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Diffstat (limited to 'fec.c')
| -rw-r--r-- | fec.c | 898 |
1 files changed, 898 insertions, 0 deletions
@@ -0,0 +1,898 @@ +/* + * 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> + +/* + * compatibility stuff + */ +#ifdef MSDOS /* but also for others, e.g. sun... */ +#define NEED_BCOPY +#define bcmp(a,b,n) memcmp(a,b,n) +#endif + +#ifdef NEED_BCOPY +#define bcopy(s, d, siz) memcpy((d), (s), (siz)) +#define bzero(d, siz) memset((d), '\0', (siz)) +#endif + +/* + * 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); + + bzero(id_row, 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 (bcmp(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 + */ + bzero(retval->enc_matrix, 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) + bcopy(src[index], fec, sz*sizeof(gf) ) ; + else if (index < code->n) { + p = &(code->enc_matrix[index*k] ); + bzero(fec, 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 ); +} + +/* + * 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) { + bzero(p, k*sizeof(gf) ); + p[i] = 1 ; + } else +#endif + if (index[i] < code->n ) + bcopy( &(code->enc_matrix[index[i]*k]), p, 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" ); + bzero(new_pkt[row], 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) { + bcopy(new_pkt[row], 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 */ |