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1 office 1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10  
11 #include <isl_map_private.h>
12 #include <isl_morph.h>
13 #include <isl/seq.h>
14 #include <isl_mat_private.h>
15 #include <isl_space_private.h>
16 #include <isl_equalities.h>
17  
18 __isl_give isl_morph *isl_morph_alloc(
19 __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
20 __isl_take isl_mat *map, __isl_take isl_mat *inv)
21 {
22 isl_morph *morph;
23  
24 if (!dom || !ran || !map || !inv)
25 goto error;
26  
27 morph = isl_alloc_type(dom->ctx, struct isl_morph);
28 if (!morph)
29 goto error;
30  
31 morph->ref = 1;
32 morph->dom = dom;
33 morph->ran = ran;
34 morph->map = map;
35 morph->inv = inv;
36  
37 return morph;
38 error:
39 isl_basic_set_free(dom);
40 isl_basic_set_free(ran);
41 isl_mat_free(map);
42 isl_mat_free(inv);
43 return NULL;
44 }
45  
46 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
47 {
48 if (!morph)
49 return NULL;
50  
51 morph->ref++;
52 return morph;
53 }
54  
55 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
56 {
57 if (!morph)
58 return NULL;
59  
60 return isl_morph_alloc(isl_basic_set_copy(morph->dom),
61 isl_basic_set_copy(morph->ran),
62 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
63 }
64  
65 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
66 {
67 if (!morph)
68 return NULL;
69  
70 if (morph->ref == 1)
71 return morph;
72 morph->ref--;
73 return isl_morph_dup(morph);
74 }
75  
76 void isl_morph_free(__isl_take isl_morph *morph)
77 {
78 if (!morph)
79 return;
80  
81 if (--morph->ref > 0)
82 return;
83  
84 isl_basic_set_free(morph->dom);
85 isl_basic_set_free(morph->ran);
86 isl_mat_free(morph->map);
87 isl_mat_free(morph->inv);
88 free(morph);
89 }
90  
91 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
92 {
93 if (!morph)
94 return NULL;
95  
96 return isl_space_copy(morph->ran->dim);
97 }
98  
99 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
100 {
101 if (!morph)
102 return 0;
103  
104 return isl_basic_set_dim(morph->dom, type);
105 }
106  
107 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
108 {
109 if (!morph)
110 return 0;
111  
112 return isl_basic_set_dim(morph->ran, type);
113 }
114  
115 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
116 enum isl_dim_type type, unsigned first, unsigned n)
117 {
118 unsigned dom_offset;
119  
120 if (n == 0)
121 return morph;
122  
123 morph = isl_morph_cow(morph);
124 if (!morph)
125 return NULL;
126  
127 dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
128  
129 morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
130  
131 morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
132  
133 morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
134  
135 if (morph->dom && morph->ran && morph->map && morph->inv)
136 return morph;
137  
138 isl_morph_free(morph);
139 return NULL;
140 }
141  
142 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
143 enum isl_dim_type type, unsigned first, unsigned n)
144 {
145 unsigned ran_offset;
146  
147 if (n == 0)
148 return morph;
149  
150 morph = isl_morph_cow(morph);
151 if (!morph)
152 return NULL;
153  
154 ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
155  
156 morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
157  
158 morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
159  
160 morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
161  
162 if (morph->dom && morph->ran && morph->map && morph->inv)
163 return morph;
164  
165 isl_morph_free(morph);
166 return NULL;
167 }
168  
169 /* Project domain of morph onto its parameter domain.
170 */
171 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
172 {
173 unsigned n;
174  
175 morph = isl_morph_cow(morph);
176 if (!morph)
177 return NULL;
178 n = isl_basic_set_dim(morph->dom, isl_dim_set);
179 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
180 if (!morph)
181 return NULL;
182 morph->dom = isl_basic_set_params(morph->dom);
183 if (morph->dom)
184 return morph;
185  
186 isl_morph_free(morph);
187 return NULL;
188 }
189  
190 /* Project range of morph onto its parameter domain.
191 */
192 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
193 {
194 unsigned n;
195  
196 morph = isl_morph_cow(morph);
197 if (!morph)
198 return NULL;
199 n = isl_basic_set_dim(morph->ran, isl_dim_set);
200 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
201 if (!morph)
202 return NULL;
203 morph->ran = isl_basic_set_params(morph->ran);
204 if (morph->ran)
205 return morph;
206  
207 isl_morph_free(morph);
208 return NULL;
209 }
210  
211 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
212 {
213 if (!morph)
214 return;
215  
216 isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
217 isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
218 isl_mat_print_internal(morph->map, out, 4);
219 isl_mat_print_internal(morph->inv, out, 4);
220 }
221  
222 void isl_morph_dump(__isl_take isl_morph *morph)
223 {
224 isl_morph_print_internal(morph, stderr);
225 }
226  
227 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
228 {
229 isl_mat *id;
230 isl_basic_set *universe;
231 unsigned total;
232  
233 if (!bset)
234 return NULL;
235  
236 total = isl_basic_set_total_dim(bset);
237 id = isl_mat_identity(bset->ctx, 1 + total);
238 universe = isl_basic_set_universe(isl_space_copy(bset->dim));
239  
240 return isl_morph_alloc(universe, isl_basic_set_copy(universe),
241 id, isl_mat_copy(id));
242 }
243  
244 /* Create a(n identity) morphism between empty sets of the same dimension
245 * a "bset".
246 */
247 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
248 {
249 isl_mat *id;
250 isl_basic_set *empty;
251 unsigned total;
252  
253 if (!bset)
254 return NULL;
255  
256 total = isl_basic_set_total_dim(bset);
257 id = isl_mat_identity(bset->ctx, 1 + total);
258 empty = isl_basic_set_empty(isl_space_copy(bset->dim));
259  
260 return isl_morph_alloc(empty, isl_basic_set_copy(empty),
261 id, isl_mat_copy(id));
262 }
263  
264 /* Given a matrix that maps a (possibly) parametric domain to
265 * a parametric domain, add in rows that map the "nparam" parameters onto
266 * themselves.
267 */
268 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
269 unsigned nparam)
270 {
271 int i;
272  
273 if (nparam == 0)
274 return mat;
275 if (!mat)
276 return NULL;
277  
278 mat = isl_mat_insert_rows(mat, 1, nparam);
279 if (!mat)
280 return NULL;
281  
282 for (i = 0; i < nparam; ++i) {
283 isl_seq_clr(mat->row[1 + i], mat->n_col);
284 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
285 }
286  
287 return mat;
288 }
289  
290 /* Construct a basic set described by the "n" equalities of "bset" starting
291 * at "first".
292 */
293 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
294 unsigned first, unsigned n)
295 {
296 int i, k;
297 isl_basic_set *eq;
298 unsigned total;
299  
300 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
301  
302 total = isl_basic_set_total_dim(bset);
303 eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
304 if (!eq)
305 return NULL;
306 for (i = 0; i < n; ++i) {
307 k = isl_basic_set_alloc_equality(eq);
308 if (k < 0)
309 goto error;
310 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
311 }
312  
313 return eq;
314 error:
315 isl_basic_set_free(eq);
316 return NULL;
317 }
318  
319 /* Given a basic set, exploit the equalties in the basic set to construct
320 * a morphishm that maps the basic set to a lower-dimensional space.
321 * Specifically, the morphism reduces the number of dimensions of type "type".
322 *
323 * This function is a slight generalization of isl_mat_variable_compression
324 * in that it allows the input to be parametric and that it allows for the
325 * compression of either parameters or set variables.
326 *
327 * We first select the equalities of interest, that is those that involve
328 * variables of type "type" and no later variables.
329 * Denote those equalities as
330 *
331 * -C(p) + M x = 0
332 *
333 * where C(p) depends on the parameters if type == isl_dim_set and
334 * is a constant if type == isl_dim_param.
335 *
336 * First compute the (left) Hermite normal form of M,
337 *
338 * M [U1 U2] = M U = H = [H1 0]
339 * or
340 * M = H Q = [H1 0] [Q1]
341 * [Q2]
342 *
343 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
344 * Define the transformed variables as
345 *
346 * x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
347 * [ x2' ] [Q2]
348 *
349 * The equalities then become
350 *
351 * -C(p) + H1 x1' = 0 or x1' = H1^{-1} C(p) = C'(p)
352 *
353 * If the denominator of the constant term does not divide the
354 * the common denominator of the parametric terms, then every
355 * integer point is mapped to a non-integer point and then the original set has no
356 * integer solutions (since the x' are a unimodular transformation
357 * of the x). In this case, an empty morphism is returned.
358 * Otherwise, the transformation is given by
359 *
360 * x = U1 H1^{-1} C(p) + U2 x2'
361 *
362 * The inverse transformation is simply
363 *
364 * x2' = Q2 x
365 *
366 * Both matrices are extended to map the full original space to the full
367 * compressed space.
368 */
369 __isl_give isl_morph *isl_basic_set_variable_compression(
370 __isl_keep isl_basic_set *bset, enum isl_dim_type type)
371 {
372 unsigned otype;
373 unsigned ntype;
374 unsigned orest;
375 unsigned nrest;
376 int f_eq, n_eq;
377 isl_space *dim;
378 isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
379 isl_basic_set *dom, *ran;
380  
381 if (!bset)
382 return NULL;
383  
384 if (isl_basic_set_plain_is_empty(bset))
385 return isl_morph_empty(bset);
386  
387 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
388  
389 otype = 1 + isl_space_offset(bset->dim, type);
390 ntype = isl_basic_set_dim(bset, type);
391 orest = otype + ntype;
392 nrest = isl_basic_set_total_dim(bset) - (orest - 1);
393  
394 for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
395 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
396 break;
397 for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
398 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
399 break;
400 if (n_eq == 0)
401 return isl_morph_identity(bset);
402  
403 H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
404 H = isl_mat_left_hermite(H, 0, &U, &Q);
405 if (!H || !U || !Q)
406 goto error;
407 Q = isl_mat_drop_rows(Q, 0, n_eq);
408 Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
409 Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
410 C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
411 if (!C)
412 goto error;
413 isl_int_set_si(C->row[0][0], 1);
414 isl_seq_clr(C->row[0] + 1, otype - 1);
415 isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
416 H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
417 H1 = isl_mat_lin_to_aff(H1);
418 C = isl_mat_inverse_product(H1, C);
419 if (!C)
420 goto error;
421 isl_mat_free(H);
422  
423 if (!isl_int_is_one(C->row[0][0])) {
424 int i;
425 isl_int g;
426  
427 isl_int_init(g);
428 for (i = 0; i < n_eq; ++i) {
429 isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
430 isl_int_gcd(g, g, C->row[0][0]);
431 if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
432 break;
433 }
434 isl_int_clear(g);
435  
436 if (i < n_eq) {
437 isl_mat_free(C);
438 isl_mat_free(U);
439 isl_mat_free(Q);
440 return isl_morph_empty(bset);
441 }
442  
443 C = isl_mat_normalize(C);
444 }
445  
446 U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
447 U1 = isl_mat_lin_to_aff(U1);
448 U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
449 U2 = isl_mat_lin_to_aff(U2);
450 isl_mat_free(U);
451  
452 C = isl_mat_product(U1, C);
453 C = isl_mat_aff_direct_sum(C, U2);
454 C = insert_parameter_rows(C, otype - 1);
455 C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
456  
457 dim = isl_space_copy(bset->dim);
458 dim = isl_space_drop_dims(dim, type, 0, ntype);
459 dim = isl_space_add_dims(dim, type, ntype - n_eq);
460 ran = isl_basic_set_universe(dim);
461 dom = copy_equalities(bset, f_eq, n_eq);
462  
463 return isl_morph_alloc(dom, ran, Q, C);
464 error:
465 isl_mat_free(C);
466 isl_mat_free(H);
467 isl_mat_free(U);
468 isl_mat_free(Q);
469 return NULL;
470 }
471  
472 /* Construct a parameter compression for "bset".
473 * We basically just call isl_mat_parameter_compression with the right input
474 * and then extend the resulting matrix to include the variables.
475 *
476 * Let the equalities be given as
477 *
478 * B(p) + A x = 0
479 *
480 * and let [H 0] be the Hermite Normal Form of A, then
481 *
482 * H^-1 B(p)
483 *
484 * needs to be integer, so we impose that each row is divisible by
485 * the denominator.
486 */
487 __isl_give isl_morph *isl_basic_set_parameter_compression(
488 __isl_keep isl_basic_set *bset)
489 {
490 unsigned nparam;
491 unsigned nvar;
492 int n_eq;
493 isl_mat *H, *B;
494 isl_vec *d;
495 isl_mat *map, *inv;
496 isl_basic_set *dom, *ran;
497  
498 if (!bset)
499 return NULL;
500  
501 if (isl_basic_set_plain_is_empty(bset))
502 return isl_morph_empty(bset);
503 if (bset->n_eq == 0)
504 return isl_morph_identity(bset);
505  
506 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
507  
508 n_eq = bset->n_eq;
509 nparam = isl_basic_set_dim(bset, isl_dim_param);
510 nvar = isl_basic_set_dim(bset, isl_dim_set);
511  
512 isl_assert(bset->ctx, n_eq <= nvar, return NULL);
513  
514 d = isl_vec_alloc(bset->ctx, n_eq);
515 B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
516 H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
517 H = isl_mat_left_hermite(H, 0, NULL, NULL);
518 H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
519 H = isl_mat_lin_to_aff(H);
520 H = isl_mat_right_inverse(H);
521 if (!H || !d)
522 goto error;
523 d = isl_vec_set(d, H->row[0][0]);
524 H = isl_mat_drop_rows(H, 0, 1);
525 H = isl_mat_drop_cols(H, 0, 1);
526 B = isl_mat_product(H, B);
527 inv = isl_mat_parameter_compression(B, d);
528 inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
529 map = isl_mat_right_inverse(isl_mat_copy(inv));
530  
531 dom = isl_basic_set_universe(isl_space_copy(bset->dim));
532 ran = isl_basic_set_universe(isl_space_copy(bset->dim));
533  
534 return isl_morph_alloc(dom, ran, map, inv);
535 error:
536 isl_mat_free(H);
537 isl_mat_free(B);
538 isl_vec_free(d);
539 return NULL;
540 }
541  
542 /* Add stride constraints to "bset" based on the inverse mapping
543 * that was plugged in. In particular, if morph maps x' to x,
544 * the the constraints of the original input
545 *
546 * A x' + b >= 0
547 *
548 * have been rewritten to
549 *
550 * A inv x + b >= 0
551 *
552 * However, this substitution may loose information on the integrality of x',
553 * so we need to impose that
554 *
555 * inv x
556 *
557 * is integral. If inv = B/d, this means that we need to impose that
558 *
559 * B x = 0 mod d
560 *
561 * or
562 *
563 * exists alpha in Z^m: B x = d alpha
564 *
565 */
566 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
567 __isl_keep isl_morph *morph)
568 {
569 int i, div, k;
570 isl_int gcd;
571  
572 if (isl_int_is_one(morph->inv->row[0][0]))
573 return bset;
574  
575 isl_int_init(gcd);
576  
577 for (i = 0; 1 + i < morph->inv->n_row; ++i) {
578 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
579 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
580 continue;
581 div = isl_basic_set_alloc_div(bset);
582 if (div < 0)
583 goto error;
584 isl_int_set_si(bset->div[div][0], 0);
585 k = isl_basic_set_alloc_equality(bset);
586 if (k < 0)
587 goto error;
588 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
589 morph->inv->n_col);
590 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
591 isl_int_set(bset->eq[k][morph->inv->n_col + div],
592 morph->inv->row[0][0]);
593 }
594  
595 isl_int_clear(gcd);
596  
597 return bset;
598 error:
599 isl_int_clear(gcd);
600 isl_basic_set_free(bset);
601 return NULL;
602 }
603  
604 /* Apply the morphism to the basic set.
605 * We basically just compute the preimage of "bset" under the inverse mapping
606 * in morph, add in stride constraints and intersect with the range
607 * of the morphism.
608 */
609 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
610 __isl_take isl_basic_set *bset)
611 {
612 isl_basic_set *res = NULL;
613 isl_mat *mat = NULL;
614 int i, k;
615 int max_stride;
616  
617 if (!morph || !bset)
618 goto error;
619  
620 isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
621 goto error);
622  
623 max_stride = morph->inv->n_row - 1;
624 if (isl_int_is_one(morph->inv->row[0][0]))
625 max_stride = 0;
626 res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
627 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
628  
629 for (i = 0; i < bset->n_div; ++i)
630 if (isl_basic_set_alloc_div(res) < 0)
631 goto error;
632  
633 mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
634 0, morph->inv->n_row);
635 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
636 if (!mat)
637 goto error;
638 for (i = 0; i < bset->n_eq; ++i) {
639 k = isl_basic_set_alloc_equality(res);
640 if (k < 0)
641 goto error;
642 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
643 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
644 morph->inv->row[0][0], bset->n_div);
645 }
646 isl_mat_free(mat);
647  
648 mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
649 0, morph->inv->n_row);
650 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
651 if (!mat)
652 goto error;
653 for (i = 0; i < bset->n_ineq; ++i) {
654 k = isl_basic_set_alloc_inequality(res);
655 if (k < 0)
656 goto error;
657 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
658 isl_seq_scale(res->ineq[k] + mat->n_col,
659 bset->ineq[i] + mat->n_col,
660 morph->inv->row[0][0], bset->n_div);
661 }
662 isl_mat_free(mat);
663  
664 mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
665 1, morph->inv->n_row);
666 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
667 if (!mat)
668 goto error;
669 for (i = 0; i < bset->n_div; ++i) {
670 isl_int_mul(res->div[i][0],
671 morph->inv->row[0][0], bset->div[i][0]);
672 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
673 isl_seq_scale(res->div[i] + 1 + mat->n_col,
674 bset->div[i] + 1 + mat->n_col,
675 morph->inv->row[0][0], bset->n_div);
676 }
677 isl_mat_free(mat);
678  
679 res = add_strides(res, morph);
680  
681 if (isl_basic_set_is_rational(bset))
682 res = isl_basic_set_set_rational(res);
683  
684 res = isl_basic_set_simplify(res);
685 res = isl_basic_set_finalize(res);
686  
687 res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
688  
689 isl_morph_free(morph);
690 isl_basic_set_free(bset);
691 return res;
692 error:
693 isl_mat_free(mat);
694 isl_morph_free(morph);
695 isl_basic_set_free(bset);
696 isl_basic_set_free(res);
697 return NULL;
698 }
699  
700 /* Apply the morphism to the set.
701 */
702 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
703 __isl_take isl_set *set)
704 {
705 int i;
706  
707 if (!morph || !set)
708 goto error;
709  
710 isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
711  
712 set = isl_set_cow(set);
713 if (!set)
714 goto error;
715  
716 isl_space_free(set->dim);
717 set->dim = isl_space_copy(morph->ran->dim);
718 if (!set->dim)
719 goto error;
720  
721 for (i = 0; i < set->n; ++i) {
722 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
723 if (!set->p[i])
724 goto error;
725 }
726  
727 isl_morph_free(morph);
728  
729 ISL_F_CLR(set, ISL_SET_NORMALIZED);
730  
731 return set;
732 error:
733 isl_set_free(set);
734 isl_morph_free(morph);
735 return NULL;
736 }
737  
738 /* Construct a morphism that first does morph2 and then morph1.
739 */
740 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
741 __isl_take isl_morph *morph2)
742 {
743 isl_mat *map, *inv;
744 isl_basic_set *dom, *ran;
745  
746 if (!morph1 || !morph2)
747 goto error;
748  
749 map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
750 inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
751 dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
752 isl_basic_set_copy(morph1->dom));
753 dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
754 ran = isl_morph_basic_set(isl_morph_copy(morph1),
755 isl_basic_set_copy(morph2->ran));
756 ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
757  
758 isl_morph_free(morph1);
759 isl_morph_free(morph2);
760  
761 return isl_morph_alloc(dom, ran, map, inv);
762 error:
763 isl_morph_free(morph1);
764 isl_morph_free(morph2);
765 return NULL;
766 }
767  
768 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
769 {
770 isl_basic_set *bset;
771 isl_mat *mat;
772  
773 morph = isl_morph_cow(morph);
774 if (!morph)
775 return NULL;
776  
777 bset = morph->dom;
778 morph->dom = morph->ran;
779 morph->ran = bset;
780  
781 mat = morph->map;
782 morph->map = morph->inv;
783 morph->inv = mat;
784  
785 return morph;
786 }
787  
788 /* We detect all the equalities first to avoid implicit equalties
789 * being discovered during the computations. In particular,
790 * the compression on the variables could expose additional stride
791 * constraints on the parameters. This would result in existentially
792 * quantified variables after applying the resulting morph, which
793 * in turn could break invariants of the calling functions.
794 */
795 __isl_give isl_morph *isl_basic_set_full_compression(
796 __isl_keep isl_basic_set *bset)
797 {
798 isl_morph *morph, *morph2;
799  
800 bset = isl_basic_set_copy(bset);
801 bset = isl_basic_set_detect_equalities(bset);
802  
803 morph = isl_basic_set_variable_compression(bset, isl_dim_param);
804 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
805  
806 morph2 = isl_basic_set_parameter_compression(bset);
807 bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
808  
809 morph = isl_morph_compose(morph2, morph);
810  
811 morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
812 isl_basic_set_free(bset);
813  
814 morph = isl_morph_compose(morph2, morph);
815  
816 return morph;
817 }
818  
819 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
820 __isl_take isl_vec *vec)
821 {
822 if (!morph)
823 goto error;
824  
825 vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
826  
827 isl_morph_free(morph);
828 return vec;
829 error:
830 isl_morph_free(morph);
831 isl_vec_free(vec);
832 return NULL;
833 }