Coverage Report

Created: 2017-03-28 09:59

/Users/buildslave/jenkins/sharedspace/clang-stage2-coverage-R@2/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 struct isl_vec *empty_sample(struct isl_basic_set *bset)
28
184
{
29
184
  struct isl_vec *vec;
30
184
31
184
  vec = isl_vec_alloc(bset->ctx, 0);
32
184
  isl_basic_set_free(bset);
33
184
  return vec;
34
184
}
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 struct isl_vec *zero_sample(struct isl_basic_set *bset)
41
43.5k
{
42
43.5k
  unsigned dim;
43
43.5k
  struct isl_vec *sample;
44
43.5k
45
43.5k
  dim = isl_basic_set_total_dim(bset);
46
43.5k
  sample = isl_vec_alloc(bset->ctx, 1 + dim);
47
43.5k
  if (
sample43.5k
)
{43.5k
48
43.5k
    isl_int_set_si(sample->el[0], 1);
49
43.5k
    isl_seq_clr(sample->el + 1, dim);
50
43.5k
  }
51
43.5k
  isl_basic_set_free(bset);
52
43.5k
  return sample;
53
43.5k
}
54
55
static struct isl_vec *interval_sample(struct isl_basic_set *bset)
56
93.2k
{
57
93.2k
  int i;
58
93.2k
  isl_int t;
59
93.2k
  struct isl_vec *sample;
60
93.2k
61
93.2k
  bset = isl_basic_set_simplify(bset);
62
93.2k
  if (!bset)
63
0
    return NULL;
64
93.2k
  
if (93.2k
isl_basic_set_plain_is_empty(bset)93.2k
)
65
0
    return empty_sample(bset);
66
93.2k
  
if (93.2k
bset->n_eq == 0 && 93.2k
bset->n_ineq == 093.1k
)
67
4.41k
    return zero_sample(bset);
68
93.2k
69
88.8k
  sample = isl_vec_alloc(bset->ctx, 2);
70
88.8k
  if (!sample)
71
0
    goto error;
72
88.8k
  
if (88.8k
!bset88.8k
)
73
0
    return NULL;
74
88.8k
  
isl_int_set_si88.8k
(sample->block.data[0], 1);88.8k
75
88.8k
76
88.8k
  if (
bset->n_eq > 088.8k
)
{72
77
72
    isl_assert(bset->ctx, bset->n_eq == 1, goto error);
78
72
    
isl_assert72
(bset->ctx, bset->n_ineq == 0, goto error);72
79
72
    
if (72
isl_int_is_one72
(bset->eq[0][1]))
80
72
      isl_int_neg(sample->el[1], bset->eq[0][0]);
81
0
    else {
82
0
      isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
83
0
           goto error);
84
0
      
isl_int_set0
(sample->el[1], bset->eq[0][0]);0
85
0
    }
86
72
    isl_basic_set_free(bset);
87
72
    return sample;
88
72
  }
89
88.8k
90
88.7k
  
isl_int_init88.7k
(t);88.7k
91
88.7k
  if (isl_int_is_one(bset->ineq[0][1]))
92
76.7k
    isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
93
88.7k
  else
94
11.9k
    isl_int_set(sample->block.data[1], bset->ineq[0][0]);
95
169k
  for (i = 1; 
i < bset->n_ineq169k
;
++i80.3k
)
{80.3k
96
80.3k
    isl_seq_inner_product(sample->block.data,
97
80.3k
          bset->ineq[i], 2, &t);
98
80.3k
    if (isl_int_is_neg(t))
99
0
      break;
100
80.3k
  }
101
88.7k
  isl_int_clear(t);
102
88.7k
  if (
i < bset->n_ineq88.7k
)
{0
103
0
    isl_vec_free(sample);
104
0
    return empty_sample(bset);
105
0
  }
106
88.7k
107
88.7k
  isl_basic_set_free(bset);
108
88.7k
  return sample;
109
0
error:
110
0
  isl_basic_set_free(bset);
111
0
  isl_vec_free(sample);
112
0
  return NULL;
113
88.7k
}
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 struct isl_vec *sample_eq(struct isl_basic_set *bset,
123
  struct isl_vec *(*recurse)(struct isl_basic_set *))
124
43.1k
{
125
43.1k
  struct isl_mat *T;
126
43.1k
  struct isl_vec *sample;
127
43.1k
128
43.1k
  if (!bset)
129
0
    return NULL;
130
43.1k
131
43.1k
  bset = isl_basic_set_remove_equalities(bset, &T, NULL);
132
43.1k
  sample = recurse(bset);
133
43.1k
  if (
!sample || 43.1k
sample->size == 043.1k
)
134
678
    isl_mat_free(T);
135
43.1k
  else
136
42.4k
    sample = isl_mat_vec_product(T, sample);
137
43.1k
  return sample;
138
43.1k
}
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
926
{
146
926
  int i, j;
147
926
  int n_eq;
148
926
  struct isl_mat *eq;
149
926
  struct isl_basic_set *bset;
150
926
151
926
  if (!tab)
152
0
    return NULL;
153
926
154
926
  bset = isl_tab_peek_bset(tab);
155
926
  isl_assert(tab->mat->ctx, bset, return NULL);
156
926
157
926
  n_eq = tab->n_var - tab->n_col + tab->n_dead;
158
926
  if (
tab->empty || 926
n_eq == 0926
)
159
132
    return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
160
794
  
if (794
n_eq == tab->n_var794
)
161
0
    return isl_mat_identity(tab->mat->ctx, tab->n_var);
162
794
163
794
  eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
164
794
  if (!eq)
165
0
    return NULL;
166
12.2k
  
for (i = 0, j = 0; 794
i < tab->n_con12.2k
;
++i11.4k
)
{11.4k
167
11.4k
    if (tab->con[i].is_row)
168
7.20k
      continue;
169
4.24k
    
if (4.24k
tab->con[i].index >= 0 && 4.24k
tab->con[i].index >= tab->n_dead3.45k
)
170
1.80k
      continue;
171
2.44k
    
if (2.44k
i < bset->n_eq2.44k
)
172
103
      isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
173
2.44k
    else
174
2.34k
      isl_seq_cpy(eq->row[j],
175
2.34k
            bset->ineq[i - bset->n_eq] + 1, tab->n_var);
176
2.44k
    ++j;
177
2.44k
  }
178
794
  isl_assert(bset->ctx, j == n_eq, goto error);
179
794
  return eq;
180
0
error:
181
0
  isl_mat_free(eq);
182
0
  return NULL;
183
794
}
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
55.9k
{
194
55.9k
  int n_eq;
195
55.9k
  struct isl_mat *eq;
196
55.9k
  struct isl_mat *Q;
197
55.9k
198
55.9k
  tab->n_unbounded = 0;
199
55.9k
  tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
200
55.9k
  if (
tab->empty || 55.9k
n_eq == 055.9k
||
n_eq == tab->n_var549
)
201
55.6k
    return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
202
55.9k
203
284
  eq = tab_equalities(tab);
204
284
  eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
205
284
  if (!eq)
206
0
    return NULL;
207
284
  isl_mat_free(eq);
208
284
209
284
  Q = isl_mat_lin_to_aff(Q);
210
284
  return Q;
211
284
}
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
78.2k
{
222
78.2k
  return isl_tab_min(tab, tab->basis->row[1 + level],
223
78.2k
          ctx->one, &min->el[level], NULL, 0);
224
78.2k
}
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
23.8k
{
235
23.8k
  enum isl_lp_result res;
236
23.8k
  unsigned dim = tab->n_var;
237
23.8k
238
23.8k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
239
23.8k
        tab->basis->row[1 + level] + 1, dim);
240
23.8k
  res = isl_tab_min(tab, tab->basis->row[1 + level],
241
23.8k
        ctx->one, &max->el[level], NULL, 0);
242
23.8k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
243
23.8k
        tab->basis->row[1 + level] + 1, dim);
244
23.8k
  isl_int_neg(max->el[level], max->el[level]);
245
23.8k
246
23.8k
  return res;
247
23.8k
}
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
5.39k
{
275
5.39k
  struct isl_tab_undo *snap;
276
5.39k
  enum isl_lp_result res;
277
5.39k
278
5.39k
  snap = isl_tab_snap(tab);
279
5.39k
280
16.8k
  do {
281
16.8k
    isl_int_add(tab->basis->row[1 + level][0],
282
16.8k
          min->el[level], max->el[level]);
283
16.8k
    isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
284
16.8k
          tab->basis->row[1 + level][0], 2);
285
16.8k
    isl_int_neg(tab->basis->row[1 + level][0],
286
16.8k
          tab->basis->row[1 + level][0]);
287
16.8k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
288
0
      return -1;
289
16.8k
    
isl_int_set_si16.8k
(tab->basis->row[1 + level][0], 0);16.8k
290
16.8k
291
16.8k
    if (++level >= tab->n_var - tab->n_unbounded)
292
1.79k
      return 1;
293
15.0k
    
if (15.0k
isl_tab_sample_is_integer(tab)15.0k
)
294
1.87k
      return 1;
295
15.0k
296
13.1k
    res = compute_min(ctx, tab, min, level);
297
13.1k
    if (res == isl_lp_error)
298
0
      return -1;
299
13.1k
    
if (13.1k
res != isl_lp_ok13.1k
)
300
0
      isl_die(ctx, isl_error_internal,
301
13.1k
        "expecting bounded rational solution",
302
13.1k
        return -1);
303
13.1k
    res = compute_max(ctx, tab, max, level);
304
13.1k
    if (res == isl_lp_error)
305
0
      return -1;
306
13.1k
    
if (13.1k
res != isl_lp_ok13.1k
)
307
0
      isl_die(ctx, isl_error_internal,
308
13.1k
        "expecting bounded rational solution",
309
13.1k
        return -1);
310
13.1k
  } while (isl_int_le(min->el[level], max->el[level]));
311
5.39k
312
1.72k
  
if (1.72k
isl_tab_rollback(tab, snap) < 01.72k
)
313
0
    return -1;
314
1.72k
315
1.72k
  return 0;
316
1.72k
}
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
64.7k
{
375
64.7k
  unsigned dim;
376
64.7k
  unsigned gbr;
377
64.7k
  struct isl_ctx *ctx;
378
64.7k
  struct isl_vec *sample;
379
64.7k
  struct isl_vec *min;
380
64.7k
  struct isl_vec *max;
381
64.7k
  enum isl_lp_result res;
382
64.7k
  int level;
383
64.7k
  int init;
384
64.7k
  int reduced;
385
64.7k
  struct isl_tab_undo **snap;
386
64.7k
387
64.7k
  if (!tab)
388
0
    return NULL;
389
64.7k
  
if (64.7k
tab->empty64.7k
)
390
4.72k
    return isl_vec_alloc(tab->mat->ctx, 0);
391
64.7k
392
60.0k
  
if (60.0k
!tab->basis60.0k
)
393
55.9k
    tab->basis = initial_basis(tab);
394
60.0k
  if (!tab->basis)
395
0
    return NULL;
396
60.0k
  
isl_assert60.0k
(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,60.0k
397
60.0k
        return NULL);
398
60.0k
  
isl_assert60.0k
(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,60.0k
399
60.0k
        return NULL);
400
60.0k
401
60.0k
  ctx = tab->mat->ctx;
402
60.0k
  dim = tab->n_var;
403
60.0k
  gbr = ctx->opt->gbr;
404
60.0k
405
60.0k
  if (
tab->n_unbounded == tab->n_var60.0k
)
{0
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
60.0k
414
60.0k
  
if (60.0k
isl_tab_extend_cons(tab, dim + 1) < 060.0k
)
415
0
    return NULL;
416
60.0k
417
60.0k
  min = isl_vec_alloc(ctx, dim);
418
60.0k
  max = isl_vec_alloc(ctx, dim);
419
60.0k
  snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
420
60.0k
421
60.0k
  if (
!min || 60.0k
!max60.0k
||
!snap60.0k
)
422
0
    goto error;
423
60.0k
424
60.0k
  level = 0;
425
60.0k
  init = 1;
426
60.0k
  reduced = 0;
427
60.0k
428
68.1k
  while (
level >= 068.1k
)
{67.4k
429
67.4k
    if (
init67.4k
)
{65.0k
430
65.0k
      int choice;
431
65.0k
432
65.0k
      res = compute_min(ctx, tab, min, level);
433
65.0k
      if (res == isl_lp_error)
434
0
        goto error;
435
65.0k
      
if (65.0k
res != isl_lp_ok65.0k
)
436
0
        isl_die(ctx, isl_error_internal,
437
65.0k
          "expecting bounded rational solution",
438
65.0k
          goto error);
439
65.0k
      
if (65.0k
isl_tab_sample_is_integer(tab)65.0k
)
440
54.4k
        break;
441
10.6k
      res = compute_max(ctx, tab, max, level);
442
10.6k
      if (res == isl_lp_error)
443
0
        goto error;
444
10.6k
      
if (10.6k
res != isl_lp_ok10.6k
)
445
0
        isl_die(ctx, isl_error_internal,
446
10.6k
          "expecting bounded rational solution",
447
10.6k
          goto error);
448
10.6k
      
if (10.6k
isl_tab_sample_is_integer(tab)10.6k
)
449
1.14k
        break;
450
9.48k
      
choice = 9.48k
isl_int_lt9.48k
(min->el[level], max->el[level]);
451
9.48k
      if (
choice9.48k
)
{5.39k
452
5.39k
        int g;
453
5.39k
        g = greedy_search(ctx, tab, min, max, level);
454
5.39k
        if (g < 0)
455
0
          goto error;
456
5.39k
        
if (5.39k
g5.39k
)
457
3.67k
          break;
458
5.39k
      }
459
5.80k
      
if (5.80k
!reduced && 5.80k
choice4.75k
&&
460
1.33k
          
ctx->opt->gbr != 1.33k
ISL_GBR_NEVER1.33k
)
{1.33k
461
1.33k
        unsigned gbr_only_first;
462
1.33k
        if (
ctx->opt->gbr == 1.33k
ISL_GBR_ONCE1.33k
)
463
0
          
ctx->opt->gbr = 0
ISL_GBR_NEVER0
;
464
1.33k
        tab->n_zero = level;
465
1.33k
        gbr_only_first = ctx->opt->gbr_only_first;
466
1.33k
        ctx->opt->gbr_only_first =
467
1.33k
          ctx->opt->gbr == ISL_GBR_ALWAYS;
468
1.33k
        tab = isl_tab_compute_reduced_basis(tab);
469
1.33k
        ctx->opt->gbr_only_first = gbr_only_first;
470
1.33k
        if (
!tab || 1.33k
!tab->basis1.33k
)
471
0
          goto error;
472
1.33k
        reduced = 1;
473
1.33k
        continue;
474
1.33k
      }
475
4.47k
      reduced = 0;
476
4.47k
      snap[level] = isl_tab_snap(tab);
477
4.47k
    } else
478
2.38k
      isl_int_add_ui(min->el[level], min->el[level], 1);
479
67.4k
480
6.85k
    
if (6.85k
isl_int_gt6.85k
(min->el[level], max->el[level]))
{3.06k
481
3.06k
      level--;
482
3.06k
      init = 0;
483
3.06k
      if (level >= 0)
484
2.38k
        
if (2.38k
isl_tab_rollback(tab, snap[level]) < 02.38k
)
485
0
          goto error;
486
3.06k
      continue;
487
3.06k
    }
488
3.78k
    
isl_int_neg3.78k
(tab->basis->row[1 + level][0], min->el[level]);3.78k
489
3.78k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
490
0
      goto error;
491
3.78k
    
isl_int_set_si3.78k
(tab->basis->row[1 + level][0], 0);3.78k
492
3.78k
    if (
level + tab->n_unbounded < dim - 13.78k
)
{3.71k
493
3.71k
      ++level;
494
3.71k
      init = 1;
495
3.71k
      continue;
496
3.71k
    }
497
71
    break;
498
3.78k
  }
499
60.0k
500
60.0k
  
if (60.0k
level >= 060.0k
)
{59.3k
501
59.3k
    sample = isl_tab_get_sample_value(tab);
502
59.3k
    if (!sample)
503
0
      goto error;
504
59.3k
    
if (59.3k
tab->n_unbounded && 59.3k
!310
isl_int_is_one310
(sample->el[0]))
{243
505
243
      sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
506
243
                 sample);
507
243
      sample = isl_vec_ceil(sample);
508
243
      sample = isl_mat_vec_inverse_product(
509
243
          isl_mat_copy(tab->basis), sample);
510
243
    }
511
59.3k
  } else
512
686
    sample = isl_vec_alloc(ctx, 0);
513
60.0k
514
60.0k
  ctx->opt->gbr = gbr;
515
60.0k
  isl_vec_free(min);
516
60.0k
  isl_vec_free(max);
517
60.0k
  free(snap);
518
60.0k
  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
60.0k
}
526
527
static struct isl_vec *sample_bounded(struct 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
21.9k
{
535
21.9k
  int i, n;
536
21.9k
  isl_vec *sample = NULL;
537
21.9k
  isl_ctx *ctx;
538
21.9k
  unsigned nparam;
539
21.9k
  unsigned nvar;
540
21.9k
541
21.9k
  ctx = isl_basic_set_get_ctx(bset);
542
21.9k
  if (!ctx)
543
0
    goto error;
544
21.9k
545
21.9k
  nparam = isl_basic_set_dim(bset, isl_dim_param);
546
21.9k
  nvar = isl_basic_set_dim(bset, isl_dim_set);
547
21.9k
548
21.9k
  sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
549
21.9k
  if (!sample)
550
0
    goto error;
551
21.9k
  
isl_int_set_si21.9k
(sample->el[0], 1);21.9k
552
21.9k
553
21.9k
  bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
554
21.9k
555
105k
  for (i = 0, n = 0; 
i < f->n_group105k
;
++i83.8k
)
{84.0k
556
84.0k
    isl_basic_set *bset_i;
557
84.0k
    isl_vec *sample_i;
558
84.0k
559
84.0k
    bset_i = isl_basic_set_copy(bset);
560
84.0k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
561
84.0k
          nparam + n + f->len[i], nvar - n - f->len[i]);
562
84.0k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
563
84.0k
          nparam, n);
564
84.0k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
565
84.0k
          n + f->len[i], nvar - n - f->len[i]);
566
84.0k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
567
84.0k
568
84.0k
    sample_i = sample_bounded(bset_i);
569
84.0k
    if (!sample_i)
570
0
      goto error;
571
84.0k
    
if (84.0k
sample_i->size == 084.0k
)
{169
572
169
      isl_basic_set_free(bset);
573
169
      isl_factorizer_free(f);
574
169
      isl_vec_free(sample);
575
169
      return sample_i;
576
169
    }
577
83.8k
    isl_seq_cpy(sample->el + 1 + nparam + n,
578
83.8k
          sample_i->el + 1, f->len[i]);
579
83.8k
    isl_vec_free(sample_i);
580
83.8k
581
83.8k
    n += f->len[i];
582
83.8k
  }
583
21.9k
584
21.7k
  f->morph = isl_morph_inverse(f->morph);
585
21.7k
  sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
586
21.7k
587
21.7k
  isl_basic_set_free(bset);
588
21.7k
  isl_factorizer_free(f);
589
21.7k
  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
21.9k
}
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 struct isl_vec *sample_bounded(struct isl_basic_set *bset)
605
163k
{
606
163k
  unsigned dim;
607
163k
  struct isl_vec *sample;
608
163k
  struct isl_tab *tab = NULL;
609
163k
  isl_factorizer *f;
610
163k
611
163k
  if (!bset)
612
0
    return NULL;
613
163k
614
163k
  
if (163k
isl_basic_set_plain_is_empty(bset)163k
)
615
7
    return empty_sample(bset);
616
163k
617
163k
  dim = isl_basic_set_total_dim(bset);
618
163k
  if (dim == 0)
619
36.4k
    return zero_sample(bset);
620
127k
  
if (127k
dim == 1127k
)
621
74.6k
    return interval_sample(bset);
622
52.4k
  
if (52.4k
bset->n_eq > 052.4k
)
623
287
    return sample_eq(bset, sample_bounded);
624
52.4k
625
52.1k
  f = isl_basic_set_factorizer(bset);
626
52.1k
  if (!f)
627
0
    goto error;
628
52.1k
  
if (52.1k
f->n_group != 052.1k
)
629
21.9k
    return factored_sample(bset, f);
630
30.2k
  isl_factorizer_free(f);
631
30.2k
632
30.2k
  tab = isl_tab_from_basic_set(bset, 1);
633
30.2k
  if (
tab && 30.2k
tab->empty30.2k
)
{3.88k
634
3.88k
    isl_tab_free(tab);
635
3.88k
    ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
636
3.88k
    sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
637
3.88k
    isl_basic_set_free(bset);
638
3.88k
    return sample;
639
3.88k
  }
640
30.2k
641
26.3k
  
if (26.3k
!26.3k
ISL_F_ISSET26.3k
(bset, ISL_BASIC_SET_NO_IMPLICIT))
642
26.2k
    
if (26.2k
isl_tab_detect_implicit_equalities(tab) < 026.2k
)
643
0
      goto error;
644
26.3k
645
26.3k
  sample = isl_tab_sample(tab);
646
26.3k
  if (!sample)
647
0
    goto error;
648
26.3k
649
26.3k
  
if (26.3k
sample->size > 026.3k
)
{26.0k
650
26.0k
    isl_vec_free(bset->sample);
651
26.0k
    bset->sample = isl_vec_copy(sample);
652
26.0k
  }
653
26.3k
654
26.3k
  isl_basic_set_free(bset);
655
26.3k
  isl_tab_free(tab);
656
26.3k
  return sample;
657
0
error:
658
0
  isl_basic_set_free(bset);
659
0
  isl_tab_free(tab);
660
0
  return NULL;
661
26.3k
}
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 struct isl_basic_set *plug_in(struct isl_basic_set *bset,
676
  struct isl_vec *sample)
677
65.4k
{
678
65.4k
  int i;
679
65.4k
  unsigned total;
680
65.4k
  struct isl_mat *T;
681
65.4k
682
65.4k
  if (
!bset || 65.4k
!sample65.4k
)
683
0
    goto error;
684
65.4k
685
65.4k
  total = isl_basic_set_total_dim(bset);
686
65.4k
  T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
687
65.4k
  if (!T)
688
0
    goto error;
689
65.4k
690
234k
  
for (i = 0; 65.4k
i < sample->size234k
;
++i169k
)
{169k
691
169k
    isl_int_set(T->row[i][0], sample->el[i]);
692
169k
    isl_seq_clr(T->row[i] + 1, T->n_col - 1);
693
169k
  }
694
329k
  for (i = 0; 
i < T->n_col - 1329k
;
++i263k
)
{263k
695
263k
    isl_seq_clr(T->row[sample->size + i], T->n_col);
696
263k
    isl_int_set_si(T->row[sample->size + i][1 + i], 1);
697
263k
  }
698
65.4k
  isl_vec_free(sample);
699
65.4k
700
65.4k
  bset = isl_basic_set_preimage(bset, T);
701
65.4k
  return bset;
702
0
error:
703
0
  isl_basic_set_free(bset);
704
0
  isl_vec_free(sample);
705
0
  return NULL;
706
65.4k
}
707
708
/* Given a basic set "bset", return any (possibly non-integer) point
709
 * in the basic set.
710
 */
711
static struct isl_vec *rational_sample(struct isl_basic_set *bset)
712
66.9k
{
713
66.9k
  struct isl_tab *tab;
714
66.9k
  struct isl_vec *sample;
715
66.9k
716
66.9k
  if (!bset)
717
0
    return NULL;
718
66.9k
719
66.9k
  tab = isl_tab_from_basic_set(bset, 0);
720
66.9k
  sample = isl_tab_get_sample_value(tab);
721
66.9k
  isl_tab_free(tab);
722
66.9k
723
66.9k
  isl_basic_set_free(bset);
724
66.9k
725
66.9k
  return sample;
726
66.9k
}
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 struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
762
  struct isl_vec *vec)
763
1.47k
{
764
1.47k
  int i, j, k;
765
1.47k
  unsigned total;
766
1.47k
767
1.47k
  struct isl_basic_set *shift = NULL;
768
1.47k
769
1.47k
  if (
!cone || 1.47k
!vec1.47k
)
770
0
    goto error;
771
1.47k
772
1.47k
  
isl_assert1.47k
(cone->ctx, cone->n_eq == 0, goto error);1.47k
773
1.47k
774
1.47k
  total = isl_basic_set_total_dim(cone);
775
1.47k
776
1.47k
  shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
777
1.47k
          0, 0, cone->n_ineq);
778
1.47k
779
4.97k
  for (i = 0; 
i < cone->n_ineq4.97k
;
++i3.50k
)
{3.50k
780
3.50k
    k = isl_basic_set_alloc_inequality(shift);
781
3.50k
    if (k < 0)
782
0
      goto error;
783
3.50k
    isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
784
3.50k
    isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
785
3.50k
              &shift->ineq[k][0]);
786
3.50k
    isl_int_cdiv_q(shift->ineq[k][0],
787
3.50k
             shift->ineq[k][0], vec->el[0]);
788
3.50k
    isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
789
13.4k
    for (j = 0; 
j < total13.4k
;
++j9.94k
)
{9.94k
790
9.94k
      if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
791
7.52k
        continue;
792
2.41k
      
isl_int_add2.41k
(shift->ineq[k][0],2.41k
793
2.41k
            shift->ineq[k][0], shift->ineq[k][1 + j]);
794
2.41k
    }
795
3.50k
  }
796
1.47k
797
1.47k
  isl_basic_set_free(cone);
798
1.47k
  isl_vec_free(vec);
799
1.47k
800
1.47k
  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
1.47k
}
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 struct isl_vec *round_up_in_cone(struct isl_vec *vec,
820
  struct isl_basic_set *cone, struct isl_mat *U)
821
65.4k
{
822
65.4k
  unsigned total;
823
65.4k
824
65.4k
  if (
!vec || 65.4k
!cone65.4k
||
!U65.4k
)
825
0
    goto error;
826
65.4k
827
65.4k
  
isl_assert65.4k
(vec->ctx, vec->size != 0, goto error);65.4k
828
65.4k
  
if (65.4k
isl_int_is_one65.4k
(vec->el[0]))
{63.9k
829
63.9k
    isl_mat_free(U);
830
63.9k
    isl_basic_set_free(cone);
831
63.9k
    return vec;
832
63.9k
  }
833
65.4k
834
1.47k
  total = isl_basic_set_total_dim(cone);
835
1.47k
  cone = isl_basic_set_preimage(cone, U);
836
1.47k
  cone = isl_basic_set_remove_dims(cone, isl_dim_set,
837
1.47k
           0, total - (vec->size - 1));
838
1.47k
839
1.47k
  cone = shift_cone(cone, vec);
840
1.47k
841
1.47k
  vec = rational_sample(cone);
842
1.47k
  vec = isl_vec_ceil(vec);
843
1.47k
  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
65.4k
}
850
851
/* Concatenate two integer vectors, i.e., two vectors with denominator
852
 * (stored in element 0) equal to 1.
853
 */
854
static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
855
65.4k
{
856
65.4k
  struct isl_vec *vec;
857
65.4k
858
65.4k
  if (
!vec1 || 65.4k
!vec265.4k
)
859
0
    goto error;
860
65.4k
  
isl_assert65.4k
(vec1->ctx, vec1->size > 0, goto error);65.4k
861
65.4k
  
isl_assert65.4k
(vec2->ctx, vec2->size > 0, goto error);65.4k
862
65.4k
  
isl_assert65.4k
(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);65.4k
863
65.4k
  
isl_assert65.4k
(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);65.4k
864
65.4k
865
65.4k
  vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
866
65.4k
  if (!vec)
867
0
    goto error;
868
65.4k
869
65.4k
  isl_seq_cpy(vec->el, vec1->el, vec1->size);
870
65.4k
  isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
871
65.4k
872
65.4k
  isl_vec_free(vec1);
873
65.4k
  isl_vec_free(vec2);
874
65.4k
875
65.4k
  return vec;
876
0
error:
877
0
  isl_vec_free(vec1);
878
0
  isl_vec_free(vec2);
879
0
  return NULL;
880
65.4k
}
881
882
/* Give a basic set "bset" with recession cone "cone", compute and
883
 * return an integer point in bset, if any.
884
 *
885
 * If the recession cone is full-dimensional, then we know that
886
 * bset contains an infinite number of integer points and it is
887
 * fairly easy to pick one of them.
888
 * If the recession cone is not full-dimensional, then we first
889
 * transform bset such that the bounded directions appear as
890
 * the first dimensions of the transformed basic set.
891
 * We do this by using a unimodular transformation that transforms
892
 * the equalities in the recession cone to equalities on the first
893
 * dimensions.
894
 *
895
 * The transformed set is then projected onto its bounded dimensions.
896
 * Note that to compute this projection, we can simply drop all constraints
897
 * involving any of the unbounded dimensions since these constraints
898
 * cannot be combined to produce a constraint on the bounded dimensions.
899
 * To see this, assume that there is such a combination of constraints
900
 * that produces a constraint on the bounded dimensions.  This means
901
 * that some combination of the unbounded dimensions has both an upper
902
 * bound and a lower bound in terms of the bounded dimensions, but then
903
 * this combination would be a bounded direction too and would have been
904
 * transformed into a bounded dimensions.
905
 *
906
 * We then compute a sample value in the bounded dimensions.
907
 * If no such value can be found, then the original set did not contain
908
 * any integer points and we are done.
909
 * Otherwise, we plug in the value we found in the bounded dimensions,
910
 * project out these bounded dimensions and end up with a set with
911
 * a full-dimensional recession cone.
912
 * A sample point in this set is computed by "rounding up" any
913
 * rational point in the set.
914
 *
915
 * The sample points in the bounded and unbounded dimensions are
916
 * then combined into a single sample point and transformed back
917
 * to the original space.
918
 */
919
__isl_give isl_vec *isl_basic_set_sample_with_cone(
920
  __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
921
68.9k
{
922
68.9k
  unsigned total;
923
68.9k
  unsigned cone_dim;
924
68.9k
  struct isl_mat *M, *U;
925
68.9k
  struct isl_vec *sample;
926
68.9k
  struct isl_vec *cone_sample;
927
68.9k
  struct isl_ctx *ctx;
928
68.9k
  struct isl_basic_set *bounded;
929
68.9k
930
68.9k
  if (
!bset || 68.9k
!cone68.9k
)
931
0
    goto error;
932
68.9k
933
68.9k
  ctx = isl_basic_set_get_ctx(bset);
934
68.9k
  total = isl_basic_set_total_dim(cone);
935
68.9k
  cone_dim = total - cone->n_eq;
936
68.9k
937
68.9k
  M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
938
68.9k
  M = isl_mat_left_hermite(M, 0, &U, NULL);
939
68.9k
  if (!M)
940
0
    goto error;
941
68.9k
  isl_mat_free(M);
942
68.9k
943
68.9k
  U = isl_mat_lin_to_aff(U);
944
68.9k
  bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
945
68.9k
946
68.9k
  bounded = isl_basic_set_copy(bset);
947
68.9k
  bounded = isl_basic_set_drop_constraints_involving(bounded,
948
68.9k
               total - cone_dim, cone_dim);
949
68.9k
  bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
950
68.9k
  sample = sample_bounded(bounded);
951
68.9k
  if (
!sample || 68.9k
sample->size == 068.9k
)
{3.46k
952
3.46k
    isl_basic_set_free(bset);
953
3.46k
    isl_basic_set_free(cone);
954
3.46k
    isl_mat_free(U);
955
3.46k
    return sample;
956
3.46k
  }
957
65.4k
  bset = plug_in(bset, isl_vec_copy(sample));
958
65.4k
  cone_sample = rational_sample(bset);
959
65.4k
  cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
960
65.4k
  sample = vec_concat(sample, cone_sample);
961
65.4k
  sample = isl_mat_vec_product(U, sample);
962
65.4k
  return sample;
963
0
error:
964
0
  isl_basic_set_free(cone);
965
0
  isl_basic_set_free(bset);
966
0
  return NULL;
967
68.9k
}
968
969
static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
970
1.45k
{
971
1.45k
  int i;
972
1.45k
973
1.45k
  isl_int_set_si(*s, 0);
974
1.45k
975
4.43k
  for (i = 0; 
i < v->size4.43k
;
++i2.98k
)
976
2.98k
    
if (2.98k
isl_int_is_neg2.98k
(v->el[i]))
977
431
      isl_int_add(*s, *s, v->el[i]);
978
1.45k
}
979
980
/* Given a tableau "tab", a tableau "tab_cone" that corresponds
981
 * to the recession cone and the inverse of a new basis U = inv(B),
982
 * with the unbounded directions in B last,
983
 * add constraints to "tab" that ensure any rational value
984
 * in the unbounded directions can be rounded up to an integer value.
985
 *
986
 * The new basis is given by x' = B x, i.e., x = U x'.
987
 * For any rational value of the last tab->n_unbounded coordinates
988
 * in the update tableau, the value that is obtained by rounding
989
 * up this value should be contained in the original tableau.
990
 * For any constraint "a x + c >= 0", we therefore need to add
991
 * a constraint "a x + c + s >= 0", with s the sum of all negative
992
 * entries in the last elements of "a U".
993
 *
994
 * Since we are not interested in the first entries of any of the "a U",
995
 * we first drop the columns of U that correpond to bounded directions.
996
 */
997
static int tab_shift_cone(struct isl_tab *tab,
998
  struct isl_tab *tab_cone, struct isl_mat *U)
999
321
{
1000
321
  int i;
1001
321
  isl_int v;
1002
321
  struct isl_basic_set *bset = NULL;
1003
321
1004
321
  if (
tab && 321
tab->n_unbounded == 0321
)
{0
1005
0
    isl_mat_free(U);
1006
0
    return 0;
1007
0
  }
1008
321
  
isl_int_init321
(v);321
1009
321
  if (
!tab || 321
!tab_cone321
||
!U321
)
1010
0
    goto error;
1011
321
  bset = isl_tab_peek_bset(tab_cone);
1012
321
  U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1013
4.64k
  for (i = 0; 
i < bset->n_ineq4.64k
;
++i4.32k
)
{4.32k
1014
4.32k
    int ok;
1015
4.32k
    struct isl_vec *row = NULL;
1016
4.32k
    if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1017
2.87k
      continue;
1018
1.45k
    row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1019
1.45k
    if (!row)
1020
0
      goto error;
1021
1.45k
    isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1022
1.45k
    row = isl_vec_mat_product(row, isl_mat_copy(U));
1023
1.45k
    if (!row)
1024
0
      goto error;
1025
1.45k
    vec_sum_of_neg(row, &v);
1026
1.45k
    isl_vec_free(row);
1027
1.45k
    if (isl_int_is_zero(v))
1028
1.08k
      continue;
1029
370
    
if (370
isl_tab_extend_cons(tab, 1) < 0370
)
1030
0
      goto error;
1031
370
    
isl_int_add370
(bset->ineq[i][0], bset->ineq[i][0], v);370
1032
370
    ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1033
370
    isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1034
370
    if (!ok)
1035
0
      goto error;
1036
370
  }
1037
321
1038
321
  isl_mat_free(U);
1039
321
  isl_int_clear(v);
1040
321
  return 0;
1041
0
error:
1042
0
  isl_mat_free(U);
1043
0
  isl_int_clear(v);
1044
0
  return -1;
1045
321
}
1046
1047
/* Compute and return an initial basis for the possibly
1048
 * unbounded tableau "tab".  "tab_cone" is a tableau
1049
 * for the corresponding recession cone.
1050
 * Additionally, add constraints to "tab" that ensure
1051
 * that any rational value for the unbounded directions
1052
 * can be rounded up to an integer value.
1053
 *
1054
 * If the tableau is bounded, i.e., if the recession cone
1055
 * is zero-dimensional, then we just use inital_basis.
1056
 * Otherwise, we construct a basis whose first directions
1057
 * correspond to equalities, followed by bounded directions,
1058
 * i.e., equalities in the recession cone.
1059
 * The remaining directions are then unbounded.
1060
 */
1061
int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1062
  struct isl_tab *tab_cone)
1063
363
{
1064
363
  struct isl_mat *eq;
1065
363
  struct isl_mat *cone_eq;
1066
363
  struct isl_mat *U, *Q;
1067
363
1068
363
  if (
!tab || 363
!tab_cone363
)
1069
0
    return -1;
1070
363
1071
363
  
if (363
tab_cone->n_col == tab_cone->n_dead363
)
{42
1072
42
    tab->basis = initial_basis(tab);
1073
42
    return tab->basis ? 
042
:
-10
;
1074
42
  }
1075
363
1076
321
  eq = tab_equalities(tab);
1077
321
  if (!eq)
1078
0
    return -1;
1079
321
  tab->n_zero = eq->n_row;
1080
321
  cone_eq = tab_equalities(tab_cone);
1081
321
  eq = isl_mat_concat(eq, cone_eq);
1082
321
  if (!eq)
1083
0
    return -1;
1084
321
  tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1085
321
  eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1086
321
  if (!eq)
1087
0
    return -1;
1088
321
  isl_mat_free(eq);
1089
321
  tab->basis = isl_mat_lin_to_aff(Q);
1090
321
  if (tab_shift_cone(tab, tab_cone, U) < 0)
1091
0
    return -1;
1092
321
  
if (321
!tab->basis321
)
1093
0
    return -1;
1094
321
  return 0;
1095
321
}
1096
1097
/* Compute and return a sample point in bset using generalized basis
1098
 * reduction.  We first check if the input set has a non-trivial
1099
 * recession cone.  If so, we perform some extra preprocessing in
1100
 * sample_with_cone.  Otherwise, we directly perform generalized basis
1101
 * reduction.
1102
 */
1103
static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1104
78.9k
{
1105
78.9k
  unsigned dim;
1106
78.9k
  struct isl_basic_set *cone;
1107
78.9k
1108
78.9k
  dim = isl_basic_set_total_dim(bset);
1109
78.9k
1110
78.9k
  cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1111
78.9k
  if (!cone)
1112
0
    goto error;
1113
78.9k
1114
78.9k
  
if (78.9k
cone->n_eq < dim78.9k
)
1115
68.6k
    return isl_basic_set_sample_with_cone(bset, cone);
1116
78.9k
1117
10.3k
  isl_basic_set_free(cone);
1118
10.3k
  return sample_bounded(bset);
1119
0
error:
1120
0
  isl_basic_set_free(bset);
1121
0
  return NULL;
1122
78.9k
}
1123
1124
static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1125
143k
{
1126
143k
  struct isl_ctx *ctx;
1127
143k
  unsigned dim;
1128
143k
  if (!bset)
1129
0
    return NULL;
1130
143k
1131
143k
  ctx = bset->ctx;
1132
143k
  if (isl_basic_set_plain_is_empty(bset))
1133
177
    return empty_sample(bset);
1134
143k
1135
143k
  dim = isl_basic_set_n_dim(bset);
1136
143k
  isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1137
143k
  
isl_assert143k
(ctx, bset->n_div == 0, goto error);143k
1138
143k
1139
143k
  
if (143k
bset->sample && 143k
bset->sample->size == 1 + dim171
)
{35
1140
35
    int contains = isl_basic_set_contains(bset, bset->sample);
1141
35
    if (contains < 0)
1142
0
      goto error;
1143
35
    
if (35
contains35
)
{0
1144
0
      struct isl_vec *sample = isl_vec_copy(bset->sample);
1145
0
      isl_basic_set_free(bset);
1146
0
      return sample;
1147
0
    }
1148
35
  }
1149
143k
  isl_vec_free(bset->sample);
1150
143k
  bset->sample = NULL;
1151
143k
1152
143k
  if (bset->n_eq > 0)
1153
42.8k
    
return sample_eq(bset, bounded ? 42.8k
isl_basic_set_sample_bounded0
1154
42.8k
                 : isl_basic_set_sample_vec);
1155
100k
  
if (100k
dim == 0100k
)
1156
2.69k
    return zero_sample(bset);
1157
97.5k
  
if (97.5k
dim == 197.5k
)
1158
18.5k
    return interval_sample(bset);
1159
97.5k
1160
78.9k
  
return bounded ? 78.9k
sample_bounded(bset)0
:
gbr_sample(bset)78.9k
;
1161
0
error:
1162
0
  isl_basic_set_free(bset);
1163
0
  return NULL;
1164
97.5k
}
1165
1166
__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1167
143k
{
1168
143k
  return basic_set_sample(bset, 0);
1169
143k
}
1170
1171
/* Compute an integer sample in "bset", where the caller guarantees
1172
 * that "bset" is bounded.
1173
 */
1174
struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1175
0
{
1176
0
  return basic_set_sample(bset, 1);
1177
0
}
1178
1179
__isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1180
130k
{
1181
130k
  int i;
1182
130k
  int k;
1183
130k
  struct isl_basic_set *bset = NULL;
1184
130k
  struct isl_ctx *ctx;
1185
130k
  unsigned dim;
1186
130k
1187
130k
  if (!vec)
1188
0
    return NULL;
1189
130k
  ctx = vec->ctx;
1190
130k
  isl_assert(ctx, vec->size != 0, goto error);
1191
130k
1192
130k
  bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1193
130k
  if (!bset)
1194
0
    goto error;
1195
130k
  dim = isl_basic_set_n_dim(bset);
1196
520k
  for (i = dim - 1; 
i >= 0520k
;
--i389k
)
{389k
1197
389k
    k = isl_basic_set_alloc_equality(bset);
1198
389k
    if (k < 0)
1199
0
      goto error;
1200
389k
    isl_seq_clr(bset->eq[k], 1 + dim);
1201
389k
    isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1202
389k
    isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1203
389k
  }
1204
130k
  bset->sample = vec;
1205
130k
1206
130k
  return bset;
1207
0
error:
1208
0
  isl_basic_set_free(bset);
1209
0
  isl_vec_free(vec);
1210
0
  return NULL;
1211
130k
}
1212
1213
__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1214
1
{
1215
1
  struct isl_basic_set *bset;
1216
1
  struct isl_vec *sample_vec;
1217
1
1218
1
  bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1219
1
  sample_vec = isl_basic_set_sample_vec(bset);
1220
1
  if (!sample_vec)
1221
0
    goto error;
1222
1
  
if (1
sample_vec->size == 01
)
{0
1223
0
    isl_vec_free(sample_vec);
1224
0
    return isl_basic_map_set_to_empty(bmap);
1225
0
  }
1226
1
  isl_vec_free(bmap->sample);
1227
1
  bmap->sample = isl_vec_copy(sample_vec);
1228
1
  bset = isl_basic_set_from_vec(sample_vec);
1229
1
  return isl_basic_map_overlying_set(bset, bmap);
1230
0
error:
1231
0
  isl_basic_map_free(bmap);
1232
0
  return NULL;
1233
1
}
1234
1235
__isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1236
1
{
1237
1
  return isl_basic_map_sample(bset);
1238
1
}
1239
1240
__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1241
0
{
1242
0
  int i;
1243
0
  isl_basic_map *sample = NULL;
1244
0
1245
0
  if (!map)
1246
0
    goto error;
1247
0
1248
0
  
for (i = 0; 0
i < map->n0
;
++i0
)
{0
1249
0
    sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1250
0
    if (!sample)
1251
0
      goto error;
1252
0
    
if (0
!0
ISL_F_ISSET0
(sample, ISL_BASIC_MAP_EMPTY))
1253
0
      break;
1254
0
    isl_basic_map_free(sample);
1255
0
  }
1256
0
  
if (0
i == map->n0
)
1257
0
    sample = isl_basic_map_empty(isl_map_get_space(map));
1258
0
  isl_map_free(map);
1259
0
  return sample;
1260
0
error:
1261
0
  isl_map_free(map);
1262
0
  return NULL;
1263
0
}
1264
1265
__isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1266
0
{
1267
0
  return bset_from_bmap(isl_map_sample(set_to_map(set)));
1268
0
}
1269
1270
__isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1271
1
{
1272
1
  isl_vec *vec;
1273
1
  isl_space *dim;
1274
1
1275
1
  dim = isl_basic_set_get_space(bset);
1276
1
  bset = isl_basic_set_underlying_set(bset);
1277
1
  vec = isl_basic_set_sample_vec(bset);
1278
1
1279
1
  return isl_point_alloc(dim, vec);
1280
1
}
1281
1282
__isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1283
2
{
1284
2
  int i;
1285
2
  isl_point *pnt;
1286
2
1287
2
  if (!set)
1288
0
    return NULL;
1289
2
1290
2
  
for (i = 0; 2
i < set->n2
;
++i0
)
{1
1291
1
    pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1292
1
    if (!pnt)
1293
0
      goto error;
1294
1
    
if (1
!isl_point_is_void(pnt)1
)
1295
1
      break;
1296
0
    isl_point_free(pnt);
1297
0
  }
1298
2
  
if (2
i == set->n2
)
1299
1
    pnt = isl_point_void(isl_set_get_space(set));
1300
2
1301
2
  isl_set_free(set);
1302
2
  return pnt;
1303
0
error:
1304
0
  isl_set_free(set);
1305
0
  return NULL;
1306
2
}