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1 /*
2  * Copyright (C) 2007 Vitor Sessak <vitor1001@gmail.com>
3  *
4  * This file is part of FFmpeg.
5  *
6  * FFmpeg is free software; you can redistribute it and/or
7  * modify it under the terms of the GNU Lesser General Public
8  * License as published by the Free Software Foundation; either
9  * version 2.1 of the License, or (at your option) any later version.
10  *
11  * FFmpeg is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
14  * Lesser General Public License for more details.
15  *
16  * You should have received a copy of the GNU Lesser General Public
17  * License along with FFmpeg; if not, write to the Free Software
18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19  */
20 
21 /**
22  * @file
23  * Codebook Generator using the ELBG algorithm
24  */
25 
26 #include <string.h>
27 
28 #include "libavutil/avassert.h"
29 #include "libavutil/common.h"
30 #include "libavutil/lfg.h"
31 #include "elbg.h"
32 
33 #define DELTA_ERR_MAX 0.1  ///< Precision of the ELBG algorithm (as percentage error)
34 
35 /**
36  * In the ELBG jargon, a cell is the set of points that are closest to a
37  * codebook entry. Not to be confused with a RoQ Video cell. */
38 typedef struct cell_s {
39     int index;
40     struct cell_s *next;
41 } cell;
42 
43 /**
44  * ELBG internal data
45  */
46 typedef struct ELBGContext {
47     int64_t error;
48     int dim;
49     int num_cb;
50     int *codebook;
51     cell **cells;
52     int64_t *utility;
53     int64_t *utility_inc;
54     int *nearest_cb;
55     int *points;
56     int *temp_points;
57     int *size_part;
58     AVLFG *rand_state;
59     int *scratchbuf;
60     cell *cell_buffer;
61 
62     /* Sizes for the buffers above. Pointers without such a field
63      * are not allocated by us and only valid for the duration
64      * of a single call to avpriv_elbg_do(). */
65     unsigned utility_allocated;
66     unsigned utility_inc_allocated;
67     unsigned size_part_allocated;
68     unsigned cells_allocated;
69     unsigned scratchbuf_allocated;
70     unsigned cell_buffer_allocated;
71     unsigned temp_points_allocated;
72 } ELBGContext;
73 
distance_limited(int * a,int * b,int dim,int limit)74 static inline int distance_limited(int *a, int *b, int dim, int limit)
75 {
76     int i, dist=0;
77     for (i=0; i<dim; i++) {
78         dist += (a[i] - b[i])*(a[i] - b[i]);
79         if (dist > limit)
80             return INT_MAX;
81     }
82 
83     return dist;
84 }
85 
vect_division(int * res,int * vect,int div,int dim)86 static inline void vect_division(int *res, int *vect, int div, int dim)
87 {
88     int i;
89     if (div > 1)
90         for (i=0; i<dim; i++)
91             res[i] = ROUNDED_DIV(vect[i],div);
92     else if (res != vect)
93         memcpy(res, vect, dim*sizeof(int));
94 
95 }
96 
eval_error_cell(ELBGContext * elbg,int * centroid,cell * cells)97 static int eval_error_cell(ELBGContext *elbg, int *centroid, cell *cells)
98 {
99     int error=0;
100     for (; cells; cells=cells->next)
101         error += distance_limited(centroid, elbg->points + cells->index*elbg->dim, elbg->dim, INT_MAX);
102 
103     return error;
104 }
105 
get_closest_codebook(ELBGContext * elbg,int index)106 static int get_closest_codebook(ELBGContext *elbg, int index)
107 {
108     int pick = 0;
109     for (int i = 0, diff_min = INT_MAX; i < elbg->num_cb; i++)
110         if (i != index) {
111             int diff;
112             diff = distance_limited(elbg->codebook + i*elbg->dim, elbg->codebook + index*elbg->dim, elbg->dim, diff_min);
113             if (diff < diff_min) {
114                 pick = i;
115                 diff_min = diff;
116             }
117         }
118     return pick;
119 }
120 
get_high_utility_cell(ELBGContext * elbg)121 static int get_high_utility_cell(ELBGContext *elbg)
122 {
123     int i=0;
124     /* Using linear search, do binary if it ever turns to be speed critical */
125     uint64_t r;
126 
127     if (elbg->utility_inc[elbg->num_cb - 1] < INT_MAX) {
128         r = av_lfg_get(elbg->rand_state) % (unsigned int)elbg->utility_inc[elbg->num_cb - 1] + 1;
129     } else {
130         r = av_lfg_get(elbg->rand_state);
131         r = (av_lfg_get(elbg->rand_state) + (r<<32)) % elbg->utility_inc[elbg->num_cb - 1] + 1;
132     }
133 
134     while (elbg->utility_inc[i] < r) {
135         i++;
136     }
137 
138     av_assert2(elbg->cells[i]);
139 
140     return i;
141 }
142 
143 /**
144  * Implementation of the simple LBG algorithm for just two codebooks
145  */
simple_lbg(ELBGContext * elbg,int dim,int * centroid[3],int newutility[3],int * points,cell * cells)146 static int simple_lbg(ELBGContext *elbg,
147                       int dim,
148                       int *centroid[3],
149                       int newutility[3],
150                       int *points,
151                       cell *cells)
152 {
153     int i, idx;
154     int numpoints[2] = {0,0};
155     int *newcentroid[2] = {
156         elbg->scratchbuf + 3*dim,
157         elbg->scratchbuf + 4*dim
158     };
159     cell *tempcell;
160 
161     memset(newcentroid[0], 0, 2 * dim * sizeof(*newcentroid[0]));
162 
163     newutility[0] =
164     newutility[1] = 0;
165 
166     for (tempcell = cells; tempcell; tempcell=tempcell->next) {
167         idx = distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX)>=
168               distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX);
169         numpoints[idx]++;
170         for (i=0; i<dim; i++)
171             newcentroid[idx][i] += points[tempcell->index*dim + i];
172     }
173 
174     vect_division(centroid[0], newcentroid[0], numpoints[0], dim);
175     vect_division(centroid[1], newcentroid[1], numpoints[1], dim);
176 
177     for (tempcell = cells; tempcell; tempcell=tempcell->next) {
178         int dist[2] = {distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX),
179                        distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX)};
180         int idx = dist[0] > dist[1];
181         newutility[idx] += dist[idx];
182     }
183 
184     return newutility[0] + newutility[1];
185 }
186 
get_new_centroids(ELBGContext * elbg,int huc,int * newcentroid_i,int * newcentroid_p)187 static void get_new_centroids(ELBGContext *elbg, int huc, int *newcentroid_i,
188                               int *newcentroid_p)
189 {
190     cell *tempcell;
191     int *min = newcentroid_i;
192     int *max = newcentroid_p;
193     int i;
194 
195     for (i=0; i< elbg->dim; i++) {
196         min[i]=INT_MAX;
197         max[i]=0;
198     }
199 
200     for (tempcell = elbg->cells[huc]; tempcell; tempcell = tempcell->next)
201         for(i=0; i<elbg->dim; i++) {
202             min[i]=FFMIN(min[i], elbg->points[tempcell->index*elbg->dim + i]);
203             max[i]=FFMAX(max[i], elbg->points[tempcell->index*elbg->dim + i]);
204         }
205 
206     for (i=0; i<elbg->dim; i++) {
207         int ni = min[i] + (max[i] - min[i])/3;
208         int np = min[i] + (2*(max[i] - min[i]))/3;
209         newcentroid_i[i] = ni;
210         newcentroid_p[i] = np;
211     }
212 }
213 
214 /**
215  * Add the points in the low utility cell to its closest cell. Split the high
216  * utility cell, putting the separated points in the (now empty) low utility
217  * cell.
218  *
219  * @param elbg         Internal elbg data
220  * @param indexes      {luc, huc, cluc}
221  * @param newcentroid  A vector with the position of the new centroids
222  */
shift_codebook(ELBGContext * elbg,int * indexes,int * newcentroid[3])223 static void shift_codebook(ELBGContext *elbg, int *indexes,
224                            int *newcentroid[3])
225 {
226     cell *tempdata;
227     cell **pp = &elbg->cells[indexes[2]];
228 
229     while(*pp)
230         pp= &(*pp)->next;
231 
232     *pp = elbg->cells[indexes[0]];
233 
234     elbg->cells[indexes[0]] = NULL;
235     tempdata = elbg->cells[indexes[1]];
236     elbg->cells[indexes[1]] = NULL;
237 
238     while(tempdata) {
239         cell *tempcell2 = tempdata->next;
240         int idx = distance_limited(elbg->points + tempdata->index*elbg->dim,
241                            newcentroid[0], elbg->dim, INT_MAX) >
242                   distance_limited(elbg->points + tempdata->index*elbg->dim,
243                            newcentroid[1], elbg->dim, INT_MAX);
244 
245         tempdata->next = elbg->cells[indexes[idx]];
246         elbg->cells[indexes[idx]] = tempdata;
247         tempdata = tempcell2;
248     }
249 }
250 
evaluate_utility_inc(ELBGContext * elbg)251 static void evaluate_utility_inc(ELBGContext *elbg)
252 {
253     int64_t inc=0;
254 
255     for (int i = 0; i < elbg->num_cb; i++) {
256         if (elbg->num_cb * elbg->utility[i] > elbg->error)
257             inc += elbg->utility[i];
258         elbg->utility_inc[i] = inc;
259     }
260 }
261 
262 
update_utility_and_n_cb(ELBGContext * elbg,int idx,int newutility)263 static void update_utility_and_n_cb(ELBGContext *elbg, int idx, int newutility)
264 {
265     cell *tempcell;
266 
267     elbg->utility[idx] = newutility;
268     for (tempcell=elbg->cells[idx]; tempcell; tempcell=tempcell->next)
269         elbg->nearest_cb[tempcell->index] = idx;
270 }
271 
272 /**
273  * Evaluate if a shift lower the error. If it does, call shift_codebooks
274  * and update elbg->error, elbg->utility and elbg->nearest_cb.
275  *
276  * @param elbg  Internal elbg data
277  * @param idx   {luc (low utility cell, huc (high utility cell), cluc (closest cell to low utility cell)}
278  */
try_shift_candidate(ELBGContext * elbg,int idx[3])279 static void try_shift_candidate(ELBGContext *elbg, int idx[3])
280 {
281     int j, k, cont=0;
282     int64_t olderror=0, newerror;
283     int newutility[3];
284     int *newcentroid[3] = {
285         elbg->scratchbuf,
286         elbg->scratchbuf + elbg->dim,
287         elbg->scratchbuf + 2*elbg->dim
288     };
289     cell *tempcell;
290 
291     for (j=0; j<3; j++)
292         olderror += elbg->utility[idx[j]];
293 
294     memset(newcentroid[2], 0, elbg->dim*sizeof(int));
295 
296     for (k=0; k<2; k++)
297         for (tempcell=elbg->cells[idx[2*k]]; tempcell; tempcell=tempcell->next) {
298             cont++;
299             for (j=0; j<elbg->dim; j++)
300                 newcentroid[2][j] += elbg->points[tempcell->index*elbg->dim + j];
301         }
302 
303     vect_division(newcentroid[2], newcentroid[2], cont, elbg->dim);
304 
305     get_new_centroids(elbg, idx[1], newcentroid[0], newcentroid[1]);
306 
307     newutility[2]  = eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[0]]);
308     newutility[2] += eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[2]]);
309 
310     newerror = newutility[2];
311 
312     newerror += simple_lbg(elbg, elbg->dim, newcentroid, newutility, elbg->points,
313                            elbg->cells[idx[1]]);
314 
315     if (olderror > newerror) {
316         shift_codebook(elbg, idx, newcentroid);
317 
318         elbg->error += newerror - olderror;
319 
320         for (j=0; j<3; j++)
321             update_utility_and_n_cb(elbg, idx[j], newutility[j]);
322 
323         evaluate_utility_inc(elbg);
324     }
325  }
326 
327 /**
328  * Implementation of the ELBG block
329  */
do_shiftings(ELBGContext * elbg)330 static void do_shiftings(ELBGContext *elbg)
331 {
332     int idx[3];
333 
334     evaluate_utility_inc(elbg);
335 
336     for (idx[0]=0; idx[0] < elbg->num_cb; idx[0]++)
337         if (elbg->num_cb * elbg->utility[idx[0]] < elbg->error) {
338             if (elbg->utility_inc[elbg->num_cb - 1] == 0)
339                 return;
340 
341             idx[1] = get_high_utility_cell(elbg);
342             idx[2] = get_closest_codebook(elbg, idx[0]);
343 
344             if (idx[1] != idx[0] && idx[1] != idx[2])
345                 try_shift_candidate(elbg, idx);
346         }
347 }
348 
do_elbg(ELBGContext * av_restrict elbg,int * points,int numpoints,int max_steps)349 static void do_elbg(ELBGContext *av_restrict elbg, int *points, int numpoints,
350                     int max_steps)
351 {
352     int *const size_part = elbg->size_part;
353     int i, j, steps = 0;
354     int best_idx = 0;
355     int64_t last_error;
356 
357     elbg->error = INT64_MAX;
358     elbg->points = points;
359 
360     do {
361         cell *free_cells = elbg->cell_buffer;
362         last_error = elbg->error;
363         steps++;
364         memset(elbg->utility, 0, elbg->num_cb * sizeof(*elbg->utility));
365         memset(elbg->cells,   0, elbg->num_cb * sizeof(*elbg->cells));
366 
367         elbg->error = 0;
368 
369         /* This loop evaluate the actual Voronoi partition. It is the most
370            costly part of the algorithm. */
371         for (i=0; i < numpoints; i++) {
372             int best_dist = distance_limited(elbg->points   + i * elbg->dim,
373                                              elbg->codebook + best_idx * elbg->dim,
374                                              elbg->dim, INT_MAX);
375             for (int k = 0; k < elbg->num_cb; k++) {
376                 int dist = distance_limited(elbg->points   + i * elbg->dim,
377                                             elbg->codebook + k * elbg->dim,
378                                             elbg->dim, best_dist);
379                 if (dist < best_dist) {
380                     best_dist = dist;
381                     best_idx = k;
382                 }
383             }
384             elbg->nearest_cb[i] = best_idx;
385             elbg->error += best_dist;
386             elbg->utility[elbg->nearest_cb[i]] += best_dist;
387             free_cells->index = i;
388             free_cells->next = elbg->cells[elbg->nearest_cb[i]];
389             elbg->cells[elbg->nearest_cb[i]] = free_cells;
390             free_cells++;
391         }
392 
393         do_shiftings(elbg);
394 
395         memset(size_part,      0, elbg->num_cb * sizeof(*size_part));
396 
397         memset(elbg->codebook, 0, elbg->num_cb * elbg->dim * sizeof(*elbg->codebook));
398 
399         for (i=0; i < numpoints; i++) {
400             size_part[elbg->nearest_cb[i]]++;
401             for (j=0; j < elbg->dim; j++)
402                 elbg->codebook[elbg->nearest_cb[i]*elbg->dim + j] +=
403                     elbg->points[i*elbg->dim + j];
404         }
405 
406         for (int i = 0; i < elbg->num_cb; i++)
407             vect_division(elbg->codebook + i*elbg->dim,
408                           elbg->codebook + i*elbg->dim, size_part[i], elbg->dim);
409 
410     } while(((last_error - elbg->error) > DELTA_ERR_MAX*elbg->error) &&
411             (steps < max_steps));
412 }
413 
414 #define BIG_PRIME 433494437LL
415 
416 /**
417  * Initialize the codebook vector for the elbg algorithm.
418  * If numpoints <= 24 * num_cb this function fills codebook with random numbers.
419  * If not, it calls do_elbg for a (smaller) random sample of the points in
420  * points.
421  */
init_elbg(ELBGContext * av_restrict elbg,int * points,int * temp_points,int numpoints,int max_steps)422 static void init_elbg(ELBGContext *av_restrict elbg, int *points, int *temp_points,
423                       int numpoints, int max_steps)
424 {
425     int dim = elbg->dim;
426 
427     if (numpoints > 24LL * elbg->num_cb) {
428         /* ELBG is very costly for a big number of points. So if we have a lot
429            of them, get a good initial codebook to save on iterations       */
430         for (int i = 0; i < numpoints / 8; i++) {
431             int k = (i*BIG_PRIME) % numpoints;
432             memcpy(temp_points + i*dim, points + k*dim, dim * sizeof(*temp_points));
433         }
434 
435         /* If anything is changed in the recursion parameters,
436          * the allocated size of temp_points will also need to be updated. */
437         init_elbg(elbg, temp_points, temp_points + numpoints / 8 * dim,
438                   numpoints / 8, 2 * max_steps);
439         do_elbg(elbg, temp_points, numpoints / 8, 2 * max_steps);
440     } else  // If not, initialize the codebook with random positions
441         for (int i = 0; i < elbg->num_cb; i++)
442             memcpy(elbg->codebook + i * dim, points + ((i*BIG_PRIME)%numpoints)*dim,
443                    dim * sizeof(*elbg->codebook));
444 }
445 
avpriv_elbg_do(ELBGContext ** elbgp,int * points,int dim,int numpoints,int * codebook,int num_cb,int max_steps,int * closest_cb,AVLFG * rand_state,uintptr_t flags)446 int avpriv_elbg_do(ELBGContext **elbgp, int *points, int dim, int numpoints,
447                    int *codebook, int num_cb, int max_steps,
448                    int *closest_cb, AVLFG *rand_state, uintptr_t flags)
449 {
450     ELBGContext *const av_restrict elbg = *elbgp ? *elbgp : av_mallocz(sizeof(*elbg));
451 
452     if (!elbg)
453         return AVERROR(ENOMEM);
454     *elbgp = elbg;
455 
456     elbg->nearest_cb = closest_cb;
457     elbg->rand_state = rand_state;
458     elbg->codebook   = codebook;
459     elbg->num_cb     = num_cb;
460     elbg->dim        = dim;
461 
462 #define ALLOCATE_IF_NECESSARY(field, new_elements, multiplicator)            \
463     if (elbg->field ## _allocated < new_elements) {                          \
464         av_freep(&elbg->field);                                              \
465         elbg->field = av_malloc_array(new_elements,                          \
466                                       multiplicator * sizeof(*elbg->field)); \
467         if (!elbg->field) {                                                  \
468             elbg->field ## _allocated = 0;                                   \
469             return AVERROR(ENOMEM);                                          \
470         }                                                                    \
471         elbg->field ## _allocated = new_elements;                            \
472     }
473     /* Allocating the buffers for do_elbg() here once relies
474      * on their size being always the same even when do_elbg()
475      * is called from init_elbg(). It also relies on do_elbg()
476      * never calling itself recursively. */
477     ALLOCATE_IF_NECESSARY(cells,       num_cb,    1)
478     ALLOCATE_IF_NECESSARY(utility,     num_cb,    1)
479     ALLOCATE_IF_NECESSARY(utility_inc, num_cb,    1)
480     ALLOCATE_IF_NECESSARY(size_part,   num_cb,    1)
481     ALLOCATE_IF_NECESSARY(cell_buffer, numpoints, 1)
482     ALLOCATE_IF_NECESSARY(scratchbuf,  dim,       5)
483     if (numpoints > 24LL * elbg->num_cb) {
484         /* The first step in the recursion in init_elbg() needs a buffer with
485         * (numpoints / 8) * dim elements; the next step needs numpoints / 8 / 8
486         * * dim elements etc. The geometric series leads to an upper bound of
487         * numpoints / 8 * 8 / 7 * dim elements. */
488         uint64_t prod = dim * (uint64_t)(numpoints / 7U);
489         if (prod > INT_MAX)
490             return AVERROR(ERANGE);
491         ALLOCATE_IF_NECESSARY(temp_points, prod, 1)
492     }
493 
494     init_elbg(elbg, points, elbg->temp_points, numpoints, max_steps);
495     do_elbg (elbg, points, numpoints, max_steps);
496     return 0;
497 }
498 
avpriv_elbg_free(ELBGContext ** elbgp)499 av_cold void avpriv_elbg_free(ELBGContext **elbgp)
500 {
501     ELBGContext *elbg = *elbgp;
502     if (!elbg)
503         return;
504 
505     av_freep(&elbg->size_part);
506     av_freep(&elbg->utility);
507     av_freep(&elbg->cell_buffer);
508     av_freep(&elbg->cells);
509     av_freep(&elbg->utility_inc);
510     av_freep(&elbg->scratchbuf);
511     av_freep(&elbg->temp_points);
512 
513     av_freep(elbgp);
514 }
515