Experimental code for polynomial construction.

abclib.dsp

@@ -5371,10 +5371,18 @@ SOURCE=.\src\proof\acec\acecOrder.c
 # End Source File
 # Begin Source File
 
+SOURCE=.\src\proof\acec\acecPo.c
+# End Source File
+# Begin Source File
+
 SOURCE=.\src\proof\acec\acecPolyn.c
 # End Source File
 # Begin Source File
 
+SOURCE=.\src\proof\acec\acecRe.c
+# End Source File
+# Begin Source File
+
 SOURCE=.\src\proof\acec\acecUtil.c
 # End Source File
 # End Group

src/proof/acec/acecPo.c

+/**CFile****************************************************************
+
+  FileName    [acecPo.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [CEC for arithmetic circuits.]
+
+  Synopsis    [Core procedures.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: acecPo.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "acecInt.h"
+#include "misc/vec/vecWec.h"
+#include "misc/vec/vecHsh.h"
+
+ABC_NAMESPACE_IMPL_START
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Prints polynomial.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Gia_PolynPrintMono( Vec_Int_t * vConst, Vec_Int_t * vMono )
+{
+    int k, Entry;
+    Vec_IntForEachEntry( vConst, Entry, k )
+        printf( "%s2^%d", Entry < 0 ? "-" : "+", Abc_AbsInt(Entry)-1 );
+    Vec_IntForEachEntry( vMono, Entry, k )
+        printf( " * %d", Entry );
+    printf( "\n" );
+}
+void Gia_PolynPrint( Vec_Wec_t * vPolyn )
+{
+    Vec_Int_t * vConst, * vMono;  int i;
+    printf( "Polynomial with %d monomials:\n", Vec_WecSize(vPolyn)/2 );
+    for ( i = 0; i < Vec_WecSize(vPolyn)/2; i++ )
+    {
+        vConst = Vec_WecEntry( vPolyn, 2*i+0 );
+        vMono  = Vec_WecEntry( vPolyn, 2*i+1 );
+        Gia_PolynPrintMono( vConst, vMono );
+    }
+}
+void Gia_PolynPrintStats( Vec_Wec_t * vPolyn )
+{
+    Vec_Int_t * vConst, * vCountsP, * vCountsN;
+    int i, Entry, Max = 0;
+    printf( "Polynomial with %d monomials:\n", Vec_WecSize(vPolyn)/2 );
+    for ( i = 0; i < Vec_WecSize(vPolyn)/2; i++ )
+    {
+        vConst = Vec_WecEntry( vPolyn, 2*i+0 );
+        Max = Abc_MaxInt( Max, Abc_AbsInt(Abc_AbsInt(Vec_IntEntry(vConst, 0))) );
+    }
+    vCountsP = Vec_IntStart( Max + 1 );
+    vCountsN = Vec_IntStart( Max + 1 );
+    for ( i = 0; i < Vec_WecSize(vPolyn)/2; i++ )
+    {
+        vConst = Vec_WecEntry( vPolyn, 2*i+0 );
+        Entry = Vec_IntEntry(vConst, 0);
+        if ( Entry > 0 )
+            Vec_IntAddToEntry( vCountsP, Entry, 1 );
+        else
+            Vec_IntAddToEntry( vCountsN, -Entry, 1 );
+    }
+    Vec_IntForEachEntry( vCountsN, Entry, i )
+        if ( Entry )
+            printf( "-2^%d appears %d times\n", Abc_AbsInt(i)-1, Entry );
+    Vec_IntForEachEntry( vCountsP, Entry, i )
+        if ( Entry )
+            printf( "+2^%d appears %d times\n", Abc_AbsInt(i)-1, Entry );
+    Vec_IntFree( vCountsP );
+    Vec_IntFree( vCountsN );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Collects polynomial.]
+
+  Description [Collects non-trivial monomials in the increasing order 
+  of the absolute value of the their first coefficients.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Wec_t * Gia_PolynGetResult( Hsh_VecMan_t * pHashC, Hsh_VecMan_t * pHashM, Vec_Int_t * vCoefs )
+{
+    Vec_Int_t * vClass, * vLevel, * vArray;
+    Vec_Wec_t * vPolyn, * vSorted;
+    int i, k, iConst, iMono;
+    // find the largest 
+    int nLargest = 0, nNonConst = 0;
+    Vec_IntForEachEntry( vCoefs, iConst, iMono )
+    {
+        //Vec_IntPrint( Hsh_VecReadEntry(pHashM, iMono) );
+        if ( iConst == 0 ) 
+            continue;
+        vArray = Hsh_VecReadEntry( pHashC, iConst );
+        nLargest = Abc_MaxInt( nLargest, Abc_AbsInt(Vec_IntEntry(vArray, 0)) );
+        nNonConst++;
+    }
+    // sort by the size of the largest coefficient
+    vSorted = Vec_WecStart( nLargest+1 );
+    Vec_IntForEachEntry( vCoefs, iConst, iMono )
+    {
+        if ( iConst == 0 ) 
+            continue;
+        vArray = Hsh_VecReadEntry( pHashC, iConst );
+        vLevel = Vec_WecEntry( vSorted, Abc_AbsInt(Vec_IntEntry(vArray, 0)) );
+        Vec_IntPushTwo( vLevel, iConst, iMono );
+    }
+    // reload in the given order
+    vPolyn = Vec_WecAlloc( 2*nNonConst );
+    Vec_WecForEachLevel( vSorted, vClass, i )
+    {
+        Vec_IntForEachEntryDouble( vClass, iConst, iMono, k )
+        {
+            vArray = Hsh_VecReadEntry( pHashC, iConst );
+            vLevel = Vec_WecPushLevel( vPolyn );
+            Vec_IntGrow( vLevel, Vec_IntSize(vArray) );
+            Vec_IntAppend( vLevel, vArray );
+
+            vArray = Hsh_VecReadEntry( pHashM, iMono );
+            vLevel = Vec_WecPushLevel( vPolyn );
+            Vec_IntGrow( vLevel, Vec_IntSize(vArray) );
+            Vec_IntAppend( vLevel, vArray );
+        }
+    }
+    assert( Vec_WecSize(vPolyn) == 2*nNonConst );
+    Vec_WecFree( vSorted );
+    return vPolyn;
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Derives new constant.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline void Gia_PolynMergeConstOne( Vec_Int_t * vConst, int New )
+{
+    int i, Old;
+    assert( New != 0 );
+    Vec_IntForEachEntry( vConst, Old, i )
+    {
+        assert( Old != 0 );
+        if ( Old == New ) // A == B
+        {
+            Vec_IntDrop( vConst, i );
+            Gia_PolynMergeConstOne( vConst, New > 0 ? New + 1 : New - 1 );
+            return;
+        }
+        if ( Abc_AbsInt(Old) == Abc_AbsInt(New) ) // A == -B
+        {
+            Vec_IntDrop( vConst, i );
+            return;
+        }
+        if ( Old + New == 1 || Old + New == -1 )  // sign(A) != sign(B)  &&  abs(abs(A)-abs(B)) == 1 
+        {
+            int Value = Abc_MinInt( Abc_AbsInt(Old), Abc_AbsInt(New) );
+            Vec_IntDrop( vConst, i );
+            Gia_PolynMergeConstOne( vConst, (Old + New == 1) ? Value : -Value );
+            return;
+        }
+    }
+    Vec_IntPushUniqueOrder( vConst, New );
+}
+static inline void Gia_PolynMergeConst( Vec_Int_t * vTempC, Hsh_VecMan_t * pHashC, int iConstAdd )
+{
+    int i, New;
+    Vec_Int_t * vConstAdd = Hsh_VecReadEntry( pHashC, iConstAdd );
+    Vec_IntForEachEntry( vConstAdd, New, i )
+    {
+        Gia_PolynMergeConstOne( vTempC, New );
+        vConstAdd = Hsh_VecReadEntry( pHashC, iConstAdd );
+    }
+}
+static inline int Gia_PolynBuildAdd( Hsh_VecMan_t * pHashC, Hsh_VecMan_t * pHashM, Vec_Int_t * vCoefs, 
+                                     Vec_Wec_t * vLit2Mono, Vec_Int_t * vTempC, Vec_Int_t * vTempM )
+{
+    int i, iLit, iConst, iConstNew;
+    int iMono = Hsh_VecManAdd(pHashM, vTempM);
+    if ( iMono == Vec_IntSize(vCoefs) ) // new monomial
+    {
+        // map monomial into a constant
+        assert( Vec_IntSize(vTempC) > 0 );
+        iConst = Hsh_VecManAdd( pHashC, vTempC );
+        Vec_IntPush( vCoefs, iConst );
+        // map literals into monomial
+        assert( Vec_IntSize(vTempM) > 0 );
+        Vec_IntForEachEntry( vTempM, iLit, i )
+            Vec_WecPush( vLit2Mono, iLit, iMono ); 
+        //printf( "New monomial: \n" );
+        //Gia_PolynPrintMono( vTempC, vTempM );
+        return 1;
+    }
+    // this monomial exists
+    iConst = Vec_IntEntry( vCoefs, iMono );
+    if ( iConst )
+        Gia_PolynMergeConst( vTempC, pHashC, iConst );
+    iConstNew = Hsh_VecManAdd( pHashC, vTempC );
+    Vec_IntWriteEntry( vCoefs, iMono, iConstNew );
+    //printf( "Old monomial: \n" );
+    //Gia_PolynPrintMono( vTempC, vTempM );
+    if ( iConst && !iConstNew )
+        return -1;
+    if ( !iConst && iConstNew )
+        return 1;
+    return 0;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computing for literals.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline int Gia_PolynHandleOne( Hsh_VecMan_t * pHashC, Hsh_VecMan_t * pHashM, Vec_Int_t * vCoefs, 
+                                      Vec_Wec_t * vLit2Mono, Vec_Int_t * vTempC, Vec_Int_t * vTempM, 
+                                      int iMono, int iLitOld, int iLitNew0, int iLitNew1 )
+{
+    int status, iConst = Vec_IntEntry( vCoefs, iMono );
+    Vec_Int_t * vArrayC = Hsh_VecReadEntry( pHashC, iConst );
+    Vec_Int_t * vArrayM = Hsh_VecReadEntry( pHashM, iMono );
+    // create new monomial
+    Vec_IntClear( vTempM );
+    Vec_IntAppend( vTempM, vArrayM );
+    status = Vec_IntRemove( vTempM, iLitOld );
+    assert( status );
+    // create new monomial
+    if ( iLitNew0 == -1 && iLitNew1 == -1 )     // no new lit - the same const
+        Vec_IntAppendMinus( vTempC, vArrayC, 0 );
+    else if ( iLitNew0 > -1 && iLitNew1 == -1 ) // one new lit - opposite const
+    {
+        Vec_IntAppendMinus( vTempC, vArrayC, 1 );
+        Vec_IntPushUniqueOrder( vTempM, iLitNew0 );
+    }
+    else if ( iLitNew0 > -1 && iLitNew1 > -1 )  // both new lit - the same const
+    {
+        Vec_IntAppendMinus( vTempC, vArrayC, 0 );
+        Vec_IntPushUniqueOrder( vTempM, iLitNew0 );
+        Vec_IntPushUniqueOrder( vTempM, iLitNew1 );
+    }
+    else assert( 0 );
+    return Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM );
+}
+
+Vec_Wec_t * Gia_PolynBuildNew2( Gia_Man_t * pGia, Vec_Int_t * vRootLits, Vec_Int_t * vLeaves, Vec_Int_t * vNodes, int fSigned, int fVerbose, int fVeryVerbose )
+{
+    abctime clk = Abc_Clock();
+    Vec_Wec_t * vPolyn;
+    Vec_Wec_t * vLit2Mono = Vec_WecStart( 2 * Gia_ManObjNum(pGia) ); // mapping AIG literals into monomials
+    Hsh_VecMan_t * pHashC = Hsh_VecManStart( 1000 );    // hash table for constants
+    Hsh_VecMan_t * pHashM = Hsh_VecManStart( 1000 );    // hash table for monomials
+    Vec_Int_t * vCoefs    = Vec_IntAlloc( 1000 );       // monomial coefficients
+    Vec_Int_t * vTempC    = Vec_IntAlloc( 10 );         // temporary array
+    Vec_Int_t * vTempM    = Vec_IntAlloc( 10 );         // temporary array
+    int i, k, iObj, iLit, iMono, nMonos = 0, nBuilds = 0;
+
+    // add 0-constant and 1-monomial
+    Hsh_VecManAdd( pHashC, vTempC );
+    Hsh_VecManAdd( pHashM, vTempM );
+    Vec_IntPush( vCoefs, 0 );
+
+    // create output signature
+    Vec_IntForEachEntry( vRootLits, iLit, i )
+    {
+        Vec_IntFill( vTempC, 1, (fSigned && i == Vec_IntSize(vRootLits)-1) ? -i-1 : i+1 );
+        Vec_IntFill( vTempM, 1, iLit );
+        nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM );
+        nBuilds++;
+    }
+
+    // perform construction for internal nodes
+    Vec_IntForEachEntryReverse( vNodes, iObj, i )
+    {
+        Gia_Obj_t * pObj = Gia_ManObj( pGia, iObj );
+        int iLits[2] = { Abc_Var2Lit(iObj, 0),         Abc_Var2Lit(iObj, 1)         };
+        int iFans[2] = { Gia_ObjFaninLit0(pObj, iObj), Gia_ObjFaninLit1(pObj, iObj) };
+        // add inverter
+        Vec_Int_t * vArray = Vec_WecEntry( vLit2Mono, iLits[1] );
+        Vec_IntForEachEntry( vArray, iMono, k )
+            if ( Vec_IntEntry(vCoefs, iMono) > 0 )
+            {
+                nMonos += Gia_PolynHandleOne( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM, iMono, iLits[1], -1, -1 );
+                nMonos += Gia_PolynHandleOne( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM, iMono, iLits[1], iLits[0], -1 );
+                Vec_IntWriteEntry( vCoefs, iMono, 0 );
+                nMonos--;
+                nBuilds++;
+                nBuilds++;
+            }
+        // add AND gate
+        vArray = Vec_WecEntry( vLit2Mono, iLits[0] );
+        Vec_IntForEachEntry( vArray, iMono, k )
+            if ( Vec_IntEntry(vCoefs, iMono) > 0 )
+            {
+                nMonos += Gia_PolynHandleOne( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM, iMono, iLits[0], iFans[0], iFans[1] );
+                Vec_IntWriteEntry( vCoefs, iMono, 0 );
+                nMonos--;
+                nBuilds++;
+            }
+        //printf( "Obj %5d : nMonos = %6d  nUsed = %6d\n", iObj, nBuilds, nMonos );
+    }
+
+    // complement leave nodes
+    Vec_IntForEachEntry( vLeaves, iObj, i )
+    {
+        Gia_Obj_t * pObj = Gia_ManObj( pGia, iObj );
+        int iLits[2] = { Abc_Var2Lit(iObj, 0),  Abc_Var2Lit(iObj, 1) };
+        // add inverter
+        Vec_Int_t * vArray = Vec_WecEntry( vLit2Mono, iLits[1] );
+        Vec_IntForEachEntry( vArray, iMono, k )
+            if ( Vec_IntEntry(vCoefs, iMono) > 0 )
+            {
+                nMonos += Gia_PolynHandleOne( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM, iMono, iLits[1], -1, -1 );
+                nMonos += Gia_PolynHandleOne( pHashC, pHashM, vCoefs, vLit2Mono, vTempC, vTempM, iMono, iLits[1], iLits[0], -1 );
+                Vec_IntWriteEntry( vCoefs, iMono, 0 );
+                nMonos--;
+                nBuilds++;
+            }
+    }
+
+    // get the results
+    vPolyn = Gia_PolynGetResult( pHashC, pHashM, vCoefs );
+
+    printf( "HashC = %d. HashM = %d.  Total = %d. Left = %d.  Used = %d.  ", 
+        Hsh_VecSize(pHashC), Hsh_VecSize(pHashM), nBuilds, nMonos, Vec_WecSize(vPolyn)/2 );
+    Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
+
+    Vec_IntFree( vTempC );
+    Vec_IntFree( vTempM );
+    Vec_IntFree( vCoefs );
+    Vec_WecFree( vLit2Mono );
+    Hsh_VecManStop( pHashC );
+    Hsh_VecManStop( pHashM );
+    return vPolyn;
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Computing for objects.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline void Gia_PolynPrepare2( Vec_Int_t * vTempC[2], Vec_Int_t * vTempM[2], int iObj, int iCst )
+{
+    Vec_IntFill( vTempC[0], 1, iCst );
+    Vec_IntFill( vTempC[1], 1, -iCst );
+    Vec_IntClear( vTempM[0] );
+    Vec_IntFill( vTempM[1], 1, iObj );
+}
+static inline void Gia_PolynPrepare4( Vec_Int_t * vTempC[4], Vec_Int_t * vTempM[4], Vec_Int_t * vConst, Vec_Int_t * vMono, int iObj, int iFan0, int iFan1 )
+{
+    int i, k, Entry;
+    for ( i = 0; i < 4; i++ )
+        Vec_IntAppendMinus( vTempC[i], vConst, i & 1 );
+    for ( i = 0; i < 4; i++ )
+        Vec_IntClear( vTempM[i] );
+    Vec_IntForEachEntry( vMono, Entry, k )
+        if ( Entry != iObj )
+            for ( i = 0; i < 4; i++ )
+                Vec_IntPush( vTempM[i], Entry );
+    Vec_IntPushUniqueOrder( vTempM[1], iFan0 );
+    Vec_IntPushUniqueOrder( vTempM[2], iFan1 );
+    Vec_IntPushUniqueOrder( vTempM[3], iFan0 );
+    Vec_IntPushUniqueOrder( vTempM[3], iFan1 );
+}
+
+Vec_Wec_t * Gia_PolynBuildNew( Gia_Man_t * pGia, Vec_Int_t * vRootLits, Vec_Int_t * vLeaves, Vec_Int_t * vNodes, int fSigned, int fVerbose, int fVeryVerbose )
+{
+    abctime clk = Abc_Clock();
+    Vec_Wec_t * vPolyn;
+    Vec_Wec_t * vLit2Mono = Vec_WecStart( Gia_ManObjNum(pGia) ); // mapping AIG literals into monomials
+    Hsh_VecMan_t * pHashC = Hsh_VecManStart( 1000 );    // hash table for constants
+    Hsh_VecMan_t * pHashM = Hsh_VecManStart( 1000 );    // hash table for monomials
+    Vec_Int_t * vCoefs    = Vec_IntAlloc( 1000 );       // monomial coefficients
+    Vec_Int_t * vTempC[4],  * vTempM[4];                // temporary array
+    int i, k, iObj, iLit, iMono, iConst, nMonos = 0, nBuilds = 0;
+    for ( i = 0; i < 4; i++ )
+        vTempC[i] = Vec_IntAlloc( 10 );
+    for ( i = 0; i < 4; i++ )
+        vTempM[i] = Vec_IntAlloc( 10 );
+
+    // add 0-constant and 1-monomial
+    Hsh_VecManAdd( pHashC, vTempC[0] );
+    Hsh_VecManAdd( pHashM, vTempM[0] );
+    Vec_IntPush( vCoefs, 0 );
+
+    // create output signature
+    Vec_IntForEachEntry( vRootLits, iLit, i )
+    {
+        Gia_PolynPrepare2( vTempC, vTempM, Abc_Lit2Var(iLit), i+1 );
+        if ( fSigned && i == Vec_IntSize(vRootLits)-1 )
+        {
+            if ( Abc_LitIsCompl(iLit) )
+            {
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[0] );   // -C
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[1] );   //  C * Driver
+                nBuilds++;
+            }
+            else
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[1] );   // -C * Driver
+        }
+        else 
+        {
+            if ( Abc_LitIsCompl(iLit) )
+            {
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[0] );   //  C
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[1] );   // -C * Driver
+                nBuilds++;
+            }
+            else
+                nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[1] );   //  C * Driver
+        }
+        nBuilds++;
+    }
+
+    // perform construction for internal nodes
+    Vec_IntForEachEntryReverse( vNodes, iObj, i )
+    {
+        Gia_Obj_t * pObj = Gia_ManObj( pGia, iObj );
+        Vec_Int_t * vArray = Vec_WecEntry( vLit2Mono, iObj );
+        Vec_IntForEachEntry( vArray, iMono, k )
+            if ( (iConst = Vec_IntEntry(vCoefs, iMono)) > 0 )
+            {
+                Vec_Int_t * vArrayC = Hsh_VecReadEntry( pHashC, iConst );
+                Vec_Int_t * vArrayM = Hsh_VecReadEntry( pHashM, iMono );
+                Gia_PolynPrepare4( vTempC, vTempM, vArrayC, vArrayM, iObj, Gia_ObjFaninId0(pObj, iObj), Gia_ObjFaninId1(pObj, iObj) );
+                if ( Gia_ObjIsXor(pObj) )
+                {
+                }
+                else if ( Gia_ObjFaninC0(pObj) && Gia_ObjFaninC1(pObj) )  //  C * (1 - x) * (1 - y)
+                {
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[0] );   //  C * 1
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[1] );   // -C * x
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[3], vTempM[2] );   // -C * y 
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[2], vTempM[3] );   //  C * x * y
+                    nBuilds += 3;
+                }
+                else if ( Gia_ObjFaninC0(pObj) && !Gia_ObjFaninC1(pObj) ) //  C * (1 - x) * y
+                {
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[2] );   //  C * y 
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[3] );   // -C * x * y
+                    nBuilds += 2;
+                }
+                else if ( !Gia_ObjFaninC0(pObj) && Gia_ObjFaninC1(pObj) ) //  C * x * (1 - y)
+                {
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[1] );   //  C * x 
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[1], vTempM[3] );   // -C * x * y
+                    nBuilds++;
+                }
+                else   
+                    nMonos += Gia_PolynBuildAdd( pHashC, pHashM, vCoefs, vLit2Mono, vTempC[0], vTempM[3] ); //  C * x * y
+                Vec_IntWriteEntry( vCoefs, iMono, 0 );
+                nMonos--;
+                nBuilds++;
+            }
+        //printf( "Obj %5d : nMonos = %6d  nUsed = %6d\n", iObj, nBuilds, nMonos );
+    }
+
+    // get the results
+    vPolyn = Gia_PolynGetResult( pHashC, pHashM, vCoefs );
+
+    printf( "HashC = %d. HashM = %d.  Total = %d. Left = %d.  Used = %d.  ", 
+        Hsh_VecSize(pHashC), Hsh_VecSize(pHashM), nBuilds, nMonos, Vec_WecSize(vPolyn)/2 );
+    Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
+
+    for ( i = 0; i < 4; i++ )
+        Vec_IntFree( vTempC[i] );
+    for ( i = 0; i < 4; i++ )
+        Vec_IntFree( vTempM[i] );
+    Vec_IntFree( vCoefs );
+    Vec_WecFree( vLit2Mono );
+    Hsh_VecManStop( pHashC );
+    Hsh_VecManStop( pHashM );
+    return vPolyn;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Gia_PolynBuild2Test( Gia_Man_t * pGia )
+{
+    Vec_Wec_t * vPolyn;
+    Vec_Int_t * vRootLits = Vec_IntAlloc( Gia_ManCoNum(pGia) );
+    Vec_Int_t * vLeaves   = Vec_IntAlloc( Gia_ManCiNum(pGia) );
+    Vec_Int_t * vNodes    = Vec_IntAlloc( Gia_ManAndNum(pGia) );
+    Gia_Obj_t * pObj;
+    int i;
+
+    Gia_ManForEachObj( pGia, pObj, i )
+        if ( Gia_ObjIsCi(pObj) )
+            Vec_IntPush( vLeaves, i );
+        else if ( Gia_ObjIsAnd(pObj) )
+            Vec_IntPush( vNodes, i );
+        else if ( Gia_ObjIsCo(pObj) )
+            Vec_IntPush( vRootLits, Gia_ObjFaninLit0p(pGia, pObj) );
+
+    vPolyn = Gia_PolynBuildNew( pGia, vRootLits, vLeaves, vNodes, 0, 0, 0 );
+//    printf( "Polynomial has %d monomials.\n", Vec_WecSize(vPolyn)/2 );
+//    Gia_PolynPrintStats( vPolyn );
+//    Gia_PolynPrint( vPolyn );
+    Vec_WecFree( vPolyn );
+
+    Vec_IntFree( vRootLits );
+    Vec_IntFree( vLeaves );
+    Vec_IntFree( vNodes );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+

src/proof/acec/acecRe.c

+/**CFile****************************************************************
+
+  FileName    [acecRe.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [CEC for arithmetic circuits.]
+
+  Synopsis    [Core procedures.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: acecRe.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "acecInt.h"
+#include "misc/vec/vecHash.h"
+#include "misc/util/utilTruth.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+#define Ree_ForEachCut( pList, pCut, i ) for ( i = 0, pCut = pList + 1; i < pList[0]; i++, pCut += pCut[0] + 2 )
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Detecting FADDs in the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ree_TruthPrecompute()
+{
+    word Truths[8] = { 0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77 };
+    word Truth;
+    int i;
+    for ( i = 0; i < 8; i++ )
+    {
+        Truth = Truths[i];
+        Truth = Abc_Tt6SwapAdjacent( Truth, 1 );
+        Abc_TtPrintHexRev( stdout, &Truth, 3 );
+        printf( "\n" );
+    }
+    printf( "\n" );
+    for ( i = 0; i < 8; i++ )
+    {
+        Truth = Truths[i];
+        Truth = Abc_Tt6SwapAdjacent( Truth, 1 );
+        Truth = Abc_Tt6SwapAdjacent( Truth, 0 );
+        Abc_TtPrintHexRev( stdout, &Truth, 3 );
+        printf( "\n" );
+    }
+    printf( "\n" );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Detecting FADDs in the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline int Ree_ManCutMergeOne( int * pCut0, int * pCut1, int * pCut )
+{
+    int i, k;
+    for ( k = 0; k <= pCut1[0]; k++ )
+        pCut[k] = pCut1[k];
+    for ( i = 1; i <= pCut0[0]; i++ )
+    {
+        for ( k = 1; k <= pCut1[0]; k++ )
+            if ( pCut0[i] == pCut1[k] )
+                break;
+        if ( k <= pCut1[0] )
+            continue;
+        if ( pCut[0] == 3 )
+            return 0;
+        pCut[1+pCut[0]++] = pCut0[i];
+    }
+    assert( pCut[0] == 2 || pCut[0] == 3 );
+    if ( pCut[1] > pCut[2] )
+        ABC_SWAP( int, pCut[1], pCut[2] );
+    assert( pCut[1] < pCut[2] );
+    if ( pCut[0] == 2 )
+        return 1;
+    if ( pCut[2] > pCut[3] )
+        ABC_SWAP( int, pCut[2], pCut[3] );
+    if ( pCut[1] > pCut[2] )
+        ABC_SWAP( int, pCut[1], pCut[2] );
+    assert( pCut[1] < pCut[2] );
+    assert( pCut[2] < pCut[3] );
+    return 1;
+}
+static inline int Ree_ManCutCheckEqual( Vec_Int_t * vCuts, int * pCutNew )
+{
+    int * pList = Vec_IntArray( vCuts );
+    int i, k, * pCut;
+    Ree_ForEachCut( pList, pCut, i )
+    {
+        for ( k = 0; k <= pCut[0]; k++ )
+            if ( pCut[k] != pCutNew[k] )
+                break;
+        if ( k > pCut[0] )
+            return 1;
+    }
+    return 0;
+}
+static inline int Ree_ManCutFind( int iObj, int * pCut )
+{
+    if ( pCut[1] == iObj ) return 0;
+    if ( pCut[2] == iObj ) return 1;
+    if ( pCut[3] == iObj ) return 2;
+    assert( 0 );
+    return -1;
+}
+static inline int Ree_ManCutNotFind( int iObj1, int iObj2, int * pCut )
+{
+    if ( pCut[3] != iObj1 && pCut[3] != iObj2 ) return 0;
+    if ( pCut[2] != iObj1 && pCut[2] != iObj2 ) return 1;
+    if ( pCut[1] != iObj1 && pCut[1] != iObj2 ) return 2;
+    assert( 0 );
+    return -1;
+}
+static inline int Ree_ManCutTruthOne( int * pCut0, int * pCut )
+{
+    int Truth0 = pCut0[pCut0[0]+1];
+    int fComp0 = (Truth0 >> 7) & 1;
+    if ( pCut0[0] == 3 )
+        return Truth0;
+    Truth0 = fComp0 ? ~Truth0 : Truth0;
+    if ( pCut0[0] == 2 )
+    {
+        int Truths[3][8] = {
+            { 0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77 }, // {0,1,-}
+            { 0x00, 0x05, 0x0A, 0x0F, 0x50, 0x55, 0x5A, 0x5F }, // {0,-,1}
+            { 0x00, 0x03, 0x0C, 0x0F, 0x30, 0x33, 0x3C, 0x3F }  // {-,0,1}
+        };
+        int Truth = Truths[Ree_ManCutNotFind(pCut0[1], pCut0[2], pCut)][Truth0 & 0x7];
+        return 0xFF & (fComp0 ? ~Truth : Truth);
+    }
+    if ( pCut0[0] == 1 )
+    {
+        int Truths[3] = { 0x55, 0x33, 0x0F };
+        int Truth = Truths[Ree_ManCutFind(pCut0[1], pCut)];
+        return 0xFF & (fComp0 ? ~Truth : Truth);
+    }
+    assert( 0 );
+    return -1;
+}
+static inline int Ree_ManCutTruth( Gia_Obj_t * pObj, int * pCut0, int * pCut1, int * pCut )
+{
+    int Truth0 = Ree_ManCutTruthOne( pCut0, pCut );
+    int Truth1 = Ree_ManCutTruthOne( pCut1, pCut );
+    Truth0 = Gia_ObjFaninC0(pObj) ? ~Truth0 : Truth0;
+    Truth1 = Gia_ObjFaninC1(pObj) ? ~Truth1 : Truth1;
+    return 0xFF & (Gia_ObjIsXor(pObj) ? Truth0 ^ Truth1 : Truth0 & Truth1); 
+}
+
+#if 0
+
+int Ree_ObjComputeTruth_rec( Gia_Obj_t * pObj )
+{
+    int Truth0, Truth1;
+    if ( pObj->Value )
+        return pObj->Value;
+    assert( Gia_ObjIsAnd(pObj) );
+    Truth0 = Ree_ObjComputeTruth_rec( Gia_ObjFanin0(pObj) );
+    Truth1 = Ree_ObjComputeTruth_rec( Gia_ObjFanin1(pObj) );
+    if ( Gia_ObjIsXor(pObj) )
+        return (pObj->Value = (Gia_ObjFaninC0(pObj) ? ~Truth0 : Truth0) ^ (Gia_ObjFaninC1(pObj) ? ~Truth1 : Truth1));
+    else
+        return (pObj->Value = (Gia_ObjFaninC0(pObj) ? ~Truth0 : Truth0) & (Gia_ObjFaninC1(pObj) ? ~Truth1 : Truth1));
+}
+void Ree_ObjCleanTruth_rec( Gia_Obj_t * pObj )
+{
+    if ( !pObj->Value )
+        return;
+    pObj->Value = 0;
+    if ( !Gia_ObjIsAnd(pObj) )
+        return;
+    Ree_ObjCleanTruth_rec( Gia_ObjFanin0(pObj) );
+    Ree_ObjCleanTruth_rec( Gia_ObjFanin1(pObj) );
+}
+int Ree_ObjComputeTruth( Gia_Man_t * p, int iObj, int * pCut )
+{
+    unsigned Truth, Truths[3] = { 0xAA, 0xCC, 0xF0 }; int i;
+    for ( i = 1; i <= pCut[0]; i++ )
+        Gia_ManObj(p, pCut[i])->Value = Truths[i-1];
+    Truth = 0xFF & Ree_ObjComputeTruth_rec( Gia_ManObj(p, iObj) );
+    Ree_ObjCleanTruth_rec( Gia_ManObj(p, iObj) );
+    return Truth;
+}
+
+#endif
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ree_ManCutPrint( int * pCut, int Count, word Truth )
+{
+    int c;
+    printf( "%d : ", Count );
+    for ( c = 1; c <= pCut[0]; c++ )
+        printf( "%3d ", pCut[c] );
+    for (      ; c <= 4; c++ )
+        printf( "    " );
+    printf( "0x" );
+    Abc_TtPrintHexRev( stdout, &Truth, 3 );
+    printf( "\n" );
+}
+void Ree_ManCutMerge( Gia_Man_t * p, int iObj, int * pList0, int * pList1, Vec_Int_t * vCuts, Hash_IntMan_t * pHash, Vec_Int_t * vData )
+{
+    int fVerbose = 0;
+    int i, k, c, Value, Truth, TruthC, * pCut0, * pCut1, pCut[5], Count = 0;
+    if ( fVerbose )
+        printf( "Object %d\n", iObj );
+    Vec_IntFill( vCuts, 2, 1 );
+    Vec_IntPush( vCuts, iObj );
+    Vec_IntPush( vCuts, 0xAA );
+    Ree_ForEachCut( pList0, pCut0, i )
+    Ree_ForEachCut( pList1, pCut1, k )
+    {
+        if ( !Ree_ManCutMergeOne(pCut0, pCut1, pCut) )
+            continue;
+        if ( Ree_ManCutCheckEqual(vCuts, pCut) )
+            continue;
+        Truth = TruthC = Ree_ManCutTruth(Gia_ManObj(p, iObj), pCut0, pCut1, pCut);
+        //assert( Truth == Ree_ObjComputeTruth(p, iObj, pCut) );
+        Vec_IntAddToEntry( vCuts, 0, 1 );  
+        for ( c = 0; c <= pCut[0]; c++ )
+            Vec_IntPush( vCuts, pCut[c] );
+        Vec_IntPush( vCuts, Truth );
+        if ( Truth & 0x80 )
+            Truth = 0xFF & ~Truth;
+        if ( (Truth == 0x66 || Truth == 0x11 || Truth == 0x22 || Truth == 0x44 || Truth == 0x77) && pCut[0] == 2 )
+        {
+            assert( pCut[0] == 2 );
+            Value = Hsh_Int3ManInsert( pHash, pCut[1], pCut[2], 0 );
+            Vec_IntPushThree( vData, iObj, Value, TruthC );
+        }
+        else if ( Truth == 0x69 || Truth == 0x17 || Truth == 0x2B || Truth == 0x4D || Truth == 0x71 )
+        {
+            assert( pCut[0] == 3 );
+            Value = Hsh_Int3ManInsert( pHash, pCut[1], pCut[2], pCut[3] );
+            Vec_IntPushThree( vData, iObj, Value, TruthC );
+        }
+        if ( fVerbose )
+            Ree_ManCutPrint( pCut, ++Count, TruthC );
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Ree_ManDeriveAdds( Hash_IntMan_t * p, Vec_Int_t * vData )
+{
+    int i, j, k, iObj, iObj2, Value, Truth, CountX, CountM, Index = 0;
+    int nEntries = Hash_IntManEntryNum(p);
+    Vec_Int_t * vAdds = Vec_IntAlloc( 1000 );
+    Vec_Int_t * vXors = Vec_IntStart( nEntries + 1 );
+    Vec_Int_t * vMajs = Vec_IntStart( nEntries + 1 );
+    Vec_Int_t * vIndex = Vec_IntStartFull( nEntries + 1 );
+    Vec_Int_t * vIndexRev = Vec_IntAlloc( 1000 );
+    Vec_Wec_t * vXorMap, * vMajMap;
+    Vec_IntForEachEntryTriple( vData, iObj, Value, Truth, i )
+    {
+        assert( Value <= nEntries );
+        if ( Truth == 0x66 || Truth == 0x99 || Truth == 0x69 || Truth == 0x96 )
+            Vec_IntAddToEntry( vXors, Value, 1 );
+        else
+            Vec_IntAddToEntry( vMajs, Value, 1 );
+    }
+    // remap these into indexes
+    Vec_IntForEachEntryTwo( vXors, vMajs, CountX, CountM, i )
+        if ( CountX && CountM )
+        {
+            Vec_IntPush( vIndexRev, i );
+            Vec_IntWriteEntry( vIndex, i, Index++ );
+        }
+    Vec_IntFree( vXors );
+    Vec_IntFree( vMajs );
+    printf( "Detected %d shared cuts among %d hashed cuts.\n", Index, nEntries );
+    // collect nodes
+    vXorMap = Vec_WecStart( Index );
+    vMajMap = Vec_WecStart( Index );
+    Vec_IntForEachEntryTriple( vData, iObj, Value, Truth, i )
+    {
+        Index = Vec_IntEntry( vIndex, Value );
+        if ( Index == -1 )
+            continue;
+        if ( Truth == 0x66 || Truth == 0x99 || Truth == 0x69 || Truth == 0x96 )
+            Vec_WecPush( vXorMap, Index, iObj );
+        else
+            Vec_WecPush( vMajMap, Index, iObj );
+    }
+    Vec_IntFree( vIndex );
+    // create pairs
+    Vec_IntForEachEntry( vIndexRev, Value, i )
+    {
+        Vec_Int_t * vXorOne = Vec_WecEntry( vXorMap, i );
+        Vec_Int_t * vMajOne = Vec_WecEntry( vMajMap, i );
+        Hash_IntObj_t * pObj = Hash_IntObj( p, Value );
+        Vec_IntForEachEntry( vXorOne, iObj, j )
+        Vec_IntForEachEntry( vMajOne, iObj2, k )
+        {
+            Vec_IntPushThree( vAdds, pObj->iData0, pObj->iData1, pObj->iData2 ); 
+            Vec_IntPushTwo( vAdds, iObj, iObj2 );
+        }
+    }
+    Vec_IntFree( vIndexRev );
+    Vec_WecFree( vXorMap );
+    Vec_WecFree( vMajMap );
+    return vAdds;
+}
+Vec_Int_t * Ree_ManComputeCuts( Gia_Man_t * p, int fVerbose )
+{
+    Gia_Obj_t * pObj; 
+    int * pList0, * pList1, i, nCuts = 0;
+    Hash_IntMan_t * pHash = Hash_IntManStart( 1000 );
+    Vec_Int_t * vAdds;
+    Vec_Int_t * vTemp = Vec_IntAlloc( 1000 );
+    Vec_Int_t * vData = Vec_IntAlloc( 1000 );
+    Vec_Int_t * vCuts = Vec_IntAlloc( 30 * Gia_ManAndNum(p) );
+    Vec_IntFill( vCuts, Gia_ManObjNum(p), 0 );
+    Gia_ManCleanValue( p );
+    Gia_ManForEachCi( p, pObj, i )
+    {
+        Vec_IntWriteEntry( vCuts, Gia_ObjId(p, pObj), Vec_IntSize(vCuts) );
+        Vec_IntPush( vCuts, 1 );
+        Vec_IntPush( vCuts, 1 );
+        Vec_IntPush( vCuts, Gia_ObjId(p, pObj) );
+        Vec_IntPush( vCuts, 0xAA );
+    }
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        pList0 = Vec_IntEntryP( vCuts, Vec_IntEntry(vCuts, Gia_ObjFaninId0(pObj, i)) );
+        pList1 = Vec_IntEntryP( vCuts, Vec_IntEntry(vCuts, Gia_ObjFaninId1(pObj, i)) );
+        Ree_ManCutMerge( p, i, pList0, pList1, vTemp, pHash, vData );
+        Vec_IntWriteEntry( vCuts, i, Vec_IntSize(vCuts) );
+        Vec_IntAppend( vCuts, vTemp );
+        nCuts += Vec_IntEntry( vTemp, 0 );
+    }
+    if ( fVerbose )
+        printf( "Nodes = %d.  Cuts = %d.  Cuts/Node = %.2f.  Ints/Node = %.2f.\n", 
+            Gia_ManAndNum(p), nCuts, 1.0*nCuts/Gia_ManAndNum(p), 1.0*Vec_IntSize(vCuts)/Gia_ManAndNum(p) );
+    Vec_IntFree( vTemp );
+    Vec_IntFree( vCuts );
+    vAdds = Ree_ManDeriveAdds( pHash, vData );
+    if ( fVerbose )
+        printf( "Adds = %d.  Total = %d.  Hashed = %d.  Hashed/Adds = %.2f.\n", 
+            Vec_IntSize(vAdds)/5, Vec_IntSize(vData)/3, Hash_IntManEntryNum(pHash), 5.0*Hash_IntManEntryNum(pHash)/Vec_IntSize(vAdds) );
+    Vec_IntFree( vData );
+    Hash_IntManStop( pHash );
+    return vAdds;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ree_ManComputeCutsTest( Gia_Man_t * p )
+{
+    abctime clk = Abc_Clock();
+    Vec_Int_t * vAdds = Ree_ManComputeCuts( p, 1 );
+    int i, Count = 0;
+    for ( i = 0; 5*i < Vec_IntSize(vAdds); i++ )
+    {
+        if ( Vec_IntEntry(vAdds, 5*i+2) == 0 )
+            continue;
+        Count++;
+        continue;
+        printf( "%6d : ", i );
+        printf( "%6d ", Vec_IntEntry(vAdds, 5*i+0) );
+        printf( "%6d ", Vec_IntEntry(vAdds, 5*i+1) );
+        printf( "%6d ", Vec_IntEntry(vAdds, 5*i+2) );
+        printf( "   ->  " );
+        printf( "%6d ", Vec_IntEntry(vAdds, 5*i+3) );
+        printf( "%6d ", Vec_IntEntry(vAdds, 5*i+4) );
+        printf( "\n" );
+    }
+    Vec_IntFree( vAdds );
+    printf( "Detected %d FAs and %d HAs.  ", Count, Vec_IntSize(vAdds)/5-Count );
+    Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
+}
+
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+