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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.h"
19 #include "./histogram.h"
20 #include "../dsp/lossless.h"
21 #include "../utils/utils.h"
22 
23 #define MAX_COST 1.e38
24 
25 // Number of partitions for the three dominant (literal, red and blue) symbol
26 // costs.
27 #define NUM_PARTITIONS 4
28 // The size of the bin-hash corresponding to the three dominant costs.
29 #define BIN_SIZE (NUM_PARTITIONS * NUM_PARTITIONS * NUM_PARTITIONS)
30 
HistogramClear(VP8LHistogram * const p)31 static void HistogramClear(VP8LHistogram* const p) {
32   uint32_t* const literal = p->literal_;
33   const int cache_bits = p->palette_code_bits_;
34   const int histo_size = VP8LGetHistogramSize(cache_bits);
35   memset(p, 0, histo_size);
36   p->palette_code_bits_ = cache_bits;
37   p->literal_ = literal;
38 }
39 
HistogramCopy(const VP8LHistogram * const src,VP8LHistogram * const dst)40 static void HistogramCopy(const VP8LHistogram* const src,
41                           VP8LHistogram* const dst) {
42   uint32_t* const dst_literal = dst->literal_;
43   const int dst_cache_bits = dst->palette_code_bits_;
44   const int histo_size = VP8LGetHistogramSize(dst_cache_bits);
45   assert(src->palette_code_bits_ == dst_cache_bits);
46   memcpy(dst, src, histo_size);
47   dst->literal_ = dst_literal;
48 }
49 
VP8LGetHistogramSize(int cache_bits)50 int VP8LGetHistogramSize(int cache_bits) {
51   const int literal_size = VP8LHistogramNumCodes(cache_bits);
52   const size_t total_size = sizeof(VP8LHistogram) + sizeof(int) * literal_size;
53   assert(total_size <= (size_t)0x7fffffff);
54   return (int)total_size;
55 }
56 
VP8LFreeHistogram(VP8LHistogram * const histo)57 void VP8LFreeHistogram(VP8LHistogram* const histo) {
58   WebPSafeFree(histo);
59 }
60 
VP8LFreeHistogramSet(VP8LHistogramSet * const histo)61 void VP8LFreeHistogramSet(VP8LHistogramSet* const histo) {
62   WebPSafeFree(histo);
63 }
64 
VP8LHistogramStoreRefs(const VP8LBackwardRefs * const refs,VP8LHistogram * const histo)65 void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
66                             VP8LHistogram* const histo) {
67   VP8LRefsCursor c = VP8LRefsCursorInit(refs);
68   while (VP8LRefsCursorOk(&c)) {
69     VP8LHistogramAddSinglePixOrCopy(histo, c.cur_pos);
70     VP8LRefsCursorNext(&c);
71   }
72 }
73 
VP8LHistogramCreate(VP8LHistogram * const p,const VP8LBackwardRefs * const refs,int palette_code_bits)74 void VP8LHistogramCreate(VP8LHistogram* const p,
75                          const VP8LBackwardRefs* const refs,
76                          int palette_code_bits) {
77   if (palette_code_bits >= 0) {
78     p->palette_code_bits_ = palette_code_bits;
79   }
80   HistogramClear(p);
81   VP8LHistogramStoreRefs(refs, p);
82 }
83 
VP8LHistogramInit(VP8LHistogram * const p,int palette_code_bits)84 void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
85   p->palette_code_bits_ = palette_code_bits;
86   HistogramClear(p);
87 }
88 
VP8LAllocateHistogram(int cache_bits)89 VP8LHistogram* VP8LAllocateHistogram(int cache_bits) {
90   VP8LHistogram* histo = NULL;
91   const int total_size = VP8LGetHistogramSize(cache_bits);
92   uint8_t* const memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
93   if (memory == NULL) return NULL;
94   histo = (VP8LHistogram*)memory;
95   // literal_ won't necessary be aligned.
96   histo->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
97   VP8LHistogramInit(histo, cache_bits);
98   return histo;
99 }
100 
VP8LAllocateHistogramSet(int size,int cache_bits)101 VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
102   int i;
103   VP8LHistogramSet* set;
104   const size_t total_size = sizeof(*set)
105                             + sizeof(*set->histograms) * size
106                             + (size_t)VP8LGetHistogramSize(cache_bits) * size;
107   uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
108   if (memory == NULL) return NULL;
109 
110   set = (VP8LHistogramSet*)memory;
111   memory += sizeof(*set);
112   set->histograms = (VP8LHistogram**)memory;
113   memory += size * sizeof(*set->histograms);
114   set->max_size = size;
115   set->size = size;
116   for (i = 0; i < size; ++i) {
117     set->histograms[i] = (VP8LHistogram*)memory;
118     // literal_ won't necessary be aligned.
119     set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
120     VP8LHistogramInit(set->histograms[i], cache_bits);
121     // There's no padding/alignment between successive histograms.
122     memory += VP8LGetHistogramSize(cache_bits);
123   }
124   return set;
125 }
126 
127 // -----------------------------------------------------------------------------
128 
VP8LHistogramAddSinglePixOrCopy(VP8LHistogram * const histo,const PixOrCopy * const v)129 void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
130                                      const PixOrCopy* const v) {
131   if (PixOrCopyIsLiteral(v)) {
132     ++histo->alpha_[PixOrCopyLiteral(v, 3)];
133     ++histo->red_[PixOrCopyLiteral(v, 2)];
134     ++histo->literal_[PixOrCopyLiteral(v, 1)];
135     ++histo->blue_[PixOrCopyLiteral(v, 0)];
136   } else if (PixOrCopyIsCacheIdx(v)) {
137     const int literal_ix =
138         NUM_LITERAL_CODES + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
139     ++histo->literal_[literal_ix];
140   } else {
141     int code, extra_bits;
142     VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
143     ++histo->literal_[NUM_LITERAL_CODES + code];
144     VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
145     ++histo->distance_[code];
146   }
147 }
148 
BitsEntropyRefine(int nonzeros,int sum,int max_val,double retval)149 static WEBP_INLINE double BitsEntropyRefine(int nonzeros, int sum, int max_val,
150                                             double retval) {
151   double mix;
152   if (nonzeros < 5) {
153     if (nonzeros <= 1) {
154       return 0;
155     }
156     // Two symbols, they will be 0 and 1 in a Huffman code.
157     // Let's mix in a bit of entropy to favor good clustering when
158     // distributions of these are combined.
159     if (nonzeros == 2) {
160       return 0.99 * sum + 0.01 * retval;
161     }
162     // No matter what the entropy says, we cannot be better than min_limit
163     // with Huffman coding. I am mixing a bit of entropy into the
164     // min_limit since it produces much better (~0.5 %) compression results
165     // perhaps because of better entropy clustering.
166     if (nonzeros == 3) {
167       mix = 0.95;
168     } else {
169       mix = 0.7;  // nonzeros == 4.
170     }
171   } else {
172     mix = 0.627;
173   }
174 
175   {
176     double min_limit = 2 * sum - max_val;
177     min_limit = mix * min_limit + (1.0 - mix) * retval;
178     return (retval < min_limit) ? min_limit : retval;
179   }
180 }
181 
BitsEntropy(const uint32_t * const array,int n)182 static double BitsEntropy(const uint32_t* const array, int n) {
183   double retval = 0.;
184   uint32_t sum = 0;
185   int nonzeros = 0;
186   uint32_t max_val = 0;
187   int i;
188   for (i = 0; i < n; ++i) {
189     if (array[i] != 0) {
190       sum += array[i];
191       ++nonzeros;
192       retval -= VP8LFastSLog2(array[i]);
193       if (max_val < array[i]) {
194         max_val = array[i];
195       }
196     }
197   }
198   retval += VP8LFastSLog2(sum);
199   return BitsEntropyRefine(nonzeros, sum, max_val, retval);
200 }
201 
BitsEntropyCombined(const uint32_t * const X,const uint32_t * const Y,int n)202 static double BitsEntropyCombined(const uint32_t* const X,
203                                   const uint32_t* const Y, int n) {
204   double retval = 0.;
205   int sum = 0;
206   int nonzeros = 0;
207   int max_val = 0;
208   int i;
209   for (i = 0; i < n; ++i) {
210     const int xy = X[i] + Y[i];
211     if (xy != 0) {
212       sum += xy;
213       ++nonzeros;
214       retval -= VP8LFastSLog2(xy);
215       if (max_val < xy) {
216         max_val = xy;
217       }
218     }
219   }
220   retval += VP8LFastSLog2(sum);
221   return BitsEntropyRefine(nonzeros, sum, max_val, retval);
222 }
223 
InitialHuffmanCost(void)224 static double InitialHuffmanCost(void) {
225   // Small bias because Huffman code length is typically not stored in
226   // full length.
227   static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
228   static const double kSmallBias = 9.1;
229   return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
230 }
231 
232 // Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
FinalHuffmanCost(const VP8LStreaks * const stats)233 static double FinalHuffmanCost(const VP8LStreaks* const stats) {
234   double retval = InitialHuffmanCost();
235   retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
236   retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
237   retval += 1.796875 * stats->streaks[0][0];
238   retval += 3.28125 * stats->streaks[1][0];
239   return retval;
240 }
241 
242 // Trampolines
HuffmanCost(const uint32_t * const population,int length)243 static double HuffmanCost(const uint32_t* const population, int length) {
244   const VP8LStreaks stats = VP8LHuffmanCostCount(population, length);
245   return FinalHuffmanCost(&stats);
246 }
247 
HuffmanCostCombined(const uint32_t * const X,const uint32_t * const Y,int length)248 static double HuffmanCostCombined(const uint32_t* const X,
249                                   const uint32_t* const Y, int length) {
250   const VP8LStreaks stats = VP8LHuffmanCostCombinedCount(X, Y, length);
251   return FinalHuffmanCost(&stats);
252 }
253 
254 // Aggregated costs
PopulationCost(const uint32_t * const population,int length)255 static double PopulationCost(const uint32_t* const population, int length) {
256   return BitsEntropy(population, length) + HuffmanCost(population, length);
257 }
258 
GetCombinedEntropy(const uint32_t * const X,const uint32_t * const Y,int length)259 static double GetCombinedEntropy(const uint32_t* const X,
260                                  const uint32_t* const Y, int length) {
261   return BitsEntropyCombined(X, Y, length) + HuffmanCostCombined(X, Y, length);
262 }
263 
264 // Estimates the Entropy + Huffman + other block overhead size cost.
VP8LHistogramEstimateBits(const VP8LHistogram * const p)265 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
266   return
267       PopulationCost(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
268       + PopulationCost(p->red_, NUM_LITERAL_CODES)
269       + PopulationCost(p->blue_, NUM_LITERAL_CODES)
270       + PopulationCost(p->alpha_, NUM_LITERAL_CODES)
271       + PopulationCost(p->distance_, NUM_DISTANCE_CODES)
272       + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
273       + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
274 }
275 
VP8LHistogramEstimateBitsBulk(const VP8LHistogram * const p)276 double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
277   return
278       BitsEntropy(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
279       + BitsEntropy(p->red_, NUM_LITERAL_CODES)
280       + BitsEntropy(p->blue_, NUM_LITERAL_CODES)
281       + BitsEntropy(p->alpha_, NUM_LITERAL_CODES)
282       + BitsEntropy(p->distance_, NUM_DISTANCE_CODES)
283       + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
284       + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
285 }
286 
287 // -----------------------------------------------------------------------------
288 // Various histogram combine/cost-eval functions
289 
GetCombinedHistogramEntropy(const VP8LHistogram * const a,const VP8LHistogram * const b,double cost_threshold,double * cost)290 static int GetCombinedHistogramEntropy(const VP8LHistogram* const a,
291                                        const VP8LHistogram* const b,
292                                        double cost_threshold,
293                                        double* cost) {
294   const int palette_code_bits = a->palette_code_bits_;
295   assert(a->palette_code_bits_ == b->palette_code_bits_);
296   *cost += GetCombinedEntropy(a->literal_, b->literal_,
297                               VP8LHistogramNumCodes(palette_code_bits));
298   *cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
299                                  b->literal_ + NUM_LITERAL_CODES,
300                                  NUM_LENGTH_CODES);
301   if (*cost > cost_threshold) return 0;
302 
303   *cost += GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES);
304   if (*cost > cost_threshold) return 0;
305 
306   *cost += GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES);
307   if (*cost > cost_threshold) return 0;
308 
309   *cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES);
310   if (*cost > cost_threshold) return 0;
311 
312   *cost += GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES);
313   *cost += VP8LExtraCostCombined(a->distance_, b->distance_,
314                                  NUM_DISTANCE_CODES);
315   if (*cost > cost_threshold) return 0;
316 
317   return 1;
318 }
319 
320 // Performs out = a + b, computing the cost C(a+b) - C(a) - C(b) while comparing
321 // to the threshold value 'cost_threshold'. The score returned is
322 //  Score = C(a+b) - C(a) - C(b), where C(a) + C(b) is known and fixed.
323 // Since the previous score passed is 'cost_threshold', we only need to compare
324 // the partial cost against 'cost_threshold + C(a) + C(b)' to possibly bail-out
325 // early.
HistogramAddEval(const VP8LHistogram * const a,const VP8LHistogram * const b,VP8LHistogram * const out,double cost_threshold)326 static double HistogramAddEval(const VP8LHistogram* const a,
327                                const VP8LHistogram* const b,
328                                VP8LHistogram* const out,
329                                double cost_threshold) {
330   double cost = 0;
331   const double sum_cost = a->bit_cost_ + b->bit_cost_;
332   cost_threshold += sum_cost;
333 
334   if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
335     VP8LHistogramAdd(a, b, out);
336     out->bit_cost_ = cost;
337     out->palette_code_bits_ = a->palette_code_bits_;
338   }
339 
340   return cost - sum_cost;
341 }
342 
343 // Same as HistogramAddEval(), except that the resulting histogram
344 // is not stored. Only the cost C(a+b) - C(a) is evaluated. We omit
345 // the term C(b) which is constant over all the evaluations.
HistogramAddThresh(const VP8LHistogram * const a,const VP8LHistogram * const b,double cost_threshold)346 static double HistogramAddThresh(const VP8LHistogram* const a,
347                                  const VP8LHistogram* const b,
348                                  double cost_threshold) {
349   double cost = -a->bit_cost_;
350   GetCombinedHistogramEntropy(a, b, cost_threshold, &cost);
351   return cost;
352 }
353 
354 // -----------------------------------------------------------------------------
355 
356 // The structure to keep track of cost range for the three dominant entropy
357 // symbols.
358 // TODO(skal): Evaluate if float can be used here instead of double for
359 // representing the entropy costs.
360 typedef struct {
361   double literal_max_;
362   double literal_min_;
363   double red_max_;
364   double red_min_;
365   double blue_max_;
366   double blue_min_;
367 } DominantCostRange;
368 
DominantCostRangeInit(DominantCostRange * const c)369 static void DominantCostRangeInit(DominantCostRange* const c) {
370   c->literal_max_ = 0.;
371   c->literal_min_ = MAX_COST;
372   c->red_max_ = 0.;
373   c->red_min_ = MAX_COST;
374   c->blue_max_ = 0.;
375   c->blue_min_ = MAX_COST;
376 }
377 
UpdateDominantCostRange(const VP8LHistogram * const h,DominantCostRange * const c)378 static void UpdateDominantCostRange(
379     const VP8LHistogram* const h, DominantCostRange* const c) {
380   if (c->literal_max_ < h->literal_cost_) c->literal_max_ = h->literal_cost_;
381   if (c->literal_min_ > h->literal_cost_) c->literal_min_ = h->literal_cost_;
382   if (c->red_max_ < h->red_cost_) c->red_max_ = h->red_cost_;
383   if (c->red_min_ > h->red_cost_) c->red_min_ = h->red_cost_;
384   if (c->blue_max_ < h->blue_cost_) c->blue_max_ = h->blue_cost_;
385   if (c->blue_min_ > h->blue_cost_) c->blue_min_ = h->blue_cost_;
386 }
387 
UpdateHistogramCost(VP8LHistogram * const h)388 static void UpdateHistogramCost(VP8LHistogram* const h) {
389   const double alpha_cost = PopulationCost(h->alpha_, NUM_LITERAL_CODES);
390   const double distance_cost =
391       PopulationCost(h->distance_, NUM_DISTANCE_CODES) +
392       VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
393   const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
394   h->literal_cost_ = PopulationCost(h->literal_, num_codes) +
395                      VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
396                                    NUM_LENGTH_CODES);
397   h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES);
398   h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES);
399   h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
400                  alpha_cost + distance_cost;
401 }
402 
GetBinIdForEntropy(double min,double max,double val)403 static int GetBinIdForEntropy(double min, double max, double val) {
404   const double range = max - min + 1e-6;
405   const double delta = val - min;
406   return (int)(NUM_PARTITIONS * delta / range);
407 }
408 
409 // TODO(vikasa): Evaluate, if there's any correlation between red & blue.
GetHistoBinIndex(const VP8LHistogram * const h,const DominantCostRange * const c)410 static int GetHistoBinIndex(
411     const VP8LHistogram* const h, const DominantCostRange* const c) {
412   const int bin_id =
413       GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_) +
414       NUM_PARTITIONS * GetBinIdForEntropy(c->red_min_, c->red_max_,
415                                           h->red_cost_) +
416       NUM_PARTITIONS * NUM_PARTITIONS * GetBinIdForEntropy(c->literal_min_,
417                                                            c->literal_max_,
418                                                            h->literal_cost_);
419   assert(bin_id < BIN_SIZE);
420   return bin_id;
421 }
422 
423 // Construct the histograms from backward references.
HistogramBuild(int xsize,int histo_bits,const VP8LBackwardRefs * const backward_refs,VP8LHistogramSet * const image_histo)424 static void HistogramBuild(
425     int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs,
426     VP8LHistogramSet* const image_histo) {
427   int x = 0, y = 0;
428   const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
429   VP8LHistogram** const histograms = image_histo->histograms;
430   VP8LRefsCursor c = VP8LRefsCursorInit(backward_refs);
431   assert(histo_bits > 0);
432   // Construct the Histo from a given backward references.
433   while (VP8LRefsCursorOk(&c)) {
434     const PixOrCopy* const v = c.cur_pos;
435     const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
436     VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
437     x += PixOrCopyLength(v);
438     while (x >= xsize) {
439       x -= xsize;
440       ++y;
441     }
442     VP8LRefsCursorNext(&c);
443   }
444 }
445 
446 // Copies the histograms and computes its bit_cost.
HistogramCopyAndAnalyze(VP8LHistogramSet * const orig_histo,VP8LHistogramSet * const image_histo)447 static void HistogramCopyAndAnalyze(
448     VP8LHistogramSet* const orig_histo, VP8LHistogramSet* const image_histo) {
449   int i;
450   const int histo_size = orig_histo->size;
451   VP8LHistogram** const orig_histograms = orig_histo->histograms;
452   VP8LHistogram** const histograms = image_histo->histograms;
453   for (i = 0; i < histo_size; ++i) {
454     VP8LHistogram* const histo = orig_histograms[i];
455     UpdateHistogramCost(histo);
456     // Copy histograms from orig_histo[] to image_histo[].
457     HistogramCopy(histo, histograms[i]);
458   }
459 }
460 
461 // Partition histograms to different entropy bins for three dominant (literal,
462 // red and blue) symbol costs and compute the histogram aggregate bit_cost.
HistogramAnalyzeEntropyBin(VP8LHistogramSet * const image_histo,int16_t * const bin_map)463 static void HistogramAnalyzeEntropyBin(
464     VP8LHistogramSet* const image_histo, int16_t* const bin_map) {
465   int i;
466   VP8LHistogram** const histograms = image_histo->histograms;
467   const int histo_size = image_histo->size;
468   const int bin_depth = histo_size + 1;
469   DominantCostRange cost_range;
470   DominantCostRangeInit(&cost_range);
471 
472   // Analyze the dominant (literal, red and blue) entropy costs.
473   for (i = 0; i < histo_size; ++i) {
474     VP8LHistogram* const histo = histograms[i];
475     UpdateDominantCostRange(histo, &cost_range);
476   }
477 
478   // bin-hash histograms on three of the dominant (literal, red and blue)
479   // symbol costs.
480   for (i = 0; i < histo_size; ++i) {
481     int num_histos;
482     VP8LHistogram* const histo = histograms[i];
483     const int16_t bin_id = (int16_t)GetHistoBinIndex(histo, &cost_range);
484     const int bin_offset = bin_id * bin_depth;
485     // bin_map[n][0] for every bin 'n' maintains the counter for the number of
486     // histograms in that bin.
487     // Get and increment the num_histos in that bin.
488     num_histos = ++bin_map[bin_offset];
489     assert(bin_offset + num_histos < bin_depth * BIN_SIZE);
490     // Add histogram i'th index at num_histos (last) position in the bin_map.
491     bin_map[bin_offset + num_histos] = i;
492   }
493 }
494 
495 // Compact the histogram set by moving the valid one left in the set to the
496 // head and moving the ones that have been merged to other histograms towards
497 // the end.
498 // TODO(vikasa): Evaluate if this method can be avoided by altering the code
499 // logic of HistogramCombineEntropyBin main loop.
HistogramCompactBins(VP8LHistogramSet * const image_histo)500 static void HistogramCompactBins(VP8LHistogramSet* const image_histo) {
501   int start = 0;
502   int end = image_histo->size - 1;
503   VP8LHistogram** const histograms = image_histo->histograms;
504   while (start < end) {
505     while (start <= end && histograms[start] != NULL &&
506            histograms[start]->bit_cost_ != 0.) {
507       ++start;
508     }
509     while (start <= end && histograms[end]->bit_cost_ == 0.) {
510       histograms[end] = NULL;
511       --end;
512     }
513     if (start < end) {
514       assert(histograms[start] != NULL);
515       assert(histograms[end] != NULL);
516       HistogramCopy(histograms[end], histograms[start]);
517       histograms[end] = NULL;
518       --end;
519     }
520   }
521   image_histo->size = end + 1;
522 }
523 
HistogramCombineEntropyBin(VP8LHistogramSet * const image_histo,VP8LHistogram * const histos,int16_t * const bin_map,int bin_depth,double combine_cost_factor)524 static void HistogramCombineEntropyBin(VP8LHistogramSet* const image_histo,
525                                        VP8LHistogram* const histos,
526                                        int16_t* const bin_map, int bin_depth,
527                                        double combine_cost_factor) {
528   int bin_id;
529   VP8LHistogram* cur_combo = histos;
530   VP8LHistogram** const histograms = image_histo->histograms;
531 
532   for (bin_id = 0; bin_id < BIN_SIZE; ++bin_id) {
533     const int bin_offset = bin_id * bin_depth;
534     const int num_histos = bin_map[bin_offset];
535     const int idx1 = bin_map[bin_offset + 1];
536     int n;
537     for (n = 2; n <= num_histos; ++n) {
538       const int idx2 = bin_map[bin_offset + n];
539       const double bit_cost_idx2 = histograms[idx2]->bit_cost_;
540       if (bit_cost_idx2 > 0.) {
541         const double bit_cost_thresh = -bit_cost_idx2 * combine_cost_factor;
542         const double curr_cost_diff =
543             HistogramAddEval(histograms[idx1], histograms[idx2],
544                              cur_combo, bit_cost_thresh);
545         if (curr_cost_diff < bit_cost_thresh) {
546           HistogramCopy(cur_combo, histograms[idx1]);
547           histograms[idx2]->bit_cost_ = 0.;
548         }
549       }
550     }
551   }
552   HistogramCompactBins(image_histo);
553 }
554 
MyRand(uint32_t * seed)555 static uint32_t MyRand(uint32_t *seed) {
556   *seed *= 16807U;
557   if (*seed == 0) {
558     *seed = 1;
559   }
560   return *seed;
561 }
562 
HistogramCombine(VP8LHistogramSet * const image_histo,VP8LHistogramSet * const histos,int quality)563 static void HistogramCombine(VP8LHistogramSet* const image_histo,
564                              VP8LHistogramSet* const histos, int quality) {
565   int iter;
566   uint32_t seed = 0;
567   int tries_with_no_success = 0;
568   int image_histo_size = image_histo->size;
569   const int iter_mult = (quality < 25) ? 2 : 2 + (quality - 25) / 8;
570   const int outer_iters = image_histo_size * iter_mult;
571   const int num_pairs = image_histo_size / 2;
572   const int num_tries_no_success = outer_iters / 2;
573   const int min_cluster_size = 2;
574   VP8LHistogram** const histograms = image_histo->histograms;
575   VP8LHistogram* cur_combo = histos->histograms[0];   // trial histogram
576   VP8LHistogram* best_combo = histos->histograms[1];  // best histogram so far
577 
578   // Collapse similar histograms in 'image_histo'.
579   for (iter = 0;
580        iter < outer_iters && image_histo_size >= min_cluster_size;
581        ++iter) {
582     double best_cost_diff = 0.;
583     int best_idx1 = -1, best_idx2 = 1;
584     int j;
585     const int num_tries =
586         (num_pairs < image_histo_size) ? num_pairs : image_histo_size;
587     seed += iter;
588     for (j = 0; j < num_tries; ++j) {
589       double curr_cost_diff;
590       // Choose two histograms at random and try to combine them.
591       const uint32_t idx1 = MyRand(&seed) % image_histo_size;
592       const uint32_t tmp = (j & 7) + 1;
593       const uint32_t diff =
594           (tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
595       const uint32_t idx2 = (idx1 + diff + 1) % image_histo_size;
596       if (idx1 == idx2) {
597         continue;
598       }
599 
600       // Calculate cost reduction on combining.
601       curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
602                                         cur_combo, best_cost_diff);
603       if (curr_cost_diff < best_cost_diff) {    // found a better pair?
604         {     // swap cur/best combo histograms
605           VP8LHistogram* const tmp_histo = cur_combo;
606           cur_combo = best_combo;
607           best_combo = tmp_histo;
608         }
609         best_cost_diff = curr_cost_diff;
610         best_idx1 = idx1;
611         best_idx2 = idx2;
612       }
613     }
614 
615     if (best_idx1 >= 0) {
616       HistogramCopy(best_combo, histograms[best_idx1]);
617       // swap best_idx2 slot with last one (which is now unused)
618       --image_histo_size;
619       if (best_idx2 != image_histo_size) {
620         HistogramCopy(histograms[image_histo_size], histograms[best_idx2]);
621         histograms[image_histo_size] = NULL;
622       }
623       tries_with_no_success = 0;
624     }
625     if (++tries_with_no_success >= num_tries_no_success) {
626       break;
627     }
628   }
629   image_histo->size = image_histo_size;
630 }
631 
632 // -----------------------------------------------------------------------------
633 // Histogram refinement
634 
635 // Find the best 'out' histogram for each of the 'in' histograms.
636 // Note: we assume that out[]->bit_cost_ is already up-to-date.
HistogramRemap(const VP8LHistogramSet * const orig_histo,const VP8LHistogramSet * const image_histo,uint16_t * const symbols)637 static void HistogramRemap(const VP8LHistogramSet* const orig_histo,
638                            const VP8LHistogramSet* const image_histo,
639                            uint16_t* const symbols) {
640   int i;
641   VP8LHistogram** const orig_histograms = orig_histo->histograms;
642   VP8LHistogram** const histograms = image_histo->histograms;
643   for (i = 0; i < orig_histo->size; ++i) {
644     int best_out = 0;
645     double best_bits =
646         HistogramAddThresh(histograms[0], orig_histograms[i], MAX_COST);
647     int k;
648     for (k = 1; k < image_histo->size; ++k) {
649       const double cur_bits =
650           HistogramAddThresh(histograms[k], orig_histograms[i], best_bits);
651       if (cur_bits < best_bits) {
652         best_bits = cur_bits;
653         best_out = k;
654       }
655     }
656     symbols[i] = best_out;
657   }
658 
659   // Recompute each out based on raw and symbols.
660   for (i = 0; i < image_histo->size; ++i) {
661     HistogramClear(histograms[i]);
662   }
663 
664   for (i = 0; i < orig_histo->size; ++i) {
665     const int idx = symbols[i];
666     VP8LHistogramAdd(orig_histograms[i], histograms[idx], histograms[idx]);
667   }
668 }
669 
GetCombineCostFactor(int histo_size,int quality)670 static double GetCombineCostFactor(int histo_size, int quality) {
671   double combine_cost_factor = 0.16;
672   if (histo_size > 256) combine_cost_factor /= 2.;
673   if (histo_size > 512) combine_cost_factor /= 2.;
674   if (histo_size > 1024) combine_cost_factor /= 2.;
675   if (quality <= 50) combine_cost_factor /= 2.;
676   return combine_cost_factor;
677 }
678 
VP8LGetHistoImageSymbols(int xsize,int ysize,const VP8LBackwardRefs * const refs,int quality,int histo_bits,int cache_bits,VP8LHistogramSet * const image_histo,uint16_t * const histogram_symbols)679 int VP8LGetHistoImageSymbols(int xsize, int ysize,
680                              const VP8LBackwardRefs* const refs,
681                              int quality, int histo_bits, int cache_bits,
682                              VP8LHistogramSet* const image_histo,
683                              uint16_t* const histogram_symbols) {
684   int ok = 0;
685   const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
686   const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
687   const int image_histo_raw_size = histo_xsize * histo_ysize;
688 
689   // The bin_map for every bin follows following semantics:
690   // bin_map[n][0] = num_histo; // The number of histograms in that bin.
691   // bin_map[n][1] = index of first histogram in that bin;
692   // bin_map[n][num_histo] = index of last histogram in that bin;
693   // bin_map[n][num_histo + 1] ... bin_map[n][bin_depth - 1] = un-used indices.
694   const int bin_depth = image_histo_raw_size + 1;
695   int16_t* bin_map = NULL;
696   VP8LHistogramSet* const histos = VP8LAllocateHistogramSet(2, cache_bits);
697   VP8LHistogramSet* const orig_histo =
698       VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
699 
700   if (orig_histo == NULL || histos == NULL) {
701     goto Error;
702   }
703 
704   // Don't attempt linear bin-partition heuristic for:
705   // histograms of small sizes, as bin_map will be very sparse and;
706   // Higher qualities (> 90), to preserve the compression gains at those
707   // quality settings.
708   if (orig_histo->size > 2 * BIN_SIZE && quality < 90) {
709     const int bin_map_size = bin_depth * BIN_SIZE;
710     bin_map = (int16_t*)WebPSafeCalloc(bin_map_size, sizeof(*bin_map));
711     if (bin_map == NULL) goto Error;
712   }
713 
714   // Construct the histograms from backward references.
715   HistogramBuild(xsize, histo_bits, refs, orig_histo);
716   // Copies the histograms and computes its bit_cost.
717   HistogramCopyAndAnalyze(orig_histo, image_histo);
718 
719   if (bin_map != NULL) {
720     const double combine_cost_factor =
721         GetCombineCostFactor(image_histo_raw_size, quality);
722     HistogramAnalyzeEntropyBin(orig_histo, bin_map);
723     // Collapse histograms with similar entropy.
724     HistogramCombineEntropyBin(image_histo, histos->histograms[0],
725                                bin_map, bin_depth, combine_cost_factor);
726   }
727 
728   // Collapse similar histograms by random histogram-pair compares.
729   HistogramCombine(image_histo, histos, quality);
730 
731   // Find the optimal map from original histograms to the final ones.
732   HistogramRemap(orig_histo, image_histo, histogram_symbols);
733 
734   ok = 1;
735 
736  Error:
737   WebPSafeFree(bin_map);
738   VP8LFreeHistogramSet(orig_histo);
739   VP8LFreeHistogramSet(histos);
740   return ok;
741 }
742