--- /dev/null
+/**
+ * zfec -- fast forward error correction library with Python interface
+ */
+
+#include "fec.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+
+/*
+ * Primitive polynomials - see Lin & Costello, Appendix A,
+ * and Lee & Messerschmitt, p. 453.
+ */
+static const char*const Pp="101110001";
+
+
+/*
+ * To speed up computations, we have tables for logarithm, exponent and
+ * inverse of a number. 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[510]; /* index->poly form conversion table */
+static int gf_log[256]; /* Poly->index form conversion table */
+static gf inverse[256]; /* 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 gf
+modnn(int x) {
+ while (x >= 255) {
+ x -= 255;
+ x = (x >> 8) + (x & 255);
+ }
+ return x;
+}
+
+#define SWAP(a,b,t) {t tmp; tmp=a; a=b; b=tmp;}
+
+/*
+ * gf_mul(x,y) multiplies two numbers. 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().
+ */
+static gf gf_mul_table[256][256];
+
+#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]
+
+/*
+ * 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
+ */
+static void
+_init_mul_table(void) {
+ int i, j;
+ for (i = 0; i < 256; i++)
+ for (j = 0; j < 256; j++)
+ gf_mul_table[i][j] = gf_exp[modnn (gf_log[i] + gf_log[j])];
+
+ for (j = 0; j < 256; j++)
+ gf_mul_table[0][j] = gf_mul_table[j][0] = 0;
+}
+
+#define NEW_GF_MATRIX(rows, cols) \
+ (gf*)malloc(rows * cols)
+
+/*
+ * initialize the data structures used for computations in GF.
+ */
+static void
+generate_gf (void) {
+ int i;
+ gf mask;
+
+ mask = 1; /* x ** 0 = 1 */
+ gf_exp[8] = 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 8 powers are simply bits shifted to the left.
+ */
+ for (i = 0; i < 8; 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[8] = \alpha ** 8
+ */
+ if (Pp[i] == '1')
+ gf_exp[8] ^= mask;
+ }
+ /*
+ * now gf_exp[8] = \alpha ** 8 is complete, so can also
+ * compute its inverse.
+ */
+ gf_log[gf_exp[8]] = 8;
+ /*
+ * Poly-repr of \alpha ** (i+1) is given by poly-repr of
+ * \alpha ** i shifted left one-bit and accounting for any
+ * \alpha ** 8 term that may occur when poly-repr of
+ * \alpha ** i is shifted.
+ */
+ mask = 1 << 7;
+ for (i = 9; i < 255; i++) {
+ if (gf_exp[i - 1] >= mask)
+ gf_exp[i] = gf_exp[8] ^ ((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] = 255;
+ /* set the extended gf_exp values for fast multiply */
+ for (i = 0; i < 255; i++)
+ gf_exp[i + 255] = gf_exp[i];
+
+ /*
+ * again special cases. 0 has no inverse. This used to
+ * be initialized to 255, but it should make no difference
+ * since noone is supposed to read from here.
+ */
+ inverse[0] = 0;
+ inverse[1] = 1;
+ for (i = 2; i <= 255; i++)
+ inverse[i] = gf_exp[255 - 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.
+ */
+#define addmul(dst, src, c, sz) \
+ if (c != 0) _addmul1(dst, src, c, sz)
+
+#define UNROLL 16 /* 1, 4, 8, 16 */
+static void
+_addmul1(register gf*restrict dst, const register gf*restrict src, gf c, size_t sz) {
+ USE_GF_MULC;
+ const 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, unsigned n, unsigned k, unsigned m) {
+ unsigned 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;
+ }
+ }
+}
+
+/*
+ * _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.
+ */
+static void
+_invert_mat(gf* src, unsigned k) {
+ gf c, *p;
+ unsigned irow = 0;
+ unsigned icol = 0;
+ unsigned row, col, i, ix;
+
+ unsigned* indxc = (unsigned*) malloc (k * sizeof(unsigned));
+ unsigned* indxr = (unsigned*) malloc (k * sizeof(unsigned));
+ unsigned* ipiv = (unsigned*) malloc (k * sizeof(unsigned));
+ gf *id_row = NEW_GF_MATRIX (1, k);
+
+ memset (id_row, '\0', k * sizeof (gf));
+ /*
+ * 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.
+ */
+ 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++) {
+ if (ipiv[ix] == 0) {
+ if (src[row * k + ix] != 0) {
+ irow = row;
+ icol = ix;
+ goto found_piv;
+ }
+ } else
+ assert (ipiv[ix] <= 1);
+ }
+ }
+ }
+ 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];
+ assert (c != 0);
+ 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)
+ */
+ 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; col > 0; col--)
+ if (indxr[col-1] != indxc[col-1])
+ for (row = 0; row < k; row++)
+ SWAP (src[row * k + indxr[col-1]], src[row * k + indxc[col-1]], gf);
+}
+
+/*
+ * fast code for inverting a vandermonde matrix.
+ *
+ * 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)
+ */
+void
+_invert_vdm (gf* src, unsigned k) {
+ unsigned i, j, row, col;
+ gf *b, *c, *p;
+ gf t, xx;
+
+ if (k == 1) /* degenerate case, matrix must be p^0 = 1 */
+ return;
+ /*
+ * 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 - 1; i > 0; i--) {
+ b[i-1] = c[i] ^ gf_mul (xx, b[i]);
+ t = gf_mul (xx, t) ^ b[i-1];
+ }
+ for (col = 0; col < k; col++)
+ src[col * k + row] = gf_mul (inverse[t], b[col]);
+ }
+ free (c);
+ free (b);
+ free (p);
+ return;
+}
+
+static int fec_initialized = 0;
+static void
+init_fec (void) {
+ generate_gf();
+ _init_mul_table();
+ 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 (fec_t *p) {
+ assert (p != NULL && p->magic == (((FEC_MAGIC ^ p->k) ^ p->n) ^ (unsigned long) (p->enc_matrix)));
+ free (p->enc_matrix);
+ free (p);
+}
+
+fec_t *
+fec_new(unsigned short k, unsigned short n) {
+ unsigned row, col;
+ gf *p, *tmp_m;
+
+ fec_t *retval;
+
+ if (fec_initialized == 0)
+ init_fec ();
+
+ retval = (fec_t *) malloc (sizeof (fec_t));
+ 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.
+ */
+ _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);
+
+ return retval;
+}
+
+/* To make sure that we stay within cache in the inner loops of fec_encode(). (It would
+ probably help to also do this for fec_decode(). */
+#ifndef STRIDE
+#define STRIDE 8192
+#endif
+
+void
+fec_encode(const fec_t* code, const gf*restrict const*restrict const src, gf*restrict const*restrict const fecs, const unsigned*restrict const block_nums, size_t num_block_nums, size_t sz) {
+ unsigned char i, j;
+ size_t k;
+ unsigned fecnum;
+ const gf* p;
+
+ for (k = 0; k < sz; k += STRIDE) {
+ size_t stride = ((sz-k) < STRIDE)?(sz-k):STRIDE;
+ for (i=0; i<num_block_nums; i++) {
+ fecnum=block_nums[i];
+ assert (fecnum >= code->k);
+ memset(fecs[i]+k, 0, stride);
+ p = &(code->enc_matrix[fecnum * code->k]);
+ for (j = 0; j < code->k; j++)
+ addmul(fecs[i]+k, src[j]+k, p[j], stride);
+ }
+ }
+}
+
+/**
+ * Build decode matrix into some memory space.
+ *
+ * @param matrix a space allocated for a k by k matrix
+ */
+void
+build_decode_matrix_into_space(const fec_t*restrict const code, const unsigned*const restrict index, const unsigned k, gf*restrict const matrix) {
+ unsigned char i;
+ gf* p;
+ for (i=0, p=matrix; i < k; i++, p += k) {
+ if (index[i] < k) {
+ memset(p, 0, k);
+ p[i] = 1;
+ } else {
+ memcpy(p, &(code->enc_matrix[index[i] * code->k]), k);
+ }
+ }
+ _invert_mat (matrix, k);
+}
+
+void
+fec_decode(const fec_t* code, const gf*restrict const*restrict const inpkts, gf*restrict const*restrict const outpkts, const unsigned*restrict const index, size_t sz) {
+ gf* m_dec = (gf*)alloca(code->k * code->k);
+ unsigned char outix=0;
+ unsigned char row=0;
+ unsigned char col=0;
+ build_decode_matrix_into_space(code, index, code->k, m_dec);
+
+ for (row=0; row<code->k; row++) {
+ assert ((index[row] >= code->k) || (index[row] == row)); /* If the block whose number is i is present, then it is required to be in the i'th element. */
+ if (index[row] >= code->k) {
+ memset(outpkts[outix], 0, sz);
+ for (col=0; col < code->k; col++)
+ addmul(outpkts[outix], inpkts[col], m_dec[row * code->k + col], sz);
+ outix++;
+ }
+ }
+}
+
+/**
+ * zfec -- fast forward error correction library with Python interface
+ *
+ * Copyright (C) 2007-2010 Zooko Wilcox-O'Hearn
+ * Author: Zooko Wilcox-O'Hearn
+ *
+ * This file is part of zfec.
+ *
+ * See README.rst for licensing information.
+ */
+
+/*
+ * This work is derived from the "fec" software by Luigi Rizzo, et al., the
+ * copyright notice and licence terms of which are included below for reference.
+ * 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
+ *
+ * Modifications by Dan Rubenstein (see Modifications.txt for
+ * their description.
+ * Modifications (C) 1998 Dan Rubenstein (drubenst@cs.umass.edu)
+ *
+ * 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.
+ */
projects / tahoe-lafs / zfec.git / blobdiff