[Mesa-dev] [PATCH 3/3] util: Change util/set to use quadratic probing

Thomas Helland thomashelland90 at gmail.com
Sat Apr 11 16:25:17 PDT 2015


The same rationale applies here as for the hash table.
Power of two size should give better performance,
and using the algorithm hash = sh + i/2 + i*i/2
should result in only distinct hash values when hitting collisions.

Difference at 95.0% confidence
     -7.9505 +/- 2.44011
   -5.04357% +/- 1.54794%

V3: Feedback from Eric Anholt
   - Don't change load factor and starting size.

V2: Feedback from Connor Abbott
   - Don't set initial hash address before potential rehash
   - Remove hash_sizes table
   - Correct the quadratic hashing algorithm
   - Use correct comment style

   Feedback from Jason Ekstrand
   - Use unreachable() to detect if we fail to insert

Signed-off-by: Thomas Helland <thomashelland90 at gmail.com>
---
 src/util/set.c | 118 ++++++++++++++++++++-------------------------------------
 src/util/set.h |   3 +-
 2 files changed, 43 insertions(+), 78 deletions(-)

diff --git a/src/util/set.c b/src/util/set.c
index f01f869..7ff9520 100644
--- a/src/util/set.c
+++ b/src/util/set.c
@@ -32,6 +32,17 @@
  *    Keith Packard <keithp at keithp.com>
  */
 
+/**
+ * Implements an open-addressing, quadratic probing hash-set.
+ *
+ * We choose set sizes that's a power of two.
+ * This is computationally less expensive than primes.
+ * As a bonus the size and free space can be calculated instead of looked up.
+ * FNV-1a has good avalanche properties, so collision is not an issue.
+ * These sets are sized to have an extra 10% free to avoid
+ * exponential performance degradation as the set fills.
+ */
+
 #include <stdlib.h>
 #include <assert.h>
 
@@ -39,51 +50,9 @@
 #include "ralloc.h"
 #include "set.h"
 
-/*
- * 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
- */
-
 uint32_t deleted_key_value;
 const void *deleted_key = &deleted_key_value;
 
-static const struct {
-   uint32_t max_entries, size, rehash;
-} 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 }
-};
-
 static int
 entry_is_free(struct set_entry *entry)
 {
@@ -114,10 +83,9 @@ _mesa_set_create(void *mem_ctx,
    if (ht == NULL)
       return NULL;
 
-   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->size_iteration = 2;
+   ht->size = 1 << ht->size_iteration;
+   ht->max_entries = ht->size * 0.9;
    ht->key_hash_function = key_hash_function;
    ht->key_equals_function = key_equals_function;
    ht->table = rzalloc_array(ht, struct set_entry, ht->size);
@@ -163,12 +131,11 @@ _mesa_set_destroy(struct set *ht, void (*delete_function)(struct set_entry *entr
 static struct set_entry *
 set_search(const struct set *ht, uint32_t hash, const void *key)
 {
-   uint32_t hash_address;
+   uint32_t start_hash_address = hash & (ht->size - 1);
+   uint32_t hash_address = start_hash_address;
+   uint32_t quad_hash = 1;
 
-   hash_address = hash % ht->size;
    do {
-      uint32_t double_hash;
-
       struct set_entry *entry = ht->table + hash_address;
 
       if (entry_is_free(entry)) {
@@ -179,10 +146,10 @@ set_search(const struct set *ht, uint32_t hash, const void *key)
          }
       }
 
-      double_hash = 1 + hash % ht->rehash;
-
-      hash_address = (hash_address + double_hash) % ht->size;
-   } while (hash_address != hash % ht->size);
+      hash_address = (start_hash_address +
+                (quad_hash + (quad_hash * quad_hash)) / 2) & (ht->size - 1);
+      quad_hash++;
+   } while (hash_address != start_hash_address);
 
    return NULL;
 }
@@ -207,35 +174,30 @@ static struct set_entry *
 set_add(struct set *ht, uint32_t hash, const void *key);
 
 static void
-set_rehash(struct set *ht, unsigned new_size_index)
+set_rehash(struct set *ht, uint32_t new_size_iteration)
 {
    struct set old_ht;
    struct set_entry *table, *entry;
 
-   if (new_size_index >= ARRAY_SIZE(hash_sizes))
+   if (new_size_iteration >= 31)
       return;
 
    table = rzalloc_array(ht, struct set_entry,
-                         hash_sizes[new_size_index].size);
+                         1 << new_size_iteration);
    if (table == NULL)
       return;
 
    old_ht = *ht;
 
    ht->table = table;
-   ht->size_index = new_size_index;
-   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->size_iteration = new_size_iteration;
+   ht->size = 1 << new_size_iteration;
+   ht->max_entries = ht->size * 0.7;
    ht->entries = 0;
    ht->deleted_entries = 0;
 
-   for (entry = old_ht.table;
-        entry != old_ht.table + old_ht.size;
-        entry++) {
-      if (entry_is_present(entry)) {
-         set_add(ht, entry->hash, entry->key);
-      }
+   set_foreach(&old_ht, entry) {
+      set_add(ht, entry->hash, entry->key);
    }
 
    ralloc_free(old_ht.table);
@@ -250,19 +212,21 @@ set_rehash(struct set *ht, unsigned new_size_index)
 static struct set_entry *
 set_add(struct set *ht, uint32_t hash, const void *key)
 {
-   uint32_t hash_address;
+   uint32_t start_hash_address, hash_address;
+   uint32_t quad_hash = 1;
    struct set_entry *available_entry = NULL;
 
    if (ht->entries >= ht->max_entries) {
-      set_rehash(ht, ht->size_index + 1);
+      set_rehash(ht, ht->size_iteration + 1);
    } else if (ht->deleted_entries + ht->entries >= ht->max_entries) {
-      set_rehash(ht, ht->size_index);
+      set_rehash(ht, ht->size_iteration);
    }
 
-   hash_address = hash % ht->size;
+   start_hash_address = hash & (ht->size - 1);
+   hash_address = start_hash_address;
+
    do {
       struct set_entry *entry = ht->table + hash_address;
-      uint32_t double_hash;
 
       if (!entry_is_present(entry)) {
          /* Stash the first available entry we find */
@@ -288,10 +252,11 @@ set_add(struct set *ht, uint32_t hash, const void *key)
          return entry;
       }
 
-      double_hash = 1 + hash % ht->rehash;
+      hash_address = (start_hash_address +
+                (quad_hash + (quad_hash * quad_hash)) / 2) & (ht->size - 1);
+      quad_hash++;
+   } while (hash_address != start_hash_address);
 
-      hash_address = (hash_address + double_hash) % ht->size;
-   } while (hash_address != hash % ht->size);
 
    if (available_entry) {
       if (entry_is_deleted(available_entry))
@@ -305,6 +270,7 @@ set_add(struct set *ht, uint32_t hash, const void *key)
    /* We could hit here if a required resize failed. An unchecked-malloc
     * application could ignore this result.
     */
+   unreachable("Failed to insert entry in hash set");
    return NULL;
 }
 
@@ -368,7 +334,7 @@ _mesa_set_random_entry(struct set *ht,
                        int (*predicate)(struct set_entry *entry))
 {
    struct set_entry *entry;
-   uint32_t i = rand() % ht->size;
+   uint32_t i = rand() & (ht->size - 1);
 
    if (ht->entries == 0)
       return NULL;
diff --git a/src/util/set.h b/src/util/set.h
index 9acd2c2..fa17d3a 100644
--- a/src/util/set.h
+++ b/src/util/set.h
@@ -46,9 +46,8 @@ struct set {
    uint32_t (*key_hash_function)(const void *key);
    bool (*key_equals_function)(const void *a, const void *b);
    uint32_t size;
-   uint32_t rehash;
    uint32_t max_entries;
-   uint32_t size_index;
+   uint32_t size_iteration;
    uint32_t entries;
    uint32_t deleted_entries;
 };
-- 
2.3.4



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