?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
hide some functions that were exposed by mistake
[isl.git] / isl_polynomial.c
blob43d79e9c5160faa6692bef5a362533ab5e89ab31
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 #include <isl_factorization.h>
13 #include <isl_lp.h>
14 #include <isl_seq.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21
22 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
23 {
24 switch (type) {
25 case isl_dim_param: return 0;
26 case isl_dim_in: return dim->nparam;
27 case isl_dim_out: return dim->nparam + dim->n_in;
28 default: return 0;
29 }
30 }
31
32 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
33 {
34 if (!up)
35 return -1;
36
37 return up->var < 0;
38 }
39
40 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return NULL;
44
45 isl_assert(up->ctx, up->var < 0, return NULL);
46
47 return (struct isl_upoly_cst *)up;
48 }
49
50 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
51 {
52 if (!up)
53 return NULL;
54
55 isl_assert(up->ctx, up->var >= 0, return NULL);
56
57 return (struct isl_upoly_rec *)up;
58 }
59
60 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
61 __isl_keep struct isl_upoly *up2)
62 {
63 int i;
64 struct isl_upoly_rec *rec1, *rec2;
65
66 if (!up1 || !up2)
67 return -1;
68 if (up1 == up2)
69 return 1;
70 if (up1->var != up2->var)
71 return 0;
72 if (isl_upoly_is_cst(up1)) {
73 struct isl_upoly_cst *cst1, *cst2;
74 cst1 = isl_upoly_as_cst(up1);
75 cst2 = isl_upoly_as_cst(up2);
76 if (!cst1 || !cst2)
77 return -1;
78 return isl_int_eq(cst1->n, cst2->n) &&
79 isl_int_eq(cst1->d, cst2->d);
80 }
81
82 rec1 = isl_upoly_as_rec(up1);
83 rec2 = isl_upoly_as_rec(up2);
84 if (!rec1 || !rec2)
85 return -1;
86
87 if (rec1->n != rec2->n)
88 return 0;
89
90 for (i = 0; i < rec1->n; ++i) {
91 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
92 if (eq < 0 || !eq)
93 return eq;
94 }
95
96 return 1;
97 }
98
99 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
100 {
101 struct isl_upoly_cst *cst;
102
103 if (!up)
104 return -1;
105 if (!isl_upoly_is_cst(up))
106 return 0;
107
108 cst = isl_upoly_as_cst(up);
109 if (!cst)
110 return -1;
111
112 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
113 }
114
115 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
116 {
117 struct isl_upoly_cst *cst;
118
119 if (!up)
120 return 0;
121 if (!isl_upoly_is_cst(up))
122 return 0;
123
124 cst = isl_upoly_as_cst(up);
125 if (!cst)
126 return 0;
127
128 return isl_int_sgn(cst->n);
129 }
130
131 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
132 {
133 struct isl_upoly_cst *cst;
134
135 if (!up)
136 return -1;
137 if (!isl_upoly_is_cst(up))
138 return 0;
139
140 cst = isl_upoly_as_cst(up);
141 if (!cst)
142 return -1;
143
144 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
145 }
146
147 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
148 {
149 struct isl_upoly_cst *cst;
150
151 if (!up)
152 return -1;
153 if (!isl_upoly_is_cst(up))
154 return 0;
155
156 cst = isl_upoly_as_cst(up);
157 if (!cst)
158 return -1;
159
160 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
161 }
162
163 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
164 {
165 struct isl_upoly_cst *cst;
166
167 if (!up)
168 return -1;
169 if (!isl_upoly_is_cst(up))
170 return 0;
171
172 cst = isl_upoly_as_cst(up);
173 if (!cst)
174 return -1;
175
176 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
177 }
178
179 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
180 {
181 struct isl_upoly_cst *cst;
182
183 if (!up)
184 return -1;
185 if (!isl_upoly_is_cst(up))
186 return 0;
187
188 cst = isl_upoly_as_cst(up);
189 if (!cst)
190 return -1;
191
192 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
193 }
194
195 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
196 {
197 struct isl_upoly_cst *cst;
198
199 if (!up)
200 return -1;
201 if (!isl_upoly_is_cst(up))
202 return 0;
203
204 cst = isl_upoly_as_cst(up);
205 if (!cst)
206 return -1;
207
208 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
209 }
210
211 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
212 {
213 struct isl_upoly_cst *cst;
214
215 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
216 if (!cst)
217 return NULL;
218
219 cst->up.ref = 1;
220 cst->up.ctx = ctx;
221 isl_ctx_ref(ctx);
222 cst->up.var = -1;
223
224 isl_int_init(cst->n);
225 isl_int_init(cst->d);
226
227 return cst;
228 }
229
230 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
231 {
232 struct isl_upoly_cst *cst;
233
234 cst = isl_upoly_cst_alloc(ctx);
235 if (!cst)
236 return NULL;
237
238 isl_int_set_si(cst->n, 0);
239 isl_int_set_si(cst->d, 1);
240
241 return &cst->up;
242 }
243
244 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
245 {
246 struct isl_upoly_cst *cst;
247
248 cst = isl_upoly_cst_alloc(ctx);
249 if (!cst)
250 return NULL;
251
252 isl_int_set_si(cst->n, 1);
253 isl_int_set_si(cst->d, 1);
254
255 return &cst->up;
256 }
257
258 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
259 {
260 struct isl_upoly_cst *cst;
261
262 cst = isl_upoly_cst_alloc(ctx);
263 if (!cst)
264 return NULL;
265
266 isl_int_set_si(cst->n, 1);
267 isl_int_set_si(cst->d, 0);
268
269 return &cst->up;
270 }
271
272 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
273 {
274 struct isl_upoly_cst *cst;
275
276 cst = isl_upoly_cst_alloc(ctx);
277 if (!cst)
278 return NULL;
279
280 isl_int_set_si(cst->n, -1);
281 isl_int_set_si(cst->d, 0);
282
283 return &cst->up;
284 }
285
286 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
287 {
288 struct isl_upoly_cst *cst;
289
290 cst = isl_upoly_cst_alloc(ctx);
291 if (!cst)
292 return NULL;
293
294 isl_int_set_si(cst->n, 0);
295 isl_int_set_si(cst->d, 0);
296
297 return &cst->up;
298 }
299
300 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
301 isl_int n, isl_int d)
302 {
303 struct isl_upoly_cst *cst;
304
305 cst = isl_upoly_cst_alloc(ctx);
306 if (!cst)
307 return NULL;
308
309 isl_int_set(cst->n, n);
310 isl_int_set(cst->d, d);
311
312 return &cst->up;
313 }
314
315 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
316 int var, int size)
317 {
318 struct isl_upoly_rec *rec;
319
320 isl_assert(ctx, var >= 0, return NULL);
321 isl_assert(ctx, size >= 0, return NULL);
322 rec = isl_calloc(ctx, struct isl_upoly_rec,
323 sizeof(struct isl_upoly_rec) +
324 (size - 1) * sizeof(struct isl_upoly *));
325 if (!rec)
326 return NULL;
327
328 rec->up.ref = 1;
329 rec->up.ctx = ctx;
330 isl_ctx_ref(ctx);
331 rec->up.var = var;
332
333 rec->n = 0;
334 rec->size = size;
335
336 return rec;
337 }
338
339 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
340 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
341 {
342 qp = isl_qpolynomial_cow(qp);
343 if (!qp || !dim)
344 goto error;
345
346 isl_dim_free(qp->dim);
347 qp->dim = dim;
348
349 return qp;
350 error:
351 isl_qpolynomial_free(qp);
352 isl_dim_free(dim);
353 return NULL;
354 }
355
356 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
357 {
358 return qp ? qp->dim->ctx : NULL;
359 }
360
361 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
362 {
363 return qp ? isl_dim_copy(qp->dim) : NULL;
364 }
365
366 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
367 enum isl_dim_type type)
368 {
369 return qp ? isl_dim_size(qp->dim, type) : 0;
370 }
371
372 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
373 {
374 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
375 }
376
377 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
378 {
379 return qp ? isl_upoly_is_one(qp->upoly) : -1;
380 }
381
382 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
385 }
386
387 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
388 {
389 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
390 }
391
392 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
393 {
394 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
395 }
396
397 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
398 {
399 return qp ? isl_upoly_sgn(qp->upoly) : 0;
400 }
401
402 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
403 {
404 isl_int_clear(cst->n);
405 isl_int_clear(cst->d);
406 }
407
408 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
409 {
410 int i;
411
412 for (i = 0; i < rec->n; ++i)
413 isl_upoly_free(rec->p[i]);
414 }
415
416 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
417 {
418 if (!up)
419 return NULL;
420
421 up->ref++;
422 return up;
423 }
424
425 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
426 {
427 struct isl_upoly_cst *cst;
428 struct isl_upoly_cst *dup;
429
430 cst = isl_upoly_as_cst(up);
431 if (!cst)
432 return NULL;
433
434 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
435 if (!dup)
436 return NULL;
437 isl_int_set(dup->n, cst->n);
438 isl_int_set(dup->d, cst->d);
439
440 return &dup->up;
441 }
442
443 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
444 {
445 int i;
446 struct isl_upoly_rec *rec;
447 struct isl_upoly_rec *dup;
448
449 rec = isl_upoly_as_rec(up);
450 if (!rec)
451 return NULL;
452
453 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
454 if (!dup)
455 return NULL;
456
457 for (i = 0; i < rec->n; ++i) {
458 dup->p[i] = isl_upoly_copy(rec->p[i]);
459 if (!dup->p[i])
460 goto error;
461 dup->n++;
462 }
463
464 return &dup->up;
465 error:
466 isl_upoly_free(&dup->up);
467 return NULL;
468 }
469
470 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
471 {
472 struct isl_upoly *dup;
473
474 if (!up)
475 return NULL;
476
477 if (isl_upoly_is_cst(up))
478 return isl_upoly_dup_cst(up);
479 else
480 return isl_upoly_dup_rec(up);
481 }
482
483 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
484 {
485 if (!up)
486 return NULL;
487
488 if (up->ref == 1)
489 return up;
490 up->ref--;
491 return isl_upoly_dup(up);
492 }
493
494 void isl_upoly_free(__isl_take struct isl_upoly *up)
495 {
496 if (!up)
497 return;
498
499 if (--up->ref > 0)
500 return;
501
502 if (up->var < 0)
503 upoly_free_cst((struct isl_upoly_cst *)up);
504 else
505 upoly_free_rec((struct isl_upoly_rec *)up);
506
507 isl_ctx_deref(up->ctx);
508 free(up);
509 }
510
511 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
512 {
513 isl_int gcd;
514
515 isl_int_init(gcd);
516 isl_int_gcd(gcd, cst->n, cst->d);
517 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
518 isl_int_divexact(cst->n, cst->n, gcd);
519 isl_int_divexact(cst->d, cst->d, gcd);
520 }
521 isl_int_clear(gcd);
522 }
523
524 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
525 __isl_take struct isl_upoly *up2)
526 {
527 struct isl_upoly_cst *cst1;
528 struct isl_upoly_cst *cst2;
529
530 up1 = isl_upoly_cow(up1);
531 if (!up1 || !up2)
532 goto error;
533
534 cst1 = isl_upoly_as_cst(up1);
535 cst2 = isl_upoly_as_cst(up2);
536
537 if (isl_int_eq(cst1->d, cst2->d))
538 isl_int_add(cst1->n, cst1->n, cst2->n);
539 else {
540 isl_int_mul(cst1->n, cst1->n, cst2->d);
541 isl_int_addmul(cst1->n, cst2->n, cst1->d);
542 isl_int_mul(cst1->d, cst1->d, cst2->d);
543 }
544
545 isl_upoly_cst_reduce(cst1);
546
547 isl_upoly_free(up2);
548 return up1;
549 error:
550 isl_upoly_free(up1);
551 isl_upoly_free(up2);
552 return NULL;
553 }
554
555 static __isl_give struct isl_upoly *replace_by_zero(
556 __isl_take struct isl_upoly *up)
557 {
558 struct isl_ctx *ctx;
559
560 if (!up)
561 return NULL;
562 ctx = up->ctx;
563 isl_upoly_free(up);
564 return isl_upoly_zero(ctx);
565 }
566
567 static __isl_give struct isl_upoly *replace_by_constant_term(
568 __isl_take struct isl_upoly *up)
569 {
570 struct isl_upoly_rec *rec;
571 struct isl_upoly *cst;
572
573 if (!up)
574 return NULL;
575
576 rec = isl_upoly_as_rec(up);
577 if (!rec)
578 goto error;
579 cst = isl_upoly_copy(rec->p[0]);
580 isl_upoly_free(up);
581 return cst;
582 error:
583 isl_upoly_free(up);
584 return NULL;
585 }
586
587 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
588 __isl_take struct isl_upoly *up2)
589 {
590 int i;
591 struct isl_upoly_rec *rec1, *rec2;
592
593 if (!up1 || !up2)
594 goto error;
595
596 if (isl_upoly_is_nan(up1)) {
597 isl_upoly_free(up2);
598 return up1;
599 }
600
601 if (isl_upoly_is_nan(up2)) {
602 isl_upoly_free(up1);
603 return up2;
604 }
605
606 if (isl_upoly_is_zero(up1)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610
611 if (isl_upoly_is_zero(up2)) {
612 isl_upoly_free(up2);
613 return up1;
614 }
615
616 if (up1->var < up2->var)
617 return isl_upoly_sum(up2, up1);
618
619 if (up2->var < up1->var) {
620 struct isl_upoly_rec *rec;
621 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
622 isl_upoly_free(up1);
623 return up2;
624 }
625 up1 = isl_upoly_cow(up1);
626 rec = isl_upoly_as_rec(up1);
627 if (!rec)
628 goto error;
629 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
630 if (rec->n == 1)
631 up1 = replace_by_constant_term(up1);
632 return up1;
633 }
634
635 if (isl_upoly_is_cst(up1))
636 return isl_upoly_sum_cst(up1, up2);
637
638 rec1 = isl_upoly_as_rec(up1);
639 rec2 = isl_upoly_as_rec(up2);
640 if (!rec1 || !rec2)
641 goto error;
642
643 if (rec1->n < rec2->n)
644 return isl_upoly_sum(up2, up1);
645
646 up1 = isl_upoly_cow(up1);
647 rec1 = isl_upoly_as_rec(up1);
648 if (!rec1)
649 goto error;
650
651 for (i = rec2->n - 1; i >= 0; --i) {
652 rec1->p[i] = isl_upoly_sum(rec1->p[i],
653 isl_upoly_copy(rec2->p[i]));
654 if (!rec1->p[i])
655 goto error;
656 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
657 isl_upoly_free(rec1->p[i]);
658 rec1->n--;
659 }
660 }
661
662 if (rec1->n == 0)
663 up1 = replace_by_zero(up1);
664 else if (rec1->n == 1)
665 up1 = replace_by_constant_term(up1);
666
667 isl_upoly_free(up2);
668
669 return up1;
670 error:
671 isl_upoly_free(up1);
672 isl_upoly_free(up2);
673 return NULL;
674 }
675
676 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
677 {
678 struct isl_upoly_cst *cst;
679
680 if (isl_upoly_is_zero(up))
681 return up;
682
683 up = isl_upoly_cow(up);
684 if (!up)
685 return NULL;
686
687 cst = isl_upoly_as_cst(up);
688
689 isl_int_neg(cst->n, cst->n);
690
691 return up;
692 }
693
694 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
695 {
696 int i;
697 struct isl_upoly_rec *rec;
698
699 if (!up)
700 return NULL;
701
702 if (isl_upoly_is_cst(up))
703 return isl_upoly_neg_cst(up);
704
705 up = isl_upoly_cow(up);
706 rec = isl_upoly_as_rec(up);
707 if (!rec)
708 goto error;
709
710 for (i = 0; i < rec->n; ++i) {
711 rec->p[i] = isl_upoly_neg(rec->p[i]);
712 if (!rec->p[i])
713 goto error;
714 }
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
723 __isl_take struct isl_upoly *up2)
724 {
725 struct isl_upoly_cst *cst1;
726 struct isl_upoly_cst *cst2;
727
728 up1 = isl_upoly_cow(up1);
729 if (!up1 || !up2)
730 goto error;
731
732 cst1 = isl_upoly_as_cst(up1);
733 cst2 = isl_upoly_as_cst(up2);
734
735 isl_int_mul(cst1->n, cst1->n, cst2->n);
736 isl_int_mul(cst1->d, cst1->d, cst2->d);
737
738 isl_upoly_cst_reduce(cst1);
739
740 isl_upoly_free(up2);
741 return up1;
742 error:
743 isl_upoly_free(up1);
744 isl_upoly_free(up2);
745 return NULL;
746 }
747
748 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
749 __isl_take struct isl_upoly *up2)
750 {
751 struct isl_upoly_rec *rec1;
752 struct isl_upoly_rec *rec2;
753 struct isl_upoly_rec *res;
754 int i, j;
755 int size;
756
757 rec1 = isl_upoly_as_rec(up1);
758 rec2 = isl_upoly_as_rec(up2);
759 if (!rec1 || !rec2)
760 goto error;
761 size = rec1->n + rec2->n - 1;
762 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
763 if (!res)
764 goto error;
765
766 for (i = 0; i < rec1->n; ++i) {
767 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
768 isl_upoly_copy(rec1->p[i]));
769 if (!res->p[i])
770 goto error;
771 res->n++;
772 }
773 for (; i < size; ++i) {
774 res->p[i] = isl_upoly_zero(up1->ctx);
775 if (!res->p[i])
776 goto error;
777 res->n++;
778 }
779 for (i = 0; i < rec1->n; ++i) {
780 for (j = 1; j < rec2->n; ++j) {
781 struct isl_upoly *up;
782 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
783 isl_upoly_copy(rec1->p[i]));
784 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
785 if (!res->p[i + j])
786 goto error;
787 }
788 }
789
790 isl_upoly_free(up1);
791 isl_upoly_free(up2);
792
793 return &res->up;
794 error:
795 isl_upoly_free(up1);
796 isl_upoly_free(up2);
797 isl_upoly_free(&res->up);
798 return NULL;
799 }
800
801 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
802 __isl_take struct isl_upoly *up2)
803 {
804 if (!up1 || !up2)
805 goto error;
806
807 if (isl_upoly_is_nan(up1)) {
808 isl_upoly_free(up2);
809 return up1;
810 }
811
812 if (isl_upoly_is_nan(up2)) {
813 isl_upoly_free(up1);
814 return up2;
815 }
816
817 if (isl_upoly_is_zero(up1)) {
818 isl_upoly_free(up2);
819 return up1;
820 }
821
822 if (isl_upoly_is_zero(up2)) {
823 isl_upoly_free(up1);
824 return up2;
825 }
826
827 if (isl_upoly_is_one(up1)) {
828 isl_upoly_free(up1);
829 return up2;
830 }
831
832 if (isl_upoly_is_one(up2)) {
833 isl_upoly_free(up2);
834 return up1;
835 }
836
837 if (up1->var < up2->var)
838 return isl_upoly_mul(up2, up1);
839
840 if (up2->var < up1->var) {
841 int i;
842 struct isl_upoly_rec *rec;
843 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
844 isl_ctx *ctx = up1->ctx;
845 isl_upoly_free(up1);
846 isl_upoly_free(up2);
847 return isl_upoly_nan(ctx);
848 }
849 up1 = isl_upoly_cow(up1);
850 rec = isl_upoly_as_rec(up1);
851 if (!rec)
852 goto error;
853
854 for (i = 0; i < rec->n; ++i) {
855 rec->p[i] = isl_upoly_mul(rec->p[i],
856 isl_upoly_copy(up2));
857 if (!rec->p[i])
858 goto error;
859 }
860 isl_upoly_free(up2);
861 return up1;
862 }
863
864 if (isl_upoly_is_cst(up1))
865 return isl_upoly_mul_cst(up1, up2);
866
867 return isl_upoly_mul_rec(up1, up2);
868 error:
869 isl_upoly_free(up1);
870 isl_upoly_free(up2);
871 return NULL;
872 }
873
874 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
875 unsigned n_div, __isl_take struct isl_upoly *up)
876 {
877 struct isl_qpolynomial *qp = NULL;
878 unsigned total;
879
880 if (!dim || !up)
881 goto error;
882
883 total = isl_dim_total(dim);
884
885 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
886 if (!qp)
887 goto error;
888
889 qp->ref = 1;
890 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
891 if (!qp->div)
892 goto error;
893
894 qp->dim = dim;
895 qp->upoly = up;
896
897 return qp;
898 error:
899 isl_dim_free(dim);
900 isl_upoly_free(up);
901 isl_qpolynomial_free(qp);
902 return NULL;
903 }
904
905 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
906 {
907 if (!qp)
908 return NULL;
909
910 qp->ref++;
911 return qp;
912 }
913
914 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
915 {
916 struct isl_qpolynomial *dup;
917
918 if (!qp)
919 return NULL;
920
921 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
922 isl_upoly_copy(qp->upoly));
923 if (!dup)
924 return NULL;
925 isl_mat_free(dup->div);
926 dup->div = isl_mat_copy(qp->div);
927 if (!dup->div)
928 goto error;
929
930 return dup;
931 error:
932 isl_qpolynomial_free(dup);
933 return NULL;
934 }
935
936 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
937 {
938 if (!qp)
939 return NULL;
940
941 if (qp->ref == 1)
942 return qp;
943 qp->ref--;
944 return isl_qpolynomial_dup(qp);
945 }
946
947 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
948 {
949 if (!qp)
950 return;
951
952 if (--qp->ref > 0)
953 return;
954
955 isl_dim_free(qp->dim);
956 isl_mat_free(qp->div);
957 isl_upoly_free(qp->upoly);
958
959 free(qp);
960 }
961
962 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
963 {
964 int i;
965 struct isl_upoly *up;
966 struct isl_upoly_rec *rec;
967 struct isl_upoly_cst *cst;
968
969 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
970 if (!rec)
971 return NULL;
972 for (i = 0; i < 1 + power; ++i) {
973 rec->p[i] = isl_upoly_zero(ctx);
974 if (!rec->p[i])
975 goto error;
976 rec->n++;
977 }
978 cst = isl_upoly_as_cst(rec->p[power]);
979 isl_int_set_si(cst->n, 1);
980
981 return &rec->up;
982 error:
983 isl_upoly_free(&rec->up);
984 return NULL;
985 }
986
987 /* r array maps original positions to new positions.
988 */
989 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
990 int *r)
991 {
992 int i;
993 struct isl_upoly_rec *rec;
994 struct isl_upoly *base;
995 struct isl_upoly *res;
996
997 if (isl_upoly_is_cst(up))
998 return up;
999
1000 rec = isl_upoly_as_rec(up);
1001 if (!rec)
1002 goto error;
1003
1004 isl_assert(up->ctx, rec->n >= 1, goto error);
1005
1006 base = isl_upoly_pow(up->ctx, r[up->var], 1);
1007 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1008
1009 for (i = rec->n - 2; i >= 0; --i) {
1010 res = isl_upoly_mul(res, isl_upoly_copy(base));
1011 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1012 }
1013
1014 isl_upoly_free(base);
1015 isl_upoly_free(up);
1016
1017 return res;
1018 error:
1019 isl_upoly_free(up);
1020 return NULL;
1021 }
1022
1023 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1024 {
1025 int n_row, n_col;
1026 int equal;
1027
1028 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1029 div1->n_col >= div2->n_col, return -1);
1030
1031 if (div1->n_row == div2->n_row)
1032 return isl_mat_is_equal(div1, div2);
1033
1034 n_row = div1->n_row;
1035 n_col = div1->n_col;
1036 div1->n_row = div2->n_row;
1037 div1->n_col = div2->n_col;
1038
1039 equal = isl_mat_is_equal(div1, div2);
1040
1041 div1->n_row = n_row;
1042 div1->n_col = n_col;
1043
1044 return equal;
1045 }
1046
1047 static void expand_row(__isl_keep isl_mat *dst, int d,
1048 __isl_keep isl_mat *src, int s, int *exp)
1049 {
1050 int i;
1051 unsigned c = src->n_col - src->n_row;
1052
1053 isl_seq_cpy(dst->row[d], src->row[s], c);
1054 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1055
1056 for (i = 0; i < s; ++i)
1057 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1058 }
1059
1060 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1061 {
1062 int li, lj;
1063
1064 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1065 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1066
1067 if (li != lj)
1068 return li - lj;
1069
1070 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1071 }
1072
1073 struct isl_div_sort_info {
1074 isl_mat *div;
1075 int row;
1076 };
1077
1078 static int div_sort_cmp(const void *p1, const void *p2)
1079 {
1080 const struct isl_div_sort_info *i1, *i2;
1081 i1 = (const struct isl_div_sort_info *) p1;
1082 i2 = (const struct isl_div_sort_info *) p2;
1083
1084 return cmp_row(i1->div, i1->row, i2->row);
1085 }
1086
1087 /* Sort divs and remove duplicates.
1088 */
1089 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1090 {
1091 int i;
1092 int skip;
1093 int len;
1094 struct isl_div_sort_info *array = NULL;
1095 int *pos = NULL, *at = NULL;
1096 int *reordering = NULL;
1097 unsigned div_pos;
1098
1099 if (!qp)
1100 return NULL;
1101 if (qp->div->n_row <= 1)
1102 return qp;
1103
1104 div_pos = isl_dim_total(qp->dim);
1105
1106 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1107 qp->div->n_row);
1108 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1109 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1110 len = qp->div->n_col - 2;
1111 reordering = isl_alloc_array(qp->div->ctx, int, len);
1112 if (!array || !pos || !at || !reordering)
1113 goto error;
1114
1115 for (i = 0; i < qp->div->n_row; ++i) {
1116 array[i].div = qp->div;
1117 array[i].row = i;
1118 pos[i] = i;
1119 at[i] = i;
1120 }
1121
1122 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1123 div_sort_cmp);
1124
1125 for (i = 0; i < div_pos; ++i)
1126 reordering[i] = i;
1127
1128 for (i = 0; i < qp->div->n_row; ++i) {
1129 if (pos[array[i].row] == i)
1130 continue;
1131 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1132 pos[at[i]] = pos[array[i].row];
1133 at[pos[array[i].row]] = at[i];
1134 at[i] = array[i].row;
1135 pos[array[i].row] = i;
1136 }
1137
1138 skip = 0;
1139 for (i = 0; i < len - div_pos; ++i) {
1140 if (i > 0 &&
1141 isl_seq_eq(qp->div->row[i - skip - 1],
1142 qp->div->row[i - skip], qp->div->n_col)) {
1143 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1144 qp->div = isl_mat_drop_cols(qp->div,
1145 2 + div_pos + i - skip, 1);
1146 skip++;
1147 }
1148 reordering[div_pos + array[i].row] = div_pos + i - skip;
1149 }
1150
1151 qp->upoly = reorder(qp->upoly, reordering);
1152
1153 if (!qp->upoly || !qp->div)
1154 goto error;
1155
1156 free(at);
1157 free(pos);
1158 free(array);
1159 free(reordering);
1160
1161 return qp;
1162 error:
1163 free(at);
1164 free(pos);
1165 free(array);
1166 free(reordering);
1167 isl_qpolynomial_free(qp);
1168 return NULL;
1169 }
1170
1171 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1172 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1173 {
1174 int i, j, k;
1175 isl_mat *div = NULL;
1176 unsigned d = div1->n_col - div1->n_row;
1177
1178 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1179 d + div1->n_row + div2->n_row);
1180 if (!div)
1181 return NULL;
1182
1183 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1184 int cmp;
1185
1186 expand_row(div, k, div1, i, exp1);
1187 expand_row(div, k + 1, div2, j, exp2);
1188
1189 cmp = cmp_row(div, k, k + 1);
1190 if (cmp == 0) {
1191 exp1[i++] = k;
1192 exp2[j++] = k;
1193 } else if (cmp < 0) {
1194 exp1[i++] = k;
1195 } else {
1196 exp2[j++] = k;
1197 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1198 }
1199 }
1200 for (; i < div1->n_row; ++i, ++k) {
1201 expand_row(div, k, div1, i, exp1);
1202 exp1[i] = k;
1203 }
1204 for (; j < div2->n_row; ++j, ++k) {
1205 expand_row(div, k, div2, j, exp2);
1206 exp2[j] = k;
1207 }
1208
1209 div->n_row = k;
1210 div->n_col = d + k;
1211
1212 return div;
1213 }
1214
1215 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1216 int *exp, int first)
1217 {
1218 int i;
1219 struct isl_upoly_rec *rec;
1220
1221 if (isl_upoly_is_cst(up))
1222 return up;
1223
1224 if (up->var < first)
1225 return up;
1226
1227 if (exp[up->var - first] == up->var - first)
1228 return up;
1229
1230 up = isl_upoly_cow(up);
1231 if (!up)
1232 goto error;
1233
1234 up->var = exp[up->var - first] + first;
1235
1236 rec = isl_upoly_as_rec(up);
1237 if (!rec)
1238 goto error;
1239
1240 for (i = 0; i < rec->n; ++i) {
1241 rec->p[i] = expand(rec->p[i], exp, first);
1242 if (!rec->p[i])
1243 goto error;
1244 }
1245
1246 return up;
1247 error:
1248 isl_upoly_free(up);
1249 return NULL;
1250 }
1251
1252 static __isl_give isl_qpolynomial *with_merged_divs(
1253 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1254 __isl_take isl_qpolynomial *qp2),
1255 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1256 {
1257 int *exp1 = NULL;
1258 int *exp2 = NULL;
1259 isl_mat *div = NULL;
1260
1261 qp1 = isl_qpolynomial_cow(qp1);
1262 qp2 = isl_qpolynomial_cow(qp2);
1263
1264 if (!qp1 || !qp2)
1265 goto error;
1266
1267 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1268 qp1->div->n_col >= qp2->div->n_col, goto error);
1269
1270 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1271 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1272 if (!exp1 || !exp2)
1273 goto error;
1274
1275 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1276 if (!div)
1277 goto error;
1278
1279 isl_mat_free(qp1->div);
1280 qp1->div = isl_mat_copy(div);
1281 isl_mat_free(qp2->div);
1282 qp2->div = isl_mat_copy(div);
1283
1284 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1285 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1286
1287 if (!qp1->upoly || !qp2->upoly)
1288 goto error;
1289
1290 isl_mat_free(div);
1291 free(exp1);
1292 free(exp2);
1293
1294 return fn(qp1, qp2);
1295 error:
1296 isl_mat_free(div);
1297 free(exp1);
1298 free(exp2);
1299 isl_qpolynomial_free(qp1);
1300 isl_qpolynomial_free(qp2);
1301 return NULL;
1302 }
1303
1304 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1305 __isl_take isl_qpolynomial *qp2)
1306 {
1307 qp1 = isl_qpolynomial_cow(qp1);
1308
1309 if (!qp1 || !qp2)
1310 goto error;
1311
1312 if (qp1->div->n_row < qp2->div->n_row)
1313 return isl_qpolynomial_add(qp2, qp1);
1314
1315 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1316 if (!compatible_divs(qp1->div, qp2->div))
1317 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1318
1319 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1320 if (!qp1->upoly)
1321 goto error;
1322
1323 isl_qpolynomial_free(qp2);
1324
1325 return qp1;
1326 error:
1327 isl_qpolynomial_free(qp1);
1328 isl_qpolynomial_free(qp2);
1329 return NULL;
1330 }
1331
1332 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1333 __isl_keep isl_set *dom,
1334 __isl_take isl_qpolynomial *qp1,
1335 __isl_take isl_qpolynomial *qp2)
1336 {
1337 return isl_qpolynomial_add(qp1, qp2);
1338 }
1339
1340 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1341 __isl_take isl_qpolynomial *qp2)
1342 {
1343 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1344 }
1345
1346 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1347 {
1348 qp = isl_qpolynomial_cow(qp);
1349
1350 if (!qp)
1351 return NULL;
1352
1353 qp->upoly = isl_upoly_neg(qp->upoly);
1354 if (!qp->upoly)
1355 goto error;
1356
1357 return qp;
1358 error:
1359 isl_qpolynomial_free(qp);
1360 return NULL;
1361 }
1362
1363 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1364 __isl_take isl_qpolynomial *qp2)
1365 {
1366 qp1 = isl_qpolynomial_cow(qp1);
1367
1368 if (!qp1 || !qp2)
1369 goto error;
1370
1371 if (qp1->div->n_row < qp2->div->n_row)
1372 return isl_qpolynomial_mul(qp2, qp1);
1373
1374 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1375 if (!compatible_divs(qp1->div, qp2->div))
1376 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1377
1378 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1379 if (!qp1->upoly)
1380 goto error;
1381
1382 isl_qpolynomial_free(qp2);
1383
1384 return qp1;
1385 error:
1386 isl_qpolynomial_free(qp1);
1387 isl_qpolynomial_free(qp2);
1388 return NULL;
1389 }
1390
1391 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1392 {
1393 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1394 }
1395
1396 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1397 {
1398 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1399 }
1400
1401 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1402 {
1403 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1404 }
1405
1406 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1407 {
1408 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1409 }
1410
1411 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1412 {
1413 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1414 }
1415
1416 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1417 isl_int v)
1418 {
1419 struct isl_qpolynomial *qp;
1420 struct isl_upoly_cst *cst;
1421
1422 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1423 if (!qp)
1424 return NULL;
1425
1426 cst = isl_upoly_as_cst(qp->upoly);
1427 isl_int_set(cst->n, v);
1428
1429 return qp;
1430 }
1431
1432 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1433 isl_int *n, isl_int *d)
1434 {
1435 struct isl_upoly_cst *cst;
1436
1437 if (!qp)
1438 return -1;
1439
1440 if (!isl_upoly_is_cst(qp->upoly))
1441 return 0;
1442
1443 cst = isl_upoly_as_cst(qp->upoly);
1444 if (!cst)
1445 return -1;
1446
1447 if (n)
1448 isl_int_set(*n, cst->n);
1449 if (d)
1450 isl_int_set(*d, cst->d);
1451
1452 return 1;
1453 }
1454
1455 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1456 {
1457 int is_cst;
1458 struct isl_upoly_rec *rec;
1459
1460 if (!up)
1461 return -1;
1462
1463 if (up->var < 0)
1464 return 1;
1465
1466 rec = isl_upoly_as_rec(up);
1467 if (!rec)
1468 return -1;
1469
1470 if (rec->n > 2)
1471 return 0;
1472
1473 isl_assert(up->ctx, rec->n > 1, return -1);
1474
1475 is_cst = isl_upoly_is_cst(rec->p[1]);
1476 if (is_cst < 0)
1477 return -1;
1478 if (!is_cst)
1479 return 0;
1480
1481 return isl_upoly_is_affine(rec->p[0]);
1482 }
1483
1484 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1485 {
1486 if (!qp)
1487 return -1;
1488
1489 if (qp->div->n_row > 0)
1490 return 0;
1491
1492 return isl_upoly_is_affine(qp->upoly);
1493 }
1494
1495 static void update_coeff(__isl_keep isl_vec *aff,
1496 __isl_keep struct isl_upoly_cst *cst, int pos)
1497 {
1498 isl_int gcd;
1499 isl_int f;
1500
1501 if (isl_int_is_zero(cst->n))
1502 return;
1503
1504 isl_int_init(gcd);
1505 isl_int_init(f);
1506 isl_int_gcd(gcd, cst->d, aff->el[0]);
1507 isl_int_divexact(f, cst->d, gcd);
1508 isl_int_divexact(gcd, aff->el[0], gcd);
1509 isl_seq_scale(aff->el, aff->el, f, aff->size);
1510 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1511 isl_int_clear(gcd);
1512 isl_int_clear(f);
1513 }
1514
1515 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1516 __isl_keep isl_vec *aff)
1517 {
1518 struct isl_upoly_cst *cst;
1519 struct isl_upoly_rec *rec;
1520
1521 if (!up || !aff)
1522 return -1;
1523
1524 if (up->var < 0) {
1525 struct isl_upoly_cst *cst;
1526
1527 cst = isl_upoly_as_cst(up);
1528 if (!cst)
1529 return -1;
1530 update_coeff(aff, cst, 0);
1531 return 0;
1532 }
1533
1534 rec = isl_upoly_as_rec(up);
1535 if (!rec)
1536 return -1;
1537 isl_assert(up->ctx, rec->n == 2, return -1);
1538
1539 cst = isl_upoly_as_cst(rec->p[1]);
1540 if (!cst)
1541 return -1;
1542 update_coeff(aff, cst, 1 + up->var);
1543
1544 return isl_upoly_update_affine(rec->p[0], aff);
1545 }
1546
1547 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1548 __isl_keep isl_qpolynomial *qp)
1549 {
1550 isl_vec *aff;
1551 unsigned d;
1552
1553 if (!qp)
1554 return NULL;
1555
1556 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1557 d = isl_dim_total(qp->dim);
1558 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1559 if (!aff)
1560 return NULL;
1561
1562 isl_seq_clr(aff->el + 1, 1 + d);
1563 isl_int_set_si(aff->el[0], 1);
1564
1565 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1566 goto error;
1567
1568 return aff;
1569 error:
1570 isl_vec_free(aff);
1571 return NULL;
1572 }
1573
1574 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1575 __isl_keep isl_qpolynomial *qp2)
1576 {
1577 if (!qp1 || !qp2)
1578 return -1;
1579
1580 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1581 }
1582
1583 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1584 {
1585 int i;
1586 struct isl_upoly_rec *rec;
1587
1588 if (isl_upoly_is_cst(up)) {
1589 struct isl_upoly_cst *cst;
1590 cst = isl_upoly_as_cst(up);
1591 if (!cst)
1592 return;
1593 isl_int_lcm(*d, *d, cst->d);
1594 return;
1595 }
1596
1597 rec = isl_upoly_as_rec(up);
1598 if (!rec)
1599 return;
1600
1601 for (i = 0; i < rec->n; ++i)
1602 upoly_update_den(rec->p[i], d);
1603 }
1604
1605 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1606 {
1607 isl_int_set_si(*d, 1);
1608 if (!qp)
1609 return;
1610 upoly_update_den(qp->upoly, d);
1611 }
1612
1613 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1614 int pos, int power)
1615 {
1616 struct isl_ctx *ctx;
1617
1618 if (!dim)
1619 return NULL;
1620
1621 ctx = dim->ctx;
1622
1623 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1624 }
1625
1626 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1627 enum isl_dim_type type, unsigned pos)
1628 {
1629 if (!dim)
1630 return NULL;
1631
1632 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1633 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1634
1635 if (type == isl_dim_set)
1636 pos += isl_dim_size(dim, isl_dim_param);
1637
1638 return isl_qpolynomial_pow(dim, pos, 1);
1639 error:
1640 isl_dim_free(dim);
1641 return NULL;
1642 }
1643
1644 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1645 int power)
1646 {
1647 struct isl_qpolynomial *qp = NULL;
1648 struct isl_upoly_rec *rec;
1649 struct isl_upoly_cst *cst;
1650 int i, d;
1651 int pos;
1652
1653 if (!div)
1654 return NULL;
1655
1656 d = div->line - div->bmap->div;
1657
1658 pos = isl_dim_total(div->bmap->dim) + d;
1659 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1660 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1661 div->bmap->n_div, &rec->up);
1662 if (!qp)
1663 goto error;
1664
1665 for (i = 0; i < div->bmap->n_div; ++i)
1666 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1667
1668 for (i = 0; i < 1 + power; ++i) {
1669 rec->p[i] = isl_upoly_zero(div->ctx);
1670 if (!rec->p[i])
1671 goto error;
1672 rec->n++;
1673 }
1674 cst = isl_upoly_as_cst(rec->p[power]);
1675 isl_int_set_si(cst->n, 1);
1676
1677 isl_div_free(div);
1678
1679 return qp;
1680 error:
1681 isl_qpolynomial_free(qp);
1682 isl_div_free(div);
1683 return NULL;
1684 }
1685
1686 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1687 {
1688 return isl_qpolynomial_div_pow(div, 1);
1689 }
1690
1691 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1692 const isl_int n, const isl_int d)
1693 {
1694 struct isl_qpolynomial *qp;
1695 struct isl_upoly_cst *cst;
1696
1697 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1698 if (!qp)
1699 return NULL;
1700
1701 cst = isl_upoly_as_cst(qp->upoly);
1702 isl_int_set(cst->n, n);
1703 isl_int_set(cst->d, d);
1704
1705 return qp;
1706 }
1707
1708 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1709 {
1710 struct isl_upoly_rec *rec;
1711 int i;
1712
1713 if (!up)
1714 return -1;
1715
1716 if (isl_upoly_is_cst(up))
1717 return 0;
1718
1719 if (up->var < d)
1720 active[up->var] = 1;
1721
1722 rec = isl_upoly_as_rec(up);
1723 for (i = 0; i < rec->n; ++i)
1724 if (up_set_active(rec->p[i], active, d) < 0)
1725 return -1;
1726
1727 return 0;
1728 }
1729
1730 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1731 {
1732 int i, j;
1733 int d = isl_dim_total(qp->dim);
1734
1735 if (!qp || !active)
1736 return -1;
1737
1738 for (i = 0; i < d; ++i)
1739 for (j = 0; j < qp->div->n_row; ++j) {
1740 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1741 continue;
1742 active[i] = 1;
1743 break;
1744 }
1745
1746 return up_set_active(qp->upoly, active, d);
1747 }
1748
1749 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1750 enum isl_dim_type type, unsigned first, unsigned n)
1751 {
1752 int i;
1753 int *active = NULL;
1754 int involves = 0;
1755
1756 if (!qp)
1757 return -1;
1758 if (n == 0)
1759 return 0;
1760
1761 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1762 return -1);
1763 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1764 type == isl_dim_set, return -1);
1765
1766 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1767 if (set_active(qp, active) < 0)
1768 goto error;
1769
1770 if (type == isl_dim_set)
1771 first += isl_dim_size(qp->dim, isl_dim_param);
1772 for (i = 0; i < n; ++i)
1773 if (active[first + i]) {
1774 involves = 1;
1775 break;
1776 }
1777
1778 free(active);
1779
1780 return involves;
1781 error:
1782 free(active);
1783 return -1;
1784 }
1785
1786 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1787 unsigned first, unsigned n)
1788 {
1789 int i;
1790 struct isl_upoly_rec *rec;
1791
1792 if (!up)
1793 return NULL;
1794 if (n == 0 || up->var < 0 || up->var < first)
1795 return up;
1796 if (up->var < first + n) {
1797 up = replace_by_constant_term(up);
1798 return isl_upoly_drop(up, first, n);
1799 }
1800 up = isl_upoly_cow(up);
1801 if (!up)
1802 return NULL;
1803 up->var -= n;
1804 rec = isl_upoly_as_rec(up);
1805 if (!rec)
1806 goto error;
1807
1808 for (i = 0; i < rec->n; ++i) {
1809 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1810 if (!rec->p[i])
1811 goto error;
1812 }
1813
1814 return up;
1815 error:
1816 isl_upoly_free(up);
1817 return NULL;
1818 }
1819
1820 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1821 __isl_take isl_qpolynomial *qp,
1822 enum isl_dim_type type, unsigned pos, const char *s)
1823 {
1824 qp = isl_qpolynomial_cow(qp);
1825 if (!qp)
1826 return NULL;
1827 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1828 if (!qp->dim)
1829 goto error;
1830 return qp;
1831 error:
1832 isl_qpolynomial_free(qp);
1833 return NULL;
1834 }
1835
1836 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1837 __isl_take isl_qpolynomial *qp,
1838 enum isl_dim_type type, unsigned first, unsigned n)
1839 {
1840 if (!qp)
1841 return NULL;
1842 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1843 return qp;
1844
1845 qp = isl_qpolynomial_cow(qp);
1846 if (!qp)
1847 return NULL;
1848
1849 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1850 goto error);
1851 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1852 type == isl_dim_set, goto error);
1853
1854 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1855 if (!qp->dim)
1856 goto error;
1857
1858 if (type == isl_dim_set)
1859 first += isl_dim_size(qp->dim, isl_dim_param);
1860
1861 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1862 if (!qp->div)
1863 goto error;
1864
1865 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1866 if (!qp->upoly)
1867 goto error;
1868
1869 return qp;
1870 error:
1871 isl_qpolynomial_free(qp);
1872 return NULL;
1873 }
1874
1875 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1876 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1877 {
1878 int i;
1879 struct isl_upoly_rec *rec;
1880 struct isl_upoly *base, *res;
1881
1882 if (!up)
1883 return NULL;
1884
1885 if (isl_upoly_is_cst(up))
1886 return up;
1887
1888 if (up->var < first)
1889 return up;
1890
1891 rec = isl_upoly_as_rec(up);
1892 if (!rec)
1893 goto error;
1894
1895 isl_assert(up->ctx, rec->n >= 1, goto error);
1896
1897 if (up->var >= first + n)
1898 base = isl_upoly_pow(up->ctx, up->var, 1);
1899 else
1900 base = isl_upoly_copy(subs[up->var - first]);
1901
1902 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1903 for (i = rec->n - 2; i >= 0; --i) {
1904 struct isl_upoly *t;
1905 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1906 res = isl_upoly_mul(res, isl_upoly_copy(base));
1907 res = isl_upoly_sum(res, t);
1908 }
1909
1910 isl_upoly_free(base);
1911 isl_upoly_free(up);
1912
1913 return res;
1914 error:
1915 isl_upoly_free(up);
1916 return NULL;
1917 }
1918
1919 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1920 isl_int denom, unsigned len)
1921 {
1922 int i;
1923 struct isl_upoly *up;
1924
1925 isl_assert(ctx, len >= 1, return NULL);
1926
1927 up = isl_upoly_rat_cst(ctx, f[0], denom);
1928 for (i = 0; i < len - 1; ++i) {
1929 struct isl_upoly *t;
1930 struct isl_upoly *c;
1931
1932 if (isl_int_is_zero(f[1 + i]))
1933 continue;
1934
1935 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1936 t = isl_upoly_pow(ctx, i, 1);
1937 t = isl_upoly_mul(c, t);
1938 up = isl_upoly_sum(up, t);
1939 }
1940
1941 return up;
1942 }
1943
1944 /* Remove common factor of non-constant terms and denominator.
1945 */
1946 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1947 {
1948 isl_ctx *ctx = qp->div->ctx;
1949 unsigned total = qp->div->n_col - 2;
1950
1951 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1952 isl_int_gcd(ctx->normalize_gcd,
1953 ctx->normalize_gcd, qp->div->row[div][0]);
1954 if (isl_int_is_one(ctx->normalize_gcd))
1955 return;
1956
1957 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1958 ctx->normalize_gcd, total);
1959 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1960 ctx->normalize_gcd);
1961 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1962 ctx->normalize_gcd);
1963 }
1964
1965 /* Replace the integer division identified by "div" by the polynomial "s".
1966 * The integer division is assumed not to appear in the definition
1967 * of any other integer divisions.
1968 */
1969 static __isl_give isl_qpolynomial *substitute_div(
1970 __isl_take isl_qpolynomial *qp,
1971 int div, __isl_take struct isl_upoly *s)
1972 {
1973 int i;
1974 int total;
1975 int *reordering;
1976
1977 if (!qp || !s)
1978 goto error;
1979
1980 qp = isl_qpolynomial_cow(qp);
1981 if (!qp)
1982 goto error;
1983
1984 total = isl_dim_total(qp->dim);
1985 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1986 if (!qp->upoly)
1987 goto error;
1988
1989 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1990 if (!reordering)
1991 goto error;
1992 for (i = 0; i < total + div; ++i)
1993 reordering[i] = i;
1994 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1995 reordering[i] = i - 1;
1996 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1997 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1998 qp->upoly = reorder(qp->upoly, reordering);
1999 free(reordering);
2000
2001 if (!qp->upoly || !qp->div)
2002 goto error;
2003
2004 isl_upoly_free(s);
2005 return qp;
2006 error:
2007 isl_qpolynomial_free(qp);
2008 isl_upoly_free(s);
2009 return NULL;
2010 }
2011
2012 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2013 * divisions because d is equal to 1 by their definition, i.e., e.
2014 */
2015 static __isl_give isl_qpolynomial *substitute_non_divs(
2016 __isl_take isl_qpolynomial *qp)
2017 {
2018 int i, j;
2019 int total;
2020 struct isl_upoly *s;
2021
2022 if (!qp)
2023 return NULL;
2024
2025 total = isl_dim_total(qp->dim);
2026 for (i = 0; qp && i < qp->div->n_row; ++i) {
2027 if (!isl_int_is_one(qp->div->row[i][0]))
2028 continue;
2029 for (j = i + 1; j < qp->div->n_row; ++j) {
2030 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2031 continue;
2032 isl_seq_combine(qp->div->row[j] + 1,
2033 qp->div->ctx->one, qp->div->row[j] + 1,
2034 qp->div->row[j][2 + total + i],
2035 qp->div->row[i] + 1, 1 + total + i);
2036 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2037 normalize_div(qp, j);
2038 }
2039 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2040 qp->div->row[i][0], qp->div->n_col - 1);
2041 qp = substitute_div(qp, i, s);
2042 --i;
2043 }
2044
2045 return qp;
2046 }
2047
2048 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2049 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2050 {
2051 int i, j, k;
2052 isl_int denom;
2053 unsigned total;
2054 unsigned n_div;
2055 struct isl_upoly *up;
2056
2057 if (!eq)
2058 goto error;
2059 if (eq->n_eq == 0) {
2060 isl_basic_set_free(eq);
2061 return qp;
2062 }
2063
2064 qp = isl_qpolynomial_cow(qp);
2065 if (!qp)
2066 goto error;
2067 qp->div = isl_mat_cow(qp->div);
2068 if (!qp->div)
2069 goto error;
2070
2071 total = 1 + isl_dim_total(eq->dim);
2072 n_div = eq->n_div;
2073 isl_int_init(denom);
2074 for (i = 0; i < eq->n_eq; ++i) {
2075 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2076 if (j < 0 || j == 0 || j >= total)
2077 continue;
2078
2079 for (k = 0; k < qp->div->n_row; ++k) {
2080 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2081 continue;
2082 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2083 &qp->div->row[k][0]);
2084 normalize_div(qp, k);
2085 }
2086
2087 if (isl_int_is_pos(eq->eq[i][j]))
2088 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2089 isl_int_abs(denom, eq->eq[i][j]);
2090 isl_int_set_si(eq->eq[i][j], 0);
2091
2092 up = isl_upoly_from_affine(qp->dim->ctx,
2093 eq->eq[i], denom, total);
2094 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2095 isl_upoly_free(up);
2096 }
2097 isl_int_clear(denom);
2098
2099 if (!qp->upoly)
2100 goto error;
2101
2102 isl_basic_set_free(eq);
2103
2104 qp = substitute_non_divs(qp);
2105 qp = sort_divs(qp);
2106
2107 return qp;
2108 error:
2109 isl_basic_set_free(eq);
2110 isl_qpolynomial_free(qp);
2111 return NULL;
2112 }
2113
2114 #undef PW
2115 #define PW isl_pw_qpolynomial
2116 #undef EL
2117 #define EL isl_qpolynomial
2118 #undef IS_ZERO
2119 #define IS_ZERO is_zero
2120 #undef FIELD
2121 #define FIELD qp
2122
2123 #include <isl_pw_templ.c>
2124
2125 #undef UNION
2126 #define UNION isl_union_pw_qpolynomial
2127 #undef PART
2128 #define PART isl_pw_qpolynomial
2129 #undef PARTS
2130 #define PARTS pw_qpolynomial
2131
2132 #include <isl_union_templ.c>
2133
2134 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2135 {
2136 if (!pwqp)
2137 return -1;
2138
2139 if (pwqp->n != -1)
2140 return 0;
2141
2142 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2143 return 0;
2144
2145 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2146 }
2147
2148 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2149 __isl_take isl_pw_qpolynomial *pwqp1,
2150 __isl_take isl_pw_qpolynomial *pwqp2)
2151 {
2152 int i, j, n;
2153 struct isl_pw_qpolynomial *res;
2154 isl_set *set;
2155
2156 if (!pwqp1 || !pwqp2)
2157 goto error;
2158
2159 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2160 goto error);
2161
2162 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2163 isl_pw_qpolynomial_free(pwqp2);
2164 return pwqp1;
2165 }
2166
2167 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2168 isl_pw_qpolynomial_free(pwqp1);
2169 return pwqp2;
2170 }
2171
2172 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2173 isl_pw_qpolynomial_free(pwqp1);
2174 return pwqp2;
2175 }
2176
2177 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2178 isl_pw_qpolynomial_free(pwqp2);
2179 return pwqp1;
2180 }
2181
2182 n = pwqp1->n * pwqp2->n;
2183 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2184
2185 for (i = 0; i < pwqp1->n; ++i) {
2186 for (j = 0; j < pwqp2->n; ++j) {
2187 struct isl_set *common;
2188 struct isl_qpolynomial *prod;
2189 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2190 isl_set_copy(pwqp2->p[j].set));
2191 if (isl_set_fast_is_empty(common)) {
2192 isl_set_free(common);
2193 continue;
2194 }
2195
2196 prod = isl_qpolynomial_mul(
2197 isl_qpolynomial_copy(pwqp1->p[i].qp),
2198 isl_qpolynomial_copy(pwqp2->p[j].qp));
2199
2200 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2201 }
2202 }
2203
2204 isl_pw_qpolynomial_free(pwqp1);
2205 isl_pw_qpolynomial_free(pwqp2);
2206
2207 return res;
2208 error:
2209 isl_pw_qpolynomial_free(pwqp1);
2210 isl_pw_qpolynomial_free(pwqp2);
2211 return NULL;
2212 }
2213
2214 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2215 __isl_take isl_pw_qpolynomial *pwqp)
2216 {
2217 int i;
2218
2219 if (!pwqp)
2220 return NULL;
2221
2222 if (isl_pw_qpolynomial_is_zero(pwqp))
2223 return pwqp;
2224
2225 pwqp = isl_pw_qpolynomial_cow(pwqp);
2226 if (!pwqp)
2227 return NULL;
2228
2229 for (i = 0; i < pwqp->n; ++i) {
2230 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2231 if (!pwqp->p[i].qp)
2232 goto error;
2233 }
2234
2235 return pwqp;
2236 error:
2237 isl_pw_qpolynomial_free(pwqp);
2238 return NULL;
2239 }
2240
2241 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2242 __isl_take isl_pw_qpolynomial *pwqp1,
2243 __isl_take isl_pw_qpolynomial *pwqp2)
2244 {
2245 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2246 }
2247
2248 __isl_give struct isl_upoly *isl_upoly_eval(
2249 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2250 {
2251 int i;
2252 struct isl_upoly_rec *rec;
2253 struct isl_upoly *res;
2254 struct isl_upoly *base;
2255
2256 if (isl_upoly_is_cst(up)) {
2257 isl_vec_free(vec);
2258 return up;
2259 }
2260
2261 rec = isl_upoly_as_rec(up);
2262 if (!rec)
2263 goto error;
2264
2265 isl_assert(up->ctx, rec->n >= 1, goto error);
2266
2267 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2268
2269 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2270 isl_vec_copy(vec));
2271
2272 for (i = rec->n - 2; i >= 0; --i) {
2273 res = isl_upoly_mul(res, isl_upoly_copy(base));
2274 res = isl_upoly_sum(res,
2275 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2276 isl_vec_copy(vec)));
2277 }
2278
2279 isl_upoly_free(base);
2280 isl_upoly_free(up);
2281 isl_vec_free(vec);
2282 return res;
2283 error:
2284 isl_upoly_free(up);
2285 isl_vec_free(vec);
2286 return NULL;
2287 }
2288
2289 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2290 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2291 {
2292 isl_vec *ext;
2293 struct isl_upoly *up;
2294 isl_dim *dim;
2295
2296 if (!qp || !pnt)
2297 goto error;
2298 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2299
2300 if (qp->div->n_row == 0)
2301 ext = isl_vec_copy(pnt->vec);
2302 else {
2303 int i;
2304 unsigned dim = isl_dim_total(qp->dim);
2305 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2306 if (!ext)
2307 goto error;
2308
2309 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2310 for (i = 0; i < qp->div->n_row; ++i) {
2311 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2312 1 + dim + i, &ext->el[1+dim+i]);
2313 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2314 qp->div->row[i][0]);
2315 }
2316 }
2317
2318 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2319 if (!up)
2320 goto error;
2321
2322 dim = isl_dim_copy(qp->dim);
2323 isl_qpolynomial_free(qp);
2324 isl_point_free(pnt);
2325
2326 return isl_qpolynomial_alloc(dim, 0, up);
2327 error:
2328 isl_qpolynomial_free(qp);
2329 isl_point_free(pnt);
2330 return NULL;
2331 }
2332
2333 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2334 __isl_keep struct isl_upoly_cst *cst2)
2335 {
2336 int cmp;
2337 isl_int t;
2338 isl_int_init(t);
2339 isl_int_mul(t, cst1->n, cst2->d);
2340 isl_int_submul(t, cst2->n, cst1->d);
2341 cmp = isl_int_sgn(t);
2342 isl_int_clear(t);
2343 return cmp;
2344 }
2345
2346 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2347 __isl_keep isl_qpolynomial *qp2)
2348 {
2349 struct isl_upoly_cst *cst1, *cst2;
2350
2351 if (!qp1 || !qp2)
2352 return -1;
2353 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2354 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2355 if (isl_qpolynomial_is_nan(qp1))
2356 return -1;
2357 if (isl_qpolynomial_is_nan(qp2))
2358 return -1;
2359 cst1 = isl_upoly_as_cst(qp1->upoly);
2360 cst2 = isl_upoly_as_cst(qp2->upoly);
2361
2362 return isl_upoly_cmp(cst1, cst2) <= 0;
2363 }
2364
2365 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2366 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2367 {
2368 struct isl_upoly_cst *cst1, *cst2;
2369 int cmp;
2370
2371 if (!qp1 || !qp2)
2372 goto error;
2373 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2374 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2375 cst1 = isl_upoly_as_cst(qp1->upoly);
2376 cst2 = isl_upoly_as_cst(qp2->upoly);
2377 cmp = isl_upoly_cmp(cst1, cst2);
2378
2379 if (cmp <= 0) {
2380 isl_qpolynomial_free(qp2);
2381 } else {
2382 isl_qpolynomial_free(qp1);
2383 qp1 = qp2;
2384 }
2385 return qp1;
2386 error:
2387 isl_qpolynomial_free(qp1);
2388 isl_qpolynomial_free(qp2);
2389 return NULL;
2390 }
2391
2392 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2393 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2394 {
2395 struct isl_upoly_cst *cst1, *cst2;
2396 int cmp;
2397
2398 if (!qp1 || !qp2)
2399 goto error;
2400 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2401 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2402 cst1 = isl_upoly_as_cst(qp1->upoly);
2403 cst2 = isl_upoly_as_cst(qp2->upoly);
2404 cmp = isl_upoly_cmp(cst1, cst2);
2405
2406 if (cmp >= 0) {
2407 isl_qpolynomial_free(qp2);
2408 } else {
2409 isl_qpolynomial_free(qp1);
2410 qp1 = qp2;
2411 }
2412 return qp1;
2413 error:
2414 isl_qpolynomial_free(qp1);
2415 isl_qpolynomial_free(qp2);
2416 return NULL;
2417 }
2418
2419 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2420 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2421 unsigned first, unsigned n)
2422 {
2423 unsigned total;
2424 unsigned g_pos;
2425 int *exp;
2426
2427 if (n == 0)
2428 return qp;
2429
2430 qp = isl_qpolynomial_cow(qp);
2431 if (!qp)
2432 return NULL;
2433
2434 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2435 goto error);
2436
2437 g_pos = pos(qp->dim, type) + first;
2438
2439 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2440 if (!qp->div)
2441 goto error;
2442
2443 total = qp->div->n_col - 2;
2444 if (total > g_pos) {
2445 int i;
2446 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2447 if (!exp)
2448 goto error;
2449 for (i = 0; i < total - g_pos; ++i)
2450 exp[i] = i + n;
2451 qp->upoly = expand(qp->upoly, exp, g_pos);
2452 free(exp);
2453 if (!qp->upoly)
2454 goto error;
2455 }
2456
2457 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2458 if (!qp->dim)
2459 goto error;
2460
2461 return qp;
2462 error:
2463 isl_qpolynomial_free(qp);
2464 return NULL;
2465 }
2466
2467 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2468 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2469 {
2470 unsigned pos;
2471
2472 pos = isl_qpolynomial_dim(qp, type);
2473
2474 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2475 }
2476
2477 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2478 __isl_take isl_pw_qpolynomial *pwqp,
2479 enum isl_dim_type type, unsigned n)
2480 {
2481 unsigned pos;
2482
2483 pos = isl_pw_qpolynomial_dim(pwqp, type);
2484
2485 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2486 }
2487
2488 static int *reordering_move(isl_ctx *ctx,
2489 unsigned len, unsigned dst, unsigned src, unsigned n)
2490 {
2491 int i;
2492 int *reordering;
2493
2494 reordering = isl_alloc_array(ctx, int, len);
2495 if (!reordering)
2496 return NULL;
2497
2498 if (dst <= src) {
2499 for (i = 0; i < dst; ++i)
2500 reordering[i] = i;
2501 for (i = 0; i < n; ++i)
2502 reordering[src + i] = dst + i;
2503 for (i = 0; i < src - dst; ++i)
2504 reordering[dst + i] = dst + n + i;
2505 for (i = 0; i < len - src - n; ++i)
2506 reordering[src + n + i] = src + n + i;
2507 } else {
2508 for (i = 0; i < src; ++i)
2509 reordering[i] = i;
2510 for (i = 0; i < n; ++i)
2511 reordering[src + i] = dst + i;
2512 for (i = 0; i < dst - src; ++i)
2513 reordering[src + n + i] = src + i;
2514 for (i = 0; i < len - dst - n; ++i)
2515 reordering[dst + n + i] = dst + n + i;
2516 }
2517
2518 return reordering;
2519 }
2520
2521 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2522 __isl_take isl_qpolynomial *qp,
2523 enum isl_dim_type dst_type, unsigned dst_pos,
2524 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2525 {
2526 unsigned g_dst_pos;
2527 unsigned g_src_pos;
2528 int *reordering;
2529
2530 qp = isl_qpolynomial_cow(qp);
2531 if (!qp)
2532 return NULL;
2533
2534 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2535 goto error);
2536
2537 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2538 g_src_pos = pos(qp->dim, src_type) + src_pos;
2539 if (dst_type > src_type)
2540 g_dst_pos -= n;
2541
2542 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2543 if (!qp->div)
2544 goto error;
2545 qp = sort_divs(qp);
2546 if (!qp)
2547 goto error;
2548
2549 reordering = reordering_move(qp->dim->ctx,
2550 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2551 if (!reordering)
2552 goto error;
2553
2554 qp->upoly = reorder(qp->upoly, reordering);
2555 free(reordering);
2556 if (!qp->upoly)
2557 goto error;
2558
2559 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2560 if (!qp->dim)
2561 goto error;
2562
2563 return qp;
2564 error:
2565 isl_qpolynomial_free(qp);
2566 return NULL;
2567 }
2568
2569 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2570 isl_int *f, isl_int denom)
2571 {
2572 struct isl_upoly *up;
2573
2574 if (!dim)
2575 return NULL;
2576
2577 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2578
2579 return isl_qpolynomial_alloc(dim, 0, up);
2580 }
2581
2582 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2583 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2584 {
2585 isl_int denom;
2586 isl_dim *dim;
2587 struct isl_upoly *up;
2588 isl_qpolynomial *qp;
2589 int sgn;
2590
2591 if (!c)
2592 return NULL;
2593
2594 isl_int_init(denom);
2595
2596 isl_constraint_get_coefficient(c, type, pos, &denom);
2597 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2598 sgn = isl_int_sgn(denom);
2599 isl_int_abs(denom, denom);
2600 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2601 1 + isl_constraint_dim(c, isl_dim_all));
2602 if (sgn < 0)
2603 isl_int_neg(denom, denom);
2604 isl_constraint_set_coefficient(c, type, pos, denom);
2605
2606 dim = isl_dim_copy(c->bmap->dim);
2607
2608 isl_int_clear(denom);
2609 isl_constraint_free(c);
2610
2611 qp = isl_qpolynomial_alloc(dim, 0, up);
2612 if (sgn > 0)
2613 qp = isl_qpolynomial_neg(qp);
2614 return qp;
2615 }
2616
2617 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2618 * in "qp" by subs[i].
2619 */
2620 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2621 __isl_take isl_qpolynomial *qp,
2622 enum isl_dim_type type, unsigned first, unsigned n,
2623 __isl_keep isl_qpolynomial **subs)
2624 {
2625 int i;
2626 struct isl_upoly **ups;
2627
2628 if (n == 0)
2629 return qp;
2630
2631 qp = isl_qpolynomial_cow(qp);
2632 if (!qp)
2633 return NULL;
2634 for (i = 0; i < n; ++i)
2635 if (!subs[i])
2636 goto error;
2637
2638 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2639 goto error);
2640
2641 for (i = 0; i < n; ++i)
2642 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2643 goto error);
2644
2645 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2646 for (i = 0; i < n; ++i)
2647 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2648
2649 first += pos(qp->dim, type);
2650
2651 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2652 if (!ups)
2653 goto error;
2654 for (i = 0; i < n; ++i)
2655 ups[i] = subs[i]->upoly;
2656
2657 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2658
2659 free(ups);
2660
2661 if (!qp->upoly)
2662 goto error;
2663
2664 return qp;
2665 error:
2666 isl_qpolynomial_free(qp);
2667 return NULL;
2668 }
2669
2670 static __isl_give isl_basic_set *add_div_constraints(
2671 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2672 {
2673 int i;
2674 unsigned total;
2675
2676 if (!bset || !div)
2677 goto error;
2678
2679 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2680 if (!bset)
2681 goto error;
2682 total = isl_basic_set_total_dim(bset);
2683 for (i = 0; i < div->n_row; ++i)
2684 if (isl_basic_set_add_div_constraints_var(bset,
2685 total - div->n_row + i, div->row[i]) < 0)
2686 goto error;
2687
2688 isl_mat_free(div);
2689 return bset;
2690 error:
2691 isl_mat_free(div);
2692 isl_basic_set_free(bset);
2693 return NULL;
2694 }
2695
2696 /* Extend "bset" with extra set dimensions for each integer division
2697 * in "qp" and then call "fn" with the extended bset and the polynomial
2698 * that results from replacing each of the integer divisions by the
2699 * corresponding extra set dimension.
2700 */
2701 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2702 __isl_keep isl_basic_set *bset,
2703 int (*fn)(__isl_take isl_basic_set *bset,
2704 __isl_take isl_qpolynomial *poly, void *user), void *user)
2705 {
2706 isl_dim *dim;
2707 isl_mat *div;
2708 isl_qpolynomial *poly;
2709
2710 if (!qp || !bset)
2711 goto error;
2712 if (qp->div->n_row == 0)
2713 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2714 user);
2715
2716 div = isl_mat_copy(qp->div);
2717 dim = isl_dim_copy(qp->dim);
2718 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2719 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2720 bset = isl_basic_set_copy(bset);
2721 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2722 bset = add_div_constraints(bset, div);
2723
2724 return fn(bset, poly, user);
2725 error:
2726 return -1;
2727 }
2728
2729 /* Return total degree in variables first (inclusive) up to last (exclusive).
2730 */
2731 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2732 {
2733 int deg = -1;
2734 int i;
2735 struct isl_upoly_rec *rec;
2736
2737 if (!up)
2738 return -2;
2739 if (isl_upoly_is_zero(up))
2740 return -1;
2741 if (isl_upoly_is_cst(up) || up->var < first)
2742 return 0;
2743
2744 rec = isl_upoly_as_rec(up);
2745 if (!rec)
2746 return -2;
2747
2748 for (i = 0; i < rec->n; ++i) {
2749 int d;
2750
2751 if (isl_upoly_is_zero(rec->p[i]))
2752 continue;
2753 d = isl_upoly_degree(rec->p[i], first, last);
2754 if (up->var < last)
2755 d += i;
2756 if (d > deg)
2757 deg = d;
2758 }
2759
2760 return deg;
2761 }
2762
2763 /* Return total degree in set variables.
2764 */
2765 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2766 {
2767 unsigned ovar;
2768 unsigned nvar;
2769
2770 if (!poly)
2771 return -2;
2772
2773 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2774 nvar = isl_dim_size(poly->dim, isl_dim_set);
2775 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2776 }
2777
2778 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2779 unsigned pos, int deg)
2780 {
2781 int i;
2782 struct isl_upoly_rec *rec;
2783
2784 if (!up)
2785 return NULL;
2786
2787 if (isl_upoly_is_cst(up) || up->var < pos) {
2788 if (deg == 0)
2789 return isl_upoly_copy(up);
2790 else
2791 return isl_upoly_zero(up->ctx);
2792 }
2793
2794 rec = isl_upoly_as_rec(up);
2795 if (!rec)
2796 return NULL;
2797
2798 if (up->var == pos) {
2799 if (deg < rec->n)
2800 return isl_upoly_copy(rec->p[deg]);
2801 else
2802 return isl_upoly_zero(up->ctx);
2803 }
2804
2805 up = isl_upoly_copy(up);
2806 up = isl_upoly_cow(up);
2807 rec = isl_upoly_as_rec(up);
2808 if (!rec)
2809 goto error;
2810
2811 for (i = 0; i < rec->n; ++i) {
2812 struct isl_upoly *t;
2813 t = isl_upoly_coeff(rec->p[i], pos, deg);
2814 if (!t)
2815 goto error;
2816 isl_upoly_free(rec->p[i]);
2817 rec->p[i] = t;
2818 }
2819
2820 return up;
2821 error:
2822 isl_upoly_free(up);
2823 return NULL;
2824 }
2825
2826 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2827 */
2828 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2829 __isl_keep isl_qpolynomial *qp,
2830 enum isl_dim_type type, unsigned t_pos, int deg)
2831 {
2832 unsigned g_pos;
2833 struct isl_upoly *up;
2834 isl_qpolynomial *c;
2835
2836 if (!qp)
2837 return NULL;
2838
2839 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2840 return NULL);
2841
2842 g_pos = pos(qp->dim, type) + t_pos;
2843 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2844
2845 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2846 if (!c)
2847 return NULL;
2848 isl_mat_free(c->div);
2849 c->div = isl_mat_copy(qp->div);
2850 if (!c->div)
2851 goto error;
2852 return c;
2853 error:
2854 isl_qpolynomial_free(c);
2855 return NULL;
2856 }
2857
2858 /* Homogenize the polynomial in the variables first (inclusive) up to
2859 * last (exclusive) by inserting powers of variable first.
2860 * Variable first is assumed not to appear in the input.
2861 */
2862 __isl_give struct isl_upoly *isl_upoly_homogenize(
2863 __isl_take struct isl_upoly *up, int deg, int target,
2864 int first, int last)
2865 {
2866 int i;
2867 struct isl_upoly_rec *rec;
2868
2869 if (!up)
2870 return NULL;
2871 if (isl_upoly_is_zero(up))
2872 return up;
2873 if (deg == target)
2874 return up;
2875 if (isl_upoly_is_cst(up) || up->var < first) {
2876 struct isl_upoly *hom;
2877
2878 hom = isl_upoly_pow(up->ctx, first, target - deg);
2879 if (!hom)
2880 goto error;
2881 rec = isl_upoly_as_rec(hom);
2882 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2883
2884 return hom;
2885 }
2886
2887 up = isl_upoly_cow(up);
2888 rec = isl_upoly_as_rec(up);
2889 if (!rec)
2890 goto error;
2891
2892 for (i = 0; i < rec->n; ++i) {
2893 if (isl_upoly_is_zero(rec->p[i]))
2894 continue;
2895 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2896 up->var < last ? deg + i : i, target,
2897 first, last);
2898 if (!rec->p[i])
2899 goto error;
2900 }
2901
2902 return up;
2903 error:
2904 isl_upoly_free(up);
2905 return NULL;
2906 }
2907
2908 /* Homogenize the polynomial in the set variables by introducing
2909 * powers of an extra set variable at position 0.
2910 */
2911 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2912 __isl_take isl_qpolynomial *poly)
2913 {
2914 unsigned ovar;
2915 unsigned nvar;
2916 int deg = isl_qpolynomial_degree(poly);
2917
2918 if (deg < -1)
2919 goto error;
2920
2921 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2922 poly = isl_qpolynomial_cow(poly);
2923 if (!poly)
2924 goto error;
2925
2926 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2927 nvar = isl_dim_size(poly->dim, isl_dim_set);
2928 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2929 ovar, ovar + nvar);
2930 if (!poly->upoly)
2931 goto error;
2932
2933 return poly;
2934 error:
2935 isl_qpolynomial_free(poly);
2936 return NULL;
2937 }
2938
2939 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2940 __isl_take isl_mat *div)
2941 {
2942 isl_term *term;
2943 int n;
2944
2945 if (!dim || !div)
2946 goto error;
2947
2948 n = isl_dim_total(dim) + div->n_row;
2949
2950 term = isl_calloc(dim->ctx, struct isl_term,
2951 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2952 if (!term)
2953 goto error;
2954
2955 term->ref = 1;
2956 term->dim = dim;
2957 term->div = div;
2958 isl_int_init(term->n);
2959 isl_int_init(term->d);
2960
2961 return term;
2962 error:
2963 isl_dim_free(dim);
2964 isl_mat_free(div);
2965 return NULL;
2966 }
2967
2968 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2969 {
2970 if (!term)
2971 return NULL;
2972
2973 term->ref++;
2974 return term;
2975 }
2976
2977 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2978 {
2979 int i;
2980 isl_term *dup;
2981 unsigned total;
2982
2983 if (term)
2984 return NULL;
2985
2986 total = isl_dim_total(term->dim) + term->div->n_row;
2987
2988 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2989 if (!dup)
2990 return NULL;
2991
2992 isl_int_set(dup->n, term->n);
2993 isl_int_set(dup->d, term->d);
2994
2995 for (i = 0; i < total; ++i)
2996 dup->pow[i] = term->pow[i];
2997
2998 return dup;
2999 }
3000
3001 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3002 {
3003 if (!term)
3004 return NULL;
3005
3006 if (term->ref == 1)
3007 return term;
3008 term->ref--;
3009 return isl_term_dup(term);
3010 }
3011
3012 void isl_term_free(__isl_take isl_term *term)
3013 {
3014 if (!term)
3015 return;
3016
3017 if (--term->ref > 0)
3018 return;
3019
3020 isl_dim_free(term->dim);
3021 isl_mat_free(term->div);
3022 isl_int_clear(term->n);
3023 isl_int_clear(term->d);
3024 free(term);
3025 }
3026
3027 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3028 {
3029 if (!term)
3030 return 0;
3031
3032 switch (type) {
3033 case isl_dim_param:
3034 case isl_dim_in:
3035 case isl_dim_out: return isl_dim_size(term->dim, type);
3036 case isl_dim_div: return term->div->n_row;
3037 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3038 default: return 0;
3039 }
3040 }
3041
3042 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3043 {
3044 return term ? term->dim->ctx : NULL;
3045 }
3046
3047 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3048 {
3049 if (!term)
3050 return;
3051 isl_int_set(*n, term->n);
3052 }
3053
3054 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3055 {
3056 if (!term)
3057 return;
3058 isl_int_set(*d, term->d);
3059 }
3060
3061 int isl_term_get_exp(__isl_keep isl_term *term,
3062 enum isl_dim_type type, unsigned pos)
3063 {
3064 if (!term)
3065 return -1;
3066
3067 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3068
3069 if (type >= isl_dim_set)
3070 pos += isl_dim_size(term->dim, isl_dim_param);
3071 if (type >= isl_dim_div)
3072 pos += isl_dim_size(term->dim, isl_dim_set);
3073
3074 return term->pow[pos];
3075 }
3076
3077 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3078 {
3079 isl_basic_map *bmap;
3080 unsigned total;
3081 int k;
3082
3083 if (!term)
3084 return NULL;
3085
3086 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3087 return NULL);
3088
3089 total = term->div->n_col - term->div->n_row - 2;
3090 /* No nested divs for now */
3091 isl_assert(term->dim->ctx,
3092 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3093 term->div->n_row) == -1,
3094 return NULL);
3095
3096 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3097 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3098 goto error;
3099
3100 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3101
3102 return isl_basic_map_div(bmap, k);
3103 error:
3104 isl_basic_map_free(bmap);
3105 return NULL;
3106 }
3107
3108 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3109 int (*fn)(__isl_take isl_term *term, void *user),
3110 __isl_take isl_term *term, void *user)
3111 {
3112 int i;
3113 struct isl_upoly_rec *rec;
3114
3115 if (!up || !term)
3116 goto error;
3117
3118 if (isl_upoly_is_zero(up))
3119 return term;
3120
3121 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3122 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3123 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3124
3125 if (isl_upoly_is_cst(up)) {
3126 struct isl_upoly_cst *cst;
3127 cst = isl_upoly_as_cst(up);
3128 if (!cst)
3129 goto error;
3130 term = isl_term_cow(term);
3131 if (!term)
3132 goto error;
3133 isl_int_set(term->n, cst->n);
3134 isl_int_set(term->d, cst->d);
3135 if (fn(isl_term_copy(term), user) < 0)
3136 goto error;
3137 return term;
3138 }
3139
3140 rec = isl_upoly_as_rec(up);
3141 if (!rec)
3142 goto error;
3143
3144 for (i = 0; i < rec->n; ++i) {
3145 term = isl_term_cow(term);
3146 if (!term)
3147 goto error;
3148 term->pow[up->var] = i;
3149 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3150 if (!term)
3151 goto error;
3152 }
3153 term->pow[up->var] = 0;
3154
3155 return term;
3156 error:
3157 isl_term_free(term);
3158 return NULL;
3159 }
3160
3161 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3162 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3163 {
3164 isl_term *term;
3165
3166 if (!qp)
3167 return -1;
3168
3169 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3170 if (!term)
3171 return -1;
3172
3173 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3174
3175 isl_term_free(term);
3176
3177 return term ? 0 : -1;
3178 }
3179
3180 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3181 {
3182 struct isl_upoly *up;
3183 isl_qpolynomial *qp;
3184 int i, n;
3185
3186 if (!term)
3187 return NULL;
3188
3189 n = isl_dim_total(term->dim) + term->div->n_row;
3190
3191 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3192 for (i = 0; i < n; ++i) {
3193 if (!term->pow[i])
3194 continue;
3195 up = isl_upoly_mul(up,
3196 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3197 }
3198
3199 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3200 if (!qp)
3201 goto error;
3202 isl_mat_free(qp->div);
3203 qp->div = isl_mat_copy(term->div);
3204 if (!qp->div)
3205 goto error;
3206
3207 isl_term_free(term);
3208 return qp;
3209 error:
3210 isl_qpolynomial_free(qp);
3211 isl_term_free(term);
3212 return NULL;
3213 }
3214
3215 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3216 __isl_take isl_dim *dim)
3217 {
3218 int i;
3219 int extra;
3220 unsigned total;
3221
3222 if (!qp || !dim)
3223 goto error;
3224
3225 if (isl_dim_equal(qp->dim, dim)) {
3226 isl_dim_free(dim);
3227 return qp;
3228 }
3229
3230 qp = isl_qpolynomial_cow(qp);
3231 if (!qp)
3232 goto error;
3233
3234 extra = isl_dim_size(dim, isl_dim_set) -
3235 isl_dim_size(qp->dim, isl_dim_set);
3236 total = isl_dim_total(qp->dim);
3237 if (qp->div->n_row) {
3238 int *exp;
3239
3240 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3241 if (!exp)
3242 goto error;
3243 for (i = 0; i < qp->div->n_row; ++i)
3244 exp[i] = extra + i;
3245 qp->upoly = expand(qp->upoly, exp, total);
3246 free(exp);
3247 if (!qp->upoly)
3248 goto error;
3249 }
3250 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3251 if (!qp->div)
3252 goto error;
3253 for (i = 0; i < qp->div->n_row; ++i)
3254 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3255
3256 isl_dim_free(qp->dim);
3257 qp->dim = dim;
3258
3259 return qp;
3260 error:
3261 isl_dim_free(dim);
3262 isl_qpolynomial_free(qp);
3263 return NULL;
3264 }
3265
3266 /* For each parameter or variable that does not appear in qp,
3267 * first eliminate the variable from all constraints and then set it to zero.
3268 */
3269 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3270 __isl_keep isl_qpolynomial *qp)
3271 {
3272 int *active = NULL;
3273 int i;
3274 int d;
3275 unsigned nparam;
3276 unsigned nvar;
3277
3278 if (!set || !qp)
3279 goto error;
3280
3281 d = isl_dim_total(set->dim);
3282 active = isl_calloc_array(set->ctx, int, d);
3283 if (set_active(qp, active) < 0)
3284 goto error;
3285
3286 for (i = 0; i < d; ++i)
3287 if (!active[i])
3288 break;
3289
3290 if (i == d) {
3291 free(active);
3292 return set;
3293 }
3294
3295 nparam = isl_dim_size(set->dim, isl_dim_param);
3296 nvar = isl_dim_size(set->dim, isl_dim_set);
3297 for (i = 0; i < nparam; ++i) {
3298 if (active[i])
3299 continue;
3300 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3301 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3302 }
3303 for (i = 0; i < nvar; ++i) {
3304 if (active[nparam + i])
3305 continue;
3306 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3307 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3308 }
3309
3310 free(active);
3311
3312 return set;
3313 error:
3314 free(active);
3315 isl_set_free(set);
3316 return NULL;
3317 }
3318
3319 struct isl_opt_data {
3320 isl_qpolynomial *qp;
3321 int first;
3322 isl_qpolynomial *opt;
3323 int max;
3324 };
3325
3326 static int opt_fn(__isl_take isl_point *pnt, void *user)
3327 {
3328 struct isl_opt_data *data = (struct isl_opt_data *)user;
3329 isl_qpolynomial *val;
3330
3331 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3332 if (data->first) {
3333 data->first = 0;
3334 data->opt = val;
3335 } else if (data->max) {
3336 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3337 } else {
3338 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3339 }
3340
3341 return 0;
3342 }
3343
3344 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3345 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3346 {
3347 struct isl_opt_data data = { NULL, 1, NULL, max };
3348
3349 if (!set || !qp)
3350 goto error;
3351
3352 if (isl_upoly_is_cst(qp->upoly)) {
3353 isl_set_free(set);
3354 return qp;
3355 }
3356
3357 set = fix_inactive(set, qp);
3358
3359 data.qp = qp;
3360 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3361 goto error;
3362
3363 if (data.first)
3364 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3365
3366 isl_set_free(set);
3367 isl_qpolynomial_free(qp);
3368 return data.opt;
3369 error:
3370 isl_set_free(set);
3371 isl_qpolynomial_free(qp);
3372 isl_qpolynomial_free(data.opt);
3373 return NULL;
3374 }
3375
3376 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3377 __isl_take isl_morph *morph)
3378 {
3379 int i;
3380 int n_sub;
3381 isl_ctx *ctx;
3382 struct isl_upoly *up;
3383 unsigned n_div;
3384 struct isl_upoly **subs;
3385 isl_mat *mat;
3386
3387 qp = isl_qpolynomial_cow(qp);
3388 if (!qp || !morph)
3389 goto error;
3390
3391 ctx = qp->dim->ctx;
3392 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3393
3394 n_sub = morph->inv->n_row - 1;
3395 if (morph->inv->n_row != morph->inv->n_col)
3396 n_sub += qp->div->n_row;
3397 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3398 if (!subs)
3399 goto error;
3400
3401 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3402 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3403 morph->inv->row[0][0], morph->inv->n_col);
3404 if (morph->inv->n_row != morph->inv->n_col)
3405 for (i = 0; i < qp->div->n_row; ++i)
3406 subs[morph->inv->n_row - 1 + i] =
3407 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3408
3409 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3410
3411 for (i = 0; i < n_sub; ++i)
3412 isl_upoly_free(subs[i]);
3413 free(subs);
3414
3415 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3416 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3417 qp->div = isl_mat_product(qp->div, mat);
3418 isl_dim_free(qp->dim);
3419 qp->dim = isl_dim_copy(morph->ran->dim);
3420
3421 if (!qp->upoly || !qp->div || !qp->dim)
3422 goto error;
3423
3424 isl_morph_free(morph);
3425
3426 return qp;
3427 error:
3428 isl_qpolynomial_free(qp);
3429 isl_morph_free(morph);
3430 return NULL;
3431 }
3432
3433 static int neg_entry(void **entry, void *user)
3434 {
3435 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3436
3437 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3438
3439 return *pwqp ? 0 : -1;
3440 }
3441
3442 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3443 __isl_take isl_union_pw_qpolynomial *upwqp)
3444 {
3445 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3446 if (!upwqp)
3447 return NULL;
3448
3449 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3450 &neg_entry, NULL) < 0)
3451 goto error;
3452
3453 return upwqp;
3454 error:
3455 isl_union_pw_qpolynomial_free(upwqp);
3456 return NULL;
3457 }
3458
3459 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3460 __isl_take isl_union_pw_qpolynomial *upwqp1,
3461 __isl_take isl_union_pw_qpolynomial *upwqp2)
3462 {
3463 return isl_union_pw_qpolynomial_add(upwqp1,
3464 isl_union_pw_qpolynomial_neg(upwqp2));
3465 }
3466
3467 static int mul_entry(void **entry, void *user)
3468 {
3469 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3470 uint32_t hash;
3471 struct isl_hash_table_entry *entry2;
3472 isl_pw_qpolynomial *pwpq = *entry;
3473 int empty;
3474
3475 hash = isl_dim_get_hash(pwpq->dim);
3476 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3477 hash, &has_dim, pwpq->dim, 0);
3478 if (!entry2)
3479 return 0;
3480
3481 pwpq = isl_pw_qpolynomial_copy(pwpq);
3482 pwpq = isl_pw_qpolynomial_mul(pwpq,
3483 isl_pw_qpolynomial_copy(entry2->data));
3484
3485 empty = isl_pw_qpolynomial_is_zero(pwpq);
3486 if (empty < 0) {
3487 isl_pw_qpolynomial_free(pwpq);
3488 return -1;
3489 }
3490 if (empty) {
3491 isl_pw_qpolynomial_free(pwpq);
3492 return 0;
3493 }
3494
3495 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3496
3497 return 0;
3498 }
3499
3500 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3501 __isl_take isl_union_pw_qpolynomial *upwqp1,
3502 __isl_take isl_union_pw_qpolynomial *upwqp2)
3503 {
3504 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3505 }
3506
3507 /* Reorder the columns of the given div definitions according to the
3508 * given reordering.
3509 */
3510 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3511 __isl_take isl_reordering *r)
3512 {
3513 int i, j;
3514 isl_mat *mat;
3515 int extra;
3516
3517 if (!div || !r)
3518 goto error;
3519
3520 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3521 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3522 if (!mat)
3523 goto error;
3524
3525 for (i = 0; i < div->n_row; ++i) {
3526 isl_seq_cpy(mat->row[i], div->row[i], 2);
3527 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3528 for (j = 0; j < r->len; ++j)
3529 isl_int_set(mat->row[i][2 + r->pos[j]],
3530 div->row[i][2 + j]);
3531 }
3532
3533 isl_reordering_free(r);
3534 isl_mat_free(div);
3535 return mat;
3536 error:
3537 isl_reordering_free(r);
3538 isl_mat_free(div);
3539 return NULL;
3540 }
3541
3542 /* Reorder the dimension of "qp" according to the given reordering.
3543 */
3544 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3545 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3546 {
3547 qp = isl_qpolynomial_cow(qp);
3548 if (!qp)
3549 goto error;
3550
3551 r = isl_reordering_extend(r, qp->div->n_row);
3552 if (!r)
3553 goto error;
3554
3555 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3556 if (!qp->div)
3557 goto error;
3558
3559 qp->upoly = reorder(qp->upoly, r->pos);
3560 if (!qp->upoly)
3561 goto error;
3562
3563 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3564
3565 isl_reordering_free(r);
3566 return qp;
3567 error:
3568 isl_qpolynomial_free(qp);
3569 isl_reordering_free(r);
3570 return NULL;
3571 }
3572
3573 struct isl_split_periods_data {
3574 int max_periods;
3575 isl_pw_qpolynomial *res;
3576 };
3577
3578 /* Create a slice where the integer division "div" has the fixed value "v".
3579 * In particular, if "div" refers to floor(f/m), then create a slice
3580 *
3581 * m v <= f <= m v + (m - 1)
3582 *
3583 * or
3584 *
3585 * f - m v >= 0
3586 * -f + m v + (m - 1) >= 0
3587 */
3588 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3589 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3590 {
3591 int total;
3592 isl_basic_set *bset = NULL;
3593 int k;
3594
3595 if (!dim || !qp)
3596 goto error;
3597
3598 total = isl_dim_total(dim);
3599 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3600
3601 k = isl_basic_set_alloc_inequality(bset);
3602 if (k < 0)
3603 goto error;
3604 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3605 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3606
3607 k = isl_basic_set_alloc_inequality(bset);
3608 if (k < 0)
3609 goto error;
3610 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3611 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3612 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3613 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3614
3615 isl_dim_free(dim);
3616 return isl_set_from_basic_set(bset);
3617 error:
3618 isl_basic_set_free(bset);
3619 isl_dim_free(dim);
3620 return NULL;
3621 }
3622
3623 static int split_periods(__isl_take isl_set *set,
3624 __isl_take isl_qpolynomial *qp, void *user);
3625
3626 /* Create a slice of the domain "set" such that integer division "div"
3627 * has the fixed value "v" and add the results to data->res,
3628 * replacing the integer division by "v" in "qp".
3629 */
3630 static int set_div(__isl_take isl_set *set,
3631 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3632 struct isl_split_periods_data *data)
3633 {
3634 int i;
3635 int total;
3636 isl_set *slice;
3637 struct isl_upoly *cst;
3638
3639 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3640 set = isl_set_intersect(set, slice);
3641
3642 if (!qp)
3643 goto error;
3644
3645 total = isl_dim_total(qp->dim);
3646
3647 for (i = div + 1; i < qp->div->n_row; ++i) {
3648 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3649 continue;
3650 isl_int_addmul(qp->div->row[i][1],
3651 qp->div->row[i][2 + total + div], v);
3652 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3653 }
3654
3655 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3656 qp = substitute_div(qp, div, cst);
3657
3658 return split_periods(set, qp, data);
3659 error:
3660 isl_set_free(set);
3661 isl_qpolynomial_free(qp);
3662 return -1;
3663 }
3664
3665 /* Split the domain "set" such that integer division "div"
3666 * has a fixed value (ranging from "min" to "max") on each slice
3667 * and add the results to data->res.
3668 */
3669 static int split_div(__isl_take isl_set *set,
3670 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3671 struct isl_split_periods_data *data)
3672 {
3673 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3674 isl_set *set_i = isl_set_copy(set);
3675 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3676
3677 if (set_div(set_i, qp_i, div, min, data) < 0)
3678 goto error;
3679 }
3680 isl_set_free(set);
3681 isl_qpolynomial_free(qp);
3682 return 0;
3683 error:
3684 isl_set_free(set);
3685 isl_qpolynomial_free(qp);
3686 return -1;
3687 }
3688
3689 /* If "qp" refers to any integer division
3690 * that can only attain "max_periods" distinct values on "set"
3691 * then split the domain along those distinct values.
3692 * Add the results (or the original if no splitting occurs)
3693 * to data->res.
3694 */
3695 static int split_periods(__isl_take isl_set *set,
3696 __isl_take isl_qpolynomial *qp, void *user)
3697 {
3698 int i;
3699 isl_pw_qpolynomial *pwqp;
3700 struct isl_split_periods_data *data;
3701 isl_int min, max;
3702 int total;
3703 int r = 0;
3704
3705 data = (struct isl_split_periods_data *)user;
3706
3707 if (!set || !qp)
3708 goto error;
3709
3710 if (qp->div->n_row == 0) {
3711 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3712 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3713 return 0;
3714 }
3715
3716 isl_int_init(min);
3717 isl_int_init(max);
3718 total = isl_dim_total(qp->dim);
3719 for (i = 0; i < qp->div->n_row; ++i) {
3720 enum isl_lp_result lp_res;
3721
3722 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3723 qp->div->n_row) != -1)
3724 continue;
3725
3726 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3727 set->ctx->one, &min, NULL, NULL);
3728 if (lp_res == isl_lp_error)
3729 goto error2;
3730 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3731 continue;
3732 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3733
3734 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3735 set->ctx->one, &max, NULL, NULL);
3736 if (lp_res == isl_lp_error)
3737 goto error2;
3738 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3739 continue;
3740 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3741
3742 isl_int_sub(max, max, min);
3743 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3744 isl_int_add(max, max, min);
3745 break;
3746 }
3747 }
3748
3749 if (i < qp->div->n_row) {
3750 r = split_div(set, qp, i, min, max, data);
3751 } else {
3752 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3753 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3754 }
3755
3756 isl_int_clear(max);
3757 isl_int_clear(min);
3758
3759 return r;
3760 error2:
3761 isl_int_clear(max);
3762 isl_int_clear(min);
3763 error:
3764 isl_set_free(set);
3765 isl_qpolynomial_free(qp);
3766 return -1;
3767 }
3768
3769 /* If any quasi-polynomial in pwqp refers to any integer division
3770 * that can only attain "max_periods" distinct values on its domain
3771 * then split the domain along those distinct values.
3772 */
3773 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3774 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3775 {
3776 struct isl_split_periods_data data;
3777
3778 data.max_periods = max_periods;
3779 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3780
3781 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3782 goto error;
3783
3784 isl_pw_qpolynomial_free(pwqp);
3785
3786 return data.res;
3787 error:
3788 isl_pw_qpolynomial_free(data.res);
3789 isl_pw_qpolynomial_free(pwqp);
3790 return NULL;
3791 }
3792
3793 /* Construct a piecewise quasipolynomial that is constant on the given
3794 * domain. In particular, it is
3795 * 0 if cst == 0
3796 * 1 if cst == 1
3797 * infinity if cst == -1
3798 */
3799 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3800 __isl_take isl_basic_set *bset, int cst)
3801 {
3802 isl_dim *dim;
3803 isl_qpolynomial *qp;
3804
3805 if (!bset)
3806 return NULL;
3807
3808 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3809 dim = isl_basic_set_get_dim(bset);
3810 if (cst < 0)
3811 qp = isl_qpolynomial_infty(dim);
3812 else if (cst == 0)
3813 qp = isl_qpolynomial_zero(dim);
3814 else
3815 qp = isl_qpolynomial_one(dim);
3816 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3817 }
3818
3819 /* Factor bset, call fn on each of the factors and return the product.
3820 *
3821 * If no factors can be found, simply call fn on the input.
3822 * Otherwise, construct the factors based on the factorizer,
3823 * call fn on each factor and compute the product.
3824 */
3825 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3826 __isl_take isl_basic_set *bset,
3827 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3828 {
3829 int i, n;
3830 isl_dim *dim;
3831 isl_set *set;
3832 isl_factorizer *f;
3833 isl_qpolynomial *qp;
3834 isl_pw_qpolynomial *pwqp;
3835 unsigned nparam;
3836 unsigned nvar;
3837
3838 f = isl_basic_set_factorizer(bset);
3839 if (!f)
3840 goto error;
3841 if (f->n_group == 0) {
3842 isl_factorizer_free(f);
3843 return fn(bset);
3844 }
3845
3846 nparam = isl_basic_set_dim(bset, isl_dim_param);
3847 nvar = isl_basic_set_dim(bset, isl_dim_set);
3848
3849 dim = isl_basic_set_get_dim(bset);
3850 dim = isl_dim_domain(dim);
3851 set = isl_set_universe(isl_dim_copy(dim));
3852 qp = isl_qpolynomial_one(dim);
3853 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3854
3855 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3856
3857 for (i = 0, n = 0; i < f->n_group; ++i) {
3858 isl_basic_set *bset_i;
3859 isl_pw_qpolynomial *pwqp_i;
3860
3861 bset_i = isl_basic_set_copy(bset);
3862 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3863 nparam + n + f->len[i], nvar - n - f->len[i]);
3864 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3865 nparam, n);
3866 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3867 n + f->len[i], nvar - n - f->len[i]);
3868 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3869
3870 pwqp_i = fn(bset_i);
3871 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3872
3873 n += f->len[i];
3874 }
3875
3876 isl_basic_set_free(bset);
3877 isl_factorizer_free(f);
3878
3879 return pwqp;
3880 error:
3881 isl_basic_set_free(bset);
3882 return NULL;
3883 }
3884
3885 /* Factor bset, call fn on each of the factors and return the product.
3886 * The function is assumed to evaluate to zero on empty domains,
3887 * to one on zero-dimensional domains and to infinity on unbounded domains
3888 * and will not be called explicitly on zero-dimensional or unbounded domains.
3889 *
3890 * We first check for some special cases and remove all equalities.
3891 * Then we hand over control to compressed_multiplicative_call.
3892 */
3893 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3894 __isl_take isl_basic_set *bset,
3895 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3896 {
3897 int bounded;
3898 isl_morph *morph;
3899 isl_pw_qpolynomial *pwqp;
3900 unsigned orig_nvar, final_nvar;
3901
3902 if (!bset)
3903 return NULL;
3904
3905 if (isl_basic_set_fast_is_empty(bset))
3906 return constant_on_domain(bset, 0);
3907
3908 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3909
3910 if (orig_nvar == 0)
3911 return constant_on_domain(bset, 1);
3912
3913 bounded = isl_basic_set_is_bounded(bset);
3914 if (bounded < 0)
3915 goto error;
3916 if (!bounded)
3917 return constant_on_domain(bset, -1);
3918
3919 if (bset->n_eq == 0)
3920 return compressed_multiplicative_call(bset, fn);
3921
3922 morph = isl_basic_set_full_compression(bset);
3923 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3924
3925 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3926
3927 pwqp = compressed_multiplicative_call(bset, fn);
3928
3929 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3930 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3931 morph = isl_morph_inverse(morph);
3932
3933 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3934
3935 return pwqp;
3936 error:
3937 isl_basic_set_free(bset);
3938 return NULL;
3939 }
Integer set library