// Copyright 2012 Google Inc. All Rights Reserved.
//
// Use of this source code is governed by a BSD-style license
// that can be found in the COPYING file in the root of the source
// tree. An additional intellectual property rights grant can be found
// in the file PATENTS. All contributing project authors may
// be found in the AUTHORS file in the root of the source tree.
// -----------------------------------------------------------------------------
//
// Author: Jyrki Alakuijala (jyrki@google.com)
//
#ifdef HAVE_CONFIG_H
#include "../webp/config.h"
#endif
#include <math.h>
#include "./backward_references_enc.h"
#include "./histogram_enc.h"
#include "../dsp/lossless.h"
#include "../dsp/lossless_common.h"
#include "../utils/utils.h"
#define MAX_COST 1.e38
// Number of partitions for the three dominant (literal, red and blue) symbol
// costs.
#define NUM_PARTITIONS 4
// The size of the bin-hash corresponding to the three dominant costs.
#define BIN_SIZE (NUM_PARTITIONS * NUM_PARTITIONS * NUM_PARTITIONS)
// Maximum number of histograms allowed in greedy combining algorithm.
#define MAX_HISTO_GREEDY 100
static void HistogramClear(VP8LHistogram* const p) {
uint32_t* const literal = p->literal_;
const int cache_bits = p->palette_code_bits_;
const int histo_size = VP8LGetHistogramSize(cache_bits);
memset(p, 0, histo_size);
p->palette_code_bits_ = cache_bits;
p->literal_ = literal;
}
// Swap two histogram pointers.
static void HistogramSwap(VP8LHistogram** const A, VP8LHistogram** const B) {
VP8LHistogram* const tmp = *A;
*A = *B;
*B = tmp;
}
static void HistogramCopy(const VP8LHistogram* const src,
VP8LHistogram* const dst) {
uint32_t* const dst_literal = dst->literal_;
const int dst_cache_bits = dst->palette_code_bits_;
const int histo_size = VP8LGetHistogramSize(dst_cache_bits);
assert(src->palette_code_bits_ == dst_cache_bits);
memcpy(dst, src, histo_size);
dst->literal_ = dst_literal;
}
int VP8LGetHistogramSize(int cache_bits) {
const int literal_size = VP8LHistogramNumCodes(cache_bits);
const size_t total_size = sizeof(VP8LHistogram) + sizeof(int) * literal_size;
assert(total_size <= (size_t)0x7fffffff);
return (int)total_size;
}
void VP8LFreeHistogram(VP8LHistogram* const histo) {
WebPSafeFree(histo);
}
void VP8LFreeHistogramSet(VP8LHistogramSet* const histo) {
WebPSafeFree(histo);
}
void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
VP8LHistogram* const histo) {
VP8LRefsCursor c = VP8LRefsCursorInit(refs);
while (VP8LRefsCursorOk(&c)) {
VP8LHistogramAddSinglePixOrCopy(histo, c.cur_pos);
VP8LRefsCursorNext(&c);
}
}
void VP8LHistogramCreate(VP8LHistogram* const p,
const VP8LBackwardRefs* const refs,
int palette_code_bits) {
if (palette_code_bits >= 0) {
p->palette_code_bits_ = palette_code_bits;
}
HistogramClear(p);
VP8LHistogramStoreRefs(refs, p);
}
void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
p->palette_code_bits_ = palette_code_bits;
HistogramClear(p);
}
VP8LHistogram* VP8LAllocateHistogram(int cache_bits) {
VP8LHistogram* histo = NULL;
const int total_size = VP8LGetHistogramSize(cache_bits);
uint8_t* const memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
if (memory == NULL) return NULL;
histo = (VP8LHistogram*)memory;
// literal_ won't necessary be aligned.
histo->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
VP8LHistogramInit(histo, cache_bits);
return histo;
}
VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
int i;
VP8LHistogramSet* set;
const int histo_size = VP8LGetHistogramSize(cache_bits);
const size_t total_size =
sizeof(*set) + size * (sizeof(*set->histograms) +
histo_size + WEBP_ALIGN_CST);
uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
if (memory == NULL) return NULL;
set = (VP8LHistogramSet*)memory;
memory += sizeof(*set);
set->histograms = (VP8LHistogram**)memory;
memory += size * sizeof(*set->histograms);
set->max_size = size;
set->size = size;
for (i = 0; i < size; ++i) {
memory = (uint8_t*)WEBP_ALIGN(memory);
set->histograms[i] = (VP8LHistogram*)memory;
// literal_ won't necessary be aligned.
set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
VP8LHistogramInit(set->histograms[i], cache_bits);
memory += histo_size;
}
return set;
}
// -----------------------------------------------------------------------------
void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
const PixOrCopy* const v) {
if (PixOrCopyIsLiteral(v)) {
++histo->alpha_[PixOrCopyLiteral(v, 3)];
++histo->red_[PixOrCopyLiteral(v, 2)];
++histo->literal_[PixOrCopyLiteral(v, 1)];
++histo->blue_[PixOrCopyLiteral(v, 0)];
} else if (PixOrCopyIsCacheIdx(v)) {
const int literal_ix =
NUM_LITERAL_CODES + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
++histo->literal_[literal_ix];
} else {
int code, extra_bits;
VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
++histo->literal_[NUM_LITERAL_CODES + code];
VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
++histo->distance_[code];
}
}
// -----------------------------------------------------------------------------
// Entropy-related functions.
static WEBP_INLINE double BitsEntropyRefine(const VP8LBitEntropy* entropy) {
double mix;
if (entropy->nonzeros < 5) {
if (entropy->nonzeros <= 1) {
return 0;
}
// Two symbols, they will be 0 and 1 in a Huffman code.
// Let's mix in a bit of entropy to favor good clustering when
// distributions of these are combined.
if (entropy->nonzeros == 2) {
return 0.99 * entropy->sum + 0.01 * entropy->entropy;
}
// No matter what the entropy says, we cannot be better than min_limit
// with Huffman coding. I am mixing a bit of entropy into the
// min_limit since it produces much better (~0.5 %) compression results
// perhaps because of better entropy clustering.
if (entropy->nonzeros == 3) {
mix = 0.95;
} else {
mix = 0.7; // nonzeros == 4.
}
} else {
mix = 0.627;
}
{
double min_limit = 2 * entropy->sum - entropy->max_val;
min_limit = mix * min_limit + (1.0 - mix) * entropy->entropy;
return (entropy->entropy < min_limit) ? min_limit : entropy->entropy;
}
}
double VP8LBitsEntropy(const uint32_t* const array, int n,
uint32_t* const trivial_symbol) {
VP8LBitEntropy entropy;
VP8LBitsEntropyUnrefined(array, n, &entropy);
if (trivial_symbol != NULL) {
*trivial_symbol =
(entropy.nonzeros == 1) ? entropy.nonzero_code : VP8L_NON_TRIVIAL_SYM;
}
return BitsEntropyRefine(&entropy);
}
static double InitialHuffmanCost(void) {
// Small bias because Huffman code length is typically not stored in
// full length.
static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
static const double kSmallBias = 9.1;
return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
}
// Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
static double FinalHuffmanCost(const VP8LStreaks* const stats) {
// The constants in this function are experimental and got rounded from
// their original values in 1/8 when switched to 1/1024.
double retval = InitialHuffmanCost();
// Second coefficient: Many zeros in the histogram are covered efficiently
// by a run-length encode. Originally 2/8.
retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
// Second coefficient: Constant values are encoded less efficiently, but still
// RLE'ed. Originally 6/8.
retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
// 0s are usually encoded more efficiently than non-0s.
// Originally 15/8.
retval += 1.796875 * stats->streaks[0][0];
// Originally 26/8.
retval += 3.28125 * stats->streaks[1][0];
return retval;
}
// Get the symbol entropy for the distribution 'population'.
// Set 'trivial_sym', if there's only one symbol present in the distribution.
static double PopulationCost(const uint32_t* const population, int length,
uint32_t* const trivial_sym) {
VP8LBitEntropy bit_entropy;
VP8LStreaks stats;
VP8LGetEntropyUnrefined(population, length, &bit_entropy, &stats);
if (trivial_sym != NULL) {
*trivial_sym = (bit_entropy.nonzeros == 1) ? bit_entropy.nonzero_code
: VP8L_NON_TRIVIAL_SYM;
}
return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
}
// trivial_at_end is 1 if the two histograms only have one element that is
// non-zero: both the zero-th one, or both the last one.
static WEBP_INLINE double GetCombinedEntropy(const uint32_t* const X,
const uint32_t* const Y,
int length, int trivial_at_end) {
VP8LStreaks stats;
if (trivial_at_end) {
// This configuration is due to palettization that transforms an indexed
// pixel into 0xff000000 | (pixel << 8) in VP8LBundleColorMap.
// BitsEntropyRefine is 0 for histograms with only one non-zero value.
// Only FinalHuffmanCost needs to be evaluated.
memset(&stats, 0, sizeof(stats));
// Deal with the non-zero value at index 0 or length-1.
stats.streaks[1][0] += 1;
// Deal with the following/previous zero streak.
stats.counts[0] += 1;
stats.streaks[0][1] += length - 1;
return FinalHuffmanCost(&stats);
} else {
VP8LBitEntropy bit_entropy;
VP8LGetCombinedEntropyUnrefined(X, Y, length, &bit_entropy, &stats);
return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
}
}
// Estimates the Entropy + Huffman + other block overhead size cost.
double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
return
PopulationCost(
p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_), NULL)
+ PopulationCost(p->red_, NUM_LITERAL_CODES, NULL)
+ PopulationCost(p->blue_, NUM_LITERAL_CODES, NULL)
+ PopulationCost(p->alpha_, NUM_LITERAL_CODES, NULL)
+ PopulationCost(p->distance_, NUM_DISTANCE_CODES, NULL)
+ VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
+ VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
}
// -----------------------------------------------------------------------------
// Various histogram combine/cost-eval functions
static int GetCombinedHistogramEntropy(const VP8LHistogram* const a,
const VP8LHistogram* const b,
double cost_threshold,
double* cost) {
const int palette_code_bits = a->palette_code_bits_;
int trivial_at_end = 0;
assert(a->palette_code_bits_ == b->palette_code_bits_);
*cost += GetCombinedEntropy(a->literal_, b->literal_,
VP8LHistogramNumCodes(palette_code_bits), 0);
*cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
b->literal_ + NUM_LITERAL_CODES,
NUM_LENGTH_CODES);
if (*cost > cost_threshold) return 0;
if (a->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM &&
a->trivial_symbol_ == b->trivial_symbol_) {
// A, R and B are all 0 or 0xff.
const uint32_t color_a = (a->trivial_symbol_ >> 24) & 0xff;
const uint32_t color_r = (a->trivial_symbol_ >> 16) & 0xff;
const uint32_t color_b = (a->trivial_symbol_ >> 0) & 0xff;
if ((color_a == 0 || color_a == 0xff) &&
(color_r == 0 || color_r == 0xff) &&
(color_b == 0 || color_b == 0xff)) {
trivial_at_end = 1;
}
}
*cost +=
GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES, trivial_at_end);
if (*cost > cost_threshold) return 0;
*cost +=
GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES, trivial_at_end);
if (*cost > cost_threshold) return 0;
*cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES,
trivial_at_end);
if (*cost > cost_threshold) return 0;
*cost +=
GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES, 0);
*cost +=
VP8LExtraCostCombined(a->distance_, b->distance_, NUM_DISTANCE_CODES);
if (*cost > cost_threshold) return 0;
return 1;
}
static WEBP_INLINE void HistogramAdd(const VP8LHistogram* const a,
const VP8LHistogram* const b,
VP8LHistogram* const out) {
VP8LHistogramAdd(a, b, out);
out->trivial_symbol_ = (a->trivial_symbol_ == b->trivial_symbol_)
? a->trivial_symbol_
: VP8L_NON_TRIVIAL_SYM;
}
// Performs out = a + b, computing the cost C(a+b) - C(a) - C(b) while comparing
// to the threshold value 'cost_threshold'. The score returned is
// Score = C(a+b) - C(a) - C(b), where C(a) + C(b) is known and fixed.
// Since the previous score passed is 'cost_threshold', we only need to compare
// the partial cost against 'cost_threshold + C(a) + C(b)' to possibly bail-out
// early.
static double HistogramAddEval(const VP8LHistogram* const a,
const VP8LHistogram* const b,
VP8LHistogram* const out,
double cost_threshold) {
double cost = 0;
const double sum_cost = a->bit_cost_ + b->bit_cost_;
cost_threshold += sum_cost;
if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
HistogramAdd(a, b, out);
out->bit_cost_ = cost;
out->palette_code_bits_ = a->palette_code_bits_;
}
return cost - sum_cost;
}
// Same as HistogramAddEval(), except that the resulting histogram
// is not stored. Only the cost C(a+b) - C(a) is evaluated. We omit
// the term C(b) which is constant over all the evaluations.
static double HistogramAddThresh(const VP8LHistogram* const a,
const VP8LHistogram* const b,
double cost_threshold) {
double cost = -a->bit_cost_;
GetCombinedHistogramEntropy(a, b, cost_threshold, &cost);
return cost;
}
// -----------------------------------------------------------------------------
// The structure to keep track of cost range for the three dominant entropy
// symbols.
// TODO(skal): Evaluate if float can be used here instead of double for
// representing the entropy costs.
typedef struct {
double literal_max_;
double literal_min_;
double red_max_;
double red_min_;
double blue_max_;
double blue_min_;
} DominantCostRange;
static void DominantCostRangeInit(DominantCostRange* const c) {
c->literal_max_ = 0.;
c->literal_min_ = MAX_COST;
c->red_max_ = 0.;
c->red_min_ = MAX_COST;
c->blue_max_ = 0.;
c->blue_min_ = MAX_COST;
}
static void UpdateDominantCostRange(
const VP8LHistogram* const h, DominantCostRange* const c) {
if (c->literal_max_ < h->literal_cost_) c->literal_max_ = h->literal_cost_;
if (c->literal_min_ > h->literal_cost_) c->literal_min_ = h->literal_cost_;
if (c->red_max_ < h->red_cost_) c->red_max_ = h->red_cost_;
if (c->red_min_ > h->red_cost_) c->red_min_ = h->red_cost_;
if (c->blue_max_ < h->blue_cost_) c->blue_max_ = h->blue_cost_;
if (c->blue_min_ > h->blue_cost_) c->blue_min_ = h->blue_cost_;
}
static void UpdateHistogramCost(VP8LHistogram* const h) {
uint32_t alpha_sym, red_sym, blue_sym;
const double alpha_cost =
PopulationCost(h->alpha_, NUM_LITERAL_CODES, &alpha_sym);
const double distance_cost =
PopulationCost(h->distance_, NUM_DISTANCE_CODES, NULL) +
VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
h->literal_cost_ = PopulationCost(h->literal_, num_codes, NULL) +
VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
NUM_LENGTH_CODES);
h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES, &red_sym);
h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES, &blue_sym);
h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
alpha_cost + distance_cost;
if ((alpha_sym | red_sym | blue_sym) == VP8L_NON_TRIVIAL_SYM) {
h->trivial_symbol_ = VP8L_NON_TRIVIAL_SYM;
} else {
h->trivial_symbol_ =
((uint32_t)alpha_sym << 24) | (red_sym << 16) | (blue_sym << 0);
}
}
static int GetBinIdForEntropy(double min, double max, double val) {
const double range = max - min;
if (range > 0.) {
const double delta = val - min;
return (int)((NUM_PARTITIONS - 1e-6) * delta / range);
} else {
return 0;
}
}
static int GetHistoBinIndex(const VP8LHistogram* const h,
const DominantCostRange* const c, int low_effort) {
int bin_id = GetBinIdForEntropy(c->literal_min_, c->literal_max_,
h->literal_cost_);
assert(bin_id < NUM_PARTITIONS);
if (!low_effort) {
bin_id = bin_id * NUM_PARTITIONS
+ GetBinIdForEntropy(c->red_min_, c->red_max_, h->red_cost_);
bin_id = bin_id * NUM_PARTITIONS
+ GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_);
assert(bin_id < BIN_SIZE);
}
return bin_id;
}
// Construct the histograms from backward references.
static void HistogramBuild(
int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs,
VP8LHistogramSet* const image_histo) {
int x = 0, y = 0;
const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
VP8LHistogram** const histograms = image_histo->histograms;
VP8LRefsCursor c = VP8LRefsCursorInit(backward_refs);
assert(histo_bits > 0);
while (VP8LRefsCursorOk(&c)) {
const PixOrCopy* const v = c.cur_pos;
const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
x += PixOrCopyLength(v);
while (x >= xsize) {
x -= xsize;
++y;
}
VP8LRefsCursorNext(&c);
}
}
// Copies the histograms and computes its bit_cost.
static void HistogramCopyAndAnalyze(
VP8LHistogramSet* const orig_histo, VP8LHistogramSet* const image_histo) {
int i;
const int histo_size = orig_histo->size;
VP8LHistogram** const orig_histograms = orig_histo->histograms;
VP8LHistogram** const histograms = image_histo->histograms;
for (i = 0; i < histo_size; ++i) {
VP8LHistogram* const histo = orig_histograms[i];
UpdateHistogramCost(histo);
// Copy histograms from orig_histo[] to image_histo[].
HistogramCopy(histo, histograms[i]);
}
}
// Partition histograms to different entropy bins for three dominant (literal,
// red and blue) symbol costs and compute the histogram aggregate bit_cost.
static void HistogramAnalyzeEntropyBin(VP8LHistogramSet* const image_histo,
uint16_t* const bin_map,
int low_effort) {
int i;
VP8LHistogram** const histograms = image_histo->histograms;
const int histo_size = image_histo->size;
DominantCostRange cost_range;
DominantCostRangeInit(&cost_range);
// Analyze the dominant (literal, red and blue) entropy costs.
for (i = 0; i < histo_size; ++i) {
UpdateDominantCostRange(histograms[i], &cost_range);
}
// bin-hash histograms on three of the dominant (literal, red and blue)
// symbol costs and store the resulting bin_id for each histogram.
for (i = 0; i < histo_size; ++i) {
bin_map[i] = GetHistoBinIndex(histograms[i], &cost_range, low_effort);
}
}
// Compact image_histo[] by merging some histograms with same bin_id together if
// it's advantageous.
static VP8LHistogram* HistogramCombineEntropyBin(
VP8LHistogramSet* const image_histo,
VP8LHistogram* cur_combo,
const uint16_t* const bin_map, int bin_map_size, int num_bins,
double combine_cost_factor, int low_effort) {
VP8LHistogram** const histograms = image_histo->histograms;
int idx;
// Work in-place: processed histograms are put at the beginning of
// image_histo[]. At the end, we just have to truncate the array.
int size = 0;
struct {
int16_t first; // position of the histogram that accumulates all
// histograms with the same bin_id
uint16_t num_combine_failures; // number of combine failures per bin_id
} bin_info[BIN_SIZE];
assert(num_bins <= BIN_SIZE);
for (idx = 0; idx < num_bins; ++idx) {
bin_info[idx].first = -1;
bin_info[idx].num_combine_failures = 0;
}
for (idx = 0; idx < bin_map_size; ++idx) {
const int bin_id = bin_map[idx];
const int first = bin_info[bin_id].first;
assert(size <= idx);
if (first == -1) {
// just move histogram #idx to its final position
histograms[size] = histograms[idx];
bin_info[bin_id].first = size++;
} else if (low_effort) {
HistogramAdd(histograms[idx], histograms[first], histograms[first]);
} else {
// try to merge #idx into #first (both share the same bin_id)
const double bit_cost = histograms[idx]->bit_cost_;
const double bit_cost_thresh = -bit_cost * combine_cost_factor;
const double curr_cost_diff =
HistogramAddEval(histograms[first], histograms[idx],
cur_combo, bit_cost_thresh);
if (curr_cost_diff < bit_cost_thresh) {
// Try to merge two histograms only if the combo is a trivial one or
// the two candidate histograms are already non-trivial.
// For some images, 'try_combine' turns out to be false for a lot of
// histogram pairs. In that case, we fallback to combining
// histograms as usual to avoid increasing the header size.
const int try_combine =
(cur_combo->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM) ||
((histograms[idx]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM) &&
(histograms[first]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM));
const int max_combine_failures = 32;
if (try_combine ||
bin_info[bin_id].num_combine_failures >= max_combine_failures) {
// move the (better) merged histogram to its final slot
HistogramSwap(&cur_combo, &histograms[first]);
} else {
histograms[size++] = histograms[idx];
++bin_info[bin_id].num_combine_failures;
}
} else {
histograms[size++] = histograms[idx];
}
}
}
image_histo->size = size;
if (low_effort) {
// for low_effort case, update the final cost when everything is merged
for (idx = 0; idx < size; ++idx) {
UpdateHistogramCost(histograms[idx]);
}
}
return cur_combo;
}
static uint32_t MyRand(uint32_t* const seed) {
*seed = (*seed * 16807ull) & 0xffffffffu;
if (*seed == 0) {
*seed = 1;
}
return *seed;
}
// -----------------------------------------------------------------------------
// Histogram pairs priority queue
// Pair of histograms. Negative idx1 value means that pair is out-of-date.
typedef struct {
int idx1;
int idx2;
double cost_diff;
double cost_combo;
} HistogramPair;
typedef struct {
HistogramPair* queue;
int size;
int max_size;
} HistoQueue;
static int HistoQueueInit(HistoQueue* const histo_queue, const int max_index) {
histo_queue->size = 0;
// max_index^2 for the queue size is safe. If you look at
// HistogramCombineGreedy, and imagine that UpdateQueueFront always pushes
// data to the queue, you insert at most:
// - max_index*(max_index-1)/2 (the first two for loops)
// - max_index - 1 in the last for loop at the first iteration of the while
// loop, max_index - 2 at the second iteration ... therefore
// max_index*(max_index-1)/2 overall too
histo_queue->max_size = max_index * max_index;
// We allocate max_size + 1 because the last element at index "size" is
// used as temporary data (and it could be up to max_size).
histo_queue->queue = (HistogramPair*)WebPSafeMalloc(
histo_queue->max_size + 1, sizeof(*histo_queue->queue));
return histo_queue->queue != NULL;
}
static void HistoQueueClear(HistoQueue* const histo_queue) {
assert(histo_queue != NULL);
WebPSafeFree(histo_queue->queue);
}
static void SwapHistogramPairs(HistogramPair *p1,
HistogramPair *p2) {
const HistogramPair tmp = *p1;
*p1 = *p2;
*p2 = tmp;
}
// Given a valid priority queue in range [0, queue_size) this function checks
// whether histo_queue[queue_size] should be accepted and swaps it with the
// front if it is smaller. Otherwise, it leaves it as is.
static void UpdateQueueFront(HistoQueue* const histo_queue) {
if (histo_queue->queue[histo_queue->size].cost_diff >= 0) return;
if (histo_queue->queue[histo_queue->size].cost_diff <
histo_queue->queue[0].cost_diff) {
SwapHistogramPairs(histo_queue->queue,
histo_queue->queue + histo_queue->size);
}
++histo_queue->size;
// We cannot add more elements than the capacity.
// The allocation adds an extra element to the official capacity so that
// histo_queue->queue[histo_queue->max_size] is read/written within bound.
assert(histo_queue->size <= histo_queue->max_size);
}
// -----------------------------------------------------------------------------
static void PreparePair(VP8LHistogram** histograms, int idx1, int idx2,
HistogramPair* const pair) {
VP8LHistogram* h1;
VP8LHistogram* h2;
double sum_cost;
if (idx1 > idx2) {
const int tmp = idx2;
idx2 = idx1;
idx1 = tmp;
}
pair->idx1 = idx1;
pair->idx2 = idx2;
h1 = histograms[idx1];
h2 = histograms[idx2];
sum_cost = h1->bit_cost_ + h2->bit_cost_;
pair->cost_combo = 0.;
GetCombinedHistogramEntropy(h1, h2, sum_cost, &pair->cost_combo);
pair->cost_diff = pair->cost_combo - sum_cost;
}
// Combines histograms by continuously choosing the one with the highest cost
// reduction.
static int HistogramCombineGreedy(VP8LHistogramSet* const image_histo) {
int ok = 0;
int image_histo_size = image_histo->size;
int i, j;
VP8LHistogram** const histograms = image_histo->histograms;
// Indexes of remaining histograms.
int* const clusters =
(int*)WebPSafeMalloc(image_histo_size, sizeof(*clusters));
// Priority queue of histogram pairs.
HistoQueue histo_queue;
if (!HistoQueueInit(&histo_queue, image_histo_size) || clusters == NULL) {
goto End;
}
for (i = 0; i < image_histo_size; ++i) {
// Initialize clusters indexes.
clusters[i] = i;
for (j = i + 1; j < image_histo_size; ++j) {
// Initialize positions array.
PreparePair(histograms, i, j, &histo_queue.queue[histo_queue.size]);
UpdateQueueFront(&histo_queue);
}
}
while (image_histo_size > 1 && histo_queue.size > 0) {
HistogramPair* copy_to;
const int idx1 = histo_queue.queue[0].idx1;
const int idx2 = histo_queue.queue[0].idx2;
HistogramAdd(histograms[idx2], histograms[idx1], histograms[idx1]);
histograms[idx1]->bit_cost_ = histo_queue.queue[0].cost_combo;
// Remove merged histogram.
for (i = 0; i + 1 < image_histo_size; ++i) {
if (clusters[i] >= idx2) {
clusters[i] = clusters[i + 1];
}
}
--image_histo_size;
// Remove pairs intersecting the just combined best pair. This will
// therefore pop the head of the queue.
copy_to = histo_queue.queue;
for (i = 0; i < histo_queue.size; ++i) {
HistogramPair* const p = histo_queue.queue + i;
if (p->idx1 == idx1 || p->idx2 == idx1 ||
p->idx1 == idx2 || p->idx2 == idx2) {
// Do not copy the invalid pair.
continue;
}
if (p->cost_diff < histo_queue.queue[0].cost_diff) {
// Replace the top of the queue if we found better.
SwapHistogramPairs(histo_queue.queue, p);
}
SwapHistogramPairs(copy_to, p);
++copy_to;
}
histo_queue.size = (int)(copy_to - histo_queue.queue);
// Push new pairs formed with combined histogram to the queue.
for (i = 0; i < image_histo_size; ++i) {
if (clusters[i] != idx1) {
PreparePair(histograms, idx1, clusters[i],
&histo_queue.queue[histo_queue.size]);
UpdateQueueFront(&histo_queue);
}
}
}
// Move remaining histograms to the beginning of the array.
for (i = 0; i < image_histo_size; ++i) {
if (i != clusters[i]) { // swap the two histograms
HistogramSwap(&histograms[i], &histograms[clusters[i]]);
}
}
image_histo->size = image_histo_size;
ok = 1;
End:
WebPSafeFree(clusters);
HistoQueueClear(&histo_queue);
return ok;
}
static void HistogramCombineStochastic(VP8LHistogramSet* const image_histo,
VP8LHistogram* tmp_histo,
VP8LHistogram* best_combo,
int quality, int min_cluster_size) {
int iter;
uint32_t seed = 0;
int tries_with_no_success = 0;
int image_histo_size = image_histo->size;
const int iter_mult = (quality < 25) ? 2 : 2 + (quality - 25) / 8;
const int outer_iters = image_histo_size * iter_mult;
const int num_pairs = image_histo_size / 2;
const int num_tries_no_success = outer_iters / 2;
int idx2_max = image_histo_size - 1;
int do_brute_dorce = 0;
VP8LHistogram** const histograms = image_histo->histograms;
// Collapse similar histograms in 'image_histo'.
++min_cluster_size;
for (iter = 0;
iter < outer_iters && image_histo_size >= min_cluster_size;
++iter) {
double best_cost_diff = 0.;
int best_idx1 = -1, best_idx2 = 1;
int j;
int num_tries =
(num_pairs < image_histo_size) ? num_pairs : image_histo_size;
// Use a brute force approach if:
// - stochastic has not worked for a while and
// - if the number of iterations for brute force is less than the number of
// iterations if we never find a match ever again stochastically (hence
// num_tries times the number of remaining outer iterations).
do_brute_dorce =
(tries_with_no_success > 10) &&
(idx2_max * (idx2_max + 1) < 2 * num_tries * (outer_iters - iter));
if (do_brute_dorce) num_tries = idx2_max;
seed += iter;
for (j = 0; j < num_tries; ++j) {
double curr_cost_diff;
// Choose two histograms at random and try to combine them.
uint32_t idx1, idx2;
if (do_brute_dorce) {
// Use a brute force approach.
idx1 = (uint32_t)j;
idx2 = (uint32_t)idx2_max;
} else {
const uint32_t tmp = (j & 7) + 1;
const uint32_t diff =
(tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
idx1 = MyRand(&seed) % image_histo_size;
idx2 = (idx1 + diff + 1) % image_histo_size;
if (idx1 == idx2) {
continue;
}
}
// Calculate cost reduction on combining.
curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
tmp_histo, best_cost_diff);
if (curr_cost_diff < best_cost_diff) { // found a better pair?
HistogramSwap(&best_combo, &tmp_histo);
best_cost_diff = curr_cost_diff;
best_idx1 = idx1;
best_idx2 = idx2;
}
}
if (do_brute_dorce) --idx2_max;
if (best_idx1 >= 0) {
HistogramSwap(&best_combo, &histograms[best_idx1]);
// swap best_idx2 slot with last one (which is now unused)
--image_histo_size;
if (idx2_max >= image_histo_size) idx2_max = image_histo_size - 1;
if (best_idx2 != image_histo_size) {
HistogramSwap(&histograms[image_histo_size], &histograms[best_idx2]);
histograms[image_histo_size] = NULL;
}
tries_with_no_success = 0;
}
if (++tries_with_no_success >= num_tries_no_success || idx2_max == 0) {
break;
}
}
image_histo->size = image_histo_size;
}
// -----------------------------------------------------------------------------
// Histogram refinement
// Find the best 'out' histogram for each of the 'in' histograms.
// Note: we assume that out[]->bit_cost_ is already up-to-date.
static void HistogramRemap(const VP8LHistogramSet* const in,
const VP8LHistogramSet* const out,
uint16_t* const symbols) {
int i;
VP8LHistogram** const in_histo = in->histograms;
VP8LHistogram** const out_histo = out->histograms;
const int in_size = in->size;
const int out_size = out->size;
if (out_size > 1) {
for (i = 0; i < in_size; ++i) {
int best_out = 0;
double best_bits = MAX_COST;
int k;
for (k = 0; k < out_size; ++k) {
const double cur_bits =
HistogramAddThresh(out_histo[k], in_histo[i], best_bits);
if (k == 0 || cur_bits < best_bits) {
best_bits = cur_bits;
best_out = k;
}
}
symbols[i] = best_out;
}
} else {
assert(out_size == 1);
for (i = 0; i < in_size; ++i) {
symbols[i] = 0;
}
}
// Recompute each out based on raw and symbols.
for (i = 0; i < out_size; ++i) {
HistogramClear(out_histo[i]);
}
for (i = 0; i < in_size; ++i) {
const int idx = symbols[i];
HistogramAdd(in_histo[i], out_histo[idx], out_histo[idx]);
}
}
static double GetCombineCostFactor(int histo_size, int quality) {
double combine_cost_factor = 0.16;
if (quality < 90) {
if (histo_size > 256) combine_cost_factor /= 2.;
if (histo_size > 512) combine_cost_factor /= 2.;
if (histo_size > 1024) combine_cost_factor /= 2.;
if (quality <= 50) combine_cost_factor /= 2.;
}
return combine_cost_factor;
}
int VP8LGetHistoImageSymbols(int xsize, int ysize,
const VP8LBackwardRefs* const refs,
int quality, int low_effort,
int histo_bits, int cache_bits,
VP8LHistogramSet* const image_histo,
VP8LHistogramSet* const tmp_histos,
uint16_t* const histogram_symbols) {
int ok = 0;
const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
const int image_histo_raw_size = histo_xsize * histo_ysize;
VP8LHistogramSet* const orig_histo =
VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
VP8LHistogram* cur_combo;
// Don't attempt linear bin-partition heuristic for
// histograms of small sizes (as bin_map will be very sparse) and
// maximum quality q==100 (to preserve the compression gains at that level).
const int entropy_combine_num_bins = low_effort ? NUM_PARTITIONS : BIN_SIZE;
const int entropy_combine =
(orig_histo->size > entropy_combine_num_bins * 2) && (quality < 100);
if (orig_histo == NULL) goto Error;
// Construct the histograms from backward references.
HistogramBuild(xsize, histo_bits, refs, orig_histo);
// Copies the histograms and computes its bit_cost.
HistogramCopyAndAnalyze(orig_histo, image_histo);
cur_combo = tmp_histos->histograms[1]; // pick up working slot
if (entropy_combine) {
const int bin_map_size = orig_histo->size;
// Reuse histogram_symbols storage. By definition, it's guaranteed to be ok.
uint16_t* const bin_map = histogram_symbols;
const double combine_cost_factor =
GetCombineCostFactor(image_histo_raw_size, quality);
HistogramAnalyzeEntropyBin(orig_histo, bin_map, low_effort);
// Collapse histograms with similar entropy.
cur_combo = HistogramCombineEntropyBin(image_histo, cur_combo,
bin_map, bin_map_size,
entropy_combine_num_bins,
combine_cost_factor, low_effort);
}
// Don't combine the histograms using stochastic and greedy heuristics for
// low-effort compression mode.
if (!low_effort || !entropy_combine) {
const float x = quality / 100.f;
// cubic ramp between 1 and MAX_HISTO_GREEDY:
const int threshold_size = (int)(1 + (x * x * x) * (MAX_HISTO_GREEDY - 1));
HistogramCombineStochastic(image_histo, tmp_histos->histograms[0],
cur_combo, quality, threshold_size);
if ((image_histo->size <= threshold_size) &&
!HistogramCombineGreedy(image_histo)) {
goto Error;
}
}
// TODO(vikasa): Optimize HistogramRemap for low-effort compression mode also.
// Find the optimal map from original histograms to the final ones.
HistogramRemap(orig_histo, image_histo, histogram_symbols);
ok = 1;
Error:
VP8LFreeHistogramSet(orig_histo);
return ok;
}