path: root/src/support/huffman.c

/*-
 * Copyright (c) 2014-2017 MongoDB, Inc.
 * Copyright (c) 2008-2014 WiredTiger, Inc.
 *	All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 4. Neither the name MongoDB or the name WiredTiger
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY MONGODB INC. ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#include "wt_internal.h"

#define	__HUFFMAN_DETAIL	0	/* Set to 1 for debugging output. */

/* Length of header in compressed message, in bits. */
#define	WT_HUFFMAN_HEADER 	3

/*
 * Maximum allowed length of Huffman code words, which otherwise can range up
 * to (#symbols - 1) bits long.  Lower value to use less memory for tables,
 * higher value for better compression.  Max value = 16 (or 32-7=25 or 64-7=57
 * if adjust data types).  FYI, JPEG uses 16.  A side effect of limiting max
 * code length is that the worst case compression (a message of the least
 * frequent symbols) is shorter.
 */
#define	MAX_CODE_LENGTH		16

typedef struct __wt_freqtree_node {
	/*
	 * Data structure representing a node of the huffman tree. It holds a
	 * 64-bit weight and pointers to the left and right child nodes.  The
	 * node either has two child nodes or none.
	 */
	uint8_t  symbol;			/* only used in leaf nodes */
	uint64_t weight;
	struct __wt_freqtree_node *left;	/* bit 0 */
	struct __wt_freqtree_node *right;	/* bit 1 */
} WT_FREQTREE_NODE;

typedef struct __wt_huffman_code {
	uint16_t pattern;		/* requirement: length of field's type
					 * in bits >= MAX_CODE_LENGTH.
					 */
	uint8_t length;
} WT_HUFFMAN_CODE;

typedef struct __wt_huffman_obj {
	/*
	 * Data structure here defines specific instance of the encoder/decoder.
	 */
	u_int	numSymbols;		/* Symbols: UINT16_MAX or UINT8_MAX */

	uint16_t max_depth, min_depth;	/* Tree max/min depths */

	/*
	 * use: codes[symbol] = struct with pattern and length.
	 * Used in encoding and decoding.
	 * memory: codes[0-to-(number of symbols - 1)]
	 */
	WT_HUFFMAN_CODE *codes;

	/*
	 * use: code2symbol[Huffman_code] = symbol.
	 * Used in decoding.
	 * memory: code2symbol[1 << max_code_length]
	 */
	uint8_t *code2symbol;
} WT_HUFFMAN_OBJ;

/*
 * Queue element data structure.
 *
 * Consists of a pointer to a huffman tree node, and a pointer to the next
 * element in the queue.
 */
typedef struct node_queue_elem {
	WT_FREQTREE_NODE *node;
	struct node_queue_elem *next;
} NODE_QUEUE_ELEM;

/*
 * Queue of huffman tree nodes.
 *
 * Contains a pointer to the beginning and the end of the queue, which is
 * implemented as a linked list.
 */
typedef struct node_queue {
	NODE_QUEUE_ELEM *first;
	NODE_QUEUE_ELEM *last;
} NODE_QUEUE;

/*
 * Internal data structure used to preserve the symbol when rearranging the
 * frequency array.
 */
typedef struct __indexed_byte {
	uint32_t symbol;	/* not uint8_t: match external data structure */
	uint32_t frequency;
} INDEXED_SYMBOL;

static int WT_CDECL indexed_freq_compare(const void *, const void *);
static int WT_CDECL indexed_symbol_compare(const void *, const void *);
static void make_table(
	WT_SESSION_IMPL *, uint8_t *, uint16_t, WT_HUFFMAN_CODE *, u_int);
static void node_queue_close(WT_SESSION_IMPL *, NODE_QUEUE *);
static void node_queue_dequeue(
	WT_SESSION_IMPL *, NODE_QUEUE *, WT_FREQTREE_NODE **);
static int  node_queue_enqueue(
	WT_SESSION_IMPL *, NODE_QUEUE *, WT_FREQTREE_NODE *);
static uint32_t profile_tree(
	WT_FREQTREE_NODE *, uint16_t, uint16_t *, uint16_t *);
static void recursive_free_node(WT_SESSION_IMPL *, WT_FREQTREE_NODE *);
static void set_codes(WT_FREQTREE_NODE *, WT_HUFFMAN_CODE *, uint16_t, uint8_t);

#define	node_queue_is_empty(queue)					\
	((queue) == NULL || (queue)->first == NULL)

/*
 * indexed_symbol_compare --
 *	Qsort comparator to order the table by symbol, lowest to highest.
 */
static int WT_CDECL
indexed_symbol_compare(const void *a, const void *b)
{
	return (((INDEXED_SYMBOL *)a)->symbol >
	    ((INDEXED_SYMBOL *)b)->symbol ? 1 :
	    (((INDEXED_SYMBOL *)a)->symbol <
	    ((INDEXED_SYMBOL *)b)->symbol ? -1 : 0));
}

/*
 * indexed_freq_compare --
 *	Qsort comparator to order the table by frequency (the most frequent
 * symbols will be at the end of the array).
 */
static int WT_CDECL
indexed_freq_compare(const void *a, const void *b)
{
	return (((INDEXED_SYMBOL *)a)->frequency >
	    ((INDEXED_SYMBOL *)b)->frequency ? 1 :
	    (((INDEXED_SYMBOL *)a)->frequency <
	    ((INDEXED_SYMBOL *)b)->frequency ? -1 : 0));
}

/*
 * profile_tree --
 *	Traverses tree to determine #leaves under each node, max depth, min
 *	depth of leaf.
 */
static uint32_t
profile_tree(WT_FREQTREE_NODE *node,
    uint16_t len, uint16_t *max_depth, uint16_t *min_depth)
{
	uint32_t leaf_cnt;

	if (node->left == NULL && node->right == NULL) {	/* leaf */
		leaf_cnt = 1;
		if (*max_depth < len)
			*max_depth = len;
		if (*min_depth > len)
			*min_depth = len;
	} else {
		/*
		 * internal node -- way tree constructed internal always has
		 * left and right children
		 */
		leaf_cnt =
		    profile_tree(node->left, len + 1, max_depth, min_depth) +
		    profile_tree(node->right, len + 1, max_depth, min_depth);
	}
	node->weight = leaf_cnt;		/* abuse weight field */
	return (leaf_cnt);
}

/*
 * set_codes --
 *	Computes Huffman code for each symbol in tree.
 *
 * Method is standard way in the literature, except that limits maximum code
 * length.  A known max code length is important for limiting memory use by
 * the tables and for knowing how large data types need to be such as the field
 * that holds the code pattern.
 */
static void
set_codes(WT_FREQTREE_NODE *node,
    WT_HUFFMAN_CODE *codes, uint16_t pattern, uint8_t len)
{
	WT_HUFFMAN_CODE *code;
	uint16_t patternleft, patternright, half;
	uint8_t remaining;

	if (node->left == NULL && node->right == NULL) {
		code = &codes[node->symbol];
		code->pattern = pattern;
		code->length = len;
#if __HUFFMAN_DETAIL
		printf("%" PRIx16 ": code %" PRIx16 ", len %" PRIu8 "\n",
		    node->symbol, pattern, len);
#endif
	} else {
		/*
		 * Check each subtree individually to see if can afford to split
		 * up bits into possibly shorter codes, or if need to employ all
		 * remaining bits up to MAX_CODE_LENGTH to consecutively number
		 * leaves.
		 */
		remaining = MAX_CODE_LENGTH - len;
		/*
		 * If not already in "low-bit mode", but need to be, open up
		 * lower-order bits for consecutive numbering.
		 */
		if (len < MAX_CODE_LENGTH &&
		    ((half = (uint16_t)(1 << (remaining - 1))) <
		    node->left->weight || half < node->right->weight)) {
			pattern = (uint16_t)(pattern << remaining);
			len = MAX_CODE_LENGTH;
		}

		if (len < MAX_CODE_LENGTH) {
			patternleft = (uint16_t)((pattern << 1) | 0);
			patternright = (uint16_t)((pattern << 1) | 1);
			len++;
		} else {			/* "low bit mode" */
			patternleft = pattern;
			patternright = (uint16_t)(pattern + node->left->weight);
						/* len unchanged */
		}

		set_codes(node->left, codes, patternleft, len);
		set_codes(node->right, codes, patternright, len);
	}
}

/*
 * make_table --
 *	Computes Huffman table used for subsequent lookups in encoding and
 * decoding.  With the table, encoding from a symbol to Huffman code and
 * decoding from a code to a symbol are simple array lookups.
 */
static void
make_table(WT_SESSION_IMPL *session, uint8_t *code2symbol,
    uint16_t max_depth, WT_HUFFMAN_CODE *codes, u_int symcnt)
{
	uint32_t j, c1, c2;	/* Exceeds uint16_t bounds at loop boundary. */
	uint16_t c, i;
	uint8_t len, shift;

	/* Zero out, for assertion below. */
	for (j = 0, c2 = (1U << max_depth); j < c2; j++)
		code2symbol[j] = 0;

	/*
	 * Here's the magic: flood all bit patterns for lower-order bits to
	 * point to same symbol.
	 */
	for (i = 0; i < symcnt; i++) {
		if ((len = codes[i].length) == 0)
			continue;

		/*
		 * The size of the array index should be enough to hold largest
		 * index into symbol table.  Pre-existing symbols were packed
		 * 0-255, so 8 bits is enough.  Don't want to make it larger
		 * than necessary, we allocate (2 ^ max-code-length) of them.
		 */
		c = codes[i].pattern;
		shift = (uint8_t)(max_depth - len);
		c1 = (uint32_t)c << shift;
		c2 = (uint32_t)(c + 1) << shift;
		for (j = c1; j < c2; j++) {
			WT_ASSERT(session, code2symbol[j] == 0);
			code2symbol[j] = (uint8_t)i;
		}
	}
}

/*
 * recursive_free_node --
 *	Recursively free the huffman frequency tree's nodes.
 */
static void
recursive_free_node(WT_SESSION_IMPL *session, WT_FREQTREE_NODE *node)
{
	if (node != NULL) {
		recursive_free_node(session, node->left);
		recursive_free_node(session, node->right);
		__wt_free(session, node);
	}
}

/*
 * __wt_huffman_open --
 *	Take a frequency table and return a pointer to a descriptor object.
 */
int
__wt_huffman_open(WT_SESSION_IMPL *session,
    void *symbol_frequency_array, u_int symcnt, u_int numbytes, void *retp)
{
	INDEXED_SYMBOL *indexed_freqs, *sym;
	NODE_QUEUE *combined_nodes, *leaves;
	WT_DECL_RET;
	WT_FREQTREE_NODE *node, *node2, **refnode, *tempnode;
	WT_HUFFMAN_OBJ *huffman;
	uint64_t w1, w2;
	uint16_t i;

	indexed_freqs = NULL;
	combined_nodes = leaves = NULL;
	node = node2 = tempnode = NULL;

	WT_RET(__wt_calloc_one(session, &huffman));

	/*
	 * The frequency table is 4B pairs of symbol and frequency.  The symbol
	 * is either 1 or 2 bytes and the frequency ranges from 1 to UINT32_MAX
	 * (a frequency of 0 means the value is never expected to appear in the
	 * input).  Validate the symbols are within range.
	 */
	if (numbytes != 1 && numbytes != 2)
		WT_ERR_MSG(session, EINVAL,
		    "illegal number of symbol bytes specified for a huffman "
		    "table");

	if (symcnt == 0)
		WT_ERR_MSG(session, EINVAL,
		    "illegal number of symbols specified for a huffman table");

	huffman->numSymbols = numbytes == 2 ? UINT16_MAX : UINT8_MAX;

	/*
	 * Order the array by symbol and check for invalid symbols and
	 * duplicates.
	 */
	sym = symbol_frequency_array;
	qsort(sym, symcnt, sizeof(INDEXED_SYMBOL), indexed_symbol_compare);
	for (i = 0; i < symcnt; ++i) {
		if (i > 0 && sym[i].symbol == sym[i - 1].symbol)
			WT_ERR_MSG(session, EINVAL,
			    "duplicate symbol %" PRIu32 " (%#" PRIx32 ") "
			    "specified in a huffman table",
			    sym[i].symbol, sym[i].symbol);
		if (sym[i].symbol > huffman->numSymbols)
			WT_ERR_MSG(session, EINVAL,
			    "out-of-range symbol %" PRIu32 " (%#" PRIx32 ") "
			    "specified in a huffman table",
			    sym[i].symbol, sym[i].symbol);
	}

	/*
	 * Massage frequencies.
	 */
	WT_ERR(__wt_calloc_def(session, 256, &indexed_freqs));

	/*
	 * Minimum of frequency==1 so everybody gets a Huffman code, in case
	 * data evolves and we need to represent this value.
	 */
	for (i = 0; i < 256; i++) {
		sym = &indexed_freqs[i];
		sym->symbol = i;
		sym->frequency = 1;
	}
	/*
	 * Avoid large tables by splitting UTF-16 frequencies into high byte
	 * and low byte.
	 */
	for (i = 0; i < symcnt; i++) {
		sym = &((INDEXED_SYMBOL *)symbol_frequency_array)[i];
		indexed_freqs[sym->symbol & 0xff].frequency += sym->frequency;
		if (numbytes == 2)
			indexed_freqs[(sym->symbol >> 8) & 0xff].frequency +=
			    sym->frequency;
	}
	huffman->numSymbols = symcnt = 256;

	/*
	 * The array must be sorted by frequency to be able to use a linear time
	 * construction algorithm.
	 */
	qsort((void *)indexed_freqs,
	    symcnt, sizeof(INDEXED_SYMBOL), indexed_freq_compare);

	/* We need two node queues to build the tree. */
	WT_ERR(__wt_calloc_one(session, &leaves));
	WT_ERR(__wt_calloc_one(session, &combined_nodes));

	/*
	 * Adding the leaves to the queue.
	 *
	 * Discard symbols with a frequency of 0; this assumes these symbols
	 * never occur in the source stream, and the purpose is to reduce the
	 * huffman tree's size.
	 */
	for (i = 0; i < symcnt; ++i)
		if (indexed_freqs[i].frequency > 0) {
			WT_ERR(__wt_calloc_one(session, &tempnode));
			tempnode->symbol = (uint8_t)indexed_freqs[i].symbol;
			tempnode->weight = indexed_freqs[i].frequency;
			WT_ERR(node_queue_enqueue(session, leaves, tempnode));
			tempnode = NULL;
		}

	while (!node_queue_is_empty(leaves) ||
	    !node_queue_is_empty(combined_nodes)) {
		/*
		 * We have to get the node with the smaller weight, examining
		 * both queues' first element.  We are collecting pairs of these
		 * items, by alternating between node and node2:
		 */
		refnode = !node ? &node : &node2;

		/*
		 * To decide which queue must be used, we get the weights of
		 * the first items from both:
		 */
		w1 = node_queue_is_empty(leaves) ?
		    UINT64_MAX : leaves->first->node->weight;
		w2 = node_queue_is_empty(combined_nodes) ?
		    UINT64_MAX : combined_nodes->first->node->weight;

		/*
		 * Based on the two weights we finally can dequeue the smaller
		 * element and place it to the alternating target node pointer:
		 */
		if (w1 < w2)
			node_queue_dequeue(session, leaves, refnode);
		else
			node_queue_dequeue(session, combined_nodes, refnode);

		/*
		 * In every second run, we have both node and node2 initialized.
		 */
		if (node != NULL && node2 != NULL) {
			WT_ERR(__wt_calloc_one(session, &tempnode));

			/* The new weight is the sum of the two weights. */
			tempnode->weight = node->weight + node2->weight;
			tempnode->left = node;
			tempnode->right = node2;

			/* Enqueue it to the combined nodes queue */
			WT_ERR(node_queue_enqueue(
			    session, combined_nodes, tempnode));
			tempnode = NULL;

			/* Reset the state pointers */
			node = node2 = NULL;
		}
	}

	/*
	 * The remaining node is in the node variable, this is the root of the
	 * tree. Calculate how many bytes it takes to hold numSymbols bytes
	 * bits.
	 */
	huffman->max_depth = 0;
	huffman->min_depth = MAX_CODE_LENGTH;
	(void)profile_tree(node, 0, &huffman->max_depth, &huffman->min_depth);
	if (huffman->max_depth > MAX_CODE_LENGTH)
		huffman->max_depth = MAX_CODE_LENGTH;

	WT_ERR(__wt_calloc_def(session, huffman->numSymbols, &huffman->codes));
	set_codes(node, huffman->codes, 0, 0);

	WT_ERR(__wt_calloc_def(
	    session, (size_t)1U << huffman->max_depth, &huffman->code2symbol));
	make_table(session, huffman->code2symbol,
	    huffman->max_depth, huffman->codes, huffman->numSymbols);

#if __HUFFMAN_DETAIL
	{
	uint8_t symbol;
	uint32_t weighted_length;

	printf("leaf depth %" PRIu16 "..%" PRIu16
	    ", memory use: codes %u# * %" WT_SIZET_FMT
	    "B + code2symbol %u# * %" WT_SIZET_FMT "B\n",
	    huffman->min_depth, huffman->max_depth,
	    huffman->numSymbols, sizeof(WT_HUFFMAN_CODE),
	    1U << huffman->max_depth, sizeof(uint16_t));

	/*
	 * measure quality of computed Huffman codes, for different max bit
	 * lengths (say, 16 vs 24 vs 32)
	 */
	weighted_length = 0;
	for (i = 0; i < symcnt; i++) {
		symbol = indexed_freqs[i].symbol;
		weighted_length +=
		    indexed_freqs[i].frequency * huffman->codes[symbol].length;
		printf(
		    "\t%" PRIu16 "->%" PRIu16 ". %" PRIu32 " * %" PRIu8 "\n",
		    i, symbol,
		    indexed_freqs[i].frequency, huffman->codes[symbol].length);
	}
	printf("weighted length of all codes (the smaller the better): "
	    "%" PRIu32 "\n", weighted_length);
	}
#endif

	*(void **)retp = huffman;

	if (0) {
err:		if (ret == 0)
			ret = WT_ERROR;
	}
	__wt_free(session, indexed_freqs);
	if (leaves != NULL)
		node_queue_close(session, leaves);
	if (combined_nodes != NULL)
		node_queue_close(session, combined_nodes);
	if (node != NULL)
		recursive_free_node(session, node);
	if (node2 != NULL)
		recursive_free_node(session, node2);
	__wt_free(session, tempnode);
	if (ret != 0)
		__wt_huffman_close(session, huffman);
	return (ret);
}

/*
 * __wt_huffman_close --
 *	Discard a Huffman descriptor object.
 */
void
__wt_huffman_close(WT_SESSION_IMPL *session, void *huffman_arg)
{
	WT_HUFFMAN_OBJ *huffman;

	huffman = huffman_arg;

	__wt_free(session, huffman->code2symbol);
	__wt_free(session, huffman->codes);
	__wt_free(session, huffman);
}

#if __HUFFMAN_DETAIL
/*
 * __wt_print_huffman_code --
 *	Prints a symbol's Huffman code.
 */
void
__wt_print_huffman_code(void *huffman_arg, uint16_t symbol)
{
	WT_HUFFMAN_CODE code;
	WT_HUFFMAN_OBJ *huffman;

	huffman = huffman_arg;

	if (symbol >= huffman->numSymbols)
		printf("symbol %" PRIu16 " out of range\n", symbol);
	else {
		code = huffman->codes[symbol];
		if (code.length == 0)
			printf(
			    "symbol %" PRIu16 " not defined -- 0 frequency\n",
			    symbol);
		else
			/* should print code as binary */
			printf(
			    "%" PRIu16 " -> code pattern "
			    "%" PRIx16 ", length %" PRIu8 "\n",
				symbol, code.pattern, code.length);
	}
}
#endif

/*
 * __wt_huffman_encode --
 *	Take a byte string, encode it into the target.
 *
 * Translation from symbol to Huffman code is a simple array lookup.
 *
 * WT_HUFFMAN_OBJ contains an array called 'codes' with one WT_HUFFMAN_CODE per
 * symbol.  Then, given a symbol:
 *	pattern = codes[symbol].pattern;
 *	length = codes[symbol].length;
 *
 * To encode byte-string, we iterate over the input symbols.  For each symbol,
 * look it up via table, shift bits onto a shift register (an int long enough
 * to hold the longest code word + up to 7 bits remaining from the previous),
 * then drain out full bytes.  Finally, at the end flush remaining bits
 * and write header bits.
 */
int
__wt_huffman_encode(WT_SESSION_IMPL *session, void *huffman_arg,
    const uint8_t *from_arg, size_t from_len, WT_ITEM *to_buf)
{
	WT_DECL_RET;
	WT_HUFFMAN_CODE code;
	WT_HUFFMAN_OBJ *huffman;
	WT_ITEM *tmp;
	size_t max_len, outlen, bytes;
	uint64_t bitpos;
	const uint8_t *from;
	uint8_t len, *out, padding_info, symbol;

	/*
	 * Shift register to accumulate bits from input.
	 * Should be >= (MAX_CODE_LENGTH + 7), but also efficient to shift bits
	 * and preferably in a machine register.
	 */
	uint32_t bits;

	/* Count of bits in shift register ('bits' above). */
	uint8_t valid;

	huffman = huffman_arg;
	from = from_arg;
	tmp = NULL;

	/*
	 * We don't want to find all of our callers and ensure they don't pass
	 * 0-length byte strings, but there's no reason to do any work.
	 */
	if (from_len == 0) {
		to_buf->size = 0;
		return (0);
	}

	/*
	 * Compute the largest compressed output size, which is if all symbols
	 * are least frequent and so have largest Huffman codes, and compressed
	 * output may be larger than the input size.  This way we don't have to
	 * worry about resizing the buffer during compression.  Use the shared
	 * system buffer while compressing, then allocate a new buffer of the
	 * right size and copy the result into it.
	 */
	max_len = (WT_HUFFMAN_HEADER +
	    from_len * huffman->max_depth + 7 /* round up to full byte */) / 8;
	WT_ERR(__wt_scr_alloc(session, max_len, &tmp));

	/*
	 * Leave the first 3 bits of the encoded value empty, it holds the
	 * number of bits actually used in the last byte of the encoded value.
	 */
	bits = 0;
	bitpos = WT_HUFFMAN_HEADER;
	valid = WT_HUFFMAN_HEADER;
	out = tmp->mem;
	for (bytes = 0; bytes < from_len; bytes++) {
		WT_ASSERT(session, WT_PTR_IN_RANGE(from, from_arg, from_len));

		symbol = *from++;

		/* Translate symbol into Huffman code and stuff into buffer. */
		code = huffman->codes[symbol];
		len = code.length;
		bits = (bits << len) | code.pattern;
		valid += len;
		bitpos += len;
		while (valid >= 8) {
			WT_ASSERT(session,
			    WT_PTR_IN_RANGE(out, tmp->mem, tmp->memsize));
			*out++ = (uint8_t)(bits >> (valid - 8));
			valid -= 8;
		}
	}
	if (valid > 0) {		/* Flush shift register. */
		WT_ASSERT(session,
		    WT_PTR_IN_RANGE(out, tmp->mem, tmp->memsize));
		*out = (uint8_t)(bits << (8 - valid));
	}

	/*
	 * At this point, bitpos is the total number of used bits (including
	 * the 3 bits at the beginning of the buffer, which we'll set now to
	 * the number of bits used in the last byte). Note if the number of
	 * bits used in the last byte is 8, we set the 3 bits to 0, in other
	 * words, the first 3 bits of the encoded value are the number of bits
	 * used in the last byte, unless they're 0, in which case there are 8
	 * bits used in the last byte.
	 */
	padding_info = (uint8_t)((bitpos % 8) << (8 - WT_HUFFMAN_HEADER));
	((uint8_t *)tmp->mem)[0] |= padding_info;

	/* Copy result of exact known size into caller's buffer. */
	outlen = (uint32_t)((bitpos + 7) / 8);
	WT_ERR(__wt_buf_initsize(session, to_buf, outlen));
	memcpy(to_buf->mem, tmp->mem, outlen);

#if __HUFFMAN_DETAIL
	printf("encode: worst case %" PRIu32 " bytes -> actual %" PRIu32 "\n",
	    max_len, outlen);
#endif

err:	__wt_scr_free(session, &tmp);
	return (ret);

}

/*
 * __wt_huffman_decode --
 *	Take a byte string, decode it into the target.
 *
 * Translation from Huffman code to symbol is a simple array lookup.
 *
 * WT_HUFFMAN_OBJ contains an array called 'code2symbol' indexed by code word
 * and whose value is the corresponding symbol.
 * From the symbol, we index into the 'codes' array to get the code length.
 *
 * When decoding a message, we don't know where the boundaries are between
 * codes.  The trick is that we collect enough bits for the longest code word,
 * and construct the table such that for codes with fewer bits we flood the
 * table with all of the bit patterns in the lower order bits.  This works
 * because the Huffman code is a unique prefix, and by the flooding we are
 * treating bits beyond the unique prefix as don't care bits.
 *
 * For example, we have table of length 2^max_code_length (1<<max_code_length).
 * For a code of length, max_code_length, the position code2symbol[code] =
 *	symbol.
 * For a code word of (max_length - 1), we fill code2symbol[code << 1] = symbol,
 * as well as code2symbol[(code << 1) | 1] = symbol.
 * And so on, so in general we fill:
 * 	code2symbol[(code) << shift inclusive .. (code+1) << shift exclusive].
 *
 * To decode a message, we read in enough bits from input to fill the shift
 * register with at least MAX_CODE_LENGTH bits.
 * We look up in the table code2symbol to obtain the symbol.
 * We look up the symbol in 'codes' to obtain the code length
 * Finally, subtract off these bits from the shift register.
 */
int
__wt_huffman_decode(WT_SESSION_IMPL *session, void *huffman_arg,
    const uint8_t *from_arg, size_t from_len, WT_ITEM *to_buf)
{
	WT_DECL_RET;
	WT_ITEM *tmp;
	WT_HUFFMAN_OBJ *huffman;
	size_t from_bytes, len, max_len, outlen;
	uint64_t from_len_bits;
	uint32_t bits, mask, max;
	uint16_t pattern;
	const uint8_t *from;
	uint8_t padding_info, symbol, *to, valid;

	huffman = huffman_arg;
	from = from_arg;
	tmp = NULL;

	/*
	 * We don't want to find all of our callers and ensure they don't pass
	 * 0-length byte strings, but there's no reason to do any work.
	 */
	if (from_len == 0) {
		to_buf->size = 0;
		return (0);
	}

	/*
	 * The first 3 bits are the number of used bits in the last byte, unless
	 * they're 0, in which case there are 8 bits used in the last byte.
	 */
	padding_info = (*from & 0xE0) >> (8 - WT_HUFFMAN_HEADER);
	from_len_bits = from_len * 8;
	if (padding_info != 0)
		from_len_bits -= 8U - padding_info;

	/* Number of bits that have codes. */
	from_len_bits -= WT_HUFFMAN_HEADER;

	/*
	 * Compute largest uncompressed output size, which is if all symbols are
	 * most frequent and so have smallest Huffman codes and therefore
	 * largest expansion.  Use the shared system buffer while uncompressing,
	 * then allocate a new buffer of exactly the right size and copy the
	 * result into it.
	 */
	max_len = (uint32_t)(from_len_bits / huffman->min_depth);
	WT_ERR(__wt_scr_alloc(session, max_len, &tmp));
	to = tmp->mem;

	/* The first byte of input is a special case because of header bits. */
	bits = *from++;
	valid = 8 - WT_HUFFMAN_HEADER;
	from_bytes = from_len - 1;

	max = huffman->max_depth;
	mask = (1U << max) - 1;
	for (outlen = 0; from_len_bits > 0; outlen++) {
		while (valid < max && from_bytes > 0) {
			WT_ASSERT(session,
			    WT_PTR_IN_RANGE(from, from_arg, from_len));
			bits = (bits << 8) | *from++;
			valid += 8;
			from_bytes--;
		}
		pattern = (uint16_t)
		    (valid >= max ?	/* short patterns near end */
		    (bits >> (valid - max)) : (bits << (max - valid)));
		symbol = huffman->code2symbol[pattern & mask];
		len = huffman->codes[symbol].length;
		valid -= (uint8_t)len;

		/*
		 * from_len_bits is the total number of input bits, reduced by
		 * the number of bits we consume from input at each step.  For
		 * all but the last step from_len_bits > len, then at the last
		 * step from_len_bits == len (in other words, from_len_bits -
		 * len = 0 input bits remaining). Generally, we cannot detect
		 * corruption during huffman decompression, this is one place
		 * where that's not true.
		 */
		if (from_len_bits < len)	/* corrupted */
			WT_ERR_MSG(session, EINVAL,
			    "huffman decompression detected input corruption");
		from_len_bits -= len;

		WT_ASSERT(session,
		    WT_PTR_IN_RANGE(to, tmp->mem, tmp->memsize));
		*to++ = symbol;
	}

	/* Return the number of bytes used. */
	WT_ERR(__wt_buf_initsize(session, to_buf, outlen));
	memcpy(to_buf->mem, tmp->mem, outlen);

#if __HUFFMAN_DETAIL
	printf("decode: worst case %" PRIu32 " bytes -> actual %" PRIu32 "\n",
	    max_len, outlen);
#endif

err:	__wt_scr_free(session, &tmp);
	return (ret);
}

/*
 * node_queue_close --
 *	Delete a queue from memory.
 *
 * It does not delete the pointed huffman tree nodes!
 */
static void
node_queue_close(WT_SESSION_IMPL *session, NODE_QUEUE *queue)
{
	NODE_QUEUE_ELEM *elem, *next_elem;

	/* Freeing each element of the queue's linked list. */
	for (elem = queue->first; elem != NULL; elem = next_elem) {
		next_elem = elem->next;
		__wt_free(session, elem);
	}

	/* Freeing the queue record itself. */
	__wt_free(session, queue);
}

/*
 * node_queue_enqueue --
 *	Push a tree node to the end of the queue.
 */
static int
node_queue_enqueue(
    WT_SESSION_IMPL *session, NODE_QUEUE *queue, WT_FREQTREE_NODE *node)
{
	NODE_QUEUE_ELEM *elem;

	/* Allocating a new linked list element */
	WT_RET(__wt_calloc_one(session, &elem));

	/* It holds the tree node, and has no next element yet */
	elem->node = node;
	elem->next = NULL;

	/* If the queue is empty, the first element will be the new one. */
	if (queue->first == NULL)
		queue->first = elem;

	/*
	 * If the queue is not empty, the last element's next pointer must be
	 * updated.
	 */
	if (queue->last != NULL)
		queue->last->next = elem;

	/* The last element is the new one */
	queue->last = elem;

	return (0);
}

/*
 * node_queue_dequeue --
 *	Removes a node from the beginning of the queue and copies the node's
 *	pointer to the location referred by the retp parameter.
 */
static void
node_queue_dequeue(
    WT_SESSION_IMPL *session, NODE_QUEUE *queue, WT_FREQTREE_NODE **retp)
{
	NODE_QUEUE_ELEM *first_elem;

	/*
	 * Getting the first element of the queue and updating it to point to
	 * the next element as first.
	 */
	first_elem = queue->first;
	*retp = first_elem->node;
	queue->first = first_elem->next;

	/*
	 * If the last element was the dequeued element, we have to update it
	 * to NULL.
	 */
	if (queue->last == first_elem)
		queue->last = NULL;

	/* Freeing the linked list element that has been dequeued */
	__wt_free(session, first_elem);
}