Bug Summary

File:tools/polly/lib/External/isl/isl_sample.c
Warning:line 1302, column 2
Undefined or garbage value returned to caller

Annotated Source Code

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
27static struct isl_vec *empty_sample(struct isl_basic_setisl_basic_map *bset)
28{
29 struct isl_vec *vec;
30
31 vec = isl_vec_alloc(bset->ctx, 0);
32 isl_basic_set_free(bset);
33 return vec;
34}
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 */
40static struct isl_vec *zero_sample(struct isl_basic_setisl_basic_map *bset)
41{
42 unsigned dim;
43 struct isl_vec *sample;
44
45 dim = isl_basic_set_total_dim(bset);
46 sample = isl_vec_alloc(bset->ctx, 1 + dim);
47 if (sample) {
48 isl_int_set_si(sample->el[0], 1)isl_sioimath_set_si((sample->el[0]), 1);
49 isl_seq_clr(sample->el + 1, dim);
50 }
51 isl_basic_set_free(bset);
52 return sample;
53}
54
55static struct isl_vec *interval_sample(struct isl_basic_setisl_basic_map *bset)
56{
57 int i;
58 isl_int t;
59 struct isl_vec *sample;
60
61 bset = isl_basic_set_simplify(bset);
62 if (!bset)
63 return NULL((void*)0);
64 if (isl_basic_set_plain_is_empty(bset))
65 return empty_sample(bset);
66 if (bset->n_eq == 0 && bset->n_ineq == 0)
67 return zero_sample(bset);
68
69 sample = isl_vec_alloc(bset->ctx, 2);
70 if (!sample)
71 goto error;
72 if (!bset)
73 return NULL((void*)0);
74 isl_int_set_si(sample->block.data[0], 1)isl_sioimath_set_si((sample->block.data[0]), 1);
75
76 if (bset->n_eq > 0) {
77 isl_assert(bset->ctx, bset->n_eq == 1, goto error)do { if (bset->n_eq == 1) break; do { isl_handle_error(bset
->ctx, isl_error_unknown, "Assertion \"" "bset->n_eq == 1"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 77); goto error; } while (0); } while (0)
;
78 isl_assert(bset->ctx, bset->n_ineq == 0, goto error)do { if (bset->n_ineq == 0) break; do { isl_handle_error(bset
->ctx, isl_error_unknown, "Assertion \"" "bset->n_ineq == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 78); goto error; } while (0); } while (0)
;
79 if (isl_int_is_one(bset->eq[0][1])(isl_sioimath_cmp_si(*(bset->eq[0][1]), 1) == 0))
80 isl_int_neg(sample->el[1], bset->eq[0][0])isl_sioimath_neg((sample->el[1]), *(bset->eq[0][0]));
81 else {
82 isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),do { if ((isl_sioimath_cmp_si(*(bset->eq[0][1]), -1) == 0)
) break; do { isl_handle_error(bset->ctx, isl_error_unknown
, "Assertion \"" "(isl_sioimath_cmp_si(*(bset->eq[0][1]), -1) == 0)"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 83); goto error; } while (0); } while (0)
83 goto error)do { if ((isl_sioimath_cmp_si(*(bset->eq[0][1]), -1) == 0)
) break; do { isl_handle_error(bset->ctx, isl_error_unknown
, "Assertion \"" "(isl_sioimath_cmp_si(*(bset->eq[0][1]), -1) == 0)"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 83); goto error; } while (0); } while (0)
;
84 isl_int_set(sample->el[1], bset->eq[0][0])isl_sioimath_set((sample->el[1]), *(bset->eq[0][0]));
85 }
86 isl_basic_set_free(bset);
87 return sample;
88 }
89
90 isl_int_init(t)isl_sioimath_init((t));
91 if (isl_int_is_one(bset->ineq[0][1])(isl_sioimath_cmp_si(*(bset->ineq[0][1]), 1) == 0))
92 isl_int_neg(sample->block.data[1], bset->ineq[0][0])isl_sioimath_neg((sample->block.data[1]), *(bset->ineq[
0][0]))
;
93 else
94 isl_int_set(sample->block.data[1], bset->ineq[0][0])isl_sioimath_set((sample->block.data[1]), *(bset->ineq[
0][0]))
;
95 for (i = 1; i < bset->n_ineq; ++i) {
96 isl_seq_inner_product(sample->block.data,
97 bset->ineq[i], 2, &t);
98 if (isl_int_is_neg(t)(isl_sioimath_sgn(*(t)) < 0))
99 break;
100 }
101 isl_int_clear(t)isl_sioimath_clear((t));
102 if (i < bset->n_ineq) {
103 isl_vec_free(sample);
104 return empty_sample(bset);
105 }
106
107 isl_basic_set_free(bset);
108 return sample;
109error:
110 isl_basic_set_free(bset);
111 isl_vec_free(sample);
112 return NULL((void*)0);
113}
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 */
122static struct isl_vec *sample_eq(struct isl_basic_setisl_basic_map *bset,
123 struct isl_vec *(*recurse)(struct isl_basic_setisl_basic_map *))
124{
125 struct isl_mat *T;
126 struct isl_vec *sample;
127
128 if (!bset)
129 return NULL((void*)0);
130
131 bset = isl_basic_set_remove_equalities(bset, &T, NULL((void*)0));
132 sample = recurse(bset);
133 if (!sample || sample->size == 0)
134 isl_mat_free(T);
135 else
136 sample = isl_mat_vec_product(T, sample);
137 return sample;
138}
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 */
144static struct isl_mat *tab_equalities(struct isl_tab *tab)
145{
146 int i, j;
147 int n_eq;
148 struct isl_mat *eq;
149 struct isl_basic_setisl_basic_map *bset;
150
151 if (!tab)
152 return NULL((void*)0);
153
154 bset = isl_tab_peek_bset(tab);
155 isl_assert(tab->mat->ctx, bset, return NULL)do { if (bset) break; do { isl_handle_error(tab->mat->ctx
, isl_error_unknown, "Assertion \"" "bset" "\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 155); return ((void*)0); } while (0); } while (0)
;
156
157 n_eq = tab->n_var - tab->n_col + tab->n_dead;
158 if (tab->empty || n_eq == 0)
159 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
160 if (n_eq == tab->n_var)
161 return isl_mat_identity(tab->mat->ctx, tab->n_var);
162
163 eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
164 if (!eq)
165 return NULL((void*)0);
166 for (i = 0, j = 0; i < tab->n_con; ++i) {
167 if (tab->con[i].is_row)
168 continue;
169 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
170 continue;
171 if (i < bset->n_eq)
172 isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
173 else
174 isl_seq_cpy(eq->row[j],
175 bset->ineq[i - bset->n_eq] + 1, tab->n_var);
176 ++j;
177 }
178 isl_assert(bset->ctx, j == n_eq, goto error)do { if (j == n_eq) break; do { isl_handle_error(bset->ctx
, isl_error_unknown, "Assertion \"" "j == n_eq" "\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 178); goto error; } while (0); } while (0)
;
179 return eq;
180error:
181 isl_mat_free(eq);
182 return NULL((void*)0);
183}
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 */
192static struct isl_mat *initial_basis(struct isl_tab *tab)
193{
194 int n_eq;
195 struct isl_mat *eq;
196 struct isl_mat *Q;
197
198 tab->n_unbounded = 0;
199 tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
200 if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
201 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
202
203 eq = tab_equalities(tab);
204 eq = isl_mat_left_hermite(eq, 0, NULL((void*)0), &Q);
205 if (!eq)
206 return NULL((void*)0);
207 isl_mat_free(eq);
208
209 Q = isl_mat_lin_to_aff(Q);
210 return Q;
211}
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 */
219static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
220 __isl_keep isl_vec *min, int level)
221{
222 return isl_tab_min(tab, tab->basis->row[1 + level],
223 ctx->one, &min->el[level], NULL((void*)0), 0);
224}
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 */
232static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
233 __isl_keep isl_vec *max, int level)
234{
235 enum isl_lp_result res;
236 unsigned dim = tab->n_var;
237
238 isl_seq_neg(tab->basis->row[1 + level] + 1,
239 tab->basis->row[1 + level] + 1, dim);
240 res = isl_tab_min(tab, tab->basis->row[1 + level],
241 ctx->one, &max->el[level], NULL((void*)0), 0);
242 isl_seq_neg(tab->basis->row[1 + level] + 1,
243 tab->basis->row[1 + level] + 1, dim);
244 isl_int_neg(max->el[level], max->el[level])isl_sioimath_neg((max->el[level]), *(max->el[level]));
245
246 return res;
247}
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 */
272static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
273 __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
274{
275 struct isl_tab_undo *snap;
276 enum isl_lp_result res;
277
278 snap = isl_tab_snap(tab);
279
280 do {
281 isl_int_add(tab->basis->row[1 + level][0],isl_sioimath_add((tab->basis->row[1 + level][0]), *(min
->el[level]), *(max->el[level]))
282 min->el[level], max->el[level])isl_sioimath_add((tab->basis->row[1 + level][0]), *(min
->el[level]), *(max->el[level]))
;
283 isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],isl_sioimath_fdiv_q_ui((tab->basis->row[1 + level][0]),
*(tab->basis->row[1 + level][0]), 2)
284 tab->basis->row[1 + level][0], 2)isl_sioimath_fdiv_q_ui((tab->basis->row[1 + level][0]),
*(tab->basis->row[1 + level][0]), 2)
;
285 isl_int_neg(tab->basis->row[1 + level][0],isl_sioimath_neg((tab->basis->row[1 + level][0]), *(tab
->basis->row[1 + level][0]))
286 tab->basis->row[1 + level][0])isl_sioimath_neg((tab->basis->row[1 + level][0]), *(tab
->basis->row[1 + level][0]))
;
287 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
288 return -1;
289 isl_int_set_si(tab->basis->row[1 + level][0], 0)isl_sioimath_set_si((tab->basis->row[1 + level][0]), 0);
290
291 if (++level >= tab->n_var - tab->n_unbounded)
292 return 1;
293 if (isl_tab_sample_is_integer(tab))
294 return 1;
295
296 res = compute_min(ctx, tab, min, level);
297 if (res == isl_lp_error)
298 return -1;
299 if (res != isl_lp_ok)
300 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 302); return -1; } while (0)
301 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 302); return -1; } while (0)
302 return -1)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 302); return -1; } while (0)
;
303 res = compute_max(ctx, tab, max, level);
304 if (res == isl_lp_error)
305 return -1;
306 if (res != isl_lp_ok)
307 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 309); return -1; } while (0)
308 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 309); return -1; } while (0)
309 return -1)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 309); return -1; } while (0)
;
310 } while (isl_int_le(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
<= 0)
);
311
312 if (isl_tab_rollback(tab, snap) < 0)
313 return -1;
314
315 return 0;
316}
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 */
373struct isl_vec *isl_tab_sample(struct isl_tab *tab)
374{
375 unsigned dim;
376 unsigned gbr;
377 struct isl_ctx *ctx;
378 struct isl_vec *sample;
379 struct isl_vec *min;
380 struct isl_vec *max;
381 enum isl_lp_result res;
382 int level;
383 int init;
384 int reduced;
385 struct isl_tab_undo **snap;
386
387 if (!tab)
388 return NULL((void*)0);
389 if (tab->empty)
390 return isl_vec_alloc(tab->mat->ctx, 0);
391
392 if (!tab->basis)
393 tab->basis = initial_basis(tab);
394 if (!tab->basis)
395 return NULL((void*)0);
396 isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,do { if (tab->basis->n_row == tab->n_var + 1) break;
do { isl_handle_error(tab->mat->ctx, isl_error_unknown
, "Assertion \"" "tab->basis->n_row == tab->n_var + 1"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 397); return ((void*)0); } while (0); } while (0)
397 return NULL)do { if (tab->basis->n_row == tab->n_var + 1) break;
do { isl_handle_error(tab->mat->ctx, isl_error_unknown
, "Assertion \"" "tab->basis->n_row == tab->n_var + 1"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 397); return ((void*)0); } while (0); } while (0)
;
398 isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,do { if (tab->basis->n_col == tab->n_var + 1) break;
do { isl_handle_error(tab->mat->ctx, isl_error_unknown
, "Assertion \"" "tab->basis->n_col == tab->n_var + 1"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 399); return ((void*)0); } while (0); } while (0)
399 return NULL)do { if (tab->basis->n_col == tab->n_var + 1) break;
do { isl_handle_error(tab->mat->ctx, isl_error_unknown
, "Assertion \"" "tab->basis->n_col == tab->n_var + 1"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 399); return ((void*)0); } while (0); } while (0)
;
400
401 ctx = tab->mat->ctx;
402 dim = tab->n_var;
403 gbr = ctx->opt->gbr;
404
405 if (tab->n_unbounded == tab->n_var) {
406 sample = isl_tab_get_sample_value(tab);
407 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
408 sample = isl_vec_ceil(sample);
409 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
410 sample);
411 return sample;
412 }
413
414 if (isl_tab_extend_cons(tab, dim + 1) < 0)
415 return NULL((void*)0);
416
417 min = isl_vec_alloc(ctx, dim);
418 max = isl_vec_alloc(ctx, dim);
419 snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim)((struct isl_tab_undo * *)isl_malloc_or_die(ctx, (dim)*sizeof
(struct isl_tab_undo *)))
;
420
421 if (!min || !max || !snap)
422 goto error;
423
424 level = 0;
425 init = 1;
426 reduced = 0;
427
428 while (level >= 0) {
429 if (init) {
430 int choice;
431
432 res = compute_min(ctx, tab, min, level);
433 if (res == isl_lp_error)
434 goto error;
435 if (res != isl_lp_ok)
436 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 438); goto error; } while (0)
437 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 438); goto error; } while (0)
438 goto error)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 438); goto error; } while (0)
;
439 if (isl_tab_sample_is_integer(tab))
440 break;
441 res = compute_max(ctx, tab, max, level);
442 if (res == isl_lp_error)
443 goto error;
444 if (res != isl_lp_ok)
445 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 447); goto error; } while (0)
446 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 447); goto error; } while (0)
447 goto error)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 447); goto error; } while (0)
;
448 if (isl_tab_sample_is_integer(tab))
449 break;
450 choice = isl_int_lt(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
< 0)
;
451 if (choice) {
452 int g;
453 g = greedy_search(ctx, tab, min, max, level);
454 if (g < 0)
455 goto error;
456 if (g)
457 break;
458 }
459 if (!reduced && choice &&
460 ctx->opt->gbr != ISL_GBR_NEVER0) {
461 unsigned gbr_only_first;
462 if (ctx->opt->gbr == ISL_GBR_ONCE1)
463 ctx->opt->gbr = ISL_GBR_NEVER0;
464 tab->n_zero = level;
465 gbr_only_first = ctx->opt->gbr_only_first;
466 ctx->opt->gbr_only_first =
467 ctx->opt->gbr == ISL_GBR_ALWAYS2;
468 tab = isl_tab_compute_reduced_basis(tab);
469 ctx->opt->gbr_only_first = gbr_only_first;
470 if (!tab || !tab->basis)
471 goto error;
472 reduced = 1;
473 continue;
474 }
475 reduced = 0;
476 snap[level] = isl_tab_snap(tab);
477 } else
478 isl_int_add_ui(min->el[level], min->el[level], 1)isl_sioimath_add_ui((min->el[level]), *(min->el[level])
, 1)
;
479
480 if (isl_int_gt(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
> 0)
) {
481 level--;
482 init = 0;
483 if (level >= 0)
484 if (isl_tab_rollback(tab, snap[level]) < 0)
485 goto error;
486 continue;
487 }
488 isl_int_neg(tab->basis->row[1 + level][0], min->el[level])isl_sioimath_neg((tab->basis->row[1 + level][0]), *(min
->el[level]))
;
489 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
490 goto error;
491 isl_int_set_si(tab->basis->row[1 + level][0], 0)isl_sioimath_set_si((tab->basis->row[1 + level][0]), 0);
492 if (level + tab->n_unbounded < dim - 1) {
493 ++level;
494 init = 1;
495 continue;
496 }
497 break;
498 }
499
500 if (level >= 0) {
501 sample = isl_tab_get_sample_value(tab);
502 if (!sample)
503 goto error;
504 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])(isl_sioimath_cmp_si(*(sample->el[0]), 1) == 0)) {
505 sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
506 sample);
507 sample = isl_vec_ceil(sample);
508 sample = isl_mat_vec_inverse_product(
509 isl_mat_copy(tab->basis), sample);
510 }
511 } else
512 sample = isl_vec_alloc(ctx, 0);
513
514 ctx->opt->gbr = gbr;
515 isl_vec_free(min);
516 isl_vec_free(max);
517 free(snap);
518 return sample;
519error:
520 ctx->opt->gbr = gbr;
521 isl_vec_free(min);
522 isl_vec_free(max);
523 free(snap);
524 return NULL((void*)0);
525}
526
527static struct isl_vec *sample_bounded(struct isl_basic_setisl_basic_map *bset);
528
529/* Compute a sample point of the given basic set, based on the given,
530 * non-trivial factorization.
531 */
532static __isl_give isl_vec *factored_sample(__isl_take isl_basic_setisl_basic_map *bset,
533 __isl_take isl_factorizer *f)
534{
535 int i, n;
536 isl_vec *sample = NULL((void*)0);
537 isl_ctx *ctx;
538 unsigned nparam;
539 unsigned nvar;
540
541 ctx = isl_basic_set_get_ctx(bset);
542 if (!ctx)
543 goto error;
544
545 nparam = isl_basic_set_dim(bset, isl_dim_param);
546 nvar = isl_basic_set_dim(bset, isl_dim_set);
547
548 sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
549 if (!sample)
550 goto error;
551 isl_int_set_si(sample->el[0], 1)isl_sioimath_set_si((sample->el[0]), 1);
552
553 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
554
555 for (i = 0, n = 0; i < f->n_group; ++i) {
556 isl_basic_setisl_basic_map *bset_i;
557 isl_vec *sample_i;
558
559 bset_i = isl_basic_set_copy(bset);
560 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
561 nparam + n + f->len[i], nvar - n - f->len[i]);
562 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
563 nparam, n);
564 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
565 n + f->len[i], nvar - n - f->len[i]);
566 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
567
568 sample_i = sample_bounded(bset_i);
569 if (!sample_i)
570 goto error;
571 if (sample_i->size == 0) {
572 isl_basic_set_free(bset);
573 isl_factorizer_free(f);
574 isl_vec_free(sample);
575 return sample_i;
576 }
577 isl_seq_cpy(sample->el + 1 + nparam + n,
578 sample_i->el + 1, f->len[i]);
579 isl_vec_free(sample_i);
580
581 n += f->len[i];
582 }
583
584 f->morph = isl_morph_inverse(f->morph);
585 sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
586
587 isl_basic_set_free(bset);
588 isl_factorizer_free(f);
589 return sample;
590error:
591 isl_basic_set_free(bset);
592 isl_factorizer_free(f);
593 isl_vec_free(sample);
594 return NULL((void*)0);
595}
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 */
604static struct isl_vec *sample_bounded(struct isl_basic_setisl_basic_map *bset)
605{
606 unsigned dim;
607 struct isl_vec *sample;
608 struct isl_tab *tab = NULL((void*)0);
609 isl_factorizer *f;
610
611 if (!bset)
612 return NULL((void*)0);
613
614 if (isl_basic_set_plain_is_empty(bset))
615 return empty_sample(bset);
616
617 dim = isl_basic_set_total_dim(bset);
618 if (dim == 0)
619 return zero_sample(bset);
620 if (dim == 1)
621 return interval_sample(bset);
622 if (bset->n_eq > 0)
623 return sample_eq(bset, sample_bounded);
624
625 f = isl_basic_set_factorizer(bset);
626 if (!f)
627 goto error;
628 if (f->n_group != 0)
629 return factored_sample(bset, f);
630 isl_factorizer_free(f);
631
632 tab = isl_tab_from_basic_set(bset, 1);
633 if (tab && tab->empty) {
634 isl_tab_free(tab);
635 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY)(((bset)->flags) |= ((1 << 1)));
636 sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
637 isl_basic_set_free(bset);
638 return sample;
639 }
640
641 if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT)(!!(((bset)->flags) & ((1 << 2)))))
642 if (isl_tab_detect_implicit_equalities(tab) < 0)
643 goto error;
644
645 sample = isl_tab_sample(tab);
646 if (!sample)
647 goto error;
648
649 if (sample->size > 0) {
650 isl_vec_free(bset->sample);
651 bset->sample = isl_vec_copy(sample);
652 }
653
654 isl_basic_set_free(bset);
655 isl_tab_free(tab);
656 return sample;
657error:
658 isl_basic_set_free(bset);
659 isl_tab_free(tab);
660 return NULL((void*)0);
661}
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 */
675static struct isl_basic_setisl_basic_map *plug_in(struct isl_basic_setisl_basic_map *bset,
676 struct isl_vec *sample)
677{
678 int i;
679 unsigned total;
680 struct isl_mat *T;
681
682 if (!bset || !sample)
683 goto error;
684
685 total = isl_basic_set_total_dim(bset);
686 T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
687 if (!T)
688 goto error;
689
690 for (i = 0; i < sample->size; ++i) {
691 isl_int_set(T->row[i][0], sample->el[i])isl_sioimath_set((T->row[i][0]), *(sample->el[i]));
692 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
693 }
694 for (i = 0; i < T->n_col - 1; ++i) {
695 isl_seq_clr(T->row[sample->size + i], T->n_col);
696 isl_int_set_si(T->row[sample->size + i][1 + i], 1)isl_sioimath_set_si((T->row[sample->size + i][1 + i]), 1
)
;
697 }
698 isl_vec_free(sample);
699
700 bset = isl_basic_set_preimage(bset, T);
701 return bset;
702error:
703 isl_basic_set_free(bset);
704 isl_vec_free(sample);
705 return NULL((void*)0);
706}
707
708/* Given a basic set "bset", return any (possibly non-integer) point
709 * in the basic set.
710 */
711static struct isl_vec *rational_sample(struct isl_basic_setisl_basic_map *bset)
712{
713 struct isl_tab *tab;
714 struct isl_vec *sample;
715
716 if (!bset)
717 return NULL((void*)0);
718
719 tab = isl_tab_from_basic_set(bset, 0);
720 sample = isl_tab_get_sample_value(tab);
721 isl_tab_free(tab);
722
723 isl_basic_set_free(bset);
724
725 return sample;
726}
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 */
761static struct isl_basic_setisl_basic_map *shift_cone(struct isl_basic_setisl_basic_map *cone,
762 struct isl_vec *vec)
763{
764 int i, j, k;
765 unsigned total;
766
767 struct isl_basic_setisl_basic_map *shift = NULL((void*)0);
768
769 if (!cone || !vec)
770 goto error;
771
772 isl_assert(cone->ctx, cone->n_eq == 0, goto error)do { if (cone->n_eq == 0) break; do { isl_handle_error(cone
->ctx, isl_error_unknown, "Assertion \"" "cone->n_eq == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 772); goto error; } while (0); } while (0)
;
773
774 total = isl_basic_set_total_dim(cone);
775
776 shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
777 0, 0, cone->n_ineq);
778
779 for (i = 0; i < cone->n_ineq; ++i) {
780 k = isl_basic_set_alloc_inequality(shift);
781 if (k < 0)
782 goto error;
783 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
784 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
785 &shift->ineq[k][0]);
786 isl_int_cdiv_q(shift->ineq[k][0],isl_sioimath_cdiv_q((shift->ineq[k][0]), *(shift->ineq[
k][0]), *(vec->el[0]))
787 shift->ineq[k][0], vec->el[0])isl_sioimath_cdiv_q((shift->ineq[k][0]), *(shift->ineq[
k][0]), *(vec->el[0]))
;
788 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0])isl_sioimath_neg((shift->ineq[k][0]), *(shift->ineq[k][
0]))
;
789 for (j = 0; j < total; ++j) {
790 if (isl_int_is_nonneg(shift->ineq[k][1 + j])(isl_sioimath_sgn(*(shift->ineq[k][1 + j])) >= 0))
791 continue;
792 isl_int_add(shift->ineq[k][0],isl_sioimath_add((shift->ineq[k][0]), *(shift->ineq[k][
0]), *(shift->ineq[k][1 + j]))
793 shift->ineq[k][0], shift->ineq[k][1 + j])isl_sioimath_add((shift->ineq[k][0]), *(shift->ineq[k][
0]), *(shift->ineq[k][1 + j]))
;
794 }
795 }
796
797 isl_basic_set_free(cone);
798 isl_vec_free(vec);
799
800 return isl_basic_set_finalize(shift);
801error:
802 isl_basic_set_free(shift);
803 isl_basic_set_free(cone);
804 isl_vec_free(vec);
805 return NULL((void*)0);
806}
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 */
819static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
820 struct isl_basic_setisl_basic_map *cone, struct isl_mat *U)
821{
822 unsigned total;
823
824 if (!vec || !cone || !U)
825 goto error;
826
827 isl_assert(vec->ctx, vec->size != 0, goto error)do { if (vec->size != 0) break; do { isl_handle_error(vec->
ctx, isl_error_unknown, "Assertion \"" "vec->size != 0" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 827); goto error; } while (0); } while (0)
;
828 if (isl_int_is_one(vec->el[0])(isl_sioimath_cmp_si(*(vec->el[0]), 1) == 0)) {
829 isl_mat_free(U);
830 isl_basic_set_free(cone);
831 return vec;
832 }
833
834 total = isl_basic_set_total_dim(cone);
835 cone = isl_basic_set_preimage(cone, U);
836 cone = isl_basic_set_remove_dims(cone, isl_dim_set,
837 0, total - (vec->size - 1));
838
839 cone = shift_cone(cone, vec);
840
841 vec = rational_sample(cone);
842 vec = isl_vec_ceil(vec);
843 return vec;
844error:
845 isl_mat_free(U);
846 isl_vec_free(vec);
847 isl_basic_set_free(cone);
848 return NULL((void*)0);
849}
850
851/* Concatenate two integer vectors, i.e., two vectors with denominator
852 * (stored in element 0) equal to 1.
853 */
854static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
855{
856 struct isl_vec *vec;
857
858 if (!vec1 || !vec2)
859 goto error;
860 isl_assert(vec1->ctx, vec1->size > 0, goto error)do { if (vec1->size > 0) break; do { isl_handle_error(vec1
->ctx, isl_error_unknown, "Assertion \"" "vec1->size > 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 860); goto error; } while (0); } while (0)
;
861 isl_assert(vec2->ctx, vec2->size > 0, goto error)do { if (vec2->size > 0) break; do { isl_handle_error(vec2
->ctx, isl_error_unknown, "Assertion \"" "vec2->size > 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 861); goto error; } while (0); } while (0)
;
862 isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error)do { if ((isl_sioimath_cmp_si(*(vec1->el[0]), 1) == 0)) break
; do { isl_handle_error(vec1->ctx, isl_error_unknown, "Assertion \""
"(isl_sioimath_cmp_si(*(vec1->el[0]), 1) == 0)" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 862); goto error; } while (0); } while (0)
;
863 isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error)do { if ((isl_sioimath_cmp_si(*(vec2->el[0]), 1) == 0)) break
; do { isl_handle_error(vec2->ctx, isl_error_unknown, "Assertion \""
"(isl_sioimath_cmp_si(*(vec2->el[0]), 1) == 0)" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 863); goto error; } while (0); } while (0)
;
864
865 vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
866 if (!vec)
867 goto error;
868
869 isl_seq_cpy(vec->el, vec1->el, vec1->size);
870 isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
871
872 isl_vec_free(vec1);
873 isl_vec_free(vec2);
874
875 return vec;
876error:
877 isl_vec_free(vec1);
878 isl_vec_free(vec2);
879 return NULL((void*)0);
880}
881
882/* Give a basic set "bset" with recession cone "cone", compute and
883 * return an integer point in bset, if any.
884 *
885 * If the recession cone is full-dimensional, then we know that
886 * bset contains an infinite number of integer points and it is
887 * fairly easy to pick one of them.
888 * If the recession cone is not full-dimensional, then we first
889 * transform bset such that the bounded directions appear as
890 * the first dimensions of the transformed basic set.
891 * We do this by using a unimodular transformation that transforms
892 * the equalities in the recession cone to equalities on the first
893 * dimensions.
894 *
895 * The transformed set is then projected onto its bounded dimensions.
896 * Note that to compute this projection, we can simply drop all constraints
897 * involving any of the unbounded dimensions since these constraints
898 * cannot be combined to produce a constraint on the bounded dimensions.
899 * To see this, assume that there is such a combination of constraints
900 * that produces a constraint on the bounded dimensions. This means
901 * that some combination of the unbounded dimensions has both an upper
902 * bound and a lower bound in terms of the bounded dimensions, but then
903 * this combination would be a bounded direction too and would have been
904 * transformed into a bounded dimensions.
905 *
906 * We then compute a sample value in the bounded dimensions.
907 * If no such value can be found, then the original set did not contain
908 * any integer points and we are done.
909 * Otherwise, we plug in the value we found in the bounded dimensions,
910 * project out these bounded dimensions and end up with a set with
911 * a full-dimensional recession cone.
912 * A sample point in this set is computed by "rounding up" any
913 * rational point in the set.
914 *
915 * The sample points in the bounded and unbounded dimensions are
916 * then combined into a single sample point and transformed back
917 * to the original space.
918 */
919__isl_give isl_vec *isl_basic_set_sample_with_cone(
920 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *cone)
921{
922 unsigned total;
923 unsigned cone_dim;
924 struct isl_mat *M, *U;
925 struct isl_vec *sample;
926 struct isl_vec *cone_sample;
927 struct isl_ctx *ctx;
928 struct isl_basic_setisl_basic_map *bounded;
929
930 if (!bset || !cone)
931 goto error;
932
933 ctx = isl_basic_set_get_ctx(bset);
934 total = isl_basic_set_total_dim(cone);
935 cone_dim = total - cone->n_eq;
936
937 M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
938 M = isl_mat_left_hermite(M, 0, &U, NULL((void*)0));
939 if (!M)
940 goto error;
941 isl_mat_free(M);
942
943 U = isl_mat_lin_to_aff(U);
944 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
945
946 bounded = isl_basic_set_copy(bset);
947 bounded = isl_basic_set_drop_constraints_involving(bounded,
948 total - cone_dim, cone_dim);
949 bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
950 sample = sample_bounded(bounded);
951 if (!sample || sample->size == 0) {
952 isl_basic_set_free(bset);
953 isl_basic_set_free(cone);
954 isl_mat_free(U);
955 return sample;
956 }
957 bset = plug_in(bset, isl_vec_copy(sample));
958 cone_sample = rational_sample(bset);
959 cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
960 sample = vec_concat(sample, cone_sample);
961 sample = isl_mat_vec_product(U, sample);
962 return sample;
963error:
964 isl_basic_set_free(cone);
965 isl_basic_set_free(bset);
966 return NULL((void*)0);
967}
968
969static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
970{
971 int i;
972
973 isl_int_set_si(*s, 0)isl_sioimath_set_si((*s), 0);
974
975 for (i = 0; i < v->size; ++i)
976 if (isl_int_is_neg(v->el[i])(isl_sioimath_sgn(*(v->el[i])) < 0))
977 isl_int_add(*s, *s, v->el[i])isl_sioimath_add((*s), *(*s), *(v->el[i]));
978}
979
980/* Given a tableau "tab", a tableau "tab_cone" that corresponds
981 * to the recession cone and the inverse of a new basis U = inv(B),
982 * with the unbounded directions in B last,
983 * add constraints to "tab" that ensure any rational value
984 * in the unbounded directions can be rounded up to an integer value.
985 *
986 * The new basis is given by x' = B x, i.e., x = U x'.
987 * For any rational value of the last tab->n_unbounded coordinates
988 * in the update tableau, the value that is obtained by rounding
989 * up this value should be contained in the original tableau.
990 * For any constraint "a x + c >= 0", we therefore need to add
991 * a constraint "a x + c + s >= 0", with s the sum of all negative
992 * entries in the last elements of "a U".
993 *
994 * Since we are not interested in the first entries of any of the "a U",
995 * we first drop the columns of U that correpond to bounded directions.
996 */
997static int tab_shift_cone(struct isl_tab *tab,
998 struct isl_tab *tab_cone, struct isl_mat *U)
999{
1000 int i;
1001 isl_int v;
1002 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
1003
1004 if (tab && tab->n_unbounded == 0) {
1005 isl_mat_free(U);
1006 return 0;
1007 }
1008 isl_int_init(v)isl_sioimath_init((v));
1009 if (!tab || !tab_cone || !U)
1010 goto error;
1011 bset = isl_tab_peek_bset(tab_cone);
1012 U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1013 for (i = 0; i < bset->n_ineq; ++i) {
1014 int ok;
1015 struct isl_vec *row = NULL((void*)0);
1016 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1017 continue;
1018 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1019 if (!row)
1020 goto error;
1021 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1022 row = isl_vec_mat_product(row, isl_mat_copy(U));
1023 if (!row)
1024 goto error;
1025 vec_sum_of_neg(row, &v);
1026 isl_vec_free(row);
1027 if (isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0))
1028 continue;
1029 if (isl_tab_extend_cons(tab, 1) < 0)
1030 goto error;
1031 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v)isl_sioimath_add((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(v))
;
1032 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1033 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(v))
;
1034 if (!ok)
1035 goto error;
1036 }
1037
1038 isl_mat_free(U);
1039 isl_int_clear(v)isl_sioimath_clear((v));
1040 return 0;
1041error:
1042 isl_mat_free(U);
1043 isl_int_clear(v)isl_sioimath_clear((v));
1044 return -1;
1045}
1046
1047/* Compute and return an initial basis for the possibly
1048 * unbounded tableau "tab". "tab_cone" is a tableau
1049 * for the corresponding recession cone.
1050 * Additionally, add constraints to "tab" that ensure
1051 * that any rational value for the unbounded directions
1052 * can be rounded up to an integer value.
1053 *
1054 * If the tableau is bounded, i.e., if the recession cone
1055 * is zero-dimensional, then we just use inital_basis.
1056 * Otherwise, we construct a basis whose first directions
1057 * correspond to equalities, followed by bounded directions,
1058 * i.e., equalities in the recession cone.
1059 * The remaining directions are then unbounded.
1060 */
1061int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1062 struct isl_tab *tab_cone)
1063{
1064 struct isl_mat *eq;
1065 struct isl_mat *cone_eq;
1066 struct isl_mat *U, *Q;
1067
1068 if (!tab || !tab_cone)
1069 return -1;
1070
1071 if (tab_cone->n_col == tab_cone->n_dead) {
1072 tab->basis = initial_basis(tab);
1073 return tab->basis ? 0 : -1;
1074 }
1075
1076 eq = tab_equalities(tab);
1077 if (!eq)
1078 return -1;
1079 tab->n_zero = eq->n_row;
1080 cone_eq = tab_equalities(tab_cone);
1081 eq = isl_mat_concat(eq, cone_eq);
1082 if (!eq)
1083 return -1;
1084 tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1085 eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1086 if (!eq)
1087 return -1;
1088 isl_mat_free(eq);
1089 tab->basis = isl_mat_lin_to_aff(Q);
1090 if (tab_shift_cone(tab, tab_cone, U) < 0)
1091 return -1;
1092 if (!tab->basis)
1093 return -1;
1094 return 0;
1095}
1096
1097/* Compute and return a sample point in bset using generalized basis
1098 * reduction. We first check if the input set has a non-trivial
1099 * recession cone. If so, we perform some extra preprocessing in
1100 * sample_with_cone. Otherwise, we directly perform generalized basis
1101 * reduction.
1102 */
1103static struct isl_vec *gbr_sample(struct isl_basic_setisl_basic_map *bset)
1104{
1105 unsigned dim;
1106 struct isl_basic_setisl_basic_map *cone;
1107
1108 dim = isl_basic_set_total_dim(bset);
1109
1110 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1111 if (!cone)
1112 goto error;
1113
1114 if (cone->n_eq < dim)
1115 return isl_basic_set_sample_with_cone(bset, cone);
1116
1117 isl_basic_set_free(cone);
1118 return sample_bounded(bset);
1119error:
1120 isl_basic_set_free(bset);
1121 return NULL((void*)0);
1122}
1123
1124static struct isl_vec *basic_set_sample(struct isl_basic_setisl_basic_map *bset, int bounded)
1125{
1126 struct isl_ctx *ctx;
1127 unsigned dim;
1128 if (!bset)
1129 return NULL((void*)0);
1130
1131 ctx = bset->ctx;
1132 if (isl_basic_set_plain_is_empty(bset))
1133 return empty_sample(bset);
1134
1135 dim = isl_basic_set_n_dim(bset);
1136 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error)do { if (isl_basic_set_n_param(bset) == 0) break; do { isl_handle_error
(ctx, isl_error_unknown, "Assertion \"" "isl_basic_set_n_param(bset) == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 1136); goto error; } while (0); } while (0)
;
1137 isl_assert(ctx, bset->n_div == 0, goto error)do { if (bset->n_div == 0) break; do { isl_handle_error(ctx
, isl_error_unknown, "Assertion \"" "bset->n_div == 0" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 1137); goto error; } while (0); } while (0)
;
1138
1139 if (bset->sample && bset->sample->size == 1 + dim) {
1140 int contains = isl_basic_set_contains(bset, bset->sample);
1141 if (contains < 0)
1142 goto error;
1143 if (contains) {
1144 struct isl_vec *sample = isl_vec_copy(bset->sample);
1145 isl_basic_set_free(bset);
1146 return sample;
1147 }
1148 }
1149 isl_vec_free(bset->sample);
1150 bset->sample = NULL((void*)0);
1151
1152 if (bset->n_eq > 0)
1153 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1154 : isl_basic_set_sample_vec);
1155 if (dim == 0)
1156 return zero_sample(bset);
1157 if (dim == 1)
1158 return interval_sample(bset);
1159
1160 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1161error:
1162 isl_basic_set_free(bset);
1163 return NULL((void*)0);
1164}
1165
1166__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_setisl_basic_map *bset)
1167{
1168 return basic_set_sample(bset, 0);
1169}
1170
1171/* Compute an integer sample in "bset", where the caller guarantees
1172 * that "bset" is bounded.
1173 */
1174struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_setisl_basic_map *bset)
1175{
1176 return basic_set_sample(bset, 1);
1177}
1178
1179__isl_give isl_basic_setisl_basic_map *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1180{
1181 int i;
1182 int k;
1183 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
1184 struct isl_ctx *ctx;
1185 unsigned dim;
1186
1187 if (!vec)
1188 return NULL((void*)0);
1189 ctx = vec->ctx;
1190 isl_assert(ctx, vec->size != 0, goto error)do { if (vec->size != 0) break; do { isl_handle_error(ctx,
isl_error_unknown, "Assertion \"" "vec->size != 0" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301389/tools/polly/lib/External/isl/isl_sample.c"
, 1190); goto error; } while (0); } while (0)
;
1191
1192 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1193 if (!bset)
1194 goto error;
1195 dim = isl_basic_set_n_dim(bset);
1196 for (i = dim - 1; i >= 0; --i) {
1197 k = isl_basic_set_alloc_equality(bset);
1198 if (k < 0)
1199 goto error;
1200 isl_seq_clr(bset->eq[k], 1 + dim);
1201 isl_int_neg(bset->eq[k][0], vec->el[1 + i])isl_sioimath_neg((bset->eq[k][0]), *(vec->el[1 + i]));
1202 isl_int_set(bset->eq[k][1 + i], vec->el[0])isl_sioimath_set((bset->eq[k][1 + i]), *(vec->el[0]));
1203 }
1204 bset->sample = vec;
1205
1206 return bset;
1207error:
1208 isl_basic_set_free(bset);
1209 isl_vec_free(vec);
1210 return NULL((void*)0);
1211}
1212
1213__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1214{
1215 struct isl_basic_setisl_basic_map *bset;
1216 struct isl_vec *sample_vec;
1217
1218 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1219 sample_vec = isl_basic_set_sample_vec(bset);
1220 if (!sample_vec)
1221 goto error;
1222 if (sample_vec->size == 0) {
1223 isl_vec_free(sample_vec);
1224 return isl_basic_map_set_to_empty(bmap);
1225 }
1226 isl_vec_free(bmap->sample);
1227 bmap->sample = isl_vec_copy(sample_vec);
1228 bset = isl_basic_set_from_vec(sample_vec);
1229 return isl_basic_map_overlying_set(bset, bmap);
1230error:
1231 isl_basic_map_free(bmap);
1232 return NULL((void*)0);
1233}
1234
1235__isl_give isl_basic_setisl_basic_map *isl_basic_set_sample(__isl_take isl_basic_setisl_basic_map *bset)
1236{
1237 return isl_basic_map_sample(bset);
1238}
1239
1240__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1241{
1242 int i;
1243 isl_basic_map *sample = NULL((void*)0);
1244
1245 if (!map)
1246 goto error;
1247
1248 for (i = 0; i < map->n; ++i) {
1249 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1250 if (!sample)
1251 goto error;
1252 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY)(!!(((sample)->flags) & ((1 << 1)))))
1253 break;
1254 isl_basic_map_free(sample);
1255 }
1256 if (i == map->n)
1257 sample = isl_basic_map_empty(isl_map_get_space(map));
1258 isl_map_free(map);
1259 return sample;
1260error:
1261 isl_map_free(map);
1262 return NULL((void*)0);
1263}
1264
1265__isl_give isl_basic_setisl_basic_map *isl_set_sample(__isl_take isl_setisl_map *set)
1266{
1267 return bset_from_bmap(isl_map_sample(set_to_map(set)));
1268}
1269
1270__isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_setisl_basic_map *bset)
1271{
1272 isl_vec *vec;
1273 isl_space *dim;
1274
1275 dim = isl_basic_set_get_space(bset);
1276 bset = isl_basic_set_underlying_set(bset);
1277 vec = isl_basic_set_sample_vec(bset);
1278
1279 return isl_point_alloc(dim, vec);
1280}
1281
1282__isl_give isl_point *isl_set_sample_point(__isl_take isl_setisl_map *set)
1283{
1284 int i;
1285 isl_point *pnt;
1
'pnt' declared without an initial value
1286
1287 if (!set)
2
Assuming 'set' is non-null
3
Taking false branch
1288 return NULL((void*)0);
1289
1290 for (i = 0; i < set->n; ++i) {
4
Assuming the condition is false
5
Loop condition is false. Execution continues on line 1298
1291 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1292 if (!pnt)
1293 goto error;
1294 if (!isl_point_is_void(pnt))
1295 break;
1296 isl_point_free(pnt);
1297 }
1298 if (i == set->n)
6
Assuming the condition is false
7
Taking false branch
1299 pnt = isl_point_void(isl_set_get_space(set));
1300
1301 isl_set_free(set);
1302 return pnt;
8
Undefined or garbage value returned to caller
1303error:
1304 isl_set_free(set);
1305 return NULL((void*)0);
1306}