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  */
41 typedef unsigned char data_t;
42 
43 
44 /**
45  * Reed-Solomon codec control block
46  */
47 struct _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 
62 static RS *rslist = NULL;
63 #ifdef HAVE_LIBPTHREAD
64 static pthread_mutex_t rslist_mutex = PTHREAD_MUTEX_INITIALIZER;
65 #endif
66 
modnn(RS * rs,int x)67 static 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  */
init_rs_char(int symsize,int gfpoly,int fcr,int prim,int nroots,int pad)99 static 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 
init_rs(int symsize,int gfpoly,int fcr,int prim,int nroots,int pad)212 RS *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 
235 DONE:
236 #ifdef HAVE_LIBPTHREAD
237 	pthread_mutex_unlock(&rslist_mutex);
238 #endif
239 	return rs;
240 }
241 
242 
free_rs_char(RS * rs)243 void 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 
free_rs_cache(void)251 void 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 
encode_rs_char(RS * rs,const data_t * data,data_t * parity)301 void 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