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isl_{in,}equality_alloc: take isl_local_space intead of isl_space
[isl.git] / isl_polynomial.c
blob2341bab09a803e6435b1b322a8f6caff4083a244
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 <stdlib.h>
12 #define ISL_DIM_H
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl/lp.h>
17 #include <isl/seq.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_div_private.h>
24 #include <isl_mat_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_config.h>
29
30 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
31 {
32 switch (type) {
33 case isl_dim_param: return 0;
34 case isl_dim_in: return dim->nparam;
35 case isl_dim_out: return dim->nparam + dim->n_in;
36 default: return 0;
37 }
38 }
39
40 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return -1;
44
45 return up->var < 0;
46 }
47
48 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
49 {
50 if (!up)
51 return NULL;
52
53 isl_assert(up->ctx, up->var < 0, return NULL);
54
55 return (struct isl_upoly_cst *)up;
56 }
57
58 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
59 {
60 if (!up)
61 return NULL;
62
63 isl_assert(up->ctx, up->var >= 0, return NULL);
64
65 return (struct isl_upoly_rec *)up;
66 }
67
68 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
69 __isl_keep struct isl_upoly *up2)
70 {
71 int i;
72 struct isl_upoly_rec *rec1, *rec2;
73
74 if (!up1 || !up2)
75 return -1;
76 if (up1 == up2)
77 return 1;
78 if (up1->var != up2->var)
79 return 0;
80 if (isl_upoly_is_cst(up1)) {
81 struct isl_upoly_cst *cst1, *cst2;
82 cst1 = isl_upoly_as_cst(up1);
83 cst2 = isl_upoly_as_cst(up2);
84 if (!cst1 || !cst2)
85 return -1;
86 return isl_int_eq(cst1->n, cst2->n) &&
87 isl_int_eq(cst1->d, cst2->d);
88 }
89
90 rec1 = isl_upoly_as_rec(up1);
91 rec2 = isl_upoly_as_rec(up2);
92 if (!rec1 || !rec2)
93 return -1;
94
95 if (rec1->n != rec2->n)
96 return 0;
97
98 for (i = 0; i < rec1->n; ++i) {
99 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
100 if (eq < 0 || !eq)
101 return eq;
102 }
103
104 return 1;
105 }
106
107 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
108 {
109 struct isl_upoly_cst *cst;
110
111 if (!up)
112 return -1;
113 if (!isl_upoly_is_cst(up))
114 return 0;
115
116 cst = isl_upoly_as_cst(up);
117 if (!cst)
118 return -1;
119
120 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
121 }
122
123 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
124 {
125 struct isl_upoly_cst *cst;
126
127 if (!up)
128 return 0;
129 if (!isl_upoly_is_cst(up))
130 return 0;
131
132 cst = isl_upoly_as_cst(up);
133 if (!cst)
134 return 0;
135
136 return isl_int_sgn(cst->n);
137 }
138
139 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
140 {
141 struct isl_upoly_cst *cst;
142
143 if (!up)
144 return -1;
145 if (!isl_upoly_is_cst(up))
146 return 0;
147
148 cst = isl_upoly_as_cst(up);
149 if (!cst)
150 return -1;
151
152 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
153 }
154
155 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
156 {
157 struct isl_upoly_cst *cst;
158
159 if (!up)
160 return -1;
161 if (!isl_upoly_is_cst(up))
162 return 0;
163
164 cst = isl_upoly_as_cst(up);
165 if (!cst)
166 return -1;
167
168 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
169 }
170
171 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
172 {
173 struct isl_upoly_cst *cst;
174
175 if (!up)
176 return -1;
177 if (!isl_upoly_is_cst(up))
178 return 0;
179
180 cst = isl_upoly_as_cst(up);
181 if (!cst)
182 return -1;
183
184 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
185 }
186
187 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
188 {
189 struct isl_upoly_cst *cst;
190
191 if (!up)
192 return -1;
193 if (!isl_upoly_is_cst(up))
194 return 0;
195
196 cst = isl_upoly_as_cst(up);
197 if (!cst)
198 return -1;
199
200 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
201 }
202
203 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
204 {
205 struct isl_upoly_cst *cst;
206
207 if (!up)
208 return -1;
209 if (!isl_upoly_is_cst(up))
210 return 0;
211
212 cst = isl_upoly_as_cst(up);
213 if (!cst)
214 return -1;
215
216 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
217 }
218
219 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
220 {
221 struct isl_upoly_cst *cst;
222
223 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
224 if (!cst)
225 return NULL;
226
227 cst->up.ref = 1;
228 cst->up.ctx = ctx;
229 isl_ctx_ref(ctx);
230 cst->up.var = -1;
231
232 isl_int_init(cst->n);
233 isl_int_init(cst->d);
234
235 return cst;
236 }
237
238 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
239 {
240 struct isl_upoly_cst *cst;
241
242 cst = isl_upoly_cst_alloc(ctx);
243 if (!cst)
244 return NULL;
245
246 isl_int_set_si(cst->n, 0);
247 isl_int_set_si(cst->d, 1);
248
249 return &cst->up;
250 }
251
252 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
253 {
254 struct isl_upoly_cst *cst;
255
256 cst = isl_upoly_cst_alloc(ctx);
257 if (!cst)
258 return NULL;
259
260 isl_int_set_si(cst->n, 1);
261 isl_int_set_si(cst->d, 1);
262
263 return &cst->up;
264 }
265
266 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
267 {
268 struct isl_upoly_cst *cst;
269
270 cst = isl_upoly_cst_alloc(ctx);
271 if (!cst)
272 return NULL;
273
274 isl_int_set_si(cst->n, 1);
275 isl_int_set_si(cst->d, 0);
276
277 return &cst->up;
278 }
279
280 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
281 {
282 struct isl_upoly_cst *cst;
283
284 cst = isl_upoly_cst_alloc(ctx);
285 if (!cst)
286 return NULL;
287
288 isl_int_set_si(cst->n, -1);
289 isl_int_set_si(cst->d, 0);
290
291 return &cst->up;
292 }
293
294 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
295 {
296 struct isl_upoly_cst *cst;
297
298 cst = isl_upoly_cst_alloc(ctx);
299 if (!cst)
300 return NULL;
301
302 isl_int_set_si(cst->n, 0);
303 isl_int_set_si(cst->d, 0);
304
305 return &cst->up;
306 }
307
308 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
309 isl_int n, isl_int d)
310 {
311 struct isl_upoly_cst *cst;
312
313 cst = isl_upoly_cst_alloc(ctx);
314 if (!cst)
315 return NULL;
316
317 isl_int_set(cst->n, n);
318 isl_int_set(cst->d, d);
319
320 return &cst->up;
321 }
322
323 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
324 int var, int size)
325 {
326 struct isl_upoly_rec *rec;
327
328 isl_assert(ctx, var >= 0, return NULL);
329 isl_assert(ctx, size >= 0, return NULL);
330 rec = isl_calloc(ctx, struct isl_upoly_rec,
331 sizeof(struct isl_upoly_rec) +
332 size * sizeof(struct isl_upoly *));
333 if (!rec)
334 return NULL;
335
336 rec->up.ref = 1;
337 rec->up.ctx = ctx;
338 isl_ctx_ref(ctx);
339 rec->up.var = var;
340
341 rec->n = 0;
342 rec->size = size;
343
344 return rec;
345 }
346
347 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
348 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
349 {
350 qp = isl_qpolynomial_cow(qp);
351 if (!qp || !dim)
352 goto error;
353
354 isl_space_free(qp->dim);
355 qp->dim = dim;
356
357 return qp;
358 error:
359 isl_qpolynomial_free(qp);
360 isl_space_free(dim);
361 return NULL;
362 }
363
364 /* Reset the space of "qp". This function is called from isl_pw_templ.c
365 * and doesn't know if the space of an element object is represented
366 * directly or through its domain. It therefore passes along both.
367 */
368 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
369 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
370 __isl_take isl_space *domain)
371 {
372 isl_space_free(space);
373 return isl_qpolynomial_reset_domain_space(qp, domain);
374 }
375
376 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
377 {
378 return qp ? qp->dim->ctx : NULL;
379 }
380
381 __isl_give isl_space *isl_qpolynomial_get_domain_space(
382 __isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_space_copy(qp->dim) : NULL;
385 }
386
387 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
388 {
389 isl_space *space;
390 if (!qp)
391 return NULL;
392 space = isl_space_copy(qp->dim);
393 space = isl_space_from_domain(space);
394 space = isl_space_add_dims(space, isl_dim_out, 1);
395 return space;
396 }
397
398 /* Externally, an isl_qpolynomial has a map space, but internally, the
399 * ls field corresponds to the domain of that space.
400 */
401 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
402 enum isl_dim_type type)
403 {
404 if (!qp)
405 return 0;
406 if (type == isl_dim_out)
407 return 1;
408 if (type == isl_dim_in)
409 type = isl_dim_set;
410 return isl_space_dim(qp->dim, type);
411 }
412
413 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
414 {
415 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
416 }
417
418 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
419 {
420 return qp ? isl_upoly_is_one(qp->upoly) : -1;
421 }
422
423 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
424 {
425 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
426 }
427
428 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
429 {
430 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
431 }
432
433 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
434 {
435 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
436 }
437
438 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
439 {
440 return qp ? isl_upoly_sgn(qp->upoly) : 0;
441 }
442
443 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
444 {
445 isl_int_clear(cst->n);
446 isl_int_clear(cst->d);
447 }
448
449 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
450 {
451 int i;
452
453 for (i = 0; i < rec->n; ++i)
454 isl_upoly_free(rec->p[i]);
455 }
456
457 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
458 {
459 if (!up)
460 return NULL;
461
462 up->ref++;
463 return up;
464 }
465
466 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
467 {
468 struct isl_upoly_cst *cst;
469 struct isl_upoly_cst *dup;
470
471 cst = isl_upoly_as_cst(up);
472 if (!cst)
473 return NULL;
474
475 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
476 if (!dup)
477 return NULL;
478 isl_int_set(dup->n, cst->n);
479 isl_int_set(dup->d, cst->d);
480
481 return &dup->up;
482 }
483
484 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
485 {
486 int i;
487 struct isl_upoly_rec *rec;
488 struct isl_upoly_rec *dup;
489
490 rec = isl_upoly_as_rec(up);
491 if (!rec)
492 return NULL;
493
494 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
495 if (!dup)
496 return NULL;
497
498 for (i = 0; i < rec->n; ++i) {
499 dup->p[i] = isl_upoly_copy(rec->p[i]);
500 if (!dup->p[i])
501 goto error;
502 dup->n++;
503 }
504
505 return &dup->up;
506 error:
507 isl_upoly_free(&dup->up);
508 return NULL;
509 }
510
511 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
512 {
513 if (!up)
514 return NULL;
515
516 if (isl_upoly_is_cst(up))
517 return isl_upoly_dup_cst(up);
518 else
519 return isl_upoly_dup_rec(up);
520 }
521
522 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
523 {
524 if (!up)
525 return NULL;
526
527 if (up->ref == 1)
528 return up;
529 up->ref--;
530 return isl_upoly_dup(up);
531 }
532
533 void isl_upoly_free(__isl_take struct isl_upoly *up)
534 {
535 if (!up)
536 return;
537
538 if (--up->ref > 0)
539 return;
540
541 if (up->var < 0)
542 upoly_free_cst((struct isl_upoly_cst *)up);
543 else
544 upoly_free_rec((struct isl_upoly_rec *)up);
545
546 isl_ctx_deref(up->ctx);
547 free(up);
548 }
549
550 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
551 {
552 isl_int gcd;
553
554 isl_int_init(gcd);
555 isl_int_gcd(gcd, cst->n, cst->d);
556 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
557 isl_int_divexact(cst->n, cst->n, gcd);
558 isl_int_divexact(cst->d, cst->d, gcd);
559 }
560 isl_int_clear(gcd);
561 }
562
563 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
564 __isl_take struct isl_upoly *up2)
565 {
566 struct isl_upoly_cst *cst1;
567 struct isl_upoly_cst *cst2;
568
569 up1 = isl_upoly_cow(up1);
570 if (!up1 || !up2)
571 goto error;
572
573 cst1 = isl_upoly_as_cst(up1);
574 cst2 = isl_upoly_as_cst(up2);
575
576 if (isl_int_eq(cst1->d, cst2->d))
577 isl_int_add(cst1->n, cst1->n, cst2->n);
578 else {
579 isl_int_mul(cst1->n, cst1->n, cst2->d);
580 isl_int_addmul(cst1->n, cst2->n, cst1->d);
581 isl_int_mul(cst1->d, cst1->d, cst2->d);
582 }
583
584 isl_upoly_cst_reduce(cst1);
585
586 isl_upoly_free(up2);
587 return up1;
588 error:
589 isl_upoly_free(up1);
590 isl_upoly_free(up2);
591 return NULL;
592 }
593
594 static __isl_give struct isl_upoly *replace_by_zero(
595 __isl_take struct isl_upoly *up)
596 {
597 struct isl_ctx *ctx;
598
599 if (!up)
600 return NULL;
601 ctx = up->ctx;
602 isl_upoly_free(up);
603 return isl_upoly_zero(ctx);
604 }
605
606 static __isl_give struct isl_upoly *replace_by_constant_term(
607 __isl_take struct isl_upoly *up)
608 {
609 struct isl_upoly_rec *rec;
610 struct isl_upoly *cst;
611
612 if (!up)
613 return NULL;
614
615 rec = isl_upoly_as_rec(up);
616 if (!rec)
617 goto error;
618 cst = isl_upoly_copy(rec->p[0]);
619 isl_upoly_free(up);
620 return cst;
621 error:
622 isl_upoly_free(up);
623 return NULL;
624 }
625
626 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
627 __isl_take struct isl_upoly *up2)
628 {
629 int i;
630 struct isl_upoly_rec *rec1, *rec2;
631
632 if (!up1 || !up2)
633 goto error;
634
635 if (isl_upoly_is_nan(up1)) {
636 isl_upoly_free(up2);
637 return up1;
638 }
639
640 if (isl_upoly_is_nan(up2)) {
641 isl_upoly_free(up1);
642 return up2;
643 }
644
645 if (isl_upoly_is_zero(up1)) {
646 isl_upoly_free(up1);
647 return up2;
648 }
649
650 if (isl_upoly_is_zero(up2)) {
651 isl_upoly_free(up2);
652 return up1;
653 }
654
655 if (up1->var < up2->var)
656 return isl_upoly_sum(up2, up1);
657
658 if (up2->var < up1->var) {
659 struct isl_upoly_rec *rec;
660 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
661 isl_upoly_free(up1);
662 return up2;
663 }
664 up1 = isl_upoly_cow(up1);
665 rec = isl_upoly_as_rec(up1);
666 if (!rec)
667 goto error;
668 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
669 if (rec->n == 1)
670 up1 = replace_by_constant_term(up1);
671 return up1;
672 }
673
674 if (isl_upoly_is_cst(up1))
675 return isl_upoly_sum_cst(up1, up2);
676
677 rec1 = isl_upoly_as_rec(up1);
678 rec2 = isl_upoly_as_rec(up2);
679 if (!rec1 || !rec2)
680 goto error;
681
682 if (rec1->n < rec2->n)
683 return isl_upoly_sum(up2, up1);
684
685 up1 = isl_upoly_cow(up1);
686 rec1 = isl_upoly_as_rec(up1);
687 if (!rec1)
688 goto error;
689
690 for (i = rec2->n - 1; i >= 0; --i) {
691 rec1->p[i] = isl_upoly_sum(rec1->p[i],
692 isl_upoly_copy(rec2->p[i]));
693 if (!rec1->p[i])
694 goto error;
695 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
696 isl_upoly_free(rec1->p[i]);
697 rec1->n--;
698 }
699 }
700
701 if (rec1->n == 0)
702 up1 = replace_by_zero(up1);
703 else if (rec1->n == 1)
704 up1 = replace_by_constant_term(up1);
705
706 isl_upoly_free(up2);
707
708 return up1;
709 error:
710 isl_upoly_free(up1);
711 isl_upoly_free(up2);
712 return NULL;
713 }
714
715 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
716 __isl_take struct isl_upoly *up, isl_int v)
717 {
718 struct isl_upoly_cst *cst;
719
720 up = isl_upoly_cow(up);
721 if (!up)
722 return NULL;
723
724 cst = isl_upoly_as_cst(up);
725
726 isl_int_addmul(cst->n, cst->d, v);
727
728 return up;
729 }
730
731 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
732 __isl_take struct isl_upoly *up, isl_int v)
733 {
734 struct isl_upoly_rec *rec;
735
736 if (!up)
737 return NULL;
738
739 if (isl_upoly_is_cst(up))
740 return isl_upoly_cst_add_isl_int(up, v);
741
742 up = isl_upoly_cow(up);
743 rec = isl_upoly_as_rec(up);
744 if (!rec)
745 goto error;
746
747 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
748 if (!rec->p[0])
749 goto error;
750
751 return up;
752 error:
753 isl_upoly_free(up);
754 return NULL;
755 }
756
757 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
758 __isl_take struct isl_upoly *up, isl_int v)
759 {
760 struct isl_upoly_cst *cst;
761
762 if (isl_upoly_is_zero(up))
763 return up;
764
765 up = isl_upoly_cow(up);
766 if (!up)
767 return NULL;
768
769 cst = isl_upoly_as_cst(up);
770
771 isl_int_mul(cst->n, cst->n, v);
772
773 return up;
774 }
775
776 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
777 __isl_take struct isl_upoly *up, isl_int v)
778 {
779 int i;
780 struct isl_upoly_rec *rec;
781
782 if (!up)
783 return NULL;
784
785 if (isl_upoly_is_cst(up))
786 return isl_upoly_cst_mul_isl_int(up, v);
787
788 up = isl_upoly_cow(up);
789 rec = isl_upoly_as_rec(up);
790 if (!rec)
791 goto error;
792
793 for (i = 0; i < rec->n; ++i) {
794 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
795 if (!rec->p[i])
796 goto error;
797 }
798
799 return up;
800 error:
801 isl_upoly_free(up);
802 return NULL;
803 }
804
805 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
806 __isl_take struct isl_upoly *up2)
807 {
808 struct isl_upoly_cst *cst1;
809 struct isl_upoly_cst *cst2;
810
811 up1 = isl_upoly_cow(up1);
812 if (!up1 || !up2)
813 goto error;
814
815 cst1 = isl_upoly_as_cst(up1);
816 cst2 = isl_upoly_as_cst(up2);
817
818 isl_int_mul(cst1->n, cst1->n, cst2->n);
819 isl_int_mul(cst1->d, cst1->d, cst2->d);
820
821 isl_upoly_cst_reduce(cst1);
822
823 isl_upoly_free(up2);
824 return up1;
825 error:
826 isl_upoly_free(up1);
827 isl_upoly_free(up2);
828 return NULL;
829 }
830
831 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
832 __isl_take struct isl_upoly *up2)
833 {
834 struct isl_upoly_rec *rec1;
835 struct isl_upoly_rec *rec2;
836 struct isl_upoly_rec *res = NULL;
837 int i, j;
838 int size;
839
840 rec1 = isl_upoly_as_rec(up1);
841 rec2 = isl_upoly_as_rec(up2);
842 if (!rec1 || !rec2)
843 goto error;
844 size = rec1->n + rec2->n - 1;
845 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
846 if (!res)
847 goto error;
848
849 for (i = 0; i < rec1->n; ++i) {
850 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
851 isl_upoly_copy(rec1->p[i]));
852 if (!res->p[i])
853 goto error;
854 res->n++;
855 }
856 for (; i < size; ++i) {
857 res->p[i] = isl_upoly_zero(up1->ctx);
858 if (!res->p[i])
859 goto error;
860 res->n++;
861 }
862 for (i = 0; i < rec1->n; ++i) {
863 for (j = 1; j < rec2->n; ++j) {
864 struct isl_upoly *up;
865 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
866 isl_upoly_copy(rec1->p[i]));
867 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
868 if (!res->p[i + j])
869 goto error;
870 }
871 }
872
873 isl_upoly_free(up1);
874 isl_upoly_free(up2);
875
876 return &res->up;
877 error:
878 isl_upoly_free(up1);
879 isl_upoly_free(up2);
880 isl_upoly_free(&res->up);
881 return NULL;
882 }
883
884 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
885 __isl_take struct isl_upoly *up2)
886 {
887 if (!up1 || !up2)
888 goto error;
889
890 if (isl_upoly_is_nan(up1)) {
891 isl_upoly_free(up2);
892 return up1;
893 }
894
895 if (isl_upoly_is_nan(up2)) {
896 isl_upoly_free(up1);
897 return up2;
898 }
899
900 if (isl_upoly_is_zero(up1)) {
901 isl_upoly_free(up2);
902 return up1;
903 }
904
905 if (isl_upoly_is_zero(up2)) {
906 isl_upoly_free(up1);
907 return up2;
908 }
909
910 if (isl_upoly_is_one(up1)) {
911 isl_upoly_free(up1);
912 return up2;
913 }
914
915 if (isl_upoly_is_one(up2)) {
916 isl_upoly_free(up2);
917 return up1;
918 }
919
920 if (up1->var < up2->var)
921 return isl_upoly_mul(up2, up1);
922
923 if (up2->var < up1->var) {
924 int i;
925 struct isl_upoly_rec *rec;
926 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
927 isl_ctx *ctx = up1->ctx;
928 isl_upoly_free(up1);
929 isl_upoly_free(up2);
930 return isl_upoly_nan(ctx);
931 }
932 up1 = isl_upoly_cow(up1);
933 rec = isl_upoly_as_rec(up1);
934 if (!rec)
935 goto error;
936
937 for (i = 0; i < rec->n; ++i) {
938 rec->p[i] = isl_upoly_mul(rec->p[i],
939 isl_upoly_copy(up2));
940 if (!rec->p[i])
941 goto error;
942 }
943 isl_upoly_free(up2);
944 return up1;
945 }
946
947 if (isl_upoly_is_cst(up1))
948 return isl_upoly_mul_cst(up1, up2);
949
950 return isl_upoly_mul_rec(up1, up2);
951 error:
952 isl_upoly_free(up1);
953 isl_upoly_free(up2);
954 return NULL;
955 }
956
957 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
958 unsigned power)
959 {
960 struct isl_upoly *res;
961
962 if (!up)
963 return NULL;
964 if (power == 1)
965 return up;
966
967 if (power % 2)
968 res = isl_upoly_copy(up);
969 else
970 res = isl_upoly_one(up->ctx);
971
972 while (power >>= 1) {
973 up = isl_upoly_mul(up, isl_upoly_copy(up));
974 if (power % 2)
975 res = isl_upoly_mul(res, isl_upoly_copy(up));
976 }
977
978 isl_upoly_free(up);
979 return res;
980 }
981
982 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
983 unsigned n_div, __isl_take struct isl_upoly *up)
984 {
985 struct isl_qpolynomial *qp = NULL;
986 unsigned total;
987
988 if (!dim || !up)
989 goto error;
990
991 if (!isl_space_is_set(dim))
992 isl_die(isl_space_get_ctx(dim), isl_error_invalid,
993 "domain of polynomial should be a set", goto error);
994
995 total = isl_space_dim(dim, isl_dim_all);
996
997 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
998 if (!qp)
999 goto error;
1000
1001 qp->ref = 1;
1002 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
1003 if (!qp->div)
1004 goto error;
1005
1006 qp->dim = dim;
1007 qp->upoly = up;
1008
1009 return qp;
1010 error:
1011 isl_space_free(dim);
1012 isl_upoly_free(up);
1013 isl_qpolynomial_free(qp);
1014 return NULL;
1015 }
1016
1017 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1018 {
1019 if (!qp)
1020 return NULL;
1021
1022 qp->ref++;
1023 return qp;
1024 }
1025
1026 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1027 {
1028 struct isl_qpolynomial *dup;
1029
1030 if (!qp)
1031 return NULL;
1032
1033 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1034 isl_upoly_copy(qp->upoly));
1035 if (!dup)
1036 return NULL;
1037 isl_mat_free(dup->div);
1038 dup->div = isl_mat_copy(qp->div);
1039 if (!dup->div)
1040 goto error;
1041
1042 return dup;
1043 error:
1044 isl_qpolynomial_free(dup);
1045 return NULL;
1046 }
1047
1048 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1049 {
1050 if (!qp)
1051 return NULL;
1052
1053 if (qp->ref == 1)
1054 return qp;
1055 qp->ref--;
1056 return isl_qpolynomial_dup(qp);
1057 }
1058
1059 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1060 {
1061 if (!qp)
1062 return NULL;
1063
1064 if (--qp->ref > 0)
1065 return NULL;
1066
1067 isl_space_free(qp->dim);
1068 isl_mat_free(qp->div);
1069 isl_upoly_free(qp->upoly);
1070
1071 free(qp);
1072 return NULL;
1073 }
1074
1075 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1076 {
1077 int i;
1078 struct isl_upoly_rec *rec;
1079 struct isl_upoly_cst *cst;
1080
1081 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1082 if (!rec)
1083 return NULL;
1084 for (i = 0; i < 1 + power; ++i) {
1085 rec->p[i] = isl_upoly_zero(ctx);
1086 if (!rec->p[i])
1087 goto error;
1088 rec->n++;
1089 }
1090 cst = isl_upoly_as_cst(rec->p[power]);
1091 isl_int_set_si(cst->n, 1);
1092
1093 return &rec->up;
1094 error:
1095 isl_upoly_free(&rec->up);
1096 return NULL;
1097 }
1098
1099 /* r array maps original positions to new positions.
1100 */
1101 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1102 int *r)
1103 {
1104 int i;
1105 struct isl_upoly_rec *rec;
1106 struct isl_upoly *base;
1107 struct isl_upoly *res;
1108
1109 if (isl_upoly_is_cst(up))
1110 return up;
1111
1112 rec = isl_upoly_as_rec(up);
1113 if (!rec)
1114 goto error;
1115
1116 isl_assert(up->ctx, rec->n >= 1, goto error);
1117
1118 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1119 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1120
1121 for (i = rec->n - 2; i >= 0; --i) {
1122 res = isl_upoly_mul(res, isl_upoly_copy(base));
1123 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1124 }
1125
1126 isl_upoly_free(base);
1127 isl_upoly_free(up);
1128
1129 return res;
1130 error:
1131 isl_upoly_free(up);
1132 return NULL;
1133 }
1134
1135 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1136 {
1137 int n_row, n_col;
1138 int equal;
1139
1140 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1141 div1->n_col >= div2->n_col, return -1);
1142
1143 if (div1->n_row == div2->n_row)
1144 return isl_mat_is_equal(div1, div2);
1145
1146 n_row = div1->n_row;
1147 n_col = div1->n_col;
1148 div1->n_row = div2->n_row;
1149 div1->n_col = div2->n_col;
1150
1151 equal = isl_mat_is_equal(div1, div2);
1152
1153 div1->n_row = n_row;
1154 div1->n_col = n_col;
1155
1156 return equal;
1157 }
1158
1159 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1160 {
1161 int li, lj;
1162
1163 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1164 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1165
1166 if (li != lj)
1167 return li - lj;
1168
1169 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1170 }
1171
1172 struct isl_div_sort_info {
1173 isl_mat *div;
1174 int row;
1175 };
1176
1177 static int div_sort_cmp(const void *p1, const void *p2)
1178 {
1179 const struct isl_div_sort_info *i1, *i2;
1180 i1 = (const struct isl_div_sort_info *) p1;
1181 i2 = (const struct isl_div_sort_info *) p2;
1182
1183 return cmp_row(i1->div, i1->row, i2->row);
1184 }
1185
1186 /* Sort divs and remove duplicates.
1187 */
1188 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1189 {
1190 int i;
1191 int skip;
1192 int len;
1193 struct isl_div_sort_info *array = NULL;
1194 int *pos = NULL, *at = NULL;
1195 int *reordering = NULL;
1196 unsigned div_pos;
1197
1198 if (!qp)
1199 return NULL;
1200 if (qp->div->n_row <= 1)
1201 return qp;
1202
1203 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1204
1205 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1206 qp->div->n_row);
1207 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1208 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1209 len = qp->div->n_col - 2;
1210 reordering = isl_alloc_array(qp->div->ctx, int, len);
1211 if (!array || !pos || !at || !reordering)
1212 goto error;
1213
1214 for (i = 0; i < qp->div->n_row; ++i) {
1215 array[i].div = qp->div;
1216 array[i].row = i;
1217 pos[i] = i;
1218 at[i] = i;
1219 }
1220
1221 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1222 div_sort_cmp);
1223
1224 for (i = 0; i < div_pos; ++i)
1225 reordering[i] = i;
1226
1227 for (i = 0; i < qp->div->n_row; ++i) {
1228 if (pos[array[i].row] == i)
1229 continue;
1230 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1231 pos[at[i]] = pos[array[i].row];
1232 at[pos[array[i].row]] = at[i];
1233 at[i] = array[i].row;
1234 pos[array[i].row] = i;
1235 }
1236
1237 skip = 0;
1238 for (i = 0; i < len - div_pos; ++i) {
1239 if (i > 0 &&
1240 isl_seq_eq(qp->div->row[i - skip - 1],
1241 qp->div->row[i - skip], qp->div->n_col)) {
1242 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1243 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1244 2 + div_pos + i - skip);
1245 qp->div = isl_mat_drop_cols(qp->div,
1246 2 + div_pos + i - skip, 1);
1247 skip++;
1248 }
1249 reordering[div_pos + array[i].row] = div_pos + i - skip;
1250 }
1251
1252 qp->upoly = reorder(qp->upoly, reordering);
1253
1254 if (!qp->upoly || !qp->div)
1255 goto error;
1256
1257 free(at);
1258 free(pos);
1259 free(array);
1260 free(reordering);
1261
1262 return qp;
1263 error:
1264 free(at);
1265 free(pos);
1266 free(array);
1267 free(reordering);
1268 isl_qpolynomial_free(qp);
1269 return NULL;
1270 }
1271
1272 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1273 int *exp, int first)
1274 {
1275 int i;
1276 struct isl_upoly_rec *rec;
1277
1278 if (isl_upoly_is_cst(up))
1279 return up;
1280
1281 if (up->var < first)
1282 return up;
1283
1284 if (exp[up->var - first] == up->var - first)
1285 return up;
1286
1287 up = isl_upoly_cow(up);
1288 if (!up)
1289 goto error;
1290
1291 up->var = exp[up->var - first] + first;
1292
1293 rec = isl_upoly_as_rec(up);
1294 if (!rec)
1295 goto error;
1296
1297 for (i = 0; i < rec->n; ++i) {
1298 rec->p[i] = expand(rec->p[i], exp, first);
1299 if (!rec->p[i])
1300 goto error;
1301 }
1302
1303 return up;
1304 error:
1305 isl_upoly_free(up);
1306 return NULL;
1307 }
1308
1309 static __isl_give isl_qpolynomial *with_merged_divs(
1310 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1311 __isl_take isl_qpolynomial *qp2),
1312 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1313 {
1314 int *exp1 = NULL;
1315 int *exp2 = NULL;
1316 isl_mat *div = NULL;
1317
1318 qp1 = isl_qpolynomial_cow(qp1);
1319 qp2 = isl_qpolynomial_cow(qp2);
1320
1321 if (!qp1 || !qp2)
1322 goto error;
1323
1324 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1325 qp1->div->n_col >= qp2->div->n_col, goto error);
1326
1327 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1328 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1329 if (!exp1 || !exp2)
1330 goto error;
1331
1332 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1333 if (!div)
1334 goto error;
1335
1336 isl_mat_free(qp1->div);
1337 qp1->div = isl_mat_copy(div);
1338 isl_mat_free(qp2->div);
1339 qp2->div = isl_mat_copy(div);
1340
1341 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1342 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1343
1344 if (!qp1->upoly || !qp2->upoly)
1345 goto error;
1346
1347 isl_mat_free(div);
1348 free(exp1);
1349 free(exp2);
1350
1351 return fn(qp1, qp2);
1352 error:
1353 isl_mat_free(div);
1354 free(exp1);
1355 free(exp2);
1356 isl_qpolynomial_free(qp1);
1357 isl_qpolynomial_free(qp2);
1358 return NULL;
1359 }
1360
1361 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1362 __isl_take isl_qpolynomial *qp2)
1363 {
1364 qp1 = isl_qpolynomial_cow(qp1);
1365
1366 if (!qp1 || !qp2)
1367 goto error;
1368
1369 if (qp1->div->n_row < qp2->div->n_row)
1370 return isl_qpolynomial_add(qp2, qp1);
1371
1372 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1373 if (!compatible_divs(qp1->div, qp2->div))
1374 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1375
1376 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1377 if (!qp1->upoly)
1378 goto error;
1379
1380 isl_qpolynomial_free(qp2);
1381
1382 return qp1;
1383 error:
1384 isl_qpolynomial_free(qp1);
1385 isl_qpolynomial_free(qp2);
1386 return NULL;
1387 }
1388
1389 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1390 __isl_keep isl_set *dom,
1391 __isl_take isl_qpolynomial *qp1,
1392 __isl_take isl_qpolynomial *qp2)
1393 {
1394 qp1 = isl_qpolynomial_add(qp1, qp2);
1395 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1396 return qp1;
1397 }
1398
1399 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1400 __isl_take isl_qpolynomial *qp2)
1401 {
1402 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1403 }
1404
1405 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1406 __isl_take isl_qpolynomial *qp, isl_int v)
1407 {
1408 if (isl_int_is_zero(v))
1409 return qp;
1410
1411 qp = isl_qpolynomial_cow(qp);
1412 if (!qp)
1413 return NULL;
1414
1415 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1416 if (!qp->upoly)
1417 goto error;
1418
1419 return qp;
1420 error:
1421 isl_qpolynomial_free(qp);
1422 return NULL;
1423
1424 }
1425
1426 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1427 {
1428 if (!qp)
1429 return NULL;
1430
1431 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1432 }
1433
1434 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1435 __isl_take isl_qpolynomial *qp, isl_int v)
1436 {
1437 if (isl_int_is_one(v))
1438 return qp;
1439
1440 if (qp && isl_int_is_zero(v)) {
1441 isl_qpolynomial *zero;
1442 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1443 isl_qpolynomial_free(qp);
1444 return zero;
1445 }
1446
1447 qp = isl_qpolynomial_cow(qp);
1448 if (!qp)
1449 return NULL;
1450
1451 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1452 if (!qp->upoly)
1453 goto error;
1454
1455 return qp;
1456 error:
1457 isl_qpolynomial_free(qp);
1458 return NULL;
1459 }
1460
1461 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1462 __isl_take isl_qpolynomial *qp, isl_int v)
1463 {
1464 return isl_qpolynomial_mul_isl_int(qp, v);
1465 }
1466
1467 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1468 __isl_take isl_qpolynomial *qp2)
1469 {
1470 qp1 = isl_qpolynomial_cow(qp1);
1471
1472 if (!qp1 || !qp2)
1473 goto error;
1474
1475 if (qp1->div->n_row < qp2->div->n_row)
1476 return isl_qpolynomial_mul(qp2, qp1);
1477
1478 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1479 if (!compatible_divs(qp1->div, qp2->div))
1480 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1481
1482 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1483 if (!qp1->upoly)
1484 goto error;
1485
1486 isl_qpolynomial_free(qp2);
1487
1488 return qp1;
1489 error:
1490 isl_qpolynomial_free(qp1);
1491 isl_qpolynomial_free(qp2);
1492 return NULL;
1493 }
1494
1495 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1496 unsigned power)
1497 {
1498 qp = isl_qpolynomial_cow(qp);
1499
1500 if (!qp)
1501 return NULL;
1502
1503 qp->upoly = isl_upoly_pow(qp->upoly, power);
1504 if (!qp->upoly)
1505 goto error;
1506
1507 return qp;
1508 error:
1509 isl_qpolynomial_free(qp);
1510 return NULL;
1511 }
1512
1513 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1514 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1515 {
1516 int i;
1517
1518 if (power == 1)
1519 return pwqp;
1520
1521 pwqp = isl_pw_qpolynomial_cow(pwqp);
1522 if (!pwqp)
1523 return NULL;
1524
1525 for (i = 0; i < pwqp->n; ++i) {
1526 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1527 if (!pwqp->p[i].qp)
1528 return isl_pw_qpolynomial_free(pwqp);
1529 }
1530
1531 return pwqp;
1532 }
1533
1534 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1535 __isl_take isl_space *dim)
1536 {
1537 if (!dim)
1538 return NULL;
1539 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1540 }
1541
1542 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1543 __isl_take isl_space *dim)
1544 {
1545 if (!dim)
1546 return NULL;
1547 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1548 }
1549
1550 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1551 __isl_take isl_space *dim)
1552 {
1553 if (!dim)
1554 return NULL;
1555 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1556 }
1557
1558 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1559 __isl_take isl_space *dim)
1560 {
1561 if (!dim)
1562 return NULL;
1563 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1564 }
1565
1566 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1567 __isl_take isl_space *dim)
1568 {
1569 if (!dim)
1570 return NULL;
1571 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1572 }
1573
1574 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1575 __isl_take isl_space *dim,
1576 isl_int v)
1577 {
1578 struct isl_qpolynomial *qp;
1579 struct isl_upoly_cst *cst;
1580
1581 if (!dim)
1582 return NULL;
1583
1584 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1585 if (!qp)
1586 return NULL;
1587
1588 cst = isl_upoly_as_cst(qp->upoly);
1589 isl_int_set(cst->n, v);
1590
1591 return qp;
1592 }
1593
1594 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1595 isl_int *n, isl_int *d)
1596 {
1597 struct isl_upoly_cst *cst;
1598
1599 if (!qp)
1600 return -1;
1601
1602 if (!isl_upoly_is_cst(qp->upoly))
1603 return 0;
1604
1605 cst = isl_upoly_as_cst(qp->upoly);
1606 if (!cst)
1607 return -1;
1608
1609 if (n)
1610 isl_int_set(*n, cst->n);
1611 if (d)
1612 isl_int_set(*d, cst->d);
1613
1614 return 1;
1615 }
1616
1617 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1618 {
1619 int is_cst;
1620 struct isl_upoly_rec *rec;
1621
1622 if (!up)
1623 return -1;
1624
1625 if (up->var < 0)
1626 return 1;
1627
1628 rec = isl_upoly_as_rec(up);
1629 if (!rec)
1630 return -1;
1631
1632 if (rec->n > 2)
1633 return 0;
1634
1635 isl_assert(up->ctx, rec->n > 1, return -1);
1636
1637 is_cst = isl_upoly_is_cst(rec->p[1]);
1638 if (is_cst < 0)
1639 return -1;
1640 if (!is_cst)
1641 return 0;
1642
1643 return isl_upoly_is_affine(rec->p[0]);
1644 }
1645
1646 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1647 {
1648 if (!qp)
1649 return -1;
1650
1651 if (qp->div->n_row > 0)
1652 return 0;
1653
1654 return isl_upoly_is_affine(qp->upoly);
1655 }
1656
1657 static void update_coeff(__isl_keep isl_vec *aff,
1658 __isl_keep struct isl_upoly_cst *cst, int pos)
1659 {
1660 isl_int gcd;
1661 isl_int f;
1662
1663 if (isl_int_is_zero(cst->n))
1664 return;
1665
1666 isl_int_init(gcd);
1667 isl_int_init(f);
1668 isl_int_gcd(gcd, cst->d, aff->el[0]);
1669 isl_int_divexact(f, cst->d, gcd);
1670 isl_int_divexact(gcd, aff->el[0], gcd);
1671 isl_seq_scale(aff->el, aff->el, f, aff->size);
1672 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1673 isl_int_clear(gcd);
1674 isl_int_clear(f);
1675 }
1676
1677 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1678 __isl_keep isl_vec *aff)
1679 {
1680 struct isl_upoly_cst *cst;
1681 struct isl_upoly_rec *rec;
1682
1683 if (!up || !aff)
1684 return -1;
1685
1686 if (up->var < 0) {
1687 struct isl_upoly_cst *cst;
1688
1689 cst = isl_upoly_as_cst(up);
1690 if (!cst)
1691 return -1;
1692 update_coeff(aff, cst, 0);
1693 return 0;
1694 }
1695
1696 rec = isl_upoly_as_rec(up);
1697 if (!rec)
1698 return -1;
1699 isl_assert(up->ctx, rec->n == 2, return -1);
1700
1701 cst = isl_upoly_as_cst(rec->p[1]);
1702 if (!cst)
1703 return -1;
1704 update_coeff(aff, cst, 1 + up->var);
1705
1706 return isl_upoly_update_affine(rec->p[0], aff);
1707 }
1708
1709 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1710 __isl_keep isl_qpolynomial *qp)
1711 {
1712 isl_vec *aff;
1713 unsigned d;
1714
1715 if (!qp)
1716 return NULL;
1717
1718 d = isl_space_dim(qp->dim, isl_dim_all);
1719 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1720 if (!aff)
1721 return NULL;
1722
1723 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1724 isl_int_set_si(aff->el[0], 1);
1725
1726 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1727 goto error;
1728
1729 return aff;
1730 error:
1731 isl_vec_free(aff);
1732 return NULL;
1733 }
1734
1735 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1736 __isl_keep isl_qpolynomial *qp2)
1737 {
1738 int equal;
1739
1740 if (!qp1 || !qp2)
1741 return -1;
1742
1743 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1744 if (equal < 0 || !equal)
1745 return equal;
1746
1747 equal = isl_mat_is_equal(qp1->div, qp2->div);
1748 if (equal < 0 || !equal)
1749 return equal;
1750
1751 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1752 }
1753
1754 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1755 {
1756 int i;
1757 struct isl_upoly_rec *rec;
1758
1759 if (isl_upoly_is_cst(up)) {
1760 struct isl_upoly_cst *cst;
1761 cst = isl_upoly_as_cst(up);
1762 if (!cst)
1763 return;
1764 isl_int_lcm(*d, *d, cst->d);
1765 return;
1766 }
1767
1768 rec = isl_upoly_as_rec(up);
1769 if (!rec)
1770 return;
1771
1772 for (i = 0; i < rec->n; ++i)
1773 upoly_update_den(rec->p[i], d);
1774 }
1775
1776 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1777 {
1778 isl_int_set_si(*d, 1);
1779 if (!qp)
1780 return;
1781 upoly_update_den(qp->upoly, d);
1782 }
1783
1784 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
1785 __isl_take isl_space *dim, int pos, int power)
1786 {
1787 struct isl_ctx *ctx;
1788
1789 if (!dim)
1790 return NULL;
1791
1792 ctx = dim->ctx;
1793
1794 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1795 }
1796
1797 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
1798 enum isl_dim_type type, unsigned pos)
1799 {
1800 if (!dim)
1801 return NULL;
1802
1803 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1804 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1805
1806 if (type == isl_dim_set)
1807 pos += isl_space_dim(dim, isl_dim_param);
1808
1809 return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
1810 error:
1811 isl_space_free(dim);
1812 return NULL;
1813 }
1814
1815 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1816 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1817 {
1818 int i;
1819 struct isl_upoly_rec *rec;
1820 struct isl_upoly *base, *res;
1821
1822 if (!up)
1823 return NULL;
1824
1825 if (isl_upoly_is_cst(up))
1826 return up;
1827
1828 if (up->var < first)
1829 return up;
1830
1831 rec = isl_upoly_as_rec(up);
1832 if (!rec)
1833 goto error;
1834
1835 isl_assert(up->ctx, rec->n >= 1, goto error);
1836
1837 if (up->var >= first + n)
1838 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1839 else
1840 base = isl_upoly_copy(subs[up->var - first]);
1841
1842 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1843 for (i = rec->n - 2; i >= 0; --i) {
1844 struct isl_upoly *t;
1845 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1846 res = isl_upoly_mul(res, isl_upoly_copy(base));
1847 res = isl_upoly_sum(res, t);
1848 }
1849
1850 isl_upoly_free(base);
1851 isl_upoly_free(up);
1852
1853 return res;
1854 error:
1855 isl_upoly_free(up);
1856 return NULL;
1857 }
1858
1859 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1860 isl_int denom, unsigned len)
1861 {
1862 int i;
1863 struct isl_upoly *up;
1864
1865 isl_assert(ctx, len >= 1, return NULL);
1866
1867 up = isl_upoly_rat_cst(ctx, f[0], denom);
1868 for (i = 0; i < len - 1; ++i) {
1869 struct isl_upoly *t;
1870 struct isl_upoly *c;
1871
1872 if (isl_int_is_zero(f[1 + i]))
1873 continue;
1874
1875 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1876 t = isl_upoly_var_pow(ctx, i, 1);
1877 t = isl_upoly_mul(c, t);
1878 up = isl_upoly_sum(up, t);
1879 }
1880
1881 return up;
1882 }
1883
1884 /* Remove common factor of non-constant terms and denominator.
1885 */
1886 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1887 {
1888 isl_ctx *ctx = qp->div->ctx;
1889 unsigned total = qp->div->n_col - 2;
1890
1891 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1892 isl_int_gcd(ctx->normalize_gcd,
1893 ctx->normalize_gcd, qp->div->row[div][0]);
1894 if (isl_int_is_one(ctx->normalize_gcd))
1895 return;
1896
1897 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1898 ctx->normalize_gcd, total);
1899 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1900 ctx->normalize_gcd);
1901 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1902 ctx->normalize_gcd);
1903 }
1904
1905 /* Replace the integer division identified by "div" by the polynomial "s".
1906 * The integer division is assumed not to appear in the definition
1907 * of any other integer divisions.
1908 */
1909 static __isl_give isl_qpolynomial *substitute_div(
1910 __isl_take isl_qpolynomial *qp,
1911 int div, __isl_take struct isl_upoly *s)
1912 {
1913 int i;
1914 int total;
1915 int *reordering;
1916
1917 if (!qp || !s)
1918 goto error;
1919
1920 qp = isl_qpolynomial_cow(qp);
1921 if (!qp)
1922 goto error;
1923
1924 total = isl_space_dim(qp->dim, isl_dim_all);
1925 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1926 if (!qp->upoly)
1927 goto error;
1928
1929 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1930 if (!reordering)
1931 goto error;
1932 for (i = 0; i < total + div; ++i)
1933 reordering[i] = i;
1934 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1935 reordering[i] = i - 1;
1936 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1937 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1938 qp->upoly = reorder(qp->upoly, reordering);
1939 free(reordering);
1940
1941 if (!qp->upoly || !qp->div)
1942 goto error;
1943
1944 isl_upoly_free(s);
1945 return qp;
1946 error:
1947 isl_qpolynomial_free(qp);
1948 isl_upoly_free(s);
1949 return NULL;
1950 }
1951
1952 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1953 * divisions because d is equal to 1 by their definition, i.e., e.
1954 */
1955 static __isl_give isl_qpolynomial *substitute_non_divs(
1956 __isl_take isl_qpolynomial *qp)
1957 {
1958 int i, j;
1959 int total;
1960 struct isl_upoly *s;
1961
1962 if (!qp)
1963 return NULL;
1964
1965 total = isl_space_dim(qp->dim, isl_dim_all);
1966 for (i = 0; qp && i < qp->div->n_row; ++i) {
1967 if (!isl_int_is_one(qp->div->row[i][0]))
1968 continue;
1969 for (j = i + 1; j < qp->div->n_row; ++j) {
1970 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1971 continue;
1972 isl_seq_combine(qp->div->row[j] + 1,
1973 qp->div->ctx->one, qp->div->row[j] + 1,
1974 qp->div->row[j][2 + total + i],
1975 qp->div->row[i] + 1, 1 + total + i);
1976 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1977 normalize_div(qp, j);
1978 }
1979 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1980 qp->div->row[i][0], qp->div->n_col - 1);
1981 qp = substitute_div(qp, i, s);
1982 --i;
1983 }
1984
1985 return qp;
1986 }
1987
1988 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1989 * with d the denominator. When replacing the coefficient e of x by
1990 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1991 * inside the division, so we need to add floor(e/d) * x outside.
1992 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1993 * to adjust the coefficient of x in each later div that depends on the
1994 * current div "div" and also in the affine expression "aff"
1995 * (if it too depends on "div").
1996 */
1997 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1998 __isl_keep isl_vec *aff)
1999 {
2000 int i, j;
2001 isl_int v;
2002 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2003
2004 isl_int_init(v);
2005 for (i = 0; i < 1 + total + div; ++i) {
2006 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2007 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2008 continue;
2009 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2010 isl_int_fdiv_r(qp->div->row[div][1 + i],
2011 qp->div->row[div][1 + i], qp->div->row[div][0]);
2012 if (!isl_int_is_zero(aff->el[1 + total + div]))
2013 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
2014 for (j = div + 1; j < qp->div->n_row; ++j) {
2015 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2016 continue;
2017 isl_int_addmul(qp->div->row[j][1 + i],
2018 v, qp->div->row[j][2 + total + div]);
2019 }
2020 }
2021 isl_int_clear(v);
2022 }
2023
2024 /* Check if the last non-zero coefficient is bigger that half of the
2025 * denominator. If so, we will invert the div to further reduce the number
2026 * of distinct divs that may appear.
2027 * If the last non-zero coefficient is exactly half the denominator,
2028 * then we continue looking for earlier coefficients that are bigger
2029 * than half the denominator.
2030 */
2031 static int needs_invert(__isl_keep isl_mat *div, int row)
2032 {
2033 int i;
2034 int cmp;
2035
2036 for (i = div->n_col - 1; i >= 1; --i) {
2037 if (isl_int_is_zero(div->row[row][i]))
2038 continue;
2039 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2040 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2041 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2042 if (cmp)
2043 return cmp > 0;
2044 if (i == 1)
2045 return 1;
2046 }
2047
2048 return 0;
2049 }
2050
2051 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2052 * We only invert the coefficients of e (and the coefficient of q in
2053 * later divs and in "aff"). After calling this function, the
2054 * coefficients of e should be reduced again.
2055 */
2056 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2057 __isl_keep isl_vec *aff)
2058 {
2059 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2060
2061 isl_seq_neg(qp->div->row[div] + 1,
2062 qp->div->row[div] + 1, qp->div->n_col - 1);
2063 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2064 isl_int_add(qp->div->row[div][1],
2065 qp->div->row[div][1], qp->div->row[div][0]);
2066 if (!isl_int_is_zero(aff->el[1 + total + div]))
2067 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2068 isl_mat_col_mul(qp->div, 2 + total + div,
2069 qp->div->ctx->negone, 2 + total + div);
2070 }
2071
2072 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2073 * in the interval [0, d-1], with d the denominator and such that the
2074 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2075 *
2076 * After the reduction, some divs may have become redundant or identical,
2077 * so we call substitute_non_divs and sort_divs. If these functions
2078 * eliminate divs or merge two or more divs into one, the coefficients
2079 * of the enclosing divs may have to be reduced again, so we call
2080 * ourselves recursively if the number of divs decreases.
2081 */
2082 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2083 {
2084 int i;
2085 isl_vec *aff = NULL;
2086 struct isl_upoly *s;
2087 unsigned n_div;
2088
2089 if (!qp)
2090 return NULL;
2091
2092 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2093 aff = isl_vec_clr(aff);
2094 if (!aff)
2095 goto error;
2096
2097 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2098
2099 for (i = 0; i < qp->div->n_row; ++i) {
2100 normalize_div(qp, i);
2101 reduce_div(qp, i, aff);
2102 if (needs_invert(qp->div, i)) {
2103 invert_div(qp, i, aff);
2104 reduce_div(qp, i, aff);
2105 }
2106 }
2107
2108 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2109 qp->div->ctx->one, aff->size);
2110 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2111 isl_upoly_free(s);
2112 if (!qp->upoly)
2113 goto error;
2114
2115 isl_vec_free(aff);
2116
2117 n_div = qp->div->n_row;
2118 qp = substitute_non_divs(qp);
2119 qp = sort_divs(qp);
2120 if (qp && qp->div->n_row < n_div)
2121 return reduce_divs(qp);
2122
2123 return qp;
2124 error:
2125 isl_qpolynomial_free(qp);
2126 isl_vec_free(aff);
2127 return NULL;
2128 }
2129
2130 /* Assumes each div only depends on earlier divs.
2131 */
2132 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2133 int power)
2134 {
2135 struct isl_qpolynomial *qp = NULL;
2136 struct isl_upoly_rec *rec;
2137 struct isl_upoly_cst *cst;
2138 int i, d;
2139 int pos;
2140
2141 if (!div)
2142 return NULL;
2143
2144 d = div->line - div->bmap->div;
2145
2146 pos = isl_space_dim(div->bmap->dim, isl_dim_all) + d;
2147 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2148 qp = isl_qpolynomial_alloc(isl_basic_map_get_space(div->bmap),
2149 div->bmap->n_div, &rec->up);
2150 if (!qp)
2151 goto error;
2152
2153 for (i = 0; i < div->bmap->n_div; ++i)
2154 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2155
2156 for (i = 0; i < 1 + power; ++i) {
2157 rec->p[i] = isl_upoly_zero(div->ctx);
2158 if (!rec->p[i])
2159 goto error;
2160 rec->n++;
2161 }
2162 cst = isl_upoly_as_cst(rec->p[power]);
2163 isl_int_set_si(cst->n, 1);
2164
2165 isl_div_free(div);
2166
2167 qp = reduce_divs(qp);
2168
2169 return qp;
2170 error:
2171 isl_qpolynomial_free(qp);
2172 isl_div_free(div);
2173 return NULL;
2174 }
2175
2176 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2177 {
2178 return isl_qpolynomial_div_pow(div, 1);
2179 }
2180
2181 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2182 __isl_take isl_space *dim, const isl_int n, const isl_int d)
2183 {
2184 struct isl_qpolynomial *qp;
2185 struct isl_upoly_cst *cst;
2186
2187 if (!dim)
2188 return NULL;
2189
2190 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2191 if (!qp)
2192 return NULL;
2193
2194 cst = isl_upoly_as_cst(qp->upoly);
2195 isl_int_set(cst->n, n);
2196 isl_int_set(cst->d, d);
2197
2198 return qp;
2199 }
2200
2201 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2202 {
2203 struct isl_upoly_rec *rec;
2204 int i;
2205
2206 if (!up)
2207 return -1;
2208
2209 if (isl_upoly_is_cst(up))
2210 return 0;
2211
2212 if (up->var < d)
2213 active[up->var] = 1;
2214
2215 rec = isl_upoly_as_rec(up);
2216 for (i = 0; i < rec->n; ++i)
2217 if (up_set_active(rec->p[i], active, d) < 0)
2218 return -1;
2219
2220 return 0;
2221 }
2222
2223 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2224 {
2225 int i, j;
2226 int d = isl_space_dim(qp->dim, isl_dim_all);
2227
2228 if (!qp || !active)
2229 return -1;
2230
2231 for (i = 0; i < d; ++i)
2232 for (j = 0; j < qp->div->n_row; ++j) {
2233 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2234 continue;
2235 active[i] = 1;
2236 break;
2237 }
2238
2239 return up_set_active(qp->upoly, active, d);
2240 }
2241
2242 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2243 enum isl_dim_type type, unsigned first, unsigned n)
2244 {
2245 int i;
2246 int *active = NULL;
2247 int involves = 0;
2248
2249 if (!qp)
2250 return -1;
2251 if (n == 0)
2252 return 0;
2253
2254 isl_assert(qp->dim->ctx,
2255 first + n <= isl_qpolynomial_dim(qp, type), return -1);
2256 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2257 type == isl_dim_in, return -1);
2258
2259 active = isl_calloc_array(qp->dim->ctx, int,
2260 isl_space_dim(qp->dim, isl_dim_all));
2261 if (set_active(qp, active) < 0)
2262 goto error;
2263
2264 if (type == isl_dim_in)
2265 first += isl_space_dim(qp->dim, isl_dim_param);
2266 for (i = 0; i < n; ++i)
2267 if (active[first + i]) {
2268 involves = 1;
2269 break;
2270 }
2271
2272 free(active);
2273
2274 return involves;
2275 error:
2276 free(active);
2277 return -1;
2278 }
2279
2280 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2281 * of the divs that do appear in the quasi-polynomial.
2282 */
2283 static __isl_give isl_qpolynomial *remove_redundant_divs(
2284 __isl_take isl_qpolynomial *qp)
2285 {
2286 int i, j;
2287 int d;
2288 int len;
2289 int skip;
2290 int *active = NULL;
2291 int *reordering = NULL;
2292 int redundant = 0;
2293 int n_div;
2294 isl_ctx *ctx;
2295
2296 if (!qp)
2297 return NULL;
2298 if (qp->div->n_row == 0)
2299 return qp;
2300
2301 d = isl_space_dim(qp->dim, isl_dim_all);
2302 len = qp->div->n_col - 2;
2303 ctx = isl_qpolynomial_get_ctx(qp);
2304 active = isl_calloc_array(ctx, int, len);
2305 if (!active)
2306 goto error;
2307
2308 if (up_set_active(qp->upoly, active, len) < 0)
2309 goto error;
2310
2311 for (i = qp->div->n_row - 1; i >= 0; --i) {
2312 if (!active[d + i]) {
2313 redundant = 1;
2314 continue;
2315 }
2316 for (j = 0; j < i; ++j) {
2317 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2318 continue;
2319 active[d + j] = 1;
2320 break;
2321 }
2322 }
2323
2324 if (!redundant) {
2325 free(active);
2326 return qp;
2327 }
2328
2329 reordering = isl_alloc_array(qp->div->ctx, int, len);
2330 if (!reordering)
2331 goto error;
2332
2333 for (i = 0; i < d; ++i)
2334 reordering[i] = i;
2335
2336 skip = 0;
2337 n_div = qp->div->n_row;
2338 for (i = 0; i < n_div; ++i) {
2339 if (!active[d + i]) {
2340 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2341 qp->div = isl_mat_drop_cols(qp->div,
2342 2 + d + i - skip, 1);
2343 skip++;
2344 }
2345 reordering[d + i] = d + i - skip;
2346 }
2347
2348 qp->upoly = reorder(qp->upoly, reordering);
2349
2350 if (!qp->upoly || !qp->div)
2351 goto error;
2352
2353 free(active);
2354 free(reordering);
2355
2356 return qp;
2357 error:
2358 free(active);
2359 free(reordering);
2360 isl_qpolynomial_free(qp);
2361 return NULL;
2362 }
2363
2364 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2365 unsigned first, unsigned n)
2366 {
2367 int i;
2368 struct isl_upoly_rec *rec;
2369
2370 if (!up)
2371 return NULL;
2372 if (n == 0 || up->var < 0 || up->var < first)
2373 return up;
2374 if (up->var < first + n) {
2375 up = replace_by_constant_term(up);
2376 return isl_upoly_drop(up, first, n);
2377 }
2378 up = isl_upoly_cow(up);
2379 if (!up)
2380 return NULL;
2381 up->var -= n;
2382 rec = isl_upoly_as_rec(up);
2383 if (!rec)
2384 goto error;
2385
2386 for (i = 0; i < rec->n; ++i) {
2387 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2388 if (!rec->p[i])
2389 goto error;
2390 }
2391
2392 return up;
2393 error:
2394 isl_upoly_free(up);
2395 return NULL;
2396 }
2397
2398 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2399 __isl_take isl_qpolynomial *qp,
2400 enum isl_dim_type type, unsigned pos, const char *s)
2401 {
2402 qp = isl_qpolynomial_cow(qp);
2403 if (!qp)
2404 return NULL;
2405 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2406 if (!qp->dim)
2407 goto error;
2408 return qp;
2409 error:
2410 isl_qpolynomial_free(qp);
2411 return NULL;
2412 }
2413
2414 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2415 __isl_take isl_qpolynomial *qp,
2416 enum isl_dim_type type, unsigned first, unsigned n)
2417 {
2418 if (!qp)
2419 return NULL;
2420 if (type == isl_dim_out)
2421 isl_die(qp->dim->ctx, isl_error_invalid,
2422 "cannot drop output/set dimension",
2423 goto error);
2424 if (type == isl_dim_in)
2425 type = isl_dim_set;
2426 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2427 return qp;
2428
2429 qp = isl_qpolynomial_cow(qp);
2430 if (!qp)
2431 return NULL;
2432
2433 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2434 goto error);
2435 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2436 type == isl_dim_set, goto error);
2437
2438 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2439 if (!qp->dim)
2440 goto error;
2441
2442 if (type == isl_dim_set)
2443 first += isl_space_dim(qp->dim, isl_dim_param);
2444
2445 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2446 if (!qp->div)
2447 goto error;
2448
2449 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2450 if (!qp->upoly)
2451 goto error;
2452
2453 return qp;
2454 error:
2455 isl_qpolynomial_free(qp);
2456 return NULL;
2457 }
2458
2459 /* Project the domain of the quasi-polynomial onto its parameter space.
2460 * The quasi-polynomial may not involve any of the domain dimensions.
2461 */
2462 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2463 __isl_take isl_qpolynomial *qp)
2464 {
2465 isl_space *space;
2466 unsigned n;
2467 int involves;
2468
2469 n = isl_qpolynomial_dim(qp, isl_dim_in);
2470 involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2471 if (involves < 0)
2472 return isl_qpolynomial_free(qp);
2473 if (involves)
2474 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2475 "polynomial involves some of the domain dimensions",
2476 return isl_qpolynomial_free(qp));
2477 qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2478 space = isl_qpolynomial_get_domain_space(qp);
2479 space = isl_space_params(space);
2480 qp = isl_qpolynomial_reset_domain_space(qp, space);
2481 return qp;
2482 }
2483
2484 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2485 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2486 {
2487 int i, j, k;
2488 isl_int denom;
2489 unsigned total;
2490 unsigned n_div;
2491 struct isl_upoly *up;
2492
2493 if (!eq)
2494 goto error;
2495 if (eq->n_eq == 0) {
2496 isl_basic_set_free(eq);
2497 return qp;
2498 }
2499
2500 qp = isl_qpolynomial_cow(qp);
2501 if (!qp)
2502 goto error;
2503 qp->div = isl_mat_cow(qp->div);
2504 if (!qp->div)
2505 goto error;
2506
2507 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2508 n_div = eq->n_div;
2509 isl_int_init(denom);
2510 for (i = 0; i < eq->n_eq; ++i) {
2511 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2512 if (j < 0 || j == 0 || j >= total)
2513 continue;
2514
2515 for (k = 0; k < qp->div->n_row; ++k) {
2516 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2517 continue;
2518 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2519 &qp->div->row[k][0]);
2520 normalize_div(qp, k);
2521 }
2522
2523 if (isl_int_is_pos(eq->eq[i][j]))
2524 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2525 isl_int_abs(denom, eq->eq[i][j]);
2526 isl_int_set_si(eq->eq[i][j], 0);
2527
2528 up = isl_upoly_from_affine(qp->dim->ctx,
2529 eq->eq[i], denom, total);
2530 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2531 isl_upoly_free(up);
2532 }
2533 isl_int_clear(denom);
2534
2535 if (!qp->upoly)
2536 goto error;
2537
2538 isl_basic_set_free(eq);
2539
2540 qp = substitute_non_divs(qp);
2541 qp = sort_divs(qp);
2542
2543 return qp;
2544 error:
2545 isl_basic_set_free(eq);
2546 isl_qpolynomial_free(qp);
2547 return NULL;
2548 }
2549
2550 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2551 */
2552 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2553 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2554 {
2555 if (!qp || !eq)
2556 goto error;
2557 if (qp->div->n_row > 0)
2558 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2559 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2560 error:
2561 isl_basic_set_free(eq);
2562 isl_qpolynomial_free(qp);
2563 return NULL;
2564 }
2565
2566 static __isl_give isl_basic_set *add_div_constraints(
2567 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2568 {
2569 int i;
2570 unsigned total;
2571
2572 if (!bset || !div)
2573 goto error;
2574
2575 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2576 if (!bset)
2577 goto error;
2578 total = isl_basic_set_total_dim(bset);
2579 for (i = 0; i < div->n_row; ++i)
2580 if (isl_basic_set_add_div_constraints_var(bset,
2581 total - div->n_row + i, div->row[i]) < 0)
2582 goto error;
2583
2584 isl_mat_free(div);
2585 return bset;
2586 error:
2587 isl_mat_free(div);
2588 isl_basic_set_free(bset);
2589 return NULL;
2590 }
2591
2592 /* Look for equalities among the variables shared by context and qp
2593 * and the integer divisions of qp, if any.
2594 * The equalities are then used to eliminate variables and/or integer
2595 * divisions from qp.
2596 */
2597 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2598 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2599 {
2600 isl_basic_set *aff;
2601
2602 if (!qp)
2603 goto error;
2604 if (qp->div->n_row > 0) {
2605 isl_basic_set *bset;
2606 context = isl_set_add_dims(context, isl_dim_set,
2607 qp->div->n_row);
2608 bset = isl_basic_set_universe(isl_set_get_space(context));
2609 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2610 context = isl_set_intersect(context,
2611 isl_set_from_basic_set(bset));
2612 }
2613
2614 aff = isl_set_affine_hull(context);
2615 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2616 error:
2617 isl_qpolynomial_free(qp);
2618 isl_set_free(context);
2619 return NULL;
2620 }
2621
2622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2623 __isl_take isl_qpolynomial *qp)
2624 {
2625 isl_set *dom;
2626
2627 if (!qp)
2628 return NULL;
2629 if (isl_qpolynomial_is_zero(qp)) {
2630 isl_space *dim = isl_qpolynomial_get_space(qp);
2631 isl_qpolynomial_free(qp);
2632 return isl_pw_qpolynomial_zero(dim);
2633 }
2634
2635 dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
2636 return isl_pw_qpolynomial_alloc(dom, qp);
2637 }
2638
2639 #undef PW
2640 #define PW isl_pw_qpolynomial
2641 #undef EL
2642 #define EL isl_qpolynomial
2643 #undef EL_IS_ZERO
2644 #define EL_IS_ZERO is_zero
2645 #undef ZERO
2646 #define ZERO zero
2647 #undef IS_ZERO
2648 #define IS_ZERO is_zero
2649 #undef FIELD
2650 #define FIELD qp
2651
2652 #include <isl_pw_templ.c>
2653
2654 #undef UNION
2655 #define UNION isl_union_pw_qpolynomial
2656 #undef PART
2657 #define PART isl_pw_qpolynomial
2658 #undef PARTS
2659 #define PARTS pw_qpolynomial
2660 #define ALIGN_DOMAIN
2661
2662 #include <isl_union_templ.c>
2663
2664 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2665 {
2666 if (!pwqp)
2667 return -1;
2668
2669 if (pwqp->n != -1)
2670 return 0;
2671
2672 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2673 return 0;
2674
2675 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2676 }
2677
2678 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2679 __isl_take isl_pw_qpolynomial *pwqp1,
2680 __isl_take isl_pw_qpolynomial *pwqp2)
2681 {
2682 int i, j, n;
2683 struct isl_pw_qpolynomial *res;
2684
2685 if (!pwqp1 || !pwqp2)
2686 goto error;
2687
2688 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2689 goto error);
2690
2691 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2692 isl_pw_qpolynomial_free(pwqp2);
2693 return pwqp1;
2694 }
2695
2696 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2697 isl_pw_qpolynomial_free(pwqp1);
2698 return pwqp2;
2699 }
2700
2701 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2702 isl_pw_qpolynomial_free(pwqp1);
2703 return pwqp2;
2704 }
2705
2706 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2707 isl_pw_qpolynomial_free(pwqp2);
2708 return pwqp1;
2709 }
2710
2711 n = pwqp1->n * pwqp2->n;
2712 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2713
2714 for (i = 0; i < pwqp1->n; ++i) {
2715 for (j = 0; j < pwqp2->n; ++j) {
2716 struct isl_set *common;
2717 struct isl_qpolynomial *prod;
2718 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2719 isl_set_copy(pwqp2->p[j].set));
2720 if (isl_set_plain_is_empty(common)) {
2721 isl_set_free(common);
2722 continue;
2723 }
2724
2725 prod = isl_qpolynomial_mul(
2726 isl_qpolynomial_copy(pwqp1->p[i].qp),
2727 isl_qpolynomial_copy(pwqp2->p[j].qp));
2728
2729 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2730 }
2731 }
2732
2733 isl_pw_qpolynomial_free(pwqp1);
2734 isl_pw_qpolynomial_free(pwqp2);
2735
2736 return res;
2737 error:
2738 isl_pw_qpolynomial_free(pwqp1);
2739 isl_pw_qpolynomial_free(pwqp2);
2740 return NULL;
2741 }
2742
2743 __isl_give struct isl_upoly *isl_upoly_eval(
2744 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2745 {
2746 int i;
2747 struct isl_upoly_rec *rec;
2748 struct isl_upoly *res;
2749 struct isl_upoly *base;
2750
2751 if (isl_upoly_is_cst(up)) {
2752 isl_vec_free(vec);
2753 return up;
2754 }
2755
2756 rec = isl_upoly_as_rec(up);
2757 if (!rec)
2758 goto error;
2759
2760 isl_assert(up->ctx, rec->n >= 1, goto error);
2761
2762 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2763
2764 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2765 isl_vec_copy(vec));
2766
2767 for (i = rec->n - 2; i >= 0; --i) {
2768 res = isl_upoly_mul(res, isl_upoly_copy(base));
2769 res = isl_upoly_sum(res,
2770 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2771 isl_vec_copy(vec)));
2772 }
2773
2774 isl_upoly_free(base);
2775 isl_upoly_free(up);
2776 isl_vec_free(vec);
2777 return res;
2778 error:
2779 isl_upoly_free(up);
2780 isl_vec_free(vec);
2781 return NULL;
2782 }
2783
2784 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2785 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2786 {
2787 isl_vec *ext;
2788 struct isl_upoly *up;
2789 isl_space *dim;
2790
2791 if (!qp || !pnt)
2792 goto error;
2793 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2794
2795 if (qp->div->n_row == 0)
2796 ext = isl_vec_copy(pnt->vec);
2797 else {
2798 int i;
2799 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2800 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2801 if (!ext)
2802 goto error;
2803
2804 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2805 for (i = 0; i < qp->div->n_row; ++i) {
2806 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2807 1 + dim + i, &ext->el[1+dim+i]);
2808 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2809 qp->div->row[i][0]);
2810 }
2811 }
2812
2813 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2814 if (!up)
2815 goto error;
2816
2817 dim = isl_space_copy(qp->dim);
2818 isl_qpolynomial_free(qp);
2819 isl_point_free(pnt);
2820
2821 return isl_qpolynomial_alloc(dim, 0, up);
2822 error:
2823 isl_qpolynomial_free(qp);
2824 isl_point_free(pnt);
2825 return NULL;
2826 }
2827
2828 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2829 __isl_keep struct isl_upoly_cst *cst2)
2830 {
2831 int cmp;
2832 isl_int t;
2833 isl_int_init(t);
2834 isl_int_mul(t, cst1->n, cst2->d);
2835 isl_int_submul(t, cst2->n, cst1->d);
2836 cmp = isl_int_sgn(t);
2837 isl_int_clear(t);
2838 return cmp;
2839 }
2840
2841 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2842 __isl_keep isl_qpolynomial *qp2)
2843 {
2844 struct isl_upoly_cst *cst1, *cst2;
2845
2846 if (!qp1 || !qp2)
2847 return -1;
2848 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2849 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2850 if (isl_qpolynomial_is_nan(qp1))
2851 return -1;
2852 if (isl_qpolynomial_is_nan(qp2))
2853 return -1;
2854 cst1 = isl_upoly_as_cst(qp1->upoly);
2855 cst2 = isl_upoly_as_cst(qp2->upoly);
2856
2857 return isl_upoly_cmp(cst1, cst2) <= 0;
2858 }
2859
2860 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2861 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2862 {
2863 struct isl_upoly_cst *cst1, *cst2;
2864 int cmp;
2865
2866 if (!qp1 || !qp2)
2867 goto error;
2868 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2869 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2870 cst1 = isl_upoly_as_cst(qp1->upoly);
2871 cst2 = isl_upoly_as_cst(qp2->upoly);
2872 cmp = isl_upoly_cmp(cst1, cst2);
2873
2874 if (cmp <= 0) {
2875 isl_qpolynomial_free(qp2);
2876 } else {
2877 isl_qpolynomial_free(qp1);
2878 qp1 = qp2;
2879 }
2880 return qp1;
2881 error:
2882 isl_qpolynomial_free(qp1);
2883 isl_qpolynomial_free(qp2);
2884 return NULL;
2885 }
2886
2887 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2888 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2889 {
2890 struct isl_upoly_cst *cst1, *cst2;
2891 int cmp;
2892
2893 if (!qp1 || !qp2)
2894 goto error;
2895 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2896 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2897 cst1 = isl_upoly_as_cst(qp1->upoly);
2898 cst2 = isl_upoly_as_cst(qp2->upoly);
2899 cmp = isl_upoly_cmp(cst1, cst2);
2900
2901 if (cmp >= 0) {
2902 isl_qpolynomial_free(qp2);
2903 } else {
2904 isl_qpolynomial_free(qp1);
2905 qp1 = qp2;
2906 }
2907 return qp1;
2908 error:
2909 isl_qpolynomial_free(qp1);
2910 isl_qpolynomial_free(qp2);
2911 return NULL;
2912 }
2913
2914 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2915 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2916 unsigned first, unsigned n)
2917 {
2918 unsigned total;
2919 unsigned g_pos;
2920 int *exp;
2921
2922 if (!qp)
2923 return NULL;
2924 if (type == isl_dim_out)
2925 isl_die(qp->div->ctx, isl_error_invalid,
2926 "cannot insert output/set dimensions",
2927 goto error);
2928 if (type == isl_dim_in)
2929 type = isl_dim_set;
2930 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2931 return qp;
2932
2933 qp = isl_qpolynomial_cow(qp);
2934 if (!qp)
2935 return NULL;
2936
2937 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2938 goto error);
2939
2940 g_pos = pos(qp->dim, type) + first;
2941
2942 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2943 if (!qp->div)
2944 goto error;
2945
2946 total = qp->div->n_col - 2;
2947 if (total > g_pos) {
2948 int i;
2949 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2950 if (!exp)
2951 goto error;
2952 for (i = 0; i < total - g_pos; ++i)
2953 exp[i] = i + n;
2954 qp->upoly = expand(qp->upoly, exp, g_pos);
2955 free(exp);
2956 if (!qp->upoly)
2957 goto error;
2958 }
2959
2960 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2961 if (!qp->dim)
2962 goto error;
2963
2964 return qp;
2965 error:
2966 isl_qpolynomial_free(qp);
2967 return NULL;
2968 }
2969
2970 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2971 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2972 {
2973 unsigned pos;
2974
2975 pos = isl_qpolynomial_dim(qp, type);
2976
2977 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2978 }
2979
2980 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2981 __isl_take isl_pw_qpolynomial *pwqp,
2982 enum isl_dim_type type, unsigned n)
2983 {
2984 unsigned pos;
2985
2986 pos = isl_pw_qpolynomial_dim(pwqp, type);
2987
2988 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2989 }
2990
2991 static int *reordering_move(isl_ctx *ctx,
2992 unsigned len, unsigned dst, unsigned src, unsigned n)
2993 {
2994 int i;
2995 int *reordering;
2996
2997 reordering = isl_alloc_array(ctx, int, len);
2998 if (!reordering)
2999 return NULL;
3000
3001 if (dst <= src) {
3002 for (i = 0; i < dst; ++i)
3003 reordering[i] = i;
3004 for (i = 0; i < n; ++i)
3005 reordering[src + i] = dst + i;
3006 for (i = 0; i < src - dst; ++i)
3007 reordering[dst + i] = dst + n + i;
3008 for (i = 0; i < len - src - n; ++i)
3009 reordering[src + n + i] = src + n + i;
3010 } else {
3011 for (i = 0; i < src; ++i)
3012 reordering[i] = i;
3013 for (i = 0; i < n; ++i)
3014 reordering[src + i] = dst + i;
3015 for (i = 0; i < dst - src; ++i)
3016 reordering[src + n + i] = src + i;
3017 for (i = 0; i < len - dst - n; ++i)
3018 reordering[dst + n + i] = dst + n + i;
3019 }
3020
3021 return reordering;
3022 }
3023
3024 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3025 __isl_take isl_qpolynomial *qp,
3026 enum isl_dim_type dst_type, unsigned dst_pos,
3027 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3028 {
3029 unsigned g_dst_pos;
3030 unsigned g_src_pos;
3031 int *reordering;
3032
3033 qp = isl_qpolynomial_cow(qp);
3034 if (!qp)
3035 return NULL;
3036
3037 if (dst_type == isl_dim_out || src_type == isl_dim_out)
3038 isl_die(qp->dim->ctx, isl_error_invalid,
3039 "cannot move output/set dimension",
3040 goto error);
3041 if (dst_type == isl_dim_in)
3042 dst_type = isl_dim_set;
3043 if (src_type == isl_dim_in)
3044 src_type = isl_dim_set;
3045
3046 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3047 goto error);
3048
3049 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3050 g_src_pos = pos(qp->dim, src_type) + src_pos;
3051 if (dst_type > src_type)
3052 g_dst_pos -= n;
3053
3054 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3055 if (!qp->div)
3056 goto error;
3057 qp = sort_divs(qp);
3058 if (!qp)
3059 goto error;
3060
3061 reordering = reordering_move(qp->dim->ctx,
3062 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3063 if (!reordering)
3064 goto error;
3065
3066 qp->upoly = reorder(qp->upoly, reordering);
3067 free(reordering);
3068 if (!qp->upoly)
3069 goto error;
3070
3071 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3072 if (!qp->dim)
3073 goto error;
3074
3075 return qp;
3076 error:
3077 isl_qpolynomial_free(qp);
3078 return NULL;
3079 }
3080
3081 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3082 isl_int *f, isl_int denom)
3083 {
3084 struct isl_upoly *up;
3085
3086 dim = isl_space_domain(dim);
3087 if (!dim)
3088 return NULL;
3089
3090 up = isl_upoly_from_affine(dim->ctx, f, denom,
3091 1 + isl_space_dim(dim, isl_dim_all));
3092
3093 return isl_qpolynomial_alloc(dim, 0, up);
3094 }
3095
3096 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3097 {
3098 isl_ctx *ctx;
3099 struct isl_upoly *up;
3100 isl_qpolynomial *qp;
3101
3102 if (!aff)
3103 return NULL;
3104
3105 ctx = isl_aff_get_ctx(aff);
3106 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3107 aff->v->size - 1);
3108
3109 qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3110 aff->ls->div->n_row, up);
3111 if (!qp)
3112 goto error;
3113
3114 isl_mat_free(qp->div);
3115 qp->div = isl_mat_copy(aff->ls->div);
3116 qp->div = isl_mat_cow(qp->div);
3117 if (!qp->div)
3118 goto error;
3119
3120 isl_aff_free(aff);
3121 qp = reduce_divs(qp);
3122 qp = remove_redundant_divs(qp);
3123 return qp;
3124 error:
3125 isl_aff_free(aff);
3126 return NULL;
3127 }
3128
3129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3130 __isl_take isl_pw_aff *pwaff)
3131 {
3132 int i;
3133 isl_pw_qpolynomial *pwqp;
3134
3135 if (!pwaff)
3136 return NULL;
3137
3138 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3139 pwaff->n);
3140
3141 for (i = 0; i < pwaff->n; ++i) {
3142 isl_set *dom;
3143 isl_qpolynomial *qp;
3144
3145 dom = isl_set_copy(pwaff->p[i].set);
3146 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3147 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3148 }
3149
3150 isl_pw_aff_free(pwaff);
3151 return pwqp;
3152 }
3153
3154 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3155 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3156 {
3157 isl_aff *aff;
3158
3159 aff = isl_constraint_get_bound(c, type, pos);
3160 isl_constraint_free(c);
3161 return isl_qpolynomial_from_aff(aff);
3162 }
3163
3164 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3165 * in "qp" by subs[i].
3166 */
3167 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3168 __isl_take isl_qpolynomial *qp,
3169 enum isl_dim_type type, unsigned first, unsigned n,
3170 __isl_keep isl_qpolynomial **subs)
3171 {
3172 int i;
3173 struct isl_upoly **ups;
3174
3175 if (n == 0)
3176 return qp;
3177
3178 qp = isl_qpolynomial_cow(qp);
3179 if (!qp)
3180 return NULL;
3181
3182 if (type == isl_dim_out)
3183 isl_die(qp->dim->ctx, isl_error_invalid,
3184 "cannot substitute output/set dimension",
3185 goto error);
3186 if (type == isl_dim_in)
3187 type = isl_dim_set;
3188
3189 for (i = 0; i < n; ++i)
3190 if (!subs[i])
3191 goto error;
3192
3193 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3194 goto error);
3195
3196 for (i = 0; i < n; ++i)
3197 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3198 goto error);
3199
3200 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3201 for (i = 0; i < n; ++i)
3202 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3203
3204 first += pos(qp->dim, type);
3205
3206 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3207 if (!ups)
3208 goto error;
3209 for (i = 0; i < n; ++i)
3210 ups[i] = subs[i]->upoly;
3211
3212 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3213
3214 free(ups);
3215
3216 if (!qp->upoly)
3217 goto error;
3218
3219 return qp;
3220 error:
3221 isl_qpolynomial_free(qp);
3222 return NULL;
3223 }
3224
3225 /* Extend "bset" with extra set dimensions for each integer division
3226 * in "qp" and then call "fn" with the extended bset and the polynomial
3227 * that results from replacing each of the integer divisions by the
3228 * corresponding extra set dimension.
3229 */
3230 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3231 __isl_keep isl_basic_set *bset,
3232 int (*fn)(__isl_take isl_basic_set *bset,
3233 __isl_take isl_qpolynomial *poly, void *user), void *user)
3234 {
3235 isl_space *dim;
3236 isl_mat *div;
3237 isl_qpolynomial *poly;
3238
3239 if (!qp || !bset)
3240 goto error;
3241 if (qp->div->n_row == 0)
3242 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3243 user);
3244
3245 div = isl_mat_copy(qp->div);
3246 dim = isl_space_copy(qp->dim);
3247 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3248 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3249 bset = isl_basic_set_copy(bset);
3250 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3251 bset = add_div_constraints(bset, div);
3252
3253 return fn(bset, poly, user);
3254 error:
3255 return -1;
3256 }
3257
3258 /* Return total degree in variables first (inclusive) up to last (exclusive).
3259 */
3260 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3261 {
3262 int deg = -1;
3263 int i;
3264 struct isl_upoly_rec *rec;
3265
3266 if (!up)
3267 return -2;
3268 if (isl_upoly_is_zero(up))
3269 return -1;
3270 if (isl_upoly_is_cst(up) || up->var < first)
3271 return 0;
3272
3273 rec = isl_upoly_as_rec(up);
3274 if (!rec)
3275 return -2;
3276
3277 for (i = 0; i < rec->n; ++i) {
3278 int d;
3279
3280 if (isl_upoly_is_zero(rec->p[i]))
3281 continue;
3282 d = isl_upoly_degree(rec->p[i], first, last);
3283 if (up->var < last)
3284 d += i;
3285 if (d > deg)
3286 deg = d;
3287 }
3288
3289 return deg;
3290 }
3291
3292 /* Return total degree in set variables.
3293 */
3294 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3295 {
3296 unsigned ovar;
3297 unsigned nvar;
3298
3299 if (!poly)
3300 return -2;
3301
3302 ovar = isl_space_offset(poly->dim, isl_dim_set);
3303 nvar = isl_space_dim(poly->dim, isl_dim_set);
3304 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3305 }
3306
3307 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3308 unsigned pos, int deg)
3309 {
3310 int i;
3311 struct isl_upoly_rec *rec;
3312
3313 if (!up)
3314 return NULL;
3315
3316 if (isl_upoly_is_cst(up) || up->var < pos) {
3317 if (deg == 0)
3318 return isl_upoly_copy(up);
3319 else
3320 return isl_upoly_zero(up->ctx);
3321 }
3322
3323 rec = isl_upoly_as_rec(up);
3324 if (!rec)
3325 return NULL;
3326
3327 if (up->var == pos) {
3328 if (deg < rec->n)
3329 return isl_upoly_copy(rec->p[deg]);
3330 else
3331 return isl_upoly_zero(up->ctx);
3332 }
3333
3334 up = isl_upoly_copy(up);
3335 up = isl_upoly_cow(up);
3336 rec = isl_upoly_as_rec(up);
3337 if (!rec)
3338 goto error;
3339
3340 for (i = 0; i < rec->n; ++i) {
3341 struct isl_upoly *t;
3342 t = isl_upoly_coeff(rec->p[i], pos, deg);
3343 if (!t)
3344 goto error;
3345 isl_upoly_free(rec->p[i]);
3346 rec->p[i] = t;
3347 }
3348
3349 return up;
3350 error:
3351 isl_upoly_free(up);
3352 return NULL;
3353 }
3354
3355 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3356 */
3357 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3358 __isl_keep isl_qpolynomial *qp,
3359 enum isl_dim_type type, unsigned t_pos, int deg)
3360 {
3361 unsigned g_pos;
3362 struct isl_upoly *up;
3363 isl_qpolynomial *c;
3364
3365 if (!qp)
3366 return NULL;
3367
3368 if (type == isl_dim_out)
3369 isl_die(qp->div->ctx, isl_error_invalid,
3370 "output/set dimension does not have a coefficient",
3371 return NULL);
3372 if (type == isl_dim_in)
3373 type = isl_dim_set;
3374
3375 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3376 return NULL);
3377
3378 g_pos = pos(qp->dim, type) + t_pos;
3379 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3380
3381 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3382 if (!c)
3383 return NULL;
3384 isl_mat_free(c->div);
3385 c->div = isl_mat_copy(qp->div);
3386 if (!c->div)
3387 goto error;
3388 return c;
3389 error:
3390 isl_qpolynomial_free(c);
3391 return NULL;
3392 }
3393
3394 /* Homogenize the polynomial in the variables first (inclusive) up to
3395 * last (exclusive) by inserting powers of variable first.
3396 * Variable first is assumed not to appear in the input.
3397 */
3398 __isl_give struct isl_upoly *isl_upoly_homogenize(
3399 __isl_take struct isl_upoly *up, int deg, int target,
3400 int first, int last)
3401 {
3402 int i;
3403 struct isl_upoly_rec *rec;
3404
3405 if (!up)
3406 return NULL;
3407 if (isl_upoly_is_zero(up))
3408 return up;
3409 if (deg == target)
3410 return up;
3411 if (isl_upoly_is_cst(up) || up->var < first) {
3412 struct isl_upoly *hom;
3413
3414 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3415 if (!hom)
3416 goto error;
3417 rec = isl_upoly_as_rec(hom);
3418 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3419
3420 return hom;
3421 }
3422
3423 up = isl_upoly_cow(up);
3424 rec = isl_upoly_as_rec(up);
3425 if (!rec)
3426 goto error;
3427
3428 for (i = 0; i < rec->n; ++i) {
3429 if (isl_upoly_is_zero(rec->p[i]))
3430 continue;
3431 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3432 up->var < last ? deg + i : i, target,
3433 first, last);
3434 if (!rec->p[i])
3435 goto error;
3436 }
3437
3438 return up;
3439 error:
3440 isl_upoly_free(up);
3441 return NULL;
3442 }
3443
3444 /* Homogenize the polynomial in the set variables by introducing
3445 * powers of an extra set variable at position 0.
3446 */
3447 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3448 __isl_take isl_qpolynomial *poly)
3449 {
3450 unsigned ovar;
3451 unsigned nvar;
3452 int deg = isl_qpolynomial_degree(poly);
3453
3454 if (deg < -1)
3455 goto error;
3456
3457 poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3458 poly = isl_qpolynomial_cow(poly);
3459 if (!poly)
3460 goto error;
3461
3462 ovar = isl_space_offset(poly->dim, isl_dim_set);
3463 nvar = isl_space_dim(poly->dim, isl_dim_set);
3464 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3465 ovar, ovar + nvar);
3466 if (!poly->upoly)
3467 goto error;
3468
3469 return poly;
3470 error:
3471 isl_qpolynomial_free(poly);
3472 return NULL;
3473 }
3474
3475 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3476 __isl_take isl_mat *div)
3477 {
3478 isl_term *term;
3479 int n;
3480
3481 if (!dim || !div)
3482 goto error;
3483
3484 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3485
3486 term = isl_calloc(dim->ctx, struct isl_term,
3487 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3488 if (!term)
3489 goto error;
3490
3491 term->ref = 1;
3492 term->dim = dim;
3493 term->div = div;
3494 isl_int_init(term->n);
3495 isl_int_init(term->d);
3496
3497 return term;
3498 error:
3499 isl_space_free(dim);
3500 isl_mat_free(div);
3501 return NULL;
3502 }
3503
3504 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3505 {
3506 if (!term)
3507 return NULL;
3508
3509 term->ref++;
3510 return term;
3511 }
3512
3513 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3514 {
3515 int i;
3516 isl_term *dup;
3517 unsigned total;
3518
3519 if (term)
3520 return NULL;
3521
3522 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3523
3524 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3525 if (!dup)
3526 return NULL;
3527
3528 isl_int_set(dup->n, term->n);
3529 isl_int_set(dup->d, term->d);
3530
3531 for (i = 0; i < total; ++i)
3532 dup->pow[i] = term->pow[i];
3533
3534 return dup;
3535 }
3536
3537 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3538 {
3539 if (!term)
3540 return NULL;
3541
3542 if (term->ref == 1)
3543 return term;
3544 term->ref--;
3545 return isl_term_dup(term);
3546 }
3547
3548 void isl_term_free(__isl_take isl_term *term)
3549 {
3550 if (!term)
3551 return;
3552
3553 if (--term->ref > 0)
3554 return;
3555
3556 isl_space_free(term->dim);
3557 isl_mat_free(term->div);
3558 isl_int_clear(term->n);
3559 isl_int_clear(term->d);
3560 free(term);
3561 }
3562
3563 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3564 {
3565 if (!term)
3566 return 0;
3567
3568 switch (type) {
3569 case isl_dim_param:
3570 case isl_dim_in:
3571 case isl_dim_out: return isl_space_dim(term->dim, type);
3572 case isl_dim_div: return term->div->n_row;
3573 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3574 term->div->n_row;
3575 default: return 0;
3576 }
3577 }
3578
3579 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3580 {
3581 return term ? term->dim->ctx : NULL;
3582 }
3583
3584 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3585 {
3586 if (!term)
3587 return;
3588 isl_int_set(*n, term->n);
3589 }
3590
3591 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3592 {
3593 if (!term)
3594 return;
3595 isl_int_set(*d, term->d);
3596 }
3597
3598 int isl_term_get_exp(__isl_keep isl_term *term,
3599 enum isl_dim_type type, unsigned pos)
3600 {
3601 if (!term)
3602 return -1;
3603
3604 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3605
3606 if (type >= isl_dim_set)
3607 pos += isl_space_dim(term->dim, isl_dim_param);
3608 if (type >= isl_dim_div)
3609 pos += isl_space_dim(term->dim, isl_dim_set);
3610
3611 return term->pow[pos];
3612 }
3613
3614 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3615 {
3616 isl_basic_map *bmap;
3617 unsigned total;
3618 int k;
3619
3620 if (!term)
3621 return NULL;
3622
3623 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3624 return NULL);
3625
3626 total = term->div->n_col - term->div->n_row - 2;
3627 /* No nested divs for now */
3628 isl_assert(term->dim->ctx,
3629 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3630 term->div->n_row) == -1,
3631 return NULL);
3632
3633 bmap = isl_basic_map_alloc_space(isl_space_copy(term->dim), 1, 0, 0);
3634 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3635 goto error;
3636
3637 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3638
3639 return isl_basic_map_div(bmap, k);
3640 error:
3641 isl_basic_map_free(bmap);
3642 return NULL;
3643 }
3644
3645 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3646 int (*fn)(__isl_take isl_term *term, void *user),
3647 __isl_take isl_term *term, void *user)
3648 {
3649 int i;
3650 struct isl_upoly_rec *rec;
3651
3652 if (!up || !term)
3653 goto error;
3654
3655 if (isl_upoly_is_zero(up))
3656 return term;
3657
3658 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3659 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3660 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3661
3662 if (isl_upoly_is_cst(up)) {
3663 struct isl_upoly_cst *cst;
3664 cst = isl_upoly_as_cst(up);
3665 if (!cst)
3666 goto error;
3667 term = isl_term_cow(term);
3668 if (!term)
3669 goto error;
3670 isl_int_set(term->n, cst->n);
3671 isl_int_set(term->d, cst->d);
3672 if (fn(isl_term_copy(term), user) < 0)
3673 goto error;
3674 return term;
3675 }
3676
3677 rec = isl_upoly_as_rec(up);
3678 if (!rec)
3679 goto error;
3680
3681 for (i = 0; i < rec->n; ++i) {
3682 term = isl_term_cow(term);
3683 if (!term)
3684 goto error;
3685 term->pow[up->var] = i;
3686 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3687 if (!term)
3688 goto error;
3689 }
3690 term->pow[up->var] = 0;
3691
3692 return term;
3693 error:
3694 isl_term_free(term);
3695 return NULL;
3696 }
3697
3698 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3699 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3700 {
3701 isl_term *term;
3702
3703 if (!qp)
3704 return -1;
3705
3706 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3707 if (!term)
3708 return -1;
3709
3710 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3711
3712 isl_term_free(term);
3713
3714 return term ? 0 : -1;
3715 }
3716
3717 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3718 {
3719 struct isl_upoly *up;
3720 isl_qpolynomial *qp;
3721 int i, n;
3722
3723 if (!term)
3724 return NULL;
3725
3726 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3727
3728 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3729 for (i = 0; i < n; ++i) {
3730 if (!term->pow[i])
3731 continue;
3732 up = isl_upoly_mul(up,
3733 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3734 }
3735
3736 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3737 if (!qp)
3738 goto error;
3739 isl_mat_free(qp->div);
3740 qp->div = isl_mat_copy(term->div);
3741 if (!qp->div)
3742 goto error;
3743
3744 isl_term_free(term);
3745 return qp;
3746 error:
3747 isl_qpolynomial_free(qp);
3748 isl_term_free(term);
3749 return NULL;
3750 }
3751
3752 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3753 __isl_take isl_space *dim)
3754 {
3755 int i;
3756 int extra;
3757 unsigned total;
3758
3759 if (!qp || !dim)
3760 goto error;
3761
3762 if (isl_space_is_equal(qp->dim, dim)) {
3763 isl_space_free(dim);
3764 return qp;
3765 }
3766
3767 qp = isl_qpolynomial_cow(qp);
3768 if (!qp)
3769 goto error;
3770
3771 extra = isl_space_dim(dim, isl_dim_set) -
3772 isl_space_dim(qp->dim, isl_dim_set);
3773 total = isl_space_dim(qp->dim, isl_dim_all);
3774 if (qp->div->n_row) {
3775 int *exp;
3776
3777 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3778 if (!exp)
3779 goto error;
3780 for (i = 0; i < qp->div->n_row; ++i)
3781 exp[i] = extra + i;
3782 qp->upoly = expand(qp->upoly, exp, total);
3783 free(exp);
3784 if (!qp->upoly)
3785 goto error;
3786 }
3787 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3788 if (!qp->div)
3789 goto error;
3790 for (i = 0; i < qp->div->n_row; ++i)
3791 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3792
3793 isl_space_free(qp->dim);
3794 qp->dim = dim;
3795
3796 return qp;
3797 error:
3798 isl_space_free(dim);
3799 isl_qpolynomial_free(qp);
3800 return NULL;
3801 }
3802
3803 /* For each parameter or variable that does not appear in qp,
3804 * first eliminate the variable from all constraints and then set it to zero.
3805 */
3806 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3807 __isl_keep isl_qpolynomial *qp)
3808 {
3809 int *active = NULL;
3810 int i;
3811 int d;
3812 unsigned nparam;
3813 unsigned nvar;
3814
3815 if (!set || !qp)
3816 goto error;
3817
3818 d = isl_space_dim(set->dim, isl_dim_all);
3819 active = isl_calloc_array(set->ctx, int, d);
3820 if (set_active(qp, active) < 0)
3821 goto error;
3822
3823 for (i = 0; i < d; ++i)
3824 if (!active[i])
3825 break;
3826
3827 if (i == d) {
3828 free(active);
3829 return set;
3830 }
3831
3832 nparam = isl_space_dim(set->dim, isl_dim_param);
3833 nvar = isl_space_dim(set->dim, isl_dim_set);
3834 for (i = 0; i < nparam; ++i) {
3835 if (active[i])
3836 continue;
3837 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3838 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3839 }
3840 for (i = 0; i < nvar; ++i) {
3841 if (active[nparam + i])
3842 continue;
3843 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3844 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3845 }
3846
3847 free(active);
3848
3849 return set;
3850 error:
3851 free(active);
3852 isl_set_free(set);
3853 return NULL;
3854 }
3855
3856 struct isl_opt_data {
3857 isl_qpolynomial *qp;
3858 int first;
3859 isl_qpolynomial *opt;
3860 int max;
3861 };
3862
3863 static int opt_fn(__isl_take isl_point *pnt, void *user)
3864 {
3865 struct isl_opt_data *data = (struct isl_opt_data *)user;
3866 isl_qpolynomial *val;
3867
3868 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3869 if (data->first) {
3870 data->first = 0;
3871 data->opt = val;
3872 } else if (data->max) {
3873 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3874 } else {
3875 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3876 }
3877
3878 return 0;
3879 }
3880
3881 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3882 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3883 {
3884 struct isl_opt_data data = { NULL, 1, NULL, max };
3885
3886 if (!set || !qp)
3887 goto error;
3888
3889 if (isl_upoly_is_cst(qp->upoly)) {
3890 isl_set_free(set);
3891 return qp;
3892 }
3893
3894 set = fix_inactive(set, qp);
3895
3896 data.qp = qp;
3897 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3898 goto error;
3899
3900 if (data.first) {
3901 isl_space *space = isl_qpolynomial_get_domain_space(qp);
3902 data.opt = isl_qpolynomial_zero_on_domain(space);
3903 }
3904
3905 isl_set_free(set);
3906 isl_qpolynomial_free(qp);
3907 return data.opt;
3908 error:
3909 isl_set_free(set);
3910 isl_qpolynomial_free(qp);
3911 isl_qpolynomial_free(data.opt);
3912 return NULL;
3913 }
3914
3915 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
3916 __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
3917 {
3918 int i;
3919 int n_sub;
3920 isl_ctx *ctx;
3921 struct isl_upoly **subs;
3922 isl_mat *mat;
3923
3924 qp = isl_qpolynomial_cow(qp);
3925 if (!qp || !morph)
3926 goto error;
3927
3928 ctx = qp->dim->ctx;
3929 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3930
3931 n_sub = morph->inv->n_row - 1;
3932 if (morph->inv->n_row != morph->inv->n_col)
3933 n_sub += qp->div->n_row;
3934 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3935 if (!subs)
3936 goto error;
3937
3938 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3939 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3940 morph->inv->row[0][0], morph->inv->n_col);
3941 if (morph->inv->n_row != morph->inv->n_col)
3942 for (i = 0; i < qp->div->n_row; ++i)
3943 subs[morph->inv->n_row - 1 + i] =
3944 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3945
3946 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3947
3948 for (i = 0; i < n_sub; ++i)
3949 isl_upoly_free(subs[i]);
3950 free(subs);
3951
3952 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3953 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3954 qp->div = isl_mat_product(qp->div, mat);
3955 isl_space_free(qp->dim);
3956 qp->dim = isl_space_copy(morph->ran->dim);
3957
3958 if (!qp->upoly || !qp->div || !qp->dim)
3959 goto error;
3960
3961 isl_morph_free(morph);
3962
3963 return qp;
3964 error:
3965 isl_qpolynomial_free(qp);
3966 isl_morph_free(morph);
3967 return NULL;
3968 }
3969
3970 static int neg_entry(void **entry, void *user)
3971 {
3972 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3973
3974 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3975
3976 return *pwqp ? 0 : -1;
3977 }
3978
3979 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3980 __isl_take isl_union_pw_qpolynomial *upwqp)
3981 {
3982 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3983 if (!upwqp)
3984 return NULL;
3985
3986 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3987 &neg_entry, NULL) < 0)
3988 goto error;
3989
3990 return upwqp;
3991 error:
3992 isl_union_pw_qpolynomial_free(upwqp);
3993 return NULL;
3994 }
3995
3996 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3997 __isl_take isl_union_pw_qpolynomial *upwqp1,
3998 __isl_take isl_union_pw_qpolynomial *upwqp2)
3999 {
4000 return isl_union_pw_qpolynomial_add(upwqp1,
4001 isl_union_pw_qpolynomial_neg(upwqp2));
4002 }
4003
4004 static int mul_entry(void **entry, void *user)
4005 {
4006 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
4007 uint32_t hash;
4008 struct isl_hash_table_entry *entry2;
4009 isl_pw_qpolynomial *pwpq = *entry;
4010 int empty;
4011
4012 hash = isl_space_get_hash(pwpq->dim);
4013 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
4014 hash, &has_dim, pwpq->dim, 0);
4015 if (!entry2)
4016 return 0;
4017
4018 pwpq = isl_pw_qpolynomial_copy(pwpq);
4019 pwpq = isl_pw_qpolynomial_mul(pwpq,
4020 isl_pw_qpolynomial_copy(entry2->data));
4021
4022 empty = isl_pw_qpolynomial_is_zero(pwpq);
4023 if (empty < 0) {
4024 isl_pw_qpolynomial_free(pwpq);
4025 return -1;
4026 }
4027 if (empty) {
4028 isl_pw_qpolynomial_free(pwpq);
4029 return 0;
4030 }
4031
4032 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
4033
4034 return 0;
4035 }
4036
4037 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4038 __isl_take isl_union_pw_qpolynomial *upwqp1,
4039 __isl_take isl_union_pw_qpolynomial *upwqp2)
4040 {
4041 return match_bin_op(upwqp1, upwqp2, &mul_entry);
4042 }
4043
4044 /* Reorder the columns of the given div definitions according to the
4045 * given reordering.
4046 */
4047 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4048 __isl_take isl_reordering *r)
4049 {
4050 int i, j;
4051 isl_mat *mat;
4052 int extra;
4053
4054 if (!div || !r)
4055 goto error;
4056
4057 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4058 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4059 if (!mat)
4060 goto error;
4061
4062 for (i = 0; i < div->n_row; ++i) {
4063 isl_seq_cpy(mat->row[i], div->row[i], 2);
4064 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4065 for (j = 0; j < r->len; ++j)
4066 isl_int_set(mat->row[i][2 + r->pos[j]],
4067 div->row[i][2 + j]);
4068 }
4069
4070 isl_reordering_free(r);
4071 isl_mat_free(div);
4072 return mat;
4073 error:
4074 isl_reordering_free(r);
4075 isl_mat_free(div);
4076 return NULL;
4077 }
4078
4079 /* Reorder the dimension of "qp" according to the given reordering.
4080 */
4081 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4082 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4083 {
4084 qp = isl_qpolynomial_cow(qp);
4085 if (!qp)
4086 goto error;
4087
4088 r = isl_reordering_extend(r, qp->div->n_row);
4089 if (!r)
4090 goto error;
4091
4092 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4093 if (!qp->div)
4094 goto error;
4095
4096 qp->upoly = reorder(qp->upoly, r->pos);
4097 if (!qp->upoly)
4098 goto error;
4099
4100 qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4101
4102 isl_reordering_free(r);
4103 return qp;
4104 error:
4105 isl_qpolynomial_free(qp);
4106 isl_reordering_free(r);
4107 return NULL;
4108 }
4109
4110 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4111 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4112 {
4113 if (!qp || !model)
4114 goto error;
4115
4116 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4117 isl_reordering *exp;
4118
4119 model = isl_space_drop_dims(model, isl_dim_in,
4120 0, isl_space_dim(model, isl_dim_in));
4121 model = isl_space_drop_dims(model, isl_dim_out,
4122 0, isl_space_dim(model, isl_dim_out));
4123 exp = isl_parameter_alignment_reordering(qp->dim, model);
4124 exp = isl_reordering_extend_space(exp,
4125 isl_qpolynomial_get_domain_space(qp));
4126 qp = isl_qpolynomial_realign_domain(qp, exp);
4127 }
4128
4129 isl_space_free(model);
4130 return qp;
4131 error:
4132 isl_space_free(model);
4133 isl_qpolynomial_free(qp);
4134 return NULL;
4135 }
4136
4137 struct isl_split_periods_data {
4138 int max_periods;
4139 isl_pw_qpolynomial *res;
4140 };
4141
4142 /* Create a slice where the integer division "div" has the fixed value "v".
4143 * In particular, if "div" refers to floor(f/m), then create a slice
4144 *
4145 * m v <= f <= m v + (m - 1)
4146 *
4147 * or
4148 *
4149 * f - m v >= 0
4150 * -f + m v + (m - 1) >= 0
4151 */
4152 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4153 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4154 {
4155 int total;
4156 isl_basic_set *bset = NULL;
4157 int k;
4158
4159 if (!dim || !qp)
4160 goto error;
4161
4162 total = isl_space_dim(dim, isl_dim_all);
4163 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4164
4165 k = isl_basic_set_alloc_inequality(bset);
4166 if (k < 0)
4167 goto error;
4168 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4169 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4170
4171 k = isl_basic_set_alloc_inequality(bset);
4172 if (k < 0)
4173 goto error;
4174 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4175 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4176 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4177 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4178
4179 isl_space_free(dim);
4180 return isl_set_from_basic_set(bset);
4181 error:
4182 isl_basic_set_free(bset);
4183 isl_space_free(dim);
4184 return NULL;
4185 }
4186
4187 static int split_periods(__isl_take isl_set *set,
4188 __isl_take isl_qpolynomial *qp, void *user);
4189
4190 /* Create a slice of the domain "set" such that integer division "div"
4191 * has the fixed value "v" and add the results to data->res,
4192 * replacing the integer division by "v" in "qp".
4193 */
4194 static int set_div(__isl_take isl_set *set,
4195 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4196 struct isl_split_periods_data *data)
4197 {
4198 int i;
4199 int total;
4200 isl_set *slice;
4201 struct isl_upoly *cst;
4202
4203 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4204 set = isl_set_intersect(set, slice);
4205
4206 if (!qp)
4207 goto error;
4208
4209 total = isl_space_dim(qp->dim, isl_dim_all);
4210
4211 for (i = div + 1; i < qp->div->n_row; ++i) {
4212 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4213 continue;
4214 isl_int_addmul(qp->div->row[i][1],
4215 qp->div->row[i][2 + total + div], v);
4216 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4217 }
4218
4219 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4220 qp = substitute_div(qp, div, cst);
4221
4222 return split_periods(set, qp, data);
4223 error:
4224 isl_set_free(set);
4225 isl_qpolynomial_free(qp);
4226 return -1;
4227 }
4228
4229 /* Split the domain "set" such that integer division "div"
4230 * has a fixed value (ranging from "min" to "max") on each slice
4231 * and add the results to data->res.
4232 */
4233 static int split_div(__isl_take isl_set *set,
4234 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4235 struct isl_split_periods_data *data)
4236 {
4237 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4238 isl_set *set_i = isl_set_copy(set);
4239 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4240
4241 if (set_div(set_i, qp_i, div, min, data) < 0)
4242 goto error;
4243 }
4244 isl_set_free(set);
4245 isl_qpolynomial_free(qp);
4246 return 0;
4247 error:
4248 isl_set_free(set);
4249 isl_qpolynomial_free(qp);
4250 return -1;
4251 }
4252
4253 /* If "qp" refers to any integer division
4254 * that can only attain "max_periods" distinct values on "set"
4255 * then split the domain along those distinct values.
4256 * Add the results (or the original if no splitting occurs)
4257 * to data->res.
4258 */
4259 static int split_periods(__isl_take isl_set *set,
4260 __isl_take isl_qpolynomial *qp, void *user)
4261 {
4262 int i;
4263 isl_pw_qpolynomial *pwqp;
4264 struct isl_split_periods_data *data;
4265 isl_int min, max;
4266 int total;
4267 int r = 0;
4268
4269 data = (struct isl_split_periods_data *)user;
4270
4271 if (!set || !qp)
4272 goto error;
4273
4274 if (qp->div->n_row == 0) {
4275 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4276 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4277 return 0;
4278 }
4279
4280 isl_int_init(min);
4281 isl_int_init(max);
4282 total = isl_space_dim(qp->dim, isl_dim_all);
4283 for (i = 0; i < qp->div->n_row; ++i) {
4284 enum isl_lp_result lp_res;
4285
4286 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4287 qp->div->n_row) != -1)
4288 continue;
4289
4290 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4291 set->ctx->one, &min, NULL, NULL);
4292 if (lp_res == isl_lp_error)
4293 goto error2;
4294 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4295 continue;
4296 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4297
4298 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4299 set->ctx->one, &max, NULL, NULL);
4300 if (lp_res == isl_lp_error)
4301 goto error2;
4302 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4303 continue;
4304 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4305
4306 isl_int_sub(max, max, min);
4307 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4308 isl_int_add(max, max, min);
4309 break;
4310 }
4311 }
4312
4313 if (i < qp->div->n_row) {
4314 r = split_div(set, qp, i, min, max, data);
4315 } else {
4316 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4317 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4318 }
4319
4320 isl_int_clear(max);
4321 isl_int_clear(min);
4322
4323 return r;
4324 error2:
4325 isl_int_clear(max);
4326 isl_int_clear(min);
4327 error:
4328 isl_set_free(set);
4329 isl_qpolynomial_free(qp);
4330 return -1;
4331 }
4332
4333 /* If any quasi-polynomial in pwqp refers to any integer division
4334 * that can only attain "max_periods" distinct values on its domain
4335 * then split the domain along those distinct values.
4336 */
4337 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4338 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4339 {
4340 struct isl_split_periods_data data;
4341
4342 data.max_periods = max_periods;
4343 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4344
4345 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4346 goto error;
4347
4348 isl_pw_qpolynomial_free(pwqp);
4349
4350 return data.res;
4351 error:
4352 isl_pw_qpolynomial_free(data.res);
4353 isl_pw_qpolynomial_free(pwqp);
4354 return NULL;
4355 }
4356
4357 /* Construct a piecewise quasipolynomial that is constant on the given
4358 * domain. In particular, it is
4359 * 0 if cst == 0
4360 * 1 if cst == 1
4361 * infinity if cst == -1
4362 */
4363 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4364 __isl_take isl_basic_set *bset, int cst)
4365 {
4366 isl_space *dim;
4367 isl_qpolynomial *qp;
4368
4369 if (!bset)
4370 return NULL;
4371
4372 bset = isl_basic_set_params(bset);
4373 dim = isl_basic_set_get_space(bset);
4374 if (cst < 0)
4375 qp = isl_qpolynomial_infty_on_domain(dim);
4376 else if (cst == 0)
4377 qp = isl_qpolynomial_zero_on_domain(dim);
4378 else
4379 qp = isl_qpolynomial_one_on_domain(dim);
4380 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4381 }
4382
4383 /* Factor bset, call fn on each of the factors and return the product.
4384 *
4385 * If no factors can be found, simply call fn on the input.
4386 * Otherwise, construct the factors based on the factorizer,
4387 * call fn on each factor and compute the product.
4388 */
4389 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4390 __isl_take isl_basic_set *bset,
4391 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4392 {
4393 int i, n;
4394 isl_space *dim;
4395 isl_set *set;
4396 isl_factorizer *f;
4397 isl_qpolynomial *qp;
4398 isl_pw_qpolynomial *pwqp;
4399 unsigned nparam;
4400 unsigned nvar;
4401
4402 f = isl_basic_set_factorizer(bset);
4403 if (!f)
4404 goto error;
4405 if (f->n_group == 0) {
4406 isl_factorizer_free(f);
4407 return fn(bset);
4408 }
4409
4410 nparam = isl_basic_set_dim(bset, isl_dim_param);
4411 nvar = isl_basic_set_dim(bset, isl_dim_set);
4412
4413 dim = isl_basic_set_get_space(bset);
4414 dim = isl_space_domain(dim);
4415 set = isl_set_universe(isl_space_copy(dim));
4416 qp = isl_qpolynomial_one_on_domain(dim);
4417 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4418
4419 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4420
4421 for (i = 0, n = 0; i < f->n_group; ++i) {
4422 isl_basic_set *bset_i;
4423 isl_pw_qpolynomial *pwqp_i;
4424
4425 bset_i = isl_basic_set_copy(bset);
4426 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4427 nparam + n + f->len[i], nvar - n - f->len[i]);
4428 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4429 nparam, n);
4430 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4431 n + f->len[i], nvar - n - f->len[i]);
4432 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4433
4434 pwqp_i = fn(bset_i);
4435 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4436
4437 n += f->len[i];
4438 }
4439
4440 isl_basic_set_free(bset);
4441 isl_factorizer_free(f);
4442
4443 return pwqp;
4444 error:
4445 isl_basic_set_free(bset);
4446 return NULL;
4447 }
4448
4449 /* Factor bset, call fn on each of the factors and return the product.
4450 * The function is assumed to evaluate to zero on empty domains,
4451 * to one on zero-dimensional domains and to infinity on unbounded domains
4452 * and will not be called explicitly on zero-dimensional or unbounded domains.
4453 *
4454 * We first check for some special cases and remove all equalities.
4455 * Then we hand over control to compressed_multiplicative_call.
4456 */
4457 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4458 __isl_take isl_basic_set *bset,
4459 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4460 {
4461 int bounded;
4462 isl_morph *morph;
4463 isl_pw_qpolynomial *pwqp;
4464
4465 if (!bset)
4466 return NULL;
4467
4468 if (isl_basic_set_plain_is_empty(bset))
4469 return constant_on_domain(bset, 0);
4470
4471 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4472 return constant_on_domain(bset, 1);
4473
4474 bounded = isl_basic_set_is_bounded(bset);
4475 if (bounded < 0)
4476 goto error;
4477 if (!bounded)
4478 return constant_on_domain(bset, -1);
4479
4480 if (bset->n_eq == 0)
4481 return compressed_multiplicative_call(bset, fn);
4482
4483 morph = isl_basic_set_full_compression(bset);
4484 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4485
4486 pwqp = compressed_multiplicative_call(bset, fn);
4487
4488 morph = isl_morph_dom_params(morph);
4489 morph = isl_morph_ran_params(morph);
4490 morph = isl_morph_inverse(morph);
4491
4492 pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4493
4494 return pwqp;
4495 error:
4496 isl_basic_set_free(bset);
4497 return NULL;
4498 }
4499
4500 /* Drop all floors in "qp", turning each integer division [a/m] into
4501 * a rational division a/m. If "down" is set, then the integer division
4502 * is replaces by (a-(m-1))/m instead.
4503 */
4504 static __isl_give isl_qpolynomial *qp_drop_floors(
4505 __isl_take isl_qpolynomial *qp, int down)
4506 {
4507 int i;
4508 struct isl_upoly *s;
4509
4510 if (!qp)
4511 return NULL;
4512 if (qp->div->n_row == 0)
4513 return qp;
4514
4515 qp = isl_qpolynomial_cow(qp);
4516 if (!qp)
4517 return NULL;
4518
4519 for (i = qp->div->n_row - 1; i >= 0; --i) {
4520 if (down) {
4521 isl_int_sub(qp->div->row[i][1],
4522 qp->div->row[i][1], qp->div->row[i][0]);
4523 isl_int_add_ui(qp->div->row[i][1],
4524 qp->div->row[i][1], 1);
4525 }
4526 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4527 qp->div->row[i][0], qp->div->n_col - 1);
4528 qp = substitute_div(qp, i, s);
4529 if (!qp)
4530 return NULL;
4531 }
4532
4533 return qp;
4534 }
4535
4536 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4537 * a rational division a/m.
4538 */
4539 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4540 __isl_take isl_pw_qpolynomial *pwqp)
4541 {
4542 int i;
4543
4544 if (!pwqp)
4545 return NULL;
4546
4547 if (isl_pw_qpolynomial_is_zero(pwqp))
4548 return pwqp;
4549
4550 pwqp = isl_pw_qpolynomial_cow(pwqp);
4551 if (!pwqp)
4552 return NULL;
4553
4554 for (i = 0; i < pwqp->n; ++i) {
4555 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4556 if (!pwqp->p[i].qp)
4557 goto error;
4558 }
4559
4560 return pwqp;
4561 error:
4562 isl_pw_qpolynomial_free(pwqp);
4563 return NULL;
4564 }
4565
4566 /* Adjust all the integer divisions in "qp" such that they are at least
4567 * one over the given orthant (identified by "signs"). This ensures
4568 * that they will still be non-negative even after subtracting (m-1)/m.
4569 *
4570 * In particular, f is replaced by f' + v, changing f = [a/m]
4571 * to f' = [(a - m v)/m].
4572 * If the constant term k in a is smaller than m,
4573 * the constant term of v is set to floor(k/m) - 1.
4574 * For any other term, if the coefficient c and the variable x have
4575 * the same sign, then no changes are needed.
4576 * Otherwise, if the variable is positive (and c is negative),
4577 * then the coefficient of x in v is set to floor(c/m).
4578 * If the variable is negative (and c is positive),
4579 * then the coefficient of x in v is set to ceil(c/m).
4580 */
4581 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4582 int *signs)
4583 {
4584 int i, j;
4585 int total;
4586 isl_vec *v = NULL;
4587 struct isl_upoly *s;
4588
4589 qp = isl_qpolynomial_cow(qp);
4590 if (!qp)
4591 return NULL;
4592 qp->div = isl_mat_cow(qp->div);
4593 if (!qp->div)
4594 goto error;
4595
4596 total = isl_space_dim(qp->dim, isl_dim_all);
4597 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4598
4599 for (i = 0; i < qp->div->n_row; ++i) {
4600 isl_int *row = qp->div->row[i];
4601 v = isl_vec_clr(v);
4602 if (!v)
4603 goto error;
4604 if (isl_int_lt(row[1], row[0])) {
4605 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4606 isl_int_sub_ui(v->el[0], v->el[0], 1);
4607 isl_int_submul(row[1], row[0], v->el[0]);
4608 }
4609 for (j = 0; j < total; ++j) {
4610 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4611 continue;
4612 if (signs[j] < 0)
4613 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4614 else
4615 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4616 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4617 }
4618 for (j = 0; j < i; ++j) {
4619 if (isl_int_sgn(row[2 + total + j]) >= 0)
4620 continue;
4621 isl_int_fdiv_q(v->el[1 + total + j],
4622 row[2 + total + j], row[0]);
4623 isl_int_submul(row[2 + total + j],
4624 row[0], v->el[1 + total + j]);
4625 }
4626 for (j = i + 1; j < qp->div->n_row; ++j) {
4627 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4628 continue;
4629 isl_seq_combine(qp->div->row[j] + 1,
4630 qp->div->ctx->one, qp->div->row[j] + 1,
4631 qp->div->row[j][2 + total + i], v->el, v->size);
4632 }
4633 isl_int_set_si(v->el[1 + total + i], 1);
4634 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4635 qp->div->ctx->one, v->size);
4636 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4637 isl_upoly_free(s);
4638 if (!qp->upoly)
4639 goto error;
4640 }
4641
4642 isl_vec_free(v);
4643 return qp;
4644 error:
4645 isl_vec_free(v);
4646 isl_qpolynomial_free(qp);
4647 return NULL;
4648 }
4649
4650 struct isl_to_poly_data {
4651 int sign;
4652 isl_pw_qpolynomial *res;
4653 isl_qpolynomial *qp;
4654 };
4655
4656 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4657 * We first make all integer divisions positive and then split the
4658 * quasipolynomials into terms with sign data->sign (the direction
4659 * of the requested approximation) and terms with the opposite sign.
4660 * In the first set of terms, each integer division [a/m] is
4661 * overapproximated by a/m, while in the second it is underapproximated
4662 * by (a-(m-1))/m.
4663 */
4664 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4665 void *user)
4666 {
4667 struct isl_to_poly_data *data = user;
4668 isl_pw_qpolynomial *t;
4669 isl_qpolynomial *qp, *up, *down;
4670
4671 qp = isl_qpolynomial_copy(data->qp);
4672 qp = make_divs_pos(qp, signs);
4673
4674 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4675 up = qp_drop_floors(up, 0);
4676 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4677 down = qp_drop_floors(down, 1);
4678
4679 isl_qpolynomial_free(qp);
4680 qp = isl_qpolynomial_add(up, down);
4681
4682 t = isl_pw_qpolynomial_alloc(orthant, qp);
4683 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4684
4685 return 0;
4686 }
4687
4688 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4689 * the polynomial will be an overapproximation. If "sign" is negative,
4690 * it will be an underapproximation. If "sign" is zero, the approximation
4691 * will lie somewhere in between.
4692 *
4693 * In particular, is sign == 0, we simply drop the floors, turning
4694 * the integer divisions into rational divisions.
4695 * Otherwise, we split the domains into orthants, make all integer divisions
4696 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4697 * depending on the requested sign and the sign of the term in which
4698 * the integer division appears.
4699 */
4700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4701 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4702 {
4703 int i;
4704 struct isl_to_poly_data data;
4705
4706 if (sign == 0)
4707 return pwqp_drop_floors(pwqp);
4708
4709 if (!pwqp)
4710 return NULL;
4711
4712 data.sign = sign;
4713 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4714
4715 for (i = 0; i < pwqp->n; ++i) {
4716 if (pwqp->p[i].qp->div->n_row == 0) {
4717 isl_pw_qpolynomial *t;
4718 t = isl_pw_qpolynomial_alloc(
4719 isl_set_copy(pwqp->p[i].set),
4720 isl_qpolynomial_copy(pwqp->p[i].qp));
4721 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4722 continue;
4723 }
4724 data.qp = pwqp->p[i].qp;
4725 if (isl_set_foreach_orthant(pwqp->p[i].set,
4726 &to_polynomial_on_orthant, &data) < 0)
4727 goto error;
4728 }
4729
4730 isl_pw_qpolynomial_free(pwqp);
4731
4732 return data.res;
4733 error:
4734 isl_pw_qpolynomial_free(pwqp);
4735 isl_pw_qpolynomial_free(data.res);
4736 return NULL;
4737 }
4738
4739 static int poly_entry(void **entry, void *user)
4740 {
4741 int *sign = user;
4742 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4743
4744 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4745
4746 return *pwqp ? 0 : -1;
4747 }
4748
4749 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4750 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4751 {
4752 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4753 if (!upwqp)
4754 return NULL;
4755
4756 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4757 &poly_entry, &sign) < 0)
4758 goto error;
4759
4760 return upwqp;
4761 error:
4762 isl_union_pw_qpolynomial_free(upwqp);
4763 return NULL;
4764 }
4765
4766 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4767 __isl_take isl_qpolynomial *qp)
4768 {
4769 int i, k;
4770 isl_space *dim;
4771 isl_vec *aff = NULL;
4772 isl_basic_map *bmap = NULL;
4773 unsigned pos;
4774 unsigned n_div;
4775
4776 if (!qp)
4777 return NULL;
4778 if (!isl_upoly_is_affine(qp->upoly))
4779 isl_die(qp->dim->ctx, isl_error_invalid,
4780 "input quasi-polynomial not affine", goto error);
4781 aff = isl_qpolynomial_extract_affine(qp);
4782 if (!aff)
4783 goto error;
4784 dim = isl_qpolynomial_get_space(qp);
4785 pos = 1 + isl_space_offset(dim, isl_dim_out);
4786 n_div = qp->div->n_row;
4787 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4788
4789 for (i = 0; i < n_div; ++i) {
4790 k = isl_basic_map_alloc_div(bmap);
4791 if (k < 0)
4792 goto error;
4793 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4794 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4795 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4796 goto error;
4797 }
4798 k = isl_basic_map_alloc_equality(bmap);
4799 if (k < 0)
4800 goto error;
4801 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4802 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4803 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4804
4805 isl_vec_free(aff);
4806 isl_qpolynomial_free(qp);
4807 bmap = isl_basic_map_finalize(bmap);
4808 return bmap;
4809 error:
4810 isl_vec_free(aff);
4811 isl_qpolynomial_free(qp);
4812 isl_basic_map_free(bmap);
4813 return NULL;
4814 }
Integer set library