1 // Copyright 2012 Google Inc. All Rights Reserved.
2 //
3 // This code is licensed under the same terms as WebM:
4 // Software License Agreement: http://www.webmproject.org/license/software/
5 // Additional IP Rights Grant: http://www.webmproject.org/license/additional/
6 // -----------------------------------------------------------------------------
7 //
8 // Author: Jyrki Alakuijala (jyrki@google.com)
9 //
10 #ifdef HAVE_CONFIG_H
11 #include "config.h"
12 #endif
13
14 #include <math.h>
15 #include <stdio.h>
16
17 #include "./backward_references.h"
18 #include "./histogram.h"
19 #include "../dsp/lossless.h"
20 #include "../utils/utils.h"
21
HistogramClear(VP8LHistogram * const p)22 static void HistogramClear(VP8LHistogram* const p) {
23 memset(p->literal_, 0, sizeof(p->literal_));
24 memset(p->red_, 0, sizeof(p->red_));
25 memset(p->blue_, 0, sizeof(p->blue_));
26 memset(p->alpha_, 0, sizeof(p->alpha_));
27 memset(p->distance_, 0, sizeof(p->distance_));
28 p->bit_cost_ = 0;
29 }
30
VP8LHistogramStoreRefs(const VP8LBackwardRefs * const refs,VP8LHistogram * const histo)31 void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
32 VP8LHistogram* const histo) {
33 int i;
34 for (i = 0; i < refs->size; ++i) {
35 VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]);
36 }
37 }
38
VP8LHistogramCreate(VP8LHistogram * const p,const VP8LBackwardRefs * const refs,int palette_code_bits)39 void VP8LHistogramCreate(VP8LHistogram* const p,
40 const VP8LBackwardRefs* const refs,
41 int palette_code_bits) {
42 if (palette_code_bits >= 0) {
43 p->palette_code_bits_ = palette_code_bits;
44 }
45 HistogramClear(p);
46 VP8LHistogramStoreRefs(refs, p);
47 }
48
VP8LHistogramInit(VP8LHistogram * const p,int palette_code_bits)49 void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
50 p->palette_code_bits_ = palette_code_bits;
51 HistogramClear(p);
52 }
53
VP8LAllocateHistogramSet(int size,int cache_bits)54 VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
55 int i;
56 VP8LHistogramSet* set;
57 VP8LHistogram* bulk;
58 const uint64_t total_size = (uint64_t)sizeof(*set)
59 + size * sizeof(*set->histograms)
60 + size * sizeof(**set->histograms);
61 uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
62 if (memory == NULL) return NULL;
63
64 set = (VP8LHistogramSet*)memory;
65 memory += sizeof(*set);
66 set->histograms = (VP8LHistogram**)memory;
67 memory += size * sizeof(*set->histograms);
68 bulk = (VP8LHistogram*)memory;
69 set->max_size = size;
70 set->size = size;
71 for (i = 0; i < size; ++i) {
72 set->histograms[i] = bulk + i;
73 VP8LHistogramInit(set->histograms[i], cache_bits);
74 }
75 return set;
76 }
77
78 // -----------------------------------------------------------------------------
79
VP8LHistogramAddSinglePixOrCopy(VP8LHistogram * const histo,const PixOrCopy * const v)80 void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
81 const PixOrCopy* const v) {
82 if (PixOrCopyIsLiteral(v)) {
83 ++histo->alpha_[PixOrCopyLiteral(v, 3)];
84 ++histo->red_[PixOrCopyLiteral(v, 2)];
85 ++histo->literal_[PixOrCopyLiteral(v, 1)];
86 ++histo->blue_[PixOrCopyLiteral(v, 0)];
87 } else if (PixOrCopyIsCacheIdx(v)) {
88 int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
89 ++histo->literal_[literal_ix];
90 } else {
91 int code, extra_bits_count, extra_bits_value;
92 PrefixEncode(PixOrCopyLength(v),
93 &code, &extra_bits_count, &extra_bits_value);
94 ++histo->literal_[256 + code];
95 PrefixEncode(PixOrCopyDistance(v),
96 &code, &extra_bits_count, &extra_bits_value);
97 ++histo->distance_[code];
98 }
99 }
100
101
102
BitsEntropy(const int * const array,int n)103 static double BitsEntropy(const int* const array, int n) {
104 double retval = 0.;
105 int sum = 0;
106 int nonzeros = 0;
107 int max_val = 0;
108 int i;
109 double mix;
110 for (i = 0; i < n; ++i) {
111 if (array[i] != 0) {
112 sum += array[i];
113 ++nonzeros;
114 retval -= VP8LFastSLog2(array[i]);
115 if (max_val < array[i]) {
116 max_val = array[i];
117 }
118 }
119 }
120 retval += VP8LFastSLog2(sum);
121
122 if (nonzeros < 5) {
123 if (nonzeros <= 1) {
124 return 0;
125 }
126 // Two symbols, they will be 0 and 1 in a Huffman code.
127 // Let's mix in a bit of entropy to favor good clustering when
128 // distributions of these are combined.
129 if (nonzeros == 2) {
130 return 0.99 * sum + 0.01 * retval;
131 }
132 // No matter what the entropy says, we cannot be better than min_limit
133 // with Huffman coding. I am mixing a bit of entropy into the
134 // min_limit since it produces much better (~0.5 %) compression results
135 // perhaps because of better entropy clustering.
136 if (nonzeros == 3) {
137 mix = 0.95;
138 } else {
139 mix = 0.7; // nonzeros == 4.
140 }
141 } else {
142 mix = 0.627;
143 }
144
145 {
146 double min_limit = 2 * sum - max_val;
147 min_limit = mix * min_limit + (1.0 - mix) * retval;
148 return (retval < min_limit) ? min_limit : retval;
149 }
150 }
151
VP8LHistogramEstimateBitsBulk(const VP8LHistogram * const p)152 double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
153 double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p))
154 + BitsEntropy(&p->red_[0], 256)
155 + BitsEntropy(&p->blue_[0], 256)
156 + BitsEntropy(&p->alpha_[0], 256)
157 + BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES);
158 // Compute the extra bits cost.
159 int i;
160 for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) {
161 retval +=
162 (i >> 1) * p->literal_[256 + i + 2];
163 }
164 for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) {
165 retval += (i >> 1) * p->distance_[i + 2];
166 }
167 return retval;
168 }
169
170
171 // Returns the cost encode the rle-encoded entropy code.
172 // The constants in this function are experimental.
HuffmanCost(const int * const population,int length)173 static double HuffmanCost(const int* const population, int length) {
174 // Small bias because Huffman code length is typically not stored in
175 // full length.
176 static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
177 static const double kSmallBias = 9.1;
178 double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
179 int streak = 0;
180 int i = 0;
181 for (; i < length - 1; ++i) {
182 ++streak;
183 if (population[i] == population[i + 1]) {
184 continue;
185 }
186 last_streak_hack:
187 // population[i] points now to the symbol in the streak of same values.
188 if (streak > 3) {
189 if (population[i] == 0) {
190 retval += 1.5625 + 0.234375 * streak;
191 } else {
192 retval += 2.578125 + 0.703125 * streak;
193 }
194 } else {
195 if (population[i] == 0) {
196 retval += 1.796875 * streak;
197 } else {
198 retval += 3.28125 * streak;
199 }
200 }
201 streak = 0;
202 }
203 if (i == length - 1) {
204 ++streak;
205 goto last_streak_hack;
206 }
207 return retval;
208 }
209
210 // Estimates the Huffman dictionary + other block overhead size.
HistogramEstimateBitsHeader(const VP8LHistogram * const p)211 static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) {
212 return HuffmanCost(&p->alpha_[0], 256) +
213 HuffmanCost(&p->red_[0], 256) +
214 HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) +
215 HuffmanCost(&p->blue_[0], 256) +
216 HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES);
217 }
218
VP8LHistogramEstimateBits(const VP8LHistogram * const p)219 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
220 return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p);
221 }
222
HistogramBuildImage(int xsize,int histo_bits,const VP8LBackwardRefs * const backward_refs,VP8LHistogramSet * const image)223 static void HistogramBuildImage(int xsize, int histo_bits,
224 const VP8LBackwardRefs* const backward_refs,
225 VP8LHistogramSet* const image) {
226 int i;
227 int x = 0, y = 0;
228 const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
229 VP8LHistogram** const histograms = image->histograms;
230 assert(histo_bits > 0);
231 for (i = 0; i < backward_refs->size; ++i) {
232 const PixOrCopy* const v = &backward_refs->refs[i];
233 const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
234 VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
235 x += PixOrCopyLength(v);
236 while (x >= xsize) {
237 x -= xsize;
238 ++y;
239 }
240 }
241 }
242
MyRand(uint32_t * seed)243 static uint32_t MyRand(uint32_t *seed) {
244 *seed *= 16807U;
245 if (*seed == 0) {
246 *seed = 1;
247 }
248 return *seed;
249 }
250
HistogramCombine(const VP8LHistogramSet * const in,VP8LHistogramSet * const out,int num_pairs)251 static int HistogramCombine(const VP8LHistogramSet* const in,
252 VP8LHistogramSet* const out, int num_pairs) {
253 int ok = 0;
254 int i, iter;
255 uint32_t seed = 0;
256 int tries_with_no_success = 0;
257 const int min_cluster_size = 2;
258 int out_size = in->size;
259 const int outer_iters = in->size * 3;
260 VP8LHistogram* const histos = (VP8LHistogram*)malloc(2 * sizeof(*histos));
261 VP8LHistogram* cur_combo = histos + 0; // trial merged histogram
262 VP8LHistogram* best_combo = histos + 1; // best merged histogram so far
263 if (histos == NULL) goto End;
264
265 // Copy histograms from in[] to out[].
266 assert(in->size <= out->size);
267 for (i = 0; i < in->size; ++i) {
268 in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]);
269 *out->histograms[i] = *in->histograms[i];
270 }
271
272 // Collapse similar histograms in 'out'.
273 for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) {
274 // We pick the best pair to be combined out of 'inner_iters' pairs.
275 double best_cost_diff = 0.;
276 int best_idx1 = 0, best_idx2 = 1;
277 int j;
278 seed += iter;
279 for (j = 0; j < num_pairs; ++j) {
280 double curr_cost_diff;
281 // Choose two histograms at random and try to combine them.
282 const uint32_t idx1 = MyRand(&seed) % out_size;
283 const uint32_t tmp = ((j & 7) + 1) % (out_size - 1);
284 const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1);
285 const uint32_t idx2 = (idx1 + diff + 1) % out_size;
286 if (idx1 == idx2) {
287 continue;
288 }
289 *cur_combo = *out->histograms[idx1];
290 VP8LHistogramAdd(cur_combo, out->histograms[idx2]);
291 cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo);
292 // Calculate cost reduction on combining.
293 curr_cost_diff = cur_combo->bit_cost_
294 - out->histograms[idx1]->bit_cost_
295 - out->histograms[idx2]->bit_cost_;
296 if (best_cost_diff > curr_cost_diff) { // found a better pair?
297 { // swap cur/best combo histograms
298 VP8LHistogram* const tmp_histo = cur_combo;
299 cur_combo = best_combo;
300 best_combo = tmp_histo;
301 }
302 best_cost_diff = curr_cost_diff;
303 best_idx1 = idx1;
304 best_idx2 = idx2;
305 }
306 }
307
308 if (best_cost_diff < 0.0) {
309 *out->histograms[best_idx1] = *best_combo;
310 // swap best_idx2 slot with last one (which is now unused)
311 --out_size;
312 if (best_idx2 != out_size) {
313 out->histograms[best_idx2] = out->histograms[out_size];
314 out->histograms[out_size] = NULL; // just for sanity check.
315 }
316 tries_with_no_success = 0;
317 }
318 if (++tries_with_no_success >= 50) {
319 break;
320 }
321 }
322 out->size = out_size;
323 ok = 1;
324
325 End:
326 free(histos);
327 return ok;
328 }
329
330 // -----------------------------------------------------------------------------
331 // Histogram refinement
332
333 // What is the bit cost of moving square_histogram from
334 // cur_symbol to candidate_symbol.
335 // TODO(skal): we don't really need to copy the histogram and Add(). Instead
336 // we just need VP8LDualHistogramEstimateBits(A, B) estimation function.
HistogramDistance(const VP8LHistogram * const square_histogram,const VP8LHistogram * const candidate)337 static double HistogramDistance(const VP8LHistogram* const square_histogram,
338 const VP8LHistogram* const candidate) {
339 const double previous_bit_cost = candidate->bit_cost_;
340 double new_bit_cost;
341 VP8LHistogram modified_histo;
342 modified_histo = *candidate;
343 VP8LHistogramAdd(&modified_histo, square_histogram);
344 new_bit_cost = VP8LHistogramEstimateBits(&modified_histo);
345
346 return new_bit_cost - previous_bit_cost;
347 }
348
349 // Find the best 'out' histogram for each of the 'in' histograms.
350 // Note: we assume that out[]->bit_cost_ is already up-to-date.
HistogramRemap(const VP8LHistogramSet * const in,const VP8LHistogramSet * const out,uint16_t * const symbols)351 static void HistogramRemap(const VP8LHistogramSet* const in,
352 const VP8LHistogramSet* const out,
353 uint16_t* const symbols) {
354 int i;
355 for (i = 0; i < in->size; ++i) {
356 int best_out = 0;
357 double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]);
358 int k;
359 for (k = 1; k < out->size; ++k) {
360 const double cur_bits =
361 HistogramDistance(in->histograms[i], out->histograms[k]);
362 if (cur_bits < best_bits) {
363 best_bits = cur_bits;
364 best_out = k;
365 }
366 }
367 symbols[i] = best_out;
368 }
369
370 // Recompute each out based on raw and symbols.
371 for (i = 0; i < out->size; ++i) {
372 HistogramClear(out->histograms[i]);
373 }
374 for (i = 0; i < in->size; ++i) {
375 VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]);
376 }
377 }
378
VP8LGetHistoImageSymbols(int xsize,int ysize,const VP8LBackwardRefs * const refs,int quality,int histo_bits,int cache_bits,VP8LHistogramSet * const image_in,uint16_t * const histogram_symbols)379 int VP8LGetHistoImageSymbols(int xsize, int ysize,
380 const VP8LBackwardRefs* const refs,
381 int quality, int histo_bits, int cache_bits,
382 VP8LHistogramSet* const image_in,
383 uint16_t* const histogram_symbols) {
384 int ok = 0;
385 const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
386 const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
387 const int num_histo_pairs = 10 + quality / 2; // For HistogramCombine().
388 const int histo_image_raw_size = histo_xsize * histo_ysize;
389 VP8LHistogramSet* const image_out =
390 VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits);
391 if (image_out == NULL) return 0;
392
393 // Build histogram image.
394 HistogramBuildImage(xsize, histo_bits, refs, image_out);
395 // Collapse similar histograms.
396 if (!HistogramCombine(image_out, image_in, num_histo_pairs)) {
397 goto Error;
398 }
399 // Find the optimal map from original histograms to the final ones.
400 HistogramRemap(image_out, image_in, histogram_symbols);
401 ok = 1;
402
403 Error:
404 free(image_out);
405 return ok;
406 }
407