• Hannes Frederic Sowa's avatar
    reciprocal_divide: update/correction of the algorithm · 809fa972
    Hannes Frederic Sowa authored
    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 aee636c4
    ("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 6a2d7a95 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.zipReported-by: 's avatarJakub 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: 's avatarDaniel Borkmann <dborkman@redhat.com>
    Signed-off-by: 's avatarHannes Frederic Sowa <hannes@stressinduktion.org>
    Signed-off-by: 's avatarDavid S. Miller <davem@davemloft.net>