/**CFile***********************************************************************
FileName [cuddSymmetry.c]
PackageName [cudd]
Synopsis [Functions for symmetry-based variable reordering.]
Description [External procedures included in this file:
<ul>
<li> Cudd_SymmProfile()
</ul>
Internal procedures included in this module:
<ul>
<li> cuddSymmCheck()
<li> cuddSymmSifting()
<li> cuddSymmSiftingConv()
</ul>
Static procedures included in this module:
<ul>
<li> ddSymmUniqueCompare()
<li> ddSymmSiftingAux()
<li> ddSymmSiftingConvAux()
<li> ddSymmSiftingUp()
<li> ddSymmSiftingDown()
<li> ddSymmGroupMove()
<li> ddSymmGroupMoveBackward()
<li> ddSymmSiftingBackward()
<li> ddSymmSummary()
</ul>]
Author [Shipra Panda, Fabio Somenzi]
Copyright [Copyright (c) 1995-2004, Regents of the University of Colorado
All rights reserved.
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.]
******************************************************************************/
#include "misc/util/util_hack.h"
#include "cuddInt.h"
ABC_NAMESPACE_IMPL_START
/*---------------------------------------------------------------------------*/
/* Constant declarations */
/*---------------------------------------------------------------------------*/
#define MV_OOM (Move *)1
/*---------------------------------------------------------------------------*/
/* Stucture declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Type declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Variable declarations */
/*---------------------------------------------------------------------------*/
#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddSymmetry.c,v 1.26 2009/02/19 16:23:54 fabio Exp $";
#endif
static int *entry;
extern int ddTotalNumberSwapping;
#ifdef DD_STATS
extern int ddTotalNISwaps;
#endif
/*---------------------------------------------------------------------------*/
/* Macro declarations */
/*---------------------------------------------------------------------------*/
/**AutomaticStart*************************************************************/
/*---------------------------------------------------------------------------*/
/* Static function prototypes */
/*---------------------------------------------------------------------------*/
static int ddSymmUniqueCompare (int *ptrX, int *ptrY);
static int ddSymmSiftingAux (DdManager *table, int x, int xLow, int xHigh);
static int ddSymmSiftingConvAux (DdManager *table, int x, int xLow, int xHigh);
static Move * ddSymmSiftingUp (DdManager *table, int y, int xLow);
static Move * ddSymmSiftingDown (DdManager *table, int x, int xHigh);
static int ddSymmGroupMove (DdManager *table, int x, int y, Move **moves);
static int ddSymmGroupMoveBackward (DdManager *table, int x, int y);
static int ddSymmSiftingBackward (DdManager *table, Move *moves, int size);
static void ddSymmSummary (DdManager *table, int lower, int upper, int *symvars, int *symgroups);
/**AutomaticEnd***************************************************************/
/*---------------------------------------------------------------------------*/
/* Definition of exported functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Prints statistics on symmetric variables.]
Description []
SideEffects [None]
******************************************************************************/
void
Cudd_SymmProfile(
DdManager * table,
int lower,
int upper)
{
int i,x,gbot;
int TotalSymm = 0;
int TotalSymmGroups = 0;
for (i = lower; i <= upper; i++) {
if (table->subtables[i].next != (unsigned) i) {
x = i;
(void) fprintf(table->out,"Group:");
do {
(void) fprintf(table->out," %d",table->invperm[x]);
TotalSymm++;
gbot = x;
x = table->subtables[x].next;
} while (x != i);
TotalSymmGroups++;
#ifdef DD_DEBUG
assert(table->subtables[gbot].next == (unsigned) i);
#endif
i = gbot;
(void) fprintf(table->out,"\n");
}
}
(void) fprintf(table->out,"Total Symmetric = %d\n",TotalSymm);
(void) fprintf(table->out,"Total Groups = %d\n",TotalSymmGroups);
} /* end of Cudd_SymmProfile */
/*---------------------------------------------------------------------------*/
/* Definition of internal functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Checks for symmetry of x and y.]
Description [Checks for symmetry of x and y. Ignores projection
functions, unless they are isolated. Returns 1 in case of symmetry; 0
otherwise.]
SideEffects [None]
******************************************************************************/
int
cuddSymmCheck(
DdManager * table,
int x,
int y)
{
DdNode *f,*f0,*f1,*f01,*f00,*f11,*f10;
int comple; /* f0 is complemented */
int xsymmy; /* x and y may be positively symmetric */
int xsymmyp; /* x and y may be negatively symmetric */
int arccount; /* number of arcs from layer x to layer y */
int TotalRefCount; /* total reference count of layer y minus 1 */
int yindex;
int i;
DdNodePtr *list;
int slots;
DdNode *sentinel = &(table->sentinel);
#ifdef DD_DEBUG
int xindex;
#endif
/* Checks that x and y are not the projection functions.
** For x it is sufficient to check whether there is only one
** node; indeed, if there is one node, it is the projection function
** and it cannot point to y. Hence, if y isn't just the projection
** function, it has one arc coming from a layer different from x.
*/
if (table->subtables[x].keys == 1) {
return(0);
}
yindex = table->invperm[y];
if (table->subtables[y].keys == 1) {
if (table->vars[yindex]->ref == 1)
return(0);
}
xsymmy = xsymmyp = 1;
arccount = 0;
slots = table->subtables[x].slots;
list = table->subtables[x].nodelist;
for (i = 0; i < slots; i++) {
f = list[i];
while (f != sentinel) {
/* Find f1, f0, f11, f10, f01, f00. */
f1 = cuddT(f);
f0 = Cudd_Regular(cuddE(f));
comple = Cudd_IsComplement(cuddE(f));
if ((int) f1->index == yindex) {
arccount++;
f11 = cuddT(f1); f10 = cuddE(f1);
} else {
if ((int) f0->index != yindex) {
/* If f is an isolated projection function it is
** allowed to bypass layer y.
*/
if (f1 != DD_ONE(table) || f0 != DD_ONE(table) || f->ref != 1)
return(0); /* f bypasses layer y */
}
f11 = f10 = f1;
}
if ((int) f0->index == yindex) {
arccount++;
f01 = cuddT(f0); f00 = cuddE(f0);
} else {
f01 = f00 = f0;
}
if (comple) {
f01 = Cudd_Not(f01);
f00 = Cudd_Not(f00);
}
if (f1 != DD_ONE(table) || f0 != DD_ONE(table) || f->ref != 1) {
xsymmy &= f01 == f10;
xsymmyp &= f11 == f00;
if ((xsymmy == 0) && (xsymmyp == 0))
return(0);
}
f = f->next;
} /* while */
} /* for */
/* Calculate the total reference counts of y */
TotalRefCount = -1; /* -1 for projection function */
slots = table->subtables[y].slots;
list = table->subtables[y].nodelist;
for (i = 0; i < slots; i++) {
f = list[i];
while (f != sentinel) {
TotalRefCount += f->ref;
f = f->next;
}
}
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
if (arccount == TotalRefCount) {
xindex = table->invperm[x];
(void) fprintf(table->out,
"Found symmetry! x =%d\ty = %d\tPos(%d,%d)\n",
xindex,yindex,x,y);
}
#endif
return(arccount == TotalRefCount);
} /* end of cuddSymmCheck */
/**Function********************************************************************
Synopsis [Symmetric sifting algorithm.]
Description [Symmetric sifting algorithm.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the DD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddSymmSiftingConv]
******************************************************************************/
int
cuddSymmSifting(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int size;
int x;
int result;
int symvars;
int symgroups;
#ifdef DD_STATS
int previousSize;
#endif
size = table->size;
/* Find order in which to sift variables. */
var = NULL;
entry = ABC_ALLOC(int,size);
if (entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingOutOfMem;
}
var = ABC_ALLOC(int,size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->perm[i];
entry[i] = table->subtables[x].keys;
var[i] = i;
}
qsort((void *)var,size,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Initialize the symmetry of each subtable to itself. */
for (i = lower; i <= upper; i++) {
table->subtables[i].next = i;
}
for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
// enable timeout during variable reodering - alanmi 2/13/11
if ( table->TimeStop && Abc_Clock() > table->TimeStop )
break;
x = table->perm[var[i]];
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
if (x < lower || x > upper) continue;
if (table->subtables[x].next == (unsigned) x) {
result = ddSymmSiftingAux(table,x,lower,upper);
if (!result) goto ddSymmSiftingOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+"); /* should never happen */
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
ABC_FREE(var);
ABC_FREE(entry);
ddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out, "\n#:S_SIFTING %8d: symmetric variables\n",
symvars);
(void) fprintf(table->out, "#:G_SIFTING %8d: symmetric groups",
symgroups);
#endif
return(1+symvars);
ddSymmSiftingOutOfMem:
if (entry != NULL) ABC_FREE(entry);
if (var != NULL) ABC_FREE(var);
return(0);
} /* end of cuddSymmSifting */
/**Function********************************************************************
Synopsis [Symmetric sifting to convergence algorithm.]
Description [Symmetric sifting to convergence algorithm.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the DD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
<li> Repeat 1-4 until no further improvement.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddSymmSifting]
******************************************************************************/
int
cuddSymmSiftingConv(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int size;
int x;
int result;
int symvars;
int symgroups;
int classes;
int initialSize;
#ifdef DD_STATS
int previousSize;
#endif
initialSize = table->keys - table->isolated;
size = table->size;
/* Find order in which to sift variables. */
var = NULL;
entry = ABC_ALLOC(int,size);
if (entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingConvOutOfMem;
}
var = ABC_ALLOC(int,size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingConvOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->perm[i];
entry[i] = table->subtables[x].keys;
var[i] = i;
}
qsort((void *)var,size,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Initialize the symmetry of each subtable to itself
** for first pass of converging symmetric sifting.
*/
for (i = lower; i <= upper; i++) {
table->subtables[i].next = i;
}
for (i = 0; i < ddMin(table->siftMaxVar, table->size); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
x = table->perm[var[i]];
if (x < lower || x > upper) continue;
/* Only sift if not in symmetry group already. */
if (table->subtables[x].next == (unsigned) x) {
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
result = ddSymmSiftingAux(table,x,lower,upper);
if (!result) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
/* Sifting now until convergence. */
while ((unsigned) initialSize > table->keys - table->isolated) {
initialSize = table->keys - table->isolated;
#ifdef DD_STATS
(void) fprintf(table->out,"\n");
#endif
/* Here we consider only one representative for each symmetry class. */
for (x = lower, classes = 0; x <= upper; x++, classes++) {
while ((unsigned) x < table->subtables[x].next) {
x = table->subtables[x].next;
}
/* Here x is the largest index in a group.
** Groups consist of adjacent variables.
** Hence, the next increment of x will move it to a new group.
*/
i = table->invperm[x];
entry[i] = table->subtables[x].keys;
var[classes] = i;
}
qsort((void *)var,classes,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar,classes); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
x = table->perm[var[i]];
if ((unsigned) x >= table->subtables[x].next) {
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
result = ddSymmSiftingConvAux(table,x,lower,upper);
if (!result ) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
} /* for */
}
ddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out, "\n#:S_SIFTING %8d: symmetric variables\n",
symvars);
(void) fprintf(table->out, "#:G_SIFTING %8d: symmetric groups",
symgroups);
#endif
ABC_FREE(var);
ABC_FREE(entry);
return(1+symvars);
ddSymmSiftingConvOutOfMem:
if (entry != NULL) ABC_FREE(entry);
if (var != NULL) ABC_FREE(var);
return(0);
} /* end of cuddSymmSiftingConv */
/*---------------------------------------------------------------------------*/
/* Definition of static functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Comparison function used by qsort.]
Description [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.]
SideEffects [None]
******************************************************************************/
static int
ddSymmUniqueCompare(
int * ptrX,
int * ptrY)
{
#if 0
if (entry[*ptrY] == entry[*ptrX]) {
return((*ptrX) - (*ptrY));
}
#endif
return(entry[*ptrY] - entry[*ptrX]);
} /* end of ddSymmUniqueCompare */
/**Function********************************************************************
Synopsis [Given xLow <= x <= xHigh moves x up and down between the
boundaries.]
Description [Given xLow <= x <= xHigh moves x up and down between the
boundaries. Finds the best position and does the required changes.
Assumes that x is not part of a symmetry group. Returns 1 if
successful; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
ddSymmSiftingAux(
DdManager * table,
int x,
int xLow,
int xHigh)
{
Move *move;
Move *moveUp; /* list of up moves */
Move *moveDown; /* list of down moves */
int initialSize;
int result;
int i;
int topbot; /* index to either top or bottom of symmetry group */
int initGroupSize, finalGroupSize;
#ifdef DD_DEBUG
/* check for previously detected symmetry */
assert(table->subtables[x].next == (unsigned) x);
#endif
initialSize = table->keys - table->isolated;
moveDown = NULL;
moveUp = NULL;
if ((x - xLow) > (xHigh - x)) {
/* Will go down first, unless x == xHigh:
** Look for consecutive symmetries above x.
*/
for (i = x; i > xLow; i--) {
if (!cuddSymmCheck(table,i-1,i))
break;
topbot = table->subtables[i-1].next; /* find top of i-1's group */
table->subtables[i-1].next = i;
table->subtables[x].next = topbot; /* x is bottom of group so its */
/* next is top of i-1's group */
i = topbot + 1; /* add 1 for i--; new i is top of symm group */
}
} else {
/* Will go up first unless x == xlow:
** Look for consecutive symmetries below x.
*/
for (i = x; i < xHigh; i++) {
if (!cuddSymmCheck(table,i,i+1))
break;
/* find bottom of i+1's symm group */
topbot = i + 1;
while ((unsigned) topbot < table->subtables[topbot].next) {
topbot = table->subtables[topbot].next;
}
table->subtables[topbot].next = table->subtables[i].next;
table->subtables[i].next = i + 1;
i = topbot - 1; /* subtract 1 for i++; new i is bottom of group */
}
}
/* Now x may be in the middle of a symmetry group.
** Find bottom of x's symm group.
*/
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
if (x == xLow) { /* Sift down */
#ifdef DD_DEBUG
/* x must be a singleton */
assert((unsigned) x == table->subtables[x].next);
#endif
if (x == xHigh) return(1); /* just one variable */
initGroupSize = 1;
moveDown = ddSymmSiftingDown(table,x,xHigh);
/* after this point x --> xHigh, unless early term */
if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveDown == NULL) return(1);
x = moveDown->y;
/* Find bottom of x's group */
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetry group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
finalGroupSize = i - x + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetry groups detected, return to best position */
result = ddSymmSiftingBackward(table,moveDown,initialSize);
} else {
initialSize = table->keys - table->isolated;
moveUp = ddSymmSiftingUp(table,x,xLow);
result = ddSymmSiftingBackward(table,moveUp,initialSize);
}
if (!result) goto ddSymmSiftingAuxOutOfMem;
} else if (cuddNextHigh(table,x) > xHigh) { /* Sift up */
/* Find top of x's symm group */
i = x; /* bottom */
x = table->subtables[x].next; /* top */
if (x == xLow) return(1); /* just one big group */
initGroupSize = i - x + 1;
moveUp = ddSymmSiftingUp(table,x,xLow);
/* after this point x --> xLow, unless early term */
if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveUp == NULL) return(1);
x = moveUp->x;
/* Find top of x's group */
i = table->subtables[x].next;
#ifdef DD_DEBUG
/* x should be the bottom of the symmetry group and i the top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
finalGroupSize = x - i + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetry groups detected, return to best position */
result = ddSymmSiftingBackward(table,moveUp,initialSize);
} else {
initialSize = table->keys - table->isolated;
moveDown = ddSymmSiftingDown(table,x,xHigh);
result = ddSymmSiftingBackward(table,moveDown,initialSize);
}
if (!result) goto ddSymmSiftingAuxOutOfMem;
} else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
moveDown = ddSymmSiftingDown(table,x,xHigh);
/* at this point x == xHigh, unless early term */
if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveDown != NULL) {
x = moveDown->y; /* x is top here */
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
} else {
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
x = table->subtables[i].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetry group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
initGroupSize = i - x + 1;
moveUp = ddSymmSiftingUp(table,x,xLow);
if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveUp != NULL) {
x = moveUp->x;
i = table->subtables[x].next;
} else {
i = x;
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x should be the bottom of the symmetry group and i the top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
finalGroupSize = x - i + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetry groups detected, return to best position */
result = ddSymmSiftingBackward(table,moveUp,initialSize);
} else {
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
initialSize = table->keys - table->isolated;
moveDown = ddSymmSiftingDown(table,x,xHigh);
result = ddSymmSiftingBackward(table,moveDown,initialSize);
}
if (!result) goto ddSymmSiftingAuxOutOfMem;
} else { /* moving up first: shorter */
/* Find top of x's symmetry group */
x = table->subtables[x].next;
moveUp = ddSymmSiftingUp(table,x,xLow);
/* at this point x == xHigh, unless early term */
if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveUp != NULL) {
x = moveUp->x;
i = table->subtables[x].next;
} else {
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
i = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x is bottom of the symmetry group and i is top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
initGroupSize = x - i + 1;
moveDown = ddSymmSiftingDown(table,x,xHigh);
if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
if (moveDown != NULL) {
x = moveDown->y;
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
} else {
i = x;
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetry group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
finalGroupSize = i - x + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetries detected, go back to best position */
result = ddSymmSiftingBackward(table,moveDown,initialSize);
} else {
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
initialSize = table->keys - table->isolated;
moveUp = ddSymmSiftingUp(table,x,xLow);
result = ddSymmSiftingBackward(table,moveUp,initialSize);
}
if (!result) goto ddSymmSiftingAuxOutOfMem;
}
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
return(1);
ddSymmSiftingAuxOutOfMem:
if (moveDown != MV_OOM) {
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
}
if (moveUp != MV_OOM) {
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
}
return(0);
} /* end of ddSymmSiftingAux */
/**Function********************************************************************
Synopsis [Given xLow <= x <= xHigh moves x up and down between the
boundaries.]
Description [Given xLow <= x <= xHigh moves x up and down between the
boundaries. Finds the best position and does the required changes.
Assumes that x is either an isolated variable, or it is the bottom of
a symmetry group. All symmetries may not have been found, because of
exceeded growth limit. Returns 1 if successful; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
ddSymmSiftingConvAux(
DdManager * table,
int x,
int xLow,
int xHigh)
{
Move *move;
Move *moveUp; /* list of up moves */
Move *moveDown; /* list of down moves */
int initialSize;
int result;
int i;
int initGroupSize, finalGroupSize;
initialSize = table->keys - table->isolated;
moveDown = NULL;
moveUp = NULL;
if (x == xLow) { /* Sift down */
#ifdef DD_DEBUG
/* x is bottom of symmetry group */
assert((unsigned) x >= table->subtables[x].next);
#endif
i = table->subtables[x].next;
initGroupSize = x - i + 1;
moveDown = ddSymmSiftingDown(table,x,xHigh);
/* at this point x == xHigh, unless early term */
if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveDown == NULL) return(1);
x = moveDown->y;
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetric group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
finalGroupSize = i - x + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetries detected, go back to best position */
result = ddSymmSiftingBackward(table,moveDown,initialSize);
} else {
initialSize = table->keys - table->isolated;
moveUp = ddSymmSiftingUp(table,x,xLow);
result = ddSymmSiftingBackward(table,moveUp,initialSize);
}
if (!result) goto ddSymmSiftingConvAuxOutOfMem;
} else if (cuddNextHigh(table,x) > xHigh) { /* Sift up */
/* Find top of x's symm group */
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
i = x; /* bottom */
x = table->subtables[x].next; /* top */
if (x == xLow) return(1);
initGroupSize = i - x + 1;
moveUp = ddSymmSiftingUp(table,x,xLow);
/* at this point x == xLow, unless early term */
if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveUp == NULL) return(1);
x = moveUp->x;
i = table->subtables[x].next;
#ifdef DD_DEBUG
/* x should be the bottom of the symmetry group and i the top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
finalGroupSize = x - i + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetry groups detected, return to best position */
result = ddSymmSiftingBackward(table,moveUp,initialSize);
} else {
initialSize = table->keys - table->isolated;
moveDown = ddSymmSiftingDown(table,x,xHigh);
result = ddSymmSiftingBackward(table,moveDown,initialSize);
}
if (!result)
goto ddSymmSiftingConvAuxOutOfMem;
} else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
moveDown = ddSymmSiftingDown(table,x,xHigh);
/* at this point x == xHigh, unless early term */
if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveDown != NULL) {
x = moveDown->y;
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
} else {
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
i = x;
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetry group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
initGroupSize = i - x + 1;
moveUp = ddSymmSiftingUp(table,x,xLow);
if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveUp != NULL) {
x = moveUp->x;
i = table->subtables[x].next;
} else {
i = x;
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x should be the bottom of the symmetry group and i the top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
finalGroupSize = x - i + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetry groups detected, return to best position */
result = ddSymmSiftingBackward(table,moveUp,initialSize);
} else {
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
initialSize = table->keys - table->isolated;
moveDown = ddSymmSiftingDown(table,x,xHigh);
result = ddSymmSiftingBackward(table,moveDown,initialSize);
}
if (!result) goto ddSymmSiftingConvAuxOutOfMem;
} else { /* moving up first: shorter */
/* Find top of x's symmetry group */
x = table->subtables[x].next;
moveUp = ddSymmSiftingUp(table,x,xLow);
/* at this point x == xHigh, unless early term */
if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveUp != NULL) {
x = moveUp->x;
i = table->subtables[x].next;
} else {
i = x;
while ((unsigned) x < table->subtables[x].next)
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x is bottom of the symmetry group and i is top */
assert((unsigned) x >= table->subtables[x].next);
assert((unsigned) i == table->subtables[x].next);
#endif
initGroupSize = x - i + 1;
moveDown = ddSymmSiftingDown(table,x,xHigh);
if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
if (moveDown != NULL) {
x = moveDown->y;
i = x;
while ((unsigned) i < table->subtables[i].next) {
i = table->subtables[i].next;
}
} else {
i = x;
x = table->subtables[x].next;
}
#ifdef DD_DEBUG
/* x should be the top of the symmetry group and i the bottom */
assert((unsigned) i >= table->subtables[i].next);
assert((unsigned) x == table->subtables[i].next);
#endif
finalGroupSize = i - x + 1;
if (initGroupSize == finalGroupSize) {
/* No new symmetries detected, go back to best position */
result = ddSymmSiftingBackward(table,moveDown,initialSize);
} else {
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
initialSize = table->keys - table->isolated;
moveUp = ddSymmSiftingUp(table,x,xLow);
result = ddSymmSiftingBackward(table,moveUp,initialSize);
}
if (!result) goto ddSymmSiftingConvAuxOutOfMem;
}
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
return(1);
ddSymmSiftingConvAuxOutOfMem:
if (moveDown != MV_OOM) {
while (moveDown != NULL) {
move = moveDown->next;
cuddDeallocMove(table, moveDown);
moveDown = move;
}
}
if (moveUp != MV_OOM) {
while (moveUp != NULL) {
move = moveUp->next;
cuddDeallocMove(table, moveUp);
moveUp = move;
}
}
return(0);
} /* end of ddSymmSiftingConvAux */
/**Function********************************************************************
Synopsis [Moves x up until either it reaches the bound (xLow) or
the size of the DD heap increases too much.]
Description [Moves x up until either it reaches the bound (xLow) or
the size of the DD heap increases too much. Assumes that x is the top
of a symmetry group. Checks x for symmetry to the adjacent
variables. If symmetry is found, the symmetry group of x is merged
with the symmetry group of the other variable. Returns the set of
moves in case of success; MV_OOM if memory is full.]
SideEffects [None]
******************************************************************************/
static Move *
ddSymmSiftingUp(
DdManager * table,
int y,
int xLow)
{
Move *moves;
Move *move;
int x;
int size;
int i;
int gxtop,gybot;
int limitSize;
int xindex, yindex;
int zindex;
int z;
int isolated;
int L; /* lower bound on DD size */
#ifdef DD_DEBUG
int checkL;
#endif
moves = NULL;
yindex = table->invperm[y];
/* Initialize the lower bound.
** The part of the DD below the bottom of y' group will not change.
** The part of the DD above y that does not interact with y will not
** change. The rest may vanish in the best case, except for
** the nodes at level xLow, which will not vanish, regardless.
*/
limitSize = L = table->keys - table->isolated;
gybot = y;
while ((unsigned) gybot < table->subtables[gybot].next)
gybot = table->subtables[gybot].next;
for (z = xLow + 1; z <= gybot; z++) {
zindex = table->invperm[z];
if (zindex == yindex || cuddTestInteract(table,zindex,yindex)) {
isolated = table->vars[zindex]->ref == 1;
L -= table->subtables[z].keys - isolated;
}
}
x = cuddNextLow(table,y);
while (x >= xLow && L <= limitSize) {
#ifdef DD_DEBUG
gybot = y;
while ((unsigned) gybot < table->subtables[gybot].next)
gybot = table->subtables[gybot].next;
checkL = table->keys - table->isolated;
for (z = xLow + 1; z <= gybot; z++) {
zindex = table->invperm[z];
if (zindex == yindex || cuddTestInteract(table,zindex,yindex)) {
isolated = table->vars[zindex]->ref == 1;
checkL -= table->subtables[z].keys - isolated;
}
}
assert(L == checkL);
#endif
gxtop = table->subtables[x].next;
if (cuddSymmCheck(table,x,y)) {
/* Symmetry found, attach symm groups */
table->subtables[x].next = y;
i = table->subtables[y].next;
while (table->subtables[i].next != (unsigned) y)
i = table->subtables[i].next;
table->subtables[i].next = gxtop;
} else if (table->subtables[x].next == (unsigned) x &&
table->subtables[y].next == (unsigned) y) {
/* x and y have self symmetry */
xindex = table->invperm[x];
size = cuddSwapInPlace(table,x,y);
#ifdef DD_DEBUG
assert(table->subtables[x].next == (unsigned) x);
assert(table->subtables[y].next == (unsigned) y);
#endif
if (size == 0) goto ddSymmSiftingUpOutOfMem;
/* Update the lower bound. */
if (cuddTestInteract(table,xindex,yindex)) {
isolated = table->vars[xindex]->ref == 1;
L += table->subtables[y].keys - isolated;
}
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL) goto ddSymmSiftingUpOutOfMem;
move->x = x;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
if ((double) size > (double) limitSize * table->maxGrowth)
return(moves);
if (size < limitSize) limitSize = size;
} else { /* Group move */
size = ddSymmGroupMove(table,x,y,&moves);
if (size == 0) goto ddSymmSiftingUpOutOfMem;
/* Update the lower bound. */
z = moves->y;
do {
zindex = table->invperm[z];
if (cuddTestInteract(table,zindex,yindex)) {
isolated = table->vars[zindex]->ref == 1;
L += table->subtables[z].keys - isolated;
}
z = table->subtables[z].next;
} while (z != (int) moves->y);
if ((double) size > (double) limitSize * table->maxGrowth)
return(moves);
if (size < limitSize) limitSize = size;
}
y = gxtop;
x = cuddNextLow(table,y);
}
return(moves);
ddSymmSiftingUpOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocMove(table, moves);
moves = move;
}
return(MV_OOM);
} /* end of ddSymmSiftingUp */
/**Function********************************************************************
Synopsis [Moves x down until either it reaches the bound (xHigh) or
the size of the DD heap increases too much.]
Description [Moves x down until either it reaches the bound (xHigh)
or the size of the DD heap increases too much. Assumes that x is the
bottom of a symmetry group. Checks x for symmetry to the adjacent
variables. If symmetry is found, the symmetry group of x is merged
with the symmetry group of the other variable. Returns the set of
moves in case of success; MV_OOM if memory is full.]
SideEffects [None]
******************************************************************************/
static Move *
ddSymmSiftingDown(
DdManager * table,
int x,
int xHigh)
{
Move *moves;
Move *move;
int y;
int size;
int limitSize;
int gxtop,gybot;
int R; /* upper bound on node decrease */
int xindex, yindex;
int isolated;
int z;
int zindex;
#ifdef DD_DEBUG
int checkR;
#endif
moves = NULL;
/* Initialize R */
xindex = table->invperm[x];
gxtop = table->subtables[x].next;
limitSize = size = table->keys - table->isolated;
R = 0;
for (z = xHigh; z > gxtop; z--) {
zindex = table->invperm[z];
if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
isolated = table->vars[zindex]->ref == 1;
R += table->subtables[z].keys - isolated;
}
}
y = cuddNextHigh(table,x);
while (y <= xHigh && size - R < limitSize) {
#ifdef DD_DEBUG
gxtop = table->subtables[x].next;
checkR = 0;
for (z = xHigh; z > gxtop; z--) {
zindex = table->invperm[z];
if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
isolated = table->vars[zindex]->ref == 1;
checkR += table->subtables[z].keys - isolated;
}
}
assert(R == checkR);
#endif
gybot = table->subtables[y].next;
while (table->subtables[gybot].next != (unsigned) y)
gybot = table->subtables[gybot].next;
if (cuddSymmCheck(table,x,y)) {
/* Symmetry found, attach symm groups */
gxtop = table->subtables[x].next;
table->subtables[x].next = y;
table->subtables[gybot].next = gxtop;
} else if (table->subtables[x].next == (unsigned) x &&
table->subtables[y].next == (unsigned) y) {
/* x and y have self symmetry */
/* Update upper bound on node decrease. */
yindex = table->invperm[y];
if (cuddTestInteract(table,xindex,yindex)) {
isolated = table->vars[yindex]->ref == 1;
R -= table->subtables[y].keys - isolated;
}
size = cuddSwapInPlace(table,x,y);
#ifdef DD_DEBUG
assert(table->subtables[x].next == (unsigned) x);
assert(table->subtables[y].next == (unsigned) y);
#endif
if (size == 0) goto ddSymmSiftingDownOutOfMem;
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL) goto ddSymmSiftingDownOutOfMem;
move->x = x;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
if ((double) size > (double) limitSize * table->maxGrowth)
return(moves);
if (size < limitSize) limitSize = size;
} else { /* Group move */
/* Update upper bound on node decrease: first phase. */
gxtop = table->subtables[x].next;
z = gxtop + 1;
do {
zindex = table->invperm[z];
if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
isolated = table->vars[zindex]->ref == 1;
R -= table->subtables[z].keys - isolated;
}
z++;
} while (z <= gybot);
size = ddSymmGroupMove(table,x,y,&moves);
if (size == 0) goto ddSymmSiftingDownOutOfMem;
if ((double) size > (double) limitSize * table->maxGrowth)
return(moves);
if (size < limitSize) limitSize = size;
/* Update upper bound on node decrease: second phase. */
gxtop = table->subtables[gybot].next;
for (z = gxtop + 1; z <= gybot; z++) {
zindex = table->invperm[z];
if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
isolated = table->vars[zindex]->ref == 1;
R += table->subtables[z].keys - isolated;
}
}
}
x = gybot;
y = cuddNextHigh(table,x);
}
return(moves);
ddSymmSiftingDownOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocMove(table, moves);
moves = move;
}
return(MV_OOM);
} /* end of ddSymmSiftingDown */
/**Function********************************************************************
Synopsis [Swaps two groups.]
Description [Swaps two groups. x is assumed to be the bottom variable
of the first group. y is assumed to be the top variable of the second
group. Updates the list of moves. Returns the number of keys in the
table if successful; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
ddSymmGroupMove(
DdManager * table,
int x,
int y,
Move ** moves)
{
Move *move;
int size = -1;
int i,j;
int xtop,xbot,xsize,ytop,ybot,ysize,newxtop;
int swapx = -1,swapy = -1;
#ifdef DD_DEBUG
assert(x < y); /* we assume that x < y */
#endif
/* Find top, bottom, and size for the two groups. */
xbot = x;
xtop = table->subtables[x].next;
xsize = xbot - xtop + 1;
ybot = y;
while ((unsigned) ybot < table->subtables[ybot].next)
ybot = table->subtables[ybot].next;
ytop = y;
ysize = ybot - ytop + 1;
/* Sift the variables of the second group up through the first group. */
for (i = 1; i <= ysize; i++) {
for (j = 1; j <= xsize; j++) {
size = cuddSwapInPlace(table,x,y);
if (size == 0) return(0);
swapx = x; swapy = y;
y = x;
x = y - 1;
}
y = ytop + i;
x = y - 1;
}
/* fix symmetries */
y = xtop; /* ytop is now where xtop used to be */
for (i = 0; i < ysize-1 ; i++) {
table->subtables[y].next = y + 1;
y = y + 1;
}
table->subtables[y].next = xtop; /* y is bottom of its group, join */
/* its symmetry to top of its group */
x = y + 1;
newxtop = x;
for (i = 0; i < xsize - 1 ; i++) {
table->subtables[x].next = x + 1;
x = x + 1;
}
table->subtables[x].next = newxtop; /* x is bottom of its group, join */
/* its symmetry to top of its group */
/* Store group move */
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL) return(0);
move->x = swapx;
move->y = swapy;
move->size = size;
move->next = *moves;
*moves = move;
return(size);
} /* end of ddSymmGroupMove */
/**Function********************************************************************
Synopsis [Undoes the swap of two groups.]
Description [Undoes the swap of two groups. x is assumed to be the
bottom variable of the first group. y is assumed to be the top
variable of the second group. Returns the number of keys in the table
if successful; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
ddSymmGroupMoveBackward(
DdManager * table,
int x,
int y)
{
int size = -1;
int i,j;
int xtop,xbot,xsize,ytop,ybot,ysize,newxtop;
#ifdef DD_DEBUG
assert(x < y); /* We assume that x < y */
#endif
/* Find top, bottom, and size for the two groups. */
xbot = x;
xtop = table->subtables[x].next;
xsize = xbot - xtop + 1;
ybot = y;
while ((unsigned) ybot < table->subtables[ybot].next)
ybot = table->subtables[ybot].next;
ytop = y;
ysize = ybot - ytop + 1;
/* Sift the variables of the second group up through the first group. */
for (i = 1; i <= ysize; i++) {
for (j = 1; j <= xsize; j++) {
size = cuddSwapInPlace(table,x,y);
if (size == 0) return(0);
y = x;
x = cuddNextLow(table,y);
}
y = ytop + i;
x = y - 1;
}
/* Fix symmetries. */
y = xtop;
for (i = 0; i < ysize-1 ; i++) {
table->subtables[y].next = y + 1;
y = y + 1;
}
table->subtables[y].next = xtop; /* y is bottom of its group, join */
/* its symmetry to top of its group */
x = y + 1;
newxtop = x;
for (i = 0; i < xsize-1 ; i++) {
table->subtables[x].next = x + 1;
x = x + 1;
}
table->subtables[x].next = newxtop; /* x is bottom of its group, join */
/* its symmetry to top of its group */
return(size);
} /* end of ddSymmGroupMoveBackward */
/**Function********************************************************************
Synopsis [Given a set of moves, returns the DD heap to the position
giving the minimum size.]
Description [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.]
SideEffects [None]
******************************************************************************/
static int
ddSymmSiftingBackward(
DdManager * table,
Move * moves,
int size)
{
Move *move;
int res = -1;
for (move = moves; move != NULL; move = move->next) {
if (move->size < size) {
size = move->size;
}
}
for (move = moves; move != NULL; move = move->next) {
if (move->size == size) return(1);
if (table->subtables[move->x].next == move->x && table->subtables[move->y].next == move->y) {
res = cuddSwapInPlace(table,(int)move->x,(int)move->y);
#ifdef DD_DEBUG
assert(table->subtables[move->x].next == move->x);
assert(table->subtables[move->y].next == move->y);
#endif
} else { /* Group move necessary */
res = ddSymmGroupMoveBackward(table,(int)move->x,(int)move->y);
}
if (!res) return(0);
}
return(1);
} /* end of ddSymmSiftingBackward */
/**Function********************************************************************
Synopsis [Counts numbers of symmetric variables and symmetry
groups.]
Description []
SideEffects [None]
******************************************************************************/
static void
ddSymmSummary(
DdManager * table,
int lower,
int upper,
int * symvars,
int * symgroups)
{
int i,x,gbot;
int TotalSymm = 0;
int TotalSymmGroups = 0;
for (i = lower; i <= upper; i++) {
if (table->subtables[i].next != (unsigned) i) {
TotalSymmGroups++;
x = i;
do {
TotalSymm++;
gbot = x;
x = table->subtables[x].next;
} while (x != i);
#ifdef DD_DEBUG
assert(table->subtables[gbot].next == (unsigned) i);
#endif
i = gbot;
}
}
*symvars = TotalSymm;
*symgroups = TotalSymmGroups;
return;
} /* end of ddSymmSummary */
ABC_NAMESPACE_IMPL_END