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-/*
- * 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 */