path: root/lib/reciprocal_div.c
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2014-01-21reciprocal_divide: update/correction of the algorithmHannes Frederic Sowa
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= [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>
2011-12-08sch_red: Adaptative RED AQMEric Dumazet
Adaptative RED AQM for linux, based on paper from Sally FLoyd, Ramakrishna Gummadi, and Scott Shenker, August 2001 : http://icir.org/floyd/papers/adaptiveRed.pdf Goal of Adaptative RED is to make max_p a dynamic value between 1% and 50% to reach the target average queue : (max_th - min_th) / 2 Every 500 ms: if (avg > target and max_p <= 0.5) increase max_p : max_p += alpha; else if (avg < target and max_p >= 0.01) decrease max_p : max_p *= beta; target :[min_th + 0.4*(min_th - max_th), min_th + 0.6*(min_th - max_th)]. alpha : min(0.01, max_p / 4) beta : 0.9 max_P is a Q0.32 fixed point number (unsigned, with 32 bits mantissa) Changes against our RED implementation are : max_p is no longer a negative power of two (1/(2^Plog)), but a Q0.32 fixed point number, to allow full range described in Adatative paper. To deliver a random number, we now use a reciprocal divide (thats really a multiply), but this operation is done once per marked/droped packet when in RED_BETWEEN_TRESH window, so added cost (compared to previous AND operation) is near zero. dump operation gives current max_p value in a new TCA_RED_MAX_P attribute. Example on a 10Mbit link : tc qdisc add dev $DEV parent 1:1 handle 10: est 1sec 8sec red \ limit 400000 min 30000 max 90000 avpkt 1000 \ burst 55 ecn adaptative bandwidth 10Mbit # tc -s -d qdisc show dev eth3 ... qdisc red 10: parent 1:1 limit 400000b min 30000b max 90000b ecn adaptative ewma 5 max_p=0.113335 Scell_log 15 Sent 50414282 bytes 34504 pkt (dropped 35, overlimits 1392 requeues 0) rate 9749Kbit 831pps backlog 72056b 16p requeues 0 marked 1357 early 35 pdrop 0 other 0 Signed-off-by: Eric Dumazet <eric.dumazet@gmail.com> Signed-off-by: David S. Miller <davem@davemloft.net>
2006-12-13[PATCH] SLAB: use a multiply instead of a divide in obj_to_index()Eric Dumazet
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>