remove unused variable in tests

Signed-off-by: Loic Dachary <loic-201408@dachary.org>

diff --git a/.gitattributes b/.gitattributes
new file mode 100644 (file)
index 0000000..f0b7445
--- /dev/null
+++ b/.gitattributes
@@ -0,0 +1,3 @@
+*.ac eol=lf
+*.am eol=lf
+*.sh eol=lf

diff --git a/.gitignore b/.gitignore
new file mode 100644 (file)
index 0000000..6c46716
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,28 @@
+/INSTALL
+Makefile
+Makefile.in
+/aclocal.m4
+/autom4te.cache/
+/autoscan.log
+/build-aux/
+/config.log
+/config.status
+/configure
+/configure.scan
+.deps/
+/include/config.h
+/include/config.h.in
+/include/stamp-h1
+.libs/
+/libtool
+/m4/libtool.m4
+/m4/ltoptions.m4
+/m4/ltsugar.m4
+/m4/ltversion.m4
+/m4/lt~obsolete.m4
+*.l[ao]
+*.[ao]
+*~
+.dirstamp
+*.log
+*.trs

diff --git a/AUTHORS b/AUTHORS
new file mode 100644 (file)
index 0000000..e69de29

diff --git a/COPYING b/COPYING
new file mode 100644 (file)
index 0000000..20ffbd2
--- /dev/null
+++ b/COPYING
@@ -0,0 +1,37 @@
+
+Copyright (c) 2013, James S. Plank and Kevin Greenan
+All rights reserved.
+
+Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure Coding Techniques
+
+Revision 2.0: Galois Field backend now links to GF-Complete
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+ - Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+
+ - 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.
+
+ - Neither the name of the University of Tennessee nor the names of its
+   contributors may be used to endorse or promote products derived
+   from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"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 COPYRIGHT
+HOLDER OR CONTRIBUTORS 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.
+

diff --git a/ChangeLog b/ChangeLog
new file mode 100644 (file)
index 0000000..e69de29

diff --git a/Examples/.gitignore b/Examples/.gitignore
new file mode 100644 (file)
index 0000000..b97ec5a
--- /dev/null
+++ b/Examples/.gitignore
@@ -0,0 +1,9 @@
+/cauchy_[0-9][0-9]
+/decoder
+/encoder
+/jerasure_[0-9][0-9]
+/liberation_[0-9][0-9]
+/reed_sol_[0-9][0-9]
+/reed_sol_test_gf
+/reed_sol_time_gf
+/test_galois

diff --git a/Examples/Makefile.am b/Examples/Makefile.am
new file mode 100644 (file)
index 0000000..9e20f1c
--- /dev/null
+++ b/Examples/Makefile.am
@@ -0,0 +1,67 @@
+# Jerasure AM file
+
+AM_CPPFLAGS = -I$(top_srcdir)/include
+AM_CFLAGS = $(SIMD_FLAGS)
+
+bin_PROGRAMS = jerasure_01 \
+               jerasure_02 \
+               jerasure_03 \
+               jerasure_04 \
+               jerasure_05 \
+               jerasure_06 \
+               jerasure_07 \
+               jerasure_08 \
+               reed_sol_01 \
+               reed_sol_02 \
+               reed_sol_03 \
+               reed_sol_04 \
+               reed_sol_test_gf \
+               reed_sol_time_gf \
+               cauchy_01 \
+               cauchy_02 \
+               cauchy_03 \
+               cauchy_04 \
+               liberation_01 \
+               encoder \
+               decoder
+
+check_PROGRAMS = 
+
+TESTS=test_all_gfs.sh $(check_PROGRAMS)
+
+dist_noinst_SCRIPTS = test_all_gfs.sh time_all_gfs_argv_init.sh
+
+test_galois_SOURCES = test_galois.c
+check_PROGRAMS += test_galois
+
+jerasure_01_SOURCES = jerasure_01.c
+jerasure_02_SOURCES = jerasure_02.c
+jerasure_03_SOURCES = jerasure_03.c
+jerasure_04_SOURCES = jerasure_04.c
+jerasure_05_SOURCES = jerasure_05.c
+jerasure_06_SOURCES = jerasure_06.c
+jerasure_07_SOURCES = jerasure_07.c
+jerasure_08_SOURCES = jerasure_08.c
+
+reed_sol_01_SOURCES = reed_sol_01.c
+reed_sol_02_SOURCES = reed_sol_02.c
+reed_sol_03_SOURCES = reed_sol_03.c
+reed_sol_04_SOURCES = reed_sol_04.c
+
+reed_sol_test_gf_SOURCES = reed_sol_test_gf.c
+reed_sol_time_gf_SOURCES = reed_sol_time_gf.c
+
+cauchy_01_SOURCES = cauchy_01.c
+cauchy_02_SOURCES = cauchy_02.c
+cauchy_03_SOURCES = cauchy_03.c
+cauchy_04_SOURCES = cauchy_04.c
+
+liberation_01_SOURCES = liberation_01.c
+
+decoder_SOURCES = decoder.c
+encoder_SOURCES = encoder.c
+
+LDADD = ../src/libJerasure.la
+decoder_LDADD = $(LDADD) ../src/libtiming.a
+encoder_LDADD = $(LDADD) ../src/libtiming.a
+reed_sol_time_gf_LDADD = $(LDADD) ../src/libtiming.a

diff --git a/Examples/cauchy_01.c b/Examples/cauchy_01.c
new file mode 100644 (file)
index 0000000..65419a0
--- /dev/null
+++ b/Examples/cauchy_01.c
@@ -0,0 +1,112 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+ 
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include "cauchy.h"
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: cauchy_01 n w - Converts the value n to a bitmatrix using GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       It prints the bitmatrix, and reports on the numberof ones.\n");
+  fprintf(stderr, "       Use 0x to input n in hexadecimal.\n");
+  fprintf(stderr, "       W must be <= 32.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: cauchy_n_ones()\n");
+  fprintf(stderr, "                   jerasure_matrix_to_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  if (s != NULL) fprintf(stderr, "\n%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  int n;
+  int i, no, w;
+  int *bitmatrix;
+  
+  if (argc != 3) usage(NULL);
+  if (sscanf(argv[1], "0x%x", &n) == 0) {
+    if (sscanf(argv[1], "%d", &n) == 0) usage("Bad n");
+  }
+  if (sscanf(argv[2], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (w == 31) {
+    if (n & 0x80000000L) usage("Bad n/w combination (n not between 0 and 2^w-1)\n");
+  } else if (w < 31) {
+    if (n >= (1 << w)) usage("Bad n/w combination (n not between 0 and 2^w-1)\n");
+  }
+
+  bitmatrix = jerasure_matrix_to_bitmatrix(1, 1, w, &n);
+  printf("<HTML><title>cauchy_01 %u %d</title>\n", w, n);
+  printf("<HTML><h3>cauchy_01 %u %d</h3>\n", w, n);
+  printf("<pre>\n");
+  if (w == 32) {
+    printf("Converted the value 0x%x to the following bitmatrix:\n\n", n);
+  } else {
+    printf("Converted the value %d (0x%x) to the following bitmatrix:\n\n", n, n);
+  }
+  jerasure_print_bitmatrix(bitmatrix, w, w, w);
+  printf("\n");
+
+  no = 0;
+  for (i = 0; i < w*w; i++) no += bitmatrix[i];
+  if (no != cauchy_n_ones(n, w)) { 
+    fprintf(stderr, "Jerasure error: # ones in the bitmatrix (%d) doesn't match cauchy_n_ones() (%d).\n",
+       no, cauchy_n_ones(n, w));
+    exit(1);
+  }
+
+  printf("# Ones: %d\n", cauchy_n_ones(n, w));
+
+  return 0;
+}

diff --git a/Examples/cauchy_02.c b/Examples/cauchy_02.c
new file mode 100644 (file)
index 0000000..45c78ab
--- /dev/null
+++ b/Examples/cauchy_02.c
@@ -0,0 +1,272 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+ 
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "cauchy.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: cauchy_02 k m w seed - CRS coding example using Bloemer's original matrix.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "k+m must be <= 2^w\n");
+  fprintf(stderr, "This sets up a generator matrix (G^T) in GF(2^w) whose last m rows are\n");
+  fprintf(stderr, "created from a Cauchy matrix, using the original definition from [Bloemer95].\n");
+  fprintf(stderr, "It converts this matrix to a bitmatrix, and then it encodes w packets from\n");
+  fprintf(stderr, "each of k disks (simulated) onto w packets on each of m disks.  Packets are \n");
+  fprintf(stderr, "simply longs.  Then, it deletes m random disks, and decodes.  \n");
+  fprintf(stderr, "\n");
+  fprintf(stderr, "The encoding and decoding are done twice, first, with jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "and jerasure_bitmatrix_decode(), and second using 'smart' scheduling with\n");
+  fprintf(stderr, "jerasure_schedule_encode() and jerasure_schedule_decode_lazy().\n");
+
+  fprintf(stderr, "\n");
+  fprintf(stderr, "This demonstrates: cauchy_original_coding_matrix()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_decode()\n");
+  fprintf(stderr, "                   cauchy_n_ones()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_lazy()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+  
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m;
+  int *matrix, *bitmatrix, **schedule;
+  char **data, **coding, **dcopy, **ccopy;
+  int no;
+  int *erasures, *erased;
+  double mstats[3], sstats[3];
+  uint32_t seed;
+  
+  if (argc != 5) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+
+  matrix = cauchy_original_coding_matrix(k, m, w);
+  if (matrix == NULL) {
+    usage("couldn't make coding matrix");
+  }
+
+  /* Print out header information to the output file. */
+  printf("<HTML>\n");
+  printf("<TITLE>Jerasure Example Output: cauchy_02 %d %d %d %d</TITLE>\n", k, m, w, seed);
+  printf("<h2>Jerasure Example Output: cauchy_02 %d %d %d %d</h3>\n", k, m, w, seed);
+
+  printf("<hr>\n");
+  printf("Parameters:\n");
+  printf("<UL><LI> Number of data disks <i>(k)</i>: %d\n", k);
+  printf("<LI> Number of coding disks <i>(m)</i>: %d\n", m);
+  printf("<LI> Word size of the Galois Field: <i>(w)</i>: %d\n", w);
+  printf("<LI> Seed for the random number generator: %d\n", seed);
+  printf("<LI> Number of bytes stored per disk: %ld\n", sizeof(long)*w);
+  printf("<LI> Number of packets stored per disk: %d\n", w);
+  printf("<LI> Number of bytes per packet: %ld\n", sizeof(long));
+  printf("</UL>\n");
+
+  /* Print out the matrix and the bitmatrix */
+  printf("<hr>\n");
+  printf("Here is the matrix, which was created with <b>cauchy_original_coding_matrix()</b>.\n");
+  printf("This is not the best matrix to use, but we include it to show an example\n");
+  printf("of <b>cauchy_original_coding_matrix()</b>.  For the best matrix and encoding/decoding\n");
+  printf("methodology, see <b>cauchy_04.</b><p><pre>\n");
+
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("</pre>\n");
+
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  no = 0;
+  for (i = 0; i < k*m; i++) {
+    no += cauchy_n_ones(matrix[i], w);
+  }
+
+  printf("The bitmatrix, which has %d one%s:<p><pre>\n", no, (no == 1) ? "" : "s");
+  jerasure_print_bitmatrix(bitmatrix, m*w, k*w, w);
+  printf("</pre>\n");
+  printf("<hr>\n");
+  MOA_Seed(seed);
+
+  data = talloc(char *, k);
+  dcopy = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    dcopy[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+    memcpy(dcopy[i], data[i], sizeof(long)*w);
+  }
+
+  printf("Here are the packets on the data disks:<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+
+  coding = talloc(char *, m);
+  ccopy = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+    ccopy[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_bitmatrix_encode(k, m, w, bitmatrix, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+  jerasure_schedule_encode(k, m, w, schedule, data, ccopy, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(sstats);
+
+  printf("<p>Encoding with jerasure_bitmatrix_encode() - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+  printf("Encoding with jerasure_schedule_encode() - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < m; i++) {
+    if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+      printf("Problem: the two encodings don't match on disk C%x\n", i);
+      exit(0);
+    }
+  }
+
+  printf("Here are the packets on the coding disks.<br>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(31, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+  printf("Erasures on the following devices:");
+  for (i = 0; erasures[i] != -1; i++) {
+    printf(" %c%x", ((erasures[i] < k) ? 'D' : 'C'), (erasures[i] < k ? erasures[i] : erasures[i]-k));
+  }
+  printf("<br>\nHere is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_bitmatrix_decode(k, m, w, bitmatrix, 0, erasures, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  printf("<p>Decoded with jerasure_bitmatrix_decode - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  for (i = 0; erasures[i] != -1; i++) {
+    bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+  }
+
+  jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, w*sizeof(long), sizeof(long), 1);
+  jerasure_get_stats(sstats);
+
+  printf("jerasure_schedule_decode_lazy - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  printf("Here is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  return 0;
+}

diff --git a/Examples/cauchy_03.c b/Examples/cauchy_03.c
new file mode 100644 (file)
index 0000000..e246e77
--- /dev/null
+++ b/Examples/cauchy_03.c
@@ -0,0 +1,290 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+ 
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "cauchy.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: cauchy_03 k m w seed - CRS coding example improving the matrix.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "k+m must be <= 2^w\n");
+  fprintf(stderr, "This sets up a generator matrix (G^T) in GF(2^w) whose last m rows are\n");
+  fprintf(stderr, "created from a Cauchy matrix, using the original definition from [Bloemer95].\n");
+  fprintf(stderr, "This is done with cauchy_xy_coding_matrix().\n");
+  fprintf(stderr, "\n");
+  fprintf(stderr, "It then it improves the matrix, which yields a different bitmatrix that is\n");
+  fprintf(stderr, "MDS like the original bitmatrix, but it will yield a bitmatrix with fewer ones.\n");
+  fprintf(stderr, "Then, it encodes w packets from each of k disks (simulated) onto w packets on\n");
+  fprintf(stderr, "on each of m disks.  Packets are longs.  Then, it deletes m random disks, and decodes.\n");
+  fprintf(stderr, "\n");
+  fprintf(stderr, "The encoding and decoding are done twice, first, with jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "and jerasure_bitmatrix_decode(), and second using 'smart' scheduling with\n");
+  fprintf(stderr, "jerasure_schedule_encode() and jerasure_schedule_decode_lazy().\n");
+
+  fprintf(stderr, "\n");
+  fprintf(stderr, "This demonstrates: cauchy_xy_coding_matrix()\n");
+  fprintf(stderr, "                   cauchy_improve_coding_matrix()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_decode()\n");
+  fprintf(stderr, "                   cauchy_n_ones()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_lazy()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+  
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m;
+  int *matrix, *bitmatrix, **schedule;
+  char **data, **coding, **dcopy, **ccopy;
+  int no;
+  int *erasures, *erased;
+  double mstats[3], sstats[3];
+  uint32_t seed;
+  int *X, *Y;
+  
+  if (argc != 5) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+
+  X = talloc(int, m);
+  Y = talloc(int, k);
+  for (i = 0; i < m; i++) X[i] = i;
+  for (i = 0; i < k; i++) Y[i] = m+i;
+
+  matrix = cauchy_xy_coding_matrix(k, m, w, X, Y);
+  if (matrix == NULL) {
+    usage("couldn't make coding matrix");
+  }
+
+  /* Print out header information to the output file. */
+  printf("<HTML>\n");
+  printf("<TITLE>Jerasure Example Output: cauchy_03 %d %d %d %d</TITLE>\n", k, m, w, seed);
+  printf("<h2>Jerasure Example Output: cauchy_03 %d %d %d %d</h3>\n", k, m, w, seed);
+
+  printf("<hr>\n");
+  printf("Parameters:\n");
+  printf("<UL><LI> Number of data disks <i>(k)</i>: %d\n", k);
+  printf("<LI> Number of coding disks <i>(m)</i>: %d\n", m);
+  printf("<LI> Word size of the Galois Field: <i>(w)</i>: %d\n", w);
+  printf("<LI> Seed for the random number generator: %d\n", seed);
+  printf("<LI> Number of bytes stored per disk: %ld\n", sizeof(long)*w);
+  printf("<LI> Number of packets stored per disk: %d\n", w);
+  printf("<LI> Number of bytes per packet: %ld\n", sizeof(long));
+  printf("</UL>\n");
+
+  /* Print out the matrix and the bitmatrix */
+  printf("<hr>\n");
+  printf("Here is the matrix, which was created with <b>cauchy_xy_coding_matrix()</b>.\n");
+
+  printf("<pre>\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("</pre>\n");
+
+  cauchy_improve_coding_matrix(k, m, w, matrix);
+
+  printf("<hr>\n");
+  printf("Here is the matrix improved with <b>cauchy_improve_coding_matrix()</b>.\n");
+
+  printf("<pre>\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("</pre>\n");
+
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  no = 0;
+  for (i = 0; i < k*m; i++) {
+    no += cauchy_n_ones(matrix[i], w);
+  }
+
+  printf("The bitmatrix, which has %d one%s:<p><pre>\n", no, (no == 1) ? "" : "s");
+  jerasure_print_bitmatrix(bitmatrix, m*w, k*w, w);
+  printf("</pre>\n");
+  printf("<hr>\n");
+
+  MOA_Seed(seed);
+
+  data = talloc(char *, k);
+  dcopy = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    dcopy[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+    memcpy(dcopy[i], data[i], sizeof(long)*w);
+  }
+
+  printf("Here are the packets on the data disks:<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+
+  coding = talloc(char *, m);
+  ccopy = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+    ccopy[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_bitmatrix_encode(k, m, w, bitmatrix, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+  jerasure_schedule_encode(k, m, w, schedule, data, ccopy, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(sstats);
+
+  printf("<p>Encoding with jerasure_bitmatrix_encode() - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+  printf("Encoding with jerasure_schedule_encode() - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < m; i++) {
+    if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+      printf("Problem: the two encodings don't match on disk C%x\n", i);
+      exit(0);
+    }
+  }
+
+  printf("Here are the packets on the coding disks.<br>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(31, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+  printf("Erasures on the following devices:");
+  for (i = 0; erasures[i] != -1; i++) {
+    printf(" %c%x", ((erasures[i] < k) ? 'D' : 'C'), (erasures[i] < k ? erasures[i] : erasures[i]-k));
+  }
+  printf("<br>\nHere is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_bitmatrix_decode(k, m, w, bitmatrix, 0, erasures, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  printf("<p>Decoded with jerasure_bitmatrix_decode - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  for (i = 0; erasures[i] != -1; i++) {
+    bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+  }
+
+  jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, w*sizeof(long), sizeof(long), 1);
+  jerasure_get_stats(sstats);
+
+  printf("jerasure_schedule_decode_lazy - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  printf("Here is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  return 0;
+}

diff --git a/Examples/cauchy_04.c b/Examples/cauchy_04.c
new file mode 100644 (file)
index 0000000..f61c614
--- /dev/null
+++ b/Examples/cauchy_04.c
@@ -0,0 +1,272 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+ 
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "cauchy.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: cauchy_04 k m w seed - CRS coding example improving the matrix.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "k+m must be <= 2^w\n");
+  fprintf(stderr, "This sets up a generator matrix (G^T) in GF(2^w) whose last m rows are\n");
+  fprintf(stderr, "a 'good' matrix, created with cauchy_good_general_coding_matrix().\n");
+  fprintf(stderr, "It converts this matrix to a bitmatrix.\n");
+  fprintf(stderr, "\n");
+  fprintf(stderr, "Then, it encodes w packets from each of k disks (simulated) onto w packets on\n");
+  fprintf(stderr, "on each of m disks.  Packets are longs.  Then, it deletes m random disks, and decodes.\n");
+  fprintf(stderr, "\n");
+  fprintf(stderr, "The encoding and decoding are done twice, first, with jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "and jerasure_bitmatrix_decode(), and second using 'smart' scheduling with\n");
+  fprintf(stderr, "jerasure_schedule_encode() and jerasure_schedule_decode_lazy().\n");
+
+  fprintf(stderr, "\n");
+  fprintf(stderr, "This demonstrates: cauchy_good_general_coding_matrix()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_decode()\n");
+  fprintf(stderr, "                   cauchy_n_ones()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_lazy()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+  
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m;
+  int *matrix, *bitmatrix, **schedule;
+  char **data, **coding, **dcopy, **ccopy;
+  int no;
+  int *erasures, *erased;
+  double mstats[3], sstats[3];
+  uint32_t seed;
+  
+  if (argc != 5) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+
+  matrix = cauchy_good_general_coding_matrix(k, m, w);
+  if (matrix == NULL) {
+    usage("couldn't make coding matrix");
+  }
+
+  /* Print out header information to the output file. */
+  printf("<HTML>\n");
+  printf("<TITLE>Jerasure Example Output: cauchy_04 %d %d %d %d</TITLE>\n", k, m, w, seed);
+  printf("<h2>Jerasure Example Output: cauchy_04 %d %d %d %d</h3>\n", k, m, w, seed);
+
+  printf("<hr>\n");
+  printf("Parameters:\n");
+  printf("<UL><LI> Number of data disks <i>(k)</i>: %d\n", k);
+  printf("<LI> Number of coding disks <i>(m)</i>: %d\n", m);
+  printf("<LI> Word size of the Galois Field: <i>(w)</i>: %d\n", w);
+  printf("<LI> Seed for the random number generator: %d\n", seed);
+  printf("<LI> Number of bytes stored per disk: %ld\n", sizeof(long)*w);
+  printf("<LI> Number of packets stored per disk: %d\n", w);
+  printf("<LI> Number of bytes per packet: %ld\n", sizeof(long));
+  printf("</UL>\n");
+
+  /* Print out the matrix and the bitmatrix */
+  printf("<hr>\n");
+  printf("Here is the matrix, which was created with <b>cauchy_good_general_coding_matrix()</b>.\n");
+
+  printf("<pre>\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("</pre>\n");
+
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  no = 0;
+  for (i = 0; i < k*m; i++) {
+    no += cauchy_n_ones(matrix[i], w);
+  }
+
+  printf("The bitmatrix, which has %d one%s:<p><pre>\n", no, (no == 1) ? "" : "s");
+  jerasure_print_bitmatrix(bitmatrix, m*w, k*w, w);
+  printf("</pre>\n");
+  printf("<hr>\n");
+
+  MOA_Seed(seed);
+
+  data = talloc(char *, k);
+  dcopy = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    dcopy[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+    memcpy(dcopy[i], data[i], sizeof(long)*w);
+  }
+
+  printf("Here are the packets on the data disks:<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+
+  coding = talloc(char *, m);
+  ccopy = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+    ccopy[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_bitmatrix_encode(k, m, w, bitmatrix, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+  jerasure_schedule_encode(k, m, w, schedule, data, ccopy, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(sstats);
+
+  printf("<p>Encoding with jerasure_bitmatrix_encode() - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+  printf("Encoding with jerasure_schedule_encode() - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < m; i++) {
+    if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+      printf("Problem: the two encodings don't match on disk C%x\n", i);
+      exit(0);
+    }
+  }
+
+  printf("Here are the packets on the coding disks.<br>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(31, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+  printf("Erasures on the following devices:");
+  for (i = 0; erasures[i] != -1; i++) {
+    printf(" %c%x", ((erasures[i] < k) ? 'D' : 'C'), (erasures[i] < k ? erasures[i] : erasures[i]-k));
+  }
+  printf("<br>\nHere is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_bitmatrix_decode(k, m, w, bitmatrix, 0, erasures, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(mstats);
+
+  printf("<p>Decoded with jerasure_bitmatrix_decode - Bytes XOR'd: %.0lf.<br>\n", mstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  for (i = 0; erasures[i] != -1; i++) {
+    bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+  }
+
+  jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, w*sizeof(long), sizeof(long), 1);
+  jerasure_get_stats(sstats);
+
+  printf("jerasure_schedule_decode_lazy - Bytes XOR'd: %.0lf.<br>\n", sstats[0]);
+
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)*w) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  printf("Here is the state of the system:\n<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  return 0;
+}

diff --git a/Examples/decoder.c b/Examples/decoder.c
new file mode 100644 (file)
index 0000000..0f6e030
--- /dev/null
+++ b/Examples/decoder.c
@@ -0,0 +1,397 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+/* 
+This program takes as input an inputfile, k, m, a coding
+technique, w, and packetsize.  It is the companion program
+of encoder.c, which creates k+m files.  This program assumes 
+that up to m erasures have occurred in the k+m files.  It
+reads in the k+m files or marks the file as erased. It then
+recreates the original file and creates a new file with the
+suffix "decoded" with the decoded contents of the file.
+
+This program does not error check command line arguments because 
+it is assumed that encoder.c has been called previously with the
+same arguments, and encoder.c does error check.
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+#include <unistd.h>
+#include <sys/time.h>
+#include <sys/stat.h>
+#include <signal.h>
+#include <unistd.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+#include "galois.h"
+#include "cauchy.h"
+#include "liberation.h"
+#include "timing.h"
+
+#define N 10
+
+enum Coding_Technique {Reed_Sol_Van, Reed_Sol_R6_Op, Cauchy_Orig, Cauchy_Good, Liberation, Blaum_Roth, Liber8tion, RDP, EVENODD, No_Coding};
+
+char *Methods[N] = {"reed_sol_van", "reed_sol_r6_op", "cauchy_orig", "cauchy_good", "liberation", "blaum_roth", "liber8tion", "rdp", "evenodd", "no_coding"};
+
+/* Global variables for signal handler */
+enum Coding_Technique method;
+int readins, n;
+
+/* Function prototype */
+void ctrl_bs_handler(int dummy);
+
+int main (int argc, char **argv) {
+       FILE *fp;                               // File pointer
+
+       /* Jerasure arguments */
+       char **data;
+       char **coding;
+       int *erasures;
+       int *erased;
+       int *matrix;
+       int *bitmatrix;
+       
+       /* Parameters */
+       int k, m, w, packetsize, buffersize;
+       int tech;
+       char *c_tech;
+       
+       int i, j;                               // loop control variable, s
+       int blocksize;                  // size of individual files
+       int origsize;                   // size of file before padding
+       int total;                              // used to write data, not padding to file
+       struct stat status;             // used to find size of individual files
+       int numerased;                  // number of erased files
+        int dummy;
+               
+       /* Used to recreate file names */
+       char *temp;
+       char *cs1, *cs2, *extension;
+       char *fname;
+       int md;
+       char *curdir;
+
+       /* Used to time decoding */
+       struct timing t1, t2, t3, t4;
+       double tsec;
+       double totalsec;
+
+       
+       signal(SIGQUIT, ctrl_bs_handler);
+
+       matrix = NULL;
+       bitmatrix = NULL;
+       totalsec = 0.0;
+       
+       /* Start timing */
+       timing_set(&t1);
+
+       /* Error checking parameters */
+       if (argc != 2) {
+               fprintf(stderr, "usage: inputfile\n");
+               exit(0);
+       }
+       curdir = (char *)malloc(sizeof(char)*100);
+       getcwd(curdir, 100);
+       
+       /* Begin recreation of file names */
+       cs1 = (char*)malloc(sizeof(char)*strlen(argv[1]));
+       cs2 = strrchr(argv[1], '/');
+       if (cs2 != NULL) {
+               cs2++;
+               strcpy(cs1, cs2);
+       }
+       else {
+               strcpy(cs1, argv[1]);
+       }
+       cs2 = strchr(cs1, '.');
+       if (cs2 != NULL) {
+                extension = strdup(cs2);
+               *cs2 = '\0';
+       } else {
+           extension = strdup("");
+        }      
+       fname = (char *)malloc(sizeof(char*)*(100+strlen(argv[1])+20));
+
+       /* Read in parameters from metadata file */
+       sprintf(fname, "%s/Coding/%s_meta.txt", curdir, cs1);
+
+       fp = fopen(fname, "rb");
+        if (fp == NULL) {
+          fprintf(stderr, "Error: no metadata file %s\n", fname);
+          exit(1);
+        }
+       temp = (char *)malloc(sizeof(char)*(strlen(argv[1])+20));
+       if (fscanf(fp, "%s", temp) != 1) {
+               fprintf(stderr, "Metadata file - bad format\n");
+               exit(0);
+       }
+       
+       if (fscanf(fp, "%d", &origsize) != 1) {
+               fprintf(stderr, "Original size is not valid\n");
+               exit(0);
+       }
+       if (fscanf(fp, "%d %d %d %d %d", &k, &m, &w, &packetsize, &buffersize) != 5) {
+               fprintf(stderr, "Parameters are not correct\n");
+               exit(0);
+       }
+       c_tech = (char *)malloc(sizeof(char)*(strlen(argv[1])+20));
+       if (fscanf(fp, "%s", c_tech) != 1) {
+               fprintf(stderr, "Metadata file - bad format\n");
+               exit(0);
+       }
+       if (fscanf(fp, "%d", &tech) != 1) {
+               fprintf(stderr, "Metadata file - bad format\n");
+               exit(0);
+       }
+       method = tech;
+       if (fscanf(fp, "%d", &readins) != 1) {
+               fprintf(stderr, "Metadata file - bad format\n");
+               exit(0);
+       }
+       fclose(fp);     
+
+       /* Allocate memory */
+       erased = (int *)malloc(sizeof(int)*(k+m));
+       for (i = 0; i < k+m; i++)
+               erased[i] = 0;
+       erasures = (int *)malloc(sizeof(int)*(k+m));
+
+       data = (char **)malloc(sizeof(char *)*k);
+       coding = (char **)malloc(sizeof(char *)*m);
+       if (buffersize != origsize) {
+               for (i = 0; i < k; i++) {
+                       data[i] = (char *)malloc(sizeof(char)*(buffersize/k));
+               }
+               for (i = 0; i < m; i++) {
+                       coding[i] = (char *)malloc(sizeof(char)*(buffersize/k));
+               }
+               blocksize = buffersize/k;
+       }
+
+       sprintf(temp, "%d", k);
+       md = strlen(temp);
+       timing_set(&t3);
+
+       /* Create coding matrix or bitmatrix */
+       switch(tech) {
+               case No_Coding:
+                       break;
+               case Reed_Sol_Van:
+                       matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+                       break;
+               case Reed_Sol_R6_Op:
+                       matrix = reed_sol_r6_coding_matrix(k, w);
+                       break;
+               case Cauchy_Orig:
+                       matrix = cauchy_original_coding_matrix(k, m, w);
+                       bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+                       break;
+               case Cauchy_Good:
+                       matrix = cauchy_good_general_coding_matrix(k, m, w);
+                       bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+                       break;
+               case Liberation:
+                       bitmatrix = liberation_coding_bitmatrix(k, w);
+                       break;
+               case Blaum_Roth:
+                       bitmatrix = blaum_roth_coding_bitmatrix(k, w);
+                       break;
+               case Liber8tion:
+                       bitmatrix = liber8tion_coding_bitmatrix(k);
+       }
+       timing_set(&t4);
+       totalsec += timing_delta(&t3, &t4);
+       
+       /* Begin decoding process */
+       total = 0;
+       n = 1;  
+       while (n <= readins) {
+               numerased = 0;
+               /* Open files, check for erasures, read in data/coding */       
+               for (i = 1; i <= k; i++) {
+                       sprintf(fname, "%s/Coding/%s_k%0*d%s", curdir, cs1, md, i, extension);
+                       fp = fopen(fname, "rb");
+                       if (fp == NULL) {
+                               erased[i-1] = 1;
+                               erasures[numerased] = i-1;
+                               numerased++;
+                               //printf("%s failed\n", fname);
+                       }
+                       else {
+                               if (buffersize == origsize) {
+                                       stat(fname, &status);
+                                       blocksize = status.st_size;
+                                       data[i-1] = (char *)malloc(sizeof(char)*blocksize);
+                                       dummy = fread(data[i-1], sizeof(char), blocksize, fp);
+                               }
+                               else {
+                                       fseek(fp, blocksize*(n-1), SEEK_SET); 
+                                       dummy = fread(data[i-1], sizeof(char), buffersize/k, fp);
+                               }
+                               fclose(fp);
+                       }
+               }
+               for (i = 1; i <= m; i++) {
+                       sprintf(fname, "%s/Coding/%s_m%0*d%s", curdir, cs1, md, i, extension);
+                               fp = fopen(fname, "rb");
+                       if (fp == NULL) {
+                               erased[k+(i-1)] = 1;
+                               erasures[numerased] = k+i-1;
+                               numerased++;
+                               //printf("%s failed\n", fname);
+                       }
+                       else {
+                               if (buffersize == origsize) {
+                                       stat(fname, &status);
+                                       blocksize = status.st_size;
+                                       coding[i-1] = (char *)malloc(sizeof(char)*blocksize);
+                                       dummy = fread(coding[i-1], sizeof(char), blocksize, fp);
+                               }
+                               else {
+                                       fseek(fp, blocksize*(n-1), SEEK_SET);
+                                       dummy = fread(coding[i-1], sizeof(char), blocksize, fp);
+                               }       
+                               fclose(fp);
+                       }
+               }
+               /* Finish allocating data/coding if needed */
+               if (n == 1) {
+                       for (i = 0; i < numerased; i++) {
+                               if (erasures[i] < k) {
+                                       data[erasures[i]] = (char *)malloc(sizeof(char)*blocksize);
+                               }
+                               else {
+                                       coding[erasures[i]-k] = (char *)malloc(sizeof(char)*blocksize);
+                               }
+                       }
+               }
+               
+               erasures[numerased] = -1;
+               timing_set(&t3);
+       
+               /* Choose proper decoding method */
+               if (tech == Reed_Sol_Van || tech == Reed_Sol_R6_Op) {
+                       i = jerasure_matrix_decode(k, m, w, matrix, 1, erasures, data, coding, blocksize);
+               }
+               else if (tech == Cauchy_Orig || tech == Cauchy_Good || tech == Liberation || tech == Blaum_Roth || tech == Liber8tion) {
+                       i = jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, blocksize, packetsize, 1);
+               }
+               else {
+                       fprintf(stderr, "Not a valid coding technique.\n");
+                       exit(0);
+               }
+               timing_set(&t4);
+       
+               /* Exit if decoding was unsuccessful */
+               if (i == -1) {
+                       fprintf(stderr, "Unsuccessful!\n");
+                       exit(0);
+               }
+       
+               /* Create decoded file */
+               sprintf(fname, "%s/Coding/%s_decoded%s", curdir, cs1, extension);
+               if (n == 1) {
+                       fp = fopen(fname, "wb");
+               }
+               else {
+                       fp = fopen(fname, "ab");
+               }
+               for (i = 0; i < k; i++) {
+                       if (total+blocksize <= origsize) {
+                               fwrite(data[i], sizeof(char), blocksize, fp);
+                               total+= blocksize;
+                       }
+                       else {
+                               for (j = 0; j < blocksize; j++) {
+                                       if (total < origsize) {
+                                               fprintf(fp, "%c", data[i][j]);
+                                               total++;
+                                       }
+                                       else {
+                                               break;
+                                       }
+                                       
+                               }
+                       }
+               }
+               n++;
+               fclose(fp);
+               totalsec += timing_delta(&t3, &t4);
+       }
+       
+       /* Free allocated memory */
+       free(cs1);
+       free(extension);
+       free(fname);
+       free(data);
+       free(coding);
+       free(erasures);
+       free(erased);
+       
+       /* Stop timing and print time */
+       timing_set(&t2);
+       tsec = timing_delta(&t1, &t2);
+       printf("Decoding (MB/sec): %0.10f\n", (((double) origsize)/1024.0/1024.0)/totalsec);
+       printf("De_Total (MB/sec): %0.10f\n\n", (((double) origsize)/1024.0/1024.0)/tsec);
+
+       return 0;
+}      
+
+void ctrl_bs_handler(int dummy) {
+       time_t mytime;
+       mytime = time(0);
+       fprintf(stderr, "\n%s\n", ctime(&mytime));
+       fprintf(stderr, "You just typed ctrl-\\ in decoder.c\n");
+       fprintf(stderr, "Total number of read ins = %d\n", readins);
+       fprintf(stderr, "Current read in: %d\n", n);
+       fprintf(stderr, "Method: %s\n\n", Methods[method]);
+       signal(SIGQUIT, ctrl_bs_handler);
+}

diff --git a/Examples/encoder.c b/Examples/encoder.c
new file mode 100644 (file)
index 0000000..8b9184f
--- /dev/null
+++ b/Examples/encoder.c
@@ -0,0 +1,627 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+/* 
+
+This program takes as input an inputfile, k, m, a coding 
+technique, w, and packetsize.  It creates k+m files from 
+the original file so that k of these files are parts of 
+the original file and m of the files are encoded based on 
+the given coding technique. The format of the created files 
+is the file name with "_k#" or "_m#" and then the extension.  
+(For example, inputfile test.txt would yield file "test_k1.txt".)
+*/
+
+#include <assert.h>
+#include <time.h>
+#include <sys/time.h>
+#include <sys/stat.h>
+#include <unistd.h>
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <errno.h>
+#include <signal.h>
+#include <gf_rand.h>
+#include <unistd.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+#include "cauchy.h"
+#include "liberation.h"
+#include "timing.h"
+
+#define N 10
+
+enum Coding_Technique {Reed_Sol_Van, Reed_Sol_R6_Op, Cauchy_Orig, Cauchy_Good, Liberation, Blaum_Roth, Liber8tion, RDP, EVENODD, No_Coding};
+
+char *Methods[N] = {"reed_sol_van", "reed_sol_r6_op", "cauchy_orig", "cauchy_good", "liberation", "blaum_roth", "liber8tion", "no_coding"};
+
+/* Global variables for signal handler */
+int readins, n;
+enum Coding_Technique method;
+
+/* Function prototypes */
+int is_prime(int w);
+void ctrl_bs_handler(int dummy);
+
+int jfread(void *ptr, int size, int nmembers, FILE *stream)
+{
+  if (stream != NULL) return fread(ptr, size, nmembers, stream);
+
+  MOA_Fill_Random_Region(ptr, size);
+  return size;
+}
+
+
+int main (int argc, char **argv) {
+       FILE *fp, *fp2;                         // file pointers
+       char *block;                            // padding file
+       int size, newsize;                      // size of file and temp size 
+       struct stat status;                     // finding file size
+
+       
+       enum Coding_Technique tech;             // coding technique (parameter)
+       int k, m, w, packetsize;                // parameters
+       int buffersize;                                 // paramter
+       int i;                                          // loop control variables
+       int blocksize;                                  // size of k+m files
+       int total;
+       int extra;
+       
+       /* Jerasure Arguments */
+       char **data;                            
+       char **coding;
+       int *matrix;
+       int *bitmatrix;
+       int **schedule;
+       
+       /* Creation of file name variables */
+       char temp[5];
+       char *s1, *s2, *extension;
+       char *fname;
+       int md;
+       char *curdir;
+       
+       /* Timing variables */
+       struct timing t1, t2, t3, t4;
+       double tsec;
+       double totalsec;
+       struct timing start;
+
+       /* Find buffersize */
+       int up, down;
+
+
+       signal(SIGQUIT, ctrl_bs_handler);
+
+       /* Start timing */
+       timing_set(&t1);
+       totalsec = 0.0;
+       matrix = NULL;
+       bitmatrix = NULL;
+       schedule = NULL;
+       
+       /* Error check Arguments*/
+       if (argc != 8) {
+               fprintf(stderr,  "usage: inputfile k m coding_technique w packetsize buffersize\n");
+               fprintf(stderr,  "\nChoose one of the following coding techniques: \nreed_sol_van, \nreed_sol_r6_op, \ncauchy_orig, \ncauchy_good, \nliberation, \nblaum_roth, \nliber8tion");
+               fprintf(stderr,  "\n\nPacketsize is ignored for the reed_sol's");
+               fprintf(stderr,  "\nBuffersize of 0 means the buffersize is chosen automatically.\n");
+               fprintf(stderr,  "\nIf you just want to test speed, use an inputfile of \"-number\" where number is the size of the fake file you want to test.\n\n");
+               exit(0);
+       }
+       /* Conversion of parameters and error checking */       
+       if (sscanf(argv[2], "%d", &k) == 0 || k <= 0) {
+               fprintf(stderr,  "Invalid value for k\n");
+               exit(0);
+       }
+       if (sscanf(argv[3], "%d", &m) == 0 || m < 0) {
+               fprintf(stderr,  "Invalid value for m\n");
+               exit(0);
+       }
+       if (sscanf(argv[5],"%d", &w) == 0 || w <= 0) {
+               fprintf(stderr,  "Invalid value for w.\n");
+               exit(0);
+       }
+       if (argc == 6) {
+               packetsize = 0;
+       }
+       else {
+               if (sscanf(argv[6], "%d", &packetsize) == 0 || packetsize < 0) {
+                       fprintf(stderr,  "Invalid value for packetsize.\n");
+                       exit(0);
+               }
+       }
+       if (argc != 8) {
+               buffersize = 0;
+       }
+       else {
+               if (sscanf(argv[7], "%d", &buffersize) == 0 || buffersize < 0) {
+                       fprintf(stderr, "Invalid value for buffersize\n");
+                       exit(0);
+               }
+               
+       }
+
+       /* Determine proper buffersize by finding the closest valid buffersize to the input value  */
+       if (buffersize != 0) {
+               if (packetsize != 0 && buffersize%(sizeof(long)*w*k*packetsize) != 0) { 
+                       up = buffersize;
+                       down = buffersize;
+                       while (up%(sizeof(long)*w*k*packetsize) != 0 && (down%(sizeof(long)*w*k*packetsize) != 0)) {
+                               up++;
+                               if (down == 0) {
+                                       down--;
+                               }
+                       }
+                       if (up%(sizeof(long)*w*k*packetsize) == 0) {
+                               buffersize = up;
+                       }
+                       else {
+                               if (down != 0) {
+                                       buffersize = down;
+                               }
+                       }
+               }
+               else if (packetsize == 0 && buffersize%(sizeof(long)*w*k) != 0) {
+                       up = buffersize;
+                       down = buffersize;
+                       while (up%(sizeof(long)*w*k) != 0 && down%(sizeof(long)*w*k) != 0) {
+                               up++;
+                               down--;
+                       }
+                       if (up%(sizeof(long)*w*k) == 0) {
+                               buffersize = up;
+                       }
+                       else {
+                               buffersize = down;
+                       }
+               }
+       }
+
+       /* Setting of coding technique and error checking */
+       
+       if (strcmp(argv[4], "no_coding") == 0) {
+               tech = No_Coding;
+       }
+       else if (strcmp(argv[4], "reed_sol_van") == 0) {
+               tech = Reed_Sol_Van;
+               if (w != 8 && w != 16 && w != 32) {
+                       fprintf(stderr,  "w must be one of {8, 16, 32}\n");
+                       exit(0);
+               }
+       }
+       else if (strcmp(argv[4], "reed_sol_r6_op") == 0) {
+               if (m != 2) {
+                       fprintf(stderr,  "m must be equal to 2\n");
+                       exit(0);
+               }
+               if (w != 8 && w != 16 && w != 32) {
+                       fprintf(stderr,  "w must be one of {8, 16, 32}\n");
+                       exit(0);
+               }
+               tech = Reed_Sol_R6_Op;
+       }
+       else if (strcmp(argv[4], "cauchy_orig") == 0) {
+               tech = Cauchy_Orig;
+               if (packetsize == 0) {
+                       fprintf(stderr, "Must include packetsize.\n");
+                       exit(0);
+               }
+       }
+       else if (strcmp(argv[4], "cauchy_good") == 0) {
+               tech = Cauchy_Good;
+               if (packetsize == 0) {
+                       fprintf(stderr, "Must include packetsize.\n");
+                       exit(0);
+               }
+       }
+       else if (strcmp(argv[4], "liberation") == 0) {
+               if (k > w) {
+                       fprintf(stderr,  "k must be less than or equal to w\n");
+                       exit(0);
+               }
+               if (w <= 2 || !(w%2) || !is_prime(w)) {
+                       fprintf(stderr,  "w must be greater than two and w must be prime\n");
+                       exit(0);
+               }
+               if (packetsize == 0) {
+                       fprintf(stderr, "Must include packetsize.\n");
+                       exit(0);
+               }
+               if ((packetsize%(sizeof(long))) != 0) {
+                       fprintf(stderr,  "packetsize must be a multiple of sizeof(long)\n");
+                       exit(0);
+               }
+               tech = Liberation;
+       }
+       else if (strcmp(argv[4], "blaum_roth") == 0) {
+               if (k > w) {
+                       fprintf(stderr,  "k must be less than or equal to w\n");
+                       exit(0);
+               }
+               if (w <= 2 || !((w+1)%2) || !is_prime(w+1)) {
+                       fprintf(stderr,  "w must be greater than two and w+1 must be prime\n");
+                       exit(0);
+               }
+               if (packetsize == 0) {
+                       fprintf(stderr, "Must include packetsize.\n");
+                       exit(0);
+               }
+               if ((packetsize%(sizeof(long))) != 0) {
+                       fprintf(stderr,  "packetsize must be a multiple of sizeof(long)\n");
+                       exit(0);
+               }
+               tech = Blaum_Roth;
+       }
+       else if (strcmp(argv[4], "liber8tion") == 0) {
+               if (packetsize == 0) {
+                       fprintf(stderr, "Must include packetsize\n");
+                       exit(0);
+               }
+               if (w != 8) {
+                       fprintf(stderr, "w must equal 8\n");
+                       exit(0);
+               }
+               if (m != 2) {
+                       fprintf(stderr, "m must equal 2\n");
+                       exit(0);
+               }
+               if (k > w) {
+                       fprintf(stderr, "k must be less than or equal to w\n");
+                       exit(0);
+               }
+               tech = Liber8tion;
+       }
+       else {
+               fprintf(stderr,  "Not a valid coding technique. Choose one of the following: reed_sol_van, reed_sol_r6_op, cauchy_orig, cauchy_good, liberation, blaum_roth, liber8tion, no_coding\n");
+               exit(0);
+       }
+
+       /* Set global variable method for signal handler */
+       method = tech;
+
+       /* Get current working directory for construction of file names */
+       curdir = (char*)malloc(sizeof(char)*1000);      
+       getcwd(curdir, 1000);
+
+        if (argv[1][0] != '-') {
+
+               /* Open file and error check */
+               fp = fopen(argv[1], "rb");
+               if (fp == NULL) {
+                       fprintf(stderr,  "Unable to open file.\n");
+                       exit(0);
+               }
+       
+               /* Create Coding directory */
+               i = mkdir("Coding", S_IRWXU);
+               if (i == -1 && errno != EEXIST) {
+                       fprintf(stderr, "Unable to create Coding directory.\n");
+                       exit(0);
+               }
+       
+               /* Determine original size of file */
+               stat(argv[1], &status); 
+               size = status.st_size;
+        } else {
+               if (sscanf(argv[1]+1, "%d", &size) != 1 || size <= 0) {
+                       fprintf(stderr, "Files starting with '-' should be sizes for randomly created input\n");
+                       exit(1);
+               }
+               fp = NULL;
+               MOA_Seed(time(0));
+        }
+
+       newsize = size;
+       
+       /* Find new size by determining next closest multiple */
+       if (packetsize != 0) {
+               if (size%(k*w*packetsize*sizeof(long)) != 0) {
+                       while (newsize%(k*w*packetsize*sizeof(long)) != 0) 
+                               newsize++;
+               }
+       }
+       else {
+               if (size%(k*w*sizeof(long)) != 0) {
+                       while (newsize%(k*w*sizeof(long)) != 0) 
+                               newsize++;
+               }
+       }
+       
+       if (buffersize != 0) {
+               while (newsize%buffersize != 0) {
+                       newsize++;
+               }
+       }
+
+
+       /* Determine size of k+m files */
+       blocksize = newsize/k;
+
+       /* Allow for buffersize and determine number of read-ins */
+       if (size > buffersize && buffersize != 0) {
+               if (newsize%buffersize != 0) {
+                       readins = newsize/buffersize;
+               }
+               else {
+                       readins = newsize/buffersize;
+               }
+               block = (char *)malloc(sizeof(char)*buffersize);
+               blocksize = buffersize/k;
+       }
+       else {
+               readins = 1;
+               buffersize = size;
+               block = (char *)malloc(sizeof(char)*newsize);
+       }
+       
+       /* Break inputfile name into the filename and extension */      
+       s1 = (char*)malloc(sizeof(char)*(strlen(argv[1])+20));
+       s2 = strrchr(argv[1], '/');
+       if (s2 != NULL) {
+               s2++;
+               strcpy(s1, s2);
+       }
+       else {
+               strcpy(s1, argv[1]);
+       }
+       s2 = strchr(s1, '.');
+       if (s2 != NULL) {
+          extension = strdup(s2);
+          *s2 = '\0';
+       } else {
+          extension = strdup("");
+        }
+       
+       /* Allocate for full file name */
+       fname = (char*)malloc(sizeof(char)*(strlen(argv[1])+strlen(curdir)+20));
+       sprintf(temp, "%d", k);
+       md = strlen(temp);
+       
+       /* Allocate data and coding */
+       data = (char **)malloc(sizeof(char*)*k);
+       coding = (char **)malloc(sizeof(char*)*m);
+       for (i = 0; i < m; i++) {
+               coding[i] = (char *)malloc(sizeof(char)*blocksize);
+                if (coding[i] == NULL) { perror("malloc"); exit(1); }
+       }
+
+       
+
+       /* Create coding matrix or bitmatrix and schedule */
+       timing_set(&t3);
+       switch(tech) {
+               case No_Coding:
+                       break;
+               case Reed_Sol_Van:
+                       matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+                       break;
+               case Reed_Sol_R6_Op:
+                       break;
+               case Cauchy_Orig:
+                       matrix = cauchy_original_coding_matrix(k, m, w);
+                       bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+                       schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+                       break;
+               case Cauchy_Good:
+                       matrix = cauchy_good_general_coding_matrix(k, m, w);
+                       bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+                       schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+                       break;  
+               case Liberation:
+                       bitmatrix = liberation_coding_bitmatrix(k, w);
+                       schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+                       break;
+               case Blaum_Roth:
+                       bitmatrix = blaum_roth_coding_bitmatrix(k, w);
+                       schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+                       break;
+               case Liber8tion:
+                       bitmatrix = liber8tion_coding_bitmatrix(k);
+                       schedule = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+                       break;
+               case RDP:
+               case EVENODD:
+                       assert(0);
+       }
+       timing_set(&start);
+       timing_set(&t4);
+       totalsec += timing_delta(&t3, &t4);
+
+       
+
+       /* Read in data until finished */
+       n = 1;
+       total = 0;
+
+       while (n <= readins) {
+               /* Check if padding is needed, if so, add appropriate 
+                  number of zeros */
+               if (total < size && total+buffersize <= size) {
+                       total += jfread(block, sizeof(char), buffersize, fp);
+               }
+               else if (total < size && total+buffersize > size) {
+                       extra = jfread(block, sizeof(char), buffersize, fp);
+                       for (i = extra; i < buffersize; i++) {
+                               block[i] = '0';
+                       }
+               }
+               else if (total == size) {
+                       for (i = 0; i < buffersize; i++) {
+                               block[i] = '0';
+                       }
+               }
+       
+               /* Set pointers to point to file data */
+               for (i = 0; i < k; i++) {
+                       data[i] = block+(i*blocksize);
+               }
+
+               timing_set(&t3);
+               /* Encode according to coding method */
+               switch(tech) {  
+                       case No_Coding:
+                               break;
+                       case Reed_Sol_Van:
+                               jerasure_matrix_encode(k, m, w, matrix, data, coding, blocksize);
+                               break;
+                       case Reed_Sol_R6_Op:
+                               reed_sol_r6_encode(k, w, data, coding, blocksize);
+                               break;
+                       case Cauchy_Orig:
+                               jerasure_schedule_encode(k, m, w, schedule, data, coding, blocksize, packetsize);
+                               break;
+                       case Cauchy_Good:
+                               jerasure_schedule_encode(k, m, w, schedule, data, coding, blocksize, packetsize);
+                               break;
+                       case Liberation:
+                               jerasure_schedule_encode(k, m, w, schedule, data, coding, blocksize, packetsize);
+                               break;
+                       case Blaum_Roth:
+                               jerasure_schedule_encode(k, m, w, schedule, data, coding, blocksize, packetsize);
+                               break;
+                       case Liber8tion:
+                               jerasure_schedule_encode(k, m, w, schedule, data, coding, blocksize, packetsize);
+                               break;
+                       case RDP:
+                       case EVENODD:
+                               assert(0);
+               }
+               timing_set(&t4);
+       
+               /* Write data and encoded data to k+m files */
+               for     (i = 1; i <= k; i++) {
+                       if (fp == NULL) {
+                               bzero(data[i-1], blocksize);
+                       } else {
+                               sprintf(fname, "%s/Coding/%s_k%0*d%s", curdir, s1, md, i, extension);
+                               if (n == 1) {
+                                       fp2 = fopen(fname, "wb");
+                               }
+                               else {
+                                       fp2 = fopen(fname, "ab");
+                               }
+                               fwrite(data[i-1], sizeof(char), blocksize, fp2);
+                               fclose(fp2);
+                       }
+                       
+               }
+               for     (i = 1; i <= m; i++) {
+                       if (fp == NULL) {
+                               bzero(data[i-1], blocksize);
+                       } else {
+                               sprintf(fname, "%s/Coding/%s_m%0*d%s", curdir, s1, md, i, extension);
+                               if (n == 1) {
+                                       fp2 = fopen(fname, "wb");
+                               }
+                               else {
+                                       fp2 = fopen(fname, "ab");
+                               }
+                               fwrite(coding[i-1], sizeof(char), blocksize, fp2);
+                               fclose(fp2);
+                       }
+               }
+               n++;
+               /* Calculate encoding time */
+               totalsec += timing_delta(&t3, &t4);
+       }
+
+       /* Create metadata file */
+        if (fp != NULL) {
+               sprintf(fname, "%s/Coding/%s_meta.txt", curdir, s1);
+               fp2 = fopen(fname, "wb");
+               fprintf(fp2, "%s\n", argv[1]);
+               fprintf(fp2, "%d\n", size);
+               fprintf(fp2, "%d %d %d %d %d\n", k, m, w, packetsize, buffersize);
+               fprintf(fp2, "%s\n", argv[4]);
+               fprintf(fp2, "%d\n", tech);
+               fprintf(fp2, "%d\n", readins);
+               fclose(fp2);
+       }
+
+
+       /* Free allocated memory */
+       free(s1);
+       free(fname);
+       free(block);
+       free(curdir);
+       
+       /* Calculate rate in MB/sec and print */
+       timing_set(&t2);
+       tsec = timing_delta(&t1, &t2);
+       printf("Encoding (MB/sec): %0.10f\n", (((double) size)/1024.0/1024.0)/totalsec);
+       printf("En_Total (MB/sec): %0.10f\n", (((double) size)/1024.0/1024.0)/tsec);
+
+       return 0;
+}
+
+/* is_prime returns 1 if number if prime, 0 if not prime */
+int is_prime(int w) {
+       int prime55[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,
+           73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
+                   181,191,193,197,199,211,223,227,229,233,239,241,251,257};
+       int i;
+       for (i = 0; i < 55; i++) {
+               if (w%prime55[i] == 0) {
+                       if (w == prime55[i]) return 1;
+                       else { return 0; }
+               }
+       }
+       assert(0);
+}
+
+/* Handles ctrl-\ event */
+void ctrl_bs_handler(int dummy) {
+       time_t mytime;
+       mytime = time(0);
+       fprintf(stderr, "\n%s\n", ctime(&mytime));
+       fprintf(stderr, "You just typed ctrl-\\ in encoder.c.\n");
+       fprintf(stderr, "Total number of read ins = %d\n", readins);
+       fprintf(stderr, "Current read in: %d\n", n);
+       fprintf(stderr, "Method: %s\n\n", Methods[method]);     
+       signal(SIGQUIT, ctrl_bs_handler);
+}

diff --git a/Examples/jerasure_01.c b/Examples/jerasure_01.c
new file mode 100644 (file)
index 0000000..20df225
--- /dev/null
+++ b/Examples/jerasure_01.c
@@ -0,0 +1,92 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_01 r c w - creates and prints out a matrix in GF(2^w).\n\n");
+  fprintf(stderr, "       Element i,j is equal to 2^(i*c+j)\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates jerasure_print_matrix().\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  int r, c, w, i, n;
+  int *matrix;
+
+  if (argc != 4) usage(NULL);
+  if (sscanf(argv[1], "%d", &r) == 0 || r <= 0) usage("Bad r");
+  if (sscanf(argv[2], "%d", &c) == 0 || c <= 0) usage("Bad c");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0) usage("Bad w");
+
+  matrix = talloc(int, r*c);
+
+  n = 1;
+  for (i = 0; i < r*c; i++) {
+    matrix[i] = n;
+    n = galois_single_multiply(n, 2, w);
+  }
+
+  printf("<HTML><TITLE>jerasure_01");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_01");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  jerasure_print_matrix(matrix, r, c, w);
+  return 0;
+}
+

diff --git a/Examples/jerasure_02.c b/Examples/jerasure_02.c
new file mode 100644 (file)
index 0000000..eb952ae
--- /dev/null
+++ b/Examples/jerasure_02.c
@@ -0,0 +1,94 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_02 r c w - Converts the matrix of jerasure_01 to a bit matrix.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates jerasure_print_bitmatrix() and jerasure_matrix_to_bitmatrix().\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  int r, c, w, i, n;
+  int *matrix;
+  int *bitmatrix;
+
+  if (argc != 4) usage(NULL);
+  if (sscanf(argv[1], "%d", &r) == 0 || r <= 0) usage("Bad r");
+  if (sscanf(argv[2], "%d", &c) == 0 || c <= 0) usage("Bad c");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0) usage("Bad w");
+
+  matrix = talloc(int, r*c);
+
+  n = 1;
+  for (i = 0; i < r*c; i++) {
+    matrix[i] = n;
+    n = galois_single_multiply(n, 2, w);
+  }
+
+  bitmatrix = jerasure_matrix_to_bitmatrix(c, r, w, matrix);
+
+  printf("<HTML><TITLE>jerasure_02");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_02");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  jerasure_print_bitmatrix(bitmatrix, r*w, c*w, w);
+  return 0;
+}
+

diff --git a/Examples/jerasure_03.c b/Examples/jerasure_03.c
new file mode 100644 (file)
index 0000000..24bd15c
--- /dev/null
+++ b/Examples/jerasure_03.c
@@ -0,0 +1,119 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_03 k w - Creates a kxk Cauchy matrix in GF(2^w). \n\n");
+  fprintf(stderr, "       k must be < 2^w.  Element i,j is 1/(i+(2^w-j-1)).  (If that is\n");
+  fprintf(stderr, "       If that is 1/0, then it sets it to zero).  \n");
+  fprintf(stderr, "       It then tests whether that matrix is invertible.\n");
+  fprintf(stderr, "       If it is invertible, then it prints out the inverse.\n");
+  fprintf(stderr, "       Finally, it prints the product of the matrix and its inverse.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_print_matrix()\n");
+  fprintf(stderr, "                   jerasure_invertible_matrix()\n");
+  fprintf(stderr, "                   jerasure_invert_matrix()\n");
+  fprintf(stderr, "                   jerasure_matrix_multiply().\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  unsigned int k, w, i, j, n;
+  int *matrix;
+  int *matrix_copy;
+  int *inverse;
+  int *identity;
+
+  if (argc != 3) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &w) == 0 || w <= 0 || w > 31) usage("Bad w");
+  if (k >= (1 << w)) usage("K too big");
+
+  matrix = talloc(int, k*k);
+  matrix_copy = talloc(int, k*k);
+  inverse = talloc(int, k*k);
+
+  for (i = 0; i < k; i++) {
+    for (j = 0; j < k; j++) {
+      n = i ^ ((1 << w)-1-j);
+      matrix[i*k+j] = (n == 0) ? 0 : galois_single_divide(1, n, w);
+    }
+  }
+
+  printf("<HTML><TITLE>jerasure_03");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_03");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  printf("The Cauchy Matrix:\n");
+  jerasure_print_matrix(matrix, k, k, w);
+  memcpy(matrix_copy, matrix, sizeof(int)*k*k);
+  i = jerasure_invertible_matrix(matrix_copy, k, w);
+  printf("\nInvertible: %s\n", (i == 1) ? "Yes" : "No");
+  if (i == 1) {
+    printf("\nInverse:\n");
+    memcpy(matrix_copy, matrix, sizeof(int)*k*k);
+    i = jerasure_invert_matrix(matrix_copy, inverse, k, w);
+    jerasure_print_matrix(inverse, k, k, w);
+    identity = jerasure_matrix_multiply(inverse, matrix, k, k, k, k, w);
+    printf("\nInverse times matrix (should be identity):\n");
+    jerasure_print_matrix(identity, k, k, w);
+  }
+  return 0;
+}
+

diff --git a/Examples/jerasure_04.c b/Examples/jerasure_04.c
new file mode 100644 (file)
index 0000000..21410a5
--- /dev/null
+++ b/Examples/jerasure_04.c
@@ -0,0 +1,118 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_04 k w - Performs the analogous bit-matrix operations to jerasure_03.\n\n");
+  fprintf(stderr, "       It converts the matrix to a kw*kw bit matrix and does the same operations.\n");
+  fprintf(stderr, "       k must be < 2^w.\n");
+  fprintf(stderr, "This demonstrates: jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_matrix_to_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_invertible_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_invert_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_matrix_multiply().\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  unsigned int k, w, i, j, n;
+  int *matrix;
+  int *bitmatrix;
+  int *bitmatrix_copy;
+  int *inverse;
+  int *identity;
+
+  if (argc != 3) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &w) == 0 || w <= 0 || w > 31) usage("Bad w");
+  if (k >= (1 << w)) usage("K too big");
+
+  matrix = talloc(int, k*k);
+  bitmatrix_copy = talloc(int, k*w*k*w);
+  inverse = talloc(int, k*w*k*w);
+
+  for (i = 0; i < k; i++) {
+    for (j = 0; j < k; j++) {
+      n = i ^ ((1 << w)-1-j);
+      matrix[i*k+j] = (n == 0) ? 0 : galois_single_divide(1, n, w);
+    }
+  }
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, k, w, matrix);
+
+  printf("<HTML><TITLE>jerasure_04");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_04");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  printf("The Cauchy Bit-Matrix:\n");
+  jerasure_print_bitmatrix(bitmatrix, k*w, k*w, w);
+  memcpy(bitmatrix_copy, bitmatrix, sizeof(int)*k*w*k*w);
+  i = jerasure_invertible_bitmatrix(bitmatrix_copy, k*w);
+  printf("\nInvertible: %s\n", (i == 1) ? "Yes" : "No");
+  if (i == 1) {
+    printf("\nInverse:\n");
+    memcpy(bitmatrix_copy, bitmatrix, sizeof(int)*k*w*k*w);
+    i = jerasure_invert_bitmatrix(bitmatrix_copy, inverse, k*w);
+    jerasure_print_bitmatrix(inverse, k*w, k*w, w);
+    identity = jerasure_matrix_multiply(inverse, bitmatrix, k*w, k*w, k*w, k*w, 2);
+    printf("\nInverse times matrix (should be identity):\n");
+    jerasure_print_bitmatrix(identity, k*w, k*w, w);
+  }
+  return 0;
+}
+

diff --git a/Examples/jerasure_05.c b/Examples/jerasure_05.c
new file mode 100644 (file)
index 0000000..20b059b
--- /dev/null
+++ b/Examples/jerasure_05.c
@@ -0,0 +1,217 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_05 k m w size seed - Does a simple Reed-Solomon coding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       k+m must be <= 2^w.  w can be 8, 16 or 32.\n");
+  fprintf(stderr, "       It sets up a Cauchy generator matrix and encodes\n");
+  fprintf(stderr, "       k devices of size bytes with it.  Then it decodes.\n");
+  fprintf(stderr, "       After that, it decodes device 0 by using jerasure_make_decoding_matrix()\n");
+  fprintf(stderr, "       and jerasure_matrix_dotprod().\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_matrix_encode()\n");
+  fprintf(stderr, "                   jerasure_matrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   jerasure_make_decoding_matrix()\n");
+  fprintf(stderr, "                   jerasure_matrix_dotprod()\n");
+  if (s != NULL) fprintf(stderr, "\n%s\n\n", s);
+  exit(1);
+}
+
+static void print_data_and_coding(int k, int m, int w, int size, 
+               char **data, char **coding) 
+{
+  int i, j, x;
+  int n, sp;
+
+  if(k > m) n = k;
+  else n = m;
+  sp = size * 2 + size/(w/8) + 8;
+
+  printf("%-*sCoding\n", sp, "Data");
+  for(i = 0; i < n; i++) {
+         if(i < k) {
+                 printf("D%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)data[i][j+x]);
+                         }
+                 }
+                 printf("    ");
+         }
+         else printf("%*s", sp, "");
+         if(i < m) {
+                 printf("C%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)coding[i][j+x]);
+                         }
+                 }
+         }
+         printf("\n");
+  }
+       printf("\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, m, w, size;
+  int i, j;
+  int *matrix;
+  char **data, **coding;
+  int *erasures, *erased;
+  int *decoding_matrix, *dm_ids;
+  uint32_t seed;
+  
+  if (argc != 6) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (w < 32 && k + m > (1 << w)) usage("k + m must be <= 2 ^ w");
+  if (sscanf(argv[4], "%d", &size) == 0 || size % sizeof(long) != 0) 
+               usage("size must be multiple of sizeof(long)");
+  if (sscanf(argv[5], "%d", &seed) == 0) usage("Bad seed");
+
+  matrix = talloc(int, m*k);
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[i*k+j] = galois_single_divide(1, i ^ (m + j), w);
+    }
+  }
+
+  printf("<HTML><TITLE>jerasure_05");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_05");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  printf("The Coding Matrix (the last m rows of the Generator Matrix G^T):\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  MOA_Seed(seed);
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, size);
+    MOA_Fill_Random_Region(data[i], size);
+  }
+
+  coding = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, size);
+  }
+
+  jerasure_matrix_encode(k, m, w, matrix, data, coding, size);
+  
+  printf("Encoding Complete:\n\n");
+  print_data_and_coding(k, m, w, size, data, coding);
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = (MOA_Random_W(w, 1))%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+         
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], size);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  print_data_and_coding(k, m, w, size, data, coding);
+  
+  i = jerasure_matrix_decode(k, m, w, matrix, 0, erasures, data, coding, size);
+
+  printf("State of the system after decoding:\n\n");
+  print_data_and_coding(k, m, w, size, data, coding);
+  
+  decoding_matrix = talloc(int, k*k);
+  dm_ids = talloc(int, k);
+
+  for (i = 0; i < m; i++) erased[i] = 1;
+  for (; i < k+m; i++) erased[i] = 0;
+
+  jerasure_make_decoding_matrix(k, m, w, matrix, erased, decoding_matrix, dm_ids);
+
+  printf("Suppose we erase the first %d devices.  Here is the decoding matrix:\n\n", m);
+  jerasure_print_matrix(decoding_matrix, k, k, w);
+  printf("\n");
+  printf("And dm_ids:\n\n");
+  jerasure_print_matrix(dm_ids, 1, k, w);
+
+  bzero(data[0], size);
+  jerasure_matrix_dotprod(k, w, decoding_matrix, dm_ids, 0, data, coding, size);
+
+  printf("\nAfter calling jerasure_matrix_dotprod, we calculate the value of device #0 to be:\n\n");
+  printf("D0 :");
+  for(i=0;i< size; i+=(w/8)) {
+         printf(" ");
+         for(j=0;j < w/8;j++){
+               printf("%02x", (unsigned char)data[0][i+j]);
+         }
+  }
+  printf("\n\n");
+
+  return 0;
+}

diff --git a/Examples/jerasure_06.c b/Examples/jerasure_06.c
new file mode 100644 (file)
index 0000000..9af9ca2
--- /dev/null
+++ b/Examples/jerasure_06.c
@@ -0,0 +1,233 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_06 k m w packetsize seed\n");
+  fprintf(stderr, "Does a simple Cauchy Reed-Solomon coding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       k+m must be < 2^w.  Packetsize must be a multiple of sizeof(long)\n");
+  fprintf(stderr, "       It sets up a Cauchy generator matrix and encodes k devices of w*packetsize bytes.\n");
+  fprintf(stderr, "       After that, it decodes device 0 by using jerasure_make_decoding_bitmatrix()\n");
+  fprintf(stderr, "       and jerasure_bitmatrix_dotprod().\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_bitmatrix_encode()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_make_decoding_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_bitmatrix_dotprod()\n");
+  if (s != NULL) fprintf(stderr, "\n%s\n\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, j, m, psize, x;
+  int *matrix, *bitmatrix;
+  char **data, **coding;
+  int *erasures, *erased;
+  int *decoding_matrix, *dm_ids;
+  uint32_t seed;
+  
+  if (argc != 6) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+  if (sscanf(argv[4], "%d", &psize) == 0 || psize <= 0) usage("Bad packetsize");
+  if(psize%sizeof(long) != 0) usage("Packetsize must be multiple of sizeof(long)");
+  if (sscanf(argv[5], "%d", &seed) == 0) usage("Bad seed");
+
+  MOA_Seed(seed);
+  matrix = talloc(int, m*k);
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[i*k+j] = galois_single_divide(1, i ^ (m + j), w);
+    }
+  }
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  printf("<HTML><TITLE>jerasure_06");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_06");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+
+  printf("<hr>\n");
+  printf("Last (m * w) rows of the Generator Matrix: (G^T):\n<pre>\n");
+  jerasure_print_bitmatrix(bitmatrix, w*m, w*k, w);
+  printf("</pre><hr>\n");
+
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, psize*w);
+    MOA_Fill_Random_Region(data[i], psize*w);
+  }
+
+  coding = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, psize*w);
+  }
+
+  jerasure_bitmatrix_encode(k, m, w, bitmatrix, data, coding, w*psize, psize);
+  
+  printf("Encoding Complete - Here is the state of the system\n\n");
+  printf("<p>\n");
+  print_array(data, k, psize*w, psize, "D");
+  printf("<p>\n");
+  print_array(coding, m, psize*w, psize, "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(w, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], psize*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:", m);
+  for (i = 0; erasures[i] != -1; i++) {
+    printf(" %c%x", ((erasures[i] < k) ? 'D' : 'C'), (erasures[i] < k ? erasures[i] : erasures[i]-k));
+  }
+  printf(". Here is the state of the system:\n");
+
+  printf("<p>\n");
+  print_array(data, k, psize*w, psize, "D");
+  printf("<p>\n");
+  print_array(coding, m, psize*w, psize, "C");
+  printf("<hr>\n");
+
+  i = jerasure_bitmatrix_decode(k, m, w, bitmatrix, 0, erasures, data, coding, 
+                 w*psize, psize);
+
+  printf("Here is the state of the system after decoding:\n\n");
+  printf("<p>\n");
+  print_array(data, k, psize*w, psize, "D");
+  printf("<p>\n");
+  print_array(coding, m, psize*w, psize, "C");
+  printf("<hr>\n");
+
+  decoding_matrix = talloc(int, k*k*w*w);
+  dm_ids = talloc(int, k);
+
+  x = (m < k) ? m : k;
+
+  for (i = 0; i < x; i++) erased[i] = 1;
+  for (; i < k+m; i++) erased[i] = 0;
+
+  jerasure_make_decoding_bitmatrix(k, m, w, bitmatrix, erased, decoding_matrix, dm_ids);
+
+  printf("Suppose we erase the first %d devices.  Here is the decoding matrix:\n<pre>\n", x);
+  jerasure_print_bitmatrix(decoding_matrix, k*w, k*w, w);
+  printf("</pre>\n");
+  printf("And dm_ids:\n<pre>\n");
+  jerasure_print_matrix(dm_ids, 1, k, w);
+  printf("</pre><hr>\n");
+
+  for (i = 0; i < x; i++) bzero(data[i], w*psize);
+
+  printf("Here is the state of the system after the erasures:\n\n");
+  printf("<p>\n");
+  print_array(data, k, psize*w, psize, "D");
+  printf("<p>\n");
+  print_array(coding, m, psize*w, psize, "C");
+  printf("<hr>\n");
+
+  for (i = 0; i < x; i++) {
+    jerasure_bitmatrix_dotprod(k, w, decoding_matrix+i*(k*w*w), dm_ids, i, data, coding, w*psize, psize);
+  }
+
+  printf("Here is the state of the system after calling <b>jerasure_bitmatrix_dotprod()</b> %d time%s with the decoding matrix:\n\n", x, (x == 1) ? "" : "s");
+  printf("<p>\n");
+  print_array(data, k, psize*w, psize, "D");
+  printf("<p>\n");
+  print_array(coding, m, psize*w, psize, "C");
+  printf("<hr>\n");
+  return 0;
+}

diff --git a/Examples/jerasure_07.c b/Examples/jerasure_07.c
new file mode 100644 (file)
index 0000000..cc57163
--- /dev/null
+++ b/Examples/jerasure_07.c
@@ -0,0 +1,223 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdint.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_07 k m w seed - Scheduled Cauchy Reed-Solomon coding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       k+m must be <= 2^w.  It sets up a Cauchy generator matrix and encodes\n");
+  fprintf(stderr, "       k sets of w*%ld bytes. It uses bit-matrix scheduling, both smart and dumb.\n", sizeof(long));
+  fprintf(stderr, "       It decodes using bit-matrix scheduling, then shows an example of\n");
+  fprintf(stderr, "       using jerasure_do_scheduled_operations().\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_dumb_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_lazy()\n");
+  fprintf(stderr, "                   jerasure_do_scheduled_operations()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, j, m;
+  int *matrix, *bitmatrix;
+  char **data, **coding, **ptrs;
+  int **smart, **dumb;
+  int *erasures, *erased;
+  double stats[3];
+  uint32_t seed;
+  
+  if (argc != 5) usage("Wrong number of arguments");
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+
+  matrix = talloc(int, m*k);
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[i*k+j] = galois_single_divide(1, i ^ (m + j), w);
+    }
+  }
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  printf("<HTML><TITLE>jerasure_07");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_07");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<hr>\n");
+
+  printf("Last m*w rows of the generator matrix (G^T):\n<pre>\n");
+  jerasure_print_bitmatrix(bitmatrix, w*m, w*k, w);
+  printf("</pre><hr>\n");
+  
+  dumb = jerasure_dumb_bitmatrix_to_schedule(k, m, w, bitmatrix);
+  smart = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+
+  MOA_Seed(seed);
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+  }
+
+  coding = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_schedule_encode(k, m, w, dumb, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+  printf("Dumb Encoding Complete: - %.0lf XOR'd bytes.  State of the system:\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_schedule_encode(k, m, w, smart, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+  printf("Smart Encoding Complete: - %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(w, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, w*sizeof(long), sizeof(long), 1);
+  jerasure_get_stats(stats);
+
+  printf("State of the system after decoding: %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  ptrs = talloc(char *, (k+m));
+  for (i = 0; i < k; i++) ptrs[i] = data[i];
+  for (i = 0; i < m; i++) ptrs[k+i] = coding[i];
+
+  for (j = 0; j < m; j++) bzero(coding[j], sizeof(long)*w);
+  printf("State of the system after erasing the coding devices:\n");
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  jerasure_do_scheduled_operations(ptrs, smart, sizeof(long));
+  printf("And using <b>jerasure_do_scheduled_operations()</b>: %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  return 0;
+}

diff --git a/Examples/jerasure_08.c b/Examples/jerasure_08.c
new file mode 100644 (file)
index 0000000..0eb5ace
--- /dev/null
+++ b/Examples/jerasure_08.c
@@ -0,0 +1,232 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: jerasure_08 k w seed - Example schedule cache usage with RAID-6\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       m=2.  k+m must be <= 2^w.  It sets up a RAID-6 generator matrix and encodes\n");
+  fprintf(stderr, "       k sets of w*%ld bytes. It creates a schedule cache for decoding.\n", sizeof(long));
+  fprintf(stderr, "       It demonstrates using the schedule cache for both encoding and decoding.\n");
+  fprintf(stderr, "       Then it demonstrates using jerasure_do_parity() to re-encode the first.\n");
+  fprintf(stderr, "       coding device\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_generate_schedule_cache()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_cache()\n");
+  fprintf(stderr, "                   jerasure_free_schedule()\n");
+  fprintf(stderr, "                   jerasure_free_schedule_cache()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  fprintf(stderr, "                   jerasure_do_parity()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, j, m;
+  int *matrix, *bitmatrix;
+  char **data, **coding;
+  int **smart, ***cache;
+  int *erasures, *erased;
+  double stats[3];
+  uint32_t seed;
+  
+  if (argc != 4) usage("Wrong number of arguments");
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad m");
+  if (sscanf(argv[3], "%d", &seed) == 0) usage("Bad seed");
+  m = 2;
+  if (w < 30 && (k+m) > (1 << w)) usage("k + m is too big");
+
+  MOA_Seed(seed);
+
+  matrix = talloc(int, m*k);
+  for (j = 0; j < k; j++) matrix[j] = 1;
+  i = 1;
+  for (j = 0; j < k; j++) {
+    matrix[k+j] = i;
+    i = galois_single_multiply(i, 2, w);
+  }
+  bitmatrix = jerasure_matrix_to_bitmatrix(k, m, w, matrix);
+
+  smart = jerasure_smart_bitmatrix_to_schedule(k, m, w, bitmatrix);
+  cache = jerasure_generate_schedule_cache(k, m, w, bitmatrix, 1);
+
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+  }
+
+  coding = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_schedule_encode(k, m, w, smart, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+
+  printf("<HTML><TITLE>jerasure_08");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>jerasure_08");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<hr>\n");
+
+  printf("Encoding Complete: - %.0lf XOR'd bytes.  Here is the state of the system:\n<p>\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erasures[0] = k;
+  erasures[1] = k+1;
+  erasures[2] = -1;
+  for (j = 0; j < m; j++) bzero(coding[j], sizeof(long)*w);
+
+  jerasure_schedule_decode_cache(k, m, w, cache, erasures, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+  printf("Encoding Using the Schedule Cache: - %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(w, 1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  jerasure_schedule_decode_cache(k, m, w, cache, erasures, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+
+  printf("State of the system after decoding: %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  bzero(coding[0], sizeof(long)*w);
+  printf("Erased the first coding device:\n\n");
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  jerasure_do_parity(k, data, coding[0], sizeof(long)*w);
+  printf("State of the system after using\n");
+  printf("<b>jerasure_do_parity()</b> to re-encode it:\n\n");
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  jerasure_free_schedule(smart);
+  jerasure_free_schedule_cache(k, m, cache);
+  
+  printf("Smart schedule and cache freed.\n\n");
+
+  return 0;
+}

diff --git a/Examples/liberation_01.c b/Examples/liberation_01.c
new file mode 100644 (file)
index 0000000..d3b4392
--- /dev/null
+++ b/Examples/liberation_01.c
@@ -0,0 +1,192 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdlib.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "liberation.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: liberation_01 k w seed - Liberation RAID-6 coding/decoding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       w must be prime and k <= w.  It sets up a Liberation bit-matrix\n");
+  fprintf(stderr, "       then it encodes k devices of w*%ld bytes using dumb bit-matrix scheduling.\n", sizeof(long));
+  fprintf(stderr, "       It decodes using smart bit-matrix scheduling.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: liberation_coding_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_smart_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_dumb_bitmatrix_to_schedule()\n");
+  fprintf(stderr, "                   jerasure_schedule_encode()\n");
+  fprintf(stderr, "                   jerasure_schedule_decode_lazy()\n");
+  fprintf(stderr, "                   jerasure_print_bitmatrix()\n");
+  fprintf(stderr, "                   jerasure_get_stats()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_array(char **ptrs, int ndevices, int size, int packetsize, char *label)
+{
+  int i, j, x;
+  unsigned char *up;
+
+  printf("<center><table border=3 cellpadding=3><tr><td></td>\n");
+
+  for (i = 0; i < ndevices; i++) printf("<td align=center>%s%x</td>\n", label, i);
+  printf("</tr>\n");
+  printf("<td align=right><pre>");
+  for (j = 0; j < size/packetsize; j++) printf("Packet %d\n", j);
+  printf("</pre></td>\n");
+  for (i = 0; i < ndevices; i++) {
+    printf("<td><pre>");
+    up = (unsigned char *) ptrs[i];
+    for (j = 0; j < size/packetsize; j++) {
+      for (x = 0; x < packetsize; x++) {
+        if (x > 0 && x%4 == 0) printf(" ");
+        printf("%02x", up[j*packetsize+x]);
+      }
+      printf("\n");
+    }
+    printf("</td>\n");
+  }
+  printf("</tr></table></center>\n");
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m;
+  int *bitmatrix;
+  char **data, **coding;
+  int **dumb;
+  int *erasures, *erased;
+  double stats[3];
+  uint32_t seed;
+  
+  if (argc != 4) usage("Wrong number of arguments");
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (sscanf(argv[3], "%u", &seed) == 0) usage("Bad seed");
+  m = 2;
+  if (w < k) usage("k is too big");
+  for (i = 2; i*i <= w; i++) if (w%i == 0) usage("w isn't prime");
+
+  bitmatrix = liberation_coding_bitmatrix(k, w);
+  if (bitmatrix == NULL) {
+    usage("couldn't make coding matrix");
+  }
+
+  printf("<HTML><TITLE>liberation_01");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>liberation_01");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<hr>\n");
+
+  printf("Coding Bit-Matrix:\n<pre>\n");
+  jerasure_print_bitmatrix(bitmatrix, w*m, w*k, w);
+  printf("</pre><hr>\n");
+
+  dumb = jerasure_dumb_bitmatrix_to_schedule(k, m, w, bitmatrix);
+
+  MOA_Seed(seed);
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long)*w);
+    MOA_Fill_Random_Region(data[i], sizeof(long)*w);
+  }
+
+  coding = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long)*w);
+  }
+
+  jerasure_schedule_encode(k, m, w, dumb, data, coding, w*sizeof(long), sizeof(long));
+  jerasure_get_stats(stats);
+  printf("Smart Encoding Complete: - %.0lf XOR'd bytes.  State of the system:\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(30,1)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], sizeof(long)*w);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  jerasure_schedule_decode_lazy(k, m, w, bitmatrix, erasures, data, coding, w*sizeof(long), sizeof(long), 1);
+  jerasure_get_stats(stats);
+
+  printf("State of the system after decoding: %.0lf XOR'd bytes\n\n", stats[0]);
+  printf("<p>\n");
+  print_array(data, k, sizeof(long)*w, sizeof(long), "D");
+  printf("<p>\n");
+  print_array(coding, m, sizeof(long)*w, sizeof(long), "C");
+  printf("<hr>\n");
+  
+  return 0;
+}

diff --git a/Examples/reed_sol_01.c b/Examples/reed_sol_01.c
new file mode 100644 (file)
index 0000000..da46aeb
--- /dev/null
+++ b/Examples/reed_sol_01.c
@@ -0,0 +1,195 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_01 k m w seed - Does a simple Reed-Solomon coding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "w must be 8, 16 or 32.  k+m must be <= 2^w.  It sets up a classic\n");
+  fprintf(stderr, "Vandermonde-based generator matrix and encodes k devices of\n");
+  fprintf(stderr, "%ld bytes each with it.  Then it decodes.\n", sizeof(long));
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: jerasure_matrix_encode()\n");
+  fprintf(stderr, "                   jerasure_matrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   reed_sol_vandermonde_coding_matrix()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+static void print_data_and_coding(int k, int m, int w, int size, 
+               char **data, char **coding) 
+{
+  int i, j, x;
+  int n, sp;
+
+  if(k > m) n = k;
+  else n = m;
+  sp = size * 2 + size/(w/8) + 8;
+
+  printf("%-*sCoding\n", sp, "Data");
+  for(i = 0; i < n; i++) {
+         if(i < k) {
+                 printf("D%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)data[i][j+x]);
+                         }
+                 }
+                 printf("    ");
+         }
+         else printf("%*s", sp, "");
+         if(i < m) {
+                 printf("C%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)coding[i][j+x]);
+                         }
+                 }
+         }
+         printf("\n");
+  }
+       printf("\n");
+}
+
+int main(int argc, char **argv)
+{
+  long l;
+  int k, w, i, j, m;
+  int *matrix;
+  char **data, **coding, **dcopy, **ccopy;
+  unsigned char uc;
+  int *erasures, *erased;
+  uint32_t seed;
+  
+  if (argc != 5) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (sscanf(argv[4], "%u", &seed) == 0) usage("Bad seed");
+  if (w <= 16 && k + m > (1 << w)) usage("k + m is too big");
+
+  matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+
+  printf("<HTML><TITLE>reed_sol_01 %d %d %d %d</title>\n", k, m, w, seed);
+  printf("<h3>reed_sol_01 %d %d %d %d</h3>\n", k, m, w, seed);
+  printf("<pre>\n");
+  printf("Last m rows of the generator Matrix (G^T):\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  MOA_Seed(seed);
+  data = talloc(char *, k);
+  dcopy = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long));
+    dcopy[i] = talloc(char, sizeof(long));
+    for (j = 0; j < sizeof(long); j++) {
+      uc = MOA_Random_W(8, 1);
+      data[i][j] = (char) uc;
+    }
+    memcpy(dcopy[i], data[i], sizeof(long));
+  }
+
+  coding = talloc(char *, m);
+  ccopy = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long));
+    ccopy[i] = talloc(char, sizeof(long));
+  }
+
+  jerasure_matrix_encode(k, m, w, matrix, data, coding, sizeof(long));
+
+  for (i = 0; i < m; i++) {
+    memcpy(ccopy[i], coding[i], sizeof(long));
+  }
+  
+  printf("Encoding Complete:\n\n");
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  l = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = MOA_Random_W(31, 0)%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      memcpy((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], &l, sizeof(long));
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+  
+  i = jerasure_matrix_decode(k, m, w, matrix, 1, erasures, data, coding, sizeof(long));
+
+  printf("State of the system after decoding:\n\n");
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+  
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  return 0;
+}

diff --git a/Examples/reed_sol_02.c b/Examples/reed_sol_02.c
new file mode 100644 (file)
index 0000000..6beb4f6
--- /dev/null
+++ b/Examples/reed_sol_02.c
@@ -0,0 +1,104 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_02 k m w - Vandermonde matrices in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       k+m must be <= 2^w.  This simply prints out the \n");
+  fprintf(stderr, "       Vandermonde matrix in GF(2^w), and then the generator\n");
+  fprintf(stderr, "       matrix that is constructed from it.  See [Plank-Ding-05] for\n");
+  fprintf(stderr, "       information on how this construction proceeds\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: reed_sol_extended_vandermonde_matrix()\n");
+  fprintf(stderr, "                   reed_sol_big_vandermonde_coding_matrix()\n");
+  fprintf(stderr, "                   reed_sol_vandermonde_coding_matrix()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, m;
+  int *matrix;
+  
+  if (argc != 4) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || w <= 0 || w > 32) usage("Bad w");
+  if (w <= 30 && k + m > (1 << w)) usage("k + m is too big");
+
+  matrix = reed_sol_extended_vandermonde_matrix(k+m, k, w);
+
+  printf("<HTML><TITLE>reed_sol_02 %d %d %d</title>\n", k, m, w);
+  printf("<h3>reed_sol_02 %d %d %d</h3>\n", k, m, w);
+  printf("<pre>\n");
+  printf("Extended Vandermonde Matrix:\n\n");
+  jerasure_print_matrix(matrix, k+m, k, w);
+  printf("\n");
+
+  matrix = reed_sol_big_vandermonde_distribution_matrix(k+m, k, w);
+  printf("Vandermonde Generator Matrix (G^T):\n\n");
+  jerasure_print_matrix(matrix, k+m, k, w);
+  printf("\n");
+
+  matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+  printf("Vandermonde Coding Matrix:\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  
+  return 0;
+}

diff --git a/Examples/reed_sol_03.c b/Examples/reed_sol_03.c
new file mode 100644 (file)
index 0000000..187cebd
--- /dev/null
+++ b/Examples/reed_sol_03.c
@@ -0,0 +1,195 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_03 k w seed - Does a simple RAID-6 coding example in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       w must be 8, 16 or 32.  k+2 must be <= 2^w.  It sets up a classic\n");
+  fprintf(stderr, "       RAID-6 coding matrix based on Anvin's optimization and encodes\n");
+  fprintf(stderr, "       %ld-byte devices with it.  Then it decodes.\n", sizeof(long));
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: reed_sol_r6_encode()\n");
+  fprintf(stderr, "                   reed_sol_r6_coding_matrix()\n");
+  fprintf(stderr, "                   jerasure_matrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+
+static void print_data_and_coding(int k, int m, int w, int size, 
+               char **data, char **coding) 
+{
+  int i, j, x;
+  int n, sp;
+
+  if(k > m) n = k;
+  else n = m;
+  sp = size * 2 + size/(w/8) + 8;
+
+  printf("%-*sCoding\n", sp, "Data");
+  for(i = 0; i < n; i++) {
+         if(i < k) {
+                 printf("D%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)data[i][j+x]);
+                         }
+                 }
+                 printf("    ");
+         }
+         else printf("%*s", sp, "");
+         if(i < m) {
+                 printf("C%-2d:", i);
+                 for(j=0;j< size; j+=(w/8)) { 
+                         printf(" ");
+                         for(x=0;x < w/8;x++){
+                               printf("%02x", (unsigned char)coding[i][j+x]);
+                         }
+                 }
+         }
+         printf("\n");
+  }
+       printf("\n");
+}
+
+int main(int argc, char **argv)
+{
+  long l;
+  unsigned char uc;
+  int k, w, i, j, m;
+  int *matrix;
+  char **data, **coding, **dcopy, **ccopy;
+  int *erasures, *erased;
+  uint32_t seed;
+  
+  if (argc != 4) usage(NULL);
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (sscanf(argv[3], "%d", &seed) == 0) usage("Bad seed");
+  m = 2;
+  if (w <= 16 && k + m > (1 << w)) usage("k + m is too big");
+
+  MOA_Seed(seed);
+  matrix = reed_sol_r6_coding_matrix(k, w);
+
+  printf("<HTML><TITLE>reed_sol_03 %d %d %d</title>\n", k, w, seed);
+  printf("<h3>reed_sol_03 %d %d %d</h3>\n", k, w, seed);
+  printf("<pre>\n");
+
+  printf("Last 2 rows of the Generator Matrix:\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  data = talloc(char *, k);
+  dcopy = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, sizeof(long));
+    dcopy[i] = talloc(char, sizeof(long));
+    for (j = 0; j < sizeof(long); j++) {
+      uc = MOA_Random_W(8, 1) %256;
+      data[i][j] = (char) uc;   
+    }
+    memcpy(dcopy[i], data[i], sizeof(long));
+  }
+
+  coding = talloc(char *, m);
+  ccopy = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, sizeof(long));
+    ccopy[i] = talloc(char, sizeof(long));
+  }
+
+  reed_sol_r6_encode(k, w, data, coding, sizeof(long));
+  for (i = 0; i < m; i++) {
+    memcpy(ccopy[i], coding[i], sizeof(long));
+  }
+  
+  printf("Encoding Complete:\n\n");
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  l = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = ((unsigned int) MOA_Random_W(w, 1))%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      memcpy((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], &l, sizeof(long));
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  printf("Erased %d random devices:\n\n", m);
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+  
+  i = jerasure_matrix_decode(k, m, w, matrix, 1, erasures, data, coding, sizeof(long));
+
+  printf("State of the system after decoding:\n\n");
+  print_data_and_coding(k, m, w, sizeof(long), data, coding);
+  
+  for (i = 0; i < k; i++) if (memcmp(data[i], dcopy[i], sizeof(long)) != 0) {
+    printf("ERROR: D%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+  for (i = 0; i < m; i++) if (memcmp(coding[i], ccopy[i], sizeof(long)) != 0) {
+    printf("ERROR: C%x after decoding does not match its state before decoding!<br>\n", i);
+  }
+
+  return 0;
+}

diff --git a/Examples/reed_sol_04.c b/Examples/reed_sol_04.c
new file mode 100644 (file)
index 0000000..f763fb0
--- /dev/null
+++ b/Examples/reed_sol_04.c
@@ -0,0 +1,120 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include <gf_rand.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_04 w seed - Shows reed_sol_galois_wXX_region_multby_2\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       w must be 8, 16 or 32.  Sets up an array of 4 random words in\n");
+  fprintf(stderr, "       GF(2^w) and multiplies them by two.  \n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This demonstrates: reed_sol_galois_w08_region_multby_2()\n");
+  fprintf(stderr, "                   reed_sol_galois_w16_region_multby_2()\n");
+  fprintf(stderr, "                   reed_sol_galois_w32_region_multby_2()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+int main(int argc, char **argv)
+{
+  unsigned char *x, *y;
+  unsigned short *xs, *ys;
+  unsigned int *xi, *yi;
+  uint32_t seed;
+  int *a32, *copy;
+  int i;
+  int w;
+  
+  if (argc != 3) usage(NULL);
+  if (sscanf(argv[1], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (sscanf(argv[2], "%d", &seed) == 0) usage("Bad seed");
+
+  printf("<HTML><TITLE>reed_sol_04 %d %d</title>\n", w, seed);
+  printf("<h3>reed_sol_04 %d %d</h3>\n", w, seed);
+  printf("<pre>\n");
+
+  MOA_Seed(seed);
+  a32 = talloc(int, 4);
+  copy = talloc(int, 4);
+  y = (unsigned char *) a32;
+  for (i = 0; i < 4*sizeof(int); i++) y[i] = MOA_Random_W(8, 1);
+  memcpy(copy, a32, sizeof(int)*4);
+
+  if (w == 8) {
+    x = (unsigned char *) copy;
+    y = (unsigned char *) a32;
+    reed_sol_galois_w08_region_multby_2((char *) a32, sizeof(int)*4);
+    for (i = 0; i < 4*sizeof(int)/sizeof(char); i++) {
+       printf("Char %2d: %3u *2 = %3u\n", i, x[i], y[i]);
+    }
+  } else if (w == 16) {
+    xs = (unsigned short *) copy;
+    ys = (unsigned short *) a32;
+    reed_sol_galois_w16_region_multby_2((char *) a32, sizeof(int)*4);
+    for (i = 0; i < 4*sizeof(int)/sizeof(short); i++) {
+       printf("Short %2d: %5u *2 = %5u\n", i, xs[i], ys[i]);
+    }
+  } else if (w == 32) {
+    xi = (unsigned int *) copy;
+    yi = (unsigned int *) a32;
+    reed_sol_galois_w16_region_multby_2((char *) a32, sizeof(int)*4);
+    for (i = 0; i < 4*sizeof(int)/sizeof(int); i++) {
+       printf("Int %2d: %10u *2 = %10u\n", i, xi[i], yi[i]);
+    }
+  } 
+
+  return 0;
+}

diff --git a/Examples/reed_sol_test_gf.c b/Examples/reed_sol_test_gf.c
new file mode 100644 (file)
index 0000000..9e8856c
--- /dev/null
+++ b/Examples/reed_sol_test_gf.c
@@ -0,0 +1,191 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gf_complete.h>
+#include <gf_method.h>
+#include <gf_rand.h>
+#include <stdint.h>
+#include <sys/time.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define BUFSIZE 4096
+
+static void *malloc16(int size) {
+    void *mem = malloc(size+16+sizeof(void*));
+    void **ptr = (void**)((long)(mem+16+sizeof(void*)) & ~(15));
+    ptr[-1] = mem;
+    return ptr;
+}
+
+#if 0
+// Unused for now.
+static void free16(void *ptr) {
+    free(((void**)ptr)[-1]);
+}
+#endif
+
+#define talloc(type, num) (type *) malloc16(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_test_gf k m w seed (additional GF args) - Tests Reed-Solomon in GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       w must be 8, 16 or 32.  k+m must be <= 2^w.\n");
+  fprintf(stderr, "       See the README for information on the additional GF args.\n");
+  fprintf(stderr, "       Set up a Vandermonde-based distribution matrix and encodes k devices of\n");
+  fprintf(stderr, "       %d bytes each with it.  Then it decodes.\n", BUFSIZE);
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This tests:        jerasure_matrix_encode()\n");
+  fprintf(stderr, "                   jerasure_matrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   galois_change_technique()\n");
+  fprintf(stderr, "                   reed_sol_vandermonde_coding_matrix()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+gf_t* get_gf(int w, int argc, char **argv, int starting)
+{
+  gf_t *gf = (gf_t*)malloc(sizeof(gf_t));
+  if (create_gf_from_argv(gf, w, argc, argv, starting) == 0) {
+    free(gf);
+    gf = NULL;
+  }
+  return gf;
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m;
+  int *matrix;
+  char **data, **coding, **old_values;
+  int *erasures, *erased;
+  gf_t *gf = NULL;
+  uint32_t seed;
+  
+  if (argc < 6) usage("Not enough command line arguments");  
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (w <= 16 && k + m > (1 << w)) usage("k + m is too big");
+
+  MOA_Seed(seed);
+
+  gf = get_gf(w, argc, argv, 5); 
+
+  if (gf == NULL) {
+    usage("Invalid arguments given for GF!\n");
+  }
+
+  galois_change_technique(gf, w); 
+
+  matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+
+  printf("<HTML><TITLE>reed_sol_test_gf");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>reed_sol_test_gf");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  printf("Last m rows of the generator matrix (G^T):\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, BUFSIZE);
+    MOA_Fill_Random_Region(data[i], BUFSIZE);
+  }
+
+  coding = talloc(char *, m);
+  old_values = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, BUFSIZE);
+    old_values[i] = talloc(char, BUFSIZE);
+  }
+
+  jerasure_matrix_encode(k, m, w, matrix, data, coding, BUFSIZE);
+  
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = ((unsigned int)MOA_Random_W(w,1))%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      memcpy(old_values[i], (erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], BUFSIZE);
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], BUFSIZE);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  i = jerasure_matrix_decode(k, m, w, matrix, 1, erasures, data, coding, BUFSIZE);
+
+  for (i = 0; i < m; i++) {
+    if (erasures[i] < k) {
+      if (memcmp(data[erasures[i]], old_values[i], BUFSIZE)) {
+        fprintf(stderr, "Decoding failed for %d!\n", erasures[i]);
+        exit(1);
+      }
+    } else {
+      if (memcmp(coding[erasures[i]-k], old_values[i], BUFSIZE)) {
+        fprintf(stderr, "Decoding failed for %d!\n", erasures[i]);
+        exit(1);
+      }
+    }
+  }
+  
+  printf("Encoding and decoding were both successful.\n");
+  return 0;
+}

diff --git a/Examples/reed_sol_time_gf.c b/Examples/reed_sol_time_gf.c
new file mode 100644 (file)
index 0000000..175de8b
--- /dev/null
+++ b/Examples/reed_sol_time_gf.c
@@ -0,0 +1,204 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan.
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank.
+ */
+
+#include <sys/time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gf_complete.h>
+#include <gf_rand.h>
+#include <gf_method.h>
+#include <stdint.h>
+#include "jerasure.h"
+#include "reed_sol.h"
+#include "timing.h"
+
+static void *malloc16(int size) {
+    void *mem = malloc(size+16+sizeof(void*));
+    void **ptr = (void**)((long)(mem+16+sizeof(void*)) & ~(15));
+    ptr[-1] = mem;
+    return ptr;
+}
+
+#if 0
+// Unused for now.
+static void free16(void *ptr) {
+    free(((void**)ptr)[-1]);
+}
+#endif
+
+#define talloc(type, num) (type *) malloc16(sizeof(type)*(num))
+
+static void usage(char *s)
+{
+  fprintf(stderr, "usage: reed_sol_time_gf k m w seed iterations bufsize (additional GF args) - Test and time Reed-Solomon in a particular GF(2^w).\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "       w must be 8, 16 or 32.  k+m must be <= 2^w.\n");
+  fprintf(stderr, "       See the README for information on the additional GF args.\n");
+  fprintf(stderr, "       Set up a Vandermonde-based distribution matrix and encodes k devices of\n");
+  fprintf(stderr, "       bufsize bytes each with it.  Then it decodes.\n");
+  fprintf(stderr, "       \n");
+  fprintf(stderr, "This tests:        jerasure_matrix_encode()\n");
+  fprintf(stderr, "                   jerasure_matrix_decode()\n");
+  fprintf(stderr, "                   jerasure_print_matrix()\n");
+  fprintf(stderr, "                   galois_change_technique()\n");
+  fprintf(stderr, "                   reed_sol_vandermonde_coding_matrix()\n");
+  if (s != NULL) fprintf(stderr, "%s\n", s);
+  exit(1);
+}
+
+gf_t* get_gf(int w, int argc, char **argv, int starting)
+{
+  gf_t *gf = (gf_t*)malloc(sizeof(gf_t));
+  if (create_gf_from_argv(gf, w, argc, argv, starting) == 0) {
+    free(gf);
+    gf = NULL;
+  }
+  return gf;
+}
+
+int main(int argc, char **argv)
+{
+  int k, w, i, m, iterations, bufsize;
+  int *matrix;
+  char **data, **coding, **old_values;
+  int *erasures, *erased;
+  uint32_t seed;
+  double t = 0, total_time = 0;
+  gf_t *gf = NULL;
+  
+  if (argc < 8) usage(NULL);  
+  if (sscanf(argv[1], "%d", &k) == 0 || k <= 0) usage("Bad k");
+  if (sscanf(argv[2], "%d", &m) == 0 || m <= 0) usage("Bad m");
+  if (sscanf(argv[3], "%d", &w) == 0 || (w != 8 && w != 16 && w != 32)) usage("Bad w");
+  if (sscanf(argv[4], "%d", &seed) == 0) usage("Bad seed");
+  if (sscanf(argv[5], "%d", &iterations) == 0) usage("Bad iterations");
+  if (sscanf(argv[6], "%d", &bufsize) == 0) usage("Bad bufsize");
+  if (w <= 16 && k + m > (1 << w)) usage("k + m is too big");
+
+  MOA_Seed(seed);
+
+  gf = get_gf(w, argc, argv, 7); 
+
+  if (gf == NULL) {
+    usage("Invalid arguments given for GF!\n");
+  }
+
+  galois_change_technique(gf, w); 
+
+  matrix = reed_sol_vandermonde_coding_matrix(k, m, w);
+
+  printf("<HTML><TITLE>reed_sol_time_gf");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</TITLE>\n");
+  printf("<h3>reed_sol_time_gf");
+  for (i = 1; i < argc; i++) printf(" %s", argv[i]);
+  printf("</h3>\n");
+  printf("<pre>\n");
+
+  printf("Last m rows of the generator matrix (G^T):\n\n");
+  jerasure_print_matrix(matrix, m, k, w);
+  printf("\n");
+
+  data = talloc(char *, k);
+  for (i = 0; i < k; i++) {
+    data[i] = talloc(char, bufsize);
+    MOA_Fill_Random_Region(data[i], bufsize);
+  }
+
+  coding = talloc(char *, m);
+  old_values = talloc(char *, m);
+  for (i = 0; i < m; i++) {
+    coding[i] = talloc(char, bufsize);
+    old_values[i] = talloc(char, bufsize);
+  }
+
+  for (i = 0; i < iterations; i++) {
+    t = timing_now();
+    jerasure_matrix_encode(k, m, w, matrix, data, coding, bufsize);
+    total_time += timing_now() - t;
+  }
+
+  printf("Encode throughput for %d iterations: %.2f MB/s (%.2f sec)\n", iterations, (double)(k*iterations*bufsize/1024/1024) / total_time, total_time);
+  
+  erasures = talloc(int, (m+1));
+  erased = talloc(int, (k+m));
+  for (i = 0; i < m+k; i++) erased[i] = 0;
+  for (i = 0; i < m; ) {
+    erasures[i] = ((unsigned int)MOA_Random_W(w, 1))%(k+m);
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      memcpy(old_values[i], (erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], bufsize);
+      bzero((erasures[i] < k) ? data[erasures[i]] : coding[erasures[i]-k], bufsize);
+      i++;
+    }
+  }
+  erasures[i] = -1;
+
+  for (i = 0; i < iterations; i++) {
+    t = timing_now();
+    jerasure_matrix_decode(k, m, w, matrix, 1, erasures, data, coding, bufsize);
+    total_time += timing_now() - t;
+  }
+  
+  printf("Decode throughput for %d iterations: %.2f MB/s (%.2f sec)\n", iterations, (double)(k*iterations*bufsize/1024/1024) / total_time, total_time);
+
+  for (i = 0; i < m; i++) {
+    if (erasures[i] < k) {
+      if (memcmp(data[erasures[i]], old_values[i], bufsize)) {
+        fprintf(stderr, "Decoding failed for %d!\n", erasures[i]);
+        exit(1);
+      }
+    } else {
+      if (memcmp(coding[erasures[i]-k], old_values[i], bufsize)) {
+        fprintf(stderr, "Decoding failed for %d!\n", erasures[i]);
+        exit(1);
+      }
+    }
+  }
+  
+  return 0;
+}

diff --git a/Examples/test_all_gfs.sh b/Examples/test_all_gfs.sh
new file mode 100755 (executable)
index 0000000..a03ee9c
--- /dev/null
+++ b/Examples/test_all_gfs.sh
@@ -0,0 +1,93 @@
+#
+#
+# Copyright (c) 2013, James S. Plank and Kevin Greenan
+# All rights reserved.
+#
+# Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+# Coding Techniques
+#
+# Revision 2.0: Galois Field backend now links to GF-Complete
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+#  - Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+#
+#  - 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.
+#
+#  - Neither the name of the University of Tennessee nor the names of its
+#    contributors may be used to endorse or promote products derived
+#    from this software without specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "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 COPYRIGHT
+# HOLDER OR CONTRIBUTORS 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.
+#
+GF_METHODS=${GF_COMPLETE_DIR:-/usr/local/bin}/gf_methods
+k=12
+m=3
+seed=1370
+
+# Test all w=8
+${GF_METHODS} 8 -B -L | awk -F: '{ if ($1 == "w=8") print $2; }' |
+while read method; do
+  echo "Testing ${k} ${m} 8 $seed ${method}"
+  $VALGRIND ./reed_sol_test_gf ${k} ${m} 8 $seed ${method} | tail -n 1
+  if [[ $? != "0" ]]; then
+    echo "Failed test for ${k} ${m} 8 $seed ${method}"
+    exit 1
+  fi
+done
+
+if [[ $? == "1" ]]; then
+  exit 1
+fi
+
+
+# Test all w=16
+${GF_METHODS} 16 -B -L | awk -F: '{ if ($1 == "w=16") print $2; }' |
+while read method; do
+  echo "Testing ${k} ${m} 16 $seed ${method}"
+  $VALGRIND ./reed_sol_test_gf ${k} ${m} 16 $seed ${method} | tail -n 1
+  if [[ $? != "0" ]]; then
+    echo "Failed test for ${k} ${m} 16 $seed ${method}"
+    exit 1
+  fi
+done
+
+
+if [[ $? == "1" ]]; then
+  exit 1
+fi
+
+# Test all w=32
+${GF_METHODS} 32 -B -L | awk -F: '{ if ($1 == "w=32") print $2; }' |
+while read method; do
+  echo "Testing ${k} ${m} 32 $seed ${method}"
+  $VALGRIND ./reed_sol_test_gf ${k} ${m} 32 $seed ${method} | tail -n 1
+  if [[ $? != "0" ]]; then
+    echo "Failed test for ${k} ${m} 32 $seed ${method}"
+    exit 1
+  fi
+done
+
+
+if [[ $? == "1" ]]; then
+  exit 1
+fi
+
+echo "Passed all tests!"

diff --git a/Examples/test_galois.c b/Examples/test_galois.c
new file mode 100644 (file)
index 0000000..a913a77
--- /dev/null
+++ b/Examples/test_galois.c
@@ -0,0 +1,23 @@
+#include <assert.h>
+#include "galois.h"
+
+int main(int argc, char **argv)
+{
+  assert(galois_init_default_field(4) == 0);
+  assert(galois_uninit_field(4) == 0);
+  assert(galois_init_default_field(4) == 0);
+  assert(galois_uninit_field(4) == 0);
+
+  assert(galois_init_default_field(8) == 0);
+  assert(galois_uninit_field(8) == 0);
+  assert(galois_init_default_field(8) == 0);
+  assert(galois_uninit_field(8) == 0);
+
+  return 0;
+}
+/*
+ * Local Variables:
+ * compile-command: "make test_galois && 
+ *    libtool --mode=execute valgrind --tool=memcheck --leak-check=full ./test_galois"
+ * End:
+ */

diff --git a/Examples/time_all_gfs_argv_init.sh b/Examples/time_all_gfs_argv_init.sh
new file mode 100755 (executable)
index 0000000..737652a
--- /dev/null
+++ b/Examples/time_all_gfs_argv_init.sh
@@ -0,0 +1,64 @@
+#
+#
+# Copyright (c) 2013, James S. Plank and Kevin Greenan
+# All rights reserved.
+#
+# Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+# Coding Techniques
+#
+# Revision 2.0: Galois Field backend now links to GF-Complete
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+#  - Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+#
+#  - 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.
+#
+#  - Neither the name of the University of Tennessee nor the names of its
+#    contributors may be used to endorse or promote products derived
+#    from this software without specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "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 COPYRIGHT
+# HOLDER OR CONTRIBUTORS 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.
+#
+GF_COMPLETE_DIR=/usr/local/bin
+GF_METHODS=${GF_COMPLETE_DIR}/gf_methods
+ITERATIONS=128
+BUFSIZE=65536
+k=12
+m=3
+seed=1370
+
+for w in 8 16 32 ; do 
+  ${GF_METHODS} $w -B -L | awk -F: '{ if ($1 == "w='$w'") print $2; }' |
+  while read method; do
+    echo "Testing ${k} ${m} ${w} ${seed} ${ITERATIONS} ${BUFSIZE} ${method}"
+    ./reed_sol_time_gf ${k} ${m} ${w} ${seed} ${ITERATIONS} ${BUFSIZE} ${method} | tail -n 2
+    if [[ $? != "0" ]]; then
+      echo "Failed test for ${k} ${m} ${w} ${seed} ${ITERATIONS} ${BUFSIZE} ${method}"
+      exit 1
+    fi
+  done
+
+  if [[ $? == "1" ]]; then
+    exit 1
+  fi
+done
+
+echo "Passed all tests!"

diff --git a/License.txt b/License.txt
new file mode 100644 (file)
index 0000000..20ffbd2
--- /dev/null
+++ b/License.txt
@@ -0,0 +1,37 @@
+
+Copyright (c) 2013, James S. Plank and Kevin Greenan
+All rights reserved.
+
+Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure Coding Techniques
+
+Revision 2.0: Galois Field backend now links to GF-Complete
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+ - Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+
+ - 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.
+
+ - Neither the name of the University of Tennessee nor the names of its
+   contributors may be used to endorse or promote products derived
+   from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"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 COPYRIGHT
+HOLDER OR CONTRIBUTORS 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.
+

diff --git a/Makefile.am b/Makefile.am
new file mode 100644 (file)
index 0000000..e79f464
--- /dev/null
+++ b/Makefile.am
@@ -0,0 +1,5 @@
+# Jerasure Automake file
+
+SUBDIRS = src Examples
+
+EXTRA_DIST = Manual.pdf PERF.txt

diff --git a/NEWS b/NEWS
new file mode 100644 (file)
index 0000000..e69de29

diff --git a/PERF.txt b/PERF.txt
new file mode 100644 (file)
index 0000000..ee27826
--- /dev/null
+++ b/PERF.txt
@@ -0,0 +1,243 @@
+This reflects time_all_gfs_argv_init.sh run on a MacBook Air with 4 GB of memory and a 1.7 GHz Intel Core i5
+
+#uname -a 
+11.4.2 Darwin Kernel Version 11.4.2: Thu Aug 23 16:25:48 PDT 2012; root:xnu-1699.32.7~1/RELEASE_X86_64 x86_64
+
+<Arguments to reed_sol_time_gf> <Throughput MB/s>
+
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diff --git a/README b/README
new file mode 100644 (file)
index 0000000..0a6a9a0
--- /dev/null
+++ b/README
@@ -0,0 +1,92 @@
+This is revision 2.0 of Jerasure.  This is pretty much Jerasure 1.2 without the
+original Galois Field backend.  Version 2.0 links directly to GF-Complete, which
+is more flexible than the original, and *much* faster, because it leverages SIMD
+instructions.
+Authors: James S. Plank (University of Tennessee)
+         Kevin M. Greenan (Box)
+
+------------------------------------------------------------
+
+External Documentation:
+
+The programmer's manual and tutorial is provided in two places:
+
+1.) A copy is hosted on BitBucket at https://bitbucket.org/jimplank/jerasure/downloads/Jerasure-Manual.pdf 
+2.) A copy is also available at http://web.eecs.utk.edu/~plank/plank/papers/UT-EECS-14-721.html
+
+See https://bitbucket.org/jimplank/gf-complete for GF-Complete.
+
+NOTE: You must have GF-Complete installed (or compiled) in order to use Jerasure 2.0.
+
+There are two directories of source code:
+
+The src directory contains the jerasure code.
+The Examples directory contains the example programs.
+
+------------------------------------------------------------
+
+If you do not have Autoconf 2.65 or later installed, you can simply build
+from the tarball distribution:
+
+http://www.kaymgee.com/Kevin_Greenan/Software_files/jerasure.tar.gz
+
+Installing if you are allowed to install GF-Complete on your machine:
+(You can skip the autoreconf step if you're using a tarball distribution.)
+
+1.) Install GF-Complete
+2.) autoreconf --force --install (*skip* if you are building from tarball)
+3.) ./configure
+4.) make
+5.) sudo make install
+
+This will install the library into your machine's lib directory,
+the headers into include, and the example programs into bin.
+
+The configuration process assumes shared objects are searched for in
+/usr/local/lib. If this is not the case on your system, you can specify a
+search path at configuration time. For example:
+  ./configure LD_LIBRARY_PATH=/usr/local/lib
+
+------------------------------------------------------------
+
+Installing if you can compile GF-Complete, but you cannot install it:
+
+1.) Install GF-Complete.  Let's suppose the full path to GF-Complete is
+    in the environment variable  GFP
+2A.) On Linux, set the environment variable LD_LIBRARY_PATH so that it
+     includes $GFP/src/.libs
+2B.) On a mac, set the environment variable DYLD_LIBRARY_PATH so that it
+     includes $GFP/src/.libs
+2.) ./configure LDFLAGS=-L$GFP/src/.libs/ CPPFLAGS=-I$GFP/include
+3.) make
+
+The examples will be in the directory Examples.  The include files will
+be in the directory include, and the library will be called libJerasure.a
+in the directory src/.libs.
+
+------------------------------------------------------------
+
+As long as GF-Complete is installed, Jerasure 2.0 can be used just as previous
+versions.  There is no need to define custom Galois Fields.  Jerasure will
+determine the default field to use, if one is not specified.
+
+If you would like to explore a using a different Galois Field implementation,
+please see the manual.
+
+------------------------------------------------------------
+
+Testing GF-Complete
+
+If the GF-Complete tools are installed in /usr/local/bin
+
+  make check
+
+If the GF-Complete tools are installed elsewhere
+
+  make GF_COMPLETE_DIR=$(pwd)/../gf-complete/tools check
+
+To run some tests with valgrind
+
+  make VALGRIND='valgrind --tool=memcheck --quiet' \
+       GF_COMPLETE_DIR=$(pwd)/../gf-complete/tools \
+       check

diff --git a/configure.ac b/configure.ac
new file mode 100644 (file)
index 0000000..32b7250
--- /dev/null
+++ b/configure.ac
@@ -0,0 +1,54 @@
+# Jerasure autoconf template
+
+AC_PREREQ([2.65])
+AC_INIT([Jerasure], [2.0], [], [],
+        [https://bitbucket.org/jimplank/jerasure])
+AC_CONFIG_SRCDIR([src/jerasure.c])
+AC_CONFIG_HEADERS([include/config.h])
+
+AC_CONFIG_AUX_DIR([build-aux])
+AC_CONFIG_MACRO_DIR([m4])
+
+AM_INIT_AUTOMAKE([1.13 -Wall -Wno-extra-portability])
+
+# Package default C compiler flags.
+dnl This must be before LT_INIT and AC_PROG_CC.
+: ${CFLAGS='-g -O3 -Wall'}
+
+LT_INIT([disable-static])
+
+# Checks for programs.
+AC_PROG_CC
+
+# Checks for libraries.
+AC_CHECK_LIB([gf_complete], [gf_init_easy], [],
+             [AC_MSG_FAILURE(
+               [You need to have gf_complete installed.
+                  gf_complete is available from http://web.eecs.utk.edu/~plank/plank/papers/CS-13-703.html])
+             ])
+
+# Checks for header files.
+AC_CHECK_HEADERS([stddef.h stdint.h stdlib.h string.h sys/time.h unistd.h])
+AC_CHECK_HEADERS([gf_complete.h gf_general.h gf_method.h gf_rand.h])
+
+# Checks for typedefs, structures, and compiler characteristics.
+AC_TYPE_UINT32_T
+AC_TYPE_UINT64_T
+AX_EXT
+
+AC_ARG_ENABLE([sse],
+              AS_HELP_STRING([--disable-sse], [Build without SSE optimizations]),
+              [if   test "x$enableval" = "xno" ; then
+                SIMD_FLAGS=""
+                echo "DISABLED SSE!!!"
+              fi]
+)
+
+# Checks for library functions.
+AC_FUNC_MALLOC
+AC_CHECK_FUNCS([bzero getcwd gettimeofday mkdir strchr strdup strrchr])
+
+AC_CONFIG_FILES([Examples/Makefile
+                 Makefile
+                 src/Makefile])
+AC_OUTPUT

diff --git a/include/cauchy.h b/include/cauchy.h
new file mode 100644 (file)
index 0000000..f8d1ae3
--- /dev/null
+++ b/include/cauchy.h
@@ -0,0 +1,54 @@
+/* *
+ * Copyright (c) 2013, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+#pragma once
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern int *cauchy_original_coding_matrix(int k, int m, int w);
+extern int *cauchy_xy_coding_matrix(int k, int m, int w, int *x, int *y);
+extern void cauchy_improve_coding_matrix(int k, int m, int w, int *matrix);
+extern int *cauchy_good_general_coding_matrix(int k, int m, int w);
+extern int cauchy_n_ones(int n, int w);
+
+#ifdef __cplusplus
+}
+#endif

diff --git a/include/galois.h b/include/galois.h
new file mode 100644 (file)
index 0000000..78e6567
--- /dev/null
+++ b/include/galois.h
@@ -0,0 +1,103 @@
+/* *
+ * Copyright (c) 2013, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+#pragma once
+
+#include <stdint.h>
+#include <gf_complete.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern int galois_init_default_field(int w);
+extern int galois_uninit_field(int w);
+extern void galois_change_technique(gf_t *gf, int w);
+
+extern int galois_single_multiply(int a, int b, int w);
+extern int galois_single_divide(int a, int b, int w);
+extern int galois_inverse(int x, int w);
+
+void galois_region_xor(           char *src,         /* Source Region */
+                                  char *dest,        /* Dest Region (holds result) */
+                                  int nbytes);      /* Number of bytes in region */
+
+/* These multiply regions in w=8, w=16 and w=32.  They are much faster
+   than calling galois_single_multiply.  The regions must be long word aligned. */
+
+void galois_w08_region_multiply(char *region,       /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,       /* Number of bytes in region */
+                                  char *r2,         /* If r2 != NULL, products go here.  
+                                                       Otherwise region is overwritten */
+                                  int add);         /* If (r2 != NULL && add) the produce is XOR'd with r2 */
+
+void galois_w16_region_multiply(char *region,       /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,       /* Number of bytes in region */
+                                  char *r2,         /* If r2 != NULL, products go here.  
+                                                       Otherwise region is overwritten */
+                                  int add);         /* If (r2 != NULL && add) the produce is XOR'd with r2 */
+
+void galois_w32_region_multiply(char *region,       /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,       /* Number of bytes in region */
+                                  char *r2,         /* If r2 != NULL, products go here.  
+                                                       Otherwise region is overwritten */
+                                  int add);         /* If (r2 != NULL && add) the produce is XOR'd with r2 */
+
+gf_t* galois_init_field(int w,
+                             int mult_type,
+                             int region_type,
+                             int divide_type,
+                             uint64_t prim_poly,
+                             int arg1,
+                             int arg2);
+
+gf_t* galois_init_composite_field(int w,
+                                int region_type,
+                                int divide_type,
+                                int degree,
+                                gf_t* base_gf);
+
+gf_t * galois_get_field_ptr(int w);
+
+#ifdef __cplusplus
+}
+#endif

diff --git a/include/jerasure.h b/include/jerasure.h
new file mode 100644 (file)
index 0000000..de874e1
--- /dev/null
+++ b/include/jerasure.h
@@ -0,0 +1,302 @@
+/* *
+ * Copyright (c) 2013, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+#pragma once
+
+#ifndef _JERASURE_H
+#define _JERASURE_H
+
+/* This uses procedures from the Galois Field arithmetic library */
+
+#include "galois.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* ------------------------------------------------------------ */
+/* In all of the routines below:
+
+   k = Number of data devices
+   m = Number of coding devices
+   w = Word size
+
+   data_ptrs = An array of k pointers to data which is size bytes.  
+               Size must be a multiple of sizeof(long).
+               Pointers must also be longword aligned.
+ 
+   coding_ptrs = An array of m pointers to coding data which is size bytes.
+
+   packetsize = The size of a coding block with bitmatrix coding. 
+                When you code with a bitmatrix, you will use w packets
+                of size packetsize.
+
+   matrix = an array of k*m integers.  
+            It represents an m by k matrix.
+            Element i,j is in matrix[i*k+j];
+
+   bitmatrix = an array of k*m*w*w integers.
+            It represents an mw by kw matrix.
+            Element i,j is in matrix[i*k*w+j];
+
+   erasures = an array of id's of erased devices. 
+              Id's are integers between 0 and k+m-1.
+              Id's 0 to k-1 are id's of data devices.
+              Id's k to k+m-1 are id's of coding devices: 
+                  Coding device id = id-k.
+              If there are e erasures, erasures[e] = -1.
+
+   schedule = an array of schedule operations.  
+
+              If there are m operations, then schedule[m][0] = -1.
+
+   operation = an array of 5 integers:
+
+          0 = operation: 0 for copy, 1 for xor (-1 for end)
+          1 = source device (0 - k+m-1)
+          2 = source packet (0 - w-1)
+          3 = destination device (0 - k+m-1)
+          4 = destination packet (0 - w-1)
+ */
+
+/* ---------------------------------------------------------------  */
+/* Bitmatrices / schedules ---------------------------------------- */
+/*
+ - jerasure_matrix_to_bitmatrix turns a m X k matrix in GF(2^w) into a
+                              wm X wk bitmatrix (in GF(2)).  This is
+                              explained in the Cauchy Reed-Solomon coding
+                              paper.
+
+ - jerasure_dumb_bitmatrix_to_schedule turns a bitmatrix into a schedule 
+                              using the straightforward algorithm -- just
+                              schedule the dot products defined by each
+                              row of the matrix.
+
+ - jerasure_smart_bitmatrix_to_schedule turns a bitmatrix into a schedule,
+                              but tries to use previous dot products to
+                              calculate new ones.  This is the optimization
+                              explained in the original Liberation code paper.
+
+ - jerasure_generate_schedule_cache precalcalculate all the schedule for the
+                              given distribution bitmatrix.  M must equal 2.
+ 
+ - jerasure_free_schedule frees a schedule that was allocated with 
+                              jerasure_XXX_bitmatrix_to_schedule.
+ 
+ - jerasure_free_schedule_cache frees a schedule cache that was created with 
+                              jerasure_generate_schedule_cache.
+ */
+
+int *jerasure_matrix_to_bitmatrix(int k, int m, int w, int *matrix);
+int **jerasure_dumb_bitmatrix_to_schedule(int k, int m, int w, int *bitmatrix);
+int **jerasure_smart_bitmatrix_to_schedule(int k, int m, int w, int *bitmatrix);
+int ***jerasure_generate_schedule_cache(int k, int m, int w, int *bitmatrix, int smart);
+
+void jerasure_free_schedule(int **schedule);
+void jerasure_free_schedule_cache(int k, int m, int ***cache);
+
+
+/* ------------------------------------------------------------ */
+/* Encoding - these are all straightforward.  jerasure_matrix_encode only 
+   works with w = 8|16|32.  */
+
+void jerasure_do_parity(int k, char **data_ptrs, char *parity_ptr, int size);
+
+void jerasure_matrix_encode(int k, int m, int w, int *matrix,
+                          char **data_ptrs, char **coding_ptrs, int size);
+
+void jerasure_bitmatrix_encode(int k, int m, int w, int *bitmatrix,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize);
+
+void jerasure_schedule_encode(int k, int m, int w, int **schedule,
+                                  char **data_ptrs, char **coding_ptrs, int size, int packetsize);
+
+/* ------------------------------------------------------------ */
+/* Decoding. -------------------------------------------------- */
+
+/* These return integers, because the matrix may not be invertible. 
+   
+   The parameter row_k_ones should be set to 1 if row k of the matrix
+   (or rows kw to (k+1)w+1) of th distribution matrix are all ones
+   (or all identity matrices).  Then you can improve the performance
+   of decoding when there is more than one failure, and the parity
+   device didn't fail.  You do it by decoding all but one of the data
+   devices, and then decoding the last data device from the data devices
+   and the parity device.
+
+   jerasure_schedule_decode_lazy generates the schedule on the fly.
+
+   jerasure_matrix_decode only works when w = 8|16|32.
+
+   jerasure_make_decoding_matrix/bitmatrix make the k*k decoding matrix
+         (or wk*wk bitmatrix) by taking the rows corresponding to k
+         non-erased devices of the distribution matrix, and then
+         inverting that matrix.
+
+         You should already have allocated the decoding matrix and
+         dm_ids, which is a vector of k integers.  These will be
+         filled in appropriately.  dm_ids[i] is the id of element
+         i of the survivors vector.  I.e. row i of the decoding matrix
+         times dm_ids equals data drive i.
+
+         Both of these routines take "erased" instead of "erasures".
+         Erased is a vector with k+m elements, which has 0 or 1 for 
+         each device's id, according to whether the device is erased.
+ 
+   jerasure_erasures_to_erased allocates and returns erased from erasures.
+    
+ */
+
+int jerasure_matrix_decode(int k, int m, int w, 
+                          int *matrix, int row_k_ones, int *erasures,
+                          char **data_ptrs, char **coding_ptrs, int size);
+                          
+int jerasure_bitmatrix_decode(int k, int m, int w, 
+                            int *bitmatrix, int row_k_ones, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize);
+
+int jerasure_schedule_decode_lazy(int k, int m, int w, int *bitmatrix, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize,
+                            int smart);
+
+int jerasure_schedule_decode_cache(int k, int m, int w, int ***scache, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize);
+
+int jerasure_make_decoding_matrix(int k, int m, int w, int *matrix, int *erased, 
+                                  int *decoding_matrix, int *dm_ids);
+
+int jerasure_make_decoding_bitmatrix(int k, int m, int w, int *matrix, int *erased, 
+                                  int *decoding_matrix, int *dm_ids);
+
+int *jerasure_erasures_to_erased(int k, int m, int *erasures);
+
+/* ------------------------------------------------------------ */
+/* These perform dot products and schedules. -------------------*/
+/*
+   src_ids is a matrix of k id's (0 - k-1 for data devices, k - k+m-1
+   for coding devices) that identify the source devices.  Dest_id is
+   the id of the destination device.
+
+   jerasure_matrix_dotprod only works when w = 8|16|32.
+
+   jerasure_do_scheduled_operations executes the schedule on w*packetsize worth of
+   bytes from each device.  ptrs is an array of pointers which should have as many
+   elements as the highest referenced device in the schedule.
+
+ */
+ 
+void jerasure_matrix_dotprod(int k, int w, int *matrix_row,
+                          int *src_ids, int dest_id,
+                          char **data_ptrs, char **coding_ptrs, int size);
+
+void jerasure_bitmatrix_dotprod(int k, int w, int *bitmatrix_row,
+                             int *src_ids, int dest_id,
+                             char **data_ptrs, char **coding_ptrs, int size, int packetsize);
+
+void jerasure_do_scheduled_operations(char **ptrs, int **schedule, int packetsize);
+
+/* ------------------------------------------------------------ */
+/* Matrix Inversion ------------------------------------------- */
+/*
+   The two matrix inversion functions work on rows*rows matrices of
+   ints.  If a bitmatrix, then each int will just be zero or one.
+   Otherwise, they will be elements of gf(2^w).  Obviously, you can
+   do bit matrices with crs_invert_matrix() and set w = 1, but
+   crs_invert_bitmatrix will be more efficient.
+
+   The two invertible functions return whether a matrix is invertible.
+   They are more efficient than the inverstion functions.
+
+   Mat will be destroyed when the matrix inversion or invertible
+   testing is done.  Sorry.
+
+   Inv must be allocated by the caller.
+
+   The two invert_matrix functions return 0 on success, and -1 if the
+   matrix is uninvertible.
+
+   The two invertible function simply return whether the matrix is
+   invertible.  (0 or 1). Mat will be destroyed.
+ */
+
+int jerasure_invert_matrix(int *mat, int *inv, int rows, int w);
+int jerasure_invert_bitmatrix(int *mat, int *inv, int rows);
+int jerasure_invertible_matrix(int *mat, int rows, int w);
+int jerasure_invertible_bitmatrix(int *mat, int rows);
+
+/* ------------------------------------------------------------ */
+/* Basic matrix operations -------------------------------------*/
+/*
+   Each of the print_matrix routines require a w.  In jerasure_print_matrix,
+   this is to calculate the field width.  In jerasure_print_bitmatrix, it is
+   to put spaces between the bits.
+
+   jerasure_matrix_multiply is a simple matrix multiplier in GF(2^w).  It returns a r1*c2
+   matrix, which is the product of the two input matrices.  It allocates
+   the product.  Obviously, c1 should equal r2.  However, this is not
+   validated by the procedure.  
+*/
+
+void jerasure_print_matrix(int *matrix, int rows, int cols, int w);
+void jerasure_print_bitmatrix(int *matrix, int rows, int cols, int w);
+
+
+int *jerasure_matrix_multiply(int *m1, int *m2, int r1, int c1, int r2, int c2, int w);
+
+/* ------------------------------------------------------------ */
+/* Stats ------------------------------------------------------ */
+/*
+  jerasure_get_stats fills in a vector of three doubles:
+
+      fill_in[0] is the number of bytes that have been XOR'd
+      fill_in[1] is the number of bytes that have been copied
+      fill_in[2] is the number of bytes that have been multiplied
+                 by a constant in GF(2^w)
+
+  When jerasure_get_stats() is called, it resets its values.
+ */
+
+void jerasure_get_stats(double *fill_in);
+
+int jerasure_autoconf_test();
+
+#ifdef __cplusplus
+}
+#endif
+#endif

diff --git a/include/liberation.h b/include/liberation.h
new file mode 100644 (file)
index 0000000..150acb9
--- /dev/null
+++ b/include/liberation.h
@@ -0,0 +1,52 @@
+/* *
+ * Copyright (c) 2013, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+#pragma once
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern int *liberation_coding_bitmatrix(int k, int w);
+extern int *liber8tion_coding_bitmatrix(int k);
+extern int *blaum_roth_coding_bitmatrix(int k, int w);
+
+#ifdef __cplusplus
+}
+#endif

diff --git a/include/reed_sol.h b/include/reed_sol.h
new file mode 100644 (file)
index 0000000..48fc4e6
--- /dev/null
+++ b/include/reed_sol.h
@@ -0,0 +1,59 @@
+/* *
+ * Copyright (c) 2013, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+#pragma once
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern int *reed_sol_vandermonde_coding_matrix(int k, int m, int w);
+extern int *reed_sol_extended_vandermonde_matrix(int rows, int cols, int w);
+extern int *reed_sol_big_vandermonde_distribution_matrix(int rows, int cols, int w);
+
+extern int reed_sol_r6_encode(int k, int w, char **data_ptrs, char **coding_ptrs, int size);
+extern int *reed_sol_r6_coding_matrix(int k, int w);
+
+extern void reed_sol_galois_w08_region_multby_2(char *region, int nbytes);
+extern void reed_sol_galois_w16_region_multby_2(char *region, int nbytes);
+extern void reed_sol_galois_w32_region_multby_2(char *region, int nbytes);
+
+#ifdef __cplusplus
+}
+#endif

diff --git a/include/timing.h b/include/timing.h
new file mode 100644 (file)
index 0000000..b489d0d
--- /dev/null
+++ b/include/timing.h
@@ -0,0 +1,43 @@
+// Timing measurement utilities.
+
+#ifndef JERASURE_INCLUDED__TIMING_H
+#define JERASURE_INCLUDED__TIMING_H
+
+// Define USE_CLOCK to use clock(). Otherwise use gettimeofday().
+#define USE_CLOCK
+
+#ifdef USE_CLOCK
+#include <time.h>
+#else
+#include <sys/time.h>
+#endif
+
+struct timing {
+#ifdef USE_CLOCK
+  clock_t clock;
+#else
+  struct timeval tv;
+#endif
+};
+
+// Get the current time as a double in seconds.
+double
+timing_now(
+  void);
+
+// Set *t to the current time.
+void
+timing_set(
+  struct timing * t);
+
+// Get *t as a double in seconds.
+double
+timing_get(
+  struct timing * t);
+
+// Return *t2 - *t1 as a double in seconds.
+double
+timing_delta(
+  struct timing * t1,
+  struct timing * t2);
+#endif

diff --git a/m4/ax_check_compile_flag.m4 b/m4/ax_check_compile_flag.m4
new file mode 100644 (file)
index 0000000..51df0c0
--- /dev/null
+++ b/m4/ax_check_compile_flag.m4
@@ -0,0 +1,74 @@
+# ===========================================================================
+#   http://www.gnu.org/software/autoconf-archive/ax_check_compile_flag.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_CHECK_COMPILE_FLAG(FLAG, [ACTION-SUCCESS], [ACTION-FAILURE], [EXTRA-FLAGS], [INPUT])
+#
+# DESCRIPTION
+#
+#   Check whether the given FLAG works with the current language's compiler
+#   or gives an error.  (Warnings, however, are ignored)
+#
+#   ACTION-SUCCESS/ACTION-FAILURE are shell commands to execute on
+#   success/failure.
+#
+#   If EXTRA-FLAGS is defined, it is added to the current language's default
+#   flags (e.g. CFLAGS) when the check is done.  The check is thus made with
+#   the flags: "CFLAGS EXTRA-FLAGS FLAG".  This can for example be used to
+#   force the compiler to issue an error when a bad flag is given.
+#
+#   INPUT gives an alternative input source to AC_COMPILE_IFELSE.
+#
+#   NOTE: Implementation based on AX_CFLAGS_GCC_OPTION. Please keep this
+#   macro in sync with AX_CHECK_{PREPROC,LINK}_FLAG.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Guido U. Draheim <guidod@gmx.de>
+#   Copyright (c) 2011 Maarten Bosmans <mkbosmans@gmail.com>
+#
+#   This program is free software: you can redistribute it and/or modify it
+#   under the terms of the GNU General Public License as published by the
+#   Free Software Foundation, either version 3 of the License, or (at your
+#   option) any later version.
+#
+#   This program is distributed in the hope that it will be useful, but
+#   WITHOUT ANY WARRANTY; without even the implied warranty of
+#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
+#   Public License for more details.
+#
+#   You should have received a copy of the GNU General Public License along
+#   with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+#   As a special exception, the respective Autoconf Macro's copyright owner
+#   gives unlimited permission to copy, distribute and modify the configure
+#   scripts that are the output of Autoconf when processing the Macro. You
+#   need not follow the terms of the GNU General Public License when using
+#   or distributing such scripts, even though portions of the text of the
+#   Macro appear in them. The GNU General Public License (GPL) does govern
+#   all other use of the material that constitutes the Autoconf Macro.
+#
+#   This special exception to the GPL applies to versions of the Autoconf
+#   Macro released by the Autoconf Archive. When you make and distribute a
+#   modified version of the Autoconf Macro, you may extend this special
+#   exception to the GPL to apply to your modified version as well.
+
+#serial 3
+
+AC_DEFUN([AX_CHECK_COMPILE_FLAG],
+[AC_PREREQ(2.59)dnl for _AC_LANG_PREFIX
+AS_VAR_PUSHDEF([CACHEVAR],[ax_cv_check_[]_AC_LANG_ABBREV[]flags_$4_$1])dnl
+AC_CACHE_CHECK([whether _AC_LANG compiler accepts $1], CACHEVAR, [
+  ax_check_save_flags=$[]_AC_LANG_PREFIX[]FLAGS
+  _AC_LANG_PREFIX[]FLAGS="$[]_AC_LANG_PREFIX[]FLAGS $4 $1"
+  AC_COMPILE_IFELSE([m4_default([$5],[AC_LANG_PROGRAM()])],
+    [AS_VAR_SET(CACHEVAR,[yes])],
+    [AS_VAR_SET(CACHEVAR,[no])])
+  _AC_LANG_PREFIX[]FLAGS=$ax_check_save_flags])
+AS_IF([test x"AS_VAR_GET(CACHEVAR)" = xyes],
+  [m4_default([$2], :)],
+  [m4_default([$3], :)])
+AS_VAR_POPDEF([CACHEVAR])dnl
+])dnl AX_CHECK_COMPILE_FLAGS

diff --git a/m4/ax_ext.m4 b/m4/ax_ext.m4
new file mode 100644 (file)
index 0000000..70a83bf
--- /dev/null
+++ b/m4/ax_ext.m4
@@ -0,0 +1,247 @@
+#
+# Modified from autoconf-archive to replace AC_REQUIRE([AX_GCC_X86_*]) with
+# AX_REQUIRE_DEFINED(...).
+#
+# ===========================================================================
+#          http://www.gnu.org/software/autoconf-archive/ax_ext.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_EXT
+#
+# DESCRIPTION
+#
+#   Find supported SIMD extensions by requesting cpuid. When an SIMD
+#   extension is found, the -m"simdextensionname" is added to SIMD_FLAGS if
+#   compiler supports it. For example, if "sse2" is available, then "-msse2"
+#   is added to SIMD_FLAGS.
+#
+#   This macro calls:
+#
+#     AC_SUBST(SIMD_FLAGS)
+#
+#   And defines:
+#
+#     HAVE_MMX / HAVE_SSE / HAVE_SSE2 / HAVE_SSE3 / HAVE_SSSE3 / HAVE_SSE4.1 / HAVE_SSE4.2 / HAVE_AVX
+#
+# LICENSE
+#
+#   Copyright (c) 2007 Christophe Tournayre <turn3r@users.sourceforge.net>
+#   Copyright (c) 2013 Michael Petch <mpetch@capp-sysware.com>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 13.1
+
+AC_DEFUN([AX_EXT],
+[
+  AC_REQUIRE([AC_CANONICAL_HOST])
+
+  case $host_cpu in
+    powerpc*)
+      AC_CACHE_CHECK([whether altivec is supported], [ax_cv_have_altivec_ext],
+          [
+            if test `/usr/sbin/sysctl -a 2>/dev/null| grep -c hw.optional.altivec` != 0; then
+                if test `/usr/sbin/sysctl -n hw.optional.altivec` = 1; then
+                  ax_cv_have_altivec_ext=yes
+                fi
+            fi
+          ])
+
+          if test "$ax_cv_have_altivec_ext" = yes; then
+            AC_DEFINE(HAVE_ALTIVEC,,[Support Altivec instructions])
+            AX_CHECK_COMPILE_FLAG(-faltivec, SIMD_FLAGS="$SIMD_FLAGS -faltivec", [])
+          fi
+    ;;
+
+
+    i[[3456]]86*|x86_64*|amd64*)
+
+      AX_REQUIRE_DEFINED([AX_GCC_X86_CPUID])
+      AX_REQUIRE_DEFINED([AX_GCC_X86_AVX_XGETBV])
+
+      AX_GCC_X86_CPUID(0x00000001)
+      ecx=0
+      edx=0
+      if test "$ax_cv_gcc_x86_cpuid_0x00000001" != "unknown";
+      then
+        ecx=`echo $ax_cv_gcc_x86_cpuid_0x00000001 | cut -d ":" -f 3`
+        edx=`echo $ax_cv_gcc_x86_cpuid_0x00000001 | cut -d ":" -f 4`
+      fi
+
+      AC_CACHE_CHECK([whether mmx is supported], [ax_cv_have_mmx_ext],
+      [
+        ax_cv_have_mmx_ext=no
+        if test "$((0x$edx>>23&0x01))" = 1; then
+          ax_cv_have_mmx_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether sse is supported], [ax_cv_have_sse_ext],
+      [
+        ax_cv_have_sse_ext=no
+        if test "$((0x$edx>>25&0x01))" = 1; then
+          ax_cv_have_sse_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether sse2 is supported], [ax_cv_have_sse2_ext],
+      [
+        ax_cv_have_sse2_ext=no
+        if test "$((0x$edx>>26&0x01))" = 1; then
+          ax_cv_have_sse2_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether sse3 is supported], [ax_cv_have_sse3_ext],
+      [
+        ax_cv_have_sse3_ext=no
+        if test "$((0x$ecx&0x01))" = 1; then
+          ax_cv_have_sse3_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether ssse3 is supported], [ax_cv_have_ssse3_ext],
+      [
+        ax_cv_have_ssse3_ext=no
+        if test "$((0x$ecx>>9&0x01))" = 1; then
+          ax_cv_have_ssse3_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether sse4.1 is supported], [ax_cv_have_sse41_ext],
+      [
+        ax_cv_have_sse41_ext=no
+        if test "$((0x$ecx>>19&0x01))" = 1; then
+          ax_cv_have_sse41_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether sse4.2 is supported], [ax_cv_have_sse42_ext],
+      [
+        ax_cv_have_sse42_ext=no
+        if test "$((0x$ecx>>20&0x01))" = 1; then
+          ax_cv_have_sse42_ext=yes
+        fi
+      ])
+
+      AC_CACHE_CHECK([whether avx is supported by processor], [ax_cv_have_avx_cpu_ext],
+      [
+        ax_cv_have_avx_cpu_ext=no
+        if test "$((0x$ecx>>28&0x01))" = 1; then
+          ax_cv_have_avx_cpu_ext=yes
+        fi
+      ])
+
+      if test x"$ax_cv_have_avx_cpu_ext" = x"yes"; then
+        AX_GCC_X86_AVX_XGETBV(0x00000000)
+
+        xgetbv_eax="0"
+        if test x"$ax_cv_gcc_x86_avx_xgetbv_0x00000000" != x"unknown"; then
+          xgetbv_eax=`echo $ax_cv_gcc_x86_avx_xgetbv_0x00000000 | cut -d ":" -f 1`
+        fi
+
+        AC_CACHE_CHECK([whether avx is supported by operating system], [ax_cv_have_avx_ext],
+        [
+          ax_cv_have_avx_ext=no
+
+          if test "$((0x$ecx>>27&0x01))" = 1; then
+            if test "$((0x$xgetbv_eax&0x6))" = 6; then
+              ax_cv_have_avx_ext=yes
+            fi
+          fi
+        ])
+        if test x"$ax_cv_have_avx_ext" = x"no"; then
+          AC_MSG_WARN([Your processor supports AVX, but your operating system doesn't])
+        fi
+      fi
+
+      if test "$ax_cv_have_mmx_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-mmmx, ax_cv_support_mmx_ext=yes, [])
+        if test x"$ax_cv_support_mmx_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -mmmx"
+          AC_DEFINE(HAVE_MMX,,[Support mmx instructions])
+        else
+          AC_MSG_WARN([Your processor supports mmx instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_sse_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-msse, ax_cv_support_sse_ext=yes, [])
+        if test x"$ax_cv_support_sse_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -msse"
+          AC_DEFINE(HAVE_SSE,,[Support SSE (Streaming SIMD Extensions) instructions])
+        else
+          AC_MSG_WARN([Your processor supports sse instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_sse2_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-msse2, ax_cv_support_sse2_ext=yes, [])
+        if test x"$ax_cv_support_sse2_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -msse2"
+          AC_DEFINE(HAVE_SSE2,,[Support SSE2 (Streaming SIMD Extensions 2) instructions])
+        else
+          AC_MSG_WARN([Your processor supports sse2 instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_sse3_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-msse3, ax_cv_support_sse3_ext=yes, [])
+        if test x"$ax_cv_support_sse3_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -msse3"
+          AC_DEFINE(HAVE_SSE3,,[Support SSE3 (Streaming SIMD Extensions 3) instructions])
+        else
+          AC_MSG_WARN([Your processor supports sse3 instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_ssse3_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-mssse3, ax_cv_support_ssse3_ext=yes, [])
+        if test x"$ax_cv_support_ssse3_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -mssse3"
+          AC_DEFINE(HAVE_SSSE3,,[Support SSSE3 (Supplemental Streaming SIMD Extensions 3) instructions])
+        else
+          AC_MSG_WARN([Your processor supports ssse3 instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_sse41_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-msse4.1, ax_cv_support_sse41_ext=yes, [])
+        if test x"$ax_cv_support_sse41_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -msse4.1"
+          AC_DEFINE(HAVE_SSE4_1,,[Support SSSE4.1 (Streaming SIMD Extensions 4.1) instructions])
+        else
+          AC_MSG_WARN([Your processor supports sse4.1 instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_sse42_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-msse4.2, ax_cv_support_sse42_ext=yes, [])
+        if test x"$ax_cv_support_sse42_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -msse4.2"
+          AC_DEFINE(HAVE_SSE4_2,,[Support SSSE4.2 (Streaming SIMD Extensions 4.2) instructions])
+        else
+          AC_MSG_WARN([Your processor supports sse4.2 instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+      if test "$ax_cv_have_avx_ext" = yes; then
+        AX_CHECK_COMPILE_FLAG(-mavx, ax_cv_support_avx_ext=yes, [])
+        if test x"$ax_cv_support_avx_ext" = x"yes"; then
+          SIMD_FLAGS="$SIMD_FLAGS -mavx"
+          AC_DEFINE(HAVE_AVX,,[Support AVX (Advanced Vector Extensions) instructions])
+        else
+          AC_MSG_WARN([Your processor supports avx instructions but not your compiler, can you try another compiler?])
+        fi
+      fi
+
+  ;;
+  esac
+
+  AC_SUBST(SIMD_FLAGS)
+])

diff --git a/m4/ax_gcc_x86_avx_xgetbv.m4 b/m4/ax_gcc_x86_avx_xgetbv.m4
new file mode 100644 (file)
index 0000000..0624eeb
--- /dev/null
+++ b/m4/ax_gcc_x86_avx_xgetbv.m4
@@ -0,0 +1,79 @@
+# ===========================================================================
+#   http://www.gnu.org/software/autoconf-archive/ax_gcc_x86_avx_xgetbv.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_GCC_X86_AVX_XGETBV
+#
+# DESCRIPTION
+#
+#   On later x86 processors with AVX SIMD support, with gcc or a compiler
+#   that has a compatible syntax for inline assembly instructions, run a
+#   small program that executes the xgetbv instruction with input OP. This
+#   can be used to detect if the OS supports AVX instruction usage.
+#
+#   On output, the values of the eax and edx registers are stored as
+#   hexadecimal strings as "eax:edx" in the cache variable
+#   ax_cv_gcc_x86_avx_xgetbv.
+#
+#   If the xgetbv instruction fails (because you are running a
+#   cross-compiler, or because you are not using gcc, or because you are on
+#   a processor that doesn't have this instruction),
+#   ax_cv_gcc_x86_avx_xgetbv_OP is set to the string "unknown".
+#
+#   This macro mainly exists to be used in AX_EXT.
+#
+# LICENSE
+#
+#   Copyright (c) 2013 Michael Petch <mpetch@capp-sysware.com>
+#
+#   This program is free software: you can redistribute it and/or modify it
+#   under the terms of the GNU General Public License as published by the
+#   Free Software Foundation, either version 3 of the License, or (at your
+#   option) any later version.
+#
+#   This program is distributed in the hope that it will be useful, but
+#   WITHOUT ANY WARRANTY; without even the implied warranty of
+#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
+#   Public License for more details.
+#
+#   You should have received a copy of the GNU General Public License along
+#   with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+#   As a special exception, the respective Autoconf Macro's copyright owner
+#   gives unlimited permission to copy, distribute and modify the configure
+#   scripts that are the output of Autoconf when processing the Macro. You
+#   need not follow the terms of the GNU General Public License when using
+#   or distributing such scripts, even though portions of the text of the
+#   Macro appear in them. The GNU General Public License (GPL) does govern
+#   all other use of the material that constitutes the Autoconf Macro.
+#
+#   This special exception to the GPL applies to versions of the Autoconf
+#   Macro released by the Autoconf Archive. When you make and distribute a
+#   modified version of the Autoconf Macro, you may extend this special
+#   exception to the GPL to apply to your modified version as well.
+
+#serial 1
+
+AC_DEFUN([AX_GCC_X86_AVX_XGETBV],
+[AC_REQUIRE([AC_PROG_CC])
+AC_LANG_PUSH([C])
+AC_CACHE_CHECK(for x86-AVX xgetbv $1 output, ax_cv_gcc_x86_avx_xgetbv_$1,
+ [AC_RUN_IFELSE([AC_LANG_PROGRAM([#include <stdio.h>], [
+     int op = $1, eax, edx;
+     FILE *f;
+      /* Opcodes for xgetbv */
+      __asm__(".byte 0x0f, 0x01, 0xd0"
+        : "=a" (eax), "=d" (edx)
+        : "c" (op));
+     f = fopen("conftest_xgetbv", "w"); if (!f) return 1;
+     fprintf(f, "%x:%x\n", eax, edx);
+     fclose(f);
+     return 0;
+])],
+     [ax_cv_gcc_x86_avx_xgetbv_$1=`cat conftest_xgetbv`; rm -f conftest_xgetbv],
+     [ax_cv_gcc_x86_avx_xgetbv_$1=unknown; rm -f conftest_xgetbv],
+     [ax_cv_gcc_x86_avx_xgetbv_$1=unknown])])
+AC_LANG_POP([C])
+])

diff --git a/m4/ax_gcc_x86_cpuid.m4 b/m4/ax_gcc_x86_cpuid.m4
new file mode 100644 (file)
index 0000000..7d46fee
--- /dev/null
+++ b/m4/ax_gcc_x86_cpuid.m4
@@ -0,0 +1,79 @@
+# ===========================================================================
+#     http://www.gnu.org/software/autoconf-archive/ax_gcc_x86_cpuid.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_GCC_X86_CPUID(OP)
+#
+# DESCRIPTION
+#
+#   On Pentium and later x86 processors, with gcc or a compiler that has a
+#   compatible syntax for inline assembly instructions, run a small program
+#   that executes the cpuid instruction with input OP. This can be used to
+#   detect the CPU type.
+#
+#   On output, the values of the eax, ebx, ecx, and edx registers are stored
+#   as hexadecimal strings as "eax:ebx:ecx:edx" in the cache variable
+#   ax_cv_gcc_x86_cpuid_OP.
+#
+#   If the cpuid instruction fails (because you are running a
+#   cross-compiler, or because you are not using gcc, or because you are on
+#   a processor that doesn't have this instruction), ax_cv_gcc_x86_cpuid_OP
+#   is set to the string "unknown".
+#
+#   This macro mainly exists to be used in AX_GCC_ARCHFLAG.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Steven G. Johnson <stevenj@alum.mit.edu>
+#   Copyright (c) 2008 Matteo Frigo
+#
+#   This program is free software: you can redistribute it and/or modify it
+#   under the terms of the GNU General Public License as published by the
+#   Free Software Foundation, either version 3 of the License, or (at your
+#   option) any later version.
+#
+#   This program is distributed in the hope that it will be useful, but
+#   WITHOUT ANY WARRANTY; without even the implied warranty of
+#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
+#   Public License for more details.
+#
+#   You should have received a copy of the GNU General Public License along
+#   with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+#   As a special exception, the respective Autoconf Macro's copyright owner
+#   gives unlimited permission to copy, distribute and modify the configure
+#   scripts that are the output of Autoconf when processing the Macro. You
+#   need not follow the terms of the GNU General Public License when using
+#   or distributing such scripts, even though portions of the text of the
+#   Macro appear in them. The GNU General Public License (GPL) does govern
+#   all other use of the material that constitutes the Autoconf Macro.
+#
+#   This special exception to the GPL applies to versions of the Autoconf
+#   Macro released by the Autoconf Archive. When you make and distribute a
+#   modified version of the Autoconf Macro, you may extend this special
+#   exception to the GPL to apply to your modified version as well.
+
+#serial 7
+
+AC_DEFUN([AX_GCC_X86_CPUID],
+[AC_REQUIRE([AC_PROG_CC])
+AC_LANG_PUSH([C])
+AC_CACHE_CHECK(for x86 cpuid $1 output, ax_cv_gcc_x86_cpuid_$1,
+ [AC_RUN_IFELSE([AC_LANG_PROGRAM([#include <stdio.h>], [
+     int op = $1, eax, ebx, ecx, edx;
+     FILE *f;
+      __asm__("cpuid"
+        : "=a" (eax), "=b" (ebx), "=c" (ecx), "=d" (edx)
+        : "a" (op));
+     f = fopen("conftest_cpuid", "w"); if (!f) return 1;
+     fprintf(f, "%x:%x:%x:%x\n", eax, ebx, ecx, edx);
+     fclose(f);
+     return 0;
+])],
+     [ax_cv_gcc_x86_cpuid_$1=`cat conftest_cpuid`; rm -f conftest_cpuid],
+     [ax_cv_gcc_x86_cpuid_$1=unknown; rm -f conftest_cpuid],
+     [ax_cv_gcc_x86_cpuid_$1=unknown])])
+AC_LANG_POP([C])
+])

diff --git a/m4/ax_require_defined.m4 b/m4/ax_require_defined.m4
new file mode 100644 (file)
index 0000000..cae1111
--- /dev/null
+++ b/m4/ax_require_defined.m4
@@ -0,0 +1,37 @@
+# ===========================================================================
+#    http://www.gnu.org/software/autoconf-archive/ax_require_defined.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_REQUIRE_DEFINED(MACRO)
+#
+# DESCRIPTION
+#
+#   AX_REQUIRE_DEFINED is a simple helper for making sure other macros have
+#   been defined and thus are available for use.  This avoids random issues
+#   where a macro isn't expanded.  Instead the configure script emits a
+#   non-fatal:
+#
+#     ./configure: line 1673: AX_CFLAGS_WARN_ALL: command not found
+#
+#   It's like AC_REQUIRE except it doesn't expand the required macro.
+#
+#   Here's an example:
+#
+#     AX_REQUIRE_DEFINED([AX_CHECK_LINK_FLAG])
+#
+# LICENSE
+#
+#   Copyright (c) 2014 Mike Frysinger <vapier@gentoo.org>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 1
+
+AC_DEFUN([AX_REQUIRE_DEFINED], [dnl
+  m4_ifndef([$1], [m4_fatal([macro ]$1[ is not defined; is a m4 file missing?])])
+])dnl AX_REQUIRE_DEFINED

diff --git a/src/Makefile.am b/src/Makefile.am
new file mode 100644 (file)
index 0000000..070f545
--- /dev/null
+++ b/src/Makefile.am
@@ -0,0 +1,22 @@
+# Jerasure AM file
+
+AM_CPPFLAGS = -I$(top_srcdir)/include
+AM_CFLAGS = $(SIMD_FLAGS)
+
+lib_LTLIBRARIES = libJerasure.la
+libJerasure_la_SOURCES = galois.c jerasure.c reed_sol.c cauchy.c liberation.c
+libJerasure_la_LDFLAGS = -version-info 2:0:0
+libJerasure_la_LIBADD = -lgf_complete
+include_HEADERS = ../include/jerasure.h
+
+# Install additional Jerasure header files in their own directory.
+jerasureincludedir = $(includedir)/jerasure
+jerasureinclude_HEADERS = \
+  ../include/cauchy.h \
+  ../include/galois.h \
+  ../include/liberation.h \
+  ../include/reed_sol.h
+
+noinst_HEADERS = ../include/timing.h
+noinst_LIBRARIES = libtiming.a
+libtiming_a_SOURCES = timing.c

diff --git a/src/cauchy.c b/src/cauchy.c
new file mode 100644 (file)
index 0000000..f63dfb7
--- /dev/null
+++ b/src/cauchy.c
@@ -0,0 +1,405 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "galois.h"
+#include "jerasure.h"
+#include "cauchy.h"
+
+static int PPs[33] = { -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1, -1 };
+static int NOs[33];
+static int ONEs[33][33];
+
+static int *cbest_0;
+static int *cbest_1;
+static int cbest_2[3];
+static int cbest_3[7];
+static int cbest_4[15];
+static int cbest_5[31];
+static int cbest_6[63];
+static int cbest_7[127];
+static int cbest_8[255];
+static int cbest_9[511];
+static int cbest_10[1023];
+static int cbest_11[1023];
+static int *cbest_12, *cbest_13, *cbest_14, *cbest_15, *cbest_16, *cbest_17, *cbest_18, *cbest_19, *cbest_20,
+           *cbest_21, *cbest_22, *cbest_23, *cbest_24, *cbest_25, *cbest_26, *cbest_27, *cbest_28, *cbest_29, *cbest_30,
+           *cbest_31, *cbest_32;
+
+static int cbest_max_k[33] = { -1, -1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 1023, -1,
+     -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+     -1, -1, -1, -1 };
+
+static int cbest_init = 0;
+
+static int *cbest_all[33];
+
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+int cauchy_n_ones(int n, int w)
+{
+  int no;
+  int cno;
+  int nones;
+  int i, j;
+  int highbit;
+
+  highbit = (1 << (w-1));
+
+  if (PPs[w] == -1) {
+    nones = 0;
+    PPs[w] = galois_single_multiply(highbit, 2, w);
+    for (i = 0; i < w; i++) {
+      if (PPs[w] & (1 << i)) {
+        ONEs[w][nones] = (1 << i);
+        nones++;
+      }
+    }
+    NOs[w] = nones;
+  }
+
+  no = 0;
+  for (i = 0; i < w; i++) if (n & (1 << i)) no++;
+  cno = no;
+  for (i = 1; i < w; i++) {
+    if (n & highbit) {
+      n ^= highbit;
+      n <<= 1;
+      n ^= PPs[w];
+      cno--;
+      for (j = 0; j < NOs[w]; j++) {
+        cno += (n & ONEs[w][j]) ? 1 : -1;
+      }
+    } else {
+      n <<= 1;
+    } 
+    no += cno;
+  }
+  return no;
+}
+  
+int *cauchy_original_coding_matrix(int k, int m, int w)
+{
+  int *matrix;
+  int i, j, index;
+
+  if (w < 31 && (k+m) > (1 << w)) return NULL;
+  matrix = talloc(int, k*m);
+  if (matrix == NULL) return NULL;
+  index = 0;
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[index] = galois_single_divide(1, (i ^ (m+j)), w);
+      index++;
+    }
+  }
+  return matrix;
+}
+
+int *cauchy_xy_coding_matrix(int k, int m, int w, int *X, int *Y)
+{
+  int index, i, j;
+  int *matrix;
+
+  matrix = talloc(int, k*m);
+  if (matrix == NULL) { return NULL; }
+  index = 0;
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[index] = galois_single_divide(1, (X[i] ^ Y[j]), w);
+      index++;
+    }
+  }
+  return matrix;
+}
+
+void cauchy_improve_coding_matrix(int k, int m, int w, int *matrix)
+{
+  int index, i, j, x;
+  int tmp;
+  int bno, tno, bno_index;
+
+  for (j = 0; j < k; j++) {
+    if (matrix[j] != 1) {
+      tmp = galois_single_divide(1, matrix[j], w);
+      index = j;
+      for (i = 0; i < m; i++) {
+        matrix[index] = galois_single_multiply(matrix[index], tmp, w);
+        index += k;
+      }
+    }
+  }
+  for (i = 1; i < m; i++) {
+    bno = 0;
+    index = i*k;
+    for (j = 0; j < k; j++) bno += cauchy_n_ones(matrix[index+j], w);
+    bno_index = -1;
+    for (j = 0; j < k; j++) {
+      if (matrix[index+j] != 1) {
+        tmp = galois_single_divide(1, matrix[index+j], w);
+        tno = 0;
+        for (x = 0; x < k; x++) {
+          tno += cauchy_n_ones(galois_single_multiply(matrix[index+x], tmp, w), w);
+        }
+        if (tno < bno) {
+          bno = tno;
+          bno_index = j;
+        }
+      }
+    }
+    if (bno_index != -1) {
+      tmp = galois_single_divide(1, matrix[index+bno_index], w);
+      for (j = 0; j < k; j++) {
+        matrix[index+j] = galois_single_multiply(matrix[index+j], tmp, w);
+      }
+    }
+  }
+}
+
+int *cauchy_good_general_coding_matrix(int k, int m, int w)
+{
+  int *matrix, i;
+
+  if (m == 2 && k <= cbest_max_k[w]) {
+    matrix = talloc(int, k*m);
+    if (matrix == NULL) return NULL;
+    if (!cbest_init) {
+      cbest_init = 1;
+      cbest_all[0] = cbest_0; cbest_all[1] = cbest_1; cbest_all[2] = cbest_2; cbest_all[3] = cbest_3; cbest_all[4] =
+      cbest_4; cbest_all[5] = cbest_5; cbest_all[6] = cbest_6; cbest_all[7] = cbest_7; cbest_all[8] = cbest_8;
+      cbest_all[9] = cbest_9; cbest_all[10] = cbest_10; cbest_all[11] = cbest_11; cbest_all[12] = cbest_12;
+      cbest_all[13] = cbest_13; cbest_all[14] = cbest_14; cbest_all[15] = cbest_15; cbest_all[16] = cbest_16;
+      cbest_all[17] = cbest_17; cbest_all[18] = cbest_18; cbest_all[19] = cbest_19; cbest_all[20] = cbest_20;
+      cbest_all[21] = cbest_21; cbest_all[22] = cbest_22; cbest_all[23] = cbest_23; cbest_all[24] = cbest_24;
+      cbest_all[25] = cbest_25; cbest_all[26] = cbest_26; cbest_all[27] = cbest_27; cbest_all[28] = cbest_28;
+      cbest_all[29] = cbest_29; cbest_all[30] = cbest_30; cbest_all[31] = cbest_31; cbest_all[32] = (int *) cbest_32;
+    }
+    for (i = 0; i < k; i++) {
+      matrix[i] = 1;
+      matrix[i+k] = cbest_all[w][i];
+    }
+    return matrix;
+  } else {
+    matrix = cauchy_original_coding_matrix(k, m, w);
+    if (matrix == NULL) return NULL;
+    cauchy_improve_coding_matrix(k, m, w, matrix);
+    return matrix;
+  }
+}
+
+static int cbest_2[3] = { 1, 2, 3 };
+static int cbest_3[7] = { 1, 2, 5, 4, 7, 3, 6 };
+
+static int cbest_4[15] = { 1, 2, 9, 4, 8, 13, 3, 6, 12, 5, 11, 15, 10, 14, 7 };
+
+static int cbest_5[31] = { 1, 2, 18, 4, 9, 8, 22, 16, 3, 11, 19, 5, 10, 6, 20, 27, 13, 23, 26, 12,
+    17, 25, 24, 31, 30, 7, 15, 21, 29, 14, 28 };
+
+static int cbest_6[63] = { 1, 2, 33, 4, 8, 49, 16, 32, 57, 3, 6, 12, 24, 48, 5, 35, 9, 37, 10, 17,
+    41, 51, 56, 61, 18, 28, 53, 14, 20, 34, 7, 13, 25, 36, 59, 26, 39, 40, 45, 50, 60, 52, 63,
+    11, 30, 55, 19, 22, 29, 43, 58, 15, 21, 38, 44, 47, 62, 27, 54, 42, 31, 23, 46 };
+
+static int cbest_7[127] = { 1, 2, 68, 4, 34, 8, 17, 16, 76, 32, 38, 3, 64, 69, 5, 19, 35, 70, 6, 9,
+    18, 102, 10, 36, 85, 12, 21, 42, 51, 72, 77, 84, 20, 25, 33, 50, 78, 98, 24, 39, 49, 100, 110
+   , 48, 65, 93, 40, 66, 71, 92, 7, 46, 55, 87, 96, 103, 106, 11, 23, 37, 54, 81, 86, 108, 13,
+    22, 27, 43, 53, 73, 80, 14, 26, 52, 74, 79, 99, 119, 44, 95, 101, 104, 111, 118, 29, 59, 89,
+    94, 117, 28, 41, 58, 67, 88, 115, 116, 47, 57, 83, 97, 107, 114, 127, 56, 82, 109, 113, 126,
+    112, 125, 15, 63, 75, 123, 124, 31, 45, 62, 91, 105, 122, 30, 61, 90, 121, 60, 120 };
+
+static int cbest_8[255] = { 1, 2, 142, 4, 71, 8, 70, 173, 3, 35, 143, 16, 17, 67, 134, 140, 172, 6, 34
+   , 69, 201, 216, 5, 33, 86, 12, 65, 138, 158, 159, 175, 10, 32, 43, 66, 108, 130, 193, 234, 9,
+    24, 25, 50, 68, 79, 100, 132, 174, 200, 217, 20, 21, 42, 48, 87, 169, 41, 54, 64, 84, 96, 117
+   , 154, 155, 165, 226, 77, 82, 135, 136, 141, 168, 192, 218, 238, 7, 18, 19, 39, 40, 78, 113,
+    116, 128, 164, 180, 195, 205, 220, 232, 14, 26, 27, 58, 109, 156, 157, 203, 235, 13, 28, 29, 38
+   , 51, 56, 75, 85, 90, 101, 110, 112, 139, 171, 11, 37, 49, 52, 76, 83, 102, 119, 131, 150, 151
+   , 167, 182, 184, 188, 197, 219, 224, 45, 55, 80, 94, 97, 133, 170, 194, 204, 221, 227, 236, 36,
+    47, 73, 92, 98, 104, 118, 152, 153, 166, 202, 207, 239, 251, 22, 23, 44, 74, 91, 148, 149, 161
+   , 181, 190, 233, 46, 59, 88, 137, 146, 147, 163, 196, 208, 212, 222, 250, 57, 81, 95, 106, 111,
+    129, 160, 176, 199, 243, 249, 15, 53, 72, 93, 103, 115, 125, 162, 183, 185, 189, 206, 225, 255,
+    186, 210, 230, 237, 242, 248, 30, 31, 62, 89, 99, 105, 114, 121, 124, 178, 209, 213, 223, 228,
+    241, 254, 60, 191, 198, 247, 120, 240, 107, 127, 144, 145, 177, 211, 214, 246, 245, 123, 126,
+    187, 231, 253, 63, 179, 229, 244, 61, 122, 215, 252 };
+
+static int cbest_9[511] = { 1, 2, 264, 4, 132, 8, 66, 16, 33, 32, 280, 64, 140, 128, 3, 70, 265, 5,
+    133, 256, 266, 6, 9, 35, 67, 134, 268, 396, 10, 17, 34, 330, 12, 18, 68, 198, 297, 20, 37, 74
+   , 136, 148, 165, 281, 296, 24, 36, 41, 65, 82, 99, 164, 272, 282, 388, 40, 49, 98, 141, 194,
+    284, 328, 412, 48, 97, 129, 142, 196, 346, 71, 72, 96, 130, 313, 392, 80, 206, 257, 267, 312,
+    334, 7, 135, 156, 173, 192, 258, 269, 397, 404, 11, 78, 144, 161, 172, 260, 270, 299, 331, 344,
+    398, 13, 19, 39, 69, 86, 103, 160, 167, 199, 202, 298, 322, 384, 14, 21, 38, 43, 75, 102, 137,
+    149, 166, 204, 289, 332, 408, 462, 22, 25, 42, 51, 83, 101, 138, 150, 273, 283, 288, 301, 350,
+    389, 429, 26, 50, 76, 100, 195, 274, 285, 300, 329, 363, 390, 413, 428, 28, 45, 84, 143, 197,
+    200, 214, 231, 276, 286, 315, 320, 347, 362, 414, 458, 44, 53, 73, 90, 107, 131, 152, 169, 181,
+    230, 314, 338, 361, 393, 400, 454, 460, 52, 57, 81, 106, 115, 168, 175, 180, 207, 229, 305, 335
+   , 348, 360, 394, 421, 478, 56, 105, 114, 157, 163, 174, 193, 210, 227, 228, 259, 304, 317, 326,
+    405, 420, 445, 79, 104, 113, 145, 158, 162, 212, 226, 261, 271, 316, 345, 379, 399, 406, 444,
+    450, 456, 87, 88, 112, 146, 203, 225, 262, 291, 323, 336, 378, 385, 425, 452, 474, 15, 205, 222
+   , 224, 239, 290, 303, 333, 367, 377, 386, 409, 424, 431, 463, 470, 476, 23, 139, 151, 189, 208,
+    238, 302, 324, 351, 366, 376, 410, 430, 437, 27, 47, 77, 94, 111, 177, 188, 237, 275, 293, 342,
+    365, 391, 436, 448, 29, 46, 55, 85, 110, 119, 171, 176, 183, 201, 215, 218, 235, 236, 277, 287,
+    292, 321, 355, 364, 415, 417, 459, 466, 472, 30, 54, 59, 91, 109, 118, 153, 170, 182, 220, 234,
+    278, 307, 339, 354, 401, 416, 423, 441, 455, 461, 468, 495, 58, 108, 117, 154, 233, 306, 319,
+    349, 353, 383, 395, 402, 422, 440, 447, 479, 494, 92, 116, 211, 232, 318, 327, 340, 352, 382,
+    446, 493, 61, 159, 213, 216, 247, 309, 381, 407, 427, 451, 457, 464, 491, 492, 60, 89, 123, 147
+   , 185, 246, 263, 308, 337, 371, 380, 426, 433, 453, 475, 487, 490, 122, 184, 191, 223, 245, 370,
+    387, 432, 439, 471, 477, 486, 489, 511, 121, 179, 190, 209, 243, 244, 295, 325, 359, 369, 411,
+    438, 485, 488, 510, 95, 120, 178, 242, 294, 343, 358, 368, 419, 449, 483, 484, 509, 219, 241,
+    357, 418, 443, 467, 473, 482, 507, 508, 31, 221, 240, 255, 279, 356, 442, 469, 481, 503, 506,
+    155, 254, 403, 480, 502, 505, 63, 93, 127, 253, 311, 341, 375, 501, 504, 62, 126, 187, 217, 251
+   , 252, 310, 374, 435, 465, 499, 500, 125, 186, 250, 373, 434, 498, 124, 249, 372, 497, 248, 496
+    };
+
+static int cbest_10[1023] = { 1, 2, 516, 4, 258, 8, 129, 16, 32, 580, 64, 128, 290, 145, 256, 3, 512,
+    517, 5, 259, 518, 588, 6, 9, 18, 36, 72, 144, 774, 10, 17, 131, 262, 288, 524, 645, 12, 33,
+    133, 266, 294, 387, 532, 576, 581, 20, 34, 65, 137, 274, 548, 582, 24, 66, 291, 838, 40, 68,
+    130, 147, 161, 322, 644, 709, 806, 48, 132, 193, 257, 386, 596, 80, 136, 298, 419, 612, 661, 772
+   , 96, 149, 260, 272, 306, 403, 513, 146, 153, 160, 264, 292, 385, 514, 519, 544, 584, 589, 708,
+    870, 7, 19, 37, 73, 192, 354, 590, 770, 775, 11, 38, 74, 177, 263, 289, 418, 520, 525, 534, 641
+   , 660, 725, 802, 836, 846, 13, 22, 76, 148, 209, 267, 295, 320, 330, 402, 526, 528, 533, 577,
+    647, 717, 804, 14, 21, 26, 35, 44, 135, 152, 165, 201, 275, 304, 384, 401, 435, 549, 578, 583,
+    604, 608, 782, 903, 25, 52, 67, 88, 139, 270, 296, 391, 417, 550, 620, 653, 790, 834, 839, 41,
+    50, 69, 104, 141, 176, 278, 302, 323, 395, 423, 540, 598, 640, 705, 724, 807, 866, 28, 42, 49,
+    70, 82, 100, 163, 208, 282, 310, 556, 592, 597, 646, 663, 677, 711, 716, 868, 878, 81, 134, 151
+   , 164, 195, 200, 299, 326, 352, 362, 400, 434, 564, 613, 657, 768, 773, 902, 967, 97, 138, 155,
+    169, 197, 261, 273, 307, 358, 390, 416, 433, 451, 614, 652, 733, 800, 814, 844, 854, 935, 56, 84
+   , 98, 140, 181, 217, 265, 293, 328, 338, 394, 422, 515, 545, 585, 704, 788, 822, 871, 919, 162,
+    179, 276, 355, 407, 427, 546, 586, 591, 616, 662, 669, 676, 710, 727, 741, 771, 780, 901, 39, 75
+   , 150, 157, 194, 211, 225, 268, 280, 308, 314, 389, 411, 439, 521, 530, 535, 628, 656, 721, 803,
+    832, 837, 842, 847, 966, 23, 77, 112, 154, 168, 196, 300, 321, 331, 393, 421, 432, 450, 522, 527
+   , 529, 552, 606, 643, 673, 693, 713, 732, 805, 864, 874, 934, 999, 15, 27, 45, 54, 78, 90, 108,
+    180, 216, 305, 483, 560, 579, 600, 605, 609, 719, 778, 783, 852, 876, 886, 899, 918, 983, 46, 53
+   , 89, 167, 178, 185, 203, 213, 271, 297, 324, 334, 336, 360, 370, 406, 426, 467, 542, 551, 610,
+    621, 649, 668, 726, 740, 786, 791, 810, 820, 835, 900, 917, 931, 951, 965, 975, 30, 51, 105, 156
+   , 205, 210, 224, 279, 303, 356, 366, 388, 405, 410, 438, 449, 459, 536, 541, 594, 599, 622, 655,
+    720, 812, 818, 862, 867, 933, 29, 43, 71, 83, 92, 101, 106, 143, 173, 283, 311, 312, 346, 392,
+    409, 420, 437, 443, 557, 566, 593, 642, 659, 672, 692, 707, 712, 737, 757, 869, 879, 911, 998,
+    60, 102, 241, 327, 353, 363, 399, 425, 482, 558, 565, 624, 679, 718, 735, 749, 769, 798, 898,
+    963, 982, 58, 86, 166, 183, 184, 202, 212, 219, 233, 286, 359, 431, 466, 615, 636, 648, 689, 729
+   , 801, 815, 840, 845, 850, 855, 884, 916, 930, 950, 964, 974, 981, 995, 1015, 57, 85, 99, 120,
+    171, 199, 204, 229, 318, 329, 339, 368, 404, 448, 458, 465, 499, 654, 671, 685, 784, 789, 823,
+    872, 882, 915, 932, 949, 997, 1007, 116, 142, 159, 172, 277, 408, 436, 442, 455, 481, 491, 547,
+    572, 587, 617, 630, 658, 665, 706, 723, 736, 756, 776, 781, 816, 860, 894, 897, 910, 947, 991,
+    114, 221, 240, 269, 281, 309, 315, 332, 342, 344, 378, 398, 424, 441, 475, 487, 531, 618, 629,
+    678, 695, 734, 743, 748, 808, 833, 843, 929, 943, 962, 973, 113, 182, 189, 218, 227, 232, 301,
+    364, 374, 430, 457, 523, 553, 562, 602, 607, 688, 728, 753, 796, 830, 865, 875, 927, 980, 994,
+    1014, 55, 79, 91, 109, 170, 187, 198, 215, 228, 284, 415, 464, 498, 554, 561, 601, 670, 675, 684
+   , 715, 745, 765, 779, 848, 853, 877, 887, 909, 914, 948, 979, 996, 1006, 1013, 47, 110, 158, 249
+   , 316, 325, 335, 337, 361, 371, 397, 447, 454, 480, 490, 497, 538, 543, 611, 632, 664, 722, 787,
+    811, 821, 880, 896, 913, 946, 961, 971, 990, 1011, 31, 94, 220, 245, 357, 367, 429, 440, 474,
+    486, 537, 595, 623, 651, 681, 694, 701, 742, 759, 813, 819, 858, 863, 892, 928, 942, 945, 972,
+    989, 993, 1003, 1023, 62, 93, 107, 188, 207, 226, 237, 243, 313, 340, 347, 376, 456, 471, 473,
+    507, 567, 568, 626, 752, 890, 907, 926, 1005, 61, 103, 124, 175, 186, 214, 372, 414, 453, 463,
+    489, 503, 559, 625, 638, 674, 691, 714, 731, 739, 744, 764, 794, 799, 828, 908, 925, 939, 959,
+    978, 1012, 59, 87, 122, 248, 287, 350, 396, 413, 446, 485, 495, 496, 637, 751, 826, 841, 851,
+    885, 912, 941, 960, 970, 977, 1010, 118, 121, 235, 244, 319, 369, 382, 428, 445, 574, 650, 667,
+    680, 700, 758, 761, 785, 873, 883, 944, 988, 992, 1002, 1009, 1022, 117, 206, 223, 231, 236, 242
+   , 470, 472, 506, 573, 631, 687, 777, 817, 856, 861, 895, 906, 987, 1004, 1021, 115, 174, 191, 333
+   , 343, 345, 379, 452, 462, 469, 488, 502, 505, 619, 690, 697, 730, 738, 755, 809, 888, 924, 938,
+    958, 969, 1019, 253, 365, 375, 412, 484, 494, 501, 563, 603, 750, 767, 792, 797, 831, 923, 940,
+    957, 976, 1001, 234, 251, 285, 348, 444, 479, 555, 634, 666, 760, 824, 849, 905, 955, 1008, 111,
+    222, 230, 247, 317, 380, 461, 511, 539, 633, 686, 703, 747, 881, 937, 986, 1020, 95, 190, 468,
+    493, 504, 570, 696, 754, 859, 893, 968, 985, 1018, 63, 126, 252, 341, 377, 500, 569, 627, 683,
+    766, 891, 922, 956, 1000, 1017, 125, 239, 250, 373, 478, 639, 795, 829, 904, 921, 954, 123, 246,
+    351, 460, 477, 510, 702, 746, 763, 827, 936, 953, 119, 383, 492, 509, 575, 984, 682, 699, 857,
+    1016, 238, 255, 889, 920, 476, 762, 793, 952, 349, 508, 635, 825, 381, 698, 254, 571, 127 };
+
+static int cbest_11[1023] = { 1,
+    2, 1026, 4, 513, 8, 16, 1282, 32, 64, 641, 128, 256, 512, 1346, 1024, 3, 673, 1027, 5, 10, 20, 40, 80, 160, 320,
+    640, 6, 9, 515, 1030, 1280, 1539, 17, 517, 1034, 1283, 12, 18, 33, 521, 1042, 1362, 34, 65, 529, 1058, 1286, 1795,
+    24, 36, 66, 129, 545, 643, 1090, 1290, 1667, 68, 130, 257, 577, 645, 672, 1154, 1298, 1344, 48, 72, 132, 258, 336,
+    649, 681, 1314, 1347, 136, 168, 260, 514, 657, 769, 1538, 1923, 84, 96, 144, 264, 516, 1025, 1350, 1410, 1859, 42,
+    272, 520, 705, 1032, 1354, 11, 21, 41, 81, 161, 192, 288, 321, 528, 675, 1028, 1537, 1699, 1794, 7, 22, 82, 162,
+    322, 544, 642, 677, 897, 1031, 1046, 1066, 1106, 1186, 1281, 1366, 1378, 1666, 14, 44, 164, 324, 384, 523, 533,
+    553, 576, 593, 644, 833, 1035, 1040, 1288, 1360, 1987, 13, 19, 28, 88, 328, 519, 648, 680, 689, 1043, 1056, 1284,
+    1363, 1474, 1543, 1793, 1955, 26, 35, 56, 176, 656, 768, 1038, 1059, 1088, 1287, 1302, 1322, 1442, 1547, 1665,
+    1922, 25, 37, 52, 67, 112, 340, 352, 525, 531, 737, 1091, 1152, 1291, 1296, 1555, 1858, 1875, 38, 69, 74, 104, 131,
+    224, 547, 651, 661, 683, 704, 721, 961, 1050, 1062, 1155, 1299, 1312, 1345, 1370, 1571, 1799, 49, 70, 73, 133, 138,
+    148, 170, 208, 259, 337, 448, 537, 549, 579, 647, 674, 929, 1094, 1294, 1315, 1352, 1536, 1603, 1671, 1698, 1803,
+    1921, 50, 134, 137, 169, 261, 266, 276, 296, 338, 416, 581, 676, 896, 1074, 1098, 1158, 1348, 1394, 1408, 1675,
+    1707, 1811, 1857, 2019, 76, 85, 97, 145, 262, 265, 522, 532, 552, 561, 585, 592, 653, 659, 685, 771, 832, 849,
+    1064, 1162, 1194, 1306, 1318, 1351, 1386, 1411, 1506, 1683, 1827, 1986, 2003, 43, 86, 98, 140, 146, 172, 273, 344,
+    518, 688, 773, 1033, 1110, 1122, 1170, 1355, 1490, 1542, 1697, 1792, 1927, 1954, 100, 193, 268, 274, 289, 597, 609,
+    665, 697, 707, 777, 1029, 1044, 1104, 1184, 1330, 1364, 1376, 1414, 1546, 1664, 1731, 1863, 1931, 1963, 23, 46, 83,
+    92, 152, 163, 184, 194, 290, 323, 368, 524, 530, 555, 693, 709, 736, 753, 785, 993, 1036, 1047, 1067, 1107, 1187,
+    1218, 1320, 1358, 1367, 1379, 1418, 1450, 1545, 1554, 1867, 1874, 1939, 1985, 15, 30, 45, 60, 90, 120, 165, 180,
+    196, 240, 280, 292, 325, 330, 360, 385, 480, 546, 650, 660, 679, 682, 713, 720, 745, 801, 899, 960, 977, 1041,
+    1289, 1361, 1426, 1472, 1541, 1570, 1703, 1798, 1953, 29, 58, 89, 116, 166, 200, 232, 326, 329, 386, 464, 535, 536,
+    548, 578, 595, 646, 835, 901, 928, 1048, 1057, 1070, 1190, 1285, 1300, 1368, 1382, 1440, 1475, 1559, 1579, 1602,
+    1619, 1670, 1802, 1879, 1891, 1920, 27, 57, 177, 304, 388, 527, 557, 580, 691, 725, 837, 905, 937, 1039, 1054,
+    1089, 1114, 1292, 1303, 1323, 1374, 1443, 1553, 1674, 1706, 1715, 1801, 1810, 1856, 1873, 1991, 2018, 2035, 53,
+    106, 113, 178, 212, 332, 341, 353, 392, 424, 541, 560, 584, 601, 652, 658, 684, 770, 841, 848, 913, 1060, 1082,
+    1096, 1153, 1202, 1297, 1402, 1478, 1522, 1569, 1673, 1682, 1705, 1797, 1826, 1959, 1995, 2002, 2027, 39, 54, 75,
+    105, 114, 225, 342, 354, 400, 539, 569, 739, 772, 1051, 1063, 1078, 1092, 1138, 1160, 1192, 1304, 1313, 1326, 1371,
+    1384, 1398, 1446, 1482, 1514, 1551, 1601, 1669, 1696, 1763, 1815, 1835, 1926, 71, 139, 149, 171, 209, 226, 298,
+    356, 449, 565, 596, 608, 625, 663, 664, 696, 706, 723, 741, 776, 853, 865, 963, 1072, 1095, 1130, 1156, 1250, 1295,
+    1310, 1353, 1392, 1687, 1730, 1747, 1809, 1862, 1930, 1962, 1971, 2007, 2017, 51, 78, 108, 135, 150, 210, 228, 267,
+    277, 297, 339, 348, 417, 450, 551, 554, 587, 617, 655, 687, 692, 708, 752, 784, 931, 965, 992, 1009, 1075, 1099,
+    1159, 1174, 1234, 1316, 1338, 1349, 1395, 1409, 1458, 1494, 1504, 1544, 1563, 1575, 1681, 1825, 1866, 1883, 1929,
+    1938, 1961, 1984, 2001, 77, 142, 174, 263, 278, 346, 376, 418, 452, 496, 583, 669, 678, 701, 712, 729, 744, 761,
+    800, 898, 933, 969, 976, 1001, 1065, 1108, 1120, 1163, 1168, 1195, 1307, 1319, 1334, 1356, 1387, 1416, 1448, 1488,
+    1507, 1540, 1607, 1702, 1807, 1865, 1925, 1952, 87, 99, 141, 147, 156, 173, 188, 216, 248, 270, 300, 345, 372, 420,
+    456, 488, 534, 563, 594, 667, 699, 757, 779, 789, 809, 834, 851, 900, 1102, 1111, 1123, 1171, 1328, 1412, 1491,
+    1558, 1578, 1587, 1611, 1618, 1679, 1711, 1729, 1861, 1878, 1890, 1907, 1943, 2023, 94, 101, 124, 154, 186, 244,
+    269, 275, 284, 526, 556, 589, 690, 724, 775, 836, 904, 936, 945, 981, 1045, 1068, 1105, 1166, 1185, 1198, 1216,
+    1331, 1365, 1377, 1390, 1415, 1430, 1510, 1552, 1577, 1714, 1800, 1819, 1831, 1872, 1899, 1937, 1990, 2034, 47, 62,
+    93, 102, 122, 153, 185, 195, 282, 291, 312, 362, 369, 432, 468, 540, 599, 600, 611, 715, 747, 840, 857, 912, 1037,
+    1052, 1112, 1126, 1219, 1321, 1359, 1372, 1419, 1424, 1451, 1568, 1623, 1635, 1672, 1691, 1701, 1704, 1723, 1796,
+    1958, 1994, 2011, 2026, 2043, 31, 61, 91, 121, 181, 197, 202, 234, 241, 281, 293, 308, 331, 361, 370, 481, 538,
+    568, 613, 695, 711, 738, 755, 781, 787, 995, 1080, 1118, 1178, 1188, 1210, 1380, 1400, 1427, 1473, 1498, 1530,
+    1550, 1557, 1600, 1617, 1668, 1719, 1735, 1762, 1779, 1814, 1834, 1843, 1877, 1889, 1935, 1967, 1993, 2025, 2039,
+    59, 117, 167, 182, 198, 201, 233, 242, 294, 327, 387, 465, 482, 559, 564, 605, 624, 662, 722, 740, 803, 852, 864,
+    881, 907, 917, 939, 962, 979, 997, 1049, 1071, 1086, 1146, 1191, 1206, 1222, 1266, 1301, 1324, 1369, 1383, 1406,
+    1422, 1441, 1454, 1480, 1512, 1526, 1549, 1686, 1713, 1739, 1746, 1771, 1808, 1833, 1871, 1970, 1989, 2006, 2016,
+    2033, 118, 305, 334, 364, 389, 394, 404, 426, 466, 484, 543, 550, 573, 586, 603, 616, 633, 654, 686, 717, 749, 793,
+    805, 843, 873, 903, 930, 964, 1008, 1055, 1115, 1128, 1142, 1200, 1226, 1258, 1293, 1308, 1375, 1476, 1520, 1562,
+    1574, 1680, 1824 };
+

diff --git a/src/cauchy_best_r6.c b/src/cauchy_best_r6.c
new file mode 100644 (file)
index 0000000..8a52e59
--- /dev/null
+++ b/src/cauchy_best_r6.c
@@ -0,0 +1,1983 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "galois.h"
+#include "jerasure.h"
+#include "cauchy.h"
+
+static int PPs[33] = { -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1,
+                       -1, -1, -1, -1, -1, -1, -1, -1, -1 };
+static int NOs[33];
+static int ONEs[33][33];
+
+static int *cbest_0;
+static int *cbest_1;
+static int cbest_2[3];
+static int cbest_3[7];
+static int cbest_4[15];
+static int cbest_5[31];
+static int cbest_6[63];
+static int cbest_7[127];
+static int cbest_8[255];
+static int cbest_9[511];
+static int cbest_10[1023];
+static int cbest_11[1023]; 
+static int cbest_12[1023], cbest_13[1023], cbest_14[1023], cbest_15[1023], cbest_16[1023], cbest_17[1023], cbest_18[1023],
+           cbest_19[1023], cbest_20[1023], cbest_21[1023], cbest_22[1023], cbest_23[1023], cbest_24[1023], cbest_25[1023],
+           cbest_26[1023], cbest_27[1023], cbest_28[1023], cbest_29[1023], cbest_30[1023], cbest_31[1023];
+static unsigned int cbest_32[1023];
+
+static int cbest_max_k[33] = { -1, -1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 1023, 
+     1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023, 1023,
+     1023, 1023, 1023, 1023 };
+
+static int cbest_init = 0;
+
+static int *cbest_all[33];
+
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+int cauchy_n_ones(int n, int w)
+{
+  int no;
+  int cno;
+  int nones;
+  int i, j;
+  int highbit;
+
+  highbit = (1 << (w-1));
+
+  if (PPs[w] == -1) {
+    nones = 0;
+    PPs[w] = galois_single_multiply(highbit, 2, w);
+    for (i = 0; i < w; i++) {
+      if (PPs[w] & (1 << i)) {
+        ONEs[w][nones] = (1 << i);
+        nones++;
+      }
+    }
+    NOs[w] = nones;
+  }
+
+  no = 0;
+  for (i = 0; i < w; i++) if (n & (1 << i)) no++;
+  cno = no;
+  for (i = 1; i < w; i++) {
+    if (n & highbit) {
+      n ^= highbit;
+      n <<= 1;
+      n ^= PPs[w];
+      cno--;
+      for (j = 0; j < NOs[w]; j++) {
+        cno += (n & ONEs[w][j]) ? 1 : -1;
+      }
+    } else {
+      n <<= 1;
+    } 
+    no += cno;
+  }
+  return no;
+}
+  
+int *cauchy_original_coding_matrix(int k, int m, int w)
+{
+  int *matrix;
+  int i, j, index;
+
+  if (w < 31 && (k+m) > (1 << w)) return NULL;
+  matrix = talloc(int, k*m);
+  if (matrix == NULL) return NULL;
+  index = 0;
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[index] = galois_single_divide(1, (i ^ (m+j)), w);
+      index++;
+    }
+  }
+  return matrix;
+}
+
+int *cauchy_xy_coding_matrix(int k, int m, int w, int *X, int *Y)
+{
+  int index, i, j;
+  int *matrix;
+
+  matrix = talloc(int, k*m);
+  if (matrix == NULL) { return NULL; }
+  index = 0;
+  for (i = 0; i < m; i++) {
+    for (j = 0; j < k; j++) {
+      matrix[index] = galois_single_divide(1, (X[i] ^ Y[j]), w);
+      index++;
+    }
+  }
+  return matrix;
+}
+
+void cauchy_improve_coding_matrix(int k, int m, int w, int *matrix)
+{
+  int index, i, j, x;
+  int tmp;
+  int bno, tno, bno_index;
+
+  for (j = 0; j < k; j++) {
+    if (matrix[j] != 1) {
+      tmp = galois_single_divide(1, matrix[j], w);
+      index = j;
+      for (i = 0; i < m; i++) {
+        matrix[index] = galois_single_multiply(matrix[index], tmp, w);
+        index += k;
+      }
+    }
+  }
+  for (i = 1; i < m; i++) {
+    bno = 0;
+    index = i*k;
+    for (j = 0; j < k; j++) bno += cauchy_n_ones(matrix[index+j], w);
+    bno_index = -1;
+    for (j = 0; j < k; j++) {
+      if (matrix[index+j] != 1) {
+        tmp = galois_single_divide(1, matrix[index+j], w);
+        tno = 0;
+        for (x = 0; x < k; x++) {
+          tno += cauchy_n_ones(galois_single_multiply(matrix[index+x], tmp, w), w);
+        }
+        if (tno < bno) {
+          bno = tno;
+          bno_index = j;
+        }
+      }
+    }
+    if (bno_index != -1) {
+      tmp = galois_single_divide(1, matrix[index+bno_index], w);
+      for (j = 0; j < k; j++) {
+        matrix[index+j] = galois_single_multiply(matrix[index+j], tmp, w);
+      }
+    }
+  }
+}
+
+int *cauchy_good_general_coding_matrix(int k, int m, int w)
+{
+  int *matrix, i;
+
+  if (m == 2 && k <= cbest_max_k[w]) {
+    matrix = talloc(int, k*m);
+    if (matrix == NULL) return NULL;
+    if (!cbest_init) {
+      cbest_init = 1;
+      cbest_all[0] = cbest_0; cbest_all[1] = cbest_1; cbest_all[2] = cbest_2; cbest_all[3] = cbest_3; cbest_all[4] =
+      cbest_4; cbest_all[5] = cbest_5; cbest_all[6] = cbest_6; cbest_all[7] = cbest_7; cbest_all[8] = cbest_8;
+      cbest_all[9] = cbest_9; cbest_all[10] = cbest_10; cbest_all[11] = cbest_11; cbest_all[12] = cbest_12;
+      cbest_all[13] = cbest_13; cbest_all[14] = cbest_14; cbest_all[15] = cbest_15; cbest_all[16] = cbest_16;
+      cbest_all[17] = cbest_17; cbest_all[18] = cbest_18; cbest_all[19] = cbest_19; cbest_all[20] = cbest_20;
+      cbest_all[21] = cbest_21; cbest_all[22] = cbest_22; cbest_all[23] = cbest_23; cbest_all[24] = cbest_24;
+      cbest_all[25] = cbest_25; cbest_all[26] = cbest_26; cbest_all[27] = cbest_27; cbest_all[28] = cbest_28;
+      cbest_all[29] = cbest_29; cbest_all[30] = cbest_30; cbest_all[31] = cbest_31; cbest_all[32] = (int *) cbest_32;
+    }
+    for (i = 0; i < k; i++) {
+      matrix[i] = 1;
+      matrix[i+k] = cbest_all[w][i];
+    }
+    return matrix;
+  } else {
+    matrix = cauchy_original_coding_matrix(k, m, w);
+    if (matrix == NULL) return NULL;
+    cauchy_improve_coding_matrix(k, m, w, matrix);
+    return matrix;
+  }
+}
+
+static int cbest_2[3] = { 1, 2, 3 };
+static int cbest_3[7] = { 1, 2, 5, 4, 7, 3, 6 };
+
+static int cbest_4[15] = { 1, 2, 9, 4, 8, 13, 3, 6, 12, 5, 11, 15, 10, 14, 7 };
+
+static int cbest_5[31] = { 1, 2, 18, 4, 9, 8, 22, 16, 3, 11, 19, 5, 10, 6, 20, 27, 13, 23, 26, 12,
+    17, 25, 24, 31, 30, 7, 15, 21, 29, 14, 28 };
+
+static int cbest_6[63] = { 1, 2, 33, 4, 8, 49, 16, 32, 57, 3, 6, 12, 24, 48, 5, 35, 9, 37, 10, 17,
+    41, 51, 56, 61, 18, 28, 53, 14, 20, 34, 7, 13, 25, 36, 59, 26, 39, 40, 45, 50, 60, 52, 63,
+    11, 30, 55, 19, 22, 29, 43, 58, 15, 21, 38, 44, 47, 62, 27, 54, 42, 31, 23, 46 };
+
+static int cbest_7[127] = { 1, 2, 68, 4, 34, 8, 17, 16, 76, 32, 38, 3, 64, 69, 5, 19, 35, 70, 6, 9,
+    18, 102, 10, 36, 85, 12, 21, 42, 51, 72, 77, 84, 20, 25, 33, 50, 78, 98, 24, 39, 49, 100, 110
+   , 48, 65, 93, 40, 66, 71, 92, 7, 46, 55, 87, 96, 103, 106, 11, 23, 37, 54, 81, 86, 108, 13,
+    22, 27, 43, 53, 73, 80, 14, 26, 52, 74, 79, 99, 119, 44, 95, 101, 104, 111, 118, 29, 59, 89,
+    94, 117, 28, 41, 58, 67, 88, 115, 116, 47, 57, 83, 97, 107, 114, 127, 56, 82, 109, 113, 126,
+    112, 125, 15, 63, 75, 123, 124, 31, 45, 62, 91, 105, 122, 30, 61, 90, 121, 60, 120 };
+
+static int cbest_8[255] = { 1, 2, 142, 4, 71, 8, 70, 173, 3, 35, 143, 16, 17, 67, 134, 140, 172, 6, 34
+   , 69, 201, 216, 5, 33, 86, 12, 65, 138, 158, 159, 175, 10, 32, 43, 66, 108, 130, 193, 234, 9,
+    24, 25, 50, 68, 79, 100, 132, 174, 200, 217, 20, 21, 42, 48, 87, 169, 41, 54, 64, 84, 96, 117
+   , 154, 155, 165, 226, 77, 82, 135, 136, 141, 168, 192, 218, 238, 7, 18, 19, 39, 40, 78, 113,
+    116, 128, 164, 180, 195, 205, 220, 232, 14, 26, 27, 58, 109, 156, 157, 203, 235, 13, 28, 29, 38
+   , 51, 56, 75, 85, 90, 101, 110, 112, 139, 171, 11, 37, 49, 52, 76, 83, 102, 119, 131, 150, 151
+   , 167, 182, 184, 188, 197, 219, 224, 45, 55, 80, 94, 97, 133, 170, 194, 204, 221, 227, 236, 36,
+    47, 73, 92, 98, 104, 118, 152, 153, 166, 202, 207, 239, 251, 22, 23, 44, 74, 91, 148, 149, 161
+   , 181, 190, 233, 46, 59, 88, 137, 146, 147, 163, 196, 208, 212, 222, 250, 57, 81, 95, 106, 111,
+    129, 160, 176, 199, 243, 249, 15, 53, 72, 93, 103, 115, 125, 162, 183, 185, 189, 206, 225, 255,
+    186, 210, 230, 237, 242, 248, 30, 31, 62, 89, 99, 105, 114, 121, 124, 178, 209, 213, 223, 228,
+    241, 254, 60, 191, 198, 247, 120, 240, 107, 127, 144, 145, 177, 211, 214, 246, 245, 123, 126,
+    187, 231, 253, 63, 179, 229, 244, 61, 122, 215, 252 };
+
+static int cbest_9[511] = { 1, 2, 264, 4, 132, 8, 66, 16, 33, 32, 280, 64, 140, 128, 3, 70, 265, 5,
+    133, 256, 266, 6, 9, 35, 67, 134, 268, 396, 10, 17, 34, 330, 12, 18, 68, 198, 297, 20, 37, 74
+   , 136, 148, 165, 281, 296, 24, 36, 41, 65, 82, 99, 164, 272, 282, 388, 40, 49, 98, 141, 194,
+    284, 328, 412, 48, 97, 129, 142, 196, 346, 71, 72, 96, 130, 313, 392, 80, 206, 257, 267, 312,
+    334, 7, 135, 156, 173, 192, 258, 269, 397, 404, 11, 78, 144, 161, 172, 260, 270, 299, 331, 344,
+    398, 13, 19, 39, 69, 86, 103, 160, 167, 199, 202, 298, 322, 384, 14, 21, 38, 43, 75, 102, 137,
+    149, 166, 204, 289, 332, 408, 462, 22, 25, 42, 51, 83, 101, 138, 150, 273, 283, 288, 301, 350,
+    389, 429, 26, 50, 76, 100, 195, 274, 285, 300, 329, 363, 390, 413, 428, 28, 45, 84, 143, 197,
+    200, 214, 231, 276, 286, 315, 320, 347, 362, 414, 458, 44, 53, 73, 90, 107, 131, 152, 169, 181,
+    230, 314, 338, 361, 393, 400, 454, 460, 52, 57, 81, 106, 115, 168, 175, 180, 207, 229, 305, 335
+   , 348, 360, 394, 421, 478, 56, 105, 114, 157, 163, 174, 193, 210, 227, 228, 259, 304, 317, 326,
+    405, 420, 445, 79, 104, 113, 145, 158, 162, 212, 226, 261, 271, 316, 345, 379, 399, 406, 444,
+    450, 456, 87, 88, 112, 146, 203, 225, 262, 291, 323, 336, 378, 385, 425, 452, 474, 15, 205, 222
+   , 224, 239, 290, 303, 333, 367, 377, 386, 409, 424, 431, 463, 470, 476, 23, 139, 151, 189, 208,
+    238, 302, 324, 351, 366, 376, 410, 430, 437, 27, 47, 77, 94, 111, 177, 188, 237, 275, 293, 342,
+    365, 391, 436, 448, 29, 46, 55, 85, 110, 119, 171, 176, 183, 201, 215, 218, 235, 236, 277, 287,
+    292, 321, 355, 364, 415, 417, 459, 466, 472, 30, 54, 59, 91, 109, 118, 153, 170, 182, 220, 234,
+    278, 307, 339, 354, 401, 416, 423, 441, 455, 461, 468, 495, 58, 108, 117, 154, 233, 306, 319,
+    349, 353, 383, 395, 402, 422, 440, 447, 479, 494, 92, 116, 211, 232, 318, 327, 340, 352, 382,
+    446, 493, 61, 159, 213, 216, 247, 309, 381, 407, 427, 451, 457, 464, 491, 492, 60, 89, 123, 147
+   , 185, 246, 263, 308, 337, 371, 380, 426, 433, 453, 475, 487, 490, 122, 184, 191, 223, 245, 370,
+    387, 432, 439, 471, 477, 486, 489, 511, 121, 179, 190, 209, 243, 244, 295, 325, 359, 369, 411,
+    438, 485, 488, 510, 95, 120, 178, 242, 294, 343, 358, 368, 419, 449, 483, 484, 509, 219, 241,
+    357, 418, 443, 467, 473, 482, 507, 508, 31, 221, 240, 255, 279, 356, 442, 469, 481, 503, 506,
+    155, 254, 403, 480, 502, 505, 63, 93, 127, 253, 311, 341, 375, 501, 504, 62, 126, 187, 217, 251
+   , 252, 310, 374, 435, 465, 499, 500, 125, 186, 250, 373, 434, 498, 124, 249, 372, 497, 248, 496
+    };
+
+static int cbest_10[1023] = { 1, 2, 516, 4, 258, 8, 129, 16, 32, 580, 64, 128, 290, 145, 256, 3, 512,
+    517, 5, 259, 518, 588, 6, 9, 18, 36, 72, 144, 774, 10, 17, 131, 262, 288, 524, 645, 12, 33,
+    133, 266, 294, 387, 532, 576, 581, 20, 34, 65, 137, 274, 548, 582, 24, 66, 291, 838, 40, 68,
+    130, 147, 161, 322, 644, 709, 806, 48, 132, 193, 257, 386, 596, 80, 136, 298, 419, 612, 661, 772
+   , 96, 149, 260, 272, 306, 403, 513, 146, 153, 160, 264, 292, 385, 514, 519, 544, 584, 589, 708,
+    870, 7, 19, 37, 73, 192, 354, 590, 770, 775, 11, 38, 74, 177, 263, 289, 418, 520, 525, 534, 641
+   , 660, 725, 802, 836, 846, 13, 22, 76, 148, 209, 267, 295, 320, 330, 402, 526, 528, 533, 577,
+    647, 717, 804, 14, 21, 26, 35, 44, 135, 152, 165, 201, 275, 304, 384, 401, 435, 549, 578, 583,
+    604, 608, 782, 903, 25, 52, 67, 88, 139, 270, 296, 391, 417, 550, 620, 653, 790, 834, 839, 41,
+    50, 69, 104, 141, 176, 278, 302, 323, 395, 423, 540, 598, 640, 705, 724, 807, 866, 28, 42, 49,
+    70, 82, 100, 163, 208, 282, 310, 556, 592, 597, 646, 663, 677, 711, 716, 868, 878, 81, 134, 151
+   , 164, 195, 200, 299, 326, 352, 362, 400, 434, 564, 613, 657, 768, 773, 902, 967, 97, 138, 155,
+    169, 197, 261, 273, 307, 358, 390, 416, 433, 451, 614, 652, 733, 800, 814, 844, 854, 935, 56, 84
+   , 98, 140, 181, 217, 265, 293, 328, 338, 394, 422, 515, 545, 585, 704, 788, 822, 871, 919, 162,
+    179, 276, 355, 407, 427, 546, 586, 591, 616, 662, 669, 676, 710, 727, 741, 771, 780, 901, 39, 75
+   , 150, 157, 194, 211, 225, 268, 280, 308, 314, 389, 411, 439, 521, 530, 535, 628, 656, 721, 803,
+    832, 837, 842, 847, 966, 23, 77, 112, 154, 168, 196, 300, 321, 331, 393, 421, 432, 450, 522, 527
+   , 529, 552, 606, 643, 673, 693, 713, 732, 805, 864, 874, 934, 999, 15, 27, 45, 54, 78, 90, 108,
+    180, 216, 305, 483, 560, 579, 600, 605, 609, 719, 778, 783, 852, 876, 886, 899, 918, 983, 46, 53
+   , 89, 167, 178, 185, 203, 213, 271, 297, 324, 334, 336, 360, 370, 406, 426, 467, 542, 551, 610,
+    621, 649, 668, 726, 740, 786, 791, 810, 820, 835, 900, 917, 931, 951, 965, 975, 30, 51, 105, 156
+   , 205, 210, 224, 279, 303, 356, 366, 388, 405, 410, 438, 449, 459, 536, 541, 594, 599, 622, 655,
+    720, 812, 818, 862, 867, 933, 29, 43, 71, 83, 92, 101, 106, 143, 173, 283, 311, 312, 346, 392,
+    409, 420, 437, 443, 557, 566, 593, 642, 659, 672, 692, 707, 712, 737, 757, 869, 879, 911, 998,
+    60, 102, 241, 327, 353, 363, 399, 425, 482, 558, 565, 624, 679, 718, 735, 749, 769, 798, 898,
+    963, 982, 58, 86, 166, 183, 184, 202, 212, 219, 233, 286, 359, 431, 466, 615, 636, 648, 689, 729
+   , 801, 815, 840, 845, 850, 855, 884, 916, 930, 950, 964, 974, 981, 995, 1015, 57, 85, 99, 120,
+    171, 199, 204, 229, 318, 329, 339, 368, 404, 448, 458, 465, 499, 654, 671, 685, 784, 789, 823,
+    872, 882, 915, 932, 949, 997, 1007, 116, 142, 159, 172, 277, 408, 436, 442, 455, 481, 491, 547,
+    572, 587, 617, 630, 658, 665, 706, 723, 736, 756, 776, 781, 816, 860, 894, 897, 910, 947, 991,
+    114, 221, 240, 269, 281, 309, 315, 332, 342, 344, 378, 398, 424, 441, 475, 487, 531, 618, 629,
+    678, 695, 734, 743, 748, 808, 833, 843, 929, 943, 962, 973, 113, 182, 189, 218, 227, 232, 301,
+    364, 374, 430, 457, 523, 553, 562, 602, 607, 688, 728, 753, 796, 830, 865, 875, 927, 980, 994,
+    1014, 55, 79, 91, 109, 170, 187, 198, 215, 228, 284, 415, 464, 498, 554, 561, 601, 670, 675, 684
+   , 715, 745, 765, 779, 848, 853, 877, 887, 909, 914, 948, 979, 996, 1006, 1013, 47, 110, 158, 249
+   , 316, 325, 335, 337, 361, 371, 397, 447, 454, 480, 490, 497, 538, 543, 611, 632, 664, 722, 787,
+    811, 821, 880, 896, 913, 946, 961, 971, 990, 1011, 31, 94, 220, 245, 357, 367, 429, 440, 474,
+    486, 537, 595, 623, 651, 681, 694, 701, 742, 759, 813, 819, 858, 863, 892, 928, 942, 945, 972,
+    989, 993, 1003, 1023, 62, 93, 107, 188, 207, 226, 237, 243, 313, 340, 347, 376, 456, 471, 473,
+    507, 567, 568, 626, 752, 890, 907, 926, 1005, 61, 103, 124, 175, 186, 214, 372, 414, 453, 463,
+    489, 503, 559, 625, 638, 674, 691, 714, 731, 739, 744, 764, 794, 799, 828, 908, 925, 939, 959,
+    978, 1012, 59, 87, 122, 248, 287, 350, 396, 413, 446, 485, 495, 496, 637, 751, 826, 841, 851,
+    885, 912, 941, 960, 970, 977, 1010, 118, 121, 235, 244, 319, 369, 382, 428, 445, 574, 650, 667,
+    680, 700, 758, 761, 785, 873, 883, 944, 988, 992, 1002, 1009, 1022, 117, 206, 223, 231, 236, 242
+   , 470, 472, 506, 573, 631, 687, 777, 817, 856, 861, 895, 906, 987, 1004, 1021, 115, 174, 191, 333
+   , 343, 345, 379, 452, 462, 469, 488, 502, 505, 619, 690, 697, 730, 738, 755, 809, 888, 924, 938,
+    958, 969, 1019, 253, 365, 375, 412, 484, 494, 501, 563, 603, 750, 767, 792, 797, 831, 923, 940,
+    957, 976, 1001, 234, 251, 285, 348, 444, 479, 555, 634, 666, 760, 824, 849, 905, 955, 1008, 111,
+    222, 230, 247, 317, 380, 461, 511, 539, 633, 686, 703, 747, 881, 937, 986, 1020, 95, 190, 468,
+    493, 504, 570, 696, 754, 859, 893, 968, 985, 1018, 63, 126, 252, 341, 377, 500, 569, 627, 683,
+    766, 891, 922, 956, 1000, 1017, 125, 239, 250, 373, 478, 639, 795, 829, 904, 921, 954, 123, 246,
+    351, 460, 477, 510, 702, 746, 763, 827, 936, 953, 119, 383, 492, 509, 575, 984, 682, 699, 857,
+    1016, 238, 255, 889, 920, 476, 762, 793, 952, 349, 508, 635, 825, 381, 698, 254, 571, 127 };
+
+static int cbest_11[1023] = { 1,
+    2, 1026, 4, 513, 8, 16, 1282, 32, 64, 641, 128, 256, 512, 1346, 1024, 3, 673, 1027, 5, 10, 20, 40, 80, 160, 320,
+    640, 6, 9, 515, 1030, 1280, 1539, 17, 517, 1034, 1283, 12, 18, 33, 521, 1042, 1362, 34, 65, 529, 1058, 1286, 1795,
+    24, 36, 66, 129, 545, 643, 1090, 1290, 1667, 68, 130, 257, 577, 645, 672, 1154, 1298, 1344, 48, 72, 132, 258, 336,
+    649, 681, 1314, 1347, 136, 168, 260, 514, 657, 769, 1538, 1923, 84, 96, 144, 264, 516, 1025, 1350, 1410, 1859, 42,
+    272, 520, 705, 1032, 1354, 11, 21, 41, 81, 161, 192, 288, 321, 528, 675, 1028, 1537, 1699, 1794, 7, 22, 82, 162,
+    322, 544, 642, 677, 897, 1031, 1046, 1066, 1106, 1186, 1281, 1366, 1378, 1666, 14, 44, 164, 324, 384, 523, 533,
+    553, 576, 593, 644, 833, 1035, 1040, 1288, 1360, 1987, 13, 19, 28, 88, 328, 519, 648, 680, 689, 1043, 1056, 1284,
+    1363, 1474, 1543, 1793, 1955, 26, 35, 56, 176, 656, 768, 1038, 1059, 1088, 1287, 1302, 1322, 1442, 1547, 1665,
+    1922, 25, 37, 52, 67, 112, 340, 352, 525, 531, 737, 1091, 1152, 1291, 1296, 1555, 1858, 1875, 38, 69, 74, 104, 131,
+    224, 547, 651, 661, 683, 704, 721, 961, 1050, 1062, 1155, 1299, 1312, 1345, 1370, 1571, 1799, 49, 70, 73, 133, 138,
+    148, 170, 208, 259, 337, 448, 537, 549, 579, 647, 674, 929, 1094, 1294, 1315, 1352, 1536, 1603, 1671, 1698, 1803,
+    1921, 50, 134, 137, 169, 261, 266, 276, 296, 338, 416, 581, 676, 896, 1074, 1098, 1158, 1348, 1394, 1408, 1675,
+    1707, 1811, 1857, 2019, 76, 85, 97, 145, 262, 265, 522, 532, 552, 561, 585, 592, 653, 659, 685, 771, 832, 849,
+    1064, 1162, 1194, 1306, 1318, 1351, 1386, 1411, 1506, 1683, 1827, 1986, 2003, 43, 86, 98, 140, 146, 172, 273, 344,
+    518, 688, 773, 1033, 1110, 1122, 1170, 1355, 1490, 1542, 1697, 1792, 1927, 1954, 100, 193, 268, 274, 289, 597, 609,
+    665, 697, 707, 777, 1029, 1044, 1104, 1184, 1330, 1364, 1376, 1414, 1546, 1664, 1731, 1863, 1931, 1963, 23, 46, 83,
+    92, 152, 163, 184, 194, 290, 323, 368, 524, 530, 555, 693, 709, 736, 753, 785, 993, 1036, 1047, 1067, 1107, 1187,
+    1218, 1320, 1358, 1367, 1379, 1418, 1450, 1545, 1554, 1867, 1874, 1939, 1985, 15, 30, 45, 60, 90, 120, 165, 180,
+    196, 240, 280, 292, 325, 330, 360, 385, 480, 546, 650, 660, 679, 682, 713, 720, 745, 801, 899, 960, 977, 1041,
+    1289, 1361, 1426, 1472, 1541, 1570, 1703, 1798, 1953, 29, 58, 89, 116, 166, 200, 232, 326, 329, 386, 464, 535, 536,
+    548, 578, 595, 646, 835, 901, 928, 1048, 1057, 1070, 1190, 1285, 1300, 1368, 1382, 1440, 1475, 1559, 1579, 1602,
+    1619, 1670, 1802, 1879, 1891, 1920, 27, 57, 177, 304, 388, 527, 557, 580, 691, 725, 837, 905, 937, 1039, 1054,
+    1089, 1114, 1292, 1303, 1323, 1374, 1443, 1553, 1674, 1706, 1715, 1801, 1810, 1856, 1873, 1991, 2018, 2035, 53,
+    106, 113, 178, 212, 332, 341, 353, 392, 424, 541, 560, 584, 601, 652, 658, 684, 770, 841, 848, 913, 1060, 1082,
+    1096, 1153, 1202, 1297, 1402, 1478, 1522, 1569, 1673, 1682, 1705, 1797, 1826, 1959, 1995, 2002, 2027, 39, 54, 75,
+    105, 114, 225, 342, 354, 400, 539, 569, 739, 772, 1051, 1063, 1078, 1092, 1138, 1160, 1192, 1304, 1313, 1326, 1371,
+    1384, 1398, 1446, 1482, 1514, 1551, 1601, 1669, 1696, 1763, 1815, 1835, 1926, 71, 139, 149, 171, 209, 226, 298,
+    356, 449, 565, 596, 608, 625, 663, 664, 696, 706, 723, 741, 776, 853, 865, 963, 1072, 1095, 1130, 1156, 1250, 1295,
+    1310, 1353, 1392, 1687, 1730, 1747, 1809, 1862, 1930, 1962, 1971, 2007, 2017, 51, 78, 108, 135, 150, 210, 228, 267,
+    277, 297, 339, 348, 417, 450, 551, 554, 587, 617, 655, 687, 692, 708, 752, 784, 931, 965, 992, 1009, 1075, 1099,
+    1159, 1174, 1234, 1316, 1338, 1349, 1395, 1409, 1458, 1494, 1504, 1544, 1563, 1575, 1681, 1825, 1866, 1883, 1929,
+    1938, 1961, 1984, 2001, 77, 142, 174, 263, 278, 346, 376, 418, 452, 496, 583, 669, 678, 701, 712, 729, 744, 761,
+    800, 898, 933, 969, 976, 1001, 1065, 1108, 1120, 1163, 1168, 1195, 1307, 1319, 1334, 1356, 1387, 1416, 1448, 1488,
+    1507, 1540, 1607, 1702, 1807, 1865, 1925, 1952, 87, 99, 141, 147, 156, 173, 188, 216, 248, 270, 300, 345, 372, 420,
+    456, 488, 534, 563, 594, 667, 699, 757, 779, 789, 809, 834, 851, 900, 1102, 1111, 1123, 1171, 1328, 1412, 1491,
+    1558, 1578, 1587, 1611, 1618, 1679, 1711, 1729, 1861, 1878, 1890, 1907, 1943, 2023, 94, 101, 124, 154, 186, 244,
+    269, 275, 284, 526, 556, 589, 690, 724, 775, 836, 904, 936, 945, 981, 1045, 1068, 1105, 1166, 1185, 1198, 1216,
+    1331, 1365, 1377, 1390, 1415, 1430, 1510, 1552, 1577, 1714, 1800, 1819, 1831, 1872, 1899, 1937, 1990, 2034, 47, 62,
+    93, 102, 122, 153, 185, 195, 282, 291, 312, 362, 369, 432, 468, 540, 599, 600, 611, 715, 747, 840, 857, 912, 1037,
+    1052, 1112, 1126, 1219, 1321, 1359, 1372, 1419, 1424, 1451, 1568, 1623, 1635, 1672, 1691, 1701, 1704, 1723, 1796,
+    1958, 1994, 2011, 2026, 2043, 31, 61, 91, 121, 181, 197, 202, 234, 241, 281, 293, 308, 331, 361, 370, 481, 538,
+    568, 613, 695, 711, 738, 755, 781, 787, 995, 1080, 1118, 1178, 1188, 1210, 1380, 1400, 1427, 1473, 1498, 1530,
+    1550, 1557, 1600, 1617, 1668, 1719, 1735, 1762, 1779, 1814, 1834, 1843, 1877, 1889, 1935, 1967, 1993, 2025, 2039,
+    59, 117, 167, 182, 198, 201, 233, 242, 294, 327, 387, 465, 482, 559, 564, 605, 624, 662, 722, 740, 803, 852, 864,
+    881, 907, 917, 939, 962, 979, 997, 1049, 1071, 1086, 1146, 1191, 1206, 1222, 1266, 1301, 1324, 1369, 1383, 1406,
+    1422, 1441, 1454, 1480, 1512, 1526, 1549, 1686, 1713, 1739, 1746, 1771, 1808, 1833, 1871, 1970, 1989, 2006, 2016,
+    2033, 118, 305, 334, 364, 389, 394, 404, 426, 466, 484, 543, 550, 573, 586, 603, 616, 633, 654, 686, 717, 749, 793,
+    805, 843, 873, 903, 930, 964, 1008, 1055, 1115, 1128, 1142, 1200, 1226, 1258, 1293, 1308, 1375, 1476, 1520, 1562,
+    1574, 1680, 1824 };
+
+static int cbest_12[1023] = {
+    1, 2, 2089, 4, 8, 3133, 16, 2088, 1044, 3, 32, 522, 261, 3639, 5, 64, 65, 2057, 2091, 6, 130, 3132, 260,
+    2219, 9, 2093, 3117, 10, 128, 257, 2081, 3890, 12, 1566, 2217, 3129, 17, 514, 520, 3135, 18, 3196, 3637, 20,
+    256, 1028, 1045, 3638, 24, 33, 523, 783, 2105, 3197, 3647, 34, 1040, 1945, 2056, 2090, 2595, 3125, 3891, 36,
+    1046, 2348, 40, 1598, 2218, 3635, 7, 48, 66, 67, 131, 263, 269, 512, 538, 782, 1076, 1174, 1819, 2049, 2059,
+    2092, 2152, 3113, 3116, 3384, 3607, 3888, 68, 69, 277, 554, 1108, 1109, 1558, 1564, 1944, 2061, 2080, 2478,
+    3894, 72, 73, 134, 265, 293, 391, 526, 586, 587, 779, 2153, 2211, 2216, 2563, 3128, 4016, 11, 14, 80, 81,
+    129, 132, 138, 530, 1172, 1692, 2073, 2095, 2223, 2316, 3101, 3109, 3119, 3134, 3645, 3874, 13, 96, 97, 146,
+    259, 262, 268, 289, 799, 1052, 1060, 1158, 1567, 1818, 2083, 2221, 2344, 2349, 2476, 2980, 3045, 3192, 3368,
+    3636, 144, 162, 276, 389, 515, 521, 578, 579, 781, 972, 1024, 1156, 2085, 2120, 2235, 2282, 2312, 3131, 3623,
+    19, 22, 28, 160, 194, 195, 264, 292, 390, 778, 846, 1238, 1239, 1562, 1596, 1684, 1937, 1947, 2104, 2233,
+    2593, 3193, 3385, 3633, 3643, 3646, 3889, 21, 26, 324, 518, 536, 909, 1029, 1297, 2008, 2121, 2209, 2283,
+    2479, 2594, 2854, 3085, 3121, 3124, 3188, 3198, 3605, 3895, 25, 136, 258, 288, 528, 552, 798, 842, 1030,
+    1140, 1141, 1490, 1556, 2470, 2603, 2626, 2721, 3892, 3898, 4017, 35, 38, 44, 56, 320, 388, 423, 486, 524,
+    570, 584, 585, 618, 619, 648, 777, 780, 1041, 1594, 1817, 2097, 2107, 2317, 2561, 3105, 3164, 3189, 3199,
+    3263, 3634, 3875, 37, 42, 52, 285, 309, 421, 1036, 1042, 1047, 1056, 1072, 1170, 1313, 1427, 1823, 1936,
+    1946, 2048, 2053, 2058, 2065, 2109, 2280, 2345, 2477, 2579, 2627, 2981, 3041, 3044, 3112, 3127, 3369, 3388,
+    3603, 3606, 3631, 3765, 3872, 41, 192, 193, 273, 399, 775, 797, 908, 968, 1104, 1105, 1168, 1236, 1237, 1281,
+    1296, 1554, 1582, 1599, 1949, 2051, 2060, 2313, 2332, 2340, 2474, 3115, 3165, 3336, 3360, 3641, 4018, 49, 70,
+    71, 76, 77, 88, 89, 112, 113, 387, 454, 484, 513, 516, 539, 640, 744, 745, 1004, 1077, 1175, 1234, 1235,
+    1550, 1668, 1680, 1694, 1803, 2063, 2112, 2210, 2215, 2227, 2281, 2472, 2562, 2784, 3261, 3449, 3547, 3591,
+    3621, 84, 85, 104, 105, 142, 154, 178, 226, 227, 242, 243, 267, 271, 385, 422, 534, 555, 771, 776, 791, 834,
+    840, 844, 973, 1068, 1078, 1166, 1425, 1488, 1559, 1560, 1565, 1688, 1816, 2072, 2077, 2094, 2136, 2144,
+    2154, 2222, 2298, 2336, 2350, 2468, 2543, 2611, 2624, 2658, 2729, 2850, 2855, 2982, 3081, 3097, 3100, 3108,
+    3118, 3184, 3247, 3326, 3376, 3644, 3702, 4024, 82, 83, 135, 164, 170, 210, 211, 279, 284, 308, 328, 356,
+    372, 417, 420, 527, 542, 576, 577, 616, 617, 656, 795, 847, 1048, 1110, 1111, 1312, 1329, 1392, 1426, 1590,
+    1592, 1822, 2082, 2113, 2128, 2156, 2187, 2220, 2364, 2466, 2471, 2785, 2976, 3077, 3111, 3180, 3245, 3882,
+    3893, 3899, 3902, 4081, 15, 30, 50, 60, 98, 99, 120, 121, 133, 139, 166, 272, 291, 295, 325, 340, 398, 419,
+    531, 558, 582, 583, 712, 713, 774, 796, 838, 1064, 1084, 1173, 1182, 1232, 1233, 1280, 1522, 1542, 1676,
+    1693, 1811, 1948, 2009, 2084, 2137, 2145, 2155, 2185, 2213, 2225, 2234, 2286, 2299, 2599, 2601, 2625, 2659,
+    2745, 2870, 2988, 3047, 3130, 3185, 3194, 3327, 3352, 3386, 3545, 3601, 3619, 3622, 3629, 3703, 3733, 3773,
+    3896, 3955, 140, 147, 152, 176, 186, 198, 199, 224, 225, 281, 305, 332, 386, 397, 532, 546, 590, 591, 680,
+    696, 843, 901, 911, 974, 1026, 1032, 1053, 1061, 1116, 1117, 1159, 1164, 1491, 1552, 1802, 1941, 2069, 2087,
+    2122, 2129, 2157, 2168, 2232, 2296, 2314, 2318, 2446, 2567, 2592, 2737, 2852, 3040, 3073, 3093, 3103, 3156,
+    3181, 3389, 3627, 3632, 3642, 3858, 3873, 4020, 74, 75, 145, 163, 168, 208, 209, 266, 270, 321, 384, 395,
+    452, 487, 502, 664, 770, 790, 905, 1025, 1054, 1148, 1149, 1152, 1157, 1301, 1360, 1424, 1578, 1686, 1821,
+    1851, 1929, 1939, 2012, 2208, 2287, 2328, 2333, 2341, 2346, 2381, 2397, 2444, 2464, 2475, 2723, 2752, 3084,
+    3120, 3195, 3337, 3361, 3370, 3417, 3514, 3579, 3604, 3615, 3780, 3878, 3984, 4019, 23, 29, 46, 92, 93, 161,
+    240, 241, 278, 348, 416, 450, 562, 568, 610, 611, 650, 769, 773, 789, 794, 1154, 1222, 1223, 1328, 1376,
+    1494, 1520, 1563, 1597, 1685, 1951, 2010, 2075, 2123, 2169, 2284, 2297, 2473, 2511, 2541, 2602, 2619, 2666,
+    2720, 3107, 3123, 3157, 3294, 3324, 3372, 3448, 3453, 3546, 3587, 3670, 3710, 27, 196, 197, 290, 294, 418,
+    482, 519, 537, 540, 574, 688, 787, 793, 969, 1062, 1142, 1143, 1435, 1548, 1588, 1662, 1663, 1801, 1810,
+    1992, 2055, 2096, 2101, 2106, 2337, 2351, 2469, 2539, 2542, 2560, 2571, 2577, 2634, 2753, 2851, 2919, 2983,
+    3013, 3043, 3104, 3259, 3262, 3322, 3377, 3380, 3441, 3625, 3717, 3767, 3781, 3880, 3900, 3939, 4025, 4049,
+    137, 174, 280, 304, 322, 326, 344, 352, 393, 396, 455, 480, 485, 529, 553, 556, 760, 761, 832, 900, 910, 964,
+    970, 1005, 1031, 1124, 1125, 1180, 1289, 1317, 1333, 1540, 1557, 1574, 1580, 1586, 1690, 1724, 1921, 1940,
+    2052, 2064, 2099, 2108, 2250, 2266, 2285, 2304, 2365, 2467, 2578, 2583, 2609, 2656, 2667, 2848, 2977, 2996,
+    3126, 3166, 3176, 3215, 3239, 3257, 3295, 3325, 3512, 3602, 3617, 3630, 3671, 3700, 3711, 3761, 3764, 3842,
+    3883, 3903, 4080, 39, 45, 57, 148, 172, 184, 287, 297, 336, 394, 448, 525, 544, 571, 588, 589, 649, 746, 747,
+    835, 841, 845, 904, 996, 1006, 1038, 1074, 1080, 1092, 1093, 1178, 1220, 1221, 1300, 1489, 1492, 1538, 1595,
+    1670, 1682, 1756, 1757, 1795, 1815, 1820, 1835, 1850, 1928, 1938, 2050, 2111, 2179, 2356, 2440, 2509, 2565,
+    2587, 2635, 2871, 2915, 2978, 2984, 2989, 3046, 3053, 3114, 3148, 3172, 3207, 3292, 3323, 3340, 3353, 3356,
+    3364, 3387, 3401, 3445, 3544, 3589, 3640, 3729, 3757, 3769, 3796, 3897, 3954, 3959, 251, 373, 581, 1057,
+    1107, 1137, 1299, 1630, 1882, 2214, 2308, 2315, 2319, 2597, 2853, 3167, 3260, 3482, 3590, 3862 };
+
+static int cbest_13[1023] = {
+    1, 2, 4109, 4, 6155, 8, 7176, 16, 3588, 4108, 32, 2054, 3, 1027, 1794, 6, 64, 4620, 6154, 5, 897, 4111, 6153,
+    7177, 12, 2310, 3077, 4105, 128, 9, 24, 513, 1155, 10, 1026, 4101, 7689, 18, 48, 256, 896, 3589, 4365, 6159,
+    7178, 17, 448, 4557, 4621, 4684, 5647, 36, 96, 224, 1025, 1792, 20, 112, 512, 769, 1538, 1795, 2052, 3076,
+    3590, 6147, 6283, 7180, 33, 56, 72, 192, 2055, 2342, 3584, 4125, 6411, 7945, 28, 34, 577, 1154, 6922, 7240,
+    14, 144, 384, 2050, 4110, 4493, 5134, 5903, 6152, 7168, 7304, 7, 40, 65, 1171, 3620, 4104, 4141, 5004, 288,
+    768, 1153, 2308, 2567, 3652, 4097, 4107, 4397, 4685, 6157, 6171, 6379, 7688, 13, 68, 1024, 1810, 2311, 3461,
+    4676, 7179, 66, 129, 576, 1826, 3079, 3844, 4100, 4173, 4622, 5646, 6347, 8073, 25, 80, 899, 905, 1031, 1091,
+    1798, 2182, 2306, 2338, 2502, 3073, 3596, 4364, 4616, 5390, 5645, 6158, 6187, 7050, 7192, 11, 26, 913, 1922,
+    4117, 4556, 4652, 5262, 6151, 6299, 6443, 6923, 7181, 19, 49, 130, 136, 257, 1169, 1283, 1536, 1793, 2062,
+    2326, 2566, 2823, 4103, 4237, 6145, 7182, 7232, 7272, 7691, 7944, 50, 449, 515, 901, 961, 1035, 1163, 1170,
+    1539, 1802, 2048, 2340, 2695, 3586, 3591, 3604, 3616, 4553, 4612, 4680, 4748, 5005, 6146, 6219, 6282, 7208,
+    7241, 7288, 22, 37, 52, 97, 160, 225, 585, 1152, 1251, 1808, 2374, 2631, 3141, 3585, 4124, 4549, 4876, 5135,
+    5902, 6281, 6410, 7169, 7172, 7305, 7320, 7560, 21, 38, 98, 113, 132, 226, 258, 452, 545, 898, 904, 1187,
+    2053, 2070, 2278, 2438, 3205, 3460, 3525, 3636, 3972, 4127, 4137, 4157, 4367, 4677, 5132, 5839, 5901, 6163,
+    6169, 6409, 6666, 7693, 57, 73, 100, 114, 193, 228, 272, 450, 456, 517, 912, 1029, 1043, 1159, 1219, 1796,
+    2343, 3078, 3333, 4113, 4121, 4361, 4381, 4393, 4492, 4559, 4623, 4686, 5518, 6275, 6920, 7721, 8137, 29, 35,
+    44, 74, 104, 146, 641, 1030, 1090, 1730, 1824, 2246, 2318, 2822, 3072, 3085, 3592, 3621, 3660, 3780, 4099,
+    4140, 4149, 4165, 4205, 4333, 4617, 4700, 5454, 5643, 6149, 6377, 7051, 7170, 7244, 7753, 7947, 15, 30, 42,
+    60, 76, 120, 145, 196, 240, 260, 292, 320, 385, 480, 514, 771, 900, 960, 1123, 1411, 1818, 1986, 2051, 2086,
+    2304, 2694, 2951, 3622, 3648, 3653, 4096, 4106, 4221, 4396, 4429, 4589, 4636, 4653, 4716, 5422, 5679, 6156,
+    6170, 6378, 6603, 7184, 7242, 7681, 8072, 41, 58, 194, 200, 521, 581, 584, 785, 865, 1059, 1139, 1168, 1282,
+    1347, 1811, 2058, 2198, 2350, 2565, 2630, 3644, 4301, 4357, 4485, 4732, 5391, 5644, 5711, 6191, 6203, 6287,
+    6297, 7193, 7296, 7306, 70, 88, 148, 208, 289, 544, 579, 801, 1034, 1089, 1099, 1162, 1315, 1570, 1827, 1830,
+    1890, 2309, 2324, 2336, 2358, 2759, 3075, 3093, 3845, 4133, 4143, 4172, 4613, 4648, 4668, 4681, 4749, 4812,
+    4996, 5263, 5278, 5388, 5639, 5775, 6167, 6175, 6185, 6315, 6346, 6383, 6415, 6427, 6447, 7194, 7949, 7961,
+    69, 84, 116, 152, 264, 290, 386, 392, 516, 593, 773, 833, 909, 993, 1033, 1161, 1175, 1250, 1542, 1602, 1799,
+    1800, 1920, 2118, 2498, 2727, 3140, 3597, 3654, 4253, 4389, 4399, 4495, 4672, 4780, 4877, 5260, 6186, 6195,
+    6211, 6251, 6345, 6441, 6794, 6926, 6938, 7018, 7183, 7233, 7256, 7273, 7624, 7690, 7977, 67, 82, 400, 529,
+    609, 640, 929, 1041, 1157, 1179, 1186, 1249, 1281, 1666, 1858, 1923, 2060, 2180, 2334, 2406, 2500, 2563,
+    2711, 3173, 3204, 3463, 3524, 3598, 3628, 3716, 4036, 4116, 4169, 4489, 4509, 4608, 4618, 4660, 4678, 4764,
+    5006, 5130, 5899, 5919, 6150, 6267, 6298, 6351, 6442, 6475, 6667, 6730, 6954, 7048, 7174, 7209, 7212, 7224,
+    7289, 7308, 7400, 7432, 81, 140, 176, 232, 296, 416, 625, 770, 915, 945, 1028, 1042, 1158, 1185, 1218, 1537,
+    1814, 2068, 2183, 2307, 2322, 2339, 2390, 2503, 2950, 3109, 3189, 3332, 3397, 3457, 3606, 3612, 3846, 4102,
+    4236, 4525, 4687, 5000, 5020, 5582, 5641, 5871, 5935, 6144, 6339, 6403, 6539, 6921, 6986, 7173, 7188, 7196,
+    7321, 7336, 7561, 7705, 7937, 8065, 8075, 27, 54, 108, 168, 216, 304, 388, 432, 520, 561, 580, 705, 777, 784,
+    864, 907, 1039, 1167, 1203, 1546, 1803, 1806, 2314, 2366, 2382, 2564, 2639, 2821, 3081, 3084, 3149, 3221,
+    3365, 3469, 3587, 3600, 3605, 3617, 3668, 3840, 4373, 4413, 4541, 4552, 4701, 5133, 5198, 5838, 5900, 6179,
+    6218, 6303, 6395, 6914, 7042, 7216, 7234, 7274, 7322, 7368, 7692, 8169, 131, 137, 164, 464, 578, 673, 800,
+    903, 1095, 1122, 1195, 1410, 1475, 1762, 1809, 1822, 1834, 2056, 2063, 2078, 2082, 2178, 2276, 2327, 2330,
+    2370, 2599, 2627, 2693, 2758, 3137, 3477, 3594, 3618, 3684, 3812, 4119, 4175, 4548, 4555, 4573, 4637, 4644,
+    4654, 4682, 4692, 4717, 5068, 5126, 5254, 5446, 5486, 5519, 5663, 5837, 5895, 6031, 6161, 6217, 6279, 6280,
+    6291, 6435, 7210, 7236, 7276, 7290, 7695, 7720, 7725, 7737, 7745, 8136, 51, 138, 280, 352, 549, 592, 657,
+    772, 832, 908, 917, 992, 1051, 1058, 1121, 1138, 1191, 1217, 1346, 1816, 1842, 2018, 2049, 2066, 2190, 2274,
+    2341, 2346, 2372, 2510, 2629, 2726, 3493, 3521, 3608, 3632, 3637, 3700, 3860, 3973, 4126, 4136, 4156, 4189,
+    4229, 4366, 4405, 4421, 4461, 4628, 4696, 4733, 5276, 5420, 5455, 5470, 5516, 5642, 5677, 6162, 6168, 6223,
+    6273, 6363, 6408, 7171, 7245, 7264, 7752, 7946, 8077, 8089, 23, 53, 134, 161, 336, 454, 496, 528, 608, 921,
+    928, 1057, 1088, 1098, 1107, 1137, 1173, 1314, 1379, 1540, 1554, 1728, 1797, 1930, 2102, 2196, 2316, 2348,
+    2375, 2436, 2562, 2710, 2819, 3074, 3092, 3509, 3638, 3876, 4112, 4120, 4360, 4380, 4392, 4445, 4545, 4558,
+    4565, 4605, 4614, 4649, 4669, 4740, 4813, 4997, 5386, 5406, 5418, 5423, 5452, 5675, 5678, 5695, 5703, 6274,
+    6285, 6371, 6664, 7054, 7066, 7185, 7200, 7243, 7246, 7280, 7324, 7680, 7685, 7729, 7881, 39, 78, 133, 156,
+    162, 227, 274, 312, 328, 453, 519, 569, 624, 914, 965, 1032, 1037, 1075, 1097, 1165, 1313, 1363, 1409, 1825,
+    1828, 1938, 2074, 2084, 2214, 2242, 2279, 2439, 2534, 2691, 3143, 3593, 3650, 3656, 3661, 3781, 4123, 4148,
+    4153, 4239, 4353, 4363, 4481, 4551, 4673, 4781, 5128, 5258, 5358, 5637, 5710, 5807, 5835, 5897, 5917, 6173,
+    6355, 6413, 6419, 6425, 6459, 6795, 6858, 6927, 7019, 7297, 7300, 7307, 7312, 7562, 7723, 7953 };
+
+static int cbest_14[1023] = {
+    1, 2, 8737, 4, 8, 13105, 16, 8736, 32, 4368, 3, 2184, 17, 1092, 15289, 34, 546, 5, 64, 68, 273, 8739, 8745,
+    6, 136, 13104, 272, 9, 8741, 128, 8873, 12, 6552, 13109, 10, 544, 13107, 256, 18, 24, 3276, 8753, 33, 1088,
+    4369, 15288, 16381, 2185, 8705, 13089, 13173, 20, 512, 1093, 2186, 4372, 8195, 8738, 8744, 13113, 35, 66,
+    547, 1094, 1638, 2188, 4370, 4376, 8752, 8865, 12832, 15291, 36, 48, 65, 69, 257, 2176, 6416, 8707, 10921, 7,
+    19, 25, 70, 137, 3208, 8740, 9008, 9829, 13088, 13169, 15281, 96, 132, 138, 277, 554, 1024, 1108, 1604, 6544,
+    8749, 8872, 50, 140, 275, 281, 562, 802, 819, 3272, 4504, 7644, 8747, 8801, 8805, 12833, 13073, 13108, 21,
+    100, 129, 192, 276, 401, 1636, 4352, 4436, 8743, 12563, 13106, 15257, 15293, 13, 38, 40, 72, 130, 200, 264,
+    274, 280, 514, 550, 818, 2216, 2252, 6553, 8193, 8875, 9009, 15259, 11, 14, 49, 384, 400, 545, 1124, 2048,
+    2218, 6554, 8761, 8877, 13075, 13111, 15273, 409, 1100, 1126, 14197, 15153, 15839, 42, 528, 768, 1109, 4097,
+    4432, 8937, 9144, 15016, 16377, 16380, 51, 76, 98, 102, 204, 408, 552, 563, 803, 1090, 2200, 2248, 3277,
+    8203, 8704, 10785, 13172, 144, 260, 548, 560, 800, 817, 1028, 1089, 1536, 3822, 4096, 4353, 8194, 8760,
+    13112, 13117, 13241, 15272, 16365, 28, 258, 265, 1606, 1634, 4380, 6556, 8864, 8869, 8993, 9136, 10913,
+    12561, 12836, 15290, 26, 80, 84, 196, 385, 513, 816, 1056, 2180, 2187, 2190, 3072, 3268, 3278, 4373, 4400,
+    4496, 6145, 7508, 8706, 8755, 8941, 9016, 9145, 9287, 10920, 12013, 12290, 13175, 15017, 22, 67, 152, 1095,
+    1639, 2189, 3212, 3292, 4371, 4374, 4377, 4568, 4572, 6418, 6536, 6584, 8225, 8929, 9825, 9828, 12849, 13093,
+    13141, 13168, 13233, 14129, 14747, 15280, 16373, 16383, 37, 529, 570, 769, 1104, 1600, 1632, 2177, 5460,
+    6144, 6417, 6586, 7636, 8466, 8713, 8748, 8867, 13091, 13097, 13171, 15837, 16313, 16364, 71, 134, 168, 285,
+    392, 520, 530, 770, 1026, 1058, 1096, 2056, 2178, 2201, 2284, 3209, 4233, 4360, 4402, 4508, 4914, 6424, 7640,
+    8709, 8721, 8746, 8757, 8800, 8804, 8992, 9121, 9137, 10923, 11809, 12837, 13072, 13115, 13137, 14193, 15566,
+    97, 133, 139, 142, 145, 261, 288, 305, 337, 555, 561, 785, 801, 1025, 1120, 1140, 1605, 1646, 2112, 2116,
+    2730, 3210, 3264, 3754, 4378, 6420, 6545, 8201, 8211, 8451, 8742, 8754, 8803, 8809, 8841, 8889, 9001, 9017,
+    9831, 10925, 12291, 12562, 12834, 12840, 15161, 15256, 15283, 15292, 29, 56, 141, 259, 268, 279, 284, 674,
+    1110, 1142, 1538, 1570, 1911, 2280, 2457, 3273, 3820, 4232, 4505, 6281, 6546, 7628, 7645, 8192, 8715, 8751,
+    8769, 8874, 9012, 9285, 9317, 12848, 12960, 13057, 13077, 13092, 14880, 15258, 15265, 15285, 15295, 27, 52,
+    74, 81, 85, 101, 160, 193, 304, 336, 516, 558, 784, 1060, 1348, 1365, 1540, 1637, 2052, 2254, 2286, 3140,
+    3200, 3274, 3818, 4225, 4437, 4506, 4560, 6480, 6528, 6548, 7440, 8190, 8199, 8467, 8723, 8807, 8876, 9010,
+    9129, 9837, 11945, 12307, 12547, 13074, 13090, 13096, 13110, 13143, 13655, 14745, 14777, 15241, 15353, 15357,
+    15831, 23, 39, 41, 44, 73, 131, 153, 194, 201, 278, 290, 307, 403, 515, 536, 551, 610, 614, 806, 823, 1116,
+    1122, 1228, 1612, 1910, 2050, 2217, 2220, 2253, 2456, 2696, 3224, 3240, 3293, 3720, 4105, 4438, 6280, 6537,
+    8331, 8720, 8756, 8773, 8879, 8881, 9120, 9761, 9845, 10849, 10853, 12288, 12593, 13157, 13297, 13617, 14196,
+    15008, 15152, 15243, 15567, 15835, 15838, 16245, 15, 58, 112, 170, 202, 283, 341, 405, 571, 682, 810, 1040,
+    1105, 1125, 1364, 1568, 1620, 1860, 1877, 2049, 2192, 2219, 2250, 3076, 4101, 4112, 4224, 4356, 4500, 5392,
+    6448, 6555, 7504, 7646, 8210, 8227, 8450, 8711, 8813, 8888, 8936, 9000, 10889, 12009, 12567, 12835, 12841,
+    12968, 13059, 13177, 13181, 13305, 13309, 14888, 15155, 16108, 16376, 104, 306, 386, 393, 402, 531, 568, 771,
+    822, 930, 1030, 1101, 1127, 1602, 1644, 2120, 2728, 3080, 3288, 3752, 3814, 4104, 4354, 4361, 4434, 4440,
+    4444, 6153, 7576, 8202, 8219, 8464, 8602, 8843, 8933, 9013, 9797, 10784, 10789, 10891, 11877, 12571, 12896,
+    12900, 12961, 13056, 13237, 14097, 14181, 14474, 14881, 15249, 15264, 15275, 16357, 16369, 43, 116, 148, 224,
+    266, 282, 289, 340, 388, 404, 411, 465, 522, 576, 580, 608, 672, 1072, 1102, 1141, 1220, 1876, 1909, 2208,
+    2222, 2240, 2244, 2282, 3136, 4100, 4433, 4468, 4564, 4912, 5456, 6273, 6400, 6484, 7444, 7620, 7632, 8323,
+    8722, 8765, 9011, 9128, 9799, 9965, 10787, 10989, 12306, 12546, 13079, 13116, 13139, 13240, 13245, 14199,
+    15033, 15240, 15251, 15261, 15564, 15869, 16317, 16361, 54, 57, 77, 99, 103, 162, 205, 232, 269, 518, 553,
+    556, 566, 787, 1062, 1091, 1111, 1143, 1542, 2060, 2210, 2232, 2249, 3788, 3816, 6152, 6450, 7629, 7783,
+    8182, 8197, 8209, 8241, 8449, 8481, 8587, 8763, 8868, 8880, 8939, 9146, 9295, 9844, 10912, 10917, 11471,
+    11813, 12005, 12289, 12560, 13153, 13156, 13301, 13653, 13685, 15009, 15018, 15157, 15242, 15562, 16379, 46,
+    53, 78, 208, 320, 410, 448, 464, 549, 612, 772, 804, 821, 938, 955, 1029, 1349, 1537, 1642, 1908, 2202, 2234,
+    3242, 3284, 3722, 3823, 4240, 4464, 6160, 6272, 6529, 6558, 6576, 7098, 7237, 8233, 8329, 8771, 8775, 8871,
+    8905, 8940, 9020, 9283, 9286, 10793, 12012, 12294, 12844, 12857, 12969, 13058, 13174, 13587, 14099, 14521,
+    14739, 14761, 14889, 15020, 15321, 15430, 15833, 16109, 16349, 82, 88, 146, 262, 291, 537, 578, 680, 776,
+    786, 807, 1032, 1074, 1117, 1160, 1574, 1607, 1635, 1654, 1894, 1907, 2124, 2182, 2204, 2440, 3084, 3225,
+    3308, 3810, 4099, 4120, 4301, 4381, 4488, 4643, 6147, 6557, 6578, 6616, 6620, 7782, 8188, 8207, 8218, 8224,
+    8465, 8603, 8833, 8928, 9249, 9824, 11873, 12305, 12337, 12545, 12565, 12577, 12853, 12897, 12901, 12977,
+    13119, 13140, 13232, 13243, 14128, 14133, 14180, 14475, 14746, 15121, 15217, 15263, 15274, 15771, 15829,
+    16177, 16356, 16372, 16382, 30, 59, 113, 197, 206, 469, 811, 820, 827, 896, 928, 954, 1041, 1057, 1136, 1216,
+    1344, 1361, 1572, 1621, 1861, 2080, 2144, 2181, 2193, 2321, 3073, 3204, 3214, 3269, 3279, 4113, 4357, 4384,
+    4404, 4420, 4497, 4922, 7236, 7492, 7509, 8579, 8600, 8712, 8729, 8866, 9138, 9319, 9827, 9833, 10915, 10985,
+    11267, 12595, 12631, 12838, 13101, 13170, 13382, 13619, 13651, 14131, 14472, 14504, 15032, 15325, 15565,
+    15827, 16125, 16312 };
+
+static int cbest_15[1023] = {
+    1, 2, 16385, 4, 8, 24577, 16, 32, 64, 28673, 128, 256, 512, 1024, 30721, 2048, 4096, 8192, 16384, 31745, 3,
+    6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 5, 16387, 9, 16389, 10, 17, 16393, 24579,
+    28672, 18, 33, 14336, 16401, 24581, 20, 34, 65, 7168, 16417, 24585, 32257, 36, 66, 129, 3584, 16449, 24593,
+    28675, 40, 68, 130, 257, 1792, 16513, 24609, 28677, 30720, 72, 132, 258, 513, 896, 16641, 24641, 28681, 80,
+    136, 260, 448, 514, 1025, 15360, 16897, 24705, 28689, 144, 224, 264, 516, 1026, 2049, 17409, 24833, 28705,
+    30723, 112, 160, 272, 520, 1028, 2050, 4097, 7680, 18433, 25089, 28737, 30725, 56, 288, 528, 1032, 2052,
+    4098, 8193, 20481, 25601, 28801, 30729, 31744, 32513, 28, 320, 544, 1040, 2056, 3840, 4100, 8194, 26625,
+    28929, 30737, 14, 576, 1056, 2064, 4104, 8196, 16386, 29185, 30753, 7, 13, 25, 49, 97, 193, 385, 640, 769,
+    1088, 1537, 1920, 2080, 3073, 4112, 6145, 8200, 12289, 15872, 16388, 29697, 30785, 31747, 26, 50, 98, 194,
+    386, 770, 1152, 1538, 2112, 3074, 4128, 6146, 8208, 12290, 16391, 16392, 16397, 16409, 16433, 16481, 16577,
+    16769, 17153, 17921, 19457, 22529, 24578, 30849, 31749, 52, 100, 196, 388, 772, 960, 1280, 1540, 2176, 3076,
+    4160, 6148, 8224, 12292, 16400, 24580, 30977, 31753, 11, 104, 200, 392, 776, 1544, 2304, 3080, 4224, 6152,
+    7936, 8256, 12296, 16416, 24583, 24584, 24589, 24601, 24625, 24673, 24769, 24961, 25345, 26113, 27649, 31233,
+    31761, 32256, 19, 22, 208, 400, 480, 784, 1552, 2560, 3088, 4352, 6160, 8320, 12304, 14337, 16395, 16448,
+    24592, 28674, 31777, 21, 35, 38, 44, 416, 800, 1568, 3104, 4608, 6176, 7169, 8448, 12320, 14338, 16403,
+    16512, 24608, 28676, 31809, 32641, 37, 67, 70, 76, 88, 240, 832, 1600, 3136, 3585, 3968, 5120, 6208, 7170,
+    8704, 12352, 14340, 16405, 16419, 16640, 23553, 24587, 24640, 28679, 28680, 28685, 28697, 28721, 28769,
+    28865, 29057, 29441, 30209, 31873, 32259, 41, 69, 131, 134, 140, 152, 176, 1664, 1793, 3200, 3586, 6272,
+    7172, 9216, 12416, 14344, 16128, 16421, 16451, 16896, 19969, 24595, 24704, 28688, 32001, 32261, 42, 73, 120,
+    133, 259, 262, 268, 280, 304, 352, 897, 1794, 3328, 3588, 6400, 7176, 10240, 12544, 14352, 16425, 16453,
+    16515, 17408, 18177, 24597, 24611, 24832, 28704, 30722, 32265, 74, 81, 137, 261, 449, 515, 518, 524, 536,
+    560, 608, 704, 898, 1796, 1984, 3592, 6656, 7184, 12800, 14368, 15361, 16457, 16517, 16643, 17281, 18432,
+    24613, 24643, 25088, 28161, 28683, 28736, 30724, 32273, 60, 82, 138, 145, 225, 265, 450, 517, 900, 1027,
+    1030, 1036, 1048, 1072, 1120, 1216, 1408, 1800, 3600, 7200, 13312, 14400, 15362, 16465, 16521, 16645, 16833,
+    16899, 20480, 24617, 24645, 24707, 25600, 26369, 28691, 28800, 30727, 30728, 30733, 30745, 30769, 30817,
+    30913, 31105, 31489, 32289, 32512, 84, 113, 146, 161, 226, 266, 273, 452, 521, 904, 1029, 1808, 2051, 2054,
+    2060, 2072, 2096, 2144, 2240, 2432, 2816, 3616, 7232, 7681, 8064, 14464, 15364, 16529, 16609, 16649, 16901,
+    17411, 24649, 24709, 24835, 25473, 26624, 28693, 28707, 28928, 30736, 32321, 30, 57, 114, 148, 162, 228, 274,
+    289, 456, 522, 529, 912, 992, 1033, 1824, 2053, 3648, 4099, 4102, 4108, 4120, 4144, 4192, 4288, 4480, 4864,
+    5632, 7296, 7682, 14592, 15368, 16497, 16545, 16657, 16905, 17413, 18435, 24065, 24657, 24713, 24837, 25025,
+    25091, 28709, 28739, 29184, 30752, 32385, 29, 58, 116, 164, 232, 276, 290, 321, 464, 530, 545, 928, 1034,
+    1041, 1856, 2057, 3712, 3841, 4101, 7424, 7684, 8195, 8198, 8204, 8216, 8240, 8288, 8384, 8576, 8960, 9728,
+    11264, 14848, 15376, 16441, 16673, 16913, 17417, 18437, 20483, 24721, 24801, 24841, 25093, 25603, 28713,
+    28741, 28803, 29696, 30465, 30731, 30784, 31746, 32515, 15, 168, 292, 322, 532, 546, 577, 1042, 1057, 2058,
+    2065, 3842, 4105, 7688, 8197, 15392, 16390, 16396, 16408, 16413, 16432, 16480, 16576, 16705, 16768, 16929,
+    17152, 17425, 17920, 18441, 19456, 20225, 20485, 22528, 24689, 24737, 24849, 25097, 25605, 26627, 28745,
+    28805, 28931, 29569, 30739, 30848, 31748, 32517, 32705, 296, 324, 496, 548, 578, 641, 1044, 1058, 1089, 1921,
+    2066, 2081, 3844, 4032, 4106, 4113, 7696, 8201, 15424, 15873, 16256, 16399, 16961, 17441, 18449, 20489,
+    24633, 24865, 25105, 25609, 26629, 28753, 28809, 28933, 29121, 29187, 30741, 30755, 30976, 31751, 31752,
+    31757, 31769, 31793, 31841, 31937, 32129, 32521, 27, 51, 54, 99, 102, 108, 195, 198, 204, 216, 328, 387, 390,
+    396, 408, 432, 552, 580, 642, 771, 774, 780, 792, 816, 864, 1060, 1090, 1153, 1539, 1542, 1548, 1560, 1584,
+    1632, 1728, 1922, 2068, 2082, 2113, 3075, 3078, 3084, 3096, 3120, 3168, 3264, 3456, 3848, 4114, 4129, 6147,
+    6150, 6156, 6168, 6192, 6240, 6336, 6528, 6912, 7712, 8202, 8209, 12291, 12294, 12300, 12312, 12336, 12384,
+    12480, 12672, 13056, 13824, 15488, 15874, 17025, 17473, 18305, 18465, 20497, 24582, 24588, 24600, 24605,
+    24624, 24672, 24768, 24897, 24960, 25121, 25344, 25617, 26112, 26633, 27648, 28417, 28817, 28897, 28937,
+    29189, 29699, 30757, 30787, 31232, 31760, 32529, 53, 101, 197, 336, 389, 584, 644, 773, 961, 1064, 1092,
+    1154, 1281, 1541, 1924, 2084, 2114, 2177, 3077, 3856, 4116, 4130, 4161, 6149, 7744, 8210, 8225, 12293, 15616,
+    15876, 16394, 16411, 16435, 16483, 16579, 16771, 17155, 17537, 17923, 18497, 19459, 20513, 22531, 24591,
+    25153, 25633, 26641, 28785, 28833, 28945, 29193, 29701, 30761, 30789, 30851, 31776, 32545, 105, 201, 248,
+    393, 592, 648, 777, 962, 1096, 1156, 1282, 1545, 1928, 2088, 2116, 2178, 2305, 3081, 3872, 4132, 4162, 4225,
+    6153, 7808, 7937, 8212, 8226, 8257, 12297, 15880, 16402, 16437, 16485, 16581, 16773, 17157, 17345, 17665,
+    17925, 18561, 19461, 20545, 22533, 25217, 25665, 26497, 26657, 28729, 28961, 29201, 29705, 30793, 30853,
+    30979, 31617, 31755, 31808, 32577, 32640, 23, 46, 92, 106, 184, 202, 209, 368, 394, 401, 481, 656, 736, 778,
+    785, 964, 1104, 1160, 1284, 1472, 1546, 1553, 1936, 2016, 2120, 2180, 2306, 2561, 2944, 3082, 3089, 3904,
+    4136, 4164, 4226, 4353, 5888, 6154, 6161, 7938, 8228, 8258, 8321, 11776, 12298, 12305, 15888, 16404, 16418,
+    16489, 16585, 16777, 17161, 17929, 18689, 19465, 20609, 22537, 23552, 24321, 24586, 24603, 24627, 24675,
+    24771, 24963, 25347, 25729, 26115, 26689, 27651, 28678, 28684, 28696, 28701, 28720, 28768, 28864, 28993,
+    29056, 29217, 29440, 29713, 30208, 30801, 30857, 30981, 31169, 31235, 31763, 31872, 32258, 45, 78, 156, 312,
+    624, 672, 801, 1554, 2562, 14384, 16593, 16785, 17937, 24677, 31237, 31765 };
+
+static int cbest_16[1023] = {
+    1, 2, 34821, 4, 8, 52231, 16, 60934, 34820, 32, 17410, 3, 8705, 17, 34, 5, 68, 34823, 34829, 6, 136, 30467,
+    34817, 39173, 52230, 64, 272, 52229, 9, 544, 52227, 10, 1088, 12, 2176, 26115, 4352, 50311, 60935, 18, 8704,
+    45956, 60932, 20, 128, 24, 34837, 47876, 17408, 30466, 33, 36, 17411, 52239, 59974, 40, 22978, 48, 256, 8707,
+    17414, 34822, 34828, 43524, 60930, 65286, 19, 35, 8709, 17418, 23938, 26114, 34816, 34836, 34853, 39172,
+    52247, 21, 69, 15233, 21762, 30465, 34825, 52225, 52228, 7, 25, 38, 72, 137, 13057, 19586, 34831, 34881,
+    52226, 42, 65, 80, 273, 10881, 26113, 29987, 34819, 34855, 39175, 50, 66, 70, 76, 545, 9793, 11489, 45957,
+    60933, 60942, 11, 14, 84, 96, 138, 1089, 11969, 34957, 37253, 50310, 52261, 13, 152, 274, 1090, 2177, 34885,
+    34949, 35093, 39169, 50309, 52246, 52263, 49, 144, 257, 546, 4353, 8713, 32643, 32901, 34845, 35365, 38341,
+    47877, 60950, 22, 28, 140, 512, 2180, 4354, 25155, 30471, 35909, 40261, 45716, 52291, 52295, 100, 129, 160,
+    276, 2178, 8706, 17426, 26123, 39717, 49351, 52235, 59975, 44, 98, 130, 168, 548, 4360, 8708, 8721, 34833,
+    51271, 52237, 60928, 81, 132, 192, 304, 514, 1092, 15232, 30464, 30475, 34839, 34861, 39181, 43525, 45958,
+    47872, 50307, 52238, 52367, 53703, 60931, 60951, 60966, 65287, 51, 88, 102, 204, 280, 408, 816, 1632, 3264,
+    6528, 8720, 13056, 17409, 17412, 26119, 45952, 47396, 52243, 52503, 59972, 60964, 26, 37, 85, 170, 196, 288,
+    340, 552, 680, 1360, 2720, 4356, 5440, 10880, 17416, 22858, 22976, 23936, 26112, 29986, 34844, 40565, 40805,
+    52245, 52775, 54663, 41, 56, 153, 162, 200, 306, 612, 1096, 1224, 2448, 4896, 7616, 8737, 9792, 11488, 17422,
+    17440, 21760, 22979, 30483, 34849, 34852, 39189, 47044, 47878, 49895, 50855, 59494, 60454, 65284, 145, 320,
+    336, 1028, 2184, 8711, 11968, 17415, 17442, 34824, 34889, 34893, 43520, 50583, 52224, 60940, 60994, 23, 29,
+    258, 392, 560, 608, 17419, 23698, 23939, 30482, 34827, 34830, 34832, 34863, 34880, 43526, 50319, 52259,
+    56583, 60943, 64806, 46, 58, 74, 176, 260, 324, 384, 1024, 1104, 3808, 8225, 8712, 14993, 17427, 17474,
+    19584, 21763, 32642, 34818, 34838, 34854, 39174, 45964, 52257, 57574, 59970, 39, 73, 82, 92, 264, 290, 2192,
+    5744, 5984, 8769, 11429, 19587, 25154, 26131, 29985, 30227, 30470, 34869, 35077, 38933, 39205, 41604, 43532,
+    52242, 52359, 58054, 60948, 61070, 63366, 65294, 43, 52, 112, 116, 400, 2056, 4368, 8739, 12577, 16450,
+    17478, 20802, 21766, 26122, 29747, 30497, 34841, 34851, 34956, 37252, 42212, 50327, 52244, 52255, 52260,
+    60998, 61206, 65282, 67, 71, 77, 89, 178, 184, 576, 672, 1904, 8773, 10401, 10883, 11425, 11849, 13061,
+    15235, 15241, 17546, 18626, 22850, 22982, 26121, 26130, 30499, 34884, 34948, 34965, 35092, 39168, 39188,
+    42692, 45700, 45717, 45972, 47884, 50191, 50308, 52233, 52262, 59014, 60938, 15, 27, 78, 97, 139, 148, 164,
+    289, 352, 356, 1120, 1216, 2992, 8717, 8841, 9313, 13059, 13065, 17538, 17682, 19594, 23522, 30469, 30474,
+    32900, 34857, 34883, 35364, 37013, 37249, 38340, 39171, 44612, 45836, 52293, 59906, 60246, 57, 86, 232, 275,
+    640, 784, 1091, 2872, 8715, 8977, 9797, 17424, 17434, 17954, 23942, 26118, 26147, 29953, 32641, 34897, 34901,
+    34945, 34981, 35908, 37255, 38221, 39233, 40260, 49349, 51127, 52290, 52294, 59766, 59982, 60110, 60929,
+    60949, 154, 224, 321, 368, 547, 648, 712, 952, 4112, 4384, 9795, 11491, 15237, 16321, 17430, 22986, 25153,
+    26117, 26145, 28787, 29027, 29955, 32403, 32897, 34871, 34887, 34951, 38337, 39207, 39716, 40533, 45596,
+    45959, 47873, 47892, 49350, 51007, 51269, 52234, 52241, 52271, 52289, 52303, 60946, 60967, 104, 118, 141,
+    156, 259, 328, 393, 513, 516, 561, 580, 704, 768, 800, 1496, 2181, 2208, 4355, 8725, 8736, 11393, 11457,
+    11971, 19590, 21106, 21346, 22306, 22918, 29507, 30473, 30535, 34868, 34917, 34959, 35009, 35013, 35076,
+    40021, 45701, 45953, 45973, 47397, 49231, 50305, 50341, 51270, 52236, 52269, 52279, 52311, 52487, 59973,
+    60965, 30, 59, 101, 142, 161, 177, 186, 261, 277, 325, 385, 464, 520, 578, 786, 1105, 1344, 1424, 2179, 2182,
+    4362, 8710, 8723, 10885, 17420, 19170, 20130, 23946, 24675, 25635, 29991, 30603, 31683, 32647, 34835, 34840,
+    34860, 34909, 34953, 34973, 35095, 35101, 35911, 39180, 39309, 39477, 40517, 40549, 40737, 50306, 50326,
+    50343, 52254, 52277, 52366, 53702, 59910, 59990, 60962, 61062, 45, 54, 83, 93, 99, 114, 131, 134, 146, 169,
+    172, 194, 236, 265, 278, 291, 358, 476, 528, 549, 650, 736, 1094, 1122, 1436, 1572, 2048, 2193, 2240, 2432,
+    2856, 4361, 8724, 8741, 11493, 17450, 17482, 19858, 21770, 22786, 22914, 22994, 30531, 32903, 32909, 34847,
+    34913, 34964, 35089, 35367, 35373, 38343, 39183, 39237, 39719, 40535, 45988, 47045, 47879, 49827, 51267,
+    52327, 52365, 52502, 53583, 53701, 54661, 59426, 59495, 60455, 60958, 65285, 53, 113, 117, 133, 193, 234,
+    305, 308, 372, 448, 468, 515, 550, 582, 642, 716, 748, 936, 1093, 1152, 1300, 1408, 1428, 2210, 2848, 3144,
+    4369, 8224, 8722, 11153, 11459, 11841, 11973, 14992, 17446, 17448, 22798, 25163, 26127, 30481, 34877, 34983,
+    35333, 35361, 35917, 39177, 39685, 40263, 40564, 40804, 43521, 43540, 45236, 45476, 45580, 45718, 47636,
+    47893, 49893, 50183, 50371, 50567, 50991, 52251, 52299, 52325, 52363, 52501, 52774, 53575, 54662, 60452,
+    60941, 60947, 60995, 65302, 103, 166, 179, 185, 205, 281, 296, 312, 354, 370, 409, 472, 714, 740, 817, 928,
+    1164, 1432, 1480, 1568, 1633, 1872, 2244, 2600, 3265, 4358, 4364, 4386, 5712, 6288, 6529, 8768, 8833, 9729,
+    10065, 10673, 10889, 11397, 11428, 11761, 17413, 17444, 22790, 22856, 23682, 23954, 26183, 29713, 29984,
+    29995, 30123, 30226, 34848, 34859, 34896, 34900, 35905, 40257, 43527, 45116, 45572, 45712, 45828, 46016,
+    47156, 47392, 47874, 49894, 50854, 50983, 52307, 52499, 52773, 60960, 60974, 60992, 64807, 90, 149, 171, 197,
+    208, 238, 282, 341, 353, 357, 518, 553, 681, 744, 770, 1098, 1156, 1280, 1296, 1361, 1472, 1634, 2188, 2328,
+    2721, 2864, 3266, 3744, 4357, 4420, 5200, 5441, 6530, 7496, 8729, 8738, 9585, 9801, 9929, 10553, 11395,
+    11497, 12576, 14977, 15249, 17417, 21778, 22794, 22859, 22977, 23696, 23818, 23937, 26129, 26251, 29715,
+    29746, 30055, 30479, 30480, 30496, 33989, 34870, 34888, 34892, 34905, 34915, 34919, 34989, 35017, 38213,
+    39191, 39713, 40741, 45954, 45965, 45990, 46924, 47908, 49347, 50317, 50582, 50735, 50853, 52240, 52267,
+    52771, 54423, 56581, 57506, 57510, 57575, 59492, 59971, 59991, 60102, 60936, 60982, 198, 374, 1097, 1225,
+    7488, 15113, 17441, 17472, 26387, 29883, 30211, 34879, 35205, 50463, 50999, 52258, 61071 };
+
+
+static int cbest_17[1023] = {
+    1, 2, 65540, 4, 32770, 8, 16385, 16, 32, 73732, 64, 128, 36866, 256, 512, 18433, 1024, 2048, 4096, 74756,
+    8192, 16384, 37378, 32768, 3, 18689, 65536, 65541, 5, 32771, 65542, 6, 9, 18, 36, 72, 144, 288, 576, 1152,
+    2304, 4608, 9216, 18432, 98310, 10, 17, 16387, 32774, 36864, 65548, 81925, 12, 33, 16389, 32778, 49155,
+    65556, 73728, 73733, 74884, 20, 34, 65, 16393, 32786, 65572, 73734, 24, 66, 129, 16401, 32802, 36867, 65604,
+    106502, 40, 68, 130, 257, 16417, 32834, 65668, 73740, 90117, 102406, 48, 132, 258, 513, 16449, 32898, 36870,
+    37442, 65796, 73748, 80, 136, 260, 514, 1025, 16513, 18435, 33026, 36874, 53251, 66052, 73764, 83973, 96,
+    264, 516, 1026, 2049, 16641, 18437, 33282, 36882, 51203, 66564, 73796, 160, 272, 520, 1028, 2050, 4097,
+    16897, 18441, 18688, 33794, 36898, 37376, 67588, 73860, 74752, 74757, 110598, 192, 528, 1032, 2052, 4098,
+    8193, 9344, 17409, 18449, 18721, 34818, 36930, 69636, 73988, 74758, 320, 544, 1040, 2056, 4100, 4672, 8194,
+    18465, 36994, 74244, 92165, 107526, 384, 1056, 2064, 2336, 4104, 8196, 16386, 18497, 20481, 37122, 37379,
+    40962, 74764, 81924, 91141, 640, 1088, 1168, 2080, 4112, 8200, 16388, 18561, 24577, 32769, 49154, 55299,
+    74772, 75780, 102918, 584, 768, 2112, 4128, 8208, 16392, 37382, 37890, 74788, 77828, 98308, 292, 1280, 2176,
+    4160, 8224, 16400, 18945, 32772, 32784, 37386, 38914, 53763, 65537, 74820, 74900, 146, 1536, 4224, 8256,
+    16416, 18691, 19457, 32776, 37394, 49153, 65538, 65543, 65568, 84229, 90116, 111622, 7, 19, 37, 73, 145, 289,
+    577, 1153, 2305, 2560, 4352, 4609, 8320, 9217, 16448, 18693, 37410, 45058, 51459, 75012, 98306, 98311,
+    111110, 11, 38, 74, 290, 578, 1154, 2306, 3072, 4610, 8448, 9218, 16512, 18434, 18697, 22529, 32775, 32800,
+    36865, 53250, 65544, 65549, 65558, 65612, 65684, 65828, 66116, 66692, 67844, 70148, 75268, 81921, 83972,
+    93189, 106500, 13, 22, 76, 148, 580, 1156, 2308, 4612, 5120, 8704, 9220, 16640, 18436, 18705, 26625, 32779,
+    32806, 32832, 32842, 32914, 33058, 33346, 33922, 35074, 37506, 41986, 51202, 65550, 65552, 65557, 73729,
+    74880, 74885, 81927, 102404, 14, 21, 26, 35, 44, 152, 296, 1160, 2312, 4616, 6144, 9224, 16391, 16403, 16421,
+    16457, 16529, 16673, 16896, 16961, 17537, 18440, 20993, 25601, 32787, 32896, 36868, 36880, 37440, 37450,
+    37634, 65573, 73730, 73735, 73760, 74886, 76804, 92421, 98318, 114695, 25, 52, 67, 88, 304, 592, 2320, 4624,
+    9232, 10240, 16395, 17408, 18448, 18720, 18753, 32782, 32803, 33024, 36872, 49159, 53249, 55811, 65574,
+    65600, 65605, 78852, 81933, 98326, 106498, 106503, 107654, 41, 50, 69, 104, 131, 176, 608, 1184, 4640, 9248,
+    12288, 16397, 18464, 18817, 32790, 32835, 33280, 38402, 49163, 51201, 55555, 65564, 65606, 65664, 65669,
+    73736, 73741, 73750, 73804, 73876, 74020, 74308, 74892, 76036, 78340, 81941, 90113, 91269, 92164, 98342,
+    102402, 102407, 28, 42, 49, 70, 82, 100, 133, 208, 259, 352, 1216, 2368, 9280, 9360, 16405, 16419, 18496,
+    20480, 32794, 32899, 33792, 36871, 36896, 37443, 39426, 49171, 65580, 65670, 65792, 65797, 73742, 73744,
+    73749, 81957, 90119, 91140, 98374, 110596, 81, 134, 137, 164, 200, 261, 416, 515, 704, 2432, 4736, 16409,
+    16451, 18560, 19201, 24576, 32810, 32838, 33027, 34816, 36875, 36902, 36928, 36938, 37010, 37154, 38018,
+    39170, 46082, 49187, 55298, 65588, 65798, 66048, 66053, 73765, 74916, 81989, 83969, 98438, 102982, 106510,
+    112134, 122887, 97, 138, 262, 265, 274, 328, 400, 517, 832, 1027, 1408, 4680, 4864, 9472, 16425, 16453,
+    16515, 18725, 19713, 32818, 32902, 33283, 36883, 36992, 37446, 45570, 49219, 65620, 65676, 66054, 66560,
+    66565, 73766, 73792, 73797, 74948, 82053, 83975, 90125, 98566, 102414, 106518, 107524, 118791, 56, 84, 98,
+    140, 161, 266, 273, 518, 521, 530, 548, 656, 800, 1029, 1664, 2051, 2816, 9728, 16433, 16517, 16643, 18439,
+    18451, 18469, 18505, 18577, 18944, 19009, 19585, 23041, 27649, 32850, 32906, 33030, 33795, 36878, 36899,
+    37120, 37377, 40960, 49283, 53255, 53762, 53827, 65636, 65804, 66566, 67584, 67589, 73756, 73798, 73856,
+    73861, 74753, 82181, 90133, 98822, 102422, 106534, 110594, 110599, 111750, 116743, 162, 193, 268, 522, 529,
+    1030, 1033, 1042, 1060, 1096, 1312, 1600, 2053, 2340, 3328, 4099, 5632, 9345, 16465, 16521, 16645, 16899,
+    18443, 18690, 19456, 22785, 32866, 33034, 33286, 34819, 36886, 36931, 37458, 49152, 49411, 51207, 53259,
+    55297, 65700, 65812, 66060, 67590, 69632, 69637, 73772, 73862, 73984, 73989, 74754, 74759, 74784, 75140,
+    82437, 83981, 84228, 90149, 93445, 99334, 102438, 102916, 106566, 194, 276, 321, 524, 545, 1034, 1041, 2054,
+    2057, 2066, 2084, 2120, 2192, 2624, 3200, 4101, 4673, 6656, 8195, 9346, 11264, 16481, 16649, 16901, 17411,
+    18445, 18692, 18723, 26881, 32930, 33042, 33290, 33798, 36890, 36995, 37380, 37392, 37474, 37888, 49667,
+    51211, 51458, 53267, 65732, 66068, 66572, 69638, 73780, 73990, 74240, 74245, 75396, 82949, 83989, 84261,
+    90181, 92161, 93317, 100358, 102470, 106630, 107522, 107527, 111174, 112, 168, 196, 280, 322, 385, 532, 546,
+    1036, 1057, 1170, 2058, 2065, 2337, 4102, 4105, 4114, 4132, 4168, 4240, 4384, 4674, 5248, 6400, 8197, 9348,
+    13312, 16545, 16657, 16905, 17413, 18453, 18467, 18696, 22528, 32962, 33298, 33802, 34822, 36906, 36934,
+    37123, 37384, 38912, 40963, 42114, 50179, 51219, 51491, 53283, 53761, 65860, 66084, 66580, 67596, 70212,
+    73812, 73868, 74246, 74760, 74765, 74774, 74828, 75044, 75332, 77060, 79364, 81920, 84005, 90245, 91137,
+    92167, 93188, 102534, 106758, 110606, 126983, 324, 386, 536, 641, 1044, 1058, 1089, 1169, 2060, 2081, 2338,
+    4106, 4113, 4676, 8198, 8201, 8210, 8228, 8264, 8336, 8480, 8768, 9352, 10496, 12800, 16577, 16913, 17417,
+    18457, 18499, 18704, 18729, 20483, 25729, 26624, 33090, 33314, 33810, 34826, 36914, 36998, 37570, 51235,
+    53315, 56067, 65924, 66596, 67604, 67876, 69644, 73828, 73996, 74766, 74768, 74773, 75776, 75781, 76932,
+    81926, 84037, 86021, 90373, 91143, 102662, 102914, 102919, 107014, 110614, 111620, 124935, 388, 552, 585,
+    642, 769, 1048, 1090, 2068, 2082, 2113, 4108, 4129, 8202, 8209, 16390, 16402, 16420, 16456, 16528, 16672,
+    16705, 16929, 16960, 17425, 17536, 18473, 18501, 18563, 18737, 20485, 20992, 21057, 24579, 25600, 32912,
+    33154, 33826, 34834, 35106, 36946, 37002, 37126, 37383, 37408, 37698, 37891, 40966, 45056, 51267, 51457,
+    53379, 65824, 66180, 66628, 66708, 67620, 69652, 73892, 74004, 74252, 74789, 74902, 75782, 77824, 77829,
+    78980, 84101, 90629, 92173, 92420, 98304, 98309, 107534, 110630, 111108, 114694, 120839, 123911, 392, 644,
+    770, 1281, 2072, 2114, 2177, 4116, 4130, 4161, 8204, 8225, 16769, 17441, 18565, 24581, 33410, 33938, 34850,
+    36962, 37130, 38530, 38915, 40970, 46594, 49158, 53248, 55303, 55810, 69668, 73924, 74260, 74790, 74821,
+    74896, 74901, 77830, 91149, 92181, 92453, 107542, 110662 };
+
+static int cbest_18[1023] = {
+    1, 2, 131136, 4, 65568, 8, 32784, 16, 16392, 32, 8196, 64, 4098, 128, 2049, 256, 512, 132160, 1024, 2048,
+    66080, 4096, 33040, 8192, 16520, 8260, 16384, 3, 4130, 32768, 131137, 5, 65569, 131138, 6, 9, 2065, 32785,
+    65536, 65570, 131140, 196704, 10, 17, 16393, 32786, 65572, 131144, 163920, 12, 18, 33, 8197, 16394, 32788,
+    65576, 98352, 131072, 131152, 147528, 20, 34, 65, 4099, 8198, 16396, 32792, 65584, 81960, 131168, 132168,
+    139332, 24, 36, 66, 129, 258, 516, 1032, 2064, 49176, 73764, 135234, 40, 68, 130, 257, 2051, 4102, 4128,
+    8204, 16408, 32816, 40980, 65632, 69666, 131264, 133185, 48, 72, 132, 513, 2053, 4106, 8212, 8256, 16424,
+    24588, 32848, 36882, 65696, 66084, 67617, 131392, 132161, 80, 136, 260, 514, 1025, 2057, 4114, 8228, 16456,
+    16512, 20490, 32912, 34833, 65824, 131648, 132162, 96, 144, 264, 1026, 12294, 18441, 33024, 66081, 132164,
+    197728, 160, 272, 520, 1028, 2050, 2081, 4162, 8324, 10245, 16648, 33042, 33296, 66048, 66082, 66592, 133184,
+    164944, 197216, 192, 288, 528, 2052, 2113, 4097, 4226, 6147, 8452, 16904, 33041, 33808, 67616, 132096,
+    132176, 148552, 320, 544, 1040, 2056, 2177, 4354, 8708, 17416, 34832, 66088, 98864, 132192, 135232, 140356,
+    164176, 384, 576, 1056, 2305, 4100, 4610, 8193, 9220, 16521, 18440, 33044, 66096, 69664, 82472, 98608,
+    136258, 640, 1088, 2080, 2561, 4104, 5122, 8194, 10244, 16522, 33048, 36880, 74276, 132288, 134209, 139268,
+    139328, 147656, 768, 1152, 2112, 3073, 4112, 6146, 8261, 16385, 16524, 20488, 49432, 66144, 69634, 70178,
+    73760, 82088, 132416, 1280, 2176, 8200, 8262, 12292, 16386, 33072, 34817, 40976, 41236, 49304, 66208, 68129,
+    132672, 147520, 1536, 2304, 4131, 4160, 4352, 8208, 16388, 16536, 24584, 32769, 33104, 37138, 66336, 73828,
+    81952, 2560, 4224, 6145, 8224, 8268, 8704, 16552, 24716, 32770, 33168, 35089, 41044, 49168, 131139, 134208,
+    135266, 148544, 163904, 198240, 7, 3072, 4134, 8276, 12290, 16400, 16584, 17408, 20618, 24652, 32772, 65537,
+    65571, 67104, 98336, 131141, 196705, 11, 2067, 4138, 4608, 8292, 8320, 10241, 16416, 18569, 24580, 32776,
+    32787, 33552, 34816, 36914, 65538, 65573, 68128, 74272, 131142, 131145, 133201, 136256, 163921, 165200,
+    196672, 196706, 13, 19, 2069, 4146, 5120, 8448, 12358, 16395, 16448, 16776, 20482, 20522, 32789, 34064,
+    49160, 65540, 65574, 65577, 67633, 98353, 131073, 131146, 131153, 147529, 163922, 196708, 14, 21, 35, 2073,
+    6144, 8199, 8388, 10309, 12326, 16397, 17032, 18433, 32790, 32793, 32800, 35088, 37136, 40964, 65544, 65578,
+    65585, 69632, 70176, 81961, 98320, 98354, 99120, 131074, 131148, 131154, 131169, 132169, 139333, 140292,
+    140352, 147530, 148680, 163924, 196712, 229488, 22, 25, 37, 67, 259, 517, 1033, 4194, 8516, 9216, 16398,
+    16640, 17544, 18457, 32794, 32832, 36866, 49177, 65552, 65580, 65586, 73765, 81928, 81962, 98356, 131076,
+    131156, 131170, 132170, 135235, 139334, 147532, 163928, 196640, 196720, 213096, 26, 38, 41, 69, 131, 518,
+    1034, 2066, 2097, 4103, 4129, 4258, 6179, 8205, 8772, 10240, 10261, 16409, 16896, 18568, 32796, 32817, 32896,
+    40981, 49178, 65588, 65633, 69667, 70146, 73732, 73766, 81964, 82600, 98360, 131080, 131160, 131172, 131265,
+    131394, 131652, 132172, 133200, 139264, 163856, 180312, 197736, 204900, 28, 42, 49, 70, 73, 133, 262, 1036,
+    2068, 2129, 4107, 4386, 6163, 8206, 8213, 8257, 9284, 16410, 16425, 24589, 32818, 32849, 36883, 40982, 49180,
+    65592, 65600, 65634, 65697, 65826, 66085, 66600, 67632, 114744, 131088, 131176, 131266, 131393, 133187,
+    135238, 135264, 139340, 147464, 147544, 163952, 164952, 172116, 200802, 44, 50, 74, 81, 134, 137, 261, 266,
+    515, 524, 2055, 2072, 2193, 4115, 4132, 4642, 8214, 8229, 8258, 10308, 12288, 16412, 16426, 16457, 16513,
+    18432, 20491, 20616, 24590, 32820, 32850, 32913, 33026, 33280, 33300, 33816, 35073, 41232, 49560, 65636,
+    65664, 65698, 65825, 66052, 66086, 67585, 67619, 69670, 73772, 74340, 81976, 82464, 106548, 131104, 131184,
+    131268, 131649, 132104, 132163, 132184, 133189, 135242, 136290, 139348, 147560, 155724, 164928, 168018,
+    196832, 197220, 198753, 52, 76, 82, 97, 138, 145, 265, 274, 532, 1027, 1048, 2059, 2321, 4110, 4136, 5154,
+    8230, 12295, 16428, 16458, 16514, 16650, 16908, 18456, 32824, 32852, 32914, 33025, 33792, 34835, 36886,
+    36912, 40988, 65640, 65700, 65792, 67621, 69674, 73780, 73824, 90156, 98416, 102450, 131272, 131396, 131650,
+    132165, 132200, 133193, 135170, 135250, 139364, 140364, 147648, 151626, 164048, 165969, 196960, 197729, 56,
+    84, 98, 140, 146, 161, 273, 290, 521, 548, 1029, 1064, 2061, 2096, 2577, 4118, 4144, 4163, 6178, 8220, 8264,
+    8325, 8454, 9228, 10260, 12356, 16460, 16516, 16649, 18443, 20480, 20494, 20520, 24712, 32856, 32916, 33043,
+    33297, 34837, 36890, 41040, 41300, 49208, 49424, 57372, 65648, 65704, 65828, 66049, 66083, 66092, 66593,
+    67625, 69682, 82024, 82080, 86058, 98480, 98848, 98868, 100401, 131200, 131280, 131400, 132166, 133121,
+    134225, 136266, 143430, 149577, 164160, 164945, 197217, 197696, 197730, 88, 100, 148, 162, 193, 268, 289,
+    322, 522, 529, 580, 1030, 1096, 2083, 2128, 3089, 4122, 4227, 4614, 5130, 6162, 8236, 8272, 8326, 8453,
+    10247, 12324, 16440, 16905, 18445, 24604, 24648, 32920, 33028, 33298, 33809, 34841, 41012, 49240, 49296,
+    53274, 65712, 65832, 66050, 66100, 66560, 66594, 77862, 82476, 84009, 98592, 131296, 131328, 131408, 131656,
+    132097, 132177, 132296, 133186, 133217, 134217, 139460, 141381, 147784, 148553, 148672, 164178, 164432,
+    164946, 197184, 197218, 197732, 104, 152, 164, 194, 276, 321, 386, 530, 545, 644, 1041, 1160, 2054, 2085,
+    2115, 2192, 2307, 2565, 3081, 4166, 4192, 4355, 4384, 8244, 8288, 8709, 8768, 12302, 16472, 16528, 16652,
+    16906, 17417, 17536, 20506, 24576, 24620, 24780, 32880, 33032, 33046, 33810, 35072, 36864, 37170, 45078,
+    51225, 65840, 66089, 66596, 67584, 67618, 68145, 69730, 73892, 75813, 82216, 98610, 98865, 131424, 131584,
+    131664, 132098, 132178, 132193, 132424, 133188, 135233, 135362, 137283, 139588, 140357, 148040, 148554,
+    164177, 164948, 198752, 230512, 112, 168, 196, 280, 292, 385, 546, 577, 772, 1042, 1057, 1288, 2058, 2089,
+    2117, 2179, 2320, 4101, 4170, 4230, 4256, 4611, 6151, 6177, 8332, 8710, 9221, 10253, 12310, 12354, 16488,
+    16544, 17418, 24708, 28686, 32944, 33045, 33050, 33304, 33812, 34834, 34865, 36946, 41108, 43029, 49416,
+    65760, 66056, 66090, 66097, 66148, 67620, 67681, 69665, 69794, 70144, 70182, 71715, 74020, 82473, 98609,
+    98832, 98866, 99376, 131680, 132100, 132180, 132194, 132680, 133192, 133313, 135490, 136259, 139844, 140358,
+    148556, 165968, 197224, 197664, 197744, 214120, 230000, 176, 200, 296, 324, 536, 641, 770, 1044, 1058, 1089,
+    1544, 2060, 2121, 2181, 4105, 4178, 4234, 4358, 8460, 9222, 10305, 16576, 17420, 18442, 18473, 20554, 20610,
+    32976, 33049, 33056, 34836, 34897, 38931, 41220, 65888, 66098, 66608, 67624, 67745, 68133, 74277, 74336,
+    82440, 82474, 131520, 132196, 132418, 133120, 133441, 134224, 135746, 164880, 181336, 197232, 205924, 229744 };
+
+
+static int cbest_19[1023] = {
+    1, 2, 262163, 4, 393242, 8, 196621, 16, 32, 360469, 64, 262162, 128, 131081, 3, 442393, 262161, 6, 256,
+    393243, 5, 327703, 12, 196620, 512, 393240, 9, 24, 98310, 262167, 426008, 10, 458782, 48, 1024, 49155,
+    196617, 17, 213004, 262171, 393234, 483359, 18, 96, 262147, 360471, 393246, 20, 2048, 16385, 196623, 286738,
+    360468, 442392, 33, 192, 32770, 106502, 229391, 34, 65540, 196613, 270355, 360465, 36, 384, 4096, 131080,
+    143369, 180234, 393226, 40, 65, 53251, 221196, 262195, 66, 768, 376852, 397338, 442395, 68, 8192, 24577,
+    49154, 90117, 503836, 72, 129, 1536, 262160, 262227, 80, 110598, 198669, 288786, 393274, 132, 3072, 16384,
+    98308, 188426, 196637, 274451, 327702, 333847, 483358, 7, 130, 136, 257, 131083, 262291, 307217, 144, 6144,
+    49153, 163851, 213005, 262165, 286739, 327699, 360477, 393241, 393306, 426010, 13, 160, 55299, 131073,
+    144393, 196616, 196653, 262166, 327701, 360453, 361493, 426009, 14, 26, 258, 264, 513, 12288, 53250, 94213,
+    131085, 196609, 262419, 399386, 442385, 458783, 25, 52, 272, 26625, 98306, 98311, 251918, 344086, 360467,
+    393370, 429080, 442397, 11, 104, 288, 24576, 32768, 90116, 106500, 196619, 196622, 196685, 229389, 262155,
+    262170, 262175, 311312, 368661, 393218, 393235, 393238, 393244, 405530, 458778, 22, 28, 49, 208, 260, 320,
+    514, 1025, 45058, 155656, 180235, 229390, 241679, 262146, 262169, 262675, 360470, 376853, 393232, 393247,
+    442394, 458780, 44, 416, 528, 22529, 77828, 172043, 180232, 196612, 199693, 213000, 221197, 262145, 262179,
+    289810, 360501, 393498, 415771, 442905, 483355, 491548, 19, 88, 97, 544, 832, 38914, 53249, 143368, 196749,
+    275475, 309265, 442377, 475167, 483357, 21, 38, 50, 56, 176, 516, 576, 1026, 1664, 2049, 19457, 71684,
+    114695, 131097, 135177, 202765, 214540, 263187, 270354, 288787, 334359, 360464, 426000, 76, 193, 352, 640,
+    3328, 32771, 35842, 49152, 106498, 106503, 139273, 213006, 229387, 262151, 278546, 286736, 327711, 352278,
+    360533, 393227, 393754, 426012, 446489, 458774, 35, 98, 152, 194, 704, 1056, 6656, 17921, 55298, 65536,
+    65541, 196629, 196877, 245774, 262194, 262259, 273427, 294929, 319504, 327687, 348182, 376854, 393224,
+    393258, 450585, 37, 42, 70, 112, 304, 385, 520, 1028, 1088, 1408, 2050, 4097, 13312, 16387, 49159, 94212,
+    110596, 125959, 131113, 144905, 188427, 196615, 212996, 262193, 264211, 270353, 315408, 329751, 360473,
+    362005, 372757, 382996, 397339, 483351, 503838, 41, 140, 608, 1152, 2816, 26624, 27649, 98318, 159752,
+    188424, 198668, 221192, 262355, 271891, 331799, 360597, 394266, 399898, 442425, 499740, 503837, 67, 100, 280,
+    388, 769, 1216, 1280, 5632, 47106, 65542, 98304, 99334, 107270, 157704, 176139, 196633, 196636, 197133,
+    262226, 363541, 376848, 393230, 406554, 409627, 425992, 427032, 442384, 69, 74, 84, 224, 386, 560, 1032,
+    2052, 2112, 2432, 4098, 8193, 11264, 16389, 49163, 49667, 79876, 90113, 122887, 131082, 131145, 143371,
+    163849, 174091, 229383, 262199, 262225, 262547, 266259, 271123, 286742, 344087, 360479, 393275, 393338,
+    397336, 428056, 429336, 442396, 458766, 470046, 483615, 503832, 73, 196, 1120, 1537, 2176, 4864, 22528,
+    23553, 32774, 55297, 78852, 81925, 98326, 163850, 213516, 221198, 262203, 274450, 307219, 311313, 327735,
+    333846, 360455, 360725, 393266, 393272, 395290, 398874, 416795, 442399, 442457, 460830, 81, 134, 770, 776,
+    2240, 2304, 9728, 39938, 53248, 110594, 110599, 131072, 137225, 143361, 144392, 180226, 196649, 196652,
+    196669, 197645, 198665, 214028, 251919, 262290, 262931, 270359, 286994, 303121, 307216, 327697, 356374,
+    360449, 393434, 434200, 442387, 483343, 133, 148, 168, 448, 1040, 2056, 2560, 3073, 4100, 4480, 8194, 16393,
+    16897, 19456, 24579, 39426, 49171, 90119, 98309, 106758, 114694, 131084, 131209, 143373, 180238, 191498,
+    196608, 199949, 221188, 249870, 251916, 262164, 262211, 262231, 275987, 286746, 288784, 289811, 323600,
+    327698, 333843, 360461, 360476, 361495, 393307, 398106, 415770, 426011, 442904, 443161, 448537, 466974,
+    483354, 485407, 131, 137, 200, 1538, 4224, 8960, 17409, 19969, 32778, 53255, 53635, 57347, 72196, 98342,
+    106510, 107014, 131077, 143497, 153608, 155657, 196639, 196717, 203277, 213020, 217100, 262235, 263699,
+    270611, 274449, 286722, 325136, 327700, 327767, 333845, 350230, 360452, 360981, 361492, 393278, 393298,
+    393304, 393626, 397330, 426040, 442376, 442521, 475166, 483356, 487455, 82, 138, 145, 268, 772, 1552, 4352,
+    6145, 17920, 18433, 19713, 33794, 45056, 53379, 65548, 106496, 166923, 180233, 196618, 196645, 196681,
+    196684, 198671, 213001, 229385, 229388, 230415, 241677, 262289, 262418, 270363, 270867, 317456, 334615,
+    349206, 360485, 397342, 397722, 399387, 417819, 429082, 442369, 442389, 443929, 458814, 503828, 146, 161,
+    296, 336, 392, 896, 2064, 3074, 4104, 4608, 8196, 16386, 16401, 20481, 24581, 34818, 36098, 49158, 49187,
+    53507, 76804, 108550, 125958, 131087, 131089, 131337, 161800, 172041, 180746, 196813, 199437, 214668, 221452,
+    241678, 262153, 262275, 262295, 265235, 270339, 271379, 273939, 278547, 286737, 290834, 311314, 327707,
+    330775, 352279, 360466, 360503, 361489, 368663, 393216, 393371, 394010, 397466, 413723, 429081, 446488,
+    458770, 458776, 15, 27, 54, 108, 162, 216, 259, 265, 432, 864, 1540, 1728, 3456, 5120, 6912, 12289, 13824,
+    27648, 32786, 36866, 38912, 49157, 53259, 67588, 94209, 98374, 106518, 131075, 172042, 178187, 196655,
+    198661, 199692, 213036, 214541, 229407, 233487, 262154, 262174, 262299, 272403, 319505, 327831, 348183,
+    360497, 368660, 376855, 393219, 393239, 393245, 393290, 393310, 393362, 397594, 401434, 405531, 426014,
+    426072, 442379, 442649, 450584, 458779, 483391, 503964, 514077, 53, 266, 273, 536, 3104, 6146, 8448, 18049,
+    24833, 38402, 40962, 54275, 65556, 69636, 86021, 90373, 98307, 114693, 124935, 145417, 158728, 188418,
+    196611, 196677, 196745, 196748, 197005, 198733, 199053, 200717, 207885, 212992, 213007, 235023, 237583,
+    251914, 262168, 262173, 262417, 262674, 268307, 288790, 288850, 315409, 339991, 344082, 376860, 377364,
+    382997, 393233, 393236, 394778, 397850, 399384, 426002, 442907, 458781, 458846, 483347, 483350, 483353,
+    491550, 30, 105, 262, 274, 289, 400, 592, 672, 1792, 2080, 3076, 4112, 8200, 8704, 16388, 16417, 24585,
+    32769, 35840, 49162, 49219, 49666, 73732, 80900, 90112, 90125, 95749, 98314, 99846, 106501, 110726, 122886,
+    131096, 131593, 135176, 143385, 144395, 175115, 180250, 184330, 188430, 198797, 202764, 223244, 245775,
+    262144, 262149, 262178, 262183, 262323, 262403, 272147, 274455, 286770, 288914, 309267, 333911, 344084,
+    360500, 360535, 360565, 362133, 368657, 376836, 388116, 393368, 393499, 397322, 398362, 400154, 407066,
+    427544, 438296, 442424, 491549, 23, 29, 46, 92, 106, 184, 209, 261, 276, 290, 321, 368, 515, 736, 1472, 1544,
+    2944, 5888, 9216, 11776, 12290, 19201, 23552, 32802, 45059, 53267, 55296, 81924, 94215, 98316, 98438, 106534,
+    139272, 163843, 174603, 196687, 197389, 198861, 198925, 212997, 213002, 213068, 221212, 225292, 229386,
+    229423, 241675, 245772, 262427, 272019, 274579, 275474, 288978, 305169, 307221, 309264, 327959, 345622,
+    360529, 362517, 363797, 376849, 378900, 393354, 393374, 393490, 396314, 405528, 409626, 426136, 436248,
+    461854, 470558, 471070, 483423, 503820, 504860, 417, 529, 1072, 6148, 10240, 92165, 101382, 125957, 144425,
+    147464, 196741, 204813, 262159, 262339, 262673, 263186, 286743, 288794, 307345, 327683, 425984, 426001,
+    432152, 442409, 458910, 505884 };
+
+static int cbest_20[1023] = {
+    1, 2, 524292, 4, 262146, 8, 131073, 16, 32, 589828, 64, 128, 294914, 256, 512, 147457, 1024, 2048, 4096,
+    598020, 8192, 16384, 32768, 299010, 65536, 131072, 149505, 262144, 3, 524288, 524293, 5, 262147, 524294,
+    599044, 6, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 786438, 10, 17,
+    131075, 262150, 294912, 524300, 655365, 12, 33, 131077, 262154, 393219, 524308, 589824, 589829, 20, 34, 65,
+    131081, 262162, 299522, 524324, 589830, 24, 66, 129, 131089, 262178, 294915, 524356, 851974, 40, 68, 130,
+    257, 131105, 262210, 524420, 589836, 720901, 819206, 48, 132, 258, 513, 131137, 262274, 294918, 524548,
+    589844, 80, 136, 260, 514, 1025, 131201, 147459, 149761, 262402, 294922, 425987, 524804, 589860, 671749, 96,
+    264, 516, 1026, 2049, 131329, 147461, 262658, 294930, 409603, 525316, 589892, 160, 272, 520, 1028, 2050,
+    4097, 131585, 147465, 149504, 263170, 294946, 299008, 526340, 589956, 598016, 598021, 884742, 192, 528, 1032,
+    2052, 4098, 8193, 74752, 132097, 147473, 264194, 294978, 528388, 590084, 598022, 320, 544, 1040, 2056, 4100,
+    8194, 16385, 37376, 133121, 147489, 266242, 295042, 532484, 590340, 737285, 860166, 384, 1056, 2064, 4104,
+    8196, 16386, 18688, 32769, 135169, 147521, 270338, 295170, 299011, 540676, 590852, 598028, 599172, 729093,
+    640, 1088, 2080, 4112, 8200, 9344, 16388, 32770, 65537, 139265, 147585, 278530, 295426, 442371, 557060,
+    591876, 598036, 823302, 768, 2112, 4128, 4672, 8208, 16392, 32772, 65538, 147713, 295938, 299014, 593924,
+    598052, 1280, 2176, 2336, 4160, 8224, 16400, 32776, 65540, 131074, 147969, 163841, 296962, 299018, 327682,
+    430083, 598084, 655364, 1168, 1536, 4224, 8256, 16416, 32784, 65544, 131076, 148481, 149507, 196609, 262145,
+    299026, 393218, 598148, 606212, 673797, 892934, 584, 2560, 4352, 8320, 16448, 32800, 65552, 131080, 149509,
+    299042, 299586, 303106, 411651, 598276, 622596, 786436, 888838, 292, 3072, 8448, 16512, 32832, 65568, 131088,
+    149513, 151553, 262148, 262160, 299074, 311298, 524289, 598532, 745477, 146, 5120, 8704, 16640, 32896, 65600,
+    131104, 149521, 155649, 262152, 299138, 393217, 524290, 524295, 524320, 599040, 599045, 720900, 7, 19, 37,
+    73, 145, 289, 577, 1153, 2305, 4609, 6144, 9217, 16896, 18433, 33024, 36865, 65664, 73729, 131136, 149537,
+    299266, 299520, 360450, 599046, 600068, 739333, 786434, 786439, 11, 38, 74, 290, 578, 1154, 2306, 4610, 9218,
+    10240, 17408, 18434, 33280, 36866, 65792, 73730, 131200, 147458, 149569, 149760, 180225, 262151, 262176,
+    294913, 425986, 446467, 524296, 524301, 524310, 524364, 524436, 524580, 524868, 525444, 526596, 528900,
+    533508, 542724, 561156, 602116, 655361, 671748, 851972, 861190, 13, 22, 76, 148, 580, 1156, 2308, 4612, 9220,
+    12288, 18436, 33792, 36868, 66048, 73732, 131328, 147460, 149633, 149793, 212993, 262155, 262182, 262208,
+    262218, 262290, 262434, 262722, 263298, 264450, 266754, 271362, 280578, 300034, 335874, 409602, 444419,
+    524302, 524304, 524309, 589825, 599052, 655367, 730117, 819204, 14, 21, 26, 35, 44, 152, 296, 1160, 2312,
+    4616, 9224, 18440, 20480, 34816, 36872, 66560, 73736, 74880, 131079, 131091, 131109, 131145, 131217, 131361,
+    131584, 131649, 132225, 133377, 135681, 140289, 147464, 167937, 204801, 262163, 262272, 294916, 294928,
+    299523, 301058, 524325, 589826, 589831, 589856, 599060, 614404, 786446, 917511, 25, 52, 67, 88, 304, 592,
+    2320, 4624, 9232, 18448, 24576, 36880, 67584, 73744, 131083, 132096, 147472, 150017, 262158, 262179, 262400,
+    294920, 393223, 425985, 524326, 524352, 524357, 599076, 630788, 655373, 786454, 823814, 851970, 851975,
+    897030, 41, 50, 69, 104, 131, 176, 608, 1184, 4640, 9248, 18464, 36896, 37440, 40960, 69632, 73760, 131085,
+    133120, 147488, 150529, 262166, 262211, 262656, 299526, 307202, 393227, 409601, 524316, 524358, 524416,
+    524421, 589832, 589837, 589846, 589900, 589972, 590116, 590404, 590980, 592132, 594436, 599108, 608260,
+    626692, 655381, 720897, 737284, 786470, 819202, 819207, 28, 42, 49, 70, 82, 100, 133, 208, 259, 352, 1216,
+    2368, 9280, 18496, 36928, 49152, 73792, 131093, 131107, 135168, 147520, 262170, 262275, 263168, 294919,
+    294944, 299530, 315394, 393235, 430595, 524332, 524422, 524544, 524549, 589838, 589840, 589845, 655397,
+    720903, 729092, 786502, 884740, 893958, 81, 134, 137, 164, 200, 261, 416, 515, 704, 2432, 4736, 18560, 18720,
+    36992, 73856, 81920, 131097, 131139, 139264, 147584, 153601, 262186, 262214, 262403, 264192, 294923, 294950,
+    294976, 294986, 295058, 295202, 295490, 296066, 297218, 299538, 304130, 313346, 368642, 393251, 442370,
+    524340, 524550, 524800, 524805, 589861, 599300, 655429, 671745, 747525, 786566, 851982, 983047, 97, 138, 262,
+    265, 274, 328, 400, 517, 832, 1027, 1408, 4864, 9472, 37120, 73984, 98304, 131113, 131141, 131203, 147712,
+    149763, 157697, 262194, 262278, 262659, 266240, 294931, 295040, 299554, 364546, 393283, 524372, 524428,
+    524806, 525312, 525317, 589862, 589888, 589893, 599188, 599556, 655493, 671751, 674053, 720909, 746501,
+    786694, 819214, 851990, 860164, 889350, 950279, 56, 84, 98, 140, 161, 266, 273, 518, 521, 530, 548, 656, 800,
+    1029, 1664, 2051, 2816, 9360, 9728, 18944, 74240, 131121, 131205, 131331, 147463, 147475, 147493, 147529,
+    147601, 147745, 147968, 148033, 148609, 149765, 152065, 156673, 163840, 184321, 221185, 262226, 262282,
+    262406, 263171, 270336, 294926, 294947, 295168, 299009, 393347, 411907, 425991, 430082, 524388, 524556,
+    525318, 526336, 526341, 589852, 589894, 589952, 589957, 598017, 655621, 720917, 786950, 819222, 852006,
+    884738, 884743, 933895, 162, 193, 268, 522, 529, 1030, 1033, 1042, 1060, 1096, 1312, 1600, 2053, 3328, 4099,
+    5632, 19456, 37888, 74753, 131153, 131209, 131333, 131587, 147467, 148480, 149506, 149769, 182273, 196608,
+    262242, 262410, 262662, 264195, 278528, 294934, 294979, 295424, 299650, 393475, 409607, 425995, 442369,
+    448515, 524452, 524564, 524812, 526342, 528384, 528389, 589868, 589958, 590080, 590085, 598018, 598023,
+    598048, 601092, 655877, 671757, 673796, 720933, 787462, 819238, 823300, 852038, 194, 276, 321, 524, 545,
+    1034, 1041, 2054, 2057, 2066, 2084, 2120, 2192, 2624, 3200, 4101, 4680, 6656, 8195, 11264, 37377, 38912,
+    74754, 75776, 131169, 131337, 131589, 132099, 147469, 149508, 149777, 215041, 262306, 262418, 262666, 263174,
+    266243, 294938, 295043, 295936, 299012, 299024, 299778, 393731, 409611, 411650, 426003, 524484, 524820,
+    525324, 528390, 532480, 532485, 589876, 590086, 590336, 590341, 603140, 656389, 671765, 720965, 737281,
+    788486, 819270, 852102, 860162, 860167, 112, 168, 196, 280, 322, 385, 532, 546, 1036, 1057, 2058, 2065, 4102,
+    4105, 4114, 4132, 4168, 4240, 4384, 5248, 6400, 8197, 13312, 16387, 18689, 22528, 37378, 74756, 77824,
+    131233, 131345, 131593, 132101, 133123, 147477, 147491, 149512, 151552, 262338, 262674, 263178, 264198,
+    270339, 294954, 294982, 295171, 296960, 299016, 327680, 336898, 394243, 409619, 426019, 430081, 446979,
+    524612, 524836, 525332, 526348, 532486, 540672, 540677, 561668, 589908, 589964, 590342, 590848, 590853,
+    598024, 598029, 598038, 598092, 598164, 598308, 598596, 599168, 599173, 600324, 602628, 616452, 634884,
+    657413, 671781, 721029, 729089, 737287, 739589, 745476, 790534, 819334, 852230, 884750, 1015815, 386, 1089,
+    4106, 8228, 8264, 8336, 10496, 131601, 147481, 147523, 149825, 155648, 262466, 263186, 295046, 300546,
+    393216, 426051, 590092, 599174, 615428, 729095, 823303 };
+
+static int cbest_21[1023] = {
+    1, 2, 1048578, 4, 524289, 8, 16, 1310722, 32, 64, 655361, 128, 256, 512, 1376258, 1024, 2048, 4096, 688129,
+    8192, 16384, 32768, 65536, 1392642, 131072, 262144, 524288, 696321, 1048576, 3, 1048579, 5, 10, 20, 40, 80,
+    160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 6, 9, 524291, 1048582,
+    1310720, 1572867, 17, 524293, 1048586, 1310723, 1396738, 12, 18, 33, 524297, 1048594, 34, 65, 524305,
+    1048610, 1310726, 1835011, 24, 36, 66, 129, 524321, 655363, 1048642, 1310730, 1703939, 68, 130, 257, 524353,
+    655365, 688128, 1048706, 1310738, 1376256, 48, 72, 132, 258, 513, 344064, 524417, 655369, 698369, 1048834,
+    1310754, 1376259, 136, 260, 514, 1025, 172032, 524545, 655377, 1049090, 1310786, 1966083, 96, 144, 264, 516,
+    1026, 2049, 86016, 524801, 655393, 1049602, 1310850, 1376262, 1900547, 272, 520, 1028, 2050, 4097, 43008,
+    525313, 655425, 1050626, 1310978, 1376266, 192, 288, 528, 1032, 2052, 4098, 8193, 21504, 526337, 655489,
+    688131, 1052674, 1311234, 1376274, 1736707, 544, 1040, 2056, 4100, 8194, 10752, 16385, 528385, 655617,
+    688133, 1056770, 1311746, 1376290, 384, 576, 1056, 2064, 4104, 5376, 8196, 16386, 32769, 532481, 655873,
+    688137, 1064962, 1312770, 1376322, 1392640, 1397762, 2031619, 1088, 2080, 2688, 4112, 8200, 16388, 32770,
+    65537, 540673, 656385, 688145, 696320, 1081346, 1314818, 1376386, 1392643, 1998851, 768, 1152, 1344, 2112,
+    4128, 8208, 16392, 32772, 65538, 131073, 557057, 657409, 688161, 1114114, 1318914, 1376514, 672, 2176, 4160,
+    8224, 16400, 32776, 65540, 131074, 262145, 348160, 589825, 659457, 688193, 1179650, 1327106, 1376770,
+    1392646, 1916931, 336, 1536, 2304, 4224, 8256, 16416, 32784, 65544, 131076, 262146, 663553, 688257, 1343490,
+    1377282, 1392650, 168, 4352, 8320, 16448, 32800, 65552, 131080, 174080, 262148, 524290, 671745, 688385,
+    786433, 1378306, 1392658, 1572866, 84, 3072, 4608, 8448, 16512, 32832, 65568, 131088, 262152, 524292, 688641,
+    696323, 698881, 1048577, 1380354, 1392674, 1441794, 1744899, 2064387, 42, 8704, 16640, 32896, 65600, 87040,
+    131104, 262160, 524296, 689153, 696325, 720897, 1048584, 1384450, 1392706, 2048003, 11, 21, 41, 81, 161, 321,
+    641, 1281, 2561, 5121, 6144, 9216, 10241, 16896, 20481, 33024, 40961, 65664, 81921, 131136, 163841, 262176,
+    327681, 524304, 690177, 696329, 1048580, 1392770, 1572865, 1835010, 7, 22, 82, 162, 322, 642, 1282, 2562,
+    5122, 10242, 17408, 20482, 33280, 40962, 43520, 65792, 81922, 131200, 163842, 262208, 327682, 524320, 655362,
+    692225, 696337, 917505, 1048583, 1048598, 1048618, 1048658, 1048738, 1048898, 1049218, 1049858, 1051138,
+    1053698, 1058818, 1069058, 1089538, 1130498, 1212418, 1310721, 1392898, 1396736, 1409026, 1703938, 2007043,
+    14, 44, 164, 324, 644, 1284, 2564, 5124, 10244, 12288, 18432, 20484, 33792, 40964, 66048, 81924, 131328,
+    163844, 262272, 327684, 524299, 524309, 524329, 524352, 524369, 524449, 524609, 524929, 525569, 526849,
+    529409, 534529, 544769, 565249, 606209, 655364, 696353, 851969, 1048587, 1048592, 1310728, 1393154, 1396739,
+    13, 19, 28, 88, 328, 648, 1288, 2568, 5128, 10248, 20488, 21760, 34816, 40968, 66560, 81928, 131584, 163848,
+    262400, 327688, 524295, 524416, 655368, 696385, 698368, 704513, 1048595, 1048608, 1310724, 1393666, 1507330,
+    1572871, 1835009, 26, 35, 56, 176, 656, 1296, 2576, 5136, 10256, 20496, 24576, 36864, 40976, 67584, 81936,
+    132096, 163856, 262656, 327696, 524544, 655376, 696449, 1048590, 1048611, 1048640, 1310727, 1310742, 1310762,
+    1310802, 1310882, 1311042, 1311362, 1312002, 1313282, 1315842, 1320962, 1331202, 1351682, 1394690, 1396742,
+    1474562, 1572875, 1703937, 1921027, 1966082, 25, 37, 52, 67, 112, 352, 1312, 2592, 5152, 10272, 10880, 20512,
+    40992, 69632, 81952, 133120, 163872, 263168, 327712, 524301, 524307, 524800, 655392, 696577, 753665, 1048643,
+    1048704, 1310731, 1310736, 1396746, 1398018, 1572883, 1900546, 2080771, 38, 69, 74, 104, 131, 224, 704, 2624,
+    5184, 10304, 20544, 41024, 49152, 73728, 81984, 135168, 163904, 264192, 327744, 349184, 524323, 525312,
+    655371, 655381, 655401, 655424, 655441, 655521, 655681, 656001, 656641, 657921, 660481, 665601, 675841,
+    696833, 737281, 983041, 1048602, 1048614, 1048707, 1048832, 1310739, 1310752, 1376257, 1396754, 1400834,
+    1572899, 1835015, 2072579, 49, 70, 73, 133, 138, 148, 208, 259, 448, 1408, 5248, 5440, 10368, 20608, 41088,
+    82048, 139264, 163968, 266240, 327808, 344065, 524313, 524325, 524355, 526336, 655367, 655488, 688130,
+    697345, 950273, 1048646, 1048835, 1049088, 1310734, 1310755, 1310784, 1376264, 1396770, 1572931, 1703943,
+    1736706, 1835019, 1966081, 50, 134, 137, 261, 266, 276, 296, 416, 515, 896, 2816, 10496, 20736, 41216, 82176,
+    98304, 147456, 164096, 172033, 270336, 327936, 344066, 524357, 524419, 528384, 655616, 688132, 698371,
+    1048626, 1048650, 1048710, 1049091, 1049600, 1310787, 1310848, 1376260, 1396802, 1425410, 1572995, 1703947,
+    1746947, 1835027, 1900545, 2052099, 76, 97, 145, 262, 265, 517, 522, 532, 552, 592, 832, 1027, 1792, 2720,
+    5632, 20992, 41472, 82432, 86017, 164352, 172034, 174592, 278528, 328192, 344068, 524337, 524361, 524421,
+    524547, 532480, 655373, 655379, 655872, 688136, 698373, 700417, 868353, 1048714, 1048838, 1049603, 1050624,
+    1220610, 1310746, 1310758, 1310851, 1310976, 1376263, 1376278, 1376298, 1376338, 1376418, 1376578, 1376898,
+    1377538, 1378818, 1381378, 1386498, 1396866, 1417218, 1540098, 1573123, 1703955, 1835043, 2031618, 98, 140,
+    146, 273, 518, 521, 1029, 1034, 1044, 1064, 1104, 1184, 1664, 2051, 3584, 11264, 41984, 43009, 82944, 86018,
+    164864, 172036, 196608, 294912, 328704, 344072, 524425, 524549, 524803, 540672, 655395, 656384, 688144,
+    698377, 1048674, 1048722, 1048842, 1049094, 1050627, 1052672, 1134594, 1310790, 1310979, 1311232, 1376267,
+    1376272, 1396994, 1523714, 1573379, 1703971, 1736705, 1835075, 1966087, 1998850, 100, 193, 268, 274, 289,
+    529, 1030, 1033, 1360, 2053, 2058, 2068, 2088, 2128, 2208, 2368, 3328, 4099, 7168, 21505, 22528, 43010,
+    83968, 86020, 165888, 172040, 329728, 344080, 524385, 524433, 524553, 524805, 525315, 557056, 610305, 655385,
+    655397, 655427, 657408, 688160, 698385, 712705, 1048850, 1049098, 1049606, 1052675, 1056768, 1091586,
+    1310770, 1310794, 1310854, 1311235, 1311744, 1376275, 1376288, 1397250, 1573891, 1704003, 1835139, 1900551,
+    1966091, 2009091, 152, 194, 290, 524, 530, 545, 1041, 2054, 2057, 4101, 4106, 4116, 4136, 4176, 4256, 4416,
+    4736, 6656, 8195, 10753, 14336, 21506, 43012, 45056, 86024, 87296, 167936, 172048, 331776, 344096, 393216,
+    524561, 524809, 525317, 526339, 567297, 589824, 655429, 655491, 659456, 688139, 688149, 688169, 688192,
+    688209, 688289, 688449, 688769, 689409, 690689, 693249, 698401, 699009, 708609, 770049, 1015809, 1048770,
+    1048866, 1049106, 1049610, 1050630, 1056771, 1064960, 1070082, 1310858, 1310982, 1311747, 1312768, 1376270,
+    1376291, 1376320, 1397760, 1482754, 1574915, 1704067, 1835267, 1900555, 1916930, 1966099, 2031617, 196, 280,
+    292, 385, 546, 577, 680, 1036, 1042, 1057, 2065, 4102, 4105, 5377, 8197, 8202, 8212, 8232, 8272, 8352, 8512,
+    8832, 9472, 10754, 13312, 16387, 21508, 28672, 43016, 86032, 90112, 172064, 335872, 344128, 524481, 524577,
+    524817, 525321, 526341, 528387, 545793, 655409, 655433, 655493, 655619, 663552, 688135, 688256, 698433,
+    761857, 999425, 1049122, 1049618, 1050634, 1052678, 1059330, 1064963, 1081344, 1310818, 1310866, 1310986,
+    1311238, 1312771, 1314816, 1376323, 1376384, 1392641, 1397763, 1398786, 1576963, 1704195, 1736711, 1835523,
+    1900563, 1966115, 1998849, 2088963, 200, 386, 548, 1058, 16394, 16424, 16544, 17664, 18944, 57344, 180224,
+    535041, 671744, 698497, 1052682, 1056774, 1353730, 1392648, 1836035 };
+
+static int cbest_22[1023] = {
+    1, 2, 2097153, 4, 8, 3145729, 16, 32, 64, 3670017, 128, 256, 512, 1024, 3932161, 2048, 4096, 8192, 16384,
+    32768, 4063233, 65536, 131072, 262144, 524288, 1048576, 2097152, 4128769, 3, 6, 12, 24, 48, 96, 192, 384,
+    768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 5, 2097155, 9,
+    2097157, 10, 17, 2097161, 3145731, 3670016, 18, 33, 1835008, 2097169, 3145733, 20, 34, 65, 917504, 2097185,
+    3145737, 4161537, 36, 66, 129, 458752, 2097217, 3145745, 3670019, 40, 68, 130, 257, 229376, 2097281, 3145761,
+    3670021, 3932160, 72, 132, 258, 513, 114688, 2097409, 3145793, 3670025, 80, 136, 260, 514, 1025, 57344,
+    1966080, 2097665, 3145857, 3670033, 144, 264, 516, 1026, 2049, 28672, 2098177, 3145985, 3670049, 3932163,
+    160, 272, 520, 1028, 2050, 4097, 14336, 983040, 2099201, 3146241, 3670081, 3932165, 288, 528, 1032, 2052,
+    4098, 7168, 8193, 2101249, 3146753, 3670145, 3932169, 4063232, 320, 544, 1040, 2056, 3584, 4100, 8194, 16385,
+    491520, 2105345, 3147777, 3670273, 3932177, 4177921, 576, 1056, 1792, 2064, 4104, 8196, 16386, 32769,
+    2113537, 3149825, 3670529, 3932193, 640, 896, 1088, 2080, 4112, 8200, 16388, 32770, 65537, 245760, 2031616,
+    2129921, 3153921, 3671041, 3932225, 4063235, 448, 1152, 2112, 4128, 8208, 16392, 32772, 65538, 131073,
+    2162689, 3162113, 3672065, 3932289, 4063237, 224, 1280, 2176, 4160, 8224, 16400, 32776, 65540, 122880,
+    131074, 262145, 2228225, 3178497, 3674113, 3932417, 4063241, 112, 2304, 4224, 8256, 16416, 32784, 65544,
+    131076, 262146, 524289, 1015808, 2359297, 3211265, 3678209, 3932673, 4063249, 4128768, 56, 2560, 4352, 8320,
+    16448, 32800, 61440, 65552, 131080, 262148, 524290, 1048577, 2621441, 3276801, 3686401, 3933185, 4063265, 28,
+    4608, 8448, 16512, 32832, 65568, 131088, 262152, 524292, 1048578, 3407873, 3702785, 3934209, 4063297, 14,
+    5120, 8704, 16640, 30720, 32896, 65600, 131104, 262160, 507904, 524296, 1048580, 2097154, 3735553, 3936257,
+    4063361, 4128771, 7, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 9216, 12289, 16896, 24577, 33024,
+    49153, 65664, 98305, 131136, 196609, 262176, 393217, 524304, 786433, 1048584, 1572865, 2064384, 2097156,
+    3801089, 3940353, 4063489, 4128773, 4186113, 26, 50, 98, 194, 386, 770, 1538, 3074, 6146, 10240, 12290,
+    15360, 17408, 24578, 33280, 49154, 65792, 98306, 131200, 196610, 262208, 393218, 524320, 786434, 1048592,
+    1572866, 2097159, 2097160, 2097165, 2097177, 2097201, 2097249, 2097345, 2097537, 2097921, 2098689, 2100225,
+    2103297, 2109441, 2121729, 2146305, 2195457, 2293761, 2490369, 2883585, 3145730, 3948545, 4063745, 4128777,
+    52, 100, 196, 388, 772, 1540, 3076, 6148, 12292, 18432, 24580, 33792, 49156, 66048, 98308, 131328, 196612,
+    253952, 262272, 393220, 524352, 786436, 1048608, 1572868, 2097168, 3145732, 3964929, 4064257, 4128785, 11,
+    104, 200, 392, 776, 1544, 3080, 6152, 7680, 12296, 20480, 24584, 34816, 49160, 66560, 98312, 131584, 196616,
+    262400, 393224, 524416, 786440, 1048640, 1572872, 2097184, 3145735, 3145736, 3145741, 3145753, 3145777,
+    3145825, 3145921, 3146113, 3146497, 3147265, 3148801, 3151873, 3158017, 3170305, 3194881, 3244033, 3342337,
+    3538945, 3997697, 4065281, 4128801, 4161536, 19, 22, 208, 400, 784, 1552, 3088, 6160, 12304, 24592, 36864,
+    49168, 67584, 98320, 132096, 196624, 262656, 393232, 524544, 786448, 1032192, 1048704, 1572880, 1835009,
+    2097163, 2097216, 3145744, 3670018, 4067329, 4128833, 21, 35, 38, 44, 416, 800, 1568, 3104, 3840, 6176,
+    12320, 24608, 40960, 49184, 69632, 98336, 126976, 133120, 196640, 263168, 393248, 524800, 786464, 917505,
+    1048832, 1572896, 1835010, 2097171, 2097280, 3145760, 3670020, 4071425, 4128897, 37, 67, 70, 76, 88, 832,
+    1600, 3136, 6208, 12352, 24640, 49216, 73728, 98368, 135168, 196672, 264192, 393280, 458753, 525312, 786496,
+    917506, 1049088, 1572928, 1835012, 2097173, 2097187, 2097408, 3014657, 3145739, 3145792, 3670023, 3670024,
+    3670029, 3670041, 3670065, 3670113, 3670209, 3670401, 3670785, 3671553, 3673089, 3676161, 3682305, 3694593,
+    3719169, 3768321, 3866625, 4079617, 4129025, 4161539, 41, 69, 131, 134, 140, 152, 176, 1664, 1920, 3200,
+    6272, 12416, 24704, 49280, 81920, 98432, 139264, 196736, 229377, 266240, 393344, 458754, 526336, 786560,
+    917508, 1049600, 1572992, 1835016, 2097189, 2097219, 2097664, 2555905, 3145747, 3145856, 3670032, 4096001,
+    4129281, 4161541, 42, 73, 133, 259, 262, 268, 280, 304, 352, 3328, 6400, 12544, 24832, 49408, 63488, 98560,
+    114689, 147456, 196864, 229378, 270336, 393472, 458756, 516096, 528384, 786688, 917512, 1050624, 1573120,
+    1835024, 2080768, 2097193, 2097221, 2097283, 2098176, 2326529, 3145749, 3145763, 3145984, 3670048, 3932162,
+    4129793, 4161545, 74, 81, 137, 261, 515, 518, 524, 536, 560, 608, 704, 960, 6656, 12800, 25088, 49664, 57345,
+    98816, 114690, 163840, 197120, 229380, 278528, 393728, 458760, 532480, 786944, 917520, 1052672, 1573376,
+    1835040, 1966081, 2097225, 2097285, 2097411, 2099200, 2211841, 3145765, 3145795, 3146240, 3604481, 3670027,
+    3670080, 3932164, 4130817, 4161553, 82, 138, 145, 265, 517, 1027, 1030, 1036, 1048, 1072, 1120, 1216, 1408,
+    13312, 25600, 28673, 50176, 57346, 99328, 114692, 197632, 229384, 294912, 394240, 458768, 540672, 787456,
+    917536, 1056768, 1573888, 1835072, 1966082, 2097233, 2097289, 2097413, 2097667, 2101248, 2154497, 3145769,
+    3145797, 3145859, 3146752, 3375105, 3670035, 3670144, 3932167, 3932168, 3932173, 3932185, 3932209, 3932257,
+    3932353, 3932545, 3932929, 3933697, 3935233, 3938305, 3944449, 3956737, 3981313, 4030465, 4132865, 4161569,
+    4190209, 84, 146, 161, 266, 273, 480, 521, 1029, 2051, 2054, 2060, 2072, 2096, 2144, 2240, 2432, 2816, 14337,
+    26624, 28674, 31744, 51200, 57348, 100352, 114696, 198656, 229392, 327680, 395264, 458784, 557056, 788480,
+    917568, 983041, 1064960, 1574912, 1835136, 1966084, 2097297, 2097417, 2097669, 2098179, 2105344, 2125825,
+    3145801, 3145861, 3145987, 3147776, 3260417, 3670037, 3670051, 3670272, 3932176, 4136961, 4161601, 4177920,
+    148, 162, 274, 289, 522, 529, 1033, 2053, 4099, 4102, 4108, 4120, 4144, 4192, 4288, 4480, 4864, 5632, 7169,
+    14338, 28676, 53248, 57352, 102400, 114704, 200704, 229408, 258048, 397312, 458816, 589824, 790528, 917632,
+    983042, 1081344, 1576960, 1835264, 1966088, 2097313, 2097425, 2097673, 2098181, 2099203, 2111489, 2113536,
+    3080193, 3145809, 3145865, 3145989, 3146243, 3149824, 3203073, 3670053, 3670083, 3670528, 3932192, 4145153,
+    4161665, 164, 240, 276, 290, 321, 530, 545, 1034, 1041, 2057, 3585, 4101, 7170, 8195, 8198, 8204, 8216, 8240,
+    8288, 8384, 8576, 8960, 9728, 11264, 14340, 28680, 57360, 106496, 114720, 204800, 229440, 401408, 458880,
+    491521, 655360, 794624, 917760, 983044, 1040384, 1114112, 1581056, 1835520, 1966096, 2097441, 2097681,
+    2098185, 2099205, 2101251, 2104321, 2129920, 3145873, 3145993, 3146245, 3146755, 3153920, 3174401, 3670057,
+    3670085, 3670147, 3671040, 3899393, 3932171, 3932224, 4063234, 4161793, 168, 292, 322, 532, 546, 577, 1042,
+    1057, 1793, 2058, 2065, 3586, 4105, 7172, 8197, 14344, 15872, 16387, 16390, 16396, 16408, 16432, 16480,
+    16576, 16768, 17152, 17920, 19456, 22528, 28688, 57376, 114752, 212992, 229504, 409600, 459008, 491522,
+    802816, 918016, 983048, 1179648, 1589248, 1836032, 1966112, 2097473, 2097697, 2098193, 2099209, 2100737,
+    2101253, 2105347, 2162688, 2588673, 3145889, 3146001, 3146249, 3146757, 3147779, 3160065, 3162112, 3670089,
+    3670149, 3670275, 3672064, 3784705, 3932179, 3932288, 4063236, 4162049, 4177923, 120, 296, 897, 1058, 1089,
+    2081, 4106, 4113, 8201, 32774, 32780, 33536, 34304, 45056, 491524, 983056, 1605632, 1966144, 2031617,
+    2098209, 2098945, 2099217, 2228224, 3146257, 3146761, 3178496, 3670153, 3670277, 3670531, 3932181, 3932416,
+    4063329, 4063425, 4069377, 4075521 };
+
+static int cbest_23[1023] = {
+    1, 2, 4194320, 4, 2097160, 8, 1048580, 16, 524290, 32, 262145, 64, 128, 4325392, 256, 512, 2162696, 1024,
+    2048, 1081348, 4096, 8192, 540674, 16384, 32768, 270337, 65536, 131072, 262144, 4329488, 524288, 2164744,
+    1048576, 3, 1082372, 2097152, 4194321, 5, 2097161, 4194322, 6, 9, 1048581, 2097162, 4194304, 4194324,
+    6291480, 10, 17, 524291, 541186, 1048582, 2097164, 4194328, 5242900, 12, 18, 33, 66, 132, 264, 528, 1056,
+    2112, 4224, 8448, 16896, 33792, 67584, 135168, 270336, 3145740, 4718610, 20, 34, 65, 262147, 524294, 540672,
+    1048588, 2097176, 2621450, 4194352, 4456465, 24, 36, 129, 262149, 270593, 524298, 1048596, 1081344, 1572870,
+    2097192, 2359305, 4194384, 4325393, 40, 68, 130, 257, 262153, 524306, 1048612, 1310725, 2097224, 2162688,
+    4194448, 4325394, 48, 72, 258, 513, 262161, 524322, 786435, 1048644, 2097288, 2162697, 4194576, 4325376,
+    4325396, 6422552, 80, 136, 260, 514, 1025, 262177, 524354, 1048708, 2097416, 2162698, 4194832, 4325400,
+    5373972, 6357016, 96, 144, 516, 1026, 2049, 262209, 524418, 1048836, 1081349, 2097672, 2162700, 4195344,
+    4329616, 4849682, 160, 272, 520, 1028, 2050, 4097, 262273, 524546, 1049092, 1081350, 2098184, 3211276,
+    4196368, 4325424, 4587537, 5275668, 192, 288, 1032, 2052, 4098, 8193, 262401, 524802, 540675, 1049604,
+    2099208, 2162712, 2686986, 3178508, 4198416, 4325456, 320, 544, 1040, 2056, 4100, 8194, 16385, 262657,
+    525314, 1050628, 1081356, 2101256, 2162728, 2424841, 4202512, 4325520, 4734994, 384, 576, 2064, 4104, 8196,
+    16386, 32769, 263169, 526338, 540678, 1052676, 1081364, 1605638, 2105352, 2162760, 2164808, 2637834, 4210704,
+    4325648, 640, 1088, 2080, 4112, 8200, 16388, 32770, 65537, 264193, 270339, 528386, 540682, 1056772, 1081380,
+    1343493, 1589254, 2113544, 2162824, 4227088, 4325904, 4464657, 6488088, 768, 1152, 4128, 8208, 16392, 32772,
+    65538, 131073, 266241, 270341, 532482, 540690, 1064964, 1081412, 2129928, 2162952, 2367497, 4259856, 4326416,
+    1280, 2176, 4160, 8224, 16400, 32776, 65540, 131074, 270345, 540706, 802819, 1081476, 1318917, 2163208,
+    4327440, 4329489, 5406740, 1536, 2304, 8256, 16416, 32784, 65544, 131076, 262146, 270353, 278529, 540738,
+    557058, 794627, 1081604, 1082404, 1114116, 2163720, 2228232, 4329490, 4456464, 2560, 4352, 8320, 16448,
+    32800, 65552, 131080, 262148, 270369, 270592, 294913, 524289, 540802, 541184, 589826, 1081860, 1082368,
+    1179652, 2164736, 2359304, 3244044, 4329472, 4329492, 4333584, 4866066, 6426648, 3072, 4608, 16512, 32832,
+    65568, 131088, 135296, 262152, 270401, 327681, 540930, 655362, 1310724, 2164745, 2166792, 4329496, 4341776,
+    4718608, 5378068, 5120, 8704, 16640, 32896, 65600, 67648, 131104, 262160, 270465, 393217, 524292, 786434,
+    1048577, 1083396, 2164746, 2170888, 2621448, 2703370, 4358160, 4595729, 4853778, 6359064, 6144, 9216, 33024,
+    33824, 65664, 131136, 262176, 524296, 541202, 541698, 1048578, 1085444, 1572868, 2164748, 2179080, 4329520,
+    4390928, 4591633, 5242896, 10240, 16912, 17408, 33280, 65792, 131200, 262208, 270849, 524304, 524352, 542722,
+    1082373, 1089540, 1622022, 2097153, 2195464, 2433033, 3145736, 3213324, 4329552, 8456, 12288, 18432, 66048,
+    131328, 262272, 271361, 524320, 544770, 786433, 1048584, 1048704, 1082374, 1097732, 2097154, 2164760,
+    2689034, 4194323, 4587536, 5276692, 6291472, 7, 4228, 20480, 34816, 66560, 131584, 262400, 272385, 548866,
+    1048592, 1351685, 1572866, 2097156, 2097163, 2097408, 2164776, 2293768, 2426889, 3179532, 4194305, 4194325,
+    4329744, 6291481, 11, 2114, 24576, 36864, 132096, 262656, 270601, 274433, 524416, 541187, 1048583, 1048608,
+    1082380, 1146884, 1310721, 2097165, 2424840, 3145732, 4194306, 4194326, 4194329, 4194816, 4330000, 4849680,
+    5242901, 6291482, 6492184, 13, 19, 67, 133, 265, 529, 1057, 2113, 4225, 8449, 16897, 33793, 40960, 67585,
+    69632, 133120, 135169, 263168, 524544, 573442, 811011, 1048640, 1082388, 1212420, 1606662, 2097166, 2097168,
+    2164872, 2621442, 3145741, 4194308, 4194330, 4330512, 4718611, 4735506, 5242902, 6291464, 6291484, 6490136,
+    14, 21, 35, 134, 266, 530, 1058, 4226, 8450, 16898, 33794, 49152, 67586, 73728, 135170, 264192, 270338,
+    286721, 524295, 524800, 540673, 541190, 606210, 1048589, 1343492, 1344517, 2097177, 2097184, 2165000,
+    2359297, 2621451, 2638346, 2686984, 3145742, 4194312, 4194332, 4194353, 4194386, 4194452, 4194584, 4195376,
+    4196432, 4198544, 4202768, 4211216, 4228112, 4261904, 4331536, 4464656, 5242884, 5373968, 5410836, 7340060,
+    22, 25, 37, 70, 268, 532, 1060, 2116, 8452, 16900, 33796, 67588, 81920, 135172, 139264, 266240, 270340,
+    303105, 524299, 525312, 541194, 671746, 1048590, 1048597, 1048832, 1081345, 1082436, 1572871, 1589766,
+    2097178, 2097193, 2097216, 2097226, 2097292, 2097688, 2098216, 2099272, 2101384, 2105608, 2114056, 2130952,
+    2165256, 2232328, 2367496, 4194354, 4194385, 4456467, 4718594, 4718614, 4734992, 5242908, 6815770, 26, 38,
+    41, 69, 74, 131, 140, 536, 1064, 2120, 4232, 16904, 33800, 67592, 98304, 135176, 147456, 262151, 270344,
+    270595, 335873, 524307, 526336, 540676, 802818, 1048598, 1048613, 1048646, 1048844, 1049088, 1049108,
+    1049636, 1050692, 1052804, 1057028, 1065476, 1081346, 1082500, 1116164, 1183748, 1318916, 1605636, 2097180,
+    2097194, 2097225, 2097280, 2162689, 2165768, 2359307, 2621454, 2637832, 3211272, 4194336, 4194356, 4194449,
+    4325395, 4337680, 4456449, 4456469, 4464913, 4718618, 4870162, 5275664, 5407764, 5767190, 6291512, 6422544,
+    6553625, 28, 42, 49, 73, 82, 148, 259, 280, 1072, 2128, 4240, 8464, 33808, 67600, 135184, 163840, 262155,
+    270352, 270597, 278528, 401409, 524302, 524323, 524422, 524554, 524818, 525346, 526402, 528384, 528514,
+    532738, 540680, 541218, 558082, 591874, 659458, 794626, 803331, 1048614, 1048645, 1049600, 1082628, 1310727,
+    1589252, 2097196, 2097289, 2162690, 2359309, 2367753, 3145756, 3178504, 3246092, 3670030, 4194360, 4194368,
+    4194388, 4194450, 4194577, 4325377, 4325397, 4329620, 4345872, 4456473, 5242932, 5505045, 6291544, 6357008,
+    6422553, 44, 50, 81, 98, 137, 164, 261, 296, 515, 560, 2144, 4256, 8480, 16928, 67616, 135200, 196608,
+    262157, 262163, 262211, 262277, 262409, 262673, 263201, 264257, 266369, 270368, 279041, 294912, 295937,
+    329729, 397313, 524310, 524355, 532480, 540688, 540736, 541250, 1048604, 1048709, 1050624, 1081352, 1081472,
+    1082884, 1319173, 1572878, 2097228, 2097290, 2097417, 2097664, 2162692, 2162699, 2162944, 2168840, 2621466,
+    3145772, 3245068, 3407885, 4194392, 4194432, 4194578, 4194833, 4325378, 4325398, 4325401, 4325888, 4362256,
+    4599825, 4718642, 4980755, 5242964, 5373973, 6291608, 6357017, 6422554, 52, 76, 97, 138, 145, 196, 262, 328,
+    517, 592, 1027, 1120, 4288, 8512, 16960, 33856, 135232, 262165, 262179, 270400, 270609, 327680, 524314,
+    524326, 524419, 540704, 541314, 786439, 794883, 802817, 1048620, 1048710, 1048837, 1052672, 1081360, 1310733,
+    1572886, 1605634, 2097208, 2097418, 2097673, 2098176, 2162701, 2172936, 2359321, 2621482, 2705418, 2883595,
+    3145804, 3211268, 4194456, 4194560, 4194580, 4194834, 4195345, 4325380, 4325402, 4329617, 4395024, 4456497,
+    4718674, 4849683, 4866578, 5243028, 5373974, 6291736, 6357018, 6422536, 6422556, 56, 84, 146, 161, 194, 273,
+    392, 518, 521, 656, 1029, 1184, 2051, 2240, 8576, 17024, 33920, 67712, 262169, 262181, 270464, 270625,
+    393216, 524330, 524358, 524547, 541442, 557056, 786443, 794625, 1048628, 1048652, 1048838, 1049093, 1056768,
+    1081351, 1081376, 1084420, 1310741, 1343489, 1572902, 1589250, 1835015, 2097240, 2097420, 2097674, 2098185,
+    2099200, 2162702, 2162704, 2181128, 2359337, 2621514, 2686978, 3145868, 3178500, 3211277, 4194416, 4194836,
+    4195346, 4196369, 4325384, 4325404, 4325425, 4325458, 4325524, 4325656, 4326448, 4327504, 4329618, 4333840,
+    4342288, 4359184, 4392976, 4456529, 4595728, 4718738, 5243156, 5275669, 5373956, 6291992, 6357000, 6357020,
+    7471132, 162, 193, 289, 1030, 1312, 2053, 4099, 34048, 262185, 262213, 524338, 524362, 524803, 786451,
+    1048716, 1049605, 1064960, 1086468, 1310757, 2097256, 2097304, 2097676, 2098186, 2099209, 2101248, 2162713,
+    2424833, 2621578, 2703882, 3145996, 3178509, 4194480, 4198417, 4325426, 4456593, 4587539, 4718866, 4849666,
+    6292504, 6426776, 7405596 };
+
+static int cbest_24[1023] = {
+    1, 2, 8388675, 4, 12583010, 8, 6291505, 16, 32, 64, 11534427, 128, 256, 8388674, 4194337, 14155886, 3, 512,
+    8388673, 6, 12583011, 5, 1024, 10485843, 12, 6291504, 12583008, 9, 24, 2048, 3145752, 8388679, 10, 7077943,
+    14680178, 48, 1572876, 13631594, 17, 4096, 8388683, 96, 786438, 12583014, 20, 6291507, 18, 33, 192, 8192,
+    393219, 7340089, 8388691, 6815797, 11534426, 12583018, 384, 131073, 6291489, 6291509, 11927640, 34, 40, 65,
+    16384, 262146, 8388707, 8585282, 12582978, 66, 768, 524292, 8388611, 8454211, 11534419, 11534425, 12583026,
+    1048584, 6291513, 36, 129, 1536, 32768, 2097168, 4292641, 5767213, 80, 130, 4194336, 6291473, 11796569,
+    12615778, 14155882, 132, 3072, 12058719, 12582946, 68, 257, 65536, 5963820, 8388803, 11534411, 11534431,
+    14155887, 258, 6144, 196609, 393218, 6307889, 7077941, 160, 260, 8388672, 72, 264, 513, 12288, 131072,
+    8388931, 10534995, 11272277, 14155878, 14155884, 786436, 8486979, 10485842, 12583138, 7, 516, 24576, 4194339,
+    6291569, 11927641, 136, 320, 514, 520, 1025, 393217, 5242921, 7077939, 7077942, 8388677, 8389187, 8585283,
+    12583009, 14418028, 13, 528, 49152, 1572872, 2981910, 8388678, 10485841, 11542619, 12583266, 14286959,
+    15466612, 14, 4194341, 6291633, 12632162, 14680179, 25, 144, 1026, 1032, 2049, 98304, 262144, 786434,
+    3145753, 8389699, 11534459, 13631595, 11, 26, 640, 1040, 3145744, 6291506, 8388682, 8388687, 11534363,
+    11927642, 12583012, 12583522, 12681314, 13656170, 14024809, 28, 49, 1056, 196608, 1572877, 4194345, 6291761,
+    7340088, 8388681, 11010135, 12583015, 14680176, 272, 1028, 2050, 4097, 1572868, 3145754, 3538971, 6291457,
+    6316081, 6815793, 6815796, 8388699, 8390723, 10485827, 10485847, 13631586, 13631592, 22, 52, 97, 2064,
+    786439, 4194305, 6291488, 6291508, 7209014, 8388690, 11534403, 12584034, 14155854, 21, 50, 56, 98, 1280,
+    2080, 1490955, 1572878, 3670044, 4194353, 5963821, 6291497, 6292017, 6340657, 7733306, 8388643, 8388723,
+    8781888, 9175109, 9961551, 12582914, 12582994, 12583019, 12583022, 14155902, 14159982, 15728762, 19, 193,
+    288, 2052, 2112, 4098, 8193, 524288, 3145736, 3145756, 3407898, 4390944, 8392771, 10485851, 11534555,
+    11796571, 12583016, 13893736, 14155874, 14352495, 15204470, 15532148, 44, 104, 393216, 2195472, 6291511,
+    6291512, 7077927, 7340081, 8388689, 8388706, 8388739, 12582979, 12583034, 12585058, 14680162, 14680182, 112,
+    196, 385, 4128, 1097736, 1835022, 4227105, 4292640, 5767209, 5767212, 6292529, 6828085, 7077937, 8388610,
+    8388695, 8454210, 11534418, 11534423, 11534424, 12583027, 13631598, 35, 41, 194, 544, 2056, 2560, 4100, 4160,
+    8194, 16385, 262147, 548868, 1703949, 2146320, 4259873, 6291472, 6291517, 7340091, 8388609, 8396867, 8519746,
+    11534417, 11534683, 11927632, 12976225, 13369444, 14155822, 42, 67, 88, 100, 208, 769, 4224, 274434, 524293,
+    1073160, 6291493, 6815799, 6946868, 7077951, 8388705, 8585280, 8650817, 10158158, 11546715, 12058715,
+    12582976, 12587106, 14155880, 14286958, 14680186, 38, 134, 224, 386, 392, 770, 131075, 137217, 536580,
+    786432, 917511, 1048585, 2883606, 3604507, 4194401, 5963816, 6291491, 6291537, 6293553, 7864381, 8389059,
+    8454209, 10502227, 11272279, 11796568, 12583024, 12583074, 12615779, 14155883, 15401079, 37, 70, 268, 576,
+    1537, 4104, 8196, 8256, 16386, 32769, 268290, 393223, 1048576, 2097169, 3866653, 6291515, 6307888, 7077911,
+    7077940, 7079991, 7340073, 7340093, 7602235, 8388715, 8405059, 10485875, 10518611, 11534429, 11534939,
+    11559003, 12058718, 12582947, 12582986, 12583030, 14680146, 81, 131, 176, 416, 536, 5120, 8320, 134145,
+    524294, 786446, 2981908, 3153944, 3538970, 5767205, 6684722, 6815781, 8388802, 8389443, 8847424, 8912967,
+    9134150, 9240645, 10485779, 11370581, 11534410, 11534430, 11927643, 12582944, 12591202, 12714083, 13631562,
+    14024808, 82, 133, 262, 388, 448, 784, 1072, 1540, 3073, 8448, 131077, 1048586, 1441803, 1572892, 1576972,
+    3473434, 4194465, 6295601, 7766074, 8388627, 8388801, 9437259, 11272273, 11534443, 11796561, 11927624,
+    11927644, 12615776, 12845152, 13631610, 14156014, 14418030, 69, 84, 140, 200, 524, 1088, 1538, 2144, 4112,
+    8200, 16388, 32770, 65537, 262150, 393227, 788486, 1490954, 1572864, 2097170, 3145784, 4292643, 4423712,
+    5767215, 5898284, 6422576, 8388711, 8390211, 8421443, 8457283, 8585286, 11535451, 12058711, 12058717,
+    12582982, 12583394, 13639786, 14696562, 15466614, 15564916, 76, 259, 352, 772, 832, 1048, 4288, 6145, 16512,
+    394243, 786454, 3211288, 4194338, 5963812, 6291475, 6291481, 6291568, 6815805, 8388615, 8388930, 8454215,
+    10534994, 11272276, 11534409, 11802713, 12599394, 13647978, 14155879, 14155885, 14876787, 74, 161, 261, 266,
+    896, 1568, 2096, 3074, 3080, 8576, 10240, 16640, 131081, 655365, 1048588, 1310730, 1572908, 1605644, 1769485,
+    2211856, 2621460, 3342361, 4194593, 5079079, 5242920, 6291697, 6299697, 7077938, 7143479, 7340057, 8388807,
+    8388929, 8391747, 8455747, 8486978, 8781889, 11534415, 12583139, 12583778, 13107302, 14155876, 14156142,
+    14418024, 14680114, 14745714, 73, 162, 265, 280, 1152, 4192, 8208, 12289, 16392, 16896, 17152, 32772, 65538,
+    132097, 262154, 393235, 802822, 1736717, 2097152, 2097172, 2981906, 3145816, 3538969, 4243489, 4292645,
+    5963822, 6029359, 6291553, 6815765, 7012404, 7209015, 8585290, 8585794, 8716353, 9109574, 10485971, 11536475,
+    11928664, 12320861, 12582962, 12583136, 13008993, 13631530, 14024811, 14155894, 14162030, 14286955, 14352494,
+    15466608, 164, 518, 704, 776, 1664, 6146, 8384, 34304, 133121, 196611, 401411, 524300, 786437, 786470,
+    1105928, 1703948, 2949142, 3145728, 4194340, 6291477, 6291632, 6291889, 6307891, 6819893, 7078007, 7209012,
+    7348281, 7733307, 8388619, 8388676, 8389186, 8394819, 8454219, 8454723, 10190926, 10534993, 11534451,
+    11796553, 11796573, 12189790, 12584546, 12615782, 14418029, 138, 168, 400, 517, 532, 1792, 3076, 3136, 6160,
+    16768, 24577, 33024, 68608, 131089, 135169, 264194, 745477, 851974, 1490953, 1572940, 4194849, 4292897,
+    4390945, 5267497, 5636138, 6553651, 6823989, 7733304, 8388835, 8388935, 8455235, 8486977, 10321997, 10485840,
+    11534395, 11542618, 12058703, 12582950, 12583106, 12583267, 12617314, 14156398, 14168174, 15466613, 16089208,
+    137, 152, 321, 515, 521, 560, 1544, 2176, 8224, 12290, 16400, 20480, 32776, 33280, 33536, 65540, 131074,
+    137216, 262162, 266242, 393251, 425987, 552964, 917510, 1572874, 2097176, 3145880, 3407896, 3604506, 4292649,
+    4567075, 6291571, 6292273, 7372857, 8388939, 8400963, 8456259, 8519747, 8585298, 8589378, 10486099, 11538523,
+    11927633, 12583142, 12583264, 12586082, 12616034, 12632163, 12779619, 12976224, 14155898, 148, 522, 529,
+    1036, 1408, 3328, 6148, 33792, 49153, 67072, 196613, 270338, 393222, 458755, 524308, 528388, 786502, 1572873,
+    2981911, 3866652, 3883037, 4194343, 4194344, 4554787, 5242913, 6291760, 6307873, 6307893, 7077925, 7077947,
+    7078071, 8388867, 8389185, 8389698, 8454227, 8585281, 8781890, 9175111, 9273413, 10158159, 10510419,
+    11010131, 11534458, 11534491, 12615786, 12616290, 12616546, 12648546, 12746851, 14073961, 14418020, 14680306,
+    15, 324, 1064, 3584, 6272, 12320, 24578, 131105, 134144, 163841, 276482, 393221, 532484, 1048600, 1474571,
+    1573004, 1835020, 3145748, 3506202, 4195361, 4292609, 4294689, 5767181, 6291456, 6293041, 6308017, 6316080,
+    6324273, 6488112, 6815792, 7077923, 7077949, 8388686, 8389191, 8413251, 8601666, 9257029, 10928208, 11403348,
+    11534347, 11534362, 11542611, 11542617, 11927672, 11960408, 12582954, 12583013, 12583523, 12589154, 12616802,
+    12681315, 13631722, 13656171, 13893738, 14155846, 14156910, 14286951, 14286957, 15401078, 15532150, 145, 322,
+    328, 1027, 1033, 1120, 1552, 2304, 12292, 16416, 32784, 65544, 66048, 98305, 131076, 262145, 262178, 393283,
+    540676, 786435, 1056776, 1441802, 2818069, 3146008, 4194304, 4194321, 4194349, 4292657, 5242923, 5767229,
+    5771309, 5964332, 6291601, 6291635, 6308145, 6946869, 7209010, 7340153, 7782458, 8388680, 8388685, 8388811,
+    8389195, 8470595, 8585314, 8618050, 10059855, 10485835, 10485845, 10486355, 10534979, 10534999, 10584147,
+    11010134, 11272261, 11534361, 11665498, 11798617, 11927576, 11927634, 11993176, 12583270, 12615746, 12632160,
+    14155790, 14155850, 14155870, 14680177, 15827066, 146, 276, 336, 641, 800, 1034, 2816, 6656, 49154, 66560,
+    196617, 197121, 524324, 720901, 786442, 786566, 3158040, 3670040, 5963817, 6291637, 6292016, 6294577,
+    6307897, 6308657, 6340656, 6815861, 7078199, 8389203, 8390722, 8454243, 8486983, 8585218, 8847425, 9134151,
+    10485846, 10535123, 12583274, 12615794, 13631587, 14159978 };
+
+static int cbest_25[1023] = {
+    1, 2, 16777220, 4, 8388610, 8, 4194305, 16, 32, 18874372, 64, 128, 9437186, 256, 512, 4718593, 1024, 2048,
+    4096, 19136516, 8192, 16384, 32768, 9568258, 65536, 131072, 262144, 4784129, 524288, 1048576, 2097152,
+    4194304, 19169284, 8388608, 3, 9584642, 16777216, 16777221, 5, 8388611, 16777222, 6, 9, 18, 36, 72, 144, 288,
+    576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 294912, 589824, 1179648, 2359296, 4718592,
+    25165830, 10, 17, 4194307, 8388614, 9437184, 16777228, 20971525, 12, 33, 4194309, 4792321, 8388618, 12582915,
+    16777236, 18874368, 18874373, 20, 34, 65, 4194313, 8388626, 16777252, 18874374, 24, 66, 129, 4194321,
+    8388642, 9437187, 16777284, 27262982, 40, 68, 130, 257, 4194337, 8388674, 16777348, 18874380, 23068677,
+    26214406, 48, 132, 258, 513, 4194369, 8388738, 9437190, 16777476, 18874388, 80, 136, 260, 514, 1025, 4194433,
+    4718595, 8388866, 9437194, 13631491, 16777732, 18874404, 19173380, 21495813, 96, 264, 516, 1026, 2049,
+    4194561, 4718597, 8389122, 9437202, 13107203, 16778244, 18874436, 160, 272, 520, 1028, 2050, 4097, 4194817,
+    4718601, 4784128, 8389634, 9437218, 9568256, 16779268, 18874500, 19136512, 19136517, 28311558, 192, 528,
+    1032, 2052, 4098, 8193, 2392064, 4195329, 4718609, 8390658, 9437250, 16781316, 18874628, 19136518, 320, 544,
+    1040, 2056, 4100, 8194, 16385, 1196032, 4196353, 4718625, 8392706, 9437314, 16785412, 18874884, 23592965,
+    27525126, 384, 1056, 2064, 4104, 8196, 16386, 32769, 598016, 4198401, 4718657, 8396802, 9437442, 9568259,
+    9586690, 16793604, 18875396, 19136524, 23330821, 640, 1088, 2080, 4112, 8200, 16388, 32770, 65537, 299008,
+    4202497, 4718721, 8404994, 9437698, 14155779, 16809988, 18876420, 19136532, 26345478, 768, 2112, 4128, 8208,
+    16392, 32772, 65538, 131073, 149504, 4210689, 4718849, 8421378, 9438210, 9568262, 16842756, 18878468,
+    19136548, 1280, 2176, 4160, 8224, 16400, 32776, 65540, 74752, 131074, 262145, 4227073, 4719105, 8454146,
+    9439234, 9568266, 13762563, 16908292, 18882564, 19136580, 1536, 4224, 8256, 16416, 32784, 37376, 65544,
+    131076, 262146, 524289, 4259841, 4719617, 4784131, 8519682, 9441282, 9568274, 17039364, 18890756, 19136644,
+    21561349, 28573702, 2560, 4352, 8320, 16448, 18688, 32800, 65552, 131080, 262148, 524290, 1048577, 4325377,
+    4720641, 4784133, 4793345, 8650754, 9445378, 9568290, 13172739, 17301508, 18907140, 19136772, 28442630, 3072,
+    8448, 9344, 16512, 32832, 65568, 131088, 262152, 524292, 1048578, 2097153, 4456449, 4722689, 4784137,
+    8912898, 9453570, 9568322, 17825796, 18939908, 19137028, 23855109, 4672, 5120, 8704, 16640, 32896, 65600,
+    131104, 262160, 524296, 1048580, 2097154, 4726785, 4784145, 9469954, 9568386, 19005444, 19137540, 19169280,
+    19169285, 2336, 6144, 16896, 33024, 65664, 131136, 262176, 524304, 1048584, 2097156, 4194306, 4734977,
+    4784161, 5242881, 9502722, 9568514, 9584640, 10485762, 19138564, 19169286, 20971524, 23658501, 1168, 10240,
+    17408, 33280, 65792, 131200, 262208, 524320, 1048592, 2097160, 4194308, 4751361, 4784193, 4792320, 6291457,
+    8388609, 9568770, 12582914, 14286851, 19140612, 19398660, 27557894, 584, 12288, 33792, 66048, 131328, 262272,
+    524352, 1048608, 2097168, 4194312, 4784257, 9569282, 9699330, 14221315, 19144708, 19169292, 19922948,
+    23363589, 25165828, 292, 20480, 34816, 66560, 131584, 262400, 524416, 1048640, 2097184, 2396160, 4194320,
+    4784385, 4849665, 8388612, 8388624, 9570306, 9584643, 9961474, 16777217, 19152900, 19169300, 19173892, 146,
+    24576, 67584, 132096, 262656, 524544, 1048704, 2097216, 4194336, 4784641, 4980737, 8388616, 9572354,
+    12582913, 16777218, 16777223, 16777248, 19169316, 23068676, 26361862, 28704774, 7, 19, 37, 73, 145, 289, 577,
+    1153, 2305, 4609, 9217, 18433, 36865, 40960, 69632, 73729, 133120, 147457, 263168, 294913, 524800, 589825,
+    1048832, 1179649, 1198080, 2097280, 2359297, 4194368, 4785153, 9576450, 9584646, 11534338, 19169348,
+    19202052, 25165826, 25165831, 11, 38, 74, 290, 578, 1154, 2306, 4610, 9218, 18434, 36866, 49152, 73730,
+    135168, 147458, 264192, 294914, 525312, 589826, 1049088, 1179650, 2097408, 2359298, 4194432, 4718594,
+    4786177, 5767169, 8388615, 8388640, 9437185, 9584650, 13631490, 13778947, 16777224, 16777229, 16777238,
+    16777292, 16777364, 16777508, 16777796, 16778372, 16779524, 16781828, 16786436, 16795652, 16814084, 16850948,
+    16924676, 17072132, 17367044, 17956868, 19169412, 19267588, 20971521, 21495812, 27262980, 28606470, 13, 22,
+    76, 148, 580, 1156, 2308, 4612, 9220, 18436, 36868, 73732, 81920, 139264, 147460, 266240, 294916, 526336,
+    589828, 599040, 1049600, 1179652, 2097664, 2359300, 4194560, 4718596, 4788225, 6815745, 8388619, 8388646,
+    8388672, 8388682, 8388754, 8388898, 8389186, 8389762, 8390914, 8393218, 8397826, 8407042, 8425474, 8462338,
+    8536066, 8683522, 8978434, 9584658, 9601026, 10747906, 13107202, 16777230, 16777232, 16777237, 18874369,
+    19169540, 20971527, 23920645, 26214404, 14, 21, 26, 35, 44, 152, 296, 1160, 2312, 4616, 9224, 18440, 36872,
+    73736, 98304, 147464, 270336, 294920, 528384, 589832, 1050624, 1179656, 2098176, 2359304, 4194311, 4194323,
+    4194341, 4194377, 4194449, 4194593, 4194816, 4194881, 4195457, 4196609, 4198913, 4203521, 4212737, 4231169,
+    4268033, 4341761, 4489217, 4718600, 4792323, 5373953, 6553601, 8388627, 8388736, 9437188, 9437200, 9584674,
+    9633794, 16777253, 18874370, 18874375, 18874400, 19169796, 19660804, 21569541, 23887877, 25165838, 28459014,
+    29360135, 25, 52, 67, 88, 304, 592, 2320, 4624, 9232, 18448, 36880, 73744, 147472, 163840, 278528, 294928,
+    299520, 532480, 589840, 1052672, 1179664, 2099200, 2359312, 4194315, 4195328, 4718608, 4792325, 4800513,
+    8388622, 8388643, 8388864, 9437192, 9584706, 9586946, 12582919, 13180931, 13631489, 16777254, 16777280,
+    16777285, 19170308, 20185092, 20971533, 25165846, 27262978, 27262983, 41, 50, 69, 104, 131, 176, 608, 1184,
+    4640, 9248, 18464, 36896, 73760, 147488, 196608, 294944, 540672, 589856, 1056768, 1179680, 2101248, 2359328,
+    4194317, 4196352, 4718624, 4792329, 4816897, 8388630, 8388675, 8389120, 9584770, 9830402, 12582923, 13107201,
+    14352387, 16777244, 16777286, 16777344, 16777349, 18874376, 18874381, 18874390, 18874444, 18874516, 18874660,
+    18874948, 18875524, 18876676, 18878980, 18883588, 18892804, 18911236, 18948100, 19021828, 19171332, 19464196,
+    20054020, 20971541, 23068673, 23592964, 25165862, 26214402, 26214407, 28, 42, 49, 70, 82, 100, 133, 208, 259,
+    352, 1216, 2368, 9280, 18496, 36928, 73792, 147520, 149760, 294976, 327680, 557056, 589888, 1064960, 1179712,
+    2105344, 2359360, 4194325, 4194339, 4198400, 4718656, 4792337, 8388634, 8388739, 8389632, 9437191, 9437216,
+    9584898, 10092546, 12582931, 16777260, 16777350, 16777472, 16777477, 18874382, 18874384, 18874389, 20971557,
+    23068679, 23330820, 25165894, 28311556, 81, 134, 137, 164, 200, 261, 416, 515, 704, 2432, 4736, 18560, 36992,
+    73856, 147584, 295040, 393216, 589952, 1081344, 1179776, 2113536, 2359424, 4194329, 4194371, 4202496,
+    4718720, 4792353, 4915201, 8388650, 8388678, 8388867, 8390656, 9437195, 9437222, 9437248, 9437258, 9437330,
+    9437474, 9437762, 9438338, 9439490, 9441794, 9446402, 9455618, 9474050, 9510914, 9585154, 9732098, 10027010,
+    11796482, 12582947, 14155778, 14303235, 16777268, 16777478, 16777728, 16777733, 18874405, 19173376, 19173381,
+    19177476, 20971589, 21495809, 23666693, 25165958, 27262990, 31457287, 97, 138, 262, 265, 274, 328, 400, 517,
+    832, 1027, 1408, 4864, 9472, 37120, 73984, 74880, 147712, 295168, 590080, 655360, 1114112, 1179904, 2129920,
+    2359552, 4194345, 4194373, 4194435, 4210688, 4718848, 4792385, 5046273, 8388658, 8388742, 8389123, 8392704,
+    9437203, 9437312, 9585666, 11665410, 12582979, 16777300, 16777356, 16777734, 16778240, 16778245, 18874406,
+    18874432, 18874437, 19173382, 19185668, 20971653, 21495815, 23068685, 25166086, 26214414, 27262998, 27525124,
+    30408711, 56, 84, 98, 140, 161, 266, 518, 521, 530, 656, 800, 1029, 1664, 2051, 9728, 18944, 74240, 147968,
+    295424, 590336, 786432, 1180160, 2162688, 2359808, 4194353, 4194437, 4194563, 4227072, 4718599, 4718611,
+    4718629, 4718665, 4718737, 4718881, 4719104, 4719169, 4720897, 4723201, 4727809, 4737025, 4755457, 4792449,
+    4866049, 5013505, 5898241, 7077889, 8388690, 8388870, 8389635, 8396800, 9437198, 9437219, 9437440, 9568257,
+    12583043, 13631495, 13762562, 14229507, 16777316, 16777484, 16778246, 16779264, 16779269, 18874396, 18874438,
+    18874496, 18874501, 19136513, 20971781, 23068693, 25166342, 26214422, 27263014, 27561990, 28311554, 28311559,
+    28737542, 29884423 };
+
+static int cbest_26[1023] = {
+    1, 2, 33554467, 4, 50331698, 8, 25165849, 16, 32, 64, 46137391, 128, 256, 56623156, 512, 33554466, 16777233,
+    3, 1024, 28311578, 33554465, 6, 50331699, 5, 41943083, 12, 2048, 25165848, 50331696, 9, 24, 12582924,
+    33554471, 10, 4096, 14155789, 58720314, 48, 6291462, 54526006, 17, 33554475, 96, 8192, 3145731, 50331702, 20,
+    25165841, 25165851, 18, 33, 192, 29360157, 33554483, 50331682, 34, 16384, 27263003, 33554435, 35127330,
+    46137387, 46137390, 50331706, 384, 25165853, 40632357, 40, 65, 66, 768, 32768, 17563665, 25165833, 46137389,
+    56623158, 68, 1048577, 50331666, 36, 129, 1536, 2097154, 23068695, 33554531, 46137383, 48234541, 80, 130,
+    65536, 4194308, 28311579, 34078755, 47185966, 56623152, 56623157, 132, 3072, 8388616, 28311576, 136, 257,
+    14155788, 16777232, 33554595, 6144, 131072, 42336299, 45088808, 50331762, 50593842, 53870641, 160, 260,
+    25165881, 72, 258, 264, 513, 12288, 1572865, 3145730, 33554723, 272, 262144, 7077894, 23592983, 25296921,
+    33554464, 50331826, 57671733, 24576, 22544404, 25165913, 47710254, 61866041, 320, 514, 520, 1025, 6291460,
+    33554979, 34340899, 41943082, 46137407, 7, 528, 49152, 524288, 16777235, 46137359, 50331954, 544, 3145729,
+    3538947, 20971541, 25165977, 33554469, 35127331, 50331697, 54722614, 56623140, 13, 144, 516, 1026, 2049,
+    98304, 11272202, 12582920, 28311570, 33554470, 33555491, 41943081, 45350952, 56623164, 14, 640, 1040,
+    1048576, 14155785, 16777237, 46202927, 50332210, 50724914, 58720315, 25, 1056, 196608, 6291458, 12582925,
+    25166105, 27263001, 41943075, 44040233, 54526002, 54526007, 11, 26, 1028, 1088, 2050, 4097, 16777217,
+    23855127, 25165825, 25165840, 25165850, 28311582, 33554474, 33554479, 33556515, 46137455, 50331700, 51118130,
+    60489787, 62390329, 28, 49, 393216, 5636101, 6291463, 16777241, 29360156, 33554473, 35323938, 46137379,
+    50331703, 50332722, 56623124, 58720312, 50, 1280, 2080, 12582916, 12582926, 22675476, 25165845, 25166361,
+    25362457, 27263002, 28311562, 33554451, 33554491, 36700192, 39845925, 40632359, 41943087, 47185967, 50331650,
+    50331690, 54526004, 22, 52, 97, 288, 1032, 2052, 2112, 4098, 8193, 786432, 14155781, 14155791, 18350096,
+    25165852, 27361307, 29360153, 33554482, 33558563, 46137385, 46137519, 50331683, 56623154, 56655924, 58720306,
+    60817464, 64487487, 21, 56, 2176, 2097152, 9175048, 14680078, 23068693, 25559065, 33554434, 33554499,
+    46137386, 50331707, 50331710, 50333746, 62914622, 19, 100, 193, 1572864, 4587524, 13631501, 17563664,
+    25165832, 25165843, 25166873, 28311577, 33554433, 40632353, 40632356, 45088809, 50331704, 53870640, 55574583,
+    35, 44, 98, 104, 2056, 2560, 4100, 4160, 8194, 16385, 2293762, 8781832, 17661969, 25165855, 33554481,
+    33562659, 36372513, 45482024, 46137647, 48234543, 50331680, 53477425, 56623220, 58720318, 42, 70, 112, 385,
+    4224, 1146881, 4390916, 7340039, 11337738, 16777265, 23068694, 30408732, 33554487, 35127328, 46137388,
+    50331686, 50335794, 56623159, 57147444, 38, 41, 140, 194, 200, 386, 4352, 2195458, 25165865, 25167897,
+    28327962, 29360149, 29360159, 33554659, 41943099, 50331667, 50331730, 57671732, 58720298, 67, 88, 208, 280,
+    576, 769, 2064, 4104, 8196, 16386, 32769, 1097729, 3145735, 23068691, 27262995, 28311610, 33554443, 33554530,
+    33570851, 37224480, 40370213, 41943051, 46137382, 46137903, 46235695, 47710255, 48234537, 48234540, 50331664,
+    54525990, 56623284, 61866040, 69, 84, 134, 224, 560, 5120, 8320, 3145728, 3538946, 4194304, 6291470,
+    11534347, 16777297, 17039377, 20316178, 31457311, 33554529, 33554851, 34078754, 45088810, 46137381, 47185962,
+    50339890, 53870643, 54526014, 56623153, 61341752, 37, 76, 196, 268, 400, 772, 1120, 1537, 8448, 2097155,
+    7077892, 12582940, 15204366, 17301521, 18612240, 22544405, 23592981, 25165837, 25169945, 26935320, 34127907,
+    34603042, 46137399, 46333999, 47235118, 64749631, 81, 131, 176, 416, 536, 770, 2240, 4112, 8200, 8704, 16388,
+    32770, 65537, 1769473, 3145739, 4194309, 5668869, 14155784, 14155805, 17563667, 22741012, 25165835, 25165880,
+    27263007, 28311642, 28573722, 33554439, 33554594, 33555235, 33587235, 35127334, 35651617, 46138415, 50331890,
+    56098871, 56623412, 63799358, 65798204, 82, 133, 138, 168, 388, 448, 1072, 3073, 4480, 1048579, 6291478,
+    8388617, 9306120, 14163981, 16777361, 24117270, 25165873, 28835866, 29360141, 33554535, 33554593, 34078753,
+    34103331, 42074155, 42336298, 45350953, 47185964, 50331674, 50331763, 50348082, 50593843, 56623160, 57671735,
+    58720282, 60293179, 137, 152, 800, 1538, 1544, 2144, 8960, 10240, 16640, 6291456, 12582956, 23592982,
+    25165945, 25174041, 25296920, 27262987, 28311568, 30933020, 33556003, 39321638, 41943147, 42205227, 42385451,
+    46137403, 48234533, 50331760, 50332082, 51740723, 53739569, 54525974, 61866043, 262, 352, 832, 1152, 4128,
+    4288, 6145, 8208, 16392, 16896, 17920, 32772, 65538, 131073, 3145747, 3538945, 4194310, 4653060, 5636100,
+    7602183, 10158089, 12648460, 14155821, 17563669, 25165912, 28311571, 28311580, 28311706, 30670876, 33554547,
+    33554722, 33620003, 35127338, 37748775, 46139439, 47185958, 49283116, 50331746, 51380275, 56623668, 56672308,
+    57409588, 74, 161, 261, 276, 336, 392, 896, 3074, 8576, 17408, 35840, 1048581, 6291494, 6324230, 7077890,
+    8388608, 8388618, 11272200, 16777489, 23592979, 25166041, 33554599, 33557539, 40632365, 42336297, 44826665,
+    50331670, 50331827, 50332466, 50364466, 50593840, 50618418, 52428848, 56623136, 56623166, 57671729, 60489786,
+    62390328, 73, 259, 265, 304, 1540, 1600, 3088, 12289, 17152, 71680, 2097158, 2326530, 2818050, 3162115,
+    12058635, 12582988, 13467660, 14155780, 14155790, 14286861, 16777234, 17563649, 21168149, 22544400, 25165883,
+    25182233, 26214424, 33554563, 33554603, 34439203, 35323939, 41943211, 46137375, 47710250, 50331766, 50331824,
+    54591542, 56623142, 56721460, 58851386, 164, 266, 273, 524, 704, 776, 1664, 6146, 8224, 16400, 20480, 32776,
+    33280, 34304, 65540, 131074, 143360, 262145, 3145763, 5242885, 7077895, 10485770, 11370506, 11796491,
+    12582912, 13107212, 14155853, 14417933, 17563673, 19660819, 20971540, 25165976, 25166233, 28311583, 28311834,
+    33554721, 33554978, 33560611, 33685539, 34078759, 34340898, 35127346, 36388897, 36700193, 37355552, 42336291,
+    45088800, 45350954, 46137351, 46137406, 46141487, 50333234, 50606130, 54657078, 56624180, 58720378, 61603896,
+    162, 552, 672, 1792, 3076, 24577, 33792, 68608, 286720, 1048585, 1163265, 1409025, 6291526, 6553606, 8388620,
+    13631500, 14155777, 15466510, 16777745, 17170449, 23068679, 23617559, 23855125, 25165897, 25165969, 28311554,
+    33554727, 35127298, 35135522, 36175905, 40632373, 40636453, 46137355, 46137358, 46137423, 50331955, 50397234,
+    54526070, 56623108, 56623148, 59244602, 64487486, 321, 515, 521, 608, 3200, 6176, 12290, 34816, 137216,
+    573440, 1572867, 2097162, 3276803, 6291461, 6815750, 12583052, 15335438, 16777236, 20971537, 22675477,
+    23068703, 24641558, 25165915, 25166617, 25198617, 28311563, 29360189, 33554468, 33554539, 33554731, 33566755,
+    40632325, 41943339, 44040235, 46137357, 46137451, 47710252, 50331830, 50334770, 54722610, 54722615, 56623126,
+    56623141, 148, 274, 322, 522, 529, 784, 1048, 1408, 2304, 3328, 6148, 8256, 16416, 32784, 49153, 65544,
+    131076, 262146, 274432, 524289, 1146880, 3145795, 3407875, 4194316, 7340038, 14155917, 17567761, 18350097,
+    18677776, 25165917, 25166104, 25296913, 25296923, 25309209, 27263000, 27263035, 27295771, 28311560, 28311574,
+    28312090, 28336154, 28704794, 29425693, 32899102, 33554739, 33554977, 33555490, 33816611, 34078763, 34340897,
+    37093408, 41943080, 42336303, 45088812, 46137405, 46145583, 50331794, 50331834, 50331938, 50593846, 53870645,
+    55574582, 56229943, 56623165, 56625204, 58720442, 62390331, 63701054, 65929276, 518, 545, 1104, 1344, 3080,
+    3584, 24578, 40960, 66560, 548864, 1048593, 3670019, 6291590, 12582922, 16777216, 16778257, 22544406,
+    23855126, 25165824, 25165885, 25165905, 25166097, 25167385, 27328539, 27361305, 31195164, 33579043, 35192866,
+    39583782, 40632355, 44138537, 45482025, 46202923, 46202926, 47710246, 50331952, 50332211, 50337842, 50462770,
+    50724915, 51904563, 53477424, 54526000, 54526134, 60424251, 61866033, 145, 328, 517, 532, 546, 1027, 1216,
+    1552, 6400, 12292, 12352, 67584, 98305, 1097728, 1572869, 2097170, 3145734, 6733830, 11272203, 12582921,
+    12583180, 14155787, 14680076, 16777225, 16777239, 16777240, 25165979, 25231385, 25303065, 28360730, 29360221,
+    29622301, 33554787, 33554947, 33554987, 35127329, 35258402, 36700194, 38633511, 39452710, 39845927, 40697893,
+    41943074, 41943079, 41943595, 42139691, 43384874, 44040232, 46137515, 46137583, 48234557, 50331958, 50593826,
+    50774066, 51216434, 51642419, 53870625, 54526003, 54722612, 54747190, 59424826, 15, 641, 6152, 6656, 49154,
+    69632, 131080, 4194324, 11534346, 14156045, 17596433, 25168921, 25296925, 25362456, 27263067, 33556514,
+    35389474, 41943073, 50331701, 50331770, 50332194, 50343986, 50593850, 60817466 };
+
+static int cbest_27[1023] = {
+    1, 2, 67108883, 4, 100663322, 8, 50331661, 16, 32, 92274709, 64, 128, 113246233, 256, 512, 67108882,
+    33554441, 3, 1024, 67108881, 123731999, 6, 100663323, 5, 2048, 83886103, 12, 50331660, 100663320, 9, 24,
+    4096, 25165830, 67108887, 109051928, 10, 117440542, 48, 12582915, 50331657, 17, 8192, 54525964, 67108891,
+    100663314, 128974876, 18, 96, 67108867, 92274711, 100663326, 20, 50331663, 73400338, 92274708, 113246232, 33,
+    192, 16384, 27262982, 58720271, 34, 50331653, 92274705, 36, 384, 36700169, 46137354, 100663306, 40, 65,
+    32768, 13631491, 56623116, 67108915, 66, 768, 96469012, 113246235, 68, 23068677, 64487438, 72, 129, 1536,
+    65536, 67108947, 80, 4194305, 28311558, 73924626, 100663354, 132, 3072, 8388610, 48234506, 50331677,
+    85458967, 123731998, 130, 136, 257, 131072, 16777220, 67109011, 69206035, 78643217, 144, 6144, 33554440,
+    92274717, 100663386, 160, 14155779, 36962313, 50331693, 92274693, 258, 264, 513, 12288, 262144, 24117253,
+    67109139, 101711898, 113246225, 272, 6291457, 12582914, 32243719, 100663450, 109838360, 113246237, 288,
+    24576, 50331725, 67108880, 260, 320, 514, 1025, 524288, 50855949, 61865999, 67109395, 528, 49152, 25165828,
+    70254611, 74186770, 83886102, 92274741, 100663578, 106430491, 123731995, 7, 544, 33554443, 50331789,
+    79167505, 113246217, 123731997, 516, 576, 1026, 2049, 98304, 1048576, 12582913, 41943051, 54525965, 54919180,
+    67108885, 67109907, 73400339, 83886099, 85590039, 100663321, 109051930, 13, 640, 33554433, 50331656,
+    67108886, 83886101, 92274773, 92536853, 100663834, 109051929, 14, 26, 1056, 196608, 13631490, 33554445,
+    50331649, 50331917, 83230736, 102236186, 117440543, 25, 52, 520, 1028, 1088, 2050, 4097, 2097152, 6815745,
+    25165826, 25165831, 37093385, 67110931, 88080406, 92274707, 98041876, 123731991, 128974878, 11, 104, 1152,
+    393216, 23068676, 27262980, 50331659, 50331662, 58720269, 67108875, 67108890, 67108895, 79691792, 92274837,
+    94371861, 100663298, 100663315, 100663318, 100663324, 100664346, 103809050, 113246265, 117440538, 128974877,
+    22, 28, 49, 208, 1280, 11534338, 27459590, 39845896, 46137355, 50332173, 58720270, 67108866, 67108889,
+    92274710, 96469013, 100663312, 100663327, 113246234, 117440540, 44, 416, 1032, 2052, 2112, 4098, 8193,
+    786432, 4194304, 5767169, 19922948, 44040203, 46137352, 50331652, 51118093, 54525960, 56623117, 67108865,
+    67108899, 67112979, 109903896, 113377305, 120324126, 125829148, 128974872, 19, 88, 97, 832, 2176, 9961474,
+    13631489, 36700168, 70516755, 92274965, 100665370, 106692635, 113246297, 121634847, 21, 38, 50, 56, 176,
+    1664, 2304, 1572864, 4980737, 18350084, 29360135, 33554457, 50332685, 51904525, 64487439, 73924627, 92274704,
+    109051920, 123731983, 76, 193, 352, 1040, 2056, 2560, 3328, 4100, 8194, 16385, 9175042, 27262978, 27262983,
+    41615368, 49020938, 54525966, 58720267, 64487436, 67108871, 67117075, 73400336, 83886111, 90177558,
+    100663307, 109051932, 114294809, 117440534, 35, 98, 152, 194, 704, 4224, 6656, 3145728, 4587521, 13729795,
+    14155778, 50331669, 62914574, 67108914, 67108979, 69992467, 81788944, 83886087, 89128982, 92275221, 96469014,
+    100663304, 100663338, 100667418, 113246361, 115343385, 37, 42, 70, 112, 304, 385, 1408, 4352, 13312,
+    12582919, 24117252, 28311556, 33554473, 48234507, 50331655, 50333709, 54525956, 67108913, 80740368, 85655575,
+    92274713, 92667925, 95420437, 128974868, 41, 140, 608, 2064, 2816, 4104, 4608, 8196, 16386, 26624, 32769,
+    6291456, 7077889, 8388608, 25165838, 32243718, 40894472, 48234504, 54951948, 56623112, 67109075, 67125267,
+    69599251, 102367258, 127926300, 67, 100, 280, 388, 769, 1216, 5120, 5632, 53248, 12058626, 40370184,
+    45088779, 50331673, 50331676, 67108946, 92275733, 93061141, 96469008, 100663310, 100671514, 104071194,
+    109051912, 113246224, 113246489, 123732031, 131596317, 69, 74, 84, 224, 386, 560, 2432, 8448, 11264, 106496,
+    12582923, 20447236, 23068673, 31457287, 33554505, 36700171, 44564491, 50335757, 58720263, 60162063, 64487434,
+    67108919, 67108945, 67109267, 69402643, 73400342, 92274719, 100663355, 100663418, 113246236, 117440526,
+    123797535, 73, 196, 1120, 1537, 2080, 4112, 4864, 8200, 8704, 16388, 22528, 32770, 65537, 212992, 6029313,
+    14155777, 20185092, 24510469, 25165846, 56623118, 67108923, 67141651, 78643219, 83886135, 85458966, 92274695,
+    99352596, 100663346, 100663352, 102105114, 113246239, 81, 134, 770, 776, 2240, 9216, 9728, 45056, 425984,
+    10223618, 20807684, 28311554, 28311559, 34603017, 36700161, 36962312, 46137346, 50331689, 50331692, 50331709,
+    67109010, 67109651, 69206034, 73973778, 78643216, 91226134, 92274689, 92276757, 100663514, 100679706,
+    113246227, 113246745, 120455198, 123732063, 128974860, 133, 148, 168, 448, 3073, 4480, 10240, 19456, 90112,
+    851968, 8388611, 10092546, 12582912, 12582931, 23068679, 32243717, 33554569, 35651593, 36700173, 46137358,
+    50339853, 51183629, 56623108, 63963150, 67108931, 67108951, 70647827, 71303186, 73400346, 73924624, 74186771,
+    82837520, 85458963, 92274701, 92274716, 100663387, 101908506, 106430490, 113442841, 114819097, 123731994,
+    124256287, 131, 137, 200, 1538, 4128, 8208, 8960, 16392, 16896, 32772, 38912, 65538, 131073, 180224, 1703936,
+    5111809, 13631495, 16121859, 16777216, 16777221, 18481156, 25165862, 27262990, 27475974, 39321608, 50331679,
+    50331757, 52035597, 54525980, 67108955, 67110419, 67174419, 73400322, 75497489, 83886167, 85458965, 89653270,
+    92274692, 100663358, 100663378, 100663384, 100663706, 109051960, 109936664, 113246216, 123731996, 124780575,
+    82, 138, 145, 268, 772, 1552, 6145, 17408, 17920, 77824, 360448, 3407872, 4194307, 5046273, 42729483,
+    50331685, 50331721, 50331724, 61865997, 64487430, 67109009, 67109138, 69206033, 81264656, 84410391, 89391126,
+    92274725, 92278805, 100696090, 101711899, 101810202, 109838362, 113246209, 113246229, 113247257, 113639449,
+    117440574, 123732127, 146, 161, 296, 336, 392, 896, 3074, 18432, 35840, 155648, 720896, 6815744, 9240578,
+    12582947, 19660804, 33554697, 41418760, 50331853, 50348045, 50855948, 51052557, 61865998, 67108995, 67109015,
+    67111955, 70123539, 84934679, 92274743, 100663451, 100664090, 109838361, 162, 259, 265, 1540, 4160, 8224,
+    12289, 16400, 20480, 32776, 65540, 71680, 131074, 262145, 311296, 1441792, 13631499, 16777222, 24117249,
+    25165824, 25165894, 25427974, 27262998, 45613067, 50331695, 54525996, 54919181, 58720287, 67109019, 67239955,
+    83230737, 83886231, 92274737, 97189908, 100663370, 100663390, 100663442, 104857627, 109051992, 109314072,
+    113246219, 128974908, 129007644, 266, 273, 536, 3104, 6146, 33792, 143360, 622592, 2883584, 4194309, 4620289,
+    9830402, 12713987, 31981575, 32243715, 33554442, 36986889, 40632328, 41943049, 48234498, 49676298, 50331717,
+    50331785, 50331788, 50332045, 50954253, 53215245, 67109137, 67109394, 67115027, 73924630, 79364113, 88080407,
+    92282901, 96469020, 98041877, 100664858, 100728858, 101711896, 109576216, 113248281, 117440606, 123731987,
+    123731990, 123731993, 123732255, 262, 274, 289, 400, 592, 672, 1792, 3076, 24577, 34816, 286720, 1245184,
+    5767168, 8388614, 10403842, 12582979, 20709380, 20971525, 23068685, 33554953, 36700185, 36962315, 41943050,
+    44826635, 46137370, 48234510, 50364429, 54657036, 67109043, 67109123, 69664787, 70254610, 73400370, 79167507,
+    79691793, 92274740, 92274775, 92274805, 92700693, 96468996, 100663448, 100663579, 102432794, 104202266,
+    113246264, 117964830, 132907037, 261, 276, 290, 321, 515, 1544, 8256, 12290, 16416, 32784, 36864, 65544,
+    131076, 262146, 524289, 573440, 2490368, 4915201, 13631488, 13631507, 13737987, 24117255, 25165958, 27263014,
+    33554432, 35127305, 44695563, 50331727, 50332429, 50855945, 50905101, 54526028, 54788108, 56623132, 58720303,
+    61865995, 67109147, 67121171, 67371027, 69206039, 69632019, 73465874, 77594641, 78643221, 79167504, 83886097,
+    83886359, 88473622, 92274769, 93126677, 100663434, 100663454, 100663570, 100666394, 109052056, 111149080,
+    128974940, 129237020, 292, 322, 529, 784, 1072, 6148, 6208, 40960, 49153, 1146880, 4194313, 4980736, 6291459,
+    20316164, 25165829, 27328518, 28311566, 29360134, 30932999, 33554444, 36962305, 50331648, 50331781, 50331916,
+    54968332, 60227599, 67108884, 67109393, 67109906, 73924634, 75169810, 83886098, 85590038, 92274901, 92291093,
+    92536855, 100794394, 109051931, 113246249, 113250329, 113377304, 117440670, 119537694, 123732511, 129499164,
+    164, 324, 518, 530, 545, 1184, 1344, 3080, 3584, 24578, 67584, 2293760, 8388618, 10354690, 12583043,
+    14155783, 14680067, 23068693, 27394054, 33554437, 33555465, 36700201, 36732937, 36962317, 37093384, 39845897,
+    46137386, 50333197, 50397197, 55574540, 64487454, 67109171, 67109379, 67133459, 70254609, 73400402, 73924610,
+    74186768, 83099664, 83230738, 83886100, 85458975, 92274772, 92536852, 92635157, 100663576, 100663835,
+    100669466, 101711890, 102170650, 106430489, 106692634, 113246267, 113246296, 121634846, 123830303, 124518431,
+    128974874, 517, 532, 16448, 69632, 524290, 1048577, 4587520, 27262976, 46137353, 50331658, 50331741,
+    54525961, 56623148, 58720268, 58982415, 67109143, 67109203, 67633171, 78643225, 100663482, 102236187,
+    106954779, 123731982 };
+
+static int cbest_28[1023] = {
+    1, 2, 134217732, 4, 67108866, 8, 33554433, 16, 32, 150994948, 64, 128, 75497474, 256, 512, 37748737, 1024,
+    2048, 4096, 153092100, 8192, 16384, 32768, 76546050, 65536, 131072, 262144, 38273025, 524288, 1048576,
+    2097152, 4194304, 153354244, 8388608, 16777216, 33554432, 76677122, 67108864, 3, 134217728, 134217733, 5,
+    38338561, 67108867, 134217734, 6, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728,
+    147456, 294912, 589824, 1179648, 2359296, 4718592, 9437184, 18874368, 37748736, 201326598, 10, 17, 33554435,
+    67108870, 75497472, 134217740, 167772165, 12, 33, 33554437, 67108874, 100663299, 134217748, 150994944,
+    150994949, 20, 34, 65, 33554441, 67108882, 134217764, 150994950, 24, 66, 129, 33554449, 67108898, 75497475,
+    134217796, 153387012, 218103814, 40, 68, 130, 257, 33554465, 67108930, 134217860, 150994956, 184549381,
+    209715206, 48, 132, 258, 513, 33554497, 67108994, 75497478, 134217988, 150994964, 80, 136, 260, 514, 1025,
+    33554561, 37748739, 67109122, 75497482, 109051907, 134218244, 150994980, 171966469, 96, 264, 516, 1026, 2049,
+    33554689, 37748741, 67109378, 75497490, 104857603, 134218756, 150995012, 160, 272, 520, 1028, 2050, 4097,
+    33554945, 37748745, 38273024, 67109890, 75497506, 76546048, 76693506, 134219780, 150995076, 153092096,
+    153092101, 226492422, 192, 528, 1032, 2052, 4098, 8193, 19136512, 33555457, 37748753, 67110914, 75497538,
+    134221828, 150995204, 153092102, 320, 544, 1040, 2056, 4100, 8194, 16385, 9568256, 33556481, 37748769,
+    67112962, 75497602, 134225924, 150995460, 188743685, 220200966, 384, 1056, 2064, 4104, 8196, 16386, 32769,
+    4784128, 33558529, 37748801, 67117058, 75497730, 76546051, 134234116, 150995972, 153092108, 186646533, 640,
+    1088, 2080, 4112, 8200, 16388, 32770, 65537, 2392064, 33562625, 37748865, 67125250, 75497986, 113246211,
+    134250500, 150996996, 153092116, 210763782, 768, 2112, 4128, 8208, 16392, 32772, 65538, 131073, 1196032,
+    33570817, 37748993, 38346753, 67141634, 75498498, 76546054, 134283268, 150999044, 153092132, 1280, 2176,
+    4160, 8224, 16400, 32776, 65540, 131074, 262145, 598016, 33587201, 37749249, 67174402, 75499522, 76546058,
+    110100483, 134348804, 151003140, 153092164, 1536, 4224, 8256, 16416, 32784, 65544, 131076, 262146, 299008,
+    524289, 33619969, 37749761, 38273027, 67239938, 75501570, 76546066, 134479876, 151011332, 153092228,
+    172490757, 228589574, 2560, 4352, 8320, 16448, 32800, 65552, 131080, 149504, 262148, 524290, 1048577,
+    33685505, 37750785, 38273029, 67371010, 75505666, 76546082, 105381891, 134742020, 151027716, 153092356,
+    227540998, 3072, 8448, 16512, 32832, 65568, 74752, 131088, 262152, 524292, 1048578, 2097153, 33816577,
+    37752833, 38273033, 67633154, 75513858, 76546114, 135266308, 151060484, 153092612, 190840837, 5120, 8704,
+    16640, 32896, 37376, 65600, 131104, 262160, 524296, 1048580, 2097154, 4194305, 34078721, 37756929, 38273041,
+    68157442, 75530242, 76546178, 136314884, 151126020, 153093124, 153354240, 153354245, 6144, 16896, 18688,
+    33024, 65664, 131136, 262176, 524304, 1048584, 2097156, 4194306, 8388609, 34603009, 37765121, 38273057,
+    69206018, 75563010, 76546306, 76677120, 138412036, 151257092, 153094148, 153354246, 153391108, 189267973,
+    9344, 10240, 17408, 33280, 65792, 131200, 262208, 524320, 1048592, 2097160, 4194308, 8388610, 16777217,
+    35651585, 37781505, 38273089, 38338560, 71303170, 75628546, 76546562, 114294787, 142606340, 151519236,
+    153096196, 220463110, 4672, 12288, 33792, 66048, 131328, 262272, 524352, 1048608, 2097168, 4194312, 8388612,
+    16777218, 37814273, 38273153, 75759618, 76547074, 113770499, 152043524, 153100292, 153354252, 186908677,
+    2336, 20480, 34816, 66560, 131584, 262400, 524416, 1048640, 2097184, 4194320, 8388616, 16777220, 19169280,
+    33554434, 37879809, 38273281, 41943041, 76021762, 76548098, 76677123, 83886082, 153108484, 153354260,
+    167772164, 1168, 24576, 67584, 132096, 262656, 524544, 1048704, 2097216, 4194336, 8388624, 16777224,
+    33554436, 38010881, 38273537, 50331649, 67108865, 76550146, 100663298, 153124868, 153354276, 155189252,
+    210894854, 229638150, 584, 40960, 69632, 133120, 263168, 524800, 1048832, 2097280, 4194368, 8388640, 9584640,
+    16777232, 33554440, 38274049, 76554242, 76677126, 77594626, 153157636, 153354308, 159383556, 201326596, 292,
+    49152, 135168, 264192, 525312, 1049088, 2097408, 4194432, 8388672, 16777248, 33554448, 38275073, 38797313,
+    67108868, 67108880, 76562434, 76677130, 76695554, 79691778, 110231555, 134217729, 153223172, 153354372,
+    228851718, 146, 81920, 139264, 266240, 526336, 1049600, 2097664, 4194560, 4792320, 8388736, 16777280,
+    33554464, 38277121, 39845889, 67108872, 76578818, 76677138, 100663297, 134217730, 134217735, 134217760,
+    153354500, 184549380, 191365125, 7, 19, 37, 73, 145, 289, 577, 1153, 2305, 4609, 9217, 18433, 36865, 73729,
+    98304, 147457, 270336, 294913, 528384, 589825, 1050624, 1179649, 2098176, 2359297, 4194816, 4718593, 8388864,
+    9437185, 16777344, 18874369, 33554496, 38281217, 38338563, 76611586, 76677154, 92274690, 153354756,
+    153616388, 172556293, 191102981, 201326594, 201326599, 227672070, 11, 38, 74, 290, 578, 1154, 2306, 4610,
+    9218, 18434, 36866, 73730, 147458, 163840, 278528, 294914, 532480, 589826, 1052672, 1179650, 2099200,
+    2359298, 2396160, 4195328, 4718594, 8389120, 9437186, 16777472, 18874370, 33554560, 37748738, 38289409,
+    38338565, 46137345, 67108871, 67108896, 75497473, 76677186, 105447427, 109051906, 134217736, 134217741,
+    134217750, 134217804, 134217876, 134218020, 134218308, 134218884, 134220036, 134222340, 134226948, 134236164,
+    134254596, 134291460, 134365188, 134512644, 134807556, 135397380, 136577028, 138936324, 143654916, 153355268,
+    154140676, 167772161, 171966468, 218103812, 13, 22, 76, 148, 580, 1156, 2308, 4612, 9220, 18436, 36868,
+    73732, 147460, 196608, 294916, 540672, 589828, 1056768, 1179652, 2101248, 2359300, 4196352, 4718596, 8389632,
+    9437188, 16777728, 18874372, 33554688, 37748740, 38305793, 38338569, 54525953, 67108875, 67108902, 67108928,
+    67108938, 67109010, 67109154, 67109442, 67110018, 67111170, 67113474, 67118082, 67127298, 67145730, 67182594,
+    67256322, 67403778, 67698690, 68288514, 69468162, 71827458, 76677250, 76808194, 85983234, 104857602,
+    114819075, 134217742, 134217744, 134217749, 150994945, 153356292, 167772167, 209715204, 14, 21, 26, 35, 44,
+    152, 296, 1160, 2312, 4616, 9224, 18440, 36872, 73736, 147464, 294920, 327680, 557056, 589832, 1064960,
+    1179656, 1198080, 2105344, 2359304, 4198400, 4718600, 8390656, 9437192, 16778240, 18874376, 33554439,
+    33554451, 33554469, 33554505, 33554577, 33554721, 33554944, 33555009, 33555585, 33556737, 33559041, 33563649,
+    33572865, 33591297, 33628161, 33701889, 33849345, 34144257, 34734081, 35913729, 37748744, 38338577, 42991617,
+    52428801, 67108883, 67108992, 75497476, 75497488, 76677378, 77070338, 134217765, 150994946, 150994951,
+    150994976, 153358340, 157286404, 201326606, 234881031, 25, 52, 67, 88, 304, 592, 2320, 4624, 9232, 18448,
+    36880, 73744, 147472, 294928, 393216, 589840, 1081344, 1179664, 2113536, 2359312, 4202496, 4718608, 8392704,
+    9437200, 16779264, 18874384, 33554443, 33555456, 37748752, 38338593, 38347777, 38404097, 67108878, 67108899,
+    67109120, 75497480, 76677634, 100663303, 109051905, 114425859, 134217766, 134217792, 134217797, 153362436,
+    153387008, 153387013, 161480708, 167772173, 189333509, 201326614, 218103810, 218103815, 41, 50, 69, 104, 131,
+    176, 608, 1184, 4640, 9248, 18464, 36896, 73760, 147488, 294944, 589856, 599040, 655360, 1114112, 1179680,
+    2129920, 2359328, 4210688, 4718624, 8396800, 9437216, 16781312, 18874400, 33554445, 33556480, 37748768,
+    38338625, 38535169, 67108886, 67108931, 67109376, 76678146, 78643202, 100663307, 104857601, 134217756,
+    134217798, 134217856, 134217861, 150994952, 150994957, 150994966, 150995020, 150995092, 150995236, 150995524,
+    150996100, 150997252, 150999556, 151004164, 151013380, 151031812, 151068676, 151142404, 151289860, 151584772,
+    152174596, 153370628, 153387014, 155713540, 160432132, 167772181, 184549377, 188743684, 201326630, 209715202,
+    209715207, 28, 42, 49, 70, 82, 100, 133, 208, 259, 352, 1216, 2368, 9280, 18496, 36928, 73792, 147520,
+    294976, 589888, 786432, 1179712, 2162688, 2359360, 4227072, 4718656, 8404992, 9437248, 16785408, 18874432,
+    33554453, 33554467, 33558528, 37748800, 38338689, 67108890, 67108995, 67109888, 75497479, 75497504, 76679170,
+    76693504, 80740354, 100663315, 113836035, 134217772, 134217862, 134217984, 134217989, 150994958, 150994960,
+    150994965, 167772197, 184549383, 186646532, 201326662, 220495878, 226492420, 229900294, 81, 134, 137, 164,
+    200, 261, 416, 515, 704, 4736, 36992, 73856, 147584, 295040, 299520, 1179776, 2228224, 2359424, 8421376,
+    9437312, 18874496, 33554457, 33554499, 33562624, 37748864, 67108906, 67108934, 67109123, 67110912, 75497483,
+    75497510, 75497536, 75497546, 75497762, 75498050, 75499778, 75502082, 75506690, 75515906, 75534338, 75571202,
+    75644930, 75792386, 76087298, 76681218, 77856770, 80216066, 94371842, 100663331, 113246210, 134217780,
+    134217990, 134218240, 150994981, 153419780, 167772229, 171966465, 201326726, 218103822, 229769222, 251658247 };
+
+static int cbest_29[1023] = {
+    1, 2, 268435458, 4, 134217729, 8, 16, 335544322, 32, 64, 167772161, 128, 256, 512, 352321538, 1024, 2048,
+    4096, 176160769, 8192, 16384, 32768, 65536, 356515842, 131072, 262144, 524288, 1048576, 178257921, 2097152,
+    4194304, 8388608, 16777216, 33554432, 357564418, 67108864, 134217728, 268435456, 3, 178782209, 268435459, 5,
+    10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720,
+    2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 6, 9, 134217731, 268435462, 335544320,
+    402653187, 17, 134217733, 268435466, 335544323, 12, 18, 33, 134217737, 268435474, 34, 65, 134217745,
+    268435490, 335544326, 469762051, 24, 36, 66, 129, 134217761, 167772163, 268435522, 335544330, 357826562,
+    436207619, 68, 130, 257, 134217793, 167772165, 176160768, 268435586, 335544338, 352321536, 48, 72, 132, 258,
+    513, 88080384, 134217857, 167772169, 268435714, 335544354, 352321539, 136, 260, 514, 1025, 44040192,
+    134217985, 167772177, 268435970, 335544386, 503316483, 96, 144, 264, 516, 1026, 2049, 22020096, 134218241,
+    167772193, 268436482, 335544450, 352321542, 486539267, 272, 520, 1028, 2050, 4097, 11010048, 134218753,
+    167772225, 268437506, 335544578, 352321546, 192, 288, 528, 1032, 2052, 4098, 8193, 5505024, 134219777,
+    167772289, 176160771, 178913281, 268439554, 335544834, 352321554, 444596227, 544, 1040, 2056, 4100, 8194,
+    16385, 2752512, 134221825, 167772417, 176160773, 268443650, 335545346, 352321570, 384, 576, 1056, 2064, 4104,
+    8196, 16386, 32769, 1376256, 134225921, 167772673, 176160777, 268451842, 335546370, 352321602, 356515840,
+    520093699, 1088, 2080, 4112, 8200, 16388, 32770, 65537, 688128, 134234113, 167773185, 176160785, 178257920,
+    268468226, 335548418, 352321666, 356515843, 511705091, 768, 1152, 2112, 4128, 8208, 16392, 32772, 65538,
+    131073, 344064, 134250497, 167774209, 176160801, 268500994, 335552514, 352321794, 2176, 4160, 8224, 16400,
+    32776, 65540, 131074, 172032, 262145, 89128960, 134283265, 167776257, 176160833, 268566530, 335560706,
+    352322050, 356515846, 490733571, 1536, 2304, 4224, 8256, 16416, 32784, 65544, 86016, 131076, 262146, 524289,
+    134348801, 167780353, 176160897, 268697602, 335577090, 352322562, 356515850, 4352, 8320, 16448, 32800, 43008,
+    65552, 131080, 262148, 524290, 1048577, 44564480, 134479873, 167788545, 176161025, 268959746, 335609858,
+    352323586, 356515858, 357892098, 3072, 4608, 8448, 16512, 21504, 32832, 65568, 131088, 262152, 524292,
+    1048578, 2097153, 134742017, 167804929, 176161281, 178257923, 269484034, 335675394, 352325634, 356515874,
+    446693379, 528482307, 8704, 10752, 16640, 32896, 65600, 131104, 262160, 524296, 1048580, 2097154, 4194305,
+    22282240, 135266305, 167837697, 176161793, 178257925, 270532610, 335806466, 352329730, 356515906, 524288003,
+    5376, 6144, 9216, 16896, 33024, 65664, 131136, 262176, 524304, 1048584, 2097156, 4194306, 8388609, 136314881,
+    167903233, 176162817, 178257929, 272629762, 336068610, 352337922, 356515970, 2688, 17408, 33280, 65792,
+    131200, 262208, 524320, 1048592, 2097160, 4194308, 8388610, 11141120, 16777217, 138412033, 168034305,
+    176164865, 178257937, 276824066, 336592898, 352354306, 356516098, 357564416, 513802243, 1344, 12288, 18432,
+    33792, 66048, 131328, 262272, 524352, 1048608, 2097168, 4194312, 8388612, 16777218, 33554433, 142606337,
+    168296449, 176168961, 178257953, 285212674, 337641474, 352387074, 356516354, 357564419, 672, 34816, 66560,
+    131584, 262400, 524416, 1048640, 2097184, 4194320, 5570560, 8388616, 16777220, 33554434, 67108865, 150994945,
+    168820737, 176177153, 178257985, 178782208, 301989890, 339738626, 352452610, 356516866, 336, 24576, 36864,
+    67584, 132096, 262656, 524544, 1048704, 2097216, 4194336, 8388624, 16777224, 33554436, 67108866, 169869313,
+    176193537, 178258049, 178946049, 343932930, 352583682, 356517890, 357564422, 491782147, 168, 69632, 133120,
+    263168, 524800, 1048832, 2097280, 2785280, 4194368, 8388640, 16777232, 33554440, 67108868, 134217730,
+    171966465, 176226305, 178258177, 201326593, 352845826, 356519938, 357564426, 402653186, 532676611, 84, 49152,
+    73728, 135168, 264192, 525312, 1049088, 2097408, 4194432, 8388672, 16777248, 33554448, 67108872, 89391104,
+    134217732, 176291841, 178258433, 268435457, 353370114, 356524034, 357564434, 369098754, 530579459, 42,
+    139264, 266240, 526336, 1049600, 1392640, 2097664, 4194560, 8388736, 16777280, 33554464, 67108880, 134217736,
+    176422913, 178258945, 184549377, 268435464, 354418690, 356532226, 357564450, 11, 21, 41, 81, 161, 321, 641,
+    1281, 2561, 5121, 10241, 20481, 40961, 81921, 98304, 147456, 163841, 270336, 327681, 528384, 655361, 1050624,
+    1310721, 2098176, 2621441, 4194816, 5242881, 8388864, 10485761, 16777344, 20971521, 33554496, 41943041,
+    67108896, 83886081, 134217744, 176685057, 178259969, 178782211, 268435460, 356548610, 357564482, 402653185,
+    447217667, 469762050, 525336579, 7, 22, 82, 162, 322, 642, 1282, 2562, 5122, 10242, 20482, 40962, 81922,
+    163842, 278528, 327682, 532480, 655362, 696320, 1052672, 1310722, 2099200, 2621442, 4195328, 5242882,
+    8389120, 10485762, 16777472, 20971522, 33554560, 41943042, 44695552, 67108928, 83886082, 134217760,
+    167772162, 177209345, 178262017, 178782213, 234881025, 268435463, 268435478, 268435498, 268435538, 268435618,
+    268435778, 268436098, 268436738, 268438018, 268440578, 268445698, 268455938, 268476418, 268517378, 268599298,
+    268763138, 269090818, 269746178, 271056898, 273678338, 278921218, 289406978, 310378498, 335544321, 356581378,
+    357564546, 360710146, 436207618, 14, 44, 164, 324, 644, 1284, 2564, 5124, 10244, 20484, 40964, 81924, 163844,
+    196608, 294912, 327684, 540672, 655364, 1056768, 1310724, 2101248, 2621444, 4196352, 5242884, 8389632,
+    10485764, 16777728, 20971524, 33554688, 41943044, 67108992, 83886084, 134217739, 134217749, 134217769,
+    134217792, 134217809, 134217889, 134218049, 134218369, 134219009, 134220289, 134222849, 134227969, 134238209,
+    134258689, 134299649, 134381569, 134545409, 134873089, 135528449, 136839169, 139460609, 144703489, 155189249,
+    167772164, 178266113, 178782217, 218103809, 268435467, 268435472, 335544328, 356646914, 357564674, 13, 19,
+    28, 88, 328, 648, 1288, 2568, 5128, 10248, 20488, 40968, 81928, 163848, 327688, 348160, 557056, 655368,
+    1064960, 1310728, 2105344, 2621448, 4198400, 5242888, 8390656, 10485768, 16778240, 20971528, 33554944,
+    41943048, 67109120, 83886088, 134217735, 134217856, 167772168, 178274305, 178782225, 180355073, 268435475,
+    268435488, 335544324, 356777986, 357564930, 385875970, 402653191, 469762049, 514326531, 26, 35, 56, 176, 656,
+    1296, 2576, 5136, 10256, 20496, 40976, 81936, 163856, 327696, 393216, 589824, 655376, 1081344, 1310736,
+    2113536, 2621456, 4202496, 5242896, 8392704, 10485776, 16779264, 20971536, 22347776, 33555456, 41943056,
+    67109376, 83886096, 134217984, 167772176, 178290689, 178782241, 268435470, 268435491, 268435520, 335544327,
+    335544342, 335544362, 335544402, 335544482, 335544642, 335544962, 335545602, 335546882, 335549442, 335554562,
+    335564802, 335585282, 335626242, 335708162, 335872002, 336199682, 336855042, 338165762, 340787202, 346030082,
+    357040130, 357565442, 357826560, 357908482, 377487362, 402653195, 436207617, 503316482, 25, 37, 52, 67, 112,
+    352, 1312, 2592, 5152, 10272, 20512, 40992, 81952, 163872, 174080, 327712, 655392, 1114112, 1310752, 2129920,
+    2621472, 4210688, 5242912, 8396800, 10485792, 16781312, 20971552, 33556480, 41943072, 67109888, 83886112,
+    134217741, 134217747, 134218240, 167772192, 178323457, 178782273, 192937985, 268435523, 268435584, 335544331,
+    335544336, 357566466, 357826563, 402653203, 486539266, 534773763, 38, 69, 74, 104, 131, 224, 704, 2624, 5184,
+    10304, 20544, 41024, 81984, 163904, 327744, 655424, 786432, 1179648, 1310784, 2162688, 2621504, 4227072,
+    5242944, 8404992, 10485824, 16785408, 20971584, 33558528, 41943104, 67110912, 83886144, 134217763, 134218752,
+    167772171, 167772181, 167772201, 167772224, 167772241, 167772321, 167772481, 167772801, 167773441, 167774721,
+    167777281, 167782401, 167792641, 167813121, 167854081, 167936001, 168099841, 168427521, 169082881, 170393601,
+    173015041, 178388993, 178782337, 188743681, 251658241, 268435482, 268435494, 268435587, 268435712, 335544339,
+    335544352, 352321537, 357568514, 358612994, 402653219, 469762055, 533725187, 49, 70, 73, 133, 138, 148, 208,
+    259, 448, 1408, 5248, 10368, 20608, 41088, 82048, 87040, 163968, 327808, 655488, 1310848, 2228224, 2621568,
+    4259840, 5243008, 8421376, 10485888, 11173888, 16793600, 20971648, 33562624, 41943168, 67112960, 83886208,
+    88080385, 134217753, 134217765, 134217795, 134219776, 167772167, 167772288, 176160770, 178520065, 178782465,
+    178913280, 243269633, 268435526, 268435715, 268435968, 335544334, 335544355, 335544384, 352321544, 357572610,
+    357826566, 402653251, 436207623, 444596226, 469762059, 492044291, 503316481, 50, 134, 137, 261, 266, 296,
+    416, 515, 896, 2816, 20736, 41216, 82176, 164096, 327936, 655616, 1310976, 1572864, 2359296, 2621696,
+    8454144, 10486016, 16809984, 20971776, 33570816, 44040193, 67117056, 83886336, 134217797, 167772416,
+    178782721, 268435506, 268435530, 268435590, 268435971, 268436480, 335544387, 335544448, 352321540, 357826570,
+    364904450, 402653315, 436207627, 469762067, 486539265 };
+
+static int cbest_30[1023] = {
+    1, 2, 541065219, 4, 811597826, 8, 405798913, 16, 32, 64, 743964675, 128, 913047554, 256, 541065218,
+    270532609, 3, 512, 456523777, 541065217, 6, 811597827, 5, 676331523, 12, 129, 405798912, 258, 811597824, 9,
+    24, 516, 1024, 202899456, 541065223, 541065283, 10, 1032, 946864130, 48, 2064, 101449728, 879230978, 17,
+    4128, 541065227, 811597858, 96, 8256, 50724864, 811597830, 20, 16512, 405798915, 18, 33, 192, 2048, 33024,
+    25362432, 405798929, 473432065, 541065235, 769327107, 66048, 439615489, 743964674, 811597834, 132096,
+    12681216, 405798917, 34, 40, 65, 264192, 541065251, 528384, 6340608, 743964673, 811597842, 384, 1056768,
+    405798921, 36, 66, 4096, 2113536, 3170304, 371982337, 743964683, 80, 4227072, 1585152, 8454144, 777781251,
+    68, 130, 768, 16908288, 541065347, 743964679, 760872963, 913047555, 792576, 33816576, 811597890, 917340162,
+    160, 67633152, 405798945, 72, 132, 257, 8192, 396288, 135266304, 913047552, 1536, 270532608, 811597954,
+    913047558, 260, 198144, 405798977, 727056387, 136, 456523776, 541065475, 743964691, 193, 386, 99072, 514,
+    3072, 405799041, 541065216, 929955842, 144, 320, 513, 16384, 49536, 743964707, 921501698, 997588994, 264,
+    520, 772, 541065315, 676331522, 811598082, 7, 24768, 270532611, 456523779, 458670081, 913047562, 385, 6144,
+    228261888, 338165761, 541065221, 541065411, 541065731, 743964739, 811597825, 13, 1028, 1544, 12384,
+    270532641, 541065222, 541065282, 676331521, 14, 259, 270532613, 270532673, 405799169, 541065346, 811597874,
+    904593410, 913047570, 946864131, 25, 272, 517, 770, 1025, 1040, 6192, 202899457, 541065473, 743964803,
+    879230979, 11, 26, 131, 640, 1026, 1033, 3088, 12288, 405798914, 456523781, 541065226, 541065231, 541065281,
+    676331539, 811597828, 811597859, 811597922, 811598338, 28, 49, 528, 2065, 3096, 101449729, 270532617,
+    405798928, 464977921, 473432064, 541065225, 676331555, 710148099, 811597831, 913047586, 946864128, 161, 288,
+    518, 1540, 2056, 4129, 32768, 114130944, 202899458, 202899464, 405798937, 439615488, 460750849, 498794497,
+    541065243, 541065735, 541066243, 676331527, 811597955, 879230976, 22, 52, 97, 133, 1034, 1548, 6176, 8257,
+    50724865, 101449732, 405798916, 456523785, 541065234, 541065299, 541066251, 769327106, 811597856, 811598080,
+    21, 50, 56, 262, 322, 2066, 2080, 16513, 24576, 50724866, 101449730, 236716032, 270532625, 405798961,
+    405799040, 405799425, 541065267, 541067283, 642514947, 811597835, 811597838, 879230986, 913047618, 946864146,
+    1014497282, 19, 774, 2049, 3080, 4130, 33025, 25362433, 202899460, 202899520, 219807744, 541065287,
+    541069347, 676331531, 743964931, 811597832, 811597866, 879230994, 980680706, 44, 98, 104, 137, 644, 1036,
+    8258, 12352, 66049, 101449760, 405798919, 405798920, 456523793, 541065233, 541065250, 541073475, 591790083,
+    769327105, 811597850, 811598342, 811598850, 946864134, 946864194, 112, 266, 387, 2052, 2068, 4112, 16514,
+    132097, 12681217, 50724880, 118358016, 371982336, 405798933, 452296705, 541065239, 541081731, 743964672,
+    811597843, 811598858, 879230982, 896139266, 913047682, 35, 41, 194, 524, 544, 1056, 1280, 2050, 4132, 6160,
+    33026, 264193, 25362434, 25362440, 57065472, 109903872, 405798925, 405798931, 405800961, 439615493,
+    473432067, 473432073, 541065291, 541067267, 541073411, 541098243, 545357827, 566427651, 770400259, 811597862,
+    811599890, 811601922, 42, 88, 100, 145, 208, 4160, 8260, 16385, 24704, 66050, 528385, 6340609, 12681220,
+    50724868, 405799171, 439615491, 439615497, 456523809, 541065249, 541131267, 743964682, 743964687, 811601954,
+    946864138, 38, 224, 274, 2072, 16516, 132098, 1056769, 6340610, 12681218, 59179008, 101449736, 185991168,
+    405799429, 405799937, 473432097, 507248641, 539017219, 541065410, 541197315, 743964681, 805355522, 811597840,
+    811606082, 862322690, 37, 67, 196, 532, 576, 1288, 4097, 4136, 12320, 33028, 49152, 65536, 264194, 2113537,
+    3170305, 25362436, 54951936, 202899472, 405798923, 405799945, 473432069, 490340353, 541065259, 541329411,
+    743964677, 743964699, 743965187, 743965699, 765165571, 769327111, 777781250, 811597846, 811614338, 81, 176,
+    388, 1048, 8224, 8264, 49408, 66052, 528386, 4227073, 50724872, 384663553, 402677761, 405798944, 405800977,
+    456523841, 541593603, 743964678, 760872962, 782073859, 811598018, 811599874, 811630850, 815890434, 836960258,
+    70, 290, 16520, 32770, 132100, 1056770, 1585153, 4227074, 8454145, 29589504, 92995584, 101449744, 270532705,
+    270532737, 371982341, 405803041, 448069633, 536903683, 541065603, 542121987, 743964802, 760872961, 811597891,
+    811597986, 811663874, 913047810, 917340163, 69, 84, 200, 548, 769, 4098, 4104, 4144, 8320, 24640, 33032,
+    264196, 2113538, 3170306, 8454146, 16908289, 27475968, 28532736, 202899488, 371982339, 405799009, 405807169,
+    541065255, 541065539, 541069315, 543178755, 544235523, 676331587, 743964929, 769327115, 771440643, 777781249,
+    809517058, 810573826, 811729922, 76, 82, 416, 1064, 2112, 8272, 66056, 528388, 792577, 6340612, 8454148,
+    16908290, 33816577, 404758529, 405798976, 405798993, 405815425, 456523905, 541065345, 777781255, 811862018,
+    913047553, 913047556, 913048066, 946864162, 134, 448, 641, 2096, 2560, 2576, 16528, 132104, 1056772, 1585154,
+    12681224, 14794752, 16908292, 46497792, 67633153, 405799105, 405831937, 407945217, 431161345, 542650371,
+    549519363, 760872967, 811597888, 812126210, 879231010, 913047559, 917340160, 73, 392, 580, 776, 1088, 4100,
+    8193, 16448, 33040, 65540, 98304, 264200, 396289, 2113540, 3170308, 13737984, 16908296, 25362448, 33816580,
+    135266305, 371982401, 388890625, 405864961, 473432081, 541065987, 557973507, 676331651, 727056386, 742404099,
+    743965191, 758824963, 769327123, 777781267, 807436290, 811598210, 812654594, 74, 140, 352, 1096, 1537, 8288,
+    66064, 98816, 528392, 792578, 4227076, 6340616, 33816578, 33816584, 50724896, 380436481, 403718145,
+    405286913, 405931009, 418480129, 439615505, 541065474, 541857795, 574881795, 727056385, 743964690, 743965707,
+    162, 168, 261, 1538, 2128, 16544, 132112, 198145, 1056776, 1585156, 7397376, 12681232, 23248896, 33816592,
+    67633154, 67633160, 101449792, 270532865, 405798947, 405798953, 406063105, 456524033, 541065379, 608698371,
+    676331571, 743444483, 743964723, 743966739, 794689539, 811597906, 811597952, 879231042, 913047566, 152, 832,
+    1152, 4192, 8194, 24577, 33056, 49280, 131072, 264208, 396290, 2113544, 3170312, 6868992, 14266368, 25362464,
+    67633168, 135266306, 202899584, 371982345, 406327297, 541065351, 541461507, 743964715, 743968803, 756711427,
+    769327139, 786235395, 813182978, 820051970, 915259394, 917876738, 929955843, 138, 896, 1160, 1282, 5152,
+    8208, 66080, 99073, 131080, 528400, 792580, 4227080, 6340624, 50724928, 67633184, 135266320, 270532610,
+    405799297, 439615521, 456523778, 458670080, 541066755, 541077507, 743964689, 743964706, 743964771, 743972931,
+    811597894, 811598594, 828506114, 913047683, 917340166, 921501699, 923713538, 929955840, 946864258, 997588995,
+    164, 268, 400, 515, 645, 784, 1290, 1552, 2192, 2580, 3073, 4224, 5160, 10320, 16576, 16640, 20640, 41280,
+    49154, 82560, 132128, 165120, 198146, 330240, 660480, 1056784, 1320960, 1585160, 2641920, 3698688, 5283840,
+    8454152, 10567680, 11624448, 12681248, 21135360, 42270720, 67633156, 84541440, 101449856, 135266336,
+    169082880, 338165760, 405798949, 405798979, 405803009, 541065314, 541065479, 541065601, 541263363, 725008387,
+    742924291, 743964695, 743981187, 777781259, 811598083, 812390402, 845414402, 879231106, 913047808, 921501696,
+    991346690, 997588992, 321, 3074, 4256, 8196, 33088, 49537, 196608, 264224, 396292, 2113552, 3170320, 3434496,
+    25362496, 135266308, 135266368, 270532640, 270532657, 363528193, 371982353, 410025985, 473432129, 541065355,
+    541065537, 541065729, 676331779, 743964867, 743966723, 743997699, 745037827, 748257283, 760872971, 769327171,
+    811603970, 912267266, 913047563, 195, 265, 280, 521, 704, 773, 3076, 5120, 8384, 66112, 99074, 197632,
+    528416, 792584, 4227088, 6340640, 50724992, 270532612, 270532672, 405799168, 414253057, 439615553, 541065220,
+    541065730, 541164291, 727056419, 743964705, 743964738, 744030723, 811597898, 811597958, 811606018, 811994114,
+    912787458, 913047560, 917340170, 148, 209, 324, 522, 1664, 24769, 32896, 132160, 198148, 262160, 1056800,
+    1585168, 1849344, 5812224, 8454160, 12681280, 270532736, 270532801, 270533121, 405798981, 405799043,
+    405799681, 405801985, 422707201, 541065313, 541068291, 541089795, 676331520, 722894851, 727056391, 741916675,
+    743708675, 744096771, 811599362, 913047578, 913048070, 913048578, 918396930, 929955850, 146, 225, 418, 1546,
+    2176, 2564, 6145, 8200, 10304, 16386, 33152, 49538, 98560, 264256, 396296, 1717248, 2113568, 3170336,
+    7133184, 16908304, 25362560, 135266312, 202899712, 228261889, 371982369, 405799057, 406591489, 456523780,
+    473432193, 541065363, 541081603, 541114755, 735510531, 744228867, 760872979, 769327235, 811597875, 811598019,
+    811598086, 811598208, 811795970, 879231002, 904593411, 913047571, 913047574, 913048586, 197, 336, 1029, 1545,
+    1568, 1792, 12385, 49153, 66176, 98308, 99076, 792592, 4227104, 270532615, 270532616, 456524289, 464977920,
+    541065409, 541065472, 541065602, 541065991, 676331547, 743964737, 811597962, 811597987, 811598336, 811610114,
+    912527362, 913049618, 917340178, 946864386 };
+
+static int cbest_31[1023] = {
+    1, 2, 1073741828, 4, 536870914, 8, 268435457, 16, 32, 1207959556, 64, 128, 603979778, 256, 512, 301989889,
+    1024, 2048, 4096, 1224736772, 8192, 16384, 32768, 612368386, 65536, 131072, 262144, 306184193, 524288,
+    1048576, 2097152, 4194304, 1226833924, 8388608, 16777216, 33554432, 67108864, 613416962, 134217728,
+    268435456, 306708481, 536870912, 3, 1073741824, 1073741829, 5, 536870915, 1073741830, 6, 9, 18, 36, 72, 144,
+    288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 294912, 589824, 1179648, 2359296, 4718592,
+    9437184, 18874368, 37748736, 75497472, 150994944, 301989888, 1610612742, 10, 17, 268435459, 536870918,
+    603979776, 1073741836, 1227096068, 1342177285, 12, 33, 268435461, 536870922, 805306371, 1073741844,
+    1207959552, 1207959557, 20, 34, 65, 268435465, 536870930, 1073741860, 1207959558, 24, 66, 129, 268435473,
+    536870946, 603979779, 1073741892, 1744830470, 40, 68, 130, 257, 268435489, 536870978, 1073741956, 1207959564,
+    1476395013, 1677721606, 48, 132, 258, 513, 268435521, 536871042, 603979782, 613548034, 1073742084,
+    1207959572, 80, 136, 260, 514, 1025, 268435585, 301989891, 536871170, 603979786, 872415235, 1073742340,
+    1207959588, 1375731717, 96, 264, 516, 1026, 2049, 268435713, 301989893, 536871426, 603979794, 838860803,
+    1073742852, 1207959620, 160, 272, 520, 1028, 2050, 4097, 268435969, 301989897, 306184192, 536871938,
+    603979810, 612368384, 1073743876, 1207959684, 1224736768, 1224736773, 1811939334, 192, 528, 1032, 2052, 4098,
+    8193, 153092096, 268436481, 301989905, 536872962, 603979842, 1073745924, 1207959812, 1224736774, 320, 544,
+    1040, 2056, 4100, 8194, 16385, 76546048, 268437505, 301989921, 306774017, 536875010, 603979906, 1073750020,
+    1207960068, 1509949445, 1761607686, 384, 1056, 2064, 4104, 8196, 16386, 32769, 38273024, 268439553,
+    301989953, 536879106, 603980034, 612368387, 1073758212, 1207960580, 1224736780, 1493172229, 640, 1088, 2080,
+    4112, 8200, 16388, 32770, 65537, 19136512, 268443649, 301990017, 536887298, 603980290, 905969667, 1073774596,
+    1207961604, 1224736788, 1686110214, 768, 2112, 4128, 8208, 16392, 32772, 65538, 131073, 9568256, 268451841,
+    301990145, 536903682, 603980802, 612368390, 1073807364, 1207963652, 1224736804, 1280, 2176, 4160, 8224,
+    16400, 32776, 65540, 131074, 262145, 4784128, 268468225, 301990401, 536936450, 603981826, 612368394,
+    880803843, 1073872900, 1207967748, 1224736836, 1536, 4224, 8256, 16416, 32784, 65544, 131076, 262146, 524289,
+    2392064, 268500993, 301990913, 306184195, 537001986, 603983874, 612368402, 1074003972, 1207975940,
+    1224736900, 1379926021, 1828716550, 2560, 4352, 8320, 16448, 32800, 65552, 131080, 262148, 524290, 1048577,
+    1196032, 268566529, 301991937, 306184197, 537133058, 603987970, 612368418, 843055107, 1074266116, 1207992324,
+    1224737028, 1227128836, 1820327942, 3072, 8448, 16512, 32832, 65568, 131088, 262152, 524292, 598016, 1048578,
+    2097153, 268697601, 301993985, 306184201, 537395202, 603996162, 612368450, 1074790404, 1208025092,
+    1224737284, 1526726661, 5120, 8704, 16640, 32896, 65600, 131104, 262160, 299008, 524296, 1048580, 2097154,
+    4194305, 268959745, 301998081, 306184209, 537919490, 604012546, 612368514, 1075838980, 1208090628,
+    1224737796, 1226833920, 1226833925, 6144, 16896, 33024, 65664, 131136, 149504, 262176, 524304, 1048584,
+    2097156, 4194306, 8388609, 269484033, 302006273, 306184225, 538968066, 604045314, 612368642, 613416960,
+    1077936132, 1208221700, 1224738820, 1226833926, 1514143749, 10240, 17408, 33280, 65792, 74752, 131200,
+    262208, 524320, 1048592, 2097160, 4194308, 8388610, 16777217, 270532609, 302022657, 306184257, 306708480,
+    541065218, 604110850, 612368898, 914358275, 1082130436, 1208483844, 1224740868, 1763704838, 12288, 33792,
+    37376, 66048, 131328, 262272, 524352, 1048608, 2097168, 4194312, 8388612, 16777218, 33554433, 272629761,
+    302055425, 306184321, 545259522, 604241922, 612369410, 910163971, 1090519044, 1209008132, 1224744964,
+    1226833932, 1495269381, 18688, 20480, 34816, 66560, 131584, 262400, 524416, 1048640, 2097184, 4194320,
+    8388616, 16777220, 33554434, 67108865, 153354240, 276824065, 302120961, 306184449, 553648130, 604504066,
+    612370434, 613416963, 613564418, 1107296260, 1210056708, 1224753156, 1226833940, 9344, 24576, 67584, 132096,
+    262656, 524544, 1048704, 2097216, 4194336, 8388624, 16777224, 33554436, 67108866, 134217729, 285212673,
+    302252033, 306184705, 570425346, 605028354, 612372482, 1140850692, 1212153860, 1224769540, 1226833956,
+    1687158790, 1837105158, 4672, 40960, 69632, 133120, 263168, 524800, 1048832, 2097280, 4194368, 8388640,
+    16777232, 33554440, 67108868, 76677120, 134217730, 302514177, 306185217, 606076930, 612376578, 613416966,
+    1216348164, 1224802308, 1226833988, 2336, 49152, 135168, 264192, 525312, 1049088, 2097408, 4194432, 8388672,
+    16777248, 33554448, 67108872, 134217732, 268435458, 303038465, 306186241, 335544321, 608174082, 612384770,
+    613416970, 671088642, 881852419, 1224867844, 1226834052, 1342177284, 1830813702, 1168, 81920, 139264, 266240,
+    526336, 1049600, 2097664, 4194560, 8388736, 16777280, 33554464, 38338560, 67108880, 134217736, 268435460,
+    304087041, 306188289, 402653185, 536870913, 612401154, 613416978, 805306370, 1224998916, 1226834180,
+    1241513988, 1530920965, 584, 98304, 270336, 528384, 1050624, 2098176, 4194816, 8388864, 16777344, 33554496,
+    67108896, 134217744, 268435464, 306192385, 306708483, 612433922, 613416994, 620756994, 1225261060,
+    1226834436, 1275068420, 1380450309, 1528823813, 1610612740, 1821376518, 292, 163840, 278528, 532480, 1052672,
+    2099200, 4195328, 8389120, 16777472, 19169280, 33554560, 67108928, 134217760, 268435472, 306200577,
+    306708485, 306782209, 310378497, 536870916, 536870928, 612499458, 613417026, 637534210, 843579395,
+    1073741825, 1225785348, 1226834948, 146, 196608, 540672, 1056768, 2101248, 4196352, 8389632, 16777728,
+    33554688, 67108992, 134217792, 268435488, 306216961, 306708489, 318767105, 536870920, 612630530, 613417090,
+    805306369, 918552579, 1073741826, 1073741831, 1073741856, 1226835972, 1476395012, 7, 19, 37, 73, 145, 289,
+    577, 1153, 2305, 4609, 9217, 18433, 36865, 73729, 147457, 294913, 327680, 557056, 589825, 1064960, 1179649,
+    2105344, 2359297, 4198400, 4718593, 8390656, 9437185, 9584640, 16778240, 18874369, 33554944, 37748737,
+    67109120, 75497473, 134217856, 150994945, 268435520, 306249729, 306708497, 612892674, 613417218, 738197506,
+    1226838020, 1228931076, 1610612738, 1610612743, 11, 38, 74, 290, 578, 1154, 2306, 4610, 9218, 18434, 36866,
+    73730, 147458, 294914, 393216, 589826, 1081344, 1179650, 2113536, 2359298, 4202496, 4718594, 8392704,
+    9437186, 16779264, 18874370, 33555456, 37748738, 67109376, 75497474, 134217984, 150994946, 268435584,
+    301989890, 306315265, 306708513, 369098753, 536870919, 536870944, 603979777, 613417474, 872415234, 915406851,
+    1073741832, 1073741837, 1073741846, 1073741900, 1073741972, 1073742116, 1073742404, 1073742980, 1073744132,
+    1073746436, 1073751044, 1073760260, 1073778692, 1073815556, 1073889284, 1074036740, 1074331652, 1074921476,
+    1076101124, 1078460420, 1083179012, 1092616196, 1111490564, 1149239300, 1226842116, 1227096064, 1227096069,
+    1233125380, 1342177281, 1375731716, 1514668037, 1744830468, 13, 22, 76, 148, 580, 1156, 2308, 4612, 9220,
+    18436, 36868, 73732, 147460, 294916, 589828, 655360, 1114112, 1179652, 2129920, 2359300, 4210688, 4718596,
+    4792320, 8396800, 9437188, 16781312, 18874372, 33556480, 37748740, 67109888, 75497476, 134218240, 150994948,
+    268435712, 301989892, 306446337, 306708545, 436207617, 536870923, 536870950, 536870976, 536870986, 536871058,
+    536871202, 536871490, 536872066, 536873218, 536875522, 536880130, 536889346, 536907778, 536944642, 537018370,
+    537165826, 537460738, 538050562, 539230210, 541589506, 546308098, 555745282, 574619650, 613417986, 614465538,
+    687865858, 838860802, 1073741838, 1073741840, 1073741845, 1207959553, 1226850308, 1227096070, 1342177287,
+    1677721604, 14, 21, 26, 35, 44, 152, 296, 1160, 2312, 4616, 9224, 18440, 36872, 73736, 147464, 294920,
+    589832, 786432, 1179656, 2162688, 2359304, 4227072, 4718600, 8404992, 9437192, 16785408, 18874376, 33558528,
+    37748744, 67110912, 75497480, 134218752, 150994952, 268435463, 268435475, 268435493, 268435529, 268435601,
+    268435745, 268435968, 268436033, 268436609, 268437761, 268440065, 268444673, 268453889, 268472321, 268509185,
+    268582913, 268730369, 269025281, 269615105, 270794753, 273154049, 277872641, 287309825, 301989896, 306708609,
+    343932929, 419430401, 536870931, 536871040, 603979780, 603979792, 613419010, 613548032, 616562690, 910688259,
+    1073741861, 1207959554, 1207959559, 1207959584, 1226866692, 1258291204, 1610612750, 1763966982, 1839202310,
+    1879048199, 25, 52, 67, 88, 304, 592, 2320, 4624, 9232, 18448, 36880, 73744, 147472, 294928, 589840, 1179664,
+    1310720, 2228224, 2359312, 2396160, 4259840, 4718608, 8421376, 9437200, 16793600, 18874384, 33562624,
+    37748752, 67112960, 75497488, 134219776, 150994960, 268435467, 268436480, 301989904, 306708737, 307232769,
+    536870926, 536870947, 536871168, 603979784, 613421058, 805306375, 872415233, 1073741862, 1073741888,
+    1073741893, 1226899460, 1227096076, 1291845636, 1342177293, 1495531525, 1610612758, 1744830466, 1744830471,
+    1838153734, 41, 50, 69, 104, 131, 176, 608, 18464, 73760, 147488, 589856, 1179680, 1572864, 2359328, 4325376,
+    4718624, 8454144, 9437216, 16809984, 18874400, 33570816, 67117056, 75497504, 134221824, 301989920, 306708993,
+    306774016, 308281345, 536870934, 536870979, 629145602, 805306379, 1073741894, 1073741952, 1207959560,
+    1207959700, 1207959844, 1207960708, 1207961860, 1207964164, 1207968772, 1207977988, 1207996420, 1208033284,
+    1208107012, 1208549380, 1209139204, 1210318852, 1212678148, 1217396740, 1226964996, 1283457028, 1342177301,
+    1476395009, 1509949444, 1610612774, 1677721607 };
+
+static unsigned int cbest_32[1023] = {
+    1, 2149580803, 2, 4, 3224371202, 8, 1612185601, 16, 32, 2955673603, 64, 128, 256, 3627417602, 512, 1024,
+    2149580802, 1074790401, 1813708801, 3, 2149580801, 2048, 3224371203, 6, 2686976003, 5, 12, 1612185600,
+    3224371200, 2149580807, 9, 24, 806092800, 3761766402, 10, 1025, 4096, 3493068802, 48, 2050, 403046400,
+    2149580811, 2149581315, 17, 4100, 3056435203, 3224371206, 96, 8200, 201523200, 20, 16400, 1612185603,
+    2149580819, 3224371458, 18, 33, 192, 32800, 100761600, 1880883201, 2955673602, 3224371210, 8192, 65600,
+    1746534401, 384, 131200, 50380800, 1612185605, 2149580835, 34, 40, 65, 262400, 1612185729, 2955673601,
+    3224371218, 768, 524800, 25190400, 1049600, 1612185609, 2149580867, 36, 66, 129, 1536, 2099200, 12595200,
+    1477836801, 3224371234, 80, 16384, 4198400, 3090022403, 6297600, 8396800, 1612185617, 2149580931, 2955673607,
+    2955673667, 3022848003, 3627417603, 68, 130, 257, 16793600, 3224371266, 3677798402, 3148800, 33587200, 160,
+    3072, 67174400, 1612185633, 2149581059, 2955673611, 3627417600, 72, 132, 258, 513, 1574400, 134348800,
+    3224371330, 32768, 268697600, 2888499203, 787200, 537395200, 1612185665, 2955673619, 136, 260, 320, 514,
+    6144, 1074790400, 1813708800, 3627417634, 393600, 3627417606, 3694592002, 2149581827, 2955673635, 3661004802,
+    3963289602, 144, 264, 516, 1026, 1537, 3074, 196800, 2149580800, 3224371714, 640, 12288, 65536, 3627417610,
+    98400, 1612185857, 2149581571, 2686976002, 272, 520, 1028, 2049, 6148, 906854400, 3224372226, 7, 49200,
+    1074790403, 1813708803, 1838899201, 2149580805, 2149582339, 3224371201, 3593830402, 3627417618, 1280, 2052,
+    3073, 24576, 1343488001, 1612186113, 1813708817, 2149580806, 2149582851, 2686976001, 2955673731, 13, 288,
+    528, 1032, 12296, 24600, 3224371586, 3761766403, 14, 131072, 1074790405, 1813708805, 3493068803, 25, 4098,
+    6146, 12300, 806092801, 1612186625, 1847296001, 2149580810, 2149580815, 2149581314, 2955673859, 3224371204,
+    3224371970, 11, 26, 544, 1040, 4097, 24592, 49152, 453427200, 1074790657, 1612185602, 1830502401, 1981644801,
+    2149580809, 2149581826, 2821324803, 3056435202, 3224371207, 3224373250, 3761766400, 28, 49, 2051, 2056, 4104,
+    6150, 403046401, 1074790409, 1074790913, 1813708809, 1880883200, 2149580827, 2149582849, 2686976007,
+    3493068800, 3627417666, 4101, 12292, 806092802, 1612185793, 1746534400, 2149580818, 2149581313, 2149584899,
+    2686976131, 2955674115, 3224371459, 22, 52, 97, 576, 1027, 1056, 2560, 3075, 8201, 49184, 201523201,
+    1612185604, 2149580851, 2552627203, 2686976259, 3056435201, 3224371211, 3224371214, 4030464002, 21, 50, 56,
+    8196, 16401, 98304, 262144, 403046402, 940441600, 1074790417, 1612185728, 1612185985, 2149584903, 2686976011,
+    3224371208, 3224372227, 3627417730, 3896115202, 19, 193, 4102, 24584, 32801, 100761601, 806092804, 806092864,
+    873267200, 1612187649, 1796915201, 2149580817, 2149580834, 2149580899, 2149582338, 2149589003, 2351104003,
+    2955674627, 3056435211, 3224371226, 3224371456, 3224373248, 3761766406, 44, 98, 104, 1029, 1088, 2064, 8193,
+    8202, 8208, 65601, 98368, 201523202, 226713600, 403046432, 1612185607, 1612185608, 2149580823, 2149597203,
+    2955673600, 3224371219, 3224375298, 3493068806, 3493068866, 3560243202, 3761766530, 112, 385, 2054, 8194,
+    16402, 131201, 50380801, 201523216, 403046404, 470220800, 1074790433, 1477836800, 1612186624, 1813708833,
+    2149580995, 2149581319, 2149613603, 2250342403, 2686976019, 3224371250, 3493068930, 3627417858, 35, 41, 194,
+    1281, 4112, 32802, 49168, 196608, 262401, 100761602, 100761608, 436633600, 806092808, 806093312, 1612185613,
+    1880883203, 2149580833, 2149580866, 2149581443, 2149588995, 2149646403, 2955673699, 3056435207, 3224375302,
+    3761766410, 3761766914, 42, 88, 100, 208, 769, 1033, 1152, 2080, 8204, 16392, 65602, 196736, 524801,
+    25190401, 50380804, 201523204, 403046656, 1074791169, 1612185616, 1746534403, 2149581187, 2149712003,
+    2199961603, 3069030403, 3224371216, 3224371235, 3224371298, 3224379402, 3425894402, 3493068810, 38, 224, 386,
+    2058, 2562, 5120, 16404, 131202, 524288, 1049601, 25190402, 50380802, 201523328, 235110400, 403046408,
+    738918400, 1074790465, 1528217601, 1612185625, 1813708865, 2015232001, 2149580843, 2149581323, 2149843203,
+    2686976035, 2955673605, 2955673795, 3073228803, 3090022402, 3224371222, 3224371462, 3224371522, 3224387602,
+    3627418114, 37, 67, 196, 4108, 16416, 32804, 98336, 262402, 2099201, 12595201, 100761604, 100761664,
+    218316800, 806092816, 1612185611, 1612185731, 1612189697, 1746534433, 1880883205, 1880883265, 1948057601,
+    2147485699, 2149580865, 2149580930, 2150105603, 2174771203, 2955673606, 2955673666, 2955675651, 3022848002,
+    3064832003, 3140403203, 3224371394, 3224404002, 3325132802, 3761766418, 81, 176, 416, 770, 1041, 2112, 5124,
+    16385, 65604, 393216, 393472, 524802, 2099202, 4198401, 50380832, 113356800, 201523208, 1612185632,
+    1612185649, 1612187651, 1746534405, 1746534465, 2150630403, 3223323650, 3224371232, 3224371267, 3224379394,
+    3224436802, 3493068818, 3677798403, 70, 388, 448, 2066, 16408, 131204, 1049602, 4198402, 6297601, 8396801,
+    25190416, 117555200, 369459200, 403046416, 1074790529, 1612185761, 1612189701, 1780121601, 1813708929,
+    1880883457, 2149580839, 2149581331, 2151684099, 2162176003, 2686976067, 3090022401, 3224371466, 3224502402,
+    3274752002, 3627418626, 69, 84, 131, 200, 1538, 4116, 16388, 32784, 32808, 196672, 262404, 4198404, 8396802,
+    12595202, 12595208, 16793601, 109158400, 806092832, 1477836803, 1611661825, 1612185697, 1612185733,
+    1612193801, 1880883209, 2149580883, 2149580929, 2149581058, 2149597187, 2153779203, 2686976387, 2955673610,
+    2955673615, 2955673665, 3022848001, 3056435219, 3224371242, 3224633602, 3627417601, 3761766434, 76, 82, 352,
+    772, 832, 1057, 2176, 4128, 8216, 8224, 16386, 65608, 524804, 786944, 3148801, 6297604, 8396804, 25190404,
+    33587201, 1612185621, 1612185664, 1612202001, 1746534409, 2148535299, 2157977603, 2955673609, 2955674626,
+    3221228546, 3222276098, 3224371264, 3224371331, 3224896002, 3249561602, 3493068834, 3677798400, 134, 161,
+    392, 896, 2082, 32832, 131208, 786432, 1048576, 1049604, 3148802, 6297602, 8396808, 16793604, 50380808,
+    58777600, 67174401, 184729600, 1477836833, 1612185619, 1612218401, 1712947201, 1813709057, 2149580871,
+    2149581347, 2166374403, 2888499202, 2955673627, 2955675649, 3048038403, 3224371474, 3627417650, 3677798406,
+    73, 133, 259, 1540, 4132, 10248, 32816, 262408, 393344, 1574401, 2099204, 12595204, 16793602, 16793608,
+    54579200, 100761616, 134348801, 1477836805, 1545011201, 1611138049, 1612185737, 1612193793, 1612251201,
+    1880883217, 2149581057, 2183168003, 2955411715, 2955673618, 2955673683, 2955677699, 3022848019, 3056435235,
+    3090022435, 3224371238, 3224372738, 3226474498, 3236966402, 3761766466, 74, 140, 704, 776, 1089, 1664, 2304,
+    3076, 4160, 8232, 10240, 32769, 65616, 524808, 1573888, 16793616, 25190408, 33587202, 33587208, 56678400,
+    201523232, 268697601, 1511424001, 1610614273, 1612316801, 1662566401, 1746534417, 2149580963, 2149583875,
+    2216755203, 2955673651, 3022848035, 3090022407, 3157196803, 3224371282, 3224371328, 3224372482, 3224387586,
+    3228569602, 3627417604, 3627417635, 3627417698, 162, 168, 262, 400, 1792, 2114, 16432, 65568, 131216, 787201,
+    1049608, 29388800, 33587216, 50380816, 67174402, 92364800, 403046464, 537395201, 1612185635, 1612185641,
+    1612448001, 1813709313, 2149580875, 2149580935, 2149581379, 2149583363, 2151155203, 2283929603, 2888499201,
+    2955673671, 2955677703, 3022848007, 3090022531, 3123609603, 3223848450, 3224371490, 3232768002, 3627417607,
+    3627419650, 3694592003, 137, 152, 261, 321, 515, 1544, 4164, 6145, 262416, 786688, 1572864, 1574402, 2099208,
+    27289600, 33587232, 67174416, 100761632, 134348802, 806092928, 1477836809, 1477837313, 1612185745,
+    1612186369, 1637376001, 1880883233, 2149613571, 2418278403, 2955149827, 2955673617, 2955673634, 2955681803,
+    3056435267, 3224371270, 3241164802, 3661004803, 3963289603, 138, 268, 784, 1153, 1408, 4224, 8264, 32770,
+    32776, 65632, 65664, 393601, 524816, 3147776, 3148804, 4198408, 33587204, 67174432, 201523264, 268697602,
+    1612185856, 1612186241, 2150368003, 2913689603, 2955673623, 2955690003, 3039641603, 3090022411, 3224371715,
+    3257958402, 3493068994, 3627417632, 164, 518, 2178, 5121, 16448, 16464, 20496, 131232, 787202, 1049616,
+    6297608, 14694400, 46182400, 67174404, 67174464, 134348832, 403046528, 537395202, 1074791425, 1612185637,
+    1612185667, 1612187137, 1613237249, 1614284801, 1624780801, 1813709825, 2149580939, 2149581063, 2149581123,
+    2149586947, 2686976515, 2888499219, 2954887939, 2955673675, 2955706403, 3022848011, 3224371362, 3224374274,
+    3291545602, 3627286658, 3627417611, 3627417614, 3694592000, 145, 265, 280, 322, 517, 1552, 3080, 4228, 6152,
+    32864, 196801, 262432, 1573376, 1574404, 2097152, 2099216, 12595216, 13644800, 134348804, 134348864,
+    806093056, 1074790402, 1444249601, 1477836817, 1612185681, 1612201985, 1616384001, 1813708802, 1838899200,
+    2149581570, 2149581825, 2149583873, 2149974403, 2955673633, 2955681795, 2955739203, 3056435331, 3224371274,
+    3224371334, 3358720002, 3627417608, 3627417642, 3627418627, 3661004800, 3677798410, 3679901698, 3686195202,
+    3761766658, 3963289600, 266, 336, 524, 641, 800, 3328, 4352, 5125, 8256, 8328, 10250, 12289, 20500, 32772,
+    41000, 65537, 82000, 131136, 164000, 328000, 393602, 524832, 656000, 1312000, 2624000, 3148808, 4198416,
+    5248000, 10496000, 20992000, 25190432, 28339200, 41984000, 83968000, 134348928, 167936000, 268697604,
+    268697664, 335872000, 671744000, 1343488000, 1611924225, 1612186112, 1618483201, 1620582401, 1813708816,
+    2149583361, 2955673987, 2955804803, 3006054403, 3090022419, 3224371712, 3224403970, 3493069058, 3627417626,
+    3627419648, 3681996802, 3719782402, 148, 304, 2306, 3584, 12290, 16528, 98401, 131264, 787204, 1049632,
+    3145728, 6297616, 8396816, 23091200, 50380864, 67174408, 268697728, 1074790785, 1612185669, 1813708825 };

diff --git a/src/galois.c b/src/galois.c
new file mode 100644 (file)
index 0000000..6dc4282
--- /dev/null
+++ b/src/galois.c
@@ -0,0 +1,376 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <errno.h>
+
+#include "galois.h"
+
+#define MAX_GF_INSTANCES 64
+gf_t *gfp_array[MAX_GF_INSTANCES] = { 0 };
+int  gfp_is_composite[MAX_GF_INSTANCES] = { 0 };
+
+gf_t *galois_get_field_ptr(int w)
+{
+  if (gfp_array[w] != NULL) {
+    return gfp_array[w];
+  }
+
+  return NULL;
+}
+
+gf_t* galois_init_field(int w,
+                        int mult_type,
+                        int region_type,
+                        int divide_type,
+                        uint64_t prim_poly,
+                        int arg1,
+                        int arg2)
+{
+  int scratch_size;
+  void *scratch_memory;
+  gf_t *gfp;
+
+  if (w <= 0 || w > 32) {
+    fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w);
+    exit(1);
+  }
+
+  gfp = (gf_t *) malloc(sizeof(gf_t));
+  if (!gfp) {
+    fprintf(stderr, "ERROR -- cannot allocate memory for Galois field w=%d\n", w);
+    exit(1);
+  }
+
+  scratch_size = gf_scratch_size(w, mult_type, region_type, divide_type, arg1, arg2);
+  if (!scratch_size) {
+    fprintf(stderr, "ERROR -- cannot get scratch size for base field w=%d\n", w);
+    exit(1);
+  }
+
+  scratch_memory = malloc(scratch_size);
+  if (!scratch_memory) {
+    fprintf(stderr, "ERROR -- cannot get scratch memory for base field w=%d\n", w);
+    exit(1);
+  }
+
+  if(!gf_init_hard(gfp,
+                   w, 
+                   mult_type, 
+                   region_type, 
+                   divide_type, 
+                   prim_poly, 
+                   arg1, 
+                   arg2, 
+                   NULL, 
+                   scratch_memory))
+  {
+    fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w);
+    exit(1);
+  }
+
+  gfp_is_composite[w] = 0;
+  return gfp;
+}
+
+gf_t* galois_init_composite_field(int w,
+                                int region_type,
+                                int divide_type,
+                                int degree,
+                                gf_t* base_gf)
+{
+  int scratch_size;
+  void *scratch_memory;
+  gf_t *gfp;
+  
+  if (w <= 0 || w > 32) {
+    fprintf(stderr, "ERROR -- cannot init composite field for w=%d\n", w);
+    exit(1);
+  }
+  
+  gfp = (gf_t *) malloc(sizeof(gf_t));
+  if (!gfp) {
+    fprintf(stderr, "ERROR -- cannot allocate memory for Galois field w=%d\n", w);
+    exit(1);
+  }
+
+  scratch_size = gf_scratch_size(w, GF_MULT_COMPOSITE, region_type, divide_type, degree, 0);
+  if (!scratch_size) {
+    fprintf(stderr, "ERROR -- cannot get scratch size for composite field w=%d\n", w);
+    exit(1);
+  }
+
+  scratch_memory = malloc(scratch_size);
+  if (!scratch_memory) {
+    fprintf(stderr, "ERROR -- cannot get scratch memory for composite field w=%d\n", w);
+    exit(1);
+  }
+
+  if(!gf_init_hard(gfp,
+                   w,
+                   GF_MULT_COMPOSITE,
+                   region_type,
+                   divide_type,
+                   0, 
+                   degree, 
+                   0, 
+                   base_gf,
+                   scratch_memory))
+  {
+    fprintf(stderr, "ERROR -- cannot init default composite field for w=%d\n", w);
+    exit(1);
+  }
+  gfp_is_composite[w] = 1;
+  return gfp;
+}
+
+int galois_init_default_field(int w)
+{
+  if (gfp_array[w] == NULL) {
+    gfp_array[w] = (gf_t*)malloc(sizeof(gf_t));
+    if(gfp_array[w] == NULL)
+      return ENOMEM;
+    if (!gf_init_easy(gfp_array[w], w))
+      return EINVAL;
+  }
+  return 0;
+}
+
+int galois_uninit_field(int w)
+{
+  int ret = 0;
+  if (gfp_array[w] != NULL) {
+    int recursive = 1;
+    ret = gf_free(gfp_array[w], recursive);
+    free(gfp_array[w]);
+    gfp_array[w] = NULL;
+  }
+  return ret;
+}
+
+static void galois_init(int w)
+{
+  if (w <= 0 || w > 32) {
+    fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w);
+    exit(1);
+  }
+
+  switch (galois_init_default_field(w)) {
+  case ENOMEM:
+    fprintf(stderr, "ERROR -- cannot allocate memory for Galois field w=%d\n", w);
+    exit(1);
+    break;
+  case EINVAL:
+    fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w);
+    exit(1);
+    break;
+  }
+}
+
+
+static int is_valid_gf(gf_t *gf, int w)
+{
+  // TODO: I assume we may eventually
+  // want to do w=64 and 128, so w
+  // will be needed to perform this check
+  (void)w;
+
+  if (gf == NULL) {
+    return 0;
+  }
+  if (gf->multiply.w32 == NULL) {
+    return 0;
+  }
+  if (gf->multiply_region.w32 == NULL) {
+    return 0;
+  }
+  if (gf->divide.w32 == NULL) {
+    return 0;
+  }
+  if (gf->inverse.w32 == NULL) {
+    return 0;
+  }
+  if (gf->extract_word.w32 == NULL) {
+    return 0;
+  }
+
+  return 1;
+}
+
+void galois_change_technique(gf_t *gf, int w)
+{
+  if (w <= 0 || w > 32) {
+    fprintf(stderr, "ERROR -- cannot support Galois field for w=%d\n", w);
+    exit(1);
+  }
+
+  if (!is_valid_gf(gf, w)) {
+    fprintf(stderr, "ERROR -- overriding with invalid Galois field for w=%d\n", w);
+    exit(1);
+  }
+
+  if (gfp_array[w] != NULL) {
+    gf_free(gfp_array[w], gfp_is_composite[w]);
+  }
+
+  gfp_array[w] = gf;
+}
+
+int galois_single_multiply(int x, int y, int w)
+{
+  if (x == 0 || y == 0) return 0;
+  
+  if (gfp_array[w] == NULL) {
+    galois_init(w);
+  }
+
+  if (w <= 32) {
+    return gfp_array[w]->multiply.w32(gfp_array[w], x, y);
+  } else {
+    fprintf(stderr, "ERROR -- Galois field not implemented for w=%d\n", w);
+    return 0;
+  }
+}
+
+int galois_single_divide(int x, int y, int w)
+{
+  if (x == 0) return 0;
+  if (y == 0) return -1;
+
+  if (gfp_array[w] == NULL) {
+    galois_init(w);
+  }
+
+  if (w <= 32) {
+    return gfp_array[w]->divide.w32(gfp_array[w], x, y);
+  } else {
+    fprintf(stderr, "ERROR -- Galois field not implemented for w=%d\n", w);
+    return 0;
+  }
+}
+
+void galois_w08_region_multiply(char *region,      /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,        /* Number of bytes in region */
+                                  char *r2,          /* If r2 != NULL, products go here */
+                                  int add)
+{
+  if (gfp_array[8] == NULL) {
+    galois_init(8);
+  }
+  gfp_array[8]->multiply_region.w32(gfp_array[8], region, r2, multby, nbytes, add);
+}
+
+void galois_w16_region_multiply(char *region,      /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,        /* Number of bytes in region */
+                                  char *r2,          /* If r2 != NULL, products go here */
+                                  int add)
+{
+  if (gfp_array[16] == NULL) {
+    galois_init(16);
+  }
+  gfp_array[16]->multiply_region.w32(gfp_array[16], region, r2, multby, nbytes, add);
+}
+
+
+void galois_w32_region_multiply(char *region,      /* Region to multiply */
+                                  int multby,       /* Number to multiply by */
+                                  int nbytes,        /* Number of bytes in region */
+                                  char *r2,          /* If r2 != NULL, products go here */
+                                  int add)
+{
+  if (gfp_array[32] == NULL) {
+    galois_init(32);
+  }
+  gfp_array[32]->multiply_region.w32(gfp_array[32], region, r2, multby, nbytes, add);
+}
+
+void galois_w8_region_xor(void *src, void *dest, int nbytes)
+{
+  if (gfp_array[8] == NULL) {
+    galois_init(8);
+  }
+  gfp_array[8]->multiply_region.w32(gfp_array[32], src, dest, 1, nbytes, 1);
+}
+
+void galois_w16_region_xor(void *src, void *dest, int nbytes)
+{
+  if (gfp_array[16] == NULL) {
+    galois_init(16);
+  }
+  gfp_array[16]->multiply_region.w32(gfp_array[16], src, dest, 1, nbytes, 1);
+}
+
+void galois_w32_region_xor(void *src, void *dest, int nbytes)
+{
+  if (gfp_array[32] == NULL) {
+    galois_init(32);
+  }
+  gfp_array[32]->multiply_region.w32(gfp_array[32], src, dest, 1, nbytes, 1);
+}
+
+void galois_region_xor(char *src, char *dest, int nbytes)
+{
+  if (nbytes >= 16) {
+    galois_w32_region_xor(src, dest, nbytes);
+  } else {
+    int i = 0;
+    for (i = 0; i < nbytes; i++) {
+      *dest ^= *src;
+      dest++;
+      src++;
+    } 
+  }
+}
+
+int galois_inverse(int y, int w)
+{
+  if (y == 0) return -1;
+  return galois_single_divide(1, y, w);
+}

diff --git a/src/jerasure.c b/src/jerasure.c
new file mode 100644 (file)
index 0000000..d8c1179
--- /dev/null
+++ b/src/jerasure.c
@@ -0,0 +1,1484 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "galois.h"
+#include "jerasure.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+static double jerasure_total_xor_bytes = 0;
+static double jerasure_total_gf_bytes = 0;
+static double jerasure_total_memcpy_bytes = 0;
+
+void jerasure_print_matrix(int *m, int rows, int cols, int w)
+{
+  int i, j;
+  int fw;
+  char s[30];
+  unsigned int w2;
+
+  if (w == 32) {
+    fw = 10;
+  } else {
+    w2 = (1 << w);
+    sprintf(s, "%u", w2-1);
+    fw = strlen(s);
+  }
+
+  for (i = 0; i < rows; i++) {
+    for (j = 0; j < cols; j++) {
+      if (j != 0) printf(" ");
+      printf("%*u", fw, m[i*cols+j]); 
+    }
+    printf("\n");
+  }
+}
+
+void jerasure_print_bitmatrix(int *m, int rows, int cols, int w)
+{
+  int i, j;
+
+  for (i = 0; i < rows; i++) {
+    if (i != 0 && i%w == 0) printf("\n");
+    for (j = 0; j < cols; j++) {
+      if (j != 0 && j%w == 0) printf(" ");
+      printf("%d", m[i*cols+j]); 
+    }
+    printf("\n");
+  }
+}
+
+int jerasure_make_decoding_matrix(int k, int m, int w, int *matrix, int *erased, int *decoding_matrix, int *dm_ids)
+{
+  int i, j, *tmpmat;
+
+  j = 0;
+  for (i = 0; j < k; i++) {
+    if (erased[i] == 0) {
+      dm_ids[j] = i;
+      j++;
+    }
+  }
+
+  tmpmat = talloc(int, k*k);
+  if (tmpmat == NULL) { return -1; }
+  for (i = 0; i < k; i++) {
+    if (dm_ids[i] < k) {
+      for (j = 0; j < k; j++) tmpmat[i*k+j] = 0;
+      tmpmat[i*k+dm_ids[i]] = 1;
+    } else {
+      for (j = 0; j < k; j++) {
+        tmpmat[i*k+j] = matrix[(dm_ids[i]-k)*k+j];
+      }
+    }
+  }
+
+  i = jerasure_invert_matrix(tmpmat, decoding_matrix, k, w);
+  free(tmpmat);
+  return i;
+}
+
+/* Internal Routine */
+int jerasure_make_decoding_bitmatrix(int k, int m, int w, int *matrix, int *erased, int *decoding_matrix, int *dm_ids)
+{
+  int i, j, *tmpmat;
+  int index, mindex;
+
+  j = 0;
+  for (i = 0; j < k; i++) {
+    if (erased[i] == 0) {
+      dm_ids[j] = i;
+      j++;
+    }
+  }
+
+  tmpmat = talloc(int, k*k*w*w);
+  if (tmpmat == NULL) { return -1; }
+  for (i = 0; i < k; i++) {
+    if (dm_ids[i] < k) {
+      index = i*k*w*w;
+      for (j = 0; j < k*w*w; j++) tmpmat[index+j] = 0;
+      index = i*k*w*w+dm_ids[i]*w;
+      for (j = 0; j < w; j++) {
+        tmpmat[index] = 1;
+        index += (k*w+1);
+      }
+    } else {
+      index = i*k*w*w;
+      mindex = (dm_ids[i]-k)*k*w*w;
+      for (j = 0; j < k*w*w; j++) {
+        tmpmat[index+j] = matrix[mindex+j];
+      }
+    }
+  }
+
+  i = jerasure_invert_bitmatrix(tmpmat, decoding_matrix, k*w);
+  free(tmpmat);
+  return i;
+}
+
+int jerasure_matrix_decode(int k, int m, int w, int *matrix, int row_k_ones, int *erasures,
+                          char **data_ptrs, char **coding_ptrs, int size)
+{
+  int i, edd, lastdrive;
+  int *tmpids;
+  int *erased, *decoding_matrix, *dm_ids;
+
+  if (w != 8 && w != 16 && w != 32) return -1;
+
+  erased = jerasure_erasures_to_erased(k, m, erasures);
+  if (erased == NULL) return -1;
+
+  /* Find the number of data drives failed */
+
+  lastdrive = k;
+
+  edd = 0;
+  for (i = 0; i < k; i++) {
+    if (erased[i]) {
+      edd++;
+      lastdrive = i;
+    }
+  }
+    
+  /* You only need to create the decoding matrix in the following cases:
+
+      1. edd > 0 and row_k_ones is false.
+      2. edd > 0 and row_k_ones is true and coding device 0 has been erased.
+      3. edd > 1
+
+      We're going to use lastdrive to denote when to stop decoding data.
+      At this point in the code, it is equal to the last erased data device.
+      However, if we can't use the parity row to decode it (i.e. row_k_ones=0
+         or erased[k] = 1, we're going to set it to k so that the decoding 
+         pass will decode all data.
+   */
+
+  if (!row_k_ones || erased[k]) lastdrive = k;
+
+  dm_ids = NULL;
+  decoding_matrix = NULL;
+
+  if (edd > 1 || (edd > 0 && (!row_k_ones || erased[k]))) {
+    dm_ids = talloc(int, k);
+    if (dm_ids == NULL) {
+      free(erased);
+      return -1;
+    }
+
+    decoding_matrix = talloc(int, k*k);
+    if (decoding_matrix == NULL) {
+      free(erased);
+      free(dm_ids);
+      return -1;
+    }
+
+    if (jerasure_make_decoding_matrix(k, m, w, matrix, erased, decoding_matrix, dm_ids) < 0) {
+      free(erased);
+      free(dm_ids);
+      free(decoding_matrix);
+      return -1;
+    }
+  }
+
+  /* Decode the data drives.  
+     If row_k_ones is true and coding device 0 is intact, then only decode edd-1 drives.
+     This is done by stopping at lastdrive.
+     We test whether edd > 0 so that we can exit the loop early if we're done.
+   */
+
+  for (i = 0; edd > 0 && i < lastdrive; i++) {
+    if (erased[i]) {
+      jerasure_matrix_dotprod(k, w, decoding_matrix+(i*k), dm_ids, i, data_ptrs, coding_ptrs, size);
+      edd--;
+    }
+  }
+
+  /* Then if necessary, decode drive lastdrive */
+
+  if (edd > 0) {
+    tmpids = talloc(int, k);
+    if (!tmpids) {
+      free(erased);
+      free(dm_ids);
+      free(decoding_matrix);
+      return -1;
+    }
+    for (i = 0; i < k; i++) {
+      tmpids[i] = (i < lastdrive) ? i : i+1;
+    }
+    jerasure_matrix_dotprod(k, w, matrix, tmpids, lastdrive, data_ptrs, coding_ptrs, size);
+    free(tmpids);
+  }
+  
+  /* Finally, re-encode any erased coding devices */
+
+  for (i = 0; i < m; i++) {
+    if (erased[k+i]) {
+      jerasure_matrix_dotprod(k, w, matrix+(i*k), NULL, i+k, data_ptrs, coding_ptrs, size);
+    }
+  }
+
+  free(erased);
+  if (dm_ids != NULL) free(dm_ids);
+  if (decoding_matrix != NULL) free(decoding_matrix);
+
+  return 0;
+}
+
+
+int *jerasure_matrix_to_bitmatrix(int k, int m, int w, int *matrix) 
+{
+  int *bitmatrix;
+  int rowelts, rowindex, colindex, elt, i, j, l, x;
+
+  if (matrix == NULL) { return NULL; }
+
+  bitmatrix = talloc(int, k*m*w*w);
+  if (!bitmatrix) return NULL;
+
+  rowelts = k * w;
+  rowindex = 0;
+
+  for (i = 0; i < m; i++) {
+    colindex = rowindex;
+    for (j = 0; j < k; j++) {
+      elt = matrix[i*k+j];
+      for (x = 0; x < w; x++) {
+        for (l = 0; l < w; l++) {
+          bitmatrix[colindex+x+l*rowelts] = ((elt & (1 << l)) ? 1 : 0);
+        }
+        elt = galois_single_multiply(elt, 2, w);
+      }
+      colindex += w;
+    }
+    rowindex += rowelts * w;
+  }
+  return bitmatrix;
+}
+
+void jerasure_matrix_encode(int k, int m, int w, int *matrix,
+                          char **data_ptrs, char **coding_ptrs, int size)
+{
+  int i;
+  
+  if (w != 8 && w != 16 && w != 32) {
+    fprintf(stderr, "ERROR: jerasure_matrix_encode() and w is not 8, 16 or 32\n");
+    exit(1);
+  }
+
+  for (i = 0; i < m; i++) {
+    jerasure_matrix_dotprod(k, w, matrix+(i*k), NULL, k+i, data_ptrs, coding_ptrs, size);
+  }
+}
+
+void jerasure_bitmatrix_dotprod(int k, int w, int *bitmatrix_row,
+                             int *src_ids, int dest_id,
+                             char **data_ptrs, char **coding_ptrs, int size, int packetsize)
+{
+  int j, sindex, pstarted, index, x, y;
+  char *dptr, *pptr, *bdptr, *bpptr;
+
+  if (size%(w*packetsize) != 0) {
+    fprintf(stderr, "jerasure_bitmatrix_dotprod - size%c(w*packetsize)) must = 0\n", '%');
+    exit(1);
+  }
+
+  bpptr = (dest_id < k) ? data_ptrs[dest_id] : coding_ptrs[dest_id-k];
+
+  for (sindex = 0; sindex < size; sindex += (packetsize*w)) {
+    index = 0;
+    for (j = 0; j < w; j++) {
+      pstarted = 0;
+      pptr = bpptr + sindex + j*packetsize;
+      for (x = 0; x < k; x++) {
+        if (src_ids == NULL) {
+          bdptr = data_ptrs[x];
+        } else if (src_ids[x] < k) {
+          bdptr = data_ptrs[src_ids[x]];
+        } else {
+          bdptr = coding_ptrs[src_ids[x]-k];
+        }
+        for (y = 0; y < w; y++) {
+          if (bitmatrix_row[index]) {
+            dptr = bdptr + sindex + y*packetsize;
+            if (!pstarted) {
+              memcpy(pptr, dptr, packetsize);
+              jerasure_total_memcpy_bytes += packetsize;
+              pstarted = 1;
+            } else {
+              galois_region_xor(dptr, pptr, packetsize);
+              jerasure_total_xor_bytes += packetsize;
+            }
+          }
+          index++;
+        }
+      }
+    }
+  }
+}
+
+void jerasure_do_parity(int k, char **data_ptrs, char *parity_ptr, int size) 
+{
+  int i;
+
+  memcpy(parity_ptr, data_ptrs[0], size);
+  jerasure_total_memcpy_bytes += size;
+  
+  for (i = 1; i < k; i++) {
+    galois_region_xor(data_ptrs[i], parity_ptr, size);
+    jerasure_total_xor_bytes += size;
+  }
+}
+
+int jerasure_invert_matrix(int *mat, int *inv, int rows, int w)
+{
+  int cols, i, j, k, x, rs2;
+  int row_start, tmp, inverse;
+ 
+  cols = rows;
+
+  k = 0;
+  for (i = 0; i < rows; i++) {
+    for (j = 0; j < cols; j++) {
+      inv[k] = (i == j) ? 1 : 0;
+      k++;
+    }
+  }
+
+  /* First -- convert into upper triangular  */
+  for (i = 0; i < cols; i++) {
+    row_start = cols*i;
+
+    /* Swap rows if we ave a zero i,i element.  If we can't swap, then the 
+       matrix was not invertible  */
+
+    if (mat[row_start+i] == 0) { 
+      for (j = i+1; j < rows && mat[cols*j+i] == 0; j++) ;
+      if (j == rows) return -1;
+      rs2 = j*cols;
+      for (k = 0; k < cols; k++) {
+        tmp = mat[row_start+k];
+        mat[row_start+k] = mat[rs2+k];
+        mat[rs2+k] = tmp;
+        tmp = inv[row_start+k];
+        inv[row_start+k] = inv[rs2+k];
+        inv[rs2+k] = tmp;
+      }
+    }
+ 
+    /* Multiply the row by 1/element i,i  */
+    tmp = mat[row_start+i];
+    if (tmp != 1) {
+      inverse = galois_single_divide(1, tmp, w);
+      for (j = 0; j < cols; j++) { 
+        mat[row_start+j] = galois_single_multiply(mat[row_start+j], inverse, w);
+        inv[row_start+j] = galois_single_multiply(inv[row_start+j], inverse, w);
+      }
+    }
+
+    /* Now for each j>i, add A_ji*Ai to Aj  */
+    k = row_start+i;
+    for (j = i+1; j != cols; j++) {
+      k += cols;
+      if (mat[k] != 0) {
+        if (mat[k] == 1) {
+          rs2 = cols*j;
+          for (x = 0; x < cols; x++) {
+            mat[rs2+x] ^= mat[row_start+x];
+            inv[rs2+x] ^= inv[row_start+x];
+          }
+        } else {
+          tmp = mat[k];
+          rs2 = cols*j;
+          for (x = 0; x < cols; x++) {
+            mat[rs2+x] ^= galois_single_multiply(tmp, mat[row_start+x], w);
+            inv[rs2+x] ^= galois_single_multiply(tmp, inv[row_start+x], w);
+          }
+        }
+      }
+    }
+  }
+
+  /* Now the matrix is upper triangular.  Start at the top and multiply down  */
+
+  for (i = rows-1; i >= 0; i--) {
+    row_start = i*cols;
+    for (j = 0; j < i; j++) {
+      rs2 = j*cols;
+      if (mat[rs2+i] != 0) {
+        tmp = mat[rs2+i];
+        mat[rs2+i] = 0; 
+        for (k = 0; k < cols; k++) {
+          inv[rs2+k] ^= galois_single_multiply(tmp, inv[row_start+k], w);
+        }
+      }
+    }
+  }
+  return 0;
+}
+
+int jerasure_invertible_matrix(int *mat, int rows, int w)
+{
+  int cols, i, j, k, x, rs2;
+  int row_start, tmp, inverse;
+ 
+  cols = rows;
+
+  /* First -- convert into upper triangular  */
+  for (i = 0; i < cols; i++) {
+    row_start = cols*i;
+
+    /* Swap rows if we ave a zero i,i element.  If we can't swap, then the 
+       matrix was not invertible  */
+
+    if (mat[row_start+i] == 0) { 
+      for (j = i+1; j < rows && mat[cols*j+i] == 0; j++) ;
+      if (j == rows) return 0;
+      rs2 = j*cols;
+      for (k = 0; k < cols; k++) {
+        tmp = mat[row_start+k];
+        mat[row_start+k] = mat[rs2+k];
+        mat[rs2+k] = tmp;
+      }
+    }
+ 
+    /* Multiply the row by 1/element i,i  */
+    tmp = mat[row_start+i];
+    if (tmp != 1) {
+      inverse = galois_single_divide(1, tmp, w);
+      for (j = 0; j < cols; j++) { 
+        mat[row_start+j] = galois_single_multiply(mat[row_start+j], inverse, w);
+      }
+    }
+
+    /* Now for each j>i, add A_ji*Ai to Aj  */
+    k = row_start+i;
+    for (j = i+1; j != cols; j++) {
+      k += cols;
+      if (mat[k] != 0) {
+        if (mat[k] == 1) {
+          rs2 = cols*j;
+          for (x = 0; x < cols; x++) {
+            mat[rs2+x] ^= mat[row_start+x];
+          }
+        } else {
+          tmp = mat[k];
+          rs2 = cols*j;
+          for (x = 0; x < cols; x++) {
+            mat[rs2+x] ^= galois_single_multiply(tmp, mat[row_start+x], w);
+          }
+        }
+      }
+    }
+  }
+  return 1;
+}
+
+/* Converts a list-style version of the erasures into an array of k+m elements
+   where the element = 1 if the index has been erased, and zero otherwise */
+
+int *jerasure_erasures_to_erased(int k, int m, int *erasures)
+{
+  int td;
+  int t_non_erased;
+  int *erased;
+  int i;
+
+  td = k+m;
+  erased = talloc(int, td);
+  if (erased == NULL) return NULL;
+  t_non_erased = td;
+
+  for (i = 0; i < td; i++) erased[i] = 0;
+
+  for (i = 0; erasures[i] != -1; i++) {
+    if (erased[erasures[i]] == 0) {
+      erased[erasures[i]] = 1;
+      t_non_erased--;
+      if (t_non_erased < k) {
+        free(erased);
+        return NULL;
+      }
+    }
+  }
+  return erased;
+}
+  
+void jerasure_free_schedule(int **schedule)
+{
+  int i;
+
+  for (i = 0; schedule[i][0] >= 0; i++) free(schedule[i]);
+  free(schedule[i]);
+  free(schedule);
+}
+
+void jerasure_free_schedule_cache(int k, int m, int ***cache)
+{
+  int e1, e2;
+
+  if (m != 2) {
+    fprintf(stderr, "jerasure_free_schedule_cache(): m must equal 2\n");
+    exit(1);
+  }
+
+  for (e1 = 0; e1 < k+m; e1++) {
+    for (e2 = 0; e2 < e1; e2++) {
+      jerasure_free_schedule(cache[e1*(k+m)+e2]);
+    }
+    jerasure_free_schedule(cache[e1*(k+m)+e1]);
+  }
+  free(cache);
+}
+
+void jerasure_matrix_dotprod(int k, int w, int *matrix_row,
+                          int *src_ids, int dest_id,
+                          char **data_ptrs, char **coding_ptrs, int size)
+{
+  int init;
+  char *dptr, *sptr;
+  int i;
+
+  if (w != 1 && w != 8 && w != 16 && w != 32) {
+    fprintf(stderr, "ERROR: jerasure_matrix_dotprod() called and w is not 1, 8, 16 or 32\n");
+    exit(1);
+  }
+
+  init = 0;
+
+  dptr = (dest_id < k) ? data_ptrs[dest_id] : coding_ptrs[dest_id-k];
+
+  /* First copy or xor any data that does not need to be multiplied by a factor */
+
+  for (i = 0; i < k; i++) {
+    if (matrix_row[i] == 1) {
+      if (src_ids == NULL) {
+        sptr = data_ptrs[i];
+      } else if (src_ids[i] < k) {
+        sptr = data_ptrs[src_ids[i]];
+      } else {
+        sptr = coding_ptrs[src_ids[i]-k];
+      }
+      if (init == 0) {
+        memcpy(dptr, sptr, size);
+        jerasure_total_memcpy_bytes += size;
+        init = 1;
+      } else {
+        galois_region_xor(sptr, dptr, size);
+        jerasure_total_xor_bytes += size;
+      }
+    }
+  }
+
+  /* Now do the data that needs to be multiplied by a factor */
+
+  for (i = 0; i < k; i++) {
+    if (matrix_row[i] != 0 && matrix_row[i] != 1) {
+      if (src_ids == NULL) {
+        sptr = data_ptrs[i];
+      } else if (src_ids[i] < k) {
+        sptr = data_ptrs[src_ids[i]];
+      } else {
+        sptr = coding_ptrs[src_ids[i]-k];
+      }
+      switch (w) {
+        case 8:  galois_w08_region_multiply(sptr, matrix_row[i], size, dptr, init); break;
+        case 16: galois_w16_region_multiply(sptr, matrix_row[i], size, dptr, init); break;
+        case 32: galois_w32_region_multiply(sptr, matrix_row[i], size, dptr, init); break;
+      }
+      jerasure_total_gf_bytes += size;
+      init = 1;
+    }
+  }
+}
+
+
+int jerasure_bitmatrix_decode(int k, int m, int w, int *bitmatrix, int row_k_ones, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize)
+{
+  int i;
+  int *erased;
+  int *decoding_matrix;
+  int *dm_ids;
+  int edd, *tmpids, lastdrive;
+  
+  erased = jerasure_erasures_to_erased(k, m, erasures);
+  if (erased == NULL) return -1;
+
+  /* See jerasure_matrix_decode for the logic of this routine.  This one works just like
+     it, but calls the bitmatrix ops instead */
+
+  lastdrive = k;
+    
+  edd = 0;
+  for (i = 0; i < k; i++) {
+    if (erased[i]) {
+      edd++;
+      lastdrive = i;
+    } 
+  }
+
+  if (row_k_ones != 1 || erased[k]) lastdrive = k;
+  
+  dm_ids = NULL;
+  decoding_matrix = NULL;
+  
+  if (edd > 1 || (edd > 0 && (row_k_ones != 1 || erased[k]))) {
+
+    dm_ids = talloc(int, k);
+    if (dm_ids == NULL) {
+      free(erased);
+      return -1;
+    }
+  
+    decoding_matrix = talloc(int, k*k*w*w);
+    if (decoding_matrix == NULL) {
+      free(erased);
+      free(dm_ids);
+      return -1;
+    }
+  
+    if (jerasure_make_decoding_bitmatrix(k, m, w, bitmatrix, erased, decoding_matrix, dm_ids) < 0) {
+      free(erased);
+      free(dm_ids);
+      free(decoding_matrix);
+      return -1;
+    }
+  }
+
+  for (i = 0; edd > 0 && i < lastdrive; i++) {
+    if (erased[i]) {
+      jerasure_bitmatrix_dotprod(k, w, decoding_matrix+i*k*w*w, dm_ids, i, data_ptrs, coding_ptrs, size, packetsize);
+      edd--;
+    }
+  }
+
+  if (edd > 0) {
+    tmpids = talloc(int, k);
+    if (!tmpids) {
+      free(erased);
+      free(dm_ids);
+      free(decoding_matrix);
+      return -1;
+    }
+    for (i = 0; i < k; i++) {
+      tmpids[i] = (i < lastdrive) ? i : i+1;
+    }
+    jerasure_bitmatrix_dotprod(k, w, bitmatrix, tmpids, lastdrive, data_ptrs, coding_ptrs, size, packetsize);
+    free(tmpids);
+  }
+
+  for (i = 0; i < m; i++) {
+    if (erased[k+i]) {
+      jerasure_bitmatrix_dotprod(k, w, bitmatrix+i*k*w*w, NULL, k+i, data_ptrs, coding_ptrs, size, packetsize);
+    }
+  }
+
+  free(erased);
+  if (dm_ids != NULL) free(dm_ids);
+  if (decoding_matrix != NULL) free(decoding_matrix);
+
+  return 0;
+}
+
+static char **set_up_ptrs_for_scheduled_decoding(int k, int m, int *erasures, char **data_ptrs, char **coding_ptrs)
+{
+  int ddf, cdf;
+  int *erased;
+  char **ptrs;
+  int i, j, x;
+
+  ddf = 0;
+  cdf = 0;
+  for (i = 0; erasures[i] != -1; i++) {
+    if (erasures[i] < k) ddf++; else cdf++;
+  }
+  
+  erased = jerasure_erasures_to_erased(k, m, erasures);
+  if (erased == NULL) return NULL;
+
+  /* Set up ptrs.  It will be as follows:
+
+       - If data drive i has not failed, then ptrs[i] = data_ptrs[i].
+       - If data drive i has failed, then ptrs[i] = coding_ptrs[j], where j is the 
+            lowest unused non-failed coding drive.
+       - Elements k to k+ddf-1 are data_ptrs[] of the failed data drives.
+       - Elements k+ddf to k+ddf+cdf-1 are coding_ptrs[] of the failed data drives.
+
+       The array row_ids contains the ids of ptrs.
+       The array ind_to_row_ids contains the row_id of drive i.
+  
+       However, we're going to set row_ids and ind_to_row in a different procedure.
+   */
+         
+  ptrs = talloc(char *, k+m);
+  if (!ptrs) {
+    free(erased);
+    return NULL;
+  }
+
+  j = k;
+  x = k;
+  for (i = 0; i < k; i++) {
+    if (erased[i] == 0) {
+      ptrs[i] = data_ptrs[i];
+    } else {
+      while (erased[j]) j++;
+      ptrs[i] = coding_ptrs[j-k];
+      j++;
+      ptrs[x] = data_ptrs[i];
+      x++;
+    }
+  }
+  for (i = k; i < k+m; i++) {
+    if (erased[i]) {
+      ptrs[x] = coding_ptrs[i-k];
+      x++;
+    }
+  }
+  free(erased);
+  return ptrs;
+}
+
+static int set_up_ids_for_scheduled_decoding(int k, int m, int *erasures, int *row_ids, int *ind_to_row)
+{
+  int ddf, cdf;
+  int *erased;
+  int i, j, x;
+
+  ddf = 0;
+  cdf = 0;
+  for (i = 0; erasures[i] != -1; i++) {
+    if (erasures[i] < k) ddf++; else cdf++;
+  }
+  
+  erased = jerasure_erasures_to_erased(k, m, erasures);
+  if (erased == NULL) return -1;
+
+  /* See set_up_ptrs_for_scheduled_decoding for how these are set */
+
+  j = k;
+  x = k;
+  for (i = 0; i < k; i++) {
+    if (erased[i] == 0) {
+      row_ids[i] = i;
+      ind_to_row[i] = i;
+    } else {
+      while (erased[j]) j++;
+      row_ids[i] = j;
+      ind_to_row[j] = i;
+      j++;
+      row_ids[x] = i;
+      ind_to_row[i] = x;
+      x++;
+    }
+  }
+  for (i = k; i < k+m; i++) {
+    if (erased[i]) {
+      row_ids[x] = i;
+      ind_to_row[i] = x;
+      x++;
+    }
+  }
+  free(erased);
+  return 0;
+}
+
+static int **jerasure_generate_decoding_schedule(int k, int m, int w, int *bitmatrix, int *erasures, int smart)
+{
+  int i, j, x, drive, y, index, z;
+  int *decoding_matrix, *inverse, *real_decoding_matrix;
+  int *ptr;
+  int *row_ids;
+  int *ind_to_row;
+  int ddf, cdf;
+  int **schedule;
+  int *b1, *b2;
+ 
+ /* First, figure out the number of data drives that have failed, and the
+    number of coding drives that have failed: ddf and cdf */
+
+  ddf = 0;
+  cdf = 0;
+  for (i = 0; erasures[i] != -1; i++) {
+    if (erasures[i] < k) ddf++; else cdf++;
+  }
+  
+  row_ids = talloc(int, k+m);
+  if (!row_ids) return NULL;
+  ind_to_row = talloc(int, k+m);
+  if (!ind_to_row) {
+    free(row_ids);
+    return NULL;
+  }
+
+  if (set_up_ids_for_scheduled_decoding(k, m, erasures, row_ids, ind_to_row) < 0) {
+    free(row_ids);
+    free(ind_to_row);
+    return NULL;
+  }
+
+  /* Now, we're going to create one decoding matrix which is going to 
+     decode everything with one call.  The hope is that the scheduler
+     will do a good job.    This matrix has w*e rows, where e is the
+     number of erasures (ddf+cdf) */
+
+  real_decoding_matrix = talloc(int, k*w*(cdf+ddf)*w);
+  if (!real_decoding_matrix) {
+    free(row_ids);
+    free(ind_to_row);
+    return NULL;
+  }
+
+  /* First, if any data drives have failed, then initialize the first
+     ddf*w rows of the decoding matrix from the standard decoding
+     matrix inversion */
+
+  if (ddf > 0) {
+    
+    decoding_matrix = talloc(int, k*k*w*w);
+    if (!decoding_matrix) {
+      free(row_ids);
+      free(ind_to_row);
+      return NULL;
+    }
+    ptr = decoding_matrix;
+    for (i = 0; i < k; i++) {
+      if (row_ids[i] == i) {
+        bzero(ptr, k*w*w*sizeof(int));
+        for (x = 0; x < w; x++) {
+          ptr[x+i*w+x*k*w] = 1;
+        } 
+      } else {
+        memcpy(ptr, bitmatrix+k*w*w*(row_ids[i]-k), k*w*w*sizeof(int));
+      }
+      ptr += (k*w*w);
+    }
+    inverse = talloc(int, k*k*w*w);
+    if (!inverse) {
+      free(row_ids);
+      free(ind_to_row);
+      free(decoding_matrix);
+      return NULL;
+    }
+    jerasure_invert_bitmatrix(decoding_matrix, inverse, k*w);
+
+/*    printf("\nMatrix to invert\n");
+    jerasure_print_bitmatrix(decoding_matrix, k*w, k*w, w);
+    printf("\n");
+    printf("\nInverse\n");
+    jerasure_print_bitmatrix(inverse, k*w, k*w, w);
+    printf("\n"); */
+
+    free(decoding_matrix);
+    ptr = real_decoding_matrix;
+    for (i = 0; i < ddf; i++) {
+      memcpy(ptr, inverse+k*w*w*row_ids[k+i], sizeof(int)*k*w*w);
+      ptr += (k*w*w);
+    }
+    free(inverse);
+  } 
+
+  /* Next, here comes the hard part.  For each coding node that needs
+     to be decoded, you start by putting its rows of the distribution
+     matrix into the decoding matrix.  If there were no failed data
+     nodes, then you're done.  However, if there have been failed
+     data nodes, then you need to modify the columns that correspond
+     to the data nodes.  You do that by first zeroing them.  Then
+     whereever there is a one in the distribution matrix, you XOR
+     in the corresponding row from the failed data node's entry in
+     the decoding matrix.  The whole process kind of makes my head
+     spin, but it works.
+   */
+
+  for (x = 0; x < cdf; x++) {
+    drive = row_ids[x+ddf+k]-k;
+    ptr = real_decoding_matrix + k*w*w*(ddf+x);
+    memcpy(ptr, bitmatrix+drive*k*w*w, sizeof(int)*k*w*w);
+
+    for (i = 0; i < k; i++) {
+      if (row_ids[i] != i) {
+        for (j = 0; j < w; j++) {
+          bzero(ptr+j*k*w+i*w, sizeof(int)*w);
+        }
+      }  
+    }
+
+    /* There's the yucky part */
+
+    index = drive*k*w*w;
+    for (i = 0; i < k; i++) {
+      if (row_ids[i] != i) {
+        b1 = real_decoding_matrix+(ind_to_row[i]-k)*k*w*w;
+        for (j = 0; j < w; j++) {
+          b2 = ptr + j*k*w;
+          for (y = 0; y < w; y++) {
+            if (bitmatrix[index+j*k*w+i*w+y]) {
+              for (z = 0; z < k*w; z++) {
+                b2[z] = b2[z] ^ b1[z+y*k*w];
+              }
+            }
+          }
+        }
+      }  
+    }
+  }
+
+/*
+  printf("\n\nReal Decoding Matrix\n\n");
+  jerasure_print_bitmatrix(real_decoding_matrix, (ddf+cdf)*w, k*w, w);
+  printf("\n"); */
+  if (smart) {
+    schedule = jerasure_smart_bitmatrix_to_schedule(k, ddf+cdf, w, real_decoding_matrix);
+  } else {
+    schedule = jerasure_dumb_bitmatrix_to_schedule(k, ddf+cdf, w, real_decoding_matrix);
+  }
+  free(row_ids);
+  free(ind_to_row);
+  free(real_decoding_matrix);
+  return schedule;
+}
+
+int jerasure_schedule_decode_lazy(int k, int m, int w, int *bitmatrix, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize, 
+                            int smart)
+{
+  int i, tdone;
+  char **ptrs;
+  int **schedule;
+ 
+  ptrs = set_up_ptrs_for_scheduled_decoding(k, m, erasures, data_ptrs, coding_ptrs);
+  if (ptrs == NULL) return -1;
+
+  schedule = jerasure_generate_decoding_schedule(k, m, w, bitmatrix, erasures, smart);
+  if (schedule == NULL) {
+    free(ptrs);
+    return -1;
+  }
+
+  for (tdone = 0; tdone < size; tdone += packetsize*w) {
+  jerasure_do_scheduled_operations(ptrs, schedule, packetsize);
+    for (i = 0; i < k+m; i++) ptrs[i] += (packetsize*w);
+  }
+
+  jerasure_free_schedule(schedule);
+  free(ptrs);
+
+  return 0;
+}
+
+int jerasure_schedule_decode_cache(int k, int m, int w, int ***scache, int *erasures,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize)
+{
+  int i, tdone;
+  char **ptrs;
+  int **schedule;
+  int index;
+ 
+  if (erasures[1] == -1) {
+    index = erasures[0]*(k+m) + erasures[0];
+  } else if (erasures[2] == -1) {
+    index = erasures[0]*(k+m) + erasures[1];
+  } else {
+    return -1;
+  }
+
+  schedule = scache[index];
+
+  ptrs = set_up_ptrs_for_scheduled_decoding(k, m, erasures, data_ptrs, coding_ptrs);
+  if (ptrs == NULL) return -1;
+
+
+  for (tdone = 0; tdone < size; tdone += packetsize*w) {
+  jerasure_do_scheduled_operations(ptrs, schedule, packetsize);
+    for (i = 0; i < k+m; i++) ptrs[i] += (packetsize*w);
+  }
+
+  free(ptrs);
+
+  return 0;
+}
+
+/* This only works when m = 2 */
+
+int ***jerasure_generate_schedule_cache(int k, int m, int w, int *bitmatrix, int smart)
+{
+  int ***scache;
+  int erasures[3];
+  int e1, e2;
+ 
+  /* Ok -- this is yucky, but it's how I'm doing it.  You will make an index out
+     of erasures, which will be  e1*(k+m)+(e2).  If there is no e2, then e2 = e1.
+     Isn't that clever and confusing.  Sorry.
+
+     We're not going to worry about ordering -- in other words, the schedule for
+     e1,e2 will be the same as e2,e1.  They will have the same pointer -- the 
+     schedule will not be duplicated. */
+
+  if (m != 2) return NULL;
+
+  scache = talloc(int **, (k+m)*(k+m+1));
+  if (scache == NULL) return NULL;
+  
+  for (e1 = 0; e1 < k+m; e1++) {
+    erasures[0] = e1;
+    for (e2 = 0; e2 < e1; e2++) {
+      erasures[1] = e2;
+      erasures[2] = -1;
+      scache[e1*(k+m)+e2] = jerasure_generate_decoding_schedule(k, m, w, bitmatrix, erasures, smart);
+      scache[e2*(k+m)+e1] = scache[e1*(k+m)+e2];
+    }
+    erasures[1] = -1;
+    scache[e1*(k+m)+e1] = jerasure_generate_decoding_schedule(k, m, w, bitmatrix, erasures, smart);
+  }
+  return scache;
+
+}
+
+int jerasure_invert_bitmatrix(int *mat, int *inv, int rows)
+{
+  int cols, i, j, k;
+  int tmp;
+ 
+  cols = rows;
+
+  k = 0;
+  for (i = 0; i < rows; i++) {
+    for (j = 0; j < cols; j++) {
+      inv[k] = (i == j) ? 1 : 0;
+      k++;
+    }
+  }
+
+  /* First -- convert into upper triangular */
+
+  for (i = 0; i < cols; i++) {
+
+    /* Swap rows if we have a zero i,i element.  If we can't swap, then the 
+       matrix was not invertible */
+
+    if ((mat[i*cols+i]) == 0) { 
+      for (j = i+1; j < rows && (mat[j*cols+i]) == 0; j++) ;
+      if (j == rows) return -1;
+      for (k = 0; k < cols; k++) {
+        tmp = mat[i*cols+k]; mat[i*cols+k] = mat[j*cols+k]; mat[j*cols+k] = tmp;
+        tmp = inv[i*cols+k]; inv[i*cols+k] = inv[j*cols+k]; inv[j*cols+k] = tmp;
+      }
+    }
+ 
+    /* Now for each j>i, add A_ji*Ai to Aj */
+    for (j = i+1; j != rows; j++) {
+      if (mat[j*cols+i] != 0) {
+        for (k = 0; k < cols; k++) {
+          mat[j*cols+k] ^= mat[i*cols+k]; 
+          inv[j*cols+k] ^= inv[i*cols+k];
+        }
+      }
+    }
+  }
+
+  /* Now the matrix is upper triangular.  Start at the top and multiply down */
+
+  for (i = rows-1; i >= 0; i--) {
+    for (j = 0; j < i; j++) {
+      if (mat[j*cols+i]) {
+        for (k = 0; k < cols; k++) {
+          mat[j*cols+k] ^= mat[i*cols+k]; 
+          inv[j*cols+k] ^= inv[i*cols+k];
+        }
+      }
+    }
+  } 
+  return 0;
+}
+
+int jerasure_invertible_bitmatrix(int *mat, int rows)
+{
+  int cols, i, j, k;
+  int tmp;
+ 
+  cols = rows;
+
+  /* First -- convert into upper triangular */
+
+  for (i = 0; i < cols; i++) {
+
+    /* Swap rows if we have a zero i,i element.  If we can't swap, then the 
+       matrix was not invertible */
+
+    if ((mat[i*cols+i]) == 0) { 
+      for (j = i+1; j < rows && (mat[j*cols+i]) == 0; j++) ;
+      if (j == rows) return 0;
+      for (k = 0; k < cols; k++) {
+        tmp = mat[i*cols+k]; mat[i*cols+k] = mat[j*cols+k]; mat[j*cols+k] = tmp;
+      }
+    }
+ 
+    /* Now for each j>i, add A_ji*Ai to Aj */
+    for (j = i+1; j != rows; j++) {
+      if (mat[j*cols+i] != 0) {
+        for (k = 0; k < cols; k++) {
+          mat[j*cols+k] ^= mat[i*cols+k]; 
+        }
+      }
+    }
+  }
+  return 1;
+}
+
+  
+int *jerasure_matrix_multiply(int *m1, int *m2, int r1, int c1, int r2, int c2, int w)
+{
+  int *product, i, j, k;
+
+  product = (int *) malloc(sizeof(int)*r1*c2);
+  for (i = 0; i < r1*c2; i++) product[i] = 0;
+
+  for (i = 0; i < r1; i++) {
+    for (j = 0; j < c2; j++) {
+      for (k = 0; k < r2; k++) {
+        product[i*c2+j] ^= galois_single_multiply(m1[i*c1+k], m2[k*c2+j], w);
+      }
+    }
+  }
+  return product;
+}
+
+void jerasure_get_stats(double *fill_in)
+{
+  fill_in[0] = jerasure_total_xor_bytes;
+  fill_in[1] = jerasure_total_gf_bytes;
+  fill_in[2] = jerasure_total_memcpy_bytes;
+  jerasure_total_xor_bytes = 0;
+  jerasure_total_gf_bytes = 0;
+  jerasure_total_memcpy_bytes = 0;
+}
+
+void jerasure_do_scheduled_operations(char **ptrs, int **operations, int packetsize)
+{
+  char *sptr;
+  char *dptr;
+  int op;
+
+  for (op = 0; operations[op][0] >= 0; op++) {
+    sptr = ptrs[operations[op][0]] + operations[op][1]*packetsize;
+    dptr = ptrs[operations[op][2]] + operations[op][3]*packetsize;
+    if (operations[op][4]) {
+/*      printf("%d,%d %d,%d\n", operations[op][0], 
+      operations[op][1], 
+      operations[op][2], 
+      operations[op][3]); 
+      printf("xor(0x%x, 0x%x -> 0x%x, %d)\n", sptr, dptr, dptr, packetsize); */
+      galois_region_xor(sptr, dptr, packetsize);
+      jerasure_total_xor_bytes += packetsize;
+    } else {
+/*      printf("memcpy(0x%x <- 0x%x)\n", dptr, sptr); */
+      memcpy(dptr, sptr, packetsize);
+      jerasure_total_memcpy_bytes += packetsize;
+    }
+  }  
+}
+
+void jerasure_schedule_encode(int k, int m, int w, int **schedule,
+                                   char **data_ptrs, char **coding_ptrs, int size, int packetsize)
+{
+  char **ptr_copy;
+  int i, tdone;
+
+  ptr_copy = talloc(char *, (k+m));
+  for (i = 0; i < k; i++) ptr_copy[i] = data_ptrs[i];
+  for (i = 0; i < m; i++) ptr_copy[i+k] = coding_ptrs[i];
+  for (tdone = 0; tdone < size; tdone += packetsize*w) {
+    jerasure_do_scheduled_operations(ptr_copy, schedule, packetsize);
+    for (i = 0; i < k+m; i++) ptr_copy[i] += (packetsize*w);
+  }
+  free(ptr_copy);
+}
+    
+int **jerasure_dumb_bitmatrix_to_schedule(int k, int m, int w, int *bitmatrix)
+{
+  int **operations;
+  int op;
+  int index, optodo, i, j;
+
+  operations = talloc(int *, k*m*w*w+1);
+  if (!operations) return NULL;
+  op = 0;
+  
+  index = 0;
+  for (i = 0; i < m*w; i++) {
+    optodo = 0;
+    for (j = 0; j < k*w; j++) {
+      if (bitmatrix[index]) {
+        operations[op] = talloc(int, 5);
+       if (!operations[op]) {
+         // -ENOMEM
+          goto error;
+        }
+        operations[op][4] = optodo;
+        operations[op][0] = j/w;
+        operations[op][1] = j%w;
+        operations[op][2] = k+i/w;
+        operations[op][3] = i%w;
+        optodo = 1;
+        op++;
+        
+      }
+      index++;
+    }
+  }
+  operations[op] = talloc(int, 5);
+  if (!operations[op]) {
+    // -ENOMEM
+    goto error;
+  }
+  operations[op][0] = -1;
+  return operations;
+
+error:
+  for (i = 0; i <= op; i++) {
+    free(operations[op]);
+  }
+  free(operations);
+  return NULL;
+}
+
+int **jerasure_smart_bitmatrix_to_schedule(int k, int m, int w, int *bitmatrix)
+{
+  int **operations;
+  int op;
+  int i, j;
+  int *diff, *from, *b1, *flink, *blink;
+  int *ptr, no, row;
+  int optodo;
+  int bestrow = 0, bestdiff, top;
+
+/*   printf("Scheduling:\n\n");
+  jerasure_print_bitmatrix(bitmatrix, m*w, k*w, w); */
+
+  operations = talloc(int *, k*m*w*w+1);
+  if (!operations) return NULL;
+  op = 0;
+  
+  diff = talloc(int, m*w);
+  if (!diff) {
+    free(operations);
+    return NULL;
+  }
+  from = talloc(int, m*w);
+  if (!from) {
+    free(operations);
+    free(diff);
+    return NULL;
+  }
+  flink = talloc(int, m*w);
+  if (!flink) {
+    free(operations);
+    free(diff);
+    free(from);
+    return NULL;
+  }
+  blink = talloc(int, m*w);
+  if (!blink) {
+    free(operations);
+    free(diff);
+    free(from);
+    free(flink);
+    return NULL;
+  }
+
+  ptr = bitmatrix;
+
+  bestdiff = k*w+1;
+  top = 0;
+  for (i = 0; i < m*w; i++) {
+    no = 0;
+    for (j = 0; j < k*w; j++) {
+      no += *ptr;
+      ptr++;
+    }
+    diff[i] = no;
+    from[i] = -1;
+    flink[i] = i+1;
+    blink[i] = i-1;
+    if (no < bestdiff) {
+      bestdiff = no;
+      bestrow = i;
+    }
+  }
+
+  flink[m*w-1] = -1;
+  
+  while (top != -1) {
+    row = bestrow;
+    /* printf("Doing row %d - %d from %d\n", row, diff[row], from[row]);  */
+
+    if (blink[row] == -1) {
+      top = flink[row];
+      if (top != -1) blink[top] = -1;
+    } else {
+      flink[blink[row]] = flink[row];
+      if (flink[row] != -1) {
+        blink[flink[row]] = blink[row];
+      }
+    }
+
+    ptr = bitmatrix + row*k*w;
+    if (from[row] == -1) {
+      optodo = 0;
+      for (j = 0; j < k*w; j++) {
+        if (ptr[j]) {
+          operations[op] = talloc(int, 5);
+          if (!operations[op]) goto error;
+          operations[op][4] = optodo;
+          operations[op][0] = j/w;
+          operations[op][1] = j%w;
+          operations[op][2] = k+row/w;
+          operations[op][3] = row%w;
+          optodo = 1;
+          op++;
+        }
+      }
+    } else {
+      operations[op] = talloc(int, 5);
+      if (!operations[op]) goto error;
+      operations[op][4] = 0;
+      operations[op][0] = k+from[row]/w;
+      operations[op][1] = from[row]%w;
+      operations[op][2] = k+row/w;
+      operations[op][3] = row%w;
+      op++;
+      b1 = bitmatrix + from[row]*k*w;
+      for (j = 0; j < k*w; j++) {
+        if (ptr[j] ^ b1[j]) {
+          operations[op] = talloc(int, 5);
+          if (!operations[op]) goto error;
+          operations[op][4] = 1;
+          operations[op][0] = j/w;
+          operations[op][1] = j%w;
+          operations[op][2] = k+row/w;
+          operations[op][3] = row%w;
+          optodo = 1;
+          op++;
+        }
+      }
+    }
+    bestdiff = k*w+1;
+    for (i = top; i != -1; i = flink[i]) {
+      no = 1;
+      b1 = bitmatrix + i*k*w;
+      for (j = 0; j < k*w; j++) no += (ptr[j] ^ b1[j]);
+      if (no < diff[i]) {
+        from[i] = row;
+        diff[i] = no;
+      }
+      if (diff[i] < bestdiff) {
+        bestdiff = diff[i];
+        bestrow = i;
+      }
+    }
+  }
+  
+  operations[op] = talloc(int, 5);
+  if (!operations[op]) goto error;
+  operations[op][0] = -1;
+  free(from);
+  free(diff);
+  free(blink);
+  free(flink);
+
+  return operations;
+
+error:
+  for (i = 0; i <= op; i++) {
+    free(operations[op]);
+  }
+  free(operations);
+  free(from);
+  free(diff);
+  free(blink);
+  free(flink);
+  return NULL;
+}
+
+void jerasure_bitmatrix_encode(int k, int m, int w, int *bitmatrix,
+                            char **data_ptrs, char **coding_ptrs, int size, int packetsize)
+{
+  int i;
+
+  if (packetsize%sizeof(long) != 0) {
+    fprintf(stderr, "jerasure_bitmatrix_encode - packetsize(%d) %c sizeof(long) != 0\n", packetsize, '%');
+    exit(1);
+  }
+  if (size%(packetsize*w) != 0) {
+    fprintf(stderr, "jerasure_bitmatrix_encode - size(%d) %c (packetsize(%d)*w(%d))) != 0\n", 
+         size, '%', packetsize, w);
+    exit(1);
+  }
+
+  for (i = 0; i < m; i++) {
+    jerasure_bitmatrix_dotprod(k, w, bitmatrix+i*k*w*w, NULL, k+i, data_ptrs, coding_ptrs, size, packetsize);
+  }
+}
+
+/*
+ * Exported function for use by autoconf to perform quick 
+ * spot-check.
+ */
+int jerasure_autoconf_test()
+{
+  int x = galois_single_multiply(1, 2, 8);
+  if (x != 2) {
+    return -1;
+  }
+  return 0;
+}
+

diff --git a/src/liberation.c b/src/liberation.c
new file mode 100644 (file)
index 0000000..11a1c4f
--- /dev/null
+++ b/src/liberation.c
@@ -0,0 +1,262 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "galois.h"
+#include "jerasure.h"
+#include "liberation.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+int *liberation_coding_bitmatrix(int k, int w)
+{
+  int *matrix, i, j, index;
+
+  if (k > w) return NULL;
+  matrix = talloc(int, 2*k*w*w);
+  if (matrix == NULL) return NULL;
+  bzero(matrix, sizeof(int)*2*k*w*w);
+  
+  /* Set up identity matrices */
+
+  for(i = 0; i < w; i++) {
+    index = i*k*w+i;
+    for (j = 0; j < k; j++) {
+      matrix[index] = 1;
+      index += w;
+    }
+  }
+
+  /* Set up liberation matrices */
+
+  for (j = 0; j < k; j++) {
+    index = k*w*w+j*w;
+    for (i = 0; i < w; i++) {
+      matrix[index+(j+i)%w] = 1;
+      index += (k*w);
+    }
+    if (j > 0) {
+      i = (j*((w-1)/2))%w;
+      matrix[k*w*w+j*w+i*k*w+(i+j-1)%w] = 1;
+    }
+  }
+  return matrix;
+}
+  
+
+int *liber8tion_coding_bitmatrix(int k)
+{
+  int *matrix, i, j, index;
+  int w;
+
+  w = 8;
+  if (k > w) return NULL;
+  matrix = talloc(int, 2*k*w*w);
+  if (matrix == NULL) return NULL;
+  bzero(matrix, sizeof(int)*2*k*w*w);
+  
+  /* Set up identity matrices */
+
+  for(i = 0; i < w; i++) {
+    index = i*k*w+i;
+    for (j = 0; j < k; j++) {
+      matrix[index] = 1;
+      index += w;
+    }
+  }
+
+  /* Set up liber8tion matrices */
+
+  index = k*w*w;
+
+  if (k == 0) return matrix;
+  matrix[index+0*k*w+0*w+0] = 1;
+  matrix[index+1*k*w+0*w+1] = 1;
+  matrix[index+2*k*w+0*w+2] = 1;
+  matrix[index+3*k*w+0*w+3] = 1;
+  matrix[index+4*k*w+0*w+4] = 1;
+  matrix[index+5*k*w+0*w+5] = 1;
+  matrix[index+6*k*w+0*w+6] = 1;
+  matrix[index+7*k*w+0*w+7] = 1;
+
+  if (k == 1) return matrix;
+  matrix[index+0*k*w+1*w+7] = 1;
+  matrix[index+1*k*w+1*w+3] = 1;
+  matrix[index+2*k*w+1*w+0] = 1;
+  matrix[index+3*k*w+1*w+2] = 1;
+  matrix[index+4*k*w+1*w+6] = 1;
+  matrix[index+5*k*w+1*w+1] = 1;
+  matrix[index+6*k*w+1*w+5] = 1;
+  matrix[index+7*k*w+1*w+4] = 1;
+  matrix[index+4*k*w+1*w+7] = 1;
+
+  if (k == 2) return matrix;
+  matrix[index+0*k*w+2*w+6] = 1;
+  matrix[index+1*k*w+2*w+2] = 1;
+  matrix[index+2*k*w+2*w+4] = 1;
+  matrix[index+3*k*w+2*w+0] = 1;
+  matrix[index+4*k*w+2*w+7] = 1;
+  matrix[index+5*k*w+2*w+3] = 1;
+  matrix[index+6*k*w+2*w+1] = 1;
+  matrix[index+7*k*w+2*w+5] = 1;
+  matrix[index+1*k*w+2*w+3] = 1;
+
+  if (k == 3) return matrix;
+  matrix[index+0*k*w+3*w+2] = 1;
+  matrix[index+1*k*w+3*w+5] = 1;
+  matrix[index+2*k*w+3*w+7] = 1;
+  matrix[index+3*k*w+3*w+6] = 1;
+  matrix[index+4*k*w+3*w+0] = 1;
+  matrix[index+5*k*w+3*w+3] = 1;
+  matrix[index+6*k*w+3*w+4] = 1;
+  matrix[index+7*k*w+3*w+1] = 1;
+  matrix[index+5*k*w+3*w+4] = 1;
+
+  if (k == 4) return matrix;
+  matrix[index+0*k*w+4*w+5] = 1;
+  matrix[index+1*k*w+4*w+6] = 1;
+  matrix[index+2*k*w+4*w+1] = 1;
+  matrix[index+3*k*w+4*w+7] = 1;
+  matrix[index+4*k*w+4*w+2] = 1;
+  matrix[index+5*k*w+4*w+4] = 1;
+  matrix[index+6*k*w+4*w+3] = 1;
+  matrix[index+7*k*w+4*w+0] = 1;
+  matrix[index+2*k*w+4*w+0] = 1;
+
+  if (k == 5) return matrix;
+  matrix[index+0*k*w+5*w+1] = 1;
+  matrix[index+1*k*w+5*w+2] = 1;
+  matrix[index+2*k*w+5*w+3] = 1;
+  matrix[index+3*k*w+5*w+4] = 1;
+  matrix[index+4*k*w+5*w+5] = 1;
+  matrix[index+5*k*w+5*w+6] = 1;
+  matrix[index+6*k*w+5*w+7] = 1;
+  matrix[index+7*k*w+5*w+0] = 1;
+  matrix[index+7*k*w+5*w+2] = 1;
+
+  if (k == 6) return matrix;
+  matrix[index+0*k*w+6*w+3] = 1;
+  matrix[index+1*k*w+6*w+0] = 1;
+  matrix[index+2*k*w+6*w+6] = 1;
+  matrix[index+3*k*w+6*w+5] = 1;
+  matrix[index+4*k*w+6*w+1] = 1;
+  matrix[index+5*k*w+6*w+7] = 1;
+  matrix[index+6*k*w+6*w+4] = 1;
+  matrix[index+7*k*w+6*w+2] = 1;
+  matrix[index+6*k*w+6*w+5] = 1;
+
+  if (k == 7) return matrix;
+  matrix[index+0*k*w+7*w+4] = 1;
+  matrix[index+1*k*w+7*w+7] = 1;
+  matrix[index+2*k*w+7*w+1] = 1;
+  matrix[index+3*k*w+7*w+5] = 1;
+  matrix[index+4*k*w+7*w+3] = 1;
+  matrix[index+5*k*w+7*w+2] = 1;
+  matrix[index+6*k*w+7*w+0] = 1;
+  matrix[index+7*k*w+7*w+6] = 1;
+  matrix[index+3*k*w+7*w+1] = 1;
+
+  return matrix;
+}
+  
+int *blaum_roth_coding_bitmatrix(int k, int w)
+{
+  int *matrix, i, j, index, l, m, p;
+
+  if (k > w) return NULL ;
+
+  matrix = talloc(int, 2*k*w*w);
+  if (matrix == NULL) return NULL;
+  bzero(matrix, sizeof(int)*2*k*w*w);
+  
+  /* Set up identity matrices */
+
+  for(i = 0; i < w; i++) {
+    index = i*k*w+i;
+    for (j = 0; j < k; j++) {
+      matrix[index] = 1;
+      index += w;
+    }
+  }
+
+  /* Set up blaum_roth matrices -- Ignore identity */
+
+  p = w+1;
+  for (j = 0; j < k; j++) {
+    index = k*w*w+j*w;
+    if (j == 0) {
+      for (l = 0; l < w; l++) {
+        matrix[index+l] = 1;
+        index += k*w;
+      }
+    } else {
+      i = j;
+      for (l = 1; l <= w; l++) {
+        if (l != p-i) {
+          m = l+i;
+          if (m >= p) m -= p;
+          m--;
+          matrix[index+m] = 1;
+        } else {
+          matrix[index+i-1] = 1;
+          if (i%2 == 0) {
+            m = i/2;
+          } else {
+            m = (p/2) + 1 + (i/2);
+          }
+          m--;
+          matrix[index+m] = 1;
+        }
+        index += k*w;
+      }
+    }
+  }
+
+  return matrix;
+}

diff --git a/src/reed_sol.c b/src/reed_sol.c
new file mode 100644 (file)
index 0000000..c0dfe83
--- /dev/null
+++ b/src/reed_sol.c
@@ -0,0 +1,301 @@
+/* *
+ * Copyright (c) 2014, James S. Plank and Kevin Greenan
+ * All rights reserved.
+ *
+ * Jerasure - A C/C++ Library for a Variety of Reed-Solomon and RAID-6 Erasure
+ * Coding Techniques
+ *
+ * Revision 2.0: Galois Field backend now links to GF-Complete
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ *  - Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ *  - 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.
+ *
+ *  - Neither the name of the University of Tennessee nor the names of its
+ *    contributors may be used to endorse or promote products derived
+ *    from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "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 COPYRIGHT
+ * HOLDER OR CONTRIBUTORS 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.
+ */
+
+/* Jerasure's authors:
+
+   Revision 2.x - 2014: James S. Plank and Kevin M. Greenan
+   Revision 1.2 - 2008: James S. Plank, Scott Simmerman and Catherine D. Schuman.
+   Revision 1.0 - 2007: James S. Plank
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include <gf_complete.h>
+#include "galois.h"
+#include "jerasure.h"
+#include "reed_sol.h"
+
+#define talloc(type, num) (type *) malloc(sizeof(type)*(num))
+
+int *reed_sol_r6_coding_matrix(int k, int w)
+{
+  int *matrix;
+  int i, tmp;
+
+  if (w != 8 && w != 16 && w != 32) return NULL;
+
+  matrix = talloc(int, 2*k);
+  if (matrix == NULL) return NULL;
+
+  for (i = 0; i < k; i++) matrix[i] = 1;
+  matrix[k] = 1;
+  tmp = 1;
+  for (i = 1; i < k; i++) {
+    tmp = galois_single_multiply(tmp, 2, w);
+    matrix[k+i] = tmp;
+  }
+  return matrix;
+}
+
+int *reed_sol_vandermonde_coding_matrix(int k, int m, int w)
+{
+  int i, j;
+  int *vdm, *dist;
+
+  vdm = reed_sol_big_vandermonde_distribution_matrix(k+m, k, w);
+  if (vdm == NULL) return NULL;
+  dist = talloc(int, m*k);
+  if (dist == NULL) {
+    free(vdm);
+    return NULL;
+  }
+
+  i = k*k;
+  for (j = 0; j < m*k; j++) {
+    dist[j] = vdm[i];
+    i++;
+  }
+  free(vdm);
+  return dist;
+}
+
+static int prim08 = -1;
+static gf_t GF08;
+
+void reed_sol_galois_w08_region_multby_2(char *region, int nbytes)
+{
+  if (prim08 == -1) {
+    prim08 = galois_single_multiply((1 << 7), 2, 8);
+    if (!gf_init_hard(&GF08, 8, GF_MULT_BYTWO_b, GF_REGION_DEFAULT, GF_DIVIDE_DEFAULT,
+                      prim08, 0, 0, NULL, NULL)) {
+      fprintf(stderr, "Error: Can't initialize the GF for reed_sol_galois_w08_region_multby_2\n");
+      exit(1);
+    }
+  }
+  GF08.multiply_region.w32(&GF08, region, region, 2, nbytes, 0);
+}
+
+static int prim16 = -1;
+static gf_t GF16;
+
+void reed_sol_galois_w16_region_multby_2(char *region, int nbytes)
+{
+  if (prim16 == -1) {
+    prim16 = galois_single_multiply((1 << 15), 2, 16);
+    if (!gf_init_hard(&GF16, 16, GF_MULT_BYTWO_b, GF_REGION_DEFAULT, GF_DIVIDE_DEFAULT,
+                      prim16, 0, 0, NULL, NULL)) {
+      fprintf(stderr, "Error: Can't initialize the GF for reed_sol_galois_w16_region_multby_2\n");
+      exit(1);
+    }
+  }
+  GF16.multiply_region.w32(&GF16, region, region, 2, nbytes, 0);
+}
+
+static int prim32 = -1;
+static gf_t GF32;
+
+void reed_sol_galois_w32_region_multby_2(char *region, int nbytes)
+{
+  if (prim32 == -1) {
+    prim32 = galois_single_multiply((1 << 31), 2, 32);
+    if (!gf_init_hard(&GF32, 32, GF_MULT_BYTWO_b, GF_REGION_DEFAULT, GF_DIVIDE_DEFAULT,
+                      prim32, 0, 0, NULL, NULL)) {
+      fprintf(stderr, "Error: Can't initialize the GF for reed_sol_galois_w32_region_multby_2\n");
+      exit(1);
+    }
+  }
+  GF32.multiply_region.w32(&GF32, region, region, 2, nbytes, 0);
+}
+
+int reed_sol_r6_encode(int k, int w, char **data_ptrs, char **coding_ptrs, int size)
+{
+  int i;
+
+  /* First, put the XOR into coding region 0 */
+
+  memcpy(coding_ptrs[0], data_ptrs[0], size);
+
+  for (i = 1; i < k; i++) galois_region_xor(data_ptrs[i], coding_ptrs[0], size);
+
+  /* Next, put the sum of (2^j)*Dj into coding region 1 */
+
+  memcpy(coding_ptrs[1], data_ptrs[k-1], size);
+
+  for (i = k-2; i >= 0; i--) {
+    switch (w) {
+      case 8:  reed_sol_galois_w08_region_multby_2(coding_ptrs[1], size); break;
+      case 16: reed_sol_galois_w16_region_multby_2(coding_ptrs[1], size); break;
+      case 32: reed_sol_galois_w32_region_multby_2(coding_ptrs[1], size); break;
+      default: return 0;
+    }
+
+    galois_region_xor(data_ptrs[i], coding_ptrs[1], size);
+  }
+  return 1;
+}
+
+int *reed_sol_extended_vandermonde_matrix(int rows, int cols, int w)
+{
+  int *vdm;
+  int i, j, k;
+
+  if (w < 30 && (1 << w) < rows) return NULL;
+  if (w < 30 && (1 << w) < cols) return NULL;
+
+  vdm = talloc(int, rows*cols);
+  if (vdm == NULL) { return NULL; }
+  
+  vdm[0] = 1;
+  for (j = 1; j < cols; j++) vdm[j] = 0;
+  if (rows == 1) return vdm;
+
+  i=(rows-1)*cols;
+  for (j = 0; j < cols-1; j++) vdm[i+j] = 0;
+  vdm[i+j] = 1;
+  if (rows == 2) return vdm;
+
+  for (i = 1; i < rows-1; i++) {
+    k = 1;
+    for (j = 0; j < cols; j++) {
+      vdm[i*cols+j] = k;
+      k = galois_single_multiply(k, i, w);
+    }
+  }
+  return vdm;
+}
+
+int *reed_sol_big_vandermonde_distribution_matrix(int rows, int cols, int w)
+{
+  int *dist;
+  int i, j, k;
+  int sindex, srindex, siindex, tmp;
+
+  if (cols >= rows) return NULL;
+  
+  dist = reed_sol_extended_vandermonde_matrix(rows, cols, w);
+  if (dist == NULL) return NULL;
+
+  sindex = 0;
+  for (i = 1; i < cols; i++) {
+    sindex += cols;
+
+    /* Find an appropriate row -- where i,i != 0 */
+    srindex = sindex+i;
+    for (j = i; j < rows && dist[srindex] == 0; j++) srindex += cols;
+    if (j >= rows) {   /* This should never happen if rows/w are correct */
+      fprintf(stderr, "reed_sol_big_vandermonde_distribution_matrix(%d,%d,%d) - couldn't make matrix\n", 
+             rows, cols, w);
+      exit(1);
+    }
+ 
+    /* If necessary, swap rows */
+    if (j != i) {
+      srindex -= i;
+      for (k = 0; k < cols; k++) {
+        tmp = dist[srindex+k];
+        dist[srindex+k] = dist[sindex+k];
+        dist[sindex+k] = tmp;
+      }
+    }
+  
+    /* If Element i,i is not equal to 1, multiply the column by 1/i */
+
+    if (dist[sindex+i] != 1) {
+      tmp = galois_single_divide(1, dist[sindex+i], w);
+      srindex = i;
+      for (j = 0; j < rows; j++) {
+        dist[srindex] = galois_single_multiply(tmp, dist[srindex], w);
+        srindex += cols;
+      }
+    }
+ 
+    /* Now, for each element in row i that is not in column 1, you need
+       to make it zero.  Suppose that this is column j, and the element
+       at i,j = e.  Then you want to replace all of column j with 
+       (col-j + col-i*e).   Note, that in row i, col-i = 1 and col-j = e.
+       So (e + 1e) = 0, which is indeed what we want. */
+
+    for (j = 0; j < cols; j++) {
+      tmp = dist[sindex+j];
+      if (j != i && tmp != 0) {
+        srindex = j;
+        siindex = i;
+        for (k = 0; k < rows; k++) {
+          dist[srindex] = dist[srindex] ^ galois_single_multiply(tmp, dist[siindex], w);
+          srindex += cols;
+          siindex += cols;
+        }
+      }
+    }
+  }
+  /* We desire to have row k be all ones.  To do that, multiply
+     the entire column j by 1/dist[k,j].  Then row j by 1/dist[j,j]. */
+
+  sindex = cols*cols;
+  for (j = 0; j < cols; j++) {
+    tmp = dist[sindex];
+    if (tmp != 1) { 
+      tmp = galois_single_divide(1, tmp, w);
+      srindex = sindex;
+      for (i = cols; i < rows; i++) {
+        dist[srindex] = galois_single_multiply(tmp, dist[srindex], w);
+        srindex += cols;
+      }
+    }
+    sindex++;
+  }
+
+  /* Finally, we'd like the first column of each row to be all ones.  To
+     do that, we multiply the row by the inverse of the first element. */
+
+  sindex = cols*(cols+1);
+  for (i = cols+1; i < rows; i++) {
+    tmp = dist[sindex];
+    if (tmp != 1) { 
+      tmp = galois_single_divide(1, tmp, w);
+      for (j = 0; j < cols; j++) dist[sindex+j] = galois_single_multiply(dist[sindex+j], tmp, w);
+    }
+    sindex += cols;
+  }
+
+  return dist;
+}
+

diff --git a/src/timing.c b/src/timing.c
new file mode 100644 (file)
index 0000000..315870a
--- /dev/null
+++ b/src/timing.c
@@ -0,0 +1,63 @@
+// Timing measurement utilities implementation.
+
+#include "timing.h"
+#include <stddef.h>
+
+void
+timing_set(
+  struct timing * t)
+{
+#ifdef USE_CLOCK
+  t->clock = clock();
+#else
+  gettimeofday(&t->tv, NULL);
+#endif
+}
+
+double
+timing_get(
+  struct timing * t)
+{
+#ifdef USE_CLOCK
+  // The clock_t type is an "arithmetic type", which could be
+  // integral, double, long double, or others.
+  //
+  // Add 0.0 to make it a double or long double, then divide (in
+  // double or long double), then convert to double for our purposes.
+  return (double) ((t->clock + 0.0) / CLOCKS_PER_SEC);
+#else
+  return (double) t->tv.tv_sec + ((double) t->tv.tv_usec) / 1000000.0;
+#endif
+}
+
+double
+timing_now()
+{
+#ifdef USE_CLOCK
+  return (double) ((clock() + 0.0) / CLOCKS_PER_SEC);
+#else
+  struct timeval tv;
+  gettimeofday(&tv, NULL);
+  return (double) tv.tv_sec + ((double) tv.tv_usec) / 1000000.0;
+#endif
+}
+
+double
+timing_delta(
+  struct timing * t1,
+  struct timing * t2)
+{
+#ifdef USE_CLOCK
+  // The clock_t type is an "arithmetic type", which could be
+  // integral, double, long double, or others.
+  //
+  // Subtract first, resulting in another clock_t, then add 0.0 to
+  // make it a double or long double, then divide (in double or long
+  // double), then convert to double for our purposes.
+  return (double) (((t2->clock - t1->clock) + 0.0) / CLOCKS_PER_SEC);
+#else
+  double const d2 = (double) t2->tv.tv_sec + ((double) t2->tv.tv_usec) / 1000000.0;
+  double const d1 = (double) t1->tv.tv_sec + ((double) t1->tv.tv_usec) / 1000000.0;
+  return d2 - d1;
+#endif
+}