* IntegerSet provides an in-memory data structure to hold a set of
* arbitrary 64-bit integers. Internally, the values are stored in a
* B-tree, with a special packed representation at the leaf level using
- * the Simple-8b algorithm, which can pack hold clusters of nearby values
+ * the Simple-8b algorithm, which can pack clusters of nearby values
* very tightly.
*
* Memory consumption depends on the number of values stored, but also
* Interface
* ---------
*
- * intset_create - Create a new empty set.
- * intset_add_member - Add an integer to the set.
+ * intset_create - Create a new, empty set
+ * intset_add_member - Add an integer to the set
* intset_is_member - Test if an integer is in the set
* intset_begin_iterate - Begin iterating through all integers in set
- * intset_iterate_next - Return next integer
+ * intset_iterate_next - Return next set member, if any
*
- * intset_create() creates the set in the current memory context. Note
- * that there is no function to free an integer set. If you need to do that,
- * create a dedicated memory context to hold it, and destroy the memory
+ * intset_create() creates the set in the current memory context. Subsequent
+ * operations that add to the data structure will continue to allocate from
+ * that same context, even if it's not current anymore.
+ *
+ * Note that there is no function to free an integer set. If you need to do
+ * that, create a dedicated memory context to hold it, and destroy the memory
* context instead.
*
*
*
* - No support for removing values.
*
- * None of these limitations are fundamental to the data structure, and
+ * None of these limitations are fundamental to the data structure, so they
* could be lifted if needed, by writing some new code. But the current
* users of this facility don't need them.
*
*
* Simple-8b encoding is based on:
*
- * Vo Ngoc Anh , Alistair Moffat, Index compression using 64-bit words,
+ * Vo Ngoc Anh, Alistair Moffat, Index compression using 64-bit words,
* Software - Practice & Experience, v.40 n.2, p.131-147, February 2010
* (https://doi.org/10.1002/spe.948)
*
/*
- * Maximum number of integers that can be encoded in a single Single-8b
+ * Maximum number of integers that can be encoded in a single Simple-8b
* codeword. (Defined here before anything else, so that we can size arrays
- * using this).
+ * using this.)
*/
#define SIMPLE8B_MAX_VALUES_PER_CODEWORD 240
* Node structures, for the in-memory B-tree.
*
* An internal node holds a number of downlink pointers to leaf nodes, or
- * to internal nodes on lower level. For each downlink, the key value
- * corresponding the lower level node is stored in a sorted array. The
+ * to internal nodes on a lower level. For each downlink, the key value
+ * corresponding to the lower level node is stored in a sorted array. The
* stored key values are low keys. In other words, if the downlink has value
* X, then all items stored on that child are >= X.
*
* Each leaf node holds a number of "items", with a varying number of
* integers packed into each item. Each item consists of two 64-bit words:
- * The first word holds first integer stored in the item, in plain format.
+ * The first word holds the first integer stored in the item, in plain format.
* The second word contains between 0 and 240 more integers, packed using
* Simple-8b encoding. By storing the first integer in plain, unpacked,
* format, we can use binary search to quickly find an item that holds (or
* with similar values.
*
* Each leaf node also has a pointer to the next leaf node, so that the leaf
- * nodes can be easily walked from beginning to end, when iterating.
+ * nodes can be easily walked from beginning to end when iterating.
*/
typedef struct intset_node intset_node;
typedef struct intset_leaf_node intset_leaf_node;
/* Common structure of both leaf and internal nodes. */
struct intset_node
{
- uint16 level;
- uint16 num_items;
+ uint16 level; /* tree level of this node */
+ uint16 num_items; /* number of items in this node */
};
/* Internal node */
/*
* We buffer insertions in a simple array, before packing and inserting them
* into the B-tree. MAX_BUFFERED_VALUES sets the size of the buffer. The
- * encoder assumes that it is large enough, that we can always fill a leaf
+ * encoder assumes that it is large enough that we can always fill a leaf
* item with buffered new items. In other words, MAX_BUFFERED_VALUES must be
* larger than MAX_VALUES_PER_LEAF_ITEM. For efficiency, make it much larger.
*/
/*
* IntegerSet is the top-level object representing the set.
*
- * The integers are stored in an in-memory B-tree structure, and an array
+ * The integers are stored in an in-memory B-tree structure, plus an array
* for newly-added integers. IntegerSet also tracks information about memory
- * usage, as well as the current position, when iterating the set with
+ * usage, as well as the current position when iterating the set with
* intset_begin_iterate / intset_iterate_next.
*/
struct IntegerSet
* Iterator support.
*
* 'iter_values' is an array of integers ready to be returned to the
- * caller. 'item_node' and 'item_itemno' point to the leaf node, and item
- * within the leaf node, to get the next batch of values from.
+ * caller; 'iter_num_values' is the length of that array, and
+ * 'iter_valueno' is the next index. 'iter_node' and 'item_itemno' point
+ * to the leaf node, and item within the leaf node, to get the next batch
+ * of values from.
*
- * Normally, 'iter_values' points 'iter_values_buf', which holds items
- * decoded from a leaf item. But after we have scanned the whole B-tree,
+ * Normally, 'iter_values' points to 'iter_values_buf', which holds items
+ * decoded from a leaf item. But after we have scanned the whole B-tree,
* we iterate through all the unbuffered values, too, by pointing
* iter_values to 'buffered_values'.
*/
- uint64 *iter_values;
+ bool iter_active; /* is iteration in progress? */
+
+ const uint64 *iter_values;
int iter_num_values; /* number of elements in 'iter_values' */
- int iter_valueno; /* index into 'iter_values' */
+ int iter_valueno; /* next index into 'iter_values' */
+
intset_leaf_node *iter_node; /* current leaf node */
- int iter_itemno; /* next item 'iter_node' to decode */
+ int iter_itemno; /* next item in 'iter_node' to decode */
uint64 iter_values_buf[MAX_VALUES_PER_LEAF_ITEM];
};
/*
- * prototypes for internal functions.
+ * Prototypes for internal functions.
*/
static void intset_update_upper(IntegerSet *intset, int level,
intset_node *new_node, uint64 new_node_item);
static int intset_binsrch_leaf(uint64 value, leaf_item *arr, int arr_elems,
bool nextkey);
-static uint64 simple8b_encode(uint64 *ints, int *num_encoded, uint64 base);
+static uint64 simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base);
static int simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base);
static bool simple8b_contains(uint64 codeword, uint64 key, uint64 base);
* Create a new, initially empty, integer set.
*
* The integer set is created in the current memory context.
+ * We will do all subsequent allocations in the same context, too, regardless
+ * of which memory context is current when new integers are added to the set.
*/
IntegerSet *
intset_create(void)
{
IntegerSet *intset;
- /*
- * Allocate the IntegerSet object in the current memory context. Remember
- * the context, so that we will do all subsequent allocations in the same
- * context, too, regardless of which memory context is current when new
- * integers are added to the set.
- */
intset = (IntegerSet *) palloc(sizeof(IntegerSet));
intset->context = CurrentMemoryContext;
intset->mem_used = GetMemoryChunkSpace(intset);
intset->num_buffered_values = 0;
+ intset->iter_active = false;
intset->iter_node = NULL;
intset->iter_itemno = 0;
intset->iter_valueno = 0;
intset->iter_num_values = 0;
+ intset->iter_values = NULL;
return intset;
}
void
intset_add_member(IntegerSet *intset, uint64 x)
{
- if (intset->iter_node)
- elog(ERROR, "cannot add new values to integer set when iteration is in progress");
+ if (intset->iter_active)
+ elog(ERROR, "cannot add new values to integer set while iteration is in progress");
if (x <= intset->highest_value && intset->num_entries > 0)
elog(ERROR, "cannot add value to integer set out of order");
if (itemno >= intset->num_buffered_values)
return false;
else
- return intset->buffered_values[itemno] == x;
+ return (intset->buffered_values[itemno] == x);
}
/*
leaf = (intset_leaf_node *) node;
/*
- * Binary search the right item on the leaf page
+ * Binary search to find the right item on the leaf page
*/
itemno = intset_binsrch_leaf(x, leaf->items, leaf->num_items, true);
if (itemno == 0)
void
intset_begin_iterate(IntegerSet *intset)
{
+ /* Note that we allow an iteration to be abandoned midway */
+ intset->iter_active = true;
intset->iter_node = intset->leftmost_leaf;
intset->iter_itemno = 0;
intset->iter_valueno = 0;
bool
intset_iterate_next(IntegerSet *intset, uint64 *next)
{
+ Assert(intset->iter_active);
for (;;)
{
+ /* Return next iter_values[] entry if any */
if (intset->iter_valueno < intset->iter_num_values)
{
*next = intset->iter_values[intset->iter_valueno++];
return true;
}
- /* Our queue is empty, decode next leaf item */
- if (intset->iter_node && intset->iter_itemno < intset->iter_node->num_items)
+ /* Decode next item in current leaf node, if any */
+ if (intset->iter_node &&
+ intset->iter_itemno < intset->iter_node->num_items)
{
- /* We have reached end of this packed item. Step to the next one. */
leaf_item *item;
int num_decoded;
item = &intset->iter_node->items[intset->iter_itemno++];
- intset->iter_values[0] = item->first;
- num_decoded = simple8b_decode(item->codeword, &intset->iter_values[1], item->first);
+ intset->iter_values_buf[0] = item->first;
+ num_decoded = simple8b_decode(item->codeword,
+ &intset->iter_values_buf[1],
+ item->first);
intset->iter_num_values = num_decoded + 1;
-
intset->iter_valueno = 0;
continue;
}
/* No more items on this leaf, step to next node */
if (intset->iter_node)
{
- /* No more matches on this bucket. Step to the next node. */
intset->iter_node = intset->iter_node->next;
intset->iter_itemno = 0;
- intset->iter_valueno = 0;
- intset->iter_num_values = 0;
continue;
}
* We have reached the end of the B-tree. But we might still have
* some integers in the buffer of newly-added values.
*/
- if (intset->iter_values == intset->iter_values_buf)
+ if (intset->iter_values == (const uint64 *) intset->iter_values_buf)
{
intset->iter_values = intset->buffered_values;
intset->iter_num_values = intset->num_buffered_values;
+ intset->iter_valueno = 0;
continue;
}
}
/* No more results. */
- *next = 0;
+ intset->iter_active = false;
+ *next = 0; /* prevent uninitialized-variable warnings */
return false;
}
/*
* Simple-8b encoding.
*
- * Simple-8b algorithm packs between 1 and 240 integers into 64-bit words,
+ * The simple-8b algorithm packs between 1 and 240 integers into 64-bit words,
* called "codewords". The number of integers packed into a single codeword
* depends on the integers being packed; small integers are encoded using
* fewer bits than large integers. A single codeword can store a single
* Since we're storing a unique, sorted, set of integers, we actually encode
* the *differences* between consecutive integers. That way, clusters of
* integers that are close to each other are packed efficiently, regardless
- * of the absolute values.
+ * of their absolute values.
*
* In Simple-8b, each codeword consists of a 4-bit selector, which indicates
* how many integers are encoded in the codeword, and the encoded integers are
* The selector 1101 is 13 in decimal. From the modes table below, we see
* that it means that the codeword encodes three 12-bit integers. In decimal,
* those integers are 18, 500000 and 20. Because we encode deltas rather than
- * absolute values, the actual values that they represent are 18, 500018 and
+ * absolute values, the actual values that they represent are 18, 500018 and
* 500038.
*
- * Modes 0 and 1 are a bit special; they encode a run of 240 or 120 zeros
+ * Modes 0 and 1 are a bit special; they encode a run of 240 or 120 zeroes
* (which means 240 or 120 consecutive integers, since we're encoding the
- * the deltas between integers), without using the rest of the codeword bits
+ * deltas between integers), without using the rest of the codeword bits
* for anything.
*
* Simple-8b cannot encode integers larger than 60 bits. Values larger than
* that are always stored in the 'first' field of a leaf item, never in the
* packed codeword. If there is a sequence of integers that are more than
* 2^60 apart, the codeword will go unused on those items. To represent that,
- * we use a magic EMPTY_CODEWORD codeword.
+ * we use a magic EMPTY_CODEWORD codeword value.
*/
-static const struct
+static const struct simple8b_mode
{
uint8 bits_per_int;
uint8 num_ints;
-} simple8b_modes[17] =
+} simple8b_modes[17] =
+
{
- {0, 240}, /* mode 0: 240 zeros */
- {0, 120}, /* mode 1: 120 zeros */
+ {0, 240}, /* mode 0: 240 zeroes */
+ {0, 120}, /* mode 1: 120 zeroes */
{1, 60}, /* mode 2: sixty 1-bit integers */
{2, 30}, /* mode 3: thirty 2-bit integers */
{3, 20}, /* mode 4: twenty 3-bit integers */
* EMPTY_CODEWORD is a special value, used to indicate "no values".
* It is used if the next value is too large to be encoded with Simple-8b.
*
- * This value looks like a 0-mode codeword, but we check for it
- * specifically. (In a real 0-mode codeword, all the unused bits are zero.)
+ * This value looks like a mode-0 codeword, but we can distinguish it
+ * because a regular mode-0 codeword would have zeroes in the unused bits.
*/
#define EMPTY_CODEWORD UINT64CONST(0x0FFFFFFFFFFFFFFF)
/*
* Encode a number of integers into a Simple-8b codeword.
*
+ * (What we actually encode are deltas between successive integers.
+ * "base" is the value before ints[0].)
+ *
* The input array must contain at least SIMPLE8B_MAX_VALUES_PER_CODEWORD
- * elements.
+ * elements, ensuring that we can produce a full codeword.
*
- * Returns the encoded codeword, and sets *num_encoded to the number
- * input integers that were encoded. It can be zero, if the first input is
- * too large to be encoded.
+ * Returns the encoded codeword, and sets *num_encoded to the number of
+ * input integers that were encoded. That can be zero, if the first delta
+ * is too large to be encoded.
*/
static uint64
-simple8b_encode(uint64 *ints, int *num_encoded, uint64 base)
+simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base)
{
int selector;
int nints;
Assert(ints[0] > base);
/*
- * Select the "mode" to use for the next codeword.
+ * Select the "mode" to use for this codeword.
*
* In each iteration, check if the next value can be represented in the
* current mode we're considering. If it's too large, then step up the
* integer. Repeat until the codeword is full, given the current mode.
*
* Note that we don't have any way to represent unused slots in the
- * codeword, so we require each codeword to be "full".
+ * codeword, so we require each codeword to be "full". It is always
+ * possible to produce a full codeword unless the very first delta is too
+ * large to be encoded. For example, if the first delta is small but the
+ * second is too large to be encoded, we'll end up using the last "mode",
+ * which has nints == 1.
*/
selector = 0;
nints = simple8b_modes[0].num_ints;
bits = simple8b_modes[0].bits_per_int;
diff = ints[0] - base - 1;
last_val = ints[0];
- i = 0;
+ i = 0; /* number of deltas we have accepted */
for (;;)
{
if (diff >= (UINT64CONST(1) << bits))
selector++;
nints = simple8b_modes[selector].num_ints;
bits = simple8b_modes[selector].bits_per_int;
-
+ /* we might already have accepted enough deltas for this mode */
if (i >= nints)
break;
}
else
{
+ /* accept this delta; then done if codeword is full */
i++;
if (i >= nints)
break;
-
+ /* examine next delta */
Assert(ints[i] > last_val);
diff = ints[i] - last_val - 1;
last_val = ints[i];
if (nints == 0)
{
/*
- * The first value is too large to be encoded with Simple-8b.
+ * The first delta is too large to be encoded with Simple-8b.
*
* If there is at least one not-too-large integer in the input, we
* will encode it using mode 15 (or a more compact mode). Hence, we
- * only get here, if the *first* input integer is >= 2^60.
+ * can only get here if the *first* delta is >= 2^60.
*/
Assert(i == 0);
*num_encoded = 0;
/*
* Decode a codeword into an array of integers.
+ * Returns the number of integers decoded.
*/
static int
simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
{
int selector = (codeword >> 60);
int nints = simple8b_modes[selector].num_ints;
- uint64 bits = simple8b_modes[selector].bits_per_int;
+ int bits = simple8b_modes[selector].bits_per_int;
uint64 mask = (UINT64CONST(1) << bits) - 1;
- uint64 prev_value;
+ uint64 curr_value;
if (codeword == EMPTY_CODEWORD)
return 0;
- prev_value = base;
+ curr_value = base;
for (int i = 0; i < nints; i++)
{
uint64 diff = codeword & mask;
- decoded[i] = prev_value + 1 + diff;
- prev_value = decoded[i];
+ curr_value += 1 + diff;
+ decoded[i] = curr_value;
codeword >>= bits;
}
return nints;
/*
* This is very similar to simple8b_decode(), but instead of decoding all
- * the values to an array, it just checks if the given integer is part of
+ * the values to an array, it just checks if the given "key" is part of
* the codeword.
*/
static bool
if (bits == 0)
{
/* Special handling for 0-bit cases. */
- return key - base <= nints;
+ return (key - base) <= nints;
}
else
{
uint64 mask = (UINT64CONST(1) << bits) - 1;
- uint64 prev_value;
+ uint64 curr_value;
- prev_value = base;
+ curr_value = base;
for (int i = 0; i < nints; i++)
{
uint64 diff = codeword & mask;
- uint64 curr_value;
- curr_value = prev_value + 1 + diff;
+ curr_value += 1 + diff;
if (curr_value >= key)
{
}
codeword >>= bits;
- prev_value = curr_value;
}
}
return false;
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