harvey/sys/src/cmd/gs/src/shcgen.c

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/*$Id: shcgen.c,v 1.2 2000/09/19 19:00:50 lpd Exp $ */
/* Generate (bounded) Huffman code definitions from frequencies, */
/* and tables from definitions. */
#include "memory_.h"
#include "stdio_.h"
#include <stdlib.h>		/* for qsort */
#include "gdebug.h"
#include "gserror.h"
#include "gserrors.h"
#include "gsmemory.h"
#include "scommon.h"
#include "shc.h"
#include "shcgen.h"

/* ------ Frequency -> definition procedure ------ */

/* Define a node for the Huffman code tree. */
typedef struct count_node_s count_node;
struct count_node_s {
    long freq;			/* frequency of value */
    uint value;			/* data value being encoded */
    uint code_length;		/* length of Huffman code */
    count_node *next;		/* next node in freq-sorted list */
    count_node *left;		/* left child in tree (smaller code_length) */
    count_node *right;		/* right child in tree (greater code_length) */
};

#ifdef DEBUG
#  define debug_print_nodes(nodes, n, tag, lengths)\
     if ( gs_debug_c('W') ) print_nodes_proc(nodes, n, tag, lengths);
private void
print_nodes_proc(const count_node * nodes, int n, const char *tag, int lengths)
{
    int i;

    dlprintf1("[w]---------------- %s ----------------\n", tag);
    for (i = 0; i < n; ++i)
	dlprintf7("[w]node %d: f=%ld v=%d len=%d N=%d L=%d R=%d\n",
		  i, nodes[i].freq, nodes[i].value, nodes[i].code_length,
		  (nodes[i].next == 0 ? -1 : (int)(nodes[i].next - nodes)),
		  (nodes[i].left == 0 ? -1 : (int)(nodes[i].left - nodes)),
		(nodes[i].right == 0 ? -1 : (int)(nodes[i].right - nodes)));
    for (i = lengths; i > 0;) {
	int j = i;
	int len = nodes[--j].code_length;

	while (j > 0 && nodes[j - 1].code_length == len)
	    --j;
	dlprintf2("[w]%d codes of length %d\n", i - j, len);
	i = j;
    }
}
#else
#  define debug_print_nodes(nodes, n, tag, lengths) DO_NOTHING
#endif

/* Node comparison procedures for sorting. */
#define pn1 ((const count_node *)p1)
#define pn2 ((const count_node *)p2)
/* Sort by decreasing frequency. */
private int
compare_freqs(const void *p1, const void *p2)
{
    long diff = pn2->freq - pn1->freq;

    return (diff < 0 ? -1 : diff > 0 ? 1 : 0);
}
/* Sort by increasing code length, and secondarily by decreasing frequency. */
private int
compare_code_lengths(const void *p1, const void *p2)
{
    int diff = pn1->code_length - pn2->code_length;

    return (diff < 0 ? -1 : diff > 0 ? 1 : compare_freqs(p1, p2));
}
/* Sort by increasing code value. */
private int
compare_values(const void *p1, const void *p2)
{
    return (pn1->value < pn2->value ? -1 :
	    pn1->value > pn2->value ? 1 : 0);
}
#undef pn1
#undef pn2

/* Adjust code lengths so that none of them exceeds max_length. */
/* We break this out just to help organize the code; it's only called */
/* from one place in hc_compute. */
private void
hc_limit_code_lengths(count_node * nodes, uint num_values, int max_length)
{
    int needed;			/* # of max_length codes we need to free up */
    count_node *longest = nodes + num_values;

    {				/* Compute the number of additional max_length codes */
	/* we need to make available. */
	int length = longest[-1].code_length;
	int next_length;
	int avail = 0;

	while ((next_length = longest[-1].code_length) > max_length) {
	    avail >>= length - next_length;
	    length = next_length;
	    (--longest)->code_length = max_length;
	    ++avail;
	}
	needed = (nodes + num_values - longest) -
	    (avail >>= (length - max_length));
	if_debug2('W', "[w]avail=%d, needed=%d\n",
		  avail, needed);
    }
    /* Skip over all max_length codes. */
    while (longest[-1].code_length == max_length)
	--longest;

    /*
     * To make available a code of length N, suppose that the next
     * shortest used code is of length M.
     * We take the lowest-frequency code of length M and change it
     * to M+1; we then have to compensate by reducing the length of
     * some of the highest-frequency codes of length N, as follows:
     *       M      new lengths for codes of length N
     *      ---     -----------
     *      N-1     (none)
     *      N-2     N-1
     *      <N-2    M+2, M+2, N-1
     * In the present situation, N = max_length.
     */
    for (; needed > 0; --needed) {	/* longest points to the first code of length max_length. */
	/* Since codes are sorted by increasing code length, */
	/* longest-1 is the desired code of length M. */
	int M1 = ++(longest[-1].code_length);

	switch (max_length - M1) {
	    case 0:		/* M == N-1 */
		--longest;
		break;
	    case 1:		/* M == N-2 */
		longest++->code_length = M1;
		break;
	    default:
		longest->code_length = M1 + 1;
		longest[1].code_length = M1 + 1;
		longest[2].code_length--;
		longest += 3;
	}
    }
}

/* Compute an optimal Huffman code from an input data set. */
/* The client must have set all the elements of *def. */
int
hc_compute(hc_definition * def, const long *freqs, gs_memory_t * mem)
{
    uint num_values = def->num_values;
    count_node *nodes =
    (count_node *) gs_alloc_byte_array(mem, num_values * 2 - 1,
				       sizeof(count_node), "hc_compute");
    int i;
    count_node *lowest;
    count_node *comb;

    if (nodes == 0)
	return_error(gs_error_VMerror);

    /* Create leaf nodes for the input data. */
    for (i = 0; i < num_values; ++i)
	nodes[i].freq = freqs[i], nodes[i].value = i;

    /* Create a list sorted by increasing frequency. */
    /* Also initialize the tree structure. */
    qsort(nodes, num_values, sizeof(count_node), compare_freqs);
    for (i = 0; i < num_values; ++i)
	nodes[i].next = &nodes[i - 1],
	    nodes[i].code_length = 0,
	    nodes[i].left = nodes[i].right = 0;
    nodes[0].next = 0;
    debug_print_nodes(nodes, num_values, "after sort", 0);

    /* Construct the Huffman code tree. */
    for (lowest = &nodes[num_values - 1], comb = &nodes[num_values];;
	 ++comb
	) {
	count_node *pn1 = lowest;
	count_node *pn2 = pn1->next;
	long freq = pn1->freq + pn2->freq;

	/* Create a parent for the two lowest-frequency nodes. */
	lowest = pn2->next;
	comb->freq = freq;
	if (pn1->code_length <= pn2->code_length)
	    comb->left = pn1, comb->right = pn2,
		comb->code_length = pn2->code_length + 1;
	else
	    comb->left = pn2, comb->right = pn1,
		comb->code_length = pn1->code_length + 1;
	if (lowest == 0)	/* no nodes left to combine */
	    break;
	/* Insert comb in the sorted list. */
	if (freq < lowest->freq)
	    comb->next = lowest, lowest = comb;
	else {
	    count_node *here = lowest;

	    while (here->next != 0 && freq >= here->next->freq)
		here = here->next;
	    comb->next = here->next;
	    here->next = comb;
	}
    }

    /* comb (i.e., &nodes[num_values * 2 - 2] is the root of the tree. */
    /* Note that the left and right children of an interior node */
    /* were constructed before, and therefore have lower indices */
    /* in the nodes array than, the parent node.  Thus we can assign */
    /* the code lengths (node depths) in a single descending-order */
    /* sweep. */
    comb++->code_length = 0;
    while (comb > nodes + num_values) {
	--comb;
	comb->left->code_length = comb->right->code_length =
	    comb->code_length + 1;
    }
    debug_print_nodes(nodes, num_values * 2 - 1, "after combine", 0);

    /* Sort the leaves again by code length. */
    qsort(nodes, num_values, sizeof(count_node), compare_code_lengths);
    debug_print_nodes(nodes, num_values, "after re-sort", num_values);

    /* Limit the code length to def->num_counts. */
    hc_limit_code_lengths(nodes, num_values, def->num_counts);
    debug_print_nodes(nodes, num_values, "after limit", num_values);

    /* Sort within each code length by increasing code value. */
    /* This doesn't affect data compression, but it makes */
    /* the code definition itself compress better using our */
    /* incremental encoding. */
    for (i = num_values; i > 0;) {
	int j = i;
	int len = nodes[--j].code_length;

	while (j > 0 && nodes[j - 1].code_length == len)
	    --j;
	qsort(&nodes[j], i - j, sizeof(count_node), compare_values);
	i = j;
    }

    /* Extract the definition from the nodes. */
    memset(def->counts, 0, sizeof(*def->counts) * (def->num_counts + 1));
    for (i = 0; i < num_values; ++i) {
	def->values[i] = nodes[i].value;
	def->counts[nodes[i].code_length]++;
    }

    /* All done, release working storage. */
    gs_free_object(mem, nodes, "hc_compute");
    return 0;
}

/* ------ Byte string <-> definition procedures ------ */

/*
 * We define a compressed representation for (well-behaved) definitions
 * as a byte string.  A "well-behaved" definition is one where if
 * code values A and B have the same code length and A < B,
 * A precedes B in the values table of the definition, and hence
 * A's encoding lexicographically precedes B's.
 *
 * The successive bytes in the compressed string  give the code lengths for
 * runs of decoded values, in the form nnnnllll where nnnn is the number of
 * consecutive values -1 and llll is the code length -1.
 */

/* Convert a definition to a byte string. */
/* The caller must provide the byte string, of length def->num_values. */
/* Assume (do not check) that the definition is well-behaved. */
/* Return the actual length of the string. */
int
hc_bytes_from_definition(byte * dbytes, const hc_definition * def)
{
    int i, j;
    byte *bp = dbytes;
    const byte *lp = dbytes;
    const byte *end = dbytes + def->num_values;
    const ushort *values = def->values;

    /* Temporarily use the output string as a map from */
    /* values to code lengths. */
    for (i = 1; i <= def->num_counts; i++)
	for (j = 0; j < def->counts[i]; j++)
	    bp[*values++] = i;

    /* Now construct the actual string. */
    while (lp < end) {
	const byte *vp;
	byte len = *lp;

	for (vp = lp + 1; vp < end && vp < lp + 16 && *vp == len;)
	    vp++;
	*bp++ = ((vp - lp - 1) << 4) + (len - 1);
	lp = vp;
    }

    return bp - dbytes;
}

/* Extract num_counts and num_values from a byte string. */
void
hc_sizes_from_bytes(hc_definition * def, const byte * dbytes, int num_bytes)
{
    uint num_counts = 0, num_values = 0;
    int i;

    for (i = 0; i < num_bytes; i++) {
	int n = (dbytes[i] >> 4) + 1;
	int l = (dbytes[i] & 15) + 1;

	if (l > num_counts)
	    num_counts = l;
	num_values += n;
    }
    def->num_counts = num_counts;
    def->num_values = num_values;
}

/* Convert a byte string back to a definition. */
/* The caller must initialize *def, including allocating counts and values. */
void
hc_definition_from_bytes(hc_definition * def, const byte * dbytes)
{
    int v, i;
    ushort counts[max_hc_length + 1];

    /* Make a first pass to set the counts for each code length. */
    memset(counts, 0, sizeof(counts[0]) * (def->num_counts + 1));
    for (i = 0, v = 0; v < def->num_values; i++) {
	int n = (dbytes[i] >> 4) + 1;
	int l = (dbytes[i] & 15) + 1;

	counts[l] += n;
	v += n;
    }

    /* Now fill in the definition. */
    memcpy(def->counts, counts, sizeof(counts[0]) * (def->num_counts + 1));
    for (i = 1, v = 0; i <= def->num_counts; i++) {
	uint prev = counts[i];

	counts[i] = v;
	v += prev;
    }
    for (i = 0, v = 0; v < def->num_values; i++) {
	int n = (dbytes[i] >> 4) + 1;
	int l = (dbytes[i] & 15) + 1;
	int j;

	for (j = 0; j < n; n++)
	    def->values[counts[l]++] = v++;
    }
}

/* ------ Definition -> table procedures ------ */

/* Generate the encoding table from the definition. */
/* The size of the encode array is def->num_values. */
void
hc_make_encoding(hce_code * encode, const hc_definition * def)
{
    uint next = 0;
    const ushort *pvalue = def->values;
    uint i, k;

    for (i = 1; i <= def->num_counts; i++) {
	for (k = 0; k < def->counts[i]; k++, pvalue++, next++) {
	    hce_code *pce = encode + *pvalue;

	    pce->code = next;
	    pce->code_length = i;
	}
	next <<= 1;
    }
}

/* We decode in two steps, first indexing into a table with */
/* a fixed number of bits from the source, and then indexing into */
/* an auxiliary table if necessary.  (See shc.h for details.) */

/* Calculate the size of the decoding table. */
uint
hc_sizeof_decoding(const hc_definition * def, int initial_bits)
{
    uint size = 1 << initial_bits;
    uint carry = 0, mask = (uint) ~ 1;
    uint i;

    for (i = initial_bits + 1; i <= def->num_counts;
	 i++, carry <<= 1, mask <<= 1
	) {
	carry += def->counts[i];
	size += carry & mask;
	carry &= ~mask;
    }
    return size;
}

/* Generate the decoding tables. */
void
hc_make_decoding(hcd_code * decode, const hc_definition * def,
		 int initial_bits)
{				/* Make entries for single-dispatch codes. */
    {
	hcd_code *pcd = decode;
	const ushort *pvalue = def->values;
	uint i, k, d;

	for (i = 0; i <= initial_bits; i++) {
	    for (k = 0; k < def->counts[i]; k++, pvalue++) {
		for (d = 1 << (initial_bits - i); d > 0;
		     d--, pcd++
		    )
		    pcd->value = *pvalue,
			pcd->code_length = i;
	    }
	}
    }
    /* Make entries for two-dispatch codes. */
    /* By working backward, we can do this more easily */
    /* in a single pass. */
    {
	uint dsize = hc_sizeof_decoding(def, initial_bits);
	hcd_code *pcd = decode + (1 << initial_bits);
	hcd_code *pcd2 = decode + dsize;
	const ushort *pvalue = def->values + def->num_values;
	uint entries_left = 0, slots_left = 0, mult_shift = 0;
	uint i = def->num_counts + 1, j;

	for (;;) {
	    if (slots_left == 0) {
		if (entries_left != 0) {
		    slots_left = 1 << (i - initial_bits);
		    mult_shift = 0;
		    continue;
		}
		if (--i <= initial_bits)
		    break;
		entries_left = def->counts[i];
		continue;
	    }
	    if (entries_left == 0) {
		entries_left = def->counts[--i];
		mult_shift++;
		continue;
	    }
	    --entries_left, --pvalue;
	    for (j = 1 << mult_shift; j > 0; j--) {
		--pcd2;
		pcd2->value = *pvalue;
		pcd2->code_length = i - initial_bits;
	    }
	    if ((slots_left -= 1 << mult_shift) == 0) {
		--pcd;
		pcd->value = pcd2 - decode;
		pcd->code_length = i + mult_shift;
	    }
	}
    }
}