[HICN-713] Transport Library Major Refactoring 2

Co-authored-by: Luca Muscariello <muscariello@ieee.org>
Co-authored-by: Michele Papalini <micpapal@cisco.com>
Co-authored-by: Olivier Roques <oroques+fdio@cisco.com>
Co-authored-by: Giulio Grassi <gigrassi@cisco.com>
Signed-off-by: Mauro Sardara <msardara@cisco.com>
Change-Id: I5b2c667bad66feb45abdb5effe22ed0f6c85d1c2

1 files changed, 838 insertions, 0 deletions

diff --git a/libtransport/src/protocols/fec/fec.cc b/libtransport/src/protocols/fec/fec.cc
new file mode 100644
index 000000000..16a04cb98
--- /dev/null
+++ b/libtransport/src/protocols/fec/fec.cc
@@ -0,0 +1,838 @@
+/*
+ * 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 "fec.h"
+
+#include <hicn/transport/portability/platform.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+/**
+ * XXX This disable a warning raising only in some platforms.
+ * TODO Check if this warning is a mistake or it is a real bug:
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=83404
+ * https://gcc.gnu.org/bugzilla//show_bug.cgi?id=88059
+ */
+#ifndef __clang__
+#pragma GCC diagnostic ignored "-Wstringop-overflow"
+#endif
+
+/*
+ * 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 ANDROID
+#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
+
+#define GF_SIZE ((1 << GF_BITS) - 1) /* powers of \alpha */
+
+/*
+ * Primitive polynomials - see Lin & Costello, Appendix A,
+ * and  Lee & Messerschmitt, p. 453.
+ */
+static const 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 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, const 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;
+  const 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;
+  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 DEBUGG
+/*
+ * 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 = (int *)my_malloc(k * sizeof(int), "indxc");
+  int *indxr = (int *)my_malloc(k * sizeof(int), "indxr");
+  int *ipiv = (int *)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
+
+void fec_free(struct fec_parms *p) {
+  if (p == NULL || p->magic != (((FEC_MAGIC ^ p->k) ^ p->n) ^
+                                (unsigned long)(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 = (struct fec_parms *)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) ^ (unsigned long)(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 = (gf **)my_malloc(k * sizeof(gf *), "new pkt pointers");
+  for (row = 0; row < k; row++) {
+    if (index[row] >= k) {
+      new_pkt[row] = (gf *)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;
+}