extraUtilMisc.c

/**CFile****************************************************************

  FileName    [extraUtilMisc.c]

  SystemName  [ABC: Logic synthesis and verification system.]

  PackageName [extra]

  Synopsis    [Misc procedures.]

  Author      [Alan Mishchenko]
  
  Affiliation [UC Berkeley]

  Date        [Ver. 1.0. Started - June 20, 2005.]

  Revision    [$Id: extraUtilMisc.c,v 1.0 2003/09/01 00:00:00 alanmi Exp $]

***********************************************************************/

#include <math.h>

#include "extra.h"

ABC_NAMESPACE_IMPL_START


/*---------------------------------------------------------------------------*/
/* Constant declarations                                                     */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Stucture declarations                                                     */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Type declarations                                                         */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Variable declarations                                                     */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Macro declarations                                                        */
/*---------------------------------------------------------------------------*/


/**AutomaticStart*************************************************************/

/*---------------------------------------------------------------------------*/
/* Static function prototypes                                                */
/*---------------------------------------------------------------------------*/

/**AutomaticEnd***************************************************************/

static void Extra_Permutations_rec( char ** pRes, int nFact, int n, char Array[] );

/*---------------------------------------------------------------------------*/
/* Definition of exported functions                                          */
/*---------------------------------------------------------------------------*/

/**Function********************************************************************

  Synopsis    [Finds the smallest integer larger of equal than the logarithm.]

  Description []

  SideEffects []

  SeeAlso     []

******************************************************************************/
int Extra_Base2LogDouble( double Num )
{
    double Res;
    int ResInt;

    Res    = log(Num)/log(2.0);
    ResInt = (int)Res;
    if ( ResInt == Res )
        return ResInt;
    else 
        return ResInt+1;
}

/**Function********************************************************************

  Synopsis    [Returns the power of two as a double.]

  Description []

  SideEffects []

  SeeAlso     []

******************************************************************************/
double Extra_Power2( int Degree )
{
    double Res;
    assert( Degree >= 0 );
    if ( Degree < 32 )
        return (double)(01<<Degree); 
    for ( Res = 1.0; Degree; Res *= 2.0, Degree-- );
    return Res;
}


/**Function*************************************************************

  Synopsis    []

  Description []

  SideEffects []

  SeeAlso     []

***********************************************************************/
int Extra_Power3( int Num )
{
    int i;
    int Res;
    Res = 1;
    for ( i = 0; i < Num; i++ )
        Res *= 3;
    return Res;
}

/**Function********************************************************************

  Synopsis    [Finds the number of combinations of k elements out of n.]

  Description []

  SideEffects []

  SeeAlso     []

******************************************************************************/
int Extra_NumCombinations( int k, int n )
{
    int i, Res = 1;
    for ( i = 1; i <= k; i++ )
            Res = Res * (n-i+1) / i;
    return Res;
} /* end of Extra_NumCombinations */

/**Function*************************************************************

  Synopsis    []

  Description []

  SideEffects []

  SeeAlso     []

***********************************************************************/
int * Extra_DeriveRadixCode( int Number, int Radix, int nDigits )
{
    static int Code[100];
    int i;
    assert( nDigits < 100 );
    for ( i = 0; i < nDigits; i++ )
    {
        Code[i] = Number % Radix;
        Number  = Number / Radix;
    }
    assert( Number == 0 );
    return Code;
}

/**Function*************************************************************

  Synopsis    [Counts the number of ones in the bitstring.]

  Description []

  SideEffects []

  SeeAlso     []

***********************************************************************/
int Extra_CountOnes( unsigned char * pBytes, int nBytes )
{
    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, Counter;
    Counter = 0;
    for ( i = 0; i < nBytes; i++ )
        Counter += bit_count[ *(pBytes+i) ];
    return Counter;
}

/**Function********************************************************************

  Synopsis    [Computes the factorial.]

  Description []

  SideEffects []

  SeeAlso     []

******************************************************************************/
int Extra_Factorial( int n )
{
    int i, Res = 1;
    for ( i = 1; i <= n; i++ )
        Res *= i;
    return Res;
}

/**Function********************************************************************

  Synopsis    [Computes the set of all permutations.]

  Description [The number of permutations in the array is n!. The number of
  entries in each permutation is n. Therefore, the resulting array is a 
  two-dimentional array of the size: n! x n. To free the resulting array,
  call ABC_FREE() on the pointer returned by this procedure.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
char ** Extra_Permutations( int n )
{
    char Array[50];
    char ** pRes;
    int nFact, i;
    // allocate memory
    nFact = Extra_Factorial( n );
    pRes  = (char **)Extra_ArrayAlloc( nFact, n, sizeof(char) );
    // fill in the permutations
    for ( i = 0; i < n; i++ )
        Array[i] = i;
    Extra_Permutations_rec( pRes, nFact, n, Array );
    // print the permutations
/*
    {
    int i, k;
    for ( i = 0; i < nFact; i++ )
    {
        printf( "{" );
        for ( k = 0; k < n; k++ )
            printf( " %d", pRes[i][k] );
        printf( " }\n" );
    }
    }
*/
    return pRes;
}

/**Function********************************************************************

  Synopsis    [Fills in the array of permutations.]

  Description []

  SideEffects []

  SeeAlso     []

******************************************************************************/
void Extra_Permutations_rec( char ** pRes, int nFact, int n, char Array[] )
{
    char ** pNext;
    int nFactNext;
    int iTemp, iCur, iLast, k;

    if ( n == 1 )
    {
        pRes[0][0] = Array[0];
        return;
    }

    // get the next factorial
    nFactNext = nFact / n;
    // get the last entry
    iLast = n - 1;

    for ( iCur = 0; iCur < n; iCur++ )
    {
        // swap Cur and Last
        iTemp        = Array[iCur];
        Array[iCur]  = Array[iLast];
        Array[iLast] = iTemp;

        // get the pointer to the current section
        pNext = pRes + (n - 1 - iCur) * nFactNext;

        // set the last entry 
        for ( k = 0; k < nFactNext; k++ )
            pNext[k][iLast] = Array[iLast];

        // call recursively for this part
        Extra_Permutations_rec( pNext, nFactNext, n - 1, Array );

        // swap them back
        iTemp        = Array[iCur];
        Array[iCur]  = Array[iLast];
        Array[iLast] = iTemp;
    }
}

/**Function*************************************************************

  Synopsis    [Permutes the given vector of minterms.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_TruthPermute_int( int * pMints, int nMints, char * pPerm, int nVars, int * pMintsP )
{
    int m, v;
    // clean the storage for minterms
    memset( pMintsP, 0, sizeof(int) * nMints );
    // go through minterms and add the variables
    for ( m = 0; m < nMints; m++ )
        for ( v = 0; v < nVars; v++ )
            if ( pMints[m] & (1 << v) )
                pMintsP[m] |= (1 << pPerm[v]);
}

/**Function*************************************************************

  Synopsis    [Permutes the function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthPermute( unsigned Truth, char * pPerms, int nVars, int fReverse )
{
    unsigned Result;
    int * pMints;
    int * pMintsP;
    int nMints;
    int i, m;

    assert( nVars < 6 );
    nMints  = (1 << nVars);
    pMints  = ABC_ALLOC( int, nMints );
    pMintsP = ABC_ALLOC( int, nMints );
    for ( i = 0; i < nMints; i++ )
        pMints[i] = i;

    Extra_TruthPermute_int( pMints, nMints, pPerms, nVars, pMintsP );

    Result = 0;
    if ( fReverse )
    {
        for ( m = 0; m < nMints; m++ )
            if ( Truth & (1 << pMintsP[m]) )
                Result |= (1 << m);
    }
    else
    {
        for ( m = 0; m < nMints; m++ )
            if ( Truth & (1 << m) )
                Result |= (1 << pMintsP[m]);
    }

    ABC_FREE( pMints );
    ABC_FREE( pMintsP );

    return Result;
}

/**Function*************************************************************

  Synopsis    [Changes the phase of the function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthPolarize( unsigned uTruth, int Polarity, int nVars )
{
    // elementary truth tables
    static unsigned Signs[5] = {
        0xAAAAAAAA,    // 1010 1010 1010 1010 1010 1010 1010 1010
        0xCCCCCCCC,    // 1010 1010 1010 1010 1010 1010 1010 1010
        0xF0F0F0F0,    // 1111 0000 1111 0000 1111 0000 1111 0000
        0xFF00FF00,    // 1111 1111 0000 0000 1111 1111 0000 0000
        0xFFFF0000     // 1111 1111 1111 1111 0000 0000 0000 0000
    };
    unsigned uTruthRes, uCof0, uCof1;
    int nMints, Shift, v;
    assert( nVars < 6 );
    nMints = (1 << nVars);
    uTruthRes = uTruth;
    for ( v = 0; v < nVars; v++ )
        if ( Polarity & (1 << v) )
        {
            uCof0  = uTruth & ~Signs[v];
            uCof1  = uTruth &  Signs[v];
            Shift  = (1 << v);
            uCof0 <<= Shift;
            uCof1 >>= Shift;
            uTruth = uCof0 | uCof1;
        }
    return uTruth;
}

/**Function*************************************************************

  Synopsis    [Computes N-canonical form using brute-force methods.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthCanonN( unsigned uTruth, int nVars )
{
    unsigned uTruthMin, uPhase;
    int nMints, i;
    nMints    = (1 << nVars);
    uTruthMin = 0xFFFFFFFF;
    for ( i = 0; i < nMints; i++ )
    {
        uPhase = Extra_TruthPolarize( uTruth, i, nVars ); 
        if ( uTruthMin > uPhase )
            uTruthMin = uPhase;
    }
    return uTruthMin;
}

/**Function*************************************************************

  Synopsis    [Computes NN-canonical form using brute-force methods.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthCanonNN( unsigned uTruth, int nVars )
{
    unsigned uTruthMin, uTruthC, uPhase;
    int nMints, i;
    nMints    = (1 << nVars);
    uTruthC   = (unsigned)( (~uTruth) & ((~((unsigned)0)) >> (32-nMints)) );
    uTruthMin = 0xFFFFFFFF;
    for ( i = 0; i < nMints; i++ )
    {
        uPhase = Extra_TruthPolarize( uTruth, i, nVars ); 
        if ( uTruthMin > uPhase )
            uTruthMin = uPhase;
        uPhase = Extra_TruthPolarize( uTruthC, i, nVars ); 
        if ( uTruthMin > uPhase )
            uTruthMin = uPhase;
    }
    return uTruthMin;
}

/**Function*************************************************************

  Synopsis    [Computes P-canonical form using brute-force methods.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthCanonP( unsigned uTruth, int nVars )
{
    static int nVarsOld, nPerms;
    static char ** pPerms = NULL;

    unsigned uTruthMin, uPerm;
    int k;

    if ( pPerms == NULL )
    {
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }
    else if ( nVarsOld != nVars )
    {
        ABC_FREE( pPerms );
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }

    uTruthMin = 0xFFFFFFFF;
    for ( k = 0; k < nPerms; k++ )
    {
        uPerm = Extra_TruthPermute( uTruth, pPerms[k], nVars, 0 );
        if ( uTruthMin > uPerm )
            uTruthMin = uPerm;
    }
    return uTruthMin;
}

/**Function*************************************************************

  Synopsis    [Computes NP-canonical form using brute-force methods.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthCanonNP( unsigned uTruth, int nVars )
{
    static int nVarsOld, nPerms;
    static char ** pPerms = NULL;

    unsigned uTruthMin, uPhase, uPerm;
    int nMints, k, i;

    if ( pPerms == NULL )
    {
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }
    else if ( nVarsOld != nVars )
    {
        ABC_FREE( pPerms );
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }

    nMints    = (1 << nVars);
    uTruthMin = 0xFFFFFFFF;
    for ( i = 0; i < nMints; i++ )
    {
        uPhase = Extra_TruthPolarize( uTruth, i, nVars ); 
        for ( k = 0; k < nPerms; k++ )
        {
            uPerm = Extra_TruthPermute( uPhase, pPerms[k], nVars, 0 );
            if ( uTruthMin > uPerm )
                uTruthMin = uPerm;
        }
    }
    return uTruthMin;
}

/**Function*************************************************************

  Synopsis    [Computes NPN-canonical form using brute-force methods.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthCanonNPN( unsigned uTruth, int nVars )
{
    static int nVarsOld, nPerms;
    static char ** pPerms = NULL;

    unsigned uTruthMin, uTruthC, uPhase, uPerm;
    int nMints, k, i;

    if ( pPerms == NULL )
    {
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }
    else if ( nVarsOld != nVars )
    {
        ABC_FREE( pPerms );
        nPerms = Extra_Factorial( nVars );   
        pPerms = Extra_Permutations( nVars );
        nVarsOld = nVars;
    }

    nMints    = (1 << nVars);
    uTruthC   = (unsigned)( (~uTruth) & ((~((unsigned)0)) >> (32-nMints)) );
    uTruthMin = 0xFFFFFFFF;
    for ( i = 0; i < nMints; i++ )
    {
        uPhase = Extra_TruthPolarize( uTruth, i, nVars ); 
        for ( k = 0; k < nPerms; k++ )
        {
            uPerm = Extra_TruthPermute( uPhase, pPerms[k], nVars, 0 );
            if ( uTruthMin > uPerm )
                uTruthMin = uPerm;
        }
        uPhase = Extra_TruthPolarize( uTruthC, i, nVars ); 
        for ( k = 0; k < nPerms; k++ )
        {
            uPerm = Extra_TruthPermute( uPhase, pPerms[k], nVars, 0 );
            if ( uTruthMin > uPerm )
                uTruthMin = uPerm;
        }
    }
    return uTruthMin;
}

/**Function*************************************************************

  Synopsis    [Computes NPN canonical forms for 4-variable functions.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_Truth4VarNPN( unsigned short ** puCanons, char ** puPhases, char ** puPerms, unsigned char ** puMap )
{
    unsigned short * uCanons;
    unsigned char * uMap;
    unsigned uTruth, uPhase, uPerm;
    char ** pPerms4, * uPhases, * uPerms;
    int nFuncs, nClasses;
    int i, k;

    nFuncs  = (1 << 16);
    uCanons = ABC_ALLOC( unsigned short, nFuncs );
    uPhases = ABC_ALLOC( char, nFuncs );
    uPerms  = ABC_ALLOC( char, nFuncs );
    uMap    = ABC_ALLOC( unsigned char, nFuncs );
    memset( uCanons, 0, sizeof(unsigned short) * nFuncs );
    memset( uPhases, 0, sizeof(char) * nFuncs );
    memset( uPerms,  0, sizeof(char) * nFuncs );
    memset( uMap,    0, sizeof(unsigned char) * nFuncs );
    pPerms4 = Extra_Permutations( 4 );

    nClasses = 1;
    nFuncs = (1 << 15);
    for ( uTruth = 1; uTruth < (unsigned)nFuncs; uTruth++ )
    {
        // skip already assigned
        if ( uCanons[uTruth] )
        {
            assert( uTruth > uCanons[uTruth] );
            uMap[~uTruth & 0xFFFF] = uMap[uTruth] = uMap[uCanons[uTruth]];
            continue;
        }
        uMap[uTruth] = nClasses++;
        for ( i = 0; i < 16; i++ )
        {
            uPhase = Extra_TruthPolarize( uTruth, i, 4 );
            for ( k = 0; k < 24; k++ )
            {
                uPerm = Extra_TruthPermute( uPhase, pPerms4[k], 4, 0 );
                if ( uCanons[uPerm] == 0 )
                {
                    uCanons[uPerm] = uTruth;
                    uPhases[uPerm] = i;
                    uPerms[uPerm]  = k;

                    uPerm = ~uPerm & 0xFFFF;
                    uCanons[uPerm] = uTruth;
                    uPhases[uPerm] = i | 16;
                    uPerms[uPerm]  = k;
                }
                else
                    assert( uCanons[uPerm] == uTruth );
            }
            uPhase = Extra_TruthPolarize( ~uTruth & 0xFFFF, i, 4 ); 
            for ( k = 0; k < 24; k++ )
            {
                uPerm = Extra_TruthPermute( uPhase, pPerms4[k], 4, 0 );
                if ( uCanons[uPerm] == 0 )
                {
                    uCanons[uPerm] = uTruth;
                    uPhases[uPerm] = i;
                    uPerms[uPerm]  = k;

                    uPerm = ~uPerm & 0xFFFF;
                    uCanons[uPerm] = uTruth;
                    uPhases[uPerm] = i | 16;
                    uPerms[uPerm]  = k;
                }
                else
                    assert( uCanons[uPerm] == uTruth );
            }
        }
    }
    uPhases[(1<<16)-1] = 16;
    assert( nClasses == 222 );
    ABC_FREE( pPerms4 );
    if ( puCanons ) 
        *puCanons = uCanons;
    else
        ABC_FREE( uCanons );
    if ( puPhases ) 
        *puPhases = uPhases;
    else
        ABC_FREE( uPhases );
    if ( puPerms ) 
        *puPerms = uPerms;
    else
        ABC_FREE( uPerms );
    if ( puMap ) 
        *puMap = uMap;
    else
        ABC_FREE( uMap );
}

/**Function*************************************************************

  Synopsis    [Computes NPN canonical forms for 4-variable functions.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_Truth3VarN( unsigned ** puCanons, char *** puPhases, char ** ppCounters )
{
    int nPhasesMax = 8;
    unsigned * uCanons;
    unsigned uTruth, uPhase, uTruth32;
    char ** uPhases, * pCounters;
    int nFuncs, nClasses, i;

    nFuncs  = (1 << 8);
    uCanons = ABC_ALLOC( unsigned, nFuncs );
    memset( uCanons, 0, sizeof(unsigned) * nFuncs );
    pCounters = ABC_ALLOC( char, nFuncs );
    memset( pCounters, 0, sizeof(char) * nFuncs );
    uPhases = (char **)Extra_ArrayAlloc( nFuncs, nPhasesMax, sizeof(char) );
    nClasses = 0;
    for ( uTruth = 0; uTruth < (unsigned)nFuncs; uTruth++ )
    {
        // skip already assigned
        uTruth32 = ((uTruth << 24) | (uTruth << 16) | (uTruth << 8) | uTruth);
        if ( uCanons[uTruth] )
        {
            assert( uTruth32 > uCanons[uTruth] );
            continue;
        }
        nClasses++;
        for ( i = 0; i < 8; i++ )
        {
            uPhase = Extra_TruthPolarize( uTruth, i, 3 );
            if ( uCanons[uPhase] == 0 && (uTruth || i==0) )
            {
                uCanons[uPhase]    = uTruth32;
                uPhases[uPhase][0] = i;
                pCounters[uPhase]  = 1;
            }
            else
            {
                assert( uCanons[uPhase] == uTruth32 );
                if ( pCounters[uPhase] < nPhasesMax )
                    uPhases[uPhase][ (int)pCounters[uPhase]++ ] = i;
            }
        }
    }
    if ( puCanons ) 
        *puCanons = uCanons;
    else
        ABC_FREE( uCanons );
    if ( puPhases ) 
        *puPhases = uPhases;
    else
        ABC_FREE( uPhases );
    if ( ppCounters ) 
        *ppCounters = pCounters;
    else
        ABC_FREE( pCounters );
//    printf( "The number of 3N-classes = %d.\n", nClasses );
}

/**Function*************************************************************

  Synopsis    [Computes NPN canonical forms for 4-variable functions.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_Truth4VarN( unsigned short ** puCanons, char *** puPhases, char ** ppCounters, int nPhasesMax )
{
    unsigned short * uCanons;
    unsigned uTruth, uPhase;
    char ** uPhases, * pCounters;
    int nFuncs, nClasses, i;

    nFuncs  = (1 << 16);
    uCanons = ABC_ALLOC( unsigned short, nFuncs );
    memset( uCanons, 0, sizeof(unsigned short) * nFuncs );
    pCounters = ABC_ALLOC( char, nFuncs );
    memset( pCounters, 0, sizeof(char) * nFuncs );
    uPhases = (char **)Extra_ArrayAlloc( nFuncs, nPhasesMax, sizeof(char) );
    nClasses = 0;
    for ( uTruth = 0; uTruth < (unsigned)nFuncs; uTruth++ )
    {
        // skip already assigned
        if ( uCanons[uTruth] )
        {
            assert( uTruth > uCanons[uTruth] );
            continue;
        }
        nClasses++;
        for ( i = 0; i < 16; i++ )
        {
            uPhase = Extra_TruthPolarize( uTruth, i, 4 );
            if ( uCanons[uPhase] == 0 && (uTruth || i==0) )
            {
                uCanons[uPhase]    = uTruth;
                uPhases[uPhase][0] = i;
                pCounters[uPhase]  = 1;
            }
            else
            {
                assert( uCanons[uPhase] == uTruth );
                if ( pCounters[uPhase] < nPhasesMax )
                    uPhases[uPhase][ (int)pCounters[uPhase]++ ] = i;
            }
        }
    }
    if ( puCanons ) 
        *puCanons = uCanons;
    else
        ABC_FREE( uCanons );
    if ( puPhases ) 
        *puPhases = uPhases;
    else
        ABC_FREE( uPhases );
    if ( ppCounters ) 
        *ppCounters = pCounters;
    else
        ABC_FREE( pCounters );
//    printf( "The number of 4N-classes = %d.\n", nClasses );
}

/**Function*************************************************************

  Synopsis    [Allocated one-memory-chunk array.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void ** Extra_ArrayAlloc( int nCols, int nRows, int Size )
{
    void ** pRes;
    char * pBuffer;
    int i;
    assert( nCols > 0 && nRows > 0 && Size > 0 );
    pBuffer = ABC_ALLOC( char, nCols * (sizeof(void *) + nRows * Size) );
    pRes = (void **)pBuffer;
    pRes[0] = pBuffer + nCols * sizeof(void *);
    for ( i = 1; i < nCols; i++ )
        pRes[i] = (void *)((char *)pRes[0] + i * nRows * Size);
    return pRes;
}

/**Function*************************************************************

  Synopsis    [Computes a phase of the 3-var function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned short Extra_TruthPerm4One( unsigned uTruth, int Phase )
{
    // cases
    static unsigned short Cases[16] = {
        0,      // 0000  - skip
        0,      // 0001  - skip
        0xCCCC, // 0010  - single var
        0,      // 0011  - skip
        0xF0F0, // 0100  - single var
        1,      // 0101
        1,      // 0110
        0,      // 0111  - skip
        0xFF00, // 1000  - single var
        1,      // 1001
        1,      // 1010
        1,      // 1011
        1,      // 1100
        1,      // 1101
        1,      // 1110
        0       // 1111  - skip
    };
    // permutations
    static int Perms[16][4] = {
        { 0, 0, 0, 0 }, // 0000  - skip
        { 0, 0, 0, 0 }, // 0001  - skip
        { 0, 0, 0, 0 }, // 0010  - single var
        { 0, 0, 0, 0 }, // 0011  - skip
        { 0, 0, 0, 0 }, // 0100  - single var
        { 0, 2, 1, 3 }, // 0101
        { 2, 0, 1, 3 }, // 0110
        { 0, 0, 0, 0 }, // 0111  - skip
        { 0, 0, 0, 0 }, // 1000  - single var
        { 0, 2, 3, 1 }, // 1001
        { 2, 0, 3, 1 }, // 1010
        { 0, 1, 3, 2 }, // 1011
        { 2, 3, 0, 1 }, // 1100
        { 0, 3, 1, 2 }, // 1101
        { 3, 0, 1, 2 }, // 1110
        { 0, 0, 0, 0 }  // 1111  - skip
    };
    int i, k, iRes;
    unsigned uTruthRes;
    assert( Phase >= 0 && Phase < 16 );
    if ( Cases[Phase] == 0 )
        return uTruth;
    if ( Cases[Phase] > 1 )
        return Cases[Phase];
    uTruthRes = 0;
    for ( i = 0; i < 16; i++ )
        if ( uTruth & (1 << i) )
        {
            for ( iRes = 0, k = 0; k < 4; k++ )
                if ( i & (1 << Perms[Phase][k]) )
                    iRes |= (1 << k);
            uTruthRes |= (1 << iRes);
        }
    return uTruthRes;
}

/**Function*************************************************************

  Synopsis    [Computes a phase of the 3-var function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned Extra_TruthPerm5One( unsigned uTruth, int Phase )
{
    // cases
    static unsigned Cases[32] = {
        0,          // 00000  - skip
        0,          // 00001  - skip
        0xCCCCCCCC, // 00010  - single var
        0,          // 00011  - skip
        0xF0F0F0F0, // 00100  - single var
        1,          // 00101
        1,          // 00110
        0,          // 00111  - skip
        0xFF00FF00, // 01000  - single var
        1,          // 01001
        1,          // 01010
        1,          // 01011
        1,          // 01100
        1,          // 01101
        1,          // 01110
        0,          // 01111  - skip
        0xFFFF0000, // 10000  - skip
        1,          // 10001
        1,          // 10010
        1,          // 10011
        1,          // 10100
        1,          // 10101
        1,          // 10110
        1,          // 10111  - four var
        1,          // 11000
        1,          // 11001
        1,          // 11010
        1,          // 11011  - four var
        1,          // 11100
        1,          // 11101  - four var
        1,          // 11110  - four var
        0           // 11111  - skip
    };
    // permutations
    static int Perms[32][5] = {
        { 0, 0, 0, 0, 0 }, // 00000  - skip
        { 0, 0, 0, 0, 0 }, // 00001  - skip
        { 0, 0, 0, 0, 0 }, // 00010  - single var
        { 0, 0, 0, 0, 0 }, // 00011  - skip
        { 0, 0, 0, 0, 0 }, // 00100  - single var
        { 0, 2, 1, 3, 4 }, // 00101
        { 2, 0, 1, 3, 4 }, // 00110
        { 0, 0, 0, 0, 0 }, // 00111  - skip
        { 0, 0, 0, 0, 0 }, // 01000  - single var
        { 0, 2, 3, 1, 4 }, // 01001
        { 2, 0, 3, 1, 4 }, // 01010
        { 0, 1, 3, 2, 4 }, // 01011
        { 2, 3, 0, 1, 4 }, // 01100
        { 0, 3, 1, 2, 4 }, // 01101
        { 3, 0, 1, 2, 4 }, // 01110
        { 0, 0, 0, 0, 0 }, // 01111  - skip
        { 0, 0, 0, 0, 0 }, // 10000  - single var
        { 0, 4, 2, 3, 1 }, // 10001
        { 4, 0, 2, 3, 1 }, // 10010
        { 0, 1, 3, 4, 2 }, // 10011
        { 2, 3, 0, 4, 1 }, // 10100
        { 0, 3, 1, 4, 2 }, // 10101
        { 3, 0, 1, 4, 2 }, // 10110
        { 0, 1, 2, 4, 3 }, // 10111  - four var
        { 2, 3, 4, 0, 1 }, // 11000
        { 0, 3, 4, 1, 2 }, // 11001
        { 3, 0, 4, 1, 2 }, // 11010
        { 0, 1, 4, 2, 3 }, // 11011  - four var
        { 3, 4, 0, 1, 2 }, // 11100
        { 0, 4, 1, 2, 3 }, // 11101  - four var
        { 4, 0, 1, 2, 3 }, // 11110  - four var
        { 0, 0, 0, 0, 0 }  // 11111  - skip
    };
    int i, k, iRes;
    unsigned uTruthRes;
    assert( Phase >= 0 && Phase < 32 );
    if ( Cases[Phase] == 0 )
        return uTruth;
    if ( Cases[Phase] > 1 )
        return Cases[Phase];
    uTruthRes = 0;
    for ( i = 0; i < 32; i++ )
        if ( uTruth & (1 << i) )
        {
            for ( iRes = 0, k = 0; k < 5; k++ )
                if ( i & (1 << Perms[Phase][k]) )
                    iRes |= (1 << k);
            uTruthRes |= (1 << iRes);
        }
    return uTruthRes;
}

/**Function*************************************************************

  Synopsis    [Computes a phase of the 3-var function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_TruthPerm6One( unsigned * uTruth, int Phase, unsigned * uTruthRes )
{
    // cases
    static unsigned Cases[64] = {
        0,          // 000000  - skip
        0,          // 000001  - skip
        0xCCCCCCCC, // 000010  - single var
        0,          // 000011  - skip
        0xF0F0F0F0, // 000100  - single var
        1,          // 000101
        1,          // 000110
        0,          // 000111  - skip
        0xFF00FF00, // 001000  - single var
        1,          // 001001
        1,          // 001010
        1,          // 001011
        1,          // 001100
        1,          // 001101
        1,          // 001110
        0,          // 001111  - skip
        0xFFFF0000, // 010000  - skip
        1,          // 010001
        1,          // 010010
        1,          // 010011
        1,          // 010100
        1,          // 010101
        1,          // 010110
        1,          // 010111  - four var
        1,          // 011000
        1,          // 011001
        1,          // 011010
        1,          // 011011  - four var
        1,          // 011100
        1,          // 011101  - four var
        1,          // 011110  - four var
        0,          // 011111  - skip
        0xFFFFFFFF, // 100000  - single var
        1,          // 100001 
        1,          // 100010  
        1,          // 100011  
        1,          // 100100  
        1,          // 100101
        1,          // 100110
        1,          // 100111  
        1,          // 101000  
        1,          // 101001
        1,          // 101010
        1,          // 101011
        1,          // 101100
        1,          // 101101
        1,          // 101110
        1,          // 101111  
        1,          // 110000  
        1,          // 110001
        1,          // 110010
        1,          // 110011
        1,          // 110100
        1,          // 110101
        1,          // 110110
        1,          // 110111  
        1,          // 111000
        1,          // 111001
        1,          // 111010
        1,          // 111011  
        1,          // 111100
        1,          // 111101  
        1,          // 111110  
        0           // 111111  - skip
    };
    // permutations
    static int Perms[64][6] = {
        { 0, 0, 0, 0, 0, 0 }, // 000000  - skip
        { 0, 0, 0, 0, 0, 0 }, // 000001  - skip
        { 0, 0, 0, 0, 0, 0 }, // 000010  - single var
        { 0, 0, 0, 0, 0, 0 }, // 000011  - skip
        { 0, 0, 0, 0, 0, 0 }, // 000100  - single var
        { 0, 2, 1, 3, 4, 5 }, // 000101
        { 2, 0, 1, 3, 4, 5 }, // 000110
        { 0, 0, 0, 0, 0, 0 }, // 000111  - skip
        { 0, 0, 0, 0, 0, 0 }, // 001000  - single var
        { 0, 2, 3, 1, 4, 5 }, // 001001
        { 2, 0, 3, 1, 4, 5 }, // 001010
        { 0, 1, 3, 2, 4, 5 }, // 001011
        { 2, 3, 0, 1, 4, 5 }, // 001100
        { 0, 3, 1, 2, 4, 5 }, // 001101
        { 3, 0, 1, 2, 4, 5 }, // 001110
        { 0, 0, 0, 0, 0, 0 }, // 001111  - skip
        { 0, 0, 0, 0, 0, 0 }, // 010000  - skip
        { 0, 4, 2, 3, 1, 5 }, // 010001
        { 4, 0, 2, 3, 1, 5 }, // 010010
        { 0, 1, 3, 4, 2, 5 }, // 010011
        { 2, 3, 0, 4, 1, 5 }, // 010100
        { 0, 3, 1, 4, 2, 5 }, // 010101
        { 3, 0, 1, 4, 2, 5 }, // 010110
        { 0, 1, 2, 4, 3, 5 }, // 010111  - four var
        { 2, 3, 4, 0, 1, 5 }, // 011000
        { 0, 3, 4, 1, 2, 5 }, // 011001
        { 3, 0, 4, 1, 2, 5 }, // 011010
        { 0, 1, 4, 2, 3, 5 }, // 011011  - four var
        { 3, 4, 0, 1, 2, 5 }, // 011100
        { 0, 4, 1, 2, 3, 5 }, // 011101  - four var
        { 4, 0, 1, 2, 3, 5 }, // 011110  - four var
        { 0, 0, 0, 0, 0, 0 }, // 011111  - skip
        { 0, 0, 0, 0, 0, 0 }, // 100000  - single var
        { 0, 2, 3, 4, 5, 1 }, // 100001 
        { 2, 0, 3, 4, 5, 1 }, // 100010  
        { 0, 1, 3, 4, 5, 2 }, // 100011  
        { 2, 3, 0, 4, 5, 1 }, // 100100  
        { 0, 3, 1, 4, 5, 2 }, // 100101
        { 3, 0, 1, 4, 5, 2 }, // 100110
        { 0, 1, 2, 4, 5, 3 }, // 100111  
        { 2, 3, 4, 0, 5, 1 }, // 101000  
        { 0, 3, 4, 1, 5, 2 }, // 101001
        { 3, 0, 4, 1, 5, 2 }, // 101010
        { 0, 1, 4, 2, 5, 3 }, // 101011
        { 3, 4, 0, 1, 5, 2 }, // 101100
        { 0, 4, 1, 2, 5, 3 }, // 101101
        { 4, 0, 1, 2, 5, 3 }, // 101110
        { 0, 1, 2, 3, 5, 4 }, // 101111  
        { 2, 3, 4, 5, 0, 1 }, // 110000  
        { 0, 3, 4, 5, 1, 2 }, // 110001
        { 3, 0, 4, 5, 1, 2 }, // 110010
        { 0, 1, 4, 5, 2, 3 }, // 110011
        { 3, 4, 0, 5, 1, 2 }, // 110100
        { 0, 4, 1, 5, 2, 3 }, // 110101
        { 4, 0, 1, 5, 2, 3 }, // 110110
        { 0, 1, 2, 5, 3, 4 }, // 110111  
        { 3, 4, 5, 0, 1, 2 }, // 111000
        { 0, 4, 5, 1, 2, 3 }, // 111001
        { 4, 0, 5, 1, 2, 3 }, // 111010
        { 0, 1, 5, 2, 3, 4 }, // 111011  
        { 4, 5, 0, 1, 2, 3 }, // 111100
        { 0, 5, 1, 2, 3, 4 }, // 111101  
        { 5, 0, 1, 2, 3, 4 }, // 111110  
        { 0, 0, 0, 0, 0, 0 }  // 111111  - skip
    };
    int i, k, iRes;
    assert( Phase >= 0 && Phase < 64 );
    if ( Cases[Phase] == 0 )
    {
        uTruthRes[0] = uTruth[0];
        uTruthRes[1] = uTruth[1];
        return;
    }
    if ( Cases[Phase] > 1 )
    {
        if ( Phase == 32 )
        {
            uTruthRes[0] = 0x00000000;
            uTruthRes[1] = 0xFFFFFFFF;
        }
        else
        {
            uTruthRes[0] = Cases[Phase];
            uTruthRes[1] = Cases[Phase];
        }
        return;
    }
    uTruthRes[0] = 0;
    uTruthRes[1] = 0;
    for ( i = 0; i < 64; i++ )
    {
        if ( i < 32 )
        {
            if ( uTruth[0] & (1 << i) )
            {
                for ( iRes = 0, k = 0; k < 6; k++ )
                    if ( i & (1 << Perms[Phase][k]) )
                        iRes |= (1 << k);
                if ( iRes < 32 )
                    uTruthRes[0] |= (1 << iRes);
                else
                    uTruthRes[1] |= (1 << (iRes-32));
            }
        }
        else
        {
            if ( uTruth[1] & (1 << (i-32)) )
            {
                for ( iRes = 0, k = 0; k < 6; k++ )
                    if ( i & (1 << Perms[Phase][k]) )
                        iRes |= (1 << k);
                if ( iRes < 32 )
                    uTruthRes[0] |= (1 << iRes);
                else
                    uTruthRes[1] |= (1 << (iRes-32));
            }
        }
    }
}

/**Function*************************************************************

  Synopsis    [Computes a phase of the 8-var function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_TruthExpand( int nVars, int nWords, unsigned * puTruth, unsigned uPhase, unsigned * puTruthR )
{
    // elementary truth tables
    static unsigned uTruths[8][8] = {
        { 0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA },
        { 0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC },
        { 0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0 },
        { 0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00 },
        { 0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000 }, 
        { 0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF }, 
        { 0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF }, 
        { 0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF } 
    };
    static char Cases[256] = {
         0, // 00000000
         0, // 00000001
         1, // 00000010
         0, // 00000011
         2, // 00000100
        -1, // 00000101
        -1, // 00000110
         0, // 00000111
         3, // 00001000
        -1, // 00001001
        -1, // 00001010
        -1, // 00001011
        -1, // 00001100
        -1, // 00001101
        -1, // 00001110
         0, // 00001111
         4, // 00010000
        -1, // 00010001
        -1, // 00010010
        -1, // 00010011
        -1, // 00010100
        -1, // 00010101
        -1, // 00010110
        -1, // 00010111
        -1, // 00011000
        -1, // 00011001
        -1, // 00011010
        -1, // 00011011
        -1, // 00011100
        -1, // 00011101
        -1, // 00011110
         0, // 00011111
         5, // 00100000
        -1, // 00100001
        -1, // 00100010
        -1, // 00100011
        -1, // 00100100
        -1, // 00100101
        -1, // 00100110
        -1, // 00100111
        -1, // 00101000
        -1, // 00101001
        -1, // 00101010
        -1, // 00101011
        -1, // 00101100
        -1, // 00101101
        -1, // 00101110
        -1, // 00101111
        -1, // 00110000
        -1, // 00110001
        -1, // 00110010
        -1, // 00110011
        -1, // 00110100
        -1, // 00110101
        -1, // 00110110
        -1, // 00110111
        -1, // 00111000
        -1, // 00111001
        -1, // 00111010
        -1, // 00111011
        -1, // 00111100
        -1, // 00111101
        -1, // 00111110
         0, // 00111111
         6, // 01000000
        -1, // 01000001
        -1, // 01000010
        -1, // 01000011
        -1, // 01000100
        -1, // 01000101
        -1, // 01000110
        -1, // 01000111
        -1, // 01001000
        -1, // 01001001
        -1, // 01001010
        -1, // 01001011
        -1, // 01001100
        -1, // 01001101
        -1, // 01001110
        -1, // 01001111
        -1, // 01010000
        -1, // 01010001
        -1, // 01010010
        -1, // 01010011
        -1, // 01010100
        -1, // 01010101
        -1, // 01010110
        -1, // 01010111
        -1, // 01011000
        -1, // 01011001
        -1, // 01011010
        -1, // 01011011
        -1, // 01011100
        -1, // 01011101
        -1, // 01011110
        -1, // 01011111
        -1, // 01100000
        -1, // 01100001
        -1, // 01100010
        -1, // 01100011
        -1, // 01100100
        -1, // 01100101
        -1, // 01100110
        -1, // 01100111
        -1, // 01101000
        -1, // 01101001
        -1, // 01101010
        -1, // 01101011
        -1, // 01101100
        -1, // 01101101
        -1, // 01101110
        -1, // 01101111
        -1, // 01110000
        -1, // 01110001
        -1, // 01110010
        -1, // 01110011
        -1, // 01110100
        -1, // 01110101
        -1, // 01110110
        -1, // 01110111
        -1, // 01111000
        -1, // 01111001
        -1, // 01111010
        -1, // 01111011
        -1, // 01111100
        -1, // 01111101
        -1, // 01111110
         0, // 01111111
         7, // 10000000
        -1, // 10000001
        -1, // 10000010
        -1, // 10000011
        -1, // 10000100
        -1, // 10000101
        -1, // 10000110
        -1, // 10000111
        -1, // 10001000
        -1, // 10001001
        -1, // 10001010
        -1, // 10001011
        -1, // 10001100
        -1, // 10001101
        -1, // 10001110
        -1, // 10001111
        -1, // 10010000
        -1, // 10010001
        -1, // 10010010
        -1, // 10010011
        -1, // 10010100
        -1, // 10010101
        -1, // 10010110
        -1, // 10010111
        -1, // 10011000
        -1, // 10011001
        -1, // 10011010
        -1, // 10011011
        -1, // 10011100
        -1, // 10011101
        -1, // 10011110
        -1, // 10011111
        -1, // 10100000
        -1, // 10100001
        -1, // 10100010
        -1, // 10100011
        -1, // 10100100
        -1, // 10100101
        -1, // 10100110
        -1, // 10100111
        -1, // 10101000
        -1, // 10101001
        -1, // 10101010
        -1, // 10101011
        -1, // 10101100
        -1, // 10101101
        -1, // 10101110
        -1, // 10101111
        -1, // 10110000
        -1, // 10110001
        -1, // 10110010
        -1, // 10110011
        -1, // 10110100
        -1, // 10110101
        -1, // 10110110
        -1, // 10110111
        -1, // 10111000
        -1, // 10111001
        -1, // 10111010
        -1, // 10111011
        -1, // 10111100
        -1, // 10111101
        -1, // 10111110
        -1, // 10111111
        -1, // 11000000
        -1, // 11000001
        -1, // 11000010
        -1, // 11000011
        -1, // 11000100
        -1, // 11000101
        -1, // 11000110
        -1, // 11000111
        -1, // 11001000
        -1, // 11001001
        -1, // 11001010
        -1, // 11001011
        -1, // 11001100
        -1, // 11001101
        -1, // 11001110
        -1, // 11001111
        -1, // 11010000
        -1, // 11010001
        -1, // 11010010
        -1, // 11010011
        -1, // 11010100
        -1, // 11010101
        -1, // 11010110
        -1, // 11010111
        -1, // 11011000
        -1, // 11011001
        -1, // 11011010
        -1, // 11011011
        -1, // 11011100
        -1, // 11011101
        -1, // 11011110
        -1, // 11011111
        -1, // 11100000
        -1, // 11100001
        -1, // 11100010
        -1, // 11100011
        -1, // 11100100
        -1, // 11100101
        -1, // 11100110
        -1, // 11100111
        -1, // 11101000
        -1, // 11101001
        -1, // 11101010
        -1, // 11101011
        -1, // 11101100
        -1, // 11101101
        -1, // 11101110
        -1, // 11101111
        -1, // 11110000
        -1, // 11110001
        -1, // 11110010
        -1, // 11110011
        -1, // 11110100
        -1, // 11110101
        -1, // 11110110
        -1, // 11110111
        -1, // 11111000
        -1, // 11111001
        -1, // 11111010
        -1, // 11111011
        -1, // 11111100
        -1, // 11111101
        -1, // 11111110
         0  // 11111111
    };
    static char Perms[256][8] = {
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00000000
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00000001
        { 1, 0, 2, 3, 4, 5, 6, 7 }, // 00000010
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00000011
        { 1, 2, 0, 3, 4, 5, 6, 7 }, // 00000100
        { 0, 2, 1, 3, 4, 5, 6, 7 }, // 00000101
        { 2, 0, 1, 3, 4, 5, 6, 7 }, // 00000110
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00000111
        { 1, 2, 3, 0, 4, 5, 6, 7 }, // 00001000
        { 0, 2, 3, 1, 4, 5, 6, 7 }, // 00001001
        { 2, 0, 3, 1, 4, 5, 6, 7 }, // 00001010
        { 0, 1, 3, 2, 4, 5, 6, 7 }, // 00001011
        { 2, 3, 0, 1, 4, 5, 6, 7 }, // 00001100
        { 0, 3, 1, 2, 4, 5, 6, 7 }, // 00001101
        { 3, 0, 1, 2, 4, 5, 6, 7 }, // 00001110
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00001111
        { 1, 2, 3, 4, 0, 5, 6, 7 }, // 00010000
        { 0, 2, 3, 4, 1, 5, 6, 7 }, // 00010001
        { 2, 0, 3, 4, 1, 5, 6, 7 }, // 00010010
        { 0, 1, 3, 4, 2, 5, 6, 7 }, // 00010011
        { 2, 3, 0, 4, 1, 5, 6, 7 }, // 00010100
        { 0, 3, 1, 4, 2, 5, 6, 7 }, // 00010101
        { 3, 0, 1, 4, 2, 5, 6, 7 }, // 00010110
        { 0, 1, 2, 4, 3, 5, 6, 7 }, // 00010111
        { 2, 3, 4, 0, 1, 5, 6, 7 }, // 00011000
        { 0, 3, 4, 1, 2, 5, 6, 7 }, // 00011001
        { 3, 0, 4, 1, 2, 5, 6, 7 }, // 00011010
        { 0, 1, 4, 2, 3, 5, 6, 7 }, // 00011011
        { 3, 4, 0, 1, 2, 5, 6, 7 }, // 00011100
        { 0, 4, 1, 2, 3, 5, 6, 7 }, // 00011101
        { 4, 0, 1, 2, 3, 5, 6, 7 }, // 00011110
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00011111
        { 1, 2, 3, 4, 5, 0, 6, 7 }, // 00100000
        { 0, 2, 3, 4, 5, 1, 6, 7 }, // 00100001
        { 2, 0, 3, 4, 5, 1, 6, 7 }, // 00100010
        { 0, 1, 3, 4, 5, 2, 6, 7 }, // 00100011
        { 2, 3, 0, 4, 5, 1, 6, 7 }, // 00100100
        { 0, 3, 1, 4, 5, 2, 6, 7 }, // 00100101
        { 3, 0, 1, 4, 5, 2, 6, 7 }, // 00100110
        { 0, 1, 2, 4, 5, 3, 6, 7 }, // 00100111
        { 2, 3, 4, 0, 5, 1, 6, 7 }, // 00101000
        { 0, 3, 4, 1, 5, 2, 6, 7 }, // 00101001
        { 3, 0, 4, 1, 5, 2, 6, 7 }, // 00101010
        { 0, 1, 4, 2, 5, 3, 6, 7 }, // 00101011
        { 3, 4, 0, 1, 5, 2, 6, 7 }, // 00101100
        { 0, 4, 1, 2, 5, 3, 6, 7 }, // 00101101
        { 4, 0, 1, 2, 5, 3, 6, 7 }, // 00101110
        { 0, 1, 2, 3, 5, 4, 6, 7 }, // 00101111
        { 2, 3, 4, 5, 0, 1, 6, 7 }, // 00110000
        { 0, 3, 4, 5, 1, 2, 6, 7 }, // 00110001
        { 3, 0, 4, 5, 1, 2, 6, 7 }, // 00110010
        { 0, 1, 4, 5, 2, 3, 6, 7 }, // 00110011
        { 3, 4, 0, 5, 1, 2, 6, 7 }, // 00110100
        { 0, 4, 1, 5, 2, 3, 6, 7 }, // 00110101
        { 4, 0, 1, 5, 2, 3, 6, 7 }, // 00110110
        { 0, 1, 2, 5, 3, 4, 6, 7 }, // 00110111
        { 3, 4, 5, 0, 1, 2, 6, 7 }, // 00111000
        { 0, 4, 5, 1, 2, 3, 6, 7 }, // 00111001
        { 4, 0, 5, 1, 2, 3, 6, 7 }, // 00111010
        { 0, 1, 5, 2, 3, 4, 6, 7 }, // 00111011
        { 4, 5, 0, 1, 2, 3, 6, 7 }, // 00111100
        { 0, 5, 1, 2, 3, 4, 6, 7 }, // 00111101
        { 5, 0, 1, 2, 3, 4, 6, 7 }, // 00111110
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 00111111
        { 1, 2, 3, 4, 5, 6, 0, 7 }, // 01000000
        { 0, 2, 3, 4, 5, 6, 1, 7 }, // 01000001
        { 2, 0, 3, 4, 5, 6, 1, 7 }, // 01000010
        { 0, 1, 3, 4, 5, 6, 2, 7 }, // 01000011
        { 2, 3, 0, 4, 5, 6, 1, 7 }, // 01000100
        { 0, 3, 1, 4, 5, 6, 2, 7 }, // 01000101
        { 3, 0, 1, 4, 5, 6, 2, 7 }, // 01000110
        { 0, 1, 2, 4, 5, 6, 3, 7 }, // 01000111
        { 2, 3, 4, 0, 5, 6, 1, 7 }, // 01001000
        { 0, 3, 4, 1, 5, 6, 2, 7 }, // 01001001
        { 3, 0, 4, 1, 5, 6, 2, 7 }, // 01001010
        { 0, 1, 4, 2, 5, 6, 3, 7 }, // 01001011
        { 3, 4, 0, 1, 5, 6, 2, 7 }, // 01001100
        { 0, 4, 1, 2, 5, 6, 3, 7 }, // 01001101
        { 4, 0, 1, 2, 5, 6, 3, 7 }, // 01001110
        { 0, 1, 2, 3, 5, 6, 4, 7 }, // 01001111
        { 2, 3, 4, 5, 0, 6, 1, 7 }, // 01010000
        { 0, 3, 4, 5, 1, 6, 2, 7 }, // 01010001
        { 3, 0, 4, 5, 1, 6, 2, 7 }, // 01010010
        { 0, 1, 4, 5, 2, 6, 3, 7 }, // 01010011
        { 3, 4, 0, 5, 1, 6, 2, 7 }, // 01010100
        { 0, 4, 1, 5, 2, 6, 3, 7 }, // 01010101
        { 4, 0, 1, 5, 2, 6, 3, 7 }, // 01010110
        { 0, 1, 2, 5, 3, 6, 4, 7 }, // 01010111
        { 3, 4, 5, 0, 1, 6, 2, 7 }, // 01011000
        { 0, 4, 5, 1, 2, 6, 3, 7 }, // 01011001
        { 4, 0, 5, 1, 2, 6, 3, 7 }, // 01011010
        { 0, 1, 5, 2, 3, 6, 4, 7 }, // 01011011
        { 4, 5, 0, 1, 2, 6, 3, 7 }, // 01011100
        { 0, 5, 1, 2, 3, 6, 4, 7 }, // 01011101
        { 5, 0, 1, 2, 3, 6, 4, 7 }, // 01011110
        { 0, 1, 2, 3, 4, 6, 5, 7 }, // 01011111
        { 2, 3, 4, 5, 6, 0, 1, 7 }, // 01100000
        { 0, 3, 4, 5, 6, 1, 2, 7 }, // 01100001
        { 3, 0, 4, 5, 6, 1, 2, 7 }, // 01100010
        { 0, 1, 4, 5, 6, 2, 3, 7 }, // 01100011
        { 3, 4, 0, 5, 6, 1, 2, 7 }, // 01100100
        { 0, 4, 1, 5, 6, 2, 3, 7 }, // 01100101
        { 4, 0, 1, 5, 6, 2, 3, 7 }, // 01100110
        { 0, 1, 2, 5, 6, 3, 4, 7 }, // 01100111
        { 3, 4, 5, 0, 6, 1, 2, 7 }, // 01101000
        { 0, 4, 5, 1, 6, 2, 3, 7 }, // 01101001
        { 4, 0, 5, 1, 6, 2, 3, 7 }, // 01101010
        { 0, 1, 5, 2, 6, 3, 4, 7 }, // 01101011
        { 4, 5, 0, 1, 6, 2, 3, 7 }, // 01101100
        { 0, 5, 1, 2, 6, 3, 4, 7 }, // 01101101
        { 5, 0, 1, 2, 6, 3, 4, 7 }, // 01101110
        { 0, 1, 2, 3, 6, 4, 5, 7 }, // 01101111
        { 3, 4, 5, 6, 0, 1, 2, 7 }, // 01110000
        { 0, 4, 5, 6, 1, 2, 3, 7 }, // 01110001
        { 4, 0, 5, 6, 1, 2, 3, 7 }, // 01110010
        { 0, 1, 5, 6, 2, 3, 4, 7 }, // 01110011
        { 4, 5, 0, 6, 1, 2, 3, 7 }, // 01110100
        { 0, 5, 1, 6, 2, 3, 4, 7 }, // 01110101
        { 5, 0, 1, 6, 2, 3, 4, 7 }, // 01110110
        { 0, 1, 2, 6, 3, 4, 5, 7 }, // 01110111
        { 4, 5, 6, 0, 1, 2, 3, 7 }, // 01111000
        { 0, 5, 6, 1, 2, 3, 4, 7 }, // 01111001
        { 5, 0, 6, 1, 2, 3, 4, 7 }, // 01111010
        { 0, 1, 6, 2, 3, 4, 5, 7 }, // 01111011
        { 5, 6, 0, 1, 2, 3, 4, 7 }, // 01111100
        { 0, 6, 1, 2, 3, 4, 5, 7 }, // 01111101
        { 6, 0, 1, 2, 3, 4, 5, 7 }, // 01111110
        { 0, 1, 2, 3, 4, 5, 6, 7 }, // 01111111
        { 1, 2, 3, 4, 5, 6, 7, 0 }, // 10000000
        { 0, 2, 3, 4, 5, 6, 7, 1 }, // 10000001
        { 2, 0, 3, 4, 5, 6, 7, 1 }, // 10000010
        { 0, 1, 3, 4, 5, 6, 7, 2 }, // 10000011
        { 2, 3, 0, 4, 5, 6, 7, 1 }, // 10000100
        { 0, 3, 1, 4, 5, 6, 7, 2 }, // 10000101
        { 3, 0, 1, 4, 5, 6, 7, 2 }, // 10000110
        { 0, 1, 2, 4, 5, 6, 7, 3 }, // 10000111
        { 2, 3, 4, 0, 5, 6, 7, 1 }, // 10001000
        { 0, 3, 4, 1, 5, 6, 7, 2 }, // 10001001
        { 3, 0, 4, 1, 5, 6, 7, 2 }, // 10001010
        { 0, 1, 4, 2, 5, 6, 7, 3 }, // 10001011
        { 3, 4, 0, 1, 5, 6, 7, 2 }, // 10001100
        { 0, 4, 1, 2, 5, 6, 7, 3 }, // 10001101
        { 4, 0, 1, 2, 5, 6, 7, 3 }, // 10001110
        { 0, 1, 2, 3, 5, 6, 7, 4 }, // 10001111
        { 2, 3, 4, 5, 0, 6, 7, 1 }, // 10010000
        { 0, 3, 4, 5, 1, 6, 7, 2 }, // 10010001
        { 3, 0, 4, 5, 1, 6, 7, 2 }, // 10010010
        { 0, 1, 4, 5, 2, 6, 7, 3 }, // 10010011
        { 3, 4, 0, 5, 1, 6, 7, 2 }, // 10010100
        { 0, 4, 1, 5, 2, 6, 7, 3 }, // 10010101
        { 4, 0, 1, 5, 2, 6, 7, 3 }, // 10010110
        { 0, 1, 2, 5, 3, 6, 7, 4 }, // 10010111
        { 3, 4, 5, 0, 1, 6, 7, 2 }, // 10011000
        { 0, 4, 5, 1, 2, 6, 7, 3 }, // 10011001
        { 4, 0, 5, 1, 2, 6, 7, 3 }, // 10011010
        { 0, 1, 5, 2, 3, 6, 7, 4 }, // 10011011
        { 4, 5, 0, 1, 2, 6, 7, 3 }, // 10011100
        { 0, 5, 1, 2, 3, 6, 7, 4 }, // 10011101
        { 5, 0, 1, 2, 3, 6, 7, 4 }, // 10011110
        { 0, 1, 2, 3, 4, 6, 7, 5 }, // 10011111
        { 2, 3, 4, 5, 6, 0, 7, 1 }, // 10100000
        { 0, 3, 4, 5, 6, 1, 7, 2 }, // 10100001
        { 3, 0, 4, 5, 6, 1, 7, 2 }, // 10100010
        { 0, 1, 4, 5, 6, 2, 7, 3 }, // 10100011
        { 3, 4, 0, 5, 6, 1, 7, 2 }, // 10100100
        { 0, 4, 1, 5, 6, 2, 7, 3 }, // 10100101
        { 4, 0, 1, 5, 6, 2, 7, 3 }, // 10100110
        { 0, 1, 2, 5, 6, 3, 7, 4 }, // 10100111
        { 3, 4, 5, 0, 6, 1, 7, 2 }, // 10101000
        { 0, 4, 5, 1, 6, 2, 7, 3 }, // 10101001
        { 4, 0, 5, 1, 6, 2, 7, 3 }, // 10101010
        { 0, 1, 5, 2, 6, 3, 7, 4 }, // 10101011
        { 4, 5, 0, 1, 6, 2, 7, 3 }, // 10101100
        { 0, 5, 1, 2, 6, 3, 7, 4 }, // 10101101
        { 5, 0, 1, 2, 6, 3, 7, 4 }, // 10101110
        { 0, 1, 2, 3, 6, 4, 7, 5 }, // 10101111
        { 3, 4, 5, 6, 0, 1, 7, 2 }, // 10110000
        { 0, 4, 5, 6, 1, 2, 7, 3 }, // 10110001
        { 4, 0, 5, 6, 1, 2, 7, 3 }, // 10110010
        { 0, 1, 5, 6, 2, 3, 7, 4 }, // 10110011
        { 4, 5, 0, 6, 1, 2, 7, 3 }, // 10110100
        { 0, 5, 1, 6, 2, 3, 7, 4 }, // 10110101
        { 5, 0, 1, 6, 2, 3, 7, 4 }, // 10110110
        { 0, 1, 2, 6, 3, 4, 7, 5 }, // 10110111
        { 4, 5, 6, 0, 1, 2, 7, 3 }, // 10111000
        { 0, 5, 6, 1, 2, 3, 7, 4 }, // 10111001
        { 5, 0, 6, 1, 2, 3, 7, 4 }, // 10111010
        { 0, 1, 6, 2, 3, 4, 7, 5 }, // 10111011
        { 5, 6, 0, 1, 2, 3, 7, 4 }, // 10111100
        { 0, 6, 1, 2, 3, 4, 7, 5 }, // 10111101
        { 6, 0, 1, 2, 3, 4, 7, 5 }, // 10111110
        { 0, 1, 2, 3, 4, 5, 7, 6 }, // 10111111
        { 2, 3, 4, 5, 6, 7, 0, 1 }, // 11000000
        { 0, 3, 4, 5, 6, 7, 1, 2 }, // 11000001
        { 3, 0, 4, 5, 6, 7, 1, 2 }, // 11000010
        { 0, 1, 4, 5, 6, 7, 2, 3 }, // 11000011
        { 3, 4, 0, 5, 6, 7, 1, 2 }, // 11000100
        { 0, 4, 1, 5, 6, 7, 2, 3 }, // 11000101
        { 4, 0, 1, 5, 6, 7, 2, 3 }, // 11000110
        { 0, 1, 2, 5, 6, 7, 3, 4 }, // 11000111
        { 3, 4, 5, 0, 6, 7, 1, 2 }, // 11001000
        { 0, 4, 5, 1, 6, 7, 2, 3 }, // 11001001
        { 4, 0, 5, 1, 6, 7, 2, 3 }, // 11001010
        { 0, 1, 5, 2, 6, 7, 3, 4 }, // 11001011
        { 4, 5, 0, 1, 6, 7, 2, 3 }, // 11001100
        { 0, 5, 1, 2, 6, 7, 3, 4 }, // 11001101
        { 5, 0, 1, 2, 6, 7, 3, 4 }, // 11001110
        { 0, 1, 2, 3, 6, 7, 4, 5 }, // 11001111
        { 3, 4, 5, 6, 0, 7, 1, 2 }, // 11010000
        { 0, 4, 5, 6, 1, 7, 2, 3 }, // 11010001
        { 4, 0, 5, 6, 1, 7, 2, 3 }, // 11010010
        { 0, 1, 5, 6, 2, 7, 3, 4 }, // 11010011
        { 4, 5, 0, 6, 1, 7, 2, 3 }, // 11010100
        { 0, 5, 1, 6, 2, 7, 3, 4 }, // 11010101
        { 5, 0, 1, 6, 2, 7, 3, 4 }, // 11010110
        { 0, 1, 2, 6, 3, 7, 4, 5 }, // 11010111
        { 4, 5, 6, 0, 1, 7, 2, 3 }, // 11011000
        { 0, 5, 6, 1, 2, 7, 3, 4 }, // 11011001
        { 5, 0, 6, 1, 2, 7, 3, 4 }, // 11011010
        { 0, 1, 6, 2, 3, 7, 4, 5 }, // 11011011
        { 5, 6, 0, 1, 2, 7, 3, 4 }, // 11011100
        { 0, 6, 1, 2, 3, 7, 4, 5 }, // 11011101
        { 6, 0, 1, 2, 3, 7, 4, 5 }, // 11011110
        { 0, 1, 2, 3, 4, 7, 5, 6 }, // 11011111
        { 3, 4, 5, 6, 7, 0, 1, 2 }, // 11100000
        { 0, 4, 5, 6, 7, 1, 2, 3 }, // 11100001
        { 4, 0, 5, 6, 7, 1, 2, 3 }, // 11100010
        { 0, 1, 5, 6, 7, 2, 3, 4 }, // 11100011
        { 4, 5, 0, 6, 7, 1, 2, 3 }, // 11100100
        { 0, 5, 1, 6, 7, 2, 3, 4 }, // 11100101
        { 5, 0, 1, 6, 7, 2, 3, 4 }, // 11100110
        { 0, 1, 2, 6, 7, 3, 4, 5 }, // 11100111
        { 4, 5, 6, 0, 7, 1, 2, 3 }, // 11101000
        { 0, 5, 6, 1, 7, 2, 3, 4 }, // 11101001
        { 5, 0, 6, 1, 7, 2, 3, 4 }, // 11101010
        { 0, 1, 6, 2, 7, 3, 4, 5 }, // 11101011
        { 5, 6, 0, 1, 7, 2, 3, 4 }, // 11101100
        { 0, 6, 1, 2, 7, 3, 4, 5 }, // 11101101
        { 6, 0, 1, 2, 7, 3, 4, 5 }, // 11101110
        { 0, 1, 2, 3, 7, 4, 5, 6 }, // 11101111
        { 4, 5, 6, 7, 0, 1, 2, 3 }, // 11110000
        { 0, 5, 6, 7, 1, 2, 3, 4 }, // 11110001
        { 5, 0, 6, 7, 1, 2, 3, 4 }, // 11110010
        { 0, 1, 6, 7, 2, 3, 4, 5 }, // 11110011
        { 5, 6, 0, 7, 1, 2, 3, 4 }, // 11110100
        { 0, 6, 1, 7, 2, 3, 4, 5 }, // 11110101
        { 6, 0, 1, 7, 2, 3, 4, 5 }, // 11110110
        { 0, 1, 2, 7, 3, 4, 5, 6 }, // 11110111
        { 5, 6, 7, 0, 1, 2, 3, 4 }, // 11111000
        { 0, 6, 7, 1, 2, 3, 4, 5 }, // 11111001
        { 6, 0, 7, 1, 2, 3, 4, 5 }, // 11111010
        { 0, 1, 7, 2, 3, 4, 5, 6 }, // 11111011
        { 6, 7, 0, 1, 2, 3, 4, 5 }, // 11111100
        { 0, 7, 1, 2, 3, 4, 5, 6 }, // 11111101
        { 7, 0, 1, 2, 3, 4, 5, 6 }, // 11111110
        { 0, 1, 2, 3, 4, 5, 6, 7 }  // 11111111
    };

    assert( uPhase > 0 && uPhase < (unsigned)(1 << nVars) );

    // the same function
    if ( Cases[uPhase] == 0 )
    {
        int i;
        for ( i = 0; i < nWords; i++ )
            puTruthR[i] = puTruth[i];
        return;
    }

    // an elementary variable
    if ( Cases[uPhase] > 0 )
    {
        int i;
        for ( i = 0; i < nWords; i++ )
            puTruthR[i] = uTruths[(int)Cases[uPhase]][i];
        return;
    }

    // truth table takes one word
    if ( nWords == 1 )
    {
        int i, k, nMints, iRes;
        char * pPerm = Perms[uPhase];
        puTruthR[0] = 0;
        nMints = (1 << nVars);
        for ( i = 0; i < nMints; i++ )
            if ( puTruth[0] & (1 << i) )
            {
                for ( iRes = 0, k = 0; k < nVars; k++ )
                    if ( i & (1 << pPerm[k]) )
                        iRes |= (1 << k);
                puTruthR[0] |= (1 << iRes);
            }
        return;
    }
    else if ( nWords == 2 )
    {
        int i, k, iRes;
        char * pPerm = Perms[uPhase];
        puTruthR[0] = puTruthR[1] = 0;
        for ( i = 0; i < 32; i++ )
        {
            if ( puTruth[0] & (1 << i) )
            {
                for ( iRes = 0, k = 0; k < 6; k++ )
                    if ( i & (1 << pPerm[k]) )
                        iRes |= (1 << k);
                if ( iRes < 32 )
                    puTruthR[0] |= (1 << iRes);
                else
                    puTruthR[1] |= (1 << (iRes-32));
            }
        }
        for ( ; i < 64; i++ )
        {
            if ( puTruth[1] & (1 << (i-32)) )
            {
                for ( iRes = 0, k = 0; k < 6; k++ )
                    if ( i & (1 << pPerm[k]) )
                        iRes |= (1 << k);
                if ( iRes < 32 )
                    puTruthR[0] |= (1 << iRes);
                else
                    puTruthR[1] |= (1 << (iRes-32));
            }
        }
    }
    // truth table takes more than one word
    else
    {
        int i, k, nMints, iRes;
        char * pPerm = Perms[uPhase];
        for ( i = 0; i < nWords; i++ )
            puTruthR[i] = 0;
        nMints = (1 << nVars);
        for ( i = 0; i < nMints; i++ )
            if ( puTruth[i>>5] & (1 << (i&31)) )
            {
                for ( iRes = 0, k = 0; k < 5; k++ )
                    if ( i & (1 << pPerm[k]) )
                        iRes |= (1 << k);
                puTruthR[iRes>>5] |= (1 << (iRes&31));
            }
    }
}

/**Function*************************************************************

  Synopsis    [Allocated lookup table for truth table permutation.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned short ** Extra_TruthPerm43()
{
    unsigned short ** pTable;
    unsigned uTruth;
    int i, k;
    pTable = (unsigned short **)Extra_ArrayAlloc( 256, 16, 2 );
    for ( i = 0; i < 256; i++ )
    {
        uTruth = (i << 8) | i;
        for ( k = 0; k < 16; k++ )
            pTable[i][k] = Extra_TruthPerm4One( uTruth, k );
    }
    return pTable;
}

/**Function*************************************************************

  Synopsis    [Allocated lookup table for truth table permutation.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned ** Extra_TruthPerm53()
{
    unsigned ** pTable;
    unsigned uTruth;
    int i, k;
    pTable = (unsigned **)Extra_ArrayAlloc( 256, 32, 4 );
    for ( i = 0; i < 256; i++ )
    {
        uTruth = (i << 24) | (i << 16) | (i << 8) | i;
        for ( k = 0; k < 32; k++ )
            pTable[i][k] = Extra_TruthPerm5One( uTruth, k );
    }
    return pTable;
}

/**Function*************************************************************

  Synopsis    [Allocated lookup table for truth table permutation.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned ** Extra_TruthPerm54()
{
    unsigned ** pTable;
    unsigned uTruth;
    int i;
    pTable = (unsigned **)Extra_ArrayAlloc( 256*256, 4, 4 );
    for ( i = 0; i < 256*256; i++ )
    {
        uTruth = (i << 16) | i;
        pTable[i][0] = Extra_TruthPerm5One( uTruth, 31-8 );
        pTable[i][1] = Extra_TruthPerm5One( uTruth, 31-4 );
        pTable[i][2] = Extra_TruthPerm5One( uTruth, 31-2 );
        pTable[i][3] = Extra_TruthPerm5One( uTruth, 31-1 );
    }
    return pTable;
}

/**Function*************************************************************

  Synopsis    [Allocated lookup table for truth table permutation.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned ** Extra_TruthPerm63()
{
    unsigned ** pTable;
    unsigned uTruth[2];
    int i, k;
    pTable = (unsigned **)Extra_ArrayAlloc( 256, 64, 8 );
    for ( i = 0; i < 256; i++ )
    {
        uTruth[0] = (i << 24) | (i << 16) | (i << 8) | i;
        uTruth[1] = uTruth[0];
        for ( k = 0; k < 64; k++ )
            Extra_TruthPerm6One( uTruth, k, &pTable[i][k] );
    }
    return pTable;
}

/**Function*************************************************************

  Synopsis    [Returns the pointer to the elementary truth tables.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
unsigned ** Extra_Truths8()
{
    static unsigned uTruths[8][8] = {
        { 0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA,0xAAAAAAAA },
        { 0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC,0xCCCCCCCC },
        { 0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0,0xF0F0F0F0 },
        { 0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00,0xFF00FF00 },
        { 0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000,0xFFFF0000 }, 
        { 0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF,0x00000000,0xFFFFFFFF }, 
        { 0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF }, 
        { 0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF } 
    };
    static unsigned * puResult[8] = {
        uTruths[0], uTruths[1], uTruths[2], uTruths[3], uTruths[4], uTruths[5], uTruths[6], uTruths[7] 
    };
    return (unsigned **)puResult;
}

/**Function*************************************************************

  Synopsis    [Bubble-sorts components by scores in increasing order.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_BubbleSort( int Order[], int Costs[], int nSize, int fIncreasing )
{
    int i, Temp, fChanges;
    assert( nSize < 1000 );
    for ( i = 0; i < nSize; i++ )
        Order[i] = i;
    if ( fIncreasing )
    {
        do {
            fChanges = 0;
            for ( i = 0; i < nSize - 1; i++ )
            {
                if ( Costs[Order[i]] <= Costs[Order[i+1]] )
                    continue;
                Temp = Order[i];
                Order[i] = Order[i+1];
                Order[i+1] = Temp;
                fChanges = 1;
            }
        } while ( fChanges );
    }
    else
    {
        do {
            fChanges = 0;
            for ( i = 0; i < nSize - 1; i++ )
            {
                if ( Costs[Order[i]] >= Costs[Order[i+1]] )
                    continue;
                Temp = Order[i];
                Order[i] = Order[i+1];
                Order[i+1] = Temp;
                fChanges = 1;
            }
        } while ( fChanges );
    }
}


/*---------------------------------------------------------------------------*/
/* Definition of internal functions                                          */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Definition of static Functions                                            */
/*---------------------------------------------------------------------------*/


/**Function*************************************************************

  Synopsis    [Computes the permutation table for 8 variables.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_TruthExpandGeneratePermTable()
{
    int i, k, nOnes, Last1, First0;
    int iOne, iZero;

    printf( "\nstatic char Cases[256] = {\n" );
    for ( i = 0; i < 256; i++ )
    {
        nOnes = 0;
        Last1 = First0 = -1;
        for ( k = 0; k < 8; k++ )
        {
            if ( i & (1 << k) )
            {
                nOnes++;
                Last1 = k;
            }
            else if ( First0 == -1 )
                First0 = k;
        }
        if ( Last1 + 1 == First0 || i == 255 )
            printf( "     %d%s", 0, (i==255? " ":",") );
        else if ( nOnes == 1 )
            printf( "     %d,", Last1 );
        else
            printf( "    -%d,", 1 );
        printf( " // " );
        Extra_PrintBinary( stdout, (unsigned*)&i, 8 );
        printf( "\n" );
    }
    printf( "};\n" );

    printf( "\nstatic char Perms[256][8] = {\n" );
    for ( i = 0; i < 256; i++ )
    {
        printf( "    {" );
        nOnes = 0;
        for ( k = 0; k < 8; k++ )
            if ( i & (1 << k) )
                nOnes++;
        iOne = 0;
        iZero = nOnes;
        for ( k = 0; k < 8; k++ )
            if ( i & (1 << k) )
                printf( "%s %d", (k==0? "":","), iOne++ );
            else
                printf( "%s %d", (k==0? "":","), iZero++ );
        assert( iOne + iZero == 8 );
        printf( " }%s // ", (i==255? " ":",") );
        Extra_PrintBinary( stdout, (unsigned*)&i, 8 );
        printf( "\n" );
    }
    printf( "};\n" );
}

/**Function*************************************************************

  Synopsis    [Computes complementation schedule for 2^n Grey codes.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int * Extra_GreyCodeSchedule( int n )
{
    int * pRes = ABC_ALLOC( int, (1<<n) );
    int i, k, b = 0;
//    pRes[b++] = -1;
    for ( k = 0; k < n; k++ )
        for ( pRes[b++] = k, i = 1; i < (1<<k); i++ )
            pRes[b++] = pRes[i-1]; // pRes[i];
    pRes[b++] = n-1;
    assert( b == (1<<n) );

    if ( 0 )
    {
        unsigned uSign = 0;
        for ( b = 0; b < (1<<n); b++ )
        {
            uSign ^= (1 << pRes[b]);
            printf( "%3d %3d  ", b, pRes[b] );
            Extra_PrintBinary( stdout, &uSign, n );
            printf( "\n" );
        }
    }
    return pRes;
}

/**Function*************************************************************

  Synopsis    [Computes permutation schedule for n! permutations.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int * Extra_PermSchedule( int n )
{
    int nFact   = Extra_Factorial(n);
    int nGroups = nFact / n / 2;
    int * pRes = ABC_ALLOC( int, nFact );
    int * pRes0, i, k, b = 0;
    assert( n > 1 );
    if ( n == 2 )
    {
        pRes[0] = pRes[1] = 0;
        return pRes;
    }
    pRes0 = Extra_PermSchedule( n-1 );
    for ( k = 0; k < nGroups; k++ )
    {
        for ( i = n-1; i > 0; i-- )
            pRes[b++] = i-1;
        pRes[b++] = pRes0[2*k]+1;
        for ( i = 0; i < n-1; i++ )
            pRes[b++] = i;
        pRes[b++] = pRes0[2*k+1];
    }
    ABC_FREE( pRes0 );
    assert( b == nFact );

    if ( 0 )
    {
        int Perm[16];
        for ( i = 0; i < n; i++ )
            Perm[i] = i;
        for ( b = 0; b < nFact; b++ )
        {
            ABC_SWAP( int, Perm[pRes[b]], Perm[pRes[b]+1] );
            printf( "%3d %3d    ", b, pRes[b] );
            for ( i = 0; i < n; i++ )
                printf( "%d", Perm[i] );
            printf( "\n" );
        }
    }
    return pRes;
}


/**Function*************************************************************

  Synopsis    [Finds minimum form of a 6-input function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline word Extra_Truth6SwapAdjacent( word t, int v )
{
    // variable swapping code
    static word PMasks[5][3] = {
        { ABC_CONST(0x9999999999999999), ABC_CONST(0x2222222222222222), ABC_CONST(0x4444444444444444) },
        { ABC_CONST(0xC3C3C3C3C3C3C3C3), ABC_CONST(0x0C0C0C0C0C0C0C0C), ABC_CONST(0x3030303030303030) },
        { ABC_CONST(0xF00FF00FF00FF00F), ABC_CONST(0x00F000F000F000F0), ABC_CONST(0x0F000F000F000F00) },
        { ABC_CONST(0xFF0000FFFF0000FF), ABC_CONST(0x0000FF000000FF00), ABC_CONST(0x00FF000000FF0000) },
        { ABC_CONST(0xFFFF00000000FFFF), ABC_CONST(0x00000000FFFF0000), ABC_CONST(0x0000FFFF00000000) }
    };
    assert( v < 5 );
    return (t & PMasks[v][0]) | ((t & PMasks[v][1]) << (1 << v)) | ((t & PMasks[v][2]) >> (1 << v));
}
static inline word Extra_Truth6ChangePhase( word t, int v )
{
    // elementary truth tables
    static word Truth6[6] = {
        ABC_CONST(0xAAAAAAAAAAAAAAAA),
        ABC_CONST(0xCCCCCCCCCCCCCCCC),
        ABC_CONST(0xF0F0F0F0F0F0F0F0),
        ABC_CONST(0xFF00FF00FF00FF00),
        ABC_CONST(0xFFFF0000FFFF0000),
        ABC_CONST(0xFFFFFFFF00000000)
    };
    assert( v < 6 );
    return ((t & ~Truth6[v]) << (1 << v)) | ((t & Truth6[v]) >> (1 << v));
}
word Extra_Truth6MinimumExact( word t, int * pComp, int * pPerm )
{
    word tMin = ~(word)0;
    word tCur, tTemp1, tTemp2;
    int i, p, c;
    for ( i = 0; i < 2; i++ )
    {
        tCur = i ? ~t : t;
        tTemp1 = tCur;
        for ( p = 0; p < 720; p++ )
        {
//            printf( "Trying perm %d:\n", p );
//            Kit_DsdPrintFromTruth( &tCur, 6 ), printf( "\n" );;
            tTemp2 = tCur;
            for ( c = 0; c < 64; c++ )
            {
                tMin = Abc_MinWord( tMin, tCur );
                tCur = Extra_Truth6ChangePhase( tCur, pComp[c] );
            }
            assert( tTemp2 == tCur );
            tCur = Extra_Truth6SwapAdjacent( tCur, pPerm[p] );
        }
        assert( tTemp1 == tCur );
    }
    return tMin;
}

/**Function*************************************************************

  Synopsis    [Perform heuristic TT minimization.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline int Extra_Truth6Ones( word t )
{
    t =    (t & ABC_CONST(0x5555555555555555)) + ((t>> 1) & ABC_CONST(0x5555555555555555));
    t =    (t & ABC_CONST(0x3333333333333333)) + ((t>> 2) & ABC_CONST(0x3333333333333333));
    t =    (t & ABC_CONST(0x0F0F0F0F0F0F0F0F)) + ((t>> 4) & ABC_CONST(0x0F0F0F0F0F0F0F0F));
    t =    (t & ABC_CONST(0x00FF00FF00FF00FF)) + ((t>> 8) & ABC_CONST(0x00FF00FF00FF00FF));
    t =    (t & ABC_CONST(0x0000FFFF0000FFFF)) + ((t>>16) & ABC_CONST(0x0000FFFF0000FFFF));
    return (t & ABC_CONST(0x00000000FFFFFFFF)) +  (t>>32);
}
static inline word Extra_Truth6MinimumRoundOne( word t, int v )
{
    word tCur, tMin = t; // ab 
    assert( v >= 0 && v < 5 );

    tCur = Extra_Truth6ChangePhase( t, v );    // !ab
    tMin = Abc_MinWord( tMin, tCur );
    tCur = Extra_Truth6ChangePhase( t, v+1 );  // a!b
    tMin = Abc_MinWord( tMin, tCur );
    tCur = Extra_Truth6ChangePhase( tCur, v ); // !a!b
    tMin = Abc_MinWord( tMin, tCur );

    t    = Extra_Truth6SwapAdjacent( t, v );   // ba
    tMin = Abc_MinWord( tMin, t );

    tCur = Extra_Truth6ChangePhase( t, v );    // !ba
    tMin = Abc_MinWord( tMin, tCur );
    tCur = Extra_Truth6ChangePhase( t, v+1 );  // b!a
    tMin = Abc_MinWord( tMin, tCur );
    tCur = Extra_Truth6ChangePhase( tCur, v ); // !b!a
    tMin = Abc_MinWord( tMin, tCur );

    return tMin;
}
static inline word Extra_Truth6MinimumRoundMany( word t )
{
    int i, k, Limit = 10;
    word tCur, tMin = t;
    for ( i = 0; i < Limit; i++ )
    {
        word tMin0 = tMin;
        for ( k = 4; k >= 0; k-- )
        {
            tCur = Extra_Truth6MinimumRoundOne( tMin, k );
            tMin = Abc_MinWord( tMin, tCur );
        }
        if ( tMin0 == tMin )
            break;
    }
    return tMin;
}
word Extra_Truth6MinimumHeuristic( word t )
{
    word tMin1, tMin2;
    int nOnes = Extra_Truth6Ones( t );
    if ( nOnes < 32 )
        return Extra_Truth6MinimumRoundMany( t );
    if ( nOnes > 32 )
        return Extra_Truth6MinimumRoundMany( ~t );
    tMin1 = Extra_Truth6MinimumRoundMany(  t );
    tMin2 = Extra_Truth6MinimumRoundMany( ~t );
    return Abc_MinWord( tMin1, tMin2 );
}
void Extra_Truth6MinimumHeuristicTest()
{
    word t = ABC_CONST(0x5555555555555555) & ~(ABC_CONST(0x3333333333333333) & ABC_CONST(0x0F0F0F0F0F0F0F0F));
    Extra_Truth6MinimumRoundMany( t );
    t = 0;
}


/**Function*************************************************************

  Synopsis    [Reads functions from file.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
word * Extra_NpnRead( char * pFileName, int nFuncs )
{
    FILE * pFile;
    word * pFuncs;
    char pBuffer[100];
    int i = 0;
    pFuncs = ABC_CALLOC( word, nFuncs );
    pFile = fopen( pFileName, "rb" );
    while ( fgets( pBuffer, 100, pFile ) )
        Extra_ReadHex( (unsigned *)(pFuncs + i++), (pBuffer[1] == 'x' ? pBuffer+2 : pBuffer), 16 );
    fclose( pFile );
    assert( i == nFuncs );
    for ( i = 0; i < Abc_MinInt(nFuncs, 10); i++ )
    {
        printf( "Line %d : ", i );
        Extra_PrintHex( stdout, (unsigned *)(pFuncs + i), 6 ), printf( "\n" );
    }
    return pFuncs;
}

/**Function*************************************************************

  Synopsis    [Comparison for words.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int CompareWords( void * p1, void * p2 )
{
    word Word1 = *(word *)p1;
    word Word2 = *(word *)p2;
    if ( Word1 < Word2 )
        return -1;
    if ( Word1 > Word2 )
        return 1;
    return 0;
}

/**Function*************************************************************

  Synopsis    [Computes the permutation table for 8 variables.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Extra_NpnTest1()
{
    int * pComp;
    pComp = Extra_PermSchedule( 5 );
//    pComp = Extra_GreyCodeSchedule( 5 );
    ABC_FREE( pComp );
}
void Extra_NpnTest2()
{
    int * pComp, * pPerm;
    word tMin, t = ABC_CONST(0xa2222aaa08888000);
    pComp = Extra_GreyCodeSchedule( 6 );
    pPerm = Extra_PermSchedule( 6 );
    tMin  = Extra_Truth6MinimumExact( t, pComp, pPerm );
    ABC_FREE( pPerm );
    ABC_FREE( pComp );

    Extra_PrintHex( stdout, (unsigned *)&t,    6 ), printf( "\n" );
    Extra_PrintHex( stdout, (unsigned *)&tMin, 6 ), printf( "\n" );
}
void Extra_NpnTest()
{
//    int nFuncs = 5687661; 
//    int nFuncs = 400777;
    int nFuncs = 10;
    abctime clk = Abc_Clock();
    word * pFuncs;
    int * pComp, * pPerm;
    int i;//, k, nUnique = 0;
/*
    // read functions
    pFuncs = Extra_NpnRead( "C:\\_projects\\abc\\_TEST\\allan\\lib6var5M.txt", nFuncs );
//    pFuncs = Extra_NpnRead( "C:\\_projects\\abc\\_TEST\\allan\\lib6var5M_out_Total_minimal.txt", nFuncs );
    qsort( (void *)pFuncs, nFuncs, sizeof(word), (int(*)(const void *,const void *))CompareWords );

    // count unique
    k = 1;
    for ( i = 1; i < nFuncs; i++ )
        if ( pFuncs[i] != pFuncs[i-1] )
            pFuncs[k++] = pFuncs[i];
    nFuncs = k;
    printf( "Total number of unique functions = %d\n", nFuncs );
*/
//    pFuncs = Extra_NpnRead( "C:\\_projects\\abc\\_TEST\\allan\\lib6var5M_out_Total_minimal.txt", nFuncs );
    pFuncs = Extra_NpnRead( "C:\\_projects\\abc\\_TEST\\allan\\test.txt", nFuncs );
    pComp = Extra_GreyCodeSchedule( 6 );
    pPerm = Extra_PermSchedule( 6 );
    // compute minimum forms
    for ( i = 0; i < nFuncs; i++ )
    {
        pFuncs[i] = Extra_Truth6MinimumExact( pFuncs[i], pComp, pPerm );
        if ( i % 10000 == 0 )
            printf( "%d\n", i );
    }
    printf( "Finished deriving minimum form\n" );
/*
    // sort them by value
    qsort( (void *)pFuncs, nFuncs, sizeof(word), (int(*)(const void *,const void *))CompareWords );
    // count unique
    nUnique = nFuncs;
    for ( i = 1; i < nFuncs; i++ )
        if ( pFuncs[i] == pFuncs[i-1] )
            nUnique--;
    printf( "Total number of unique ones = %d\n", nUnique );
*/
    for ( i = 0; i < Abc_MinInt(nFuncs, 10); i++ )
    {
        printf( "Line %d : ", i );
        Extra_PrintHex( stdout, (unsigned *)(pFuncs + i), 6 ), printf( "\n" );
    }
    ABC_FREE( pPerm );
    ABC_FREE( pComp );
    ABC_FREE( pFuncs );
    Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
}


////////////////////////////////////////////////////////////////////////
///                       END OF FILE                                ///
////////////////////////////////////////////////////////////////////////


ABC_NAMESPACE_IMPL_END