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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=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>