Avoid use of float arithmetic in bipartite_match.c.

tglsfdc · tglsfdc · commit 44ed65a54597 · 2015-08-23T13:02:18.000-04:00
Since the distances used in this algorithm are small integers (not more
than the size of the U set, in fact), there is no good reason to use float
arithmetic for them.  Use short ints instead: they're smaller, faster, and
require no special portability assumptions.

Per testing by Greg Stark, which disclosed that the code got into an
infinite loop on VAX for lack of IEEE-style float infinities.  We don't
really care all that much whether Postgres can run on a VAX anymore,
but there seems sufficient reason to change this code anyway.

In passing, make a few other small adjustments to make the code match
usual Postgres coding style a bit better.
diff --git a/src/backend/lib/bipartite_match.c b/src/backend/lib/bipartite_match.c
@@ -16,17 +16,20 @@
  */
 #include "postgres.h"
 
-#include <float.h>
-#include <math.h>
 #include <limits.h>
 
 #include "lib/bipartite_match.h"
 #include "miscadmin.h"
-#include "utils/builtins.h"
 
+/*
+ * The distances computed in hk_breadth_search can easily be seen to never
+ * exceed u_size.  Since we restrict u_size to be less than SHRT_MAX, we
+ * can therefore use SHRT_MAX as the "infinity" distance needed as a marker.
+ */
+#define HK_INFINITY  SHRT_MAX
 
 static bool hk_breadth_search(BipartiteMatchState *state);
-static bool hk_depth_search(BipartiteMatchState *state, int u, int depth);
+static bool hk_depth_search(BipartiteMatchState *state, int u);
 
 /*
  * Given the size of U and V, where each is indexed 1..size, and an adjacency
@@ -37,26 +40,29 @@ BipartiteMatch(int u_size, int v_size, short **adjacency)
 {
 	BipartiteMatchState *state = palloc(sizeof(BipartiteMatchState));
 
-	Assert(u_size < SHRT_MAX);
-	Assert(v_size < SHRT_MAX);
+	if (u_size < 0 || u_size >= SHRT_MAX ||
+		v_size < 0 || v_size >= SHRT_MAX)
+		elog(ERROR, "invalid set size for BipartiteMatch");
 
 	state->u_size = u_size;
 	state->v_size = v_size;
-	state->matching = 0;
 	state->adjacency = adjacency;
-	state->pair_uv = palloc0((u_size + 1) * sizeof(short));
-	state->pair_vu = palloc0((v_size + 1) * sizeof(short));
-	state->distance = palloc((u_size + 1) * sizeof(float));
-	state->queue = palloc((u_size + 2) * sizeof(short));
+	state->matching = 0;
+	state->pair_uv = (short *) palloc0((u_size + 1) * sizeof(short));
+	state->pair_vu = (short *) palloc0((v_size + 1) * sizeof(short));
+	state->distance = (short *) palloc((u_size + 1) * sizeof(short));
+	state->queue = (short *) palloc((u_size + 2) * sizeof(short));
 
 	while (hk_breadth_search(state))
 	{
 		int			u;
 
-		for (u = 1; u <= u_size; ++u)
+		for (u = 1; u <= u_size; u++)
+		{
 			if (state->pair_uv[u] == 0)
-				if (hk_depth_search(state, u, 1))
+				if (hk_depth_search(state, u))
 					state->matching++;
+		}
 
 		CHECK_FOR_INTERRUPTS(); /* just in case */
 	}
@@ -79,27 +85,31 @@ BipartiteMatchFree(BipartiteMatchState *state)
 	pfree(state);
 }
 
+/*
+ * Perform the breadth-first search step of H-K matching.
+ * Returns true if successful.
+ */
 static bool
 hk_breadth_search(BipartiteMatchState *state)
 {
 	int			usize = state->u_size;
 	short	   *queue = state->queue;
-	float	   *distance = state->distance;
+	short	   *distance = state->distance;
 	int			qhead = 0;		/* we never enqueue any node more than once */
 	int			qtail = 0;		/* so don't have to worry about wrapping */
 	int			u;
 
-	distance[0] = get_float4_infinity();
+	distance[0] = HK_INFINITY;
 
-	for (u = 1; u <= usize; ++u)
+	for (u = 1; u <= usize; u++)
 	{
 		if (state->pair_uv[u] == 0)
 		{
 			distance[u] = 0;
 			queue[qhead++] = u;
 		}
 		else
-			distance[u] = get_float4_infinity();
+			distance[u] = HK_INFINITY;
 	}
 
 	while (qtail < qhead)
@@ -111,45 +121,52 @@ hk_breadth_search(BipartiteMatchState *state)
 			short	   *u_adj = state->adjacency[u];
 			int			i = u_adj ? u_adj[0] : 0;
 
-			for (; i > 0; --i)
+			for (; i > 0; i--)
 			{
 				int			u_next = state->pair_vu[u_adj[i]];
 
-				if (isinf(distance[u_next]))
+				if (distance[u_next] == HK_INFINITY)
 				{
 					distance[u_next] = 1 + distance[u];
+					Assert(qhead < usize + 2);
 					queue[qhead++] = u_next;
-					Assert(qhead <= usize + 2);
 				}
 			}
 		}
 	}
 
-	return !isinf(distance[0]);
+	return (distance[0] != HK_INFINITY);
 }
 
+/*
+ * Perform the depth-first search step of H-K matching.
+ * Returns true if successful.
+ */
 static bool
-hk_depth_search(BipartiteMatchState *state, int u, int depth)
+hk_depth_search(BipartiteMatchState *state, int u)
 {
-	float	   *distance = state->distance;
+	short	   *distance = state->distance;
 	short	   *pair_uv = state->pair_uv;
 	short	   *pair_vu = state->pair_vu;
 	short	   *u_adj = state->adjacency[u];
 	int			i = u_adj ? u_adj[0] : 0;
+	short		nextdist;
 
 	if (u == 0)
 		return true;
+	if (distance[u] == HK_INFINITY)
+		return false;
+	nextdist = distance[u] + 1;
 
-	if ((depth % 8) == 0)
-		check_stack_depth();
+	check_stack_depth();
 
-	for (; i > 0; --i)
+	for (; i > 0; i--)
 	{
 		int			v = u_adj[i];
 
-		if (distance[pair_vu[v]] == distance[u] + 1)
+		if (distance[pair_vu[v]] == nextdist)
 		{
-			if (hk_depth_search(state, pair_vu[v], depth + 1))
+			if (hk_depth_search(state, pair_vu[v]))
 			{
 				pair_vu[v] = u;
 				pair_uv[u] = v;
@@ -158,6 +175,6 @@ hk_depth_search(BipartiteMatchState *state, int u, int depth)
 		}
 	}
 
-	distance[u] = get_float4_infinity();
+	distance[u] = HK_INFINITY;
 	return false;
 }
diff --git a/src/include/lib/bipartite_match.h b/src/include/lib/bipartite_match.h
@@ -11,7 +11,7 @@
 /*
  * Given a bipartite graph consisting of nodes U numbered 1..nU, nodes V
  * numbered 1..nV, and an adjacency map of undirected edges in the form
- * adjacency[u] = [n, v1, v2, v3, ... vn], we wish to find a "maximum
+ * adjacency[u] = [k, v1, v2, v3, ... vk], we wish to find a "maximum
  * cardinality matching", which is defined as follows: a matching is a subset
  * of the original edges such that no node has more than one edge, and a
  * matching has maximum cardinality if there exists no other matching with a
@@ -24,21 +24,23 @@
  * the problem of planning a collection of grouping sets with the provably
  * minimal number of sort operations.
  */
-typedef struct bipartite_match_state
+typedef struct BipartiteMatchState
 {
+	/* inputs: */
 	int			u_size;			/* size of U */
 	int			v_size;			/* size of V */
+	short	  **adjacency;		/* adjacency[u] = [k, v1,v2,v3,...,vk] */
+	/* outputs: */
 	int			matching;		/* number of edges in matching */
-	short	  **adjacency;		/* adjacency[u] = [n, v1,v2,v3,...,vn] */
 	short	   *pair_uv;		/* pair_uv[u] -> v */
 	short	   *pair_vu;		/* pair_vu[v] -> u */
-
-	float	   *distance;		/* distance[u], float so we can have +inf */
+	/* private state for matching algorithm: */
+	short	   *distance;		/* distance[u] */
 	short	   *queue;			/* queue storage for breadth search */
 } BipartiteMatchState;
 
-BipartiteMatchState *BipartiteMatch(int u_size, int v_size, short **adjacency);
+extern BipartiteMatchState *BipartiteMatch(int u_size, int v_size, short **adjacency);
 
-void		BipartiteMatchFree(BipartiteMatchState *state);
+extern void BipartiteMatchFree(BipartiteMatchState *state);
 
 #endif   /* BIPARTITE_MATCH_H */
