Coverage Report

Created: 2017-10-03 07:32

/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 __isl_give isl_vec *empty_sample(__isl_take isl_basic_set *bset)
28
410
{
29
410
  struct isl_vec *vec;
30
410
31
410
  vec = isl_vec_alloc(bset->ctx, 0);
32
410
  isl_basic_set_free(bset);
33
410
  return vec;
34
410
}
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
62.1k
{
42
62.1k
  unsigned dim;
43
62.1k
  struct isl_vec *sample;
44
62.1k
45
62.1k
  dim = isl_basic_set_total_dim(bset);
46
62.1k
  sample = isl_vec_alloc(bset->ctx, 1 + dim);
47
62.1k
  if (
sample62.1k
) {
48
62.1k
    isl_int_set_si(sample->el[0], 1);
49
62.1k
    isl_seq_clr(sample->el + 1, dim);
50
62.1k
  }
51
62.1k
  isl_basic_set_free(bset);
52
62.1k
  return sample;
53
62.1k
}
54
55
static __isl_give isl_vec *interval_sample(__isl_take isl_basic_set *bset)
56
163k
{
57
163k
  int i;
58
163k
  isl_int t;
59
163k
  struct isl_vec *sample;
60
163k
61
163k
  bset = isl_basic_set_simplify(bset);
62
163k
  if (!bset)
63
0
    return NULL;
64
163k
  
if (163k
isl_basic_set_plain_is_empty(bset)163k
)
65
0
    return empty_sample(bset);
66
163k
  
if (163k
bset->n_eq == 0 && 163k
bset->n_ineq == 0162k
)
67
7.78k
    return zero_sample(bset);
68
155k
69
155k
  sample = isl_vec_alloc(bset->ctx, 2);
70
155k
  if (!sample)
71
0
    goto error;
72
155k
  
if (155k
!bset155k
)
73
0
    return NULL;
74
155k
  
isl_int_set_si155k
(sample->block.data[0], 1);
75
155k
76
155k
  if (
bset->n_eq > 0155k
) {
77
940
    isl_assert(bset->ctx, bset->n_eq == 1, goto error);
78
940
    
isl_assert940
(bset->ctx, bset->n_ineq == 0, goto error);
79
940
    
if (940
isl_int_is_one940
(bset->eq[0][1]))
80
940
      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]);
85
0
    }
86
940
    isl_basic_set_free(bset);
87
940
    return sample;
88
154k
  }
89
154k
90
154k
  
isl_int_init154k
(t);
91
154k
  if (isl_int_is_one(bset->ineq[0][1]))
92
132k
    isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
93
154k
  else
94
22.1k
    isl_int_set(sample->block.data[1], bset->ineq[0][0]);
95
298k
  for (i = 1; 
i < bset->n_ineq298k
;
++i143k
) {
96
143k
    isl_seq_inner_product(sample->block.data,
97
143k
          bset->ineq[i], 2, &t);
98
143k
    if (isl_int_is_neg(t))
99
0
      break;
100
143k
  }
101
154k
  isl_int_clear(t);
102
154k
  if (
i < bset->n_ineq154k
) {
103
0
    isl_vec_free(sample);
104
0
    return empty_sample(bset);
105
0
  }
106
154k
107
154k
  isl_basic_set_free(bset);
108
154k
  return sample;
109
0
error:
110
0
  isl_basic_set_free(bset);
111
0
  isl_vec_free(sample);
112
0
  return NULL;
113
163k
}
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
88.0k
{
125
88.0k
  struct isl_mat *T;
126
88.0k
  struct isl_vec *sample;
127
88.0k
128
88.0k
  if (!bset)
129
0
    return NULL;
130
88.0k
131
88.0k
  bset = isl_basic_set_remove_equalities(bset, &T, NULL);
132
88.0k
  sample = recurse(bset);
133
88.0k
  if (
!sample || 88.0k
sample->size == 088.0k
)
134
1.49k
    isl_mat_free(T);
135
88.0k
  else
136
86.5k
    sample = isl_mat_vec_product(T, sample);
137
88.0k
  return sample;
138
88.0k
}
139
140
/* Return a matrix containing the equalities of the tableau
141
 * in constraint form.  The tableau is assumed to have
142
 * an associated bset that has been kept up-to-date.
143
 */
144
static struct isl_mat *tab_equalities(struct isl_tab *tab)
145
1.44k
{
146
1.44k
  int i, j;
147
1.44k
  int n_eq;
148
1.44k
  struct isl_mat *eq;
149
1.44k
  struct isl_basic_set *bset;
150
1.44k
151
1.44k
  if (!tab)
152
0
    return NULL;
153
1.44k
154
1.44k
  bset = isl_tab_peek_bset(tab);
155
1.44k
  isl_assert(tab->mat->ctx, bset, return NULL);
156
1.44k
157
1.44k
  n_eq = tab->n_var - tab->n_col + tab->n_dead;
158
1.44k
  if (
tab->empty || 1.44k
n_eq == 01.44k
)
159
344
    return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
160
1.10k
  
if (1.10k
n_eq == tab->n_var1.10k
)
161
0
    return isl_mat_identity(tab->mat->ctx, tab->n_var);
162
1.10k
163
1.10k
  eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
164
1.10k
  if (!eq)
165
0
    return NULL;
166
11.2k
  
for (i = 0, j = 0; 1.10k
i < tab->n_con11.2k
;
++i10.1k
) {
167
10.1k
    if (tab->con[i].is_row)
168
6.34k
      continue;
169
3.80k
    
if (3.80k
tab->con[i].index >= 0 && 3.80k
tab->con[i].index >= tab->n_dead2.30k
)
170
1.79k
      continue;
171
2.01k
    
if (2.01k
i < bset->n_eq2.01k
)
172
448
      isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
173
2.01k
    else
174
1.56k
      isl_seq_cpy(eq->row[j],
175
1.56k
            bset->ineq[i - bset->n_eq] + 1, tab->n_var);
176
10.1k
    ++j;
177
10.1k
  }
178
1.10k
  isl_assert(bset->ctx, j == n_eq, goto error);
179
1.10k
  return eq;
180
0
error:
181
0
  isl_mat_free(eq);
182
0
  return NULL;
183
1.44k
}
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
115k
{
194
115k
  int n_eq;
195
115k
  struct isl_mat *eq;
196
115k
  struct isl_mat *Q;
197
115k
198
115k
  tab->n_unbounded = 0;
199
115k
  tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
200
115k
  if (
tab->empty || 115k
n_eq == 0115k
||
n_eq == tab->n_var1.08k
)
201
115k
    return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
202
694
203
694
  eq = tab_equalities(tab);
204
694
  eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
205
694
  if (!eq)
206
0
    return NULL;
207
694
  isl_mat_free(eq);
208
694
209
694
  Q = isl_mat_lin_to_aff(Q);
210
694
  return Q;
211
694
}
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
166k
{
222
166k
  return isl_tab_min(tab, tab->basis->row[1 + level],
223
166k
          ctx->one, &min->el[level], NULL, 0);
224
166k
}
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
58.0k
{
235
58.0k
  enum isl_lp_result res;
236
58.0k
  unsigned dim = tab->n_var;
237
58.0k
238
58.0k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
239
58.0k
        tab->basis->row[1 + level] + 1, dim);
240
58.0k
  res = isl_tab_min(tab, tab->basis->row[1 + level],
241
58.0k
        ctx->one, &max->el[level], NULL, 0);
242
58.0k
  isl_seq_neg(tab->basis->row[1 + level] + 1,
243
58.0k
        tab->basis->row[1 + level] + 1, dim);
244
58.0k
  isl_int_neg(max->el[level], max->el[level]);
245
58.0k
246
58.0k
  return res;
247
58.0k
}
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
13.9k
{
275
13.9k
  struct isl_tab_undo *snap;
276
13.9k
  enum isl_lp_result res;
277
13.9k
278
13.9k
  snap = isl_tab_snap(tab);
279
13.9k
280
46.9k
  do {
281
46.9k
    isl_int_add(tab->basis->row[1 + level][0],
282
46.9k
          min->el[level], max->el[level]);
283
46.9k
    isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
284
46.9k
          tab->basis->row[1 + level][0], 2);
285
46.9k
    isl_int_neg(tab->basis->row[1 + level][0],
286
46.9k
          tab->basis->row[1 + level][0]);
287
46.9k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
288
0
      return -1;
289
46.9k
    
isl_int_set_si46.9k
(tab->basis->row[1 + level][0], 0);
290
46.9k
291
46.9k
    if (++level >= tab->n_var - tab->n_unbounded)
292
4.53k
      return 1;
293
42.4k
    
if (42.4k
isl_tab_sample_is_integer(tab)42.4k
)
294
6.35k
      return 1;
295
36.0k
296
36.0k
    res = compute_min(ctx, tab, min, level);
297
36.0k
    if (res == isl_lp_error)
298
0
      return -1;
299
36.0k
    
if (36.0k
res != isl_lp_ok36.0k
)
300
0
      isl_die(ctx, isl_error_internal,
301
36.0k
        "expecting bounded rational solution",
302
36.0k
        return -1);
303
36.0k
    res = compute_max(ctx, tab, max, level);
304
36.0k
    if (res == isl_lp_error)
305
0
      return -1;
306
36.0k
    
if (36.0k
res != isl_lp_ok36.0k
)
307
0
      isl_die(ctx, isl_error_internal,
308
46.9k
        "expecting bounded rational solution",
309
46.9k
        return -1);
310
36.0k
  } while (isl_int_le(min->el[level], max->el[level]));
311
13.9k
312
3.09k
  
if (3.09k
isl_tab_rollback(tab, snap) < 03.09k
)
313
0
    return -1;
314
3.09k
315
3.09k
  return 0;
316
3.09k
}
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
132k
{
375
132k
  unsigned dim;
376
132k
  unsigned gbr;
377
132k
  struct isl_ctx *ctx;
378
132k
  struct isl_vec *sample;
379
132k
  struct isl_vec *min;
380
132k
  struct isl_vec *max;
381
132k
  enum isl_lp_result res;
382
132k
  int level;
383
132k
  int init;
384
132k
  int reduced;
385
132k
  struct isl_tab_undo **snap;
386
132k
387
132k
  if (!tab)
388
0
    return NULL;
389
132k
  
if (132k
tab->empty132k
)
390
8.98k
    return isl_vec_alloc(tab->mat->ctx, 0);
391
123k
392
123k
  
if (123k
!tab->basis123k
)
393
115k
    tab->basis = initial_basis(tab);
394
123k
  if (!tab->basis)
395
0
    return NULL;
396
123k
  
isl_assert123k
(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
397
123k
        return NULL);
398
123k
  
isl_assert123k
(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
399
123k
        return NULL);
400
123k
401
123k
  ctx = tab->mat->ctx;
402
123k
  dim = tab->n_var;
403
123k
  gbr = ctx->opt->gbr;
404
123k
405
123k
  if (
tab->n_unbounded == tab->n_var123k
) {
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
123k
414
123k
  
if (123k
isl_tab_extend_cons(tab, dim + 1) < 0123k
)
415
0
    return NULL;
416
123k
417
123k
  min = isl_vec_alloc(ctx, dim);
418
123k
  max = isl_vec_alloc(ctx, dim);
419
123k
  snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
420
123k
421
123k
  if (
!min || 123k
!max123k
||
!snap123k
)
422
0
    goto error;
423
123k
424
123k
  level = 0;
425
123k
  init = 1;
426
123k
  reduced = 0;
427
123k
428
131k
  while (
level >= 0131k
) {
429
130k
    if (
init130k
) {
430
129k
      int choice;
431
129k
432
129k
      res = compute_min(ctx, tab, min, level);
433
129k
      if (res == isl_lp_error)
434
0
        goto error;
435
129k
      
if (129k
res != isl_lp_ok129k
)
436
0
        isl_die(ctx, isl_error_internal,
437
129k
          "expecting bounded rational solution",
438
129k
          goto error);
439
129k
      
if (129k
isl_tab_sample_is_integer(tab)129k
)
440
107k
        break;
441
21.9k
      res = compute_max(ctx, tab, max, level);
442
21.9k
      if (res == isl_lp_error)
443
0
        goto error;
444
21.9k
      
if (21.9k
res != isl_lp_ok21.9k
)
445
0
        isl_die(ctx, isl_error_internal,
446
21.9k
          "expecting bounded rational solution",
447
21.9k
          goto error);
448
21.9k
      
if (21.9k
isl_tab_sample_is_integer(tab)21.9k
)
449
4.09k
        break;
450
17.9k
      
choice = 17.9k
isl_int_lt17.9k
(min->el[level], max->el[level]);
451
17.9k
      if (
choice17.9k
) {
452
13.9k
        int g;
453
13.9k
        g = greedy_search(ctx, tab, min, max, level);
454
13.9k
        if (g < 0)
455
0
          goto error;
456
13.9k
        
if (13.9k
g13.9k
)
457
10.8k
          break;
458
7.02k
      }
459
7.02k
      
if (7.02k
!reduced && 7.02k
choice5.33k
&&
460
7.02k
          
ctx->opt->gbr != 2.84k
ISL_GBR_NEVER2.84k
) {
461
2.84k
        unsigned gbr_only_first;
462
2.84k
        if (
ctx->opt->gbr == 2.84k
ISL_GBR_ONCE2.84k
)
463
0
          
ctx->opt->gbr = 0
ISL_GBR_NEVER0
;
464
2.84k
        tab->n_zero = level;
465
2.84k
        gbr_only_first = ctx->opt->gbr_only_first;
466
2.84k
        ctx->opt->gbr_only_first =
467
2.84k
          ctx->opt->gbr == ISL_GBR_ALWAYS;
468
2.84k
        tab = isl_tab_compute_reduced_basis(tab);
469
2.84k
        ctx->opt->gbr_only_first = gbr_only_first;
470
2.84k
        if (
!tab || 2.84k
!tab->basis2.84k
)
471
0
          goto error;
472
2.84k
        reduced = 1;
473
2.84k
        continue;
474
2.84k
      }
475
4.17k
      reduced = 0;
476
4.17k
      snap[level] = isl_tab_snap(tab);
477
4.17k
    } else
478
1.03k
      isl_int_add_ui(min->el[level], min->el[level], 1);
479
130k
480
5.21k
    
if (5.21k
isl_int_gt5.21k
(min->el[level], max->el[level])) {
481
1.81k
      level--;
482
1.81k
      init = 0;
483
1.81k
      if (level >= 0)
484
1.03k
        
if (1.03k
isl_tab_rollback(tab, snap[level]) < 01.03k
)
485
0
          goto error;
486
1.81k
      continue;
487
1.81k
    }
488
3.40k
    
isl_int_neg3.40k
(tab->basis->row[1 + level][0], min->el[level]);
489
3.40k
    if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
490
0
      goto error;
491
3.40k
    
isl_int_set_si3.40k
(tab->basis->row[1 + level][0], 0);
492
3.40k
    if (
level + tab->n_unbounded < dim - 13.40k
) {
493
3.39k
      ++level;
494
3.39k
      init = 1;
495
3.39k
      continue;
496
3.39k
    }
497
7
    break;
498
7
  }
499
123k
500
123k
  
if (123k
level >= 0123k
) {
501
122k
    sample = isl_tab_get_sample_value(tab);
502
122k
    if (!sample)
503
0
      goto error;
504
122k
    
if (122k
tab->n_unbounded && 122k
!682
isl_int_is_one682
(sample->el[0])) {
505
160
      sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
506
160
                 sample);
507
160
      sample = isl_vec_ceil(sample);
508
160
      sample = isl_mat_vec_inverse_product(
509
160
          isl_mat_copy(tab->basis), sample);
510
160
    }
511
122k
  } else
512
773
    sample = isl_vec_alloc(ctx, 0);
513
123k
514
123k
  ctx->opt->gbr = gbr;
515
123k
  isl_vec_free(min);
516
123k
  isl_vec_free(max);
517
123k
  free(snap);
518
123k
  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
132k
}
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
44.4k
{
535
44.4k
  int i, n;
536
44.4k
  isl_vec *sample = NULL;
537
44.4k
  isl_ctx *ctx;
538
44.4k
  unsigned nparam;
539
44.4k
  unsigned nvar;
540
44.4k
541
44.4k
  ctx = isl_basic_set_get_ctx(bset);
542
44.4k
  if (!ctx)
543
0
    goto error;
544
44.4k
545
44.4k
  nparam = isl_basic_set_dim(bset, isl_dim_param);
546
44.4k
  nvar = isl_basic_set_dim(bset, isl_dim_set);
547
44.4k
548
44.4k
  sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
549
44.4k
  if (!sample)
550
0
    goto error;
551
44.4k
  
isl_int_set_si44.4k
(sample->el[0], 1);
552
44.4k
553
44.4k
  bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
554
44.4k
555
217k
  for (i = 0, n = 0; 
i < f->n_group217k
;
++i172k
) {
556
173k
    isl_basic_set *bset_i;
557
173k
    isl_vec *sample_i;
558
173k
559
173k
    bset_i = isl_basic_set_copy(bset);
560
173k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
561
173k
          nparam + n + f->len[i], nvar - n - f->len[i]);
562
173k
    bset_i = isl_basic_set_drop_constraints_involving(bset_i,
563
173k
          nparam, n);
564
173k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
565
173k
          n + f->len[i], nvar - n - f->len[i]);
566
173k
    bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
567
173k
568
173k
    sample_i = sample_bounded(bset_i);
569
173k
    if (!sample_i)
570
0
      goto error;
571
173k
    
if (173k
sample_i->size == 0173k
) {
572
420
      isl_basic_set_free(bset);
573
420
      isl_factorizer_free(f);
574
420
      isl_vec_free(sample);
575
420
      return sample_i;
576
420
    }
577
172k
    isl_seq_cpy(sample->el + 1 + nparam + n,
578
172k
          sample_i->el + 1, f->len[i]);
579
172k
    isl_vec_free(sample_i);
580
172k
581
172k
    n += f->len[i];
582
172k
  }
583
44.4k
584
44.0k
  f->morph = isl_morph_inverse(f->morph);
585
44.0k
  sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
586
44.0k
587
44.0k
  isl_basic_set_free(bset);
588
44.0k
  isl_factorizer_free(f);
589
44.0k
  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
44.4k
}
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
298k
{
606
298k
  unsigned dim;
607
298k
  struct isl_vec *sample;
608
298k
  struct isl_tab *tab = NULL;
609
298k
  isl_factorizer *f;
610
298k
611
298k
  if (!bset)
612
0
    return NULL;
613
298k
614
298k
  
if (298k
isl_basic_set_plain_is_empty(bset)298k
)
615
24
    return empty_sample(bset);
616
298k
617
298k
  dim = isl_basic_set_total_dim(bset);
618
298k
  if (dim == 0)
619
50.2k
    return zero_sample(bset);
620
248k
  
if (248k
dim == 1248k
)
621
133k
    return interval_sample(bset);
622
114k
  
if (114k
bset->n_eq > 0114k
)
623
1.30k
    return sample_eq(bset, sample_bounded);
624
112k
625
112k
  f = isl_basic_set_factorizer(bset);
626
112k
  if (!f)
627
0
    goto error;
628
112k
  
if (112k
f->n_group != 0112k
)
629
44.4k
    return factored_sample(bset, f);
630
68.4k
  isl_factorizer_free(f);
631
68.4k
632
68.4k
  tab = isl_tab_from_basic_set(bset, 1);
633
68.4k
  if (
tab && 68.4k
tab->empty68.4k
) {
634
3.93k
    isl_tab_free(tab);
635
3.93k
    ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
636
3.93k
    sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
637
3.93k
    isl_basic_set_free(bset);
638
3.93k
    return sample;
639
3.93k
  }
640
64.5k
641
64.5k
  
if (64.5k
!64.5k
ISL_F_ISSET64.5k
(bset, ISL_BASIC_SET_NO_IMPLICIT))
642
64.4k
    
if (64.4k
isl_tab_detect_implicit_equalities(tab) < 064.4k
)
643
0
      goto error;
644
64.5k
645
64.5k
  sample = isl_tab_sample(tab);
646
64.5k
  if (!sample)
647
0
    goto error;
648
64.5k
649
64.5k
  
if (64.5k
sample->size > 064.5k
) {
650
63.9k
    isl_vec_free(bset->sample);
651
63.9k
    bset->sample = isl_vec_copy(sample);
652
63.9k
  }
653
64.5k
654
64.5k
  isl_basic_set_free(bset);
655
64.5k
  isl_tab_free(tab);
656
64.5k
  return sample;
657
0
error:
658
0
  isl_basic_set_free(bset);
659
0
  isl_tab_free(tab);
660
0
  return NULL;
661
298k
}
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
103k
{
678
103k
  int i;
679
103k
  unsigned total;
680
103k
  struct isl_mat *T;
681
103k
682
103k
  if (
!bset || 103k
!sample103k
)
683
0
    goto error;
684
103k
685
103k
  total = isl_basic_set_total_dim(bset);
686
103k
  T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
687
103k
  if (!T)
688
0
    goto error;
689
103k
690
420k
  
for (i = 0; 103k
i < sample->size420k
;
++i316k
) {
691
316k
    isl_int_set(T->row[i][0], sample->el[i]);
692
316k
    isl_seq_clr(T->row[i] + 1, T->n_col - 1);
693
316k
  }
694
476k
  for (i = 0; 
i < T->n_col - 1476k
;
++i373k
) {
695
373k
    isl_seq_clr(T->row[sample->size + i], T->n_col);
696
373k
    isl_int_set_si(T->row[sample->size + i][1 + i], 1);
697
373k
  }
698
103k
  isl_vec_free(sample);
699
103k
700
103k
  bset = isl_basic_set_preimage(bset, T);
701
103k
  return bset;
702
0
error:
703
0
  isl_basic_set_free(bset);
704
0
  isl_vec_free(sample);
705
0
  return NULL;
706
103k
}
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
106k
{
713
106k
  struct isl_tab *tab;
714
106k
  struct isl_vec *sample;
715
106k
716
106k
  if (!bset)
717
0
    return NULL;
718
106k
719
106k
  tab = isl_tab_from_basic_set(bset, 0);
720
106k
  sample = isl_tab_get_sample_value(tab);
721
106k
  isl_tab_free(tab);
722
106k
723
106k
  isl_basic_set_free(bset);
724
106k
725
106k
  return sample;
726
106k
}
727
728
/* Given a linear cone "cone" and a rational point "vec",
729
 * construct a polyhedron with shifted copies of the constraints in "cone",
730
 * i.e., a polyhedron with "cone" as its recession cone, such that each
731
 * point x in this polyhedron is such that the unit box positioned at x
732
 * lies entirely inside the affine cone 'vec + cone'.
733
 * Any rational point in this polyhedron may therefore be rounded up
734
 * to yield an integer point that lies inside said affine cone.
735
 *
736
 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
737
 * point "vec" by v/d.
738
 * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
739
 * by <a_i, x> - b/d >= 0.
740
 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
741
 * We prefer this polyhedron over the actual affine cone because it doesn't
742
 * require a scaling of the constraints.
743
 * If each of the vertices of the unit cube positioned at x lies inside
744
 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
745
 * We therefore impose that x' = x + \sum e_i, for any selection of unit
746
 * vectors lies inside the polyhedron, i.e.,
747
 *
748
 *  <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
749
 *
750
 * The most stringent of these constraints is the one that selects
751
 * all negative a_i, so the polyhedron we are looking for has constraints
752
 *
753
 *  <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
754
 *
755
 * Note that if cone were known to have only non-negative rays
756
 * (which can be accomplished by a unimodular transformation),
757
 * then we would only have to check the points x' = x + e_i
758
 * and we only have to add the smallest negative a_i (if any)
759
 * instead of the sum of all negative a_i.
760
 */
761
static __isl_give isl_basic_set *shift_cone(__isl_take isl_basic_set *cone,
762
  __isl_take isl_vec *vec)
763
3.02k
{
764
3.02k
  int i, j, k;
765
3.02k
  unsigned total;
766
3.02k
767
3.02k
  struct isl_basic_set *shift = NULL;
768
3.02k
769
3.02k
  if (
!cone || 3.02k
!vec3.02k
)
770
0
    goto error;
771
3.02k
772
3.02k
  
isl_assert3.02k
(cone->ctx, cone->n_eq == 0, goto error);
773
3.02k
774
3.02k
  total = isl_basic_set_total_dim(cone);
775
3.02k
776
3.02k
  shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
777
3.02k
          0, 0, cone->n_ineq);
778
3.02k
779
9.69k
  for (i = 0; 
i < cone->n_ineq9.69k
;
++i6.66k
) {
780
6.66k
    k = isl_basic_set_alloc_inequality(shift);
781
6.66k
    if (k < 0)
782
0
      goto error;
783
6.66k
    isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
784
6.66k
    isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
785
6.66k
              &shift->ineq[k][0]);
786
6.66k
    isl_int_cdiv_q(shift->ineq[k][0],
787
6.66k
             shift->ineq[k][0], vec->el[0]);
788
6.66k
    isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
789
24.1k
    for (j = 0; 
j < total24.1k
;
++j17.4k
) {
790
17.4k
      if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
791
13.3k
        continue;
792
4.10k
      
isl_int_add4.10k
(shift->ineq[k][0],
793
4.10k
            shift->ineq[k][0], shift->ineq[k][1 + j]);
794
4.10k
    }
795
6.66k
  }
796
3.02k
797
3.02k
  isl_basic_set_free(cone);
798
3.02k
  isl_vec_free(vec);
799
3.02k
800
3.02k
  return isl_basic_set_finalize(shift);
801
0
error:
802
0
  isl_basic_set_free(shift);
803
0
  isl_basic_set_free(cone);
804
0
  isl_vec_free(vec);
805
0
  return NULL;
806
3.02k
}
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
103k
{
822
103k
  unsigned total;
823
103k
824
103k
  if (
!vec || 103k
!cone103k
||
!U103k
)
825
0
    goto error;
826
103k
827
103k
  
isl_assert103k
(vec->ctx, vec->size != 0, goto error);
828
103k
  
if (103k
isl_int_is_one103k
(vec->el[0])) {
829
100k
    isl_mat_free(U);
830
100k
    isl_basic_set_free(cone);
831
100k
    return vec;
832
100k
  }
833
3.02k
834
3.02k
  total = isl_basic_set_total_dim(cone);
835
3.02k
  cone = isl_basic_set_preimage(cone, U);
836
3.02k
  cone = isl_basic_set_remove_dims(cone, isl_dim_set,
837
3.02k
           0, total - (vec->size - 1));
838
3.02k
839
3.02k
  cone = shift_cone(cone, vec);
840
3.02k
841
3.02k
  vec = rational_sample(cone);
842
3.02k
  vec = isl_vec_ceil(vec);
843
3.02k
  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
103k
}
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
103k
{
857
103k
  struct isl_vec *vec;
858
103k
859
103k
  if (
!vec1 || 103k
!vec2103k
)
860
0
    goto error;
861
103k
  
isl_assert103k
(vec1->ctx, vec1->size > 0, goto error);
862
103k
  
isl_assert103k
(vec2->ctx, vec2->size > 0, goto error);
863
103k
  
isl_assert103k
(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
864
103k
  
isl_assert103k
(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
865
103k
866
103k
  vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
867
103k
  if (!vec)
868
0
    goto error;
869
103k
870
103k
  isl_seq_cpy(vec->el, vec1->el, vec1->size);
871
103k
  isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
872
103k
873
103k
  isl_vec_free(vec1);
874
103k
  isl_vec_free(vec2);
875
103k
876
103k
  return vec;
877
0
error:
878
0
  isl_vec_free(vec1);
879
0
  isl_vec_free(vec2);
880
0
  return NULL;
881
103k
}
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
107k
{
923
107k
  unsigned total;
924
107k
  unsigned cone_dim;
925
107k
  struct isl_mat *M, *U;
926
107k
  struct isl_vec *sample;
927
107k
  struct isl_vec *cone_sample;
928
107k
  struct isl_ctx *ctx;
929
107k
  struct isl_basic_set *bounded;
930
107k
931
107k
  if (
!bset || 107k
!cone107k
)
932
0
    goto error;
933
107k
934
107k
  ctx = isl_basic_set_get_ctx(bset);
935
107k
  total = isl_basic_set_total_dim(cone);
936
107k
  cone_dim = total - cone->n_eq;
937
107k
938
107k
  M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
939
107k
  M = isl_mat_left_hermite(M, 0, &U, NULL);
940
107k
  if (!M)
941
0
    goto error;
942
107k
  isl_mat_free(M);
943
107k
944
107k
  U = isl_mat_lin_to_aff(U);
945
107k
  bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
946
107k
947
107k
  bounded = isl_basic_set_copy(bset);
948
107k
  bounded = isl_basic_set_drop_constraints_involving(bounded,
949
107k
               total - cone_dim, cone_dim);
950
107k
  bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
951
107k
  sample = sample_bounded(bounded);
952
107k
  if (
!sample || 107k
sample->size == 0107k
) {
953
3.33k
    isl_basic_set_free(bset);
954
3.33k
    isl_basic_set_free(cone);
955
3.33k
    isl_mat_free(U);
956
3.33k
    return sample;
957
3.33k
  }
958
103k
  bset = plug_in(bset, isl_vec_copy(sample));
959
103k
  cone_sample = rational_sample(bset);
960
103k
  cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
961
103k
  sample = vec_concat(sample, cone_sample);
962
103k
  sample = isl_mat_vec_product(U, sample);
963
103k
  return sample;
964
0
error:
965
0
  isl_basic_set_free(cone);
966
0
  isl_basic_set_free(bset);
967
0
  return NULL;
968
107k
}
969
970
static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
971
621
{
972
621
  int i;
973
621
974
621
  isl_int_set_si(*s, 0);
975
621
976
1.70k
  for (i = 0; 
i < v->size1.70k
;
++i1.08k
)
977
1.08k
    
if (1.08k
isl_int_is_neg1.08k
(v->el[i]))
978
222
      isl_int_add(*s, *s, v->el[i]);
979
621
}
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
375
{
1001
375
  int i;
1002
375
  isl_int v;
1003
375
  struct isl_basic_set *bset = NULL;
1004
375
1005
375
  if (
tab && 375
tab->n_unbounded == 0375
) {
1006
0
    isl_mat_free(U);
1007
0
    return 0;
1008
0
  }
1009
375
  
isl_int_init375
(v);
1010
375
  if (
!tab || 375
!tab_cone375
||
!U375
)
1011
0
    goto error;
1012
375
  bset = isl_tab_peek_bset(tab_cone);
1013
375
  U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1014
3.04k
  for (i = 0; 
i < bset->n_ineq3.04k
;
++i2.66k
) {
1015
2.66k
    int ok;
1016
2.66k
    struct isl_vec *row = NULL;
1017
2.66k
    if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1018
2.04k
      continue;
1019
621
    row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1020
621
    if (!row)
1021
0
      goto error;
1022
621
    isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1023
621
    row = isl_vec_mat_product(row, isl_mat_copy(U));
1024
621
    if (!row)
1025
0
      goto error;
1026
621
    vec_sum_of_neg(row, &v);
1027
621
    isl_vec_free(row);
1028
621
    if (isl_int_is_zero(v))
1029
424
      continue;
1030
197
    
if (197
isl_tab_extend_cons(tab, 1) < 0197
)
1031
0
      goto error;
1032
197
    
isl_int_add197
(bset->ineq[i][0], bset->ineq[i][0], v);
1033
197
    ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1034
197
    isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1035
197
    if (!ok)
1036
0
      goto error;
1037
2.66k
  }
1038
375
1039
375
  isl_mat_free(U);
1040
375
  isl_int_clear(v);
1041
375
  return 0;
1042
0
error:
1043
0
  isl_mat_free(U);
1044
0
  isl_int_clear(v);
1045
0
  return -1;
1046
375
}
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
502
{
1065
502
  struct isl_mat *eq;
1066
502
  struct isl_mat *cone_eq;
1067
502
  struct isl_mat *U, *Q;
1068
502
1069
502
  if (
!tab || 502
!tab_cone502
)
1070
0
    return -1;
1071
502
1072
502
  
if (502
tab_cone->n_col == tab_cone->n_dead502
) {
1073
127
    tab->basis = initial_basis(tab);
1074
127
    return tab->basis ? 
0127
:
-10
;
1075
127
  }
1076
375
1077
375
  eq = tab_equalities(tab);
1078
375
  if (!eq)
1079
0
    return -1;
1080
375
  tab->n_zero = eq->n_row;
1081
375
  cone_eq = tab_equalities(tab_cone);
1082
375
  eq = isl_mat_concat(eq, cone_eq);
1083
375
  if (!eq)
1084
0
    return -1;
1085
375
  tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1086
375
  eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1087
375
  if (!eq)
1088
0
    return -1;
1089
375
  isl_mat_free(eq);
1090
375
  tab->basis = isl_mat_lin_to_aff(Q);
1091
375
  if (tab_shift_cone(tab, tab_cone, U) < 0)
1092
0
    return -1;
1093
375
  
if (375
!tab->basis375
)
1094
0
    return -1;
1095
375
  return 0;
1096
375
}
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
123k
{
1106
123k
  unsigned dim;
1107
123k
  struct isl_basic_set *cone;
1108
123k
1109
123k
  dim = isl_basic_set_total_dim(bset);
1110
123k
1111
123k
  cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1112
123k
  if (!cone)
1113
0
    goto error;
1114
123k
1115
123k
  
if (123k
cone->n_eq < dim123k
)
1116
106k
    return isl_basic_set_sample_with_cone(bset, cone);
1117
16.8k
1118
16.8k
  isl_basic_set_free(cone);
1119
16.8k
  return sample_bounded(bset);
1120
0
error:
1121
0
  isl_basic_set_free(bset);
1122
0
  return NULL;
1123
123k
}
1124
1125
static __isl_give isl_vec *basic_set_sample(__isl_take isl_basic_set *bset,
1126
  int bounded)
1127
244k
{
1128
244k
  struct isl_ctx *ctx;
1129
244k
  unsigned dim;
1130
244k
  if (!bset)
1131
0
    return NULL;
1132
244k
1133
244k
  ctx = bset->ctx;
1134
244k
  if (isl_basic_set_plain_is_empty(bset))
1135
386
    return empty_sample(bset);
1136
243k
1137
243k
  dim = isl_basic_set_n_dim(bset);
1138
243k
  isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1139
243k
  
isl_assert243k
(ctx, bset->n_div == 0, goto error);
1140
243k
1141
243k
  
if (243k
bset->sample && 243k
bset->sample->size == 1 + dim282
) {
1142
125
    int contains = isl_basic_set_contains(bset, bset->sample);
1143
125
    if (contains < 0)
1144
0
      goto error;
1145
125
    
if (125
contains125
) {
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
243k
  }
1151
243k
  isl_vec_free(bset->sample);
1152
243k
  bset->sample = NULL;
1153
243k
1154
243k
  if (bset->n_eq > 0)
1155
86.7k
    
return sample_eq(bset, bounded ? 86.7k
isl_basic_set_sample_bounded0
1156
86.7k
                 : isl_basic_set_sample_vec);
1157
156k
  
if (156k
dim == 0156k
)
1158
4.13k
    return zero_sample(bset);
1159
152k
  
if (152k
dim == 1152k
)
1160
29.6k
    return interval_sample(bset);
1161
123k
1162
123k
  
return bounded ? 123k
sample_bounded(bset)0
:
gbr_sample(bset)123k
;
1163
0
error:
1164
0
  isl_basic_set_free(bset);
1165
0
  return NULL;
1166
244k
}
1167
1168
__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1169
244k
{
1170
244k
  return basic_set_sample(bset, 0);
1171
244k
}
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
260k
{
1183
260k
  int i;
1184
260k
  int k;
1185
260k
  struct isl_basic_set *bset = NULL;
1186
260k
  struct isl_ctx *ctx;
1187
260k
  unsigned dim;
1188
260k
1189
260k
  if (!vec)
1190
0
    return NULL;
1191
260k
  ctx = vec->ctx;
1192
260k
  isl_assert(ctx, vec->size != 0, goto error);
1193
260k
1194
260k
  bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1195
260k
  if (!bset)
1196
0
    goto error;
1197
260k
  dim = isl_basic_set_n_dim(bset);
1198
1.22M
  for (i = dim - 1; 
i >= 01.22M
;
--i968k
) {
1199
968k
    k = isl_basic_set_alloc_equality(bset);
1200
968k
    if (k < 0)
1201
0
      goto error;
1202
968k
    isl_seq_clr(bset->eq[k], 1 + dim);
1203
968k
    isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1204
968k
    isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1205
968k
  }
1206
260k
  bset->sample = vec;
1207
260k
1208
260k
  return bset;
1209
0
error:
1210
0
  isl_basic_set_free(bset);
1211
0
  isl_vec_free(vec);
1212
0
  return NULL;
1213
260k
}
1214
1215
__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1216
1
{
1217
1
  struct isl_basic_set *bset;
1218
1
  struct isl_vec *sample_vec;
1219
1
1220
1
  bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1221
1
  sample_vec = isl_basic_set_sample_vec(bset);
1222
1
  if (!sample_vec)
1223
0
    goto error;
1224
1
  
if (1
sample_vec->size == 01
) {
1225
0
    isl_vec_free(sample_vec);
1226
0
    return isl_basic_map_set_to_empty(bmap);
1227
0
  }
1228
1
  isl_vec_free(bmap->sample);
1229
1
  bmap->sample = isl_vec_copy(sample_vec);
1230
1
  bset = isl_basic_set_from_vec(sample_vec);
1231
1
  return isl_basic_map_overlying_set(bset, bmap);
1232
0
error:
1233
0
  isl_basic_map_free(bmap);
1234
0
  return NULL;
1235
1
}
1236
1237
__isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1238
1
{
1239
1
  return isl_basic_map_sample(bset);
1240
1
}
1241
1242
__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1243
0
{
1244
0
  int i;
1245
0
  isl_basic_map *sample = NULL;
1246
0
1247
0
  if (!map)
1248
0
    goto error;
1249
0
1250
0
  
for (i = 0; 0
i < map->n0
;
++i0
) {
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 (0
!0
ISL_F_ISSET0
(sample, ISL_BASIC_MAP_EMPTY))
1255
0
      break;
1256
0
    isl_basic_map_free(sample);
1257
0
  }
1258
0
  
if (0
i == map->n0
)
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
1
{
1274
1
  isl_vec *vec;
1275
1
  isl_space *dim;
1276
1
1277
1
  dim = isl_basic_set_get_space(bset);
1278
1
  bset = isl_basic_set_underlying_set(bset);
1279
1
  vec = isl_basic_set_sample_vec(bset);
1280
1
1281
1
  return isl_point_alloc(dim, vec);
1282
1
}
1283
1284
__isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1285
2
{
1286
2
  int i;
1287
2
  isl_point *pnt;
1288
2
1289
2
  if (!set)
1290
0
    return NULL;
1291
2
1292
2
  
for (i = 0; 2
i < set->n2
;
++i0
) {
1293
1
    pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1294
1
    if (!pnt)
1295
0
      goto error;
1296
1
    
if (1
!isl_point_is_void(pnt)1
)
1297
1
      break;
1298
0
    isl_point_free(pnt);
1299
0
  }
1300
2
  
if (2
i == set->n2
)
1301
1
    pnt = isl_point_void(isl_set_get_space(set));
1302
2
1303
2
  isl_set_free(set);
1304
2
  return pnt;
1305
0
error:
1306
0
  isl_set_free(set);
1307
0
  return NULL;
1308
2
}