[sheepdog] [PATCH 1/9] add forward error correction for erasure code
Liu Yuan
namei.unix at gmail.com
Thu Sep 19 12:42:45 CEST 2013
This is imported and based on zfec
Signed-off-by: Liu Yuan <namei.unix at gmail.com>
---
include/Makefile.am | 2 +-
include/fec.h | 170 +++++++++++++++
lib/Makefile.am | 2 +-
lib/fec.c | 578 +++++++++++++++++++++++++++++++++++++++++++++++++++
4 files changed, 750 insertions(+), 2 deletions(-)
create mode 100644 include/fec.h
create mode 100644 lib/fec.c
diff --git a/include/Makefile.am b/include/Makefile.am
index 06e97a6..2c86984 100644
--- a/include/Makefile.am
+++ b/include/Makefile.am
@@ -3,4 +3,4 @@ MAINTAINERCLEANFILES = Makefile.in config.h.in
noinst_HEADERS = bitops.h event.h logger.h sheepdog_proto.h util.h \
list.h net.h sheep.h exits.h strbuf.h rbtree.h \
sha1.h option.h internal_proto.h shepherd.h work.h \
- sockfd_cache.h compiler.h
+ sockfd_cache.h compiler.h fec.h
diff --git a/include/fec.h b/include/fec.h
new file mode 100644
index 0000000..e10802d
--- /dev/null
+++ b/include/fec.h
@@ -0,0 +1,170 @@
+/*
+ * zfec -- fast forward error correction library
+ *
+ * Copyright (C) 2007-2008 Allmyds, Inc.
+ * Author: Zooko Wilcox-O'Hearn
+ *
+ * This file is part of zfec.
+ *
+ * See README.rst for licensing information.
+ */
+
+/*
+ * Much of 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.h -- forward error correction based on Vandermonde matrices
+ * 980614
+ * (C) 1997-98 Luigi Rizzo (luigi at iet.unipi.it)
+ *
+ * Portions derived from code by Phil Karn (karn at ka9q.ampr.org),
+ * Robert Morelos-Zaragoza (robert at spectra.eng.hawaii.edu) and Hari
+ * Thirumoorthy (harit at spectra.eng.hawaii.edu), Aug 1995
+ *
+ * Modifications by Dan Rubenstein (see Modifications.txt for
+ * their description.
+ * Modifications (C) 1998 Dan Rubenstein (drubenst at 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.
+ */
+
+#include <stddef.h>
+#include <stdint.h>
+
+#ifdef __GNUC__
+#ifndef alloca
+#define alloca(x) __builtin_alloca(x)
+#endif
+#else
+#include <alloca.h>
+#endif
+
+struct fec {
+ unsigned long magic;
+ unsigned short k, n; /* parameters of the code */
+ uint8_t *enc_matrix;
+};
+
+/*
+ * param k the number of blocks required to reconstruct
+ * param m the total number of blocks created
+ */
+struct fec *fec_new(unsigned short k, unsigned short m);
+void fec_free(struct fec *p);
+
+/*
+ * @param inpkts the "primary blocks" i.e. the chunks of the input data
+ * @param fecs buffers into which the secondary blocks will be written
+ * @param block_nums the numbers of the desired check blocks (the id >= k) which
+ * fec_encode() will produce and store into the buffers of the fecs parameter
+ * @param num_block_nums the length of the block_nums array
+ * @param sz size of a packet in bytes
+ */
+void fec_encode(const struct fec *code,
+ const uint8_t *const *const src,
+ uint8_t *const *const fecs,
+ const int *const block_nums,
+ size_t num_block_nums, size_t sz);
+
+/*
+ * @param inpkts an array of packets (size k); If a primary block, i, is present
+ * then it must be at index i. Secondary blocks can appear anywhere.
+ * @param outpkts an array of buffers into which the reconstructed output
+ * packets will be written (only packets which are not present in the inpkts
+ * input will be reconstructed and written to outpkts)
+ * @param index an array of the blocknums of the packets in inpkts
+ * @param sz size of a packet in bytes
+ */
+void fec_decode(const struct fec *code,
+ const uint8_t *const *const inpkts,
+ uint8_t *const *const outpkts,
+ const int *const index, size_t sz);
+
+#define SD_EC_D 4 /* No. of data strips */
+#define SD_EC_P 2 /* No. of parity strips */
+#define SD_EC_DP (SD_EC_D + SD_EC_P)
+#define SD_EC_STRIP_SIZE (1*1024) /* 1k best empirical value */
+#define SD_EC_D_SIZE (SD_EC_STRIP_SIZE * SD_EC_D)
+#define SD_EC_OBJECT_SIZE (SD_DATA_OBJ_SIZE / SD_EC_D)
+#define SD_EC_STRIPE (SD_EC_STRIP_SIZE * SD_EC_DP)
+#define STRIP_PER_OBJECT (SD_DATA_OBJ_SIZE / SD_EC_STRIP_SIZE)
+
+/*
+ * Stripe: data strips + parity strips, spread on all replica
+ * DS: data strip
+ * PS: parity strip
+ * R: Replica
+ *
+ * +--------------------stripe ----------------------+
+ * v v
+ * +----+----------------------------------------------+
+ * | ds | ds | ds | ds | ds | ... | ps | ps | ... | ps |
+ * +----+----------------------------------------------+
+ * | .. | .. | .. | .. | .. | ... | .. | .. | ... | .. |
+ * +----+----+----+----+----+ ... +----+----+-----+----+
+ * R1 R2 R3 R4 R5 ... Rn Rn+1 Rn+2 Rn+3
+ */
+
+/* Return the erasure code context to encode|decode */
+static inline void *ec_init(void)
+{
+ return fec_new(SD_EC_D, SD_EC_DP);
+}
+
+/*
+ * This function decodes the data strips and return the parity strips
+ *
+ * @ds: data strips to generate parity strips
+ * @ps: parity strips to return
+ */
+static inline void ec_encode(void *ctx, const uint8_t *ds[SD_EC_D],
+ uint8_t *ps[SD_EC_P])
+{
+ int total = SD_EC_D + SD_EC_P;
+ const int pidx[SD_EC_P] = { total - 2, total - 1 };
+
+ fec_encode(ctx, ds, ps, pidx, SD_EC_P, SD_EC_STRIP_SIZE);
+}
+
+/*
+ * This function takes input strips and return the lost strips
+ *
+ * @input: strips (either ds or ps) that are used to generate lost strips
+ * @output: the lost ds or ps to return
+ * @idx: indexes of each input strip in the whole stripe
+ */
+static inline void ec_decode(void *ctx, const uint8_t *input[SD_EC_D],
+ uint8_t *output[],
+ const int idx[])
+{
+ fec_decode(ctx, input, output, idx, SD_EC_STRIP_SIZE);
+}
+
+/* Destroy the erasure code context */
+static inline void ec_destroy(void *ctx)
+{
+ fec_free(ctx);
+}
diff --git a/lib/Makefile.am b/lib/Makefile.am
index 496c588..4cc1a17 100644
--- a/lib/Makefile.am
+++ b/lib/Makefile.am
@@ -5,7 +5,7 @@ INCLUDES = -I$(top_builddir)/include -I$(top_srcdir)/include
noinst_LIBRARIES = libsheepdog.a
libsheepdog_a_SOURCES = event.c logger.c net.c util.c rbtree.c strbuf.c \
- sha1.c option.c work.c sockfd_cache.c
+ sha1.c option.c work.c sockfd_cache.c fec.c
if BUILD_SHA1_HW
libsheepdog_a_SOURCES += sha1_ssse3.S
diff --git a/lib/fec.c b/lib/fec.c
new file mode 100644
index 0000000..331c7b7
--- /dev/null
+++ b/lib/fec.c
@@ -0,0 +1,578 @@
+/*
+ * zfec -- fast forward error correction
+ *
+ * Copyright (C) 2007-2010 Zooko Wilcox-O'Hearn
+ * Author: Zooko Wilcox-O'Hearn
+ *
+ * This file is part of zfec.
+ *
+ * Imported by Liu Yuan <namei.unix at gmail.com>
+ *
+ */
+
+/*
+ * 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 at iet.unipi.it)
+ *
+ * Portions derived from code by Phil Karn (karn at ka9q.ampr.org),
+ * Robert Morelos-Zaragoza (robert at spectra.eng.hawaii.edu) and Hari
+ * Thirumoorthy (harit at spectra.eng.hawaii.edu), Aug 1995
+ *
+ * Modifications by Dan Rubenstein (see Modifications.txt for
+ * their description.
+ * Modifications (C) 1998 Dan Rubenstein (drubenst at 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.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "fec.h"
+#include "util.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 uint8_t gf_exp[510]; /* idx->poly form conversion table */
+static int gf_log[256]; /* Poly->idx form conversion table */
+static uint8_t 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 uint8_t 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 uint8_t gf_mul_table[256][256];
+
+#define gf_mul(x, y) gf_mul_table[x][y]
+
+#define USE_GF_MULC register uint8_t *__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:
+ * idx->polynomial form gf_exp[] contains j= \alpha^i;
+ * polynomial form -> idx 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) \
+ (uint8_t *)malloc(rows * cols)
+
+/* initialize the data structures used for computations in GF. */
+static void generate_gf(void)
+{
+ int i;
+ uint8_t 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 uint8_t *dst,
+ const register uint8_t *src,
+ uint8_t c, size_t sz)
+{
+ USE_GF_MULC;
+ const uint8_t *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(uint8_t *a, uint8_t *b, uint8_t *c, unsigned n, unsigned k,
+ unsigned m)
+{
+ unsigned row, col, i;
+
+ for (row = 0; row < n; row++) {
+ for (col = 0; col < m; col++) {
+ uint8_t *pa = &a[row * k];
+ uint8_t *pb = &b[col];
+ uint8_t 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(uint8_t *src, unsigned k)
+{
+ uint8_t 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));
+ uint8_t *id_row = NEW_GF_MATRIX(1, k);
+
+ memset(id_row, '\0', k * sizeof(uint8_t));
+ /* ipiv marks elements already used as pivots. */
+ for (i = 0; i < k; i++)
+ ipiv[i] = 0;
+
+ for (col = 0; col < k; col++) {
+ uint8_t *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],
+ uint8_t);
+ 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(uint8_t)) != 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]], uint8_t);
+}
+
+/*
+ * 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)
+ */
+static void _invert_vdm(uint8_t *src, unsigned k)
+{
+ unsigned i, j, row, col;
+ uint8_t *b, *c, *p;
+ uint8_t 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++) {
+ uint8_t 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;
+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(struct fec *p)
+{
+ assert(p != NULL && p->magic == (((FEC_MAGIC ^ p->k) ^ p->n) ^
+ (unsigned long) (p->enc_matrix)));
+ free(p->enc_matrix);
+ free(p);
+}
+
+struct fec *fec_new(unsigned short k, unsigned short n)
+{
+ unsigned row, col;
+ uint8_t *p, *tmp_m;
+
+ struct fec *retval;
+
+ if (fec_initialized == 0)
+ init_fec();
+
+ retval = (struct fec *)malloc(sizeof(struct fec));
+ 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(uint8_t));
+ 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 struct fec *code,
+ const uint8_t *const *const src,
+ uint8_t *const *const fecs,
+ const int *const block_nums,
+ size_t num_block_nums, size_t sz)
+{
+ unsigned char i, j;
+ size_t k;
+ unsigned fecnum;
+ const uint8_t *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
+ */
+static void
+build_decode_matrix_into_space(const struct fec *const code,
+ const int *const idx,
+ const unsigned k, uint8_t *const matrix)
+{
+ unsigned char i;
+ uint8_t *p;
+ for (i = 0, p = matrix; i < k; i++, p += k) {
+ if (idx[i] < k) {
+ memset(p, 0, k);
+ p[i] = 1;
+ } else {
+ memcpy(p, &(code->enc_matrix[idx[i] * code->k]), k);
+ }
+ }
+ _invert_mat(matrix, k);
+}
+
+void fec_decode(const struct fec *code,
+ const uint8_t *const *const inpkts,
+ uint8_t *const *const outpkts,
+ const int *const idx, size_t sz)
+{
+ uint8_t *m_dec = (uint8_t *)alloca(code->k * code->k);
+ unsigned char outix = 0;
+ unsigned char row = 0;
+ unsigned char col = 0;
+ build_decode_matrix_into_space(code, idx, code->k, m_dec);
+
+ for (row = 0; row < code->k; row++) {
+ /*
+ * If the block whose number is i is present, then it is
+ * required to be in the i'th element.
+ */
+ assert((idx[row] >= code->k) || (idx[row] == row));
+ if (idx[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++;
+ }
+ }
+}
--
1.7.9.5
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