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add isl_pw_qpolynomial_project_out
[isl.git] / isl_polynomial.c
blob1597a63eb631a31ec997753d56cd1a811d8e0f69
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #define ISL_DIM_H
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl/lp.h>
17 #include <isl/seq.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_div_private.h>
24 #include <isl_mat_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_config.h>
29
30 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
31 {
32 switch (type) {
33 case isl_dim_param: return 0;
34 case isl_dim_in: return dim->nparam;
35 case isl_dim_out: return dim->nparam + dim->n_in;
36 default: return 0;
37 }
38 }
39
40 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
41 {
42 if (!up)
43 return -1;
44
45 return up->var < 0;
46 }
47
48 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
49 {
50 if (!up)
51 return NULL;
52
53 isl_assert(up->ctx, up->var < 0, return NULL);
54
55 return (struct isl_upoly_cst *)up;
56 }
57
58 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
59 {
60 if (!up)
61 return NULL;
62
63 isl_assert(up->ctx, up->var >= 0, return NULL);
64
65 return (struct isl_upoly_rec *)up;
66 }
67
68 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
69 __isl_keep struct isl_upoly *up2)
70 {
71 int i;
72 struct isl_upoly_rec *rec1, *rec2;
73
74 if (!up1 || !up2)
75 return -1;
76 if (up1 == up2)
77 return 1;
78 if (up1->var != up2->var)
79 return 0;
80 if (isl_upoly_is_cst(up1)) {
81 struct isl_upoly_cst *cst1, *cst2;
82 cst1 = isl_upoly_as_cst(up1);
83 cst2 = isl_upoly_as_cst(up2);
84 if (!cst1 || !cst2)
85 return -1;
86 return isl_int_eq(cst1->n, cst2->n) &&
87 isl_int_eq(cst1->d, cst2->d);
88 }
89
90 rec1 = isl_upoly_as_rec(up1);
91 rec2 = isl_upoly_as_rec(up2);
92 if (!rec1 || !rec2)
93 return -1;
94
95 if (rec1->n != rec2->n)
96 return 0;
97
98 for (i = 0; i < rec1->n; ++i) {
99 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
100 if (eq < 0 || !eq)
101 return eq;
102 }
103
104 return 1;
105 }
106
107 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
108 {
109 struct isl_upoly_cst *cst;
110
111 if (!up)
112 return -1;
113 if (!isl_upoly_is_cst(up))
114 return 0;
115
116 cst = isl_upoly_as_cst(up);
117 if (!cst)
118 return -1;
119
120 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
121 }
122
123 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
124 {
125 struct isl_upoly_cst *cst;
126
127 if (!up)
128 return 0;
129 if (!isl_upoly_is_cst(up))
130 return 0;
131
132 cst = isl_upoly_as_cst(up);
133 if (!cst)
134 return 0;
135
136 return isl_int_sgn(cst->n);
137 }
138
139 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
140 {
141 struct isl_upoly_cst *cst;
142
143 if (!up)
144 return -1;
145 if (!isl_upoly_is_cst(up))
146 return 0;
147
148 cst = isl_upoly_as_cst(up);
149 if (!cst)
150 return -1;
151
152 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
153 }
154
155 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
156 {
157 struct isl_upoly_cst *cst;
158
159 if (!up)
160 return -1;
161 if (!isl_upoly_is_cst(up))
162 return 0;
163
164 cst = isl_upoly_as_cst(up);
165 if (!cst)
166 return -1;
167
168 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
169 }
170
171 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
172 {
173 struct isl_upoly_cst *cst;
174
175 if (!up)
176 return -1;
177 if (!isl_upoly_is_cst(up))
178 return 0;
179
180 cst = isl_upoly_as_cst(up);
181 if (!cst)
182 return -1;
183
184 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
185 }
186
187 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
188 {
189 struct isl_upoly_cst *cst;
190
191 if (!up)
192 return -1;
193 if (!isl_upoly_is_cst(up))
194 return 0;
195
196 cst = isl_upoly_as_cst(up);
197 if (!cst)
198 return -1;
199
200 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
201 }
202
203 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
204 {
205 struct isl_upoly_cst *cst;
206
207 if (!up)
208 return -1;
209 if (!isl_upoly_is_cst(up))
210 return 0;
211
212 cst = isl_upoly_as_cst(up);
213 if (!cst)
214 return -1;
215
216 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
217 }
218
219 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
220 {
221 struct isl_upoly_cst *cst;
222
223 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
224 if (!cst)
225 return NULL;
226
227 cst->up.ref = 1;
228 cst->up.ctx = ctx;
229 isl_ctx_ref(ctx);
230 cst->up.var = -1;
231
232 isl_int_init(cst->n);
233 isl_int_init(cst->d);
234
235 return cst;
236 }
237
238 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
239 {
240 struct isl_upoly_cst *cst;
241
242 cst = isl_upoly_cst_alloc(ctx);
243 if (!cst)
244 return NULL;
245
246 isl_int_set_si(cst->n, 0);
247 isl_int_set_si(cst->d, 1);
248
249 return &cst->up;
250 }
251
252 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
253 {
254 struct isl_upoly_cst *cst;
255
256 cst = isl_upoly_cst_alloc(ctx);
257 if (!cst)
258 return NULL;
259
260 isl_int_set_si(cst->n, 1);
261 isl_int_set_si(cst->d, 1);
262
263 return &cst->up;
264 }
265
266 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
267 {
268 struct isl_upoly_cst *cst;
269
270 cst = isl_upoly_cst_alloc(ctx);
271 if (!cst)
272 return NULL;
273
274 isl_int_set_si(cst->n, 1);
275 isl_int_set_si(cst->d, 0);
276
277 return &cst->up;
278 }
279
280 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
281 {
282 struct isl_upoly_cst *cst;
283
284 cst = isl_upoly_cst_alloc(ctx);
285 if (!cst)
286 return NULL;
287
288 isl_int_set_si(cst->n, -1);
289 isl_int_set_si(cst->d, 0);
290
291 return &cst->up;
292 }
293
294 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
295 {
296 struct isl_upoly_cst *cst;
297
298 cst = isl_upoly_cst_alloc(ctx);
299 if (!cst)
300 return NULL;
301
302 isl_int_set_si(cst->n, 0);
303 isl_int_set_si(cst->d, 0);
304
305 return &cst->up;
306 }
307
308 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
309 isl_int n, isl_int d)
310 {
311 struct isl_upoly_cst *cst;
312
313 cst = isl_upoly_cst_alloc(ctx);
314 if (!cst)
315 return NULL;
316
317 isl_int_set(cst->n, n);
318 isl_int_set(cst->d, d);
319
320 return &cst->up;
321 }
322
323 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
324 int var, int size)
325 {
326 struct isl_upoly_rec *rec;
327
328 isl_assert(ctx, var >= 0, return NULL);
329 isl_assert(ctx, size >= 0, return NULL);
330 rec = isl_calloc(ctx, struct isl_upoly_rec,
331 sizeof(struct isl_upoly_rec) +
332 size * sizeof(struct isl_upoly *));
333 if (!rec)
334 return NULL;
335
336 rec->up.ref = 1;
337 rec->up.ctx = ctx;
338 isl_ctx_ref(ctx);
339 rec->up.var = var;
340
341 rec->n = 0;
342 rec->size = size;
343
344 return rec;
345 }
346
347 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space(
348 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
349 {
350 qp = isl_qpolynomial_cow(qp);
351 if (!qp || !dim)
352 goto error;
353
354 isl_space_free(qp->dim);
355 qp->dim = dim;
356
357 return qp;
358 error:
359 isl_qpolynomial_free(qp);
360 isl_space_free(dim);
361 return NULL;
362 }
363
364 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
365 {
366 return qp ? qp->dim->ctx : NULL;
367 }
368
369 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
370 {
371 return qp ? isl_space_copy(qp->dim) : NULL;
372 }
373
374 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
375 enum isl_dim_type type)
376 {
377 return qp ? isl_space_dim(qp->dim, type) : 0;
378 }
379
380 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
381 {
382 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
383 }
384
385 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
386 {
387 return qp ? isl_upoly_is_one(qp->upoly) : -1;
388 }
389
390 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
391 {
392 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
393 }
394
395 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
396 {
397 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
398 }
399
400 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
401 {
402 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
403 }
404
405 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
406 {
407 return qp ? isl_upoly_sgn(qp->upoly) : 0;
408 }
409
410 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
411 {
412 isl_int_clear(cst->n);
413 isl_int_clear(cst->d);
414 }
415
416 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
417 {
418 int i;
419
420 for (i = 0; i < rec->n; ++i)
421 isl_upoly_free(rec->p[i]);
422 }
423
424 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
425 {
426 if (!up)
427 return NULL;
428
429 up->ref++;
430 return up;
431 }
432
433 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
434 {
435 struct isl_upoly_cst *cst;
436 struct isl_upoly_cst *dup;
437
438 cst = isl_upoly_as_cst(up);
439 if (!cst)
440 return NULL;
441
442 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
443 if (!dup)
444 return NULL;
445 isl_int_set(dup->n, cst->n);
446 isl_int_set(dup->d, cst->d);
447
448 return &dup->up;
449 }
450
451 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
452 {
453 int i;
454 struct isl_upoly_rec *rec;
455 struct isl_upoly_rec *dup;
456
457 rec = isl_upoly_as_rec(up);
458 if (!rec)
459 return NULL;
460
461 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
462 if (!dup)
463 return NULL;
464
465 for (i = 0; i < rec->n; ++i) {
466 dup->p[i] = isl_upoly_copy(rec->p[i]);
467 if (!dup->p[i])
468 goto error;
469 dup->n++;
470 }
471
472 return &dup->up;
473 error:
474 isl_upoly_free(&dup->up);
475 return NULL;
476 }
477
478 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
479 {
480 if (!up)
481 return NULL;
482
483 if (isl_upoly_is_cst(up))
484 return isl_upoly_dup_cst(up);
485 else
486 return isl_upoly_dup_rec(up);
487 }
488
489 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
490 {
491 if (!up)
492 return NULL;
493
494 if (up->ref == 1)
495 return up;
496 up->ref--;
497 return isl_upoly_dup(up);
498 }
499
500 void isl_upoly_free(__isl_take struct isl_upoly *up)
501 {
502 if (!up)
503 return;
504
505 if (--up->ref > 0)
506 return;
507
508 if (up->var < 0)
509 upoly_free_cst((struct isl_upoly_cst *)up);
510 else
511 upoly_free_rec((struct isl_upoly_rec *)up);
512
513 isl_ctx_deref(up->ctx);
514 free(up);
515 }
516
517 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
518 {
519 isl_int gcd;
520
521 isl_int_init(gcd);
522 isl_int_gcd(gcd, cst->n, cst->d);
523 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
524 isl_int_divexact(cst->n, cst->n, gcd);
525 isl_int_divexact(cst->d, cst->d, gcd);
526 }
527 isl_int_clear(gcd);
528 }
529
530 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
531 __isl_take struct isl_upoly *up2)
532 {
533 struct isl_upoly_cst *cst1;
534 struct isl_upoly_cst *cst2;
535
536 up1 = isl_upoly_cow(up1);
537 if (!up1 || !up2)
538 goto error;
539
540 cst1 = isl_upoly_as_cst(up1);
541 cst2 = isl_upoly_as_cst(up2);
542
543 if (isl_int_eq(cst1->d, cst2->d))
544 isl_int_add(cst1->n, cst1->n, cst2->n);
545 else {
546 isl_int_mul(cst1->n, cst1->n, cst2->d);
547 isl_int_addmul(cst1->n, cst2->n, cst1->d);
548 isl_int_mul(cst1->d, cst1->d, cst2->d);
549 }
550
551 isl_upoly_cst_reduce(cst1);
552
553 isl_upoly_free(up2);
554 return up1;
555 error:
556 isl_upoly_free(up1);
557 isl_upoly_free(up2);
558 return NULL;
559 }
560
561 static __isl_give struct isl_upoly *replace_by_zero(
562 __isl_take struct isl_upoly *up)
563 {
564 struct isl_ctx *ctx;
565
566 if (!up)
567 return NULL;
568 ctx = up->ctx;
569 isl_upoly_free(up);
570 return isl_upoly_zero(ctx);
571 }
572
573 static __isl_give struct isl_upoly *replace_by_constant_term(
574 __isl_take struct isl_upoly *up)
575 {
576 struct isl_upoly_rec *rec;
577 struct isl_upoly *cst;
578
579 if (!up)
580 return NULL;
581
582 rec = isl_upoly_as_rec(up);
583 if (!rec)
584 goto error;
585 cst = isl_upoly_copy(rec->p[0]);
586 isl_upoly_free(up);
587 return cst;
588 error:
589 isl_upoly_free(up);
590 return NULL;
591 }
592
593 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
594 __isl_take struct isl_upoly *up2)
595 {
596 int i;
597 struct isl_upoly_rec *rec1, *rec2;
598
599 if (!up1 || !up2)
600 goto error;
601
602 if (isl_upoly_is_nan(up1)) {
603 isl_upoly_free(up2);
604 return up1;
605 }
606
607 if (isl_upoly_is_nan(up2)) {
608 isl_upoly_free(up1);
609 return up2;
610 }
611
612 if (isl_upoly_is_zero(up1)) {
613 isl_upoly_free(up1);
614 return up2;
615 }
616
617 if (isl_upoly_is_zero(up2)) {
618 isl_upoly_free(up2);
619 return up1;
620 }
621
622 if (up1->var < up2->var)
623 return isl_upoly_sum(up2, up1);
624
625 if (up2->var < up1->var) {
626 struct isl_upoly_rec *rec;
627 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
628 isl_upoly_free(up1);
629 return up2;
630 }
631 up1 = isl_upoly_cow(up1);
632 rec = isl_upoly_as_rec(up1);
633 if (!rec)
634 goto error;
635 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
636 if (rec->n == 1)
637 up1 = replace_by_constant_term(up1);
638 return up1;
639 }
640
641 if (isl_upoly_is_cst(up1))
642 return isl_upoly_sum_cst(up1, up2);
643
644 rec1 = isl_upoly_as_rec(up1);
645 rec2 = isl_upoly_as_rec(up2);
646 if (!rec1 || !rec2)
647 goto error;
648
649 if (rec1->n < rec2->n)
650 return isl_upoly_sum(up2, up1);
651
652 up1 = isl_upoly_cow(up1);
653 rec1 = isl_upoly_as_rec(up1);
654 if (!rec1)
655 goto error;
656
657 for (i = rec2->n - 1; i >= 0; --i) {
658 rec1->p[i] = isl_upoly_sum(rec1->p[i],
659 isl_upoly_copy(rec2->p[i]));
660 if (!rec1->p[i])
661 goto error;
662 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
663 isl_upoly_free(rec1->p[i]);
664 rec1->n--;
665 }
666 }
667
668 if (rec1->n == 0)
669 up1 = replace_by_zero(up1);
670 else if (rec1->n == 1)
671 up1 = replace_by_constant_term(up1);
672
673 isl_upoly_free(up2);
674
675 return up1;
676 error:
677 isl_upoly_free(up1);
678 isl_upoly_free(up2);
679 return NULL;
680 }
681
682 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
683 __isl_take struct isl_upoly *up, isl_int v)
684 {
685 struct isl_upoly_cst *cst;
686
687 up = isl_upoly_cow(up);
688 if (!up)
689 return NULL;
690
691 cst = isl_upoly_as_cst(up);
692
693 isl_int_addmul(cst->n, cst->d, v);
694
695 return up;
696 }
697
698 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
699 __isl_take struct isl_upoly *up, isl_int v)
700 {
701 struct isl_upoly_rec *rec;
702
703 if (!up)
704 return NULL;
705
706 if (isl_upoly_is_cst(up))
707 return isl_upoly_cst_add_isl_int(up, v);
708
709 up = isl_upoly_cow(up);
710 rec = isl_upoly_as_rec(up);
711 if (!rec)
712 goto error;
713
714 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
715 if (!rec->p[0])
716 goto error;
717
718 return up;
719 error:
720 isl_upoly_free(up);
721 return NULL;
722 }
723
724 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
725 __isl_take struct isl_upoly *up, isl_int v)
726 {
727 struct isl_upoly_cst *cst;
728
729 if (isl_upoly_is_zero(up))
730 return up;
731
732 up = isl_upoly_cow(up);
733 if (!up)
734 return NULL;
735
736 cst = isl_upoly_as_cst(up);
737
738 isl_int_mul(cst->n, cst->n, v);
739
740 return up;
741 }
742
743 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
744 __isl_take struct isl_upoly *up, isl_int v)
745 {
746 int i;
747 struct isl_upoly_rec *rec;
748
749 if (!up)
750 return NULL;
751
752 if (isl_upoly_is_cst(up))
753 return isl_upoly_cst_mul_isl_int(up, v);
754
755 up = isl_upoly_cow(up);
756 rec = isl_upoly_as_rec(up);
757 if (!rec)
758 goto error;
759
760 for (i = 0; i < rec->n; ++i) {
761 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
762 if (!rec->p[i])
763 goto error;
764 }
765
766 return up;
767 error:
768 isl_upoly_free(up);
769 return NULL;
770 }
771
772 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
773 __isl_take struct isl_upoly *up2)
774 {
775 struct isl_upoly_cst *cst1;
776 struct isl_upoly_cst *cst2;
777
778 up1 = isl_upoly_cow(up1);
779 if (!up1 || !up2)
780 goto error;
781
782 cst1 = isl_upoly_as_cst(up1);
783 cst2 = isl_upoly_as_cst(up2);
784
785 isl_int_mul(cst1->n, cst1->n, cst2->n);
786 isl_int_mul(cst1->d, cst1->d, cst2->d);
787
788 isl_upoly_cst_reduce(cst1);
789
790 isl_upoly_free(up2);
791 return up1;
792 error:
793 isl_upoly_free(up1);
794 isl_upoly_free(up2);
795 return NULL;
796 }
797
798 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
799 __isl_take struct isl_upoly *up2)
800 {
801 struct isl_upoly_rec *rec1;
802 struct isl_upoly_rec *rec2;
803 struct isl_upoly_rec *res = NULL;
804 int i, j;
805 int size;
806
807 rec1 = isl_upoly_as_rec(up1);
808 rec2 = isl_upoly_as_rec(up2);
809 if (!rec1 || !rec2)
810 goto error;
811 size = rec1->n + rec2->n - 1;
812 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
813 if (!res)
814 goto error;
815
816 for (i = 0; i < rec1->n; ++i) {
817 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
818 isl_upoly_copy(rec1->p[i]));
819 if (!res->p[i])
820 goto error;
821 res->n++;
822 }
823 for (; i < size; ++i) {
824 res->p[i] = isl_upoly_zero(up1->ctx);
825 if (!res->p[i])
826 goto error;
827 res->n++;
828 }
829 for (i = 0; i < rec1->n; ++i) {
830 for (j = 1; j < rec2->n; ++j) {
831 struct isl_upoly *up;
832 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
833 isl_upoly_copy(rec1->p[i]));
834 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
835 if (!res->p[i + j])
836 goto error;
837 }
838 }
839
840 isl_upoly_free(up1);
841 isl_upoly_free(up2);
842
843 return &res->up;
844 error:
845 isl_upoly_free(up1);
846 isl_upoly_free(up2);
847 isl_upoly_free(&res->up);
848 return NULL;
849 }
850
851 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
852 __isl_take struct isl_upoly *up2)
853 {
854 if (!up1 || !up2)
855 goto error;
856
857 if (isl_upoly_is_nan(up1)) {
858 isl_upoly_free(up2);
859 return up1;
860 }
861
862 if (isl_upoly_is_nan(up2)) {
863 isl_upoly_free(up1);
864 return up2;
865 }
866
867 if (isl_upoly_is_zero(up1)) {
868 isl_upoly_free(up2);
869 return up1;
870 }
871
872 if (isl_upoly_is_zero(up2)) {
873 isl_upoly_free(up1);
874 return up2;
875 }
876
877 if (isl_upoly_is_one(up1)) {
878 isl_upoly_free(up1);
879 return up2;
880 }
881
882 if (isl_upoly_is_one(up2)) {
883 isl_upoly_free(up2);
884 return up1;
885 }
886
887 if (up1->var < up2->var)
888 return isl_upoly_mul(up2, up1);
889
890 if (up2->var < up1->var) {
891 int i;
892 struct isl_upoly_rec *rec;
893 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
894 isl_ctx *ctx = up1->ctx;
895 isl_upoly_free(up1);
896 isl_upoly_free(up2);
897 return isl_upoly_nan(ctx);
898 }
899 up1 = isl_upoly_cow(up1);
900 rec = isl_upoly_as_rec(up1);
901 if (!rec)
902 goto error;
903
904 for (i = 0; i < rec->n; ++i) {
905 rec->p[i] = isl_upoly_mul(rec->p[i],
906 isl_upoly_copy(up2));
907 if (!rec->p[i])
908 goto error;
909 }
910 isl_upoly_free(up2);
911 return up1;
912 }
913
914 if (isl_upoly_is_cst(up1))
915 return isl_upoly_mul_cst(up1, up2);
916
917 return isl_upoly_mul_rec(up1, up2);
918 error:
919 isl_upoly_free(up1);
920 isl_upoly_free(up2);
921 return NULL;
922 }
923
924 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
925 unsigned power)
926 {
927 struct isl_upoly *res;
928
929 if (!up)
930 return NULL;
931 if (power == 1)
932 return up;
933
934 if (power % 2)
935 res = isl_upoly_copy(up);
936 else
937 res = isl_upoly_one(up->ctx);
938
939 while (power >>= 1) {
940 up = isl_upoly_mul(up, isl_upoly_copy(up));
941 if (power % 2)
942 res = isl_upoly_mul(res, isl_upoly_copy(up));
943 }
944
945 isl_upoly_free(up);
946 return res;
947 }
948
949 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
950 unsigned n_div, __isl_take struct isl_upoly *up)
951 {
952 struct isl_qpolynomial *qp = NULL;
953 unsigned total;
954
955 if (!dim || !up)
956 goto error;
957
958 total = isl_space_dim(dim, isl_dim_all);
959
960 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
961 if (!qp)
962 goto error;
963
964 qp->ref = 1;
965 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
966 if (!qp->div)
967 goto error;
968
969 qp->dim = dim;
970 qp->upoly = up;
971
972 return qp;
973 error:
974 isl_space_free(dim);
975 isl_upoly_free(up);
976 isl_qpolynomial_free(qp);
977 return NULL;
978 }
979
980 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
981 {
982 if (!qp)
983 return NULL;
984
985 qp->ref++;
986 return qp;
987 }
988
989 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
990 {
991 struct isl_qpolynomial *dup;
992
993 if (!qp)
994 return NULL;
995
996 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
997 isl_upoly_copy(qp->upoly));
998 if (!dup)
999 return NULL;
1000 isl_mat_free(dup->div);
1001 dup->div = isl_mat_copy(qp->div);
1002 if (!dup->div)
1003 goto error;
1004
1005 return dup;
1006 error:
1007 isl_qpolynomial_free(dup);
1008 return NULL;
1009 }
1010
1011 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1012 {
1013 if (!qp)
1014 return NULL;
1015
1016 if (qp->ref == 1)
1017 return qp;
1018 qp->ref--;
1019 return isl_qpolynomial_dup(qp);
1020 }
1021
1022 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1023 {
1024 if (!qp)
1025 return NULL;
1026
1027 if (--qp->ref > 0)
1028 return NULL;
1029
1030 isl_space_free(qp->dim);
1031 isl_mat_free(qp->div);
1032 isl_upoly_free(qp->upoly);
1033
1034 free(qp);
1035 return NULL;
1036 }
1037
1038 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1039 {
1040 int i;
1041 struct isl_upoly_rec *rec;
1042 struct isl_upoly_cst *cst;
1043
1044 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1045 if (!rec)
1046 return NULL;
1047 for (i = 0; i < 1 + power; ++i) {
1048 rec->p[i] = isl_upoly_zero(ctx);
1049 if (!rec->p[i])
1050 goto error;
1051 rec->n++;
1052 }
1053 cst = isl_upoly_as_cst(rec->p[power]);
1054 isl_int_set_si(cst->n, 1);
1055
1056 return &rec->up;
1057 error:
1058 isl_upoly_free(&rec->up);
1059 return NULL;
1060 }
1061
1062 /* r array maps original positions to new positions.
1063 */
1064 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1065 int *r)
1066 {
1067 int i;
1068 struct isl_upoly_rec *rec;
1069 struct isl_upoly *base;
1070 struct isl_upoly *res;
1071
1072 if (isl_upoly_is_cst(up))
1073 return up;
1074
1075 rec = isl_upoly_as_rec(up);
1076 if (!rec)
1077 goto error;
1078
1079 isl_assert(up->ctx, rec->n >= 1, goto error);
1080
1081 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1082 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1083
1084 for (i = rec->n - 2; i >= 0; --i) {
1085 res = isl_upoly_mul(res, isl_upoly_copy(base));
1086 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1087 }
1088
1089 isl_upoly_free(base);
1090 isl_upoly_free(up);
1091
1092 return res;
1093 error:
1094 isl_upoly_free(up);
1095 return NULL;
1096 }
1097
1098 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1099 {
1100 int n_row, n_col;
1101 int equal;
1102
1103 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1104 div1->n_col >= div2->n_col, return -1);
1105
1106 if (div1->n_row == div2->n_row)
1107 return isl_mat_is_equal(div1, div2);
1108
1109 n_row = div1->n_row;
1110 n_col = div1->n_col;
1111 div1->n_row = div2->n_row;
1112 div1->n_col = div2->n_col;
1113
1114 equal = isl_mat_is_equal(div1, div2);
1115
1116 div1->n_row = n_row;
1117 div1->n_col = n_col;
1118
1119 return equal;
1120 }
1121
1122 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1123 {
1124 int li, lj;
1125
1126 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1127 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1128
1129 if (li != lj)
1130 return li - lj;
1131
1132 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1133 }
1134
1135 struct isl_div_sort_info {
1136 isl_mat *div;
1137 int row;
1138 };
1139
1140 static int div_sort_cmp(const void *p1, const void *p2)
1141 {
1142 const struct isl_div_sort_info *i1, *i2;
1143 i1 = (const struct isl_div_sort_info *) p1;
1144 i2 = (const struct isl_div_sort_info *) p2;
1145
1146 return cmp_row(i1->div, i1->row, i2->row);
1147 }
1148
1149 /* Sort divs and remove duplicates.
1150 */
1151 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1152 {
1153 int i;
1154 int skip;
1155 int len;
1156 struct isl_div_sort_info *array = NULL;
1157 int *pos = NULL, *at = NULL;
1158 int *reordering = NULL;
1159 unsigned div_pos;
1160
1161 if (!qp)
1162 return NULL;
1163 if (qp->div->n_row <= 1)
1164 return qp;
1165
1166 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1167
1168 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1169 qp->div->n_row);
1170 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1171 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1172 len = qp->div->n_col - 2;
1173 reordering = isl_alloc_array(qp->div->ctx, int, len);
1174 if (!array || !pos || !at || !reordering)
1175 goto error;
1176
1177 for (i = 0; i < qp->div->n_row; ++i) {
1178 array[i].div = qp->div;
1179 array[i].row = i;
1180 pos[i] = i;
1181 at[i] = i;
1182 }
1183
1184 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1185 div_sort_cmp);
1186
1187 for (i = 0; i < div_pos; ++i)
1188 reordering[i] = i;
1189
1190 for (i = 0; i < qp->div->n_row; ++i) {
1191 if (pos[array[i].row] == i)
1192 continue;
1193 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1194 pos[at[i]] = pos[array[i].row];
1195 at[pos[array[i].row]] = at[i];
1196 at[i] = array[i].row;
1197 pos[array[i].row] = i;
1198 }
1199
1200 skip = 0;
1201 for (i = 0; i < len - div_pos; ++i) {
1202 if (i > 0 &&
1203 isl_seq_eq(qp->div->row[i - skip - 1],
1204 qp->div->row[i - skip], qp->div->n_col)) {
1205 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1206 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1207 2 + div_pos + i - skip);
1208 qp->div = isl_mat_drop_cols(qp->div,
1209 2 + div_pos + i - skip, 1);
1210 skip++;
1211 }
1212 reordering[div_pos + array[i].row] = div_pos + i - skip;
1213 }
1214
1215 qp->upoly = reorder(qp->upoly, reordering);
1216
1217 if (!qp->upoly || !qp->div)
1218 goto error;
1219
1220 free(at);
1221 free(pos);
1222 free(array);
1223 free(reordering);
1224
1225 return qp;
1226 error:
1227 free(at);
1228 free(pos);
1229 free(array);
1230 free(reordering);
1231 isl_qpolynomial_free(qp);
1232 return NULL;
1233 }
1234
1235 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1236 int *exp, int first)
1237 {
1238 int i;
1239 struct isl_upoly_rec *rec;
1240
1241 if (isl_upoly_is_cst(up))
1242 return up;
1243
1244 if (up->var < first)
1245 return up;
1246
1247 if (exp[up->var - first] == up->var - first)
1248 return up;
1249
1250 up = isl_upoly_cow(up);
1251 if (!up)
1252 goto error;
1253
1254 up->var = exp[up->var - first] + first;
1255
1256 rec = isl_upoly_as_rec(up);
1257 if (!rec)
1258 goto error;
1259
1260 for (i = 0; i < rec->n; ++i) {
1261 rec->p[i] = expand(rec->p[i], exp, first);
1262 if (!rec->p[i])
1263 goto error;
1264 }
1265
1266 return up;
1267 error:
1268 isl_upoly_free(up);
1269 return NULL;
1270 }
1271
1272 static __isl_give isl_qpolynomial *with_merged_divs(
1273 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1274 __isl_take isl_qpolynomial *qp2),
1275 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1276 {
1277 int *exp1 = NULL;
1278 int *exp2 = NULL;
1279 isl_mat *div = NULL;
1280
1281 qp1 = isl_qpolynomial_cow(qp1);
1282 qp2 = isl_qpolynomial_cow(qp2);
1283
1284 if (!qp1 || !qp2)
1285 goto error;
1286
1287 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1288 qp1->div->n_col >= qp2->div->n_col, goto error);
1289
1290 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1291 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1292 if (!exp1 || !exp2)
1293 goto error;
1294
1295 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1296 if (!div)
1297 goto error;
1298
1299 isl_mat_free(qp1->div);
1300 qp1->div = isl_mat_copy(div);
1301 isl_mat_free(qp2->div);
1302 qp2->div = isl_mat_copy(div);
1303
1304 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1305 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1306
1307 if (!qp1->upoly || !qp2->upoly)
1308 goto error;
1309
1310 isl_mat_free(div);
1311 free(exp1);
1312 free(exp2);
1313
1314 return fn(qp1, qp2);
1315 error:
1316 isl_mat_free(div);
1317 free(exp1);
1318 free(exp2);
1319 isl_qpolynomial_free(qp1);
1320 isl_qpolynomial_free(qp2);
1321 return NULL;
1322 }
1323
1324 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1325 __isl_take isl_qpolynomial *qp2)
1326 {
1327 qp1 = isl_qpolynomial_cow(qp1);
1328
1329 if (!qp1 || !qp2)
1330 goto error;
1331
1332 if (qp1->div->n_row < qp2->div->n_row)
1333 return isl_qpolynomial_add(qp2, qp1);
1334
1335 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1336 if (!compatible_divs(qp1->div, qp2->div))
1337 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1338
1339 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1340 if (!qp1->upoly)
1341 goto error;
1342
1343 isl_qpolynomial_free(qp2);
1344
1345 return qp1;
1346 error:
1347 isl_qpolynomial_free(qp1);
1348 isl_qpolynomial_free(qp2);
1349 return NULL;
1350 }
1351
1352 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1353 __isl_keep isl_set *dom,
1354 __isl_take isl_qpolynomial *qp1,
1355 __isl_take isl_qpolynomial *qp2)
1356 {
1357 qp1 = isl_qpolynomial_add(qp1, qp2);
1358 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1359 return qp1;
1360 }
1361
1362 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1363 __isl_take isl_qpolynomial *qp2)
1364 {
1365 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1366 }
1367
1368 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1369 __isl_take isl_qpolynomial *qp, isl_int v)
1370 {
1371 if (isl_int_is_zero(v))
1372 return qp;
1373
1374 qp = isl_qpolynomial_cow(qp);
1375 if (!qp)
1376 return NULL;
1377
1378 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1379 if (!qp->upoly)
1380 goto error;
1381
1382 return qp;
1383 error:
1384 isl_qpolynomial_free(qp);
1385 return NULL;
1386
1387 }
1388
1389 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1390 {
1391 if (!qp)
1392 return NULL;
1393
1394 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1395 }
1396
1397 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1398 __isl_take isl_qpolynomial *qp, isl_int v)
1399 {
1400 if (isl_int_is_one(v))
1401 return qp;
1402
1403 if (qp && isl_int_is_zero(v)) {
1404 isl_qpolynomial *zero;
1405 zero = isl_qpolynomial_zero(isl_space_copy(qp->dim));
1406 isl_qpolynomial_free(qp);
1407 return zero;
1408 }
1409
1410 qp = isl_qpolynomial_cow(qp);
1411 if (!qp)
1412 return NULL;
1413
1414 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1415 if (!qp->upoly)
1416 goto error;
1417
1418 return qp;
1419 error:
1420 isl_qpolynomial_free(qp);
1421 return NULL;
1422 }
1423
1424 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1425 __isl_take isl_qpolynomial *qp, isl_int v)
1426 {
1427 return isl_qpolynomial_mul_isl_int(qp, v);
1428 }
1429
1430 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1431 __isl_take isl_qpolynomial *qp2)
1432 {
1433 qp1 = isl_qpolynomial_cow(qp1);
1434
1435 if (!qp1 || !qp2)
1436 goto error;
1437
1438 if (qp1->div->n_row < qp2->div->n_row)
1439 return isl_qpolynomial_mul(qp2, qp1);
1440
1441 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1442 if (!compatible_divs(qp1->div, qp2->div))
1443 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1444
1445 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1446 if (!qp1->upoly)
1447 goto error;
1448
1449 isl_qpolynomial_free(qp2);
1450
1451 return qp1;
1452 error:
1453 isl_qpolynomial_free(qp1);
1454 isl_qpolynomial_free(qp2);
1455 return NULL;
1456 }
1457
1458 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1459 unsigned power)
1460 {
1461 qp = isl_qpolynomial_cow(qp);
1462
1463 if (!qp)
1464 return NULL;
1465
1466 qp->upoly = isl_upoly_pow(qp->upoly, power);
1467 if (!qp->upoly)
1468 goto error;
1469
1470 return qp;
1471 error:
1472 isl_qpolynomial_free(qp);
1473 return NULL;
1474 }
1475
1476 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1477 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1478 {
1479 int i;
1480
1481 if (power == 1)
1482 return pwqp;
1483
1484 pwqp = isl_pw_qpolynomial_cow(pwqp);
1485 if (!pwqp)
1486 return NULL;
1487
1488 for (i = 0; i < pwqp->n; ++i) {
1489 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1490 if (!pwqp->p[i].qp)
1491 return isl_pw_qpolynomial_free(pwqp);
1492 }
1493
1494 return pwqp;
1495 }
1496
1497 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_space *dim)
1498 {
1499 if (!dim)
1500 return NULL;
1501 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1502 }
1503
1504 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_space *dim)
1505 {
1506 if (!dim)
1507 return NULL;
1508 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1509 }
1510
1511 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_space *dim)
1512 {
1513 if (!dim)
1514 return NULL;
1515 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1516 }
1517
1518 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_space *dim)
1519 {
1520 if (!dim)
1521 return NULL;
1522 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1523 }
1524
1525 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_space *dim)
1526 {
1527 if (!dim)
1528 return NULL;
1529 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1530 }
1531
1532 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_space *dim,
1533 isl_int v)
1534 {
1535 struct isl_qpolynomial *qp;
1536 struct isl_upoly_cst *cst;
1537
1538 if (!dim)
1539 return NULL;
1540
1541 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1542 if (!qp)
1543 return NULL;
1544
1545 cst = isl_upoly_as_cst(qp->upoly);
1546 isl_int_set(cst->n, v);
1547
1548 return qp;
1549 }
1550
1551 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1552 isl_int *n, isl_int *d)
1553 {
1554 struct isl_upoly_cst *cst;
1555
1556 if (!qp)
1557 return -1;
1558
1559 if (!isl_upoly_is_cst(qp->upoly))
1560 return 0;
1561
1562 cst = isl_upoly_as_cst(qp->upoly);
1563 if (!cst)
1564 return -1;
1565
1566 if (n)
1567 isl_int_set(*n, cst->n);
1568 if (d)
1569 isl_int_set(*d, cst->d);
1570
1571 return 1;
1572 }
1573
1574 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1575 {
1576 int is_cst;
1577 struct isl_upoly_rec *rec;
1578
1579 if (!up)
1580 return -1;
1581
1582 if (up->var < 0)
1583 return 1;
1584
1585 rec = isl_upoly_as_rec(up);
1586 if (!rec)
1587 return -1;
1588
1589 if (rec->n > 2)
1590 return 0;
1591
1592 isl_assert(up->ctx, rec->n > 1, return -1);
1593
1594 is_cst = isl_upoly_is_cst(rec->p[1]);
1595 if (is_cst < 0)
1596 return -1;
1597 if (!is_cst)
1598 return 0;
1599
1600 return isl_upoly_is_affine(rec->p[0]);
1601 }
1602
1603 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1604 {
1605 if (!qp)
1606 return -1;
1607
1608 if (qp->div->n_row > 0)
1609 return 0;
1610
1611 return isl_upoly_is_affine(qp->upoly);
1612 }
1613
1614 static void update_coeff(__isl_keep isl_vec *aff,
1615 __isl_keep struct isl_upoly_cst *cst, int pos)
1616 {
1617 isl_int gcd;
1618 isl_int f;
1619
1620 if (isl_int_is_zero(cst->n))
1621 return;
1622
1623 isl_int_init(gcd);
1624 isl_int_init(f);
1625 isl_int_gcd(gcd, cst->d, aff->el[0]);
1626 isl_int_divexact(f, cst->d, gcd);
1627 isl_int_divexact(gcd, aff->el[0], gcd);
1628 isl_seq_scale(aff->el, aff->el, f, aff->size);
1629 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1630 isl_int_clear(gcd);
1631 isl_int_clear(f);
1632 }
1633
1634 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1635 __isl_keep isl_vec *aff)
1636 {
1637 struct isl_upoly_cst *cst;
1638 struct isl_upoly_rec *rec;
1639
1640 if (!up || !aff)
1641 return -1;
1642
1643 if (up->var < 0) {
1644 struct isl_upoly_cst *cst;
1645
1646 cst = isl_upoly_as_cst(up);
1647 if (!cst)
1648 return -1;
1649 update_coeff(aff, cst, 0);
1650 return 0;
1651 }
1652
1653 rec = isl_upoly_as_rec(up);
1654 if (!rec)
1655 return -1;
1656 isl_assert(up->ctx, rec->n == 2, return -1);
1657
1658 cst = isl_upoly_as_cst(rec->p[1]);
1659 if (!cst)
1660 return -1;
1661 update_coeff(aff, cst, 1 + up->var);
1662
1663 return isl_upoly_update_affine(rec->p[0], aff);
1664 }
1665
1666 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1667 __isl_keep isl_qpolynomial *qp)
1668 {
1669 isl_vec *aff;
1670 unsigned d;
1671
1672 if (!qp)
1673 return NULL;
1674
1675 d = isl_space_dim(qp->dim, isl_dim_all);
1676 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1677 if (!aff)
1678 return NULL;
1679
1680 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1681 isl_int_set_si(aff->el[0], 1);
1682
1683 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1684 goto error;
1685
1686 return aff;
1687 error:
1688 isl_vec_free(aff);
1689 return NULL;
1690 }
1691
1692 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1693 __isl_keep isl_qpolynomial *qp2)
1694 {
1695 int equal;
1696
1697 if (!qp1 || !qp2)
1698 return -1;
1699
1700 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1701 if (equal < 0 || !equal)
1702 return equal;
1703
1704 equal = isl_mat_is_equal(qp1->div, qp2->div);
1705 if (equal < 0 || !equal)
1706 return equal;
1707
1708 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1709 }
1710
1711 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1712 {
1713 int i;
1714 struct isl_upoly_rec *rec;
1715
1716 if (isl_upoly_is_cst(up)) {
1717 struct isl_upoly_cst *cst;
1718 cst = isl_upoly_as_cst(up);
1719 if (!cst)
1720 return;
1721 isl_int_lcm(*d, *d, cst->d);
1722 return;
1723 }
1724
1725 rec = isl_upoly_as_rec(up);
1726 if (!rec)
1727 return;
1728
1729 for (i = 0; i < rec->n; ++i)
1730 upoly_update_den(rec->p[i], d);
1731 }
1732
1733 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1734 {
1735 isl_int_set_si(*d, 1);
1736 if (!qp)
1737 return;
1738 upoly_update_den(qp->upoly, d);
1739 }
1740
1741 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_space *dim,
1742 int pos, int power)
1743 {
1744 struct isl_ctx *ctx;
1745
1746 if (!dim)
1747 return NULL;
1748
1749 ctx = dim->ctx;
1750
1751 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1752 }
1753
1754 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_space *dim,
1755 enum isl_dim_type type, unsigned pos)
1756 {
1757 if (!dim)
1758 return NULL;
1759
1760 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1761 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1762
1763 if (type == isl_dim_set)
1764 pos += isl_space_dim(dim, isl_dim_param);
1765
1766 return isl_qpolynomial_var_pow(dim, pos, 1);
1767 error:
1768 isl_space_free(dim);
1769 return NULL;
1770 }
1771
1772 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1773 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1774 {
1775 int i;
1776 struct isl_upoly_rec *rec;
1777 struct isl_upoly *base, *res;
1778
1779 if (!up)
1780 return NULL;
1781
1782 if (isl_upoly_is_cst(up))
1783 return up;
1784
1785 if (up->var < first)
1786 return up;
1787
1788 rec = isl_upoly_as_rec(up);
1789 if (!rec)
1790 goto error;
1791
1792 isl_assert(up->ctx, rec->n >= 1, goto error);
1793
1794 if (up->var >= first + n)
1795 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1796 else
1797 base = isl_upoly_copy(subs[up->var - first]);
1798
1799 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1800 for (i = rec->n - 2; i >= 0; --i) {
1801 struct isl_upoly *t;
1802 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1803 res = isl_upoly_mul(res, isl_upoly_copy(base));
1804 res = isl_upoly_sum(res, t);
1805 }
1806
1807 isl_upoly_free(base);
1808 isl_upoly_free(up);
1809
1810 return res;
1811 error:
1812 isl_upoly_free(up);
1813 return NULL;
1814 }
1815
1816 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1817 isl_int denom, unsigned len)
1818 {
1819 int i;
1820 struct isl_upoly *up;
1821
1822 isl_assert(ctx, len >= 1, return NULL);
1823
1824 up = isl_upoly_rat_cst(ctx, f[0], denom);
1825 for (i = 0; i < len - 1; ++i) {
1826 struct isl_upoly *t;
1827 struct isl_upoly *c;
1828
1829 if (isl_int_is_zero(f[1 + i]))
1830 continue;
1831
1832 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1833 t = isl_upoly_var_pow(ctx, i, 1);
1834 t = isl_upoly_mul(c, t);
1835 up = isl_upoly_sum(up, t);
1836 }
1837
1838 return up;
1839 }
1840
1841 /* Remove common factor of non-constant terms and denominator.
1842 */
1843 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1844 {
1845 isl_ctx *ctx = qp->div->ctx;
1846 unsigned total = qp->div->n_col - 2;
1847
1848 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1849 isl_int_gcd(ctx->normalize_gcd,
1850 ctx->normalize_gcd, qp->div->row[div][0]);
1851 if (isl_int_is_one(ctx->normalize_gcd))
1852 return;
1853
1854 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1855 ctx->normalize_gcd, total);
1856 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1857 ctx->normalize_gcd);
1858 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1859 ctx->normalize_gcd);
1860 }
1861
1862 /* Replace the integer division identified by "div" by the polynomial "s".
1863 * The integer division is assumed not to appear in the definition
1864 * of any other integer divisions.
1865 */
1866 static __isl_give isl_qpolynomial *substitute_div(
1867 __isl_take isl_qpolynomial *qp,
1868 int div, __isl_take struct isl_upoly *s)
1869 {
1870 int i;
1871 int total;
1872 int *reordering;
1873
1874 if (!qp || !s)
1875 goto error;
1876
1877 qp = isl_qpolynomial_cow(qp);
1878 if (!qp)
1879 goto error;
1880
1881 total = isl_space_dim(qp->dim, isl_dim_all);
1882 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1883 if (!qp->upoly)
1884 goto error;
1885
1886 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1887 if (!reordering)
1888 goto error;
1889 for (i = 0; i < total + div; ++i)
1890 reordering[i] = i;
1891 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1892 reordering[i] = i - 1;
1893 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1894 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1895 qp->upoly = reorder(qp->upoly, reordering);
1896 free(reordering);
1897
1898 if (!qp->upoly || !qp->div)
1899 goto error;
1900
1901 isl_upoly_free(s);
1902 return qp;
1903 error:
1904 isl_qpolynomial_free(qp);
1905 isl_upoly_free(s);
1906 return NULL;
1907 }
1908
1909 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1910 * divisions because d is equal to 1 by their definition, i.e., e.
1911 */
1912 static __isl_give isl_qpolynomial *substitute_non_divs(
1913 __isl_take isl_qpolynomial *qp)
1914 {
1915 int i, j;
1916 int total;
1917 struct isl_upoly *s;
1918
1919 if (!qp)
1920 return NULL;
1921
1922 total = isl_space_dim(qp->dim, isl_dim_all);
1923 for (i = 0; qp && i < qp->div->n_row; ++i) {
1924 if (!isl_int_is_one(qp->div->row[i][0]))
1925 continue;
1926 for (j = i + 1; j < qp->div->n_row; ++j) {
1927 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1928 continue;
1929 isl_seq_combine(qp->div->row[j] + 1,
1930 qp->div->ctx->one, qp->div->row[j] + 1,
1931 qp->div->row[j][2 + total + i],
1932 qp->div->row[i] + 1, 1 + total + i);
1933 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1934 normalize_div(qp, j);
1935 }
1936 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1937 qp->div->row[i][0], qp->div->n_col - 1);
1938 qp = substitute_div(qp, i, s);
1939 --i;
1940 }
1941
1942 return qp;
1943 }
1944
1945 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1946 * with d the denominator. When replacing the coefficient e of x by
1947 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1948 * inside the division, so we need to add floor(e/d) * x outside.
1949 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1950 * to adjust the coefficient of x in each later div that depends on the
1951 * current div "div" and also in the affine expression "aff"
1952 * (if it too depends on "div").
1953 */
1954 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1955 __isl_keep isl_vec *aff)
1956 {
1957 int i, j;
1958 isl_int v;
1959 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1960
1961 isl_int_init(v);
1962 for (i = 0; i < 1 + total + div; ++i) {
1963 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1964 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1965 continue;
1966 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1967 isl_int_fdiv_r(qp->div->row[div][1 + i],
1968 qp->div->row[div][1 + i], qp->div->row[div][0]);
1969 if (!isl_int_is_zero(aff->el[1 + total + div]))
1970 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1971 for (j = div + 1; j < qp->div->n_row; ++j) {
1972 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1973 continue;
1974 isl_int_addmul(qp->div->row[j][1 + i],
1975 v, qp->div->row[j][2 + total + div]);
1976 }
1977 }
1978 isl_int_clear(v);
1979 }
1980
1981 /* Check if the last non-zero coefficient is bigger that half of the
1982 * denominator. If so, we will invert the div to further reduce the number
1983 * of distinct divs that may appear.
1984 * If the last non-zero coefficient is exactly half the denominator,
1985 * then we continue looking for earlier coefficients that are bigger
1986 * than half the denominator.
1987 */
1988 static int needs_invert(__isl_keep isl_mat *div, int row)
1989 {
1990 int i;
1991 int cmp;
1992
1993 for (i = div->n_col - 1; i >= 1; --i) {
1994 if (isl_int_is_zero(div->row[row][i]))
1995 continue;
1996 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1997 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1998 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1999 if (cmp)
2000 return cmp > 0;
2001 if (i == 1)
2002 return 1;
2003 }
2004
2005 return 0;
2006 }
2007
2008 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2009 * We only invert the coefficients of e (and the coefficient of q in
2010 * later divs and in "aff"). After calling this function, the
2011 * coefficients of e should be reduced again.
2012 */
2013 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2014 __isl_keep isl_vec *aff)
2015 {
2016 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2017
2018 isl_seq_neg(qp->div->row[div] + 1,
2019 qp->div->row[div] + 1, qp->div->n_col - 1);
2020 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2021 isl_int_add(qp->div->row[div][1],
2022 qp->div->row[div][1], qp->div->row[div][0]);
2023 if (!isl_int_is_zero(aff->el[1 + total + div]))
2024 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2025 isl_mat_col_mul(qp->div, 2 + total + div,
2026 qp->div->ctx->negone, 2 + total + div);
2027 }
2028
2029 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2030 * in the interval [0, d-1], with d the denominator and such that the
2031 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2032 *
2033 * After the reduction, some divs may have become redundant or identical,
2034 * so we call substitute_non_divs and sort_divs. If these functions
2035 * eliminate divs or merge two or more divs into one, the coefficients
2036 * of the enclosing divs may have to be reduced again, so we call
2037 * ourselves recursively if the number of divs decreases.
2038 */
2039 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2040 {
2041 int i;
2042 isl_vec *aff = NULL;
2043 struct isl_upoly *s;
2044 unsigned n_div;
2045
2046 if (!qp)
2047 return NULL;
2048
2049 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2050 aff = isl_vec_clr(aff);
2051 if (!aff)
2052 goto error;
2053
2054 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2055
2056 for (i = 0; i < qp->div->n_row; ++i) {
2057 normalize_div(qp, i);
2058 reduce_div(qp, i, aff);
2059 if (needs_invert(qp->div, i)) {
2060 invert_div(qp, i, aff);
2061 reduce_div(qp, i, aff);
2062 }
2063 }
2064
2065 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2066 qp->div->ctx->one, aff->size);
2067 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2068 isl_upoly_free(s);
2069 if (!qp->upoly)
2070 goto error;
2071
2072 isl_vec_free(aff);
2073
2074 n_div = qp->div->n_row;
2075 qp = substitute_non_divs(qp);
2076 qp = sort_divs(qp);
2077 if (qp && qp->div->n_row < n_div)
2078 return reduce_divs(qp);
2079
2080 return qp;
2081 error:
2082 isl_qpolynomial_free(qp);
2083 isl_vec_free(aff);
2084 return NULL;
2085 }
2086
2087 /* Assumes each div only depends on earlier divs.
2088 */
2089 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2090 int power)
2091 {
2092 struct isl_qpolynomial *qp = NULL;
2093 struct isl_upoly_rec *rec;
2094 struct isl_upoly_cst *cst;
2095 int i, d;
2096 int pos;
2097
2098 if (!div)
2099 return NULL;
2100
2101 d = div->line - div->bmap->div;
2102
2103 pos = isl_space_dim(div->bmap->dim, isl_dim_all) + d;
2104 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2105 qp = isl_qpolynomial_alloc(isl_basic_map_get_space(div->bmap),
2106 div->bmap->n_div, &rec->up);
2107 if (!qp)
2108 goto error;
2109
2110 for (i = 0; i < div->bmap->n_div; ++i)
2111 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2112
2113 for (i = 0; i < 1 + power; ++i) {
2114 rec->p[i] = isl_upoly_zero(div->ctx);
2115 if (!rec->p[i])
2116 goto error;
2117 rec->n++;
2118 }
2119 cst = isl_upoly_as_cst(rec->p[power]);
2120 isl_int_set_si(cst->n, 1);
2121
2122 isl_div_free(div);
2123
2124 qp = reduce_divs(qp);
2125
2126 return qp;
2127 error:
2128 isl_qpolynomial_free(qp);
2129 isl_div_free(div);
2130 return NULL;
2131 }
2132
2133 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2134 {
2135 return isl_qpolynomial_div_pow(div, 1);
2136 }
2137
2138 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_space *dim,
2139 const isl_int n, const isl_int d)
2140 {
2141 struct isl_qpolynomial *qp;
2142 struct isl_upoly_cst *cst;
2143
2144 if (!dim)
2145 return NULL;
2146
2147 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2148 if (!qp)
2149 return NULL;
2150
2151 cst = isl_upoly_as_cst(qp->upoly);
2152 isl_int_set(cst->n, n);
2153 isl_int_set(cst->d, d);
2154
2155 return qp;
2156 }
2157
2158 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2159 {
2160 struct isl_upoly_rec *rec;
2161 int i;
2162
2163 if (!up)
2164 return -1;
2165
2166 if (isl_upoly_is_cst(up))
2167 return 0;
2168
2169 if (up->var < d)
2170 active[up->var] = 1;
2171
2172 rec = isl_upoly_as_rec(up);
2173 for (i = 0; i < rec->n; ++i)
2174 if (up_set_active(rec->p[i], active, d) < 0)
2175 return -1;
2176
2177 return 0;
2178 }
2179
2180 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2181 {
2182 int i, j;
2183 int d = isl_space_dim(qp->dim, isl_dim_all);
2184
2185 if (!qp || !active)
2186 return -1;
2187
2188 for (i = 0; i < d; ++i)
2189 for (j = 0; j < qp->div->n_row; ++j) {
2190 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2191 continue;
2192 active[i] = 1;
2193 break;
2194 }
2195
2196 return up_set_active(qp->upoly, active, d);
2197 }
2198
2199 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2200 enum isl_dim_type type, unsigned first, unsigned n)
2201 {
2202 int i;
2203 int *active = NULL;
2204 int involves = 0;
2205
2206 if (!qp)
2207 return -1;
2208 if (n == 0)
2209 return 0;
2210
2211 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2212 return -1);
2213 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2214 type == isl_dim_set, return -1);
2215
2216 active = isl_calloc_array(qp->dim->ctx, int,
2217 isl_space_dim(qp->dim, isl_dim_all));
2218 if (set_active(qp, active) < 0)
2219 goto error;
2220
2221 if (type == isl_dim_set)
2222 first += isl_space_dim(qp->dim, isl_dim_param);
2223 for (i = 0; i < n; ++i)
2224 if (active[first + i]) {
2225 involves = 1;
2226 break;
2227 }
2228
2229 free(active);
2230
2231 return involves;
2232 error:
2233 free(active);
2234 return -1;
2235 }
2236
2237 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2238 * of the divs that do appear in the quasi-polynomial.
2239 */
2240 static __isl_give isl_qpolynomial *remove_redundant_divs(
2241 __isl_take isl_qpolynomial *qp)
2242 {
2243 int i, j;
2244 int d;
2245 int len;
2246 int skip;
2247 int *active = NULL;
2248 int *reordering = NULL;
2249 int redundant = 0;
2250 int n_div;
2251 isl_ctx *ctx;
2252
2253 if (!qp)
2254 return NULL;
2255 if (qp->div->n_row == 0)
2256 return qp;
2257
2258 d = isl_space_dim(qp->dim, isl_dim_all);
2259 len = qp->div->n_col - 2;
2260 ctx = isl_qpolynomial_get_ctx(qp);
2261 active = isl_calloc_array(ctx, int, len);
2262 if (!active)
2263 goto error;
2264
2265 if (up_set_active(qp->upoly, active, len) < 0)
2266 goto error;
2267
2268 for (i = qp->div->n_row - 1; i >= 0; --i) {
2269 if (!active[d + i]) {
2270 redundant = 1;
2271 continue;
2272 }
2273 for (j = 0; j < i; ++j) {
2274 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2275 continue;
2276 active[d + j] = 1;
2277 break;
2278 }
2279 }
2280
2281 if (!redundant) {
2282 free(active);
2283 return qp;
2284 }
2285
2286 reordering = isl_alloc_array(qp->div->ctx, int, len);
2287 if (!reordering)
2288 goto error;
2289
2290 for (i = 0; i < d; ++i)
2291 reordering[i] = i;
2292
2293 skip = 0;
2294 n_div = qp->div->n_row;
2295 for (i = 0; i < n_div; ++i) {
2296 if (!active[d + i]) {
2297 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2298 qp->div = isl_mat_drop_cols(qp->div,
2299 2 + d + i - skip, 1);
2300 skip++;
2301 }
2302 reordering[d + i] = d + i - skip;
2303 }
2304
2305 qp->upoly = reorder(qp->upoly, reordering);
2306
2307 if (!qp->upoly || !qp->div)
2308 goto error;
2309
2310 free(active);
2311 free(reordering);
2312
2313 return qp;
2314 error:
2315 free(active);
2316 free(reordering);
2317 isl_qpolynomial_free(qp);
2318 return NULL;
2319 }
2320
2321 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2322 unsigned first, unsigned n)
2323 {
2324 int i;
2325 struct isl_upoly_rec *rec;
2326
2327 if (!up)
2328 return NULL;
2329 if (n == 0 || up->var < 0 || up->var < first)
2330 return up;
2331 if (up->var < first + n) {
2332 up = replace_by_constant_term(up);
2333 return isl_upoly_drop(up, first, n);
2334 }
2335 up = isl_upoly_cow(up);
2336 if (!up)
2337 return NULL;
2338 up->var -= n;
2339 rec = isl_upoly_as_rec(up);
2340 if (!rec)
2341 goto error;
2342
2343 for (i = 0; i < rec->n; ++i) {
2344 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2345 if (!rec->p[i])
2346 goto error;
2347 }
2348
2349 return up;
2350 error:
2351 isl_upoly_free(up);
2352 return NULL;
2353 }
2354
2355 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2356 __isl_take isl_qpolynomial *qp,
2357 enum isl_dim_type type, unsigned pos, const char *s)
2358 {
2359 qp = isl_qpolynomial_cow(qp);
2360 if (!qp)
2361 return NULL;
2362 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2363 if (!qp->dim)
2364 goto error;
2365 return qp;
2366 error:
2367 isl_qpolynomial_free(qp);
2368 return NULL;
2369 }
2370
2371 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2372 __isl_take isl_qpolynomial *qp,
2373 enum isl_dim_type type, unsigned first, unsigned n)
2374 {
2375 if (!qp)
2376 return NULL;
2377 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2378 return qp;
2379
2380 qp = isl_qpolynomial_cow(qp);
2381 if (!qp)
2382 return NULL;
2383
2384 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2385 goto error);
2386 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2387 type == isl_dim_set, goto error);
2388
2389 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2390 if (!qp->dim)
2391 goto error;
2392
2393 if (type == isl_dim_set)
2394 first += isl_space_dim(qp->dim, isl_dim_param);
2395
2396 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2397 if (!qp->div)
2398 goto error;
2399
2400 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2401 if (!qp->upoly)
2402 goto error;
2403
2404 return qp;
2405 error:
2406 isl_qpolynomial_free(qp);
2407 return NULL;
2408 }
2409
2410 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2411 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2412 {
2413 int i, j, k;
2414 isl_int denom;
2415 unsigned total;
2416 unsigned n_div;
2417 struct isl_upoly *up;
2418
2419 if (!eq)
2420 goto error;
2421 if (eq->n_eq == 0) {
2422 isl_basic_set_free(eq);
2423 return qp;
2424 }
2425
2426 qp = isl_qpolynomial_cow(qp);
2427 if (!qp)
2428 goto error;
2429 qp->div = isl_mat_cow(qp->div);
2430 if (!qp->div)
2431 goto error;
2432
2433 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2434 n_div = eq->n_div;
2435 isl_int_init(denom);
2436 for (i = 0; i < eq->n_eq; ++i) {
2437 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2438 if (j < 0 || j == 0 || j >= total)
2439 continue;
2440
2441 for (k = 0; k < qp->div->n_row; ++k) {
2442 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2443 continue;
2444 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2445 &qp->div->row[k][0]);
2446 normalize_div(qp, k);
2447 }
2448
2449 if (isl_int_is_pos(eq->eq[i][j]))
2450 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2451 isl_int_abs(denom, eq->eq[i][j]);
2452 isl_int_set_si(eq->eq[i][j], 0);
2453
2454 up = isl_upoly_from_affine(qp->dim->ctx,
2455 eq->eq[i], denom, total);
2456 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2457 isl_upoly_free(up);
2458 }
2459 isl_int_clear(denom);
2460
2461 if (!qp->upoly)
2462 goto error;
2463
2464 isl_basic_set_free(eq);
2465
2466 qp = substitute_non_divs(qp);
2467 qp = sort_divs(qp);
2468
2469 return qp;
2470 error:
2471 isl_basic_set_free(eq);
2472 isl_qpolynomial_free(qp);
2473 return NULL;
2474 }
2475
2476 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2477 */
2478 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2479 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2480 {
2481 if (!qp || !eq)
2482 goto error;
2483 if (qp->div->n_row > 0)
2484 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2485 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2486 error:
2487 isl_basic_set_free(eq);
2488 isl_qpolynomial_free(qp);
2489 return NULL;
2490 }
2491
2492 static __isl_give isl_basic_set *add_div_constraints(
2493 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2494 {
2495 int i;
2496 unsigned total;
2497
2498 if (!bset || !div)
2499 goto error;
2500
2501 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2502 if (!bset)
2503 goto error;
2504 total = isl_basic_set_total_dim(bset);
2505 for (i = 0; i < div->n_row; ++i)
2506 if (isl_basic_set_add_div_constraints_var(bset,
2507 total - div->n_row + i, div->row[i]) < 0)
2508 goto error;
2509
2510 isl_mat_free(div);
2511 return bset;
2512 error:
2513 isl_mat_free(div);
2514 isl_basic_set_free(bset);
2515 return NULL;
2516 }
2517
2518 /* Look for equalities among the variables shared by context and qp
2519 * and the integer divisions of qp, if any.
2520 * The equalities are then used to eliminate variables and/or integer
2521 * divisions from qp.
2522 */
2523 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2524 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2525 {
2526 isl_basic_set *aff;
2527
2528 if (!qp)
2529 goto error;
2530 if (qp->div->n_row > 0) {
2531 isl_basic_set *bset;
2532 context = isl_set_add_dims(context, isl_dim_set,
2533 qp->div->n_row);
2534 bset = isl_basic_set_universe(isl_set_get_space(context));
2535 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2536 context = isl_set_intersect(context,
2537 isl_set_from_basic_set(bset));
2538 }
2539
2540 aff = isl_set_affine_hull(context);
2541 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2542 error:
2543 isl_qpolynomial_free(qp);
2544 isl_set_free(context);
2545 return NULL;
2546 }
2547
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2549 __isl_take isl_qpolynomial *qp)
2550 {
2551 isl_set *dom;
2552
2553 if (!qp)
2554 return NULL;
2555 if (isl_qpolynomial_is_zero(qp)) {
2556 isl_space *dim = isl_qpolynomial_get_space(qp);
2557 isl_qpolynomial_free(qp);
2558 return isl_pw_qpolynomial_zero(dim);
2559 }
2560
2561 dom = isl_set_universe(isl_qpolynomial_get_space(qp));
2562 return isl_pw_qpolynomial_alloc(dom, qp);
2563 }
2564
2565 #undef PW
2566 #define PW isl_pw_qpolynomial
2567 #undef EL
2568 #define EL isl_qpolynomial
2569 #undef EL_IS_ZERO
2570 #define EL_IS_ZERO is_zero
2571 #undef ZERO
2572 #define ZERO zero
2573 #undef IS_ZERO
2574 #define IS_ZERO is_zero
2575 #undef FIELD
2576 #define FIELD qp
2577
2578 #include <isl_pw_templ.c>
2579
2580 #undef UNION
2581 #define UNION isl_union_pw_qpolynomial
2582 #undef PART
2583 #define PART isl_pw_qpolynomial
2584 #undef PARTS
2585 #define PARTS pw_qpolynomial
2586
2587 #include <isl_union_templ.c>
2588
2589 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2590 {
2591 if (!pwqp)
2592 return -1;
2593
2594 if (pwqp->n != -1)
2595 return 0;
2596
2597 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2598 return 0;
2599
2600 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2601 }
2602
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2604 __isl_take isl_pw_qpolynomial *pwqp1,
2605 __isl_take isl_pw_qpolynomial *pwqp2)
2606 {
2607 int i, j, n;
2608 struct isl_pw_qpolynomial *res;
2609
2610 if (!pwqp1 || !pwqp2)
2611 goto error;
2612
2613 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2614 goto error);
2615
2616 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2617 isl_pw_qpolynomial_free(pwqp2);
2618 return pwqp1;
2619 }
2620
2621 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2622 isl_pw_qpolynomial_free(pwqp1);
2623 return pwqp2;
2624 }
2625
2626 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2627 isl_pw_qpolynomial_free(pwqp1);
2628 return pwqp2;
2629 }
2630
2631 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2632 isl_pw_qpolynomial_free(pwqp2);
2633 return pwqp1;
2634 }
2635
2636 n = pwqp1->n * pwqp2->n;
2637 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2638
2639 for (i = 0; i < pwqp1->n; ++i) {
2640 for (j = 0; j < pwqp2->n; ++j) {
2641 struct isl_set *common;
2642 struct isl_qpolynomial *prod;
2643 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2644 isl_set_copy(pwqp2->p[j].set));
2645 if (isl_set_plain_is_empty(common)) {
2646 isl_set_free(common);
2647 continue;
2648 }
2649
2650 prod = isl_qpolynomial_mul(
2651 isl_qpolynomial_copy(pwqp1->p[i].qp),
2652 isl_qpolynomial_copy(pwqp2->p[j].qp));
2653
2654 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2655 }
2656 }
2657
2658 isl_pw_qpolynomial_free(pwqp1);
2659 isl_pw_qpolynomial_free(pwqp2);
2660
2661 return res;
2662 error:
2663 isl_pw_qpolynomial_free(pwqp1);
2664 isl_pw_qpolynomial_free(pwqp2);
2665 return NULL;
2666 }
2667
2668 __isl_give struct isl_upoly *isl_upoly_eval(
2669 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2670 {
2671 int i;
2672 struct isl_upoly_rec *rec;
2673 struct isl_upoly *res;
2674 struct isl_upoly *base;
2675
2676 if (isl_upoly_is_cst(up)) {
2677 isl_vec_free(vec);
2678 return up;
2679 }
2680
2681 rec = isl_upoly_as_rec(up);
2682 if (!rec)
2683 goto error;
2684
2685 isl_assert(up->ctx, rec->n >= 1, goto error);
2686
2687 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2688
2689 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2690 isl_vec_copy(vec));
2691
2692 for (i = rec->n - 2; i >= 0; --i) {
2693 res = isl_upoly_mul(res, isl_upoly_copy(base));
2694 res = isl_upoly_sum(res,
2695 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2696 isl_vec_copy(vec)));
2697 }
2698
2699 isl_upoly_free(base);
2700 isl_upoly_free(up);
2701 isl_vec_free(vec);
2702 return res;
2703 error:
2704 isl_upoly_free(up);
2705 isl_vec_free(vec);
2706 return NULL;
2707 }
2708
2709 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2710 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2711 {
2712 isl_vec *ext;
2713 struct isl_upoly *up;
2714 isl_space *dim;
2715
2716 if (!qp || !pnt)
2717 goto error;
2718 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2719
2720 if (qp->div->n_row == 0)
2721 ext = isl_vec_copy(pnt->vec);
2722 else {
2723 int i;
2724 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2725 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2726 if (!ext)
2727 goto error;
2728
2729 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2730 for (i = 0; i < qp->div->n_row; ++i) {
2731 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2732 1 + dim + i, &ext->el[1+dim+i]);
2733 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2734 qp->div->row[i][0]);
2735 }
2736 }
2737
2738 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2739 if (!up)
2740 goto error;
2741
2742 dim = isl_space_copy(qp->dim);
2743 isl_qpolynomial_free(qp);
2744 isl_point_free(pnt);
2745
2746 return isl_qpolynomial_alloc(dim, 0, up);
2747 error:
2748 isl_qpolynomial_free(qp);
2749 isl_point_free(pnt);
2750 return NULL;
2751 }
2752
2753 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2754 __isl_keep struct isl_upoly_cst *cst2)
2755 {
2756 int cmp;
2757 isl_int t;
2758 isl_int_init(t);
2759 isl_int_mul(t, cst1->n, cst2->d);
2760 isl_int_submul(t, cst2->n, cst1->d);
2761 cmp = isl_int_sgn(t);
2762 isl_int_clear(t);
2763 return cmp;
2764 }
2765
2766 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2767 __isl_keep isl_qpolynomial *qp2)
2768 {
2769 struct isl_upoly_cst *cst1, *cst2;
2770
2771 if (!qp1 || !qp2)
2772 return -1;
2773 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2774 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2775 if (isl_qpolynomial_is_nan(qp1))
2776 return -1;
2777 if (isl_qpolynomial_is_nan(qp2))
2778 return -1;
2779 cst1 = isl_upoly_as_cst(qp1->upoly);
2780 cst2 = isl_upoly_as_cst(qp2->upoly);
2781
2782 return isl_upoly_cmp(cst1, cst2) <= 0;
2783 }
2784
2785 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2786 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2787 {
2788 struct isl_upoly_cst *cst1, *cst2;
2789 int cmp;
2790
2791 if (!qp1 || !qp2)
2792 goto error;
2793 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2794 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2795 cst1 = isl_upoly_as_cst(qp1->upoly);
2796 cst2 = isl_upoly_as_cst(qp2->upoly);
2797 cmp = isl_upoly_cmp(cst1, cst2);
2798
2799 if (cmp <= 0) {
2800 isl_qpolynomial_free(qp2);
2801 } else {
2802 isl_qpolynomial_free(qp1);
2803 qp1 = qp2;
2804 }
2805 return qp1;
2806 error:
2807 isl_qpolynomial_free(qp1);
2808 isl_qpolynomial_free(qp2);
2809 return NULL;
2810 }
2811
2812 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2813 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2814 {
2815 struct isl_upoly_cst *cst1, *cst2;
2816 int cmp;
2817
2818 if (!qp1 || !qp2)
2819 goto error;
2820 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2821 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2822 cst1 = isl_upoly_as_cst(qp1->upoly);
2823 cst2 = isl_upoly_as_cst(qp2->upoly);
2824 cmp = isl_upoly_cmp(cst1, cst2);
2825
2826 if (cmp >= 0) {
2827 isl_qpolynomial_free(qp2);
2828 } else {
2829 isl_qpolynomial_free(qp1);
2830 qp1 = qp2;
2831 }
2832 return qp1;
2833 error:
2834 isl_qpolynomial_free(qp1);
2835 isl_qpolynomial_free(qp2);
2836 return NULL;
2837 }
2838
2839 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2840 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2841 unsigned first, unsigned n)
2842 {
2843 unsigned total;
2844 unsigned g_pos;
2845 int *exp;
2846
2847 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2848 return qp;
2849
2850 qp = isl_qpolynomial_cow(qp);
2851 if (!qp)
2852 return NULL;
2853
2854 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2855 goto error);
2856
2857 g_pos = pos(qp->dim, type) + first;
2858
2859 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2860 if (!qp->div)
2861 goto error;
2862
2863 total = qp->div->n_col - 2;
2864 if (total > g_pos) {
2865 int i;
2866 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2867 if (!exp)
2868 goto error;
2869 for (i = 0; i < total - g_pos; ++i)
2870 exp[i] = i + n;
2871 qp->upoly = expand(qp->upoly, exp, g_pos);
2872 free(exp);
2873 if (!qp->upoly)
2874 goto error;
2875 }
2876
2877 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2878 if (!qp->dim)
2879 goto error;
2880
2881 return qp;
2882 error:
2883 isl_qpolynomial_free(qp);
2884 return NULL;
2885 }
2886
2887 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2888 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2889 {
2890 unsigned pos;
2891
2892 pos = isl_qpolynomial_dim(qp, type);
2893
2894 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2895 }
2896
2897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2898 __isl_take isl_pw_qpolynomial *pwqp,
2899 enum isl_dim_type type, unsigned n)
2900 {
2901 unsigned pos;
2902
2903 pos = isl_pw_qpolynomial_dim(pwqp, type);
2904
2905 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2906 }
2907
2908 static int *reordering_move(isl_ctx *ctx,
2909 unsigned len, unsigned dst, unsigned src, unsigned n)
2910 {
2911 int i;
2912 int *reordering;
2913
2914 reordering = isl_alloc_array(ctx, int, len);
2915 if (!reordering)
2916 return NULL;
2917
2918 if (dst <= src) {
2919 for (i = 0; i < dst; ++i)
2920 reordering[i] = i;
2921 for (i = 0; i < n; ++i)
2922 reordering[src + i] = dst + i;
2923 for (i = 0; i < src - dst; ++i)
2924 reordering[dst + i] = dst + n + i;
2925 for (i = 0; i < len - src - n; ++i)
2926 reordering[src + n + i] = src + n + i;
2927 } else {
2928 for (i = 0; i < src; ++i)
2929 reordering[i] = i;
2930 for (i = 0; i < n; ++i)
2931 reordering[src + i] = dst + i;
2932 for (i = 0; i < dst - src; ++i)
2933 reordering[src + n + i] = src + i;
2934 for (i = 0; i < len - dst - n; ++i)
2935 reordering[dst + n + i] = dst + n + i;
2936 }
2937
2938 return reordering;
2939 }
2940
2941 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2942 __isl_take isl_qpolynomial *qp,
2943 enum isl_dim_type dst_type, unsigned dst_pos,
2944 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2945 {
2946 unsigned g_dst_pos;
2947 unsigned g_src_pos;
2948 int *reordering;
2949
2950 qp = isl_qpolynomial_cow(qp);
2951 if (!qp)
2952 return NULL;
2953
2954 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
2955 goto error);
2956
2957 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2958 g_src_pos = pos(qp->dim, src_type) + src_pos;
2959 if (dst_type > src_type)
2960 g_dst_pos -= n;
2961
2962 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2963 if (!qp->div)
2964 goto error;
2965 qp = sort_divs(qp);
2966 if (!qp)
2967 goto error;
2968
2969 reordering = reordering_move(qp->dim->ctx,
2970 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2971 if (!reordering)
2972 goto error;
2973
2974 qp->upoly = reorder(qp->upoly, reordering);
2975 free(reordering);
2976 if (!qp->upoly)
2977 goto error;
2978
2979 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2980 if (!qp->dim)
2981 goto error;
2982
2983 return qp;
2984 error:
2985 isl_qpolynomial_free(qp);
2986 return NULL;
2987 }
2988
2989 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
2990 isl_int *f, isl_int denom)
2991 {
2992 struct isl_upoly *up;
2993
2994 if (!dim)
2995 return NULL;
2996
2997 up = isl_upoly_from_affine(dim->ctx, f, denom,
2998 1 + isl_space_dim(dim, isl_dim_all));
2999
3000 return isl_qpolynomial_alloc(dim, 0, up);
3001 }
3002
3003 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3004 {
3005 isl_ctx *ctx;
3006 struct isl_upoly *up;
3007 isl_qpolynomial *qp;
3008
3009 if (!aff)
3010 return NULL;
3011
3012 ctx = isl_aff_get_ctx(aff);
3013 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3014 aff->v->size - 1);
3015
3016 qp = isl_qpolynomial_alloc(isl_aff_get_space(aff),
3017 aff->ls->div->n_row, up);
3018 if (!qp)
3019 goto error;
3020
3021 isl_mat_free(qp->div);
3022 qp->div = isl_mat_copy(aff->ls->div);
3023 qp->div = isl_mat_cow(qp->div);
3024 if (!qp->div)
3025 goto error;
3026
3027 isl_aff_free(aff);
3028 qp = reduce_divs(qp);
3029 qp = remove_redundant_divs(qp);
3030 return qp;
3031 error:
3032 isl_aff_free(aff);
3033 return NULL;
3034 }
3035
3036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3037 __isl_take isl_pw_aff *pwaff)
3038 {
3039 int i;
3040 isl_pw_qpolynomial *pwqp;
3041
3042 if (!pwaff)
3043 return NULL;
3044
3045 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3046 pwaff->n);
3047
3048 for (i = 0; i < pwaff->n; ++i) {
3049 isl_set *dom;
3050 isl_qpolynomial *qp;
3051
3052 dom = isl_set_copy(pwaff->p[i].set);
3053 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3054 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3055 }
3056
3057 isl_pw_aff_free(pwaff);
3058 return pwqp;
3059 }
3060
3061 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3062 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3063 {
3064 isl_aff *aff;
3065
3066 aff = isl_constraint_get_bound(c, type, pos);
3067 isl_constraint_free(c);
3068 return isl_qpolynomial_from_aff(aff);
3069 }
3070
3071 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3072 * in "qp" by subs[i].
3073 */
3074 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3075 __isl_take isl_qpolynomial *qp,
3076 enum isl_dim_type type, unsigned first, unsigned n,
3077 __isl_keep isl_qpolynomial **subs)
3078 {
3079 int i;
3080 struct isl_upoly **ups;
3081
3082 if (n == 0)
3083 return qp;
3084
3085 qp = isl_qpolynomial_cow(qp);
3086 if (!qp)
3087 return NULL;
3088 for (i = 0; i < n; ++i)
3089 if (!subs[i])
3090 goto error;
3091
3092 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3093 goto error);
3094
3095 for (i = 0; i < n; ++i)
3096 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3097 goto error);
3098
3099 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3100 for (i = 0; i < n; ++i)
3101 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3102
3103 first += pos(qp->dim, type);
3104
3105 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3106 if (!ups)
3107 goto error;
3108 for (i = 0; i < n; ++i)
3109 ups[i] = subs[i]->upoly;
3110
3111 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3112
3113 free(ups);
3114
3115 if (!qp->upoly)
3116 goto error;
3117
3118 return qp;
3119 error:
3120 isl_qpolynomial_free(qp);
3121 return NULL;
3122 }
3123
3124 /* Extend "bset" with extra set dimensions for each integer division
3125 * in "qp" and then call "fn" with the extended bset and the polynomial
3126 * that results from replacing each of the integer divisions by the
3127 * corresponding extra set dimension.
3128 */
3129 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3130 __isl_keep isl_basic_set *bset,
3131 int (*fn)(__isl_take isl_basic_set *bset,
3132 __isl_take isl_qpolynomial *poly, void *user), void *user)
3133 {
3134 isl_space *dim;
3135 isl_mat *div;
3136 isl_qpolynomial *poly;
3137
3138 if (!qp || !bset)
3139 goto error;
3140 if (qp->div->n_row == 0)
3141 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3142 user);
3143
3144 div = isl_mat_copy(qp->div);
3145 dim = isl_space_copy(qp->dim);
3146 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3147 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3148 bset = isl_basic_set_copy(bset);
3149 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3150 bset = add_div_constraints(bset, div);
3151
3152 return fn(bset, poly, user);
3153 error:
3154 return -1;
3155 }
3156
3157 /* Return total degree in variables first (inclusive) up to last (exclusive).
3158 */
3159 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3160 {
3161 int deg = -1;
3162 int i;
3163 struct isl_upoly_rec *rec;
3164
3165 if (!up)
3166 return -2;
3167 if (isl_upoly_is_zero(up))
3168 return -1;
3169 if (isl_upoly_is_cst(up) || up->var < first)
3170 return 0;
3171
3172 rec = isl_upoly_as_rec(up);
3173 if (!rec)
3174 return -2;
3175
3176 for (i = 0; i < rec->n; ++i) {
3177 int d;
3178
3179 if (isl_upoly_is_zero(rec->p[i]))
3180 continue;
3181 d = isl_upoly_degree(rec->p[i], first, last);
3182 if (up->var < last)
3183 d += i;
3184 if (d > deg)
3185 deg = d;
3186 }
3187
3188 return deg;
3189 }
3190
3191 /* Return total degree in set variables.
3192 */
3193 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3194 {
3195 unsigned ovar;
3196 unsigned nvar;
3197
3198 if (!poly)
3199 return -2;
3200
3201 ovar = isl_space_offset(poly->dim, isl_dim_set);
3202 nvar = isl_space_dim(poly->dim, isl_dim_set);
3203 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3204 }
3205
3206 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3207 unsigned pos, int deg)
3208 {
3209 int i;
3210 struct isl_upoly_rec *rec;
3211
3212 if (!up)
3213 return NULL;
3214
3215 if (isl_upoly_is_cst(up) || up->var < pos) {
3216 if (deg == 0)
3217 return isl_upoly_copy(up);
3218 else
3219 return isl_upoly_zero(up->ctx);
3220 }
3221
3222 rec = isl_upoly_as_rec(up);
3223 if (!rec)
3224 return NULL;
3225
3226 if (up->var == pos) {
3227 if (deg < rec->n)
3228 return isl_upoly_copy(rec->p[deg]);
3229 else
3230 return isl_upoly_zero(up->ctx);
3231 }
3232
3233 up = isl_upoly_copy(up);
3234 up = isl_upoly_cow(up);
3235 rec = isl_upoly_as_rec(up);
3236 if (!rec)
3237 goto error;
3238
3239 for (i = 0; i < rec->n; ++i) {
3240 struct isl_upoly *t;
3241 t = isl_upoly_coeff(rec->p[i], pos, deg);
3242 if (!t)
3243 goto error;
3244 isl_upoly_free(rec->p[i]);
3245 rec->p[i] = t;
3246 }
3247
3248 return up;
3249 error:
3250 isl_upoly_free(up);
3251 return NULL;
3252 }
3253
3254 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3255 */
3256 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3257 __isl_keep isl_qpolynomial *qp,
3258 enum isl_dim_type type, unsigned t_pos, int deg)
3259 {
3260 unsigned g_pos;
3261 struct isl_upoly *up;
3262 isl_qpolynomial *c;
3263
3264 if (!qp)
3265 return NULL;
3266
3267 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3268 return NULL);
3269
3270 g_pos = pos(qp->dim, type) + t_pos;
3271 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3272
3273 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3274 if (!c)
3275 return NULL;
3276 isl_mat_free(c->div);
3277 c->div = isl_mat_copy(qp->div);
3278 if (!c->div)
3279 goto error;
3280 return c;
3281 error:
3282 isl_qpolynomial_free(c);
3283 return NULL;
3284 }
3285
3286 /* Homogenize the polynomial in the variables first (inclusive) up to
3287 * last (exclusive) by inserting powers of variable first.
3288 * Variable first is assumed not to appear in the input.
3289 */
3290 __isl_give struct isl_upoly *isl_upoly_homogenize(
3291 __isl_take struct isl_upoly *up, int deg, int target,
3292 int first, int last)
3293 {
3294 int i;
3295 struct isl_upoly_rec *rec;
3296
3297 if (!up)
3298 return NULL;
3299 if (isl_upoly_is_zero(up))
3300 return up;
3301 if (deg == target)
3302 return up;
3303 if (isl_upoly_is_cst(up) || up->var < first) {
3304 struct isl_upoly *hom;
3305
3306 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3307 if (!hom)
3308 goto error;
3309 rec = isl_upoly_as_rec(hom);
3310 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3311
3312 return hom;
3313 }
3314
3315 up = isl_upoly_cow(up);
3316 rec = isl_upoly_as_rec(up);
3317 if (!rec)
3318 goto error;
3319
3320 for (i = 0; i < rec->n; ++i) {
3321 if (isl_upoly_is_zero(rec->p[i]))
3322 continue;
3323 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3324 up->var < last ? deg + i : i, target,
3325 first, last);
3326 if (!rec->p[i])
3327 goto error;
3328 }
3329
3330 return up;
3331 error:
3332 isl_upoly_free(up);
3333 return NULL;
3334 }
3335
3336 /* Homogenize the polynomial in the set variables by introducing
3337 * powers of an extra set variable at position 0.
3338 */
3339 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3340 __isl_take isl_qpolynomial *poly)
3341 {
3342 unsigned ovar;
3343 unsigned nvar;
3344 int deg = isl_qpolynomial_degree(poly);
3345
3346 if (deg < -1)
3347 goto error;
3348
3349 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3350 poly = isl_qpolynomial_cow(poly);
3351 if (!poly)
3352 goto error;
3353
3354 ovar = isl_space_offset(poly->dim, isl_dim_set);
3355 nvar = isl_space_dim(poly->dim, isl_dim_set);
3356 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3357 ovar, ovar + nvar);
3358 if (!poly->upoly)
3359 goto error;
3360
3361 return poly;
3362 error:
3363 isl_qpolynomial_free(poly);
3364 return NULL;
3365 }
3366
3367 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3368 __isl_take isl_mat *div)
3369 {
3370 isl_term *term;
3371 int n;
3372
3373 if (!dim || !div)
3374 goto error;
3375
3376 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3377
3378 term = isl_calloc(dim->ctx, struct isl_term,
3379 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3380 if (!term)
3381 goto error;
3382
3383 term->ref = 1;
3384 term->dim = dim;
3385 term->div = div;
3386 isl_int_init(term->n);
3387 isl_int_init(term->d);
3388
3389 return term;
3390 error:
3391 isl_space_free(dim);
3392 isl_mat_free(div);
3393 return NULL;
3394 }
3395
3396 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3397 {
3398 if (!term)
3399 return NULL;
3400
3401 term->ref++;
3402 return term;
3403 }
3404
3405 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3406 {
3407 int i;
3408 isl_term *dup;
3409 unsigned total;
3410
3411 if (term)
3412 return NULL;
3413
3414 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3415
3416 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3417 if (!dup)
3418 return NULL;
3419
3420 isl_int_set(dup->n, term->n);
3421 isl_int_set(dup->d, term->d);
3422
3423 for (i = 0; i < total; ++i)
3424 dup->pow[i] = term->pow[i];
3425
3426 return dup;
3427 }
3428
3429 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3430 {
3431 if (!term)
3432 return NULL;
3433
3434 if (term->ref == 1)
3435 return term;
3436 term->ref--;
3437 return isl_term_dup(term);
3438 }
3439
3440 void isl_term_free(__isl_take isl_term *term)
3441 {
3442 if (!term)
3443 return;
3444
3445 if (--term->ref > 0)
3446 return;
3447
3448 isl_space_free(term->dim);
3449 isl_mat_free(term->div);
3450 isl_int_clear(term->n);
3451 isl_int_clear(term->d);
3452 free(term);
3453 }
3454
3455 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3456 {
3457 if (!term)
3458 return 0;
3459
3460 switch (type) {
3461 case isl_dim_param:
3462 case isl_dim_in:
3463 case isl_dim_out: return isl_space_dim(term->dim, type);
3464 case isl_dim_div: return term->div->n_row;
3465 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3466 term->div->n_row;
3467 default: return 0;
3468 }
3469 }
3470
3471 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3472 {
3473 return term ? term->dim->ctx : NULL;
3474 }
3475
3476 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3477 {
3478 if (!term)
3479 return;
3480 isl_int_set(*n, term->n);
3481 }
3482
3483 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3484 {
3485 if (!term)
3486 return;
3487 isl_int_set(*d, term->d);
3488 }
3489
3490 int isl_term_get_exp(__isl_keep isl_term *term,
3491 enum isl_dim_type type, unsigned pos)
3492 {
3493 if (!term)
3494 return -1;
3495
3496 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3497
3498 if (type >= isl_dim_set)
3499 pos += isl_space_dim(term->dim, isl_dim_param);
3500 if (type >= isl_dim_div)
3501 pos += isl_space_dim(term->dim, isl_dim_set);
3502
3503 return term->pow[pos];
3504 }
3505
3506 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3507 {
3508 isl_basic_map *bmap;
3509 unsigned total;
3510 int k;
3511
3512 if (!term)
3513 return NULL;
3514
3515 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3516 return NULL);
3517
3518 total = term->div->n_col - term->div->n_row - 2;
3519 /* No nested divs for now */
3520 isl_assert(term->dim->ctx,
3521 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3522 term->div->n_row) == -1,
3523 return NULL);
3524
3525 bmap = isl_basic_map_alloc_space(isl_space_copy(term->dim), 1, 0, 0);
3526 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3527 goto error;
3528
3529 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3530
3531 return isl_basic_map_div(bmap, k);
3532 error:
3533 isl_basic_map_free(bmap);
3534 return NULL;
3535 }
3536
3537 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3538 int (*fn)(__isl_take isl_term *term, void *user),
3539 __isl_take isl_term *term, void *user)
3540 {
3541 int i;
3542 struct isl_upoly_rec *rec;
3543
3544 if (!up || !term)
3545 goto error;
3546
3547 if (isl_upoly_is_zero(up))
3548 return term;
3549
3550 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3551 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3552 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3553
3554 if (isl_upoly_is_cst(up)) {
3555 struct isl_upoly_cst *cst;
3556 cst = isl_upoly_as_cst(up);
3557 if (!cst)
3558 goto error;
3559 term = isl_term_cow(term);
3560 if (!term)
3561 goto error;
3562 isl_int_set(term->n, cst->n);
3563 isl_int_set(term->d, cst->d);
3564 if (fn(isl_term_copy(term), user) < 0)
3565 goto error;
3566 return term;
3567 }
3568
3569 rec = isl_upoly_as_rec(up);
3570 if (!rec)
3571 goto error;
3572
3573 for (i = 0; i < rec->n; ++i) {
3574 term = isl_term_cow(term);
3575 if (!term)
3576 goto error;
3577 term->pow[up->var] = i;
3578 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3579 if (!term)
3580 goto error;
3581 }
3582 term->pow[up->var] = 0;
3583
3584 return term;
3585 error:
3586 isl_term_free(term);
3587 return NULL;
3588 }
3589
3590 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3591 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3592 {
3593 isl_term *term;
3594
3595 if (!qp)
3596 return -1;
3597
3598 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3599 if (!term)
3600 return -1;
3601
3602 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3603
3604 isl_term_free(term);
3605
3606 return term ? 0 : -1;
3607 }
3608
3609 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3610 {
3611 struct isl_upoly *up;
3612 isl_qpolynomial *qp;
3613 int i, n;
3614
3615 if (!term)
3616 return NULL;
3617
3618 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3619
3620 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3621 for (i = 0; i < n; ++i) {
3622 if (!term->pow[i])
3623 continue;
3624 up = isl_upoly_mul(up,
3625 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3626 }
3627
3628 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3629 if (!qp)
3630 goto error;
3631 isl_mat_free(qp->div);
3632 qp->div = isl_mat_copy(term->div);
3633 if (!qp->div)
3634 goto error;
3635
3636 isl_term_free(term);
3637 return qp;
3638 error:
3639 isl_qpolynomial_free(qp);
3640 isl_term_free(term);
3641 return NULL;
3642 }
3643
3644 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3645 __isl_take isl_space *dim)
3646 {
3647 int i;
3648 int extra;
3649 unsigned total;
3650
3651 if (!qp || !dim)
3652 goto error;
3653
3654 if (isl_space_is_equal(qp->dim, dim)) {
3655 isl_space_free(dim);
3656 return qp;
3657 }
3658
3659 qp = isl_qpolynomial_cow(qp);
3660 if (!qp)
3661 goto error;
3662
3663 extra = isl_space_dim(dim, isl_dim_set) -
3664 isl_space_dim(qp->dim, isl_dim_set);
3665 total = isl_space_dim(qp->dim, isl_dim_all);
3666 if (qp->div->n_row) {
3667 int *exp;
3668
3669 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3670 if (!exp)
3671 goto error;
3672 for (i = 0; i < qp->div->n_row; ++i)
3673 exp[i] = extra + i;
3674 qp->upoly = expand(qp->upoly, exp, total);
3675 free(exp);
3676 if (!qp->upoly)
3677 goto error;
3678 }
3679 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3680 if (!qp->div)
3681 goto error;
3682 for (i = 0; i < qp->div->n_row; ++i)
3683 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3684
3685 isl_space_free(qp->dim);
3686 qp->dim = dim;
3687
3688 return qp;
3689 error:
3690 isl_space_free(dim);
3691 isl_qpolynomial_free(qp);
3692 return NULL;
3693 }
3694
3695 /* For each parameter or variable that does not appear in qp,
3696 * first eliminate the variable from all constraints and then set it to zero.
3697 */
3698 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3699 __isl_keep isl_qpolynomial *qp)
3700 {
3701 int *active = NULL;
3702 int i;
3703 int d;
3704 unsigned nparam;
3705 unsigned nvar;
3706
3707 if (!set || !qp)
3708 goto error;
3709
3710 d = isl_space_dim(set->dim, isl_dim_all);
3711 active = isl_calloc_array(set->ctx, int, d);
3712 if (set_active(qp, active) < 0)
3713 goto error;
3714
3715 for (i = 0; i < d; ++i)
3716 if (!active[i])
3717 break;
3718
3719 if (i == d) {
3720 free(active);
3721 return set;
3722 }
3723
3724 nparam = isl_space_dim(set->dim, isl_dim_param);
3725 nvar = isl_space_dim(set->dim, isl_dim_set);
3726 for (i = 0; i < nparam; ++i) {
3727 if (active[i])
3728 continue;
3729 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3730 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3731 }
3732 for (i = 0; i < nvar; ++i) {
3733 if (active[nparam + i])
3734 continue;
3735 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3736 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3737 }
3738
3739 free(active);
3740
3741 return set;
3742 error:
3743 free(active);
3744 isl_set_free(set);
3745 return NULL;
3746 }
3747
3748 struct isl_opt_data {
3749 isl_qpolynomial *qp;
3750 int first;
3751 isl_qpolynomial *opt;
3752 int max;
3753 };
3754
3755 static int opt_fn(__isl_take isl_point *pnt, void *user)
3756 {
3757 struct isl_opt_data *data = (struct isl_opt_data *)user;
3758 isl_qpolynomial *val;
3759
3760 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3761 if (data->first) {
3762 data->first = 0;
3763 data->opt = val;
3764 } else if (data->max) {
3765 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3766 } else {
3767 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3768 }
3769
3770 return 0;
3771 }
3772
3773 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3774 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3775 {
3776 struct isl_opt_data data = { NULL, 1, NULL, max };
3777
3778 if (!set || !qp)
3779 goto error;
3780
3781 if (isl_upoly_is_cst(qp->upoly)) {
3782 isl_set_free(set);
3783 return qp;
3784 }
3785
3786 set = fix_inactive(set, qp);
3787
3788 data.qp = qp;
3789 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3790 goto error;
3791
3792 if (data.first)
3793 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_space(qp));
3794
3795 isl_set_free(set);
3796 isl_qpolynomial_free(qp);
3797 return data.opt;
3798 error:
3799 isl_set_free(set);
3800 isl_qpolynomial_free(qp);
3801 isl_qpolynomial_free(data.opt);
3802 return NULL;
3803 }
3804
3805 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3806 __isl_take isl_morph *morph)
3807 {
3808 int i;
3809 int n_sub;
3810 isl_ctx *ctx;
3811 struct isl_upoly **subs;
3812 isl_mat *mat;
3813
3814 qp = isl_qpolynomial_cow(qp);
3815 if (!qp || !morph)
3816 goto error;
3817
3818 ctx = qp->dim->ctx;
3819 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3820
3821 n_sub = morph->inv->n_row - 1;
3822 if (morph->inv->n_row != morph->inv->n_col)
3823 n_sub += qp->div->n_row;
3824 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3825 if (!subs)
3826 goto error;
3827
3828 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3829 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3830 morph->inv->row[0][0], morph->inv->n_col);
3831 if (morph->inv->n_row != morph->inv->n_col)
3832 for (i = 0; i < qp->div->n_row; ++i)
3833 subs[morph->inv->n_row - 1 + i] =
3834 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3835
3836 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3837
3838 for (i = 0; i < n_sub; ++i)
3839 isl_upoly_free(subs[i]);
3840 free(subs);
3841
3842 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3843 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3844 qp->div = isl_mat_product(qp->div, mat);
3845 isl_space_free(qp->dim);
3846 qp->dim = isl_space_copy(morph->ran->dim);
3847
3848 if (!qp->upoly || !qp->div || !qp->dim)
3849 goto error;
3850
3851 isl_morph_free(morph);
3852
3853 return qp;
3854 error:
3855 isl_qpolynomial_free(qp);
3856 isl_morph_free(morph);
3857 return NULL;
3858 }
3859
3860 static int neg_entry(void **entry, void *user)
3861 {
3862 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3863
3864 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3865
3866 return *pwqp ? 0 : -1;
3867 }
3868
3869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3870 __isl_take isl_union_pw_qpolynomial *upwqp)
3871 {
3872 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3873 if (!upwqp)
3874 return NULL;
3875
3876 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3877 &neg_entry, NULL) < 0)
3878 goto error;
3879
3880 return upwqp;
3881 error:
3882 isl_union_pw_qpolynomial_free(upwqp);
3883 return NULL;
3884 }
3885
3886 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3887 __isl_take isl_union_pw_qpolynomial *upwqp1,
3888 __isl_take isl_union_pw_qpolynomial *upwqp2)
3889 {
3890 return isl_union_pw_qpolynomial_add(upwqp1,
3891 isl_union_pw_qpolynomial_neg(upwqp2));
3892 }
3893
3894 static int mul_entry(void **entry, void *user)
3895 {
3896 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3897 uint32_t hash;
3898 struct isl_hash_table_entry *entry2;
3899 isl_pw_qpolynomial *pwpq = *entry;
3900 int empty;
3901
3902 hash = isl_space_get_hash(pwpq->dim);
3903 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3904 hash, &has_dim, pwpq->dim, 0);
3905 if (!entry2)
3906 return 0;
3907
3908 pwpq = isl_pw_qpolynomial_copy(pwpq);
3909 pwpq = isl_pw_qpolynomial_mul(pwpq,
3910 isl_pw_qpolynomial_copy(entry2->data));
3911
3912 empty = isl_pw_qpolynomial_is_zero(pwpq);
3913 if (empty < 0) {
3914 isl_pw_qpolynomial_free(pwpq);
3915 return -1;
3916 }
3917 if (empty) {
3918 isl_pw_qpolynomial_free(pwpq);
3919 return 0;
3920 }
3921
3922 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3923
3924 return 0;
3925 }
3926
3927 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3928 __isl_take isl_union_pw_qpolynomial *upwqp1,
3929 __isl_take isl_union_pw_qpolynomial *upwqp2)
3930 {
3931 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3932 }
3933
3934 /* Reorder the columns of the given div definitions according to the
3935 * given reordering.
3936 */
3937 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3938 __isl_take isl_reordering *r)
3939 {
3940 int i, j;
3941 isl_mat *mat;
3942 int extra;
3943
3944 if (!div || !r)
3945 goto error;
3946
3947 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
3948 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3949 if (!mat)
3950 goto error;
3951
3952 for (i = 0; i < div->n_row; ++i) {
3953 isl_seq_cpy(mat->row[i], div->row[i], 2);
3954 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3955 for (j = 0; j < r->len; ++j)
3956 isl_int_set(mat->row[i][2 + r->pos[j]],
3957 div->row[i][2 + j]);
3958 }
3959
3960 isl_reordering_free(r);
3961 isl_mat_free(div);
3962 return mat;
3963 error:
3964 isl_reordering_free(r);
3965 isl_mat_free(div);
3966 return NULL;
3967 }
3968
3969 /* Reorder the dimension of "qp" according to the given reordering.
3970 */
3971 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3972 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3973 {
3974 qp = isl_qpolynomial_cow(qp);
3975 if (!qp)
3976 goto error;
3977
3978 r = isl_reordering_extend(r, qp->div->n_row);
3979 if (!r)
3980 goto error;
3981
3982 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3983 if (!qp->div)
3984 goto error;
3985
3986 qp->upoly = reorder(qp->upoly, r->pos);
3987 if (!qp->upoly)
3988 goto error;
3989
3990 qp = isl_qpolynomial_reset_space(qp, isl_space_copy(r->dim));
3991
3992 isl_reordering_free(r);
3993 return qp;
3994 error:
3995 isl_qpolynomial_free(qp);
3996 isl_reordering_free(r);
3997 return NULL;
3998 }
3999
4000 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4001 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4002 {
4003 if (!qp || !model)
4004 goto error;
4005
4006 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4007 isl_reordering *exp;
4008
4009 model = isl_space_drop_dims(model, isl_dim_in,
4010 0, isl_space_dim(model, isl_dim_in));
4011 model = isl_space_drop_dims(model, isl_dim_out,
4012 0, isl_space_dim(model, isl_dim_out));
4013 exp = isl_parameter_alignment_reordering(qp->dim, model);
4014 exp = isl_reordering_extend_space(exp,
4015 isl_qpolynomial_get_space(qp));
4016 qp = isl_qpolynomial_realign(qp, exp);
4017 }
4018
4019 isl_space_free(model);
4020 return qp;
4021 error:
4022 isl_space_free(model);
4023 isl_qpolynomial_free(qp);
4024 return NULL;
4025 }
4026
4027 struct isl_split_periods_data {
4028 int max_periods;
4029 isl_pw_qpolynomial *res;
4030 };
4031
4032 /* Create a slice where the integer division "div" has the fixed value "v".
4033 * In particular, if "div" refers to floor(f/m), then create a slice
4034 *
4035 * m v <= f <= m v + (m - 1)
4036 *
4037 * or
4038 *
4039 * f - m v >= 0
4040 * -f + m v + (m - 1) >= 0
4041 */
4042 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4043 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4044 {
4045 int total;
4046 isl_basic_set *bset = NULL;
4047 int k;
4048
4049 if (!dim || !qp)
4050 goto error;
4051
4052 total = isl_space_dim(dim, isl_dim_all);
4053 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4054
4055 k = isl_basic_set_alloc_inequality(bset);
4056 if (k < 0)
4057 goto error;
4058 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4059 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4060
4061 k = isl_basic_set_alloc_inequality(bset);
4062 if (k < 0)
4063 goto error;
4064 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4065 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4066 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4067 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4068
4069 isl_space_free(dim);
4070 return isl_set_from_basic_set(bset);
4071 error:
4072 isl_basic_set_free(bset);
4073 isl_space_free(dim);
4074 return NULL;
4075 }
4076
4077 static int split_periods(__isl_take isl_set *set,
4078 __isl_take isl_qpolynomial *qp, void *user);
4079
4080 /* Create a slice of the domain "set" such that integer division "div"
4081 * has the fixed value "v" and add the results to data->res,
4082 * replacing the integer division by "v" in "qp".
4083 */
4084 static int set_div(__isl_take isl_set *set,
4085 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4086 struct isl_split_periods_data *data)
4087 {
4088 int i;
4089 int total;
4090 isl_set *slice;
4091 struct isl_upoly *cst;
4092
4093 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4094 set = isl_set_intersect(set, slice);
4095
4096 if (!qp)
4097 goto error;
4098
4099 total = isl_space_dim(qp->dim, isl_dim_all);
4100
4101 for (i = div + 1; i < qp->div->n_row; ++i) {
4102 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4103 continue;
4104 isl_int_addmul(qp->div->row[i][1],
4105 qp->div->row[i][2 + total + div], v);
4106 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4107 }
4108
4109 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4110 qp = substitute_div(qp, div, cst);
4111
4112 return split_periods(set, qp, data);
4113 error:
4114 isl_set_free(set);
4115 isl_qpolynomial_free(qp);
4116 return -1;
4117 }
4118
4119 /* Split the domain "set" such that integer division "div"
4120 * has a fixed value (ranging from "min" to "max") on each slice
4121 * and add the results to data->res.
4122 */
4123 static int split_div(__isl_take isl_set *set,
4124 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4125 struct isl_split_periods_data *data)
4126 {
4127 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4128 isl_set *set_i = isl_set_copy(set);
4129 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4130
4131 if (set_div(set_i, qp_i, div, min, data) < 0)
4132 goto error;
4133 }
4134 isl_set_free(set);
4135 isl_qpolynomial_free(qp);
4136 return 0;
4137 error:
4138 isl_set_free(set);
4139 isl_qpolynomial_free(qp);
4140 return -1;
4141 }
4142
4143 /* If "qp" refers to any integer division
4144 * that can only attain "max_periods" distinct values on "set"
4145 * then split the domain along those distinct values.
4146 * Add the results (or the original if no splitting occurs)
4147 * to data->res.
4148 */
4149 static int split_periods(__isl_take isl_set *set,
4150 __isl_take isl_qpolynomial *qp, void *user)
4151 {
4152 int i;
4153 isl_pw_qpolynomial *pwqp;
4154 struct isl_split_periods_data *data;
4155 isl_int min, max;
4156 int total;
4157 int r = 0;
4158
4159 data = (struct isl_split_periods_data *)user;
4160
4161 if (!set || !qp)
4162 goto error;
4163
4164 if (qp->div->n_row == 0) {
4165 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4166 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4167 return 0;
4168 }
4169
4170 isl_int_init(min);
4171 isl_int_init(max);
4172 total = isl_space_dim(qp->dim, isl_dim_all);
4173 for (i = 0; i < qp->div->n_row; ++i) {
4174 enum isl_lp_result lp_res;
4175
4176 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4177 qp->div->n_row) != -1)
4178 continue;
4179
4180 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4181 set->ctx->one, &min, NULL, NULL);
4182 if (lp_res == isl_lp_error)
4183 goto error2;
4184 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4185 continue;
4186 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4187
4188 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4189 set->ctx->one, &max, NULL, NULL);
4190 if (lp_res == isl_lp_error)
4191 goto error2;
4192 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4193 continue;
4194 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4195
4196 isl_int_sub(max, max, min);
4197 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4198 isl_int_add(max, max, min);
4199 break;
4200 }
4201 }
4202
4203 if (i < qp->div->n_row) {
4204 r = split_div(set, qp, i, min, max, data);
4205 } else {
4206 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4207 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4208 }
4209
4210 isl_int_clear(max);
4211 isl_int_clear(min);
4212
4213 return r;
4214 error2:
4215 isl_int_clear(max);
4216 isl_int_clear(min);
4217 error:
4218 isl_set_free(set);
4219 isl_qpolynomial_free(qp);
4220 return -1;
4221 }
4222
4223 /* If any quasi-polynomial in pwqp refers to any integer division
4224 * that can only attain "max_periods" distinct values on its domain
4225 * then split the domain along those distinct values.
4226 */
4227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4228 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4229 {
4230 struct isl_split_periods_data data;
4231
4232 data.max_periods = max_periods;
4233 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4234
4235 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4236 goto error;
4237
4238 isl_pw_qpolynomial_free(pwqp);
4239
4240 return data.res;
4241 error:
4242 isl_pw_qpolynomial_free(data.res);
4243 isl_pw_qpolynomial_free(pwqp);
4244 return NULL;
4245 }
4246
4247 /* Construct a piecewise quasipolynomial that is constant on the given
4248 * domain. In particular, it is
4249 * 0 if cst == 0
4250 * 1 if cst == 1
4251 * infinity if cst == -1
4252 */
4253 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4254 __isl_take isl_basic_set *bset, int cst)
4255 {
4256 isl_space *dim;
4257 isl_qpolynomial *qp;
4258
4259 if (!bset)
4260 return NULL;
4261
4262 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4263 dim = isl_basic_set_get_space(bset);
4264 if (cst < 0)
4265 qp = isl_qpolynomial_infty(dim);
4266 else if (cst == 0)
4267 qp = isl_qpolynomial_zero(dim);
4268 else
4269 qp = isl_qpolynomial_one(dim);
4270 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4271 }
4272
4273 /* Factor bset, call fn on each of the factors and return the product.
4274 *
4275 * If no factors can be found, simply call fn on the input.
4276 * Otherwise, construct the factors based on the factorizer,
4277 * call fn on each factor and compute the product.
4278 */
4279 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4280 __isl_take isl_basic_set *bset,
4281 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4282 {
4283 int i, n;
4284 isl_space *dim;
4285 isl_set *set;
4286 isl_factorizer *f;
4287 isl_qpolynomial *qp;
4288 isl_pw_qpolynomial *pwqp;
4289 unsigned nparam;
4290 unsigned nvar;
4291
4292 f = isl_basic_set_factorizer(bset);
4293 if (!f)
4294 goto error;
4295 if (f->n_group == 0) {
4296 isl_factorizer_free(f);
4297 return fn(bset);
4298 }
4299
4300 nparam = isl_basic_set_dim(bset, isl_dim_param);
4301 nvar = isl_basic_set_dim(bset, isl_dim_set);
4302
4303 dim = isl_basic_set_get_space(bset);
4304 dim = isl_space_domain(dim);
4305 set = isl_set_universe(isl_space_copy(dim));
4306 qp = isl_qpolynomial_one(dim);
4307 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4308
4309 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4310
4311 for (i = 0, n = 0; i < f->n_group; ++i) {
4312 isl_basic_set *bset_i;
4313 isl_pw_qpolynomial *pwqp_i;
4314
4315 bset_i = isl_basic_set_copy(bset);
4316 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4317 nparam + n + f->len[i], nvar - n - f->len[i]);
4318 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4319 nparam, n);
4320 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4321 n + f->len[i], nvar - n - f->len[i]);
4322 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4323
4324 pwqp_i = fn(bset_i);
4325 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4326
4327 n += f->len[i];
4328 }
4329
4330 isl_basic_set_free(bset);
4331 isl_factorizer_free(f);
4332
4333 return pwqp;
4334 error:
4335 isl_basic_set_free(bset);
4336 return NULL;
4337 }
4338
4339 /* Factor bset, call fn on each of the factors and return the product.
4340 * The function is assumed to evaluate to zero on empty domains,
4341 * to one on zero-dimensional domains and to infinity on unbounded domains
4342 * and will not be called explicitly on zero-dimensional or unbounded domains.
4343 *
4344 * We first check for some special cases and remove all equalities.
4345 * Then we hand over control to compressed_multiplicative_call.
4346 */
4347 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4348 __isl_take isl_basic_set *bset,
4349 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4350 {
4351 int bounded;
4352 isl_morph *morph;
4353 isl_pw_qpolynomial *pwqp;
4354 unsigned orig_nvar, final_nvar;
4355
4356 if (!bset)
4357 return NULL;
4358
4359 if (isl_basic_set_plain_is_empty(bset))
4360 return constant_on_domain(bset, 0);
4361
4362 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4363
4364 if (orig_nvar == 0)
4365 return constant_on_domain(bset, 1);
4366
4367 bounded = isl_basic_set_is_bounded(bset);
4368 if (bounded < 0)
4369 goto error;
4370 if (!bounded)
4371 return constant_on_domain(bset, -1);
4372
4373 if (bset->n_eq == 0)
4374 return compressed_multiplicative_call(bset, fn);
4375
4376 morph = isl_basic_set_full_compression(bset);
4377 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4378
4379 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4380
4381 pwqp = compressed_multiplicative_call(bset, fn);
4382
4383 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4384 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4385 morph = isl_morph_inverse(morph);
4386
4387 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4388
4389 return pwqp;
4390 error:
4391 isl_basic_set_free(bset);
4392 return NULL;
4393 }
4394
4395 /* Drop all floors in "qp", turning each integer division [a/m] into
4396 * a rational division a/m. If "down" is set, then the integer division
4397 * is replaces by (a-(m-1))/m instead.
4398 */
4399 static __isl_give isl_qpolynomial *qp_drop_floors(
4400 __isl_take isl_qpolynomial *qp, int down)
4401 {
4402 int i;
4403 struct isl_upoly *s;
4404
4405 if (!qp)
4406 return NULL;
4407 if (qp->div->n_row == 0)
4408 return qp;
4409
4410 qp = isl_qpolynomial_cow(qp);
4411 if (!qp)
4412 return NULL;
4413
4414 for (i = qp->div->n_row - 1; i >= 0; --i) {
4415 if (down) {
4416 isl_int_sub(qp->div->row[i][1],
4417 qp->div->row[i][1], qp->div->row[i][0]);
4418 isl_int_add_ui(qp->div->row[i][1],
4419 qp->div->row[i][1], 1);
4420 }
4421 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4422 qp->div->row[i][0], qp->div->n_col - 1);
4423 qp = substitute_div(qp, i, s);
4424 if (!qp)
4425 return NULL;
4426 }
4427
4428 return qp;
4429 }
4430
4431 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4432 * a rational division a/m.
4433 */
4434 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4435 __isl_take isl_pw_qpolynomial *pwqp)
4436 {
4437 int i;
4438
4439 if (!pwqp)
4440 return NULL;
4441
4442 if (isl_pw_qpolynomial_is_zero(pwqp))
4443 return pwqp;
4444
4445 pwqp = isl_pw_qpolynomial_cow(pwqp);
4446 if (!pwqp)
4447 return NULL;
4448
4449 for (i = 0; i < pwqp->n; ++i) {
4450 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4451 if (!pwqp->p[i].qp)
4452 goto error;
4453 }
4454
4455 return pwqp;
4456 error:
4457 isl_pw_qpolynomial_free(pwqp);
4458 return NULL;
4459 }
4460
4461 /* Adjust all the integer divisions in "qp" such that they are at least
4462 * one over the given orthant (identified by "signs"). This ensures
4463 * that they will still be non-negative even after subtracting (m-1)/m.
4464 *
4465 * In particular, f is replaced by f' + v, changing f = [a/m]
4466 * to f' = [(a - m v)/m].
4467 * If the constant term k in a is smaller than m,
4468 * the constant term of v is set to floor(k/m) - 1.
4469 * For any other term, if the coefficient c and the variable x have
4470 * the same sign, then no changes are needed.
4471 * Otherwise, if the variable is positive (and c is negative),
4472 * then the coefficient of x in v is set to floor(c/m).
4473 * If the variable is negative (and c is positive),
4474 * then the coefficient of x in v is set to ceil(c/m).
4475 */
4476 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4477 int *signs)
4478 {
4479 int i, j;
4480 int total;
4481 isl_vec *v = NULL;
4482 struct isl_upoly *s;
4483
4484 qp = isl_qpolynomial_cow(qp);
4485 if (!qp)
4486 return NULL;
4487 qp->div = isl_mat_cow(qp->div);
4488 if (!qp->div)
4489 goto error;
4490
4491 total = isl_space_dim(qp->dim, isl_dim_all);
4492 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4493
4494 for (i = 0; i < qp->div->n_row; ++i) {
4495 isl_int *row = qp->div->row[i];
4496 v = isl_vec_clr(v);
4497 if (!v)
4498 goto error;
4499 if (isl_int_lt(row[1], row[0])) {
4500 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4501 isl_int_sub_ui(v->el[0], v->el[0], 1);
4502 isl_int_submul(row[1], row[0], v->el[0]);
4503 }
4504 for (j = 0; j < total; ++j) {
4505 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4506 continue;
4507 if (signs[j] < 0)
4508 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4509 else
4510 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4511 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4512 }
4513 for (j = 0; j < i; ++j) {
4514 if (isl_int_sgn(row[2 + total + j]) >= 0)
4515 continue;
4516 isl_int_fdiv_q(v->el[1 + total + j],
4517 row[2 + total + j], row[0]);
4518 isl_int_submul(row[2 + total + j],
4519 row[0], v->el[1 + total + j]);
4520 }
4521 for (j = i + 1; j < qp->div->n_row; ++j) {
4522 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4523 continue;
4524 isl_seq_combine(qp->div->row[j] + 1,
4525 qp->div->ctx->one, qp->div->row[j] + 1,
4526 qp->div->row[j][2 + total + i], v->el, v->size);
4527 }
4528 isl_int_set_si(v->el[1 + total + i], 1);
4529 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4530 qp->div->ctx->one, v->size);
4531 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4532 isl_upoly_free(s);
4533 if (!qp->upoly)
4534 goto error;
4535 }
4536
4537 isl_vec_free(v);
4538 return qp;
4539 error:
4540 isl_vec_free(v);
4541 isl_qpolynomial_free(qp);
4542 return NULL;
4543 }
4544
4545 struct isl_to_poly_data {
4546 int sign;
4547 isl_pw_qpolynomial *res;
4548 isl_qpolynomial *qp;
4549 };
4550
4551 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4552 * We first make all integer divisions positive and then split the
4553 * quasipolynomials into terms with sign data->sign (the direction
4554 * of the requested approximation) and terms with the opposite sign.
4555 * In the first set of terms, each integer division [a/m] is
4556 * overapproximated by a/m, while in the second it is underapproximated
4557 * by (a-(m-1))/m.
4558 */
4559 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4560 void *user)
4561 {
4562 struct isl_to_poly_data *data = user;
4563 isl_pw_qpolynomial *t;
4564 isl_qpolynomial *qp, *up, *down;
4565
4566 qp = isl_qpolynomial_copy(data->qp);
4567 qp = make_divs_pos(qp, signs);
4568
4569 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4570 up = qp_drop_floors(up, 0);
4571 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4572 down = qp_drop_floors(down, 1);
4573
4574 isl_qpolynomial_free(qp);
4575 qp = isl_qpolynomial_add(up, down);
4576
4577 t = isl_pw_qpolynomial_alloc(orthant, qp);
4578 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4579
4580 return 0;
4581 }
4582
4583 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4584 * the polynomial will be an overapproximation. If "sign" is negative,
4585 * it will be an underapproximation. If "sign" is zero, the approximation
4586 * will lie somewhere in between.
4587 *
4588 * In particular, is sign == 0, we simply drop the floors, turning
4589 * the integer divisions into rational divisions.
4590 * Otherwise, we split the domains into orthants, make all integer divisions
4591 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4592 * depending on the requested sign and the sign of the term in which
4593 * the integer division appears.
4594 */
4595 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4596 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4597 {
4598 int i;
4599 struct isl_to_poly_data data;
4600
4601 if (sign == 0)
4602 return pwqp_drop_floors(pwqp);
4603
4604 if (!pwqp)
4605 return NULL;
4606
4607 data.sign = sign;
4608 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4609
4610 for (i = 0; i < pwqp->n; ++i) {
4611 if (pwqp->p[i].qp->div->n_row == 0) {
4612 isl_pw_qpolynomial *t;
4613 t = isl_pw_qpolynomial_alloc(
4614 isl_set_copy(pwqp->p[i].set),
4615 isl_qpolynomial_copy(pwqp->p[i].qp));
4616 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4617 continue;
4618 }
4619 data.qp = pwqp->p[i].qp;
4620 if (isl_set_foreach_orthant(pwqp->p[i].set,
4621 &to_polynomial_on_orthant, &data) < 0)
4622 goto error;
4623 }
4624
4625 isl_pw_qpolynomial_free(pwqp);
4626
4627 return data.res;
4628 error:
4629 isl_pw_qpolynomial_free(pwqp);
4630 isl_pw_qpolynomial_free(data.res);
4631 return NULL;
4632 }
4633
4634 static int poly_entry(void **entry, void *user)
4635 {
4636 int *sign = user;
4637 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4638
4639 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4640
4641 return *pwqp ? 0 : -1;
4642 }
4643
4644 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4645 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4646 {
4647 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4648 if (!upwqp)
4649 return NULL;
4650
4651 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4652 &poly_entry, &sign) < 0)
4653 goto error;
4654
4655 return upwqp;
4656 error:
4657 isl_union_pw_qpolynomial_free(upwqp);
4658 return NULL;
4659 }
4660
4661 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4662 __isl_take isl_qpolynomial *qp)
4663 {
4664 int i, k;
4665 isl_space *dim;
4666 isl_vec *aff = NULL;
4667 isl_basic_map *bmap = NULL;
4668 unsigned pos;
4669 unsigned n_div;
4670
4671 if (!qp)
4672 return NULL;
4673 if (!isl_upoly_is_affine(qp->upoly))
4674 isl_die(qp->dim->ctx, isl_error_invalid,
4675 "input quasi-polynomial not affine", goto error);
4676 aff = isl_qpolynomial_extract_affine(qp);
4677 if (!aff)
4678 goto error;
4679 dim = isl_qpolynomial_get_space(qp);
4680 dim = isl_space_from_domain(dim);
4681 pos = 1 + isl_space_offset(dim, isl_dim_out);
4682 dim = isl_space_add_dims(dim, isl_dim_out, 1);
4683 n_div = qp->div->n_row;
4684 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4685
4686 for (i = 0; i < n_div; ++i) {
4687 k = isl_basic_map_alloc_div(bmap);
4688 if (k < 0)
4689 goto error;
4690 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4691 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4692 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4693 goto error;
4694 }
4695 k = isl_basic_map_alloc_equality(bmap);
4696 if (k < 0)
4697 goto error;
4698 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4699 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4700 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4701
4702 isl_vec_free(aff);
4703 isl_qpolynomial_free(qp);
4704 bmap = isl_basic_map_finalize(bmap);
4705 return bmap;
4706 error:
4707 isl_vec_free(aff);
4708 isl_qpolynomial_free(qp);
4709 isl_basic_map_free(bmap);
4710 return NULL;
4711 }
Integer set library