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Diffstat (limited to 'fec.c')
| -rw-r--r-- | fec.c | 904 |
1 files changed, 0 insertions, 904 deletions
@@ -1,904 +0,0 @@ -/* - * fec.c -- forward error correction based on Vandermonde matrices - * 980624 - * (C) 1997-98 Luigi Rizzo (luigi@iet.unipi.it) - * - * Portions derived from code by Phil Karn (karn@ka9q.ampr.org), - * Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari - * Thirumoorthy (harit@spectra.eng.hawaii.edu), Aug 1995 - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above - * copyright notice, this list of conditions and the following - * disclaimer in the documentation and/or other materials - * provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, - * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A - * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS - * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, - * OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, - * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, - * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY - * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR - * TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT - * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY - * OF SUCH DAMAGE. - */ - -/* - * The following parameter defines how many bits are used for - * field elements. The code supports any value from 2 to 16 - * but fastest operation is achieved with 8 bit elements - * This is the only parameter you may want to change. - */ -#ifndef GF_BITS -#define GF_BITS 8 /* code over GF(2**GF_BITS) - change to suit */ -#endif - -#include <stdio.h> -#include <stdlib.h> -#include <string.h> - -/* - * stuff used for testing purposes only - */ - -#ifdef TEST -#define DEB(x) -#define DDB(x) x -#define DEBUG 0 /* minimal debugging */ -#ifdef MSDOS -#include <time.h> -struct timeval { - unsigned long ticks; -}; -#define gettimeofday(x, dummy) { (x)->ticks = clock() ; } -#define DIFF_T(a,b) (1+ 1000000*(a.ticks - b.ticks) / CLOCKS_PER_SEC ) -typedef unsigned long u_long ; -typedef unsigned short u_short ; -#else /* typically, unix systems */ -#include <sys/time.h> -#define DIFF_T(a,b) \ - (1+ 1000000*(a.tv_sec - b.tv_sec) + (a.tv_usec - b.tv_usec) ) -#endif - -#define TICK(t) \ - {struct timeval x ; \ - gettimeofday(&x, NULL) ; \ - t = x.tv_usec + 1000000* (x.tv_sec & 0xff ) ; \ - } -#define TOCK(t) \ - { u_long t1 ; TICK(t1) ; \ - if (t1 < t) t = 256000000 + t1 - t ; \ - else t = t1 - t ; \ - if (t == 0) t = 1 ;} - -u_long ticks[10]; /* vars for timekeeping */ -#else -#define DEB(x) -#define DDB(x) -#define TICK(x) -#define TOCK(x) -#endif /* TEST */ - -/* - * You should not need to change anything beyond this point. - * The first part of the file implements linear algebra in GF. - * - * gf is the type used to store an element of the Galois Field. - * Must constain at least GF_BITS bits. - * - * Note: unsigned char will work up to GF(256) but int seems to run - * faster on the Pentium. We use int whenever have to deal with an - * index, since they are generally faster. - */ -#if (GF_BITS < 2 && GF_BITS >16) -#error "GF_BITS must be 2 .. 16" -#endif -#if (GF_BITS <= 8) -typedef unsigned char gf; -#else -typedef unsigned short gf; -#endif - -#define GF_SIZE ((1 << GF_BITS) - 1) /* powers of \alpha */ - -/* - * Primitive polynomials - see Lin & Costello, Appendix A, - * and Lee & Messerschmitt, p. 453. - */ -static char *allPp[] = { /* GF_BITS polynomial */ - NULL, /* 0 no code */ - NULL, /* 1 no code */ - "111", /* 2 1+x+x^2 */ - "1101", /* 3 1+x+x^3 */ - "11001", /* 4 1+x+x^4 */ - "101001", /* 5 1+x^2+x^5 */ - "1100001", /* 6 1+x+x^6 */ - "10010001", /* 7 1 + x^3 + x^7 */ - "101110001", /* 8 1+x^2+x^3+x^4+x^8 */ - "1000100001", /* 9 1+x^4+x^9 */ - "10010000001", /* 10 1+x^3+x^10 */ - "101000000001", /* 11 1+x^2+x^11 */ - "1100101000001", /* 12 1+x+x^4+x^6+x^12 */ - "11011000000001", /* 13 1+x+x^3+x^4+x^13 */ - "110000100010001", /* 14 1+x+x^6+x^10+x^14 */ - "1100000000000001", /* 15 1+x+x^15 */ - "11010000000010001" /* 16 1+x+x^3+x^12+x^16 */ -}; - - -/* - * To speed up computations, we have tables for logarithm, exponent - * and inverse of a number. If GF_BITS <= 8, we use a table for - * multiplication as well (it takes 64K, no big deal even on a PDA, - * especially because it can be pre-initialized an put into a ROM!), - * otherwhise we use a table of logarithms. - * In any case the macro gf_mul(x,y) takes care of multiplications. - */ - -static gf gf_exp[2*GF_SIZE]; /* index->poly form conversion table */ -static int gf_log[GF_SIZE + 1]; /* Poly->index form conversion table */ -static gf inverse[GF_SIZE+1]; /* inverse of field elem. */ - /* inv[\alpha**i]=\alpha**(GF_SIZE-i-1) */ - -/* - * modnn(x) computes x % GF_SIZE, where GF_SIZE is 2**GF_BITS - 1, - * without a slow divide. - */ -static inline gf -modnn(int x) -{ - while (x >= GF_SIZE) { - x -= GF_SIZE; - x = (x >> GF_BITS) + (x & GF_SIZE); - } - return x; -} - -#define SWAP(a,b,t) {t tmp; tmp=a; a=b; b=tmp;} - -/* - * gf_mul(x,y) multiplies two numbers. If GF_BITS<=8, it is much - * faster to use a multiplication table. - * - * USE_GF_MULC, GF_MULC0(c) and GF_ADDMULC(x) can be used when multiplying - * many numbers by the same constant. In this case the first - * call sets the constant, and others perform the multiplications. - * A value related to the multiplication is held in a local variable - * declared with USE_GF_MULC . See usage in addmul1(). - */ -#if (GF_BITS <= 8) -static gf gf_mul_table[GF_SIZE + 1][GF_SIZE + 1]; - -#define gf_mul(x,y) gf_mul_table[x][y] - -#define USE_GF_MULC register gf * __gf_mulc_ -#define GF_MULC0(c) __gf_mulc_ = gf_mul_table[c] -#define GF_ADDMULC(dst, x) dst ^= __gf_mulc_[x] - -static void -init_mul_table() -{ - int i, j; - for (i=0; i< GF_SIZE+1; i++) - for (j=0; j< GF_SIZE+1; j++) - gf_mul_table[i][j] = gf_exp[modnn(gf_log[i] + gf_log[j]) ] ; - - for (j=0; j< GF_SIZE+1; j++) - gf_mul_table[0][j] = gf_mul_table[j][0] = 0; -} -#else /* GF_BITS > 8 */ -static inline gf -gf_mul(x,y) -{ - if ( (x) == 0 || (y)==0 ) return 0; - - return gf_exp[gf_log[x] + gf_log[y] ] ; -} -#define init_mul_table() - -#define USE_GF_MULC register gf * __gf_mulc_ -#define GF_MULC0(c) __gf_mulc_ = &gf_exp[ gf_log[c] ] -#define GF_ADDMULC(dst, x) { if (x) dst ^= __gf_mulc_[ gf_log[x] ] ; } -#endif - -/* - * Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m] - * Lookup tables: - * index->polynomial form gf_exp[] contains j= \alpha^i; - * polynomial form -> index form gf_log[ j = \alpha^i ] = i - * \alpha=x is the primitive element of GF(2^m) - * - * For efficiency, gf_exp[] has size 2*GF_SIZE, so that a simple - * multiplication of two numbers can be resolved without calling modnn - */ - -/* - * i use malloc so many times, it is easier to put checks all in - * one place. - */ -static void * -my_malloc(int sz, char *err_string) -{ - void *p = malloc( sz ); - if (p == NULL) { - fprintf(stderr, "-- malloc failure allocating %s\n", err_string); - exit(1) ; - } - return p ; -} - -#define NEW_GF_MATRIX(rows, cols) \ - (gf *)my_malloc(rows * cols * sizeof(gf), " ## __LINE__ ## " ) - -/* - * initialize the data structures used for computations in GF. - */ -static void -generate_gf(void) -{ - int i; - gf mask; - char *Pp = allPp[GF_BITS] ; - - mask = 1; /* x ** 0 = 1 */ - gf_exp[GF_BITS] = 0; /* will be updated at the end of the 1st loop */ - /* - * first, generate the (polynomial representation of) powers of \alpha, - * which are stored in gf_exp[i] = \alpha ** i . - * At the same time build gf_log[gf_exp[i]] = i . - * The first GF_BITS powers are simply bits shifted to the left. - */ - for (i = 0; i < GF_BITS; i++, mask <<= 1 ) { - gf_exp[i] = mask; - gf_log[gf_exp[i]] = i; - /* - * If Pp[i] == 1 then \alpha ** i occurs in poly-repr - * gf_exp[GF_BITS] = \alpha ** GF_BITS - */ - if ( Pp[i] == '1' ) - gf_exp[GF_BITS] ^= mask; - } - /* - * now gf_exp[GF_BITS] = \alpha ** GF_BITS is complete, so can als - * compute its inverse. - */ - gf_log[gf_exp[GF_BITS]] = GF_BITS; - /* - * Poly-repr of \alpha ** (i+1) is given by poly-repr of - * \alpha ** i shifted left one-bit and accounting for any - * \alpha ** GF_BITS term that may occur when poly-repr of - * \alpha ** i is shifted. - */ - mask = 1 << (GF_BITS - 1 ) ; - for (i = GF_BITS + 1; i < GF_SIZE; i++) { - if (gf_exp[i - 1] >= mask) - gf_exp[i] = gf_exp[GF_BITS] ^ ((gf_exp[i - 1] ^ mask) << 1); - else - gf_exp[i] = gf_exp[i - 1] << 1; - gf_log[gf_exp[i]] = i; - } - /* - * log(0) is not defined, so use a special value - */ - gf_log[0] = GF_SIZE ; - /* set the extended gf_exp values for fast multiply */ - for (i = 0 ; i < GF_SIZE ; i++) - gf_exp[i + GF_SIZE] = gf_exp[i] ; - - /* - * again special cases. 0 has no inverse. This used to - * be initialized to GF_SIZE, but it should make no difference - * since noone is supposed to read from here. - */ - inverse[0] = 0 ; - inverse[1] = 1; - for (i=2; i<=GF_SIZE; i++) - inverse[i] = gf_exp[GF_SIZE-gf_log[i]]; -} - -/* - * Various linear algebra operations that i use often. - */ - -/* - * addmul() computes dst[] = dst[] + c * src[] - * This is used often, so better optimize it! Currently the loop is - * unrolled 16 times, a good value for 486 and pentium-class machines. - * The case c=0 is also optimized, whereas c=1 is not. These - * calls are unfrequent in my typical apps so I did not bother. - * - * Note that gcc on - */ -#define addmul(dst, src, c, sz) \ - if (c != 0) addmul1(dst, src, c, sz) - -#define UNROLL 16 /* 1, 4, 8, 16 */ -static void -addmul1(gf *dst1, gf *src1, gf c, int sz) -{ - USE_GF_MULC ; - register gf *dst = dst1, *src = src1 ; - gf *lim = &dst[sz - UNROLL + 1] ; - - GF_MULC0(c) ; - -#if (UNROLL > 1) /* unrolling by 8/16 is quite effective on the pentium */ - for (; dst < lim ; dst += UNROLL, src += UNROLL ) { - GF_ADDMULC( dst[0] , src[0] ); - GF_ADDMULC( dst[1] , src[1] ); - GF_ADDMULC( dst[2] , src[2] ); - GF_ADDMULC( dst[3] , src[3] ); -#if (UNROLL > 4) - GF_ADDMULC( dst[4] , src[4] ); - GF_ADDMULC( dst[5] , src[5] ); - GF_ADDMULC( dst[6] , src[6] ); - GF_ADDMULC( dst[7] , src[7] ); -#endif -#if (UNROLL > 8) - GF_ADDMULC( dst[8] , src[8] ); - GF_ADDMULC( dst[9] , src[9] ); - GF_ADDMULC( dst[10] , src[10] ); - GF_ADDMULC( dst[11] , src[11] ); - GF_ADDMULC( dst[12] , src[12] ); - GF_ADDMULC( dst[13] , src[13] ); - GF_ADDMULC( dst[14] , src[14] ); - GF_ADDMULC( dst[15] , src[15] ); -#endif - } -#endif - lim += UNROLL - 1 ; - for (; dst < lim; dst++, src++ ) /* final components */ - GF_ADDMULC( *dst , *src ); -} - -/* - * computes C = AB where A is n*k, B is k*m, C is n*m - */ -static void -matmul(gf *a, gf *b, gf *c, int n, int k, int m) -{ - int row, col, i ; - - for (row = 0; row < n ; row++) { - for (col = 0; col < m ; col++) { - gf *pa = &a[ row * k ]; - gf *pb = &b[ col ]; - gf acc = 0 ; - for (i = 0; i < k ; i++, pa++, pb += m ) - acc ^= gf_mul( *pa, *pb ) ; - c[ row * m + col ] = acc ; - } - } -} - -#ifdef DEBUG -/* - * returns 1 if the square matrix is identiy - * (only for test) - */ -static int -is_identity(gf *m, int k) -{ - int row, col ; - for (row=0; row<k; row++) - for (col=0; col<k; col++) - if ( (row==col && *m != 1) || - (row!=col && *m != 0) ) - return 0 ; - else - m++ ; - return 1 ; -} -#endif /* debug */ - -/* - * invert_mat() takes a matrix and produces its inverse - * k is the size of the matrix. - * (Gauss-Jordan, adapted from Numerical Recipes in C) - * Return non-zero if singular. - */ -DEB( int pivloops=0; int pivswaps=0 ; /* diagnostic */) -static int -invert_mat(gf *src, int k) -{ - gf c, *p ; - int irow, icol, row, col, i, ix ; - - int error = 1 ; - int *indxc = my_malloc(k*sizeof(int), "indxc"); - int *indxr = my_malloc(k*sizeof(int), "indxr"); - int *ipiv = my_malloc(k*sizeof(int), "ipiv"); - gf *id_row = NEW_GF_MATRIX(1, k); - gf *temp_row = NEW_GF_MATRIX(1, k); - - memset(id_row, '\0', k*sizeof(gf)); - DEB( pivloops=0; pivswaps=0 ; /* diagnostic */ ) - /* - * ipiv marks elements already used as pivots. - */ - for (i = 0; i < k ; i++) - ipiv[i] = 0 ; - - for (col = 0; col < k ; col++) { - gf *pivot_row ; - /* - * Zeroing column 'col', look for a non-zero element. - * First try on the diagonal, if it fails, look elsewhere. - */ - irow = icol = -1 ; - if (ipiv[col] != 1 && src[col*k + col] != 0) { - irow = col ; - icol = col ; - goto found_piv ; - } - for (row = 0 ; row < k ; row++) { - if (ipiv[row] != 1) { - for (ix = 0 ; ix < k ; ix++) { - DEB( pivloops++ ; ) - if (ipiv[ix] == 0) { - if (src[row*k + ix] != 0) { - irow = row ; - icol = ix ; - goto found_piv ; - } - } else if (ipiv[ix] > 1) { - fprintf(stderr, "singular matrix\n"); - goto fail ; - } - } - } - } - if (icol == -1) { - fprintf(stderr, "XXX pivot not found!\n"); - goto fail ; - } -found_piv: - ++(ipiv[icol]) ; - /* - * swap rows irow and icol, so afterwards the diagonal - * element will be correct. Rarely done, not worth - * optimizing. - */ - if (irow != icol) { - for (ix = 0 ; ix < k ; ix++ ) { - SWAP( src[irow*k + ix], src[icol*k + ix], gf) ; - } - } - indxr[col] = irow ; - indxc[col] = icol ; - pivot_row = &src[icol*k] ; - c = pivot_row[icol] ; - if (c == 0) { - fprintf(stderr, "singular matrix 2\n"); - goto fail ; - } - if (c != 1 ) { /* otherwhise this is a NOP */ - /* - * this is done often , but optimizing is not so - * fruitful, at least in the obvious ways (unrolling) - */ - DEB( pivswaps++ ; ) - c = inverse[ c ] ; - pivot_row[icol] = 1 ; - for (ix = 0 ; ix < k ; ix++ ) - pivot_row[ix] = gf_mul(c, pivot_row[ix] ); - } - /* - * from all rows, remove multiples of the selected row - * to zero the relevant entry (in fact, the entry is not zero - * because we know it must be zero). - * (Here, if we know that the pivot_row is the identity, - * we can optimize the addmul). - */ - id_row[icol] = 1; - if (memcmp(pivot_row, id_row, k*sizeof(gf)) != 0) { - for (p = src, ix = 0 ; ix < k ; ix++, p += k ) { - if (ix != icol) { - c = p[icol] ; - p[icol] = 0 ; - addmul(p, pivot_row, c, k ); - } - } - } - id_row[icol] = 0; - } /* done all columns */ - for (col = k-1 ; col >= 0 ; col-- ) { - if (indxr[col] <0 || indxr[col] >= k) - fprintf(stderr, "AARGH, indxr[col] %d\n", indxr[col]); - else if (indxc[col] <0 || indxc[col] >= k) - fprintf(stderr, "AARGH, indxc[col] %d\n", indxc[col]); - else - if (indxr[col] != indxc[col] ) { - for (row = 0 ; row < k ; row++ ) { - SWAP( src[row*k + indxr[col]], src[row*k + indxc[col]], gf) ; - } - } - } - error = 0 ; -fail: - free(indxc); - free(indxr); - free(ipiv); - free(id_row); - free(temp_row); - return error ; -} - -/* - * fast code for inverting a vandermonde matrix. - * XXX NOTE: It assumes that the matrix - * is not singular and _IS_ a vandermonde matrix. Only uses - * the second column of the matrix, containing the p_i's. - * - * Algorithm borrowed from "Numerical recipes in C" -- sec.2.8, but - * largely revised for my purposes. - * p = coefficients of the matrix (p_i) - * q = values of the polynomial (known) - */ - -int -invert_vdm(gf *src, int k) -{ - int i, j, row, col ; - gf *b, *c, *p; - gf t, xx ; - - if (k == 1) /* degenerate case, matrix must be p^0 = 1 */ - return 0 ; - /* - * c holds the coefficient of P(x) = Prod (x - p_i), i=0..k-1 - * b holds the coefficient for the matrix inversion - */ - c = NEW_GF_MATRIX(1, k); - b = NEW_GF_MATRIX(1, k); - - p = NEW_GF_MATRIX(1, k); - - for ( j=1, i = 0 ; i < k ; i++, j+=k ) { - c[i] = 0 ; - p[i] = src[j] ; /* p[i] */ - } - /* - * construct coeffs. recursively. We know c[k] = 1 (implicit) - * and start P_0 = x - p_0, then at each stage multiply by - * x - p_i generating P_i = x P_{i-1} - p_i P_{i-1} - * After k steps we are done. - */ - c[k-1] = p[0] ; /* really -p(0), but x = -x in GF(2^m) */ - for (i = 1 ; i < k ; i++ ) { - gf p_i = p[i] ; /* see above comment */ - for (j = k-1 - ( i - 1 ) ; j < k-1 ; j++ ) - c[j] ^= gf_mul( p_i, c[j+1] ) ; - c[k-1] ^= p_i ; - } - - for (row = 0 ; row < k ; row++ ) { - /* - * synthetic division etc. - */ - xx = p[row] ; - t = 1 ; - b[k-1] = 1 ; /* this is in fact c[k] */ - for (i = k-2 ; i >= 0 ; i-- ) { - b[i] = c[i+1] ^ gf_mul(xx, b[i+1]) ; - t = gf_mul(xx, t) ^ b[i] ; - } - for (col = 0 ; col < k ; col++ ) - src[col*k + row] = gf_mul(inverse[t], b[col] ); - } - free(c) ; - free(b) ; - free(p) ; - return 0 ; -} - -static int fec_initialized = 0 ; -static void -init_fec() -{ - TICK(ticks[0]); - generate_gf(); - TOCK(ticks[0]); - DDB(fprintf(stderr, "generate_gf took %ldus\n", ticks[0]);) - TICK(ticks[0]); - init_mul_table(); - TOCK(ticks[0]); - DDB(fprintf(stderr, "init_mul_table took %ldus\n", ticks[0]);) - fec_initialized = 1 ; -} - -/* - * This section contains the proper FEC encoding/decoding routines. - * The encoding matrix is computed starting with a Vandermonde matrix, - * and then transforming it into a systematic matrix. - */ - -#define FEC_MAGIC 0xFECC0DEC - -struct fec_parms { - u_long magic ; - int k, n ; /* parameters of the code */ - gf *enc_matrix ; -} ; - -void -fec_free(struct fec_parms *p) -{ - if (p==NULL || - p->magic != ( ( (FEC_MAGIC ^ p->k) ^ p->n) ^ (int)(p->enc_matrix)) ) { - fprintf(stderr, "bad parameters to fec_free\n"); - return ; - } - free(p->enc_matrix); - free(p); -} - -/* - * create a new encoder, returning a descriptor. This contains k,n and - * the encoding matrix. - */ -struct fec_parms * -fec_new(int k, int n) -{ - int row, col ; - gf *p, *tmp_m ; - - struct fec_parms *retval ; - - if (fec_initialized == 0) - init_fec(); - - if (k > GF_SIZE + 1 || n > GF_SIZE + 1 || k > n ) { - fprintf(stderr, "Invalid parameters k %d n %d GF_SIZE %d\n", - k, n, GF_SIZE ); - return NULL ; - } - retval = my_malloc(sizeof(struct fec_parms), "new_code"); - retval->k = k ; - retval->n = n ; - retval->enc_matrix = NEW_GF_MATRIX(n, k); - retval->magic = ( ( FEC_MAGIC ^ k) ^ n) ^ (int)(retval->enc_matrix) ; - tmp_m = NEW_GF_MATRIX(n, k); - /* - * fill the matrix with powers of field elements, starting from 0. - * The first row is special, cannot be computed with exp. table. - */ - tmp_m[0] = 1 ; - for (col = 1; col < k ; col++) - tmp_m[col] = 0 ; - for (p = tmp_m + k, row = 0; row < n-1 ; row++, p += k) { - for ( col = 0 ; col < k ; col ++ ) - p[col] = gf_exp[modnn(row*col)]; - } - - /* - * quick code to build systematic matrix: invert the top - * k*k vandermonde matrix, multiply right the bottom n-k rows - * by the inverse, and construct the identity matrix at the top. - */ - TICK(ticks[3]); - invert_vdm(tmp_m, k); /* much faster than invert_mat */ - matmul(tmp_m + k*k, tmp_m, retval->enc_matrix + k*k, n - k, k, k); - /* - * the upper matrix is I so do not bother with a slow multiply - */ - memset(retval->enc_matrix, '\0', k*k*sizeof(gf) ); - for (p = retval->enc_matrix, col = 0 ; col < k ; col++, p += k+1 ) - *p = 1 ; - free(tmp_m); - TOCK(ticks[3]); - - DDB(fprintf(stderr, "--- %ld us to build encoding matrix\n", - ticks[3]);) - DEB(pr_matrix(retval->enc_matrix, n, k, "encoding_matrix");) - return retval ; -} - -/* - * fec_encode accepts as input pointers to n data packets of size sz, - * and produces as output a packet pointed to by fec, computed - * with index "index". - */ -void -fec_encode(struct fec_parms *code, gf *src[], gf *fec, int index, int sz) -{ - int i, k = code->k ; - gf *p ; - - if (GF_BITS > 8) - sz /= 2 ; - - if (index < k) - memcpy(fec, src[index], sz*sizeof(gf) ) ; - else if (index < code->n) { - p = &(code->enc_matrix[index*k] ); - memset(fec, '\0', sz*sizeof(gf)); - for (i = 0; i < k ; i++) - addmul(fec, src[i], p[i], sz ) ; - } else - fprintf(stderr, "Invalid index %d (max %d)\n", - index, code->n - 1 ); -} - -void fec_encode_linear(struct fec_parms *code, gf *src, gf *fec, int index, int sz) -{ - int i, k = code->k ; - gf *p ; - - if (GF_BITS > 8) - sz /= 2 ; - - if (index < k) - memcpy(fec, src + (index * sz), sz*sizeof(gf) ) ; - else if (index < code->n) { - p = &(code->enc_matrix[index*k] ); - memset(fec, '\0', sz*sizeof(gf)); - for (i = 0; i < k ; i++) - addmul(fec, src + (i * sz), p[i], sz ) ; - } else - fprintf(stderr, "Invalid index %d (max %d)\n", - index, code->n - 1 ); -} -/* - * shuffle move src packets in their position - */ -static int -shuffle(gf *pkt[], int index[], int k) -{ - int i; - - for ( i = 0 ; i < k ; ) { - if (index[i] >= k || index[i] == i) - i++ ; - else { - /* - * put pkt in the right position (first check for conflicts). - */ - int c = index[i] ; - - if (index[c] == c) { - DEB(fprintf(stderr, "\nshuffle, error at %d\n", i);) - return 1 ; - } - SWAP(index[i], index[c], int) ; - SWAP(pkt[i], pkt[c], gf *) ; - } - } - DEB( /* just test that it works... */ - for ( i = 0 ; i < k ; i++ ) { - if (index[i] < k && index[i] != i) { - fprintf(stderr, "shuffle: after\n"); - for (i=0; i<k ; i++) fprintf(stderr, "%3d ", index[i]); - fprintf(stderr, "\n"); - return 1 ; - } - } - ) - return 0 ; -} - -/* - * build_decode_matrix constructs the encoding matrix given the - * indexes. The matrix must be already allocated as - * a vector of k*k elements, in row-major order - */ -static gf * -build_decode_matrix(struct fec_parms *code, gf *pkt[], int index[]) -{ - int i , k = code->k ; - gf *p, *matrix = NEW_GF_MATRIX(k, k); - - TICK(ticks[9]); - for (i = 0, p = matrix ; i < k ; i++, p += k ) { -#if 1 /* this is simply an optimization, not very useful indeed */ - if (index[i] < k) { - memset(p, '\0', k*sizeof(gf) ); - p[i] = 1 ; - } else -#endif - if (index[i] < code->n ) - memcpy(p, &(code->enc_matrix[index[i]*k]), k*sizeof(gf) ); - else { - fprintf(stderr, "decode: invalid index %d (max %d)\n", - index[i], code->n - 1 ); - free(matrix) ; - return NULL ; - } - } - TICK(ticks[9]); - if (invert_mat(matrix, k)) { - free(matrix); - matrix = NULL ; - } - TOCK(ticks[9]); - return matrix ; -} - -/* - * fec_decode receives as input a vector of packets, the indexes of - * packets, and produces the correct vector as output. - * - * Input: - * code: pointer to code descriptor - * pkt: pointers to received packets. They are modified - * to store the output packets (in place) - * index: pointer to packet indexes (modified) - * sz: size of each packet - */ -int -fec_decode(struct fec_parms *code, gf *pkt[], int index[], int sz) -{ - gf *m_dec ; - gf **new_pkt ; - int row, col , k = code->k ; - - if (GF_BITS > 8) - sz /= 2 ; - - if (shuffle(pkt, index, k)) /* error if true */ - return 1 ; - m_dec = build_decode_matrix(code, pkt, index); - - if (m_dec == NULL) - return 1 ; /* error */ - /* - * do the actual decoding - */ - new_pkt = my_malloc (k * sizeof (gf * ), "new pkt pointers" ); - for (row = 0 ; row < k ; row++ ) { - if (index[row] >= k) { - new_pkt[row] = my_malloc (sz * sizeof (gf), "new pkt buffer" ); - memset(new_pkt[row], '\0', sz * sizeof(gf) ) ; - for (col = 0 ; col < k ; col++ ) - addmul(new_pkt[row], pkt[col], m_dec[row*k + col], sz) ; - } - } - /* - * move pkts to their final destination - */ - for (row = 0 ; row < k ; row++ ) { - if (index[row] >= k) { - memcpy(pkt[row], new_pkt[row], sz*sizeof(gf)); - free(new_pkt[row]); - } - } - free(new_pkt); - free(m_dec); - - return 0; -} - -/*********** end of FEC code -- beginning of test code ************/ - -#if (TEST || DEBUG) -void -test_gf() -{ - int i ; - /* - * test gf tables. Sufficiently tested... - */ - for (i=0; i<= GF_SIZE; i++) { - if (gf_exp[gf_log[i]] != i) - fprintf(stderr, "bad exp/log i %d log %d exp(log) %d\n", - i, gf_log[i], gf_exp[gf_log[i]]); - - if (i != 0 && gf_mul(i, inverse[i]) != 1) - fprintf(stderr, "bad mul/inv i %d inv %d i*inv(i) %d\n", - i, inverse[i], gf_mul(i, inverse[i]) ); - if (gf_mul(0,i) != 0) - fprintf(stderr, "bad mul table 0,%d\n",i); - if (gf_mul(i,0) != 0) - fprintf(stderr, "bad mul table %d,0\n",i); - } -} -#endif /* TEST */ |