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