Re: [Qemu-devel] [PATCH] page_cache: use multiplicative hash for page position calculation

[Laszlo Ersek <lersek@redhat.com>]

On 03/01/13 12:53, Peter Lieven wrote:
> instead of a linear mapping we use a multiplicative hash
> with the golden ratio to derive the cache bucket from the
> address. this helps to reduce collisions if memory positions
> are multiple of the cache size and it avoids a division
> in the position calculation.
> 
> Signed-off-by: Peter Lieven <pl@kamp.de>
> ---
>  page_cache.c |    5 ++++-
>  1 file changed, 4 insertions(+), 1 deletion(-)
> 
> diff --git a/page_cache.c b/page_cache.c
> index 376f1db..45d769a 100644
> --- a/page_cache.c
> +++ b/page_cache.c
> @@ -24,6 +24,7 @@
>  #include <strings.h>
> 
>  #include "qemu-common.h"
> +#include "qemu/host-utils.h"
>  #include "migration/page_cache.h"
> 
>  #ifdef DEBUG_CACHE
> @@ -48,6 +49,7 @@ struct PageCache {
>      int64_t max_num_items;
>      uint64_t max_item_age;
>      int64_t num_items;
> +    uint64_t hash_shift_bits;
>  };
> 
>  PageCache *cache_init(int64_t num_pages, unsigned int page_size)
> @@ -72,6 +74,7 @@ PageCache *cache_init(int64_t num_pages, unsigned int
> page_size)
>      cache->num_items = 0;
>      cache->max_item_age = 0;
>      cache->max_num_items = num_pages;
> +    cache->hash_shift_bits = clz64(num_pages-1);
> 
>      DPRINTF("Setting cache buckets to %" PRId64 "\n",
> cache->max_num_items);
> 
> @@ -108,7 +111,7 @@ static size_t cache_get_cache_pos(const PageCache
> *cache,
>      size_t pos;
> 
>      g_assert(cache->max_num_items);
> -    pos = (address / cache->page_size) & (cache->max_num_items - 1);
> +    pos = (address * 0x9e3779b97f4a7c13) >> cache->hash_shift_bits;
>      return pos;
>  }
> 

According to <http://www.brpreiss.com/books/opus4/html/page214.html>,
the multiplier "is chosen as the integer that is relatively prime to"
2^64 "which is closest to" (sqrt(5)-1)/2 * 2^64.

(sqrt(5)-1)/2 * 2^64 ~= 11400714819323198485.86699842797038469120

hence the constant would be a=0x9e3779b97f4a7c15. Any reason why a-2 is
used in the patch?

(Note: this is not a review or any suggestion to change the patch; I'm
just curious.)

A google-fight between "a" and "a-2" is inconclusive. So is stackoverflow:

http://stackoverflow.com/questions/4113278/64-bit-multiplicative-hashing
http://stackoverflow.com/questions/8513911/how-to-create-a-good-hash-combine-with-64-bit-output-inspired-by-boosthash-co

Thanks
Laszlo