Exact synthesis of majority gates.

1 files changed, 373 insertions, 0 deletions

diff --git a/src/sat/bmc/bmcMaj.c b/src/sat/bmc/bmcMaj.c
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+/**CFile****************************************************************
+
+  FileName    [bmcMaj.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/util/utilTruth.h"
+#include "sat/glucose/AbcGlucose.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
+    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
+    bmcg_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     []
+
+***********************************************************************/
+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);
+}
+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;
+}
+int Maj_ManMarkup( Maj_Man_t * p )
+{
+    int i, k, j;
+    p->iVar = 1;
+    assert( p->nObjs <= MAJ_NOBJS );
+    // 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++ )
+        {
+            for ( j = (p->fUseConst && k == 2) ? 0 : 2; 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 + 2; i < p->nObjs; i++ )
+    {
+        printf( "Node %d\n", i );
+        for ( j = 0; j < p->nObjs; j++ )
+        {
+            for ( k = 0; k < 3; k++ )
+                printf( "%2d ", p->VarMarks[i][k][j] );
+            printf( "\n" );
+        }
+    }
+    return p->iVar;
+}
+Maj_Man_t * Maj_ManAlloc( int nVars, int nNodes, int fUseConst )
+{
+    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->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       = bmcg_sat_solver_start();
+    bmcg_sat_solver_set_nvars( p->pSat, p->iVar );
+    return p;
+}
+void Maj_ManFree( Maj_Man_t * p )
+{
+    bmcg_sat_solver_stop( 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] && bmcg_sat_solver_read_cex_varvalue(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 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 );
+    }
+    iMint = Abc_TtFindFirstDiffBit( Maj_ManTruth(p, p->nObjs-1), Maj_ManTruth(p, p->nObjs), p->nWords );
+    return iMint;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+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++ )
+    {
+        printf( "%02d = MAJ(", i-2 );
+        for ( k = 0; k < 3; 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     []
+
+***********************************************************************/
+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 ( !bmcg_sat_solver_addclause( p->pSat, 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 ( !bmcg_sat_solver_addclause( p->pSat, pLits2, 2 ) )
+                    return 0;
+            }
+            if ( k == 2 )
+                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 ( !bmcg_sat_solver_addclause( p->pSat, 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 ( !bmcg_sat_solver_addclause( p->pSat, Vec_IntArray(vArray), Vec_IntSize(vArray) ) )
+            return 0;
+    }
+    return 1;
+}
+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;
+    bmcg_sat_solver_set_nvars( 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++ )
+        {
+            int nLits2 = 0;
+            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 ( !bmcg_sat_solver_addclause( p->pSat, 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 ( !bmcg_sat_solver_addclause( p->pSat, pLits, nLits ) )
+                    return 0;
+            }
+        }
+    }
+    p->iVar += 4*p->nNodes;
+    return 1;
+}
+void Maj_ManExactSynthesis( int nVars, int nNodes, int fUseConst, int fVerbose )
+{
+    int i, iMint = 0;
+    abctime clkTotal = Abc_Clock();
+    Maj_Man_t * p = Maj_ManAlloc( nVars, nNodes, fUseConst );
+    int status = Maj_ManAddCnfStart( p );
+    assert( status );
+    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 ) )
+            break;
+        status = bmcg_sat_solver_solve( p->pSat, NULL, 0 );
+        if ( fVerbose )
+        {
+            printf( "Iter %3d : ", i );
+            printf( "Vars = %5d  ", p->iVar );
+            printf( "Clauses = %5d  ", bmcg_sat_solver_clausenum(p->pSat) );
+            printf( "Conflicts = %7d  ", bmcg_sat_solver_conflictnum(p->pSat) );
+            Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
+        }
+        if ( status == GLUCOSE_UNSAT )
+        {
+            printf( "The problem has no solution.\n" );
+            break;
+        }
+        iMint = Maj_ManEval( p );
+    }
+    if ( iMint == -1 )
+        Maj_ManPrintSolution( p );
+    Maj_ManFree( p );
+    Abc_PrintTime( 1, "Total runtime", Abc_Clock() - clkTotal );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+