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isl_qpolynomial: properly merge identical nested divs
[isl.git] / isl_polynomial.c
blob92e8b2f6af9e690ee2fd6dfe6950ce9aeb1ebe2e
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 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1146 2 + div_pos + i - skip);
1147 qp->div = isl_mat_drop_cols(qp->div,
1148 2 + div_pos + i - skip, 1);
1149 skip++;
1150 }
1151 reordering[div_pos + array[i].row] = div_pos + i - skip;
1152 }
1153
1154 qp->upoly = reorder(qp->upoly, reordering);
1155
1156 if (!qp->upoly || !qp->div)
1157 goto error;
1158
1159 free(at);
1160 free(pos);
1161 free(array);
1162 free(reordering);
1163
1164 return qp;
1165 error:
1166 free(at);
1167 free(pos);
1168 free(array);
1169 free(reordering);
1170 isl_qpolynomial_free(qp);
1171 return NULL;
1172 }
1173
1174 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1175 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1176 {
1177 int i, j, k;
1178 isl_mat *div = NULL;
1179 unsigned d = div1->n_col - div1->n_row;
1180
1181 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1182 d + div1->n_row + div2->n_row);
1183 if (!div)
1184 return NULL;
1185
1186 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1187 int cmp;
1188
1189 expand_row(div, k, div1, i, exp1);
1190 expand_row(div, k + 1, div2, j, exp2);
1191
1192 cmp = cmp_row(div, k, k + 1);
1193 if (cmp == 0) {
1194 exp1[i++] = k;
1195 exp2[j++] = k;
1196 } else if (cmp < 0) {
1197 exp1[i++] = k;
1198 } else {
1199 exp2[j++] = k;
1200 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1201 }
1202 }
1203 for (; i < div1->n_row; ++i, ++k) {
1204 expand_row(div, k, div1, i, exp1);
1205 exp1[i] = k;
1206 }
1207 for (; j < div2->n_row; ++j, ++k) {
1208 expand_row(div, k, div2, j, exp2);
1209 exp2[j] = k;
1210 }
1211
1212 div->n_row = k;
1213 div->n_col = d + k;
1214
1215 return div;
1216 }
1217
1218 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1219 int *exp, int first)
1220 {
1221 int i;
1222 struct isl_upoly_rec *rec;
1223
1224 if (isl_upoly_is_cst(up))
1225 return up;
1226
1227 if (up->var < first)
1228 return up;
1229
1230 if (exp[up->var - first] == up->var - first)
1231 return up;
1232
1233 up = isl_upoly_cow(up);
1234 if (!up)
1235 goto error;
1236
1237 up->var = exp[up->var - first] + first;
1238
1239 rec = isl_upoly_as_rec(up);
1240 if (!rec)
1241 goto error;
1242
1243 for (i = 0; i < rec->n; ++i) {
1244 rec->p[i] = expand(rec->p[i], exp, first);
1245 if (!rec->p[i])
1246 goto error;
1247 }
1248
1249 return up;
1250 error:
1251 isl_upoly_free(up);
1252 return NULL;
1253 }
1254
1255 static __isl_give isl_qpolynomial *with_merged_divs(
1256 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1257 __isl_take isl_qpolynomial *qp2),
1258 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1259 {
1260 int *exp1 = NULL;
1261 int *exp2 = NULL;
1262 isl_mat *div = NULL;
1263
1264 qp1 = isl_qpolynomial_cow(qp1);
1265 qp2 = isl_qpolynomial_cow(qp2);
1266
1267 if (!qp1 || !qp2)
1268 goto error;
1269
1270 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1271 qp1->div->n_col >= qp2->div->n_col, goto error);
1272
1273 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1274 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1275 if (!exp1 || !exp2)
1276 goto error;
1277
1278 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1279 if (!div)
1280 goto error;
1281
1282 isl_mat_free(qp1->div);
1283 qp1->div = isl_mat_copy(div);
1284 isl_mat_free(qp2->div);
1285 qp2->div = isl_mat_copy(div);
1286
1287 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1288 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1289
1290 if (!qp1->upoly || !qp2->upoly)
1291 goto error;
1292
1293 isl_mat_free(div);
1294 free(exp1);
1295 free(exp2);
1296
1297 return fn(qp1, qp2);
1298 error:
1299 isl_mat_free(div);
1300 free(exp1);
1301 free(exp2);
1302 isl_qpolynomial_free(qp1);
1303 isl_qpolynomial_free(qp2);
1304 return NULL;
1305 }
1306
1307 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1308 __isl_take isl_qpolynomial *qp2)
1309 {
1310 qp1 = isl_qpolynomial_cow(qp1);
1311
1312 if (!qp1 || !qp2)
1313 goto error;
1314
1315 if (qp1->div->n_row < qp2->div->n_row)
1316 return isl_qpolynomial_add(qp2, qp1);
1317
1318 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1319 if (!compatible_divs(qp1->div, qp2->div))
1320 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1321
1322 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1323 if (!qp1->upoly)
1324 goto error;
1325
1326 isl_qpolynomial_free(qp2);
1327
1328 return qp1;
1329 error:
1330 isl_qpolynomial_free(qp1);
1331 isl_qpolynomial_free(qp2);
1332 return NULL;
1333 }
1334
1335 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1336 __isl_keep isl_set *dom,
1337 __isl_take isl_qpolynomial *qp1,
1338 __isl_take isl_qpolynomial *qp2)
1339 {
1340 return isl_qpolynomial_add(qp1, qp2);
1341 }
1342
1343 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1344 __isl_take isl_qpolynomial *qp2)
1345 {
1346 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1347 }
1348
1349 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1350 {
1351 qp = isl_qpolynomial_cow(qp);
1352
1353 if (!qp)
1354 return NULL;
1355
1356 qp->upoly = isl_upoly_neg(qp->upoly);
1357 if (!qp->upoly)
1358 goto error;
1359
1360 return qp;
1361 error:
1362 isl_qpolynomial_free(qp);
1363 return NULL;
1364 }
1365
1366 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1367 __isl_take isl_qpolynomial *qp2)
1368 {
1369 qp1 = isl_qpolynomial_cow(qp1);
1370
1371 if (!qp1 || !qp2)
1372 goto error;
1373
1374 if (qp1->div->n_row < qp2->div->n_row)
1375 return isl_qpolynomial_mul(qp2, qp1);
1376
1377 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1378 if (!compatible_divs(qp1->div, qp2->div))
1379 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1380
1381 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1382 if (!qp1->upoly)
1383 goto error;
1384
1385 isl_qpolynomial_free(qp2);
1386
1387 return qp1;
1388 error:
1389 isl_qpolynomial_free(qp1);
1390 isl_qpolynomial_free(qp2);
1391 return NULL;
1392 }
1393
1394 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1395 {
1396 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1397 }
1398
1399 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1400 {
1401 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1402 }
1403
1404 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1405 {
1406 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1407 }
1408
1409 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1410 {
1411 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1412 }
1413
1414 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1415 {
1416 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1417 }
1418
1419 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1420 isl_int v)
1421 {
1422 struct isl_qpolynomial *qp;
1423 struct isl_upoly_cst *cst;
1424
1425 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1426 if (!qp)
1427 return NULL;
1428
1429 cst = isl_upoly_as_cst(qp->upoly);
1430 isl_int_set(cst->n, v);
1431
1432 return qp;
1433 }
1434
1435 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1436 isl_int *n, isl_int *d)
1437 {
1438 struct isl_upoly_cst *cst;
1439
1440 if (!qp)
1441 return -1;
1442
1443 if (!isl_upoly_is_cst(qp->upoly))
1444 return 0;
1445
1446 cst = isl_upoly_as_cst(qp->upoly);
1447 if (!cst)
1448 return -1;
1449
1450 if (n)
1451 isl_int_set(*n, cst->n);
1452 if (d)
1453 isl_int_set(*d, cst->d);
1454
1455 return 1;
1456 }
1457
1458 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1459 {
1460 int is_cst;
1461 struct isl_upoly_rec *rec;
1462
1463 if (!up)
1464 return -1;
1465
1466 if (up->var < 0)
1467 return 1;
1468
1469 rec = isl_upoly_as_rec(up);
1470 if (!rec)
1471 return -1;
1472
1473 if (rec->n > 2)
1474 return 0;
1475
1476 isl_assert(up->ctx, rec->n > 1, return -1);
1477
1478 is_cst = isl_upoly_is_cst(rec->p[1]);
1479 if (is_cst < 0)
1480 return -1;
1481 if (!is_cst)
1482 return 0;
1483
1484 return isl_upoly_is_affine(rec->p[0]);
1485 }
1486
1487 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1488 {
1489 if (!qp)
1490 return -1;
1491
1492 if (qp->div->n_row > 0)
1493 return 0;
1494
1495 return isl_upoly_is_affine(qp->upoly);
1496 }
1497
1498 static void update_coeff(__isl_keep isl_vec *aff,
1499 __isl_keep struct isl_upoly_cst *cst, int pos)
1500 {
1501 isl_int gcd;
1502 isl_int f;
1503
1504 if (isl_int_is_zero(cst->n))
1505 return;
1506
1507 isl_int_init(gcd);
1508 isl_int_init(f);
1509 isl_int_gcd(gcd, cst->d, aff->el[0]);
1510 isl_int_divexact(f, cst->d, gcd);
1511 isl_int_divexact(gcd, aff->el[0], gcd);
1512 isl_seq_scale(aff->el, aff->el, f, aff->size);
1513 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1514 isl_int_clear(gcd);
1515 isl_int_clear(f);
1516 }
1517
1518 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1519 __isl_keep isl_vec *aff)
1520 {
1521 struct isl_upoly_cst *cst;
1522 struct isl_upoly_rec *rec;
1523
1524 if (!up || !aff)
1525 return -1;
1526
1527 if (up->var < 0) {
1528 struct isl_upoly_cst *cst;
1529
1530 cst = isl_upoly_as_cst(up);
1531 if (!cst)
1532 return -1;
1533 update_coeff(aff, cst, 0);
1534 return 0;
1535 }
1536
1537 rec = isl_upoly_as_rec(up);
1538 if (!rec)
1539 return -1;
1540 isl_assert(up->ctx, rec->n == 2, return -1);
1541
1542 cst = isl_upoly_as_cst(rec->p[1]);
1543 if (!cst)
1544 return -1;
1545 update_coeff(aff, cst, 1 + up->var);
1546
1547 return isl_upoly_update_affine(rec->p[0], aff);
1548 }
1549
1550 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1551 __isl_keep isl_qpolynomial *qp)
1552 {
1553 isl_vec *aff;
1554 unsigned d;
1555
1556 if (!qp)
1557 return NULL;
1558
1559 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1560 d = isl_dim_total(qp->dim);
1561 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1562 if (!aff)
1563 return NULL;
1564
1565 isl_seq_clr(aff->el + 1, 1 + d);
1566 isl_int_set_si(aff->el[0], 1);
1567
1568 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1569 goto error;
1570
1571 return aff;
1572 error:
1573 isl_vec_free(aff);
1574 return NULL;
1575 }
1576
1577 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1578 __isl_keep isl_qpolynomial *qp2)
1579 {
1580 if (!qp1 || !qp2)
1581 return -1;
1582
1583 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1584 }
1585
1586 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1587 {
1588 int i;
1589 struct isl_upoly_rec *rec;
1590
1591 if (isl_upoly_is_cst(up)) {
1592 struct isl_upoly_cst *cst;
1593 cst = isl_upoly_as_cst(up);
1594 if (!cst)
1595 return;
1596 isl_int_lcm(*d, *d, cst->d);
1597 return;
1598 }
1599
1600 rec = isl_upoly_as_rec(up);
1601 if (!rec)
1602 return;
1603
1604 for (i = 0; i < rec->n; ++i)
1605 upoly_update_den(rec->p[i], d);
1606 }
1607
1608 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1609 {
1610 isl_int_set_si(*d, 1);
1611 if (!qp)
1612 return;
1613 upoly_update_den(qp->upoly, d);
1614 }
1615
1616 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1617 int pos, int power)
1618 {
1619 struct isl_ctx *ctx;
1620
1621 if (!dim)
1622 return NULL;
1623
1624 ctx = dim->ctx;
1625
1626 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1627 }
1628
1629 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1630 enum isl_dim_type type, unsigned pos)
1631 {
1632 if (!dim)
1633 return NULL;
1634
1635 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1636 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1637
1638 if (type == isl_dim_set)
1639 pos += isl_dim_size(dim, isl_dim_param);
1640
1641 return isl_qpolynomial_pow(dim, pos, 1);
1642 error:
1643 isl_dim_free(dim);
1644 return NULL;
1645 }
1646
1647 /* Remove common factor of non-constant terms and denominator.
1648 */
1649 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1650 {
1651 isl_ctx *ctx = qp->div->ctx;
1652 unsigned total = qp->div->n_col - 2;
1653
1654 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1655 isl_int_gcd(ctx->normalize_gcd,
1656 ctx->normalize_gcd, qp->div->row[div][0]);
1657 if (isl_int_is_one(ctx->normalize_gcd))
1658 return;
1659
1660 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1661 ctx->normalize_gcd, total);
1662 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1663 ctx->normalize_gcd);
1664 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1665 ctx->normalize_gcd);
1666 }
1667
1668 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1669 int power)
1670 {
1671 struct isl_qpolynomial *qp = NULL;
1672 struct isl_upoly_rec *rec;
1673 struct isl_upoly_cst *cst;
1674 int i, d;
1675 int pos;
1676
1677 if (!div)
1678 return NULL;
1679
1680 d = div->line - div->bmap->div;
1681
1682 pos = isl_dim_total(div->bmap->dim) + d;
1683 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1684 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1685 div->bmap->n_div, &rec->up);
1686 if (!qp)
1687 goto error;
1688
1689 for (i = 0; i < div->bmap->n_div; ++i) {
1690 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1691 normalize_div(qp, i);
1692 }
1693
1694 for (i = 0; i < 1 + power; ++i) {
1695 rec->p[i] = isl_upoly_zero(div->ctx);
1696 if (!rec->p[i])
1697 goto error;
1698 rec->n++;
1699 }
1700 cst = isl_upoly_as_cst(rec->p[power]);
1701 isl_int_set_si(cst->n, 1);
1702
1703 isl_div_free(div);
1704
1705 qp = sort_divs(qp);
1706
1707 return qp;
1708 error:
1709 isl_qpolynomial_free(qp);
1710 isl_div_free(div);
1711 return NULL;
1712 }
1713
1714 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1715 {
1716 return isl_qpolynomial_div_pow(div, 1);
1717 }
1718
1719 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1720 const isl_int n, const isl_int d)
1721 {
1722 struct isl_qpolynomial *qp;
1723 struct isl_upoly_cst *cst;
1724
1725 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1726 if (!qp)
1727 return NULL;
1728
1729 cst = isl_upoly_as_cst(qp->upoly);
1730 isl_int_set(cst->n, n);
1731 isl_int_set(cst->d, d);
1732
1733 return qp;
1734 }
1735
1736 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1737 {
1738 struct isl_upoly_rec *rec;
1739 int i;
1740
1741 if (!up)
1742 return -1;
1743
1744 if (isl_upoly_is_cst(up))
1745 return 0;
1746
1747 if (up->var < d)
1748 active[up->var] = 1;
1749
1750 rec = isl_upoly_as_rec(up);
1751 for (i = 0; i < rec->n; ++i)
1752 if (up_set_active(rec->p[i], active, d) < 0)
1753 return -1;
1754
1755 return 0;
1756 }
1757
1758 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1759 {
1760 int i, j;
1761 int d = isl_dim_total(qp->dim);
1762
1763 if (!qp || !active)
1764 return -1;
1765
1766 for (i = 0; i < d; ++i)
1767 for (j = 0; j < qp->div->n_row; ++j) {
1768 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1769 continue;
1770 active[i] = 1;
1771 break;
1772 }
1773
1774 return up_set_active(qp->upoly, active, d);
1775 }
1776
1777 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1778 enum isl_dim_type type, unsigned first, unsigned n)
1779 {
1780 int i;
1781 int *active = NULL;
1782 int involves = 0;
1783
1784 if (!qp)
1785 return -1;
1786 if (n == 0)
1787 return 0;
1788
1789 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1790 return -1);
1791 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1792 type == isl_dim_set, return -1);
1793
1794 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1795 if (set_active(qp, active) < 0)
1796 goto error;
1797
1798 if (type == isl_dim_set)
1799 first += isl_dim_size(qp->dim, isl_dim_param);
1800 for (i = 0; i < n; ++i)
1801 if (active[first + i]) {
1802 involves = 1;
1803 break;
1804 }
1805
1806 free(active);
1807
1808 return involves;
1809 error:
1810 free(active);
1811 return -1;
1812 }
1813
1814 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1815 unsigned first, unsigned n)
1816 {
1817 int i;
1818 struct isl_upoly_rec *rec;
1819
1820 if (!up)
1821 return NULL;
1822 if (n == 0 || up->var < 0 || up->var < first)
1823 return up;
1824 if (up->var < first + n) {
1825 up = replace_by_constant_term(up);
1826 return isl_upoly_drop(up, first, n);
1827 }
1828 up = isl_upoly_cow(up);
1829 if (!up)
1830 return NULL;
1831 up->var -= n;
1832 rec = isl_upoly_as_rec(up);
1833 if (!rec)
1834 goto error;
1835
1836 for (i = 0; i < rec->n; ++i) {
1837 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1838 if (!rec->p[i])
1839 goto error;
1840 }
1841
1842 return up;
1843 error:
1844 isl_upoly_free(up);
1845 return NULL;
1846 }
1847
1848 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1849 __isl_take isl_qpolynomial *qp,
1850 enum isl_dim_type type, unsigned pos, const char *s)
1851 {
1852 qp = isl_qpolynomial_cow(qp);
1853 if (!qp)
1854 return NULL;
1855 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1856 if (!qp->dim)
1857 goto error;
1858 return qp;
1859 error:
1860 isl_qpolynomial_free(qp);
1861 return NULL;
1862 }
1863
1864 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1865 __isl_take isl_qpolynomial *qp,
1866 enum isl_dim_type type, unsigned first, unsigned n)
1867 {
1868 if (!qp)
1869 return NULL;
1870 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1871 return qp;
1872
1873 qp = isl_qpolynomial_cow(qp);
1874 if (!qp)
1875 return NULL;
1876
1877 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1878 goto error);
1879 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1880 type == isl_dim_set, goto error);
1881
1882 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1883 if (!qp->dim)
1884 goto error;
1885
1886 if (type == isl_dim_set)
1887 first += isl_dim_size(qp->dim, isl_dim_param);
1888
1889 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1890 if (!qp->div)
1891 goto error;
1892
1893 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1894 if (!qp->upoly)
1895 goto error;
1896
1897 return qp;
1898 error:
1899 isl_qpolynomial_free(qp);
1900 return NULL;
1901 }
1902
1903 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1904 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1905 {
1906 int i;
1907 struct isl_upoly_rec *rec;
1908 struct isl_upoly *base, *res;
1909
1910 if (!up)
1911 return NULL;
1912
1913 if (isl_upoly_is_cst(up))
1914 return up;
1915
1916 if (up->var < first)
1917 return up;
1918
1919 rec = isl_upoly_as_rec(up);
1920 if (!rec)
1921 goto error;
1922
1923 isl_assert(up->ctx, rec->n >= 1, goto error);
1924
1925 if (up->var >= first + n)
1926 base = isl_upoly_pow(up->ctx, up->var, 1);
1927 else
1928 base = isl_upoly_copy(subs[up->var - first]);
1929
1930 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1931 for (i = rec->n - 2; i >= 0; --i) {
1932 struct isl_upoly *t;
1933 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1934 res = isl_upoly_mul(res, isl_upoly_copy(base));
1935 res = isl_upoly_sum(res, t);
1936 }
1937
1938 isl_upoly_free(base);
1939 isl_upoly_free(up);
1940
1941 return res;
1942 error:
1943 isl_upoly_free(up);
1944 return NULL;
1945 }
1946
1947 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1948 isl_int denom, unsigned len)
1949 {
1950 int i;
1951 struct isl_upoly *up;
1952
1953 isl_assert(ctx, len >= 1, return NULL);
1954
1955 up = isl_upoly_rat_cst(ctx, f[0], denom);
1956 for (i = 0; i < len - 1; ++i) {
1957 struct isl_upoly *t;
1958 struct isl_upoly *c;
1959
1960 if (isl_int_is_zero(f[1 + i]))
1961 continue;
1962
1963 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1964 t = isl_upoly_pow(ctx, i, 1);
1965 t = isl_upoly_mul(c, t);
1966 up = isl_upoly_sum(up, t);
1967 }
1968
1969 return up;
1970 }
1971
1972 /* Replace the integer division identified by "div" by the polynomial "s".
1973 * The integer division is assumed not to appear in the definition
1974 * of any other integer divisions.
1975 */
1976 static __isl_give isl_qpolynomial *substitute_div(
1977 __isl_take isl_qpolynomial *qp,
1978 int div, __isl_take struct isl_upoly *s)
1979 {
1980 int i;
1981 int total;
1982 int *reordering;
1983
1984 if (!qp || !s)
1985 goto error;
1986
1987 qp = isl_qpolynomial_cow(qp);
1988 if (!qp)
1989 goto error;
1990
1991 total = isl_dim_total(qp->dim);
1992 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1993 if (!qp->upoly)
1994 goto error;
1995
1996 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1997 if (!reordering)
1998 goto error;
1999 for (i = 0; i < total + div; ++i)
2000 reordering[i] = i;
2001 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
2002 reordering[i] = i - 1;
2003 qp->div = isl_mat_drop_rows(qp->div, div, 1);
2004 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2005 qp->upoly = reorder(qp->upoly, reordering);
2006 free(reordering);
2007
2008 if (!qp->upoly || !qp->div)
2009 goto error;
2010
2011 isl_upoly_free(s);
2012 return qp;
2013 error:
2014 isl_qpolynomial_free(qp);
2015 isl_upoly_free(s);
2016 return NULL;
2017 }
2018
2019 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2020 * divisions because d is equal to 1 by their definition, i.e., e.
2021 */
2022 static __isl_give isl_qpolynomial *substitute_non_divs(
2023 __isl_take isl_qpolynomial *qp)
2024 {
2025 int i, j;
2026 int total;
2027 struct isl_upoly *s;
2028
2029 if (!qp)
2030 return NULL;
2031
2032 total = isl_dim_total(qp->dim);
2033 for (i = 0; qp && i < qp->div->n_row; ++i) {
2034 if (!isl_int_is_one(qp->div->row[i][0]))
2035 continue;
2036 for (j = i + 1; j < qp->div->n_row; ++j) {
2037 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2038 continue;
2039 isl_seq_combine(qp->div->row[j] + 1,
2040 qp->div->ctx->one, qp->div->row[j] + 1,
2041 qp->div->row[j][2 + total + i],
2042 qp->div->row[i] + 1, 1 + total + i);
2043 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2044 normalize_div(qp, j);
2045 }
2046 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2047 qp->div->row[i][0], qp->div->n_col - 1);
2048 qp = substitute_div(qp, i, s);
2049 --i;
2050 }
2051
2052 return qp;
2053 }
2054
2055 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2056 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2057 {
2058 int i, j, k;
2059 isl_int denom;
2060 unsigned total;
2061 unsigned n_div;
2062 struct isl_upoly *up;
2063
2064 if (!eq)
2065 goto error;
2066 if (eq->n_eq == 0) {
2067 isl_basic_set_free(eq);
2068 return qp;
2069 }
2070
2071 qp = isl_qpolynomial_cow(qp);
2072 if (!qp)
2073 goto error;
2074 qp->div = isl_mat_cow(qp->div);
2075 if (!qp->div)
2076 goto error;
2077
2078 total = 1 + isl_dim_total(eq->dim);
2079 n_div = eq->n_div;
2080 isl_int_init(denom);
2081 for (i = 0; i < eq->n_eq; ++i) {
2082 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2083 if (j < 0 || j == 0 || j >= total)
2084 continue;
2085
2086 for (k = 0; k < qp->div->n_row; ++k) {
2087 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2088 continue;
2089 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2090 &qp->div->row[k][0]);
2091 normalize_div(qp, k);
2092 }
2093
2094 if (isl_int_is_pos(eq->eq[i][j]))
2095 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2096 isl_int_abs(denom, eq->eq[i][j]);
2097 isl_int_set_si(eq->eq[i][j], 0);
2098
2099 up = isl_upoly_from_affine(qp->dim->ctx,
2100 eq->eq[i], denom, total);
2101 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2102 isl_upoly_free(up);
2103 }
2104 isl_int_clear(denom);
2105
2106 if (!qp->upoly)
2107 goto error;
2108
2109 isl_basic_set_free(eq);
2110
2111 qp = substitute_non_divs(qp);
2112 qp = sort_divs(qp);
2113
2114 return qp;
2115 error:
2116 isl_basic_set_free(eq);
2117 isl_qpolynomial_free(qp);
2118 return NULL;
2119 }
2120
2121 static __isl_give isl_basic_set *add_div_constraints(
2122 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2123 {
2124 int i;
2125 unsigned total;
2126
2127 if (!bset || !div)
2128 goto error;
2129
2130 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2131 if (!bset)
2132 goto error;
2133 total = isl_basic_set_total_dim(bset);
2134 for (i = 0; i < div->n_row; ++i)
2135 if (isl_basic_set_add_div_constraints_var(bset,
2136 total - div->n_row + i, div->row[i]) < 0)
2137 goto error;
2138
2139 isl_mat_free(div);
2140 return bset;
2141 error:
2142 isl_mat_free(div);
2143 isl_basic_set_free(bset);
2144 return NULL;
2145 }
2146
2147 /* Look for equalities among the variables shared by context and qp
2148 * and the integer divisions of qp, if any.
2149 * The equalities are then used to eliminate variables and/or integer
2150 * divisions from qp.
2151 */
2152 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2153 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2154 {
2155 isl_basic_set *aff;
2156
2157 if (!qp)
2158 goto error;
2159 if (qp->div->n_row > 0) {
2160 isl_basic_set *bset;
2161 context = isl_set_add_dims(context, isl_dim_set,
2162 qp->div->n_row);
2163 bset = isl_basic_set_universe(isl_set_get_dim(context));
2164 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2165 context = isl_set_intersect(context,
2166 isl_set_from_basic_set(bset));
2167 }
2168
2169 aff = isl_set_affine_hull(context);
2170 return isl_qpolynomial_substitute_equalities(qp, aff);
2171 error:
2172 isl_qpolynomial_free(qp);
2173 isl_set_free(context);
2174 return NULL;
2175 }
2176
2177 #undef PW
2178 #define PW isl_pw_qpolynomial
2179 #undef EL
2180 #define EL isl_qpolynomial
2181 #undef IS_ZERO
2182 #define IS_ZERO is_zero
2183 #undef FIELD
2184 #define FIELD qp
2185
2186 #include <isl_pw_templ.c>
2187
2188 #undef UNION
2189 #define UNION isl_union_pw_qpolynomial
2190 #undef PART
2191 #define PART isl_pw_qpolynomial
2192 #undef PARTS
2193 #define PARTS pw_qpolynomial
2194
2195 #include <isl_union_templ.c>
2196
2197 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2198 {
2199 if (!pwqp)
2200 return -1;
2201
2202 if (pwqp->n != -1)
2203 return 0;
2204
2205 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2206 return 0;
2207
2208 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2209 }
2210
2211 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2212 __isl_take isl_pw_qpolynomial *pwqp1,
2213 __isl_take isl_pw_qpolynomial *pwqp2)
2214 {
2215 int i, j, n;
2216 struct isl_pw_qpolynomial *res;
2217 isl_set *set;
2218
2219 if (!pwqp1 || !pwqp2)
2220 goto error;
2221
2222 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2223 goto error);
2224
2225 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2226 isl_pw_qpolynomial_free(pwqp2);
2227 return pwqp1;
2228 }
2229
2230 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2231 isl_pw_qpolynomial_free(pwqp1);
2232 return pwqp2;
2233 }
2234
2235 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2236 isl_pw_qpolynomial_free(pwqp1);
2237 return pwqp2;
2238 }
2239
2240 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2241 isl_pw_qpolynomial_free(pwqp2);
2242 return pwqp1;
2243 }
2244
2245 n = pwqp1->n * pwqp2->n;
2246 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2247
2248 for (i = 0; i < pwqp1->n; ++i) {
2249 for (j = 0; j < pwqp2->n; ++j) {
2250 struct isl_set *common;
2251 struct isl_qpolynomial *prod;
2252 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2253 isl_set_copy(pwqp2->p[j].set));
2254 if (isl_set_fast_is_empty(common)) {
2255 isl_set_free(common);
2256 continue;
2257 }
2258
2259 prod = isl_qpolynomial_mul(
2260 isl_qpolynomial_copy(pwqp1->p[i].qp),
2261 isl_qpolynomial_copy(pwqp2->p[j].qp));
2262
2263 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2264 }
2265 }
2266
2267 isl_pw_qpolynomial_free(pwqp1);
2268 isl_pw_qpolynomial_free(pwqp2);
2269
2270 return res;
2271 error:
2272 isl_pw_qpolynomial_free(pwqp1);
2273 isl_pw_qpolynomial_free(pwqp2);
2274 return NULL;
2275 }
2276
2277 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2278 __isl_take isl_pw_qpolynomial *pwqp)
2279 {
2280 int i;
2281
2282 if (!pwqp)
2283 return NULL;
2284
2285 if (isl_pw_qpolynomial_is_zero(pwqp))
2286 return pwqp;
2287
2288 pwqp = isl_pw_qpolynomial_cow(pwqp);
2289 if (!pwqp)
2290 return NULL;
2291
2292 for (i = 0; i < pwqp->n; ++i) {
2293 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2294 if (!pwqp->p[i].qp)
2295 goto error;
2296 }
2297
2298 return pwqp;
2299 error:
2300 isl_pw_qpolynomial_free(pwqp);
2301 return NULL;
2302 }
2303
2304 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2305 __isl_take isl_pw_qpolynomial *pwqp1,
2306 __isl_take isl_pw_qpolynomial *pwqp2)
2307 {
2308 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2309 }
2310
2311 __isl_give struct isl_upoly *isl_upoly_eval(
2312 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2313 {
2314 int i;
2315 struct isl_upoly_rec *rec;
2316 struct isl_upoly *res;
2317 struct isl_upoly *base;
2318
2319 if (isl_upoly_is_cst(up)) {
2320 isl_vec_free(vec);
2321 return up;
2322 }
2323
2324 rec = isl_upoly_as_rec(up);
2325 if (!rec)
2326 goto error;
2327
2328 isl_assert(up->ctx, rec->n >= 1, goto error);
2329
2330 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2331
2332 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2333 isl_vec_copy(vec));
2334
2335 for (i = rec->n - 2; i >= 0; --i) {
2336 res = isl_upoly_mul(res, isl_upoly_copy(base));
2337 res = isl_upoly_sum(res,
2338 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2339 isl_vec_copy(vec)));
2340 }
2341
2342 isl_upoly_free(base);
2343 isl_upoly_free(up);
2344 isl_vec_free(vec);
2345 return res;
2346 error:
2347 isl_upoly_free(up);
2348 isl_vec_free(vec);
2349 return NULL;
2350 }
2351
2352 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2353 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2354 {
2355 isl_vec *ext;
2356 struct isl_upoly *up;
2357 isl_dim *dim;
2358
2359 if (!qp || !pnt)
2360 goto error;
2361 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2362
2363 if (qp->div->n_row == 0)
2364 ext = isl_vec_copy(pnt->vec);
2365 else {
2366 int i;
2367 unsigned dim = isl_dim_total(qp->dim);
2368 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2369 if (!ext)
2370 goto error;
2371
2372 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2373 for (i = 0; i < qp->div->n_row; ++i) {
2374 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2375 1 + dim + i, &ext->el[1+dim+i]);
2376 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2377 qp->div->row[i][0]);
2378 }
2379 }
2380
2381 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2382 if (!up)
2383 goto error;
2384
2385 dim = isl_dim_copy(qp->dim);
2386 isl_qpolynomial_free(qp);
2387 isl_point_free(pnt);
2388
2389 return isl_qpolynomial_alloc(dim, 0, up);
2390 error:
2391 isl_qpolynomial_free(qp);
2392 isl_point_free(pnt);
2393 return NULL;
2394 }
2395
2396 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2397 __isl_keep struct isl_upoly_cst *cst2)
2398 {
2399 int cmp;
2400 isl_int t;
2401 isl_int_init(t);
2402 isl_int_mul(t, cst1->n, cst2->d);
2403 isl_int_submul(t, cst2->n, cst1->d);
2404 cmp = isl_int_sgn(t);
2405 isl_int_clear(t);
2406 return cmp;
2407 }
2408
2409 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2410 __isl_keep isl_qpolynomial *qp2)
2411 {
2412 struct isl_upoly_cst *cst1, *cst2;
2413
2414 if (!qp1 || !qp2)
2415 return -1;
2416 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2417 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2418 if (isl_qpolynomial_is_nan(qp1))
2419 return -1;
2420 if (isl_qpolynomial_is_nan(qp2))
2421 return -1;
2422 cst1 = isl_upoly_as_cst(qp1->upoly);
2423 cst2 = isl_upoly_as_cst(qp2->upoly);
2424
2425 return isl_upoly_cmp(cst1, cst2) <= 0;
2426 }
2427
2428 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2429 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2430 {
2431 struct isl_upoly_cst *cst1, *cst2;
2432 int cmp;
2433
2434 if (!qp1 || !qp2)
2435 goto error;
2436 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2437 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2438 cst1 = isl_upoly_as_cst(qp1->upoly);
2439 cst2 = isl_upoly_as_cst(qp2->upoly);
2440 cmp = isl_upoly_cmp(cst1, cst2);
2441
2442 if (cmp <= 0) {
2443 isl_qpolynomial_free(qp2);
2444 } else {
2445 isl_qpolynomial_free(qp1);
2446 qp1 = qp2;
2447 }
2448 return qp1;
2449 error:
2450 isl_qpolynomial_free(qp1);
2451 isl_qpolynomial_free(qp2);
2452 return NULL;
2453 }
2454
2455 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2456 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2457 {
2458 struct isl_upoly_cst *cst1, *cst2;
2459 int cmp;
2460
2461 if (!qp1 || !qp2)
2462 goto error;
2463 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2464 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2465 cst1 = isl_upoly_as_cst(qp1->upoly);
2466 cst2 = isl_upoly_as_cst(qp2->upoly);
2467 cmp = isl_upoly_cmp(cst1, cst2);
2468
2469 if (cmp >= 0) {
2470 isl_qpolynomial_free(qp2);
2471 } else {
2472 isl_qpolynomial_free(qp1);
2473 qp1 = qp2;
2474 }
2475 return qp1;
2476 error:
2477 isl_qpolynomial_free(qp1);
2478 isl_qpolynomial_free(qp2);
2479 return NULL;
2480 }
2481
2482 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2483 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2484 unsigned first, unsigned n)
2485 {
2486 unsigned total;
2487 unsigned g_pos;
2488 int *exp;
2489
2490 if (n == 0)
2491 return qp;
2492
2493 qp = isl_qpolynomial_cow(qp);
2494 if (!qp)
2495 return NULL;
2496
2497 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2498 goto error);
2499
2500 g_pos = pos(qp->dim, type) + first;
2501
2502 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2503 if (!qp->div)
2504 goto error;
2505
2506 total = qp->div->n_col - 2;
2507 if (total > g_pos) {
2508 int i;
2509 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2510 if (!exp)
2511 goto error;
2512 for (i = 0; i < total - g_pos; ++i)
2513 exp[i] = i + n;
2514 qp->upoly = expand(qp->upoly, exp, g_pos);
2515 free(exp);
2516 if (!qp->upoly)
2517 goto error;
2518 }
2519
2520 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2521 if (!qp->dim)
2522 goto error;
2523
2524 return qp;
2525 error:
2526 isl_qpolynomial_free(qp);
2527 return NULL;
2528 }
2529
2530 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2531 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2532 {
2533 unsigned pos;
2534
2535 pos = isl_qpolynomial_dim(qp, type);
2536
2537 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2538 }
2539
2540 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2541 __isl_take isl_pw_qpolynomial *pwqp,
2542 enum isl_dim_type type, unsigned n)
2543 {
2544 unsigned pos;
2545
2546 pos = isl_pw_qpolynomial_dim(pwqp, type);
2547
2548 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2549 }
2550
2551 static int *reordering_move(isl_ctx *ctx,
2552 unsigned len, unsigned dst, unsigned src, unsigned n)
2553 {
2554 int i;
2555 int *reordering;
2556
2557 reordering = isl_alloc_array(ctx, int, len);
2558 if (!reordering)
2559 return NULL;
2560
2561 if (dst <= src) {
2562 for (i = 0; i < dst; ++i)
2563 reordering[i] = i;
2564 for (i = 0; i < n; ++i)
2565 reordering[src + i] = dst + i;
2566 for (i = 0; i < src - dst; ++i)
2567 reordering[dst + i] = dst + n + i;
2568 for (i = 0; i < len - src - n; ++i)
2569 reordering[src + n + i] = src + n + i;
2570 } else {
2571 for (i = 0; i < src; ++i)
2572 reordering[i] = i;
2573 for (i = 0; i < n; ++i)
2574 reordering[src + i] = dst + i;
2575 for (i = 0; i < dst - src; ++i)
2576 reordering[src + n + i] = src + i;
2577 for (i = 0; i < len - dst - n; ++i)
2578 reordering[dst + n + i] = dst + n + i;
2579 }
2580
2581 return reordering;
2582 }
2583
2584 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2585 __isl_take isl_qpolynomial *qp,
2586 enum isl_dim_type dst_type, unsigned dst_pos,
2587 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2588 {
2589 unsigned g_dst_pos;
2590 unsigned g_src_pos;
2591 int *reordering;
2592
2593 qp = isl_qpolynomial_cow(qp);
2594 if (!qp)
2595 return NULL;
2596
2597 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2598 goto error);
2599
2600 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2601 g_src_pos = pos(qp->dim, src_type) + src_pos;
2602 if (dst_type > src_type)
2603 g_dst_pos -= n;
2604
2605 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2606 if (!qp->div)
2607 goto error;
2608 qp = sort_divs(qp);
2609 if (!qp)
2610 goto error;
2611
2612 reordering = reordering_move(qp->dim->ctx,
2613 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2614 if (!reordering)
2615 goto error;
2616
2617 qp->upoly = reorder(qp->upoly, reordering);
2618 free(reordering);
2619 if (!qp->upoly)
2620 goto error;
2621
2622 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2623 if (!qp->dim)
2624 goto error;
2625
2626 return qp;
2627 error:
2628 isl_qpolynomial_free(qp);
2629 return NULL;
2630 }
2631
2632 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2633 isl_int *f, isl_int denom)
2634 {
2635 struct isl_upoly *up;
2636
2637 if (!dim)
2638 return NULL;
2639
2640 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2641
2642 return isl_qpolynomial_alloc(dim, 0, up);
2643 }
2644
2645 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2646 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2647 {
2648 isl_int denom;
2649 isl_dim *dim;
2650 struct isl_upoly *up;
2651 isl_qpolynomial *qp;
2652 int sgn;
2653
2654 if (!c)
2655 return NULL;
2656
2657 isl_int_init(denom);
2658
2659 isl_constraint_get_coefficient(c, type, pos, &denom);
2660 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2661 sgn = isl_int_sgn(denom);
2662 isl_int_abs(denom, denom);
2663 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2664 1 + isl_constraint_dim(c, isl_dim_all));
2665 if (sgn < 0)
2666 isl_int_neg(denom, denom);
2667 isl_constraint_set_coefficient(c, type, pos, denom);
2668
2669 dim = isl_dim_copy(c->bmap->dim);
2670
2671 isl_int_clear(denom);
2672 isl_constraint_free(c);
2673
2674 qp = isl_qpolynomial_alloc(dim, 0, up);
2675 if (sgn > 0)
2676 qp = isl_qpolynomial_neg(qp);
2677 return qp;
2678 }
2679
2680 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2681 * in "qp" by subs[i].
2682 */
2683 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2684 __isl_take isl_qpolynomial *qp,
2685 enum isl_dim_type type, unsigned first, unsigned n,
2686 __isl_keep isl_qpolynomial **subs)
2687 {
2688 int i;
2689 struct isl_upoly **ups;
2690
2691 if (n == 0)
2692 return qp;
2693
2694 qp = isl_qpolynomial_cow(qp);
2695 if (!qp)
2696 return NULL;
2697 for (i = 0; i < n; ++i)
2698 if (!subs[i])
2699 goto error;
2700
2701 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2702 goto error);
2703
2704 for (i = 0; i < n; ++i)
2705 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2706 goto error);
2707
2708 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2709 for (i = 0; i < n; ++i)
2710 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2711
2712 first += pos(qp->dim, type);
2713
2714 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2715 if (!ups)
2716 goto error;
2717 for (i = 0; i < n; ++i)
2718 ups[i] = subs[i]->upoly;
2719
2720 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2721
2722 free(ups);
2723
2724 if (!qp->upoly)
2725 goto error;
2726
2727 return qp;
2728 error:
2729 isl_qpolynomial_free(qp);
2730 return NULL;
2731 }
2732
2733 /* Extend "bset" with extra set dimensions for each integer division
2734 * in "qp" and then call "fn" with the extended bset and the polynomial
2735 * that results from replacing each of the integer divisions by the
2736 * corresponding extra set dimension.
2737 */
2738 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2739 __isl_keep isl_basic_set *bset,
2740 int (*fn)(__isl_take isl_basic_set *bset,
2741 __isl_take isl_qpolynomial *poly, void *user), void *user)
2742 {
2743 isl_dim *dim;
2744 isl_mat *div;
2745 isl_qpolynomial *poly;
2746
2747 if (!qp || !bset)
2748 goto error;
2749 if (qp->div->n_row == 0)
2750 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2751 user);
2752
2753 div = isl_mat_copy(qp->div);
2754 dim = isl_dim_copy(qp->dim);
2755 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2756 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2757 bset = isl_basic_set_copy(bset);
2758 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2759 bset = add_div_constraints(bset, div);
2760
2761 return fn(bset, poly, user);
2762 error:
2763 return -1;
2764 }
2765
2766 /* Return total degree in variables first (inclusive) up to last (exclusive).
2767 */
2768 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2769 {
2770 int deg = -1;
2771 int i;
2772 struct isl_upoly_rec *rec;
2773
2774 if (!up)
2775 return -2;
2776 if (isl_upoly_is_zero(up))
2777 return -1;
2778 if (isl_upoly_is_cst(up) || up->var < first)
2779 return 0;
2780
2781 rec = isl_upoly_as_rec(up);
2782 if (!rec)
2783 return -2;
2784
2785 for (i = 0; i < rec->n; ++i) {
2786 int d;
2787
2788 if (isl_upoly_is_zero(rec->p[i]))
2789 continue;
2790 d = isl_upoly_degree(rec->p[i], first, last);
2791 if (up->var < last)
2792 d += i;
2793 if (d > deg)
2794 deg = d;
2795 }
2796
2797 return deg;
2798 }
2799
2800 /* Return total degree in set variables.
2801 */
2802 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2803 {
2804 unsigned ovar;
2805 unsigned nvar;
2806
2807 if (!poly)
2808 return -2;
2809
2810 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2811 nvar = isl_dim_size(poly->dim, isl_dim_set);
2812 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2813 }
2814
2815 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2816 unsigned pos, int deg)
2817 {
2818 int i;
2819 struct isl_upoly_rec *rec;
2820
2821 if (!up)
2822 return NULL;
2823
2824 if (isl_upoly_is_cst(up) || up->var < pos) {
2825 if (deg == 0)
2826 return isl_upoly_copy(up);
2827 else
2828 return isl_upoly_zero(up->ctx);
2829 }
2830
2831 rec = isl_upoly_as_rec(up);
2832 if (!rec)
2833 return NULL;
2834
2835 if (up->var == pos) {
2836 if (deg < rec->n)
2837 return isl_upoly_copy(rec->p[deg]);
2838 else
2839 return isl_upoly_zero(up->ctx);
2840 }
2841
2842 up = isl_upoly_copy(up);
2843 up = isl_upoly_cow(up);
2844 rec = isl_upoly_as_rec(up);
2845 if (!rec)
2846 goto error;
2847
2848 for (i = 0; i < rec->n; ++i) {
2849 struct isl_upoly *t;
2850 t = isl_upoly_coeff(rec->p[i], pos, deg);
2851 if (!t)
2852 goto error;
2853 isl_upoly_free(rec->p[i]);
2854 rec->p[i] = t;
2855 }
2856
2857 return up;
2858 error:
2859 isl_upoly_free(up);
2860 return NULL;
2861 }
2862
2863 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2864 */
2865 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2866 __isl_keep isl_qpolynomial *qp,
2867 enum isl_dim_type type, unsigned t_pos, int deg)
2868 {
2869 unsigned g_pos;
2870 struct isl_upoly *up;
2871 isl_qpolynomial *c;
2872
2873 if (!qp)
2874 return NULL;
2875
2876 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2877 return NULL);
2878
2879 g_pos = pos(qp->dim, type) + t_pos;
2880 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2881
2882 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2883 if (!c)
2884 return NULL;
2885 isl_mat_free(c->div);
2886 c->div = isl_mat_copy(qp->div);
2887 if (!c->div)
2888 goto error;
2889 return c;
2890 error:
2891 isl_qpolynomial_free(c);
2892 return NULL;
2893 }
2894
2895 /* Homogenize the polynomial in the variables first (inclusive) up to
2896 * last (exclusive) by inserting powers of variable first.
2897 * Variable first is assumed not to appear in the input.
2898 */
2899 __isl_give struct isl_upoly *isl_upoly_homogenize(
2900 __isl_take struct isl_upoly *up, int deg, int target,
2901 int first, int last)
2902 {
2903 int i;
2904 struct isl_upoly_rec *rec;
2905
2906 if (!up)
2907 return NULL;
2908 if (isl_upoly_is_zero(up))
2909 return up;
2910 if (deg == target)
2911 return up;
2912 if (isl_upoly_is_cst(up) || up->var < first) {
2913 struct isl_upoly *hom;
2914
2915 hom = isl_upoly_pow(up->ctx, first, target - deg);
2916 if (!hom)
2917 goto error;
2918 rec = isl_upoly_as_rec(hom);
2919 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2920
2921 return hom;
2922 }
2923
2924 up = isl_upoly_cow(up);
2925 rec = isl_upoly_as_rec(up);
2926 if (!rec)
2927 goto error;
2928
2929 for (i = 0; i < rec->n; ++i) {
2930 if (isl_upoly_is_zero(rec->p[i]))
2931 continue;
2932 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2933 up->var < last ? deg + i : i, target,
2934 first, last);
2935 if (!rec->p[i])
2936 goto error;
2937 }
2938
2939 return up;
2940 error:
2941 isl_upoly_free(up);
2942 return NULL;
2943 }
2944
2945 /* Homogenize the polynomial in the set variables by introducing
2946 * powers of an extra set variable at position 0.
2947 */
2948 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2949 __isl_take isl_qpolynomial *poly)
2950 {
2951 unsigned ovar;
2952 unsigned nvar;
2953 int deg = isl_qpolynomial_degree(poly);
2954
2955 if (deg < -1)
2956 goto error;
2957
2958 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2959 poly = isl_qpolynomial_cow(poly);
2960 if (!poly)
2961 goto error;
2962
2963 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2964 nvar = isl_dim_size(poly->dim, isl_dim_set);
2965 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2966 ovar, ovar + nvar);
2967 if (!poly->upoly)
2968 goto error;
2969
2970 return poly;
2971 error:
2972 isl_qpolynomial_free(poly);
2973 return NULL;
2974 }
2975
2976 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2977 __isl_take isl_mat *div)
2978 {
2979 isl_term *term;
2980 int n;
2981
2982 if (!dim || !div)
2983 goto error;
2984
2985 n = isl_dim_total(dim) + div->n_row;
2986
2987 term = isl_calloc(dim->ctx, struct isl_term,
2988 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2989 if (!term)
2990 goto error;
2991
2992 term->ref = 1;
2993 term->dim = dim;
2994 term->div = div;
2995 isl_int_init(term->n);
2996 isl_int_init(term->d);
2997
2998 return term;
2999 error:
3000 isl_dim_free(dim);
3001 isl_mat_free(div);
3002 return NULL;
3003 }
3004
3005 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3006 {
3007 if (!term)
3008 return NULL;
3009
3010 term->ref++;
3011 return term;
3012 }
3013
3014 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3015 {
3016 int i;
3017 isl_term *dup;
3018 unsigned total;
3019
3020 if (term)
3021 return NULL;
3022
3023 total = isl_dim_total(term->dim) + term->div->n_row;
3024
3025 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3026 if (!dup)
3027 return NULL;
3028
3029 isl_int_set(dup->n, term->n);
3030 isl_int_set(dup->d, term->d);
3031
3032 for (i = 0; i < total; ++i)
3033 dup->pow[i] = term->pow[i];
3034
3035 return dup;
3036 }
3037
3038 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3039 {
3040 if (!term)
3041 return NULL;
3042
3043 if (term->ref == 1)
3044 return term;
3045 term->ref--;
3046 return isl_term_dup(term);
3047 }
3048
3049 void isl_term_free(__isl_take isl_term *term)
3050 {
3051 if (!term)
3052 return;
3053
3054 if (--term->ref > 0)
3055 return;
3056
3057 isl_dim_free(term->dim);
3058 isl_mat_free(term->div);
3059 isl_int_clear(term->n);
3060 isl_int_clear(term->d);
3061 free(term);
3062 }
3063
3064 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3065 {
3066 if (!term)
3067 return 0;
3068
3069 switch (type) {
3070 case isl_dim_param:
3071 case isl_dim_in:
3072 case isl_dim_out: return isl_dim_size(term->dim, type);
3073 case isl_dim_div: return term->div->n_row;
3074 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3075 default: return 0;
3076 }
3077 }
3078
3079 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3080 {
3081 return term ? term->dim->ctx : NULL;
3082 }
3083
3084 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3085 {
3086 if (!term)
3087 return;
3088 isl_int_set(*n, term->n);
3089 }
3090
3091 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3092 {
3093 if (!term)
3094 return;
3095 isl_int_set(*d, term->d);
3096 }
3097
3098 int isl_term_get_exp(__isl_keep isl_term *term,
3099 enum isl_dim_type type, unsigned pos)
3100 {
3101 if (!term)
3102 return -1;
3103
3104 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3105
3106 if (type >= isl_dim_set)
3107 pos += isl_dim_size(term->dim, isl_dim_param);
3108 if (type >= isl_dim_div)
3109 pos += isl_dim_size(term->dim, isl_dim_set);
3110
3111 return term->pow[pos];
3112 }
3113
3114 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3115 {
3116 isl_basic_map *bmap;
3117 unsigned total;
3118 int k;
3119
3120 if (!term)
3121 return NULL;
3122
3123 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3124 return NULL);
3125
3126 total = term->div->n_col - term->div->n_row - 2;
3127 /* No nested divs for now */
3128 isl_assert(term->dim->ctx,
3129 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3130 term->div->n_row) == -1,
3131 return NULL);
3132
3133 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3134 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3135 goto error;
3136
3137 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3138
3139 return isl_basic_map_div(bmap, k);
3140 error:
3141 isl_basic_map_free(bmap);
3142 return NULL;
3143 }
3144
3145 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3146 int (*fn)(__isl_take isl_term *term, void *user),
3147 __isl_take isl_term *term, void *user)
3148 {
3149 int i;
3150 struct isl_upoly_rec *rec;
3151
3152 if (!up || !term)
3153 goto error;
3154
3155 if (isl_upoly_is_zero(up))
3156 return term;
3157
3158 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3159 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3160 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3161
3162 if (isl_upoly_is_cst(up)) {
3163 struct isl_upoly_cst *cst;
3164 cst = isl_upoly_as_cst(up);
3165 if (!cst)
3166 goto error;
3167 term = isl_term_cow(term);
3168 if (!term)
3169 goto error;
3170 isl_int_set(term->n, cst->n);
3171 isl_int_set(term->d, cst->d);
3172 if (fn(isl_term_copy(term), user) < 0)
3173 goto error;
3174 return term;
3175 }
3176
3177 rec = isl_upoly_as_rec(up);
3178 if (!rec)
3179 goto error;
3180
3181 for (i = 0; i < rec->n; ++i) {
3182 term = isl_term_cow(term);
3183 if (!term)
3184 goto error;
3185 term->pow[up->var] = i;
3186 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3187 if (!term)
3188 goto error;
3189 }
3190 term->pow[up->var] = 0;
3191
3192 return term;
3193 error:
3194 isl_term_free(term);
3195 return NULL;
3196 }
3197
3198 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3199 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3200 {
3201 isl_term *term;
3202
3203 if (!qp)
3204 return -1;
3205
3206 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3207 if (!term)
3208 return -1;
3209
3210 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3211
3212 isl_term_free(term);
3213
3214 return term ? 0 : -1;
3215 }
3216
3217 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3218 {
3219 struct isl_upoly *up;
3220 isl_qpolynomial *qp;
3221 int i, n;
3222
3223 if (!term)
3224 return NULL;
3225
3226 n = isl_dim_total(term->dim) + term->div->n_row;
3227
3228 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3229 for (i = 0; i < n; ++i) {
3230 if (!term->pow[i])
3231 continue;
3232 up = isl_upoly_mul(up,
3233 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3234 }
3235
3236 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3237 if (!qp)
3238 goto error;
3239 isl_mat_free(qp->div);
3240 qp->div = isl_mat_copy(term->div);
3241 if (!qp->div)
3242 goto error;
3243
3244 isl_term_free(term);
3245 return qp;
3246 error:
3247 isl_qpolynomial_free(qp);
3248 isl_term_free(term);
3249 return NULL;
3250 }
3251
3252 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3253 __isl_take isl_dim *dim)
3254 {
3255 int i;
3256 int extra;
3257 unsigned total;
3258
3259 if (!qp || !dim)
3260 goto error;
3261
3262 if (isl_dim_equal(qp->dim, dim)) {
3263 isl_dim_free(dim);
3264 return qp;
3265 }
3266
3267 qp = isl_qpolynomial_cow(qp);
3268 if (!qp)
3269 goto error;
3270
3271 extra = isl_dim_size(dim, isl_dim_set) -
3272 isl_dim_size(qp->dim, isl_dim_set);
3273 total = isl_dim_total(qp->dim);
3274 if (qp->div->n_row) {
3275 int *exp;
3276
3277 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3278 if (!exp)
3279 goto error;
3280 for (i = 0; i < qp->div->n_row; ++i)
3281 exp[i] = extra + i;
3282 qp->upoly = expand(qp->upoly, exp, total);
3283 free(exp);
3284 if (!qp->upoly)
3285 goto error;
3286 }
3287 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3288 if (!qp->div)
3289 goto error;
3290 for (i = 0; i < qp->div->n_row; ++i)
3291 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3292
3293 isl_dim_free(qp->dim);
3294 qp->dim = dim;
3295
3296 return qp;
3297 error:
3298 isl_dim_free(dim);
3299 isl_qpolynomial_free(qp);
3300 return NULL;
3301 }
3302
3303 /* For each parameter or variable that does not appear in qp,
3304 * first eliminate the variable from all constraints and then set it to zero.
3305 */
3306 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3307 __isl_keep isl_qpolynomial *qp)
3308 {
3309 int *active = NULL;
3310 int i;
3311 int d;
3312 unsigned nparam;
3313 unsigned nvar;
3314
3315 if (!set || !qp)
3316 goto error;
3317
3318 d = isl_dim_total(set->dim);
3319 active = isl_calloc_array(set->ctx, int, d);
3320 if (set_active(qp, active) < 0)
3321 goto error;
3322
3323 for (i = 0; i < d; ++i)
3324 if (!active[i])
3325 break;
3326
3327 if (i == d) {
3328 free(active);
3329 return set;
3330 }
3331
3332 nparam = isl_dim_size(set->dim, isl_dim_param);
3333 nvar = isl_dim_size(set->dim, isl_dim_set);
3334 for (i = 0; i < nparam; ++i) {
3335 if (active[i])
3336 continue;
3337 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3338 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3339 }
3340 for (i = 0; i < nvar; ++i) {
3341 if (active[nparam + i])
3342 continue;
3343 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3344 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3345 }
3346
3347 free(active);
3348
3349 return set;
3350 error:
3351 free(active);
3352 isl_set_free(set);
3353 return NULL;
3354 }
3355
3356 struct isl_opt_data {
3357 isl_qpolynomial *qp;
3358 int first;
3359 isl_qpolynomial *opt;
3360 int max;
3361 };
3362
3363 static int opt_fn(__isl_take isl_point *pnt, void *user)
3364 {
3365 struct isl_opt_data *data = (struct isl_opt_data *)user;
3366 isl_qpolynomial *val;
3367
3368 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3369 if (data->first) {
3370 data->first = 0;
3371 data->opt = val;
3372 } else if (data->max) {
3373 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3374 } else {
3375 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3376 }
3377
3378 return 0;
3379 }
3380
3381 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3382 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3383 {
3384 struct isl_opt_data data = { NULL, 1, NULL, max };
3385
3386 if (!set || !qp)
3387 goto error;
3388
3389 if (isl_upoly_is_cst(qp->upoly)) {
3390 isl_set_free(set);
3391 return qp;
3392 }
3393
3394 set = fix_inactive(set, qp);
3395
3396 data.qp = qp;
3397 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3398 goto error;
3399
3400 if (data.first)
3401 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3402
3403 isl_set_free(set);
3404 isl_qpolynomial_free(qp);
3405 return data.opt;
3406 error:
3407 isl_set_free(set);
3408 isl_qpolynomial_free(qp);
3409 isl_qpolynomial_free(data.opt);
3410 return NULL;
3411 }
3412
3413 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3414 __isl_take isl_morph *morph)
3415 {
3416 int i;
3417 int n_sub;
3418 isl_ctx *ctx;
3419 struct isl_upoly *up;
3420 unsigned n_div;
3421 struct isl_upoly **subs;
3422 isl_mat *mat;
3423
3424 qp = isl_qpolynomial_cow(qp);
3425 if (!qp || !morph)
3426 goto error;
3427
3428 ctx = qp->dim->ctx;
3429 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3430
3431 n_sub = morph->inv->n_row - 1;
3432 if (morph->inv->n_row != morph->inv->n_col)
3433 n_sub += qp->div->n_row;
3434 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3435 if (!subs)
3436 goto error;
3437
3438 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3439 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3440 morph->inv->row[0][0], morph->inv->n_col);
3441 if (morph->inv->n_row != morph->inv->n_col)
3442 for (i = 0; i < qp->div->n_row; ++i)
3443 subs[morph->inv->n_row - 1 + i] =
3444 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3445
3446 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3447
3448 for (i = 0; i < n_sub; ++i)
3449 isl_upoly_free(subs[i]);
3450 free(subs);
3451
3452 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3453 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3454 qp->div = isl_mat_product(qp->div, mat);
3455 isl_dim_free(qp->dim);
3456 qp->dim = isl_dim_copy(morph->ran->dim);
3457
3458 if (!qp->upoly || !qp->div || !qp->dim)
3459 goto error;
3460
3461 isl_morph_free(morph);
3462
3463 return qp;
3464 error:
3465 isl_qpolynomial_free(qp);
3466 isl_morph_free(morph);
3467 return NULL;
3468 }
3469
3470 static int neg_entry(void **entry, void *user)
3471 {
3472 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3473
3474 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3475
3476 return *pwqp ? 0 : -1;
3477 }
3478
3479 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3480 __isl_take isl_union_pw_qpolynomial *upwqp)
3481 {
3482 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3483 if (!upwqp)
3484 return NULL;
3485
3486 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3487 &neg_entry, NULL) < 0)
3488 goto error;
3489
3490 return upwqp;
3491 error:
3492 isl_union_pw_qpolynomial_free(upwqp);
3493 return NULL;
3494 }
3495
3496 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3497 __isl_take isl_union_pw_qpolynomial *upwqp1,
3498 __isl_take isl_union_pw_qpolynomial *upwqp2)
3499 {
3500 return isl_union_pw_qpolynomial_add(upwqp1,
3501 isl_union_pw_qpolynomial_neg(upwqp2));
3502 }
3503
3504 static int mul_entry(void **entry, void *user)
3505 {
3506 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3507 uint32_t hash;
3508 struct isl_hash_table_entry *entry2;
3509 isl_pw_qpolynomial *pwpq = *entry;
3510 int empty;
3511
3512 hash = isl_dim_get_hash(pwpq->dim);
3513 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3514 hash, &has_dim, pwpq->dim, 0);
3515 if (!entry2)
3516 return 0;
3517
3518 pwpq = isl_pw_qpolynomial_copy(pwpq);
3519 pwpq = isl_pw_qpolynomial_mul(pwpq,
3520 isl_pw_qpolynomial_copy(entry2->data));
3521
3522 empty = isl_pw_qpolynomial_is_zero(pwpq);
3523 if (empty < 0) {
3524 isl_pw_qpolynomial_free(pwpq);
3525 return -1;
3526 }
3527 if (empty) {
3528 isl_pw_qpolynomial_free(pwpq);
3529 return 0;
3530 }
3531
3532 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3533
3534 return 0;
3535 }
3536
3537 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3538 __isl_take isl_union_pw_qpolynomial *upwqp1,
3539 __isl_take isl_union_pw_qpolynomial *upwqp2)
3540 {
3541 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3542 }
3543
3544 /* Reorder the columns of the given div definitions according to the
3545 * given reordering.
3546 */
3547 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3548 __isl_take isl_reordering *r)
3549 {
3550 int i, j;
3551 isl_mat *mat;
3552 int extra;
3553
3554 if (!div || !r)
3555 goto error;
3556
3557 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3558 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3559 if (!mat)
3560 goto error;
3561
3562 for (i = 0; i < div->n_row; ++i) {
3563 isl_seq_cpy(mat->row[i], div->row[i], 2);
3564 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3565 for (j = 0; j < r->len; ++j)
3566 isl_int_set(mat->row[i][2 + r->pos[j]],
3567 div->row[i][2 + j]);
3568 }
3569
3570 isl_reordering_free(r);
3571 isl_mat_free(div);
3572 return mat;
3573 error:
3574 isl_reordering_free(r);
3575 isl_mat_free(div);
3576 return NULL;
3577 }
3578
3579 /* Reorder the dimension of "qp" according to the given reordering.
3580 */
3581 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3582 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3583 {
3584 qp = isl_qpolynomial_cow(qp);
3585 if (!qp)
3586 goto error;
3587
3588 r = isl_reordering_extend(r, qp->div->n_row);
3589 if (!r)
3590 goto error;
3591
3592 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3593 if (!qp->div)
3594 goto error;
3595
3596 qp->upoly = reorder(qp->upoly, r->pos);
3597 if (!qp->upoly)
3598 goto error;
3599
3600 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3601
3602 isl_reordering_free(r);
3603 return qp;
3604 error:
3605 isl_qpolynomial_free(qp);
3606 isl_reordering_free(r);
3607 return NULL;
3608 }
3609
3610 struct isl_split_periods_data {
3611 int max_periods;
3612 isl_pw_qpolynomial *res;
3613 };
3614
3615 /* Create a slice where the integer division "div" has the fixed value "v".
3616 * In particular, if "div" refers to floor(f/m), then create a slice
3617 *
3618 * m v <= f <= m v + (m - 1)
3619 *
3620 * or
3621 *
3622 * f - m v >= 0
3623 * -f + m v + (m - 1) >= 0
3624 */
3625 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3626 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3627 {
3628 int total;
3629 isl_basic_set *bset = NULL;
3630 int k;
3631
3632 if (!dim || !qp)
3633 goto error;
3634
3635 total = isl_dim_total(dim);
3636 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3637
3638 k = isl_basic_set_alloc_inequality(bset);
3639 if (k < 0)
3640 goto error;
3641 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3642 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3643
3644 k = isl_basic_set_alloc_inequality(bset);
3645 if (k < 0)
3646 goto error;
3647 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3648 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3649 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3650 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3651
3652 isl_dim_free(dim);
3653 return isl_set_from_basic_set(bset);
3654 error:
3655 isl_basic_set_free(bset);
3656 isl_dim_free(dim);
3657 return NULL;
3658 }
3659
3660 static int split_periods(__isl_take isl_set *set,
3661 __isl_take isl_qpolynomial *qp, void *user);
3662
3663 /* Create a slice of the domain "set" such that integer division "div"
3664 * has the fixed value "v" and add the results to data->res,
3665 * replacing the integer division by "v" in "qp".
3666 */
3667 static int set_div(__isl_take isl_set *set,
3668 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3669 struct isl_split_periods_data *data)
3670 {
3671 int i;
3672 int total;
3673 isl_set *slice;
3674 struct isl_upoly *cst;
3675
3676 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3677 set = isl_set_intersect(set, slice);
3678
3679 if (!qp)
3680 goto error;
3681
3682 total = isl_dim_total(qp->dim);
3683
3684 for (i = div + 1; i < qp->div->n_row; ++i) {
3685 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3686 continue;
3687 isl_int_addmul(qp->div->row[i][1],
3688 qp->div->row[i][2 + total + div], v);
3689 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3690 }
3691
3692 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3693 qp = substitute_div(qp, div, cst);
3694
3695 return split_periods(set, qp, data);
3696 error:
3697 isl_set_free(set);
3698 isl_qpolynomial_free(qp);
3699 return -1;
3700 }
3701
3702 /* Split the domain "set" such that integer division "div"
3703 * has a fixed value (ranging from "min" to "max") on each slice
3704 * and add the results to data->res.
3705 */
3706 static int split_div(__isl_take isl_set *set,
3707 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3708 struct isl_split_periods_data *data)
3709 {
3710 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3711 isl_set *set_i = isl_set_copy(set);
3712 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3713
3714 if (set_div(set_i, qp_i, div, min, data) < 0)
3715 goto error;
3716 }
3717 isl_set_free(set);
3718 isl_qpolynomial_free(qp);
3719 return 0;
3720 error:
3721 isl_set_free(set);
3722 isl_qpolynomial_free(qp);
3723 return -1;
3724 }
3725
3726 /* If "qp" refers to any integer division
3727 * that can only attain "max_periods" distinct values on "set"
3728 * then split the domain along those distinct values.
3729 * Add the results (or the original if no splitting occurs)
3730 * to data->res.
3731 */
3732 static int split_periods(__isl_take isl_set *set,
3733 __isl_take isl_qpolynomial *qp, void *user)
3734 {
3735 int i;
3736 isl_pw_qpolynomial *pwqp;
3737 struct isl_split_periods_data *data;
3738 isl_int min, max;
3739 int total;
3740 int r = 0;
3741
3742 data = (struct isl_split_periods_data *)user;
3743
3744 if (!set || !qp)
3745 goto error;
3746
3747 if (qp->div->n_row == 0) {
3748 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3749 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3750 return 0;
3751 }
3752
3753 isl_int_init(min);
3754 isl_int_init(max);
3755 total = isl_dim_total(qp->dim);
3756 for (i = 0; i < qp->div->n_row; ++i) {
3757 enum isl_lp_result lp_res;
3758
3759 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3760 qp->div->n_row) != -1)
3761 continue;
3762
3763 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3764 set->ctx->one, &min, NULL, NULL);
3765 if (lp_res == isl_lp_error)
3766 goto error2;
3767 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3768 continue;
3769 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3770
3771 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3772 set->ctx->one, &max, NULL, NULL);
3773 if (lp_res == isl_lp_error)
3774 goto error2;
3775 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3776 continue;
3777 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3778
3779 isl_int_sub(max, max, min);
3780 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3781 isl_int_add(max, max, min);
3782 break;
3783 }
3784 }
3785
3786 if (i < qp->div->n_row) {
3787 r = split_div(set, qp, i, min, max, data);
3788 } else {
3789 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3790 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3791 }
3792
3793 isl_int_clear(max);
3794 isl_int_clear(min);
3795
3796 return r;
3797 error2:
3798 isl_int_clear(max);
3799 isl_int_clear(min);
3800 error:
3801 isl_set_free(set);
3802 isl_qpolynomial_free(qp);
3803 return -1;
3804 }
3805
3806 /* If any quasi-polynomial in pwqp refers to any integer division
3807 * that can only attain "max_periods" distinct values on its domain
3808 * then split the domain along those distinct values.
3809 */
3810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3811 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3812 {
3813 struct isl_split_periods_data data;
3814
3815 data.max_periods = max_periods;
3816 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3817
3818 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3819 goto error;
3820
3821 isl_pw_qpolynomial_free(pwqp);
3822
3823 return data.res;
3824 error:
3825 isl_pw_qpolynomial_free(data.res);
3826 isl_pw_qpolynomial_free(pwqp);
3827 return NULL;
3828 }
3829
3830 /* Construct a piecewise quasipolynomial that is constant on the given
3831 * domain. In particular, it is
3832 * 0 if cst == 0
3833 * 1 if cst == 1
3834 * infinity if cst == -1
3835 */
3836 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3837 __isl_take isl_basic_set *bset, int cst)
3838 {
3839 isl_dim *dim;
3840 isl_qpolynomial *qp;
3841
3842 if (!bset)
3843 return NULL;
3844
3845 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3846 dim = isl_basic_set_get_dim(bset);
3847 if (cst < 0)
3848 qp = isl_qpolynomial_infty(dim);
3849 else if (cst == 0)
3850 qp = isl_qpolynomial_zero(dim);
3851 else
3852 qp = isl_qpolynomial_one(dim);
3853 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3854 }
3855
3856 /* Factor bset, call fn on each of the factors and return the product.
3857 *
3858 * If no factors can be found, simply call fn on the input.
3859 * Otherwise, construct the factors based on the factorizer,
3860 * call fn on each factor and compute the product.
3861 */
3862 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3863 __isl_take isl_basic_set *bset,
3864 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3865 {
3866 int i, n;
3867 isl_dim *dim;
3868 isl_set *set;
3869 isl_factorizer *f;
3870 isl_qpolynomial *qp;
3871 isl_pw_qpolynomial *pwqp;
3872 unsigned nparam;
3873 unsigned nvar;
3874
3875 f = isl_basic_set_factorizer(bset);
3876 if (!f)
3877 goto error;
3878 if (f->n_group == 0) {
3879 isl_factorizer_free(f);
3880 return fn(bset);
3881 }
3882
3883 nparam = isl_basic_set_dim(bset, isl_dim_param);
3884 nvar = isl_basic_set_dim(bset, isl_dim_set);
3885
3886 dim = isl_basic_set_get_dim(bset);
3887 dim = isl_dim_domain(dim);
3888 set = isl_set_universe(isl_dim_copy(dim));
3889 qp = isl_qpolynomial_one(dim);
3890 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3891
3892 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3893
3894 for (i = 0, n = 0; i < f->n_group; ++i) {
3895 isl_basic_set *bset_i;
3896 isl_pw_qpolynomial *pwqp_i;
3897
3898 bset_i = isl_basic_set_copy(bset);
3899 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3900 nparam + n + f->len[i], nvar - n - f->len[i]);
3901 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3902 nparam, n);
3903 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3904 n + f->len[i], nvar - n - f->len[i]);
3905 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3906
3907 pwqp_i = fn(bset_i);
3908 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3909
3910 n += f->len[i];
3911 }
3912
3913 isl_basic_set_free(bset);
3914 isl_factorizer_free(f);
3915
3916 return pwqp;
3917 error:
3918 isl_basic_set_free(bset);
3919 return NULL;
3920 }
3921
3922 /* Factor bset, call fn on each of the factors and return the product.
3923 * The function is assumed to evaluate to zero on empty domains,
3924 * to one on zero-dimensional domains and to infinity on unbounded domains
3925 * and will not be called explicitly on zero-dimensional or unbounded domains.
3926 *
3927 * We first check for some special cases and remove all equalities.
3928 * Then we hand over control to compressed_multiplicative_call.
3929 */
3930 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3931 __isl_take isl_basic_set *bset,
3932 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3933 {
3934 int bounded;
3935 isl_morph *morph;
3936 isl_pw_qpolynomial *pwqp;
3937 unsigned orig_nvar, final_nvar;
3938
3939 if (!bset)
3940 return NULL;
3941
3942 if (isl_basic_set_fast_is_empty(bset))
3943 return constant_on_domain(bset, 0);
3944
3945 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3946
3947 if (orig_nvar == 0)
3948 return constant_on_domain(bset, 1);
3949
3950 bounded = isl_basic_set_is_bounded(bset);
3951 if (bounded < 0)
3952 goto error;
3953 if (!bounded)
3954 return constant_on_domain(bset, -1);
3955
3956 if (bset->n_eq == 0)
3957 return compressed_multiplicative_call(bset, fn);
3958
3959 morph = isl_basic_set_full_compression(bset);
3960 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3961
3962 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3963
3964 pwqp = compressed_multiplicative_call(bset, fn);
3965
3966 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3967 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3968 morph = isl_morph_inverse(morph);
3969
3970 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3971
3972 return pwqp;
3973 error:
3974 isl_basic_set_free(bset);
3975 return NULL;
3976 }
3977
3978 /* Drop all floors in "qp", turning each integer division [a/m] into
3979 * a rational division a/m. If "down" is set, then the integer division
3980 * is replaces by (a-(m-1))/m instead.
3981 */
3982 static __isl_give isl_qpolynomial *qp_drop_floors(
3983 __isl_take isl_qpolynomial *qp, int down)
3984 {
3985 int i;
3986 struct isl_upoly *s;
3987
3988 if (!qp)
3989 return NULL;
3990 if (qp->div->n_row == 0)
3991 return qp;
3992
3993 qp = isl_qpolynomial_cow(qp);
3994 if (!qp)
3995 return NULL;
3996
3997 for (i = qp->div->n_row - 1; i >= 0; --i) {
3998 if (down) {
3999 isl_int_sub(qp->div->row[i][1],
4000 qp->div->row[i][1], qp->div->row[i][0]);
4001 isl_int_add_ui(qp->div->row[i][1],
4002 qp->div->row[i][1], 1);
4003 }
4004 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4005 qp->div->row[i][0], qp->div->n_col - 1);
4006 qp = substitute_div(qp, i, s);
4007 if (!qp)
4008 return NULL;
4009 }
4010
4011 return qp;
4012 }
4013
4014 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4015 * a rational division a/m.
4016 */
4017 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4018 __isl_take isl_pw_qpolynomial *pwqp)
4019 {
4020 int i;
4021
4022 if (!pwqp)
4023 return NULL;
4024
4025 if (isl_pw_qpolynomial_is_zero(pwqp))
4026 return pwqp;
4027
4028 pwqp = isl_pw_qpolynomial_cow(pwqp);
4029 if (!pwqp)
4030 return NULL;
4031
4032 for (i = 0; i < pwqp->n; ++i) {
4033 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4034 if (!pwqp->p[i].qp)
4035 goto error;
4036 }
4037
4038 return pwqp;
4039 error:
4040 isl_pw_qpolynomial_free(pwqp);
4041 return NULL;
4042 }
4043
4044 /* Adjust all the integer divisions in "qp" such that they are at least
4045 * one over the given orthant (identified by "signs"). This ensures
4046 * that they will still be non-negative even after subtracting (m-1)/m.
4047 *
4048 * In particular, f is replaced by f' + v, changing f = [a/m]
4049 * to f' = [(a - m v)/m].
4050 * If the constant term k in a is smaller than m,
4051 * the constant term of v is set to floor(k/m) - 1.
4052 * For any other term, if the coefficient c and the variable x have
4053 * the same sign, then no changes are needed.
4054 * Otherwise, if the variable is positive (and c is negative),
4055 * then the coefficient of x in v is set to floor(c/m).
4056 * If the variable is negative (and c is positive),
4057 * then the coefficient of x in v is set to ceil(c/m).
4058 */
4059 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4060 int *signs)
4061 {
4062 int i, j;
4063 int total;
4064 isl_vec *v = NULL;
4065 struct isl_upoly *s;
4066
4067 qp = isl_qpolynomial_cow(qp);
4068 if (!qp)
4069 return NULL;
4070 qp->div = isl_mat_cow(qp->div);
4071 if (!qp->div)
4072 goto error;
4073
4074 total = isl_dim_total(qp->dim);
4075 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4076
4077 for (i = 0; i < qp->div->n_row; ++i) {
4078 isl_int *row = qp->div->row[i];
4079 v = isl_vec_clr(v);
4080 if (!v)
4081 goto error;
4082 if (isl_int_lt(row[1], row[0])) {
4083 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4084 isl_int_sub_ui(v->el[0], v->el[0], 1);
4085 isl_int_submul(row[1], row[0], v->el[0]);
4086 }
4087 for (j = 0; j < total; ++j) {
4088 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4089 continue;
4090 if (signs[j] < 0)
4091 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4092 else
4093 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4094 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4095 }
4096 for (j = 0; j < i; ++j) {
4097 if (isl_int_sgn(row[2 + total + j]) >= 0)
4098 continue;
4099 isl_int_fdiv_q(v->el[1 + total + j],
4100 row[2 + total + j], row[0]);
4101 isl_int_submul(row[2 + total + j],
4102 row[0], v->el[1 + total + j]);
4103 }
4104 for (j = i + 1; j < qp->div->n_row; ++j) {
4105 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4106 continue;
4107 isl_seq_combine(qp->div->row[j] + 1,
4108 qp->div->ctx->one, qp->div->row[j] + 1,
4109 qp->div->row[j][2 + total + i], v->el, v->size);
4110 }
4111 isl_int_set_si(v->el[1 + total + i], 1);
4112 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4113 qp->div->ctx->one, v->size);
4114 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4115 isl_upoly_free(s);
4116 if (!qp->upoly)
4117 goto error;
4118 }
4119
4120 isl_vec_free(v);
4121 return qp;
4122 error:
4123 isl_vec_free(v);
4124 isl_qpolynomial_free(qp);
4125 return NULL;
4126 }
4127
4128 struct isl_to_poly_data {
4129 int sign;
4130 isl_pw_qpolynomial *res;
4131 isl_qpolynomial *qp;
4132 };
4133
4134 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4135 * We first make all integer divisions positive and then split the
4136 * quasipolynomials into terms with sign data->sign (the direction
4137 * of the requested approximation) and terms with the opposite sign.
4138 * In the first set of terms, each integer division [a/m] is
4139 * overapproximated by a/m, while in the second it is underapproximated
4140 * by (a-(m-1))/m.
4141 */
4142 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4143 void *user)
4144 {
4145 struct isl_to_poly_data *data = user;
4146 isl_pw_qpolynomial *t;
4147 isl_qpolynomial *qp, *up, *down;
4148
4149 qp = isl_qpolynomial_copy(data->qp);
4150 qp = make_divs_pos(qp, signs);
4151
4152 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4153 up = qp_drop_floors(up, 0);
4154 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4155 down = qp_drop_floors(down, 1);
4156
4157 isl_qpolynomial_free(qp);
4158 qp = isl_qpolynomial_add(up, down);
4159
4160 t = isl_pw_qpolynomial_alloc(orthant, qp);
4161 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4162
4163 return 0;
4164 }
4165
4166 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4167 * the polynomial will be an overapproximation. If "sign" is negative,
4168 * it will be an underapproximation. If "sign" is zero, the approximation
4169 * will lie somewhere in between.
4170 *
4171 * In particular, is sign == 0, we simply drop the floors, turning
4172 * the integer divisions into rational divisions.
4173 * Otherwise, we split the domains into orthants, make all integer divisions
4174 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4175 * depending on the requested sign and the sign of the term in which
4176 * the integer division appears.
4177 */
4178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4179 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4180 {
4181 int i;
4182 struct isl_to_poly_data data;
4183
4184 if (sign == 0)
4185 return pwqp_drop_floors(pwqp);
4186
4187 if (!pwqp)
4188 return NULL;
4189
4190 data.sign = sign;
4191 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4192
4193 for (i = 0; i < pwqp->n; ++i) {
4194 if (pwqp->p[i].qp->div->n_row == 0) {
4195 isl_pw_qpolynomial *t;
4196 t = isl_pw_qpolynomial_alloc(
4197 isl_set_copy(pwqp->p[i].set),
4198 isl_qpolynomial_copy(pwqp->p[i].qp));
4199 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4200 continue;
4201 }
4202 data.qp = pwqp->p[i].qp;
4203 if (isl_set_foreach_orthant(pwqp->p[i].set,
4204 &to_polynomial_on_orthant, &data) < 0)
4205 goto error;
4206 }
4207
4208 isl_pw_qpolynomial_free(pwqp);
4209
4210 return data.res;
4211 error:
4212 isl_pw_qpolynomial_free(pwqp);
4213 isl_pw_qpolynomial_free(data.res);
4214 return NULL;
4215 }
4216
4217 static int poly_entry(void **entry, void *user)
4218 {
4219 int *sign = user;
4220 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4221
4222 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4223
4224 return *pwqp ? 0 : -1;
4225 }
4226
4227 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4228 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4229 {
4230 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4231 if (!upwqp)
4232 return NULL;
4233
4234 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4235 &poly_entry, &sign) < 0)
4236 goto error;
4237
4238 return upwqp;
4239 error:
4240 isl_union_pw_qpolynomial_free(upwqp);
4241 return NULL;
4242 }
Integer set library