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=10.1.1.1.2556
  [6] http://www.agner.org/optimize/asmlib.zipReported-by: NJakub 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: NDaniel Borkmann <dborkman@redhat.com>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

On most architectures division is an expensive operation and accessing an
element currently requires four of them.  This performance penalty
effectively precludes flex arrays from being used on any kind of fast
path.  However, two of these divisions can be handled at creation time and
the others can be replaced by a reciprocal divide, completely avoiding
real divisions on access.

[eparis@redhat.com: rebase on top of changes to support 0 len elements]
[eparis@redhat.com: initialize part_nr when array fits entirely in base]
Signed-off-by: NJesse Gross <jesse@nicira.com>
Signed-off-by: NEric Paris <eparis@redhat.com>
Cc: Dave Hansen <dave@linux.vnet.ibm.com>
Cc: David Rientjes <rientjes@google.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

Change flex_array_prealloc to take the number of elements for which space
should be allocated instead of the last (inclusive) element. Users
and documentation are updated accordingly.  flex_arrays got introduced before
they had users.  When folks started using it, they ended up needing a
different API than was coded up originally.  This swaps over to the API that
folks apparently need.
Based-on-patch-by: NSteffen Klassert <steffen.klassert@secunet.com>
Signed-off-by: NEric Paris <eparis@redhat.com>
Tested-by: NChris Richards <gizmo@giz-works.com>
Acked-by: NDave Hansen <dave@linux.vnet.ibm.com>
Cc: stable@kernel.org [2.6.38+]

Change flex_array_prealloc to take the number of elements for which space
should be allocated instead of the last (inclusive) element. Users
and documentation are updated accordingly.  flex_arrays got introduced before
they had users.  When folks started using it, they ended up needing a
different API than was coded up originally.  This swaps over to the API that
folks apparently need.
Based-on-patch-by: NSteffen Klassert <steffen.klassert@secunet.com>
Signed-off-by: NEric Paris <eparis@redhat.com>
Tested-by: NChris Richards <gizmo@giz-works.com>
Acked-by: NDave Hansen <dave@linux.vnet.ibm.com>
Cc: stable@kernel.org [2.6.38+]

Using flex_array_put_ptr() results in a compile error "error: lvalue
required as unary ‘&’ operand"  fix the casting order to fix this.
Signed-off-by: NEric Paris <eparis@redhat.com>

Getting and putting arrays of pointers with flex arrays is a PITA.  You
have to remember to pass &ptr to the _put and you have to do weird and
wacky casting to get the ptr back from the _get.  Add two functions
flex_array_get_ptr() and flex_array_put_ptr() to handle all of the magic.

[akpm@linux-foundation.org: simplification suggested by Joe]
Signed-off-by: NEric Paris <eparis@redhat.com>
Cc: David Rientjes <rientjes@google.com>
Cc: Dave Hansen <dave@linux.vnet.ibm.com>
Cc: Joe Perches <joe@perches.com>
Cc: James Morris <jmorris@namei.org>
Cc: Joe Perches <joe@perches.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

FLEX_ARRAY_INIT(element_size, total_nr_elements) cannot determine if
either parameter is valid, so flex arrays which are statically allocated
with this interface can easily become corrupted or reference beyond its
allocated memory.

This removes FLEX_ARRAY_INIT() as a struct flex_array initializer since no
initializer may perform the required checking.  Instead, the array is now
defined with a new interface:

	DEFINE_FLEX_ARRAY(name, element_size, total_nr_elements)

This may be prefixed with `static' for file scope.

This interface includes compile-time checking of the parameters to ensure
they are valid.  Since the validity of both element_size and
total_nr_elements depend on FLEX_ARRAY_BASE_SIZE and FLEX_ARRAY_PART_SIZE,
the kernel build will fail if either of these predefined values changes
such that the array parameters are no longer valid.

Since BUILD_BUG_ON() requires compile time constants, several of the
static inline functions that were once local to lib/flex_array.c had to be
moved to include/linux/flex_array.h.
Signed-off-by: NDavid Rientjes <rientjes@google.com>
Acked-by: NDave Hansen <dave@linux.vnet.ibm.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

Add a new function to the flex_array API:

	int flex_array_shrink(struct flex_array *fa)

This function will free all unused second-level pages.  Since elements are
now poisoned if they are not allocated with __GFP_ZERO, it's possible to
identify parts that consist solely of unused elements.

flex_array_shrink() returns the number of pages freed.
Signed-off-by: NDavid Rientjes <rientjes@google.com>
Cc: Dave Hansen <dave@linux.vnet.ibm.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

Add a new function to the flex_array API:

	int flex_array_clear(struct flex_array *fa,
				unsigned int element_nr)

This function will zero the element at element_nr in the flex_array.

Although this is equivalent to using flex_array_put() and passing a
pointer to zero'd memory, flex_array_clear() does not require such a
pointer to memory that would most likely need to be allocated on the
caller's stack which could be significantly large depending on
element_size.
Signed-off-by: NDavid Rientjes <rientjes@google.com>
Cc: Dave Hansen <dave@linux.vnet.ibm.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

It's problematic to allow signed element_nr's or total's to be passed as
part of the flex array API.

flex_array_alloc() allows total_nr_elements to be set to a negative
quantity, which is obviously erroneous.

flex_array_get() and flex_array_put() allows negative array indices in
dereferencing an array part, which could address memory mapped before
struct flex_array.

The fix is to convert all existing element_nr formals to be qualified as
unsigned.  Existing checks to compare it to total_nr_elements or the max
array size based on element_size need not be changed.
Signed-off-by: NDavid Rientjes <rientjes@google.com>
Cc: Dave Hansen <dave@linux.vnet.ibm.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

The `parts' member of struct flex_array should evaluate to an incomplete
type so that sizeof() cannot be used and C99 does not require the
zero-length specification.
Signed-off-by: NDavid Rientjes <rientjes@google.com>
Acked-by: NDave Hansen <dave@linux.vnet.ibm.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

Once a structure goes over PAGE_SIZE*2, we see occasional allocation
failures.  Some people have chosen to switch over to things like vmalloc()
that will let them keep array-like access to such a large structures.
But, vmalloc() has plenty of downsides.

Here's an alternative.  I think it's what Andrew was suggesting here:

	http://lkml.org/lkml/2009/7/2/518

I call it a flexible array.  It does all of its work in PAGE_SIZE bits, so
never does an order>0 allocation.  The base level has
PAGE_SIZE-2*sizeof(int) bytes of storage for pointers to the second level.
 So, with a 32-bit arch, you get about 4MB (4183112 bytes) of total
storage when the objects pack nicely into a page.  It is half that on
64-bit because the pointers are twice the size.  There's a table detailing
this in the code.

There are kerneldocs for the functions, but here's an
overview:

flex_array_alloc() - dynamically allocate a base structure
flex_array_free() - free the array and all of the
		    second-level pages
flex_array_free_parts() - free the second-level pages, but
			  not the base (for static bases)
flex_array_put() - copy into the array at the given index
flex_array_get() - copy out of the array at the given index
flex_array_prealloc() - preallocate the second-level pages
			between the given indexes to
			guarantee no allocs will occur at
			put() time.

We could also potentially just pass the "element_size" into each of the
API functions instead of storing it internally.  That would get us one
more base pointer on 32-bit.

I've been testing this by running it in userspace.  The header and patch
that I've been using are here, as well as the little script I'm using to
generate the size table which goes in the kerneldocs.

	http://sr71.net/~dave/linux/flexarray/

[akpm@linux-foundation.org: coding-style fixes]
Signed-off-by: NDave Hansen <dave@linux.vnet.ibm.com>
Reviewed-by: NKAMEZAWA Hiroyuki <kamezawa.hiroyu@jp.fujitsu.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>