Functions for dynamic variable reordering. More...

#include "util.h"
#include "mtrInt.h"
#include "cuddInt.h"

Include dependency graph for cuddReorder.c:

Functions
int	Cudd_ReduceHeap (DdManager *table, Cudd_ReorderingType heuristic, int minsize)
	Main dynamic reordering routine. More...

int	Cudd_ShuffleHeap (DdManager table, int permutation)
	Reorders variables according to given permutation. More...

DdNode *	cuddDynamicAllocNode (DdManager *table)
	Dynamically allocates a Node. More...

int	cuddSifting (DdManager *table, int lower, int upper)
	Implementation of Rudell's sifting algorithm. More...

int	cuddSwapping (DdManager *table, int lower, int upper, Cudd_ReorderingType heuristic)
	Reorders variables by a sequence of (non-adjacent) swaps. More...

int	cuddNextHigh (DdManager *table, int x)
	Finds the next subtable with a larger index. More...

int	cuddNextLow (DdManager *table, int x)
	Finds the next subtable with a smaller index. More...

int	cuddSwapInPlace (DdManager *table, int x, int y)
	Swaps two adjacent variables. More...

int	cuddBddAlignToZdd (DdManager *table)
	Reorders BDD variables according to the order of the ZDD variables. More...

static int	ddUniqueCompare (void const ptrX, void const ptrY)
	Comparison function used by qsort. More...

static Move *	ddSwapAny (DdManager *table, int x, int y)
	Swaps any two variables. More...

static int	ddSiftingAux (DdManager *table, int x, int xLow, int xHigh)
	Given xLow <= x <= xHigh moves x up and down between the boundaries. More...

static Move *	ddSiftingUp (DdManager *table, int y, int xLow)
	Sifts a variable up. More...

static Move *	ddSiftingDown (DdManager *table, int x, int xHigh)
	Sifts a variable down. More...

static int	ddSiftingBackward (DdManager table, int size, Move moves)
	Given a set of moves, returns the DD heap to the position giving the minimum size. More...

static int	ddReorderPreprocess (DdManager *table)
	Prepares the DD heap for dynamic reordering. More...

static int	ddReorderPostprocess (DdManager *table)
	Cleans up at the end of reordering. More...

static int	ddShuffle (DdManager table, int permutation)
	Reorders variables according to a given permutation. More...

static int	ddSiftUp (DdManager *table, int x, int xLow)
	Moves one variable up. More...

static void	bddFixTree (DdManager table, MtrNode treenode)
	Fixes the BDD variable group tree after a shuffle. More...

static int	ddUpdateMtrTree (DdManager table, MtrNode treenode, int perm, int invperm)
	Updates the BDD variable group tree before a shuffle. More...

static int	ddCheckPermuation (DdManager table, MtrNode treenode, int perm, int invperm)
	Checks the BDD variable group tree before a shuffle. More...

Detailed Description

Functions for dynamic variable reordering.

Author: Shipra Panda, Bernard Plessier, Fabio Somenzi

Copyright

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Function Documentation

◆ bddFixTree()

static void bddFixTree	(	DdManager *	table,
		MtrNode *	treenode
	)

static

Fixes the BDD variable group tree after a shuffle.

Assumes that the order of the variables in a terminal node has not been changed.

Side effects Changes the BDD variable group tree.

◆ Cudd_ReduceHeap()

int Cudd_ReduceHeap	(	DdManager *	table,
		Cudd_ReorderingType	heuristic,
		int	minsize
	)

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.

Parameters

table	DD manager
heuristic	method used for reordering
minsize	bound below which no reordering occurs

◆ Cudd_ShuffleHeap()

int Cudd_ShuffleHeap	(	DdManager *	table,
		int *	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

Parameters

table	DD manager
permutation	required variable permutation

◆ cuddBddAlignToZdd()

int cuddBddAlignToZdd ( DdManager * table )

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

Parameters

table DD manager

◆ cuddDynamicAllocNode()

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

◆ cuddNextHigh()

int cuddNextHigh	(	DdManager *	table,
		int	x
	)

Finds the next subtable with a larger index.

Returns: the index.

Side effects None

See also: cuddNextLow

◆ cuddNextLow()

int cuddNextLow	(	DdManager *	table,
		int	x
	)

Finds the next subtable with a smaller index.

Returns: the index.

Side effects None

See also: cuddNextHigh

◆ cuddSifting()

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

Implementation of Rudell's sifting algorithm.

Assumes that no dead nodes are present.

Order all the variables according to the number of entries in each unique table.
Sift the variable up and down, remembering each time the total size of the DD heap.
Select the best permutation.
Repeat 3 and 4 for all variables.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ cuddSwapInPlace()

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

◆ cuddSwapping()

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

Reorders variables by a sequence of (non-adjacent) swaps.

Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.

Select two variables (RANDOM or HEURISTIC).
Permute these variables.
If the nodes have decreased accept the permutation.
Otherwise reconstruct the original heap.
Loop.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ ddCheckPermuation()

static int ddCheckPermuation	(	DdManager *	table,
		MtrNode *	treenode,
		int *	perm,
		int *	invperm
	)

static

Checks the BDD variable group tree before a shuffle.

Returns: 1 if successful; 0 otherwise.

Side effects Changes the BDD variable group tree.

◆ ddReorderPostprocess()

static int ddReorderPostprocess ( DdManager * table )

static

Cleans up at the end of reordering.

Side effects None

◆ ddReorderPreprocess()

static int ddReorderPreprocess ( DdManager * table )

static

Prepares the DD heap for dynamic reordering.

Does garbage collection, to guarantee that there are no dead nodes; clears the cache, which is invalidated by dynamic reordering; initializes the number of isolated projection functions; and initializes the interaction matrix.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ ddShuffle()

static int ddShuffle	(	DdManager *	table,
		int *	permutation
	)

static

Reorders variables according to a given permutation.

The i-th permutation array contains the index of the variable that should be brought to the i-th level. ddShuffle assumes that no dead nodes are present and that the interaction matrix is properly initialized. The reordering is achieved by a series of upward sifts.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ ddSiftingAux()

static int ddSiftingAux	(	DdManager *	table,
		int	x,
		int	xLow,
		int	xHigh
	)

static

Given xLow <= x <= xHigh moves x up and down between the boundaries.

Finds the best position and does the required changes.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ ddSiftingBackward()

static int ddSiftingBackward	(	DdManager *	table,
		int	size,
		Move *	moves
	)

static

Given a set of moves, returns the DD heap to the position giving the minimum size.

In case of ties, returns to the closest position giving the minimum size.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ ddSiftingDown()

static Move* ddSiftingDown	(	DdManager *	table,
		int	x,
		int	xHigh
	)

static

Sifts a variable down.

Moves x down until either it reaches the bound (xHigh) or the size of the DD heap increases too much.

Returns: the set of moves in case of success; NULL if memory is full.

Side effects None

◆ ddSiftingUp()

static Move* ddSiftingUp	(	DdManager *	table,
		int	y,
		int	xLow
	)

static

Sifts a variable up.

Moves y up until either it reaches the bound (xLow) or the size of the DD heap increases too much.

Returns: the set of moves in case of success; NULL if memory is full.

Side effects None

◆ ddSiftUp()

static int ddSiftUp	(	DdManager *	table,
		int	x,
		int	xLow
	)

static

Moves one variable up.

Takes a variable from position x and sifts it up to position xLow; xLow should be less than or equal to x.

Returns: 1 if successful; 0 otherwise

Side effects None

◆ ddSwapAny()

static Move* ddSwapAny	(	DdManager *	table,
		int	x,
		int	y
	)

static

Swaps any two variables.

Returns: the set of moves.

Side effects None

◆ ddUniqueCompare()

static int ddUniqueCompare	(	void const *	ptrX,
		void const *	ptrY
	)

static

Comparison function used by qsort.

Used 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

◆ ddUpdateMtrTree()

static int ddUpdateMtrTree	(	DdManager *	table,
		MtrNode *	treenode,
		int *	perm,
		int *	invperm
	)

static

Updates the BDD variable group tree before a shuffle.

Returns: 1 if successful; 0 otherwise.

Side effects Changes the BDD variable group tree.