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>

2 files changed, 26 insertions, 5 deletions

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);