reciprocal_divide: update/correction of the algorithm

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>
Signed-off-by: David S. Miller <davem@davemloft.net>

1 files changed, 3 insertions, 1 deletions

diff --git a/include/linux/slab_def.h b/include/linux/slab_def.h
index 09bfffb08a56..96e8abae19a9 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 */