1 |
/* |
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* fec.c -- forward error correction based on Vandermonde matrices |
3 |
* 980624 |
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* (C) 1997-98 Luigi Rizzo (luigi@iet.unipi.it) |
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* |
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* Portions derived from code by Phil Karn (karn@ka9q.ampr.org), |
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* Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari |
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* Thirumoorthy (harit@spectra.eng.hawaii.edu), Aug 1995 |
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* modified by Marc Lehmann <fec@schmorp.de>, Sep 2003. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions |
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* are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* 2. Redistributions in binary form must reproduce the above |
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* copyright notice, this list of conditions and the following |
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* disclaimer in the documentation and/or other materials |
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* provided with the distribution. |
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* |
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* THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND |
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, |
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* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A |
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* PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS |
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* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, |
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* OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, |
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* OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR |
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* TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT |
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* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY |
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* OF SUCH DAMAGE. |
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*/ |
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|
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#include <stdio.h> |
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#include <stdlib.h> |
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#include <string.h> |
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#include <stdint.h> |
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|
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#define MSDOS /* LEAVE THIS IN PLACE EVEN ON UNIX! */ |
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|
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/* |
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* compatibility stuff |
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*/ |
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#ifdef MSDOS /* but also for others, e.g. sun... */ |
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#define NEED_BCOPY |
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#define bcmp(a,b,n) memcmp(a,b,n) |
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#endif |
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|
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#ifdef NEED_BCOPY |
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#define bcopy(s, d, siz) memcpy((d), (s), (siz)) |
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#define bzero(d, siz) memset((d), '\0', (siz)) |
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#endif |
55 |
|
56 |
/* |
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* stuff used for testing purposes only |
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*/ |
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|
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#ifdef TEST |
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#define DEB(x) |
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#define DDB(x) x |
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#define DEBUG 0 /* minimal debugging */ |
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|
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#ifdef MSDOS |
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#include <time.h> |
67 |
struct timeval { |
68 |
unsigned long ticks; |
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}; |
70 |
#define gettimeofday(x, dummy) { (x)->ticks = clock() ; } |
71 |
#define DIFF_T(a,b) (1+ 1000000*(a.ticks - b.ticks) / CLOCKS_PER_SEC ) |
72 |
typedef unsigned long u_long ; |
73 |
typedef unsigned short u_short ; |
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#else /* typically, unix systems */ |
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#include <sys/time.h> |
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#define DIFF_T(a,b) \ |
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(1+ 1000000*(a.tv_sec - b.tv_sec) + (a.tv_usec - b.tv_usec) ) |
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#endif |
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|
80 |
#define TICK(t) \ |
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{struct timeval x ; \ |
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gettimeofday(&x, NULL) ; \ |
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t = x.tv_usec + 1000000* (x.tv_sec & 0xff ) ; \ |
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} |
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#define TOCK(t) \ |
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{ u_long t1 ; TICK(t1) ; \ |
87 |
if (t1 < t) t = 256000000 + t1 - t ; \ |
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else t = t1 - t ; \ |
89 |
if (t == 0) t = 1 ;} |
90 |
|
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u_long ticks[10]; /* vars for timekeeping */ |
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#else |
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#define DEB(x) |
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#define DDB(x) |
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#define TICK(x) |
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#define TOCK(x) |
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#endif /* TEST */ |
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|
99 |
/* |
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* You should not need to change anything beyond this point. |
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* The first part of the file implements linear algebra in GF. |
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* |
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* gf is the type used to store an element of the Galois Field. |
104 |
* Must constain at least GF_BITS bits. |
105 |
* |
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* Note: unsigned char will work up to GF(256) but int seems to run |
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* faster on the Pentium. We use int whenever have to deal with an |
108 |
* index, since they are generally faster. |
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*/ |
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#if (GF_BITS < 2 && GF_BITS >16) |
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#error "GF_BITS must be 2 .. 16" |
112 |
#endif |
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#if (GF_BITS <= 8) |
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typedef uint8_t gf; |
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#else |
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typedef uint16_t gf; |
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#endif |
118 |
|
119 |
#define GF_SIZE ((1 << GF_BITS) - 1) /* powers of \alpha */ |
120 |
|
121 |
/* |
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* Primitive polynomials - see Lin & Costello, Appendix A, |
123 |
* and Lee & Messerschmitt, p. 453. |
124 |
*/ |
125 |
static char *allPp[] = { /* GF_BITS polynomial */ |
126 |
NULL, /* 0 no code */ |
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NULL, /* 1 no code */ |
128 |
"111", /* 2 1+x+x^2 */ |
129 |
"1101", /* 3 1+x+x^3 */ |
130 |
"11001", /* 4 1+x+x^4 */ |
131 |
"101001", /* 5 1+x^2+x^5 */ |
132 |
"1100001", /* 6 1+x+x^6 */ |
133 |
"10010001", /* 7 1 + x^3 + x^7 */ |
134 |
"101110001", /* 8 1+x^2+x^3+x^4+x^8 */ |
135 |
"1000100001", /* 9 1+x^4+x^9 */ |
136 |
"10010000001", /* 10 1+x^3+x^10 */ |
137 |
"101000000001", /* 11 1+x^2+x^11 */ |
138 |
"1100101000001", /* 12 1+x+x^4+x^6+x^12 */ |
139 |
"11011000000001", /* 13 1+x+x^3+x^4+x^13 */ |
140 |
"110000100010001", /* 14 1+x+x^6+x^10+x^14 */ |
141 |
"1100000000000001", /* 15 1+x+x^15 */ |
142 |
"11010000000010001" /* 16 1+x+x^3+x^12+x^16 */ |
143 |
}; |
144 |
|
145 |
|
146 |
/* |
147 |
* To speed up computations, we have tables for logarithm, exponent |
148 |
* and inverse of a number. If GF_BITS <= 8, we use a table for |
149 |
* multiplication as well (it takes 64K, no big deal even on a PDA, |
150 |
* especially because it can be pre-initialized an put into a ROM!), |
151 |
* otherwhise we use a table of logarithms. |
152 |
* In any case the macro gf_mul(x,y) takes care of multiplications. |
153 |
*/ |
154 |
|
155 |
static gf gf_exp[2*GF_SIZE]; /* index->poly form conversion table */ |
156 |
static int gf_log[GF_SIZE + 1]; /* Poly->index form conversion table */ |
157 |
static gf inverse[GF_SIZE+1]; /* inverse of field elem. */ |
158 |
/* inv[\alpha**i]=\alpha**(GF_SIZE-i-1) */ |
159 |
|
160 |
/* |
161 |
* modnn(x) computes x % GF_SIZE, where GF_SIZE is 2**GF_BITS - 1, |
162 |
* without a slow divide. |
163 |
*/ |
164 |
static inline gf |
165 |
modnn(int x) |
166 |
{ |
167 |
while (x >= GF_SIZE) { |
168 |
x -= GF_SIZE; |
169 |
x = (x >> GF_BITS) + (x & GF_SIZE); |
170 |
} |
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return x; |
172 |
} |
173 |
|
174 |
#define SWAP(a,b,t) {t tmp; tmp=a; a=b; b=tmp;} |
175 |
|
176 |
/* |
177 |
* gf_mul(x,y) multiplies two numbers. If GF_BITS<=8, it is much |
178 |
* faster to use a multiplication table. |
179 |
* |
180 |
* USE_GF_MULC, GF_MULC0(c) and GF_ADDMULC(x) can be used when multiplying |
181 |
* many numbers by the same constant. In this case the first |
182 |
* call sets the constant, and others perform the multiplications. |
183 |
* A value related to the multiplication is held in a local variable |
184 |
* declared with USE_GF_MULC . See usage in addmul1(). |
185 |
*/ |
186 |
#if (GF_BITS <= 8) |
187 |
static gf gf_mul_table[GF_SIZE + 1][GF_SIZE + 1]; |
188 |
|
189 |
#define gf_mul(x,y) gf_mul_table[x][y] |
190 |
|
191 |
#define USE_GF_MULC register gf * __gf_mulc_ |
192 |
#define GF_MULC0(c) __gf_mulc_ = gf_mul_table[c] |
193 |
#define GF_ADDMULC(dst, x) dst ^= __gf_mulc_[x] |
194 |
|
195 |
static void |
196 |
init_mul_table() |
197 |
{ |
198 |
int i, j; |
199 |
for (i=0; i< GF_SIZE+1; i++) |
200 |
for (j=0; j< GF_SIZE+1; j++) |
201 |
gf_mul_table[i][j] = gf_exp[modnn(gf_log[i] + gf_log[j]) ] ; |
202 |
|
203 |
for (j=0; j< GF_SIZE+1; j++) |
204 |
gf_mul_table[0][j] = gf_mul_table[j][0] = 0; |
205 |
} |
206 |
#else /* GF_BITS > 8 */ |
207 |
static inline gf |
208 |
gf_mul(x,y) |
209 |
{ |
210 |
if ( (x) == 0 || (y)==0 ) return 0; |
211 |
|
212 |
return gf_exp[gf_log[x] + gf_log[y] ] ; |
213 |
} |
214 |
#define init_mul_table() |
215 |
|
216 |
#define USE_GF_MULC register gf * __gf_mulc_ |
217 |
#define GF_MULC0(c) __gf_mulc_ = &gf_exp[ gf_log[c] ] |
218 |
#define GF_ADDMULC(dst, x) { if (x) dst ^= __gf_mulc_[ gf_log[x] ] ; } |
219 |
#endif |
220 |
|
221 |
/* |
222 |
* Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m] |
223 |
* Lookup tables: |
224 |
* index->polynomial form gf_exp[] contains j= \alpha^i; |
225 |
* polynomial form -> index form gf_log[ j = \alpha^i ] = i |
226 |
* \alpha=x is the primitive element of GF(2^m) |
227 |
* |
228 |
* For efficiency, gf_exp[] has size 2*GF_SIZE, so that a simple |
229 |
* multiplication of two numbers can be resolved without calling modnn |
230 |
*/ |
231 |
|
232 |
/* |
233 |
* i use malloc so many times, it is easier to put checks all in |
234 |
* one place. |
235 |
*/ |
236 |
static void * |
237 |
my_malloc(int sz, char *err_string) |
238 |
{ |
239 |
void *p = malloc( sz ); |
240 |
if (p == NULL) { |
241 |
fprintf(stderr, "-- malloc failure allocating %s\n", err_string); |
242 |
exit(1) ; |
243 |
} |
244 |
return p ; |
245 |
} |
246 |
|
247 |
#define NEW_GF_MATRIX(rows, cols) \ |
248 |
(gf *)my_malloc(rows * cols * sizeof(gf), " ## __LINE__ ## " ) |
249 |
|
250 |
/* |
251 |
* initialize the data structures used for computations in GF. |
252 |
*/ |
253 |
static void |
254 |
generate_gf(void) |
255 |
{ |
256 |
int i; |
257 |
gf mask; |
258 |
char *Pp = allPp[GF_BITS] ; |
259 |
|
260 |
mask = 1; /* x ** 0 = 1 */ |
261 |
gf_exp[GF_BITS] = 0; /* will be updated at the end of the 1st loop */ |
262 |
/* |
263 |
* first, generate the (polynomial representation of) powers of \alpha, |
264 |
* which are stored in gf_exp[i] = \alpha ** i . |
265 |
* At the same time build gf_log[gf_exp[i]] = i . |
266 |
* The first GF_BITS powers are simply bits shifted to the left. |
267 |
*/ |
268 |
for (i = 0; i < GF_BITS; i++, mask <<= 1 ) { |
269 |
gf_exp[i] = mask; |
270 |
gf_log[gf_exp[i]] = i; |
271 |
/* |
272 |
* If Pp[i] == 1 then \alpha ** i occurs in poly-repr |
273 |
* gf_exp[GF_BITS] = \alpha ** GF_BITS |
274 |
*/ |
275 |
if ( Pp[i] == '1' ) |
276 |
gf_exp[GF_BITS] ^= mask; |
277 |
} |
278 |
/* |
279 |
* now gf_exp[GF_BITS] = \alpha ** GF_BITS is complete, so can als |
280 |
* compute its inverse. |
281 |
*/ |
282 |
gf_log[gf_exp[GF_BITS]] = GF_BITS; |
283 |
/* |
284 |
* Poly-repr of \alpha ** (i+1) is given by poly-repr of |
285 |
* \alpha ** i shifted left one-bit and accounting for any |
286 |
* \alpha ** GF_BITS term that may occur when poly-repr of |
287 |
* \alpha ** i is shifted. |
288 |
*/ |
289 |
mask = 1 << (GF_BITS - 1 ) ; |
290 |
for (i = GF_BITS + 1; i < GF_SIZE; i++) { |
291 |
if (gf_exp[i - 1] >= mask) |
292 |
gf_exp[i] = gf_exp[GF_BITS] ^ ((gf_exp[i - 1] ^ mask) << 1); |
293 |
else |
294 |
gf_exp[i] = gf_exp[i - 1] << 1; |
295 |
gf_log[gf_exp[i]] = i; |
296 |
} |
297 |
/* |
298 |
* log(0) is not defined, so use a special value |
299 |
*/ |
300 |
gf_log[0] = GF_SIZE ; |
301 |
/* set the extended gf_exp values for fast multiply */ |
302 |
for (i = 0 ; i < GF_SIZE ; i++) |
303 |
gf_exp[i + GF_SIZE] = gf_exp[i] ; |
304 |
|
305 |
/* |
306 |
* again special cases. 0 has no inverse. This used to |
307 |
* be initialized to GF_SIZE, but it should make no difference |
308 |
* since noone is supposed to read from here. |
309 |
*/ |
310 |
inverse[0] = 0 ; |
311 |
inverse[1] = 1; |
312 |
for (i=2; i<=GF_SIZE; i++) |
313 |
inverse[i] = gf_exp[GF_SIZE-gf_log[i]]; |
314 |
} |
315 |
|
316 |
/* |
317 |
* Various linear algebra operations that i use often. |
318 |
*/ |
319 |
|
320 |
/* |
321 |
* addmul() computes dst[] = dst[] + c * src[] |
322 |
* This is used often, so better optimize it! Currently the loop is |
323 |
* unrolled 16 times, a good value for 486 and pentium-class machines. |
324 |
* The case c=0 is also optimized, whereas c=1 is not. These |
325 |
* calls are unfrequent in my typical apps so I did not bother. |
326 |
* |
327 |
* Note that gcc on |
328 |
*/ |
329 |
#define addmul(dst, src, c, sz) \ |
330 |
if (c != 0) addmul1(dst, src, c, sz) |
331 |
|
332 |
#define UNROLL 16 /* 1, 4, 8, 16 */ |
333 |
static void |
334 |
addmul1(gf *dst1, gf *src1, gf c, int sz) |
335 |
{ |
336 |
USE_GF_MULC ; |
337 |
register gf *dst = dst1, *src = src1 ; |
338 |
gf *lim = &dst[sz - UNROLL + 1] ; |
339 |
|
340 |
GF_MULC0(c) ; |
341 |
|
342 |
#if (UNROLL > 1) /* unrolling by 8/16 is quite effective on the pentium */ |
343 |
for (; dst < lim ; dst += UNROLL, src += UNROLL ) { |
344 |
GF_ADDMULC( dst[0] , src[0] ); |
345 |
GF_ADDMULC( dst[1] , src[1] ); |
346 |
GF_ADDMULC( dst[2] , src[2] ); |
347 |
GF_ADDMULC( dst[3] , src[3] ); |
348 |
#if (UNROLL > 4) |
349 |
GF_ADDMULC( dst[4] , src[4] ); |
350 |
GF_ADDMULC( dst[5] , src[5] ); |
351 |
GF_ADDMULC( dst[6] , src[6] ); |
352 |
GF_ADDMULC( dst[7] , src[7] ); |
353 |
#endif |
354 |
#if (UNROLL > 8) |
355 |
GF_ADDMULC( dst[8] , src[8] ); |
356 |
GF_ADDMULC( dst[9] , src[9] ); |
357 |
GF_ADDMULC( dst[10] , src[10] ); |
358 |
GF_ADDMULC( dst[11] , src[11] ); |
359 |
GF_ADDMULC( dst[12] , src[12] ); |
360 |
GF_ADDMULC( dst[13] , src[13] ); |
361 |
GF_ADDMULC( dst[14] , src[14] ); |
362 |
GF_ADDMULC( dst[15] , src[15] ); |
363 |
#endif |
364 |
} |
365 |
#endif |
366 |
lim += UNROLL - 1 ; |
367 |
for (; dst < lim; dst++, src++ ) /* final components */ |
368 |
GF_ADDMULC( *dst , *src ); |
369 |
} |
370 |
|
371 |
/* |
372 |
* computes C = AB where A is n*k, B is k*m, C is n*m |
373 |
*/ |
374 |
static void |
375 |
matmul(gf *a, gf *b, gf *c, int n, int k, int m) |
376 |
{ |
377 |
int row, col, i ; |
378 |
|
379 |
for (row = 0; row < n ; row++) { |
380 |
for (col = 0; col < m ; col++) { |
381 |
gf *pa = &a[ row * k ]; |
382 |
gf *pb = &b[ col ]; |
383 |
gf acc = 0 ; |
384 |
for (i = 0; i < k ; i++, pa++, pb += m ) |
385 |
acc ^= gf_mul( *pa, *pb ) ; |
386 |
c[ row * m + col ] = acc ; |
387 |
} |
388 |
} |
389 |
} |
390 |
|
391 |
#ifdef DEBUG |
392 |
/* |
393 |
* returns 1 if the square matrix is identiy |
394 |
* (only for test) |
395 |
*/ |
396 |
static int |
397 |
is_identity(gf *m, int k) |
398 |
{ |
399 |
int row, col ; |
400 |
for (row=0; row<k; row++) |
401 |
for (col=0; col<k; col++) |
402 |
if ( (row==col && *m != 1) || |
403 |
(row!=col && *m != 0) ) |
404 |
return 0 ; |
405 |
else |
406 |
m++ ; |
407 |
return 1 ; |
408 |
} |
409 |
#endif /* debug */ |
410 |
|
411 |
/* |
412 |
* invert_mat() takes a matrix and produces its inverse |
413 |
* k is the size of the matrix. |
414 |
* (Gauss-Jordan, adapted from Numerical Recipes in C) |
415 |
* Return non-zero if singular. |
416 |
*/ |
417 |
DEB( int pivloops=0; int pivswaps=0 ; /* diagnostic */) |
418 |
static int |
419 |
invert_mat(gf *src, int k) |
420 |
{ |
421 |
gf c, *p ; |
422 |
int irow, icol, row, col, i, ix ; |
423 |
|
424 |
int error = 1 ; |
425 |
int *indxc = my_malloc(k*sizeof(int), "indxc"); |
426 |
int *indxr = my_malloc(k*sizeof(int), "indxr"); |
427 |
int *ipiv = my_malloc(k*sizeof(int), "ipiv"); |
428 |
gf *id_row = NEW_GF_MATRIX(1, k); |
429 |
gf *temp_row = NEW_GF_MATRIX(1, k); |
430 |
|
431 |
bzero(id_row, k*sizeof(gf)); |
432 |
DEB( pivloops=0; pivswaps=0 ; /* diagnostic */ ) |
433 |
/* |
434 |
* ipiv marks elements already used as pivots. |
435 |
*/ |
436 |
for (i = 0; i < k ; i++) |
437 |
ipiv[i] = 0 ; |
438 |
|
439 |
for (col = 0; col < k ; col++) { |
440 |
gf *pivot_row ; |
441 |
/* |
442 |
* Zeroing column 'col', look for a non-zero element. |
443 |
* First try on the diagonal, if it fails, look elsewhere. |
444 |
*/ |
445 |
irow = icol = -1 ; |
446 |
if (ipiv[col] != 1 && src[col*k + col] != 0) { |
447 |
irow = col ; |
448 |
icol = col ; |
449 |
goto found_piv ; |
450 |
} |
451 |
for (row = 0 ; row < k ; row++) { |
452 |
if (ipiv[row] != 1) { |
453 |
for (ix = 0 ; ix < k ; ix++) { |
454 |
DEB( pivloops++ ; ) |
455 |
if (ipiv[ix] == 0) { |
456 |
if (src[row*k + ix] != 0) { |
457 |
irow = row ; |
458 |
icol = ix ; |
459 |
goto found_piv ; |
460 |
} |
461 |
} else if (ipiv[ix] > 1) { |
462 |
fprintf(stderr, "singular matrix\n"); |
463 |
goto fail ; |
464 |
} |
465 |
} |
466 |
} |
467 |
} |
468 |
if (icol == -1) { |
469 |
fprintf(stderr, "XXX pivot not found!\n"); |
470 |
goto fail ; |
471 |
} |
472 |
found_piv: |
473 |
++(ipiv[icol]) ; |
474 |
/* |
475 |
* swap rows irow and icol, so afterwards the diagonal |
476 |
* element will be correct. Rarely done, not worth |
477 |
* optimizing. |
478 |
*/ |
479 |
if (irow != icol) { |
480 |
for (ix = 0 ; ix < k ; ix++ ) { |
481 |
SWAP( src[irow*k + ix], src[icol*k + ix], gf) ; |
482 |
} |
483 |
} |
484 |
indxr[col] = irow ; |
485 |
indxc[col] = icol ; |
486 |
pivot_row = &src[icol*k] ; |
487 |
c = pivot_row[icol] ; |
488 |
if (c == 0) { |
489 |
fprintf(stderr, "singular matrix 2\n"); |
490 |
goto fail ; |
491 |
} |
492 |
if (c != 1 ) { /* otherwhise this is a NOP */ |
493 |
/* |
494 |
* this is done often , but optimizing is not so |
495 |
* fruitful, at least in the obvious ways (unrolling) |
496 |
*/ |
497 |
DEB( pivswaps++ ; ) |
498 |
c = inverse[ c ] ; |
499 |
pivot_row[icol] = 1 ; |
500 |
for (ix = 0 ; ix < k ; ix++ ) |
501 |
pivot_row[ix] = gf_mul(c, pivot_row[ix] ); |
502 |
} |
503 |
/* |
504 |
* from all rows, remove multiples of the selected row |
505 |
* to zero the relevant entry (in fact, the entry is not zero |
506 |
* because we know it must be zero). |
507 |
* (Here, if we know that the pivot_row is the identity, |
508 |
* we can optimize the addmul). |
509 |
*/ |
510 |
id_row[icol] = 1; |
511 |
if (bcmp(pivot_row, id_row, k*sizeof(gf)) != 0) { |
512 |
for (p = src, ix = 0 ; ix < k ; ix++, p += k ) { |
513 |
if (ix != icol) { |
514 |
c = p[icol] ; |
515 |
p[icol] = 0 ; |
516 |
addmul(p, pivot_row, c, k ); |
517 |
} |
518 |
} |
519 |
} |
520 |
id_row[icol] = 0; |
521 |
} /* done all columns */ |
522 |
for (col = k-1 ; col >= 0 ; col-- ) { |
523 |
if (indxr[col] <0 || indxr[col] >= k) |
524 |
fprintf(stderr, "AARGH, indxr[col] %d\n", indxr[col]); |
525 |
else if (indxc[col] <0 || indxc[col] >= k) |
526 |
fprintf(stderr, "AARGH, indxc[col] %d\n", indxc[col]); |
527 |
else |
528 |
if (indxr[col] != indxc[col] ) { |
529 |
for (row = 0 ; row < k ; row++ ) { |
530 |
SWAP( src[row*k + indxr[col]], src[row*k + indxc[col]], gf) ; |
531 |
} |
532 |
} |
533 |
} |
534 |
error = 0 ; |
535 |
fail: |
536 |
free(indxc); |
537 |
free(indxr); |
538 |
free(ipiv); |
539 |
free(id_row); |
540 |
free(temp_row); |
541 |
return error ; |
542 |
} |
543 |
|
544 |
/* |
545 |
* fast code for inverting a vandermonde matrix. |
546 |
* XXX NOTE: It assumes that the matrix |
547 |
* is not singular and _IS_ a vandermonde matrix. Only uses |
548 |
* the second column of the matrix, containing the p_i's. |
549 |
* |
550 |
* Algorithm borrowed from "Numerical recipes in C" -- sec.2.8, but |
551 |
* largely revised for my purposes. |
552 |
* p = coefficients of the matrix (p_i) |
553 |
* q = values of the polynomial (known) |
554 |
*/ |
555 |
|
556 |
static int |
557 |
invert_vdm(gf *src, int k) |
558 |
{ |
559 |
int i, j, row, col ; |
560 |
gf *b, *c, *p; |
561 |
gf t, xx ; |
562 |
|
563 |
if (k == 1) /* degenerate case, matrix must be p^0 = 1 */ |
564 |
return 0 ; |
565 |
/* |
566 |
* c holds the coefficient of P(x) = Prod (x - p_i), i=0..k-1 |
567 |
* b holds the coefficient for the matrix inversion |
568 |
*/ |
569 |
c = NEW_GF_MATRIX(1, k); |
570 |
b = NEW_GF_MATRIX(1, k); |
571 |
|
572 |
p = NEW_GF_MATRIX(1, k); |
573 |
|
574 |
for ( j=1, i = 0 ; i < k ; i++, j+=k ) { |
575 |
c[i] = 0 ; |
576 |
p[i] = src[j] ; /* p[i] */ |
577 |
} |
578 |
/* |
579 |
* construct coeffs. recursively. We know c[k] = 1 (implicit) |
580 |
* and start P_0 = x - p_0, then at each stage multiply by |
581 |
* x - p_i generating P_i = x P_{i-1} - p_i P_{i-1} |
582 |
* After k steps we are done. |
583 |
*/ |
584 |
c[k-1] = p[0] ; /* really -p(0), but x = -x in GF(2^m) */ |
585 |
for (i = 1 ; i < k ; i++ ) { |
586 |
gf p_i = p[i] ; /* see above comment */ |
587 |
for (j = k-1 - ( i - 1 ) ; j < k-1 ; j++ ) |
588 |
c[j] ^= gf_mul( p_i, c[j+1] ) ; |
589 |
c[k-1] ^= p_i ; |
590 |
} |
591 |
|
592 |
for (row = 0 ; row < k ; row++ ) { |
593 |
/* |
594 |
* synthetic division etc. |
595 |
*/ |
596 |
xx = p[row] ; |
597 |
t = 1 ; |
598 |
b[k-1] = 1 ; /* this is in fact c[k] */ |
599 |
for (i = k-2 ; i >= 0 ; i-- ) { |
600 |
b[i] = c[i+1] ^ gf_mul(xx, b[i+1]) ; |
601 |
t = gf_mul(xx, t) ^ b[i] ; |
602 |
} |
603 |
for (col = 0 ; col < k ; col++ ) |
604 |
src[col*k + row] = gf_mul(inverse[t], b[col] ); |
605 |
} |
606 |
free(c) ; |
607 |
free(b) ; |
608 |
free(p) ; |
609 |
return 0 ; |
610 |
} |
611 |
|
612 |
static int fec_initialized = 0 ; |
613 |
|
614 |
static void init_fec() |
615 |
{ |
616 |
TICK(ticks[0]); |
617 |
generate_gf(); |
618 |
TOCK(ticks[0]); |
619 |
DDB(fprintf(stderr, "generate_gf took %ldus\n", ticks[0]);) |
620 |
TICK(ticks[0]); |
621 |
init_mul_table(); |
622 |
TOCK(ticks[0]); |
623 |
DDB(fprintf(stderr, "init_mul_table took %ldus\n", ticks[0]);) |
624 |
fec_initialized = 1 ; |
625 |
} |
626 |
|
627 |
/* |
628 |
* This section contains the proper FEC encoding/decoding routines. |
629 |
* The encoding matrix is computed starting with a Vandermonde matrix, |
630 |
* and then transforming it into a systematic matrix. |
631 |
*/ |
632 |
|
633 |
struct fec_parms { |
634 |
int k, n ; /* parameters of the code */ |
635 |
gf *enc_matrix ; |
636 |
} ; |
637 |
|
638 |
void |
639 |
fec_free(struct fec_parms *p) |
640 |
{ |
641 |
if (p==NULL) { |
642 |
fprintf(stderr, "bad parameters to fec_free\n"); |
643 |
return ; |
644 |
} |
645 |
free(p->enc_matrix); |
646 |
free(p); |
647 |
} |
648 |
|
649 |
/* |
650 |
* create a new encoder, returning a descriptor. This contains k,n and |
651 |
* the encoding matrix. |
652 |
*/ |
653 |
struct fec_parms * |
654 |
fec_new(int k, int n) |
655 |
{ |
656 |
int row, col ; |
657 |
gf *p, *tmp_m ; |
658 |
|
659 |
struct fec_parms *retval ; |
660 |
|
661 |
if (fec_initialized == 0) |
662 |
init_fec(); |
663 |
|
664 |
if (k > GF_SIZE + 1 || n > GF_SIZE + 1 || k > n ) { |
665 |
fprintf(stderr, "Invalid parameters k %d n %d GF_SIZE %d\n", |
666 |
k, n, GF_SIZE ); |
667 |
return NULL ; |
668 |
} |
669 |
retval = my_malloc(sizeof(struct fec_parms), "new_code"); |
670 |
retval->k = k ; |
671 |
retval->n = n ; |
672 |
retval->enc_matrix = NEW_GF_MATRIX(n, k); |
673 |
tmp_m = NEW_GF_MATRIX(n, k); |
674 |
/* |
675 |
* fill the matrix with powers of field elements, starting from 0. |
676 |
* The first row is special, cannot be computed with exp. table. |
677 |
*/ |
678 |
tmp_m[0] = 1 ; |
679 |
for (col = 1; col < k ; col++) |
680 |
tmp_m[col] = 0 ; |
681 |
for (p = tmp_m + k, row = 0; row < n-1 ; row++, p += k) { |
682 |
for ( col = 0 ; col < k ; col ++ ) |
683 |
p[col] = gf_exp[modnn(row*col)]; |
684 |
} |
685 |
|
686 |
/* |
687 |
* quick code to build systematic matrix: invert the top |
688 |
* k*k vandermonde matrix, multiply right the bottom n-k rows |
689 |
* by the inverse, and construct the identity matrix at the top. |
690 |
*/ |
691 |
TICK(ticks[3]); |
692 |
invert_vdm(tmp_m, k); /* much faster than invert_mat */ |
693 |
matmul(tmp_m + k*k, tmp_m, retval->enc_matrix + k*k, n - k, k, k); |
694 |
/* |
695 |
* the upper matrix is I so do not bother with a slow multiply |
696 |
*/ |
697 |
bzero(retval->enc_matrix, k*k*sizeof(gf) ); |
698 |
for (p = retval->enc_matrix, col = 0 ; col < k ; col++, p += k+1 ) |
699 |
*p = 1 ; |
700 |
free(tmp_m); |
701 |
TOCK(ticks[3]); |
702 |
|
703 |
DDB(fprintf(stderr, "--- %ld us to build encoding matrix\n", |
704 |
ticks[3]);) |
705 |
DEB(pr_matrix(retval->enc_matrix, n, k, "encoding_matrix");) |
706 |
return retval ; |
707 |
} |
708 |
|
709 |
/* |
710 |
* fec_encode accepts as input pointers to n data packets of size sz, |
711 |
* and produces as output a packet pointed to by fec, computed |
712 |
* with index "index". |
713 |
*/ |
714 |
void |
715 |
fec_encode(struct fec_parms *code, gf *src[], gf *fec, int index, int sz) |
716 |
{ |
717 |
int i, k = code->k ; |
718 |
gf *p ; |
719 |
|
720 |
if (GF_BITS > 8) |
721 |
sz /= 2 ; |
722 |
|
723 |
if (index < k) |
724 |
bcopy(src[index], fec, sz*sizeof(gf) ) ; |
725 |
else if (index < code->n) { |
726 |
p = &(code->enc_matrix[index*k] ); |
727 |
bzero(fec, sz*sizeof(gf)); |
728 |
for (i = 0; i < k ; i++) |
729 |
addmul(fec, src[i], p[i], sz ) ; |
730 |
} else |
731 |
fprintf(stderr, "Invalid index %d (max %d)\n", |
732 |
index, code->n - 1 ); |
733 |
} |
734 |
|
735 |
/* |
736 |
* shuffle move src packets in their position |
737 |
*/ |
738 |
static int |
739 |
shuffle(gf *pkt[], int index[], int k) |
740 |
{ |
741 |
int i; |
742 |
|
743 |
for ( i = 0 ; i < k ; ) { |
744 |
if (index[i] >= k || index[i] == i) |
745 |
i++ ; |
746 |
else { |
747 |
/* |
748 |
* put pkt in the right position (first check for conflicts). |
749 |
*/ |
750 |
int c = index[i] ; |
751 |
|
752 |
if (index[c] == c) { |
753 |
DEB(fprintf(stderr, "\nshuffle, error at %d\n", i);) |
754 |
return 1 ; |
755 |
} |
756 |
SWAP(index[i], index[c], int) ; |
757 |
SWAP(pkt[i], pkt[c], gf *) ; |
758 |
} |
759 |
} |
760 |
DEB( /* just test that it works... */ |
761 |
for ( i = 0 ; i < k ; i++ ) { |
762 |
if (index[i] < k && index[i] != i) { |
763 |
fprintf(stderr, "shuffle: after\n"); |
764 |
for (i=0; i<k ; i++) fprintf(stderr, "%3d ", index[i]); |
765 |
fprintf(stderr, "\n"); |
766 |
return 1 ; |
767 |
} |
768 |
} |
769 |
) |
770 |
return 0 ; |
771 |
} |
772 |
|
773 |
/* |
774 |
* build_decode_matrix constructs the encoding matrix given the |
775 |
* indexes. The matrix must be already allocated as |
776 |
* a vector of k*k elements, in row-major order |
777 |
*/ |
778 |
static gf * |
779 |
build_decode_matrix(struct fec_parms *code, gf *pkt[], int index[]) |
780 |
{ |
781 |
int i , k = code->k ; |
782 |
gf *p, *matrix = NEW_GF_MATRIX(k, k); |
783 |
|
784 |
TICK(ticks[9]); |
785 |
for (i = 0, p = matrix ; i < k ; i++, p += k ) { |
786 |
#if 1 /* this is simply an optimization, not very useful indeed */ |
787 |
if (index[i] < k) { |
788 |
bzero(p, k*sizeof(gf) ); |
789 |
p[i] = 1 ; |
790 |
} else |
791 |
#endif |
792 |
if (index[i] < code->n ) |
793 |
bcopy( &(code->enc_matrix[index[i]*k]), p, k*sizeof(gf) ); |
794 |
else { |
795 |
fprintf(stderr, "decode: invalid index %d (max %d)\n", |
796 |
index[i], code->n - 1 ); |
797 |
free(matrix) ; |
798 |
return NULL ; |
799 |
} |
800 |
} |
801 |
TICK(ticks[9]); |
802 |
if (invert_mat(matrix, k)) { |
803 |
free(matrix); |
804 |
matrix = NULL ; |
805 |
} |
806 |
TOCK(ticks[9]); |
807 |
return matrix ; |
808 |
} |
809 |
|
810 |
/* |
811 |
* fec_decode receives as input a vector of packets, the indexes of |
812 |
* packets, and produces the correct vector as output. |
813 |
* |
814 |
* Input: |
815 |
* code: pointer to code descriptor |
816 |
* pkt: pointers to received packets. They are modified |
817 |
* to store the output packets (in place) |
818 |
* index: pointer to packet indexes (modified) |
819 |
* sz: size of each packet |
820 |
*/ |
821 |
int |
822 |
fec_decode(struct fec_parms *code, gf *pkt[], int index[], int sz) |
823 |
{ |
824 |
gf *m_dec ; |
825 |
gf **new_pkt ; |
826 |
int row, col , k = code->k ; |
827 |
|
828 |
if (GF_BITS > 8) |
829 |
sz /= 2 ; |
830 |
|
831 |
if (shuffle(pkt, index, k)) /* error if true */ |
832 |
return 1 ; |
833 |
m_dec = build_decode_matrix(code, pkt, index); |
834 |
|
835 |
if (m_dec == NULL) |
836 |
return 1 ; /* error */ |
837 |
/* |
838 |
* do the actual decoding |
839 |
*/ |
840 |
new_pkt = my_malloc (k * sizeof (gf * ), "new pkt pointers" ); |
841 |
for (row = 0 ; row < k ; row++ ) { |
842 |
if (index[row] >= k) { |
843 |
new_pkt[row] = my_malloc (sz * sizeof (gf), "new pkt buffer" ); |
844 |
bzero(new_pkt[row], sz * sizeof(gf) ) ; |
845 |
for (col = 0 ; col < k ; col++ ) |
846 |
addmul(new_pkt[row], pkt[col], m_dec[row*k + col], sz) ; |
847 |
} |
848 |
} |
849 |
/* |
850 |
* move pkts to their final destination |
851 |
*/ |
852 |
for (row = 0 ; row < k ; row++ ) { |
853 |
if (index[row] >= k) { |
854 |
bcopy(new_pkt[row], pkt[row], sz*sizeof(gf)); |
855 |
free(new_pkt[row]); |
856 |
index[row] = row; |
857 |
} |
858 |
} |
859 |
free(new_pkt); |
860 |
free(m_dec); |
861 |
|
862 |
return 0; |
863 |
} |
864 |
|
865 |
/*********** end of FEC code -- beginning of test code ************/ |
866 |
|
867 |
#if (TEST || DEBUG) |
868 |
void |
869 |
test_gf() |
870 |
{ |
871 |
int i ; |
872 |
/* |
873 |
* test gf tables. Sufficiently tested... |
874 |
*/ |
875 |
for (i=0; i<= GF_SIZE; i++) { |
876 |
if (gf_exp[gf_log[i]] != i) |
877 |
fprintf(stderr, "bad exp/log i %d log %d exp(log) %d\n", |
878 |
i, gf_log[i], gf_exp[gf_log[i]]); |
879 |
|
880 |
if (i != 0 && gf_mul(i, inverse[i]) != 1) |
881 |
fprintf(stderr, "bad mul/inv i %d inv %d i*inv(i) %d\n", |
882 |
i, inverse[i], gf_mul(i, inverse[i]) ); |
883 |
if (gf_mul(0,i) != 0) |
884 |
fprintf(stderr, "bad mul table 0,%d\n",i); |
885 |
if (gf_mul(i,0) != 0) |
886 |
fprintf(stderr, "bad mul table %d,0\n",i); |
887 |
} |
888 |
} |
889 |
#endif /* TEST */ |