rscode.c

/*
 * qrencode - QR Code encoder
 *
 * Reed solomon encoder. This code is taken from Phil Karn's libfec then
 * editted and packed into a pair of .c and .h files.
 *
 * Copyright (C) 2002, 2003, 2004, 2006 Phil Karn, KA9Q
 * (libfec is released under the GNU Lesser General Public License.)
 *
 * Copyright (C) 2006, 2007, 2008, 2009 Kentaro Fukuchi <fukuchi@megaui.net>
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or any later version.
 *
 * This library 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 */

#include <stdlib.h>
#include <string.h>
#include "rscode.h"

/* Stuff specific to the 8-bit symbol version of the general purpose RS codecs
 *
 */
typedef unsigned char data_t;


/**
 * Reed-Solomon codec control block
 */
struct _RS {
	int mm;              /* Bits per symbol */
	int nn;              /* Symbols per block (= (1<<mm)-1) */
	data_t *alpha_to;     /* log lookup table */
	data_t *index_of;     /* Antilog lookup table */
	data_t *genpoly;      /* Generator polynomial */
	int nroots;     /* Number of generator roots = number of parity symbols */
	int fcr;        /* First consecutive root, index form */
	int prim;       /* Primitive element, index form */
	int iprim;      /* prim-th root of 1, index form */
	int pad;        /* Padding bytes in shortened block */
	int gfpoly;
	struct _RS *next;
};

static RS *rslist = NULL;

static inline int modnn(RS *rs, int x){
	while (x >= rs->nn) {
		x -= rs->nn;
		x = (x >> rs->mm) + (x & rs->nn);
	}
	return x;
}


#define MODNN(x) modnn(rs,x)

#define MM (rs->mm)
#define NN (rs->nn)
#define ALPHA_TO (rs->alpha_to) 
#define INDEX_OF (rs->index_of)
#define GENPOLY (rs->genpoly)
#define NROOTS (rs->nroots)
#define FCR (rs->fcr)
#define PRIM (rs->prim)
#define IPRIM (rs->iprim)
#define PAD (rs->pad)
#define A0 (NN)


/* Initialize a Reed-Solomon codec
 * symsize = symbol size, bits
 * gfpoly = Field generator polynomial coefficients
 * fcr = first root of RS code generator polynomial, index form
 * prim = primitive element to generate polynomial roots
 * nroots = RS code generator polynomial degree (number of roots)
 * pad = padding bytes at front of shortened block
 */
static RS *init_rs_char(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad)
{
  RS *rs;


/* Common code for intializing a Reed-Solomon control block (char or int symbols)
 * Copyright 2004 Phil Karn, KA9Q
 * May be used under the terms of the GNU Lesser General Public License (LGPL)
 */
//#undef NULL
//#define NULL ((void *)0)

  int i, j, sr,root,iprim;

  rs = NULL;
  /* Check parameter ranges */
  if(symsize < 0 || symsize > (int)(8*sizeof(data_t))){
    goto done;
  }

  if(fcr < 0 || fcr >= (1<<symsize))
    goto done;
  if(prim <= 0 || prim >= (1<<symsize))
    goto done;
  if(nroots < 0 || nroots >= (1<<symsize))
    goto done; /* Can't have more roots than symbol values! */
  if(pad < 0 || pad >= ((1<<symsize) -1 - nroots))
    goto done; /* Too much padding */

  rs = (RS *)calloc(1,sizeof(RS));
  if(rs == NULL)
    goto done;

  rs->mm = symsize;
  rs->nn = (1<<symsize)-1;
  rs->pad = pad;

  rs->alpha_to = (data_t *)malloc(sizeof(data_t)*(rs->nn+1));
  if(rs->alpha_to == NULL){
    free(rs);
    rs = NULL;
    goto done;
  }
  rs->index_of = (data_t *)malloc(sizeof(data_t)*(rs->nn+1));
  if(rs->index_of == NULL){
    free(rs->alpha_to);
    free(rs);
    rs = NULL;
    goto done;
  }

  /* Generate Galois field lookup tables */
  rs->index_of[0] = A0; /* log(zero) = -inf */
  rs->alpha_to[A0] = 0; /* alpha**-inf = 0 */
  sr = 1;
  for(i=0;i<rs->nn;i++){
    rs->index_of[sr] = i;
    rs->alpha_to[i] = sr;
    sr <<= 1;
    if(sr & (1<<symsize))
      sr ^= gfpoly;
    sr &= rs->nn;
  }
  if(sr != 1){
    /* field generator polynomial is not primitive! */
    free(rs->alpha_to);
    free(rs->index_of);
    free(rs);
    rs = NULL;
    goto done;
  }

  /* Form RS code generator polynomial from its roots */
  rs->genpoly = (data_t *)malloc(sizeof(data_t)*(nroots+1));
  if(rs->genpoly == NULL){
    free(rs->alpha_to);
    free(rs->index_of);
    free(rs);
    rs = NULL;
    goto done;
  }
  rs->fcr = fcr;
  rs->prim = prim;
  rs->nroots = nroots;
  rs->gfpoly = gfpoly;

  /* Find prim-th root of 1, used in decoding */
  for(iprim=1;(iprim % prim) != 0;iprim += rs->nn)
    ;
  rs->iprim = iprim / prim;

  rs->genpoly[0] = 1;
  for (i = 0,root=fcr*prim; i < nroots; i++,root += prim) {
    rs->genpoly[i+1] = 1;

    /* Multiply rs->genpoly[] by  @**(root + x) */
    for (j = i; j > 0; j--){
      if (rs->genpoly[j] != 0)
	rs->genpoly[j] = rs->genpoly[j-1] ^ rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[j]] + root)];
      else
	rs->genpoly[j] = rs->genpoly[j-1];
    }
    /* rs->genpoly[0] can never be zero */
    rs->genpoly[0] = rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[0]] + root)];
  }
  /* convert rs->genpoly[] to index form for quicker encoding */
  for (i = 0; i <= nroots; i++)
    rs->genpoly[i] = rs->index_of[rs->genpoly[i]];
 done:;

  return rs;
}

RS *init_rs(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad)
{
	RS *rs;

	for(rs = rslist; rs != NULL; rs = rs->next) {
		if(rs->pad != pad) continue;
		if(rs->nroots != nroots) continue;
		if(rs->mm != symsize) continue;
		if(rs->gfpoly != gfpoly) continue;
		if(rs->fcr != fcr) continue;
		if(rs->prim != prim) continue;

		goto DONE;
	}

	rs = init_rs_char(symsize, gfpoly, fcr, prim, nroots, pad);
	if(rs == NULL) goto DONE;
	rs->next = rslist;
	rslist = rs;

DONE:
	return rs;
}


void free_rs_char(RS *rs)
{
	free(rs->alpha_to);
	free(rs->index_of);
	free(rs->genpoly);
	free(rs);
}

void free_rs_cache(void)
{
	RS *rs, *next;

	rs = rslist;
	while(rs != NULL) {
		next = rs->next;
		free_rs_char(rs);
		rs = next;
	}
}

/* The guts of the Reed-Solomon encoder, meant to be #included
 * into a function body with the following typedefs, macros and variables supplied
 * according to the code parameters:

 * data_t - a typedef for the data symbol
 * data_t data[] - array of NN-NROOTS-PAD and type data_t to be encoded
 * data_t parity[] - an array of NROOTS and type data_t to be written with parity symbols
 * NROOTS - the number of roots in the RS code generator polynomial,
 *          which is the same as the number of parity symbols in a block.
            Integer variable or literal.
	    * 
 * NN - the total number of symbols in a RS block. Integer variable or literal.
 * PAD - the number of pad symbols in a block. Integer variable or literal.
 * ALPHA_TO - The address of an array of NN elements to convert Galois field
 *            elements in index (log) form to polynomial form. Read only.
 * INDEX_OF - The address of an array of NN elements to convert Galois field
 *            elements in polynomial form to index (log) form. Read only.
 * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
 * GENPOLY - an array of NROOTS+1 elements containing the generator polynomial in index form

 * The memset() and memmove() functions are used. The appropriate header
 * file declaring these functions (usually <string.h>) must be included by the calling
 * program.

 * Copyright 2004, Phil Karn, KA9Q
 * May be used under the terms of the GNU Lesser General Public License (LGPL)
 */

#undef A0
#define A0 (NN) /* Special reserved value encoding zero in index form */

void encode_rs_char(RS *rs, const data_t *data, data_t *parity)
{
  int i, j;
  data_t feedback;

  memset(parity,0,NROOTS*sizeof(data_t));

  for(i=0;i<NN-NROOTS-PAD;i++){
    feedback = INDEX_OF[data[i] ^ parity[0]];
    if(feedback != A0){      /* feedback term is non-zero */
#ifdef UNNORMALIZED
      /* This line is unnecessary when GENPOLY[NROOTS] is unity, as it must
       * always be for the polynomials constructed by init_rs()
       */
      feedback = MODNN(NN - GENPOLY[NROOTS] + feedback);
#endif
      for(j=1;j<NROOTS;j++)
	parity[j] ^= ALPHA_TO[MODNN(feedback + GENPOLY[NROOTS-j])];
    }
    /* Shift */
    memmove(&parity[0],&parity[1],sizeof(data_t)*(NROOTS-1));
    if(feedback != A0)
      parity[NROOTS-1] = ALPHA_TO[MODNN(feedback + GENPOLY[0])];
    else
      parity[NROOTS-1] = 0;
  }
}