/**CFile****************************************************************
FileName [dauCanon.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [DAG-aware unmapping.]
Synopsis [Canonical form computation.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - June 20, 2005.]
Revision [$Id: dauCanon.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
***********************************************************************/
#include "dauInt.h"
#include "misc/util/utilTruth.h"
#include "misc/vec/vecMem.h"
#include "bool/lucky/lucky.h"
#include <math.h>
ABC_NAMESPACE_IMPL_START
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
static word s_CMasks6[5] = {
ABC_CONST(0x1111111111111111),
ABC_CONST(0x0303030303030303),
ABC_CONST(0x000F000F000F000F),
ABC_CONST(0x000000FF000000FF),
ABC_CONST(0x000000000000FFFF)
};
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Compares Cof0 and Cof1.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
/*
static inline int Abc_TtCompare1VarCofs( word * pTruth, int nWords, int iVar )
{
if ( nWords == 1 )
{
word Cof0 = pTruth[0] & s_Truths6Neg[iVar];
word Cof1 = (pTruth[0] >> (1 << iVar)) & s_Truths6Neg[iVar];
if ( Cof0 != Cof1 )
return Cof0 < Cof1 ? -1 : 1;
return 0;
}
if ( iVar <= 5 )
{
word Cof0, Cof1;
int w, shift = (1 << iVar);
for ( w = 0; w < nWords; w++ )
{
Cof0 = pTruth[w] & s_Truths6Neg[iVar];
Cof1 = (pTruth[w] >> shift) & s_Truths6Neg[iVar];
if ( Cof0 != Cof1 )
return Cof0 < Cof1 ? -1 : 1;
}
return 0;
}
// if ( iVar > 5 )
{
word * pLimit = pTruth + nWords;
int i, iStep = Abc_TtWordNum(iVar);
assert( nWords >= 2 );
for ( ; pTruth < pLimit; pTruth += 2*iStep )
for ( i = 0; i < iStep; i++ )
if ( pTruth[i] != pTruth[i + iStep] )
return pTruth[i] < pTruth[i + iStep] ? -1 : 1;
return 0;
}
}
static inline int Abc_TtCompare1VarCofsRev( word * pTruth, int nWords, int iVar )
{
if ( nWords == 1 )
{
word Cof0 = pTruth[0] & s_Truths6Neg[iVar];
word Cof1 = (pTruth[0] >> (1 << iVar)) & s_Truths6Neg[iVar];
if ( Cof0 != Cof1 )
return Cof0 < Cof1 ? -1 : 1;
return 0;
}
if ( iVar <= 5 )
{
word Cof0, Cof1;
int w, shift = (1 << iVar);
for ( w = nWords - 1; w >= 0; w-- )
{
Cof0 = pTruth[w] & s_Truths6Neg[iVar];
Cof1 = (pTruth[w] >> shift) & s_Truths6Neg[iVar];
if ( Cof0 != Cof1 )
return Cof0 < Cof1 ? -1 : 1;
}
return 0;
}
// if ( iVar > 5 )
{
word * pLimit = pTruth + nWords;
int i, iStep = Abc_TtWordNum(iVar);
assert( nWords >= 2 );
for ( pLimit -= 2*iStep; pLimit >= pTruth; pLimit -= 2*iStep )
for ( i = iStep - 1; i >= 0; i-- )
if ( pLimit[i] != pLimit[i + iStep] )
return pLimit[i] < pLimit[i + iStep] ? -1 : 1;
return 0;
}
}
*/
/**Function*************************************************************
Synopsis [Checks equality of pairs of cofactors w.r.t. adjacent variables.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline int Abc_TtCheckEqual2VarCofs( word * pTruth, int nWords, int iVar, int Num1, int Num2 )
{
assert( Num1 < Num2 && Num2 < 4 );
if ( nWords == 1 )
return ((pTruth[0] >> (Num2 * (1 << iVar))) & s_CMasks6[iVar]) == ((pTruth[0] >> (Num1 * (1 << iVar))) & s_CMasks6[iVar]);
if ( iVar <= 4 )
{
int w, shift = (1 << iVar);
for ( w = 0; w < nWords; w++ )
if ( ((pTruth[w] >> Num2 * shift) & s_CMasks6[iVar]) != ((pTruth[w] >> Num1 * shift) & s_CMasks6[iVar]) )
return 0;
return 1;
}
if ( iVar == 5 )
{
unsigned * pTruthU = (unsigned *)pTruth;
unsigned * pLimitU = (unsigned *)(pTruth + nWords);
assert( nWords >= 2 );
for ( ; pTruthU < pLimitU; pTruthU += 4 )
if ( pTruthU[Num2] != pTruthU[Num1] )
return 0;
return 1;
}
// if ( iVar > 5 )
{
word * pLimit = pTruth + nWords;
int i, iStep = Abc_TtWordNum(iVar);
assert( nWords >= 4 );
for ( ; pTruth < pLimit; pTruth += 4*iStep )
for ( i = 0; i < iStep; i++ )
if ( pTruth[i+Num2*iStep] != pTruth[i+Num1*iStep] )
return 0;
return 1;
}
}
/**Function*************************************************************
Synopsis [Compares pairs of cofactors w.r.t. adjacent variables.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline int Abc_TtCompare2VarCofs( word * pTruth, int nWords, int iVar, int Num1, int Num2 )
{
assert( Num1 < Num2 && Num2 < 4 );
if ( nWords == 1 )
{
word Cof1 = (pTruth[0] >> (Num1 * (1 << iVar))) & s_CMasks6[iVar];
word Cof2 = (pTruth[0] >> (Num2 * (1 << iVar))) & s_CMasks6[iVar];
if ( Cof1 != Cof2 )
return Cof1 < Cof2 ? -1 : 1;
return 0;
}
if ( iVar <= 4 )
{
word Cof1, Cof2;
int w, shift = (1 << iVar);
for ( w = 0; w < nWords; w++ )
{
Cof1 = (pTruth[w] >> Num1 * shift) & s_CMasks6[iVar];
Cof2 = (pTruth[w] >> Num2 * shift) & s_CMasks6[iVar];
if ( Cof1 != Cof2 )
return Cof1 < Cof2 ? -1 : 1;
}
return 0;
}
if ( iVar == 5 )
{
unsigned * pTruthU = (unsigned *)pTruth;
unsigned * pLimitU = (unsigned *)(pTruth + nWords);
assert( nWords >= 2 );
for ( ; pTruthU < pLimitU; pTruthU += 4 )
if ( pTruthU[Num1] != pTruthU[Num2] )
return pTruthU[Num1] < pTruthU[Num2] ? -1 : 1;
return 0;
}
// if ( iVar > 5 )
{
word * pLimit = pTruth + nWords;
int i, iStep = Abc_TtWordNum(iVar);
int Offset1 = Num1*iStep;
int Offset2 = Num2*iStep;
assert( nWords >= 4 );
for ( ; pTruth < pLimit; pTruth += 4*iStep )
for ( i = 0; i < iStep; i++ )
if ( pTruth[i + Offset1] != pTruth[i + Offset2] )
return pTruth[i + Offset1] < pTruth[i + Offset2] ? -1 : 1;
return 0;
}
}
static inline int Abc_TtCompare2VarCofsRev( word * pTruth, int nWords, int iVar, int Num1, int Num2 )
{
assert( Num1 < Num2 && Num2 < 4 );
if ( nWords == 1 )
{
word Cof1 = (pTruth[0] >> (Num1 * (1 << iVar))) & s_CMasks6[iVar];
word Cof2 = (pTruth[0] >> (Num2 * (1 << iVar))) & s_CMasks6[iVar];
if ( Cof1 != Cof2 )
return Cof1 < Cof2 ? -1 : 1;
return 0;
}
if ( iVar <= 4 )
{
word Cof1, Cof2;
int w, shift = (1 << iVar);
for ( w = nWords - 1; w >= 0; w-- )
{
Cof1 = (pTruth[w] >> Num1 * shift) & s_CMasks6[iVar];
Cof2 = (pTruth[w] >> Num2 * shift) & s_CMasks6[iVar];
if ( Cof1 != Cof2 )
return Cof1 < Cof2 ? -1 : 1;
}
return 0;
}
if ( iVar == 5 )
{
unsigned * pTruthU = (unsigned *)pTruth;
unsigned * pLimitU = (unsigned *)(pTruth + nWords);
assert( nWords >= 2 );
for ( pLimitU -= 4; pLimitU >= pTruthU; pLimitU -= 4 )
if ( pLimitU[Num1] != pLimitU[Num2] )
return pLimitU[Num1] < pLimitU[Num2] ? -1 : 1;
return 0;
}
// if ( iVar > 5 )
{
word * pLimit = pTruth + nWords;
int i, iStep = Abc_TtWordNum(iVar);
int Offset1 = Num1*iStep;
int Offset2 = Num2*iStep;
assert( nWords >= 4 );
for ( pLimit -= 4*iStep; pLimit >= pTruth; pLimit -= 4*iStep )
for ( i = iStep - 1; i >= 0; i-- )
if ( pLimit[i + Offset1] != pLimit[i + Offset2] )
return pLimit[i + Offset1] < pLimit[i + Offset2] ? -1 : 1;
return 0;
}
}
/**Function*************************************************************
Synopsis [Minterm counting in all cofactors.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Abc_TtNormalizeSmallTruth(word * pTruth, int nVars)
{
if (nVars < 6) {
int shift, bits = (1 << nVars);
word base = *pTruth = *pTruth & ((((word)1) << bits) - 1);
for (shift = bits; shift < 64; shift += bits)
*pTruth |= base << shift;
}
}
static inline void Abc_TtVerifySmallTruth(word * pTruth, int nVars)
{
#ifndef NDEBUG
if (nVars < 6) {
word nTruth = *pTruth;
Abc_TtNormalizeSmallTruth(&nTruth, nVars);
assert(*pTruth == nTruth);
}
#endif
}
static inline int Abc_TtCountOnesInTruth( word * pTruth, int nVars )
{
int nWords = Abc_TtWordNum( nVars );
int k, Counter = 0;
Abc_TtVerifySmallTruth(pTruth, nVars);
for ( k = 0; k < nWords; k++ )
if ( pTruth[k] )
Counter += Abc_TtCountOnes( pTruth[k] );
return Counter;
}
static inline void Abc_TtCountOnesInCofs( word * pTruth, int nVars, int * pStore )
{
word Temp;
int i, k, Counter, nWords;
if ( nVars <= 6 )
{
Abc_TtVerifySmallTruth(pTruth, nVars);
for ( i = 0; i < nVars; i++ )
pStore[i] = Abc_TtCountOnes( pTruth[0] & s_Truths6Neg[i] );
return;
}
assert( nVars > 6 );
nWords = Abc_TtWordNum( nVars );
memset( pStore, 0, sizeof(int) * nVars );
for ( k = 0; k < nWords; k++ )
{
// count 1's for the first six variables
for ( i = 0; i < 6; i++ )
if ( (Temp = (pTruth[k] & s_Truths6Neg[i]) | ((pTruth[k+1] & s_Truths6Neg[i]) << (1 << i))) )
pStore[i] += Abc_TtCountOnes( Temp );
// count 1's for all other variables
if ( pTruth[k] )
{
Counter = Abc_TtCountOnes( pTruth[k] );
for ( i = 6; i < nVars; i++ )
if ( (k & (1 << (i-6))) == 0 )
pStore[i] += Counter;
}
k++;
// count 1's for all other variables
if ( pTruth[k] )
{
Counter = Abc_TtCountOnes( pTruth[k] );
for ( i = 6; i < nVars; i++ )
if ( (k & (1 << (i-6))) == 0 )
pStore[i] += Counter;
}
}
}
int Abc_TtCountOnesInCofsSimple( word * pTruth, int nVars, int * pStore )
{
Abc_TtCountOnesInCofs( pTruth, nVars, pStore );
return Abc_TtCountOnesInTruth( pTruth, nVars );
}
// Shifted Cofactor Coefficient
static inline int shiftFunc(int ci)
//{ return ci * ci; }
{ return 1 << ci; }
static int Abc_TtScc6(word wTruth, int ck)
{
int i;
int sum = 0;
if (!wTruth) return 0;
for (i = 0; i < 64; i++)
if (wTruth & (word)1 << i) {
int ci = Abc_TtBitCount8[i] + ck;
sum += shiftFunc(ci);
}
return sum;
}
int Abc_TtScc(word * pTruth, int nVars)
{
int k, nWords = Abc_TtWordNum(nVars);
int sum = 0;
Abc_TtNormalizeSmallTruth(pTruth, nVars);
for (k = 0; k < nWords; k++)
sum += Abc_TtScc6(pTruth[k], Abc_TtBitCount16(k));
return sum;
}
static inline void Abc_TtSccInCofs6(word wTruth, int nVars, int ck, int * pStore)
{
int i, j, v;
assert(nVars <= 6);
for (v = 0; v < nVars; v++)
{
int sum = 0;
for (i = j = 0; j < 64; j++)
if (s_Truths6Neg[v] & (word)1 << j)
{
if (wTruth & (word)1 << j)
{
int ci = Abc_TtBitCount8[i] + ck;
sum += shiftFunc(ci);
}
i++;
}
pStore[v] += sum;
}
}
static inline void Abc_TtSccInCofs(word * pTruth, int nVars, int * pStore)
{
int k, v, nWords;
int kv[10] = { 0 };
memset(pStore, 0, sizeof(int) * nVars);
if (nVars <= 6)
{
Abc_TtNormalizeSmallTruth(pTruth, nVars);
Abc_TtSccInCofs6(pTruth[0], nVars, 0, pStore);
return;
}
assert(nVars > 6);
nWords = Abc_TtWordNum(nVars);
for (k = 0; k < nWords; k++)
{
// count 1's for the first six variables
Abc_TtSccInCofs6(pTruth[k], 6, Abc_TtBitCount16(k), pStore);
// count 1's for all other variables
for (v = 6; v < nVars; v++)
if ((k & (1 << (v - 6))) == 0)
{
pStore[v] += Abc_TtScc6(pTruth[k], Abc_TtBitCount16(kv[v - 6]));
kv[v - 6]++;
}
}
}
/**Function*************************************************************
Synopsis [Minterm counting in all cofactors.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline void Abc_TtCountOnesInCofsSlow( word * pTruth, int nVars, int * pStore )
{
static int bit_count[256] = {
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8
};
int i, k, nBytes;
unsigned char * pTruthC = (unsigned char *)pTruth;
nBytes = 8 * Abc_TtWordNum( nVars );
memset( pStore, 0, sizeof(int) * nVars );
for ( k = 0; k < nBytes; k++ )
{
pStore[0] += bit_count[ pTruthC[k] & 0x55 ];
pStore[1] += bit_count[ pTruthC[k] & 0x33 ];
pStore[2] += bit_count[ pTruthC[k] & 0x0F ];
for ( i = 3; i < nVars; i++ )
if ( (k & (1 << (i-3))) == 0 )
pStore[i] += bit_count[pTruthC[k]];
}
}
/**Function*************************************************************
Synopsis [Minterm counting in all cofactors.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Abc_TtCountOnesInCofsFast6_rec( word Truth, int iVar, int nBytes, int * pStore )
{
static int bit_count[256] = {
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8
};
int nMints0, nMints1;
if ( Truth == 0 )
return 0;
if ( ~Truth == 0 )
{
int i;
for ( i = 0; i <= iVar; i++ )
pStore[i] += nBytes * 4;
return nBytes * 8;
}
if ( nBytes == 1 )
{
assert( iVar == 2 );
pStore[0] += bit_count[ Truth & 0x55 ];
pStore[1] += bit_count[ Truth & 0x33 ];
pStore[2] += bit_count[ Truth & 0x0F ];
return bit_count[ Truth & 0xFF ];
}
nMints0 = Abc_TtCountOnesInCofsFast6_rec( Abc_Tt6Cofactor0(Truth, iVar), iVar - 1, nBytes/2, pStore );
nMints1 = Abc_TtCountOnesInCofsFast6_rec( Abc_Tt6Cofactor1(Truth, iVar), iVar - 1, nBytes/2, pStore );
pStore[iVar] += nMints0;
return nMints0 + nMints1;
}
int Abc_TtCountOnesInCofsFast_rec( word * pTruth, int iVar, int nWords, int * pStore )
{
int nMints0, nMints1;
if ( nWords == 1 )
{
assert( iVar == 5 );
return Abc_TtCountOnesInCofsFast6_rec( pTruth[0], iVar, 8, pStore );
}
assert( nWords > 1 );
assert( iVar > 5 );
if ( pTruth[0] & 1 )
{
if ( Abc_TtIsConst1( pTruth, nWords ) )
{
int i;
for ( i = 0; i <= iVar; i++ )
pStore[i] += nWords * 32;
return nWords * 64;
}
}
else
{
if ( Abc_TtIsConst0( pTruth, nWords ) )
return 0;
}
nMints0 = Abc_TtCountOnesInCofsFast_rec( pTruth, iVar - 1, nWords/2, pStore );
nMints1 = Abc_TtCountOnesInCofsFast_rec( pTruth + nWords/2, iVar - 1, nWords/2, pStore );
pStore[iVar] += nMints0;
return nMints0 + nMints1;
}
int Abc_TtCountOnesInCofsFast( word * pTruth, int nVars, int * pStore )
{
memset( pStore, 0, sizeof(int) * nVars );
assert( nVars >= 3 );
if ( nVars <= 6 )
return Abc_TtCountOnesInCofsFast6_rec( pTruth[0], nVars - 1, Abc_TtByteNum( nVars ), pStore );
else
return Abc_TtCountOnesInCofsFast_rec( pTruth, nVars - 1, Abc_TtWordNum( nVars ), pStore );
}
/**Function*************************************************************
Synopsis []
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline unsigned Abc_TtSemiCanonicize( word * pTruth, int nVars, char * pCanonPerm, int * pStoreOut, int fOnlySwap )
{
int fUseOld = 1;
int fOldSwap = 0;
int pStoreIn[17];
int * pStore = pStoreOut ? pStoreOut : pStoreIn;
int i, nOnes, nWords = Abc_TtWordNum( nVars );
unsigned uCanonPhase = 0;
assert( nVars <= 16 );
for ( i = 0; i < nVars; i++ )
pCanonPerm[i] = i;
if ( fUseOld )
{
// normalize polarity
nOnes = Abc_TtCountOnesInTruth( pTruth, nVars );
if ( nOnes > nWords * 32 && !fOnlySwap )
{
Abc_TtNot( pTruth, nWords );
nOnes = nWords*64 - nOnes;
uCanonPhase |= (1 << nVars);
}
// normalize phase
Abc_TtCountOnesInCofs( pTruth, nVars, pStore );
pStore[nVars] = nOnes;
for ( i = 0; i < nVars; i++ )
{
if ( pStore[i] >= nOnes - pStore[i] || fOnlySwap )
continue;
Abc_TtFlip( pTruth, nWords, i );
uCanonPhase |= (1 << i);
pStore[i] = nOnes - pStore[i];
}
}
else
{
nOnes = Abc_TtCountOnesInCofsQuick( pTruth, nVars, pStore );
// normalize polarity
if ( nOnes > nWords * 32 && !fOnlySwap )
{
for ( i = 0; i < nVars; i++ )
pStore[i] = nWords * 32 - pStore[i];
Abc_TtNot( pTruth, nWords );
nOnes = nWords*64 - nOnes;
uCanonPhase |= (1 << nVars);
}
// normalize phase
pStore[nVars] = nOnes;
for ( i = 0; i < nVars; i++ )
{
if ( pStore[i] >= nOnes - pStore[i] || fOnlySwap )
continue;
Abc_TtFlip( pTruth, nWords, i );
uCanonPhase |= (1 << i);
pStore[i] = nOnes - pStore[i];
}
}
// normalize permutation
if ( fOldSwap )
{
int fChange;
do {
fChange = 0;
for ( i = 0; i < nVars-1; i++ )
{
if ( pStore[i] <= pStore[i+1] )
// if ( pStore[i] >= pStore[i+1] )
continue;
ABC_SWAP( int, pCanonPerm[i], pCanonPerm[i+1] );
ABC_SWAP( int, pStore[i], pStore[i+1] );
if ( ((uCanonPhase >> i) & 1) != ((uCanonPhase >> (i+1)) & 1) )
{
uCanonPhase ^= (1 << i);
uCanonPhase ^= (1 << (i+1));
}
Abc_TtSwapAdjacent( pTruth, nWords, i );
fChange = 1;
// nSwaps++;
}
}
while ( fChange );
}
else
{
int k, BestK;
for ( i = 0; i < nVars - 1; i++ )
{
BestK = i + 1;
for ( k = i + 2; k < nVars; k++ )
if ( pStore[BestK] > pStore[k] )
// if ( pStore[BestK] < pStore[k] )
BestK = k;
if ( pStore[i] <= pStore[BestK] )
// if ( pStore[i] >= pStore[BestK] )
continue;
ABC_SWAP( int, pCanonPerm[i], pCanonPerm[BestK] );
ABC_SWAP( int, pStore[i], pStore[BestK] );
if ( ((uCanonPhase >> i) & 1) != ((uCanonPhase >> BestK) & 1) )
{
uCanonPhase ^= (1 << i);
uCanonPhase ^= (1 << BestK);
}
Abc_TtSwapVars( pTruth, nVars, i, BestK );
// nSwaps++;
}
}
return uCanonPhase;
}
/**Function*************************************************************
Synopsis []
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Abc_TtCofactorTest10( word * pTruth, int nVars, int N )
{
static word pCopy1[1024];
static word pCopy2[1024];
int nWords = Abc_TtWordNum( nVars );
int i;
for ( i = 0; i < nVars - 1; i++ )
{
// Kit_DsdPrintFromTruth( pTruth, nVars ); printf( "\n" );
Abc_TtCopy( pCopy1, pTruth, nWords, 0 );
Abc_TtSwapAdjacent( pCopy1, nWords, i );
// Kit_DsdPrintFromTruth( pCopy1, nVars ); printf( "\n" );
Abc_TtCopy( pCopy2, pTruth, nWords, 0 );
Abc_TtSwapVars( pCopy2, nVars, i, i+1 );
// Kit_DsdPrintFromTruth( pCopy2, nVars ); printf( "\n" );
assert( Abc_TtEqual( pCopy1, pCopy2, nWords ) );
}
}
/**Function*************************************************************
Synopsis [Naive evaluation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Abc_Tt6CofactorPermNaive( word * pTruth, int i, int fSwapOnly )
{
if ( fSwapOnly )
{
word Copy = Abc_Tt6SwapAdjacent( pTruth[0], i );
if ( pTruth[0] > Copy )
{
pTruth[0] = Copy;
return 4;
}
return 0;
}
{
word Copy = pTruth[0];
word Best = pTruth[0];
int Config = 0;
// PXY
// 001
Copy = Abc_Tt6Flip( Copy, i );
if ( Best > Copy )
Best = Copy, Config = 1;
// PXY
// 011
Copy = Abc_Tt6Flip( Copy, i+1 );
if ( Best > Copy )
Best = Copy, Config = 3;
// PXY
// 010
Copy = Abc_Tt6Flip( Copy, i );
if ( Best > Copy )
Best = Copy, Config = 2;
// PXY
// 110
Copy = Abc_Tt6SwapAdjacent( Copy, i );
if ( Best > Copy )
Best = Copy, Config = 6;
// PXY
// 111
Copy = Abc_Tt6Flip( Copy, i+1 );
if ( Best > Copy )
Best = Copy, Config = 7;
// PXY
// 101
Copy = Abc_Tt6Flip( Copy, i );
if ( Best > Copy )
Best = Copy, Config = 5;
// PXY
// 100
Copy = Abc_Tt6Flip( Copy, i+1 );
if ( Best > Copy )
Best = Copy, Config = 4;
// PXY
// 000
Copy = Abc_Tt6SwapAdjacent( Copy, i );
assert( Copy == pTruth[0] );
assert( Best <= pTruth[0] );
pTruth[0] = Best;
return Config;
}
}
int Abc_TtCofactorPermNaive( word * pTruth, int i, int nWords, int fSwapOnly )
{
if ( fSwapOnly )
{
static word pCopy[1024];
Abc_TtCopy( pCopy, pTruth, nWords, 0 );
Abc_TtSwapAdjacent( pCopy, nWords, i );
if ( Abc_TtCompareRev(pTruth, pCopy, nWords) == 1 )
{
Abc_TtCopy( pTruth, pCopy, nWords, 0 );
return 4;
}
return 0;
}
{
static word pCopy[1024];
static word pBest[1024];
int Config = 0;
// save two copies
Abc_TtCopy( pCopy, pTruth, nWords, 0 );
Abc_TtCopy( pBest, pTruth, nWords, 0 );
// PXY
// 001
Abc_TtFlip( pCopy, nWords, i );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 1;
// PXY
// 011
Abc_TtFlip( pCopy, nWords, i+1 );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 3;
// PXY
// 010
Abc_TtFlip( pCopy, nWords, i );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 2;
// PXY
// 110
Abc_TtSwapAdjacent( pCopy, nWords, i );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 6;
// PXY
// 111
Abc_TtFlip( pCopy, nWords, i+1 );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 7;
// PXY
// 101
Abc_TtFlip( pCopy, nWords, i );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 5;
// PXY
// 100
Abc_TtFlip( pCopy, nWords, i+1 );
if ( Abc_TtCompareRev(pBest, pCopy, nWords) == 1 )
Abc_TtCopy( pBest, pCopy, nWords, 0 ), Config = 4;
// PXY
// 000
Abc_TtSwapAdjacent( pCopy, nWords, i );
assert( Abc_TtEqual( pTruth, pCopy, nWords ) );
if ( Config == 0 )
return 0;
assert( Abc_TtCompareRev(pTruth, pBest, nWords) == 1 );
Abc_TtCopy( pTruth, pBest, nWords, 0 );
return Config;
}
}
/**Function*************************************************************
Synopsis [Smart evaluation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Abc_TtCofactorPermConfig( word * pTruth, int i, int nWords, int fSwapOnly, int fNaive )
{
if ( nWords == 1 )
return Abc_Tt6CofactorPermNaive( pTruth, i, fSwapOnly );
if ( fNaive )
return Abc_TtCofactorPermNaive( pTruth, i, nWords, fSwapOnly );
if ( fSwapOnly )
{
if ( Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 1, 2 ) < 0 ) // Cof1 < Cof2
{
Abc_TtSwapAdjacent( pTruth, nWords, i );
return 4;
}
return 0;
}
{
int fComp01, fComp02, fComp03, fComp12, fComp13, fComp23, Config = 0;
fComp01 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 0, 1 );
fComp23 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 2, 3 );
if ( fComp23 >= 0 ) // Cof2 >= Cof3
{
if ( fComp01 >= 0 ) // Cof0 >= Cof1
{
fComp13 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 1, 3 );
if ( fComp13 < 0 ) // Cof1 < Cof3
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 2;
else if ( fComp13 == 0 ) // Cof1 == Cof3
{
fComp02 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 0, 2 );
if ( fComp02 < 0 )
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 2;
}
// else Cof1 > Cof3 -- do nothing
}
else // Cof0 < Cof1
{
fComp03 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 0, 3 );
if ( fComp03 < 0 ) // Cof0 < Cof3
{
Abc_TtFlip( pTruth, nWords, i );
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 3;
}
else // Cof0 >= Cof3
{
if ( fComp23 == 0 ) // can flip Cof0 and Cof1
Abc_TtFlip( pTruth, nWords, i ), Config = 1;
}
}
}
else // Cof2 < Cof3
{
if ( fComp01 >= 0 ) // Cof0 >= Cof1
{
fComp12 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 1, 2 );
if ( fComp12 > 0 ) // Cof1 > Cof2
Abc_TtFlip( pTruth, nWords, i ), Config = 1;
else if ( fComp12 == 0 ) // Cof1 == Cof2
{
Abc_TtFlip( pTruth, nWords, i );
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 3;
}
else // Cof1 < Cof2
{
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 2;
if ( fComp01 == 0 )
Abc_TtFlip( pTruth, nWords, i ), Config ^= 1;
}
}
else // Cof0 < Cof1
{
fComp02 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 0, 2 );
if ( fComp02 == -1 ) // Cof0 < Cof2
{
Abc_TtFlip( pTruth, nWords, i );
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 3;
}
else if ( fComp02 == 0 ) // Cof0 == Cof2
{
fComp13 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 1, 3 );
if ( fComp13 >= 0 ) // Cof1 >= Cof3
Abc_TtFlip( pTruth, nWords, i ), Config = 1;
else // Cof1 < Cof3
{
Abc_TtFlip( pTruth, nWords, i );
Abc_TtFlip( pTruth, nWords, i + 1 ), Config = 3;
}
}
else // Cof0 > Cof2
Abc_TtFlip( pTruth, nWords, i ), Config = 1;
}
}
// perform final swap if needed
fComp12 = Abc_TtCompare2VarCofsRev( pTruth, nWords, i, 1, 2 );
if ( fComp12 < 0 ) // Cof1 < Cof2
Abc_TtSwapAdjacent( pTruth, nWords, i ), Config ^= 4;
return Config;
}
}
int Abc_TtCofactorPerm( word * pTruth, int i, int nWords, int fSwapOnly, char * pCanonPerm, unsigned * puCanonPhase, int fNaive )
{
if ( fSwapOnly )
{
int Config = Abc_TtCofactorPermConfig( pTruth, i, nWords, 1, 0 );
if ( Config )
{
if ( ((*puCanonPhase >> i) & 1) != ((*puCanonPhase >> (i+1)) & 1) )
{
*puCanonPhase ^= (1 << i);
*puCanonPhase ^= (1 << (i+1));
}
ABC_SWAP( int, pCanonPerm[i], pCanonPerm[i+1] );
}
return Config;
}
{
static word pCopy1[1024];
int Config;
Abc_TtCopy( pCopy1, pTruth, nWords, 0 );
Config = Abc_TtCofactorPermConfig( pTruth, i, nWords, 0, fNaive );
if ( Config == 0 )
return 0;
if ( Abc_TtCompareRev(pTruth, pCopy1, nWords) == 1 ) // made it worse
{
Abc_TtCopy( pTruth, pCopy1, nWords, 0 );
return 0;
}
// improved
if ( Config & 1 )
*puCanonPhase ^= (1 << i);
if ( Config & 2 )
*puCanonPhase ^= (1 << (i+1));
if ( Config & 4 )
{
if ( ((*puCanonPhase >> i) & 1) != ((*puCanonPhase >> (i+1)) & 1) )
{
*puCanonPhase ^= (1 << i);
*puCanonPhase ^= (1 << (i+1));
}
ABC_SWAP( int, pCanonPerm[i], pCanonPerm[i+1] );
}
return Config;
}
}
/**Function*************************************************************
Synopsis [Semi-canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
//#define CANON_VERIFY
unsigned Abc_TtCanonicize( word * pTruth, int nVars, char * pCanonPerm )
{
int pStoreIn[17];
unsigned uCanonPhase;
int i, k, nWords = Abc_TtWordNum( nVars );
int fNaive = 1;
#ifdef CANON_VERIFY
char pCanonPermCopy[16];
static word pCopy1[1024];
static word pCopy2[1024];
Abc_TtCopy( pCopy1, pTruth, nWords, 0 );
#endif
uCanonPhase = Abc_TtSemiCanonicize( pTruth, nVars, pCanonPerm, pStoreIn, 0 );
for ( k = 0; k < 5; k++ )
{
int fChanges = 0;
for ( i = nVars - 2; i >= 0; i-- )
if ( pStoreIn[i] == pStoreIn[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, pStoreIn[i] != pStoreIn[nVars]/2, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
fChanges = 0;
for ( i = 1; i < nVars - 1; i++ )
if ( pStoreIn[i] == pStoreIn[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, pStoreIn[i] != pStoreIn[nVars]/2, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
}
#ifdef CANON_VERIFY
Abc_TtCopy( pCopy2, pTruth, nWords, 0 );
memcpy( pCanonPermCopy, pCanonPerm, sizeof(char) * nVars );
Abc_TtImplementNpnConfig( pCopy2, nVars, pCanonPermCopy, uCanonPhase );
if ( !Abc_TtEqual( pCopy1, pCopy2, nWords ) )
printf( "Canonical form verification failed!\n" );
#endif
/*
if ( !Abc_TtEqual( pCopy1, pCopy2, nWords ) )
{
Kit_DsdPrintFromTruth( pCopy1, nVars ); printf( "\n" );
Kit_DsdPrintFromTruth( pCopy2, nVars ); printf( "\n" );
i = 0;
}
*/
return uCanonPhase;
}
unsigned Abc_TtCanonicizePerm( word * pTruth, int nVars, char * pCanonPerm )
{
int pStoreIn[17];
unsigned uCanonPhase;
int i, k, nWords = Abc_TtWordNum( nVars );
int fNaive = 1;
#ifdef CANON_VERIFY
char pCanonPermCopy[16];
static word pCopy1[1024];
static word pCopy2[1024];
Abc_TtCopy( pCopy1, pTruth, nWords, 0 );
#endif
assert( nVars <= 16 );
for ( i = 0; i < nVars; i++ )
pCanonPerm[i] = i;
uCanonPhase = Abc_TtSemiCanonicize( pTruth, nVars, pCanonPerm, pStoreIn, 1 );
for ( k = 0; k < 5; k++ )
{
int fChanges = 0;
for ( i = nVars - 2; i >= 0; i-- )
if ( pStoreIn[i] == pStoreIn[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, 1, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
fChanges = 0;
for ( i = 1; i < nVars - 1; i++ )
if ( pStoreIn[i] == pStoreIn[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, 1, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
}
#ifdef CANON_VERIFY
Abc_TtCopy( pCopy2, pTruth, nWords, 0 );
memcpy( pCanonPermCopy, pCanonPerm, sizeof(char) * nVars );
Abc_TtImplementNpnConfig( pCopy2, nVars, pCanonPermCopy, uCanonPhase );
if ( !Abc_TtEqual( pCopy1, pCopy2, nWords ) )
printf( "Canonical form verification failed!\n" );
#endif
assert( uCanonPhase == 0 );
return uCanonPhase;
}
/**Function*************************************************************
Synopsis [Semi-canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline int Abc_TtCanonicizePhaseVar6( word * pTruth, int nVars, int v )
{
int w, nWords = Abc_TtWordNum( nVars );
int s, nStep = 1 << (v-6);
assert( v >= 6 );
for ( w = nWords - 1, s = nWords - nStep; w > 0; w-- )
{
if ( pTruth[w-nStep] == pTruth[w] )
{
if ( w == s ) { w = s - nStep; s = w - nStep; }
continue;
}
if ( pTruth[w-nStep] > pTruth[w] )
return -1;
for ( ; w > 0; w-- )
{
ABC_SWAP( word, pTruth[w-nStep], pTruth[w] );
if ( w == s ) { w = s - nStep; s = w - nStep; }
}
assert( w == -1 );
return 1;
}
return 0;
}
static inline int Abc_TtCanonicizePhaseVar5( word * pTruth, int nVars, int v )
{
int w, nWords = Abc_TtWordNum( nVars );
int Shift = 1 << v;
word Mask = s_Truths6[v];
assert( v < 6 );
for ( w = nWords - 1; w >= 0; w-- )
{
if ( ((pTruth[w] << Shift) & Mask) == (pTruth[w] & Mask) )
continue;
if ( ((pTruth[w] << Shift) & Mask) > (pTruth[w] & Mask) )
return -1;
// Extra_PrintHex( stdout, (unsigned *)pTruth, nVars ); printf("\n" );
for ( ; w >= 0; w-- )
pTruth[w] = ((pTruth[w] << Shift) & Mask) | ((pTruth[w] & Mask) >> Shift);
// Extra_PrintHex( stdout, (unsigned *)pTruth, nVars ); printf( " changed %d", v ), printf("\n" );
return 1;
}
return 0;
}
unsigned Abc_TtCanonicizePhase( word * pTruth, int nVars )
{
unsigned uCanonPhase = 0;
int v, nWords = Abc_TtWordNum( nVars );
// static int Counter = 0;
// Counter++;
#ifdef CANON_VERIFY
static word pCopy1[1024];
static word pCopy2[1024];
Abc_TtCopy( pCopy1, pTruth, nWords, 0 );
#endif
if ( (pTruth[nWords-1] >> 63) & 1 )
{
Abc_TtNot( pTruth, nWords );
uCanonPhase ^= (1 << nVars);
}
// while ( 1 )
// {
// unsigned uCanonPhase2 = uCanonPhase;
for ( v = nVars - 1; v >= 6; v-- )
if ( Abc_TtCanonicizePhaseVar6( pTruth, nVars, v ) == 1 )
uCanonPhase ^= 1 << v;
for ( ; v >= 0; v-- )
if ( Abc_TtCanonicizePhaseVar5( pTruth, nVars, v ) == 1 )
uCanonPhase ^= 1 << v;
// if ( uCanonPhase2 == uCanonPhase )
// break;
// }
// for ( v = 5; v >= 0; v-- )
// assert( Abc_TtCanonicizePhaseVar5( pTruth, nVars, v ) != 1 );
#ifdef CANON_VERIFY
Abc_TtCopy( pCopy2, pTruth, nWords, 0 );
Abc_TtImplementNpnConfig( pCopy2, nVars, NULL, uCanonPhase );
if ( !Abc_TtEqual( pCopy1, pCopy2, nWords ) )
printf( "Canonical form verification failed!\n" );
#endif
return uCanonPhase;
}
/**Function*************************************************************
Synopsis [Hierarchical semi-canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
#define TT_MAX_LEVELS 5
struct Abc_TtHieMan_t_
{
int nLastLevel, nWords;
Vec_Mem_t * vTtMem[TT_MAX_LEVELS]; // truth table memory and hash tables
Vec_Int_t * vRepres[TT_MAX_LEVELS]; // pointers to the representatives from the last hierarchical level
int vTruthId[TT_MAX_LEVELS];
Vec_Int_t * vPhase;
};
Abc_TtHieMan_t * Abc_TtHieManStart(int nVars, int nLevels)
{
Abc_TtHieMan_t * p = NULL;
int i;
if (nLevels > TT_MAX_LEVELS) return p;
p = ABC_CALLOC(Abc_TtHieMan_t, 1);
p->nLastLevel = nLevels - 1;
p->nWords = Abc_TtWordNum(nVars);
for (i = 0; i < nLevels; i++)
{
p->vTtMem[i] = Vec_MemAlloc(p->nWords, 12);
Vec_MemHashAlloc(p->vTtMem[i], 10000);
p->vRepres[i] = Vec_IntAlloc(1);
}
p->vPhase = Vec_IntAlloc(2500);
return p;
}
void Abc_TtHieManStop(Abc_TtHieMan_t * p)
{
int i;
for (i = 0; i <= p->nLastLevel; i++)
{
Vec_MemHashFree(p->vTtMem[i]);
Vec_MemFreeP(&p->vTtMem[i]);
Vec_IntFree(p->vRepres[i]);
}
Vec_IntFree( p->vPhase );
ABC_FREE(p);
}
int Abc_TtHieRetrieveOrInsert(Abc_TtHieMan_t * p, int level, word * pTruth, word * pResult)
{
int i, iSpot, truthId;
word * pRepTruth;
if (!p) return -1;
if (level < 0) level += p->nLastLevel + 1;
if (level < 0 || level > p->nLastLevel) return -1;
iSpot = *Vec_MemHashLookup(p->vTtMem[level], pTruth);
if (iSpot == -1) {
p->vTruthId[level] = Vec_MemHashInsert(p->vTtMem[level], pTruth);
if (level < p->nLastLevel) return 0;
iSpot = p->vTruthId[level];
}
// return the class representative
if (level < p->nLastLevel)
truthId = Vec_IntEntry(p->vRepres[level], iSpot);
else
truthId = iSpot;
for (i = 0; i < level; i++)
Vec_IntSetEntry(p->vRepres[i], p->vTruthId[i], truthId);
pRepTruth = Vec_MemReadEntry(p->vTtMem[p->nLastLevel], truthId);
if (level < p->nLastLevel) {
Abc_TtCopy(pResult, pRepTruth, p->nWords, 0);
return 1;
}
assert(Abc_TtEqual(pTruth, pRepTruth, p->nWords));
if (pTruth != pResult)
Abc_TtCopy(pResult, pRepTruth, p->nWords, 0);
return 0;
}
unsigned Abc_TtCanonicizeHie( Abc_TtHieMan_t * p, word * pTruthInit, int nVars, char * pCanonPerm, int fExact )
{
int fNaive = 1;
int pStore[17];
//static word pTruth[1024];
word * pTruth = pTruthInit;
unsigned uCanonPhase = 0;
int nOnes, nWords = Abc_TtWordNum( nVars );
int i, k;
assert( nVars <= 16 );
// handle constant
if ( nVars == 0 )
{
Abc_TtClear( pTruthInit, nWords );
return 0;
}
//Abc_TtCopy( pTruth, pTruthInit, nWords, 0 );
for ( i = 0; i < nVars; i++ )
pCanonPerm[i] = i;
// normalize polarity
nOnes = Abc_TtCountOnesInTruth( pTruth, nVars );
if ( nOnes > nWords * 32 )
{
Abc_TtNot( pTruth, nWords );
nOnes = nWords*64 - nOnes;
uCanonPhase |= (1 << nVars);
}
// check cache
if (Abc_TtHieRetrieveOrInsert(p, 0, pTruth, pTruthInit) > 0) return 0;
// normalize phase
Abc_TtCountOnesInCofs( pTruth, nVars, pStore );
pStore[nVars] = nOnes;
for ( i = 0; i < nVars; i++ )
{
if ( pStore[i] >= nOnes - pStore[i] )
continue;
Abc_TtFlip( pTruth, nWords, i );
uCanonPhase |= (1 << i);
pStore[i] = nOnes - pStore[i];
}
// check cache
if (Abc_TtHieRetrieveOrInsert(p, 1, pTruth, pTruthInit) > 0) return 0;
// normalize permutation
{
int k, BestK;
for ( i = 0; i < nVars - 1; i++ )
{
BestK = i + 1;
for ( k = i + 2; k < nVars; k++ )
if ( pStore[BestK] > pStore[k] )
BestK = k;
if ( pStore[i] <= pStore[BestK] )
continue;
ABC_SWAP( int, pCanonPerm[i], pCanonPerm[BestK] );
ABC_SWAP( int, pStore[i], pStore[BestK] );
if ( ((uCanonPhase >> i) & 1) != ((uCanonPhase >> BestK) & 1) )
{
uCanonPhase ^= (1 << i);
uCanonPhase ^= (1 << BestK);
}
Abc_TtSwapVars( pTruth, nVars, i, BestK );
}
}
// check cache
if (Abc_TtHieRetrieveOrInsert(p, 2, pTruth, pTruthInit) > 0) return 0;
// iterate TT permutations for tied variables
for ( k = 0; k < 5; k++ )
{
int fChanges = 0;
for ( i = nVars - 2; i >= 0; i-- )
if ( pStore[i] == pStore[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, pStore[i] != pStore[nVars]/2, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
fChanges = 0;
for ( i = 1; i < nVars - 1; i++ )
if ( pStore[i] == pStore[i+1] )
fChanges |= Abc_TtCofactorPerm( pTruth, i, nWords, pStore[i] != pStore[nVars]/2, pCanonPerm, &uCanonPhase, fNaive );
if ( !fChanges )
break;
}
// check cache
if (Abc_TtHieRetrieveOrInsert(p, 3, pTruth, pTruthInit) > 0) return 0;
// perform exact NPN using groups
if ( fExact ) {
extern void simpleMinimalGroups(word* x, word* pAux, word* minimal, int* pGroups, int nGroups, permInfo** pis, int nVars, int fFlipOutput, int fFlipInput);
word pAuxWord[1024], pAuxWord1[1024];
int pGroups[16];
int nGroups = 0;
permInfo * pis[17];
// get groups
pGroups[0] = 0;
for (i = 0; i < nVars - 1; i++) {
if (pStore[i] == pStore[i + 1]) {
pGroups[nGroups]++;
} else {
pGroups[nGroups]++;
nGroups++;
pGroups[nGroups] = 0;
}
}
pGroups[nGroups]++;
nGroups++;
// compute permInfo from 0 to nVars (incl.)
for (i = 0; i <= nVars; i++) {
pis[i] = setPermInfoPtr(i);
}
// do the exact matching
if (nOnes == nWords * 32) /* balanced output */
simpleMinimalGroups(pTruth, pAuxWord, pAuxWord1, pGroups, nGroups, pis, nVars, 1, 1);
else if (pStore[0] != pStore[1] && pStore[0] == (nOnes - pStore[0])) /* balanced singleton input */
simpleMinimalGroups(pTruth, pAuxWord, pAuxWord1, pGroups, nGroups, pis, nVars, 0, 1);
else
simpleMinimalGroups(pTruth, pAuxWord, pAuxWord1, pGroups, nGroups, pis, nVars, 0, 0);
// cleanup
for (i = 0; i <= nVars; i++) {
freePermInfoPtr(pis[i]);
}
}
// update cache
Abc_TtHieRetrieveOrInsert(p, 4, pTruth, pTruthInit);
return 0;
}
/**Function*************************************************************
Synopsis [Adaptive exact/semi-canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
typedef struct TiedGroup_
{
char iStart; // index of Abc_TgMan_t::pPerm
char nGVars; // the number of variables in the group
} TiedGroup;
typedef struct Abc_TgMan_t_
{
word *pTruth;
int nVars; // the number of variables
int nGVars; // the number of variables in groups ( symmetric variables purged )
int nGroups; // the number of tied groups
unsigned uPhase; // phase of each variable and the function
int fPhased; // if the phases of all the variables are determined
char pPerm[16]; // permutation of variables, symmetric variables purged, for grouping
char pPermT[16]; // permutation of variables, symmetric variables expanded, actual transformation for pTruth
char pPermTRev[16]; // reverse permutation of pPermT
signed char pPermDir[16]; // for generating the next permutation
TiedGroup pGroup[16]; // tied groups
// symemtric group attributes
char symPhase[16]; // phase type of symemtric groups
signed char symLink[17]; // singly linked list, indicate the variables in symemtric groups
int nAlgorithm; // 0: AdjCE, 1: AdjSE, 2: E: Cost-Aware
char pFGrps[16]; // tied groups to be flipped
Vec_Int_t * vPhase; // candidate phase assignments
} Abc_TgMan_t;
#if !defined(NDEBUG) && !defined(CANON_VERIFY)
#define CANON_VERIFY
#endif
/**Function*************************************************************
Synopsis [Utilities.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
// Johnson�CTrotter algorithm
static int Abc_NextPermSwapC(char * pData, signed char * pDir, int size)
{
int i, j, k = -1;
for (i = 0; i < size; i++)
{
j = i + pDir[i];
if (j >= 0 && j < size && pData[i] > pData[j] && (k < 0 || pData[i] > pData[k]))
k = i;
}
if (k < 0) k = 0;
for (i = 0; i < size; i++)
if (pData[i] > pData[k])
pDir[i] = -pDir[i];
j = k + pDir[k];
return j < k ? j : k;
}
//typedef unsigned(*TtCanonicizeFunc)(Abc_TtHieMan_t * p, word * pTruth, int nVars, char * pCanonPerm, int flag);
unsigned Abc_TtCanonicizeWrap(TtCanonicizeFunc func, Abc_TtHieMan_t * p, word * pTruth, int nVars, char * pCanonPerm, int flag)
{
int nWords = Abc_TtWordNum(nVars);
unsigned uCanonPhase1, uCanonPhase2;
char pCanonPerm2[16];
static word pTruth2[1024];
Abc_TtNormalizeSmallTruth(pTruth, nVars);
if (Abc_TtCountOnesInTruth(pTruth, nVars) != nWords * 32)
return func(p, pTruth, nVars, pCanonPerm, flag);
Abc_TtCopy(pTruth2, pTruth, nWords, 1);
uCanonPhase1 = func(p, pTruth, nVars, pCanonPerm, flag);
uCanonPhase2 = func(p, pTruth2, nVars, pCanonPerm2, flag);
if (Abc_TtCompareRev(pTruth, pTruth2, nWords) <= 0)
return uCanonPhase1;
Abc_TtCopy(pTruth, pTruth2, nWords, 0);
memcpy(pCanonPerm, pCanonPerm2, nVars);
return uCanonPhase2;
}
word gpVerCopy[1024];
static int Abc_TtCannonVerify(word* pTruth, int nVars, char * pCanonPerm, unsigned uCanonPhase)
{
#ifdef CANON_VERIFY
int nWords = Abc_TtWordNum(nVars);
char pCanonPermCopy[16];
static word pCopy2[1024];
Abc_TtVerifySmallTruth(pTruth, nVars);
Abc_TtCopy(pCopy2, pTruth, nWords, 0);
memcpy(pCanonPermCopy, pCanonPerm, sizeof(char) * nVars);
Abc_TtImplementNpnConfig(pCopy2, nVars, pCanonPermCopy, uCanonPhase);
return Abc_TtEqual(gpVerCopy, pCopy2, nWords);
#else
return 1;
#endif
}
/**Function*************************************************************
Synopsis [Tied group management.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static void Abc_TgInitMan(Abc_TgMan_t * pMan, word * pTruth, int nVars, int nAlg, Vec_Int_t * vPhase)
{
int i;
pMan->pTruth = pTruth;
pMan->uPhase = 0;
pMan->fPhased = 0;
pMan->nVars = pMan->nGVars = nVars;
pMan->nGroups = 1;
pMan->pGroup[0].iStart = 0;
pMan->pGroup[0].nGVars = nVars;
for (i = 0; i < nVars; i++)
{
pMan->pPerm[i] = i;
pMan->pPermT[i] = i;
pMan->pPermTRev[i] = i;
pMan->symPhase[i] = 1;
pMan->symLink[i] = -1;
}
pMan->symLink[i] = -1;
pMan->nAlgorithm = nAlg;
pMan->vPhase = vPhase;
Vec_IntClear(vPhase);
}
static int Abc_TgSplitGroup(Abc_TgMan_t * pMan, TiedGroup * pGrp, int * pCoef)
{
int i, j, n = 0;
int nGVars = pGrp->nGVars;
char * pVars = pMan->pPerm + pGrp->iStart;
int iGrp = pGrp - pMan->pGroup;
// sort variables
for (i = 1; i < nGVars; i++)
{
int a = pCoef[i]; char aa = pVars[i];
for (j = i; j > 0 && pCoef[j - 1] > a; j--)
pCoef[j] = pCoef[j - 1], pVars[j] = pVars[j - 1];
pCoef[j] = a; pVars[j] = aa;
}
for (i = 1; i < nGVars; i++)
if (pCoef[i] != pCoef[i - 1]) n++;
if (n == 0) return 0;
memmove(pGrp + n + 1, pGrp + 1, (pMan->nGroups - iGrp - 1) * sizeof(TiedGroup));
// group variables
for (i = j = 1; i < nGVars; i++)
{
if (pCoef[i] == pCoef[i - 1]) continue;
pGrp[j].iStart = pGrp->iStart + i;
pGrp[j - 1].nGVars = pGrp[j].iStart - pGrp[j - 1].iStart;
j++;
}
assert(j == n + 1);
pGrp[n].nGVars = pGrp->iStart + i - pGrp[n].iStart;
pMan->nGroups += n;
return n;
}
static inline void Abc_TgManCopy(Abc_TgMan_t* pDst, word* pDstTruth, Abc_TgMan_t* pSrc)
{
*pDst = *pSrc;
Abc_TtCopy(pDstTruth, pSrc->pTruth, Abc_TtWordNum(pSrc->nVars), 0);
pDst->pTruth = pDstTruth;
}
static inline int Abc_TgCannonVerify(Abc_TgMan_t* pMan)
{
return Abc_TtCannonVerify(pMan->pTruth, pMan->nVars, pMan->pPermT, pMan->uPhase);
}
extern int Abc_TgExpendSymmetry(Abc_TgMan_t * pMan, char * pDest);
static void CheckConfig(Abc_TgMan_t * pMan)
{
#ifndef NDEBUG
int i;
char pPermE[16];
Abc_TgExpendSymmetry(pMan, pPermE);
for (i = 0; i < pMan->nVars; i++)
{
assert(pPermE[i] == pMan->pPermT[i]);
assert(pMan->pPermTRev[(int)pMan->pPermT[i]] == i);
}
assert(Abc_TgCannonVerify(pMan));
#endif
}
/**Function*************************************************************
Synopsis [Truthtable manipulation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline void Abc_TgFlipVar(Abc_TgMan_t* pMan, int iVar)
{
int nWords = Abc_TtWordNum(pMan->nVars);
int ivp = pMan->pPermTRev[iVar];
Abc_TtFlip(pMan->pTruth, nWords, ivp);
pMan->uPhase ^= 1 << ivp;
}
static inline void Abc_TgFlipSymGroupByVar(Abc_TgMan_t* pMan, int iVar)
{
for (; iVar >= 0; iVar = pMan->symLink[iVar])
if (pMan->symPhase[iVar])
Abc_TgFlipVar(pMan, iVar);
}
static inline void Abc_TgFlipSymGroup(Abc_TgMan_t* pMan, int idx)
{
Abc_TgFlipSymGroupByVar(pMan, pMan->pPerm[idx]);
}
static inline void Abc_TgClearSymGroupPhase(Abc_TgMan_t* pMan, int iVar)
{
for (; iVar >= 0; iVar = pMan->symLink[iVar])
pMan->symPhase[iVar] = 0;
}
static void Abc_TgImplementPerm(Abc_TgMan_t* pMan, const char *pPermDest)
{
int i, nVars = pMan->nVars;
char *pPerm = pMan->pPermT;
char *pRev = pMan->pPermTRev;
unsigned uPhase = pMan->uPhase & (1 << nVars);
for (i = 0; i < nVars; i++)
pRev[(int)pPerm[i]] = i;
for (i = 0; i < nVars; i++)
pPerm[i] = pRev[(int)pPermDest[i]];
for (i = 0; i < nVars; i++)
pRev[(int)pPerm[i]] = i;
Abc_TtImplementNpnConfig(pMan->pTruth, nVars, pRev, 0);
// Abc_TtVerifySmallTruth(pMan->pTruth, nVars);
for (i = 0; i < nVars; i++)
{
if (pMan->uPhase & (1 << pPerm[i]))
uPhase |= (1 << i);
pPerm[i] = pPermDest[i];
pRev[(int)pPerm[i]] = i;
}
pMan->uPhase = uPhase;
}
static void Abc_TgSwapAdjacentSymGroups(Abc_TgMan_t* pMan, int idx)
{
int iVar, jVar, ix;
char pPermNew[16];
assert(idx < pMan->nGVars - 1);
iVar = pMan->pPerm[idx];
jVar = pMan->pPerm[idx + 1];
pMan->pPerm[idx] = jVar;
pMan->pPerm[idx + 1] = iVar;
ABC_SWAP(char, pMan->pPermDir[idx], pMan->pPermDir[idx + 1]);
if (pMan->symLink[iVar] >= 0 || pMan->symLink[jVar] >= 0)
{
Abc_TgExpendSymmetry(pMan, pPermNew);
Abc_TgImplementPerm(pMan, pPermNew);
return;
}
// plain variable swap
ix = pMan->pPermTRev[iVar];
assert(pMan->pPermT[ix] == iVar && pMan->pPermT[ix + 1] == jVar);
Abc_TtSwapAdjacent(pMan->pTruth, Abc_TtWordNum(pMan->nVars), ix);
pMan->pPermT[ix] = jVar;
pMan->pPermT[ix + 1] = iVar;
pMan->pPermTRev[iVar] = ix + 1;
pMan->pPermTRev[jVar] = ix;
if (((pMan->uPhase >> ix) & 1) != ((pMan->uPhase >> (ix + 1)) & 1))
pMan->uPhase ^= 1 << ix | 1 << (ix + 1);
assert(Abc_TgCannonVerify(pMan));
}
/**Function*************************************************************
Synopsis [semmetry of two variables.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static word pSymCopy[1024];
static int Abc_TtIsSymmetric(word * pTruth, int nVars, int iVar, int jVar, int fPhase)
{
int rv;
int nWords = Abc_TtWordNum(nVars);
Abc_TtCopy(pSymCopy, pTruth, nWords, 0);
Abc_TtSwapVars(pSymCopy, nVars, iVar, jVar);
rv = Abc_TtEqual(pTruth, pSymCopy, nWords) * 2;
if (!fPhase) return rv;
Abc_TtFlip(pSymCopy, nWords, iVar);
Abc_TtFlip(pSymCopy, nWords, jVar);
return rv + Abc_TtEqual(pTruth, pSymCopy, nWords);
}
static int Abc_TtIsSymmetricHigh(Abc_TgMan_t * pMan, int iVar, int jVar, int fPhase)
{
int rv, iv, jv, n;
int nWords = Abc_TtWordNum(pMan->nVars);
Abc_TtCopy(pSymCopy, pMan->pTruth, nWords, 0);
for (n = 0, iv = iVar, jv = jVar; iv >= 0 && jv >= 0; iv = pMan->symLink[iv], jv = pMan->symLink[jv], n++)
Abc_TtSwapVars(pSymCopy, pMan->nVars, iv, jv);
assert(iv < 0 && jv < 0); // two symmetric groups must have the same size
rv = Abc_TtEqual(pMan->pTruth, pSymCopy, nWords) * 2;
if (!fPhase) return rv;
for (iv = iVar, jv = jVar; iv >= 0 && jv >= 0; iv = pMan->symLink[iv], jv = pMan->symLink[jv])
{
if (pMan->symPhase[iv]) Abc_TtFlip(pSymCopy, nWords, iv);
if (pMan->symPhase[jv]) Abc_TtFlip(pSymCopy, nWords, jv);
}
return rv + Abc_TtEqual(pMan->pTruth, pSymCopy, nWords);
}
/**Function*************************************************************
Synopsis [Create groups by cofactor signatures]
Description [Similar to Abc_TtSemiCanonicize.
Use stable insertion sort to keep the order of the variables in the groups.
Defer permutation. ]
SideEffects []
SeeAlso []
***********************************************************************/
static void Abc_TgCreateGroups(Abc_TgMan_t * pMan)
{
int pStore[17];
int i, nOnes;
int nVars = pMan->nVars, nWords = Abc_TtWordNum(nVars);
//TiedGroup * pGrp = pMan->pGroup;
assert(nVars <= 16);
// normalize polarity
nOnes = Abc_TtCountOnesInTruth(pMan->pTruth, nVars);
if (nOnes > nWords * 32)
{
Abc_TtNot(pMan->pTruth, nWords);
nOnes = nWords * 64 - nOnes;
pMan->uPhase |= (1 << nVars);
}
// normalize phase
Abc_TtCountOnesInCofs(pMan->pTruth, nVars, pStore);
pStore[nVars] = nOnes;
for (i = 0; i < nVars; i++)
{
if (pStore[i] >= nOnes - pStore[i])
continue;
Abc_TtFlip(pMan->pTruth, nWords, i);
pMan->uPhase |= (1 << i);
pStore[i] = nOnes - pStore[i];
}
Abc_TgSplitGroup(pMan, pMan->pGroup, pStore);
pMan->fPhased = pStore[0] * 2 != nOnes;
}
/**Function*************************************************************
Synopsis [Group symmetric variables.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static int Abc_TgGroupSymmetry(Abc_TgMan_t * pMan, TiedGroup * pGrp, int fHigh)
{
int i, j, iVar, jVar, nsym = 0;
int fDone[16], scnt[16], stype[16];
signed char *symLink = pMan->symLink;
// char * symPhase = pMan->symPhase;
int nGVars = pGrp->nGVars;
int fPhase = (pGrp == pMan->pGroup) && !pMan->fPhased;
char * pVars = pMan->pPerm + pGrp->iStart;
int modified;
for (i = 0; i < nGVars; i++)
fDone[i] = 0, scnt[i] = 1;
do {
modified = 0;
for (i = 0; i < nGVars - 1; i++)
{
iVar = pVars[i];
if (iVar < 0 || fDone[i]) continue;
// if (!pGrp->fPhased && !Abc_TtHasVar(pMan->pTruth, pMan->nVars, iVar)) continue;
// Mark symmetric variables/groups
for (j = i + 1; j < nGVars; j++)
{
jVar = pVars[j];
if (jVar < 0 || scnt[j] != scnt[i]) // || pMan->symPhase[jVar] != pMan->symPhase[iVar])
stype[j] = 0;
else if (scnt[j] == 1)
stype[j] = Abc_TtIsSymmetric(pMan->pTruth, pMan->nVars, iVar, jVar, fPhase);
else
stype[j] = Abc_TtIsSymmetricHigh(pMan, iVar, jVar, fPhase);
}
fDone[i] = 1;
// Merge symmetric groups
for (j = i + 1; j < nGVars; j++)
{
int ii;
jVar = pVars[j];
switch (stype[j])
{
case 1: // E-Symmetry
Abc_TgFlipSymGroupByVar(pMan, jVar);
// fallthrough
case 2: // NE-Symmetry
pMan->symPhase[iVar] += pMan->symPhase[jVar];
break;
case 3: // multiform Symmetry
Abc_TgClearSymGroupPhase(pMan, jVar);
break;
default: // case 0: No Symmetry
continue;
}
for (ii = iVar; symLink[ii] >= 0; ii = symLink[ii])
;
symLink[ii] = jVar;
pVars[j] = -1;
scnt[i] += scnt[j];
modified = 1;
fDone[i] = 0;
nsym++;
}
}
// if (++order > 3) printf("%d", order);
} while (fHigh && modified);
return nsym;
}
static void Abc_TgPurgeSymmetry(Abc_TgMan_t * pMan, int fHigh)
{
int i, j, k, sum = 0, nVars = pMan->nVars;
signed char *symLink = pMan->symLink;
char gcnt[16] = { 0 };
char * pPerm = pMan->pPerm;
// purge unsupported variables
if (!pMan->fPhased)
{
int iVar = pMan->nVars;
for (j = 0; j < pMan->pGroup[0].nGVars; j++)
{
int jVar = pPerm[j];
assert(jVar >= 0);
if (!Abc_TtHasVar(pMan->pTruth, nVars, jVar))
{
symLink[jVar] = symLink[iVar];
symLink[iVar] = jVar;
pPerm[j] = -1;
gcnt[0]++;
}
}
}
for (k = 0; k < pMan->nGroups; k++)
gcnt[k] += Abc_TgGroupSymmetry(pMan, pMan->pGroup + k, fHigh);
for (i = 0; i < nVars && pPerm[i] >= 0; i++)
;
for (j = i + 1; ; i++, j++)
{
while (j < nVars && pPerm[j] < 0) j++;
if (j >= nVars) break;
pPerm[i] = pPerm[j];
}
for (k = 0; k < pMan->nGroups; k++)
{
pMan->pGroup[k].nGVars -= gcnt[k];
pMan->pGroup[k].iStart -= sum;
sum += gcnt[k];
}
if (pMan->pGroup[0].nGVars == 0)
{
pMan->nGroups--;
memmove(pMan->pGroup, pMan->pGroup + 1, sizeof(TiedGroup) * pMan->nGroups);
assert(pMan->pGroup[0].iStart == 0);
}
pMan->nGVars -= sum;
}
int Abc_TgExpendSymmetry(Abc_TgMan_t * pMan, char * pDest)
{
int i = 0, j, k, s;
char * pPerm = pMan->pPerm;
for (j = 0; j < pMan->nGVars; j++)
for (k = pPerm[j]; k >= 0; k = pMan->symLink[k])
pDest[i++] = k;
s = i;
for (k = pMan->symLink[pMan->nVars]; k >= 0; k = pMan->symLink[k])
pDest[i++] = k;
assert(i == pMan->nVars);
return s;
}
static void Abc_TgResetGroup(Abc_TgMan_t * pMan)
{
int i, j;
char * pPerm = pMan->pPerm;
char pPermNew[16];
int nGVars = pMan->nGVars;
for (i = 1; i < nGVars; i++)
{
char t = pPerm[i];
for (j = i; j > 0 && pPerm[j - 1] > t; j--)
pPerm[j] = pPerm[j - 1];
pPerm[j] = t;
}
Abc_TgExpendSymmetry(pMan, pPermNew);
Abc_TgImplementPerm(pMan, pPermNew);
pMan->fPhased = 0;
pMan->nGroups = 1;
pMan->pGroup->nGVars = nGVars;
Vec_IntClear(pMan->vPhase);
}
static void Abc_TgResetGroup1(Abc_TgMan_t * pMan)
{
int i, j;
char pPermNew[16];
int nSVars = Abc_TgExpendSymmetry(pMan, pPermNew);
for (i = 1; i < nSVars; i++)
{
char t = pPermNew[i];
for (j = i; j > 0 && pPermNew[j - 1] > t; j--)
pPermNew[j] = pPermNew[j - 1];
pPermNew[j] = t;
}
Abc_TgImplementPerm(pMan, pPermNew);
pMan->fPhased = 0;
pMan->nGroups = 1;
pMan->nGVars = pMan->pGroup->nGVars = nSVars;
for (i = 0; i < pMan->nVars; i++)
{
pMan->pPerm[i] = pPermNew[i];
pMan->symPhase[i] = 1;
pMan->symLink[i] = -1;
}
Vec_IntClear(pMan->vPhase);
}
/**Function*************************************************************
Synopsis [Semi-canonical form computation.]
Description [simple config enumeration]
SideEffects []
SeeAlso []
***********************************************************************/
static int Abc_TgSymGroupPerm(Abc_TgMan_t* pMan, int idx, int fSwapOnly)
{
word* pTruth = pMan->pTruth;
static word pCopy[1024];
static word pBest[1024];
int Config = 0;
int nWords = Abc_TtWordNum(pMan->nVars);
Abc_TgMan_t tgManCopy, tgManBest;
CheckConfig(pMan);
if (fSwapOnly)
{
Abc_TgManCopy(&tgManCopy, pCopy, pMan);
Abc_TgSwapAdjacentSymGroups(&tgManCopy, idx);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pTruth, pCopy, nWords) < 0)
{
Abc_TgManCopy(pMan, pTruth, &tgManCopy);
return 4;
}
return 0;
}
// save two copies
Abc_TgManCopy(&tgManCopy, pCopy, pMan);
Abc_TgManCopy(&tgManBest, pBest, pMan);
// PXY
// 001
Abc_TgFlipSymGroup(&tgManCopy, idx);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 1;
// PXY
// 011
Abc_TgFlipSymGroup(&tgManCopy, idx + 1);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 3;
// PXY
// 010
Abc_TgFlipSymGroup(&tgManCopy, idx);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 2;
// PXY
// 110
Abc_TgSwapAdjacentSymGroups(&tgManCopy, idx);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 6;
// PXY
// 111
Abc_TgFlipSymGroup(&tgManCopy, idx + 1);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 7;
// PXY
// 101
Abc_TgFlipSymGroup(&tgManCopy, idx);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 5;
// PXY
// 100
Abc_TgFlipSymGroup(&tgManCopy, idx + 1);
CheckConfig(&tgManCopy);
if (Abc_TtCompareRev(pBest, pCopy, nWords) == 1)
Abc_TgManCopy(&tgManBest, pBest, &tgManCopy), Config = 4;
// PXY
// 000
Abc_TgSwapAdjacentSymGroups(&tgManCopy, idx);
CheckConfig(&tgManCopy);
assert(Abc_TtEqual(pTruth, pCopy, nWords));
if (Config == 0)
return 0;
assert(Abc_TtCompareRev(pTruth, pBest, nWords) == 1);
Abc_TgManCopy(pMan, pTruth, &tgManBest);
return Config;
}
static int Abc_TgPermPhase(Abc_TgMan_t* pMan, int iVar)
{
static word pCopy[1024];
int nWords = Abc_TtWordNum(pMan->nVars);
int ivp = pMan->pPermTRev[iVar];
Abc_TtCopy(pCopy, pMan->pTruth, nWords, 0);
Abc_TtFlip(pCopy, nWords, ivp);
if (Abc_TtCompareRev(pMan->pTruth, pCopy, nWords) == 1)
{
Abc_TtCopy(pMan->pTruth, pCopy, nWords, 0);
pMan->uPhase ^= 1 << ivp;
return 16;
}
return 0;
}
static void Abc_TgSimpleEnumeration(Abc_TgMan_t * pMan)
{
int i, j, k;
int pGid[16];
for (k = j = 0; j < pMan->nGroups; j++)
for (i = 0; i < pMan->pGroup[j].nGVars; i++, k++)
pGid[k] = j;
assert(k == pMan->nGVars);
for (k = 0; k < 5; k++)
{
int fChanges = 0;
for (i = pMan->nGVars - 2; i >= 0; i--)
if (pGid[i] == pGid[i + 1])
fChanges |= Abc_TgSymGroupPerm(pMan, i, pGid[i] > 0 || pMan->fPhased);
for (i = 1; i < pMan->nGVars - 1; i++)
if (pGid[i] == pGid[i + 1])
fChanges |= Abc_TgSymGroupPerm(pMan, i, pGid[i] > 0 || pMan->fPhased);
for (i = pMan->nVars - 1; i >= 0; i--)
if (pMan->symPhase[i])
fChanges |= Abc_TgPermPhase(pMan, i);
for (i = 1; i < pMan->nVars; i++)
if (pMan->symPhase[i])
fChanges |= Abc_TgPermPhase(pMan, i);
if (!fChanges) break;
}
assert(Abc_TgCannonVerify(pMan));
}
/**Function*************************************************************
Synopsis [Exact canonical form computation.]
Description [full config enumeration]
SideEffects []
SeeAlso []
***********************************************************************/
static int Abc_TgIsInitPerm(char * pData, signed char * pDir, int size)
{
int i;
if (pDir[0] != -1) return 0;
for (i = 1; i < size; i++)
if (pDir[i] != -1 || pData[i] < pData[i - 1])
return 0;
return 1;
}
static void Abc_TgFirstPermutation(Abc_TgMan_t * pMan)
{
int i;
for (i = 0; i < pMan->nGVars; i++)
pMan->pPermDir[i] = -1;
#ifndef NDEBUG
for (i = 0; i < pMan->nGroups; i++)
{
TiedGroup * pGrp = pMan->pGroup + i;
int nGvars = pGrp->nGVars;
char * pVars = pMan->pPerm + pGrp->iStart;
signed char * pDirs = pMan->pPermDir + pGrp->iStart;
assert(Abc_TgIsInitPerm(pVars, pDirs, nGvars));
}
#endif
}
static int Abc_TgNextPermutation(Abc_TgMan_t * pMan)
{
int i, j, nGvars;
TiedGroup * pGrp;
char * pVars;
signed char * pDirs;
for (i = 0; i < pMan->nGroups; i++)
{
pGrp = pMan->pGroup + i;
nGvars = pGrp->nGVars;
if (nGvars == 1) continue;
pVars = pMan->pPerm + pGrp->iStart;
pDirs = pMan->pPermDir + pGrp->iStart;
j = Abc_NextPermSwapC(pVars, pDirs, nGvars);
if (j >= 0)
{
Abc_TgSwapAdjacentSymGroups(pMan, j + pGrp->iStart);
return 1;
}
Abc_TgSwapAdjacentSymGroups(pMan, pGrp->iStart);
assert(Abc_TgIsInitPerm(pVars, pDirs, nGvars));
}
return 0;
}
static inline unsigned grayCode(unsigned a) { return a ^ (a >> 1); }
static int grayFlip(unsigned a)
{
int i;
for (i = 0, a++; ; i++)
if (a & (1 << i)) return i;
}
static inline void Abc_TgSaveBest(Abc_TgMan_t * pMan, Abc_TgMan_t * pBest)
{
if (Abc_TtCompareRev(pBest->pTruth, pMan->pTruth, Abc_TtWordNum(pMan->nVars)) == 1)
Abc_TgManCopy(pBest, pBest->pTruth, pMan);
}
static void Abc_TgPhaseEnumeration(Abc_TgMan_t * pMan, Abc_TgMan_t * pBest)
{
char pFGrps[16];
int i, j, n = pMan->pGroup->nGVars;
Abc_TgSaveBest(pMan, pBest);
if (pMan->fPhased) return;
// sort by symPhase
for (i = 0; i < n; i++)
{
char iv = pMan->pPerm[i];
for (j = i; j > 0 && pMan->symPhase[(int)pFGrps[j-1]] > pMan->symPhase[(int)iv]; j--)
pFGrps[j] = pFGrps[j - 1];
pFGrps[j] = iv;
}
for (i = 0; i < (1 << n) - 1; i++)
{
Abc_TgFlipSymGroupByVar(pMan, pFGrps[grayFlip(i)]);
Abc_TgSaveBest(pMan, pBest);
}
}
/**Function*************************************************************
Synopsis [Hybrid exact canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static void Abc_TgCalcScc(Abc_TgMan_t * pMan, int * pOut, int fSort)
{
int i, j, k;
TiedGroup * pGrp;
Abc_TtSccInCofs(pMan->pTruth, pMan->nVars, pOut);
for (i = j = 0; j < pMan->nGVars; j++)
{
pOut[j] = pOut[i];
for (k = pMan->pPerm[j]; k >= 0; k = pMan->symLink[k])
{
i++;
assert(pMan->symLink[k] < 0 || pOut[j] == pOut[i]);
}
}
if (!fSort) return;
for (pGrp = pMan->pGroup; pGrp < pMan->pGroup + pMan->nGroups; pGrp++)
{
int vb = pGrp->iStart, ve = vb + pGrp->nGVars;
for (i = vb + 1; i < ve; i++)
{
int a = pOut[i];
for (j = i; j > vb && pOut[j - 1] > a; j--)
pOut[j] = pOut[j - 1];
pOut[j] = a;
}
}
}
static void Abc_TgSplitGroupsByScc(Abc_TgMan_t * pMan)
{
int pScc[16];
char pPermT[16];
TiedGroup * pGrp;
Abc_TgCalcScc(pMan, pScc, 0);
for (pGrp = pMan->pGroup; pGrp < pMan->pGroup + pMan->nGroups; pGrp++)
pGrp += Abc_TgSplitGroup(pMan, pGrp, pScc + pGrp->iStart);
Abc_TgExpendSymmetry(pMan, pPermT);
Abc_TgImplementPerm(pMan, pPermT);
assert(Abc_TgCannonVerify(pMan));
}
static int Abc_TgCompareCoef(int * pIn1, int * pIn2, int n)
{
int i;
for (i = 0; i < n; i++)
if (pIn1[i] != pIn2[i])
return (pIn1[i] < pIn2[i]) ? -1 : 1;
return 0;
}
// log2(n!)*100
static const int log2fn[17] = { 0, 0, 100, 258, 458, 691, 949, 1230, 1530, 1847, 2179, 2525, 2884, 3254, 3634, 4025, 4425 };
static int Abc_TgPermCostScc(Abc_TgMan_t * pMan, int *pScc)
{
int i, j, k, cost = 0;
for (i = k = 0; i < pMan->nGroups; i++)
{
int n = pMan->pGroup[i].nGVars;
int d = 1;
for (j = 1, k++; j < n; j++, k++)
if (pScc[k] == pScc[k - 1]) d++;
else {
cost += log2fn[d];
d = 1;
}
cost += log2fn[d];
}
return cost;
}
static void Abc_TgPermEnumerationScc(Abc_TgMan_t * pMan, Abc_TgMan_t * pBest)
{
static word pCopy[1024];
Abc_TgMan_t tgManCopy;
Abc_TgManCopy(&tgManCopy, pCopy, pMan);
if (pMan->nAlgorithm > 1)
Abc_TgSplitGroupsByScc(&tgManCopy);
Abc_TgFirstPermutation(&tgManCopy);
do {
Abc_TgSaveBest(&tgManCopy, pBest);
} while (Abc_TgNextPermutation(&tgManCopy));
}
static void Abc_TgReorderFGrps(Abc_TgMan_t * pMan)
{
char * pFGrps = pMan->pFGrps;
int i, j, n = pMan->fPhased ? 0 : pMan->pGroup->nGVars;
// sort by symPhase
for (i = 0; i < n; i++)
{
char iv = pMan->pPerm[i];
for (j = i; j > 0 && pMan->symPhase[(int)pFGrps[j - 1]] > pMan->symPhase[(int)iv]; j--)
pFGrps[j] = pFGrps[j - 1];
pFGrps[j] = iv;
}
}
static int ilog2(int n)
{
int i;
for (i = 0; n /= 2; i++)
;
return i;
}
typedef struct Abc_SccCost_t_ {
int cNeg, cPhase, cPerm;
} Abc_SccCost_t;
static Abc_SccCost_t Abc_TgRecordPhase(Abc_TgMan_t * pMan, int mode)
{
Vec_Int_t * vPhase = pMan->vPhase;
int i, j, n = pMan->pGroup->nGVars;
int nStart = mode == 0 ? 1 : 0;
int nCoefs = pMan->nGVars + 2 - nStart;
int pScc[18], pMinScc[18];
Abc_SccCost_t ret;
if (pMan->fPhased)
{
ret.cNeg = 0;
ret.cPhase = 0;
Abc_TgCalcScc(pMan, pScc + 2, 1);
ret.cPerm = Abc_TgPermCostScc(pMan, pScc + 2);
return ret;
}
Abc_TgReorderFGrps(pMan);
pMinScc[1] = Abc_TtScc(pMan->pTruth, pMan->nVars);
Abc_TgCalcScc(pMan, pMinScc + 2, 1);
pMinScc[0] = mode == 0 ? 0 : Abc_TgPermCostScc(pMan, pMinScc + 2);
Vec_IntPush(vPhase, 0);
for (i = 0; (j = grayFlip(i)) < n; i++)
{
Abc_TgFlipSymGroupByVar(pMan, pMan->pFGrps[j]);
pScc[1] = Abc_TtScc(pMan->pTruth, pMan->nVars);
if (mode == 0 && pScc[1] > pMinScc[1]) continue;
Abc_TgCalcScc(pMan, pScc + 2, 1);
if (mode > 0)
pScc[0] = Abc_TgPermCostScc(pMan, pScc + 2);
if (Abc_TgCompareCoef(pScc + nStart, pMinScc + nStart, nCoefs) < 0)
{
memcpy(pMinScc + nStart, pScc + nStart, nCoefs * sizeof(int));
Vec_IntClear(vPhase);
}
if (Abc_TgCompareCoef(pScc + nStart, pMinScc + nStart, nCoefs) == 0)
Vec_IntPush(vPhase, grayCode(i+1));
}
Abc_TgFlipSymGroupByVar(pMan, pMan->pFGrps[n - 1]);
ret.cNeg = n;
ret.cPhase = ilog2(Vec_IntSize(vPhase));
ret.cPerm = Abc_TgPermCostScc(pMan, pMinScc + 2);
return ret;
}
static int Abc_TgRecordPhase1(Abc_TgMan_t * pMan) // for AdjSE
{
Vec_Int_t * vPhase = pMan->vPhase;
int i, j, n = pMan->pGroup->nGVars;
//int nCoefs = pMan->nGVars + 2;
int nScc, nMinScc;
assert (Vec_IntSize(vPhase) == 0);
if (pMan->fPhased) return 0;
Abc_TgReorderFGrps(pMan);
nMinScc = Abc_TtScc(pMan->pTruth, pMan->nVars);
Vec_IntPush(vPhase, 0);
for (i = 0; (j = grayFlip(i)) < n; i++)
{
Abc_TgFlipSymGroupByVar(pMan, pMan->pFGrps[j]);
nScc = Abc_TtScc(pMan->pTruth, pMan->nVars);
if (nScc > nMinScc) continue;
if (nScc < nMinScc)
{
nMinScc = nScc;
Vec_IntClear(vPhase);
}
Vec_IntPush(vPhase, grayCode(i + 1));
}
Abc_TgFlipSymGroupByVar(pMan, pMan->pFGrps[n - 1]);
return ilog2(Vec_IntSize(vPhase));
}
static void Abc_TgPhaseEnumerationScc(Abc_TgMan_t * pMan, Abc_TgMan_t * pBest)
{
Vec_Int_t * vPhase = pMan->vPhase;
int i, j, n = pMan->pGroup->nGVars;
int ph0 = 0, ph, flp;
static word pCopy[1024];
Abc_TgMan_t tgManCopy;
if (pMan->fPhased)
{
Abc_TgPermEnumerationScc(pMan, pBest);
return;
}
Abc_TgManCopy(&tgManCopy, pCopy, pMan);
Vec_IntForEachEntry(vPhase, ph, i)
{
flp = ph ^ ph0;
for (j = 0; j < n; j++)
if (flp & (1 << j))
Abc_TgFlipSymGroupByVar(&tgManCopy, pMan->pFGrps[j]);
ph0 = ph;
Abc_TgPermEnumerationScc(&tgManCopy, pBest);
}
}
static void Abc_TgFullEnumeration(Abc_TgMan_t * pWork, Abc_TgMan_t * pBest)
{
if (pWork->nAlgorithm > 0)
{
Abc_TtFill(pBest->pTruth, Abc_TtWordNum(pBest->nVars));
Abc_TgPhaseEnumerationScc(pWork, pBest);
}
else
{
Abc_TgFirstPermutation(pWork);
do Abc_TgPhaseEnumeration(pWork, pBest);
while (Abc_TgNextPermutation(pWork));
}
pBest->uPhase |= 1 << 30;
}
// runtime cost for Abc_TgRecordPhase (mode = 1)
static inline double Abc_SccPhaseCost(Abc_TgMan_t * pMan)
{
return pMan->nVars * 0.997 + pMan->nGVars * 1.043 - 15.9;
}
// runtime cost for Abc_TgFullEnumeration
static inline double Abc_SccEnumCost(Abc_TgMan_t * pMan, Abc_SccCost_t c)
{
switch (pMan->nAlgorithm)
{
case 0: return pMan->nVars + c.cPhase * 1.09 + c.cPerm * 0.01144;
case 1: return pMan->nVars + c.cPhase * 0.855 + c.cPerm * 0.00797;
case 2: return pMan->nVars * 0.94 + c.cPhase * 0.885 + c.cPerm * 0.00855 - 20.59;
}
return 0;
}
static int Abc_TgEnumerationCost(Abc_TgMan_t * pMan)
{
int i;
Abc_SccCost_t c = { 0,0,0 };
if (pMan->nGroups == 0) return 0;
for (i = 0; i < pMan->nGroups; i++)
c.cPerm += log2fn[(int)pMan->pGroup[i].nGVars];
c.cPhase = pMan->fPhased ? 0
: pMan->nAlgorithm == 0 ? pMan->pGroup->nGVars
: Abc_TgRecordPhase1(pMan);
// coefficients computed by linear regression
return Abc_SccEnumCost(pMan, c) + 0.5;
}
/**Function*************************************************************
Synopsis [Adaptive heuristic/exact canonical form computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
unsigned Abc_TtCanonicizeAda(Abc_TtHieMan_t * p, word * pTruth, int nVars, char * pCanonPerm, int iThres)
{
int nWords = Abc_TtWordNum(nVars);
unsigned fExac = 0, fHash = 1 << 29;
static word pCopy[1024];
Abc_TgMan_t tgMan, tgManCopy;
int iCost;
const int MaxCost = 84; // maximun posible cost for function with 16 inputs
const int nAlg = iThres >= 1000 ? 1 : 0;
const int fHigh = (iThres % 1000) >= 100, nEnumThres = iThres % 100;
// handle constant
if ( nVars == 0 ) {
Abc_TtClear( pTruth, nWords );
return 0;
}
Abc_TtVerifySmallTruth(pTruth, nVars);
#ifdef CANON_VERIFY
Abc_TtCopy(gpVerCopy, pTruth, nWords, 0);
#endif
assert(nVars <= 16);
assert(!(nAlg && p == NULL));
if (p && Abc_TtHieRetrieveOrInsert(p, -5, pTruth, pTruth) > 0) return fHash;
Abc_TgInitMan(&tgMan, pTruth, nVars, nAlg, p ? p->vPhase : NULL);
Abc_TgCreateGroups(&tgMan);
if (p && Abc_TtHieRetrieveOrInsert(p, -4, pTruth, pTruth) > 0) return fHash;
Abc_TgPurgeSymmetry(&tgMan, fHigh);
Abc_TgExpendSymmetry(&tgMan, pCanonPerm);
Abc_TgImplementPerm(&tgMan, pCanonPerm);
assert(Abc_TgCannonVerify(&tgMan));
iCost = Abc_TgEnumerationCost(&tgMan);
if (p == NULL || p->nLastLevel == 0) {
if (nEnumThres > MaxCost || iCost < nEnumThres) {
Abc_TgManCopy(&tgManCopy, pCopy, &tgMan);
Abc_TgFullEnumeration(&tgManCopy, &tgMan);
}
else
Abc_TgSimpleEnumeration(&tgMan);
}
else {
if (nEnumThres > MaxCost || iCost < nEnumThres) fExac = 1 << 30;
if (Abc_TtHieRetrieveOrInsert(p, -3, pTruth, pTruth) > 0) return fHash + fExac;
Abc_TgManCopy(&tgManCopy, pCopy, &tgMan);
Abc_TgSimpleEnumeration(&tgMan);
if (Abc_TtHieRetrieveOrInsert(p, -2, pTruth, pTruth) > 0) return fHash + fExac;
if (fExac) {
Abc_TgManCopy(&tgMan, pTruth, &tgManCopy);
Abc_TgFullEnumeration(&tgManCopy, &tgMan);
}
Abc_TtHieRetrieveOrInsert(p, -1, pTruth, pTruth);
}
memcpy(pCanonPerm, tgMan.pPermT, sizeof(char) * nVars);
#ifdef CANON_VERIFY
if (!Abc_TgCannonVerify(&tgMan))
printf("Canonical form verification failed!\n");
#endif
return tgMan.uPhase;
}
unsigned Abc_TtCanonicizeCA(Abc_TtHieMan_t * p, word * pTruth, int nVars, char * pCanonPerm, int fCA)
{
int nWords = Abc_TtWordNum(nVars);
unsigned fHard = 0, fHash = 1 << 29;
static word pCopy[1024];
Abc_TgMan_t tgMan, tgManCopy;
Abc_SccCost_t sc;
// handle constant
if (nVars == 0) {
Abc_TtClear(pTruth, nWords);
return 0;
}
Abc_TtVerifySmallTruth(pTruth, nVars);
#ifdef CANON_VERIFY
Abc_TtCopy(gpVerCopy, pTruth, nWords, 0);
#endif
assert(nVars <= 16);
assert(p != NULL);
if (Abc_TtHieRetrieveOrInsert(p, -5, pTruth, pTruth) > 0) return fHash;
Abc_TgInitMan(&tgMan, pTruth, nVars, 2, p->vPhase);
Abc_TgCreateGroups(&tgMan);
if (p && Abc_TtHieRetrieveOrInsert(p, -4, pTruth, pTruth) > 0) return fHash;
Abc_TgPurgeSymmetry(&tgMan, 1);
Abc_TgExpendSymmetry(&tgMan, pCanonPerm);
Abc_TgImplementPerm(&tgMan, pCanonPerm);
assert(Abc_TgCannonVerify(&tgMan));
if (Abc_TtHieRetrieveOrInsert(p, -3, pTruth, pTruth) > 0) return fHash;
Abc_TgManCopy(&tgManCopy, pCopy, &tgMan);
Abc_TgSimpleEnumeration(&tgMan);
if (Abc_TtHieRetrieveOrInsert(p, -2, pTruth, pTruth) > 0) return fHash;
Abc_TgManCopy(&tgMan, pTruth, &tgManCopy);
Abc_TtFill(pTruth, nWords);
assert(Abc_TgCannonVerify(&tgManCopy));
sc = Abc_TgRecordPhase(&tgManCopy, 0);
if (fCA && Abc_SccEnumCost(&tgManCopy, sc) > Abc_SccPhaseCost(&tgManCopy))
{
Abc_TgResetGroup(&tgManCopy);
sc = Abc_TgRecordPhase(&tgManCopy, 1);
fHard = 1 << 28;
}
Abc_TgFullEnumeration(&tgManCopy, &tgMan);
Abc_TtHieRetrieveOrInsert(p, -1, pTruth, pTruth);
memcpy(pCanonPerm, tgMan.pPermT, sizeof(char) * nVars);
#ifdef CANON_VERIFY
if (!Abc_TgCannonVerify(&tgMan))
printf("Canonical form verification failed!\n");
#endif
return tgMan.uPhase | fHard;
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END