FIX: fixed a little bug I introduced from last commit in fskdemod

[proxmark3-svn] / common / lfdemod.c

//-----------------------------------------------------------------------------
// Copyright (C) 2014 
//
// This code is licensed to you under the terms of the GNU GPL, version 2 or,
// at your option, any later version. See the LICENSE.txt file for the text of
// the license.
//-----------------------------------------------------------------------------
// Low frequency commands
//-----------------------------------------------------------------------------

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "lfdemod.h"

//by marshmellow
//takes 1s and 0s and searches for EM410x format - output EM ID
uint64_t Em410xDecode(uint8_t *BitStream, uint32_t BitLen)
{
        //no arguments needed - built this way in case we want this to be a direct call from "data " cmds in the future
        //  otherwise could be a void with no arguments
        //set defaults
        int high = 0, low = 128;
        uint64_t lo = 0; 
        uint32_t i = 0;
        uint32_t initLoopMax = 65;

        if (initLoopMax > BitLen) 
                initLoopMax = BitLen;

        for (; i < initLoopMax; ++i) //65 samples should be plenty to find high and low values
        {
                if (BitStream[i] > high)
                        high = BitStream[i];
                else if (BitStream[i] < low)
                        low = BitStream[i];
        }

        if (((high !=1)||(low !=0))){  //allow only 1s and 0s 
                return 0;
        }

        uint8_t parityTest = 0;
        // 111111111 bit pattern represent start of frame
        uint8_t frame_marker_mask[] = {1,1,1,1,1,1,1,1,1};
        uint32_t idx = 0;
        uint32_t j = 0;
        uint8_t resetCnt = 0;
        while( (idx + 64) < BitLen) {

        restart:

    // search for a start of frame marker
    if ( memcmp(BitStream+idx, frame_marker_mask, sizeof(frame_marker_mask)) == 0) {
                // frame marker found
                idx += 9;//sizeof(frame_marker_mask);
                for ( i = 0; i < 10; ++i){
                        for( j = 0; j < 5; ++j){
                                parityTest += BitStream[(i*5) + j + idx];        
                        }
                        if (parityTest == ( (parityTest >> 1) << 1)){
                                parityTest = 0;
                                for (j = 0; j < 4; ++j){
                                        lo = ( lo << 1LL)|( BitStream[( i * 5 ) + j + idx]);
                                }
                        } else {
                                //parity failed
                                parityTest = 0;
                                idx -= 8;
                                if (resetCnt > 5) return 0;
                                resetCnt++;
                                goto restart;//continue;
                        }
                }
                //skip last 5 bit parity test for simplicity.
                return lo;
                } else {
                        idx++;
                }
        }       
        return 0;
}

//by marshmellow
//takes 2 arguments - clock and invert both as integers
//attempts to demodulate ask while decoding manchester 
//prints binary found and saves in graphbuffer for further commands
int askmandemod(uint8_t *BinStream, uint32_t *BitLen, int *clk, int *invert)
{
        int i;
        int high = 0, low = 128;
        *clk = DetectASKClock(BinStream, (size_t)*BitLen, *clk); //clock default
        
        if (*clk < 8 )    *clk = 64;
        if (*clk < 32 )   *clk = 32;
        if (*invert != 1) *invert = 0;
        
        uint32_t initLoopMax = 200;
        if (initLoopMax > *BitLen) 
                initLoopMax = *BitLen;
  
        // Detect high and lows 
        // 200 samples should be enough to find high and low values
        for (i = 0; i < initLoopMax; ++i) {
                if (BinStream[i] > high)
                        high = BinStream[i];
                else if (BinStream[i] < low)
                        low = BinStream[i];
        }
  
        //throw away static 
        if ((high < 158) )
                return -2;

        //25% fuzz in case highs and lows aren't clipped [marshmellow]
        high = (int)(high * .75);
        low  = (int)(low+128 * .25);
 
        int lastBit = 0;      // set first clock check
        uint32_t bitnum = 0;  // output counter

        // clock tolerance adjust - waves will be accepted as within the clock if they fall + or - this value + clock from last valid wave
        //clock tolerance may not be needed anymore currently set to + or - 1 but could be increased for poor waves or removed entirely 
        int tol = ( *clk == 32 ) ? 1 : 0;  

        int j = 0;
        uint32_t gLen = *BitLen;

        if (gLen > 3000) gLen = 3000;

        uint8_t errCnt = 0;
        uint32_t bestStart = *BitLen;
        uint32_t bestErrCnt = (*BitLen/1000);
        uint32_t maxErr = bestErrCnt;

  //loop to find first wave that works
        for (j=0; j < gLen; ++j){
  
                if ((BinStream[j] >= high)||(BinStream[j] <= low)){
                  lastBit = j - *clk;    
                  errCnt = 0;
          
      //loop through to see if this start location works
      for (i = j; i < *BitLen; ++i) {   
        if ((BinStream[i] >= high) && ((i-lastBit)>(*clk-tol))){
          lastBit += *clk;
        } else if ((BinStream[i] <= low) && ((i-lastBit)>(*clk-tol))){
          //low found and we are expecting a bar
          lastBit += *clk;
        } else {
          //mid value found or no bar supposed to be here
          if ((i-lastBit) > (*clk + tol)){
            //should have hit a high or low based on clock!!
           
            errCnt++;
            lastBit += *clk;//skip over until hit too many errors
            if (errCnt > maxErr) break;  //allow 1 error for every 1000 samples else start over
          }
        }
        if ((i-j) >(400 * *clk)) break; //got plenty of bits
      }
      //we got more than 64 good bits and not all errors
      if ((((i-j)/ *clk) > (64 + errCnt)) && (errCnt < maxErr)) {
        //possible good read
        if (errCnt == 0){
                        bestStart = j;
                        bestErrCnt = errCnt;
                        break;  //great read - finish
        } 
        if (errCnt < bestErrCnt){  //set this as new best run
          bestErrCnt = errCnt;
          bestStart = j;
        }
      }
    }
  }
  if (bestErrCnt < maxErr){
        //best run is good enough set to best run and set overwrite BinStream
        j = bestStart;
        lastBit = bestStart - *clk;
        bitnum = 0;
    for (i = j; i < *BitLen; ++i) {   
                if ((BinStream[i] >= high) && ((i-lastBit)>(*clk-tol))){
                        lastBit += *clk;
                        BinStream[bitnum] = *invert;
                        bitnum++;
                } else if ((BinStream[i] <= low) && ((i-lastBit)>(*clk-tol))){
                        //low found and we are expecting a bar
                        lastBit += *clk;
                        BinStream[bitnum] = 1 - *invert; 
                        bitnum++;
                } else {
                        //mid value found or no bar supposed to be here
                        if ((i-lastBit) > (*clk+tol)){
                                //should have hit a high or low based on clock!!
                                if (bitnum > 0){
                                        BinStream[bitnum] = 77;
                                        bitnum++;
                                }
                                lastBit += *clk;//skip over error
                        }
                }
                if (bitnum >= 400) break;
                }
                *BitLen = bitnum;
        } else {
                *invert = bestStart;
                *clk = j;
                return -1; 
        }       
  return bestErrCnt;
}

//by marshmellow
//take 10 and 01 and manchester decode
//run through 2 times and take least errCnt
int manrawdecode(uint8_t * bits, int *bitlen)
{
  int bitnum = 0;
  int errCnt = 0;
  int bestErr = 1000;
  int bestRun = 0;
  int i = 1;
  int j = 1;

        for (; j < 3; ++j){
                i = 1;
                for ( i = i + j; i < *bitlen-2; i += 2){
                        if ( bits[i]==1 && (bits[i+1]==0)){
                        } else if ((bits[i]==0)&& bits[i+1]==1){
                        } else {
                                errCnt++;
                        }
                        if(bitnum > 300) break;
                }
                if (bestErr > errCnt){
                        bestErr = errCnt;
                        bestRun = j;
                }       
                errCnt = 0;
        }
        errCnt = bestErr;
        if (errCnt < 20){
                j = bestRun;
                i = 1;
                for ( i = i+j; i < *bitlen-2; i += 2){
                        if ( bits[i] == 1 && bits[i + 1] == 0 ){
                                        bits[bitnum++] = 0;
                        } else if ( bits[i] == 0 && bits[i + 1] == 1 ){
                                        bits[bitnum++] = 1;
                        } else {
                                bits[bitnum++] = 77;
                        }
                        if ( bitnum > 300 ) break;
                }
                *bitlen = bitnum;
        }   
        return errCnt;
}


//by marshmellow
//take 01 or 10 = 0 and 11 or 00 = 1
int BiphaseRawDecode(uint8_t * bits, int *bitlen, int offset)
{
        uint8_t bitnum = 0;
        uint32_t errCnt = 0;
        uint32_t i = offset;
        
        for (; i < *bitlen-2; i += 2 ){
                if ( (bits[i]==1 && bits[i+1]==0)||
                         (bits[i]==0 && bits[i+1]==1)){
                        bits[bitnum++] = 1;
                } else if ( (bits[i]==0 && bits[i+1]==0)||
                                        (bits[i]==1 && bits[i+1]==1)){
                        bits[bitnum++] = 0;
                } else {
                        bits[bitnum++] = 77;
                        errCnt++;
                }
                if ( bitnum > 250) break;
        }  
        *bitlen = bitnum;
        return errCnt;
}

//by marshmellow
//takes 2 arguments - clock and invert both as integers
//attempts to demodulate ask only
//prints binary found and saves in graphbuffer for further commands
int askrawdemod(uint8_t *BinStream, int *bitLen, int *clk, int *invert)
{
  uint32_t i;
  uint32_t initLoopMax = 200;
  int high = 0, low = 128;
  uint8_t BitStream[502] = {0x00};
  
  *clk = DetectASKClock(BinStream, *bitLen, *clk); //clock default
  
  if (*clk < 8)         *clk = 64;      
  if (*clk < 32)        *clk = 32;      
  if (*invert != 1) *invert = 0;

  if (initLoopMax > *bitLen) 
        initLoopMax = *bitLen;
  
  // Detect high and lows 
  for (i = 0; i < initLoopMax; ++i) //200 samples should be plenty to find high and low values
  {
    if (BinStream[i] > high)
                high = BinStream[i];
    else if (BinStream[i] < low)
                low = BinStream[i];
  }
  
  //throw away static
        if ((high < 158)){  
                return -2;
        }
  
        //25% fuzz in case highs and lows aren't clipped [marshmellow]
        high = (int)(high * .75);
        low  = (int)(low+128 * .25);

  int lastBit = 0;                      //set first clock check
  uint32_t bitnum = 0;          //output counter
  
  uint8_t tol = 0;                      //clock tolerance adjust - waves will be accepted as within the clock if they fall + or - this value + clock from last valid wave
  if (*clk==32) tol = 1;        //clock tolerance may not be needed anymore currently set to + or - 1 but could be increased for poor waves or removed entirely 

  uint32_t gLen = *bitLen;
  if (gLen > 500) gLen = 500;

  uint32_t j = 0;
  uint8_t errCnt = 0;
  uint32_t bestStart = *bitLen;
  uint32_t bestErrCnt = (*bitLen / 1000);
  uint32_t errCntLimit = bestErrCnt;
  uint8_t midBit = 0;
  
  //loop to find first wave that works
  for (j = 0; j < gLen; ++j){
  
    if ((BinStream[j] >= high)||(BinStream[j] <= low)){
      lastBit = j - *clk;    
      //loop through to see if this start location works
      for (i = j; i < *bitLen; ++i) {  
        if ((BinStream[i] >= high) && ((i-lastBit)>(*clk-tol))){
          lastBit += *clk;
          BitStream[bitnum] =  *invert;
          bitnum++;
          midBit = 0;
        } else if ((BinStream[i] <= low) && ((i-lastBit)>(*clk-tol))){
          //low found and we are expecting a bar
          lastBit += *clk;
          BitStream[bitnum] = 1-*invert; 
          bitnum++;
          midBit=0;
        } else if ((BinStream[i]<=low) && (midBit==0) && ((i-lastBit)>((*clk/2)-tol))){
          //mid bar?
          midBit = 1;
          BitStream[bitnum] = 1 - *invert;
          bitnum++;
        } else if ((BinStream[i]>=high)&&(midBit==0) && ((i-lastBit)>((*clk/2)-tol))){
          //mid bar?
          midBit = 1;
          BitStream[bitnum] = *invert;
          bitnum++;
        } else if ((i-lastBit)>((*clk/2)+tol)&&(midBit==0)){
          //no mid bar found
          midBit = 1;
          BitStream[bitnum] = BitStream[bitnum-1];
          bitnum++;
        } else {
          //mid value found or no bar supposed to be here

          if (( i - lastBit) > ( *clk + tol)){
            //should have hit a high or low based on clock!!

            if (bitnum > 0){
              BitStream[bitnum] = 77;
              bitnum++;
            }

            errCnt++;
            lastBit += *clk;//skip over until hit too many errors
            if (errCnt > errCntLimit){  //allow 1 error for every 1000 samples else start over
              errCnt = 0;
              bitnum = 0;//start over
              break;
            }
          }          
        }
        if (bitnum > 500) break;
      }
      //we got more than 64 good bits and not all errors
          //possible good read
      if ((bitnum > (64 + errCnt)) && (errCnt < errCntLimit)) {

                //great read - finish
        if (errCnt == 0) break;  
                
                //if current run == bestErrCnt run (after exhausted testing) then finish 
        if (bestStart == j) break;  
        
                //set this as new best run
                if (errCnt < bestErrCnt){
          bestErrCnt = errCnt;
          bestStart = j;
        }
      }
    }
    if (j >= gLen){ //exhausted test
      //if there was a ok test go back to that one and re-run the best run (then dump after that run)
      if (bestErrCnt < errCntLimit) 
                j = bestStart;
    }
  }
        if (bitnum > 16){

                for (i = 0; i < bitnum; ++i){
                        BinStream[i] = BitStream[i];
                }
                *bitLen = bitnum;
        } else {
                return -1;
        }
  return errCnt;
}
//translate wave to 11111100000 (1 for each short wave 0 for each long wave) 
size_t fsk_wave_demod(uint8_t * dest, size_t size, uint8_t fchigh, uint8_t fclow)
{
        uint32_t last_transition = 0;
        uint32_t idx = 1;
        uint32_t maxVal = 0;
        
        if (fchigh == 0) fchigh = 10;
        if (fclow == 0) fclow = 8;
        
        // we do care about the actual theshold value as sometimes near the center of the
        // wave we may get static that changes direction of wave for one value
        // if our value is too low it might affect the read.  and if our tag or
        // antenna is weak a setting too high might not see anything. [marshmellow]
        if ( size < 100)
                return 0;
        
        // Find high from first 100 samples
        for ( idx = 1; idx < 100; idx++ ){
                if ( maxVal < dest[idx]) 
                        maxVal = dest[idx];
        }
        
    // set close to the top of the wave threshold with 25% margin for error
    // less likely to get a false transition up there. 
    // (but have to be careful not to go too high and miss some short waves)
        uint8_t threshold_value = (uint8_t)(maxVal * .75);
        
        // sync to first lo-hi transition, and threshold
        // Need to threshold first sample
        
        dest[0] = (dest[0] < threshold_value) ? 0 : 1;

        size_t numBits = 0;
        
        // count cycles between consecutive lo-hi transitions, there should be either 8 (fc/8)
        // or 10 (fc/10) cycles but in practice due to noise etc we may end up with with anywhere
        // between 7 to 11 cycles so fuzz it by treat anything <9 as 8 and anything else as 10
        for(idx = 1; idx < size; idx++) {

                // threshold current value
                dest[idx] = (dest[idx] < threshold_value) ? 0 : 1;

                // Check for 0->1 transition
                if (dest[idx-1] < dest[idx]) { // 0 -> 1 transition
                        if ( ( idx - last_transition ) <( fclow - 2 ) ) {      //0-5 = garbage noise
                                //do nothing with extra garbage
                        } else if ((idx - last_transition) < ( fchigh - 1 )) { //6-8 = 8 waves
                                dest[numBits]=1;
                        } else {                                                        //9+ = 10 waves
                                dest[numBits]=0;
                        }
                        last_transition = idx;
                        numBits++;
                }
        }
        //it returns the number of bytes, but each byte represents a bit: 1 or 0
        return numBits; 
}

uint32_t myround2(float f)
{
  if (f >= 2000) return 2000;//something bad happened
  return (uint32_t) (f + (float)0.5);
}

//translate 11111100000 to 10 
size_t aggregate_bits(uint8_t *dest, size_t size, uint8_t rfLen, uint8_t maxConsequtiveBits, uint8_t invert, uint8_t fchigh, uint8_t fclow )
{
        uint8_t lastval = dest[0];
        uint32_t idx = 0;
        uint32_t n = 1;
        size_t numBits = 0;

        for( idx = 1; idx < size; idx++) {

                if (dest[idx] == lastval) {
                        n++;
                        continue;
                }
                //if lastval was 1, we have a 1->0 crossing
                if ( dest[idx-1] == 1 ) {
                        n = myround2( (float)( n + 1 ) / ((float)(rfLen)/(float)fclow));
                } else { // 0->1 crossing
                        n = myround2( (float)( n + 1 ) / ((float)(rfLen-2)/(float)fchigh));  //-2 for fudge factor
                }
                if (n == 0) n = 1;

                if(n < maxConsequtiveBits) //Consecutive 
                {
                        if(invert == 0){ //invert bits 
                                memset(dest+numBits, dest[idx-1] , n);
                        }else{
                                memset(dest+numBits, dest[idx-1]^1 , n);        
                        }                       
                        numBits += n;
                }
                n = 0;
                lastval = dest[idx];
        }//end for
        return numBits;
}

//by marshmellow  (from holiman's base)
// full fsk demod from GraphBuffer wave to decoded 1s and 0s (no mandemod)
int fskdemod(uint8_t *dest, size_t size, uint8_t rfLen, uint8_t invert, uint8_t fchigh, uint8_t fclow)
{
        // FSK demodulator
        size = fsk_wave_demod(dest, size, fchigh, fclow);
        if ( size > 0 )
                size = aggregate_bits(dest, size, rfLen, 192, invert, fchigh, fclow);
        return size;
}

// loop to get raw HID waveform then FSK demodulate the TAG ID from it
int HIDdemodFSK(uint8_t *dest, size_t size, uint32_t *hi2, uint32_t *hi, uint32_t *lo)
{
        size_t idx = 0;
        int numshifts = 0;

        // FSK demodulator
        size = fskdemod(dest, size, 50, 0, 10, 8);

        // final loop, go over previously decoded manchester data and decode into usable tag ID
        // 111000 bit pattern represent start of frame, 01 pattern represents a 1 and 10 represents a 0
        uint8_t frame_marker_mask[] = {1,1,1,0,0,0};

        uint8_t mask_len =  sizeof frame_marker_mask /  sizeof frame_marker_mask[0];
        
        //one scan
        while( idx + mask_len < size) {
        // search for a start of frame marker
                if ( memcmp(dest+idx, frame_marker_mask, sizeof(frame_marker_mask)) == 0)
                { // frame marker found
                        idx += mask_len;
                        while(dest[idx] != dest[idx+1] && idx < size-2)
                        {       
                                // Keep going until next frame marker (or error)
                                // Shift in a bit. Start by shifting high registers
                                *hi2 = ( *hi2 << 1 ) | ( *hi >> 31 );
                                *hi = ( *hi << 1 ) | ( *lo >> 31 );
                                //Then, shift in a 0 or one into low
                                if (dest[idx] && !dest[idx+1])  // 1 0
                                        *lo = ( *lo << 1 ) | 0;
                                else // 0 1
                                        *lo = ( *lo << 1 ) | 1;
                                numshifts++;
                                idx += 2;
                        }
                        // Hopefully, we read a tag and  hit upon the next frame marker
                        if(idx + mask_len < size)
                        {
                                if ( memcmp(dest+idx, frame_marker_mask, sizeof(frame_marker_mask)) == 0)
                                {
                                        //good return 
                                        return idx;
                                }
                        }
                        // reset
                        *hi2 = *hi = *lo = 0;
                        numshifts = 0;
                }else   {
                        idx++;
                }
        }
        return -1;
}

uint32_t bytebits_to_byte(uint8_t *src, int numbits)
{
        //HACK:  potential overflow in numbits is larger then uint32 bits.
        
        uint32_t num = 0;
        for(int i = 0 ; i < numbits ; ++i)      {
                num = (num << 1) | (*src);
                src++;
        }
        return num;
}

int IOdemodFSK(uint8_t *dest, size_t size)
{
        //make sure buffer has data
        if (size < 100) return -1;
        
        uint32_t idx = 0;
        uint8_t testMax = 0;
        
        //test samples are not just noise
        for (; idx < 65; ++idx ){
                if (testMax < dest[idx])
                        testMax = dest[idx];
        }

        //if not just noise
        if (testMax < 170) return -2;
                
        // FSK demodulator
        size = fskdemod(dest, size, 64, 1, 10, 8);  //  RF/64 and invert
        
        //did we get a good demod?
        if (size < 65) return -3;
        
        //Index map
        //0           10          20          30          40          50          60
        //|           |           |           |           |           |           |
        //01234567 8 90123456 7 89012345 6 78901234 5 67890123 4 56789012 3 45678901 23
        //-----------------------------------------------------------------------------
        //00000000 0 11110000 1 facility 1 version* 1 code*one 1 code*two 1 ???????? 11
        //
        //XSF(version)facility:codeone+codetwo
        //Handle the data
        
        uint8_t mask[] = {0,0,0,0,0,0,0,0,0,1};
        
        for( idx = 0; idx < (size - 65); ++idx) {
        if ( memcmp(dest + idx, mask, sizeof(mask))==0) {
                //frame marker found
                if (!dest[idx+8] && 
                        dest[idx+17] == 1 &&
                        dest[idx+26] == 1 &&
                        dest[idx+35] == 1 &&
                        dest[idx+44] == 1 &&
                        dest[idx+53] == 1){
                                //confirmed proper separator bits found
                                //return start position
                                return (int) idx;
                        }
                }               
        }
        return 0;
}

// by marshmellow
// not perfect especially with lower clocks or VERY good antennas (heavy wave clipping)
// maybe somehow adjust peak trimming value based on samples to fix?
int DetectASKClock(uint8_t dest[], size_t size, int clock)
{
        int i = 0;
        int clk[] = {16,32,40,50,64,100,128,256};
        uint8_t clkLen = sizeof clk / sizeof clk[0];
        
        //if we already have a valid clock quit
        for (; i < clkLen; ++i)
                if (clk[i] == clock) 
                        return clock;
                        
        int peak = 0;
        int low = 128;  
        int loopCnt = 256;
        if (size < loopCnt) 
                loopCnt = size;
        
        //get high and low peak
        for ( i = 0; i < loopCnt; ++i ){
                if(dest[i] > peak) 
                        peak = dest[i]; 
                if(dest[i] < low) 
                        low = dest[i];
        }

        peak = (int)(peak * .75);
        low  = (int)(low+128 * .25);
 
        int ii, cnt, bestErr, tol = 0;
        int errCnt[clkLen];
        memset(errCnt, 0x00, clkLen);
        
        int tmpIndex, tmphigh, tmplow;
        
        //test each valid clock from smallest to greatest to see which lines up
        for( cnt = 0; cnt < clkLen; ++cnt ){

                tol = (clk[cnt] == 32) ? 1 : 0;
                bestErr = 1000;
                tmpIndex = tmphigh = tmplow = 0;

                //try lining up the peaks by moving starting point (try first 256) 
                for (ii=0; ii < loopCnt; ++ii){
                
                        // not a peak? continue
                        if ( (dest[ii] < peak) && (dest[ii] > low)) 
                                continue;

                        errCnt[cnt] = 0;
                        
                        // now that we have the first one lined up test rest of wave array
                        for ( i = 0; i < ((int)(size / clk[cnt]) - 1); ++i){
                          
                                tmpIndex = ii + (i * clk[cnt] );
                                tmplow  = dest[ tmpIndex - tol];
                                tmphigh = dest[ tmpIndex + tol];
                                
                                if ( dest[tmpIndex] >= peak || dest[tmpIndex] <= low ) {
                                }
                                else if ( tmplow >= peak || tmplow <= low){
                                }                                       
                                else if ( tmphigh >= peak || tmphigh <= low){
                                }
                                else 
                                        errCnt[cnt]++; //error no peak detected
                        }

                        //if we found no errors this is correct one - return this clock
                        if ( errCnt[cnt] == 0 )
                                return clk[cnt];

                        if ( errCnt[cnt] < bestErr) 
                                bestErr = errCnt[cnt];
                }
                // save the least error.
                errCnt[cnt] = bestErr;
        }
        // find best clock which has lowest number of errors
        int j = 0, bestIndex = 0;
        for (; j < clkLen; ++j){
                if ( errCnt[j] < errCnt[bestIndex] )
                        bestIndex = j;
        }
        return clk[bestIndex];
}