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add isl_map_flat_domain_product
[isl.git] / isl_polynomial.c
blobc83dc72b286cf9f3ad34954aa25ec7a61d5380c1
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 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2411 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2412 {
2413 int i, j, k;
2414 isl_int denom;
2415 unsigned total;
2416 unsigned n_div;
2417 struct isl_upoly *up;
2418
2419 if (!eq)
2420 goto error;
2421 if (eq->n_eq == 0) {
2422 isl_basic_set_free(eq);
2423 return qp;
2424 }
2425
2426 qp = isl_qpolynomial_cow(qp);
2427 if (!qp)
2428 goto error;
2429 qp->div = isl_mat_cow(qp->div);
2430 if (!qp->div)
2431 goto error;
2432
2433 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2434 n_div = eq->n_div;
2435 isl_int_init(denom);
2436 for (i = 0; i < eq->n_eq; ++i) {
2437 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2438 if (j < 0 || j == 0 || j >= total)
2439 continue;
2440
2441 for (k = 0; k < qp->div->n_row; ++k) {
2442 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2443 continue;
2444 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2445 &qp->div->row[k][0]);
2446 normalize_div(qp, k);
2447 }
2448
2449 if (isl_int_is_pos(eq->eq[i][j]))
2450 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2451 isl_int_abs(denom, eq->eq[i][j]);
2452 isl_int_set_si(eq->eq[i][j], 0);
2453
2454 up = isl_upoly_from_affine(qp->dim->ctx,
2455 eq->eq[i], denom, total);
2456 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2457 isl_upoly_free(up);
2458 }
2459 isl_int_clear(denom);
2460
2461 if (!qp->upoly)
2462 goto error;
2463
2464 isl_basic_set_free(eq);
2465
2466 qp = substitute_non_divs(qp);
2467 qp = sort_divs(qp);
2468
2469 return qp;
2470 error:
2471 isl_basic_set_free(eq);
2472 isl_qpolynomial_free(qp);
2473 return NULL;
2474 }
2475
2476 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2477 */
2478 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2479 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2480 {
2481 if (!qp || !eq)
2482 goto error;
2483 if (qp->div->n_row > 0)
2484 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2485 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2486 error:
2487 isl_basic_set_free(eq);
2488 isl_qpolynomial_free(qp);
2489 return NULL;
2490 }
2491
2492 static __isl_give isl_basic_set *add_div_constraints(
2493 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2494 {
2495 int i;
2496 unsigned total;
2497
2498 if (!bset || !div)
2499 goto error;
2500
2501 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2502 if (!bset)
2503 goto error;
2504 total = isl_basic_set_total_dim(bset);
2505 for (i = 0; i < div->n_row; ++i)
2506 if (isl_basic_set_add_div_constraints_var(bset,
2507 total - div->n_row + i, div->row[i]) < 0)
2508 goto error;
2509
2510 isl_mat_free(div);
2511 return bset;
2512 error:
2513 isl_mat_free(div);
2514 isl_basic_set_free(bset);
2515 return NULL;
2516 }
2517
2518 /* Look for equalities among the variables shared by context and qp
2519 * and the integer divisions of qp, if any.
2520 * The equalities are then used to eliminate variables and/or integer
2521 * divisions from qp.
2522 */
2523 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2524 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2525 {
2526 isl_basic_set *aff;
2527
2528 if (!qp)
2529 goto error;
2530 if (qp->div->n_row > 0) {
2531 isl_basic_set *bset;
2532 context = isl_set_add_dims(context, isl_dim_set,
2533 qp->div->n_row);
2534 bset = isl_basic_set_universe(isl_set_get_space(context));
2535 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2536 context = isl_set_intersect(context,
2537 isl_set_from_basic_set(bset));
2538 }
2539
2540 aff = isl_set_affine_hull(context);
2541 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2542 error:
2543 isl_qpolynomial_free(qp);
2544 isl_set_free(context);
2545 return NULL;
2546 }
2547
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2549 __isl_take isl_qpolynomial *qp)
2550 {
2551 isl_set *dom;
2552
2553 if (!qp)
2554 return NULL;
2555 if (isl_qpolynomial_is_zero(qp)) {
2556 isl_space *dim = isl_qpolynomial_get_space(qp);
2557 isl_qpolynomial_free(qp);
2558 return isl_pw_qpolynomial_zero(dim);
2559 }
2560
2561 dom = isl_set_universe(isl_qpolynomial_get_space(qp));
2562 return isl_pw_qpolynomial_alloc(dom, qp);
2563 }
2564
2565 #undef PW
2566 #define PW isl_pw_qpolynomial
2567 #undef EL
2568 #define EL isl_qpolynomial
2569 #undef EL_IS_ZERO
2570 #define EL_IS_ZERO is_zero
2571 #undef ZERO
2572 #define ZERO zero
2573 #undef IS_ZERO
2574 #define IS_ZERO is_zero
2575 #undef FIELD
2576 #define FIELD qp
2577
2578 #include <isl_pw_templ.c>
2579
2580 #undef UNION
2581 #define UNION isl_union_pw_qpolynomial
2582 #undef PART
2583 #define PART isl_pw_qpolynomial
2584 #undef PARTS
2585 #define PARTS pw_qpolynomial
2586
2587 #include <isl_union_templ.c>
2588
2589 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2590 {
2591 if (!pwqp)
2592 return -1;
2593
2594 if (pwqp->n != -1)
2595 return 0;
2596
2597 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2598 return 0;
2599
2600 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2601 }
2602
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2604 __isl_take isl_pw_qpolynomial *pwqp1,
2605 __isl_take isl_pw_qpolynomial *pwqp2)
2606 {
2607 int i, j, n;
2608 struct isl_pw_qpolynomial *res;
2609
2610 if (!pwqp1 || !pwqp2)
2611 goto error;
2612
2613 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2614 goto error);
2615
2616 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2617 isl_pw_qpolynomial_free(pwqp2);
2618 return pwqp1;
2619 }
2620
2621 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2622 isl_pw_qpolynomial_free(pwqp1);
2623 return pwqp2;
2624 }
2625
2626 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2627 isl_pw_qpolynomial_free(pwqp1);
2628 return pwqp2;
2629 }
2630
2631 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2632 isl_pw_qpolynomial_free(pwqp2);
2633 return pwqp1;
2634 }
2635
2636 n = pwqp1->n * pwqp2->n;
2637 res = isl_pw_qpolynomial_alloc_(isl_space_copy(pwqp1->dim), n);
2638
2639 for (i = 0; i < pwqp1->n; ++i) {
2640 for (j = 0; j < pwqp2->n; ++j) {
2641 struct isl_set *common;
2642 struct isl_qpolynomial *prod;
2643 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2644 isl_set_copy(pwqp2->p[j].set));
2645 if (isl_set_plain_is_empty(common)) {
2646 isl_set_free(common);
2647 continue;
2648 }
2649
2650 prod = isl_qpolynomial_mul(
2651 isl_qpolynomial_copy(pwqp1->p[i].qp),
2652 isl_qpolynomial_copy(pwqp2->p[j].qp));
2653
2654 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2655 }
2656 }
2657
2658 isl_pw_qpolynomial_free(pwqp1);
2659 isl_pw_qpolynomial_free(pwqp2);
2660
2661 return res;
2662 error:
2663 isl_pw_qpolynomial_free(pwqp1);
2664 isl_pw_qpolynomial_free(pwqp2);
2665 return NULL;
2666 }
2667
2668 __isl_give struct isl_upoly *isl_upoly_eval(
2669 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2670 {
2671 int i;
2672 struct isl_upoly_rec *rec;
2673 struct isl_upoly *res;
2674 struct isl_upoly *base;
2675
2676 if (isl_upoly_is_cst(up)) {
2677 isl_vec_free(vec);
2678 return up;
2679 }
2680
2681 rec = isl_upoly_as_rec(up);
2682 if (!rec)
2683 goto error;
2684
2685 isl_assert(up->ctx, rec->n >= 1, goto error);
2686
2687 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2688
2689 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2690 isl_vec_copy(vec));
2691
2692 for (i = rec->n - 2; i >= 0; --i) {
2693 res = isl_upoly_mul(res, isl_upoly_copy(base));
2694 res = isl_upoly_sum(res,
2695 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2696 isl_vec_copy(vec)));
2697 }
2698
2699 isl_upoly_free(base);
2700 isl_upoly_free(up);
2701 isl_vec_free(vec);
2702 return res;
2703 error:
2704 isl_upoly_free(up);
2705 isl_vec_free(vec);
2706 return NULL;
2707 }
2708
2709 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2710 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2711 {
2712 isl_vec *ext;
2713 struct isl_upoly *up;
2714 isl_space *dim;
2715
2716 if (!qp || !pnt)
2717 goto error;
2718 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2719
2720 if (qp->div->n_row == 0)
2721 ext = isl_vec_copy(pnt->vec);
2722 else {
2723 int i;
2724 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2725 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2726 if (!ext)
2727 goto error;
2728
2729 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2730 for (i = 0; i < qp->div->n_row; ++i) {
2731 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2732 1 + dim + i, &ext->el[1+dim+i]);
2733 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2734 qp->div->row[i][0]);
2735 }
2736 }
2737
2738 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2739 if (!up)
2740 goto error;
2741
2742 dim = isl_space_copy(qp->dim);
2743 isl_qpolynomial_free(qp);
2744 isl_point_free(pnt);
2745
2746 return isl_qpolynomial_alloc(dim, 0, up);
2747 error:
2748 isl_qpolynomial_free(qp);
2749 isl_point_free(pnt);
2750 return NULL;
2751 }
2752
2753 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2754 __isl_keep struct isl_upoly_cst *cst2)
2755 {
2756 int cmp;
2757 isl_int t;
2758 isl_int_init(t);
2759 isl_int_mul(t, cst1->n, cst2->d);
2760 isl_int_submul(t, cst2->n, cst1->d);
2761 cmp = isl_int_sgn(t);
2762 isl_int_clear(t);
2763 return cmp;
2764 }
2765
2766 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2767 __isl_keep isl_qpolynomial *qp2)
2768 {
2769 struct isl_upoly_cst *cst1, *cst2;
2770
2771 if (!qp1 || !qp2)
2772 return -1;
2773 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2774 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2775 if (isl_qpolynomial_is_nan(qp1))
2776 return -1;
2777 if (isl_qpolynomial_is_nan(qp2))
2778 return -1;
2779 cst1 = isl_upoly_as_cst(qp1->upoly);
2780 cst2 = isl_upoly_as_cst(qp2->upoly);
2781
2782 return isl_upoly_cmp(cst1, cst2) <= 0;
2783 }
2784
2785 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2786 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2787 {
2788 struct isl_upoly_cst *cst1, *cst2;
2789 int cmp;
2790
2791 if (!qp1 || !qp2)
2792 goto error;
2793 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2794 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2795 cst1 = isl_upoly_as_cst(qp1->upoly);
2796 cst2 = isl_upoly_as_cst(qp2->upoly);
2797 cmp = isl_upoly_cmp(cst1, cst2);
2798
2799 if (cmp <= 0) {
2800 isl_qpolynomial_free(qp2);
2801 } else {
2802 isl_qpolynomial_free(qp1);
2803 qp1 = qp2;
2804 }
2805 return qp1;
2806 error:
2807 isl_qpolynomial_free(qp1);
2808 isl_qpolynomial_free(qp2);
2809 return NULL;
2810 }
2811
2812 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2813 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2814 {
2815 struct isl_upoly_cst *cst1, *cst2;
2816 int cmp;
2817
2818 if (!qp1 || !qp2)
2819 goto error;
2820 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2821 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2822 cst1 = isl_upoly_as_cst(qp1->upoly);
2823 cst2 = isl_upoly_as_cst(qp2->upoly);
2824 cmp = isl_upoly_cmp(cst1, cst2);
2825
2826 if (cmp >= 0) {
2827 isl_qpolynomial_free(qp2);
2828 } else {
2829 isl_qpolynomial_free(qp1);
2830 qp1 = qp2;
2831 }
2832 return qp1;
2833 error:
2834 isl_qpolynomial_free(qp1);
2835 isl_qpolynomial_free(qp2);
2836 return NULL;
2837 }
2838
2839 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2840 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2841 unsigned first, unsigned n)
2842 {
2843 unsigned total;
2844 unsigned g_pos;
2845 int *exp;
2846
2847 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2848 return qp;
2849
2850 qp = isl_qpolynomial_cow(qp);
2851 if (!qp)
2852 return NULL;
2853
2854 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2855 goto error);
2856
2857 g_pos = pos(qp->dim, type) + first;
2858
2859 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2860 if (!qp->div)
2861 goto error;
2862
2863 total = qp->div->n_col - 2;
2864 if (total > g_pos) {
2865 int i;
2866 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2867 if (!exp)
2868 goto error;
2869 for (i = 0; i < total - g_pos; ++i)
2870 exp[i] = i + n;
2871 qp->upoly = expand(qp->upoly, exp, g_pos);
2872 free(exp);
2873 if (!qp->upoly)
2874 goto error;
2875 }
2876
2877 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2878 if (!qp->dim)
2879 goto error;
2880
2881 return qp;
2882 error:
2883 isl_qpolynomial_free(qp);
2884 return NULL;
2885 }
2886
2887 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2888 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2889 {
2890 unsigned pos;
2891
2892 pos = isl_qpolynomial_dim(qp, type);
2893
2894 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2895 }
2896
2897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2898 __isl_take isl_pw_qpolynomial *pwqp,
2899 enum isl_dim_type type, unsigned n)
2900 {
2901 unsigned pos;
2902
2903 pos = isl_pw_qpolynomial_dim(pwqp, type);
2904
2905 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2906 }
2907
2908 static int *reordering_move(isl_ctx *ctx,
2909 unsigned len, unsigned dst, unsigned src, unsigned n)
2910 {
2911 int i;
2912 int *reordering;
2913
2914 reordering = isl_alloc_array(ctx, int, len);
2915 if (!reordering)
2916 return NULL;
2917
2918 if (dst <= src) {
2919 for (i = 0; i < dst; ++i)
2920 reordering[i] = i;
2921 for (i = 0; i < n; ++i)
2922 reordering[src + i] = dst + i;
2923 for (i = 0; i < src - dst; ++i)
2924 reordering[dst + i] = dst + n + i;
2925 for (i = 0; i < len - src - n; ++i)
2926 reordering[src + n + i] = src + n + i;
2927 } else {
2928 for (i = 0; i < src; ++i)
2929 reordering[i] = i;
2930 for (i = 0; i < n; ++i)
2931 reordering[src + i] = dst + i;
2932 for (i = 0; i < dst - src; ++i)
2933 reordering[src + n + i] = src + i;
2934 for (i = 0; i < len - dst - n; ++i)
2935 reordering[dst + n + i] = dst + n + i;
2936 }
2937
2938 return reordering;
2939 }
2940
2941 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2942 __isl_take isl_qpolynomial *qp,
2943 enum isl_dim_type dst_type, unsigned dst_pos,
2944 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2945 {
2946 unsigned g_dst_pos;
2947 unsigned g_src_pos;
2948 int *reordering;
2949
2950 qp = isl_qpolynomial_cow(qp);
2951 if (!qp)
2952 return NULL;
2953
2954 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
2955 goto error);
2956
2957 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2958 g_src_pos = pos(qp->dim, src_type) + src_pos;
2959 if (dst_type > src_type)
2960 g_dst_pos -= n;
2961
2962 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2963 if (!qp->div)
2964 goto error;
2965 qp = sort_divs(qp);
2966 if (!qp)
2967 goto error;
2968
2969 reordering = reordering_move(qp->dim->ctx,
2970 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2971 if (!reordering)
2972 goto error;
2973
2974 qp->upoly = reorder(qp->upoly, reordering);
2975 free(reordering);
2976 if (!qp->upoly)
2977 goto error;
2978
2979 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2980 if (!qp->dim)
2981 goto error;
2982
2983 return qp;
2984 error:
2985 isl_qpolynomial_free(qp);
2986 return NULL;
2987 }
2988
2989 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
2990 isl_int *f, isl_int denom)
2991 {
2992 struct isl_upoly *up;
2993
2994 if (!dim)
2995 return NULL;
2996
2997 up = isl_upoly_from_affine(dim->ctx, f, denom,
2998 1 + isl_space_dim(dim, isl_dim_all));
2999
3000 return isl_qpolynomial_alloc(dim, 0, up);
3001 }
3002
3003 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3004 {
3005 isl_ctx *ctx;
3006 struct isl_upoly *up;
3007 isl_qpolynomial *qp;
3008
3009 if (!aff)
3010 return NULL;
3011
3012 ctx = isl_aff_get_ctx(aff);
3013 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3014 aff->v->size - 1);
3015
3016 qp = isl_qpolynomial_alloc(isl_aff_get_space(aff),
3017 aff->ls->div->n_row, up);
3018 if (!qp)
3019 goto error;
3020
3021 isl_mat_free(qp->div);
3022 qp->div = isl_mat_copy(aff->ls->div);
3023 qp->div = isl_mat_cow(qp->div);
3024 if (!qp->div)
3025 goto error;
3026
3027 isl_aff_free(aff);
3028 qp = reduce_divs(qp);
3029 qp = remove_redundant_divs(qp);
3030 return qp;
3031 error:
3032 isl_aff_free(aff);
3033 return NULL;
3034 }
3035
3036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3037 __isl_take isl_pw_aff *pwaff)
3038 {
3039 int i;
3040 isl_pw_qpolynomial *pwqp;
3041
3042 if (!pwaff)
3043 return NULL;
3044
3045 pwqp = isl_pw_qpolynomial_alloc_(isl_pw_aff_get_space(pwaff), pwaff->n);
3046
3047 for (i = 0; i < pwaff->n; ++i) {
3048 isl_set *dom;
3049 isl_qpolynomial *qp;
3050
3051 dom = isl_set_copy(pwaff->p[i].set);
3052 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3053 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3054 }
3055
3056 isl_pw_aff_free(pwaff);
3057 return pwqp;
3058 }
3059
3060 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3061 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3062 {
3063 isl_aff *aff;
3064
3065 aff = isl_constraint_get_bound(c, type, pos);
3066 isl_constraint_free(c);
3067 return isl_qpolynomial_from_aff(aff);
3068 }
3069
3070 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3071 * in "qp" by subs[i].
3072 */
3073 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3074 __isl_take isl_qpolynomial *qp,
3075 enum isl_dim_type type, unsigned first, unsigned n,
3076 __isl_keep isl_qpolynomial **subs)
3077 {
3078 int i;
3079 struct isl_upoly **ups;
3080
3081 if (n == 0)
3082 return qp;
3083
3084 qp = isl_qpolynomial_cow(qp);
3085 if (!qp)
3086 return NULL;
3087 for (i = 0; i < n; ++i)
3088 if (!subs[i])
3089 goto error;
3090
3091 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3092 goto error);
3093
3094 for (i = 0; i < n; ++i)
3095 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3096 goto error);
3097
3098 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3099 for (i = 0; i < n; ++i)
3100 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3101
3102 first += pos(qp->dim, type);
3103
3104 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3105 if (!ups)
3106 goto error;
3107 for (i = 0; i < n; ++i)
3108 ups[i] = subs[i]->upoly;
3109
3110 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3111
3112 free(ups);
3113
3114 if (!qp->upoly)
3115 goto error;
3116
3117 return qp;
3118 error:
3119 isl_qpolynomial_free(qp);
3120 return NULL;
3121 }
3122
3123 /* Extend "bset" with extra set dimensions for each integer division
3124 * in "qp" and then call "fn" with the extended bset and the polynomial
3125 * that results from replacing each of the integer divisions by the
3126 * corresponding extra set dimension.
3127 */
3128 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3129 __isl_keep isl_basic_set *bset,
3130 int (*fn)(__isl_take isl_basic_set *bset,
3131 __isl_take isl_qpolynomial *poly, void *user), void *user)
3132 {
3133 isl_space *dim;
3134 isl_mat *div;
3135 isl_qpolynomial *poly;
3136
3137 if (!qp || !bset)
3138 goto error;
3139 if (qp->div->n_row == 0)
3140 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3141 user);
3142
3143 div = isl_mat_copy(qp->div);
3144 dim = isl_space_copy(qp->dim);
3145 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3146 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3147 bset = isl_basic_set_copy(bset);
3148 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3149 bset = add_div_constraints(bset, div);
3150
3151 return fn(bset, poly, user);
3152 error:
3153 return -1;
3154 }
3155
3156 /* Return total degree in variables first (inclusive) up to last (exclusive).
3157 */
3158 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3159 {
3160 int deg = -1;
3161 int i;
3162 struct isl_upoly_rec *rec;
3163
3164 if (!up)
3165 return -2;
3166 if (isl_upoly_is_zero(up))
3167 return -1;
3168 if (isl_upoly_is_cst(up) || up->var < first)
3169 return 0;
3170
3171 rec = isl_upoly_as_rec(up);
3172 if (!rec)
3173 return -2;
3174
3175 for (i = 0; i < rec->n; ++i) {
3176 int d;
3177
3178 if (isl_upoly_is_zero(rec->p[i]))
3179 continue;
3180 d = isl_upoly_degree(rec->p[i], first, last);
3181 if (up->var < last)
3182 d += i;
3183 if (d > deg)
3184 deg = d;
3185 }
3186
3187 return deg;
3188 }
3189
3190 /* Return total degree in set variables.
3191 */
3192 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3193 {
3194 unsigned ovar;
3195 unsigned nvar;
3196
3197 if (!poly)
3198 return -2;
3199
3200 ovar = isl_space_offset(poly->dim, isl_dim_set);
3201 nvar = isl_space_dim(poly->dim, isl_dim_set);
3202 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3203 }
3204
3205 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3206 unsigned pos, int deg)
3207 {
3208 int i;
3209 struct isl_upoly_rec *rec;
3210
3211 if (!up)
3212 return NULL;
3213
3214 if (isl_upoly_is_cst(up) || up->var < pos) {
3215 if (deg == 0)
3216 return isl_upoly_copy(up);
3217 else
3218 return isl_upoly_zero(up->ctx);
3219 }
3220
3221 rec = isl_upoly_as_rec(up);
3222 if (!rec)
3223 return NULL;
3224
3225 if (up->var == pos) {
3226 if (deg < rec->n)
3227 return isl_upoly_copy(rec->p[deg]);
3228 else
3229 return isl_upoly_zero(up->ctx);
3230 }
3231
3232 up = isl_upoly_copy(up);
3233 up = isl_upoly_cow(up);
3234 rec = isl_upoly_as_rec(up);
3235 if (!rec)
3236 goto error;
3237
3238 for (i = 0; i < rec->n; ++i) {
3239 struct isl_upoly *t;
3240 t = isl_upoly_coeff(rec->p[i], pos, deg);
3241 if (!t)
3242 goto error;
3243 isl_upoly_free(rec->p[i]);
3244 rec->p[i] = t;
3245 }
3246
3247 return up;
3248 error:
3249 isl_upoly_free(up);
3250 return NULL;
3251 }
3252
3253 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3254 */
3255 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3256 __isl_keep isl_qpolynomial *qp,
3257 enum isl_dim_type type, unsigned t_pos, int deg)
3258 {
3259 unsigned g_pos;
3260 struct isl_upoly *up;
3261 isl_qpolynomial *c;
3262
3263 if (!qp)
3264 return NULL;
3265
3266 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3267 return NULL);
3268
3269 g_pos = pos(qp->dim, type) + t_pos;
3270 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3271
3272 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3273 if (!c)
3274 return NULL;
3275 isl_mat_free(c->div);
3276 c->div = isl_mat_copy(qp->div);
3277 if (!c->div)
3278 goto error;
3279 return c;
3280 error:
3281 isl_qpolynomial_free(c);
3282 return NULL;
3283 }
3284
3285 /* Homogenize the polynomial in the variables first (inclusive) up to
3286 * last (exclusive) by inserting powers of variable first.
3287 * Variable first is assumed not to appear in the input.
3288 */
3289 __isl_give struct isl_upoly *isl_upoly_homogenize(
3290 __isl_take struct isl_upoly *up, int deg, int target,
3291 int first, int last)
3292 {
3293 int i;
3294 struct isl_upoly_rec *rec;
3295
3296 if (!up)
3297 return NULL;
3298 if (isl_upoly_is_zero(up))
3299 return up;
3300 if (deg == target)
3301 return up;
3302 if (isl_upoly_is_cst(up) || up->var < first) {
3303 struct isl_upoly *hom;
3304
3305 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3306 if (!hom)
3307 goto error;
3308 rec = isl_upoly_as_rec(hom);
3309 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3310
3311 return hom;
3312 }
3313
3314 up = isl_upoly_cow(up);
3315 rec = isl_upoly_as_rec(up);
3316 if (!rec)
3317 goto error;
3318
3319 for (i = 0; i < rec->n; ++i) {
3320 if (isl_upoly_is_zero(rec->p[i]))
3321 continue;
3322 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3323 up->var < last ? deg + i : i, target,
3324 first, last);
3325 if (!rec->p[i])
3326 goto error;
3327 }
3328
3329 return up;
3330 error:
3331 isl_upoly_free(up);
3332 return NULL;
3333 }
3334
3335 /* Homogenize the polynomial in the set variables by introducing
3336 * powers of an extra set variable at position 0.
3337 */
3338 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3339 __isl_take isl_qpolynomial *poly)
3340 {
3341 unsigned ovar;
3342 unsigned nvar;
3343 int deg = isl_qpolynomial_degree(poly);
3344
3345 if (deg < -1)
3346 goto error;
3347
3348 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3349 poly = isl_qpolynomial_cow(poly);
3350 if (!poly)
3351 goto error;
3352
3353 ovar = isl_space_offset(poly->dim, isl_dim_set);
3354 nvar = isl_space_dim(poly->dim, isl_dim_set);
3355 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3356 ovar, ovar + nvar);
3357 if (!poly->upoly)
3358 goto error;
3359
3360 return poly;
3361 error:
3362 isl_qpolynomial_free(poly);
3363 return NULL;
3364 }
3365
3366 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3367 __isl_take isl_mat *div)
3368 {
3369 isl_term *term;
3370 int n;
3371
3372 if (!dim || !div)
3373 goto error;
3374
3375 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3376
3377 term = isl_calloc(dim->ctx, struct isl_term,
3378 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3379 if (!term)
3380 goto error;
3381
3382 term->ref = 1;
3383 term->dim = dim;
3384 term->div = div;
3385 isl_int_init(term->n);
3386 isl_int_init(term->d);
3387
3388 return term;
3389 error:
3390 isl_space_free(dim);
3391 isl_mat_free(div);
3392 return NULL;
3393 }
3394
3395 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3396 {
3397 if (!term)
3398 return NULL;
3399
3400 term->ref++;
3401 return term;
3402 }
3403
3404 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3405 {
3406 int i;
3407 isl_term *dup;
3408 unsigned total;
3409
3410 if (term)
3411 return NULL;
3412
3413 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3414
3415 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3416 if (!dup)
3417 return NULL;
3418
3419 isl_int_set(dup->n, term->n);
3420 isl_int_set(dup->d, term->d);
3421
3422 for (i = 0; i < total; ++i)
3423 dup->pow[i] = term->pow[i];
3424
3425 return dup;
3426 }
3427
3428 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3429 {
3430 if (!term)
3431 return NULL;
3432
3433 if (term->ref == 1)
3434 return term;
3435 term->ref--;
3436 return isl_term_dup(term);
3437 }
3438
3439 void isl_term_free(__isl_take isl_term *term)
3440 {
3441 if (!term)
3442 return;
3443
3444 if (--term->ref > 0)
3445 return;
3446
3447 isl_space_free(term->dim);
3448 isl_mat_free(term->div);
3449 isl_int_clear(term->n);
3450 isl_int_clear(term->d);
3451 free(term);
3452 }
3453
3454 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3455 {
3456 if (!term)
3457 return 0;
3458
3459 switch (type) {
3460 case isl_dim_param:
3461 case isl_dim_in:
3462 case isl_dim_out: return isl_space_dim(term->dim, type);
3463 case isl_dim_div: return term->div->n_row;
3464 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3465 term->div->n_row;
3466 default: return 0;
3467 }
3468 }
3469
3470 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3471 {
3472 return term ? term->dim->ctx : NULL;
3473 }
3474
3475 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3476 {
3477 if (!term)
3478 return;
3479 isl_int_set(*n, term->n);
3480 }
3481
3482 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3483 {
3484 if (!term)
3485 return;
3486 isl_int_set(*d, term->d);
3487 }
3488
3489 int isl_term_get_exp(__isl_keep isl_term *term,
3490 enum isl_dim_type type, unsigned pos)
3491 {
3492 if (!term)
3493 return -1;
3494
3495 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3496
3497 if (type >= isl_dim_set)
3498 pos += isl_space_dim(term->dim, isl_dim_param);
3499 if (type >= isl_dim_div)
3500 pos += isl_space_dim(term->dim, isl_dim_set);
3501
3502 return term->pow[pos];
3503 }
3504
3505 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3506 {
3507 isl_basic_map *bmap;
3508 unsigned total;
3509 int k;
3510
3511 if (!term)
3512 return NULL;
3513
3514 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3515 return NULL);
3516
3517 total = term->div->n_col - term->div->n_row - 2;
3518 /* No nested divs for now */
3519 isl_assert(term->dim->ctx,
3520 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3521 term->div->n_row) == -1,
3522 return NULL);
3523
3524 bmap = isl_basic_map_alloc_space(isl_space_copy(term->dim), 1, 0, 0);
3525 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3526 goto error;
3527
3528 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3529
3530 return isl_basic_map_div(bmap, k);
3531 error:
3532 isl_basic_map_free(bmap);
3533 return NULL;
3534 }
3535
3536 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3537 int (*fn)(__isl_take isl_term *term, void *user),
3538 __isl_take isl_term *term, void *user)
3539 {
3540 int i;
3541 struct isl_upoly_rec *rec;
3542
3543 if (!up || !term)
3544 goto error;
3545
3546 if (isl_upoly_is_zero(up))
3547 return term;
3548
3549 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3550 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3551 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3552
3553 if (isl_upoly_is_cst(up)) {
3554 struct isl_upoly_cst *cst;
3555 cst = isl_upoly_as_cst(up);
3556 if (!cst)
3557 goto error;
3558 term = isl_term_cow(term);
3559 if (!term)
3560 goto error;
3561 isl_int_set(term->n, cst->n);
3562 isl_int_set(term->d, cst->d);
3563 if (fn(isl_term_copy(term), user) < 0)
3564 goto error;
3565 return term;
3566 }
3567
3568 rec = isl_upoly_as_rec(up);
3569 if (!rec)
3570 goto error;
3571
3572 for (i = 0; i < rec->n; ++i) {
3573 term = isl_term_cow(term);
3574 if (!term)
3575 goto error;
3576 term->pow[up->var] = i;
3577 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3578 if (!term)
3579 goto error;
3580 }
3581 term->pow[up->var] = 0;
3582
3583 return term;
3584 error:
3585 isl_term_free(term);
3586 return NULL;
3587 }
3588
3589 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3590 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3591 {
3592 isl_term *term;
3593
3594 if (!qp)
3595 return -1;
3596
3597 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3598 if (!term)
3599 return -1;
3600
3601 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3602
3603 isl_term_free(term);
3604
3605 return term ? 0 : -1;
3606 }
3607
3608 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3609 {
3610 struct isl_upoly *up;
3611 isl_qpolynomial *qp;
3612 int i, n;
3613
3614 if (!term)
3615 return NULL;
3616
3617 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3618
3619 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3620 for (i = 0; i < n; ++i) {
3621 if (!term->pow[i])
3622 continue;
3623 up = isl_upoly_mul(up,
3624 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3625 }
3626
3627 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3628 if (!qp)
3629 goto error;
3630 isl_mat_free(qp->div);
3631 qp->div = isl_mat_copy(term->div);
3632 if (!qp->div)
3633 goto error;
3634
3635 isl_term_free(term);
3636 return qp;
3637 error:
3638 isl_qpolynomial_free(qp);
3639 isl_term_free(term);
3640 return NULL;
3641 }
3642
3643 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3644 __isl_take isl_space *dim)
3645 {
3646 int i;
3647 int extra;
3648 unsigned total;
3649
3650 if (!qp || !dim)
3651 goto error;
3652
3653 if (isl_space_is_equal(qp->dim, dim)) {
3654 isl_space_free(dim);
3655 return qp;
3656 }
3657
3658 qp = isl_qpolynomial_cow(qp);
3659 if (!qp)
3660 goto error;
3661
3662 extra = isl_space_dim(dim, isl_dim_set) -
3663 isl_space_dim(qp->dim, isl_dim_set);
3664 total = isl_space_dim(qp->dim, isl_dim_all);
3665 if (qp->div->n_row) {
3666 int *exp;
3667
3668 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3669 if (!exp)
3670 goto error;
3671 for (i = 0; i < qp->div->n_row; ++i)
3672 exp[i] = extra + i;
3673 qp->upoly = expand(qp->upoly, exp, total);
3674 free(exp);
3675 if (!qp->upoly)
3676 goto error;
3677 }
3678 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3679 if (!qp->div)
3680 goto error;
3681 for (i = 0; i < qp->div->n_row; ++i)
3682 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3683
3684 isl_space_free(qp->dim);
3685 qp->dim = dim;
3686
3687 return qp;
3688 error:
3689 isl_space_free(dim);
3690 isl_qpolynomial_free(qp);
3691 return NULL;
3692 }
3693
3694 /* For each parameter or variable that does not appear in qp,
3695 * first eliminate the variable from all constraints and then set it to zero.
3696 */
3697 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3698 __isl_keep isl_qpolynomial *qp)
3699 {
3700 int *active = NULL;
3701 int i;
3702 int d;
3703 unsigned nparam;
3704 unsigned nvar;
3705
3706 if (!set || !qp)
3707 goto error;
3708
3709 d = isl_space_dim(set->dim, isl_dim_all);
3710 active = isl_calloc_array(set->ctx, int, d);
3711 if (set_active(qp, active) < 0)
3712 goto error;
3713
3714 for (i = 0; i < d; ++i)
3715 if (!active[i])
3716 break;
3717
3718 if (i == d) {
3719 free(active);
3720 return set;
3721 }
3722
3723 nparam = isl_space_dim(set->dim, isl_dim_param);
3724 nvar = isl_space_dim(set->dim, isl_dim_set);
3725 for (i = 0; i < nparam; ++i) {
3726 if (active[i])
3727 continue;
3728 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3729 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3730 }
3731 for (i = 0; i < nvar; ++i) {
3732 if (active[nparam + i])
3733 continue;
3734 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3735 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3736 }
3737
3738 free(active);
3739
3740 return set;
3741 error:
3742 free(active);
3743 isl_set_free(set);
3744 return NULL;
3745 }
3746
3747 struct isl_opt_data {
3748 isl_qpolynomial *qp;
3749 int first;
3750 isl_qpolynomial *opt;
3751 int max;
3752 };
3753
3754 static int opt_fn(__isl_take isl_point *pnt, void *user)
3755 {
3756 struct isl_opt_data *data = (struct isl_opt_data *)user;
3757 isl_qpolynomial *val;
3758
3759 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3760 if (data->first) {
3761 data->first = 0;
3762 data->opt = val;
3763 } else if (data->max) {
3764 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3765 } else {
3766 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3767 }
3768
3769 return 0;
3770 }
3771
3772 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3773 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3774 {
3775 struct isl_opt_data data = { NULL, 1, NULL, max };
3776
3777 if (!set || !qp)
3778 goto error;
3779
3780 if (isl_upoly_is_cst(qp->upoly)) {
3781 isl_set_free(set);
3782 return qp;
3783 }
3784
3785 set = fix_inactive(set, qp);
3786
3787 data.qp = qp;
3788 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3789 goto error;
3790
3791 if (data.first)
3792 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_space(qp));
3793
3794 isl_set_free(set);
3795 isl_qpolynomial_free(qp);
3796 return data.opt;
3797 error:
3798 isl_set_free(set);
3799 isl_qpolynomial_free(qp);
3800 isl_qpolynomial_free(data.opt);
3801 return NULL;
3802 }
3803
3804 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3805 __isl_take isl_morph *morph)
3806 {
3807 int i;
3808 int n_sub;
3809 isl_ctx *ctx;
3810 struct isl_upoly **subs;
3811 isl_mat *mat;
3812
3813 qp = isl_qpolynomial_cow(qp);
3814 if (!qp || !morph)
3815 goto error;
3816
3817 ctx = qp->dim->ctx;
3818 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3819
3820 n_sub = morph->inv->n_row - 1;
3821 if (morph->inv->n_row != morph->inv->n_col)
3822 n_sub += qp->div->n_row;
3823 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3824 if (!subs)
3825 goto error;
3826
3827 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3828 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3829 morph->inv->row[0][0], morph->inv->n_col);
3830 if (morph->inv->n_row != morph->inv->n_col)
3831 for (i = 0; i < qp->div->n_row; ++i)
3832 subs[morph->inv->n_row - 1 + i] =
3833 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3834
3835 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3836
3837 for (i = 0; i < n_sub; ++i)
3838 isl_upoly_free(subs[i]);
3839 free(subs);
3840
3841 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3842 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3843 qp->div = isl_mat_product(qp->div, mat);
3844 isl_space_free(qp->dim);
3845 qp->dim = isl_space_copy(morph->ran->dim);
3846
3847 if (!qp->upoly || !qp->div || !qp->dim)
3848 goto error;
3849
3850 isl_morph_free(morph);
3851
3852 return qp;
3853 error:
3854 isl_qpolynomial_free(qp);
3855 isl_morph_free(morph);
3856 return NULL;
3857 }
3858
3859 static int neg_entry(void **entry, void *user)
3860 {
3861 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3862
3863 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3864
3865 return *pwqp ? 0 : -1;
3866 }
3867
3868 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3869 __isl_take isl_union_pw_qpolynomial *upwqp)
3870 {
3871 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3872 if (!upwqp)
3873 return NULL;
3874
3875 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3876 &neg_entry, NULL) < 0)
3877 goto error;
3878
3879 return upwqp;
3880 error:
3881 isl_union_pw_qpolynomial_free(upwqp);
3882 return NULL;
3883 }
3884
3885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3886 __isl_take isl_union_pw_qpolynomial *upwqp1,
3887 __isl_take isl_union_pw_qpolynomial *upwqp2)
3888 {
3889 return isl_union_pw_qpolynomial_add(upwqp1,
3890 isl_union_pw_qpolynomial_neg(upwqp2));
3891 }
3892
3893 static int mul_entry(void **entry, void *user)
3894 {
3895 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3896 uint32_t hash;
3897 struct isl_hash_table_entry *entry2;
3898 isl_pw_qpolynomial *pwpq = *entry;
3899 int empty;
3900
3901 hash = isl_space_get_hash(pwpq->dim);
3902 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3903 hash, &has_dim, pwpq->dim, 0);
3904 if (!entry2)
3905 return 0;
3906
3907 pwpq = isl_pw_qpolynomial_copy(pwpq);
3908 pwpq = isl_pw_qpolynomial_mul(pwpq,
3909 isl_pw_qpolynomial_copy(entry2->data));
3910
3911 empty = isl_pw_qpolynomial_is_zero(pwpq);
3912 if (empty < 0) {
3913 isl_pw_qpolynomial_free(pwpq);
3914 return -1;
3915 }
3916 if (empty) {
3917 isl_pw_qpolynomial_free(pwpq);
3918 return 0;
3919 }
3920
3921 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3922
3923 return 0;
3924 }
3925
3926 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3927 __isl_take isl_union_pw_qpolynomial *upwqp1,
3928 __isl_take isl_union_pw_qpolynomial *upwqp2)
3929 {
3930 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3931 }
3932
3933 /* Reorder the columns of the given div definitions according to the
3934 * given reordering.
3935 */
3936 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3937 __isl_take isl_reordering *r)
3938 {
3939 int i, j;
3940 isl_mat *mat;
3941 int extra;
3942
3943 if (!div || !r)
3944 goto error;
3945
3946 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
3947 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3948 if (!mat)
3949 goto error;
3950
3951 for (i = 0; i < div->n_row; ++i) {
3952 isl_seq_cpy(mat->row[i], div->row[i], 2);
3953 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3954 for (j = 0; j < r->len; ++j)
3955 isl_int_set(mat->row[i][2 + r->pos[j]],
3956 div->row[i][2 + j]);
3957 }
3958
3959 isl_reordering_free(r);
3960 isl_mat_free(div);
3961 return mat;
3962 error:
3963 isl_reordering_free(r);
3964 isl_mat_free(div);
3965 return NULL;
3966 }
3967
3968 /* Reorder the dimension of "qp" according to the given reordering.
3969 */
3970 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3971 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3972 {
3973 qp = isl_qpolynomial_cow(qp);
3974 if (!qp)
3975 goto error;
3976
3977 r = isl_reordering_extend(r, qp->div->n_row);
3978 if (!r)
3979 goto error;
3980
3981 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3982 if (!qp->div)
3983 goto error;
3984
3985 qp->upoly = reorder(qp->upoly, r->pos);
3986 if (!qp->upoly)
3987 goto error;
3988
3989 qp = isl_qpolynomial_reset_space(qp, isl_space_copy(r->dim));
3990
3991 isl_reordering_free(r);
3992 return qp;
3993 error:
3994 isl_qpolynomial_free(qp);
3995 isl_reordering_free(r);
3996 return NULL;
3997 }
3998
3999 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4000 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4001 {
4002 if (!qp || !model)
4003 goto error;
4004
4005 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4006 isl_reordering *exp;
4007
4008 model = isl_space_drop_dims(model, isl_dim_in,
4009 0, isl_space_dim(model, isl_dim_in));
4010 model = isl_space_drop_dims(model, isl_dim_out,
4011 0, isl_space_dim(model, isl_dim_out));
4012 exp = isl_parameter_alignment_reordering(qp->dim, model);
4013 exp = isl_reordering_extend_space(exp,
4014 isl_qpolynomial_get_space(qp));
4015 qp = isl_qpolynomial_realign(qp, exp);
4016 }
4017
4018 isl_space_free(model);
4019 return qp;
4020 error:
4021 isl_space_free(model);
4022 isl_qpolynomial_free(qp);
4023 return NULL;
4024 }
4025
4026 struct isl_split_periods_data {
4027 int max_periods;
4028 isl_pw_qpolynomial *res;
4029 };
4030
4031 /* Create a slice where the integer division "div" has the fixed value "v".
4032 * In particular, if "div" refers to floor(f/m), then create a slice
4033 *
4034 * m v <= f <= m v + (m - 1)
4035 *
4036 * or
4037 *
4038 * f - m v >= 0
4039 * -f + m v + (m - 1) >= 0
4040 */
4041 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4042 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4043 {
4044 int total;
4045 isl_basic_set *bset = NULL;
4046 int k;
4047
4048 if (!dim || !qp)
4049 goto error;
4050
4051 total = isl_space_dim(dim, isl_dim_all);
4052 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4053
4054 k = isl_basic_set_alloc_inequality(bset);
4055 if (k < 0)
4056 goto error;
4057 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4058 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4059
4060 k = isl_basic_set_alloc_inequality(bset);
4061 if (k < 0)
4062 goto error;
4063 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4064 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4065 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4066 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4067
4068 isl_space_free(dim);
4069 return isl_set_from_basic_set(bset);
4070 error:
4071 isl_basic_set_free(bset);
4072 isl_space_free(dim);
4073 return NULL;
4074 }
4075
4076 static int split_periods(__isl_take isl_set *set,
4077 __isl_take isl_qpolynomial *qp, void *user);
4078
4079 /* Create a slice of the domain "set" such that integer division "div"
4080 * has the fixed value "v" and add the results to data->res,
4081 * replacing the integer division by "v" in "qp".
4082 */
4083 static int set_div(__isl_take isl_set *set,
4084 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4085 struct isl_split_periods_data *data)
4086 {
4087 int i;
4088 int total;
4089 isl_set *slice;
4090 struct isl_upoly *cst;
4091
4092 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4093 set = isl_set_intersect(set, slice);
4094
4095 if (!qp)
4096 goto error;
4097
4098 total = isl_space_dim(qp->dim, isl_dim_all);
4099
4100 for (i = div + 1; i < qp->div->n_row; ++i) {
4101 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4102 continue;
4103 isl_int_addmul(qp->div->row[i][1],
4104 qp->div->row[i][2 + total + div], v);
4105 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4106 }
4107
4108 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4109 qp = substitute_div(qp, div, cst);
4110
4111 return split_periods(set, qp, data);
4112 error:
4113 isl_set_free(set);
4114 isl_qpolynomial_free(qp);
4115 return -1;
4116 }
4117
4118 /* Split the domain "set" such that integer division "div"
4119 * has a fixed value (ranging from "min" to "max") on each slice
4120 * and add the results to data->res.
4121 */
4122 static int split_div(__isl_take isl_set *set,
4123 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4124 struct isl_split_periods_data *data)
4125 {
4126 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4127 isl_set *set_i = isl_set_copy(set);
4128 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4129
4130 if (set_div(set_i, qp_i, div, min, data) < 0)
4131 goto error;
4132 }
4133 isl_set_free(set);
4134 isl_qpolynomial_free(qp);
4135 return 0;
4136 error:
4137 isl_set_free(set);
4138 isl_qpolynomial_free(qp);
4139 return -1;
4140 }
4141
4142 /* If "qp" refers to any integer division
4143 * that can only attain "max_periods" distinct values on "set"
4144 * then split the domain along those distinct values.
4145 * Add the results (or the original if no splitting occurs)
4146 * to data->res.
4147 */
4148 static int split_periods(__isl_take isl_set *set,
4149 __isl_take isl_qpolynomial *qp, void *user)
4150 {
4151 int i;
4152 isl_pw_qpolynomial *pwqp;
4153 struct isl_split_periods_data *data;
4154 isl_int min, max;
4155 int total;
4156 int r = 0;
4157
4158 data = (struct isl_split_periods_data *)user;
4159
4160 if (!set || !qp)
4161 goto error;
4162
4163 if (qp->div->n_row == 0) {
4164 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4165 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4166 return 0;
4167 }
4168
4169 isl_int_init(min);
4170 isl_int_init(max);
4171 total = isl_space_dim(qp->dim, isl_dim_all);
4172 for (i = 0; i < qp->div->n_row; ++i) {
4173 enum isl_lp_result lp_res;
4174
4175 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4176 qp->div->n_row) != -1)
4177 continue;
4178
4179 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4180 set->ctx->one, &min, NULL, NULL);
4181 if (lp_res == isl_lp_error)
4182 goto error2;
4183 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4184 continue;
4185 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4186
4187 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4188 set->ctx->one, &max, NULL, NULL);
4189 if (lp_res == isl_lp_error)
4190 goto error2;
4191 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4192 continue;
4193 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4194
4195 isl_int_sub(max, max, min);
4196 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4197 isl_int_add(max, max, min);
4198 break;
4199 }
4200 }
4201
4202 if (i < qp->div->n_row) {
4203 r = split_div(set, qp, i, min, max, data);
4204 } else {
4205 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4206 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4207 }
4208
4209 isl_int_clear(max);
4210 isl_int_clear(min);
4211
4212 return r;
4213 error2:
4214 isl_int_clear(max);
4215 isl_int_clear(min);
4216 error:
4217 isl_set_free(set);
4218 isl_qpolynomial_free(qp);
4219 return -1;
4220 }
4221
4222 /* If any quasi-polynomial in pwqp refers to any integer division
4223 * that can only attain "max_periods" distinct values on its domain
4224 * then split the domain along those distinct values.
4225 */
4226 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4227 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4228 {
4229 struct isl_split_periods_data data;
4230
4231 data.max_periods = max_periods;
4232 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4233
4234 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4235 goto error;
4236
4237 isl_pw_qpolynomial_free(pwqp);
4238
4239 return data.res;
4240 error:
4241 isl_pw_qpolynomial_free(data.res);
4242 isl_pw_qpolynomial_free(pwqp);
4243 return NULL;
4244 }
4245
4246 /* Construct a piecewise quasipolynomial that is constant on the given
4247 * domain. In particular, it is
4248 * 0 if cst == 0
4249 * 1 if cst == 1
4250 * infinity if cst == -1
4251 */
4252 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4253 __isl_take isl_basic_set *bset, int cst)
4254 {
4255 isl_space *dim;
4256 isl_qpolynomial *qp;
4257
4258 if (!bset)
4259 return NULL;
4260
4261 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4262 dim = isl_basic_set_get_space(bset);
4263 if (cst < 0)
4264 qp = isl_qpolynomial_infty(dim);
4265 else if (cst == 0)
4266 qp = isl_qpolynomial_zero(dim);
4267 else
4268 qp = isl_qpolynomial_one(dim);
4269 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4270 }
4271
4272 /* Factor bset, call fn on each of the factors and return the product.
4273 *
4274 * If no factors can be found, simply call fn on the input.
4275 * Otherwise, construct the factors based on the factorizer,
4276 * call fn on each factor and compute the product.
4277 */
4278 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4279 __isl_take isl_basic_set *bset,
4280 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4281 {
4282 int i, n;
4283 isl_space *dim;
4284 isl_set *set;
4285 isl_factorizer *f;
4286 isl_qpolynomial *qp;
4287 isl_pw_qpolynomial *pwqp;
4288 unsigned nparam;
4289 unsigned nvar;
4290
4291 f = isl_basic_set_factorizer(bset);
4292 if (!f)
4293 goto error;
4294 if (f->n_group == 0) {
4295 isl_factorizer_free(f);
4296 return fn(bset);
4297 }
4298
4299 nparam = isl_basic_set_dim(bset, isl_dim_param);
4300 nvar = isl_basic_set_dim(bset, isl_dim_set);
4301
4302 dim = isl_basic_set_get_space(bset);
4303 dim = isl_space_domain(dim);
4304 set = isl_set_universe(isl_space_copy(dim));
4305 qp = isl_qpolynomial_one(dim);
4306 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4307
4308 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4309
4310 for (i = 0, n = 0; i < f->n_group; ++i) {
4311 isl_basic_set *bset_i;
4312 isl_pw_qpolynomial *pwqp_i;
4313
4314 bset_i = isl_basic_set_copy(bset);
4315 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4316 nparam + n + f->len[i], nvar - n - f->len[i]);
4317 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4318 nparam, n);
4319 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4320 n + f->len[i], nvar - n - f->len[i]);
4321 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4322
4323 pwqp_i = fn(bset_i);
4324 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4325
4326 n += f->len[i];
4327 }
4328
4329 isl_basic_set_free(bset);
4330 isl_factorizer_free(f);
4331
4332 return pwqp;
4333 error:
4334 isl_basic_set_free(bset);
4335 return NULL;
4336 }
4337
4338 /* Factor bset, call fn on each of the factors and return the product.
4339 * The function is assumed to evaluate to zero on empty domains,
4340 * to one on zero-dimensional domains and to infinity on unbounded domains
4341 * and will not be called explicitly on zero-dimensional or unbounded domains.
4342 *
4343 * We first check for some special cases and remove all equalities.
4344 * Then we hand over control to compressed_multiplicative_call.
4345 */
4346 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4347 __isl_take isl_basic_set *bset,
4348 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4349 {
4350 int bounded;
4351 isl_morph *morph;
4352 isl_pw_qpolynomial *pwqp;
4353 unsigned orig_nvar, final_nvar;
4354
4355 if (!bset)
4356 return NULL;
4357
4358 if (isl_basic_set_plain_is_empty(bset))
4359 return constant_on_domain(bset, 0);
4360
4361 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4362
4363 if (orig_nvar == 0)
4364 return constant_on_domain(bset, 1);
4365
4366 bounded = isl_basic_set_is_bounded(bset);
4367 if (bounded < 0)
4368 goto error;
4369 if (!bounded)
4370 return constant_on_domain(bset, -1);
4371
4372 if (bset->n_eq == 0)
4373 return compressed_multiplicative_call(bset, fn);
4374
4375 morph = isl_basic_set_full_compression(bset);
4376 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4377
4378 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4379
4380 pwqp = compressed_multiplicative_call(bset, fn);
4381
4382 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4383 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4384 morph = isl_morph_inverse(morph);
4385
4386 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4387
4388 return pwqp;
4389 error:
4390 isl_basic_set_free(bset);
4391 return NULL;
4392 }
4393
4394 /* Drop all floors in "qp", turning each integer division [a/m] into
4395 * a rational division a/m. If "down" is set, then the integer division
4396 * is replaces by (a-(m-1))/m instead.
4397 */
4398 static __isl_give isl_qpolynomial *qp_drop_floors(
4399 __isl_take isl_qpolynomial *qp, int down)
4400 {
4401 int i;
4402 struct isl_upoly *s;
4403
4404 if (!qp)
4405 return NULL;
4406 if (qp->div->n_row == 0)
4407 return qp;
4408
4409 qp = isl_qpolynomial_cow(qp);
4410 if (!qp)
4411 return NULL;
4412
4413 for (i = qp->div->n_row - 1; i >= 0; --i) {
4414 if (down) {
4415 isl_int_sub(qp->div->row[i][1],
4416 qp->div->row[i][1], qp->div->row[i][0]);
4417 isl_int_add_ui(qp->div->row[i][1],
4418 qp->div->row[i][1], 1);
4419 }
4420 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4421 qp->div->row[i][0], qp->div->n_col - 1);
4422 qp = substitute_div(qp, i, s);
4423 if (!qp)
4424 return NULL;
4425 }
4426
4427 return qp;
4428 }
4429
4430 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4431 * a rational division a/m.
4432 */
4433 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4434 __isl_take isl_pw_qpolynomial *pwqp)
4435 {
4436 int i;
4437
4438 if (!pwqp)
4439 return NULL;
4440
4441 if (isl_pw_qpolynomial_is_zero(pwqp))
4442 return pwqp;
4443
4444 pwqp = isl_pw_qpolynomial_cow(pwqp);
4445 if (!pwqp)
4446 return NULL;
4447
4448 for (i = 0; i < pwqp->n; ++i) {
4449 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4450 if (!pwqp->p[i].qp)
4451 goto error;
4452 }
4453
4454 return pwqp;
4455 error:
4456 isl_pw_qpolynomial_free(pwqp);
4457 return NULL;
4458 }
4459
4460 /* Adjust all the integer divisions in "qp" such that they are at least
4461 * one over the given orthant (identified by "signs"). This ensures
4462 * that they will still be non-negative even after subtracting (m-1)/m.
4463 *
4464 * In particular, f is replaced by f' + v, changing f = [a/m]
4465 * to f' = [(a - m v)/m].
4466 * If the constant term k in a is smaller than m,
4467 * the constant term of v is set to floor(k/m) - 1.
4468 * For any other term, if the coefficient c and the variable x have
4469 * the same sign, then no changes are needed.
4470 * Otherwise, if the variable is positive (and c is negative),
4471 * then the coefficient of x in v is set to floor(c/m).
4472 * If the variable is negative (and c is positive),
4473 * then the coefficient of x in v is set to ceil(c/m).
4474 */
4475 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4476 int *signs)
4477 {
4478 int i, j;
4479 int total;
4480 isl_vec *v = NULL;
4481 struct isl_upoly *s;
4482
4483 qp = isl_qpolynomial_cow(qp);
4484 if (!qp)
4485 return NULL;
4486 qp->div = isl_mat_cow(qp->div);
4487 if (!qp->div)
4488 goto error;
4489
4490 total = isl_space_dim(qp->dim, isl_dim_all);
4491 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4492
4493 for (i = 0; i < qp->div->n_row; ++i) {
4494 isl_int *row = qp->div->row[i];
4495 v = isl_vec_clr(v);
4496 if (!v)
4497 goto error;
4498 if (isl_int_lt(row[1], row[0])) {
4499 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4500 isl_int_sub_ui(v->el[0], v->el[0], 1);
4501 isl_int_submul(row[1], row[0], v->el[0]);
4502 }
4503 for (j = 0; j < total; ++j) {
4504 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4505 continue;
4506 if (signs[j] < 0)
4507 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4508 else
4509 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4510 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4511 }
4512 for (j = 0; j < i; ++j) {
4513 if (isl_int_sgn(row[2 + total + j]) >= 0)
4514 continue;
4515 isl_int_fdiv_q(v->el[1 + total + j],
4516 row[2 + total + j], row[0]);
4517 isl_int_submul(row[2 + total + j],
4518 row[0], v->el[1 + total + j]);
4519 }
4520 for (j = i + 1; j < qp->div->n_row; ++j) {
4521 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4522 continue;
4523 isl_seq_combine(qp->div->row[j] + 1,
4524 qp->div->ctx->one, qp->div->row[j] + 1,
4525 qp->div->row[j][2 + total + i], v->el, v->size);
4526 }
4527 isl_int_set_si(v->el[1 + total + i], 1);
4528 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4529 qp->div->ctx->one, v->size);
4530 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4531 isl_upoly_free(s);
4532 if (!qp->upoly)
4533 goto error;
4534 }
4535
4536 isl_vec_free(v);
4537 return qp;
4538 error:
4539 isl_vec_free(v);
4540 isl_qpolynomial_free(qp);
4541 return NULL;
4542 }
4543
4544 struct isl_to_poly_data {
4545 int sign;
4546 isl_pw_qpolynomial *res;
4547 isl_qpolynomial *qp;
4548 };
4549
4550 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4551 * We first make all integer divisions positive and then split the
4552 * quasipolynomials into terms with sign data->sign (the direction
4553 * of the requested approximation) and terms with the opposite sign.
4554 * In the first set of terms, each integer division [a/m] is
4555 * overapproximated by a/m, while in the second it is underapproximated
4556 * by (a-(m-1))/m.
4557 */
4558 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4559 void *user)
4560 {
4561 struct isl_to_poly_data *data = user;
4562 isl_pw_qpolynomial *t;
4563 isl_qpolynomial *qp, *up, *down;
4564
4565 qp = isl_qpolynomial_copy(data->qp);
4566 qp = make_divs_pos(qp, signs);
4567
4568 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4569 up = qp_drop_floors(up, 0);
4570 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4571 down = qp_drop_floors(down, 1);
4572
4573 isl_qpolynomial_free(qp);
4574 qp = isl_qpolynomial_add(up, down);
4575
4576 t = isl_pw_qpolynomial_alloc(orthant, qp);
4577 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4578
4579 return 0;
4580 }
4581
4582 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4583 * the polynomial will be an overapproximation. If "sign" is negative,
4584 * it will be an underapproximation. If "sign" is zero, the approximation
4585 * will lie somewhere in between.
4586 *
4587 * In particular, is sign == 0, we simply drop the floors, turning
4588 * the integer divisions into rational divisions.
4589 * Otherwise, we split the domains into orthants, make all integer divisions
4590 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4591 * depending on the requested sign and the sign of the term in which
4592 * the integer division appears.
4593 */
4594 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4595 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4596 {
4597 int i;
4598 struct isl_to_poly_data data;
4599
4600 if (sign == 0)
4601 return pwqp_drop_floors(pwqp);
4602
4603 if (!pwqp)
4604 return NULL;
4605
4606 data.sign = sign;
4607 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4608
4609 for (i = 0; i < pwqp->n; ++i) {
4610 if (pwqp->p[i].qp->div->n_row == 0) {
4611 isl_pw_qpolynomial *t;
4612 t = isl_pw_qpolynomial_alloc(
4613 isl_set_copy(pwqp->p[i].set),
4614 isl_qpolynomial_copy(pwqp->p[i].qp));
4615 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4616 continue;
4617 }
4618 data.qp = pwqp->p[i].qp;
4619 if (isl_set_foreach_orthant(pwqp->p[i].set,
4620 &to_polynomial_on_orthant, &data) < 0)
4621 goto error;
4622 }
4623
4624 isl_pw_qpolynomial_free(pwqp);
4625
4626 return data.res;
4627 error:
4628 isl_pw_qpolynomial_free(pwqp);
4629 isl_pw_qpolynomial_free(data.res);
4630 return NULL;
4631 }
4632
4633 static int poly_entry(void **entry, void *user)
4634 {
4635 int *sign = user;
4636 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4637
4638 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4639
4640 return *pwqp ? 0 : -1;
4641 }
4642
4643 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4644 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4645 {
4646 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4647 if (!upwqp)
4648 return NULL;
4649
4650 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4651 &poly_entry, &sign) < 0)
4652 goto error;
4653
4654 return upwqp;
4655 error:
4656 isl_union_pw_qpolynomial_free(upwqp);
4657 return NULL;
4658 }
4659
4660 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4661 __isl_take isl_qpolynomial *qp)
4662 {
4663 int i, k;
4664 isl_space *dim;
4665 isl_vec *aff = NULL;
4666 isl_basic_map *bmap = NULL;
4667 unsigned pos;
4668 unsigned n_div;
4669
4670 if (!qp)
4671 return NULL;
4672 if (!isl_upoly_is_affine(qp->upoly))
4673 isl_die(qp->dim->ctx, isl_error_invalid,
4674 "input quasi-polynomial not affine", goto error);
4675 aff = isl_qpolynomial_extract_affine(qp);
4676 if (!aff)
4677 goto error;
4678 dim = isl_qpolynomial_get_space(qp);
4679 dim = isl_space_from_domain(dim);
4680 pos = 1 + isl_space_offset(dim, isl_dim_out);
4681 dim = isl_space_add_dims(dim, isl_dim_out, 1);
4682 n_div = qp->div->n_row;
4683 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4684
4685 for (i = 0; i < n_div; ++i) {
4686 k = isl_basic_map_alloc_div(bmap);
4687 if (k < 0)
4688 goto error;
4689 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4690 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4691 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4692 goto error;
4693 }
4694 k = isl_basic_map_alloc_equality(bmap);
4695 if (k < 0)
4696 goto error;
4697 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4698 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4699 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4700
4701 isl_vec_free(aff);
4702 isl_qpolynomial_free(qp);
4703 bmap = isl_basic_map_finalize(bmap);
4704 return bmap;
4705 error:
4706 isl_vec_free(aff);
4707 isl_qpolynomial_free(qp);
4708 isl_basic_map_free(bmap);
4709 return NULL;
4710 }
Integer set library