2006-12-13 15:34:27 +07:00
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#ifndef _LINUX_RECIPROCAL_DIV_H
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#define _LINUX_RECIPROCAL_DIV_H
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#include <linux/types.h>
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/*
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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>
2014-01-22 08:29:41 +07:00
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* This algorithm is based on the paper "Division by Invariant
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* Integers Using Multiplication" by Torbjörn Granlund and Peter
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* L. Montgomery.
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2006-12-13 15:34:27 +07:00
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*
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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>
2014-01-22 08:29:41 +07:00
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* The assembler implementation from Agner Fog, which this code is
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* based on, can be found here:
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* http://www.agner.org/optimize/asmlib.zip
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2006-12-13 15:34:27 +07:00
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*
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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>
2014-01-22 08:29:41 +07:00
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* This optimization for A/B is helpful if the divisor B is mostly
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* runtime invariant. The reciprocal of B is calculated in the
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* slow-path with reciprocal_value(). The fast-path can then just use
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* a much faster multiplication operation with a variable dividend A
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* to calculate the division A/B.
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2006-12-13 15:34:27 +07:00
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*/
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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>
2014-01-22 08:29:41 +07:00
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struct reciprocal_value {
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u32 m;
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u8 sh1, sh2;
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};
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2006-12-13 15:34:27 +07:00
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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>
2014-01-22 08:29:41 +07:00
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struct reciprocal_value reciprocal_value(u32 d);
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2006-12-13 15:34:27 +07:00
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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>
2014-01-22 08:29:41 +07:00
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static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
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2006-12-13 15:34:27 +07:00
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{
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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>
2014-01-22 08:29:41 +07:00
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u32 t = (u32)(((u64)a * R.m) >> 32);
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return (t + ((a - t) >> R.sh1)) >> R.sh2;
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2006-12-13 15:34:27 +07:00
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}
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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>
2014-01-22 08:29:41 +07:00
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#endif /* _LINUX_RECIPROCAL_DIV_H */
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