1// Copyright 2012 Google Inc. All Rights Reserved.
2//
3// Use of this source code is governed by a BSD-style license
4// that can be found in the COPYING file in the root of the source
5// tree. An additional intellectual property rights grant can be found
6// in the file PATENTS. All contributing project authors may
7// be found in the AUTHORS file in the root of the source tree.
8// -----------------------------------------------------------------------------
9//
10// Author: Jyrki Alakuijala (jyrki@google.com)
11//
12#ifdef HAVE_CONFIG_H
13#include "../webp/config.h"
14#endif
15
16#include <math.h>
17
18#include "./backward_references_enc.h"
19#include "./histogram_enc.h"
20#include "../dsp/lossless.h"
21#include "../dsp/lossless_common.h"
22#include "../utils/utils.h"
23
24#define MAX_COST 1.e38
25
26// Number of partitions for the three dominant (literal, red and blue) symbol
27// costs.
28#define NUM_PARTITIONS 4
29// The size of the bin-hash corresponding to the three dominant costs.
30#define BIN_SIZE (NUM_PARTITIONS * NUM_PARTITIONS * NUM_PARTITIONS)
31// Maximum number of histograms allowed in greedy combining algorithm.
32#define MAX_HISTO_GREEDY 100
33
34static void HistogramClear(VP8LHistogram* const p) {
35 uint32_t* const literal = p->literal_;
36 const int cache_bits = p->palette_code_bits_;
37 const int histo_size = VP8LGetHistogramSize(cache_bits);
38 memset(p, 0, histo_size);
39 p->palette_code_bits_ = cache_bits;
40 p->literal_ = literal;
41}
42
43// Swap two histogram pointers.
44static void HistogramSwap(VP8LHistogram** const A, VP8LHistogram** const B) {
45 VP8LHistogram* const tmp = *A;
46 *A = *B;
47 *B = tmp;
48}
49
50static void HistogramCopy(const VP8LHistogram* const src,
51 VP8LHistogram* const dst) {
52 uint32_t* const dst_literal = dst->literal_;
53 const int dst_cache_bits = dst->palette_code_bits_;
54 const int histo_size = VP8LGetHistogramSize(dst_cache_bits);
55 assert(src->palette_code_bits_ == dst_cache_bits);
56 memcpy(dst, src, histo_size);
57 dst->literal_ = dst_literal;
58}
59
60int VP8LGetHistogramSize(int cache_bits) {
61 const int literal_size = VP8LHistogramNumCodes(cache_bits);
62 const size_t total_size = sizeof(VP8LHistogram) + sizeof(int) * literal_size;
63 assert(total_size <= (size_t)0x7fffffff);
64 return (int)total_size;
65}
66
67void VP8LFreeHistogram(VP8LHistogram* const histo) {
68 WebPSafeFree(histo);
69}
70
71void VP8LFreeHistogramSet(VP8LHistogramSet* const histo) {
72 WebPSafeFree(histo);
73}
74
75void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
76 VP8LHistogram* const histo) {
77 VP8LRefsCursor c = VP8LRefsCursorInit(refs);
78 while (VP8LRefsCursorOk(&c)) {
79 VP8LHistogramAddSinglePixOrCopy(histo, c.cur_pos);
80 VP8LRefsCursorNext(&c);
81 }
82}
83
84void VP8LHistogramCreate(VP8LHistogram* const p,
85 const VP8LBackwardRefs* const refs,
86 int palette_code_bits) {
87 if (palette_code_bits >= 0) {
88 p->palette_code_bits_ = palette_code_bits;
89 }
90 HistogramClear(p);
91 VP8LHistogramStoreRefs(refs, p);
92}
93
94void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
95 p->palette_code_bits_ = palette_code_bits;
96 HistogramClear(p);
97}
98
99VP8LHistogram* VP8LAllocateHistogram(int cache_bits) {
100 VP8LHistogram* histo = NULL;
101 const int total_size = VP8LGetHistogramSize(cache_bits);
102 uint8_t* const memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
103 if (memory == NULL) return NULL;
104 histo = (VP8LHistogram*)memory;
105 // literal_ won't necessary be aligned.
106 histo->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
107 VP8LHistogramInit(histo, cache_bits);
108 return histo;
109}
110
111VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
112 int i;
113 VP8LHistogramSet* set;
114 const int histo_size = VP8LGetHistogramSize(cache_bits);
115 const size_t total_size =
116 sizeof(*set) + size * (sizeof(*set->histograms) +
117 histo_size + WEBP_ALIGN_CST);
118 uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
119 if (memory == NULL) return NULL;
120
121 set = (VP8LHistogramSet*)memory;
122 memory += sizeof(*set);
123 set->histograms = (VP8LHistogram**)memory;
124 memory += size * sizeof(*set->histograms);
125 set->max_size = size;
126 set->size = size;
127 for (i = 0; i < size; ++i) {
128 memory = (uint8_t*)WEBP_ALIGN(memory);
129 set->histograms[i] = (VP8LHistogram*)memory;
130 // literal_ won't necessary be aligned.
131 set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
132 VP8LHistogramInit(set->histograms[i], cache_bits);
133 memory += histo_size;
134 }
135 return set;
136}
137
138// -----------------------------------------------------------------------------
139
140void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
141 const PixOrCopy* const v) {
142 if (PixOrCopyIsLiteral(v)) {
143 ++histo->alpha_[PixOrCopyLiteral(v, 3)];
144 ++histo->red_[PixOrCopyLiteral(v, 2)];
145 ++histo->literal_[PixOrCopyLiteral(v, 1)];
146 ++histo->blue_[PixOrCopyLiteral(v, 0)];
147 } else if (PixOrCopyIsCacheIdx(v)) {
148 const int literal_ix =
149 NUM_LITERAL_CODES + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
150 ++histo->literal_[literal_ix];
151 } else {
152 int code, extra_bits;
153 VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
154 ++histo->literal_[NUM_LITERAL_CODES + code];
155 VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
156 ++histo->distance_[code];
157 }
158}
159
160// -----------------------------------------------------------------------------
161// Entropy-related functions.
162
163static WEBP_INLINE double BitsEntropyRefine(const VP8LBitEntropy* entropy) {
164 double mix;
165 if (entropy->nonzeros < 5) {
166 if (entropy->nonzeros <= 1) {
167 return 0;
168 }
169 // Two symbols, they will be 0 and 1 in a Huffman code.
170 // Let's mix in a bit of entropy to favor good clustering when
171 // distributions of these are combined.
172 if (entropy->nonzeros == 2) {
173 return 0.99 * entropy->sum + 0.01 * entropy->entropy;
174 }
175 // No matter what the entropy says, we cannot be better than min_limit
176 // with Huffman coding. I am mixing a bit of entropy into the
177 // min_limit since it produces much better (~0.5 %) compression results
178 // perhaps because of better entropy clustering.
179 if (entropy->nonzeros == 3) {
180 mix = 0.95;
181 } else {
182 mix = 0.7; // nonzeros == 4.
183 }
184 } else {
185 mix = 0.627;
186 }
187
188 {
189 double min_limit = 2 * entropy->sum - entropy->max_val;
190 min_limit = mix * min_limit + (1.0 - mix) * entropy->entropy;
191 return (entropy->entropy < min_limit) ? min_limit : entropy->entropy;
192 }
193}
194
195double VP8LBitsEntropy(const uint32_t* const array, int n,
196 uint32_t* const trivial_symbol) {
197 VP8LBitEntropy entropy;
198 VP8LBitsEntropyUnrefined(array, n, &entropy);
199 if (trivial_symbol != NULL) {
200 *trivial_symbol =
201 (entropy.nonzeros == 1) ? entropy.nonzero_code : VP8L_NON_TRIVIAL_SYM;
202 }
203
204 return BitsEntropyRefine(&entropy);
205}
206
207static double InitialHuffmanCost(void) {
208 // Small bias because Huffman code length is typically not stored in
209 // full length.
210 static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
211 static const double kSmallBias = 9.1;
212 return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
213}
214
215// Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
216static double FinalHuffmanCost(const VP8LStreaks* const stats) {
217 // The constants in this function are experimental and got rounded from
218 // their original values in 1/8 when switched to 1/1024.
219 double retval = InitialHuffmanCost();
220 // Second coefficient: Many zeros in the histogram are covered efficiently
221 // by a run-length encode. Originally 2/8.
222 retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
223 // Second coefficient: Constant values are encoded less efficiently, but still
224 // RLE'ed. Originally 6/8.
225 retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
226 // 0s are usually encoded more efficiently than non-0s.
227 // Originally 15/8.
228 retval += 1.796875 * stats->streaks[0][0];
229 // Originally 26/8.
230 retval += 3.28125 * stats->streaks[1][0];
231 return retval;
232}
233
234// Get the symbol entropy for the distribution 'population'.
235// Set 'trivial_sym', if there's only one symbol present in the distribution.
236static double PopulationCost(const uint32_t* const population, int length,
237 uint32_t* const trivial_sym) {
238 VP8LBitEntropy bit_entropy;
239 VP8LStreaks stats;
240 VP8LGetEntropyUnrefined(population, length, &bit_entropy, &stats);
241 if (trivial_sym != NULL) {
242 *trivial_sym = (bit_entropy.nonzeros == 1) ? bit_entropy.nonzero_code
243 : VP8L_NON_TRIVIAL_SYM;
244 }
245
246 return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
247}
248
249// trivial_at_end is 1 if the two histograms only have one element that is
250// non-zero: both the zero-th one, or both the last one.
251static WEBP_INLINE double GetCombinedEntropy(const uint32_t* const X,
252 const uint32_t* const Y,
253 int length, int trivial_at_end) {
254 VP8LStreaks stats;
255 if (trivial_at_end) {
256 // This configuration is due to palettization that transforms an indexed
257 // pixel into 0xff000000 | (pixel << 8) in VP8LBundleColorMap.
258 // BitsEntropyRefine is 0 for histograms with only one non-zero value.
259 // Only FinalHuffmanCost needs to be evaluated.
260 memset(&stats, 0, sizeof(stats));
261 // Deal with the non-zero value at index 0 or length-1.
262 stats.streaks[1][0] += 1;
263 // Deal with the following/previous zero streak.
264 stats.counts[0] += 1;
265 stats.streaks[0][1] += length - 1;
266 return FinalHuffmanCost(&stats);
267 } else {
268 VP8LBitEntropy bit_entropy;
269 VP8LGetCombinedEntropyUnrefined(X, Y, length, &bit_entropy, &stats);
270
271 return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
272 }
273}
274
275// Estimates the Entropy + Huffman + other block overhead size cost.
276double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
277 return
278 PopulationCost(
279 p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_), NULL)
280 + PopulationCost(p->red_, NUM_LITERAL_CODES, NULL)
281 + PopulationCost(p->blue_, NUM_LITERAL_CODES, NULL)
282 + PopulationCost(p->alpha_, NUM_LITERAL_CODES, NULL)
283 + PopulationCost(p->distance_, NUM_DISTANCE_CODES, NULL)
284 + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
285 + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
286}
287
288// -----------------------------------------------------------------------------
289// Various histogram combine/cost-eval functions
290
291static int GetCombinedHistogramEntropy(const VP8LHistogram* const a,
292 const VP8LHistogram* const b,
293 double cost_threshold,
294 double* cost) {
295 const int palette_code_bits = a->palette_code_bits_;
296 int trivial_at_end = 0;
297 assert(a->palette_code_bits_ == b->palette_code_bits_);
298 *cost += GetCombinedEntropy(a->literal_, b->literal_,
299 VP8LHistogramNumCodes(palette_code_bits), 0);
300 *cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
301 b->literal_ + NUM_LITERAL_CODES,
302 NUM_LENGTH_CODES);
303 if (*cost > cost_threshold) return 0;
304
305 if (a->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM &&
306 a->trivial_symbol_ == b->trivial_symbol_) {
307 // A, R and B are all 0 or 0xff.
308 const uint32_t color_a = (a->trivial_symbol_ >> 24) & 0xff;
309 const uint32_t color_r = (a->trivial_symbol_ >> 16) & 0xff;
310 const uint32_t color_b = (a->trivial_symbol_ >> 0) & 0xff;
311 if ((color_a == 0 || color_a == 0xff) &&
312 (color_r == 0 || color_r == 0xff) &&
313 (color_b == 0 || color_b == 0xff)) {
314 trivial_at_end = 1;
315 }
316 }
317
318 *cost +=
319 GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES, trivial_at_end);
320 if (*cost > cost_threshold) return 0;
321
322 *cost +=
323 GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES, trivial_at_end);
324 if (*cost > cost_threshold) return 0;
325
326 *cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES,
327 trivial_at_end);
328 if (*cost > cost_threshold) return 0;
329
330 *cost +=
331 GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES, 0);
332 *cost +=
333 VP8LExtraCostCombined(a->distance_, b->distance_, NUM_DISTANCE_CODES);
334 if (*cost > cost_threshold) return 0;
335
336 return 1;
337}
338
339static WEBP_INLINE void HistogramAdd(const VP8LHistogram* const a,
340 const VP8LHistogram* const b,
341 VP8LHistogram* const out) {
342 VP8LHistogramAdd(a, b, out);
343 out->trivial_symbol_ = (a->trivial_symbol_ == b->trivial_symbol_)
344 ? a->trivial_symbol_
345 : VP8L_NON_TRIVIAL_SYM;
346}
347
348// Performs out = a + b, computing the cost C(a+b) - C(a) - C(b) while comparing
349// to the threshold value 'cost_threshold'. The score returned is
350// Score = C(a+b) - C(a) - C(b), where C(a) + C(b) is known and fixed.
351// Since the previous score passed is 'cost_threshold', we only need to compare
352// the partial cost against 'cost_threshold + C(a) + C(b)' to possibly bail-out
353// early.
354static double HistogramAddEval(const VP8LHistogram* const a,
355 const VP8LHistogram* const b,
356 VP8LHistogram* const out,
357 double cost_threshold) {
358 double cost = 0;
359 const double sum_cost = a->bit_cost_ + b->bit_cost_;
360 cost_threshold += sum_cost;
361
362 if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
363 HistogramAdd(a, b, out);
364 out->bit_cost_ = cost;
365 out->palette_code_bits_ = a->palette_code_bits_;
366 }
367
368 return cost - sum_cost;
369}
370
371// Same as HistogramAddEval(), except that the resulting histogram
372// is not stored. Only the cost C(a+b) - C(a) is evaluated. We omit
373// the term C(b) which is constant over all the evaluations.
374static double HistogramAddThresh(const VP8LHistogram* const a,
375 const VP8LHistogram* const b,
376 double cost_threshold) {
377 double cost = -a->bit_cost_;
378 GetCombinedHistogramEntropy(a, b, cost_threshold, &cost);
379 return cost;
380}
381
382// -----------------------------------------------------------------------------
383
384// The structure to keep track of cost range for the three dominant entropy
385// symbols.
386// TODO(skal): Evaluate if float can be used here instead of double for
387// representing the entropy costs.
388typedef struct {
389 double literal_max_;
390 double literal_min_;
391 double red_max_;
392 double red_min_;
393 double blue_max_;
394 double blue_min_;
395} DominantCostRange;
396
397static void DominantCostRangeInit(DominantCostRange* const c) {
398 c->literal_max_ = 0.;
399 c->literal_min_ = MAX_COST;
400 c->red_max_ = 0.;
401 c->red_min_ = MAX_COST;
402 c->blue_max_ = 0.;
403 c->blue_min_ = MAX_COST;
404}
405
406static void UpdateDominantCostRange(
407 const VP8LHistogram* const h, DominantCostRange* const c) {
408 if (c->literal_max_ < h->literal_cost_) c->literal_max_ = h->literal_cost_;
409 if (c->literal_min_ > h->literal_cost_) c->literal_min_ = h->literal_cost_;
410 if (c->red_max_ < h->red_cost_) c->red_max_ = h->red_cost_;
411 if (c->red_min_ > h->red_cost_) c->red_min_ = h->red_cost_;
412 if (c->blue_max_ < h->blue_cost_) c->blue_max_ = h->blue_cost_;
413 if (c->blue_min_ > h->blue_cost_) c->blue_min_ = h->blue_cost_;
414}
415
416static void UpdateHistogramCost(VP8LHistogram* const h) {
417 uint32_t alpha_sym, red_sym, blue_sym;
418 const double alpha_cost =
419 PopulationCost(h->alpha_, NUM_LITERAL_CODES, &alpha_sym);
420 const double distance_cost =
421 PopulationCost(h->distance_, NUM_DISTANCE_CODES, NULL) +
422 VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
423 const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
424 h->literal_cost_ = PopulationCost(h->literal_, num_codes, NULL) +
425 VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
426 NUM_LENGTH_CODES);
427 h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES, &red_sym);
428 h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES, &blue_sym);
429 h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
430 alpha_cost + distance_cost;
431 if ((alpha_sym | red_sym | blue_sym) == VP8L_NON_TRIVIAL_SYM) {
432 h->trivial_symbol_ = VP8L_NON_TRIVIAL_SYM;
433 } else {
434 h->trivial_symbol_ =
435 ((uint32_t)alpha_sym << 24) | (red_sym << 16) | (blue_sym << 0);
436 }
437}
438
439static int GetBinIdForEntropy(double min, double max, double val) {
440 const double range = max - min;
441 if (range > 0.) {
442 const double delta = val - min;
443 return (int)((NUM_PARTITIONS - 1e-6) * delta / range);
444 } else {
445 return 0;
446 }
447}
448
449static int GetHistoBinIndex(const VP8LHistogram* const h,
450 const DominantCostRange* const c, int low_effort) {
451 int bin_id = GetBinIdForEntropy(c->literal_min_, c->literal_max_,
452 h->literal_cost_);
453 assert(bin_id < NUM_PARTITIONS);
454 if (!low_effort) {
455 bin_id = bin_id * NUM_PARTITIONS
456 + GetBinIdForEntropy(c->red_min_, c->red_max_, h->red_cost_);
457 bin_id = bin_id * NUM_PARTITIONS
458 + GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_);
459 assert(bin_id < BIN_SIZE);
460 }
461 return bin_id;
462}
463
464// Construct the histograms from backward references.
465static void HistogramBuild(
466 int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs,
467 VP8LHistogramSet* const image_histo) {
468 int x = 0, y = 0;
469 const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
470 VP8LHistogram** const histograms = image_histo->histograms;
471 VP8LRefsCursor c = VP8LRefsCursorInit(backward_refs);
472 assert(histo_bits > 0);
473 while (VP8LRefsCursorOk(&c)) {
474 const PixOrCopy* const v = c.cur_pos;
475 const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
476 VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
477 x += PixOrCopyLength(v);
478 while (x >= xsize) {
479 x -= xsize;
480 ++y;
481 }
482 VP8LRefsCursorNext(&c);
483 }
484}
485
486// Copies the histograms and computes its bit_cost.
487static void HistogramCopyAndAnalyze(
488 VP8LHistogramSet* const orig_histo, VP8LHistogramSet* const image_histo) {
489 int i;
490 const int histo_size = orig_histo->size;
491 VP8LHistogram** const orig_histograms = orig_histo->histograms;
492 VP8LHistogram** const histograms = image_histo->histograms;
493 for (i = 0; i < histo_size; ++i) {
494 VP8LHistogram* const histo = orig_histograms[i];
495 UpdateHistogramCost(histo);
496 // Copy histograms from orig_histo[] to image_histo[].
497 HistogramCopy(histo, histograms[i]);
498 }
499}
500
501// Partition histograms to different entropy bins for three dominant (literal,
502// red and blue) symbol costs and compute the histogram aggregate bit_cost.
503static void HistogramAnalyzeEntropyBin(VP8LHistogramSet* const image_histo,
504 uint16_t* const bin_map,
505 int low_effort) {
506 int i;
507 VP8LHistogram** const histograms = image_histo->histograms;
508 const int histo_size = image_histo->size;
509 DominantCostRange cost_range;
510 DominantCostRangeInit(&cost_range);
511
512 // Analyze the dominant (literal, red and blue) entropy costs.
513 for (i = 0; i < histo_size; ++i) {
514 UpdateDominantCostRange(histograms[i], &cost_range);
515 }
516
517 // bin-hash histograms on three of the dominant (literal, red and blue)
518 // symbol costs and store the resulting bin_id for each histogram.
519 for (i = 0; i < histo_size; ++i) {
520 bin_map[i] = GetHistoBinIndex(histograms[i], &cost_range, low_effort);
521 }
522}
523
524// Compact image_histo[] by merging some histograms with same bin_id together if
525// it's advantageous.
526static VP8LHistogram* HistogramCombineEntropyBin(
527 VP8LHistogramSet* const image_histo,
528 VP8LHistogram* cur_combo,
529 const uint16_t* const bin_map, int bin_map_size, int num_bins,
530 double combine_cost_factor, int low_effort) {
531 VP8LHistogram** const histograms = image_histo->histograms;
532 int idx;
533 // Work in-place: processed histograms are put at the beginning of
534 // image_histo[]. At the end, we just have to truncate the array.
535 int size = 0;
536 struct {
537 int16_t first; // position of the histogram that accumulates all
538 // histograms with the same bin_id
539 uint16_t num_combine_failures; // number of combine failures per bin_id
540 } bin_info[BIN_SIZE];
541
542 assert(num_bins <= BIN_SIZE);
543 for (idx = 0; idx < num_bins; ++idx) {
544 bin_info[idx].first = -1;
545 bin_info[idx].num_combine_failures = 0;
546 }
547
548 for (idx = 0; idx < bin_map_size; ++idx) {
549 const int bin_id = bin_map[idx];
550 const int first = bin_info[bin_id].first;
551 assert(size <= idx);
552 if (first == -1) {
553 // just move histogram #idx to its final position
554 histograms[size] = histograms[idx];
555 bin_info[bin_id].first = size++;
556 } else if (low_effort) {
557 HistogramAdd(histograms[idx], histograms[first], histograms[first]);
558 } else {
559 // try to merge #idx into #first (both share the same bin_id)
560 const double bit_cost = histograms[idx]->bit_cost_;
561 const double bit_cost_thresh = -bit_cost * combine_cost_factor;
562 const double curr_cost_diff =
563 HistogramAddEval(histograms[first], histograms[idx],
564 cur_combo, bit_cost_thresh);
565 if (curr_cost_diff < bit_cost_thresh) {
566 // Try to merge two histograms only if the combo is a trivial one or
567 // the two candidate histograms are already non-trivial.
568 // For some images, 'try_combine' turns out to be false for a lot of
569 // histogram pairs. In that case, we fallback to combining
570 // histograms as usual to avoid increasing the header size.
571 const int try_combine =
572 (cur_combo->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM) ||
573 ((histograms[idx]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM) &&
574 (histograms[first]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM));
575 const int max_combine_failures = 32;
576 if (try_combine ||
577 bin_info[bin_id].num_combine_failures >= max_combine_failures) {
578 // move the (better) merged histogram to its final slot
579 HistogramSwap(&cur_combo, &histograms[first]);
580 } else {
581 histograms[size++] = histograms[idx];
582 ++bin_info[bin_id].num_combine_failures;
583 }
584 } else {
585 histograms[size++] = histograms[idx];
586 }
587 }
588 }
589 image_histo->size = size;
590 if (low_effort) {
591 // for low_effort case, update the final cost when everything is merged
592 for (idx = 0; idx < size; ++idx) {
593 UpdateHistogramCost(histograms[idx]);
594 }
595 }
596 return cur_combo;
597}
598
599static uint32_t MyRand(uint32_t* const seed) {
600 *seed = (*seed * 16807ull) & 0xffffffffu;
601 if (*seed == 0) {
602 *seed = 1;
603 }
604 return *seed;
605}
606
607// -----------------------------------------------------------------------------
608// Histogram pairs priority queue
609
610// Pair of histograms. Negative idx1 value means that pair is out-of-date.
611typedef struct {
612 int idx1;
613 int idx2;
614 double cost_diff;
615 double cost_combo;
616} HistogramPair;
617
618typedef struct {
619 HistogramPair* queue;
620 int size;
621 int max_size;
622} HistoQueue;
623
624static int HistoQueueInit(HistoQueue* const histo_queue, const int max_index) {
625 histo_queue->size = 0;
626 // max_index^2 for the queue size is safe. If you look at
627 // HistogramCombineGreedy, and imagine that UpdateQueueFront always pushes
628 // data to the queue, you insert at most:
629 // - max_index*(max_index-1)/2 (the first two for loops)
630 // - max_index - 1 in the last for loop at the first iteration of the while
631 // loop, max_index - 2 at the second iteration ... therefore
632 // max_index*(max_index-1)/2 overall too
633 histo_queue->max_size = max_index * max_index;
634 // We allocate max_size + 1 because the last element at index "size" is
635 // used as temporary data (and it could be up to max_size).
636 histo_queue->queue = (HistogramPair*)WebPSafeMalloc(
637 histo_queue->max_size + 1, sizeof(*histo_queue->queue));
638 return histo_queue->queue != NULL;
639}
640
641static void HistoQueueClear(HistoQueue* const histo_queue) {
642 assert(histo_queue != NULL);
643 WebPSafeFree(histo_queue->queue);
644}
645
646static void SwapHistogramPairs(HistogramPair *p1,
647 HistogramPair *p2) {
648 const HistogramPair tmp = *p1;
649 *p1 = *p2;
650 *p2 = tmp;
651}
652
653// Given a valid priority queue in range [0, queue_size) this function checks
654// whether histo_queue[queue_size] should be accepted and swaps it with the
655// front if it is smaller. Otherwise, it leaves it as is.
656static void UpdateQueueFront(HistoQueue* const histo_queue) {
657 if (histo_queue->queue[histo_queue->size].cost_diff >= 0) return;
658
659 if (histo_queue->queue[histo_queue->size].cost_diff <
660 histo_queue->queue[0].cost_diff) {
661 SwapHistogramPairs(histo_queue->queue,
662 histo_queue->queue + histo_queue->size);
663 }
664 ++histo_queue->size;
665
666 // We cannot add more elements than the capacity.
667 // The allocation adds an extra element to the official capacity so that
668 // histo_queue->queue[histo_queue->max_size] is read/written within bound.
669 assert(histo_queue->size <= histo_queue->max_size);
670}
671
672// -----------------------------------------------------------------------------
673
674static void PreparePair(VP8LHistogram** histograms, int idx1, int idx2,
675 HistogramPair* const pair) {
676 VP8LHistogram* h1;
677 VP8LHistogram* h2;
678 double sum_cost;
679
680 if (idx1 > idx2) {
681 const int tmp = idx2;
682 idx2 = idx1;
683 idx1 = tmp;
684 }
685 pair->idx1 = idx1;
686 pair->idx2 = idx2;
687 h1 = histograms[idx1];
688 h2 = histograms[idx2];
689 sum_cost = h1->bit_cost_ + h2->bit_cost_;
690 pair->cost_combo = 0.;
691 GetCombinedHistogramEntropy(h1, h2, sum_cost, &pair->cost_combo);
692 pair->cost_diff = pair->cost_combo - sum_cost;
693}
694
695// Combines histograms by continuously choosing the one with the highest cost
696// reduction.
697static int HistogramCombineGreedy(VP8LHistogramSet* const image_histo) {
698 int ok = 0;
699 int image_histo_size = image_histo->size;
700 int i, j;
701 VP8LHistogram** const histograms = image_histo->histograms;
702 // Indexes of remaining histograms.
703 int* const clusters =
704 (int*)WebPSafeMalloc(image_histo_size, sizeof(*clusters));
705 // Priority queue of histogram pairs.
706 HistoQueue histo_queue;
707
708 if (!HistoQueueInit(&histo_queue, image_histo_size) || clusters == NULL) {
709 goto End;
710 }
711
712 for (i = 0; i < image_histo_size; ++i) {
713 // Initialize clusters indexes.
714 clusters[i] = i;
715 for (j = i + 1; j < image_histo_size; ++j) {
716 // Initialize positions array.
717 PreparePair(histograms, i, j, &histo_queue.queue[histo_queue.size]);
718 UpdateQueueFront(&histo_queue);
719 }
720 }
721
722 while (image_histo_size > 1 && histo_queue.size > 0) {
723 HistogramPair* copy_to;
724 const int idx1 = histo_queue.queue[0].idx1;
725 const int idx2 = histo_queue.queue[0].idx2;
726 HistogramAdd(histograms[idx2], histograms[idx1], histograms[idx1]);
727 histograms[idx1]->bit_cost_ = histo_queue.queue[0].cost_combo;
728 // Remove merged histogram.
729 for (i = 0; i + 1 < image_histo_size; ++i) {
730 if (clusters[i] >= idx2) {
731 clusters[i] = clusters[i + 1];
732 }
733 }
734 --image_histo_size;
735
736 // Remove pairs intersecting the just combined best pair. This will
737 // therefore pop the head of the queue.
738 copy_to = histo_queue.queue;
739 for (i = 0; i < histo_queue.size; ++i) {
740 HistogramPair* const p = histo_queue.queue + i;
741 if (p->idx1 == idx1 || p->idx2 == idx1 ||
742 p->idx1 == idx2 || p->idx2 == idx2) {
743 // Do not copy the invalid pair.
744 continue;
745 }
746 if (p->cost_diff < histo_queue.queue[0].cost_diff) {
747 // Replace the top of the queue if we found better.
748 SwapHistogramPairs(histo_queue.queue, p);
749 }
750 SwapHistogramPairs(copy_to, p);
751 ++copy_to;
752 }
753 histo_queue.size = (int)(copy_to - histo_queue.queue);
754
755 // Push new pairs formed with combined histogram to the queue.
756 for (i = 0; i < image_histo_size; ++i) {
757 if (clusters[i] != idx1) {
758 PreparePair(histograms, idx1, clusters[i],
759 &histo_queue.queue[histo_queue.size]);
760 UpdateQueueFront(&histo_queue);
761 }
762 }
763 }
764 // Move remaining histograms to the beginning of the array.
765 for (i = 0; i < image_histo_size; ++i) {
766 if (i != clusters[i]) { // swap the two histograms
767 HistogramSwap(&histograms[i], &histograms[clusters[i]]);
768 }
769 }
770
771 image_histo->size = image_histo_size;
772 ok = 1;
773
774 End:
775 WebPSafeFree(clusters);
776 HistoQueueClear(&histo_queue);
777 return ok;
778}
779
780static void HistogramCombineStochastic(VP8LHistogramSet* const image_histo,
781 VP8LHistogram* tmp_histo,
782 VP8LHistogram* best_combo,
783 int quality, int min_cluster_size) {
784 int iter;
785 uint32_t seed = 0;
786 int tries_with_no_success = 0;
787 int image_histo_size = image_histo->size;
788 const int iter_mult = (quality < 25) ? 2 : 2 + (quality - 25) / 8;
789 const int outer_iters = image_histo_size * iter_mult;
790 const int num_pairs = image_histo_size / 2;
791 const int num_tries_no_success = outer_iters / 2;
792 int idx2_max = image_histo_size - 1;
793 int do_brute_dorce = 0;
794 VP8LHistogram** const histograms = image_histo->histograms;
795
796 // Collapse similar histograms in 'image_histo'.
797 ++min_cluster_size;
798 for (iter = 0;
799 iter < outer_iters && image_histo_size >= min_cluster_size;
800 ++iter) {
801 double best_cost_diff = 0.;
802 int best_idx1 = -1, best_idx2 = 1;
803 int j;
804 int num_tries =
805 (num_pairs < image_histo_size) ? num_pairs : image_histo_size;
806 // Use a brute force approach if:
807 // - stochastic has not worked for a while and
808 // - if the number of iterations for brute force is less than the number of
809 // iterations if we never find a match ever again stochastically (hence
810 // num_tries times the number of remaining outer iterations).
811 do_brute_dorce =
812 (tries_with_no_success > 10) &&
813 (idx2_max * (idx2_max + 1) < 2 * num_tries * (outer_iters - iter));
814 if (do_brute_dorce) num_tries = idx2_max;
815
816 seed += iter;
817 for (j = 0; j < num_tries; ++j) {
818 double curr_cost_diff;
819 // Choose two histograms at random and try to combine them.
820 uint32_t idx1, idx2;
821 if (do_brute_dorce) {
822 // Use a brute force approach.
823 idx1 = (uint32_t)j;
824 idx2 = (uint32_t)idx2_max;
825 } else {
826 const uint32_t tmp = (j & 7) + 1;
827 const uint32_t diff =
828 (tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
829 idx1 = MyRand(&seed) % image_histo_size;
830 idx2 = (idx1 + diff + 1) % image_histo_size;
831 if (idx1 == idx2) {
832 continue;
833 }
834 }
835
836 // Calculate cost reduction on combining.
837 curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
838 tmp_histo, best_cost_diff);
839 if (curr_cost_diff < best_cost_diff) { // found a better pair?
840 HistogramSwap(&best_combo, &tmp_histo);
841 best_cost_diff = curr_cost_diff;
842 best_idx1 = idx1;
843 best_idx2 = idx2;
844 }
845 }
846 if (do_brute_dorce) --idx2_max;
847
848 if (best_idx1 >= 0) {
849 HistogramSwap(&best_combo, &histograms[best_idx1]);
850 // swap best_idx2 slot with last one (which is now unused)
851 --image_histo_size;
852 if (idx2_max >= image_histo_size) idx2_max = image_histo_size - 1;
853 if (best_idx2 != image_histo_size) {
854 HistogramSwap(&histograms[image_histo_size], &histograms[best_idx2]);
855 histograms[image_histo_size] = NULL;
856 }
857 tries_with_no_success = 0;
858 }
859 if (++tries_with_no_success >= num_tries_no_success || idx2_max == 0) {
860 break;
861 }
862 }
863 image_histo->size = image_histo_size;
864}
865
866// -----------------------------------------------------------------------------
867// Histogram refinement
868
869// Find the best 'out' histogram for each of the 'in' histograms.
870// Note: we assume that out[]->bit_cost_ is already up-to-date.
871static void HistogramRemap(const VP8LHistogramSet* const in,
872 const VP8LHistogramSet* const out,
873 uint16_t* const symbols) {
874 int i;
875 VP8LHistogram** const in_histo = in->histograms;
876 VP8LHistogram** const out_histo = out->histograms;
877 const int in_size = in->size;
878 const int out_size = out->size;
879 if (out_size > 1) {
880 for (i = 0; i < in_size; ++i) {
881 int best_out = 0;
882 double best_bits = MAX_COST;
883 int k;
884 for (k = 0; k < out_size; ++k) {
885 const double cur_bits =
886 HistogramAddThresh(out_histo[k], in_histo[i], best_bits);
887 if (k == 0 || cur_bits < best_bits) {
888 best_bits = cur_bits;
889 best_out = k;
890 }
891 }
892 symbols[i] = best_out;
893 }
894 } else {
895 assert(out_size == 1);
896 for (i = 0; i < in_size; ++i) {
897 symbols[i] = 0;
898 }
899 }
900
901 // Recompute each out based on raw and symbols.
902 for (i = 0; i < out_size; ++i) {
903 HistogramClear(out_histo[i]);
904 }
905
906 for (i = 0; i < in_size; ++i) {
907 const int idx = symbols[i];
908 HistogramAdd(in_histo[i], out_histo[idx], out_histo[idx]);
909 }
910}
911
912static double GetCombineCostFactor(int histo_size, int quality) {
913 double combine_cost_factor = 0.16;
914 if (quality < 90) {
915 if (histo_size > 256) combine_cost_factor /= 2.;
916 if (histo_size > 512) combine_cost_factor /= 2.;
917 if (histo_size > 1024) combine_cost_factor /= 2.;
918 if (quality <= 50) combine_cost_factor /= 2.;
919 }
920 return combine_cost_factor;
921}
922
923int VP8LGetHistoImageSymbols(int xsize, int ysize,
924 const VP8LBackwardRefs* const refs,
925 int quality, int low_effort,
926 int histo_bits, int cache_bits,
927 VP8LHistogramSet* const image_histo,
928 VP8LHistogramSet* const tmp_histos,
929 uint16_t* const histogram_symbols) {
930 int ok = 0;
931 const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
932 const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
933 const int image_histo_raw_size = histo_xsize * histo_ysize;
934 VP8LHistogramSet* const orig_histo =
935 VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
936 VP8LHistogram* cur_combo;
937 // Don't attempt linear bin-partition heuristic for
938 // histograms of small sizes (as bin_map will be very sparse) and
939 // maximum quality q==100 (to preserve the compression gains at that level).
940 const int entropy_combine_num_bins = low_effort ? NUM_PARTITIONS : BIN_SIZE;
941 const int entropy_combine =
942 (orig_histo->size > entropy_combine_num_bins * 2) && (quality < 100);
943
944 if (orig_histo == NULL) goto Error;
945
946 // Construct the histograms from backward references.
947 HistogramBuild(xsize, histo_bits, refs, orig_histo);
948 // Copies the histograms and computes its bit_cost.
949 HistogramCopyAndAnalyze(orig_histo, image_histo);
950
951 cur_combo = tmp_histos->histograms[1]; // pick up working slot
952 if (entropy_combine) {
953 const int bin_map_size = orig_histo->size;
954 // Reuse histogram_symbols storage. By definition, it's guaranteed to be ok.
955 uint16_t* const bin_map = histogram_symbols;
956 const double combine_cost_factor =
957 GetCombineCostFactor(image_histo_raw_size, quality);
958
959 HistogramAnalyzeEntropyBin(orig_histo, bin_map, low_effort);
960 // Collapse histograms with similar entropy.
961 cur_combo = HistogramCombineEntropyBin(image_histo, cur_combo,
962 bin_map, bin_map_size,
963 entropy_combine_num_bins,
964 combine_cost_factor, low_effort);
965 }
966
967 // Don't combine the histograms using stochastic and greedy heuristics for
968 // low-effort compression mode.
969 if (!low_effort || !entropy_combine) {
970 const float x = quality / 100.f;
971 // cubic ramp between 1 and MAX_HISTO_GREEDY:
972 const int threshold_size = (int)(1 + (x * x * x) * (MAX_HISTO_GREEDY - 1));
973 HistogramCombineStochastic(image_histo, tmp_histos->histograms[0],
974 cur_combo, quality, threshold_size);
975 if ((image_histo->size <= threshold_size) &&
976 !HistogramCombineGreedy(image_histo)) {
977 goto Error;
978 }
979 }
980
981 // TODO(vikasa): Optimize HistogramRemap for low-effort compression mode also.
982 // Find the optimal map from original histograms to the final ones.
983 HistogramRemap(orig_histo, image_histo, histogram_symbols);
984
985 ok = 1;
986
987 Error:
988 VP8LFreeHistogramSet(orig_histo);
989 return ok;
990}
991