/********************************************************************
**                Image Component Library (ICL)                    **
**                                                                 **
** Copyright (C) 2006-2013 CITEC, University of Bielefeld          **
**                         Neuroinformatics Group                  **
** Website: www.iclcv.org and                                      **
**          http://opensource.cit-ec.de/projects/icl               **
**                                                                 **
** File   : ICLMarkers/src/ICLMarkers/BCHCode.cpp                  **
** Module : ICLMarkers                                             **
** Authors: Christof Elbrechter                                    **
**                                                                 **
**                                                                 **
** GNU LESSER GENERAL PUBLIC LICENSE                               **
** This file may be used under the terms of the GNU Lesser General **
** Public License version 3.0 as published by the                  **
**                                                                 **
** Free Software Foundation and appearing in the file LICENSE.LGPL **
** included in the packaging of this file.  Please review the      **
** following information to ensure the license requirements will   **
** be met: http://www.gnu.org/licenses/lgpl-3.0.txt                **
**                                                                 **
** The development of this software was supported by the           **
** Excellence Cluster EXC 277 Cognitive Interaction Technology.    **
** The Excellence Cluster EXC 277 is a grant of the Deutsche       **
** Forschungsgemeinschaft (DFG) in the context of the German       **
** Excellence Initiative.                                          **
**                                                                 **
********************************************************************/

#include <vector>
#include <algorithm>

#include <ICLUtils/SmartPtr.h>
#include <ICLUtils/Exception.h>
#include <ICLMath/FixedVector.h>
#include <ICLUtils/Mutex.h>

#include <ICLMarkers/BCHCode.h>

using namespace icl::utils;
using namespace icl::math;
using namespace icl::core;


namespace icl {
  namespace markers{
    
    /** source copyright: (source code found at http://www.eccpage.com/bch3.c)
        
        COPYRIGHT NOTICE: This computer program is free for non-commercial purposes.
        You may implement this program for any non-commercial application. You may 
        also implement this program for commercial purposes, provided that you
        obtain my written permission. Any modification of this program is covered
        by this copyright.
        == Copyright (c) 1994-7,  Robert Morelos-Zaragoza. All rights reserved.  ==
        
        
        Our code design was also inspired by the ARToolkitPlus implementation
        that also uses Robert Morelos-Zaragoza's BCH-En/Decoder.
        
        ARToolkitPlusSRC/src/extra/BCH_original.txt for details/orig. copyright notice
        Copyright of the derived and new portions of this work
        (C) 2006 Graz University of Technology
        author: Thomas Pintaric
        ARToolkitPlus can also be used under the terms of the GNU public license
    */
  
  
    static SmartPtr<icl8u> static_indices;
    static const char **static_bch_codes=0;
    
    static void init_static_data(){
      if(static_indices) return;
      
      static const char *all_codes[4096]={
        "XhqhUc","XNlua5","XxMD3K","X39ozF","XplQIr","XVq5mQ","XF9W73","X-MJvm","XdMcMW","XJ9ril","Xtqy-w","XZllrT","Xl9VQJ","XRM8ey","XBl1Zf","X7qMD+","XfRfQB","XLWweG","XvDFZ9","X1gmDg","XnWOMi","XTR7iZ","XDgY-U","X9DHrv","XbDaIP","XHgtms","XrRA7p","XXWjv0","XjgTU6","XPD+ab","XzW33C","X5RKzN","XgwvI1","XMngmo","XwGp7t","X27CvO","Xon4UM","XUwRaD","XE7I3a","X+GXz7","XcGqQh","XI7de8","XswkZH","XYnzDA","Xk79Mu","XQGUiV","XAnN-Y","X6w0rj","XeTxMS","XK2eix","XuBn-k","X0aErX","Xm26Q-","XSTPee","XCaGZz","X8BZDI","XaBsUE","XGabaL","XqTi34","XW2Bzd","Xia-In","XOBSm2","Xy2L7R","X4T2vq",
        "rhtoiz","rNiDMI","rxLur-","r3+h-e","rpiJek","rVtWQX","rF+5DS","r-LQZx","rdLlaR","rJ+yUq","rttrzn","rZic32","rl+Mm4","rRL1Id","rBi8vE","r7tV7L","rfOmma","rLZFI7","rvEwvM","r1ff7D","rnZHat","rTOYUO","rDf7z1","r9EO3o","rbEjeY","rHfAQj","rrOtDu","rXZaZV","rjfKiH","rPE3MA","rzZ+rh","r5OT-8","rgvCeU","rMopQv","rwJgDi","r24vZZ","rooXi9","rUvIMg","rE4RrB","r+J4-G","rcJzmC","rI4kIN","rsvdv6","rYoq7b","rk40ap","rQJNU0","rAoUzP","r6v93s","reUEa3","rK1nUm","ruyezr","r0dx3Q","rm1ZmK","rSUGIF","rCdPvc","r8y675","rayBif","rGdiM+","rqUbrJ","rW1s-y","rid2ew","rOyLQT","ry1SDW","r4U-Zl",
        "HhQqZ0","HNXdDp","HxCkQs","H3hzeP","HpX9-N","HVQUrC","HFhNMb","H-C0i6","HdCv7g","HJhgv9","HtQpIG","HZXCmB","Hlh43v","HRCRzU","HBXIUZ","H7QXai","Hfrs3T","HLkbzw","HvNiUl","H18BaW","Hnk-7+","HTrSvf","HD8LIy","H9N2mJ","HbNx-F","HH8erK","HrrnM5","HXkEic","Hj86Zm","HPNPD3","HzkGQQ","H5rZer","HgSc-d","HM3rr4","HwAyML","H2bliE","Ho3VZq","HUS8DR","HEb1Q2","H+AMen","HcAh3X","HIbuzk","HsSDUx","HY3oaS","HkbQ7I","HQA5vz","HA3WIe","H6SJm-","Hexa7A","HKmtvH","HuHAI8","H06jmh","HmmT3j","HSx+zY","HC63UV","H8HKau","HaHfZO","HG6wDt","HqxFQo","HWmme1","Hi6O-7","HOH7ra","HymYMD","H4xHiM",
        "bhPzvV","bNYk7u","bxFdmj","b3eqIY","bpY0z8","bVPN3h","bFeUaA","b-F9UH","bdFCDD","bJepZM","btPge7","bZYvQa","bleXro","bRFI-1","bBYRiO","b7P4Mt","bfsBr2","bLji-n","bvKbiq","b1-sMR","bnj2DL","bTsLZE","bD-Sed","b9K-Q4","bbKEze","bH-n3-","brseaI","bXjxUz","bj-Zvx","bPKG7S","bzjPmX","b5s6Ik","bgVlzy","bM0y3J","bwzra+","b2ccUf","bo0Mvl","bUV17W","bEc8mT","b+zVIw","bczorQ","bIcD-r","bsVuim","bY0hM3","bkcJD5","bQzWZc","bA05eF","b6VQQK","beujDb","bKpAZ6","buIteN","b05aQC","bmpKrs","bSu3-P","bC5+i0","b8ITMp","baImvZ","bG5F7i","bquwmv","bWpfIU","bi5HzG","bOIY3B","byp7ag","b4uOU9",
        "5hTSGz","5N2-oI","5xB25-","53aLxe","5p2bSk","5VTscX","5FaB1S","5-BiBx","5dBPOR","5Ja6gq","5tTZXn","5Z2GF2","5laeK4","5RBxkd","5B2E9E","57TntL","5fwUKa","5Ln9k7","5vG09M","517NtD","5nndOt","5TwqgO","5D7zX1","59GkFo","5bGRSY","5H74cj","5rwX1u","5XnIBV","5j7gGH","5PGvoA","5znC5h","55wpx8","5gR+SU","5MWTcv","5wDK1i","52g3BZ","5oWtG9","5URaog","5Egj5B","5+DAxG","5cD7KC","5IgOkN","5sRH96","5YWYtb","5kgwOp","5QDfg0","5AWmXP","56RFFs","5eq8O3","5KlVgm","5uMMXr","5091FQ","5mlrKK","5SqckF","5C9l9c","58Myt5","5aM5Gf","5G9Qo+","5qqJ5J","5WlWxy","5i9uSw","5OMhcT","5ylo1W","54qDBl",
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        "jhuYB0","jNpH1p","jxIOcs","j357SP","jppFxN","jVum5C","jF5fob","j-IwG6","jdI3tg","jJ5K99","jtuTkG","jZp+KB","jl5AFv","jRIjXU","jBpagZ","j7utOi","jfVWFT","jL0JXw","jvzQgl","j1c5OW","jn0Dt+","jTVo9f","jDchky","j9zuKJ","jbz1xF","jHcM5K","jrVVo5","jX08Gc","jjcyBm","jPzl13","jz0ccQ","j5VrSr","jgsGxd","jMjZ54","jwK6oL","j2-PGE","jojnBq","jUsE1R","jE-xc2","j+KeSn","jcKLFX","jI-2Xk","jss-gx","jYjSOS","jk-itI","jQKB9z","jAjske","j6sbK-","jePItA","jKYX9H","juF4k8","j0eRKh","jmYpFj","jSPCXY","jCevgV","j8FgOu","jaFNBO","jGe01t","jqP9co","jWYUS1","jiekx7","jOFz5a","jyYqoD","j4PdGM",
        "1h1bN0","1NUsjp","1xdB+s","13yiqP","1pUSRN","1V1-fC","1Fy2Yb","1-dLC6","1ddeVg","1Jyxb9","1t1E2G","1ZUnyB","1lyPJv","1Rd6nU","1BUZ6Z","171Gui","1fodJT","1Lvqnw","1v4z6l","11JkuW","1nvUV+","1To9bf","1DJ02y","194NyJ","1b4gRF","1HJvfK","1roCY5","1XvpCc","1jJRNm","1P44j3","1zvX+Q","15oIqr","1gZtRd","1MOaf4","1wfjYL","12EACE","1oO+Nq","1UZTjR","1EEK+2","1+f3qn","1cfwJX","1IEfnk","1sZm6x","1YOFuS","1kE7VI","1QfObz","1AOH2e","16ZYy-","1eirVA","1KtcbH","1u+l28","10Lyyh","1mt8Jj","1SiVnY","1CLM6V","18+1uu","1a+uNO","1GLhjt","1qio+o","1WtDq1","1iL5R7","1O+Qfa","1ytJYD","14iWCM",
        "vh2ibV","vNTBVu","vxasyj","v3Bb2Y","vpTLn8","vV22Jh","vFB-uA","v-aS6H","vdanjD","vJBENM","vt2xq7","vZTe+a","vlBGfo","vRaZR1","vBT6CO","v72PYt","vfnkf2","vLwzRn","vv7qCq","v1GdYR","vnwNjL","vTn0NE","vDG9qd","v97U+4","vb7pne","vHGCJ-","vrnvuI","vXwg6z","vjGIbx","vP7XVS","vzw4yX","v5nR2k","vgWAny","vMRjJJ","vwgau+","v2Dt6f","voR3bl","vUWKVW","vEDTyT","v+g+2w","vcgFfQ","vIDmRr","vsWfCm","vYRwY3","vkDYj5","vQgHNc","vAROqF","v6W7+K","velyjb","vKqlN6","vu9cqN","v0Mr+C","vmq1fs","vSlMRP","vCMVC0","v898Yp","va9DbZ","vGMoVi","vqlhyv","vWqu2U","viMWnG","vO9JJB","vyqQug","v4l569",
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        "+hEr4K","+NfcwF","+xOlHc","+3Zyp5","+pf803","+VEVAm","+FZMTr","+-O1dQ","+dOuWw","+JZhET","+tEoPW","+ZfDhl","+lZ58f","+ROQs+","+BfJLJ","+7EWly","+fLt89","+L+asg","+vtjLB","+1iAlG","+n++WU","+TLTEv","+DiKPi","+9t3hZ","+btw0p","+HifA0","+rLmTP","+X+Fds","+ji74C","+PtOwN","+z+HH6","+5LYpb","+gyd0t","+MdqAO","+wUzT1","+21kdo","+odU4a","+Uy9w7","+E10HM","++UNpD","+cUg8H","+I1vsA","+syCLh","+Ydpl8","+k1RWY","+QU4Ej","+AdXPu","+6yIhV","+eJbWk","+K4sEX","+uvBPS","+0oihx","+m4S8z","+SJ-sI","+Co2L-","+8vLle","+ave44","+Goxwd","+qJEHE","+W4npL","+ioP0R","+Ov6Aq","+y4ZTn","+4JGd2",
        "EhDyE-","ENglWe","ExRchz","E3WrPI","Epg1sS","EVDM8x","EFWVlk","E-R8LX","EdRDwn","EJWo42","EtDhpR","EZguHq","ElWWAE","ERRJ0L","EBgQd4","E7D5Td","EfMAAM","EL9j0D","Evqada","E1ltT7","En93w1","ETMK4o","EDlTpt","E9q+HO","EbqFsu","EHlm8V","ErMflY","EX9wLj","EjlYEh","EPqHW8","Ez9OhH","E5M7PA","EgBksi","EMaz8Z","EwTqlU","E22dLv","EoaNEB","EUB0WG","EE29h9","E+TUPg","EcTpA6","EI2C0b","EsBvdC","EYagTN","Ek2IwP","EQTX4s","EAa4pp","E6BRH0","EeGiwr","EK7B4Q","Euwsp3","E0nbHm","Em7LAc","ESG205","ECn-dK","E8wSTF","EawnEJ","EGnEWy","EqGxhf","EW7eP+","EinGsW","EOwZ8l","Ey76lw","E4GPLT",
        "UhKgLs","UN-vlP","UxsC80","U3jpsp","Up-RPb","UVK4h6","UFjXWN","U-sIEC","UdsdTG","UJjqdB","UtKz0g","UZ-kA9","UljUHZ","URs9pi","UB-04v","U7KNwU","UfFeHl","ULexpW","UvPE4T","U1Ynww","UnePTy","UTF6dJ","UDYZ0+","U9PGAf","UbPbP5","UHYshc","UrFBWF","UXeiEK","UjYSLQ","UPP-lr","Uze28m","U5FLs3","UgIuPL","UM5hhE","UwuoWd","U2pDE4","Uo55L2","UUIQln","UEpJ8q","U+uWsR","UcurHx","UIpcpS","UsIl4X","UY5ywk","Ukp8Te","UQuVd-","UA5M0I","U6I1Az","UezwT8","UKcfdh","UuVm0A","U00FAH","Umc7HV","USzOpu","UC0H4j","U8VYwY","UaVtLo","UG0al1","Uqzj8O","UWcAst","Ui0+PD","UOVThM","UycKW7","U4z3Ea",
        "ohNpdj","oN8CTY","oxrvAV","o3kg0u","op8IpA","oVNXHH","oFk4w8","o-rR4h","odrkl7","oJkzLa","otNqsD","oZ8d8M","olkNhO","oRr0Pt","oB89Eo","o7NUW1","ofCnhq","oLhEPR","ovQxE2","o1XeWn","onhGld","oTCZL4","oDX6sL","o9QP8E","obQipI","oHXBHz","orCswe","oXhb4-","ojXLdX","oPQ2Tk","ozh-Ax","o5CS0S","ogHDp+","oM6oHf","owxhwy","o2mu4J","oo6WdT","oUHJTw","oEmQAl","o+x50W","ocxyhm","oImlP3","osHcEQ","oY6rWr","okm1lF","oQxMLK","oA6Vs5","o6H88c","oeAFlN","oKbmLC","ouSfsb","o03w86","ombYh0","oSAHPp","oC3OEs","o8S7WP","oaSAdv","oG3jTU","oqAaAZ","oWbt0i","oi33pg","oOSKH9","oybTwG","o4A+4B"
      };
      
      static_bch_codes = all_codes;
      const char *lut = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789+-\0";
      static_indices = new icl8u[256];
      for(const char *p=lut;*p;++p){
        static_indices.get()[(int)*p] = (icl8u)(p-lut);
      }
    }
  
    /// this class implements a (36-bit binary BCH en/decoder)
    /** the code can carry 12 bits of information and it can be
        extracted event if 4 errors occur */
    class BCHCoder::Impl{
      public:
      enum Constants{
        BCH_DEFAULT_M      = 6,
        BCH_DEFAULT_LENGTH = 36,
        BCH_DEFAULT_T      = 4,
        BCH_DEFAULT_K      = 12,
        BCH_MAX_M          = 6,
        BCH_MAX_P          = 7,   // MAX_M+1
        BCH_MAX_LUT        = 64,  // 2^MAX_M
        BCH_MAX_SQ         = 8    // SQRT(MAX_LUT) -- (?)
      };
      int t, m, n, length, k, d;
      FixedMatrix<int,BCH_MAX_LUT,BCH_MAX_LUT> m_elp; 
      FixedColVector<int,BCH_MAX_P> p;
      FixedColVector<int,BCH_MAX_LUT> alpha_to,index_of,g,m_d,m_l,m_ulu,m_s,m_root,m_loc,m_reg;
      
      typedef int64_t _64bits;
  
      Impl(){
        init_static_data();
  
        // {{{ open
        m = BCH_DEFAULT_M;
        length = BCH_DEFAULT_LENGTH;
        t = BCH_DEFAULT_T;
        std::fill(p.begin(),p.begin()+m+1,0);
        p[0] = p[1] = 1;
        n = (1 << m) - 1;
        
        // generate galois field GF(2**m)
          int mask = 1;
          alpha_to[m] = 0;
          for (int i = 0; i < m; i++) {
            alpha_to[i] = mask;
            index_of[alpha_to[i]] = i;
            if (p[i] != 0){
              alpha_to[m] ^= mask;
            }
            mask <<= 1;
          }
          index_of[alpha_to[m]] = m;
          mask >>= 1;
          for (int i = m + 1; i < n; i++) {
            if (alpha_to[i - 1] >= mask){
              alpha_to[i] = alpha_to[m] ^ ((alpha_to[i - 1] ^ mask) << 1);
            }else{
              alpha_to[i] = alpha_to[i - 1] << 1;
            }
            index_of[alpha_to[i]] = i;
          }
          index_of[0] = -1;
          
          gen_poly();   
          
          std::fill(m_elp.begin(),m_elp.end(),0);
      }
      // }}}
      
      bool gen_poly(){
        // {{{ open
        int ii, jj, ll, kaux;
        int test, aux, nocycles, root, noterms, rdncy;
        int cycle[1024][21], size[1024], min[1024], zeros[1024];
        
        /* Generate cycle sets modulo n, n = 2**m - 1 */
        cycle[0][0] = 0;
        size[0] = 1;
        cycle[1][0] = 1;
        size[1] = 1;
        jj = 1;			/* cycle set index */
        
        
        do {
          /* Generate the jj-th cycle set */
          ii = 0;
          do {
            ii++;
            cycle[jj][ii] = (cycle[jj][ii - 1] * 2) % n;
            size[jj]++;
            aux = (cycle[jj][ii] * 2) % n;
          } while (aux != cycle[jj][0]);
          /* Next cycle set representative */
          ll = 0;
          do {
            ll++;
            test = 0;
            for (ii = 1; ((ii <= jj) && (!test)); ii++)	
              /* Examine previous cycle sets */
              for (kaux = 0; ((kaux < size[ii]) && (!test)); kaux++)
                if (ll == cycle[ii][kaux])
                  test = 1;
          } while ((test) && (ll < (n - 1)));
          if (!(test)) {
            jj++;	/* next cycle set index */
            cycle[jj][0] = ll;
            size[jj] = 1;
          }
        } while (ll < (n - 1));
        nocycles = jj;		/* number of cycle sets modulo n */
        d = 2 * t + 1;
          
        /* Search for roots 1, 2, ..., d-1 in cycle sets */
        kaux = 0;
        rdncy = 0;
        for (ii = 1; ii <= nocycles; ii++) {
          min[kaux] = 0;
          test = 0;
          for (jj = 0; ((jj < size[ii]) && (!test)); jj++)
            for (root = 1; ((root < d) && (!test)); root++)
              if (root == cycle[ii][jj])  {
                test = 1;
                min[kaux] = ii;
              }
          if (min[kaux]) {
            rdncy += size[min[kaux]];
            kaux++;
          }
        }
        noterms = kaux;
        kaux = 1;
        for (ii = 0; ii < noterms; ii++)
          for (jj = 0; jj < size[min[ii]]; jj++) {
            zeros[kaux] = cycle[min[ii]][jj];
            kaux++;
          }
          
        k = length - rdncy;
          
        if (k<0){
          return false;
        }
          
        /* Compute the generator polynomial */
        g[0] = alpha_to[zeros[1]];
        g[1] = 1;		/* g(x) = (X + zeros[1]) initially */
        for (ii = 2; ii <= rdncy; ii++) {
          g[ii] = 1;
          for (jj = ii - 1; jj > 0; jj--)
            if (g[jj] != 0)
              g[jj] = g[jj - 1] ^ alpha_to[(index_of[g[jj]] + zeros[ii]) % n];
            else
              g[jj] = g[jj - 1];
          g[0] = alpha_to[(index_of[g[0]] + zeros[ii]) % n];
        }
        return true;
      }
      // }}}
  
      
      /// not used because, we pre-encoded the whole data-set
      void encode_bch(int *bb, const int *data){
        // {{{ open
        int    i, j;
        int    feedback;
        
        for (i = 0; i < length - k; i++)
          bb[i] = 0;
        for (i = k - 1; i >= 0; i--) {
          feedback = data[i] ^ bb[length - k - 1];
          if (feedback != 0) {
            for (j = length - k - 1; j > 0; j--)
              if (g[j] != 0)
                bb[j] = bb[j - 1] ^ feedback;
              else
                bb[j] = bb[j - 1];
            bb[0] = g[0] && feedback;
          } else {
            for (j = length - k - 1; j > 0; j--)
              bb[j] = bb[j - 1];
            bb[0] = 0;
          }
        }
      }
      // }}}
      
      // adapted version that works on an encoded int64_t,
      // the original version got an int[]
      int decode_bch_2(int64_t &code){
        // {{{ open
        
        int i, j, u, q, t2, count = 0, syn_error = 0;
        bool too_many_errors = false;
        int64_t one = 1;
        t2 = 2 * t;
        
        /* first form the syndromes */
        for (i = 1; i <= t2; i++) {
          m_s[i] = 0;
          for (j = 0; j < length; j++)
            if ((code&(one<<j)))  //TODO check
              m_s[i] ^= alpha_to[(i * j) % n];
          if (m_s[i] != 0)
            syn_error = 1; /* set error flag if non-zero syndrome */
          /*
              * Note:    If the code is used only for ERROR DETECTION, then
              *          exit program here indicating the presence of errors.
              */
          /* convert syndrome from polynomial form to index form  */
          m_s[i] = index_of[m_s[i]];
        }
        
        
        if (syn_error) {	/* if there are errors, try to correct them */
          /*
              * Compute the error location polynomial via the Berlekamp
              * iterative algorithm. Following the terminology of Lin and
              * Costello's book :   d[u] is the 'mu'th discrepancy, where
              * u='mu'+1 and 'mu' (the Greek letter!) is the step number
              * ranging from -1 to 2*t (see L&C),  l[u] is the degree of
              * the elp at that step, and u_l[u] is the difference between
              * the step number and the degree of the elp. 
              */
          /* initialise table entries */
          m_d[0] = 0;			/* index form */
          m_d[1] = m_s[1];		/* index form */
          m_elp(0,0) = 0;//[0][0] = 0;		/* index form */
          m_elp(1,0) = 1;		/* polynomial form */
          for (i = 1; i < t2; i++) {
            m_elp(0,i) = -1;	/* index form */
            m_elp(1,i) = 0;	/* polynomial form */
          }
          m_l[0] = 0;
          m_l[1] = 0;
          m_ulu[0] = -1;
          m_ulu[1] = 0;
          u = 0;
            
          do {
            u++;
            if (m_d[u] == -1) {
              m_l[u + 1] = m_l[u];
              for (i = 0; i <= m_l[u]; i++) {
                m_elp(u + 1,i) = m_elp(u,i);
                m_elp(u,i) = index_of[m_elp(u,i)];
              }
            } else
              /*
                  * search for words with greatest m_ulu[q] for
                  * which m_d[q]!=0 
                  */
              {
                q = u - 1;
                while ((m_d[q] == -1) && (q > 0))
                  q--;
                /* have found first non-zero m_d[q]  */
                if (q > 0) {
                  j = q;
                  do {
                    j--;
                    if ((m_d[j] != -1) && (m_ulu[q] < m_ulu[j]))
                      q = j;
                  } while (j > 0);
                }
              
                /*
                    * have now found q such that m_d[u]!=0 and
                    * m_ulu[q] is maximum 
                    */
                /* store degree of new elp polynomial */
                if (m_l[u] > m_l[q] + u - q)
                  m_l[u + 1] = m_l[u];
                else
                  m_l[u + 1] = m_l[q] + u - q;
              
                /* form new elp(x) */
                for (i = 0; i < t2; i++)
                  m_elp(u + 1,i) = 0;
                for (i = 0; i <= m_l[q]; i++)
                  if (m_elp(q,i) != -1)
                    m_elp(u + 1,i + u - q) = 
                    alpha_to[(m_d[u] + n - m_d[q] + m_elp(q,i)) % n];
                for (i = 0; i <= m_l[u]; i++) {
                  m_elp(u + 1,i) ^= m_elp(u,i);
                  m_elp(u,i) = index_of[m_elp(u,i)];
                }
              }
            m_ulu[u + 1] = u - m_l[u + 1];
          
            /* form (u+1)th discrepancy */
            if (u < t2) {	
              /* no discrepancy computed on last iteration */
              if (m_s[u + 1] != -1)
                m_d[u + 1] = alpha_to[m_s[u + 1]];
              else
                m_d[u + 1] = 0;
              for (i = 1; i <= m_l[u + 1]; i++)
                if ((m_s[u + 1 - i] != -1) && (m_elp(u + 1,i) != 0))
                  m_d[u + 1] ^= alpha_to[(m_s[u + 1 - i] 
                                          + index_of[m_elp(u + 1,i)]) % n];
              /* put m_d[u+1] into index form */
              m_d[u + 1] = index_of[m_d[u + 1]];	
            }
          } while ((u < t2) && (m_l[u + 1] <= t));
        
          u++;
          if (m_l[u] <= t) {/* Can correct errors */
            /* put elp into index form */
            for (i = 0; i <= m_l[u]; i++)
              m_elp(u,i) = index_of[m_elp(u,i)];
          
            /* Chien search: find roots of the error location polynomial */
            for (i = 1; i <= m_l[u]; i++)
              m_reg[i] = m_elp(u,i);
            count = 0;
            for (i = 1; i <= n; i++) {
              q = 1;
              for (j = 1; j <= m_l[u]; j++)
                if (m_reg[j] != -1) {
                  m_reg[j] = (m_reg[j] + j) % n;
                  q ^= alpha_to[m_reg[j]];
                }
              if (!q) {	/* store root and error
                              * location number indices */
                m_root[count] = i;
                m_loc[count] = n - i;
                count++;
              }
            }
            if (count == m_l[u])	
              {
                /* no. roots = degree of elp hence <= t errors */
                for (i = 0; i < m_l[u]; i++)
                  {
                    int li = m_loc[i];
                    if(li<BCH_DEFAULT_LENGTH){
                      //code[m_loc[i]].flip(); //^= 1;
                      code ^= (one << li);
                    }
                    else too_many_errors = true;
                  }
              }
            else	/* elp has degree >t hence cannot solve */
              {
                return(m_l[u]); // number of errors
              
              }
          }
        }
        if(too_many_errors) return(BCH_DEFAULT_T+1);
        else return(syn_error == 0 ? 0 : m_l[u]); // number of errors
      }
      // }}}
    };
    
    BCHCoder::BCHCoder():impl(new Impl){ }
  
    BCHCoder::~BCHCoder(){ delete impl; }
  
    
    BCHCode BCHCoder::encode(int idx){
      // {{{ open
      init_static_data();
      
      if(idx < 0 || idx > 4095) throw ICLException("invalid bch code ID (allowed: 0 <= index <= 4095)");
      
      const char *pc = static_bch_codes[idx];
      
      BCHCode c;
      for(int i=0;i<6;++i){
        int idx = static_indices.get()[(int)pc[i]];
        for(int j=0;j<6;++j){
          c[i*6+j] = idx & (1<<j);
        }
        // next 6 bits of c are used from ?? 
      }
      return c;
    }
    // }}}
    
    DecodedBCHCode BCHCoder::decode(const BCHCode &code){
      // {{{ open
      int64_t c=0,o=1;
      for(int i=0;i<36;++i){
        if(code[35-i]){
          c |= o << i;
        }
      }
      c ^= 0x8f80b8750ll;
      int err = impl->decode_bch_2(c);// BCHCoder::getInstance()->decode_bch_2(c);
  
      DecodedBCHCode ret;
      ret.origCode = code;
      
      if(err > BCHCoder::Impl::BCH_DEFAULT_T){
        ret.errors = 36;
        ret.id = -1;
      }else{
        ret.errors = err;
        ret.id = 0;
        for(int i=24,j=0;i<36;++i,++j){
          if(c & (o<<i)){
            ret.id |= (1 << j);
          }
        }
        ret.correctedCode = err ? encode(ret.id) : ret.origCode;
      }
      return ret;
    }
    // }}}
  
  
  
    
    DecodedBCHCode BCHCoder::decode(const icl8u data[36]){
      BCHCode code(0);
      for(unsigned int i=0;i<36;++i){
        code[i] = data[i];
      }
      return decode(code);
    }
    
    
    static BCHCode code_from_image(const Img8u &image, bool useROI) throw (ICLException){
      BCHCode code(0);
      ICLASSERT_THROW(image.getChannels(), ICLException("code_from_image(const Img8u&,bool): input image has not channels"));
      if(useROI){
        ICLASSERT_THROW(image.getROISize().getDim() == 36, ICLException("code_from_image(const Img8u&,true): images ROI dim must be 36"));
        Img8u::const_roi_iterator it = image.beginROI(0);
        for(unsigned int i=0;i<36;++i,++it){
          code[i] = *it;
        }
      }else{
        ICLASSERT_THROW(image.getSize().getDim() == 36, ICLException("decode_bch(const Img8u&,false): image dim must be 36"));
        Img8u::const_iterator it = image.begin(0);
        for(unsigned int i=0;i<36;++i,++it){
          code[i] = *it;
        }
      }    
      return code;
    }
    
    DecodedBCHCode BCHCoder::decode(const Img8u &image, bool useROI) throw (ICLException){
      return decode(code_from_image(image,useROI));
    }
    
    
    BCHCode BCHCoder::rotateCode(const BCHCode &in){
      BCHCode out(0);
      for(int y=0;y<6;++y){
        for(int x=0;x<6;++x){
          if(in[x+6*y]) out.set(5+6*x-y);
        }
      }
      return out;
    }
  
    DecodedBCHCode2D BCHCoder::decode2D(const Img8u &image, int maxID, bool useROI) throw (ICLException){
      BCHCode last = code_from_image(image,useROI);
      DecodedBCHCode2D best = decode(last);
      if(best.id > maxID){
        best.errors = 36;
        best.id = -1;
      }
      best.rot = DecodedBCHCode2D::Rot0;
      if(!best.errors) return best;
  
      for(int i=1;i<4;++i){
        last = rotateCode(last);
        DecodedBCHCode2D curr = decode(last);
        if(curr.id > maxID) continue; //curr.errors = 36;
        curr.rot = (DecodedBCHCode2D::Rotation)i;
        if(!curr.errors) return curr;
        if(curr < best){
          best = curr;
        }
      }
      return best;
    }
  
    std::ostream &operator<<(std::ostream &s, const DecodedBCHCode2D::Rotation &r){
      return s << (r == DecodedBCHCode2D::Rot0 ? "0 Degree" :
                   r == DecodedBCHCode2D::Rot90 ? "90 Degree" :
                   r == DecodedBCHCode2D::Rot180 ? "180 Degree" :
                   r == DecodedBCHCode2D::Rot270 ? "270 Degree" :
                   "??? Degree");
    }
  
  
    Img8u BCHCoder::createMarkerImage(int idx, int border, const Size &resultSize){
      if(border < 0) throw ICLException("create_bch_marker_image: border must be >= 0");
      BCHCode c = encode(idx);
      Img8u im(Size(6+2*border,6+2*border),1);
      Channel8u ch=im[0];
      im.fill(0);
      for(int y=0;y<6;++y){
        for(int x=0;x<6;++x){
          ch(border+x,border+y) = 255 * (c[x+6*y]);
        }
      }
      if(resultSize != Size::null){
        im.scale(resultSize,interpolateNN);
      }
      return im;
    }
  } // namespace markers
}