Bug Summary

File:polly/lib/External/isl/isl_affine_hull.c
Warning:line 513, column 6
Access to field 'sample' results in a dereference of a null pointer (loaded from variable 'bset')

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_affine_hull.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_affine_hull.c
1/*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012 Ecole Normale Superieure
5 *
6 * Use of this software is governed by the MIT license
7 *
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13 */
14
15#include <isl_ctx_private.h>
16#include <isl_map_private.h>
17#include <isl_seq.h>
18#include <isl/set.h>
19#include <isl/lp.h>
20#include <isl/map.h>
21#include "isl_equalities.h"
22#include "isl_sample.h"
23#include "isl_tab.h"
24#include <isl_mat_private.h>
25#include <isl_vec_private.h>
26
27#include <bset_to_bmap.c>
28#include <bset_from_bmap.c>
29#include <set_to_map.c>
30#include <set_from_map.c>
31
32__isl_give isl_basic_map *isl_basic_map_implicit_equalities(
33 __isl_take isl_basic_map *bmap)
34{
35 struct isl_tab *tab;
36
37 if (!bmap)
38 return bmap;
39
40 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
41 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
42 return bmap;
43 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT)(!!(((bmap)->flags) & ((1 << 2)))))
44 return bmap;
45 if (bmap->n_ineq <= 1)
46 return bmap;
47
48 tab = isl_tab_from_basic_map(bmap, 0);
49 if (isl_tab_detect_implicit_equalities(tab) < 0)
50 goto error;
51 bmap = isl_basic_map_update_from_tab(bmap, tab);
52 isl_tab_free(tab);
53 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
54 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT)(((bmap)->flags) |= ((1 << 2)));
55 return bmap;
56error:
57 isl_tab_free(tab);
58 isl_basic_map_free(bmap);
59 return NULL((void*)0);
60}
61
62__isl_give isl_basic_setisl_basic_map *isl_basic_set_implicit_equalities(
63 __isl_take isl_basic_setisl_basic_map *bset)
64{
65 return bset_from_bmap(
66 isl_basic_map_implicit_equalities(bset_to_bmap(bset)));
67}
68
69/* Make eq[row][col] of both bmaps equal so we can add the row
70 * add the column to the common matrix.
71 * Note that because of the echelon form, the columns of row row
72 * after column col are zero.
73 */
74static void set_common_multiple(
75 struct isl_basic_setisl_basic_map *bset1, struct isl_basic_setisl_basic_map *bset2,
76 unsigned row, unsigned col)
77{
78 isl_int m, c;
79
80 if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col])(isl_sioimath_cmp(*(bset1->eq[row][col]), *(bset2->eq[row
][col])) == 0)
)
81 return;
82
83 isl_int_init(c)isl_sioimath_init((c));
84 isl_int_init(m)isl_sioimath_init((m));
85 isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col])isl_sioimath_lcm((m), *(bset1->eq[row][col]), *(bset2->
eq[row][col]))
;
86 isl_int_divexact(c, m, bset1->eq[row][col])isl_sioimath_tdiv_q((c), *(m), *(bset1->eq[row][col]));
87 isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
88 isl_int_divexact(c, m, bset2->eq[row][col])isl_sioimath_tdiv_q((c), *(m), *(bset2->eq[row][col]));
89 isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
90 isl_int_clear(c)isl_sioimath_clear((c));
91 isl_int_clear(m)isl_sioimath_clear((m));
92}
93
94/* Delete a given equality, moving all the following equalities one up.
95 */
96static void delete_row(__isl_keep isl_basic_setisl_basic_map *bset, unsigned row)
97{
98 isl_int *t;
99 int r;
100
101 t = bset->eq[row];
102 bset->n_eq--;
103 for (r = row; r < bset->n_eq; ++r)
104 bset->eq[r] = bset->eq[r+1];
105 bset->eq[bset->n_eq] = t;
106}
107
108/* Make first row entries in column col of bset1 identical to
109 * those of bset2, using the fact that entry bset1->eq[row][col]=a
110 * is non-zero. Initially, these elements of bset1 are all zero.
111 * For each row i < row, we set
112 * A[i] = a * A[i] + B[i][col] * A[row]
113 * B[i] = a * B[i]
114 * so that
115 * A[i][col] = B[i][col] = a * old(B[i][col])
116 */
117static isl_stat construct_column(
118 __isl_keep isl_basic_setisl_basic_map *bset1, __isl_keep isl_basic_setisl_basic_map *bset2,
119 unsigned row, unsigned col)
120{
121 int r;
122 isl_int a;
123 isl_int b;
124 isl_size total;
125
126 total = isl_basic_set_dim(bset1, isl_dim_set);
127 if (total < 0)
128 return isl_stat_error;
129
130 isl_int_init(a)isl_sioimath_init((a));
131 isl_int_init(b)isl_sioimath_init((b));
132 for (r = 0; r < row; ++r) {
133 if (isl_int_is_zero(bset2->eq[r][col])(isl_sioimath_sgn(*(bset2->eq[r][col])) == 0))
134 continue;
135 isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col])isl_sioimath_gcd((b), *(bset2->eq[r][col]), *(bset1->eq
[row][col]))
;
136 isl_int_divexact(a, bset1->eq[row][col], b)isl_sioimath_tdiv_q((a), *(bset1->eq[row][col]), *(b));
137 isl_int_divexact(b, bset2->eq[r][col], b)isl_sioimath_tdiv_q((b), *(bset2->eq[r][col]), *(b));
138 isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
139 b, bset1->eq[row], 1 + total);
140 isl_seq_scale(bset2->eq[r], bset2->eq[r], a, 1 + total);
141 }
142 isl_int_clear(a)isl_sioimath_clear((a));
143 isl_int_clear(b)isl_sioimath_clear((b));
144 delete_row(bset1, row);
145
146 return isl_stat_ok;
147}
148
149/* Make first row entries in column col of bset1 identical to
150 * those of bset2, using only these entries of the two matrices.
151 * Let t be the last row with different entries.
152 * For each row i < t, we set
153 * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
154 * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
155 * so that
156 * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
157 */
158static isl_bool transform_column(
159 __isl_keep isl_basic_setisl_basic_map *bset1, __isl_keep isl_basic_setisl_basic_map *bset2,
160 unsigned row, unsigned col)
161{
162 int i, t;
163 isl_int a, b, g;
164 isl_size total;
165
166 for (t = row-1; t >= 0; --t)
167 if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col])(isl_sioimath_cmp(*(bset1->eq[t][col]), *(bset2->eq[t][
col])) != 0)
)
168 break;
169 if (t < 0)
170 return isl_bool_false;
171
172 total = isl_basic_set_dim(bset1, isl_dim_set);
173 if (total < 0)
174 return isl_bool_error;
175 isl_int_init(a)isl_sioimath_init((a));
176 isl_int_init(b)isl_sioimath_init((b));
177 isl_int_init(g)isl_sioimath_init((g));
178 isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col])isl_sioimath_sub((b), *(bset1->eq[t][col]), *(bset2->eq
[t][col]))
;
179 for (i = 0; i < t; ++i) {
180 isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col])isl_sioimath_sub((a), *(bset2->eq[i][col]), *(bset1->eq
[i][col]))
;
181 isl_int_gcd(g, a, b)isl_sioimath_gcd((g), *(a), *(b));
182 isl_int_divexact(a, a, g)isl_sioimath_tdiv_q((a), *(a), *(g));
183 isl_int_divexact(g, b, g)isl_sioimath_tdiv_q((g), *(b), *(g));
184 isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
185 1 + total);
186 isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
187 1 + total);
188 }
189 isl_int_clear(a)isl_sioimath_clear((a));
190 isl_int_clear(b)isl_sioimath_clear((b));
191 isl_int_clear(g)isl_sioimath_clear((g));
192 delete_row(bset1, t);
193 delete_row(bset2, t);
194 return isl_bool_true;
195}
196
197/* The implementation is based on Section 5.2 of Michael Karr,
198 * "Affine Relationships Among Variables of a Program",
199 * except that the echelon form we use starts from the last column
200 * and that we are dealing with integer coefficients.
201 */
202static __isl_give isl_basic_setisl_basic_map *affine_hull(
203 __isl_take isl_basic_setisl_basic_map *bset1, __isl_take isl_basic_setisl_basic_map *bset2)
204{
205 isl_size dim;
206 unsigned total;
207 int col;
208 int row;
209
210 dim = isl_basic_set_dim(bset1, isl_dim_set);
211 if (dim < 0 || !bset2)
212 goto error;
213
214 total = 1 + dim;
215
216 row = 0;
217 for (col = total-1; col >= 0; --col) {
218 int is_zero1 = row >= bset1->n_eq ||
219 isl_int_is_zero(bset1->eq[row][col])(isl_sioimath_sgn(*(bset1->eq[row][col])) == 0);
220 int is_zero2 = row >= bset2->n_eq ||
221 isl_int_is_zero(bset2->eq[row][col])(isl_sioimath_sgn(*(bset2->eq[row][col])) == 0);
222 if (!is_zero1 && !is_zero2) {
223 set_common_multiple(bset1, bset2, row, col);
224 ++row;
225 } else if (!is_zero1 && is_zero2) {
226 if (construct_column(bset1, bset2, row, col) < 0)
227 goto error;
228 } else if (is_zero1 && !is_zero2) {
229 if (construct_column(bset2, bset1, row, col) < 0)
230 goto error;
231 } else {
232 isl_bool transform;
233
234 transform = transform_column(bset1, bset2, row, col);
235 if (transform < 0)
236 goto error;
237 if (transform)
238 --row;
239 }
240 }
241 isl_assert(bset1->ctx, row == bset1->n_eq, goto error)do { if (row == bset1->n_eq) break; do { isl_handle_error(
bset1->ctx, isl_error_unknown, "Assertion \"" "row == bset1->n_eq"
"\" failed", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_affine_hull.c"
, 241); goto error; } while (0); } while (0)
;
242 isl_basic_set_free(bset2);
243 bset1 = isl_basic_set_normalize_constraints(bset1);
244 return bset1;
245error:
246 isl_basic_set_free(bset1);
247 isl_basic_set_free(bset2);
248 return NULL((void*)0);
249}
250
251/* Find an integer point in the set represented by "tab"
252 * that lies outside of the equality "eq" e(x) = 0.
253 * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
254 * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
255 * The point, if found, is returned.
256 * If no point can be found, a zero-length vector is returned.
257 *
258 * Before solving an ILP problem, we first check if simply
259 * adding the normal of the constraint to one of the known
260 * integer points in the basic set represented by "tab"
261 * yields another point inside the basic set.
262 *
263 * The caller of this function ensures that the tableau is bounded or
264 * that tab->basis and tab->n_unbounded have been set appropriately.
265 */
266static __isl_give isl_vec *outside_point(struct isl_tab *tab, isl_int *eq,
267 int up)
268{
269 struct isl_ctx *ctx;
270 struct isl_vec *sample = NULL((void*)0);
271 struct isl_tab_undo *snap;
272 unsigned dim;
273
274 if (!tab)
275 return NULL((void*)0);
276 ctx = tab->mat->ctx;
277
278 dim = tab->n_var;
279 sample = isl_vec_alloc(ctx, 1 + dim);
280 if (!sample)
281 return NULL((void*)0);
282 isl_int_set_si(sample->el[0], 1)isl_sioimath_set_si((sample->el[0]), 1);
283 isl_seq_combine(sample->el + 1,
284 ctx->one, tab->bmap->sample->el + 1,
285 up ? ctx->one : ctx->negone, eq + 1, dim);
286 if (isl_basic_map_contains(tab->bmap, sample))
287 return sample;
288 isl_vec_free(sample);
289 sample = NULL((void*)0);
290
291 snap = isl_tab_snap(tab);
292
293 if (!up)
294 isl_seq_neg(eq, eq, 1 + dim);
295 isl_int_sub_ui(eq[0], eq[0], 1)isl_sioimath_sub_ui((eq[0]), *(eq[0]), 1);
296
297 if (isl_tab_extend_cons(tab, 1) < 0)
298 goto error;
299 if (isl_tab_add_ineq(tab, eq) < 0)
300 goto error;
301
302 sample = isl_tab_sample(tab);
303
304 isl_int_add_ui(eq[0], eq[0], 1)isl_sioimath_add_ui((eq[0]), *(eq[0]), 1);
305 if (!up)
306 isl_seq_neg(eq, eq, 1 + dim);
307
308 if (sample && isl_tab_rollback(tab, snap) < 0)
309 goto error;
310
311 return sample;
312error:
313 isl_vec_free(sample);
314 return NULL((void*)0);
315}
316
317__isl_give isl_basic_setisl_basic_map *isl_basic_set_recession_cone(
318 __isl_take isl_basic_setisl_basic_map *bset)
319{
320 int i;
321 isl_bool empty;
322
323 empty = isl_basic_set_plain_is_empty(bset);
324 if (empty < 0)
325 return isl_basic_set_free(bset);
326 if (empty)
327 return bset;
328
329 bset = isl_basic_set_cow(bset);
330 if (isl_basic_set_check_no_locals(bset) < 0)
331 return isl_basic_set_free(bset);
332
333 for (i = 0; i < bset->n_eq; ++i)
334 isl_int_set_si(bset->eq[i][0], 0)isl_sioimath_set_si((bset->eq[i][0]), 0);
335
336 for (i = 0; i < bset->n_ineq; ++i)
337 isl_int_set_si(bset->ineq[i][0], 0)isl_sioimath_set_si((bset->ineq[i][0]), 0);
338
339 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) &= ~((1 << 2)));
340 return isl_basic_set_implicit_equalities(bset);
341}
342
343/* Move "sample" to a point that is one up (or down) from the original
344 * point in dimension "pos".
345 */
346static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up)
347{
348 if (up)
349 isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1)isl_sioimath_add_ui((sample->el[1 + pos]), *(sample->el
[1 + pos]), 1)
;
350 else
351 isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1)isl_sioimath_sub_ui((sample->el[1 + pos]), *(sample->el
[1 + pos]), 1)
;
352}
353
354/* Check if any points that are adjacent to "sample" also belong to "bset".
355 * If so, add them to "hull" and return the updated hull.
356 *
357 * Before checking whether and adjacent point belongs to "bset", we first
358 * check whether it already belongs to "hull" as this test is typically
359 * much cheaper.
360 */
361static __isl_give isl_basic_setisl_basic_map *add_adjacent_points(
362 __isl_take isl_basic_setisl_basic_map *hull, __isl_take isl_vec *sample,
363 __isl_keep isl_basic_setisl_basic_map *bset)
364{
365 int i, up;
366 isl_size dim;
367
368 dim = isl_basic_set_dim(hull, isl_dim_set);
369 if (!sample || dim < 0)
370 goto error;
371
372 for (i = 0; i < dim; ++i) {
373 for (up = 0; up <= 1; ++up) {
374 int contains;
375 isl_basic_setisl_basic_map *point;
376
377 adjacent_point(sample, i, up);
378 contains = isl_basic_set_contains(hull, sample);
379 if (contains < 0)
380 goto error;
381 if (contains) {
382 adjacent_point(sample, i, !up);
383 continue;
384 }
385 contains = isl_basic_set_contains(bset, sample);
386 if (contains < 0)
387 goto error;
388 if (contains) {
389 point = isl_basic_set_from_vec(
390 isl_vec_copy(sample));
391 hull = affine_hull(hull, point);
392 }
393 adjacent_point(sample, i, !up);
394 if (contains)
395 break;
396 }
397 }
398
399 isl_vec_free(sample);
400
401 return hull;
402error:
403 isl_vec_free(sample);
404 isl_basic_set_free(hull);
405 return NULL((void*)0);
406}
407
408/* Extend an initial (under-)approximation of the affine hull of basic
409 * set represented by the tableau "tab"
410 * by looking for points that do not satisfy one of the equalities
411 * in the current approximation and adding them to that approximation
412 * until no such points can be found any more.
413 *
414 * The caller of this function ensures that "tab" is bounded or
415 * that tab->basis and tab->n_unbounded have been set appropriately.
416 *
417 * "bset" may be either NULL or the basic set represented by "tab".
418 * If "bset" is not NULL, we check for any point we find if any
419 * of its adjacent points also belong to "bset".
420 */
421static __isl_give isl_basic_setisl_basic_map *extend_affine_hull(struct isl_tab *tab,
422 __isl_take isl_basic_setisl_basic_map *hull, __isl_keep isl_basic_setisl_basic_map *bset)
423{
424 int i, j;
425 unsigned dim;
426
427 if (!tab || !hull)
428 goto error;
429
430 dim = tab->n_var;
431
432 if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
433 goto error;
434
435 for (i = 0; i < dim; ++i) {
436 struct isl_vec *sample;
437 struct isl_basic_setisl_basic_map *point;
438 for (j = 0; j < hull->n_eq; ++j) {
439 sample = outside_point(tab, hull->eq[j], 1);
440 if (!sample)
441 goto error;
442 if (sample->size > 0)
443 break;
444 isl_vec_free(sample);
445 sample = outside_point(tab, hull->eq[j], 0);
446 if (!sample)
447 goto error;
448 if (sample->size > 0)
449 break;
450 isl_vec_free(sample);
451
452 if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
453 goto error;
454 }
455 if (j == hull->n_eq)
456 break;
457 if (tab->samples &&
458 isl_tab_add_sample(tab, isl_vec_copy(sample)) < 0)
459 hull = isl_basic_set_free(hull);
460 if (bset)
461 hull = add_adjacent_points(hull, isl_vec_copy(sample),
462 bset);
463 point = isl_basic_set_from_vec(sample);
464 hull = affine_hull(hull, point);
465 if (!hull)
466 return NULL((void*)0);
467 }
468
469 return hull;
470error:
471 isl_basic_set_free(hull);
472 return NULL((void*)0);
473}
474
475/* Construct an initial underapproximation of the hull of "bset"
476 * from "sample" and any of its adjacent points that also belong to "bset".
477 */
478static __isl_give isl_basic_setisl_basic_map *initialize_hull(__isl_keep isl_basic_setisl_basic_map *bset,
479 __isl_take isl_vec *sample)
480{
481 isl_basic_setisl_basic_map *hull;
482
483 hull = isl_basic_set_from_vec(isl_vec_copy(sample));
484 hull = add_adjacent_points(hull, sample, bset);
485
486 return hull;
487}
488
489/* Look for all equalities satisfied by the integer points in bset,
490 * which is assumed to be bounded.
491 *
492 * The equalities are obtained by successively looking for
493 * a point that is affinely independent of the points found so far.
494 * In particular, for each equality satisfied by the points so far,
495 * we check if there is any point on a hyperplane parallel to the
496 * corresponding hyperplane shifted by at least one (in either direction).
497 */
498static __isl_give isl_basic_setisl_basic_map *uset_affine_hull_bounded(
499 __isl_take isl_basic_setisl_basic_map *bset)
500{
501 struct isl_vec *sample = NULL((void*)0);
502 struct isl_basic_setisl_basic_map *hull;
503 struct isl_tab *tab = NULL((void*)0);
504 isl_size dim;
505
506 if (isl_basic_set_plain_is_empty(bset))
10
Assuming the condition is false
11
Taking false branch
507 return bset;
508
509 dim = isl_basic_set_dim(bset, isl_dim_set);
510 if (dim < 0)
12
Assuming 'dim' is >= 0
511 return isl_basic_set_free(bset);
512
513 if (bset->sample && bset->sample->size == 1 + dim) {
13
Access to field 'sample' results in a dereference of a null pointer (loaded from variable 'bset')
514 int contains = isl_basic_set_contains(bset, bset->sample);
515 if (contains < 0)
516 goto error;
517 if (contains) {
518 if (dim == 0)
519 return bset;
520 sample = isl_vec_copy(bset->sample);
521 } else {
522 isl_vec_free(bset->sample);
523 bset->sample = NULL((void*)0);
524 }
525 }
526
527 tab = isl_tab_from_basic_set(bset, 1);
528 if (!tab)
529 goto error;
530 if (tab->empty) {
531 isl_tab_free(tab);
532 isl_vec_free(sample);
533 return isl_basic_set_set_to_empty(bset);
534 }
535
536 if (!sample) {
537 struct isl_tab_undo *snap;
538 snap = isl_tab_snap(tab);
539 sample = isl_tab_sample(tab);
540 if (isl_tab_rollback(tab, snap) < 0)
541 goto error;
542 isl_vec_free(tab->bmap->sample);
543 tab->bmap->sample = isl_vec_copy(sample);
544 }
545
546 if (!sample)
547 goto error;
548 if (sample->size == 0) {
549 isl_tab_free(tab);
550 isl_vec_free(sample);
551 return isl_basic_set_set_to_empty(bset);
552 }
553
554 hull = initialize_hull(bset, sample);
555
556 hull = extend_affine_hull(tab, hull, bset);
557 isl_basic_set_free(bset);
558 isl_tab_free(tab);
559
560 return hull;
561error:
562 isl_vec_free(sample);
563 isl_tab_free(tab);
564 isl_basic_set_free(bset);
565 return NULL((void*)0);
566}
567
568/* Given an unbounded tableau and an integer point satisfying the tableau,
569 * construct an initial affine hull containing the recession cone
570 * shifted to the given point.
571 *
572 * The unbounded directions are taken from the last rows of the basis,
573 * which is assumed to have been initialized appropriately.
574 */
575static __isl_give isl_basic_setisl_basic_map *initial_hull(struct isl_tab *tab,
576 __isl_take isl_vec *vec)
577{
578 int i;
579 int k;
580 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
581 struct isl_ctx *ctx;
582 isl_size dim;
583
584 if (!vec || !tab)
585 return NULL((void*)0);
586 ctx = vec->ctx;
587 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_affine_hull.c"
, 587); goto error; } while (0); } while (0)
;
588
589 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
590 dim = isl_basic_set_dim(bset, isl_dim_set);
591 if (dim < 0)
592 goto error;
593 dim -= tab->n_unbounded;
594 for (i = 0; i < dim; ++i) {
595 k = isl_basic_set_alloc_equality(bset);
596 if (k < 0)
597 goto error;
598 isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
599 vec->size - 1);
600 isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
601 vec->size - 1, &bset->eq[k][0]);
602 isl_int_neg(bset->eq[k][0], bset->eq[k][0])isl_sioimath_neg((bset->eq[k][0]), *(bset->eq[k][0]));
603 }
604 bset->sample = vec;
605 bset = isl_basic_set_gauss(bset, NULL((void*)0));
606
607 return bset;
608error:
609 isl_basic_set_free(bset);
610 isl_vec_free(vec);
611 return NULL((void*)0);
612}
613
614/* Given a tableau of a set and a tableau of the corresponding
615 * recession cone, detect and add all equalities to the tableau.
616 * If the tableau is bounded, then we can simply keep the
617 * tableau in its state after the return from extend_affine_hull.
618 * However, if the tableau is unbounded, then
619 * isl_tab_set_initial_basis_with_cone will add some additional
620 * constraints to the tableau that have to be removed again.
621 * In this case, we therefore rollback to the state before
622 * any constraints were added and then add the equalities back in.
623 */
624struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
625 struct isl_tab *tab_cone)
626{
627 int j;
628 struct isl_vec *sample;
629 struct isl_basic_setisl_basic_map *hull = NULL((void*)0);
630 struct isl_tab_undo *snap;
631
632 if (!tab || !tab_cone)
633 goto error;
634
635 snap = isl_tab_snap(tab);
636
637 isl_mat_free(tab->basis);
638 tab->basis = NULL((void*)0);
639
640 isl_assert(tab->mat->ctx, tab->bmap, goto error)do { if (tab->bmap) break; do { isl_handle_error(tab->mat
->ctx, isl_error_unknown, "Assertion \"" "tab->bmap" "\" failed"
, "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_affine_hull.c"
, 640); goto error; } while (0); } while (0)
;
641 isl_assert(tab->mat->ctx, tab->samples, goto error)do { if (tab->samples) break; do { isl_handle_error(tab->
mat->ctx, isl_error_unknown, "Assertion \"" "tab->samples"
"\" failed", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_affine_hull.c"
, 641); goto error; } while (0); } while (0)
;
642 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error)do { if (tab->samples->n_col == 1 + tab->n_var) break
; do { isl_handle_error(tab->mat->ctx, isl_error_unknown
, "Assertion \"" "tab->samples->n_col == 1 + tab->n_var"
"\" failed", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_affine_hull.c"
, 642); goto error; } while (0); } while (0)
;
643 isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error)do { if (tab->n_sample > tab->n_outside) break; do {
isl_handle_error(tab->mat->ctx, isl_error_unknown, "Assertion \""
"tab->n_sample > tab->n_outside" "\" failed", "/build/llvm-toolchain-snapshot-14~++20210926122410+d23fd8ae8906/polly/lib/External/isl/isl_affine_hull.c"
, 643); goto error; } while (0); } while (0)
;
644
645 if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
646 goto error;
647
648 sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
649 if (!sample)
650 goto error;
651
652 isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
653
654 isl_vec_free(tab->bmap->sample);
655 tab->bmap->sample = isl_vec_copy(sample);
656
657 if (tab->n_unbounded == 0)
658 hull = isl_basic_set_from_vec(isl_vec_copy(sample));
659 else
660 hull = initial_hull(tab, isl_vec_copy(sample));
661
662 for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
663 isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
664 hull = affine_hull(hull,
665 isl_basic_set_from_vec(isl_vec_copy(sample)));
666 }
667
668 isl_vec_free(sample);
669
670 hull = extend_affine_hull(tab, hull, NULL((void*)0));
671 if (!hull)
672 goto error;
673
674 if (tab->n_unbounded == 0) {
675 isl_basic_set_free(hull);
676 return tab;
677 }
678
679 if (isl_tab_rollback(tab, snap) < 0)
680 goto error;
681
682 if (hull->n_eq > tab->n_zero) {
683 for (j = 0; j < hull->n_eq; ++j) {
684 isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
685 if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
686 goto error;
687 }
688 }
689
690 isl_basic_set_free(hull);
691
692 return tab;
693error:
694 isl_basic_set_free(hull);
695 isl_tab_free(tab);
696 return NULL((void*)0);
697}
698
699/* Compute the affine hull of "bset", where "cone" is the recession cone
700 * of "bset".
701 *
702 * We first compute a unimodular transformation that puts the unbounded
703 * directions in the last dimensions. In particular, we take a transformation
704 * that maps all equalities to equalities (in HNF) on the first dimensions.
705 * Let x be the original dimensions and y the transformed, with y_1 bounded
706 * and y_2 unbounded.
707 *
708 * [ y_1 ] [ y_1 ] [ Q_1 ]
709 * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
710 *
711 * Let's call the input basic set S. We compute S' = preimage(S, U)
712 * and drop the final dimensions including any constraints involving them.
713 * This results in set S''.
714 * Then we compute the affine hull A'' of S''.
715 * Let F y_1 >= g be the constraint system of A''. In the transformed
716 * space the y_2 are unbounded, so we can add them back without any constraints,
717 * resulting in
718 *
719 * [ y_1 ]
720 * [ F 0 ] [ y_2 ] >= g
721 * or
722 * [ Q_1 ]
723 * [ F 0 ] [ Q_2 ] x >= g
724 * or
725 * F Q_1 x >= g
726 *
727 * The affine hull in the original space is then obtained as
728 * A = preimage(A'', Q_1).
729 */
730static __isl_give isl_basic_setisl_basic_map *affine_hull_with_cone(
731 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *cone)
732{
733 isl_size total;
734 unsigned cone_dim;
735 struct isl_basic_setisl_basic_map *hull;
736 struct isl_mat *M, *U, *Q;
737
738 total = isl_basic_set_dim(cone, isl_dim_all);
739 if (!bset || total < 0)
1
Assuming 'bset' is non-null
2
Assuming 'total' is >= 0
3
Taking false branch
740 goto error;
741
742 cone_dim = total - cone->n_eq;
743
744 M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
745 M = isl_mat_left_hermite(M, 0, &U, &Q);
746 if (!M)
4
Assuming 'M' is non-null
5
Taking false branch
747 goto error;
748 isl_mat_free(M);
749
750 U = isl_mat_lin_to_aff(U);
751 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
752
753 bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
754 cone_dim);
755 bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
6
Value assigned to 'bset'
756
757 Q = isl_mat_lin_to_aff(Q);
758 Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
759
760 if (bset && bset->sample && bset->sample->size == 1 + total)
7
Assuming 'bset' is null
761 bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
762
763 hull = uset_affine_hull_bounded(bset);
8
Passing null pointer value via 1st parameter 'bset'
9
Calling 'uset_affine_hull_bounded'
764
765 if (!hull) {
766 isl_mat_free(Q);
767 isl_mat_free(U);
768 } else {
769 struct isl_vec *sample = isl_vec_copy(hull->sample);
770 U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
771 if (sample && sample->size > 0)
772 sample = isl_mat_vec_product(U, sample);
773 else
774 isl_mat_free(U);
775 hull = isl_basic_set_preimage(hull, Q);
776 if (hull) {
777 isl_vec_free(hull->sample);
778 hull->sample = sample;
779 } else
780 isl_vec_free(sample);
781 }
782
783 isl_basic_set_free(cone);
784
785 return hull;
786error:
787 isl_basic_set_free(bset);
788 isl_basic_set_free(cone);
789 return NULL((void*)0);
790}
791
792/* Look for all equalities satisfied by the integer points in bset,
793 * which is assumed not to have any explicit equalities.
794 *
795 * The equalities are obtained by successively looking for
796 * a point that is affinely independent of the points found so far.
797 * In particular, for each equality satisfied by the points so far,
798 * we check if there is any point on a hyperplane parallel to the
799 * corresponding hyperplane shifted by at least one (in either direction).
800 *
801 * Before looking for any outside points, we first compute the recession
802 * cone. The directions of this recession cone will always be part
803 * of the affine hull, so there is no need for looking for any points
804 * in these directions.
805 * In particular, if the recession cone is full-dimensional, then
806 * the affine hull is simply the whole universe.
807 */
808static __isl_give isl_basic_setisl_basic_map *uset_affine_hull(
809 __isl_take isl_basic_setisl_basic_map *bset)
810{
811 struct isl_basic_setisl_basic_map *cone;
812 isl_size total;
813
814 if (isl_basic_set_plain_is_empty(bset))
815 return bset;
816
817 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
818 if (!cone)
819 goto error;
820 if (cone->n_eq == 0) {
821 isl_space *space;
822 space = isl_basic_set_get_space(bset);
823 isl_basic_set_free(cone);
824 isl_basic_set_free(bset);
825 return isl_basic_set_universe(space);
826 }
827
828 total = isl_basic_set_dim(cone, isl_dim_all);
829 if (total < 0)
830 bset = isl_basic_set_free(bset);
831 if (cone->n_eq < total)
832 return affine_hull_with_cone(bset, cone);
833
834 isl_basic_set_free(cone);
835 return uset_affine_hull_bounded(bset);
836error:
837 isl_basic_set_free(bset);
838 return NULL((void*)0);
839}
840
841/* Look for all equalities satisfied by the integer points in bmap
842 * that are independent of the equalities already explicitly available
843 * in bmap.
844 *
845 * We first remove all equalities already explicitly available,
846 * then look for additional equalities in the reduced space
847 * and then transform the result to the original space.
848 * The original equalities are _not_ added to this set. This is
849 * the responsibility of the calling function.
850 * The resulting basic set has all meaning about the dimensions removed.
851 * In particular, dimensions that correspond to existential variables
852 * in bmap and that are found to be fixed are not removed.
853 */
854static __isl_give isl_basic_setisl_basic_map *equalities_in_underlying_set(
855 __isl_take isl_basic_map *bmap)
856{
857 struct isl_mat *T1 = NULL((void*)0);
858 struct isl_mat *T2 = NULL((void*)0);
859 struct isl_basic_setisl_basic_map *bset = NULL((void*)0);
860 struct isl_basic_setisl_basic_map *hull = NULL((void*)0);
861
862 bset = isl_basic_map_underlying_set(bmap);
863 if (!bset)
864 return NULL((void*)0);
865 if (bset->n_eq)
866 bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
867 if (!bset)
868 goto error;
869
870 hull = uset_affine_hull(bset);
871 if (!T2)
872 return hull;
873
874 if (!hull) {
875 isl_mat_free(T1);
876 isl_mat_free(T2);
877 } else {
878 struct isl_vec *sample = isl_vec_copy(hull->sample);
879 if (sample && sample->size > 0)
880 sample = isl_mat_vec_product(T1, sample);
881 else
882 isl_mat_free(T1);
883 hull = isl_basic_set_preimage(hull, T2);
884 if (hull) {
885 isl_vec_free(hull->sample);
886 hull->sample = sample;
887 } else
888 isl_vec_free(sample);
889 }
890
891 return hull;
892error:
893 isl_mat_free(T1);
894 isl_mat_free(T2);
895 isl_basic_set_free(bset);
896 isl_basic_set_free(hull);
897 return NULL((void*)0);
898}
899
900/* Detect and make explicit all equalities satisfied by the (integer)
901 * points in bmap.
902 */
903__isl_give isl_basic_map *isl_basic_map_detect_equalities(
904 __isl_take isl_basic_map *bmap)
905{
906 int i, j;
907 isl_size total;
908 struct isl_basic_setisl_basic_map *hull = NULL((void*)0);
909
910 if (!bmap)
911 return NULL((void*)0);
912 if (bmap->n_ineq == 0)
913 return bmap;
914 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
915 return bmap;
916 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES)(!!(((bmap)->flags) & ((1 << 7)))))
917 return bmap;
918 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4)))))
919 return isl_basic_map_implicit_equalities(bmap);
920
921 hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
922 if (!hull)
923 goto error;
924 if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)(!!(((hull)->flags) & ((1 << 1))))) {
925 isl_basic_set_free(hull);
926 return isl_basic_map_set_to_empty(bmap);
927 }
928 bmap = isl_basic_map_extend(bmap, 0, hull->n_eq, 0);
929 total = isl_basic_set_dim(hull, isl_dim_all);
930 if (total < 0)
931 goto error;
932 for (i = 0; i < hull->n_eq; ++i) {
933 j = isl_basic_map_alloc_equality(bmap);
934 if (j < 0)
935 goto error;
936 isl_seq_cpy(bmap->eq[j], hull->eq[i], 1 + total);
937 }
938 isl_vec_free(bmap->sample);
939 bmap->sample = isl_vec_copy(hull->sample);
940 isl_basic_set_free(hull);
941 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES)(((bmap)->flags) |= ((1 << 2) | (1 << 7)));
942 bmap = isl_basic_map_simplify(bmap);
943 return isl_basic_map_finalize(bmap);
944error:
945 isl_basic_set_free(hull);
946 isl_basic_map_free(bmap);
947 return NULL((void*)0);
948}
949
950__isl_give isl_basic_setisl_basic_map *isl_basic_set_detect_equalities(
951 __isl_take isl_basic_setisl_basic_map *bset)
952{
953 return bset_from_bmap(
954 isl_basic_map_detect_equalities(bset_to_bmap(bset)));
955}
956
957__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
958{
959 return isl_map_inline_foreach_basic_map(map,
960 &isl_basic_map_detect_equalities);
961}
962
963__isl_give isl_setisl_map *isl_set_detect_equalities(__isl_take isl_setisl_map *set)
964{
965 return set_from_map(isl_map_detect_equalities(set_to_map(set)));
966}
967
968/* Return the superset of "bmap" described by the equalities
969 * satisfied by "bmap" that are already known.
970 */
971__isl_give isl_basic_map *isl_basic_map_plain_affine_hull(
972 __isl_take isl_basic_map *bmap)
973{
974 bmap = isl_basic_map_cow(bmap);
975 if (bmap)
976 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
977 bmap = isl_basic_map_finalize(bmap);
978 return bmap;
979}
980
981/* Return the superset of "bset" described by the equalities
982 * satisfied by "bset" that are already known.
983 */
984__isl_give isl_basic_setisl_basic_map *isl_basic_set_plain_affine_hull(
985 __isl_take isl_basic_setisl_basic_map *bset)
986{
987 return isl_basic_map_plain_affine_hull(bset);
988}
989
990/* After computing the rational affine hull (by detecting the implicit
991 * equalities), we compute the additional equalities satisfied by
992 * the integer points (if any) and add the original equalities back in.
993 */
994__isl_give isl_basic_map *isl_basic_map_affine_hull(
995 __isl_take isl_basic_map *bmap)
996{
997 bmap = isl_basic_map_detect_equalities(bmap);
998 bmap = isl_basic_map_plain_affine_hull(bmap);
999 return bmap;
1000}
1001
1002__isl_give isl_basic_setisl_basic_map *isl_basic_set_affine_hull(
1003 __isl_take isl_basic_setisl_basic_map *bset)
1004{
1005 return bset_from_bmap(isl_basic_map_affine_hull(bset_to_bmap(bset)));
1006}
1007
1008/* Given a rational affine matrix "M", add stride constraints to "bmap"
1009 * that ensure that
1010 *
1011 * M(x)
1012 *
1013 * is an integer vector. The variables x include all the variables
1014 * of "bmap" except the unknown divs.
1015 *
1016 * If d is the common denominator of M, then we need to impose that
1017 *
1018 * d M(x) = 0 mod d
1019 *
1020 * or
1021 *
1022 * exists alpha : d M(x) = d alpha
1023 *
1024 * This function is similar to add_strides in isl_morph.c
1025 */
1026static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap,
1027 __isl_keep isl_mat *M, int n_known)
1028{
1029 int i, div, k;
1030 isl_int gcd;
1031
1032 if (isl_int_is_one(M->row[0][0])(isl_sioimath_cmp_si(*(M->row[0][0]), 1) == 0))
1033 return bmap;
1034
1035 bmap = isl_basic_map_extend(bmap, M->n_row - 1, M->n_row - 1, 0);
1036
1037 isl_int_init(gcd)isl_sioimath_init((gcd));
1038 for (i = 1; i < M->n_row; ++i) {
1039 isl_seq_gcd(M->row[i], M->n_col, &gcd);
1040 if (isl_int_is_divisible_by(gcd, M->row[0][0])isl_sioimath_is_divisible_by(*(gcd), *(M->row[0][0])))
1041 continue;
1042 div = isl_basic_map_alloc_div(bmap);
1043 if (div < 0)
1044 goto error;
1045 isl_int_set_si(bmap->div[div][0], 0)isl_sioimath_set_si((bmap->div[div][0]), 0);
1046 k = isl_basic_map_alloc_equality(bmap);
1047 if (k < 0)
1048 goto error;
1049 isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col);
1050 isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known);
1051 isl_int_set(bmap->eq[k][M->n_col - n_known + div],isl_sioimath_set((bmap->eq[k][M->n_col - n_known + div]
), *(M->row[0][0]))
1052 M->row[0][0])isl_sioimath_set((bmap->eq[k][M->n_col - n_known + div]
), *(M->row[0][0]))
;
1053 }
1054 isl_int_clear(gcd)isl_sioimath_clear((gcd));
1055
1056 return bmap;
1057error:
1058 isl_int_clear(gcd)isl_sioimath_clear((gcd));
1059 isl_basic_map_free(bmap);
1060 return NULL((void*)0);
1061}
1062
1063/* If there are any equalities that involve (multiple) unknown divs,
1064 * then extract the stride information encoded by those equalities
1065 * and make it explicitly available in "bmap".
1066 *
1067 * We first sort the divs so that the unknown divs appear last and
1068 * then we count how many equalities involve these divs.
1069 *
1070 * Let these equalities be of the form
1071 *
1072 * A(x) + B y = 0
1073 *
1074 * where y represents the unknown divs and x the remaining variables.
1075 * Let [H 0] be the Hermite Normal Form of B, i.e.,
1076 *
1077 * B = [H 0] Q
1078 *
1079 * Then x is a solution of the equalities iff
1080 *
1081 * H^-1 A(x) (= - [I 0] Q y)
1082 *
1083 * is an integer vector. Let d be the common denominator of H^-1.
1084 * We impose
1085 *
1086 * d H^-1 A(x) = d alpha
1087 *
1088 * in add_strides, with alpha fresh existentially quantified variables.
1089 */
1090static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit(
1091 __isl_take isl_basic_map *bmap)
1092{
1093 isl_bool known;
1094 int n_known;
1095 int n, n_col;
1096 isl_size v_div;
1097 isl_ctx *ctx;
1098 isl_mat *A, *B, *M;
1099
1100 known = isl_basic_map_divs_known(bmap);
1101 if (known < 0)
1102 return isl_basic_map_free(bmap);
1103 if (known)
1104 return bmap;
1105 bmap = isl_basic_map_sort_divs(bmap);
1106 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
1107 if (!bmap)
1108 return NULL((void*)0);
1109
1110 for (n_known = 0; n_known < bmap->n_div; ++n_known)
1111 if (isl_int_is_zero(bmap->div[n_known][0])(isl_sioimath_sgn(*(bmap->div[n_known][0])) == 0))
1112 break;
1113 v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
1114 if (v_div < 0)
1115 return isl_basic_map_free(bmap);
1116 for (n = 0; n < bmap->n_eq; ++n)
1117 if (isl_seq_first_non_zero(bmap->eq[n] + 1 + v_div + n_known,
1118 bmap->n_div - n_known) == -1)
1119 break;
1120 if (n == 0)
1121 return bmap;
1122 ctx = isl_basic_map_get_ctx(bmap);
1123 B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + v_div + n_known);
1124 n_col = bmap->n_div - n_known;
1125 A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + v_div + n_known, n_col);
1126 A = isl_mat_left_hermite(A, 0, NULL((void*)0), NULL((void*)0));
1127 A = isl_mat_drop_cols(A, n, n_col - n);
1128 A = isl_mat_lin_to_aff(A);
1129 A = isl_mat_right_inverse(A);
1130 B = isl_mat_insert_zero_rows(B, 0, 1);
1131 B = isl_mat_set_element_si(B, 0, 0, 1);
1132 M = isl_mat_product(A, B);
1133 if (!M)
1134 return isl_basic_map_free(bmap);
1135 bmap = add_strides(bmap, M, n_known);
1136 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
1137 isl_mat_free(M);
1138
1139 return bmap;
1140}
1141
1142/* Compute the affine hull of each basic map in "map" separately
1143 * and make all stride information explicit so that we can remove
1144 * all unknown divs without losing this information.
1145 * The result is also guaranteed to be gaussed.
1146 *
1147 * In simple cases where a div is determined by an equality,
1148 * calling isl_basic_map_gauss is enough to make the stride information
1149 * explicit, as it will derive an explicit representation for the div
1150 * from the equality. If, however, the stride information
1151 * is encoded through multiple unknown divs then we need to make
1152 * some extra effort in isl_basic_map_make_strides_explicit.
1153 */
1154static __isl_give isl_map *isl_map_local_affine_hull(__isl_take isl_map *map)
1155{
1156 int i;
1157
1158 map = isl_map_cow(map);
1159 if (!map)
1160 return NULL((void*)0);
1161
1162 for (i = 0; i < map->n; ++i) {
1163 map->p[i] = isl_basic_map_affine_hull(map->p[i]);
1164 map->p[i] = isl_basic_map_gauss(map->p[i], NULL((void*)0));
1165 map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]);
1166 if (!map->p[i])
1167 return isl_map_free(map);
1168 }
1169
1170 return map;
1171}
1172
1173static __isl_give isl_setisl_map *isl_set_local_affine_hull(__isl_take isl_setisl_map *set)
1174{
1175 return isl_map_local_affine_hull(set);
1176}
1177
1178/* Return an empty basic map living in the same space as "map".
1179 */
1180static __isl_give isl_basic_map *replace_map_by_empty_basic_map(
1181 __isl_take isl_map *map)
1182{
1183 isl_space *space;
1184
1185 space = isl_map_get_space(map);
1186 isl_map_free(map);
1187 return isl_basic_map_empty(space);
1188}
1189
1190/* Compute the affine hull of "map".
1191 *
1192 * We first compute the affine hull of each basic map separately.
1193 * Then we align the divs and recompute the affine hulls of the basic
1194 * maps since some of them may now have extra divs.
1195 * In order to avoid performing parametric integer programming to
1196 * compute explicit expressions for the divs, possible leading to
1197 * an explosion in the number of basic maps, we first drop all unknown
1198 * divs before aligning the divs. Note that isl_map_local_affine_hull tries
1199 * to make sure that all stride information is explicitly available
1200 * in terms of known divs. This involves calling isl_basic_set_gauss,
1201 * which is also needed because affine_hull assumes its input has been gaussed,
1202 * while isl_map_affine_hull may be called on input that has not been gaussed,
1203 * in particular from initial_facet_constraint.
1204 * Similarly, align_divs may reorder some divs so that we need to
1205 * gauss the result again.
1206 * Finally, we combine the individual affine hulls into a single
1207 * affine hull.
1208 */
1209__isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map)
1210{
1211 struct isl_basic_map *model = NULL((void*)0);
1212 struct isl_basic_map *hull = NULL((void*)0);
1213 struct isl_setisl_map *set;
1214 isl_basic_setisl_basic_map *bset;
1215
1216 map = isl_map_detect_equalities(map);
1217 map = isl_map_local_affine_hull(map);
1218 map = isl_map_remove_empty_parts(map);
1219 map = isl_map_remove_unknown_divs(map);
1220 map = isl_map_align_divs_internal(map);
1221
1222 if (!map)
1223 return NULL((void*)0);
1224
1225 if (map->n == 0)
1226 return replace_map_by_empty_basic_map(map);
1227
1228 model = isl_basic_map_copy(map->p[0]);
1229 set = isl_map_underlying_set(map);
1230 set = isl_set_cow(set);
1231 set = isl_set_local_affine_hull(set);
1232 if (!set)
1233 goto error;
1234
1235 while (set->n > 1)
1236 set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
1237
1238 bset = isl_basic_set_copy(set->p[0]);
1239 hull = isl_basic_map_overlying_set(bset, model);
1240 isl_set_free(set);
1241 hull = isl_basic_map_simplify(hull);
1242 return isl_basic_map_finalize(hull);
1243error:
1244 isl_basic_map_free(model);
1245 isl_set_free(set);
1246 return NULL((void*)0);
1247}
1248
1249__isl_give isl_basic_setisl_basic_map *isl_set_affine_hull(__isl_take isl_setisl_map *set)
1250{
1251 return bset_from_bmap(isl_map_affine_hull(set_to_map(set)));
1252}