faster state sets merge in grep utility, dfa.c (avoid O(N^2) algorithms)

fast_grep_patch3.diff

Index: dfa.c
===================================================================
--- dfa.c       (revision grep-2.14-faster-dfa)
+++ dfa.c	(revision grep-2.14)
@@ -1992,6 +1992,133 @@
       s->elems[i] = s->elems[i + 1];
 }
 
+/* Merge implementation of sorted sets, then number of sets smore than 2.
+   Priority queue aka 'heap' data structure used to select maximum of
+   many elements */
+
+typedef struct {
+  position p;
+  size_t set_index; /* Remember which set this element was taken from */
+} heap_elem;
+
+
+static void
+heap_add (heap_elem *heap, size_t *heap_size, heap_elem e)
+{
+  size_t i = *heap_size;
+  while (i)
+    {
+      size_t parent = (i-1) / 2;
+      if (e.p.index < heap[parent].p.index)
+        break;
+
+      heap[i] = heap[parent];
+      i = parent;
+    }
+  heap[i] = e;
+  *heap_size += 1;
+}
+
+static void
+heap_remove_top_and_add (heap_elem *heap, size_t heap_size, heap_elem e)
+{
+  size_t i = 0;
+  size_t lchild  = 2*i + 1;
+  size_t n = heap_size;
+  while (lchild < n)
+    {
+      size_t rchild = lchild + 1;
+      size_t nextchild = lchild;
+      if (rchild < n && heap[lchild].p.index < heap[rchild].p.index)
+        nextchild = rchild;
+      if (e.p.index >= heap[nextchild].p.index)
+        break;
+      heap[i] = heap[nextchild];
+      i = nextchild;
+      lchild = 2*i + 1;
+    }
+  heap[i] = e;
+}
+
+
+static void
+heap_remove_top (heap_elem *heap, size_t *heap_size)
+{
+  *heap_size -= 1;
+  if (*heap_size == 0)
+    return;
+  heap_remove_top_and_add (heap, *heap_size, heap[*heap_size]);
+}
+
+static void
+heap_merge_many_sets (position_set *sets, size_t n, position_set *result)
+{
+  size_t heap_size = 0;
+  position_set r; /* faster access to local variables */
+  heap_elem *heap = XNMALLOC (n, heap_elem);
+  size_t *ids = XNMALLOC (n, size_t);
+  size_t sum_of_sizes = 0;
+  size_t i;
+
+  for (i = 0; i < n; ++i)
+    {
+      sum_of_sizes += sets[i].nelem;
+      /* special value for "end of set", to reduce
+         dependent memory reads */
+      ids[i] = ~(size_t)0;
+      if (sets[i].nelem)
+        {
+          heap_elem e = { sets[i].elems[0], i };
+          heap_add (heap, &heap_size, e);
+          if (sets[i].nelem > 1)
+            ids[i] = 1;
+        }
+    }
+
+  REALLOC_IF_NECESSARY(result->elems, result->alloc, sum_of_sizes);
+  r = *result;
+  r.nelem = 0;
+
+  while (heap_size)
+    {
+      heap_elem e = heap[0];
+      if (r.nelem && r.elems[r.nelem-1].index == e.p.index)
+        r.elems[r.nelem-1].constraint |= e.p.constraint;
+      else
+        r.elems[r.nelem++] = e.p;
+      i = e.set_index;
+      if (ids[i] != ~(size_t)0)
+        {
+          heap_elem e2 = { sets[i].elems[ids[i]], i };
+          heap_remove_top_and_add (heap, heap_size, e2);
+          ++ids[i];
+          if (ids[i] == sets[i].nelem)
+            ids[i] = ~(size_t)0;
+        }
+      else
+        {
+          heap_remove_top (heap, &heap_size);
+        }
+    }
+  *result = r;
+  free (ids);
+  free (heap);
+}
+
+static void
+merge_many_sets (position_set *sets, size_t n, position_set *result)
+{
+  /* optimized solutions for special/trivial cases */
+  if (n == 0)
+    result->nelem = 0;
+  else if (n == 1)
+    copy (&sets[0], result);
+  else if (n == 2)
+    merge (&sets[0], &sets[1], result);
+  else
+    heap_merge_many_sets(sets, n, result);
+}
+
 /* Find the index of the state corresponding to the given position set with
    the given preceding context, or create a new state if there is no such
    state.  Context tells whether we got here on a newline or letter. */
@@ -2482,13 +2609,16 @@
   charclass leftovers;          /* Stuff in the label that didn't match. */
   int leftoversf;               /* True if leftovers is nonempty. */
   position_set follows;         /* Union of the follows of some group. */
-  position_set tmp;             /* Temporary space for merging sets. */
+  position_set follows_tmp;     /* Temporary space for merging sets. */
   int possible_contexts;        /* Contexts that this group can match. */
   int separate_contexts;        /* Context that new state wants to know. */
   state_num state;              /* New state. */
   state_num state_newline;      /* New state on a newline transition. */
   state_num state_letter;       /* New state on a letter transition. */
   int next_isnt_1st_byte = 0;   /* Flag if we can't add state0.  */
+  position_set *sets = 0;       /* Temporary array of sets, to pass many sets to merge function */
+  size_t sets_n = 0;            /* Sets array size */
+  size_t sets_alloc = 0;        /* Sets array capacity   */
   size_t i, j, k;
 
   MALLOC (grps, NOTCHAR);
@@ -2607,7 +2737,7 @@
     }
 
   alloc_position_set (&follows, d->nleaves);
-  alloc_position_set (&tmp, d->nleaves);
+  alloc_position_set (&follows_tmp, d->nleaves);
 
   /* If we are a searching matcher, the default transition is to a state
      containing the positions of state 0, otherwise the default transition
@@ -2637,13 +2767,12 @@
 
   for (i = 0; i < ngrps; ++i)
     {
-      follows.nelem = 0;
-
-      /* Find the union of the follows of the positions of the group.
-         This is a hideously inefficient loop.  Fix it someday. */
+      /* Find the union of the follows of the positions of the group.  */
+      sets_n = grps[i].nelem;
+      REALLOC_IF_NECESSARY(sets, sets_alloc, sets_n);
       for (j = 0; j < grps[i].nelem; ++j)
-        for (k = 0; k < d->follows[grps[i].elems[j]].nelem; ++k)
-          insert (d->follows[grps[i].elems[j]].elems[k], &follows);
+        sets[j] = d->follows[grps[i].elems[j]];
+      merge_many_sets (sets, sets_n, &follows_tmp);
 
       if (d->mb_cur_max > 1)
         {
@@ -2666,9 +2795,9 @@
              <mb A>, so we cannot add state[0].  */
 
           next_isnt_1st_byte = 0;
-          for (j = 0; j < follows.nelem; ++j)
+          for (j = 0; j < follows_tmp.nelem; ++j)
             {
-              if (!(d->multibyte_prop[follows.elems[j].index] & 1))
+              if (!(d->multibyte_prop[follows_tmp.elems[j].index] & 1))
                 {
                   next_isnt_1st_byte = 1;
                   break;
@@ -2680,8 +2809,7 @@
          of state 0 as well. */
       if (d->searchflag
           && (!MBS_SUPPORT || (d->mb_cur_max == 1 || !next_isnt_1st_byte)))
-        for (j = 0; j < d->states[0].elems.nelem; ++j)
-          insert (d->states[0].elems.elems[j], &follows);
+        merge (&follows_tmp, &d->states[0].elems, &follows);
 
       /* Find out if the new state will want any context information. */
       possible_contexts = charclass_context (labels[i]);
@@ -2720,7 +2848,8 @@
   for (i = 0; i < ngrps; ++i)
     free (grps[i].elems);
   free (follows.elems);
-  free (tmp.elems);
+  free (sets);
+  free (follows_tmp.elems);
   free (grps);
   free (labels);
 }