Priority functions. More...
#include "util.h"
#include "cuddInt.h"
Functions | |
DdNode * | Cudd_PrioritySelect (DdManager *dd, DdNode *R, DdNode **x, DdNode **y, DdNode **z, DdNode *Pi, int n, DD_PRFP Pifunc) |
Selects pairs from R using a priority function. | |
DdNode * | Cudd_Xgty (DdManager *dd, int N, DdNode **z, DdNode **x, DdNode **y) |
Generates a BDD for the function x > y. | |
DdNode * | Cudd_Xeqy (DdManager *dd, int N, DdNode **x, DdNode **y) |
Generates a BDD for the function x==y. | |
DdNode * | Cudd_addXeqy (DdManager *dd, int N, DdNode **x, DdNode **y) |
Generates an ADD for the function x==y. | |
DdNode * | Cudd_Dxygtdxz (DdManager *dd, int N, DdNode **x, DdNode **y, DdNode **z) |
Generates a BDD for the function d(x,y) > d(x,z). | |
DdNode * | Cudd_Dxygtdyz (DdManager *dd, int N, DdNode **x, DdNode **y, DdNode **z) |
Generates a BDD for the function d(x,y) > d(y,z). | |
DdNode * | Cudd_Inequality (DdManager *dd, int N, int c, DdNode **x, DdNode **y) |
Generates a BDD for the function x - y c. | |
DdNode * | Cudd_Disequality (DdManager *dd, int N, int c, DdNode **x, DdNode **y) |
Generates a BDD for the function x - y != c. | |
DdNode * | Cudd_bddInterval (DdManager *dd, int N, DdNode **x, unsigned int lowerB, unsigned int upperB) |
Generates a BDD for the function lowerB x upperB. | |
DdNode * | Cudd_CProjection (DdManager *dd, DdNode *R, DdNode *Y) |
Computes the compatible projection of R w.r.t. cube Y. | |
DdNode * | Cudd_addHamming (DdManager *dd, DdNode **xVars, DdNode **yVars, int nVars) |
Computes the Hamming distance ADD. | |
int | Cudd_MinHammingDist (DdManager *dd, DdNode *f, int *minterm, int upperBound) |
Returns the minimum Hamming distance between f and minterm. | |
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. | |
DdNode * | cuddCProjectionRecur (DdManager *dd, DdNode *R, DdNode *Y, DdNode *Ysupp) |
Performs the recursive step of Cudd_CProjection. | |
DdNode * | cuddBddClosestCube (DdManager *dd, DdNode *f, DdNode *g, CUDD_VALUE_TYPE bound) |
Performs the recursive step of Cudd_bddClosestCube. | |
static int | cuddMinHammingDistRecur (DdNode *f, int *minterm, DdHashTable *table, int upperBound) |
Performs the recursive step of Cudd_MinHammingDist. | |
static DdNode * | separateCube (DdManager *dd, DdNode *f, CUDD_VALUE_TYPE *distance) |
Separates cube from distance. | |
static DdNode * | createResult (DdManager *dd, unsigned int index, unsigned int phase, DdNode *cube, CUDD_VALUE_TYPE distance) |
Builds a result for cache storage. |
Priority functions.
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static DdNode* createResult | ( | DdManager * | dd, | |
unsigned int | index, | |||
unsigned int | phase, | |||
DdNode * | cube, | |||
CUDD_VALUE_TYPE | distance | |||
) | [static] |
Builds a result for cache storage.
Computes the Hamming distance ADD.
The two vectors xVars and yVars identify the variables that form the two arguments.
Generates an ADD for the function x==y.
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\[N-1\]. 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\[N-1\].
dd | DD manager | |
N | number of x and y variables | |
x | array of x variables | |
y | array of y variables |
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.
DdNode* Cudd_bddInterval | ( | DdManager * | dd, | |
int | N, | |||
DdNode ** | x, | |||
unsigned int | lowerB, | |||
unsigned int | upperB | |||
) |
Generates a BDD for the function lowerB x upperB.
This function generates a BDD for the function lowerB x upperB, where x is an N-bit number, x\[0\] x\[1\] ... x\[N-1\], with 0 the most significant bit (important!). The number of variables N should be sufficient to represent the bounds; otherwise, the bounds are truncated to their N least significant bits. Two BDDs are built bottom-up for lowerB x and x upperB, and they are finally conjoined.
dd | DD manager | |
N | number of x variables | |
x | array of x variables | |
lowerB | lower bound | |
upperB | upper bound |
Computes the compatible projection of R w.r.t. cube Y.
Computes the compatible projection of relation R with respect to cube Y. For a comparison between Cudd_CProjection and Cudd_PrioritySelect, see the documentation of the latter.
Generates a BDD for the function x - y != c.
This function generates a BDD for the function x -y != c. 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 a linear number of nodes if the variables are ordered as follows: x\[0\] y\[0\] x\[1\] y\[1\] ... x\[N-1\] y\[N-1\].
dd | DD manager | |
N | number of x and y variables | |
c | right-hand side constant | |
x | array of x variables | |
y | array of y variables |
Generates a BDD for the function d(x,y) > d(x,z).
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: . 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\[N-1\].
dd | DD manager | |
N | number of x, y, and z variables | |
x | array of x variables | |
y | array of y variables | |
z | array of z variables |
Generates a BDD for the function d(x,y) > d(y,z).
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: . 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\[N-1\].
dd | DD manager | |
N | number of x, y, and z variables | |
x | array of x variables | |
y | array of y variables | |
z | array of z variables |
Generates a BDD for the function x - y c.
This function generates a BDD for the function x -y c. 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 a linear number of nodes if the variables are ordered as follows: x\[0\] y\[0\] x\[1\] y\[1\] ... x\[N-1\] y\[N-1\].
dd | DD manager | |
N | number of x and y variables | |
c | right-hand side constant | |
x | array of x variables | |
y | array of y variables |
Returns the minimum Hamming distance between f and minterm.
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.
dd | DD manager | |
f | function to examine | |
minterm | reference minterm | |
upperBound | distance above which an approximate answer is OK |
DdNode* Cudd_PrioritySelect | ( | DdManager * | dd, | |
DdNode * | R, | |||
DdNode ** | x, | |||
DdNode ** | y, | |||
DdNode ** | z, | |||
DdNode * | Pi, | |||
int | n, | |||
DD_PRFP | Pifunc | |||
) |
Selects pairs from R using a priority function.
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. 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 vector 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:
dd | manager | |
R | BDD of the relation | |
x | array of x variables | |
y | array of y variables | |
z | array of z variables (optional: may be NULL) | |
Pi | BDD of the priority function (optional: may be NULL) | |
n | size of x, y, and z | |
Pifunc | function used to build Pi if it is NULL |
Generates a BDD for the function x==y.
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\[N-1\]. 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\[N-1\].
dd | DD manager | |
N | number of x and y variables | |
x | array of x variables | |
y | array of y variables |
Generates a BDD for the function x > y.
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.
dd | DD manager | |
N | number of x and y variables | |
z | array of z variables: unused | |
x | array of x variables | |
y | array of y variables |
DdNode* cuddBddClosestCube | ( | DdManager * | dd, | |
DdNode * | f, | |||
DdNode * | g, | |||
CUDD_VALUE_TYPE | bound | |||
) |
Performs the recursive step of Cudd_bddClosestCube.
The procedure uses a four-way recursion to examine all four combinations of cofactors of f
and g
according to the following formula.
H(f,g) = min(H(ft,gt), H(fe,ge), H(ft,ge)+1, H(fe,gt)+1)
Bounding is based on the following observations.
The variable bound
is set at the largest value of the distance that we are still interested in. Therefore, we desist when
(bound == -1) and (F != not(G)) or (bound == 0) and (F == not(G)).
If we were maximally aggressive in using the bound, we would always set the bound to the minimum distance seen thus far minus one. That is, we would maintain the invariant
bound < minD,
except at the very beginning, when we have no value for minD
.
However, we do not use bound < minD
when examining the two negative cofactors, because we try to find a large cube at minimum distance. To do so, we try to find a cube in the negative cofactors at the same or smaller distance from the cube found in the positive cofactors.
When we compute H(ft,ge)
and H(fe,gt)
we know that we are going to add 1 to the result of the recursive call to account for the difference in the splitting variable. Therefore, we decrease the bound correspondingly.
Another important observation concerns the need of examining all four pairs of cofators only when both f
and g
depend on the top variable.
Suppose gt == ge == g
. (That is, g
does not depend on the top variable.) Then
H(f,g) = min(H(ft,g), H(fe,g), H(ft,g)+1, H(fe,g)+1) = min(H(ft,g), H(fe,g)) .
Therefore, under these circumstances, we skip the two "cross" cases.
An 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).
Performs the recursive step of Cudd_CProjection.
static int cuddMinHammingDistRecur | ( | DdNode * | f, | |
int * | minterm, | |||
DdHashTable * | table, | |||
int | upperBound | |||
) | [static] |
Performs the recursive step of Cudd_MinHammingDist.
It is based on the following identity. Let H(f) be the minimum Hamming distance of the minterms of f from the reference minterm. Then:
H(f) = min(H(f0)+h0,H(f1)+h1)
where f0 and f1 are the two cofactors of f with respect to its top variable; h0 is 1 if the minterm assigns 1 to the top variable of f; h1 is 1 if the minterm assigns 0 to the top variable of f. The upper bound on the distance is used to bound the depth of the recursion.
static DdNode* separateCube | ( | DdManager * | dd, | |
DdNode * | f, | |||
CUDD_VALUE_TYPE * | distance | |||
) | [static] |
Separates cube from distance.