Coverage Report

Created: 2018-06-24 14:39

/Users/buildslave/jenkins/workspace/clang-stage2-coverage-R/llvm/tools/polly/lib/External/isl/isl_sample.c
Line
Count
Source (jump to first uncovered line)
1
/*
2
 * Copyright 2008-2009 Katholieke Universiteit Leuven
3
 *
4
 * Use of this software is governed by the MIT license
5
 *
6
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8
 */
9
10
#include <isl_ctx_private.h>
11
#include <isl_map_private.h>
12
#include "isl_sample.h"
13
#include <isl/vec.h>
14
#include <isl/mat.h>
15
#include <isl_seq.h>
16
#include "isl_equalities.h"
17
#include "isl_tab.h"
18
#include "isl_basis_reduction.h"
19
#include <isl_factorization.h>
20
#include <isl_point_private.h>
21
#include <isl_options_private.h>
22
#include <isl_vec_private.h>
23
24
#include <bset_from_bmap.c>
25
#include <set_to_map.c>
26
27
static __isl_give isl_vec *empty_sample(__isl_take isl_basic_set *bset)
28
481
{
29
481
  struct isl_vec *vec;
30
481
31
481
  vec = isl_vec_alloc(bset->ctx, 0);
32
481
  isl_basic_set_free(bset);
33
481
  return vec;
34
481
}
35
36
/* Construct a zero sample of the same dimension as bset.
37
 * As a special case, if bset is zero-dimensional, this
38
 * function creates a zero-dimensional sample point.
39
 */
40
static __isl_give isl_vec *zero_sample(__isl_take isl_basic_set *bset)
41
63.2k
{
42
63.2k
  unsigned dim;
43
63.2k
  struct isl_vec *sample;
44
63.2k
45
63.2k
  dim = isl_basic_set_total_dim(bset);
46
63.2k
  sample = isl_vec_alloc(bset->ctx, 1 + dim);
47
63.2k
  if (sample) {
48
63.2k
    isl_int_set_si(sample->el[0], 1);
49
63.2k
    isl_seq_clr(sample->el + 1, dim);
50
63.2k
  }
51
63.2k
  isl_basic_set_free(bset);
52
63.2k
  return sample;
53
63.2k
}
54
55
static __isl_give isl_vec *interval_sample(__isl_take isl_basic_set *bset)
56
171k
{
57
171k
  int i;
58
171k
  isl_int t;
59
171k
  struct isl_vec *sample;
60
171k
61
171k
  bset = isl_basic_set_simplify(bset);
62
171k
  if (!bset)
63
0
    return NULL;
64
171k
  if (isl_basic_set_plain_is_empty(bset))
65
0
    return empty_sample(bset);
66
171k
  if (bset->n_eq == 0 && 
bset->n_ineq == 0171k
)
67
8.14k
    return zero_sample(bset);
68
163k
69
163k
  sample = isl_vec_alloc(bset->ctx, 2);
70
163k
  if (!sample)
71
0
    goto error;
72
163k
  if (!bset)
73
0
    return NULL;
74
163k
  isl_int_set_si(sample->block.data[0], 1);
75
163k
76
163k
  if (bset->n_eq > 0) {
77
959
    isl_assert(bset->ctx, bset->n_eq == 1, goto error);
78
959
    isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
79
959
    if (isl_int_is_one(bset->eq[0][1]))
80
959
      isl_int_neg(sample->el[1], bset->eq[0][0]);
81
959
    else {
82
0
      isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
83
0
           goto error);
84
0
      isl_int_set(sample->el[1], bset->eq[0][0]);
85
0
    }
86
959
    isl_basic_set_free(bset);
87
959
    return sample;
88
162k
  }
89
162k
90
162k
  isl_int_init(t);
91
162k
  if (isl_int_is_one(bset->ineq[0][1]))
92
162k
    
isl_int_neg141k
(sample->block.data[1], bset->ineq[0][0]);
93
162k
  else
94
162k
    
isl_int_set21.3k
(sample->block.data[1], bset->ineq[0][0]);
95
316k
  for (i = 1; i < bset->n_ineq; 
++i153k
) {
96
153k
    isl_seq_inner_product(sample->block.data,
97
153k
          bset->ineq[i], 2, &t);
98
153k
    if (isl_int_is_neg(t))
99
153k
      
break0
;
100
153k
  }
101
162k
  isl_int_clear(t);
102
162k
  if (i < bset->n_ineq) {
103
0
    isl_vec_free(sample);
104
0
    return empty_sample(bset);
105
0
  }
106
162k
107
162k
  isl_basic_set_free(bset);
108
162k
  return sample;
109
0
error:
110
0
  isl_basic_set_free(bset);
111
0
  isl_vec_free(sample);
112
0
  return NULL;
113
162k
}
114
115
/* Find a sample integer point, if any, in bset, which is known
116
 * to have equalities.  If bset contains no integer points, then
117
 * return a zero-length vector.
118
 * We simply remove the known equalities, compute a sample
119
 * in the resulting bset, using the specified recurse function,
120
 * and then transform the sample back to the original space.
121
 */
122
static __isl_give isl_vec *sample_eq(__isl_take isl_basic_set *bset,
123
  __isl_give isl_vec *(*recurse)(__isl_take isl_basic_set *))
124
91.0k
{
125
91.0k
  struct isl_mat *T;
126
91.0k
  struct isl_vec *sample;
127
91.0k
128
91.0k
  if (!bset)
129
0
    return NULL;
130
91.0k
131
91.0k
  bset = isl_basic_set_remove_equalities(bset, &T, NULL);
132
91.0k
  sample = recurse(bset);
133
91.0k
  if (!sample || sample->size == 0)
134
1.60k
    isl_mat_free(T);
135
89.4k
  else
136
89.4k
    sample = isl_mat_vec_product(T, sample);
137
91.0k
  return sample;
138
91.0k
}
139
140
/* Return a matrix containing the equalities of the tableau
141
 * in constraint form.  The tableau is assumed to have
142
 * an associated bset that has been kept up-to-date.
143
 */
144
static struct isl_mat *tab_equalities(struct isl_tab *tab)
145
1.60k
{
146
1.60k
  int i, j;
147
1.60k
  int n_eq;
148
1.60k
  struct isl_mat *eq;
149
1.60k
  struct isl_basic_set *bset;
150
1.60k
151
1.60k
  if (!tab)
152
0
    return NULL;
153
1.60k
154
1.60k
  bset = isl_tab_peek_bset(tab);
155
1.60k
  isl_assert(tab->mat->ctx, bset, return NULL);
156
1.60k
157
1.60k
  n_eq = tab->n_var - tab->n_col + tab->n_dead;
158
1.60k
  if (tab->empty || n_eq == 0)
159
367
    return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
160
1.23k
  if (n_eq == tab->n_var)
161
0
    return isl_mat_identity(tab->mat->ctx, tab->n_var);
162
1.23k
163
1.23k
  eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
164
1.23k
  if (!eq)
165
0
    return NULL;
166
12.4k
  
for (i = 0, j = 0; 1.23k
i < tab->n_con;
++i11.1k
) {
167
11.1k
    if (tab->con[i].is_row)
168
6.91k
      continue;
169
4.27k
    if (tab->con[i].index >= 0 && 
tab->con[i].index >= tab->n_dead2.59k
)
170
2.00k
      continue;
171
2.27k
    if (i < bset->n_eq)
172
496
      isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
173
1.77k
    else
174
1.77k
      isl_seq_cpy(eq->row[j],
175
1.77k
            bset->ineq[i - bset->n_eq] + 1, tab->n_var);
176
2.27k
    ++j;
177
2.27k
  }
178
1.23k
  isl_assert(bset->ctx, j == n_eq, goto error);
179
1.23k
  return eq;
180
0
error:
181
0
  isl_mat_free(eq);
182
0
  return NULL;
183
1.23k
}
184
185
/* Compute and return an initial basis for the bounded tableau "tab".
186
 *
187
 * If the tableau is either full-dimensional or zero-dimensional,
188
 * the we simply return an identity matrix.
189
 * Otherwise, we construct a basis whose first directions correspond
190
 * to equalities.
191
 */
192
static struct isl_mat *initial_basis(struct isl_tab *tab)
193
119k
{
194
119k
  int n_eq;
195
119k
  struct isl_mat *eq;
196
119k
  struct isl_mat *Q;
197
119k
198
119k
  tab->n_unbounded = 0;
199
119k
  tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
200
119k
  if (tab->empty || n_eq == 0 || 
n_eq == tab->n_var1.17k
)
201
119k
    return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
202
778
203
778
  eq = tab_equalities(tab);
204
778
  eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
205
778
  if (!eq)
206
0
    return NULL;
207
778
  isl_mat_free(eq);
208
778
209
778
  Q = isl_mat_lin_to_aff(Q);
210
778
  return Q;
211
778
}
212
213
/* Compute the minimum of the current ("level") basis row over "tab"
214
 * and store the result in position "level" of "min".
215
 *
216
 * This function assumes that at least one more row and at least
217
 * one more element in the constraint array are available in the tableau.
218
 */
219
static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
220
  __isl_keep isl_vec *min, int level)
221
173k
{
222
173k
  return isl_tab_min(tab, tab->basis->row[1 + level],
223
173k
          ctx->one, &min->el[level], NULL, 0);
224
173k
}
225
226
/* Compute the maximum of the current ("level") basis row over "tab"
227
 * and store the result in position "level" of "max".
228
 *
229
 * This function assumes that at least one more row and at least
230
 * one more element in the constraint array are available in the tableau.
231
 */
232
static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
233
  __isl_keep isl_vec *max, int level)
234
61.2k
{
235
61.2k
  enum isl_lp_result res;
236
61.2k
  unsigned dim = tab->n_var;
237
61.2k
238
61.2k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
239
61.2k
        tab->basis->row[1 + level] + 1, dim);
240
61.2k
  res = isl_tab_min(tab, tab->basis->row[1 + level],
241
61.2k
        ctx->one, &max->el[level], NULL, 0);
242
61.2k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
243
61.2k
        tab->basis->row[1 + level] + 1, dim);
244
61.2k
  isl_int_neg(max->el[level], max->el[level]);
245
61.2k
246
61.2k
  return res;
247
61.2k
}
248
249
/* Perform a greedy search for an integer point in the set represented
250
 * by "tab", given that the minimal rational value (rounded up to the
251
 * nearest integer) at "level" is smaller than the maximal rational
252
 * value (rounded down to the nearest integer).
253
 *
254
 * Return 1 if we have found an integer point (if tab->n_unbounded > 0
255
 * then we may have only found integer values for the bounded dimensions
256
 * and it is the responsibility of the caller to extend this solution
257
 * to the unbounded dimensions).
258
 * Return 0 if greedy search did not result in a solution.
259
 * Return -1 if some error occurred.
260
 *
261
 * We assign a value half-way between the minimum and the maximum
262
 * to the current dimension and check if the minimal value of the
263
 * next dimension is still smaller than (or equal) to the maximal value.
264
 * We continue this process until either
265
 * - the minimal value (rounded up) is greater than the maximal value
266
 *  (rounded down).  In this case, greedy search has failed.
267
 * - we have exhausted all bounded dimensions, meaning that we have
268
 *  found a solution.
269
 * - the sample value of the tableau is integral.
270
 * - some error has occurred.
271
 */
272
static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
273
  __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
274
14.8k
{
275
14.8k
  struct isl_tab_undo *snap;
276
14.8k
  enum isl_lp_result res;
277
14.8k
278
14.8k
  snap = isl_tab_snap(tab);
279
14.8k
280
49.0k
  do {
281
49.0k
    isl_int_add(tab->basis->row[1 + level][0],
282
49.0k
          min->el[level], max->el[level]);
283
49.0k
    isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
284
49.0k
          tab->basis->row[1 + level][0], 2);
285
49.0k
    isl_int_neg(tab->basis->row[1 + level][0],
286
49.0k
          tab->basis->row[1 + level][0]);
287
49.0k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
288
0
      return -1;
289
49.0k
    isl_int_set_si(tab->basis->row[1 + level][0], 0);
290
49.0k
291
49.0k
    if (++level >= tab->n_var - tab->n_unbounded)
292
4.66k
      return 1;
293
44.4k
    if (isl_tab_sample_is_integer(tab))
294
6.72k
      return 1;
295
37.7k
296
37.7k
    res = compute_min(ctx, tab, min, level);
297
37.7k
    if (res == isl_lp_error)
298
0
      return -1;
299
37.7k
    if (res != isl_lp_ok)
300
37.7k
      
isl_die0
(ctx, isl_error_internal,
301
37.7k
        "expecting bounded rational solution",
302
37.7k
        return -1);
303
37.7k
    res = compute_max(ctx, tab, max, level);
304
37.7k
    if (res == isl_lp_error)
305
0
      return -1;
306
37.7k
    if (res != isl_lp_ok)
307
37.7k
      
isl_die0
(ctx, isl_error_internal,
308
37.7k
        "expecting bounded rational solution",
309
37.7k
        return -1);
310
37.7k
  } while (isl_int_le(min->el[level], max->el[level]));
311
14.8k
312
14.8k
  
if (3.45k
isl_tab_rollback(tab, snap) < 03.45k
)
313
0
    return -1;
314
3.45k
315
3.45k
  return 0;
316
3.45k
}
317
318
/* Given a tableau representing a set, find and return
319
 * an integer point in the set, if there is any.
320
 *
321
 * We perform a depth first search
322
 * for an integer point, by scanning all possible values in the range
323
 * attained by a basis vector, where an initial basis may have been set
324
 * by the calling function.  Otherwise an initial basis that exploits
325
 * the equalities in the tableau is created.
326
 * tab->n_zero is currently ignored and is clobbered by this function.
327
 *
328
 * The tableau is allowed to have unbounded direction, but then
329
 * the calling function needs to set an initial basis, with the
330
 * unbounded directions last and with tab->n_unbounded set
331
 * to the number of unbounded directions.
332
 * Furthermore, the calling functions needs to add shifted copies
333
 * of all constraints involving unbounded directions to ensure
334
 * that any feasible rational value in these directions can be rounded
335
 * up to yield a feasible integer value.
336
 * In particular, let B define the given basis x' = B x
337
 * and let T be the inverse of B, i.e., X = T x'.
338
 * Let a x + c >= 0 be a constraint of the set represented by the tableau,
339
 * or a T x' + c >= 0 in terms of the given basis.  Assume that
340
 * the bounded directions have an integer value, then we can safely
341
 * round up the values for the unbounded directions if we make sure
342
 * that x' not only satisfies the original constraint, but also
343
 * the constraint "a T x' + c + s >= 0" with s the sum of all
344
 * negative values in the last n_unbounded entries of "a T".
345
 * The calling function therefore needs to add the constraint
346
 * a x + c + s >= 0.  The current function then scans the first
347
 * directions for an integer value and once those have been found,
348
 * it can compute "T ceil(B x)" to yield an integer point in the set.
349
 * Note that during the search, the first rows of B may be changed
350
 * by a basis reduction, but the last n_unbounded rows of B remain
351
 * unaltered and are also not mixed into the first rows.
352
 *
353
 * The search is implemented iteratively.  "level" identifies the current
354
 * basis vector.  "init" is true if we want the first value at the current
355
 * level and false if we want the next value.
356
 *
357
 * At the start of each level, we first check if we can find a solution
358
 * using greedy search.  If not, we continue with the exhaustive search.
359
 *
360
 * The initial basis is the identity matrix.  If the range in some direction
361
 * contains more than one integer value, we perform basis reduction based
362
 * on the value of ctx->opt->gbr
363
 *  - ISL_GBR_NEVER:  never perform basis reduction
364
 *  - ISL_GBR_ONCE:   only perform basis reduction the first
365
 *        time such a range is encountered
366
 *  - ISL_GBR_ALWAYS: always perform basis reduction when
367
 *        such a range is encountered
368
 *
369
 * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
370
 * reduction computation to return early.  That is, as soon as it
371
 * finds a reasonable first direction.
372
 */ 
373
struct isl_vec *isl_tab_sample(struct isl_tab *tab)
374
138k
{
375
138k
  unsigned dim;
376
138k
  unsigned gbr;
377
138k
  struct isl_ctx *ctx;
378
138k
  struct isl_vec *sample;
379
138k
  struct isl_vec *min;
380
138k
  struct isl_vec *max;
381
138k
  enum isl_lp_result res;
382
138k
  int level;
383
138k
  int init;
384
138k
  int reduced;
385
138k
  struct isl_tab_undo **snap;
386
138k
387
138k
  if (!tab)
388
0
    return NULL;
389
138k
  if (tab->empty)
390
10.5k
    return isl_vec_alloc(tab->mat->ctx, 0);
391
128k
392
128k
  if (!tab->basis)
393
119k
    tab->basis = initial_basis(tab);
394
128k
  if (!tab->basis)
395
0
    return NULL;
396
128k
  isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
397
128k
        return NULL);
398
128k
  isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
399
128k
        return NULL);
400
128k
401
128k
  ctx = tab->mat->ctx;
402
128k
  dim = tab->n_var;
403
128k
  gbr = ctx->opt->gbr;
404
128k
405
128k
  if (tab->n_unbounded == tab->n_var) {
406
0
    sample = isl_tab_get_sample_value(tab);
407
0
    sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
408
0
    sample = isl_vec_ceil(sample);
409
0
    sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
410
0
              sample);
411
0
    return sample;
412
0
  }
413
128k
414
128k
  if (isl_tab_extend_cons(tab, dim + 1) < 0)
415
0
    return NULL;
416
128k
417
128k
  min = isl_vec_alloc(ctx, dim);
418
128k
  max = isl_vec_alloc(ctx, dim);
419
128k
  snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
420
128k
421
128k
  if (!min || !max || !snap)
422
0
    goto error;
423
128k
424
128k
  level = 0;
425
128k
  init = 1;
426
128k
  reduced = 0;
427
128k
428
137k
  while (level >= 0) {
429
136k
    if (init) {
430
135k
      int choice;
431
135k
432
135k
      res = compute_min(ctx, tab, min, level);
433
135k
      if (res == isl_lp_error)
434
0
        goto error;
435
135k
      if (res != isl_lp_ok)
436
135k
        
isl_die0
(ctx, isl_error_internal,
437
135k
          "expecting bounded rational solution",
438
135k
          goto error);
439
135k
      if (isl_tab_sample_is_integer(tab))
440
111k
        break;
441
23.5k
      res = compute_max(ctx, tab, max, level);
442
23.5k
      if (res == isl_lp_error)
443
0
        goto error;
444
23.5k
      if (res != isl_lp_ok)
445
23.5k
        
isl_die0
(ctx, isl_error_internal,
446
23.5k
          "expecting bounded rational solution",
447
23.5k
          goto error);
448
23.5k
      if (isl_tab_sample_is_integer(tab))
449
4.34k
        break;
450
19.2k
      choice = isl_int_lt(min->el[level], max->el[level]);
451
19.2k
      if (choice) {
452
14.8k
        int g;
453
14.8k
        g = greedy_search(ctx, tab, min, max, level);
454
14.8k
        if (g < 0)
455
0
          goto error;
456
14.8k
        if (g)
457
11.3k
          break;
458
7.82k
      }
459
7.82k
      if (!reduced && 
choice5.90k
&&
460
7.82k
          
ctx->opt->gbr != 3.12k
ISL_GBR_NEVER3.12k
) {
461
3.12k
        unsigned gbr_only_first;
462
3.12k
        if (ctx->opt->gbr == ISL_GBR_ONCE)
463
3.12k
          
ctx->opt->gbr = 0
ISL_GBR_NEVER0
;
464
3.12k
        tab->n_zero = level;
465
3.12k
        gbr_only_first = ctx->opt->gbr_only_first;
466
3.12k
        ctx->opt->gbr_only_first =
467
3.12k
          ctx->opt->gbr == ISL_GBR_ALWAYS;
468
3.12k
        tab = isl_tab_compute_reduced_basis(tab);
469
3.12k
        ctx->opt->gbr_only_first = gbr_only_first;
470
3.12k
        if (!tab || !tab->basis)
471
0
          goto error;
472
3.12k
        reduced = 1;
473
3.12k
        continue;
474
3.12k
      }
475
4.69k
      reduced = 0;
476
4.69k
      snap[level] = isl_tab_snap(tab);
477
4.69k
    } else
478
136k
      
isl_int_add_ui1.37k
(min->el[level], min->el[level], 1);
479
136k
480
136k
    
if (6.07k
isl_int_gt6.07k
(min->el[level], max->el[level])) {
481
2.25k
      level--;
482
2.25k
      init = 0;
483
2.25k
      if (level >= 0)
484
1.37k
        if (isl_tab_rollback(tab, snap[level]) < 0)
485
0
          goto error;
486
2.25k
      continue;
487
2.25k
    }
488
3.82k
    isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
489
3.82k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
490
0
      goto error;
491
3.82k
    isl_int_set_si(tab->basis->row[1 + level][0], 0);
492
3.82k
    if (level + tab->n_unbounded < dim - 1) {
493
3.81k
      ++level;
494
3.81k
      init = 1;
495
3.81k
      continue;
496
3.81k
    }
497
11
    break;
498
11
  }
499
128k
500
128k
  if (level >= 0) {
501
127k
    sample = isl_tab_get_sample_value(tab);
502
127k
    if (!sample)
503
0
      goto error;
504
127k
    if (tab->n_unbounded && 
!754
isl_int_is_one754
(sample->el[0])) {
505
188
      sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
506
188
                 sample);
507
188
      sample = isl_vec_ceil(sample);
508
188
      sample = isl_mat_vec_inverse_product(
509
188
          isl_mat_copy(tab->basis), sample);
510
188
    }
511
127k
  } else
512
876
    sample = isl_vec_alloc(ctx, 0);
513
128k
514
128k
  ctx->opt->gbr = gbr;
515
128k
  isl_vec_free(min);
516
128k
  isl_vec_free(max);
517
128k
  free(snap);
518
128k
  return sample;
519
0
error:
520
0
  ctx->opt->gbr = gbr;
521
0
  isl_vec_free(min);
522
0
  isl_vec_free(max);
523
0
  free(snap);
524
0
  return NULL;
525
128k
}
526
527
static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_set *bset);
528
529
/* Compute a sample point of the given basic set, based on the given,
530
 * non-trivial factorization.
531
 */
532
static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
533
  __isl_take isl_factorizer *f)
534
46.2k
{
535
46.2k
  int i, n;
536
46.2k
  isl_vec *sample = NULL;
537
46.2k
  isl_ctx *ctx;
538
46.2k
  unsigned nparam;
539
46.2k
  unsigned nvar;
540
46.2k
541
46.2k
  ctx = isl_basic_set_get_ctx(bset);
542
46.2k
  if (!ctx)
543
0
    goto error;
544
46.2k
545
46.2k
  nparam = isl_basic_set_dim(bset, isl_dim_param);
546
46.2k
  nvar = isl_basic_set_dim(bset, isl_dim_set);
547
46.2k
548
46.2k
  sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
549
46.2k
  if (!sample)
550
0
    goto error;
551
46.2k
  isl_int_set_si(sample->el[0], 1);
552
46.2k
553
46.2k
  bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
554
46.2k
555
227k
  for (i = 0, n = 0; i < f->n_group; 
++i181k
) {
556
181k
    isl_basic_set *bset_i;
557
181k
    isl_vec *sample_i;
558
181k
559
181k
    bset_i = isl_basic_set_copy(bset);
560
181k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
561
181k
          nparam + n + f->len[i], nvar - n - f->len[i]);
562
181k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
563
181k
          nparam, n);
564
181k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
565
181k
          n + f->len[i], nvar - n - f->len[i]);
566
181k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
567
181k
568
181k
    sample_i = sample_bounded(bset_i);
569
181k
    if (!sample_i)
570
0
      goto error;
571
181k
    if (sample_i->size == 0) {
572
451
      isl_basic_set_free(bset);
573
451
      isl_factorizer_free(f);
574
451
      isl_vec_free(sample);
575
451
      return sample_i;
576
451
    }
577
181k
    isl_seq_cpy(sample->el + 1 + nparam + n,
578
181k
          sample_i->el + 1, f->len[i]);
579
181k
    isl_vec_free(sample_i);
580
181k
581
181k
    n += f->len[i];
582
181k
  }
583
46.2k
584
46.2k
  f->morph = isl_morph_inverse(f->morph);
585
45.7k
  sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
586
45.7k
587
45.7k
  isl_basic_set_free(bset);
588
45.7k
  isl_factorizer_free(f);
589
45.7k
  return sample;
590
0
error:
591
0
  isl_basic_set_free(bset);
592
0
  isl_factorizer_free(f);
593
0
  isl_vec_free(sample);
594
0
  return NULL;
595
46.2k
}
596
597
/* Given a basic set that is known to be bounded, find and return
598
 * an integer point in the basic set, if there is any.
599
 *
600
 * After handling some trivial cases, we construct a tableau
601
 * and then use isl_tab_sample to find a sample, passing it
602
 * the identity matrix as initial basis.
603
 */ 
604
static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_set *bset)
605
311k
{
606
311k
  unsigned dim;
607
311k
  struct isl_vec *sample;
608
311k
  struct isl_tab *tab = NULL;
609
311k
  isl_factorizer *f;
610
311k
611
311k
  if (!bset)
612
0
    return NULL;
613
311k
614
311k
  if (isl_basic_set_plain_is_empty(bset))
615
44
    return empty_sample(bset);
616
311k
617
311k
  dim = isl_basic_set_total_dim(bset);
618
311k
  if (dim == 0)
619
51.3k
    return zero_sample(bset);
620
260k
  if (dim == 1)
621
142k
    return interval_sample(bset);
622
117k
  if (bset->n_eq > 0)
623
1.11k
    return sample_eq(bset, sample_bounded);
624
116k
625
116k
  f = isl_basic_set_factorizer(bset);
626
116k
  if (!f)
627
0
    goto error;
628
116k
  if (f->n_group != 0)
629
46.2k
    return factored_sample(bset, f);
630
70.3k
  isl_factorizer_free(f);
631
70.3k
632
70.3k
  tab = isl_tab_from_basic_set(bset, 1);
633
70.3k
  if (tab && tab->empty) {
634
4.07k
    isl_tab_free(tab);
635
4.07k
    ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
636
4.07k
    sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
637
4.07k
    isl_basic_set_free(bset);
638
4.07k
    return sample;
639
4.07k
  }
640
66.2k
641
66.2k
  if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
642
66.2k
    
if (66.1k
isl_tab_detect_implicit_equalities(tab) < 066.1k
)
643
0
      goto error;
644
66.2k
645
66.2k
  sample = isl_tab_sample(tab);
646
66.2k
  if (!sample)
647
0
    goto error;
648
66.2k
649
66.2k
  if (sample->size > 0) {
650
65.6k
    isl_vec_free(bset->sample);
651
65.6k
    bset->sample = isl_vec_copy(sample);
652
65.6k
  }
653
66.2k
654
66.2k
  isl_basic_set_free(bset);
655
66.2k
  isl_tab_free(tab);
656
66.2k
  return sample;
657
0
error:
658
0
  isl_basic_set_free(bset);
659
0
  isl_tab_free(tab);
660
0
  return NULL;
661
66.2k
}
662
663
/* Given a basic set "bset" and a value "sample" for the first coordinates
664
 * of bset, plug in these values and drop the corresponding coordinates.
665
 *
666
 * We do this by computing the preimage of the transformation
667
 *
668
 *       [ 1 0 ]
669
 *  x =  [ s 0 ] x'
670
 *       [ 0 I ]
671
 *
672
 * where [1 s] is the sample value and I is the identity matrix of the
673
 * appropriate dimension.
674
 */
675
static __isl_give isl_basic_set *plug_in(__isl_take isl_basic_set *bset,
676
  __isl_take isl_vec *sample)
677
107k
{
678
107k
  int i;
679
107k
  unsigned total;
680
107k
  struct isl_mat *T;
681
107k
682
107k
  if (!bset || !sample)
683
0
    goto error;
684
107k
685
107k
  total = isl_basic_set_total_dim(bset);
686
107k
  T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
687
107k
  if (!T)
688
0
    goto error;
689
107k
690
437k
  
for (i = 0; 107k
i < sample->size;
++i330k
) {
691
330k
    isl_int_set(T->row[i][0], sample->el[i]);
692
330k
    isl_seq_clr(T->row[i] + 1, T->n_col - 1);
693
330k
  }
694
497k
  for (i = 0; i < T->n_col - 1; 
++i389k
) {
695
389k
    isl_seq_clr(T->row[sample->size + i], T->n_col);
696
389k
    isl_int_set_si(T->row[sample->size + i][1 + i], 1);
697
389k
  }
698
107k
  isl_vec_free(sample);
699
107k
700
107k
  bset = isl_basic_set_preimage(bset, T);
701
107k
  return bset;
702
0
error:
703
0
  isl_basic_set_free(bset);
704
0
  isl_vec_free(sample);
705
0
  return NULL;
706
107k
}
707
708
/* Given a basic set "bset", return any (possibly non-integer) point
709
 * in the basic set.
710
 */
711
static __isl_give isl_vec *rational_sample(__isl_take isl_basic_set *bset)
712
110k
{
713
110k
  struct isl_tab *tab;
714
110k
  struct isl_vec *sample;
715
110k
716
110k
  if (!bset)
717
0
    return NULL;
718
110k
719
110k
  tab = isl_tab_from_basic_set(bset, 0);
720
110k
  sample = isl_tab_get_sample_value(tab);
721
110k
  isl_tab_free(tab);
722
110k
723
110k
  isl_basic_set_free(bset);
724
110k
725
110k
  return sample;
726
110k
}
727
728
/* Given a linear cone "cone" and a rational point "vec",
729
 * construct a polyhedron with shifted copies of the constraints in "cone",
730
 * i.e., a polyhedron with "cone" as its recession cone, such that each
731
 * point x in this polyhedron is such that the unit box positioned at x
732
 * lies entirely inside the affine cone 'vec + cone'.
733
 * Any rational point in this polyhedron may therefore be rounded up
734
 * to yield an integer point that lies inside said affine cone.
735
 *
736
 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
737
 * point "vec" by v/d.
738
 * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
739
 * by <a_i, x> - b/d >= 0.
740
 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
741
 * We prefer this polyhedron over the actual affine cone because it doesn't
742
 * require a scaling of the constraints.
743
 * If each of the vertices of the unit cube positioned at x lies inside
744
 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
745
 * We therefore impose that x' = x + \sum e_i, for any selection of unit
746
 * vectors lies inside the polyhedron, i.e.,
747
 *
748
 *  <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
749
 *
750
 * The most stringent of these constraints is the one that selects
751
 * all negative a_i, so the polyhedron we are looking for has constraints
752
 *
753
 *  <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
754
 *
755
 * Note that if cone were known to have only non-negative rays
756
 * (which can be accomplished by a unimodular transformation),
757
 * then we would only have to check the points x' = x + e_i
758
 * and we only have to add the smallest negative a_i (if any)
759
 * instead of the sum of all negative a_i.
760
 */
761
static __isl_give isl_basic_set *shift_cone(__isl_take isl_basic_set *cone,
762
  __isl_take isl_vec *vec)
763
3.20k
{
764
3.20k
  int i, j, k;
765
3.20k
  unsigned total;
766
3.20k
767
3.20k
  struct isl_basic_set *shift = NULL;
768
3.20k
769
3.20k
  if (!cone || !vec)
770
0
    goto error;
771
3.20k
772
3.20k
  isl_assert(cone->ctx, cone->n_eq == 0, goto error);
773
3.20k
774
3.20k
  total = isl_basic_set_total_dim(cone);
775
3.20k
776
3.20k
  shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
777
3.20k
          0, 0, cone->n_ineq);
778
3.20k
779
10.0k
  for (i = 0; i < cone->n_ineq; 
++i6.88k
) {
780
6.88k
    k = isl_basic_set_alloc_inequality(shift);
781
6.88k
    if (k < 0)
782
0
      goto error;
783
6.88k
    isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
784
6.88k
    isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
785
6.88k
              &shift->ineq[k][0]);
786
6.88k
    isl_int_cdiv_q(shift->ineq[k][0],
787
6.88k
             shift->ineq[k][0], vec->el[0]);
788
6.88k
    isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
789
25.6k
    for (j = 0; j < total; 
++j18.7k
) {
790
18.7k
      if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
791
18.7k
        
continue14.2k
;
792
4.45k
      isl_int_add(shift->ineq[k][0],
793
4.45k
            shift->ineq[k][0], shift->ineq[k][1 + j]);
794
4.45k
    }
795
6.88k
  }
796
3.20k
797
3.20k
  isl_basic_set_free(cone);
798
3.20k
  isl_vec_free(vec);
799
3.20k
800
3.20k
  return isl_basic_set_finalize(shift);
801
0
error:
802
0
  isl_basic_set_free(shift);
803
0
  isl_basic_set_free(cone);
804
0
  isl_vec_free(vec);
805
0
  return NULL;
806
3.20k
}
807
808
/* Given a rational point vec in a (transformed) basic set,
809
 * such that cone is the recession cone of the original basic set,
810
 * "round up" the rational point to an integer point.
811
 *
812
 * We first check if the rational point just happens to be integer.
813
 * If not, we transform the cone in the same way as the basic set,
814
 * pick a point x in this cone shifted to the rational point such that
815
 * the whole unit cube at x is also inside this affine cone.
816
 * Then we simply round up the coordinates of x and return the
817
 * resulting integer point.
818
 */
819
static __isl_give isl_vec *round_up_in_cone(__isl_take isl_vec *vec,
820
  __isl_take isl_basic_set *cone, __isl_take isl_mat *U)
821
107k
{
822
107k
  unsigned total;
823
107k
824
107k
  if (!vec || !cone || !U)
825
0
    goto error;
826
107k
827
107k
  isl_assert(vec->ctx, vec->size != 0, goto error);
828
107k
  if (isl_int_is_one(vec->el[0])) {
829
104k
    isl_mat_free(U);
830
104k
    isl_basic_set_free(cone);
831
104k
    return vec;
832
104k
  }
833
3.20k
834
3.20k
  total = isl_basic_set_total_dim(cone);
835
3.20k
  cone = isl_basic_set_preimage(cone, U);
836
3.20k
  cone = isl_basic_set_remove_dims(cone, isl_dim_set,
837
3.20k
           0, total - (vec->size - 1));
838
3.20k
839
3.20k
  cone = shift_cone(cone, vec);
840
3.20k
841
3.20k
  vec = rational_sample(cone);
842
3.20k
  vec = isl_vec_ceil(vec);
843
3.20k
  return vec;
844
0
error:
845
0
  isl_mat_free(U);
846
0
  isl_vec_free(vec);
847
0
  isl_basic_set_free(cone);
848
0
  return NULL;
849
3.20k
}
850
851
/* Concatenate two integer vectors, i.e., two vectors with denominator
852
 * (stored in element 0) equal to 1.
853
 */
854
static __isl_give isl_vec *vec_concat(__isl_take isl_vec *vec1,
855
  __isl_take isl_vec *vec2)
856
107k
{
857
107k
  struct isl_vec *vec;
858
107k
859
107k
  if (!vec1 || !vec2)
860
0
    goto error;
861
107k
  isl_assert(vec1->ctx, vec1->size > 0, goto error);
862
107k
  isl_assert(vec2->ctx, vec2->size > 0, goto error);
863
107k
  isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
864
107k
  isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
865
107k
866
107k
  vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
867
107k
  if (!vec)
868
0
    goto error;
869
107k
870
107k
  isl_seq_cpy(vec->el, vec1->el, vec1->size);
871
107k
  isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
872
107k
873
107k
  isl_vec_free(vec1);
874
107k
  isl_vec_free(vec2);
875
107k
876
107k
  return vec;
877
0
error:
878
0
  isl_vec_free(vec1);
879
0
  isl_vec_free(vec2);
880
0
  return NULL;
881
107k
}
882
883
/* Give a basic set "bset" with recession cone "cone", compute and
884
 * return an integer point in bset, if any.
885
 *
886
 * If the recession cone is full-dimensional, then we know that
887
 * bset contains an infinite number of integer points and it is
888
 * fairly easy to pick one of them.
889
 * If the recession cone is not full-dimensional, then we first
890
 * transform bset such that the bounded directions appear as
891
 * the first dimensions of the transformed basic set.
892
 * We do this by using a unimodular transformation that transforms
893
 * the equalities in the recession cone to equalities on the first
894
 * dimensions.
895
 *
896
 * The transformed set is then projected onto its bounded dimensions.
897
 * Note that to compute this projection, we can simply drop all constraints
898
 * involving any of the unbounded dimensions since these constraints
899
 * cannot be combined to produce a constraint on the bounded dimensions.
900
 * To see this, assume that there is such a combination of constraints
901
 * that produces a constraint on the bounded dimensions.  This means
902
 * that some combination of the unbounded dimensions has both an upper
903
 * bound and a lower bound in terms of the bounded dimensions, but then
904
 * this combination would be a bounded direction too and would have been
905
 * transformed into a bounded dimensions.
906
 *
907
 * We then compute a sample value in the bounded dimensions.
908
 * If no such value can be found, then the original set did not contain
909
 * any integer points and we are done.
910
 * Otherwise, we plug in the value we found in the bounded dimensions,
911
 * project out these bounded dimensions and end up with a set with
912
 * a full-dimensional recession cone.
913
 * A sample point in this set is computed by "rounding up" any
914
 * rational point in the set.
915
 *
916
 * The sample points in the bounded and unbounded dimensions are
917
 * then combined into a single sample point and transformed back
918
 * to the original space.
919
 */
920
__isl_give isl_vec *isl_basic_set_sample_with_cone(
921
  __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
922
110k
{
923
110k
  unsigned total;
924
110k
  unsigned cone_dim;
925
110k
  struct isl_mat *M, *U;
926
110k
  struct isl_vec *sample;
927
110k
  struct isl_vec *cone_sample;
928
110k
  struct isl_ctx *ctx;
929
110k
  struct isl_basic_set *bounded;
930
110k
931
110k
  if (!bset || !cone)
932
0
    goto error;
933
110k
934
110k
  ctx = isl_basic_set_get_ctx(bset);
935
110k
  total = isl_basic_set_total_dim(cone);
936
110k
  cone_dim = total - cone->n_eq;
937
110k
938
110k
  M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
939
110k
  M = isl_mat_left_hermite(M, 0, &U, NULL);
940
110k
  if (!M)
941
0
    goto error;
942
110k
  isl_mat_free(M);
943
110k
944
110k
  U = isl_mat_lin_to_aff(U);
945
110k
  bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
946
110k
947
110k
  bounded = isl_basic_set_copy(bset);
948
110k
  bounded = isl_basic_set_drop_constraints_involving(bounded,
949
110k
               total - cone_dim, cone_dim);
950
110k
  bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
951
110k
  sample = sample_bounded(bounded);
952
110k
  if (!sample || sample->size == 0) {
953
3.37k
    isl_basic_set_free(bset);
954
3.37k
    isl_basic_set_free(cone);
955
3.37k
    isl_mat_free(U);
956
3.37k
    return sample;
957
3.37k
  }
958
107k
  bset = plug_in(bset, isl_vec_copy(sample));
959
107k
  cone_sample = rational_sample(bset);
960
107k
  cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
961
107k
  sample = vec_concat(sample, cone_sample);
962
107k
  sample = isl_mat_vec_product(U, sample);
963
107k
  return sample;
964
0
error:
965
0
  isl_basic_set_free(cone);
966
0
  isl_basic_set_free(bset);
967
0
  return NULL;
968
107k
}
969
970
static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
971
722
{
972
722
  int i;
973
722
974
722
  isl_int_set_si(*s, 0);
975
722
976
2.24k
  for (i = 0; i < v->size; 
++i1.52k
)
977
1.52k
    if (isl_int_is_neg(v->el[i]))
978
1.52k
      
isl_int_add255
(*s, *s, v->el[i]);
979
722
}
980
981
/* Given a tableau "tab", a tableau "tab_cone" that corresponds
982
 * to the recession cone and the inverse of a new basis U = inv(B),
983
 * with the unbounded directions in B last,
984
 * add constraints to "tab" that ensure any rational value
985
 * in the unbounded directions can be rounded up to an integer value.
986
 *
987
 * The new basis is given by x' = B x, i.e., x = U x'.
988
 * For any rational value of the last tab->n_unbounded coordinates
989
 * in the update tableau, the value that is obtained by rounding
990
 * up this value should be contained in the original tableau.
991
 * For any constraint "a x + c >= 0", we therefore need to add
992
 * a constraint "a x + c + s >= 0", with s the sum of all negative
993
 * entries in the last elements of "a U".
994
 *
995
 * Since we are not interested in the first entries of any of the "a U",
996
 * we first drop the columns of U that correpond to bounded directions.
997
 */
998
static int tab_shift_cone(struct isl_tab *tab,
999
  struct isl_tab *tab_cone, struct isl_mat *U)
1000
411
{
1001
411
  int i;
1002
411
  isl_int v;
1003
411
  struct isl_basic_set *bset = NULL;
1004
411
1005
411
  if (tab && tab->n_unbounded == 0) {
1006
0
    isl_mat_free(U);
1007
0
    return 0;
1008
0
  }
1009
411
  isl_int_init(v);
1010
411
  if (!tab || !tab_cone || !U)
1011
0
    goto error;
1012
411
  bset = isl_tab_peek_bset(tab_cone);
1013
411
  U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1014
3.47k
  for (i = 0; i < bset->n_ineq; 
++i3.06k
) {
1015
3.06k
    int ok;
1016
3.06k
    struct isl_vec *row = NULL;
1017
3.06k
    if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1018
2.34k
      continue;
1019
722
    row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1020
722
    if (!row)
1021
0
      goto error;
1022
722
    isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1023
722
    row = isl_vec_mat_product(row, isl_mat_copy(U));
1024
722
    if (!row)
1025
0
      goto error;
1026
722
    vec_sum_of_neg(row, &v);
1027
722
    isl_vec_free(row);
1028
722
    if (isl_int_is_zero(v))
1029
722
      
continue492
;
1030
230
    if (isl_tab_extend_cons(tab, 1) < 0)
1031
0
      goto error;
1032
230
    isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1033
230
    ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1034
230
    isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1035
230
    if (!ok)
1036
0
      goto error;
1037
230
  }
1038
411
1039
411
  isl_mat_free(U);
1040
411
  isl_int_clear(v);
1041
411
  return 0;
1042
0
error:
1043
0
  isl_mat_free(U);
1044
0
  isl_int_clear(v);
1045
0
  return -1;
1046
411
}
1047
1048
/* Compute and return an initial basis for the possibly
1049
 * unbounded tableau "tab".  "tab_cone" is a tableau
1050
 * for the corresponding recession cone.
1051
 * Additionally, add constraints to "tab" that ensure
1052
 * that any rational value for the unbounded directions
1053
 * can be rounded up to an integer value.
1054
 *
1055
 * If the tableau is bounded, i.e., if the recession cone
1056
 * is zero-dimensional, then we just use inital_basis.
1057
 * Otherwise, we construct a basis whose first directions
1058
 * correspond to equalities, followed by bounded directions,
1059
 * i.e., equalities in the recession cone.
1060
 * The remaining directions are then unbounded.
1061
 */
1062
int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1063
  struct isl_tab *tab_cone)
1064
558
{
1065
558
  struct isl_mat *eq;
1066
558
  struct isl_mat *cone_eq;
1067
558
  struct isl_mat *U, *Q;
1068
558
1069
558
  if (!tab || !tab_cone)
1070
0
    return -1;
1071
558
1072
558
  if (tab_cone->n_col == tab_cone->n_dead) {
1073
147
    tab->basis = initial_basis(tab);
1074
147
    return tab->basis ? 0 : 
-10
;
1075
147
  }
1076
411
1077
411
  eq = tab_equalities(tab);
1078
411
  if (!eq)
1079
0
    return -1;
1080
411
  tab->n_zero = eq->n_row;
1081
411
  cone_eq = tab_equalities(tab_cone);
1082
411
  eq = isl_mat_concat(eq, cone_eq);
1083
411
  if (!eq)
1084
0
    return -1;
1085
411
  tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1086
411
  eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1087
411
  if (!eq)
1088
0
    return -1;
1089
411
  isl_mat_free(eq);
1090
411
  tab->basis = isl_mat_lin_to_aff(Q);
1091
411
  if (tab_shift_cone(tab, tab_cone, U) < 0)
1092
0
    return -1;
1093
411
  if (!tab->basis)
1094
0
    return -1;
1095
411
  return 0;
1096
411
}
1097
1098
/* Compute and return a sample point in bset using generalized basis
1099
 * reduction.  We first check if the input set has a non-trivial
1100
 * recession cone.  If so, we perform some extra preprocessing in
1101
 * sample_with_cone.  Otherwise, we directly perform generalized basis
1102
 * reduction.
1103
 */
1104
static __isl_give isl_vec *gbr_sample(__isl_take isl_basic_set *bset)
1105
128k
{
1106
128k
  unsigned dim;
1107
128k
  struct isl_basic_set *cone;
1108
128k
1109
128k
  dim = isl_basic_set_total_dim(bset);
1110
128k
1111
128k
  cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1112
128k
  if (!cone)
1113
0
    goto error;
1114
128k
1115
128k
  if (cone->n_eq < dim)
1116
110k
    return isl_basic_set_sample_with_cone(bset, cone);
1117
18.2k
1118
18.2k
  isl_basic_set_free(cone);
1119
18.2k
  return sample_bounded(bset);
1120
0
error:
1121
0
  isl_basic_set_free(bset);
1122
0
  return NULL;
1123
18.2k
}
1124
1125
static __isl_give isl_vec *basic_set_sample(__isl_take isl_basic_set *bset,
1126
  int bounded)
1127
251k
{
1128
251k
  struct isl_ctx *ctx;
1129
251k
  unsigned dim;
1130
251k
  if (!bset)
1131
0
    return NULL;
1132
251k
1133
251k
  ctx = bset->ctx;
1134
251k
  if (isl_basic_set_plain_is_empty(bset))
1135
437
    return empty_sample(bset);
1136
251k
1137
251k
  dim = isl_basic_set_n_dim(bset);
1138
251k
  isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1139
251k
  isl_assert(ctx, bset->n_div == 0, goto error);
1140
251k
1141
251k
  if (bset->sample && 
bset->sample->size == 1 + dim283
) {
1142
125
    int contains = isl_basic_set_contains(bset, bset->sample);
1143
125
    if (contains < 0)
1144
0
      goto error;
1145
125
    if (contains) {
1146
8
      struct isl_vec *sample = isl_vec_copy(bset->sample);
1147
8
      isl_basic_set_free(bset);
1148
8
      return sample;
1149
8
    }
1150
251k
  }
1151
251k
  isl_vec_free(bset->sample);
1152
251k
  bset->sample = NULL;
1153
251k
1154
251k
  if (bset->n_eq > 0)
1155
89.9k
    return sample_eq(bset, bounded ? 
isl_basic_set_sample_bounded0
1156
89.9k
                 : isl_basic_set_sample_vec);
1157
161k
  if (dim == 0)
1158
3.80k
    return zero_sample(bset);
1159
157k
  if (dim == 1)
1160
29.0k
    return interval_sample(bset);
1161
128k
1162
128k
  return bounded ? 
sample_bounded(bset)0
: gbr_sample(bset);
1163
0
error:
1164
0
  isl_basic_set_free(bset);
1165
0
  return NULL;
1166
128k
}
1167
1168
__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1169
251k
{
1170
251k
  return basic_set_sample(bset, 0);
1171
251k
}
1172
1173
/* Compute an integer sample in "bset", where the caller guarantees
1174
 * that "bset" is bounded.
1175
 */
1176
__isl_give isl_vec *isl_basic_set_sample_bounded(__isl_take isl_basic_set *bset)
1177
0
{
1178
0
  return basic_set_sample(bset, 1);
1179
0
}
1180
1181
__isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1182
267k
{
1183
267k
  int i;
1184
267k
  int k;
1185
267k
  struct isl_basic_set *bset = NULL;
1186
267k
  struct isl_ctx *ctx;
1187
267k
  unsigned dim;
1188
267k
1189
267k
  if (!vec)
1190
0
    return NULL;
1191
267k
  ctx = vec->ctx;
1192
267k
  isl_assert(ctx, vec->size != 0, goto error);
1193
267k
1194
267k
  bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1195
267k
  if (!bset)
1196
0
    goto error;
1197
267k
  dim = isl_basic_set_n_dim(bset);
1198
1.25M
  for (i = dim - 1; i >= 0; 
--i983k
) {
1199
983k
    k = isl_basic_set_alloc_equality(bset);
1200
983k
    if (k < 0)
1201
0
      goto error;
1202
983k
    isl_seq_clr(bset->eq[k], 1 + dim);
1203
983k
    isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1204
983k
    isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1205
983k
  }
1206
267k
  bset->sample = vec;
1207
267k
1208
267k
  return bset;
1209
0
error:
1210
0
  isl_basic_set_free(bset);
1211
0
  isl_vec_free(vec);
1212
0
  return NULL;
1213
267k
}
1214
1215
__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1216
1
{
1217
1
  struct isl_basic_set *bset;
1218
1
  struct isl_vec *sample_vec;
1219
1
1220
1
  bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1221
1
  sample_vec = isl_basic_set_sample_vec(bset);
1222
1
  if (!sample_vec)
1223
0
    goto error;
1224
1
  if (sample_vec->size == 0) {
1225
0
    isl_vec_free(sample_vec);
1226
0
    return isl_basic_map_set_to_empty(bmap);
1227
0
  }
1228
1
  isl_vec_free(bmap->sample);
1229
1
  bmap->sample = isl_vec_copy(sample_vec);
1230
1
  bset = isl_basic_set_from_vec(sample_vec);
1231
1
  return isl_basic_map_overlying_set(bset, bmap);
1232
0
error:
1233
0
  isl_basic_map_free(bmap);
1234
0
  return NULL;
1235
1
}
1236
1237
__isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1238
1
{
1239
1
  return isl_basic_map_sample(bset);
1240
1
}
1241
1242
__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1243
0
{
1244
0
  int i;
1245
0
  isl_basic_map *sample = NULL;
1246
0
1247
0
  if (!map)
1248
0
    goto error;
1249
0
1250
0
  for (i = 0; i < map->n; ++i) {
1251
0
    sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1252
0
    if (!sample)
1253
0
      goto error;
1254
0
    if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1255
0
      break;
1256
0
    isl_basic_map_free(sample);
1257
0
  }
1258
0
  if (i == map->n)
1259
0
    sample = isl_basic_map_empty(isl_map_get_space(map));
1260
0
  isl_map_free(map);
1261
0
  return sample;
1262
0
error:
1263
0
  isl_map_free(map);
1264
0
  return NULL;
1265
0
}
1266
1267
__isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1268
0
{
1269
0
  return bset_from_bmap(isl_map_sample(set_to_map(set)));
1270
0
}
1271
1272
__isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1273
22
{
1274
22
  isl_vec *vec;
1275
22
  isl_space *dim;
1276
22
1277
22
  dim = isl_basic_set_get_space(bset);
1278
22
  bset = isl_basic_set_underlying_set(bset);
1279
22
  vec = isl_basic_set_sample_vec(bset);
1280
22
1281
22
  return isl_point_alloc(dim, vec);
1282
22
}
1283
1284
__isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1285
25
{
1286
25
  int i;
1287
25
  isl_point *pnt;
1288
25
1289
25
  if (!set)
1290
0
    return NULL;
1291
25
1292
25
  for (i = 0; i < set->n; 
++i0
) {
1293
22
    pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1294
22
    if (!pnt)
1295
0
      goto error;
1296
22
    if (!isl_point_is_void(pnt))
1297
22
      break;
1298
0
    isl_point_free(pnt);
1299
0
  }
1300
25
  if (i == set->n)
1301
3
    pnt = isl_point_void(isl_set_get_space(set));
1302
25
1303
25
  isl_set_free(set);
1304
25
  return pnt;
1305
0
error:
1306
0
  isl_set_free(set);
1307
0
  return NULL;
1308
25
}