// Copyright 2012 Google Inc. All Rights Reserved. // // This code is licensed under the same terms as WebM: // Software License Agreement: http://www.webmproject.org/license/software/ // Additional IP Rights Grant: http://www.webmproject.org/license/additional/ // ----------------------------------------------------------------------------- // // Author: Jyrki Alakuijala (jyrki@google.com) // #ifdef HAVE_CONFIG_H #include "config.h" #endif #include <math.h> #include <stdio.h> #include "./backward_references.h" #include "./histogram.h" #include "../dsp/lossless.h" #include "../utils/utils.h" static void HistogramClear(VP8LHistogram* const p) { memset(p->literal_, 0, sizeof(p->literal_)); memset(p->red_, 0, sizeof(p->red_)); memset(p->blue_, 0, sizeof(p->blue_)); memset(p->alpha_, 0, sizeof(p->alpha_)); memset(p->distance_, 0, sizeof(p->distance_)); p->bit_cost_ = 0; } void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs, VP8LHistogram* const histo) { int i; for (i = 0; i < refs->size; ++i) { VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]); } } void VP8LHistogramCreate(VP8LHistogram* const p, const VP8LBackwardRefs* const refs, int palette_code_bits) { if (palette_code_bits >= 0) { p->palette_code_bits_ = palette_code_bits; } HistogramClear(p); VP8LHistogramStoreRefs(refs, p); } void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) { p->palette_code_bits_ = palette_code_bits; HistogramClear(p); } VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) { int i; VP8LHistogramSet* set; VP8LHistogram* bulk; const uint64_t total_size = (uint64_t)sizeof(*set) + size * sizeof(*set->histograms) + size * sizeof(**set->histograms); uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory)); if (memory == NULL) return NULL; set = (VP8LHistogramSet*)memory; memory += sizeof(*set); set->histograms = (VP8LHistogram**)memory; memory += size * sizeof(*set->histograms); bulk = (VP8LHistogram*)memory; set->max_size = size; set->size = size; for (i = 0; i < size; ++i) { set->histograms[i] = bulk + i; VP8LHistogramInit(set->histograms[i], cache_bits); } return set; } // ----------------------------------------------------------------------------- void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo, const PixOrCopy* const v) { if (PixOrCopyIsLiteral(v)) { ++histo->alpha_[PixOrCopyLiteral(v, 3)]; ++histo->red_[PixOrCopyLiteral(v, 2)]; ++histo->literal_[PixOrCopyLiteral(v, 1)]; ++histo->blue_[PixOrCopyLiteral(v, 0)]; } else if (PixOrCopyIsCacheIdx(v)) { int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v); ++histo->literal_[literal_ix]; } else { int code, extra_bits_count, extra_bits_value; PrefixEncode(PixOrCopyLength(v), &code, &extra_bits_count, &extra_bits_value); ++histo->literal_[256 + code]; PrefixEncode(PixOrCopyDistance(v), &code, &extra_bits_count, &extra_bits_value); ++histo->distance_[code]; } } static double BitsEntropy(const int* const array, int n) { double retval = 0.; int sum = 0; int nonzeros = 0; int max_val = 0; int i; double mix; for (i = 0; i < n; ++i) { if (array[i] != 0) { sum += array[i]; ++nonzeros; retval -= VP8LFastSLog2(array[i]); if (max_val < array[i]) { max_val = array[i]; } } } retval += VP8LFastSLog2(sum); if (nonzeros < 5) { if (nonzeros <= 1) { return 0; } // Two symbols, they will be 0 and 1 in a Huffman code. // Let's mix in a bit of entropy to favor good clustering when // distributions of these are combined. if (nonzeros == 2) { return 0.99 * sum + 0.01 * retval; } // No matter what the entropy says, we cannot be better than min_limit // with Huffman coding. I am mixing a bit of entropy into the // min_limit since it produces much better (~0.5 %) compression results // perhaps because of better entropy clustering. if (nonzeros == 3) { mix = 0.95; } else { mix = 0.7; // nonzeros == 4. } } else { mix = 0.627; } { double min_limit = 2 * sum - max_val; min_limit = mix * min_limit + (1.0 - mix) * retval; return (retval < min_limit) ? min_limit : retval; } } double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) { double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p)) + BitsEntropy(&p->red_[0], 256) + BitsEntropy(&p->blue_[0], 256) + BitsEntropy(&p->alpha_[0], 256) + BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES); // Compute the extra bits cost. int i; for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) { retval += (i >> 1) * p->literal_[256 + i + 2]; } for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) { retval += (i >> 1) * p->distance_[i + 2]; } return retval; } // Returns the cost encode the rle-encoded entropy code. // The constants in this function are experimental. static double HuffmanCost(const int* const population, int length) { // Small bias because Huffman code length is typically not stored in // full length. static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3; static const double kSmallBias = 9.1; double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias; int streak = 0; int i = 0; for (; i < length - 1; ++i) { ++streak; if (population[i] == population[i + 1]) { continue; } last_streak_hack: // population[i] points now to the symbol in the streak of same values. if (streak > 3) { if (population[i] == 0) { retval += 1.5625 + 0.234375 * streak; } else { retval += 2.578125 + 0.703125 * streak; } } else { if (population[i] == 0) { retval += 1.796875 * streak; } else { retval += 3.28125 * streak; } } streak = 0; } if (i == length - 1) { ++streak; goto last_streak_hack; } return retval; } // Estimates the Huffman dictionary + other block overhead size. static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) { return HuffmanCost(&p->alpha_[0], 256) + HuffmanCost(&p->red_[0], 256) + HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) + HuffmanCost(&p->blue_[0], 256) + HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES); } double VP8LHistogramEstimateBits(const VP8LHistogram* const p) { return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p); } static void HistogramBuildImage(int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs, VP8LHistogramSet* const image) { int i; int x = 0, y = 0; const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits); VP8LHistogram** const histograms = image->histograms; assert(histo_bits > 0); for (i = 0; i < backward_refs->size; ++i) { const PixOrCopy* const v = &backward_refs->refs[i]; const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits); VP8LHistogramAddSinglePixOrCopy(histograms[ix], v); x += PixOrCopyLength(v); while (x >= xsize) { x -= xsize; ++y; } } } static uint32_t MyRand(uint32_t *seed) { *seed *= 16807U; if (*seed == 0) { *seed = 1; } return *seed; } static int HistogramCombine(const VP8LHistogramSet* const in, VP8LHistogramSet* const out, int num_pairs) { int ok = 0; int i, iter; uint32_t seed = 0; int tries_with_no_success = 0; const int min_cluster_size = 2; int out_size = in->size; const int outer_iters = in->size * 3; VP8LHistogram* const histos = (VP8LHistogram*)malloc(2 * sizeof(*histos)); VP8LHistogram* cur_combo = histos + 0; // trial merged histogram VP8LHistogram* best_combo = histos + 1; // best merged histogram so far if (histos == NULL) goto End; // Copy histograms from in[] to out[]. assert(in->size <= out->size); for (i = 0; i < in->size; ++i) { in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]); *out->histograms[i] = *in->histograms[i]; } // Collapse similar histograms in 'out'. for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) { // We pick the best pair to be combined out of 'inner_iters' pairs. double best_cost_diff = 0.; int best_idx1 = 0, best_idx2 = 1; int j; seed += iter; for (j = 0; j < num_pairs; ++j) { double curr_cost_diff; // Choose two histograms at random and try to combine them. const uint32_t idx1 = MyRand(&seed) % out_size; const uint32_t tmp = ((j & 7) + 1) % (out_size - 1); const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1); const uint32_t idx2 = (idx1 + diff + 1) % out_size; if (idx1 == idx2) { continue; } *cur_combo = *out->histograms[idx1]; VP8LHistogramAdd(cur_combo, out->histograms[idx2]); cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo); // Calculate cost reduction on combining. curr_cost_diff = cur_combo->bit_cost_ - out->histograms[idx1]->bit_cost_ - out->histograms[idx2]->bit_cost_; if (best_cost_diff > curr_cost_diff) { // found a better pair? { // swap cur/best combo histograms VP8LHistogram* const tmp_histo = cur_combo; cur_combo = best_combo; best_combo = tmp_histo; } best_cost_diff = curr_cost_diff; best_idx1 = idx1; best_idx2 = idx2; } } if (best_cost_diff < 0.0) { *out->histograms[best_idx1] = *best_combo; // swap best_idx2 slot with last one (which is now unused) --out_size; if (best_idx2 != out_size) { out->histograms[best_idx2] = out->histograms[out_size]; out->histograms[out_size] = NULL; // just for sanity check. } tries_with_no_success = 0; } if (++tries_with_no_success >= 50) { break; } } out->size = out_size; ok = 1; End: free(histos); return ok; } // ----------------------------------------------------------------------------- // Histogram refinement // What is the bit cost of moving square_histogram from // cur_symbol to candidate_symbol. // TODO(skal): we don't really need to copy the histogram and Add(). Instead // we just need VP8LDualHistogramEstimateBits(A, B) estimation function. static double HistogramDistance(const VP8LHistogram* const square_histogram, const VP8LHistogram* const candidate) { const double previous_bit_cost = candidate->bit_cost_; double new_bit_cost; VP8LHistogram modified_histo; modified_histo = *candidate; VP8LHistogramAdd(&modified_histo, square_histogram); new_bit_cost = VP8LHistogramEstimateBits(&modified_histo); return new_bit_cost - previous_bit_cost; } // Find the best 'out' histogram for each of the 'in' histograms. // Note: we assume that out[]->bit_cost_ is already up-to-date. static void HistogramRemap(const VP8LHistogramSet* const in, const VP8LHistogramSet* const out, uint16_t* const symbols) { int i; for (i = 0; i < in->size; ++i) { int best_out = 0; double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]); int k; for (k = 1; k < out->size; ++k) { const double cur_bits = HistogramDistance(in->histograms[i], out->histograms[k]); if (cur_bits < best_bits) { best_bits = cur_bits; best_out = k; } } symbols[i] = best_out; } // Recompute each out based on raw and symbols. for (i = 0; i < out->size; ++i) { HistogramClear(out->histograms[i]); } for (i = 0; i < in->size; ++i) { VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]); } } int 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) { int ok = 0; const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1; const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1; const int num_histo_pairs = 10 + quality / 2; // For HistogramCombine(). const int histo_image_raw_size = histo_xsize * histo_ysize; VP8LHistogramSet* const image_out = VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits); if (image_out == NULL) return 0; // Build histogram image. HistogramBuildImage(xsize, histo_bits, refs, image_out); // Collapse similar histograms. if (!HistogramCombine(image_out, image_in, num_histo_pairs)) { goto Error; } // Find the optimal map from original histograms to the final ones. HistogramRemap(image_out, image_in, histogram_symbols); ok = 1; Error: free(image_out); return ok; }