Coverage Report

Created: 2017-11-21 16:49

/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
147
{
29
147
  struct isl_vec *vec;
30
147
31
147
  vec = isl_vec_alloc(bset->ctx, 0);
32
147
  isl_basic_set_free(bset);
33
147
  return vec;
34
147
}
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
20.9k
{
42
20.9k
  unsigned dim;
43
20.9k
  struct isl_vec *sample;
44
20.9k
45
20.9k
  dim = isl_basic_set_total_dim(bset);
46
20.9k
  sample = isl_vec_alloc(bset->ctx, 1 + dim);
47
20.9k
  if (sample) {
48
20.9k
    isl_int_set_si(sample->el[0], 1);
49
20.9k
    isl_seq_clr(sample->el + 1, dim);
50
20.9k
  }
51
20.9k
  isl_basic_set_free(bset);
52
20.9k
  return sample;
53
20.9k
}
54
55
static __isl_give isl_vec *interval_sample(__isl_take isl_basic_set *bset)
56
66.4k
{
57
66.4k
  int i;
58
66.4k
  isl_int t;
59
66.4k
  struct isl_vec *sample;
60
66.4k
61
66.4k
  bset = isl_basic_set_simplify(bset);
62
66.4k
  if (!bset)
63
0
    return NULL;
64
66.4k
  if (isl_basic_set_plain_is_empty(bset))
65
0
    return empty_sample(bset);
66
66.4k
  if (bset->n_eq == 0 && 
bset->n_ineq == 065.6k
)
67
2.07k
    return zero_sample(bset);
68
64.4k
69
64.4k
  sample = isl_vec_alloc(bset->ctx, 2);
70
64.4k
  if (!sample)
71
0
    goto error;
72
64.4k
  if (!bset)
73
0
    return NULL;
74
64.4k
  isl_int_set_si(sample->block.data[0], 1);
75
64.4k
76
64.4k
  if (bset->n_eq > 0) {
77
880
    isl_assert(bset->ctx, bset->n_eq == 1, goto error);
78
880
    isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
79
880
    if (isl_int_is_one(bset->eq[0][1]))
80
880
      isl_int_neg(sample->el[1], bset->eq[0][0]);
81
880
    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
880
    isl_basic_set_free(bset);
87
880
    return sample;
88
63.5k
  }
89
63.5k
90
63.5k
  isl_int_init(t);
91
63.5k
  if (isl_int_is_one(bset->ineq[0][1]))
92
63.5k
    
isl_int_neg57.0k
(sample->block.data[1], bset->ineq[0][0]);
93
63.5k
  else
94
63.5k
    
isl_int_set6.45k
(sample->block.data[1], bset->ineq[0][0]);
95
123k
  for (i = 1; i < bset->n_ineq; 
++i59.5k
) {
96
59.5k
    isl_seq_inner_product(sample->block.data,
97
59.5k
          bset->ineq[i], 2, &t);
98
59.5k
    if (isl_int_is_neg(t))
99
59.5k
      
break0
;
100
59.5k
  }
101
63.5k
  isl_int_clear(t);
102
63.5k
  if (i < bset->n_ineq) {
103
0
    isl_vec_free(sample);
104
0
    return empty_sample(bset);
105
0
  }
106
63.5k
107
63.5k
  isl_basic_set_free(bset);
108
63.5k
  return sample;
109
0
error:
110
0
  isl_basic_set_free(bset);
111
0
  isl_vec_free(sample);
112
0
  return NULL;
113
66.4k
}
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
35.7k
{
125
35.7k
  struct isl_mat *T;
126
35.7k
  struct isl_vec *sample;
127
35.7k
128
35.7k
  if (!bset)
129
0
    return NULL;
130
35.7k
131
35.7k
  bset = isl_basic_set_remove_equalities(bset, &T, NULL);
132
35.7k
  sample = recurse(bset);
133
35.7k
  if (!sample || sample->size == 0)
134
523
    isl_mat_free(T);
135
35.2k
  else
136
35.2k
    sample = isl_mat_vec_product(T, sample);
137
35.7k
  return sample;
138
35.7k
}
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
868
{
146
868
  int i, j;
147
868
  int n_eq;
148
868
  struct isl_mat *eq;
149
868
  struct isl_basic_set *bset;
150
868
151
868
  if (!tab)
152
0
    return NULL;
153
868
154
868
  bset = isl_tab_peek_bset(tab);
155
868
  isl_assert(tab->mat->ctx, bset, return NULL);
156
868
157
868
  n_eq = tab->n_var - tab->n_col + tab->n_dead;
158
868
  if (tab->empty || n_eq == 0)
159
211
    return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
160
657
  if (n_eq == tab->n_var)
161
0
    return isl_mat_identity(tab->mat->ctx, tab->n_var);
162
657
163
657
  eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
164
657
  if (!eq)
165
0
    return NULL;
166
7.02k
  
for (i = 0, j = 0; 657
i < tab->n_con;
++i6.36k
) {
167
6.36k
    if (tab->con[i].is_row)
168
4.09k
      continue;
169
2.27k
    if (tab->con[i].index >= 0 && 
tab->con[i].index >= tab->n_dead1.44k
)
170
1.12k
      continue;
171
1.14k
    if (i < bset->n_eq)
172
271
      isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
173
875
    else
174
875
      isl_seq_cpy(eq->row[j],
175
875
            bset->ineq[i - bset->n_eq] + 1, tab->n_var);
176
6.36k
    ++j;
177
6.36k
  }
178
657
  isl_assert(bset->ctx, j == n_eq, goto error);
179
657
  return eq;
180
0
error:
181
0
  isl_mat_free(eq);
182
0
  return NULL;
183
868
}
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
58.5k
{
194
58.5k
  int n_eq;
195
58.5k
  struct isl_mat *eq;
196
58.5k
  struct isl_mat *Q;
197
58.5k
198
58.5k
  tab->n_unbounded = 0;
199
58.5k
  tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
200
58.5k
  if (tab->empty || n_eq == 0 || 
n_eq == tab->n_var528
)
201
58.1k
    return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
202
402
203
402
  eq = tab_equalities(tab);
204
402
  eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
205
402
  if (!eq)
206
0
    return NULL;
207
402
  isl_mat_free(eq);
208
402
209
402
  Q = isl_mat_lin_to_aff(Q);
210
402
  return Q;
211
402
}
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
95.0k
{
222
95.0k
  return isl_tab_min(tab, tab->basis->row[1 + level],
223
95.0k
          ctx->one, &min->el[level], NULL, 0);
224
95.0k
}
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
43.3k
{
235
43.3k
  enum isl_lp_result res;
236
43.3k
  unsigned dim = tab->n_var;
237
43.3k
238
43.3k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
239
43.3k
        tab->basis->row[1 + level] + 1, dim);
240
43.3k
  res = isl_tab_min(tab, tab->basis->row[1 + level],
241
43.3k
        ctx->one, &max->el[level], NULL, 0);
242
43.3k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
243
43.3k
        tab->basis->row[1 + level] + 1, dim);
244
43.3k
  isl_int_neg(max->el[level], max->el[level]);
245
43.3k
246
43.3k
  return res;
247
43.3k
}
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
9.81k
{
275
9.81k
  struct isl_tab_undo *snap;
276
9.81k
  enum isl_lp_result res;
277
9.81k
278
9.81k
  snap = isl_tab_snap(tab);
279
9.81k
280
36.2k
  do {
281
36.2k
    isl_int_add(tab->basis->row[1 + level][0],
282
36.2k
          min->el[level], max->el[level]);
283
36.2k
    isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
284
36.2k
          tab->basis->row[1 + level][0], 2);
285
36.2k
    isl_int_neg(tab->basis->row[1 + level][0],
286
36.2k
          tab->basis->row[1 + level][0]);
287
36.2k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
288
0
      return -1;
289
36.2k
    isl_int_set_si(tab->basis->row[1 + level][0], 0);
290
36.2k
291
36.2k
    if (++level >= tab->n_var - tab->n_unbounded)
292
2.78k
      return 1;
293
33.4k
    if (isl_tab_sample_is_integer(tab))
294
5.09k
      return 1;
295
28.3k
296
28.3k
    res = compute_min(ctx, tab, min, level);
297
28.3k
    if (res == isl_lp_error)
298
0
      return -1;
299
28.3k
    if (res != isl_lp_ok)
300
28.3k
      
isl_die0
(ctx, isl_error_internal,
301
28.3k
        "expecting bounded rational solution",
302
28.3k
        return -1);
303
28.3k
    res = compute_max(ctx, tab, max, level);
304
28.3k
    if (res == isl_lp_error)
305
0
      return -1;
306
28.3k
    if (res != isl_lp_ok)
307
28.3k
      
isl_die0
(ctx, isl_error_internal,
308
36.2k
        "expecting bounded rational solution",
309
36.2k
        return -1);
310
36.2k
  } while (
isl_int_le28.3k
(min->el[level], max->el[level]));
311
9.81k
312
9.81k
  
if (1.93k
isl_tab_rollback(tab, snap) < 01.93k
)
313
0
    return -1;
314
1.93k
315
1.93k
  return 0;
316
1.93k
}
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
68.3k
{
375
68.3k
  unsigned dim;
376
68.3k
  unsigned gbr;
377
68.3k
  struct isl_ctx *ctx;
378
68.3k
  struct isl_vec *sample;
379
68.3k
  struct isl_vec *min;
380
68.3k
  struct isl_vec *max;
381
68.3k
  enum isl_lp_result res;
382
68.3k
  int level;
383
68.3k
  int init;
384
68.3k
  int reduced;
385
68.3k
  struct isl_tab_undo **snap;
386
68.3k
387
68.3k
  if (!tab)
388
0
    return NULL;
389
68.3k
  if (tab->empty)
390
5.27k
    return isl_vec_alloc(tab->mat->ctx, 0);
391
63.0k
392
63.0k
  if (!tab->basis)
393
58.4k
    tab->basis = initial_basis(tab);
394
63.0k
  if (!tab->basis)
395
0
    return NULL;
396
63.0k
  isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
397
63.0k
        return NULL);
398
63.0k
  isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
399
63.0k
        return NULL);
400
63.0k
401
63.0k
  ctx = tab->mat->ctx;
402
63.0k
  dim = tab->n_var;
403
63.0k
  gbr = ctx->opt->gbr;
404
63.0k
405
63.0k
  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
63.0k
414
63.0k
  if (isl_tab_extend_cons(tab, dim + 1) < 0)
415
0
    return NULL;
416
63.0k
417
63.0k
  min = isl_vec_alloc(ctx, dim);
418
63.0k
  max = isl_vec_alloc(ctx, dim);
419
63.0k
  snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
420
63.0k
421
63.0k
  if (!min || !max || !snap)
422
0
    goto error;
423
63.0k
424
63.0k
  level = 0;
425
63.0k
  init = 1;
426
63.0k
  reduced = 0;
427
63.0k
428
67.4k
  while (level >= 0) {
429
67.1k
    if (init) {
430
66.6k
      int choice;
431
66.6k
432
66.6k
      res = compute_min(ctx, tab, min, level);
433
66.6k
      if (res == isl_lp_error)
434
0
        goto error;
435
66.6k
      if (res != isl_lp_ok)
436
66.6k
        
isl_die0
(ctx, isl_error_internal,
437
66.6k
          "expecting bounded rational solution",
438
66.6k
          goto error);
439
66.6k
      if (isl_tab_sample_is_integer(tab))
440
51.6k
        break;
441
15.0k
      res = compute_max(ctx, tab, max, level);
442
15.0k
      if (res == isl_lp_error)
443
0
        goto error;
444
15.0k
      if (res != isl_lp_ok)
445
15.0k
        
isl_die0
(ctx, isl_error_internal,
446
15.0k
          "expecting bounded rational solution",
447
15.0k
          goto error);
448
15.0k
      if (isl_tab_sample_is_integer(tab))
449
3.12k
        break;
450
11.9k
      choice = isl_int_lt(min->el[level], max->el[level]);
451
11.9k
      if (choice) {
452
9.81k
        int g;
453
9.81k
        g = greedy_search(ctx, tab, min, max, level);
454
9.81k
        if (g < 0)
455
0
          goto error;
456
9.81k
        if (g)
457
7.87k
          break;
458
4.02k
      }
459
4.02k
      if (!reduced && 
choice3.05k
&&
460
4.02k
          
ctx->opt->gbr != 1.85k
ISL_GBR_NEVER1.85k
) {
461
1.85k
        unsigned gbr_only_first;
462
1.85k
        if (ctx->opt->gbr == ISL_GBR_ONCE)
463
1.85k
          
ctx->opt->gbr = 0
ISL_GBR_NEVER0
;
464
1.85k
        tab->n_zero = level;
465
1.85k
        gbr_only_first = ctx->opt->gbr_only_first;
466
1.85k
        ctx->opt->gbr_only_first =
467
1.85k
          ctx->opt->gbr == ISL_GBR_ALWAYS;
468
1.85k
        tab = isl_tab_compute_reduced_basis(tab);
469
1.85k
        ctx->opt->gbr_only_first = gbr_only_first;
470
1.85k
        if (!tab || !tab->basis)
471
0
          goto error;
472
1.85k
        reduced = 1;
473
1.85k
        continue;
474
1.85k
      }
475
2.17k
      reduced = 0;
476
2.17k
      snap[level] = isl_tab_snap(tab);
477
2.17k
    } else
478
67.1k
      
isl_int_add_ui443
(min->el[level], min->el[level], 1);
479
67.1k
480
67.1k
    
if (2.61k
isl_int_gt2.61k
(min->el[level], max->el[level])) {
481
828
      level--;
482
828
      init = 0;
483
828
      if (level >= 0)
484
443
        if (isl_tab_rollback(tab, snap[level]) < 0)
485
0
          goto error;
486
828
      continue;
487
828
    }
488
1.79k
    isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
489
1.79k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
490
0
      goto error;
491
1.79k
    isl_int_set_si(tab->basis->row[1 + level][0], 0);
492
1.79k
    if (level + tab->n_unbounded < dim - 1) {
493
1.79k
      ++level;
494
1.79k
      init = 1;
495
1.79k
      continue;
496
1.79k
    }
497
0
    break;
498
0
  }
499
63.0k
500
63.0k
  if (level >= 0) {
501
62.6k
    sample = isl_tab_get_sample_value(tab);
502
62.6k
    if (!sample)
503
0
      goto error;
504
62.6k
    if (tab->n_unbounded && 
!407
isl_int_is_one407
(sample->el[0])) {
505
106
      sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
506
106
                 sample);
507
106
      sample = isl_vec_ceil(sample);
508
106
      sample = isl_mat_vec_inverse_product(
509
106
          isl_mat_copy(tab->basis), sample);
510
106
    }
511
62.6k
  } else
512
385
    sample = isl_vec_alloc(ctx, 0);
513
63.0k
514
63.0k
  ctx->opt->gbr = gbr;
515
63.0k
  isl_vec_free(min);
516
63.0k
  isl_vec_free(max);
517
63.0k
  free(snap);
518
63.0k
  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
68.3k
}
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
21.6k
{
535
21.6k
  int i, n;
536
21.6k
  isl_vec *sample = NULL;
537
21.6k
  isl_ctx *ctx;
538
21.6k
  unsigned nparam;
539
21.6k
  unsigned nvar;
540
21.6k
541
21.6k
  ctx = isl_basic_set_get_ctx(bset);
542
21.6k
  if (!ctx)
543
0
    goto error;
544
21.6k
545
21.6k
  nparam = isl_basic_set_dim(bset, isl_dim_param);
546
21.6k
  nvar = isl_basic_set_dim(bset, isl_dim_set);
547
21.6k
548
21.6k
  sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
549
21.6k
  if (!sample)
550
0
    goto error;
551
21.6k
  isl_int_set_si(sample->el[0], 1);
552
21.6k
553
21.6k
  bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
554
21.6k
555
105k
  for (i = 0, n = 0; i < f->n_group; 
++i83.4k
) {
556
83.7k
    isl_basic_set *bset_i;
557
83.7k
    isl_vec *sample_i;
558
83.7k
559
83.7k
    bset_i = isl_basic_set_copy(bset);
560
83.7k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
561
83.7k
          nparam + n + f->len[i], nvar - n - f->len[i]);
562
83.7k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
563
83.7k
          nparam, n);
564
83.7k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
565
83.7k
          n + f->len[i], nvar - n - f->len[i]);
566
83.7k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
567
83.7k
568
83.7k
    sample_i = sample_bounded(bset_i);
569
83.7k
    if (!sample_i)
570
0
      goto error;
571
83.7k
    if (sample_i->size == 0) {
572
240
      isl_basic_set_free(bset);
573
240
      isl_factorizer_free(f);
574
240
      isl_vec_free(sample);
575
240
      return sample_i;
576
240
    }
577
83.4k
    isl_seq_cpy(sample->el + 1 + nparam + n,
578
83.4k
          sample_i->el + 1, f->len[i]);
579
83.4k
    isl_vec_free(sample_i);
580
83.4k
581
83.4k
    n += f->len[i];
582
83.4k
  }
583
21.6k
584
21.6k
  f->morph = isl_morph_inverse(f->morph);
585
21.3k
  sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
586
21.3k
587
21.3k
  isl_basic_set_free(bset);
588
21.3k
  isl_factorizer_free(f);
589
21.3k
  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
21.6k
}
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
135k
{
606
135k
  unsigned dim;
607
135k
  struct isl_vec *sample;
608
135k
  struct isl_tab *tab = NULL;
609
135k
  isl_factorizer *f;
610
135k
611
135k
  if (!bset)
612
0
    return NULL;
613
135k
614
135k
  if (isl_basic_set_plain_is_empty(bset))
615
16
    return empty_sample(bset);
616
135k
617
135k
  dim = isl_basic_set_total_dim(bset);
618
135k
  if (dim == 0)
619
17.1k
    return zero_sample(bset);
620
117k
  if (dim == 1)
621
57.2k
    return interval_sample(bset);
622
60.6k
  if (bset->n_eq > 0)
623
979
    return sample_eq(bset, sample_bounded);
624
59.6k
625
59.6k
  f = isl_basic_set_factorizer(bset);
626
59.6k
  if (!f)
627
0
    goto error;
628
59.6k
  if (f->n_group != 0)
629
21.6k
    return factored_sample(bset, f);
630
38.0k
  isl_factorizer_free(f);
631
38.0k
632
38.0k
  tab = isl_tab_from_basic_set(bset, 1);
633
38.0k
  if (tab && tab->empty) {
634
2.63k
    isl_tab_free(tab);
635
2.63k
    ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
636
2.63k
    sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
637
2.63k
    isl_basic_set_free(bset);
638
2.63k
    return sample;
639
2.63k
  }
640
35.4k
641
35.4k
  if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
642
35.4k
    
if (35.3k
isl_tab_detect_implicit_equalities(tab) < 035.3k
)
643
0
      goto error;
644
35.4k
645
35.4k
  sample = isl_tab_sample(tab);
646
35.4k
  if (!sample)
647
0
    goto error;
648
35.4k
649
35.4k
  if (sample->size > 0) {
650
35.1k
    isl_vec_free(bset->sample);
651
35.1k
    bset->sample = isl_vec_copy(sample);
652
35.1k
  }
653
35.4k
654
35.4k
  isl_basic_set_free(bset);
655
35.4k
  isl_tab_free(tab);
656
35.4k
  return sample;
657
0
error:
658
0
  isl_basic_set_free(bset);
659
0
  isl_tab_free(tab);
660
0
  return NULL;
661
135k
}
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
42.1k
{
678
42.1k
  int i;
679
42.1k
  unsigned total;
680
42.1k
  struct isl_mat *T;
681
42.1k
682
42.1k
  if (!bset || !sample)
683
0
    goto error;
684
42.1k
685
42.1k
  total = isl_basic_set_total_dim(bset);
686
42.1k
  T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
687
42.1k
  if (!T)
688
0
    goto error;
689
42.1k
690
194k
  
for (i = 0; 42.1k
i < sample->size;
++i152k
) {
691
152k
    isl_int_set(T->row[i][0], sample->el[i]);
692
152k
    isl_seq_clr(T->row[i] + 1, T->n_col - 1);
693
152k
  }
694
228k
  for (i = 0; i < T->n_col - 1; 
++i185k
) {
695
185k
    isl_seq_clr(T->row[sample->size + i], T->n_col);
696
185k
    isl_int_set_si(T->row[sample->size + i][1 + i], 1);
697
185k
  }
698
42.1k
  isl_vec_free(sample);
699
42.1k
700
42.1k
  bset = isl_basic_set_preimage(bset, T);
701
42.1k
  return bset;
702
0
error:
703
0
  isl_basic_set_free(bset);
704
0
  isl_vec_free(sample);
705
0
  return NULL;
706
42.1k
}
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
43.0k
{
713
43.0k
  struct isl_tab *tab;
714
43.0k
  struct isl_vec *sample;
715
43.0k
716
43.0k
  if (!bset)
717
0
    return NULL;
718
43.0k
719
43.0k
  tab = isl_tab_from_basic_set(bset, 0);
720
43.0k
  sample = isl_tab_get_sample_value(tab);
721
43.0k
  isl_tab_free(tab);
722
43.0k
723
43.0k
  isl_basic_set_free(bset);
724
43.0k
725
43.0k
  return sample;
726
43.0k
}
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
978
{
764
978
  int i, j, k;
765
978
  unsigned total;
766
978
767
978
  struct isl_basic_set *shift = NULL;
768
978
769
978
  if (!cone || !vec)
770
0
    goto error;
771
978
772
978
  isl_assert(cone->ctx, cone->n_eq == 0, goto error);
773
978
774
978
  total = isl_basic_set_total_dim(cone);
775
978
776
978
  shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
777
978
          0, 0, cone->n_ineq);
778
978
779
3.06k
  for (i = 0; i < cone->n_ineq; 
++i2.08k
) {
780
2.08k
    k = isl_basic_set_alloc_inequality(shift);
781
2.08k
    if (k < 0)
782
0
      goto error;
783
2.08k
    isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
784
2.08k
    isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
785
2.08k
              &shift->ineq[k][0]);
786
2.08k
    isl_int_cdiv_q(shift->ineq[k][0],
787
2.08k
             shift->ineq[k][0], vec->el[0]);
788
2.08k
    isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
789
7.44k
    for (j = 0; j < total; 
++j5.36k
) {
790
5.36k
      if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
791
5.36k
        
continue4.17k
;
792
1.18k
      isl_int_add(shift->ineq[k][0],
793
1.18k
            shift->ineq[k][0], shift->ineq[k][1 + j]);
794
1.18k
    }
795
2.08k
  }
796
978
797
978
  isl_basic_set_free(cone);
798
978
  isl_vec_free(vec);
799
978
800
978
  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
978
}
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
42.1k
{
822
42.1k
  unsigned total;
823
42.1k
824
42.1k
  if (!vec || !cone || !U)
825
0
    goto error;
826
42.1k
827
42.1k
  isl_assert(vec->ctx, vec->size != 0, goto error);
828
42.1k
  if (isl_int_is_one(vec->el[0])) {
829
41.1k
    isl_mat_free(U);
830
41.1k
    isl_basic_set_free(cone);
831
41.1k
    return vec;
832
41.1k
  }
833
978
834
978
  total = isl_basic_set_total_dim(cone);
835
978
  cone = isl_basic_set_preimage(cone, U);
836
978
  cone = isl_basic_set_remove_dims(cone, isl_dim_set,
837
978
           0, total - (vec->size - 1));
838
978
839
978
  cone = shift_cone(cone, vec);
840
978
841
978
  vec = rational_sample(cone);
842
978
  vec = isl_vec_ceil(vec);
843
978
  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
42.1k
}
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
42.1k
{
857
42.1k
  struct isl_vec *vec;
858
42.1k
859
42.1k
  if (!vec1 || !vec2)
860
0
    goto error;
861
42.1k
  isl_assert(vec1->ctx, vec1->size > 0, goto error);
862
42.1k
  isl_assert(vec2->ctx, vec2->size > 0, goto error);
863
42.1k
  isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
864
42.1k
  isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
865
42.1k
866
42.1k
  vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
867
42.1k
  if (!vec)
868
0
    goto error;
869
42.1k
870
42.1k
  isl_seq_cpy(vec->el, vec1->el, vec1->size);
871
42.1k
  isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
872
42.1k
873
42.1k
  isl_vec_free(vec1);
874
42.1k
  isl_vec_free(vec2);
875
42.1k
876
42.1k
  return vec;
877
0
error:
878
0
  isl_vec_free(vec1);
879
0
  isl_vec_free(vec2);
880
0
  return NULL;
881
42.1k
}
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
44.6k
{
923
44.6k
  unsigned total;
924
44.6k
  unsigned cone_dim;
925
44.6k
  struct isl_mat *M, *U;
926
44.6k
  struct isl_vec *sample;
927
44.6k
  struct isl_vec *cone_sample;
928
44.6k
  struct isl_ctx *ctx;
929
44.6k
  struct isl_basic_set *bounded;
930
44.6k
931
44.6k
  if (!bset || !cone)
932
0
    goto error;
933
44.6k
934
44.6k
  ctx = isl_basic_set_get_ctx(bset);
935
44.6k
  total = isl_basic_set_total_dim(cone);
936
44.6k
  cone_dim = total - cone->n_eq;
937
44.6k
938
44.6k
  M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
939
44.6k
  M = isl_mat_left_hermite(M, 0, &U, NULL);
940
44.6k
  if (!M)
941
0
    goto error;
942
44.6k
  isl_mat_free(M);
943
44.6k
944
44.6k
  U = isl_mat_lin_to_aff(U);
945
44.6k
  bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
946
44.6k
947
44.6k
  bounded = isl_basic_set_copy(bset);
948
44.6k
  bounded = isl_basic_set_drop_constraints_involving(bounded,
949
44.6k
               total - cone_dim, cone_dim);
950
44.6k
  bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
951
44.6k
  sample = sample_bounded(bounded);
952
44.6k
  if (!sample || sample->size == 0) {
953
2.51k
    isl_basic_set_free(bset);
954
2.51k
    isl_basic_set_free(cone);
955
2.51k
    isl_mat_free(U);
956
2.51k
    return sample;
957
2.51k
  }
958
42.1k
  bset = plug_in(bset, isl_vec_copy(sample));
959
42.1k
  cone_sample = rational_sample(bset);
960
42.1k
  cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
961
42.1k
  sample = vec_concat(sample, cone_sample);
962
42.1k
  sample = isl_mat_vec_product(U, sample);
963
42.1k
  return sample;
964
0
error:
965
0
  isl_basic_set_free(cone);
966
0
  isl_basic_set_free(bset);
967
0
  return NULL;
968
44.6k
}
969
970
static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
971
255
{
972
255
  int i;
973
255
974
255
  isl_int_set_si(*s, 0);
975
255
976
617
  for (i = 0; i < v->size; 
++i362
)
977
362
    if (isl_int_is_neg(v->el[i]))
978
362
      
isl_int_add63
(*s, *s, v->el[i]);
979
255
}
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
233
{
1001
233
  int i;
1002
233
  isl_int v;
1003
233
  struct isl_basic_set *bset = NULL;
1004
233
1005
233
  if (tab && tab->n_unbounded == 0) {
1006
0
    isl_mat_free(U);
1007
0
    return 0;
1008
0
  }
1009
233
  isl_int_init(v);
1010
233
  if (!tab || !tab_cone || !U)
1011
0
    goto error;
1012
233
  bset = isl_tab_peek_bset(tab_cone);
1013
233
  U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1014
1.73k
  for (i = 0; i < bset->n_ineq; 
++i1.49k
) {
1015
1.49k
    int ok;
1016
1.49k
    struct isl_vec *row = NULL;
1017
1.49k
    if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1018
1.24k
      continue;
1019
255
    row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1020
255
    if (!row)
1021
0
      goto error;
1022
255
    isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1023
255
    row = isl_vec_mat_product(row, isl_mat_copy(U));
1024
255
    if (!row)
1025
0
      goto error;
1026
255
    vec_sum_of_neg(row, &v);
1027
255
    isl_vec_free(row);
1028
255
    if (isl_int_is_zero(v))
1029
255
      
continue196
;
1030
59
    if (isl_tab_extend_cons(tab, 1) < 0)
1031
0
      goto error;
1032
59
    isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1033
59
    ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1034
59
    isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1035
59
    if (!ok)
1036
0
      goto error;
1037
1.49k
  }
1038
233
1039
233
  isl_mat_free(U);
1040
233
  isl_int_clear(v);
1041
233
  return 0;
1042
0
error:
1043
0
  isl_mat_free(U);
1044
0
  isl_int_clear(v);
1045
0
  return -1;
1046
233
}
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
290
{
1065
290
  struct isl_mat *eq;
1066
290
  struct isl_mat *cone_eq;
1067
290
  struct isl_mat *U, *Q;
1068
290
1069
290
  if (!tab || !tab_cone)
1070
0
    return -1;
1071
290
1072
290
  if (tab_cone->n_col == tab_cone->n_dead) {
1073
57
    tab->basis = initial_basis(tab);
1074
57
    return tab->basis ? 0 : 
-10
;
1075
57
  }
1076
233
1077
233
  eq = tab_equalities(tab);
1078
233
  if (!eq)
1079
0
    return -1;
1080
233
  tab->n_zero = eq->n_row;
1081
233
  cone_eq = tab_equalities(tab_cone);
1082
233
  eq = isl_mat_concat(eq, cone_eq);
1083
233
  if (!eq)
1084
0
    return -1;
1085
233
  tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1086
233
  eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1087
233
  if (!eq)
1088
0
    return -1;
1089
233
  isl_mat_free(eq);
1090
233
  tab->basis = isl_mat_lin_to_aff(Q);
1091
233
  if (tab_shift_cone(tab, tab_cone, U) < 0)
1092
0
    return -1;
1093
233
  if (!tab->basis)
1094
0
    return -1;
1095
233
  return 0;
1096
233
}
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
49.9k
{
1106
49.9k
  unsigned dim;
1107
49.9k
  struct isl_basic_set *cone;
1108
49.9k
1109
49.9k
  dim = isl_basic_set_total_dim(bset);
1110
49.9k
1111
49.9k
  cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1112
49.9k
  if (!cone)
1113
0
    goto error;
1114
49.9k
1115
49.9k
  if (cone->n_eq < dim)
1116
44.2k
    return isl_basic_set_sample_with_cone(bset, cone);
1117
5.76k
1118
5.76k
  isl_basic_set_free(cone);
1119
5.76k
  return sample_bounded(bset);
1120
0
error:
1121
0
  isl_basic_set_free(bset);
1122
0
  return NULL;
1123
49.9k
}
1124
1125
static __isl_give isl_vec *basic_set_sample(__isl_take isl_basic_set *bset,
1126
  int bounded)
1127
95.8k
{
1128
95.8k
  struct isl_ctx *ctx;
1129
95.8k
  unsigned dim;
1130
95.8k
  if (!bset)
1131
0
    return NULL;
1132
95.8k
1133
95.8k
  ctx = bset->ctx;
1134
95.8k
  if (isl_basic_set_plain_is_empty(bset))
1135
131
    return empty_sample(bset);
1136
95.7k
1137
95.7k
  dim = isl_basic_set_n_dim(bset);
1138
95.7k
  isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1139
95.7k
  isl_assert(ctx, bset->n_div == 0, goto error);
1140
95.7k
1141
95.7k
  if (bset->sample && 
bset->sample->size == 1 + dim137
) {
1142
122
    int contains = isl_basic_set_contains(bset, bset->sample);
1143
122
    if (contains < 0)
1144
0
      goto error;
1145
122
    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
95.6k
  }
1151
95.6k
  isl_vec_free(bset->sample);
1152
95.6k
  bset->sample = NULL;
1153
95.6k
1154
95.6k
  if (bset->n_eq > 0)
1155
34.7k
    return sample_eq(bset, bounded ? 
isl_basic_set_sample_bounded0
1156
34.7k
                 : isl_basic_set_sample_vec);
1157
60.9k
  if (dim == 0)
1158
1.69k
    return zero_sample(bset);
1159
59.2k
  if (dim == 1)
1160
9.22k
    return interval_sample(bset);
1161
49.9k
1162
49.9k
  return bounded ? 
sample_bounded(bset)0
: gbr_sample(bset);
1163
0
error:
1164
0
  isl_basic_set_free(bset);
1165
0
  return NULL;
1166
95.8k
}
1167
1168
__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1169
95.8k
{
1170
95.8k
  return basic_set_sample(bset, 0);
1171
95.8k
}
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
126k
{
1183
126k
  int i;
1184
126k
  int k;
1185
126k
  struct isl_basic_set *bset = NULL;
1186
126k
  struct isl_ctx *ctx;
1187
126k
  unsigned dim;
1188
126k
1189
126k
  if (!vec)
1190
0
    return NULL;
1191
126k
  ctx = vec->ctx;
1192
126k
  isl_assert(ctx, vec->size != 0, goto error);
1193
126k
1194
126k
  bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1195
126k
  if (!bset)
1196
0
    goto error;
1197
126k
  dim = isl_basic_set_n_dim(bset);
1198
685k
  for (i = dim - 1; i >= 0; 
--i558k
) {
1199
558k
    k = isl_basic_set_alloc_equality(bset);
1200
558k
    if (k < 0)
1201
0
      goto error;
1202
558k
    isl_seq_clr(bset->eq[k], 1 + dim);
1203
558k
    isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1204
558k
    isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1205
558k
  }
1206
126k
  bset->sample = vec;
1207
126k
1208
126k
  return bset;
1209
0
error:
1210
0
  isl_basic_set_free(bset);
1211
0
  isl_vec_free(vec);
1212
0
  return NULL;
1213
126k
}
1214
1215
__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1216
0
{
1217
0
  struct isl_basic_set *bset;
1218
0
  struct isl_vec *sample_vec;
1219
0
1220
0
  bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1221
0
  sample_vec = isl_basic_set_sample_vec(bset);
1222
0
  if (!sample_vec)
1223
0
    goto error;
1224
0
  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
0
  isl_vec_free(bmap->sample);
1229
0
  bmap->sample = isl_vec_copy(sample_vec);
1230
0
  bset = isl_basic_set_from_vec(sample_vec);
1231
0
  return isl_basic_map_overlying_set(bset, bmap);
1232
0
error:
1233
0
  isl_basic_map_free(bmap);
1234
0
  return NULL;
1235
0
}
1236
1237
__isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1238
0
{
1239
0
  return isl_basic_map_sample(bset);
1240
0
}
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
0
{
1274
0
  isl_vec *vec;
1275
0
  isl_space *dim;
1276
0
1277
0
  dim = isl_basic_set_get_space(bset);
1278
0
  bset = isl_basic_set_underlying_set(bset);
1279
0
  vec = isl_basic_set_sample_vec(bset);
1280
0
1281
0
  return isl_point_alloc(dim, vec);
1282
0
}
1283
1284
__isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1285
0
{
1286
0
  int i;
1287
0
  isl_point *pnt;
1288
0
1289
0
  if (!set)
1290
0
    return NULL;
1291
0
1292
0
  for (i = 0; i < set->n; ++i) {
1293
0
    pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1294
0
    if (!pnt)
1295
0
      goto error;
1296
0
    if (!isl_point_is_void(pnt))
1297
0
      break;
1298
0
    isl_point_free(pnt);
1299
0
  }
1300
0
  if (i == set->n)
1301
0
    pnt = isl_point_void(isl_set_get_space(set));
1302
0
1303
0
  isl_set_free(set);
1304
0
  return pnt;
1305
0
error:
1306
0
  isl_set_free(set);
1307
0
  return NULL;
1308
0
}