X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=96f945cf0efd8f91a425997222536638d75e1ef1;hp=0cc8d9b8317012885e665c15767d51b9874a8976;hb=25b3132348e1f5964f4ec4bc4e1226f21d14bb3f;hpb=f133b2f3b3a6ccaedeced7420b68a0ae5918cf22

diff --git a/main.c b/main.c
index 0cc8d9b..96f945c 100644
--- a/main.c
+++ b/main.c
@@ -5,7 +5,13 @@
  *
  * Invoke as   ./main n m
  *
- * The algorithm is faster if the arguments are ordered so that n > m.
+ * The arguments must be ordered so that n > m:
+ *   n is the number of (more, shorter) input matches of length m
+ *   m is the number of (fewer, longer) output matches of length n
+ *
+ * Options:
+ *  -j<jobs>     run in parallel on <jobs> cores
+ *  -b<best>     search only for better than <best>
  */
 
 /*
@@ -22,6 +28,10 @@
  * GNU General Public License for more details.
  */
 
+#define _GNU_SOURCE
+
+#include <publib.h>
+
 #include <stdio.h>
 #include <stdint.h>
 #include <stdlib.h>
@@ -30,10 +40,18 @@
 #include <unistd.h>
 #include <stdbool.h>
 #include <inttypes.h>
+#include <math.h>
+#include <sys/types.h>
+#include <sys/wait.h>
+#include <sys/uio.h>
+#include <sys/fcntl.h>
 
-#include <publib.h>
 #include <glpk.h>
 
+#ifndef VERSION
+#define VERSION "(unknown-version)"
+#endif
+
 /*
  * Algorithm.
  *
@@ -46,7 +64,8 @@
  *
  * We search all possible adjacency matrices, and for each one we run
  * GLPK's simplex solver.  We represent the adjacency matrix as an
- * array of bitmaps.
+ * array of bitmaps: one word per input stick, with one bit per output
+ * stick.
  *
  * However, there are a couple of wrinkles:
  *
@@ -64,11 +83,18 @@
  * nondecreasing in array order.
  *
  * Once we have a solution, we also avoid considering any candidate
- * which involves dividing one of the output sticks into so many
+ * which involves dividing one of the input sticks into so many
  * fragment that the smallest fragment would necessarily be no bigger
  * than our best solution.  That is, we reject candidates where any of
  * the hamming weights of the adjacency bitmap words are too large.
  *
+ * We further winnow the set of possible adjacency matrices, by
+ * ensuring the same bit is not set in too many entries of adjmatrix
+ * (ie, as above, only considering output sticks); and by ensuring
+ * that it is not set in too few: each output stick must consist
+ * of at least two fragments since the output sticks are longer than
+ * the input ones.
+ *
  * And, we want to do the search in order of increasing maximum
  * hamming weight.  This is because in practice optimal solutions tend
  * to have low hamming weight, and having found a reasonable solution
@@ -79,6 +105,8 @@
 typedef uint32_t AdjWord;
 #define PRADJ "08"PRIx32
 
+#define FOR_BITS(j,m) for (j=0, j##bit=1; j < (m); j++, j##bit<<=1)
+
 static int n, m, maxhamweight;
 static AdjWord *adjmatrix;
 static AdjWord adjall;
@@ -87,9 +115,272 @@ static double best;
 static glp_prob *best_prob;
 static AdjWord *best_adjmatrix;
 
+static int n_max_frags=INT_MAX, m_max_frags=INT_MAX;
+static int *weight;
+
 static unsigned printcounter;
 
-static int ncpus = 1;
+static void iterate(void);
+static void iterate_recurse(int i, AdjWord min);
+static bool preconsider_ok(int nwords, bool doprint);
+static bool maxhamweight_ok(void);
+static void optimise(bool doprint);
+
+static void progress_eol(void) {
+  fprintf(stderr,"        \r");
+  fflush(stderr);
+}
+
+static void set_best(double new_best) {
+  best = new_best;
+  /*
+   * When computing n_max_frags, we want to set a value that will skip
+   * anything that won't provide strictly better solutions.  So we
+   * want
+   *             frags <      n / best
+   *                        _          _
+   *   <=>       frags <   |  n / best  |
+   *                        _          _
+   *   <=>       frags <=  |  n / best  | - 1
+   *
+   * But best values from glpk are slightly approximate, so we
+   * subtract a fudge factor from our target.
+   */
+  double near_best = best * 0.98 - 0.02;
+  if (near_best > 0) {
+    n_max_frags = ceil(n / near_best) - 1;
+    m_max_frags = ceil(m / near_best) - 1;
+  }
+}
+
+/*----- multicore support -----*/
+
+/*
+ * Multicore protocol
+ *
+ * We fork into:
+ *   - master (parent)
+ *   - generator
+ *   - ncpu workers
+ *
+ * ipc facilities:
+ *   - one pipe ("work") from generator to workers
+ *   - ever-extending file ("bus") containing new "best" values
+ *   - one file for each worker giving maxhamweight and adjmatrix for best
+ *
+ * generator runs iterate_recurse to a certain depth and writes the
+ * candidates to a pipe
+ *
+ * workers read candidates from the pipe and resume iterate_recurse
+ * halfway through the recursion
+ *
+ * whenever a worker does a doprint, it checks the bus for new best
+ * value; actual best values are appended
+ *
+ * master waits for generator and all workers to finish and then
+ * runs optimise() for each worker's best, then prints
+ */ 
+
+static int ncpus = 0, multicore_iteration_boundary = INT_MAX;
+
+static int mc_bus, mc_work[2];
+static off_t mc_bus_read;
+
+typedef struct {
+  int w;
+  FILE *results;
+  pid_t pid;
+} Worker;
+static Worker *mc_us;
+static bool mc_am_generator;
+
+static void multicore_check_for_new_best(void);
+
+#define MAX_NIOVS 4
+static AdjWord mc_iter_min;
+static int mc_niovs;
+static size_t mc_iovlen;
+static struct iovec mc_iov[MAX_NIOVS];
+
+#define IOV0 (mc_niovs = mc_iovlen = 0)
+
+#define IOV(obj, count) ({				\
+    assert(mc_niovs < MAX_NIOVS);			\
+    mc_iov[mc_niovs].iov_base = &(obj);			\
+    mc_iov[mc_niovs].iov_len = sizeof(obj) * (count);	\
+    mc_iovlen += mc_iov[mc_niovs].iov_len;              \
+    mc_niovs++;						\
+  })
+
+static void mc_rwvsetup_outer(void) {
+  IOV0;
+  IOV(maxhamweight, 1);
+  IOV(mc_iter_min, 1);
+  IOV(*adjmatrix, multicore_iteration_boundary);
+  IOV(*weight, m);
+}
+
+static void mc_rwvsetup_full(void) {
+  IOV0;
+  IOV(*adjmatrix, n);
+}
+
+static void vlprintf(const char *fmt, va_list al) {
+  vfprintf(stderr,fmt,al);
+  progress_eol();
+}
+
+static void LPRINTF(const char *fmt, ...) {
+  va_list al;
+  va_start(al,fmt);
+  vlprintf(fmt,al);
+  va_end(al);
+}
+
+static void mc_awaitpid(int wnum, pid_t pid) {
+  LPRINTF("master awaiting %2d [%ld]",wnum,(long)pid);
+  int status;
+  pid_t got = waitpid(pid, &status, 0);
+  assert(got == pid);
+  if (status) {
+    fprintf(stderr,"\nFAILED SUBPROC %2d [%ld] %d\n",
+	    wnum, (long)pid, status);
+    exit(-1);
+  }
+}
+
+static void multicore_outer_iteration(int i, AdjWord min) {
+  static unsigned check_counter;
+
+  assert(i == multicore_iteration_boundary);
+  mc_iter_min = min;
+  mc_rwvsetup_outer();
+  ssize_t r = writev(mc_work[1], mc_iov, mc_niovs);
+  assert(r == mc_iovlen);
+  /* effectively, this writev arranges to transfers control
+   * to some worker's instance of iterate_recurse via mc_iterate_worker */
+
+  if (!(check_counter++ & 0xff))
+    multicore_check_for_new_best();
+}
+
+static void mc_iterate_worker(void) {
+  static time_t lastprint;
+
+  for (;;) {
+    mc_rwvsetup_outer();
+    ssize_t r = readv(mc_work[0], mc_iov, mc_niovs);
+    if (r == 0) break;
+    assert(r == mc_iovlen);
+    
+    bool ok = maxhamweight_ok();
+    if (!ok) continue;
+
+    time_t now = time(0);
+    bool doprint = now != lastprint;
+    lastprint = now;
+
+    ok = preconsider_ok(multicore_iteration_boundary, doprint);
+    if (doprint) progress_eol();
+    if (!ok) continue;
+
+    /* stop iterate_recurse from trying to run multicore_outer_iteration */
+    int mc_org_it_bound = multicore_iteration_boundary;
+    multicore_iteration_boundary = INT_MAX;
+    iterate_recurse(mc_org_it_bound, mc_iter_min);
+    multicore_iteration_boundary = mc_org_it_bound;
+  }
+  if (best_adjmatrix) {
+    LPRINTF("worker %2d reporting",mc_us->w);
+    adjmatrix = best_adjmatrix;
+    mc_rwvsetup_full();
+    ssize_t r = writev(fileno(mc_us->results), mc_iov, mc_niovs);
+    assert(r == mc_iovlen);
+  }
+  LPRINTF("worker %2d ending",mc_us->w);
+  exit(0);
+}
+
+static void multicore(void) {
+  Worker *mc_workers;
+  int w;
+  pid_t genpid;
+
+  multicore_iteration_boundary = n / 2;
+
+  FILE *busf = tmpfile();  assert(busf);
+  mc_bus = fileno(busf);
+  int r = fcntl(mc_bus, F_GETFL);  assert(r >= 0);
+  r |= O_APPEND;
+  r = fcntl(mc_bus, F_SETFL, r);  assert(r >= 0);
+
+  r = pipe(mc_work);  assert(!r);
+
+  mc_workers = xmalloc(sizeof(*mc_workers) * ncpus);
+  for (w=0; w<ncpus; w++) {
+    mc_workers[w].w = w;
+    mc_workers[w].results = tmpfile();  assert(mc_workers[w].results);
+    mc_workers[w].pid = fork();  assert(mc_workers[w].pid >= 0);
+    if (!mc_workers[w].pid) {
+      mc_us = &mc_workers[w];
+      close(mc_work[1]);
+      LPRINTF("worker %2d running", w);
+      mc_iterate_worker();
+      exit(0);
+    }
+  }
+
+  close(mc_work[0]);
+
+  genpid = fork();  assert(genpid >= 0);
+  if (!genpid) {
+    mc_am_generator = 1;
+    LPRINTF("generator running");
+    iterate();
+    exit(0);
+  }
+
+  close(mc_work[1]);
+  mc_awaitpid(-1, genpid);
+  for (w=0; w<ncpus; w++)
+    mc_awaitpid(w, mc_workers[w].pid);
+
+  for (w=0; w<ncpus; w++) {
+    mc_rwvsetup_full();
+    LPRINTF("reading report from %2d",w);
+    ssize_t sr = preadv(fileno(mc_workers[w].results), mc_iov, mc_niovs, 0);
+    if (!sr) continue;
+    LPRINTF("got report from %2d",w);
+    maxhamweight = 0;
+    optimise(1);
+  }
+}
+
+static void multicore_check_for_new_best(void) {
+  if (!(mc_us || mc_am_generator))
+    return;
+
+  for (;;) {
+    double msg;
+    ssize_t got = pread(mc_bus, &msg, sizeof(msg), mc_bus_read);
+    if (!got) break;
+    assert(got == sizeof(msg));
+    if (msg > best)
+      set_best(msg);
+    mc_bus_read += sizeof(msg);
+  }
+}
+
+static void multicore_found_new_best(void) {
+  if (!mc_us)
+    return;
+
+  if (mc_us /* might be master */) fprintf(stderr,"    w%-2d ",mc_us->w);
+  ssize_t wrote = write(mc_bus, &best, sizeof(best));
+  assert(wrote == sizeof(best));
+}
+
+/*----- end of multicore support -----*/
 
 static AdjWord *xalloc_adjmatrix(void) {
   return xmalloc(sizeof(*adjmatrix)*n);
@@ -99,16 +390,21 @@ static void prep(void) {
   adjall = ~((~(AdjWord)0) << m);
   adjmatrix = xalloc_adjmatrix();
   glp_term_out(GLP_OFF);
+  setlinebuf(stderr);
+  weight = calloc(sizeof(*weight), m);  assert(weight);
 }
 
+#if 0
 static AdjWord one_adj_bit(int bitnum) {
   return (AdjWord)1 << bitnum;
 }
+#endif
 
 static int count_set_adj_bits(AdjWord w) {
-  int j, total;
-  for (j=0, total=0; j<m; j++)
-    total += !!(w & one_adj_bit(j));
+  int j, total = 0;
+  AdjWord jbit;
+  FOR_BITS(j,m)
+    total += !!(w & jbit);
   return total;
 }
 
@@ -116,6 +412,10 @@ static int count_set_adj_bits(AdjWord w) {
 
 static int totalfrags;
 
+static bool maxhamweight_ok(void) {
+  return maxhamweight <= m_max_frags;
+}
+
 static bool preconsider_ok(int nwords, bool doprint) {
   int i;
 
@@ -124,14 +424,13 @@ static bool preconsider_ok(int nwords, bool doprint) {
   bool had_max = 0;
   for (i=0, totalfrags=0; i<nwords; i++) {
     int frags = count_set_adj_bits(adjmatrix[i]);
-    had_max += (frags >= maxhamweight);
-    totalfrags += frags;
     PRINTF("%"PRADJ" ", adjmatrix[i]);
-    double maxminsize = (double)m / frags;
-    if (maxminsize <= best) {
+    if (frags > m_max_frags) {
       PRINTF(" too fine");
       goto out;
     }
+    had_max += (frags >= maxhamweight);
+    totalfrags += frags;
   }
   if (!had_max) {
     /* Skip this candidate as its max hamming weight is lower than
@@ -151,6 +450,7 @@ static void optimise(bool doprint) {
   /* Consider the best answer (if any) for a given adjacency matrix */
   glp_prob *prob = 0;
   int i, j;
+  AdjWord jbit;
 
   /*
    * Up to a certain point, optimise() can be restarted.  We use this
@@ -236,8 +536,8 @@ static void optimise(bool doprint) {
   glp_set_obj_coef(prob, X_minimum, 1);
 
   for (i=0; i<n; i++) {
-    for (j=0; j<m; j++) {
-      if (!(adjmatrix[i] & one_adj_bit(j)))
+    FOR_BITS(j,m) {
+      if (!(adjmatrix[i] & jbit))
 	continue;
       /* x_total_i += x_minimum */
       /* x_total_j += x_minimum */
@@ -316,7 +616,8 @@ static void optimise(bool doprint) {
 
   HAVE_PRINTED;
 
-  best = got;
+  set_best(got);
+  multicore_found_new_best();
 
   if (best_prob) glp_delete_prob(best_prob);
   best_prob = prob;
@@ -332,15 +633,27 @@ static void optimise(bool doprint) {
  out:
   if (prob)
     glp_delete_prob(prob);
-  if (doprint) { PRINTF("        \r"); fflush(stdout); }
+  if (doprint) progress_eol();
+  if (doprint) multicore_check_for_new_best();
 }
 
 static void iterate_recurse(int i, AdjWord min) {
+  int j;
+  AdjWord jbit;
+
   if (i >= n) {
+    for (j=0; j<m; j++)
+      if (weight[j] < 2)
+	return;
+
     printcounter++;
     optimise(!(printcounter & 0xfff));
     return;
   }
+  if (i >= multicore_iteration_boundary) {
+    multicore_outer_iteration(i, min);
+    return;
+  }
   for (adjmatrix[i] = min;
        ;
        adjmatrix[i]++) {
@@ -349,8 +662,20 @@ static void iterate_recurse(int i, AdjWord min) {
     if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
       goto again;
 
+    FOR_BITS(j,m)
+      if (adjmatrix[i] & jbit)
+        weight[j]++;
+    for (int j = 0; j < m; j++)
+      if (weight[j] > n_max_frags)
+        goto takeout;
+
     iterate_recurse(i+1, adjmatrix[i]);
 
+  takeout:
+    FOR_BITS(j,m)
+      if (adjmatrix[i] & jbit)
+        weight[j]--;
+
   again:
     if (adjmatrix[i] == adjall)
       return;
@@ -359,20 +684,66 @@ static void iterate_recurse(int i, AdjWord min) {
 
 static void iterate(void) {
   for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
-    double maxminsize = (double)m / maxhamweight;
-    if (maxminsize <= best)
+    if (!maxhamweight_ok())
       continue;
 
     iterate_recurse(0, 1);
   }
 }
 
+static int gcd(int a, int b)
+{
+  assert(a>0);
+  assert(b>0);
+  while (b) {
+    int t = a % b;
+    a = b;
+    b = t;
+  }
+  return a;
+}
+
+static void print_rational(int n, int d)
+{
+  int g = gcd(n, d);
+  n /= g;
+  d /= g;
+  printf("%d", n);
+  if (d > 1)
+    printf("/%d", d);
+}
+
+#define MAKE_INT_VECTOR_COMPARATOR(thing)                               \
+  static int compare_ints_##thing(const void *av, const void *bv)       \
+  {                                                                     \
+    const int *a = (const int *)av;                                     \
+    const int *b = (const int *)bv;                                     \
+    int i;                                                              \
+    for (i = 0; i < (thing); i++)                                       \
+      if (a[i] != b[i])                                                 \
+        return a[i] > b[i] ? -1 : +1;                                   \
+    return 0;                                                           \
+  }
+/* Good grief, if only qsort let me pass a context parameter */
+MAKE_INT_VECTOR_COMPARATOR(1)
+MAKE_INT_VECTOR_COMPARATOR(m)
+MAKE_INT_VECTOR_COMPARATOR(n)
+
 static void report(void) {
   fprintf(stderr, "\n");
+  if (best_adjmatrix) {
+    int i;
+    fprintf(stderr,"  ");
+    for (i=0; i<n; i++) fprintf(stderr, " %"PRADJ, best_adjmatrix[i]);
+  }
+  fprintf(stderr, " best=%-12.8f nf<=%d mf<=%d\n",
+	  best, n_max_frags, m_max_frags);
+  printf("%d into %d: ", n, m);
   if (best_prob) {
     double min = glp_get_obj_val(best_prob);
     double a[n][m];
-    int i, j, cols;
+    int ai[n][m];
+    int i, j, k, d, cols, imin;
     for (i = 0; i < n; i++)
       for (j = 0; j < m; j++)
         a[i][j] = 0;
@@ -383,25 +754,115 @@ static void report(void) {
         continue;
       a[x][y] = min + glp_get_col_prim(best_prob, i);
     }
-    printf("%d into %d: min fragment %g\n", n, m, min);
-    for (i = 0; i < n; i++) {
+
+    /*
+     * Try to find a denominator over which all these numbers turn
+     * sensibly into rationals.
+     */
+    for (d = 1;; d++) {
+      /*
+       * Round everything to the nearest multiple of d.
+       */
+      for (i = 0; i < n; i++)
+        for (j = 0; j < m; j++)
+          ai[i][j] = a[i][j] * d + 0.5;
+
+      /*
+       * Ensure the rows and columns add up correctly.
+       */
+      for (i = 0; i < n; i++) {
+        int total = 0;
+        for (j = 0; j < m; j++)
+          total += ai[i][j];
+        if (total != d*m)
+          goto next_d;
+      }
       for (j = 0; j < m; j++) {
-        if (a[i][j])
-          printf(" %9.3f", a[i][j]);
-        else
-          printf("          ");
+        int total = 0;
+        for (i = 0; i < n; i++)
+          total += ai[i][j];
+        if (total != d*n)
+          goto next_d;
       }
-      printf("\n");
+
+      /*
+       * Ensure we haven't rounded a good solution to a worse one, by
+       * finding the new minimum fragment and making sure it's at
+       * least the one we previously had.
+       */
+      imin = d*n;
+      for (i = 0; i < n; i++)
+        for (j = 0; j < m; j++)
+          if (ai[i][j] > 0 && ai[i][j] < imin)
+            imin = ai[i][j];
+
+      if (abs((double)imin / d - min) > 1e-10)
+        goto next_d;
+
+      /*
+       * Got it! We've found a rational-valued dissection.
+       */
+      printf("min fragment ");
+      print_rational(imin, d);
+      printf("   [%s]\n", VERSION);
+
+      /*
+       * We don't really want to output the matrix, so instead let's
+       * output the ways in which the sticks are cut up.
+       */
+      {
+        int ai2[m][n];
+        for (i = 0; i < n; i++) {
+          for (j = 0; j < m; j++)
+            ai2[j][i] = ai[i][j];
+        }
+        for (i = 0; i < n; i++)
+          qsort(ai+i, m, sizeof(int), compare_ints_1);
+        qsort(ai, n, m*sizeof(int), compare_ints_m);
+        printf("  Cut up %d sticks of length %d like this:\n", n, m);
+        for (i = 0; i < n ;) {
+          for (j = 1; i+j < n && compare_ints_m(ai+i, ai+i+j) == 0; j++);
+          printf("    %d x (", j);
+          for (k = 0; k < m && ai[i][k] > 0; k++) {
+            if (k > 0) printf(" + ");
+            print_rational(ai[i][k], d);
+          }
+          printf(")\n");
+          i += j;
+        }
+
+        for (j = 0; j < m; j++)
+          qsort(ai2+j, n, sizeof(int), compare_ints_1);
+        qsort(ai2, m, n*sizeof(int), compare_ints_n);
+        printf("  Reassemble as %d sticks of length %d like this:\n", m, n);
+        for (j = 0; j < m ;) {
+          for (i = 1; i+j < m && compare_ints_n(ai2+j, ai2+j+i) == 0; i++);
+          printf("    %d x (", i);
+          for (k = 0; k < n && ai2[j][k] > 0; k++) {
+            if (k > 0) printf(" + ");
+            print_rational(ai2[j][k], d);
+          }
+          printf(")\n");
+          j += i;
+        }
+      }
+      return;
+
+     next_d:;
     }
+  } else {
+    printf(" none better than %9.3f    [%s]\n", best, VERSION);
   }
   if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
 }
  
 int main(int argc, char **argv) {
   int opt;
-  while ((opt = getopt(argc,argv,"j:")) >= 0) {
+  double best_to_set = -1.0; /* means 'don't' */
+  while ((opt = getopt(argc,argv,"j:b:")) >= 0) {
     switch (opt) {
     case 'j': ncpus = atoi(optarg); break;
+    case 'b': best_to_set = atof(optarg); break;
     case '+': assert(!"bad option");
     default: abort();
     }
@@ -411,9 +872,14 @@ int main(int argc, char **argv) {
   assert(argc==3);
   n = atoi(argv[1]);
   m = atoi(argv[2]);
+  assert(n > m);
+  if (best_to_set > 0) set_best(best_to_set);
 
   prep();
-  iterate();
+
+  if (ncpus) multicore();
+  else iterate();
+
   report();
   return 0;
 }