libgo/go/compress/flate/huffman_code.go

   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         "sort"
  10 )
  11
  12 type huffmanEncoder struct {
  13         codeBits []uint8
  14         code     []uint16
  15 }
  16
  17 type literalNode struct {
  18         literal uint16
  19         freq    int32
  20 }
  21
  22 type chain struct {
  23         // The sum of the leaves in this tree
  24         freq int32
  25
  26         // The number of literals to the left of this item at this level
  27         leafCount int32
  28
  29         // The right child of this chain in the previous level.
  30         up *chain
  31 }
  32
  33 type levelInfo struct {
  34         // Our level.  for better printing
  35         level int32
  36
  37         // The most recent chain generated for this level
  38         lastChain *chain
  39
  40         // The frequency of the next character to add to this level
  41         nextCharFreq int32
  42
  43         // The frequency of the next pair (from level below) to add to this level.
  44         // Only valid if the "needed" value of the next lower level is 0.
  45         nextPairFreq int32
  46
  47         // The number of chains remaining to generate for this level before moving
  48         // up to the next level
  49         needed int32
  50
  51         // The levelInfo for level+1
  52         up *levelInfo
  53
  54         // The levelInfo for level-1
  55         down *levelInfo
  56 }
  57
  58 func maxNode() literalNode { return literalNode{math.MaxUint16, math.MaxInt32} }
  59
  60 func newHuffmanEncoder(size int) *huffmanEncoder {
  61         return &huffmanEncoder{make([]uint8, size), make([]uint16, size)}
  62 }
  63
  64 // Generates a HuffmanCode corresponding to the fixed literal table
  65 func generateFixedLiteralEncoding() *huffmanEncoder {
  66         h := newHuffmanEncoder(maxLit)
  67         codeBits := h.codeBits
  68         code := h.code
  69         var ch uint16
  70         for ch = 0; ch < maxLit; ch++ {
  71                 var bits uint16
  72                 var size uint8
  73                 switch {
  74                 case ch < 144:
  75                         // size 8, 000110000  .. 10111111
  76                         bits = ch + 48
  77                         size = 8
  78                         break
  79                 case ch < 256:
  80                         // size 9, 110010000 .. 111111111
  81                         bits = ch + 400 - 144
  82                         size = 9
  83                         break
  84                 case ch < 280:
  85                         // size 7, 0000000 .. 0010111
  86                         bits = ch - 256
  87                         size = 7
  88                         break
  89                 default:
  90                         // size 8, 11000000 .. 11000111
  91                         bits = ch + 192 - 280
  92                         size = 8
  93                 }
  94                 codeBits[ch] = size
  95                 code[ch] = reverseBits(bits, size)
  96         }
  97         return h
  98 }
  99
 100 func generateFixedOffsetEncoding() *huffmanEncoder {
 101         h := newHuffmanEncoder(30)
 102         codeBits := h.codeBits
 103         code := h.code
 104         for ch := uint16(0); ch < 30; ch++ {
 105                 codeBits[ch] = 5
 106                 code[ch] = reverseBits(ch, 5)
 107         }
 108         return h
 109 }
 110
 111 var fixedLiteralEncoding *huffmanEncoder = generateFixedLiteralEncoding()
 112 var fixedOffsetEncoding *huffmanEncoder = generateFixedOffsetEncoding()
 113
 114 func (h *huffmanEncoder) bitLength(freq []int32) int64 {
 115         var total int64
 116         for i, f := range freq {
 117                 if f != 0 {
 118                         total += int64(f) * int64(h.codeBits[i])
 119                 }
 120         }
 121         return total
 122 }
 123
 124 // Return the number of literals assigned to each bit size in the Huffman encoding
 125 //
 126 // This method is only called when list.length >= 3
 127 // The cases of 0, 1, and 2 literals are handled by special case code.
 128 //
 129 // list  An array of the literals with non-zero frequencies
 130 //             and their associated frequencies.  The array is in order of increasing
 131 //             frequency, and has as its last element a special element with frequency
 132 //             MaxInt32
 133 // maxBits     The maximum number of bits that should be used to encode any literal.
 134 // return      An integer array in which array[i] indicates the number of literals
 135 //             that should be encoded in i bits.
 136 func (h *huffmanEncoder) bitCounts(list []literalNode, maxBits int32) []int32 {
 137         n := int32(len(list))
 138         list = list[0 : n+1]
 139         list[n] = maxNode()
 140
 141         // The tree can't have greater depth than n - 1, no matter what.  This
 142         // saves a little bit of work in some small cases
 143         if maxBits > n-1 {
 144                 maxBits = n - 1
 145         }
 146
 147         // Create information about each of the levels.
 148         // A bogus "Level 0" whose sole purpose is so that
 149         // level1.prev.needed==0.  This makes level1.nextPairFreq
 150         // be a legitimate value that never gets chosen.
 151         top := &levelInfo{needed: 0}
 152         chain2 := &chain{list[1].freq, 2, new(chain)}
 153         for level := int32(1); level <= maxBits; level++ {
 154                 // For every level, the first two items are the first two characters.
 155                 // We initialize the levels as if we had already figured this out.
 156                 top = &levelInfo{
 157                         level:        level,
 158                         lastChain:    chain2,
 159                         nextCharFreq: list[2].freq,
 160                         nextPairFreq: list[0].freq + list[1].freq,
 161                         down:         top,
 162                 }
 163                 top.down.up = top
 164                 if level == 1 {
 165                         top.nextPairFreq = math.MaxInt32
 166                 }
 167         }
 168
 169         // We need a total of 2*n - 2 items at top level and have already generated 2.
 170         top.needed = 2*n - 4
 171
 172         l := top
 173         for {
 174                 if l.nextPairFreq == math.MaxInt32 && l.nextCharFreq == math.MaxInt32 {
 175                         // We've run out of both leafs and pairs.
 176                         // End all calculations for this level.
 177                         // To m sure we never come back to this level or any lower level,
 178                         // set nextPairFreq impossibly large.
 179                         l.lastChain = nil
 180                         l.needed = 0
 181                         l = l.up
 182                         l.nextPairFreq = math.MaxInt32
 183                         continue
 184                 }
 185
 186                 prevFreq := l.lastChain.freq
 187                 if l.nextCharFreq < l.nextPairFreq {
 188                         // The next item on this row is a leaf node.
 189                         n := l.lastChain.leafCount + 1
 190                         l.lastChain = &chain{l.nextCharFreq, n, l.lastChain.up}
 191                         l.nextCharFreq = list[n].freq
 192                 } else {
 193                         // The next item on this row is a pair from the previous row.
 194                         // nextPairFreq isn't valid until we generate two
 195                         // more values in the level below
 196                         l.lastChain = &chain{l.nextPairFreq, l.lastChain.leafCount, l.down.lastChain}
 197                         l.down.needed = 2
 198                 }
 199
 200                 if l.needed--; l.needed == 0 {
 201                         // We've done everything we need to do for this level.
 202                         // Continue calculating one level up.  Fill in nextPairFreq
 203                         // of that level with the sum of the two nodes we've just calculated on
 204                         // this level.
 205                         up := l.up
 206                         if up == nil {
 207                                 // All done!
 208                                 break
 209                         }
 210                         up.nextPairFreq = prevFreq + l.lastChain.freq
 211                         l = up
 212                 } else {
 213                         // If we stole from below, move down temporarily to replenish it.
 214                         for l.down.needed > 0 {
 215                                 l = l.down
 216                         }
 217                 }
 218         }
 219
 220         // Somethings is wrong if at the end, the top level is null or hasn't used
 221         // all of the leaves.
 222         if top.lastChain.leafCount != n {
 223                 panic("top.lastChain.leafCount != n")
 224         }
 225
 226         bitCount := make([]int32, maxBits+1)
 227         bits := 1
 228         for chain := top.lastChain; chain.up != nil; chain = chain.up {
 229                 // chain.leafCount gives the number of literals requiring at least "bits"
 230                 // bits to encode.
 231                 bitCount[bits] = chain.leafCount - chain.up.leafCount
 232                 bits++
 233         }
 234         return bitCount
 235 }
 236
 237 // Look at the leaves and assign them a bit count and an encoding as specified
 238 // in RFC 1951 3.2.2
 239 func (h *huffmanEncoder) assignEncodingAndSize(bitCount []int32, list []literalNode) {
 240         code := uint16(0)
 241         for n, bits := range bitCount {
 242                 code <<= 1
 243                 if n == 0 || bits == 0 {
 244                         continue
 245                 }
 246                 // The literals list[len(list)-bits] .. list[len(list)-bits]
 247                 // are encoded using "bits" bits, and get the values
 248                 // code, code + 1, ....  The code values are
 249                 // assigned in literal order (not frequency order).
 250                 chunk := list[len(list)-int(bits):]
 251                 sortByLiteral(chunk)
 252                 for _, node := range chunk {
 253                         h.codeBits[node.literal] = uint8(n)
 254                         h.code[node.literal] = reverseBits(code, uint8(n))
 255                         code++
 256                 }
 257                 list = list[0 : len(list)-int(bits)]
 258         }
 259 }
 260
 261 // Update this Huffman Code object to be the minimum code for the specified frequency count.
 262 //
 263 // freq  An array of frequencies, in which frequency[i] gives the frequency of literal i.
 264 // maxBits  The maximum number of bits to use for any literal.
 265 func (h *huffmanEncoder) generate(freq []int32, maxBits int32) {
 266         list := make([]literalNode, len(freq)+1)
 267         // Number of non-zero literals
 268         count := 0
 269         // Set list to be the set of all non-zero literals and their frequencies
 270         for i, f := range freq {
 271                 if f != 0 {
 272                         list[count] = literalNode{uint16(i), f}
 273                         count++
 274                 } else {
 275                         h.codeBits[i] = 0
 276                 }
 277         }
 278         // If freq[] is shorter than codeBits[], fill rest of codeBits[] with zeros
 279         h.codeBits = h.codeBits[0:len(freq)]
 280         list = list[0:count]
 281         if count <= 2 {
 282                 // Handle the small cases here, because they are awkward for the general case code.  With
 283                 // two or fewer literals, everything has bit length 1.
 284                 for i, node := range list {
 285                         // "list" is in order of increasing literal value.
 286                         h.codeBits[node.literal] = 1
 287                         h.code[node.literal] = uint16(i)
 288                 }
 289                 return
 290         }
 291         sortByFreq(list)
 292
 293         // Get the number of literals for each bit count
 294         bitCount := h.bitCounts(list, maxBits)
 295         // And do the assignment
 296         h.assignEncodingAndSize(bitCount, list)
 297 }
 298
 299 type literalNodeSorter struct {
 300         a    []literalNode
 301         less func(i, j int) bool
 302 }
 303
 304 func (s literalNodeSorter) Len() int { return len(s.a) }
 305
 306 func (s literalNodeSorter) Less(i, j int) bool {
 307         return s.less(i, j)
 308 }
 309
 310 func (s literalNodeSorter) Swap(i, j int) { s.a[i], s.a[j] = s.a[j], s.a[i] }
 311
 312 func sortByFreq(a []literalNode) {
 313         s := &literalNodeSorter{a, func(i, j int) bool {
 314                 if a[i].freq == a[j].freq {
 315                         return a[i].literal < a[j].literal
 316                 }
 317                 return a[i].freq < a[j].freq
 318         }}
 319         sort.Sort(s)
 320 }
 321
 322 func sortByLiteral(a []literalNode) {
 323         s := &literalNodeSorter{a, func(i, j int) bool { return a[i].literal < a[j].literal }}
 324         sort.Sort(s)
 325 }