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[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
#ifndef _LINUX_RECIPROCAL_DIV_H
#define _LINUX_RECIPROCAL_DIV_H
#include <linux/types.h>
/*
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 09:29:41 +08:00
* This algorithm is based on the paper "Division by Invariant
* Integers Using Multiplication" by Torbjörn Granlund and Peter
* L. Montgomery.
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
*
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 09:29:41 +08:00
* The assembler implementation from Agner Fog, which this code is
* based on, can be found here:
* http://www.agner.org/optimize/asmlib.zip
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
*
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 09:29:41 +08:00
* 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.
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
*/
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 09:29:41 +08:00
struct reciprocal_value {
u32 m;
u8 sh1, sh2;
};
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
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 09:29:41 +08:00
struct reciprocal_value reciprocal_value(u32 d);
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
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 09:29:41 +08:00
static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
{
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 09:29:41 +08:00
u32 t = (u32)(((u64)a * R.m) >> 32);
return (t + ((a - t) >> R.sh1)) >> R.sh2;
[PATCH] SLAB: use a multiply instead of a divide in obj_to_index() 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>
2006-12-13 16:34:27 +08:00
}
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 09:29:41 +08:00
#endif /* _LINUX_RECIPROCAL_DIV_H */