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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>
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When some objects are allocated by one CPU but freed by another CPU we can
consume lot of cycles doing divides in obj_to_index().
(Typical load on a dual processor machine where network interrupts are
handled by one particular CPU (allocating skbufs), and the other CPU is
running the application (consuming and freeing skbufs))
Here on one production server (dual-core AMD Opteron 285), I noticed this
divide took 1.20 % of CPU_CLK_UNHALTED events in kernel. But Opteron are
quite modern cpus and the divide is much more expensive on oldest
architectures :
On a 200 MHz sparcv9 machine, the division takes 64 cycles instead of 1
cycle for a multiply.
Doing some math, we can use a reciprocal multiplication instead of a divide.
If we want to compute V = (A / B) (A and B being u32 quantities)
we can instead use :
V = ((u64)A * RECIPROCAL(B)) >> 32 ;
where RECIPROCAL(B) is precalculated to ((1LL << 32) + (B - 1)) / B
Note :
I wrote pure C code for clarity. gcc output for i386 is not optimal but
acceptable :
mull 0x14(%ebx)
mov %edx,%eax // part of the >> 32
xor %edx,%edx // useless
mov %eax,(%esp) // could be avoided
mov %edx,0x4(%esp) // useless
mov (%esp),%ebx
[akpm@osdl.org: small cleanups]
Signed-off-by: Eric Dumazet <dada1@cosmosbay.com>
Cc: Christoph Lameter <clameter@sgi.com>
Cc: David Miller <davem@davemloft.net>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
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Hannes Frederic Sowa
Eric Dumazet