greenplumn integerset 源码
greenplumn integerset 代码
文件路径：/src/backend/lib/integerset.c
/*-------------------------------------------------------------------------
*
* integerset.c
* Data structure to hold a large set of 64-bit integers efficiently
*
* 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 clusters of nearby values
* very tightly.
*
* Memory consumption depends on the number of values stored, but also
* on how far the values are from each other. In the best case, with
* long runs of consecutive integers, memory consumption can be as low as
* 0.1 bytes per integer. In the worst case, if integers are more than
* 2^32 apart, it uses about 8 bytes per integer. In typical use, the
* consumption per integer is somewhere between those extremes, depending
* on the range of integers stored, and how "clustered" they are.
*
*
* Interface
* ---------
*
* 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 set member, if any
*
* 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.
*
*
* Limitations
* -----------
*
* - Values must be added in order. (Random insertions would require
* splitting nodes, which hasn't been implemented.)
*
* - Values cannot be added while iteration is in progress.
*
* - No support for removing values.
*
* 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.
*
*
* References
* ----------
*
* Simple-8b encoding is based on:
*
* 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)
*
*
* Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
* IDENTIFICATION
* src/backend/lib/integerset.c
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include "access/htup_details.h"
#include "lib/integerset.h"
#include "port/pg_bitutils.h"
#include "utils/memutils.h"
/*
* 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.)
*/
#define SIMPLE8B_MAX_VALUES_PER_CODEWORD 240
/*
* Parameters for shape of the in-memory B-tree.
*
* These set the size of each internal and leaf node. They don't necessarily
* need to be the same, because the tree is just an in-memory structure.
* With the default 64, each node is about 1 kb.
*
* If you change these, you must recalculate MAX_TREE_LEVELS, too!
*/
#define MAX_INTERNAL_ITEMS 64
#define MAX_LEAF_ITEMS 64
/*
* Maximum height of the tree.
*
* MAX_TREE_ITEMS is calculated from the "fan-out" of the B-tree. The
* theoretical maximum number of items that we can store in a set is 2^64,
* so MAX_TREE_LEVELS should be set so that:
*
* MAX_LEAF_ITEMS * MAX_INTERNAL_ITEMS ^ (MAX_TREE_LEVELS - 1) >= 2^64.
*
* In practice, we'll need far fewer levels, because you will run out of
* memory long before reaching that number, but let's be conservative.
*/
#define MAX_TREE_LEVELS 11
/*
* 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 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 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
* would hold) a particular integer. And by storing the rest in packed form,
* we still get pretty good memory density, if there are clusters of integers
* 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.
*/
typedef struct intset_node intset_node;
typedef struct intset_leaf_node intset_leaf_node;
typedef struct intset_internal_node intset_internal_node;
/* Common structure of both leaf and internal nodes. */
struct intset_node
{
uint16 level; /* tree level of this node */
uint16 num_items; /* number of items in this node */
};
/* Internal node */
struct intset_internal_node
{
/* common header, must match intset_node */
uint16 level; /* >= 1 on internal nodes */
uint16 num_items;
/*
* 'values' is an array of key values, and 'downlinks' are pointers to
* lower-level nodes, corresponding to the key values.
*/
uint64 values[MAX_INTERNAL_ITEMS];
intset_node *downlinks[MAX_INTERNAL_ITEMS];
};
/* Leaf node */
typedef struct
{
uint64 first; /* first integer in this item */
uint64 codeword; /* simple8b encoded differences from 'first' */
} leaf_item;
#define MAX_VALUES_PER_LEAF_ITEM (1 + SIMPLE8B_MAX_VALUES_PER_CODEWORD)
struct intset_leaf_node
{
/* common header, must match intset_node */
uint16 level; /* 0 on leafs */
uint16 num_items;
intset_leaf_node *next; /* right sibling, if any */
leaf_item items[MAX_LEAF_ITEMS];
};
/*
* 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
* 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.
*/
#define MAX_BUFFERED_VALUES (MAX_VALUES_PER_LEAF_ITEM * 2)
/*
* IntegerSet is the top-level object representing the set.
*
* 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
* intset_begin_iterate / intset_iterate_next.
*/
struct IntegerSet
{
/*
* 'context' is the memory context holding this integer set and all its
* tree nodes.
*
* 'mem_used' tracks the amount of memory used. We don't do anything with
* it in integerset.c itself, but the callers can ask for it with
* intset_memory_usage().
*/
MemoryContext context;
uint64 mem_used;
uint64 num_entries; /* total # of values in the set */
uint64 highest_value; /* highest value stored in this set */
/*
* B-tree to hold the packed values.
*
* 'rightmost_nodes' hold pointers to the rightmost node on each level.
* rightmost_parent[0] is rightmost leaf, rightmost_parent[1] is its
* parent, and so forth, all the way up to the root. These are needed when
* adding new values. (Currently, we require that new values are added at
* the end.)
*/
int num_levels; /* height of the tree */
intset_node *root; /* root node */
intset_node *rightmost_nodes[MAX_TREE_LEVELS];
intset_leaf_node *leftmost_leaf; /* leftmost leaf node */
/*
* Holding area for new items that haven't been inserted to the tree yet.
*/
uint64 buffered_values[MAX_BUFFERED_VALUES];
int num_buffered_values;
/*
* Iterator support.
*
* 'iter_values' is an array of integers ready to be returned to the
* caller; 'iter_num_values' is the length of that array, and
* 'iter_valueno' is the next index. 'iter_node' and 'iter_itemno' point
* to the leaf node, and item within the leaf node, to get the next batch
* of values from.
*
* 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'.
*/
bool iter_active; /* is iteration in progress? */
const uint64 *iter_values;
int iter_num_values; /* number of elements in 'iter_values' */
int iter_valueno; /* next index into 'iter_values' */
intset_leaf_node *iter_node; /* current leaf node */
int iter_itemno; /* next item in 'iter_node' to decode */
uint64 iter_values_buf[MAX_VALUES_PER_LEAF_ITEM];
};
/*
* Prototypes for internal functions.
*/
static void intset_update_upper(IntegerSet *intset, int level,
intset_node *child, uint64 child_key);
static void intset_flush_buffered_values(IntegerSet *intset);
static int intset_binsrch_uint64(uint64 value, uint64 *arr, int arr_elems,
bool nextkey);
static int intset_binsrch_leaf(uint64 value, leaf_item *arr, int arr_elems,
bool nextkey);
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;
intset = (IntegerSet *) palloc(sizeof(IntegerSet));
intset->context = CurrentMemoryContext;
intset->mem_used = GetMemoryChunkSpace(intset);
intset->num_entries = 0;
intset->highest_value = 0;
intset->num_levels = 0;
intset->root = NULL;
memset(intset->rightmost_nodes, 0, sizeof(intset->rightmost_nodes));
intset->leftmost_leaf = NULL;
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;
}
/*
* Allocate a new node.
*/
static intset_internal_node *
intset_new_internal_node(IntegerSet *intset)
{
intset_internal_node *n;
n = (intset_internal_node *) MemoryContextAlloc(intset->context,
sizeof(intset_internal_node));
intset->mem_used += GetMemoryChunkSpace(n);
n->level = 0; /* caller must set */
n->num_items = 0;
return n;
}
static intset_leaf_node *
intset_new_leaf_node(IntegerSet *intset)
{
intset_leaf_node *n;
n = (intset_leaf_node *) MemoryContextAlloc(intset->context,
sizeof(intset_leaf_node));
intset->mem_used += GetMemoryChunkSpace(n);
n->level = 0;
n->num_items = 0;
n->next = NULL;
return n;
}
/*
* Return the number of entries in the integer set.
*/
uint64
intset_num_entries(IntegerSet *intset)
{
return intset->num_entries;
}
/*
* Return the amount of memory used by the integer set.
*/
uint64
intset_memory_usage(IntegerSet *intset)
{
return intset->mem_used;
}
/*
* Add a value to the set.
*
* Values must be added in order.
*/
void
intset_add_member(IntegerSet *intset, uint64 x)
{
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 (intset->num_buffered_values >= MAX_BUFFERED_VALUES)
{
/* Time to flush our buffer */
intset_flush_buffered_values(intset);
Assert(intset->num_buffered_values < MAX_BUFFERED_VALUES);
}
/* Add it to the buffer of newly-added values */
intset->buffered_values[intset->num_buffered_values] = x;
intset->num_buffered_values++;
intset->num_entries++;
intset->highest_value = x;
}
/*
* Take a batch of buffered values, and pack them into the B-tree.
*/
static void
intset_flush_buffered_values(IntegerSet *intset)
{
uint64 *values = intset->buffered_values;
uint64 num_values = intset->num_buffered_values;
int num_packed = 0;
intset_leaf_node *leaf;
leaf = (intset_leaf_node *) intset->rightmost_nodes[0];
/*
* If the tree is completely empty, create the first leaf page, which is
* also the root.
*/
if (leaf == NULL)
{
/*
* This is the very first item in the set.
*
* Allocate root node. It's also a leaf.
*/
leaf = intset_new_leaf_node(intset);
intset->root = (intset_node *) leaf;
intset->leftmost_leaf = leaf;
intset->rightmost_nodes[0] = (intset_node *) leaf;
intset->num_levels = 1;
}
/*
* If there are less than MAX_VALUES_PER_LEAF_ITEM values in the buffer,
* stop. In most cases, we cannot encode that many values in a single
* value, but this way, the encoder doesn't have to worry about running
* out of input.
*/
while (num_values - num_packed >= MAX_VALUES_PER_LEAF_ITEM)
{
leaf_item item;
int num_encoded;
/*
* Construct the next leaf item, packing as many buffered values as
* possible.
*/
item.first = values[num_packed];
item.codeword = simple8b_encode(&values[num_packed + 1],
&num_encoded,
item.first);
/*
* Add the item to the node, allocating a new node if the old one is
* full.
*/
if (leaf->num_items >= MAX_LEAF_ITEMS)
{
/* Allocate new leaf and link it to the tree */
intset_leaf_node *old_leaf = leaf;
leaf = intset_new_leaf_node(intset);
old_leaf->next = leaf;
intset->rightmost_nodes[0] = (intset_node *) leaf;
intset_update_upper(intset, 1, (intset_node *) leaf, item.first);
}
leaf->items[leaf->num_items++] = item;
num_packed += 1 + num_encoded;
}
/*
* Move any remaining buffered values to the beginning of the array.
*/
if (num_packed < intset->num_buffered_values)
{
memmove(&intset->buffered_values[0],
&intset->buffered_values[num_packed],
(intset->num_buffered_values - num_packed) * sizeof(uint64));
}
intset->num_buffered_values -= num_packed;
}
/*
* Insert a downlink into parent node, after creating a new node.
*
* Recurses if the parent node is full, too.
*/
static void
intset_update_upper(IntegerSet *intset, int level, intset_node *child,
uint64 child_key)
{
intset_internal_node *parent;
Assert(level > 0);
/*
* Create a new root node, if necessary.
*/
if (level >= intset->num_levels)
{
intset_node *oldroot = intset->root;
uint64 downlink_key;
/* MAX_TREE_LEVELS should be more than enough, this shouldn't happen */
if (intset->num_levels == MAX_TREE_LEVELS)
elog(ERROR, "could not expand integer set, maximum number of levels reached");
intset->num_levels++;
/*
* Get the first value on the old root page, to be used as the
* downlink.
*/
if (intset->root->level == 0)
downlink_key = ((intset_leaf_node *) oldroot)->items[0].first;
else
downlink_key = ((intset_internal_node *) oldroot)->values[0];
parent = intset_new_internal_node(intset);
parent->level = level;
parent->values[0] = downlink_key;
parent->downlinks[0] = oldroot;
parent->num_items = 1;
intset->root = (intset_node *) parent;
intset->rightmost_nodes[level] = (intset_node *) parent;
}
/*
* Place the downlink on the parent page.
*/
parent = (intset_internal_node *) intset->rightmost_nodes[level];
if (parent->num_items < MAX_INTERNAL_ITEMS)
{
parent->values[parent->num_items] = child_key;
parent->downlinks[parent->num_items] = child;
parent->num_items++;
}
else
{
/*
* Doesn't fit. Allocate new parent, with the downlink as the first
* item on it, and recursively insert the downlink to the new parent
* to the grandparent.
*/
parent = intset_new_internal_node(intset);
parent->level = level;
parent->values[0] = child_key;
parent->downlinks[0] = child;
parent->num_items = 1;
intset->rightmost_nodes[level] = (intset_node *) parent;
intset_update_upper(intset, level + 1, (intset_node *) parent, child_key);
}
}
/*
* Does the set contain the given value?
*/
bool
intset_is_member(IntegerSet *intset, uint64 x)
{
intset_node *node;
intset_leaf_node *leaf;
int level;
int itemno;
leaf_item *item;
/*
* The value might be in the buffer of newly-added values.
*/
if (intset->num_buffered_values > 0 && x >= intset->buffered_values[0])
{
int itemno;
itemno = intset_binsrch_uint64(x,
intset->buffered_values,
intset->num_buffered_values,
false);
if (itemno >= intset->num_buffered_values)
return false;
else
return (intset->buffered_values[itemno] == x);
}
/*
* Start from the root, and walk down the B-tree to find the right leaf
* node.
*/
if (!intset->root)
return false;
node = intset->root;
for (level = intset->num_levels - 1; level > 0; level--)
{
intset_internal_node *n = (intset_internal_node *) node;
Assert(node->level == level);
itemno = intset_binsrch_uint64(x, n->values, n->num_items, true);
if (itemno == 0)
return false;
node = n->downlinks[itemno - 1];
}
Assert(node->level == 0);
leaf = (intset_leaf_node *) node;
/*
* 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)
return false;
item = &leaf->items[itemno - 1];
/* Is this a match to the first value on the item? */
if (item->first == x)
return true;
Assert(x > item->first);
/* Is it in the packed codeword? */
if (simple8b_contains(item->codeword, x, item->first))
return true;
return false;
}
/*
* Begin in-order scan through all the values.
*
* While the iteration is in-progress, you cannot add new values to the set.
*/
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;
intset->iter_num_values = 0;
intset->iter_values = intset->iter_values_buf;
}
/*
* Returns the next integer, when iterating.
*
* intset_begin_iterate() must be called first. intset_iterate_next() returns
* the next value in the set. Returns true, if there was another value, and
* stores the value in *next. Otherwise, returns false.
*/
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;
}
/* Decode next item in current leaf node, if any */
if (intset->iter_node &&
intset->iter_itemno < intset->iter_node->num_items)
{
leaf_item *item;
int num_decoded;
item = &intset->iter_node->items[intset->iter_itemno++];
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)
{
intset->iter_node = intset->iter_node->next;
intset->iter_itemno = 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 == (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;
}
break;
}
/* No more results. */
intset->iter_active = false;
*next = 0; /* prevent uninitialized-variable warnings */
return false;
}
/*
* intset_binsrch_uint64() -- search a sorted array of uint64s
*
* Returns the first position with key equal or less than the given key.
* The returned position would be the "insert" location for the given key,
* that is, the position where the new key should be inserted to.
*
* 'nextkey' affects the behavior on equal keys. If true, and there is an
* equal key in the array, this returns the position immediately after the
* equal key. If false, this returns the position of the equal key itself.
*/
static int
intset_binsrch_uint64(uint64 item, uint64 *arr, int arr_elems, bool nextkey)
{
int low,
high,
mid;
low = 0;
high = arr_elems;
while (high > low)
{
mid = low + (high - low) / 2;
if (nextkey)
{
if (item >= arr[mid])
low = mid + 1;
else
high = mid;
}
else
{
if (item > arr[mid])
low = mid + 1;
else
high = mid;
}
}
return low;
}
/* same, but for an array of leaf items */
static int
intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems, bool nextkey)
{
int low,
high,
mid;
low = 0;
high = arr_elems;
while (high > low)
{
mid = low + (high - low) / 2;
if (nextkey)
{
if (item >= arr[mid].first)
low = mid + 1;
else
high = mid;
}
else
{
if (item > arr[mid].first)
low = mid + 1;
else
high = mid;
}
}
return low;
}
/*
* Simple-8b encoding.
*
* 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
* 60-bit integer, or two 30-bit integers, for example.
*
* 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 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
* packed into the remaining 60 bits. The selector allows for 16 different
* ways of using the remaining 60 bits, called "modes". The number of integers
* packed into a single codeword in each mode is listed in the simple8b_modes
* table below. For example, consider the following codeword:
*
* 20-bit integer 20-bit integer 20-bit integer
* 1101 00000000000000010010 01111010000100100000 00000000000000010100
* ^
* selector
*
* The selector 1101 is 13 in decimal. From the modes table below, we see
* that it means that the codeword encodes three 20-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
* 500038.
*
* 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
* 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 value.
*/
static const struct simple8b_mode
{
uint8 bits_per_int;
uint8 num_ints;
} simple8b_modes[17] =
{
{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 */
{4, 15}, /* mode 5: fifteen 4-bit integers */
{5, 12}, /* mode 6: twelve 5-bit integers */
{6, 10}, /* mode 7: ten 6-bit integers */
{7, 8}, /* mode 8: eight 7-bit integers (four bits
* are wasted) */
{8, 7}, /* mode 9: seven 8-bit integers (four bits
* are wasted) */
{10, 6}, /* mode 10: six 10-bit integers */
{12, 5}, /* mode 11: five 12-bit integers */
{15, 4}, /* mode 12: four 15-bit integers */
{20, 3}, /* mode 13: three 20-bit integers */
{30, 2}, /* mode 14: two 30-bit integers */
{60, 1}, /* mode 15: one 60-bit integer */
{0, 0} /* sentinel value */
};
/*
* 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 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, ensuring that we can produce a full codeword.
*
* 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(const uint64 *ints, int *num_encoded, uint64 base)
{
int selector;
int nints;
int bits;
uint64 diff;
uint64 last_val;
uint64 codeword;
int i;
Assert(ints[0] > base);
/*
* 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
* mode to a wider one, and repeat. If it fits, move on to the next
* 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". 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; /* number of deltas we have accepted */
for (;;)
{
if (diff >= (UINT64CONST(1) << bits))
{
/* too large, step up to next mode */
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 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
* can only get here if the *first* delta is >= 2^60.
*/
Assert(i == 0);
*num_encoded = 0;
return EMPTY_CODEWORD;
}
/*
* Encode the integers using the selected mode. Note that we shift them
* into the codeword in reverse order, so that they will come out in the
* correct order in the decoder.
*/
codeword = 0;
if (bits > 0)
{
for (i = nints - 1; i > 0; i--)
{
diff = ints[i] - ints[i - 1] - 1;
codeword |= diff;
codeword <<= bits;
}
diff = ints[0] - base - 1;
codeword |= diff;
}
/* add selector to the codeword, and return */
codeword |= (uint64) selector << 60;
*num_encoded = nints;
return codeword;
}
/*
* 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;
int bits = simple8b_modes[selector].bits_per_int;
uint64 mask = (UINT64CONST(1) << bits) - 1;
uint64 curr_value;
if (codeword == EMPTY_CODEWORD)
return 0;
curr_value = base;
for (int i = 0; i < nints; i++)
{
uint64 diff = codeword & mask;
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 "key" is part of
* the codeword.
*/
static bool
simple8b_contains(uint64 codeword, uint64 key, uint64 base)
{
int selector = (codeword >> 60);
int nints = simple8b_modes[selector].num_ints;
int bits = simple8b_modes[selector].bits_per_int;
if (codeword == EMPTY_CODEWORD)
return false;
if (bits == 0)
{
/* Special handling for 0-bit cases. */
return (key - base) <= nints;
}
else
{
uint64 mask = (UINT64CONST(1) << bits) - 1;
uint64 curr_value;
curr_value = base;
for (int i = 0; i < nints; i++)
{
uint64 diff = codeword & mask;
curr_value += 1 + diff;
if (curr_value >= key)
{
if (curr_value == key)
return true;
else
return false;
}
codeword >>= bits;
}
}
return false;
}
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