437 lines
11 KiB
Go
437 lines
11 KiB
Go
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package brotli
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/* Copyright 2013 Google Inc. All Rights Reserved.
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Distributed under MIT license.
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See file LICENSE for detail or copy at https://opensource.org/licenses/MIT
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*/
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/* Functions to estimate the bit cost of Huffman trees. */
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func shannonEntropy(population []uint32, size uint, total *uint) float64 {
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var sum uint = 0
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var retval float64 = 0
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var population_end []uint32 = population[size:]
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var p uint
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for -cap(population) < -cap(population_end) {
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p = uint(population[0])
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population = population[1:]
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sum += p
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retval -= float64(p) * fastLog2(p)
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}
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if sum != 0 {
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retval += float64(sum) * fastLog2(sum)
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}
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*total = sum
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return retval
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}
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func bitsEntropy(population []uint32, size uint) float64 {
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var sum uint
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var retval float64 = shannonEntropy(population, size, &sum)
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if retval < float64(sum) {
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/* At least one bit per literal is needed. */
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retval = float64(sum)
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}
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return retval
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}
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const kOneSymbolHistogramCost float64 = 12
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const kTwoSymbolHistogramCost float64 = 20
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const kThreeSymbolHistogramCost float64 = 28
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const kFourSymbolHistogramCost float64 = 37
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func populationCostLiteral(histogram *histogramLiteral) float64 {
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var data_size uint = histogramDataSizeLiteral()
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var count int = 0
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var s [5]uint
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var bits float64 = 0.0
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var i uint
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if histogram.total_count_ == 0 {
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return kOneSymbolHistogramCost
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}
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for i = 0; i < data_size; i++ {
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if histogram.data_[i] > 0 {
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s[count] = i
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count++
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if count > 4 {
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break
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}
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}
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}
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if count == 1 {
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return kOneSymbolHistogramCost
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}
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if count == 2 {
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return kTwoSymbolHistogramCost + float64(histogram.total_count_)
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}
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if count == 3 {
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var histo0 uint32 = histogram.data_[s[0]]
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var histo1 uint32 = histogram.data_[s[1]]
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var histo2 uint32 = histogram.data_[s[2]]
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var histomax uint32 = brotli_max_uint32_t(histo0, brotli_max_uint32_t(histo1, histo2))
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return kThreeSymbolHistogramCost + 2*(float64(histo0)+float64(histo1)+float64(histo2)) - float64(histomax)
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}
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if count == 4 {
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var histo [4]uint32
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var h23 uint32
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var histomax uint32
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for i = 0; i < 4; i++ {
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histo[i] = histogram.data_[s[i]]
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}
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/* Sort */
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for i = 0; i < 4; i++ {
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var j uint
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for j = i + 1; j < 4; j++ {
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if histo[j] > histo[i] {
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var tmp uint32 = histo[j]
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histo[j] = histo[i]
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histo[i] = tmp
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}
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}
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}
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h23 = histo[2] + histo[3]
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histomax = brotli_max_uint32_t(h23, histo[0])
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return kFourSymbolHistogramCost + 3*float64(h23) + 2*(float64(histo[0])+float64(histo[1])) - float64(histomax)
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}
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{
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var max_depth uint = 1
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var depth_histo = [codeLengthCodes]uint32{0}
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/* In this loop we compute the entropy of the histogram and simultaneously
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build a simplified histogram of the code length codes where we use the
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zero repeat code 17, but we don't use the non-zero repeat code 16. */
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var log2total float64 = fastLog2(histogram.total_count_)
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for i = 0; i < data_size; {
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if histogram.data_[i] > 0 {
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var log2p float64 = log2total - fastLog2(uint(histogram.data_[i]))
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/* Compute -log2(P(symbol)) = -log2(count(symbol)/total_count) =
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= log2(total_count) - log2(count(symbol)) */
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var depth uint = uint(log2p + 0.5)
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/* Approximate the bit depth by round(-log2(P(symbol))) */
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bits += float64(histogram.data_[i]) * log2p
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if depth > 15 {
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depth = 15
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}
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if depth > max_depth {
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max_depth = depth
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}
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depth_histo[depth]++
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i++
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} else {
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var reps uint32 = 1
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/* Compute the run length of zeros and add the appropriate number of 0
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and 17 code length codes to the code length code histogram. */
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var k uint
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for k = i + 1; k < data_size && histogram.data_[k] == 0; k++ {
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reps++
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}
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i += uint(reps)
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if i == data_size {
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/* Don't add any cost for the last zero run, since these are encoded
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only implicitly. */
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break
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}
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if reps < 3 {
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depth_histo[0] += reps
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} else {
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reps -= 2
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for reps > 0 {
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depth_histo[repeatZeroCodeLength]++
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/* Add the 3 extra bits for the 17 code length code. */
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bits += 3
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reps >>= 3
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}
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}
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}
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}
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/* Add the estimated encoding cost of the code length code histogram. */
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bits += float64(18 + 2*max_depth)
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/* Add the entropy of the code length code histogram. */
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bits += bitsEntropy(depth_histo[:], codeLengthCodes)
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}
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return bits
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}
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func populationCostCommand(histogram *histogramCommand) float64 {
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var data_size uint = histogramDataSizeCommand()
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var count int = 0
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var s [5]uint
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var bits float64 = 0.0
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var i uint
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if histogram.total_count_ == 0 {
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return kOneSymbolHistogramCost
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}
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for i = 0; i < data_size; i++ {
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if histogram.data_[i] > 0 {
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s[count] = i
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count++
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if count > 4 {
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break
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}
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}
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}
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if count == 1 {
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return kOneSymbolHistogramCost
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}
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if count == 2 {
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return kTwoSymbolHistogramCost + float64(histogram.total_count_)
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}
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if count == 3 {
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var histo0 uint32 = histogram.data_[s[0]]
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var histo1 uint32 = histogram.data_[s[1]]
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var histo2 uint32 = histogram.data_[s[2]]
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var histomax uint32 = brotli_max_uint32_t(histo0, brotli_max_uint32_t(histo1, histo2))
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return kThreeSymbolHistogramCost + 2*(float64(histo0)+float64(histo1)+float64(histo2)) - float64(histomax)
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}
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if count == 4 {
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var histo [4]uint32
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var h23 uint32
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var histomax uint32
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for i = 0; i < 4; i++ {
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histo[i] = histogram.data_[s[i]]
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}
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/* Sort */
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for i = 0; i < 4; i++ {
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var j uint
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for j = i + 1; j < 4; j++ {
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if histo[j] > histo[i] {
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var tmp uint32 = histo[j]
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histo[j] = histo[i]
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histo[i] = tmp
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}
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}
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}
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h23 = histo[2] + histo[3]
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histomax = brotli_max_uint32_t(h23, histo[0])
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return kFourSymbolHistogramCost + 3*float64(h23) + 2*(float64(histo[0])+float64(histo[1])) - float64(histomax)
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}
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{
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var max_depth uint = 1
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var depth_histo = [codeLengthCodes]uint32{0}
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/* In this loop we compute the entropy of the histogram and simultaneously
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build a simplified histogram of the code length codes where we use the
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zero repeat code 17, but we don't use the non-zero repeat code 16. */
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var log2total float64 = fastLog2(histogram.total_count_)
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for i = 0; i < data_size; {
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if histogram.data_[i] > 0 {
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var log2p float64 = log2total - fastLog2(uint(histogram.data_[i]))
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/* Compute -log2(P(symbol)) = -log2(count(symbol)/total_count) =
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= log2(total_count) - log2(count(symbol)) */
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var depth uint = uint(log2p + 0.5)
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/* Approximate the bit depth by round(-log2(P(symbol))) */
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bits += float64(histogram.data_[i]) * log2p
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if depth > 15 {
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depth = 15
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}
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if depth > max_depth {
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max_depth = depth
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}
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depth_histo[depth]++
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i++
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} else {
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var reps uint32 = 1
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/* Compute the run length of zeros and add the appropriate number of 0
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and 17 code length codes to the code length code histogram. */
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var k uint
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for k = i + 1; k < data_size && histogram.data_[k] == 0; k++ {
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reps++
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}
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i += uint(reps)
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if i == data_size {
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/* Don't add any cost for the last zero run, since these are encoded
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only implicitly. */
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break
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}
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if reps < 3 {
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depth_histo[0] += reps
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} else {
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reps -= 2
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for reps > 0 {
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depth_histo[repeatZeroCodeLength]++
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/* Add the 3 extra bits for the 17 code length code. */
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bits += 3
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reps >>= 3
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}
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}
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}
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}
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/* Add the estimated encoding cost of the code length code histogram. */
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bits += float64(18 + 2*max_depth)
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/* Add the entropy of the code length code histogram. */
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bits += bitsEntropy(depth_histo[:], codeLengthCodes)
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}
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return bits
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}
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func populationCostDistance(histogram *histogramDistance) float64 {
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var data_size uint = histogramDataSizeDistance()
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var count int = 0
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var s [5]uint
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var bits float64 = 0.0
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var i uint
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if histogram.total_count_ == 0 {
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return kOneSymbolHistogramCost
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}
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for i = 0; i < data_size; i++ {
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if histogram.data_[i] > 0 {
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s[count] = i
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count++
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if count > 4 {
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break
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}
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}
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}
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if count == 1 {
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return kOneSymbolHistogramCost
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}
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if count == 2 {
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return kTwoSymbolHistogramCost + float64(histogram.total_count_)
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}
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if count == 3 {
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var histo0 uint32 = histogram.data_[s[0]]
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var histo1 uint32 = histogram.data_[s[1]]
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var histo2 uint32 = histogram.data_[s[2]]
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var histomax uint32 = brotli_max_uint32_t(histo0, brotli_max_uint32_t(histo1, histo2))
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return kThreeSymbolHistogramCost + 2*(float64(histo0)+float64(histo1)+float64(histo2)) - float64(histomax)
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}
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if count == 4 {
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var histo [4]uint32
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var h23 uint32
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var histomax uint32
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for i = 0; i < 4; i++ {
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histo[i] = histogram.data_[s[i]]
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}
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/* Sort */
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for i = 0; i < 4; i++ {
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var j uint
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for j = i + 1; j < 4; j++ {
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if histo[j] > histo[i] {
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var tmp uint32 = histo[j]
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histo[j] = histo[i]
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histo[i] = tmp
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}
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}
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}
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h23 = histo[2] + histo[3]
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histomax = brotli_max_uint32_t(h23, histo[0])
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return kFourSymbolHistogramCost + 3*float64(h23) + 2*(float64(histo[0])+float64(histo[1])) - float64(histomax)
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}
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{
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var max_depth uint = 1
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var depth_histo = [codeLengthCodes]uint32{0}
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/* In this loop we compute the entropy of the histogram and simultaneously
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build a simplified histogram of the code length codes where we use the
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zero repeat code 17, but we don't use the non-zero repeat code 16. */
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||
|
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|
||
|
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var log2total float64 = fastLog2(histogram.total_count_)
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for i = 0; i < data_size; {
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if histogram.data_[i] > 0 {
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var log2p float64 = log2total - fastLog2(uint(histogram.data_[i]))
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/* Compute -log2(P(symbol)) = -log2(count(symbol)/total_count) =
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= log2(total_count) - log2(count(symbol)) */
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var depth uint = uint(log2p + 0.5)
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/* Approximate the bit depth by round(-log2(P(symbol))) */
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bits += float64(histogram.data_[i]) * log2p
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|
|
|
||
|
|
if depth > 15 {
|
||
|
|
depth = 15
|
||
|
|
}
|
||
|
|
|
||
|
|
if depth > max_depth {
|
||
|
|
max_depth = depth
|
||
|
|
}
|
||
|
|
|
||
|
|
depth_histo[depth]++
|
||
|
|
i++
|
||
|
|
} else {
|
||
|
|
var reps uint32 = 1
|
||
|
|
/* Compute the run length of zeros and add the appropriate number of 0
|
||
|
|
and 17 code length codes to the code length code histogram. */
|
||
|
|
|
||
|
|
var k uint
|
||
|
|
for k = i + 1; k < data_size && histogram.data_[k] == 0; k++ {
|
||
|
|
reps++
|
||
|
|
}
|
||
|
|
|
||
|
|
i += uint(reps)
|
||
|
|
if i == data_size {
|
||
|
|
/* Don't add any cost for the last zero run, since these are encoded
|
||
|
|
only implicitly. */
|
||
|
|
break
|
||
|
|
}
|
||
|
|
|
||
|
|
if reps < 3 {
|
||
|
|
depth_histo[0] += reps
|
||
|
|
} else {
|
||
|
|
reps -= 2
|
||
|
|
for reps > 0 {
|
||
|
|
depth_histo[repeatZeroCodeLength]++
|
||
|
|
|
||
|
|
/* Add the 3 extra bits for the 17 code length code. */
|
||
|
|
bits += 3
|
||
|
|
|
||
|
|
reps >>= 3
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Add the estimated encoding cost of the code length code histogram. */
|
||
|
|
bits += float64(18 + 2*max_depth)
|
||
|
|
|
||
|
|
/* Add the entropy of the code length code histogram. */
|
||
|
|
bits += bitsEntropy(depth_histo[:], codeLengthCodes)
|
||
|
|
}
|
||
|
|
|
||
|
|
return bits
|
||
|
|
}
|