger than either one of T or one of E, cuddUniqueInterIVO is called, here IVO stands for independent variable ordering.

  See Also `Cudd_MakeBddFromZddCover`

    int
    cuddNextHigh(
      DdManager * table,
      int  x
    )

  Finds the next subtable with a larger index. Returns the index.

  Side Effects None

  See Also `cuddNextLow`

    int
    cuddNextLow(
      DdManager * table,
      int  x
    )

  Finds the next subtable with a smaller index. Returns the index.

  Side Effects None

  See Also `cuddNextHigh`

    void
    cuddPrintNode(
      DdNode * f,
      FILE * fp
    )

  Prints out information on a node.

  Side Effects None

    void
    cuddPrintVarGroups(
      DdManager * dd, manager
      MtrNode * root, root of the group tree
      int  zdd, 0: BDD; 1: ZDD
      int  silent flag to check tree syntax only
    )

  Prints the variable groups as a parenthesized list. For each group the level range that it represents is printed. After each group, the group's flags are printed, preceded by a `|'. For each flag (except MTR_TERMINAL) a character is printed.
  - F: MTR_FIXED
  - N: MTR_NEWNODE
  - S: MTR_SOFT
  The second argument, silent, if different from 0, causes Cudd_PrintVarGroups to only check the syntax of the group tree.

  Side Effects None

    int
    cuddP(
      DdManager * dd,
      DdNode * f
    )

  Prints a DD to the standard output. One line per node is printed. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_PrintDebug`

    void
    cuddReclaimZdd(
      DdManager * table,
      DdNode * n
    )

  Brings children of a dead ZDD node back.

  Side Effects None

  See Also `cuddReclaim`

    void
    cuddReclaim(
      DdManager * table,
      DdNode * n
    )

  Brings children of a dead node back.

  Side Effects None

  See Also `cuddReclaimZdd`

    cuddRef(
       n
    )

  Increases the reference count of a node, if it is not saturated. This being a macro, it is faster than Cudd_Ref, but it cannot be used in constructs like cuddRef(a = b()).

  Side Effects none

  See Also `Cudd_Ref`

    void
    cuddRehash(
      DdManager * unique,
      int  i
    )

  Doubles the size of a unique subtable and rehashes its contents.

  Side Effects None

    DdNode *
    cuddRemapUnderApprox(
      DdManager * dd, DD manager
      DdNode * f, current DD
      int  numVars, maximum number of variables
      int  threshold, threshold under which approximation stops
      double  quality minimum improvement for accepted changes
    )

  Applies the remapping underappoximation algorithm. Proceeds in three phases:
  - collect information on each node in the BDD; this is done via DFS.
  - traverse the BDD in top-down fashion and compute for each node whether remapping increases density.
  - traverse the BDD via DFS and actually perform the elimination.
  Returns the approximated BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_RemapUnderApprox`

    int
    cuddResizeTableZdd(
      DdManager * unique,
      int  index
    )

  Increases the number of ZDD subtables in a unique table so that it meets or exceeds index. When new ZDD variables are created, it is possible to preserve the functions unchanged, or it is possible to preserve the covers unchanged, but not both. cuddResizeTableZdd preserves the covers. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `ddResizeTable`

    cuddSatDec(
       x
    )

  Saturating decrement operator.

  Side Effects none

  See Also `cuddSatInc`

    cuddSatInc(
       x
    )

  Saturating increment operator.

  Side Effects none

  See Also `cuddSatDec`

    void
    cuddSetInteract(
      DdManager * table,
      int  x,
      int  y
    )

  Given a pair of variables 0 <= x < y < table->size, sets the corresponding bit of the interaction matrix to 1.

  Side Effects None

    void
    cuddShrinkDeathRow(
      DdManager * table
    )

  Shrinks the death row by a factor of four.

  Side Effects None

  See Also `cuddClearDeathRow`

    void
    cuddShrinkSubtable(
      DdManager * unique,
      int  i
    )

  Shrinks a subtable.

  Side Effects None

  See Also `cuddRehash`

    int
    cuddSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  Implementation of Rudell's sifting algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique table.
  2. Sift the variable up and down, remembering each time the total size of the DD heap.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 if successful; 0 otherwise.

  Side Effects None

    void
    cuddSlowTableGrowth(
      DdManager * unique
    )

  Adjusts parameters of a table to slow down its growth.

  Side Effects None

    DdNode *
    cuddSolveEqnRecur(
      DdManager * bdd,
      DdNode * F, the left-hand side of the equation
      DdNode * Y, the cube of remaining y variables
      DdNode ** G, the array of solutions
      int  n, number of unknowns
      int * yIndex, array holding the y variable indices
      int  i level of recursion
    )

  Implements the recursive step of Cudd_SolveEqn. Returns NULL if the intermediate solution blows up or reordering occurs. The parametric solutions are stored in the array G.

  Side Effects none

  See Also `Cudd_SolveEqn Cudd_VerifySol`

    DdNode*
    cuddSplitSetRecur(
      DdManager * manager,
      st_table * mtable,
      int * varSeen,
      DdNode * p,
      double  n,
      double  max,
      int  index
    )

  Implements the recursive step of Cudd_SplitSet. The procedure recursively traverses the BDD and checks to see if any node satisfies the minterm requirements as specified by 'n'. At any node X, n is compared to the number of minterms in the onset of X's children. If either of the child nodes have exactly n minterms, then that node is returned; else, if n is greater than the onset of one of the child nodes, that node is retained and the difference in the number of minterms is extracted from the other child. In case n minterms can be extracted from constant 1, the algorithm returns the result with at most log(n) nodes.

  Side Effects The array 'varSeen' is updated at every recursive call to set the variables traversed by the procedure.

    enum st_retval
    cuddStCountfree(
      char * key,
      char * value,
      char * arg
    )

  Frees the memory used to store the minterm counts recorded in the visited table. Returns ST_CONTINUE.

  Side Effects None

    DdNode *
    cuddSubsetHeavyBranch(
      DdManager * dd, DD manager
      DdNode * f, current DD
      int  numVars, maximum number of variables
      int  threshold threshold size for the subset
    )

  Here a subset BDD is built by throwing away one of the children. Starting at root, annotate each node with the number of minterms (in terms of the total number of variables specified - numVars), number of nodes taken by the DAG rooted at this node and number of additional nodes taken by the child that has the lesser minterms. The child with the lower number of minterms is thrown away and a dyanmic count of the nodes of the subset is kept. Once the threshold is reached the subset is returned to the calling procedure.

  Side Effects None

  See Also `Cudd_SubsetHeavyBranch`

    DdNode *
    cuddSubsetShortPaths(
      DdManager * dd, DD manager
      DdNode * f, function to be subset
      int  numVars, total number of variables in consideration
      int  threshold, maximum number of nodes allowed in the subset
      int  hardlimit flag determining whether thershold should be respected strictly
    )

  The outermost procedure to return a subset of the given BDD with the largest cubes. The path lengths are calculated, the maximum allowable path length is determined and the number of nodes of this path length that can be used to build a subset. If the threshold is larger than the size of the original BDD, the original BDD is returned.

  Side Effects None

  See Also `Cudd_SubsetShortPaths`

    int
    cuddSwapInPlace(
      DdManager * table,
      int  x,
      int  y
    )

  Swaps two adjacent variables. It assumes that no dead nodes are present on entry to this procedure. The procedure then guarantees that no dead nodes will be present when it terminates. cuddSwapInPlace assumes that x < y. Returns the number of keys in the table if successful; 0 otherwise.

  Side Effects None

    int
    cuddSwapping(
      DdManager * table,
      int  lower,
      int  upper,
      Cudd_ReorderingType  heuristic
    )

  Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.
  1. Select two variables (RANDOM or HEURISTIC).
  2. Permute these variables.
  3. If the nodes have decreased accept the permutation.
  4. Otherwise reconstruct the original heap.
  5. Loop.
  Returns 1 in case of success; 0 otherwise.

  Side Effects None

    int
    cuddSymmCheck(
      DdManager * table,
      int  x,
      int  y
    )

  Checks for symmetry of x and y. Ignores projection functions, unless they are isolated. Returns 1 in case of symmetry; 0 otherwise.

  Side Effects None

    int
    cuddSymmSiftingConv(
      DdManager * table,
      int  lower,
      int  upper
    )

  Symmetric sifting to convergence algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique subtable.
  2. Sift the variable up and down, remembering each time the total size of the DD heap and grouping variables that are symmetric.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  5. Repeat 1-4 until no further improvement.
  Returns 1 plus the number of symmetric variables if successful; 0 otherwise.

  Side Effects None

  See Also `cuddSymmSifting`

    int
    cuddSymmSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  Symmetric sifting algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique subtable.
  2. Sift the variable up and down, remembering each time the total size of the DD heap and grouping variables that are symmetric.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 plus the number of symmetric variables if successful; 0 otherwise.

  Side Effects None

  See Also `cuddSymmSiftingConv`

    int
    cuddTestInteract(
      DdManager * table,
      int  x,
      int  y
    )

  Given a pair of variables 0 <= x < y < table->size, tests whether the corresponding bit of the interaction matrix is 1. Returns the value of the bit.

  Side Effects None

    int
    cuddTimesInDeathRow(
      DdManager * dd,
      DdNode * f
    )

  Counts how many times a node is in the death row.

  Side Effects None

  See Also `Cudd_DelayedDerefBdd cuddClearDeathRow cuddIsInDeathRow`

    int
    cuddTreeSifting(
      DdManager * table, DD table
      Cudd_ReorderingType  method reordering method for the groups of leaves
    )

  Tree sifting algorithm. Assumes that a tree representing a group hierarchy is passed as a parameter. It then reorders each group in postorder fashion by calling ddTreeSiftingAux. Assumes that no dead nodes are present. Returns 1 if successful; 0 otherwise.

  Side Effects None

    cuddT(
       node
    )

  Returns the then child of an internal node. If `node` is a constant node, the result is unpredictable. The pointer passed to cuddT must be regular.

  Side Effects none

  See Also `Cudd_T`

    DdNode *
    cuddUnderApprox(
      DdManager * dd, DD manager
      DdNode * f, current DD
      int  numVars, maximum number of variables
      int  threshold, threshold under which approximation stops
      int  safe, enforce safe approximation
      double  quality minimum improvement for accepted changes
    )

  Applies Tom Shiple's underappoximation algorithm. Proceeds in three phases:
  - collect information on each node in the BDD; this is done via DFS.
  - traverse the BDD in top-down fashion and compute for each node whether its elimination increases density.
  - traverse the BDD via DFS and actually perform the elimination.
  Returns the approximated BDD if successful; NULL otherwise.

  Side Effects None

  See Also `Cudd_UnderApprox`

    DdNode *
    cuddUniqueConst(
      DdManager * unique,
      CUDD_VALUE_TYPE  value
    )

  Checks the unique table for the existence of a constant node. If it does not exist, it creates a new one. Does not modify the reference count of whatever is returned. A newly created internal node comes back with a reference count 0. Returns a pointer to the new node.

  Side Effects None

    DdNode *
    cuddUniqueInterIVO(
      DdManager * unique,
      int  index,
      DdNode * T,
      DdNode * E
    )

  Wrapper for cuddUniqueInter that is independent of variable ordering (IVO). This function does not require parameter index to precede the indices of the top nodes of T and E in the variable order. Returns a pointer to the result node under normal conditions; NULL if reordering occurred or memory was exhausted.

  Side Effects None

  See Also `cuddUniqueInter Cudd_MakeBddFromZddCover`

    DdNode *
    cuddUniqueInterZdd(
      DdManager * unique,
      int  index,
      DdNode * T,
      DdNode * E
    )

  Checks the unique table for the existence of an internal ZDD node. If it does not exist, it creates a new one. Does not modify the reference count of whatever is returned. A newly created internal node comes back with a reference count 0. For a newly created node, increments the reference counts of what T and E point to. Returns a pointer to the new node if successful; NULL if memory is exhausted or if reordering took place.

  Side Effects None

  See Also `cuddUniqueInter`

    DdNode *
    cuddUniqueInter(
      DdManager * unique,
      int  index,
      DdNode * T,
      DdNode * E
    )

  Checks the unique table for the existence of an internal node. If it does not exist, it creates a new one. Does not modify the reference count of whatever is returned. A newly created internal node comes back with a reference count 0. For a newly created node, increments the reference counts of what T and E point to. Returns a pointer to the new node if successful; NULL if memory is exhausted or if reordering took place.

  Side Effects None

  See Also `cuddUniqueInterZdd`

    DdNode *
    cuddVerifySol(
      DdManager * bdd,
      DdNode * F, the left-hand side of the equation
      DdNode ** G, the array of solutions
      int * yIndex, array holding the y variable indices
      int  n number of unknowns
    )

  Implements the recursive step of Cudd_VerifySol.

  Side Effects none

  See Also `Cudd_VerifySol`

    cuddV(
       node
    )

  Returns the value of a constant node. If `node` is an internal node, the result is unpredictable. The pointer passed to cuddV must be regular.

  Side Effects none

  See Also `Cudd_V`

    int
    cuddWindowReorder(
      DdManager * table, DD table
      int  low, lowest index to reorder
      int  high, highest index to reorder
      Cudd_ReorderingType  submethod window reordering option
    )

  Reorders by applying the method of the sliding window. Tries all possible permutations to the variables in a window that slides from low to high. The size of the window is determined by submethod. Assumes that no dead nodes are present. Returns 1 in case of success; 0 otherwise.

  Side Effects None

    int
    cuddZddAlignToBdd(
      DdManager * table DD manager
    )

  Reorders ZDD variables according to the order of the BDD variables. This function can be called at the end of BDD reordering to insure that the order of the ZDD variables is consistent with the order of the BDD variables. The number of ZDD variables must be a multiple of the number of BDD variables. Let `M` be the ratio of the two numbers. cuddZddAlignToBdd then considers the ZDD variables from `M*i` to `(M+1)*i-1` as corresponding to BDD variable `i`. This function should be normally called from Cudd_ReduceHeap, which clears the cache. Returns 1 in case of success; 0 otherwise.

  Side Effects Changes the ZDD variable order for all diagrams and performs garbage collection of the ZDD unique table.

  See Also `Cudd_zddShuffleHeap Cudd_ReduceHeap`

    DdNode *
    cuddZddChangeAux(
      DdManager * zdd,
      DdNode * P,
      DdNode * zvar
    )

  Performs the recursive step of Cudd_zddChange.

  Side Effects None

    DdNode *
    cuddZddChange(
      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. cuddZddChange performs the same function as Cudd_zddChange, but does not restart if reordering has taken place. Therefore it can be called from within a recursive procedure.

  Side Effects None

  See Also `Cudd_zddChange`

    DdNode	*
    cuddZddComplement(
      DdManager * dd,
      DdNode * node
    )

  Computes the complement of a ZDD node. So far, since we couldn't find a direct way to get the complement of a ZDD cover, we first convert a ZDD cover to a BDD, then make the complement of the ZDD cover from the complement of the BDD node by using ISOP.

  Side Effects The result depends on current variable order.

    DdNode *
    cuddZddDiff(
      DdManager * zdd,
      DdNode * P,
      DdNode * Q
    )

  Performs the recursive step of Cudd_zddDiff.

  Side Effects None

    DdNode	*
    cuddZddDivideF(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddDivideF.

  Side Effects None

  See Also `Cudd_zddDivideF`

    DdNode	*
    cuddZddDivide(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddDivide.

  Side Effects None

  See Also `Cudd_zddDivide`

    void
    cuddZddFreeUniv(
      DdManager * zdd
    )

  Frees the ZDD universe.

  Side Effects None

  See Also `cuddZddInitUniv`

    int
    cuddZddGetCofactors2(
      DdManager * dd,
      DdNode * f,
      int  v,
      DdNode ** f1,
      DdNode ** f0
    )

  Computes the two-way decomposition of f w.r.t. v.

  Side Effects The results are returned in f1 and f0.

  See Also `cuddZddGetCofactors3`

    int
    cuddZddGetCofactors3(
      DdManager * dd,
      DdNode * f,
      int  v,
      DdNode ** f1,
      DdNode ** f0,
      DdNode ** fd
    )

  Computes the three-way decomposition of function f (represented by a ZDD) wit respect to variable v.

  Side Effects The results are returned in f1, f0, and fd.

  See Also `cuddZddGetCofactors2`

    int
    cuddZddGetNegVarIndex(
      DdManager * dd,
      int  index
    )

  Returns the index of negative ZDD variable.

    int
    cuddZddGetNegVarLevel(
      DdManager * dd,
      int  index
    )

  Returns the level of negative ZDD variable.

    DdNode *
    cuddZddGetNodeIVO(
      DdManager * dd,
      int  index,
      DdNode * g,
      DdNode * h
    )

  Wrapper for cuddUniqueInterZdd that is independent of variable ordering (IVO). This function does not require parameter index to precede the indices of the top nodes of g and h in the variable order. Returns a pointer to the result node under normal conditions; NULL if reordering occurred or memory was exhausted.

  Side Effects None

  See Also `cuddZddGetNode cuddZddIsop`

    DdNode *
    cuddZddGetNode(
      DdManager * zdd,
      int  id,
      DdNode * T,
      DdNode * E
    )

  Wrapper for cuddUniqueInterZdd, which applies the ZDD reduction rule. Returns a pointer to the result node under normal conditions; NULL if reordering occurred or memory was exhausted.

  Side Effects None

  See Also `cuddUniqueInterZdd`

    int
    cuddZddGetPosVarIndex(
      DdManager * dd,
      int  index
    )

  Returns the index of positive ZDD variable.

    int
    cuddZddGetPosVarLevel(
      DdManager * dd,
      int  index
    )

  Returns the level of positive ZDD variable.

    int
    cuddZddInitUniv(
      DdManager * zdd
    )

  Initializes the ZDD universe. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `cuddZddFreeUniv`

    DdNode *
    cuddZddIntersect(
      DdManager * zdd,
      DdNode * P,
      DdNode * Q
    )

  Performs the recursive step of Cudd_zddIntersect.

  Side Effects None

    DdNode	*
    cuddZddIsop(
      DdManager * dd,
      DdNode * L,
      DdNode * U,
      DdNode ** zdd_I
    )

  Performs the recursive step of Cudd_zddIsop.

  Side Effects None

  See Also `Cudd_zddIsop`

    DdNode *
    cuddZddIte(
      DdManager * dd,
      DdNode * f,
      DdNode * g,
      DdNode * h
    )

  Performs the recursive step of Cudd_zddIte.

  Side Effects None

    int
    cuddZddLinearInPlace(
      DdManager * table,
      int  x,
      int  y
    )

  Linearly combines two adjacent variables. It assumes that no dead nodes are present on entry to this procedure. The procedure then guarantees that no dead nodes will be present when it terminates. cuddZddLinearInPlace assumes that x < y. Returns the number of keys in the table if successful; 0 otherwise.

  Side Effects None

  See Also `cuddZddSwapInPlace cuddLinearInPlace`

    int
    cuddZddLinearSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  Implementation of the linear sifting algorithm for ZDDs. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique table.
  2. Sift the variable up and down and applies the XOR transformation, remembering each time the total size of the DD heap.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 if successful; 0 otherwise.

  Side Effects None

    int
    cuddZddNextHigh(
      DdManager * table,
      int  x
    )

  Finds the next subtable with a larger index. Returns the index.

  Side Effects None

    int
    cuddZddNextLow(
      DdManager * table,
      int  x
    )

  Finds the next subtable with a smaller index. Returns the index.

  Side Effects None

    DdNode	*
    cuddZddProduct(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddProduct.

  Side Effects None

  See Also `Cudd_zddProduct`

    int
    cuddZddP(
      DdManager * zdd,
      DdNode * f
    )

  Prints a ZDD to the standard output. One line per node is printed. Returns 1 if successful; 0 otherwise.

  Side Effects None

  See Also `Cudd_zddPrintDebug`

    int
    cuddZddSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  Implementation of Rudell's sifting algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique table.
  2. Sift the variable up and down, remembering each time the total size of the DD heap.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 if successful; 0 otherwise.

  Side Effects None

    DdNode *
    cuddZddSubset0(
      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. cuddZddSubset0 performs the same function as Cudd_zddSubset0, but does not restart if reordering has taken place. Therefore it can be called from within a recursive procedure.

  Side Effects None

  See Also `cuddZddSubset1 Cudd_zddSubset0`

    DdNode *
    cuddZddSubset1(
      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. cuddZddSubset1 performs the same function as Cudd_zddSubset1, but does not restart if reordering has taken place. Therefore it can be called from within a recursive procedure.

  Side Effects None

  See Also `cuddZddSubset0 Cudd_zddSubset1`

    int
    cuddZddSwapInPlace(
      DdManager * table,
      int  x,
      int  y
    )

  Swaps two adjacent variables. It assumes that no dead nodes are present on entry to this procedure. The procedure then guarantees that no dead nodes will be present when it terminates. cuddZddSwapInPlace assumes that x < y. Returns the number of keys in the table if successful; 0 otherwise.

  Side Effects None

    int
    cuddZddSwapping(
      DdManager * table,
      int  lower,
      int  upper,
      Cudd_ReorderingType  heuristic
    )

  Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.
  1. Select two variables (RANDOM or HEURISTIC).
  2. Permute these variables.
  3. If the nodes have decreased accept the permutation.
  4. Otherwise reconstruct the original heap.
  5. Loop.
  Returns 1 in case of success; 0 otherwise.

  Side Effects None

    int
    cuddZddSymmCheck(
      DdManager * table,
      int  x,
      int  y
    )

  Checks for symmetry of x and y. Ignores projection functions, unless they are isolated. Returns 1 in case of symmetry; 0 otherwise.

  Side Effects None

    int
    cuddZddSymmSiftingConv(
      DdManager * table,
      int  lower,
      int  upper
    )

  Symmetric sifting to convergence algorithm for ZDDs. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique subtable.
  2. Sift the variable up and down, remembering each time the total size of the ZDD heap and grouping variables that are symmetric.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  5. Repeat 1-4 until no further improvement.
  Returns 1 plus the number of symmetric variables if successful; 0 otherwise.

  Side Effects None

  See Also `cuddZddSymmSifting`

    int
    cuddZddSymmSifting(
      DdManager * table,
      int  lower,
      int  upper
    )

  Symmetric sifting algorithm. Assumes that no dead nodes are present.
  1. Order all the variables according to the number of entries in each unique subtable.
  2. Sift the variable up and down, remembering each time the total size of the ZDD heap and grouping variables that are symmetric.
  3. Select the best permutation.
  4. Repeat 3 and 4 for all variables.
  Returns 1 plus the number of symmetric variables if successful; 0 otherwise.

  Side Effects None

  See Also `cuddZddSymmSiftingConv`

    int
    cuddZddTreeSifting(
      DdManager * table, DD table
      Cudd_ReorderingType  method reordering method for the groups of leaves
    )

  Tree sifting algorithm for ZDDs. Assumes that a tree representing a group hierarchy is passed as a parameter. It then reorders each group in postorder fashion by calling zddTreeSiftingAux. Assumes that no dead nodes are present. Returns 1 if successful; 0 otherwise.

  Side Effects None

    DdNode	*
    cuddZddUnateProduct(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddUnateProduct.

  Side Effects None

  See Also `Cudd_zddUnateProduct`

    DdNode *
    cuddZddUnion(
      DdManager * zdd,
      DdNode * P,
      DdNode * Q
    )

  Performs the recursive step of Cudd_zddUnion.

  Side Effects None

    int
    cuddZddUniqueCompare(
      int * ptr_x,
      int * ptr_y
    )

  Comparison function used by qsort to order the variables according to the number of keys in the subtables. Returns the difference in number of keys between the two variables being compared.

  Side Effects None

    DdNode	*
    cuddZddWeakDivF(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddWeakDivF.

  Side Effects None

  See Also `Cudd_zddWeakDivF`

    DdNode	*
    cuddZddWeakDiv(
      DdManager * dd,
      DdNode * f,
      DdNode * g
    )

  Performs the recursive step of Cudd_zddWeakDiv.

  Side Effects None

  See Also `Cudd_zddWeakDiv`

    ddAbs(
       x
    )

  Computes the absolute value of a number.

  Side Effects none

    ddCHash2(
       o,
       f,
       g,
       s
    )

  Hash function for the cache for functions with two operands.

  Side Effects none

  See Also `ddHash ddCHash`

    ddCHash(
       o,
       f,
       g,
       h,
       s
    )

  Hash function for the cache.

  Side Effects none

  See Also `ddHash ddCHash2`

    ddEqualVal(
       x,
       y,
       e
    )

  Returns 1 if the absolute value of the difference of the two arguments x and y is less than e.

  Side Effects none

    ddHash(
       f,
       g,
       s
    )

  Hash function for the unique table.

  Side Effects none

  See Also `ddCHash ddCHash2`

    ddLCHash2(
       f,
       g,
       shift
    )

  Computes hash function for keys of two operands.

  Side Effects None

  See Also `ddLCHash3 ddLCHash`

    ddLCHash3(
       f,
       g,
       h,
       shift
    )

  Computes hash function for keys of three operands.

  Side Effects None

  See Also `ddLCHash2 ddLCHash`

    ddMax(
       x,
       y
    )

  Computes the maximum of two numbers.

  Side Effects none

  See Also `ddMin`

    ddMin(
       x,
       y
    )

  Computes the minimum of two numbers.

  Side Effects none

  See Also `ddMax`

    lqHash(
       key,
       shift
    )

  Hash function for the table of a level queue.

  Side Effects None

  See Also `hashInsert hashLookup hashDelete`

    statLine(
       dd
    )

  Outputs a line of stats if DD_COUNT and DD_STATS are defined. Increments the number of recursive calls if DD_COUNT is defined.

  Side Effects None

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