?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
hide isl_set internals
[isl.git] / isl_polynomial.c
blob8acfa9878b0d270ea1a2981cbcebc304dff9d263
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 #include <isl_range.h>
22
23 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
24 {
25 switch (type) {
26 case isl_dim_param: return 0;
27 case isl_dim_in: return dim->nparam;
28 case isl_dim_out: return dim->nparam + dim->n_in;
29 default: return 0;
30 }
31 }
32
33 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
34 {
35 if (!up)
36 return -1;
37
38 return up->var < 0;
39 }
40
41 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
42 {
43 if (!up)
44 return NULL;
45
46 isl_assert(up->ctx, up->var < 0, return NULL);
47
48 return (struct isl_upoly_cst *)up;
49 }
50
51 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
52 {
53 if (!up)
54 return NULL;
55
56 isl_assert(up->ctx, up->var >= 0, return NULL);
57
58 return (struct isl_upoly_rec *)up;
59 }
60
61 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
62 __isl_keep struct isl_upoly *up2)
63 {
64 int i;
65 struct isl_upoly_rec *rec1, *rec2;
66
67 if (!up1 || !up2)
68 return -1;
69 if (up1 == up2)
70 return 1;
71 if (up1->var != up2->var)
72 return 0;
73 if (isl_upoly_is_cst(up1)) {
74 struct isl_upoly_cst *cst1, *cst2;
75 cst1 = isl_upoly_as_cst(up1);
76 cst2 = isl_upoly_as_cst(up2);
77 if (!cst1 || !cst2)
78 return -1;
79 return isl_int_eq(cst1->n, cst2->n) &&
80 isl_int_eq(cst1->d, cst2->d);
81 }
82
83 rec1 = isl_upoly_as_rec(up1);
84 rec2 = isl_upoly_as_rec(up2);
85 if (!rec1 || !rec2)
86 return -1;
87
88 if (rec1->n != rec2->n)
89 return 0;
90
91 for (i = 0; i < rec1->n; ++i) {
92 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
93 if (eq < 0 || !eq)
94 return eq;
95 }
96
97 return 1;
98 }
99
100 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
101 {
102 struct isl_upoly_cst *cst;
103
104 if (!up)
105 return -1;
106 if (!isl_upoly_is_cst(up))
107 return 0;
108
109 cst = isl_upoly_as_cst(up);
110 if (!cst)
111 return -1;
112
113 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
114 }
115
116 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
117 {
118 struct isl_upoly_cst *cst;
119
120 if (!up)
121 return 0;
122 if (!isl_upoly_is_cst(up))
123 return 0;
124
125 cst = isl_upoly_as_cst(up);
126 if (!cst)
127 return 0;
128
129 return isl_int_sgn(cst->n);
130 }
131
132 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
133 {
134 struct isl_upoly_cst *cst;
135
136 if (!up)
137 return -1;
138 if (!isl_upoly_is_cst(up))
139 return 0;
140
141 cst = isl_upoly_as_cst(up);
142 if (!cst)
143 return -1;
144
145 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
146 }
147
148 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
149 {
150 struct isl_upoly_cst *cst;
151
152 if (!up)
153 return -1;
154 if (!isl_upoly_is_cst(up))
155 return 0;
156
157 cst = isl_upoly_as_cst(up);
158 if (!cst)
159 return -1;
160
161 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
162 }
163
164 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
165 {
166 struct isl_upoly_cst *cst;
167
168 if (!up)
169 return -1;
170 if (!isl_upoly_is_cst(up))
171 return 0;
172
173 cst = isl_upoly_as_cst(up);
174 if (!cst)
175 return -1;
176
177 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
178 }
179
180 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
181 {
182 struct isl_upoly_cst *cst;
183
184 if (!up)
185 return -1;
186 if (!isl_upoly_is_cst(up))
187 return 0;
188
189 cst = isl_upoly_as_cst(up);
190 if (!cst)
191 return -1;
192
193 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
194 }
195
196 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
197 {
198 struct isl_upoly_cst *cst;
199
200 if (!up)
201 return -1;
202 if (!isl_upoly_is_cst(up))
203 return 0;
204
205 cst = isl_upoly_as_cst(up);
206 if (!cst)
207 return -1;
208
209 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
210 }
211
212 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
213 {
214 struct isl_upoly_cst *cst;
215
216 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
217 if (!cst)
218 return NULL;
219
220 cst->up.ref = 1;
221 cst->up.ctx = ctx;
222 isl_ctx_ref(ctx);
223 cst->up.var = -1;
224
225 isl_int_init(cst->n);
226 isl_int_init(cst->d);
227
228 return cst;
229 }
230
231 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
232 {
233 struct isl_upoly_cst *cst;
234
235 cst = isl_upoly_cst_alloc(ctx);
236 if (!cst)
237 return NULL;
238
239 isl_int_set_si(cst->n, 0);
240 isl_int_set_si(cst->d, 1);
241
242 return &cst->up;
243 }
244
245 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
246 {
247 struct isl_upoly_cst *cst;
248
249 cst = isl_upoly_cst_alloc(ctx);
250 if (!cst)
251 return NULL;
252
253 isl_int_set_si(cst->n, 1);
254 isl_int_set_si(cst->d, 1);
255
256 return &cst->up;
257 }
258
259 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
260 {
261 struct isl_upoly_cst *cst;
262
263 cst = isl_upoly_cst_alloc(ctx);
264 if (!cst)
265 return NULL;
266
267 isl_int_set_si(cst->n, 1);
268 isl_int_set_si(cst->d, 0);
269
270 return &cst->up;
271 }
272
273 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
274 {
275 struct isl_upoly_cst *cst;
276
277 cst = isl_upoly_cst_alloc(ctx);
278 if (!cst)
279 return NULL;
280
281 isl_int_set_si(cst->n, -1);
282 isl_int_set_si(cst->d, 0);
283
284 return &cst->up;
285 }
286
287 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
288 {
289 struct isl_upoly_cst *cst;
290
291 cst = isl_upoly_cst_alloc(ctx);
292 if (!cst)
293 return NULL;
294
295 isl_int_set_si(cst->n, 0);
296 isl_int_set_si(cst->d, 0);
297
298 return &cst->up;
299 }
300
301 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
302 isl_int n, isl_int d)
303 {
304 struct isl_upoly_cst *cst;
305
306 cst = isl_upoly_cst_alloc(ctx);
307 if (!cst)
308 return NULL;
309
310 isl_int_set(cst->n, n);
311 isl_int_set(cst->d, d);
312
313 return &cst->up;
314 }
315
316 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
317 int var, int size)
318 {
319 struct isl_upoly_rec *rec;
320
321 isl_assert(ctx, var >= 0, return NULL);
322 isl_assert(ctx, size >= 0, return NULL);
323 rec = isl_calloc(ctx, struct isl_upoly_rec,
324 sizeof(struct isl_upoly_rec) +
325 (size - 1) * sizeof(struct isl_upoly *));
326 if (!rec)
327 return NULL;
328
329 rec->up.ref = 1;
330 rec->up.ctx = ctx;
331 isl_ctx_ref(ctx);
332 rec->up.var = var;
333
334 rec->n = 0;
335 rec->size = size;
336
337 return rec;
338 }
339
340 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
342 {
343 qp = isl_qpolynomial_cow(qp);
344 if (!qp || !dim)
345 goto error;
346
347 isl_dim_free(qp->dim);
348 qp->dim = dim;
349
350 return qp;
351 error:
352 isl_qpolynomial_free(qp);
353 isl_dim_free(dim);
354 return NULL;
355 }
356
357 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
358 {
359 return qp ? qp->dim->ctx : NULL;
360 }
361
362 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? isl_dim_copy(qp->dim) : NULL;
365 }
366
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
368 enum isl_dim_type type)
369 {
370 return qp ? isl_dim_size(qp->dim, type) : 0;
371 }
372
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
374 {
375 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
376 }
377
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? isl_upoly_is_one(qp->upoly) : -1;
381 }
382
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
384 {
385 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
386 }
387
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
389 {
390 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
391 }
392
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
394 {
395 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
396 }
397
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
399 {
400 return qp ? isl_upoly_sgn(qp->upoly) : 0;
401 }
402
403 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
404 {
405 isl_int_clear(cst->n);
406 isl_int_clear(cst->d);
407 }
408
409 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
410 {
411 int i;
412
413 for (i = 0; i < rec->n; ++i)
414 isl_upoly_free(rec->p[i]);
415 }
416
417 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
418 {
419 if (!up)
420 return NULL;
421
422 up->ref++;
423 return up;
424 }
425
426 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
427 {
428 struct isl_upoly_cst *cst;
429 struct isl_upoly_cst *dup;
430
431 cst = isl_upoly_as_cst(up);
432 if (!cst)
433 return NULL;
434
435 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
436 if (!dup)
437 return NULL;
438 isl_int_set(dup->n, cst->n);
439 isl_int_set(dup->d, cst->d);
440
441 return &dup->up;
442 }
443
444 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
445 {
446 int i;
447 struct isl_upoly_rec *rec;
448 struct isl_upoly_rec *dup;
449
450 rec = isl_upoly_as_rec(up);
451 if (!rec)
452 return NULL;
453
454 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
455 if (!dup)
456 return NULL;
457
458 for (i = 0; i < rec->n; ++i) {
459 dup->p[i] = isl_upoly_copy(rec->p[i]);
460 if (!dup->p[i])
461 goto error;
462 dup->n++;
463 }
464
465 return &dup->up;
466 error:
467 isl_upoly_free(&dup->up);
468 return NULL;
469 }
470
471 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
472 {
473 struct isl_upoly *dup;
474
475 if (!up)
476 return NULL;
477
478 if (isl_upoly_is_cst(up))
479 return isl_upoly_dup_cst(up);
480 else
481 return isl_upoly_dup_rec(up);
482 }
483
484 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
485 {
486 if (!up)
487 return NULL;
488
489 if (up->ref == 1)
490 return up;
491 up->ref--;
492 return isl_upoly_dup(up);
493 }
494
495 void isl_upoly_free(__isl_take struct isl_upoly *up)
496 {
497 if (!up)
498 return;
499
500 if (--up->ref > 0)
501 return;
502
503 if (up->var < 0)
504 upoly_free_cst((struct isl_upoly_cst *)up);
505 else
506 upoly_free_rec((struct isl_upoly_rec *)up);
507
508 isl_ctx_deref(up->ctx);
509 free(up);
510 }
511
512 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
513 {
514 isl_int gcd;
515
516 isl_int_init(gcd);
517 isl_int_gcd(gcd, cst->n, cst->d);
518 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
519 isl_int_divexact(cst->n, cst->n, gcd);
520 isl_int_divexact(cst->d, cst->d, gcd);
521 }
522 isl_int_clear(gcd);
523 }
524
525 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
526 __isl_take struct isl_upoly *up2)
527 {
528 struct isl_upoly_cst *cst1;
529 struct isl_upoly_cst *cst2;
530
531 up1 = isl_upoly_cow(up1);
532 if (!up1 || !up2)
533 goto error;
534
535 cst1 = isl_upoly_as_cst(up1);
536 cst2 = isl_upoly_as_cst(up2);
537
538 if (isl_int_eq(cst1->d, cst2->d))
539 isl_int_add(cst1->n, cst1->n, cst2->n);
540 else {
541 isl_int_mul(cst1->n, cst1->n, cst2->d);
542 isl_int_addmul(cst1->n, cst2->n, cst1->d);
543 isl_int_mul(cst1->d, cst1->d, cst2->d);
544 }
545
546 isl_upoly_cst_reduce(cst1);
547
548 isl_upoly_free(up2);
549 return up1;
550 error:
551 isl_upoly_free(up1);
552 isl_upoly_free(up2);
553 return NULL;
554 }
555
556 static __isl_give struct isl_upoly *replace_by_zero(
557 __isl_take struct isl_upoly *up)
558 {
559 struct isl_ctx *ctx;
560
561 if (!up)
562 return NULL;
563 ctx = up->ctx;
564 isl_upoly_free(up);
565 return isl_upoly_zero(ctx);
566 }
567
568 static __isl_give struct isl_upoly *replace_by_constant_term(
569 __isl_take struct isl_upoly *up)
570 {
571 struct isl_upoly_rec *rec;
572 struct isl_upoly *cst;
573
574 if (!up)
575 return NULL;
576
577 rec = isl_upoly_as_rec(up);
578 if (!rec)
579 goto error;
580 cst = isl_upoly_copy(rec->p[0]);
581 isl_upoly_free(up);
582 return cst;
583 error:
584 isl_upoly_free(up);
585 return NULL;
586 }
587
588 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
589 __isl_take struct isl_upoly *up2)
590 {
591 int i;
592 struct isl_upoly_rec *rec1, *rec2;
593
594 if (!up1 || !up2)
595 goto error;
596
597 if (isl_upoly_is_nan(up1)) {
598 isl_upoly_free(up2);
599 return up1;
600 }
601
602 if (isl_upoly_is_nan(up2)) {
603 isl_upoly_free(up1);
604 return up2;
605 }
606
607 if (isl_upoly_is_zero(up1)) {
608 isl_upoly_free(up1);
609 return up2;
610 }
611
612 if (isl_upoly_is_zero(up2)) {
613 isl_upoly_free(up2);
614 return up1;
615 }
616
617 if (up1->var < up2->var)
618 return isl_upoly_sum(up2, up1);
619
620 if (up2->var < up1->var) {
621 struct isl_upoly_rec *rec;
622 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
623 isl_upoly_free(up1);
624 return up2;
625 }
626 up1 = isl_upoly_cow(up1);
627 rec = isl_upoly_as_rec(up1);
628 if (!rec)
629 goto error;
630 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
631 if (rec->n == 1)
632 up1 = replace_by_constant_term(up1);
633 return up1;
634 }
635
636 if (isl_upoly_is_cst(up1))
637 return isl_upoly_sum_cst(up1, up2);
638
639 rec1 = isl_upoly_as_rec(up1);
640 rec2 = isl_upoly_as_rec(up2);
641 if (!rec1 || !rec2)
642 goto error;
643
644 if (rec1->n < rec2->n)
645 return isl_upoly_sum(up2, up1);
646
647 up1 = isl_upoly_cow(up1);
648 rec1 = isl_upoly_as_rec(up1);
649 if (!rec1)
650 goto error;
651
652 for (i = rec2->n - 1; i >= 0; --i) {
653 rec1->p[i] = isl_upoly_sum(rec1->p[i],
654 isl_upoly_copy(rec2->p[i]));
655 if (!rec1->p[i])
656 goto error;
657 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
658 isl_upoly_free(rec1->p[i]);
659 rec1->n--;
660 }
661 }
662
663 if (rec1->n == 0)
664 up1 = replace_by_zero(up1);
665 else if (rec1->n == 1)
666 up1 = replace_by_constant_term(up1);
667
668 isl_upoly_free(up2);
669
670 return up1;
671 error:
672 isl_upoly_free(up1);
673 isl_upoly_free(up2);
674 return NULL;
675 }
676
677 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
678 {
679 struct isl_upoly_cst *cst;
680
681 if (isl_upoly_is_zero(up))
682 return up;
683
684 up = isl_upoly_cow(up);
685 if (!up)
686 return NULL;
687
688 cst = isl_upoly_as_cst(up);
689
690 isl_int_neg(cst->n, cst->n);
691
692 return up;
693 }
694
695 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
696 {
697 int i;
698 struct isl_upoly_rec *rec;
699
700 if (!up)
701 return NULL;
702
703 if (isl_upoly_is_cst(up))
704 return isl_upoly_neg_cst(up);
705
706 up = isl_upoly_cow(up);
707 rec = isl_upoly_as_rec(up);
708 if (!rec)
709 goto error;
710
711 for (i = 0; i < rec->n; ++i) {
712 rec->p[i] = isl_upoly_neg(rec->p[i]);
713 if (!rec->p[i])
714 goto error;
715 }
716
717 return up;
718 error:
719 isl_upoly_free(up);
720 return NULL;
721 }
722
723 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
724 __isl_take struct isl_upoly *up2)
725 {
726 struct isl_upoly_cst *cst1;
727 struct isl_upoly_cst *cst2;
728
729 up1 = isl_upoly_cow(up1);
730 if (!up1 || !up2)
731 goto error;
732
733 cst1 = isl_upoly_as_cst(up1);
734 cst2 = isl_upoly_as_cst(up2);
735
736 isl_int_mul(cst1->n, cst1->n, cst2->n);
737 isl_int_mul(cst1->d, cst1->d, cst2->d);
738
739 isl_upoly_cst_reduce(cst1);
740
741 isl_upoly_free(up2);
742 return up1;
743 error:
744 isl_upoly_free(up1);
745 isl_upoly_free(up2);
746 return NULL;
747 }
748
749 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
750 __isl_take struct isl_upoly *up2)
751 {
752 struct isl_upoly_rec *rec1;
753 struct isl_upoly_rec *rec2;
754 struct isl_upoly_rec *res;
755 int i, j;
756 int size;
757
758 rec1 = isl_upoly_as_rec(up1);
759 rec2 = isl_upoly_as_rec(up2);
760 if (!rec1 || !rec2)
761 goto error;
762 size = rec1->n + rec2->n - 1;
763 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
764 if (!res)
765 goto error;
766
767 for (i = 0; i < rec1->n; ++i) {
768 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
769 isl_upoly_copy(rec1->p[i]));
770 if (!res->p[i])
771 goto error;
772 res->n++;
773 }
774 for (; i < size; ++i) {
775 res->p[i] = isl_upoly_zero(up1->ctx);
776 if (!res->p[i])
777 goto error;
778 res->n++;
779 }
780 for (i = 0; i < rec1->n; ++i) {
781 for (j = 1; j < rec2->n; ++j) {
782 struct isl_upoly *up;
783 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
784 isl_upoly_copy(rec1->p[i]));
785 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
786 if (!res->p[i + j])
787 goto error;
788 }
789 }
790
791 isl_upoly_free(up1);
792 isl_upoly_free(up2);
793
794 return &res->up;
795 error:
796 isl_upoly_free(up1);
797 isl_upoly_free(up2);
798 isl_upoly_free(&res->up);
799 return NULL;
800 }
801
802 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
803 __isl_take struct isl_upoly *up2)
804 {
805 if (!up1 || !up2)
806 goto error;
807
808 if (isl_upoly_is_nan(up1)) {
809 isl_upoly_free(up2);
810 return up1;
811 }
812
813 if (isl_upoly_is_nan(up2)) {
814 isl_upoly_free(up1);
815 return up2;
816 }
817
818 if (isl_upoly_is_zero(up1)) {
819 isl_upoly_free(up2);
820 return up1;
821 }
822
823 if (isl_upoly_is_zero(up2)) {
824 isl_upoly_free(up1);
825 return up2;
826 }
827
828 if (isl_upoly_is_one(up1)) {
829 isl_upoly_free(up1);
830 return up2;
831 }
832
833 if (isl_upoly_is_one(up2)) {
834 isl_upoly_free(up2);
835 return up1;
836 }
837
838 if (up1->var < up2->var)
839 return isl_upoly_mul(up2, up1);
840
841 if (up2->var < up1->var) {
842 int i;
843 struct isl_upoly_rec *rec;
844 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
845 isl_ctx *ctx = up1->ctx;
846 isl_upoly_free(up1);
847 isl_upoly_free(up2);
848 return isl_upoly_nan(ctx);
849 }
850 up1 = isl_upoly_cow(up1);
851 rec = isl_upoly_as_rec(up1);
852 if (!rec)
853 goto error;
854
855 for (i = 0; i < rec->n; ++i) {
856 rec->p[i] = isl_upoly_mul(rec->p[i],
857 isl_upoly_copy(up2));
858 if (!rec->p[i])
859 goto error;
860 }
861 isl_upoly_free(up2);
862 return up1;
863 }
864
865 if (isl_upoly_is_cst(up1))
866 return isl_upoly_mul_cst(up1, up2);
867
868 return isl_upoly_mul_rec(up1, up2);
869 error:
870 isl_upoly_free(up1);
871 isl_upoly_free(up2);
872 return NULL;
873 }
874
875 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
876 unsigned n_div, __isl_take struct isl_upoly *up)
877 {
878 struct isl_qpolynomial *qp = NULL;
879 unsigned total;
880
881 if (!dim || !up)
882 goto error;
883
884 total = isl_dim_total(dim);
885
886 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
887 if (!qp)
888 goto error;
889
890 qp->ref = 1;
891 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
892 if (!qp->div)
893 goto error;
894
895 qp->dim = dim;
896 qp->upoly = up;
897
898 return qp;
899 error:
900 isl_dim_free(dim);
901 isl_upoly_free(up);
902 isl_qpolynomial_free(qp);
903 return NULL;
904 }
905
906 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
907 {
908 if (!qp)
909 return NULL;
910
911 qp->ref++;
912 return qp;
913 }
914
915 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
916 {
917 struct isl_qpolynomial *dup;
918
919 if (!qp)
920 return NULL;
921
922 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
923 isl_upoly_copy(qp->upoly));
924 if (!dup)
925 return NULL;
926 isl_mat_free(dup->div);
927 dup->div = isl_mat_copy(qp->div);
928 if (!dup->div)
929 goto error;
930
931 return dup;
932 error:
933 isl_qpolynomial_free(dup);
934 return NULL;
935 }
936
937 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
938 {
939 if (!qp)
940 return NULL;
941
942 if (qp->ref == 1)
943 return qp;
944 qp->ref--;
945 return isl_qpolynomial_dup(qp);
946 }
947
948 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
949 {
950 if (!qp)
951 return;
952
953 if (--qp->ref > 0)
954 return;
955
956 isl_dim_free(qp->dim);
957 isl_mat_free(qp->div);
958 isl_upoly_free(qp->upoly);
959
960 free(qp);
961 }
962
963 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
964 {
965 int i;
966 struct isl_upoly *up;
967 struct isl_upoly_rec *rec;
968 struct isl_upoly_cst *cst;
969
970 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
971 if (!rec)
972 return NULL;
973 for (i = 0; i < 1 + power; ++i) {
974 rec->p[i] = isl_upoly_zero(ctx);
975 if (!rec->p[i])
976 goto error;
977 rec->n++;
978 }
979 cst = isl_upoly_as_cst(rec->p[power]);
980 isl_int_set_si(cst->n, 1);
981
982 return &rec->up;
983 error:
984 isl_upoly_free(&rec->up);
985 return NULL;
986 }
987
988 /* r array maps original positions to new positions.
989 */
990 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
991 int *r)
992 {
993 int i;
994 struct isl_upoly_rec *rec;
995 struct isl_upoly *base;
996 struct isl_upoly *res;
997
998 if (isl_upoly_is_cst(up))
999 return up;
1000
1001 rec = isl_upoly_as_rec(up);
1002 if (!rec)
1003 goto error;
1004
1005 isl_assert(up->ctx, rec->n >= 1, goto error);
1006
1007 base = isl_upoly_pow(up->ctx, r[up->var], 1);
1008 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1009
1010 for (i = rec->n - 2; i >= 0; --i) {
1011 res = isl_upoly_mul(res, isl_upoly_copy(base));
1012 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1013 }
1014
1015 isl_upoly_free(base);
1016 isl_upoly_free(up);
1017
1018 return res;
1019 error:
1020 isl_upoly_free(up);
1021 return NULL;
1022 }
1023
1024 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1025 {
1026 int n_row, n_col;
1027 int equal;
1028
1029 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1030 div1->n_col >= div2->n_col, return -1);
1031
1032 if (div1->n_row == div2->n_row)
1033 return isl_mat_is_equal(div1, div2);
1034
1035 n_row = div1->n_row;
1036 n_col = div1->n_col;
1037 div1->n_row = div2->n_row;
1038 div1->n_col = div2->n_col;
1039
1040 equal = isl_mat_is_equal(div1, div2);
1041
1042 div1->n_row = n_row;
1043 div1->n_col = n_col;
1044
1045 return equal;
1046 }
1047
1048 static void expand_row(__isl_keep isl_mat *dst, int d,
1049 __isl_keep isl_mat *src, int s, int *exp)
1050 {
1051 int i;
1052 unsigned c = src->n_col - src->n_row;
1053
1054 isl_seq_cpy(dst->row[d], src->row[s], c);
1055 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1056
1057 for (i = 0; i < s; ++i)
1058 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1059 }
1060
1061 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1062 {
1063 int li, lj;
1064
1065 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1066 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1067
1068 if (li != lj)
1069 return li - lj;
1070
1071 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1072 }
1073
1074 struct isl_div_sort_info {
1075 isl_mat *div;
1076 int row;
1077 };
1078
1079 static int div_sort_cmp(const void *p1, const void *p2)
1080 {
1081 const struct isl_div_sort_info *i1, *i2;
1082 i1 = (const struct isl_div_sort_info *) p1;
1083 i2 = (const struct isl_div_sort_info *) p2;
1084
1085 return cmp_row(i1->div, i1->row, i2->row);
1086 }
1087
1088 /* Sort divs and remove duplicates.
1089 */
1090 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1091 {
1092 int i;
1093 int skip;
1094 int len;
1095 struct isl_div_sort_info *array = NULL;
1096 int *pos = NULL, *at = NULL;
1097 int *reordering = NULL;
1098 unsigned div_pos;
1099
1100 if (!qp)
1101 return NULL;
1102 if (qp->div->n_row <= 1)
1103 return qp;
1104
1105 div_pos = isl_dim_total(qp->dim);
1106
1107 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1108 qp->div->n_row);
1109 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1110 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1111 len = qp->div->n_col - 2;
1112 reordering = isl_alloc_array(qp->div->ctx, int, len);
1113 if (!array || !pos || !at || !reordering)
1114 goto error;
1115
1116 for (i = 0; i < qp->div->n_row; ++i) {
1117 array[i].div = qp->div;
1118 array[i].row = i;
1119 pos[i] = i;
1120 at[i] = i;
1121 }
1122
1123 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1124 div_sort_cmp);
1125
1126 for (i = 0; i < div_pos; ++i)
1127 reordering[i] = i;
1128
1129 for (i = 0; i < qp->div->n_row; ++i) {
1130 if (pos[array[i].row] == i)
1131 continue;
1132 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1133 pos[at[i]] = pos[array[i].row];
1134 at[pos[array[i].row]] = at[i];
1135 at[i] = array[i].row;
1136 pos[array[i].row] = i;
1137 }
1138
1139 skip = 0;
1140 for (i = 0; i < len - div_pos; ++i) {
1141 if (i > 0 &&
1142 isl_seq_eq(qp->div->row[i - skip - 1],
1143 qp->div->row[i - skip], qp->div->n_col)) {
1144 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1145 qp->div = isl_mat_drop_cols(qp->div,
1146 2 + div_pos + i - skip, 1);
1147 skip++;
1148 }
1149 reordering[div_pos + array[i].row] = div_pos + i - skip;
1150 }
1151
1152 qp->upoly = reorder(qp->upoly, reordering);
1153
1154 if (!qp->upoly || !qp->div)
1155 goto error;
1156
1157 free(at);
1158 free(pos);
1159 free(array);
1160 free(reordering);
1161
1162 return qp;
1163 error:
1164 free(at);
1165 free(pos);
1166 free(array);
1167 free(reordering);
1168 isl_qpolynomial_free(qp);
1169 return NULL;
1170 }
1171
1172 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1173 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1174 {
1175 int i, j, k;
1176 isl_mat *div = NULL;
1177 unsigned d = div1->n_col - div1->n_row;
1178
1179 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1180 d + div1->n_row + div2->n_row);
1181 if (!div)
1182 return NULL;
1183
1184 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1185 int cmp;
1186
1187 expand_row(div, k, div1, i, exp1);
1188 expand_row(div, k + 1, div2, j, exp2);
1189
1190 cmp = cmp_row(div, k, k + 1);
1191 if (cmp == 0) {
1192 exp1[i++] = k;
1193 exp2[j++] = k;
1194 } else if (cmp < 0) {
1195 exp1[i++] = k;
1196 } else {
1197 exp2[j++] = k;
1198 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1199 }
1200 }
1201 for (; i < div1->n_row; ++i, ++k) {
1202 expand_row(div, k, div1, i, exp1);
1203 exp1[i] = k;
1204 }
1205 for (; j < div2->n_row; ++j, ++k) {
1206 expand_row(div, k, div2, j, exp2);
1207 exp2[j] = k;
1208 }
1209
1210 div->n_row = k;
1211 div->n_col = d + k;
1212
1213 return div;
1214 }
1215
1216 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1217 int *exp, int first)
1218 {
1219 int i;
1220 struct isl_upoly_rec *rec;
1221
1222 if (isl_upoly_is_cst(up))
1223 return up;
1224
1225 if (up->var < first)
1226 return up;
1227
1228 if (exp[up->var - first] == up->var - first)
1229 return up;
1230
1231 up = isl_upoly_cow(up);
1232 if (!up)
1233 goto error;
1234
1235 up->var = exp[up->var - first] + first;
1236
1237 rec = isl_upoly_as_rec(up);
1238 if (!rec)
1239 goto error;
1240
1241 for (i = 0; i < rec->n; ++i) {
1242 rec->p[i] = expand(rec->p[i], exp, first);
1243 if (!rec->p[i])
1244 goto error;
1245 }
1246
1247 return up;
1248 error:
1249 isl_upoly_free(up);
1250 return NULL;
1251 }
1252
1253 static __isl_give isl_qpolynomial *with_merged_divs(
1254 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1255 __isl_take isl_qpolynomial *qp2),
1256 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1257 {
1258 int *exp1 = NULL;
1259 int *exp2 = NULL;
1260 isl_mat *div = NULL;
1261
1262 qp1 = isl_qpolynomial_cow(qp1);
1263 qp2 = isl_qpolynomial_cow(qp2);
1264
1265 if (!qp1 || !qp2)
1266 goto error;
1267
1268 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1269 qp1->div->n_col >= qp2->div->n_col, goto error);
1270
1271 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1272 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1273 if (!exp1 || !exp2)
1274 goto error;
1275
1276 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1277 if (!div)
1278 goto error;
1279
1280 isl_mat_free(qp1->div);
1281 qp1->div = isl_mat_copy(div);
1282 isl_mat_free(qp2->div);
1283 qp2->div = isl_mat_copy(div);
1284
1285 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1286 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1287
1288 if (!qp1->upoly || !qp2->upoly)
1289 goto error;
1290
1291 isl_mat_free(div);
1292 free(exp1);
1293 free(exp2);
1294
1295 return fn(qp1, qp2);
1296 error:
1297 isl_mat_free(div);
1298 free(exp1);
1299 free(exp2);
1300 isl_qpolynomial_free(qp1);
1301 isl_qpolynomial_free(qp2);
1302 return NULL;
1303 }
1304
1305 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1306 __isl_take isl_qpolynomial *qp2)
1307 {
1308 qp1 = isl_qpolynomial_cow(qp1);
1309
1310 if (!qp1 || !qp2)
1311 goto error;
1312
1313 if (qp1->div->n_row < qp2->div->n_row)
1314 return isl_qpolynomial_add(qp2, qp1);
1315
1316 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1317 if (!compatible_divs(qp1->div, qp2->div))
1318 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1319
1320 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1321 if (!qp1->upoly)
1322 goto error;
1323
1324 isl_qpolynomial_free(qp2);
1325
1326 return qp1;
1327 error:
1328 isl_qpolynomial_free(qp1);
1329 isl_qpolynomial_free(qp2);
1330 return NULL;
1331 }
1332
1333 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1334 __isl_keep isl_set *dom,
1335 __isl_take isl_qpolynomial *qp1,
1336 __isl_take isl_qpolynomial *qp2)
1337 {
1338 return isl_qpolynomial_add(qp1, qp2);
1339 }
1340
1341 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1342 __isl_take isl_qpolynomial *qp2)
1343 {
1344 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1345 }
1346
1347 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1348 {
1349 qp = isl_qpolynomial_cow(qp);
1350
1351 if (!qp)
1352 return NULL;
1353
1354 qp->upoly = isl_upoly_neg(qp->upoly);
1355 if (!qp->upoly)
1356 goto error;
1357
1358 return qp;
1359 error:
1360 isl_qpolynomial_free(qp);
1361 return NULL;
1362 }
1363
1364 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1365 __isl_take isl_qpolynomial *qp2)
1366 {
1367 qp1 = isl_qpolynomial_cow(qp1);
1368
1369 if (!qp1 || !qp2)
1370 goto error;
1371
1372 if (qp1->div->n_row < qp2->div->n_row)
1373 return isl_qpolynomial_mul(qp2, qp1);
1374
1375 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1376 if (!compatible_divs(qp1->div, qp2->div))
1377 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1378
1379 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1380 if (!qp1->upoly)
1381 goto error;
1382
1383 isl_qpolynomial_free(qp2);
1384
1385 return qp1;
1386 error:
1387 isl_qpolynomial_free(qp1);
1388 isl_qpolynomial_free(qp2);
1389 return NULL;
1390 }
1391
1392 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1393 {
1394 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1395 }
1396
1397 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1398 {
1399 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1400 }
1401
1402 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1403 {
1404 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1405 }
1406
1407 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1408 {
1409 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1410 }
1411
1412 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1413 {
1414 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1415 }
1416
1417 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1418 isl_int v)
1419 {
1420 struct isl_qpolynomial *qp;
1421 struct isl_upoly_cst *cst;
1422
1423 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1424 if (!qp)
1425 return NULL;
1426
1427 cst = isl_upoly_as_cst(qp->upoly);
1428 isl_int_set(cst->n, v);
1429
1430 return qp;
1431 }
1432
1433 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1434 isl_int *n, isl_int *d)
1435 {
1436 struct isl_upoly_cst *cst;
1437
1438 if (!qp)
1439 return -1;
1440
1441 if (!isl_upoly_is_cst(qp->upoly))
1442 return 0;
1443
1444 cst = isl_upoly_as_cst(qp->upoly);
1445 if (!cst)
1446 return -1;
1447
1448 if (n)
1449 isl_int_set(*n, cst->n);
1450 if (d)
1451 isl_int_set(*d, cst->d);
1452
1453 return 1;
1454 }
1455
1456 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1457 {
1458 int is_cst;
1459 struct isl_upoly_rec *rec;
1460
1461 if (!up)
1462 return -1;
1463
1464 if (up->var < 0)
1465 return 1;
1466
1467 rec = isl_upoly_as_rec(up);
1468 if (!rec)
1469 return -1;
1470
1471 if (rec->n > 2)
1472 return 0;
1473
1474 isl_assert(up->ctx, rec->n > 1, return -1);
1475
1476 is_cst = isl_upoly_is_cst(rec->p[1]);
1477 if (is_cst < 0)
1478 return -1;
1479 if (!is_cst)
1480 return 0;
1481
1482 return isl_upoly_is_affine(rec->p[0]);
1483 }
1484
1485 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1486 {
1487 if (!qp)
1488 return -1;
1489
1490 if (qp->div->n_row > 0)
1491 return 0;
1492
1493 return isl_upoly_is_affine(qp->upoly);
1494 }
1495
1496 static void update_coeff(__isl_keep isl_vec *aff,
1497 __isl_keep struct isl_upoly_cst *cst, int pos)
1498 {
1499 isl_int gcd;
1500 isl_int f;
1501
1502 if (isl_int_is_zero(cst->n))
1503 return;
1504
1505 isl_int_init(gcd);
1506 isl_int_init(f);
1507 isl_int_gcd(gcd, cst->d, aff->el[0]);
1508 isl_int_divexact(f, cst->d, gcd);
1509 isl_int_divexact(gcd, aff->el[0], gcd);
1510 isl_seq_scale(aff->el, aff->el, f, aff->size);
1511 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1512 isl_int_clear(gcd);
1513 isl_int_clear(f);
1514 }
1515
1516 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1517 __isl_keep isl_vec *aff)
1518 {
1519 struct isl_upoly_cst *cst;
1520 struct isl_upoly_rec *rec;
1521
1522 if (!up || !aff)
1523 return -1;
1524
1525 if (up->var < 0) {
1526 struct isl_upoly_cst *cst;
1527
1528 cst = isl_upoly_as_cst(up);
1529 if (!cst)
1530 return -1;
1531 update_coeff(aff, cst, 0);
1532 return 0;
1533 }
1534
1535 rec = isl_upoly_as_rec(up);
1536 if (!rec)
1537 return -1;
1538 isl_assert(up->ctx, rec->n == 2, return -1);
1539
1540 cst = isl_upoly_as_cst(rec->p[1]);
1541 if (!cst)
1542 return -1;
1543 update_coeff(aff, cst, 1 + up->var);
1544
1545 return isl_upoly_update_affine(rec->p[0], aff);
1546 }
1547
1548 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1549 __isl_keep isl_qpolynomial *qp)
1550 {
1551 isl_vec *aff;
1552 unsigned d;
1553
1554 if (!qp)
1555 return NULL;
1556
1557 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1558 d = isl_dim_total(qp->dim);
1559 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1560 if (!aff)
1561 return NULL;
1562
1563 isl_seq_clr(aff->el + 1, 1 + d);
1564 isl_int_set_si(aff->el[0], 1);
1565
1566 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1567 goto error;
1568
1569 return aff;
1570 error:
1571 isl_vec_free(aff);
1572 return NULL;
1573 }
1574
1575 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1576 __isl_keep isl_qpolynomial *qp2)
1577 {
1578 if (!qp1 || !qp2)
1579 return -1;
1580
1581 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1582 }
1583
1584 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1585 {
1586 int i;
1587 struct isl_upoly_rec *rec;
1588
1589 if (isl_upoly_is_cst(up)) {
1590 struct isl_upoly_cst *cst;
1591 cst = isl_upoly_as_cst(up);
1592 if (!cst)
1593 return;
1594 isl_int_lcm(*d, *d, cst->d);
1595 return;
1596 }
1597
1598 rec = isl_upoly_as_rec(up);
1599 if (!rec)
1600 return;
1601
1602 for (i = 0; i < rec->n; ++i)
1603 upoly_update_den(rec->p[i], d);
1604 }
1605
1606 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1607 {
1608 isl_int_set_si(*d, 1);
1609 if (!qp)
1610 return;
1611 upoly_update_den(qp->upoly, d);
1612 }
1613
1614 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1615 int pos, int power)
1616 {
1617 struct isl_ctx *ctx;
1618
1619 if (!dim)
1620 return NULL;
1621
1622 ctx = dim->ctx;
1623
1624 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1625 }
1626
1627 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1628 enum isl_dim_type type, unsigned pos)
1629 {
1630 if (!dim)
1631 return NULL;
1632
1633 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1634 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1635
1636 if (type == isl_dim_set)
1637 pos += isl_dim_size(dim, isl_dim_param);
1638
1639 return isl_qpolynomial_pow(dim, pos, 1);
1640 error:
1641 isl_dim_free(dim);
1642 return NULL;
1643 }
1644
1645 /* Remove common factor of non-constant terms and denominator.
1646 */
1647 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1648 {
1649 isl_ctx *ctx = qp->div->ctx;
1650 unsigned total = qp->div->n_col - 2;
1651
1652 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1653 isl_int_gcd(ctx->normalize_gcd,
1654 ctx->normalize_gcd, qp->div->row[div][0]);
1655 if (isl_int_is_one(ctx->normalize_gcd))
1656 return;
1657
1658 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1659 ctx->normalize_gcd, total);
1660 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1661 ctx->normalize_gcd);
1662 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1663 ctx->normalize_gcd);
1664 }
1665
1666 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1667 int power)
1668 {
1669 struct isl_qpolynomial *qp = NULL;
1670 struct isl_upoly_rec *rec;
1671 struct isl_upoly_cst *cst;
1672 int i, d;
1673 int pos;
1674
1675 if (!div)
1676 return NULL;
1677
1678 d = div->line - div->bmap->div;
1679
1680 pos = isl_dim_total(div->bmap->dim) + d;
1681 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1682 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1683 div->bmap->n_div, &rec->up);
1684 if (!qp)
1685 goto error;
1686
1687 for (i = 0; i < div->bmap->n_div; ++i) {
1688 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1689 normalize_div(qp, i);
1690 }
1691
1692 for (i = 0; i < 1 + power; ++i) {
1693 rec->p[i] = isl_upoly_zero(div->ctx);
1694 if (!rec->p[i])
1695 goto error;
1696 rec->n++;
1697 }
1698 cst = isl_upoly_as_cst(rec->p[power]);
1699 isl_int_set_si(cst->n, 1);
1700
1701 isl_div_free(div);
1702
1703 return qp;
1704 error:
1705 isl_qpolynomial_free(qp);
1706 isl_div_free(div);
1707 return NULL;
1708 }
1709
1710 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1711 {
1712 return isl_qpolynomial_div_pow(div, 1);
1713 }
1714
1715 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1716 const isl_int n, const isl_int d)
1717 {
1718 struct isl_qpolynomial *qp;
1719 struct isl_upoly_cst *cst;
1720
1721 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1722 if (!qp)
1723 return NULL;
1724
1725 cst = isl_upoly_as_cst(qp->upoly);
1726 isl_int_set(cst->n, n);
1727 isl_int_set(cst->d, d);
1728
1729 return qp;
1730 }
1731
1732 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1733 {
1734 struct isl_upoly_rec *rec;
1735 int i;
1736
1737 if (!up)
1738 return -1;
1739
1740 if (isl_upoly_is_cst(up))
1741 return 0;
1742
1743 if (up->var < d)
1744 active[up->var] = 1;
1745
1746 rec = isl_upoly_as_rec(up);
1747 for (i = 0; i < rec->n; ++i)
1748 if (up_set_active(rec->p[i], active, d) < 0)
1749 return -1;
1750
1751 return 0;
1752 }
1753
1754 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1755 {
1756 int i, j;
1757 int d = isl_dim_total(qp->dim);
1758
1759 if (!qp || !active)
1760 return -1;
1761
1762 for (i = 0; i < d; ++i)
1763 for (j = 0; j < qp->div->n_row; ++j) {
1764 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1765 continue;
1766 active[i] = 1;
1767 break;
1768 }
1769
1770 return up_set_active(qp->upoly, active, d);
1771 }
1772
1773 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1774 enum isl_dim_type type, unsigned first, unsigned n)
1775 {
1776 int i;
1777 int *active = NULL;
1778 int involves = 0;
1779
1780 if (!qp)
1781 return -1;
1782 if (n == 0)
1783 return 0;
1784
1785 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1786 return -1);
1787 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1788 type == isl_dim_set, return -1);
1789
1790 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1791 if (set_active(qp, active) < 0)
1792 goto error;
1793
1794 if (type == isl_dim_set)
1795 first += isl_dim_size(qp->dim, isl_dim_param);
1796 for (i = 0; i < n; ++i)
1797 if (active[first + i]) {
1798 involves = 1;
1799 break;
1800 }
1801
1802 free(active);
1803
1804 return involves;
1805 error:
1806 free(active);
1807 return -1;
1808 }
1809
1810 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1811 unsigned first, unsigned n)
1812 {
1813 int i;
1814 struct isl_upoly_rec *rec;
1815
1816 if (!up)
1817 return NULL;
1818 if (n == 0 || up->var < 0 || up->var < first)
1819 return up;
1820 if (up->var < first + n) {
1821 up = replace_by_constant_term(up);
1822 return isl_upoly_drop(up, first, n);
1823 }
1824 up = isl_upoly_cow(up);
1825 if (!up)
1826 return NULL;
1827 up->var -= n;
1828 rec = isl_upoly_as_rec(up);
1829 if (!rec)
1830 goto error;
1831
1832 for (i = 0; i < rec->n; ++i) {
1833 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1834 if (!rec->p[i])
1835 goto error;
1836 }
1837
1838 return up;
1839 error:
1840 isl_upoly_free(up);
1841 return NULL;
1842 }
1843
1844 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1845 __isl_take isl_qpolynomial *qp,
1846 enum isl_dim_type type, unsigned pos, const char *s)
1847 {
1848 qp = isl_qpolynomial_cow(qp);
1849 if (!qp)
1850 return NULL;
1851 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1852 if (!qp->dim)
1853 goto error;
1854 return qp;
1855 error:
1856 isl_qpolynomial_free(qp);
1857 return NULL;
1858 }
1859
1860 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1861 __isl_take isl_qpolynomial *qp,
1862 enum isl_dim_type type, unsigned first, unsigned n)
1863 {
1864 if (!qp)
1865 return NULL;
1866 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1867 return qp;
1868
1869 qp = isl_qpolynomial_cow(qp);
1870 if (!qp)
1871 return NULL;
1872
1873 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1874 goto error);
1875 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1876 type == isl_dim_set, goto error);
1877
1878 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1879 if (!qp->dim)
1880 goto error;
1881
1882 if (type == isl_dim_set)
1883 first += isl_dim_size(qp->dim, isl_dim_param);
1884
1885 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1886 if (!qp->div)
1887 goto error;
1888
1889 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1890 if (!qp->upoly)
1891 goto error;
1892
1893 return qp;
1894 error:
1895 isl_qpolynomial_free(qp);
1896 return NULL;
1897 }
1898
1899 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1900 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1901 {
1902 int i;
1903 struct isl_upoly_rec *rec;
1904 struct isl_upoly *base, *res;
1905
1906 if (!up)
1907 return NULL;
1908
1909 if (isl_upoly_is_cst(up))
1910 return up;
1911
1912 if (up->var < first)
1913 return up;
1914
1915 rec = isl_upoly_as_rec(up);
1916 if (!rec)
1917 goto error;
1918
1919 isl_assert(up->ctx, rec->n >= 1, goto error);
1920
1921 if (up->var >= first + n)
1922 base = isl_upoly_pow(up->ctx, up->var, 1);
1923 else
1924 base = isl_upoly_copy(subs[up->var - first]);
1925
1926 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1927 for (i = rec->n - 2; i >= 0; --i) {
1928 struct isl_upoly *t;
1929 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1930 res = isl_upoly_mul(res, isl_upoly_copy(base));
1931 res = isl_upoly_sum(res, t);
1932 }
1933
1934 isl_upoly_free(base);
1935 isl_upoly_free(up);
1936
1937 return res;
1938 error:
1939 isl_upoly_free(up);
1940 return NULL;
1941 }
1942
1943 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1944 isl_int denom, unsigned len)
1945 {
1946 int i;
1947 struct isl_upoly *up;
1948
1949 isl_assert(ctx, len >= 1, return NULL);
1950
1951 up = isl_upoly_rat_cst(ctx, f[0], denom);
1952 for (i = 0; i < len - 1; ++i) {
1953 struct isl_upoly *t;
1954 struct isl_upoly *c;
1955
1956 if (isl_int_is_zero(f[1 + i]))
1957 continue;
1958
1959 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1960 t = isl_upoly_pow(ctx, i, 1);
1961 t = isl_upoly_mul(c, t);
1962 up = isl_upoly_sum(up, t);
1963 }
1964
1965 return up;
1966 }
1967
1968 /* Replace the integer division identified by "div" by the polynomial "s".
1969 * The integer division is assumed not to appear in the definition
1970 * of any other integer divisions.
1971 */
1972 static __isl_give isl_qpolynomial *substitute_div(
1973 __isl_take isl_qpolynomial *qp,
1974 int div, __isl_take struct isl_upoly *s)
1975 {
1976 int i;
1977 int total;
1978 int *reordering;
1979
1980 if (!qp || !s)
1981 goto error;
1982
1983 qp = isl_qpolynomial_cow(qp);
1984 if (!qp)
1985 goto error;
1986
1987 total = isl_dim_total(qp->dim);
1988 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1989 if (!qp->upoly)
1990 goto error;
1991
1992 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1993 if (!reordering)
1994 goto error;
1995 for (i = 0; i < total + div; ++i)
1996 reordering[i] = i;
1997 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1998 reordering[i] = i - 1;
1999 qp->div = isl_mat_drop_rows(qp->div, div, 1);
2000 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2001 qp->upoly = reorder(qp->upoly, reordering);
2002 free(reordering);
2003
2004 if (!qp->upoly || !qp->div)
2005 goto error;
2006
2007 isl_upoly_free(s);
2008 return qp;
2009 error:
2010 isl_qpolynomial_free(qp);
2011 isl_upoly_free(s);
2012 return NULL;
2013 }
2014
2015 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2016 * divisions because d is equal to 1 by their definition, i.e., e.
2017 */
2018 static __isl_give isl_qpolynomial *substitute_non_divs(
2019 __isl_take isl_qpolynomial *qp)
2020 {
2021 int i, j;
2022 int total;
2023 struct isl_upoly *s;
2024
2025 if (!qp)
2026 return NULL;
2027
2028 total = isl_dim_total(qp->dim);
2029 for (i = 0; qp && i < qp->div->n_row; ++i) {
2030 if (!isl_int_is_one(qp->div->row[i][0]))
2031 continue;
2032 for (j = i + 1; j < qp->div->n_row; ++j) {
2033 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2034 continue;
2035 isl_seq_combine(qp->div->row[j] + 1,
2036 qp->div->ctx->one, qp->div->row[j] + 1,
2037 qp->div->row[j][2 + total + i],
2038 qp->div->row[i] + 1, 1 + total + i);
2039 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2040 normalize_div(qp, j);
2041 }
2042 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2043 qp->div->row[i][0], qp->div->n_col - 1);
2044 qp = substitute_div(qp, i, s);
2045 --i;
2046 }
2047
2048 return qp;
2049 }
2050
2051 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2052 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2053 {
2054 int i, j, k;
2055 isl_int denom;
2056 unsigned total;
2057 unsigned n_div;
2058 struct isl_upoly *up;
2059
2060 if (!eq)
2061 goto error;
2062 if (eq->n_eq == 0) {
2063 isl_basic_set_free(eq);
2064 return qp;
2065 }
2066
2067 qp = isl_qpolynomial_cow(qp);
2068 if (!qp)
2069 goto error;
2070 qp->div = isl_mat_cow(qp->div);
2071 if (!qp->div)
2072 goto error;
2073
2074 total = 1 + isl_dim_total(eq->dim);
2075 n_div = eq->n_div;
2076 isl_int_init(denom);
2077 for (i = 0; i < eq->n_eq; ++i) {
2078 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2079 if (j < 0 || j == 0 || j >= total)
2080 continue;
2081
2082 for (k = 0; k < qp->div->n_row; ++k) {
2083 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2084 continue;
2085 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2086 &qp->div->row[k][0]);
2087 normalize_div(qp, k);
2088 }
2089
2090 if (isl_int_is_pos(eq->eq[i][j]))
2091 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2092 isl_int_abs(denom, eq->eq[i][j]);
2093 isl_int_set_si(eq->eq[i][j], 0);
2094
2095 up = isl_upoly_from_affine(qp->dim->ctx,
2096 eq->eq[i], denom, total);
2097 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2098 isl_upoly_free(up);
2099 }
2100 isl_int_clear(denom);
2101
2102 if (!qp->upoly)
2103 goto error;
2104
2105 isl_basic_set_free(eq);
2106
2107 qp = substitute_non_divs(qp);
2108 qp = sort_divs(qp);
2109
2110 return qp;
2111 error:
2112 isl_basic_set_free(eq);
2113 isl_qpolynomial_free(qp);
2114 return NULL;
2115 }
2116
2117 static __isl_give isl_basic_set *add_div_constraints(
2118 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2119 {
2120 int i;
2121 unsigned total;
2122
2123 if (!bset || !div)
2124 goto error;
2125
2126 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2127 if (!bset)
2128 goto error;
2129 total = isl_basic_set_total_dim(bset);
2130 for (i = 0; i < div->n_row; ++i)
2131 if (isl_basic_set_add_div_constraints_var(bset,
2132 total - div->n_row + i, div->row[i]) < 0)
2133 goto error;
2134
2135 isl_mat_free(div);
2136 return bset;
2137 error:
2138 isl_mat_free(div);
2139 isl_basic_set_free(bset);
2140 return NULL;
2141 }
2142
2143 /* Look for equalities among the variables shared by context and qp
2144 * and the integer divisions of qp, if any.
2145 * The equalities are then used to eliminate variables and/or integer
2146 * divisions from qp.
2147 */
2148 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2149 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2150 {
2151 isl_basic_set *aff;
2152
2153 if (!qp)
2154 goto error;
2155 if (qp->div->n_row > 0) {
2156 isl_basic_set *bset;
2157 context = isl_set_add_dims(context, isl_dim_set,
2158 qp->div->n_row);
2159 bset = isl_basic_set_universe(isl_set_get_dim(context));
2160 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2161 context = isl_set_intersect(context,
2162 isl_set_from_basic_set(bset));
2163 }
2164
2165 aff = isl_set_affine_hull(context);
2166 return isl_qpolynomial_substitute_equalities(qp, aff);
2167 error:
2168 isl_qpolynomial_free(qp);
2169 isl_set_free(context);
2170 return NULL;
2171 }
2172
2173 #undef PW
2174 #define PW isl_pw_qpolynomial
2175 #undef EL
2176 #define EL isl_qpolynomial
2177 #undef IS_ZERO
2178 #define IS_ZERO is_zero
2179 #undef FIELD
2180 #define FIELD qp
2181
2182 #include <isl_pw_templ.c>
2183
2184 #undef UNION
2185 #define UNION isl_union_pw_qpolynomial
2186 #undef PART
2187 #define PART isl_pw_qpolynomial
2188 #undef PARTS
2189 #define PARTS pw_qpolynomial
2190
2191 #include <isl_union_templ.c>
2192
2193 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2194 {
2195 if (!pwqp)
2196 return -1;
2197
2198 if (pwqp->n != -1)
2199 return 0;
2200
2201 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2202 return 0;
2203
2204 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2205 }
2206
2207 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2208 __isl_take isl_pw_qpolynomial *pwqp1,
2209 __isl_take isl_pw_qpolynomial *pwqp2)
2210 {
2211 int i, j, n;
2212 struct isl_pw_qpolynomial *res;
2213 isl_set *set;
2214
2215 if (!pwqp1 || !pwqp2)
2216 goto error;
2217
2218 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2219 goto error);
2220
2221 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2222 isl_pw_qpolynomial_free(pwqp2);
2223 return pwqp1;
2224 }
2225
2226 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2227 isl_pw_qpolynomial_free(pwqp1);
2228 return pwqp2;
2229 }
2230
2231 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2232 isl_pw_qpolynomial_free(pwqp1);
2233 return pwqp2;
2234 }
2235
2236 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2237 isl_pw_qpolynomial_free(pwqp2);
2238 return pwqp1;
2239 }
2240
2241 n = pwqp1->n * pwqp2->n;
2242 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2243
2244 for (i = 0; i < pwqp1->n; ++i) {
2245 for (j = 0; j < pwqp2->n; ++j) {
2246 struct isl_set *common;
2247 struct isl_qpolynomial *prod;
2248 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2249 isl_set_copy(pwqp2->p[j].set));
2250 if (isl_set_fast_is_empty(common)) {
2251 isl_set_free(common);
2252 continue;
2253 }
2254
2255 prod = isl_qpolynomial_mul(
2256 isl_qpolynomial_copy(pwqp1->p[i].qp),
2257 isl_qpolynomial_copy(pwqp2->p[j].qp));
2258
2259 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2260 }
2261 }
2262
2263 isl_pw_qpolynomial_free(pwqp1);
2264 isl_pw_qpolynomial_free(pwqp2);
2265
2266 return res;
2267 error:
2268 isl_pw_qpolynomial_free(pwqp1);
2269 isl_pw_qpolynomial_free(pwqp2);
2270 return NULL;
2271 }
2272
2273 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2274 __isl_take isl_pw_qpolynomial *pwqp)
2275 {
2276 int i;
2277
2278 if (!pwqp)
2279 return NULL;
2280
2281 if (isl_pw_qpolynomial_is_zero(pwqp))
2282 return pwqp;
2283
2284 pwqp = isl_pw_qpolynomial_cow(pwqp);
2285 if (!pwqp)
2286 return NULL;
2287
2288 for (i = 0; i < pwqp->n; ++i) {
2289 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2290 if (!pwqp->p[i].qp)
2291 goto error;
2292 }
2293
2294 return pwqp;
2295 error:
2296 isl_pw_qpolynomial_free(pwqp);
2297 return NULL;
2298 }
2299
2300 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2301 __isl_take isl_pw_qpolynomial *pwqp1,
2302 __isl_take isl_pw_qpolynomial *pwqp2)
2303 {
2304 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2305 }
2306
2307 __isl_give struct isl_upoly *isl_upoly_eval(
2308 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2309 {
2310 int i;
2311 struct isl_upoly_rec *rec;
2312 struct isl_upoly *res;
2313 struct isl_upoly *base;
2314
2315 if (isl_upoly_is_cst(up)) {
2316 isl_vec_free(vec);
2317 return up;
2318 }
2319
2320 rec = isl_upoly_as_rec(up);
2321 if (!rec)
2322 goto error;
2323
2324 isl_assert(up->ctx, rec->n >= 1, goto error);
2325
2326 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2327
2328 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2329 isl_vec_copy(vec));
2330
2331 for (i = rec->n - 2; i >= 0; --i) {
2332 res = isl_upoly_mul(res, isl_upoly_copy(base));
2333 res = isl_upoly_sum(res,
2334 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2335 isl_vec_copy(vec)));
2336 }
2337
2338 isl_upoly_free(base);
2339 isl_upoly_free(up);
2340 isl_vec_free(vec);
2341 return res;
2342 error:
2343 isl_upoly_free(up);
2344 isl_vec_free(vec);
2345 return NULL;
2346 }
2347
2348 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2349 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2350 {
2351 isl_vec *ext;
2352 struct isl_upoly *up;
2353 isl_dim *dim;
2354
2355 if (!qp || !pnt)
2356 goto error;
2357 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2358
2359 if (qp->div->n_row == 0)
2360 ext = isl_vec_copy(pnt->vec);
2361 else {
2362 int i;
2363 unsigned dim = isl_dim_total(qp->dim);
2364 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2365 if (!ext)
2366 goto error;
2367
2368 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2369 for (i = 0; i < qp->div->n_row; ++i) {
2370 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2371 1 + dim + i, &ext->el[1+dim+i]);
2372 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2373 qp->div->row[i][0]);
2374 }
2375 }
2376
2377 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2378 if (!up)
2379 goto error;
2380
2381 dim = isl_dim_copy(qp->dim);
2382 isl_qpolynomial_free(qp);
2383 isl_point_free(pnt);
2384
2385 return isl_qpolynomial_alloc(dim, 0, up);
2386 error:
2387 isl_qpolynomial_free(qp);
2388 isl_point_free(pnt);
2389 return NULL;
2390 }
2391
2392 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2393 __isl_keep struct isl_upoly_cst *cst2)
2394 {
2395 int cmp;
2396 isl_int t;
2397 isl_int_init(t);
2398 isl_int_mul(t, cst1->n, cst2->d);
2399 isl_int_submul(t, cst2->n, cst1->d);
2400 cmp = isl_int_sgn(t);
2401 isl_int_clear(t);
2402 return cmp;
2403 }
2404
2405 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2406 __isl_keep isl_qpolynomial *qp2)
2407 {
2408 struct isl_upoly_cst *cst1, *cst2;
2409
2410 if (!qp1 || !qp2)
2411 return -1;
2412 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2413 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2414 if (isl_qpolynomial_is_nan(qp1))
2415 return -1;
2416 if (isl_qpolynomial_is_nan(qp2))
2417 return -1;
2418 cst1 = isl_upoly_as_cst(qp1->upoly);
2419 cst2 = isl_upoly_as_cst(qp2->upoly);
2420
2421 return isl_upoly_cmp(cst1, cst2) <= 0;
2422 }
2423
2424 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2425 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2426 {
2427 struct isl_upoly_cst *cst1, *cst2;
2428 int cmp;
2429
2430 if (!qp1 || !qp2)
2431 goto error;
2432 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2433 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2434 cst1 = isl_upoly_as_cst(qp1->upoly);
2435 cst2 = isl_upoly_as_cst(qp2->upoly);
2436 cmp = isl_upoly_cmp(cst1, cst2);
2437
2438 if (cmp <= 0) {
2439 isl_qpolynomial_free(qp2);
2440 } else {
2441 isl_qpolynomial_free(qp1);
2442 qp1 = qp2;
2443 }
2444 return qp1;
2445 error:
2446 isl_qpolynomial_free(qp1);
2447 isl_qpolynomial_free(qp2);
2448 return NULL;
2449 }
2450
2451 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2452 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2453 {
2454 struct isl_upoly_cst *cst1, *cst2;
2455 int cmp;
2456
2457 if (!qp1 || !qp2)
2458 goto error;
2459 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2460 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2461 cst1 = isl_upoly_as_cst(qp1->upoly);
2462 cst2 = isl_upoly_as_cst(qp2->upoly);
2463 cmp = isl_upoly_cmp(cst1, cst2);
2464
2465 if (cmp >= 0) {
2466 isl_qpolynomial_free(qp2);
2467 } else {
2468 isl_qpolynomial_free(qp1);
2469 qp1 = qp2;
2470 }
2471 return qp1;
2472 error:
2473 isl_qpolynomial_free(qp1);
2474 isl_qpolynomial_free(qp2);
2475 return NULL;
2476 }
2477
2478 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2479 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2480 unsigned first, unsigned n)
2481 {
2482 unsigned total;
2483 unsigned g_pos;
2484 int *exp;
2485
2486 if (n == 0)
2487 return qp;
2488
2489 qp = isl_qpolynomial_cow(qp);
2490 if (!qp)
2491 return NULL;
2492
2493 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2494 goto error);
2495
2496 g_pos = pos(qp->dim, type) + first;
2497
2498 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2499 if (!qp->div)
2500 goto error;
2501
2502 total = qp->div->n_col - 2;
2503 if (total > g_pos) {
2504 int i;
2505 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2506 if (!exp)
2507 goto error;
2508 for (i = 0; i < total - g_pos; ++i)
2509 exp[i] = i + n;
2510 qp->upoly = expand(qp->upoly, exp, g_pos);
2511 free(exp);
2512 if (!qp->upoly)
2513 goto error;
2514 }
2515
2516 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2517 if (!qp->dim)
2518 goto error;
2519
2520 return qp;
2521 error:
2522 isl_qpolynomial_free(qp);
2523 return NULL;
2524 }
2525
2526 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2527 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2528 {
2529 unsigned pos;
2530
2531 pos = isl_qpolynomial_dim(qp, type);
2532
2533 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2534 }
2535
2536 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2537 __isl_take isl_pw_qpolynomial *pwqp,
2538 enum isl_dim_type type, unsigned n)
2539 {
2540 unsigned pos;
2541
2542 pos = isl_pw_qpolynomial_dim(pwqp, type);
2543
2544 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2545 }
2546
2547 static int *reordering_move(isl_ctx *ctx,
2548 unsigned len, unsigned dst, unsigned src, unsigned n)
2549 {
2550 int i;
2551 int *reordering;
2552
2553 reordering = isl_alloc_array(ctx, int, len);
2554 if (!reordering)
2555 return NULL;
2556
2557 if (dst <= src) {
2558 for (i = 0; i < dst; ++i)
2559 reordering[i] = i;
2560 for (i = 0; i < n; ++i)
2561 reordering[src + i] = dst + i;
2562 for (i = 0; i < src - dst; ++i)
2563 reordering[dst + i] = dst + n + i;
2564 for (i = 0; i < len - src - n; ++i)
2565 reordering[src + n + i] = src + n + i;
2566 } else {
2567 for (i = 0; i < src; ++i)
2568 reordering[i] = i;
2569 for (i = 0; i < n; ++i)
2570 reordering[src + i] = dst + i;
2571 for (i = 0; i < dst - src; ++i)
2572 reordering[src + n + i] = src + i;
2573 for (i = 0; i < len - dst - n; ++i)
2574 reordering[dst + n + i] = dst + n + i;
2575 }
2576
2577 return reordering;
2578 }
2579
2580 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2581 __isl_take isl_qpolynomial *qp,
2582 enum isl_dim_type dst_type, unsigned dst_pos,
2583 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2584 {
2585 unsigned g_dst_pos;
2586 unsigned g_src_pos;
2587 int *reordering;
2588
2589 qp = isl_qpolynomial_cow(qp);
2590 if (!qp)
2591 return NULL;
2592
2593 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2594 goto error);
2595
2596 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2597 g_src_pos = pos(qp->dim, src_type) + src_pos;
2598 if (dst_type > src_type)
2599 g_dst_pos -= n;
2600
2601 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2602 if (!qp->div)
2603 goto error;
2604 qp = sort_divs(qp);
2605 if (!qp)
2606 goto error;
2607
2608 reordering = reordering_move(qp->dim->ctx,
2609 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2610 if (!reordering)
2611 goto error;
2612
2613 qp->upoly = reorder(qp->upoly, reordering);
2614 free(reordering);
2615 if (!qp->upoly)
2616 goto error;
2617
2618 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2619 if (!qp->dim)
2620 goto error;
2621
2622 return qp;
2623 error:
2624 isl_qpolynomial_free(qp);
2625 return NULL;
2626 }
2627
2628 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2629 isl_int *f, isl_int denom)
2630 {
2631 struct isl_upoly *up;
2632
2633 if (!dim)
2634 return NULL;
2635
2636 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2637
2638 return isl_qpolynomial_alloc(dim, 0, up);
2639 }
2640
2641 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2642 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2643 {
2644 isl_int denom;
2645 isl_dim *dim;
2646 struct isl_upoly *up;
2647 isl_qpolynomial *qp;
2648 int sgn;
2649
2650 if (!c)
2651 return NULL;
2652
2653 isl_int_init(denom);
2654
2655 isl_constraint_get_coefficient(c, type, pos, &denom);
2656 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2657 sgn = isl_int_sgn(denom);
2658 isl_int_abs(denom, denom);
2659 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2660 1 + isl_constraint_dim(c, isl_dim_all));
2661 if (sgn < 0)
2662 isl_int_neg(denom, denom);
2663 isl_constraint_set_coefficient(c, type, pos, denom);
2664
2665 dim = isl_dim_copy(c->bmap->dim);
2666
2667 isl_int_clear(denom);
2668 isl_constraint_free(c);
2669
2670 qp = isl_qpolynomial_alloc(dim, 0, up);
2671 if (sgn > 0)
2672 qp = isl_qpolynomial_neg(qp);
2673 return qp;
2674 }
2675
2676 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2677 * in "qp" by subs[i].
2678 */
2679 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2680 __isl_take isl_qpolynomial *qp,
2681 enum isl_dim_type type, unsigned first, unsigned n,
2682 __isl_keep isl_qpolynomial **subs)
2683 {
2684 int i;
2685 struct isl_upoly **ups;
2686
2687 if (n == 0)
2688 return qp;
2689
2690 qp = isl_qpolynomial_cow(qp);
2691 if (!qp)
2692 return NULL;
2693 for (i = 0; i < n; ++i)
2694 if (!subs[i])
2695 goto error;
2696
2697 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2698 goto error);
2699
2700 for (i = 0; i < n; ++i)
2701 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2702 goto error);
2703
2704 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2705 for (i = 0; i < n; ++i)
2706 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2707
2708 first += pos(qp->dim, type);
2709
2710 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2711 if (!ups)
2712 goto error;
2713 for (i = 0; i < n; ++i)
2714 ups[i] = subs[i]->upoly;
2715
2716 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2717
2718 free(ups);
2719
2720 if (!qp->upoly)
2721 goto error;
2722
2723 return qp;
2724 error:
2725 isl_qpolynomial_free(qp);
2726 return NULL;
2727 }
2728
2729 /* Extend "bset" with extra set dimensions for each integer division
2730 * in "qp" and then call "fn" with the extended bset and the polynomial
2731 * that results from replacing each of the integer divisions by the
2732 * corresponding extra set dimension.
2733 */
2734 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2735 __isl_keep isl_basic_set *bset,
2736 int (*fn)(__isl_take isl_basic_set *bset,
2737 __isl_take isl_qpolynomial *poly, void *user), void *user)
2738 {
2739 isl_dim *dim;
2740 isl_mat *div;
2741 isl_qpolynomial *poly;
2742
2743 if (!qp || !bset)
2744 goto error;
2745 if (qp->div->n_row == 0)
2746 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2747 user);
2748
2749 div = isl_mat_copy(qp->div);
2750 dim = isl_dim_copy(qp->dim);
2751 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2752 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2753 bset = isl_basic_set_copy(bset);
2754 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2755 bset = add_div_constraints(bset, div);
2756
2757 return fn(bset, poly, user);
2758 error:
2759 return -1;
2760 }
2761
2762 /* Return total degree in variables first (inclusive) up to last (exclusive).
2763 */
2764 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2765 {
2766 int deg = -1;
2767 int i;
2768 struct isl_upoly_rec *rec;
2769
2770 if (!up)
2771 return -2;
2772 if (isl_upoly_is_zero(up))
2773 return -1;
2774 if (isl_upoly_is_cst(up) || up->var < first)
2775 return 0;
2776
2777 rec = isl_upoly_as_rec(up);
2778 if (!rec)
2779 return -2;
2780
2781 for (i = 0; i < rec->n; ++i) {
2782 int d;
2783
2784 if (isl_upoly_is_zero(rec->p[i]))
2785 continue;
2786 d = isl_upoly_degree(rec->p[i], first, last);
2787 if (up->var < last)
2788 d += i;
2789 if (d > deg)
2790 deg = d;
2791 }
2792
2793 return deg;
2794 }
2795
2796 /* Return total degree in set variables.
2797 */
2798 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2799 {
2800 unsigned ovar;
2801 unsigned nvar;
2802
2803 if (!poly)
2804 return -2;
2805
2806 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2807 nvar = isl_dim_size(poly->dim, isl_dim_set);
2808 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2809 }
2810
2811 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2812 unsigned pos, int deg)
2813 {
2814 int i;
2815 struct isl_upoly_rec *rec;
2816
2817 if (!up)
2818 return NULL;
2819
2820 if (isl_upoly_is_cst(up) || up->var < pos) {
2821 if (deg == 0)
2822 return isl_upoly_copy(up);
2823 else
2824 return isl_upoly_zero(up->ctx);
2825 }
2826
2827 rec = isl_upoly_as_rec(up);
2828 if (!rec)
2829 return NULL;
2830
2831 if (up->var == pos) {
2832 if (deg < rec->n)
2833 return isl_upoly_copy(rec->p[deg]);
2834 else
2835 return isl_upoly_zero(up->ctx);
2836 }
2837
2838 up = isl_upoly_copy(up);
2839 up = isl_upoly_cow(up);
2840 rec = isl_upoly_as_rec(up);
2841 if (!rec)
2842 goto error;
2843
2844 for (i = 0; i < rec->n; ++i) {
2845 struct isl_upoly *t;
2846 t = isl_upoly_coeff(rec->p[i], pos, deg);
2847 if (!t)
2848 goto error;
2849 isl_upoly_free(rec->p[i]);
2850 rec->p[i] = t;
2851 }
2852
2853 return up;
2854 error:
2855 isl_upoly_free(up);
2856 return NULL;
2857 }
2858
2859 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2860 */
2861 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2862 __isl_keep isl_qpolynomial *qp,
2863 enum isl_dim_type type, unsigned t_pos, int deg)
2864 {
2865 unsigned g_pos;
2866 struct isl_upoly *up;
2867 isl_qpolynomial *c;
2868
2869 if (!qp)
2870 return NULL;
2871
2872 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2873 return NULL);
2874
2875 g_pos = pos(qp->dim, type) + t_pos;
2876 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2877
2878 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2879 if (!c)
2880 return NULL;
2881 isl_mat_free(c->div);
2882 c->div = isl_mat_copy(qp->div);
2883 if (!c->div)
2884 goto error;
2885 return c;
2886 error:
2887 isl_qpolynomial_free(c);
2888 return NULL;
2889 }
2890
2891 /* Homogenize the polynomial in the variables first (inclusive) up to
2892 * last (exclusive) by inserting powers of variable first.
2893 * Variable first is assumed not to appear in the input.
2894 */
2895 __isl_give struct isl_upoly *isl_upoly_homogenize(
2896 __isl_take struct isl_upoly *up, int deg, int target,
2897 int first, int last)
2898 {
2899 int i;
2900 struct isl_upoly_rec *rec;
2901
2902 if (!up)
2903 return NULL;
2904 if (isl_upoly_is_zero(up))
2905 return up;
2906 if (deg == target)
2907 return up;
2908 if (isl_upoly_is_cst(up) || up->var < first) {
2909 struct isl_upoly *hom;
2910
2911 hom = isl_upoly_pow(up->ctx, first, target - deg);
2912 if (!hom)
2913 goto error;
2914 rec = isl_upoly_as_rec(hom);
2915 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2916
2917 return hom;
2918 }
2919
2920 up = isl_upoly_cow(up);
2921 rec = isl_upoly_as_rec(up);
2922 if (!rec)
2923 goto error;
2924
2925 for (i = 0; i < rec->n; ++i) {
2926 if (isl_upoly_is_zero(rec->p[i]))
2927 continue;
2928 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2929 up->var < last ? deg + i : i, target,
2930 first, last);
2931 if (!rec->p[i])
2932 goto error;
2933 }
2934
2935 return up;
2936 error:
2937 isl_upoly_free(up);
2938 return NULL;
2939 }
2940
2941 /* Homogenize the polynomial in the set variables by introducing
2942 * powers of an extra set variable at position 0.
2943 */
2944 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2945 __isl_take isl_qpolynomial *poly)
2946 {
2947 unsigned ovar;
2948 unsigned nvar;
2949 int deg = isl_qpolynomial_degree(poly);
2950
2951 if (deg < -1)
2952 goto error;
2953
2954 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2955 poly = isl_qpolynomial_cow(poly);
2956 if (!poly)
2957 goto error;
2958
2959 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2960 nvar = isl_dim_size(poly->dim, isl_dim_set);
2961 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2962 ovar, ovar + nvar);
2963 if (!poly->upoly)
2964 goto error;
2965
2966 return poly;
2967 error:
2968 isl_qpolynomial_free(poly);
2969 return NULL;
2970 }
2971
2972 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2973 __isl_take isl_mat *div)
2974 {
2975 isl_term *term;
2976 int n;
2977
2978 if (!dim || !div)
2979 goto error;
2980
2981 n = isl_dim_total(dim) + div->n_row;
2982
2983 term = isl_calloc(dim->ctx, struct isl_term,
2984 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2985 if (!term)
2986 goto error;
2987
2988 term->ref = 1;
2989 term->dim = dim;
2990 term->div = div;
2991 isl_int_init(term->n);
2992 isl_int_init(term->d);
2993
2994 return term;
2995 error:
2996 isl_dim_free(dim);
2997 isl_mat_free(div);
2998 return NULL;
2999 }
3000
3001 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3002 {
3003 if (!term)
3004 return NULL;
3005
3006 term->ref++;
3007 return term;
3008 }
3009
3010 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3011 {
3012 int i;
3013 isl_term *dup;
3014 unsigned total;
3015
3016 if (term)
3017 return NULL;
3018
3019 total = isl_dim_total(term->dim) + term->div->n_row;
3020
3021 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3022 if (!dup)
3023 return NULL;
3024
3025 isl_int_set(dup->n, term->n);
3026 isl_int_set(dup->d, term->d);
3027
3028 for (i = 0; i < total; ++i)
3029 dup->pow[i] = term->pow[i];
3030
3031 return dup;
3032 }
3033
3034 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3035 {
3036 if (!term)
3037 return NULL;
3038
3039 if (term->ref == 1)
3040 return term;
3041 term->ref--;
3042 return isl_term_dup(term);
3043 }
3044
3045 void isl_term_free(__isl_take isl_term *term)
3046 {
3047 if (!term)
3048 return;
3049
3050 if (--term->ref > 0)
3051 return;
3052
3053 isl_dim_free(term->dim);
3054 isl_mat_free(term->div);
3055 isl_int_clear(term->n);
3056 isl_int_clear(term->d);
3057 free(term);
3058 }
3059
3060 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3061 {
3062 if (!term)
3063 return 0;
3064
3065 switch (type) {
3066 case isl_dim_param:
3067 case isl_dim_in:
3068 case isl_dim_out: return isl_dim_size(term->dim, type);
3069 case isl_dim_div: return term->div->n_row;
3070 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3071 default: return 0;
3072 }
3073 }
3074
3075 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3076 {
3077 return term ? term->dim->ctx : NULL;
3078 }
3079
3080 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3081 {
3082 if (!term)
3083 return;
3084 isl_int_set(*n, term->n);
3085 }
3086
3087 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3088 {
3089 if (!term)
3090 return;
3091 isl_int_set(*d, term->d);
3092 }
3093
3094 int isl_term_get_exp(__isl_keep isl_term *term,
3095 enum isl_dim_type type, unsigned pos)
3096 {
3097 if (!term)
3098 return -1;
3099
3100 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3101
3102 if (type >= isl_dim_set)
3103 pos += isl_dim_size(term->dim, isl_dim_param);
3104 if (type >= isl_dim_div)
3105 pos += isl_dim_size(term->dim, isl_dim_set);
3106
3107 return term->pow[pos];
3108 }
3109
3110 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3111 {
3112 isl_basic_map *bmap;
3113 unsigned total;
3114 int k;
3115
3116 if (!term)
3117 return NULL;
3118
3119 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3120 return NULL);
3121
3122 total = term->div->n_col - term->div->n_row - 2;
3123 /* No nested divs for now */
3124 isl_assert(term->dim->ctx,
3125 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3126 term->div->n_row) == -1,
3127 return NULL);
3128
3129 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3130 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3131 goto error;
3132
3133 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3134
3135 return isl_basic_map_div(bmap, k);
3136 error:
3137 isl_basic_map_free(bmap);
3138 return NULL;
3139 }
3140
3141 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3142 int (*fn)(__isl_take isl_term *term, void *user),
3143 __isl_take isl_term *term, void *user)
3144 {
3145 int i;
3146 struct isl_upoly_rec *rec;
3147
3148 if (!up || !term)
3149 goto error;
3150
3151 if (isl_upoly_is_zero(up))
3152 return term;
3153
3154 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3155 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3156 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3157
3158 if (isl_upoly_is_cst(up)) {
3159 struct isl_upoly_cst *cst;
3160 cst = isl_upoly_as_cst(up);
3161 if (!cst)
3162 goto error;
3163 term = isl_term_cow(term);
3164 if (!term)
3165 goto error;
3166 isl_int_set(term->n, cst->n);
3167 isl_int_set(term->d, cst->d);
3168 if (fn(isl_term_copy(term), user) < 0)
3169 goto error;
3170 return term;
3171 }
3172
3173 rec = isl_upoly_as_rec(up);
3174 if (!rec)
3175 goto error;
3176
3177 for (i = 0; i < rec->n; ++i) {
3178 term = isl_term_cow(term);
3179 if (!term)
3180 goto error;
3181 term->pow[up->var] = i;
3182 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3183 if (!term)
3184 goto error;
3185 }
3186 term->pow[up->var] = 0;
3187
3188 return term;
3189 error:
3190 isl_term_free(term);
3191 return NULL;
3192 }
3193
3194 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3195 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3196 {
3197 isl_term *term;
3198
3199 if (!qp)
3200 return -1;
3201
3202 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3203 if (!term)
3204 return -1;
3205
3206 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3207
3208 isl_term_free(term);
3209
3210 return term ? 0 : -1;
3211 }
3212
3213 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3214 {
3215 struct isl_upoly *up;
3216 isl_qpolynomial *qp;
3217 int i, n;
3218
3219 if (!term)
3220 return NULL;
3221
3222 n = isl_dim_total(term->dim) + term->div->n_row;
3223
3224 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3225 for (i = 0; i < n; ++i) {
3226 if (!term->pow[i])
3227 continue;
3228 up = isl_upoly_mul(up,
3229 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3230 }
3231
3232 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3233 if (!qp)
3234 goto error;
3235 isl_mat_free(qp->div);
3236 qp->div = isl_mat_copy(term->div);
3237 if (!qp->div)
3238 goto error;
3239
3240 isl_term_free(term);
3241 return qp;
3242 error:
3243 isl_qpolynomial_free(qp);
3244 isl_term_free(term);
3245 return NULL;
3246 }
3247
3248 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3249 __isl_take isl_dim *dim)
3250 {
3251 int i;
3252 int extra;
3253 unsigned total;
3254
3255 if (!qp || !dim)
3256 goto error;
3257
3258 if (isl_dim_equal(qp->dim, dim)) {
3259 isl_dim_free(dim);
3260 return qp;
3261 }
3262
3263 qp = isl_qpolynomial_cow(qp);
3264 if (!qp)
3265 goto error;
3266
3267 extra = isl_dim_size(dim, isl_dim_set) -
3268 isl_dim_size(qp->dim, isl_dim_set);
3269 total = isl_dim_total(qp->dim);
3270 if (qp->div->n_row) {
3271 int *exp;
3272
3273 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3274 if (!exp)
3275 goto error;
3276 for (i = 0; i < qp->div->n_row; ++i)
3277 exp[i] = extra + i;
3278 qp->upoly = expand(qp->upoly, exp, total);
3279 free(exp);
3280 if (!qp->upoly)
3281 goto error;
3282 }
3283 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3284 if (!qp->div)
3285 goto error;
3286 for (i = 0; i < qp->div->n_row; ++i)
3287 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3288
3289 isl_dim_free(qp->dim);
3290 qp->dim = dim;
3291
3292 return qp;
3293 error:
3294 isl_dim_free(dim);
3295 isl_qpolynomial_free(qp);
3296 return NULL;
3297 }
3298
3299 /* For each parameter or variable that does not appear in qp,
3300 * first eliminate the variable from all constraints and then set it to zero.
3301 */
3302 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3303 __isl_keep isl_qpolynomial *qp)
3304 {
3305 int *active = NULL;
3306 int i;
3307 int d;
3308 unsigned nparam;
3309 unsigned nvar;
3310
3311 if (!set || !qp)
3312 goto error;
3313
3314 d = isl_dim_total(set->dim);
3315 active = isl_calloc_array(set->ctx, int, d);
3316 if (set_active(qp, active) < 0)
3317 goto error;
3318
3319 for (i = 0; i < d; ++i)
3320 if (!active[i])
3321 break;
3322
3323 if (i == d) {
3324 free(active);
3325 return set;
3326 }
3327
3328 nparam = isl_dim_size(set->dim, isl_dim_param);
3329 nvar = isl_dim_size(set->dim, isl_dim_set);
3330 for (i = 0; i < nparam; ++i) {
3331 if (active[i])
3332 continue;
3333 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3334 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3335 }
3336 for (i = 0; i < nvar; ++i) {
3337 if (active[nparam + i])
3338 continue;
3339 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3340 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3341 }
3342
3343 free(active);
3344
3345 return set;
3346 error:
3347 free(active);
3348 isl_set_free(set);
3349 return NULL;
3350 }
3351
3352 struct isl_opt_data {
3353 isl_qpolynomial *qp;
3354 int first;
3355 isl_qpolynomial *opt;
3356 int max;
3357 };
3358
3359 static int opt_fn(__isl_take isl_point *pnt, void *user)
3360 {
3361 struct isl_opt_data *data = (struct isl_opt_data *)user;
3362 isl_qpolynomial *val;
3363
3364 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3365 if (data->first) {
3366 data->first = 0;
3367 data->opt = val;
3368 } else if (data->max) {
3369 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3370 } else {
3371 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3372 }
3373
3374 return 0;
3375 }
3376
3377 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3378 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3379 {
3380 struct isl_opt_data data = { NULL, 1, NULL, max };
3381
3382 if (!set || !qp)
3383 goto error;
3384
3385 if (isl_upoly_is_cst(qp->upoly)) {
3386 isl_set_free(set);
3387 return qp;
3388 }
3389
3390 set = fix_inactive(set, qp);
3391
3392 data.qp = qp;
3393 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3394 goto error;
3395
3396 if (data.first)
3397 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3398
3399 isl_set_free(set);
3400 isl_qpolynomial_free(qp);
3401 return data.opt;
3402 error:
3403 isl_set_free(set);
3404 isl_qpolynomial_free(qp);
3405 isl_qpolynomial_free(data.opt);
3406 return NULL;
3407 }
3408
3409 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3410 __isl_take isl_morph *morph)
3411 {
3412 int i;
3413 int n_sub;
3414 isl_ctx *ctx;
3415 struct isl_upoly *up;
3416 unsigned n_div;
3417 struct isl_upoly **subs;
3418 isl_mat *mat;
3419
3420 qp = isl_qpolynomial_cow(qp);
3421 if (!qp || !morph)
3422 goto error;
3423
3424 ctx = qp->dim->ctx;
3425 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3426
3427 n_sub = morph->inv->n_row - 1;
3428 if (morph->inv->n_row != morph->inv->n_col)
3429 n_sub += qp->div->n_row;
3430 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3431 if (!subs)
3432 goto error;
3433
3434 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3435 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3436 morph->inv->row[0][0], morph->inv->n_col);
3437 if (morph->inv->n_row != morph->inv->n_col)
3438 for (i = 0; i < qp->div->n_row; ++i)
3439 subs[morph->inv->n_row - 1 + i] =
3440 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3441
3442 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3443
3444 for (i = 0; i < n_sub; ++i)
3445 isl_upoly_free(subs[i]);
3446 free(subs);
3447
3448 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3449 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3450 qp->div = isl_mat_product(qp->div, mat);
3451 isl_dim_free(qp->dim);
3452 qp->dim = isl_dim_copy(morph->ran->dim);
3453
3454 if (!qp->upoly || !qp->div || !qp->dim)
3455 goto error;
3456
3457 isl_morph_free(morph);
3458
3459 return qp;
3460 error:
3461 isl_qpolynomial_free(qp);
3462 isl_morph_free(morph);
3463 return NULL;
3464 }
3465
3466 static int neg_entry(void **entry, void *user)
3467 {
3468 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3469
3470 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3471
3472 return *pwqp ? 0 : -1;
3473 }
3474
3475 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3476 __isl_take isl_union_pw_qpolynomial *upwqp)
3477 {
3478 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3479 if (!upwqp)
3480 return NULL;
3481
3482 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3483 &neg_entry, NULL) < 0)
3484 goto error;
3485
3486 return upwqp;
3487 error:
3488 isl_union_pw_qpolynomial_free(upwqp);
3489 return NULL;
3490 }
3491
3492 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3493 __isl_take isl_union_pw_qpolynomial *upwqp1,
3494 __isl_take isl_union_pw_qpolynomial *upwqp2)
3495 {
3496 return isl_union_pw_qpolynomial_add(upwqp1,
3497 isl_union_pw_qpolynomial_neg(upwqp2));
3498 }
3499
3500 static int mul_entry(void **entry, void *user)
3501 {
3502 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3503 uint32_t hash;
3504 struct isl_hash_table_entry *entry2;
3505 isl_pw_qpolynomial *pwpq = *entry;
3506 int empty;
3507
3508 hash = isl_dim_get_hash(pwpq->dim);
3509 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3510 hash, &has_dim, pwpq->dim, 0);
3511 if (!entry2)
3512 return 0;
3513
3514 pwpq = isl_pw_qpolynomial_copy(pwpq);
3515 pwpq = isl_pw_qpolynomial_mul(pwpq,
3516 isl_pw_qpolynomial_copy(entry2->data));
3517
3518 empty = isl_pw_qpolynomial_is_zero(pwpq);
3519 if (empty < 0) {
3520 isl_pw_qpolynomial_free(pwpq);
3521 return -1;
3522 }
3523 if (empty) {
3524 isl_pw_qpolynomial_free(pwpq);
3525 return 0;
3526 }
3527
3528 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3529
3530 return 0;
3531 }
3532
3533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3534 __isl_take isl_union_pw_qpolynomial *upwqp1,
3535 __isl_take isl_union_pw_qpolynomial *upwqp2)
3536 {
3537 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3538 }
3539
3540 /* Reorder the columns of the given div definitions according to the
3541 * given reordering.
3542 */
3543 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3544 __isl_take isl_reordering *r)
3545 {
3546 int i, j;
3547 isl_mat *mat;
3548 int extra;
3549
3550 if (!div || !r)
3551 goto error;
3552
3553 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3554 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3555 if (!mat)
3556 goto error;
3557
3558 for (i = 0; i < div->n_row; ++i) {
3559 isl_seq_cpy(mat->row[i], div->row[i], 2);
3560 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3561 for (j = 0; j < r->len; ++j)
3562 isl_int_set(mat->row[i][2 + r->pos[j]],
3563 div->row[i][2 + j]);
3564 }
3565
3566 isl_reordering_free(r);
3567 isl_mat_free(div);
3568 return mat;
3569 error:
3570 isl_reordering_free(r);
3571 isl_mat_free(div);
3572 return NULL;
3573 }
3574
3575 /* Reorder the dimension of "qp" according to the given reordering.
3576 */
3577 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3578 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3579 {
3580 qp = isl_qpolynomial_cow(qp);
3581 if (!qp)
3582 goto error;
3583
3584 r = isl_reordering_extend(r, qp->div->n_row);
3585 if (!r)
3586 goto error;
3587
3588 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3589 if (!qp->div)
3590 goto error;
3591
3592 qp->upoly = reorder(qp->upoly, r->pos);
3593 if (!qp->upoly)
3594 goto error;
3595
3596 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3597
3598 isl_reordering_free(r);
3599 return qp;
3600 error:
3601 isl_qpolynomial_free(qp);
3602 isl_reordering_free(r);
3603 return NULL;
3604 }
3605
3606 struct isl_split_periods_data {
3607 int max_periods;
3608 isl_pw_qpolynomial *res;
3609 };
3610
3611 /* Create a slice where the integer division "div" has the fixed value "v".
3612 * In particular, if "div" refers to floor(f/m), then create a slice
3613 *
3614 * m v <= f <= m v + (m - 1)
3615 *
3616 * or
3617 *
3618 * f - m v >= 0
3619 * -f + m v + (m - 1) >= 0
3620 */
3621 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3622 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3623 {
3624 int total;
3625 isl_basic_set *bset = NULL;
3626 int k;
3627
3628 if (!dim || !qp)
3629 goto error;
3630
3631 total = isl_dim_total(dim);
3632 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3633
3634 k = isl_basic_set_alloc_inequality(bset);
3635 if (k < 0)
3636 goto error;
3637 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3638 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3639
3640 k = isl_basic_set_alloc_inequality(bset);
3641 if (k < 0)
3642 goto error;
3643 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3644 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3645 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3646 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3647
3648 isl_dim_free(dim);
3649 return isl_set_from_basic_set(bset);
3650 error:
3651 isl_basic_set_free(bset);
3652 isl_dim_free(dim);
3653 return NULL;
3654 }
3655
3656 static int split_periods(__isl_take isl_set *set,
3657 __isl_take isl_qpolynomial *qp, void *user);
3658
3659 /* Create a slice of the domain "set" such that integer division "div"
3660 * has the fixed value "v" and add the results to data->res,
3661 * replacing the integer division by "v" in "qp".
3662 */
3663 static int set_div(__isl_take isl_set *set,
3664 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3665 struct isl_split_periods_data *data)
3666 {
3667 int i;
3668 int total;
3669 isl_set *slice;
3670 struct isl_upoly *cst;
3671
3672 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3673 set = isl_set_intersect(set, slice);
3674
3675 if (!qp)
3676 goto error;
3677
3678 total = isl_dim_total(qp->dim);
3679
3680 for (i = div + 1; i < qp->div->n_row; ++i) {
3681 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3682 continue;
3683 isl_int_addmul(qp->div->row[i][1],
3684 qp->div->row[i][2 + total + div], v);
3685 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3686 }
3687
3688 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3689 qp = substitute_div(qp, div, cst);
3690
3691 return split_periods(set, qp, data);
3692 error:
3693 isl_set_free(set);
3694 isl_qpolynomial_free(qp);
3695 return -1;
3696 }
3697
3698 /* Split the domain "set" such that integer division "div"
3699 * has a fixed value (ranging from "min" to "max") on each slice
3700 * and add the results to data->res.
3701 */
3702 static int split_div(__isl_take isl_set *set,
3703 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3704 struct isl_split_periods_data *data)
3705 {
3706 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3707 isl_set *set_i = isl_set_copy(set);
3708 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3709
3710 if (set_div(set_i, qp_i, div, min, data) < 0)
3711 goto error;
3712 }
3713 isl_set_free(set);
3714 isl_qpolynomial_free(qp);
3715 return 0;
3716 error:
3717 isl_set_free(set);
3718 isl_qpolynomial_free(qp);
3719 return -1;
3720 }
3721
3722 /* If "qp" refers to any integer division
3723 * that can only attain "max_periods" distinct values on "set"
3724 * then split the domain along those distinct values.
3725 * Add the results (or the original if no splitting occurs)
3726 * to data->res.
3727 */
3728 static int split_periods(__isl_take isl_set *set,
3729 __isl_take isl_qpolynomial *qp, void *user)
3730 {
3731 int i;
3732 isl_pw_qpolynomial *pwqp;
3733 struct isl_split_periods_data *data;
3734 isl_int min, max;
3735 int total;
3736 int r = 0;
3737
3738 data = (struct isl_split_periods_data *)user;
3739
3740 if (!set || !qp)
3741 goto error;
3742
3743 if (qp->div->n_row == 0) {
3744 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3745 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3746 return 0;
3747 }
3748
3749 isl_int_init(min);
3750 isl_int_init(max);
3751 total = isl_dim_total(qp->dim);
3752 for (i = 0; i < qp->div->n_row; ++i) {
3753 enum isl_lp_result lp_res;
3754
3755 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3756 qp->div->n_row) != -1)
3757 continue;
3758
3759 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3760 set->ctx->one, &min, NULL, NULL);
3761 if (lp_res == isl_lp_error)
3762 goto error2;
3763 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3764 continue;
3765 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3766
3767 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3768 set->ctx->one, &max, NULL, NULL);
3769 if (lp_res == isl_lp_error)
3770 goto error2;
3771 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3772 continue;
3773 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3774
3775 isl_int_sub(max, max, min);
3776 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3777 isl_int_add(max, max, min);
3778 break;
3779 }
3780 }
3781
3782 if (i < qp->div->n_row) {
3783 r = split_div(set, qp, i, min, max, data);
3784 } else {
3785 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3786 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3787 }
3788
3789 isl_int_clear(max);
3790 isl_int_clear(min);
3791
3792 return r;
3793 error2:
3794 isl_int_clear(max);
3795 isl_int_clear(min);
3796 error:
3797 isl_set_free(set);
3798 isl_qpolynomial_free(qp);
3799 return -1;
3800 }
3801
3802 /* If any quasi-polynomial in pwqp refers to any integer division
3803 * that can only attain "max_periods" distinct values on its domain
3804 * then split the domain along those distinct values.
3805 */
3806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3807 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3808 {
3809 struct isl_split_periods_data data;
3810
3811 data.max_periods = max_periods;
3812 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3813
3814 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3815 goto error;
3816
3817 isl_pw_qpolynomial_free(pwqp);
3818
3819 return data.res;
3820 error:
3821 isl_pw_qpolynomial_free(data.res);
3822 isl_pw_qpolynomial_free(pwqp);
3823 return NULL;
3824 }
3825
3826 /* Construct a piecewise quasipolynomial that is constant on the given
3827 * domain. In particular, it is
3828 * 0 if cst == 0
3829 * 1 if cst == 1
3830 * infinity if cst == -1
3831 */
3832 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3833 __isl_take isl_basic_set *bset, int cst)
3834 {
3835 isl_dim *dim;
3836 isl_qpolynomial *qp;
3837
3838 if (!bset)
3839 return NULL;
3840
3841 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3842 dim = isl_basic_set_get_dim(bset);
3843 if (cst < 0)
3844 qp = isl_qpolynomial_infty(dim);
3845 else if (cst == 0)
3846 qp = isl_qpolynomial_zero(dim);
3847 else
3848 qp = isl_qpolynomial_one(dim);
3849 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3850 }
3851
3852 /* Factor bset, call fn on each of the factors and return the product.
3853 *
3854 * If no factors can be found, simply call fn on the input.
3855 * Otherwise, construct the factors based on the factorizer,
3856 * call fn on each factor and compute the product.
3857 */
3858 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3859 __isl_take isl_basic_set *bset,
3860 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3861 {
3862 int i, n;
3863 isl_dim *dim;
3864 isl_set *set;
3865 isl_factorizer *f;
3866 isl_qpolynomial *qp;
3867 isl_pw_qpolynomial *pwqp;
3868 unsigned nparam;
3869 unsigned nvar;
3870
3871 f = isl_basic_set_factorizer(bset);
3872 if (!f)
3873 goto error;
3874 if (f->n_group == 0) {
3875 isl_factorizer_free(f);
3876 return fn(bset);
3877 }
3878
3879 nparam = isl_basic_set_dim(bset, isl_dim_param);
3880 nvar = isl_basic_set_dim(bset, isl_dim_set);
3881
3882 dim = isl_basic_set_get_dim(bset);
3883 dim = isl_dim_domain(dim);
3884 set = isl_set_universe(isl_dim_copy(dim));
3885 qp = isl_qpolynomial_one(dim);
3886 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3887
3888 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3889
3890 for (i = 0, n = 0; i < f->n_group; ++i) {
3891 isl_basic_set *bset_i;
3892 isl_pw_qpolynomial *pwqp_i;
3893
3894 bset_i = isl_basic_set_copy(bset);
3895 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3896 nparam + n + f->len[i], nvar - n - f->len[i]);
3897 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3898 nparam, n);
3899 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3900 n + f->len[i], nvar - n - f->len[i]);
3901 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3902
3903 pwqp_i = fn(bset_i);
3904 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3905
3906 n += f->len[i];
3907 }
3908
3909 isl_basic_set_free(bset);
3910 isl_factorizer_free(f);
3911
3912 return pwqp;
3913 error:
3914 isl_basic_set_free(bset);
3915 return NULL;
3916 }
3917
3918 /* Factor bset, call fn on each of the factors and return the product.
3919 * The function is assumed to evaluate to zero on empty domains,
3920 * to one on zero-dimensional domains and to infinity on unbounded domains
3921 * and will not be called explicitly on zero-dimensional or unbounded domains.
3922 *
3923 * We first check for some special cases and remove all equalities.
3924 * Then we hand over control to compressed_multiplicative_call.
3925 */
3926 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3927 __isl_take isl_basic_set *bset,
3928 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3929 {
3930 int bounded;
3931 isl_morph *morph;
3932 isl_pw_qpolynomial *pwqp;
3933 unsigned orig_nvar, final_nvar;
3934
3935 if (!bset)
3936 return NULL;
3937
3938 if (isl_basic_set_fast_is_empty(bset))
3939 return constant_on_domain(bset, 0);
3940
3941 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3942
3943 if (orig_nvar == 0)
3944 return constant_on_domain(bset, 1);
3945
3946 bounded = isl_basic_set_is_bounded(bset);
3947 if (bounded < 0)
3948 goto error;
3949 if (!bounded)
3950 return constant_on_domain(bset, -1);
3951
3952 if (bset->n_eq == 0)
3953 return compressed_multiplicative_call(bset, fn);
3954
3955 morph = isl_basic_set_full_compression(bset);
3956 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3957
3958 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3959
3960 pwqp = compressed_multiplicative_call(bset, fn);
3961
3962 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3963 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3964 morph = isl_morph_inverse(morph);
3965
3966 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3967
3968 return pwqp;
3969 error:
3970 isl_basic_set_free(bset);
3971 return NULL;
3972 }
3973
3974 /* Drop all floors in "qp", turning each integer division [a/m] into
3975 * a rational division a/m. If "down" is set, then the integer division
3976 * is replaces by (a-(m-1))/m instead.
3977 */
3978 static __isl_give isl_qpolynomial *qp_drop_floors(
3979 __isl_take isl_qpolynomial *qp, int down)
3980 {
3981 int i;
3982 struct isl_upoly *s;
3983
3984 if (!qp)
3985 return NULL;
3986 if (qp->div->n_row == 0)
3987 return qp;
3988
3989 qp = isl_qpolynomial_cow(qp);
3990 if (!qp)
3991 return NULL;
3992
3993 for (i = qp->div->n_row - 1; i >= 0; --i) {
3994 if (down) {
3995 isl_int_sub(qp->div->row[i][1],
3996 qp->div->row[i][1], qp->div->row[i][0]);
3997 isl_int_add_ui(qp->div->row[i][1],
3998 qp->div->row[i][1], 1);
3999 }
4000 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4001 qp->div->row[i][0], qp->div->n_col - 1);
4002 qp = substitute_div(qp, i, s);
4003 if (!qp)
4004 return NULL;
4005 }
4006
4007 return qp;
4008 }
4009
4010 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4011 * a rational division a/m.
4012 */
4013 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4014 __isl_take isl_pw_qpolynomial *pwqp)
4015 {
4016 int i;
4017
4018 if (!pwqp)
4019 return NULL;
4020
4021 if (isl_pw_qpolynomial_is_zero(pwqp))
4022 return pwqp;
4023
4024 pwqp = isl_pw_qpolynomial_cow(pwqp);
4025 if (!pwqp)
4026 return NULL;
4027
4028 for (i = 0; i < pwqp->n; ++i) {
4029 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4030 if (!pwqp->p[i].qp)
4031 goto error;
4032 }
4033
4034 return pwqp;
4035 error:
4036 isl_pw_qpolynomial_free(pwqp);
4037 return NULL;
4038 }
4039
4040 /* Adjust all the integer divisions in "qp" such that they are at least
4041 * one over the given orthant (identified by "signs"). This ensures
4042 * that they will still be non-negative even after subtracting (m-1)/m.
4043 *
4044 * In particular, f is replaced by f' + v, changing f = [a/m]
4045 * to f' = [(a - m v)/m].
4046 * If the constant term k in a is smaller than m,
4047 * the constant term of v is set to floor(k/m) - 1.
4048 * For any other term, if the coefficient c and the variable x have
4049 * the same sign, then no changes are needed.
4050 * Otherwise, if the variable is positive (and c is negative),
4051 * then the coefficient of x in v is set to floor(c/m).
4052 * If the variable is negative (and c is positive),
4053 * then the coefficient of x in v is set to ceil(c/m).
4054 */
4055 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4056 int *signs)
4057 {
4058 int i, j;
4059 int total;
4060 isl_vec *v = NULL;
4061 struct isl_upoly *s;
4062
4063 qp = isl_qpolynomial_cow(qp);
4064 if (!qp)
4065 return NULL;
4066 qp->div = isl_mat_cow(qp->div);
4067 if (!qp->div)
4068 goto error;
4069
4070 total = isl_dim_total(qp->dim);
4071 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4072
4073 for (i = 0; i < qp->div->n_row; ++i) {
4074 isl_int *row = qp->div->row[i];
4075 v = isl_vec_clr(v);
4076 if (!v)
4077 goto error;
4078 if (isl_int_lt(row[1], row[0])) {
4079 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4080 isl_int_sub_ui(v->el[0], v->el[0], 1);
4081 isl_int_submul(row[1], row[0], v->el[0]);
4082 }
4083 for (j = 0; j < total; ++j) {
4084 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4085 continue;
4086 if (signs[j] < 0)
4087 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4088 else
4089 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4090 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4091 }
4092 for (j = 0; j < i; ++j) {
4093 if (isl_int_sgn(row[2 + total + j]) >= 0)
4094 continue;
4095 isl_int_fdiv_q(v->el[1 + total + j],
4096 row[2 + total + j], row[0]);
4097 isl_int_submul(row[2 + total + j],
4098 row[0], v->el[1 + total + j]);
4099 }
4100 for (j = i + 1; j < qp->div->n_row; ++j) {
4101 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4102 continue;
4103 isl_seq_combine(qp->div->row[j] + 1,
4104 qp->div->ctx->one, qp->div->row[j] + 1,
4105 qp->div->row[j][2 + total + i], v->el, v->size);
4106 }
4107 isl_int_set_si(v->el[1 + total + i], 1);
4108 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4109 qp->div->ctx->one, v->size);
4110 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4111 isl_upoly_free(s);
4112 if (!qp->upoly)
4113 goto error;
4114 }
4115
4116 isl_vec_free(v);
4117 return qp;
4118 error:
4119 isl_vec_free(v);
4120 isl_qpolynomial_free(qp);
4121 return NULL;
4122 }
4123
4124 struct isl_to_poly_data {
4125 int sign;
4126 isl_pw_qpolynomial *res;
4127 isl_qpolynomial *qp;
4128 };
4129
4130 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4131 * We first make all integer divisions positive and then split the
4132 * quasipolynomials into terms with sign data->sign (the direction
4133 * of the requested approximation) and terms with the opposite sign.
4134 * In the first set of terms, each integer division [a/m] is
4135 * overapproximated by a/m, while in the second it is underapproximated
4136 * by (a-(m-1))/m.
4137 */
4138 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4139 void *user)
4140 {
4141 struct isl_to_poly_data *data = user;
4142 isl_pw_qpolynomial *t;
4143 isl_qpolynomial *qp, *up, *down;
4144
4145 qp = isl_qpolynomial_copy(data->qp);
4146 qp = make_divs_pos(qp, signs);
4147
4148 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4149 up = qp_drop_floors(up, 0);
4150 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4151 down = qp_drop_floors(down, 1);
4152
4153 isl_qpolynomial_free(qp);
4154 qp = isl_qpolynomial_add(up, down);
4155
4156 t = isl_pw_qpolynomial_alloc(orthant, qp);
4157 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4158
4159 return 0;
4160 }
4161
4162 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4163 * the polynomial will be an overapproximation. If "sign" is negative,
4164 * it will be an underapproximation. If "sign" is zero, the approximation
4165 * will lie somewhere in between.
4166 *
4167 * In particular, is sign == 0, we simply drop the floors, turning
4168 * the integer divisions into rational divisions.
4169 * Otherwise, we split the domains into orthants, make all integer divisions
4170 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4171 * depending on the requested sign and the sign of the term in which
4172 * the integer division appears.
4173 */
4174 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4175 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4176 {
4177 int i;
4178 struct isl_to_poly_data data;
4179
4180 if (sign == 0)
4181 return pwqp_drop_floors(pwqp);
4182
4183 if (!pwqp)
4184 return NULL;
4185
4186 data.sign = sign;
4187 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4188
4189 for (i = 0; i < pwqp->n; ++i) {
4190 if (pwqp->p[i].qp->div->n_row == 0) {
4191 isl_pw_qpolynomial *t;
4192 t = isl_pw_qpolynomial_alloc(
4193 isl_set_copy(pwqp->p[i].set),
4194 isl_qpolynomial_copy(pwqp->p[i].qp));
4195 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4196 continue;
4197 }
4198 data.qp = pwqp->p[i].qp;
4199 if (isl_set_foreach_orthant(pwqp->p[i].set,
4200 &to_polynomial_on_orthant, &data) < 0)
4201 goto error;
4202 }
4203
4204 isl_pw_qpolynomial_free(pwqp);
4205
4206 return data.res;
4207 error:
4208 isl_pw_qpolynomial_free(pwqp);
4209 isl_pw_qpolynomial_free(data.res);
4210 return NULL;
4211 }
4212
4213 static int poly_entry(void **entry, void *user)
4214 {
4215 int *sign = user;
4216 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4217
4218 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4219
4220 return *pwqp ? 0 : -1;
4221 }
4222
4223 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4224 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4225 {
4226 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4227 if (!upwqp)
4228 return NULL;
4229
4230 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4231 &poly_entry, &sign) < 0)
4232 goto error;
4233
4234 return upwqp;
4235 error:
4236 isl_union_pw_qpolynomial_free(upwqp);
4237 return NULL;
4238 }
Integer set library