Coverage Report

Created: 2017-11-23 03:11

/Users/buildslave/jenkins/workspace/clang-stage2-coverage-R/llvm/tools/polly/lib/External/isl/isl_farkas.c
Line
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1
/*
2
 * Copyright 2010      INRIA Saclay
3
 *
4
 * Use of this software is governed by the MIT license
5
 *
6
 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7
 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8
 * 91893 Orsay, France 
9
 */
10
11
#include <isl_map_private.h>
12
#include <isl/set.h>
13
#include <isl_space_private.h>
14
#include <isl_seq.h>
15
16
/*
17
 * Let C be a cone and define
18
 *
19
 *  C' := { y | forall x in C : y x >= 0 }
20
 *
21
 * C' contains the coefficients of all linear constraints
22
 * that are valid for C.
23
 * Furthermore, C'' = C.
24
 *
25
 * If C is defined as { x | A x >= 0 }
26
 * then any element in C' must be a non-negative combination
27
 * of the rows of A, i.e., y = t A with t >= 0.  That is,
28
 *
29
 *  C' = { y | exists t >= 0 : y = t A }
30
 *
31
 * If any of the rows in A actually represents an equality, then
32
 * also negative combinations of this row are allowed and so the
33
 * non-negativity constraint on the corresponding element of t
34
 * can be dropped.
35
 *
36
 * A polyhedron P = { x | b + A x >= 0 } can be represented
37
 * in homogeneous coordinates by the cone
38
 * C = { [z,x] | b z + A x >= and z >= 0 }
39
 * The valid linear constraints on C correspond to the valid affine
40
 * constraints on P.
41
 * This is essentially Farkas' lemma.
42
 *
43
 * Since
44
 *          [ 1 0 ]
45
 *    [ w y ] = [t_0 t] [ b A ]
46
 *
47
 * we have
48
 *
49
 *  C' = { w, y | exists t_0, t >= 0 : y = t A and w = t_0 + t b }
50
 * or
51
 *
52
 *  C' = { w, y | exists t >= 0 : y = t A and w - t b >= 0 }
53
 *
54
 * In practice, we introduce an extra variable (w), shifting all
55
 * other variables to the right, and an extra inequality
56
 * (w - t b >= 0) corresponding to the positivity constraint on
57
 * the homogeneous coordinate.
58
 *
59
 * When going back from coefficients to solutions, we immediately
60
 * plug in 1 for z, which corresponds to shifting all variables
61
 * to the left, with the leftmost ending up in the constant position.
62
 */
63
64
/* Add the given prefix to all named isl_dim_set dimensions in "dim".
65
 */
66
static __isl_give isl_space *isl_space_prefix(__isl_take isl_space *dim,
67
  const char *prefix)
68
884
{
69
884
  int i;
70
884
  isl_ctx *ctx;
71
884
  unsigned nvar;
72
884
  size_t prefix_len = strlen(prefix);
73
884
74
884
  if (!dim)
75
0
    return NULL;
76
884
77
884
  ctx = isl_space_get_ctx(dim);
78
884
  nvar = isl_space_dim(dim, isl_dim_set);
79
884
80
2.02k
  for (i = 0; i < nvar; 
++i1.14k
) {
81
1.14k
    const char *name;
82
1.14k
    char *prefix_name;
83
1.14k
84
1.14k
    name = isl_space_get_dim_name(dim, isl_dim_set, i);
85
1.14k
    if (!name)
86
442
      continue;
87
700
88
700
    prefix_name = isl_alloc_array(ctx, char,
89
700
                prefix_len + strlen(name) + 1);
90
700
    if (!prefix_name)
91
0
      goto error;
92
700
    memcpy(prefix_name, prefix, prefix_len);
93
700
    strcpy(prefix_name + prefix_len, name);
94
700
95
700
    dim = isl_space_set_dim_name(dim, isl_dim_set, i, prefix_name);
96
700
    free(prefix_name);
97
700
  }
98
884
99
884
  return dim;
100
0
error:
101
0
  isl_space_free(dim);
102
0
  return NULL;
103
884
}
104
105
/* Given a dimension specification of the solutions space, construct
106
 * a dimension specification for the space of coefficients.
107
 *
108
 * In particular transform
109
 *
110
 *  [params] -> { S }
111
 *
112
 * to
113
 *
114
 *  { coefficients[[cst, params] -> S] }
115
 *
116
 * and prefix each dimension name with "c_".
117
 */
118
static __isl_give isl_space *isl_space_coefficients(__isl_take isl_space *dim)
119
442
{
120
442
  isl_space *dim_param;
121
442
  unsigned nvar;
122
442
  unsigned nparam;
123
442
124
442
  nvar = isl_space_dim(dim, isl_dim_set);
125
442
  nparam = isl_space_dim(dim, isl_dim_param);
126
442
  dim_param = isl_space_copy(dim);
127
442
  dim_param = isl_space_drop_dims(dim_param, isl_dim_set, 0, nvar);
128
442
  dim_param = isl_space_move_dims(dim_param, isl_dim_set, 0,
129
442
         isl_dim_param, 0, nparam);
130
442
  dim_param = isl_space_prefix(dim_param, "c_");
131
442
  dim_param = isl_space_insert_dims(dim_param, isl_dim_set, 0, 1);
132
442
  dim_param = isl_space_set_dim_name(dim_param, isl_dim_set, 0, "c_cst");
133
442
  dim = isl_space_drop_dims(dim, isl_dim_param, 0, nparam);
134
442
  dim = isl_space_prefix(dim, "c_");
135
442
  dim = isl_space_join(isl_space_from_domain(dim_param),
136
442
         isl_space_from_range(dim));
137
442
  dim = isl_space_wrap(dim);
138
442
  dim = isl_space_set_tuple_name(dim, isl_dim_set, "coefficients");
139
442
140
442
  return dim;
141
442
}
142
143
/* Drop the given prefix from all named dimensions of type "type" in "dim".
144
 */
145
static __isl_give isl_space *isl_space_unprefix(__isl_take isl_space *dim,
146
  enum isl_dim_type type, const char *prefix)
147
6
{
148
6
  int i;
149
6
  unsigned n;
150
6
  size_t prefix_len = strlen(prefix);
151
6
152
6
  n = isl_space_dim(dim, type);
153
6
154
9
  for (i = 0; i < n; 
++i3
) {
155
3
    const char *name;
156
3
157
3
    name = isl_space_get_dim_name(dim, type, i);
158
3
    if (!name)
159
0
      continue;
160
3
    if (strncmp(name, prefix, prefix_len))
161
3
      continue;
162
0
163
0
    dim = isl_space_set_dim_name(dim, type, i, name + prefix_len);
164
0
  }
165
6
166
6
  return dim;
167
6
}
168
169
/* Given a dimension specification of the space of coefficients, construct
170
 * a dimension specification for the space of solutions.
171
 *
172
 * In particular transform
173
 *
174
 *  { coefficients[[cst, params] -> S] }
175
 *
176
 * to
177
 *
178
 *  [params] -> { S }
179
 *
180
 * and drop the "c_" prefix from the dimension names.
181
 */
182
static __isl_give isl_space *isl_space_solutions(__isl_take isl_space *dim)
183
3
{
184
3
  unsigned nparam;
185
3
186
3
  dim = isl_space_unwrap(dim);
187
3
  dim = isl_space_drop_dims(dim, isl_dim_in, 0, 1);
188
3
  dim = isl_space_unprefix(dim, isl_dim_in, "c_");
189
3
  dim = isl_space_unprefix(dim, isl_dim_out, "c_");
190
3
  nparam = isl_space_dim(dim, isl_dim_in);
191
3
  dim = isl_space_move_dims(dim, isl_dim_param, 0, isl_dim_in, 0, nparam);
192
3
  dim = isl_space_range(dim);
193
3
194
3
  return dim;
195
3
}
196
197
/* Return the rational universe basic set in the given space.
198
 */
199
static __isl_give isl_basic_set *rational_universe(__isl_take isl_space *space)
200
7
{
201
7
  isl_basic_set *bset;
202
7
203
7
  bset = isl_basic_set_universe(space);
204
7
  bset = isl_basic_set_set_rational(bset);
205
7
206
7
  return bset;
207
7
}
208
209
/* Compute the dual of "bset" by applying Farkas' lemma.
210
 * As explained above, we add an extra dimension to represent
211
 * the coefficient of the constant term when going from solutions
212
 * to coefficients (shift == 1) and we drop the extra dimension when going
213
 * in the opposite direction (shift == -1).  "dim" is the space in which
214
 * the dual should be created.
215
 *
216
 * If "bset" is (obviously) empty, then the way this emptiness
217
 * is represented by the constraints does not allow for the application
218
 * of the standard farkas algorithm.  We therefore handle this case
219
 * specifically and return the universe basic set.
220
 */
221
static __isl_give isl_basic_set *farkas(__isl_take isl_space *space,
222
  __isl_take isl_basic_set *bset, int shift)
223
440
{
224
440
  int i, j, k;
225
440
  isl_basic_set *dual = NULL;
226
440
  unsigned total;
227
440
228
440
  if (isl_basic_set_plain_is_empty(bset)) {
229
2
    isl_basic_set_free(bset);
230
2
    return rational_universe(space);
231
2
  }
232
438
233
438
  total = isl_basic_set_total_dim(bset);
234
438
235
438
  dual = isl_basic_set_alloc_space(space, bset->n_eq + bset->n_ineq,
236
438
          total, bset->n_ineq + (shift > 0));
237
438
  dual = isl_basic_set_set_rational(dual);
238
438
239
1.57k
  for (i = 0; i < bset->n_eq + bset->n_ineq; 
++i1.13k
) {
240
1.13k
    k = isl_basic_set_alloc_div(dual);
241
1.13k
    if (k < 0)
242
0
      goto error;
243
1.13k
    isl_int_set_si(dual->div[k][0], 0);
244
1.13k
  }
245
438
246
1.57k
  
for (i = 0; 438
i < total;
++i1.13k
) {
247
1.13k
    k = isl_basic_set_alloc_equality(dual);
248
1.13k
    if (k < 0)
249
0
      goto error;
250
1.13k
    isl_seq_clr(dual->eq[k], 1 + shift + total);
251
1.13k
    isl_int_set_si(dual->eq[k][1 + shift + i], -1);
252
3.42k
    for (j = 0; j < bset->n_eq; 
++j2.28k
)
253
2.28k
      isl_int_set(dual->eq[k][1 + shift + total + j],
254
1.13k
            bset->eq[j][1 + i]);
255
2.43k
    for (j = 0; j < bset->n_ineq; 
++j1.29k
)
256
1.29k
      isl_int_set(dual->eq[k][1 + shift + total + bset->n_eq + j],
257
1.13k
            bset->ineq[j][1 + i]);
258
1.13k
  }
259
438
260
790
  
for (i = 0; 438
i < bset->n_ineq;
++i352
) {
261
352
    k = isl_basic_set_alloc_inequality(dual);
262
352
    if (k < 0)
263
0
      goto error;
264
352
    isl_seq_clr(dual->ineq[k],
265
352
          1 + shift + total + bset->n_eq + bset->n_ineq);
266
352
    isl_int_set_si(dual->ineq[k][1 + shift + total + bset->n_eq + i], 1);
267
352
  }
268
438
269
438
  if (shift > 0) {
270
436
    k = isl_basic_set_alloc_inequality(dual);
271
436
    if (k < 0)
272
0
      goto error;
273
436
    isl_seq_clr(dual->ineq[k], 2 + total);
274
436
    isl_int_set_si(dual->ineq[k][1], 1);
275
1.22k
    for (j = 0; j < bset->n_eq; 
++j784
)
276
784
      isl_int_neg(dual->ineq[k][2 + total + j],
277
436
            bset->eq[j][0]);
278
786
    for (j = 0; j < bset->n_ineq; 
++j350
)
279
436
      
isl_int_neg350
(dual->ineq[k][2 + total + bset->n_eq + j],
280
436
            bset->ineq[j][0]);
281
436
  }
282
438
283
438
  dual = isl_basic_set_remove_divs(dual);
284
438
  dual = isl_basic_set_simplify(dual);
285
438
  dual = isl_basic_set_finalize(dual);
286
438
287
438
  isl_basic_set_free(bset);
288
438
  return dual;
289
0
error:
290
0
  isl_basic_set_free(bset);
291
0
  isl_basic_set_free(dual);
292
0
  return NULL;
293
440
}
294
295
/* Construct a basic set containing the tuples of coefficients of all
296
 * valid affine constraints on the given basic set.
297
 */
298
__isl_give isl_basic_set *isl_basic_set_coefficients(
299
  __isl_take isl_basic_set *bset)
300
437
{
301
437
  isl_space *dim;
302
437
303
437
  if (!bset)
304
0
    return NULL;
305
437
  if (bset->n_div)
306
437
    
isl_die0
(bset->ctx, isl_error_invalid,
307
437
      "input set not allowed to have local variables",
308
437
      goto error);
309
437
310
437
  dim = isl_basic_set_get_space(bset);
311
437
  dim = isl_space_coefficients(dim);
312
437
313
437
  return farkas(dim, bset, 1);
314
0
error:
315
0
  isl_basic_set_free(bset);
316
0
  return NULL;
317
437
}
318
319
/* Construct a basic set containing the elements that satisfy all
320
 * affine constraints whose coefficient tuples are
321
 * contained in the given basic set.
322
 */
323
__isl_give isl_basic_set *isl_basic_set_solutions(
324
  __isl_take isl_basic_set *bset)
325
3
{
326
3
  isl_space *dim;
327
3
328
3
  if (!bset)
329
0
    return NULL;
330
3
  if (bset->n_div)
331
3
    
isl_die0
(bset->ctx, isl_error_invalid,
332
3
      "input set not allowed to have local variables",
333
3
      goto error);
334
3
335
3
  dim = isl_basic_set_get_space(bset);
336
3
  dim = isl_space_solutions(dim);
337
3
338
3
  return farkas(dim, bset, -1);
339
0
error:
340
0
  isl_basic_set_free(bset);
341
0
  return NULL;
342
3
}
343
344
/* Construct a basic set containing the tuples of coefficients of all
345
 * valid affine constraints on the given set.
346
 */
347
__isl_give isl_basic_set *isl_set_coefficients(__isl_take isl_set *set)
348
285
{
349
285
  int i;
350
285
  isl_basic_set *coeff;
351
285
352
285
  if (!set)
353
0
    return NULL;
354
285
  if (set->n == 0) {
355
5
    isl_space *space = isl_set_get_space(set);
356
5
    space = isl_space_coefficients(space);
357
5
    isl_set_free(set);
358
5
    return rational_universe(space);
359
5
  }
360
280
361
280
  coeff = isl_basic_set_coefficients(isl_basic_set_copy(set->p[0]));
362
280
363
370
  for (i = 1; i < set->n; 
++i90
) {
364
90
    isl_basic_set *bset, *coeff_i;
365
90
    bset = isl_basic_set_copy(set->p[i]);
366
90
    coeff_i = isl_basic_set_coefficients(bset);
367
90
    coeff = isl_basic_set_intersect(coeff, coeff_i);
368
90
  }
369
285
370
285
  isl_set_free(set);
371
285
  return coeff;
372
285
}
373
374
/* Wrapper around isl_basic_set_coefficients for use
375
 * as a isl_basic_set_list_map callback.
376
 */
377
static __isl_give isl_basic_set *coefficients_wrap(
378
  __isl_take isl_basic_set *bset, void *user)
379
64
{
380
64
  return isl_basic_set_coefficients(bset);
381
64
}
382
383
/* Replace the elements of "list" by the result of applying
384
 * isl_basic_set_coefficients to them.
385
 */
386
__isl_give isl_basic_set_list *isl_basic_set_list_coefficients(
387
  __isl_take isl_basic_set_list *list)
388
64
{
389
64
  return isl_basic_set_list_map(list, &coefficients_wrap, NULL);
390
64
}
391
392
/* Construct a basic set containing the elements that satisfy all
393
 * affine constraints whose coefficient tuples are
394
 * contained in the given set.
395
 */
396
__isl_give isl_basic_set *isl_set_solutions(__isl_take isl_set *set)
397
0
{
398
0
  int i;
399
0
  isl_basic_set *sol;
400
0
401
0
  if (!set)
402
0
    return NULL;
403
0
  if (set->n == 0) {
404
0
    isl_space *space = isl_set_get_space(set);
405
0
    space = isl_space_solutions(space);
406
0
    isl_set_free(set);
407
0
    return rational_universe(space);
408
0
  }
409
0
410
0
  sol = isl_basic_set_solutions(isl_basic_set_copy(set->p[0]));
411
0
412
0
  for (i = 1; i < set->n; ++i) {
413
0
    isl_basic_set *bset, *sol_i;
414
0
    bset = isl_basic_set_copy(set->p[i]);
415
0
    sol_i = isl_basic_set_solutions(bset);
416
0
    sol = isl_basic_set_intersect(sol, sol_i);
417
0
  }
418
0
419
0
  isl_set_free(set);
420
0
  return sol;
421
0
}