sha1-lookup: make selection of 'middle' less aggressive

If we pick 'mi' between 'lo' and 'hi' at 50%, which was what the
simple binary search did, we are halving the search space
whether the entry at 'mi' is lower or higher than the target.

The previous patch was about picking not the middle but closer
to 'hi', when we know the target is a lot closer to 'hi' than it
is to 'lo'.  However, if it turns out that the entry at 'mi' is
higher than the target, we would end up reducing the search
space only by the difference between 'mi' and 'hi' (which by
definition is less than 50% --- that was the whole point of not
using the simple binary search), which made the search less
efficient.  And the risk of overshooting becomes very high, if
we try to be too precise.

This tweaks the selection of 'mi' to be a bit closer to the
middle than we would otherwise pick to avoid the problem.

Signed-off-by: Junio C Hamano <gitster@pobox.com>

sha1-lookup.c

@@ -50,6 +50,12 @@
  * the midway of the table.  It can reasonably be expected to be near
  * 87% (222/256) from the top of the table.
  *
+ * However, we do not want to pick "mi" too precisely.  If the entry at
+ * the 87% in the above example turns out to be higher than the target
+ * we are looking for, we would end up narrowing the search space down
+ * only by 13%, instead of 50% we would get if we did a simple binary
+ * search.  So we would want to hedge our bets by being less aggressive.
+ *
  * The table at "table" holds at least "nr" entries of "elem_size"
  * bytes each.  Each entry has the SHA-1 key at "key_offset".  The
  * table is sorted by the SHA-1 key of the entries.  The caller wants
@@ -119,11 +125,25 @@ int sha1_entry_pos(const void *table,
 		if (hiv < kyv)
 			return -1 - hi;
 
-		if (kyv == lov && lov < hiv - 1)
+		/*
-			kyv++;
+		 * Even if we know the target is much closer to 'hi'
-		else if (kyv == hiv - 1 && lov < kyv)
+		 * than 'lo', if we pick too precisely and overshoot
-			kyv--;
+		 * (e.g. when we know 'mi' is closer to 'hi' than to
-
+		 * 'lo', pick 'mi' that is higher than the target), we
+		 * end up narrowing the search space by a smaller
+		 * amount (i.e. the distance between 'mi' and 'hi')
+		 * than what we would have (i.e. about half of 'lo'
+		 * and 'hi').  Hedge our bets to pick 'mi' less
+		 * aggressively, i.e. make 'mi' a bit closer to the
+		 * middle than we would otherwise pick.
+		 */
+		kyv = (kyv * 6 + lov + hiv) / 8;
+		if (lov < hiv - 1) {
+			if (kyv == lov)
+				kyv++;
+			else if (kyv == hiv)
+				kyv--;
+		}
 		mi = (range - 1) * (kyv - lov) / (hiv - lov) + lo;
 
 		if (debug_lookup) {
@@ -142,8 +162,7 @@ int sha1_entry_pos(const void *table,
 		if (cmp > 0) {
 			hi = mi;
 			hi_key = mi_key;
-		}
+		} else {
-		else {
 			lo = mi + 1;
 			lo_key = mi_key + elem_size;
 		}