/**CFile****************************************************************
FileName [dsc.h]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [Disjoint support decomposition - ICCD'15]
Synopsis [Disjoint-support decomposition with cofactoring and boolean difference analysis
from V. Callegaro, F. S. Marranghello, M. G. A. Martins, R. P. Ribas and A. I. Reis,
"Bottom-up disjoint-support decomposition based on cofactor and boolean difference analysis," ICCD'15]
Author [Vinicius Callegaro, Mayler G. A. Martins, Felipe S. Marranghello, Renato P. Ribas and Andre I. Reis]
Affiliation [UFRGS - Federal University of Rio Grande do Sul - Brazil]
Date [Ver. 1.0. Started - October 24, 2014.]
Revision [$Id: dsc.h,v 1.00 2014/10/24 00:00:00 vcallegaro Exp $]
***********************************************************************/
#include "dsc.h"
#include <assert.h>
#include "misc/util/utilTruth.h"
ABC_NAMESPACE_IMPL_START
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
/*
This code performs truth-table-based decomposition for 6-variable functions.
Representation of operations:
! = not;
(ab) = a and b;
[ab] = a xor b;
*/
typedef struct Dsc_node_t_ Dsc_node_t;
struct Dsc_node_t_
{
word *pNegCof;
word *pPosCof;
word *pBoolDiff;
unsigned int on[DSC_MAX_VAR+1]; // pos cofactor spec - first element denotes the size of the array
unsigned int off[DSC_MAX_VAR+1]; // neg cofactor spec - first element denotes the size of the array
char exp[DSC_MAX_STR];
};
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
static inline void xorInPlace( word * pOut, word * pIn2, int nWords)
{
int w;
for ( w = 0; w < nWords; w++ )
pOut[w] ^= pIn2[w];
}
static inline void dsc_debug_node(Dsc_node_t * pNode, int nVars, const int TRUTH_WORDS) {
int i;
printf("Node:\t%s\n",pNode->exp);
printf("\tneg cof:\t");Abc_TtPrintHexRev(stdout, pNode->pNegCof, nVars);
printf("\tpos cof:\t");Abc_TtPrintHexRev(stdout, pNode->pPosCof, nVars);
printf("\tbool diff:\t");Abc_TtPrintHexRev(stdout, pNode->pBoolDiff, nVars);
printf("\toff:\t");
for (i=1;i<=(int)pNode->off[0];i++) {
printf("%c%c", (pNode->off[i] & 1U) ? ' ' : '!', 'a'+(pNode->off[i] >> 1));
}
printf("\ton:\t");
for (i=1;i<=(int)pNode->on[0];i++) {
printf("%c%c", (pNode->on[i] & 1U) ? ' ' : '!', 'a'+(pNode->on[i] >> 1));
}
printf("\n");
}
static inline int dsc_and_test(Dsc_node_t *ni, Dsc_node_t *nj, const int TRUTH_WORDS, int* ci, int* cj) {
if (Abc_TtEqual(ni->pNegCof, nj->pNegCof, TRUTH_WORDS)) {*ci=1; *cj=1; return 1;}
else if (Abc_TtEqual(ni->pNegCof, nj->pPosCof, TRUTH_WORDS)) {*ci=1; *cj=0; return 1;}
else if (Abc_TtEqual(ni->pPosCof, nj->pNegCof, TRUTH_WORDS)) {*ci=0; *cj=1; return 1;}
else if (Abc_TtEqual(ni->pPosCof, nj->pPosCof, TRUTH_WORDS)) {*ci=0; *cj=0; return 1;}
return 0;
}
static inline int dsc_xor_test(Dsc_node_t *ni, Dsc_node_t *nj, const int TRUTH_WORDS) {
return Abc_TtEqual(ni->pBoolDiff, nj->pBoolDiff, TRUTH_WORDS);
}
static inline void concat(char* target, char begin, char end, char* s1, int s1Polarity, char* s2, int s2Polarity) {
*target++ = begin;
//s1
if (!s1Polarity)
*target++ = '!';
while (*s1 != '\0')
*target++ = *s1++;
// s2
if (!s2Polarity)
*target++ = '!';
while (*s2 != '\0')
*target++ = *s2++;
// end
*target++ = end;
*target = '\0';
}
static inline void cubeCofactor(word * const pTruth, const unsigned int * const cubeCof, const int TRUTH_WORDS) {
int size = cubeCof[0];
int i;
for (i = 1; i <= size; i++) {
unsigned int c = cubeCof[i];
if (c & 1U) {
Abc_TtCofactor1(pTruth, TRUTH_WORDS, c >> 1);
} else {
Abc_TtCofactor0(pTruth, TRUTH_WORDS, c >> 1);
}
}
}
static inline void merge(unsigned int * const pOut, const unsigned int * const pIn) {
const int elementsToCopy = pIn[0];
int i, j;
for (i = pOut[0]+1, j = 1; j <= elementsToCopy; i++, j++) {
pOut[i] = pIn[j];
}
pOut[0] += elementsToCopy;
}
void dsc_and_group(Dsc_node_t * pOut, Dsc_node_t * ni, int niPolarity, Dsc_node_t * nj, int njPolarity, int nVars, const int TRUTH_WORDS) {
unsigned int* xiOFF, * xiON, * xjOFF, * xjON;
// expression
concat(pOut->exp, '(', ')', ni->exp, niPolarity, nj->exp, njPolarity);
// ON-OFF
if (niPolarity) {
xiOFF = ni->off;
xiON = ni->on;
} else {
xiOFF = ni->on;
xiON = ni->off;
}
if (njPolarity) {
xjOFF = nj->off;
xjON = nj->on;
} else {
xjOFF = nj->on;
xjON = nj->off;
}
// creating both the new OFF specification and negative cofactor of the new group
{
// first element of the array represents the size of the cube-cofactor
int xiOFFSize = xiOFF[0];
int xjOFFSize = xjOFF[0];
if (xiOFFSize <= xjOFFSize) {
int i;
pOut->off[0] = xiOFFSize; // set the number of elements
for (i = 1; i <= xiOFFSize; i++) {
pOut->off[i] = xiOFF[i];
}
} else {
int i;
pOut->off[0] = xjOFFSize; // set the number of elements
for (i = 1; i <= xjOFFSize; i++) {
pOut->off[i] = xjOFF[i];
}
}
// set the negative cofactor of the new group
pOut->pNegCof = niPolarity ? ni->pNegCof : ni->pPosCof;
}
// creating both new ON specification and positive cofactor of the new group
{
int i;
int j;
unsigned int xiONSize = xiON[0];
unsigned int xjONSize = xjON[0];
pOut->on[0] = xiONSize + xjONSize;
for (i = 1; i <= (int)xiONSize; i++) {
pOut->on[i] = xiON[i];
}
for (j = 1; j <= (int)xjONSize; j++) {
pOut->on[i++] = xjON[j];
}
// set the positive cofactor of the new group
if (xiONSize >= xjONSize) {
pOut->pPosCof = niPolarity ? ni->pPosCof : ni->pNegCof;
cubeCofactor(pOut->pPosCof, xjON, TRUTH_WORDS);
} else {
pOut->pPosCof = njPolarity ? nj->pPosCof : nj->pNegCof;
cubeCofactor(pOut->pPosCof, xiON, TRUTH_WORDS);
}
}
// set the boolean difference of the new group
pOut->pBoolDiff = njPolarity ? nj->pNegCof : nj->pPosCof;
xorInPlace(pOut->pBoolDiff, pOut->pPosCof, TRUTH_WORDS);
}
void dsc_xor_group(Dsc_node_t * pOut, Dsc_node_t * ni, Dsc_node_t * nj, int nVars, const int TRUTH_WORDS) {
//
const unsigned int * xiOFF = ni->off;
const unsigned int * xiON = ni->on;
const unsigned int * xjOFF = nj->off;
const unsigned int * xjON = nj->on;
//
const int xiOFFSize = xiOFF[0];
const int xiONSize = xiON[0];
const int xjOFFSize = xjOFF[0];
const int xjONSize = xjON[0];
// minCubeCofs
int minCCSize = xiOFFSize;
int minCCPolarity = 0;
Dsc_node_t * minCCNode = ni;
// expression
concat(pOut->exp, '[', ']', ni->exp, 1, nj->exp, 1);
if (minCCSize > xiONSize) {
minCCSize = xiONSize;
minCCPolarity = 1;
//minCCNode = ni;
}
if (minCCSize > xjOFFSize) {
minCCSize = xjOFFSize;
minCCPolarity = 0;
minCCNode = nj;
}
if (minCCSize > xjONSize) {
minCCSize = xjONSize;
minCCPolarity = 1;
minCCNode = nj;
}
//
if (minCCNode == ni) {
if (minCCPolarity) {
// gOFF = xiON, xjON
pOut->pNegCof = nj->pPosCof;
cubeCofactor(pOut->pNegCof, xiON, TRUTH_WORDS);
// gON = xiON, xjOFF
pOut->pPosCof = nj->pNegCof;
cubeCofactor(pOut->pPosCof, xiON, TRUTH_WORDS);
} else {
// gOFF = xiOFF, xjOFF
pOut->pNegCof = nj->pNegCof;
cubeCofactor(pOut->pNegCof, xiOFF, TRUTH_WORDS);
// gON = xiOFF, xjON
pOut->pPosCof = nj->pPosCof;
cubeCofactor(pOut->pPosCof, xiOFF, TRUTH_WORDS);
}
}else {
if (minCCPolarity) {
// gOFF = xjON, xiON
pOut->pNegCof = ni->pPosCof;
cubeCofactor(pOut->pNegCof, xjON, TRUTH_WORDS);
// gON = xjON, xiOFF
pOut->pPosCof = ni->pNegCof;
cubeCofactor(pOut->pPosCof, xjON, TRUTH_WORDS);
} else {
// gOFF = xjOFF, xiOFF
pOut->pNegCof = ni->pNegCof;
cubeCofactor(pOut->pNegCof, xjOFF, TRUTH_WORDS);
// gON = xjOFF, xiON
pOut->pPosCof = ni->pPosCof;
cubeCofactor(pOut->pPosCof, xjOFF, TRUTH_WORDS);
}
}
// bool diff
pOut->pBoolDiff = ni->pBoolDiff;
// evaluating specs
// off spec
pOut->off[0] = 0;
if ((xiOFFSize+xjOFFSize) <= (xiONSize+xjONSize)) {
merge(pOut->off, xiOFF);
merge(pOut->off, xjOFF);
} else {
merge(pOut->off, xiON);
merge(pOut->off, xjON);
}
// on spec
pOut->on[0] = 0;
if ((xiOFFSize+xjONSize) <= (xiONSize+xjOFFSize)) {
merge(pOut->on, xiOFF);
merge(pOut->on, xjON);
} else {
merge(pOut->on, xiON);
merge(pOut->on, xjOFF);
}
}
/**
* memory allocator with a capacity of storing 3*nVars
* truth-tables for negative and positive cofactors and
* the boolean difference for each input variable
*/
extern word * Dsc_alloc_pool(int nVars) {
return ABC_ALLOC(word, 3 * Abc_TtWordNum(nVars) * nVars);
}
/**
* just free the memory pool
*/
extern void Dsc_free_pool(word * pool) {
ABC_FREE(pool);
}
/**
* This method implements the paper proposed by V. Callegaro, F. S. Marranghello, M. G. A. Martins, R. P. Ribas and A. I. Reis,
* entitled "Bottom-up disjoint-support decomposition based on cofactor and boolean difference analysis", presented at ICCD 2015.
* pTruth: pointer for the truth table representing the target function.
* nVarsInit: the number of variables of the truth table of the target function.
* pRes: pointer for storing the resulting decomposition, whenever a decomposition can be found.
* pool: NULL or a pointer for with a capacity of storing 3*nVars truth-tables. IF NULL, the function will allocate and free the memory of each call.
* (the results presented on ICCD paper are running this method with NULL for the memory pool).
* The method returns 0 if a full decomposition was found and a negative value otherwise.
*/
extern int Dsc_Decompose(word * pTruth, const int nVarsInit, char * const pRes, word *pool) {
const int TRUTH_WORDS = Abc_TtWordNum(nVarsInit);
const int NEED_POOL_ALLOC = (pool == NULL);
Dsc_node_t nodes[DSC_MAX_VAR];
Dsc_node_t *newNodes[DSC_MAX_VAR];
Dsc_node_t *oldNodes[DSC_MAX_VAR];
Dsc_node_t freeNodes[DSC_MAX_VAR]; // N is the maximum number of possible groups.
int f = 0; // f represent the next free position in the freeNodes array
int o = 0; // o stands for the number of already tested nodes
int n = 0; // n will represent the number of current nodes (i.e. support)
pRes[0] = '\0';
pRes[1] = '\0';
if (NEED_POOL_ALLOC)
pool = ABC_ALLOC(word, 3 * TRUTH_WORDS * nVarsInit);
// block for the node data allocation
{
// pointer for the next free truth word
word *pNextTruth = pool;
int iVar;
for (iVar = 0; iVar < nVarsInit; iVar++) {
// negative cofactor
Abc_TtCofactor0p(pNextTruth, pTruth, TRUTH_WORDS, iVar);
// dont care test
if (!Abc_TtEqual(pNextTruth, pTruth, TRUTH_WORDS)) {
Dsc_node_t *node = &nodes[iVar];
node->pNegCof = pNextTruth;
// increment next truth pointer
pNextTruth += TRUTH_WORDS;
// positive cofactor
node->pPosCof = pNextTruth;
Abc_TtCofactor1p(node->pPosCof, pTruth, TRUTH_WORDS, iVar);
// increment next truth pointer
pNextTruth += TRUTH_WORDS;
// boolean difference
node->pBoolDiff = pNextTruth;
Abc_TtXor(node->pBoolDiff, node->pNegCof, node->pPosCof, TRUTH_WORDS, 0);
// increment next truth pointer
pNextTruth += TRUTH_WORDS;
// define on spec -
node->on[0] = 1; node->on[1] = (iVar << 1) | 1u; // lit = i*2+1, when polarity=true
// define off spec
node->off[0] = 1; node->off[1] = iVar << 1;// lit=i*2 otherwise
// store the node expression
node->exp[0] = 'a'+iVar; // TODO fix the variable names
node->exp[1] = '\0';
// add the node to the newNodes array
newNodes[n++] = node;
}
}
}
//const int initialSupport = n;
if (n == 0) {
if (NEED_POOL_ALLOC)
ABC_FREE(pool);
if (Abc_TtIsConst0(pTruth, TRUTH_WORDS)) {
{ if ( pRes ) pRes[0] = '0', pRes[1] = '\0'; }
return 0;
} else if (Abc_TtIsConst1(pTruth, TRUTH_WORDS)) {
{ if ( pRes ) pRes[0] = '1', pRes[1] = '\0'; }
return 0;
} else {
Abc_Print(-1, "ERROR. No variable in the support of f, but f isn't constant!\n");
return -1;
}
}
while (n > 0) {
int tempN = 0;
int i, j, iPolarity, jPolarity;
Dsc_node_t *ni, *nj, *newNode = NULL;
for (i = 0; i < n; i++) {
ni = newNodes[i];
newNode = NULL;
j = 0;
while (j < o) {
nj = oldNodes[j];
if (dsc_and_test(ni, nj, TRUTH_WORDS, &iPolarity, &jPolarity)) {
newNode = &freeNodes[f++];
dsc_and_group(newNode, ni, iPolarity, nj, jPolarity, nVarsInit, TRUTH_WORDS);
}
// XOR test
if ((newNode == NULL) && (dsc_xor_test(ni, nj, TRUTH_WORDS))) {
newNode = &freeNodes[f++];
dsc_xor_group(newNode, ni, nj, nVarsInit, TRUTH_WORDS);
}
if (newNode != NULL) {
oldNodes[j] = oldNodes[--o];
break;
} else {
j++;
}
}
if (newNode != NULL) {
newNodes[tempN++] = newNode;
} else {
oldNodes[o++] = ni;
}
}
n = tempN;
}
if (o == 1) {
Dsc_node_t * solution = oldNodes[0];
if (Abc_TtIsConst0(solution->pNegCof, TRUTH_WORDS) && Abc_TtIsConst1(solution->pPosCof, TRUTH_WORDS)) {
// Direct solution found
if ( pRes )
strcpy( pRes, solution->exp);
if (NEED_POOL_ALLOC)
ABC_FREE(pool);
return 0;
} else if (Abc_TtIsConst1(solution->pNegCof, TRUTH_WORDS) && Abc_TtIsConst0(solution->pPosCof, TRUTH_WORDS)) {
// Complementary solution found
if ( pRes ) {
pRes[0] = '!';
strcpy( &pRes[1], solution->exp);
}
if (NEED_POOL_ALLOC)
ABC_FREE(pool);
return 0;
} else {
printf("DSC ERROR: Final DSC node found, but differs from target function.\n");
if (NEED_POOL_ALLOC)
ABC_FREE(pool);
return -1;
}
}
if (NEED_POOL_ALLOC)
ABC_FREE(pool);
return -1;
}
/**Function*************************************************************
Synopsis [DSD formula manipulation.]
Description [Code copied from dauDsd.c but changed DAU_MAX_VAR to DSC_MAX_VAR]
***********************************************************************/
int * Dsc_ComputeMatches( char * p )
{
static int pMatches[DSC_MAX_VAR];
int pNested[DSC_MAX_VAR];
int v, nNested = 0;
for ( v = 0; p[v]; v++ )
{
pMatches[v] = 0;
if ( p[v] == '(' || p[v] == '[' || p[v] == '<' || p[v] == '{' )
pNested[nNested++] = v;
else if ( p[v] == ')' || p[v] == ']' || p[v] == '>' || p[v] == '}' )
pMatches[pNested[--nNested]] = v;
assert( nNested < DSC_MAX_VAR );
}
assert( nNested == 0 );
return pMatches;
}
/**Function*************************************************************
Synopsis [DSD formula manipulation.]
Description [Code copied from dauDsd.c but changed DAU_MAX_VAR to DSC_MAX_VAR]
***********************************************************************/
int Dsc_CountAnds_rec( char * pStr, char ** p, int * pMatches )
{
if ( **p == '!' )
(*p)++;
while ( (**p >= 'A' && **p <= 'F') || (**p >= '0' && **p <= '9') )
(*p)++;
if ( **p == '<' )
{
char * q = pStr + pMatches[*p - pStr];
if ( *(q+1) == '{' )
*p = q+1;
}
if ( **p >= 'a' && **p <= 'z' ) // var
return 0;
if ( **p == '(' || **p == '[' ) // and/or/xor
{
int Counter = 0, AddOn = (**p == '(')? 1 : 3;
char * q = pStr + pMatches[ *p - pStr ];
assert( *q == **p + 1 + (**p != '(') );
for ( (*p)++; *p < q; (*p)++ )
Counter += AddOn + Dsc_CountAnds_rec( pStr, p, pMatches );
assert( *p == q );
return Counter - AddOn;
}
if ( **p == '<' || **p == '{' ) // mux
{
int Counter = 3;
char * q = pStr + pMatches[ *p - pStr ];
assert( *q == **p + 1 + (**p != '(') );
for ( (*p)++; *p < q; (*p)++ )
Counter += Dsc_CountAnds_rec( pStr, p, pMatches );
assert( *p == q );
return Counter;
}
assert( 0 );
return 0;
}
/**Function*************************************************************
Synopsis [DSD formula manipulation.]
Description [Code copied from dauDsd.c but changed DAU_MAX_VAR to DSC_MAX_VAR]
***********************************************************************/
extern int Dsc_CountAnds( char * pDsd )
{
if ( pDsd[1] == 0 )
return 0;
return Dsc_CountAnds_rec( pDsd, &pDsd, Dsc_ComputeMatches(pDsd) );
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END