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Source file src/compress/flate/huffman_code.go

Documentation: compress/flate

  // Copyright 2009 The Go Authors. All rights reserved.
  // Use of this source code is governed by a BSD-style
  // license that can be found in the LICENSE file.
  
  package flate
  
  import (
  	"math"
  	"math/bits"
  	"sort"
  )
  
  // hcode is a huffman code with a bit code and bit length.
  type hcode struct {
  	code, len uint16
  }
  
  type huffmanEncoder struct {
  	codes     []hcode
  	freqcache []literalNode
  	bitCount  [17]int32
  	lns       byLiteral // stored to avoid repeated allocation in generate
  	lfs       byFreq    // stored to avoid repeated allocation in generate
  }
  
  type literalNode struct {
  	literal uint16
  	freq    int32
  }
  
  // A levelInfo describes the state of the constructed tree for a given depth.
  type levelInfo struct {
  	// Our level.  for better printing
  	level int32
  
  	// The frequency of the last node at this level
  	lastFreq int32
  
  	// The frequency of the next character to add to this level
  	nextCharFreq int32
  
  	// The frequency of the next pair (from level below) to add to this level.
  	// Only valid if the "needed" value of the next lower level is 0.
  	nextPairFreq int32
  
  	// The number of chains remaining to generate for this level before moving
  	// up to the next level
  	needed int32
  }
  
  // set sets the code and length of an hcode.
  func (h *hcode) set(code uint16, length uint16) {
  	h.len = length
  	h.code = code
  }
  
  func maxNode() literalNode { return literalNode{math.MaxUint16, math.MaxInt32} }
  
  func newHuffmanEncoder(size int) *huffmanEncoder {
  	return &huffmanEncoder{codes: make([]hcode, size)}
  }
  
  // Generates a HuffmanCode corresponding to the fixed literal table
  func generateFixedLiteralEncoding() *huffmanEncoder {
  	h := newHuffmanEncoder(maxNumLit)
  	codes := h.codes
  	var ch uint16
  	for ch = 0; ch < maxNumLit; ch++ {
  		var bits uint16
  		var size uint16
  		switch {
  		case ch < 144:
  			// size 8, 000110000  .. 10111111
  			bits = ch + 48
  			size = 8
  			break
  		case ch < 256:
  			// size 9, 110010000 .. 111111111
  			bits = ch + 400 - 144
  			size = 9
  			break
  		case ch < 280:
  			// size 7, 0000000 .. 0010111
  			bits = ch - 256
  			size = 7
  			break
  		default:
  			// size 8, 11000000 .. 11000111
  			bits = ch + 192 - 280
  			size = 8
  		}
  		codes[ch] = hcode{code: reverseBits(bits, byte(size)), len: size}
  	}
  	return h
  }
  
  func generateFixedOffsetEncoding() *huffmanEncoder {
  	h := newHuffmanEncoder(30)
  	codes := h.codes
  	for ch := range codes {
  		codes[ch] = hcode{code: reverseBits(uint16(ch), 5), len: 5}
  	}
  	return h
  }
  
  var fixedLiteralEncoding *huffmanEncoder = generateFixedLiteralEncoding()
  var fixedOffsetEncoding *huffmanEncoder = generateFixedOffsetEncoding()
  
  func (h *huffmanEncoder) bitLength(freq []int32) int {
  	var total int
  	for i, f := range freq {
  		if f != 0 {
  			total += int(f) * int(h.codes[i].len)
  		}
  	}
  	return total
  }
  
  const maxBitsLimit = 16
  
  // Return the number of literals assigned to each bit size in the Huffman encoding
  //
  // This method is only called when list.length >= 3
  // The cases of 0, 1, and 2 literals are handled by special case code.
  //
  // list  An array of the literals with non-zero frequencies
  //             and their associated frequencies. The array is in order of increasing
  //             frequency, and has as its last element a special element with frequency
  //             MaxInt32
  // maxBits     The maximum number of bits that should be used to encode any literal.
  //             Must be less than 16.
  // return      An integer array in which array[i] indicates the number of literals
  //             that should be encoded in i bits.
  func (h *huffmanEncoder) bitCounts(list []literalNode, maxBits int32) []int32 {
  	if maxBits >= maxBitsLimit {
  		panic("flate: maxBits too large")
  	}
  	n := int32(len(list))
  	list = list[0 : n+1]
  	list[n] = maxNode()
  
  	// The tree can't have greater depth than n - 1, no matter what. This
  	// saves a little bit of work in some small cases
  	if maxBits > n-1 {
  		maxBits = n - 1
  	}
  
  	// Create information about each of the levels.
  	// A bogus "Level 0" whose sole purpose is so that
  	// level1.prev.needed==0.  This makes level1.nextPairFreq
  	// be a legitimate value that never gets chosen.
  	var levels [maxBitsLimit]levelInfo
  	// leafCounts[i] counts the number of literals at the left
  	// of ancestors of the rightmost node at level i.
  	// leafCounts[i][j] is the number of literals at the left
  	// of the level j ancestor.
  	var leafCounts [maxBitsLimit][maxBitsLimit]int32
  
  	for level := int32(1); level <= maxBits; level++ {
  		// For every level, the first two items are the first two characters.
  		// We initialize the levels as if we had already figured this out.
  		levels[level] = levelInfo{
  			level:        level,
  			lastFreq:     list[1].freq,
  			nextCharFreq: list[2].freq,
  			nextPairFreq: list[0].freq + list[1].freq,
  		}
  		leafCounts[level][level] = 2
  		if level == 1 {
  			levels[level].nextPairFreq = math.MaxInt32
  		}
  	}
  
  	// We need a total of 2*n - 2 items at top level and have already generated 2.
  	levels[maxBits].needed = 2*n - 4
  
  	level := maxBits
  	for {
  		l := &levels[level]
  		if l.nextPairFreq == math.MaxInt32 && l.nextCharFreq == math.MaxInt32 {
  			// We've run out of both leafs and pairs.
  			// End all calculations for this level.
  			// To make sure we never come back to this level or any lower level,
  			// set nextPairFreq impossibly large.
  			l.needed = 0
  			levels[level+1].nextPairFreq = math.MaxInt32
  			level++
  			continue
  		}
  
  		prevFreq := l.lastFreq
  		if l.nextCharFreq < l.nextPairFreq {
  			// The next item on this row is a leaf node.
  			n := leafCounts[level][level] + 1
  			l.lastFreq = l.nextCharFreq
  			// Lower leafCounts are the same of the previous node.
  			leafCounts[level][level] = n
  			l.nextCharFreq = list[n].freq
  		} else {
  			// The next item on this row is a pair from the previous row.
  			// nextPairFreq isn't valid until we generate two
  			// more values in the level below
  			l.lastFreq = l.nextPairFreq
  			// Take leaf counts from the lower level, except counts[level] remains the same.
  			copy(leafCounts[level][:level], leafCounts[level-1][:level])
  			levels[l.level-1].needed = 2
  		}
  
  		if l.needed--; l.needed == 0 {
  			// We've done everything we need to do for this level.
  			// Continue calculating one level up. Fill in nextPairFreq
  			// of that level with the sum of the two nodes we've just calculated on
  			// this level.
  			if l.level == maxBits {
  				// All done!
  				break
  			}
  			levels[l.level+1].nextPairFreq = prevFreq + l.lastFreq
  			level++
  		} else {
  			// If we stole from below, move down temporarily to replenish it.
  			for levels[level-1].needed > 0 {
  				level--
  			}
  		}
  	}
  
  	// Somethings is wrong if at the end, the top level is null or hasn't used
  	// all of the leaves.
  	if leafCounts[maxBits][maxBits] != n {
  		panic("leafCounts[maxBits][maxBits] != n")
  	}
  
  	bitCount := h.bitCount[:maxBits+1]
  	bits := 1
  	counts := &leafCounts[maxBits]
  	for level := maxBits; level > 0; level-- {
  		// chain.leafCount gives the number of literals requiring at least "bits"
  		// bits to encode.
  		bitCount[bits] = counts[level] - counts[level-1]
  		bits++
  	}
  	return bitCount
  }
  
  // Look at the leaves and assign them a bit count and an encoding as specified
  // in RFC 1951 3.2.2
  func (h *huffmanEncoder) assignEncodingAndSize(bitCount []int32, list []literalNode) {
  	code := uint16(0)
  	for n, bits := range bitCount {
  		code <<= 1
  		if n == 0 || bits == 0 {
  			continue
  		}
  		// The literals list[len(list)-bits] .. list[len(list)-bits]
  		// are encoded using "bits" bits, and get the values
  		// code, code + 1, ....  The code values are
  		// assigned in literal order (not frequency order).
  		chunk := list[len(list)-int(bits):]
  
  		h.lns.sort(chunk)
  		for _, node := range chunk {
  			h.codes[node.literal] = hcode{code: reverseBits(code, uint8(n)), len: uint16(n)}
  			code++
  		}
  		list = list[0 : len(list)-int(bits)]
  	}
  }
  
  // Update this Huffman Code object to be the minimum code for the specified frequency count.
  //
  // freq  An array of frequencies, in which frequency[i] gives the frequency of literal i.
  // maxBits  The maximum number of bits to use for any literal.
  func (h *huffmanEncoder) generate(freq []int32, maxBits int32) {
  	if h.freqcache == nil {
  		// Allocate a reusable buffer with the longest possible frequency table.
  		// Possible lengths are codegenCodeCount, offsetCodeCount and maxNumLit.
  		// The largest of these is maxNumLit, so we allocate for that case.
  		h.freqcache = make([]literalNode, maxNumLit+1)
  	}
  	list := h.freqcache[:len(freq)+1]
  	// Number of non-zero literals
  	count := 0
  	// Set list to be the set of all non-zero literals and their frequencies
  	for i, f := range freq {
  		if f != 0 {
  			list[count] = literalNode{uint16(i), f}
  			count++
  		} else {
  			list[count] = literalNode{}
  			h.codes[i].len = 0
  		}
  	}
  	list[len(freq)] = literalNode{}
  
  	list = list[:count]
  	if count <= 2 {
  		// Handle the small cases here, because they are awkward for the general case code. With
  		// two or fewer literals, everything has bit length 1.
  		for i, node := range list {
  			// "list" is in order of increasing literal value.
  			h.codes[node.literal].set(uint16(i), 1)
  		}
  		return
  	}
  	h.lfs.sort(list)
  
  	// Get the number of literals for each bit count
  	bitCount := h.bitCounts(list, maxBits)
  	// And do the assignment
  	h.assignEncodingAndSize(bitCount, list)
  }
  
  type byLiteral []literalNode
  
  func (s *byLiteral) sort(a []literalNode) {
  	*s = byLiteral(a)
  	sort.Sort(s)
  }
  
  func (s byLiteral) Len() int { return len(s) }
  
  func (s byLiteral) Less(i, j int) bool {
  	return s[i].literal < s[j].literal
  }
  
  func (s byLiteral) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
  
  type byFreq []literalNode
  
  func (s *byFreq) sort(a []literalNode) {
  	*s = byFreq(a)
  	sort.Sort(s)
  }
  
  func (s byFreq) Len() int { return len(s) }
  
  func (s byFreq) Less(i, j int) bool {
  	if s[i].freq == s[j].freq {
  		return s[i].literal < s[j].literal
  	}
  	return s[i].freq < s[j].freq
  }
  
  func (s byFreq) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
  
  func reverseBits(number uint16, bitLength byte) uint16 {
  	return bits.Reverse16(number << (16 - bitLength))
  }
  

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