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deflate.c
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deflate.c
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/*
* Reimplementation of Deflate (RFC1951) compression. Adapted from
* the version in PuTTY, and extended to write dynamic Huffman
* trees and choose block boundaries usefully.
*/
/*
* TODO:
*
* - Feature: could do with forms of flush other than SYNC_FLUSH.
* I'm not sure exactly how those work when you don't know in
* advance that your next block will be static (as we did in
* PuTTY). And remember the 9-bit limitation of zlib.
* + also, zlib has FULL_FLUSH which clears the LZ77 state as
* well, for random access.
*
* - Compression quality: chooseblock() appears to be computing
* wildly inaccurate block size estimates. Possible resolutions:
* + find and fix some trivial bug I haven't spotted yet
* + abandon the entropic approximation and go with trial
* Huffman runs
*
* - Compression quality: see if increasing SYMLIMIT causes
* dynamic blocks to start being consistently smaller than it.
* + actually we seem to be there already, but check on a
* larger corpus.
*
* - Compression quality: we ought to be able to fall right back
* to actual uncompressed blocks if really necessary, though
* it's not clear what the criterion for doing so would be.
*/
/*
* This software is copyright 2000-2006 Simon Tatham.
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or
* sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
* IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <stdio.h>
#include <stddef.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#include "deflate.h"
#define snew(type) ( (type *) malloc(sizeof(type)) )
#define snewn(n, type) ( (type *) malloc((n) * sizeof(type)) )
#define sresize(x, n, type) ( (type *) realloc((x), (n) * sizeof(type)) )
#define sfree(x) ( free((x)) )
#define lenof(x) (sizeof((x)) / sizeof(*(x)))
#ifndef FALSE
#define FALSE 0
#define TRUE (!FALSE)
#endif
/* ----------------------------------------------------------------------
* This file can be compiled in a number of modes.
*
* With -DSTANDALONE, it builds a self-contained deflate tool which
* can compress, decompress, and also analyse a deflated file to
* print out the sequence of literals and copy commands it
* contains.
*
* With -DTESTMODE, it builds a test application which is given a
* file on standard input, both compresses and decompresses it, and
* outputs the re-decompressed result so it can be conveniently
* diffed against the original. Define -DTESTDBG as well for lots
* of diagnostics.
*/
#if defined TESTDBG
/* gcc-specific diagnostic macro */
#define debug_int(x...) ( fprintf(stderr, x) )
#define debug(x) ( debug_int x )
#else
#define debug(x) ((void)0)
#endif
#ifdef STANDALONE
#define ANALYSIS
#endif
#ifdef ANALYSIS
int analyse_level = 0;
#endif
/* ----------------------------------------------------------------------
* Basic LZ77 code. This bit is designed modularly, so it could be
* ripped out and used in a different LZ77 compressor. Go to it,
* and good luck :-)
*/
struct LZ77InternalContext;
struct LZ77Context {
struct LZ77InternalContext *ictx;
void *userdata;
void (*literal) (struct LZ77Context * ctx, unsigned char c);
void (*match) (struct LZ77Context * ctx, int distance, int len);
};
/*
* Initialise the private fields of an LZ77Context. It's up to the
* user to initialise the public fields.
*/
static int lz77_init(struct LZ77Context *ctx);
/*
* Supply data to be compressed. Will update the private fields of
* the LZ77Context, and will call literal() and match() to output.
* If `compress' is FALSE, it will never emit a match, but will
* instead call literal() for everything.
*/
static void lz77_compress(struct LZ77Context *ctx,
const unsigned char *data, int len, int compress);
/*
* Modifiable parameters.
*/
#define WINSIZE 32768 /* window size. Must be power of 2! */
#define HASHMAX 2039 /* one more than max hash value */
#define MAXMATCH 32 /* how many matches we track */
#define HASHCHARS 3 /* how many chars make a hash */
/*
* This compressor takes a less slapdash approach than the
* gzip/zlib one. Rather than allowing our hash chains to fall into
* disuse near the far end, we keep them doubly linked so we can
* _find_ the far end, and then every time we add a new byte to the
* window (thus rolling round by one and removing the previous
* byte), we can carefully remove the hash chain entry.
*/
#define INVALID -1 /* invalid hash _and_ invalid offset */
struct WindowEntry {
short next, prev; /* array indices within the window */
short hashval;
};
struct HashEntry {
short first; /* window index of first in chain */
};
struct Match {
int distance, len;
};
struct LZ77InternalContext {
struct WindowEntry win[WINSIZE];
unsigned char data[WINSIZE];
int winpos;
struct HashEntry hashtab[HASHMAX];
unsigned char pending[HASHCHARS];
int npending;
};
static int lz77_hash(const unsigned char *data)
{
return (257 * data[0] + 263 * data[1] + 269 * data[2]) % HASHMAX;
}
static int lz77_init(struct LZ77Context *ctx)
{
struct LZ77InternalContext *st;
int i;
st = snew(struct LZ77InternalContext);
if (!st)
return 0;
ctx->ictx = st;
for (i = 0; i < WINSIZE; i++)
st->win[i].next = st->win[i].prev = st->win[i].hashval = INVALID;
for (i = 0; i < HASHMAX; i++)
st->hashtab[i].first = INVALID;
st->winpos = 0;
st->npending = 0;
return 1;
}
static void lz77_advance(struct LZ77InternalContext *st,
unsigned char c, int hash)
{
int off;
/*
* Remove the hash entry at winpos from the tail of its chain,
* or empty the chain if it's the only thing on the chain.
*/
if (st->win[st->winpos].prev != INVALID) {
st->win[st->win[st->winpos].prev].next = INVALID;
} else if (st->win[st->winpos].hashval != INVALID) {
st->hashtab[st->win[st->winpos].hashval].first = INVALID;
}
/*
* Create a new entry at winpos and add it to the head of its
* hash chain.
*/
st->win[st->winpos].hashval = hash;
st->win[st->winpos].prev = INVALID;
off = st->win[st->winpos].next = st->hashtab[hash].first;
st->hashtab[hash].first = st->winpos;
if (off != INVALID)
st->win[off].prev = st->winpos;
st->data[st->winpos] = c;
/*
* Advance the window pointer.
*/
st->winpos = (st->winpos + 1) & (WINSIZE - 1);
}
#define CHARAT(k) ( (k)<0 ? st->data[(st->winpos+k)&(WINSIZE-1)] : data[k] )
static void lz77_compress(struct LZ77Context *ctx,
const unsigned char *data, int len, int compress)
{
struct LZ77InternalContext *st = ctx->ictx;
int i, hash, distance, off, nmatch, matchlen, advance;
struct Match defermatch, matches[MAXMATCH];
int deferchr;
/*
* Add any pending characters from last time to the window. (We
* might not be able to.)
*/
for (i = 0; i < st->npending; i++) {
unsigned char foo[HASHCHARS];
int j;
if (len + st->npending - i < HASHCHARS) {
/* Update the pending array. */
for (j = i; j < st->npending; j++)
st->pending[j - i] = st->pending[j];
break;
}
for (j = 0; j < HASHCHARS; j++)
foo[j] = (i + j < st->npending ? st->pending[i + j] :
data[i + j - st->npending]);
lz77_advance(st, foo[0], lz77_hash(foo));
}
st->npending -= i;
defermatch.len = 0;
deferchr = '\0';
while (len > 0) {
/* Don't even look for a match, if we're not compressing. */
if (compress && len >= HASHCHARS) {
/*
* Hash the next few characters.
*/
hash = lz77_hash(data);
/*
* Look the hash up in the corresponding hash chain and see
* what we can find.
*/
nmatch = 0;
for (off = st->hashtab[hash].first;
off != INVALID; off = st->win[off].next) {
/* distance = 1 if off == st->winpos-1 */
/* distance = WINSIZE if off == st->winpos */
distance =
WINSIZE - (off + WINSIZE - st->winpos) % WINSIZE;
for (i = 0; i < HASHCHARS; i++)
if (CHARAT(i) != CHARAT(i - distance))
break;
if (i == HASHCHARS) {
matches[nmatch].distance = distance;
matches[nmatch].len = 3;
if (++nmatch >= MAXMATCH)
break;
}
}
} else {
nmatch = 0;
hash = INVALID;
}
if (nmatch > 0) {
/*
* We've now filled up matches[] with nmatch potential
* matches. Follow them down to find the longest. (We
* assume here that it's always worth favouring a
* longer match over a shorter one.)
*/
matchlen = HASHCHARS;
while (matchlen < len) {
int j;
for (i = j = 0; i < nmatch; i++) {
if (CHARAT(matchlen) ==
CHARAT(matchlen - matches[i].distance)) {
matches[j++] = matches[i];
}
}
if (j == 0)
break;
matchlen++;
nmatch = j;
}
/*
* We've now got all the longest matches. We favour the
* shorter distances, which means we go with matches[0].
* So see if we want to defer it or throw it away.
*/
matches[0].len = matchlen;
if (defermatch.len > 0) {
if (matches[0].len > defermatch.len + 1) {
/* We have a better match. Emit the deferred char,
* and defer this match. */
ctx->literal(ctx, (unsigned char) deferchr);
defermatch = matches[0];
deferchr = data[0];
advance = 1;
} else {
/* We don't have a better match. Do the deferred one. */
ctx->match(ctx, defermatch.distance, defermatch.len);
advance = defermatch.len - 1;
defermatch.len = 0;
}
} else {
/* There was no deferred match. Defer this one. */
defermatch = matches[0];
deferchr = data[0];
advance = 1;
}
} else {
/*
* We found no matches. Emit the deferred match, if
* any; otherwise emit a literal.
*/
if (defermatch.len > 0) {
ctx->match(ctx, defermatch.distance, defermatch.len);
advance = defermatch.len - 1;
defermatch.len = 0;
} else {
ctx->literal(ctx, data[0]);
advance = 1;
}
}
/*
* Now advance the position by `advance' characters,
* keeping the window and hash chains consistent.
*/
while (advance > 0) {
if (len >= HASHCHARS) {
lz77_advance(st, *data, lz77_hash(data));
} else {
st->pending[st->npending++] = *data;
}
data++;
len--;
advance--;
}
}
}
/* ----------------------------------------------------------------------
* Deflate functionality common to both compression and decompression.
*/
static const unsigned char lenlenmap[] = {
16, 17, 18, 0, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3, 13, 2, 14, 1, 15
};
#define MAXCODELEN 16
/*
* Given a sequence of Huffman code lengths, compute the actual
* codes, in the final form suitable for feeding to outbits (i.e.
* already bit-mirrored).
*
* Returns the maximum code length found. Can also return -1 to
* indicate the table was overcommitted (too many or too short
* codes to exactly cover the possible space), or -2 to indicate it
* was undercommitted (too few or too long codes).
*/
static int hufcodes(const unsigned char *lengths, int *codes, int nsyms)
{
int count[MAXCODELEN], startcode[MAXCODELEN];
int code, maxlen;
int i, j;
/* Count the codes of each length. */
maxlen = 0;
for (i = 1; i < MAXCODELEN; i++)
count[i] = 0;
for (i = 0; i < nsyms; i++) {
count[lengths[i]]++;
if (maxlen < lengths[i])
maxlen = lengths[i];
}
/* Determine the starting code for each length block. */
code = 0;
for (i = 1; i < MAXCODELEN; i++) {
startcode[i] = code;
code += count[i];
if (code > (1 << i))
maxlen = -1; /* overcommitted */
code <<= 1;
}
if (code < (1 << MAXCODELEN))
maxlen = -2; /* undercommitted */
/* Determine the code for each symbol. Mirrored, of course. */
for (i = 0; i < nsyms; i++) {
code = startcode[lengths[i]]++;
codes[i] = 0;
for (j = 0; j < lengths[i]; j++) {
codes[i] = (codes[i] << 1) | (code & 1);
code >>= 1;
}
}
return maxlen;
}
/*
* Adler32 checksum function.
*/
static unsigned long adler32_update(unsigned long s,
const unsigned char *data, int len)
{
unsigned s1 = s & 0xFFFF, s2 = (s >> 16) & 0xFFFF;
int i;
for (i = 0; i < len; i++) {
s1 += data[i];
s2 += s1;
if (!(i & 0xFFF)) {
s1 %= 65521;
s2 %= 65521;
}
}
return ((s2 % 65521) << 16) | (s1 % 65521);
}
/*
* CRC32 checksum function.
*/
static unsigned long crc32_update(unsigned long crcword,
const unsigned char *data, int len)
{
static const unsigned long crc32_table[256] = {
0x00000000L, 0x77073096L, 0xEE0E612CL, 0x990951BAL,
0x076DC419L, 0x706AF48FL, 0xE963A535L, 0x9E6495A3L,
0x0EDB8832L, 0x79DCB8A4L, 0xE0D5E91EL, 0x97D2D988L,
0x09B64C2BL, 0x7EB17CBDL, 0xE7B82D07L, 0x90BF1D91L,
0x1DB71064L, 0x6AB020F2L, 0xF3B97148L, 0x84BE41DEL,
0x1ADAD47DL, 0x6DDDE4EBL, 0xF4D4B551L, 0x83D385C7L,
0x136C9856L, 0x646BA8C0L, 0xFD62F97AL, 0x8A65C9ECL,
0x14015C4FL, 0x63066CD9L, 0xFA0F3D63L, 0x8D080DF5L,
0x3B6E20C8L, 0x4C69105EL, 0xD56041E4L, 0xA2677172L,
0x3C03E4D1L, 0x4B04D447L, 0xD20D85FDL, 0xA50AB56BL,
0x35B5A8FAL, 0x42B2986CL, 0xDBBBC9D6L, 0xACBCF940L,
0x32D86CE3L, 0x45DF5C75L, 0xDCD60DCFL, 0xABD13D59L,
0x26D930ACL, 0x51DE003AL, 0xC8D75180L, 0xBFD06116L,
0x21B4F4B5L, 0x56B3C423L, 0xCFBA9599L, 0xB8BDA50FL,
0x2802B89EL, 0x5F058808L, 0xC60CD9B2L, 0xB10BE924L,
0x2F6F7C87L, 0x58684C11L, 0xC1611DABL, 0xB6662D3DL,
0x76DC4190L, 0x01DB7106L, 0x98D220BCL, 0xEFD5102AL,
0x71B18589L, 0x06B6B51FL, 0x9FBFE4A5L, 0xE8B8D433L,
0x7807C9A2L, 0x0F00F934L, 0x9609A88EL, 0xE10E9818L,
0x7F6A0DBBL, 0x086D3D2DL, 0x91646C97L, 0xE6635C01L,
0x6B6B51F4L, 0x1C6C6162L, 0x856530D8L, 0xF262004EL,
0x6C0695EDL, 0x1B01A57BL, 0x8208F4C1L, 0xF50FC457L,
0x65B0D9C6L, 0x12B7E950L, 0x8BBEB8EAL, 0xFCB9887CL,
0x62DD1DDFL, 0x15DA2D49L, 0x8CD37CF3L, 0xFBD44C65L,
0x4DB26158L, 0x3AB551CEL, 0xA3BC0074L, 0xD4BB30E2L,
0x4ADFA541L, 0x3DD895D7L, 0xA4D1C46DL, 0xD3D6F4FBL,
0x4369E96AL, 0x346ED9FCL, 0xAD678846L, 0xDA60B8D0L,
0x44042D73L, 0x33031DE5L, 0xAA0A4C5FL, 0xDD0D7CC9L,
0x5005713CL, 0x270241AAL, 0xBE0B1010L, 0xC90C2086L,
0x5768B525L, 0x206F85B3L, 0xB966D409L, 0xCE61E49FL,
0x5EDEF90EL, 0x29D9C998L, 0xB0D09822L, 0xC7D7A8B4L,
0x59B33D17L, 0x2EB40D81L, 0xB7BD5C3BL, 0xC0BA6CADL,
0xEDB88320L, 0x9ABFB3B6L, 0x03B6E20CL, 0x74B1D29AL,
0xEAD54739L, 0x9DD277AFL, 0x04DB2615L, 0x73DC1683L,
0xE3630B12L, 0x94643B84L, 0x0D6D6A3EL, 0x7A6A5AA8L,
0xE40ECF0BL, 0x9309FF9DL, 0x0A00AE27L, 0x7D079EB1L,
0xF00F9344L, 0x8708A3D2L, 0x1E01F268L, 0x6906C2FEL,
0xF762575DL, 0x806567CBL, 0x196C3671L, 0x6E6B06E7L,
0xFED41B76L, 0x89D32BE0L, 0x10DA7A5AL, 0x67DD4ACCL,
0xF9B9DF6FL, 0x8EBEEFF9L, 0x17B7BE43L, 0x60B08ED5L,
0xD6D6A3E8L, 0xA1D1937EL, 0x38D8C2C4L, 0x4FDFF252L,
0xD1BB67F1L, 0xA6BC5767L, 0x3FB506DDL, 0x48B2364BL,
0xD80D2BDAL, 0xAF0A1B4CL, 0x36034AF6L, 0x41047A60L,
0xDF60EFC3L, 0xA867DF55L, 0x316E8EEFL, 0x4669BE79L,
0xCB61B38CL, 0xBC66831AL, 0x256FD2A0L, 0x5268E236L,
0xCC0C7795L, 0xBB0B4703L, 0x220216B9L, 0x5505262FL,
0xC5BA3BBEL, 0xB2BD0B28L, 0x2BB45A92L, 0x5CB36A04L,
0xC2D7FFA7L, 0xB5D0CF31L, 0x2CD99E8BL, 0x5BDEAE1DL,
0x9B64C2B0L, 0xEC63F226L, 0x756AA39CL, 0x026D930AL,
0x9C0906A9L, 0xEB0E363FL, 0x72076785L, 0x05005713L,
0x95BF4A82L, 0xE2B87A14L, 0x7BB12BAEL, 0x0CB61B38L,
0x92D28E9BL, 0xE5D5BE0DL, 0x7CDCEFB7L, 0x0BDBDF21L,
0x86D3D2D4L, 0xF1D4E242L, 0x68DDB3F8L, 0x1FDA836EL,
0x81BE16CDL, 0xF6B9265BL, 0x6FB077E1L, 0x18B74777L,
0x88085AE6L, 0xFF0F6A70L, 0x66063BCAL, 0x11010B5CL,
0x8F659EFFL, 0xF862AE69L, 0x616BFFD3L, 0x166CCF45L,
0xA00AE278L, 0xD70DD2EEL, 0x4E048354L, 0x3903B3C2L,
0xA7672661L, 0xD06016F7L, 0x4969474DL, 0x3E6E77DBL,
0xAED16A4AL, 0xD9D65ADCL, 0x40DF0B66L, 0x37D83BF0L,
0xA9BCAE53L, 0xDEBB9EC5L, 0x47B2CF7FL, 0x30B5FFE9L,
0xBDBDF21CL, 0xCABAC28AL, 0x53B39330L, 0x24B4A3A6L,
0xBAD03605L, 0xCDD70693L, 0x54DE5729L, 0x23D967BFL,
0xB3667A2EL, 0xC4614AB8L, 0x5D681B02L, 0x2A6F2B94L,
0xB40BBE37L, 0xC30C8EA1L, 0x5A05DF1BL, 0x2D02EF8DL
};
crcword ^= 0xFFFFFFFFL;
while (len--) {
unsigned long newbyte = *data++;
newbyte ^= crcword & 0xFFL;
crcword = (crcword >> 8) ^ crc32_table[newbyte];
}
return crcword ^ 0xFFFFFFFFL;
}
typedef struct {
short code, extrabits;
int min, max;
} coderecord;
static const coderecord lencodes[] = {
{257, 0, 3, 3},
{258, 0, 4, 4},
{259, 0, 5, 5},
{260, 0, 6, 6},
{261, 0, 7, 7},
{262, 0, 8, 8},
{263, 0, 9, 9},
{264, 0, 10, 10},
{265, 1, 11, 12},
{266, 1, 13, 14},
{267, 1, 15, 16},
{268, 1, 17, 18},
{269, 2, 19, 22},
{270, 2, 23, 26},
{271, 2, 27, 30},
{272, 2, 31, 34},
{273, 3, 35, 42},
{274, 3, 43, 50},
{275, 3, 51, 58},
{276, 3, 59, 66},
{277, 4, 67, 82},
{278, 4, 83, 98},
{279, 4, 99, 114},
{280, 4, 115, 130},
{281, 5, 131, 162},
{282, 5, 163, 194},
{283, 5, 195, 226},
{284, 5, 227, 257},
{285, 0, 258, 258},
};
static const coderecord distcodes[] = {
{0, 0, 1, 1},
{1, 0, 2, 2},
{2, 0, 3, 3},
{3, 0, 4, 4},
{4, 1, 5, 6},
{5, 1, 7, 8},
{6, 2, 9, 12},
{7, 2, 13, 16},
{8, 3, 17, 24},
{9, 3, 25, 32},
{10, 4, 33, 48},
{11, 4, 49, 64},
{12, 5, 65, 96},
{13, 5, 97, 128},
{14, 6, 129, 192},
{15, 6, 193, 256},
{16, 7, 257, 384},
{17, 7, 385, 512},
{18, 8, 513, 768},
{19, 8, 769, 1024},
{20, 9, 1025, 1536},
{21, 9, 1537, 2048},
{22, 10, 2049, 3072},
{23, 10, 3073, 4096},
{24, 11, 4097, 6144},
{25, 11, 6145, 8192},
{26, 12, 8193, 12288},
{27, 12, 12289, 16384},
{28, 13, 16385, 24576},
{29, 13, 24577, 32768},
};
/* ----------------------------------------------------------------------
* Deflate compression.
*/
#define SYMLIMIT 65536
#define SYMPFX_LITLEN 0x00000000U
#define SYMPFX_DIST 0x40000000U
#define SYMPFX_EXTRABITS 0x80000000U
#define SYMPFX_CODELEN 0xC0000000U
#define SYMPFX_MASK 0xC0000000U
#define SYM_EXTRABITS_MASK 0x3C000000U
#define SYM_EXTRABITS_SHIFT 26
struct huftrees {
unsigned char *len_litlen;
int *code_litlen;
unsigned char *len_dist;
int *code_dist;
unsigned char *len_codelen;
int *code_codelen;
};
struct deflate_compress_ctx {
struct LZ77Context *lzc;
unsigned char *outbuf;
int outlen, outsize;
unsigned long outbits;
int noutbits;
int firstblock;
unsigned long *syms;
int symstart, nsyms;
int type;
unsigned long checksum;
unsigned long datasize;
int lastblock;
int finished;
unsigned char static_len1[288], static_len2[30];
int static_code1[288], static_code2[30];
struct huftrees sht;
#ifdef STATISTICS
unsigned long bitcount;
#endif
};
static void outbits(deflate_compress_ctx *out,
unsigned long bits, int nbits)
{
assert(out->noutbits + nbits <= 32);
out->outbits |= bits << out->noutbits;
out->noutbits += nbits;
while (out->noutbits >= 8) {
if (out->outlen >= out->outsize) {
out->outsize = out->outlen + 64;
out->outbuf = sresize(out->outbuf, out->outsize, unsigned char);
}
out->outbuf[out->outlen++] = (unsigned char) (out->outbits & 0xFF);
out->outbits >>= 8;
out->noutbits -= 8;
}
#ifdef STATISTICS
out->bitcount += nbits;
#endif
}
/*
* Binary heap functions used by buildhuf(). Each one assumes the
* heap to be stored in an array of ints, with two ints per node
* (user data and key). They take in the old heap length, and
* return the new one.
*/
#define HEAPPARENT(x) (((x)-2)/4*2)
#define HEAPLEFT(x) ((x)*2+2)
#define HEAPRIGHT(x) ((x)*2+4)
static int addheap(int *heap, int len, int userdata, int key)
{
int me, dad, tmp;
me = len;
heap[len++] = userdata;
heap[len++] = key;
while (me > 0) {
dad = HEAPPARENT(me);
if (heap[me+1] < heap[dad+1]) {
tmp = heap[me]; heap[me] = heap[dad]; heap[dad] = tmp;
tmp = heap[me+1]; heap[me+1] = heap[dad+1]; heap[dad+1] = tmp;
me = dad;
} else
break;
}
return len;
}
static int rmheap(int *heap, int len, int *userdata, int *key)
{
int me, lc, rc, c, tmp;
len -= 2;
*userdata = heap[0];
*key = heap[1];
heap[0] = heap[len];
heap[1] = heap[len+1];
me = 0;
while (1) {
lc = HEAPLEFT(me);
rc = HEAPRIGHT(me);
if (lc >= len)
break;
else if (rc >= len || heap[lc+1] < heap[rc+1])
c = lc;
else
c = rc;
if (heap[me+1] > heap[c+1]) {
tmp = heap[me]; heap[me] = heap[c]; heap[c] = tmp;
tmp = heap[me+1]; heap[me+1] = heap[c+1]; heap[c+1] = tmp;
} else
break;
me = c;
}
return len;
}
/*
* The core of the Huffman algorithm: takes an input array of
* symbol frequencies, and produces an output array of code
* lengths.
*
* This is basically a generic Huffman implementation, but it has
* one zlib-related quirk which is that it caps the output code
* lengths to fit in an unsigned char (which is safe since Deflate
* will reject anything longer than 15 anyway). Anyone wanting to
* rip it out and use it in another context should find that easy
* to remove.
*/
#define HUFMAX 286
static void buildhuf(const int *freqs, unsigned char *lengths, int nsyms)
{
int parent[2*HUFMAX-1];
int length[2*HUFMAX-1];
int heap[2*HUFMAX];
int heapsize;
int i, j, n;
int si, sj;
assert(nsyms <= HUFMAX);
memset(parent, 0, sizeof(parent));
/*
* Begin by building the heap.
*/
heapsize = 0;
for (i = 0; i < nsyms; i++)
if (freqs[i] > 0) /* leave unused symbols out totally */
heapsize = addheap(heap, heapsize, i, freqs[i]);
/*
* Now repeatedly take two elements off the heap and merge
* them.
*/
n = HUFMAX;
while (heapsize > 2) {
heapsize = rmheap(heap, heapsize, &i, &si);
heapsize = rmheap(heap, heapsize, &j, &sj);
parent[i] = n;
parent[j] = n;
heapsize = addheap(heap, heapsize, n, si + sj);
n++;
}
/*
* Now we have our tree, in the form of a link from each node
* to the index of its parent. Count back down the tree to
* determine the code lengths.
*/
memset(length, 0, sizeof(length));
/* The tree root has length 0 after that, which is correct. */
for (i = n-1; i-- ;)
if (parent[i] > 0)
length[i] = 1 + length[parent[i]];
/*
* And that's it. (Simple, wasn't it?) Copy the lengths into
* the output array and leave.
*
* Here we cap lengths to fit in unsigned char.
*/
for (i = 0; i < nsyms; i++)
lengths[i] = (length[i] > 255 ? 255 : length[i]);
}
/*
* Wrapper around buildhuf() which enforces the Deflate restriction
* that no code length may exceed 15 bits, or 7 for the auxiliary
* code length alphabet. This function has the same calling
* semantics as buildhuf(), except that it might modify the freqs
* array.
*/
static void deflate_buildhuf(int *freqs, unsigned char *lengths,
int nsyms, int limit)
{
int smallestfreq, totalfreq, nactivesyms;
int num, denom, adjust;
int i;
int maxprob;
/*
* Nasty special case: if the frequency table has fewer than
* two non-zero elements, we must invent some, because we can't
* have fewer than one bit encoding a symbol.
*/
assert(nsyms >= 2);
{
int count = 0;
for (i = 0; i < nsyms; i++)
if (freqs[i] > 0)
count++;
if (count < 2) {
for (i = 0; i < nsyms && count > 0; i++)
if (freqs[i] == 0) {
freqs[i] = 1;
count--;
}
}
}
/*
* First, try building the Huffman table the normal way. If
* this works, it's optimal, so we don't want to mess with it.
*/
buildhuf(freqs, lengths, nsyms);
for (i = 0; i < nsyms; i++)
if (lengths[i] > limit)
break;
if (i == nsyms)
return; /* OK */
/*
* The Huffman algorithm can only ever generate a code length
* of N bits or more if there is a symbol whose probability is
* less than the reciprocal of the (N+2)th Fibonacci number
* (counting from F_0=0 and F_1=1), i.e. 1/2584 for N=16, or
* 1/55 for N=8. (This is a necessary though not sufficient
* condition.)
*
* Why is this? Well, consider the input symbol with the
* smallest probability. Let that probability be x. In order
* for this symbol to have a code length of at least 1, the
* Huffman algorithm will have to merge it with some other
* node; and since x is the smallest probability, the node it
* gets merged with must be at least x. Thus, the probability
* of the resulting combined node will be at least 2x. Now in
* order for our node to reach depth 2, this 2x-node must be
* merged again. But what with? We can't assume the node it
* merges with is at least 2x, because this one might only be
* the _second_ smallest remaining node. But we do know the
* node it merges with must be at least x, so our order-2
* internal node is at least 3x.
*
* How small a node can merge with _that_ to get an order-3
* internal node? Well, it must be at least 2x, because if it
* was smaller than that then it would have been one of the two
* smallest nodes in the previous step and been merged at that
* point. So at least 3x, plus at least 2x, comes to at least
* 5x for an order-3 node.
*
* And so it goes on: at every stage we must merge our current
* node with a node at least as big as the bigger of this one's
* two parents, and from this starting point that gives rise to
* the Fibonacci sequence. So we find that in order to have a
* node n levels deep (i.e. a maximum code length of n), the
* overall probability of the root of the entire tree must be
* at least F_{n+2} times the probability of the rarest symbol.
* In other words, since the overall probability is 1, it is a
* necessary condition for a code length of 16 or more that
* there must be at least one symbol with probability <=
* 1/F_18.
*
* (To demonstrate that a probability this big really can give
* rise to a code length of 16, consider the set of input
* frequencies { 1-epsilon, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
* 89, 144, 233, 377, 610, 987 }, for arbitrarily small
* epsilon.)
*
* So here buildhuf() has returned us an overlong code. So to
* ensure it doesn't do it again, we add a constant to all the
* (non-zero) symbol frequencies, causing them to become more
* balanced and removing the danger. We can then feed the
* results back to the standard buildhuf() and be
* assert()-level confident that the resulting code lengths
* contain nothing outside the permitted range.
*/
assert(limit == 15 || limit == 7);
maxprob = (limit == 15 ? 2584 : 55); /* no point in computing full F_n */
totalfreq = nactivesyms = 0;
smallestfreq = -1;
for (i = 0; i < nsyms; i++) {
if (freqs[i] == 0)
continue;
if (smallestfreq < 0 || smallestfreq > freqs[i])
smallestfreq = freqs[i];
totalfreq += freqs[i];
nactivesyms++;
}
assert(smallestfreq <= totalfreq / maxprob);
/*
* We want to find the smallest integer `adjust' such that
* (totalfreq + nactivesyms * adjust) / (smallestfreq +
* adjust) is less than maxprob. A bit of algebra tells us
* that the threshold value is equal to
*
* totalfreq - maxprob * smallestfreq
* ----------------------------------
* maxprob - nactivesyms
*
* rounded up, of course. And we'll only even be trying
* this if
*/
num = totalfreq - smallestfreq * maxprob;
denom = maxprob - nactivesyms;
adjust = (num + denom - 1) / denom;
/*
* Now add `adjust' to all the input symbol frequencies.
*/
for (i = 0; i < nsyms; i++)
if (freqs[i] != 0)
freqs[i] += adjust;
/*
* Rebuild the Huffman tree...
*/
buildhuf(freqs, lengths, nsyms);
/*
* ... and this time it ought to be OK.
*/
for (i = 0; i < nsyms; i++)
assert(lengths[i] <= limit);
}
/*
* Compute the bit length of a symbol, given the three Huffman
* trees.
*/
static int symsize(unsigned sym, const struct huftrees *trees)
{
unsigned basesym = sym &~ SYMPFX_MASK;
switch (sym & SYMPFX_MASK) {
case SYMPFX_LITLEN:
return trees->len_litlen[basesym];
case SYMPFX_DIST:
return trees->len_dist[basesym];
case SYMPFX_CODELEN:
return trees->len_codelen[basesym];
default /*case SYMPFX_EXTRABITS*/:
return basesym >> SYM_EXTRABITS_SHIFT;
}
}
/*
* Write out a single symbol, given the three Huffman trees.
*/
static void writesym(deflate_compress_ctx *out,
unsigned sym, const struct huftrees *trees)
{
unsigned basesym = sym &~ SYMPFX_MASK;
int i;
switch (sym & SYMPFX_MASK) {
case SYMPFX_LITLEN:
debug(("send: litlen %d\n", basesym));
outbits(out, trees->code_litlen[basesym], trees->len_litlen[basesym]);
break;
case SYMPFX_DIST:
debug(("send: dist %d\n", basesym));