Coverage Report

Created: 2017-06-28 17:40

/Users/buildslave/jenkins/sharedspace/clang-stage2-coverage-R@2/llvm/tools/polly/lib/External/isl/isl_affine_hull.c
Line
Count
Source (jump to first uncovered line)
1
/*
2
 * Copyright 2008-2009 Katholieke Universiteit Leuven
3
 * Copyright 2010      INRIA Saclay
4
 * Copyright 2012      Ecole Normale Superieure
5
 *
6
 * Use of this software is governed by the MIT license
7
 *
8
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12
 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13
 */
14
15
#include <isl_ctx_private.h>
16
#include <isl_map_private.h>
17
#include <isl_seq.h>
18
#include <isl/set.h>
19
#include <isl/lp.h>
20
#include <isl/map.h>
21
#include "isl_equalities.h"
22
#include "isl_sample.h"
23
#include "isl_tab.h"
24
#include <isl_mat_private.h>
25
#include <isl_vec_private.h>
26
27
#include <bset_to_bmap.c>
28
#include <bset_from_bmap.c>
29
#include <set_to_map.c>
30
#include <set_from_map.c>
31
32
__isl_give isl_basic_map *isl_basic_map_implicit_equalities(
33
  __isl_take isl_basic_map *bmap)
34
182k
{
35
182k
  struct isl_tab *tab;
36
182k
37
182k
  if (!bmap)
38
0
    return bmap;
39
182k
40
182k
  bmap = isl_basic_map_gauss(bmap, NULL);
41
182k
  if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
42
785
    return bmap;
43
181k
  
if (181k
ISL_F_ISSET181k
(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
44
5.13k
    return bmap;
45
176k
  
if (176k
bmap->n_ineq <= 1176k
)
46
23.4k
    return bmap;
47
176k
48
153k
  tab = isl_tab_from_basic_map(bmap, 0);
49
153k
  if (isl_tab_detect_implicit_equalities(tab) < 0)
50
0
    goto error;
51
153k
  bmap = isl_basic_map_update_from_tab(bmap, tab);
52
153k
  isl_tab_free(tab);
53
153k
  bmap = isl_basic_map_gauss(bmap, NULL);
54
153k
  ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
55
153k
  return bmap;
56
0
error:
57
0
  isl_tab_free(tab);
58
0
  isl_basic_map_free(bmap);
59
0
  return NULL;
60
153k
}
61
62
struct isl_basic_set *isl_basic_set_implicit_equalities(
63
            struct isl_basic_set *bset)
64
164k
{
65
164k
  return bset_from_bmap(
66
164k
    isl_basic_map_implicit_equalities(bset_to_bmap(bset)));
67
164k
}
68
69
/* Make eq[row][col] of both bmaps equal so we can add the row
70
 * add the column to the common matrix.
71
 * Note that because of the echelon form, the columns of row row
72
 * after column col are zero.
73
 */
74
static void set_common_multiple(
75
  struct isl_basic_set *bset1, struct isl_basic_set *bset2,
76
  unsigned row, unsigned col)
77
223k
{
78
223k
  isl_int m, c;
79
223k
80
223k
  if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col]))
81
191k
    return;
82
223k
83
32.2k
  
isl_int_init32.2k
(c);32.2k
84
32.2k
  isl_int_init(m);
85
32.2k
  isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]);
86
32.2k
  isl_int_divexact(c, m, bset1->eq[row][col]);
87
32.2k
  isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
88
32.2k
  isl_int_divexact(c, m, bset2->eq[row][col]);
89
32.2k
  isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
90
32.2k
  isl_int_clear(c);
91
32.2k
  isl_int_clear(m);
92
32.2k
}
93
94
/* Delete a given equality, moving all the following equalities one up.
95
 */
96
static void delete_row(struct isl_basic_set *bset, unsigned row)
97
334k
{
98
334k
  isl_int *t;
99
334k
  int r;
100
334k
101
334k
  t = bset->eq[row];
102
334k
  bset->n_eq--;
103
606k
  for (r = row; 
r < bset->n_eq606k
;
++r272k
)
104
272k
    bset->eq[r] = bset->eq[r+1];
105
334k
  bset->eq[bset->n_eq] = t;
106
334k
}
107
108
/* Make first row entries in column col of bset1 identical to
109
 * those of bset2, using the fact that entry bset1->eq[row][col]=a
110
 * is non-zero.  Initially, these elements of bset1 are all zero.
111
 * For each row i < row, we set
112
 *    A[i] = a * A[i] + B[i][col] * A[row]
113
 *    B[i] = a * B[i]
114
 * so that
115
 *    A[i][col] = B[i][col] = a * old(B[i][col])
116
 */
117
static void construct_column(
118
  struct isl_basic_set *bset1, struct isl_basic_set *bset2,
119
  unsigned row, unsigned col)
120
133k
{
121
133k
  int r;
122
133k
  isl_int a;
123
133k
  isl_int b;
124
133k
  unsigned total;
125
133k
126
133k
  isl_int_init(a);
127
133k
  isl_int_init(b);
128
133k
  total = 1 + isl_basic_set_n_dim(bset1);
129
394k
  for (r = 0; 
r < row394k
;
++r260k
)
{260k
130
260k
    if (isl_int_is_zero(bset2->eq[r][col]))
131
247k
      continue;
132
12.7k
    
isl_int_gcd12.7k
(b, bset2->eq[r][col], bset1->eq[row][col]);12.7k
133
12.7k
    isl_int_divexact(a, bset1->eq[row][col], b);
134
12.7k
    isl_int_divexact(b, bset2->eq[r][col], b);
135
12.7k
    isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
136
12.7k
                b, bset1->eq[row], total);
137
12.7k
    isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
138
12.7k
  }
139
133k
  isl_int_clear(a);
140
133k
  isl_int_clear(b);
141
133k
  delete_row(bset1, row);
142
133k
}
143
144
/* Make first row entries in column col of bset1 identical to
145
 * those of bset2, using only these entries of the two matrices.
146
 * Let t be the last row with different entries.
147
 * For each row i < t, we set
148
 *  A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
149
 *  B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
150
 * so that
151
 *  A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
152
 */
153
static int transform_column(
154
  struct isl_basic_set *bset1, struct isl_basic_set *bset2,
155
  unsigned row, unsigned col)
156
143k
{
157
143k
  int i, t;
158
143k
  isl_int a, b, g;
159
143k
  unsigned total;
160
143k
161
169k
  for (t = row-1; 
t >= 0169k
;
--t26.0k
)
162
126k
    
if (126k
isl_int_ne126k
(bset1->eq[t][col], bset2->eq[t][col]))
163
100k
      break;
164
143k
  if (t < 0)
165
43.5k
    return 0;
166
143k
167
100k
  total = 1 + isl_basic_set_n_dim(bset1);
168
100k
  isl_int_init(a);
169
100k
  isl_int_init(b);
170
100k
  isl_int_init(g);
171
100k
  isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
172
203k
  for (i = 0; 
i < t203k
;
++i103k
)
{103k
173
103k
    isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
174
103k
    isl_int_gcd(g, a, b);
175
103k
    isl_int_divexact(a, a, g);
176
103k
    isl_int_divexact(g, b, g);
177
103k
    isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
178
103k
        total);
179
103k
    isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
180
103k
        total);
181
103k
  }
182
100k
  isl_int_clear(a);
183
100k
  isl_int_clear(b);
184
100k
  isl_int_clear(g);
185
100k
  delete_row(bset1, t);
186
100k
  delete_row(bset2, t);
187
100k
  return 1;
188
143k
}
189
190
/* The implementation is based on Section 5.2 of Michael Karr,
191
 * "Affine Relationships Among Variables of a Program",
192
 * except that the echelon form we use starts from the last column
193
 * and that we are dealing with integer coefficients.
194
 */
195
static struct isl_basic_set *affine_hull(
196
  struct isl_basic_set *bset1, struct isl_basic_set *bset2)
197
113k
{
198
113k
  unsigned total;
199
113k
  int col;
200
113k
  int row;
201
113k
202
113k
  if (
!bset1 || 113k
!bset2113k
)
203
0
    goto error;
204
113k
205
113k
  total = 1 + isl_basic_set_n_dim(bset1);
206
113k
207
113k
  row = 0;
208
614k
  for (col = total-1; 
col >= 0614k
;
--col501k
)
{501k
209
501k
    int is_zero1 = row >= bset1->n_eq ||
210
247k
      isl_int_is_zero(bset1->eq[row][col]);
211
501k
    int is_zero2 = row >= bset2->n_eq ||
212
356k
      isl_int_is_zero(bset2->eq[row][col]);
213
501k
    if (
!is_zero1 && 501k
!is_zero2225k
)
{223k
214
223k
      set_common_multiple(bset1, bset2, row, col);
215
223k
      ++row;
216
277k
    } else 
if (277k
!is_zero1 && 277k
is_zero21.54k
)
{1.54k
217
1.54k
      construct_column(bset1, bset2, row, col);
218
275k
    } else 
if (275k
is_zero1 && 275k
!is_zero2275k
)
{132k
219
132k
      construct_column(bset2, bset1, row, col);
220
143k
    } else {
221
143k
      if (transform_column(bset1, bset2, row, col))
222
100k
        --row;
223
143k
    }
224
501k
  }
225
113k
  isl_assert(bset1->ctx, row == bset1->n_eq, goto error);
226
113k
  isl_basic_set_free(bset2);
227
113k
  bset1 = isl_basic_set_normalize_constraints(bset1);
228
113k
  return bset1;
229
0
error:
230
0
  isl_basic_set_free(bset1);
231
0
  isl_basic_set_free(bset2);
232
0
  return NULL;
233
113k
}
234
235
/* Find an integer point in the set represented by "tab"
236
 * that lies outside of the equality "eq" e(x) = 0.
237
 * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
238
 * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
239
 * The point, if found, is returned.
240
 * If no point can be found, a zero-length vector is returned.
241
 *
242
 * Before solving an ILP problem, we first check if simply
243
 * adding the normal of the constraint to one of the known
244
 * integer points in the basic set represented by "tab"
245
 * yields another point inside the basic set.
246
 *
247
 * The caller of this function ensures that the tableau is bounded or
248
 * that tab->basis and tab->n_unbounded have been set appropriately.
249
 */
250
static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
251
13.9k
{
252
13.9k
  struct isl_ctx *ctx;
253
13.9k
  struct isl_vec *sample = NULL;
254
13.9k
  struct isl_tab_undo *snap;
255
13.9k
  unsigned dim;
256
13.9k
257
13.9k
  if (!tab)
258
0
    return NULL;
259
13.9k
  ctx = tab->mat->ctx;
260
13.9k
261
13.9k
  dim = tab->n_var;
262
13.9k
  sample = isl_vec_alloc(ctx, 1 + dim);
263
13.9k
  if (!sample)
264
0
    return NULL;
265
13.9k
  
isl_int_set_si13.9k
(sample->el[0], 1);13.9k
266
13.9k
  isl_seq_combine(sample->el + 1,
267
13.9k
    ctx->one, tab->bmap->sample->el + 1,
268
9.49k
    up ? 
ctx->one9.49k
:
ctx->negone4.46k
, eq + 1, dim);
269
13.9k
  if (isl_basic_map_contains(tab->bmap, sample))
270
51
    return sample;
271
13.9k
  isl_vec_free(sample);
272
13.9k
  sample = NULL;
273
13.9k
274
13.9k
  snap = isl_tab_snap(tab);
275
13.9k
276
13.9k
  if (!up)
277
4.44k
    isl_seq_neg(eq, eq, 1 + dim);
278
13.9k
  isl_int_sub_ui(eq[0], eq[0], 1);
279
13.9k
280
13.9k
  if (isl_tab_extend_cons(tab, 1) < 0)
281
0
    goto error;
282
13.9k
  
if (13.9k
isl_tab_add_ineq(tab, eq) < 013.9k
)
283
0
    goto error;
284
13.9k
285
13.9k
  sample = isl_tab_sample(tab);
286
13.9k
287
13.9k
  isl_int_add_ui(eq[0], eq[0], 1);
288
13.9k
  if (!up)
289
4.44k
    isl_seq_neg(eq, eq, 1 + dim);
290
13.9k
291
13.9k
  if (
sample && 13.9k
isl_tab_rollback(tab, snap) < 013.9k
)
292
0
    goto error;
293
13.9k
294
13.9k
  return sample;
295
0
error:
296
0
  isl_vec_free(sample);
297
0
  return NULL;
298
13.9k
}
299
300
__isl_give isl_basic_set *isl_basic_set_recession_cone(
301
  __isl_take isl_basic_set *bset)
302
164k
{
303
164k
  int i;
304
164k
305
164k
  bset = isl_basic_set_cow(bset);
306
164k
  if (!bset)
307
0
    return NULL;
308
164k
  
isl_assert164k
(bset->ctx, bset->n_div == 0, goto error);164k
309
164k
310
164k
  
for (i = 0; 164k
i < bset->n_eq164k
;
++i228
)
311
228
    isl_int_set_si(bset->eq[i][0], 0);
312
164k
313
938k
  for (i = 0; 
i < bset->n_ineq938k
;
++i774k
)
314
774k
    isl_int_set_si(bset->ineq[i][0], 0);
315
164k
316
164k
  ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
317
164k
  return isl_basic_set_implicit_equalities(bset);
318
0
error:
319
0
  isl_basic_set_free(bset);
320
0
  return NULL;
321
164k
}
322
323
/* Move "sample" to a point that is one up (or down) from the original
324
 * point in dimension "pos".
325
 */
326
static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up)
327
455k
{
328
455k
  if (up)
329
227k
    isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
330
455k
  else
331
227k
    isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
332
455k
}
333
334
/* Check if any points that are adjacent to "sample" also belong to "bset".
335
 * If so, add them to "hull" and return the updated hull.
336
 *
337
 * Before checking whether and adjacent point belongs to "bset", we first
338
 * check whether it already belongs to "hull" as this test is typically
339
 * much cheaper.
340
 */
341
static __isl_give isl_basic_set *add_adjacent_points(
342
  __isl_take isl_basic_set *hull, __isl_take isl_vec *sample,
343
  __isl_keep isl_basic_set *bset)
344
57.5k
{
345
57.5k
  int i, up;
346
57.5k
  int dim;
347
57.5k
348
57.5k
  if (!sample)
349
0
    goto error;
350
57.5k
351
57.5k
  dim = isl_basic_set_dim(hull, isl_dim_set);
352
57.5k
353
180k
  for (i = 0; 
i < dim180k
;
++i122k
)
{122k
354
253k
    for (up = 0; 
up <= 1253k
;
++up130k
)
{227k
355
227k
      int contains;
356
227k
      isl_basic_set *point;
357
227k
358
227k
      adjacent_point(sample, i, up);
359
227k
      contains = isl_basic_set_contains(hull, sample);
360
227k
      if (contains < 0)
361
0
        goto error;
362
227k
      
if (227k
contains227k
)
{24.3k
363
24.3k
        adjacent_point(sample, i, !up);
364
24.3k
        continue;
365
24.3k
      }
366
203k
      contains = isl_basic_set_contains(bset, sample);
367
203k
      if (contains < 0)
368
0
        goto error;
369
203k
      
if (203k
contains203k
)
{96.7k
370
96.7k
        point = isl_basic_set_from_vec(
371
96.7k
              isl_vec_copy(sample));
372
96.7k
        hull = affine_hull(hull, point);
373
96.7k
      }
374
203k
      adjacent_point(sample, i, !up);
375
203k
      if (contains)
376
96.7k
        break;
377
203k
    }
378
122k
  }
379
57.5k
380
57.5k
  isl_vec_free(sample);
381
57.5k
382
57.5k
  return hull;
383
0
error:
384
0
  isl_vec_free(sample);
385
0
  isl_basic_set_free(hull);
386
0
  return NULL;
387
57.5k
}
388
389
/* Extend an initial (under-)approximation of the affine hull of basic
390
 * set represented by the tableau "tab"
391
 * by looking for points that do not satisfy one of the equalities
392
 * in the current approximation and adding them to that approximation
393
 * until no such points can be found any more.
394
 *
395
 * The caller of this function ensures that "tab" is bounded or
396
 * that tab->basis and tab->n_unbounded have been set appropriately.
397
 *
398
 * "bset" may be either NULL or the basic set represented by "tab".
399
 * If "bset" is not NULL, we check for any point we find if any
400
 * of its adjacent points also belong to "bset".
401
 */
402
static __isl_give isl_basic_set *extend_affine_hull(struct isl_tab *tab,
403
  __isl_take isl_basic_set *hull, __isl_keep isl_basic_set *bset)
404
52.4k
{
405
52.4k
  int i, j;
406
52.4k
  unsigned dim;
407
52.4k
408
52.4k
  if (
!tab || 52.4k
!hull52.4k
)
409
0
    goto error;
410
52.4k
411
52.4k
  dim = tab->n_var;
412
52.4k
413
52.4k
  if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
414
0
    goto error;
415
52.4k
416
58.8k
  
for (i = 0; 52.4k
i < dim58.8k
;
++i6.48k
)
{58.8k
417
58.8k
    struct isl_vec *sample;
418
58.8k
    struct isl_basic_set *point;
419
61.8k
    for (j = 0; 
j < hull->n_eq61.8k
;
++j3.01k
)
{9.49k
420
9.49k
      sample = outside_point(tab, hull->eq[j], 1);
421
9.49k
      if (!sample)
422
0
        goto error;
423
9.49k
      
if (9.49k
sample->size > 09.49k
)
424
5.03k
        break;
425
4.46k
      isl_vec_free(sample);
426
4.46k
      sample = outside_point(tab, hull->eq[j], 0);
427
4.46k
      if (!sample)
428
0
        goto error;
429
4.46k
      
if (4.46k
sample->size > 04.46k
)
430
1.44k
        break;
431
3.01k
      isl_vec_free(sample);
432
3.01k
433
3.01k
      if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
434
0
        goto error;
435
3.01k
    }
436
58.8k
    
if (58.8k
j == hull->n_eq58.8k
)
437
52.3k
      break;
438
6.48k
    
if (6.48k
tab->samples &&6.48k
439
842
        isl_tab_add_sample(tab, isl_vec_copy(sample)) < 0)
440
0
      hull = isl_basic_set_free(hull);
441
6.48k
    if (bset)
442
5.63k
      hull = add_adjacent_points(hull, isl_vec_copy(sample),
443
5.63k
                bset);
444
6.48k
    point = isl_basic_set_from_vec(sample);
445
6.48k
    hull = affine_hull(hull, point);
446
6.48k
    if (!hull)
447
0
      return NULL;
448
6.48k
  }
449
52.4k
450
52.4k
  return hull;
451
0
error:
452
0
  isl_basic_set_free(hull);
453
0
  return NULL;
454
52.4k
}
455
456
/* Construct an initial underapproximation of the hull of "bset"
457
 * from "sample" and any of its adjacent points that also belong to "bset".
458
 */
459
static __isl_give isl_basic_set *initialize_hull(__isl_keep isl_basic_set *bset,
460
  __isl_take isl_vec *sample)
461
51.8k
{
462
51.8k
  isl_basic_set *hull;
463
51.8k
464
51.8k
  hull = isl_basic_set_from_vec(isl_vec_copy(sample));
465
51.8k
  hull = add_adjacent_points(hull, sample, bset);
466
51.8k
467
51.8k
  return hull;
468
51.8k
}
469
470
/* Look for all equalities satisfied by the integer points in bset,
471
 * which is assumed to be bounded.
472
 *
473
 * The equalities are obtained by successively looking for
474
 * a point that is affinely independent of the points found so far.
475
 * In particular, for each equality satisfied by the points so far,
476
 * we check if there is any point on a hyperplane parallel to the
477
 * corresponding hyperplane shifted by at least one (in either direction).
478
 */
479
static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset)
480
52.0k
{
481
52.0k
  struct isl_vec *sample = NULL;
482
52.0k
  struct isl_basic_set *hull;
483
52.0k
  struct isl_tab *tab = NULL;
484
52.0k
  unsigned dim;
485
52.0k
486
52.0k
  if (isl_basic_set_plain_is_empty(bset))
487
0
    return bset;
488
52.0k
489
52.0k
  dim = isl_basic_set_n_dim(bset);
490
52.0k
491
52.0k
  if (
bset->sample && 52.0k
bset->sample->size == 1 + dim27.3k
)
{19.0k
492
19.0k
    int contains = isl_basic_set_contains(bset, bset->sample);
493
19.0k
    if (contains < 0)
494
0
      goto error;
495
19.0k
    
if (19.0k
contains19.0k
)
{18.7k
496
18.7k
      if (dim == 0)
497
0
        return bset;
498
18.7k
      sample = isl_vec_copy(bset->sample);
499
232
    } else {
500
232
      isl_vec_free(bset->sample);
501
232
      bset->sample = NULL;
502
232
    }
503
19.0k
  }
504
52.0k
505
52.0k
  tab = isl_tab_from_basic_set(bset, 1);
506
52.0k
  if (!tab)
507
0
    goto error;
508
52.0k
  
if (52.0k
tab->empty52.0k
)
{130
509
130
    isl_tab_free(tab);
510
130
    isl_vec_free(sample);
511
130
    return isl_basic_set_set_to_empty(bset);
512
130
  }
513
52.0k
514
51.8k
  
if (51.8k
!sample51.8k
)
{33.1k
515
33.1k
    struct isl_tab_undo *snap;
516
33.1k
    snap = isl_tab_snap(tab);
517
33.1k
    sample = isl_tab_sample(tab);
518
33.1k
    if (isl_tab_rollback(tab, snap) < 0)
519
0
      goto error;
520
33.1k
    isl_vec_free(tab->bmap->sample);
521
33.1k
    tab->bmap->sample = isl_vec_copy(sample);
522
33.1k
  }
523
51.8k
524
51.8k
  
if (51.8k
!sample51.8k
)
525
0
    goto error;
526
51.8k
  
if (51.8k
sample->size == 051.8k
)
{15
527
15
    isl_tab_free(tab);
528
15
    isl_vec_free(sample);
529
15
    return isl_basic_set_set_to_empty(bset);
530
15
  }
531
51.8k
532
51.8k
  hull = initialize_hull(bset, sample);
533
51.8k
534
51.8k
  hull = extend_affine_hull(tab, hull, bset);
535
51.8k
  isl_basic_set_free(bset);
536
51.8k
  isl_tab_free(tab);
537
51.8k
538
51.8k
  return hull;
539
0
error:
540
0
  isl_vec_free(sample);
541
0
  isl_tab_free(tab);
542
0
  isl_basic_set_free(bset);
543
0
  return NULL;
544
51.8k
}
545
546
/* Given an unbounded tableau and an integer point satisfying the tableau,
547
 * construct an initial affine hull containing the recession cone
548
 * shifted to the given point.
549
 *
550
 * The unbounded directions are taken from the last rows of the basis,
551
 * which is assumed to have been initialized appropriately.
552
 */
553
static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab,
554
  __isl_take isl_vec *vec)
555
419
{
556
419
  int i;
557
419
  int k;
558
419
  struct isl_basic_set *bset = NULL;
559
419
  struct isl_ctx *ctx;
560
419
  unsigned dim;
561
419
562
419
  if (
!vec || 419
!tab419
)
563
0
    return NULL;
564
419
  ctx = vec->ctx;
565
419
  isl_assert(ctx, vec->size != 0, goto error);
566
419
567
419
  bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
568
419
  if (!bset)
569
0
    goto error;
570
419
  dim = isl_basic_set_n_dim(bset) - tab->n_unbounded;
571
2.33k
  for (i = 0; 
i < dim2.33k
;
++i1.91k
)
{1.91k
572
1.91k
    k = isl_basic_set_alloc_equality(bset);
573
1.91k
    if (k < 0)
574
0
      goto error;
575
1.91k
    isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
576
1.91k
          vec->size - 1);
577
1.91k
    isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
578
1.91k
              vec->size - 1, &bset->eq[k][0]);
579
1.91k
    isl_int_neg(bset->eq[k][0], bset->eq[k][0]);
580
1.91k
  }
581
419
  bset->sample = vec;
582
419
  bset = isl_basic_set_gauss(bset, NULL);
583
419
584
419
  return bset;
585
0
error:
586
0
  isl_basic_set_free(bset);
587
0
  isl_vec_free(vec);
588
0
  return NULL;
589
419
}
590
591
/* Given a tableau of a set and a tableau of the corresponding
592
 * recession cone, detect and add all equalities to the tableau.
593
 * If the tableau is bounded, then we can simply keep the
594
 * tableau in its state after the return from extend_affine_hull.
595
 * However, if the tableau is unbounded, then
596
 * isl_tab_set_initial_basis_with_cone will add some additional
597
 * constraints to the tableau that have to be removed again.
598
 * In this case, we therefore rollback to the state before
599
 * any constraints were added and then add the equalities back in.
600
 */
601
struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
602
  struct isl_tab *tab_cone)
603
534
{
604
534
  int j;
605
534
  struct isl_vec *sample;
606
534
  struct isl_basic_set *hull = NULL;
607
534
  struct isl_tab_undo *snap;
608
534
609
534
  if (
!tab || 534
!tab_cone534
)
610
0
    goto error;
611
534
612
534
  snap = isl_tab_snap(tab);
613
534
614
534
  isl_mat_free(tab->basis);
615
534
  tab->basis = NULL;
616
534
617
534
  isl_assert(tab->mat->ctx, tab->bmap, goto error);
618
534
  
isl_assert534
(tab->mat->ctx, tab->samples, goto error);534
619
534
  
isl_assert534
(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);534
620
534
  
isl_assert534
(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);534
621
534
622
534
  
if (534
isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0534
)
623
0
    goto error;
624
534
625
534
  sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
626
534
  if (!sample)
627
0
    goto error;
628
534
629
534
  isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
630
534
631
534
  isl_vec_free(tab->bmap->sample);
632
534
  tab->bmap->sample = isl_vec_copy(sample);
633
534
634
534
  if (tab->n_unbounded == 0)
635
115
    hull = isl_basic_set_from_vec(isl_vec_copy(sample));
636
534
  else
637
419
    hull = initial_hull(tab, isl_vec_copy(sample));
638
534
639
964
  for (j = tab->n_outside + 1; 
j < tab->n_sample964
;
++j430
)
{430
640
430
    isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
641
430
    hull = affine_hull(hull,
642
430
        isl_basic_set_from_vec(isl_vec_copy(sample)));
643
430
  }
644
534
645
534
  isl_vec_free(sample);
646
534
647
534
  hull = extend_affine_hull(tab, hull, NULL);
648
534
  if (!hull)
649
0
    goto error;
650
534
651
534
  
if (534
tab->n_unbounded == 0534
)
{115
652
115
    isl_basic_set_free(hull);
653
115
    return tab;
654
115
  }
655
534
656
419
  
if (419
isl_tab_rollback(tab, snap) < 0419
)
657
0
    goto error;
658
419
659
419
  
if (419
hull->n_eq > tab->n_zero419
)
{184
660
1.01k
    for (j = 0; 
j < hull->n_eq1.01k
;
++j826
)
{826
661
826
      isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
662
826
      if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
663
0
        goto error;
664
826
    }
665
184
  }
666
419
667
419
  isl_basic_set_free(hull);
668
419
669
419
  return tab;
670
0
error:
671
0
  isl_basic_set_free(hull);
672
0
  isl_tab_free(tab);
673
0
  return NULL;
674
419
}
675
676
/* Compute the affine hull of "bset", where "cone" is the recession cone
677
 * of "bset".
678
 *
679
 * We first compute a unimodular transformation that puts the unbounded
680
 * directions in the last dimensions.  In particular, we take a transformation
681
 * that maps all equalities to equalities (in HNF) on the first dimensions.
682
 * Let x be the original dimensions and y the transformed, with y_1 bounded
683
 * and y_2 unbounded.
684
 *
685
 *         [ y_1 ]      [ y_1 ]   [ Q_1 ]
686
 *  x = U  [ y_2 ]      [ y_2 ] = [ Q_2 ] x
687
 *
688
 * Let's call the input basic set S.  We compute S' = preimage(S, U)
689
 * and drop the final dimensions including any constraints involving them.
690
 * This results in set S''.
691
 * Then we compute the affine hull A'' of S''.
692
 * Let F y_1 >= g be the constraint system of A''.  In the transformed
693
 * space the y_2 are unbounded, so we can add them back without any constraints,
694
 * resulting in
695
 *
696
 *            [ y_1 ]
697
 *    [ F 0 ] [ y_2 ] >= g
698
 * or
699
 *            [ Q_1 ]
700
 *    [ F 0 ] [ Q_2 ] x >= g
701
 * or
702
 *    F Q_1 x >= g
703
 *
704
 * The affine hull in the original space is then obtained as
705
 * A = preimage(A'', Q_1).
706
 */
707
static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
708
  struct isl_basic_set *cone)
709
41.3k
{
710
41.3k
  unsigned total;
711
41.3k
  unsigned cone_dim;
712
41.3k
  struct isl_basic_set *hull;
713
41.3k
  struct isl_mat *M, *U, *Q;
714
41.3k
715
41.3k
  if (
!bset || 41.3k
!cone41.3k
)
716
0
    goto error;
717
41.3k
718
41.3k
  total = isl_basic_set_total_dim(cone);
719
41.3k
  cone_dim = total - cone->n_eq;
720
41.3k
721
41.3k
  M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
722
41.3k
  M = isl_mat_left_hermite(M, 0, &U, &Q);
723
41.3k
  if (!M)
724
0
    goto error;
725
41.3k
  isl_mat_free(M);
726
41.3k
727
41.3k
  U = isl_mat_lin_to_aff(U);
728
41.3k
  bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
729
41.3k
730
41.3k
  bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
731
41.3k
              cone_dim);
732
41.3k
  bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
733
41.3k
734
41.3k
  Q = isl_mat_lin_to_aff(Q);
735
41.3k
  Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
736
41.3k
737
41.3k
  if (
bset && 41.3k
bset->sample41.3k
&&
bset->sample->size == 1 + total19.3k
)
738
14.2k
    bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
739
41.3k
740
41.3k
  hull = uset_affine_hull_bounded(bset);
741
41.3k
742
41.3k
  if (
!hull41.3k
)
{0
743
0
    isl_mat_free(Q);
744
0
    isl_mat_free(U);
745
41.3k
  } else {
746
41.3k
    struct isl_vec *sample = isl_vec_copy(hull->sample);
747
41.3k
    U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
748
41.3k
    if (
sample && 41.3k
sample->size > 041.3k
)
749
41.3k
      sample = isl_mat_vec_product(U, sample);
750
41.3k
    else
751
38
      isl_mat_free(U);
752
41.3k
    hull = isl_basic_set_preimage(hull, Q);
753
41.3k
    if (
hull41.3k
)
{41.3k
754
41.3k
      isl_vec_free(hull->sample);
755
41.3k
      hull->sample = sample;
756
41.3k
    } else
757
0
      isl_vec_free(sample);
758
41.3k
  }
759
41.3k
760
41.3k
  isl_basic_set_free(cone);
761
41.3k
762
41.3k
  return hull;
763
0
error:
764
0
  isl_basic_set_free(bset);
765
0
  isl_basic_set_free(cone);
766
0
  return NULL;
767
41.3k
}
768
769
/* Look for all equalities satisfied by the integer points in bset,
770
 * which is assumed not to have any explicit equalities.
771
 *
772
 * The equalities are obtained by successively looking for
773
 * a point that is affinely independent of the points found so far.
774
 * In particular, for each equality satisfied by the points so far,
775
 * we check if there is any point on a hyperplane parallel to the
776
 * corresponding hyperplane shifted by at least one (in either direction).
777
 *
778
 * Before looking for any outside points, we first compute the recession
779
 * cone.  The directions of this recession cone will always be part
780
 * of the affine hull, so there is no need for looking for any points
781
 * in these directions.
782
 * In particular, if the recession cone is full-dimensional, then
783
 * the affine hull is simply the whole universe.
784
 */
785
static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
786
70.1k
{
787
70.1k
  struct isl_basic_set *cone;
788
70.1k
789
70.1k
  if (isl_basic_set_plain_is_empty(bset))
790
6
    return bset;
791
70.1k
792
70.1k
  cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
793
70.1k
  if (!cone)
794
0
    goto error;
795
70.1k
  
if (70.1k
cone->n_eq == 070.1k
)
{18.0k
796
18.0k
    isl_space *space;
797
18.0k
    space = isl_basic_set_get_space(bset);
798
18.0k
    isl_basic_set_free(cone);
799
18.0k
    isl_basic_set_free(bset);
800
18.0k
    return isl_basic_set_universe(space);
801
18.0k
  }
802
70.1k
803
52.0k
  
if (52.0k
cone->n_eq < isl_basic_set_total_dim(cone)52.0k
)
804
41.3k
    return affine_hull_with_cone(bset, cone);
805
52.0k
806
10.6k
  isl_basic_set_free(cone);
807
10.6k
  return uset_affine_hull_bounded(bset);
808
0
error:
809
0
  isl_basic_set_free(bset);
810
0
  return NULL;
811
52.0k
}
812
813
/* Look for all equalities satisfied by the integer points in bmap
814
 * that are independent of the equalities already explicitly available
815
 * in bmap.
816
 *
817
 * We first remove all equalities already explicitly available,
818
 * then look for additional equalities in the reduced space
819
 * and then transform the result to the original space.
820
 * The original equalities are _not_ added to this set.  This is
821
 * the responsibility of the calling function.
822
 * The resulting basic set has all meaning about the dimensions removed.
823
 * In particular, dimensions that correspond to existential variables
824
 * in bmap and that are found to be fixed are not removed.
825
 */
826
static struct isl_basic_set *equalities_in_underlying_set(
827
            struct isl_basic_map *bmap)
828
70.1k
{
829
70.1k
  struct isl_mat *T1 = NULL;
830
70.1k
  struct isl_mat *T2 = NULL;
831
70.1k
  struct isl_basic_set *bset = NULL;
832
70.1k
  struct isl_basic_set *hull = NULL;
833
70.1k
834
70.1k
  bset = isl_basic_map_underlying_set(bmap);
835
70.1k
  if (!bset)
836
0
    return NULL;
837
70.1k
  
if (70.1k
bset->n_eq70.1k
)
838
14.6k
    bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
839
70.1k
  if (!bset)
840
0
    goto error;
841
70.1k
842
70.1k
  hull = uset_affine_hull(bset);
843
70.1k
  if (!T2)
844
55.5k
    return hull;
845
70.1k
846
14.6k
  
if (14.6k
!hull14.6k
)
{0
847
0
    isl_mat_free(T1);
848
0
    isl_mat_free(T2);
849
14.6k
  } else {
850
14.6k
    struct isl_vec *sample = isl_vec_copy(hull->sample);
851
14.6k
    if (
sample && 14.6k
sample->size > 010.8k
)
852
10.8k
      sample = isl_mat_vec_product(T1, sample);
853
14.6k
    else
854
3.72k
      isl_mat_free(T1);
855
14.6k
    hull = isl_basic_set_preimage(hull, T2);
856
14.6k
    if (
hull14.6k
)
{14.6k
857
14.6k
      isl_vec_free(hull->sample);
858
14.6k
      hull->sample = sample;
859
14.6k
    } else
860
0
      isl_vec_free(sample);
861
14.6k
  }
862
14.6k
863
14.6k
  return hull;
864
0
error:
865
0
  isl_mat_free(T1);
866
0
  isl_mat_free(T2);
867
0
  isl_basic_set_free(bset);
868
0
  isl_basic_set_free(hull);
869
0
  return NULL;
870
70.1k
}
871
872
/* Detect and make explicit all equalities satisfied by the (integer)
873
 * points in bmap.
874
 */
875
__isl_give isl_basic_map *isl_basic_map_detect_equalities(
876
  __isl_take isl_basic_map *bmap)
877
491k
{
878
491k
  int i, j;
879
491k
  struct isl_basic_set *hull = NULL;
880
491k
881
491k
  if (!bmap)
882
0
    return NULL;
883
491k
  
if (491k
bmap->n_ineq == 0491k
)
884
332k
    return bmap;
885
158k
  
if (158k
ISL_F_ISSET158k
(bmap, ISL_BASIC_MAP_EMPTY))
886
0
    return bmap;
887
158k
  
if (158k
ISL_F_ISSET158k
(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
888
70.6k
    return bmap;
889
88.2k
  
if (88.2k
ISL_F_ISSET88.2k
(bmap, ISL_BASIC_MAP_RATIONAL))
890
18.1k
    return isl_basic_map_implicit_equalities(bmap);
891
88.2k
892
70.1k
  hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
893
70.1k
  if (!hull)
894
0
    goto error;
895
70.1k
  
if (70.1k
ISL_F_ISSET70.1k
(hull, ISL_BASIC_SET_EMPTY))
{151
896
151
    isl_basic_set_free(hull);
897
151
    return isl_basic_map_set_to_empty(bmap);
898
151
  }
899
69.9k
  bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0,
900
69.9k
          hull->n_eq, 0);
901
71.5k
  for (i = 0; 
i < hull->n_eq71.5k
;
++i1.57k
)
{1.57k
902
1.57k
    j = isl_basic_map_alloc_equality(bmap);
903
1.57k
    if (j < 0)
904
0
      goto error;
905
1.57k
    isl_seq_cpy(bmap->eq[j], hull->eq[i],
906
1.57k
        1 + isl_basic_set_total_dim(hull));
907
1.57k
  }
908
69.9k
  isl_vec_free(bmap->sample);
909
69.9k
  bmap->sample = isl_vec_copy(hull->sample);
910
69.9k
  isl_basic_set_free(hull);
911
69.9k
  ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
912
69.9k
  bmap = isl_basic_map_simplify(bmap);
913
69.9k
  return isl_basic_map_finalize(bmap);
914
0
error:
915
0
  isl_basic_set_free(hull);
916
0
  isl_basic_map_free(bmap);
917
0
  return NULL;
918
69.9k
}
919
920
__isl_give isl_basic_set *isl_basic_set_detect_equalities(
921
            __isl_take isl_basic_set *bset)
922
30.9k
{
923
30.9k
  return bset_from_bmap(
924
30.9k
    isl_basic_map_detect_equalities(bset_to_bmap(bset)));
925
30.9k
}
926
927
__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
928
146k
{
929
146k
  return isl_map_inline_foreach_basic_map(map,
930
146k
              &isl_basic_map_detect_equalities);
931
146k
}
932
933
__isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
934
11.4k
{
935
11.4k
  return set_from_map(isl_map_detect_equalities(set_to_map(set)));
936
11.4k
}
937
938
/* Return the superset of "bmap" described by the equalities
939
 * satisfied by "bmap" that are already known.
940
 */
941
__isl_give isl_basic_map *isl_basic_map_plain_affine_hull(
942
  __isl_take isl_basic_map *bmap)
943
388k
{
944
388k
  bmap = isl_basic_map_cow(bmap);
945
388k
  if (bmap)
946
388k
    isl_basic_map_free_inequality(bmap, bmap->n_ineq);
947
388k
  bmap = isl_basic_map_finalize(bmap);
948
388k
  return bmap;
949
388k
}
950
951
/* Return the superset of "bset" described by the equalities
952
 * satisfied by "bset" that are already known.
953
 */
954
__isl_give isl_basic_set *isl_basic_set_plain_affine_hull(
955
  __isl_take isl_basic_set *bset)
956
30.9k
{
957
30.9k
  return isl_basic_map_plain_affine_hull(bset);
958
30.9k
}
959
960
/* After computing the rational affine hull (by detecting the implicit
961
 * equalities), we compute the additional equalities satisfied by
962
 * the integer points (if any) and add the original equalities back in.
963
 */
964
__isl_give isl_basic_map *isl_basic_map_affine_hull(
965
  __isl_take isl_basic_map *bmap)
966
289k
{
967
289k
  bmap = isl_basic_map_detect_equalities(bmap);
968
289k
  bmap = isl_basic_map_plain_affine_hull(bmap);
969
289k
  return bmap;
970
289k
}
971
972
struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
973
7.10k
{
974
7.10k
  return bset_from_bmap(isl_basic_map_affine_hull(bset_to_bmap(bset)));
975
7.10k
}
976
977
/* Given a rational affine matrix "M", add stride constraints to "bmap"
978
 * that ensure that
979
 *
980
 *    M(x)
981
 *
982
 * is an integer vector.  The variables x include all the variables
983
 * of "bmap" except the unknown divs.
984
 *
985
 * If d is the common denominator of M, then we need to impose that
986
 *
987
 *    d M(x) = 0  mod d
988
 *
989
 * or
990
 *
991
 *    exists alpha : d M(x) = d alpha
992
 *
993
 * This function is similar to add_strides in isl_morph.c
994
 */
995
static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap,
996
  __isl_keep isl_mat *M, int n_known)
997
0
{
998
0
  int i, div, k;
999
0
  isl_int gcd;
1000
0
1001
0
  if (isl_int_is_one(M->row[0][0]))
1002
0
    return bmap;
1003
0
1004
0
  bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
1005
0
          M->n_row - 1, M->n_row - 1, 0);
1006
0
1007
0
  isl_int_init(gcd);
1008
0
  for (i = 1; 
i < M->n_row0
;
++i0
)
{0
1009
0
    isl_seq_gcd(M->row[i], M->n_col, &gcd);
1010
0
    if (isl_int_is_divisible_by(gcd, M->row[0][0]))
1011
0
      continue;
1012
0
    div = isl_basic_map_alloc_div(bmap);
1013
0
    if (div < 0)
1014
0
      goto error;
1015
0
    
isl_int_set_si0
(bmap->div[div][0], 0);0
1016
0
    k = isl_basic_map_alloc_equality(bmap);
1017
0
    if (k < 0)
1018
0
      goto error;
1019
0
    isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col);
1020
0
    isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known);
1021
0
    isl_int_set(bmap->eq[k][M->n_col - n_known + div],
1022
0
          M->row[0][0]);
1023
0
  }
1024
0
  
isl_int_clear0
(gcd);0
1025
0
1026
0
  return bmap;
1027
0
error:
1028
0
  isl_int_clear(gcd);
1029
0
  isl_basic_map_free(bmap);
1030
0
  return NULL;
1031
0
}
1032
1033
/* If there are any equalities that involve (multiple) unknown divs,
1034
 * then extract the stride information encoded by those equalities
1035
 * and make it explicitly available in "bmap".
1036
 *
1037
 * We first sort the divs so that the unknown divs appear last and
1038
 * then we count how many equalities involve these divs.
1039
 *
1040
 * Let these equalities be of the form
1041
 *
1042
 *    A(x) + B y = 0
1043
 *
1044
 * where y represents the unknown divs and x the remaining variables.
1045
 * Let [H 0] be the Hermite Normal Form of B, i.e.,
1046
 *
1047
 *    B = [H 0] Q
1048
 *
1049
 * Then x is a solution of the equalities iff
1050
 *
1051
 *    H^-1 A(x) (= - [I 0] Q y)
1052
 *
1053
 * is an integer vector.  Let d be the common denominator of H^-1.
1054
 * We impose
1055
 *
1056
 *    d H^-1 A(x) = d alpha
1057
 *
1058
 * in add_strides, with alpha fresh existentially quantified variables.
1059
 */
1060
static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit(
1061
  __isl_take isl_basic_map *bmap)
1062
281k
{
1063
281k
  int known;
1064
281k
  int n_known;
1065
281k
  int n, n_col;
1066
281k
  int total;
1067
281k
  isl_ctx *ctx;
1068
281k
  isl_mat *A, *B, *M;
1069
281k
1070
281k
  known = isl_basic_map_divs_known(bmap);
1071
281k
  if (known < 0)
1072
0
    return isl_basic_map_free(bmap);
1073
281k
  
if (281k
known281k
)
1074
281k
    return bmap;
1075
0
  bmap = isl_basic_map_sort_divs(bmap);
1076
0
  bmap = isl_basic_map_gauss(bmap, NULL);
1077
0
  if (!bmap)
1078
0
    return NULL;
1079
0
1080
0
  
for (n_known = 0; 0
n_known < bmap->n_div0
;
++n_known0
)
1081
0
    
if (0
isl_int_is_zero0
(bmap->div[n_known][0]))
1082
0
      break;
1083
0
  ctx = isl_basic_map_get_ctx(bmap);
1084
0
  total = isl_space_dim(bmap->dim, isl_dim_all);
1085
0
  for (n = 0; 
n < bmap->n_eq0
;
++n0
)
1086
0
    
if (0
isl_seq_first_non_zero(bmap->eq[n] + 1 + total + n_known,0
1087
0
              bmap->n_div - n_known) == -1)
1088
0
      break;
1089
0
  if (n == 0)
1090
0
    return bmap;
1091
0
  B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + total + n_known);
1092
0
  n_col = bmap->n_div - n_known;
1093
0
  A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + total + n_known, n_col);
1094
0
  A = isl_mat_left_hermite(A, 0, NULL, NULL);
1095
0
  A = isl_mat_drop_cols(A, n, n_col - n);
1096
0
  A = isl_mat_lin_to_aff(A);
1097
0
  A = isl_mat_right_inverse(A);
1098
0
  B = isl_mat_insert_zero_rows(B, 0, 1);
1099
0
  B = isl_mat_set_element_si(B, 0, 0, 1);
1100
0
  M = isl_mat_product(A, B);
1101
0
  if (!M)
1102
0
    return isl_basic_map_free(bmap);
1103
0
  bmap = add_strides(bmap, M, n_known);
1104
0
  bmap = isl_basic_map_gauss(bmap, NULL);
1105
0
  isl_mat_free(M);
1106
0
1107
0
  return bmap;
1108
0
}
1109
1110
/* Compute the affine hull of each basic map in "map" separately
1111
 * and make all stride information explicit so that we can remove
1112
 * all unknown divs without losing this information.
1113
 * The result is also guaranteed to be gaussed.
1114
 *
1115
 * In simple cases where a div is determined by an equality,
1116
 * calling isl_basic_map_gauss is enough to make the stride information
1117
 * explicit, as it will derive an explicit representation for the div
1118
 * from the equality.  If, however, the stride information
1119
 * is encoded through multiple unknown divs then we need to make
1120
 * some extra effort in isl_basic_map_make_strides_explicit.
1121
 */
1122
static __isl_give isl_map *isl_map_local_affine_hull(__isl_take isl_map *map)
1123
260k
{
1124
260k
  int i;
1125
260k
1126
260k
  map = isl_map_cow(map);
1127
260k
  if (!map)
1128
0
    return NULL;
1129
260k
1130
542k
  
for (i = 0; 260k
i < map->n542k
;
++i281k
)
{281k
1131
281k
    map->p[i] = isl_basic_map_affine_hull(map->p[i]);
1132
281k
    map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
1133
281k
    map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]);
1134
281k
    if (!map->p[i])
1135
0
      return isl_map_free(map);
1136
281k
  }
1137
260k
1138
260k
  return map;
1139
260k
}
1140
1141
static __isl_give isl_set *isl_set_local_affine_hull(__isl_take isl_set *set)
1142
130k
{
1143
130k
  return isl_map_local_affine_hull(set);
1144
130k
}
1145
1146
/* Return an empty basic map living in the same space as "map".
1147
 */
1148
static __isl_give isl_basic_map *replace_map_by_empty_basic_map(
1149
  __isl_take isl_map *map)
1150
0
{
1151
0
  isl_space *space;
1152
0
1153
0
  space = isl_map_get_space(map);
1154
0
  isl_map_free(map);
1155
0
  return isl_basic_map_empty(space);
1156
0
}
1157
1158
/* Compute the affine hull of "map".
1159
 *
1160
 * We first compute the affine hull of each basic map separately.
1161
 * Then we align the divs and recompute the affine hulls of the basic
1162
 * maps since some of them may now have extra divs.
1163
 * In order to avoid performing parametric integer programming to
1164
 * compute explicit expressions for the divs, possible leading to
1165
 * an explosion in the number of basic maps, we first drop all unknown
1166
 * divs before aligning the divs.  Note that isl_map_local_affine_hull tries
1167
 * to make sure that all stride information is explicitly available
1168
 * in terms of known divs.  This involves calling isl_basic_set_gauss,
1169
 * which is also needed because affine_hull assumes its input has been gaussed,
1170
 * while isl_map_affine_hull may be called on input that has not been gaussed,
1171
 * in particular from initial_facet_constraint.
1172
 * Similarly, align_divs may reorder some divs so that we need to
1173
 * gauss the result again.
1174
 * Finally, we combine the individual affine hulls into a single
1175
 * affine hull.
1176
 */
1177
__isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map)
1178
130k
{
1179
130k
  struct isl_basic_map *model = NULL;
1180
130k
  struct isl_basic_map *hull = NULL;
1181
130k
  struct isl_set *set;
1182
130k
  isl_basic_set *bset;
1183
130k
1184
130k
  map = isl_map_detect_equalities(map);
1185
130k
  map = isl_map_local_affine_hull(map);
1186
130k
  map = isl_map_remove_empty_parts(map);
1187
130k
  map = isl_map_remove_unknown_divs(map);
1188
130k
  map = isl_map_align_divs_internal(map);
1189
130k
1190
130k
  if (!map)
1191
0
    return NULL;
1192
130k
1193
130k
  
if (130k
map->n == 0130k
)
1194
0
    return replace_map_by_empty_basic_map(map);
1195
130k
1196
130k
  model = isl_basic_map_copy(map->p[0]);
1197
130k
  set = isl_map_underlying_set(map);
1198
130k
  set = isl_set_cow(set);
1199
130k
  set = isl_set_local_affine_hull(set);
1200
130k
  if (!set)
1201
0
    goto error;
1202
130k
1203
140k
  
while (130k
set->n > 1140k
)
1204
10.1k
    set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
1205
130k
1206
130k
  bset = isl_basic_set_copy(set->p[0]);
1207
130k
  hull = isl_basic_map_overlying_set(bset, model);
1208
130k
  isl_set_free(set);
1209
130k
  hull = isl_basic_map_simplify(hull);
1210
130k
  return isl_basic_map_finalize(hull);
1211
0
error:
1212
0
  isl_basic_map_free(model);
1213
0
  isl_set_free(set);
1214
0
  return NULL;
1215
130k
}
1216
1217
struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
1218
128k
{
1219
128k
  return bset_from_bmap(isl_map_affine_hull(set_to_map(set)));
1220
128k
}