From cd50d72afd7a54ec57827049c8bb934cfbb5a42c Mon Sep 17 00:00:00 2001 From: "Steinar H. Gunderson" Date: Sun, 17 Sep 2017 11:06:32 +0200 Subject: [PATCH] Add some code for (semi-)optimal assignment of rANS coefficients to streams. --- qdc.cpp | 165 ++++++++++++++++++++++++++++++++++++++++++++++++-------- 1 file changed, 143 insertions(+), 22 deletions(-) diff --git a/qdc.cpp b/qdc.cpp index a0fe2e7..b5594b7 100644 --- a/qdc.cpp +++ b/qdc.cpp @@ -9,14 +9,24 @@ #include "ryg_rans/rans_byte.h" #include "ryg_rans/renormalize.h" +#include #include +#include +#include #include +#include #define WIDTH 1280 #define HEIGHT 720 #define NUM_SYMS 256 #define ESCAPE_LIMIT (NUM_SYMS - 1) +// If you set this to 1, the program will try to optimize the placement +// of coefficients to rANS probability distributions. This is randomized, +// so you might want to run it a few times. +#define FIND_OPTIMAL_STREAM_ASSIGNMENT 0 +#define NUM_CLUSTERS 8 + static constexpr uint32_t prob_bits = 12; static constexpr uint32_t prob_scale = 1 << prob_bits; @@ -137,22 +147,19 @@ void SymbolStats::normalize_freqs(uint32_t target_total) calc_cost, (calc_cost - ideal_cost) / 8.0, total_loss / 8.0, total_loss_with_dp / 8.0); } -SymbolStats stats[64]; +SymbolStats stats[128]; + +#if FIND_OPTIMAL_STREAM_ASSIGNMENT +// Distance from one stream to the other, based on a hacked-up K-L divergence. +float kl_dist[64][64]; +#endif -int pick_stats_for(int y, int x) +int pick_stats_for(int x, int y, bool is_chroma) { - //return 0; - //return std::min(hypot(x, y), 7); - return std::min(x + y, 7); - //if (x + y >= 7) return 7; - //return x + y; - //return y * 8 + x; -#if 0 - if (y == 0 && x == 0) { - return 0; - } else { - return 1; - } +#if FIND_OPTIMAL_STREAM_ASSIGNMENT + return y * 8 + x + is_chroma * 64; +#else + return std::min(x + y, 7) + is_chroma * 8; #endif } @@ -348,6 +355,114 @@ void convert_ycbcr() } } +#if FIND_OPTIMAL_STREAM_ASSIGNMENT +double find_best_assignment(const int *medoids, int *assignment) +{ + double current_score = 0.0; + for (int i = 0; i < 64; ++i) { + int best_medoid = medoids[0]; + float best_medoid_score = kl_dist[i][medoids[0]]; + for (int j = 1; j < NUM_CLUSTERS; ++j) { + if (kl_dist[i][medoids[j]] < best_medoid_score) { + best_medoid = medoids[j]; + best_medoid_score = kl_dist[i][medoids[j]]; + } + } + assignment[i] = best_medoid; + current_score += best_medoid_score; + } + return current_score; +} + +void find_optimal_stream_assignment(int base) +{ + double inv_sum[64]; + for (unsigned i = 0; i < 64; ++i) { + double s = 0.0; + for (unsigned k = 0; k < 256; ++k) { + s += stats[i + base].freqs[k] + 0.5; + } + inv_sum[i] = 1.0 / s; + } + + for (unsigned i = 0; i < 64; ++i) { + for (unsigned j = 0; j < 64; ++j) { + double d = 0.0; + for (unsigned k = 0; k < 256; ++k) { + double p1 = (stats[i + base].freqs[k] + 0.5) * inv_sum[i]; + double p2 = (stats[j + base].freqs[k] + 0.5) * inv_sum[j]; + + // K-L divergence is asymmetric; this is a hack. + d += p1 * log(p1 / p2); + d += p2 * log(p2 / p1); + } + kl_dist[i][j] = d; + //printf("%.3f ", d); + } + //printf("\n"); + } + + // k-medoids init + int medoids[64]; // only the first NUM_CLUSTERS matter + bool is_medoid[64] = { false }; + std::iota(medoids, medoids + 64, 0); + std::random_device rd; + std::mt19937 g(rd()); + std::shuffle(medoids, medoids + 64, g); + for (int i = 0; i < NUM_CLUSTERS; ++i) { + printf("%d ", medoids[i]); + is_medoid[medoids[i]] = true; + } + printf("\n"); + + // assign each data point to the closest medoid + int assignment[64]; + double current_score = find_best_assignment(medoids, assignment); + + for (int i = 0; i < 1000; ++i) { + printf("iter %d\n", i); + bool any_changed = false; + for (int m = 0; m < NUM_CLUSTERS; ++m) { + for (int o = 0; o < 64; ++o) { + if (is_medoid[o]) continue; + int old_medoid = medoids[m]; + medoids[m] = o; + + int new_assignment[64]; + double candidate_score = find_best_assignment(medoids, new_assignment); + + if (candidate_score < current_score) { + current_score = candidate_score; + memcpy(assignment, new_assignment, sizeof(assignment)); + + is_medoid[old_medoid] = false; + is_medoid[medoids[m]] = true; + printf("%f: ", current_score); + for (int i = 0; i < 64; ++i) { + printf("%d ", assignment[i]); + } + printf("\n"); + any_changed = true; + } else { + medoids[m] = old_medoid; + } + } + } + if (!any_changed) break; + } + printf("\n"); + std::unordered_map rmap; + for (int i = 0; i < 64; ++i) { + if (i % 8 == 0) printf("\n"); + if (!rmap.count(assignment[i])) { + rmap.emplace(assignment[i], rmap.size()); + } + printf("%d, ", rmap[assignment[i]]); + } + printf("\n"); +} +#endif + int main(int argc, char **argv) { if (argc >= 2) @@ -620,9 +735,8 @@ int main(int argc, char **argv) } for (unsigned y = 0; y < 8; ++y) { for (unsigned x = 0; x < 8; ++x) { - SymbolStats &s_luma = stats[pick_stats_for(x, y)]; - SymbolStats &s_chroma = stats[pick_stats_for(x, y) + 8]; // HACK - //SymbolStats &s_chroma = stats[pick_stats_for(x, y)]; + SymbolStats &s_luma = stats[pick_stats_for(x, y, false)]; + SymbolStats &s_chroma = stats[pick_stats_for(x, y, true)]; // Luma for (unsigned yb = 0; yb < HEIGHT; yb += 8) { @@ -654,6 +768,15 @@ int main(int argc, char **argv) } } } + +#if FIND_OPTIMAL_STREAM_ASSIGNMENT + printf("Luma:\n"); + find_optimal_stream_assignment(0); + printf("Chroma:\n"); + find_optimal_stream_assignment(64); + exit(0); +#endif + for (unsigned i = 0; i < 64; ++i) { stats[i].freqs[255] /= 2; // zero, has no sign bits (yes, this is trickery) stats[i].normalize_freqs(prob_scale); @@ -685,7 +808,7 @@ int main(int argc, char **argv) // Luma for (unsigned y = 0; y < 8; ++y) { for (unsigned x = 0; x < 8; ++x) { - SymbolStats &s_luma = stats[pick_stats_for(x, y)]; + SymbolStats &s_luma = stats[pick_stats_for(x, y, false)]; rans_encoder.init_prob(s_luma); // Luma @@ -730,8 +853,7 @@ int main(int argc, char **argv) // Cb for (unsigned y = 0; y < 8; ++y) { for (unsigned x = 0; x < 8; ++x) { - SymbolStats &s_chroma = stats[pick_stats_for(x, y) + 8]; - //SymbolStats &s_chroma = stats[pick_stats_for(x, y)]; + SymbolStats &s_chroma = stats[pick_stats_for(x, y, true)]; rans_encoder.init_prob(s_chroma); rans_encoder.clear(); @@ -756,8 +878,7 @@ int main(int argc, char **argv) // Cr for (unsigned y = 0; y < 8; ++y) { for (unsigned x = 0; x < 8; ++x) { - SymbolStats &s_chroma = stats[pick_stats_for(x, y) + 8]; - //SymbolStats &s_chroma = stats[pick_stats_for(x, y)]; + SymbolStats &s_chroma = stats[pick_stats_for(x, y, true)]; rans_encoder.init_prob(s_chroma); rans_encoder.clear(); -- 2.39.2