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add isl_basic_map_from_range
[isl.git] / isl_polynomial.c
blob2d52894dc5b981f1e2a6a2148bd7677618889d20
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_lp.h>
13 #include <isl_seq.h>
14 #include <isl_union_map_private.h>
15 #include <isl_polynomial_private.h>
16 #include <isl_point_private.h>
17 #include <isl_dim_private.h>
18 #include <isl_map_private.h>
19 #include <isl_mat_private.h>
20
21 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
22 {
23 switch (type) {
24 case isl_dim_param: return 0;
25 case isl_dim_in: return dim->nparam;
26 case isl_dim_out: return dim->nparam + dim->n_in;
27 default: return 0;
28 }
29 }
30
31 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
32 {
33 if (!up)
34 return -1;
35
36 return up->var < 0;
37 }
38
39 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
40 {
41 if (!up)
42 return NULL;
43
44 isl_assert(up->ctx, up->var < 0, return NULL);
45
46 return (struct isl_upoly_cst *)up;
47 }
48
49 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
50 {
51 if (!up)
52 return NULL;
53
54 isl_assert(up->ctx, up->var >= 0, return NULL);
55
56 return (struct isl_upoly_rec *)up;
57 }
58
59 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
60 __isl_keep struct isl_upoly *up2)
61 {
62 int i;
63 struct isl_upoly_rec *rec1, *rec2;
64
65 if (!up1 || !up2)
66 return -1;
67 if (up1 == up2)
68 return 1;
69 if (up1->var != up2->var)
70 return 0;
71 if (isl_upoly_is_cst(up1)) {
72 struct isl_upoly_cst *cst1, *cst2;
73 cst1 = isl_upoly_as_cst(up1);
74 cst2 = isl_upoly_as_cst(up2);
75 if (!cst1 || !cst2)
76 return -1;
77 return isl_int_eq(cst1->n, cst2->n) &&
78 isl_int_eq(cst1->d, cst2->d);
79 }
80
81 rec1 = isl_upoly_as_rec(up1);
82 rec2 = isl_upoly_as_rec(up2);
83 if (!rec1 || !rec2)
84 return -1;
85
86 if (rec1->n != rec2->n)
87 return 0;
88
89 for (i = 0; i < rec1->n; ++i) {
90 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
91 if (eq < 0 || !eq)
92 return eq;
93 }
94
95 return 1;
96 }
97
98 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
99 {
100 struct isl_upoly_cst *cst;
101
102 if (!up)
103 return -1;
104 if (!isl_upoly_is_cst(up))
105 return 0;
106
107 cst = isl_upoly_as_cst(up);
108 if (!cst)
109 return -1;
110
111 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
112 }
113
114 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
115 {
116 struct isl_upoly_cst *cst;
117
118 if (!up)
119 return 0;
120 if (!isl_upoly_is_cst(up))
121 return 0;
122
123 cst = isl_upoly_as_cst(up);
124 if (!cst)
125 return 0;
126
127 return isl_int_sgn(cst->n);
128 }
129
130 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
131 {
132 struct isl_upoly_cst *cst;
133
134 if (!up)
135 return -1;
136 if (!isl_upoly_is_cst(up))
137 return 0;
138
139 cst = isl_upoly_as_cst(up);
140 if (!cst)
141 return -1;
142
143 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
144 }
145
146 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
147 {
148 struct isl_upoly_cst *cst;
149
150 if (!up)
151 return -1;
152 if (!isl_upoly_is_cst(up))
153 return 0;
154
155 cst = isl_upoly_as_cst(up);
156 if (!cst)
157 return -1;
158
159 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
160 }
161
162 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
163 {
164 struct isl_upoly_cst *cst;
165
166 if (!up)
167 return -1;
168 if (!isl_upoly_is_cst(up))
169 return 0;
170
171 cst = isl_upoly_as_cst(up);
172 if (!cst)
173 return -1;
174
175 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
176 }
177
178 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
179 {
180 struct isl_upoly_cst *cst;
181
182 if (!up)
183 return -1;
184 if (!isl_upoly_is_cst(up))
185 return 0;
186
187 cst = isl_upoly_as_cst(up);
188 if (!cst)
189 return -1;
190
191 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
192 }
193
194 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
195 {
196 struct isl_upoly_cst *cst;
197
198 if (!up)
199 return -1;
200 if (!isl_upoly_is_cst(up))
201 return 0;
202
203 cst = isl_upoly_as_cst(up);
204 if (!cst)
205 return -1;
206
207 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
208 }
209
210 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
211 {
212 struct isl_upoly_cst *cst;
213
214 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
215 if (!cst)
216 return NULL;
217
218 cst->up.ref = 1;
219 cst->up.ctx = ctx;
220 isl_ctx_ref(ctx);
221 cst->up.var = -1;
222
223 isl_int_init(cst->n);
224 isl_int_init(cst->d);
225
226 return cst;
227 }
228
229 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
230 {
231 struct isl_upoly_cst *cst;
232
233 cst = isl_upoly_cst_alloc(ctx);
234 if (!cst)
235 return NULL;
236
237 isl_int_set_si(cst->n, 0);
238 isl_int_set_si(cst->d, 1);
239
240 return &cst->up;
241 }
242
243 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
244 {
245 struct isl_upoly_cst *cst;
246
247 cst = isl_upoly_cst_alloc(ctx);
248 if (!cst)
249 return NULL;
250
251 isl_int_set_si(cst->n, 1);
252 isl_int_set_si(cst->d, 0);
253
254 return &cst->up;
255 }
256
257 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
258 {
259 struct isl_upoly_cst *cst;
260
261 cst = isl_upoly_cst_alloc(ctx);
262 if (!cst)
263 return NULL;
264
265 isl_int_set_si(cst->n, -1);
266 isl_int_set_si(cst->d, 0);
267
268 return &cst->up;
269 }
270
271 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
272 {
273 struct isl_upoly_cst *cst;
274
275 cst = isl_upoly_cst_alloc(ctx);
276 if (!cst)
277 return NULL;
278
279 isl_int_set_si(cst->n, 0);
280 isl_int_set_si(cst->d, 0);
281
282 return &cst->up;
283 }
284
285 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
286 isl_int n, isl_int d)
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(cst->n, n);
295 isl_int_set(cst->d, d);
296
297 return &cst->up;
298 }
299
300 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
301 int var, int size)
302 {
303 struct isl_upoly_rec *rec;
304
305 isl_assert(ctx, var >= 0, return NULL);
306 isl_assert(ctx, size >= 0, return NULL);
307 rec = isl_calloc(ctx, struct isl_upoly_rec,
308 sizeof(struct isl_upoly_rec) +
309 (size - 1) * sizeof(struct isl_upoly *));
310 if (!rec)
311 return NULL;
312
313 rec->up.ref = 1;
314 rec->up.ctx = ctx;
315 isl_ctx_ref(ctx);
316 rec->up.var = var;
317
318 rec->n = 0;
319 rec->size = size;
320
321 return rec;
322 }
323
324 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
325 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
326 {
327 qp = isl_qpolynomial_cow(qp);
328 if (!qp || !dim)
329 goto error;
330
331 isl_dim_free(qp->dim);
332 qp->dim = dim;
333
334 return qp;
335 error:
336 isl_qpolynomial_free(qp);
337 isl_dim_free(dim);
338 return NULL;
339 }
340
341 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
342 {
343 return qp ? qp->dim->ctx : NULL;
344 }
345
346 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
347 {
348 return qp ? isl_dim_copy(qp->dim) : NULL;
349 }
350
351 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
352 enum isl_dim_type type)
353 {
354 return qp ? isl_dim_size(qp->dim, type) : 0;
355 }
356
357 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
358 {
359 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
360 }
361
362 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? isl_upoly_is_one(qp->upoly) : -1;
365 }
366
367 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
368 {
369 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
370 }
371
372 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
373 {
374 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
375 }
376
377 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
378 {
379 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
380 }
381
382 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_upoly_sgn(qp->upoly) : 0;
385 }
386
387 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
388 {
389 isl_int_clear(cst->n);
390 isl_int_clear(cst->d);
391 }
392
393 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
394 {
395 int i;
396
397 for (i = 0; i < rec->n; ++i)
398 isl_upoly_free(rec->p[i]);
399 }
400
401 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
402 {
403 if (!up)
404 return NULL;
405
406 up->ref++;
407 return up;
408 }
409
410 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
411 {
412 struct isl_upoly_cst *cst;
413 struct isl_upoly_cst *dup;
414
415 cst = isl_upoly_as_cst(up);
416 if (!cst)
417 return NULL;
418
419 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
420 if (!dup)
421 return NULL;
422 isl_int_set(dup->n, cst->n);
423 isl_int_set(dup->d, cst->d);
424
425 return &dup->up;
426 }
427
428 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
429 {
430 int i;
431 struct isl_upoly_rec *rec;
432 struct isl_upoly_rec *dup;
433
434 rec = isl_upoly_as_rec(up);
435 if (!rec)
436 return NULL;
437
438 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
439 if (!dup)
440 return NULL;
441
442 for (i = 0; i < rec->n; ++i) {
443 dup->p[i] = isl_upoly_copy(rec->p[i]);
444 if (!dup->p[i])
445 goto error;
446 dup->n++;
447 }
448
449 return &dup->up;
450 error:
451 isl_upoly_free(&dup->up);
452 return NULL;
453 }
454
455 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
456 {
457 struct isl_upoly *dup;
458
459 if (!up)
460 return NULL;
461
462 if (isl_upoly_is_cst(up))
463 return isl_upoly_dup_cst(up);
464 else
465 return isl_upoly_dup_rec(up);
466 }
467
468 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
469 {
470 if (!up)
471 return NULL;
472
473 if (up->ref == 1)
474 return up;
475 up->ref--;
476 return isl_upoly_dup(up);
477 }
478
479 void isl_upoly_free(__isl_take struct isl_upoly *up)
480 {
481 if (!up)
482 return;
483
484 if (--up->ref > 0)
485 return;
486
487 if (up->var < 0)
488 upoly_free_cst((struct isl_upoly_cst *)up);
489 else
490 upoly_free_rec((struct isl_upoly_rec *)up);
491
492 isl_ctx_deref(up->ctx);
493 free(up);
494 }
495
496 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
497 {
498 isl_int gcd;
499
500 isl_int_init(gcd);
501 isl_int_gcd(gcd, cst->n, cst->d);
502 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
503 isl_int_divexact(cst->n, cst->n, gcd);
504 isl_int_divexact(cst->d, cst->d, gcd);
505 }
506 isl_int_clear(gcd);
507 }
508
509 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
510 __isl_take struct isl_upoly *up2)
511 {
512 struct isl_upoly_cst *cst1;
513 struct isl_upoly_cst *cst2;
514
515 up1 = isl_upoly_cow(up1);
516 if (!up1 || !up2)
517 goto error;
518
519 cst1 = isl_upoly_as_cst(up1);
520 cst2 = isl_upoly_as_cst(up2);
521
522 if (isl_int_eq(cst1->d, cst2->d))
523 isl_int_add(cst1->n, cst1->n, cst2->n);
524 else {
525 isl_int_mul(cst1->n, cst1->n, cst2->d);
526 isl_int_addmul(cst1->n, cst2->n, cst1->d);
527 isl_int_mul(cst1->d, cst1->d, cst2->d);
528 }
529
530 isl_upoly_cst_reduce(cst1);
531
532 isl_upoly_free(up2);
533 return up1;
534 error:
535 isl_upoly_free(up1);
536 isl_upoly_free(up2);
537 return NULL;
538 }
539
540 static __isl_give struct isl_upoly *replace_by_zero(
541 __isl_take struct isl_upoly *up)
542 {
543 struct isl_ctx *ctx;
544
545 if (!up)
546 return NULL;
547 ctx = up->ctx;
548 isl_upoly_free(up);
549 return isl_upoly_zero(ctx);
550 }
551
552 static __isl_give struct isl_upoly *replace_by_constant_term(
553 __isl_take struct isl_upoly *up)
554 {
555 struct isl_upoly_rec *rec;
556 struct isl_upoly *cst;
557
558 if (!up)
559 return NULL;
560
561 rec = isl_upoly_as_rec(up);
562 if (!rec)
563 goto error;
564 cst = isl_upoly_copy(rec->p[0]);
565 isl_upoly_free(up);
566 return cst;
567 error:
568 isl_upoly_free(up);
569 return NULL;
570 }
571
572 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
573 __isl_take struct isl_upoly *up2)
574 {
575 int i;
576 struct isl_upoly_rec *rec1, *rec2;
577
578 if (!up1 || !up2)
579 goto error;
580
581 if (isl_upoly_is_nan(up1)) {
582 isl_upoly_free(up2);
583 return up1;
584 }
585
586 if (isl_upoly_is_nan(up2)) {
587 isl_upoly_free(up1);
588 return up2;
589 }
590
591 if (isl_upoly_is_zero(up1)) {
592 isl_upoly_free(up1);
593 return up2;
594 }
595
596 if (isl_upoly_is_zero(up2)) {
597 isl_upoly_free(up2);
598 return up1;
599 }
600
601 if (up1->var < up2->var)
602 return isl_upoly_sum(up2, up1);
603
604 if (up2->var < up1->var) {
605 struct isl_upoly_rec *rec;
606 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610 up1 = isl_upoly_cow(up1);
611 rec = isl_upoly_as_rec(up1);
612 if (!rec)
613 goto error;
614 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
615 if (rec->n == 1)
616 up1 = replace_by_constant_term(up1);
617 return up1;
618 }
619
620 if (isl_upoly_is_cst(up1))
621 return isl_upoly_sum_cst(up1, up2);
622
623 rec1 = isl_upoly_as_rec(up1);
624 rec2 = isl_upoly_as_rec(up2);
625 if (!rec1 || !rec2)
626 goto error;
627
628 if (rec1->n < rec2->n)
629 return isl_upoly_sum(up2, up1);
630
631 up1 = isl_upoly_cow(up1);
632 rec1 = isl_upoly_as_rec(up1);
633 if (!rec1)
634 goto error;
635
636 for (i = rec2->n - 1; i >= 0; --i) {
637 rec1->p[i] = isl_upoly_sum(rec1->p[i],
638 isl_upoly_copy(rec2->p[i]));
639 if (!rec1->p[i])
640 goto error;
641 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
642 isl_upoly_free(rec1->p[i]);
643 rec1->n--;
644 }
645 }
646
647 if (rec1->n == 0)
648 up1 = replace_by_zero(up1);
649 else if (rec1->n == 1)
650 up1 = replace_by_constant_term(up1);
651
652 isl_upoly_free(up2);
653
654 return up1;
655 error:
656 isl_upoly_free(up1);
657 isl_upoly_free(up2);
658 return NULL;
659 }
660
661 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
662 {
663 struct isl_upoly_cst *cst;
664
665 if (isl_upoly_is_zero(up))
666 return up;
667
668 up = isl_upoly_cow(up);
669 if (!up)
670 return NULL;
671
672 cst = isl_upoly_as_cst(up);
673
674 isl_int_neg(cst->n, cst->n);
675
676 return up;
677 }
678
679 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
680 {
681 int i;
682 struct isl_upoly_rec *rec;
683
684 if (!up)
685 return NULL;
686
687 if (isl_upoly_is_cst(up))
688 return isl_upoly_neg_cst(up);
689
690 up = isl_upoly_cow(up);
691 rec = isl_upoly_as_rec(up);
692 if (!rec)
693 goto error;
694
695 for (i = 0; i < rec->n; ++i) {
696 rec->p[i] = isl_upoly_neg(rec->p[i]);
697 if (!rec->p[i])
698 goto error;
699 }
700
701 return up;
702 error:
703 isl_upoly_free(up);
704 return NULL;
705 }
706
707 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
708 __isl_take struct isl_upoly *up2)
709 {
710 struct isl_upoly_cst *cst1;
711 struct isl_upoly_cst *cst2;
712
713 up1 = isl_upoly_cow(up1);
714 if (!up1 || !up2)
715 goto error;
716
717 cst1 = isl_upoly_as_cst(up1);
718 cst2 = isl_upoly_as_cst(up2);
719
720 isl_int_mul(cst1->n, cst1->n, cst2->n);
721 isl_int_mul(cst1->d, cst1->d, cst2->d);
722
723 isl_upoly_cst_reduce(cst1);
724
725 isl_upoly_free(up2);
726 return up1;
727 error:
728 isl_upoly_free(up1);
729 isl_upoly_free(up2);
730 return NULL;
731 }
732
733 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
734 __isl_take struct isl_upoly *up2)
735 {
736 struct isl_upoly_rec *rec1;
737 struct isl_upoly_rec *rec2;
738 struct isl_upoly_rec *res;
739 int i, j;
740 int size;
741
742 rec1 = isl_upoly_as_rec(up1);
743 rec2 = isl_upoly_as_rec(up2);
744 if (!rec1 || !rec2)
745 goto error;
746 size = rec1->n + rec2->n - 1;
747 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
748 if (!res)
749 goto error;
750
751 for (i = 0; i < rec1->n; ++i) {
752 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
753 isl_upoly_copy(rec1->p[i]));
754 if (!res->p[i])
755 goto error;
756 res->n++;
757 }
758 for (; i < size; ++i) {
759 res->p[i] = isl_upoly_zero(up1->ctx);
760 if (!res->p[i])
761 goto error;
762 res->n++;
763 }
764 for (i = 0; i < rec1->n; ++i) {
765 for (j = 1; j < rec2->n; ++j) {
766 struct isl_upoly *up;
767 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
768 isl_upoly_copy(rec1->p[i]));
769 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
770 if (!res->p[i + j])
771 goto error;
772 }
773 }
774
775 isl_upoly_free(up1);
776 isl_upoly_free(up2);
777
778 return &res->up;
779 error:
780 isl_upoly_free(up1);
781 isl_upoly_free(up2);
782 isl_upoly_free(&res->up);
783 return NULL;
784 }
785
786 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
787 __isl_take struct isl_upoly *up2)
788 {
789 if (!up1 || !up2)
790 goto error;
791
792 if (isl_upoly_is_nan(up1)) {
793 isl_upoly_free(up2);
794 return up1;
795 }
796
797 if (isl_upoly_is_nan(up2)) {
798 isl_upoly_free(up1);
799 return up2;
800 }
801
802 if (isl_upoly_is_zero(up1)) {
803 isl_upoly_free(up2);
804 return up1;
805 }
806
807 if (isl_upoly_is_zero(up2)) {
808 isl_upoly_free(up1);
809 return up2;
810 }
811
812 if (isl_upoly_is_one(up1)) {
813 isl_upoly_free(up1);
814 return up2;
815 }
816
817 if (isl_upoly_is_one(up2)) {
818 isl_upoly_free(up2);
819 return up1;
820 }
821
822 if (up1->var < up2->var)
823 return isl_upoly_mul(up2, up1);
824
825 if (up2->var < up1->var) {
826 int i;
827 struct isl_upoly_rec *rec;
828 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
829 isl_ctx *ctx = up1->ctx;
830 isl_upoly_free(up1);
831 isl_upoly_free(up2);
832 return isl_upoly_nan(ctx);
833 }
834 up1 = isl_upoly_cow(up1);
835 rec = isl_upoly_as_rec(up1);
836 if (!rec)
837 goto error;
838
839 for (i = 0; i < rec->n; ++i) {
840 rec->p[i] = isl_upoly_mul(rec->p[i],
841 isl_upoly_copy(up2));
842 if (!rec->p[i])
843 goto error;
844 }
845 isl_upoly_free(up2);
846 return up1;
847 }
848
849 if (isl_upoly_is_cst(up1))
850 return isl_upoly_mul_cst(up1, up2);
851
852 return isl_upoly_mul_rec(up1, up2);
853 error:
854 isl_upoly_free(up1);
855 isl_upoly_free(up2);
856 return NULL;
857 }
858
859 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
860 unsigned n_div, __isl_take struct isl_upoly *up)
861 {
862 struct isl_qpolynomial *qp = NULL;
863 unsigned total;
864
865 if (!dim || !up)
866 goto error;
867
868 total = isl_dim_total(dim);
869
870 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
871 if (!qp)
872 goto error;
873
874 qp->ref = 1;
875 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
876 if (!qp->div)
877 goto error;
878
879 qp->dim = dim;
880 qp->upoly = up;
881
882 return qp;
883 error:
884 isl_dim_free(dim);
885 isl_upoly_free(up);
886 isl_qpolynomial_free(qp);
887 return NULL;
888 }
889
890 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
891 {
892 if (!qp)
893 return NULL;
894
895 qp->ref++;
896 return qp;
897 }
898
899 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
900 {
901 struct isl_qpolynomial *dup;
902
903 if (!qp)
904 return NULL;
905
906 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
907 isl_upoly_copy(qp->upoly));
908 if (!dup)
909 return NULL;
910 isl_mat_free(dup->div);
911 dup->div = isl_mat_copy(qp->div);
912 if (!dup->div)
913 goto error;
914
915 return dup;
916 error:
917 isl_qpolynomial_free(dup);
918 return NULL;
919 }
920
921 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
922 {
923 if (!qp)
924 return NULL;
925
926 if (qp->ref == 1)
927 return qp;
928 qp->ref--;
929 return isl_qpolynomial_dup(qp);
930 }
931
932 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
933 {
934 if (!qp)
935 return;
936
937 if (--qp->ref > 0)
938 return;
939
940 isl_dim_free(qp->dim);
941 isl_mat_free(qp->div);
942 isl_upoly_free(qp->upoly);
943
944 free(qp);
945 }
946
947 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
948 {
949 int i;
950 struct isl_upoly *up;
951 struct isl_upoly_rec *rec;
952 struct isl_upoly_cst *cst;
953
954 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
955 if (!rec)
956 return NULL;
957 for (i = 0; i < 1 + power; ++i) {
958 rec->p[i] = isl_upoly_zero(ctx);
959 if (!rec->p[i])
960 goto error;
961 rec->n++;
962 }
963 cst = isl_upoly_as_cst(rec->p[power]);
964 isl_int_set_si(cst->n, 1);
965
966 return &rec->up;
967 error:
968 isl_upoly_free(&rec->up);
969 return NULL;
970 }
971
972 /* r array maps original positions to new positions.
973 */
974 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
975 int *r)
976 {
977 int i;
978 struct isl_upoly_rec *rec;
979 struct isl_upoly *base;
980 struct isl_upoly *res;
981
982 if (isl_upoly_is_cst(up))
983 return up;
984
985 rec = isl_upoly_as_rec(up);
986 if (!rec)
987 goto error;
988
989 isl_assert(up->ctx, rec->n >= 1, goto error);
990
991 base = isl_upoly_pow(up->ctx, r[up->var], 1);
992 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
993
994 for (i = rec->n - 2; i >= 0; --i) {
995 res = isl_upoly_mul(res, isl_upoly_copy(base));
996 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
997 }
998
999 isl_upoly_free(base);
1000 isl_upoly_free(up);
1001
1002 return res;
1003 error:
1004 isl_upoly_free(up);
1005 return NULL;
1006 }
1007
1008 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1009 {
1010 int n_row, n_col;
1011 int equal;
1012
1013 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1014 div1->n_col >= div2->n_col, return -1);
1015
1016 if (div1->n_row == div2->n_row)
1017 return isl_mat_is_equal(div1, div2);
1018
1019 n_row = div1->n_row;
1020 n_col = div1->n_col;
1021 div1->n_row = div2->n_row;
1022 div1->n_col = div2->n_col;
1023
1024 equal = isl_mat_is_equal(div1, div2);
1025
1026 div1->n_row = n_row;
1027 div1->n_col = n_col;
1028
1029 return equal;
1030 }
1031
1032 static void expand_row(__isl_keep isl_mat *dst, int d,
1033 __isl_keep isl_mat *src, int s, int *exp)
1034 {
1035 int i;
1036 unsigned c = src->n_col - src->n_row;
1037
1038 isl_seq_cpy(dst->row[d], src->row[s], c);
1039 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1040
1041 for (i = 0; i < s; ++i)
1042 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1043 }
1044
1045 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1046 {
1047 int li, lj;
1048
1049 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1050 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1051
1052 if (li != lj)
1053 return li - lj;
1054
1055 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1056 }
1057
1058 struct isl_div_sort_info {
1059 isl_mat *div;
1060 int row;
1061 };
1062
1063 static int div_sort_cmp(const void *p1, const void *p2)
1064 {
1065 const struct isl_div_sort_info *i1, *i2;
1066 i1 = (const struct isl_div_sort_info *) p1;
1067 i2 = (const struct isl_div_sort_info *) p2;
1068
1069 return cmp_row(i1->div, i1->row, i2->row);
1070 }
1071
1072 /* Sort divs and remove duplicates.
1073 */
1074 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1075 {
1076 int i;
1077 int skip;
1078 int len;
1079 struct isl_div_sort_info *array = NULL;
1080 int *pos = NULL, *at = NULL;
1081 int *reordering = NULL;
1082 unsigned div_pos;
1083
1084 if (!qp)
1085 return NULL;
1086 if (qp->div->n_row <= 1)
1087 return qp;
1088
1089 div_pos = isl_dim_total(qp->dim);
1090
1091 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1092 qp->div->n_row);
1093 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1094 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1095 len = qp->div->n_col - 2;
1096 reordering = isl_alloc_array(qp->div->ctx, int, len);
1097 if (!array || !pos || !at || !reordering)
1098 goto error;
1099
1100 for (i = 0; i < qp->div->n_row; ++i) {
1101 array[i].div = qp->div;
1102 array[i].row = i;
1103 pos[i] = i;
1104 at[i] = i;
1105 }
1106
1107 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1108 div_sort_cmp);
1109
1110 for (i = 0; i < div_pos; ++i)
1111 reordering[i] = i;
1112
1113 for (i = 0; i < qp->div->n_row; ++i) {
1114 if (pos[array[i].row] == i)
1115 continue;
1116 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1117 pos[at[i]] = pos[array[i].row];
1118 at[pos[array[i].row]] = at[i];
1119 at[i] = array[i].row;
1120 pos[array[i].row] = i;
1121 }
1122
1123 skip = 0;
1124 for (i = 0; i < len - div_pos; ++i) {
1125 if (i > 0 &&
1126 isl_seq_eq(qp->div->row[i - skip - 1],
1127 qp->div->row[i - skip], qp->div->n_col)) {
1128 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1129 qp->div = isl_mat_drop_cols(qp->div,
1130 2 + div_pos + i - skip, 1);
1131 skip++;
1132 }
1133 reordering[div_pos + array[i].row] = div_pos + i - skip;
1134 }
1135
1136 qp->upoly = reorder(qp->upoly, reordering);
1137
1138 if (!qp->upoly || !qp->div)
1139 goto error;
1140
1141 free(at);
1142 free(pos);
1143 free(array);
1144 free(reordering);
1145
1146 return qp;
1147 error:
1148 free(at);
1149 free(pos);
1150 free(array);
1151 free(reordering);
1152 isl_qpolynomial_free(qp);
1153 return NULL;
1154 }
1155
1156 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1157 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1158 {
1159 int i, j, k;
1160 isl_mat *div = NULL;
1161 unsigned d = div1->n_col - div1->n_row;
1162
1163 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1164 d + div1->n_row + div2->n_row);
1165 if (!div)
1166 return NULL;
1167
1168 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1169 int cmp;
1170
1171 expand_row(div, k, div1, i, exp1);
1172 expand_row(div, k + 1, div2, j, exp2);
1173
1174 cmp = cmp_row(div, k, k + 1);
1175 if (cmp == 0) {
1176 exp1[i++] = k;
1177 exp2[j++] = k;
1178 } else if (cmp < 0) {
1179 exp1[i++] = k;
1180 } else {
1181 exp2[j++] = k;
1182 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1183 }
1184 }
1185 for (; i < div1->n_row; ++i, ++k) {
1186 expand_row(div, k, div1, i, exp1);
1187 exp1[i] = k;
1188 }
1189 for (; j < div2->n_row; ++j, ++k) {
1190 expand_row(div, k, div2, j, exp2);
1191 exp2[j] = k;
1192 }
1193
1194 div->n_row = k;
1195 div->n_col = d + k;
1196
1197 return div;
1198 }
1199
1200 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1201 int *exp, int first)
1202 {
1203 int i;
1204 struct isl_upoly_rec *rec;
1205
1206 if (isl_upoly_is_cst(up))
1207 return up;
1208
1209 if (up->var < first)
1210 return up;
1211
1212 if (exp[up->var - first] == up->var - first)
1213 return up;
1214
1215 up = isl_upoly_cow(up);
1216 if (!up)
1217 goto error;
1218
1219 up->var = exp[up->var - first] + first;
1220
1221 rec = isl_upoly_as_rec(up);
1222 if (!rec)
1223 goto error;
1224
1225 for (i = 0; i < rec->n; ++i) {
1226 rec->p[i] = expand(rec->p[i], exp, first);
1227 if (!rec->p[i])
1228 goto error;
1229 }
1230
1231 return up;
1232 error:
1233 isl_upoly_free(up);
1234 return NULL;
1235 }
1236
1237 static __isl_give isl_qpolynomial *with_merged_divs(
1238 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1239 __isl_take isl_qpolynomial *qp2),
1240 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1241 {
1242 int *exp1 = NULL;
1243 int *exp2 = NULL;
1244 isl_mat *div = NULL;
1245
1246 qp1 = isl_qpolynomial_cow(qp1);
1247 qp2 = isl_qpolynomial_cow(qp2);
1248
1249 if (!qp1 || !qp2)
1250 goto error;
1251
1252 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1253 qp1->div->n_col >= qp2->div->n_col, goto error);
1254
1255 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1256 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1257 if (!exp1 || !exp2)
1258 goto error;
1259
1260 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1261 if (!div)
1262 goto error;
1263
1264 isl_mat_free(qp1->div);
1265 qp1->div = isl_mat_copy(div);
1266 isl_mat_free(qp2->div);
1267 qp2->div = isl_mat_copy(div);
1268
1269 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1270 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1271
1272 if (!qp1->upoly || !qp2->upoly)
1273 goto error;
1274
1275 isl_mat_free(div);
1276 free(exp1);
1277 free(exp2);
1278
1279 return fn(qp1, qp2);
1280 error:
1281 isl_mat_free(div);
1282 free(exp1);
1283 free(exp2);
1284 isl_qpolynomial_free(qp1);
1285 isl_qpolynomial_free(qp2);
1286 return NULL;
1287 }
1288
1289 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1290 __isl_take isl_qpolynomial *qp2)
1291 {
1292 qp1 = isl_qpolynomial_cow(qp1);
1293
1294 if (!qp1 || !qp2)
1295 goto error;
1296
1297 if (qp1->div->n_row < qp2->div->n_row)
1298 return isl_qpolynomial_add(qp2, qp1);
1299
1300 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1301 if (!compatible_divs(qp1->div, qp2->div))
1302 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1303
1304 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1305 if (!qp1->upoly)
1306 goto error;
1307
1308 isl_qpolynomial_free(qp2);
1309
1310 return qp1;
1311 error:
1312 isl_qpolynomial_free(qp1);
1313 isl_qpolynomial_free(qp2);
1314 return NULL;
1315 }
1316
1317 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1318 __isl_keep isl_set *dom,
1319 __isl_take isl_qpolynomial *qp1,
1320 __isl_take isl_qpolynomial *qp2)
1321 {
1322 return isl_qpolynomial_add(qp1, qp2);
1323 }
1324
1325 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1326 __isl_take isl_qpolynomial *qp2)
1327 {
1328 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1329 }
1330
1331 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1332 {
1333 qp = isl_qpolynomial_cow(qp);
1334
1335 if (!qp)
1336 return NULL;
1337
1338 qp->upoly = isl_upoly_neg(qp->upoly);
1339 if (!qp->upoly)
1340 goto error;
1341
1342 return qp;
1343 error:
1344 isl_qpolynomial_free(qp);
1345 return NULL;
1346 }
1347
1348 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1349 __isl_take isl_qpolynomial *qp2)
1350 {
1351 qp1 = isl_qpolynomial_cow(qp1);
1352
1353 if (!qp1 || !qp2)
1354 goto error;
1355
1356 if (qp1->div->n_row < qp2->div->n_row)
1357 return isl_qpolynomial_mul(qp2, qp1);
1358
1359 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1360 if (!compatible_divs(qp1->div, qp2->div))
1361 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1362
1363 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1364 if (!qp1->upoly)
1365 goto error;
1366
1367 isl_qpolynomial_free(qp2);
1368
1369 return qp1;
1370 error:
1371 isl_qpolynomial_free(qp1);
1372 isl_qpolynomial_free(qp2);
1373 return NULL;
1374 }
1375
1376 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1377 {
1378 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1379 }
1380
1381 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1382 {
1383 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1384 }
1385
1386 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1387 {
1388 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1389 }
1390
1391 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1392 {
1393 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1394 }
1395
1396 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1397 isl_int v)
1398 {
1399 struct isl_qpolynomial *qp;
1400 struct isl_upoly_cst *cst;
1401
1402 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1403 if (!qp)
1404 return NULL;
1405
1406 cst = isl_upoly_as_cst(qp->upoly);
1407 isl_int_set(cst->n, v);
1408
1409 return qp;
1410 }
1411
1412 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1413 isl_int *n, isl_int *d)
1414 {
1415 struct isl_upoly_cst *cst;
1416
1417 if (!qp)
1418 return -1;
1419
1420 if (!isl_upoly_is_cst(qp->upoly))
1421 return 0;
1422
1423 cst = isl_upoly_as_cst(qp->upoly);
1424 if (!cst)
1425 return -1;
1426
1427 if (n)
1428 isl_int_set(*n, cst->n);
1429 if (d)
1430 isl_int_set(*d, cst->d);
1431
1432 return 1;
1433 }
1434
1435 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1436 {
1437 int is_cst;
1438 struct isl_upoly_rec *rec;
1439
1440 if (!up)
1441 return -1;
1442
1443 if (up->var < 0)
1444 return 1;
1445
1446 rec = isl_upoly_as_rec(up);
1447 if (!rec)
1448 return -1;
1449
1450 if (rec->n > 2)
1451 return 0;
1452
1453 isl_assert(up->ctx, rec->n > 1, return -1);
1454
1455 is_cst = isl_upoly_is_cst(rec->p[1]);
1456 if (is_cst < 0)
1457 return -1;
1458 if (!is_cst)
1459 return 0;
1460
1461 return isl_upoly_is_affine(rec->p[0]);
1462 }
1463
1464 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1465 {
1466 if (!qp)
1467 return -1;
1468
1469 if (qp->div->n_row > 0)
1470 return 0;
1471
1472 return isl_upoly_is_affine(qp->upoly);
1473 }
1474
1475 static void update_coeff(__isl_keep isl_vec *aff,
1476 __isl_keep struct isl_upoly_cst *cst, int pos)
1477 {
1478 isl_int gcd;
1479 isl_int f;
1480
1481 if (isl_int_is_zero(cst->n))
1482 return;
1483
1484 isl_int_init(gcd);
1485 isl_int_init(f);
1486 isl_int_gcd(gcd, cst->d, aff->el[0]);
1487 isl_int_divexact(f, cst->d, gcd);
1488 isl_int_divexact(gcd, aff->el[0], gcd);
1489 isl_seq_scale(aff->el, aff->el, f, aff->size);
1490 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1491 isl_int_clear(gcd);
1492 isl_int_clear(f);
1493 }
1494
1495 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1496 __isl_keep isl_vec *aff)
1497 {
1498 struct isl_upoly_cst *cst;
1499 struct isl_upoly_rec *rec;
1500
1501 if (!up || !aff)
1502 return -1;
1503
1504 if (up->var < 0) {
1505 struct isl_upoly_cst *cst;
1506
1507 cst = isl_upoly_as_cst(up);
1508 if (!cst)
1509 return -1;
1510 update_coeff(aff, cst, 0);
1511 return 0;
1512 }
1513
1514 rec = isl_upoly_as_rec(up);
1515 if (!rec)
1516 return -1;
1517 isl_assert(up->ctx, rec->n == 2, return -1);
1518
1519 cst = isl_upoly_as_cst(rec->p[1]);
1520 if (!cst)
1521 return -1;
1522 update_coeff(aff, cst, 1 + up->var);
1523
1524 return isl_upoly_update_affine(rec->p[0], aff);
1525 }
1526
1527 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1528 __isl_keep isl_qpolynomial *qp)
1529 {
1530 isl_vec *aff;
1531 unsigned d;
1532
1533 if (!qp)
1534 return NULL;
1535
1536 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1537 d = isl_dim_total(qp->dim);
1538 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1539 if (!aff)
1540 return NULL;
1541
1542 isl_seq_clr(aff->el + 1, 1 + d);
1543 isl_int_set_si(aff->el[0], 1);
1544
1545 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1546 goto error;
1547
1548 return aff;
1549 error:
1550 isl_vec_free(aff);
1551 return NULL;
1552 }
1553
1554 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1555 __isl_keep isl_qpolynomial *qp2)
1556 {
1557 if (!qp1 || !qp2)
1558 return -1;
1559
1560 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1561 }
1562
1563 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1564 {
1565 int i;
1566 struct isl_upoly_rec *rec;
1567
1568 if (isl_upoly_is_cst(up)) {
1569 struct isl_upoly_cst *cst;
1570 cst = isl_upoly_as_cst(up);
1571 if (!cst)
1572 return;
1573 isl_int_lcm(*d, *d, cst->d);
1574 return;
1575 }
1576
1577 rec = isl_upoly_as_rec(up);
1578 if (!rec)
1579 return;
1580
1581 for (i = 0; i < rec->n; ++i)
1582 upoly_update_den(rec->p[i], d);
1583 }
1584
1585 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1586 {
1587 isl_int_set_si(*d, 1);
1588 if (!qp)
1589 return;
1590 upoly_update_den(qp->upoly, d);
1591 }
1592
1593 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1594 int pos, int power)
1595 {
1596 struct isl_ctx *ctx;
1597
1598 if (!dim)
1599 return NULL;
1600
1601 ctx = dim->ctx;
1602
1603 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1604 }
1605
1606 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1607 enum isl_dim_type type, unsigned pos)
1608 {
1609 if (!dim)
1610 return NULL;
1611
1612 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1613 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1614
1615 if (type == isl_dim_set)
1616 pos += isl_dim_size(dim, isl_dim_param);
1617
1618 return isl_qpolynomial_pow(dim, pos, 1);
1619 error:
1620 isl_dim_free(dim);
1621 return NULL;
1622 }
1623
1624 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1625 int power)
1626 {
1627 struct isl_qpolynomial *qp = NULL;
1628 struct isl_upoly_rec *rec;
1629 struct isl_upoly_cst *cst;
1630 int i;
1631 int pos;
1632
1633 if (!div)
1634 return NULL;
1635 isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
1636
1637 pos = isl_dim_total(div->bmap->dim);
1638 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1639 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1,
1640 &rec->up);
1641 if (!qp)
1642 goto error;
1643
1644 isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
1645 isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
1646
1647 for (i = 0; i < 1 + power; ++i) {
1648 rec->p[i] = isl_upoly_zero(div->ctx);
1649 if (!rec->p[i])
1650 goto error;
1651 rec->n++;
1652 }
1653 cst = isl_upoly_as_cst(rec->p[power]);
1654 isl_int_set_si(cst->n, 1);
1655
1656 isl_div_free(div);
1657
1658 return qp;
1659 error:
1660 isl_qpolynomial_free(qp);
1661 isl_div_free(div);
1662 return NULL;
1663 }
1664
1665 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1666 {
1667 return isl_qpolynomial_div_pow(div, 1);
1668 }
1669
1670 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1671 const isl_int n, const isl_int d)
1672 {
1673 struct isl_qpolynomial *qp;
1674 struct isl_upoly_cst *cst;
1675
1676 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1677 if (!qp)
1678 return NULL;
1679
1680 cst = isl_upoly_as_cst(qp->upoly);
1681 isl_int_set(cst->n, n);
1682 isl_int_set(cst->d, d);
1683
1684 return qp;
1685 }
1686
1687 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1688 {
1689 struct isl_upoly_rec *rec;
1690 int i;
1691
1692 if (!up)
1693 return -1;
1694
1695 if (isl_upoly_is_cst(up))
1696 return 0;
1697
1698 if (up->var < d)
1699 active[up->var] = 1;
1700
1701 rec = isl_upoly_as_rec(up);
1702 for (i = 0; i < rec->n; ++i)
1703 if (up_set_active(rec->p[i], active, d) < 0)
1704 return -1;
1705
1706 return 0;
1707 }
1708
1709 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1710 {
1711 int i, j;
1712 int d = isl_dim_total(qp->dim);
1713
1714 if (!qp || !active)
1715 return -1;
1716
1717 for (i = 0; i < d; ++i)
1718 for (j = 0; j < qp->div->n_row; ++j) {
1719 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1720 continue;
1721 active[i] = 1;
1722 break;
1723 }
1724
1725 return up_set_active(qp->upoly, active, d);
1726 }
1727
1728 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1729 enum isl_dim_type type, unsigned first, unsigned n)
1730 {
1731 int i;
1732 int *active = NULL;
1733 int involves = 0;
1734
1735 if (!qp)
1736 return -1;
1737 if (n == 0)
1738 return 0;
1739
1740 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1741 return -1);
1742 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1743 type == isl_dim_set, return -1);
1744
1745 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1746 if (set_active(qp, active) < 0)
1747 goto error;
1748
1749 if (type == isl_dim_set)
1750 first += isl_dim_size(qp->dim, isl_dim_param);
1751 for (i = 0; i < n; ++i)
1752 if (active[first + i]) {
1753 involves = 1;
1754 break;
1755 }
1756
1757 free(active);
1758
1759 return involves;
1760 error:
1761 free(active);
1762 return -1;
1763 }
1764
1765 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1766 unsigned first, unsigned n)
1767 {
1768 int i;
1769 struct isl_upoly_rec *rec;
1770
1771 if (!up)
1772 return NULL;
1773 if (n == 0 || up->var < 0 || up->var < first)
1774 return up;
1775 if (up->var < first + n) {
1776 up = replace_by_constant_term(up);
1777 return isl_upoly_drop(up, first, n);
1778 }
1779 up = isl_upoly_cow(up);
1780 if (!up)
1781 return NULL;
1782 up->var -= n;
1783 rec = isl_upoly_as_rec(up);
1784 if (!rec)
1785 goto error;
1786
1787 for (i = 0; i < rec->n; ++i) {
1788 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1789 if (!rec->p[i])
1790 goto error;
1791 }
1792
1793 return up;
1794 error:
1795 isl_upoly_free(up);
1796 return NULL;
1797 }
1798
1799 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1800 __isl_take isl_qpolynomial *qp,
1801 enum isl_dim_type type, unsigned first, unsigned n)
1802 {
1803 if (!qp)
1804 return NULL;
1805 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1806 return qp;
1807
1808 qp = isl_qpolynomial_cow(qp);
1809 if (!qp)
1810 return NULL;
1811
1812 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1813 goto error);
1814 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1815 type == isl_dim_set, goto error);
1816
1817 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1818 if (!qp->dim)
1819 goto error;
1820
1821 if (type == isl_dim_set)
1822 first += isl_dim_size(qp->dim, isl_dim_param);
1823
1824 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1825 if (!qp->div)
1826 goto error;
1827
1828 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1829 if (!qp->upoly)
1830 goto error;
1831
1832 return qp;
1833 error:
1834 isl_qpolynomial_free(qp);
1835 return NULL;
1836 }
1837
1838 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1839 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1840 {
1841 int i;
1842 struct isl_upoly_rec *rec;
1843 struct isl_upoly *base, *res;
1844
1845 if (!up)
1846 return NULL;
1847
1848 if (isl_upoly_is_cst(up))
1849 return up;
1850
1851 if (up->var < first)
1852 return up;
1853
1854 rec = isl_upoly_as_rec(up);
1855 if (!rec)
1856 goto error;
1857
1858 isl_assert(up->ctx, rec->n >= 1, goto error);
1859
1860 if (up->var >= first + n)
1861 base = isl_upoly_pow(up->ctx, up->var, 1);
1862 else
1863 base = isl_upoly_copy(subs[up->var - first]);
1864
1865 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1866 for (i = rec->n - 2; i >= 0; --i) {
1867 struct isl_upoly *t;
1868 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1869 res = isl_upoly_mul(res, isl_upoly_copy(base));
1870 res = isl_upoly_sum(res, t);
1871 }
1872
1873 isl_upoly_free(base);
1874 isl_upoly_free(up);
1875
1876 return res;
1877 error:
1878 isl_upoly_free(up);
1879 return NULL;
1880 }
1881
1882 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1883 isl_int denom, unsigned len)
1884 {
1885 int i;
1886 struct isl_upoly *up;
1887
1888 isl_assert(ctx, len >= 1, return NULL);
1889
1890 up = isl_upoly_rat_cst(ctx, f[0], denom);
1891 for (i = 0; i < len - 1; ++i) {
1892 struct isl_upoly *t;
1893 struct isl_upoly *c;
1894
1895 if (isl_int_is_zero(f[1 + i]))
1896 continue;
1897
1898 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1899 t = isl_upoly_pow(ctx, i, 1);
1900 t = isl_upoly_mul(c, t);
1901 up = isl_upoly_sum(up, t);
1902 }
1903
1904 return up;
1905 }
1906
1907 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
1908 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
1909 {
1910 int i, j, k;
1911 isl_int denom;
1912 unsigned total;
1913 struct isl_upoly *up;
1914
1915 if (!eq)
1916 goto error;
1917 if (eq->n_eq == 0) {
1918 isl_basic_set_free(eq);
1919 return qp;
1920 }
1921
1922 qp = isl_qpolynomial_cow(qp);
1923 if (!qp)
1924 goto error;
1925 qp->div = isl_mat_cow(qp->div);
1926 if (!qp->div)
1927 goto error;
1928
1929 total = 1 + isl_dim_total(eq->dim);
1930 isl_int_init(denom);
1931 for (i = 0; i < eq->n_eq; ++i) {
1932 j = isl_seq_last_non_zero(eq->eq[i], total);
1933 if (j < 0 || j == 0)
1934 continue;
1935
1936 for (k = 0; k < qp->div->n_row; ++k) {
1937 if (isl_int_is_zero(qp->div->row[k][1 + j]))
1938 continue;
1939 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
1940 &qp->div->row[k][0]);
1941 isl_seq_normalize(qp->div->ctx,
1942 qp->div->row[k], 1 + total);
1943 }
1944
1945 if (isl_int_is_pos(eq->eq[i][j]))
1946 isl_seq_neg(eq->eq[i], eq->eq[i], total);
1947 isl_int_abs(denom, eq->eq[i][j]);
1948 isl_int_set_si(eq->eq[i][j], 0);
1949
1950 up = isl_upoly_from_affine(qp->dim->ctx,
1951 eq->eq[i], denom, total);
1952 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
1953 isl_upoly_free(up);
1954 }
1955 isl_int_clear(denom);
1956
1957 if (!qp->upoly)
1958 goto error;
1959
1960 isl_basic_set_free(eq);
1961
1962 qp = sort_divs(qp);
1963
1964 return qp;
1965 error:
1966 isl_basic_set_free(eq);
1967 isl_qpolynomial_free(qp);
1968 return NULL;
1969 }
1970
1971 #undef PW
1972 #define PW isl_pw_qpolynomial
1973 #undef EL
1974 #define EL isl_qpolynomial
1975 #undef IS_ZERO
1976 #define IS_ZERO is_zero
1977 #undef FIELD
1978 #define FIELD qp
1979
1980 #include <isl_pw_templ.c>
1981
1982 #undef UNION
1983 #define UNION isl_union_pw_qpolynomial
1984 #undef PART
1985 #define PART isl_pw_qpolynomial
1986 #undef PARTS
1987 #define PARTS pw_qpolynomial
1988
1989 #include <isl_union_templ.c>
1990
1991 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
1992 {
1993 if (!pwqp)
1994 return -1;
1995
1996 if (pwqp->n != -1)
1997 return 0;
1998
1999 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2000 return 0;
2001
2002 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2003 }
2004
2005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2006 __isl_take isl_pw_qpolynomial *pwqp1,
2007 __isl_take isl_pw_qpolynomial *pwqp2)
2008 {
2009 int i, j, n;
2010 struct isl_pw_qpolynomial *res;
2011 isl_set *set;
2012
2013 if (!pwqp1 || !pwqp2)
2014 goto error;
2015
2016 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2017 goto error);
2018
2019 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2020 isl_pw_qpolynomial_free(pwqp2);
2021 return pwqp1;
2022 }
2023
2024 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2025 isl_pw_qpolynomial_free(pwqp1);
2026 return pwqp2;
2027 }
2028
2029 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2030 isl_pw_qpolynomial_free(pwqp1);
2031 return pwqp2;
2032 }
2033
2034 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2035 isl_pw_qpolynomial_free(pwqp2);
2036 return pwqp1;
2037 }
2038
2039 n = pwqp1->n * pwqp2->n;
2040 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2041
2042 for (i = 0; i < pwqp1->n; ++i) {
2043 for (j = 0; j < pwqp2->n; ++j) {
2044 struct isl_set *common;
2045 struct isl_qpolynomial *prod;
2046 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2047 isl_set_copy(pwqp2->p[j].set));
2048 if (isl_set_fast_is_empty(common)) {
2049 isl_set_free(common);
2050 continue;
2051 }
2052
2053 prod = isl_qpolynomial_mul(
2054 isl_qpolynomial_copy(pwqp1->p[i].qp),
2055 isl_qpolynomial_copy(pwqp2->p[j].qp));
2056
2057 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2058 }
2059 }
2060
2061 isl_pw_qpolynomial_free(pwqp1);
2062 isl_pw_qpolynomial_free(pwqp2);
2063
2064 return res;
2065 error:
2066 isl_pw_qpolynomial_free(pwqp1);
2067 isl_pw_qpolynomial_free(pwqp2);
2068 return NULL;
2069 }
2070
2071 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2072 __isl_take isl_pw_qpolynomial *pwqp)
2073 {
2074 int i;
2075
2076 if (!pwqp)
2077 return NULL;
2078
2079 if (isl_pw_qpolynomial_is_zero(pwqp))
2080 return pwqp;
2081
2082 pwqp = isl_pw_qpolynomial_cow(pwqp);
2083 if (!pwqp)
2084 return NULL;
2085
2086 for (i = 0; i < pwqp->n; ++i) {
2087 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2088 if (!pwqp->p[i].qp)
2089 goto error;
2090 }
2091
2092 return pwqp;
2093 error:
2094 isl_pw_qpolynomial_free(pwqp);
2095 return NULL;
2096 }
2097
2098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2099 __isl_take isl_pw_qpolynomial *pwqp1,
2100 __isl_take isl_pw_qpolynomial *pwqp2)
2101 {
2102 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2103 }
2104
2105 __isl_give struct isl_upoly *isl_upoly_eval(
2106 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2107 {
2108 int i;
2109 struct isl_upoly_rec *rec;
2110 struct isl_upoly *res;
2111 struct isl_upoly *base;
2112
2113 if (isl_upoly_is_cst(up)) {
2114 isl_vec_free(vec);
2115 return up;
2116 }
2117
2118 rec = isl_upoly_as_rec(up);
2119 if (!rec)
2120 goto error;
2121
2122 isl_assert(up->ctx, rec->n >= 1, goto error);
2123
2124 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2125
2126 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2127 isl_vec_copy(vec));
2128
2129 for (i = rec->n - 2; i >= 0; --i) {
2130 res = isl_upoly_mul(res, isl_upoly_copy(base));
2131 res = isl_upoly_sum(res,
2132 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2133 isl_vec_copy(vec)));
2134 }
2135
2136 isl_upoly_free(base);
2137 isl_upoly_free(up);
2138 isl_vec_free(vec);
2139 return res;
2140 error:
2141 isl_upoly_free(up);
2142 isl_vec_free(vec);
2143 return NULL;
2144 }
2145
2146 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2147 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2148 {
2149 isl_vec *ext;
2150 struct isl_upoly *up;
2151 isl_dim *dim;
2152
2153 if (!qp || !pnt)
2154 goto error;
2155 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2156
2157 if (qp->div->n_row == 0)
2158 ext = isl_vec_copy(pnt->vec);
2159 else {
2160 int i;
2161 unsigned dim = isl_dim_total(qp->dim);
2162 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2163 if (!ext)
2164 goto error;
2165
2166 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2167 for (i = 0; i < qp->div->n_row; ++i) {
2168 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2169 1 + dim + i, &ext->el[1+dim+i]);
2170 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2171 qp->div->row[i][0]);
2172 }
2173 }
2174
2175 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2176 if (!up)
2177 goto error;
2178
2179 dim = isl_dim_copy(qp->dim);
2180 isl_qpolynomial_free(qp);
2181 isl_point_free(pnt);
2182
2183 return isl_qpolynomial_alloc(dim, 0, up);
2184 error:
2185 isl_qpolynomial_free(qp);
2186 isl_point_free(pnt);
2187 return NULL;
2188 }
2189
2190 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2191 __isl_keep struct isl_upoly_cst *cst2)
2192 {
2193 int cmp;
2194 isl_int t;
2195 isl_int_init(t);
2196 isl_int_mul(t, cst1->n, cst2->d);
2197 isl_int_submul(t, cst2->n, cst1->d);
2198 cmp = isl_int_sgn(t);
2199 isl_int_clear(t);
2200 return cmp;
2201 }
2202
2203 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2204 __isl_keep isl_qpolynomial *qp2)
2205 {
2206 struct isl_upoly_cst *cst1, *cst2;
2207
2208 if (!qp1 || !qp2)
2209 return -1;
2210 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2211 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2212 if (isl_qpolynomial_is_nan(qp1))
2213 return -1;
2214 if (isl_qpolynomial_is_nan(qp2))
2215 return -1;
2216 cst1 = isl_upoly_as_cst(qp1->upoly);
2217 cst2 = isl_upoly_as_cst(qp2->upoly);
2218
2219 return isl_upoly_cmp(cst1, cst2) <= 0;
2220 }
2221
2222 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2223 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2224 {
2225 struct isl_upoly_cst *cst1, *cst2;
2226 int cmp;
2227
2228 if (!qp1 || !qp2)
2229 goto error;
2230 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2231 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2232 cst1 = isl_upoly_as_cst(qp1->upoly);
2233 cst2 = isl_upoly_as_cst(qp2->upoly);
2234 cmp = isl_upoly_cmp(cst1, cst2);
2235
2236 if (cmp <= 0) {
2237 isl_qpolynomial_free(qp2);
2238 } else {
2239 isl_qpolynomial_free(qp1);
2240 qp1 = qp2;
2241 }
2242 return qp1;
2243 error:
2244 isl_qpolynomial_free(qp1);
2245 isl_qpolynomial_free(qp2);
2246 return NULL;
2247 }
2248
2249 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2250 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2251 {
2252 struct isl_upoly_cst *cst1, *cst2;
2253 int cmp;
2254
2255 if (!qp1 || !qp2)
2256 goto error;
2257 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2258 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2259 cst1 = isl_upoly_as_cst(qp1->upoly);
2260 cst2 = isl_upoly_as_cst(qp2->upoly);
2261 cmp = isl_upoly_cmp(cst1, cst2);
2262
2263 if (cmp >= 0) {
2264 isl_qpolynomial_free(qp2);
2265 } else {
2266 isl_qpolynomial_free(qp1);
2267 qp1 = qp2;
2268 }
2269 return qp1;
2270 error:
2271 isl_qpolynomial_free(qp1);
2272 isl_qpolynomial_free(qp2);
2273 return NULL;
2274 }
2275
2276 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2277 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2278 unsigned first, unsigned n)
2279 {
2280 unsigned total;
2281 unsigned g_pos;
2282 int *exp;
2283
2284 if (n == 0)
2285 return qp;
2286
2287 qp = isl_qpolynomial_cow(qp);
2288 if (!qp)
2289 return NULL;
2290
2291 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2292 goto error);
2293
2294 g_pos = pos(qp->dim, type) + first;
2295
2296 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2297 if (!qp->div)
2298 goto error;
2299
2300 total = qp->div->n_col - 2;
2301 if (total > g_pos) {
2302 int i;
2303 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2304 if (!exp)
2305 goto error;
2306 for (i = 0; i < total - g_pos; ++i)
2307 exp[i] = i + n;
2308 qp->upoly = expand(qp->upoly, exp, g_pos);
2309 free(exp);
2310 if (!qp->upoly)
2311 goto error;
2312 }
2313
2314 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2315 if (!qp->dim)
2316 goto error;
2317
2318 return qp;
2319 error:
2320 isl_qpolynomial_free(qp);
2321 return NULL;
2322 }
2323
2324 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2325 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2326 {
2327 unsigned pos;
2328
2329 pos = isl_qpolynomial_dim(qp, type);
2330
2331 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2332 }
2333
2334 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2335 __isl_take isl_pw_qpolynomial *pwqp,
2336 enum isl_dim_type type, unsigned n)
2337 {
2338 unsigned pos;
2339
2340 pos = isl_pw_qpolynomial_dim(pwqp, type);
2341
2342 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2343 }
2344
2345 static int *reordering_move(isl_ctx *ctx,
2346 unsigned len, unsigned dst, unsigned src, unsigned n)
2347 {
2348 int i;
2349 int *reordering;
2350
2351 reordering = isl_alloc_array(ctx, int, len);
2352 if (!reordering)
2353 return NULL;
2354
2355 if (dst <= src) {
2356 for (i = 0; i < dst; ++i)
2357 reordering[i] = i;
2358 for (i = 0; i < n; ++i)
2359 reordering[src + i] = dst + i;
2360 for (i = 0; i < src - dst; ++i)
2361 reordering[dst + i] = dst + n + i;
2362 for (i = 0; i < len - src - n; ++i)
2363 reordering[src + n + i] = src + n + i;
2364 } else {
2365 for (i = 0; i < src; ++i)
2366 reordering[i] = i;
2367 for (i = 0; i < n; ++i)
2368 reordering[src + i] = dst + i;
2369 for (i = 0; i < dst - src; ++i)
2370 reordering[src + n + i] = src + i;
2371 for (i = 0; i < len - dst - n; ++i)
2372 reordering[dst + n + i] = dst + n + i;
2373 }
2374
2375 return reordering;
2376 }
2377
2378 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2379 __isl_take isl_qpolynomial *qp,
2380 enum isl_dim_type dst_type, unsigned dst_pos,
2381 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2382 {
2383 unsigned g_dst_pos;
2384 unsigned g_src_pos;
2385 int *reordering;
2386
2387 qp = isl_qpolynomial_cow(qp);
2388 if (!qp)
2389 return NULL;
2390
2391 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2392 goto error);
2393
2394 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2395 g_src_pos = pos(qp->dim, src_type) + src_pos;
2396 if (dst_type > src_type)
2397 g_dst_pos -= n;
2398
2399 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2400 if (!qp->div)
2401 goto error;
2402 qp = sort_divs(qp);
2403 if (!qp)
2404 goto error;
2405
2406 reordering = reordering_move(qp->dim->ctx,
2407 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2408 if (!reordering)
2409 goto error;
2410
2411 qp->upoly = reorder(qp->upoly, reordering);
2412 free(reordering);
2413 if (!qp->upoly)
2414 goto error;
2415
2416 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2417 if (!qp->dim)
2418 goto error;
2419
2420 return qp;
2421 error:
2422 isl_qpolynomial_free(qp);
2423 return NULL;
2424 }
2425
2426 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2427 isl_int *f, isl_int denom)
2428 {
2429 struct isl_upoly *up;
2430
2431 if (!dim)
2432 return NULL;
2433
2434 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2435
2436 return isl_qpolynomial_alloc(dim, 0, up);
2437 }
2438
2439 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2440 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2441 {
2442 isl_int denom;
2443 isl_dim *dim;
2444 struct isl_upoly *up;
2445 isl_qpolynomial *qp;
2446 int sgn;
2447
2448 if (!c)
2449 return NULL;
2450
2451 isl_int_init(denom);
2452
2453 isl_constraint_get_coefficient(c, type, pos, &denom);
2454 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2455 sgn = isl_int_sgn(denom);
2456 isl_int_abs(denom, denom);
2457 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2458 1 + isl_constraint_dim(c, isl_dim_all));
2459 if (sgn < 0)
2460 isl_int_neg(denom, denom);
2461 isl_constraint_set_coefficient(c, type, pos, denom);
2462
2463 dim = isl_dim_copy(c->bmap->dim);
2464
2465 isl_int_clear(denom);
2466 isl_constraint_free(c);
2467
2468 qp = isl_qpolynomial_alloc(dim, 0, up);
2469 if (sgn > 0)
2470 qp = isl_qpolynomial_neg(qp);
2471 return qp;
2472 }
2473
2474 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2475 * in "qp" by subs[i].
2476 */
2477 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2478 __isl_take isl_qpolynomial *qp,
2479 enum isl_dim_type type, unsigned first, unsigned n,
2480 __isl_keep isl_qpolynomial **subs)
2481 {
2482 int i;
2483 struct isl_upoly **ups;
2484
2485 if (n == 0)
2486 return qp;
2487
2488 qp = isl_qpolynomial_cow(qp);
2489 if (!qp)
2490 return NULL;
2491 for (i = 0; i < n; ++i)
2492 if (!subs[i])
2493 goto error;
2494
2495 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2496 goto error);
2497
2498 for (i = 0; i < n; ++i)
2499 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2500 goto error);
2501
2502 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2503 for (i = 0; i < n; ++i)
2504 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2505
2506 first += pos(qp->dim, type);
2507
2508 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2509 if (!ups)
2510 goto error;
2511 for (i = 0; i < n; ++i)
2512 ups[i] = subs[i]->upoly;
2513
2514 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2515
2516 free(ups);
2517
2518 if (!qp->upoly)
2519 goto error;
2520
2521 return qp;
2522 error:
2523 isl_qpolynomial_free(qp);
2524 return NULL;
2525 }
2526
2527 __isl_give isl_basic_set *add_div_constraints(__isl_take isl_basic_set *bset,
2528 __isl_take isl_mat *div)
2529 {
2530 int i;
2531 unsigned total;
2532
2533 if (!bset || !div)
2534 goto error;
2535
2536 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2537 if (!bset)
2538 goto error;
2539 total = isl_basic_set_total_dim(bset);
2540 for (i = 0; i < div->n_row; ++i)
2541 if (isl_basic_set_add_div_constraints_var(bset,
2542 total - div->n_row + i, div->row[i]) < 0)
2543 goto error;
2544
2545 isl_mat_free(div);
2546 return bset;
2547 error:
2548 isl_mat_free(div);
2549 isl_basic_set_free(bset);
2550 return NULL;
2551 }
2552
2553 /* Extend "bset" with extra set dimensions for each integer division
2554 * in "qp" and then call "fn" with the extended bset and the polynomial
2555 * that results from replacing each of the integer divisions by the
2556 * corresponding extra set dimension.
2557 */
2558 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2559 __isl_keep isl_basic_set *bset,
2560 int (*fn)(__isl_take isl_basic_set *bset,
2561 __isl_take isl_qpolynomial *poly, void *user), void *user)
2562 {
2563 isl_dim *dim;
2564 isl_mat *div;
2565 isl_qpolynomial *poly;
2566
2567 if (!qp || !bset)
2568 goto error;
2569 if (qp->div->n_row == 0)
2570 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2571 user);
2572
2573 div = isl_mat_copy(qp->div);
2574 dim = isl_dim_copy(qp->dim);
2575 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2576 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2577 bset = isl_basic_set_copy(bset);
2578 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2579 bset = add_div_constraints(bset, div);
2580
2581 return fn(bset, poly, user);
2582 error:
2583 return -1;
2584 }
2585
2586 /* Return total degree in variables first (inclusive) up to last (exclusive).
2587 */
2588 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2589 {
2590 int deg = -1;
2591 int i;
2592 struct isl_upoly_rec *rec;
2593
2594 if (!up)
2595 return -2;
2596 if (isl_upoly_is_zero(up))
2597 return -1;
2598 if (isl_upoly_is_cst(up) || up->var < first)
2599 return 0;
2600
2601 rec = isl_upoly_as_rec(up);
2602 if (!rec)
2603 return -2;
2604
2605 for (i = 0; i < rec->n; ++i) {
2606 int d;
2607
2608 if (isl_upoly_is_zero(rec->p[i]))
2609 continue;
2610 d = isl_upoly_degree(rec->p[i], first, last);
2611 if (up->var < last)
2612 d += i;
2613 if (d > deg)
2614 deg = d;
2615 }
2616
2617 return deg;
2618 }
2619
2620 /* Return total degree in set variables.
2621 */
2622 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2623 {
2624 unsigned ovar;
2625 unsigned nvar;
2626
2627 if (!poly)
2628 return -2;
2629
2630 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2631 nvar = isl_dim_size(poly->dim, isl_dim_set);
2632 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2633 }
2634
2635 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2636 unsigned pos, int deg)
2637 {
2638 int i;
2639 struct isl_upoly_rec *rec;
2640
2641 if (!up)
2642 return NULL;
2643
2644 if (isl_upoly_is_cst(up) || up->var < pos) {
2645 if (deg == 0)
2646 return isl_upoly_copy(up);
2647 else
2648 return isl_upoly_zero(up->ctx);
2649 }
2650
2651 rec = isl_upoly_as_rec(up);
2652 if (!rec)
2653 return NULL;
2654
2655 if (up->var == pos) {
2656 if (deg < rec->n)
2657 return isl_upoly_copy(rec->p[deg]);
2658 else
2659 return isl_upoly_zero(up->ctx);
2660 }
2661
2662 up = isl_upoly_copy(up);
2663 up = isl_upoly_cow(up);
2664 rec = isl_upoly_as_rec(up);
2665 if (!rec)
2666 goto error;
2667
2668 for (i = 0; i < rec->n; ++i) {
2669 struct isl_upoly *t;
2670 t = isl_upoly_coeff(rec->p[i], pos, deg);
2671 if (!t)
2672 goto error;
2673 isl_upoly_free(rec->p[i]);
2674 rec->p[i] = t;
2675 }
2676
2677 return up;
2678 error:
2679 isl_upoly_free(up);
2680 return NULL;
2681 }
2682
2683 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2684 */
2685 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2686 __isl_keep isl_qpolynomial *qp,
2687 enum isl_dim_type type, unsigned t_pos, int deg)
2688 {
2689 unsigned g_pos;
2690 struct isl_upoly *up;
2691 isl_qpolynomial *c;
2692
2693 if (!qp)
2694 return NULL;
2695
2696 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2697 return NULL);
2698
2699 g_pos = pos(qp->dim, type) + t_pos;
2700 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2701
2702 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2703 if (!c)
2704 return NULL;
2705 isl_mat_free(c->div);
2706 c->div = isl_mat_copy(qp->div);
2707 if (!c->div)
2708 goto error;
2709 return c;
2710 error:
2711 isl_qpolynomial_free(c);
2712 return NULL;
2713 }
2714
2715 /* Homogenize the polynomial in the variables first (inclusive) up to
2716 * last (exclusive) by inserting powers of variable first.
2717 * Variable first is assumed not to appear in the input.
2718 */
2719 __isl_give struct isl_upoly *isl_upoly_homogenize(
2720 __isl_take struct isl_upoly *up, int deg, int target,
2721 int first, int last)
2722 {
2723 int i;
2724 struct isl_upoly_rec *rec;
2725
2726 if (!up)
2727 return NULL;
2728 if (isl_upoly_is_zero(up))
2729 return up;
2730 if (deg == target)
2731 return up;
2732 if (isl_upoly_is_cst(up) || up->var < first) {
2733 struct isl_upoly *hom;
2734
2735 hom = isl_upoly_pow(up->ctx, first, target - deg);
2736 if (!hom)
2737 goto error;
2738 rec = isl_upoly_as_rec(hom);
2739 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2740
2741 return hom;
2742 }
2743
2744 up = isl_upoly_cow(up);
2745 rec = isl_upoly_as_rec(up);
2746 if (!rec)
2747 goto error;
2748
2749 for (i = 0; i < rec->n; ++i) {
2750 if (isl_upoly_is_zero(rec->p[i]))
2751 continue;
2752 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2753 up->var < last ? deg + i : i, target,
2754 first, last);
2755 if (!rec->p[i])
2756 goto error;
2757 }
2758
2759 return up;
2760 error:
2761 isl_upoly_free(up);
2762 return NULL;
2763 }
2764
2765 /* Homogenize the polynomial in the set variables by introducing
2766 * powers of an extra set variable at position 0.
2767 */
2768 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2769 __isl_take isl_qpolynomial *poly)
2770 {
2771 unsigned ovar;
2772 unsigned nvar;
2773 int deg = isl_qpolynomial_degree(poly);
2774
2775 if (deg < -1)
2776 goto error;
2777
2778 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2779 poly = isl_qpolynomial_cow(poly);
2780 if (!poly)
2781 goto error;
2782
2783 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2784 nvar = isl_dim_size(poly->dim, isl_dim_set);
2785 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2786 ovar, ovar + nvar);
2787 if (!poly->upoly)
2788 goto error;
2789
2790 return poly;
2791 error:
2792 isl_qpolynomial_free(poly);
2793 return NULL;
2794 }
2795
2796 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2797 __isl_take isl_mat *div)
2798 {
2799 isl_term *term;
2800 int n;
2801
2802 if (!dim || !div)
2803 goto error;
2804
2805 n = isl_dim_total(dim) + div->n_row;
2806
2807 term = isl_calloc(dim->ctx, struct isl_term,
2808 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2809 if (!term)
2810 goto error;
2811
2812 term->ref = 1;
2813 term->dim = dim;
2814 term->div = div;
2815 isl_int_init(term->n);
2816 isl_int_init(term->d);
2817
2818 return term;
2819 error:
2820 isl_dim_free(dim);
2821 isl_mat_free(div);
2822 return NULL;
2823 }
2824
2825 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2826 {
2827 if (!term)
2828 return NULL;
2829
2830 term->ref++;
2831 return term;
2832 }
2833
2834 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2835 {
2836 int i;
2837 isl_term *dup;
2838 unsigned total;
2839
2840 if (term)
2841 return NULL;
2842
2843 total = isl_dim_total(term->dim) + term->div->n_row;
2844
2845 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2846 if (!dup)
2847 return NULL;
2848
2849 isl_int_set(dup->n, term->n);
2850 isl_int_set(dup->d, term->d);
2851
2852 for (i = 0; i < total; ++i)
2853 dup->pow[i] = term->pow[i];
2854
2855 return dup;
2856 }
2857
2858 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
2859 {
2860 if (!term)
2861 return NULL;
2862
2863 if (term->ref == 1)
2864 return term;
2865 term->ref--;
2866 return isl_term_dup(term);
2867 }
2868
2869 void isl_term_free(__isl_take isl_term *term)
2870 {
2871 if (!term)
2872 return;
2873
2874 if (--term->ref > 0)
2875 return;
2876
2877 isl_dim_free(term->dim);
2878 isl_mat_free(term->div);
2879 isl_int_clear(term->n);
2880 isl_int_clear(term->d);
2881 free(term);
2882 }
2883
2884 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
2885 {
2886 if (!term)
2887 return 0;
2888
2889 switch (type) {
2890 case isl_dim_param:
2891 case isl_dim_in:
2892 case isl_dim_out: return isl_dim_size(term->dim, type);
2893 case isl_dim_div: return term->div->n_row;
2894 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
2895 default: return 0;
2896 }
2897 }
2898
2899 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
2900 {
2901 return term ? term->dim->ctx : NULL;
2902 }
2903
2904 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
2905 {
2906 if (!term)
2907 return;
2908 isl_int_set(*n, term->n);
2909 }
2910
2911 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
2912 {
2913 if (!term)
2914 return;
2915 isl_int_set(*d, term->d);
2916 }
2917
2918 int isl_term_get_exp(__isl_keep isl_term *term,
2919 enum isl_dim_type type, unsigned pos)
2920 {
2921 if (!term)
2922 return -1;
2923
2924 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
2925
2926 if (type >= isl_dim_set)
2927 pos += isl_dim_size(term->dim, isl_dim_param);
2928 if (type >= isl_dim_div)
2929 pos += isl_dim_size(term->dim, isl_dim_set);
2930
2931 return term->pow[pos];
2932 }
2933
2934 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
2935 {
2936 isl_basic_map *bmap;
2937 unsigned total;
2938 int k;
2939
2940 if (!term)
2941 return NULL;
2942
2943 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
2944 return NULL);
2945
2946 total = term->div->n_col - term->div->n_row - 2;
2947 /* No nested divs for now */
2948 isl_assert(term->dim->ctx,
2949 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
2950 term->div->n_row) == -1,
2951 return NULL);
2952
2953 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
2954 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
2955 goto error;
2956
2957 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
2958
2959 return isl_basic_map_div(bmap, k);
2960 error:
2961 isl_basic_map_free(bmap);
2962 return NULL;
2963 }
2964
2965 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
2966 int (*fn)(__isl_take isl_term *term, void *user),
2967 __isl_take isl_term *term, void *user)
2968 {
2969 int i;
2970 struct isl_upoly_rec *rec;
2971
2972 if (!up || !term)
2973 goto error;
2974
2975 if (isl_upoly_is_zero(up))
2976 return term;
2977
2978 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
2979 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
2980 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
2981
2982 if (isl_upoly_is_cst(up)) {
2983 struct isl_upoly_cst *cst;
2984 cst = isl_upoly_as_cst(up);
2985 if (!cst)
2986 goto error;
2987 term = isl_term_cow(term);
2988 if (!term)
2989 goto error;
2990 isl_int_set(term->n, cst->n);
2991 isl_int_set(term->d, cst->d);
2992 if (fn(isl_term_copy(term), user) < 0)
2993 goto error;
2994 return term;
2995 }
2996
2997 rec = isl_upoly_as_rec(up);
2998 if (!rec)
2999 goto error;
3000
3001 for (i = 0; i < rec->n; ++i) {
3002 term = isl_term_cow(term);
3003 if (!term)
3004 goto error;
3005 term->pow[up->var] = i;
3006 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3007 if (!term)
3008 goto error;
3009 }
3010 term->pow[up->var] = 0;
3011
3012 return term;
3013 error:
3014 isl_term_free(term);
3015 return NULL;
3016 }
3017
3018 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3019 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3020 {
3021 isl_term *term;
3022
3023 if (!qp)
3024 return -1;
3025
3026 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3027 if (!term)
3028 return -1;
3029
3030 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3031
3032 isl_term_free(term);
3033
3034 return term ? 0 : -1;
3035 }
3036
3037 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3038 {
3039 struct isl_upoly *up;
3040 isl_qpolynomial *qp;
3041 int i, n;
3042
3043 if (!term)
3044 return NULL;
3045
3046 n = isl_dim_total(term->dim) + term->div->n_row;
3047
3048 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3049 for (i = 0; i < n; ++i) {
3050 if (!term->pow[i])
3051 continue;
3052 up = isl_upoly_mul(up,
3053 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3054 }
3055
3056 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3057 if (!qp)
3058 goto error;
3059 isl_mat_free(qp->div);
3060 qp->div = isl_mat_copy(term->div);
3061 if (!qp->div)
3062 goto error;
3063
3064 isl_term_free(term);
3065 return qp;
3066 error:
3067 isl_qpolynomial_free(qp);
3068 isl_term_free(term);
3069 return NULL;
3070 }
3071
3072 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3073 __isl_take isl_dim *dim)
3074 {
3075 int i;
3076 int extra;
3077 unsigned total;
3078
3079 if (!qp || !dim)
3080 goto error;
3081
3082 if (isl_dim_equal(qp->dim, dim)) {
3083 isl_dim_free(dim);
3084 return qp;
3085 }
3086
3087 qp = isl_qpolynomial_cow(qp);
3088 if (!qp)
3089 goto error;
3090
3091 extra = isl_dim_size(dim, isl_dim_set) -
3092 isl_dim_size(qp->dim, isl_dim_set);
3093 total = isl_dim_total(qp->dim);
3094 if (qp->div->n_row) {
3095 int *exp;
3096
3097 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3098 if (!exp)
3099 goto error;
3100 for (i = 0; i < qp->div->n_row; ++i)
3101 exp[i] = extra + i;
3102 qp->upoly = expand(qp->upoly, exp, total);
3103 free(exp);
3104 if (!qp->upoly)
3105 goto error;
3106 }
3107 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3108 if (!qp->div)
3109 goto error;
3110 for (i = 0; i < qp->div->n_row; ++i)
3111 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3112
3113 isl_dim_free(qp->dim);
3114 qp->dim = dim;
3115
3116 return qp;
3117 error:
3118 isl_dim_free(dim);
3119 isl_qpolynomial_free(qp);
3120 return NULL;
3121 }
3122
3123 /* For each parameter or variable that does not appear in qp,
3124 * first eliminate the variable from all constraints and then set it to zero.
3125 */
3126 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3127 __isl_keep isl_qpolynomial *qp)
3128 {
3129 int *active = NULL;
3130 int i;
3131 int d;
3132 unsigned nparam;
3133 unsigned nvar;
3134
3135 if (!set || !qp)
3136 goto error;
3137
3138 d = isl_dim_total(set->dim);
3139 active = isl_calloc_array(set->ctx, int, d);
3140 if (set_active(qp, active) < 0)
3141 goto error;
3142
3143 for (i = 0; i < d; ++i)
3144 if (!active[i])
3145 break;
3146
3147 if (i == d) {
3148 free(active);
3149 return set;
3150 }
3151
3152 nparam = isl_dim_size(set->dim, isl_dim_param);
3153 nvar = isl_dim_size(set->dim, isl_dim_set);
3154 for (i = 0; i < nparam; ++i) {
3155 if (active[i])
3156 continue;
3157 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3158 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3159 }
3160 for (i = 0; i < nvar; ++i) {
3161 if (active[nparam + i])
3162 continue;
3163 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3164 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3165 }
3166
3167 free(active);
3168
3169 return set;
3170 error:
3171 free(active);
3172 isl_set_free(set);
3173 return NULL;
3174 }
3175
3176 struct isl_opt_data {
3177 isl_qpolynomial *qp;
3178 int first;
3179 isl_qpolynomial *opt;
3180 int max;
3181 };
3182
3183 static int opt_fn(__isl_take isl_point *pnt, void *user)
3184 {
3185 struct isl_opt_data *data = (struct isl_opt_data *)user;
3186 isl_qpolynomial *val;
3187
3188 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3189 if (data->first) {
3190 data->first = 0;
3191 data->opt = val;
3192 } else if (data->max) {
3193 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3194 } else {
3195 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3196 }
3197
3198 return 0;
3199 }
3200
3201 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3202 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3203 {
3204 struct isl_opt_data data = { NULL, 1, NULL, max };
3205
3206 if (!set || !qp)
3207 goto error;
3208
3209 if (isl_upoly_is_cst(qp->upoly)) {
3210 isl_set_free(set);
3211 return qp;
3212 }
3213
3214 set = fix_inactive(set, qp);
3215
3216 data.qp = qp;
3217 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3218 goto error;
3219
3220 if (data.first)
3221 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3222
3223 isl_set_free(set);
3224 isl_qpolynomial_free(qp);
3225 return data.opt;
3226 error:
3227 isl_set_free(set);
3228 isl_qpolynomial_free(qp);
3229 isl_qpolynomial_free(data.opt);
3230 return NULL;
3231 }
3232
3233 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3234 __isl_take isl_morph *morph)
3235 {
3236 int i;
3237 isl_ctx *ctx;
3238 struct isl_upoly *up;
3239 unsigned n_div;
3240 struct isl_upoly **subs;
3241 isl_mat *mat;
3242
3243 qp = isl_qpolynomial_cow(qp);
3244 if (!qp || !morph)
3245 goto error;
3246
3247 ctx = qp->dim->ctx;
3248 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3249
3250 subs = isl_calloc_array(ctx, struct isl_upoly *, morph->inv->n_row - 1);
3251 if (!subs)
3252 goto error;
3253
3254 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3255 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3256 morph->inv->row[0][0], morph->inv->n_col);
3257
3258 qp->upoly = isl_upoly_subs(qp->upoly, 0, morph->inv->n_row - 1, subs);
3259
3260 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3261 isl_upoly_free(subs[i]);
3262 free(subs);
3263
3264 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3265 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3266 qp->div = isl_mat_product(qp->div, mat);
3267 isl_dim_free(qp->dim);
3268 qp->dim = isl_dim_copy(morph->ran->dim);
3269
3270 if (!qp->upoly || !qp->div || !qp->dim)
3271 goto error;
3272
3273 isl_morph_free(morph);
3274
3275 return qp;
3276 error:
3277 isl_qpolynomial_free(qp);
3278 isl_morph_free(morph);
3279 return NULL;
3280 }
3281
3282 static int neg_entry(void **entry, void *user)
3283 {
3284 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3285
3286 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3287
3288 return *pwqp ? 0 : -1;
3289 }
3290
3291 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3292 __isl_take isl_union_pw_qpolynomial *upwqp)
3293 {
3294 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3295 if (!upwqp)
3296 return NULL;
3297
3298 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3299 &neg_entry, NULL) < 0)
3300 goto error;
3301
3302 return upwqp;
3303 error:
3304 isl_union_pw_qpolynomial_free(upwqp);
3305 return NULL;
3306 }
3307
3308 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3309 __isl_take isl_union_pw_qpolynomial *upwqp1,
3310 __isl_take isl_union_pw_qpolynomial *upwqp2)
3311 {
3312 return isl_union_pw_qpolynomial_add(upwqp1,
3313 isl_union_pw_qpolynomial_neg(upwqp2));
3314 }
3315
3316 static int mul_entry(void **entry, void *user)
3317 {
3318 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3319 uint32_t hash;
3320 struct isl_hash_table_entry *entry2;
3321 isl_pw_qpolynomial *pwpq = *entry;
3322 int empty;
3323
3324 hash = isl_dim_get_hash(pwpq->dim);
3325 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3326 hash, &has_dim, pwpq->dim, 0);
3327 if (!entry2)
3328 return 0;
3329
3330 pwpq = isl_pw_qpolynomial_copy(pwpq);
3331 pwpq = isl_pw_qpolynomial_mul(pwpq,
3332 isl_pw_qpolynomial_copy(entry2->data));
3333
3334 empty = isl_pw_qpolynomial_is_zero(pwpq);
3335 if (empty < 0) {
3336 isl_pw_qpolynomial_free(pwpq);
3337 return -1;
3338 }
3339 if (empty) {
3340 isl_pw_qpolynomial_free(pwpq);
3341 return 0;
3342 }
3343
3344 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3345
3346 return 0;
3347 }
3348
3349 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3350 __isl_take isl_union_pw_qpolynomial *upwqp1,
3351 __isl_take isl_union_pw_qpolynomial *upwqp2)
3352 {
3353 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3354 }
3355
3356 /* Reorder the columns of the given div definitions according to the
3357 * given reordering.
3358 */
3359 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3360 __isl_take isl_reordering *r)
3361 {
3362 int i, j;
3363 isl_mat *mat;
3364 int extra;
3365
3366 if (!div || !r)
3367 goto error;
3368
3369 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3370 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3371 if (!mat)
3372 goto error;
3373
3374 for (i = 0; i < div->n_row; ++i) {
3375 isl_seq_cpy(mat->row[i], div->row[i], 2);
3376 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3377 for (j = 0; j < r->len; ++j)
3378 isl_int_set(mat->row[i][2 + r->pos[j]],
3379 div->row[i][2 + j]);
3380 }
3381
3382 isl_reordering_free(r);
3383 isl_mat_free(div);
3384 return mat;
3385 error:
3386 isl_reordering_free(r);
3387 isl_mat_free(div);
3388 return NULL;
3389 }
3390
3391 /* Reorder the dimension of "qp" according to the given reordering.
3392 */
3393 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3394 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3395 {
3396 qp = isl_qpolynomial_cow(qp);
3397 if (!qp)
3398 goto error;
3399
3400 r = isl_reordering_extend(r, qp->div->n_row);
3401 if (!r)
3402 goto error;
3403
3404 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3405 if (!qp->div)
3406 goto error;
3407
3408 qp->upoly = reorder(qp->upoly, r->pos);
3409 if (!qp->upoly)
3410 goto error;
3411
3412 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3413
3414 isl_reordering_free(r);
3415 return qp;
3416 error:
3417 isl_qpolynomial_free(qp);
3418 isl_reordering_free(r);
3419 return NULL;
3420 }
3421
3422 struct isl_split_periods_data {
3423 int max_periods;
3424 isl_pw_qpolynomial *res;
3425 };
3426
3427 /* Create a slice where the integer division "div" has the fixed value "v".
3428 * In particular, if "div" refers to floor(f/m), then create a slice
3429 *
3430 * m v <= f <= m v + (m - 1)
3431 *
3432 * or
3433 *
3434 * f - m v >= 0
3435 * -f + m v + (m - 1) >= 0
3436 */
3437 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3438 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3439 {
3440 int total;
3441 isl_basic_set *bset = NULL;
3442 int k;
3443
3444 if (!dim || !qp)
3445 goto error;
3446
3447 total = isl_dim_total(dim);
3448 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3449
3450 k = isl_basic_set_alloc_inequality(bset);
3451 if (k < 0)
3452 goto error;
3453 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3454 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3455
3456 k = isl_basic_set_alloc_inequality(bset);
3457 if (k < 0)
3458 goto error;
3459 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3460 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3461 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3462 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3463
3464 isl_dim_free(dim);
3465 return isl_set_from_basic_set(bset);
3466 error:
3467 isl_basic_set_free(bset);
3468 isl_dim_free(dim);
3469 return NULL;
3470 }
3471
3472 static int split_periods(__isl_take isl_set *set,
3473 __isl_take isl_qpolynomial *qp, void *user);
3474
3475 /* Create a slice of the domain "set" such that integer division "div"
3476 * has the fixed value "v" and add the results to data->res,
3477 * replacing the integer division by "v" in "qp".
3478 */
3479 static int set_div(__isl_take isl_set *set,
3480 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3481 struct isl_split_periods_data *data)
3482 {
3483 int i;
3484 int *reordering;
3485 isl_set *slice;
3486 struct isl_upoly *cst;
3487 int total;
3488
3489 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3490 set = isl_set_intersect(set, slice);
3491
3492 qp = isl_qpolynomial_cow(qp);
3493 if (!qp)
3494 goto error;
3495
3496 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3497 if (!cst)
3498 goto error;
3499 total = isl_dim_total(qp->dim);
3500 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &cst);
3501 isl_upoly_free(cst);
3502 if (!qp->upoly)
3503 goto error;
3504
3505 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
3506 if (!reordering)
3507 goto error;
3508 for (i = 0; i < total + div; ++i)
3509 reordering[i] = i;
3510 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
3511 reordering[i] = i - 1;
3512 qp->div = isl_mat_drop_rows(qp->div, div, 1);
3513 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
3514 qp->upoly = reorder(qp->upoly, reordering);
3515 free(reordering);
3516
3517 if (!qp->upoly || !qp->div)
3518 goto error;
3519
3520 return split_periods(set, qp, data);
3521 error:
3522 isl_set_free(set);
3523 isl_qpolynomial_free(qp);
3524 return -1;
3525 }
3526
3527 /* Split the domain "set" such that integer division "div"
3528 * has a fixed value (ranging from "min" to "max") on each slice
3529 * and add the results to data->res.
3530 */
3531 static int split_div(__isl_take isl_set *set,
3532 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3533 struct isl_split_periods_data *data)
3534 {
3535 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3536 isl_set *set_i = isl_set_copy(set);
3537 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3538
3539 if (set_div(set_i, qp_i, div, min, data) < 0)
3540 goto error;
3541 }
3542 isl_set_free(set);
3543 isl_qpolynomial_free(qp);
3544 return 0;
3545 error:
3546 isl_set_free(set);
3547 isl_qpolynomial_free(qp);
3548 return -1;
3549 }
3550
3551 /* If "qp" refers to any integer division
3552 * that can only attain "max_periods" distinct values on "set"
3553 * then split the domain along those distinct values.
3554 * Add the results (or the original if no splitting occurs)
3555 * to data->res.
3556 */
3557 static int split_periods(__isl_take isl_set *set,
3558 __isl_take isl_qpolynomial *qp, void *user)
3559 {
3560 int i;
3561 isl_pw_qpolynomial *pwqp;
3562 struct isl_split_periods_data *data;
3563 isl_int min, max;
3564 int total;
3565 int r = 0;
3566
3567 data = (struct isl_split_periods_data *)user;
3568
3569 if (!set || !qp)
3570 goto error;
3571
3572 if (qp->div->n_row == 0) {
3573 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3574 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3575 return 0;
3576 }
3577
3578 isl_int_init(min);
3579 isl_int_init(max);
3580 total = isl_dim_total(qp->dim);
3581 for (i = 0; i < qp->div->n_row; ++i) {
3582 enum isl_lp_result lp_res;
3583
3584 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3585 qp->div->n_row) != -1)
3586 continue;
3587
3588 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3589 set->ctx->one, &min, NULL, NULL);
3590 if (lp_res == isl_lp_error)
3591 goto error2;
3592 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3593 continue;
3594 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3595
3596 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3597 set->ctx->one, &max, NULL, NULL);
3598 if (lp_res == isl_lp_error)
3599 goto error2;
3600 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3601 continue;
3602 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3603
3604 isl_int_sub(max, max, min);
3605 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3606 isl_int_add(max, max, min);
3607 break;
3608 }
3609 }
3610
3611 if (i < qp->div->n_row) {
3612 r = split_div(set, qp, i, min, max, data);
3613 } else {
3614 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3615 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3616 }
3617
3618 isl_int_clear(max);
3619 isl_int_clear(min);
3620
3621 return r;
3622 error2:
3623 isl_int_clear(max);
3624 isl_int_clear(min);
3625 error:
3626 isl_set_free(set);
3627 isl_qpolynomial_free(qp);
3628 return -1;
3629 }
3630
3631 /* If any quasi-polynomial in pwqp refers to any integer division
3632 * that can only attain "max_periods" distinct values on its domain
3633 * then split the domain along those distinct values.
3634 */
3635 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3636 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3637 {
3638 struct isl_split_periods_data data;
3639
3640 data.max_periods = max_periods;
3641 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3642
3643 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3644 goto error;
3645
3646 isl_pw_qpolynomial_free(pwqp);
3647
3648 return data.res;
3649 error:
3650 isl_pw_qpolynomial_free(data.res);
3651 isl_pw_qpolynomial_free(pwqp);
3652 return NULL;
3653 }
Integer set library