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authorHannes Frederic Sowa <hannes@stressinduktion.org>2014-01-22 02:29:41 +0100
committerDavid S. Miller <davem@davemloft.net>2014-01-21 23:17:20 -0800
commit809fa972fd90ff27225294b17a027e908b2d7b7a (patch)
tree3bb15ec5b897df4ea197339478bb5d76049a2761 /include
parent89770b0a69ee0e0e5e99c722192d535115f73778 (diff)
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>
Diffstat (limited to 'include')
-rw-r--r--include/linux/flex_array.h3
-rw-r--r--include/linux/reciprocal_div.h39
-rw-r--r--include/linux/slab_def.h4
-rw-r--r--include/net/red.h3
4 files changed, 28 insertions, 21 deletions
diff --git a/include/linux/flex_array.h b/include/linux/flex_array.h
index 6843cf193a44..b6efb0c64408 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 f9c90b33285b..8c5a3fb6c6c5 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 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 */
diff --git a/include/net/red.h b/include/net/red.h
index 168bb2f495f2..76e0b5f922c6 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) */