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isl_transitive_closure.c: remove unused variable
[isl.git] / isl_polynomial.c
blobba9179c0fa2f5e5a8a01338cd5740dbd1526cbd1
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl/lp.h>
16 #include <isl/seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
26
27 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
28 {
29 switch (type) {
30 case isl_dim_param: return 0;
31 case isl_dim_in: return dim->nparam;
32 case isl_dim_out: return dim->nparam + dim->n_in;
33 default: return 0;
34 }
35 }
36
37 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
38 {
39 if (!up)
40 return -1;
41
42 return up->var < 0;
43 }
44
45 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
46 {
47 if (!up)
48 return NULL;
49
50 isl_assert(up->ctx, up->var < 0, return NULL);
51
52 return (struct isl_upoly_cst *)up;
53 }
54
55 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
56 {
57 if (!up)
58 return NULL;
59
60 isl_assert(up->ctx, up->var >= 0, return NULL);
61
62 return (struct isl_upoly_rec *)up;
63 }
64
65 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
66 __isl_keep struct isl_upoly *up2)
67 {
68 int i;
69 struct isl_upoly_rec *rec1, *rec2;
70
71 if (!up1 || !up2)
72 return -1;
73 if (up1 == up2)
74 return 1;
75 if (up1->var != up2->var)
76 return 0;
77 if (isl_upoly_is_cst(up1)) {
78 struct isl_upoly_cst *cst1, *cst2;
79 cst1 = isl_upoly_as_cst(up1);
80 cst2 = isl_upoly_as_cst(up2);
81 if (!cst1 || !cst2)
82 return -1;
83 return isl_int_eq(cst1->n, cst2->n) &&
84 isl_int_eq(cst1->d, cst2->d);
85 }
86
87 rec1 = isl_upoly_as_rec(up1);
88 rec2 = isl_upoly_as_rec(up2);
89 if (!rec1 || !rec2)
90 return -1;
91
92 if (rec1->n != rec2->n)
93 return 0;
94
95 for (i = 0; i < rec1->n; ++i) {
96 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
97 if (eq < 0 || !eq)
98 return eq;
99 }
100
101 return 1;
102 }
103
104 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
105 {
106 struct isl_upoly_cst *cst;
107
108 if (!up)
109 return -1;
110 if (!isl_upoly_is_cst(up))
111 return 0;
112
113 cst = isl_upoly_as_cst(up);
114 if (!cst)
115 return -1;
116
117 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
118 }
119
120 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
121 {
122 struct isl_upoly_cst *cst;
123
124 if (!up)
125 return 0;
126 if (!isl_upoly_is_cst(up))
127 return 0;
128
129 cst = isl_upoly_as_cst(up);
130 if (!cst)
131 return 0;
132
133 return isl_int_sgn(cst->n);
134 }
135
136 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
137 {
138 struct isl_upoly_cst *cst;
139
140 if (!up)
141 return -1;
142 if (!isl_upoly_is_cst(up))
143 return 0;
144
145 cst = isl_upoly_as_cst(up);
146 if (!cst)
147 return -1;
148
149 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
150 }
151
152 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
153 {
154 struct isl_upoly_cst *cst;
155
156 if (!up)
157 return -1;
158 if (!isl_upoly_is_cst(up))
159 return 0;
160
161 cst = isl_upoly_as_cst(up);
162 if (!cst)
163 return -1;
164
165 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
166 }
167
168 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
169 {
170 struct isl_upoly_cst *cst;
171
172 if (!up)
173 return -1;
174 if (!isl_upoly_is_cst(up))
175 return 0;
176
177 cst = isl_upoly_as_cst(up);
178 if (!cst)
179 return -1;
180
181 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
182 }
183
184 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
185 {
186 struct isl_upoly_cst *cst;
187
188 if (!up)
189 return -1;
190 if (!isl_upoly_is_cst(up))
191 return 0;
192
193 cst = isl_upoly_as_cst(up);
194 if (!cst)
195 return -1;
196
197 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
198 }
199
200 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
201 {
202 struct isl_upoly_cst *cst;
203
204 if (!up)
205 return -1;
206 if (!isl_upoly_is_cst(up))
207 return 0;
208
209 cst = isl_upoly_as_cst(up);
210 if (!cst)
211 return -1;
212
213 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
214 }
215
216 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
217 {
218 struct isl_upoly_cst *cst;
219
220 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
221 if (!cst)
222 return NULL;
223
224 cst->up.ref = 1;
225 cst->up.ctx = ctx;
226 isl_ctx_ref(ctx);
227 cst->up.var = -1;
228
229 isl_int_init(cst->n);
230 isl_int_init(cst->d);
231
232 return cst;
233 }
234
235 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
236 {
237 struct isl_upoly_cst *cst;
238
239 cst = isl_upoly_cst_alloc(ctx);
240 if (!cst)
241 return NULL;
242
243 isl_int_set_si(cst->n, 0);
244 isl_int_set_si(cst->d, 1);
245
246 return &cst->up;
247 }
248
249 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
250 {
251 struct isl_upoly_cst *cst;
252
253 cst = isl_upoly_cst_alloc(ctx);
254 if (!cst)
255 return NULL;
256
257 isl_int_set_si(cst->n, 1);
258 isl_int_set_si(cst->d, 1);
259
260 return &cst->up;
261 }
262
263 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
264 {
265 struct isl_upoly_cst *cst;
266
267 cst = isl_upoly_cst_alloc(ctx);
268 if (!cst)
269 return NULL;
270
271 isl_int_set_si(cst->n, 1);
272 isl_int_set_si(cst->d, 0);
273
274 return &cst->up;
275 }
276
277 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
278 {
279 struct isl_upoly_cst *cst;
280
281 cst = isl_upoly_cst_alloc(ctx);
282 if (!cst)
283 return NULL;
284
285 isl_int_set_si(cst->n, -1);
286 isl_int_set_si(cst->d, 0);
287
288 return &cst->up;
289 }
290
291 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
292 {
293 struct isl_upoly_cst *cst;
294
295 cst = isl_upoly_cst_alloc(ctx);
296 if (!cst)
297 return NULL;
298
299 isl_int_set_si(cst->n, 0);
300 isl_int_set_si(cst->d, 0);
301
302 return &cst->up;
303 }
304
305 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
306 isl_int n, isl_int d)
307 {
308 struct isl_upoly_cst *cst;
309
310 cst = isl_upoly_cst_alloc(ctx);
311 if (!cst)
312 return NULL;
313
314 isl_int_set(cst->n, n);
315 isl_int_set(cst->d, d);
316
317 return &cst->up;
318 }
319
320 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
321 int var, int size)
322 {
323 struct isl_upoly_rec *rec;
324
325 isl_assert(ctx, var >= 0, return NULL);
326 isl_assert(ctx, size >= 0, return NULL);
327 rec = isl_calloc(ctx, struct isl_upoly_rec,
328 sizeof(struct isl_upoly_rec) +
329 (size - 1) * sizeof(struct isl_upoly *));
330 if (!rec)
331 return NULL;
332
333 rec->up.ref = 1;
334 rec->up.ctx = ctx;
335 isl_ctx_ref(ctx);
336 rec->up.var = var;
337
338 rec->n = 0;
339 rec->size = size;
340
341 return rec;
342 }
343
344 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
345 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
346 {
347 qp = isl_qpolynomial_cow(qp);
348 if (!qp || !dim)
349 goto error;
350
351 isl_dim_free(qp->dim);
352 qp->dim = dim;
353
354 return qp;
355 error:
356 isl_qpolynomial_free(qp);
357 isl_dim_free(dim);
358 return NULL;
359 }
360
361 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
362 {
363 return qp ? qp->dim->ctx : NULL;
364 }
365
366 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
367 {
368 return qp ? isl_dim_copy(qp->dim) : NULL;
369 }
370
371 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
372 enum isl_dim_type type)
373 {
374 return qp ? isl_dim_size(qp->dim, type) : 0;
375 }
376
377 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
378 {
379 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
380 }
381
382 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
383 {
384 return qp ? isl_upoly_is_one(qp->upoly) : -1;
385 }
386
387 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
388 {
389 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
390 }
391
392 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
393 {
394 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
395 }
396
397 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
398 {
399 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
400 }
401
402 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
403 {
404 return qp ? isl_upoly_sgn(qp->upoly) : 0;
405 }
406
407 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
408 {
409 isl_int_clear(cst->n);
410 isl_int_clear(cst->d);
411 }
412
413 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
414 {
415 int i;
416
417 for (i = 0; i < rec->n; ++i)
418 isl_upoly_free(rec->p[i]);
419 }
420
421 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
422 {
423 if (!up)
424 return NULL;
425
426 up->ref++;
427 return up;
428 }
429
430 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
431 {
432 struct isl_upoly_cst *cst;
433 struct isl_upoly_cst *dup;
434
435 cst = isl_upoly_as_cst(up);
436 if (!cst)
437 return NULL;
438
439 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
440 if (!dup)
441 return NULL;
442 isl_int_set(dup->n, cst->n);
443 isl_int_set(dup->d, cst->d);
444
445 return &dup->up;
446 }
447
448 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
449 {
450 int i;
451 struct isl_upoly_rec *rec;
452 struct isl_upoly_rec *dup;
453
454 rec = isl_upoly_as_rec(up);
455 if (!rec)
456 return NULL;
457
458 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
459 if (!dup)
460 return NULL;
461
462 for (i = 0; i < rec->n; ++i) {
463 dup->p[i] = isl_upoly_copy(rec->p[i]);
464 if (!dup->p[i])
465 goto error;
466 dup->n++;
467 }
468
469 return &dup->up;
470 error:
471 isl_upoly_free(&dup->up);
472 return NULL;
473 }
474
475 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
476 {
477 if (!up)
478 return NULL;
479
480 if (isl_upoly_is_cst(up))
481 return isl_upoly_dup_cst(up);
482 else
483 return isl_upoly_dup_rec(up);
484 }
485
486 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
487 {
488 if (!up)
489 return NULL;
490
491 if (up->ref == 1)
492 return up;
493 up->ref--;
494 return isl_upoly_dup(up);
495 }
496
497 void isl_upoly_free(__isl_take struct isl_upoly *up)
498 {
499 if (!up)
500 return;
501
502 if (--up->ref > 0)
503 return;
504
505 if (up->var < 0)
506 upoly_free_cst((struct isl_upoly_cst *)up);
507 else
508 upoly_free_rec((struct isl_upoly_rec *)up);
509
510 isl_ctx_deref(up->ctx);
511 free(up);
512 }
513
514 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
515 {
516 isl_int gcd;
517
518 isl_int_init(gcd);
519 isl_int_gcd(gcd, cst->n, cst->d);
520 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
521 isl_int_divexact(cst->n, cst->n, gcd);
522 isl_int_divexact(cst->d, cst->d, gcd);
523 }
524 isl_int_clear(gcd);
525 }
526
527 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
528 __isl_take struct isl_upoly *up2)
529 {
530 struct isl_upoly_cst *cst1;
531 struct isl_upoly_cst *cst2;
532
533 up1 = isl_upoly_cow(up1);
534 if (!up1 || !up2)
535 goto error;
536
537 cst1 = isl_upoly_as_cst(up1);
538 cst2 = isl_upoly_as_cst(up2);
539
540 if (isl_int_eq(cst1->d, cst2->d))
541 isl_int_add(cst1->n, cst1->n, cst2->n);
542 else {
543 isl_int_mul(cst1->n, cst1->n, cst2->d);
544 isl_int_addmul(cst1->n, cst2->n, cst1->d);
545 isl_int_mul(cst1->d, cst1->d, cst2->d);
546 }
547
548 isl_upoly_cst_reduce(cst1);
549
550 isl_upoly_free(up2);
551 return up1;
552 error:
553 isl_upoly_free(up1);
554 isl_upoly_free(up2);
555 return NULL;
556 }
557
558 static __isl_give struct isl_upoly *replace_by_zero(
559 __isl_take struct isl_upoly *up)
560 {
561 struct isl_ctx *ctx;
562
563 if (!up)
564 return NULL;
565 ctx = up->ctx;
566 isl_upoly_free(up);
567 return isl_upoly_zero(ctx);
568 }
569
570 static __isl_give struct isl_upoly *replace_by_constant_term(
571 __isl_take struct isl_upoly *up)
572 {
573 struct isl_upoly_rec *rec;
574 struct isl_upoly *cst;
575
576 if (!up)
577 return NULL;
578
579 rec = isl_upoly_as_rec(up);
580 if (!rec)
581 goto error;
582 cst = isl_upoly_copy(rec->p[0]);
583 isl_upoly_free(up);
584 return cst;
585 error:
586 isl_upoly_free(up);
587 return NULL;
588 }
589
590 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
591 __isl_take struct isl_upoly *up2)
592 {
593 int i;
594 struct isl_upoly_rec *rec1, *rec2;
595
596 if (!up1 || !up2)
597 goto error;
598
599 if (isl_upoly_is_nan(up1)) {
600 isl_upoly_free(up2);
601 return up1;
602 }
603
604 if (isl_upoly_is_nan(up2)) {
605 isl_upoly_free(up1);
606 return up2;
607 }
608
609 if (isl_upoly_is_zero(up1)) {
610 isl_upoly_free(up1);
611 return up2;
612 }
613
614 if (isl_upoly_is_zero(up2)) {
615 isl_upoly_free(up2);
616 return up1;
617 }
618
619 if (up1->var < up2->var)
620 return isl_upoly_sum(up2, up1);
621
622 if (up2->var < up1->var) {
623 struct isl_upoly_rec *rec;
624 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
625 isl_upoly_free(up1);
626 return up2;
627 }
628 up1 = isl_upoly_cow(up1);
629 rec = isl_upoly_as_rec(up1);
630 if (!rec)
631 goto error;
632 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
633 if (rec->n == 1)
634 up1 = replace_by_constant_term(up1);
635 return up1;
636 }
637
638 if (isl_upoly_is_cst(up1))
639 return isl_upoly_sum_cst(up1, up2);
640
641 rec1 = isl_upoly_as_rec(up1);
642 rec2 = isl_upoly_as_rec(up2);
643 if (!rec1 || !rec2)
644 goto error;
645
646 if (rec1->n < rec2->n)
647 return isl_upoly_sum(up2, up1);
648
649 up1 = isl_upoly_cow(up1);
650 rec1 = isl_upoly_as_rec(up1);
651 if (!rec1)
652 goto error;
653
654 for (i = rec2->n - 1; i >= 0; --i) {
655 rec1->p[i] = isl_upoly_sum(rec1->p[i],
656 isl_upoly_copy(rec2->p[i]));
657 if (!rec1->p[i])
658 goto error;
659 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
660 isl_upoly_free(rec1->p[i]);
661 rec1->n--;
662 }
663 }
664
665 if (rec1->n == 0)
666 up1 = replace_by_zero(up1);
667 else if (rec1->n == 1)
668 up1 = replace_by_constant_term(up1);
669
670 isl_upoly_free(up2);
671
672 return up1;
673 error:
674 isl_upoly_free(up1);
675 isl_upoly_free(up2);
676 return NULL;
677 }
678
679 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
680 __isl_take struct isl_upoly *up, isl_int v)
681 {
682 struct isl_upoly_cst *cst;
683
684 up = isl_upoly_cow(up);
685 if (!up)
686 return NULL;
687
688 cst = isl_upoly_as_cst(up);
689
690 isl_int_addmul(cst->n, cst->d, v);
691
692 return up;
693 }
694
695 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
696 __isl_take struct isl_upoly *up, isl_int v)
697 {
698 struct isl_upoly_rec *rec;
699
700 if (!up)
701 return NULL;
702
703 if (isl_upoly_is_cst(up))
704 return isl_upoly_cst_add_isl_int(up, v);
705
706 up = isl_upoly_cow(up);
707 rec = isl_upoly_as_rec(up);
708 if (!rec)
709 goto error;
710
711 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
712 if (!rec->p[0])
713 goto error;
714
715 return up;
716 error:
717 isl_upoly_free(up);
718 return NULL;
719 }
720
721 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
722 __isl_take struct isl_upoly *up, isl_int v)
723 {
724 struct isl_upoly_cst *cst;
725
726 if (isl_upoly_is_zero(up))
727 return up;
728
729 up = isl_upoly_cow(up);
730 if (!up)
731 return NULL;
732
733 cst = isl_upoly_as_cst(up);
734
735 isl_int_mul(cst->n, cst->n, v);
736
737 return up;
738 }
739
740 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
741 __isl_take struct isl_upoly *up, isl_int v)
742 {
743 int i;
744 struct isl_upoly_rec *rec;
745
746 if (!up)
747 return NULL;
748
749 if (isl_upoly_is_cst(up))
750 return isl_upoly_cst_mul_isl_int(up, v);
751
752 up = isl_upoly_cow(up);
753 rec = isl_upoly_as_rec(up);
754 if (!rec)
755 goto error;
756
757 for (i = 0; i < rec->n; ++i) {
758 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
759 if (!rec->p[i])
760 goto error;
761 }
762
763 return up;
764 error:
765 isl_upoly_free(up);
766 return NULL;
767 }
768
769 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
770 __isl_take struct isl_upoly *up2)
771 {
772 struct isl_upoly_cst *cst1;
773 struct isl_upoly_cst *cst2;
774
775 up1 = isl_upoly_cow(up1);
776 if (!up1 || !up2)
777 goto error;
778
779 cst1 = isl_upoly_as_cst(up1);
780 cst2 = isl_upoly_as_cst(up2);
781
782 isl_int_mul(cst1->n, cst1->n, cst2->n);
783 isl_int_mul(cst1->d, cst1->d, cst2->d);
784
785 isl_upoly_cst_reduce(cst1);
786
787 isl_upoly_free(up2);
788 return up1;
789 error:
790 isl_upoly_free(up1);
791 isl_upoly_free(up2);
792 return NULL;
793 }
794
795 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
796 __isl_take struct isl_upoly *up2)
797 {
798 struct isl_upoly_rec *rec1;
799 struct isl_upoly_rec *rec2;
800 struct isl_upoly_rec *res;
801 int i, j;
802 int size;
803
804 rec1 = isl_upoly_as_rec(up1);
805 rec2 = isl_upoly_as_rec(up2);
806 if (!rec1 || !rec2)
807 goto error;
808 size = rec1->n + rec2->n - 1;
809 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
810 if (!res)
811 goto error;
812
813 for (i = 0; i < rec1->n; ++i) {
814 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
815 isl_upoly_copy(rec1->p[i]));
816 if (!res->p[i])
817 goto error;
818 res->n++;
819 }
820 for (; i < size; ++i) {
821 res->p[i] = isl_upoly_zero(up1->ctx);
822 if (!res->p[i])
823 goto error;
824 res->n++;
825 }
826 for (i = 0; i < rec1->n; ++i) {
827 for (j = 1; j < rec2->n; ++j) {
828 struct isl_upoly *up;
829 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
830 isl_upoly_copy(rec1->p[i]));
831 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
832 if (!res->p[i + j])
833 goto error;
834 }
835 }
836
837 isl_upoly_free(up1);
838 isl_upoly_free(up2);
839
840 return &res->up;
841 error:
842 isl_upoly_free(up1);
843 isl_upoly_free(up2);
844 isl_upoly_free(&res->up);
845 return NULL;
846 }
847
848 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
849 __isl_take struct isl_upoly *up2)
850 {
851 if (!up1 || !up2)
852 goto error;
853
854 if (isl_upoly_is_nan(up1)) {
855 isl_upoly_free(up2);
856 return up1;
857 }
858
859 if (isl_upoly_is_nan(up2)) {
860 isl_upoly_free(up1);
861 return up2;
862 }
863
864 if (isl_upoly_is_zero(up1)) {
865 isl_upoly_free(up2);
866 return up1;
867 }
868
869 if (isl_upoly_is_zero(up2)) {
870 isl_upoly_free(up1);
871 return up2;
872 }
873
874 if (isl_upoly_is_one(up1)) {
875 isl_upoly_free(up1);
876 return up2;
877 }
878
879 if (isl_upoly_is_one(up2)) {
880 isl_upoly_free(up2);
881 return up1;
882 }
883
884 if (up1->var < up2->var)
885 return isl_upoly_mul(up2, up1);
886
887 if (up2->var < up1->var) {
888 int i;
889 struct isl_upoly_rec *rec;
890 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
891 isl_ctx *ctx = up1->ctx;
892 isl_upoly_free(up1);
893 isl_upoly_free(up2);
894 return isl_upoly_nan(ctx);
895 }
896 up1 = isl_upoly_cow(up1);
897 rec = isl_upoly_as_rec(up1);
898 if (!rec)
899 goto error;
900
901 for (i = 0; i < rec->n; ++i) {
902 rec->p[i] = isl_upoly_mul(rec->p[i],
903 isl_upoly_copy(up2));
904 if (!rec->p[i])
905 goto error;
906 }
907 isl_upoly_free(up2);
908 return up1;
909 }
910
911 if (isl_upoly_is_cst(up1))
912 return isl_upoly_mul_cst(up1, up2);
913
914 return isl_upoly_mul_rec(up1, up2);
915 error:
916 isl_upoly_free(up1);
917 isl_upoly_free(up2);
918 return NULL;
919 }
920
921 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
922 unsigned power)
923 {
924 struct isl_upoly *res;
925
926 if (!up)
927 return NULL;
928 if (power == 1)
929 return up;
930
931 if (power % 2)
932 res = isl_upoly_copy(up);
933 else
934 res = isl_upoly_one(up->ctx);
935
936 while (power >>= 1) {
937 up = isl_upoly_mul(up, isl_upoly_copy(up));
938 if (power % 2)
939 res = isl_upoly_mul(res, isl_upoly_copy(up));
940 }
941
942 isl_upoly_free(up);
943 return res;
944 }
945
946 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
947 unsigned n_div, __isl_take struct isl_upoly *up)
948 {
949 struct isl_qpolynomial *qp = NULL;
950 unsigned total;
951
952 if (!dim || !up)
953 goto error;
954
955 total = isl_dim_total(dim);
956
957 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
958 if (!qp)
959 goto error;
960
961 qp->ref = 1;
962 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
963 if (!qp->div)
964 goto error;
965
966 qp->dim = dim;
967 qp->upoly = up;
968
969 return qp;
970 error:
971 isl_dim_free(dim);
972 isl_upoly_free(up);
973 isl_qpolynomial_free(qp);
974 return NULL;
975 }
976
977 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
978 {
979 if (!qp)
980 return NULL;
981
982 qp->ref++;
983 return qp;
984 }
985
986 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
987 {
988 struct isl_qpolynomial *dup;
989
990 if (!qp)
991 return NULL;
992
993 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
994 isl_upoly_copy(qp->upoly));
995 if (!dup)
996 return NULL;
997 isl_mat_free(dup->div);
998 dup->div = isl_mat_copy(qp->div);
999 if (!dup->div)
1000 goto error;
1001
1002 return dup;
1003 error:
1004 isl_qpolynomial_free(dup);
1005 return NULL;
1006 }
1007
1008 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1009 {
1010 if (!qp)
1011 return NULL;
1012
1013 if (qp->ref == 1)
1014 return qp;
1015 qp->ref--;
1016 return isl_qpolynomial_dup(qp);
1017 }
1018
1019 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1020 {
1021 if (!qp)
1022 return;
1023
1024 if (--qp->ref > 0)
1025 return;
1026
1027 isl_dim_free(qp->dim);
1028 isl_mat_free(qp->div);
1029 isl_upoly_free(qp->upoly);
1030
1031 free(qp);
1032 }
1033
1034 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1035 {
1036 int i;
1037 struct isl_upoly_rec *rec;
1038 struct isl_upoly_cst *cst;
1039
1040 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1041 if (!rec)
1042 return NULL;
1043 for (i = 0; i < 1 + power; ++i) {
1044 rec->p[i] = isl_upoly_zero(ctx);
1045 if (!rec->p[i])
1046 goto error;
1047 rec->n++;
1048 }
1049 cst = isl_upoly_as_cst(rec->p[power]);
1050 isl_int_set_si(cst->n, 1);
1051
1052 return &rec->up;
1053 error:
1054 isl_upoly_free(&rec->up);
1055 return NULL;
1056 }
1057
1058 /* r array maps original positions to new positions.
1059 */
1060 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1061 int *r)
1062 {
1063 int i;
1064 struct isl_upoly_rec *rec;
1065 struct isl_upoly *base;
1066 struct isl_upoly *res;
1067
1068 if (isl_upoly_is_cst(up))
1069 return up;
1070
1071 rec = isl_upoly_as_rec(up);
1072 if (!rec)
1073 goto error;
1074
1075 isl_assert(up->ctx, rec->n >= 1, goto error);
1076
1077 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1078 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1079
1080 for (i = rec->n - 2; i >= 0; --i) {
1081 res = isl_upoly_mul(res, isl_upoly_copy(base));
1082 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1083 }
1084
1085 isl_upoly_free(base);
1086 isl_upoly_free(up);
1087
1088 return res;
1089 error:
1090 isl_upoly_free(up);
1091 return NULL;
1092 }
1093
1094 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1095 {
1096 int n_row, n_col;
1097 int equal;
1098
1099 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1100 div1->n_col >= div2->n_col, return -1);
1101
1102 if (div1->n_row == div2->n_row)
1103 return isl_mat_is_equal(div1, div2);
1104
1105 n_row = div1->n_row;
1106 n_col = div1->n_col;
1107 div1->n_row = div2->n_row;
1108 div1->n_col = div2->n_col;
1109
1110 equal = isl_mat_is_equal(div1, div2);
1111
1112 div1->n_row = n_row;
1113 div1->n_col = n_col;
1114
1115 return equal;
1116 }
1117
1118 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1119 {
1120 int li, lj;
1121
1122 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1123 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1124
1125 if (li != lj)
1126 return li - lj;
1127
1128 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1129 }
1130
1131 struct isl_div_sort_info {
1132 isl_mat *div;
1133 int row;
1134 };
1135
1136 static int div_sort_cmp(const void *p1, const void *p2)
1137 {
1138 const struct isl_div_sort_info *i1, *i2;
1139 i1 = (const struct isl_div_sort_info *) p1;
1140 i2 = (const struct isl_div_sort_info *) p2;
1141
1142 return cmp_row(i1->div, i1->row, i2->row);
1143 }
1144
1145 /* Sort divs and remove duplicates.
1146 */
1147 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1148 {
1149 int i;
1150 int skip;
1151 int len;
1152 struct isl_div_sort_info *array = NULL;
1153 int *pos = NULL, *at = NULL;
1154 int *reordering = NULL;
1155 unsigned div_pos;
1156
1157 if (!qp)
1158 return NULL;
1159 if (qp->div->n_row <= 1)
1160 return qp;
1161
1162 div_pos = isl_dim_total(qp->dim);
1163
1164 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1165 qp->div->n_row);
1166 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1167 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1168 len = qp->div->n_col - 2;
1169 reordering = isl_alloc_array(qp->div->ctx, int, len);
1170 if (!array || !pos || !at || !reordering)
1171 goto error;
1172
1173 for (i = 0; i < qp->div->n_row; ++i) {
1174 array[i].div = qp->div;
1175 array[i].row = i;
1176 pos[i] = i;
1177 at[i] = i;
1178 }
1179
1180 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1181 div_sort_cmp);
1182
1183 for (i = 0; i < div_pos; ++i)
1184 reordering[i] = i;
1185
1186 for (i = 0; i < qp->div->n_row; ++i) {
1187 if (pos[array[i].row] == i)
1188 continue;
1189 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1190 pos[at[i]] = pos[array[i].row];
1191 at[pos[array[i].row]] = at[i];
1192 at[i] = array[i].row;
1193 pos[array[i].row] = i;
1194 }
1195
1196 skip = 0;
1197 for (i = 0; i < len - div_pos; ++i) {
1198 if (i > 0 &&
1199 isl_seq_eq(qp->div->row[i - skip - 1],
1200 qp->div->row[i - skip], qp->div->n_col)) {
1201 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1202 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1203 2 + div_pos + i - skip);
1204 qp->div = isl_mat_drop_cols(qp->div,
1205 2 + div_pos + i - skip, 1);
1206 skip++;
1207 }
1208 reordering[div_pos + array[i].row] = div_pos + i - skip;
1209 }
1210
1211 qp->upoly = reorder(qp->upoly, reordering);
1212
1213 if (!qp->upoly || !qp->div)
1214 goto error;
1215
1216 free(at);
1217 free(pos);
1218 free(array);
1219 free(reordering);
1220
1221 return qp;
1222 error:
1223 free(at);
1224 free(pos);
1225 free(array);
1226 free(reordering);
1227 isl_qpolynomial_free(qp);
1228 return NULL;
1229 }
1230
1231 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1232 int *exp, int first)
1233 {
1234 int i;
1235 struct isl_upoly_rec *rec;
1236
1237 if (isl_upoly_is_cst(up))
1238 return up;
1239
1240 if (up->var < first)
1241 return up;
1242
1243 if (exp[up->var - first] == up->var - first)
1244 return up;
1245
1246 up = isl_upoly_cow(up);
1247 if (!up)
1248 goto error;
1249
1250 up->var = exp[up->var - first] + first;
1251
1252 rec = isl_upoly_as_rec(up);
1253 if (!rec)
1254 goto error;
1255
1256 for (i = 0; i < rec->n; ++i) {
1257 rec->p[i] = expand(rec->p[i], exp, first);
1258 if (!rec->p[i])
1259 goto error;
1260 }
1261
1262 return up;
1263 error:
1264 isl_upoly_free(up);
1265 return NULL;
1266 }
1267
1268 static __isl_give isl_qpolynomial *with_merged_divs(
1269 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1270 __isl_take isl_qpolynomial *qp2),
1271 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1272 {
1273 int *exp1 = NULL;
1274 int *exp2 = NULL;
1275 isl_mat *div = NULL;
1276
1277 qp1 = isl_qpolynomial_cow(qp1);
1278 qp2 = isl_qpolynomial_cow(qp2);
1279
1280 if (!qp1 || !qp2)
1281 goto error;
1282
1283 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1284 qp1->div->n_col >= qp2->div->n_col, goto error);
1285
1286 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1287 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1288 if (!exp1 || !exp2)
1289 goto error;
1290
1291 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1292 if (!div)
1293 goto error;
1294
1295 isl_mat_free(qp1->div);
1296 qp1->div = isl_mat_copy(div);
1297 isl_mat_free(qp2->div);
1298 qp2->div = isl_mat_copy(div);
1299
1300 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1301 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1302
1303 if (!qp1->upoly || !qp2->upoly)
1304 goto error;
1305
1306 isl_mat_free(div);
1307 free(exp1);
1308 free(exp2);
1309
1310 return fn(qp1, qp2);
1311 error:
1312 isl_mat_free(div);
1313 free(exp1);
1314 free(exp2);
1315 isl_qpolynomial_free(qp1);
1316 isl_qpolynomial_free(qp2);
1317 return NULL;
1318 }
1319
1320 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1321 __isl_take isl_qpolynomial *qp2)
1322 {
1323 qp1 = isl_qpolynomial_cow(qp1);
1324
1325 if (!qp1 || !qp2)
1326 goto error;
1327
1328 if (qp1->div->n_row < qp2->div->n_row)
1329 return isl_qpolynomial_add(qp2, qp1);
1330
1331 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1332 if (!compatible_divs(qp1->div, qp2->div))
1333 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1334
1335 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1336 if (!qp1->upoly)
1337 goto error;
1338
1339 isl_qpolynomial_free(qp2);
1340
1341 return qp1;
1342 error:
1343 isl_qpolynomial_free(qp1);
1344 isl_qpolynomial_free(qp2);
1345 return NULL;
1346 }
1347
1348 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1349 __isl_keep isl_set *dom,
1350 __isl_take isl_qpolynomial *qp1,
1351 __isl_take isl_qpolynomial *qp2)
1352 {
1353 qp1 = isl_qpolynomial_add(qp1, qp2);
1354 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1355 return qp1;
1356 }
1357
1358 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1359 __isl_take isl_qpolynomial *qp2)
1360 {
1361 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1362 }
1363
1364 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1365 __isl_take isl_qpolynomial *qp, isl_int v)
1366 {
1367 if (isl_int_is_zero(v))
1368 return qp;
1369
1370 qp = isl_qpolynomial_cow(qp);
1371 if (!qp)
1372 return NULL;
1373
1374 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1375 if (!qp->upoly)
1376 goto error;
1377
1378 return qp;
1379 error:
1380 isl_qpolynomial_free(qp);
1381 return NULL;
1382
1383 }
1384
1385 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1386 {
1387 if (!qp)
1388 return NULL;
1389
1390 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1391 }
1392
1393 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1394 __isl_take isl_qpolynomial *qp, isl_int v)
1395 {
1396 if (isl_int_is_one(v))
1397 return qp;
1398
1399 if (qp && isl_int_is_zero(v)) {
1400 isl_qpolynomial *zero;
1401 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1402 isl_qpolynomial_free(qp);
1403 return zero;
1404 }
1405
1406 qp = isl_qpolynomial_cow(qp);
1407 if (!qp)
1408 return NULL;
1409
1410 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1411 if (!qp->upoly)
1412 goto error;
1413
1414 return qp;
1415 error:
1416 isl_qpolynomial_free(qp);
1417 return NULL;
1418 }
1419
1420 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1421 __isl_take isl_qpolynomial *qp2)
1422 {
1423 qp1 = isl_qpolynomial_cow(qp1);
1424
1425 if (!qp1 || !qp2)
1426 goto error;
1427
1428 if (qp1->div->n_row < qp2->div->n_row)
1429 return isl_qpolynomial_mul(qp2, qp1);
1430
1431 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1432 if (!compatible_divs(qp1->div, qp2->div))
1433 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1434
1435 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1436 if (!qp1->upoly)
1437 goto error;
1438
1439 isl_qpolynomial_free(qp2);
1440
1441 return qp1;
1442 error:
1443 isl_qpolynomial_free(qp1);
1444 isl_qpolynomial_free(qp2);
1445 return NULL;
1446 }
1447
1448 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1449 unsigned power)
1450 {
1451 qp = isl_qpolynomial_cow(qp);
1452
1453 if (!qp)
1454 return NULL;
1455
1456 qp->upoly = isl_upoly_pow(qp->upoly, power);
1457 if (!qp->upoly)
1458 goto error;
1459
1460 return qp;
1461 error:
1462 isl_qpolynomial_free(qp);
1463 return NULL;
1464 }
1465
1466 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1467 {
1468 if (!dim)
1469 return NULL;
1470 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1471 }
1472
1473 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1474 {
1475 if (!dim)
1476 return NULL;
1477 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1478 }
1479
1480 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1481 {
1482 if (!dim)
1483 return NULL;
1484 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1485 }
1486
1487 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1488 {
1489 if (!dim)
1490 return NULL;
1491 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1495 {
1496 if (!dim)
1497 return NULL;
1498 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1499 }
1500
1501 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1502 isl_int v)
1503 {
1504 struct isl_qpolynomial *qp;
1505 struct isl_upoly_cst *cst;
1506
1507 if (!dim)
1508 return NULL;
1509
1510 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1511 if (!qp)
1512 return NULL;
1513
1514 cst = isl_upoly_as_cst(qp->upoly);
1515 isl_int_set(cst->n, v);
1516
1517 return qp;
1518 }
1519
1520 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1521 isl_int *n, isl_int *d)
1522 {
1523 struct isl_upoly_cst *cst;
1524
1525 if (!qp)
1526 return -1;
1527
1528 if (!isl_upoly_is_cst(qp->upoly))
1529 return 0;
1530
1531 cst = isl_upoly_as_cst(qp->upoly);
1532 if (!cst)
1533 return -1;
1534
1535 if (n)
1536 isl_int_set(*n, cst->n);
1537 if (d)
1538 isl_int_set(*d, cst->d);
1539
1540 return 1;
1541 }
1542
1543 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1544 {
1545 int is_cst;
1546 struct isl_upoly_rec *rec;
1547
1548 if (!up)
1549 return -1;
1550
1551 if (up->var < 0)
1552 return 1;
1553
1554 rec = isl_upoly_as_rec(up);
1555 if (!rec)
1556 return -1;
1557
1558 if (rec->n > 2)
1559 return 0;
1560
1561 isl_assert(up->ctx, rec->n > 1, return -1);
1562
1563 is_cst = isl_upoly_is_cst(rec->p[1]);
1564 if (is_cst < 0)
1565 return -1;
1566 if (!is_cst)
1567 return 0;
1568
1569 return isl_upoly_is_affine(rec->p[0]);
1570 }
1571
1572 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1573 {
1574 if (!qp)
1575 return -1;
1576
1577 if (qp->div->n_row > 0)
1578 return 0;
1579
1580 return isl_upoly_is_affine(qp->upoly);
1581 }
1582
1583 static void update_coeff(__isl_keep isl_vec *aff,
1584 __isl_keep struct isl_upoly_cst *cst, int pos)
1585 {
1586 isl_int gcd;
1587 isl_int f;
1588
1589 if (isl_int_is_zero(cst->n))
1590 return;
1591
1592 isl_int_init(gcd);
1593 isl_int_init(f);
1594 isl_int_gcd(gcd, cst->d, aff->el[0]);
1595 isl_int_divexact(f, cst->d, gcd);
1596 isl_int_divexact(gcd, aff->el[0], gcd);
1597 isl_seq_scale(aff->el, aff->el, f, aff->size);
1598 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1599 isl_int_clear(gcd);
1600 isl_int_clear(f);
1601 }
1602
1603 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1604 __isl_keep isl_vec *aff)
1605 {
1606 struct isl_upoly_cst *cst;
1607 struct isl_upoly_rec *rec;
1608
1609 if (!up || !aff)
1610 return -1;
1611
1612 if (up->var < 0) {
1613 struct isl_upoly_cst *cst;
1614
1615 cst = isl_upoly_as_cst(up);
1616 if (!cst)
1617 return -1;
1618 update_coeff(aff, cst, 0);
1619 return 0;
1620 }
1621
1622 rec = isl_upoly_as_rec(up);
1623 if (!rec)
1624 return -1;
1625 isl_assert(up->ctx, rec->n == 2, return -1);
1626
1627 cst = isl_upoly_as_cst(rec->p[1]);
1628 if (!cst)
1629 return -1;
1630 update_coeff(aff, cst, 1 + up->var);
1631
1632 return isl_upoly_update_affine(rec->p[0], aff);
1633 }
1634
1635 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1636 __isl_keep isl_qpolynomial *qp)
1637 {
1638 isl_vec *aff;
1639 unsigned d;
1640
1641 if (!qp)
1642 return NULL;
1643
1644 d = isl_dim_total(qp->dim);
1645 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1646 if (!aff)
1647 return NULL;
1648
1649 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1650 isl_int_set_si(aff->el[0], 1);
1651
1652 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1653 goto error;
1654
1655 return aff;
1656 error:
1657 isl_vec_free(aff);
1658 return NULL;
1659 }
1660
1661 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1662 __isl_keep isl_qpolynomial *qp2)
1663 {
1664 if (!qp1 || !qp2)
1665 return -1;
1666
1667 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1668 }
1669
1670 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1671 {
1672 int i;
1673 struct isl_upoly_rec *rec;
1674
1675 if (isl_upoly_is_cst(up)) {
1676 struct isl_upoly_cst *cst;
1677 cst = isl_upoly_as_cst(up);
1678 if (!cst)
1679 return;
1680 isl_int_lcm(*d, *d, cst->d);
1681 return;
1682 }
1683
1684 rec = isl_upoly_as_rec(up);
1685 if (!rec)
1686 return;
1687
1688 for (i = 0; i < rec->n; ++i)
1689 upoly_update_den(rec->p[i], d);
1690 }
1691
1692 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1693 {
1694 isl_int_set_si(*d, 1);
1695 if (!qp)
1696 return;
1697 upoly_update_den(qp->upoly, d);
1698 }
1699
1700 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1701 int pos, int power)
1702 {
1703 struct isl_ctx *ctx;
1704
1705 if (!dim)
1706 return NULL;
1707
1708 ctx = dim->ctx;
1709
1710 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1711 }
1712
1713 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1714 enum isl_dim_type type, unsigned pos)
1715 {
1716 if (!dim)
1717 return NULL;
1718
1719 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1720 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1721
1722 if (type == isl_dim_set)
1723 pos += isl_dim_size(dim, isl_dim_param);
1724
1725 return isl_qpolynomial_var_pow(dim, pos, 1);
1726 error:
1727 isl_dim_free(dim);
1728 return NULL;
1729 }
1730
1731 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1732 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1733 {
1734 int i;
1735 struct isl_upoly_rec *rec;
1736 struct isl_upoly *base, *res;
1737
1738 if (!up)
1739 return NULL;
1740
1741 if (isl_upoly_is_cst(up))
1742 return up;
1743
1744 if (up->var < first)
1745 return up;
1746
1747 rec = isl_upoly_as_rec(up);
1748 if (!rec)
1749 goto error;
1750
1751 isl_assert(up->ctx, rec->n >= 1, goto error);
1752
1753 if (up->var >= first + n)
1754 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1755 else
1756 base = isl_upoly_copy(subs[up->var - first]);
1757
1758 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1759 for (i = rec->n - 2; i >= 0; --i) {
1760 struct isl_upoly *t;
1761 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1762 res = isl_upoly_mul(res, isl_upoly_copy(base));
1763 res = isl_upoly_sum(res, t);
1764 }
1765
1766 isl_upoly_free(base);
1767 isl_upoly_free(up);
1768
1769 return res;
1770 error:
1771 isl_upoly_free(up);
1772 return NULL;
1773 }
1774
1775 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1776 isl_int denom, unsigned len)
1777 {
1778 int i;
1779 struct isl_upoly *up;
1780
1781 isl_assert(ctx, len >= 1, return NULL);
1782
1783 up = isl_upoly_rat_cst(ctx, f[0], denom);
1784 for (i = 0; i < len - 1; ++i) {
1785 struct isl_upoly *t;
1786 struct isl_upoly *c;
1787
1788 if (isl_int_is_zero(f[1 + i]))
1789 continue;
1790
1791 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1792 t = isl_upoly_var_pow(ctx, i, 1);
1793 t = isl_upoly_mul(c, t);
1794 up = isl_upoly_sum(up, t);
1795 }
1796
1797 return up;
1798 }
1799
1800 /* Remove common factor of non-constant terms and denominator.
1801 */
1802 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1803 {
1804 isl_ctx *ctx = qp->div->ctx;
1805 unsigned total = qp->div->n_col - 2;
1806
1807 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1808 isl_int_gcd(ctx->normalize_gcd,
1809 ctx->normalize_gcd, qp->div->row[div][0]);
1810 if (isl_int_is_one(ctx->normalize_gcd))
1811 return;
1812
1813 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1814 ctx->normalize_gcd, total);
1815 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1816 ctx->normalize_gcd);
1817 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1818 ctx->normalize_gcd);
1819 }
1820
1821 /* Replace the integer division identified by "div" by the polynomial "s".
1822 * The integer division is assumed not to appear in the definition
1823 * of any other integer divisions.
1824 */
1825 static __isl_give isl_qpolynomial *substitute_div(
1826 __isl_take isl_qpolynomial *qp,
1827 int div, __isl_take struct isl_upoly *s)
1828 {
1829 int i;
1830 int total;
1831 int *reordering;
1832
1833 if (!qp || !s)
1834 goto error;
1835
1836 qp = isl_qpolynomial_cow(qp);
1837 if (!qp)
1838 goto error;
1839
1840 total = isl_dim_total(qp->dim);
1841 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1842 if (!qp->upoly)
1843 goto error;
1844
1845 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1846 if (!reordering)
1847 goto error;
1848 for (i = 0; i < total + div; ++i)
1849 reordering[i] = i;
1850 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1851 reordering[i] = i - 1;
1852 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1853 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1854 qp->upoly = reorder(qp->upoly, reordering);
1855 free(reordering);
1856
1857 if (!qp->upoly || !qp->div)
1858 goto error;
1859
1860 isl_upoly_free(s);
1861 return qp;
1862 error:
1863 isl_qpolynomial_free(qp);
1864 isl_upoly_free(s);
1865 return NULL;
1866 }
1867
1868 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1869 * divisions because d is equal to 1 by their definition, i.e., e.
1870 */
1871 static __isl_give isl_qpolynomial *substitute_non_divs(
1872 __isl_take isl_qpolynomial *qp)
1873 {
1874 int i, j;
1875 int total;
1876 struct isl_upoly *s;
1877
1878 if (!qp)
1879 return NULL;
1880
1881 total = isl_dim_total(qp->dim);
1882 for (i = 0; qp && i < qp->div->n_row; ++i) {
1883 if (!isl_int_is_one(qp->div->row[i][0]))
1884 continue;
1885 for (j = i + 1; j < qp->div->n_row; ++j) {
1886 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1887 continue;
1888 isl_seq_combine(qp->div->row[j] + 1,
1889 qp->div->ctx->one, qp->div->row[j] + 1,
1890 qp->div->row[j][2 + total + i],
1891 qp->div->row[i] + 1, 1 + total + i);
1892 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1893 normalize_div(qp, j);
1894 }
1895 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1896 qp->div->row[i][0], qp->div->n_col - 1);
1897 qp = substitute_div(qp, i, s);
1898 --i;
1899 }
1900
1901 return qp;
1902 }
1903
1904 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1905 * with d the denominator. When replacing the coefficient e of x by
1906 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1907 * inside the division, so we need to add floor(e/d) * x outside.
1908 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1909 * to adjust the coefficient of x in each later div that depends on the
1910 * current div "div" and also in the affine expression "aff"
1911 * (if it too depends on "div").
1912 */
1913 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1914 __isl_keep isl_vec *aff)
1915 {
1916 int i, j;
1917 isl_int v;
1918 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1919
1920 isl_int_init(v);
1921 for (i = 0; i < 1 + total + div; ++i) {
1922 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1923 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1924 continue;
1925 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1926 isl_int_fdiv_r(qp->div->row[div][1 + i],
1927 qp->div->row[div][1 + i], qp->div->row[div][0]);
1928 if (!isl_int_is_zero(aff->el[1 + total + div]))
1929 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1930 for (j = div + 1; j < qp->div->n_row; ++j) {
1931 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1932 continue;
1933 isl_int_addmul(qp->div->row[j][1 + i],
1934 v, qp->div->row[j][2 + total + div]);
1935 }
1936 }
1937 isl_int_clear(v);
1938 }
1939
1940 /* Check if the last non-zero coefficient is bigger that half of the
1941 * denominator. If so, we will invert the div to further reduce the number
1942 * of distinct divs that may appear.
1943 * If the last non-zero coefficient is exactly half the denominator,
1944 * then we continue looking for earlier coefficients that are bigger
1945 * than half the denominator.
1946 */
1947 static int needs_invert(__isl_keep isl_mat *div, int row)
1948 {
1949 int i;
1950 int cmp;
1951
1952 for (i = div->n_col - 1; i >= 1; --i) {
1953 if (isl_int_is_zero(div->row[row][i]))
1954 continue;
1955 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1956 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1957 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1958 if (cmp)
1959 return cmp > 0;
1960 if (i == 1)
1961 return 1;
1962 }
1963
1964 return 0;
1965 }
1966
1967 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1968 * We only invert the coefficients of e (and the coefficient of q in
1969 * later divs and in "aff"). After calling this function, the
1970 * coefficients of e should be reduced again.
1971 */
1972 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1973 __isl_keep isl_vec *aff)
1974 {
1975 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1976
1977 isl_seq_neg(qp->div->row[div] + 1,
1978 qp->div->row[div] + 1, qp->div->n_col - 1);
1979 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1980 isl_int_add(qp->div->row[div][1],
1981 qp->div->row[div][1], qp->div->row[div][0]);
1982 if (!isl_int_is_zero(aff->el[1 + total + div]))
1983 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1984 isl_mat_col_mul(qp->div, 2 + total + div,
1985 qp->div->ctx->negone, 2 + total + div);
1986 }
1987
1988 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1989 * in the interval [0, d-1], with d the denominator and such that the
1990 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1991 *
1992 * After the reduction, some divs may have become redundant or identical,
1993 * so we call substitute_non_divs and sort_divs. If these functions
1994 * eliminate divs or merge two or more divs into one, the coefficients
1995 * of the enclosing divs may have to be reduced again, so we call
1996 * ourselves recursively if the number of divs decreases.
1997 */
1998 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
1999 {
2000 int i;
2001 isl_vec *aff = NULL;
2002 struct isl_upoly *s;
2003 unsigned n_div;
2004
2005 if (!qp)
2006 return NULL;
2007
2008 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2009 aff = isl_vec_clr(aff);
2010 if (!aff)
2011 goto error;
2012
2013 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2014
2015 for (i = 0; i < qp->div->n_row; ++i) {
2016 normalize_div(qp, i);
2017 reduce_div(qp, i, aff);
2018 if (needs_invert(qp->div, i)) {
2019 invert_div(qp, i, aff);
2020 reduce_div(qp, i, aff);
2021 }
2022 }
2023
2024 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2025 qp->div->ctx->one, aff->size);
2026 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2027 isl_upoly_free(s);
2028 if (!qp->upoly)
2029 goto error;
2030
2031 isl_vec_free(aff);
2032
2033 n_div = qp->div->n_row;
2034 qp = substitute_non_divs(qp);
2035 qp = sort_divs(qp);
2036 if (qp && qp->div->n_row < n_div)
2037 return reduce_divs(qp);
2038
2039 return qp;
2040 error:
2041 isl_qpolynomial_free(qp);
2042 isl_vec_free(aff);
2043 return NULL;
2044 }
2045
2046 /* Assumes each div only depends on earlier divs.
2047 */
2048 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2049 int power)
2050 {
2051 struct isl_qpolynomial *qp = NULL;
2052 struct isl_upoly_rec *rec;
2053 struct isl_upoly_cst *cst;
2054 int i, d;
2055 int pos;
2056
2057 if (!div)
2058 return NULL;
2059
2060 d = div->line - div->bmap->div;
2061
2062 pos = isl_dim_total(div->bmap->dim) + d;
2063 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2064 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2065 div->bmap->n_div, &rec->up);
2066 if (!qp)
2067 goto error;
2068
2069 for (i = 0; i < div->bmap->n_div; ++i)
2070 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2071
2072 for (i = 0; i < 1 + power; ++i) {
2073 rec->p[i] = isl_upoly_zero(div->ctx);
2074 if (!rec->p[i])
2075 goto error;
2076 rec->n++;
2077 }
2078 cst = isl_upoly_as_cst(rec->p[power]);
2079 isl_int_set_si(cst->n, 1);
2080
2081 isl_div_free(div);
2082
2083 qp = reduce_divs(qp);
2084
2085 return qp;
2086 error:
2087 isl_qpolynomial_free(qp);
2088 isl_div_free(div);
2089 return NULL;
2090 }
2091
2092 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2093 {
2094 return isl_qpolynomial_div_pow(div, 1);
2095 }
2096
2097 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2098 const isl_int n, const isl_int d)
2099 {
2100 struct isl_qpolynomial *qp;
2101 struct isl_upoly_cst *cst;
2102
2103 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2104 if (!qp)
2105 return NULL;
2106
2107 cst = isl_upoly_as_cst(qp->upoly);
2108 isl_int_set(cst->n, n);
2109 isl_int_set(cst->d, d);
2110
2111 return qp;
2112 }
2113
2114 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2115 {
2116 struct isl_upoly_rec *rec;
2117 int i;
2118
2119 if (!up)
2120 return -1;
2121
2122 if (isl_upoly_is_cst(up))
2123 return 0;
2124
2125 if (up->var < d)
2126 active[up->var] = 1;
2127
2128 rec = isl_upoly_as_rec(up);
2129 for (i = 0; i < rec->n; ++i)
2130 if (up_set_active(rec->p[i], active, d) < 0)
2131 return -1;
2132
2133 return 0;
2134 }
2135
2136 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2137 {
2138 int i, j;
2139 int d = isl_dim_total(qp->dim);
2140
2141 if (!qp || !active)
2142 return -1;
2143
2144 for (i = 0; i < d; ++i)
2145 for (j = 0; j < qp->div->n_row; ++j) {
2146 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2147 continue;
2148 active[i] = 1;
2149 break;
2150 }
2151
2152 return up_set_active(qp->upoly, active, d);
2153 }
2154
2155 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2156 enum isl_dim_type type, unsigned first, unsigned n)
2157 {
2158 int i;
2159 int *active = NULL;
2160 int involves = 0;
2161
2162 if (!qp)
2163 return -1;
2164 if (n == 0)
2165 return 0;
2166
2167 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2168 return -1);
2169 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2170 type == isl_dim_set, return -1);
2171
2172 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2173 if (set_active(qp, active) < 0)
2174 goto error;
2175
2176 if (type == isl_dim_set)
2177 first += isl_dim_size(qp->dim, isl_dim_param);
2178 for (i = 0; i < n; ++i)
2179 if (active[first + i]) {
2180 involves = 1;
2181 break;
2182 }
2183
2184 free(active);
2185
2186 return involves;
2187 error:
2188 free(active);
2189 return -1;
2190 }
2191
2192 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2193 * of the divs that do appear in the quasi-polynomial.
2194 */
2195 static __isl_give isl_qpolynomial *remove_redundant_divs(
2196 __isl_take isl_qpolynomial *qp)
2197 {
2198 int i, j;
2199 int d;
2200 int len;
2201 int skip;
2202 int *active = NULL;
2203 int *reordering = NULL;
2204 int redundant = 0;
2205 int n_div;
2206
2207 if (!qp)
2208 return NULL;
2209 if (qp->div->n_row == 0)
2210 return qp;
2211
2212 d = isl_dim_total(qp->dim);
2213 len = qp->div->n_col - 2;
2214 active = isl_calloc_array(qp->ctx, int, len);
2215 if (!active)
2216 goto error;
2217
2218 if (up_set_active(qp->upoly, active, len) < 0)
2219 goto error;
2220
2221 for (i = qp->div->n_row - 1; i >= 0; --i) {
2222 if (!active[d + i]) {
2223 redundant = 1;
2224 continue;
2225 }
2226 for (j = 0; j < i; ++j) {
2227 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2228 continue;
2229 active[d + j] = 1;
2230 break;
2231 }
2232 }
2233
2234 if (!redundant) {
2235 free(active);
2236 return qp;
2237 }
2238
2239 reordering = isl_alloc_array(qp->div->ctx, int, len);
2240 if (!reordering)
2241 goto error;
2242
2243 for (i = 0; i < d; ++i)
2244 reordering[i] = i;
2245
2246 skip = 0;
2247 n_div = qp->div->n_row;
2248 for (i = 0; i < n_div; ++i) {
2249 if (!active[d + i]) {
2250 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2251 qp->div = isl_mat_drop_cols(qp->div,
2252 2 + d + i - skip, 1);
2253 skip++;
2254 }
2255 reordering[d + i] = d + i - skip;
2256 }
2257
2258 qp->upoly = reorder(qp->upoly, reordering);
2259
2260 if (!qp->upoly || !qp->div)
2261 goto error;
2262
2263 free(active);
2264 free(reordering);
2265
2266 return qp;
2267 error:
2268 free(active);
2269 free(reordering);
2270 isl_qpolynomial_free(qp);
2271 return NULL;
2272 }
2273
2274 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2275 unsigned first, unsigned n)
2276 {
2277 int i;
2278 struct isl_upoly_rec *rec;
2279
2280 if (!up)
2281 return NULL;
2282 if (n == 0 || up->var < 0 || up->var < first)
2283 return up;
2284 if (up->var < first + n) {
2285 up = replace_by_constant_term(up);
2286 return isl_upoly_drop(up, first, n);
2287 }
2288 up = isl_upoly_cow(up);
2289 if (!up)
2290 return NULL;
2291 up->var -= n;
2292 rec = isl_upoly_as_rec(up);
2293 if (!rec)
2294 goto error;
2295
2296 for (i = 0; i < rec->n; ++i) {
2297 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2298 if (!rec->p[i])
2299 goto error;
2300 }
2301
2302 return up;
2303 error:
2304 isl_upoly_free(up);
2305 return NULL;
2306 }
2307
2308 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2309 __isl_take isl_qpolynomial *qp,
2310 enum isl_dim_type type, unsigned pos, const char *s)
2311 {
2312 qp = isl_qpolynomial_cow(qp);
2313 if (!qp)
2314 return NULL;
2315 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2316 if (!qp->dim)
2317 goto error;
2318 return qp;
2319 error:
2320 isl_qpolynomial_free(qp);
2321 return NULL;
2322 }
2323
2324 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2325 __isl_take isl_qpolynomial *qp,
2326 enum isl_dim_type type, unsigned first, unsigned n)
2327 {
2328 if (!qp)
2329 return NULL;
2330 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2331 return qp;
2332
2333 qp = isl_qpolynomial_cow(qp);
2334 if (!qp)
2335 return NULL;
2336
2337 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2338 goto error);
2339 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2340 type == isl_dim_set, goto error);
2341
2342 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2343 if (!qp->dim)
2344 goto error;
2345
2346 if (type == isl_dim_set)
2347 first += isl_dim_size(qp->dim, isl_dim_param);
2348
2349 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2350 if (!qp->div)
2351 goto error;
2352
2353 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2354 if (!qp->upoly)
2355 goto error;
2356
2357 return qp;
2358 error:
2359 isl_qpolynomial_free(qp);
2360 return NULL;
2361 }
2362
2363 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2364 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2365 {
2366 int i, j, k;
2367 isl_int denom;
2368 unsigned total;
2369 unsigned n_div;
2370 struct isl_upoly *up;
2371
2372 if (!eq)
2373 goto error;
2374 if (eq->n_eq == 0) {
2375 isl_basic_set_free(eq);
2376 return qp;
2377 }
2378
2379 qp = isl_qpolynomial_cow(qp);
2380 if (!qp)
2381 goto error;
2382 qp->div = isl_mat_cow(qp->div);
2383 if (!qp->div)
2384 goto error;
2385
2386 total = 1 + isl_dim_total(eq->dim);
2387 n_div = eq->n_div;
2388 isl_int_init(denom);
2389 for (i = 0; i < eq->n_eq; ++i) {
2390 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2391 if (j < 0 || j == 0 || j >= total)
2392 continue;
2393
2394 for (k = 0; k < qp->div->n_row; ++k) {
2395 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2396 continue;
2397 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2398 &qp->div->row[k][0]);
2399 normalize_div(qp, k);
2400 }
2401
2402 if (isl_int_is_pos(eq->eq[i][j]))
2403 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2404 isl_int_abs(denom, eq->eq[i][j]);
2405 isl_int_set_si(eq->eq[i][j], 0);
2406
2407 up = isl_upoly_from_affine(qp->dim->ctx,
2408 eq->eq[i], denom, total);
2409 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2410 isl_upoly_free(up);
2411 }
2412 isl_int_clear(denom);
2413
2414 if (!qp->upoly)
2415 goto error;
2416
2417 isl_basic_set_free(eq);
2418
2419 qp = substitute_non_divs(qp);
2420 qp = sort_divs(qp);
2421
2422 return qp;
2423 error:
2424 isl_basic_set_free(eq);
2425 isl_qpolynomial_free(qp);
2426 return NULL;
2427 }
2428
2429 static __isl_give isl_basic_set *add_div_constraints(
2430 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2431 {
2432 int i;
2433 unsigned total;
2434
2435 if (!bset || !div)
2436 goto error;
2437
2438 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2439 if (!bset)
2440 goto error;
2441 total = isl_basic_set_total_dim(bset);
2442 for (i = 0; i < div->n_row; ++i)
2443 if (isl_basic_set_add_div_constraints_var(bset,
2444 total - div->n_row + i, div->row[i]) < 0)
2445 goto error;
2446
2447 isl_mat_free(div);
2448 return bset;
2449 error:
2450 isl_mat_free(div);
2451 isl_basic_set_free(bset);
2452 return NULL;
2453 }
2454
2455 /* Look for equalities among the variables shared by context and qp
2456 * and the integer divisions of qp, if any.
2457 * The equalities are then used to eliminate variables and/or integer
2458 * divisions from qp.
2459 */
2460 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2461 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2462 {
2463 isl_basic_set *aff;
2464
2465 if (!qp)
2466 goto error;
2467 if (qp->div->n_row > 0) {
2468 isl_basic_set *bset;
2469 context = isl_set_add_dims(context, isl_dim_set,
2470 qp->div->n_row);
2471 bset = isl_basic_set_universe(isl_set_get_dim(context));
2472 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2473 context = isl_set_intersect(context,
2474 isl_set_from_basic_set(bset));
2475 }
2476
2477 aff = isl_set_affine_hull(context);
2478 return isl_qpolynomial_substitute_equalities(qp, aff);
2479 error:
2480 isl_qpolynomial_free(qp);
2481 isl_set_free(context);
2482 return NULL;
2483 }
2484
2485 #undef PW
2486 #define PW isl_pw_qpolynomial
2487 #undef EL
2488 #define EL isl_qpolynomial
2489 #undef IS_ZERO
2490 #define IS_ZERO is_zero
2491 #undef FIELD
2492 #define FIELD qp
2493
2494 #include <isl_pw_templ.c>
2495
2496 #undef UNION
2497 #define UNION isl_union_pw_qpolynomial
2498 #undef PART
2499 #define PART isl_pw_qpolynomial
2500 #undef PARTS
2501 #define PARTS pw_qpolynomial
2502
2503 #include <isl_union_templ.c>
2504
2505 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2506 {
2507 if (!pwqp)
2508 return -1;
2509
2510 if (pwqp->n != -1)
2511 return 0;
2512
2513 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2514 return 0;
2515
2516 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2517 }
2518
2519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2520 __isl_take isl_pw_qpolynomial *pwqp1,
2521 __isl_take isl_pw_qpolynomial *pwqp2)
2522 {
2523 int i, j, n;
2524 struct isl_pw_qpolynomial *res;
2525
2526 if (!pwqp1 || !pwqp2)
2527 goto error;
2528
2529 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2530 goto error);
2531
2532 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2533 isl_pw_qpolynomial_free(pwqp2);
2534 return pwqp1;
2535 }
2536
2537 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2538 isl_pw_qpolynomial_free(pwqp1);
2539 return pwqp2;
2540 }
2541
2542 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2543 isl_pw_qpolynomial_free(pwqp1);
2544 return pwqp2;
2545 }
2546
2547 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2548 isl_pw_qpolynomial_free(pwqp2);
2549 return pwqp1;
2550 }
2551
2552 n = pwqp1->n * pwqp2->n;
2553 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2554
2555 for (i = 0; i < pwqp1->n; ++i) {
2556 for (j = 0; j < pwqp2->n; ++j) {
2557 struct isl_set *common;
2558 struct isl_qpolynomial *prod;
2559 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2560 isl_set_copy(pwqp2->p[j].set));
2561 if (isl_set_plain_is_empty(common)) {
2562 isl_set_free(common);
2563 continue;
2564 }
2565
2566 prod = isl_qpolynomial_mul(
2567 isl_qpolynomial_copy(pwqp1->p[i].qp),
2568 isl_qpolynomial_copy(pwqp2->p[j].qp));
2569
2570 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2571 }
2572 }
2573
2574 isl_pw_qpolynomial_free(pwqp1);
2575 isl_pw_qpolynomial_free(pwqp2);
2576
2577 return res;
2578 error:
2579 isl_pw_qpolynomial_free(pwqp1);
2580 isl_pw_qpolynomial_free(pwqp2);
2581 return NULL;
2582 }
2583
2584 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2585 __isl_take isl_pw_qpolynomial *pwqp)
2586 {
2587 int i;
2588
2589 if (!pwqp)
2590 return NULL;
2591
2592 if (isl_pw_qpolynomial_is_zero(pwqp))
2593 return pwqp;
2594
2595 pwqp = isl_pw_qpolynomial_cow(pwqp);
2596 if (!pwqp)
2597 return NULL;
2598
2599 for (i = 0; i < pwqp->n; ++i) {
2600 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2601 if (!pwqp->p[i].qp)
2602 goto error;
2603 }
2604
2605 return pwqp;
2606 error:
2607 isl_pw_qpolynomial_free(pwqp);
2608 return NULL;
2609 }
2610
2611 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2612 __isl_take isl_pw_qpolynomial *pwqp1,
2613 __isl_take isl_pw_qpolynomial *pwqp2)
2614 {
2615 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2616 }
2617
2618 __isl_give struct isl_upoly *isl_upoly_eval(
2619 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2620 {
2621 int i;
2622 struct isl_upoly_rec *rec;
2623 struct isl_upoly *res;
2624 struct isl_upoly *base;
2625
2626 if (isl_upoly_is_cst(up)) {
2627 isl_vec_free(vec);
2628 return up;
2629 }
2630
2631 rec = isl_upoly_as_rec(up);
2632 if (!rec)
2633 goto error;
2634
2635 isl_assert(up->ctx, rec->n >= 1, goto error);
2636
2637 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2638
2639 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2640 isl_vec_copy(vec));
2641
2642 for (i = rec->n - 2; i >= 0; --i) {
2643 res = isl_upoly_mul(res, isl_upoly_copy(base));
2644 res = isl_upoly_sum(res,
2645 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2646 isl_vec_copy(vec)));
2647 }
2648
2649 isl_upoly_free(base);
2650 isl_upoly_free(up);
2651 isl_vec_free(vec);
2652 return res;
2653 error:
2654 isl_upoly_free(up);
2655 isl_vec_free(vec);
2656 return NULL;
2657 }
2658
2659 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2660 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2661 {
2662 isl_vec *ext;
2663 struct isl_upoly *up;
2664 isl_dim *dim;
2665
2666 if (!qp || !pnt)
2667 goto error;
2668 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2669
2670 if (qp->div->n_row == 0)
2671 ext = isl_vec_copy(pnt->vec);
2672 else {
2673 int i;
2674 unsigned dim = isl_dim_total(qp->dim);
2675 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2676 if (!ext)
2677 goto error;
2678
2679 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2680 for (i = 0; i < qp->div->n_row; ++i) {
2681 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2682 1 + dim + i, &ext->el[1+dim+i]);
2683 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2684 qp->div->row[i][0]);
2685 }
2686 }
2687
2688 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2689 if (!up)
2690 goto error;
2691
2692 dim = isl_dim_copy(qp->dim);
2693 isl_qpolynomial_free(qp);
2694 isl_point_free(pnt);
2695
2696 return isl_qpolynomial_alloc(dim, 0, up);
2697 error:
2698 isl_qpolynomial_free(qp);
2699 isl_point_free(pnt);
2700 return NULL;
2701 }
2702
2703 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2704 __isl_keep struct isl_upoly_cst *cst2)
2705 {
2706 int cmp;
2707 isl_int t;
2708 isl_int_init(t);
2709 isl_int_mul(t, cst1->n, cst2->d);
2710 isl_int_submul(t, cst2->n, cst1->d);
2711 cmp = isl_int_sgn(t);
2712 isl_int_clear(t);
2713 return cmp;
2714 }
2715
2716 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2717 __isl_keep isl_qpolynomial *qp2)
2718 {
2719 struct isl_upoly_cst *cst1, *cst2;
2720
2721 if (!qp1 || !qp2)
2722 return -1;
2723 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2724 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2725 if (isl_qpolynomial_is_nan(qp1))
2726 return -1;
2727 if (isl_qpolynomial_is_nan(qp2))
2728 return -1;
2729 cst1 = isl_upoly_as_cst(qp1->upoly);
2730 cst2 = isl_upoly_as_cst(qp2->upoly);
2731
2732 return isl_upoly_cmp(cst1, cst2) <= 0;
2733 }
2734
2735 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2736 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2737 {
2738 struct isl_upoly_cst *cst1, *cst2;
2739 int cmp;
2740
2741 if (!qp1 || !qp2)
2742 goto error;
2743 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2744 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2745 cst1 = isl_upoly_as_cst(qp1->upoly);
2746 cst2 = isl_upoly_as_cst(qp2->upoly);
2747 cmp = isl_upoly_cmp(cst1, cst2);
2748
2749 if (cmp <= 0) {
2750 isl_qpolynomial_free(qp2);
2751 } else {
2752 isl_qpolynomial_free(qp1);
2753 qp1 = qp2;
2754 }
2755 return qp1;
2756 error:
2757 isl_qpolynomial_free(qp1);
2758 isl_qpolynomial_free(qp2);
2759 return NULL;
2760 }
2761
2762 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2763 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2764 {
2765 struct isl_upoly_cst *cst1, *cst2;
2766 int cmp;
2767
2768 if (!qp1 || !qp2)
2769 goto error;
2770 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2771 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2772 cst1 = isl_upoly_as_cst(qp1->upoly);
2773 cst2 = isl_upoly_as_cst(qp2->upoly);
2774 cmp = isl_upoly_cmp(cst1, cst2);
2775
2776 if (cmp >= 0) {
2777 isl_qpolynomial_free(qp2);
2778 } else {
2779 isl_qpolynomial_free(qp1);
2780 qp1 = qp2;
2781 }
2782 return qp1;
2783 error:
2784 isl_qpolynomial_free(qp1);
2785 isl_qpolynomial_free(qp2);
2786 return NULL;
2787 }
2788
2789 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2790 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2791 unsigned first, unsigned n)
2792 {
2793 unsigned total;
2794 unsigned g_pos;
2795 int *exp;
2796
2797 if (n == 0)
2798 return qp;
2799
2800 qp = isl_qpolynomial_cow(qp);
2801 if (!qp)
2802 return NULL;
2803
2804 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2805 goto error);
2806
2807 g_pos = pos(qp->dim, type) + first;
2808
2809 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2810 if (!qp->div)
2811 goto error;
2812
2813 total = qp->div->n_col - 2;
2814 if (total > g_pos) {
2815 int i;
2816 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2817 if (!exp)
2818 goto error;
2819 for (i = 0; i < total - g_pos; ++i)
2820 exp[i] = i + n;
2821 qp->upoly = expand(qp->upoly, exp, g_pos);
2822 free(exp);
2823 if (!qp->upoly)
2824 goto error;
2825 }
2826
2827 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2828 if (!qp->dim)
2829 goto error;
2830
2831 return qp;
2832 error:
2833 isl_qpolynomial_free(qp);
2834 return NULL;
2835 }
2836
2837 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2838 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2839 {
2840 unsigned pos;
2841
2842 pos = isl_qpolynomial_dim(qp, type);
2843
2844 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2845 }
2846
2847 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2848 __isl_take isl_pw_qpolynomial *pwqp,
2849 enum isl_dim_type type, unsigned n)
2850 {
2851 unsigned pos;
2852
2853 pos = isl_pw_qpolynomial_dim(pwqp, type);
2854
2855 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2856 }
2857
2858 static int *reordering_move(isl_ctx *ctx,
2859 unsigned len, unsigned dst, unsigned src, unsigned n)
2860 {
2861 int i;
2862 int *reordering;
2863
2864 reordering = isl_alloc_array(ctx, int, len);
2865 if (!reordering)
2866 return NULL;
2867
2868 if (dst <= src) {
2869 for (i = 0; i < dst; ++i)
2870 reordering[i] = i;
2871 for (i = 0; i < n; ++i)
2872 reordering[src + i] = dst + i;
2873 for (i = 0; i < src - dst; ++i)
2874 reordering[dst + i] = dst + n + i;
2875 for (i = 0; i < len - src - n; ++i)
2876 reordering[src + n + i] = src + n + i;
2877 } else {
2878 for (i = 0; i < src; ++i)
2879 reordering[i] = i;
2880 for (i = 0; i < n; ++i)
2881 reordering[src + i] = dst + i;
2882 for (i = 0; i < dst - src; ++i)
2883 reordering[src + n + i] = src + i;
2884 for (i = 0; i < len - dst - n; ++i)
2885 reordering[dst + n + i] = dst + n + i;
2886 }
2887
2888 return reordering;
2889 }
2890
2891 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2892 __isl_take isl_qpolynomial *qp,
2893 enum isl_dim_type dst_type, unsigned dst_pos,
2894 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2895 {
2896 unsigned g_dst_pos;
2897 unsigned g_src_pos;
2898 int *reordering;
2899
2900 qp = isl_qpolynomial_cow(qp);
2901 if (!qp)
2902 return NULL;
2903
2904 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2905 goto error);
2906
2907 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2908 g_src_pos = pos(qp->dim, src_type) + src_pos;
2909 if (dst_type > src_type)
2910 g_dst_pos -= n;
2911
2912 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2913 if (!qp->div)
2914 goto error;
2915 qp = sort_divs(qp);
2916 if (!qp)
2917 goto error;
2918
2919 reordering = reordering_move(qp->dim->ctx,
2920 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2921 if (!reordering)
2922 goto error;
2923
2924 qp->upoly = reorder(qp->upoly, reordering);
2925 free(reordering);
2926 if (!qp->upoly)
2927 goto error;
2928
2929 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2930 if (!qp->dim)
2931 goto error;
2932
2933 return qp;
2934 error:
2935 isl_qpolynomial_free(qp);
2936 return NULL;
2937 }
2938
2939 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2940 isl_int *f, isl_int denom)
2941 {
2942 struct isl_upoly *up;
2943
2944 if (!dim)
2945 return NULL;
2946
2947 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2948
2949 return isl_qpolynomial_alloc(dim, 0, up);
2950 }
2951
2952 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2953 {
2954 isl_ctx *ctx;
2955 struct isl_upoly *up;
2956 isl_qpolynomial *qp;
2957
2958 if (!aff)
2959 return NULL;
2960
2961 ctx = isl_aff_get_ctx(aff);
2962 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2963 aff->v->size - 1);
2964
2965 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2966 aff->ls->div->n_row, up);
2967 if (!qp)
2968 goto error;
2969
2970 isl_mat_free(qp->div);
2971 qp->div = isl_mat_copy(aff->ls->div);
2972 qp->div = isl_mat_cow(qp->div);
2973 if (!qp->div)
2974 goto error;
2975
2976 isl_aff_free(aff);
2977 qp = reduce_divs(qp);
2978 qp = remove_redundant_divs(qp);
2979 return qp;
2980 error:
2981 isl_aff_free(aff);
2982 return NULL;
2983 }
2984
2985 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2986 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2987 {
2988 isl_int denom;
2989 isl_dim *dim;
2990 struct isl_upoly *up;
2991 isl_qpolynomial *qp;
2992 int sgn;
2993
2994 if (!c)
2995 return NULL;
2996
2997 isl_int_init(denom);
2998
2999 isl_constraint_get_coefficient(c, type, pos, &denom);
3000 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3001 sgn = isl_int_sgn(denom);
3002 isl_int_abs(denom, denom);
3003 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3004 1 + isl_constraint_dim(c, isl_dim_all));
3005 if (sgn < 0)
3006 isl_int_neg(denom, denom);
3007 isl_constraint_set_coefficient(c, type, pos, denom);
3008
3009 dim = isl_dim_copy(c->bmap->dim);
3010
3011 isl_int_clear(denom);
3012 isl_constraint_free(c);
3013
3014 qp = isl_qpolynomial_alloc(dim, 0, up);
3015 if (sgn > 0)
3016 qp = isl_qpolynomial_neg(qp);
3017 return qp;
3018 }
3019
3020 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3021 * in "qp" by subs[i].
3022 */
3023 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3024 __isl_take isl_qpolynomial *qp,
3025 enum isl_dim_type type, unsigned first, unsigned n,
3026 __isl_keep isl_qpolynomial **subs)
3027 {
3028 int i;
3029 struct isl_upoly **ups;
3030
3031 if (n == 0)
3032 return qp;
3033
3034 qp = isl_qpolynomial_cow(qp);
3035 if (!qp)
3036 return NULL;
3037 for (i = 0; i < n; ++i)
3038 if (!subs[i])
3039 goto error;
3040
3041 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3042 goto error);
3043
3044 for (i = 0; i < n; ++i)
3045 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3046 goto error);
3047
3048 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3049 for (i = 0; i < n; ++i)
3050 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3051
3052 first += pos(qp->dim, type);
3053
3054 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3055 if (!ups)
3056 goto error;
3057 for (i = 0; i < n; ++i)
3058 ups[i] = subs[i]->upoly;
3059
3060 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3061
3062 free(ups);
3063
3064 if (!qp->upoly)
3065 goto error;
3066
3067 return qp;
3068 error:
3069 isl_qpolynomial_free(qp);
3070 return NULL;
3071 }
3072
3073 /* Extend "bset" with extra set dimensions for each integer division
3074 * in "qp" and then call "fn" with the extended bset and the polynomial
3075 * that results from replacing each of the integer divisions by the
3076 * corresponding extra set dimension.
3077 */
3078 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3079 __isl_keep isl_basic_set *bset,
3080 int (*fn)(__isl_take isl_basic_set *bset,
3081 __isl_take isl_qpolynomial *poly, void *user), void *user)
3082 {
3083 isl_dim *dim;
3084 isl_mat *div;
3085 isl_qpolynomial *poly;
3086
3087 if (!qp || !bset)
3088 goto error;
3089 if (qp->div->n_row == 0)
3090 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3091 user);
3092
3093 div = isl_mat_copy(qp->div);
3094 dim = isl_dim_copy(qp->dim);
3095 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3096 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3097 bset = isl_basic_set_copy(bset);
3098 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3099 bset = add_div_constraints(bset, div);
3100
3101 return fn(bset, poly, user);
3102 error:
3103 return -1;
3104 }
3105
3106 /* Return total degree in variables first (inclusive) up to last (exclusive).
3107 */
3108 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3109 {
3110 int deg = -1;
3111 int i;
3112 struct isl_upoly_rec *rec;
3113
3114 if (!up)
3115 return -2;
3116 if (isl_upoly_is_zero(up))
3117 return -1;
3118 if (isl_upoly_is_cst(up) || up->var < first)
3119 return 0;
3120
3121 rec = isl_upoly_as_rec(up);
3122 if (!rec)
3123 return -2;
3124
3125 for (i = 0; i < rec->n; ++i) {
3126 int d;
3127
3128 if (isl_upoly_is_zero(rec->p[i]))
3129 continue;
3130 d = isl_upoly_degree(rec->p[i], first, last);
3131 if (up->var < last)
3132 d += i;
3133 if (d > deg)
3134 deg = d;
3135 }
3136
3137 return deg;
3138 }
3139
3140 /* Return total degree in set variables.
3141 */
3142 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3143 {
3144 unsigned ovar;
3145 unsigned nvar;
3146
3147 if (!poly)
3148 return -2;
3149
3150 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3151 nvar = isl_dim_size(poly->dim, isl_dim_set);
3152 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3153 }
3154
3155 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3156 unsigned pos, int deg)
3157 {
3158 int i;
3159 struct isl_upoly_rec *rec;
3160
3161 if (!up)
3162 return NULL;
3163
3164 if (isl_upoly_is_cst(up) || up->var < pos) {
3165 if (deg == 0)
3166 return isl_upoly_copy(up);
3167 else
3168 return isl_upoly_zero(up->ctx);
3169 }
3170
3171 rec = isl_upoly_as_rec(up);
3172 if (!rec)
3173 return NULL;
3174
3175 if (up->var == pos) {
3176 if (deg < rec->n)
3177 return isl_upoly_copy(rec->p[deg]);
3178 else
3179 return isl_upoly_zero(up->ctx);
3180 }
3181
3182 up = isl_upoly_copy(up);
3183 up = isl_upoly_cow(up);
3184 rec = isl_upoly_as_rec(up);
3185 if (!rec)
3186 goto error;
3187
3188 for (i = 0; i < rec->n; ++i) {
3189 struct isl_upoly *t;
3190 t = isl_upoly_coeff(rec->p[i], pos, deg);
3191 if (!t)
3192 goto error;
3193 isl_upoly_free(rec->p[i]);
3194 rec->p[i] = t;
3195 }
3196
3197 return up;
3198 error:
3199 isl_upoly_free(up);
3200 return NULL;
3201 }
3202
3203 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3204 */
3205 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3206 __isl_keep isl_qpolynomial *qp,
3207 enum isl_dim_type type, unsigned t_pos, int deg)
3208 {
3209 unsigned g_pos;
3210 struct isl_upoly *up;
3211 isl_qpolynomial *c;
3212
3213 if (!qp)
3214 return NULL;
3215
3216 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3217 return NULL);
3218
3219 g_pos = pos(qp->dim, type) + t_pos;
3220 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3221
3222 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3223 if (!c)
3224 return NULL;
3225 isl_mat_free(c->div);
3226 c->div = isl_mat_copy(qp->div);
3227 if (!c->div)
3228 goto error;
3229 return c;
3230 error:
3231 isl_qpolynomial_free(c);
3232 return NULL;
3233 }
3234
3235 /* Homogenize the polynomial in the variables first (inclusive) up to
3236 * last (exclusive) by inserting powers of variable first.
3237 * Variable first is assumed not to appear in the input.
3238 */
3239 __isl_give struct isl_upoly *isl_upoly_homogenize(
3240 __isl_take struct isl_upoly *up, int deg, int target,
3241 int first, int last)
3242 {
3243 int i;
3244 struct isl_upoly_rec *rec;
3245
3246 if (!up)
3247 return NULL;
3248 if (isl_upoly_is_zero(up))
3249 return up;
3250 if (deg == target)
3251 return up;
3252 if (isl_upoly_is_cst(up) || up->var < first) {
3253 struct isl_upoly *hom;
3254
3255 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3256 if (!hom)
3257 goto error;
3258 rec = isl_upoly_as_rec(hom);
3259 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3260
3261 return hom;
3262 }
3263
3264 up = isl_upoly_cow(up);
3265 rec = isl_upoly_as_rec(up);
3266 if (!rec)
3267 goto error;
3268
3269 for (i = 0; i < rec->n; ++i) {
3270 if (isl_upoly_is_zero(rec->p[i]))
3271 continue;
3272 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3273 up->var < last ? deg + i : i, target,
3274 first, last);
3275 if (!rec->p[i])
3276 goto error;
3277 }
3278
3279 return up;
3280 error:
3281 isl_upoly_free(up);
3282 return NULL;
3283 }
3284
3285 /* Homogenize the polynomial in the set variables by introducing
3286 * powers of an extra set variable at position 0.
3287 */
3288 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3289 __isl_take isl_qpolynomial *poly)
3290 {
3291 unsigned ovar;
3292 unsigned nvar;
3293 int deg = isl_qpolynomial_degree(poly);
3294
3295 if (deg < -1)
3296 goto error;
3297
3298 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3299 poly = isl_qpolynomial_cow(poly);
3300 if (!poly)
3301 goto error;
3302
3303 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3304 nvar = isl_dim_size(poly->dim, isl_dim_set);
3305 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3306 ovar, ovar + nvar);
3307 if (!poly->upoly)
3308 goto error;
3309
3310 return poly;
3311 error:
3312 isl_qpolynomial_free(poly);
3313 return NULL;
3314 }
3315
3316 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3317 __isl_take isl_mat *div)
3318 {
3319 isl_term *term;
3320 int n;
3321
3322 if (!dim || !div)
3323 goto error;
3324
3325 n = isl_dim_total(dim) + div->n_row;
3326
3327 term = isl_calloc(dim->ctx, struct isl_term,
3328 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3329 if (!term)
3330 goto error;
3331
3332 term->ref = 1;
3333 term->dim = dim;
3334 term->div = div;
3335 isl_int_init(term->n);
3336 isl_int_init(term->d);
3337
3338 return term;
3339 error:
3340 isl_dim_free(dim);
3341 isl_mat_free(div);
3342 return NULL;
3343 }
3344
3345 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3346 {
3347 if (!term)
3348 return NULL;
3349
3350 term->ref++;
3351 return term;
3352 }
3353
3354 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3355 {
3356 int i;
3357 isl_term *dup;
3358 unsigned total;
3359
3360 if (term)
3361 return NULL;
3362
3363 total = isl_dim_total(term->dim) + term->div->n_row;
3364
3365 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3366 if (!dup)
3367 return NULL;
3368
3369 isl_int_set(dup->n, term->n);
3370 isl_int_set(dup->d, term->d);
3371
3372 for (i = 0; i < total; ++i)
3373 dup->pow[i] = term->pow[i];
3374
3375 return dup;
3376 }
3377
3378 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3379 {
3380 if (!term)
3381 return NULL;
3382
3383 if (term->ref == 1)
3384 return term;
3385 term->ref--;
3386 return isl_term_dup(term);
3387 }
3388
3389 void isl_term_free(__isl_take isl_term *term)
3390 {
3391 if (!term)
3392 return;
3393
3394 if (--term->ref > 0)
3395 return;
3396
3397 isl_dim_free(term->dim);
3398 isl_mat_free(term->div);
3399 isl_int_clear(term->n);
3400 isl_int_clear(term->d);
3401 free(term);
3402 }
3403
3404 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3405 {
3406 if (!term)
3407 return 0;
3408
3409 switch (type) {
3410 case isl_dim_param:
3411 case isl_dim_in:
3412 case isl_dim_out: return isl_dim_size(term->dim, type);
3413 case isl_dim_div: return term->div->n_row;
3414 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3415 default: return 0;
3416 }
3417 }
3418
3419 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3420 {
3421 return term ? term->dim->ctx : NULL;
3422 }
3423
3424 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3425 {
3426 if (!term)
3427 return;
3428 isl_int_set(*n, term->n);
3429 }
3430
3431 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3432 {
3433 if (!term)
3434 return;
3435 isl_int_set(*d, term->d);
3436 }
3437
3438 int isl_term_get_exp(__isl_keep isl_term *term,
3439 enum isl_dim_type type, unsigned pos)
3440 {
3441 if (!term)
3442 return -1;
3443
3444 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3445
3446 if (type >= isl_dim_set)
3447 pos += isl_dim_size(term->dim, isl_dim_param);
3448 if (type >= isl_dim_div)
3449 pos += isl_dim_size(term->dim, isl_dim_set);
3450
3451 return term->pow[pos];
3452 }
3453
3454 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3455 {
3456 isl_basic_map *bmap;
3457 unsigned total;
3458 int k;
3459
3460 if (!term)
3461 return NULL;
3462
3463 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3464 return NULL);
3465
3466 total = term->div->n_col - term->div->n_row - 2;
3467 /* No nested divs for now */
3468 isl_assert(term->dim->ctx,
3469 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3470 term->div->n_row) == -1,
3471 return NULL);
3472
3473 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3474 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3475 goto error;
3476
3477 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3478
3479 return isl_basic_map_div(bmap, k);
3480 error:
3481 isl_basic_map_free(bmap);
3482 return NULL;
3483 }
3484
3485 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3486 int (*fn)(__isl_take isl_term *term, void *user),
3487 __isl_take isl_term *term, void *user)
3488 {
3489 int i;
3490 struct isl_upoly_rec *rec;
3491
3492 if (!up || !term)
3493 goto error;
3494
3495 if (isl_upoly_is_zero(up))
3496 return term;
3497
3498 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3499 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3500 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3501
3502 if (isl_upoly_is_cst(up)) {
3503 struct isl_upoly_cst *cst;
3504 cst = isl_upoly_as_cst(up);
3505 if (!cst)
3506 goto error;
3507 term = isl_term_cow(term);
3508 if (!term)
3509 goto error;
3510 isl_int_set(term->n, cst->n);
3511 isl_int_set(term->d, cst->d);
3512 if (fn(isl_term_copy(term), user) < 0)
3513 goto error;
3514 return term;
3515 }
3516
3517 rec = isl_upoly_as_rec(up);
3518 if (!rec)
3519 goto error;
3520
3521 for (i = 0; i < rec->n; ++i) {
3522 term = isl_term_cow(term);
3523 if (!term)
3524 goto error;
3525 term->pow[up->var] = i;
3526 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3527 if (!term)
3528 goto error;
3529 }
3530 term->pow[up->var] = 0;
3531
3532 return term;
3533 error:
3534 isl_term_free(term);
3535 return NULL;
3536 }
3537
3538 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3539 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3540 {
3541 isl_term *term;
3542
3543 if (!qp)
3544 return -1;
3545
3546 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3547 if (!term)
3548 return -1;
3549
3550 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3551
3552 isl_term_free(term);
3553
3554 return term ? 0 : -1;
3555 }
3556
3557 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3558 {
3559 struct isl_upoly *up;
3560 isl_qpolynomial *qp;
3561 int i, n;
3562
3563 if (!term)
3564 return NULL;
3565
3566 n = isl_dim_total(term->dim) + term->div->n_row;
3567
3568 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3569 for (i = 0; i < n; ++i) {
3570 if (!term->pow[i])
3571 continue;
3572 up = isl_upoly_mul(up,
3573 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3574 }
3575
3576 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3577 if (!qp)
3578 goto error;
3579 isl_mat_free(qp->div);
3580 qp->div = isl_mat_copy(term->div);
3581 if (!qp->div)
3582 goto error;
3583
3584 isl_term_free(term);
3585 return qp;
3586 error:
3587 isl_qpolynomial_free(qp);
3588 isl_term_free(term);
3589 return NULL;
3590 }
3591
3592 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3593 __isl_take isl_dim *dim)
3594 {
3595 int i;
3596 int extra;
3597 unsigned total;
3598
3599 if (!qp || !dim)
3600 goto error;
3601
3602 if (isl_dim_equal(qp->dim, dim)) {
3603 isl_dim_free(dim);
3604 return qp;
3605 }
3606
3607 qp = isl_qpolynomial_cow(qp);
3608 if (!qp)
3609 goto error;
3610
3611 extra = isl_dim_size(dim, isl_dim_set) -
3612 isl_dim_size(qp->dim, isl_dim_set);
3613 total = isl_dim_total(qp->dim);
3614 if (qp->div->n_row) {
3615 int *exp;
3616
3617 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3618 if (!exp)
3619 goto error;
3620 for (i = 0; i < qp->div->n_row; ++i)
3621 exp[i] = extra + i;
3622 qp->upoly = expand(qp->upoly, exp, total);
3623 free(exp);
3624 if (!qp->upoly)
3625 goto error;
3626 }
3627 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3628 if (!qp->div)
3629 goto error;
3630 for (i = 0; i < qp->div->n_row; ++i)
3631 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3632
3633 isl_dim_free(qp->dim);
3634 qp->dim = dim;
3635
3636 return qp;
3637 error:
3638 isl_dim_free(dim);
3639 isl_qpolynomial_free(qp);
3640 return NULL;
3641 }
3642
3643 /* For each parameter or variable that does not appear in qp,
3644 * first eliminate the variable from all constraints and then set it to zero.
3645 */
3646 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3647 __isl_keep isl_qpolynomial *qp)
3648 {
3649 int *active = NULL;
3650 int i;
3651 int d;
3652 unsigned nparam;
3653 unsigned nvar;
3654
3655 if (!set || !qp)
3656 goto error;
3657
3658 d = isl_dim_total(set->dim);
3659 active = isl_calloc_array(set->ctx, int, d);
3660 if (set_active(qp, active) < 0)
3661 goto error;
3662
3663 for (i = 0; i < d; ++i)
3664 if (!active[i])
3665 break;
3666
3667 if (i == d) {
3668 free(active);
3669 return set;
3670 }
3671
3672 nparam = isl_dim_size(set->dim, isl_dim_param);
3673 nvar = isl_dim_size(set->dim, isl_dim_set);
3674 for (i = 0; i < nparam; ++i) {
3675 if (active[i])
3676 continue;
3677 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3678 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3679 }
3680 for (i = 0; i < nvar; ++i) {
3681 if (active[nparam + i])
3682 continue;
3683 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3684 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3685 }
3686
3687 free(active);
3688
3689 return set;
3690 error:
3691 free(active);
3692 isl_set_free(set);
3693 return NULL;
3694 }
3695
3696 struct isl_opt_data {
3697 isl_qpolynomial *qp;
3698 int first;
3699 isl_qpolynomial *opt;
3700 int max;
3701 };
3702
3703 static int opt_fn(__isl_take isl_point *pnt, void *user)
3704 {
3705 struct isl_opt_data *data = (struct isl_opt_data *)user;
3706 isl_qpolynomial *val;
3707
3708 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3709 if (data->first) {
3710 data->first = 0;
3711 data->opt = val;
3712 } else if (data->max) {
3713 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3714 } else {
3715 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3716 }
3717
3718 return 0;
3719 }
3720
3721 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3722 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3723 {
3724 struct isl_opt_data data = { NULL, 1, NULL, max };
3725
3726 if (!set || !qp)
3727 goto error;
3728
3729 if (isl_upoly_is_cst(qp->upoly)) {
3730 isl_set_free(set);
3731 return qp;
3732 }
3733
3734 set = fix_inactive(set, qp);
3735
3736 data.qp = qp;
3737 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3738 goto error;
3739
3740 if (data.first)
3741 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3742
3743 isl_set_free(set);
3744 isl_qpolynomial_free(qp);
3745 return data.opt;
3746 error:
3747 isl_set_free(set);
3748 isl_qpolynomial_free(qp);
3749 isl_qpolynomial_free(data.opt);
3750 return NULL;
3751 }
3752
3753 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3754 __isl_take isl_morph *morph)
3755 {
3756 int i;
3757 int n_sub;
3758 isl_ctx *ctx;
3759 struct isl_upoly **subs;
3760 isl_mat *mat;
3761
3762 qp = isl_qpolynomial_cow(qp);
3763 if (!qp || !morph)
3764 goto error;
3765
3766 ctx = qp->dim->ctx;
3767 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3768
3769 n_sub = morph->inv->n_row - 1;
3770 if (morph->inv->n_row != morph->inv->n_col)
3771 n_sub += qp->div->n_row;
3772 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3773 if (!subs)
3774 goto error;
3775
3776 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3777 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3778 morph->inv->row[0][0], morph->inv->n_col);
3779 if (morph->inv->n_row != morph->inv->n_col)
3780 for (i = 0; i < qp->div->n_row; ++i)
3781 subs[morph->inv->n_row - 1 + i] =
3782 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3783
3784 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3785
3786 for (i = 0; i < n_sub; ++i)
3787 isl_upoly_free(subs[i]);
3788 free(subs);
3789
3790 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3791 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3792 qp->div = isl_mat_product(qp->div, mat);
3793 isl_dim_free(qp->dim);
3794 qp->dim = isl_dim_copy(morph->ran->dim);
3795
3796 if (!qp->upoly || !qp->div || !qp->dim)
3797 goto error;
3798
3799 isl_morph_free(morph);
3800
3801 return qp;
3802 error:
3803 isl_qpolynomial_free(qp);
3804 isl_morph_free(morph);
3805 return NULL;
3806 }
3807
3808 static int neg_entry(void **entry, void *user)
3809 {
3810 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3811
3812 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3813
3814 return *pwqp ? 0 : -1;
3815 }
3816
3817 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3818 __isl_take isl_union_pw_qpolynomial *upwqp)
3819 {
3820 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3821 if (!upwqp)
3822 return NULL;
3823
3824 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3825 &neg_entry, NULL) < 0)
3826 goto error;
3827
3828 return upwqp;
3829 error:
3830 isl_union_pw_qpolynomial_free(upwqp);
3831 return NULL;
3832 }
3833
3834 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3835 __isl_take isl_union_pw_qpolynomial *upwqp1,
3836 __isl_take isl_union_pw_qpolynomial *upwqp2)
3837 {
3838 return isl_union_pw_qpolynomial_add(upwqp1,
3839 isl_union_pw_qpolynomial_neg(upwqp2));
3840 }
3841
3842 static int mul_entry(void **entry, void *user)
3843 {
3844 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3845 uint32_t hash;
3846 struct isl_hash_table_entry *entry2;
3847 isl_pw_qpolynomial *pwpq = *entry;
3848 int empty;
3849
3850 hash = isl_dim_get_hash(pwpq->dim);
3851 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3852 hash, &has_dim, pwpq->dim, 0);
3853 if (!entry2)
3854 return 0;
3855
3856 pwpq = isl_pw_qpolynomial_copy(pwpq);
3857 pwpq = isl_pw_qpolynomial_mul(pwpq,
3858 isl_pw_qpolynomial_copy(entry2->data));
3859
3860 empty = isl_pw_qpolynomial_is_zero(pwpq);
3861 if (empty < 0) {
3862 isl_pw_qpolynomial_free(pwpq);
3863 return -1;
3864 }
3865 if (empty) {
3866 isl_pw_qpolynomial_free(pwpq);
3867 return 0;
3868 }
3869
3870 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3871
3872 return 0;
3873 }
3874
3875 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3876 __isl_take isl_union_pw_qpolynomial *upwqp1,
3877 __isl_take isl_union_pw_qpolynomial *upwqp2)
3878 {
3879 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3880 }
3881
3882 /* Reorder the columns of the given div definitions according to the
3883 * given reordering.
3884 */
3885 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3886 __isl_take isl_reordering *r)
3887 {
3888 int i, j;
3889 isl_mat *mat;
3890 int extra;
3891
3892 if (!div || !r)
3893 goto error;
3894
3895 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3896 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3897 if (!mat)
3898 goto error;
3899
3900 for (i = 0; i < div->n_row; ++i) {
3901 isl_seq_cpy(mat->row[i], div->row[i], 2);
3902 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3903 for (j = 0; j < r->len; ++j)
3904 isl_int_set(mat->row[i][2 + r->pos[j]],
3905 div->row[i][2 + j]);
3906 }
3907
3908 isl_reordering_free(r);
3909 isl_mat_free(div);
3910 return mat;
3911 error:
3912 isl_reordering_free(r);
3913 isl_mat_free(div);
3914 return NULL;
3915 }
3916
3917 /* Reorder the dimension of "qp" according to the given reordering.
3918 */
3919 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3920 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3921 {
3922 qp = isl_qpolynomial_cow(qp);
3923 if (!qp)
3924 goto error;
3925
3926 r = isl_reordering_extend(r, qp->div->n_row);
3927 if (!r)
3928 goto error;
3929
3930 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3931 if (!qp->div)
3932 goto error;
3933
3934 qp->upoly = reorder(qp->upoly, r->pos);
3935 if (!qp->upoly)
3936 goto error;
3937
3938 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3939
3940 isl_reordering_free(r);
3941 return qp;
3942 error:
3943 isl_qpolynomial_free(qp);
3944 isl_reordering_free(r);
3945 return NULL;
3946 }
3947
3948 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3949 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3950 {
3951 if (!qp || !model)
3952 goto error;
3953
3954 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3955 isl_reordering *exp;
3956
3957 model = isl_dim_drop(model, isl_dim_in,
3958 0, isl_dim_size(model, isl_dim_in));
3959 model = isl_dim_drop(model, isl_dim_out,
3960 0, isl_dim_size(model, isl_dim_out));
3961 exp = isl_parameter_alignment_reordering(qp->dim, model);
3962 exp = isl_reordering_extend_dim(exp,
3963 isl_qpolynomial_get_dim(qp));
3964 qp = isl_qpolynomial_realign(qp, exp);
3965 }
3966
3967 isl_dim_free(model);
3968 return qp;
3969 error:
3970 isl_dim_free(model);
3971 isl_qpolynomial_free(qp);
3972 return NULL;
3973 }
3974
3975 struct isl_split_periods_data {
3976 int max_periods;
3977 isl_pw_qpolynomial *res;
3978 };
3979
3980 /* Create a slice where the integer division "div" has the fixed value "v".
3981 * In particular, if "div" refers to floor(f/m), then create a slice
3982 *
3983 * m v <= f <= m v + (m - 1)
3984 *
3985 * or
3986 *
3987 * f - m v >= 0
3988 * -f + m v + (m - 1) >= 0
3989 */
3990 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3991 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3992 {
3993 int total;
3994 isl_basic_set *bset = NULL;
3995 int k;
3996
3997 if (!dim || !qp)
3998 goto error;
3999
4000 total = isl_dim_total(dim);
4001 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4002
4003 k = isl_basic_set_alloc_inequality(bset);
4004 if (k < 0)
4005 goto error;
4006 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4007 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4008
4009 k = isl_basic_set_alloc_inequality(bset);
4010 if (k < 0)
4011 goto error;
4012 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4013 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4014 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4015 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4016
4017 isl_dim_free(dim);
4018 return isl_set_from_basic_set(bset);
4019 error:
4020 isl_basic_set_free(bset);
4021 isl_dim_free(dim);
4022 return NULL;
4023 }
4024
4025 static int split_periods(__isl_take isl_set *set,
4026 __isl_take isl_qpolynomial *qp, void *user);
4027
4028 /* Create a slice of the domain "set" such that integer division "div"
4029 * has the fixed value "v" and add the results to data->res,
4030 * replacing the integer division by "v" in "qp".
4031 */
4032 static int set_div(__isl_take isl_set *set,
4033 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4034 struct isl_split_periods_data *data)
4035 {
4036 int i;
4037 int total;
4038 isl_set *slice;
4039 struct isl_upoly *cst;
4040
4041 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4042 set = isl_set_intersect(set, slice);
4043
4044 if (!qp)
4045 goto error;
4046
4047 total = isl_dim_total(qp->dim);
4048
4049 for (i = div + 1; i < qp->div->n_row; ++i) {
4050 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4051 continue;
4052 isl_int_addmul(qp->div->row[i][1],
4053 qp->div->row[i][2 + total + div], v);
4054 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4055 }
4056
4057 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4058 qp = substitute_div(qp, div, cst);
4059
4060 return split_periods(set, qp, data);
4061 error:
4062 isl_set_free(set);
4063 isl_qpolynomial_free(qp);
4064 return -1;
4065 }
4066
4067 /* Split the domain "set" such that integer division "div"
4068 * has a fixed value (ranging from "min" to "max") on each slice
4069 * and add the results to data->res.
4070 */
4071 static int split_div(__isl_take isl_set *set,
4072 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4073 struct isl_split_periods_data *data)
4074 {
4075 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4076 isl_set *set_i = isl_set_copy(set);
4077 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4078
4079 if (set_div(set_i, qp_i, div, min, data) < 0)
4080 goto error;
4081 }
4082 isl_set_free(set);
4083 isl_qpolynomial_free(qp);
4084 return 0;
4085 error:
4086 isl_set_free(set);
4087 isl_qpolynomial_free(qp);
4088 return -1;
4089 }
4090
4091 /* If "qp" refers to any integer division
4092 * that can only attain "max_periods" distinct values on "set"
4093 * then split the domain along those distinct values.
4094 * Add the results (or the original if no splitting occurs)
4095 * to data->res.
4096 */
4097 static int split_periods(__isl_take isl_set *set,
4098 __isl_take isl_qpolynomial *qp, void *user)
4099 {
4100 int i;
4101 isl_pw_qpolynomial *pwqp;
4102 struct isl_split_periods_data *data;
4103 isl_int min, max;
4104 int total;
4105 int r = 0;
4106
4107 data = (struct isl_split_periods_data *)user;
4108
4109 if (!set || !qp)
4110 goto error;
4111
4112 if (qp->div->n_row == 0) {
4113 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4114 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4115 return 0;
4116 }
4117
4118 isl_int_init(min);
4119 isl_int_init(max);
4120 total = isl_dim_total(qp->dim);
4121 for (i = 0; i < qp->div->n_row; ++i) {
4122 enum isl_lp_result lp_res;
4123
4124 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4125 qp->div->n_row) != -1)
4126 continue;
4127
4128 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4129 set->ctx->one, &min, NULL, NULL);
4130 if (lp_res == isl_lp_error)
4131 goto error2;
4132 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4133 continue;
4134 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4135
4136 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4137 set->ctx->one, &max, NULL, NULL);
4138 if (lp_res == isl_lp_error)
4139 goto error2;
4140 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4141 continue;
4142 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4143
4144 isl_int_sub(max, max, min);
4145 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4146 isl_int_add(max, max, min);
4147 break;
4148 }
4149 }
4150
4151 if (i < qp->div->n_row) {
4152 r = split_div(set, qp, i, min, max, data);
4153 } else {
4154 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4155 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4156 }
4157
4158 isl_int_clear(max);
4159 isl_int_clear(min);
4160
4161 return r;
4162 error2:
4163 isl_int_clear(max);
4164 isl_int_clear(min);
4165 error:
4166 isl_set_free(set);
4167 isl_qpolynomial_free(qp);
4168 return -1;
4169 }
4170
4171 /* If any quasi-polynomial in pwqp refers to any integer division
4172 * that can only attain "max_periods" distinct values on its domain
4173 * then split the domain along those distinct values.
4174 */
4175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4176 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4177 {
4178 struct isl_split_periods_data data;
4179
4180 data.max_periods = max_periods;
4181 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4182
4183 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4184 goto error;
4185
4186 isl_pw_qpolynomial_free(pwqp);
4187
4188 return data.res;
4189 error:
4190 isl_pw_qpolynomial_free(data.res);
4191 isl_pw_qpolynomial_free(pwqp);
4192 return NULL;
4193 }
4194
4195 /* Construct a piecewise quasipolynomial that is constant on the given
4196 * domain. In particular, it is
4197 * 0 if cst == 0
4198 * 1 if cst == 1
4199 * infinity if cst == -1
4200 */
4201 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4202 __isl_take isl_basic_set *bset, int cst)
4203 {
4204 isl_dim *dim;
4205 isl_qpolynomial *qp;
4206
4207 if (!bset)
4208 return NULL;
4209
4210 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4211 dim = isl_basic_set_get_dim(bset);
4212 if (cst < 0)
4213 qp = isl_qpolynomial_infty(dim);
4214 else if (cst == 0)
4215 qp = isl_qpolynomial_zero(dim);
4216 else
4217 qp = isl_qpolynomial_one(dim);
4218 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4219 }
4220
4221 /* Factor bset, call fn on each of the factors and return the product.
4222 *
4223 * If no factors can be found, simply call fn on the input.
4224 * Otherwise, construct the factors based on the factorizer,
4225 * call fn on each factor and compute the product.
4226 */
4227 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4228 __isl_take isl_basic_set *bset,
4229 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4230 {
4231 int i, n;
4232 isl_dim *dim;
4233 isl_set *set;
4234 isl_factorizer *f;
4235 isl_qpolynomial *qp;
4236 isl_pw_qpolynomial *pwqp;
4237 unsigned nparam;
4238 unsigned nvar;
4239
4240 f = isl_basic_set_factorizer(bset);
4241 if (!f)
4242 goto error;
4243 if (f->n_group == 0) {
4244 isl_factorizer_free(f);
4245 return fn(bset);
4246 }
4247
4248 nparam = isl_basic_set_dim(bset, isl_dim_param);
4249 nvar = isl_basic_set_dim(bset, isl_dim_set);
4250
4251 dim = isl_basic_set_get_dim(bset);
4252 dim = isl_dim_domain(dim);
4253 set = isl_set_universe(isl_dim_copy(dim));
4254 qp = isl_qpolynomial_one(dim);
4255 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4256
4257 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4258
4259 for (i = 0, n = 0; i < f->n_group; ++i) {
4260 isl_basic_set *bset_i;
4261 isl_pw_qpolynomial *pwqp_i;
4262
4263 bset_i = isl_basic_set_copy(bset);
4264 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4265 nparam + n + f->len[i], nvar - n - f->len[i]);
4266 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4267 nparam, n);
4268 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4269 n + f->len[i], nvar - n - f->len[i]);
4270 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4271
4272 pwqp_i = fn(bset_i);
4273 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4274
4275 n += f->len[i];
4276 }
4277
4278 isl_basic_set_free(bset);
4279 isl_factorizer_free(f);
4280
4281 return pwqp;
4282 error:
4283 isl_basic_set_free(bset);
4284 return NULL;
4285 }
4286
4287 /* Factor bset, call fn on each of the factors and return the product.
4288 * The function is assumed to evaluate to zero on empty domains,
4289 * to one on zero-dimensional domains and to infinity on unbounded domains
4290 * and will not be called explicitly on zero-dimensional or unbounded domains.
4291 *
4292 * We first check for some special cases and remove all equalities.
4293 * Then we hand over control to compressed_multiplicative_call.
4294 */
4295 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4296 __isl_take isl_basic_set *bset,
4297 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4298 {
4299 int bounded;
4300 isl_morph *morph;
4301 isl_pw_qpolynomial *pwqp;
4302 unsigned orig_nvar, final_nvar;
4303
4304 if (!bset)
4305 return NULL;
4306
4307 if (isl_basic_set_plain_is_empty(bset))
4308 return constant_on_domain(bset, 0);
4309
4310 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4311
4312 if (orig_nvar == 0)
4313 return constant_on_domain(bset, 1);
4314
4315 bounded = isl_basic_set_is_bounded(bset);
4316 if (bounded < 0)
4317 goto error;
4318 if (!bounded)
4319 return constant_on_domain(bset, -1);
4320
4321 if (bset->n_eq == 0)
4322 return compressed_multiplicative_call(bset, fn);
4323
4324 morph = isl_basic_set_full_compression(bset);
4325 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4326
4327 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4328
4329 pwqp = compressed_multiplicative_call(bset, fn);
4330
4331 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4332 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4333 morph = isl_morph_inverse(morph);
4334
4335 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4336
4337 return pwqp;
4338 error:
4339 isl_basic_set_free(bset);
4340 return NULL;
4341 }
4342
4343 /* Drop all floors in "qp", turning each integer division [a/m] into
4344 * a rational division a/m. If "down" is set, then the integer division
4345 * is replaces by (a-(m-1))/m instead.
4346 */
4347 static __isl_give isl_qpolynomial *qp_drop_floors(
4348 __isl_take isl_qpolynomial *qp, int down)
4349 {
4350 int i;
4351 struct isl_upoly *s;
4352
4353 if (!qp)
4354 return NULL;
4355 if (qp->div->n_row == 0)
4356 return qp;
4357
4358 qp = isl_qpolynomial_cow(qp);
4359 if (!qp)
4360 return NULL;
4361
4362 for (i = qp->div->n_row - 1; i >= 0; --i) {
4363 if (down) {
4364 isl_int_sub(qp->div->row[i][1],
4365 qp->div->row[i][1], qp->div->row[i][0]);
4366 isl_int_add_ui(qp->div->row[i][1],
4367 qp->div->row[i][1], 1);
4368 }
4369 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4370 qp->div->row[i][0], qp->div->n_col - 1);
4371 qp = substitute_div(qp, i, s);
4372 if (!qp)
4373 return NULL;
4374 }
4375
4376 return qp;
4377 }
4378
4379 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4380 * a rational division a/m.
4381 */
4382 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4383 __isl_take isl_pw_qpolynomial *pwqp)
4384 {
4385 int i;
4386
4387 if (!pwqp)
4388 return NULL;
4389
4390 if (isl_pw_qpolynomial_is_zero(pwqp))
4391 return pwqp;
4392
4393 pwqp = isl_pw_qpolynomial_cow(pwqp);
4394 if (!pwqp)
4395 return NULL;
4396
4397 for (i = 0; i < pwqp->n; ++i) {
4398 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4399 if (!pwqp->p[i].qp)
4400 goto error;
4401 }
4402
4403 return pwqp;
4404 error:
4405 isl_pw_qpolynomial_free(pwqp);
4406 return NULL;
4407 }
4408
4409 /* Adjust all the integer divisions in "qp" such that they are at least
4410 * one over the given orthant (identified by "signs"). This ensures
4411 * that they will still be non-negative even after subtracting (m-1)/m.
4412 *
4413 * In particular, f is replaced by f' + v, changing f = [a/m]
4414 * to f' = [(a - m v)/m].
4415 * If the constant term k in a is smaller than m,
4416 * the constant term of v is set to floor(k/m) - 1.
4417 * For any other term, if the coefficient c and the variable x have
4418 * the same sign, then no changes are needed.
4419 * Otherwise, if the variable is positive (and c is negative),
4420 * then the coefficient of x in v is set to floor(c/m).
4421 * If the variable is negative (and c is positive),
4422 * then the coefficient of x in v is set to ceil(c/m).
4423 */
4424 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4425 int *signs)
4426 {
4427 int i, j;
4428 int total;
4429 isl_vec *v = NULL;
4430 struct isl_upoly *s;
4431
4432 qp = isl_qpolynomial_cow(qp);
4433 if (!qp)
4434 return NULL;
4435 qp->div = isl_mat_cow(qp->div);
4436 if (!qp->div)
4437 goto error;
4438
4439 total = isl_dim_total(qp->dim);
4440 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4441
4442 for (i = 0; i < qp->div->n_row; ++i) {
4443 isl_int *row = qp->div->row[i];
4444 v = isl_vec_clr(v);
4445 if (!v)
4446 goto error;
4447 if (isl_int_lt(row[1], row[0])) {
4448 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4449 isl_int_sub_ui(v->el[0], v->el[0], 1);
4450 isl_int_submul(row[1], row[0], v->el[0]);
4451 }
4452 for (j = 0; j < total; ++j) {
4453 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4454 continue;
4455 if (signs[j] < 0)
4456 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4457 else
4458 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4459 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4460 }
4461 for (j = 0; j < i; ++j) {
4462 if (isl_int_sgn(row[2 + total + j]) >= 0)
4463 continue;
4464 isl_int_fdiv_q(v->el[1 + total + j],
4465 row[2 + total + j], row[0]);
4466 isl_int_submul(row[2 + total + j],
4467 row[0], v->el[1 + total + j]);
4468 }
4469 for (j = i + 1; j < qp->div->n_row; ++j) {
4470 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4471 continue;
4472 isl_seq_combine(qp->div->row[j] + 1,
4473 qp->div->ctx->one, qp->div->row[j] + 1,
4474 qp->div->row[j][2 + total + i], v->el, v->size);
4475 }
4476 isl_int_set_si(v->el[1 + total + i], 1);
4477 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4478 qp->div->ctx->one, v->size);
4479 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4480 isl_upoly_free(s);
4481 if (!qp->upoly)
4482 goto error;
4483 }
4484
4485 isl_vec_free(v);
4486 return qp;
4487 error:
4488 isl_vec_free(v);
4489 isl_qpolynomial_free(qp);
4490 return NULL;
4491 }
4492
4493 struct isl_to_poly_data {
4494 int sign;
4495 isl_pw_qpolynomial *res;
4496 isl_qpolynomial *qp;
4497 };
4498
4499 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4500 * We first make all integer divisions positive and then split the
4501 * quasipolynomials into terms with sign data->sign (the direction
4502 * of the requested approximation) and terms with the opposite sign.
4503 * In the first set of terms, each integer division [a/m] is
4504 * overapproximated by a/m, while in the second it is underapproximated
4505 * by (a-(m-1))/m.
4506 */
4507 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4508 void *user)
4509 {
4510 struct isl_to_poly_data *data = user;
4511 isl_pw_qpolynomial *t;
4512 isl_qpolynomial *qp, *up, *down;
4513
4514 qp = isl_qpolynomial_copy(data->qp);
4515 qp = make_divs_pos(qp, signs);
4516
4517 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4518 up = qp_drop_floors(up, 0);
4519 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4520 down = qp_drop_floors(down, 1);
4521
4522 isl_qpolynomial_free(qp);
4523 qp = isl_qpolynomial_add(up, down);
4524
4525 t = isl_pw_qpolynomial_alloc(orthant, qp);
4526 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4527
4528 return 0;
4529 }
4530
4531 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4532 * the polynomial will be an overapproximation. If "sign" is negative,
4533 * it will be an underapproximation. If "sign" is zero, the approximation
4534 * will lie somewhere in between.
4535 *
4536 * In particular, is sign == 0, we simply drop the floors, turning
4537 * the integer divisions into rational divisions.
4538 * Otherwise, we split the domains into orthants, make all integer divisions
4539 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4540 * depending on the requested sign and the sign of the term in which
4541 * the integer division appears.
4542 */
4543 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4544 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4545 {
4546 int i;
4547 struct isl_to_poly_data data;
4548
4549 if (sign == 0)
4550 return pwqp_drop_floors(pwqp);
4551
4552 if (!pwqp)
4553 return NULL;
4554
4555 data.sign = sign;
4556 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4557
4558 for (i = 0; i < pwqp->n; ++i) {
4559 if (pwqp->p[i].qp->div->n_row == 0) {
4560 isl_pw_qpolynomial *t;
4561 t = isl_pw_qpolynomial_alloc(
4562 isl_set_copy(pwqp->p[i].set),
4563 isl_qpolynomial_copy(pwqp->p[i].qp));
4564 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4565 continue;
4566 }
4567 data.qp = pwqp->p[i].qp;
4568 if (isl_set_foreach_orthant(pwqp->p[i].set,
4569 &to_polynomial_on_orthant, &data) < 0)
4570 goto error;
4571 }
4572
4573 isl_pw_qpolynomial_free(pwqp);
4574
4575 return data.res;
4576 error:
4577 isl_pw_qpolynomial_free(pwqp);
4578 isl_pw_qpolynomial_free(data.res);
4579 return NULL;
4580 }
4581
4582 static int poly_entry(void **entry, void *user)
4583 {
4584 int *sign = user;
4585 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4586
4587 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4588
4589 return *pwqp ? 0 : -1;
4590 }
4591
4592 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4593 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4594 {
4595 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4596 if (!upwqp)
4597 return NULL;
4598
4599 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4600 &poly_entry, &sign) < 0)
4601 goto error;
4602
4603 return upwqp;
4604 error:
4605 isl_union_pw_qpolynomial_free(upwqp);
4606 return NULL;
4607 }
4608
4609 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4610 __isl_take isl_qpolynomial *qp)
4611 {
4612 int i, k;
4613 isl_dim *dim;
4614 isl_vec *aff = NULL;
4615 isl_basic_map *bmap = NULL;
4616 unsigned pos;
4617 unsigned n_div;
4618
4619 if (!qp)
4620 return NULL;
4621 if (!isl_upoly_is_affine(qp->upoly))
4622 isl_die(qp->dim->ctx, isl_error_invalid,
4623 "input quasi-polynomial not affine", goto error);
4624 aff = isl_qpolynomial_extract_affine(qp);
4625 if (!aff)
4626 goto error;
4627 dim = isl_qpolynomial_get_dim(qp);
4628 dim = isl_dim_from_domain(dim);
4629 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4630 dim = isl_dim_add(dim, isl_dim_out, 1);
4631 n_div = qp->div->n_row;
4632 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4633
4634 for (i = 0; i < n_div; ++i) {
4635 k = isl_basic_map_alloc_div(bmap);
4636 if (k < 0)
4637 goto error;
4638 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4639 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4640 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4641 goto error;
4642 }
4643 k = isl_basic_map_alloc_equality(bmap);
4644 if (k < 0)
4645 goto error;
4646 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4647 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4648 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4649
4650 isl_vec_free(aff);
4651 isl_qpolynomial_free(qp);
4652 bmap = isl_basic_map_finalize(bmap);
4653 return bmap;
4654 error:
4655 isl_vec_free(aff);
4656 isl_qpolynomial_free(qp);
4657 isl_basic_map_free(bmap);
4658 return NULL;
4659 }
Integer set library