Bug Summary

File:polly/lib/External/isl/isl_sample.c
Warning:line 1331, column 2
Undefined or garbage value returned to caller

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name isl_sample.c -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mframe-pointer=none -fmath-errno -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/build-llvm -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I tools/polly/lib/External -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/imath -I tools/polly/lib/External/isl -I tools/polly/include -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/pet/include -I tools/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/include -I include -I /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/llvm/include -D NDEBUG -U NDEBUG -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-command-line-argument -Wno-unknown-warning-option -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=gnu99 -fconst-strings -fdebug-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/build-llvm -ferror-limit 19 -fgnuc-version=4.2.1 -fcolor-diagnostics -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2021-09-26-234817-15343-1 -x c /build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c
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 __isl_give isl_vec *empty_sample(__isl_take 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 __isl_give isl_vec *zero_sample(__isl_take isl_basic_setisl_basic_map *bset)
41{
42 isl_size dim;
43 struct isl_vec *sample;
44
45 dim = isl_basic_set_dim(bset, isl_dim_all);
46 if (dim < 0)
47 goto error;
48 sample = isl_vec_alloc(bset->ctx, 1 + dim);
49 if (sample) {
50 isl_int_set_si(sample->el[0], 1)isl_sioimath_set_si((sample->el[0]), 1);
51 isl_seq_clr(sample->el + 1, dim);
52 }
53 isl_basic_set_free(bset);
54 return sample;
55error:
56 isl_basic_set_free(bset);
57 return NULL((void*)0);
58}
59
60static __isl_give isl_vec *interval_sample(__isl_take isl_basic_setisl_basic_map *bset)
61{
62 int i;
63 isl_int t;
64 struct isl_vec *sample;
65
66 bset = isl_basic_set_simplify(bset);
67 if (!bset)
68 return NULL((void*)0);
69 if (isl_basic_set_plain_is_empty(bset))
70 return empty_sample(bset);
71 if (bset->n_eq == 0 && bset->n_ineq == 0)
72 return zero_sample(bset);
73
74 sample = isl_vec_alloc(bset->ctx, 2);
75 if (!sample)
76 goto error;
77 if (!bset)
78 return NULL((void*)0);
79 isl_int_set_si(sample->block.data[0], 1)isl_sioimath_set_si((sample->block.data[0]), 1);
80
81 if (bset->n_eq > 0) {
82 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 82); goto error; } while (0); } while (0)
;
83 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 83); goto error; } while (0); } while (0)
;
84 if (isl_int_is_one(bset->eq[0][1])(isl_sioimath_cmp_si(*(bset->eq[0][1]), 1) == 0))
85 isl_int_neg(sample->el[1], bset->eq[0][0])isl_sioimath_neg((sample->el[1]), *(bset->eq[0][0]));
86 else {
87 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 88); goto error; } while (0); } while (0)
88 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 88); goto error; } while (0); } while (0)
;
89 isl_int_set(sample->el[1], bset->eq[0][0])isl_sioimath_set((sample->el[1]), *(bset->eq[0][0]));
90 }
91 isl_basic_set_free(bset);
92 return sample;
93 }
94
95 isl_int_init(t)isl_sioimath_init((t));
96 if (isl_int_is_one(bset->ineq[0][1])(isl_sioimath_cmp_si(*(bset->ineq[0][1]), 1) == 0))
97 isl_int_neg(sample->block.data[1], bset->ineq[0][0])isl_sioimath_neg((sample->block.data[1]), *(bset->ineq[
0][0]))
;
98 else
99 isl_int_set(sample->block.data[1], bset->ineq[0][0])isl_sioimath_set((sample->block.data[1]), *(bset->ineq[
0][0]))
;
100 for (i = 1; i < bset->n_ineq; ++i) {
101 isl_seq_inner_product(sample->block.data,
102 bset->ineq[i], 2, &t);
103 if (isl_int_is_neg(t)(isl_sioimath_sgn(*(t)) < 0))
104 break;
105 }
106 isl_int_clear(t)isl_sioimath_clear((t));
107 if (i < bset->n_ineq) {
108 isl_vec_free(sample);
109 return empty_sample(bset);
110 }
111
112 isl_basic_set_free(bset);
113 return sample;
114error:
115 isl_basic_set_free(bset);
116 isl_vec_free(sample);
117 return NULL((void*)0);
118}
119
120/* Find a sample integer point, if any, in bset, which is known
121 * to have equalities. If bset contains no integer points, then
122 * return a zero-length vector.
123 * We simply remove the known equalities, compute a sample
124 * in the resulting bset, using the specified recurse function,
125 * and then transform the sample back to the original space.
126 */
127static __isl_give isl_vec *sample_eq(__isl_take isl_basic_setisl_basic_map *bset,
128 __isl_give isl_vec *(*recurse)(__isl_take isl_basic_setisl_basic_map *))
129{
130 struct isl_mat *T;
131 struct isl_vec *sample;
132
133 if (!bset)
134 return NULL((void*)0);
135
136 bset = isl_basic_set_remove_equalities(bset, &T, NULL((void*)0));
137 sample = recurse(bset);
138 if (!sample || sample->size == 0)
139 isl_mat_free(T);
140 else
141 sample = isl_mat_vec_product(T, sample);
142 return sample;
143}
144
145/* Return a matrix containing the equalities of the tableau
146 * in constraint form. The tableau is assumed to have
147 * an associated bset that has been kept up-to-date.
148 */
149static struct isl_mat *tab_equalities(struct isl_tab *tab)
150{
151 int i, j;
152 int n_eq;
153 struct isl_mat *eq;
154 struct isl_basic_setisl_basic_map *bset;
155
156 if (!tab)
157 return NULL((void*)0);
158
159 bset = isl_tab_peek_bset(tab);
160 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 160); return ((void*)0); } while (0); } while (0)
;
161
162 n_eq = tab->n_var - tab->n_col + tab->n_dead;
163 if (tab->empty || n_eq == 0)
164 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
165 if (n_eq == tab->n_var)
166 return isl_mat_identity(tab->mat->ctx, tab->n_var);
167
168 eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
169 if (!eq)
170 return NULL((void*)0);
171 for (i = 0, j = 0; i < tab->n_con; ++i) {
172 if (tab->con[i].is_row)
173 continue;
174 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
175 continue;
176 if (i < bset->n_eq)
177 isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
178 else
179 isl_seq_cpy(eq->row[j],
180 bset->ineq[i - bset->n_eq] + 1, tab->n_var);
181 ++j;
182 }
183 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 183); goto error; } while (0); } while (0)
;
184 return eq;
185error:
186 isl_mat_free(eq);
187 return NULL((void*)0);
188}
189
190/* Compute and return an initial basis for the bounded tableau "tab".
191 *
192 * If the tableau is either full-dimensional or zero-dimensional,
193 * the we simply return an identity matrix.
194 * Otherwise, we construct a basis whose first directions correspond
195 * to equalities.
196 */
197static struct isl_mat *initial_basis(struct isl_tab *tab)
198{
199 int n_eq;
200 struct isl_mat *eq;
201 struct isl_mat *Q;
202
203 tab->n_unbounded = 0;
204 tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
205 if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
206 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
207
208 eq = tab_equalities(tab);
209 eq = isl_mat_left_hermite(eq, 0, NULL((void*)0), &Q);
210 if (!eq)
211 return NULL((void*)0);
212 isl_mat_free(eq);
213
214 Q = isl_mat_lin_to_aff(Q);
215 return Q;
216}
217
218/* Compute the minimum of the current ("level") basis row over "tab"
219 * and store the result in position "level" of "min".
220 *
221 * This function assumes that at least one more row and at least
222 * one more element in the constraint array are available in the tableau.
223 */
224static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
225 __isl_keep isl_vec *min, int level)
226{
227 return isl_tab_min(tab, tab->basis->row[1 + level],
228 ctx->one, &min->el[level], NULL((void*)0), 0);
229}
230
231/* Compute the maximum of the current ("level") basis row over "tab"
232 * and store the result in position "level" of "max".
233 *
234 * This function assumes that at least one more row and at least
235 * one more element in the constraint array are available in the tableau.
236 */
237static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
238 __isl_keep isl_vec *max, int level)
239{
240 enum isl_lp_result res;
241 unsigned dim = tab->n_var;
242
243 isl_seq_neg(tab->basis->row[1 + level] + 1,
244 tab->basis->row[1 + level] + 1, dim);
245 res = isl_tab_min(tab, tab->basis->row[1 + level],
246 ctx->one, &max->el[level], NULL((void*)0), 0);
247 isl_seq_neg(tab->basis->row[1 + level] + 1,
248 tab->basis->row[1 + level] + 1, dim);
249 isl_int_neg(max->el[level], max->el[level])isl_sioimath_neg((max->el[level]), *(max->el[level]));
250
251 return res;
252}
253
254/* Perform a greedy search for an integer point in the set represented
255 * by "tab", given that the minimal rational value (rounded up to the
256 * nearest integer) at "level" is smaller than the maximal rational
257 * value (rounded down to the nearest integer).
258 *
259 * Return 1 if we have found an integer point (if tab->n_unbounded > 0
260 * then we may have only found integer values for the bounded dimensions
261 * and it is the responsibility of the caller to extend this solution
262 * to the unbounded dimensions).
263 * Return 0 if greedy search did not result in a solution.
264 * Return -1 if some error occurred.
265 *
266 * We assign a value half-way between the minimum and the maximum
267 * to the current dimension and check if the minimal value of the
268 * next dimension is still smaller than (or equal) to the maximal value.
269 * We continue this process until either
270 * - the minimal value (rounded up) is greater than the maximal value
271 * (rounded down). In this case, greedy search has failed.
272 * - we have exhausted all bounded dimensions, meaning that we have
273 * found a solution.
274 * - the sample value of the tableau is integral.
275 * - some error has occurred.
276 */
277static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
278 __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
279{
280 struct isl_tab_undo *snap;
281 enum isl_lp_result res;
282
283 snap = isl_tab_snap(tab);
284
285 do {
286 isl_int_add(tab->basis->row[1 + level][0],isl_sioimath_add((tab->basis->row[1 + level][0]), *(min
->el[level]), *(max->el[level]))
287 min->el[level], max->el[level])isl_sioimath_add((tab->basis->row[1 + level][0]), *(min
->el[level]), *(max->el[level]))
;
288 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)
289 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)
;
290 isl_int_neg(tab->basis->row[1 + level][0],isl_sioimath_neg((tab->basis->row[1 + level][0]), *(tab
->basis->row[1 + level][0]))
291 tab->basis->row[1 + level][0])isl_sioimath_neg((tab->basis->row[1 + level][0]), *(tab
->basis->row[1 + level][0]))
;
292 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
293 return -1;
294 isl_int_set_si(tab->basis->row[1 + level][0], 0)isl_sioimath_set_si((tab->basis->row[1 + level][0]), 0);
295
296 if (++level >= tab->n_var - tab->n_unbounded)
297 return 1;
298 if (isl_tab_sample_is_integer(tab))
299 return 1;
300
301 res = compute_min(ctx, tab, min, level);
302 if (res == isl_lp_error)
303 return -1;
304 if (res != isl_lp_ok)
305 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 307); return -1; } while (0)
306 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 307); return -1; } while (0)
307 return -1)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 307); return -1; } while (0)
;
308 res = compute_max(ctx, tab, max, level);
309 if (res == isl_lp_error)
310 return -1;
311 if (res != isl_lp_ok)
312 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 314); return -1; } while (0)
313 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 314); return -1; } while (0)
314 return -1)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 314); return -1; } while (0)
;
315 } while (isl_int_le(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
<= 0)
);
316
317 if (isl_tab_rollback(tab, snap) < 0)
318 return -1;
319
320 return 0;
321}
322
323/* Given a tableau representing a set, find and return
324 * an integer point in the set, if there is any.
325 *
326 * We perform a depth first search
327 * for an integer point, by scanning all possible values in the range
328 * attained by a basis vector, where an initial basis may have been set
329 * by the calling function. Otherwise an initial basis that exploits
330 * the equalities in the tableau is created.
331 * tab->n_zero is currently ignored and is clobbered by this function.
332 *
333 * The tableau is allowed to have unbounded direction, but then
334 * the calling function needs to set an initial basis, with the
335 * unbounded directions last and with tab->n_unbounded set
336 * to the number of unbounded directions.
337 * Furthermore, the calling functions needs to add shifted copies
338 * of all constraints involving unbounded directions to ensure
339 * that any feasible rational value in these directions can be rounded
340 * up to yield a feasible integer value.
341 * In particular, let B define the given basis x' = B x
342 * and let T be the inverse of B, i.e., X = T x'.
343 * Let a x + c >= 0 be a constraint of the set represented by the tableau,
344 * or a T x' + c >= 0 in terms of the given basis. Assume that
345 * the bounded directions have an integer value, then we can safely
346 * round up the values for the unbounded directions if we make sure
347 * that x' not only satisfies the original constraint, but also
348 * the constraint "a T x' + c + s >= 0" with s the sum of all
349 * negative values in the last n_unbounded entries of "a T".
350 * The calling function therefore needs to add the constraint
351 * a x + c + s >= 0. The current function then scans the first
352 * directions for an integer value and once those have been found,
353 * it can compute "T ceil(B x)" to yield an integer point in the set.
354 * Note that during the search, the first rows of B may be changed
355 * by a basis reduction, but the last n_unbounded rows of B remain
356 * unaltered and are also not mixed into the first rows.
357 *
358 * The search is implemented iteratively. "level" identifies the current
359 * basis vector. "init" is true if we want the first value at the current
360 * level and false if we want the next value.
361 *
362 * At the start of each level, we first check if we can find a solution
363 * using greedy search. If not, we continue with the exhaustive search.
364 *
365 * The initial basis is the identity matrix. If the range in some direction
366 * contains more than one integer value, we perform basis reduction based
367 * on the value of ctx->opt->gbr
368 * - ISL_GBR_NEVER: never perform basis reduction
369 * - ISL_GBR_ONCE: only perform basis reduction the first
370 * time such a range is encountered
371 * - ISL_GBR_ALWAYS: always perform basis reduction when
372 * such a range is encountered
373 *
374 * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
375 * reduction computation to return early. That is, as soon as it
376 * finds a reasonable first direction.
377 */
378__isl_give isl_vec *isl_tab_sample(struct isl_tab *tab)
379{
380 unsigned dim;
381 unsigned gbr;
382 struct isl_ctx *ctx;
383 struct isl_vec *sample;
384 struct isl_vec *min;
385 struct isl_vec *max;
386 enum isl_lp_result res;
387 int level;
388 int init;
389 int reduced;
390 struct isl_tab_undo **snap;
391
392 if (!tab)
393 return NULL((void*)0);
394 if (tab->empty)
395 return isl_vec_alloc(tab->mat->ctx, 0);
396
397 if (!tab->basis)
398 tab->basis = initial_basis(tab);
399 if (!tab->basis)
400 return NULL((void*)0);
401 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 402); return ((void*)0); } while (0); } while (0)
402 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 402); return ((void*)0); } while (0); } while (0)
;
403 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 404); return ((void*)0); } while (0); } while (0)
404 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 404); return ((void*)0); } while (0); } while (0)
;
405
406 ctx = tab->mat->ctx;
407 dim = tab->n_var;
408 gbr = ctx->opt->gbr;
409
410 if (tab->n_unbounded == tab->n_var) {
411 sample = isl_tab_get_sample_value(tab);
412 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
413 sample = isl_vec_ceil(sample);
414 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
415 sample);
416 return sample;
417 }
418
419 if (isl_tab_extend_cons(tab, dim + 1) < 0)
420 return NULL((void*)0);
421
422 min = isl_vec_alloc(ctx, dim);
423 max = isl_vec_alloc(ctx, dim);
424 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 *)))
;
425
426 if (!min || !max || !snap)
427 goto error;
428
429 level = 0;
430 init = 1;
431 reduced = 0;
432
433 while (level >= 0) {
434 if (init) {
435 int choice;
436
437 res = compute_min(ctx, tab, min, level);
438 if (res == isl_lp_error)
439 goto error;
440 if (res != isl_lp_ok)
441 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 443); goto error; } while (0)
442 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 443); goto error; } while (0)
443 goto error)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 443); goto error; } while (0)
;
444 if (isl_tab_sample_is_integer(tab))
445 break;
446 res = compute_max(ctx, tab, max, level);
447 if (res == isl_lp_error)
448 goto error;
449 if (res != isl_lp_ok)
450 isl_die(ctx, isl_error_internal,do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 452); goto error; } while (0)
451 "expecting bounded rational solution",do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 452); goto error; } while (0)
452 goto error)do { isl_handle_error(ctx, isl_error_internal, "expecting bounded rational solution"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 452); goto error; } while (0)
;
453 if (isl_tab_sample_is_integer(tab))
454 break;
455 choice = isl_int_lt(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
< 0)
;
456 if (choice) {
457 int g;
458 g = greedy_search(ctx, tab, min, max, level);
459 if (g < 0)
460 goto error;
461 if (g)
462 break;
463 }
464 if (!reduced && choice &&
465 ctx->opt->gbr != ISL_GBR_NEVER0) {
466 unsigned gbr_only_first;
467 if (ctx->opt->gbr == ISL_GBR_ONCE1)
468 ctx->opt->gbr = ISL_GBR_NEVER0;
469 tab->n_zero = level;
470 gbr_only_first = ctx->opt->gbr_only_first;
471 ctx->opt->gbr_only_first =
472 ctx->opt->gbr == ISL_GBR_ALWAYS2;
473 tab = isl_tab_compute_reduced_basis(tab);
474 ctx->opt->gbr_only_first = gbr_only_first;
475 if (!tab || !tab->basis)
476 goto error;
477 reduced = 1;
478 continue;
479 }
480 reduced = 0;
481 snap[level] = isl_tab_snap(tab);
482 } else
483 isl_int_add_ui(min->el[level], min->el[level], 1)isl_sioimath_add_ui((min->el[level]), *(min->el[level])
, 1)
;
484
485 if (isl_int_gt(min->el[level], max->el[level])(isl_sioimath_cmp(*(min->el[level]), *(max->el[level]))
> 0)
) {
486 level--;
487 init = 0;
488 if (level >= 0)
489 if (isl_tab_rollback(tab, snap[level]) < 0)
490 goto error;
491 continue;
492 }
493 isl_int_neg(tab->basis->row[1 + level][0], min->el[level])isl_sioimath_neg((tab->basis->row[1 + level][0]), *(min
->el[level]))
;
494 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
495 goto error;
496 isl_int_set_si(tab->basis->row[1 + level][0], 0)isl_sioimath_set_si((tab->basis->row[1 + level][0]), 0);
497 if (level + tab->n_unbounded < dim - 1) {
498 ++level;
499 init = 1;
500 continue;
501 }
502 break;
503 }
504
505 if (level >= 0) {
506 sample = isl_tab_get_sample_value(tab);
507 if (!sample)
508 goto error;
509 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])(isl_sioimath_cmp_si(*(sample->el[0]), 1) == 0)) {
510 sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
511 sample);
512 sample = isl_vec_ceil(sample);
513 sample = isl_mat_vec_inverse_product(
514 isl_mat_copy(tab->basis), sample);
515 }
516 } else
517 sample = isl_vec_alloc(ctx, 0);
518
519 ctx->opt->gbr = gbr;
520 isl_vec_free(min);
521 isl_vec_free(max);
522 free(snap);
523 return sample;
524error:
525 ctx->opt->gbr = gbr;
526 isl_vec_free(min);
527 isl_vec_free(max);
528 free(snap);
529 return NULL((void*)0);
530}
531
532static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_setisl_basic_map *bset);
533
534/* Internal data for factored_sample.
535 * "sample" collects the sample and may get reset to a zero-length vector
536 * signaling the absence of a sample vector.
537 * "pos" is the position of the contribution of the next factor.
538 */
539struct isl_factored_sample_data {
540 isl_vec *sample;
541 int pos;
542};
543
544/* isl_factorizer_every_factor_basic_set callback that extends
545 * the sample in data->sample with the contribution
546 * of the factor "bset".
547 * If "bset" turns out to be empty, then the product is empty too and
548 * no further factors need to be considered.
549 */
550static isl_bool factor_sample(__isl_keep isl_basic_setisl_basic_map *bset, void *user)
551{
552 struct isl_factored_sample_data *data = user;
553 isl_vec *sample;
554 isl_size n;
555
556 n = isl_basic_set_dim(bset, isl_dim_set);
557 if (n < 0)
558 return isl_bool_error;
559
560 sample = sample_bounded(isl_basic_set_copy(bset));
561 if (!sample)
562 return isl_bool_error;
563 if (sample->size == 0) {
564 isl_vec_free(data->sample);
565 data->sample = sample;
566 return isl_bool_false;
567 }
568 isl_seq_cpy(data->sample->el + data->pos, sample->el + 1, n);
569 isl_vec_free(sample);
570 data->pos += n;
571
572 return isl_bool_true;
573}
574
575/* Compute a sample point of the given basic set, based on the given,
576 * non-trivial factorization.
577 */
578static __isl_give isl_vec *factored_sample(__isl_take isl_basic_setisl_basic_map *bset,
579 __isl_take isl_factorizer *f)
580{
581 struct isl_factored_sample_data data = { NULL((void*)0) };
582 isl_ctx *ctx;
583 isl_size total;
584 isl_bool every;
585
586 ctx = isl_basic_set_get_ctx(bset);
587 total = isl_basic_set_dim(bset, isl_dim_all);
588 if (!ctx || total < 0)
589 goto error;
590
591 data.sample = isl_vec_alloc(ctx, 1 + total);
592 if (!data.sample)
593 goto error;
594 isl_int_set_si(data.sample->el[0], 1)isl_sioimath_set_si((data.sample->el[0]), 1);
595 data.pos = 1;
596
597 every = isl_factorizer_every_factor_basic_set(f, &factor_sample, &data);
598 if (every < 0) {
599 data.sample = isl_vec_free(data.sample);
600 } else if (every) {
601 isl_morph *morph;
602
603 morph = isl_morph_inverse(isl_morph_copy(f->morph));
604 data.sample = isl_morph_vec(morph, data.sample);
605 }
606
607 isl_basic_set_free(bset);
608 isl_factorizer_free(f);
609 return data.sample;
610error:
611 isl_basic_set_free(bset);
612 isl_factorizer_free(f);
613 isl_vec_free(data.sample);
614 return NULL((void*)0);
615}
616
617/* Given a basic set that is known to be bounded, find and return
618 * an integer point in the basic set, if there is any.
619 *
620 * After handling some trivial cases, we construct a tableau
621 * and then use isl_tab_sample to find a sample, passing it
622 * the identity matrix as initial basis.
623 */
624static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_setisl_basic_map *bset)
625{
626 isl_size dim;
627 struct isl_vec *sample;
628 struct isl_tab *tab = NULL((void*)0);
629 isl_factorizer *f;
630
631 if (!bset)
632 return NULL((void*)0);
633
634 if (isl_basic_set_plain_is_empty(bset))
635 return empty_sample(bset);
636
637 dim = isl_basic_set_dim(bset, isl_dim_all);
638 if (dim < 0)
639 bset = isl_basic_set_free(bset);
640 if (dim == 0)
641 return zero_sample(bset);
642 if (dim == 1)
643 return interval_sample(bset);
644 if (bset->n_eq > 0)
645 return sample_eq(bset, sample_bounded);
646
647 f = isl_basic_set_factorizer(bset);
648 if (!f)
649 goto error;
650 if (f->n_group != 0)
651 return factored_sample(bset, f);
652 isl_factorizer_free(f);
653
654 tab = isl_tab_from_basic_set(bset, 1);
655 if (tab && tab->empty) {
656 isl_tab_free(tab);
657 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY)(((bset)->flags) |= ((1 << 1)));
658 sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
659 isl_basic_set_free(bset);
660 return sample;
661 }
662
663 if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT)(!!(((bset)->flags) & ((1 << 2)))))
664 if (isl_tab_detect_implicit_equalities(tab) < 0)
665 goto error;
666
667 sample = isl_tab_sample(tab);
668 if (!sample)
669 goto error;
670
671 if (sample->size > 0) {
672 isl_vec_free(bset->sample);
673 bset->sample = isl_vec_copy(sample);
674 }
675
676 isl_basic_set_free(bset);
677 isl_tab_free(tab);
678 return sample;
679error:
680 isl_basic_set_free(bset);
681 isl_tab_free(tab);
682 return NULL((void*)0);
683}
684
685/* Given a basic set "bset" and a value "sample" for the first coordinates
686 * of bset, plug in these values and drop the corresponding coordinates.
687 *
688 * We do this by computing the preimage of the transformation
689 *
690 * [ 1 0 ]
691 * x = [ s 0 ] x'
692 * [ 0 I ]
693 *
694 * where [1 s] is the sample value and I is the identity matrix of the
695 * appropriate dimension.
696 */
697static __isl_give isl_basic_setisl_basic_map *plug_in(__isl_take isl_basic_setisl_basic_map *bset,
698 __isl_take isl_vec *sample)
699{
700 int i;
701 isl_size total;
702 struct isl_mat *T;
703
704 total = isl_basic_set_dim(bset, isl_dim_all);
705 if (total < 0 || !sample)
706 goto error;
707
708 T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
709 if (!T)
710 goto error;
711
712 for (i = 0; i < sample->size; ++i) {
713 isl_int_set(T->row[i][0], sample->el[i])isl_sioimath_set((T->row[i][0]), *(sample->el[i]));
714 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
715 }
716 for (i = 0; i < T->n_col - 1; ++i) {
717 isl_seq_clr(T->row[sample->size + i], T->n_col);
718 isl_int_set_si(T->row[sample->size + i][1 + i], 1)isl_sioimath_set_si((T->row[sample->size + i][1 + i]), 1
)
;
719 }
720 isl_vec_free(sample);
721
722 bset = isl_basic_set_preimage(bset, T);
723 return bset;
724error:
725 isl_basic_set_free(bset);
726 isl_vec_free(sample);
727 return NULL((void*)0);
728}
729
730/* Given a basic set "bset", return any (possibly non-integer) point
731 * in the basic set.
732 */
733static __isl_give isl_vec *rational_sample(__isl_take isl_basic_setisl_basic_map *bset)
734{
735 struct isl_tab *tab;
736 struct isl_vec *sample;
737
738 if (!bset)
739 return NULL((void*)0);
740
741 tab = isl_tab_from_basic_set(bset, 0);
742 sample = isl_tab_get_sample_value(tab);
743 isl_tab_free(tab);
744
745 isl_basic_set_free(bset);
746
747 return sample;
748}
749
750/* Given a linear cone "cone" and a rational point "vec",
751 * construct a polyhedron with shifted copies of the constraints in "cone",
752 * i.e., a polyhedron with "cone" as its recession cone, such that each
753 * point x in this polyhedron is such that the unit box positioned at x
754 * lies entirely inside the affine cone 'vec + cone'.
755 * Any rational point in this polyhedron may therefore be rounded up
756 * to yield an integer point that lies inside said affine cone.
757 *
758 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
759 * point "vec" by v/d.
760 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
761 * by <a_i, x> - b/d >= 0.
762 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
763 * We prefer this polyhedron over the actual affine cone because it doesn't
764 * require a scaling of the constraints.
765 * If each of the vertices of the unit cube positioned at x lies inside
766 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
767 * We therefore impose that x' = x + \sum e_i, for any selection of unit
768 * vectors lies inside the polyhedron, i.e.,
769 *
770 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
771 *
772 * The most stringent of these constraints is the one that selects
773 * all negative a_i, so the polyhedron we are looking for has constraints
774 *
775 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
776 *
777 * Note that if cone were known to have only non-negative rays
778 * (which can be accomplished by a unimodular transformation),
779 * then we would only have to check the points x' = x + e_i
780 * and we only have to add the smallest negative a_i (if any)
781 * instead of the sum of all negative a_i.
782 */
783static __isl_give isl_basic_setisl_basic_map *shift_cone(__isl_take isl_basic_setisl_basic_map *cone,
784 __isl_take isl_vec *vec)
785{
786 int i, j, k;
787 isl_size total;
788
789 struct isl_basic_setisl_basic_map *shift = NULL((void*)0);
790
791 total = isl_basic_set_dim(cone, isl_dim_all);
792 if (total < 0 || !vec)
793 goto error;
794
795 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 795); goto error; } while (0); } while (0)
;
796
797 shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
798 0, 0, cone->n_ineq);
799
800 for (i = 0; i < cone->n_ineq; ++i) {
801 k = isl_basic_set_alloc_inequality(shift);
802 if (k < 0)
803 goto error;
804 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
805 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
806 &shift->ineq[k][0]);
807 isl_int_cdiv_q(shift->ineq[k][0],isl_sioimath_cdiv_q((shift->ineq[k][0]), *(shift->ineq[
k][0]), *(vec->el[0]))
808 shift->ineq[k][0], vec->el[0])isl_sioimath_cdiv_q((shift->ineq[k][0]), *(shift->ineq[
k][0]), *(vec->el[0]))
;
809 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0])isl_sioimath_neg((shift->ineq[k][0]), *(shift->ineq[k][
0]))
;
810 for (j = 0; j < total; ++j) {
811 if (isl_int_is_nonneg(shift->ineq[k][1 + j])(isl_sioimath_sgn(*(shift->ineq[k][1 + j])) >= 0))
812 continue;
813 isl_int_add(shift->ineq[k][0],isl_sioimath_add((shift->ineq[k][0]), *(shift->ineq[k][
0]), *(shift->ineq[k][1 + j]))
814 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]))
;
815 }
816 }
817
818 isl_basic_set_free(cone);
819 isl_vec_free(vec);
820
821 return isl_basic_set_finalize(shift);
822error:
823 isl_basic_set_free(shift);
824 isl_basic_set_free(cone);
825 isl_vec_free(vec);
826 return NULL((void*)0);
827}
828
829/* Given a rational point vec in a (transformed) basic set,
830 * such that cone is the recession cone of the original basic set,
831 * "round up" the rational point to an integer point.
832 *
833 * We first check if the rational point just happens to be integer.
834 * If not, we transform the cone in the same way as the basic set,
835 * pick a point x in this cone shifted to the rational point such that
836 * the whole unit cube at x is also inside this affine cone.
837 * Then we simply round up the coordinates of x and return the
838 * resulting integer point.
839 */
840static __isl_give isl_vec *round_up_in_cone(__isl_take isl_vec *vec,
841 __isl_take isl_basic_setisl_basic_map *cone, __isl_take isl_mat *U)
842{
843 isl_size total;
844
845 if (!vec || !cone || !U)
846 goto error;
847
848 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"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 848); goto error; } while (0); } while (0)
;
849 if (isl_int_is_one(vec->el[0])(isl_sioimath_cmp_si(*(vec->el[0]), 1) == 0)) {
850 isl_mat_free(U);
851 isl_basic_set_free(cone);
852 return vec;
853 }
854
855 total = isl_basic_set_dim(cone, isl_dim_all);
856 if (total < 0)
857 goto error;
858 cone = isl_basic_set_preimage(cone, U);
859 cone = isl_basic_set_remove_dims(cone, isl_dim_set,
860 0, total - (vec->size - 1));
861
862 cone = shift_cone(cone, vec);
863
864 vec = rational_sample(cone);
865 vec = isl_vec_ceil(vec);
866 return vec;
867error:
868 isl_mat_free(U);
869 isl_vec_free(vec);
870 isl_basic_set_free(cone);
871 return NULL((void*)0);
872}
873
874/* Concatenate two integer vectors, i.e., two vectors with denominator
875 * (stored in element 0) equal to 1.
876 */
877static __isl_give isl_vec *vec_concat(__isl_take isl_vec *vec1,
878 __isl_take isl_vec *vec2)
879{
880 struct isl_vec *vec;
881
882 if (!vec1 || !vec2)
883 goto error;
884 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 884); goto error; } while (0); } while (0)
;
885 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", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 885); goto error; } while (0); } while (0)
;
886 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"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 886); goto error; } while (0); } while (0)
;
887 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"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 887); goto error; } while (0); } while (0)
;
888
889 vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
890 if (!vec)
891 goto error;
892
893 isl_seq_cpy(vec->el, vec1->el, vec1->size);
894 isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
895
896 isl_vec_free(vec1);
897 isl_vec_free(vec2);
898
899 return vec;
900error:
901 isl_vec_free(vec1);
902 isl_vec_free(vec2);
903 return NULL((void*)0);
904}
905
906/* Give a basic set "bset" with recession cone "cone", compute and
907 * return an integer point in bset, if any.
908 *
909 * If the recession cone is full-dimensional, then we know that
910 * bset contains an infinite number of integer points and it is
911 * fairly easy to pick one of them.
912 * If the recession cone is not full-dimensional, then we first
913 * transform bset such that the bounded directions appear as
914 * the first dimensions of the transformed basic set.
915 * We do this by using a unimodular transformation that transforms
916 * the equalities in the recession cone to equalities on the first
917 * dimensions.
918 *
919 * The transformed set is then projected onto its bounded dimensions.
920 * Note that to compute this projection, we can simply drop all constraints
921 * involving any of the unbounded dimensions since these constraints
922 * cannot be combined to produce a constraint on the bounded dimensions.
923 * To see this, assume that there is such a combination of constraints
924 * that produces a constraint on the bounded dimensions. This means
925 * that some combination of the unbounded dimensions has both an upper
926 * bound and a lower bound in terms of the bounded dimensions, but then
927 * this combination would be a bounded direction too and would have been
928 * transformed into a bounded dimensions.
929 *
930 * We then compute a sample value in the bounded dimensions.
931 * If no such value can be found, then the original set did not contain
932 * any integer points and we are done.
933 * Otherwise, we plug in the value we found in the bounded dimensions,
934 * project out these bounded dimensions and end up with a set with
935 * a full-dimensional recession cone.
936 * A sample point in this set is computed by "rounding up" any
937 * rational point in the set.
938 *
939 * The sample points in the bounded and unbounded dimensions are
940 * then combined into a single sample point and transformed back
941 * to the original space.
942 */
943__isl_give isl_vec *isl_basic_set_sample_with_cone(
944 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *cone)
945{
946 isl_size total;
947 unsigned cone_dim;
948 struct isl_mat *M, *U;
949 struct isl_vec *sample;
950 struct isl_vec *cone_sample;
951 struct isl_ctx *ctx;
952 struct isl_basic_setisl_basic_map *bounded;
953
954 total = isl_basic_set_dim(cone, isl_dim_all);
955 if (!bset || total < 0)
956 goto error;
957
958 ctx = isl_basic_set_get_ctx(bset);
959 cone_dim = total - cone->n_eq;
960
961 M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
962 M = isl_mat_left_hermite(M, 0, &U, NULL((void*)0));
963 if (!M)
964 goto error;
965 isl_mat_free(M);
966
967 U = isl_mat_lin_to_aff(U);
968 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
969
970 bounded = isl_basic_set_copy(bset);
971 bounded = isl_basic_set_drop_constraints_involving(bounded,
972 total - cone_dim, cone_dim);
973 bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
974 sample = sample_bounded(bounded);
975 if (!sample || sample->size == 0) {
976 isl_basic_set_free(bset);
977 isl_basic_set_free(cone);
978 isl_mat_free(U);
979 return sample;
980 }
981 bset = plug_in(bset, isl_vec_copy(sample));
982 cone_sample = rational_sample(bset);
983 cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
984 sample = vec_concat(sample, cone_sample);
985 sample = isl_mat_vec_product(U, sample);
986 return sample;
987error:
988 isl_basic_set_free(cone);
989 isl_basic_set_free(bset);
990 return NULL((void*)0);
991}
992
993static void vec_sum_of_neg(__isl_keep isl_vec *v, isl_int *s)
994{
995 int i;
996
997 isl_int_set_si(*s, 0)isl_sioimath_set_si((*s), 0);
998
999 for (i = 0; i < v->size; ++i)
1000 if (isl_int_is_neg(v->el[i])(isl_sioimath_sgn(*(v->el[i])) < 0))
1001 isl_int_add(*s, *s, v->el[i])isl_sioimath_add((*s), *(*s), *(v->el[i]));
1002}
1003
1004/* Given a tableau "tab", a tableau "tab_cone" that corresponds
1005 * to the recession cone and the inverse of a new basis U = inv(B),
1006 * with the unbounded directions in B last,
1007 * add constraints to "tab" that ensure any rational value
1008 * in the unbounded directions can be rounded up to an integer value.
1009 *
1010 * The new basis is given by x' = B x, i.e., x = U x'.
1011 * For any rational value of the last tab->n_unbounded coordinates
1012 * in the update tableau, the value that is obtained by rounding
1013 * up this value should be contained in the original tableau.
1014 * For any constraint "a x + c >= 0", we therefore need to add
1015 * a constraint "a x + c + s >= 0", with s the sum of all negative
1016 * entries in the last elements of "a U".
1017 *
1018 * Since we are not interested in the first entries of any of the "a U",
1019 * we first drop the columns of U that correpond to bounded directions.
1020 */
1021static int tab_shift_cone(struct isl_tab *tab,
1022 struct isl_tab *tab_cone, struct isl_mat *U)
1023{
1024 int i;
1025 isl_int v;
1026 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
1027
1028 if (tab && tab->n_unbounded == 0) {
1029 isl_mat_free(U);
1030 return 0;
1031 }
1032 isl_int_init(v)isl_sioimath_init((v));
1033 if (!tab || !tab_cone || !U)
1034 goto error;
1035 bset = isl_tab_peek_bset(tab_cone);
1036 U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1037 for (i = 0; i < bset->n_ineq; ++i) {
1038 int ok;
1039 struct isl_vec *row = NULL((void*)0);
1040 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1041 continue;
1042 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1043 if (!row)
1044 goto error;
1045 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1046 row = isl_vec_mat_product(row, isl_mat_copy(U));
1047 if (!row)
1048 goto error;
1049 vec_sum_of_neg(row, &v);
1050 isl_vec_free(row);
1051 if (isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0))
1052 continue;
1053 if (isl_tab_extend_cons(tab, 1) < 0)
1054 goto error;
1055 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v)isl_sioimath_add((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(v))
;
1056 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1057 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(v))
;
1058 if (!ok)
1059 goto error;
1060 }
1061
1062 isl_mat_free(U);
1063 isl_int_clear(v)isl_sioimath_clear((v));
1064 return 0;
1065error:
1066 isl_mat_free(U);
1067 isl_int_clear(v)isl_sioimath_clear((v));
1068 return -1;
1069}
1070
1071/* Compute and return an initial basis for the possibly
1072 * unbounded tableau "tab". "tab_cone" is a tableau
1073 * for the corresponding recession cone.
1074 * Additionally, add constraints to "tab" that ensure
1075 * that any rational value for the unbounded directions
1076 * can be rounded up to an integer value.
1077 *
1078 * If the tableau is bounded, i.e., if the recession cone
1079 * is zero-dimensional, then we just use inital_basis.
1080 * Otherwise, we construct a basis whose first directions
1081 * correspond to equalities, followed by bounded directions,
1082 * i.e., equalities in the recession cone.
1083 * The remaining directions are then unbounded.
1084 */
1085int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1086 struct isl_tab *tab_cone)
1087{
1088 struct isl_mat *eq;
1089 struct isl_mat *cone_eq;
1090 struct isl_mat *U, *Q;
1091
1092 if (!tab || !tab_cone)
1093 return -1;
1094
1095 if (tab_cone->n_col == tab_cone->n_dead) {
1096 tab->basis = initial_basis(tab);
1097 return tab->basis ? 0 : -1;
1098 }
1099
1100 eq = tab_equalities(tab);
1101 if (!eq)
1102 return -1;
1103 tab->n_zero = eq->n_row;
1104 cone_eq = tab_equalities(tab_cone);
1105 eq = isl_mat_concat(eq, cone_eq);
1106 if (!eq)
1107 return -1;
1108 tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1109 eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1110 if (!eq)
1111 return -1;
1112 isl_mat_free(eq);
1113 tab->basis = isl_mat_lin_to_aff(Q);
1114 if (tab_shift_cone(tab, tab_cone, U) < 0)
1115 return -1;
1116 if (!tab->basis)
1117 return -1;
1118 return 0;
1119}
1120
1121/* Compute and return a sample point in bset using generalized basis
1122 * reduction. We first check if the input set has a non-trivial
1123 * recession cone. If so, we perform some extra preprocessing in
1124 * sample_with_cone. Otherwise, we directly perform generalized basis
1125 * reduction.
1126 */
1127static __isl_give isl_vec *gbr_sample(__isl_take isl_basic_setisl_basic_map *bset)
1128{
1129 isl_size dim;
1130 struct isl_basic_setisl_basic_map *cone;
1131
1132 dim = isl_basic_set_dim(bset, isl_dim_all);
1133 if (dim < 0)
1134 goto error;
1135
1136 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1137 if (!cone)
1138 goto error;
1139
1140 if (cone->n_eq < dim)
1141 return isl_basic_set_sample_with_cone(bset, cone);
1142
1143 isl_basic_set_free(cone);
1144 return sample_bounded(bset);
1145error:
1146 isl_basic_set_free(bset);
1147 return NULL((void*)0);
1148}
1149
1150static __isl_give isl_vec *basic_set_sample(__isl_take isl_basic_setisl_basic_map *bset,
1151 int bounded)
1152{
1153 struct isl_ctx *ctx;
1154 isl_size dim;
1155 if (!bset)
1156 return NULL((void*)0);
1157
1158 ctx = bset->ctx;
1159 if (isl_basic_set_plain_is_empty(bset))
1160 return empty_sample(bset);
1161
1162 dim = isl_basic_set_dim(bset, isl_dim_set);
1163 if (dim < 0 ||
1164 isl_basic_set_check_no_params(bset) < 0 ||
1165 isl_basic_set_check_no_locals(bset) < 0)
1166 goto error;
1167
1168 if (bset->sample && bset->sample->size == 1 + dim) {
1169 int contains = isl_basic_set_contains(bset, bset->sample);
1170 if (contains < 0)
1171 goto error;
1172 if (contains) {
1173 struct isl_vec *sample = isl_vec_copy(bset->sample);
1174 isl_basic_set_free(bset);
1175 return sample;
1176 }
1177 }
1178 isl_vec_free(bset->sample);
1179 bset->sample = NULL((void*)0);
1180
1181 if (bset->n_eq > 0)
1182 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1183 : isl_basic_set_sample_vec);
1184 if (dim == 0)
1185 return zero_sample(bset);
1186 if (dim == 1)
1187 return interval_sample(bset);
1188
1189 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1190error:
1191 isl_basic_set_free(bset);
1192 return NULL((void*)0);
1193}
1194
1195__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_setisl_basic_map *bset)
1196{
1197 return basic_set_sample(bset, 0);
1198}
1199
1200/* Compute an integer sample in "bset", where the caller guarantees
1201 * that "bset" is bounded.
1202 */
1203__isl_give isl_vec *isl_basic_set_sample_bounded(__isl_take isl_basic_setisl_basic_map *bset)
1204{
1205 return basic_set_sample(bset, 1);
1206}
1207
1208__isl_give isl_basic_setisl_basic_map *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1209{
1210 int i;
1211 int k;
1212 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
1213 struct isl_ctx *ctx;
1214 isl_size dim;
1215
1216 if (!vec)
1217 return NULL((void*)0);
1218 ctx = vec->ctx;
1219 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"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_sample.c"
, 1219); goto error; } while (0); } while (0)
;
1220
1221 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1222 dim = isl_basic_set_dim(bset, isl_dim_set);
1223 if (dim < 0)
1224 goto error;
1225 for (i = dim - 1; i >= 0; --i) {
1226 k = isl_basic_set_alloc_equality(bset);
1227 if (k < 0)
1228 goto error;
1229 isl_seq_clr(bset->eq[k], 1 + dim);
1230 isl_int_neg(bset->eq[k][0], vec->el[1 + i])isl_sioimath_neg((bset->eq[k][0]), *(vec->el[1 + i]));
1231 isl_int_set(bset->eq[k][1 + i], vec->el[0])isl_sioimath_set((bset->eq[k][1 + i]), *(vec->el[0]));
1232 }
1233 bset->sample = vec;
1234
1235 return bset;
1236error:
1237 isl_basic_set_free(bset);
1238 isl_vec_free(vec);
1239 return NULL((void*)0);
1240}
1241
1242__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1243{
1244 struct isl_basic_setisl_basic_map *bset;
1245 struct isl_vec *sample_vec;
1246
1247 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1248 sample_vec = isl_basic_set_sample_vec(bset);
1249 if (!sample_vec)
1250 goto error;
1251 if (sample_vec->size == 0) {
1252 isl_vec_free(sample_vec);
1253 return isl_basic_map_set_to_empty(bmap);
1254 }
1255 isl_vec_free(bmap->sample);
1256 bmap->sample = isl_vec_copy(sample_vec);
1257 bset = isl_basic_set_from_vec(sample_vec);
1258 return isl_basic_map_overlying_set(bset, bmap);
1259error:
1260 isl_basic_map_free(bmap);
1261 return NULL((void*)0);
1262}
1263
1264__isl_give isl_basic_setisl_basic_map *isl_basic_set_sample(__isl_take isl_basic_setisl_basic_map *bset)
1265{
1266 return isl_basic_map_sample(bset);
1267}
1268
1269__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1270{
1271 int i;
1272 isl_basic_map *sample = NULL((void*)0);
1273
1274 if (!map)
1275 goto error;
1276
1277 for (i = 0; i < map->n; ++i) {
1278 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1279 if (!sample)
1280 goto error;
1281 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY)(!!(((sample)->flags) & ((1 << 1)))))
1282 break;
1283 isl_basic_map_free(sample);
1284 }
1285 if (i == map->n)
1286 sample = isl_basic_map_empty(isl_map_get_space(map));
1287 isl_map_free(map);
1288 return sample;
1289error:
1290 isl_map_free(map);
1291 return NULL((void*)0);
1292}
1293
1294__isl_give isl_basic_setisl_basic_map *isl_set_sample(__isl_take isl_setisl_map *set)
1295{
1296 return bset_from_bmap(isl_map_sample(set_to_map(set)));
1297}
1298
1299__isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_setisl_basic_map *bset)
1300{
1301 isl_vec *vec;
1302 isl_space *space;
1303
1304 space = isl_basic_set_get_space(bset);
1305 bset = isl_basic_set_underlying_set(bset);
1306 vec = isl_basic_set_sample_vec(bset);
1307
1308 return isl_point_alloc(space, vec);
1309}
1310
1311__isl_give isl_point *isl_set_sample_point(__isl_take isl_setisl_map *set)
1312{
1313 int i;
1314 isl_point *pnt;
1
'pnt' declared without an initial value
1315
1316 if (!set)
2
Assuming 'set' is non-null
3
Taking false branch
1317 return NULL((void*)0);
1318
1319 for (i = 0; i < set->n; ++i) {
4
Assuming 'i' is >= field 'n'
5
Loop condition is false. Execution continues on line 1327
1320 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1321 if (!pnt)
1322 goto error;
1323 if (!isl_point_is_void(pnt))
1324 break;
1325 isl_point_free(pnt);
1326 }
1327 if (i == set->n)
6
Assuming 'i' is not equal to field 'n'
7
Taking false branch
1328 pnt = isl_point_void(isl_set_get_space(set));
1329
1330 isl_set_free(set);
1331 return pnt;
8
Undefined or garbage value returned to caller
1332error:
1333 isl_set_free(set);
1334 return NULL((void*)0);
1335}