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add isl_space_extend_domain_with_range
[isl.git] / isl_polynomial.c
blob78296097ba74fa15e61703327daff2b540d94bd1
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 #define ISL_DIM_H
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl/lp.h>
17 #include <isl/seq.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_div_private.h>
24 #include <isl_mat_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_config.h>
29
30 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
31 {
32 switch (type) {
33 case isl_dim_param: return 0;
34 case isl_dim_in: return dim->nparam;
35 case isl_dim_out: return dim->nparam + dim->n_in;
36 default: return 0;
37 }
38 }
39
40 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return -1;
44
45 return up->var < 0;
46 }
47
48 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
49 {
50 if (!up)
51 return NULL;
52
53 isl_assert(up->ctx, up->var < 0, return NULL);
54
55 return (struct isl_upoly_cst *)up;
56 }
57
58 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
59 {
60 if (!up)
61 return NULL;
62
63 isl_assert(up->ctx, up->var >= 0, return NULL);
64
65 return (struct isl_upoly_rec *)up;
66 }
67
68 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
69 __isl_keep struct isl_upoly *up2)
70 {
71 int i;
72 struct isl_upoly_rec *rec1, *rec2;
73
74 if (!up1 || !up2)
75 return -1;
76 if (up1 == up2)
77 return 1;
78 if (up1->var != up2->var)
79 return 0;
80 if (isl_upoly_is_cst(up1)) {
81 struct isl_upoly_cst *cst1, *cst2;
82 cst1 = isl_upoly_as_cst(up1);
83 cst2 = isl_upoly_as_cst(up2);
84 if (!cst1 || !cst2)
85 return -1;
86 return isl_int_eq(cst1->n, cst2->n) &&
87 isl_int_eq(cst1->d, cst2->d);
88 }
89
90 rec1 = isl_upoly_as_rec(up1);
91 rec2 = isl_upoly_as_rec(up2);
92 if (!rec1 || !rec2)
93 return -1;
94
95 if (rec1->n != rec2->n)
96 return 0;
97
98 for (i = 0; i < rec1->n; ++i) {
99 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
100 if (eq < 0 || !eq)
101 return eq;
102 }
103
104 return 1;
105 }
106
107 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
108 {
109 struct isl_upoly_cst *cst;
110
111 if (!up)
112 return -1;
113 if (!isl_upoly_is_cst(up))
114 return 0;
115
116 cst = isl_upoly_as_cst(up);
117 if (!cst)
118 return -1;
119
120 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
121 }
122
123 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
124 {
125 struct isl_upoly_cst *cst;
126
127 if (!up)
128 return 0;
129 if (!isl_upoly_is_cst(up))
130 return 0;
131
132 cst = isl_upoly_as_cst(up);
133 if (!cst)
134 return 0;
135
136 return isl_int_sgn(cst->n);
137 }
138
139 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
140 {
141 struct isl_upoly_cst *cst;
142
143 if (!up)
144 return -1;
145 if (!isl_upoly_is_cst(up))
146 return 0;
147
148 cst = isl_upoly_as_cst(up);
149 if (!cst)
150 return -1;
151
152 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
153 }
154
155 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
156 {
157 struct isl_upoly_cst *cst;
158
159 if (!up)
160 return -1;
161 if (!isl_upoly_is_cst(up))
162 return 0;
163
164 cst = isl_upoly_as_cst(up);
165 if (!cst)
166 return -1;
167
168 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
169 }
170
171 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
172 {
173 struct isl_upoly_cst *cst;
174
175 if (!up)
176 return -1;
177 if (!isl_upoly_is_cst(up))
178 return 0;
179
180 cst = isl_upoly_as_cst(up);
181 if (!cst)
182 return -1;
183
184 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
185 }
186
187 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
188 {
189 struct isl_upoly_cst *cst;
190
191 if (!up)
192 return -1;
193 if (!isl_upoly_is_cst(up))
194 return 0;
195
196 cst = isl_upoly_as_cst(up);
197 if (!cst)
198 return -1;
199
200 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
201 }
202
203 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
204 {
205 struct isl_upoly_cst *cst;
206
207 if (!up)
208 return -1;
209 if (!isl_upoly_is_cst(up))
210 return 0;
211
212 cst = isl_upoly_as_cst(up);
213 if (!cst)
214 return -1;
215
216 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
217 }
218
219 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
220 {
221 struct isl_upoly_cst *cst;
222
223 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
224 if (!cst)
225 return NULL;
226
227 cst->up.ref = 1;
228 cst->up.ctx = ctx;
229 isl_ctx_ref(ctx);
230 cst->up.var = -1;
231
232 isl_int_init(cst->n);
233 isl_int_init(cst->d);
234
235 return cst;
236 }
237
238 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
239 {
240 struct isl_upoly_cst *cst;
241
242 cst = isl_upoly_cst_alloc(ctx);
243 if (!cst)
244 return NULL;
245
246 isl_int_set_si(cst->n, 0);
247 isl_int_set_si(cst->d, 1);
248
249 return &cst->up;
250 }
251
252 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
253 {
254 struct isl_upoly_cst *cst;
255
256 cst = isl_upoly_cst_alloc(ctx);
257 if (!cst)
258 return NULL;
259
260 isl_int_set_si(cst->n, 1);
261 isl_int_set_si(cst->d, 1);
262
263 return &cst->up;
264 }
265
266 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
267 {
268 struct isl_upoly_cst *cst;
269
270 cst = isl_upoly_cst_alloc(ctx);
271 if (!cst)
272 return NULL;
273
274 isl_int_set_si(cst->n, 1);
275 isl_int_set_si(cst->d, 0);
276
277 return &cst->up;
278 }
279
280 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
281 {
282 struct isl_upoly_cst *cst;
283
284 cst = isl_upoly_cst_alloc(ctx);
285 if (!cst)
286 return NULL;
287
288 isl_int_set_si(cst->n, -1);
289 isl_int_set_si(cst->d, 0);
290
291 return &cst->up;
292 }
293
294 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
295 {
296 struct isl_upoly_cst *cst;
297
298 cst = isl_upoly_cst_alloc(ctx);
299 if (!cst)
300 return NULL;
301
302 isl_int_set_si(cst->n, 0);
303 isl_int_set_si(cst->d, 0);
304
305 return &cst->up;
306 }
307
308 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
309 isl_int n, isl_int d)
310 {
311 struct isl_upoly_cst *cst;
312
313 cst = isl_upoly_cst_alloc(ctx);
314 if (!cst)
315 return NULL;
316
317 isl_int_set(cst->n, n);
318 isl_int_set(cst->d, d);
319
320 return &cst->up;
321 }
322
323 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
324 int var, int size)
325 {
326 struct isl_upoly_rec *rec;
327
328 isl_assert(ctx, var >= 0, return NULL);
329 isl_assert(ctx, size >= 0, return NULL);
330 rec = isl_calloc(ctx, struct isl_upoly_rec,
331 sizeof(struct isl_upoly_rec) +
332 size * sizeof(struct isl_upoly *));
333 if (!rec)
334 return NULL;
335
336 rec->up.ref = 1;
337 rec->up.ctx = ctx;
338 isl_ctx_ref(ctx);
339 rec->up.var = var;
340
341 rec->n = 0;
342 rec->size = size;
343
344 return rec;
345 }
346
347 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space(
348 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
349 {
350 qp = isl_qpolynomial_cow(qp);
351 if (!qp || !dim)
352 goto error;
353
354 isl_space_free(qp->dim);
355 qp->dim = dim;
356
357 return qp;
358 error:
359 isl_qpolynomial_free(qp);
360 isl_space_free(dim);
361 return NULL;
362 }
363
364 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
365 {
366 return qp ? qp->dim->ctx : NULL;
367 }
368
369 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
370 {
371 return qp ? isl_space_copy(qp->dim) : NULL;
372 }
373
374 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
375 enum isl_dim_type type)
376 {
377 return qp ? isl_space_dim(qp->dim, type) : 0;
378 }
379
380 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
381 {
382 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
383 }
384
385 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
386 {
387 return qp ? isl_upoly_is_one(qp->upoly) : -1;
388 }
389
390 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
391 {
392 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
393 }
394
395 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
396 {
397 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
398 }
399
400 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
401 {
402 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
403 }
404
405 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
406 {
407 return qp ? isl_upoly_sgn(qp->upoly) : 0;
408 }
409
410 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
411 {
412 isl_int_clear(cst->n);
413 isl_int_clear(cst->d);
414 }
415
416 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
417 {
418 int i;
419
420 for (i = 0; i < rec->n; ++i)
421 isl_upoly_free(rec->p[i]);
422 }
423
424 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
425 {
426 if (!up)
427 return NULL;
428
429 up->ref++;
430 return up;
431 }
432
433 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
434 {
435 struct isl_upoly_cst *cst;
436 struct isl_upoly_cst *dup;
437
438 cst = isl_upoly_as_cst(up);
439 if (!cst)
440 return NULL;
441
442 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
443 if (!dup)
444 return NULL;
445 isl_int_set(dup->n, cst->n);
446 isl_int_set(dup->d, cst->d);
447
448 return &dup->up;
449 }
450
451 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
452 {
453 int i;
454 struct isl_upoly_rec *rec;
455 struct isl_upoly_rec *dup;
456
457 rec = isl_upoly_as_rec(up);
458 if (!rec)
459 return NULL;
460
461 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
462 if (!dup)
463 return NULL;
464
465 for (i = 0; i < rec->n; ++i) {
466 dup->p[i] = isl_upoly_copy(rec->p[i]);
467 if (!dup->p[i])
468 goto error;
469 dup->n++;
470 }
471
472 return &dup->up;
473 error:
474 isl_upoly_free(&dup->up);
475 return NULL;
476 }
477
478 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
479 {
480 if (!up)
481 return NULL;
482
483 if (isl_upoly_is_cst(up))
484 return isl_upoly_dup_cst(up);
485 else
486 return isl_upoly_dup_rec(up);
487 }
488
489 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
490 {
491 if (!up)
492 return NULL;
493
494 if (up->ref == 1)
495 return up;
496 up->ref--;
497 return isl_upoly_dup(up);
498 }
499
500 void isl_upoly_free(__isl_take struct isl_upoly *up)
501 {
502 if (!up)
503 return;
504
505 if (--up->ref > 0)
506 return;
507
508 if (up->var < 0)
509 upoly_free_cst((struct isl_upoly_cst *)up);
510 else
511 upoly_free_rec((struct isl_upoly_rec *)up);
512
513 isl_ctx_deref(up->ctx);
514 free(up);
515 }
516
517 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
518 {
519 isl_int gcd;
520
521 isl_int_init(gcd);
522 isl_int_gcd(gcd, cst->n, cst->d);
523 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
524 isl_int_divexact(cst->n, cst->n, gcd);
525 isl_int_divexact(cst->d, cst->d, gcd);
526 }
527 isl_int_clear(gcd);
528 }
529
530 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
531 __isl_take struct isl_upoly *up2)
532 {
533 struct isl_upoly_cst *cst1;
534 struct isl_upoly_cst *cst2;
535
536 up1 = isl_upoly_cow(up1);
537 if (!up1 || !up2)
538 goto error;
539
540 cst1 = isl_upoly_as_cst(up1);
541 cst2 = isl_upoly_as_cst(up2);
542
543 if (isl_int_eq(cst1->d, cst2->d))
544 isl_int_add(cst1->n, cst1->n, cst2->n);
545 else {
546 isl_int_mul(cst1->n, cst1->n, cst2->d);
547 isl_int_addmul(cst1->n, cst2->n, cst1->d);
548 isl_int_mul(cst1->d, cst1->d, cst2->d);
549 }
550
551 isl_upoly_cst_reduce(cst1);
552
553 isl_upoly_free(up2);
554 return up1;
555 error:
556 isl_upoly_free(up1);
557 isl_upoly_free(up2);
558 return NULL;
559 }
560
561 static __isl_give struct isl_upoly *replace_by_zero(
562 __isl_take struct isl_upoly *up)
563 {
564 struct isl_ctx *ctx;
565
566 if (!up)
567 return NULL;
568 ctx = up->ctx;
569 isl_upoly_free(up);
570 return isl_upoly_zero(ctx);
571 }
572
573 static __isl_give struct isl_upoly *replace_by_constant_term(
574 __isl_take struct isl_upoly *up)
575 {
576 struct isl_upoly_rec *rec;
577 struct isl_upoly *cst;
578
579 if (!up)
580 return NULL;
581
582 rec = isl_upoly_as_rec(up);
583 if (!rec)
584 goto error;
585 cst = isl_upoly_copy(rec->p[0]);
586 isl_upoly_free(up);
587 return cst;
588 error:
589 isl_upoly_free(up);
590 return NULL;
591 }
592
593 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
594 __isl_take struct isl_upoly *up2)
595 {
596 int i;
597 struct isl_upoly_rec *rec1, *rec2;
598
599 if (!up1 || !up2)
600 goto error;
601
602 if (isl_upoly_is_nan(up1)) {
603 isl_upoly_free(up2);
604 return up1;
605 }
606
607 if (isl_upoly_is_nan(up2)) {
608 isl_upoly_free(up1);
609 return up2;
610 }
611
612 if (isl_upoly_is_zero(up1)) {
613 isl_upoly_free(up1);
614 return up2;
615 }
616
617 if (isl_upoly_is_zero(up2)) {
618 isl_upoly_free(up2);
619 return up1;
620 }
621
622 if (up1->var < up2->var)
623 return isl_upoly_sum(up2, up1);
624
625 if (up2->var < up1->var) {
626 struct isl_upoly_rec *rec;
627 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
628 isl_upoly_free(up1);
629 return up2;
630 }
631 up1 = isl_upoly_cow(up1);
632 rec = isl_upoly_as_rec(up1);
633 if (!rec)
634 goto error;
635 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
636 if (rec->n == 1)
637 up1 = replace_by_constant_term(up1);
638 return up1;
639 }
640
641 if (isl_upoly_is_cst(up1))
642 return isl_upoly_sum_cst(up1, up2);
643
644 rec1 = isl_upoly_as_rec(up1);
645 rec2 = isl_upoly_as_rec(up2);
646 if (!rec1 || !rec2)
647 goto error;
648
649 if (rec1->n < rec2->n)
650 return isl_upoly_sum(up2, up1);
651
652 up1 = isl_upoly_cow(up1);
653 rec1 = isl_upoly_as_rec(up1);
654 if (!rec1)
655 goto error;
656
657 for (i = rec2->n - 1; i >= 0; --i) {
658 rec1->p[i] = isl_upoly_sum(rec1->p[i],
659 isl_upoly_copy(rec2->p[i]));
660 if (!rec1->p[i])
661 goto error;
662 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
663 isl_upoly_free(rec1->p[i]);
664 rec1->n--;
665 }
666 }
667
668 if (rec1->n == 0)
669 up1 = replace_by_zero(up1);
670 else if (rec1->n == 1)
671 up1 = replace_by_constant_term(up1);
672
673 isl_upoly_free(up2);
674
675 return up1;
676 error:
677 isl_upoly_free(up1);
678 isl_upoly_free(up2);
679 return NULL;
680 }
681
682 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
683 __isl_take struct isl_upoly *up, isl_int v)
684 {
685 struct isl_upoly_cst *cst;
686
687 up = isl_upoly_cow(up);
688 if (!up)
689 return NULL;
690
691 cst = isl_upoly_as_cst(up);
692
693 isl_int_addmul(cst->n, cst->d, v);
694
695 return up;
696 }
697
698 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
699 __isl_take struct isl_upoly *up, isl_int v)
700 {
701 struct isl_upoly_rec *rec;
702
703 if (!up)
704 return NULL;
705
706 if (isl_upoly_is_cst(up))
707 return isl_upoly_cst_add_isl_int(up, v);
708
709 up = isl_upoly_cow(up);
710 rec = isl_upoly_as_rec(up);
711 if (!rec)
712 goto error;
713
714 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
715 if (!rec->p[0])
716 goto error;
717
718 return up;
719 error:
720 isl_upoly_free(up);
721 return NULL;
722 }
723
724 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
725 __isl_take struct isl_upoly *up, isl_int v)
726 {
727 struct isl_upoly_cst *cst;
728
729 if (isl_upoly_is_zero(up))
730 return up;
731
732 up = isl_upoly_cow(up);
733 if (!up)
734 return NULL;
735
736 cst = isl_upoly_as_cst(up);
737
738 isl_int_mul(cst->n, cst->n, v);
739
740 return up;
741 }
742
743 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
744 __isl_take struct isl_upoly *up, isl_int v)
745 {
746 int i;
747 struct isl_upoly_rec *rec;
748
749 if (!up)
750 return NULL;
751
752 if (isl_upoly_is_cst(up))
753 return isl_upoly_cst_mul_isl_int(up, v);
754
755 up = isl_upoly_cow(up);
756 rec = isl_upoly_as_rec(up);
757 if (!rec)
758 goto error;
759
760 for (i = 0; i < rec->n; ++i) {
761 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
762 if (!rec->p[i])
763 goto error;
764 }
765
766 return up;
767 error:
768 isl_upoly_free(up);
769 return NULL;
770 }
771
772 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
773 __isl_take struct isl_upoly *up2)
774 {
775 struct isl_upoly_cst *cst1;
776 struct isl_upoly_cst *cst2;
777
778 up1 = isl_upoly_cow(up1);
779 if (!up1 || !up2)
780 goto error;
781
782 cst1 = isl_upoly_as_cst(up1);
783 cst2 = isl_upoly_as_cst(up2);
784
785 isl_int_mul(cst1->n, cst1->n, cst2->n);
786 isl_int_mul(cst1->d, cst1->d, cst2->d);
787
788 isl_upoly_cst_reduce(cst1);
789
790 isl_upoly_free(up2);
791 return up1;
792 error:
793 isl_upoly_free(up1);
794 isl_upoly_free(up2);
795 return NULL;
796 }
797
798 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
799 __isl_take struct isl_upoly *up2)
800 {
801 struct isl_upoly_rec *rec1;
802 struct isl_upoly_rec *rec2;
803 struct isl_upoly_rec *res = NULL;
804 int i, j;
805 int size;
806
807 rec1 = isl_upoly_as_rec(up1);
808 rec2 = isl_upoly_as_rec(up2);
809 if (!rec1 || !rec2)
810 goto error;
811 size = rec1->n + rec2->n - 1;
812 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
813 if (!res)
814 goto error;
815
816 for (i = 0; i < rec1->n; ++i) {
817 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
818 isl_upoly_copy(rec1->p[i]));
819 if (!res->p[i])
820 goto error;
821 res->n++;
822 }
823 for (; i < size; ++i) {
824 res->p[i] = isl_upoly_zero(up1->ctx);
825 if (!res->p[i])
826 goto error;
827 res->n++;
828 }
829 for (i = 0; i < rec1->n; ++i) {
830 for (j = 1; j < rec2->n; ++j) {
831 struct isl_upoly *up;
832 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
833 isl_upoly_copy(rec1->p[i]));
834 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
835 if (!res->p[i + j])
836 goto error;
837 }
838 }
839
840 isl_upoly_free(up1);
841 isl_upoly_free(up2);
842
843 return &res->up;
844 error:
845 isl_upoly_free(up1);
846 isl_upoly_free(up2);
847 isl_upoly_free(&res->up);
848 return NULL;
849 }
850
851 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
852 __isl_take struct isl_upoly *up2)
853 {
854 if (!up1 || !up2)
855 goto error;
856
857 if (isl_upoly_is_nan(up1)) {
858 isl_upoly_free(up2);
859 return up1;
860 }
861
862 if (isl_upoly_is_nan(up2)) {
863 isl_upoly_free(up1);
864 return up2;
865 }
866
867 if (isl_upoly_is_zero(up1)) {
868 isl_upoly_free(up2);
869 return up1;
870 }
871
872 if (isl_upoly_is_zero(up2)) {
873 isl_upoly_free(up1);
874 return up2;
875 }
876
877 if (isl_upoly_is_one(up1)) {
878 isl_upoly_free(up1);
879 return up2;
880 }
881
882 if (isl_upoly_is_one(up2)) {
883 isl_upoly_free(up2);
884 return up1;
885 }
886
887 if (up1->var < up2->var)
888 return isl_upoly_mul(up2, up1);
889
890 if (up2->var < up1->var) {
891 int i;
892 struct isl_upoly_rec *rec;
893 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
894 isl_ctx *ctx = up1->ctx;
895 isl_upoly_free(up1);
896 isl_upoly_free(up2);
897 return isl_upoly_nan(ctx);
898 }
899 up1 = isl_upoly_cow(up1);
900 rec = isl_upoly_as_rec(up1);
901 if (!rec)
902 goto error;
903
904 for (i = 0; i < rec->n; ++i) {
905 rec->p[i] = isl_upoly_mul(rec->p[i],
906 isl_upoly_copy(up2));
907 if (!rec->p[i])
908 goto error;
909 }
910 isl_upoly_free(up2);
911 return up1;
912 }
913
914 if (isl_upoly_is_cst(up1))
915 return isl_upoly_mul_cst(up1, up2);
916
917 return isl_upoly_mul_rec(up1, up2);
918 error:
919 isl_upoly_free(up1);
920 isl_upoly_free(up2);
921 return NULL;
922 }
923
924 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
925 unsigned power)
926 {
927 struct isl_upoly *res;
928
929 if (!up)
930 return NULL;
931 if (power == 1)
932 return up;
933
934 if (power % 2)
935 res = isl_upoly_copy(up);
936 else
937 res = isl_upoly_one(up->ctx);
938
939 while (power >>= 1) {
940 up = isl_upoly_mul(up, isl_upoly_copy(up));
941 if (power % 2)
942 res = isl_upoly_mul(res, isl_upoly_copy(up));
943 }
944
945 isl_upoly_free(up);
946 return res;
947 }
948
949 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
950 unsigned n_div, __isl_take struct isl_upoly *up)
951 {
952 struct isl_qpolynomial *qp = NULL;
953 unsigned total;
954
955 if (!dim || !up)
956 goto error;
957
958 total = isl_space_dim(dim, isl_dim_all);
959
960 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
961 if (!qp)
962 goto error;
963
964 qp->ref = 1;
965 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
966 if (!qp->div)
967 goto error;
968
969 qp->dim = dim;
970 qp->upoly = up;
971
972 return qp;
973 error:
974 isl_space_free(dim);
975 isl_upoly_free(up);
976 isl_qpolynomial_free(qp);
977 return NULL;
978 }
979
980 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
981 {
982 if (!qp)
983 return NULL;
984
985 qp->ref++;
986 return qp;
987 }
988
989 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
990 {
991 struct isl_qpolynomial *dup;
992
993 if (!qp)
994 return NULL;
995
996 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
997 isl_upoly_copy(qp->upoly));
998 if (!dup)
999 return NULL;
1000 isl_mat_free(dup->div);
1001 dup->div = isl_mat_copy(qp->div);
1002 if (!dup->div)
1003 goto error;
1004
1005 return dup;
1006 error:
1007 isl_qpolynomial_free(dup);
1008 return NULL;
1009 }
1010
1011 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1012 {
1013 if (!qp)
1014 return NULL;
1015
1016 if (qp->ref == 1)
1017 return qp;
1018 qp->ref--;
1019 return isl_qpolynomial_dup(qp);
1020 }
1021
1022 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1023 {
1024 if (!qp)
1025 return NULL;
1026
1027 if (--qp->ref > 0)
1028 return NULL;
1029
1030 isl_space_free(qp->dim);
1031 isl_mat_free(qp->div);
1032 isl_upoly_free(qp->upoly);
1033
1034 free(qp);
1035 return NULL;
1036 }
1037
1038 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1039 {
1040 int i;
1041 struct isl_upoly_rec *rec;
1042 struct isl_upoly_cst *cst;
1043
1044 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1045 if (!rec)
1046 return NULL;
1047 for (i = 0; i < 1 + power; ++i) {
1048 rec->p[i] = isl_upoly_zero(ctx);
1049 if (!rec->p[i])
1050 goto error;
1051 rec->n++;
1052 }
1053 cst = isl_upoly_as_cst(rec->p[power]);
1054 isl_int_set_si(cst->n, 1);
1055
1056 return &rec->up;
1057 error:
1058 isl_upoly_free(&rec->up);
1059 return NULL;
1060 }
1061
1062 /* r array maps original positions to new positions.
1063 */
1064 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1065 int *r)
1066 {
1067 int i;
1068 struct isl_upoly_rec *rec;
1069 struct isl_upoly *base;
1070 struct isl_upoly *res;
1071
1072 if (isl_upoly_is_cst(up))
1073 return up;
1074
1075 rec = isl_upoly_as_rec(up);
1076 if (!rec)
1077 goto error;
1078
1079 isl_assert(up->ctx, rec->n >= 1, goto error);
1080
1081 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1082 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1083
1084 for (i = rec->n - 2; i >= 0; --i) {
1085 res = isl_upoly_mul(res, isl_upoly_copy(base));
1086 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1087 }
1088
1089 isl_upoly_free(base);
1090 isl_upoly_free(up);
1091
1092 return res;
1093 error:
1094 isl_upoly_free(up);
1095 return NULL;
1096 }
1097
1098 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1099 {
1100 int n_row, n_col;
1101 int equal;
1102
1103 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1104 div1->n_col >= div2->n_col, return -1);
1105
1106 if (div1->n_row == div2->n_row)
1107 return isl_mat_is_equal(div1, div2);
1108
1109 n_row = div1->n_row;
1110 n_col = div1->n_col;
1111 div1->n_row = div2->n_row;
1112 div1->n_col = div2->n_col;
1113
1114 equal = isl_mat_is_equal(div1, div2);
1115
1116 div1->n_row = n_row;
1117 div1->n_col = n_col;
1118
1119 return equal;
1120 }
1121
1122 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1123 {
1124 int li, lj;
1125
1126 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1127 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1128
1129 if (li != lj)
1130 return li - lj;
1131
1132 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1133 }
1134
1135 struct isl_div_sort_info {
1136 isl_mat *div;
1137 int row;
1138 };
1139
1140 static int div_sort_cmp(const void *p1, const void *p2)
1141 {
1142 const struct isl_div_sort_info *i1, *i2;
1143 i1 = (const struct isl_div_sort_info *) p1;
1144 i2 = (const struct isl_div_sort_info *) p2;
1145
1146 return cmp_row(i1->div, i1->row, i2->row);
1147 }
1148
1149 /* Sort divs and remove duplicates.
1150 */
1151 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1152 {
1153 int i;
1154 int skip;
1155 int len;
1156 struct isl_div_sort_info *array = NULL;
1157 int *pos = NULL, *at = NULL;
1158 int *reordering = NULL;
1159 unsigned div_pos;
1160
1161 if (!qp)
1162 return NULL;
1163 if (qp->div->n_row <= 1)
1164 return qp;
1165
1166 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1167
1168 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1169 qp->div->n_row);
1170 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1171 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1172 len = qp->div->n_col - 2;
1173 reordering = isl_alloc_array(qp->div->ctx, int, len);
1174 if (!array || !pos || !at || !reordering)
1175 goto error;
1176
1177 for (i = 0; i < qp->div->n_row; ++i) {
1178 array[i].div = qp->div;
1179 array[i].row = i;
1180 pos[i] = i;
1181 at[i] = i;
1182 }
1183
1184 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1185 div_sort_cmp);
1186
1187 for (i = 0; i < div_pos; ++i)
1188 reordering[i] = i;
1189
1190 for (i = 0; i < qp->div->n_row; ++i) {
1191 if (pos[array[i].row] == i)
1192 continue;
1193 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1194 pos[at[i]] = pos[array[i].row];
1195 at[pos[array[i].row]] = at[i];
1196 at[i] = array[i].row;
1197 pos[array[i].row] = i;
1198 }
1199
1200 skip = 0;
1201 for (i = 0; i < len - div_pos; ++i) {
1202 if (i > 0 &&
1203 isl_seq_eq(qp->div->row[i - skip - 1],
1204 qp->div->row[i - skip], qp->div->n_col)) {
1205 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1206 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1207 2 + div_pos + i - skip);
1208 qp->div = isl_mat_drop_cols(qp->div,
1209 2 + div_pos + i - skip, 1);
1210 skip++;
1211 }
1212 reordering[div_pos + array[i].row] = div_pos + i - skip;
1213 }
1214
1215 qp->upoly = reorder(qp->upoly, reordering);
1216
1217 if (!qp->upoly || !qp->div)
1218 goto error;
1219
1220 free(at);
1221 free(pos);
1222 free(array);
1223 free(reordering);
1224
1225 return qp;
1226 error:
1227 free(at);
1228 free(pos);
1229 free(array);
1230 free(reordering);
1231 isl_qpolynomial_free(qp);
1232 return NULL;
1233 }
1234
1235 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1236 int *exp, int first)
1237 {
1238 int i;
1239 struct isl_upoly_rec *rec;
1240
1241 if (isl_upoly_is_cst(up))
1242 return up;
1243
1244 if (up->var < first)
1245 return up;
1246
1247 if (exp[up->var - first] == up->var - first)
1248 return up;
1249
1250 up = isl_upoly_cow(up);
1251 if (!up)
1252 goto error;
1253
1254 up->var = exp[up->var - first] + first;
1255
1256 rec = isl_upoly_as_rec(up);
1257 if (!rec)
1258 goto error;
1259
1260 for (i = 0; i < rec->n; ++i) {
1261 rec->p[i] = expand(rec->p[i], exp, first);
1262 if (!rec->p[i])
1263 goto error;
1264 }
1265
1266 return up;
1267 error:
1268 isl_upoly_free(up);
1269 return NULL;
1270 }
1271
1272 static __isl_give isl_qpolynomial *with_merged_divs(
1273 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1274 __isl_take isl_qpolynomial *qp2),
1275 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1276 {
1277 int *exp1 = NULL;
1278 int *exp2 = NULL;
1279 isl_mat *div = NULL;
1280
1281 qp1 = isl_qpolynomial_cow(qp1);
1282 qp2 = isl_qpolynomial_cow(qp2);
1283
1284 if (!qp1 || !qp2)
1285 goto error;
1286
1287 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1288 qp1->div->n_col >= qp2->div->n_col, goto error);
1289
1290 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1291 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1292 if (!exp1 || !exp2)
1293 goto error;
1294
1295 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1296 if (!div)
1297 goto error;
1298
1299 isl_mat_free(qp1->div);
1300 qp1->div = isl_mat_copy(div);
1301 isl_mat_free(qp2->div);
1302 qp2->div = isl_mat_copy(div);
1303
1304 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1305 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1306
1307 if (!qp1->upoly || !qp2->upoly)
1308 goto error;
1309
1310 isl_mat_free(div);
1311 free(exp1);
1312 free(exp2);
1313
1314 return fn(qp1, qp2);
1315 error:
1316 isl_mat_free(div);
1317 free(exp1);
1318 free(exp2);
1319 isl_qpolynomial_free(qp1);
1320 isl_qpolynomial_free(qp2);
1321 return NULL;
1322 }
1323
1324 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1325 __isl_take isl_qpolynomial *qp2)
1326 {
1327 qp1 = isl_qpolynomial_cow(qp1);
1328
1329 if (!qp1 || !qp2)
1330 goto error;
1331
1332 if (qp1->div->n_row < qp2->div->n_row)
1333 return isl_qpolynomial_add(qp2, qp1);
1334
1335 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1336 if (!compatible_divs(qp1->div, qp2->div))
1337 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1338
1339 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1340 if (!qp1->upoly)
1341 goto error;
1342
1343 isl_qpolynomial_free(qp2);
1344
1345 return qp1;
1346 error:
1347 isl_qpolynomial_free(qp1);
1348 isl_qpolynomial_free(qp2);
1349 return NULL;
1350 }
1351
1352 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1353 __isl_keep isl_set *dom,
1354 __isl_take isl_qpolynomial *qp1,
1355 __isl_take isl_qpolynomial *qp2)
1356 {
1357 qp1 = isl_qpolynomial_add(qp1, qp2);
1358 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1359 return qp1;
1360 }
1361
1362 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1363 __isl_take isl_qpolynomial *qp2)
1364 {
1365 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1366 }
1367
1368 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1369 __isl_take isl_qpolynomial *qp, isl_int v)
1370 {
1371 if (isl_int_is_zero(v))
1372 return qp;
1373
1374 qp = isl_qpolynomial_cow(qp);
1375 if (!qp)
1376 return NULL;
1377
1378 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1379 if (!qp->upoly)
1380 goto error;
1381
1382 return qp;
1383 error:
1384 isl_qpolynomial_free(qp);
1385 return NULL;
1386
1387 }
1388
1389 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1390 {
1391 if (!qp)
1392 return NULL;
1393
1394 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1395 }
1396
1397 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1398 __isl_take isl_qpolynomial *qp, isl_int v)
1399 {
1400 if (isl_int_is_one(v))
1401 return qp;
1402
1403 if (qp && isl_int_is_zero(v)) {
1404 isl_qpolynomial *zero;
1405 zero = isl_qpolynomial_zero(isl_space_copy(qp->dim));
1406 isl_qpolynomial_free(qp);
1407 return zero;
1408 }
1409
1410 qp = isl_qpolynomial_cow(qp);
1411 if (!qp)
1412 return NULL;
1413
1414 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1415 if (!qp->upoly)
1416 goto error;
1417
1418 return qp;
1419 error:
1420 isl_qpolynomial_free(qp);
1421 return NULL;
1422 }
1423
1424 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1425 __isl_take isl_qpolynomial *qp, isl_int v)
1426 {
1427 return isl_qpolynomial_mul_isl_int(qp, v);
1428 }
1429
1430 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1431 __isl_take isl_qpolynomial *qp2)
1432 {
1433 qp1 = isl_qpolynomial_cow(qp1);
1434
1435 if (!qp1 || !qp2)
1436 goto error;
1437
1438 if (qp1->div->n_row < qp2->div->n_row)
1439 return isl_qpolynomial_mul(qp2, qp1);
1440
1441 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1442 if (!compatible_divs(qp1->div, qp2->div))
1443 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1444
1445 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1446 if (!qp1->upoly)
1447 goto error;
1448
1449 isl_qpolynomial_free(qp2);
1450
1451 return qp1;
1452 error:
1453 isl_qpolynomial_free(qp1);
1454 isl_qpolynomial_free(qp2);
1455 return NULL;
1456 }
1457
1458 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1459 unsigned power)
1460 {
1461 qp = isl_qpolynomial_cow(qp);
1462
1463 if (!qp)
1464 return NULL;
1465
1466 qp->upoly = isl_upoly_pow(qp->upoly, power);
1467 if (!qp->upoly)
1468 goto error;
1469
1470 return qp;
1471 error:
1472 isl_qpolynomial_free(qp);
1473 return NULL;
1474 }
1475
1476 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1477 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1478 {
1479 int i;
1480
1481 if (power == 1)
1482 return pwqp;
1483
1484 pwqp = isl_pw_qpolynomial_cow(pwqp);
1485 if (!pwqp)
1486 return NULL;
1487
1488 for (i = 0; i < pwqp->n; ++i) {
1489 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1490 if (!pwqp->p[i].qp)
1491 return isl_pw_qpolynomial_free(pwqp);
1492 }
1493
1494 return pwqp;
1495 }
1496
1497 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_space *dim)
1498 {
1499 if (!dim)
1500 return NULL;
1501 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1502 }
1503
1504 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_space *dim)
1505 {
1506 if (!dim)
1507 return NULL;
1508 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1509 }
1510
1511 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_space *dim)
1512 {
1513 if (!dim)
1514 return NULL;
1515 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1516 }
1517
1518 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_space *dim)
1519 {
1520 if (!dim)
1521 return NULL;
1522 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1523 }
1524
1525 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_space *dim)
1526 {
1527 if (!dim)
1528 return NULL;
1529 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1530 }
1531
1532 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_space *dim,
1533 isl_int v)
1534 {
1535 struct isl_qpolynomial *qp;
1536 struct isl_upoly_cst *cst;
1537
1538 if (!dim)
1539 return NULL;
1540
1541 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1542 if (!qp)
1543 return NULL;
1544
1545 cst = isl_upoly_as_cst(qp->upoly);
1546 isl_int_set(cst->n, v);
1547
1548 return qp;
1549 }
1550
1551 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1552 isl_int *n, isl_int *d)
1553 {
1554 struct isl_upoly_cst *cst;
1555
1556 if (!qp)
1557 return -1;
1558
1559 if (!isl_upoly_is_cst(qp->upoly))
1560 return 0;
1561
1562 cst = isl_upoly_as_cst(qp->upoly);
1563 if (!cst)
1564 return -1;
1565
1566 if (n)
1567 isl_int_set(*n, cst->n);
1568 if (d)
1569 isl_int_set(*d, cst->d);
1570
1571 return 1;
1572 }
1573
1574 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1575 {
1576 int is_cst;
1577 struct isl_upoly_rec *rec;
1578
1579 if (!up)
1580 return -1;
1581
1582 if (up->var < 0)
1583 return 1;
1584
1585 rec = isl_upoly_as_rec(up);
1586 if (!rec)
1587 return -1;
1588
1589 if (rec->n > 2)
1590 return 0;
1591
1592 isl_assert(up->ctx, rec->n > 1, return -1);
1593
1594 is_cst = isl_upoly_is_cst(rec->p[1]);
1595 if (is_cst < 0)
1596 return -1;
1597 if (!is_cst)
1598 return 0;
1599
1600 return isl_upoly_is_affine(rec->p[0]);
1601 }
1602
1603 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1604 {
1605 if (!qp)
1606 return -1;
1607
1608 if (qp->div->n_row > 0)
1609 return 0;
1610
1611 return isl_upoly_is_affine(qp->upoly);
1612 }
1613
1614 static void update_coeff(__isl_keep isl_vec *aff,
1615 __isl_keep struct isl_upoly_cst *cst, int pos)
1616 {
1617 isl_int gcd;
1618 isl_int f;
1619
1620 if (isl_int_is_zero(cst->n))
1621 return;
1622
1623 isl_int_init(gcd);
1624 isl_int_init(f);
1625 isl_int_gcd(gcd, cst->d, aff->el[0]);
1626 isl_int_divexact(f, cst->d, gcd);
1627 isl_int_divexact(gcd, aff->el[0], gcd);
1628 isl_seq_scale(aff->el, aff->el, f, aff->size);
1629 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1630 isl_int_clear(gcd);
1631 isl_int_clear(f);
1632 }
1633
1634 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1635 __isl_keep isl_vec *aff)
1636 {
1637 struct isl_upoly_cst *cst;
1638 struct isl_upoly_rec *rec;
1639
1640 if (!up || !aff)
1641 return -1;
1642
1643 if (up->var < 0) {
1644 struct isl_upoly_cst *cst;
1645
1646 cst = isl_upoly_as_cst(up);
1647 if (!cst)
1648 return -1;
1649 update_coeff(aff, cst, 0);
1650 return 0;
1651 }
1652
1653 rec = isl_upoly_as_rec(up);
1654 if (!rec)
1655 return -1;
1656 isl_assert(up->ctx, rec->n == 2, return -1);
1657
1658 cst = isl_upoly_as_cst(rec->p[1]);
1659 if (!cst)
1660 return -1;
1661 update_coeff(aff, cst, 1 + up->var);
1662
1663 return isl_upoly_update_affine(rec->p[0], aff);
1664 }
1665
1666 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1667 __isl_keep isl_qpolynomial *qp)
1668 {
1669 isl_vec *aff;
1670 unsigned d;
1671
1672 if (!qp)
1673 return NULL;
1674
1675 d = isl_space_dim(qp->dim, isl_dim_all);
1676 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1677 if (!aff)
1678 return NULL;
1679
1680 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1681 isl_int_set_si(aff->el[0], 1);
1682
1683 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1684 goto error;
1685
1686 return aff;
1687 error:
1688 isl_vec_free(aff);
1689 return NULL;
1690 }
1691
1692 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1693 __isl_keep isl_qpolynomial *qp2)
1694 {
1695 int equal;
1696
1697 if (!qp1 || !qp2)
1698 return -1;
1699
1700 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1701 if (equal < 0 || !equal)
1702 return equal;
1703
1704 equal = isl_mat_is_equal(qp1->div, qp2->div);
1705 if (equal < 0 || !equal)
1706 return equal;
1707
1708 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1709 }
1710
1711 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1712 {
1713 int i;
1714 struct isl_upoly_rec *rec;
1715
1716 if (isl_upoly_is_cst(up)) {
1717 struct isl_upoly_cst *cst;
1718 cst = isl_upoly_as_cst(up);
1719 if (!cst)
1720 return;
1721 isl_int_lcm(*d, *d, cst->d);
1722 return;
1723 }
1724
1725 rec = isl_upoly_as_rec(up);
1726 if (!rec)
1727 return;
1728
1729 for (i = 0; i < rec->n; ++i)
1730 upoly_update_den(rec->p[i], d);
1731 }
1732
1733 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1734 {
1735 isl_int_set_si(*d, 1);
1736 if (!qp)
1737 return;
1738 upoly_update_den(qp->upoly, d);
1739 }
1740
1741 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_space *dim,
1742 int pos, int power)
1743 {
1744 struct isl_ctx *ctx;
1745
1746 if (!dim)
1747 return NULL;
1748
1749 ctx = dim->ctx;
1750
1751 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1752 }
1753
1754 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_space *dim,
1755 enum isl_dim_type type, unsigned pos)
1756 {
1757 if (!dim)
1758 return NULL;
1759
1760 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1761 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1762
1763 if (type == isl_dim_set)
1764 pos += isl_space_dim(dim, isl_dim_param);
1765
1766 return isl_qpolynomial_var_pow(dim, pos, 1);
1767 error:
1768 isl_space_free(dim);
1769 return NULL;
1770 }
1771
1772 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1773 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1774 {
1775 int i;
1776 struct isl_upoly_rec *rec;
1777 struct isl_upoly *base, *res;
1778
1779 if (!up)
1780 return NULL;
1781
1782 if (isl_upoly_is_cst(up))
1783 return up;
1784
1785 if (up->var < first)
1786 return up;
1787
1788 rec = isl_upoly_as_rec(up);
1789 if (!rec)
1790 goto error;
1791
1792 isl_assert(up->ctx, rec->n >= 1, goto error);
1793
1794 if (up->var >= first + n)
1795 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1796 else
1797 base = isl_upoly_copy(subs[up->var - first]);
1798
1799 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1800 for (i = rec->n - 2; i >= 0; --i) {
1801 struct isl_upoly *t;
1802 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1803 res = isl_upoly_mul(res, isl_upoly_copy(base));
1804 res = isl_upoly_sum(res, t);
1805 }
1806
1807 isl_upoly_free(base);
1808 isl_upoly_free(up);
1809
1810 return res;
1811 error:
1812 isl_upoly_free(up);
1813 return NULL;
1814 }
1815
1816 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1817 isl_int denom, unsigned len)
1818 {
1819 int i;
1820 struct isl_upoly *up;
1821
1822 isl_assert(ctx, len >= 1, return NULL);
1823
1824 up = isl_upoly_rat_cst(ctx, f[0], denom);
1825 for (i = 0; i < len - 1; ++i) {
1826 struct isl_upoly *t;
1827 struct isl_upoly *c;
1828
1829 if (isl_int_is_zero(f[1 + i]))
1830 continue;
1831
1832 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1833 t = isl_upoly_var_pow(ctx, i, 1);
1834 t = isl_upoly_mul(c, t);
1835 up = isl_upoly_sum(up, t);
1836 }
1837
1838 return up;
1839 }
1840
1841 /* Remove common factor of non-constant terms and denominator.
1842 */
1843 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1844 {
1845 isl_ctx *ctx = qp->div->ctx;
1846 unsigned total = qp->div->n_col - 2;
1847
1848 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1849 isl_int_gcd(ctx->normalize_gcd,
1850 ctx->normalize_gcd, qp->div->row[div][0]);
1851 if (isl_int_is_one(ctx->normalize_gcd))
1852 return;
1853
1854 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1855 ctx->normalize_gcd, total);
1856 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1857 ctx->normalize_gcd);
1858 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1859 ctx->normalize_gcd);
1860 }
1861
1862 /* Replace the integer division identified by "div" by the polynomial "s".
1863 * The integer division is assumed not to appear in the definition
1864 * of any other integer divisions.
1865 */
1866 static __isl_give isl_qpolynomial *substitute_div(
1867 __isl_take isl_qpolynomial *qp,
1868 int div, __isl_take struct isl_upoly *s)
1869 {
1870 int i;
1871 int total;
1872 int *reordering;
1873
1874 if (!qp || !s)
1875 goto error;
1876
1877 qp = isl_qpolynomial_cow(qp);
1878 if (!qp)
1879 goto error;
1880
1881 total = isl_space_dim(qp->dim, isl_dim_all);
1882 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1883 if (!qp->upoly)
1884 goto error;
1885
1886 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1887 if (!reordering)
1888 goto error;
1889 for (i = 0; i < total + div; ++i)
1890 reordering[i] = i;
1891 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1892 reordering[i] = i - 1;
1893 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1894 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1895 qp->upoly = reorder(qp->upoly, reordering);
1896 free(reordering);
1897
1898 if (!qp->upoly || !qp->div)
1899 goto error;
1900
1901 isl_upoly_free(s);
1902 return qp;
1903 error:
1904 isl_qpolynomial_free(qp);
1905 isl_upoly_free(s);
1906 return NULL;
1907 }
1908
1909 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1910 * divisions because d is equal to 1 by their definition, i.e., e.
1911 */
1912 static __isl_give isl_qpolynomial *substitute_non_divs(
1913 __isl_take isl_qpolynomial *qp)
1914 {
1915 int i, j;
1916 int total;
1917 struct isl_upoly *s;
1918
1919 if (!qp)
1920 return NULL;
1921
1922 total = isl_space_dim(qp->dim, isl_dim_all);
1923 for (i = 0; qp && i < qp->div->n_row; ++i) {
1924 if (!isl_int_is_one(qp->div->row[i][0]))
1925 continue;
1926 for (j = i + 1; j < qp->div->n_row; ++j) {
1927 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1928 continue;
1929 isl_seq_combine(qp->div->row[j] + 1,
1930 qp->div->ctx->one, qp->div->row[j] + 1,
1931 qp->div->row[j][2 + total + i],
1932 qp->div->row[i] + 1, 1 + total + i);
1933 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1934 normalize_div(qp, j);
1935 }
1936 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1937 qp->div->row[i][0], qp->div->n_col - 1);
1938 qp = substitute_div(qp, i, s);
1939 --i;
1940 }
1941
1942 return qp;
1943 }
1944
1945 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1946 * with d the denominator. When replacing the coefficient e of x by
1947 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1948 * inside the division, so we need to add floor(e/d) * x outside.
1949 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1950 * to adjust the coefficient of x in each later div that depends on the
1951 * current div "div" and also in the affine expression "aff"
1952 * (if it too depends on "div").
1953 */
1954 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1955 __isl_keep isl_vec *aff)
1956 {
1957 int i, j;
1958 isl_int v;
1959 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1960
1961 isl_int_init(v);
1962 for (i = 0; i < 1 + total + div; ++i) {
1963 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1964 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1965 continue;
1966 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1967 isl_int_fdiv_r(qp->div->row[div][1 + i],
1968 qp->div->row[div][1 + i], qp->div->row[div][0]);
1969 if (!isl_int_is_zero(aff->el[1 + total + div]))
1970 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1971 for (j = div + 1; j < qp->div->n_row; ++j) {
1972 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1973 continue;
1974 isl_int_addmul(qp->div->row[j][1 + i],
1975 v, qp->div->row[j][2 + total + div]);
1976 }
1977 }
1978 isl_int_clear(v);
1979 }
1980
1981 /* Check if the last non-zero coefficient is bigger that half of the
1982 * denominator. If so, we will invert the div to further reduce the number
1983 * of distinct divs that may appear.
1984 * If the last non-zero coefficient is exactly half the denominator,
1985 * then we continue looking for earlier coefficients that are bigger
1986 * than half the denominator.
1987 */
1988 static int needs_invert(__isl_keep isl_mat *div, int row)
1989 {
1990 int i;
1991 int cmp;
1992
1993 for (i = div->n_col - 1; i >= 1; --i) {
1994 if (isl_int_is_zero(div->row[row][i]))
1995 continue;
1996 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1997 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1998 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1999 if (cmp)
2000 return cmp > 0;
2001 if (i == 1)
2002 return 1;
2003 }
2004
2005 return 0;
2006 }
2007
2008 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2009 * We only invert the coefficients of e (and the coefficient of q in
2010 * later divs and in "aff"). After calling this function, the
2011 * coefficients of e should be reduced again.
2012 */
2013 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2014 __isl_keep isl_vec *aff)
2015 {
2016 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2017
2018 isl_seq_neg(qp->div->row[div] + 1,
2019 qp->div->row[div] + 1, qp->div->n_col - 1);
2020 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2021 isl_int_add(qp->div->row[div][1],
2022 qp->div->row[div][1], qp->div->row[div][0]);
2023 if (!isl_int_is_zero(aff->el[1 + total + div]))
2024 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2025 isl_mat_col_mul(qp->div, 2 + total + div,
2026 qp->div->ctx->negone, 2 + total + div);
2027 }
2028
2029 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2030 * in the interval [0, d-1], with d the denominator and such that the
2031 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2032 *
2033 * After the reduction, some divs may have become redundant or identical,
2034 * so we call substitute_non_divs and sort_divs. If these functions
2035 * eliminate divs or merge two or more divs into one, the coefficients
2036 * of the enclosing divs may have to be reduced again, so we call
2037 * ourselves recursively if the number of divs decreases.
2038 */
2039 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2040 {
2041 int i;
2042 isl_vec *aff = NULL;
2043 struct isl_upoly *s;
2044 unsigned n_div;
2045
2046 if (!qp)
2047 return NULL;
2048
2049 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2050 aff = isl_vec_clr(aff);
2051 if (!aff)
2052 goto error;
2053
2054 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2055
2056 for (i = 0; i < qp->div->n_row; ++i) {
2057 normalize_div(qp, i);
2058 reduce_div(qp, i, aff);
2059 if (needs_invert(qp->div, i)) {
2060 invert_div(qp, i, aff);
2061 reduce_div(qp, i, aff);
2062 }
2063 }
2064
2065 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2066 qp->div->ctx->one, aff->size);
2067 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2068 isl_upoly_free(s);
2069 if (!qp->upoly)
2070 goto error;
2071
2072 isl_vec_free(aff);
2073
2074 n_div = qp->div->n_row;
2075 qp = substitute_non_divs(qp);
2076 qp = sort_divs(qp);
2077 if (qp && qp->div->n_row < n_div)
2078 return reduce_divs(qp);
2079
2080 return qp;
2081 error:
2082 isl_qpolynomial_free(qp);
2083 isl_vec_free(aff);
2084 return NULL;
2085 }
2086
2087 /* Assumes each div only depends on earlier divs.
2088 */
2089 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2090 int power)
2091 {
2092 struct isl_qpolynomial *qp = NULL;
2093 struct isl_upoly_rec *rec;
2094 struct isl_upoly_cst *cst;
2095 int i, d;
2096 int pos;
2097
2098 if (!div)
2099 return NULL;
2100
2101 d = div->line - div->bmap->div;
2102
2103 pos = isl_space_dim(div->bmap->dim, isl_dim_all) + d;
2104 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2105 qp = isl_qpolynomial_alloc(isl_basic_map_get_space(div->bmap),
2106 div->bmap->n_div, &rec->up);
2107 if (!qp)
2108 goto error;
2109
2110 for (i = 0; i < div->bmap->n_div; ++i)
2111 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2112
2113 for (i = 0; i < 1 + power; ++i) {
2114 rec->p[i] = isl_upoly_zero(div->ctx);
2115 if (!rec->p[i])
2116 goto error;
2117 rec->n++;
2118 }
2119 cst = isl_upoly_as_cst(rec->p[power]);
2120 isl_int_set_si(cst->n, 1);
2121
2122 isl_div_free(div);
2123
2124 qp = reduce_divs(qp);
2125
2126 return qp;
2127 error:
2128 isl_qpolynomial_free(qp);
2129 isl_div_free(div);
2130 return NULL;
2131 }
2132
2133 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2134 {
2135 return isl_qpolynomial_div_pow(div, 1);
2136 }
2137
2138 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_space *dim,
2139 const isl_int n, const isl_int d)
2140 {
2141 struct isl_qpolynomial *qp;
2142 struct isl_upoly_cst *cst;
2143
2144 if (!dim)
2145 return NULL;
2146
2147 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2148 if (!qp)
2149 return NULL;
2150
2151 cst = isl_upoly_as_cst(qp->upoly);
2152 isl_int_set(cst->n, n);
2153 isl_int_set(cst->d, d);
2154
2155 return qp;
2156 }
2157
2158 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2159 {
2160 struct isl_upoly_rec *rec;
2161 int i;
2162
2163 if (!up)
2164 return -1;
2165
2166 if (isl_upoly_is_cst(up))
2167 return 0;
2168
2169 if (up->var < d)
2170 active[up->var] = 1;
2171
2172 rec = isl_upoly_as_rec(up);
2173 for (i = 0; i < rec->n; ++i)
2174 if (up_set_active(rec->p[i], active, d) < 0)
2175 return -1;
2176
2177 return 0;
2178 }
2179
2180 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2181 {
2182 int i, j;
2183 int d = isl_space_dim(qp->dim, isl_dim_all);
2184
2185 if (!qp || !active)
2186 return -1;
2187
2188 for (i = 0; i < d; ++i)
2189 for (j = 0; j < qp->div->n_row; ++j) {
2190 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2191 continue;
2192 active[i] = 1;
2193 break;
2194 }
2195
2196 return up_set_active(qp->upoly, active, d);
2197 }
2198
2199 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2200 enum isl_dim_type type, unsigned first, unsigned n)
2201 {
2202 int i;
2203 int *active = NULL;
2204 int involves = 0;
2205
2206 if (!qp)
2207 return -1;
2208 if (n == 0)
2209 return 0;
2210
2211 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2212 return -1);
2213 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2214 type == isl_dim_set, return -1);
2215
2216 active = isl_calloc_array(qp->dim->ctx, int,
2217 isl_space_dim(qp->dim, isl_dim_all));
2218 if (set_active(qp, active) < 0)
2219 goto error;
2220
2221 if (type == isl_dim_set)
2222 first += isl_space_dim(qp->dim, isl_dim_param);
2223 for (i = 0; i < n; ++i)
2224 if (active[first + i]) {
2225 involves = 1;
2226 break;
2227 }
2228
2229 free(active);
2230
2231 return involves;
2232 error:
2233 free(active);
2234 return -1;
2235 }
2236
2237 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2238 * of the divs that do appear in the quasi-polynomial.
2239 */
2240 static __isl_give isl_qpolynomial *remove_redundant_divs(
2241 __isl_take isl_qpolynomial *qp)
2242 {
2243 int i, j;
2244 int d;
2245 int len;
2246 int skip;
2247 int *active = NULL;
2248 int *reordering = NULL;
2249 int redundant = 0;
2250 int n_div;
2251 isl_ctx *ctx;
2252
2253 if (!qp)
2254 return NULL;
2255 if (qp->div->n_row == 0)
2256 return qp;
2257
2258 d = isl_space_dim(qp->dim, isl_dim_all);
2259 len = qp->div->n_col - 2;
2260 ctx = isl_qpolynomial_get_ctx(qp);
2261 active = isl_calloc_array(ctx, int, len);
2262 if (!active)
2263 goto error;
2264
2265 if (up_set_active(qp->upoly, active, len) < 0)
2266 goto error;
2267
2268 for (i = qp->div->n_row - 1; i >= 0; --i) {
2269 if (!active[d + i]) {
2270 redundant = 1;
2271 continue;
2272 }
2273 for (j = 0; j < i; ++j) {
2274 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2275 continue;
2276 active[d + j] = 1;
2277 break;
2278 }
2279 }
2280
2281 if (!redundant) {
2282 free(active);
2283 return qp;
2284 }
2285
2286 reordering = isl_alloc_array(qp->div->ctx, int, len);
2287 if (!reordering)
2288 goto error;
2289
2290 for (i = 0; i < d; ++i)
2291 reordering[i] = i;
2292
2293 skip = 0;
2294 n_div = qp->div->n_row;
2295 for (i = 0; i < n_div; ++i) {
2296 if (!active[d + i]) {
2297 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2298 qp->div = isl_mat_drop_cols(qp->div,
2299 2 + d + i - skip, 1);
2300 skip++;
2301 }
2302 reordering[d + i] = d + i - skip;
2303 }
2304
2305 qp->upoly = reorder(qp->upoly, reordering);
2306
2307 if (!qp->upoly || !qp->div)
2308 goto error;
2309
2310 free(active);
2311 free(reordering);
2312
2313 return qp;
2314 error:
2315 free(active);
2316 free(reordering);
2317 isl_qpolynomial_free(qp);
2318 return NULL;
2319 }
2320
2321 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2322 unsigned first, unsigned n)
2323 {
2324 int i;
2325 struct isl_upoly_rec *rec;
2326
2327 if (!up)
2328 return NULL;
2329 if (n == 0 || up->var < 0 || up->var < first)
2330 return up;
2331 if (up->var < first + n) {
2332 up = replace_by_constant_term(up);
2333 return isl_upoly_drop(up, first, n);
2334 }
2335 up = isl_upoly_cow(up);
2336 if (!up)
2337 return NULL;
2338 up->var -= n;
2339 rec = isl_upoly_as_rec(up);
2340 if (!rec)
2341 goto error;
2342
2343 for (i = 0; i < rec->n; ++i) {
2344 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2345 if (!rec->p[i])
2346 goto error;
2347 }
2348
2349 return up;
2350 error:
2351 isl_upoly_free(up);
2352 return NULL;
2353 }
2354
2355 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2356 __isl_take isl_qpolynomial *qp,
2357 enum isl_dim_type type, unsigned pos, const char *s)
2358 {
2359 qp = isl_qpolynomial_cow(qp);
2360 if (!qp)
2361 return NULL;
2362 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2363 if (!qp->dim)
2364 goto error;
2365 return qp;
2366 error:
2367 isl_qpolynomial_free(qp);
2368 return NULL;
2369 }
2370
2371 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2372 __isl_take isl_qpolynomial *qp,
2373 enum isl_dim_type type, unsigned first, unsigned n)
2374 {
2375 if (!qp)
2376 return NULL;
2377 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2378 return qp;
2379
2380 qp = isl_qpolynomial_cow(qp);
2381 if (!qp)
2382 return NULL;
2383
2384 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2385 goto error);
2386 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2387 type == isl_dim_set, goto error);
2388
2389 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2390 if (!qp->dim)
2391 goto error;
2392
2393 if (type == isl_dim_set)
2394 first += isl_space_dim(qp->dim, isl_dim_param);
2395
2396 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2397 if (!qp->div)
2398 goto error;
2399
2400 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2401 if (!qp->upoly)
2402 goto error;
2403
2404 return qp;
2405 error:
2406 isl_qpolynomial_free(qp);
2407 return NULL;
2408 }
2409
2410 /* Project the domain of the quasi-polynomial onto its parameter space.
2411 * The quasi-polynomial may not involve any of the domain dimensions.
2412 */
2413 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2414 __isl_take isl_qpolynomial *qp)
2415 {
2416 isl_space *space;
2417 unsigned n;
2418 int involves;
2419
2420 n = isl_qpolynomial_dim(qp, isl_dim_set);
2421 involves = isl_qpolynomial_involves_dims(qp, isl_dim_set, 0, n);
2422 if (involves < 0)
2423 return isl_qpolynomial_free(qp);
2424 if (involves)
2425 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2426 "polynomial involves some of the domain dimensions",
2427 return isl_qpolynomial_free(qp));
2428 qp = isl_qpolynomial_drop_dims(qp, isl_dim_set, 0, n);
2429 space = isl_qpolynomial_get_space(qp);
2430 space = isl_space_params(space);
2431 qp = isl_qpolynomial_reset_space(qp, space);
2432 return qp;
2433 }
2434
2435 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2436 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2437 {
2438 int i, j, k;
2439 isl_int denom;
2440 unsigned total;
2441 unsigned n_div;
2442 struct isl_upoly *up;
2443
2444 if (!eq)
2445 goto error;
2446 if (eq->n_eq == 0) {
2447 isl_basic_set_free(eq);
2448 return qp;
2449 }
2450
2451 qp = isl_qpolynomial_cow(qp);
2452 if (!qp)
2453 goto error;
2454 qp->div = isl_mat_cow(qp->div);
2455 if (!qp->div)
2456 goto error;
2457
2458 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2459 n_div = eq->n_div;
2460 isl_int_init(denom);
2461 for (i = 0; i < eq->n_eq; ++i) {
2462 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2463 if (j < 0 || j == 0 || j >= total)
2464 continue;
2465
2466 for (k = 0; k < qp->div->n_row; ++k) {
2467 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2468 continue;
2469 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2470 &qp->div->row[k][0]);
2471 normalize_div(qp, k);
2472 }
2473
2474 if (isl_int_is_pos(eq->eq[i][j]))
2475 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2476 isl_int_abs(denom, eq->eq[i][j]);
2477 isl_int_set_si(eq->eq[i][j], 0);
2478
2479 up = isl_upoly_from_affine(qp->dim->ctx,
2480 eq->eq[i], denom, total);
2481 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2482 isl_upoly_free(up);
2483 }
2484 isl_int_clear(denom);
2485
2486 if (!qp->upoly)
2487 goto error;
2488
2489 isl_basic_set_free(eq);
2490
2491 qp = substitute_non_divs(qp);
2492 qp = sort_divs(qp);
2493
2494 return qp;
2495 error:
2496 isl_basic_set_free(eq);
2497 isl_qpolynomial_free(qp);
2498 return NULL;
2499 }
2500
2501 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2502 */
2503 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2504 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2505 {
2506 if (!qp || !eq)
2507 goto error;
2508 if (qp->div->n_row > 0)
2509 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2510 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2511 error:
2512 isl_basic_set_free(eq);
2513 isl_qpolynomial_free(qp);
2514 return NULL;
2515 }
2516
2517 static __isl_give isl_basic_set *add_div_constraints(
2518 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2519 {
2520 int i;
2521 unsigned total;
2522
2523 if (!bset || !div)
2524 goto error;
2525
2526 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2527 if (!bset)
2528 goto error;
2529 total = isl_basic_set_total_dim(bset);
2530 for (i = 0; i < div->n_row; ++i)
2531 if (isl_basic_set_add_div_constraints_var(bset,
2532 total - div->n_row + i, div->row[i]) < 0)
2533 goto error;
2534
2535 isl_mat_free(div);
2536 return bset;
2537 error:
2538 isl_mat_free(div);
2539 isl_basic_set_free(bset);
2540 return NULL;
2541 }
2542
2543 /* Look for equalities among the variables shared by context and qp
2544 * and the integer divisions of qp, if any.
2545 * The equalities are then used to eliminate variables and/or integer
2546 * divisions from qp.
2547 */
2548 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2549 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2550 {
2551 isl_basic_set *aff;
2552
2553 if (!qp)
2554 goto error;
2555 if (qp->div->n_row > 0) {
2556 isl_basic_set *bset;
2557 context = isl_set_add_dims(context, isl_dim_set,
2558 qp->div->n_row);
2559 bset = isl_basic_set_universe(isl_set_get_space(context));
2560 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2561 context = isl_set_intersect(context,
2562 isl_set_from_basic_set(bset));
2563 }
2564
2565 aff = isl_set_affine_hull(context);
2566 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2567 error:
2568 isl_qpolynomial_free(qp);
2569 isl_set_free(context);
2570 return NULL;
2571 }
2572
2573 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2574 __isl_take isl_qpolynomial *qp)
2575 {
2576 isl_set *dom;
2577
2578 if (!qp)
2579 return NULL;
2580 if (isl_qpolynomial_is_zero(qp)) {
2581 isl_space *dim = isl_qpolynomial_get_space(qp);
2582 isl_qpolynomial_free(qp);
2583 return isl_pw_qpolynomial_zero(dim);
2584 }
2585
2586 dom = isl_set_universe(isl_qpolynomial_get_space(qp));
2587 return isl_pw_qpolynomial_alloc(dom, qp);
2588 }
2589
2590 #undef PW
2591 #define PW isl_pw_qpolynomial
2592 #undef EL
2593 #define EL isl_qpolynomial
2594 #undef EL_IS_ZERO
2595 #define EL_IS_ZERO is_zero
2596 #undef ZERO
2597 #define ZERO zero
2598 #undef IS_ZERO
2599 #define IS_ZERO is_zero
2600 #undef FIELD
2601 #define FIELD qp
2602
2603 #include <isl_pw_templ.c>
2604
2605 #undef UNION
2606 #define UNION isl_union_pw_qpolynomial
2607 #undef PART
2608 #define PART isl_pw_qpolynomial
2609 #undef PARTS
2610 #define PARTS pw_qpolynomial
2611
2612 #include <isl_union_templ.c>
2613
2614 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2615 {
2616 if (!pwqp)
2617 return -1;
2618
2619 if (pwqp->n != -1)
2620 return 0;
2621
2622 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2623 return 0;
2624
2625 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2626 }
2627
2628 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2629 __isl_take isl_pw_qpolynomial *pwqp1,
2630 __isl_take isl_pw_qpolynomial *pwqp2)
2631 {
2632 int i, j, n;
2633 struct isl_pw_qpolynomial *res;
2634
2635 if (!pwqp1 || !pwqp2)
2636 goto error;
2637
2638 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2639 goto error);
2640
2641 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2642 isl_pw_qpolynomial_free(pwqp2);
2643 return pwqp1;
2644 }
2645
2646 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2647 isl_pw_qpolynomial_free(pwqp1);
2648 return pwqp2;
2649 }
2650
2651 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2652 isl_pw_qpolynomial_free(pwqp1);
2653 return pwqp2;
2654 }
2655
2656 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2657 isl_pw_qpolynomial_free(pwqp2);
2658 return pwqp1;
2659 }
2660
2661 n = pwqp1->n * pwqp2->n;
2662 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2663
2664 for (i = 0; i < pwqp1->n; ++i) {
2665 for (j = 0; j < pwqp2->n; ++j) {
2666 struct isl_set *common;
2667 struct isl_qpolynomial *prod;
2668 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2669 isl_set_copy(pwqp2->p[j].set));
2670 if (isl_set_plain_is_empty(common)) {
2671 isl_set_free(common);
2672 continue;
2673 }
2674
2675 prod = isl_qpolynomial_mul(
2676 isl_qpolynomial_copy(pwqp1->p[i].qp),
2677 isl_qpolynomial_copy(pwqp2->p[j].qp));
2678
2679 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2680 }
2681 }
2682
2683 isl_pw_qpolynomial_free(pwqp1);
2684 isl_pw_qpolynomial_free(pwqp2);
2685
2686 return res;
2687 error:
2688 isl_pw_qpolynomial_free(pwqp1);
2689 isl_pw_qpolynomial_free(pwqp2);
2690 return NULL;
2691 }
2692
2693 __isl_give struct isl_upoly *isl_upoly_eval(
2694 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2695 {
2696 int i;
2697 struct isl_upoly_rec *rec;
2698 struct isl_upoly *res;
2699 struct isl_upoly *base;
2700
2701 if (isl_upoly_is_cst(up)) {
2702 isl_vec_free(vec);
2703 return up;
2704 }
2705
2706 rec = isl_upoly_as_rec(up);
2707 if (!rec)
2708 goto error;
2709
2710 isl_assert(up->ctx, rec->n >= 1, goto error);
2711
2712 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2713
2714 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2715 isl_vec_copy(vec));
2716
2717 for (i = rec->n - 2; i >= 0; --i) {
2718 res = isl_upoly_mul(res, isl_upoly_copy(base));
2719 res = isl_upoly_sum(res,
2720 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2721 isl_vec_copy(vec)));
2722 }
2723
2724 isl_upoly_free(base);
2725 isl_upoly_free(up);
2726 isl_vec_free(vec);
2727 return res;
2728 error:
2729 isl_upoly_free(up);
2730 isl_vec_free(vec);
2731 return NULL;
2732 }
2733
2734 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2735 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2736 {
2737 isl_vec *ext;
2738 struct isl_upoly *up;
2739 isl_space *dim;
2740
2741 if (!qp || !pnt)
2742 goto error;
2743 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2744
2745 if (qp->div->n_row == 0)
2746 ext = isl_vec_copy(pnt->vec);
2747 else {
2748 int i;
2749 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2750 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2751 if (!ext)
2752 goto error;
2753
2754 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2755 for (i = 0; i < qp->div->n_row; ++i) {
2756 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2757 1 + dim + i, &ext->el[1+dim+i]);
2758 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2759 qp->div->row[i][0]);
2760 }
2761 }
2762
2763 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2764 if (!up)
2765 goto error;
2766
2767 dim = isl_space_copy(qp->dim);
2768 isl_qpolynomial_free(qp);
2769 isl_point_free(pnt);
2770
2771 return isl_qpolynomial_alloc(dim, 0, up);
2772 error:
2773 isl_qpolynomial_free(qp);
2774 isl_point_free(pnt);
2775 return NULL;
2776 }
2777
2778 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2779 __isl_keep struct isl_upoly_cst *cst2)
2780 {
2781 int cmp;
2782 isl_int t;
2783 isl_int_init(t);
2784 isl_int_mul(t, cst1->n, cst2->d);
2785 isl_int_submul(t, cst2->n, cst1->d);
2786 cmp = isl_int_sgn(t);
2787 isl_int_clear(t);
2788 return cmp;
2789 }
2790
2791 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2792 __isl_keep isl_qpolynomial *qp2)
2793 {
2794 struct isl_upoly_cst *cst1, *cst2;
2795
2796 if (!qp1 || !qp2)
2797 return -1;
2798 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2799 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2800 if (isl_qpolynomial_is_nan(qp1))
2801 return -1;
2802 if (isl_qpolynomial_is_nan(qp2))
2803 return -1;
2804 cst1 = isl_upoly_as_cst(qp1->upoly);
2805 cst2 = isl_upoly_as_cst(qp2->upoly);
2806
2807 return isl_upoly_cmp(cst1, cst2) <= 0;
2808 }
2809
2810 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2811 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2812 {
2813 struct isl_upoly_cst *cst1, *cst2;
2814 int cmp;
2815
2816 if (!qp1 || !qp2)
2817 goto error;
2818 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2819 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2820 cst1 = isl_upoly_as_cst(qp1->upoly);
2821 cst2 = isl_upoly_as_cst(qp2->upoly);
2822 cmp = isl_upoly_cmp(cst1, cst2);
2823
2824 if (cmp <= 0) {
2825 isl_qpolynomial_free(qp2);
2826 } else {
2827 isl_qpolynomial_free(qp1);
2828 qp1 = qp2;
2829 }
2830 return qp1;
2831 error:
2832 isl_qpolynomial_free(qp1);
2833 isl_qpolynomial_free(qp2);
2834 return NULL;
2835 }
2836
2837 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2838 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2839 {
2840 struct isl_upoly_cst *cst1, *cst2;
2841 int cmp;
2842
2843 if (!qp1 || !qp2)
2844 goto error;
2845 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2846 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2847 cst1 = isl_upoly_as_cst(qp1->upoly);
2848 cst2 = isl_upoly_as_cst(qp2->upoly);
2849 cmp = isl_upoly_cmp(cst1, cst2);
2850
2851 if (cmp >= 0) {
2852 isl_qpolynomial_free(qp2);
2853 } else {
2854 isl_qpolynomial_free(qp1);
2855 qp1 = qp2;
2856 }
2857 return qp1;
2858 error:
2859 isl_qpolynomial_free(qp1);
2860 isl_qpolynomial_free(qp2);
2861 return NULL;
2862 }
2863
2864 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2865 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2866 unsigned first, unsigned n)
2867 {
2868 unsigned total;
2869 unsigned g_pos;
2870 int *exp;
2871
2872 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2873 return qp;
2874
2875 qp = isl_qpolynomial_cow(qp);
2876 if (!qp)
2877 return NULL;
2878
2879 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2880 goto error);
2881
2882 g_pos = pos(qp->dim, type) + first;
2883
2884 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2885 if (!qp->div)
2886 goto error;
2887
2888 total = qp->div->n_col - 2;
2889 if (total > g_pos) {
2890 int i;
2891 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2892 if (!exp)
2893 goto error;
2894 for (i = 0; i < total - g_pos; ++i)
2895 exp[i] = i + n;
2896 qp->upoly = expand(qp->upoly, exp, g_pos);
2897 free(exp);
2898 if (!qp->upoly)
2899 goto error;
2900 }
2901
2902 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2903 if (!qp->dim)
2904 goto error;
2905
2906 return qp;
2907 error:
2908 isl_qpolynomial_free(qp);
2909 return NULL;
2910 }
2911
2912 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2913 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2914 {
2915 unsigned pos;
2916
2917 pos = isl_qpolynomial_dim(qp, type);
2918
2919 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2920 }
2921
2922 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2923 __isl_take isl_pw_qpolynomial *pwqp,
2924 enum isl_dim_type type, unsigned n)
2925 {
2926 unsigned pos;
2927
2928 pos = isl_pw_qpolynomial_dim(pwqp, type);
2929
2930 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2931 }
2932
2933 static int *reordering_move(isl_ctx *ctx,
2934 unsigned len, unsigned dst, unsigned src, unsigned n)
2935 {
2936 int i;
2937 int *reordering;
2938
2939 reordering = isl_alloc_array(ctx, int, len);
2940 if (!reordering)
2941 return NULL;
2942
2943 if (dst <= src) {
2944 for (i = 0; i < dst; ++i)
2945 reordering[i] = i;
2946 for (i = 0; i < n; ++i)
2947 reordering[src + i] = dst + i;
2948 for (i = 0; i < src - dst; ++i)
2949 reordering[dst + i] = dst + n + i;
2950 for (i = 0; i < len - src - n; ++i)
2951 reordering[src + n + i] = src + n + i;
2952 } else {
2953 for (i = 0; i < src; ++i)
2954 reordering[i] = i;
2955 for (i = 0; i < n; ++i)
2956 reordering[src + i] = dst + i;
2957 for (i = 0; i < dst - src; ++i)
2958 reordering[src + n + i] = src + i;
2959 for (i = 0; i < len - dst - n; ++i)
2960 reordering[dst + n + i] = dst + n + i;
2961 }
2962
2963 return reordering;
2964 }
2965
2966 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2967 __isl_take isl_qpolynomial *qp,
2968 enum isl_dim_type dst_type, unsigned dst_pos,
2969 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2970 {
2971 unsigned g_dst_pos;
2972 unsigned g_src_pos;
2973 int *reordering;
2974
2975 qp = isl_qpolynomial_cow(qp);
2976 if (!qp)
2977 return NULL;
2978
2979 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
2980 goto error);
2981
2982 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2983 g_src_pos = pos(qp->dim, src_type) + src_pos;
2984 if (dst_type > src_type)
2985 g_dst_pos -= n;
2986
2987 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2988 if (!qp->div)
2989 goto error;
2990 qp = sort_divs(qp);
2991 if (!qp)
2992 goto error;
2993
2994 reordering = reordering_move(qp->dim->ctx,
2995 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2996 if (!reordering)
2997 goto error;
2998
2999 qp->upoly = reorder(qp->upoly, reordering);
3000 free(reordering);
3001 if (!qp->upoly)
3002 goto error;
3003
3004 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3005 if (!qp->dim)
3006 goto error;
3007
3008 return qp;
3009 error:
3010 isl_qpolynomial_free(qp);
3011 return NULL;
3012 }
3013
3014 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3015 isl_int *f, isl_int denom)
3016 {
3017 struct isl_upoly *up;
3018
3019 if (!dim)
3020 return NULL;
3021
3022 up = isl_upoly_from_affine(dim->ctx, f, denom,
3023 1 + isl_space_dim(dim, isl_dim_all));
3024
3025 return isl_qpolynomial_alloc(dim, 0, up);
3026 }
3027
3028 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3029 {
3030 isl_ctx *ctx;
3031 struct isl_upoly *up;
3032 isl_qpolynomial *qp;
3033
3034 if (!aff)
3035 return NULL;
3036
3037 ctx = isl_aff_get_ctx(aff);
3038 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3039 aff->v->size - 1);
3040
3041 qp = isl_qpolynomial_alloc(isl_aff_get_space(aff),
3042 aff->ls->div->n_row, up);
3043 if (!qp)
3044 goto error;
3045
3046 isl_mat_free(qp->div);
3047 qp->div = isl_mat_copy(aff->ls->div);
3048 qp->div = isl_mat_cow(qp->div);
3049 if (!qp->div)
3050 goto error;
3051
3052 isl_aff_free(aff);
3053 qp = reduce_divs(qp);
3054 qp = remove_redundant_divs(qp);
3055 return qp;
3056 error:
3057 isl_aff_free(aff);
3058 return NULL;
3059 }
3060
3061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3062 __isl_take isl_pw_aff *pwaff)
3063 {
3064 int i;
3065 isl_pw_qpolynomial *pwqp;
3066
3067 if (!pwaff)
3068 return NULL;
3069
3070 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3071 pwaff->n);
3072
3073 for (i = 0; i < pwaff->n; ++i) {
3074 isl_set *dom;
3075 isl_qpolynomial *qp;
3076
3077 dom = isl_set_copy(pwaff->p[i].set);
3078 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3079 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3080 }
3081
3082 isl_pw_aff_free(pwaff);
3083 return pwqp;
3084 }
3085
3086 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3087 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3088 {
3089 isl_aff *aff;
3090
3091 aff = isl_constraint_get_bound(c, type, pos);
3092 isl_constraint_free(c);
3093 return isl_qpolynomial_from_aff(aff);
3094 }
3095
3096 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3097 * in "qp" by subs[i].
3098 */
3099 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3100 __isl_take isl_qpolynomial *qp,
3101 enum isl_dim_type type, unsigned first, unsigned n,
3102 __isl_keep isl_qpolynomial **subs)
3103 {
3104 int i;
3105 struct isl_upoly **ups;
3106
3107 if (n == 0)
3108 return qp;
3109
3110 qp = isl_qpolynomial_cow(qp);
3111 if (!qp)
3112 return NULL;
3113 for (i = 0; i < n; ++i)
3114 if (!subs[i])
3115 goto error;
3116
3117 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3118 goto error);
3119
3120 for (i = 0; i < n; ++i)
3121 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3122 goto error);
3123
3124 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3125 for (i = 0; i < n; ++i)
3126 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3127
3128 first += pos(qp->dim, type);
3129
3130 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3131 if (!ups)
3132 goto error;
3133 for (i = 0; i < n; ++i)
3134 ups[i] = subs[i]->upoly;
3135
3136 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3137
3138 free(ups);
3139
3140 if (!qp->upoly)
3141 goto error;
3142
3143 return qp;
3144 error:
3145 isl_qpolynomial_free(qp);
3146 return NULL;
3147 }
3148
3149 /* Extend "bset" with extra set dimensions for each integer division
3150 * in "qp" and then call "fn" with the extended bset and the polynomial
3151 * that results from replacing each of the integer divisions by the
3152 * corresponding extra set dimension.
3153 */
3154 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3155 __isl_keep isl_basic_set *bset,
3156 int (*fn)(__isl_take isl_basic_set *bset,
3157 __isl_take isl_qpolynomial *poly, void *user), void *user)
3158 {
3159 isl_space *dim;
3160 isl_mat *div;
3161 isl_qpolynomial *poly;
3162
3163 if (!qp || !bset)
3164 goto error;
3165 if (qp->div->n_row == 0)
3166 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3167 user);
3168
3169 div = isl_mat_copy(qp->div);
3170 dim = isl_space_copy(qp->dim);
3171 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3172 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3173 bset = isl_basic_set_copy(bset);
3174 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3175 bset = add_div_constraints(bset, div);
3176
3177 return fn(bset, poly, user);
3178 error:
3179 return -1;
3180 }
3181
3182 /* Return total degree in variables first (inclusive) up to last (exclusive).
3183 */
3184 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3185 {
3186 int deg = -1;
3187 int i;
3188 struct isl_upoly_rec *rec;
3189
3190 if (!up)
3191 return -2;
3192 if (isl_upoly_is_zero(up))
3193 return -1;
3194 if (isl_upoly_is_cst(up) || up->var < first)
3195 return 0;
3196
3197 rec = isl_upoly_as_rec(up);
3198 if (!rec)
3199 return -2;
3200
3201 for (i = 0; i < rec->n; ++i) {
3202 int d;
3203
3204 if (isl_upoly_is_zero(rec->p[i]))
3205 continue;
3206 d = isl_upoly_degree(rec->p[i], first, last);
3207 if (up->var < last)
3208 d += i;
3209 if (d > deg)
3210 deg = d;
3211 }
3212
3213 return deg;
3214 }
3215
3216 /* Return total degree in set variables.
3217 */
3218 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3219 {
3220 unsigned ovar;
3221 unsigned nvar;
3222
3223 if (!poly)
3224 return -2;
3225
3226 ovar = isl_space_offset(poly->dim, isl_dim_set);
3227 nvar = isl_space_dim(poly->dim, isl_dim_set);
3228 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3229 }
3230
3231 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3232 unsigned pos, int deg)
3233 {
3234 int i;
3235 struct isl_upoly_rec *rec;
3236
3237 if (!up)
3238 return NULL;
3239
3240 if (isl_upoly_is_cst(up) || up->var < pos) {
3241 if (deg == 0)
3242 return isl_upoly_copy(up);
3243 else
3244 return isl_upoly_zero(up->ctx);
3245 }
3246
3247 rec = isl_upoly_as_rec(up);
3248 if (!rec)
3249 return NULL;
3250
3251 if (up->var == pos) {
3252 if (deg < rec->n)
3253 return isl_upoly_copy(rec->p[deg]);
3254 else
3255 return isl_upoly_zero(up->ctx);
3256 }
3257
3258 up = isl_upoly_copy(up);
3259 up = isl_upoly_cow(up);
3260 rec = isl_upoly_as_rec(up);
3261 if (!rec)
3262 goto error;
3263
3264 for (i = 0; i < rec->n; ++i) {
3265 struct isl_upoly *t;
3266 t = isl_upoly_coeff(rec->p[i], pos, deg);
3267 if (!t)
3268 goto error;
3269 isl_upoly_free(rec->p[i]);
3270 rec->p[i] = t;
3271 }
3272
3273 return up;
3274 error:
3275 isl_upoly_free(up);
3276 return NULL;
3277 }
3278
3279 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3280 */
3281 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3282 __isl_keep isl_qpolynomial *qp,
3283 enum isl_dim_type type, unsigned t_pos, int deg)
3284 {
3285 unsigned g_pos;
3286 struct isl_upoly *up;
3287 isl_qpolynomial *c;
3288
3289 if (!qp)
3290 return NULL;
3291
3292 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3293 return NULL);
3294
3295 g_pos = pos(qp->dim, type) + t_pos;
3296 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3297
3298 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3299 if (!c)
3300 return NULL;
3301 isl_mat_free(c->div);
3302 c->div = isl_mat_copy(qp->div);
3303 if (!c->div)
3304 goto error;
3305 return c;
3306 error:
3307 isl_qpolynomial_free(c);
3308 return NULL;
3309 }
3310
3311 /* Homogenize the polynomial in the variables first (inclusive) up to
3312 * last (exclusive) by inserting powers of variable first.
3313 * Variable first is assumed not to appear in the input.
3314 */
3315 __isl_give struct isl_upoly *isl_upoly_homogenize(
3316 __isl_take struct isl_upoly *up, int deg, int target,
3317 int first, int last)
3318 {
3319 int i;
3320 struct isl_upoly_rec *rec;
3321
3322 if (!up)
3323 return NULL;
3324 if (isl_upoly_is_zero(up))
3325 return up;
3326 if (deg == target)
3327 return up;
3328 if (isl_upoly_is_cst(up) || up->var < first) {
3329 struct isl_upoly *hom;
3330
3331 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3332 if (!hom)
3333 goto error;
3334 rec = isl_upoly_as_rec(hom);
3335 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3336
3337 return hom;
3338 }
3339
3340 up = isl_upoly_cow(up);
3341 rec = isl_upoly_as_rec(up);
3342 if (!rec)
3343 goto error;
3344
3345 for (i = 0; i < rec->n; ++i) {
3346 if (isl_upoly_is_zero(rec->p[i]))
3347 continue;
3348 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3349 up->var < last ? deg + i : i, target,
3350 first, last);
3351 if (!rec->p[i])
3352 goto error;
3353 }
3354
3355 return up;
3356 error:
3357 isl_upoly_free(up);
3358 return NULL;
3359 }
3360
3361 /* Homogenize the polynomial in the set variables by introducing
3362 * powers of an extra set variable at position 0.
3363 */
3364 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3365 __isl_take isl_qpolynomial *poly)
3366 {
3367 unsigned ovar;
3368 unsigned nvar;
3369 int deg = isl_qpolynomial_degree(poly);
3370
3371 if (deg < -1)
3372 goto error;
3373
3374 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3375 poly = isl_qpolynomial_cow(poly);
3376 if (!poly)
3377 goto error;
3378
3379 ovar = isl_space_offset(poly->dim, isl_dim_set);
3380 nvar = isl_space_dim(poly->dim, isl_dim_set);
3381 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3382 ovar, ovar + nvar);
3383 if (!poly->upoly)
3384 goto error;
3385
3386 return poly;
3387 error:
3388 isl_qpolynomial_free(poly);
3389 return NULL;
3390 }
3391
3392 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3393 __isl_take isl_mat *div)
3394 {
3395 isl_term *term;
3396 int n;
3397
3398 if (!dim || !div)
3399 goto error;
3400
3401 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3402
3403 term = isl_calloc(dim->ctx, struct isl_term,
3404 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3405 if (!term)
3406 goto error;
3407
3408 term->ref = 1;
3409 term->dim = dim;
3410 term->div = div;
3411 isl_int_init(term->n);
3412 isl_int_init(term->d);
3413
3414 return term;
3415 error:
3416 isl_space_free(dim);
3417 isl_mat_free(div);
3418 return NULL;
3419 }
3420
3421 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3422 {
3423 if (!term)
3424 return NULL;
3425
3426 term->ref++;
3427 return term;
3428 }
3429
3430 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3431 {
3432 int i;
3433 isl_term *dup;
3434 unsigned total;
3435
3436 if (term)
3437 return NULL;
3438
3439 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3440
3441 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3442 if (!dup)
3443 return NULL;
3444
3445 isl_int_set(dup->n, term->n);
3446 isl_int_set(dup->d, term->d);
3447
3448 for (i = 0; i < total; ++i)
3449 dup->pow[i] = term->pow[i];
3450
3451 return dup;
3452 }
3453
3454 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3455 {
3456 if (!term)
3457 return NULL;
3458
3459 if (term->ref == 1)
3460 return term;
3461 term->ref--;
3462 return isl_term_dup(term);
3463 }
3464
3465 void isl_term_free(__isl_take isl_term *term)
3466 {
3467 if (!term)
3468 return;
3469
3470 if (--term->ref > 0)
3471 return;
3472
3473 isl_space_free(term->dim);
3474 isl_mat_free(term->div);
3475 isl_int_clear(term->n);
3476 isl_int_clear(term->d);
3477 free(term);
3478 }
3479
3480 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3481 {
3482 if (!term)
3483 return 0;
3484
3485 switch (type) {
3486 case isl_dim_param:
3487 case isl_dim_in:
3488 case isl_dim_out: return isl_space_dim(term->dim, type);
3489 case isl_dim_div: return term->div->n_row;
3490 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3491 term->div->n_row;
3492 default: return 0;
3493 }
3494 }
3495
3496 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3497 {
3498 return term ? term->dim->ctx : NULL;
3499 }
3500
3501 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3502 {
3503 if (!term)
3504 return;
3505 isl_int_set(*n, term->n);
3506 }
3507
3508 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3509 {
3510 if (!term)
3511 return;
3512 isl_int_set(*d, term->d);
3513 }
3514
3515 int isl_term_get_exp(__isl_keep isl_term *term,
3516 enum isl_dim_type type, unsigned pos)
3517 {
3518 if (!term)
3519 return -1;
3520
3521 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3522
3523 if (type >= isl_dim_set)
3524 pos += isl_space_dim(term->dim, isl_dim_param);
3525 if (type >= isl_dim_div)
3526 pos += isl_space_dim(term->dim, isl_dim_set);
3527
3528 return term->pow[pos];
3529 }
3530
3531 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3532 {
3533 isl_basic_map *bmap;
3534 unsigned total;
3535 int k;
3536
3537 if (!term)
3538 return NULL;
3539
3540 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3541 return NULL);
3542
3543 total = term->div->n_col - term->div->n_row - 2;
3544 /* No nested divs for now */
3545 isl_assert(term->dim->ctx,
3546 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3547 term->div->n_row) == -1,
3548 return NULL);
3549
3550 bmap = isl_basic_map_alloc_space(isl_space_copy(term->dim), 1, 0, 0);
3551 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3552 goto error;
3553
3554 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3555
3556 return isl_basic_map_div(bmap, k);
3557 error:
3558 isl_basic_map_free(bmap);
3559 return NULL;
3560 }
3561
3562 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3563 int (*fn)(__isl_take isl_term *term, void *user),
3564 __isl_take isl_term *term, void *user)
3565 {
3566 int i;
3567 struct isl_upoly_rec *rec;
3568
3569 if (!up || !term)
3570 goto error;
3571
3572 if (isl_upoly_is_zero(up))
3573 return term;
3574
3575 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3576 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3577 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3578
3579 if (isl_upoly_is_cst(up)) {
3580 struct isl_upoly_cst *cst;
3581 cst = isl_upoly_as_cst(up);
3582 if (!cst)
3583 goto error;
3584 term = isl_term_cow(term);
3585 if (!term)
3586 goto error;
3587 isl_int_set(term->n, cst->n);
3588 isl_int_set(term->d, cst->d);
3589 if (fn(isl_term_copy(term), user) < 0)
3590 goto error;
3591 return term;
3592 }
3593
3594 rec = isl_upoly_as_rec(up);
3595 if (!rec)
3596 goto error;
3597
3598 for (i = 0; i < rec->n; ++i) {
3599 term = isl_term_cow(term);
3600 if (!term)
3601 goto error;
3602 term->pow[up->var] = i;
3603 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3604 if (!term)
3605 goto error;
3606 }
3607 term->pow[up->var] = 0;
3608
3609 return term;
3610 error:
3611 isl_term_free(term);
3612 return NULL;
3613 }
3614
3615 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3616 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3617 {
3618 isl_term *term;
3619
3620 if (!qp)
3621 return -1;
3622
3623 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3624 if (!term)
3625 return -1;
3626
3627 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3628
3629 isl_term_free(term);
3630
3631 return term ? 0 : -1;
3632 }
3633
3634 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3635 {
3636 struct isl_upoly *up;
3637 isl_qpolynomial *qp;
3638 int i, n;
3639
3640 if (!term)
3641 return NULL;
3642
3643 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3644
3645 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3646 for (i = 0; i < n; ++i) {
3647 if (!term->pow[i])
3648 continue;
3649 up = isl_upoly_mul(up,
3650 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3651 }
3652
3653 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3654 if (!qp)
3655 goto error;
3656 isl_mat_free(qp->div);
3657 qp->div = isl_mat_copy(term->div);
3658 if (!qp->div)
3659 goto error;
3660
3661 isl_term_free(term);
3662 return qp;
3663 error:
3664 isl_qpolynomial_free(qp);
3665 isl_term_free(term);
3666 return NULL;
3667 }
3668
3669 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3670 __isl_take isl_space *dim)
3671 {
3672 int i;
3673 int extra;
3674 unsigned total;
3675
3676 if (!qp || !dim)
3677 goto error;
3678
3679 if (isl_space_is_equal(qp->dim, dim)) {
3680 isl_space_free(dim);
3681 return qp;
3682 }
3683
3684 qp = isl_qpolynomial_cow(qp);
3685 if (!qp)
3686 goto error;
3687
3688 extra = isl_space_dim(dim, isl_dim_set) -
3689 isl_space_dim(qp->dim, isl_dim_set);
3690 total = isl_space_dim(qp->dim, isl_dim_all);
3691 if (qp->div->n_row) {
3692 int *exp;
3693
3694 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3695 if (!exp)
3696 goto error;
3697 for (i = 0; i < qp->div->n_row; ++i)
3698 exp[i] = extra + i;
3699 qp->upoly = expand(qp->upoly, exp, total);
3700 free(exp);
3701 if (!qp->upoly)
3702 goto error;
3703 }
3704 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3705 if (!qp->div)
3706 goto error;
3707 for (i = 0; i < qp->div->n_row; ++i)
3708 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3709
3710 isl_space_free(qp->dim);
3711 qp->dim = dim;
3712
3713 return qp;
3714 error:
3715 isl_space_free(dim);
3716 isl_qpolynomial_free(qp);
3717 return NULL;
3718 }
3719
3720 /* For each parameter or variable that does not appear in qp,
3721 * first eliminate the variable from all constraints and then set it to zero.
3722 */
3723 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3724 __isl_keep isl_qpolynomial *qp)
3725 {
3726 int *active = NULL;
3727 int i;
3728 int d;
3729 unsigned nparam;
3730 unsigned nvar;
3731
3732 if (!set || !qp)
3733 goto error;
3734
3735 d = isl_space_dim(set->dim, isl_dim_all);
3736 active = isl_calloc_array(set->ctx, int, d);
3737 if (set_active(qp, active) < 0)
3738 goto error;
3739
3740 for (i = 0; i < d; ++i)
3741 if (!active[i])
3742 break;
3743
3744 if (i == d) {
3745 free(active);
3746 return set;
3747 }
3748
3749 nparam = isl_space_dim(set->dim, isl_dim_param);
3750 nvar = isl_space_dim(set->dim, isl_dim_set);
3751 for (i = 0; i < nparam; ++i) {
3752 if (active[i])
3753 continue;
3754 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3755 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3756 }
3757 for (i = 0; i < nvar; ++i) {
3758 if (active[nparam + i])
3759 continue;
3760 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3761 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3762 }
3763
3764 free(active);
3765
3766 return set;
3767 error:
3768 free(active);
3769 isl_set_free(set);
3770 return NULL;
3771 }
3772
3773 struct isl_opt_data {
3774 isl_qpolynomial *qp;
3775 int first;
3776 isl_qpolynomial *opt;
3777 int max;
3778 };
3779
3780 static int opt_fn(__isl_take isl_point *pnt, void *user)
3781 {
3782 struct isl_opt_data *data = (struct isl_opt_data *)user;
3783 isl_qpolynomial *val;
3784
3785 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3786 if (data->first) {
3787 data->first = 0;
3788 data->opt = val;
3789 } else if (data->max) {
3790 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3791 } else {
3792 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3793 }
3794
3795 return 0;
3796 }
3797
3798 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3799 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3800 {
3801 struct isl_opt_data data = { NULL, 1, NULL, max };
3802
3803 if (!set || !qp)
3804 goto error;
3805
3806 if (isl_upoly_is_cst(qp->upoly)) {
3807 isl_set_free(set);
3808 return qp;
3809 }
3810
3811 set = fix_inactive(set, qp);
3812
3813 data.qp = qp;
3814 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3815 goto error;
3816
3817 if (data.first)
3818 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_space(qp));
3819
3820 isl_set_free(set);
3821 isl_qpolynomial_free(qp);
3822 return data.opt;
3823 error:
3824 isl_set_free(set);
3825 isl_qpolynomial_free(qp);
3826 isl_qpolynomial_free(data.opt);
3827 return NULL;
3828 }
3829
3830 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3831 __isl_take isl_morph *morph)
3832 {
3833 int i;
3834 int n_sub;
3835 isl_ctx *ctx;
3836 struct isl_upoly **subs;
3837 isl_mat *mat;
3838
3839 qp = isl_qpolynomial_cow(qp);
3840 if (!qp || !morph)
3841 goto error;
3842
3843 ctx = qp->dim->ctx;
3844 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3845
3846 n_sub = morph->inv->n_row - 1;
3847 if (morph->inv->n_row != morph->inv->n_col)
3848 n_sub += qp->div->n_row;
3849 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3850 if (!subs)
3851 goto error;
3852
3853 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3854 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3855 morph->inv->row[0][0], morph->inv->n_col);
3856 if (morph->inv->n_row != morph->inv->n_col)
3857 for (i = 0; i < qp->div->n_row; ++i)
3858 subs[morph->inv->n_row - 1 + i] =
3859 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3860
3861 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3862
3863 for (i = 0; i < n_sub; ++i)
3864 isl_upoly_free(subs[i]);
3865 free(subs);
3866
3867 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3868 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3869 qp->div = isl_mat_product(qp->div, mat);
3870 isl_space_free(qp->dim);
3871 qp->dim = isl_space_copy(morph->ran->dim);
3872
3873 if (!qp->upoly || !qp->div || !qp->dim)
3874 goto error;
3875
3876 isl_morph_free(morph);
3877
3878 return qp;
3879 error:
3880 isl_qpolynomial_free(qp);
3881 isl_morph_free(morph);
3882 return NULL;
3883 }
3884
3885 static int neg_entry(void **entry, void *user)
3886 {
3887 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3888
3889 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3890
3891 return *pwqp ? 0 : -1;
3892 }
3893
3894 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3895 __isl_take isl_union_pw_qpolynomial *upwqp)
3896 {
3897 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3898 if (!upwqp)
3899 return NULL;
3900
3901 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3902 &neg_entry, NULL) < 0)
3903 goto error;
3904
3905 return upwqp;
3906 error:
3907 isl_union_pw_qpolynomial_free(upwqp);
3908 return NULL;
3909 }
3910
3911 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3912 __isl_take isl_union_pw_qpolynomial *upwqp1,
3913 __isl_take isl_union_pw_qpolynomial *upwqp2)
3914 {
3915 return isl_union_pw_qpolynomial_add(upwqp1,
3916 isl_union_pw_qpolynomial_neg(upwqp2));
3917 }
3918
3919 static int mul_entry(void **entry, void *user)
3920 {
3921 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3922 uint32_t hash;
3923 struct isl_hash_table_entry *entry2;
3924 isl_pw_qpolynomial *pwpq = *entry;
3925 int empty;
3926
3927 hash = isl_space_get_hash(pwpq->dim);
3928 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3929 hash, &has_dim, pwpq->dim, 0);
3930 if (!entry2)
3931 return 0;
3932
3933 pwpq = isl_pw_qpolynomial_copy(pwpq);
3934 pwpq = isl_pw_qpolynomial_mul(pwpq,
3935 isl_pw_qpolynomial_copy(entry2->data));
3936
3937 empty = isl_pw_qpolynomial_is_zero(pwpq);
3938 if (empty < 0) {
3939 isl_pw_qpolynomial_free(pwpq);
3940 return -1;
3941 }
3942 if (empty) {
3943 isl_pw_qpolynomial_free(pwpq);
3944 return 0;
3945 }
3946
3947 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3948
3949 return 0;
3950 }
3951
3952 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3953 __isl_take isl_union_pw_qpolynomial *upwqp1,
3954 __isl_take isl_union_pw_qpolynomial *upwqp2)
3955 {
3956 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3957 }
3958
3959 /* Reorder the columns of the given div definitions according to the
3960 * given reordering.
3961 */
3962 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3963 __isl_take isl_reordering *r)
3964 {
3965 int i, j;
3966 isl_mat *mat;
3967 int extra;
3968
3969 if (!div || !r)
3970 goto error;
3971
3972 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
3973 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3974 if (!mat)
3975 goto error;
3976
3977 for (i = 0; i < div->n_row; ++i) {
3978 isl_seq_cpy(mat->row[i], div->row[i], 2);
3979 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3980 for (j = 0; j < r->len; ++j)
3981 isl_int_set(mat->row[i][2 + r->pos[j]],
3982 div->row[i][2 + j]);
3983 }
3984
3985 isl_reordering_free(r);
3986 isl_mat_free(div);
3987 return mat;
3988 error:
3989 isl_reordering_free(r);
3990 isl_mat_free(div);
3991 return NULL;
3992 }
3993
3994 /* Reorder the dimension of "qp" according to the given reordering.
3995 */
3996 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3997 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3998 {
3999 qp = isl_qpolynomial_cow(qp);
4000 if (!qp)
4001 goto error;
4002
4003 r = isl_reordering_extend(r, qp->div->n_row);
4004 if (!r)
4005 goto error;
4006
4007 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4008 if (!qp->div)
4009 goto error;
4010
4011 qp->upoly = reorder(qp->upoly, r->pos);
4012 if (!qp->upoly)
4013 goto error;
4014
4015 qp = isl_qpolynomial_reset_space(qp, isl_space_copy(r->dim));
4016
4017 isl_reordering_free(r);
4018 return qp;
4019 error:
4020 isl_qpolynomial_free(qp);
4021 isl_reordering_free(r);
4022 return NULL;
4023 }
4024
4025 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4026 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4027 {
4028 if (!qp || !model)
4029 goto error;
4030
4031 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4032 isl_reordering *exp;
4033
4034 model = isl_space_drop_dims(model, isl_dim_in,
4035 0, isl_space_dim(model, isl_dim_in));
4036 model = isl_space_drop_dims(model, isl_dim_out,
4037 0, isl_space_dim(model, isl_dim_out));
4038 exp = isl_parameter_alignment_reordering(qp->dim, model);
4039 exp = isl_reordering_extend_space(exp,
4040 isl_qpolynomial_get_space(qp));
4041 qp = isl_qpolynomial_realign(qp, exp);
4042 }
4043
4044 isl_space_free(model);
4045 return qp;
4046 error:
4047 isl_space_free(model);
4048 isl_qpolynomial_free(qp);
4049 return NULL;
4050 }
4051
4052 struct isl_split_periods_data {
4053 int max_periods;
4054 isl_pw_qpolynomial *res;
4055 };
4056
4057 /* Create a slice where the integer division "div" has the fixed value "v".
4058 * In particular, if "div" refers to floor(f/m), then create a slice
4059 *
4060 * m v <= f <= m v + (m - 1)
4061 *
4062 * or
4063 *
4064 * f - m v >= 0
4065 * -f + m v + (m - 1) >= 0
4066 */
4067 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4068 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4069 {
4070 int total;
4071 isl_basic_set *bset = NULL;
4072 int k;
4073
4074 if (!dim || !qp)
4075 goto error;
4076
4077 total = isl_space_dim(dim, isl_dim_all);
4078 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4079
4080 k = isl_basic_set_alloc_inequality(bset);
4081 if (k < 0)
4082 goto error;
4083 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4084 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4085
4086 k = isl_basic_set_alloc_inequality(bset);
4087 if (k < 0)
4088 goto error;
4089 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4090 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4091 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4092 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4093
4094 isl_space_free(dim);
4095 return isl_set_from_basic_set(bset);
4096 error:
4097 isl_basic_set_free(bset);
4098 isl_space_free(dim);
4099 return NULL;
4100 }
4101
4102 static int split_periods(__isl_take isl_set *set,
4103 __isl_take isl_qpolynomial *qp, void *user);
4104
4105 /* Create a slice of the domain "set" such that integer division "div"
4106 * has the fixed value "v" and add the results to data->res,
4107 * replacing the integer division by "v" in "qp".
4108 */
4109 static int set_div(__isl_take isl_set *set,
4110 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4111 struct isl_split_periods_data *data)
4112 {
4113 int i;
4114 int total;
4115 isl_set *slice;
4116 struct isl_upoly *cst;
4117
4118 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4119 set = isl_set_intersect(set, slice);
4120
4121 if (!qp)
4122 goto error;
4123
4124 total = isl_space_dim(qp->dim, isl_dim_all);
4125
4126 for (i = div + 1; i < qp->div->n_row; ++i) {
4127 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4128 continue;
4129 isl_int_addmul(qp->div->row[i][1],
4130 qp->div->row[i][2 + total + div], v);
4131 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4132 }
4133
4134 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4135 qp = substitute_div(qp, div, cst);
4136
4137 return split_periods(set, qp, data);
4138 error:
4139 isl_set_free(set);
4140 isl_qpolynomial_free(qp);
4141 return -1;
4142 }
4143
4144 /* Split the domain "set" such that integer division "div"
4145 * has a fixed value (ranging from "min" to "max") on each slice
4146 * and add the results to data->res.
4147 */
4148 static int split_div(__isl_take isl_set *set,
4149 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4150 struct isl_split_periods_data *data)
4151 {
4152 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4153 isl_set *set_i = isl_set_copy(set);
4154 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4155
4156 if (set_div(set_i, qp_i, div, min, data) < 0)
4157 goto error;
4158 }
4159 isl_set_free(set);
4160 isl_qpolynomial_free(qp);
4161 return 0;
4162 error:
4163 isl_set_free(set);
4164 isl_qpolynomial_free(qp);
4165 return -1;
4166 }
4167
4168 /* If "qp" refers to any integer division
4169 * that can only attain "max_periods" distinct values on "set"
4170 * then split the domain along those distinct values.
4171 * Add the results (or the original if no splitting occurs)
4172 * to data->res.
4173 */
4174 static int split_periods(__isl_take isl_set *set,
4175 __isl_take isl_qpolynomial *qp, void *user)
4176 {
4177 int i;
4178 isl_pw_qpolynomial *pwqp;
4179 struct isl_split_periods_data *data;
4180 isl_int min, max;
4181 int total;
4182 int r = 0;
4183
4184 data = (struct isl_split_periods_data *)user;
4185
4186 if (!set || !qp)
4187 goto error;
4188
4189 if (qp->div->n_row == 0) {
4190 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4191 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4192 return 0;
4193 }
4194
4195 isl_int_init(min);
4196 isl_int_init(max);
4197 total = isl_space_dim(qp->dim, isl_dim_all);
4198 for (i = 0; i < qp->div->n_row; ++i) {
4199 enum isl_lp_result lp_res;
4200
4201 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4202 qp->div->n_row) != -1)
4203 continue;
4204
4205 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4206 set->ctx->one, &min, NULL, NULL);
4207 if (lp_res == isl_lp_error)
4208 goto error2;
4209 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4210 continue;
4211 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4212
4213 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4214 set->ctx->one, &max, NULL, NULL);
4215 if (lp_res == isl_lp_error)
4216 goto error2;
4217 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4218 continue;
4219 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4220
4221 isl_int_sub(max, max, min);
4222 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4223 isl_int_add(max, max, min);
4224 break;
4225 }
4226 }
4227
4228 if (i < qp->div->n_row) {
4229 r = split_div(set, qp, i, min, max, data);
4230 } else {
4231 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4232 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4233 }
4234
4235 isl_int_clear(max);
4236 isl_int_clear(min);
4237
4238 return r;
4239 error2:
4240 isl_int_clear(max);
4241 isl_int_clear(min);
4242 error:
4243 isl_set_free(set);
4244 isl_qpolynomial_free(qp);
4245 return -1;
4246 }
4247
4248 /* If any quasi-polynomial in pwqp refers to any integer division
4249 * that can only attain "max_periods" distinct values on its domain
4250 * then split the domain along those distinct values.
4251 */
4252 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4253 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4254 {
4255 struct isl_split_periods_data data;
4256
4257 data.max_periods = max_periods;
4258 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4259
4260 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4261 goto error;
4262
4263 isl_pw_qpolynomial_free(pwqp);
4264
4265 return data.res;
4266 error:
4267 isl_pw_qpolynomial_free(data.res);
4268 isl_pw_qpolynomial_free(pwqp);
4269 return NULL;
4270 }
4271
4272 /* Construct a piecewise quasipolynomial that is constant on the given
4273 * domain. In particular, it is
4274 * 0 if cst == 0
4275 * 1 if cst == 1
4276 * infinity if cst == -1
4277 */
4278 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4279 __isl_take isl_basic_set *bset, int cst)
4280 {
4281 isl_space *dim;
4282 isl_qpolynomial *qp;
4283
4284 if (!bset)
4285 return NULL;
4286
4287 bset = isl_basic_set_params(bset);
4288 dim = isl_basic_set_get_space(bset);
4289 if (cst < 0)
4290 qp = isl_qpolynomial_infty(dim);
4291 else if (cst == 0)
4292 qp = isl_qpolynomial_zero(dim);
4293 else
4294 qp = isl_qpolynomial_one(dim);
4295 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4296 }
4297
4298 /* Factor bset, call fn on each of the factors and return the product.
4299 *
4300 * If no factors can be found, simply call fn on the input.
4301 * Otherwise, construct the factors based on the factorizer,
4302 * call fn on each factor and compute the product.
4303 */
4304 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4305 __isl_take isl_basic_set *bset,
4306 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4307 {
4308 int i, n;
4309 isl_space *dim;
4310 isl_set *set;
4311 isl_factorizer *f;
4312 isl_qpolynomial *qp;
4313 isl_pw_qpolynomial *pwqp;
4314 unsigned nparam;
4315 unsigned nvar;
4316
4317 f = isl_basic_set_factorizer(bset);
4318 if (!f)
4319 goto error;
4320 if (f->n_group == 0) {
4321 isl_factorizer_free(f);
4322 return fn(bset);
4323 }
4324
4325 nparam = isl_basic_set_dim(bset, isl_dim_param);
4326 nvar = isl_basic_set_dim(bset, isl_dim_set);
4327
4328 dim = isl_basic_set_get_space(bset);
4329 dim = isl_space_domain(dim);
4330 set = isl_set_universe(isl_space_copy(dim));
4331 qp = isl_qpolynomial_one(dim);
4332 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4333
4334 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4335
4336 for (i = 0, n = 0; i < f->n_group; ++i) {
4337 isl_basic_set *bset_i;
4338 isl_pw_qpolynomial *pwqp_i;
4339
4340 bset_i = isl_basic_set_copy(bset);
4341 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4342 nparam + n + f->len[i], nvar - n - f->len[i]);
4343 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4344 nparam, n);
4345 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4346 n + f->len[i], nvar - n - f->len[i]);
4347 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4348
4349 pwqp_i = fn(bset_i);
4350 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4351
4352 n += f->len[i];
4353 }
4354
4355 isl_basic_set_free(bset);
4356 isl_factorizer_free(f);
4357
4358 return pwqp;
4359 error:
4360 isl_basic_set_free(bset);
4361 return NULL;
4362 }
4363
4364 /* Factor bset, call fn on each of the factors and return the product.
4365 * The function is assumed to evaluate to zero on empty domains,
4366 * to one on zero-dimensional domains and to infinity on unbounded domains
4367 * and will not be called explicitly on zero-dimensional or unbounded domains.
4368 *
4369 * We first check for some special cases and remove all equalities.
4370 * Then we hand over control to compressed_multiplicative_call.
4371 */
4372 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4373 __isl_take isl_basic_set *bset,
4374 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4375 {
4376 int bounded;
4377 isl_morph *morph;
4378 isl_pw_qpolynomial *pwqp;
4379
4380 if (!bset)
4381 return NULL;
4382
4383 if (isl_basic_set_plain_is_empty(bset))
4384 return constant_on_domain(bset, 0);
4385
4386 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4387 return constant_on_domain(bset, 1);
4388
4389 bounded = isl_basic_set_is_bounded(bset);
4390 if (bounded < 0)
4391 goto error;
4392 if (!bounded)
4393 return constant_on_domain(bset, -1);
4394
4395 if (bset->n_eq == 0)
4396 return compressed_multiplicative_call(bset, fn);
4397
4398 morph = isl_basic_set_full_compression(bset);
4399 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4400
4401 pwqp = compressed_multiplicative_call(bset, fn);
4402
4403 morph = isl_morph_dom_params(morph);
4404 morph = isl_morph_ran_params(morph);
4405 morph = isl_morph_inverse(morph);
4406
4407 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4408
4409 return pwqp;
4410 error:
4411 isl_basic_set_free(bset);
4412 return NULL;
4413 }
4414
4415 /* Drop all floors in "qp", turning each integer division [a/m] into
4416 * a rational division a/m. If "down" is set, then the integer division
4417 * is replaces by (a-(m-1))/m instead.
4418 */
4419 static __isl_give isl_qpolynomial *qp_drop_floors(
4420 __isl_take isl_qpolynomial *qp, int down)
4421 {
4422 int i;
4423 struct isl_upoly *s;
4424
4425 if (!qp)
4426 return NULL;
4427 if (qp->div->n_row == 0)
4428 return qp;
4429
4430 qp = isl_qpolynomial_cow(qp);
4431 if (!qp)
4432 return NULL;
4433
4434 for (i = qp->div->n_row - 1; i >= 0; --i) {
4435 if (down) {
4436 isl_int_sub(qp->div->row[i][1],
4437 qp->div->row[i][1], qp->div->row[i][0]);
4438 isl_int_add_ui(qp->div->row[i][1],
4439 qp->div->row[i][1], 1);
4440 }
4441 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4442 qp->div->row[i][0], qp->div->n_col - 1);
4443 qp = substitute_div(qp, i, s);
4444 if (!qp)
4445 return NULL;
4446 }
4447
4448 return qp;
4449 }
4450
4451 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4452 * a rational division a/m.
4453 */
4454 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4455 __isl_take isl_pw_qpolynomial *pwqp)
4456 {
4457 int i;
4458
4459 if (!pwqp)
4460 return NULL;
4461
4462 if (isl_pw_qpolynomial_is_zero(pwqp))
4463 return pwqp;
4464
4465 pwqp = isl_pw_qpolynomial_cow(pwqp);
4466 if (!pwqp)
4467 return NULL;
4468
4469 for (i = 0; i < pwqp->n; ++i) {
4470 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4471 if (!pwqp->p[i].qp)
4472 goto error;
4473 }
4474
4475 return pwqp;
4476 error:
4477 isl_pw_qpolynomial_free(pwqp);
4478 return NULL;
4479 }
4480
4481 /* Adjust all the integer divisions in "qp" such that they are at least
4482 * one over the given orthant (identified by "signs"). This ensures
4483 * that they will still be non-negative even after subtracting (m-1)/m.
4484 *
4485 * In particular, f is replaced by f' + v, changing f = [a/m]
4486 * to f' = [(a - m v)/m].
4487 * If the constant term k in a is smaller than m,
4488 * the constant term of v is set to floor(k/m) - 1.
4489 * For any other term, if the coefficient c and the variable x have
4490 * the same sign, then no changes are needed.
4491 * Otherwise, if the variable is positive (and c is negative),
4492 * then the coefficient of x in v is set to floor(c/m).
4493 * If the variable is negative (and c is positive),
4494 * then the coefficient of x in v is set to ceil(c/m).
4495 */
4496 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4497 int *signs)
4498 {
4499 int i, j;
4500 int total;
4501 isl_vec *v = NULL;
4502 struct isl_upoly *s;
4503
4504 qp = isl_qpolynomial_cow(qp);
4505 if (!qp)
4506 return NULL;
4507 qp->div = isl_mat_cow(qp->div);
4508 if (!qp->div)
4509 goto error;
4510
4511 total = isl_space_dim(qp->dim, isl_dim_all);
4512 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4513
4514 for (i = 0; i < qp->div->n_row; ++i) {
4515 isl_int *row = qp->div->row[i];
4516 v = isl_vec_clr(v);
4517 if (!v)
4518 goto error;
4519 if (isl_int_lt(row[1], row[0])) {
4520 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4521 isl_int_sub_ui(v->el[0], v->el[0], 1);
4522 isl_int_submul(row[1], row[0], v->el[0]);
4523 }
4524 for (j = 0; j < total; ++j) {
4525 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4526 continue;
4527 if (signs[j] < 0)
4528 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4529 else
4530 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4531 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4532 }
4533 for (j = 0; j < i; ++j) {
4534 if (isl_int_sgn(row[2 + total + j]) >= 0)
4535 continue;
4536 isl_int_fdiv_q(v->el[1 + total + j],
4537 row[2 + total + j], row[0]);
4538 isl_int_submul(row[2 + total + j],
4539 row[0], v->el[1 + total + j]);
4540 }
4541 for (j = i + 1; j < qp->div->n_row; ++j) {
4542 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4543 continue;
4544 isl_seq_combine(qp->div->row[j] + 1,
4545 qp->div->ctx->one, qp->div->row[j] + 1,
4546 qp->div->row[j][2 + total + i], v->el, v->size);
4547 }
4548 isl_int_set_si(v->el[1 + total + i], 1);
4549 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4550 qp->div->ctx->one, v->size);
4551 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4552 isl_upoly_free(s);
4553 if (!qp->upoly)
4554 goto error;
4555 }
4556
4557 isl_vec_free(v);
4558 return qp;
4559 error:
4560 isl_vec_free(v);
4561 isl_qpolynomial_free(qp);
4562 return NULL;
4563 }
4564
4565 struct isl_to_poly_data {
4566 int sign;
4567 isl_pw_qpolynomial *res;
4568 isl_qpolynomial *qp;
4569 };
4570
4571 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4572 * We first make all integer divisions positive and then split the
4573 * quasipolynomials into terms with sign data->sign (the direction
4574 * of the requested approximation) and terms with the opposite sign.
4575 * In the first set of terms, each integer division [a/m] is
4576 * overapproximated by a/m, while in the second it is underapproximated
4577 * by (a-(m-1))/m.
4578 */
4579 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4580 void *user)
4581 {
4582 struct isl_to_poly_data *data = user;
4583 isl_pw_qpolynomial *t;
4584 isl_qpolynomial *qp, *up, *down;
4585
4586 qp = isl_qpolynomial_copy(data->qp);
4587 qp = make_divs_pos(qp, signs);
4588
4589 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4590 up = qp_drop_floors(up, 0);
4591 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4592 down = qp_drop_floors(down, 1);
4593
4594 isl_qpolynomial_free(qp);
4595 qp = isl_qpolynomial_add(up, down);
4596
4597 t = isl_pw_qpolynomial_alloc(orthant, qp);
4598 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4599
4600 return 0;
4601 }
4602
4603 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4604 * the polynomial will be an overapproximation. If "sign" is negative,
4605 * it will be an underapproximation. If "sign" is zero, the approximation
4606 * will lie somewhere in between.
4607 *
4608 * In particular, is sign == 0, we simply drop the floors, turning
4609 * the integer divisions into rational divisions.
4610 * Otherwise, we split the domains into orthants, make all integer divisions
4611 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4612 * depending on the requested sign and the sign of the term in which
4613 * the integer division appears.
4614 */
4615 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4616 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4617 {
4618 int i;
4619 struct isl_to_poly_data data;
4620
4621 if (sign == 0)
4622 return pwqp_drop_floors(pwqp);
4623
4624 if (!pwqp)
4625 return NULL;
4626
4627 data.sign = sign;
4628 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4629
4630 for (i = 0; i < pwqp->n; ++i) {
4631 if (pwqp->p[i].qp->div->n_row == 0) {
4632 isl_pw_qpolynomial *t;
4633 t = isl_pw_qpolynomial_alloc(
4634 isl_set_copy(pwqp->p[i].set),
4635 isl_qpolynomial_copy(pwqp->p[i].qp));
4636 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4637 continue;
4638 }
4639 data.qp = pwqp->p[i].qp;
4640 if (isl_set_foreach_orthant(pwqp->p[i].set,
4641 &to_polynomial_on_orthant, &data) < 0)
4642 goto error;
4643 }
4644
4645 isl_pw_qpolynomial_free(pwqp);
4646
4647 return data.res;
4648 error:
4649 isl_pw_qpolynomial_free(pwqp);
4650 isl_pw_qpolynomial_free(data.res);
4651 return NULL;
4652 }
4653
4654 static int poly_entry(void **entry, void *user)
4655 {
4656 int *sign = user;
4657 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4658
4659 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4660
4661 return *pwqp ? 0 : -1;
4662 }
4663
4664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4665 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4666 {
4667 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4668 if (!upwqp)
4669 return NULL;
4670
4671 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4672 &poly_entry, &sign) < 0)
4673 goto error;
4674
4675 return upwqp;
4676 error:
4677 isl_union_pw_qpolynomial_free(upwqp);
4678 return NULL;
4679 }
4680
4681 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4682 __isl_take isl_qpolynomial *qp)
4683 {
4684 int i, k;
4685 isl_space *dim;
4686 isl_vec *aff = NULL;
4687 isl_basic_map *bmap = NULL;
4688 unsigned pos;
4689 unsigned n_div;
4690
4691 if (!qp)
4692 return NULL;
4693 if (!isl_upoly_is_affine(qp->upoly))
4694 isl_die(qp->dim->ctx, isl_error_invalid,
4695 "input quasi-polynomial not affine", goto error);
4696 aff = isl_qpolynomial_extract_affine(qp);
4697 if (!aff)
4698 goto error;
4699 dim = isl_qpolynomial_get_space(qp);
4700 dim = isl_space_from_domain(dim);
4701 pos = 1 + isl_space_offset(dim, isl_dim_out);
4702 dim = isl_space_add_dims(dim, isl_dim_out, 1);
4703 n_div = qp->div->n_row;
4704 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4705
4706 for (i = 0; i < n_div; ++i) {
4707 k = isl_basic_map_alloc_div(bmap);
4708 if (k < 0)
4709 goto error;
4710 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4711 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4712 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4713 goto error;
4714 }
4715 k = isl_basic_map_alloc_equality(bmap);
4716 if (k < 0)
4717 goto error;
4718 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4719 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4720 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4721
4722 isl_vec_free(aff);
4723 isl_qpolynomial_free(qp);
4724 bmap = isl_basic_map_finalize(bmap);
4725 return bmap;
4726 error:
4727 isl_vec_free(aff);
4728 isl_qpolynomial_free(qp);
4729 isl_basic_map_free(bmap);
4730 return NULL;
4731 }
Integer set library