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dataflow analysis: allow absence of "textual" order during sorting of sources
[isl.git] / isl_polynomial.c
blobf0ca4347bb936d8f6087d64a85edfb263f81747b
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_factorization.h>
13 #include <isl/lp.h>
14 #include <isl/seq.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_range.h>
22
23 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
24 {
25 switch (type) {
26 case isl_dim_param: return 0;
27 case isl_dim_in: return dim->nparam;
28 case isl_dim_out: return dim->nparam + dim->n_in;
29 default: return 0;
30 }
31 }
32
33 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
34 {
35 if (!up)
36 return -1;
37
38 return up->var < 0;
39 }
40
41 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
42 {
43 if (!up)
44 return NULL;
45
46 isl_assert(up->ctx, up->var < 0, return NULL);
47
48 return (struct isl_upoly_cst *)up;
49 }
50
51 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
52 {
53 if (!up)
54 return NULL;
55
56 isl_assert(up->ctx, up->var >= 0, return NULL);
57
58 return (struct isl_upoly_rec *)up;
59 }
60
61 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
62 __isl_keep struct isl_upoly *up2)
63 {
64 int i;
65 struct isl_upoly_rec *rec1, *rec2;
66
67 if (!up1 || !up2)
68 return -1;
69 if (up1 == up2)
70 return 1;
71 if (up1->var != up2->var)
72 return 0;
73 if (isl_upoly_is_cst(up1)) {
74 struct isl_upoly_cst *cst1, *cst2;
75 cst1 = isl_upoly_as_cst(up1);
76 cst2 = isl_upoly_as_cst(up2);
77 if (!cst1 || !cst2)
78 return -1;
79 return isl_int_eq(cst1->n, cst2->n) &&
80 isl_int_eq(cst1->d, cst2->d);
81 }
82
83 rec1 = isl_upoly_as_rec(up1);
84 rec2 = isl_upoly_as_rec(up2);
85 if (!rec1 || !rec2)
86 return -1;
87
88 if (rec1->n != rec2->n)
89 return 0;
90
91 for (i = 0; i < rec1->n; ++i) {
92 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
93 if (eq < 0 || !eq)
94 return eq;
95 }
96
97 return 1;
98 }
99
100 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
101 {
102 struct isl_upoly_cst *cst;
103
104 if (!up)
105 return -1;
106 if (!isl_upoly_is_cst(up))
107 return 0;
108
109 cst = isl_upoly_as_cst(up);
110 if (!cst)
111 return -1;
112
113 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
114 }
115
116 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
117 {
118 struct isl_upoly_cst *cst;
119
120 if (!up)
121 return 0;
122 if (!isl_upoly_is_cst(up))
123 return 0;
124
125 cst = isl_upoly_as_cst(up);
126 if (!cst)
127 return 0;
128
129 return isl_int_sgn(cst->n);
130 }
131
132 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
133 {
134 struct isl_upoly_cst *cst;
135
136 if (!up)
137 return -1;
138 if (!isl_upoly_is_cst(up))
139 return 0;
140
141 cst = isl_upoly_as_cst(up);
142 if (!cst)
143 return -1;
144
145 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
146 }
147
148 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
149 {
150 struct isl_upoly_cst *cst;
151
152 if (!up)
153 return -1;
154 if (!isl_upoly_is_cst(up))
155 return 0;
156
157 cst = isl_upoly_as_cst(up);
158 if (!cst)
159 return -1;
160
161 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
162 }
163
164 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
165 {
166 struct isl_upoly_cst *cst;
167
168 if (!up)
169 return -1;
170 if (!isl_upoly_is_cst(up))
171 return 0;
172
173 cst = isl_upoly_as_cst(up);
174 if (!cst)
175 return -1;
176
177 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
178 }
179
180 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
181 {
182 struct isl_upoly_cst *cst;
183
184 if (!up)
185 return -1;
186 if (!isl_upoly_is_cst(up))
187 return 0;
188
189 cst = isl_upoly_as_cst(up);
190 if (!cst)
191 return -1;
192
193 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
194 }
195
196 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
197 {
198 struct isl_upoly_cst *cst;
199
200 if (!up)
201 return -1;
202 if (!isl_upoly_is_cst(up))
203 return 0;
204
205 cst = isl_upoly_as_cst(up);
206 if (!cst)
207 return -1;
208
209 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
210 }
211
212 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
213 {
214 struct isl_upoly_cst *cst;
215
216 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
217 if (!cst)
218 return NULL;
219
220 cst->up.ref = 1;
221 cst->up.ctx = ctx;
222 isl_ctx_ref(ctx);
223 cst->up.var = -1;
224
225 isl_int_init(cst->n);
226 isl_int_init(cst->d);
227
228 return cst;
229 }
230
231 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
232 {
233 struct isl_upoly_cst *cst;
234
235 cst = isl_upoly_cst_alloc(ctx);
236 if (!cst)
237 return NULL;
238
239 isl_int_set_si(cst->n, 0);
240 isl_int_set_si(cst->d, 1);
241
242 return &cst->up;
243 }
244
245 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
246 {
247 struct isl_upoly_cst *cst;
248
249 cst = isl_upoly_cst_alloc(ctx);
250 if (!cst)
251 return NULL;
252
253 isl_int_set_si(cst->n, 1);
254 isl_int_set_si(cst->d, 1);
255
256 return &cst->up;
257 }
258
259 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
260 {
261 struct isl_upoly_cst *cst;
262
263 cst = isl_upoly_cst_alloc(ctx);
264 if (!cst)
265 return NULL;
266
267 isl_int_set_si(cst->n, 1);
268 isl_int_set_si(cst->d, 0);
269
270 return &cst->up;
271 }
272
273 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
274 {
275 struct isl_upoly_cst *cst;
276
277 cst = isl_upoly_cst_alloc(ctx);
278 if (!cst)
279 return NULL;
280
281 isl_int_set_si(cst->n, -1);
282 isl_int_set_si(cst->d, 0);
283
284 return &cst->up;
285 }
286
287 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
288 {
289 struct isl_upoly_cst *cst;
290
291 cst = isl_upoly_cst_alloc(ctx);
292 if (!cst)
293 return NULL;
294
295 isl_int_set_si(cst->n, 0);
296 isl_int_set_si(cst->d, 0);
297
298 return &cst->up;
299 }
300
301 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
302 isl_int n, isl_int d)
303 {
304 struct isl_upoly_cst *cst;
305
306 cst = isl_upoly_cst_alloc(ctx);
307 if (!cst)
308 return NULL;
309
310 isl_int_set(cst->n, n);
311 isl_int_set(cst->d, d);
312
313 return &cst->up;
314 }
315
316 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
317 int var, int size)
318 {
319 struct isl_upoly_rec *rec;
320
321 isl_assert(ctx, var >= 0, return NULL);
322 isl_assert(ctx, size >= 0, return NULL);
323 rec = isl_calloc(ctx, struct isl_upoly_rec,
324 sizeof(struct isl_upoly_rec) +
325 (size - 1) * sizeof(struct isl_upoly *));
326 if (!rec)
327 return NULL;
328
329 rec->up.ref = 1;
330 rec->up.ctx = ctx;
331 isl_ctx_ref(ctx);
332 rec->up.var = var;
333
334 rec->n = 0;
335 rec->size = size;
336
337 return rec;
338 }
339
340 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
342 {
343 qp = isl_qpolynomial_cow(qp);
344 if (!qp || !dim)
345 goto error;
346
347 isl_dim_free(qp->dim);
348 qp->dim = dim;
349
350 return qp;
351 error:
352 isl_qpolynomial_free(qp);
353 isl_dim_free(dim);
354 return NULL;
355 }
356
357 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
358 {
359 return qp ? qp->dim->ctx : NULL;
360 }
361
362 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? isl_dim_copy(qp->dim) : NULL;
365 }
366
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
368 enum isl_dim_type type)
369 {
370 return qp ? isl_dim_size(qp->dim, type) : 0;
371 }
372
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
374 {
375 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
376 }
377
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? isl_upoly_is_one(qp->upoly) : -1;
381 }
382
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
384 {
385 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
386 }
387
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
389 {
390 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
391 }
392
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
394 {
395 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
396 }
397
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
399 {
400 return qp ? isl_upoly_sgn(qp->upoly) : 0;
401 }
402
403 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
404 {
405 isl_int_clear(cst->n);
406 isl_int_clear(cst->d);
407 }
408
409 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
410 {
411 int i;
412
413 for (i = 0; i < rec->n; ++i)
414 isl_upoly_free(rec->p[i]);
415 }
416
417 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
418 {
419 if (!up)
420 return NULL;
421
422 up->ref++;
423 return up;
424 }
425
426 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
427 {
428 struct isl_upoly_cst *cst;
429 struct isl_upoly_cst *dup;
430
431 cst = isl_upoly_as_cst(up);
432 if (!cst)
433 return NULL;
434
435 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
436 if (!dup)
437 return NULL;
438 isl_int_set(dup->n, cst->n);
439 isl_int_set(dup->d, cst->d);
440
441 return &dup->up;
442 }
443
444 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
445 {
446 int i;
447 struct isl_upoly_rec *rec;
448 struct isl_upoly_rec *dup;
449
450 rec = isl_upoly_as_rec(up);
451 if (!rec)
452 return NULL;
453
454 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
455 if (!dup)
456 return NULL;
457
458 for (i = 0; i < rec->n; ++i) {
459 dup->p[i] = isl_upoly_copy(rec->p[i]);
460 if (!dup->p[i])
461 goto error;
462 dup->n++;
463 }
464
465 return &dup->up;
466 error:
467 isl_upoly_free(&dup->up);
468 return NULL;
469 }
470
471 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
472 {
473 struct isl_upoly *dup;
474
475 if (!up)
476 return NULL;
477
478 if (isl_upoly_is_cst(up))
479 return isl_upoly_dup_cst(up);
480 else
481 return isl_upoly_dup_rec(up);
482 }
483
484 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
485 {
486 if (!up)
487 return NULL;
488
489 if (up->ref == 1)
490 return up;
491 up->ref--;
492 return isl_upoly_dup(up);
493 }
494
495 void isl_upoly_free(__isl_take struct isl_upoly *up)
496 {
497 if (!up)
498 return;
499
500 if (--up->ref > 0)
501 return;
502
503 if (up->var < 0)
504 upoly_free_cst((struct isl_upoly_cst *)up);
505 else
506 upoly_free_rec((struct isl_upoly_rec *)up);
507
508 isl_ctx_deref(up->ctx);
509 free(up);
510 }
511
512 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
513 {
514 isl_int gcd;
515
516 isl_int_init(gcd);
517 isl_int_gcd(gcd, cst->n, cst->d);
518 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
519 isl_int_divexact(cst->n, cst->n, gcd);
520 isl_int_divexact(cst->d, cst->d, gcd);
521 }
522 isl_int_clear(gcd);
523 }
524
525 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
526 __isl_take struct isl_upoly *up2)
527 {
528 struct isl_upoly_cst *cst1;
529 struct isl_upoly_cst *cst2;
530
531 up1 = isl_upoly_cow(up1);
532 if (!up1 || !up2)
533 goto error;
534
535 cst1 = isl_upoly_as_cst(up1);
536 cst2 = isl_upoly_as_cst(up2);
537
538 if (isl_int_eq(cst1->d, cst2->d))
539 isl_int_add(cst1->n, cst1->n, cst2->n);
540 else {
541 isl_int_mul(cst1->n, cst1->n, cst2->d);
542 isl_int_addmul(cst1->n, cst2->n, cst1->d);
543 isl_int_mul(cst1->d, cst1->d, cst2->d);
544 }
545
546 isl_upoly_cst_reduce(cst1);
547
548 isl_upoly_free(up2);
549 return up1;
550 error:
551 isl_upoly_free(up1);
552 isl_upoly_free(up2);
553 return NULL;
554 }
555
556 static __isl_give struct isl_upoly *replace_by_zero(
557 __isl_take struct isl_upoly *up)
558 {
559 struct isl_ctx *ctx;
560
561 if (!up)
562 return NULL;
563 ctx = up->ctx;
564 isl_upoly_free(up);
565 return isl_upoly_zero(ctx);
566 }
567
568 static __isl_give struct isl_upoly *replace_by_constant_term(
569 __isl_take struct isl_upoly *up)
570 {
571 struct isl_upoly_rec *rec;
572 struct isl_upoly *cst;
573
574 if (!up)
575 return NULL;
576
577 rec = isl_upoly_as_rec(up);
578 if (!rec)
579 goto error;
580 cst = isl_upoly_copy(rec->p[0]);
581 isl_upoly_free(up);
582 return cst;
583 error:
584 isl_upoly_free(up);
585 return NULL;
586 }
587
588 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
589 __isl_take struct isl_upoly *up2)
590 {
591 int i;
592 struct isl_upoly_rec *rec1, *rec2;
593
594 if (!up1 || !up2)
595 goto error;
596
597 if (isl_upoly_is_nan(up1)) {
598 isl_upoly_free(up2);
599 return up1;
600 }
601
602 if (isl_upoly_is_nan(up2)) {
603 isl_upoly_free(up1);
604 return up2;
605 }
606
607 if (isl_upoly_is_zero(up1)) {
608 isl_upoly_free(up1);
609 return up2;
610 }
611
612 if (isl_upoly_is_zero(up2)) {
613 isl_upoly_free(up2);
614 return up1;
615 }
616
617 if (up1->var < up2->var)
618 return isl_upoly_sum(up2, up1);
619
620 if (up2->var < up1->var) {
621 struct isl_upoly_rec *rec;
622 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
623 isl_upoly_free(up1);
624 return up2;
625 }
626 up1 = isl_upoly_cow(up1);
627 rec = isl_upoly_as_rec(up1);
628 if (!rec)
629 goto error;
630 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
631 if (rec->n == 1)
632 up1 = replace_by_constant_term(up1);
633 return up1;
634 }
635
636 if (isl_upoly_is_cst(up1))
637 return isl_upoly_sum_cst(up1, up2);
638
639 rec1 = isl_upoly_as_rec(up1);
640 rec2 = isl_upoly_as_rec(up2);
641 if (!rec1 || !rec2)
642 goto error;
643
644 if (rec1->n < rec2->n)
645 return isl_upoly_sum(up2, up1);
646
647 up1 = isl_upoly_cow(up1);
648 rec1 = isl_upoly_as_rec(up1);
649 if (!rec1)
650 goto error;
651
652 for (i = rec2->n - 1; i >= 0; --i) {
653 rec1->p[i] = isl_upoly_sum(rec1->p[i],
654 isl_upoly_copy(rec2->p[i]));
655 if (!rec1->p[i])
656 goto error;
657 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
658 isl_upoly_free(rec1->p[i]);
659 rec1->n--;
660 }
661 }
662
663 if (rec1->n == 0)
664 up1 = replace_by_zero(up1);
665 else if (rec1->n == 1)
666 up1 = replace_by_constant_term(up1);
667
668 isl_upoly_free(up2);
669
670 return up1;
671 error:
672 isl_upoly_free(up1);
673 isl_upoly_free(up2);
674 return NULL;
675 }
676
677 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
678 {
679 struct isl_upoly_cst *cst;
680
681 if (isl_upoly_is_zero(up))
682 return up;
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_neg(cst->n, cst->n);
691
692 return up;
693 }
694
695 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
696 {
697 int i;
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_neg_cst(up);
705
706 up = isl_upoly_cow(up);
707 rec = isl_upoly_as_rec(up);
708 if (!rec)
709 goto error;
710
711 for (i = 0; i < rec->n; ++i) {
712 rec->p[i] = isl_upoly_neg(rec->p[i]);
713 if (!rec->p[i])
714 goto error;
715 }
716
717 return up;
718 error:
719 isl_upoly_free(up);
720 return NULL;
721 }
722
723 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
724 __isl_take struct isl_upoly *up2)
725 {
726 struct isl_upoly_cst *cst1;
727 struct isl_upoly_cst *cst2;
728
729 up1 = isl_upoly_cow(up1);
730 if (!up1 || !up2)
731 goto error;
732
733 cst1 = isl_upoly_as_cst(up1);
734 cst2 = isl_upoly_as_cst(up2);
735
736 isl_int_mul(cst1->n, cst1->n, cst2->n);
737 isl_int_mul(cst1->d, cst1->d, cst2->d);
738
739 isl_upoly_cst_reduce(cst1);
740
741 isl_upoly_free(up2);
742 return up1;
743 error:
744 isl_upoly_free(up1);
745 isl_upoly_free(up2);
746 return NULL;
747 }
748
749 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
750 __isl_take struct isl_upoly *up2)
751 {
752 struct isl_upoly_rec *rec1;
753 struct isl_upoly_rec *rec2;
754 struct isl_upoly_rec *res;
755 int i, j;
756 int size;
757
758 rec1 = isl_upoly_as_rec(up1);
759 rec2 = isl_upoly_as_rec(up2);
760 if (!rec1 || !rec2)
761 goto error;
762 size = rec1->n + rec2->n - 1;
763 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
764 if (!res)
765 goto error;
766
767 for (i = 0; i < rec1->n; ++i) {
768 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
769 isl_upoly_copy(rec1->p[i]));
770 if (!res->p[i])
771 goto error;
772 res->n++;
773 }
774 for (; i < size; ++i) {
775 res->p[i] = isl_upoly_zero(up1->ctx);
776 if (!res->p[i])
777 goto error;
778 res->n++;
779 }
780 for (i = 0; i < rec1->n; ++i) {
781 for (j = 1; j < rec2->n; ++j) {
782 struct isl_upoly *up;
783 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
784 isl_upoly_copy(rec1->p[i]));
785 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
786 if (!res->p[i + j])
787 goto error;
788 }
789 }
790
791 isl_upoly_free(up1);
792 isl_upoly_free(up2);
793
794 return &res->up;
795 error:
796 isl_upoly_free(up1);
797 isl_upoly_free(up2);
798 isl_upoly_free(&res->up);
799 return NULL;
800 }
801
802 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
803 __isl_take struct isl_upoly *up2)
804 {
805 if (!up1 || !up2)
806 goto error;
807
808 if (isl_upoly_is_nan(up1)) {
809 isl_upoly_free(up2);
810 return up1;
811 }
812
813 if (isl_upoly_is_nan(up2)) {
814 isl_upoly_free(up1);
815 return up2;
816 }
817
818 if (isl_upoly_is_zero(up1)) {
819 isl_upoly_free(up2);
820 return up1;
821 }
822
823 if (isl_upoly_is_zero(up2)) {
824 isl_upoly_free(up1);
825 return up2;
826 }
827
828 if (isl_upoly_is_one(up1)) {
829 isl_upoly_free(up1);
830 return up2;
831 }
832
833 if (isl_upoly_is_one(up2)) {
834 isl_upoly_free(up2);
835 return up1;
836 }
837
838 if (up1->var < up2->var)
839 return isl_upoly_mul(up2, up1);
840
841 if (up2->var < up1->var) {
842 int i;
843 struct isl_upoly_rec *rec;
844 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
845 isl_ctx *ctx = up1->ctx;
846 isl_upoly_free(up1);
847 isl_upoly_free(up2);
848 return isl_upoly_nan(ctx);
849 }
850 up1 = isl_upoly_cow(up1);
851 rec = isl_upoly_as_rec(up1);
852 if (!rec)
853 goto error;
854
855 for (i = 0; i < rec->n; ++i) {
856 rec->p[i] = isl_upoly_mul(rec->p[i],
857 isl_upoly_copy(up2));
858 if (!rec->p[i])
859 goto error;
860 }
861 isl_upoly_free(up2);
862 return up1;
863 }
864
865 if (isl_upoly_is_cst(up1))
866 return isl_upoly_mul_cst(up1, up2);
867
868 return isl_upoly_mul_rec(up1, up2);
869 error:
870 isl_upoly_free(up1);
871 isl_upoly_free(up2);
872 return NULL;
873 }
874
875 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
876 unsigned power)
877 {
878 struct isl_upoly *res;
879
880 if (!up)
881 return NULL;
882 if (power == 1)
883 return up;
884
885 if (power % 2)
886 res = isl_upoly_copy(up);
887 else
888 res = isl_upoly_one(up->ctx);
889
890 while (power >>= 1) {
891 up = isl_upoly_mul(up, isl_upoly_copy(up));
892 if (power % 2)
893 res = isl_upoly_mul(res, isl_upoly_copy(up));
894 }
895
896 isl_upoly_free(up);
897 return res;
898 }
899
900 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
901 unsigned n_div, __isl_take struct isl_upoly *up)
902 {
903 struct isl_qpolynomial *qp = NULL;
904 unsigned total;
905
906 if (!dim || !up)
907 goto error;
908
909 total = isl_dim_total(dim);
910
911 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
912 if (!qp)
913 goto error;
914
915 qp->ref = 1;
916 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
917 if (!qp->div)
918 goto error;
919
920 qp->dim = dim;
921 qp->upoly = up;
922
923 return qp;
924 error:
925 isl_dim_free(dim);
926 isl_upoly_free(up);
927 isl_qpolynomial_free(qp);
928 return NULL;
929 }
930
931 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
932 {
933 if (!qp)
934 return NULL;
935
936 qp->ref++;
937 return qp;
938 }
939
940 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
941 {
942 struct isl_qpolynomial *dup;
943
944 if (!qp)
945 return NULL;
946
947 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
948 isl_upoly_copy(qp->upoly));
949 if (!dup)
950 return NULL;
951 isl_mat_free(dup->div);
952 dup->div = isl_mat_copy(qp->div);
953 if (!dup->div)
954 goto error;
955
956 return dup;
957 error:
958 isl_qpolynomial_free(dup);
959 return NULL;
960 }
961
962 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
963 {
964 if (!qp)
965 return NULL;
966
967 if (qp->ref == 1)
968 return qp;
969 qp->ref--;
970 return isl_qpolynomial_dup(qp);
971 }
972
973 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
974 {
975 if (!qp)
976 return;
977
978 if (--qp->ref > 0)
979 return;
980
981 isl_dim_free(qp->dim);
982 isl_mat_free(qp->div);
983 isl_upoly_free(qp->upoly);
984
985 free(qp);
986 }
987
988 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
989 {
990 int i;
991 struct isl_upoly *up;
992 struct isl_upoly_rec *rec;
993 struct isl_upoly_cst *cst;
994
995 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
996 if (!rec)
997 return NULL;
998 for (i = 0; i < 1 + power; ++i) {
999 rec->p[i] = isl_upoly_zero(ctx);
1000 if (!rec->p[i])
1001 goto error;
1002 rec->n++;
1003 }
1004 cst = isl_upoly_as_cst(rec->p[power]);
1005 isl_int_set_si(cst->n, 1);
1006
1007 return &rec->up;
1008 error:
1009 isl_upoly_free(&rec->up);
1010 return NULL;
1011 }
1012
1013 /* r array maps original positions to new positions.
1014 */
1015 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1016 int *r)
1017 {
1018 int i;
1019 struct isl_upoly_rec *rec;
1020 struct isl_upoly *base;
1021 struct isl_upoly *res;
1022
1023 if (isl_upoly_is_cst(up))
1024 return up;
1025
1026 rec = isl_upoly_as_rec(up);
1027 if (!rec)
1028 goto error;
1029
1030 isl_assert(up->ctx, rec->n >= 1, goto error);
1031
1032 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1033 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1034
1035 for (i = rec->n - 2; i >= 0; --i) {
1036 res = isl_upoly_mul(res, isl_upoly_copy(base));
1037 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1038 }
1039
1040 isl_upoly_free(base);
1041 isl_upoly_free(up);
1042
1043 return res;
1044 error:
1045 isl_upoly_free(up);
1046 return NULL;
1047 }
1048
1049 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1050 {
1051 int n_row, n_col;
1052 int equal;
1053
1054 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1055 div1->n_col >= div2->n_col, return -1);
1056
1057 if (div1->n_row == div2->n_row)
1058 return isl_mat_is_equal(div1, div2);
1059
1060 n_row = div1->n_row;
1061 n_col = div1->n_col;
1062 div1->n_row = div2->n_row;
1063 div1->n_col = div2->n_col;
1064
1065 equal = isl_mat_is_equal(div1, div2);
1066
1067 div1->n_row = n_row;
1068 div1->n_col = n_col;
1069
1070 return equal;
1071 }
1072
1073 static void expand_row(__isl_keep isl_mat *dst, int d,
1074 __isl_keep isl_mat *src, int s, int *exp)
1075 {
1076 int i;
1077 unsigned c = src->n_col - src->n_row;
1078
1079 isl_seq_cpy(dst->row[d], src->row[s], c);
1080 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1081
1082 for (i = 0; i < s; ++i)
1083 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1084 }
1085
1086 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1087 {
1088 int li, lj;
1089
1090 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1091 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1092
1093 if (li != lj)
1094 return li - lj;
1095
1096 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1097 }
1098
1099 struct isl_div_sort_info {
1100 isl_mat *div;
1101 int row;
1102 };
1103
1104 static int div_sort_cmp(const void *p1, const void *p2)
1105 {
1106 const struct isl_div_sort_info *i1, *i2;
1107 i1 = (const struct isl_div_sort_info *) p1;
1108 i2 = (const struct isl_div_sort_info *) p2;
1109
1110 return cmp_row(i1->div, i1->row, i2->row);
1111 }
1112
1113 /* Sort divs and remove duplicates.
1114 */
1115 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1116 {
1117 int i;
1118 int skip;
1119 int len;
1120 struct isl_div_sort_info *array = NULL;
1121 int *pos = NULL, *at = NULL;
1122 int *reordering = NULL;
1123 unsigned div_pos;
1124
1125 if (!qp)
1126 return NULL;
1127 if (qp->div->n_row <= 1)
1128 return qp;
1129
1130 div_pos = isl_dim_total(qp->dim);
1131
1132 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1133 qp->div->n_row);
1134 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1135 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1136 len = qp->div->n_col - 2;
1137 reordering = isl_alloc_array(qp->div->ctx, int, len);
1138 if (!array || !pos || !at || !reordering)
1139 goto error;
1140
1141 for (i = 0; i < qp->div->n_row; ++i) {
1142 array[i].div = qp->div;
1143 array[i].row = i;
1144 pos[i] = i;
1145 at[i] = i;
1146 }
1147
1148 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1149 div_sort_cmp);
1150
1151 for (i = 0; i < div_pos; ++i)
1152 reordering[i] = i;
1153
1154 for (i = 0; i < qp->div->n_row; ++i) {
1155 if (pos[array[i].row] == i)
1156 continue;
1157 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1158 pos[at[i]] = pos[array[i].row];
1159 at[pos[array[i].row]] = at[i];
1160 at[i] = array[i].row;
1161 pos[array[i].row] = i;
1162 }
1163
1164 skip = 0;
1165 for (i = 0; i < len - div_pos; ++i) {
1166 if (i > 0 &&
1167 isl_seq_eq(qp->div->row[i - skip - 1],
1168 qp->div->row[i - skip], qp->div->n_col)) {
1169 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1170 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1171 2 + div_pos + i - skip);
1172 qp->div = isl_mat_drop_cols(qp->div,
1173 2 + div_pos + i - skip, 1);
1174 skip++;
1175 }
1176 reordering[div_pos + array[i].row] = div_pos + i - skip;
1177 }
1178
1179 qp->upoly = reorder(qp->upoly, reordering);
1180
1181 if (!qp->upoly || !qp->div)
1182 goto error;
1183
1184 free(at);
1185 free(pos);
1186 free(array);
1187 free(reordering);
1188
1189 return qp;
1190 error:
1191 free(at);
1192 free(pos);
1193 free(array);
1194 free(reordering);
1195 isl_qpolynomial_free(qp);
1196 return NULL;
1197 }
1198
1199 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1200 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1201 {
1202 int i, j, k;
1203 isl_mat *div = NULL;
1204 unsigned d = div1->n_col - div1->n_row;
1205
1206 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1207 d + div1->n_row + div2->n_row);
1208 if (!div)
1209 return NULL;
1210
1211 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1212 int cmp;
1213
1214 expand_row(div, k, div1, i, exp1);
1215 expand_row(div, k + 1, div2, j, exp2);
1216
1217 cmp = cmp_row(div, k, k + 1);
1218 if (cmp == 0) {
1219 exp1[i++] = k;
1220 exp2[j++] = k;
1221 } else if (cmp < 0) {
1222 exp1[i++] = k;
1223 } else {
1224 exp2[j++] = k;
1225 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1226 }
1227 }
1228 for (; i < div1->n_row; ++i, ++k) {
1229 expand_row(div, k, div1, i, exp1);
1230 exp1[i] = k;
1231 }
1232 for (; j < div2->n_row; ++j, ++k) {
1233 expand_row(div, k, div2, j, exp2);
1234 exp2[j] = k;
1235 }
1236
1237 div->n_row = k;
1238 div->n_col = d + k;
1239
1240 return div;
1241 }
1242
1243 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1244 int *exp, int first)
1245 {
1246 int i;
1247 struct isl_upoly_rec *rec;
1248
1249 if (isl_upoly_is_cst(up))
1250 return up;
1251
1252 if (up->var < first)
1253 return up;
1254
1255 if (exp[up->var - first] == up->var - first)
1256 return up;
1257
1258 up = isl_upoly_cow(up);
1259 if (!up)
1260 goto error;
1261
1262 up->var = exp[up->var - first] + first;
1263
1264 rec = isl_upoly_as_rec(up);
1265 if (!rec)
1266 goto error;
1267
1268 for (i = 0; i < rec->n; ++i) {
1269 rec->p[i] = expand(rec->p[i], exp, first);
1270 if (!rec->p[i])
1271 goto error;
1272 }
1273
1274 return up;
1275 error:
1276 isl_upoly_free(up);
1277 return NULL;
1278 }
1279
1280 static __isl_give isl_qpolynomial *with_merged_divs(
1281 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1282 __isl_take isl_qpolynomial *qp2),
1283 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1284 {
1285 int *exp1 = NULL;
1286 int *exp2 = NULL;
1287 isl_mat *div = NULL;
1288
1289 qp1 = isl_qpolynomial_cow(qp1);
1290 qp2 = isl_qpolynomial_cow(qp2);
1291
1292 if (!qp1 || !qp2)
1293 goto error;
1294
1295 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1296 qp1->div->n_col >= qp2->div->n_col, goto error);
1297
1298 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1299 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1300 if (!exp1 || !exp2)
1301 goto error;
1302
1303 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1304 if (!div)
1305 goto error;
1306
1307 isl_mat_free(qp1->div);
1308 qp1->div = isl_mat_copy(div);
1309 isl_mat_free(qp2->div);
1310 qp2->div = isl_mat_copy(div);
1311
1312 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1313 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1314
1315 if (!qp1->upoly || !qp2->upoly)
1316 goto error;
1317
1318 isl_mat_free(div);
1319 free(exp1);
1320 free(exp2);
1321
1322 return fn(qp1, qp2);
1323 error:
1324 isl_mat_free(div);
1325 free(exp1);
1326 free(exp2);
1327 isl_qpolynomial_free(qp1);
1328 isl_qpolynomial_free(qp2);
1329 return NULL;
1330 }
1331
1332 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1333 __isl_take isl_qpolynomial *qp2)
1334 {
1335 qp1 = isl_qpolynomial_cow(qp1);
1336
1337 if (!qp1 || !qp2)
1338 goto error;
1339
1340 if (qp1->div->n_row < qp2->div->n_row)
1341 return isl_qpolynomial_add(qp2, qp1);
1342
1343 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1344 if (!compatible_divs(qp1->div, qp2->div))
1345 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1346
1347 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1348 if (!qp1->upoly)
1349 goto error;
1350
1351 isl_qpolynomial_free(qp2);
1352
1353 return qp1;
1354 error:
1355 isl_qpolynomial_free(qp1);
1356 isl_qpolynomial_free(qp2);
1357 return NULL;
1358 }
1359
1360 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1361 __isl_keep isl_set *dom,
1362 __isl_take isl_qpolynomial *qp1,
1363 __isl_take isl_qpolynomial *qp2)
1364 {
1365 return isl_qpolynomial_add(qp1, qp2);
1366 }
1367
1368 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1369 __isl_take isl_qpolynomial *qp2)
1370 {
1371 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1372 }
1373
1374 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1375 {
1376 qp = isl_qpolynomial_cow(qp);
1377
1378 if (!qp)
1379 return NULL;
1380
1381 qp->upoly = isl_upoly_neg(qp->upoly);
1382 if (!qp->upoly)
1383 goto error;
1384
1385 return qp;
1386 error:
1387 isl_qpolynomial_free(qp);
1388 return NULL;
1389 }
1390
1391 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1392 __isl_take isl_qpolynomial *qp2)
1393 {
1394 qp1 = isl_qpolynomial_cow(qp1);
1395
1396 if (!qp1 || !qp2)
1397 goto error;
1398
1399 if (qp1->div->n_row < qp2->div->n_row)
1400 return isl_qpolynomial_mul(qp2, qp1);
1401
1402 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1403 if (!compatible_divs(qp1->div, qp2->div))
1404 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1405
1406 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1407 if (!qp1->upoly)
1408 goto error;
1409
1410 isl_qpolynomial_free(qp2);
1411
1412 return qp1;
1413 error:
1414 isl_qpolynomial_free(qp1);
1415 isl_qpolynomial_free(qp2);
1416 return NULL;
1417 }
1418
1419 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1420 unsigned power)
1421 {
1422 qp = isl_qpolynomial_cow(qp);
1423
1424 if (!qp)
1425 return NULL;
1426
1427 qp->upoly = isl_upoly_pow(qp->upoly, power);
1428 if (!qp->upoly)
1429 goto error;
1430
1431 return qp;
1432 error:
1433 isl_qpolynomial_free(qp);
1434 return NULL;
1435 }
1436
1437 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1438 {
1439 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1440 }
1441
1442 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1443 {
1444 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1445 }
1446
1447 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1448 {
1449 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1450 }
1451
1452 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1453 {
1454 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1455 }
1456
1457 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1458 {
1459 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1460 }
1461
1462 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1463 isl_int v)
1464 {
1465 struct isl_qpolynomial *qp;
1466 struct isl_upoly_cst *cst;
1467
1468 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1469 if (!qp)
1470 return NULL;
1471
1472 cst = isl_upoly_as_cst(qp->upoly);
1473 isl_int_set(cst->n, v);
1474
1475 return qp;
1476 }
1477
1478 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1479 isl_int *n, isl_int *d)
1480 {
1481 struct isl_upoly_cst *cst;
1482
1483 if (!qp)
1484 return -1;
1485
1486 if (!isl_upoly_is_cst(qp->upoly))
1487 return 0;
1488
1489 cst = isl_upoly_as_cst(qp->upoly);
1490 if (!cst)
1491 return -1;
1492
1493 if (n)
1494 isl_int_set(*n, cst->n);
1495 if (d)
1496 isl_int_set(*d, cst->d);
1497
1498 return 1;
1499 }
1500
1501 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1502 {
1503 int is_cst;
1504 struct isl_upoly_rec *rec;
1505
1506 if (!up)
1507 return -1;
1508
1509 if (up->var < 0)
1510 return 1;
1511
1512 rec = isl_upoly_as_rec(up);
1513 if (!rec)
1514 return -1;
1515
1516 if (rec->n > 2)
1517 return 0;
1518
1519 isl_assert(up->ctx, rec->n > 1, return -1);
1520
1521 is_cst = isl_upoly_is_cst(rec->p[1]);
1522 if (is_cst < 0)
1523 return -1;
1524 if (!is_cst)
1525 return 0;
1526
1527 return isl_upoly_is_affine(rec->p[0]);
1528 }
1529
1530 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1531 {
1532 if (!qp)
1533 return -1;
1534
1535 if (qp->div->n_row > 0)
1536 return 0;
1537
1538 return isl_upoly_is_affine(qp->upoly);
1539 }
1540
1541 static void update_coeff(__isl_keep isl_vec *aff,
1542 __isl_keep struct isl_upoly_cst *cst, int pos)
1543 {
1544 isl_int gcd;
1545 isl_int f;
1546
1547 if (isl_int_is_zero(cst->n))
1548 return;
1549
1550 isl_int_init(gcd);
1551 isl_int_init(f);
1552 isl_int_gcd(gcd, cst->d, aff->el[0]);
1553 isl_int_divexact(f, cst->d, gcd);
1554 isl_int_divexact(gcd, aff->el[0], gcd);
1555 isl_seq_scale(aff->el, aff->el, f, aff->size);
1556 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1557 isl_int_clear(gcd);
1558 isl_int_clear(f);
1559 }
1560
1561 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1562 __isl_keep isl_vec *aff)
1563 {
1564 struct isl_upoly_cst *cst;
1565 struct isl_upoly_rec *rec;
1566
1567 if (!up || !aff)
1568 return -1;
1569
1570 if (up->var < 0) {
1571 struct isl_upoly_cst *cst;
1572
1573 cst = isl_upoly_as_cst(up);
1574 if (!cst)
1575 return -1;
1576 update_coeff(aff, cst, 0);
1577 return 0;
1578 }
1579
1580 rec = isl_upoly_as_rec(up);
1581 if (!rec)
1582 return -1;
1583 isl_assert(up->ctx, rec->n == 2, return -1);
1584
1585 cst = isl_upoly_as_cst(rec->p[1]);
1586 if (!cst)
1587 return -1;
1588 update_coeff(aff, cst, 1 + up->var);
1589
1590 return isl_upoly_update_affine(rec->p[0], aff);
1591 }
1592
1593 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1594 __isl_keep isl_qpolynomial *qp)
1595 {
1596 isl_vec *aff;
1597 unsigned d;
1598
1599 if (!qp)
1600 return NULL;
1601
1602 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1603 d = isl_dim_total(qp->dim);
1604 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1605 if (!aff)
1606 return NULL;
1607
1608 isl_seq_clr(aff->el + 1, 1 + d);
1609 isl_int_set_si(aff->el[0], 1);
1610
1611 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1612 goto error;
1613
1614 return aff;
1615 error:
1616 isl_vec_free(aff);
1617 return NULL;
1618 }
1619
1620 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1621 __isl_keep isl_qpolynomial *qp2)
1622 {
1623 if (!qp1 || !qp2)
1624 return -1;
1625
1626 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1627 }
1628
1629 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1630 {
1631 int i;
1632 struct isl_upoly_rec *rec;
1633
1634 if (isl_upoly_is_cst(up)) {
1635 struct isl_upoly_cst *cst;
1636 cst = isl_upoly_as_cst(up);
1637 if (!cst)
1638 return;
1639 isl_int_lcm(*d, *d, cst->d);
1640 return;
1641 }
1642
1643 rec = isl_upoly_as_rec(up);
1644 if (!rec)
1645 return;
1646
1647 for (i = 0; i < rec->n; ++i)
1648 upoly_update_den(rec->p[i], d);
1649 }
1650
1651 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1652 {
1653 isl_int_set_si(*d, 1);
1654 if (!qp)
1655 return;
1656 upoly_update_den(qp->upoly, d);
1657 }
1658
1659 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1660 int pos, int power)
1661 {
1662 struct isl_ctx *ctx;
1663
1664 if (!dim)
1665 return NULL;
1666
1667 ctx = dim->ctx;
1668
1669 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1670 }
1671
1672 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1673 enum isl_dim_type type, unsigned pos)
1674 {
1675 if (!dim)
1676 return NULL;
1677
1678 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1679 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1680
1681 if (type == isl_dim_set)
1682 pos += isl_dim_size(dim, isl_dim_param);
1683
1684 return isl_qpolynomial_var_pow(dim, pos, 1);
1685 error:
1686 isl_dim_free(dim);
1687 return NULL;
1688 }
1689
1690 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1691 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1692 {
1693 int i;
1694 struct isl_upoly_rec *rec;
1695 struct isl_upoly *base, *res;
1696
1697 if (!up)
1698 return NULL;
1699
1700 if (isl_upoly_is_cst(up))
1701 return up;
1702
1703 if (up->var < first)
1704 return up;
1705
1706 rec = isl_upoly_as_rec(up);
1707 if (!rec)
1708 goto error;
1709
1710 isl_assert(up->ctx, rec->n >= 1, goto error);
1711
1712 if (up->var >= first + n)
1713 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1714 else
1715 base = isl_upoly_copy(subs[up->var - first]);
1716
1717 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1718 for (i = rec->n - 2; i >= 0; --i) {
1719 struct isl_upoly *t;
1720 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1721 res = isl_upoly_mul(res, isl_upoly_copy(base));
1722 res = isl_upoly_sum(res, t);
1723 }
1724
1725 isl_upoly_free(base);
1726 isl_upoly_free(up);
1727
1728 return res;
1729 error:
1730 isl_upoly_free(up);
1731 return NULL;
1732 }
1733
1734 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1735 isl_int denom, unsigned len)
1736 {
1737 int i;
1738 struct isl_upoly *up;
1739
1740 isl_assert(ctx, len >= 1, return NULL);
1741
1742 up = isl_upoly_rat_cst(ctx, f[0], denom);
1743 for (i = 0; i < len - 1; ++i) {
1744 struct isl_upoly *t;
1745 struct isl_upoly *c;
1746
1747 if (isl_int_is_zero(f[1 + i]))
1748 continue;
1749
1750 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1751 t = isl_upoly_var_pow(ctx, i, 1);
1752 t = isl_upoly_mul(c, t);
1753 up = isl_upoly_sum(up, t);
1754 }
1755
1756 return up;
1757 }
1758
1759 /* Remove common factor of non-constant terms and denominator.
1760 */
1761 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1762 {
1763 isl_ctx *ctx = qp->div->ctx;
1764 unsigned total = qp->div->n_col - 2;
1765
1766 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1767 isl_int_gcd(ctx->normalize_gcd,
1768 ctx->normalize_gcd, qp->div->row[div][0]);
1769 if (isl_int_is_one(ctx->normalize_gcd))
1770 return;
1771
1772 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1773 ctx->normalize_gcd, total);
1774 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1775 ctx->normalize_gcd);
1776 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1777 ctx->normalize_gcd);
1778 }
1779
1780 /* Replace the integer division identified by "div" by the polynomial "s".
1781 * The integer division is assumed not to appear in the definition
1782 * of any other integer divisions.
1783 */
1784 static __isl_give isl_qpolynomial *substitute_div(
1785 __isl_take isl_qpolynomial *qp,
1786 int div, __isl_take struct isl_upoly *s)
1787 {
1788 int i;
1789 int total;
1790 int *reordering;
1791
1792 if (!qp || !s)
1793 goto error;
1794
1795 qp = isl_qpolynomial_cow(qp);
1796 if (!qp)
1797 goto error;
1798
1799 total = isl_dim_total(qp->dim);
1800 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1801 if (!qp->upoly)
1802 goto error;
1803
1804 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1805 if (!reordering)
1806 goto error;
1807 for (i = 0; i < total + div; ++i)
1808 reordering[i] = i;
1809 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1810 reordering[i] = i - 1;
1811 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1812 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1813 qp->upoly = reorder(qp->upoly, reordering);
1814 free(reordering);
1815
1816 if (!qp->upoly || !qp->div)
1817 goto error;
1818
1819 isl_upoly_free(s);
1820 return qp;
1821 error:
1822 isl_qpolynomial_free(qp);
1823 isl_upoly_free(s);
1824 return NULL;
1825 }
1826
1827 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1828 * divisions because d is equal to 1 by their definition, i.e., e.
1829 */
1830 static __isl_give isl_qpolynomial *substitute_non_divs(
1831 __isl_take isl_qpolynomial *qp)
1832 {
1833 int i, j;
1834 int total;
1835 struct isl_upoly *s;
1836
1837 if (!qp)
1838 return NULL;
1839
1840 total = isl_dim_total(qp->dim);
1841 for (i = 0; qp && i < qp->div->n_row; ++i) {
1842 if (!isl_int_is_one(qp->div->row[i][0]))
1843 continue;
1844 for (j = i + 1; j < qp->div->n_row; ++j) {
1845 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1846 continue;
1847 isl_seq_combine(qp->div->row[j] + 1,
1848 qp->div->ctx->one, qp->div->row[j] + 1,
1849 qp->div->row[j][2 + total + i],
1850 qp->div->row[i] + 1, 1 + total + i);
1851 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1852 normalize_div(qp, j);
1853 }
1854 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1855 qp->div->row[i][0], qp->div->n_col - 1);
1856 qp = substitute_div(qp, i, s);
1857 --i;
1858 }
1859
1860 return qp;
1861 }
1862
1863 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1864 * with d the denominator. When replacing the coefficient e of x by
1865 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1866 * inside the division, so we need to add floor(e/d) * x outside.
1867 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1868 * to adjust the coefficient of x in each later div that depends on the
1869 * current div "div" and also in the affine expression "aff"
1870 * (if it too depends on "div").
1871 */
1872 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1873 __isl_keep isl_vec *aff)
1874 {
1875 int i, j;
1876 isl_int v;
1877 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1878
1879 isl_int_init(v);
1880 for (i = 0; i < 1 + total + div; ++i) {
1881 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1882 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1883 continue;
1884 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1885 isl_int_fdiv_r(qp->div->row[div][1 + i],
1886 qp->div->row[div][1 + i], qp->div->row[div][0]);
1887 if (!isl_int_is_zero(aff->el[1 + total + div]))
1888 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1889 for (j = div + 1; j < qp->div->n_row; ++j) {
1890 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1891 continue;
1892 isl_int_addmul(qp->div->row[j][1 + i],
1893 v, qp->div->row[j][2 + total + div]);
1894 }
1895 }
1896 isl_int_clear(v);
1897 }
1898
1899 /* Check if the last non-zero coefficient is bigger that half of the
1900 * denominator. If so, we will invert the div to further reduce the number
1901 * of distinct divs that may appear.
1902 * If the last non-zero coefficient is exactly half the denominator,
1903 * then we continue looking for earlier coefficients that are bigger
1904 * than half the denominator.
1905 */
1906 static int needs_invert(__isl_keep isl_mat *div, int row)
1907 {
1908 int i;
1909 int cmp;
1910
1911 for (i = div->n_col - 1; i >= 1; --i) {
1912 if (isl_int_is_zero(div->row[row][i]))
1913 continue;
1914 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1915 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1916 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1917 if (cmp)
1918 return cmp > 0;
1919 if (i == 1)
1920 return 1;
1921 }
1922
1923 return 0;
1924 }
1925
1926 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1927 * We only invert the coefficients of e (and the coefficient of q in
1928 * later divs and in "aff"). After calling this function, the
1929 * coefficients of e should be reduced again.
1930 */
1931 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1932 __isl_keep isl_vec *aff)
1933 {
1934 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1935
1936 isl_seq_neg(qp->div->row[div] + 1,
1937 qp->div->row[div] + 1, qp->div->n_col - 1);
1938 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1939 isl_int_add(qp->div->row[div][1],
1940 qp->div->row[div][1], qp->div->row[div][0]);
1941 if (!isl_int_is_zero(aff->el[1 + total + div]))
1942 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1943 isl_mat_col_mul(qp->div, 2 + total + div,
1944 qp->div->ctx->negone, 2 + total + div);
1945 }
1946
1947 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1948 * in the interval [0, d-1], with d the denominator and such that the
1949 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1950 *
1951 * After the reduction, some divs may have become redundant or identical,
1952 * so we call substitute_non_divs and sort_divs. If these functions
1953 * eliminate divs of merge * two or more divs into one, the coefficients
1954 * of the enclosing divs may have to be reduced again, so we call
1955 * ourselves recursively if the number of divs decreases.
1956 */
1957 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
1958 {
1959 int i, j;
1960 isl_vec *aff = NULL;
1961 struct isl_upoly *s;
1962 unsigned n_div;
1963
1964 if (!qp)
1965 return NULL;
1966
1967 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
1968 aff = isl_vec_clr(aff);
1969 if (!aff)
1970 goto error;
1971
1972 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
1973
1974 for (i = 0; i < qp->div->n_row; ++i) {
1975 normalize_div(qp, i);
1976 reduce_div(qp, i, aff);
1977 if (needs_invert(qp->div, i)) {
1978 invert_div(qp, i, aff);
1979 reduce_div(qp, i, aff);
1980 }
1981 }
1982
1983 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
1984 qp->div->ctx->one, aff->size);
1985 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
1986 isl_upoly_free(s);
1987 if (!qp->upoly)
1988 goto error;
1989
1990 isl_vec_free(aff);
1991
1992 n_div = qp->div->n_row;
1993 qp = substitute_non_divs(qp);
1994 qp = sort_divs(qp);
1995 if (qp && qp->div->n_row < n_div)
1996 return reduce_divs(qp);
1997
1998 return qp;
1999 error:
2000 isl_qpolynomial_free(qp);
2001 isl_vec_free(aff);
2002 return NULL;
2003 }
2004
2005 /* Assumes each div only depends on earlier divs.
2006 */
2007 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2008 int power)
2009 {
2010 struct isl_qpolynomial *qp = NULL;
2011 struct isl_upoly_rec *rec;
2012 struct isl_upoly_cst *cst;
2013 int i, d;
2014 int pos;
2015
2016 if (!div)
2017 return NULL;
2018
2019 d = div->line - div->bmap->div;
2020
2021 pos = isl_dim_total(div->bmap->dim) + d;
2022 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2023 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2024 div->bmap->n_div, &rec->up);
2025 if (!qp)
2026 goto error;
2027
2028 for (i = 0; i < div->bmap->n_div; ++i)
2029 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2030
2031 for (i = 0; i < 1 + power; ++i) {
2032 rec->p[i] = isl_upoly_zero(div->ctx);
2033 if (!rec->p[i])
2034 goto error;
2035 rec->n++;
2036 }
2037 cst = isl_upoly_as_cst(rec->p[power]);
2038 isl_int_set_si(cst->n, 1);
2039
2040 isl_div_free(div);
2041
2042 qp = reduce_divs(qp);
2043
2044 return qp;
2045 error:
2046 isl_qpolynomial_free(qp);
2047 isl_div_free(div);
2048 return NULL;
2049 }
2050
2051 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2052 {
2053 return isl_qpolynomial_div_pow(div, 1);
2054 }
2055
2056 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2057 const isl_int n, const isl_int d)
2058 {
2059 struct isl_qpolynomial *qp;
2060 struct isl_upoly_cst *cst;
2061
2062 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2063 if (!qp)
2064 return NULL;
2065
2066 cst = isl_upoly_as_cst(qp->upoly);
2067 isl_int_set(cst->n, n);
2068 isl_int_set(cst->d, d);
2069
2070 return qp;
2071 }
2072
2073 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2074 {
2075 struct isl_upoly_rec *rec;
2076 int i;
2077
2078 if (!up)
2079 return -1;
2080
2081 if (isl_upoly_is_cst(up))
2082 return 0;
2083
2084 if (up->var < d)
2085 active[up->var] = 1;
2086
2087 rec = isl_upoly_as_rec(up);
2088 for (i = 0; i < rec->n; ++i)
2089 if (up_set_active(rec->p[i], active, d) < 0)
2090 return -1;
2091
2092 return 0;
2093 }
2094
2095 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2096 {
2097 int i, j;
2098 int d = isl_dim_total(qp->dim);
2099
2100 if (!qp || !active)
2101 return -1;
2102
2103 for (i = 0; i < d; ++i)
2104 for (j = 0; j < qp->div->n_row; ++j) {
2105 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2106 continue;
2107 active[i] = 1;
2108 break;
2109 }
2110
2111 return up_set_active(qp->upoly, active, d);
2112 }
2113
2114 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2115 enum isl_dim_type type, unsigned first, unsigned n)
2116 {
2117 int i;
2118 int *active = NULL;
2119 int involves = 0;
2120
2121 if (!qp)
2122 return -1;
2123 if (n == 0)
2124 return 0;
2125
2126 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2127 return -1);
2128 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2129 type == isl_dim_set, return -1);
2130
2131 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2132 if (set_active(qp, active) < 0)
2133 goto error;
2134
2135 if (type == isl_dim_set)
2136 first += isl_dim_size(qp->dim, isl_dim_param);
2137 for (i = 0; i < n; ++i)
2138 if (active[first + i]) {
2139 involves = 1;
2140 break;
2141 }
2142
2143 free(active);
2144
2145 return involves;
2146 error:
2147 free(active);
2148 return -1;
2149 }
2150
2151 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2152 unsigned first, unsigned n)
2153 {
2154 int i;
2155 struct isl_upoly_rec *rec;
2156
2157 if (!up)
2158 return NULL;
2159 if (n == 0 || up->var < 0 || up->var < first)
2160 return up;
2161 if (up->var < first + n) {
2162 up = replace_by_constant_term(up);
2163 return isl_upoly_drop(up, first, n);
2164 }
2165 up = isl_upoly_cow(up);
2166 if (!up)
2167 return NULL;
2168 up->var -= n;
2169 rec = isl_upoly_as_rec(up);
2170 if (!rec)
2171 goto error;
2172
2173 for (i = 0; i < rec->n; ++i) {
2174 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2175 if (!rec->p[i])
2176 goto error;
2177 }
2178
2179 return up;
2180 error:
2181 isl_upoly_free(up);
2182 return NULL;
2183 }
2184
2185 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2186 __isl_take isl_qpolynomial *qp,
2187 enum isl_dim_type type, unsigned pos, const char *s)
2188 {
2189 qp = isl_qpolynomial_cow(qp);
2190 if (!qp)
2191 return NULL;
2192 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2193 if (!qp->dim)
2194 goto error;
2195 return qp;
2196 error:
2197 isl_qpolynomial_free(qp);
2198 return NULL;
2199 }
2200
2201 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2202 __isl_take isl_qpolynomial *qp,
2203 enum isl_dim_type type, unsigned first, unsigned n)
2204 {
2205 if (!qp)
2206 return NULL;
2207 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2208 return qp;
2209
2210 qp = isl_qpolynomial_cow(qp);
2211 if (!qp)
2212 return NULL;
2213
2214 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2215 goto error);
2216 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2217 type == isl_dim_set, goto error);
2218
2219 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2220 if (!qp->dim)
2221 goto error;
2222
2223 if (type == isl_dim_set)
2224 first += isl_dim_size(qp->dim, isl_dim_param);
2225
2226 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2227 if (!qp->div)
2228 goto error;
2229
2230 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2231 if (!qp->upoly)
2232 goto error;
2233
2234 return qp;
2235 error:
2236 isl_qpolynomial_free(qp);
2237 return NULL;
2238 }
2239
2240 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2241 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2242 {
2243 int i, j, k;
2244 isl_int denom;
2245 unsigned total;
2246 unsigned n_div;
2247 struct isl_upoly *up;
2248
2249 if (!eq)
2250 goto error;
2251 if (eq->n_eq == 0) {
2252 isl_basic_set_free(eq);
2253 return qp;
2254 }
2255
2256 qp = isl_qpolynomial_cow(qp);
2257 if (!qp)
2258 goto error;
2259 qp->div = isl_mat_cow(qp->div);
2260 if (!qp->div)
2261 goto error;
2262
2263 total = 1 + isl_dim_total(eq->dim);
2264 n_div = eq->n_div;
2265 isl_int_init(denom);
2266 for (i = 0; i < eq->n_eq; ++i) {
2267 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2268 if (j < 0 || j == 0 || j >= total)
2269 continue;
2270
2271 for (k = 0; k < qp->div->n_row; ++k) {
2272 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2273 continue;
2274 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2275 &qp->div->row[k][0]);
2276 normalize_div(qp, k);
2277 }
2278
2279 if (isl_int_is_pos(eq->eq[i][j]))
2280 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2281 isl_int_abs(denom, eq->eq[i][j]);
2282 isl_int_set_si(eq->eq[i][j], 0);
2283
2284 up = isl_upoly_from_affine(qp->dim->ctx,
2285 eq->eq[i], denom, total);
2286 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2287 isl_upoly_free(up);
2288 }
2289 isl_int_clear(denom);
2290
2291 if (!qp->upoly)
2292 goto error;
2293
2294 isl_basic_set_free(eq);
2295
2296 qp = substitute_non_divs(qp);
2297 qp = sort_divs(qp);
2298
2299 return qp;
2300 error:
2301 isl_basic_set_free(eq);
2302 isl_qpolynomial_free(qp);
2303 return NULL;
2304 }
2305
2306 static __isl_give isl_basic_set *add_div_constraints(
2307 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2308 {
2309 int i;
2310 unsigned total;
2311
2312 if (!bset || !div)
2313 goto error;
2314
2315 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2316 if (!bset)
2317 goto error;
2318 total = isl_basic_set_total_dim(bset);
2319 for (i = 0; i < div->n_row; ++i)
2320 if (isl_basic_set_add_div_constraints_var(bset,
2321 total - div->n_row + i, div->row[i]) < 0)
2322 goto error;
2323
2324 isl_mat_free(div);
2325 return bset;
2326 error:
2327 isl_mat_free(div);
2328 isl_basic_set_free(bset);
2329 return NULL;
2330 }
2331
2332 /* Look for equalities among the variables shared by context and qp
2333 * and the integer divisions of qp, if any.
2334 * The equalities are then used to eliminate variables and/or integer
2335 * divisions from qp.
2336 */
2337 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2338 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2339 {
2340 isl_basic_set *aff;
2341
2342 if (!qp)
2343 goto error;
2344 if (qp->div->n_row > 0) {
2345 isl_basic_set *bset;
2346 context = isl_set_add_dims(context, isl_dim_set,
2347 qp->div->n_row);
2348 bset = isl_basic_set_universe(isl_set_get_dim(context));
2349 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2350 context = isl_set_intersect(context,
2351 isl_set_from_basic_set(bset));
2352 }
2353
2354 aff = isl_set_affine_hull(context);
2355 return isl_qpolynomial_substitute_equalities(qp, aff);
2356 error:
2357 isl_qpolynomial_free(qp);
2358 isl_set_free(context);
2359 return NULL;
2360 }
2361
2362 #undef PW
2363 #define PW isl_pw_qpolynomial
2364 #undef EL
2365 #define EL isl_qpolynomial
2366 #undef IS_ZERO
2367 #define IS_ZERO is_zero
2368 #undef FIELD
2369 #define FIELD qp
2370
2371 #include <isl_pw_templ.c>
2372
2373 #undef UNION
2374 #define UNION isl_union_pw_qpolynomial
2375 #undef PART
2376 #define PART isl_pw_qpolynomial
2377 #undef PARTS
2378 #define PARTS pw_qpolynomial
2379
2380 #include <isl_union_templ.c>
2381
2382 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2383 {
2384 if (!pwqp)
2385 return -1;
2386
2387 if (pwqp->n != -1)
2388 return 0;
2389
2390 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2391 return 0;
2392
2393 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2394 }
2395
2396 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2397 __isl_take isl_pw_qpolynomial *pwqp1,
2398 __isl_take isl_pw_qpolynomial *pwqp2)
2399 {
2400 int i, j, n;
2401 struct isl_pw_qpolynomial *res;
2402 isl_set *set;
2403
2404 if (!pwqp1 || !pwqp2)
2405 goto error;
2406
2407 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2408 goto error);
2409
2410 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2411 isl_pw_qpolynomial_free(pwqp2);
2412 return pwqp1;
2413 }
2414
2415 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2416 isl_pw_qpolynomial_free(pwqp1);
2417 return pwqp2;
2418 }
2419
2420 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2421 isl_pw_qpolynomial_free(pwqp1);
2422 return pwqp2;
2423 }
2424
2425 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2426 isl_pw_qpolynomial_free(pwqp2);
2427 return pwqp1;
2428 }
2429
2430 n = pwqp1->n * pwqp2->n;
2431 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2432
2433 for (i = 0; i < pwqp1->n; ++i) {
2434 for (j = 0; j < pwqp2->n; ++j) {
2435 struct isl_set *common;
2436 struct isl_qpolynomial *prod;
2437 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2438 isl_set_copy(pwqp2->p[j].set));
2439 if (isl_set_fast_is_empty(common)) {
2440 isl_set_free(common);
2441 continue;
2442 }
2443
2444 prod = isl_qpolynomial_mul(
2445 isl_qpolynomial_copy(pwqp1->p[i].qp),
2446 isl_qpolynomial_copy(pwqp2->p[j].qp));
2447
2448 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2449 }
2450 }
2451
2452 isl_pw_qpolynomial_free(pwqp1);
2453 isl_pw_qpolynomial_free(pwqp2);
2454
2455 return res;
2456 error:
2457 isl_pw_qpolynomial_free(pwqp1);
2458 isl_pw_qpolynomial_free(pwqp2);
2459 return NULL;
2460 }
2461
2462 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2463 __isl_take isl_pw_qpolynomial *pwqp)
2464 {
2465 int i;
2466
2467 if (!pwqp)
2468 return NULL;
2469
2470 if (isl_pw_qpolynomial_is_zero(pwqp))
2471 return pwqp;
2472
2473 pwqp = isl_pw_qpolynomial_cow(pwqp);
2474 if (!pwqp)
2475 return NULL;
2476
2477 for (i = 0; i < pwqp->n; ++i) {
2478 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2479 if (!pwqp->p[i].qp)
2480 goto error;
2481 }
2482
2483 return pwqp;
2484 error:
2485 isl_pw_qpolynomial_free(pwqp);
2486 return NULL;
2487 }
2488
2489 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2490 __isl_take isl_pw_qpolynomial *pwqp1,
2491 __isl_take isl_pw_qpolynomial *pwqp2)
2492 {
2493 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2494 }
2495
2496 __isl_give struct isl_upoly *isl_upoly_eval(
2497 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2498 {
2499 int i;
2500 struct isl_upoly_rec *rec;
2501 struct isl_upoly *res;
2502 struct isl_upoly *base;
2503
2504 if (isl_upoly_is_cst(up)) {
2505 isl_vec_free(vec);
2506 return up;
2507 }
2508
2509 rec = isl_upoly_as_rec(up);
2510 if (!rec)
2511 goto error;
2512
2513 isl_assert(up->ctx, rec->n >= 1, goto error);
2514
2515 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2516
2517 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2518 isl_vec_copy(vec));
2519
2520 for (i = rec->n - 2; i >= 0; --i) {
2521 res = isl_upoly_mul(res, isl_upoly_copy(base));
2522 res = isl_upoly_sum(res,
2523 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2524 isl_vec_copy(vec)));
2525 }
2526
2527 isl_upoly_free(base);
2528 isl_upoly_free(up);
2529 isl_vec_free(vec);
2530 return res;
2531 error:
2532 isl_upoly_free(up);
2533 isl_vec_free(vec);
2534 return NULL;
2535 }
2536
2537 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2538 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2539 {
2540 isl_vec *ext;
2541 struct isl_upoly *up;
2542 isl_dim *dim;
2543
2544 if (!qp || !pnt)
2545 goto error;
2546 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2547
2548 if (qp->div->n_row == 0)
2549 ext = isl_vec_copy(pnt->vec);
2550 else {
2551 int i;
2552 unsigned dim = isl_dim_total(qp->dim);
2553 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2554 if (!ext)
2555 goto error;
2556
2557 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2558 for (i = 0; i < qp->div->n_row; ++i) {
2559 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2560 1 + dim + i, &ext->el[1+dim+i]);
2561 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2562 qp->div->row[i][0]);
2563 }
2564 }
2565
2566 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2567 if (!up)
2568 goto error;
2569
2570 dim = isl_dim_copy(qp->dim);
2571 isl_qpolynomial_free(qp);
2572 isl_point_free(pnt);
2573
2574 return isl_qpolynomial_alloc(dim, 0, up);
2575 error:
2576 isl_qpolynomial_free(qp);
2577 isl_point_free(pnt);
2578 return NULL;
2579 }
2580
2581 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2582 __isl_keep struct isl_upoly_cst *cst2)
2583 {
2584 int cmp;
2585 isl_int t;
2586 isl_int_init(t);
2587 isl_int_mul(t, cst1->n, cst2->d);
2588 isl_int_submul(t, cst2->n, cst1->d);
2589 cmp = isl_int_sgn(t);
2590 isl_int_clear(t);
2591 return cmp;
2592 }
2593
2594 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2595 __isl_keep isl_qpolynomial *qp2)
2596 {
2597 struct isl_upoly_cst *cst1, *cst2;
2598
2599 if (!qp1 || !qp2)
2600 return -1;
2601 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2602 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2603 if (isl_qpolynomial_is_nan(qp1))
2604 return -1;
2605 if (isl_qpolynomial_is_nan(qp2))
2606 return -1;
2607 cst1 = isl_upoly_as_cst(qp1->upoly);
2608 cst2 = isl_upoly_as_cst(qp2->upoly);
2609
2610 return isl_upoly_cmp(cst1, cst2) <= 0;
2611 }
2612
2613 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2614 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2615 {
2616 struct isl_upoly_cst *cst1, *cst2;
2617 int cmp;
2618
2619 if (!qp1 || !qp2)
2620 goto error;
2621 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2622 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2623 cst1 = isl_upoly_as_cst(qp1->upoly);
2624 cst2 = isl_upoly_as_cst(qp2->upoly);
2625 cmp = isl_upoly_cmp(cst1, cst2);
2626
2627 if (cmp <= 0) {
2628 isl_qpolynomial_free(qp2);
2629 } else {
2630 isl_qpolynomial_free(qp1);
2631 qp1 = qp2;
2632 }
2633 return qp1;
2634 error:
2635 isl_qpolynomial_free(qp1);
2636 isl_qpolynomial_free(qp2);
2637 return NULL;
2638 }
2639
2640 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2641 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2642 {
2643 struct isl_upoly_cst *cst1, *cst2;
2644 int cmp;
2645
2646 if (!qp1 || !qp2)
2647 goto error;
2648 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2649 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2650 cst1 = isl_upoly_as_cst(qp1->upoly);
2651 cst2 = isl_upoly_as_cst(qp2->upoly);
2652 cmp = isl_upoly_cmp(cst1, cst2);
2653
2654 if (cmp >= 0) {
2655 isl_qpolynomial_free(qp2);
2656 } else {
2657 isl_qpolynomial_free(qp1);
2658 qp1 = qp2;
2659 }
2660 return qp1;
2661 error:
2662 isl_qpolynomial_free(qp1);
2663 isl_qpolynomial_free(qp2);
2664 return NULL;
2665 }
2666
2667 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2668 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2669 unsigned first, unsigned n)
2670 {
2671 unsigned total;
2672 unsigned g_pos;
2673 int *exp;
2674
2675 if (n == 0)
2676 return qp;
2677
2678 qp = isl_qpolynomial_cow(qp);
2679 if (!qp)
2680 return NULL;
2681
2682 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2683 goto error);
2684
2685 g_pos = pos(qp->dim, type) + first;
2686
2687 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2688 if (!qp->div)
2689 goto error;
2690
2691 total = qp->div->n_col - 2;
2692 if (total > g_pos) {
2693 int i;
2694 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2695 if (!exp)
2696 goto error;
2697 for (i = 0; i < total - g_pos; ++i)
2698 exp[i] = i + n;
2699 qp->upoly = expand(qp->upoly, exp, g_pos);
2700 free(exp);
2701 if (!qp->upoly)
2702 goto error;
2703 }
2704
2705 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2706 if (!qp->dim)
2707 goto error;
2708
2709 return qp;
2710 error:
2711 isl_qpolynomial_free(qp);
2712 return NULL;
2713 }
2714
2715 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2716 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2717 {
2718 unsigned pos;
2719
2720 pos = isl_qpolynomial_dim(qp, type);
2721
2722 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2723 }
2724
2725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2726 __isl_take isl_pw_qpolynomial *pwqp,
2727 enum isl_dim_type type, unsigned n)
2728 {
2729 unsigned pos;
2730
2731 pos = isl_pw_qpolynomial_dim(pwqp, type);
2732
2733 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2734 }
2735
2736 static int *reordering_move(isl_ctx *ctx,
2737 unsigned len, unsigned dst, unsigned src, unsigned n)
2738 {
2739 int i;
2740 int *reordering;
2741
2742 reordering = isl_alloc_array(ctx, int, len);
2743 if (!reordering)
2744 return NULL;
2745
2746 if (dst <= src) {
2747 for (i = 0; i < dst; ++i)
2748 reordering[i] = i;
2749 for (i = 0; i < n; ++i)
2750 reordering[src + i] = dst + i;
2751 for (i = 0; i < src - dst; ++i)
2752 reordering[dst + i] = dst + n + i;
2753 for (i = 0; i < len - src - n; ++i)
2754 reordering[src + n + i] = src + n + i;
2755 } else {
2756 for (i = 0; i < src; ++i)
2757 reordering[i] = i;
2758 for (i = 0; i < n; ++i)
2759 reordering[src + i] = dst + i;
2760 for (i = 0; i < dst - src; ++i)
2761 reordering[src + n + i] = src + i;
2762 for (i = 0; i < len - dst - n; ++i)
2763 reordering[dst + n + i] = dst + n + i;
2764 }
2765
2766 return reordering;
2767 }
2768
2769 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2770 __isl_take isl_qpolynomial *qp,
2771 enum isl_dim_type dst_type, unsigned dst_pos,
2772 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2773 {
2774 unsigned g_dst_pos;
2775 unsigned g_src_pos;
2776 int *reordering;
2777
2778 qp = isl_qpolynomial_cow(qp);
2779 if (!qp)
2780 return NULL;
2781
2782 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2783 goto error);
2784
2785 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2786 g_src_pos = pos(qp->dim, src_type) + src_pos;
2787 if (dst_type > src_type)
2788 g_dst_pos -= n;
2789
2790 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2791 if (!qp->div)
2792 goto error;
2793 qp = sort_divs(qp);
2794 if (!qp)
2795 goto error;
2796
2797 reordering = reordering_move(qp->dim->ctx,
2798 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2799 if (!reordering)
2800 goto error;
2801
2802 qp->upoly = reorder(qp->upoly, reordering);
2803 free(reordering);
2804 if (!qp->upoly)
2805 goto error;
2806
2807 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2808 if (!qp->dim)
2809 goto error;
2810
2811 return qp;
2812 error:
2813 isl_qpolynomial_free(qp);
2814 return NULL;
2815 }
2816
2817 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2818 isl_int *f, isl_int denom)
2819 {
2820 struct isl_upoly *up;
2821
2822 if (!dim)
2823 return NULL;
2824
2825 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2826
2827 return isl_qpolynomial_alloc(dim, 0, up);
2828 }
2829
2830 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2831 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2832 {
2833 isl_int denom;
2834 isl_dim *dim;
2835 struct isl_upoly *up;
2836 isl_qpolynomial *qp;
2837 int sgn;
2838
2839 if (!c)
2840 return NULL;
2841
2842 isl_int_init(denom);
2843
2844 isl_constraint_get_coefficient(c, type, pos, &denom);
2845 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2846 sgn = isl_int_sgn(denom);
2847 isl_int_abs(denom, denom);
2848 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2849 1 + isl_constraint_dim(c, isl_dim_all));
2850 if (sgn < 0)
2851 isl_int_neg(denom, denom);
2852 isl_constraint_set_coefficient(c, type, pos, denom);
2853
2854 dim = isl_dim_copy(c->bmap->dim);
2855
2856 isl_int_clear(denom);
2857 isl_constraint_free(c);
2858
2859 qp = isl_qpolynomial_alloc(dim, 0, up);
2860 if (sgn > 0)
2861 qp = isl_qpolynomial_neg(qp);
2862 return qp;
2863 }
2864
2865 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2866 * in "qp" by subs[i].
2867 */
2868 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2869 __isl_take isl_qpolynomial *qp,
2870 enum isl_dim_type type, unsigned first, unsigned n,
2871 __isl_keep isl_qpolynomial **subs)
2872 {
2873 int i;
2874 struct isl_upoly **ups;
2875
2876 if (n == 0)
2877 return qp;
2878
2879 qp = isl_qpolynomial_cow(qp);
2880 if (!qp)
2881 return NULL;
2882 for (i = 0; i < n; ++i)
2883 if (!subs[i])
2884 goto error;
2885
2886 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2887 goto error);
2888
2889 for (i = 0; i < n; ++i)
2890 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2891 goto error);
2892
2893 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2894 for (i = 0; i < n; ++i)
2895 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2896
2897 first += pos(qp->dim, type);
2898
2899 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2900 if (!ups)
2901 goto error;
2902 for (i = 0; i < n; ++i)
2903 ups[i] = subs[i]->upoly;
2904
2905 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2906
2907 free(ups);
2908
2909 if (!qp->upoly)
2910 goto error;
2911
2912 return qp;
2913 error:
2914 isl_qpolynomial_free(qp);
2915 return NULL;
2916 }
2917
2918 /* Extend "bset" with extra set dimensions for each integer division
2919 * in "qp" and then call "fn" with the extended bset and the polynomial
2920 * that results from replacing each of the integer divisions by the
2921 * corresponding extra set dimension.
2922 */
2923 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2924 __isl_keep isl_basic_set *bset,
2925 int (*fn)(__isl_take isl_basic_set *bset,
2926 __isl_take isl_qpolynomial *poly, void *user), void *user)
2927 {
2928 isl_dim *dim;
2929 isl_mat *div;
2930 isl_qpolynomial *poly;
2931
2932 if (!qp || !bset)
2933 goto error;
2934 if (qp->div->n_row == 0)
2935 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2936 user);
2937
2938 div = isl_mat_copy(qp->div);
2939 dim = isl_dim_copy(qp->dim);
2940 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2941 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2942 bset = isl_basic_set_copy(bset);
2943 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2944 bset = add_div_constraints(bset, div);
2945
2946 return fn(bset, poly, user);
2947 error:
2948 return -1;
2949 }
2950
2951 /* Return total degree in variables first (inclusive) up to last (exclusive).
2952 */
2953 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2954 {
2955 int deg = -1;
2956 int i;
2957 struct isl_upoly_rec *rec;
2958
2959 if (!up)
2960 return -2;
2961 if (isl_upoly_is_zero(up))
2962 return -1;
2963 if (isl_upoly_is_cst(up) || up->var < first)
2964 return 0;
2965
2966 rec = isl_upoly_as_rec(up);
2967 if (!rec)
2968 return -2;
2969
2970 for (i = 0; i < rec->n; ++i) {
2971 int d;
2972
2973 if (isl_upoly_is_zero(rec->p[i]))
2974 continue;
2975 d = isl_upoly_degree(rec->p[i], first, last);
2976 if (up->var < last)
2977 d += i;
2978 if (d > deg)
2979 deg = d;
2980 }
2981
2982 return deg;
2983 }
2984
2985 /* Return total degree in set variables.
2986 */
2987 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2988 {
2989 unsigned ovar;
2990 unsigned nvar;
2991
2992 if (!poly)
2993 return -2;
2994
2995 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2996 nvar = isl_dim_size(poly->dim, isl_dim_set);
2997 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2998 }
2999
3000 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3001 unsigned pos, int deg)
3002 {
3003 int i;
3004 struct isl_upoly_rec *rec;
3005
3006 if (!up)
3007 return NULL;
3008
3009 if (isl_upoly_is_cst(up) || up->var < pos) {
3010 if (deg == 0)
3011 return isl_upoly_copy(up);
3012 else
3013 return isl_upoly_zero(up->ctx);
3014 }
3015
3016 rec = isl_upoly_as_rec(up);
3017 if (!rec)
3018 return NULL;
3019
3020 if (up->var == pos) {
3021 if (deg < rec->n)
3022 return isl_upoly_copy(rec->p[deg]);
3023 else
3024 return isl_upoly_zero(up->ctx);
3025 }
3026
3027 up = isl_upoly_copy(up);
3028 up = isl_upoly_cow(up);
3029 rec = isl_upoly_as_rec(up);
3030 if (!rec)
3031 goto error;
3032
3033 for (i = 0; i < rec->n; ++i) {
3034 struct isl_upoly *t;
3035 t = isl_upoly_coeff(rec->p[i], pos, deg);
3036 if (!t)
3037 goto error;
3038 isl_upoly_free(rec->p[i]);
3039 rec->p[i] = t;
3040 }
3041
3042 return up;
3043 error:
3044 isl_upoly_free(up);
3045 return NULL;
3046 }
3047
3048 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3049 */
3050 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3051 __isl_keep isl_qpolynomial *qp,
3052 enum isl_dim_type type, unsigned t_pos, int deg)
3053 {
3054 unsigned g_pos;
3055 struct isl_upoly *up;
3056 isl_qpolynomial *c;
3057
3058 if (!qp)
3059 return NULL;
3060
3061 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3062 return NULL);
3063
3064 g_pos = pos(qp->dim, type) + t_pos;
3065 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3066
3067 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3068 if (!c)
3069 return NULL;
3070 isl_mat_free(c->div);
3071 c->div = isl_mat_copy(qp->div);
3072 if (!c->div)
3073 goto error;
3074 return c;
3075 error:
3076 isl_qpolynomial_free(c);
3077 return NULL;
3078 }
3079
3080 /* Homogenize the polynomial in the variables first (inclusive) up to
3081 * last (exclusive) by inserting powers of variable first.
3082 * Variable first is assumed not to appear in the input.
3083 */
3084 __isl_give struct isl_upoly *isl_upoly_homogenize(
3085 __isl_take struct isl_upoly *up, int deg, int target,
3086 int first, int last)
3087 {
3088 int i;
3089 struct isl_upoly_rec *rec;
3090
3091 if (!up)
3092 return NULL;
3093 if (isl_upoly_is_zero(up))
3094 return up;
3095 if (deg == target)
3096 return up;
3097 if (isl_upoly_is_cst(up) || up->var < first) {
3098 struct isl_upoly *hom;
3099
3100 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3101 if (!hom)
3102 goto error;
3103 rec = isl_upoly_as_rec(hom);
3104 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3105
3106 return hom;
3107 }
3108
3109 up = isl_upoly_cow(up);
3110 rec = isl_upoly_as_rec(up);
3111 if (!rec)
3112 goto error;
3113
3114 for (i = 0; i < rec->n; ++i) {
3115 if (isl_upoly_is_zero(rec->p[i]))
3116 continue;
3117 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3118 up->var < last ? deg + i : i, target,
3119 first, last);
3120 if (!rec->p[i])
3121 goto error;
3122 }
3123
3124 return up;
3125 error:
3126 isl_upoly_free(up);
3127 return NULL;
3128 }
3129
3130 /* Homogenize the polynomial in the set variables by introducing
3131 * powers of an extra set variable at position 0.
3132 */
3133 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3134 __isl_take isl_qpolynomial *poly)
3135 {
3136 unsigned ovar;
3137 unsigned nvar;
3138 int deg = isl_qpolynomial_degree(poly);
3139
3140 if (deg < -1)
3141 goto error;
3142
3143 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3144 poly = isl_qpolynomial_cow(poly);
3145 if (!poly)
3146 goto error;
3147
3148 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3149 nvar = isl_dim_size(poly->dim, isl_dim_set);
3150 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3151 ovar, ovar + nvar);
3152 if (!poly->upoly)
3153 goto error;
3154
3155 return poly;
3156 error:
3157 isl_qpolynomial_free(poly);
3158 return NULL;
3159 }
3160
3161 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3162 __isl_take isl_mat *div)
3163 {
3164 isl_term *term;
3165 int n;
3166
3167 if (!dim || !div)
3168 goto error;
3169
3170 n = isl_dim_total(dim) + div->n_row;
3171
3172 term = isl_calloc(dim->ctx, struct isl_term,
3173 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3174 if (!term)
3175 goto error;
3176
3177 term->ref = 1;
3178 term->dim = dim;
3179 term->div = div;
3180 isl_int_init(term->n);
3181 isl_int_init(term->d);
3182
3183 return term;
3184 error:
3185 isl_dim_free(dim);
3186 isl_mat_free(div);
3187 return NULL;
3188 }
3189
3190 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3191 {
3192 if (!term)
3193 return NULL;
3194
3195 term->ref++;
3196 return term;
3197 }
3198
3199 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3200 {
3201 int i;
3202 isl_term *dup;
3203 unsigned total;
3204
3205 if (term)
3206 return NULL;
3207
3208 total = isl_dim_total(term->dim) + term->div->n_row;
3209
3210 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3211 if (!dup)
3212 return NULL;
3213
3214 isl_int_set(dup->n, term->n);
3215 isl_int_set(dup->d, term->d);
3216
3217 for (i = 0; i < total; ++i)
3218 dup->pow[i] = term->pow[i];
3219
3220 return dup;
3221 }
3222
3223 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3224 {
3225 if (!term)
3226 return NULL;
3227
3228 if (term->ref == 1)
3229 return term;
3230 term->ref--;
3231 return isl_term_dup(term);
3232 }
3233
3234 void isl_term_free(__isl_take isl_term *term)
3235 {
3236 if (!term)
3237 return;
3238
3239 if (--term->ref > 0)
3240 return;
3241
3242 isl_dim_free(term->dim);
3243 isl_mat_free(term->div);
3244 isl_int_clear(term->n);
3245 isl_int_clear(term->d);
3246 free(term);
3247 }
3248
3249 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3250 {
3251 if (!term)
3252 return 0;
3253
3254 switch (type) {
3255 case isl_dim_param:
3256 case isl_dim_in:
3257 case isl_dim_out: return isl_dim_size(term->dim, type);
3258 case isl_dim_div: return term->div->n_row;
3259 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3260 default: return 0;
3261 }
3262 }
3263
3264 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3265 {
3266 return term ? term->dim->ctx : NULL;
3267 }
3268
3269 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3270 {
3271 if (!term)
3272 return;
3273 isl_int_set(*n, term->n);
3274 }
3275
3276 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3277 {
3278 if (!term)
3279 return;
3280 isl_int_set(*d, term->d);
3281 }
3282
3283 int isl_term_get_exp(__isl_keep isl_term *term,
3284 enum isl_dim_type type, unsigned pos)
3285 {
3286 if (!term)
3287 return -1;
3288
3289 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3290
3291 if (type >= isl_dim_set)
3292 pos += isl_dim_size(term->dim, isl_dim_param);
3293 if (type >= isl_dim_div)
3294 pos += isl_dim_size(term->dim, isl_dim_set);
3295
3296 return term->pow[pos];
3297 }
3298
3299 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3300 {
3301 isl_basic_map *bmap;
3302 unsigned total;
3303 int k;
3304
3305 if (!term)
3306 return NULL;
3307
3308 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3309 return NULL);
3310
3311 total = term->div->n_col - term->div->n_row - 2;
3312 /* No nested divs for now */
3313 isl_assert(term->dim->ctx,
3314 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3315 term->div->n_row) == -1,
3316 return NULL);
3317
3318 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3319 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3320 goto error;
3321
3322 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3323
3324 return isl_basic_map_div(bmap, k);
3325 error:
3326 isl_basic_map_free(bmap);
3327 return NULL;
3328 }
3329
3330 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3331 int (*fn)(__isl_take isl_term *term, void *user),
3332 __isl_take isl_term *term, void *user)
3333 {
3334 int i;
3335 struct isl_upoly_rec *rec;
3336
3337 if (!up || !term)
3338 goto error;
3339
3340 if (isl_upoly_is_zero(up))
3341 return term;
3342
3343 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3344 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3345 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3346
3347 if (isl_upoly_is_cst(up)) {
3348 struct isl_upoly_cst *cst;
3349 cst = isl_upoly_as_cst(up);
3350 if (!cst)
3351 goto error;
3352 term = isl_term_cow(term);
3353 if (!term)
3354 goto error;
3355 isl_int_set(term->n, cst->n);
3356 isl_int_set(term->d, cst->d);
3357 if (fn(isl_term_copy(term), user) < 0)
3358 goto error;
3359 return term;
3360 }
3361
3362 rec = isl_upoly_as_rec(up);
3363 if (!rec)
3364 goto error;
3365
3366 for (i = 0; i < rec->n; ++i) {
3367 term = isl_term_cow(term);
3368 if (!term)
3369 goto error;
3370 term->pow[up->var] = i;
3371 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3372 if (!term)
3373 goto error;
3374 }
3375 term->pow[up->var] = 0;
3376
3377 return term;
3378 error:
3379 isl_term_free(term);
3380 return NULL;
3381 }
3382
3383 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3384 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3385 {
3386 isl_term *term;
3387
3388 if (!qp)
3389 return -1;
3390
3391 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3392 if (!term)
3393 return -1;
3394
3395 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3396
3397 isl_term_free(term);
3398
3399 return term ? 0 : -1;
3400 }
3401
3402 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3403 {
3404 struct isl_upoly *up;
3405 isl_qpolynomial *qp;
3406 int i, n;
3407
3408 if (!term)
3409 return NULL;
3410
3411 n = isl_dim_total(term->dim) + term->div->n_row;
3412
3413 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3414 for (i = 0; i < n; ++i) {
3415 if (!term->pow[i])
3416 continue;
3417 up = isl_upoly_mul(up,
3418 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3419 }
3420
3421 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3422 if (!qp)
3423 goto error;
3424 isl_mat_free(qp->div);
3425 qp->div = isl_mat_copy(term->div);
3426 if (!qp->div)
3427 goto error;
3428
3429 isl_term_free(term);
3430 return qp;
3431 error:
3432 isl_qpolynomial_free(qp);
3433 isl_term_free(term);
3434 return NULL;
3435 }
3436
3437 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3438 __isl_take isl_dim *dim)
3439 {
3440 int i;
3441 int extra;
3442 unsigned total;
3443
3444 if (!qp || !dim)
3445 goto error;
3446
3447 if (isl_dim_equal(qp->dim, dim)) {
3448 isl_dim_free(dim);
3449 return qp;
3450 }
3451
3452 qp = isl_qpolynomial_cow(qp);
3453 if (!qp)
3454 goto error;
3455
3456 extra = isl_dim_size(dim, isl_dim_set) -
3457 isl_dim_size(qp->dim, isl_dim_set);
3458 total = isl_dim_total(qp->dim);
3459 if (qp->div->n_row) {
3460 int *exp;
3461
3462 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3463 if (!exp)
3464 goto error;
3465 for (i = 0; i < qp->div->n_row; ++i)
3466 exp[i] = extra + i;
3467 qp->upoly = expand(qp->upoly, exp, total);
3468 free(exp);
3469 if (!qp->upoly)
3470 goto error;
3471 }
3472 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3473 if (!qp->div)
3474 goto error;
3475 for (i = 0; i < qp->div->n_row; ++i)
3476 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3477
3478 isl_dim_free(qp->dim);
3479 qp->dim = dim;
3480
3481 return qp;
3482 error:
3483 isl_dim_free(dim);
3484 isl_qpolynomial_free(qp);
3485 return NULL;
3486 }
3487
3488 /* For each parameter or variable that does not appear in qp,
3489 * first eliminate the variable from all constraints and then set it to zero.
3490 */
3491 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3492 __isl_keep isl_qpolynomial *qp)
3493 {
3494 int *active = NULL;
3495 int i;
3496 int d;
3497 unsigned nparam;
3498 unsigned nvar;
3499
3500 if (!set || !qp)
3501 goto error;
3502
3503 d = isl_dim_total(set->dim);
3504 active = isl_calloc_array(set->ctx, int, d);
3505 if (set_active(qp, active) < 0)
3506 goto error;
3507
3508 for (i = 0; i < d; ++i)
3509 if (!active[i])
3510 break;
3511
3512 if (i == d) {
3513 free(active);
3514 return set;
3515 }
3516
3517 nparam = isl_dim_size(set->dim, isl_dim_param);
3518 nvar = isl_dim_size(set->dim, isl_dim_set);
3519 for (i = 0; i < nparam; ++i) {
3520 if (active[i])
3521 continue;
3522 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3523 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3524 }
3525 for (i = 0; i < nvar; ++i) {
3526 if (active[nparam + i])
3527 continue;
3528 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3529 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3530 }
3531
3532 free(active);
3533
3534 return set;
3535 error:
3536 free(active);
3537 isl_set_free(set);
3538 return NULL;
3539 }
3540
3541 struct isl_opt_data {
3542 isl_qpolynomial *qp;
3543 int first;
3544 isl_qpolynomial *opt;
3545 int max;
3546 };
3547
3548 static int opt_fn(__isl_take isl_point *pnt, void *user)
3549 {
3550 struct isl_opt_data *data = (struct isl_opt_data *)user;
3551 isl_qpolynomial *val;
3552
3553 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3554 if (data->first) {
3555 data->first = 0;
3556 data->opt = val;
3557 } else if (data->max) {
3558 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3559 } else {
3560 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3561 }
3562
3563 return 0;
3564 }
3565
3566 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3567 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3568 {
3569 struct isl_opt_data data = { NULL, 1, NULL, max };
3570
3571 if (!set || !qp)
3572 goto error;
3573
3574 if (isl_upoly_is_cst(qp->upoly)) {
3575 isl_set_free(set);
3576 return qp;
3577 }
3578
3579 set = fix_inactive(set, qp);
3580
3581 data.qp = qp;
3582 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3583 goto error;
3584
3585 if (data.first)
3586 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3587
3588 isl_set_free(set);
3589 isl_qpolynomial_free(qp);
3590 return data.opt;
3591 error:
3592 isl_set_free(set);
3593 isl_qpolynomial_free(qp);
3594 isl_qpolynomial_free(data.opt);
3595 return NULL;
3596 }
3597
3598 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3599 __isl_take isl_morph *morph)
3600 {
3601 int i;
3602 int n_sub;
3603 isl_ctx *ctx;
3604 struct isl_upoly *up;
3605 unsigned n_div;
3606 struct isl_upoly **subs;
3607 isl_mat *mat;
3608
3609 qp = isl_qpolynomial_cow(qp);
3610 if (!qp || !morph)
3611 goto error;
3612
3613 ctx = qp->dim->ctx;
3614 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3615
3616 n_sub = morph->inv->n_row - 1;
3617 if (morph->inv->n_row != morph->inv->n_col)
3618 n_sub += qp->div->n_row;
3619 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3620 if (!subs)
3621 goto error;
3622
3623 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3624 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3625 morph->inv->row[0][0], morph->inv->n_col);
3626 if (morph->inv->n_row != morph->inv->n_col)
3627 for (i = 0; i < qp->div->n_row; ++i)
3628 subs[morph->inv->n_row - 1 + i] =
3629 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3630
3631 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3632
3633 for (i = 0; i < n_sub; ++i)
3634 isl_upoly_free(subs[i]);
3635 free(subs);
3636
3637 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3638 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3639 qp->div = isl_mat_product(qp->div, mat);
3640 isl_dim_free(qp->dim);
3641 qp->dim = isl_dim_copy(morph->ran->dim);
3642
3643 if (!qp->upoly || !qp->div || !qp->dim)
3644 goto error;
3645
3646 isl_morph_free(morph);
3647
3648 return qp;
3649 error:
3650 isl_qpolynomial_free(qp);
3651 isl_morph_free(morph);
3652 return NULL;
3653 }
3654
3655 static int neg_entry(void **entry, void *user)
3656 {
3657 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3658
3659 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3660
3661 return *pwqp ? 0 : -1;
3662 }
3663
3664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3665 __isl_take isl_union_pw_qpolynomial *upwqp)
3666 {
3667 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3668 if (!upwqp)
3669 return NULL;
3670
3671 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3672 &neg_entry, NULL) < 0)
3673 goto error;
3674
3675 return upwqp;
3676 error:
3677 isl_union_pw_qpolynomial_free(upwqp);
3678 return NULL;
3679 }
3680
3681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3682 __isl_take isl_union_pw_qpolynomial *upwqp1,
3683 __isl_take isl_union_pw_qpolynomial *upwqp2)
3684 {
3685 return isl_union_pw_qpolynomial_add(upwqp1,
3686 isl_union_pw_qpolynomial_neg(upwqp2));
3687 }
3688
3689 static int mul_entry(void **entry, void *user)
3690 {
3691 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3692 uint32_t hash;
3693 struct isl_hash_table_entry *entry2;
3694 isl_pw_qpolynomial *pwpq = *entry;
3695 int empty;
3696
3697 hash = isl_dim_get_hash(pwpq->dim);
3698 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3699 hash, &has_dim, pwpq->dim, 0);
3700 if (!entry2)
3701 return 0;
3702
3703 pwpq = isl_pw_qpolynomial_copy(pwpq);
3704 pwpq = isl_pw_qpolynomial_mul(pwpq,
3705 isl_pw_qpolynomial_copy(entry2->data));
3706
3707 empty = isl_pw_qpolynomial_is_zero(pwpq);
3708 if (empty < 0) {
3709 isl_pw_qpolynomial_free(pwpq);
3710 return -1;
3711 }
3712 if (empty) {
3713 isl_pw_qpolynomial_free(pwpq);
3714 return 0;
3715 }
3716
3717 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3718
3719 return 0;
3720 }
3721
3722 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3723 __isl_take isl_union_pw_qpolynomial *upwqp1,
3724 __isl_take isl_union_pw_qpolynomial *upwqp2)
3725 {
3726 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3727 }
3728
3729 /* Reorder the columns of the given div definitions according to the
3730 * given reordering.
3731 */
3732 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3733 __isl_take isl_reordering *r)
3734 {
3735 int i, j;
3736 isl_mat *mat;
3737 int extra;
3738
3739 if (!div || !r)
3740 goto error;
3741
3742 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3743 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3744 if (!mat)
3745 goto error;
3746
3747 for (i = 0; i < div->n_row; ++i) {
3748 isl_seq_cpy(mat->row[i], div->row[i], 2);
3749 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3750 for (j = 0; j < r->len; ++j)
3751 isl_int_set(mat->row[i][2 + r->pos[j]],
3752 div->row[i][2 + j]);
3753 }
3754
3755 isl_reordering_free(r);
3756 isl_mat_free(div);
3757 return mat;
3758 error:
3759 isl_reordering_free(r);
3760 isl_mat_free(div);
3761 return NULL;
3762 }
3763
3764 /* Reorder the dimension of "qp" according to the given reordering.
3765 */
3766 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3767 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3768 {
3769 qp = isl_qpolynomial_cow(qp);
3770 if (!qp)
3771 goto error;
3772
3773 r = isl_reordering_extend(r, qp->div->n_row);
3774 if (!r)
3775 goto error;
3776
3777 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3778 if (!qp->div)
3779 goto error;
3780
3781 qp->upoly = reorder(qp->upoly, r->pos);
3782 if (!qp->upoly)
3783 goto error;
3784
3785 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3786
3787 isl_reordering_free(r);
3788 return qp;
3789 error:
3790 isl_qpolynomial_free(qp);
3791 isl_reordering_free(r);
3792 return NULL;
3793 }
3794
3795 struct isl_split_periods_data {
3796 int max_periods;
3797 isl_pw_qpolynomial *res;
3798 };
3799
3800 /* Create a slice where the integer division "div" has the fixed value "v".
3801 * In particular, if "div" refers to floor(f/m), then create a slice
3802 *
3803 * m v <= f <= m v + (m - 1)
3804 *
3805 * or
3806 *
3807 * f - m v >= 0
3808 * -f + m v + (m - 1) >= 0
3809 */
3810 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3811 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3812 {
3813 int total;
3814 isl_basic_set *bset = NULL;
3815 int k;
3816
3817 if (!dim || !qp)
3818 goto error;
3819
3820 total = isl_dim_total(dim);
3821 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3822
3823 k = isl_basic_set_alloc_inequality(bset);
3824 if (k < 0)
3825 goto error;
3826 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3827 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3828
3829 k = isl_basic_set_alloc_inequality(bset);
3830 if (k < 0)
3831 goto error;
3832 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3833 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3834 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3835 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3836
3837 isl_dim_free(dim);
3838 return isl_set_from_basic_set(bset);
3839 error:
3840 isl_basic_set_free(bset);
3841 isl_dim_free(dim);
3842 return NULL;
3843 }
3844
3845 static int split_periods(__isl_take isl_set *set,
3846 __isl_take isl_qpolynomial *qp, void *user);
3847
3848 /* Create a slice of the domain "set" such that integer division "div"
3849 * has the fixed value "v" and add the results to data->res,
3850 * replacing the integer division by "v" in "qp".
3851 */
3852 static int set_div(__isl_take isl_set *set,
3853 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3854 struct isl_split_periods_data *data)
3855 {
3856 int i;
3857 int total;
3858 isl_set *slice;
3859 struct isl_upoly *cst;
3860
3861 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3862 set = isl_set_intersect(set, slice);
3863
3864 if (!qp)
3865 goto error;
3866
3867 total = isl_dim_total(qp->dim);
3868
3869 for (i = div + 1; i < qp->div->n_row; ++i) {
3870 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3871 continue;
3872 isl_int_addmul(qp->div->row[i][1],
3873 qp->div->row[i][2 + total + div], v);
3874 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3875 }
3876
3877 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3878 qp = substitute_div(qp, div, cst);
3879
3880 return split_periods(set, qp, data);
3881 error:
3882 isl_set_free(set);
3883 isl_qpolynomial_free(qp);
3884 return -1;
3885 }
3886
3887 /* Split the domain "set" such that integer division "div"
3888 * has a fixed value (ranging from "min" to "max") on each slice
3889 * and add the results to data->res.
3890 */
3891 static int split_div(__isl_take isl_set *set,
3892 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3893 struct isl_split_periods_data *data)
3894 {
3895 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3896 isl_set *set_i = isl_set_copy(set);
3897 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3898
3899 if (set_div(set_i, qp_i, div, min, data) < 0)
3900 goto error;
3901 }
3902 isl_set_free(set);
3903 isl_qpolynomial_free(qp);
3904 return 0;
3905 error:
3906 isl_set_free(set);
3907 isl_qpolynomial_free(qp);
3908 return -1;
3909 }
3910
3911 /* If "qp" refers to any integer division
3912 * that can only attain "max_periods" distinct values on "set"
3913 * then split the domain along those distinct values.
3914 * Add the results (or the original if no splitting occurs)
3915 * to data->res.
3916 */
3917 static int split_periods(__isl_take isl_set *set,
3918 __isl_take isl_qpolynomial *qp, void *user)
3919 {
3920 int i;
3921 isl_pw_qpolynomial *pwqp;
3922 struct isl_split_periods_data *data;
3923 isl_int min, max;
3924 int total;
3925 int r = 0;
3926
3927 data = (struct isl_split_periods_data *)user;
3928
3929 if (!set || !qp)
3930 goto error;
3931
3932 if (qp->div->n_row == 0) {
3933 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3934 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3935 return 0;
3936 }
3937
3938 isl_int_init(min);
3939 isl_int_init(max);
3940 total = isl_dim_total(qp->dim);
3941 for (i = 0; i < qp->div->n_row; ++i) {
3942 enum isl_lp_result lp_res;
3943
3944 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3945 qp->div->n_row) != -1)
3946 continue;
3947
3948 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3949 set->ctx->one, &min, NULL, NULL);
3950 if (lp_res == isl_lp_error)
3951 goto error2;
3952 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3953 continue;
3954 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3955
3956 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3957 set->ctx->one, &max, NULL, NULL);
3958 if (lp_res == isl_lp_error)
3959 goto error2;
3960 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3961 continue;
3962 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3963
3964 isl_int_sub(max, max, min);
3965 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3966 isl_int_add(max, max, min);
3967 break;
3968 }
3969 }
3970
3971 if (i < qp->div->n_row) {
3972 r = split_div(set, qp, i, min, max, data);
3973 } else {
3974 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3975 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3976 }
3977
3978 isl_int_clear(max);
3979 isl_int_clear(min);
3980
3981 return r;
3982 error2:
3983 isl_int_clear(max);
3984 isl_int_clear(min);
3985 error:
3986 isl_set_free(set);
3987 isl_qpolynomial_free(qp);
3988 return -1;
3989 }
3990
3991 /* If any quasi-polynomial in pwqp refers to any integer division
3992 * that can only attain "max_periods" distinct values on its domain
3993 * then split the domain along those distinct values.
3994 */
3995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3996 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3997 {
3998 struct isl_split_periods_data data;
3999
4000 data.max_periods = max_periods;
4001 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4002
4003 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4004 goto error;
4005
4006 isl_pw_qpolynomial_free(pwqp);
4007
4008 return data.res;
4009 error:
4010 isl_pw_qpolynomial_free(data.res);
4011 isl_pw_qpolynomial_free(pwqp);
4012 return NULL;
4013 }
4014
4015 /* Construct a piecewise quasipolynomial that is constant on the given
4016 * domain. In particular, it is
4017 * 0 if cst == 0
4018 * 1 if cst == 1
4019 * infinity if cst == -1
4020 */
4021 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4022 __isl_take isl_basic_set *bset, int cst)
4023 {
4024 isl_dim *dim;
4025 isl_qpolynomial *qp;
4026
4027 if (!bset)
4028 return NULL;
4029
4030 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4031 dim = isl_basic_set_get_dim(bset);
4032 if (cst < 0)
4033 qp = isl_qpolynomial_infty(dim);
4034 else if (cst == 0)
4035 qp = isl_qpolynomial_zero(dim);
4036 else
4037 qp = isl_qpolynomial_one(dim);
4038 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4039 }
4040
4041 /* Factor bset, call fn on each of the factors and return the product.
4042 *
4043 * If no factors can be found, simply call fn on the input.
4044 * Otherwise, construct the factors based on the factorizer,
4045 * call fn on each factor and compute the product.
4046 */
4047 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4048 __isl_take isl_basic_set *bset,
4049 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4050 {
4051 int i, n;
4052 isl_dim *dim;
4053 isl_set *set;
4054 isl_factorizer *f;
4055 isl_qpolynomial *qp;
4056 isl_pw_qpolynomial *pwqp;
4057 unsigned nparam;
4058 unsigned nvar;
4059
4060 f = isl_basic_set_factorizer(bset);
4061 if (!f)
4062 goto error;
4063 if (f->n_group == 0) {
4064 isl_factorizer_free(f);
4065 return fn(bset);
4066 }
4067
4068 nparam = isl_basic_set_dim(bset, isl_dim_param);
4069 nvar = isl_basic_set_dim(bset, isl_dim_set);
4070
4071 dim = isl_basic_set_get_dim(bset);
4072 dim = isl_dim_domain(dim);
4073 set = isl_set_universe(isl_dim_copy(dim));
4074 qp = isl_qpolynomial_one(dim);
4075 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4076
4077 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4078
4079 for (i = 0, n = 0; i < f->n_group; ++i) {
4080 isl_basic_set *bset_i;
4081 isl_pw_qpolynomial *pwqp_i;
4082
4083 bset_i = isl_basic_set_copy(bset);
4084 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4085 nparam + n + f->len[i], nvar - n - f->len[i]);
4086 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4087 nparam, n);
4088 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4089 n + f->len[i], nvar - n - f->len[i]);
4090 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4091
4092 pwqp_i = fn(bset_i);
4093 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4094
4095 n += f->len[i];
4096 }
4097
4098 isl_basic_set_free(bset);
4099 isl_factorizer_free(f);
4100
4101 return pwqp;
4102 error:
4103 isl_basic_set_free(bset);
4104 return NULL;
4105 }
4106
4107 /* Factor bset, call fn on each of the factors and return the product.
4108 * The function is assumed to evaluate to zero on empty domains,
4109 * to one on zero-dimensional domains and to infinity on unbounded domains
4110 * and will not be called explicitly on zero-dimensional or unbounded domains.
4111 *
4112 * We first check for some special cases and remove all equalities.
4113 * Then we hand over control to compressed_multiplicative_call.
4114 */
4115 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4116 __isl_take isl_basic_set *bset,
4117 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4118 {
4119 int bounded;
4120 isl_morph *morph;
4121 isl_pw_qpolynomial *pwqp;
4122 unsigned orig_nvar, final_nvar;
4123
4124 if (!bset)
4125 return NULL;
4126
4127 if (isl_basic_set_fast_is_empty(bset))
4128 return constant_on_domain(bset, 0);
4129
4130 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4131
4132 if (orig_nvar == 0)
4133 return constant_on_domain(bset, 1);
4134
4135 bounded = isl_basic_set_is_bounded(bset);
4136 if (bounded < 0)
4137 goto error;
4138 if (!bounded)
4139 return constant_on_domain(bset, -1);
4140
4141 if (bset->n_eq == 0)
4142 return compressed_multiplicative_call(bset, fn);
4143
4144 morph = isl_basic_set_full_compression(bset);
4145 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4146
4147 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4148
4149 pwqp = compressed_multiplicative_call(bset, fn);
4150
4151 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4152 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4153 morph = isl_morph_inverse(morph);
4154
4155 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4156
4157 return pwqp;
4158 error:
4159 isl_basic_set_free(bset);
4160 return NULL;
4161 }
4162
4163 /* Drop all floors in "qp", turning each integer division [a/m] into
4164 * a rational division a/m. If "down" is set, then the integer division
4165 * is replaces by (a-(m-1))/m instead.
4166 */
4167 static __isl_give isl_qpolynomial *qp_drop_floors(
4168 __isl_take isl_qpolynomial *qp, int down)
4169 {
4170 int i;
4171 struct isl_upoly *s;
4172
4173 if (!qp)
4174 return NULL;
4175 if (qp->div->n_row == 0)
4176 return qp;
4177
4178 qp = isl_qpolynomial_cow(qp);
4179 if (!qp)
4180 return NULL;
4181
4182 for (i = qp->div->n_row - 1; i >= 0; --i) {
4183 if (down) {
4184 isl_int_sub(qp->div->row[i][1],
4185 qp->div->row[i][1], qp->div->row[i][0]);
4186 isl_int_add_ui(qp->div->row[i][1],
4187 qp->div->row[i][1], 1);
4188 }
4189 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4190 qp->div->row[i][0], qp->div->n_col - 1);
4191 qp = substitute_div(qp, i, s);
4192 if (!qp)
4193 return NULL;
4194 }
4195
4196 return qp;
4197 }
4198
4199 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4200 * a rational division a/m.
4201 */
4202 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4203 __isl_take isl_pw_qpolynomial *pwqp)
4204 {
4205 int i;
4206
4207 if (!pwqp)
4208 return NULL;
4209
4210 if (isl_pw_qpolynomial_is_zero(pwqp))
4211 return pwqp;
4212
4213 pwqp = isl_pw_qpolynomial_cow(pwqp);
4214 if (!pwqp)
4215 return NULL;
4216
4217 for (i = 0; i < pwqp->n; ++i) {
4218 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4219 if (!pwqp->p[i].qp)
4220 goto error;
4221 }
4222
4223 return pwqp;
4224 error:
4225 isl_pw_qpolynomial_free(pwqp);
4226 return NULL;
4227 }
4228
4229 /* Adjust all the integer divisions in "qp" such that they are at least
4230 * one over the given orthant (identified by "signs"). This ensures
4231 * that they will still be non-negative even after subtracting (m-1)/m.
4232 *
4233 * In particular, f is replaced by f' + v, changing f = [a/m]
4234 * to f' = [(a - m v)/m].
4235 * If the constant term k in a is smaller than m,
4236 * the constant term of v is set to floor(k/m) - 1.
4237 * For any other term, if the coefficient c and the variable x have
4238 * the same sign, then no changes are needed.
4239 * Otherwise, if the variable is positive (and c is negative),
4240 * then the coefficient of x in v is set to floor(c/m).
4241 * If the variable is negative (and c is positive),
4242 * then the coefficient of x in v is set to ceil(c/m).
4243 */
4244 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4245 int *signs)
4246 {
4247 int i, j;
4248 int total;
4249 isl_vec *v = NULL;
4250 struct isl_upoly *s;
4251
4252 qp = isl_qpolynomial_cow(qp);
4253 if (!qp)
4254 return NULL;
4255 qp->div = isl_mat_cow(qp->div);
4256 if (!qp->div)
4257 goto error;
4258
4259 total = isl_dim_total(qp->dim);
4260 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4261
4262 for (i = 0; i < qp->div->n_row; ++i) {
4263 isl_int *row = qp->div->row[i];
4264 v = isl_vec_clr(v);
4265 if (!v)
4266 goto error;
4267 if (isl_int_lt(row[1], row[0])) {
4268 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4269 isl_int_sub_ui(v->el[0], v->el[0], 1);
4270 isl_int_submul(row[1], row[0], v->el[0]);
4271 }
4272 for (j = 0; j < total; ++j) {
4273 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4274 continue;
4275 if (signs[j] < 0)
4276 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4277 else
4278 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4279 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4280 }
4281 for (j = 0; j < i; ++j) {
4282 if (isl_int_sgn(row[2 + total + j]) >= 0)
4283 continue;
4284 isl_int_fdiv_q(v->el[1 + total + j],
4285 row[2 + total + j], row[0]);
4286 isl_int_submul(row[2 + total + j],
4287 row[0], v->el[1 + total + j]);
4288 }
4289 for (j = i + 1; j < qp->div->n_row; ++j) {
4290 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4291 continue;
4292 isl_seq_combine(qp->div->row[j] + 1,
4293 qp->div->ctx->one, qp->div->row[j] + 1,
4294 qp->div->row[j][2 + total + i], v->el, v->size);
4295 }
4296 isl_int_set_si(v->el[1 + total + i], 1);
4297 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4298 qp->div->ctx->one, v->size);
4299 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4300 isl_upoly_free(s);
4301 if (!qp->upoly)
4302 goto error;
4303 }
4304
4305 isl_vec_free(v);
4306 return qp;
4307 error:
4308 isl_vec_free(v);
4309 isl_qpolynomial_free(qp);
4310 return NULL;
4311 }
4312
4313 struct isl_to_poly_data {
4314 int sign;
4315 isl_pw_qpolynomial *res;
4316 isl_qpolynomial *qp;
4317 };
4318
4319 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4320 * We first make all integer divisions positive and then split the
4321 * quasipolynomials into terms with sign data->sign (the direction
4322 * of the requested approximation) and terms with the opposite sign.
4323 * In the first set of terms, each integer division [a/m] is
4324 * overapproximated by a/m, while in the second it is underapproximated
4325 * by (a-(m-1))/m.
4326 */
4327 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4328 void *user)
4329 {
4330 struct isl_to_poly_data *data = user;
4331 isl_pw_qpolynomial *t;
4332 isl_qpolynomial *qp, *up, *down;
4333
4334 qp = isl_qpolynomial_copy(data->qp);
4335 qp = make_divs_pos(qp, signs);
4336
4337 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4338 up = qp_drop_floors(up, 0);
4339 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4340 down = qp_drop_floors(down, 1);
4341
4342 isl_qpolynomial_free(qp);
4343 qp = isl_qpolynomial_add(up, down);
4344
4345 t = isl_pw_qpolynomial_alloc(orthant, qp);
4346 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4347
4348 return 0;
4349 }
4350
4351 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4352 * the polynomial will be an overapproximation. If "sign" is negative,
4353 * it will be an underapproximation. If "sign" is zero, the approximation
4354 * will lie somewhere in between.
4355 *
4356 * In particular, is sign == 0, we simply drop the floors, turning
4357 * the integer divisions into rational divisions.
4358 * Otherwise, we split the domains into orthants, make all integer divisions
4359 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4360 * depending on the requested sign and the sign of the term in which
4361 * the integer division appears.
4362 */
4363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4364 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4365 {
4366 int i;
4367 struct isl_to_poly_data data;
4368
4369 if (sign == 0)
4370 return pwqp_drop_floors(pwqp);
4371
4372 if (!pwqp)
4373 return NULL;
4374
4375 data.sign = sign;
4376 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4377
4378 for (i = 0; i < pwqp->n; ++i) {
4379 if (pwqp->p[i].qp->div->n_row == 0) {
4380 isl_pw_qpolynomial *t;
4381 t = isl_pw_qpolynomial_alloc(
4382 isl_set_copy(pwqp->p[i].set),
4383 isl_qpolynomial_copy(pwqp->p[i].qp));
4384 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4385 continue;
4386 }
4387 data.qp = pwqp->p[i].qp;
4388 if (isl_set_foreach_orthant(pwqp->p[i].set,
4389 &to_polynomial_on_orthant, &data) < 0)
4390 goto error;
4391 }
4392
4393 isl_pw_qpolynomial_free(pwqp);
4394
4395 return data.res;
4396 error:
4397 isl_pw_qpolynomial_free(pwqp);
4398 isl_pw_qpolynomial_free(data.res);
4399 return NULL;
4400 }
4401
4402 static int poly_entry(void **entry, void *user)
4403 {
4404 int *sign = user;
4405 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4406
4407 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4408
4409 return *pwqp ? 0 : -1;
4410 }
4411
4412 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4413 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4414 {
4415 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4416 if (!upwqp)
4417 return NULL;
4418
4419 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4420 &poly_entry, &sign) < 0)
4421 goto error;
4422
4423 return upwqp;
4424 error:
4425 isl_union_pw_qpolynomial_free(upwqp);
4426 return NULL;
4427 }
Integer set library