1/*
2 * qrencode - QR Code encoder
3 *
4 * Reed solomon encoder. This code is taken from Phil Karn's libfec then
5 * editted and packed into a pair of .c and .h files.
6 *
7 * Copyright (C) 2002, 2003, 2004, 2006 Phil Karn, KA9Q
8 * (libfec is released under the GNU Lesser General Public License.)
9 *
10 * Copyright (C) 2006-2011 Kentaro Fukuchi <kentaro@fukuchi.org>
11 *
12 * This library is free software; you can redistribute it and/or
13 * modify it under the terms of the GNU Lesser General Public
14 * License as published by the Free Software Foundation; either
15 * version 2.1 of the License, or any later version.
16 *
17 * This library is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20 * Lesser General Public License for more details.
21 *
22 * You should have received a copy of the GNU Lesser General Public
23 * License along with this library; if not, write to the Free Software
24 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
25 */
26
27#if HAVE_CONFIG_H
28# include "config.h"
29#endif
30#include <stdlib.h>
31#include <string.h>
32#ifdef HAVE_LIBPTHREAD
33#  include <pthread.h>
34#endif
35
36#include "rscode.h"
37
38/* Stuff specific to the 8-bit symbol version of the general purpose RS codecs
39 *
40 */
41typedef unsigned char data_t;
42
43
44/**
45 * Reed-Solomon codec control block
46 */
47struct _RS {
48	int mm;              /* Bits per symbol */
49	int nn;              /* Symbols per block (= (1<<mm)-1) */
50	data_t *alpha_to;     /* log lookup table */
51	data_t *index_of;     /* Antilog lookup table */
52	data_t *genpoly;      /* Generator polynomial */
53	int nroots;     /* Number of generator roots = number of parity symbols */
54	int fcr;        /* First consecutive root, index form */
55	int prim;       /* Primitive element, index form */
56	int iprim;      /* prim-th root of 1, index form */
57	int pad;        /* Padding bytes in shortened block */
58	int gfpoly;
59	struct _RS *next;
60};
61
62static RS *rslist = NULL;
63#ifdef HAVE_LIBPTHREAD
64static pthread_mutex_t rslist_mutex = PTHREAD_MUTEX_INITIALIZER;
65#endif
66
67static inline int modnn(RS *rs, int x){
68	while (x >= rs->nn) {
69		x -= rs->nn;
70		x = (x >> rs->mm) + (x & rs->nn);
71	}
72	return x;
73}
74
75
76#define MODNN(x) modnn(rs,x)
77
78#define MM (rs->mm)
79#define NN (rs->nn)
80#define ALPHA_TO (rs->alpha_to)
81#define INDEX_OF (rs->index_of)
82#define GENPOLY (rs->genpoly)
83#define NROOTS (rs->nroots)
84#define FCR (rs->fcr)
85#define PRIM (rs->prim)
86#define IPRIM (rs->iprim)
87#define PAD (rs->pad)
88#define A0 (NN)
89
90
91/* Initialize a Reed-Solomon codec
92 * symsize = symbol size, bits
93 * gfpoly = Field generator polynomial coefficients
94 * fcr = first root of RS code generator polynomial, index form
95 * prim = primitive element to generate polynomial roots
96 * nroots = RS code generator polynomial degree (number of roots)
97 * pad = padding bytes at front of shortened block
98 */
99static RS *init_rs_char(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad)
100{
101  RS *rs;
102
103
104/* Common code for intializing a Reed-Solomon control block (char or int symbols)
105 * Copyright 2004 Phil Karn, KA9Q
106 * May be used under the terms of the GNU Lesser General Public License (LGPL)
107 */
108//#undef NULL
109//#define NULL ((void *)0)
110
111  int i, j, sr,root,iprim;
112
113  rs = NULL;
114  /* Check parameter ranges */
115  if(symsize < 0 || symsize > (int)(8*sizeof(data_t))){
116    goto done;
117  }
118
119  if(fcr < 0 || fcr >= (1<<symsize))
120    goto done;
121  if(prim <= 0 || prim >= (1<<symsize))
122    goto done;
123  if(nroots < 0 || nroots >= (1<<symsize))
124    goto done; /* Can't have more roots than symbol values! */
125  if(pad < 0 || pad >= ((1<<symsize) -1 - nroots))
126    goto done; /* Too much padding */
127
128  rs = (RS *)calloc(1,sizeof(RS));
129  if(rs == NULL)
130    goto done;
131
132  rs->mm = symsize;
133  rs->nn = (1<<symsize)-1;
134  rs->pad = pad;
135
136  rs->alpha_to = (data_t *)malloc(sizeof(data_t)*(rs->nn+1));
137  if(rs->alpha_to == NULL){
138    free(rs);
139    rs = NULL;
140    goto done;
141  }
142  rs->index_of = (data_t *)malloc(sizeof(data_t)*(rs->nn+1));
143  if(rs->index_of == NULL){
144    free(rs->alpha_to);
145    free(rs);
146    rs = NULL;
147    goto done;
148  }
149
150  /* Generate Galois field lookup tables */
151  rs->index_of[0] = A0; /* log(zero) = -inf */
152  rs->alpha_to[A0] = 0; /* alpha**-inf = 0 */
153  sr = 1;
154  for(i=0;i<rs->nn;i++){
155    rs->index_of[sr] = i;
156    rs->alpha_to[i] = sr;
157    sr <<= 1;
158    if(sr & (1<<symsize))
159      sr ^= gfpoly;
160    sr &= rs->nn;
161  }
162  if(sr != 1){
163    /* field generator polynomial is not primitive! */
164    free(rs->alpha_to);
165    free(rs->index_of);
166    free(rs);
167    rs = NULL;
168    goto done;
169  }
170
171  /* Form RS code generator polynomial from its roots */
172  rs->genpoly = (data_t *)malloc(sizeof(data_t)*(nroots+1));
173  if(rs->genpoly == NULL){
174    free(rs->alpha_to);
175    free(rs->index_of);
176    free(rs);
177    rs = NULL;
178    goto done;
179  }
180  rs->fcr = fcr;
181  rs->prim = prim;
182  rs->nroots = nroots;
183  rs->gfpoly = gfpoly;
184
185  /* Find prim-th root of 1, used in decoding */
186  for(iprim=1;(iprim % prim) != 0;iprim += rs->nn)
187    ;
188  rs->iprim = iprim / prim;
189
190  rs->genpoly[0] = 1;
191  for (i = 0,root=fcr*prim; i < nroots; i++,root += prim) {
192    rs->genpoly[i+1] = 1;
193
194    /* Multiply rs->genpoly[] by  @**(root + x) */
195    for (j = i; j > 0; j--){
196      if (rs->genpoly[j] != 0)
197	rs->genpoly[j] = rs->genpoly[j-1] ^ rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[j]] + root)];
198      else
199	rs->genpoly[j] = rs->genpoly[j-1];
200    }
201    /* rs->genpoly[0] can never be zero */
202    rs->genpoly[0] = rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[0]] + root)];
203  }
204  /* convert rs->genpoly[] to index form for quicker encoding */
205  for (i = 0; i <= nroots; i++)
206    rs->genpoly[i] = rs->index_of[rs->genpoly[i]];
207 done:;
208
209  return rs;
210}
211
212RS *init_rs(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad)
213{
214	RS *rs;
215
216#ifdef HAVE_LIBPTHREAD
217	pthread_mutex_lock(&rslist_mutex);
218#endif
219	for(rs = rslist; rs != NULL; rs = rs->next) {
220		if(rs->pad != pad) continue;
221		if(rs->nroots != nroots) continue;
222		if(rs->mm != symsize) continue;
223		if(rs->gfpoly != gfpoly) continue;
224		if(rs->fcr != fcr) continue;
225		if(rs->prim != prim) continue;
226
227		goto DONE;
228	}
229
230	rs = init_rs_char(symsize, gfpoly, fcr, prim, nroots, pad);
231	if(rs == NULL) goto DONE;
232	rs->next = rslist;
233	rslist = rs;
234
235DONE:
236#ifdef HAVE_LIBPTHREAD
237	pthread_mutex_unlock(&rslist_mutex);
238#endif
239	return rs;
240}
241
242
243void free_rs_char(RS *rs)
244{
245	free(rs->alpha_to);
246	free(rs->index_of);
247	free(rs->genpoly);
248	free(rs);
249}
250
251void free_rs_cache(void)
252{
253	RS *rs, *next;
254
255#ifdef HAVE_LIBPTHREAD
256	pthread_mutex_lock(&rslist_mutex);
257#endif
258	rs = rslist;
259	while(rs != NULL) {
260		next = rs->next;
261		free_rs_char(rs);
262		rs = next;
263	}
264	rslist = NULL;
265#ifdef HAVE_LIBPTHREAD
266	pthread_mutex_unlock(&rslist_mutex);
267#endif
268}
269
270/* The guts of the Reed-Solomon encoder, meant to be #included
271 * into a function body with the following typedefs, macros and variables supplied
272 * according to the code parameters:
273
274 * data_t - a typedef for the data symbol
275 * data_t data[] - array of NN-NROOTS-PAD and type data_t to be encoded
276 * data_t parity[] - an array of NROOTS and type data_t to be written with parity symbols
277 * NROOTS - the number of roots in the RS code generator polynomial,
278 *          which is the same as the number of parity symbols in a block.
279            Integer variable or literal.
280	    *
281 * NN - the total number of symbols in a RS block. Integer variable or literal.
282 * PAD - the number of pad symbols in a block. Integer variable or literal.
283 * ALPHA_TO - The address of an array of NN elements to convert Galois field
284 *            elements in index (log) form to polynomial form. Read only.
285 * INDEX_OF - The address of an array of NN elements to convert Galois field
286 *            elements in polynomial form to index (log) form. Read only.
287 * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
288 * GENPOLY - an array of NROOTS+1 elements containing the generator polynomial in index form
289
290 * The memset() and memmove() functions are used. The appropriate header
291 * file declaring these functions (usually <string.h>) must be included by the calling
292 * program.
293
294 * Copyright 2004, Phil Karn, KA9Q
295 * May be used under the terms of the GNU Lesser General Public License (LGPL)
296 */
297
298#undef A0
299#define A0 (NN) /* Special reserved value encoding zero in index form */
300
301void encode_rs_char(RS *rs, const data_t *data, data_t *parity)
302{
303  int i, j;
304  data_t feedback;
305
306  memset(parity,0,NROOTS*sizeof(data_t));
307
308  for(i=0;i<NN-NROOTS-PAD;i++){
309    feedback = INDEX_OF[data[i] ^ parity[0]];
310    if(feedback != A0){      /* feedback term is non-zero */
311#ifdef UNNORMALIZED
312      /* This line is unnecessary when GENPOLY[NROOTS] is unity, as it must
313       * always be for the polynomials constructed by init_rs()
314       */
315      feedback = MODNN(NN - GENPOLY[NROOTS] + feedback);
316#endif
317      for(j=1;j<NROOTS;j++)
318	parity[j] ^= ALPHA_TO[MODNN(feedback + GENPOLY[NROOTS-j])];
319    }
320    /* Shift */
321    memmove(&parity[0],&parity[1],sizeof(data_t)*(NROOTS-1));
322    if(feedback != A0)
323      parity[NROOTS-1] = ALPHA_TO[MODNN(feedback + GENPOLY[0])];
324    else
325      parity[NROOTS-1] = 0;
326  }
327}
328