Merge commit 'meins/next' into next
[paraslash.git] / fec.c
1 /** \file fec.c Forward error correction based on Vandermonde matrices. */
2
3 /*
4 * 980624
5 * (C) 1997-98 Luigi Rizzo (luigi@iet.unipi.it)
6 *
7 * Portions derived from code by Phil Karn (karn@ka9q.ampr.org),
8 * Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari
9 * Thirumoorthy (harit@spectra.eng.hawaii.edu), Aug 1995
10 *
11 * Redistribution and use in source and binary forms, with or without
12 * modification, are permitted provided that the following conditions
13 * are met:
14 *
15 * 1. Redistributions of source code must retain the above copyright
16 * notice, this list of conditions and the following disclaimer.
17 * 2. Redistributions in binary form must reproduce the above
18 * copyright notice, this list of conditions and the following
19 * disclaimer in the documentation and/or other materials
20 * provided with the distribution.
21 *
22 * THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND
23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
24 * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
25 * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS
26 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
27 * OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
28 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
29 * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
30 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
31 * TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
32 * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
33 * OF SUCH DAMAGE.
34 */
35
36 #include <regex.h>
37
38 #include "para.h"
39 #include "error.h"
40 #include "portable_io.h"
41 #include "string.h"
42 #include "fec.h"
43
44 #define GF_BITS 8 /* code over GF(256) */
45 #define GF_SIZE ((1 << GF_BITS) - 1)
46
47 /*
48 * To speed up computations, we have tables for logarithm, exponent and inverse
49 * of a number. We use a table for multiplication as well (it takes 64K, no big
50 * deal even on a PDA, especially because it can be pre-initialized an put into
51 * a ROM!). The macro gf_mul(x,y) takes care of multiplications.
52 */
53 static unsigned char gf_exp[2 * GF_SIZE]; /* index->poly form conversion table */
54 static int gf_log[GF_SIZE + 1]; /* Poly->index form conversion table */
55 static unsigned char inverse[GF_SIZE + 1]; /* inverse of field elem. */
56 static unsigned char gf_mul_table[GF_SIZE + 1][GF_SIZE + 1];
57 /* Multiply two numbers. */
58 #define gf_mul(x,y) gf_mul_table[x][y]
59
60 /* Compute x % GF_SIZE without a slow divide. */
61 static inline unsigned char modnn(int x)
62 {
63 while (x >= GF_SIZE) {
64 x -= GF_SIZE;
65 x = (x >> GF_BITS) + (x & GF_SIZE);
66 }
67 return x;
68 }
69
70 static void init_mul_table(void)
71 {
72 int i, j;
73 for (i = 0; i < GF_SIZE + 1; i++)
74 for (j = 0; j < GF_SIZE + 1; j++)
75 gf_mul_table[i][j] =
76 gf_exp[modnn(gf_log[i] + gf_log[j])];
77
78 for (j = 0; j < GF_SIZE + 1; j++)
79 gf_mul_table[0][j] = gf_mul_table[j][0] = 0;
80 }
81
82 static unsigned char *alloc_matrix(int rows, int cols)
83 {
84 return para_malloc(rows * cols);
85 }
86
87 /*
88 * Initialize the data structures used for computations in GF.
89 *
90 * This generates GF(2**GF_BITS) from the irreducible polynomial p(X) in
91 * p[0]..p[m].
92 *
93 * Lookup tables:
94 * index->polynomial form gf_exp[] contains j= \alpha^i;
95 * polynomial form -> index form gf_log[ j = \alpha^i ] = i
96 * \alpha=x is the primitive element of GF(2^m)
97 *
98 * For efficiency, gf_exp[] has size 2*GF_SIZE, so that a simple
99 * multiplication of two numbers can be resolved without calling modnn
100 */
101 static void generate_gf(void)
102 {
103 int i;
104 unsigned char mask = 1;
105 char *pp = "101110001"; /* The primitive polynomial 1+x^2+x^3+x^4+x^8 */
106 gf_exp[GF_BITS] = 0; /* will be updated at the end of the 1st loop */
107
108 /*
109 * first, generate the (polynomial representation of) powers of \alpha,
110 * which are stored in gf_exp[i] = \alpha ** i .
111 * At the same time build gf_log[gf_exp[i]] = i .
112 * The first GF_BITS powers are simply bits shifted to the left.
113 */
114 for (i = 0; i < GF_BITS; i++, mask <<= 1) {
115 gf_exp[i] = mask;
116 gf_log[gf_exp[i]] = i;
117 /*
118 * If pp[i] == 1 then \alpha ** i occurs in poly-repr
119 * gf_exp[GF_BITS] = \alpha ** GF_BITS
120 */
121 if (pp[i] == '1')
122 gf_exp[GF_BITS] ^= mask;
123 }
124 /*
125 * now gf_exp[GF_BITS] = \alpha ** GF_BITS is complete, so can also
126 * compute its inverse.
127 */
128 gf_log[gf_exp[GF_BITS]] = GF_BITS;
129 /*
130 * Poly-repr of \alpha ** (i+1) is given by poly-repr of \alpha ** i
131 * shifted left one-bit and accounting for any \alpha ** GF_BITS term
132 * that may occur when poly-repr of \alpha ** i is shifted.
133 */
134 mask = 1 << (GF_BITS - 1);
135 for (i = GF_BITS + 1; i < GF_SIZE; i++) {
136 if (gf_exp[i - 1] >= mask)
137 gf_exp[i] =
138 gf_exp[GF_BITS] ^ ((gf_exp[i - 1] ^ mask) << 1);
139 else
140 gf_exp[i] = gf_exp[i - 1] << 1;
141 gf_log[gf_exp[i]] = i;
142 }
143 /*
144 * log(0) is not defined, so use a special value
145 */
146 gf_log[0] = GF_SIZE;
147 /* set the extended gf_exp values for fast multiply */
148 for (i = 0; i < GF_SIZE; i++)
149 gf_exp[i + GF_SIZE] = gf_exp[i];
150
151 inverse[0] = 0; /* 0 has no inverse. */
152 inverse[1] = 1;
153 for (i = 2; i <= GF_SIZE; i++)
154 inverse[i] = gf_exp[GF_SIZE - gf_log[i]];
155 }
156
157 /*
158 * Compute dst[] = dst[] + c * src[]
159 *
160 * This is used often, so better optimize it! Currently the loop is unrolled 16
161 * times. The case c=0 is also optimized, whereas c=1 is not.
162 */
163 #define UNROLL 16
164 static void addmul(unsigned char *dst1, const unsigned char const *src1,
165 unsigned char c, int sz)
166 {
167 if (c == 0)
168 return;
169 unsigned char *dst = dst1, *lim = &dst[sz - UNROLL + 1],
170 *col = gf_mul_table[c];
171 const unsigned char const *src = src1;
172
173 for (; dst < lim; dst += UNROLL, src += UNROLL) {
174 dst[0] ^= col[src[0]];
175 dst[1] ^= col[src[1]];
176 dst[2] ^= col[src[2]];
177 dst[3] ^= col[src[3]];
178 dst[4] ^= col[src[4]];
179 dst[5] ^= col[src[5]];
180 dst[6] ^= col[src[6]];
181 dst[7] ^= col[src[7]];
182 dst[8] ^= col[src[8]];
183 dst[9] ^= col[src[9]];
184 dst[10] ^= col[src[10]];
185 dst[11] ^= col[src[11]];
186 dst[12] ^= col[src[12]];
187 dst[13] ^= col[src[13]];
188 dst[14] ^= col[src[14]];
189 dst[15] ^= col[src[15]];
190 }
191 lim += UNROLL - 1;
192 for (; dst < lim; dst++, src++) /* final components */
193 *dst ^= col[*src];
194 }
195
196 /*
197 * Compute C = AB where A is n*k, B is k*m, C is n*m
198 */
199 static void matmul(unsigned char *a, unsigned char *b, unsigned char *c,
200 int n, int k, int m)
201 {
202 int row, col, i;
203
204 for (row = 0; row < n; row++) {
205 for (col = 0; col < m; col++) {
206 unsigned char *pa = &a[row * k], *pb = &b[col], acc = 0;
207 for (i = 0; i < k; i++, pa++, pb += m)
208 acc ^= gf_mul(*pa, *pb);
209 c[row * m + col] = acc;
210 }
211 }
212 }
213
214 #define FEC_SWAP(a,b) {typeof(a) tmp = a; a = b; b = tmp;}
215
216 /*
217 * Compute the inverse of a matrix.
218 *
219 * k is the size of the matrix 'src' (Gauss-Jordan, adapted from Numerical
220 * Recipes in C). Returns negative on errors.
221 */
222 static int invert_mat(unsigned char *src, int k)
223 {
224 int irow, icol, row, col, ix, error;
225 int *indxc = para_malloc(k * sizeof(int));
226 int *indxr = para_malloc(k * sizeof(int));
227 int *ipiv = para_malloc(k * sizeof(int)); /* elements used as pivots */
228 unsigned char c, *p, *id_row = alloc_matrix(1, k),
229 *temp_row = alloc_matrix(1, k);
230
231 memset(id_row, 0, k);
232 memset(ipiv, 0, k * sizeof(int));
233
234 for (col = 0; col < k; col++) {
235 unsigned char *pivot_row;
236 /*
237 * Zeroing column 'col', look for a non-zero element.
238 * First try on the diagonal, if it fails, look elsewhere.
239 */
240 irow = icol = -1;
241 if (ipiv[col] != 1 && src[col * k + col] != 0) {
242 irow = col;
243 icol = col;
244 goto found_piv;
245 }
246 for (row = 0; row < k; row++) {
247 if (ipiv[row] != 1) {
248 for (ix = 0; ix < k; ix++) {
249 if (ipiv[ix] == 0) {
250 if (src[row * k + ix] != 0) {
251 irow = row;
252 icol = ix;
253 goto found_piv;
254 }
255 } else if (ipiv[ix] > 1) {
256 error = -E_FEC_PIVOT;
257 goto fail;
258 }
259 }
260 }
261 }
262 error = -E_FEC_PIVOT;
263 if (icol == -1)
264 goto fail;
265 found_piv:
266 ++(ipiv[icol]);
267 /*
268 * swap rows irow and icol, so afterwards the diagonal element
269 * will be correct. Rarely done, not worth optimizing.
270 */
271 if (irow != icol)
272 for (ix = 0; ix < k; ix++)
273 FEC_SWAP(src[irow * k + ix], src[icol * k + ix]);
274 indxr[col] = irow;
275 indxc[col] = icol;
276 pivot_row = &src[icol * k];
277 error = -E_FEC_SINGULAR;
278 c = pivot_row[icol];
279 if (c == 0)
280 goto fail;
281 if (c != 1) { /* otherwise this is a NOP */
282 /*
283 * this is done often , but optimizing is not so
284 * fruitful, at least in the obvious ways (unrolling)
285 */
286 c = inverse[c];
287 pivot_row[icol] = 1;
288 for (ix = 0; ix < k; ix++)
289 pivot_row[ix] = gf_mul(c, pivot_row[ix]);
290 }
291 /*
292 * from all rows, remove multiples of the selected row to zero
293 * the relevant entry (in fact, the entry is not zero because
294 * we know it must be zero). (Here, if we know that the
295 * pivot_row is the identity, we can optimize the addmul).
296 */
297 id_row[icol] = 1;
298 if (memcmp(pivot_row, id_row, k) != 0) {
299 for (p = src, ix = 0; ix < k; ix++, p += k) {
300 if (ix != icol) {
301 c = p[icol];
302 p[icol] = 0;
303 addmul(p, pivot_row, c, k);
304 }
305 }
306 }
307 id_row[icol] = 0;
308 }
309 for (col = k - 1; col >= 0; col--) {
310 if (indxr[col] < 0 || indxr[col] >= k)
311 PARA_CRIT_LOG("AARGH, indxr[col] %d\n", indxr[col]);
312 else if (indxc[col] < 0 || indxc[col] >= k)
313 PARA_CRIT_LOG("AARGH, indxc[col] %d\n", indxc[col]);
314 else if (indxr[col] != indxc[col]) {
315 for (row = 0; row < k; row++) {
316 FEC_SWAP(src[row * k + indxr[col]],
317 src[row * k + indxc[col]]);
318 }
319 }
320 }
321 error = 0;
322 fail:
323 free(indxc);
324 free(indxr);
325 free(ipiv);
326 free(id_row);
327 free(temp_row);
328 return error;
329 }
330
331 /*
332 * Invert a Vandermonde matrix.
333 *
334 * It assumes that the matrix is not singular and _IS_ a Vandermonde matrix.
335 * Only uses the second column of the matrix, containing the p_i's.
336 *
337 * Algorithm borrowed from "Numerical recipes in C" -- sec.2.8, but largely
338 * revised for GF purposes.
339 */
340 static void invert_vdm(unsigned char *src, int k)
341 {
342 int i, j, row, col;
343 unsigned char *b, *c, *p, t, xx;
344
345 if (k == 1) /* degenerate */
346 return;
347 /*
348 * c holds the coefficient of P(x) = Prod (x - p_i), i=0..k-1
349 * b holds the coefficient for the matrix inversion
350 */
351 c = para_malloc(k);
352 b = para_malloc(k);
353 p = para_malloc(k);
354
355 for (j = 1, i = 0; i < k; i++, j += k) {
356 c[i] = 0;
357 p[i] = src[j];
358 }
359 /*
360 * construct coeffs recursively. We know c[k] = 1 (implicit) and start
361 * P_0 = x - p_0, then at each stage multiply by x - p_i generating P_i
362 * = x P_{i-1} - p_i P_{i-1} After k steps we are done.
363 */
364 c[k - 1] = p[0]; /* really -p(0), but x = -x in GF(2^m) */
365 for (i = 1; i < k; i++) {
366 unsigned char p_i = p[i];
367 for (j = k - 1 - (i - 1); j < k - 1; j++)
368 c[j] ^= gf_mul(p_i, c[j + 1]);
369 c[k - 1] ^= p_i;
370 }
371
372 for (row = 0; row < k; row++) {
373 /*
374 * synthetic division etc.
375 */
376 xx = p[row];
377 t = 1;
378 b[k - 1] = 1; /* this is in fact c[k] */
379 for (i = k - 2; i >= 0; i--) {
380 b[i] = c[i + 1] ^ gf_mul(xx, b[i + 1]);
381 t = gf_mul(xx, t) ^ b[i];
382 }
383 for (col = 0; col < k; col++)
384 src[col * k + row] = gf_mul(inverse[t], b[col]);
385 }
386 free(c);
387 free(b);
388 free(p);
389 }
390
391 static int fec_initialized;
392
393 static void init_fec(void)
394 {
395 generate_gf();
396 init_mul_table();
397 fec_initialized = 1;
398 }
399
400 /** Internal FEC parameters. */
401 struct fec_parms {
402 /** Number of data slices. */
403 int k;
404 /** Number of slices (including redundant slices). */
405 int n;
406 /** The encoding matrix, computed by init_fec(). */
407 unsigned char *enc_matrix;
408 };
409
410 /**
411 * Deallocate a fec params structure.
412 *
413 * \param p The structure to free.
414 */
415 void fec_free(struct fec_parms *p)
416 {
417 if (!p)
418 return;
419 free(p->enc_matrix);
420 free(p);
421 }
422
423 /**
424 * Create a new encoder and return an opaque descriptor to it.
425 *
426 * \param k Number of input slices.
427 * \param n Number of output slices.
428 * \param result On success the Fec descriptor is returned here.
429 *
430 * \return Standard.
431 *
432 * This creates the k*n encoding matrix. It is computed starting with a
433 * Vandermonde matrix, and then transformed into a systematic matrix.
434 */
435 int fec_new(int k, int n, struct fec_parms **result)
436 {
437 int row, col;
438 unsigned char *p, *tmp_m;
439 struct fec_parms *parms;
440
441 if (!fec_initialized)
442 init_fec();
443
444 if (k < 1 || k > GF_SIZE + 1 || n > GF_SIZE + 1 || k > n)
445 return -E_FEC_PARMS;
446 parms = para_malloc(sizeof(struct fec_parms));
447 parms->k = k;
448 parms->n = n;
449 parms->enc_matrix = alloc_matrix(n, k);
450 tmp_m = alloc_matrix(n, k);
451 /*
452 * fill the matrix with powers of field elements, starting from 0.
453 * The first row is special, cannot be computed with exp. table.
454 */
455 tmp_m[0] = 1;
456 for (col = 1; col < k; col++)
457 tmp_m[col] = 0;
458 for (p = tmp_m + k, row = 0; row < n - 1; row++, p += k) {
459 for (col = 0; col < k; col++)
460 p[col] = gf_exp[modnn(row * col)];
461 }
462
463 /*
464 * quick code to build systematic matrix: invert the top
465 * k*k vandermonde matrix, multiply right the bottom n-k rows
466 * by the inverse, and construct the identity matrix at the top.
467 */
468 invert_vdm(tmp_m, k); /* much faster than invert_mat */
469 matmul(tmp_m + k * k, tmp_m, parms->enc_matrix + k * k, n - k, k, k);
470 /*
471 * the upper matrix is I so do not bother with a slow multiply
472 */
473 memset(parms->enc_matrix, 0, k * k);
474 for (p = parms->enc_matrix, col = 0; col < k; col++, p += k + 1)
475 *p = 1;
476 free(tmp_m);
477 *result = parms;
478 return 0;
479 }
480
481 /**
482 * Compute one encoded slice of the given input.
483 *
484 * \param parms The fec parameters returned earlier by fec_new().
485 * \param src The \a k data slices to encode.
486 * \param dst Result pointer.
487 * \param idx The index of the slice to compute.
488 * \param sz The size of the input data packets.
489 *
490 * Encode the \a k slices of size \a sz given by \a src and store the output
491 * slice number \a idx in \a dst.
492 */
493 void fec_encode(struct fec_parms *parms, const unsigned char * const *src,
494 unsigned char *dst, int idx, int sz)
495 {
496 int i, k = parms->k;
497 unsigned char *p;
498
499 assert(idx <= parms->n);
500
501 if (idx < k) {
502 memcpy(dst, src[idx], sz);
503 return;
504 }
505 p = &(parms->enc_matrix[idx * k]);
506 memset(dst, 0, sz);
507 for (i = 0; i < k; i++)
508 addmul(dst, src[i], p[i], sz);
509 }
510
511 /* Move src packets in their position. */
512 static int shuffle(unsigned char **data, int *idx, int k)
513 {
514 int i;
515
516 for (i = 0; i < k;) {
517 if (idx[i] >= k || idx[i] == i)
518 i++;
519 else { /* put index and data at the right position */
520 int c = idx[i];
521
522 if (idx[c] == c) /* conflict */
523 return -E_FEC_BAD_IDX;
524 FEC_SWAP(idx[i], idx[c]);
525 FEC_SWAP(data[i], data[c]);
526 }
527 }
528 return 0;
529 }
530
531 /*
532 * Construct the decoding matrix given the indices. The encoding matrix must
533 * already be allocated.
534 */
535 static int build_decode_matrix(struct fec_parms *parms, int *idx,
536 unsigned char **result)
537 {
538 int ret = -E_FEC_BAD_IDX, i, k = parms->k;
539 unsigned char *p, *matrix = alloc_matrix(k, k);
540
541 for (i = 0, p = matrix; i < k; i++, p += k) {
542 if (idx[i] >= parms->n) /* invalid index */
543 goto err;
544 if (idx[i] < k) {
545 memset(p, 0, k);
546 p[i] = 1;
547 } else
548 memcpy(p, &(parms->enc_matrix[idx[i] * k]), k);
549 }
550 ret = invert_mat(matrix, k);
551 if (ret < 0)
552 goto err;
553 *result = matrix;
554 return 0;
555 err:
556 free(matrix);
557 *result = NULL;
558 return ret;
559 }
560
561 /**
562 * Decode one slice from the group of received slices.
563 *
564 * \param parms Pointer to fec params structure.
565 * \param data Pointers to received packets.
566 * \param idx Pointer to packet indices (gets modified).
567 * \param sz Size of each packet.
568 *
569 * \return Zero on success, -1 on errors.
570 *
571 * The \a data vector of received slices and the indices of slices are used to
572 * produce the correct output slice. The data slices are modified in-place.
573 */
574 int fec_decode(struct fec_parms *parms, unsigned char **data, int *idx,
575 int sz)
576 {
577 unsigned char *m_dec, **slice;
578 int ret, row, col, k = parms->k;
579
580 ret = shuffle(data, idx, k);
581 if (ret < 0)
582 return ret;
583 ret = build_decode_matrix(parms, idx, &m_dec);
584 if (ret < 0)
585 return ret;
586 /* do the actual decoding */
587 slice = para_malloc(k * sizeof(unsigned char *));
588 for (row = 0; row < k; row++) {
589 if (idx[row] >= k) {
590 slice[row] = para_calloc(sz);
591 for (col = 0; col < k; col++)
592 addmul(slice[row], data[col],
593 m_dec[row * k + col], sz);
594 }
595 }
596 /* move slices to their final destination */
597 for (row = 0; row < k; row++) {
598 if (idx[row] >= k) {
599 memcpy(data[row], slice[row], sz);
600 free(slice[row]);
601 }
602 }
603 free(slice);
604 free(m_dec);
605 return 0;
606 }