Merge pull request #552 from ThomasWaldmann/hashtable-resizing

Hashtable resizing

.coveragerc

@@ -8,6 +8,7 @@ omit =
     */borg/fuse.py
     */borg/support/*
     */borg/testsuite/*
+    */borg/hash_sizes.py
 
 [report]
 exclude_lines =

borg/_hashindex.c

@@ -40,20 +40,43 @@ typedef struct {
     int upper_limit;
 } HashIndex;
 
+/* prime (or w/ big prime factors) hash table sizes
+ * not sure we need primes for borg's usage (as we have a hash function based
+ * on sha256, we can assume an even, seemingly random distribution of values),
+ * but OTOH primes don't harm.
+ * also, growth of the sizes starts with fast-growing 2x steps, but slows down
+ * more and more down to 1.1x. this is to avoid huge jumps in memory allocation,
+ * like e.g. 4G -> 8G.
+ * these values are generated by hash_sizes.py.
+ */
+static int hash_sizes[] = {
+    1031, 2053, 4099, 8209, 16411, 32771, 65537, 131101, 262147, 445649,
+    757607, 1287917, 2189459, 3065243, 4291319, 6007867, 8410991,
+    11775359, 16485527, 23079703, 27695653, 33234787, 39881729, 47858071,
+    57429683, 68915617, 82698751, 99238507, 119086189, 144378011, 157223263,
+    173476439, 190253911, 209915011, 230493629, 253169431, 278728861,
+    306647623, 337318939, 370742809, 408229973, 449387209, 493428073,
+    543105119, 596976533, 657794869, 722676499, 795815791, 874066969,
+    962279771, 1057701643, 1164002657, 1280003147, 1407800297, 1548442699,
+    1703765389, 1873768367, 2062383853, /* 32bit int ends about here */
+};
+
+#define HASH_MIN_LOAD .25
+#define HASH_MAX_LOAD .75  /* don't go higher than 0.75, otherwise performance severely suffers! */
+
+#define MAX(x, y) ((x) > (y) ? (x): (y))
+#define NELEMS(x) (sizeof(x) / sizeof((x)[0]))
+
 #define EMPTY _htole32(0xffffffff)
 #define DELETED _htole32(0xfffffffe)
-#define MAX_BUCKET_SIZE 512
-#define BUCKET_LOWER_LIMIT .25
-#define BUCKET_UPPER_LIMIT .75  /* don't go higher than 0.75, otherwise performance severely suffers! */
-#define MIN_BUCKETS 1031  /* must be prime, otherwise performance breaks down! */
-#define MAX(x, y) ((x) > (y) ? (x): (y))
+
 #define BUCKET_ADDR(index, idx) (index->buckets + (idx * index->bucket_size))
 
+#define BUCKET_MATCHES_KEY(index, idx, key) (memcmp(key, BUCKET_ADDR(index, idx), index->key_size) == 0)
+
 #define BUCKET_IS_DELETED(index, idx) (*((uint32_t *)(BUCKET_ADDR(index, idx) + index->key_size)) == DELETED)
 #define BUCKET_IS_EMPTY(index, idx) (*((uint32_t *)(BUCKET_ADDR(index, idx) + index->key_size)) == EMPTY)
 
-#define BUCKET_MATCHES_KEY(index, idx, key) (memcmp(key, BUCKET_ADDR(index, idx), index->key_size) == 0)
-
 #define BUCKET_MARK_DELETED(index, idx) (*((uint32_t *)(BUCKET_ADDR(index, idx) + index->key_size)) = DELETED)
 #define BUCKET_MARK_EMPTY(index, idx) (*((uint32_t *)(BUCKET_ADDR(index, idx) + index->key_size)) = EMPTY)
 
@@ -130,6 +153,53 @@ hashindex_resize(HashIndex *index, int capacity)
     return 1;
 }
 
+int get_lower_limit(int num_buckets){
+    int min_buckets = hash_sizes[0];
+    if (num_buckets <= min_buckets)
+        return 0;
+    return (int)(num_buckets * HASH_MIN_LOAD);
+}
+
+int get_upper_limit(int num_buckets){
+    int max_buckets = hash_sizes[NELEMS(hash_sizes) - 1];
+    if (num_buckets >= max_buckets)
+        return num_buckets;
+    return (int)(num_buckets * HASH_MAX_LOAD);
+}
+
+int size_idx(int size){
+    /* find the hash_sizes index with entry >= size */
+    int elems = NELEMS(hash_sizes);
+    int entry, i=0;
+    do{
+        entry = hash_sizes[i++];
+    }while((entry < size) && (i < elems));
+    if (i >= elems)
+        return elems - 1;
+    i--;
+    return i;
+}
+
+int fit_size(int current){
+    int i = size_idx(current);
+    return hash_sizes[i];
+}
+
+int grow_size(int current){
+    int i = size_idx(current) + 1;
+    int elems = NELEMS(hash_sizes);
+    if (i >= elems)
+        return hash_sizes[elems - 1];
+    return hash_sizes[i];
+}
+
+int shrink_size(int current){
+    int i = size_idx(current) - 1;
+    if (i < 0)
+        return hash_sizes[0];
+    return hash_sizes[i];
+}
+
 /* Public API */
 static HashIndex *
 hashindex_read(const char *path)
@@ -207,8 +277,8 @@ hashindex_read(const char *path)
     index->key_size = header.key_size;
     index->value_size = header.value_size;
     index->bucket_size = index->key_size + index->value_size;
-    index->lower_limit = index->num_buckets > MIN_BUCKETS ? ((int)(index->num_buckets * BUCKET_LOWER_LIMIT)) : 0;
-    index->upper_limit = (int)(index->num_buckets * BUCKET_UPPER_LIMIT);
+    index->lower_limit = get_lower_limit(index->num_buckets);
+    index->upper_limit = get_upper_limit(index->num_buckets);
 fail:
     if(fclose(fd) < 0) {
         EPRINTF_PATH(path, "fclose failed");
@@ -221,7 +291,7 @@ hashindex_init(int capacity, int key_size, int value_size)
 {
     HashIndex *index;
     int i;
-    capacity = MAX(MIN_BUCKETS, capacity);
+    capacity = fit_size(capacity);
 
     if(!(index = malloc(sizeof(HashIndex)))) {
         EPRINTF("malloc header failed");
@@ -237,8 +307,8 @@ hashindex_init(int capacity, int key_size, int value_size)
     index->value_size = value_size;
     index->num_buckets = capacity;
     index->bucket_size = index->key_size + index->value_size;
-    index->lower_limit = index->num_buckets > MIN_BUCKETS ? ((int)(index->num_buckets * BUCKET_LOWER_LIMIT)) : 0;
-    index->upper_limit = (int)(index->num_buckets * BUCKET_UPPER_LIMIT);
+    index->lower_limit = get_lower_limit(index->num_buckets);
+    index->upper_limit = get_upper_limit(index->num_buckets);
     for(i = 0; i < capacity; i++) {
         BUCKET_MARK_EMPTY(index, i);
     }
@@ -302,7 +372,7 @@ hashindex_set(HashIndex *index, const void *key, const void *value)
     if(idx < 0)
     {
         if(index->num_entries > index->upper_limit) {
-            if(!hashindex_resize(index, index->num_buckets * 2)) {
+            if(!hashindex_resize(index, grow_size(index->num_buckets))) {
                 return 0;
             }
         }
@@ -332,7 +402,7 @@ hashindex_delete(HashIndex *index, const void *key)
     BUCKET_MARK_DELETED(index, idx);
     index->num_entries -= 1;
     if(index->num_entries < index->lower_limit) {
-        if(!hashindex_resize(index, index->num_buckets / 2)) {
+        if(!hashindex_resize(index, shrink_size(index->num_buckets))) {
             return 0;
         }
     }

borg/hash_sizes.py

@@ -0,0 +1,103 @@
+"""
+Compute hashtable sizes with nices properties
+- prime sizes (for small to medium sizes)
+- 2 prime-factor sizes (for big sizes)
+- fast growth for small sizes
+- slow growth for big sizes
+
+Note:
+     this is just a tool for developers.
+     within borgbackup, it is just used to generate hash_sizes definition for _hashindex.c.
+"""
+
+from collections import namedtuple
+
+K, M, G = 2**10, 2**20, 2**30
+
+# hash table size (in number of buckets)
+start, end_p1, end_p2 = 1 * K, 127 * M, 2 * G - 10 * M  # stay well below 2^31 - 1
+
+Policy = namedtuple("Policy", "upto grow")
+
+policies = [
+    # which growth factor to use when growing a hashtable of size < upto
+    # grow fast (*2.0) at the start so we do not have to resize too often (expensive).
+    # grow slow (*1.1) for huge hash tables (do not jump too much in memory usage)
+    Policy(256*K, 2.0),
+    Policy(2*M, 1.7),
+    Policy(16*M, 1.4),
+    Policy(128*M, 1.2),
+    Policy(2*G-1, 1.1),
+]
+
+
+# slightly modified version of:
+# http://www.macdevcenter.com/pub/a/python/excerpt/pythonckbk_chap1/index1.html?page=2
+def eratosthenes():
+    """Yields the sequence of prime numbers via the Sieve of Eratosthenes."""
+    D = {}  # map each composite integer to its first-found prime factor
+    q = 2  # q gets 2, 3, 4, 5, ... ad infinitum
+    while True:
+        p = D.pop(q, None)
+        if p is None:
+            # q not a key in D, so q is prime, therefore, yield it
+            yield q
+            # mark q squared as not-prime (with q as first-found prime factor)
+            D[q * q] = q
+        else:
+            # let x <- smallest (N*p)+q which wasn't yet known to be composite
+            # we just learned x is composite, with p first-found prime factor,
+            # since p is the first-found prime factor of q -- find and mark it
+            x = p + q
+            while x in D:
+                x += p
+            D[x] = p
+        q += 1
+
+
+def two_prime_factors(pfix=65537):
+    """Yields numbers with 2 prime factors pfix and p."""
+    for p in eratosthenes():
+        yield pfix * p
+
+
+def get_grow_factor(size):
+    for p in policies:
+        if size < p.upto:
+            return p.grow
+
+
+def find_bigger_prime(gen, i):
+    while True:
+        p = next(gen)
+        if p >= i:
+            return p
+
+
+def main():
+    sizes = []
+    i = start
+
+    gen = eratosthenes()
+    while i < end_p1:
+        grow_factor = get_grow_factor(i)
+        p = find_bigger_prime(gen, i)
+        sizes.append(p)
+        i = int(i * grow_factor)
+
+    gen = two_prime_factors()  # for lower ram consumption
+    while i < end_p2:
+        grow_factor = get_grow_factor(i)
+        p = find_bigger_prime(gen, i)
+        sizes.append(p)
+        i = int(i * grow_factor)
+
+    print("""\
+static int hash_sizes[] = {
+    %s
+};
+""" % ', '.join(str(size) for size in sizes))
+
+
+if __name__ == '__main__':
+    main()