[Mesa-dev] [PATCH 2/4] util: Change hash_table to use quadratic probing

Eric Anholt eric at anholt.net
Mon Mar 16 15:46:02 PDT 2015


Thomas Helland <thomashelland90 at gmail.com> writes:

> This should give better cache locality, less memory consumption,
> and should also be faster since we avoid a modulo operation.
> Also change table size to be power of two.
> This gives better performance as we can do bitmasking instead of
> modulo operations for fitting the hash in the address space.
> By using the algorithm hash = sh + i/2 + i*i/2
> ee are guaranteed that all retries from the quad probing
> are distinct, and so should be able to completely fill the table.
> This passes the test added to exercise a worst case collision scenario.
> ---
>  src/util/hash_table.c | 101 +++++++++++++++++++++++++-------------------------
>  src/util/hash_table.h |   1 -
>  2 files changed, 50 insertions(+), 52 deletions(-)
>
> diff --git a/src/util/hash_table.c b/src/util/hash_table.c
> index 3247593..92ffc10 100644
> --- a/src/util/hash_table.c
> +++ b/src/util/hash_table.c
> @@ -33,7 +33,7 @@
>   */
>  
>  /**
> - * Implements an open-addressing, linear-reprobing hash table.
> + * Implements an open-addressing, quadratic probing hash table.
>   *
>   * For more information, see:
>   *
> @@ -51,44 +51,45 @@
>  static const uint32_t deleted_key_value;
>  
>  /**
> - * From Knuth -- a good choice for hash/rehash values is p, p-2 where
> - * p and p-2 are both prime.  These tables are sized to have an extra 10%
> - * free to avoid exponential performance degradation as the hash table fills
> + * We chose table sizes that's a power of two.
> + * This is computationally less expensive than primes.
> + * FNV-1a has good avalanche properties, so collision is not an issue.
> + * These tables are sized to have an extra 10% free to avoid
> + * exponential performance degradation as the hash table fills
>   */
>  static const struct {
> -   uint32_t max_entries, size, rehash;
> +   uint32_t max_entries, size;
>  } hash_sizes[] = {
> -   { 2,			5,		3	  },
> -   { 4,			7,		5	  },
> -   { 8,			13,		11	  },
> -   { 16,		19,		17	  },
> -   { 32,		43,		41        },
> -   { 64,		73,		71        },
> -   { 128,		151,		149       },
> -   { 256,		283,		281       },
> -   { 512,		571,		569       },
> -   { 1024,		1153,		1151      },
> -   { 2048,		2269,		2267      },
> -   { 4096,		4519,		4517      },
> -   { 8192,		9013,		9011      },
> -   { 16384,		18043,		18041     },
> -   { 32768,		36109,		36107     },
> -   { 65536,		72091,		72089     },
> -   { 131072,		144409,		144407    },
> -   { 262144,		288361,		288359    },
> -   { 524288,		576883,		576881    },
> -   { 1048576,		1153459,	1153457   },
> -   { 2097152,		2307163,	2307161   },
> -   { 4194304,		4613893,	4613891   },
> -   { 8388608,		9227641,	9227639   },
> -   { 16777216,		18455029,	18455027  },
> -   { 33554432,		36911011,	36911009  },
> -   { 67108864,		73819861,	73819859  },
> -   { 134217728,		147639589,	147639587 },
> -   { 268435456,		295279081,	295279079 },
> -   { 536870912,		590559793,	590559791 },
> -   { 1073741824,	1181116273,	1181116271},
> -   { 2147483648ul,	2362232233ul,	2362232231ul}
> +      { 3,            4            },
> +      { 7,            8            },
> +      { 14,           16           },
> +      { 28,           32           },
> +      { 57,           64           },
> +      { 115,          128          },
> +      { 230,          256          },
> +      { 460,          512          },
> +      { 921,          1024         },
> +      { 1843,         2048         },
> +      { 3686,         4096         },
> +      { 7372,         8192         },
> +      { 14745,        16384        },
> +      { 29491,        32768        },
> +      { 58982,        65536        },
> +      { 117964,       131072       },
> +      { 235929,       262144       },
> +      { 471859,       524288       },
> +      { 943718,       1048576      },
> +      { 1887436,      2097152      },
> +      { 3774873,      4194304      },
> +      { 7549747,      8388608      },
> +      { 15099494,     16777216     },
> +      { 30198988,     33554432     },
> +      { 60397977,     67108864     },
> +      { 120795955,    134217728    },
> +      { 241591910,    268435456    },
> +      { 483183820,    536870912    },
> +      { 966367641,    1073741824   },
> +      { 1932735283ul, 2147483648ul }
>  };
>  
>  static int
> @@ -123,7 +124,6 @@ _mesa_hash_table_create(void *mem_ctx,
>  
>     ht->size_index = 0;
>     ht->size = hash_sizes[ht->size_index].size;
> -   ht->rehash = hash_sizes[ht->size_index].rehash;
>     ht->max_entries = hash_sizes[ht->size_index].max_entries;
>     ht->key_hash_function = key_hash_function;
>     ht->key_equals_function = key_equals_function;
> @@ -182,12 +182,12 @@ _mesa_hash_table_set_deleted_key(struct hash_table *ht, const void *deleted_key)
>  static struct hash_entry *
>  hash_table_search(struct hash_table *ht, uint32_t hash, const void *key)
>  {
> -   uint32_t start_hash_address = hash % ht->size;
> +   uint32_t start_hash_address = hash & (ht->size - 1);
>     uint32_t hash_address = start_hash_address;
> +   // Start at 2, or we will match start_hash_address initially and bail
> +   uint32_t quad_hash = 2;
>  
>     do {
> -      uint32_t double_hash;
> -
>        struct hash_entry *entry = ht->table + hash_address;
>  
>        if (entry_is_free(entry)) {
> @@ -198,9 +198,9 @@ hash_table_search(struct hash_table *ht, uint32_t hash, const void *key)
>           }
>        }
>  
> -      double_hash = 1 + hash % ht->rehash;
> -
> -      hash_address = (hash_address + double_hash) % ht->size;
> +      hash_address = (start_hash_address + (quad_hash / 2) +
> +                      ((quad_hash * quad_hash) / 2)) & (ht->size - 1);
> +      quad_hash++;

I'm assuming you wanted the sequence quoted at:

http://en.wikipedia.org/wiki/Quadratic_probing

But looking at the iterations of your quad_hash, since you're using
integer math:

(2 / 2) + (2 * 2) / 2 = 1 + 2 = 3
(3 / 2) + (3 * 3) / 2 = 1 + 4 = 5
(4 / 2) + (4 * 4) / 2 = 2 + 8 = 10
(5 / 2) + (5 * 5) / 2 = 2 + 12 = 14

I think what you wanted as your probe is:

uint32_t double_hash = 1;
...
hash_address = (start_hash_address + ((quad_hash + quad_hash *
quad_hash) >> 1)) & (ht->size - 1)
quad_hash++;

Then you get:
(1 + 1 * 1) / 2 = 3 / 2 = 1
(2 + 2 * 2) / 2 = 6 / 2 = 3
(3 + 3 * 3) / 2 = 12 / 2 = 6
(4 + 4 * 4) / 2 = 20 / 2 = 10

-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 818 bytes
Desc: not available
URL: <http://lists.freedesktop.org/archives/mesa-dev/attachments/20150316/4d11eb92/attachment-0001.sig>


More information about the mesa-dev mailing list