/*
* 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 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;
};
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->nroots != nroots) continue;
if(rs->pad != pad) continue;
if(rs->mm != symsize) continue;
if(rs->gfpoly != gfpoly) continue;
if(rs->fcr != fcr) continue;
if(rs->prim != prim) continue;
return rs;
}
rs = init_rs_char(symsize, gfpoly, fcr, prim, nroots, pad);
rs->next = rslist;
rslist = rs;
return rs;
}
void free_rs_char(RS *rs)
{
free(rs->alpha_to);
free(rs->index_of);
free(rs->genpoly);
free(rs);
}
/* 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;
}
}
