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export isl_basic_set_remove_redundancies
[isl.git] / isl_polynomial.c
blob5ad0952f01e8141432e5044cd00e9135da9d02a9
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
25 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
26 {
27 switch (type) {
28 case isl_dim_param: return 0;
29 case isl_dim_in: return dim->nparam;
30 case isl_dim_out: return dim->nparam + dim->n_in;
31 default: return 0;
32 }
33 }
34
35 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
36 {
37 if (!up)
38 return -1;
39
40 return up->var < 0;
41 }
42
43 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
44 {
45 if (!up)
46 return NULL;
47
48 isl_assert(up->ctx, up->var < 0, return NULL);
49
50 return (struct isl_upoly_cst *)up;
51 }
52
53 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
54 {
55 if (!up)
56 return NULL;
57
58 isl_assert(up->ctx, up->var >= 0, return NULL);
59
60 return (struct isl_upoly_rec *)up;
61 }
62
63 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
64 __isl_keep struct isl_upoly *up2)
65 {
66 int i;
67 struct isl_upoly_rec *rec1, *rec2;
68
69 if (!up1 || !up2)
70 return -1;
71 if (up1 == up2)
72 return 1;
73 if (up1->var != up2->var)
74 return 0;
75 if (isl_upoly_is_cst(up1)) {
76 struct isl_upoly_cst *cst1, *cst2;
77 cst1 = isl_upoly_as_cst(up1);
78 cst2 = isl_upoly_as_cst(up2);
79 if (!cst1 || !cst2)
80 return -1;
81 return isl_int_eq(cst1->n, cst2->n) &&
82 isl_int_eq(cst1->d, cst2->d);
83 }
84
85 rec1 = isl_upoly_as_rec(up1);
86 rec2 = isl_upoly_as_rec(up2);
87 if (!rec1 || !rec2)
88 return -1;
89
90 if (rec1->n != rec2->n)
91 return 0;
92
93 for (i = 0; i < rec1->n; ++i) {
94 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
95 if (eq < 0 || !eq)
96 return eq;
97 }
98
99 return 1;
100 }
101
102 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
103 {
104 struct isl_upoly_cst *cst;
105
106 if (!up)
107 return -1;
108 if (!isl_upoly_is_cst(up))
109 return 0;
110
111 cst = isl_upoly_as_cst(up);
112 if (!cst)
113 return -1;
114
115 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
116 }
117
118 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
119 {
120 struct isl_upoly_cst *cst;
121
122 if (!up)
123 return 0;
124 if (!isl_upoly_is_cst(up))
125 return 0;
126
127 cst = isl_upoly_as_cst(up);
128 if (!cst)
129 return 0;
130
131 return isl_int_sgn(cst->n);
132 }
133
134 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
135 {
136 struct isl_upoly_cst *cst;
137
138 if (!up)
139 return -1;
140 if (!isl_upoly_is_cst(up))
141 return 0;
142
143 cst = isl_upoly_as_cst(up);
144 if (!cst)
145 return -1;
146
147 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
148 }
149
150 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
151 {
152 struct isl_upoly_cst *cst;
153
154 if (!up)
155 return -1;
156 if (!isl_upoly_is_cst(up))
157 return 0;
158
159 cst = isl_upoly_as_cst(up);
160 if (!cst)
161 return -1;
162
163 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
164 }
165
166 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
167 {
168 struct isl_upoly_cst *cst;
169
170 if (!up)
171 return -1;
172 if (!isl_upoly_is_cst(up))
173 return 0;
174
175 cst = isl_upoly_as_cst(up);
176 if (!cst)
177 return -1;
178
179 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
180 }
181
182 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
183 {
184 struct isl_upoly_cst *cst;
185
186 if (!up)
187 return -1;
188 if (!isl_upoly_is_cst(up))
189 return 0;
190
191 cst = isl_upoly_as_cst(up);
192 if (!cst)
193 return -1;
194
195 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
196 }
197
198 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
199 {
200 struct isl_upoly_cst *cst;
201
202 if (!up)
203 return -1;
204 if (!isl_upoly_is_cst(up))
205 return 0;
206
207 cst = isl_upoly_as_cst(up);
208 if (!cst)
209 return -1;
210
211 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
212 }
213
214 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
215 {
216 struct isl_upoly_cst *cst;
217
218 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
219 if (!cst)
220 return NULL;
221
222 cst->up.ref = 1;
223 cst->up.ctx = ctx;
224 isl_ctx_ref(ctx);
225 cst->up.var = -1;
226
227 isl_int_init(cst->n);
228 isl_int_init(cst->d);
229
230 return cst;
231 }
232
233 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
234 {
235 struct isl_upoly_cst *cst;
236
237 cst = isl_upoly_cst_alloc(ctx);
238 if (!cst)
239 return NULL;
240
241 isl_int_set_si(cst->n, 0);
242 isl_int_set_si(cst->d, 1);
243
244 return &cst->up;
245 }
246
247 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
248 {
249 struct isl_upoly_cst *cst;
250
251 cst = isl_upoly_cst_alloc(ctx);
252 if (!cst)
253 return NULL;
254
255 isl_int_set_si(cst->n, 1);
256 isl_int_set_si(cst->d, 1);
257
258 return &cst->up;
259 }
260
261 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
262 {
263 struct isl_upoly_cst *cst;
264
265 cst = isl_upoly_cst_alloc(ctx);
266 if (!cst)
267 return NULL;
268
269 isl_int_set_si(cst->n, 1);
270 isl_int_set_si(cst->d, 0);
271
272 return &cst->up;
273 }
274
275 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
276 {
277 struct isl_upoly_cst *cst;
278
279 cst = isl_upoly_cst_alloc(ctx);
280 if (!cst)
281 return NULL;
282
283 isl_int_set_si(cst->n, -1);
284 isl_int_set_si(cst->d, 0);
285
286 return &cst->up;
287 }
288
289 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
290 {
291 struct isl_upoly_cst *cst;
292
293 cst = isl_upoly_cst_alloc(ctx);
294 if (!cst)
295 return NULL;
296
297 isl_int_set_si(cst->n, 0);
298 isl_int_set_si(cst->d, 0);
299
300 return &cst->up;
301 }
302
303 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
304 isl_int n, isl_int d)
305 {
306 struct isl_upoly_cst *cst;
307
308 cst = isl_upoly_cst_alloc(ctx);
309 if (!cst)
310 return NULL;
311
312 isl_int_set(cst->n, n);
313 isl_int_set(cst->d, d);
314
315 return &cst->up;
316 }
317
318 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
319 int var, int size)
320 {
321 struct isl_upoly_rec *rec;
322
323 isl_assert(ctx, var >= 0, return NULL);
324 isl_assert(ctx, size >= 0, return NULL);
325 rec = isl_calloc(ctx, struct isl_upoly_rec,
326 sizeof(struct isl_upoly_rec) +
327 (size - 1) * sizeof(struct isl_upoly *));
328 if (!rec)
329 return NULL;
330
331 rec->up.ref = 1;
332 rec->up.ctx = ctx;
333 isl_ctx_ref(ctx);
334 rec->up.var = var;
335
336 rec->n = 0;
337 rec->size = size;
338
339 return rec;
340 }
341
342 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
343 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
344 {
345 qp = isl_qpolynomial_cow(qp);
346 if (!qp || !dim)
347 goto error;
348
349 isl_dim_free(qp->dim);
350 qp->dim = dim;
351
352 return qp;
353 error:
354 isl_qpolynomial_free(qp);
355 isl_dim_free(dim);
356 return NULL;
357 }
358
359 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
360 {
361 return qp ? qp->dim->ctx : NULL;
362 }
363
364 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
365 {
366 return qp ? isl_dim_copy(qp->dim) : NULL;
367 }
368
369 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
370 enum isl_dim_type type)
371 {
372 return qp ? isl_dim_size(qp->dim, type) : 0;
373 }
374
375 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
376 {
377 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
378 }
379
380 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
381 {
382 return qp ? isl_upoly_is_one(qp->upoly) : -1;
383 }
384
385 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
386 {
387 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
388 }
389
390 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
391 {
392 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
393 }
394
395 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
396 {
397 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
398 }
399
400 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
401 {
402 return qp ? isl_upoly_sgn(qp->upoly) : 0;
403 }
404
405 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
406 {
407 isl_int_clear(cst->n);
408 isl_int_clear(cst->d);
409 }
410
411 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
412 {
413 int i;
414
415 for (i = 0; i < rec->n; ++i)
416 isl_upoly_free(rec->p[i]);
417 }
418
419 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
420 {
421 if (!up)
422 return NULL;
423
424 up->ref++;
425 return up;
426 }
427
428 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
429 {
430 struct isl_upoly_cst *cst;
431 struct isl_upoly_cst *dup;
432
433 cst = isl_upoly_as_cst(up);
434 if (!cst)
435 return NULL;
436
437 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
438 if (!dup)
439 return NULL;
440 isl_int_set(dup->n, cst->n);
441 isl_int_set(dup->d, cst->d);
442
443 return &dup->up;
444 }
445
446 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
447 {
448 int i;
449 struct isl_upoly_rec *rec;
450 struct isl_upoly_rec *dup;
451
452 rec = isl_upoly_as_rec(up);
453 if (!rec)
454 return NULL;
455
456 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
457 if (!dup)
458 return NULL;
459
460 for (i = 0; i < rec->n; ++i) {
461 dup->p[i] = isl_upoly_copy(rec->p[i]);
462 if (!dup->p[i])
463 goto error;
464 dup->n++;
465 }
466
467 return &dup->up;
468 error:
469 isl_upoly_free(&dup->up);
470 return NULL;
471 }
472
473 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
474 {
475 struct isl_upoly *dup;
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 *up;
1038 struct isl_upoly_rec *rec;
1039 struct isl_upoly_cst *cst;
1040
1041 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1042 if (!rec)
1043 return NULL;
1044 for (i = 0; i < 1 + power; ++i) {
1045 rec->p[i] = isl_upoly_zero(ctx);
1046 if (!rec->p[i])
1047 goto error;
1048 rec->n++;
1049 }
1050 cst = isl_upoly_as_cst(rec->p[power]);
1051 isl_int_set_si(cst->n, 1);
1052
1053 return &rec->up;
1054 error:
1055 isl_upoly_free(&rec->up);
1056 return NULL;
1057 }
1058
1059 /* r array maps original positions to new positions.
1060 */
1061 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1062 int *r)
1063 {
1064 int i;
1065 struct isl_upoly_rec *rec;
1066 struct isl_upoly *base;
1067 struct isl_upoly *res;
1068
1069 if (isl_upoly_is_cst(up))
1070 return up;
1071
1072 rec = isl_upoly_as_rec(up);
1073 if (!rec)
1074 goto error;
1075
1076 isl_assert(up->ctx, rec->n >= 1, goto error);
1077
1078 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1079 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1080
1081 for (i = rec->n - 2; i >= 0; --i) {
1082 res = isl_upoly_mul(res, isl_upoly_copy(base));
1083 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1084 }
1085
1086 isl_upoly_free(base);
1087 isl_upoly_free(up);
1088
1089 return res;
1090 error:
1091 isl_upoly_free(up);
1092 return NULL;
1093 }
1094
1095 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1096 {
1097 int n_row, n_col;
1098 int equal;
1099
1100 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1101 div1->n_col >= div2->n_col, return -1);
1102
1103 if (div1->n_row == div2->n_row)
1104 return isl_mat_is_equal(div1, div2);
1105
1106 n_row = div1->n_row;
1107 n_col = div1->n_col;
1108 div1->n_row = div2->n_row;
1109 div1->n_col = div2->n_col;
1110
1111 equal = isl_mat_is_equal(div1, div2);
1112
1113 div1->n_row = n_row;
1114 div1->n_col = n_col;
1115
1116 return equal;
1117 }
1118
1119 static void expand_row(__isl_keep isl_mat *dst, int d,
1120 __isl_keep isl_mat *src, int s, int *exp)
1121 {
1122 int i;
1123 unsigned c = src->n_col - src->n_row;
1124
1125 isl_seq_cpy(dst->row[d], src->row[s], c);
1126 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1127
1128 for (i = 0; i < s; ++i)
1129 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1130 }
1131
1132 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1133 {
1134 int li, lj;
1135
1136 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1137 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1138
1139 if (li != lj)
1140 return li - lj;
1141
1142 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1143 }
1144
1145 struct isl_div_sort_info {
1146 isl_mat *div;
1147 int row;
1148 };
1149
1150 static int div_sort_cmp(const void *p1, const void *p2)
1151 {
1152 const struct isl_div_sort_info *i1, *i2;
1153 i1 = (const struct isl_div_sort_info *) p1;
1154 i2 = (const struct isl_div_sort_info *) p2;
1155
1156 return cmp_row(i1->div, i1->row, i2->row);
1157 }
1158
1159 /* Sort divs and remove duplicates.
1160 */
1161 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1162 {
1163 int i;
1164 int skip;
1165 int len;
1166 struct isl_div_sort_info *array = NULL;
1167 int *pos = NULL, *at = NULL;
1168 int *reordering = NULL;
1169 unsigned div_pos;
1170
1171 if (!qp)
1172 return NULL;
1173 if (qp->div->n_row <= 1)
1174 return qp;
1175
1176 div_pos = isl_dim_total(qp->dim);
1177
1178 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1179 qp->div->n_row);
1180 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1181 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1182 len = qp->div->n_col - 2;
1183 reordering = isl_alloc_array(qp->div->ctx, int, len);
1184 if (!array || !pos || !at || !reordering)
1185 goto error;
1186
1187 for (i = 0; i < qp->div->n_row; ++i) {
1188 array[i].div = qp->div;
1189 array[i].row = i;
1190 pos[i] = i;
1191 at[i] = i;
1192 }
1193
1194 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1195 div_sort_cmp);
1196
1197 for (i = 0; i < div_pos; ++i)
1198 reordering[i] = i;
1199
1200 for (i = 0; i < qp->div->n_row; ++i) {
1201 if (pos[array[i].row] == i)
1202 continue;
1203 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1204 pos[at[i]] = pos[array[i].row];
1205 at[pos[array[i].row]] = at[i];
1206 at[i] = array[i].row;
1207 pos[array[i].row] = i;
1208 }
1209
1210 skip = 0;
1211 for (i = 0; i < len - div_pos; ++i) {
1212 if (i > 0 &&
1213 isl_seq_eq(qp->div->row[i - skip - 1],
1214 qp->div->row[i - skip], qp->div->n_col)) {
1215 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1216 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1217 2 + div_pos + i - skip);
1218 qp->div = isl_mat_drop_cols(qp->div,
1219 2 + div_pos + i - skip, 1);
1220 skip++;
1221 }
1222 reordering[div_pos + array[i].row] = div_pos + i - skip;
1223 }
1224
1225 qp->upoly = reorder(qp->upoly, reordering);
1226
1227 if (!qp->upoly || !qp->div)
1228 goto error;
1229
1230 free(at);
1231 free(pos);
1232 free(array);
1233 free(reordering);
1234
1235 return qp;
1236 error:
1237 free(at);
1238 free(pos);
1239 free(array);
1240 free(reordering);
1241 isl_qpolynomial_free(qp);
1242 return NULL;
1243 }
1244
1245 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1246 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1247 {
1248 int i, j, k;
1249 isl_mat *div = NULL;
1250 unsigned d = div1->n_col - div1->n_row;
1251
1252 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1253 d + div1->n_row + div2->n_row);
1254 if (!div)
1255 return NULL;
1256
1257 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1258 int cmp;
1259
1260 expand_row(div, k, div1, i, exp1);
1261 expand_row(div, k + 1, div2, j, exp2);
1262
1263 cmp = cmp_row(div, k, k + 1);
1264 if (cmp == 0) {
1265 exp1[i++] = k;
1266 exp2[j++] = k;
1267 } else if (cmp < 0) {
1268 exp1[i++] = k;
1269 } else {
1270 exp2[j++] = k;
1271 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1272 }
1273 }
1274 for (; i < div1->n_row; ++i, ++k) {
1275 expand_row(div, k, div1, i, exp1);
1276 exp1[i] = k;
1277 }
1278 for (; j < div2->n_row; ++j, ++k) {
1279 expand_row(div, k, div2, j, exp2);
1280 exp2[j] = k;
1281 }
1282
1283 div->n_row = k;
1284 div->n_col = d + k;
1285
1286 return div;
1287 }
1288
1289 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1290 int *exp, int first)
1291 {
1292 int i;
1293 struct isl_upoly_rec *rec;
1294
1295 if (isl_upoly_is_cst(up))
1296 return up;
1297
1298 if (up->var < first)
1299 return up;
1300
1301 if (exp[up->var - first] == up->var - first)
1302 return up;
1303
1304 up = isl_upoly_cow(up);
1305 if (!up)
1306 goto error;
1307
1308 up->var = exp[up->var - first] + first;
1309
1310 rec = isl_upoly_as_rec(up);
1311 if (!rec)
1312 goto error;
1313
1314 for (i = 0; i < rec->n; ++i) {
1315 rec->p[i] = expand(rec->p[i], exp, first);
1316 if (!rec->p[i])
1317 goto error;
1318 }
1319
1320 return up;
1321 error:
1322 isl_upoly_free(up);
1323 return NULL;
1324 }
1325
1326 static __isl_give isl_qpolynomial *with_merged_divs(
1327 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1328 __isl_take isl_qpolynomial *qp2),
1329 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1330 {
1331 int *exp1 = NULL;
1332 int *exp2 = NULL;
1333 isl_mat *div = NULL;
1334
1335 qp1 = isl_qpolynomial_cow(qp1);
1336 qp2 = isl_qpolynomial_cow(qp2);
1337
1338 if (!qp1 || !qp2)
1339 goto error;
1340
1341 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1342 qp1->div->n_col >= qp2->div->n_col, goto error);
1343
1344 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1345 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1346 if (!exp1 || !exp2)
1347 goto error;
1348
1349 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1350 if (!div)
1351 goto error;
1352
1353 isl_mat_free(qp1->div);
1354 qp1->div = isl_mat_copy(div);
1355 isl_mat_free(qp2->div);
1356 qp2->div = isl_mat_copy(div);
1357
1358 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1359 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1360
1361 if (!qp1->upoly || !qp2->upoly)
1362 goto error;
1363
1364 isl_mat_free(div);
1365 free(exp1);
1366 free(exp2);
1367
1368 return fn(qp1, qp2);
1369 error:
1370 isl_mat_free(div);
1371 free(exp1);
1372 free(exp2);
1373 isl_qpolynomial_free(qp1);
1374 isl_qpolynomial_free(qp2);
1375 return NULL;
1376 }
1377
1378 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1379 __isl_take isl_qpolynomial *qp2)
1380 {
1381 qp1 = isl_qpolynomial_cow(qp1);
1382
1383 if (!qp1 || !qp2)
1384 goto error;
1385
1386 if (qp1->div->n_row < qp2->div->n_row)
1387 return isl_qpolynomial_add(qp2, qp1);
1388
1389 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1390 if (!compatible_divs(qp1->div, qp2->div))
1391 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1392
1393 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1394 if (!qp1->upoly)
1395 goto error;
1396
1397 isl_qpolynomial_free(qp2);
1398
1399 return qp1;
1400 error:
1401 isl_qpolynomial_free(qp1);
1402 isl_qpolynomial_free(qp2);
1403 return NULL;
1404 }
1405
1406 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1407 __isl_keep isl_set *dom,
1408 __isl_take isl_qpolynomial *qp1,
1409 __isl_take isl_qpolynomial *qp2)
1410 {
1411 qp1 = isl_qpolynomial_add(qp1, qp2);
1412 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1413 return qp1;
1414 }
1415
1416 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1417 __isl_take isl_qpolynomial *qp2)
1418 {
1419 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1420 }
1421
1422 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1423 __isl_take isl_qpolynomial *qp, isl_int v)
1424 {
1425 if (isl_int_is_zero(v))
1426 return qp;
1427
1428 qp = isl_qpolynomial_cow(qp);
1429 if (!qp)
1430 return NULL;
1431
1432 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1433 if (!qp->upoly)
1434 goto error;
1435
1436 return qp;
1437 error:
1438 isl_qpolynomial_free(qp);
1439 return NULL;
1440
1441 }
1442
1443 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1444 {
1445 if (!qp)
1446 return NULL;
1447
1448 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1449 }
1450
1451 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1452 __isl_take isl_qpolynomial *qp, isl_int v)
1453 {
1454 if (isl_int_is_one(v))
1455 return qp;
1456
1457 if (qp && isl_int_is_zero(v)) {
1458 isl_qpolynomial *zero;
1459 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1460 isl_qpolynomial_free(qp);
1461 return zero;
1462 }
1463
1464 qp = isl_qpolynomial_cow(qp);
1465 if (!qp)
1466 return NULL;
1467
1468 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1469 if (!qp->upoly)
1470 goto error;
1471
1472 return qp;
1473 error:
1474 isl_qpolynomial_free(qp);
1475 return NULL;
1476 }
1477
1478 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1479 __isl_take isl_qpolynomial *qp2)
1480 {
1481 qp1 = isl_qpolynomial_cow(qp1);
1482
1483 if (!qp1 || !qp2)
1484 goto error;
1485
1486 if (qp1->div->n_row < qp2->div->n_row)
1487 return isl_qpolynomial_mul(qp2, qp1);
1488
1489 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1490 if (!compatible_divs(qp1->div, qp2->div))
1491 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1492
1493 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1494 if (!qp1->upoly)
1495 goto error;
1496
1497 isl_qpolynomial_free(qp2);
1498
1499 return qp1;
1500 error:
1501 isl_qpolynomial_free(qp1);
1502 isl_qpolynomial_free(qp2);
1503 return NULL;
1504 }
1505
1506 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1507 unsigned power)
1508 {
1509 qp = isl_qpolynomial_cow(qp);
1510
1511 if (!qp)
1512 return NULL;
1513
1514 qp->upoly = isl_upoly_pow(qp->upoly, power);
1515 if (!qp->upoly)
1516 goto error;
1517
1518 return qp;
1519 error:
1520 isl_qpolynomial_free(qp);
1521 return NULL;
1522 }
1523
1524 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1525 {
1526 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1527 }
1528
1529 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1530 {
1531 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1532 }
1533
1534 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1535 {
1536 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1537 }
1538
1539 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1540 {
1541 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1542 }
1543
1544 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1545 {
1546 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1547 }
1548
1549 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1550 isl_int v)
1551 {
1552 struct isl_qpolynomial *qp;
1553 struct isl_upoly_cst *cst;
1554
1555 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1556 if (!qp)
1557 return NULL;
1558
1559 cst = isl_upoly_as_cst(qp->upoly);
1560 isl_int_set(cst->n, v);
1561
1562 return qp;
1563 }
1564
1565 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1566 isl_int *n, isl_int *d)
1567 {
1568 struct isl_upoly_cst *cst;
1569
1570 if (!qp)
1571 return -1;
1572
1573 if (!isl_upoly_is_cst(qp->upoly))
1574 return 0;
1575
1576 cst = isl_upoly_as_cst(qp->upoly);
1577 if (!cst)
1578 return -1;
1579
1580 if (n)
1581 isl_int_set(*n, cst->n);
1582 if (d)
1583 isl_int_set(*d, cst->d);
1584
1585 return 1;
1586 }
1587
1588 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1589 {
1590 int is_cst;
1591 struct isl_upoly_rec *rec;
1592
1593 if (!up)
1594 return -1;
1595
1596 if (up->var < 0)
1597 return 1;
1598
1599 rec = isl_upoly_as_rec(up);
1600 if (!rec)
1601 return -1;
1602
1603 if (rec->n > 2)
1604 return 0;
1605
1606 isl_assert(up->ctx, rec->n > 1, return -1);
1607
1608 is_cst = isl_upoly_is_cst(rec->p[1]);
1609 if (is_cst < 0)
1610 return -1;
1611 if (!is_cst)
1612 return 0;
1613
1614 return isl_upoly_is_affine(rec->p[0]);
1615 }
1616
1617 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1618 {
1619 if (!qp)
1620 return -1;
1621
1622 if (qp->div->n_row > 0)
1623 return 0;
1624
1625 return isl_upoly_is_affine(qp->upoly);
1626 }
1627
1628 static void update_coeff(__isl_keep isl_vec *aff,
1629 __isl_keep struct isl_upoly_cst *cst, int pos)
1630 {
1631 isl_int gcd;
1632 isl_int f;
1633
1634 if (isl_int_is_zero(cst->n))
1635 return;
1636
1637 isl_int_init(gcd);
1638 isl_int_init(f);
1639 isl_int_gcd(gcd, cst->d, aff->el[0]);
1640 isl_int_divexact(f, cst->d, gcd);
1641 isl_int_divexact(gcd, aff->el[0], gcd);
1642 isl_seq_scale(aff->el, aff->el, f, aff->size);
1643 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1644 isl_int_clear(gcd);
1645 isl_int_clear(f);
1646 }
1647
1648 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1649 __isl_keep isl_vec *aff)
1650 {
1651 struct isl_upoly_cst *cst;
1652 struct isl_upoly_rec *rec;
1653
1654 if (!up || !aff)
1655 return -1;
1656
1657 if (up->var < 0) {
1658 struct isl_upoly_cst *cst;
1659
1660 cst = isl_upoly_as_cst(up);
1661 if (!cst)
1662 return -1;
1663 update_coeff(aff, cst, 0);
1664 return 0;
1665 }
1666
1667 rec = isl_upoly_as_rec(up);
1668 if (!rec)
1669 return -1;
1670 isl_assert(up->ctx, rec->n == 2, return -1);
1671
1672 cst = isl_upoly_as_cst(rec->p[1]);
1673 if (!cst)
1674 return -1;
1675 update_coeff(aff, cst, 1 + up->var);
1676
1677 return isl_upoly_update_affine(rec->p[0], aff);
1678 }
1679
1680 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1681 __isl_keep isl_qpolynomial *qp)
1682 {
1683 isl_vec *aff;
1684 unsigned d;
1685
1686 if (!qp)
1687 return NULL;
1688
1689 d = isl_dim_total(qp->dim);
1690 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1691 if (!aff)
1692 return NULL;
1693
1694 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1695 isl_int_set_si(aff->el[0], 1);
1696
1697 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1698 goto error;
1699
1700 return aff;
1701 error:
1702 isl_vec_free(aff);
1703 return NULL;
1704 }
1705
1706 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1707 __isl_keep isl_qpolynomial *qp2)
1708 {
1709 if (!qp1 || !qp2)
1710 return -1;
1711
1712 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1713 }
1714
1715 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1716 {
1717 int i;
1718 struct isl_upoly_rec *rec;
1719
1720 if (isl_upoly_is_cst(up)) {
1721 struct isl_upoly_cst *cst;
1722 cst = isl_upoly_as_cst(up);
1723 if (!cst)
1724 return;
1725 isl_int_lcm(*d, *d, cst->d);
1726 return;
1727 }
1728
1729 rec = isl_upoly_as_rec(up);
1730 if (!rec)
1731 return;
1732
1733 for (i = 0; i < rec->n; ++i)
1734 upoly_update_den(rec->p[i], d);
1735 }
1736
1737 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1738 {
1739 isl_int_set_si(*d, 1);
1740 if (!qp)
1741 return;
1742 upoly_update_den(qp->upoly, d);
1743 }
1744
1745 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1746 int pos, int power)
1747 {
1748 struct isl_ctx *ctx;
1749
1750 if (!dim)
1751 return NULL;
1752
1753 ctx = dim->ctx;
1754
1755 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1756 }
1757
1758 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1759 enum isl_dim_type type, unsigned pos)
1760 {
1761 if (!dim)
1762 return NULL;
1763
1764 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1765 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1766
1767 if (type == isl_dim_set)
1768 pos += isl_dim_size(dim, isl_dim_param);
1769
1770 return isl_qpolynomial_var_pow(dim, pos, 1);
1771 error:
1772 isl_dim_free(dim);
1773 return NULL;
1774 }
1775
1776 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1777 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1778 {
1779 int i;
1780 struct isl_upoly_rec *rec;
1781 struct isl_upoly *base, *res;
1782
1783 if (!up)
1784 return NULL;
1785
1786 if (isl_upoly_is_cst(up))
1787 return up;
1788
1789 if (up->var < first)
1790 return up;
1791
1792 rec = isl_upoly_as_rec(up);
1793 if (!rec)
1794 goto error;
1795
1796 isl_assert(up->ctx, rec->n >= 1, goto error);
1797
1798 if (up->var >= first + n)
1799 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1800 else
1801 base = isl_upoly_copy(subs[up->var - first]);
1802
1803 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1804 for (i = rec->n - 2; i >= 0; --i) {
1805 struct isl_upoly *t;
1806 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1807 res = isl_upoly_mul(res, isl_upoly_copy(base));
1808 res = isl_upoly_sum(res, t);
1809 }
1810
1811 isl_upoly_free(base);
1812 isl_upoly_free(up);
1813
1814 return res;
1815 error:
1816 isl_upoly_free(up);
1817 return NULL;
1818 }
1819
1820 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1821 isl_int denom, unsigned len)
1822 {
1823 int i;
1824 struct isl_upoly *up;
1825
1826 isl_assert(ctx, len >= 1, return NULL);
1827
1828 up = isl_upoly_rat_cst(ctx, f[0], denom);
1829 for (i = 0; i < len - 1; ++i) {
1830 struct isl_upoly *t;
1831 struct isl_upoly *c;
1832
1833 if (isl_int_is_zero(f[1 + i]))
1834 continue;
1835
1836 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1837 t = isl_upoly_var_pow(ctx, i, 1);
1838 t = isl_upoly_mul(c, t);
1839 up = isl_upoly_sum(up, t);
1840 }
1841
1842 return up;
1843 }
1844
1845 /* Remove common factor of non-constant terms and denominator.
1846 */
1847 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1848 {
1849 isl_ctx *ctx = qp->div->ctx;
1850 unsigned total = qp->div->n_col - 2;
1851
1852 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1853 isl_int_gcd(ctx->normalize_gcd,
1854 ctx->normalize_gcd, qp->div->row[div][0]);
1855 if (isl_int_is_one(ctx->normalize_gcd))
1856 return;
1857
1858 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1859 ctx->normalize_gcd, total);
1860 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1861 ctx->normalize_gcd);
1862 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1863 ctx->normalize_gcd);
1864 }
1865
1866 /* Replace the integer division identified by "div" by the polynomial "s".
1867 * The integer division is assumed not to appear in the definition
1868 * of any other integer divisions.
1869 */
1870 static __isl_give isl_qpolynomial *substitute_div(
1871 __isl_take isl_qpolynomial *qp,
1872 int div, __isl_take struct isl_upoly *s)
1873 {
1874 int i;
1875 int total;
1876 int *reordering;
1877
1878 if (!qp || !s)
1879 goto error;
1880
1881 qp = isl_qpolynomial_cow(qp);
1882 if (!qp)
1883 goto error;
1884
1885 total = isl_dim_total(qp->dim);
1886 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1887 if (!qp->upoly)
1888 goto error;
1889
1890 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1891 if (!reordering)
1892 goto error;
1893 for (i = 0; i < total + div; ++i)
1894 reordering[i] = i;
1895 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1896 reordering[i] = i - 1;
1897 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1898 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1899 qp->upoly = reorder(qp->upoly, reordering);
1900 free(reordering);
1901
1902 if (!qp->upoly || !qp->div)
1903 goto error;
1904
1905 isl_upoly_free(s);
1906 return qp;
1907 error:
1908 isl_qpolynomial_free(qp);
1909 isl_upoly_free(s);
1910 return NULL;
1911 }
1912
1913 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1914 * divisions because d is equal to 1 by their definition, i.e., e.
1915 */
1916 static __isl_give isl_qpolynomial *substitute_non_divs(
1917 __isl_take isl_qpolynomial *qp)
1918 {
1919 int i, j;
1920 int total;
1921 struct isl_upoly *s;
1922
1923 if (!qp)
1924 return NULL;
1925
1926 total = isl_dim_total(qp->dim);
1927 for (i = 0; qp && i < qp->div->n_row; ++i) {
1928 if (!isl_int_is_one(qp->div->row[i][0]))
1929 continue;
1930 for (j = i + 1; j < qp->div->n_row; ++j) {
1931 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1932 continue;
1933 isl_seq_combine(qp->div->row[j] + 1,
1934 qp->div->ctx->one, qp->div->row[j] + 1,
1935 qp->div->row[j][2 + total + i],
1936 qp->div->row[i] + 1, 1 + total + i);
1937 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1938 normalize_div(qp, j);
1939 }
1940 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1941 qp->div->row[i][0], qp->div->n_col - 1);
1942 qp = substitute_div(qp, i, s);
1943 --i;
1944 }
1945
1946 return qp;
1947 }
1948
1949 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1950 * with d the denominator. When replacing the coefficient e of x by
1951 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1952 * inside the division, so we need to add floor(e/d) * x outside.
1953 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1954 * to adjust the coefficient of x in each later div that depends on the
1955 * current div "div" and also in the affine expression "aff"
1956 * (if it too depends on "div").
1957 */
1958 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1959 __isl_keep isl_vec *aff)
1960 {
1961 int i, j;
1962 isl_int v;
1963 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1964
1965 isl_int_init(v);
1966 for (i = 0; i < 1 + total + div; ++i) {
1967 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1968 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1969 continue;
1970 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1971 isl_int_fdiv_r(qp->div->row[div][1 + i],
1972 qp->div->row[div][1 + i], qp->div->row[div][0]);
1973 if (!isl_int_is_zero(aff->el[1 + total + div]))
1974 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1975 for (j = div + 1; j < qp->div->n_row; ++j) {
1976 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1977 continue;
1978 isl_int_addmul(qp->div->row[j][1 + i],
1979 v, qp->div->row[j][2 + total + div]);
1980 }
1981 }
1982 isl_int_clear(v);
1983 }
1984
1985 /* Check if the last non-zero coefficient is bigger that half of the
1986 * denominator. If so, we will invert the div to further reduce the number
1987 * of distinct divs that may appear.
1988 * If the last non-zero coefficient is exactly half the denominator,
1989 * then we continue looking for earlier coefficients that are bigger
1990 * than half the denominator.
1991 */
1992 static int needs_invert(__isl_keep isl_mat *div, int row)
1993 {
1994 int i;
1995 int cmp;
1996
1997 for (i = div->n_col - 1; i >= 1; --i) {
1998 if (isl_int_is_zero(div->row[row][i]))
1999 continue;
2000 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2001 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2002 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2003 if (cmp)
2004 return cmp > 0;
2005 if (i == 1)
2006 return 1;
2007 }
2008
2009 return 0;
2010 }
2011
2012 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2013 * We only invert the coefficients of e (and the coefficient of q in
2014 * later divs and in "aff"). After calling this function, the
2015 * coefficients of e should be reduced again.
2016 */
2017 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2018 __isl_keep isl_vec *aff)
2019 {
2020 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2021
2022 isl_seq_neg(qp->div->row[div] + 1,
2023 qp->div->row[div] + 1, qp->div->n_col - 1);
2024 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2025 isl_int_add(qp->div->row[div][1],
2026 qp->div->row[div][1], qp->div->row[div][0]);
2027 if (!isl_int_is_zero(aff->el[1 + total + div]))
2028 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2029 isl_mat_col_mul(qp->div, 2 + total + div,
2030 qp->div->ctx->negone, 2 + total + div);
2031 }
2032
2033 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2034 * in the interval [0, d-1], with d the denominator and such that the
2035 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2036 *
2037 * After the reduction, some divs may have become redundant or identical,
2038 * so we call substitute_non_divs and sort_divs. If these functions
2039 * eliminate divs of merge * two or more divs into one, the coefficients
2040 * of the enclosing divs may have to be reduced again, so we call
2041 * ourselves recursively if the number of divs decreases.
2042 */
2043 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2044 {
2045 int i, j;
2046 isl_vec *aff = NULL;
2047 struct isl_upoly *s;
2048 unsigned n_div;
2049
2050 if (!qp)
2051 return NULL;
2052
2053 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2054 aff = isl_vec_clr(aff);
2055 if (!aff)
2056 goto error;
2057
2058 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2059
2060 for (i = 0; i < qp->div->n_row; ++i) {
2061 normalize_div(qp, i);
2062 reduce_div(qp, i, aff);
2063 if (needs_invert(qp->div, i)) {
2064 invert_div(qp, i, aff);
2065 reduce_div(qp, i, aff);
2066 }
2067 }
2068
2069 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2070 qp->div->ctx->one, aff->size);
2071 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2072 isl_upoly_free(s);
2073 if (!qp->upoly)
2074 goto error;
2075
2076 isl_vec_free(aff);
2077
2078 n_div = qp->div->n_row;
2079 qp = substitute_non_divs(qp);
2080 qp = sort_divs(qp);
2081 if (qp && qp->div->n_row < n_div)
2082 return reduce_divs(qp);
2083
2084 return qp;
2085 error:
2086 isl_qpolynomial_free(qp);
2087 isl_vec_free(aff);
2088 return NULL;
2089 }
2090
2091 /* Assumes each div only depends on earlier divs.
2092 */
2093 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2094 int power)
2095 {
2096 struct isl_qpolynomial *qp = NULL;
2097 struct isl_upoly_rec *rec;
2098 struct isl_upoly_cst *cst;
2099 int i, d;
2100 int pos;
2101
2102 if (!div)
2103 return NULL;
2104
2105 d = div->line - div->bmap->div;
2106
2107 pos = isl_dim_total(div->bmap->dim) + d;
2108 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2109 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2110 div->bmap->n_div, &rec->up);
2111 if (!qp)
2112 goto error;
2113
2114 for (i = 0; i < div->bmap->n_div; ++i)
2115 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2116
2117 for (i = 0; i < 1 + power; ++i) {
2118 rec->p[i] = isl_upoly_zero(div->ctx);
2119 if (!rec->p[i])
2120 goto error;
2121 rec->n++;
2122 }
2123 cst = isl_upoly_as_cst(rec->p[power]);
2124 isl_int_set_si(cst->n, 1);
2125
2126 isl_div_free(div);
2127
2128 qp = reduce_divs(qp);
2129
2130 return qp;
2131 error:
2132 isl_qpolynomial_free(qp);
2133 isl_div_free(div);
2134 return NULL;
2135 }
2136
2137 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2138 {
2139 return isl_qpolynomial_div_pow(div, 1);
2140 }
2141
2142 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2143 const isl_int n, const isl_int d)
2144 {
2145 struct isl_qpolynomial *qp;
2146 struct isl_upoly_cst *cst;
2147
2148 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2149 if (!qp)
2150 return NULL;
2151
2152 cst = isl_upoly_as_cst(qp->upoly);
2153 isl_int_set(cst->n, n);
2154 isl_int_set(cst->d, d);
2155
2156 return qp;
2157 }
2158
2159 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2160 {
2161 struct isl_upoly_rec *rec;
2162 int i;
2163
2164 if (!up)
2165 return -1;
2166
2167 if (isl_upoly_is_cst(up))
2168 return 0;
2169
2170 if (up->var < d)
2171 active[up->var] = 1;
2172
2173 rec = isl_upoly_as_rec(up);
2174 for (i = 0; i < rec->n; ++i)
2175 if (up_set_active(rec->p[i], active, d) < 0)
2176 return -1;
2177
2178 return 0;
2179 }
2180
2181 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2182 {
2183 int i, j;
2184 int d = isl_dim_total(qp->dim);
2185
2186 if (!qp || !active)
2187 return -1;
2188
2189 for (i = 0; i < d; ++i)
2190 for (j = 0; j < qp->div->n_row; ++j) {
2191 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2192 continue;
2193 active[i] = 1;
2194 break;
2195 }
2196
2197 return up_set_active(qp->upoly, active, d);
2198 }
2199
2200 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2201 enum isl_dim_type type, unsigned first, unsigned n)
2202 {
2203 int i;
2204 int *active = NULL;
2205 int involves = 0;
2206
2207 if (!qp)
2208 return -1;
2209 if (n == 0)
2210 return 0;
2211
2212 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2213 return -1);
2214 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2215 type == isl_dim_set, return -1);
2216
2217 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2218 if (set_active(qp, active) < 0)
2219 goto error;
2220
2221 if (type == isl_dim_set)
2222 first += isl_dim_size(qp->dim, isl_dim_param);
2223 for (i = 0; i < n; ++i)
2224 if (active[first + i]) {
2225 involves = 1;
2226 break;
2227 }
2228
2229 free(active);
2230
2231 return involves;
2232 error:
2233 free(active);
2234 return -1;
2235 }
2236
2237 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2238 unsigned first, unsigned n)
2239 {
2240 int i;
2241 struct isl_upoly_rec *rec;
2242
2243 if (!up)
2244 return NULL;
2245 if (n == 0 || up->var < 0 || up->var < first)
2246 return up;
2247 if (up->var < first + n) {
2248 up = replace_by_constant_term(up);
2249 return isl_upoly_drop(up, first, n);
2250 }
2251 up = isl_upoly_cow(up);
2252 if (!up)
2253 return NULL;
2254 up->var -= n;
2255 rec = isl_upoly_as_rec(up);
2256 if (!rec)
2257 goto error;
2258
2259 for (i = 0; i < rec->n; ++i) {
2260 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2261 if (!rec->p[i])
2262 goto error;
2263 }
2264
2265 return up;
2266 error:
2267 isl_upoly_free(up);
2268 return NULL;
2269 }
2270
2271 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2272 __isl_take isl_qpolynomial *qp,
2273 enum isl_dim_type type, unsigned pos, const char *s)
2274 {
2275 qp = isl_qpolynomial_cow(qp);
2276 if (!qp)
2277 return NULL;
2278 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2279 if (!qp->dim)
2280 goto error;
2281 return qp;
2282 error:
2283 isl_qpolynomial_free(qp);
2284 return NULL;
2285 }
2286
2287 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2288 __isl_take isl_qpolynomial *qp,
2289 enum isl_dim_type type, unsigned first, unsigned n)
2290 {
2291 if (!qp)
2292 return NULL;
2293 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2294 return qp;
2295
2296 qp = isl_qpolynomial_cow(qp);
2297 if (!qp)
2298 return NULL;
2299
2300 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2301 goto error);
2302 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2303 type == isl_dim_set, goto error);
2304
2305 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2306 if (!qp->dim)
2307 goto error;
2308
2309 if (type == isl_dim_set)
2310 first += isl_dim_size(qp->dim, isl_dim_param);
2311
2312 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2313 if (!qp->div)
2314 goto error;
2315
2316 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2317 if (!qp->upoly)
2318 goto error;
2319
2320 return qp;
2321 error:
2322 isl_qpolynomial_free(qp);
2323 return NULL;
2324 }
2325
2326 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2327 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2328 {
2329 int i, j, k;
2330 isl_int denom;
2331 unsigned total;
2332 unsigned n_div;
2333 struct isl_upoly *up;
2334
2335 if (!eq)
2336 goto error;
2337 if (eq->n_eq == 0) {
2338 isl_basic_set_free(eq);
2339 return qp;
2340 }
2341
2342 qp = isl_qpolynomial_cow(qp);
2343 if (!qp)
2344 goto error;
2345 qp->div = isl_mat_cow(qp->div);
2346 if (!qp->div)
2347 goto error;
2348
2349 total = 1 + isl_dim_total(eq->dim);
2350 n_div = eq->n_div;
2351 isl_int_init(denom);
2352 for (i = 0; i < eq->n_eq; ++i) {
2353 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2354 if (j < 0 || j == 0 || j >= total)
2355 continue;
2356
2357 for (k = 0; k < qp->div->n_row; ++k) {
2358 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2359 continue;
2360 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2361 &qp->div->row[k][0]);
2362 normalize_div(qp, k);
2363 }
2364
2365 if (isl_int_is_pos(eq->eq[i][j]))
2366 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2367 isl_int_abs(denom, eq->eq[i][j]);
2368 isl_int_set_si(eq->eq[i][j], 0);
2369
2370 up = isl_upoly_from_affine(qp->dim->ctx,
2371 eq->eq[i], denom, total);
2372 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2373 isl_upoly_free(up);
2374 }
2375 isl_int_clear(denom);
2376
2377 if (!qp->upoly)
2378 goto error;
2379
2380 isl_basic_set_free(eq);
2381
2382 qp = substitute_non_divs(qp);
2383 qp = sort_divs(qp);
2384
2385 return qp;
2386 error:
2387 isl_basic_set_free(eq);
2388 isl_qpolynomial_free(qp);
2389 return NULL;
2390 }
2391
2392 static __isl_give isl_basic_set *add_div_constraints(
2393 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2394 {
2395 int i;
2396 unsigned total;
2397
2398 if (!bset || !div)
2399 goto error;
2400
2401 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2402 if (!bset)
2403 goto error;
2404 total = isl_basic_set_total_dim(bset);
2405 for (i = 0; i < div->n_row; ++i)
2406 if (isl_basic_set_add_div_constraints_var(bset,
2407 total - div->n_row + i, div->row[i]) < 0)
2408 goto error;
2409
2410 isl_mat_free(div);
2411 return bset;
2412 error:
2413 isl_mat_free(div);
2414 isl_basic_set_free(bset);
2415 return NULL;
2416 }
2417
2418 /* Look for equalities among the variables shared by context and qp
2419 * and the integer divisions of qp, if any.
2420 * The equalities are then used to eliminate variables and/or integer
2421 * divisions from qp.
2422 */
2423 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2424 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2425 {
2426 isl_basic_set *aff;
2427
2428 if (!qp)
2429 goto error;
2430 if (qp->div->n_row > 0) {
2431 isl_basic_set *bset;
2432 context = isl_set_add_dims(context, isl_dim_set,
2433 qp->div->n_row);
2434 bset = isl_basic_set_universe(isl_set_get_dim(context));
2435 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2436 context = isl_set_intersect(context,
2437 isl_set_from_basic_set(bset));
2438 }
2439
2440 aff = isl_set_affine_hull(context);
2441 return isl_qpolynomial_substitute_equalities(qp, aff);
2442 error:
2443 isl_qpolynomial_free(qp);
2444 isl_set_free(context);
2445 return NULL;
2446 }
2447
2448 #undef PW
2449 #define PW isl_pw_qpolynomial
2450 #undef EL
2451 #define EL isl_qpolynomial
2452 #undef IS_ZERO
2453 #define IS_ZERO is_zero
2454 #undef FIELD
2455 #define FIELD qp
2456
2457 #include <isl_pw_templ.c>
2458
2459 #undef UNION
2460 #define UNION isl_union_pw_qpolynomial
2461 #undef PART
2462 #define PART isl_pw_qpolynomial
2463 #undef PARTS
2464 #define PARTS pw_qpolynomial
2465
2466 #include <isl_union_templ.c>
2467
2468 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2469 {
2470 if (!pwqp)
2471 return -1;
2472
2473 if (pwqp->n != -1)
2474 return 0;
2475
2476 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2477 return 0;
2478
2479 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2480 }
2481
2482 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2483 __isl_take isl_pw_qpolynomial *pwqp1,
2484 __isl_take isl_pw_qpolynomial *pwqp2)
2485 {
2486 int i, j, n;
2487 struct isl_pw_qpolynomial *res;
2488 isl_set *set;
2489
2490 if (!pwqp1 || !pwqp2)
2491 goto error;
2492
2493 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2494 goto error);
2495
2496 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2497 isl_pw_qpolynomial_free(pwqp2);
2498 return pwqp1;
2499 }
2500
2501 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2502 isl_pw_qpolynomial_free(pwqp1);
2503 return pwqp2;
2504 }
2505
2506 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2507 isl_pw_qpolynomial_free(pwqp1);
2508 return pwqp2;
2509 }
2510
2511 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2512 isl_pw_qpolynomial_free(pwqp2);
2513 return pwqp1;
2514 }
2515
2516 n = pwqp1->n * pwqp2->n;
2517 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2518
2519 for (i = 0; i < pwqp1->n; ++i) {
2520 for (j = 0; j < pwqp2->n; ++j) {
2521 struct isl_set *common;
2522 struct isl_qpolynomial *prod;
2523 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2524 isl_set_copy(pwqp2->p[j].set));
2525 if (isl_set_plain_is_empty(common)) {
2526 isl_set_free(common);
2527 continue;
2528 }
2529
2530 prod = isl_qpolynomial_mul(
2531 isl_qpolynomial_copy(pwqp1->p[i].qp),
2532 isl_qpolynomial_copy(pwqp2->p[j].qp));
2533
2534 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2535 }
2536 }
2537
2538 isl_pw_qpolynomial_free(pwqp1);
2539 isl_pw_qpolynomial_free(pwqp2);
2540
2541 return res;
2542 error:
2543 isl_pw_qpolynomial_free(pwqp1);
2544 isl_pw_qpolynomial_free(pwqp2);
2545 return NULL;
2546 }
2547
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2549 __isl_take isl_pw_qpolynomial *pwqp)
2550 {
2551 int i;
2552
2553 if (!pwqp)
2554 return NULL;
2555
2556 if (isl_pw_qpolynomial_is_zero(pwqp))
2557 return pwqp;
2558
2559 pwqp = isl_pw_qpolynomial_cow(pwqp);
2560 if (!pwqp)
2561 return NULL;
2562
2563 for (i = 0; i < pwqp->n; ++i) {
2564 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2565 if (!pwqp->p[i].qp)
2566 goto error;
2567 }
2568
2569 return pwqp;
2570 error:
2571 isl_pw_qpolynomial_free(pwqp);
2572 return NULL;
2573 }
2574
2575 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2576 __isl_take isl_pw_qpolynomial *pwqp1,
2577 __isl_take isl_pw_qpolynomial *pwqp2)
2578 {
2579 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2580 }
2581
2582 __isl_give struct isl_upoly *isl_upoly_eval(
2583 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2584 {
2585 int i;
2586 struct isl_upoly_rec *rec;
2587 struct isl_upoly *res;
2588 struct isl_upoly *base;
2589
2590 if (isl_upoly_is_cst(up)) {
2591 isl_vec_free(vec);
2592 return up;
2593 }
2594
2595 rec = isl_upoly_as_rec(up);
2596 if (!rec)
2597 goto error;
2598
2599 isl_assert(up->ctx, rec->n >= 1, goto error);
2600
2601 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2602
2603 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2604 isl_vec_copy(vec));
2605
2606 for (i = rec->n - 2; i >= 0; --i) {
2607 res = isl_upoly_mul(res, isl_upoly_copy(base));
2608 res = isl_upoly_sum(res,
2609 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2610 isl_vec_copy(vec)));
2611 }
2612
2613 isl_upoly_free(base);
2614 isl_upoly_free(up);
2615 isl_vec_free(vec);
2616 return res;
2617 error:
2618 isl_upoly_free(up);
2619 isl_vec_free(vec);
2620 return NULL;
2621 }
2622
2623 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2624 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2625 {
2626 isl_vec *ext;
2627 struct isl_upoly *up;
2628 isl_dim *dim;
2629
2630 if (!qp || !pnt)
2631 goto error;
2632 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2633
2634 if (qp->div->n_row == 0)
2635 ext = isl_vec_copy(pnt->vec);
2636 else {
2637 int i;
2638 unsigned dim = isl_dim_total(qp->dim);
2639 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2640 if (!ext)
2641 goto error;
2642
2643 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2644 for (i = 0; i < qp->div->n_row; ++i) {
2645 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2646 1 + dim + i, &ext->el[1+dim+i]);
2647 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2648 qp->div->row[i][0]);
2649 }
2650 }
2651
2652 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2653 if (!up)
2654 goto error;
2655
2656 dim = isl_dim_copy(qp->dim);
2657 isl_qpolynomial_free(qp);
2658 isl_point_free(pnt);
2659
2660 return isl_qpolynomial_alloc(dim, 0, up);
2661 error:
2662 isl_qpolynomial_free(qp);
2663 isl_point_free(pnt);
2664 return NULL;
2665 }
2666
2667 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2668 __isl_keep struct isl_upoly_cst *cst2)
2669 {
2670 int cmp;
2671 isl_int t;
2672 isl_int_init(t);
2673 isl_int_mul(t, cst1->n, cst2->d);
2674 isl_int_submul(t, cst2->n, cst1->d);
2675 cmp = isl_int_sgn(t);
2676 isl_int_clear(t);
2677 return cmp;
2678 }
2679
2680 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2681 __isl_keep isl_qpolynomial *qp2)
2682 {
2683 struct isl_upoly_cst *cst1, *cst2;
2684
2685 if (!qp1 || !qp2)
2686 return -1;
2687 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2688 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2689 if (isl_qpolynomial_is_nan(qp1))
2690 return -1;
2691 if (isl_qpolynomial_is_nan(qp2))
2692 return -1;
2693 cst1 = isl_upoly_as_cst(qp1->upoly);
2694 cst2 = isl_upoly_as_cst(qp2->upoly);
2695
2696 return isl_upoly_cmp(cst1, cst2) <= 0;
2697 }
2698
2699 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2700 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2701 {
2702 struct isl_upoly_cst *cst1, *cst2;
2703 int cmp;
2704
2705 if (!qp1 || !qp2)
2706 goto error;
2707 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2708 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2709 cst1 = isl_upoly_as_cst(qp1->upoly);
2710 cst2 = isl_upoly_as_cst(qp2->upoly);
2711 cmp = isl_upoly_cmp(cst1, cst2);
2712
2713 if (cmp <= 0) {
2714 isl_qpolynomial_free(qp2);
2715 } else {
2716 isl_qpolynomial_free(qp1);
2717 qp1 = qp2;
2718 }
2719 return qp1;
2720 error:
2721 isl_qpolynomial_free(qp1);
2722 isl_qpolynomial_free(qp2);
2723 return NULL;
2724 }
2725
2726 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2727 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2728 {
2729 struct isl_upoly_cst *cst1, *cst2;
2730 int cmp;
2731
2732 if (!qp1 || !qp2)
2733 goto error;
2734 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2735 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2736 cst1 = isl_upoly_as_cst(qp1->upoly);
2737 cst2 = isl_upoly_as_cst(qp2->upoly);
2738 cmp = isl_upoly_cmp(cst1, cst2);
2739
2740 if (cmp >= 0) {
2741 isl_qpolynomial_free(qp2);
2742 } else {
2743 isl_qpolynomial_free(qp1);
2744 qp1 = qp2;
2745 }
2746 return qp1;
2747 error:
2748 isl_qpolynomial_free(qp1);
2749 isl_qpolynomial_free(qp2);
2750 return NULL;
2751 }
2752
2753 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2754 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2755 unsigned first, unsigned n)
2756 {
2757 unsigned total;
2758 unsigned g_pos;
2759 int *exp;
2760
2761 if (n == 0)
2762 return qp;
2763
2764 qp = isl_qpolynomial_cow(qp);
2765 if (!qp)
2766 return NULL;
2767
2768 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2769 goto error);
2770
2771 g_pos = pos(qp->dim, type) + first;
2772
2773 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2774 if (!qp->div)
2775 goto error;
2776
2777 total = qp->div->n_col - 2;
2778 if (total > g_pos) {
2779 int i;
2780 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2781 if (!exp)
2782 goto error;
2783 for (i = 0; i < total - g_pos; ++i)
2784 exp[i] = i + n;
2785 qp->upoly = expand(qp->upoly, exp, g_pos);
2786 free(exp);
2787 if (!qp->upoly)
2788 goto error;
2789 }
2790
2791 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2792 if (!qp->dim)
2793 goto error;
2794
2795 return qp;
2796 error:
2797 isl_qpolynomial_free(qp);
2798 return NULL;
2799 }
2800
2801 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2802 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2803 {
2804 unsigned pos;
2805
2806 pos = isl_qpolynomial_dim(qp, type);
2807
2808 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2809 }
2810
2811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2812 __isl_take isl_pw_qpolynomial *pwqp,
2813 enum isl_dim_type type, unsigned n)
2814 {
2815 unsigned pos;
2816
2817 pos = isl_pw_qpolynomial_dim(pwqp, type);
2818
2819 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2820 }
2821
2822 static int *reordering_move(isl_ctx *ctx,
2823 unsigned len, unsigned dst, unsigned src, unsigned n)
2824 {
2825 int i;
2826 int *reordering;
2827
2828 reordering = isl_alloc_array(ctx, int, len);
2829 if (!reordering)
2830 return NULL;
2831
2832 if (dst <= src) {
2833 for (i = 0; i < dst; ++i)
2834 reordering[i] = i;
2835 for (i = 0; i < n; ++i)
2836 reordering[src + i] = dst + i;
2837 for (i = 0; i < src - dst; ++i)
2838 reordering[dst + i] = dst + n + i;
2839 for (i = 0; i < len - src - n; ++i)
2840 reordering[src + n + i] = src + n + i;
2841 } else {
2842 for (i = 0; i < src; ++i)
2843 reordering[i] = i;
2844 for (i = 0; i < n; ++i)
2845 reordering[src + i] = dst + i;
2846 for (i = 0; i < dst - src; ++i)
2847 reordering[src + n + i] = src + i;
2848 for (i = 0; i < len - dst - n; ++i)
2849 reordering[dst + n + i] = dst + n + i;
2850 }
2851
2852 return reordering;
2853 }
2854
2855 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2856 __isl_take isl_qpolynomial *qp,
2857 enum isl_dim_type dst_type, unsigned dst_pos,
2858 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2859 {
2860 unsigned g_dst_pos;
2861 unsigned g_src_pos;
2862 int *reordering;
2863
2864 qp = isl_qpolynomial_cow(qp);
2865 if (!qp)
2866 return NULL;
2867
2868 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2869 goto error);
2870
2871 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2872 g_src_pos = pos(qp->dim, src_type) + src_pos;
2873 if (dst_type > src_type)
2874 g_dst_pos -= n;
2875
2876 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2877 if (!qp->div)
2878 goto error;
2879 qp = sort_divs(qp);
2880 if (!qp)
2881 goto error;
2882
2883 reordering = reordering_move(qp->dim->ctx,
2884 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2885 if (!reordering)
2886 goto error;
2887
2888 qp->upoly = reorder(qp->upoly, reordering);
2889 free(reordering);
2890 if (!qp->upoly)
2891 goto error;
2892
2893 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2894 if (!qp->dim)
2895 goto error;
2896
2897 return qp;
2898 error:
2899 isl_qpolynomial_free(qp);
2900 return NULL;
2901 }
2902
2903 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2904 isl_int *f, isl_int denom)
2905 {
2906 struct isl_upoly *up;
2907
2908 if (!dim)
2909 return NULL;
2910
2911 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2912
2913 return isl_qpolynomial_alloc(dim, 0, up);
2914 }
2915
2916 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2917 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2918 {
2919 isl_int denom;
2920 isl_dim *dim;
2921 struct isl_upoly *up;
2922 isl_qpolynomial *qp;
2923 int sgn;
2924
2925 if (!c)
2926 return NULL;
2927
2928 isl_int_init(denom);
2929
2930 isl_constraint_get_coefficient(c, type, pos, &denom);
2931 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2932 sgn = isl_int_sgn(denom);
2933 isl_int_abs(denom, denom);
2934 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2935 1 + isl_constraint_dim(c, isl_dim_all));
2936 if (sgn < 0)
2937 isl_int_neg(denom, denom);
2938 isl_constraint_set_coefficient(c, type, pos, denom);
2939
2940 dim = isl_dim_copy(c->bmap->dim);
2941
2942 isl_int_clear(denom);
2943 isl_constraint_free(c);
2944
2945 qp = isl_qpolynomial_alloc(dim, 0, up);
2946 if (sgn > 0)
2947 qp = isl_qpolynomial_neg(qp);
2948 return qp;
2949 }
2950
2951 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2952 * in "qp" by subs[i].
2953 */
2954 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2955 __isl_take isl_qpolynomial *qp,
2956 enum isl_dim_type type, unsigned first, unsigned n,
2957 __isl_keep isl_qpolynomial **subs)
2958 {
2959 int i;
2960 struct isl_upoly **ups;
2961
2962 if (n == 0)
2963 return qp;
2964
2965 qp = isl_qpolynomial_cow(qp);
2966 if (!qp)
2967 return NULL;
2968 for (i = 0; i < n; ++i)
2969 if (!subs[i])
2970 goto error;
2971
2972 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2973 goto error);
2974
2975 for (i = 0; i < n; ++i)
2976 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2977 goto error);
2978
2979 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2980 for (i = 0; i < n; ++i)
2981 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2982
2983 first += pos(qp->dim, type);
2984
2985 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2986 if (!ups)
2987 goto error;
2988 for (i = 0; i < n; ++i)
2989 ups[i] = subs[i]->upoly;
2990
2991 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2992
2993 free(ups);
2994
2995 if (!qp->upoly)
2996 goto error;
2997
2998 return qp;
2999 error:
3000 isl_qpolynomial_free(qp);
3001 return NULL;
3002 }
3003
3004 /* Extend "bset" with extra set dimensions for each integer division
3005 * in "qp" and then call "fn" with the extended bset and the polynomial
3006 * that results from replacing each of the integer divisions by the
3007 * corresponding extra set dimension.
3008 */
3009 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3010 __isl_keep isl_basic_set *bset,
3011 int (*fn)(__isl_take isl_basic_set *bset,
3012 __isl_take isl_qpolynomial *poly, void *user), void *user)
3013 {
3014 isl_dim *dim;
3015 isl_mat *div;
3016 isl_qpolynomial *poly;
3017
3018 if (!qp || !bset)
3019 goto error;
3020 if (qp->div->n_row == 0)
3021 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3022 user);
3023
3024 div = isl_mat_copy(qp->div);
3025 dim = isl_dim_copy(qp->dim);
3026 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3027 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3028 bset = isl_basic_set_copy(bset);
3029 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3030 bset = add_div_constraints(bset, div);
3031
3032 return fn(bset, poly, user);
3033 error:
3034 return -1;
3035 }
3036
3037 /* Return total degree in variables first (inclusive) up to last (exclusive).
3038 */
3039 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3040 {
3041 int deg = -1;
3042 int i;
3043 struct isl_upoly_rec *rec;
3044
3045 if (!up)
3046 return -2;
3047 if (isl_upoly_is_zero(up))
3048 return -1;
3049 if (isl_upoly_is_cst(up) || up->var < first)
3050 return 0;
3051
3052 rec = isl_upoly_as_rec(up);
3053 if (!rec)
3054 return -2;
3055
3056 for (i = 0; i < rec->n; ++i) {
3057 int d;
3058
3059 if (isl_upoly_is_zero(rec->p[i]))
3060 continue;
3061 d = isl_upoly_degree(rec->p[i], first, last);
3062 if (up->var < last)
3063 d += i;
3064 if (d > deg)
3065 deg = d;
3066 }
3067
3068 return deg;
3069 }
3070
3071 /* Return total degree in set variables.
3072 */
3073 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3074 {
3075 unsigned ovar;
3076 unsigned nvar;
3077
3078 if (!poly)
3079 return -2;
3080
3081 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3082 nvar = isl_dim_size(poly->dim, isl_dim_set);
3083 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3084 }
3085
3086 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3087 unsigned pos, int deg)
3088 {
3089 int i;
3090 struct isl_upoly_rec *rec;
3091
3092 if (!up)
3093 return NULL;
3094
3095 if (isl_upoly_is_cst(up) || up->var < pos) {
3096 if (deg == 0)
3097 return isl_upoly_copy(up);
3098 else
3099 return isl_upoly_zero(up->ctx);
3100 }
3101
3102 rec = isl_upoly_as_rec(up);
3103 if (!rec)
3104 return NULL;
3105
3106 if (up->var == pos) {
3107 if (deg < rec->n)
3108 return isl_upoly_copy(rec->p[deg]);
3109 else
3110 return isl_upoly_zero(up->ctx);
3111 }
3112
3113 up = isl_upoly_copy(up);
3114 up = isl_upoly_cow(up);
3115 rec = isl_upoly_as_rec(up);
3116 if (!rec)
3117 goto error;
3118
3119 for (i = 0; i < rec->n; ++i) {
3120 struct isl_upoly *t;
3121 t = isl_upoly_coeff(rec->p[i], pos, deg);
3122 if (!t)
3123 goto error;
3124 isl_upoly_free(rec->p[i]);
3125 rec->p[i] = t;
3126 }
3127
3128 return up;
3129 error:
3130 isl_upoly_free(up);
3131 return NULL;
3132 }
3133
3134 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3135 */
3136 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3137 __isl_keep isl_qpolynomial *qp,
3138 enum isl_dim_type type, unsigned t_pos, int deg)
3139 {
3140 unsigned g_pos;
3141 struct isl_upoly *up;
3142 isl_qpolynomial *c;
3143
3144 if (!qp)
3145 return NULL;
3146
3147 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3148 return NULL);
3149
3150 g_pos = pos(qp->dim, type) + t_pos;
3151 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3152
3153 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3154 if (!c)
3155 return NULL;
3156 isl_mat_free(c->div);
3157 c->div = isl_mat_copy(qp->div);
3158 if (!c->div)
3159 goto error;
3160 return c;
3161 error:
3162 isl_qpolynomial_free(c);
3163 return NULL;
3164 }
3165
3166 /* Homogenize the polynomial in the variables first (inclusive) up to
3167 * last (exclusive) by inserting powers of variable first.
3168 * Variable first is assumed not to appear in the input.
3169 */
3170 __isl_give struct isl_upoly *isl_upoly_homogenize(
3171 __isl_take struct isl_upoly *up, int deg, int target,
3172 int first, int last)
3173 {
3174 int i;
3175 struct isl_upoly_rec *rec;
3176
3177 if (!up)
3178 return NULL;
3179 if (isl_upoly_is_zero(up))
3180 return up;
3181 if (deg == target)
3182 return up;
3183 if (isl_upoly_is_cst(up) || up->var < first) {
3184 struct isl_upoly *hom;
3185
3186 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3187 if (!hom)
3188 goto error;
3189 rec = isl_upoly_as_rec(hom);
3190 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3191
3192 return hom;
3193 }
3194
3195 up = isl_upoly_cow(up);
3196 rec = isl_upoly_as_rec(up);
3197 if (!rec)
3198 goto error;
3199
3200 for (i = 0; i < rec->n; ++i) {
3201 if (isl_upoly_is_zero(rec->p[i]))
3202 continue;
3203 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3204 up->var < last ? deg + i : i, target,
3205 first, last);
3206 if (!rec->p[i])
3207 goto error;
3208 }
3209
3210 return up;
3211 error:
3212 isl_upoly_free(up);
3213 return NULL;
3214 }
3215
3216 /* Homogenize the polynomial in the set variables by introducing
3217 * powers of an extra set variable at position 0.
3218 */
3219 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3220 __isl_take isl_qpolynomial *poly)
3221 {
3222 unsigned ovar;
3223 unsigned nvar;
3224 int deg = isl_qpolynomial_degree(poly);
3225
3226 if (deg < -1)
3227 goto error;
3228
3229 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3230 poly = isl_qpolynomial_cow(poly);
3231 if (!poly)
3232 goto error;
3233
3234 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3235 nvar = isl_dim_size(poly->dim, isl_dim_set);
3236 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3237 ovar, ovar + nvar);
3238 if (!poly->upoly)
3239 goto error;
3240
3241 return poly;
3242 error:
3243 isl_qpolynomial_free(poly);
3244 return NULL;
3245 }
3246
3247 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3248 __isl_take isl_mat *div)
3249 {
3250 isl_term *term;
3251 int n;
3252
3253 if (!dim || !div)
3254 goto error;
3255
3256 n = isl_dim_total(dim) + div->n_row;
3257
3258 term = isl_calloc(dim->ctx, struct isl_term,
3259 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3260 if (!term)
3261 goto error;
3262
3263 term->ref = 1;
3264 term->dim = dim;
3265 term->div = div;
3266 isl_int_init(term->n);
3267 isl_int_init(term->d);
3268
3269 return term;
3270 error:
3271 isl_dim_free(dim);
3272 isl_mat_free(div);
3273 return NULL;
3274 }
3275
3276 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3277 {
3278 if (!term)
3279 return NULL;
3280
3281 term->ref++;
3282 return term;
3283 }
3284
3285 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3286 {
3287 int i;
3288 isl_term *dup;
3289 unsigned total;
3290
3291 if (term)
3292 return NULL;
3293
3294 total = isl_dim_total(term->dim) + term->div->n_row;
3295
3296 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3297 if (!dup)
3298 return NULL;
3299
3300 isl_int_set(dup->n, term->n);
3301 isl_int_set(dup->d, term->d);
3302
3303 for (i = 0; i < total; ++i)
3304 dup->pow[i] = term->pow[i];
3305
3306 return dup;
3307 }
3308
3309 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3310 {
3311 if (!term)
3312 return NULL;
3313
3314 if (term->ref == 1)
3315 return term;
3316 term->ref--;
3317 return isl_term_dup(term);
3318 }
3319
3320 void isl_term_free(__isl_take isl_term *term)
3321 {
3322 if (!term)
3323 return;
3324
3325 if (--term->ref > 0)
3326 return;
3327
3328 isl_dim_free(term->dim);
3329 isl_mat_free(term->div);
3330 isl_int_clear(term->n);
3331 isl_int_clear(term->d);
3332 free(term);
3333 }
3334
3335 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3336 {
3337 if (!term)
3338 return 0;
3339
3340 switch (type) {
3341 case isl_dim_param:
3342 case isl_dim_in:
3343 case isl_dim_out: return isl_dim_size(term->dim, type);
3344 case isl_dim_div: return term->div->n_row;
3345 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3346 default: return 0;
3347 }
3348 }
3349
3350 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3351 {
3352 return term ? term->dim->ctx : NULL;
3353 }
3354
3355 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3356 {
3357 if (!term)
3358 return;
3359 isl_int_set(*n, term->n);
3360 }
3361
3362 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3363 {
3364 if (!term)
3365 return;
3366 isl_int_set(*d, term->d);
3367 }
3368
3369 int isl_term_get_exp(__isl_keep isl_term *term,
3370 enum isl_dim_type type, unsigned pos)
3371 {
3372 if (!term)
3373 return -1;
3374
3375 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3376
3377 if (type >= isl_dim_set)
3378 pos += isl_dim_size(term->dim, isl_dim_param);
3379 if (type >= isl_dim_div)
3380 pos += isl_dim_size(term->dim, isl_dim_set);
3381
3382 return term->pow[pos];
3383 }
3384
3385 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3386 {
3387 isl_basic_map *bmap;
3388 unsigned total;
3389 int k;
3390
3391 if (!term)
3392 return NULL;
3393
3394 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3395 return NULL);
3396
3397 total = term->div->n_col - term->div->n_row - 2;
3398 /* No nested divs for now */
3399 isl_assert(term->dim->ctx,
3400 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3401 term->div->n_row) == -1,
3402 return NULL);
3403
3404 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3405 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3406 goto error;
3407
3408 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3409
3410 return isl_basic_map_div(bmap, k);
3411 error:
3412 isl_basic_map_free(bmap);
3413 return NULL;
3414 }
3415
3416 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3417 int (*fn)(__isl_take isl_term *term, void *user),
3418 __isl_take isl_term *term, void *user)
3419 {
3420 int i;
3421 struct isl_upoly_rec *rec;
3422
3423 if (!up || !term)
3424 goto error;
3425
3426 if (isl_upoly_is_zero(up))
3427 return term;
3428
3429 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3430 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3431 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3432
3433 if (isl_upoly_is_cst(up)) {
3434 struct isl_upoly_cst *cst;
3435 cst = isl_upoly_as_cst(up);
3436 if (!cst)
3437 goto error;
3438 term = isl_term_cow(term);
3439 if (!term)
3440 goto error;
3441 isl_int_set(term->n, cst->n);
3442 isl_int_set(term->d, cst->d);
3443 if (fn(isl_term_copy(term), user) < 0)
3444 goto error;
3445 return term;
3446 }
3447
3448 rec = isl_upoly_as_rec(up);
3449 if (!rec)
3450 goto error;
3451
3452 for (i = 0; i < rec->n; ++i) {
3453 term = isl_term_cow(term);
3454 if (!term)
3455 goto error;
3456 term->pow[up->var] = i;
3457 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3458 if (!term)
3459 goto error;
3460 }
3461 term->pow[up->var] = 0;
3462
3463 return term;
3464 error:
3465 isl_term_free(term);
3466 return NULL;
3467 }
3468
3469 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3470 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3471 {
3472 isl_term *term;
3473
3474 if (!qp)
3475 return -1;
3476
3477 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3478 if (!term)
3479 return -1;
3480
3481 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3482
3483 isl_term_free(term);
3484
3485 return term ? 0 : -1;
3486 }
3487
3488 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3489 {
3490 struct isl_upoly *up;
3491 isl_qpolynomial *qp;
3492 int i, n;
3493
3494 if (!term)
3495 return NULL;
3496
3497 n = isl_dim_total(term->dim) + term->div->n_row;
3498
3499 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3500 for (i = 0; i < n; ++i) {
3501 if (!term->pow[i])
3502 continue;
3503 up = isl_upoly_mul(up,
3504 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3505 }
3506
3507 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3508 if (!qp)
3509 goto error;
3510 isl_mat_free(qp->div);
3511 qp->div = isl_mat_copy(term->div);
3512 if (!qp->div)
3513 goto error;
3514
3515 isl_term_free(term);
3516 return qp;
3517 error:
3518 isl_qpolynomial_free(qp);
3519 isl_term_free(term);
3520 return NULL;
3521 }
3522
3523 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3524 __isl_take isl_dim *dim)
3525 {
3526 int i;
3527 int extra;
3528 unsigned total;
3529
3530 if (!qp || !dim)
3531 goto error;
3532
3533 if (isl_dim_equal(qp->dim, dim)) {
3534 isl_dim_free(dim);
3535 return qp;
3536 }
3537
3538 qp = isl_qpolynomial_cow(qp);
3539 if (!qp)
3540 goto error;
3541
3542 extra = isl_dim_size(dim, isl_dim_set) -
3543 isl_dim_size(qp->dim, isl_dim_set);
3544 total = isl_dim_total(qp->dim);
3545 if (qp->div->n_row) {
3546 int *exp;
3547
3548 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3549 if (!exp)
3550 goto error;
3551 for (i = 0; i < qp->div->n_row; ++i)
3552 exp[i] = extra + i;
3553 qp->upoly = expand(qp->upoly, exp, total);
3554 free(exp);
3555 if (!qp->upoly)
3556 goto error;
3557 }
3558 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3559 if (!qp->div)
3560 goto error;
3561 for (i = 0; i < qp->div->n_row; ++i)
3562 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3563
3564 isl_dim_free(qp->dim);
3565 qp->dim = dim;
3566
3567 return qp;
3568 error:
3569 isl_dim_free(dim);
3570 isl_qpolynomial_free(qp);
3571 return NULL;
3572 }
3573
3574 /* For each parameter or variable that does not appear in qp,
3575 * first eliminate the variable from all constraints and then set it to zero.
3576 */
3577 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3578 __isl_keep isl_qpolynomial *qp)
3579 {
3580 int *active = NULL;
3581 int i;
3582 int d;
3583 unsigned nparam;
3584 unsigned nvar;
3585
3586 if (!set || !qp)
3587 goto error;
3588
3589 d = isl_dim_total(set->dim);
3590 active = isl_calloc_array(set->ctx, int, d);
3591 if (set_active(qp, active) < 0)
3592 goto error;
3593
3594 for (i = 0; i < d; ++i)
3595 if (!active[i])
3596 break;
3597
3598 if (i == d) {
3599 free(active);
3600 return set;
3601 }
3602
3603 nparam = isl_dim_size(set->dim, isl_dim_param);
3604 nvar = isl_dim_size(set->dim, isl_dim_set);
3605 for (i = 0; i < nparam; ++i) {
3606 if (active[i])
3607 continue;
3608 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3609 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3610 }
3611 for (i = 0; i < nvar; ++i) {
3612 if (active[nparam + i])
3613 continue;
3614 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3615 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3616 }
3617
3618 free(active);
3619
3620 return set;
3621 error:
3622 free(active);
3623 isl_set_free(set);
3624 return NULL;
3625 }
3626
3627 struct isl_opt_data {
3628 isl_qpolynomial *qp;
3629 int first;
3630 isl_qpolynomial *opt;
3631 int max;
3632 };
3633
3634 static int opt_fn(__isl_take isl_point *pnt, void *user)
3635 {
3636 struct isl_opt_data *data = (struct isl_opt_data *)user;
3637 isl_qpolynomial *val;
3638
3639 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3640 if (data->first) {
3641 data->first = 0;
3642 data->opt = val;
3643 } else if (data->max) {
3644 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3645 } else {
3646 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3647 }
3648
3649 return 0;
3650 }
3651
3652 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3653 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3654 {
3655 struct isl_opt_data data = { NULL, 1, NULL, max };
3656
3657 if (!set || !qp)
3658 goto error;
3659
3660 if (isl_upoly_is_cst(qp->upoly)) {
3661 isl_set_free(set);
3662 return qp;
3663 }
3664
3665 set = fix_inactive(set, qp);
3666
3667 data.qp = qp;
3668 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3669 goto error;
3670
3671 if (data.first)
3672 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3673
3674 isl_set_free(set);
3675 isl_qpolynomial_free(qp);
3676 return data.opt;
3677 error:
3678 isl_set_free(set);
3679 isl_qpolynomial_free(qp);
3680 isl_qpolynomial_free(data.opt);
3681 return NULL;
3682 }
3683
3684 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3685 __isl_take isl_morph *morph)
3686 {
3687 int i;
3688 int n_sub;
3689 isl_ctx *ctx;
3690 struct isl_upoly *up;
3691 unsigned n_div;
3692 struct isl_upoly **subs;
3693 isl_mat *mat;
3694
3695 qp = isl_qpolynomial_cow(qp);
3696 if (!qp || !morph)
3697 goto error;
3698
3699 ctx = qp->dim->ctx;
3700 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3701
3702 n_sub = morph->inv->n_row - 1;
3703 if (morph->inv->n_row != morph->inv->n_col)
3704 n_sub += qp->div->n_row;
3705 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3706 if (!subs)
3707 goto error;
3708
3709 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3710 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3711 morph->inv->row[0][0], morph->inv->n_col);
3712 if (morph->inv->n_row != morph->inv->n_col)
3713 for (i = 0; i < qp->div->n_row; ++i)
3714 subs[morph->inv->n_row - 1 + i] =
3715 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3716
3717 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3718
3719 for (i = 0; i < n_sub; ++i)
3720 isl_upoly_free(subs[i]);
3721 free(subs);
3722
3723 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3724 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3725 qp->div = isl_mat_product(qp->div, mat);
3726 isl_dim_free(qp->dim);
3727 qp->dim = isl_dim_copy(morph->ran->dim);
3728
3729 if (!qp->upoly || !qp->div || !qp->dim)
3730 goto error;
3731
3732 isl_morph_free(morph);
3733
3734 return qp;
3735 error:
3736 isl_qpolynomial_free(qp);
3737 isl_morph_free(morph);
3738 return NULL;
3739 }
3740
3741 static int neg_entry(void **entry, void *user)
3742 {
3743 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3744
3745 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3746
3747 return *pwqp ? 0 : -1;
3748 }
3749
3750 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3751 __isl_take isl_union_pw_qpolynomial *upwqp)
3752 {
3753 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3754 if (!upwqp)
3755 return NULL;
3756
3757 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3758 &neg_entry, NULL) < 0)
3759 goto error;
3760
3761 return upwqp;
3762 error:
3763 isl_union_pw_qpolynomial_free(upwqp);
3764 return NULL;
3765 }
3766
3767 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3768 __isl_take isl_union_pw_qpolynomial *upwqp1,
3769 __isl_take isl_union_pw_qpolynomial *upwqp2)
3770 {
3771 return isl_union_pw_qpolynomial_add(upwqp1,
3772 isl_union_pw_qpolynomial_neg(upwqp2));
3773 }
3774
3775 static int mul_entry(void **entry, void *user)
3776 {
3777 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3778 uint32_t hash;
3779 struct isl_hash_table_entry *entry2;
3780 isl_pw_qpolynomial *pwpq = *entry;
3781 int empty;
3782
3783 hash = isl_dim_get_hash(pwpq->dim);
3784 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3785 hash, &has_dim, pwpq->dim, 0);
3786 if (!entry2)
3787 return 0;
3788
3789 pwpq = isl_pw_qpolynomial_copy(pwpq);
3790 pwpq = isl_pw_qpolynomial_mul(pwpq,
3791 isl_pw_qpolynomial_copy(entry2->data));
3792
3793 empty = isl_pw_qpolynomial_is_zero(pwpq);
3794 if (empty < 0) {
3795 isl_pw_qpolynomial_free(pwpq);
3796 return -1;
3797 }
3798 if (empty) {
3799 isl_pw_qpolynomial_free(pwpq);
3800 return 0;
3801 }
3802
3803 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3804
3805 return 0;
3806 }
3807
3808 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3809 __isl_take isl_union_pw_qpolynomial *upwqp1,
3810 __isl_take isl_union_pw_qpolynomial *upwqp2)
3811 {
3812 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3813 }
3814
3815 /* Reorder the columns of the given div definitions according to the
3816 * given reordering.
3817 */
3818 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3819 __isl_take isl_reordering *r)
3820 {
3821 int i, j;
3822 isl_mat *mat;
3823 int extra;
3824
3825 if (!div || !r)
3826 goto error;
3827
3828 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3829 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3830 if (!mat)
3831 goto error;
3832
3833 for (i = 0; i < div->n_row; ++i) {
3834 isl_seq_cpy(mat->row[i], div->row[i], 2);
3835 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3836 for (j = 0; j < r->len; ++j)
3837 isl_int_set(mat->row[i][2 + r->pos[j]],
3838 div->row[i][2 + j]);
3839 }
3840
3841 isl_reordering_free(r);
3842 isl_mat_free(div);
3843 return mat;
3844 error:
3845 isl_reordering_free(r);
3846 isl_mat_free(div);
3847 return NULL;
3848 }
3849
3850 /* Reorder the dimension of "qp" according to the given reordering.
3851 */
3852 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3853 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3854 {
3855 qp = isl_qpolynomial_cow(qp);
3856 if (!qp)
3857 goto error;
3858
3859 r = isl_reordering_extend(r, qp->div->n_row);
3860 if (!r)
3861 goto error;
3862
3863 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3864 if (!qp->div)
3865 goto error;
3866
3867 qp->upoly = reorder(qp->upoly, r->pos);
3868 if (!qp->upoly)
3869 goto error;
3870
3871 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3872
3873 isl_reordering_free(r);
3874 return qp;
3875 error:
3876 isl_qpolynomial_free(qp);
3877 isl_reordering_free(r);
3878 return NULL;
3879 }
3880
3881 struct isl_split_periods_data {
3882 int max_periods;
3883 isl_pw_qpolynomial *res;
3884 };
3885
3886 /* Create a slice where the integer division "div" has the fixed value "v".
3887 * In particular, if "div" refers to floor(f/m), then create a slice
3888 *
3889 * m v <= f <= m v + (m - 1)
3890 *
3891 * or
3892 *
3893 * f - m v >= 0
3894 * -f + m v + (m - 1) >= 0
3895 */
3896 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3897 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3898 {
3899 int total;
3900 isl_basic_set *bset = NULL;
3901 int k;
3902
3903 if (!dim || !qp)
3904 goto error;
3905
3906 total = isl_dim_total(dim);
3907 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3908
3909 k = isl_basic_set_alloc_inequality(bset);
3910 if (k < 0)
3911 goto error;
3912 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3913 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3914
3915 k = isl_basic_set_alloc_inequality(bset);
3916 if (k < 0)
3917 goto error;
3918 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3919 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3920 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3921 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3922
3923 isl_dim_free(dim);
3924 return isl_set_from_basic_set(bset);
3925 error:
3926 isl_basic_set_free(bset);
3927 isl_dim_free(dim);
3928 return NULL;
3929 }
3930
3931 static int split_periods(__isl_take isl_set *set,
3932 __isl_take isl_qpolynomial *qp, void *user);
3933
3934 /* Create a slice of the domain "set" such that integer division "div"
3935 * has the fixed value "v" and add the results to data->res,
3936 * replacing the integer division by "v" in "qp".
3937 */
3938 static int set_div(__isl_take isl_set *set,
3939 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3940 struct isl_split_periods_data *data)
3941 {
3942 int i;
3943 int total;
3944 isl_set *slice;
3945 struct isl_upoly *cst;
3946
3947 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3948 set = isl_set_intersect(set, slice);
3949
3950 if (!qp)
3951 goto error;
3952
3953 total = isl_dim_total(qp->dim);
3954
3955 for (i = div + 1; i < qp->div->n_row; ++i) {
3956 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3957 continue;
3958 isl_int_addmul(qp->div->row[i][1],
3959 qp->div->row[i][2 + total + div], v);
3960 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3961 }
3962
3963 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3964 qp = substitute_div(qp, div, cst);
3965
3966 return split_periods(set, qp, data);
3967 error:
3968 isl_set_free(set);
3969 isl_qpolynomial_free(qp);
3970 return -1;
3971 }
3972
3973 /* Split the domain "set" such that integer division "div"
3974 * has a fixed value (ranging from "min" to "max") on each slice
3975 * and add the results to data->res.
3976 */
3977 static int split_div(__isl_take isl_set *set,
3978 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3979 struct isl_split_periods_data *data)
3980 {
3981 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3982 isl_set *set_i = isl_set_copy(set);
3983 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3984
3985 if (set_div(set_i, qp_i, div, min, data) < 0)
3986 goto error;
3987 }
3988 isl_set_free(set);
3989 isl_qpolynomial_free(qp);
3990 return 0;
3991 error:
3992 isl_set_free(set);
3993 isl_qpolynomial_free(qp);
3994 return -1;
3995 }
3996
3997 /* If "qp" refers to any integer division
3998 * that can only attain "max_periods" distinct values on "set"
3999 * then split the domain along those distinct values.
4000 * Add the results (or the original if no splitting occurs)
4001 * to data->res.
4002 */
4003 static int split_periods(__isl_take isl_set *set,
4004 __isl_take isl_qpolynomial *qp, void *user)
4005 {
4006 int i;
4007 isl_pw_qpolynomial *pwqp;
4008 struct isl_split_periods_data *data;
4009 isl_int min, max;
4010 int total;
4011 int r = 0;
4012
4013 data = (struct isl_split_periods_data *)user;
4014
4015 if (!set || !qp)
4016 goto error;
4017
4018 if (qp->div->n_row == 0) {
4019 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4020 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4021 return 0;
4022 }
4023
4024 isl_int_init(min);
4025 isl_int_init(max);
4026 total = isl_dim_total(qp->dim);
4027 for (i = 0; i < qp->div->n_row; ++i) {
4028 enum isl_lp_result lp_res;
4029
4030 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4031 qp->div->n_row) != -1)
4032 continue;
4033
4034 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4035 set->ctx->one, &min, NULL, NULL);
4036 if (lp_res == isl_lp_error)
4037 goto error2;
4038 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4039 continue;
4040 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4041
4042 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4043 set->ctx->one, &max, NULL, NULL);
4044 if (lp_res == isl_lp_error)
4045 goto error2;
4046 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4047 continue;
4048 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4049
4050 isl_int_sub(max, max, min);
4051 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4052 isl_int_add(max, max, min);
4053 break;
4054 }
4055 }
4056
4057 if (i < qp->div->n_row) {
4058 r = split_div(set, qp, i, min, max, data);
4059 } else {
4060 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4061 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4062 }
4063
4064 isl_int_clear(max);
4065 isl_int_clear(min);
4066
4067 return r;
4068 error2:
4069 isl_int_clear(max);
4070 isl_int_clear(min);
4071 error:
4072 isl_set_free(set);
4073 isl_qpolynomial_free(qp);
4074 return -1;
4075 }
4076
4077 /* If any quasi-polynomial in pwqp refers to any integer division
4078 * that can only attain "max_periods" distinct values on its domain
4079 * then split the domain along those distinct values.
4080 */
4081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4082 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4083 {
4084 struct isl_split_periods_data data;
4085
4086 data.max_periods = max_periods;
4087 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4088
4089 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4090 goto error;
4091
4092 isl_pw_qpolynomial_free(pwqp);
4093
4094 return data.res;
4095 error:
4096 isl_pw_qpolynomial_free(data.res);
4097 isl_pw_qpolynomial_free(pwqp);
4098 return NULL;
4099 }
4100
4101 /* Construct a piecewise quasipolynomial that is constant on the given
4102 * domain. In particular, it is
4103 * 0 if cst == 0
4104 * 1 if cst == 1
4105 * infinity if cst == -1
4106 */
4107 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4108 __isl_take isl_basic_set *bset, int cst)
4109 {
4110 isl_dim *dim;
4111 isl_qpolynomial *qp;
4112
4113 if (!bset)
4114 return NULL;
4115
4116 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4117 dim = isl_basic_set_get_dim(bset);
4118 if (cst < 0)
4119 qp = isl_qpolynomial_infty(dim);
4120 else if (cst == 0)
4121 qp = isl_qpolynomial_zero(dim);
4122 else
4123 qp = isl_qpolynomial_one(dim);
4124 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4125 }
4126
4127 /* Factor bset, call fn on each of the factors and return the product.
4128 *
4129 * If no factors can be found, simply call fn on the input.
4130 * Otherwise, construct the factors based on the factorizer,
4131 * call fn on each factor and compute the product.
4132 */
4133 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4134 __isl_take isl_basic_set *bset,
4135 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4136 {
4137 int i, n;
4138 isl_dim *dim;
4139 isl_set *set;
4140 isl_factorizer *f;
4141 isl_qpolynomial *qp;
4142 isl_pw_qpolynomial *pwqp;
4143 unsigned nparam;
4144 unsigned nvar;
4145
4146 f = isl_basic_set_factorizer(bset);
4147 if (!f)
4148 goto error;
4149 if (f->n_group == 0) {
4150 isl_factorizer_free(f);
4151 return fn(bset);
4152 }
4153
4154 nparam = isl_basic_set_dim(bset, isl_dim_param);
4155 nvar = isl_basic_set_dim(bset, isl_dim_set);
4156
4157 dim = isl_basic_set_get_dim(bset);
4158 dim = isl_dim_domain(dim);
4159 set = isl_set_universe(isl_dim_copy(dim));
4160 qp = isl_qpolynomial_one(dim);
4161 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4162
4163 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4164
4165 for (i = 0, n = 0; i < f->n_group; ++i) {
4166 isl_basic_set *bset_i;
4167 isl_pw_qpolynomial *pwqp_i;
4168
4169 bset_i = isl_basic_set_copy(bset);
4170 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4171 nparam + n + f->len[i], nvar - n - f->len[i]);
4172 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4173 nparam, n);
4174 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4175 n + f->len[i], nvar - n - f->len[i]);
4176 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4177
4178 pwqp_i = fn(bset_i);
4179 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4180
4181 n += f->len[i];
4182 }
4183
4184 isl_basic_set_free(bset);
4185 isl_factorizer_free(f);
4186
4187 return pwqp;
4188 error:
4189 isl_basic_set_free(bset);
4190 return NULL;
4191 }
4192
4193 /* Factor bset, call fn on each of the factors and return the product.
4194 * The function is assumed to evaluate to zero on empty domains,
4195 * to one on zero-dimensional domains and to infinity on unbounded domains
4196 * and will not be called explicitly on zero-dimensional or unbounded domains.
4197 *
4198 * We first check for some special cases and remove all equalities.
4199 * Then we hand over control to compressed_multiplicative_call.
4200 */
4201 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4202 __isl_take isl_basic_set *bset,
4203 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4204 {
4205 int bounded;
4206 isl_morph *morph;
4207 isl_pw_qpolynomial *pwqp;
4208 unsigned orig_nvar, final_nvar;
4209
4210 if (!bset)
4211 return NULL;
4212
4213 if (isl_basic_set_plain_is_empty(bset))
4214 return constant_on_domain(bset, 0);
4215
4216 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4217
4218 if (orig_nvar == 0)
4219 return constant_on_domain(bset, 1);
4220
4221 bounded = isl_basic_set_is_bounded(bset);
4222 if (bounded < 0)
4223 goto error;
4224 if (!bounded)
4225 return constant_on_domain(bset, -1);
4226
4227 if (bset->n_eq == 0)
4228 return compressed_multiplicative_call(bset, fn);
4229
4230 morph = isl_basic_set_full_compression(bset);
4231 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4232
4233 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4234
4235 pwqp = compressed_multiplicative_call(bset, fn);
4236
4237 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4238 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4239 morph = isl_morph_inverse(morph);
4240
4241 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4242
4243 return pwqp;
4244 error:
4245 isl_basic_set_free(bset);
4246 return NULL;
4247 }
4248
4249 /* Drop all floors in "qp", turning each integer division [a/m] into
4250 * a rational division a/m. If "down" is set, then the integer division
4251 * is replaces by (a-(m-1))/m instead.
4252 */
4253 static __isl_give isl_qpolynomial *qp_drop_floors(
4254 __isl_take isl_qpolynomial *qp, int down)
4255 {
4256 int i;
4257 struct isl_upoly *s;
4258
4259 if (!qp)
4260 return NULL;
4261 if (qp->div->n_row == 0)
4262 return qp;
4263
4264 qp = isl_qpolynomial_cow(qp);
4265 if (!qp)
4266 return NULL;
4267
4268 for (i = qp->div->n_row - 1; i >= 0; --i) {
4269 if (down) {
4270 isl_int_sub(qp->div->row[i][1],
4271 qp->div->row[i][1], qp->div->row[i][0]);
4272 isl_int_add_ui(qp->div->row[i][1],
4273 qp->div->row[i][1], 1);
4274 }
4275 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4276 qp->div->row[i][0], qp->div->n_col - 1);
4277 qp = substitute_div(qp, i, s);
4278 if (!qp)
4279 return NULL;
4280 }
4281
4282 return qp;
4283 }
4284
4285 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4286 * a rational division a/m.
4287 */
4288 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4289 __isl_take isl_pw_qpolynomial *pwqp)
4290 {
4291 int i;
4292
4293 if (!pwqp)
4294 return NULL;
4295
4296 if (isl_pw_qpolynomial_is_zero(pwqp))
4297 return pwqp;
4298
4299 pwqp = isl_pw_qpolynomial_cow(pwqp);
4300 if (!pwqp)
4301 return NULL;
4302
4303 for (i = 0; i < pwqp->n; ++i) {
4304 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4305 if (!pwqp->p[i].qp)
4306 goto error;
4307 }
4308
4309 return pwqp;
4310 error:
4311 isl_pw_qpolynomial_free(pwqp);
4312 return NULL;
4313 }
4314
4315 /* Adjust all the integer divisions in "qp" such that they are at least
4316 * one over the given orthant (identified by "signs"). This ensures
4317 * that they will still be non-negative even after subtracting (m-1)/m.
4318 *
4319 * In particular, f is replaced by f' + v, changing f = [a/m]
4320 * to f' = [(a - m v)/m].
4321 * If the constant term k in a is smaller than m,
4322 * the constant term of v is set to floor(k/m) - 1.
4323 * For any other term, if the coefficient c and the variable x have
4324 * the same sign, then no changes are needed.
4325 * Otherwise, if the variable is positive (and c is negative),
4326 * then the coefficient of x in v is set to floor(c/m).
4327 * If the variable is negative (and c is positive),
4328 * then the coefficient of x in v is set to ceil(c/m).
4329 */
4330 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4331 int *signs)
4332 {
4333 int i, j;
4334 int total;
4335 isl_vec *v = NULL;
4336 struct isl_upoly *s;
4337
4338 qp = isl_qpolynomial_cow(qp);
4339 if (!qp)
4340 return NULL;
4341 qp->div = isl_mat_cow(qp->div);
4342 if (!qp->div)
4343 goto error;
4344
4345 total = isl_dim_total(qp->dim);
4346 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4347
4348 for (i = 0; i < qp->div->n_row; ++i) {
4349 isl_int *row = qp->div->row[i];
4350 v = isl_vec_clr(v);
4351 if (!v)
4352 goto error;
4353 if (isl_int_lt(row[1], row[0])) {
4354 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4355 isl_int_sub_ui(v->el[0], v->el[0], 1);
4356 isl_int_submul(row[1], row[0], v->el[0]);
4357 }
4358 for (j = 0; j < total; ++j) {
4359 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4360 continue;
4361 if (signs[j] < 0)
4362 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4363 else
4364 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4365 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4366 }
4367 for (j = 0; j < i; ++j) {
4368 if (isl_int_sgn(row[2 + total + j]) >= 0)
4369 continue;
4370 isl_int_fdiv_q(v->el[1 + total + j],
4371 row[2 + total + j], row[0]);
4372 isl_int_submul(row[2 + total + j],
4373 row[0], v->el[1 + total + j]);
4374 }
4375 for (j = i + 1; j < qp->div->n_row; ++j) {
4376 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4377 continue;
4378 isl_seq_combine(qp->div->row[j] + 1,
4379 qp->div->ctx->one, qp->div->row[j] + 1,
4380 qp->div->row[j][2 + total + i], v->el, v->size);
4381 }
4382 isl_int_set_si(v->el[1 + total + i], 1);
4383 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4384 qp->div->ctx->one, v->size);
4385 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4386 isl_upoly_free(s);
4387 if (!qp->upoly)
4388 goto error;
4389 }
4390
4391 isl_vec_free(v);
4392 return qp;
4393 error:
4394 isl_vec_free(v);
4395 isl_qpolynomial_free(qp);
4396 return NULL;
4397 }
4398
4399 struct isl_to_poly_data {
4400 int sign;
4401 isl_pw_qpolynomial *res;
4402 isl_qpolynomial *qp;
4403 };
4404
4405 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4406 * We first make all integer divisions positive and then split the
4407 * quasipolynomials into terms with sign data->sign (the direction
4408 * of the requested approximation) and terms with the opposite sign.
4409 * In the first set of terms, each integer division [a/m] is
4410 * overapproximated by a/m, while in the second it is underapproximated
4411 * by (a-(m-1))/m.
4412 */
4413 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4414 void *user)
4415 {
4416 struct isl_to_poly_data *data = user;
4417 isl_pw_qpolynomial *t;
4418 isl_qpolynomial *qp, *up, *down;
4419
4420 qp = isl_qpolynomial_copy(data->qp);
4421 qp = make_divs_pos(qp, signs);
4422
4423 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4424 up = qp_drop_floors(up, 0);
4425 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4426 down = qp_drop_floors(down, 1);
4427
4428 isl_qpolynomial_free(qp);
4429 qp = isl_qpolynomial_add(up, down);
4430
4431 t = isl_pw_qpolynomial_alloc(orthant, qp);
4432 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4433
4434 return 0;
4435 }
4436
4437 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4438 * the polynomial will be an overapproximation. If "sign" is negative,
4439 * it will be an underapproximation. If "sign" is zero, the approximation
4440 * will lie somewhere in between.
4441 *
4442 * In particular, is sign == 0, we simply drop the floors, turning
4443 * the integer divisions into rational divisions.
4444 * Otherwise, we split the domains into orthants, make all integer divisions
4445 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4446 * depending on the requested sign and the sign of the term in which
4447 * the integer division appears.
4448 */
4449 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4450 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4451 {
4452 int i;
4453 struct isl_to_poly_data data;
4454
4455 if (sign == 0)
4456 return pwqp_drop_floors(pwqp);
4457
4458 if (!pwqp)
4459 return NULL;
4460
4461 data.sign = sign;
4462 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4463
4464 for (i = 0; i < pwqp->n; ++i) {
4465 if (pwqp->p[i].qp->div->n_row == 0) {
4466 isl_pw_qpolynomial *t;
4467 t = isl_pw_qpolynomial_alloc(
4468 isl_set_copy(pwqp->p[i].set),
4469 isl_qpolynomial_copy(pwqp->p[i].qp));
4470 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4471 continue;
4472 }
4473 data.qp = pwqp->p[i].qp;
4474 if (isl_set_foreach_orthant(pwqp->p[i].set,
4475 &to_polynomial_on_orthant, &data) < 0)
4476 goto error;
4477 }
4478
4479 isl_pw_qpolynomial_free(pwqp);
4480
4481 return data.res;
4482 error:
4483 isl_pw_qpolynomial_free(pwqp);
4484 isl_pw_qpolynomial_free(data.res);
4485 return NULL;
4486 }
4487
4488 static int poly_entry(void **entry, void *user)
4489 {
4490 int *sign = user;
4491 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4492
4493 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4494
4495 return *pwqp ? 0 : -1;
4496 }
4497
4498 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4499 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4500 {
4501 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4502 if (!upwqp)
4503 return NULL;
4504
4505 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4506 &poly_entry, &sign) < 0)
4507 goto error;
4508
4509 return upwqp;
4510 error:
4511 isl_union_pw_qpolynomial_free(upwqp);
4512 return NULL;
4513 }
4514
4515 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4516 __isl_take isl_qpolynomial *qp)
4517 {
4518 int i, k;
4519 isl_dim *dim;
4520 isl_vec *aff = NULL;
4521 isl_basic_map *bmap = NULL;
4522 unsigned pos;
4523 unsigned n_div;
4524
4525 if (!qp)
4526 return NULL;
4527 if (!isl_upoly_is_affine(qp->upoly))
4528 isl_die(qp->dim->ctx, isl_error_invalid,
4529 "input quasi-polynomial not affine", goto error);
4530 aff = isl_qpolynomial_extract_affine(qp);
4531 if (!aff)
4532 goto error;
4533 dim = isl_qpolynomial_get_dim(qp);
4534 dim = isl_dim_from_domain(dim);
4535 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4536 dim = isl_dim_add(dim, isl_dim_out, 1);
4537 n_div = qp->div->n_row;
4538 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4539
4540 for (i = 0; i < n_div; ++i) {
4541 k = isl_basic_map_alloc_div(bmap);
4542 if (k < 0)
4543 goto error;
4544 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4545 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4546 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4547 goto error;
4548 }
4549 k = isl_basic_map_alloc_equality(bmap);
4550 if (k < 0)
4551 goto error;
4552 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4553 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4554 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4555
4556 isl_vec_free(aff);
4557 isl_qpolynomial_free(qp);
4558 bmap = isl_basic_map_finalize(bmap);
4559 return bmap;
4560 error:
4561 isl_vec_free(aff);
4562 isl_qpolynomial_free(qp);
4563 isl_basic_map_free(bmap);
4564 return NULL;
4565 }
Integer set library