?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
export isl_pw_qpolynomial_fold_fix_dim
[isl.git] / isl_polynomial.c
bloba9de8813bb4611f7e1870885aaad7326d71bf9eb
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_factorization.h>
13 #include <isl_lp.h>
14 #include <isl_seq.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21
22 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
23 {
24 switch (type) {
25 case isl_dim_param: return 0;
26 case isl_dim_in: return dim->nparam;
27 case isl_dim_out: return dim->nparam + dim->n_in;
28 default: return 0;
29 }
30 }
31
32 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
33 {
34 if (!up)
35 return -1;
36
37 return up->var < 0;
38 }
39
40 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return NULL;
44
45 isl_assert(up->ctx, up->var < 0, return NULL);
46
47 return (struct isl_upoly_cst *)up;
48 }
49
50 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
51 {
52 if (!up)
53 return NULL;
54
55 isl_assert(up->ctx, up->var >= 0, return NULL);
56
57 return (struct isl_upoly_rec *)up;
58 }
59
60 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
61 __isl_keep struct isl_upoly *up2)
62 {
63 int i;
64 struct isl_upoly_rec *rec1, *rec2;
65
66 if (!up1 || !up2)
67 return -1;
68 if (up1 == up2)
69 return 1;
70 if (up1->var != up2->var)
71 return 0;
72 if (isl_upoly_is_cst(up1)) {
73 struct isl_upoly_cst *cst1, *cst2;
74 cst1 = isl_upoly_as_cst(up1);
75 cst2 = isl_upoly_as_cst(up2);
76 if (!cst1 || !cst2)
77 return -1;
78 return isl_int_eq(cst1->n, cst2->n) &&
79 isl_int_eq(cst1->d, cst2->d);
80 }
81
82 rec1 = isl_upoly_as_rec(up1);
83 rec2 = isl_upoly_as_rec(up2);
84 if (!rec1 || !rec2)
85 return -1;
86
87 if (rec1->n != rec2->n)
88 return 0;
89
90 for (i = 0; i < rec1->n; ++i) {
91 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
92 if (eq < 0 || !eq)
93 return eq;
94 }
95
96 return 1;
97 }
98
99 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
100 {
101 struct isl_upoly_cst *cst;
102
103 if (!up)
104 return -1;
105 if (!isl_upoly_is_cst(up))
106 return 0;
107
108 cst = isl_upoly_as_cst(up);
109 if (!cst)
110 return -1;
111
112 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
113 }
114
115 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
116 {
117 struct isl_upoly_cst *cst;
118
119 if (!up)
120 return 0;
121 if (!isl_upoly_is_cst(up))
122 return 0;
123
124 cst = isl_upoly_as_cst(up);
125 if (!cst)
126 return 0;
127
128 return isl_int_sgn(cst->n);
129 }
130
131 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
132 {
133 struct isl_upoly_cst *cst;
134
135 if (!up)
136 return -1;
137 if (!isl_upoly_is_cst(up))
138 return 0;
139
140 cst = isl_upoly_as_cst(up);
141 if (!cst)
142 return -1;
143
144 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
145 }
146
147 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
148 {
149 struct isl_upoly_cst *cst;
150
151 if (!up)
152 return -1;
153 if (!isl_upoly_is_cst(up))
154 return 0;
155
156 cst = isl_upoly_as_cst(up);
157 if (!cst)
158 return -1;
159
160 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
161 }
162
163 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
164 {
165 struct isl_upoly_cst *cst;
166
167 if (!up)
168 return -1;
169 if (!isl_upoly_is_cst(up))
170 return 0;
171
172 cst = isl_upoly_as_cst(up);
173 if (!cst)
174 return -1;
175
176 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
177 }
178
179 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
180 {
181 struct isl_upoly_cst *cst;
182
183 if (!up)
184 return -1;
185 if (!isl_upoly_is_cst(up))
186 return 0;
187
188 cst = isl_upoly_as_cst(up);
189 if (!cst)
190 return -1;
191
192 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
193 }
194
195 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
196 {
197 struct isl_upoly_cst *cst;
198
199 if (!up)
200 return -1;
201 if (!isl_upoly_is_cst(up))
202 return 0;
203
204 cst = isl_upoly_as_cst(up);
205 if (!cst)
206 return -1;
207
208 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
209 }
210
211 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
212 {
213 struct isl_upoly_cst *cst;
214
215 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
216 if (!cst)
217 return NULL;
218
219 cst->up.ref = 1;
220 cst->up.ctx = ctx;
221 isl_ctx_ref(ctx);
222 cst->up.var = -1;
223
224 isl_int_init(cst->n);
225 isl_int_init(cst->d);
226
227 return cst;
228 }
229
230 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
231 {
232 struct isl_upoly_cst *cst;
233
234 cst = isl_upoly_cst_alloc(ctx);
235 if (!cst)
236 return NULL;
237
238 isl_int_set_si(cst->n, 0);
239 isl_int_set_si(cst->d, 1);
240
241 return &cst->up;
242 }
243
244 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
245 {
246 struct isl_upoly_cst *cst;
247
248 cst = isl_upoly_cst_alloc(ctx);
249 if (!cst)
250 return NULL;
251
252 isl_int_set_si(cst->n, 1);
253 isl_int_set_si(cst->d, 1);
254
255 return &cst->up;
256 }
257
258 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
259 {
260 struct isl_upoly_cst *cst;
261
262 cst = isl_upoly_cst_alloc(ctx);
263 if (!cst)
264 return NULL;
265
266 isl_int_set_si(cst->n, 1);
267 isl_int_set_si(cst->d, 0);
268
269 return &cst->up;
270 }
271
272 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
273 {
274 struct isl_upoly_cst *cst;
275
276 cst = isl_upoly_cst_alloc(ctx);
277 if (!cst)
278 return NULL;
279
280 isl_int_set_si(cst->n, -1);
281 isl_int_set_si(cst->d, 0);
282
283 return &cst->up;
284 }
285
286 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
287 {
288 struct isl_upoly_cst *cst;
289
290 cst = isl_upoly_cst_alloc(ctx);
291 if (!cst)
292 return NULL;
293
294 isl_int_set_si(cst->n, 0);
295 isl_int_set_si(cst->d, 0);
296
297 return &cst->up;
298 }
299
300 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
301 isl_int n, isl_int d)
302 {
303 struct isl_upoly_cst *cst;
304
305 cst = isl_upoly_cst_alloc(ctx);
306 if (!cst)
307 return NULL;
308
309 isl_int_set(cst->n, n);
310 isl_int_set(cst->d, d);
311
312 return &cst->up;
313 }
314
315 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
316 int var, int size)
317 {
318 struct isl_upoly_rec *rec;
319
320 isl_assert(ctx, var >= 0, return NULL);
321 isl_assert(ctx, size >= 0, return NULL);
322 rec = isl_calloc(ctx, struct isl_upoly_rec,
323 sizeof(struct isl_upoly_rec) +
324 (size - 1) * sizeof(struct isl_upoly *));
325 if (!rec)
326 return NULL;
327
328 rec->up.ref = 1;
329 rec->up.ctx = ctx;
330 isl_ctx_ref(ctx);
331 rec->up.var = var;
332
333 rec->n = 0;
334 rec->size = size;
335
336 return rec;
337 }
338
339 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
340 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
341 {
342 qp = isl_qpolynomial_cow(qp);
343 if (!qp || !dim)
344 goto error;
345
346 isl_dim_free(qp->dim);
347 qp->dim = dim;
348
349 return qp;
350 error:
351 isl_qpolynomial_free(qp);
352 isl_dim_free(dim);
353 return NULL;
354 }
355
356 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
357 {
358 return qp ? qp->dim->ctx : NULL;
359 }
360
361 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
362 {
363 return qp ? isl_dim_copy(qp->dim) : NULL;
364 }
365
366 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
367 enum isl_dim_type type)
368 {
369 return qp ? isl_dim_size(qp->dim, type) : 0;
370 }
371
372 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
373 {
374 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
375 }
376
377 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
378 {
379 return qp ? isl_upoly_is_one(qp->upoly) : -1;
380 }
381
382 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
385 }
386
387 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
388 {
389 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
390 }
391
392 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
393 {
394 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
395 }
396
397 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
398 {
399 return qp ? isl_upoly_sgn(qp->upoly) : 0;
400 }
401
402 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
403 {
404 isl_int_clear(cst->n);
405 isl_int_clear(cst->d);
406 }
407
408 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
409 {
410 int i;
411
412 for (i = 0; i < rec->n; ++i)
413 isl_upoly_free(rec->p[i]);
414 }
415
416 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
417 {
418 if (!up)
419 return NULL;
420
421 up->ref++;
422 return up;
423 }
424
425 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
426 {
427 struct isl_upoly_cst *cst;
428 struct isl_upoly_cst *dup;
429
430 cst = isl_upoly_as_cst(up);
431 if (!cst)
432 return NULL;
433
434 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
435 if (!dup)
436 return NULL;
437 isl_int_set(dup->n, cst->n);
438 isl_int_set(dup->d, cst->d);
439
440 return &dup->up;
441 }
442
443 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
444 {
445 int i;
446 struct isl_upoly_rec *rec;
447 struct isl_upoly_rec *dup;
448
449 rec = isl_upoly_as_rec(up);
450 if (!rec)
451 return NULL;
452
453 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
454 if (!dup)
455 return NULL;
456
457 for (i = 0; i < rec->n; ++i) {
458 dup->p[i] = isl_upoly_copy(rec->p[i]);
459 if (!dup->p[i])
460 goto error;
461 dup->n++;
462 }
463
464 return &dup->up;
465 error:
466 isl_upoly_free(&dup->up);
467 return NULL;
468 }
469
470 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
471 {
472 struct isl_upoly *dup;
473
474 if (!up)
475 return NULL;
476
477 if (isl_upoly_is_cst(up))
478 return isl_upoly_dup_cst(up);
479 else
480 return isl_upoly_dup_rec(up);
481 }
482
483 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
484 {
485 if (!up)
486 return NULL;
487
488 if (up->ref == 1)
489 return up;
490 up->ref--;
491 return isl_upoly_dup(up);
492 }
493
494 void isl_upoly_free(__isl_take struct isl_upoly *up)
495 {
496 if (!up)
497 return;
498
499 if (--up->ref > 0)
500 return;
501
502 if (up->var < 0)
503 upoly_free_cst((struct isl_upoly_cst *)up);
504 else
505 upoly_free_rec((struct isl_upoly_rec *)up);
506
507 isl_ctx_deref(up->ctx);
508 free(up);
509 }
510
511 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
512 {
513 isl_int gcd;
514
515 isl_int_init(gcd);
516 isl_int_gcd(gcd, cst->n, cst->d);
517 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
518 isl_int_divexact(cst->n, cst->n, gcd);
519 isl_int_divexact(cst->d, cst->d, gcd);
520 }
521 isl_int_clear(gcd);
522 }
523
524 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
525 __isl_take struct isl_upoly *up2)
526 {
527 struct isl_upoly_cst *cst1;
528 struct isl_upoly_cst *cst2;
529
530 up1 = isl_upoly_cow(up1);
531 if (!up1 || !up2)
532 goto error;
533
534 cst1 = isl_upoly_as_cst(up1);
535 cst2 = isl_upoly_as_cst(up2);
536
537 if (isl_int_eq(cst1->d, cst2->d))
538 isl_int_add(cst1->n, cst1->n, cst2->n);
539 else {
540 isl_int_mul(cst1->n, cst1->n, cst2->d);
541 isl_int_addmul(cst1->n, cst2->n, cst1->d);
542 isl_int_mul(cst1->d, cst1->d, cst2->d);
543 }
544
545 isl_upoly_cst_reduce(cst1);
546
547 isl_upoly_free(up2);
548 return up1;
549 error:
550 isl_upoly_free(up1);
551 isl_upoly_free(up2);
552 return NULL;
553 }
554
555 static __isl_give struct isl_upoly *replace_by_zero(
556 __isl_take struct isl_upoly *up)
557 {
558 struct isl_ctx *ctx;
559
560 if (!up)
561 return NULL;
562 ctx = up->ctx;
563 isl_upoly_free(up);
564 return isl_upoly_zero(ctx);
565 }
566
567 static __isl_give struct isl_upoly *replace_by_constant_term(
568 __isl_take struct isl_upoly *up)
569 {
570 struct isl_upoly_rec *rec;
571 struct isl_upoly *cst;
572
573 if (!up)
574 return NULL;
575
576 rec = isl_upoly_as_rec(up);
577 if (!rec)
578 goto error;
579 cst = isl_upoly_copy(rec->p[0]);
580 isl_upoly_free(up);
581 return cst;
582 error:
583 isl_upoly_free(up);
584 return NULL;
585 }
586
587 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
588 __isl_take struct isl_upoly *up2)
589 {
590 int i;
591 struct isl_upoly_rec *rec1, *rec2;
592
593 if (!up1 || !up2)
594 goto error;
595
596 if (isl_upoly_is_nan(up1)) {
597 isl_upoly_free(up2);
598 return up1;
599 }
600
601 if (isl_upoly_is_nan(up2)) {
602 isl_upoly_free(up1);
603 return up2;
604 }
605
606 if (isl_upoly_is_zero(up1)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610
611 if (isl_upoly_is_zero(up2)) {
612 isl_upoly_free(up2);
613 return up1;
614 }
615
616 if (up1->var < up2->var)
617 return isl_upoly_sum(up2, up1);
618
619 if (up2->var < up1->var) {
620 struct isl_upoly_rec *rec;
621 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
622 isl_upoly_free(up1);
623 return up2;
624 }
625 up1 = isl_upoly_cow(up1);
626 rec = isl_upoly_as_rec(up1);
627 if (!rec)
628 goto error;
629 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
630 if (rec->n == 1)
631 up1 = replace_by_constant_term(up1);
632 return up1;
633 }
634
635 if (isl_upoly_is_cst(up1))
636 return isl_upoly_sum_cst(up1, up2);
637
638 rec1 = isl_upoly_as_rec(up1);
639 rec2 = isl_upoly_as_rec(up2);
640 if (!rec1 || !rec2)
641 goto error;
642
643 if (rec1->n < rec2->n)
644 return isl_upoly_sum(up2, up1);
645
646 up1 = isl_upoly_cow(up1);
647 rec1 = isl_upoly_as_rec(up1);
648 if (!rec1)
649 goto error;
650
651 for (i = rec2->n - 1; i >= 0; --i) {
652 rec1->p[i] = isl_upoly_sum(rec1->p[i],
653 isl_upoly_copy(rec2->p[i]));
654 if (!rec1->p[i])
655 goto error;
656 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
657 isl_upoly_free(rec1->p[i]);
658 rec1->n--;
659 }
660 }
661
662 if (rec1->n == 0)
663 up1 = replace_by_zero(up1);
664 else if (rec1->n == 1)
665 up1 = replace_by_constant_term(up1);
666
667 isl_upoly_free(up2);
668
669 return up1;
670 error:
671 isl_upoly_free(up1);
672 isl_upoly_free(up2);
673 return NULL;
674 }
675
676 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
677 {
678 struct isl_upoly_cst *cst;
679
680 if (isl_upoly_is_zero(up))
681 return up;
682
683 up = isl_upoly_cow(up);
684 if (!up)
685 return NULL;
686
687 cst = isl_upoly_as_cst(up);
688
689 isl_int_neg(cst->n, cst->n);
690
691 return up;
692 }
693
694 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
695 {
696 int i;
697 struct isl_upoly_rec *rec;
698
699 if (!up)
700 return NULL;
701
702 if (isl_upoly_is_cst(up))
703 return isl_upoly_neg_cst(up);
704
705 up = isl_upoly_cow(up);
706 rec = isl_upoly_as_rec(up);
707 if (!rec)
708 goto error;
709
710 for (i = 0; i < rec->n; ++i) {
711 rec->p[i] = isl_upoly_neg(rec->p[i]);
712 if (!rec->p[i])
713 goto error;
714 }
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
723 __isl_take struct isl_upoly *up2)
724 {
725 struct isl_upoly_cst *cst1;
726 struct isl_upoly_cst *cst2;
727
728 up1 = isl_upoly_cow(up1);
729 if (!up1 || !up2)
730 goto error;
731
732 cst1 = isl_upoly_as_cst(up1);
733 cst2 = isl_upoly_as_cst(up2);
734
735 isl_int_mul(cst1->n, cst1->n, cst2->n);
736 isl_int_mul(cst1->d, cst1->d, cst2->d);
737
738 isl_upoly_cst_reduce(cst1);
739
740 isl_upoly_free(up2);
741 return up1;
742 error:
743 isl_upoly_free(up1);
744 isl_upoly_free(up2);
745 return NULL;
746 }
747
748 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
749 __isl_take struct isl_upoly *up2)
750 {
751 struct isl_upoly_rec *rec1;
752 struct isl_upoly_rec *rec2;
753 struct isl_upoly_rec *res;
754 int i, j;
755 int size;
756
757 rec1 = isl_upoly_as_rec(up1);
758 rec2 = isl_upoly_as_rec(up2);
759 if (!rec1 || !rec2)
760 goto error;
761 size = rec1->n + rec2->n - 1;
762 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
763 if (!res)
764 goto error;
765
766 for (i = 0; i < rec1->n; ++i) {
767 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
768 isl_upoly_copy(rec1->p[i]));
769 if (!res->p[i])
770 goto error;
771 res->n++;
772 }
773 for (; i < size; ++i) {
774 res->p[i] = isl_upoly_zero(up1->ctx);
775 if (!res->p[i])
776 goto error;
777 res->n++;
778 }
779 for (i = 0; i < rec1->n; ++i) {
780 for (j = 1; j < rec2->n; ++j) {
781 struct isl_upoly *up;
782 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
783 isl_upoly_copy(rec1->p[i]));
784 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
785 if (!res->p[i + j])
786 goto error;
787 }
788 }
789
790 isl_upoly_free(up1);
791 isl_upoly_free(up2);
792
793 return &res->up;
794 error:
795 isl_upoly_free(up1);
796 isl_upoly_free(up2);
797 isl_upoly_free(&res->up);
798 return NULL;
799 }
800
801 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
802 __isl_take struct isl_upoly *up2)
803 {
804 if (!up1 || !up2)
805 goto error;
806
807 if (isl_upoly_is_nan(up1)) {
808 isl_upoly_free(up2);
809 return up1;
810 }
811
812 if (isl_upoly_is_nan(up2)) {
813 isl_upoly_free(up1);
814 return up2;
815 }
816
817 if (isl_upoly_is_zero(up1)) {
818 isl_upoly_free(up2);
819 return up1;
820 }
821
822 if (isl_upoly_is_zero(up2)) {
823 isl_upoly_free(up1);
824 return up2;
825 }
826
827 if (isl_upoly_is_one(up1)) {
828 isl_upoly_free(up1);
829 return up2;
830 }
831
832 if (isl_upoly_is_one(up2)) {
833 isl_upoly_free(up2);
834 return up1;
835 }
836
837 if (up1->var < up2->var)
838 return isl_upoly_mul(up2, up1);
839
840 if (up2->var < up1->var) {
841 int i;
842 struct isl_upoly_rec *rec;
843 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
844 isl_ctx *ctx = up1->ctx;
845 isl_upoly_free(up1);
846 isl_upoly_free(up2);
847 return isl_upoly_nan(ctx);
848 }
849 up1 = isl_upoly_cow(up1);
850 rec = isl_upoly_as_rec(up1);
851 if (!rec)
852 goto error;
853
854 for (i = 0; i < rec->n; ++i) {
855 rec->p[i] = isl_upoly_mul(rec->p[i],
856 isl_upoly_copy(up2));
857 if (!rec->p[i])
858 goto error;
859 }
860 isl_upoly_free(up2);
861 return up1;
862 }
863
864 if (isl_upoly_is_cst(up1))
865 return isl_upoly_mul_cst(up1, up2);
866
867 return isl_upoly_mul_rec(up1, up2);
868 error:
869 isl_upoly_free(up1);
870 isl_upoly_free(up2);
871 return NULL;
872 }
873
874 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
875 unsigned n_div, __isl_take struct isl_upoly *up)
876 {
877 struct isl_qpolynomial *qp = NULL;
878 unsigned total;
879
880 if (!dim || !up)
881 goto error;
882
883 total = isl_dim_total(dim);
884
885 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
886 if (!qp)
887 goto error;
888
889 qp->ref = 1;
890 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
891 if (!qp->div)
892 goto error;
893
894 qp->dim = dim;
895 qp->upoly = up;
896
897 return qp;
898 error:
899 isl_dim_free(dim);
900 isl_upoly_free(up);
901 isl_qpolynomial_free(qp);
902 return NULL;
903 }
904
905 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
906 {
907 if (!qp)
908 return NULL;
909
910 qp->ref++;
911 return qp;
912 }
913
914 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
915 {
916 struct isl_qpolynomial *dup;
917
918 if (!qp)
919 return NULL;
920
921 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
922 isl_upoly_copy(qp->upoly));
923 if (!dup)
924 return NULL;
925 isl_mat_free(dup->div);
926 dup->div = isl_mat_copy(qp->div);
927 if (!dup->div)
928 goto error;
929
930 return dup;
931 error:
932 isl_qpolynomial_free(dup);
933 return NULL;
934 }
935
936 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
937 {
938 if (!qp)
939 return NULL;
940
941 if (qp->ref == 1)
942 return qp;
943 qp->ref--;
944 return isl_qpolynomial_dup(qp);
945 }
946
947 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
948 {
949 if (!qp)
950 return;
951
952 if (--qp->ref > 0)
953 return;
954
955 isl_dim_free(qp->dim);
956 isl_mat_free(qp->div);
957 isl_upoly_free(qp->upoly);
958
959 free(qp);
960 }
961
962 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
963 {
964 int i;
965 struct isl_upoly *up;
966 struct isl_upoly_rec *rec;
967 struct isl_upoly_cst *cst;
968
969 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
970 if (!rec)
971 return NULL;
972 for (i = 0; i < 1 + power; ++i) {
973 rec->p[i] = isl_upoly_zero(ctx);
974 if (!rec->p[i])
975 goto error;
976 rec->n++;
977 }
978 cst = isl_upoly_as_cst(rec->p[power]);
979 isl_int_set_si(cst->n, 1);
980
981 return &rec->up;
982 error:
983 isl_upoly_free(&rec->up);
984 return NULL;
985 }
986
987 /* r array maps original positions to new positions.
988 */
989 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
990 int *r)
991 {
992 int i;
993 struct isl_upoly_rec *rec;
994 struct isl_upoly *base;
995 struct isl_upoly *res;
996
997 if (isl_upoly_is_cst(up))
998 return up;
999
1000 rec = isl_upoly_as_rec(up);
1001 if (!rec)
1002 goto error;
1003
1004 isl_assert(up->ctx, rec->n >= 1, goto error);
1005
1006 base = isl_upoly_pow(up->ctx, r[up->var], 1);
1007 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1008
1009 for (i = rec->n - 2; i >= 0; --i) {
1010 res = isl_upoly_mul(res, isl_upoly_copy(base));
1011 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1012 }
1013
1014 isl_upoly_free(base);
1015 isl_upoly_free(up);
1016
1017 return res;
1018 error:
1019 isl_upoly_free(up);
1020 return NULL;
1021 }
1022
1023 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1024 {
1025 int n_row, n_col;
1026 int equal;
1027
1028 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1029 div1->n_col >= div2->n_col, return -1);
1030
1031 if (div1->n_row == div2->n_row)
1032 return isl_mat_is_equal(div1, div2);
1033
1034 n_row = div1->n_row;
1035 n_col = div1->n_col;
1036 div1->n_row = div2->n_row;
1037 div1->n_col = div2->n_col;
1038
1039 equal = isl_mat_is_equal(div1, div2);
1040
1041 div1->n_row = n_row;
1042 div1->n_col = n_col;
1043
1044 return equal;
1045 }
1046
1047 static void expand_row(__isl_keep isl_mat *dst, int d,
1048 __isl_keep isl_mat *src, int s, int *exp)
1049 {
1050 int i;
1051 unsigned c = src->n_col - src->n_row;
1052
1053 isl_seq_cpy(dst->row[d], src->row[s], c);
1054 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1055
1056 for (i = 0; i < s; ++i)
1057 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1058 }
1059
1060 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1061 {
1062 int li, lj;
1063
1064 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1065 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1066
1067 if (li != lj)
1068 return li - lj;
1069
1070 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1071 }
1072
1073 struct isl_div_sort_info {
1074 isl_mat *div;
1075 int row;
1076 };
1077
1078 static int div_sort_cmp(const void *p1, const void *p2)
1079 {
1080 const struct isl_div_sort_info *i1, *i2;
1081 i1 = (const struct isl_div_sort_info *) p1;
1082 i2 = (const struct isl_div_sort_info *) p2;
1083
1084 return cmp_row(i1->div, i1->row, i2->row);
1085 }
1086
1087 /* Sort divs and remove duplicates.
1088 */
1089 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1090 {
1091 int i;
1092 int skip;
1093 int len;
1094 struct isl_div_sort_info *array = NULL;
1095 int *pos = NULL, *at = NULL;
1096 int *reordering = NULL;
1097 unsigned div_pos;
1098
1099 if (!qp)
1100 return NULL;
1101 if (qp->div->n_row <= 1)
1102 return qp;
1103
1104 div_pos = isl_dim_total(qp->dim);
1105
1106 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1107 qp->div->n_row);
1108 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1109 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1110 len = qp->div->n_col - 2;
1111 reordering = isl_alloc_array(qp->div->ctx, int, len);
1112 if (!array || !pos || !at || !reordering)
1113 goto error;
1114
1115 for (i = 0; i < qp->div->n_row; ++i) {
1116 array[i].div = qp->div;
1117 array[i].row = i;
1118 pos[i] = i;
1119 at[i] = i;
1120 }
1121
1122 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1123 div_sort_cmp);
1124
1125 for (i = 0; i < div_pos; ++i)
1126 reordering[i] = i;
1127
1128 for (i = 0; i < qp->div->n_row; ++i) {
1129 if (pos[array[i].row] == i)
1130 continue;
1131 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1132 pos[at[i]] = pos[array[i].row];
1133 at[pos[array[i].row]] = at[i];
1134 at[i] = array[i].row;
1135 pos[array[i].row] = i;
1136 }
1137
1138 skip = 0;
1139 for (i = 0; i < len - div_pos; ++i) {
1140 if (i > 0 &&
1141 isl_seq_eq(qp->div->row[i - skip - 1],
1142 qp->div->row[i - skip], qp->div->n_col)) {
1143 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1144 qp->div = isl_mat_drop_cols(qp->div,
1145 2 + div_pos + i - skip, 1);
1146 skip++;
1147 }
1148 reordering[div_pos + array[i].row] = div_pos + i - skip;
1149 }
1150
1151 qp->upoly = reorder(qp->upoly, reordering);
1152
1153 if (!qp->upoly || !qp->div)
1154 goto error;
1155
1156 free(at);
1157 free(pos);
1158 free(array);
1159 free(reordering);
1160
1161 return qp;
1162 error:
1163 free(at);
1164 free(pos);
1165 free(array);
1166 free(reordering);
1167 isl_qpolynomial_free(qp);
1168 return NULL;
1169 }
1170
1171 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1172 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1173 {
1174 int i, j, k;
1175 isl_mat *div = NULL;
1176 unsigned d = div1->n_col - div1->n_row;
1177
1178 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1179 d + div1->n_row + div2->n_row);
1180 if (!div)
1181 return NULL;
1182
1183 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1184 int cmp;
1185
1186 expand_row(div, k, div1, i, exp1);
1187 expand_row(div, k + 1, div2, j, exp2);
1188
1189 cmp = cmp_row(div, k, k + 1);
1190 if (cmp == 0) {
1191 exp1[i++] = k;
1192 exp2[j++] = k;
1193 } else if (cmp < 0) {
1194 exp1[i++] = k;
1195 } else {
1196 exp2[j++] = k;
1197 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1198 }
1199 }
1200 for (; i < div1->n_row; ++i, ++k) {
1201 expand_row(div, k, div1, i, exp1);
1202 exp1[i] = k;
1203 }
1204 for (; j < div2->n_row; ++j, ++k) {
1205 expand_row(div, k, div2, j, exp2);
1206 exp2[j] = k;
1207 }
1208
1209 div->n_row = k;
1210 div->n_col = d + k;
1211
1212 return div;
1213 }
1214
1215 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1216 int *exp, int first)
1217 {
1218 int i;
1219 struct isl_upoly_rec *rec;
1220
1221 if (isl_upoly_is_cst(up))
1222 return up;
1223
1224 if (up->var < first)
1225 return up;
1226
1227 if (exp[up->var - first] == up->var - first)
1228 return up;
1229
1230 up = isl_upoly_cow(up);
1231 if (!up)
1232 goto error;
1233
1234 up->var = exp[up->var - first] + first;
1235
1236 rec = isl_upoly_as_rec(up);
1237 if (!rec)
1238 goto error;
1239
1240 for (i = 0; i < rec->n; ++i) {
1241 rec->p[i] = expand(rec->p[i], exp, first);
1242 if (!rec->p[i])
1243 goto error;
1244 }
1245
1246 return up;
1247 error:
1248 isl_upoly_free(up);
1249 return NULL;
1250 }
1251
1252 static __isl_give isl_qpolynomial *with_merged_divs(
1253 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1254 __isl_take isl_qpolynomial *qp2),
1255 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1256 {
1257 int *exp1 = NULL;
1258 int *exp2 = NULL;
1259 isl_mat *div = NULL;
1260
1261 qp1 = isl_qpolynomial_cow(qp1);
1262 qp2 = isl_qpolynomial_cow(qp2);
1263
1264 if (!qp1 || !qp2)
1265 goto error;
1266
1267 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1268 qp1->div->n_col >= qp2->div->n_col, goto error);
1269
1270 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1271 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1272 if (!exp1 || !exp2)
1273 goto error;
1274
1275 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1276 if (!div)
1277 goto error;
1278
1279 isl_mat_free(qp1->div);
1280 qp1->div = isl_mat_copy(div);
1281 isl_mat_free(qp2->div);
1282 qp2->div = isl_mat_copy(div);
1283
1284 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1285 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1286
1287 if (!qp1->upoly || !qp2->upoly)
1288 goto error;
1289
1290 isl_mat_free(div);
1291 free(exp1);
1292 free(exp2);
1293
1294 return fn(qp1, qp2);
1295 error:
1296 isl_mat_free(div);
1297 free(exp1);
1298 free(exp2);
1299 isl_qpolynomial_free(qp1);
1300 isl_qpolynomial_free(qp2);
1301 return NULL;
1302 }
1303
1304 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1305 __isl_take isl_qpolynomial *qp2)
1306 {
1307 qp1 = isl_qpolynomial_cow(qp1);
1308
1309 if (!qp1 || !qp2)
1310 goto error;
1311
1312 if (qp1->div->n_row < qp2->div->n_row)
1313 return isl_qpolynomial_add(qp2, qp1);
1314
1315 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1316 if (!compatible_divs(qp1->div, qp2->div))
1317 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1318
1319 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1320 if (!qp1->upoly)
1321 goto error;
1322
1323 isl_qpolynomial_free(qp2);
1324
1325 return qp1;
1326 error:
1327 isl_qpolynomial_free(qp1);
1328 isl_qpolynomial_free(qp2);
1329 return NULL;
1330 }
1331
1332 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1333 __isl_keep isl_set *dom,
1334 __isl_take isl_qpolynomial *qp1,
1335 __isl_take isl_qpolynomial *qp2)
1336 {
1337 return isl_qpolynomial_add(qp1, qp2);
1338 }
1339
1340 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1341 __isl_take isl_qpolynomial *qp2)
1342 {
1343 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1344 }
1345
1346 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1347 {
1348 qp = isl_qpolynomial_cow(qp);
1349
1350 if (!qp)
1351 return NULL;
1352
1353 qp->upoly = isl_upoly_neg(qp->upoly);
1354 if (!qp->upoly)
1355 goto error;
1356
1357 return qp;
1358 error:
1359 isl_qpolynomial_free(qp);
1360 return NULL;
1361 }
1362
1363 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1364 __isl_take isl_qpolynomial *qp2)
1365 {
1366 qp1 = isl_qpolynomial_cow(qp1);
1367
1368 if (!qp1 || !qp2)
1369 goto error;
1370
1371 if (qp1->div->n_row < qp2->div->n_row)
1372 return isl_qpolynomial_mul(qp2, qp1);
1373
1374 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1375 if (!compatible_divs(qp1->div, qp2->div))
1376 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1377
1378 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1379 if (!qp1->upoly)
1380 goto error;
1381
1382 isl_qpolynomial_free(qp2);
1383
1384 return qp1;
1385 error:
1386 isl_qpolynomial_free(qp1);
1387 isl_qpolynomial_free(qp2);
1388 return NULL;
1389 }
1390
1391 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1392 {
1393 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1394 }
1395
1396 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1397 {
1398 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1399 }
1400
1401 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1402 {
1403 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1404 }
1405
1406 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1407 {
1408 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1409 }
1410
1411 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1412 {
1413 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1414 }
1415
1416 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1417 isl_int v)
1418 {
1419 struct isl_qpolynomial *qp;
1420 struct isl_upoly_cst *cst;
1421
1422 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1423 if (!qp)
1424 return NULL;
1425
1426 cst = isl_upoly_as_cst(qp->upoly);
1427 isl_int_set(cst->n, v);
1428
1429 return qp;
1430 }
1431
1432 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1433 isl_int *n, isl_int *d)
1434 {
1435 struct isl_upoly_cst *cst;
1436
1437 if (!qp)
1438 return -1;
1439
1440 if (!isl_upoly_is_cst(qp->upoly))
1441 return 0;
1442
1443 cst = isl_upoly_as_cst(qp->upoly);
1444 if (!cst)
1445 return -1;
1446
1447 if (n)
1448 isl_int_set(*n, cst->n);
1449 if (d)
1450 isl_int_set(*d, cst->d);
1451
1452 return 1;
1453 }
1454
1455 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1456 {
1457 int is_cst;
1458 struct isl_upoly_rec *rec;
1459
1460 if (!up)
1461 return -1;
1462
1463 if (up->var < 0)
1464 return 1;
1465
1466 rec = isl_upoly_as_rec(up);
1467 if (!rec)
1468 return -1;
1469
1470 if (rec->n > 2)
1471 return 0;
1472
1473 isl_assert(up->ctx, rec->n > 1, return -1);
1474
1475 is_cst = isl_upoly_is_cst(rec->p[1]);
1476 if (is_cst < 0)
1477 return -1;
1478 if (!is_cst)
1479 return 0;
1480
1481 return isl_upoly_is_affine(rec->p[0]);
1482 }
1483
1484 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1485 {
1486 if (!qp)
1487 return -1;
1488
1489 if (qp->div->n_row > 0)
1490 return 0;
1491
1492 return isl_upoly_is_affine(qp->upoly);
1493 }
1494
1495 static void update_coeff(__isl_keep isl_vec *aff,
1496 __isl_keep struct isl_upoly_cst *cst, int pos)
1497 {
1498 isl_int gcd;
1499 isl_int f;
1500
1501 if (isl_int_is_zero(cst->n))
1502 return;
1503
1504 isl_int_init(gcd);
1505 isl_int_init(f);
1506 isl_int_gcd(gcd, cst->d, aff->el[0]);
1507 isl_int_divexact(f, cst->d, gcd);
1508 isl_int_divexact(gcd, aff->el[0], gcd);
1509 isl_seq_scale(aff->el, aff->el, f, aff->size);
1510 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1511 isl_int_clear(gcd);
1512 isl_int_clear(f);
1513 }
1514
1515 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1516 __isl_keep isl_vec *aff)
1517 {
1518 struct isl_upoly_cst *cst;
1519 struct isl_upoly_rec *rec;
1520
1521 if (!up || !aff)
1522 return -1;
1523
1524 if (up->var < 0) {
1525 struct isl_upoly_cst *cst;
1526
1527 cst = isl_upoly_as_cst(up);
1528 if (!cst)
1529 return -1;
1530 update_coeff(aff, cst, 0);
1531 return 0;
1532 }
1533
1534 rec = isl_upoly_as_rec(up);
1535 if (!rec)
1536 return -1;
1537 isl_assert(up->ctx, rec->n == 2, return -1);
1538
1539 cst = isl_upoly_as_cst(rec->p[1]);
1540 if (!cst)
1541 return -1;
1542 update_coeff(aff, cst, 1 + up->var);
1543
1544 return isl_upoly_update_affine(rec->p[0], aff);
1545 }
1546
1547 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1548 __isl_keep isl_qpolynomial *qp)
1549 {
1550 isl_vec *aff;
1551 unsigned d;
1552
1553 if (!qp)
1554 return NULL;
1555
1556 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1557 d = isl_dim_total(qp->dim);
1558 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1559 if (!aff)
1560 return NULL;
1561
1562 isl_seq_clr(aff->el + 1, 1 + d);
1563 isl_int_set_si(aff->el[0], 1);
1564
1565 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1566 goto error;
1567
1568 return aff;
1569 error:
1570 isl_vec_free(aff);
1571 return NULL;
1572 }
1573
1574 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1575 __isl_keep isl_qpolynomial *qp2)
1576 {
1577 if (!qp1 || !qp2)
1578 return -1;
1579
1580 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1581 }
1582
1583 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1584 {
1585 int i;
1586 struct isl_upoly_rec *rec;
1587
1588 if (isl_upoly_is_cst(up)) {
1589 struct isl_upoly_cst *cst;
1590 cst = isl_upoly_as_cst(up);
1591 if (!cst)
1592 return;
1593 isl_int_lcm(*d, *d, cst->d);
1594 return;
1595 }
1596
1597 rec = isl_upoly_as_rec(up);
1598 if (!rec)
1599 return;
1600
1601 for (i = 0; i < rec->n; ++i)
1602 upoly_update_den(rec->p[i], d);
1603 }
1604
1605 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1606 {
1607 isl_int_set_si(*d, 1);
1608 if (!qp)
1609 return;
1610 upoly_update_den(qp->upoly, d);
1611 }
1612
1613 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1614 int pos, int power)
1615 {
1616 struct isl_ctx *ctx;
1617
1618 if (!dim)
1619 return NULL;
1620
1621 ctx = dim->ctx;
1622
1623 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1624 }
1625
1626 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1627 enum isl_dim_type type, unsigned pos)
1628 {
1629 if (!dim)
1630 return NULL;
1631
1632 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1633 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1634
1635 if (type == isl_dim_set)
1636 pos += isl_dim_size(dim, isl_dim_param);
1637
1638 return isl_qpolynomial_pow(dim, pos, 1);
1639 error:
1640 isl_dim_free(dim);
1641 return NULL;
1642 }
1643
1644 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1645 int power)
1646 {
1647 struct isl_qpolynomial *qp = NULL;
1648 struct isl_upoly_rec *rec;
1649 struct isl_upoly_cst *cst;
1650 int i, d;
1651 int pos;
1652
1653 if (!div)
1654 return NULL;
1655
1656 d = div->line - div->bmap->div;
1657
1658 pos = isl_dim_total(div->bmap->dim) + d;
1659 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1660 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1661 div->bmap->n_div, &rec->up);
1662 if (!qp)
1663 goto error;
1664
1665 for (i = 0; i < div->bmap->n_div; ++i)
1666 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1667
1668 for (i = 0; i < 1 + power; ++i) {
1669 rec->p[i] = isl_upoly_zero(div->ctx);
1670 if (!rec->p[i])
1671 goto error;
1672 rec->n++;
1673 }
1674 cst = isl_upoly_as_cst(rec->p[power]);
1675 isl_int_set_si(cst->n, 1);
1676
1677 isl_div_free(div);
1678
1679 return qp;
1680 error:
1681 isl_qpolynomial_free(qp);
1682 isl_div_free(div);
1683 return NULL;
1684 }
1685
1686 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1687 {
1688 return isl_qpolynomial_div_pow(div, 1);
1689 }
1690
1691 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1692 const isl_int n, const isl_int d)
1693 {
1694 struct isl_qpolynomial *qp;
1695 struct isl_upoly_cst *cst;
1696
1697 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1698 if (!qp)
1699 return NULL;
1700
1701 cst = isl_upoly_as_cst(qp->upoly);
1702 isl_int_set(cst->n, n);
1703 isl_int_set(cst->d, d);
1704
1705 return qp;
1706 }
1707
1708 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1709 {
1710 struct isl_upoly_rec *rec;
1711 int i;
1712
1713 if (!up)
1714 return -1;
1715
1716 if (isl_upoly_is_cst(up))
1717 return 0;
1718
1719 if (up->var < d)
1720 active[up->var] = 1;
1721
1722 rec = isl_upoly_as_rec(up);
1723 for (i = 0; i < rec->n; ++i)
1724 if (up_set_active(rec->p[i], active, d) < 0)
1725 return -1;
1726
1727 return 0;
1728 }
1729
1730 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1731 {
1732 int i, j;
1733 int d = isl_dim_total(qp->dim);
1734
1735 if (!qp || !active)
1736 return -1;
1737
1738 for (i = 0; i < d; ++i)
1739 for (j = 0; j < qp->div->n_row; ++j) {
1740 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1741 continue;
1742 active[i] = 1;
1743 break;
1744 }
1745
1746 return up_set_active(qp->upoly, active, d);
1747 }
1748
1749 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1750 enum isl_dim_type type, unsigned first, unsigned n)
1751 {
1752 int i;
1753 int *active = NULL;
1754 int involves = 0;
1755
1756 if (!qp)
1757 return -1;
1758 if (n == 0)
1759 return 0;
1760
1761 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1762 return -1);
1763 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1764 type == isl_dim_set, return -1);
1765
1766 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1767 if (set_active(qp, active) < 0)
1768 goto error;
1769
1770 if (type == isl_dim_set)
1771 first += isl_dim_size(qp->dim, isl_dim_param);
1772 for (i = 0; i < n; ++i)
1773 if (active[first + i]) {
1774 involves = 1;
1775 break;
1776 }
1777
1778 free(active);
1779
1780 return involves;
1781 error:
1782 free(active);
1783 return -1;
1784 }
1785
1786 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1787 unsigned first, unsigned n)
1788 {
1789 int i;
1790 struct isl_upoly_rec *rec;
1791
1792 if (!up)
1793 return NULL;
1794 if (n == 0 || up->var < 0 || up->var < first)
1795 return up;
1796 if (up->var < first + n) {
1797 up = replace_by_constant_term(up);
1798 return isl_upoly_drop(up, first, n);
1799 }
1800 up = isl_upoly_cow(up);
1801 if (!up)
1802 return NULL;
1803 up->var -= n;
1804 rec = isl_upoly_as_rec(up);
1805 if (!rec)
1806 goto error;
1807
1808 for (i = 0; i < rec->n; ++i) {
1809 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1810 if (!rec->p[i])
1811 goto error;
1812 }
1813
1814 return up;
1815 error:
1816 isl_upoly_free(up);
1817 return NULL;
1818 }
1819
1820 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1821 __isl_take isl_qpolynomial *qp,
1822 enum isl_dim_type type, unsigned pos, const char *s)
1823 {
1824 qp = isl_qpolynomial_cow(qp);
1825 if (!qp)
1826 return NULL;
1827 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1828 if (!qp->dim)
1829 goto error;
1830 return qp;
1831 error:
1832 isl_qpolynomial_free(qp);
1833 return NULL;
1834 }
1835
1836 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1837 __isl_take isl_qpolynomial *qp,
1838 enum isl_dim_type type, unsigned first, unsigned n)
1839 {
1840 if (!qp)
1841 return NULL;
1842 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1843 return qp;
1844
1845 qp = isl_qpolynomial_cow(qp);
1846 if (!qp)
1847 return NULL;
1848
1849 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1850 goto error);
1851 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1852 type == isl_dim_set, goto error);
1853
1854 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1855 if (!qp->dim)
1856 goto error;
1857
1858 if (type == isl_dim_set)
1859 first += isl_dim_size(qp->dim, isl_dim_param);
1860
1861 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1862 if (!qp->div)
1863 goto error;
1864
1865 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1866 if (!qp->upoly)
1867 goto error;
1868
1869 return qp;
1870 error:
1871 isl_qpolynomial_free(qp);
1872 return NULL;
1873 }
1874
1875 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1876 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1877 {
1878 int i;
1879 struct isl_upoly_rec *rec;
1880 struct isl_upoly *base, *res;
1881
1882 if (!up)
1883 return NULL;
1884
1885 if (isl_upoly_is_cst(up))
1886 return up;
1887
1888 if (up->var < first)
1889 return up;
1890
1891 rec = isl_upoly_as_rec(up);
1892 if (!rec)
1893 goto error;
1894
1895 isl_assert(up->ctx, rec->n >= 1, goto error);
1896
1897 if (up->var >= first + n)
1898 base = isl_upoly_pow(up->ctx, up->var, 1);
1899 else
1900 base = isl_upoly_copy(subs[up->var - first]);
1901
1902 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1903 for (i = rec->n - 2; i >= 0; --i) {
1904 struct isl_upoly *t;
1905 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1906 res = isl_upoly_mul(res, isl_upoly_copy(base));
1907 res = isl_upoly_sum(res, t);
1908 }
1909
1910 isl_upoly_free(base);
1911 isl_upoly_free(up);
1912
1913 return res;
1914 error:
1915 isl_upoly_free(up);
1916 return NULL;
1917 }
1918
1919 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1920 isl_int denom, unsigned len)
1921 {
1922 int i;
1923 struct isl_upoly *up;
1924
1925 isl_assert(ctx, len >= 1, return NULL);
1926
1927 up = isl_upoly_rat_cst(ctx, f[0], denom);
1928 for (i = 0; i < len - 1; ++i) {
1929 struct isl_upoly *t;
1930 struct isl_upoly *c;
1931
1932 if (isl_int_is_zero(f[1 + i]))
1933 continue;
1934
1935 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1936 t = isl_upoly_pow(ctx, i, 1);
1937 t = isl_upoly_mul(c, t);
1938 up = isl_upoly_sum(up, t);
1939 }
1940
1941 return up;
1942 }
1943
1944 /* Remove common factor of non-constant terms and denominator.
1945 */
1946 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1947 {
1948 isl_ctx *ctx = qp->div->ctx;
1949 unsigned total = qp->div->n_col - 2;
1950
1951 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1952 isl_int_gcd(ctx->normalize_gcd,
1953 ctx->normalize_gcd, qp->div->row[div][0]);
1954 if (isl_int_is_one(ctx->normalize_gcd))
1955 return;
1956
1957 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1958 ctx->normalize_gcd, total);
1959 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1960 ctx->normalize_gcd);
1961 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1962 ctx->normalize_gcd);
1963 }
1964
1965 /* Replace the integer division identified by "div" by the polynomial "s".
1966 * The integer division is assumed not to appear in the definition
1967 * of any other integer divisions.
1968 */
1969 static __isl_give isl_qpolynomial *substitute_div(
1970 __isl_take isl_qpolynomial *qp,
1971 int div, __isl_take struct isl_upoly *s)
1972 {
1973 int i;
1974 int total;
1975 int *reordering;
1976
1977 if (!qp || !s)
1978 goto error;
1979
1980 qp = isl_qpolynomial_cow(qp);
1981 if (!qp)
1982 goto error;
1983
1984 total = isl_dim_total(qp->dim);
1985 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1986 if (!qp->upoly)
1987 goto error;
1988
1989 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1990 if (!reordering)
1991 goto error;
1992 for (i = 0; i < total + div; ++i)
1993 reordering[i] = i;
1994 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1995 reordering[i] = i - 1;
1996 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1997 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1998 qp->upoly = reorder(qp->upoly, reordering);
1999 free(reordering);
2000
2001 if (!qp->upoly || !qp->div)
2002 goto error;
2003
2004 isl_upoly_free(s);
2005 return qp;
2006 error:
2007 isl_qpolynomial_free(qp);
2008 isl_upoly_free(s);
2009 return NULL;
2010 }
2011
2012 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2013 * divisions because d is equal to 1 by their definition, i.e., e.
2014 */
2015 static __isl_give isl_qpolynomial *substitute_non_divs(
2016 __isl_take isl_qpolynomial *qp)
2017 {
2018 int i, j;
2019 int total;
2020 struct isl_upoly *s;
2021
2022 if (!qp)
2023 return NULL;
2024
2025 total = isl_dim_total(qp->dim);
2026 for (i = 0; qp && i < qp->div->n_row; ++i) {
2027 if (!isl_int_is_one(qp->div->row[i][0]))
2028 continue;
2029 for (j = i + 1; j < qp->div->n_row; ++j) {
2030 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2031 continue;
2032 isl_seq_combine(qp->div->row[j] + 1,
2033 qp->div->ctx->one, qp->div->row[j] + 1,
2034 qp->div->row[j][2 + total + i],
2035 qp->div->row[i] + 1, 1 + total + i);
2036 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2037 normalize_div(qp, j);
2038 }
2039 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2040 qp->div->row[i][0], qp->div->n_col - 1);
2041 qp = substitute_div(qp, i, s);
2042 --i;
2043 }
2044
2045 return qp;
2046 }
2047
2048 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2049 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2050 {
2051 int i, j, k;
2052 isl_int denom;
2053 unsigned total;
2054 unsigned n_div;
2055 struct isl_upoly *up;
2056
2057 if (!eq)
2058 goto error;
2059 if (eq->n_eq == 0) {
2060 isl_basic_set_free(eq);
2061 return qp;
2062 }
2063
2064 qp = isl_qpolynomial_cow(qp);
2065 if (!qp)
2066 goto error;
2067 qp->div = isl_mat_cow(qp->div);
2068 if (!qp->div)
2069 goto error;
2070
2071 total = 1 + isl_dim_total(eq->dim);
2072 n_div = eq->n_div;
2073 isl_int_init(denom);
2074 for (i = 0; i < eq->n_eq; ++i) {
2075 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2076 if (j < 0 || j == 0 || j >= total)
2077 continue;
2078
2079 for (k = 0; k < qp->div->n_row; ++k) {
2080 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2081 continue;
2082 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2083 &qp->div->row[k][0]);
2084 normalize_div(qp, k);
2085 }
2086
2087 if (isl_int_is_pos(eq->eq[i][j]))
2088 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2089 isl_int_abs(denom, eq->eq[i][j]);
2090 isl_int_set_si(eq->eq[i][j], 0);
2091
2092 up = isl_upoly_from_affine(qp->dim->ctx,
2093 eq->eq[i], denom, total);
2094 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2095 isl_upoly_free(up);
2096 }
2097 isl_int_clear(denom);
2098
2099 if (!qp->upoly)
2100 goto error;
2101
2102 isl_basic_set_free(eq);
2103
2104 qp = substitute_non_divs(qp);
2105 qp = sort_divs(qp);
2106
2107 return qp;
2108 error:
2109 isl_basic_set_free(eq);
2110 isl_qpolynomial_free(qp);
2111 return NULL;
2112 }
2113
2114 static __isl_give isl_basic_set *add_div_constraints(
2115 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2116 {
2117 int i;
2118 unsigned total;
2119
2120 if (!bset || !div)
2121 goto error;
2122
2123 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2124 if (!bset)
2125 goto error;
2126 total = isl_basic_set_total_dim(bset);
2127 for (i = 0; i < div->n_row; ++i)
2128 if (isl_basic_set_add_div_constraints_var(bset,
2129 total - div->n_row + i, div->row[i]) < 0)
2130 goto error;
2131
2132 isl_mat_free(div);
2133 return bset;
2134 error:
2135 isl_mat_free(div);
2136 isl_basic_set_free(bset);
2137 return NULL;
2138 }
2139
2140 /* Look for equalities among the variables shared by context and qp
2141 * and the integer divisions of qp, if any.
2142 * The equalities are then used to eliminate variables and/or integer
2143 * divisions from qp.
2144 */
2145 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2146 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2147 {
2148 isl_basic_set *aff;
2149
2150 if (!qp)
2151 goto error;
2152 if (qp->div->n_row > 0) {
2153 isl_basic_set *bset;
2154 context = isl_set_add_dims(context, isl_dim_set,
2155 qp->div->n_row);
2156 bset = isl_basic_set_universe(isl_set_get_dim(context));
2157 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2158 context = isl_set_intersect(context,
2159 isl_set_from_basic_set(bset));
2160 }
2161
2162 aff = isl_set_affine_hull(context);
2163 return isl_qpolynomial_substitute_equalities(qp, aff);
2164 error:
2165 isl_qpolynomial_free(qp);
2166 isl_set_free(context);
2167 return NULL;
2168 }
2169
2170 #undef PW
2171 #define PW isl_pw_qpolynomial
2172 #undef EL
2173 #define EL isl_qpolynomial
2174 #undef IS_ZERO
2175 #define IS_ZERO is_zero
2176 #undef FIELD
2177 #define FIELD qp
2178
2179 #include <isl_pw_templ.c>
2180
2181 #undef UNION
2182 #define UNION isl_union_pw_qpolynomial
2183 #undef PART
2184 #define PART isl_pw_qpolynomial
2185 #undef PARTS
2186 #define PARTS pw_qpolynomial
2187
2188 #include <isl_union_templ.c>
2189
2190 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2191 {
2192 if (!pwqp)
2193 return -1;
2194
2195 if (pwqp->n != -1)
2196 return 0;
2197
2198 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2199 return 0;
2200
2201 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2202 }
2203
2204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2205 __isl_take isl_pw_qpolynomial *pwqp1,
2206 __isl_take isl_pw_qpolynomial *pwqp2)
2207 {
2208 int i, j, n;
2209 struct isl_pw_qpolynomial *res;
2210 isl_set *set;
2211
2212 if (!pwqp1 || !pwqp2)
2213 goto error;
2214
2215 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2216 goto error);
2217
2218 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2219 isl_pw_qpolynomial_free(pwqp2);
2220 return pwqp1;
2221 }
2222
2223 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2224 isl_pw_qpolynomial_free(pwqp1);
2225 return pwqp2;
2226 }
2227
2228 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2229 isl_pw_qpolynomial_free(pwqp1);
2230 return pwqp2;
2231 }
2232
2233 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2234 isl_pw_qpolynomial_free(pwqp2);
2235 return pwqp1;
2236 }
2237
2238 n = pwqp1->n * pwqp2->n;
2239 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2240
2241 for (i = 0; i < pwqp1->n; ++i) {
2242 for (j = 0; j < pwqp2->n; ++j) {
2243 struct isl_set *common;
2244 struct isl_qpolynomial *prod;
2245 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2246 isl_set_copy(pwqp2->p[j].set));
2247 if (isl_set_fast_is_empty(common)) {
2248 isl_set_free(common);
2249 continue;
2250 }
2251
2252 prod = isl_qpolynomial_mul(
2253 isl_qpolynomial_copy(pwqp1->p[i].qp),
2254 isl_qpolynomial_copy(pwqp2->p[j].qp));
2255
2256 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2257 }
2258 }
2259
2260 isl_pw_qpolynomial_free(pwqp1);
2261 isl_pw_qpolynomial_free(pwqp2);
2262
2263 return res;
2264 error:
2265 isl_pw_qpolynomial_free(pwqp1);
2266 isl_pw_qpolynomial_free(pwqp2);
2267 return NULL;
2268 }
2269
2270 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2271 __isl_take isl_pw_qpolynomial *pwqp)
2272 {
2273 int i;
2274
2275 if (!pwqp)
2276 return NULL;
2277
2278 if (isl_pw_qpolynomial_is_zero(pwqp))
2279 return pwqp;
2280
2281 pwqp = isl_pw_qpolynomial_cow(pwqp);
2282 if (!pwqp)
2283 return NULL;
2284
2285 for (i = 0; i < pwqp->n; ++i) {
2286 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2287 if (!pwqp->p[i].qp)
2288 goto error;
2289 }
2290
2291 return pwqp;
2292 error:
2293 isl_pw_qpolynomial_free(pwqp);
2294 return NULL;
2295 }
2296
2297 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2298 __isl_take isl_pw_qpolynomial *pwqp1,
2299 __isl_take isl_pw_qpolynomial *pwqp2)
2300 {
2301 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2302 }
2303
2304 __isl_give struct isl_upoly *isl_upoly_eval(
2305 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2306 {
2307 int i;
2308 struct isl_upoly_rec *rec;
2309 struct isl_upoly *res;
2310 struct isl_upoly *base;
2311
2312 if (isl_upoly_is_cst(up)) {
2313 isl_vec_free(vec);
2314 return up;
2315 }
2316
2317 rec = isl_upoly_as_rec(up);
2318 if (!rec)
2319 goto error;
2320
2321 isl_assert(up->ctx, rec->n >= 1, goto error);
2322
2323 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2324
2325 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2326 isl_vec_copy(vec));
2327
2328 for (i = rec->n - 2; i >= 0; --i) {
2329 res = isl_upoly_mul(res, isl_upoly_copy(base));
2330 res = isl_upoly_sum(res,
2331 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2332 isl_vec_copy(vec)));
2333 }
2334
2335 isl_upoly_free(base);
2336 isl_upoly_free(up);
2337 isl_vec_free(vec);
2338 return res;
2339 error:
2340 isl_upoly_free(up);
2341 isl_vec_free(vec);
2342 return NULL;
2343 }
2344
2345 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2346 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2347 {
2348 isl_vec *ext;
2349 struct isl_upoly *up;
2350 isl_dim *dim;
2351
2352 if (!qp || !pnt)
2353 goto error;
2354 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2355
2356 if (qp->div->n_row == 0)
2357 ext = isl_vec_copy(pnt->vec);
2358 else {
2359 int i;
2360 unsigned dim = isl_dim_total(qp->dim);
2361 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2362 if (!ext)
2363 goto error;
2364
2365 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2366 for (i = 0; i < qp->div->n_row; ++i) {
2367 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2368 1 + dim + i, &ext->el[1+dim+i]);
2369 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2370 qp->div->row[i][0]);
2371 }
2372 }
2373
2374 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2375 if (!up)
2376 goto error;
2377
2378 dim = isl_dim_copy(qp->dim);
2379 isl_qpolynomial_free(qp);
2380 isl_point_free(pnt);
2381
2382 return isl_qpolynomial_alloc(dim, 0, up);
2383 error:
2384 isl_qpolynomial_free(qp);
2385 isl_point_free(pnt);
2386 return NULL;
2387 }
2388
2389 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2390 __isl_keep struct isl_upoly_cst *cst2)
2391 {
2392 int cmp;
2393 isl_int t;
2394 isl_int_init(t);
2395 isl_int_mul(t, cst1->n, cst2->d);
2396 isl_int_submul(t, cst2->n, cst1->d);
2397 cmp = isl_int_sgn(t);
2398 isl_int_clear(t);
2399 return cmp;
2400 }
2401
2402 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2403 __isl_keep isl_qpolynomial *qp2)
2404 {
2405 struct isl_upoly_cst *cst1, *cst2;
2406
2407 if (!qp1 || !qp2)
2408 return -1;
2409 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2410 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2411 if (isl_qpolynomial_is_nan(qp1))
2412 return -1;
2413 if (isl_qpolynomial_is_nan(qp2))
2414 return -1;
2415 cst1 = isl_upoly_as_cst(qp1->upoly);
2416 cst2 = isl_upoly_as_cst(qp2->upoly);
2417
2418 return isl_upoly_cmp(cst1, cst2) <= 0;
2419 }
2420
2421 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2422 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2423 {
2424 struct isl_upoly_cst *cst1, *cst2;
2425 int cmp;
2426
2427 if (!qp1 || !qp2)
2428 goto error;
2429 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2430 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2431 cst1 = isl_upoly_as_cst(qp1->upoly);
2432 cst2 = isl_upoly_as_cst(qp2->upoly);
2433 cmp = isl_upoly_cmp(cst1, cst2);
2434
2435 if (cmp <= 0) {
2436 isl_qpolynomial_free(qp2);
2437 } else {
2438 isl_qpolynomial_free(qp1);
2439 qp1 = qp2;
2440 }
2441 return qp1;
2442 error:
2443 isl_qpolynomial_free(qp1);
2444 isl_qpolynomial_free(qp2);
2445 return NULL;
2446 }
2447
2448 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2449 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2450 {
2451 struct isl_upoly_cst *cst1, *cst2;
2452 int cmp;
2453
2454 if (!qp1 || !qp2)
2455 goto error;
2456 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2457 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2458 cst1 = isl_upoly_as_cst(qp1->upoly);
2459 cst2 = isl_upoly_as_cst(qp2->upoly);
2460 cmp = isl_upoly_cmp(cst1, cst2);
2461
2462 if (cmp >= 0) {
2463 isl_qpolynomial_free(qp2);
2464 } else {
2465 isl_qpolynomial_free(qp1);
2466 qp1 = qp2;
2467 }
2468 return qp1;
2469 error:
2470 isl_qpolynomial_free(qp1);
2471 isl_qpolynomial_free(qp2);
2472 return NULL;
2473 }
2474
2475 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2476 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2477 unsigned first, unsigned n)
2478 {
2479 unsigned total;
2480 unsigned g_pos;
2481 int *exp;
2482
2483 if (n == 0)
2484 return qp;
2485
2486 qp = isl_qpolynomial_cow(qp);
2487 if (!qp)
2488 return NULL;
2489
2490 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2491 goto error);
2492
2493 g_pos = pos(qp->dim, type) + first;
2494
2495 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2496 if (!qp->div)
2497 goto error;
2498
2499 total = qp->div->n_col - 2;
2500 if (total > g_pos) {
2501 int i;
2502 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2503 if (!exp)
2504 goto error;
2505 for (i = 0; i < total - g_pos; ++i)
2506 exp[i] = i + n;
2507 qp->upoly = expand(qp->upoly, exp, g_pos);
2508 free(exp);
2509 if (!qp->upoly)
2510 goto error;
2511 }
2512
2513 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2514 if (!qp->dim)
2515 goto error;
2516
2517 return qp;
2518 error:
2519 isl_qpolynomial_free(qp);
2520 return NULL;
2521 }
2522
2523 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2524 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2525 {
2526 unsigned pos;
2527
2528 pos = isl_qpolynomial_dim(qp, type);
2529
2530 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2531 }
2532
2533 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2534 __isl_take isl_pw_qpolynomial *pwqp,
2535 enum isl_dim_type type, unsigned n)
2536 {
2537 unsigned pos;
2538
2539 pos = isl_pw_qpolynomial_dim(pwqp, type);
2540
2541 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2542 }
2543
2544 static int *reordering_move(isl_ctx *ctx,
2545 unsigned len, unsigned dst, unsigned src, unsigned n)
2546 {
2547 int i;
2548 int *reordering;
2549
2550 reordering = isl_alloc_array(ctx, int, len);
2551 if (!reordering)
2552 return NULL;
2553
2554 if (dst <= src) {
2555 for (i = 0; i < dst; ++i)
2556 reordering[i] = i;
2557 for (i = 0; i < n; ++i)
2558 reordering[src + i] = dst + i;
2559 for (i = 0; i < src - dst; ++i)
2560 reordering[dst + i] = dst + n + i;
2561 for (i = 0; i < len - src - n; ++i)
2562 reordering[src + n + i] = src + n + i;
2563 } else {
2564 for (i = 0; i < src; ++i)
2565 reordering[i] = i;
2566 for (i = 0; i < n; ++i)
2567 reordering[src + i] = dst + i;
2568 for (i = 0; i < dst - src; ++i)
2569 reordering[src + n + i] = src + i;
2570 for (i = 0; i < len - dst - n; ++i)
2571 reordering[dst + n + i] = dst + n + i;
2572 }
2573
2574 return reordering;
2575 }
2576
2577 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2578 __isl_take isl_qpolynomial *qp,
2579 enum isl_dim_type dst_type, unsigned dst_pos,
2580 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2581 {
2582 unsigned g_dst_pos;
2583 unsigned g_src_pos;
2584 int *reordering;
2585
2586 qp = isl_qpolynomial_cow(qp);
2587 if (!qp)
2588 return NULL;
2589
2590 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2591 goto error);
2592
2593 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2594 g_src_pos = pos(qp->dim, src_type) + src_pos;
2595 if (dst_type > src_type)
2596 g_dst_pos -= n;
2597
2598 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2599 if (!qp->div)
2600 goto error;
2601 qp = sort_divs(qp);
2602 if (!qp)
2603 goto error;
2604
2605 reordering = reordering_move(qp->dim->ctx,
2606 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2607 if (!reordering)
2608 goto error;
2609
2610 qp->upoly = reorder(qp->upoly, reordering);
2611 free(reordering);
2612 if (!qp->upoly)
2613 goto error;
2614
2615 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2616 if (!qp->dim)
2617 goto error;
2618
2619 return qp;
2620 error:
2621 isl_qpolynomial_free(qp);
2622 return NULL;
2623 }
2624
2625 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2626 isl_int *f, isl_int denom)
2627 {
2628 struct isl_upoly *up;
2629
2630 if (!dim)
2631 return NULL;
2632
2633 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2634
2635 return isl_qpolynomial_alloc(dim, 0, up);
2636 }
2637
2638 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2639 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2640 {
2641 isl_int denom;
2642 isl_dim *dim;
2643 struct isl_upoly *up;
2644 isl_qpolynomial *qp;
2645 int sgn;
2646
2647 if (!c)
2648 return NULL;
2649
2650 isl_int_init(denom);
2651
2652 isl_constraint_get_coefficient(c, type, pos, &denom);
2653 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2654 sgn = isl_int_sgn(denom);
2655 isl_int_abs(denom, denom);
2656 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2657 1 + isl_constraint_dim(c, isl_dim_all));
2658 if (sgn < 0)
2659 isl_int_neg(denom, denom);
2660 isl_constraint_set_coefficient(c, type, pos, denom);
2661
2662 dim = isl_dim_copy(c->bmap->dim);
2663
2664 isl_int_clear(denom);
2665 isl_constraint_free(c);
2666
2667 qp = isl_qpolynomial_alloc(dim, 0, up);
2668 if (sgn > 0)
2669 qp = isl_qpolynomial_neg(qp);
2670 return qp;
2671 }
2672
2673 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2674 * in "qp" by subs[i].
2675 */
2676 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2677 __isl_take isl_qpolynomial *qp,
2678 enum isl_dim_type type, unsigned first, unsigned n,
2679 __isl_keep isl_qpolynomial **subs)
2680 {
2681 int i;
2682 struct isl_upoly **ups;
2683
2684 if (n == 0)
2685 return qp;
2686
2687 qp = isl_qpolynomial_cow(qp);
2688 if (!qp)
2689 return NULL;
2690 for (i = 0; i < n; ++i)
2691 if (!subs[i])
2692 goto error;
2693
2694 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2695 goto error);
2696
2697 for (i = 0; i < n; ++i)
2698 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2699 goto error);
2700
2701 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2702 for (i = 0; i < n; ++i)
2703 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2704
2705 first += pos(qp->dim, type);
2706
2707 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2708 if (!ups)
2709 goto error;
2710 for (i = 0; i < n; ++i)
2711 ups[i] = subs[i]->upoly;
2712
2713 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2714
2715 free(ups);
2716
2717 if (!qp->upoly)
2718 goto error;
2719
2720 return qp;
2721 error:
2722 isl_qpolynomial_free(qp);
2723 return NULL;
2724 }
2725
2726 /* Extend "bset" with extra set dimensions for each integer division
2727 * in "qp" and then call "fn" with the extended bset and the polynomial
2728 * that results from replacing each of the integer divisions by the
2729 * corresponding extra set dimension.
2730 */
2731 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2732 __isl_keep isl_basic_set *bset,
2733 int (*fn)(__isl_take isl_basic_set *bset,
2734 __isl_take isl_qpolynomial *poly, void *user), void *user)
2735 {
2736 isl_dim *dim;
2737 isl_mat *div;
2738 isl_qpolynomial *poly;
2739
2740 if (!qp || !bset)
2741 goto error;
2742 if (qp->div->n_row == 0)
2743 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2744 user);
2745
2746 div = isl_mat_copy(qp->div);
2747 dim = isl_dim_copy(qp->dim);
2748 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2749 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2750 bset = isl_basic_set_copy(bset);
2751 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2752 bset = add_div_constraints(bset, div);
2753
2754 return fn(bset, poly, user);
2755 error:
2756 return -1;
2757 }
2758
2759 /* Return total degree in variables first (inclusive) up to last (exclusive).
2760 */
2761 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2762 {
2763 int deg = -1;
2764 int i;
2765 struct isl_upoly_rec *rec;
2766
2767 if (!up)
2768 return -2;
2769 if (isl_upoly_is_zero(up))
2770 return -1;
2771 if (isl_upoly_is_cst(up) || up->var < first)
2772 return 0;
2773
2774 rec = isl_upoly_as_rec(up);
2775 if (!rec)
2776 return -2;
2777
2778 for (i = 0; i < rec->n; ++i) {
2779 int d;
2780
2781 if (isl_upoly_is_zero(rec->p[i]))
2782 continue;
2783 d = isl_upoly_degree(rec->p[i], first, last);
2784 if (up->var < last)
2785 d += i;
2786 if (d > deg)
2787 deg = d;
2788 }
2789
2790 return deg;
2791 }
2792
2793 /* Return total degree in set variables.
2794 */
2795 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2796 {
2797 unsigned ovar;
2798 unsigned nvar;
2799
2800 if (!poly)
2801 return -2;
2802
2803 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2804 nvar = isl_dim_size(poly->dim, isl_dim_set);
2805 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2806 }
2807
2808 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2809 unsigned pos, int deg)
2810 {
2811 int i;
2812 struct isl_upoly_rec *rec;
2813
2814 if (!up)
2815 return NULL;
2816
2817 if (isl_upoly_is_cst(up) || up->var < pos) {
2818 if (deg == 0)
2819 return isl_upoly_copy(up);
2820 else
2821 return isl_upoly_zero(up->ctx);
2822 }
2823
2824 rec = isl_upoly_as_rec(up);
2825 if (!rec)
2826 return NULL;
2827
2828 if (up->var == pos) {
2829 if (deg < rec->n)
2830 return isl_upoly_copy(rec->p[deg]);
2831 else
2832 return isl_upoly_zero(up->ctx);
2833 }
2834
2835 up = isl_upoly_copy(up);
2836 up = isl_upoly_cow(up);
2837 rec = isl_upoly_as_rec(up);
2838 if (!rec)
2839 goto error;
2840
2841 for (i = 0; i < rec->n; ++i) {
2842 struct isl_upoly *t;
2843 t = isl_upoly_coeff(rec->p[i], pos, deg);
2844 if (!t)
2845 goto error;
2846 isl_upoly_free(rec->p[i]);
2847 rec->p[i] = t;
2848 }
2849
2850 return up;
2851 error:
2852 isl_upoly_free(up);
2853 return NULL;
2854 }
2855
2856 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2857 */
2858 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2859 __isl_keep isl_qpolynomial *qp,
2860 enum isl_dim_type type, unsigned t_pos, int deg)
2861 {
2862 unsigned g_pos;
2863 struct isl_upoly *up;
2864 isl_qpolynomial *c;
2865
2866 if (!qp)
2867 return NULL;
2868
2869 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2870 return NULL);
2871
2872 g_pos = pos(qp->dim, type) + t_pos;
2873 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2874
2875 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2876 if (!c)
2877 return NULL;
2878 isl_mat_free(c->div);
2879 c->div = isl_mat_copy(qp->div);
2880 if (!c->div)
2881 goto error;
2882 return c;
2883 error:
2884 isl_qpolynomial_free(c);
2885 return NULL;
2886 }
2887
2888 /* Homogenize the polynomial in the variables first (inclusive) up to
2889 * last (exclusive) by inserting powers of variable first.
2890 * Variable first is assumed not to appear in the input.
2891 */
2892 __isl_give struct isl_upoly *isl_upoly_homogenize(
2893 __isl_take struct isl_upoly *up, int deg, int target,
2894 int first, int last)
2895 {
2896 int i;
2897 struct isl_upoly_rec *rec;
2898
2899 if (!up)
2900 return NULL;
2901 if (isl_upoly_is_zero(up))
2902 return up;
2903 if (deg == target)
2904 return up;
2905 if (isl_upoly_is_cst(up) || up->var < first) {
2906 struct isl_upoly *hom;
2907
2908 hom = isl_upoly_pow(up->ctx, first, target - deg);
2909 if (!hom)
2910 goto error;
2911 rec = isl_upoly_as_rec(hom);
2912 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2913
2914 return hom;
2915 }
2916
2917 up = isl_upoly_cow(up);
2918 rec = isl_upoly_as_rec(up);
2919 if (!rec)
2920 goto error;
2921
2922 for (i = 0; i < rec->n; ++i) {
2923 if (isl_upoly_is_zero(rec->p[i]))
2924 continue;
2925 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2926 up->var < last ? deg + i : i, target,
2927 first, last);
2928 if (!rec->p[i])
2929 goto error;
2930 }
2931
2932 return up;
2933 error:
2934 isl_upoly_free(up);
2935 return NULL;
2936 }
2937
2938 /* Homogenize the polynomial in the set variables by introducing
2939 * powers of an extra set variable at position 0.
2940 */
2941 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2942 __isl_take isl_qpolynomial *poly)
2943 {
2944 unsigned ovar;
2945 unsigned nvar;
2946 int deg = isl_qpolynomial_degree(poly);
2947
2948 if (deg < -1)
2949 goto error;
2950
2951 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2952 poly = isl_qpolynomial_cow(poly);
2953 if (!poly)
2954 goto error;
2955
2956 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2957 nvar = isl_dim_size(poly->dim, isl_dim_set);
2958 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2959 ovar, ovar + nvar);
2960 if (!poly->upoly)
2961 goto error;
2962
2963 return poly;
2964 error:
2965 isl_qpolynomial_free(poly);
2966 return NULL;
2967 }
2968
2969 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2970 __isl_take isl_mat *div)
2971 {
2972 isl_term *term;
2973 int n;
2974
2975 if (!dim || !div)
2976 goto error;
2977
2978 n = isl_dim_total(dim) + div->n_row;
2979
2980 term = isl_calloc(dim->ctx, struct isl_term,
2981 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2982 if (!term)
2983 goto error;
2984
2985 term->ref = 1;
2986 term->dim = dim;
2987 term->div = div;
2988 isl_int_init(term->n);
2989 isl_int_init(term->d);
2990
2991 return term;
2992 error:
2993 isl_dim_free(dim);
2994 isl_mat_free(div);
2995 return NULL;
2996 }
2997
2998 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2999 {
3000 if (!term)
3001 return NULL;
3002
3003 term->ref++;
3004 return term;
3005 }
3006
3007 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3008 {
3009 int i;
3010 isl_term *dup;
3011 unsigned total;
3012
3013 if (term)
3014 return NULL;
3015
3016 total = isl_dim_total(term->dim) + term->div->n_row;
3017
3018 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3019 if (!dup)
3020 return NULL;
3021
3022 isl_int_set(dup->n, term->n);
3023 isl_int_set(dup->d, term->d);
3024
3025 for (i = 0; i < total; ++i)
3026 dup->pow[i] = term->pow[i];
3027
3028 return dup;
3029 }
3030
3031 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3032 {
3033 if (!term)
3034 return NULL;
3035
3036 if (term->ref == 1)
3037 return term;
3038 term->ref--;
3039 return isl_term_dup(term);
3040 }
3041
3042 void isl_term_free(__isl_take isl_term *term)
3043 {
3044 if (!term)
3045 return;
3046
3047 if (--term->ref > 0)
3048 return;
3049
3050 isl_dim_free(term->dim);
3051 isl_mat_free(term->div);
3052 isl_int_clear(term->n);
3053 isl_int_clear(term->d);
3054 free(term);
3055 }
3056
3057 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3058 {
3059 if (!term)
3060 return 0;
3061
3062 switch (type) {
3063 case isl_dim_param:
3064 case isl_dim_in:
3065 case isl_dim_out: return isl_dim_size(term->dim, type);
3066 case isl_dim_div: return term->div->n_row;
3067 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3068 default: return 0;
3069 }
3070 }
3071
3072 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3073 {
3074 return term ? term->dim->ctx : NULL;
3075 }
3076
3077 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3078 {
3079 if (!term)
3080 return;
3081 isl_int_set(*n, term->n);
3082 }
3083
3084 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3085 {
3086 if (!term)
3087 return;
3088 isl_int_set(*d, term->d);
3089 }
3090
3091 int isl_term_get_exp(__isl_keep isl_term *term,
3092 enum isl_dim_type type, unsigned pos)
3093 {
3094 if (!term)
3095 return -1;
3096
3097 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3098
3099 if (type >= isl_dim_set)
3100 pos += isl_dim_size(term->dim, isl_dim_param);
3101 if (type >= isl_dim_div)
3102 pos += isl_dim_size(term->dim, isl_dim_set);
3103
3104 return term->pow[pos];
3105 }
3106
3107 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3108 {
3109 isl_basic_map *bmap;
3110 unsigned total;
3111 int k;
3112
3113 if (!term)
3114 return NULL;
3115
3116 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3117 return NULL);
3118
3119 total = term->div->n_col - term->div->n_row - 2;
3120 /* No nested divs for now */
3121 isl_assert(term->dim->ctx,
3122 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3123 term->div->n_row) == -1,
3124 return NULL);
3125
3126 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3127 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3128 goto error;
3129
3130 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3131
3132 return isl_basic_map_div(bmap, k);
3133 error:
3134 isl_basic_map_free(bmap);
3135 return NULL;
3136 }
3137
3138 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3139 int (*fn)(__isl_take isl_term *term, void *user),
3140 __isl_take isl_term *term, void *user)
3141 {
3142 int i;
3143 struct isl_upoly_rec *rec;
3144
3145 if (!up || !term)
3146 goto error;
3147
3148 if (isl_upoly_is_zero(up))
3149 return term;
3150
3151 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3152 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3153 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3154
3155 if (isl_upoly_is_cst(up)) {
3156 struct isl_upoly_cst *cst;
3157 cst = isl_upoly_as_cst(up);
3158 if (!cst)
3159 goto error;
3160 term = isl_term_cow(term);
3161 if (!term)
3162 goto error;
3163 isl_int_set(term->n, cst->n);
3164 isl_int_set(term->d, cst->d);
3165 if (fn(isl_term_copy(term), user) < 0)
3166 goto error;
3167 return term;
3168 }
3169
3170 rec = isl_upoly_as_rec(up);
3171 if (!rec)
3172 goto error;
3173
3174 for (i = 0; i < rec->n; ++i) {
3175 term = isl_term_cow(term);
3176 if (!term)
3177 goto error;
3178 term->pow[up->var] = i;
3179 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3180 if (!term)
3181 goto error;
3182 }
3183 term->pow[up->var] = 0;
3184
3185 return term;
3186 error:
3187 isl_term_free(term);
3188 return NULL;
3189 }
3190
3191 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3192 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3193 {
3194 isl_term *term;
3195
3196 if (!qp)
3197 return -1;
3198
3199 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3200 if (!term)
3201 return -1;
3202
3203 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3204
3205 isl_term_free(term);
3206
3207 return term ? 0 : -1;
3208 }
3209
3210 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3211 {
3212 struct isl_upoly *up;
3213 isl_qpolynomial *qp;
3214 int i, n;
3215
3216 if (!term)
3217 return NULL;
3218
3219 n = isl_dim_total(term->dim) + term->div->n_row;
3220
3221 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3222 for (i = 0; i < n; ++i) {
3223 if (!term->pow[i])
3224 continue;
3225 up = isl_upoly_mul(up,
3226 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3227 }
3228
3229 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3230 if (!qp)
3231 goto error;
3232 isl_mat_free(qp->div);
3233 qp->div = isl_mat_copy(term->div);
3234 if (!qp->div)
3235 goto error;
3236
3237 isl_term_free(term);
3238 return qp;
3239 error:
3240 isl_qpolynomial_free(qp);
3241 isl_term_free(term);
3242 return NULL;
3243 }
3244
3245 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3246 __isl_take isl_dim *dim)
3247 {
3248 int i;
3249 int extra;
3250 unsigned total;
3251
3252 if (!qp || !dim)
3253 goto error;
3254
3255 if (isl_dim_equal(qp->dim, dim)) {
3256 isl_dim_free(dim);
3257 return qp;
3258 }
3259
3260 qp = isl_qpolynomial_cow(qp);
3261 if (!qp)
3262 goto error;
3263
3264 extra = isl_dim_size(dim, isl_dim_set) -
3265 isl_dim_size(qp->dim, isl_dim_set);
3266 total = isl_dim_total(qp->dim);
3267 if (qp->div->n_row) {
3268 int *exp;
3269
3270 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3271 if (!exp)
3272 goto error;
3273 for (i = 0; i < qp->div->n_row; ++i)
3274 exp[i] = extra + i;
3275 qp->upoly = expand(qp->upoly, exp, total);
3276 free(exp);
3277 if (!qp->upoly)
3278 goto error;
3279 }
3280 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3281 if (!qp->div)
3282 goto error;
3283 for (i = 0; i < qp->div->n_row; ++i)
3284 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3285
3286 isl_dim_free(qp->dim);
3287 qp->dim = dim;
3288
3289 return qp;
3290 error:
3291 isl_dim_free(dim);
3292 isl_qpolynomial_free(qp);
3293 return NULL;
3294 }
3295
3296 /* For each parameter or variable that does not appear in qp,
3297 * first eliminate the variable from all constraints and then set it to zero.
3298 */
3299 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3300 __isl_keep isl_qpolynomial *qp)
3301 {
3302 int *active = NULL;
3303 int i;
3304 int d;
3305 unsigned nparam;
3306 unsigned nvar;
3307
3308 if (!set || !qp)
3309 goto error;
3310
3311 d = isl_dim_total(set->dim);
3312 active = isl_calloc_array(set->ctx, int, d);
3313 if (set_active(qp, active) < 0)
3314 goto error;
3315
3316 for (i = 0; i < d; ++i)
3317 if (!active[i])
3318 break;
3319
3320 if (i == d) {
3321 free(active);
3322 return set;
3323 }
3324
3325 nparam = isl_dim_size(set->dim, isl_dim_param);
3326 nvar = isl_dim_size(set->dim, isl_dim_set);
3327 for (i = 0; i < nparam; ++i) {
3328 if (active[i])
3329 continue;
3330 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3331 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3332 }
3333 for (i = 0; i < nvar; ++i) {
3334 if (active[nparam + i])
3335 continue;
3336 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3337 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3338 }
3339
3340 free(active);
3341
3342 return set;
3343 error:
3344 free(active);
3345 isl_set_free(set);
3346 return NULL;
3347 }
3348
3349 struct isl_opt_data {
3350 isl_qpolynomial *qp;
3351 int first;
3352 isl_qpolynomial *opt;
3353 int max;
3354 };
3355
3356 static int opt_fn(__isl_take isl_point *pnt, void *user)
3357 {
3358 struct isl_opt_data *data = (struct isl_opt_data *)user;
3359 isl_qpolynomial *val;
3360
3361 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3362 if (data->first) {
3363 data->first = 0;
3364 data->opt = val;
3365 } else if (data->max) {
3366 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3367 } else {
3368 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3369 }
3370
3371 return 0;
3372 }
3373
3374 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3375 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3376 {
3377 struct isl_opt_data data = { NULL, 1, NULL, max };
3378
3379 if (!set || !qp)
3380 goto error;
3381
3382 if (isl_upoly_is_cst(qp->upoly)) {
3383 isl_set_free(set);
3384 return qp;
3385 }
3386
3387 set = fix_inactive(set, qp);
3388
3389 data.qp = qp;
3390 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3391 goto error;
3392
3393 if (data.first)
3394 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3395
3396 isl_set_free(set);
3397 isl_qpolynomial_free(qp);
3398 return data.opt;
3399 error:
3400 isl_set_free(set);
3401 isl_qpolynomial_free(qp);
3402 isl_qpolynomial_free(data.opt);
3403 return NULL;
3404 }
3405
3406 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3407 __isl_take isl_morph *morph)
3408 {
3409 int i;
3410 int n_sub;
3411 isl_ctx *ctx;
3412 struct isl_upoly *up;
3413 unsigned n_div;
3414 struct isl_upoly **subs;
3415 isl_mat *mat;
3416
3417 qp = isl_qpolynomial_cow(qp);
3418 if (!qp || !morph)
3419 goto error;
3420
3421 ctx = qp->dim->ctx;
3422 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3423
3424 n_sub = morph->inv->n_row - 1;
3425 if (morph->inv->n_row != morph->inv->n_col)
3426 n_sub += qp->div->n_row;
3427 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3428 if (!subs)
3429 goto error;
3430
3431 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3432 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3433 morph->inv->row[0][0], morph->inv->n_col);
3434 if (morph->inv->n_row != morph->inv->n_col)
3435 for (i = 0; i < qp->div->n_row; ++i)
3436 subs[morph->inv->n_row - 1 + i] =
3437 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3438
3439 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3440
3441 for (i = 0; i < n_sub; ++i)
3442 isl_upoly_free(subs[i]);
3443 free(subs);
3444
3445 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3446 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3447 qp->div = isl_mat_product(qp->div, mat);
3448 isl_dim_free(qp->dim);
3449 qp->dim = isl_dim_copy(morph->ran->dim);
3450
3451 if (!qp->upoly || !qp->div || !qp->dim)
3452 goto error;
3453
3454 isl_morph_free(morph);
3455
3456 return qp;
3457 error:
3458 isl_qpolynomial_free(qp);
3459 isl_morph_free(morph);
3460 return NULL;
3461 }
3462
3463 static int neg_entry(void **entry, void *user)
3464 {
3465 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3466
3467 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3468
3469 return *pwqp ? 0 : -1;
3470 }
3471
3472 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3473 __isl_take isl_union_pw_qpolynomial *upwqp)
3474 {
3475 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3476 if (!upwqp)
3477 return NULL;
3478
3479 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3480 &neg_entry, NULL) < 0)
3481 goto error;
3482
3483 return upwqp;
3484 error:
3485 isl_union_pw_qpolynomial_free(upwqp);
3486 return NULL;
3487 }
3488
3489 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3490 __isl_take isl_union_pw_qpolynomial *upwqp1,
3491 __isl_take isl_union_pw_qpolynomial *upwqp2)
3492 {
3493 return isl_union_pw_qpolynomial_add(upwqp1,
3494 isl_union_pw_qpolynomial_neg(upwqp2));
3495 }
3496
3497 static int mul_entry(void **entry, void *user)
3498 {
3499 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3500 uint32_t hash;
3501 struct isl_hash_table_entry *entry2;
3502 isl_pw_qpolynomial *pwpq = *entry;
3503 int empty;
3504
3505 hash = isl_dim_get_hash(pwpq->dim);
3506 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3507 hash, &has_dim, pwpq->dim, 0);
3508 if (!entry2)
3509 return 0;
3510
3511 pwpq = isl_pw_qpolynomial_copy(pwpq);
3512 pwpq = isl_pw_qpolynomial_mul(pwpq,
3513 isl_pw_qpolynomial_copy(entry2->data));
3514
3515 empty = isl_pw_qpolynomial_is_zero(pwpq);
3516 if (empty < 0) {
3517 isl_pw_qpolynomial_free(pwpq);
3518 return -1;
3519 }
3520 if (empty) {
3521 isl_pw_qpolynomial_free(pwpq);
3522 return 0;
3523 }
3524
3525 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3526
3527 return 0;
3528 }
3529
3530 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3531 __isl_take isl_union_pw_qpolynomial *upwqp1,
3532 __isl_take isl_union_pw_qpolynomial *upwqp2)
3533 {
3534 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3535 }
3536
3537 /* Reorder the columns of the given div definitions according to the
3538 * given reordering.
3539 */
3540 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3541 __isl_take isl_reordering *r)
3542 {
3543 int i, j;
3544 isl_mat *mat;
3545 int extra;
3546
3547 if (!div || !r)
3548 goto error;
3549
3550 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3551 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3552 if (!mat)
3553 goto error;
3554
3555 for (i = 0; i < div->n_row; ++i) {
3556 isl_seq_cpy(mat->row[i], div->row[i], 2);
3557 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3558 for (j = 0; j < r->len; ++j)
3559 isl_int_set(mat->row[i][2 + r->pos[j]],
3560 div->row[i][2 + j]);
3561 }
3562
3563 isl_reordering_free(r);
3564 isl_mat_free(div);
3565 return mat;
3566 error:
3567 isl_reordering_free(r);
3568 isl_mat_free(div);
3569 return NULL;
3570 }
3571
3572 /* Reorder the dimension of "qp" according to the given reordering.
3573 */
3574 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3575 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3576 {
3577 qp = isl_qpolynomial_cow(qp);
3578 if (!qp)
3579 goto error;
3580
3581 r = isl_reordering_extend(r, qp->div->n_row);
3582 if (!r)
3583 goto error;
3584
3585 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3586 if (!qp->div)
3587 goto error;
3588
3589 qp->upoly = reorder(qp->upoly, r->pos);
3590 if (!qp->upoly)
3591 goto error;
3592
3593 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3594
3595 isl_reordering_free(r);
3596 return qp;
3597 error:
3598 isl_qpolynomial_free(qp);
3599 isl_reordering_free(r);
3600 return NULL;
3601 }
3602
3603 struct isl_split_periods_data {
3604 int max_periods;
3605 isl_pw_qpolynomial *res;
3606 };
3607
3608 /* Create a slice where the integer division "div" has the fixed value "v".
3609 * In particular, if "div" refers to floor(f/m), then create a slice
3610 *
3611 * m v <= f <= m v + (m - 1)
3612 *
3613 * or
3614 *
3615 * f - m v >= 0
3616 * -f + m v + (m - 1) >= 0
3617 */
3618 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3619 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3620 {
3621 int total;
3622 isl_basic_set *bset = NULL;
3623 int k;
3624
3625 if (!dim || !qp)
3626 goto error;
3627
3628 total = isl_dim_total(dim);
3629 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3630
3631 k = isl_basic_set_alloc_inequality(bset);
3632 if (k < 0)
3633 goto error;
3634 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3635 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3636
3637 k = isl_basic_set_alloc_inequality(bset);
3638 if (k < 0)
3639 goto error;
3640 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3641 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3642 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3643 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3644
3645 isl_dim_free(dim);
3646 return isl_set_from_basic_set(bset);
3647 error:
3648 isl_basic_set_free(bset);
3649 isl_dim_free(dim);
3650 return NULL;
3651 }
3652
3653 static int split_periods(__isl_take isl_set *set,
3654 __isl_take isl_qpolynomial *qp, void *user);
3655
3656 /* Create a slice of the domain "set" such that integer division "div"
3657 * has the fixed value "v" and add the results to data->res,
3658 * replacing the integer division by "v" in "qp".
3659 */
3660 static int set_div(__isl_take isl_set *set,
3661 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3662 struct isl_split_periods_data *data)
3663 {
3664 int i;
3665 int total;
3666 isl_set *slice;
3667 struct isl_upoly *cst;
3668
3669 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3670 set = isl_set_intersect(set, slice);
3671
3672 if (!qp)
3673 goto error;
3674
3675 total = isl_dim_total(qp->dim);
3676
3677 for (i = div + 1; i < qp->div->n_row; ++i) {
3678 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3679 continue;
3680 isl_int_addmul(qp->div->row[i][1],
3681 qp->div->row[i][2 + total + div], v);
3682 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3683 }
3684
3685 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3686 qp = substitute_div(qp, div, cst);
3687
3688 return split_periods(set, qp, data);
3689 error:
3690 isl_set_free(set);
3691 isl_qpolynomial_free(qp);
3692 return -1;
3693 }
3694
3695 /* Split the domain "set" such that integer division "div"
3696 * has a fixed value (ranging from "min" to "max") on each slice
3697 * and add the results to data->res.
3698 */
3699 static int split_div(__isl_take isl_set *set,
3700 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3701 struct isl_split_periods_data *data)
3702 {
3703 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3704 isl_set *set_i = isl_set_copy(set);
3705 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3706
3707 if (set_div(set_i, qp_i, div, min, data) < 0)
3708 goto error;
3709 }
3710 isl_set_free(set);
3711 isl_qpolynomial_free(qp);
3712 return 0;
3713 error:
3714 isl_set_free(set);
3715 isl_qpolynomial_free(qp);
3716 return -1;
3717 }
3718
3719 /* If "qp" refers to any integer division
3720 * that can only attain "max_periods" distinct values on "set"
3721 * then split the domain along those distinct values.
3722 * Add the results (or the original if no splitting occurs)
3723 * to data->res.
3724 */
3725 static int split_periods(__isl_take isl_set *set,
3726 __isl_take isl_qpolynomial *qp, void *user)
3727 {
3728 int i;
3729 isl_pw_qpolynomial *pwqp;
3730 struct isl_split_periods_data *data;
3731 isl_int min, max;
3732 int total;
3733 int r = 0;
3734
3735 data = (struct isl_split_periods_data *)user;
3736
3737 if (!set || !qp)
3738 goto error;
3739
3740 if (qp->div->n_row == 0) {
3741 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3742 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3743 return 0;
3744 }
3745
3746 isl_int_init(min);
3747 isl_int_init(max);
3748 total = isl_dim_total(qp->dim);
3749 for (i = 0; i < qp->div->n_row; ++i) {
3750 enum isl_lp_result lp_res;
3751
3752 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3753 qp->div->n_row) != -1)
3754 continue;
3755
3756 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3757 set->ctx->one, &min, NULL, NULL);
3758 if (lp_res == isl_lp_error)
3759 goto error2;
3760 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3761 continue;
3762 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3763
3764 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3765 set->ctx->one, &max, NULL, NULL);
3766 if (lp_res == isl_lp_error)
3767 goto error2;
3768 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3769 continue;
3770 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3771
3772 isl_int_sub(max, max, min);
3773 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3774 isl_int_add(max, max, min);
3775 break;
3776 }
3777 }
3778
3779 if (i < qp->div->n_row) {
3780 r = split_div(set, qp, i, min, max, data);
3781 } else {
3782 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3783 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3784 }
3785
3786 isl_int_clear(max);
3787 isl_int_clear(min);
3788
3789 return r;
3790 error2:
3791 isl_int_clear(max);
3792 isl_int_clear(min);
3793 error:
3794 isl_set_free(set);
3795 isl_qpolynomial_free(qp);
3796 return -1;
3797 }
3798
3799 /* If any quasi-polynomial in pwqp refers to any integer division
3800 * that can only attain "max_periods" distinct values on its domain
3801 * then split the domain along those distinct values.
3802 */
3803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3804 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3805 {
3806 struct isl_split_periods_data data;
3807
3808 data.max_periods = max_periods;
3809 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3810
3811 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3812 goto error;
3813
3814 isl_pw_qpolynomial_free(pwqp);
3815
3816 return data.res;
3817 error:
3818 isl_pw_qpolynomial_free(data.res);
3819 isl_pw_qpolynomial_free(pwqp);
3820 return NULL;
3821 }
3822
3823 /* Construct a piecewise quasipolynomial that is constant on the given
3824 * domain. In particular, it is
3825 * 0 if cst == 0
3826 * 1 if cst == 1
3827 * infinity if cst == -1
3828 */
3829 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3830 __isl_take isl_basic_set *bset, int cst)
3831 {
3832 isl_dim *dim;
3833 isl_qpolynomial *qp;
3834
3835 if (!bset)
3836 return NULL;
3837
3838 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3839 dim = isl_basic_set_get_dim(bset);
3840 if (cst < 0)
3841 qp = isl_qpolynomial_infty(dim);
3842 else if (cst == 0)
3843 qp = isl_qpolynomial_zero(dim);
3844 else
3845 qp = isl_qpolynomial_one(dim);
3846 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3847 }
3848
3849 /* Factor bset, call fn on each of the factors and return the product.
3850 *
3851 * If no factors can be found, simply call fn on the input.
3852 * Otherwise, construct the factors based on the factorizer,
3853 * call fn on each factor and compute the product.
3854 */
3855 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3856 __isl_take isl_basic_set *bset,
3857 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3858 {
3859 int i, n;
3860 isl_dim *dim;
3861 isl_set *set;
3862 isl_factorizer *f;
3863 isl_qpolynomial *qp;
3864 isl_pw_qpolynomial *pwqp;
3865 unsigned nparam;
3866 unsigned nvar;
3867
3868 f = isl_basic_set_factorizer(bset);
3869 if (!f)
3870 goto error;
3871 if (f->n_group == 0) {
3872 isl_factorizer_free(f);
3873 return fn(bset);
3874 }
3875
3876 nparam = isl_basic_set_dim(bset, isl_dim_param);
3877 nvar = isl_basic_set_dim(bset, isl_dim_set);
3878
3879 dim = isl_basic_set_get_dim(bset);
3880 dim = isl_dim_domain(dim);
3881 set = isl_set_universe(isl_dim_copy(dim));
3882 qp = isl_qpolynomial_one(dim);
3883 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3884
3885 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3886
3887 for (i = 0, n = 0; i < f->n_group; ++i) {
3888 isl_basic_set *bset_i;
3889 isl_pw_qpolynomial *pwqp_i;
3890
3891 bset_i = isl_basic_set_copy(bset);
3892 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3893 nparam + n + f->len[i], nvar - n - f->len[i]);
3894 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3895 nparam, n);
3896 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3897 n + f->len[i], nvar - n - f->len[i]);
3898 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3899
3900 pwqp_i = fn(bset_i);
3901 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3902
3903 n += f->len[i];
3904 }
3905
3906 isl_basic_set_free(bset);
3907 isl_factorizer_free(f);
3908
3909 return pwqp;
3910 error:
3911 isl_basic_set_free(bset);
3912 return NULL;
3913 }
3914
3915 /* Factor bset, call fn on each of the factors and return the product.
3916 * The function is assumed to evaluate to zero on empty domains,
3917 * to one on zero-dimensional domains and to infinity on unbounded domains
3918 * and will not be called explicitly on zero-dimensional or unbounded domains.
3919 *
3920 * We first check for some special cases and remove all equalities.
3921 * Then we hand over control to compressed_multiplicative_call.
3922 */
3923 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3924 __isl_take isl_basic_set *bset,
3925 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3926 {
3927 int bounded;
3928 isl_morph *morph;
3929 isl_pw_qpolynomial *pwqp;
3930 unsigned orig_nvar, final_nvar;
3931
3932 if (!bset)
3933 return NULL;
3934
3935 if (isl_basic_set_fast_is_empty(bset))
3936 return constant_on_domain(bset, 0);
3937
3938 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3939
3940 if (orig_nvar == 0)
3941 return constant_on_domain(bset, 1);
3942
3943 bounded = isl_basic_set_is_bounded(bset);
3944 if (bounded < 0)
3945 goto error;
3946 if (!bounded)
3947 return constant_on_domain(bset, -1);
3948
3949 if (bset->n_eq == 0)
3950 return compressed_multiplicative_call(bset, fn);
3951
3952 morph = isl_basic_set_full_compression(bset);
3953 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3954
3955 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3956
3957 pwqp = compressed_multiplicative_call(bset, fn);
3958
3959 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3960 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3961 morph = isl_morph_inverse(morph);
3962
3963 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3964
3965 return pwqp;
3966 error:
3967 isl_basic_set_free(bset);
3968 return NULL;
3969 }
Integer set library