File: reedsol.c

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/** 
 *
 * This is a simple Reed-Solomon encoder
 * (C) Cliff Hones 2004
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA
 *
 */ 


// It is not written with high efficiency in mind, so is probably
// not suitable for real-time encoding.  The aim was to keep it
// simple, general and clear.
//
// <Some notes on the theory and implementation need to be added here>

// Usage:
// First call rs_init_gf(poly) to set up the Galois Field parameters.
// Then  call rs_init_code(size, index) to set the encoding size
// Then  call rs_encode(datasize, data, out) to encode the data.
//
// These can be called repeatedly as required - but note that
// rs_init_code must be called following any rs_init_gf call.
//
// If the parameters are fixed, some of the statics below can be
// replaced with constants in the obvious way, and additionally
// malloc/free can be avoided by using static arrays of a suitable
// size.

#include <stdio.h>              // only needed for debug (main)
#include <stdlib.h>             // only needed for malloc/free

static int gfpoly;
static int symsize;             // in bits
static int logmod;              // 2**symsize - 1
static int rlen;

static int *log = NULL,
   *alog = NULL,
   *rspoly = NULL;

// rs_init_gf(poly) initialises the parameters for the Galois Field.
// The symbol size is determined from the highest bit set in poly
// This implementation will support sizes up to 30 bits (though that
// will result in very large log/antilog tables) - bit sizes of
// 8 or 4 are typical
//
// The poly is the bit pattern representing the GF characteristic
// polynomial.  e.g. for ECC200 (8-bit symbols) the polynomial is
// a**8 + a**5 + a**3 + a**2 + 1, which translates to 0x12d.

void rs_init_gf (int poly)
{
   int m,
     b,
     p,
     v;

   // Return storage from previous setup
   if (log)
   {
      free (log);
      free (alog);
      free (rspoly);
      rspoly = NULL;
   }
   // Find the top bit, and hence the symbol size
   for (b = 1, m = 0; b <= poly; b <<= 1)
      m++;
   b >>= 1;
   m--;
   gfpoly = poly;
   symsize = m;

   // Calculate the log/alog tables
   logmod = (1 << m) - 1;
   log = (int *) malloc (sizeof (int) * (logmod + 1));
   alog = (int *) malloc (sizeof (int) * logmod);

   for (p = 1, v = 0; v < logmod; v++)
   {
      alog[v] = p;
      log[p] = v;
      p <<= 1;
      if (p & b)
         p ^= poly;
   }
}

// rs_init_code(nsym, index) initialises the Reed-Solomon encoder
// nsym is the number of symbols to be generated (to be appended
// to the input data).  index is usually 1 - it is the index of
// the constant in the first term (i) of the RS generator polynomial:
// (x + 2**i)*(x + 2**(i+1))*...   [nsym terms]
// For ECC200, index is 1.

void rs_init_code (int nsym, int index)
{
   int i,
     k;

   if (rspoly)
      free (rspoly);
   rspoly = (int *) malloc (sizeof (int) * (nsym + 1));

   rlen = nsym;

   rspoly[0] = 1;
   for (i = 1; i <= nsym; i++)
   {
      rspoly[i] = 1;
      for (k = i - 1; k > 0; k--)
      {
         if (rspoly[k])
            rspoly[k] = alog[(log[rspoly[k]] + index) % logmod];
         rspoly[k] ^= rspoly[k - 1];
      }
      rspoly[0] = alog[(log[rspoly[0]] + index) % logmod];
      index++;
   }
}

// Note that the following uses byte arrays, so is only suitable for
// symbol sizes up to 8 bits.  Just change the data type of data and res
// to unsigned int * for larger symbols.

void rs_encode (int len, unsigned char *data, unsigned char *res)
{
   int i,
     k,
     m;
   for (i = 0; i < rlen; i++)
      res[i] = 0;
   for (i = 0; i < len; i++)
   {
      m = res[rlen - 1] ^ data[i];
      for (k = rlen - 1; k > 0; k--)
      {
         if (m && rspoly[k])
            res[k] = res[k - 1] ^ alog[(log[m] + log[rspoly[k]]) % logmod];
         else
            res[k] = res[k - 1];
      }
      if (m && rspoly[0])
         res[0] = alog[(log[m] + log[rspoly[0]]) % logmod];
      else
         res[0] = 0;
   }
}

#ifndef LIB
// The following tests the routines with the ISO/IEC 16022 Annexe R data
int main (void)
{
   register int i;

   unsigned char data[9] = { 142, 164, 186 };
   unsigned char out[5];

   rs_init_gf (0x12d);
   rs_init_code (5, 1);

   rs_encode (3, data, out);

   printf ("Result of Annexe R encoding:\n");
   for (i = 4; i >= 0; i--)
      printf ("  %d\n", out[i]);

   return 0;
}
#endif