[PATCH net-next v3 0/3] reciprocal_divide update

[PATCH net-next v3 0/3] reciprocal_divide update

[Daniel Borkmann]

This patch is on top of aee636c4809fa5 ("bpf: do not use reciprocal
divide") from Eric that sits in net tree. It will not create a merge
conflict, but it depends on this one, so we suggest, if possible, to
merge net into net-next.

We are proposing this change with only small modifications from the
v2 version, namely updating the name of trim to reciprocal_scale
(as commented on by Ben Hutchings and Eric Dumazet, thanks!).

We thought about introducing the reciprocal_divide algorithm in
parallel to the one already used by the kernel but faced organizational
issues, leading us to the conclusion that it is best to just replace
the old one: We could not come up with names for the different
implementations and also with a way to describe the differences to
guide developers which one to choose in which situation. This is
because we cannot specify the correct semantics for the version
which is currently used by the kernel. Altough it seems to not be
causing problems in the kernel, we cannot surely say so in the
case of flex_array for the future. Current usage seems ok, but
future users could run into problems.

Changelog:

v1->v2:
 - changed name to prandom_u32_max in p1
 - changed name to trim in p2
 - reworked code in p3
v2->v3:
 - p1 and p3 stays unchanged, only small update in commit
   message in p3
 - changed name to reciprocal_scale in p2
 - fixed kernel doc format

Thanks !

Daniel Borkmann (2):
  random32: add prandom_u32_max and convert open coded users
  net: introduce reciprocal_scale helper and convert users

Hannes Frederic Sowa (1):
  reciprocal_divide: update/correction of the algorithm

 drivers/net/bonding/bond_main.c     | 24 ++++++++++++++++-------
 drivers/net/bonding/bond_netlink.c  |  4 ----
 drivers/net/bonding/bond_options.c  | 15 +++++++++-----
 drivers/net/bonding/bond_sysfs.c    |  5 -----
 drivers/net/bonding/bonding.h       |  3 +++
 drivers/net/team/team_mode_random.c |  8 +-------
 include/linux/flex_array.h          |  3 ++-
 include/linux/kernel.h              | 19 ++++++++++++++++++
 include/linux/random.h              | 18 ++++++++++++++++-
 include/linux/reciprocal_div.h      | 39 ++++++++++++++++++++-----------------
 include/linux/slab_def.h            |  4 +++-
 include/net/codel.h                 |  4 +---
 include/net/red.h                   |  3 ++-
 lib/flex_array.c                    |  7 ++++++-
 lib/reciprocal_div.c                | 24 +++++++++++++++++++----
 net/packet/af_packet.c              |  5 ++---
 net/sched/sch_choke.c               |  9 +--------
 net/sched/sch_netem.c               |  6 ++++--
 18 files changed, 129 insertions(+), 71 deletions(-)

-- 
1.8.3.1

[PATCH net-next v3 1/3] random32: add prandom_u32_max and convert open coded users

[Daniel Borkmann]

Many functions have open coded a function that returns a random
number in range [0,N-1]. Under the assumption that we have a PRNG
such as taus113 with being well distributed in [0, ~0U] space,
we can implement such a function as uword t = (n*m')>>32, where
m' is a random number obtained from PRNG, n the right open interval
border and t our resulting random number, with n,m',t in u32 universe.

Lets go with Joe and simply call it prandom_u32_max(), although
technically we have an right open interval endpoint, but that we
have documented. Other users can further be migrated to the new
prandom_u32_max() function later on; for now, we need to make sure
to migrate reciprocal_divide() users for the reciprocal_divide()
follow-up fixup since their function signatures are going to change.

Joint work with Hannes Frederic Sowa.

Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl>
Cc: Eric Dumazet <eric.dumazet@gmail.com>
Cc: linux-kernel@vger.kernel.org
Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: Daniel Borkmann <dborkman@redhat.com>
---
 drivers/net/team/team_mode_random.c |  8 +-------
 include/linux/random.h              | 18 +++++++++++++++++-
 net/packet/af_packet.c              |  2 +-
 net/sched/sch_choke.c               |  9 +--------
 4 files changed, 20 insertions(+), 17 deletions(-)

diff --git a/drivers/net/team/team_mode_random.c b/drivers/net/team/team_mode_random.c
index 7f032e2..cd2f692 100644
--- a/drivers/net/team/team_mode_random.c
+++ b/drivers/net/team/team_mode_random.c
@@ -13,20 +13,14 @@
 #include <linux/module.h>
 #include <linux/init.h>
 #include <linux/skbuff.h>
-#include <linux/reciprocal_div.h>
 #include <linux/if_team.h>
 
-static u32 random_N(unsigned int N)
-{
-	return reciprocal_divide(prandom_u32(), N);
-}
-
 static bool rnd_transmit(struct team *team, struct sk_buff *skb)
 {
 	struct team_port *port;
 	int port_index;
 
-	port_index = random_N(team->en_port_count);
+	port_index = prandom_u32_max(team->en_port_count);
 	port = team_get_port_by_index_rcu(team, port_index);
 	if (unlikely(!port))
 		goto drop;
diff --git a/include/linux/random.h b/include/linux/random.h
index 4002b3d..3e89ac9 100644
--- a/include/linux/random.h
+++ b/include/linux/random.h
@@ -8,7 +8,6 @@
 
 #include <uapi/linux/random.h>
 
-
 extern void add_device_randomness(const void *, unsigned int);
 extern void add_input_randomness(unsigned int type, unsigned int code,
 				 unsigned int value);
@@ -38,6 +37,23 @@ struct rnd_state {
 u32 prandom_u32_state(struct rnd_state *state);
 void prandom_bytes_state(struct rnd_state *state, void *buf, int nbytes);
 
+/**
+ * prandom_u32_max - returns a pseduo-random number in interval [0, ep_ro)
+ * @ep_ro: right open interval endpoint
+ *
+ * Returns a pseduo-random number that is in interval [0, ep_ro). Note
+ * that the result depends on PRNG being well distributed in [0, ~0U]
+ * u32 space. Here we use maximally equidistributed combined Tausworthe
+ * generator, that is, prandom_u32(). This is useful when requesting a
+ * random index of an array containing ep_ro elements, for example.
+ *
+ * Returns: pseduo-random number in interval [0, ep_ro)
+ */
+static inline u32 prandom_u32_max(u32 ep_ro)
+{
+	return (u32)(((u64) prandom_u32() * ep_ro) >> 32);
+}
+
 /*
  * Handle minimum values for seeds
  */
diff --git a/net/packet/af_packet.c b/net/packet/af_packet.c
index 12f2f72..266c311 100644
--- a/net/packet/af_packet.c
+++ b/net/packet/af_packet.c
@@ -1289,7 +1289,7 @@ static unsigned int fanout_demux_rnd(struct packet_fanout *f,
 				     struct sk_buff *skb,
 				     unsigned int num)
 {
-	return reciprocal_divide(prandom_u32(), num);
+	return prandom_u32_max(num);
 }
 
 static unsigned int fanout_demux_rollover(struct packet_fanout *f,
diff --git a/net/sched/sch_choke.c b/net/sched/sch_choke.c
index ddd73cb..2aee028 100644
--- a/net/sched/sch_choke.c
+++ b/net/sched/sch_choke.c
@@ -14,7 +14,6 @@
 #include <linux/types.h>
 #include <linux/kernel.h>
 #include <linux/skbuff.h>
-#include <linux/reciprocal_div.h>
 #include <linux/vmalloc.h>
 #include <net/pkt_sched.h>
 #include <net/inet_ecn.h>
@@ -77,12 +76,6 @@ struct choke_sched_data {
 	struct sk_buff **tab;
 };
 
-/* deliver a random number between 0 and N - 1 */
-static u32 random_N(unsigned int N)
-{
-	return reciprocal_divide(prandom_u32(), N);
-}
-
 /* number of elements in queue including holes */
 static unsigned int choke_len(const struct choke_sched_data *q)
 {
@@ -233,7 +226,7 @@ static struct sk_buff *choke_peek_random(const struct choke_sched_data *q,
 	int retrys = 3;
 
 	do {
-		*pidx = (q->head + random_N(choke_len(q))) & q->tab_mask;
+		*pidx = (q->head + prandom_u32_max(choke_len(q))) & q->tab_mask;
 		skb = q->tab[*pidx];
 		if (skb)
 			return skb;
-- 
1.8.3.1

Re: [PATCH net-next v3 1/3] random32: add prandom_u32_max and convert open coded users

[Tilman Schmidt]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 19.01.2014 00:40, schrieb Daniel Borkmann:

> @@ -38,6 +37,23 @@ struct rnd_state { u32 prandom_u32_state(struct
> rnd_state *state); void prandom_bytes_state(struct rnd_state
> *state, void *buf, int nbytes);
> 
> +/** + * prandom_u32_max - returns a pseduo-random number in
> interval [0, ep_ro) + * @ep_ro: right open interval endpoint + * +
> * Returns a pseduo-random number that is in interval [0, ep_ro).
> Note + * that the result depends on PRNG being well distributed in
> [0, ~0U] + * u32 space. Here we use maximally equidistributed
> combined Tausworthe + * generator, that is, prandom_u32(). This is
> useful when requesting a + * random index of an array containing
> ep_ro elements, for example. + * + * Returns: pseduo-random number
> in interval [0, ep_ro) + */

The word "pseudo" is consistently mistyped as "pseduo" in this comment.
(Three occurrences.) You may want to correct this before it gets merged.

Thanks,
Tilman

- -- 
Tilman Schmidt                              E-Mail: tilman@imap.cc
Bonn, Germany
Diese Nachricht besteht zu 100% aus wiederverwerteten Bits.
Ungeöffnet mindestens haltbar bis: (siehe Rückseite)
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[PATCH net-next v3 2/3] net: introduce reciprocal_scale helper and convert users

[Daniel Borkmann]

As David Laight suggests, we shouldn't necessarily call this
reciprocal_divide() when users didn't requested a reciprocal_value();
lets keep the basic idea and call it reciprocal_scale(). More
background information on this topic can be found in [1].

Joint work with Hannes Frederic Sowa.

  [1] http://homepage.cs.uiowa.edu/~jones/bcd/divide.html

Suggested-by: David Laight <david.laight@aculab.com>
Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl>
Cc: Eric Dumazet <eric.dumazet@gmail.com>
Cc: linux-kernel@vger.kernel.org
Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: Daniel Borkmann <dborkman@redhat.com>
---
 include/linux/kernel.h | 19 +++++++++++++++++++
 include/net/codel.h    |  4 +---
 net/packet/af_packet.c |  3 +--
 3 files changed, 21 insertions(+), 5 deletions(-)

diff --git a/include/linux/kernel.h b/include/linux/kernel.h
index ecb8754..7afdbd2 100644
--- a/include/linux/kernel.h
+++ b/include/linux/kernel.h
@@ -193,6 +193,25 @@ extern int _cond_resched(void);
 		(__x < 0) ? -__x : __x;		\
 	})
 
+/**
+ * reciprocal_scale - "scale" a value into range [0, ep_ro)
+ * @val: value
+ * @ep_ro: right open interval endpoint
+ *
+ * Perform a "reciprocal multiplication" in order to "scale" a value into
+ * range [0, ep_ro), where the upper interval endpoint is right-open.
+ * This is useful, e.g. for accessing a index of an array containing
+ * ep_ro elements, for example. Think of it as sort of modulus, only that
+ * the result isn't that of modulo. ;) Note that if initial input is a
+ * small value, then result will return 0.
+ *
+ * Return: a result based on val in interval [0, ep_ro).
+ */
+static inline u32 reciprocal_scale(u32 val, u32 ep_ro)
+{
+	return (u32)(((u64) val * ep_ro) >> 32);
+}
+
 #if defined(CONFIG_MMU) && \
 	(defined(CONFIG_PROVE_LOCKING) || defined(CONFIG_DEBUG_ATOMIC_SLEEP))
 void might_fault(void);
diff --git a/include/net/codel.h b/include/net/codel.h
index 3b04ff5..fe0eab3 100644
--- a/include/net/codel.h
+++ b/include/net/codel.h
@@ -46,7 +46,6 @@
 #include <linux/skbuff.h>
 #include <net/pkt_sched.h>
 #include <net/inet_ecn.h>
-#include <linux/reciprocal_div.h>
 
 /* Controlling Queue Delay (CoDel) algorithm
  * =========================================
@@ -211,10 +210,9 @@ static codel_time_t codel_control_law(codel_time_t t,
 				      codel_time_t interval,
 				      u32 rec_inv_sqrt)
 {
-	return t + reciprocal_divide(interval, rec_inv_sqrt << REC_INV_SQRT_SHIFT);
+	return t + reciprocal_scale(interval, rec_inv_sqrt << REC_INV_SQRT_SHIFT);
 }
 
-
 static bool codel_should_drop(const struct sk_buff *skb,
 			      struct Qdisc *sch,
 			      struct codel_vars *vars,
diff --git a/net/packet/af_packet.c b/net/packet/af_packet.c
index 266c311..141b019 100644
--- a/net/packet/af_packet.c
+++ b/net/packet/af_packet.c
@@ -88,7 +88,6 @@
 #include <linux/virtio_net.h>
 #include <linux/errqueue.h>
 #include <linux/net_tstamp.h>
-#include <linux/reciprocal_div.h>
 #include <linux/percpu.h>
 #ifdef CONFIG_INET
 #include <net/inet_common.h>
@@ -1262,7 +1261,7 @@ static unsigned int fanout_demux_hash(struct packet_fanout *f,
 				      struct sk_buff *skb,
 				      unsigned int num)
 {
-	return reciprocal_divide(skb->rxhash, num);
+	return reciprocal_scale(skb->rxhash, num);
 }
 
 static unsigned int fanout_demux_lb(struct packet_fanout *f,
-- 
1.8.3.1

[PATCH net-next v3 3/3] reciprocal_divide: update/correction of the algorithm

[Daniel Borkmann]

From: Hannes Frederic Sowa <hannes@stressinduktion.org>

Jakub Zawadzki noticed that some divisions by reciprocal_divide()
were not correct [1][2], which he could also show with BPF code
after divisions are transformed into reciprocal_value() for runtime
invariance which can be passed to reciprocal_divide() later on;
reverse in BPF dump ended up with a different, off-by-one K in
some situations.

This has been fixed by Eric Dumazet in commit aee636c4809fa5
("bpf: do not use reciprocal divide"). This follow-up patch
improves reciprocal_value() and reciprocal_divide() to work in
all cases by using Granlund and Montgomery method, so that also
future use is safe and without any non-obvious side-effects.
Known problems with the old implementation were that division by 1
always returned 0 and some off-by-ones when the dividend and divisor
where very large. This seemed to not be problematic with its
current users, as far as we can tell. Eric Dumazet checked for
the slab usage, we cannot surely say so in the case of flex_array.
Still, in order to fix that, we propose an extension from the
original implementation from commit 6a2d7a955d8d resp. [3][4],
by using the algorithm proposed in "Division by Invariant Integers
Using Multiplication" [5], Torbjörn Granlund and Peter L.
Montgomery, that is, pseudocode for q = n/d where q, n, d is in
u32 universe:

1) Initialization:

  int l = ceil(log_2 d)
  uword m' = floor((1<<32)*((1<<l)-d)/d)+1
  int sh_1 = min(l,1)
  int sh_2 = max(l-1,0)

2) For q = n/d, all uword:

  uword t = (n*m')>>32
  q = (t+((n-t)>>sh_1))>>sh_2

The assembler implementation from Agner Fog [6] also helped a lot
while implementing. We have tested the implementation on x86_64,
ppc64, i686, s390x; on x86_64/haswell we're still half the latency
compared to normal divide.

Joint work with Daniel Borkmann.

  [1] http://www.wireshark.org/~darkjames/reciprocal-buggy.c
  [2] http://www.wireshark.org/~darkjames/set-and-dump-filter-k-bug.c
  [3] https://gmplib.org/~tege/division-paper.pdf
  [4] http://homepage.cs.uiowa.edu/~jones/bcd/divide.html
  [5] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2556
  [6] http://www.agner.org/optimize/asmlib.zip

Reported-by: Jakub Zawadzki <darkjames-ws@darkjames.pl>
Cc: Eric Dumazet <eric.dumazet@gmail.com>
Cc: Austin S Hemmelgarn <ahferroin7@gmail.com>
Cc: linux-kernel@vger.kernel.org
Cc: Jesse Gross <jesse@nicira.com>
Cc: Jamal Hadi Salim <jhs@mojatatu.com>
Cc: Stephen Hemminger <stephen@networkplumber.org>
Cc: Matt Mackall <mpm@selenic.com>
Cc: Pekka Enberg <penberg@kernel.org>
Cc: Christoph Lameter <cl@linux-foundation.org>
Cc: Andy Gospodarek <andy@greyhouse.net>
Cc: Veaceslav Falico <vfalico@redhat.com>
Cc: Jay Vosburgh <fubar@us.ibm.com>
Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl>
Signed-off-by: Daniel Borkmann <dborkman@redhat.com>
Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org>
---
 drivers/net/bonding/bond_main.c    | 24 ++++++++++++++++-------
 drivers/net/bonding/bond_netlink.c |  4 ----
 drivers/net/bonding/bond_options.c | 15 ++++++++++-----
 drivers/net/bonding/bond_sysfs.c   |  5 -----
 drivers/net/bonding/bonding.h      |  3 +++
 include/linux/flex_array.h         |  3 ++-
 include/linux/reciprocal_div.h     | 39 ++++++++++++++++++++------------------
 include/linux/slab_def.h           |  4 +++-
 include/net/red.h                  |  3 ++-
 lib/flex_array.c                   |  7 ++++++-
 lib/reciprocal_div.c               | 24 +++++++++++++++++++----
 net/sched/sch_netem.c              |  6 ++++--
 12 files changed, 88 insertions(+), 49 deletions(-)

diff --git a/drivers/net/bonding/bond_main.c b/drivers/net/bonding/bond_main.c
index 3220b48..f100bd9 100644
--- a/drivers/net/bonding/bond_main.c
+++ b/drivers/net/bonding/bond_main.c
@@ -79,7 +79,6 @@
 #include <net/pkt_sched.h>
 #include <linux/rculist.h>
 #include <net/flow_keys.h>
-#include <linux/reciprocal_div.h>
 #include "bonding.h"
 #include "bond_3ad.h"
 #include "bond_alb.h"
@@ -3596,8 +3595,9 @@ static void bond_xmit_slave_id(struct bonding *bond, struct sk_buff *skb, int sl
  */
 static u32 bond_rr_gen_slave_id(struct bonding *bond)
 {
-	int packets_per_slave = bond->params.packets_per_slave;
 	u32 slave_id;
+	struct reciprocal_value reciprocal_packets_per_slave;
+	int packets_per_slave = bond->params.packets_per_slave;
 
 	switch (packets_per_slave) {
 	case 0:
@@ -3607,8 +3607,10 @@ static u32 bond_rr_gen_slave_id(struct bonding *bond)
 		slave_id = bond->rr_tx_counter;
 		break;
 	default:
+		reciprocal_packets_per_slave =
+			bond->params.reciprocal_packets_per_slave;
 		slave_id = reciprocal_divide(bond->rr_tx_counter,
-					     packets_per_slave);
+					     reciprocal_packets_per_slave);
 		break;
 	}
 	bond->rr_tx_counter++;
@@ -4343,10 +4345,18 @@ static int bond_check_params(struct bond_params *params)
 	params->resend_igmp = resend_igmp;
 	params->min_links = min_links;
 	params->lp_interval = lp_interval;
-	if (packets_per_slave > 1)
-		params->packets_per_slave = reciprocal_value(packets_per_slave);
-	else
-		params->packets_per_slave = packets_per_slave;
+	params->packets_per_slave = packets_per_slave;
+	if (packets_per_slave > 0) {
+		params->reciprocal_packets_per_slave =
+			reciprocal_value(packets_per_slave);
+	} else {
+		/* reciprocal_packets_per_slave is unused if
+		 * packets_per_slave is 0 or 1, just initialize it
+		 */
+		params->reciprocal_packets_per_slave =
+			(struct reciprocal_value) { 0 };
+	}
+
 	if (primary) {
 		strncpy(params->primary, primary, IFNAMSIZ);
 		params->primary[IFNAMSIZ - 1] = 0;
diff --git a/drivers/net/bonding/bond_netlink.c b/drivers/net/bonding/bond_netlink.c
index 21c6488..e852655 100644
--- a/drivers/net/bonding/bond_netlink.c
+++ b/drivers/net/bonding/bond_netlink.c
@@ -19,7 +19,6 @@
 #include <linux/if_ether.h>
 #include <net/netlink.h>
 #include <net/rtnetlink.h>
-#include <linux/reciprocal_div.h>
 #include "bonding.h"
 
 int bond_get_slave(struct net_device *slave_dev, struct sk_buff *skb)
@@ -452,9 +451,6 @@ static int bond_fill_info(struct sk_buff *skb,
 		goto nla_put_failure;
 
 	packets_per_slave = bond->params.packets_per_slave;
-	if (packets_per_slave > 1)
-		packets_per_slave = reciprocal_value(packets_per_slave);
-
 	if (nla_put_u32(skb, IFLA_BOND_PACKETS_PER_SLAVE,
 			packets_per_slave))
 		goto nla_put_failure;
diff --git a/drivers/net/bonding/bond_options.c b/drivers/net/bonding/bond_options.c
index 945a666..85e4348 100644
--- a/drivers/net/bonding/bond_options.c
+++ b/drivers/net/bonding/bond_options.c
@@ -16,7 +16,6 @@
 #include <linux/netdevice.h>
 #include <linux/rwlock.h>
 #include <linux/rcupdate.h>
-#include <linux/reciprocal_div.h>
 #include "bonding.h"
 
 int bond_option_mode_set(struct bonding *bond, int mode)
@@ -671,11 +670,17 @@ int bond_option_packets_per_slave_set(struct bonding *bond,
 		pr_warn("%s: Warning: packets_per_slave has effect only in balance-rr mode\n",
 			bond->dev->name);
 
-	if (packets_per_slave > 1)
-		bond->params.packets_per_slave =
+	bond->params.packets_per_slave = packets_per_slave;
+	if (packets_per_slave > 0) {
+		bond->params.reciprocal_packets_per_slave =
 			reciprocal_value(packets_per_slave);
-	else
-		bond->params.packets_per_slave = packets_per_slave;
+	} else {
+		/* reciprocal_packets_per_slave is unused if
+		 * packets_per_slave is 0 or 1, just initialize it
+		 */
+		bond->params.reciprocal_packets_per_slave =
+			(struct reciprocal_value) { 0 };
+	}
 
 	return 0;
 }
diff --git a/drivers/net/bonding/bond_sysfs.c b/drivers/net/bonding/bond_sysfs.c
index 011f163..c083e9a 100644
--- a/drivers/net/bonding/bond_sysfs.c
+++ b/drivers/net/bonding/bond_sysfs.c
@@ -39,7 +39,6 @@
 #include <net/net_namespace.h>
 #include <net/netns/generic.h>
 #include <linux/nsproxy.h>
-#include <linux/reciprocal_div.h>
 
 #include "bonding.h"
 
@@ -1374,10 +1373,6 @@ static ssize_t bonding_show_packets_per_slave(struct device *d,
 {
 	struct bonding *bond = to_bond(d);
 	unsigned int packets_per_slave = bond->params.packets_per_slave;
-
-	if (packets_per_slave > 1)
-		packets_per_slave = reciprocal_value(packets_per_slave);
-
 	return sprintf(buf, "%u\n", packets_per_slave);
 }
 
diff --git a/drivers/net/bonding/bonding.h b/drivers/net/bonding/bonding.h
index 8a935f8..0a616c4 100644
--- a/drivers/net/bonding/bonding.h
+++ b/drivers/net/bonding/bonding.h
@@ -23,6 +23,8 @@
 #include <linux/netpoll.h>
 #include <linux/inetdevice.h>
 #include <linux/etherdevice.h>
+#include <linux/reciprocal_div.h>
+
 #include "bond_3ad.h"
 #include "bond_alb.h"
 
@@ -171,6 +173,7 @@ struct bond_params {
 	int resend_igmp;
 	int lp_interval;
 	int packets_per_slave;
+	struct reciprocal_value reciprocal_packets_per_slave;
 };
 
 struct bond_parm_tbl {
diff --git a/include/linux/flex_array.h b/include/linux/flex_array.h
index 6843cf1..b6efb0c 100644
--- a/include/linux/flex_array.h
+++ b/include/linux/flex_array.h
@@ -2,6 +2,7 @@
 #define _FLEX_ARRAY_H
 
 #include <linux/types.h>
+#include <linux/reciprocal_div.h>
 #include <asm/page.h>
 
 #define FLEX_ARRAY_PART_SIZE PAGE_SIZE
@@ -22,7 +23,7 @@ struct flex_array {
 			int element_size;
 			int total_nr_elements;
 			int elems_per_part;
-			u32 reciprocal_elems;
+			struct reciprocal_value reciprocal_elems;
 			struct flex_array_part *parts[];
 		};
 		/*
diff --git a/include/linux/reciprocal_div.h b/include/linux/reciprocal_div.h
index f9c90b3..8c5a3fb 100644
--- a/include/linux/reciprocal_div.h
+++ b/include/linux/reciprocal_div.h
@@ -4,29 +4,32 @@
 #include <linux/types.h>
 
 /*
- * This file describes reciprocical division.
+ * This algorithm is based on the paper "Division by Invariant
+ * Integers Using Multiplication" by Torbjörn Granlund and Peter
+ * L. Montgomery.
  *
- * This optimizes the (A/B) problem, when A and B are two u32
- * and B is a known value (but not known at compile time)
+ * The assembler implementation from Agner Fog, which this code is
+ * based on, can be found here:
+ * http://www.agner.org/optimize/asmlib.zip
  *
- * The math principle used is :
- *   Let RECIPROCAL_VALUE(B) be (((1LL << 32) + (B - 1))/ B)
- *   Then A / B = (u32)(((u64)(A) * (R)) >> 32)
- *
- * This replaces a divide by a multiply (and a shift), and
- * is generally less expensive in CPU cycles.
+ * This optimization for A/B is helpful if the divisor B is mostly
+ * runtime invariant. The reciprocal of B is calculated in the
+ * slow-path with reciprocal_value(). The fast-path can then just use
+ * a much faster multiplication operation with a variable dividend A
+ * to calculate the division A/B.
  */
 
-/*
- * Computes the reciprocal value (R) for the value B of the divisor.
- * Should not be called before each reciprocal_divide(),
- * or else the performance is slower than a normal divide.
- */
-extern u32 reciprocal_value(u32 B);
+struct reciprocal_value {
+	u32 m;
+	u8 sh1, sh2;
+};
 
+struct reciprocal_value reciprocal_value(u32 d);
 
-static inline u32 reciprocal_divide(u32 A, u32 R)
+static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
 {
-	return (u32)(((u64)A * R) >> 32);
+	u32 t = (u32)(((u64)a * R.m) >> 32);
+	return (t + ((a - t) >> R.sh1)) >> R.sh2;
 }
-#endif
+
+#endif /* _LINUX_RECIPROCAL_DIV_H */
diff --git a/include/linux/slab_def.h b/include/linux/slab_def.h
index 09bfffb..96e8aba 100644
--- a/include/linux/slab_def.h
+++ b/include/linux/slab_def.h
@@ -1,6 +1,8 @@
 #ifndef _LINUX_SLAB_DEF_H
 #define	_LINUX_SLAB_DEF_H
 
+#include <linux/reciprocal_div.h>
+
 /*
  * Definitions unique to the original Linux SLAB allocator.
  */
@@ -12,7 +14,7 @@ struct kmem_cache {
 	unsigned int shared;
 
 	unsigned int size;
-	u32 reciprocal_buffer_size;
+	struct reciprocal_value reciprocal_buffer_size;
 /* 2) touched by every alloc & free from the backend */
 
 	unsigned int flags;		/* constant flags */
diff --git a/include/net/red.h b/include/net/red.h
index 168bb2f..76e0b5f 100644
--- a/include/net/red.h
+++ b/include/net/red.h
@@ -130,7 +130,8 @@ struct red_parms {
 	u32		qth_max;	/* Max avg length threshold: Wlog scaled */
 	u32		Scell_max;
 	u32		max_P;		/* probability, [0 .. 1.0] 32 scaled */
-	u32		max_P_reciprocal; /* reciprocal_value(max_P / qth_delta) */
+	/* reciprocal_value(max_P / qth_delta) */
+	struct reciprocal_value	max_P_reciprocal;
 	u32		qth_delta;	/* max_th - min_th */
 	u32		target_min;	/* min_th + 0.4*(max_th - min_th) */
 	u32		target_max;	/* min_th + 0.6*(max_th - min_th) */
diff --git a/lib/flex_array.c b/lib/flex_array.c
index 6948a66..2eed22f 100644
--- a/lib/flex_array.c
+++ b/lib/flex_array.c
@@ -90,8 +90,8 @@ struct flex_array *flex_array_alloc(int element_size, unsigned int total,
 {
 	struct flex_array *ret;
 	int elems_per_part = 0;
-	int reciprocal_elems = 0;
 	int max_size = 0;
+	struct reciprocal_value reciprocal_elems = { 0 };
 
 	if (element_size) {
 		elems_per_part = FLEX_ARRAY_ELEMENTS_PER_PART(element_size);
@@ -119,6 +119,11 @@ EXPORT_SYMBOL(flex_array_alloc);
 static int fa_element_to_part_nr(struct flex_array *fa,
 					unsigned int element_nr)
 {
+	/*
+	 * if element_size == 0 we don't get here, so we never touch
+	 * the zeroed fa->reciprocal_elems, which would yield invalid
+	 * results
+	 */
 	return reciprocal_divide(element_nr, fa->reciprocal_elems);
 }
 
diff --git a/lib/reciprocal_div.c b/lib/reciprocal_div.c
index 75510e9..4641524 100644
--- a/lib/reciprocal_div.c
+++ b/lib/reciprocal_div.c
@@ -1,11 +1,27 @@
+#include <linux/kernel.h>
 #include <asm/div64.h>
 #include <linux/reciprocal_div.h>
 #include <linux/export.h>
 
-u32 reciprocal_value(u32 k)
+/*
+ * For a description of the algorithm please have a look at
+ * include/linux/reciprocal_div.h
+ */
+
+struct reciprocal_value reciprocal_value(u32 d)
 {
-	u64 val = (1LL << 32) + (k - 1);
-	do_div(val, k);
-	return (u32)val;
+	struct reciprocal_value R;
+	u64 m;
+	int l;
+
+	l = fls(d - 1);
+	m = ((1ULL << 32) * ((1ULL << l) - d));
+	do_div(m, d);
+	++m;
+	R.m = (u32)m;
+	R.sh1 = min(l, 1);
+	R.sh2 = max(l - 1, 0);
+
+	return R;
 }
 EXPORT_SYMBOL(reciprocal_value);
diff --git a/net/sched/sch_netem.c b/net/sched/sch_netem.c
index 3019c10..81fc5b0 100644
--- a/net/sched/sch_netem.c
+++ b/net/sched/sch_netem.c
@@ -91,7 +91,7 @@ struct netem_sched_data {
 	u64 rate;
 	s32 packet_overhead;
 	u32 cell_size;
-	u32 cell_size_reciprocal;
+	struct reciprocal_value cell_size_reciprocal;
 	s32 cell_overhead;
 
 	struct crndstate {
@@ -716,9 +716,11 @@ static void get_rate(struct Qdisc *sch, const struct nlattr *attr)
 	q->rate = r->rate;
 	q->packet_overhead = r->packet_overhead;
 	q->cell_size = r->cell_size;
+	q->cell_overhead = r->cell_overhead;
 	if (q->cell_size)
 		q->cell_size_reciprocal = reciprocal_value(q->cell_size);
-	q->cell_overhead = r->cell_overhead;
+	else
+		q->cell_size_reciprocal = (struct reciprocal_value) { 0 };
 }
 
 static int get_loss_clg(struct Qdisc *sch, const struct nlattr *attr)
-- 
1.8.3.1