Eliminate divide in new fast-path locking code

c4d5cb71d2 adjusted the fast-path locking code to allow some
configuration of the number of fast-path locking slots via the
max_locks_per_transaction GUC.  In that commit the FAST_PATH_REL_GROUP()
macro used integer division to determine the fast-path locking group slot
to use for the lock.

The divisor in this case is always a power-of-two value.  Here we swap
out the divide by a bitwise-AND, which is a significantly faster
operation to perform.

In passing, adjust the code that's setting FastPathLockGroupsPerBackend
so that it's more clear that the value being set is a power-of-two.

Also, adjust some comments in the area which contained some magic
numbers.  It seems better to justify the 1024 upper limit in the
location where the #define is made instead of where it is used.

Author: David Rowley <drowleyml@gmail.com>
Reviewed-by: Tomas Vondra <tomas@vondra.me>
Discussion: https://postgr.es/m/CAApHDvodr3bcnpxcs7+k-3cFwYR0tP-BYhyd2PpDhe-bCx9i=g@mail.gmail.com

src/backend/storage/lmgr/lock.c

@@ -210,9 +210,12 @@ int			FastPathLockGroupsPerBackend = 0;
  *
  * The selected constant (49157) is a prime not too close to 2^k, and it's
  * small enough to not cause overflows (in 64-bit).
+ *
+ * We can assume that FastPathLockGroupsPerBackend is a power-of-two per
+ * InitializeFastPathLocks().
  */
 #define FAST_PATH_REL_GROUP(rel) \
-	(((uint64) (rel) * 49157) % FastPathLockGroupsPerBackend)
+	(((uint64) (rel) * 49157) & (FastPathLockGroupsPerBackend - 1))
 
 /*
  * Given the group/slot indexes, calculate the slot index in the whole array

src/backend/utils/init/postinit.c

@@ -575,13 +575,6 @@ InitializeMaxBackends(void)
  *
  * This must be called after modules have had the chance to alter GUCs in
  * shared_preload_libraries and before shared memory size is determined.
- *
- * The default max_locks_per_xact=64 means 4 groups by default.
- *
- * We allow anything between 1 and 1024 groups, with the usual power-of-2
- * logic. The 1 is the "old" size with only 16 slots, 1024 is an arbitrary
- * limit (matching max_locks_per_xact = 16k). Values over 1024 are unlikely
- * to be beneficial - there are bottlenecks we'll hit way before that.
  */
 void
 InitializeFastPathLocks(void)
@@ -589,19 +582,22 @@ InitializeFastPathLocks(void)
 	/* Should be initialized only once. */
 	Assert(FastPathLockGroupsPerBackend == 0);
 
-	/* we need at least one group */
+	/*
-	FastPathLockGroupsPerBackend = 1;
+	 * Based on the max_locks_per_transaction GUC, as that's a good indicator
+	 * of the expected number of locks, figure out the value for
+	 * FastPathLockGroupsPerBackend.  This must be a power-of-two.  We cap the
+	 * value at FP_LOCK_GROUPS_PER_BACKEND_MAX and insist the value is at
+	 * least 1.
+	 *
+	 * The default max_locks_per_transaction = 64 means 4 groups by default.
+	 */
+	FastPathLockGroupsPerBackend =
+		Max(Min(pg_nextpower2_32(max_locks_per_xact) / FP_LOCK_SLOTS_PER_GROUP,
+				FP_LOCK_GROUPS_PER_BACKEND_MAX), 1);
 
-	while (FastPathLockGroupsPerBackend < FP_LOCK_GROUPS_PER_BACKEND_MAX)
+	/* Validate we did get a power-of-two */
-	{
+	Assert(FastPathLockGroupsPerBackend ==
-		/* stop once we exceed max_locks_per_xact */
+		   pg_nextpower2_32(FastPathLockGroupsPerBackend));
-		if (FastPathLockSlotsPerBackend() >= max_locks_per_xact)
-			break;
-
-		FastPathLockGroupsPerBackend *= 2;
-	}
-
-	Assert(FastPathLockGroupsPerBackend <= FP_LOCK_GROUPS_PER_BACKEND_MAX);
 }
 
 /*

src/include/storage/proc.h

@@ -86,6 +86,14 @@ struct XidCache
  */
 extern PGDLLIMPORT int FastPathLockGroupsPerBackend;
 
+/*
+ * Define the maximum number of fast-path locking groups per backend.
+ * This must be a power-of-two value.  The actual number of fast-path
+ * lock groups is calculated in InitializeFastPathLocks() based on
+ * max_locks_per_transaction.  1024 is an arbitrary upper limit (matching
+ * max_locks_per_transaction = 16k).  Values over 1024 are unlikely to be
+ * beneficial as there are bottlenecks we'll hit way before that.
+ */
 #define		FP_LOCK_GROUPS_PER_BACKEND_MAX	1024
 #define		FP_LOCK_SLOTS_PER_GROUP		16	/* don't change */
 #define		FastPathLockSlotsPerBackend() \