Date:	Wed,  7 Aug 2013 19:32:36 +0300 (EEST)
From:	"Kirill A. Shutemov" <kirill.shutemov@...ux.intel.com>
To:	Jan Kara <jack@...e.cz>
Cc:	"Kirill A. Shutemov" <kirill.shutemov@...ux.intel.com>,
	Andrea Arcangeli <aarcange@...hat.com>,
	Andrew Morton <akpm@...ux-foundation.org>,
	Al Viro <viro@...iv.linux.org.uk>,
	Hugh Dickins <hughd@...gle.com>,
	Wu Fengguang <fengguang.wu@...el.com>, Jan Kara <jack@...e.cz>,
	Mel Gorman <mgorman@...e.de>, linux-mm@...ck.org,
	Andi Kleen <ak@...ux.intel.com>,
	Matthew Wilcox <willy@...ux.intel.com>,
	"Kirill A. Shutemov" <kirill@...temov.name>,
	Hillf Danton <dhillf@...il.com>, Dave Hansen <dave@...1.net>,
	Ning Qu <quning@...gle.com>, linux-fsdevel@...r.kernel.org,
	linux-kernel@...r.kernel.org
Subject: Re: [PATCH 01/23] radix-tree: implement preload for multiple
 contiguous elements

Jan Kara wrote:
> On Sun 04-08-13 05:17:03, Kirill A. Shutemov wrote:
> > From: "Kirill A. Shutemov" <kirill.shutemov@...ux.intel.com>
> > 
> > The radix tree is variable-height, so an insert operation not only has
> > to build the branch to its corresponding item, it also has to build the
> > branch to existing items if the size has to be increased (by
> > radix_tree_extend).
> > 
> > The worst case is a zero height tree with just a single item at index 0,
> > and then inserting an item at index ULONG_MAX. This requires 2 new branches
> > of RADIX_TREE_MAX_PATH size to be created, with only the root node shared.
> > 
> > Radix tree is usually protected by spin lock. It means we want to
> > pre-allocate required memory before taking the lock.
> > 
> > Currently radix_tree_preload() only guarantees enough nodes to insert
> > one element. It's a hard limit. For transparent huge page cache we want
> > to insert HPAGE_PMD_NR (512 on x86-64) entries to address_space at once.
> > 
> > This patch introduces radix_tree_preload_count(). It allows to
> > preallocate nodes enough to insert a number of *contiguous* elements.
> > The feature costs about 5KiB per-CPU, details below.
> > 
> > Worst case for adding N contiguous items is adding entries at indexes
> > (ULONG_MAX - N) to ULONG_MAX. It requires nodes to insert single worst-case
> > item plus extra nodes if you cross the boundary from one node to the next.
> > 
> > Preload uses per-CPU array to store nodes. The total cost of preload is
> > "array size" * sizeof(void*) * NR_CPUS. We want to increase array size
> > to be able to handle 512 entries at once.
> > 
> > Size of array depends on system bitness and on RADIX_TREE_MAP_SHIFT.
> > 
> > We have three possible RADIX_TREE_MAP_SHIFT:
> > 
> >  #ifdef __KERNEL__
> >  #define RADIX_TREE_MAP_SHIFT	(CONFIG_BASE_SMALL ? 4 : 6)
> >  #else
> >  #define RADIX_TREE_MAP_SHIFT	3	/* For more stressful testing */
> >  #endif
> > 
> > On 64-bit system:
> > For RADIX_TREE_MAP_SHIFT=3, old array size is 43, new is 107.
> > For RADIX_TREE_MAP_SHIFT=4, old array size is 31, new is 63.
> > For RADIX_TREE_MAP_SHIFT=6, old array size is 21, new is 30.
> > 
> > On 32-bit system:
> > For RADIX_TREE_MAP_SHIFT=3, old array size is 21, new is 84.
> > For RADIX_TREE_MAP_SHIFT=4, old array size is 15, new is 46.
> > For RADIX_TREE_MAP_SHIFT=6, old array size is 11, new is 19.
> > 
> > On most machines we will have RADIX_TREE_MAP_SHIFT=6. In this case,
> > on 64-bit system the per-CPU feature overhead is
> >  for preload array:
> >    (30 - 21) * sizeof(void*) = 72 bytes
> >  plus, if the preload array is full
> >    (30 - 21) * sizeof(struct radix_tree_node) = 9 * 560 = 5040 bytes
> >  total: 5112 bytes
> > 
> > on 32-bit system the per-CPU feature overhead is
> >  for preload array:
> >    (19 - 11) * sizeof(void*) = 32 bytes
> >  plus, if the preload array is full
> >    (19 - 11) * sizeof(struct radix_tree_node) = 8 * 296 = 2368 bytes
> >  total: 2400 bytes
> > 
> > Since only THP uses batched preload at the moment, we disable (set max
> > preload to 1) it if !CONFIG_TRANSPARENT_HUGEPAGE_PAGECACHE. This can be
> > changed in the future.
> > 
> > Signed-off-by: Matthew Wilcox <willy@...ux.intel.com>
> > Signed-off-by: Kirill A. Shutemov <kirill.shutemov@...ux.intel.com>
> > Acked-by: Dave Hansen <dave.hansen@...ux.intel.com>
> > ---
> >  include/linux/radix-tree.h | 11 +++++++++++
> >  lib/radix-tree.c           | 41 ++++++++++++++++++++++++++++++++---------
> >  2 files changed, 43 insertions(+), 9 deletions(-)
> ...
> > diff --git a/lib/radix-tree.c b/lib/radix-tree.c
> > index 7811ed3..99ab73c 100644
> > --- a/lib/radix-tree.c
> > +++ b/lib/radix-tree.c
> > @@ -82,16 +82,24 @@ static struct kmem_cache *radix_tree_node_cachep;
> >   * The worst case is a zero height tree with just a single item at index 0,
> >   * and then inserting an item at index ULONG_MAX. This requires 2 new branches
> >   * of RADIX_TREE_MAX_PATH size to be created, with only the root node shared.
> > + *
> > + * Worst case for adding N contiguous items is adding entries at indexes
> > + * (ULONG_MAX - N) to ULONG_MAX. It requires nodes to insert single worst-case
> > + * item plus extra nodes if you cross the boundary from one node to the next.
> > + *
> >   * Hence:
> >   */
> > -#define RADIX_TREE_PRELOAD_SIZE (RADIX_TREE_MAX_PATH * 2 - 1)
> > +#define RADIX_TREE_PRELOAD_MIN (RADIX_TREE_MAX_PATH * 2 - 1)
> > +#define RADIX_TREE_PRELOAD_MAX \
> > +	(RADIX_TREE_PRELOAD_MIN + \
> > +	 DIV_ROUND_UP(RADIX_TREE_PRELOAD_NR - 1, RADIX_TREE_MAP_SIZE))
>   Umm, is this really correct? I see two problems:
> 1) You may need internal tree nodes at various levels but you seem to
> account only for the level 1.
> 2) The rounding doesn't seem right because RADIX_TREE_MAP_SIZE+2 nodes may
> require 3 nodes at level 1 if the indexes are like:
> i_0 | i_1 .. i_{RADIX_TREE_MAP_SIZE} | i_{RADIX_TREE_MAP_SIZE+1}
>     ^                                ^
>     node boundary                    node boundary

My bad. Let's try to calculate once again.

We want to insert N contiguous items without restriction on alignment.

Let's limit N <= 1UL << (2 * RADIX_TREE_MAP_SHIFT), without
CONFIG_BASE_SMALL it's 4096. It will simplify calculation a bit.

Worst case scenario, I can imagine, is tree with only one element at index
0 and we add N items where at least one index requires max tree high and
we cross boundary between items in root node.

Basically, at least one index is less then

1UL << ((RADIX_TREE_MAX_PATH - 1) * RADIX_TREE_MAP_SHIFT)

and one equal or more.

In this case we need:

- RADIX_TREE_MAX_PATH nodes to build new path to item with index 0;
- DIV_ROUND_UP(N, RADIX_TREE_MAP_SIZE) nodes for last level nodes for new
  items;
- 2 * (RADIX_TREE_MAX_PATH - 2) nodes to build path to last level nodes.
  (-2, because root node and last level nodes are already accounted).

The macro:

#define RADIX_TREE_PRELOAD_MAX \
	( RADIX_TREE_MAX_PATH + \
	  DIV_ROUND_UP(RADIX_TREE_PRELOAD_NR, RADIX_TREE_MAP_SIZE) + \
	  2 * (RADIX_TREE_MAX_PATH - 2) )

For 64-bit system and N=512, RADIX_TREE_PRELOAD_MAX is 37.

Does it sound correct? Any thoughts?

-- 
 Kirill A. Shutemov
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