Re: [PATCH 1/3] tcp: Switch hash table to linear probing instead of chaining

[David Gibson <david@gibson.dropbear.id.au>]

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On Wed, Dec 06, 2023 at 11:43:29PM +0100, Stefano Brivio wrote:
> On Mon,  4 Dec 2023 14:16:09 +1100
> David Gibson <david@gibson.dropbear.id.au> wrote:
> 
> > Currently we deal with hash collisions by letting a hash bucket contain
> > multiple entries, forming a linked list using an index in the connection
> > structure.
> > 
> > That's a pretty standard and simple approach, but in our case we can use
> > an even simpler one: linear probing.  Here if a hash bucket is occupied
> > we just move onto the next one until we find a feww one.  This slightly
> > simplifies lookup and more importantly saves some precious bytes in the
> > connection structure by removing the need for a link.  It does require some
> > additional complexity for hash removal.
> > 
> > This approach can perform poorly with hash table load is high.  However, we
> > already size our hash table of pointers larger than the connection table,
> > which puts an upper bound on the load.  It's relatively cheap to decrease
> > that bound if we find we need to.
> > 
> > I adapted the linear probing operations from Knuth's The Art of Computer
> > Programming, Volume 3, 2nd Edition.  Specifically Algorithm L and Algorithm
> > R in Section 6.4.  Note that there is an error in Algorithm R as printed,
> > see errata at [0].
> > 
> > [0] https://www-cs-faculty.stanford.edu/~knuth/all3-prepre.ps.gz
> > 
> > Signed-off-by: David Gibson <david@gibson.dropbear.id.au>
> > ---
> >  tcp.c      | 111 +++++++++++++++++++++++++++--------------------------
> >  tcp_conn.h |   2 -
> >  util.h     |  13 +++++++
> >  3 files changed, 69 insertions(+), 57 deletions(-)
> > 
> > diff --git a/tcp.c b/tcp.c
> > index 17c7cba..09acf7f 100644
> > --- a/tcp.c
> > +++ b/tcp.c
> > @@ -573,22 +573,12 @@ static unsigned int tcp6_l2_flags_buf_used;
> >  
> >  #define CONN(idx)		(&(FLOW(idx)->tcp))
> >  
> > -/** conn_at_idx() - Find a connection by index, if present
> > - * @idx:	Index of connection to lookup
> > - *
> > - * Return: pointer to connection, or NULL if @idx is out of bounds
> > - */
> > -static inline struct tcp_tap_conn *conn_at_idx(unsigned idx)
> > -{
> > -	if (idx >= FLOW_MAX)
> > -		return NULL;
> > -	ASSERT(CONN(idx)->f.type == FLOW_TCP);
> > -	return CONN(idx);
> > -}
> > -
> >  /* Table for lookup from remote address, local port, remote port */
> >  static struct tcp_tap_conn *tc_hash[TCP_HASH_TABLE_SIZE];
> >  
> > +static_assert(ARRAY_SIZE(tc_hash) >= FLOW_MAX,
> > +	"Safe linear probing requires hash table larger than connection table");
> > +
> >  /* Pools for pre-opened sockets (in init) */
> >  int init_sock_pool4		[TCP_SOCK_POOL_SIZE];
> >  int init_sock_pool6		[TCP_SOCK_POOL_SIZE];
> > @@ -1196,6 +1186,27 @@ static unsigned int tcp_conn_hash(const struct ctx *c,
> >  	return tcp_hash(c, &conn->faddr, conn->eport, conn->fport);
> >  }
> >  
> > +/**
> > + * tcp_hash_probe() - Find hash bucket for a connection
> > + * @c:		Execution context
> > + * @conn:	Connection to find bucket for
> > + *
> > + * Return: If @conn is in the table, its current bucket, otherwise a suitable
> > + *         free bucket for it.
> > + */
> > +static inline unsigned tcp_hash_probe(const struct ctx *c,
> > +				      const struct tcp_tap_conn *conn)
> > +{
> > +	unsigned b;
> > +
> > +	/* Linear probing */
> > +	for (b = tcp_conn_hash(c, conn); tc_hash[b] && tc_hash[b] != conn;
> > +	     b = (b + 1) % TCP_HASH_TABLE_SIZE)
> > +		;
> > +
> > +	return b;
> > +}
> > +
> >  /**
> >   * tcp_hash_insert() - Insert connection into hash table, chain link
> >   * @c:		Execution context
> > @@ -1203,14 +1214,10 @@ static unsigned int tcp_conn_hash(const struct ctx *c,
> >   */
> >  static void tcp_hash_insert(const struct ctx *c, struct tcp_tap_conn *conn)
> >  {
> > -	int b;
> > +	unsigned b = tcp_hash_probe(c, conn);
> >  
> > -	b = tcp_hash(c, &conn->faddr, conn->eport, conn->fport);
> > -	conn->next_index = tc_hash[b] ? FLOW_IDX(tc_hash[b]) : -1U;
> >  	tc_hash[b] = conn;
> > -
> > -	flow_dbg(conn, "hash table insert: sock %i, bucket: %i, next: %p",
> > -		 conn->sock, b, (void *)conn_at_idx(conn->next_index));
> > +	flow_dbg(conn, "hash table insert: sock %i, bucket: %u", conn->sock, b);
> >  }
> >  
> >  /**
> > @@ -1221,23 +1228,27 @@ static void tcp_hash_insert(const struct ctx *c, struct tcp_tap_conn *conn)
> >  static void tcp_hash_remove(const struct ctx *c,
> >  			    const struct tcp_tap_conn *conn)
> >  {
> > -	struct tcp_tap_conn *entry, *prev = NULL;
> > -	int b = tcp_conn_hash(c, conn);
> > +	unsigned b = tcp_hash_probe(c, conn), s;
> >  
> > -	for (entry = tc_hash[b]; entry;
> > -	     prev = entry, entry = conn_at_idx(entry->next_index)) {
> > -		if (entry == conn) {
> > -			if (prev)
> > -				prev->next_index = conn->next_index;
> > -			else
> > -				tc_hash[b] = conn_at_idx(conn->next_index);
> > -			break;
> > +	if (!tc_hash[b])
> > +		return; /* Redundant remove */
> > +
> > +	flow_dbg(conn, "hash table remove: sock %i, bucket: %u", conn->sock, b);
> > +
> > +	/* Scan the remainder of the cluster */
> > +	for (s = (b + 1) % TCP_HASH_TABLE_SIZE; tc_hash[s];
> > +	     s = (s + 1) % TCP_HASH_TABLE_SIZE) {
> > +		unsigned h = tcp_conn_hash(c, tc_hash[s]);
> > +
> > +		if (in_mod_range(h, b, s, TCP_HASH_TABLE_SIZE)) {
> > +			/* tc_hash[s] can live in tc_hash[b]'s slot */
> > +			debug("hash table remove: shuffle %u -> %u", s, b);
> > +			tc_hash[b] = tc_hash[s];
> > +			b = s;
> >  		}
> >  	}
> 
> This makes intuitively sense to me, but I can't wrap my head around the
> fact that it corresponds to algorithm R. Step R3 implies that, if h *is*
> (cyclically) between b and s, you should skip the move and go back to R2
> right away. The condition here seems to be reversed, though. What am I
> missing?

Ugh... this is doing my head in a bit, because there are a bunch of
stacked negatives.  Ok, so the original is:

	"If r lies cyclically between i and j, go back to R2"

Or equivalently a loop body of

	if (in_mod_range(r, i, j))
		continue;
	/* Step R4/R1 stuff */

Now in this version we have r => h, i => s and j => b, so

	if (in_mod_range(h, s, b))
		continue;
	/* Step R4/R1 stuff */

Or equivalently

	if (!in_mod_range(h, s, b))
		/* Step R4/R1 stuff */;

And because of how "cyclically between" works, that becomes:

	if (in_mod_range(h, b, s))
		/* Step R4/R1 stuff */;

Which is what I have.

But... the original is probing backwards through buckets whereas I'm
probing forwards, which I think reverses it again.  Yeah.. I'm pretty
sure my version is wrong.  If h == (s-1) > b, for example, it
definitely can't live in slot b, because probing would start at slot
s-1, and never reach b.

Hrm.. I'm going to switch mine to stepping backwards, like the Knuth,
just so I'm less confused.

-- 
David Gibson			| I'll have my music baroque, and my code
david AT gibson.dropbear.id.au	| minimalist, thank you.  NOT _the_ _other_
				| _way_ _around_!
http://www.ozlabs.org/~dgibson

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