Detection of threshold functions.

2 files changed, 334 insertions, 0 deletions

diff --git a/src/misc/extra/extraUtilThresh.c b/src/misc/extra/extraUtilThresh.c
new file mode 100644
index 00000000..88752b7d
--- /dev/null
+++ b/src/misc/extra/extraUtilThresh.c
@@ -0,0 +1,333 @@
+/**CFile****************************************************************
+
+  FileName    [extraUtilThresh.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [extra]
+
+  Synopsis    [Dealing with threshold functions.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - October 7, 2014.]
+
+  Revision    [$Id: extraUtilThresh.c,v 1.0 2014/10/07 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+
+#include "misc/vec/vec.h"
+#include "misc/util/utilTruth.h"
+
+ABC_NAMESPACE_IMPL_START
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Checks thresholdness of the function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Extra_ThreshPrintChow( int Chow0, int * pChow, int nVars )
+{
+    int i;
+    for ( i = 0; i < nVars; i++ )
+        printf( "%d ", pChow[i] );
+    printf( "  %d\n", Chow0 );
+}
+int Extra_ThreshComputeChow( word * t, int nVars, int * pChow )
+{
+    int i, k, Chow0 = 0, nMints = (1 << nVars);
+    memset( pChow, 0, sizeof(int) * nVars );
+    // compute Chow coefs
+    for ( i = 0; i < nMints; i++ )
+        if ( Abc_TtGetBit(t, i) )
+            for ( Chow0++, k = 0; k < nVars; k++ )
+                if ( (i >> k) & 1 )
+                    pChow[k]++;
+    // compute modified Chow coefs
+    for ( k = 0; k < nVars; k++ )
+        pChow[k] = 2 * pChow[k] - Chow0;
+    return Chow0 - (1 << (nVars-1));
+}
+void Extra_ThreshSortByChow( word * t, int nVars, int * pChow )
+{
+    int i, nWords = Abc_TtWordNum(nVars);
+    while ( 1 )
+    {
+        int fChange = 0;
+        for ( i = 0; i < nVars - 1; i++ )
+        {
+            if ( pChow[i] >= pChow[i+1] )
+                continue;
+            ABC_SWAP( int, pChow[i], pChow[i+1] );
+            Abc_TtSwapAdjacent( t, nWords, i );
+            fChange = 1;
+        }
+        if ( !fChange )
+            return;
+    }
+}
+static inline int Extra_ThreshWeightedSum( int * pW, int nVars, int m )
+{
+    int i, Cost = 0;
+    for ( i = 0; i < nVars; i++ )
+        if ( (m >> i) & 1 )
+            Cost += pW[i];
+    return Cost;
+}
+int Extra_ThreshSelectWeights3( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars);
+    assert( nVars == 3 );
+    for ( pW[2] = 1;     pW[2] <= nVars; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= nVars; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= nVars; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+//            printf( "%c%d ", Abc_TtGetBit(t, m) ? '+' : '-', Extra_ThreshWeightedSum(pW, nVars, m) );
+        }
+//        printf( "  -%d +%d\n", Lmax, Lmin );
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights4( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars);
+    assert( nVars == 4 );
+    for ( pW[3] = 1;     pW[3] <= nVars; pW[3]++ )
+    for ( pW[2] = pW[3]; pW[2] <= nVars; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= nVars; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= nVars; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+        }
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights5( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 0;
+    assert( nVars == 5 );
+    for ( pW[4] = 1;     pW[4] <= Limit; pW[4]++ )
+    for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
+    for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+        }
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights6( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 3;
+    assert( nVars == 6 );
+    for ( pW[5] = 1;     pW[5] <= Limit; pW[5]++ )
+    for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
+    for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
+    for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+        }
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights7( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 6;
+    assert( nVars == 7 );
+    for ( pW[6] = 1;     pW[6] <= Limit; pW[6]++ )
+    for ( pW[5] = pW[6]; pW[5] <= Limit; pW[5]++ )
+    for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
+    for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
+    for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+        }
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights8( word * t, int nVars, int * pW )
+{
+    int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 1; // <<-- incomplete detection to save runtime!
+    assert( nVars == 8 );
+    for ( pW[7] = 1;     pW[7] <= Limit; pW[7]++ )
+    for ( pW[6] = pW[7]; pW[6] <= Limit; pW[6]++ )
+    for ( pW[5] = pW[6]; pW[5] <= Limit; pW[5]++ )
+    for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
+    for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
+    for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
+    for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
+    for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
+    {
+        Lmin = 10000; Lmax = 0;
+        for ( m = 0; m < nMints; m++ )
+        {
+            if ( Abc_TtGetBit(t, m) )
+                Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
+            else
+                Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
+            if ( Lmax >= Lmin )
+                break;
+        }
+        if ( m < nMints )
+            continue;
+        assert( Lmax < Lmin );
+        return Lmin;
+    }
+    return 0;
+}
+int Extra_ThreshSelectWeights( word * t, int nVars, int * pW )
+{
+    if ( nVars <= 2 )
+        return (t[0] & 0xF) != 6 && (t[0] & 0xF) != 9;
+    if ( nVars == 3 )
+        return Extra_ThreshSelectWeights3( t, nVars, pW );
+    if ( nVars == 4 )
+        return Extra_ThreshSelectWeights4( t, nVars, pW );
+    if ( nVars == 5 )
+        return Extra_ThreshSelectWeights5( t, nVars, pW );
+    if ( nVars == 6 )
+        return Extra_ThreshSelectWeights6( t, nVars, pW );
+    if ( nVars == 7 )
+        return Extra_ThreshSelectWeights7( t, nVars, pW );
+    if ( nVars == 8 )
+        return Extra_ThreshSelectWeights8( t, nVars, pW );
+    return 0;
+}
+int Extra_ThreshCheck( word * t, int nVars, int * pW )
+{
+    int Chow[16], Chow0, nMints = (1 << nVars);
+    if ( !Abc_TtIsUnate(t, nVars) )
+        return 0;
+    Abc_TtMakePosUnate( t, nVars );
+    Chow0 = Extra_ThreshComputeChow( t, nVars, Chow );
+    Extra_ThreshSortByChow( t, nVars, Chow );
+    return Extra_ThreshSelectWeights( t, nVars, pW );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks unateness of a function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Extra_ThreshCheckTest()
+{
+    int nVars = 5;
+    int T, Chow0, Chow[16], Weights[16];
+//    word t =  s_Truths6[0] & s_Truths6[1] & s_Truths6[2] & s_Truths6[3] & s_Truths6[4];
+//    word t =  (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[4]);
+    word t =  (s_Truths6[2] & s_Truths6[1]) | (s_Truths6[2] & s_Truths6[0] & s_Truths6[3]) | (s_Truths6[2] & s_Truths6[0] & ~s_Truths6[4]);
+//    word t =  (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[4]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[3]);
+//    word t =  (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2]) | (s_Truths6[0] & s_Truths6[3] & s_Truths6[4] & s_Truths6[5]) | 
+//        (s_Truths6[1] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[4]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[5]);
+    int i;
+    assert( nVars <= 8 );
+    for ( i = 0; i < nVars; i++ )
+        printf( "%d %d %d\n", i, Abc_TtPosVar(&t, nVars, i), Abc_TtNegVar(&t, nVars, i) );
+//    word t = s_Truths6[0] & s_Truths6[1] & s_Truths6[2];
+    Chow0 = Extra_ThreshComputeChow( &t, nVars, Chow );
+    if ( (T = Extra_ThreshCheck(&t, nVars, Weights)) )
+        Extra_ThreshPrintChow( T, Weights, nVars );
+    else
+        printf( "No threshold\n" );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+
diff --git a/src/misc/extra/module.make b/src/misc/extra/module.make
index 1503cec1..87ba8559 100644
--- a/src/misc/extra/module.make
+++ b/src/misc/extra/module.make
@@ -18,5 +18,6 @@ SRC +=    src/misc/extra/extraBddAuto.c \
     src/misc/extra/extraUtilProgress.c \
     src/misc/extra/extraUtilReader.c \
     src/misc/extra/extraUtilSupp.c \
+    src/misc/extra/extraUtilTrash.c \
     src/misc/extra/extraUtilTruth.c \
     src/misc/extra/extraUtilUtil.c