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 (at) 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 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 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 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 49 void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) { 50 p->palette_code_bits_ = palette_code_bits; 51 HistogramClear(p); 52 } 53 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 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 } 100 101 102 103 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 } 151 152 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. 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. 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 } 218 219 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) { 220 return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p); 221 } 222 223 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 } 242 243 static uint32_t MyRand(uint32_t *seed) { 244 *seed *= 16807U; 245 if (*seed == 0) { 246 *seed = 1; 247 } 248 return *seed; 249 } 250 251 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. 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. 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 } 378 379 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
