source: code/trunk/vendor/github.com/klauspost/compress/flate/huffman_code.go@ 822

// 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"
)

const (
        maxBitsLimit = 16
        // number of valid literals
        literalCount = 286
)

// 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
}

type literalNode struct {
        literal uint16
        freq    uint16
}

// 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 reverseBits(number uint16, bitLength byte) uint16 {
        return bits.Reverse16(number << ((16 - bitLength) & 15))
}

func maxNode() literalNode { return literalNode{math.MaxUint16, math.MaxUint16} }

func newHuffmanEncoder(size int) *huffmanEncoder {
        // Make capacity to next power of two.
        c := uint(bits.Len32(uint32(size - 1)))
        return &huffmanEncoder{codes: make([]hcode, size, 1<<c)}
}

// Generates a HuffmanCode corresponding to the fixed literal table
func generateFixedLiteralEncoding() *huffmanEncoder {
        h := newHuffmanEncoder(literalCount)
        codes := h.codes
        var ch uint16
        for ch = 0; ch < literalCount; ch++ {
                var bits uint16
                var size uint16
                switch {
                case ch < 144:
                        // size 8, 000110000  .. 10111111
                        bits = ch + 48
                        size = 8
                case ch < 256:
                        // size 9, 110010000 .. 111111111
                        bits = ch + 400 - 144
                        size = 9
                case ch < 280:
                        // size 7, 0000000 .. 0010111
                        bits = ch - 256
                        size = 7
                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 = generateFixedLiteralEncoding()
var fixedOffsetEncoding = generateFixedOffsetEncoding()

func (h *huffmanEncoder) bitLength(freq []uint16) int {
        var total int
        for i, f := range freq {
                if f != 0 {
                        total += int(f) * int(h.codes[i].len)
                }
        }
        return total
}

// 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:     int32(list[1].freq),
                        nextCharFreq: int32(list[2].freq),
                        nextPairFreq: int32(list[0].freq) + int32(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
                        e := list[n]
                        if e.literal < math.MaxUint16 {
                                l.nextCharFreq = int32(e.freq)
                        } else {
                                l.nextCharFreq = math.MaxInt32
                        }
                } 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):]

                sortByLiteral(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 []uint16, maxBits int32) {
        if h.freqcache == nil {
                // Allocate a reusable buffer with the longest possible frequency table.
                // Possible lengths are codegenCodeCount, offsetCodeCount and literalCount.
                // The largest of these is literalCount, so we allocate for that case.
                h.freqcache = make([]literalNode, literalCount+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
        }
        sortByFreq(list)

        // Get the number of literals for each bit count
        bitCount := h.bitCounts(list, maxBits)
        // And do the assignment
        h.assignEncodingAndSize(bitCount, list)
}

func atLeastOne(v float32) float32 {
        if v < 1 {
                return 1
        }
        return v
}

// histogramSize accumulates a histogram of b in h.
// An estimated size in bits is returned.
// Unassigned values are assigned '1' in the histogram.
// len(h) must be >= 256, and h's elements must be all zeroes.
func histogramSize(b []byte, h []uint16, fill bool) (int, int) {
        h = h[:256]
        for _, t := range b {
                h[t]++
        }
        invTotal := 1.0 / float32(len(b))
        shannon := float32(0.0)
        var extra float32
        if fill {
                oneBits := atLeastOne(-mFastLog2(invTotal))
                for i, v := range h[:] {
                        if v > 0 {
                                n := float32(v)
                                shannon += atLeastOne(-mFastLog2(n*invTotal)) * n
                        } else {
                                h[i] = 1
                                extra += oneBits
                        }
                }
        } else {
                for _, v := range h[:] {
                        if v > 0 {
                                n := float32(v)
                                shannon += atLeastOne(-mFastLog2(n*invTotal)) * n
                        }
                }
        }

        return int(shannon + 0.99), int(extra + 0.99)
}