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add isl_set_upper_bound_si
[isl.git] / isl_polynomial.c
blob83724adfd97b0619769ab2e6d82e04c410ff50cc
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_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_config.h>
28
29 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
30 {
31 switch (type) {
32 case isl_dim_param: return 0;
33 case isl_dim_in: return dim->nparam;
34 case isl_dim_out: return dim->nparam + dim->n_in;
35 default: return 0;
36 }
37 }
38
39 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
40 {
41 if (!up)
42 return -1;
43
44 return up->var < 0;
45 }
46
47 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
48 {
49 if (!up)
50 return NULL;
51
52 isl_assert(up->ctx, up->var < 0, return NULL);
53
54 return (struct isl_upoly_cst *)up;
55 }
56
57 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
58 {
59 if (!up)
60 return NULL;
61
62 isl_assert(up->ctx, up->var >= 0, return NULL);
63
64 return (struct isl_upoly_rec *)up;
65 }
66
67 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
68 __isl_keep struct isl_upoly *up2)
69 {
70 int i;
71 struct isl_upoly_rec *rec1, *rec2;
72
73 if (!up1 || !up2)
74 return -1;
75 if (up1 == up2)
76 return 1;
77 if (up1->var != up2->var)
78 return 0;
79 if (isl_upoly_is_cst(up1)) {
80 struct isl_upoly_cst *cst1, *cst2;
81 cst1 = isl_upoly_as_cst(up1);
82 cst2 = isl_upoly_as_cst(up2);
83 if (!cst1 || !cst2)
84 return -1;
85 return isl_int_eq(cst1->n, cst2->n) &&
86 isl_int_eq(cst1->d, cst2->d);
87 }
88
89 rec1 = isl_upoly_as_rec(up1);
90 rec2 = isl_upoly_as_rec(up2);
91 if (!rec1 || !rec2)
92 return -1;
93
94 if (rec1->n != rec2->n)
95 return 0;
96
97 for (i = 0; i < rec1->n; ++i) {
98 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
99 if (eq < 0 || !eq)
100 return eq;
101 }
102
103 return 1;
104 }
105
106 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
107 {
108 struct isl_upoly_cst *cst;
109
110 if (!up)
111 return -1;
112 if (!isl_upoly_is_cst(up))
113 return 0;
114
115 cst = isl_upoly_as_cst(up);
116 if (!cst)
117 return -1;
118
119 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
120 }
121
122 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
123 {
124 struct isl_upoly_cst *cst;
125
126 if (!up)
127 return 0;
128 if (!isl_upoly_is_cst(up))
129 return 0;
130
131 cst = isl_upoly_as_cst(up);
132 if (!cst)
133 return 0;
134
135 return isl_int_sgn(cst->n);
136 }
137
138 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
139 {
140 struct isl_upoly_cst *cst;
141
142 if (!up)
143 return -1;
144 if (!isl_upoly_is_cst(up))
145 return 0;
146
147 cst = isl_upoly_as_cst(up);
148 if (!cst)
149 return -1;
150
151 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
152 }
153
154 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
155 {
156 struct isl_upoly_cst *cst;
157
158 if (!up)
159 return -1;
160 if (!isl_upoly_is_cst(up))
161 return 0;
162
163 cst = isl_upoly_as_cst(up);
164 if (!cst)
165 return -1;
166
167 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
168 }
169
170 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
171 {
172 struct isl_upoly_cst *cst;
173
174 if (!up)
175 return -1;
176 if (!isl_upoly_is_cst(up))
177 return 0;
178
179 cst = isl_upoly_as_cst(up);
180 if (!cst)
181 return -1;
182
183 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
184 }
185
186 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
187 {
188 struct isl_upoly_cst *cst;
189
190 if (!up)
191 return -1;
192 if (!isl_upoly_is_cst(up))
193 return 0;
194
195 cst = isl_upoly_as_cst(up);
196 if (!cst)
197 return -1;
198
199 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
200 }
201
202 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
203 {
204 struct isl_upoly_cst *cst;
205
206 if (!up)
207 return -1;
208 if (!isl_upoly_is_cst(up))
209 return 0;
210
211 cst = isl_upoly_as_cst(up);
212 if (!cst)
213 return -1;
214
215 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
216 }
217
218 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
219 {
220 struct isl_upoly_cst *cst;
221
222 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
223 if (!cst)
224 return NULL;
225
226 cst->up.ref = 1;
227 cst->up.ctx = ctx;
228 isl_ctx_ref(ctx);
229 cst->up.var = -1;
230
231 isl_int_init(cst->n);
232 isl_int_init(cst->d);
233
234 return cst;
235 }
236
237 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
238 {
239 struct isl_upoly_cst *cst;
240
241 cst = isl_upoly_cst_alloc(ctx);
242 if (!cst)
243 return NULL;
244
245 isl_int_set_si(cst->n, 0);
246 isl_int_set_si(cst->d, 1);
247
248 return &cst->up;
249 }
250
251 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
252 {
253 struct isl_upoly_cst *cst;
254
255 cst = isl_upoly_cst_alloc(ctx);
256 if (!cst)
257 return NULL;
258
259 isl_int_set_si(cst->n, 1);
260 isl_int_set_si(cst->d, 1);
261
262 return &cst->up;
263 }
264
265 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
266 {
267 struct isl_upoly_cst *cst;
268
269 cst = isl_upoly_cst_alloc(ctx);
270 if (!cst)
271 return NULL;
272
273 isl_int_set_si(cst->n, 1);
274 isl_int_set_si(cst->d, 0);
275
276 return &cst->up;
277 }
278
279 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
280 {
281 struct isl_upoly_cst *cst;
282
283 cst = isl_upoly_cst_alloc(ctx);
284 if (!cst)
285 return NULL;
286
287 isl_int_set_si(cst->n, -1);
288 isl_int_set_si(cst->d, 0);
289
290 return &cst->up;
291 }
292
293 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
294 {
295 struct isl_upoly_cst *cst;
296
297 cst = isl_upoly_cst_alloc(ctx);
298 if (!cst)
299 return NULL;
300
301 isl_int_set_si(cst->n, 0);
302 isl_int_set_si(cst->d, 0);
303
304 return &cst->up;
305 }
306
307 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
308 isl_int n, isl_int d)
309 {
310 struct isl_upoly_cst *cst;
311
312 cst = isl_upoly_cst_alloc(ctx);
313 if (!cst)
314 return NULL;
315
316 isl_int_set(cst->n, n);
317 isl_int_set(cst->d, d);
318
319 return &cst->up;
320 }
321
322 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
323 int var, int size)
324 {
325 struct isl_upoly_rec *rec;
326
327 isl_assert(ctx, var >= 0, return NULL);
328 isl_assert(ctx, size >= 0, return NULL);
329 rec = isl_calloc(ctx, struct isl_upoly_rec,
330 sizeof(struct isl_upoly_rec) +
331 size * sizeof(struct isl_upoly *));
332 if (!rec)
333 return NULL;
334
335 rec->up.ref = 1;
336 rec->up.ctx = ctx;
337 isl_ctx_ref(ctx);
338 rec->up.var = var;
339
340 rec->n = 0;
341 rec->size = size;
342
343 return rec;
344 }
345
346 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
347 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
348 {
349 qp = isl_qpolynomial_cow(qp);
350 if (!qp || !dim)
351 goto error;
352
353 isl_space_free(qp->dim);
354 qp->dim = dim;
355
356 return qp;
357 error:
358 isl_qpolynomial_free(qp);
359 isl_space_free(dim);
360 return NULL;
361 }
362
363 /* Reset the space of "qp". This function is called from isl_pw_templ.c
364 * and doesn't know if the space of an element object is represented
365 * directly or through its domain. It therefore passes along both.
366 */
367 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
368 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
369 __isl_take isl_space *domain)
370 {
371 isl_space_free(space);
372 return isl_qpolynomial_reset_domain_space(qp, domain);
373 }
374
375 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
376 {
377 return qp ? qp->dim->ctx : NULL;
378 }
379
380 __isl_give isl_space *isl_qpolynomial_get_domain_space(
381 __isl_keep isl_qpolynomial *qp)
382 {
383 return qp ? isl_space_copy(qp->dim) : NULL;
384 }
385
386 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
387 {
388 isl_space *space;
389 if (!qp)
390 return NULL;
391 space = isl_space_copy(qp->dim);
392 space = isl_space_from_domain(space);
393 space = isl_space_add_dims(space, isl_dim_out, 1);
394 return space;
395 }
396
397 /* Externally, an isl_qpolynomial has a map space, but internally, the
398 * ls field corresponds to the domain of that space.
399 */
400 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
401 enum isl_dim_type type)
402 {
403 if (!qp)
404 return 0;
405 if (type == isl_dim_out)
406 return 1;
407 if (type == isl_dim_in)
408 type = isl_dim_set;
409 return isl_space_dim(qp->dim, type);
410 }
411
412 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
413 {
414 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
415 }
416
417 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
418 {
419 return qp ? isl_upoly_is_one(qp->upoly) : -1;
420 }
421
422 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
423 {
424 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
425 }
426
427 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
428 {
429 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
430 }
431
432 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
433 {
434 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
435 }
436
437 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
438 {
439 return qp ? isl_upoly_sgn(qp->upoly) : 0;
440 }
441
442 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
443 {
444 isl_int_clear(cst->n);
445 isl_int_clear(cst->d);
446 }
447
448 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
449 {
450 int i;
451
452 for (i = 0; i < rec->n; ++i)
453 isl_upoly_free(rec->p[i]);
454 }
455
456 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
457 {
458 if (!up)
459 return NULL;
460
461 up->ref++;
462 return up;
463 }
464
465 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
466 {
467 struct isl_upoly_cst *cst;
468 struct isl_upoly_cst *dup;
469
470 cst = isl_upoly_as_cst(up);
471 if (!cst)
472 return NULL;
473
474 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
475 if (!dup)
476 return NULL;
477 isl_int_set(dup->n, cst->n);
478 isl_int_set(dup->d, cst->d);
479
480 return &dup->up;
481 }
482
483 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
484 {
485 int i;
486 struct isl_upoly_rec *rec;
487 struct isl_upoly_rec *dup;
488
489 rec = isl_upoly_as_rec(up);
490 if (!rec)
491 return NULL;
492
493 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
494 if (!dup)
495 return NULL;
496
497 for (i = 0; i < rec->n; ++i) {
498 dup->p[i] = isl_upoly_copy(rec->p[i]);
499 if (!dup->p[i])
500 goto error;
501 dup->n++;
502 }
503
504 return &dup->up;
505 error:
506 isl_upoly_free(&dup->up);
507 return NULL;
508 }
509
510 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
511 {
512 if (!up)
513 return NULL;
514
515 if (isl_upoly_is_cst(up))
516 return isl_upoly_dup_cst(up);
517 else
518 return isl_upoly_dup_rec(up);
519 }
520
521 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
522 {
523 if (!up)
524 return NULL;
525
526 if (up->ref == 1)
527 return up;
528 up->ref--;
529 return isl_upoly_dup(up);
530 }
531
532 void isl_upoly_free(__isl_take struct isl_upoly *up)
533 {
534 if (!up)
535 return;
536
537 if (--up->ref > 0)
538 return;
539
540 if (up->var < 0)
541 upoly_free_cst((struct isl_upoly_cst *)up);
542 else
543 upoly_free_rec((struct isl_upoly_rec *)up);
544
545 isl_ctx_deref(up->ctx);
546 free(up);
547 }
548
549 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
550 {
551 isl_int gcd;
552
553 isl_int_init(gcd);
554 isl_int_gcd(gcd, cst->n, cst->d);
555 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
556 isl_int_divexact(cst->n, cst->n, gcd);
557 isl_int_divexact(cst->d, cst->d, gcd);
558 }
559 isl_int_clear(gcd);
560 }
561
562 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
563 __isl_take struct isl_upoly *up2)
564 {
565 struct isl_upoly_cst *cst1;
566 struct isl_upoly_cst *cst2;
567
568 up1 = isl_upoly_cow(up1);
569 if (!up1 || !up2)
570 goto error;
571
572 cst1 = isl_upoly_as_cst(up1);
573 cst2 = isl_upoly_as_cst(up2);
574
575 if (isl_int_eq(cst1->d, cst2->d))
576 isl_int_add(cst1->n, cst1->n, cst2->n);
577 else {
578 isl_int_mul(cst1->n, cst1->n, cst2->d);
579 isl_int_addmul(cst1->n, cst2->n, cst1->d);
580 isl_int_mul(cst1->d, cst1->d, cst2->d);
581 }
582
583 isl_upoly_cst_reduce(cst1);
584
585 isl_upoly_free(up2);
586 return up1;
587 error:
588 isl_upoly_free(up1);
589 isl_upoly_free(up2);
590 return NULL;
591 }
592
593 static __isl_give struct isl_upoly *replace_by_zero(
594 __isl_take struct isl_upoly *up)
595 {
596 struct isl_ctx *ctx;
597
598 if (!up)
599 return NULL;
600 ctx = up->ctx;
601 isl_upoly_free(up);
602 return isl_upoly_zero(ctx);
603 }
604
605 static __isl_give struct isl_upoly *replace_by_constant_term(
606 __isl_take struct isl_upoly *up)
607 {
608 struct isl_upoly_rec *rec;
609 struct isl_upoly *cst;
610
611 if (!up)
612 return NULL;
613
614 rec = isl_upoly_as_rec(up);
615 if (!rec)
616 goto error;
617 cst = isl_upoly_copy(rec->p[0]);
618 isl_upoly_free(up);
619 return cst;
620 error:
621 isl_upoly_free(up);
622 return NULL;
623 }
624
625 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
626 __isl_take struct isl_upoly *up2)
627 {
628 int i;
629 struct isl_upoly_rec *rec1, *rec2;
630
631 if (!up1 || !up2)
632 goto error;
633
634 if (isl_upoly_is_nan(up1)) {
635 isl_upoly_free(up2);
636 return up1;
637 }
638
639 if (isl_upoly_is_nan(up2)) {
640 isl_upoly_free(up1);
641 return up2;
642 }
643
644 if (isl_upoly_is_zero(up1)) {
645 isl_upoly_free(up1);
646 return up2;
647 }
648
649 if (isl_upoly_is_zero(up2)) {
650 isl_upoly_free(up2);
651 return up1;
652 }
653
654 if (up1->var < up2->var)
655 return isl_upoly_sum(up2, up1);
656
657 if (up2->var < up1->var) {
658 struct isl_upoly_rec *rec;
659 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
660 isl_upoly_free(up1);
661 return up2;
662 }
663 up1 = isl_upoly_cow(up1);
664 rec = isl_upoly_as_rec(up1);
665 if (!rec)
666 goto error;
667 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
668 if (rec->n == 1)
669 up1 = replace_by_constant_term(up1);
670 return up1;
671 }
672
673 if (isl_upoly_is_cst(up1))
674 return isl_upoly_sum_cst(up1, up2);
675
676 rec1 = isl_upoly_as_rec(up1);
677 rec2 = isl_upoly_as_rec(up2);
678 if (!rec1 || !rec2)
679 goto error;
680
681 if (rec1->n < rec2->n)
682 return isl_upoly_sum(up2, up1);
683
684 up1 = isl_upoly_cow(up1);
685 rec1 = isl_upoly_as_rec(up1);
686 if (!rec1)
687 goto error;
688
689 for (i = rec2->n - 1; i >= 0; --i) {
690 rec1->p[i] = isl_upoly_sum(rec1->p[i],
691 isl_upoly_copy(rec2->p[i]));
692 if (!rec1->p[i])
693 goto error;
694 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
695 isl_upoly_free(rec1->p[i]);
696 rec1->n--;
697 }
698 }
699
700 if (rec1->n == 0)
701 up1 = replace_by_zero(up1);
702 else if (rec1->n == 1)
703 up1 = replace_by_constant_term(up1);
704
705 isl_upoly_free(up2);
706
707 return up1;
708 error:
709 isl_upoly_free(up1);
710 isl_upoly_free(up2);
711 return NULL;
712 }
713
714 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
715 __isl_take struct isl_upoly *up, isl_int v)
716 {
717 struct isl_upoly_cst *cst;
718
719 up = isl_upoly_cow(up);
720 if (!up)
721 return NULL;
722
723 cst = isl_upoly_as_cst(up);
724
725 isl_int_addmul(cst->n, cst->d, v);
726
727 return up;
728 }
729
730 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
731 __isl_take struct isl_upoly *up, isl_int v)
732 {
733 struct isl_upoly_rec *rec;
734
735 if (!up)
736 return NULL;
737
738 if (isl_upoly_is_cst(up))
739 return isl_upoly_cst_add_isl_int(up, v);
740
741 up = isl_upoly_cow(up);
742 rec = isl_upoly_as_rec(up);
743 if (!rec)
744 goto error;
745
746 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
747 if (!rec->p[0])
748 goto error;
749
750 return up;
751 error:
752 isl_upoly_free(up);
753 return NULL;
754 }
755
756 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
757 __isl_take struct isl_upoly *up, isl_int v)
758 {
759 struct isl_upoly_cst *cst;
760
761 if (isl_upoly_is_zero(up))
762 return up;
763
764 up = isl_upoly_cow(up);
765 if (!up)
766 return NULL;
767
768 cst = isl_upoly_as_cst(up);
769
770 isl_int_mul(cst->n, cst->n, v);
771
772 return up;
773 }
774
775 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
776 __isl_take struct isl_upoly *up, isl_int v)
777 {
778 int i;
779 struct isl_upoly_rec *rec;
780
781 if (!up)
782 return NULL;
783
784 if (isl_upoly_is_cst(up))
785 return isl_upoly_cst_mul_isl_int(up, v);
786
787 up = isl_upoly_cow(up);
788 rec = isl_upoly_as_rec(up);
789 if (!rec)
790 goto error;
791
792 for (i = 0; i < rec->n; ++i) {
793 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
794 if (!rec->p[i])
795 goto error;
796 }
797
798 return up;
799 error:
800 isl_upoly_free(up);
801 return NULL;
802 }
803
804 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
805 __isl_take struct isl_upoly *up2)
806 {
807 struct isl_upoly_cst *cst1;
808 struct isl_upoly_cst *cst2;
809
810 up1 = isl_upoly_cow(up1);
811 if (!up1 || !up2)
812 goto error;
813
814 cst1 = isl_upoly_as_cst(up1);
815 cst2 = isl_upoly_as_cst(up2);
816
817 isl_int_mul(cst1->n, cst1->n, cst2->n);
818 isl_int_mul(cst1->d, cst1->d, cst2->d);
819
820 isl_upoly_cst_reduce(cst1);
821
822 isl_upoly_free(up2);
823 return up1;
824 error:
825 isl_upoly_free(up1);
826 isl_upoly_free(up2);
827 return NULL;
828 }
829
830 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
831 __isl_take struct isl_upoly *up2)
832 {
833 struct isl_upoly_rec *rec1;
834 struct isl_upoly_rec *rec2;
835 struct isl_upoly_rec *res = NULL;
836 int i, j;
837 int size;
838
839 rec1 = isl_upoly_as_rec(up1);
840 rec2 = isl_upoly_as_rec(up2);
841 if (!rec1 || !rec2)
842 goto error;
843 size = rec1->n + rec2->n - 1;
844 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
845 if (!res)
846 goto error;
847
848 for (i = 0; i < rec1->n; ++i) {
849 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
850 isl_upoly_copy(rec1->p[i]));
851 if (!res->p[i])
852 goto error;
853 res->n++;
854 }
855 for (; i < size; ++i) {
856 res->p[i] = isl_upoly_zero(up1->ctx);
857 if (!res->p[i])
858 goto error;
859 res->n++;
860 }
861 for (i = 0; i < rec1->n; ++i) {
862 for (j = 1; j < rec2->n; ++j) {
863 struct isl_upoly *up;
864 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
865 isl_upoly_copy(rec1->p[i]));
866 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
867 if (!res->p[i + j])
868 goto error;
869 }
870 }
871
872 isl_upoly_free(up1);
873 isl_upoly_free(up2);
874
875 return &res->up;
876 error:
877 isl_upoly_free(up1);
878 isl_upoly_free(up2);
879 isl_upoly_free(&res->up);
880 return NULL;
881 }
882
883 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
884 __isl_take struct isl_upoly *up2)
885 {
886 if (!up1 || !up2)
887 goto error;
888
889 if (isl_upoly_is_nan(up1)) {
890 isl_upoly_free(up2);
891 return up1;
892 }
893
894 if (isl_upoly_is_nan(up2)) {
895 isl_upoly_free(up1);
896 return up2;
897 }
898
899 if (isl_upoly_is_zero(up1)) {
900 isl_upoly_free(up2);
901 return up1;
902 }
903
904 if (isl_upoly_is_zero(up2)) {
905 isl_upoly_free(up1);
906 return up2;
907 }
908
909 if (isl_upoly_is_one(up1)) {
910 isl_upoly_free(up1);
911 return up2;
912 }
913
914 if (isl_upoly_is_one(up2)) {
915 isl_upoly_free(up2);
916 return up1;
917 }
918
919 if (up1->var < up2->var)
920 return isl_upoly_mul(up2, up1);
921
922 if (up2->var < up1->var) {
923 int i;
924 struct isl_upoly_rec *rec;
925 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
926 isl_ctx *ctx = up1->ctx;
927 isl_upoly_free(up1);
928 isl_upoly_free(up2);
929 return isl_upoly_nan(ctx);
930 }
931 up1 = isl_upoly_cow(up1);
932 rec = isl_upoly_as_rec(up1);
933 if (!rec)
934 goto error;
935
936 for (i = 0; i < rec->n; ++i) {
937 rec->p[i] = isl_upoly_mul(rec->p[i],
938 isl_upoly_copy(up2));
939 if (!rec->p[i])
940 goto error;
941 }
942 isl_upoly_free(up2);
943 return up1;
944 }
945
946 if (isl_upoly_is_cst(up1))
947 return isl_upoly_mul_cst(up1, up2);
948
949 return isl_upoly_mul_rec(up1, up2);
950 error:
951 isl_upoly_free(up1);
952 isl_upoly_free(up2);
953 return NULL;
954 }
955
956 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
957 unsigned power)
958 {
959 struct isl_upoly *res;
960
961 if (!up)
962 return NULL;
963 if (power == 1)
964 return up;
965
966 if (power % 2)
967 res = isl_upoly_copy(up);
968 else
969 res = isl_upoly_one(up->ctx);
970
971 while (power >>= 1) {
972 up = isl_upoly_mul(up, isl_upoly_copy(up));
973 if (power % 2)
974 res = isl_upoly_mul(res, isl_upoly_copy(up));
975 }
976
977 isl_upoly_free(up);
978 return res;
979 }
980
981 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
982 unsigned n_div, __isl_take struct isl_upoly *up)
983 {
984 struct isl_qpolynomial *qp = NULL;
985 unsigned total;
986
987 if (!dim || !up)
988 goto error;
989
990 if (!isl_space_is_set(dim))
991 isl_die(isl_space_get_ctx(dim), isl_error_invalid,
992 "domain of polynomial should be a set", goto error);
993
994 total = isl_space_dim(dim, isl_dim_all);
995
996 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
997 if (!qp)
998 goto error;
999
1000 qp->ref = 1;
1001 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
1002 if (!qp->div)
1003 goto error;
1004
1005 qp->dim = dim;
1006 qp->upoly = up;
1007
1008 return qp;
1009 error:
1010 isl_space_free(dim);
1011 isl_upoly_free(up);
1012 isl_qpolynomial_free(qp);
1013 return NULL;
1014 }
1015
1016 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1017 {
1018 if (!qp)
1019 return NULL;
1020
1021 qp->ref++;
1022 return qp;
1023 }
1024
1025 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1026 {
1027 struct isl_qpolynomial *dup;
1028
1029 if (!qp)
1030 return NULL;
1031
1032 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1033 isl_upoly_copy(qp->upoly));
1034 if (!dup)
1035 return NULL;
1036 isl_mat_free(dup->div);
1037 dup->div = isl_mat_copy(qp->div);
1038 if (!dup->div)
1039 goto error;
1040
1041 return dup;
1042 error:
1043 isl_qpolynomial_free(dup);
1044 return NULL;
1045 }
1046
1047 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1048 {
1049 if (!qp)
1050 return NULL;
1051
1052 if (qp->ref == 1)
1053 return qp;
1054 qp->ref--;
1055 return isl_qpolynomial_dup(qp);
1056 }
1057
1058 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1059 {
1060 if (!qp)
1061 return NULL;
1062
1063 if (--qp->ref > 0)
1064 return NULL;
1065
1066 isl_space_free(qp->dim);
1067 isl_mat_free(qp->div);
1068 isl_upoly_free(qp->upoly);
1069
1070 free(qp);
1071 return NULL;
1072 }
1073
1074 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1075 {
1076 int i;
1077 struct isl_upoly_rec *rec;
1078 struct isl_upoly_cst *cst;
1079
1080 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1081 if (!rec)
1082 return NULL;
1083 for (i = 0; i < 1 + power; ++i) {
1084 rec->p[i] = isl_upoly_zero(ctx);
1085 if (!rec->p[i])
1086 goto error;
1087 rec->n++;
1088 }
1089 cst = isl_upoly_as_cst(rec->p[power]);
1090 isl_int_set_si(cst->n, 1);
1091
1092 return &rec->up;
1093 error:
1094 isl_upoly_free(&rec->up);
1095 return NULL;
1096 }
1097
1098 /* r array maps original positions to new positions.
1099 */
1100 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1101 int *r)
1102 {
1103 int i;
1104 struct isl_upoly_rec *rec;
1105 struct isl_upoly *base;
1106 struct isl_upoly *res;
1107
1108 if (isl_upoly_is_cst(up))
1109 return up;
1110
1111 rec = isl_upoly_as_rec(up);
1112 if (!rec)
1113 goto error;
1114
1115 isl_assert(up->ctx, rec->n >= 1, goto error);
1116
1117 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1118 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1119
1120 for (i = rec->n - 2; i >= 0; --i) {
1121 res = isl_upoly_mul(res, isl_upoly_copy(base));
1122 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1123 }
1124
1125 isl_upoly_free(base);
1126 isl_upoly_free(up);
1127
1128 return res;
1129 error:
1130 isl_upoly_free(up);
1131 return NULL;
1132 }
1133
1134 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1135 {
1136 int n_row, n_col;
1137 int equal;
1138
1139 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1140 div1->n_col >= div2->n_col, return -1);
1141
1142 if (div1->n_row == div2->n_row)
1143 return isl_mat_is_equal(div1, div2);
1144
1145 n_row = div1->n_row;
1146 n_col = div1->n_col;
1147 div1->n_row = div2->n_row;
1148 div1->n_col = div2->n_col;
1149
1150 equal = isl_mat_is_equal(div1, div2);
1151
1152 div1->n_row = n_row;
1153 div1->n_col = n_col;
1154
1155 return equal;
1156 }
1157
1158 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1159 {
1160 int li, lj;
1161
1162 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1163 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1164
1165 if (li != lj)
1166 return li - lj;
1167
1168 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1169 }
1170
1171 struct isl_div_sort_info {
1172 isl_mat *div;
1173 int row;
1174 };
1175
1176 static int div_sort_cmp(const void *p1, const void *p2)
1177 {
1178 const struct isl_div_sort_info *i1, *i2;
1179 i1 = (const struct isl_div_sort_info *) p1;
1180 i2 = (const struct isl_div_sort_info *) p2;
1181
1182 return cmp_row(i1->div, i1->row, i2->row);
1183 }
1184
1185 /* Sort divs and remove duplicates.
1186 */
1187 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1188 {
1189 int i;
1190 int skip;
1191 int len;
1192 struct isl_div_sort_info *array = NULL;
1193 int *pos = NULL, *at = NULL;
1194 int *reordering = NULL;
1195 unsigned div_pos;
1196
1197 if (!qp)
1198 return NULL;
1199 if (qp->div->n_row <= 1)
1200 return qp;
1201
1202 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1203
1204 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1205 qp->div->n_row);
1206 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1207 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1208 len = qp->div->n_col - 2;
1209 reordering = isl_alloc_array(qp->div->ctx, int, len);
1210 if (!array || !pos || !at || !reordering)
1211 goto error;
1212
1213 for (i = 0; i < qp->div->n_row; ++i) {
1214 array[i].div = qp->div;
1215 array[i].row = i;
1216 pos[i] = i;
1217 at[i] = i;
1218 }
1219
1220 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1221 div_sort_cmp);
1222
1223 for (i = 0; i < div_pos; ++i)
1224 reordering[i] = i;
1225
1226 for (i = 0; i < qp->div->n_row; ++i) {
1227 if (pos[array[i].row] == i)
1228 continue;
1229 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1230 pos[at[i]] = pos[array[i].row];
1231 at[pos[array[i].row]] = at[i];
1232 at[i] = array[i].row;
1233 pos[array[i].row] = i;
1234 }
1235
1236 skip = 0;
1237 for (i = 0; i < len - div_pos; ++i) {
1238 if (i > 0 &&
1239 isl_seq_eq(qp->div->row[i - skip - 1],
1240 qp->div->row[i - skip], qp->div->n_col)) {
1241 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1242 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1243 2 + div_pos + i - skip);
1244 qp->div = isl_mat_drop_cols(qp->div,
1245 2 + div_pos + i - skip, 1);
1246 skip++;
1247 }
1248 reordering[div_pos + array[i].row] = div_pos + i - skip;
1249 }
1250
1251 qp->upoly = reorder(qp->upoly, reordering);
1252
1253 if (!qp->upoly || !qp->div)
1254 goto error;
1255
1256 free(at);
1257 free(pos);
1258 free(array);
1259 free(reordering);
1260
1261 return qp;
1262 error:
1263 free(at);
1264 free(pos);
1265 free(array);
1266 free(reordering);
1267 isl_qpolynomial_free(qp);
1268 return NULL;
1269 }
1270
1271 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1272 int *exp, int first)
1273 {
1274 int i;
1275 struct isl_upoly_rec *rec;
1276
1277 if (isl_upoly_is_cst(up))
1278 return up;
1279
1280 if (up->var < first)
1281 return up;
1282
1283 if (exp[up->var - first] == up->var - first)
1284 return up;
1285
1286 up = isl_upoly_cow(up);
1287 if (!up)
1288 goto error;
1289
1290 up->var = exp[up->var - first] + first;
1291
1292 rec = isl_upoly_as_rec(up);
1293 if (!rec)
1294 goto error;
1295
1296 for (i = 0; i < rec->n; ++i) {
1297 rec->p[i] = expand(rec->p[i], exp, first);
1298 if (!rec->p[i])
1299 goto error;
1300 }
1301
1302 return up;
1303 error:
1304 isl_upoly_free(up);
1305 return NULL;
1306 }
1307
1308 static __isl_give isl_qpolynomial *with_merged_divs(
1309 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1310 __isl_take isl_qpolynomial *qp2),
1311 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1312 {
1313 int *exp1 = NULL;
1314 int *exp2 = NULL;
1315 isl_mat *div = NULL;
1316
1317 qp1 = isl_qpolynomial_cow(qp1);
1318 qp2 = isl_qpolynomial_cow(qp2);
1319
1320 if (!qp1 || !qp2)
1321 goto error;
1322
1323 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1324 qp1->div->n_col >= qp2->div->n_col, goto error);
1325
1326 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1327 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1328 if (!exp1 || !exp2)
1329 goto error;
1330
1331 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1332 if (!div)
1333 goto error;
1334
1335 isl_mat_free(qp1->div);
1336 qp1->div = isl_mat_copy(div);
1337 isl_mat_free(qp2->div);
1338 qp2->div = isl_mat_copy(div);
1339
1340 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1341 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1342
1343 if (!qp1->upoly || !qp2->upoly)
1344 goto error;
1345
1346 isl_mat_free(div);
1347 free(exp1);
1348 free(exp2);
1349
1350 return fn(qp1, qp2);
1351 error:
1352 isl_mat_free(div);
1353 free(exp1);
1354 free(exp2);
1355 isl_qpolynomial_free(qp1);
1356 isl_qpolynomial_free(qp2);
1357 return NULL;
1358 }
1359
1360 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1361 __isl_take isl_qpolynomial *qp2)
1362 {
1363 qp1 = isl_qpolynomial_cow(qp1);
1364
1365 if (!qp1 || !qp2)
1366 goto error;
1367
1368 if (qp1->div->n_row < qp2->div->n_row)
1369 return isl_qpolynomial_add(qp2, qp1);
1370
1371 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1372 if (!compatible_divs(qp1->div, qp2->div))
1373 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1374
1375 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1376 if (!qp1->upoly)
1377 goto error;
1378
1379 isl_qpolynomial_free(qp2);
1380
1381 return qp1;
1382 error:
1383 isl_qpolynomial_free(qp1);
1384 isl_qpolynomial_free(qp2);
1385 return NULL;
1386 }
1387
1388 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1389 __isl_keep isl_set *dom,
1390 __isl_take isl_qpolynomial *qp1,
1391 __isl_take isl_qpolynomial *qp2)
1392 {
1393 qp1 = isl_qpolynomial_add(qp1, qp2);
1394 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1395 return qp1;
1396 }
1397
1398 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1399 __isl_take isl_qpolynomial *qp2)
1400 {
1401 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1402 }
1403
1404 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1405 __isl_take isl_qpolynomial *qp, isl_int v)
1406 {
1407 if (isl_int_is_zero(v))
1408 return qp;
1409
1410 qp = isl_qpolynomial_cow(qp);
1411 if (!qp)
1412 return NULL;
1413
1414 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1415 if (!qp->upoly)
1416 goto error;
1417
1418 return qp;
1419 error:
1420 isl_qpolynomial_free(qp);
1421 return NULL;
1422
1423 }
1424
1425 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1426 {
1427 if (!qp)
1428 return NULL;
1429
1430 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1431 }
1432
1433 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1434 __isl_take isl_qpolynomial *qp, isl_int v)
1435 {
1436 if (isl_int_is_one(v))
1437 return qp;
1438
1439 if (qp && isl_int_is_zero(v)) {
1440 isl_qpolynomial *zero;
1441 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1442 isl_qpolynomial_free(qp);
1443 return zero;
1444 }
1445
1446 qp = isl_qpolynomial_cow(qp);
1447 if (!qp)
1448 return NULL;
1449
1450 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1451 if (!qp->upoly)
1452 goto error;
1453
1454 return qp;
1455 error:
1456 isl_qpolynomial_free(qp);
1457 return NULL;
1458 }
1459
1460 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1461 __isl_take isl_qpolynomial *qp, isl_int v)
1462 {
1463 return isl_qpolynomial_mul_isl_int(qp, v);
1464 }
1465
1466 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1467 __isl_take isl_qpolynomial *qp2)
1468 {
1469 qp1 = isl_qpolynomial_cow(qp1);
1470
1471 if (!qp1 || !qp2)
1472 goto error;
1473
1474 if (qp1->div->n_row < qp2->div->n_row)
1475 return isl_qpolynomial_mul(qp2, qp1);
1476
1477 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1478 if (!compatible_divs(qp1->div, qp2->div))
1479 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1480
1481 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1482 if (!qp1->upoly)
1483 goto error;
1484
1485 isl_qpolynomial_free(qp2);
1486
1487 return qp1;
1488 error:
1489 isl_qpolynomial_free(qp1);
1490 isl_qpolynomial_free(qp2);
1491 return NULL;
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1495 unsigned power)
1496 {
1497 qp = isl_qpolynomial_cow(qp);
1498
1499 if (!qp)
1500 return NULL;
1501
1502 qp->upoly = isl_upoly_pow(qp->upoly, power);
1503 if (!qp->upoly)
1504 goto error;
1505
1506 return qp;
1507 error:
1508 isl_qpolynomial_free(qp);
1509 return NULL;
1510 }
1511
1512 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1513 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1514 {
1515 int i;
1516
1517 if (power == 1)
1518 return pwqp;
1519
1520 pwqp = isl_pw_qpolynomial_cow(pwqp);
1521 if (!pwqp)
1522 return NULL;
1523
1524 for (i = 0; i < pwqp->n; ++i) {
1525 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1526 if (!pwqp->p[i].qp)
1527 return isl_pw_qpolynomial_free(pwqp);
1528 }
1529
1530 return pwqp;
1531 }
1532
1533 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1534 __isl_take isl_space *dim)
1535 {
1536 if (!dim)
1537 return NULL;
1538 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1539 }
1540
1541 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1542 __isl_take isl_space *dim)
1543 {
1544 if (!dim)
1545 return NULL;
1546 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1547 }
1548
1549 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1550 __isl_take isl_space *dim)
1551 {
1552 if (!dim)
1553 return NULL;
1554 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1555 }
1556
1557 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1558 __isl_take isl_space *dim)
1559 {
1560 if (!dim)
1561 return NULL;
1562 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1563 }
1564
1565 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1566 __isl_take isl_space *dim)
1567 {
1568 if (!dim)
1569 return NULL;
1570 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1571 }
1572
1573 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1574 __isl_take isl_space *dim,
1575 isl_int v)
1576 {
1577 struct isl_qpolynomial *qp;
1578 struct isl_upoly_cst *cst;
1579
1580 if (!dim)
1581 return NULL;
1582
1583 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1584 if (!qp)
1585 return NULL;
1586
1587 cst = isl_upoly_as_cst(qp->upoly);
1588 isl_int_set(cst->n, v);
1589
1590 return qp;
1591 }
1592
1593 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1594 isl_int *n, isl_int *d)
1595 {
1596 struct isl_upoly_cst *cst;
1597
1598 if (!qp)
1599 return -1;
1600
1601 if (!isl_upoly_is_cst(qp->upoly))
1602 return 0;
1603
1604 cst = isl_upoly_as_cst(qp->upoly);
1605 if (!cst)
1606 return -1;
1607
1608 if (n)
1609 isl_int_set(*n, cst->n);
1610 if (d)
1611 isl_int_set(*d, cst->d);
1612
1613 return 1;
1614 }
1615
1616 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1617 {
1618 int is_cst;
1619 struct isl_upoly_rec *rec;
1620
1621 if (!up)
1622 return -1;
1623
1624 if (up->var < 0)
1625 return 1;
1626
1627 rec = isl_upoly_as_rec(up);
1628 if (!rec)
1629 return -1;
1630
1631 if (rec->n > 2)
1632 return 0;
1633
1634 isl_assert(up->ctx, rec->n > 1, return -1);
1635
1636 is_cst = isl_upoly_is_cst(rec->p[1]);
1637 if (is_cst < 0)
1638 return -1;
1639 if (!is_cst)
1640 return 0;
1641
1642 return isl_upoly_is_affine(rec->p[0]);
1643 }
1644
1645 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1646 {
1647 if (!qp)
1648 return -1;
1649
1650 if (qp->div->n_row > 0)
1651 return 0;
1652
1653 return isl_upoly_is_affine(qp->upoly);
1654 }
1655
1656 static void update_coeff(__isl_keep isl_vec *aff,
1657 __isl_keep struct isl_upoly_cst *cst, int pos)
1658 {
1659 isl_int gcd;
1660 isl_int f;
1661
1662 if (isl_int_is_zero(cst->n))
1663 return;
1664
1665 isl_int_init(gcd);
1666 isl_int_init(f);
1667 isl_int_gcd(gcd, cst->d, aff->el[0]);
1668 isl_int_divexact(f, cst->d, gcd);
1669 isl_int_divexact(gcd, aff->el[0], gcd);
1670 isl_seq_scale(aff->el, aff->el, f, aff->size);
1671 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1672 isl_int_clear(gcd);
1673 isl_int_clear(f);
1674 }
1675
1676 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1677 __isl_keep isl_vec *aff)
1678 {
1679 struct isl_upoly_cst *cst;
1680 struct isl_upoly_rec *rec;
1681
1682 if (!up || !aff)
1683 return -1;
1684
1685 if (up->var < 0) {
1686 struct isl_upoly_cst *cst;
1687
1688 cst = isl_upoly_as_cst(up);
1689 if (!cst)
1690 return -1;
1691 update_coeff(aff, cst, 0);
1692 return 0;
1693 }
1694
1695 rec = isl_upoly_as_rec(up);
1696 if (!rec)
1697 return -1;
1698 isl_assert(up->ctx, rec->n == 2, return -1);
1699
1700 cst = isl_upoly_as_cst(rec->p[1]);
1701 if (!cst)
1702 return -1;
1703 update_coeff(aff, cst, 1 + up->var);
1704
1705 return isl_upoly_update_affine(rec->p[0], aff);
1706 }
1707
1708 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1709 __isl_keep isl_qpolynomial *qp)
1710 {
1711 isl_vec *aff;
1712 unsigned d;
1713
1714 if (!qp)
1715 return NULL;
1716
1717 d = isl_space_dim(qp->dim, isl_dim_all);
1718 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1719 if (!aff)
1720 return NULL;
1721
1722 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1723 isl_int_set_si(aff->el[0], 1);
1724
1725 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1726 goto error;
1727
1728 return aff;
1729 error:
1730 isl_vec_free(aff);
1731 return NULL;
1732 }
1733
1734 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1735 __isl_keep isl_qpolynomial *qp2)
1736 {
1737 int equal;
1738
1739 if (!qp1 || !qp2)
1740 return -1;
1741
1742 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1743 if (equal < 0 || !equal)
1744 return equal;
1745
1746 equal = isl_mat_is_equal(qp1->div, qp2->div);
1747 if (equal < 0 || !equal)
1748 return equal;
1749
1750 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1751 }
1752
1753 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1754 {
1755 int i;
1756 struct isl_upoly_rec *rec;
1757
1758 if (isl_upoly_is_cst(up)) {
1759 struct isl_upoly_cst *cst;
1760 cst = isl_upoly_as_cst(up);
1761 if (!cst)
1762 return;
1763 isl_int_lcm(*d, *d, cst->d);
1764 return;
1765 }
1766
1767 rec = isl_upoly_as_rec(up);
1768 if (!rec)
1769 return;
1770
1771 for (i = 0; i < rec->n; ++i)
1772 upoly_update_den(rec->p[i], d);
1773 }
1774
1775 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1776 {
1777 isl_int_set_si(*d, 1);
1778 if (!qp)
1779 return;
1780 upoly_update_den(qp->upoly, d);
1781 }
1782
1783 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
1784 __isl_take isl_space *dim, int pos, int power)
1785 {
1786 struct isl_ctx *ctx;
1787
1788 if (!dim)
1789 return NULL;
1790
1791 ctx = dim->ctx;
1792
1793 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1794 }
1795
1796 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
1797 enum isl_dim_type type, unsigned pos)
1798 {
1799 if (!dim)
1800 return NULL;
1801
1802 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1803 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1804
1805 if (type == isl_dim_set)
1806 pos += isl_space_dim(dim, isl_dim_param);
1807
1808 return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
1809 error:
1810 isl_space_free(dim);
1811 return NULL;
1812 }
1813
1814 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1815 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1816 {
1817 int i;
1818 struct isl_upoly_rec *rec;
1819 struct isl_upoly *base, *res;
1820
1821 if (!up)
1822 return NULL;
1823
1824 if (isl_upoly_is_cst(up))
1825 return up;
1826
1827 if (up->var < first)
1828 return up;
1829
1830 rec = isl_upoly_as_rec(up);
1831 if (!rec)
1832 goto error;
1833
1834 isl_assert(up->ctx, rec->n >= 1, goto error);
1835
1836 if (up->var >= first + n)
1837 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1838 else
1839 base = isl_upoly_copy(subs[up->var - first]);
1840
1841 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1842 for (i = rec->n - 2; i >= 0; --i) {
1843 struct isl_upoly *t;
1844 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1845 res = isl_upoly_mul(res, isl_upoly_copy(base));
1846 res = isl_upoly_sum(res, t);
1847 }
1848
1849 isl_upoly_free(base);
1850 isl_upoly_free(up);
1851
1852 return res;
1853 error:
1854 isl_upoly_free(up);
1855 return NULL;
1856 }
1857
1858 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1859 isl_int denom, unsigned len)
1860 {
1861 int i;
1862 struct isl_upoly *up;
1863
1864 isl_assert(ctx, len >= 1, return NULL);
1865
1866 up = isl_upoly_rat_cst(ctx, f[0], denom);
1867 for (i = 0; i < len - 1; ++i) {
1868 struct isl_upoly *t;
1869 struct isl_upoly *c;
1870
1871 if (isl_int_is_zero(f[1 + i]))
1872 continue;
1873
1874 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1875 t = isl_upoly_var_pow(ctx, i, 1);
1876 t = isl_upoly_mul(c, t);
1877 up = isl_upoly_sum(up, t);
1878 }
1879
1880 return up;
1881 }
1882
1883 /* Remove common factor of non-constant terms and denominator.
1884 */
1885 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1886 {
1887 isl_ctx *ctx = qp->div->ctx;
1888 unsigned total = qp->div->n_col - 2;
1889
1890 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1891 isl_int_gcd(ctx->normalize_gcd,
1892 ctx->normalize_gcd, qp->div->row[div][0]);
1893 if (isl_int_is_one(ctx->normalize_gcd))
1894 return;
1895
1896 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1897 ctx->normalize_gcd, total);
1898 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1899 ctx->normalize_gcd);
1900 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1901 ctx->normalize_gcd);
1902 }
1903
1904 /* Replace the integer division identified by "div" by the polynomial "s".
1905 * The integer division is assumed not to appear in the definition
1906 * of any other integer divisions.
1907 */
1908 static __isl_give isl_qpolynomial *substitute_div(
1909 __isl_take isl_qpolynomial *qp,
1910 int div, __isl_take struct isl_upoly *s)
1911 {
1912 int i;
1913 int total;
1914 int *reordering;
1915
1916 if (!qp || !s)
1917 goto error;
1918
1919 qp = isl_qpolynomial_cow(qp);
1920 if (!qp)
1921 goto error;
1922
1923 total = isl_space_dim(qp->dim, isl_dim_all);
1924 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1925 if (!qp->upoly)
1926 goto error;
1927
1928 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1929 if (!reordering)
1930 goto error;
1931 for (i = 0; i < total + div; ++i)
1932 reordering[i] = i;
1933 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1934 reordering[i] = i - 1;
1935 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1936 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1937 qp->upoly = reorder(qp->upoly, reordering);
1938 free(reordering);
1939
1940 if (!qp->upoly || !qp->div)
1941 goto error;
1942
1943 isl_upoly_free(s);
1944 return qp;
1945 error:
1946 isl_qpolynomial_free(qp);
1947 isl_upoly_free(s);
1948 return NULL;
1949 }
1950
1951 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1952 * divisions because d is equal to 1 by their definition, i.e., e.
1953 */
1954 static __isl_give isl_qpolynomial *substitute_non_divs(
1955 __isl_take isl_qpolynomial *qp)
1956 {
1957 int i, j;
1958 int total;
1959 struct isl_upoly *s;
1960
1961 if (!qp)
1962 return NULL;
1963
1964 total = isl_space_dim(qp->dim, isl_dim_all);
1965 for (i = 0; qp && i < qp->div->n_row; ++i) {
1966 if (!isl_int_is_one(qp->div->row[i][0]))
1967 continue;
1968 for (j = i + 1; j < qp->div->n_row; ++j) {
1969 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1970 continue;
1971 isl_seq_combine(qp->div->row[j] + 1,
1972 qp->div->ctx->one, qp->div->row[j] + 1,
1973 qp->div->row[j][2 + total + i],
1974 qp->div->row[i] + 1, 1 + total + i);
1975 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1976 normalize_div(qp, j);
1977 }
1978 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1979 qp->div->row[i][0], qp->div->n_col - 1);
1980 qp = substitute_div(qp, i, s);
1981 --i;
1982 }
1983
1984 return qp;
1985 }
1986
1987 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1988 * with d the denominator. When replacing the coefficient e of x by
1989 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1990 * inside the division, so we need to add floor(e/d) * x outside.
1991 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1992 * to adjust the coefficient of x in each later div that depends on the
1993 * current div "div" and also in the affine expression "aff"
1994 * (if it too depends on "div").
1995 */
1996 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1997 __isl_keep isl_vec *aff)
1998 {
1999 int i, j;
2000 isl_int v;
2001 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2002
2003 isl_int_init(v);
2004 for (i = 0; i < 1 + total + div; ++i) {
2005 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2006 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2007 continue;
2008 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2009 isl_int_fdiv_r(qp->div->row[div][1 + i],
2010 qp->div->row[div][1 + i], qp->div->row[div][0]);
2011 if (!isl_int_is_zero(aff->el[1 + total + div]))
2012 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
2013 for (j = div + 1; j < qp->div->n_row; ++j) {
2014 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2015 continue;
2016 isl_int_addmul(qp->div->row[j][1 + i],
2017 v, qp->div->row[j][2 + total + div]);
2018 }
2019 }
2020 isl_int_clear(v);
2021 }
2022
2023 /* Check if the last non-zero coefficient is bigger that half of the
2024 * denominator. If so, we will invert the div to further reduce the number
2025 * of distinct divs that may appear.
2026 * If the last non-zero coefficient is exactly half the denominator,
2027 * then we continue looking for earlier coefficients that are bigger
2028 * than half the denominator.
2029 */
2030 static int needs_invert(__isl_keep isl_mat *div, int row)
2031 {
2032 int i;
2033 int cmp;
2034
2035 for (i = div->n_col - 1; i >= 1; --i) {
2036 if (isl_int_is_zero(div->row[row][i]))
2037 continue;
2038 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2039 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2040 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2041 if (cmp)
2042 return cmp > 0;
2043 if (i == 1)
2044 return 1;
2045 }
2046
2047 return 0;
2048 }
2049
2050 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2051 * We only invert the coefficients of e (and the coefficient of q in
2052 * later divs and in "aff"). After calling this function, the
2053 * coefficients of e should be reduced again.
2054 */
2055 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2056 __isl_keep isl_vec *aff)
2057 {
2058 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2059
2060 isl_seq_neg(qp->div->row[div] + 1,
2061 qp->div->row[div] + 1, qp->div->n_col - 1);
2062 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2063 isl_int_add(qp->div->row[div][1],
2064 qp->div->row[div][1], qp->div->row[div][0]);
2065 if (!isl_int_is_zero(aff->el[1 + total + div]))
2066 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2067 isl_mat_col_mul(qp->div, 2 + total + div,
2068 qp->div->ctx->negone, 2 + total + div);
2069 }
2070
2071 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2072 * in the interval [0, d-1], with d the denominator and such that the
2073 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2074 *
2075 * After the reduction, some divs may have become redundant or identical,
2076 * so we call substitute_non_divs and sort_divs. If these functions
2077 * eliminate divs or merge two or more divs into one, the coefficients
2078 * of the enclosing divs may have to be reduced again, so we call
2079 * ourselves recursively if the number of divs decreases.
2080 */
2081 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2082 {
2083 int i;
2084 isl_vec *aff = NULL;
2085 struct isl_upoly *s;
2086 unsigned n_div;
2087
2088 if (!qp)
2089 return NULL;
2090
2091 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2092 aff = isl_vec_clr(aff);
2093 if (!aff)
2094 goto error;
2095
2096 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2097
2098 for (i = 0; i < qp->div->n_row; ++i) {
2099 normalize_div(qp, i);
2100 reduce_div(qp, i, aff);
2101 if (needs_invert(qp->div, i)) {
2102 invert_div(qp, i, aff);
2103 reduce_div(qp, i, aff);
2104 }
2105 }
2106
2107 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2108 qp->div->ctx->one, aff->size);
2109 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2110 isl_upoly_free(s);
2111 if (!qp->upoly)
2112 goto error;
2113
2114 isl_vec_free(aff);
2115
2116 n_div = qp->div->n_row;
2117 qp = substitute_non_divs(qp);
2118 qp = sort_divs(qp);
2119 if (qp && qp->div->n_row < n_div)
2120 return reduce_divs(qp);
2121
2122 return qp;
2123 error:
2124 isl_qpolynomial_free(qp);
2125 isl_vec_free(aff);
2126 return NULL;
2127 }
2128
2129 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2130 __isl_take isl_space *dim, const isl_int n, const isl_int d)
2131 {
2132 struct isl_qpolynomial *qp;
2133 struct isl_upoly_cst *cst;
2134
2135 if (!dim)
2136 return NULL;
2137
2138 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2139 if (!qp)
2140 return NULL;
2141
2142 cst = isl_upoly_as_cst(qp->upoly);
2143 isl_int_set(cst->n, n);
2144 isl_int_set(cst->d, d);
2145
2146 return qp;
2147 }
2148
2149 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2150 {
2151 struct isl_upoly_rec *rec;
2152 int i;
2153
2154 if (!up)
2155 return -1;
2156
2157 if (isl_upoly_is_cst(up))
2158 return 0;
2159
2160 if (up->var < d)
2161 active[up->var] = 1;
2162
2163 rec = isl_upoly_as_rec(up);
2164 for (i = 0; i < rec->n; ++i)
2165 if (up_set_active(rec->p[i], active, d) < 0)
2166 return -1;
2167
2168 return 0;
2169 }
2170
2171 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2172 {
2173 int i, j;
2174 int d = isl_space_dim(qp->dim, isl_dim_all);
2175
2176 if (!qp || !active)
2177 return -1;
2178
2179 for (i = 0; i < d; ++i)
2180 for (j = 0; j < qp->div->n_row; ++j) {
2181 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2182 continue;
2183 active[i] = 1;
2184 break;
2185 }
2186
2187 return up_set_active(qp->upoly, active, d);
2188 }
2189
2190 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2191 enum isl_dim_type type, unsigned first, unsigned n)
2192 {
2193 int i;
2194 int *active = NULL;
2195 int involves = 0;
2196
2197 if (!qp)
2198 return -1;
2199 if (n == 0)
2200 return 0;
2201
2202 isl_assert(qp->dim->ctx,
2203 first + n <= isl_qpolynomial_dim(qp, type), return -1);
2204 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2205 type == isl_dim_in, return -1);
2206
2207 active = isl_calloc_array(qp->dim->ctx, int,
2208 isl_space_dim(qp->dim, isl_dim_all));
2209 if (set_active(qp, active) < 0)
2210 goto error;
2211
2212 if (type == isl_dim_in)
2213 first += isl_space_dim(qp->dim, isl_dim_param);
2214 for (i = 0; i < n; ++i)
2215 if (active[first + i]) {
2216 involves = 1;
2217 break;
2218 }
2219
2220 free(active);
2221
2222 return involves;
2223 error:
2224 free(active);
2225 return -1;
2226 }
2227
2228 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2229 * of the divs that do appear in the quasi-polynomial.
2230 */
2231 static __isl_give isl_qpolynomial *remove_redundant_divs(
2232 __isl_take isl_qpolynomial *qp)
2233 {
2234 int i, j;
2235 int d;
2236 int len;
2237 int skip;
2238 int *active = NULL;
2239 int *reordering = NULL;
2240 int redundant = 0;
2241 int n_div;
2242 isl_ctx *ctx;
2243
2244 if (!qp)
2245 return NULL;
2246 if (qp->div->n_row == 0)
2247 return qp;
2248
2249 d = isl_space_dim(qp->dim, isl_dim_all);
2250 len = qp->div->n_col - 2;
2251 ctx = isl_qpolynomial_get_ctx(qp);
2252 active = isl_calloc_array(ctx, int, len);
2253 if (!active)
2254 goto error;
2255
2256 if (up_set_active(qp->upoly, active, len) < 0)
2257 goto error;
2258
2259 for (i = qp->div->n_row - 1; i >= 0; --i) {
2260 if (!active[d + i]) {
2261 redundant = 1;
2262 continue;
2263 }
2264 for (j = 0; j < i; ++j) {
2265 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2266 continue;
2267 active[d + j] = 1;
2268 break;
2269 }
2270 }
2271
2272 if (!redundant) {
2273 free(active);
2274 return qp;
2275 }
2276
2277 reordering = isl_alloc_array(qp->div->ctx, int, len);
2278 if (!reordering)
2279 goto error;
2280
2281 for (i = 0; i < d; ++i)
2282 reordering[i] = i;
2283
2284 skip = 0;
2285 n_div = qp->div->n_row;
2286 for (i = 0; i < n_div; ++i) {
2287 if (!active[d + i]) {
2288 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2289 qp->div = isl_mat_drop_cols(qp->div,
2290 2 + d + i - skip, 1);
2291 skip++;
2292 }
2293 reordering[d + i] = d + i - skip;
2294 }
2295
2296 qp->upoly = reorder(qp->upoly, reordering);
2297
2298 if (!qp->upoly || !qp->div)
2299 goto error;
2300
2301 free(active);
2302 free(reordering);
2303
2304 return qp;
2305 error:
2306 free(active);
2307 free(reordering);
2308 isl_qpolynomial_free(qp);
2309 return NULL;
2310 }
2311
2312 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2313 unsigned first, unsigned n)
2314 {
2315 int i;
2316 struct isl_upoly_rec *rec;
2317
2318 if (!up)
2319 return NULL;
2320 if (n == 0 || up->var < 0 || up->var < first)
2321 return up;
2322 if (up->var < first + n) {
2323 up = replace_by_constant_term(up);
2324 return isl_upoly_drop(up, first, n);
2325 }
2326 up = isl_upoly_cow(up);
2327 if (!up)
2328 return NULL;
2329 up->var -= n;
2330 rec = isl_upoly_as_rec(up);
2331 if (!rec)
2332 goto error;
2333
2334 for (i = 0; i < rec->n; ++i) {
2335 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2336 if (!rec->p[i])
2337 goto error;
2338 }
2339
2340 return up;
2341 error:
2342 isl_upoly_free(up);
2343 return NULL;
2344 }
2345
2346 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2347 __isl_take isl_qpolynomial *qp,
2348 enum isl_dim_type type, unsigned pos, const char *s)
2349 {
2350 qp = isl_qpolynomial_cow(qp);
2351 if (!qp)
2352 return NULL;
2353 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2354 if (!qp->dim)
2355 goto error;
2356 return qp;
2357 error:
2358 isl_qpolynomial_free(qp);
2359 return NULL;
2360 }
2361
2362 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2363 __isl_take isl_qpolynomial *qp,
2364 enum isl_dim_type type, unsigned first, unsigned n)
2365 {
2366 if (!qp)
2367 return NULL;
2368 if (type == isl_dim_out)
2369 isl_die(qp->dim->ctx, isl_error_invalid,
2370 "cannot drop output/set dimension",
2371 goto error);
2372 if (type == isl_dim_in)
2373 type = isl_dim_set;
2374 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2375 return qp;
2376
2377 qp = isl_qpolynomial_cow(qp);
2378 if (!qp)
2379 return NULL;
2380
2381 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2382 goto error);
2383 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2384 type == isl_dim_set, goto error);
2385
2386 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2387 if (!qp->dim)
2388 goto error;
2389
2390 if (type == isl_dim_set)
2391 first += isl_space_dim(qp->dim, isl_dim_param);
2392
2393 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2394 if (!qp->div)
2395 goto error;
2396
2397 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2398 if (!qp->upoly)
2399 goto error;
2400
2401 return qp;
2402 error:
2403 isl_qpolynomial_free(qp);
2404 return NULL;
2405 }
2406
2407 /* Project the domain of the quasi-polynomial onto its parameter space.
2408 * The quasi-polynomial may not involve any of the domain dimensions.
2409 */
2410 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2411 __isl_take isl_qpolynomial *qp)
2412 {
2413 isl_space *space;
2414 unsigned n;
2415 int involves;
2416
2417 n = isl_qpolynomial_dim(qp, isl_dim_in);
2418 involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2419 if (involves < 0)
2420 return isl_qpolynomial_free(qp);
2421 if (involves)
2422 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2423 "polynomial involves some of the domain dimensions",
2424 return isl_qpolynomial_free(qp));
2425 qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2426 space = isl_qpolynomial_get_domain_space(qp);
2427 space = isl_space_params(space);
2428 qp = isl_qpolynomial_reset_domain_space(qp, space);
2429 return qp;
2430 }
2431
2432 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2433 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2434 {
2435 int i, j, k;
2436 isl_int denom;
2437 unsigned total;
2438 unsigned n_div;
2439 struct isl_upoly *up;
2440
2441 if (!eq)
2442 goto error;
2443 if (eq->n_eq == 0) {
2444 isl_basic_set_free(eq);
2445 return qp;
2446 }
2447
2448 qp = isl_qpolynomial_cow(qp);
2449 if (!qp)
2450 goto error;
2451 qp->div = isl_mat_cow(qp->div);
2452 if (!qp->div)
2453 goto error;
2454
2455 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2456 n_div = eq->n_div;
2457 isl_int_init(denom);
2458 for (i = 0; i < eq->n_eq; ++i) {
2459 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2460 if (j < 0 || j == 0 || j >= total)
2461 continue;
2462
2463 for (k = 0; k < qp->div->n_row; ++k) {
2464 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2465 continue;
2466 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2467 &qp->div->row[k][0]);
2468 normalize_div(qp, k);
2469 }
2470
2471 if (isl_int_is_pos(eq->eq[i][j]))
2472 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2473 isl_int_abs(denom, eq->eq[i][j]);
2474 isl_int_set_si(eq->eq[i][j], 0);
2475
2476 up = isl_upoly_from_affine(qp->dim->ctx,
2477 eq->eq[i], denom, total);
2478 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2479 isl_upoly_free(up);
2480 }
2481 isl_int_clear(denom);
2482
2483 if (!qp->upoly)
2484 goto error;
2485
2486 isl_basic_set_free(eq);
2487
2488 qp = substitute_non_divs(qp);
2489 qp = sort_divs(qp);
2490
2491 return qp;
2492 error:
2493 isl_basic_set_free(eq);
2494 isl_qpolynomial_free(qp);
2495 return NULL;
2496 }
2497
2498 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2499 */
2500 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2501 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2502 {
2503 if (!qp || !eq)
2504 goto error;
2505 if (qp->div->n_row > 0)
2506 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2507 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2508 error:
2509 isl_basic_set_free(eq);
2510 isl_qpolynomial_free(qp);
2511 return NULL;
2512 }
2513
2514 static __isl_give isl_basic_set *add_div_constraints(
2515 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2516 {
2517 int i;
2518 unsigned total;
2519
2520 if (!bset || !div)
2521 goto error;
2522
2523 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2524 if (!bset)
2525 goto error;
2526 total = isl_basic_set_total_dim(bset);
2527 for (i = 0; i < div->n_row; ++i)
2528 if (isl_basic_set_add_div_constraints_var(bset,
2529 total - div->n_row + i, div->row[i]) < 0)
2530 goto error;
2531
2532 isl_mat_free(div);
2533 return bset;
2534 error:
2535 isl_mat_free(div);
2536 isl_basic_set_free(bset);
2537 return NULL;
2538 }
2539
2540 /* Look for equalities among the variables shared by context and qp
2541 * and the integer divisions of qp, if any.
2542 * The equalities are then used to eliminate variables and/or integer
2543 * divisions from qp.
2544 */
2545 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2546 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2547 {
2548 isl_basic_set *aff;
2549
2550 if (!qp)
2551 goto error;
2552 if (qp->div->n_row > 0) {
2553 isl_basic_set *bset;
2554 context = isl_set_add_dims(context, isl_dim_set,
2555 qp->div->n_row);
2556 bset = isl_basic_set_universe(isl_set_get_space(context));
2557 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2558 context = isl_set_intersect(context,
2559 isl_set_from_basic_set(bset));
2560 }
2561
2562 aff = isl_set_affine_hull(context);
2563 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2564 error:
2565 isl_qpolynomial_free(qp);
2566 isl_set_free(context);
2567 return NULL;
2568 }
2569
2570 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
2571 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2572 {
2573 isl_space *space = isl_qpolynomial_get_domain_space(qp);
2574 isl_set *dom_context = isl_set_universe(space);
2575 dom_context = isl_set_intersect_params(dom_context, context);
2576 return isl_qpolynomial_gist(qp, dom_context);
2577 }
2578
2579 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2580 __isl_take isl_qpolynomial *qp)
2581 {
2582 isl_set *dom;
2583
2584 if (!qp)
2585 return NULL;
2586 if (isl_qpolynomial_is_zero(qp)) {
2587 isl_space *dim = isl_qpolynomial_get_space(qp);
2588 isl_qpolynomial_free(qp);
2589 return isl_pw_qpolynomial_zero(dim);
2590 }
2591
2592 dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
2593 return isl_pw_qpolynomial_alloc(dom, qp);
2594 }
2595
2596 #undef PW
2597 #define PW isl_pw_qpolynomial
2598 #undef EL
2599 #define EL isl_qpolynomial
2600 #undef EL_IS_ZERO
2601 #define EL_IS_ZERO is_zero
2602 #undef ZERO
2603 #define ZERO zero
2604 #undef IS_ZERO
2605 #define IS_ZERO is_zero
2606 #undef FIELD
2607 #define FIELD qp
2608
2609 #include <isl_pw_templ.c>
2610
2611 #undef UNION
2612 #define UNION isl_union_pw_qpolynomial
2613 #undef PART
2614 #define PART isl_pw_qpolynomial
2615 #undef PARTS
2616 #define PARTS pw_qpolynomial
2617 #define ALIGN_DOMAIN
2618
2619 #include <isl_union_templ.c>
2620
2621 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2622 {
2623 if (!pwqp)
2624 return -1;
2625
2626 if (pwqp->n != -1)
2627 return 0;
2628
2629 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2630 return 0;
2631
2632 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2633 }
2634
2635 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2636 __isl_take isl_pw_qpolynomial *pwqp1,
2637 __isl_take isl_pw_qpolynomial *pwqp2)
2638 {
2639 return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
2640 }
2641
2642 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2643 __isl_take isl_pw_qpolynomial *pwqp1,
2644 __isl_take isl_pw_qpolynomial *pwqp2)
2645 {
2646 int i, j, n;
2647 struct isl_pw_qpolynomial *res;
2648
2649 if (!pwqp1 || !pwqp2)
2650 goto error;
2651
2652 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2653 goto error);
2654
2655 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2656 isl_pw_qpolynomial_free(pwqp2);
2657 return pwqp1;
2658 }
2659
2660 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2661 isl_pw_qpolynomial_free(pwqp1);
2662 return pwqp2;
2663 }
2664
2665 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2666 isl_pw_qpolynomial_free(pwqp1);
2667 return pwqp2;
2668 }
2669
2670 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2671 isl_pw_qpolynomial_free(pwqp2);
2672 return pwqp1;
2673 }
2674
2675 n = pwqp1->n * pwqp2->n;
2676 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2677
2678 for (i = 0; i < pwqp1->n; ++i) {
2679 for (j = 0; j < pwqp2->n; ++j) {
2680 struct isl_set *common;
2681 struct isl_qpolynomial *prod;
2682 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2683 isl_set_copy(pwqp2->p[j].set));
2684 if (isl_set_plain_is_empty(common)) {
2685 isl_set_free(common);
2686 continue;
2687 }
2688
2689 prod = isl_qpolynomial_mul(
2690 isl_qpolynomial_copy(pwqp1->p[i].qp),
2691 isl_qpolynomial_copy(pwqp2->p[j].qp));
2692
2693 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2694 }
2695 }
2696
2697 isl_pw_qpolynomial_free(pwqp1);
2698 isl_pw_qpolynomial_free(pwqp2);
2699
2700 return res;
2701 error:
2702 isl_pw_qpolynomial_free(pwqp1);
2703 isl_pw_qpolynomial_free(pwqp2);
2704 return NULL;
2705 }
2706
2707 __isl_give struct isl_upoly *isl_upoly_eval(
2708 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2709 {
2710 int i;
2711 struct isl_upoly_rec *rec;
2712 struct isl_upoly *res;
2713 struct isl_upoly *base;
2714
2715 if (isl_upoly_is_cst(up)) {
2716 isl_vec_free(vec);
2717 return up;
2718 }
2719
2720 rec = isl_upoly_as_rec(up);
2721 if (!rec)
2722 goto error;
2723
2724 isl_assert(up->ctx, rec->n >= 1, goto error);
2725
2726 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2727
2728 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2729 isl_vec_copy(vec));
2730
2731 for (i = rec->n - 2; i >= 0; --i) {
2732 res = isl_upoly_mul(res, isl_upoly_copy(base));
2733 res = isl_upoly_sum(res,
2734 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2735 isl_vec_copy(vec)));
2736 }
2737
2738 isl_upoly_free(base);
2739 isl_upoly_free(up);
2740 isl_vec_free(vec);
2741 return res;
2742 error:
2743 isl_upoly_free(up);
2744 isl_vec_free(vec);
2745 return NULL;
2746 }
2747
2748 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2749 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2750 {
2751 isl_vec *ext;
2752 struct isl_upoly *up;
2753 isl_space *dim;
2754
2755 if (!qp || !pnt)
2756 goto error;
2757 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2758
2759 if (qp->div->n_row == 0)
2760 ext = isl_vec_copy(pnt->vec);
2761 else {
2762 int i;
2763 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2764 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2765 if (!ext)
2766 goto error;
2767
2768 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2769 for (i = 0; i < qp->div->n_row; ++i) {
2770 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2771 1 + dim + i, &ext->el[1+dim+i]);
2772 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2773 qp->div->row[i][0]);
2774 }
2775 }
2776
2777 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2778 if (!up)
2779 goto error;
2780
2781 dim = isl_space_copy(qp->dim);
2782 isl_qpolynomial_free(qp);
2783 isl_point_free(pnt);
2784
2785 return isl_qpolynomial_alloc(dim, 0, up);
2786 error:
2787 isl_qpolynomial_free(qp);
2788 isl_point_free(pnt);
2789 return NULL;
2790 }
2791
2792 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2793 __isl_keep struct isl_upoly_cst *cst2)
2794 {
2795 int cmp;
2796 isl_int t;
2797 isl_int_init(t);
2798 isl_int_mul(t, cst1->n, cst2->d);
2799 isl_int_submul(t, cst2->n, cst1->d);
2800 cmp = isl_int_sgn(t);
2801 isl_int_clear(t);
2802 return cmp;
2803 }
2804
2805 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2806 __isl_keep isl_qpolynomial *qp2)
2807 {
2808 struct isl_upoly_cst *cst1, *cst2;
2809
2810 if (!qp1 || !qp2)
2811 return -1;
2812 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2813 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2814 if (isl_qpolynomial_is_nan(qp1))
2815 return -1;
2816 if (isl_qpolynomial_is_nan(qp2))
2817 return -1;
2818 cst1 = isl_upoly_as_cst(qp1->upoly);
2819 cst2 = isl_upoly_as_cst(qp2->upoly);
2820
2821 return isl_upoly_cmp(cst1, cst2) <= 0;
2822 }
2823
2824 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2825 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2826 {
2827 struct isl_upoly_cst *cst1, *cst2;
2828 int cmp;
2829
2830 if (!qp1 || !qp2)
2831 goto error;
2832 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2833 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2834 cst1 = isl_upoly_as_cst(qp1->upoly);
2835 cst2 = isl_upoly_as_cst(qp2->upoly);
2836 cmp = isl_upoly_cmp(cst1, cst2);
2837
2838 if (cmp <= 0) {
2839 isl_qpolynomial_free(qp2);
2840 } else {
2841 isl_qpolynomial_free(qp1);
2842 qp1 = qp2;
2843 }
2844 return qp1;
2845 error:
2846 isl_qpolynomial_free(qp1);
2847 isl_qpolynomial_free(qp2);
2848 return NULL;
2849 }
2850
2851 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2852 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2853 {
2854 struct isl_upoly_cst *cst1, *cst2;
2855 int cmp;
2856
2857 if (!qp1 || !qp2)
2858 goto error;
2859 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2860 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2861 cst1 = isl_upoly_as_cst(qp1->upoly);
2862 cst2 = isl_upoly_as_cst(qp2->upoly);
2863 cmp = isl_upoly_cmp(cst1, cst2);
2864
2865 if (cmp >= 0) {
2866 isl_qpolynomial_free(qp2);
2867 } else {
2868 isl_qpolynomial_free(qp1);
2869 qp1 = qp2;
2870 }
2871 return qp1;
2872 error:
2873 isl_qpolynomial_free(qp1);
2874 isl_qpolynomial_free(qp2);
2875 return NULL;
2876 }
2877
2878 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2879 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2880 unsigned first, unsigned n)
2881 {
2882 unsigned total;
2883 unsigned g_pos;
2884 int *exp;
2885
2886 if (!qp)
2887 return NULL;
2888 if (type == isl_dim_out)
2889 isl_die(qp->div->ctx, isl_error_invalid,
2890 "cannot insert output/set dimensions",
2891 goto error);
2892 if (type == isl_dim_in)
2893 type = isl_dim_set;
2894 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2895 return qp;
2896
2897 qp = isl_qpolynomial_cow(qp);
2898 if (!qp)
2899 return NULL;
2900
2901 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2902 goto error);
2903
2904 g_pos = pos(qp->dim, type) + first;
2905
2906 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2907 if (!qp->div)
2908 goto error;
2909
2910 total = qp->div->n_col - 2;
2911 if (total > g_pos) {
2912 int i;
2913 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2914 if (!exp)
2915 goto error;
2916 for (i = 0; i < total - g_pos; ++i)
2917 exp[i] = i + n;
2918 qp->upoly = expand(qp->upoly, exp, g_pos);
2919 free(exp);
2920 if (!qp->upoly)
2921 goto error;
2922 }
2923
2924 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2925 if (!qp->dim)
2926 goto error;
2927
2928 return qp;
2929 error:
2930 isl_qpolynomial_free(qp);
2931 return NULL;
2932 }
2933
2934 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2935 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2936 {
2937 unsigned pos;
2938
2939 pos = isl_qpolynomial_dim(qp, type);
2940
2941 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2942 }
2943
2944 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2945 __isl_take isl_pw_qpolynomial *pwqp,
2946 enum isl_dim_type type, unsigned n)
2947 {
2948 unsigned pos;
2949
2950 pos = isl_pw_qpolynomial_dim(pwqp, type);
2951
2952 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2953 }
2954
2955 static int *reordering_move(isl_ctx *ctx,
2956 unsigned len, unsigned dst, unsigned src, unsigned n)
2957 {
2958 int i;
2959 int *reordering;
2960
2961 reordering = isl_alloc_array(ctx, int, len);
2962 if (!reordering)
2963 return NULL;
2964
2965 if (dst <= src) {
2966 for (i = 0; i < dst; ++i)
2967 reordering[i] = i;
2968 for (i = 0; i < n; ++i)
2969 reordering[src + i] = dst + i;
2970 for (i = 0; i < src - dst; ++i)
2971 reordering[dst + i] = dst + n + i;
2972 for (i = 0; i < len - src - n; ++i)
2973 reordering[src + n + i] = src + n + i;
2974 } else {
2975 for (i = 0; i < src; ++i)
2976 reordering[i] = i;
2977 for (i = 0; i < n; ++i)
2978 reordering[src + i] = dst + i;
2979 for (i = 0; i < dst - src; ++i)
2980 reordering[src + n + i] = src + i;
2981 for (i = 0; i < len - dst - n; ++i)
2982 reordering[dst + n + i] = dst + n + i;
2983 }
2984
2985 return reordering;
2986 }
2987
2988 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2989 __isl_take isl_qpolynomial *qp,
2990 enum isl_dim_type dst_type, unsigned dst_pos,
2991 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2992 {
2993 unsigned g_dst_pos;
2994 unsigned g_src_pos;
2995 int *reordering;
2996
2997 qp = isl_qpolynomial_cow(qp);
2998 if (!qp)
2999 return NULL;
3000
3001 if (dst_type == isl_dim_out || src_type == isl_dim_out)
3002 isl_die(qp->dim->ctx, isl_error_invalid,
3003 "cannot move output/set dimension",
3004 goto error);
3005 if (dst_type == isl_dim_in)
3006 dst_type = isl_dim_set;
3007 if (src_type == isl_dim_in)
3008 src_type = isl_dim_set;
3009
3010 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3011 goto error);
3012
3013 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3014 g_src_pos = pos(qp->dim, src_type) + src_pos;
3015 if (dst_type > src_type)
3016 g_dst_pos -= n;
3017
3018 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3019 if (!qp->div)
3020 goto error;
3021 qp = sort_divs(qp);
3022 if (!qp)
3023 goto error;
3024
3025 reordering = reordering_move(qp->dim->ctx,
3026 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3027 if (!reordering)
3028 goto error;
3029
3030 qp->upoly = reorder(qp->upoly, reordering);
3031 free(reordering);
3032 if (!qp->upoly)
3033 goto error;
3034
3035 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3036 if (!qp->dim)
3037 goto error;
3038
3039 return qp;
3040 error:
3041 isl_qpolynomial_free(qp);
3042 return NULL;
3043 }
3044
3045 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3046 isl_int *f, isl_int denom)
3047 {
3048 struct isl_upoly *up;
3049
3050 dim = isl_space_domain(dim);
3051 if (!dim)
3052 return NULL;
3053
3054 up = isl_upoly_from_affine(dim->ctx, f, denom,
3055 1 + isl_space_dim(dim, isl_dim_all));
3056
3057 return isl_qpolynomial_alloc(dim, 0, up);
3058 }
3059
3060 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3061 {
3062 isl_ctx *ctx;
3063 struct isl_upoly *up;
3064 isl_qpolynomial *qp;
3065
3066 if (!aff)
3067 return NULL;
3068
3069 ctx = isl_aff_get_ctx(aff);
3070 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3071 aff->v->size - 1);
3072
3073 qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3074 aff->ls->div->n_row, up);
3075 if (!qp)
3076 goto error;
3077
3078 isl_mat_free(qp->div);
3079 qp->div = isl_mat_copy(aff->ls->div);
3080 qp->div = isl_mat_cow(qp->div);
3081 if (!qp->div)
3082 goto error;
3083
3084 isl_aff_free(aff);
3085 qp = reduce_divs(qp);
3086 qp = remove_redundant_divs(qp);
3087 return qp;
3088 error:
3089 isl_aff_free(aff);
3090 return NULL;
3091 }
3092
3093 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3094 __isl_take isl_pw_aff *pwaff)
3095 {
3096 int i;
3097 isl_pw_qpolynomial *pwqp;
3098
3099 if (!pwaff)
3100 return NULL;
3101
3102 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3103 pwaff->n);
3104
3105 for (i = 0; i < pwaff->n; ++i) {
3106 isl_set *dom;
3107 isl_qpolynomial *qp;
3108
3109 dom = isl_set_copy(pwaff->p[i].set);
3110 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3111 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3112 }
3113
3114 isl_pw_aff_free(pwaff);
3115 return pwqp;
3116 }
3117
3118 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3119 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3120 {
3121 isl_aff *aff;
3122
3123 aff = isl_constraint_get_bound(c, type, pos);
3124 isl_constraint_free(c);
3125 return isl_qpolynomial_from_aff(aff);
3126 }
3127
3128 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3129 * in "qp" by subs[i].
3130 */
3131 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3132 __isl_take isl_qpolynomial *qp,
3133 enum isl_dim_type type, unsigned first, unsigned n,
3134 __isl_keep isl_qpolynomial **subs)
3135 {
3136 int i;
3137 struct isl_upoly **ups;
3138
3139 if (n == 0)
3140 return qp;
3141
3142 qp = isl_qpolynomial_cow(qp);
3143 if (!qp)
3144 return NULL;
3145
3146 if (type == isl_dim_out)
3147 isl_die(qp->dim->ctx, isl_error_invalid,
3148 "cannot substitute output/set dimension",
3149 goto error);
3150 if (type == isl_dim_in)
3151 type = isl_dim_set;
3152
3153 for (i = 0; i < n; ++i)
3154 if (!subs[i])
3155 goto error;
3156
3157 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3158 goto error);
3159
3160 for (i = 0; i < n; ++i)
3161 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3162 goto error);
3163
3164 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3165 for (i = 0; i < n; ++i)
3166 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3167
3168 first += pos(qp->dim, type);
3169
3170 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3171 if (!ups)
3172 goto error;
3173 for (i = 0; i < n; ++i)
3174 ups[i] = subs[i]->upoly;
3175
3176 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3177
3178 free(ups);
3179
3180 if (!qp->upoly)
3181 goto error;
3182
3183 return qp;
3184 error:
3185 isl_qpolynomial_free(qp);
3186 return NULL;
3187 }
3188
3189 /* Extend "bset" with extra set dimensions for each integer division
3190 * in "qp" and then call "fn" with the extended bset and the polynomial
3191 * that results from replacing each of the integer divisions by the
3192 * corresponding extra set dimension.
3193 */
3194 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3195 __isl_keep isl_basic_set *bset,
3196 int (*fn)(__isl_take isl_basic_set *bset,
3197 __isl_take isl_qpolynomial *poly, void *user), void *user)
3198 {
3199 isl_space *dim;
3200 isl_mat *div;
3201 isl_qpolynomial *poly;
3202
3203 if (!qp || !bset)
3204 goto error;
3205 if (qp->div->n_row == 0)
3206 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3207 user);
3208
3209 div = isl_mat_copy(qp->div);
3210 dim = isl_space_copy(qp->dim);
3211 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3212 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3213 bset = isl_basic_set_copy(bset);
3214 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3215 bset = add_div_constraints(bset, div);
3216
3217 return fn(bset, poly, user);
3218 error:
3219 return -1;
3220 }
3221
3222 /* Return total degree in variables first (inclusive) up to last (exclusive).
3223 */
3224 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3225 {
3226 int deg = -1;
3227 int i;
3228 struct isl_upoly_rec *rec;
3229
3230 if (!up)
3231 return -2;
3232 if (isl_upoly_is_zero(up))
3233 return -1;
3234 if (isl_upoly_is_cst(up) || up->var < first)
3235 return 0;
3236
3237 rec = isl_upoly_as_rec(up);
3238 if (!rec)
3239 return -2;
3240
3241 for (i = 0; i < rec->n; ++i) {
3242 int d;
3243
3244 if (isl_upoly_is_zero(rec->p[i]))
3245 continue;
3246 d = isl_upoly_degree(rec->p[i], first, last);
3247 if (up->var < last)
3248 d += i;
3249 if (d > deg)
3250 deg = d;
3251 }
3252
3253 return deg;
3254 }
3255
3256 /* Return total degree in set variables.
3257 */
3258 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3259 {
3260 unsigned ovar;
3261 unsigned nvar;
3262
3263 if (!poly)
3264 return -2;
3265
3266 ovar = isl_space_offset(poly->dim, isl_dim_set);
3267 nvar = isl_space_dim(poly->dim, isl_dim_set);
3268 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3269 }
3270
3271 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3272 unsigned pos, int deg)
3273 {
3274 int i;
3275 struct isl_upoly_rec *rec;
3276
3277 if (!up)
3278 return NULL;
3279
3280 if (isl_upoly_is_cst(up) || up->var < pos) {
3281 if (deg == 0)
3282 return isl_upoly_copy(up);
3283 else
3284 return isl_upoly_zero(up->ctx);
3285 }
3286
3287 rec = isl_upoly_as_rec(up);
3288 if (!rec)
3289 return NULL;
3290
3291 if (up->var == pos) {
3292 if (deg < rec->n)
3293 return isl_upoly_copy(rec->p[deg]);
3294 else
3295 return isl_upoly_zero(up->ctx);
3296 }
3297
3298 up = isl_upoly_copy(up);
3299 up = isl_upoly_cow(up);
3300 rec = isl_upoly_as_rec(up);
3301 if (!rec)
3302 goto error;
3303
3304 for (i = 0; i < rec->n; ++i) {
3305 struct isl_upoly *t;
3306 t = isl_upoly_coeff(rec->p[i], pos, deg);
3307 if (!t)
3308 goto error;
3309 isl_upoly_free(rec->p[i]);
3310 rec->p[i] = t;
3311 }
3312
3313 return up;
3314 error:
3315 isl_upoly_free(up);
3316 return NULL;
3317 }
3318
3319 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3320 */
3321 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3322 __isl_keep isl_qpolynomial *qp,
3323 enum isl_dim_type type, unsigned t_pos, int deg)
3324 {
3325 unsigned g_pos;
3326 struct isl_upoly *up;
3327 isl_qpolynomial *c;
3328
3329 if (!qp)
3330 return NULL;
3331
3332 if (type == isl_dim_out)
3333 isl_die(qp->div->ctx, isl_error_invalid,
3334 "output/set dimension does not have a coefficient",
3335 return NULL);
3336 if (type == isl_dim_in)
3337 type = isl_dim_set;
3338
3339 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3340 return NULL);
3341
3342 g_pos = pos(qp->dim, type) + t_pos;
3343 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3344
3345 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3346 if (!c)
3347 return NULL;
3348 isl_mat_free(c->div);
3349 c->div = isl_mat_copy(qp->div);
3350 if (!c->div)
3351 goto error;
3352 return c;
3353 error:
3354 isl_qpolynomial_free(c);
3355 return NULL;
3356 }
3357
3358 /* Homogenize the polynomial in the variables first (inclusive) up to
3359 * last (exclusive) by inserting powers of variable first.
3360 * Variable first is assumed not to appear in the input.
3361 */
3362 __isl_give struct isl_upoly *isl_upoly_homogenize(
3363 __isl_take struct isl_upoly *up, int deg, int target,
3364 int first, int last)
3365 {
3366 int i;
3367 struct isl_upoly_rec *rec;
3368
3369 if (!up)
3370 return NULL;
3371 if (isl_upoly_is_zero(up))
3372 return up;
3373 if (deg == target)
3374 return up;
3375 if (isl_upoly_is_cst(up) || up->var < first) {
3376 struct isl_upoly *hom;
3377
3378 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3379 if (!hom)
3380 goto error;
3381 rec = isl_upoly_as_rec(hom);
3382 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3383
3384 return hom;
3385 }
3386
3387 up = isl_upoly_cow(up);
3388 rec = isl_upoly_as_rec(up);
3389 if (!rec)
3390 goto error;
3391
3392 for (i = 0; i < rec->n; ++i) {
3393 if (isl_upoly_is_zero(rec->p[i]))
3394 continue;
3395 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3396 up->var < last ? deg + i : i, target,
3397 first, last);
3398 if (!rec->p[i])
3399 goto error;
3400 }
3401
3402 return up;
3403 error:
3404 isl_upoly_free(up);
3405 return NULL;
3406 }
3407
3408 /* Homogenize the polynomial in the set variables by introducing
3409 * powers of an extra set variable at position 0.
3410 */
3411 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3412 __isl_take isl_qpolynomial *poly)
3413 {
3414 unsigned ovar;
3415 unsigned nvar;
3416 int deg = isl_qpolynomial_degree(poly);
3417
3418 if (deg < -1)
3419 goto error;
3420
3421 poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3422 poly = isl_qpolynomial_cow(poly);
3423 if (!poly)
3424 goto error;
3425
3426 ovar = isl_space_offset(poly->dim, isl_dim_set);
3427 nvar = isl_space_dim(poly->dim, isl_dim_set);
3428 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3429 ovar, ovar + nvar);
3430 if (!poly->upoly)
3431 goto error;
3432
3433 return poly;
3434 error:
3435 isl_qpolynomial_free(poly);
3436 return NULL;
3437 }
3438
3439 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3440 __isl_take isl_mat *div)
3441 {
3442 isl_term *term;
3443 int n;
3444
3445 if (!dim || !div)
3446 goto error;
3447
3448 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3449
3450 term = isl_calloc(dim->ctx, struct isl_term,
3451 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3452 if (!term)
3453 goto error;
3454
3455 term->ref = 1;
3456 term->dim = dim;
3457 term->div = div;
3458 isl_int_init(term->n);
3459 isl_int_init(term->d);
3460
3461 return term;
3462 error:
3463 isl_space_free(dim);
3464 isl_mat_free(div);
3465 return NULL;
3466 }
3467
3468 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3469 {
3470 if (!term)
3471 return NULL;
3472
3473 term->ref++;
3474 return term;
3475 }
3476
3477 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3478 {
3479 int i;
3480 isl_term *dup;
3481 unsigned total;
3482
3483 if (term)
3484 return NULL;
3485
3486 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3487
3488 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3489 if (!dup)
3490 return NULL;
3491
3492 isl_int_set(dup->n, term->n);
3493 isl_int_set(dup->d, term->d);
3494
3495 for (i = 0; i < total; ++i)
3496 dup->pow[i] = term->pow[i];
3497
3498 return dup;
3499 }
3500
3501 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3502 {
3503 if (!term)
3504 return NULL;
3505
3506 if (term->ref == 1)
3507 return term;
3508 term->ref--;
3509 return isl_term_dup(term);
3510 }
3511
3512 void isl_term_free(__isl_take isl_term *term)
3513 {
3514 if (!term)
3515 return;
3516
3517 if (--term->ref > 0)
3518 return;
3519
3520 isl_space_free(term->dim);
3521 isl_mat_free(term->div);
3522 isl_int_clear(term->n);
3523 isl_int_clear(term->d);
3524 free(term);
3525 }
3526
3527 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3528 {
3529 if (!term)
3530 return 0;
3531
3532 switch (type) {
3533 case isl_dim_param:
3534 case isl_dim_in:
3535 case isl_dim_out: return isl_space_dim(term->dim, type);
3536 case isl_dim_div: return term->div->n_row;
3537 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3538 term->div->n_row;
3539 default: return 0;
3540 }
3541 }
3542
3543 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3544 {
3545 return term ? term->dim->ctx : NULL;
3546 }
3547
3548 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3549 {
3550 if (!term)
3551 return;
3552 isl_int_set(*n, term->n);
3553 }
3554
3555 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3556 {
3557 if (!term)
3558 return;
3559 isl_int_set(*d, term->d);
3560 }
3561
3562 int isl_term_get_exp(__isl_keep isl_term *term,
3563 enum isl_dim_type type, unsigned pos)
3564 {
3565 if (!term)
3566 return -1;
3567
3568 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3569
3570 if (type >= isl_dim_set)
3571 pos += isl_space_dim(term->dim, isl_dim_param);
3572 if (type >= isl_dim_div)
3573 pos += isl_space_dim(term->dim, isl_dim_set);
3574
3575 return term->pow[pos];
3576 }
3577
3578 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3579 {
3580 isl_local_space *ls;
3581 isl_aff *aff;
3582 unsigned total;
3583
3584 if (!term)
3585 return NULL;
3586
3587 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3588 return NULL);
3589
3590 total = term->div->n_col - term->div->n_row - 2;
3591 /* No nested divs for now */
3592 isl_assert(term->dim->ctx,
3593 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3594 term->div->n_row) == -1,
3595 return NULL);
3596
3597 ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
3598 isl_mat_copy(term->div));
3599 aff = isl_aff_alloc(ls);
3600 if (!aff)
3601 return NULL;
3602
3603 isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
3604
3605 return aff;
3606 }
3607
3608 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3609 int (*fn)(__isl_take isl_term *term, void *user),
3610 __isl_take isl_term *term, void *user)
3611 {
3612 int i;
3613 struct isl_upoly_rec *rec;
3614
3615 if (!up || !term)
3616 goto error;
3617
3618 if (isl_upoly_is_zero(up))
3619 return term;
3620
3621 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3622 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3623 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3624
3625 if (isl_upoly_is_cst(up)) {
3626 struct isl_upoly_cst *cst;
3627 cst = isl_upoly_as_cst(up);
3628 if (!cst)
3629 goto error;
3630 term = isl_term_cow(term);
3631 if (!term)
3632 goto error;
3633 isl_int_set(term->n, cst->n);
3634 isl_int_set(term->d, cst->d);
3635 if (fn(isl_term_copy(term), user) < 0)
3636 goto error;
3637 return term;
3638 }
3639
3640 rec = isl_upoly_as_rec(up);
3641 if (!rec)
3642 goto error;
3643
3644 for (i = 0; i < rec->n; ++i) {
3645 term = isl_term_cow(term);
3646 if (!term)
3647 goto error;
3648 term->pow[up->var] = i;
3649 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3650 if (!term)
3651 goto error;
3652 }
3653 term->pow[up->var] = 0;
3654
3655 return term;
3656 error:
3657 isl_term_free(term);
3658 return NULL;
3659 }
3660
3661 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3662 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3663 {
3664 isl_term *term;
3665
3666 if (!qp)
3667 return -1;
3668
3669 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3670 if (!term)
3671 return -1;
3672
3673 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3674
3675 isl_term_free(term);
3676
3677 return term ? 0 : -1;
3678 }
3679
3680 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3681 {
3682 struct isl_upoly *up;
3683 isl_qpolynomial *qp;
3684 int i, n;
3685
3686 if (!term)
3687 return NULL;
3688
3689 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3690
3691 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3692 for (i = 0; i < n; ++i) {
3693 if (!term->pow[i])
3694 continue;
3695 up = isl_upoly_mul(up,
3696 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3697 }
3698
3699 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3700 if (!qp)
3701 goto error;
3702 isl_mat_free(qp->div);
3703 qp->div = isl_mat_copy(term->div);
3704 if (!qp->div)
3705 goto error;
3706
3707 isl_term_free(term);
3708 return qp;
3709 error:
3710 isl_qpolynomial_free(qp);
3711 isl_term_free(term);
3712 return NULL;
3713 }
3714
3715 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3716 __isl_take isl_space *dim)
3717 {
3718 int i;
3719 int extra;
3720 unsigned total;
3721
3722 if (!qp || !dim)
3723 goto error;
3724
3725 if (isl_space_is_equal(qp->dim, dim)) {
3726 isl_space_free(dim);
3727 return qp;
3728 }
3729
3730 qp = isl_qpolynomial_cow(qp);
3731 if (!qp)
3732 goto error;
3733
3734 extra = isl_space_dim(dim, isl_dim_set) -
3735 isl_space_dim(qp->dim, isl_dim_set);
3736 total = isl_space_dim(qp->dim, isl_dim_all);
3737 if (qp->div->n_row) {
3738 int *exp;
3739
3740 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3741 if (!exp)
3742 goto error;
3743 for (i = 0; i < qp->div->n_row; ++i)
3744 exp[i] = extra + i;
3745 qp->upoly = expand(qp->upoly, exp, total);
3746 free(exp);
3747 if (!qp->upoly)
3748 goto error;
3749 }
3750 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3751 if (!qp->div)
3752 goto error;
3753 for (i = 0; i < qp->div->n_row; ++i)
3754 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3755
3756 isl_space_free(qp->dim);
3757 qp->dim = dim;
3758
3759 return qp;
3760 error:
3761 isl_space_free(dim);
3762 isl_qpolynomial_free(qp);
3763 return NULL;
3764 }
3765
3766 /* For each parameter or variable that does not appear in qp,
3767 * first eliminate the variable from all constraints and then set it to zero.
3768 */
3769 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3770 __isl_keep isl_qpolynomial *qp)
3771 {
3772 int *active = NULL;
3773 int i;
3774 int d;
3775 unsigned nparam;
3776 unsigned nvar;
3777
3778 if (!set || !qp)
3779 goto error;
3780
3781 d = isl_space_dim(set->dim, isl_dim_all);
3782 active = isl_calloc_array(set->ctx, int, d);
3783 if (set_active(qp, active) < 0)
3784 goto error;
3785
3786 for (i = 0; i < d; ++i)
3787 if (!active[i])
3788 break;
3789
3790 if (i == d) {
3791 free(active);
3792 return set;
3793 }
3794
3795 nparam = isl_space_dim(set->dim, isl_dim_param);
3796 nvar = isl_space_dim(set->dim, isl_dim_set);
3797 for (i = 0; i < nparam; ++i) {
3798 if (active[i])
3799 continue;
3800 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3801 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3802 }
3803 for (i = 0; i < nvar; ++i) {
3804 if (active[nparam + i])
3805 continue;
3806 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3807 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3808 }
3809
3810 free(active);
3811
3812 return set;
3813 error:
3814 free(active);
3815 isl_set_free(set);
3816 return NULL;
3817 }
3818
3819 struct isl_opt_data {
3820 isl_qpolynomial *qp;
3821 int first;
3822 isl_qpolynomial *opt;
3823 int max;
3824 };
3825
3826 static int opt_fn(__isl_take isl_point *pnt, void *user)
3827 {
3828 struct isl_opt_data *data = (struct isl_opt_data *)user;
3829 isl_qpolynomial *val;
3830
3831 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3832 if (data->first) {
3833 data->first = 0;
3834 data->opt = val;
3835 } else if (data->max) {
3836 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3837 } else {
3838 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3839 }
3840
3841 return 0;
3842 }
3843
3844 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3845 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3846 {
3847 struct isl_opt_data data = { NULL, 1, NULL, max };
3848
3849 if (!set || !qp)
3850 goto error;
3851
3852 if (isl_upoly_is_cst(qp->upoly)) {
3853 isl_set_free(set);
3854 return qp;
3855 }
3856
3857 set = fix_inactive(set, qp);
3858
3859 data.qp = qp;
3860 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3861 goto error;
3862
3863 if (data.first) {
3864 isl_space *space = isl_qpolynomial_get_domain_space(qp);
3865 data.opt = isl_qpolynomial_zero_on_domain(space);
3866 }
3867
3868 isl_set_free(set);
3869 isl_qpolynomial_free(qp);
3870 return data.opt;
3871 error:
3872 isl_set_free(set);
3873 isl_qpolynomial_free(qp);
3874 isl_qpolynomial_free(data.opt);
3875 return NULL;
3876 }
3877
3878 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
3879 __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
3880 {
3881 int i;
3882 int n_sub;
3883 isl_ctx *ctx;
3884 struct isl_upoly **subs;
3885 isl_mat *mat, *diag;
3886
3887 qp = isl_qpolynomial_cow(qp);
3888 if (!qp || !morph)
3889 goto error;
3890
3891 ctx = qp->dim->ctx;
3892 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3893
3894 n_sub = morph->inv->n_row - 1;
3895 if (morph->inv->n_row != morph->inv->n_col)
3896 n_sub += qp->div->n_row;
3897 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3898 if (!subs)
3899 goto error;
3900
3901 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3902 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3903 morph->inv->row[0][0], morph->inv->n_col);
3904 if (morph->inv->n_row != morph->inv->n_col)
3905 for (i = 0; i < qp->div->n_row; ++i)
3906 subs[morph->inv->n_row - 1 + i] =
3907 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3908
3909 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3910
3911 for (i = 0; i < n_sub; ++i)
3912 isl_upoly_free(subs[i]);
3913 free(subs);
3914
3915 diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
3916 mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
3917 diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
3918 mat = isl_mat_diagonal(mat, diag);
3919 qp->div = isl_mat_product(qp->div, mat);
3920 isl_space_free(qp->dim);
3921 qp->dim = isl_space_copy(morph->ran->dim);
3922
3923 if (!qp->upoly || !qp->div || !qp->dim)
3924 goto error;
3925
3926 isl_morph_free(morph);
3927
3928 return qp;
3929 error:
3930 isl_qpolynomial_free(qp);
3931 isl_morph_free(morph);
3932 return NULL;
3933 }
3934
3935 static int neg_entry(void **entry, void *user)
3936 {
3937 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3938
3939 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3940
3941 return *pwqp ? 0 : -1;
3942 }
3943
3944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3945 __isl_take isl_union_pw_qpolynomial *upwqp)
3946 {
3947 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3948 if (!upwqp)
3949 return NULL;
3950
3951 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3952 &neg_entry, NULL) < 0)
3953 goto error;
3954
3955 return upwqp;
3956 error:
3957 isl_union_pw_qpolynomial_free(upwqp);
3958 return NULL;
3959 }
3960
3961 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3962 __isl_take isl_union_pw_qpolynomial *upwqp1,
3963 __isl_take isl_union_pw_qpolynomial *upwqp2)
3964 {
3965 return isl_union_pw_qpolynomial_add(upwqp1,
3966 isl_union_pw_qpolynomial_neg(upwqp2));
3967 }
3968
3969 static int mul_entry(void **entry, void *user)
3970 {
3971 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3972 uint32_t hash;
3973 struct isl_hash_table_entry *entry2;
3974 isl_pw_qpolynomial *pwpq = *entry;
3975 int empty;
3976
3977 hash = isl_space_get_hash(pwpq->dim);
3978 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3979 hash, &has_dim, pwpq->dim, 0);
3980 if (!entry2)
3981 return 0;
3982
3983 pwpq = isl_pw_qpolynomial_copy(pwpq);
3984 pwpq = isl_pw_qpolynomial_mul(pwpq,
3985 isl_pw_qpolynomial_copy(entry2->data));
3986
3987 empty = isl_pw_qpolynomial_is_zero(pwpq);
3988 if (empty < 0) {
3989 isl_pw_qpolynomial_free(pwpq);
3990 return -1;
3991 }
3992 if (empty) {
3993 isl_pw_qpolynomial_free(pwpq);
3994 return 0;
3995 }
3996
3997 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3998
3999 return 0;
4000 }
4001
4002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4003 __isl_take isl_union_pw_qpolynomial *upwqp1,
4004 __isl_take isl_union_pw_qpolynomial *upwqp2)
4005 {
4006 return match_bin_op(upwqp1, upwqp2, &mul_entry);
4007 }
4008
4009 /* Reorder the columns of the given div definitions according to the
4010 * given reordering.
4011 */
4012 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4013 __isl_take isl_reordering *r)
4014 {
4015 int i, j;
4016 isl_mat *mat;
4017 int extra;
4018
4019 if (!div || !r)
4020 goto error;
4021
4022 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4023 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4024 if (!mat)
4025 goto error;
4026
4027 for (i = 0; i < div->n_row; ++i) {
4028 isl_seq_cpy(mat->row[i], div->row[i], 2);
4029 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4030 for (j = 0; j < r->len; ++j)
4031 isl_int_set(mat->row[i][2 + r->pos[j]],
4032 div->row[i][2 + j]);
4033 }
4034
4035 isl_reordering_free(r);
4036 isl_mat_free(div);
4037 return mat;
4038 error:
4039 isl_reordering_free(r);
4040 isl_mat_free(div);
4041 return NULL;
4042 }
4043
4044 /* Reorder the dimension of "qp" according to the given reordering.
4045 */
4046 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4047 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4048 {
4049 qp = isl_qpolynomial_cow(qp);
4050 if (!qp)
4051 goto error;
4052
4053 r = isl_reordering_extend(r, qp->div->n_row);
4054 if (!r)
4055 goto error;
4056
4057 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4058 if (!qp->div)
4059 goto error;
4060
4061 qp->upoly = reorder(qp->upoly, r->pos);
4062 if (!qp->upoly)
4063 goto error;
4064
4065 qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4066
4067 isl_reordering_free(r);
4068 return qp;
4069 error:
4070 isl_qpolynomial_free(qp);
4071 isl_reordering_free(r);
4072 return NULL;
4073 }
4074
4075 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4076 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4077 {
4078 if (!qp || !model)
4079 goto error;
4080
4081 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4082 isl_reordering *exp;
4083
4084 model = isl_space_drop_dims(model, isl_dim_in,
4085 0, isl_space_dim(model, isl_dim_in));
4086 model = isl_space_drop_dims(model, isl_dim_out,
4087 0, isl_space_dim(model, isl_dim_out));
4088 exp = isl_parameter_alignment_reordering(qp->dim, model);
4089 exp = isl_reordering_extend_space(exp,
4090 isl_qpolynomial_get_domain_space(qp));
4091 qp = isl_qpolynomial_realign_domain(qp, exp);
4092 }
4093
4094 isl_space_free(model);
4095 return qp;
4096 error:
4097 isl_space_free(model);
4098 isl_qpolynomial_free(qp);
4099 return NULL;
4100 }
4101
4102 struct isl_split_periods_data {
4103 int max_periods;
4104 isl_pw_qpolynomial *res;
4105 };
4106
4107 /* Create a slice where the integer division "div" has the fixed value "v".
4108 * In particular, if "div" refers to floor(f/m), then create a slice
4109 *
4110 * m v <= f <= m v + (m - 1)
4111 *
4112 * or
4113 *
4114 * f - m v >= 0
4115 * -f + m v + (m - 1) >= 0
4116 */
4117 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4118 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4119 {
4120 int total;
4121 isl_basic_set *bset = NULL;
4122 int k;
4123
4124 if (!dim || !qp)
4125 goto error;
4126
4127 total = isl_space_dim(dim, isl_dim_all);
4128 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4129
4130 k = isl_basic_set_alloc_inequality(bset);
4131 if (k < 0)
4132 goto error;
4133 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4134 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4135
4136 k = isl_basic_set_alloc_inequality(bset);
4137 if (k < 0)
4138 goto error;
4139 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4140 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4141 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4142 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4143
4144 isl_space_free(dim);
4145 return isl_set_from_basic_set(bset);
4146 error:
4147 isl_basic_set_free(bset);
4148 isl_space_free(dim);
4149 return NULL;
4150 }
4151
4152 static int split_periods(__isl_take isl_set *set,
4153 __isl_take isl_qpolynomial *qp, void *user);
4154
4155 /* Create a slice of the domain "set" such that integer division "div"
4156 * has the fixed value "v" and add the results to data->res,
4157 * replacing the integer division by "v" in "qp".
4158 */
4159 static int set_div(__isl_take isl_set *set,
4160 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4161 struct isl_split_periods_data *data)
4162 {
4163 int i;
4164 int total;
4165 isl_set *slice;
4166 struct isl_upoly *cst;
4167
4168 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4169 set = isl_set_intersect(set, slice);
4170
4171 if (!qp)
4172 goto error;
4173
4174 total = isl_space_dim(qp->dim, isl_dim_all);
4175
4176 for (i = div + 1; i < qp->div->n_row; ++i) {
4177 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4178 continue;
4179 isl_int_addmul(qp->div->row[i][1],
4180 qp->div->row[i][2 + total + div], v);
4181 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4182 }
4183
4184 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4185 qp = substitute_div(qp, div, cst);
4186
4187 return split_periods(set, qp, data);
4188 error:
4189 isl_set_free(set);
4190 isl_qpolynomial_free(qp);
4191 return -1;
4192 }
4193
4194 /* Split the domain "set" such that integer division "div"
4195 * has a fixed value (ranging from "min" to "max") on each slice
4196 * and add the results to data->res.
4197 */
4198 static int split_div(__isl_take isl_set *set,
4199 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4200 struct isl_split_periods_data *data)
4201 {
4202 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4203 isl_set *set_i = isl_set_copy(set);
4204 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4205
4206 if (set_div(set_i, qp_i, div, min, data) < 0)
4207 goto error;
4208 }
4209 isl_set_free(set);
4210 isl_qpolynomial_free(qp);
4211 return 0;
4212 error:
4213 isl_set_free(set);
4214 isl_qpolynomial_free(qp);
4215 return -1;
4216 }
4217
4218 /* If "qp" refers to any integer division
4219 * that can only attain "max_periods" distinct values on "set"
4220 * then split the domain along those distinct values.
4221 * Add the results (or the original if no splitting occurs)
4222 * to data->res.
4223 */
4224 static int split_periods(__isl_take isl_set *set,
4225 __isl_take isl_qpolynomial *qp, void *user)
4226 {
4227 int i;
4228 isl_pw_qpolynomial *pwqp;
4229 struct isl_split_periods_data *data;
4230 isl_int min, max;
4231 int total;
4232 int r = 0;
4233
4234 data = (struct isl_split_periods_data *)user;
4235
4236 if (!set || !qp)
4237 goto error;
4238
4239 if (qp->div->n_row == 0) {
4240 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4241 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4242 return 0;
4243 }
4244
4245 isl_int_init(min);
4246 isl_int_init(max);
4247 total = isl_space_dim(qp->dim, isl_dim_all);
4248 for (i = 0; i < qp->div->n_row; ++i) {
4249 enum isl_lp_result lp_res;
4250
4251 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4252 qp->div->n_row) != -1)
4253 continue;
4254
4255 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4256 set->ctx->one, &min, NULL, NULL);
4257 if (lp_res == isl_lp_error)
4258 goto error2;
4259 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4260 continue;
4261 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4262
4263 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4264 set->ctx->one, &max, NULL, NULL);
4265 if (lp_res == isl_lp_error)
4266 goto error2;
4267 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4268 continue;
4269 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4270
4271 isl_int_sub(max, max, min);
4272 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4273 isl_int_add(max, max, min);
4274 break;
4275 }
4276 }
4277
4278 if (i < qp->div->n_row) {
4279 r = split_div(set, qp, i, min, max, data);
4280 } else {
4281 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4282 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4283 }
4284
4285 isl_int_clear(max);
4286 isl_int_clear(min);
4287
4288 return r;
4289 error2:
4290 isl_int_clear(max);
4291 isl_int_clear(min);
4292 error:
4293 isl_set_free(set);
4294 isl_qpolynomial_free(qp);
4295 return -1;
4296 }
4297
4298 /* If any quasi-polynomial in pwqp refers to any integer division
4299 * that can only attain "max_periods" distinct values on its domain
4300 * then split the domain along those distinct values.
4301 */
4302 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4303 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4304 {
4305 struct isl_split_periods_data data;
4306
4307 data.max_periods = max_periods;
4308 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4309
4310 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4311 goto error;
4312
4313 isl_pw_qpolynomial_free(pwqp);
4314
4315 return data.res;
4316 error:
4317 isl_pw_qpolynomial_free(data.res);
4318 isl_pw_qpolynomial_free(pwqp);
4319 return NULL;
4320 }
4321
4322 /* Construct a piecewise quasipolynomial that is constant on the given
4323 * domain. In particular, it is
4324 * 0 if cst == 0
4325 * 1 if cst == 1
4326 * infinity if cst == -1
4327 */
4328 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4329 __isl_take isl_basic_set *bset, int cst)
4330 {
4331 isl_space *dim;
4332 isl_qpolynomial *qp;
4333
4334 if (!bset)
4335 return NULL;
4336
4337 bset = isl_basic_set_params(bset);
4338 dim = isl_basic_set_get_space(bset);
4339 if (cst < 0)
4340 qp = isl_qpolynomial_infty_on_domain(dim);
4341 else if (cst == 0)
4342 qp = isl_qpolynomial_zero_on_domain(dim);
4343 else
4344 qp = isl_qpolynomial_one_on_domain(dim);
4345 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4346 }
4347
4348 /* Factor bset, call fn on each of the factors and return the product.
4349 *
4350 * If no factors can be found, simply call fn on the input.
4351 * Otherwise, construct the factors based on the factorizer,
4352 * call fn on each factor and compute the product.
4353 */
4354 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4355 __isl_take isl_basic_set *bset,
4356 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4357 {
4358 int i, n;
4359 isl_space *dim;
4360 isl_set *set;
4361 isl_factorizer *f;
4362 isl_qpolynomial *qp;
4363 isl_pw_qpolynomial *pwqp;
4364 unsigned nparam;
4365 unsigned nvar;
4366
4367 f = isl_basic_set_factorizer(bset);
4368 if (!f)
4369 goto error;
4370 if (f->n_group == 0) {
4371 isl_factorizer_free(f);
4372 return fn(bset);
4373 }
4374
4375 nparam = isl_basic_set_dim(bset, isl_dim_param);
4376 nvar = isl_basic_set_dim(bset, isl_dim_set);
4377
4378 dim = isl_basic_set_get_space(bset);
4379 dim = isl_space_domain(dim);
4380 set = isl_set_universe(isl_space_copy(dim));
4381 qp = isl_qpolynomial_one_on_domain(dim);
4382 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4383
4384 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4385
4386 for (i = 0, n = 0; i < f->n_group; ++i) {
4387 isl_basic_set *bset_i;
4388 isl_pw_qpolynomial *pwqp_i;
4389
4390 bset_i = isl_basic_set_copy(bset);
4391 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4392 nparam + n + f->len[i], nvar - n - f->len[i]);
4393 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4394 nparam, n);
4395 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4396 n + f->len[i], nvar - n - f->len[i]);
4397 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4398
4399 pwqp_i = fn(bset_i);
4400 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4401
4402 n += f->len[i];
4403 }
4404
4405 isl_basic_set_free(bset);
4406 isl_factorizer_free(f);
4407
4408 return pwqp;
4409 error:
4410 isl_basic_set_free(bset);
4411 return NULL;
4412 }
4413
4414 /* Factor bset, call fn on each of the factors and return the product.
4415 * The function is assumed to evaluate to zero on empty domains,
4416 * to one on zero-dimensional domains and to infinity on unbounded domains
4417 * and will not be called explicitly on zero-dimensional or unbounded domains.
4418 *
4419 * We first check for some special cases and remove all equalities.
4420 * Then we hand over control to compressed_multiplicative_call.
4421 */
4422 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4423 __isl_take isl_basic_set *bset,
4424 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4425 {
4426 int bounded;
4427 isl_morph *morph;
4428 isl_pw_qpolynomial *pwqp;
4429
4430 if (!bset)
4431 return NULL;
4432
4433 if (isl_basic_set_plain_is_empty(bset))
4434 return constant_on_domain(bset, 0);
4435
4436 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4437 return constant_on_domain(bset, 1);
4438
4439 bounded = isl_basic_set_is_bounded(bset);
4440 if (bounded < 0)
4441 goto error;
4442 if (!bounded)
4443 return constant_on_domain(bset, -1);
4444
4445 if (bset->n_eq == 0)
4446 return compressed_multiplicative_call(bset, fn);
4447
4448 morph = isl_basic_set_full_compression(bset);
4449 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4450
4451 pwqp = compressed_multiplicative_call(bset, fn);
4452
4453 morph = isl_morph_dom_params(morph);
4454 morph = isl_morph_ran_params(morph);
4455 morph = isl_morph_inverse(morph);
4456
4457 pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4458
4459 return pwqp;
4460 error:
4461 isl_basic_set_free(bset);
4462 return NULL;
4463 }
4464
4465 /* Drop all floors in "qp", turning each integer division [a/m] into
4466 * a rational division a/m. If "down" is set, then the integer division
4467 * is replaces by (a-(m-1))/m instead.
4468 */
4469 static __isl_give isl_qpolynomial *qp_drop_floors(
4470 __isl_take isl_qpolynomial *qp, int down)
4471 {
4472 int i;
4473 struct isl_upoly *s;
4474
4475 if (!qp)
4476 return NULL;
4477 if (qp->div->n_row == 0)
4478 return qp;
4479
4480 qp = isl_qpolynomial_cow(qp);
4481 if (!qp)
4482 return NULL;
4483
4484 for (i = qp->div->n_row - 1; i >= 0; --i) {
4485 if (down) {
4486 isl_int_sub(qp->div->row[i][1],
4487 qp->div->row[i][1], qp->div->row[i][0]);
4488 isl_int_add_ui(qp->div->row[i][1],
4489 qp->div->row[i][1], 1);
4490 }
4491 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4492 qp->div->row[i][0], qp->div->n_col - 1);
4493 qp = substitute_div(qp, i, s);
4494 if (!qp)
4495 return NULL;
4496 }
4497
4498 return qp;
4499 }
4500
4501 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4502 * a rational division a/m.
4503 */
4504 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4505 __isl_take isl_pw_qpolynomial *pwqp)
4506 {
4507 int i;
4508
4509 if (!pwqp)
4510 return NULL;
4511
4512 if (isl_pw_qpolynomial_is_zero(pwqp))
4513 return pwqp;
4514
4515 pwqp = isl_pw_qpolynomial_cow(pwqp);
4516 if (!pwqp)
4517 return NULL;
4518
4519 for (i = 0; i < pwqp->n; ++i) {
4520 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4521 if (!pwqp->p[i].qp)
4522 goto error;
4523 }
4524
4525 return pwqp;
4526 error:
4527 isl_pw_qpolynomial_free(pwqp);
4528 return NULL;
4529 }
4530
4531 /* Adjust all the integer divisions in "qp" such that they are at least
4532 * one over the given orthant (identified by "signs"). This ensures
4533 * that they will still be non-negative even after subtracting (m-1)/m.
4534 *
4535 * In particular, f is replaced by f' + v, changing f = [a/m]
4536 * to f' = [(a - m v)/m].
4537 * If the constant term k in a is smaller than m,
4538 * the constant term of v is set to floor(k/m) - 1.
4539 * For any other term, if the coefficient c and the variable x have
4540 * the same sign, then no changes are needed.
4541 * Otherwise, if the variable is positive (and c is negative),
4542 * then the coefficient of x in v is set to floor(c/m).
4543 * If the variable is negative (and c is positive),
4544 * then the coefficient of x in v is set to ceil(c/m).
4545 */
4546 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4547 int *signs)
4548 {
4549 int i, j;
4550 int total;
4551 isl_vec *v = NULL;
4552 struct isl_upoly *s;
4553
4554 qp = isl_qpolynomial_cow(qp);
4555 if (!qp)
4556 return NULL;
4557 qp->div = isl_mat_cow(qp->div);
4558 if (!qp->div)
4559 goto error;
4560
4561 total = isl_space_dim(qp->dim, isl_dim_all);
4562 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4563
4564 for (i = 0; i < qp->div->n_row; ++i) {
4565 isl_int *row = qp->div->row[i];
4566 v = isl_vec_clr(v);
4567 if (!v)
4568 goto error;
4569 if (isl_int_lt(row[1], row[0])) {
4570 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4571 isl_int_sub_ui(v->el[0], v->el[0], 1);
4572 isl_int_submul(row[1], row[0], v->el[0]);
4573 }
4574 for (j = 0; j < total; ++j) {
4575 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4576 continue;
4577 if (signs[j] < 0)
4578 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4579 else
4580 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4581 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4582 }
4583 for (j = 0; j < i; ++j) {
4584 if (isl_int_sgn(row[2 + total + j]) >= 0)
4585 continue;
4586 isl_int_fdiv_q(v->el[1 + total + j],
4587 row[2 + total + j], row[0]);
4588 isl_int_submul(row[2 + total + j],
4589 row[0], v->el[1 + total + j]);
4590 }
4591 for (j = i + 1; j < qp->div->n_row; ++j) {
4592 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4593 continue;
4594 isl_seq_combine(qp->div->row[j] + 1,
4595 qp->div->ctx->one, qp->div->row[j] + 1,
4596 qp->div->row[j][2 + total + i], v->el, v->size);
4597 }
4598 isl_int_set_si(v->el[1 + total + i], 1);
4599 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4600 qp->div->ctx->one, v->size);
4601 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4602 isl_upoly_free(s);
4603 if (!qp->upoly)
4604 goto error;
4605 }
4606
4607 isl_vec_free(v);
4608 return qp;
4609 error:
4610 isl_vec_free(v);
4611 isl_qpolynomial_free(qp);
4612 return NULL;
4613 }
4614
4615 struct isl_to_poly_data {
4616 int sign;
4617 isl_pw_qpolynomial *res;
4618 isl_qpolynomial *qp;
4619 };
4620
4621 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4622 * We first make all integer divisions positive and then split the
4623 * quasipolynomials into terms with sign data->sign (the direction
4624 * of the requested approximation) and terms with the opposite sign.
4625 * In the first set of terms, each integer division [a/m] is
4626 * overapproximated by a/m, while in the second it is underapproximated
4627 * by (a-(m-1))/m.
4628 */
4629 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4630 void *user)
4631 {
4632 struct isl_to_poly_data *data = user;
4633 isl_pw_qpolynomial *t;
4634 isl_qpolynomial *qp, *up, *down;
4635
4636 qp = isl_qpolynomial_copy(data->qp);
4637 qp = make_divs_pos(qp, signs);
4638
4639 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4640 up = qp_drop_floors(up, 0);
4641 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4642 down = qp_drop_floors(down, 1);
4643
4644 isl_qpolynomial_free(qp);
4645 qp = isl_qpolynomial_add(up, down);
4646
4647 t = isl_pw_qpolynomial_alloc(orthant, qp);
4648 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4649
4650 return 0;
4651 }
4652
4653 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4654 * the polynomial will be an overapproximation. If "sign" is negative,
4655 * it will be an underapproximation. If "sign" is zero, the approximation
4656 * will lie somewhere in between.
4657 *
4658 * In particular, is sign == 0, we simply drop the floors, turning
4659 * the integer divisions into rational divisions.
4660 * Otherwise, we split the domains into orthants, make all integer divisions
4661 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4662 * depending on the requested sign and the sign of the term in which
4663 * the integer division appears.
4664 */
4665 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4666 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4667 {
4668 int i;
4669 struct isl_to_poly_data data;
4670
4671 if (sign == 0)
4672 return pwqp_drop_floors(pwqp);
4673
4674 if (!pwqp)
4675 return NULL;
4676
4677 data.sign = sign;
4678 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4679
4680 for (i = 0; i < pwqp->n; ++i) {
4681 if (pwqp->p[i].qp->div->n_row == 0) {
4682 isl_pw_qpolynomial *t;
4683 t = isl_pw_qpolynomial_alloc(
4684 isl_set_copy(pwqp->p[i].set),
4685 isl_qpolynomial_copy(pwqp->p[i].qp));
4686 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4687 continue;
4688 }
4689 data.qp = pwqp->p[i].qp;
4690 if (isl_set_foreach_orthant(pwqp->p[i].set,
4691 &to_polynomial_on_orthant, &data) < 0)
4692 goto error;
4693 }
4694
4695 isl_pw_qpolynomial_free(pwqp);
4696
4697 return data.res;
4698 error:
4699 isl_pw_qpolynomial_free(pwqp);
4700 isl_pw_qpolynomial_free(data.res);
4701 return NULL;
4702 }
4703
4704 static int poly_entry(void **entry, void *user)
4705 {
4706 int *sign = user;
4707 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4708
4709 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4710
4711 return *pwqp ? 0 : -1;
4712 }
4713
4714 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4715 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4716 {
4717 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4718 if (!upwqp)
4719 return NULL;
4720
4721 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4722 &poly_entry, &sign) < 0)
4723 goto error;
4724
4725 return upwqp;
4726 error:
4727 isl_union_pw_qpolynomial_free(upwqp);
4728 return NULL;
4729 }
4730
4731 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4732 __isl_take isl_qpolynomial *qp)
4733 {
4734 int i, k;
4735 isl_space *dim;
4736 isl_vec *aff = NULL;
4737 isl_basic_map *bmap = NULL;
4738 unsigned pos;
4739 unsigned n_div;
4740
4741 if (!qp)
4742 return NULL;
4743 if (!isl_upoly_is_affine(qp->upoly))
4744 isl_die(qp->dim->ctx, isl_error_invalid,
4745 "input quasi-polynomial not affine", goto error);
4746 aff = isl_qpolynomial_extract_affine(qp);
4747 if (!aff)
4748 goto error;
4749 dim = isl_qpolynomial_get_space(qp);
4750 pos = 1 + isl_space_offset(dim, isl_dim_out);
4751 n_div = qp->div->n_row;
4752 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4753
4754 for (i = 0; i < n_div; ++i) {
4755 k = isl_basic_map_alloc_div(bmap);
4756 if (k < 0)
4757 goto error;
4758 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4759 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4760 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4761 goto error;
4762 }
4763 k = isl_basic_map_alloc_equality(bmap);
4764 if (k < 0)
4765 goto error;
4766 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4767 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4768 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4769
4770 isl_vec_free(aff);
4771 isl_qpolynomial_free(qp);
4772 bmap = isl_basic_map_finalize(bmap);
4773 return bmap;
4774 error:
4775 isl_vec_free(aff);
4776 isl_qpolynomial_free(qp);
4777 isl_basic_map_free(bmap);
4778 return NULL;
4779 }
Integer set library