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isl_set_split_dims: extract out half-space creation
[isl.git] / isl_polynomial.c
blob050f666cebc2496b1a3e2cba52bfe3a1b277ac22
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_factorization.h>
13 #include <isl_lp.h>
14 #include <isl_seq.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21
22 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
23 {
24 switch (type) {
25 case isl_dim_param: return 0;
26 case isl_dim_in: return dim->nparam;
27 case isl_dim_out: return dim->nparam + dim->n_in;
28 default: return 0;
29 }
30 }
31
32 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
33 {
34 if (!up)
35 return -1;
36
37 return up->var < 0;
38 }
39
40 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return NULL;
44
45 isl_assert(up->ctx, up->var < 0, return NULL);
46
47 return (struct isl_upoly_cst *)up;
48 }
49
50 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
51 {
52 if (!up)
53 return NULL;
54
55 isl_assert(up->ctx, up->var >= 0, return NULL);
56
57 return (struct isl_upoly_rec *)up;
58 }
59
60 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
61 __isl_keep struct isl_upoly *up2)
62 {
63 int i;
64 struct isl_upoly_rec *rec1, *rec2;
65
66 if (!up1 || !up2)
67 return -1;
68 if (up1 == up2)
69 return 1;
70 if (up1->var != up2->var)
71 return 0;
72 if (isl_upoly_is_cst(up1)) {
73 struct isl_upoly_cst *cst1, *cst2;
74 cst1 = isl_upoly_as_cst(up1);
75 cst2 = isl_upoly_as_cst(up2);
76 if (!cst1 || !cst2)
77 return -1;
78 return isl_int_eq(cst1->n, cst2->n) &&
79 isl_int_eq(cst1->d, cst2->d);
80 }
81
82 rec1 = isl_upoly_as_rec(up1);
83 rec2 = isl_upoly_as_rec(up2);
84 if (!rec1 || !rec2)
85 return -1;
86
87 if (rec1->n != rec2->n)
88 return 0;
89
90 for (i = 0; i < rec1->n; ++i) {
91 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
92 if (eq < 0 || !eq)
93 return eq;
94 }
95
96 return 1;
97 }
98
99 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
100 {
101 struct isl_upoly_cst *cst;
102
103 if (!up)
104 return -1;
105 if (!isl_upoly_is_cst(up))
106 return 0;
107
108 cst = isl_upoly_as_cst(up);
109 if (!cst)
110 return -1;
111
112 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
113 }
114
115 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
116 {
117 struct isl_upoly_cst *cst;
118
119 if (!up)
120 return 0;
121 if (!isl_upoly_is_cst(up))
122 return 0;
123
124 cst = isl_upoly_as_cst(up);
125 if (!cst)
126 return 0;
127
128 return isl_int_sgn(cst->n);
129 }
130
131 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
132 {
133 struct isl_upoly_cst *cst;
134
135 if (!up)
136 return -1;
137 if (!isl_upoly_is_cst(up))
138 return 0;
139
140 cst = isl_upoly_as_cst(up);
141 if (!cst)
142 return -1;
143
144 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
145 }
146
147 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
148 {
149 struct isl_upoly_cst *cst;
150
151 if (!up)
152 return -1;
153 if (!isl_upoly_is_cst(up))
154 return 0;
155
156 cst = isl_upoly_as_cst(up);
157 if (!cst)
158 return -1;
159
160 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
161 }
162
163 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
164 {
165 struct isl_upoly_cst *cst;
166
167 if (!up)
168 return -1;
169 if (!isl_upoly_is_cst(up))
170 return 0;
171
172 cst = isl_upoly_as_cst(up);
173 if (!cst)
174 return -1;
175
176 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
177 }
178
179 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
180 {
181 struct isl_upoly_cst *cst;
182
183 if (!up)
184 return -1;
185 if (!isl_upoly_is_cst(up))
186 return 0;
187
188 cst = isl_upoly_as_cst(up);
189 if (!cst)
190 return -1;
191
192 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
193 }
194
195 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
196 {
197 struct isl_upoly_cst *cst;
198
199 if (!up)
200 return -1;
201 if (!isl_upoly_is_cst(up))
202 return 0;
203
204 cst = isl_upoly_as_cst(up);
205 if (!cst)
206 return -1;
207
208 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
209 }
210
211 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
212 {
213 struct isl_upoly_cst *cst;
214
215 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
216 if (!cst)
217 return NULL;
218
219 cst->up.ref = 1;
220 cst->up.ctx = ctx;
221 isl_ctx_ref(ctx);
222 cst->up.var = -1;
223
224 isl_int_init(cst->n);
225 isl_int_init(cst->d);
226
227 return cst;
228 }
229
230 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
231 {
232 struct isl_upoly_cst *cst;
233
234 cst = isl_upoly_cst_alloc(ctx);
235 if (!cst)
236 return NULL;
237
238 isl_int_set_si(cst->n, 0);
239 isl_int_set_si(cst->d, 1);
240
241 return &cst->up;
242 }
243
244 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
245 {
246 struct isl_upoly_cst *cst;
247
248 cst = isl_upoly_cst_alloc(ctx);
249 if (!cst)
250 return NULL;
251
252 isl_int_set_si(cst->n, 1);
253 isl_int_set_si(cst->d, 1);
254
255 return &cst->up;
256 }
257
258 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
259 {
260 struct isl_upoly_cst *cst;
261
262 cst = isl_upoly_cst_alloc(ctx);
263 if (!cst)
264 return NULL;
265
266 isl_int_set_si(cst->n, 1);
267 isl_int_set_si(cst->d, 0);
268
269 return &cst->up;
270 }
271
272 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
273 {
274 struct isl_upoly_cst *cst;
275
276 cst = isl_upoly_cst_alloc(ctx);
277 if (!cst)
278 return NULL;
279
280 isl_int_set_si(cst->n, -1);
281 isl_int_set_si(cst->d, 0);
282
283 return &cst->up;
284 }
285
286 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
287 {
288 struct isl_upoly_cst *cst;
289
290 cst = isl_upoly_cst_alloc(ctx);
291 if (!cst)
292 return NULL;
293
294 isl_int_set_si(cst->n, 0);
295 isl_int_set_si(cst->d, 0);
296
297 return &cst->up;
298 }
299
300 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
301 isl_int n, isl_int d)
302 {
303 struct isl_upoly_cst *cst;
304
305 cst = isl_upoly_cst_alloc(ctx);
306 if (!cst)
307 return NULL;
308
309 isl_int_set(cst->n, n);
310 isl_int_set(cst->d, d);
311
312 return &cst->up;
313 }
314
315 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
316 int var, int size)
317 {
318 struct isl_upoly_rec *rec;
319
320 isl_assert(ctx, var >= 0, return NULL);
321 isl_assert(ctx, size >= 0, return NULL);
322 rec = isl_calloc(ctx, struct isl_upoly_rec,
323 sizeof(struct isl_upoly_rec) +
324 (size - 1) * sizeof(struct isl_upoly *));
325 if (!rec)
326 return NULL;
327
328 rec->up.ref = 1;
329 rec->up.ctx = ctx;
330 isl_ctx_ref(ctx);
331 rec->up.var = var;
332
333 rec->n = 0;
334 rec->size = size;
335
336 return rec;
337 }
338
339 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
340 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
341 {
342 qp = isl_qpolynomial_cow(qp);
343 if (!qp || !dim)
344 goto error;
345
346 isl_dim_free(qp->dim);
347 qp->dim = dim;
348
349 return qp;
350 error:
351 isl_qpolynomial_free(qp);
352 isl_dim_free(dim);
353 return NULL;
354 }
355
356 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
357 {
358 return qp ? qp->dim->ctx : NULL;
359 }
360
361 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
362 {
363 return qp ? isl_dim_copy(qp->dim) : NULL;
364 }
365
366 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
367 enum isl_dim_type type)
368 {
369 return qp ? isl_dim_size(qp->dim, type) : 0;
370 }
371
372 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
373 {
374 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
375 }
376
377 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
378 {
379 return qp ? isl_upoly_is_one(qp->upoly) : -1;
380 }
381
382 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
385 }
386
387 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
388 {
389 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
390 }
391
392 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
393 {
394 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
395 }
396
397 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
398 {
399 return qp ? isl_upoly_sgn(qp->upoly) : 0;
400 }
401
402 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
403 {
404 isl_int_clear(cst->n);
405 isl_int_clear(cst->d);
406 }
407
408 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
409 {
410 int i;
411
412 for (i = 0; i < rec->n; ++i)
413 isl_upoly_free(rec->p[i]);
414 }
415
416 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
417 {
418 if (!up)
419 return NULL;
420
421 up->ref++;
422 return up;
423 }
424
425 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
426 {
427 struct isl_upoly_cst *cst;
428 struct isl_upoly_cst *dup;
429
430 cst = isl_upoly_as_cst(up);
431 if (!cst)
432 return NULL;
433
434 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
435 if (!dup)
436 return NULL;
437 isl_int_set(dup->n, cst->n);
438 isl_int_set(dup->d, cst->d);
439
440 return &dup->up;
441 }
442
443 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
444 {
445 int i;
446 struct isl_upoly_rec *rec;
447 struct isl_upoly_rec *dup;
448
449 rec = isl_upoly_as_rec(up);
450 if (!rec)
451 return NULL;
452
453 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
454 if (!dup)
455 return NULL;
456
457 for (i = 0; i < rec->n; ++i) {
458 dup->p[i] = isl_upoly_copy(rec->p[i]);
459 if (!dup->p[i])
460 goto error;
461 dup->n++;
462 }
463
464 return &dup->up;
465 error:
466 isl_upoly_free(&dup->up);
467 return NULL;
468 }
469
470 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
471 {
472 struct isl_upoly *dup;
473
474 if (!up)
475 return NULL;
476
477 if (isl_upoly_is_cst(up))
478 return isl_upoly_dup_cst(up);
479 else
480 return isl_upoly_dup_rec(up);
481 }
482
483 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
484 {
485 if (!up)
486 return NULL;
487
488 if (up->ref == 1)
489 return up;
490 up->ref--;
491 return isl_upoly_dup(up);
492 }
493
494 void isl_upoly_free(__isl_take struct isl_upoly *up)
495 {
496 if (!up)
497 return;
498
499 if (--up->ref > 0)
500 return;
501
502 if (up->var < 0)
503 upoly_free_cst((struct isl_upoly_cst *)up);
504 else
505 upoly_free_rec((struct isl_upoly_rec *)up);
506
507 isl_ctx_deref(up->ctx);
508 free(up);
509 }
510
511 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
512 {
513 isl_int gcd;
514
515 isl_int_init(gcd);
516 isl_int_gcd(gcd, cst->n, cst->d);
517 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
518 isl_int_divexact(cst->n, cst->n, gcd);
519 isl_int_divexact(cst->d, cst->d, gcd);
520 }
521 isl_int_clear(gcd);
522 }
523
524 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
525 __isl_take struct isl_upoly *up2)
526 {
527 struct isl_upoly_cst *cst1;
528 struct isl_upoly_cst *cst2;
529
530 up1 = isl_upoly_cow(up1);
531 if (!up1 || !up2)
532 goto error;
533
534 cst1 = isl_upoly_as_cst(up1);
535 cst2 = isl_upoly_as_cst(up2);
536
537 if (isl_int_eq(cst1->d, cst2->d))
538 isl_int_add(cst1->n, cst1->n, cst2->n);
539 else {
540 isl_int_mul(cst1->n, cst1->n, cst2->d);
541 isl_int_addmul(cst1->n, cst2->n, cst1->d);
542 isl_int_mul(cst1->d, cst1->d, cst2->d);
543 }
544
545 isl_upoly_cst_reduce(cst1);
546
547 isl_upoly_free(up2);
548 return up1;
549 error:
550 isl_upoly_free(up1);
551 isl_upoly_free(up2);
552 return NULL;
553 }
554
555 static __isl_give struct isl_upoly *replace_by_zero(
556 __isl_take struct isl_upoly *up)
557 {
558 struct isl_ctx *ctx;
559
560 if (!up)
561 return NULL;
562 ctx = up->ctx;
563 isl_upoly_free(up);
564 return isl_upoly_zero(ctx);
565 }
566
567 static __isl_give struct isl_upoly *replace_by_constant_term(
568 __isl_take struct isl_upoly *up)
569 {
570 struct isl_upoly_rec *rec;
571 struct isl_upoly *cst;
572
573 if (!up)
574 return NULL;
575
576 rec = isl_upoly_as_rec(up);
577 if (!rec)
578 goto error;
579 cst = isl_upoly_copy(rec->p[0]);
580 isl_upoly_free(up);
581 return cst;
582 error:
583 isl_upoly_free(up);
584 return NULL;
585 }
586
587 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
588 __isl_take struct isl_upoly *up2)
589 {
590 int i;
591 struct isl_upoly_rec *rec1, *rec2;
592
593 if (!up1 || !up2)
594 goto error;
595
596 if (isl_upoly_is_nan(up1)) {
597 isl_upoly_free(up2);
598 return up1;
599 }
600
601 if (isl_upoly_is_nan(up2)) {
602 isl_upoly_free(up1);
603 return up2;
604 }
605
606 if (isl_upoly_is_zero(up1)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610
611 if (isl_upoly_is_zero(up2)) {
612 isl_upoly_free(up2);
613 return up1;
614 }
615
616 if (up1->var < up2->var)
617 return isl_upoly_sum(up2, up1);
618
619 if (up2->var < up1->var) {
620 struct isl_upoly_rec *rec;
621 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
622 isl_upoly_free(up1);
623 return up2;
624 }
625 up1 = isl_upoly_cow(up1);
626 rec = isl_upoly_as_rec(up1);
627 if (!rec)
628 goto error;
629 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
630 if (rec->n == 1)
631 up1 = replace_by_constant_term(up1);
632 return up1;
633 }
634
635 if (isl_upoly_is_cst(up1))
636 return isl_upoly_sum_cst(up1, up2);
637
638 rec1 = isl_upoly_as_rec(up1);
639 rec2 = isl_upoly_as_rec(up2);
640 if (!rec1 || !rec2)
641 goto error;
642
643 if (rec1->n < rec2->n)
644 return isl_upoly_sum(up2, up1);
645
646 up1 = isl_upoly_cow(up1);
647 rec1 = isl_upoly_as_rec(up1);
648 if (!rec1)
649 goto error;
650
651 for (i = rec2->n - 1; i >= 0; --i) {
652 rec1->p[i] = isl_upoly_sum(rec1->p[i],
653 isl_upoly_copy(rec2->p[i]));
654 if (!rec1->p[i])
655 goto error;
656 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
657 isl_upoly_free(rec1->p[i]);
658 rec1->n--;
659 }
660 }
661
662 if (rec1->n == 0)
663 up1 = replace_by_zero(up1);
664 else if (rec1->n == 1)
665 up1 = replace_by_constant_term(up1);
666
667 isl_upoly_free(up2);
668
669 return up1;
670 error:
671 isl_upoly_free(up1);
672 isl_upoly_free(up2);
673 return NULL;
674 }
675
676 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
677 {
678 struct isl_upoly_cst *cst;
679
680 if (isl_upoly_is_zero(up))
681 return up;
682
683 up = isl_upoly_cow(up);
684 if (!up)
685 return NULL;
686
687 cst = isl_upoly_as_cst(up);
688
689 isl_int_neg(cst->n, cst->n);
690
691 return up;
692 }
693
694 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
695 {
696 int i;
697 struct isl_upoly_rec *rec;
698
699 if (!up)
700 return NULL;
701
702 if (isl_upoly_is_cst(up))
703 return isl_upoly_neg_cst(up);
704
705 up = isl_upoly_cow(up);
706 rec = isl_upoly_as_rec(up);
707 if (!rec)
708 goto error;
709
710 for (i = 0; i < rec->n; ++i) {
711 rec->p[i] = isl_upoly_neg(rec->p[i]);
712 if (!rec->p[i])
713 goto error;
714 }
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
723 __isl_take struct isl_upoly *up2)
724 {
725 struct isl_upoly_cst *cst1;
726 struct isl_upoly_cst *cst2;
727
728 up1 = isl_upoly_cow(up1);
729 if (!up1 || !up2)
730 goto error;
731
732 cst1 = isl_upoly_as_cst(up1);
733 cst2 = isl_upoly_as_cst(up2);
734
735 isl_int_mul(cst1->n, cst1->n, cst2->n);
736 isl_int_mul(cst1->d, cst1->d, cst2->d);
737
738 isl_upoly_cst_reduce(cst1);
739
740 isl_upoly_free(up2);
741 return up1;
742 error:
743 isl_upoly_free(up1);
744 isl_upoly_free(up2);
745 return NULL;
746 }
747
748 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
749 __isl_take struct isl_upoly *up2)
750 {
751 struct isl_upoly_rec *rec1;
752 struct isl_upoly_rec *rec2;
753 struct isl_upoly_rec *res;
754 int i, j;
755 int size;
756
757 rec1 = isl_upoly_as_rec(up1);
758 rec2 = isl_upoly_as_rec(up2);
759 if (!rec1 || !rec2)
760 goto error;
761 size = rec1->n + rec2->n - 1;
762 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
763 if (!res)
764 goto error;
765
766 for (i = 0; i < rec1->n; ++i) {
767 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
768 isl_upoly_copy(rec1->p[i]));
769 if (!res->p[i])
770 goto error;
771 res->n++;
772 }
773 for (; i < size; ++i) {
774 res->p[i] = isl_upoly_zero(up1->ctx);
775 if (!res->p[i])
776 goto error;
777 res->n++;
778 }
779 for (i = 0; i < rec1->n; ++i) {
780 for (j = 1; j < rec2->n; ++j) {
781 struct isl_upoly *up;
782 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
783 isl_upoly_copy(rec1->p[i]));
784 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
785 if (!res->p[i + j])
786 goto error;
787 }
788 }
789
790 isl_upoly_free(up1);
791 isl_upoly_free(up2);
792
793 return &res->up;
794 error:
795 isl_upoly_free(up1);
796 isl_upoly_free(up2);
797 isl_upoly_free(&res->up);
798 return NULL;
799 }
800
801 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
802 __isl_take struct isl_upoly *up2)
803 {
804 if (!up1 || !up2)
805 goto error;
806
807 if (isl_upoly_is_nan(up1)) {
808 isl_upoly_free(up2);
809 return up1;
810 }
811
812 if (isl_upoly_is_nan(up2)) {
813 isl_upoly_free(up1);
814 return up2;
815 }
816
817 if (isl_upoly_is_zero(up1)) {
818 isl_upoly_free(up2);
819 return up1;
820 }
821
822 if (isl_upoly_is_zero(up2)) {
823 isl_upoly_free(up1);
824 return up2;
825 }
826
827 if (isl_upoly_is_one(up1)) {
828 isl_upoly_free(up1);
829 return up2;
830 }
831
832 if (isl_upoly_is_one(up2)) {
833 isl_upoly_free(up2);
834 return up1;
835 }
836
837 if (up1->var < up2->var)
838 return isl_upoly_mul(up2, up1);
839
840 if (up2->var < up1->var) {
841 int i;
842 struct isl_upoly_rec *rec;
843 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
844 isl_ctx *ctx = up1->ctx;
845 isl_upoly_free(up1);
846 isl_upoly_free(up2);
847 return isl_upoly_nan(ctx);
848 }
849 up1 = isl_upoly_cow(up1);
850 rec = isl_upoly_as_rec(up1);
851 if (!rec)
852 goto error;
853
854 for (i = 0; i < rec->n; ++i) {
855 rec->p[i] = isl_upoly_mul(rec->p[i],
856 isl_upoly_copy(up2));
857 if (!rec->p[i])
858 goto error;
859 }
860 isl_upoly_free(up2);
861 return up1;
862 }
863
864 if (isl_upoly_is_cst(up1))
865 return isl_upoly_mul_cst(up1, up2);
866
867 return isl_upoly_mul_rec(up1, up2);
868 error:
869 isl_upoly_free(up1);
870 isl_upoly_free(up2);
871 return NULL;
872 }
873
874 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
875 unsigned n_div, __isl_take struct isl_upoly *up)
876 {
877 struct isl_qpolynomial *qp = NULL;
878 unsigned total;
879
880 if (!dim || !up)
881 goto error;
882
883 total = isl_dim_total(dim);
884
885 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
886 if (!qp)
887 goto error;
888
889 qp->ref = 1;
890 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
891 if (!qp->div)
892 goto error;
893
894 qp->dim = dim;
895 qp->upoly = up;
896
897 return qp;
898 error:
899 isl_dim_free(dim);
900 isl_upoly_free(up);
901 isl_qpolynomial_free(qp);
902 return NULL;
903 }
904
905 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
906 {
907 if (!qp)
908 return NULL;
909
910 qp->ref++;
911 return qp;
912 }
913
914 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
915 {
916 struct isl_qpolynomial *dup;
917
918 if (!qp)
919 return NULL;
920
921 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
922 isl_upoly_copy(qp->upoly));
923 if (!dup)
924 return NULL;
925 isl_mat_free(dup->div);
926 dup->div = isl_mat_copy(qp->div);
927 if (!dup->div)
928 goto error;
929
930 return dup;
931 error:
932 isl_qpolynomial_free(dup);
933 return NULL;
934 }
935
936 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
937 {
938 if (!qp)
939 return NULL;
940
941 if (qp->ref == 1)
942 return qp;
943 qp->ref--;
944 return isl_qpolynomial_dup(qp);
945 }
946
947 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
948 {
949 if (!qp)
950 return;
951
952 if (--qp->ref > 0)
953 return;
954
955 isl_dim_free(qp->dim);
956 isl_mat_free(qp->div);
957 isl_upoly_free(qp->upoly);
958
959 free(qp);
960 }
961
962 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
963 {
964 int i;
965 struct isl_upoly *up;
966 struct isl_upoly_rec *rec;
967 struct isl_upoly_cst *cst;
968
969 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
970 if (!rec)
971 return NULL;
972 for (i = 0; i < 1 + power; ++i) {
973 rec->p[i] = isl_upoly_zero(ctx);
974 if (!rec->p[i])
975 goto error;
976 rec->n++;
977 }
978 cst = isl_upoly_as_cst(rec->p[power]);
979 isl_int_set_si(cst->n, 1);
980
981 return &rec->up;
982 error:
983 isl_upoly_free(&rec->up);
984 return NULL;
985 }
986
987 /* r array maps original positions to new positions.
988 */
989 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
990 int *r)
991 {
992 int i;
993 struct isl_upoly_rec *rec;
994 struct isl_upoly *base;
995 struct isl_upoly *res;
996
997 if (isl_upoly_is_cst(up))
998 return up;
999
1000 rec = isl_upoly_as_rec(up);
1001 if (!rec)
1002 goto error;
1003
1004 isl_assert(up->ctx, rec->n >= 1, goto error);
1005
1006 base = isl_upoly_pow(up->ctx, r[up->var], 1);
1007 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1008
1009 for (i = rec->n - 2; i >= 0; --i) {
1010 res = isl_upoly_mul(res, isl_upoly_copy(base));
1011 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1012 }
1013
1014 isl_upoly_free(base);
1015 isl_upoly_free(up);
1016
1017 return res;
1018 error:
1019 isl_upoly_free(up);
1020 return NULL;
1021 }
1022
1023 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1024 {
1025 int n_row, n_col;
1026 int equal;
1027
1028 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1029 div1->n_col >= div2->n_col, return -1);
1030
1031 if (div1->n_row == div2->n_row)
1032 return isl_mat_is_equal(div1, div2);
1033
1034 n_row = div1->n_row;
1035 n_col = div1->n_col;
1036 div1->n_row = div2->n_row;
1037 div1->n_col = div2->n_col;
1038
1039 equal = isl_mat_is_equal(div1, div2);
1040
1041 div1->n_row = n_row;
1042 div1->n_col = n_col;
1043
1044 return equal;
1045 }
1046
1047 static void expand_row(__isl_keep isl_mat *dst, int d,
1048 __isl_keep isl_mat *src, int s, int *exp)
1049 {
1050 int i;
1051 unsigned c = src->n_col - src->n_row;
1052
1053 isl_seq_cpy(dst->row[d], src->row[s], c);
1054 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1055
1056 for (i = 0; i < s; ++i)
1057 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1058 }
1059
1060 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1061 {
1062 int li, lj;
1063
1064 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1065 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1066
1067 if (li != lj)
1068 return li - lj;
1069
1070 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1071 }
1072
1073 struct isl_div_sort_info {
1074 isl_mat *div;
1075 int row;
1076 };
1077
1078 static int div_sort_cmp(const void *p1, const void *p2)
1079 {
1080 const struct isl_div_sort_info *i1, *i2;
1081 i1 = (const struct isl_div_sort_info *) p1;
1082 i2 = (const struct isl_div_sort_info *) p2;
1083
1084 return cmp_row(i1->div, i1->row, i2->row);
1085 }
1086
1087 /* Sort divs and remove duplicates.
1088 */
1089 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1090 {
1091 int i;
1092 int skip;
1093 int len;
1094 struct isl_div_sort_info *array = NULL;
1095 int *pos = NULL, *at = NULL;
1096 int *reordering = NULL;
1097 unsigned div_pos;
1098
1099 if (!qp)
1100 return NULL;
1101 if (qp->div->n_row <= 1)
1102 return qp;
1103
1104 div_pos = isl_dim_total(qp->dim);
1105
1106 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1107 qp->div->n_row);
1108 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1109 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1110 len = qp->div->n_col - 2;
1111 reordering = isl_alloc_array(qp->div->ctx, int, len);
1112 if (!array || !pos || !at || !reordering)
1113 goto error;
1114
1115 for (i = 0; i < qp->div->n_row; ++i) {
1116 array[i].div = qp->div;
1117 array[i].row = i;
1118 pos[i] = i;
1119 at[i] = i;
1120 }
1121
1122 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1123 div_sort_cmp);
1124
1125 for (i = 0; i < div_pos; ++i)
1126 reordering[i] = i;
1127
1128 for (i = 0; i < qp->div->n_row; ++i) {
1129 if (pos[array[i].row] == i)
1130 continue;
1131 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1132 pos[at[i]] = pos[array[i].row];
1133 at[pos[array[i].row]] = at[i];
1134 at[i] = array[i].row;
1135 pos[array[i].row] = i;
1136 }
1137
1138 skip = 0;
1139 for (i = 0; i < len - div_pos; ++i) {
1140 if (i > 0 &&
1141 isl_seq_eq(qp->div->row[i - skip - 1],
1142 qp->div->row[i - skip], qp->div->n_col)) {
1143 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1144 qp->div = isl_mat_drop_cols(qp->div,
1145 2 + div_pos + i - skip, 1);
1146 skip++;
1147 }
1148 reordering[div_pos + array[i].row] = div_pos + i - skip;
1149 }
1150
1151 qp->upoly = reorder(qp->upoly, reordering);
1152
1153 if (!qp->upoly || !qp->div)
1154 goto error;
1155
1156 free(at);
1157 free(pos);
1158 free(array);
1159 free(reordering);
1160
1161 return qp;
1162 error:
1163 free(at);
1164 free(pos);
1165 free(array);
1166 free(reordering);
1167 isl_qpolynomial_free(qp);
1168 return NULL;
1169 }
1170
1171 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1172 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1173 {
1174 int i, j, k;
1175 isl_mat *div = NULL;
1176 unsigned d = div1->n_col - div1->n_row;
1177
1178 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1179 d + div1->n_row + div2->n_row);
1180 if (!div)
1181 return NULL;
1182
1183 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1184 int cmp;
1185
1186 expand_row(div, k, div1, i, exp1);
1187 expand_row(div, k + 1, div2, j, exp2);
1188
1189 cmp = cmp_row(div, k, k + 1);
1190 if (cmp == 0) {
1191 exp1[i++] = k;
1192 exp2[j++] = k;
1193 } else if (cmp < 0) {
1194 exp1[i++] = k;
1195 } else {
1196 exp2[j++] = k;
1197 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1198 }
1199 }
1200 for (; i < div1->n_row; ++i, ++k) {
1201 expand_row(div, k, div1, i, exp1);
1202 exp1[i] = k;
1203 }
1204 for (; j < div2->n_row; ++j, ++k) {
1205 expand_row(div, k, div2, j, exp2);
1206 exp2[j] = k;
1207 }
1208
1209 div->n_row = k;
1210 div->n_col = d + k;
1211
1212 return div;
1213 }
1214
1215 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1216 int *exp, int first)
1217 {
1218 int i;
1219 struct isl_upoly_rec *rec;
1220
1221 if (isl_upoly_is_cst(up))
1222 return up;
1223
1224 if (up->var < first)
1225 return up;
1226
1227 if (exp[up->var - first] == up->var - first)
1228 return up;
1229
1230 up = isl_upoly_cow(up);
1231 if (!up)
1232 goto error;
1233
1234 up->var = exp[up->var - first] + first;
1235
1236 rec = isl_upoly_as_rec(up);
1237 if (!rec)
1238 goto error;
1239
1240 for (i = 0; i < rec->n; ++i) {
1241 rec->p[i] = expand(rec->p[i], exp, first);
1242 if (!rec->p[i])
1243 goto error;
1244 }
1245
1246 return up;
1247 error:
1248 isl_upoly_free(up);
1249 return NULL;
1250 }
1251
1252 static __isl_give isl_qpolynomial *with_merged_divs(
1253 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1254 __isl_take isl_qpolynomial *qp2),
1255 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1256 {
1257 int *exp1 = NULL;
1258 int *exp2 = NULL;
1259 isl_mat *div = NULL;
1260
1261 qp1 = isl_qpolynomial_cow(qp1);
1262 qp2 = isl_qpolynomial_cow(qp2);
1263
1264 if (!qp1 || !qp2)
1265 goto error;
1266
1267 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1268 qp1->div->n_col >= qp2->div->n_col, goto error);
1269
1270 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1271 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1272 if (!exp1 || !exp2)
1273 goto error;
1274
1275 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1276 if (!div)
1277 goto error;
1278
1279 isl_mat_free(qp1->div);
1280 qp1->div = isl_mat_copy(div);
1281 isl_mat_free(qp2->div);
1282 qp2->div = isl_mat_copy(div);
1283
1284 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1285 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1286
1287 if (!qp1->upoly || !qp2->upoly)
1288 goto error;
1289
1290 isl_mat_free(div);
1291 free(exp1);
1292 free(exp2);
1293
1294 return fn(qp1, qp2);
1295 error:
1296 isl_mat_free(div);
1297 free(exp1);
1298 free(exp2);
1299 isl_qpolynomial_free(qp1);
1300 isl_qpolynomial_free(qp2);
1301 return NULL;
1302 }
1303
1304 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1305 __isl_take isl_qpolynomial *qp2)
1306 {
1307 qp1 = isl_qpolynomial_cow(qp1);
1308
1309 if (!qp1 || !qp2)
1310 goto error;
1311
1312 if (qp1->div->n_row < qp2->div->n_row)
1313 return isl_qpolynomial_add(qp2, qp1);
1314
1315 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1316 if (!compatible_divs(qp1->div, qp2->div))
1317 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1318
1319 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1320 if (!qp1->upoly)
1321 goto error;
1322
1323 isl_qpolynomial_free(qp2);
1324
1325 return qp1;
1326 error:
1327 isl_qpolynomial_free(qp1);
1328 isl_qpolynomial_free(qp2);
1329 return NULL;
1330 }
1331
1332 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1333 __isl_keep isl_set *dom,
1334 __isl_take isl_qpolynomial *qp1,
1335 __isl_take isl_qpolynomial *qp2)
1336 {
1337 return isl_qpolynomial_add(qp1, qp2);
1338 }
1339
1340 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1341 __isl_take isl_qpolynomial *qp2)
1342 {
1343 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1344 }
1345
1346 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1347 {
1348 qp = isl_qpolynomial_cow(qp);
1349
1350 if (!qp)
1351 return NULL;
1352
1353 qp->upoly = isl_upoly_neg(qp->upoly);
1354 if (!qp->upoly)
1355 goto error;
1356
1357 return qp;
1358 error:
1359 isl_qpolynomial_free(qp);
1360 return NULL;
1361 }
1362
1363 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1364 __isl_take isl_qpolynomial *qp2)
1365 {
1366 qp1 = isl_qpolynomial_cow(qp1);
1367
1368 if (!qp1 || !qp2)
1369 goto error;
1370
1371 if (qp1->div->n_row < qp2->div->n_row)
1372 return isl_qpolynomial_mul(qp2, qp1);
1373
1374 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1375 if (!compatible_divs(qp1->div, qp2->div))
1376 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1377
1378 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1379 if (!qp1->upoly)
1380 goto error;
1381
1382 isl_qpolynomial_free(qp2);
1383
1384 return qp1;
1385 error:
1386 isl_qpolynomial_free(qp1);
1387 isl_qpolynomial_free(qp2);
1388 return NULL;
1389 }
1390
1391 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1392 {
1393 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1394 }
1395
1396 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1397 {
1398 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1399 }
1400
1401 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1402 {
1403 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1404 }
1405
1406 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1407 {
1408 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1409 }
1410
1411 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1412 {
1413 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1414 }
1415
1416 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1417 isl_int v)
1418 {
1419 struct isl_qpolynomial *qp;
1420 struct isl_upoly_cst *cst;
1421
1422 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1423 if (!qp)
1424 return NULL;
1425
1426 cst = isl_upoly_as_cst(qp->upoly);
1427 isl_int_set(cst->n, v);
1428
1429 return qp;
1430 }
1431
1432 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1433 isl_int *n, isl_int *d)
1434 {
1435 struct isl_upoly_cst *cst;
1436
1437 if (!qp)
1438 return -1;
1439
1440 if (!isl_upoly_is_cst(qp->upoly))
1441 return 0;
1442
1443 cst = isl_upoly_as_cst(qp->upoly);
1444 if (!cst)
1445 return -1;
1446
1447 if (n)
1448 isl_int_set(*n, cst->n);
1449 if (d)
1450 isl_int_set(*d, cst->d);
1451
1452 return 1;
1453 }
1454
1455 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1456 {
1457 int is_cst;
1458 struct isl_upoly_rec *rec;
1459
1460 if (!up)
1461 return -1;
1462
1463 if (up->var < 0)
1464 return 1;
1465
1466 rec = isl_upoly_as_rec(up);
1467 if (!rec)
1468 return -1;
1469
1470 if (rec->n > 2)
1471 return 0;
1472
1473 isl_assert(up->ctx, rec->n > 1, return -1);
1474
1475 is_cst = isl_upoly_is_cst(rec->p[1]);
1476 if (is_cst < 0)
1477 return -1;
1478 if (!is_cst)
1479 return 0;
1480
1481 return isl_upoly_is_affine(rec->p[0]);
1482 }
1483
1484 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1485 {
1486 if (!qp)
1487 return -1;
1488
1489 if (qp->div->n_row > 0)
1490 return 0;
1491
1492 return isl_upoly_is_affine(qp->upoly);
1493 }
1494
1495 static void update_coeff(__isl_keep isl_vec *aff,
1496 __isl_keep struct isl_upoly_cst *cst, int pos)
1497 {
1498 isl_int gcd;
1499 isl_int f;
1500
1501 if (isl_int_is_zero(cst->n))
1502 return;
1503
1504 isl_int_init(gcd);
1505 isl_int_init(f);
1506 isl_int_gcd(gcd, cst->d, aff->el[0]);
1507 isl_int_divexact(f, cst->d, gcd);
1508 isl_int_divexact(gcd, aff->el[0], gcd);
1509 isl_seq_scale(aff->el, aff->el, f, aff->size);
1510 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1511 isl_int_clear(gcd);
1512 isl_int_clear(f);
1513 }
1514
1515 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1516 __isl_keep isl_vec *aff)
1517 {
1518 struct isl_upoly_cst *cst;
1519 struct isl_upoly_rec *rec;
1520
1521 if (!up || !aff)
1522 return -1;
1523
1524 if (up->var < 0) {
1525 struct isl_upoly_cst *cst;
1526
1527 cst = isl_upoly_as_cst(up);
1528 if (!cst)
1529 return -1;
1530 update_coeff(aff, cst, 0);
1531 return 0;
1532 }
1533
1534 rec = isl_upoly_as_rec(up);
1535 if (!rec)
1536 return -1;
1537 isl_assert(up->ctx, rec->n == 2, return -1);
1538
1539 cst = isl_upoly_as_cst(rec->p[1]);
1540 if (!cst)
1541 return -1;
1542 update_coeff(aff, cst, 1 + up->var);
1543
1544 return isl_upoly_update_affine(rec->p[0], aff);
1545 }
1546
1547 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1548 __isl_keep isl_qpolynomial *qp)
1549 {
1550 isl_vec *aff;
1551 unsigned d;
1552
1553 if (!qp)
1554 return NULL;
1555
1556 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1557 d = isl_dim_total(qp->dim);
1558 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1559 if (!aff)
1560 return NULL;
1561
1562 isl_seq_clr(aff->el + 1, 1 + d);
1563 isl_int_set_si(aff->el[0], 1);
1564
1565 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1566 goto error;
1567
1568 return aff;
1569 error:
1570 isl_vec_free(aff);
1571 return NULL;
1572 }
1573
1574 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1575 __isl_keep isl_qpolynomial *qp2)
1576 {
1577 if (!qp1 || !qp2)
1578 return -1;
1579
1580 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1581 }
1582
1583 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1584 {
1585 int i;
1586 struct isl_upoly_rec *rec;
1587
1588 if (isl_upoly_is_cst(up)) {
1589 struct isl_upoly_cst *cst;
1590 cst = isl_upoly_as_cst(up);
1591 if (!cst)
1592 return;
1593 isl_int_lcm(*d, *d, cst->d);
1594 return;
1595 }
1596
1597 rec = isl_upoly_as_rec(up);
1598 if (!rec)
1599 return;
1600
1601 for (i = 0; i < rec->n; ++i)
1602 upoly_update_den(rec->p[i], d);
1603 }
1604
1605 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1606 {
1607 isl_int_set_si(*d, 1);
1608 if (!qp)
1609 return;
1610 upoly_update_den(qp->upoly, d);
1611 }
1612
1613 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1614 int pos, int power)
1615 {
1616 struct isl_ctx *ctx;
1617
1618 if (!dim)
1619 return NULL;
1620
1621 ctx = dim->ctx;
1622
1623 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1624 }
1625
1626 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1627 enum isl_dim_type type, unsigned pos)
1628 {
1629 if (!dim)
1630 return NULL;
1631
1632 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1633 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1634
1635 if (type == isl_dim_set)
1636 pos += isl_dim_size(dim, isl_dim_param);
1637
1638 return isl_qpolynomial_pow(dim, pos, 1);
1639 error:
1640 isl_dim_free(dim);
1641 return NULL;
1642 }
1643
1644 /* Remove common factor of non-constant terms and denominator.
1645 */
1646 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1647 {
1648 isl_ctx *ctx = qp->div->ctx;
1649 unsigned total = qp->div->n_col - 2;
1650
1651 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1652 isl_int_gcd(ctx->normalize_gcd,
1653 ctx->normalize_gcd, qp->div->row[div][0]);
1654 if (isl_int_is_one(ctx->normalize_gcd))
1655 return;
1656
1657 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1658 ctx->normalize_gcd, total);
1659 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1660 ctx->normalize_gcd);
1661 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1662 ctx->normalize_gcd);
1663 }
1664
1665 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1666 int power)
1667 {
1668 struct isl_qpolynomial *qp = NULL;
1669 struct isl_upoly_rec *rec;
1670 struct isl_upoly_cst *cst;
1671 int i, d;
1672 int pos;
1673
1674 if (!div)
1675 return NULL;
1676
1677 d = div->line - div->bmap->div;
1678
1679 pos = isl_dim_total(div->bmap->dim) + d;
1680 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1681 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1682 div->bmap->n_div, &rec->up);
1683 if (!qp)
1684 goto error;
1685
1686 for (i = 0; i < div->bmap->n_div; ++i) {
1687 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1688 normalize_div(qp, i);
1689 }
1690
1691 for (i = 0; i < 1 + power; ++i) {
1692 rec->p[i] = isl_upoly_zero(div->ctx);
1693 if (!rec->p[i])
1694 goto error;
1695 rec->n++;
1696 }
1697 cst = isl_upoly_as_cst(rec->p[power]);
1698 isl_int_set_si(cst->n, 1);
1699
1700 isl_div_free(div);
1701
1702 return qp;
1703 error:
1704 isl_qpolynomial_free(qp);
1705 isl_div_free(div);
1706 return NULL;
1707 }
1708
1709 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1710 {
1711 return isl_qpolynomial_div_pow(div, 1);
1712 }
1713
1714 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1715 const isl_int n, const isl_int d)
1716 {
1717 struct isl_qpolynomial *qp;
1718 struct isl_upoly_cst *cst;
1719
1720 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1721 if (!qp)
1722 return NULL;
1723
1724 cst = isl_upoly_as_cst(qp->upoly);
1725 isl_int_set(cst->n, n);
1726 isl_int_set(cst->d, d);
1727
1728 return qp;
1729 }
1730
1731 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1732 {
1733 struct isl_upoly_rec *rec;
1734 int i;
1735
1736 if (!up)
1737 return -1;
1738
1739 if (isl_upoly_is_cst(up))
1740 return 0;
1741
1742 if (up->var < d)
1743 active[up->var] = 1;
1744
1745 rec = isl_upoly_as_rec(up);
1746 for (i = 0; i < rec->n; ++i)
1747 if (up_set_active(rec->p[i], active, d) < 0)
1748 return -1;
1749
1750 return 0;
1751 }
1752
1753 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1754 {
1755 int i, j;
1756 int d = isl_dim_total(qp->dim);
1757
1758 if (!qp || !active)
1759 return -1;
1760
1761 for (i = 0; i < d; ++i)
1762 for (j = 0; j < qp->div->n_row; ++j) {
1763 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1764 continue;
1765 active[i] = 1;
1766 break;
1767 }
1768
1769 return up_set_active(qp->upoly, active, d);
1770 }
1771
1772 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1773 enum isl_dim_type type, unsigned first, unsigned n)
1774 {
1775 int i;
1776 int *active = NULL;
1777 int involves = 0;
1778
1779 if (!qp)
1780 return -1;
1781 if (n == 0)
1782 return 0;
1783
1784 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1785 return -1);
1786 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1787 type == isl_dim_set, return -1);
1788
1789 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1790 if (set_active(qp, active) < 0)
1791 goto error;
1792
1793 if (type == isl_dim_set)
1794 first += isl_dim_size(qp->dim, isl_dim_param);
1795 for (i = 0; i < n; ++i)
1796 if (active[first + i]) {
1797 involves = 1;
1798 break;
1799 }
1800
1801 free(active);
1802
1803 return involves;
1804 error:
1805 free(active);
1806 return -1;
1807 }
1808
1809 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1810 unsigned first, unsigned n)
1811 {
1812 int i;
1813 struct isl_upoly_rec *rec;
1814
1815 if (!up)
1816 return NULL;
1817 if (n == 0 || up->var < 0 || up->var < first)
1818 return up;
1819 if (up->var < first + n) {
1820 up = replace_by_constant_term(up);
1821 return isl_upoly_drop(up, first, n);
1822 }
1823 up = isl_upoly_cow(up);
1824 if (!up)
1825 return NULL;
1826 up->var -= n;
1827 rec = isl_upoly_as_rec(up);
1828 if (!rec)
1829 goto error;
1830
1831 for (i = 0; i < rec->n; ++i) {
1832 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1833 if (!rec->p[i])
1834 goto error;
1835 }
1836
1837 return up;
1838 error:
1839 isl_upoly_free(up);
1840 return NULL;
1841 }
1842
1843 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1844 __isl_take isl_qpolynomial *qp,
1845 enum isl_dim_type type, unsigned pos, const char *s)
1846 {
1847 qp = isl_qpolynomial_cow(qp);
1848 if (!qp)
1849 return NULL;
1850 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1851 if (!qp->dim)
1852 goto error;
1853 return qp;
1854 error:
1855 isl_qpolynomial_free(qp);
1856 return NULL;
1857 }
1858
1859 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1860 __isl_take isl_qpolynomial *qp,
1861 enum isl_dim_type type, unsigned first, unsigned n)
1862 {
1863 if (!qp)
1864 return NULL;
1865 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1866 return qp;
1867
1868 qp = isl_qpolynomial_cow(qp);
1869 if (!qp)
1870 return NULL;
1871
1872 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1873 goto error);
1874 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1875 type == isl_dim_set, goto error);
1876
1877 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1878 if (!qp->dim)
1879 goto error;
1880
1881 if (type == isl_dim_set)
1882 first += isl_dim_size(qp->dim, isl_dim_param);
1883
1884 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1885 if (!qp->div)
1886 goto error;
1887
1888 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1889 if (!qp->upoly)
1890 goto error;
1891
1892 return qp;
1893 error:
1894 isl_qpolynomial_free(qp);
1895 return NULL;
1896 }
1897
1898 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1899 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1900 {
1901 int i;
1902 struct isl_upoly_rec *rec;
1903 struct isl_upoly *base, *res;
1904
1905 if (!up)
1906 return NULL;
1907
1908 if (isl_upoly_is_cst(up))
1909 return up;
1910
1911 if (up->var < first)
1912 return up;
1913
1914 rec = isl_upoly_as_rec(up);
1915 if (!rec)
1916 goto error;
1917
1918 isl_assert(up->ctx, rec->n >= 1, goto error);
1919
1920 if (up->var >= first + n)
1921 base = isl_upoly_pow(up->ctx, up->var, 1);
1922 else
1923 base = isl_upoly_copy(subs[up->var - first]);
1924
1925 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1926 for (i = rec->n - 2; i >= 0; --i) {
1927 struct isl_upoly *t;
1928 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1929 res = isl_upoly_mul(res, isl_upoly_copy(base));
1930 res = isl_upoly_sum(res, t);
1931 }
1932
1933 isl_upoly_free(base);
1934 isl_upoly_free(up);
1935
1936 return res;
1937 error:
1938 isl_upoly_free(up);
1939 return NULL;
1940 }
1941
1942 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1943 isl_int denom, unsigned len)
1944 {
1945 int i;
1946 struct isl_upoly *up;
1947
1948 isl_assert(ctx, len >= 1, return NULL);
1949
1950 up = isl_upoly_rat_cst(ctx, f[0], denom);
1951 for (i = 0; i < len - 1; ++i) {
1952 struct isl_upoly *t;
1953 struct isl_upoly *c;
1954
1955 if (isl_int_is_zero(f[1 + i]))
1956 continue;
1957
1958 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1959 t = isl_upoly_pow(ctx, i, 1);
1960 t = isl_upoly_mul(c, t);
1961 up = isl_upoly_sum(up, t);
1962 }
1963
1964 return up;
1965 }
1966
1967 /* Replace the integer division identified by "div" by the polynomial "s".
1968 * The integer division is assumed not to appear in the definition
1969 * of any other integer divisions.
1970 */
1971 static __isl_give isl_qpolynomial *substitute_div(
1972 __isl_take isl_qpolynomial *qp,
1973 int div, __isl_take struct isl_upoly *s)
1974 {
1975 int i;
1976 int total;
1977 int *reordering;
1978
1979 if (!qp || !s)
1980 goto error;
1981
1982 qp = isl_qpolynomial_cow(qp);
1983 if (!qp)
1984 goto error;
1985
1986 total = isl_dim_total(qp->dim);
1987 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1988 if (!qp->upoly)
1989 goto error;
1990
1991 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1992 if (!reordering)
1993 goto error;
1994 for (i = 0; i < total + div; ++i)
1995 reordering[i] = i;
1996 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1997 reordering[i] = i - 1;
1998 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1999 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2000 qp->upoly = reorder(qp->upoly, reordering);
2001 free(reordering);
2002
2003 if (!qp->upoly || !qp->div)
2004 goto error;
2005
2006 isl_upoly_free(s);
2007 return qp;
2008 error:
2009 isl_qpolynomial_free(qp);
2010 isl_upoly_free(s);
2011 return NULL;
2012 }
2013
2014 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2015 * divisions because d is equal to 1 by their definition, i.e., e.
2016 */
2017 static __isl_give isl_qpolynomial *substitute_non_divs(
2018 __isl_take isl_qpolynomial *qp)
2019 {
2020 int i, j;
2021 int total;
2022 struct isl_upoly *s;
2023
2024 if (!qp)
2025 return NULL;
2026
2027 total = isl_dim_total(qp->dim);
2028 for (i = 0; qp && i < qp->div->n_row; ++i) {
2029 if (!isl_int_is_one(qp->div->row[i][0]))
2030 continue;
2031 for (j = i + 1; j < qp->div->n_row; ++j) {
2032 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2033 continue;
2034 isl_seq_combine(qp->div->row[j] + 1,
2035 qp->div->ctx->one, qp->div->row[j] + 1,
2036 qp->div->row[j][2 + total + i],
2037 qp->div->row[i] + 1, 1 + total + i);
2038 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2039 normalize_div(qp, j);
2040 }
2041 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2042 qp->div->row[i][0], qp->div->n_col - 1);
2043 qp = substitute_div(qp, i, s);
2044 --i;
2045 }
2046
2047 return qp;
2048 }
2049
2050 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2051 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2052 {
2053 int i, j, k;
2054 isl_int denom;
2055 unsigned total;
2056 unsigned n_div;
2057 struct isl_upoly *up;
2058
2059 if (!eq)
2060 goto error;
2061 if (eq->n_eq == 0) {
2062 isl_basic_set_free(eq);
2063 return qp;
2064 }
2065
2066 qp = isl_qpolynomial_cow(qp);
2067 if (!qp)
2068 goto error;
2069 qp->div = isl_mat_cow(qp->div);
2070 if (!qp->div)
2071 goto error;
2072
2073 total = 1 + isl_dim_total(eq->dim);
2074 n_div = eq->n_div;
2075 isl_int_init(denom);
2076 for (i = 0; i < eq->n_eq; ++i) {
2077 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2078 if (j < 0 || j == 0 || j >= total)
2079 continue;
2080
2081 for (k = 0; k < qp->div->n_row; ++k) {
2082 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2083 continue;
2084 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2085 &qp->div->row[k][0]);
2086 normalize_div(qp, k);
2087 }
2088
2089 if (isl_int_is_pos(eq->eq[i][j]))
2090 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2091 isl_int_abs(denom, eq->eq[i][j]);
2092 isl_int_set_si(eq->eq[i][j], 0);
2093
2094 up = isl_upoly_from_affine(qp->dim->ctx,
2095 eq->eq[i], denom, total);
2096 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2097 isl_upoly_free(up);
2098 }
2099 isl_int_clear(denom);
2100
2101 if (!qp->upoly)
2102 goto error;
2103
2104 isl_basic_set_free(eq);
2105
2106 qp = substitute_non_divs(qp);
2107 qp = sort_divs(qp);
2108
2109 return qp;
2110 error:
2111 isl_basic_set_free(eq);
2112 isl_qpolynomial_free(qp);
2113 return NULL;
2114 }
2115
2116 static __isl_give isl_basic_set *add_div_constraints(
2117 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2118 {
2119 int i;
2120 unsigned total;
2121
2122 if (!bset || !div)
2123 goto error;
2124
2125 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2126 if (!bset)
2127 goto error;
2128 total = isl_basic_set_total_dim(bset);
2129 for (i = 0; i < div->n_row; ++i)
2130 if (isl_basic_set_add_div_constraints_var(bset,
2131 total - div->n_row + i, div->row[i]) < 0)
2132 goto error;
2133
2134 isl_mat_free(div);
2135 return bset;
2136 error:
2137 isl_mat_free(div);
2138 isl_basic_set_free(bset);
2139 return NULL;
2140 }
2141
2142 /* Look for equalities among the variables shared by context and qp
2143 * and the integer divisions of qp, if any.
2144 * The equalities are then used to eliminate variables and/or integer
2145 * divisions from qp.
2146 */
2147 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2148 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2149 {
2150 isl_basic_set *aff;
2151
2152 if (!qp)
2153 goto error;
2154 if (qp->div->n_row > 0) {
2155 isl_basic_set *bset;
2156 context = isl_set_add_dims(context, isl_dim_set,
2157 qp->div->n_row);
2158 bset = isl_basic_set_universe(isl_set_get_dim(context));
2159 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2160 context = isl_set_intersect(context,
2161 isl_set_from_basic_set(bset));
2162 }
2163
2164 aff = isl_set_affine_hull(context);
2165 return isl_qpolynomial_substitute_equalities(qp, aff);
2166 error:
2167 isl_qpolynomial_free(qp);
2168 isl_set_free(context);
2169 return NULL;
2170 }
2171
2172 #undef PW
2173 #define PW isl_pw_qpolynomial
2174 #undef EL
2175 #define EL isl_qpolynomial
2176 #undef IS_ZERO
2177 #define IS_ZERO is_zero
2178 #undef FIELD
2179 #define FIELD qp
2180
2181 #include <isl_pw_templ.c>
2182
2183 #undef UNION
2184 #define UNION isl_union_pw_qpolynomial
2185 #undef PART
2186 #define PART isl_pw_qpolynomial
2187 #undef PARTS
2188 #define PARTS pw_qpolynomial
2189
2190 #include <isl_union_templ.c>
2191
2192 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2193 {
2194 if (!pwqp)
2195 return -1;
2196
2197 if (pwqp->n != -1)
2198 return 0;
2199
2200 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2201 return 0;
2202
2203 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2204 }
2205
2206 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2207 __isl_take isl_pw_qpolynomial *pwqp1,
2208 __isl_take isl_pw_qpolynomial *pwqp2)
2209 {
2210 int i, j, n;
2211 struct isl_pw_qpolynomial *res;
2212 isl_set *set;
2213
2214 if (!pwqp1 || !pwqp2)
2215 goto error;
2216
2217 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2218 goto error);
2219
2220 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2221 isl_pw_qpolynomial_free(pwqp2);
2222 return pwqp1;
2223 }
2224
2225 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2226 isl_pw_qpolynomial_free(pwqp1);
2227 return pwqp2;
2228 }
2229
2230 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2231 isl_pw_qpolynomial_free(pwqp1);
2232 return pwqp2;
2233 }
2234
2235 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2236 isl_pw_qpolynomial_free(pwqp2);
2237 return pwqp1;
2238 }
2239
2240 n = pwqp1->n * pwqp2->n;
2241 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2242
2243 for (i = 0; i < pwqp1->n; ++i) {
2244 for (j = 0; j < pwqp2->n; ++j) {
2245 struct isl_set *common;
2246 struct isl_qpolynomial *prod;
2247 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2248 isl_set_copy(pwqp2->p[j].set));
2249 if (isl_set_fast_is_empty(common)) {
2250 isl_set_free(common);
2251 continue;
2252 }
2253
2254 prod = isl_qpolynomial_mul(
2255 isl_qpolynomial_copy(pwqp1->p[i].qp),
2256 isl_qpolynomial_copy(pwqp2->p[j].qp));
2257
2258 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2259 }
2260 }
2261
2262 isl_pw_qpolynomial_free(pwqp1);
2263 isl_pw_qpolynomial_free(pwqp2);
2264
2265 return res;
2266 error:
2267 isl_pw_qpolynomial_free(pwqp1);
2268 isl_pw_qpolynomial_free(pwqp2);
2269 return NULL;
2270 }
2271
2272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2273 __isl_take isl_pw_qpolynomial *pwqp)
2274 {
2275 int i;
2276
2277 if (!pwqp)
2278 return NULL;
2279
2280 if (isl_pw_qpolynomial_is_zero(pwqp))
2281 return pwqp;
2282
2283 pwqp = isl_pw_qpolynomial_cow(pwqp);
2284 if (!pwqp)
2285 return NULL;
2286
2287 for (i = 0; i < pwqp->n; ++i) {
2288 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2289 if (!pwqp->p[i].qp)
2290 goto error;
2291 }
2292
2293 return pwqp;
2294 error:
2295 isl_pw_qpolynomial_free(pwqp);
2296 return NULL;
2297 }
2298
2299 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2300 __isl_take isl_pw_qpolynomial *pwqp1,
2301 __isl_take isl_pw_qpolynomial *pwqp2)
2302 {
2303 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2304 }
2305
2306 __isl_give struct isl_upoly *isl_upoly_eval(
2307 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2308 {
2309 int i;
2310 struct isl_upoly_rec *rec;
2311 struct isl_upoly *res;
2312 struct isl_upoly *base;
2313
2314 if (isl_upoly_is_cst(up)) {
2315 isl_vec_free(vec);
2316 return up;
2317 }
2318
2319 rec = isl_upoly_as_rec(up);
2320 if (!rec)
2321 goto error;
2322
2323 isl_assert(up->ctx, rec->n >= 1, goto error);
2324
2325 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2326
2327 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2328 isl_vec_copy(vec));
2329
2330 for (i = rec->n - 2; i >= 0; --i) {
2331 res = isl_upoly_mul(res, isl_upoly_copy(base));
2332 res = isl_upoly_sum(res,
2333 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2334 isl_vec_copy(vec)));
2335 }
2336
2337 isl_upoly_free(base);
2338 isl_upoly_free(up);
2339 isl_vec_free(vec);
2340 return res;
2341 error:
2342 isl_upoly_free(up);
2343 isl_vec_free(vec);
2344 return NULL;
2345 }
2346
2347 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2348 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2349 {
2350 isl_vec *ext;
2351 struct isl_upoly *up;
2352 isl_dim *dim;
2353
2354 if (!qp || !pnt)
2355 goto error;
2356 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2357
2358 if (qp->div->n_row == 0)
2359 ext = isl_vec_copy(pnt->vec);
2360 else {
2361 int i;
2362 unsigned dim = isl_dim_total(qp->dim);
2363 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2364 if (!ext)
2365 goto error;
2366
2367 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2368 for (i = 0; i < qp->div->n_row; ++i) {
2369 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2370 1 + dim + i, &ext->el[1+dim+i]);
2371 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2372 qp->div->row[i][0]);
2373 }
2374 }
2375
2376 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2377 if (!up)
2378 goto error;
2379
2380 dim = isl_dim_copy(qp->dim);
2381 isl_qpolynomial_free(qp);
2382 isl_point_free(pnt);
2383
2384 return isl_qpolynomial_alloc(dim, 0, up);
2385 error:
2386 isl_qpolynomial_free(qp);
2387 isl_point_free(pnt);
2388 return NULL;
2389 }
2390
2391 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2392 __isl_keep struct isl_upoly_cst *cst2)
2393 {
2394 int cmp;
2395 isl_int t;
2396 isl_int_init(t);
2397 isl_int_mul(t, cst1->n, cst2->d);
2398 isl_int_submul(t, cst2->n, cst1->d);
2399 cmp = isl_int_sgn(t);
2400 isl_int_clear(t);
2401 return cmp;
2402 }
2403
2404 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2405 __isl_keep isl_qpolynomial *qp2)
2406 {
2407 struct isl_upoly_cst *cst1, *cst2;
2408
2409 if (!qp1 || !qp2)
2410 return -1;
2411 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2412 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2413 if (isl_qpolynomial_is_nan(qp1))
2414 return -1;
2415 if (isl_qpolynomial_is_nan(qp2))
2416 return -1;
2417 cst1 = isl_upoly_as_cst(qp1->upoly);
2418 cst2 = isl_upoly_as_cst(qp2->upoly);
2419
2420 return isl_upoly_cmp(cst1, cst2) <= 0;
2421 }
2422
2423 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2424 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2425 {
2426 struct isl_upoly_cst *cst1, *cst2;
2427 int cmp;
2428
2429 if (!qp1 || !qp2)
2430 goto error;
2431 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2432 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2433 cst1 = isl_upoly_as_cst(qp1->upoly);
2434 cst2 = isl_upoly_as_cst(qp2->upoly);
2435 cmp = isl_upoly_cmp(cst1, cst2);
2436
2437 if (cmp <= 0) {
2438 isl_qpolynomial_free(qp2);
2439 } else {
2440 isl_qpolynomial_free(qp1);
2441 qp1 = qp2;
2442 }
2443 return qp1;
2444 error:
2445 isl_qpolynomial_free(qp1);
2446 isl_qpolynomial_free(qp2);
2447 return NULL;
2448 }
2449
2450 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2451 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2452 {
2453 struct isl_upoly_cst *cst1, *cst2;
2454 int cmp;
2455
2456 if (!qp1 || !qp2)
2457 goto error;
2458 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2459 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2460 cst1 = isl_upoly_as_cst(qp1->upoly);
2461 cst2 = isl_upoly_as_cst(qp2->upoly);
2462 cmp = isl_upoly_cmp(cst1, cst2);
2463
2464 if (cmp >= 0) {
2465 isl_qpolynomial_free(qp2);
2466 } else {
2467 isl_qpolynomial_free(qp1);
2468 qp1 = qp2;
2469 }
2470 return qp1;
2471 error:
2472 isl_qpolynomial_free(qp1);
2473 isl_qpolynomial_free(qp2);
2474 return NULL;
2475 }
2476
2477 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2478 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2479 unsigned first, unsigned n)
2480 {
2481 unsigned total;
2482 unsigned g_pos;
2483 int *exp;
2484
2485 if (n == 0)
2486 return qp;
2487
2488 qp = isl_qpolynomial_cow(qp);
2489 if (!qp)
2490 return NULL;
2491
2492 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2493 goto error);
2494
2495 g_pos = pos(qp->dim, type) + first;
2496
2497 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2498 if (!qp->div)
2499 goto error;
2500
2501 total = qp->div->n_col - 2;
2502 if (total > g_pos) {
2503 int i;
2504 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2505 if (!exp)
2506 goto error;
2507 for (i = 0; i < total - g_pos; ++i)
2508 exp[i] = i + n;
2509 qp->upoly = expand(qp->upoly, exp, g_pos);
2510 free(exp);
2511 if (!qp->upoly)
2512 goto error;
2513 }
2514
2515 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2516 if (!qp->dim)
2517 goto error;
2518
2519 return qp;
2520 error:
2521 isl_qpolynomial_free(qp);
2522 return NULL;
2523 }
2524
2525 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2526 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2527 {
2528 unsigned pos;
2529
2530 pos = isl_qpolynomial_dim(qp, type);
2531
2532 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2533 }
2534
2535 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2536 __isl_take isl_pw_qpolynomial *pwqp,
2537 enum isl_dim_type type, unsigned n)
2538 {
2539 unsigned pos;
2540
2541 pos = isl_pw_qpolynomial_dim(pwqp, type);
2542
2543 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2544 }
2545
2546 static int *reordering_move(isl_ctx *ctx,
2547 unsigned len, unsigned dst, unsigned src, unsigned n)
2548 {
2549 int i;
2550 int *reordering;
2551
2552 reordering = isl_alloc_array(ctx, int, len);
2553 if (!reordering)
2554 return NULL;
2555
2556 if (dst <= src) {
2557 for (i = 0; i < dst; ++i)
2558 reordering[i] = i;
2559 for (i = 0; i < n; ++i)
2560 reordering[src + i] = dst + i;
2561 for (i = 0; i < src - dst; ++i)
2562 reordering[dst + i] = dst + n + i;
2563 for (i = 0; i < len - src - n; ++i)
2564 reordering[src + n + i] = src + n + i;
2565 } else {
2566 for (i = 0; i < src; ++i)
2567 reordering[i] = i;
2568 for (i = 0; i < n; ++i)
2569 reordering[src + i] = dst + i;
2570 for (i = 0; i < dst - src; ++i)
2571 reordering[src + n + i] = src + i;
2572 for (i = 0; i < len - dst - n; ++i)
2573 reordering[dst + n + i] = dst + n + i;
2574 }
2575
2576 return reordering;
2577 }
2578
2579 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2580 __isl_take isl_qpolynomial *qp,
2581 enum isl_dim_type dst_type, unsigned dst_pos,
2582 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2583 {
2584 unsigned g_dst_pos;
2585 unsigned g_src_pos;
2586 int *reordering;
2587
2588 qp = isl_qpolynomial_cow(qp);
2589 if (!qp)
2590 return NULL;
2591
2592 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2593 goto error);
2594
2595 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2596 g_src_pos = pos(qp->dim, src_type) + src_pos;
2597 if (dst_type > src_type)
2598 g_dst_pos -= n;
2599
2600 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2601 if (!qp->div)
2602 goto error;
2603 qp = sort_divs(qp);
2604 if (!qp)
2605 goto error;
2606
2607 reordering = reordering_move(qp->dim->ctx,
2608 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2609 if (!reordering)
2610 goto error;
2611
2612 qp->upoly = reorder(qp->upoly, reordering);
2613 free(reordering);
2614 if (!qp->upoly)
2615 goto error;
2616
2617 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2618 if (!qp->dim)
2619 goto error;
2620
2621 return qp;
2622 error:
2623 isl_qpolynomial_free(qp);
2624 return NULL;
2625 }
2626
2627 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2628 isl_int *f, isl_int denom)
2629 {
2630 struct isl_upoly *up;
2631
2632 if (!dim)
2633 return NULL;
2634
2635 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2636
2637 return isl_qpolynomial_alloc(dim, 0, up);
2638 }
2639
2640 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2641 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2642 {
2643 isl_int denom;
2644 isl_dim *dim;
2645 struct isl_upoly *up;
2646 isl_qpolynomial *qp;
2647 int sgn;
2648
2649 if (!c)
2650 return NULL;
2651
2652 isl_int_init(denom);
2653
2654 isl_constraint_get_coefficient(c, type, pos, &denom);
2655 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2656 sgn = isl_int_sgn(denom);
2657 isl_int_abs(denom, denom);
2658 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2659 1 + isl_constraint_dim(c, isl_dim_all));
2660 if (sgn < 0)
2661 isl_int_neg(denom, denom);
2662 isl_constraint_set_coefficient(c, type, pos, denom);
2663
2664 dim = isl_dim_copy(c->bmap->dim);
2665
2666 isl_int_clear(denom);
2667 isl_constraint_free(c);
2668
2669 qp = isl_qpolynomial_alloc(dim, 0, up);
2670 if (sgn > 0)
2671 qp = isl_qpolynomial_neg(qp);
2672 return qp;
2673 }
2674
2675 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2676 * in "qp" by subs[i].
2677 */
2678 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2679 __isl_take isl_qpolynomial *qp,
2680 enum isl_dim_type type, unsigned first, unsigned n,
2681 __isl_keep isl_qpolynomial **subs)
2682 {
2683 int i;
2684 struct isl_upoly **ups;
2685
2686 if (n == 0)
2687 return qp;
2688
2689 qp = isl_qpolynomial_cow(qp);
2690 if (!qp)
2691 return NULL;
2692 for (i = 0; i < n; ++i)
2693 if (!subs[i])
2694 goto error;
2695
2696 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2697 goto error);
2698
2699 for (i = 0; i < n; ++i)
2700 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2701 goto error);
2702
2703 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2704 for (i = 0; i < n; ++i)
2705 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2706
2707 first += pos(qp->dim, type);
2708
2709 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2710 if (!ups)
2711 goto error;
2712 for (i = 0; i < n; ++i)
2713 ups[i] = subs[i]->upoly;
2714
2715 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2716
2717 free(ups);
2718
2719 if (!qp->upoly)
2720 goto error;
2721
2722 return qp;
2723 error:
2724 isl_qpolynomial_free(qp);
2725 return NULL;
2726 }
2727
2728 /* Extend "bset" with extra set dimensions for each integer division
2729 * in "qp" and then call "fn" with the extended bset and the polynomial
2730 * that results from replacing each of the integer divisions by the
2731 * corresponding extra set dimension.
2732 */
2733 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2734 __isl_keep isl_basic_set *bset,
2735 int (*fn)(__isl_take isl_basic_set *bset,
2736 __isl_take isl_qpolynomial *poly, void *user), void *user)
2737 {
2738 isl_dim *dim;
2739 isl_mat *div;
2740 isl_qpolynomial *poly;
2741
2742 if (!qp || !bset)
2743 goto error;
2744 if (qp->div->n_row == 0)
2745 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2746 user);
2747
2748 div = isl_mat_copy(qp->div);
2749 dim = isl_dim_copy(qp->dim);
2750 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2751 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2752 bset = isl_basic_set_copy(bset);
2753 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2754 bset = add_div_constraints(bset, div);
2755
2756 return fn(bset, poly, user);
2757 error:
2758 return -1;
2759 }
2760
2761 /* Return total degree in variables first (inclusive) up to last (exclusive).
2762 */
2763 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2764 {
2765 int deg = -1;
2766 int i;
2767 struct isl_upoly_rec *rec;
2768
2769 if (!up)
2770 return -2;
2771 if (isl_upoly_is_zero(up))
2772 return -1;
2773 if (isl_upoly_is_cst(up) || up->var < first)
2774 return 0;
2775
2776 rec = isl_upoly_as_rec(up);
2777 if (!rec)
2778 return -2;
2779
2780 for (i = 0; i < rec->n; ++i) {
2781 int d;
2782
2783 if (isl_upoly_is_zero(rec->p[i]))
2784 continue;
2785 d = isl_upoly_degree(rec->p[i], first, last);
2786 if (up->var < last)
2787 d += i;
2788 if (d > deg)
2789 deg = d;
2790 }
2791
2792 return deg;
2793 }
2794
2795 /* Return total degree in set variables.
2796 */
2797 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2798 {
2799 unsigned ovar;
2800 unsigned nvar;
2801
2802 if (!poly)
2803 return -2;
2804
2805 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2806 nvar = isl_dim_size(poly->dim, isl_dim_set);
2807 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2808 }
2809
2810 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2811 unsigned pos, int deg)
2812 {
2813 int i;
2814 struct isl_upoly_rec *rec;
2815
2816 if (!up)
2817 return NULL;
2818
2819 if (isl_upoly_is_cst(up) || up->var < pos) {
2820 if (deg == 0)
2821 return isl_upoly_copy(up);
2822 else
2823 return isl_upoly_zero(up->ctx);
2824 }
2825
2826 rec = isl_upoly_as_rec(up);
2827 if (!rec)
2828 return NULL;
2829
2830 if (up->var == pos) {
2831 if (deg < rec->n)
2832 return isl_upoly_copy(rec->p[deg]);
2833 else
2834 return isl_upoly_zero(up->ctx);
2835 }
2836
2837 up = isl_upoly_copy(up);
2838 up = isl_upoly_cow(up);
2839 rec = isl_upoly_as_rec(up);
2840 if (!rec)
2841 goto error;
2842
2843 for (i = 0; i < rec->n; ++i) {
2844 struct isl_upoly *t;
2845 t = isl_upoly_coeff(rec->p[i], pos, deg);
2846 if (!t)
2847 goto error;
2848 isl_upoly_free(rec->p[i]);
2849 rec->p[i] = t;
2850 }
2851
2852 return up;
2853 error:
2854 isl_upoly_free(up);
2855 return NULL;
2856 }
2857
2858 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2859 */
2860 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2861 __isl_keep isl_qpolynomial *qp,
2862 enum isl_dim_type type, unsigned t_pos, int deg)
2863 {
2864 unsigned g_pos;
2865 struct isl_upoly *up;
2866 isl_qpolynomial *c;
2867
2868 if (!qp)
2869 return NULL;
2870
2871 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2872 return NULL);
2873
2874 g_pos = pos(qp->dim, type) + t_pos;
2875 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2876
2877 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2878 if (!c)
2879 return NULL;
2880 isl_mat_free(c->div);
2881 c->div = isl_mat_copy(qp->div);
2882 if (!c->div)
2883 goto error;
2884 return c;
2885 error:
2886 isl_qpolynomial_free(c);
2887 return NULL;
2888 }
2889
2890 /* Homogenize the polynomial in the variables first (inclusive) up to
2891 * last (exclusive) by inserting powers of variable first.
2892 * Variable first is assumed not to appear in the input.
2893 */
2894 __isl_give struct isl_upoly *isl_upoly_homogenize(
2895 __isl_take struct isl_upoly *up, int deg, int target,
2896 int first, int last)
2897 {
2898 int i;
2899 struct isl_upoly_rec *rec;
2900
2901 if (!up)
2902 return NULL;
2903 if (isl_upoly_is_zero(up))
2904 return up;
2905 if (deg == target)
2906 return up;
2907 if (isl_upoly_is_cst(up) || up->var < first) {
2908 struct isl_upoly *hom;
2909
2910 hom = isl_upoly_pow(up->ctx, first, target - deg);
2911 if (!hom)
2912 goto error;
2913 rec = isl_upoly_as_rec(hom);
2914 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2915
2916 return hom;
2917 }
2918
2919 up = isl_upoly_cow(up);
2920 rec = isl_upoly_as_rec(up);
2921 if (!rec)
2922 goto error;
2923
2924 for (i = 0; i < rec->n; ++i) {
2925 if (isl_upoly_is_zero(rec->p[i]))
2926 continue;
2927 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2928 up->var < last ? deg + i : i, target,
2929 first, last);
2930 if (!rec->p[i])
2931 goto error;
2932 }
2933
2934 return up;
2935 error:
2936 isl_upoly_free(up);
2937 return NULL;
2938 }
2939
2940 /* Homogenize the polynomial in the set variables by introducing
2941 * powers of an extra set variable at position 0.
2942 */
2943 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2944 __isl_take isl_qpolynomial *poly)
2945 {
2946 unsigned ovar;
2947 unsigned nvar;
2948 int deg = isl_qpolynomial_degree(poly);
2949
2950 if (deg < -1)
2951 goto error;
2952
2953 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2954 poly = isl_qpolynomial_cow(poly);
2955 if (!poly)
2956 goto error;
2957
2958 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2959 nvar = isl_dim_size(poly->dim, isl_dim_set);
2960 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2961 ovar, ovar + nvar);
2962 if (!poly->upoly)
2963 goto error;
2964
2965 return poly;
2966 error:
2967 isl_qpolynomial_free(poly);
2968 return NULL;
2969 }
2970
2971 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2972 __isl_take isl_mat *div)
2973 {
2974 isl_term *term;
2975 int n;
2976
2977 if (!dim || !div)
2978 goto error;
2979
2980 n = isl_dim_total(dim) + div->n_row;
2981
2982 term = isl_calloc(dim->ctx, struct isl_term,
2983 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2984 if (!term)
2985 goto error;
2986
2987 term->ref = 1;
2988 term->dim = dim;
2989 term->div = div;
2990 isl_int_init(term->n);
2991 isl_int_init(term->d);
2992
2993 return term;
2994 error:
2995 isl_dim_free(dim);
2996 isl_mat_free(div);
2997 return NULL;
2998 }
2999
3000 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3001 {
3002 if (!term)
3003 return NULL;
3004
3005 term->ref++;
3006 return term;
3007 }
3008
3009 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3010 {
3011 int i;
3012 isl_term *dup;
3013 unsigned total;
3014
3015 if (term)
3016 return NULL;
3017
3018 total = isl_dim_total(term->dim) + term->div->n_row;
3019
3020 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3021 if (!dup)
3022 return NULL;
3023
3024 isl_int_set(dup->n, term->n);
3025 isl_int_set(dup->d, term->d);
3026
3027 for (i = 0; i < total; ++i)
3028 dup->pow[i] = term->pow[i];
3029
3030 return dup;
3031 }
3032
3033 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3034 {
3035 if (!term)
3036 return NULL;
3037
3038 if (term->ref == 1)
3039 return term;
3040 term->ref--;
3041 return isl_term_dup(term);
3042 }
3043
3044 void isl_term_free(__isl_take isl_term *term)
3045 {
3046 if (!term)
3047 return;
3048
3049 if (--term->ref > 0)
3050 return;
3051
3052 isl_dim_free(term->dim);
3053 isl_mat_free(term->div);
3054 isl_int_clear(term->n);
3055 isl_int_clear(term->d);
3056 free(term);
3057 }
3058
3059 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3060 {
3061 if (!term)
3062 return 0;
3063
3064 switch (type) {
3065 case isl_dim_param:
3066 case isl_dim_in:
3067 case isl_dim_out: return isl_dim_size(term->dim, type);
3068 case isl_dim_div: return term->div->n_row;
3069 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3070 default: return 0;
3071 }
3072 }
3073
3074 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3075 {
3076 return term ? term->dim->ctx : NULL;
3077 }
3078
3079 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3080 {
3081 if (!term)
3082 return;
3083 isl_int_set(*n, term->n);
3084 }
3085
3086 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3087 {
3088 if (!term)
3089 return;
3090 isl_int_set(*d, term->d);
3091 }
3092
3093 int isl_term_get_exp(__isl_keep isl_term *term,
3094 enum isl_dim_type type, unsigned pos)
3095 {
3096 if (!term)
3097 return -1;
3098
3099 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3100
3101 if (type >= isl_dim_set)
3102 pos += isl_dim_size(term->dim, isl_dim_param);
3103 if (type >= isl_dim_div)
3104 pos += isl_dim_size(term->dim, isl_dim_set);
3105
3106 return term->pow[pos];
3107 }
3108
3109 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3110 {
3111 isl_basic_map *bmap;
3112 unsigned total;
3113 int k;
3114
3115 if (!term)
3116 return NULL;
3117
3118 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3119 return NULL);
3120
3121 total = term->div->n_col - term->div->n_row - 2;
3122 /* No nested divs for now */
3123 isl_assert(term->dim->ctx,
3124 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3125 term->div->n_row) == -1,
3126 return NULL);
3127
3128 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3129 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3130 goto error;
3131
3132 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3133
3134 return isl_basic_map_div(bmap, k);
3135 error:
3136 isl_basic_map_free(bmap);
3137 return NULL;
3138 }
3139
3140 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3141 int (*fn)(__isl_take isl_term *term, void *user),
3142 __isl_take isl_term *term, void *user)
3143 {
3144 int i;
3145 struct isl_upoly_rec *rec;
3146
3147 if (!up || !term)
3148 goto error;
3149
3150 if (isl_upoly_is_zero(up))
3151 return term;
3152
3153 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3154 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3155 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3156
3157 if (isl_upoly_is_cst(up)) {
3158 struct isl_upoly_cst *cst;
3159 cst = isl_upoly_as_cst(up);
3160 if (!cst)
3161 goto error;
3162 term = isl_term_cow(term);
3163 if (!term)
3164 goto error;
3165 isl_int_set(term->n, cst->n);
3166 isl_int_set(term->d, cst->d);
3167 if (fn(isl_term_copy(term), user) < 0)
3168 goto error;
3169 return term;
3170 }
3171
3172 rec = isl_upoly_as_rec(up);
3173 if (!rec)
3174 goto error;
3175
3176 for (i = 0; i < rec->n; ++i) {
3177 term = isl_term_cow(term);
3178 if (!term)
3179 goto error;
3180 term->pow[up->var] = i;
3181 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3182 if (!term)
3183 goto error;
3184 }
3185 term->pow[up->var] = 0;
3186
3187 return term;
3188 error:
3189 isl_term_free(term);
3190 return NULL;
3191 }
3192
3193 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3194 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3195 {
3196 isl_term *term;
3197
3198 if (!qp)
3199 return -1;
3200
3201 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3202 if (!term)
3203 return -1;
3204
3205 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3206
3207 isl_term_free(term);
3208
3209 return term ? 0 : -1;
3210 }
3211
3212 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3213 {
3214 struct isl_upoly *up;
3215 isl_qpolynomial *qp;
3216 int i, n;
3217
3218 if (!term)
3219 return NULL;
3220
3221 n = isl_dim_total(term->dim) + term->div->n_row;
3222
3223 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3224 for (i = 0; i < n; ++i) {
3225 if (!term->pow[i])
3226 continue;
3227 up = isl_upoly_mul(up,
3228 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3229 }
3230
3231 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3232 if (!qp)
3233 goto error;
3234 isl_mat_free(qp->div);
3235 qp->div = isl_mat_copy(term->div);
3236 if (!qp->div)
3237 goto error;
3238
3239 isl_term_free(term);
3240 return qp;
3241 error:
3242 isl_qpolynomial_free(qp);
3243 isl_term_free(term);
3244 return NULL;
3245 }
3246
3247 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3248 __isl_take isl_dim *dim)
3249 {
3250 int i;
3251 int extra;
3252 unsigned total;
3253
3254 if (!qp || !dim)
3255 goto error;
3256
3257 if (isl_dim_equal(qp->dim, dim)) {
3258 isl_dim_free(dim);
3259 return qp;
3260 }
3261
3262 qp = isl_qpolynomial_cow(qp);
3263 if (!qp)
3264 goto error;
3265
3266 extra = isl_dim_size(dim, isl_dim_set) -
3267 isl_dim_size(qp->dim, isl_dim_set);
3268 total = isl_dim_total(qp->dim);
3269 if (qp->div->n_row) {
3270 int *exp;
3271
3272 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3273 if (!exp)
3274 goto error;
3275 for (i = 0; i < qp->div->n_row; ++i)
3276 exp[i] = extra + i;
3277 qp->upoly = expand(qp->upoly, exp, total);
3278 free(exp);
3279 if (!qp->upoly)
3280 goto error;
3281 }
3282 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3283 if (!qp->div)
3284 goto error;
3285 for (i = 0; i < qp->div->n_row; ++i)
3286 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3287
3288 isl_dim_free(qp->dim);
3289 qp->dim = dim;
3290
3291 return qp;
3292 error:
3293 isl_dim_free(dim);
3294 isl_qpolynomial_free(qp);
3295 return NULL;
3296 }
3297
3298 /* For each parameter or variable that does not appear in qp,
3299 * first eliminate the variable from all constraints and then set it to zero.
3300 */
3301 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3302 __isl_keep isl_qpolynomial *qp)
3303 {
3304 int *active = NULL;
3305 int i;
3306 int d;
3307 unsigned nparam;
3308 unsigned nvar;
3309
3310 if (!set || !qp)
3311 goto error;
3312
3313 d = isl_dim_total(set->dim);
3314 active = isl_calloc_array(set->ctx, int, d);
3315 if (set_active(qp, active) < 0)
3316 goto error;
3317
3318 for (i = 0; i < d; ++i)
3319 if (!active[i])
3320 break;
3321
3322 if (i == d) {
3323 free(active);
3324 return set;
3325 }
3326
3327 nparam = isl_dim_size(set->dim, isl_dim_param);
3328 nvar = isl_dim_size(set->dim, isl_dim_set);
3329 for (i = 0; i < nparam; ++i) {
3330 if (active[i])
3331 continue;
3332 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3333 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3334 }
3335 for (i = 0; i < nvar; ++i) {
3336 if (active[nparam + i])
3337 continue;
3338 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3339 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3340 }
3341
3342 free(active);
3343
3344 return set;
3345 error:
3346 free(active);
3347 isl_set_free(set);
3348 return NULL;
3349 }
3350
3351 struct isl_opt_data {
3352 isl_qpolynomial *qp;
3353 int first;
3354 isl_qpolynomial *opt;
3355 int max;
3356 };
3357
3358 static int opt_fn(__isl_take isl_point *pnt, void *user)
3359 {
3360 struct isl_opt_data *data = (struct isl_opt_data *)user;
3361 isl_qpolynomial *val;
3362
3363 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3364 if (data->first) {
3365 data->first = 0;
3366 data->opt = val;
3367 } else if (data->max) {
3368 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3369 } else {
3370 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3371 }
3372
3373 return 0;
3374 }
3375
3376 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3377 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3378 {
3379 struct isl_opt_data data = { NULL, 1, NULL, max };
3380
3381 if (!set || !qp)
3382 goto error;
3383
3384 if (isl_upoly_is_cst(qp->upoly)) {
3385 isl_set_free(set);
3386 return qp;
3387 }
3388
3389 set = fix_inactive(set, qp);
3390
3391 data.qp = qp;
3392 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3393 goto error;
3394
3395 if (data.first)
3396 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3397
3398 isl_set_free(set);
3399 isl_qpolynomial_free(qp);
3400 return data.opt;
3401 error:
3402 isl_set_free(set);
3403 isl_qpolynomial_free(qp);
3404 isl_qpolynomial_free(data.opt);
3405 return NULL;
3406 }
3407
3408 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3409 __isl_take isl_morph *morph)
3410 {
3411 int i;
3412 int n_sub;
3413 isl_ctx *ctx;
3414 struct isl_upoly *up;
3415 unsigned n_div;
3416 struct isl_upoly **subs;
3417 isl_mat *mat;
3418
3419 qp = isl_qpolynomial_cow(qp);
3420 if (!qp || !morph)
3421 goto error;
3422
3423 ctx = qp->dim->ctx;
3424 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3425
3426 n_sub = morph->inv->n_row - 1;
3427 if (morph->inv->n_row != morph->inv->n_col)
3428 n_sub += qp->div->n_row;
3429 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3430 if (!subs)
3431 goto error;
3432
3433 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3434 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3435 morph->inv->row[0][0], morph->inv->n_col);
3436 if (morph->inv->n_row != morph->inv->n_col)
3437 for (i = 0; i < qp->div->n_row; ++i)
3438 subs[morph->inv->n_row - 1 + i] =
3439 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3440
3441 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3442
3443 for (i = 0; i < n_sub; ++i)
3444 isl_upoly_free(subs[i]);
3445 free(subs);
3446
3447 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3448 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3449 qp->div = isl_mat_product(qp->div, mat);
3450 isl_dim_free(qp->dim);
3451 qp->dim = isl_dim_copy(morph->ran->dim);
3452
3453 if (!qp->upoly || !qp->div || !qp->dim)
3454 goto error;
3455
3456 isl_morph_free(morph);
3457
3458 return qp;
3459 error:
3460 isl_qpolynomial_free(qp);
3461 isl_morph_free(morph);
3462 return NULL;
3463 }
3464
3465 static int neg_entry(void **entry, void *user)
3466 {
3467 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3468
3469 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3470
3471 return *pwqp ? 0 : -1;
3472 }
3473
3474 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3475 __isl_take isl_union_pw_qpolynomial *upwqp)
3476 {
3477 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3478 if (!upwqp)
3479 return NULL;
3480
3481 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3482 &neg_entry, NULL) < 0)
3483 goto error;
3484
3485 return upwqp;
3486 error:
3487 isl_union_pw_qpolynomial_free(upwqp);
3488 return NULL;
3489 }
3490
3491 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3492 __isl_take isl_union_pw_qpolynomial *upwqp1,
3493 __isl_take isl_union_pw_qpolynomial *upwqp2)
3494 {
3495 return isl_union_pw_qpolynomial_add(upwqp1,
3496 isl_union_pw_qpolynomial_neg(upwqp2));
3497 }
3498
3499 static int mul_entry(void **entry, void *user)
3500 {
3501 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3502 uint32_t hash;
3503 struct isl_hash_table_entry *entry2;
3504 isl_pw_qpolynomial *pwpq = *entry;
3505 int empty;
3506
3507 hash = isl_dim_get_hash(pwpq->dim);
3508 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3509 hash, &has_dim, pwpq->dim, 0);
3510 if (!entry2)
3511 return 0;
3512
3513 pwpq = isl_pw_qpolynomial_copy(pwpq);
3514 pwpq = isl_pw_qpolynomial_mul(pwpq,
3515 isl_pw_qpolynomial_copy(entry2->data));
3516
3517 empty = isl_pw_qpolynomial_is_zero(pwpq);
3518 if (empty < 0) {
3519 isl_pw_qpolynomial_free(pwpq);
3520 return -1;
3521 }
3522 if (empty) {
3523 isl_pw_qpolynomial_free(pwpq);
3524 return 0;
3525 }
3526
3527 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3528
3529 return 0;
3530 }
3531
3532 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3533 __isl_take isl_union_pw_qpolynomial *upwqp1,
3534 __isl_take isl_union_pw_qpolynomial *upwqp2)
3535 {
3536 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3537 }
3538
3539 /* Reorder the columns of the given div definitions according to the
3540 * given reordering.
3541 */
3542 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3543 __isl_take isl_reordering *r)
3544 {
3545 int i, j;
3546 isl_mat *mat;
3547 int extra;
3548
3549 if (!div || !r)
3550 goto error;
3551
3552 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3553 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3554 if (!mat)
3555 goto error;
3556
3557 for (i = 0; i < div->n_row; ++i) {
3558 isl_seq_cpy(mat->row[i], div->row[i], 2);
3559 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3560 for (j = 0; j < r->len; ++j)
3561 isl_int_set(mat->row[i][2 + r->pos[j]],
3562 div->row[i][2 + j]);
3563 }
3564
3565 isl_reordering_free(r);
3566 isl_mat_free(div);
3567 return mat;
3568 error:
3569 isl_reordering_free(r);
3570 isl_mat_free(div);
3571 return NULL;
3572 }
3573
3574 /* Reorder the dimension of "qp" according to the given reordering.
3575 */
3576 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3577 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3578 {
3579 qp = isl_qpolynomial_cow(qp);
3580 if (!qp)
3581 goto error;
3582
3583 r = isl_reordering_extend(r, qp->div->n_row);
3584 if (!r)
3585 goto error;
3586
3587 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3588 if (!qp->div)
3589 goto error;
3590
3591 qp->upoly = reorder(qp->upoly, r->pos);
3592 if (!qp->upoly)
3593 goto error;
3594
3595 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3596
3597 isl_reordering_free(r);
3598 return qp;
3599 error:
3600 isl_qpolynomial_free(qp);
3601 isl_reordering_free(r);
3602 return NULL;
3603 }
3604
3605 struct isl_split_periods_data {
3606 int max_periods;
3607 isl_pw_qpolynomial *res;
3608 };
3609
3610 /* Create a slice where the integer division "div" has the fixed value "v".
3611 * In particular, if "div" refers to floor(f/m), then create a slice
3612 *
3613 * m v <= f <= m v + (m - 1)
3614 *
3615 * or
3616 *
3617 * f - m v >= 0
3618 * -f + m v + (m - 1) >= 0
3619 */
3620 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3621 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3622 {
3623 int total;
3624 isl_basic_set *bset = NULL;
3625 int k;
3626
3627 if (!dim || !qp)
3628 goto error;
3629
3630 total = isl_dim_total(dim);
3631 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3632
3633 k = isl_basic_set_alloc_inequality(bset);
3634 if (k < 0)
3635 goto error;
3636 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3637 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3638
3639 k = isl_basic_set_alloc_inequality(bset);
3640 if (k < 0)
3641 goto error;
3642 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3643 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3644 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3645 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3646
3647 isl_dim_free(dim);
3648 return isl_set_from_basic_set(bset);
3649 error:
3650 isl_basic_set_free(bset);
3651 isl_dim_free(dim);
3652 return NULL;
3653 }
3654
3655 static int split_periods(__isl_take isl_set *set,
3656 __isl_take isl_qpolynomial *qp, void *user);
3657
3658 /* Create a slice of the domain "set" such that integer division "div"
3659 * has the fixed value "v" and add the results to data->res,
3660 * replacing the integer division by "v" in "qp".
3661 */
3662 static int set_div(__isl_take isl_set *set,
3663 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3664 struct isl_split_periods_data *data)
3665 {
3666 int i;
3667 int total;
3668 isl_set *slice;
3669 struct isl_upoly *cst;
3670
3671 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3672 set = isl_set_intersect(set, slice);
3673
3674 if (!qp)
3675 goto error;
3676
3677 total = isl_dim_total(qp->dim);
3678
3679 for (i = div + 1; i < qp->div->n_row; ++i) {
3680 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3681 continue;
3682 isl_int_addmul(qp->div->row[i][1],
3683 qp->div->row[i][2 + total + div], v);
3684 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3685 }
3686
3687 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3688 qp = substitute_div(qp, div, cst);
3689
3690 return split_periods(set, qp, data);
3691 error:
3692 isl_set_free(set);
3693 isl_qpolynomial_free(qp);
3694 return -1;
3695 }
3696
3697 /* Split the domain "set" such that integer division "div"
3698 * has a fixed value (ranging from "min" to "max") on each slice
3699 * and add the results to data->res.
3700 */
3701 static int split_div(__isl_take isl_set *set,
3702 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3703 struct isl_split_periods_data *data)
3704 {
3705 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3706 isl_set *set_i = isl_set_copy(set);
3707 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3708
3709 if (set_div(set_i, qp_i, div, min, data) < 0)
3710 goto error;
3711 }
3712 isl_set_free(set);
3713 isl_qpolynomial_free(qp);
3714 return 0;
3715 error:
3716 isl_set_free(set);
3717 isl_qpolynomial_free(qp);
3718 return -1;
3719 }
3720
3721 /* If "qp" refers to any integer division
3722 * that can only attain "max_periods" distinct values on "set"
3723 * then split the domain along those distinct values.
3724 * Add the results (or the original if no splitting occurs)
3725 * to data->res.
3726 */
3727 static int split_periods(__isl_take isl_set *set,
3728 __isl_take isl_qpolynomial *qp, void *user)
3729 {
3730 int i;
3731 isl_pw_qpolynomial *pwqp;
3732 struct isl_split_periods_data *data;
3733 isl_int min, max;
3734 int total;
3735 int r = 0;
3736
3737 data = (struct isl_split_periods_data *)user;
3738
3739 if (!set || !qp)
3740 goto error;
3741
3742 if (qp->div->n_row == 0) {
3743 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3744 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3745 return 0;
3746 }
3747
3748 isl_int_init(min);
3749 isl_int_init(max);
3750 total = isl_dim_total(qp->dim);
3751 for (i = 0; i < qp->div->n_row; ++i) {
3752 enum isl_lp_result lp_res;
3753
3754 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3755 qp->div->n_row) != -1)
3756 continue;
3757
3758 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3759 set->ctx->one, &min, NULL, NULL);
3760 if (lp_res == isl_lp_error)
3761 goto error2;
3762 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3763 continue;
3764 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3765
3766 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3767 set->ctx->one, &max, NULL, NULL);
3768 if (lp_res == isl_lp_error)
3769 goto error2;
3770 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3771 continue;
3772 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3773
3774 isl_int_sub(max, max, min);
3775 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3776 isl_int_add(max, max, min);
3777 break;
3778 }
3779 }
3780
3781 if (i < qp->div->n_row) {
3782 r = split_div(set, qp, i, min, max, data);
3783 } else {
3784 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3785 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3786 }
3787
3788 isl_int_clear(max);
3789 isl_int_clear(min);
3790
3791 return r;
3792 error2:
3793 isl_int_clear(max);
3794 isl_int_clear(min);
3795 error:
3796 isl_set_free(set);
3797 isl_qpolynomial_free(qp);
3798 return -1;
3799 }
3800
3801 /* If any quasi-polynomial in pwqp refers to any integer division
3802 * that can only attain "max_periods" distinct values on its domain
3803 * then split the domain along those distinct values.
3804 */
3805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3806 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3807 {
3808 struct isl_split_periods_data data;
3809
3810 data.max_periods = max_periods;
3811 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3812
3813 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3814 goto error;
3815
3816 isl_pw_qpolynomial_free(pwqp);
3817
3818 return data.res;
3819 error:
3820 isl_pw_qpolynomial_free(data.res);
3821 isl_pw_qpolynomial_free(pwqp);
3822 return NULL;
3823 }
3824
3825 /* Construct a piecewise quasipolynomial that is constant on the given
3826 * domain. In particular, it is
3827 * 0 if cst == 0
3828 * 1 if cst == 1
3829 * infinity if cst == -1
3830 */
3831 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3832 __isl_take isl_basic_set *bset, int cst)
3833 {
3834 isl_dim *dim;
3835 isl_qpolynomial *qp;
3836
3837 if (!bset)
3838 return NULL;
3839
3840 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3841 dim = isl_basic_set_get_dim(bset);
3842 if (cst < 0)
3843 qp = isl_qpolynomial_infty(dim);
3844 else if (cst == 0)
3845 qp = isl_qpolynomial_zero(dim);
3846 else
3847 qp = isl_qpolynomial_one(dim);
3848 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3849 }
3850
3851 /* Factor bset, call fn on each of the factors and return the product.
3852 *
3853 * If no factors can be found, simply call fn on the input.
3854 * Otherwise, construct the factors based on the factorizer,
3855 * call fn on each factor and compute the product.
3856 */
3857 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3858 __isl_take isl_basic_set *bset,
3859 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3860 {
3861 int i, n;
3862 isl_dim *dim;
3863 isl_set *set;
3864 isl_factorizer *f;
3865 isl_qpolynomial *qp;
3866 isl_pw_qpolynomial *pwqp;
3867 unsigned nparam;
3868 unsigned nvar;
3869
3870 f = isl_basic_set_factorizer(bset);
3871 if (!f)
3872 goto error;
3873 if (f->n_group == 0) {
3874 isl_factorizer_free(f);
3875 return fn(bset);
3876 }
3877
3878 nparam = isl_basic_set_dim(bset, isl_dim_param);
3879 nvar = isl_basic_set_dim(bset, isl_dim_set);
3880
3881 dim = isl_basic_set_get_dim(bset);
3882 dim = isl_dim_domain(dim);
3883 set = isl_set_universe(isl_dim_copy(dim));
3884 qp = isl_qpolynomial_one(dim);
3885 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3886
3887 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3888
3889 for (i = 0, n = 0; i < f->n_group; ++i) {
3890 isl_basic_set *bset_i;
3891 isl_pw_qpolynomial *pwqp_i;
3892
3893 bset_i = isl_basic_set_copy(bset);
3894 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3895 nparam + n + f->len[i], nvar - n - f->len[i]);
3896 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3897 nparam, n);
3898 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3899 n + f->len[i], nvar - n - f->len[i]);
3900 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3901
3902 pwqp_i = fn(bset_i);
3903 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3904
3905 n += f->len[i];
3906 }
3907
3908 isl_basic_set_free(bset);
3909 isl_factorizer_free(f);
3910
3911 return pwqp;
3912 error:
3913 isl_basic_set_free(bset);
3914 return NULL;
3915 }
3916
3917 /* Factor bset, call fn on each of the factors and return the product.
3918 * The function is assumed to evaluate to zero on empty domains,
3919 * to one on zero-dimensional domains and to infinity on unbounded domains
3920 * and will not be called explicitly on zero-dimensional or unbounded domains.
3921 *
3922 * We first check for some special cases and remove all equalities.
3923 * Then we hand over control to compressed_multiplicative_call.
3924 */
3925 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3926 __isl_take isl_basic_set *bset,
3927 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3928 {
3929 int bounded;
3930 isl_morph *morph;
3931 isl_pw_qpolynomial *pwqp;
3932 unsigned orig_nvar, final_nvar;
3933
3934 if (!bset)
3935 return NULL;
3936
3937 if (isl_basic_set_fast_is_empty(bset))
3938 return constant_on_domain(bset, 0);
3939
3940 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3941
3942 if (orig_nvar == 0)
3943 return constant_on_domain(bset, 1);
3944
3945 bounded = isl_basic_set_is_bounded(bset);
3946 if (bounded < 0)
3947 goto error;
3948 if (!bounded)
3949 return constant_on_domain(bset, -1);
3950
3951 if (bset->n_eq == 0)
3952 return compressed_multiplicative_call(bset, fn);
3953
3954 morph = isl_basic_set_full_compression(bset);
3955 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3956
3957 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3958
3959 pwqp = compressed_multiplicative_call(bset, fn);
3960
3961 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3962 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3963 morph = isl_morph_inverse(morph);
3964
3965 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3966
3967 return pwqp;
3968 error:
3969 isl_basic_set_free(bset);
3970 return NULL;
3971 }
Integer set library