/**CFile**************************************************************** FileName [bmcMaj2.c] SystemName [ABC: Logic synthesis and verification system.] PackageName [SAT-based bounded model checking.] Synopsis [Exact synthesis with majority gates.] Author [Alan Mishchenko] Affiliation [UC Berkeley] Date [Ver. 1.0. Started - October 1, 2017.] Revision [$Id: bmcMaj.c,v 1.00 2017/10/01 00:00:00 alanmi Exp $] ***********************************************************************/ #include "bmc.h" #include "misc/extra/extra.h" #include "misc/util/utilTruth.h" #include "sat/cnf/cnf.h" #include "sat/bsat/satStore.h" ABC_NAMESPACE_IMPL_START //////////////////////////////////////////////////////////////////////// /// DECLARATIONS /// //////////////////////////////////////////////////////////////////////// #define MAJ_NOBJS 32 // Const0 + Const1 + nVars + nNodes typedef struct Maj_Man_t_ Maj_Man_t; struct Maj_Man_t_ { int nVars; // inputs int nNodes; // internal nodes int nObjs; // total objects (2 consts, nVars inputs, nNodes internal nodes) int nWords; // the truth table size in 64-bit words int iVar; // the next available SAT variable int fUseConst; // use constant fanins int fUseLine; // use cascade topology int fUseRand; // use random topology int nRands; // number of random connections int fVerbose; // verbose flag Vec_Wrd_t * vInfo; // Const0 + Const1 + nVars + nNodes + Maj(nVars) int VarMarks[MAJ_NOBJS][3][MAJ_NOBJS]; // variable marks int VarVals[MAJ_NOBJS+2]; // values of the first 2 + nVars variables Vec_Wec_t * vOutLits; // output vars sat_solver * pSat; // SAT solver }; static inline word * Maj_ManTruth( Maj_Man_t * p, int v ) { return Vec_WrdEntryP( p->vInfo, p->nWords * v ); } //////////////////////////////////////////////////////////////////////// /// FUNCTION DEFINITIONS /// //////////////////////////////////////////////////////////////////////// /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static int Maj_ManValue( int iMint, int nVars ) { int k, Count = 0; for ( k = 0; k < nVars; k++ ) Count += (iMint >> k) & 1; return (int)(Count > nVars/2); } static Vec_Wrd_t * Maj_ManTruthTables( Maj_Man_t * p ) { Vec_Wrd_t * vInfo = p->vInfo = Vec_WrdStart( p->nWords * (p->nObjs + 1) ); int i, nMints = Abc_MaxInt( 64, 1 << p->nVars ); Abc_TtFill( Maj_ManTruth(p, 1), p->nWords ); for ( i = 0; i < p->nVars; i++ ) Abc_TtIthVar( Maj_ManTruth(p, i+2), i, p->nVars ); for ( i = 0; i < nMints; i++ ) if ( Maj_ManValue(i, p->nVars) ) Abc_TtSetBit( Maj_ManTruth(p, p->nObjs), i ); //Dau_DsdPrintFromTruth( Maj_ManTruth(p, p->nObjs), p->nVars ); return vInfo; } static void Maj_ManConnect( int VarCons[MAJ_NOBJS][3], int nVars, int nObjs, int nRands, int fVerbose ) { int i, v, r, x; srand(clock()); for ( i = nObjs-2; i >= nVars + 2; i-- ) { while ( 1 ) { int Index = 1 + (rand() % (nObjs-1-i)); for ( v = 2; v >= 0; v-- ) // for ( v = 0; v < 3; v++ ) if ( VarCons[i+Index][v] == 0 ) { VarCons[i+Index][v] = i; if ( fVerbose ) printf( "%d -> %d ", i, i+Index ); break; } if ( v >= 0 ) break; } } for ( r = 0; r < nRands; r++ ) { i = nVars+2 + (rand() % ((nObjs-1)-(nVars+2))); for ( x = 0; x < 100; x++ ) { int Index = 1 + (rand() % (nObjs-1-i)); for ( v = 2; v >= 0; v-- ) // for ( v = 0; v < 3; v++ ) { if ( VarCons[i+Index][v] == i ) { v = -1; break; } if ( VarCons[i+Index][v] == 0 ) { VarCons[i+Index][v] = i; if ( fVerbose ) printf( "+%d -> %d ", i, i+Index ); break; } } if ( v >= 0 ) break; } if ( x == 100 ) r--; } if ( fVerbose ) printf( "\n" ); } static void Maj_ManConnect2( int VarCons[MAJ_NOBJS][3], int nVars, int nObjs, int nRands ) { VarCons[8+2][2] = 7+2; VarCons[10+2][2] = 9+2; VarCons[11+2][2] = 7+2; VarCons[11+2][1] = 8+2; VarCons[12+2][2] = 9+2; VarCons[12+2][1] = 10+2; VarCons[13+2][2] = 11+2; VarCons[13+2][1] = 12+2; } static int Maj_ManMarkup( Maj_Man_t * p ) { int VarCons[MAJ_NOBJS][3] = {{0}}; int i, k, j, m; p->iVar = 1; assert( p->nObjs <= MAJ_NOBJS ); // create connections if ( p->fUseRand ) Maj_ManConnect( VarCons, p->nVars, p->nObjs, p->nRands, p->fVerbose ); // make exception for the first node i = p->nVars + 2; for ( k = 0; k < 3; k++ ) { j = 4-k; Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; } // assign variables for other nodes for ( i = p->nVars + 3; i < p->nObjs; i++ ) { for ( k = 0; k < 3; k++ ) { if ( p->fUseLine && k == 0 ) { j = i-1; Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; continue; } if ( p->fUseRand && VarCons[i][k] > 0 ) { j = VarCons[i][k]; Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; continue; } for ( j = (p->fUseConst && k == 2) ? 0 : 2; j < (p->fUseRand ? p->nVars+2-k : i-k); j++ ) { Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; } } } printf( "The number of parameter variables = %d.\n", p->iVar ); if ( !p->fVerbose ) return p->iVar; // printout printf( " " ); for ( i = p->nVars + 2; i < p->nObjs; i++ ) printf( " Node %2d ", i ); printf( "\n" ); for ( m = 0; m < p->nObjs; m++ ) { printf( "%2d : ", m ); for ( i = p->nVars + 2; i < p->nObjs; i++ ) { for ( j = 0; j < p->nObjs; j++ ) { if ( j != m ) continue; for ( k = 0; k < 3; k++ ) if ( p->VarMarks[i][k][j] ) printf( "%3d ", p->VarMarks[i][k][j] ); else printf( "%3c ", '.' ); printf( " " ); } } printf( "\n" ); } return p->iVar; } static Maj_Man_t * Maj_ManAlloc( int nVars, int nNodes, int fUseConst, int fUseLine, int fUseRand, int nRands, int fVerbose ) { Maj_Man_t * p = ABC_CALLOC( Maj_Man_t, 1 ); p->nVars = nVars; p->nNodes = nNodes; p->nObjs = 2 + nVars + nNodes; p->fUseConst = fUseConst; p->fUseLine = fUseLine; p->fUseRand = fUseRand; p->fVerbose = fVerbose; p->nRands = nRands; p->nWords = Abc_TtWordNum(nVars); p->vOutLits = Vec_WecStart( p->nObjs ); p->iVar = Maj_ManMarkup( p ); p->VarVals[1] = 1; p->vInfo = Maj_ManTruthTables( p ); p->pSat = sat_solver_new(); sat_solver_setnvars( p->pSat, p->iVar ); return p; } static void Maj_ManFree( Maj_Man_t * p ) { sat_solver_delete( p->pSat ); Vec_WrdFree( p->vInfo ); Vec_WecFree( p->vOutLits ); ABC_FREE( p ); } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static inline int Maj_ManFindFanin( Maj_Man_t * p, int i, int k ) { int j, Count = 0, iVar = -1; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] && sat_solver_var_value(p->pSat, p->VarMarks[i][k][j]) ) { iVar = j; Count++; } assert( Count == 1 ); return iVar; } static inline int Maj_ManEval( Maj_Man_t * p ) { int fUseMiddle = 1; static int Flag = 0; int i, k, iMint; word * pFanins[3]; for ( i = p->nVars + 2; i < p->nObjs; i++ ) { for ( k = 0; k < 3; k++ ) pFanins[k] = Maj_ManTruth( p, Maj_ManFindFanin(p, i, k) ); Abc_TtMaj( Maj_ManTruth(p, i), pFanins[0], pFanins[1], pFanins[2], p->nWords ); } if ( fUseMiddle ) { iMint = -1; for ( i = 0; i < (1 << p->nVars); i++ ) { int nOnes = Abc_TtBitCount16(i); if ( nOnes < p->nVars/2 || nOnes > p->nVars/2+1 ) continue; if ( Abc_TtGetBit(Maj_ManTruth(p, p->nObjs), i) == Abc_TtGetBit(Maj_ManTruth(p, p->nObjs-1), i) ) continue; iMint = i; break; } } else { if ( Flag && p->nVars >= 6 ) iMint = Abc_TtFindLastDiffBit( Maj_ManTruth(p, p->nObjs-1), Maj_ManTruth(p, p->nObjs), p->nVars ); else iMint = Abc_TtFindFirstDiffBit( Maj_ManTruth(p, p->nObjs-1), Maj_ManTruth(p, p->nObjs), p->nVars ); } //Flag ^= 1; assert( iMint < (1 << p->nVars) ); return iMint; } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static void Maj_ManPrintSolution( Maj_Man_t * p ) { int i, k, iVar; printf( "Realization of %d-input majority using %d MAJ3 gates:\n", p->nVars, p->nNodes ); // for ( i = p->nVars + 2; i < p->nObjs; i++ ) for ( i = p->nObjs - 1; i >= p->nVars + 2; i-- ) { printf( "%02d = MAJ(", i-2 ); for ( k = 2; k >= 0; k-- ) { iVar = Maj_ManFindFanin( p, i, k ); if ( iVar >= 2 && iVar < p->nVars + 2 ) printf( " %c", 'a'+iVar-2 ); else if ( iVar < 2 ) printf( " %d", iVar ); else printf( " %02d", iVar-2 ); } printf( " )\n" ); } } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static int Maj_ManAddCnfStart( Maj_Man_t * p ) { int pLits[MAJ_NOBJS], pLits2[2], i, j, k, n, m; // input constraints for ( i = p->nVars + 2; i < p->nObjs; i++ ) { for ( k = 0; k < 3; k++ ) { int nLits = 0; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 0 ); assert( nLits > 0 ); // input uniqueness if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; for ( n = 0; n < nLits; n++ ) for ( m = n+1; m < nLits; m++ ) { pLits2[0] = Abc_LitNot(pLits[n]); pLits2[1] = Abc_LitNot(pLits[m]); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } if ( k == 2 || p->VarMarks[i][k][2] == 0 || p->VarMarks[i][k+1][2] == 0 ) continue; // symmetry breaking for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) for ( n = j; n < p->nObjs; n++ ) if ( p->VarMarks[i][k+1][n] ) { pLits2[0] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits2[1] = Abc_Var2Lit( p->VarMarks[i][k+1][n], 1 ); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } } } // outputs should be used for ( i = 2; i < p->nObjs - 1; i++ ) { Vec_Int_t * vArray = Vec_WecEntry(p->vOutLits, i); assert( Vec_IntSize(vArray) > 0 ); if ( !sat_solver_addclause( p->pSat, Vec_IntArray(vArray), Vec_IntLimit(vArray) ) ) return 0; } return 1; } static int Maj_ManAddCnf( Maj_Man_t * p, int iMint ) { // save minterm values int i, k, n, j, Value = Maj_ManValue(iMint, p->nVars); for ( i = 0; i < p->nVars; i++ ) p->VarVals[i+2] = (iMint >> i) & 1; sat_solver_setnvars( p->pSat, p->iVar + 4*p->nNodes ); //printf( "Adding clauses for minterm %d.\n", iMint ); for ( i = p->nVars + 2; i < p->nObjs; i++ ) { // fanin connectivity int iBaseSatVarI = p->iVar + 4*(i - p->nVars - 2); for ( k = 0; k < 3; k++ ) { for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) { int iBaseSatVarJ = p->iVar + 4*(j - p->nVars - 2); for ( n = 0; n < 2; n++ ) { int pLits[3], nLits = 0; pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + k, n ); if ( j >= p->nVars + 2 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarJ + 3, !n ); else if ( p->VarVals[j] == n ) continue; if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } // node functionality for ( n = 0; n < 2; n++ ) { if ( i == p->nObjs - 1 && n == Value ) continue; for ( k = 0; k < 3; k++ ) { int pLits[3], nLits = 0; if ( k != 0 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 0, n ); if ( k != 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 1, n ); if ( k != 2 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 2, n ); if ( i != p->nObjs - 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 3, !n ); assert( nLits <= 3 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } p->iVar += 4*p->nNodes; return 1; } int Maj_ManExactSynthesis2( int nVars, int nNodes, int fUseConst, int fUseLine, int fUseRand, int nRands, int fVerbose ) { int i, iMint = 0; abctime clkTotal = Abc_Clock(); Maj_Man_t * p = Maj_ManAlloc( nVars, nNodes, fUseConst, fUseLine, fUseRand, nRands, fVerbose ); int status = Maj_ManAddCnfStart( p ); assert( status ); if ( fVerbose ) printf( "Running exact synthesis for %d-input majority with %d MAJ3 gates...\n", p->nVars, p->nNodes ); for ( i = 0; iMint != -1; i++ ) { abctime clk = Abc_Clock(); if ( !Maj_ManAddCnf( p, iMint ) ) { printf( "The problem has no solution after %2d iterations. ", i+1 ); break; } status = sat_solver_solve( p->pSat, NULL, NULL, 0, 0, 0, 0 ); if ( fVerbose ) { printf( "Iter %3d : ", i ); Extra_PrintBinary( stdout, (unsigned *)&iMint, p->nVars ); printf( " Var =%5d ", p->iVar ); printf( "Cla =%6d ", sat_solver_nclauses(p->pSat) ); printf( "Conf =%9d ", sat_solver_nconflicts(p->pSat) ); Abc_PrintTime( 1, "Time", Abc_Clock() - clk ); } if ( status == l_False ) { printf( "The problem has no solution after %2d iterations. ", i+1 ); break; } iMint = Maj_ManEval( p ); } if ( iMint == -1 ) Maj_ManPrintSolution( p ); Maj_ManFree( p ); Abc_PrintTime( 1, "Total runtime", Abc_Clock() - clkTotal ); return iMint == -1; } int Maj_ManExactSynthesisTest() { // while ( !Maj_ManExactSynthesis2( 5, 4, 0, 0, 1, 1, 0 ) ); // while ( !Maj_ManExactSynthesis2( 7, 7, 0, 0, 1, 2, 0 ) ); while ( !Maj_ManExactSynthesis2( 9, 10, 0, 0, 1, 3, 0 ) ); return 1; } typedef struct Exa_Man_t_ Exa_Man_t; struct Exa_Man_t_ { Bmc_EsPar_t * pPars; // parameters int nVars; // inputs int nNodes; // internal nodes int nObjs; // total objects (nVars inputs + nNodes internal nodes) int nWords; // the truth table size in 64-bit words int iVar; // the next available SAT variable word * pTruth; // truth table Vec_Wrd_t * vInfo; // nVars + nNodes + 1 int VarMarks[MAJ_NOBJS][2][MAJ_NOBJS]; // variable marks int VarVals[MAJ_NOBJS]; // values of the first nVars variables Vec_Wec_t * vOutLits; // output vars sat_solver * pSat; // SAT solver }; static inline word * Exa_ManTruth( Exa_Man_t * p, int v ) { return Vec_WrdEntryP( p->vInfo, p->nWords * v ); } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static Vec_Wrd_t * Exa_ManTruthTables( Exa_Man_t * p ) { Vec_Wrd_t * vInfo = p->vInfo = Vec_WrdStart( p->nWords * (p->nObjs+1) ); int i; for ( i = 0; i < p->nVars; i++ ) Abc_TtIthVar( Exa_ManTruth(p, i), i, p->nVars ); //Dau_DsdPrintFromTruth( Exa_ManTruth(p, p->nObjs), p->nVars ); return vInfo; } static int Exa_ManMarkup( Exa_Man_t * p ) { int i, k, j; assert( p->nObjs <= MAJ_NOBJS ); // assign functionality p->iVar = 1 + p->nNodes * 3; // assign connectivity variables for ( i = p->nVars; i < p->nObjs; i++ ) { for ( k = 0; k < 2; k++ ) { if ( p->pPars->fFewerVars && i == p->nObjs - 1 && k == 0 ) { j = p->nObjs - 2; Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; continue; } for ( j = p->pPars->fFewerVars ? 1 - k : 0; j < i - k; j++ ) { Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; } } } printf( "The number of parameter variables = %d.\n", p->iVar ); return p->iVar; // printout for ( i = p->nVars; i < p->nObjs; i++ ) { printf( "Node %d\n", i ); for ( j = 0; j < p->nObjs; j++ ) { for ( k = 0; k < 2; k++ ) printf( "%3d ", p->VarMarks[i][k][j] ); printf( "\n" ); } } return p->iVar; } static Exa_Man_t * Exa_ManAlloc( Bmc_EsPar_t * pPars, word * pTruth ) { Exa_Man_t * p = ABC_CALLOC( Exa_Man_t, 1 ); p->pPars = pPars; p->nVars = pPars->nVars; p->nNodes = pPars->nNodes; p->nObjs = pPars->nVars + pPars->nNodes; p->nWords = Abc_TtWordNum(pPars->nVars); p->pTruth = pTruth; p->vOutLits = Vec_WecStart( p->nObjs ); p->iVar = Exa_ManMarkup( p ); p->vInfo = Exa_ManTruthTables( p ); p->pSat = sat_solver_new(); sat_solver_setnvars( p->pSat, p->iVar ); return p; } static void Exa_ManFree( Exa_Man_t * p ) { sat_solver_delete( p->pSat ); Vec_WrdFree( p->vInfo ); Vec_WecFree( p->vOutLits ); ABC_FREE( p ); } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static inline int Exa_ManFindFanin( Exa_Man_t * p, int i, int k ) { int j, Count = 0, iVar = -1; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] && sat_solver_var_value(p->pSat, p->VarMarks[i][k][j]) ) { iVar = j; Count++; } assert( Count == 1 ); return iVar; } static inline int Exa_ManEval( Exa_Man_t * p ) { static int Flag = 0; int i, k, iMint; word * pFanins[2]; for ( i = p->nVars; i < p->nObjs; i++ ) { int iVarStart = 1 + 3*(i - p->nVars); for ( k = 0; k < 2; k++ ) pFanins[k] = Exa_ManTruth( p, Exa_ManFindFanin(p, i, k) ); Abc_TtConst0( Exa_ManTruth(p, i), p->nWords ); for ( k = 1; k < 4; k++ ) { if ( !sat_solver_var_value(p->pSat, iVarStart+k-1) ) continue; Abc_TtAndCompl( Exa_ManTruth(p, p->nObjs), pFanins[0], !(k&1), pFanins[1], !(k>>1), p->nWords ); Abc_TtOr( Exa_ManTruth(p, i), Exa_ManTruth(p, i), Exa_ManTruth(p, p->nObjs), p->nWords ); } } if ( Flag && p->nVars >= 6 ) iMint = Abc_TtFindLastDiffBit( Exa_ManTruth(p, p->nObjs-1), p->pTruth, p->nVars ); else iMint = Abc_TtFindFirstDiffBit( Exa_ManTruth(p, p->nObjs-1), p->pTruth, p->nVars ); //Flag ^= 1; assert( iMint < (1 << p->nVars) ); return iMint; } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static void Exa_ManPrintSolution( Exa_Man_t * p, int fCompl ) { int i, k, iVar; printf( "Realization of given %d-input function using %d two-input gates:\n", p->nVars, p->nNodes ); // for ( i = p->nVars + 2; i < p->nObjs; i++ ) for ( i = p->nObjs - 1; i >= p->nVars; i-- ) { int iVarStart = 1 + 3*(i - p->nVars); int Val1 = sat_solver_var_value(p->pSat, iVarStart); int Val2 = sat_solver_var_value(p->pSat, iVarStart+1); int Val3 = sat_solver_var_value(p->pSat, iVarStart+2); if ( i == p->nObjs - 1 && fCompl ) printf( "%02d = 4\'b%d%d%d1(", i, !Val3, !Val2, !Val1 ); else printf( "%02d = 4\'b%d%d%d0(", i, Val3, Val2, Val1 ); for ( k = 1; k >= 0; k-- ) { iVar = Exa_ManFindFanin( p, i, k ); if ( iVar >= 0 && iVar < p->nVars ) printf( " %c", 'a'+iVar ); else printf( " %02d", iVar ); } printf( " )\n" ); } } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static int Exa_ManAddCnfStart( Exa_Man_t * p, int fOnlyAnd ) { int pLits[MAJ_NOBJS], pLits2[2], i, j, k, n, m; // input constraints for ( i = p->nVars; i < p->nObjs; i++ ) { int iVarStart = 1 + 3*(i - p->nVars); for ( k = 0; k < 2; k++ ) { int nLits = 0; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 0 ); assert( nLits > 0 ); // input uniqueness if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; for ( n = 0; n < nLits; n++ ) for ( m = n+1; m < nLits; m++ ) { pLits2[0] = Abc_LitNot(pLits[n]); pLits2[1] = Abc_LitNot(pLits[m]); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } if ( k == 1 ) break; // symmetry breaking for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) for ( n = j; n < p->nObjs; n++ ) if ( p->VarMarks[i][k+1][n] ) { pLits2[0] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits2[1] = Abc_Var2Lit( p->VarMarks[i][k+1][n], 1 ); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } } #ifdef USE_NODE_ORDER // node ordering for ( j = p->nVars; j < i; j++ ) for ( n = 0; n < p->nObjs; n++ ) if ( p->VarMarks[i][0][n] ) for ( m = n+1; m < p->nObjs; m++ ) if ( p->VarMarks[j][0][m] ) { pLits2[0] = Abc_Var2Lit( p->VarMarks[i][0][n], 1 ); pLits2[1] = Abc_Var2Lit( p->VarMarks[j][0][m], 1 ); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } #endif // two input functions for ( k = 0; k < 3; k++ ) { pLits[0] = Abc_Var2Lit( iVarStart, k==1 ); pLits[1] = Abc_Var2Lit( iVarStart+1, k==2 ); pLits[2] = Abc_Var2Lit( iVarStart+2, k!=0 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+3 ) ) return 0; } if ( fOnlyAnd ) { pLits[0] = Abc_Var2Lit( iVarStart, 1 ); pLits[1] = Abc_Var2Lit( iVarStart+1, 1 ); pLits[2] = Abc_Var2Lit( iVarStart+2, 0 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+3 ) ) return 0; } } // outputs should be used for ( i = 0; i < p->nObjs - 1; i++ ) { Vec_Int_t * vArray = Vec_WecEntry(p->vOutLits, i); assert( Vec_IntSize(vArray) > 0 ); if ( !sat_solver_addclause( p->pSat, Vec_IntArray(vArray), Vec_IntLimit(vArray) ) ) return 0; } return 1; } static int Exa_ManAddCnf( Exa_Man_t * p, int iMint ) { // save minterm values int i, k, n, j, Value = Abc_TtGetBit(p->pTruth, iMint); for ( i = 0; i < p->nVars; i++ ) p->VarVals[i] = (iMint >> i) & 1; sat_solver_setnvars( p->pSat, p->iVar + 3*p->nNodes ); //printf( "Adding clauses for minterm %d with value %d.\n", iMint, Value ); for ( i = p->nVars; i < p->nObjs; i++ ) { // fanin connectivity int iVarStart = 1 + 3*(i - p->nVars); int iBaseSatVarI = p->iVar + 3*(i - p->nVars); for ( k = 0; k < 2; k++ ) { for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) { int iBaseSatVarJ = p->iVar + 3*(j - p->nVars); for ( n = 0; n < 2; n++ ) { int pLits[3], nLits = 0; pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + k, n ); if ( j >= p->nVars ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarJ + 2, !n ); else if ( p->VarVals[j] == n ) continue; if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } // node functionality for ( n = 0; n < 2; n++ ) { if ( i == p->nObjs - 1 && n == Value ) continue; for ( k = 0; k < 4; k++ ) { int pLits[4], nLits = 0; if ( k == 0 && n == 1 ) continue; pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 0, (k&1) ); pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 1, (k>>1) ); if ( i != p->nObjs - 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 2, !n ); if ( k > 0 ) pLits[nLits++] = Abc_Var2Lit( iVarStart + k-1, n ); assert( nLits <= 4 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } p->iVar += 3*p->nNodes; return 1; } void Exa_ManExactSynthesis2( Bmc_EsPar_t * pPars ) { int i, status, iMint = 1; abctime clkTotal = Abc_Clock(); Exa_Man_t * p; int fCompl = 0; word pTruth[16]; Abc_TtReadHex( pTruth, pPars->pTtStr ); assert( pPars->nVars <= 10 ); p = Exa_ManAlloc( pPars, pTruth ); if ( pTruth[0] & 1 ) { fCompl = 1; Abc_TtNot( pTruth, p->nWords ); } status = Exa_ManAddCnfStart( p, pPars->fOnlyAnd ); assert( status ); printf( "Running exact synthesis for %d-input function with %d two-input gates...\n", p->nVars, p->nNodes ); for ( i = 0; iMint != -1; i++ ) { abctime clk = Abc_Clock(); if ( !Exa_ManAddCnf( p, iMint ) ) break; status = sat_solver_solve( p->pSat, NULL, NULL, 0, 0, 0, 0 ); if ( pPars->fVerbose ) { printf( "Iter %3d : ", i ); Extra_PrintBinary( stdout, (unsigned *)&iMint, p->nVars ); printf( " Var =%5d ", p->iVar ); printf( "Cla =%6d ", sat_solver_nclauses(p->pSat) ); printf( "Conf =%9d ", sat_solver_nconflicts(p->pSat) ); Abc_PrintTime( 1, "Time", Abc_Clock() - clk ); } if ( status == l_False ) { printf( "The problem has no solution.\n" ); break; } iMint = Exa_ManEval( p ); } if ( iMint == -1 ) Exa_ManPrintSolution( p, fCompl ); Exa_ManFree( p ); Abc_PrintTime( 1, "Total runtime", Abc_Clock() - clkTotal ); } typedef struct Exa3_Man_t_ Exa3_Man_t; struct Exa3_Man_t_ { Bmc_EsPar_t * pPars; // parameters int nVars; // inputs int nNodes; // internal nodes int nLutSize; // lut size int LutMask; // lut mask int nObjs; // total objects (nVars inputs + nNodes internal nodes) int nWords; // the truth table size in 64-bit words int iVar; // the next available SAT variable word * pTruth; // truth table Vec_Wrd_t * vInfo; // nVars + nNodes + 1 int VarMarks[MAJ_NOBJS][6][MAJ_NOBJS]; // variable marks int VarVals[MAJ_NOBJS]; // values of the first nVars variables Vec_Wec_t * vOutLits; // output vars sat_solver * pSat; // SAT solver }; static inline word * Exa3_ManTruth( Exa3_Man_t * p, int v ) { return Vec_WrdEntryP( p->vInfo, p->nWords * v ); } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static Vec_Wrd_t * Exa3_ManTruthTables( Exa3_Man_t * p ) { Vec_Wrd_t * vInfo = p->vInfo = Vec_WrdStart( p->nWords * (p->nObjs+1) ); int i; for ( i = 0; i < p->nVars; i++ ) Abc_TtIthVar( Exa3_ManTruth(p, i), i, p->nVars ); //Dau_DsdPrintFromTruth( Exa3_ManTruth(p, p->nObjs), p->nVars ); return vInfo; } static int Exa3_ManMarkup( Exa3_Man_t * p ) { int i, k, j; assert( p->nObjs <= MAJ_NOBJS ); // assign functionality variables p->iVar = 1 + p->LutMask * p->nNodes; // assign connectivity variables for ( i = p->nVars; i < p->nObjs; i++ ) { for ( k = 0; k < p->nLutSize; k++ ) { if ( p->pPars->fFewerVars && i == p->nObjs - 1 && k == 0 ) { j = p->nObjs - 2; Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; continue; } for ( j = p->pPars->fFewerVars ? p->nLutSize - 1 - k : 0; j < i - k; j++ ) { Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) ); p->VarMarks[i][k][j] = p->iVar++; } } } printf( "The number of parameter variables = %d.\n", p->iVar ); return p->iVar; // printout // for ( i = p->nVars; i < p->nObjs; i++ ) for ( i = p->nObjs - 1; i >= p->nVars; i-- ) { printf( " Node %2d\n", i ); for ( j = 0; j < p->nObjs; j++ ) { printf( "Fanin %2d : ", j ); for ( k = 0; k < p->nLutSize; k++ ) printf( "%3d ", p->VarMarks[i][k][j] ); printf( "\n" ); } } return p->iVar; } static int Exa3_ManInitPolarityFindVar( Exa3_Man_t * p, int i, int k, int * pIndex ) { int iVar; do { iVar = p->VarMarks[i][k][*pIndex]; *pIndex = (*pIndex + 1) % p->nVars; } while ( iVar <= 0 ); //intf( "Setting var %d.\n", iVar ); return iVar; } static void Exa3_ManInitPolarity( Exa3_Man_t * p ) { int i, k, iVar, nInputs = 0; for ( i = p->nVars; i < p->nObjs; i++ ) { // create AND-gate int iVarStart = 1 + p->LutMask*(i - p->nVars); iVar = iVarStart + p->LutMask-1; p->pSat->polarity[iVar] = 1; //printf( "Setting var %d.\n", iVar ); } for ( i = p->nVars; i < p->nObjs; i++ ) { // connect first fanin to previous if ( i == p->nVars ) { for ( k = p->nLutSize - 1; k >= 0; k-- ) { iVar = Exa3_ManInitPolarityFindVar( p, i, k, &nInputs ); p->pSat->polarity[iVar] = 1; } } else { for ( k = p->nLutSize - 1; k > 0; k-- ) { iVar = Exa3_ManInitPolarityFindVar( p, i, k, &nInputs ); p->pSat->polarity[iVar] = 1; } iVar = p->VarMarks[i][0][i-1]; if ( iVar <= 0 ) printf( "Variable mapping error.\n" ), fflush(stdout); assert( iVar > 0 ); p->pSat->polarity[iVar] = 1; //intf( "Setting var %d.\n", iVar ); } //intf( "\n" ); } } static Exa3_Man_t * Exa3_ManAlloc( Bmc_EsPar_t * pPars, word * pTruth ) { Exa3_Man_t * p = ABC_CALLOC( Exa3_Man_t, 1 ); p->pPars = pPars; p->nVars = pPars->nVars; p->nNodes = pPars->nNodes; p->nLutSize = pPars->nLutSize; p->LutMask = (1 << pPars->nLutSize) - 1; p->nObjs = pPars->nVars + pPars->nNodes; p->nWords = Abc_TtWordNum(pPars->nVars); p->pTruth = pTruth; p->vOutLits = Vec_WecStart( p->nObjs ); p->iVar = Exa3_ManMarkup( p ); p->vInfo = Exa3_ManTruthTables( p ); p->pSat = sat_solver_new(); sat_solver_setnvars( p->pSat, p->iVar ); //Exa3_ManInitPolarity( p ); return p; } static void Exa3_ManFree( Exa3_Man_t * p ) { sat_solver_delete( p->pSat ); Vec_WrdFree( p->vInfo ); Vec_WecFree( p->vOutLits ); ABC_FREE( p ); } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static inline int Exa3_ManFindFanin( Exa3_Man_t * p, int i, int k ) { int j, Count = 0, iVar = -1; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] && sat_solver_var_value(p->pSat, p->VarMarks[i][k][j]) ) { iVar = j; Count++; } assert( Count == 1 ); return iVar; } static inline int Exa3_ManEval( Exa3_Man_t * p ) { static int Flag = 0; int i, k, j, iMint; word * pFanins[6]; for ( i = p->nVars; i < p->nObjs; i++ ) { int iVarStart = 1 + p->LutMask*(i - p->nVars); for ( k = 0; k < p->nLutSize; k++ ) pFanins[k] = Exa3_ManTruth( p, Exa3_ManFindFanin(p, i, k) ); Abc_TtConst0( Exa3_ManTruth(p, i), p->nWords ); for ( k = 1; k <= p->LutMask; k++ ) { if ( !sat_solver_var_value(p->pSat, iVarStart+k-1) ) continue; // Abc_TtAndCompl( Exa3_ManTruth(p, p->nObjs), pFanins[0], !(k&1), pFanins[1], !(k>>1), p->nWords ); Abc_TtConst1( Exa3_ManTruth(p, p->nObjs), p->nWords ); for ( j = 0; j < p->nLutSize; j++ ) Abc_TtAndCompl( Exa3_ManTruth(p, p->nObjs), Exa3_ManTruth(p, p->nObjs), 0, pFanins[j], !((k >> j) & 1), p->nWords ); Abc_TtOr( Exa3_ManTruth(p, i), Exa3_ManTruth(p, i), Exa3_ManTruth(p, p->nObjs), p->nWords ); } } if ( Flag && p->nVars >= 6 ) iMint = Abc_TtFindLastDiffBit( Exa3_ManTruth(p, p->nObjs-1), p->pTruth, p->nVars ); else iMint = Abc_TtFindFirstDiffBit( Exa3_ManTruth(p, p->nObjs-1), p->pTruth, p->nVars ); //Flag ^= 1; assert( iMint < (1 << p->nVars) ); return iMint; } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static void Exa3_ManPrintSolution( Exa3_Man_t * p, int fCompl ) { int i, k, iVar; printf( "Realization of given %d-input function using %d %d-input LUTs:\n", p->nVars, p->nNodes, p->nLutSize ); for ( i = p->nObjs - 1; i >= p->nVars; i-- ) { int Val, iVarStart = 1 + p->LutMask*(i - p->nVars); // int Val1 = sat_solver_var_value(p->pSat, iVarStart); // int Val2 = sat_solver_var_value(p->pSat, iVarStart+1); // int Val3 = sat_solver_var_value(p->pSat, iVarStart+2); // if ( i == p->nObjs - 1 && fCompl ) // printf( "%02d = 4\'b%d%d%d1(", i, !Val3, !Val2, !Val1 ); // else // printf( "%02d = 4\'b%d%d%d0(", i, Val3, Val2, Val1 ); printf( "%02d = %d\'b", i, 1 << p->nLutSize ); for ( k = p->LutMask - 1; k >= 0; k-- ) { Val = sat_solver_var_value(p->pSat, iVarStart+k); if ( i == p->nObjs - 1 && fCompl ) printf( "%d", !Val ); else printf( "%d", Val ); } if ( i == p->nObjs - 1 && fCompl ) printf( "1(" ); else printf( "0(" ); for ( k = p->nLutSize - 1; k >= 0; k-- ) { iVar = Exa3_ManFindFanin( p, i, k ); if ( iVar >= 0 && iVar < p->nVars ) printf( " %c", 'a'+iVar ); else printf( " %02d", iVar ); } printf( " )\n" ); } } /**Function************************************************************* Synopsis [] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ static int Exa3_ManAddCnfStart( Exa3_Man_t * p, int fOnlyAnd ) { int pLits[MAJ_NOBJS], pLits2[2], i, j, k, n, m; // input constraints for ( i = p->nVars; i < p->nObjs; i++ ) { int iVarStart = 1 + p->LutMask*(i - p->nVars); for ( k = 0; k < p->nLutSize; k++ ) { int nLits = 0; for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 0 ); assert( nLits > 0 ); // input uniqueness if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; for ( n = 0; n < nLits; n++ ) for ( m = n+1; m < nLits; m++ ) { pLits2[0] = Abc_LitNot(pLits[n]); pLits2[1] = Abc_LitNot(pLits[m]); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } if ( k == p->nLutSize - 1 ) break; // symmetry breaking for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) for ( n = j; n < p->nObjs; n++ ) if ( p->VarMarks[i][k+1][n] ) { pLits2[0] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits2[1] = Abc_Var2Lit( p->VarMarks[i][k+1][n], 1 ); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } } //printf( "Node %d:\n", i ); //sat_solver_flip_print_clause( p->pSat ); #ifdef USE_NODE_ORDER // node ordering for ( j = p->nVars; j < i; j++ ) for ( n = 0; n < p->nObjs; n++ ) if ( p->VarMarks[i][0][n] ) for ( m = n+1; m < p->nObjs; m++ ) if ( p->VarMarks[j][0][m] ) { pLits2[0] = Abc_Var2Lit( p->VarMarks[i][0][n], 1 ); pLits2[1] = Abc_Var2Lit( p->VarMarks[j][0][m], 1 ); if ( !sat_solver_addclause( p->pSat, pLits2, pLits2+2 ) ) return 0; } #endif if ( p->nLutSize != 2 ) continue; // two-input functions for ( k = 0; k < 3; k++ ) { pLits[0] = Abc_Var2Lit( iVarStart, k==1 ); pLits[1] = Abc_Var2Lit( iVarStart+1, k==2 ); pLits[2] = Abc_Var2Lit( iVarStart+2, k!=0 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+3 ) ) return 0; } if ( fOnlyAnd ) { pLits[0] = Abc_Var2Lit( iVarStart, 1 ); pLits[1] = Abc_Var2Lit( iVarStart+1, 1 ); pLits[2] = Abc_Var2Lit( iVarStart+2, 0 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+3 ) ) return 0; } } // outputs should be used for ( i = 0; i < p->nObjs - 1; i++ ) { Vec_Int_t * vArray = Vec_WecEntry(p->vOutLits, i); assert( Vec_IntSize(vArray) > 0 ); if ( !sat_solver_addclause( p->pSat, Vec_IntArray(vArray), Vec_IntLimit(vArray) ) ) return 0; } return 1; } static int Exa3_ManAddCnf( Exa3_Man_t * p, int iMint ) { // save minterm values int i, k, n, j, Value = Abc_TtGetBit(p->pTruth, iMint); for ( i = 0; i < p->nVars; i++ ) p->VarVals[i] = (iMint >> i) & 1; sat_solver_setnvars( p->pSat, p->iVar + (p->nLutSize+1)*p->nNodes ); //printf( "Adding clauses for minterm %d with value %d.\n", iMint, Value ); for ( i = p->nVars; i < p->nObjs; i++ ) { // fanin connectivity int iVarStart = 1 + p->LutMask*(i - p->nVars); int iBaseSatVarI = p->iVar + (p->nLutSize+1)*(i - p->nVars); for ( k = 0; k < p->nLutSize; k++ ) { for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] ) { int iBaseSatVarJ = p->iVar + (p->nLutSize+1)*(j - p->nVars); for ( n = 0; n < 2; n++ ) { int pLits[3], nLits = 0; pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 ); pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + k, n ); if ( j >= p->nVars ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarJ + p->nLutSize, !n ); else if ( p->VarVals[j] == n ) continue; if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } // node functionality for ( n = 0; n < 2; n++ ) { if ( i == p->nObjs - 1 && n == Value ) continue; for ( k = 0; k <= p->LutMask; k++ ) { int pLits[8], nLits = 0; if ( k == 0 && n == 1 ) continue; //pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 0, (k&1) ); //pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 1, (k>>1) ); //if ( i != p->nObjs - 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 2, !n ); for ( j = 0; j < p->nLutSize; j++ ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + j, (k >> j) & 1 ); if ( i != p->nObjs - 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + j, !n ); if ( k > 0 ) pLits[nLits++] = Abc_Var2Lit( iVarStart + k-1, n ); assert( nLits <= p->nLutSize+2 ); if ( !sat_solver_addclause( p->pSat, pLits, pLits+nLits ) ) return 0; } } } p->iVar += (p->nLutSize+1)*p->nNodes; return 1; } void Exa3_ManExactSynthesis2( Bmc_EsPar_t * pPars ) { int i, status, iMint = 1; abctime clkTotal = Abc_Clock(); Exa3_Man_t * p; int fCompl = 0; word pTruth[16]; Abc_TtReadHex( pTruth, pPars->pTtStr ); assert( pPars->nVars <= 10 ); assert( pPars->nLutSize <= 6 ); p = Exa3_ManAlloc( pPars, pTruth ); if ( pTruth[0] & 1 ) { fCompl = 1; Abc_TtNot( pTruth, p->nWords ); } status = Exa3_ManAddCnfStart( p, pPars->fOnlyAnd ); assert( status ); printf( "Running exact synthesis for %d-input function with %d %d-input LUTs...\n", p->nVars, p->nNodes, p->nLutSize ); for ( i = 0; iMint != -1; i++ ) { abctime clk = Abc_Clock(); if ( !Exa3_ManAddCnf( p, iMint ) ) break; status = sat_solver_solve( p->pSat, NULL, NULL, 0, 0, 0, 0 ); if ( pPars->fVerbose ) { printf( "Iter %3d : ", i ); Extra_PrintBinary( stdout, (unsigned *)&iMint, p->nVars ); printf( " Var =%5d ", p->iVar ); printf( "Cla =%6d ", sat_solver_nclauses(p->pSat) ); printf( "Conf =%9d ", sat_solver_nconflicts(p->pSat) ); Abc_PrintTime( 1, "Time", Abc_Clock() - clk ); } if ( status == l_False ) { printf( "The problem has no solution.\n" ); break; } iMint = Exa3_ManEval( p ); } if ( iMint == -1 ) Exa3_ManPrintSolution( p, fCompl ); Exa3_ManFree( p ); Abc_PrintTime( 1, "Total runtime", Abc_Clock() - clkTotal ); } //////////////////////////////////////////////////////////////////////// /// END OF FILE /// //////////////////////////////////////////////////////////////////////// ABC_NAMESPACE_IMPL_END