huffman_code.mx raw

   1  // Copyright 2009 The Go Authors. All rights reserved.
   2  // Use of this source code is governed by a BSD-style
   3  // license that can be found in the LICENSE file.
   4  
   5  package flate
   6  
   7  import (
   8  	"math"
   9  	"math/bits"
  10  	"sort"
  11  )
  12  
  13  // hcode is a huffman code with a bit code and bit length.
  14  type hcode struct {
  15  	code, len uint16
  16  }
  17  
  18  type huffmanEncoder struct {
  19  	codes     []hcode
  20  	freqcache []literalNode
  21  	bitCount  [17]int32
  22  	lns       byLiteral // stored to avoid repeated allocation in generate
  23  	lfs       byFreq    // stored to avoid repeated allocation in generate
  24  }
  25  
  26  type literalNode struct {
  27  	literal uint16
  28  	freq    int32
  29  }
  30  
  31  // A levelInfo describes the state of the constructed tree for a given depth.
  32  type levelInfo struct {
  33  	// Our level.  for better printing
  34  	level int32
  35  
  36  	// The frequency of the last node at this level
  37  	lastFreq int32
  38  
  39  	// The frequency of the next character to add to this level
  40  	nextCharFreq int32
  41  
  42  	// The frequency of the next pair (from level below) to add to this level.
  43  	// Only valid if the "needed" value of the next lower level is 0.
  44  	nextPairFreq int32
  45  
  46  	// The number of chains remaining to generate for this level before moving
  47  	// up to the next level
  48  	needed int32
  49  }
  50  
  51  // set sets the code and length of an hcode.
  52  func (h *hcode) set(code uint16, length uint16) {
  53  	h.len = length
  54  	h.code = code
  55  }
  56  
  57  func maxNode() literalNode { return literalNode{math.MaxUint16, math.MaxInt32} }
  58  
  59  func newHuffmanEncoder(size int) *huffmanEncoder {
  60  	return &huffmanEncoder{codes: []hcode{:size}}
  61  }
  62  
  63  // Generates a HuffmanCode corresponding to the fixed literal table.
  64  func generateFixedLiteralEncoding() *huffmanEncoder {
  65  	h := newHuffmanEncoder(maxNumLit)
  66  	codes := h.codes
  67  	var ch uint16
  68  	for ch = 0; ch < maxNumLit; ch++ {
  69  		var bits uint16
  70  		var size uint16
  71  		switch {
  72  		case ch < 144:
  73  			// size 8, 000110000  .. 10111111
  74  			bits = ch + 48
  75  			size = 8
  76  		case ch < 256:
  77  			// size 9, 110010000 .. 111111111
  78  			bits = ch + 400 - 144
  79  			size = 9
  80  		case ch < 280:
  81  			// size 7, 0000000 .. 0010111
  82  			bits = ch - 256
  83  			size = 7
  84  		default:
  85  			// size 8, 11000000 .. 11000111
  86  			bits = ch + 192 - 280
  87  			size = 8
  88  		}
  89  		codes[ch] = hcode{code: reverseBits(bits, byte(size)), len: size}
  90  	}
  91  	return h
  92  }
  93  
  94  func generateFixedOffsetEncoding() *huffmanEncoder {
  95  	h := newHuffmanEncoder(30)
  96  	codes := h.codes
  97  	for ch := range codes {
  98  		codes[ch] = hcode{code: reverseBits(uint16(ch), 5), len: 5}
  99  	}
 100  	return h
 101  }
 102  
 103  var fixedLiteralEncoding *huffmanEncoder = generateFixedLiteralEncoding()
 104  var fixedOffsetEncoding *huffmanEncoder = generateFixedOffsetEncoding()
 105  
 106  func (h *huffmanEncoder) bitLength(freq []int32) int {
 107  	var total int
 108  	for i, f := range freq {
 109  		if f != 0 {
 110  			total += int(f) * int(h.codes[i].len)
 111  		}
 112  	}
 113  	return total
 114  }
 115  
 116  const maxBitsLimit = 16
 117  
 118  // bitCounts computes the number of literals assigned to each bit size in the Huffman encoding.
 119  // It is only called when list.length >= 3.
 120  // The cases of 0, 1, and 2 literals are handled by special case code.
 121  //
 122  // list is an array of the literals with non-zero frequencies
 123  // and their associated frequencies. The array is in order of increasing
 124  // frequency and has as its last element a special element with frequency
 125  // MaxInt32.
 126  //
 127  // maxBits is the maximum number of bits that should be used to encode any literal.
 128  // It must be less than 16.
 129  //
 130  // bitCounts returns an integer slice in which slice[i] indicates the number of literals
 131  // that should be encoded in i bits.
 132  func (h *huffmanEncoder) bitCounts(list []literalNode, maxBits int32) []int32 {
 133  	if maxBits >= maxBitsLimit {
 134  		panic("flate: maxBits too large")
 135  	}
 136  	n := int32(len(list))
 137  	list = list[0 : n+1]
 138  	list[n] = maxNode()
 139  
 140  	// The tree can't have greater depth than n - 1, no matter what. This
 141  	// saves a little bit of work in some small cases
 142  	if maxBits > n-1 {
 143  		maxBits = n - 1
 144  	}
 145  
 146  	// Create information about each of the levels.
 147  	// A bogus "Level 0" whose sole purpose is so that
 148  	// level1.prev.needed==0.  This makes level1.nextPairFreq
 149  	// be a legitimate value that never gets chosen.
 150  	var levels [maxBitsLimit]levelInfo
 151  	// leafCounts[i] counts the number of literals at the left
 152  	// of ancestors of the rightmost node at level i.
 153  	// leafCounts[i][j] is the number of literals at the left
 154  	// of the level j ancestor.
 155  	var leafCounts [maxBitsLimit][maxBitsLimit]int32
 156  
 157  	for level := int32(1); level <= maxBits; level++ {
 158  		// For every level, the first two items are the first two characters.
 159  		// We initialize the levels as if we had already figured this out.
 160  		levels[level] = levelInfo{
 161  			level:        level,
 162  			lastFreq:     list[1].freq,
 163  			nextCharFreq: list[2].freq,
 164  			nextPairFreq: list[0].freq + list[1].freq,
 165  		}
 166  		leafCounts[level][level] = 2
 167  		if level == 1 {
 168  			levels[level].nextPairFreq = math.MaxInt32
 169  		}
 170  	}
 171  
 172  	// We need a total of 2*n - 2 items at top level and have already generated 2.
 173  	levels[maxBits].needed = 2*n - 4
 174  
 175  	level := maxBits
 176  	for {
 177  		l := &levels[level]
 178  		if l.nextPairFreq == math.MaxInt32 && l.nextCharFreq == math.MaxInt32 {
 179  			// We've run out of both leaves and pairs.
 180  			// End all calculations for this level.
 181  			// To make sure we never come back to this level or any lower level,
 182  			// set nextPairFreq impossibly large.
 183  			l.needed = 0
 184  			levels[level+1].nextPairFreq = math.MaxInt32
 185  			level++
 186  			continue
 187  		}
 188  
 189  		prevFreq := l.lastFreq
 190  		if l.nextCharFreq < l.nextPairFreq {
 191  			// The next item on this row is a leaf node.
 192  			n := leafCounts[level][level] + 1
 193  			l.lastFreq = l.nextCharFreq
 194  			// Lower leafCounts are the same of the previous node.
 195  			leafCounts[level][level] = n
 196  			l.nextCharFreq = list[n].freq
 197  		} else {
 198  			// The next item on this row is a pair from the previous row.
 199  			// nextPairFreq isn't valid until we generate two
 200  			// more values in the level below
 201  			l.lastFreq = l.nextPairFreq
 202  			// Take leaf counts from the lower level, except counts[level] remains the same.
 203  			copy(leafCounts[level][:level], leafCounts[level-1][:level])
 204  			levels[l.level-1].needed = 2
 205  		}
 206  
 207  		if l.needed--; l.needed == 0 {
 208  			// We've done everything we need to do for this level.
 209  			// Continue calculating one level up. Fill in nextPairFreq
 210  			// of that level with the sum of the two nodes we've just calculated on
 211  			// this level.
 212  			if l.level == maxBits {
 213  				// All done!
 214  				break
 215  			}
 216  			levels[l.level+1].nextPairFreq = prevFreq + l.lastFreq
 217  			level++
 218  		} else {
 219  			// If we stole from below, move down temporarily to replenish it.
 220  			for levels[level-1].needed > 0 {
 221  				level--
 222  			}
 223  		}
 224  	}
 225  
 226  	// Somethings is wrong if at the end, the top level is null or hasn't used
 227  	// all of the leaves.
 228  	if leafCounts[maxBits][maxBits] != n {
 229  		panic("leafCounts[maxBits][maxBits] != n")
 230  	}
 231  
 232  	bitCount := h.bitCount[:maxBits+1]
 233  	bits := 1
 234  	counts := &leafCounts[maxBits]
 235  	for level := maxBits; level > 0; level-- {
 236  		// chain.leafCount gives the number of literals requiring at least "bits"
 237  		// bits to encode.
 238  		bitCount[bits] = counts[level] - counts[level-1]
 239  		bits++
 240  	}
 241  	return bitCount
 242  }
 243  
 244  // Look at the leaves and assign them a bit count and an encoding as specified
 245  // in RFC 1951 3.2.2
 246  func (h *huffmanEncoder) assignEncodingAndSize(bitCount []int32, list []literalNode) {
 247  	code := uint16(0)
 248  	for n, bits := range bitCount {
 249  		code <<= 1
 250  		if n == 0 || bits == 0 {
 251  			continue
 252  		}
 253  		// The literals list[len(list)-bits] .. list[len(list)-bits]
 254  		// are encoded using "bits" bits, and get the values
 255  		// code, code + 1, ....  The code values are
 256  		// assigned in literal order (not frequency order).
 257  		chunk := list[len(list)-int(bits):]
 258  
 259  		h.lns.sort(chunk)
 260  		for _, node := range chunk {
 261  			h.codes[node.literal] = hcode{code: reverseBits(code, uint8(n)), len: uint16(n)}
 262  			code++
 263  		}
 264  		list = list[0 : len(list)-int(bits)]
 265  	}
 266  }
 267  
 268  // Update this Huffman Code object to be the minimum code for the specified frequency count.
 269  //
 270  // freq is an array of frequencies, in which freq[i] gives the frequency of literal i.
 271  // maxBits  The maximum number of bits to use for any literal.
 272  func (h *huffmanEncoder) generate(freq []int32, maxBits int32) {
 273  	if h.freqcache == nil {
 274  		// Allocate a reusable buffer with the longest possible frequency table.
 275  		// Possible lengths are codegenCodeCount, offsetCodeCount and maxNumLit.
 276  		// The largest of these is maxNumLit, so we allocate for that case.
 277  		h.freqcache = []literalNode{:maxNumLit+1}
 278  	}
 279  	list := h.freqcache[:len(freq)+1]
 280  	// Number of non-zero literals
 281  	count := 0
 282  	// Set list to be the set of all non-zero literals and their frequencies
 283  	for i, f := range freq {
 284  		if f != 0 {
 285  			list[count] = literalNode{uint16(i), f}
 286  			count++
 287  		} else {
 288  			h.codes[i].len = 0
 289  		}
 290  	}
 291  
 292  	list = list[:count]
 293  	if count <= 2 {
 294  		// Handle the small cases here, because they are awkward for the general case code. With
 295  		// two or fewer literals, everything has bit length 1.
 296  		for i, node := range list {
 297  			// "list" is in order of increasing literal value.
 298  			h.codes[node.literal].set(uint16(i), 1)
 299  		}
 300  		return
 301  	}
 302  	h.lfs.sort(list)
 303  
 304  	// Get the number of literals for each bit count
 305  	bitCount := h.bitCounts(list, maxBits)
 306  	// And do the assignment
 307  	h.assignEncodingAndSize(bitCount, list)
 308  }
 309  
 310  type byLiteral []literalNode
 311  
 312  func (s *byLiteral) sort(a []literalNode) {
 313  	*s = byLiteral(a)
 314  	sort.Sort(s)
 315  }
 316  
 317  func (s byLiteral) Len() int { return len(s) }
 318  
 319  func (s byLiteral) Less(i, j int) bool {
 320  	return s[i].literal < s[j].literal
 321  }
 322  
 323  func (s byLiteral) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
 324  
 325  type byFreq []literalNode
 326  
 327  func (s *byFreq) sort(a []literalNode) {
 328  	*s = byFreq(a)
 329  	sort.Sort(s)
 330  }
 331  
 332  func (s byFreq) Len() int { return len(s) }
 333  
 334  func (s byFreq) Less(i, j int) bool {
 335  	if s[i].freq == s[j].freq {
 336  		return s[i].literal < s[j].literal
 337  	}
 338  	return s[i].freq < s[j].freq
 339  }
 340  
 341  func (s byFreq) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
 342  
 343  func reverseBits(number uint16, bitLength byte) uint16 {
 344  	return bits.Reverse16(number << (16 - bitLength))
 345  }
 346