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document isl_dim_move
[isl.git] / isl_polynomial.c
blob0d2a125ab911f9f80415762484f3f855f4778477
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl/lp.h>
16 #include <isl/seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_dim_private.h>
22 #include <isl_div_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_config.h>
28
29 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
30 {
31 switch (type) {
32 case isl_dim_param: return 0;
33 case isl_dim_in: return dim->nparam;
34 case isl_dim_out: return dim->nparam + dim->n_in;
35 default: return 0;
36 }
37 }
38
39 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
40 {
41 if (!up)
42 return -1;
43
44 return up->var < 0;
45 }
46
47 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
48 {
49 if (!up)
50 return NULL;
51
52 isl_assert(up->ctx, up->var < 0, return NULL);
53
54 return (struct isl_upoly_cst *)up;
55 }
56
57 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
58 {
59 if (!up)
60 return NULL;
61
62 isl_assert(up->ctx, up->var >= 0, return NULL);
63
64 return (struct isl_upoly_rec *)up;
65 }
66
67 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
68 __isl_keep struct isl_upoly *up2)
69 {
70 int i;
71 struct isl_upoly_rec *rec1, *rec2;
72
73 if (!up1 || !up2)
74 return -1;
75 if (up1 == up2)
76 return 1;
77 if (up1->var != up2->var)
78 return 0;
79 if (isl_upoly_is_cst(up1)) {
80 struct isl_upoly_cst *cst1, *cst2;
81 cst1 = isl_upoly_as_cst(up1);
82 cst2 = isl_upoly_as_cst(up2);
83 if (!cst1 || !cst2)
84 return -1;
85 return isl_int_eq(cst1->n, cst2->n) &&
86 isl_int_eq(cst1->d, cst2->d);
87 }
88
89 rec1 = isl_upoly_as_rec(up1);
90 rec2 = isl_upoly_as_rec(up2);
91 if (!rec1 || !rec2)
92 return -1;
93
94 if (rec1->n != rec2->n)
95 return 0;
96
97 for (i = 0; i < rec1->n; ++i) {
98 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
99 if (eq < 0 || !eq)
100 return eq;
101 }
102
103 return 1;
104 }
105
106 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
107 {
108 struct isl_upoly_cst *cst;
109
110 if (!up)
111 return -1;
112 if (!isl_upoly_is_cst(up))
113 return 0;
114
115 cst = isl_upoly_as_cst(up);
116 if (!cst)
117 return -1;
118
119 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
120 }
121
122 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
123 {
124 struct isl_upoly_cst *cst;
125
126 if (!up)
127 return 0;
128 if (!isl_upoly_is_cst(up))
129 return 0;
130
131 cst = isl_upoly_as_cst(up);
132 if (!cst)
133 return 0;
134
135 return isl_int_sgn(cst->n);
136 }
137
138 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
139 {
140 struct isl_upoly_cst *cst;
141
142 if (!up)
143 return -1;
144 if (!isl_upoly_is_cst(up))
145 return 0;
146
147 cst = isl_upoly_as_cst(up);
148 if (!cst)
149 return -1;
150
151 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
152 }
153
154 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
155 {
156 struct isl_upoly_cst *cst;
157
158 if (!up)
159 return -1;
160 if (!isl_upoly_is_cst(up))
161 return 0;
162
163 cst = isl_upoly_as_cst(up);
164 if (!cst)
165 return -1;
166
167 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
168 }
169
170 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
171 {
172 struct isl_upoly_cst *cst;
173
174 if (!up)
175 return -1;
176 if (!isl_upoly_is_cst(up))
177 return 0;
178
179 cst = isl_upoly_as_cst(up);
180 if (!cst)
181 return -1;
182
183 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
184 }
185
186 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
187 {
188 struct isl_upoly_cst *cst;
189
190 if (!up)
191 return -1;
192 if (!isl_upoly_is_cst(up))
193 return 0;
194
195 cst = isl_upoly_as_cst(up);
196 if (!cst)
197 return -1;
198
199 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
200 }
201
202 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
203 {
204 struct isl_upoly_cst *cst;
205
206 if (!up)
207 return -1;
208 if (!isl_upoly_is_cst(up))
209 return 0;
210
211 cst = isl_upoly_as_cst(up);
212 if (!cst)
213 return -1;
214
215 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
216 }
217
218 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
219 {
220 struct isl_upoly_cst *cst;
221
222 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
223 if (!cst)
224 return NULL;
225
226 cst->up.ref = 1;
227 cst->up.ctx = ctx;
228 isl_ctx_ref(ctx);
229 cst->up.var = -1;
230
231 isl_int_init(cst->n);
232 isl_int_init(cst->d);
233
234 return cst;
235 }
236
237 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
238 {
239 struct isl_upoly_cst *cst;
240
241 cst = isl_upoly_cst_alloc(ctx);
242 if (!cst)
243 return NULL;
244
245 isl_int_set_si(cst->n, 0);
246 isl_int_set_si(cst->d, 1);
247
248 return &cst->up;
249 }
250
251 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
252 {
253 struct isl_upoly_cst *cst;
254
255 cst = isl_upoly_cst_alloc(ctx);
256 if (!cst)
257 return NULL;
258
259 isl_int_set_si(cst->n, 1);
260 isl_int_set_si(cst->d, 1);
261
262 return &cst->up;
263 }
264
265 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
266 {
267 struct isl_upoly_cst *cst;
268
269 cst = isl_upoly_cst_alloc(ctx);
270 if (!cst)
271 return NULL;
272
273 isl_int_set_si(cst->n, 1);
274 isl_int_set_si(cst->d, 0);
275
276 return &cst->up;
277 }
278
279 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
280 {
281 struct isl_upoly_cst *cst;
282
283 cst = isl_upoly_cst_alloc(ctx);
284 if (!cst)
285 return NULL;
286
287 isl_int_set_si(cst->n, -1);
288 isl_int_set_si(cst->d, 0);
289
290 return &cst->up;
291 }
292
293 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
294 {
295 struct isl_upoly_cst *cst;
296
297 cst = isl_upoly_cst_alloc(ctx);
298 if (!cst)
299 return NULL;
300
301 isl_int_set_si(cst->n, 0);
302 isl_int_set_si(cst->d, 0);
303
304 return &cst->up;
305 }
306
307 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
308 isl_int n, isl_int d)
309 {
310 struct isl_upoly_cst *cst;
311
312 cst = isl_upoly_cst_alloc(ctx);
313 if (!cst)
314 return NULL;
315
316 isl_int_set(cst->n, n);
317 isl_int_set(cst->d, d);
318
319 return &cst->up;
320 }
321
322 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
323 int var, int size)
324 {
325 struct isl_upoly_rec *rec;
326
327 isl_assert(ctx, var >= 0, return NULL);
328 isl_assert(ctx, size >= 0, return NULL);
329 rec = isl_calloc(ctx, struct isl_upoly_rec,
330 sizeof(struct isl_upoly_rec) +
331 size * sizeof(struct isl_upoly *));
332 if (!rec)
333 return NULL;
334
335 rec->up.ref = 1;
336 rec->up.ctx = ctx;
337 isl_ctx_ref(ctx);
338 rec->up.var = var;
339
340 rec->n = 0;
341 rec->size = size;
342
343 return rec;
344 }
345
346 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
347 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
348 {
349 qp = isl_qpolynomial_cow(qp);
350 if (!qp || !dim)
351 goto error;
352
353 isl_dim_free(qp->dim);
354 qp->dim = dim;
355
356 return qp;
357 error:
358 isl_qpolynomial_free(qp);
359 isl_dim_free(dim);
360 return NULL;
361 }
362
363 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
364 {
365 return qp ? qp->dim->ctx : NULL;
366 }
367
368 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
369 {
370 return qp ? isl_dim_copy(qp->dim) : NULL;
371 }
372
373 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
374 enum isl_dim_type type)
375 {
376 return qp ? isl_dim_size(qp->dim, type) : 0;
377 }
378
379 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
380 {
381 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
382 }
383
384 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
385 {
386 return qp ? isl_upoly_is_one(qp->upoly) : -1;
387 }
388
389 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
390 {
391 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
392 }
393
394 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
395 {
396 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
397 }
398
399 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
400 {
401 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
402 }
403
404 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
405 {
406 return qp ? isl_upoly_sgn(qp->upoly) : 0;
407 }
408
409 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
410 {
411 isl_int_clear(cst->n);
412 isl_int_clear(cst->d);
413 }
414
415 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
416 {
417 int i;
418
419 for (i = 0; i < rec->n; ++i)
420 isl_upoly_free(rec->p[i]);
421 }
422
423 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
424 {
425 if (!up)
426 return NULL;
427
428 up->ref++;
429 return up;
430 }
431
432 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
433 {
434 struct isl_upoly_cst *cst;
435 struct isl_upoly_cst *dup;
436
437 cst = isl_upoly_as_cst(up);
438 if (!cst)
439 return NULL;
440
441 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
442 if (!dup)
443 return NULL;
444 isl_int_set(dup->n, cst->n);
445 isl_int_set(dup->d, cst->d);
446
447 return &dup->up;
448 }
449
450 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
451 {
452 int i;
453 struct isl_upoly_rec *rec;
454 struct isl_upoly_rec *dup;
455
456 rec = isl_upoly_as_rec(up);
457 if (!rec)
458 return NULL;
459
460 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
461 if (!dup)
462 return NULL;
463
464 for (i = 0; i < rec->n; ++i) {
465 dup->p[i] = isl_upoly_copy(rec->p[i]);
466 if (!dup->p[i])
467 goto error;
468 dup->n++;
469 }
470
471 return &dup->up;
472 error:
473 isl_upoly_free(&dup->up);
474 return NULL;
475 }
476
477 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
478 {
479 if (!up)
480 return NULL;
481
482 if (isl_upoly_is_cst(up))
483 return isl_upoly_dup_cst(up);
484 else
485 return isl_upoly_dup_rec(up);
486 }
487
488 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
489 {
490 if (!up)
491 return NULL;
492
493 if (up->ref == 1)
494 return up;
495 up->ref--;
496 return isl_upoly_dup(up);
497 }
498
499 void isl_upoly_free(__isl_take struct isl_upoly *up)
500 {
501 if (!up)
502 return;
503
504 if (--up->ref > 0)
505 return;
506
507 if (up->var < 0)
508 upoly_free_cst((struct isl_upoly_cst *)up);
509 else
510 upoly_free_rec((struct isl_upoly_rec *)up);
511
512 isl_ctx_deref(up->ctx);
513 free(up);
514 }
515
516 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
517 {
518 isl_int gcd;
519
520 isl_int_init(gcd);
521 isl_int_gcd(gcd, cst->n, cst->d);
522 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
523 isl_int_divexact(cst->n, cst->n, gcd);
524 isl_int_divexact(cst->d, cst->d, gcd);
525 }
526 isl_int_clear(gcd);
527 }
528
529 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
530 __isl_take struct isl_upoly *up2)
531 {
532 struct isl_upoly_cst *cst1;
533 struct isl_upoly_cst *cst2;
534
535 up1 = isl_upoly_cow(up1);
536 if (!up1 || !up2)
537 goto error;
538
539 cst1 = isl_upoly_as_cst(up1);
540 cst2 = isl_upoly_as_cst(up2);
541
542 if (isl_int_eq(cst1->d, cst2->d))
543 isl_int_add(cst1->n, cst1->n, cst2->n);
544 else {
545 isl_int_mul(cst1->n, cst1->n, cst2->d);
546 isl_int_addmul(cst1->n, cst2->n, cst1->d);
547 isl_int_mul(cst1->d, cst1->d, cst2->d);
548 }
549
550 isl_upoly_cst_reduce(cst1);
551
552 isl_upoly_free(up2);
553 return up1;
554 error:
555 isl_upoly_free(up1);
556 isl_upoly_free(up2);
557 return NULL;
558 }
559
560 static __isl_give struct isl_upoly *replace_by_zero(
561 __isl_take struct isl_upoly *up)
562 {
563 struct isl_ctx *ctx;
564
565 if (!up)
566 return NULL;
567 ctx = up->ctx;
568 isl_upoly_free(up);
569 return isl_upoly_zero(ctx);
570 }
571
572 static __isl_give struct isl_upoly *replace_by_constant_term(
573 __isl_take struct isl_upoly *up)
574 {
575 struct isl_upoly_rec *rec;
576 struct isl_upoly *cst;
577
578 if (!up)
579 return NULL;
580
581 rec = isl_upoly_as_rec(up);
582 if (!rec)
583 goto error;
584 cst = isl_upoly_copy(rec->p[0]);
585 isl_upoly_free(up);
586 return cst;
587 error:
588 isl_upoly_free(up);
589 return NULL;
590 }
591
592 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
593 __isl_take struct isl_upoly *up2)
594 {
595 int i;
596 struct isl_upoly_rec *rec1, *rec2;
597
598 if (!up1 || !up2)
599 goto error;
600
601 if (isl_upoly_is_nan(up1)) {
602 isl_upoly_free(up2);
603 return up1;
604 }
605
606 if (isl_upoly_is_nan(up2)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610
611 if (isl_upoly_is_zero(up1)) {
612 isl_upoly_free(up1);
613 return up2;
614 }
615
616 if (isl_upoly_is_zero(up2)) {
617 isl_upoly_free(up2);
618 return up1;
619 }
620
621 if (up1->var < up2->var)
622 return isl_upoly_sum(up2, up1);
623
624 if (up2->var < up1->var) {
625 struct isl_upoly_rec *rec;
626 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
627 isl_upoly_free(up1);
628 return up2;
629 }
630 up1 = isl_upoly_cow(up1);
631 rec = isl_upoly_as_rec(up1);
632 if (!rec)
633 goto error;
634 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
635 if (rec->n == 1)
636 up1 = replace_by_constant_term(up1);
637 return up1;
638 }
639
640 if (isl_upoly_is_cst(up1))
641 return isl_upoly_sum_cst(up1, up2);
642
643 rec1 = isl_upoly_as_rec(up1);
644 rec2 = isl_upoly_as_rec(up2);
645 if (!rec1 || !rec2)
646 goto error;
647
648 if (rec1->n < rec2->n)
649 return isl_upoly_sum(up2, up1);
650
651 up1 = isl_upoly_cow(up1);
652 rec1 = isl_upoly_as_rec(up1);
653 if (!rec1)
654 goto error;
655
656 for (i = rec2->n - 1; i >= 0; --i) {
657 rec1->p[i] = isl_upoly_sum(rec1->p[i],
658 isl_upoly_copy(rec2->p[i]));
659 if (!rec1->p[i])
660 goto error;
661 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
662 isl_upoly_free(rec1->p[i]);
663 rec1->n--;
664 }
665 }
666
667 if (rec1->n == 0)
668 up1 = replace_by_zero(up1);
669 else if (rec1->n == 1)
670 up1 = replace_by_constant_term(up1);
671
672 isl_upoly_free(up2);
673
674 return up1;
675 error:
676 isl_upoly_free(up1);
677 isl_upoly_free(up2);
678 return NULL;
679 }
680
681 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
682 __isl_take struct isl_upoly *up, isl_int v)
683 {
684 struct isl_upoly_cst *cst;
685
686 up = isl_upoly_cow(up);
687 if (!up)
688 return NULL;
689
690 cst = isl_upoly_as_cst(up);
691
692 isl_int_addmul(cst->n, cst->d, v);
693
694 return up;
695 }
696
697 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
698 __isl_take struct isl_upoly *up, isl_int v)
699 {
700 struct isl_upoly_rec *rec;
701
702 if (!up)
703 return NULL;
704
705 if (isl_upoly_is_cst(up))
706 return isl_upoly_cst_add_isl_int(up, v);
707
708 up = isl_upoly_cow(up);
709 rec = isl_upoly_as_rec(up);
710 if (!rec)
711 goto error;
712
713 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
714 if (!rec->p[0])
715 goto error;
716
717 return up;
718 error:
719 isl_upoly_free(up);
720 return NULL;
721 }
722
723 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
724 __isl_take struct isl_upoly *up, isl_int v)
725 {
726 struct isl_upoly_cst *cst;
727
728 if (isl_upoly_is_zero(up))
729 return up;
730
731 up = isl_upoly_cow(up);
732 if (!up)
733 return NULL;
734
735 cst = isl_upoly_as_cst(up);
736
737 isl_int_mul(cst->n, cst->n, v);
738
739 return up;
740 }
741
742 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
743 __isl_take struct isl_upoly *up, isl_int v)
744 {
745 int i;
746 struct isl_upoly_rec *rec;
747
748 if (!up)
749 return NULL;
750
751 if (isl_upoly_is_cst(up))
752 return isl_upoly_cst_mul_isl_int(up, v);
753
754 up = isl_upoly_cow(up);
755 rec = isl_upoly_as_rec(up);
756 if (!rec)
757 goto error;
758
759 for (i = 0; i < rec->n; ++i) {
760 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
761 if (!rec->p[i])
762 goto error;
763 }
764
765 return up;
766 error:
767 isl_upoly_free(up);
768 return NULL;
769 }
770
771 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
772 __isl_take struct isl_upoly *up2)
773 {
774 struct isl_upoly_cst *cst1;
775 struct isl_upoly_cst *cst2;
776
777 up1 = isl_upoly_cow(up1);
778 if (!up1 || !up2)
779 goto error;
780
781 cst1 = isl_upoly_as_cst(up1);
782 cst2 = isl_upoly_as_cst(up2);
783
784 isl_int_mul(cst1->n, cst1->n, cst2->n);
785 isl_int_mul(cst1->d, cst1->d, cst2->d);
786
787 isl_upoly_cst_reduce(cst1);
788
789 isl_upoly_free(up2);
790 return up1;
791 error:
792 isl_upoly_free(up1);
793 isl_upoly_free(up2);
794 return NULL;
795 }
796
797 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
798 __isl_take struct isl_upoly *up2)
799 {
800 struct isl_upoly_rec *rec1;
801 struct isl_upoly_rec *rec2;
802 struct isl_upoly_rec *res = NULL;
803 int i, j;
804 int size;
805
806 rec1 = isl_upoly_as_rec(up1);
807 rec2 = isl_upoly_as_rec(up2);
808 if (!rec1 || !rec2)
809 goto error;
810 size = rec1->n + rec2->n - 1;
811 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
812 if (!res)
813 goto error;
814
815 for (i = 0; i < rec1->n; ++i) {
816 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
817 isl_upoly_copy(rec1->p[i]));
818 if (!res->p[i])
819 goto error;
820 res->n++;
821 }
822 for (; i < size; ++i) {
823 res->p[i] = isl_upoly_zero(up1->ctx);
824 if (!res->p[i])
825 goto error;
826 res->n++;
827 }
828 for (i = 0; i < rec1->n; ++i) {
829 for (j = 1; j < rec2->n; ++j) {
830 struct isl_upoly *up;
831 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
832 isl_upoly_copy(rec1->p[i]));
833 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
834 if (!res->p[i + j])
835 goto error;
836 }
837 }
838
839 isl_upoly_free(up1);
840 isl_upoly_free(up2);
841
842 return &res->up;
843 error:
844 isl_upoly_free(up1);
845 isl_upoly_free(up2);
846 isl_upoly_free(&res->up);
847 return NULL;
848 }
849
850 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
851 __isl_take struct isl_upoly *up2)
852 {
853 if (!up1 || !up2)
854 goto error;
855
856 if (isl_upoly_is_nan(up1)) {
857 isl_upoly_free(up2);
858 return up1;
859 }
860
861 if (isl_upoly_is_nan(up2)) {
862 isl_upoly_free(up1);
863 return up2;
864 }
865
866 if (isl_upoly_is_zero(up1)) {
867 isl_upoly_free(up2);
868 return up1;
869 }
870
871 if (isl_upoly_is_zero(up2)) {
872 isl_upoly_free(up1);
873 return up2;
874 }
875
876 if (isl_upoly_is_one(up1)) {
877 isl_upoly_free(up1);
878 return up2;
879 }
880
881 if (isl_upoly_is_one(up2)) {
882 isl_upoly_free(up2);
883 return up1;
884 }
885
886 if (up1->var < up2->var)
887 return isl_upoly_mul(up2, up1);
888
889 if (up2->var < up1->var) {
890 int i;
891 struct isl_upoly_rec *rec;
892 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
893 isl_ctx *ctx = up1->ctx;
894 isl_upoly_free(up1);
895 isl_upoly_free(up2);
896 return isl_upoly_nan(ctx);
897 }
898 up1 = isl_upoly_cow(up1);
899 rec = isl_upoly_as_rec(up1);
900 if (!rec)
901 goto error;
902
903 for (i = 0; i < rec->n; ++i) {
904 rec->p[i] = isl_upoly_mul(rec->p[i],
905 isl_upoly_copy(up2));
906 if (!rec->p[i])
907 goto error;
908 }
909 isl_upoly_free(up2);
910 return up1;
911 }
912
913 if (isl_upoly_is_cst(up1))
914 return isl_upoly_mul_cst(up1, up2);
915
916 return isl_upoly_mul_rec(up1, up2);
917 error:
918 isl_upoly_free(up1);
919 isl_upoly_free(up2);
920 return NULL;
921 }
922
923 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
924 unsigned power)
925 {
926 struct isl_upoly *res;
927
928 if (!up)
929 return NULL;
930 if (power == 1)
931 return up;
932
933 if (power % 2)
934 res = isl_upoly_copy(up);
935 else
936 res = isl_upoly_one(up->ctx);
937
938 while (power >>= 1) {
939 up = isl_upoly_mul(up, isl_upoly_copy(up));
940 if (power % 2)
941 res = isl_upoly_mul(res, isl_upoly_copy(up));
942 }
943
944 isl_upoly_free(up);
945 return res;
946 }
947
948 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
949 unsigned n_div, __isl_take struct isl_upoly *up)
950 {
951 struct isl_qpolynomial *qp = NULL;
952 unsigned total;
953
954 if (!dim || !up)
955 goto error;
956
957 total = isl_dim_total(dim);
958
959 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
960 if (!qp)
961 goto error;
962
963 qp->ref = 1;
964 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
965 if (!qp->div)
966 goto error;
967
968 qp->dim = dim;
969 qp->upoly = up;
970
971 return qp;
972 error:
973 isl_dim_free(dim);
974 isl_upoly_free(up);
975 isl_qpolynomial_free(qp);
976 return NULL;
977 }
978
979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
980 {
981 if (!qp)
982 return NULL;
983
984 qp->ref++;
985 return qp;
986 }
987
988 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
989 {
990 struct isl_qpolynomial *dup;
991
992 if (!qp)
993 return NULL;
994
995 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
996 isl_upoly_copy(qp->upoly));
997 if (!dup)
998 return NULL;
999 isl_mat_free(dup->div);
1000 dup->div = isl_mat_copy(qp->div);
1001 if (!dup->div)
1002 goto error;
1003
1004 return dup;
1005 error:
1006 isl_qpolynomial_free(dup);
1007 return NULL;
1008 }
1009
1010 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1011 {
1012 if (!qp)
1013 return NULL;
1014
1015 if (qp->ref == 1)
1016 return qp;
1017 qp->ref--;
1018 return isl_qpolynomial_dup(qp);
1019 }
1020
1021 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1022 {
1023 if (!qp)
1024 return NULL;
1025
1026 if (--qp->ref > 0)
1027 return NULL;
1028
1029 isl_dim_free(qp->dim);
1030 isl_mat_free(qp->div);
1031 isl_upoly_free(qp->upoly);
1032
1033 free(qp);
1034 return NULL;
1035 }
1036
1037 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1038 {
1039 int i;
1040 struct isl_upoly_rec *rec;
1041 struct isl_upoly_cst *cst;
1042
1043 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1044 if (!rec)
1045 return NULL;
1046 for (i = 0; i < 1 + power; ++i) {
1047 rec->p[i] = isl_upoly_zero(ctx);
1048 if (!rec->p[i])
1049 goto error;
1050 rec->n++;
1051 }
1052 cst = isl_upoly_as_cst(rec->p[power]);
1053 isl_int_set_si(cst->n, 1);
1054
1055 return &rec->up;
1056 error:
1057 isl_upoly_free(&rec->up);
1058 return NULL;
1059 }
1060
1061 /* r array maps original positions to new positions.
1062 */
1063 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1064 int *r)
1065 {
1066 int i;
1067 struct isl_upoly_rec *rec;
1068 struct isl_upoly *base;
1069 struct isl_upoly *res;
1070
1071 if (isl_upoly_is_cst(up))
1072 return up;
1073
1074 rec = isl_upoly_as_rec(up);
1075 if (!rec)
1076 goto error;
1077
1078 isl_assert(up->ctx, rec->n >= 1, goto error);
1079
1080 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1081 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1082
1083 for (i = rec->n - 2; i >= 0; --i) {
1084 res = isl_upoly_mul(res, isl_upoly_copy(base));
1085 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1086 }
1087
1088 isl_upoly_free(base);
1089 isl_upoly_free(up);
1090
1091 return res;
1092 error:
1093 isl_upoly_free(up);
1094 return NULL;
1095 }
1096
1097 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1098 {
1099 int n_row, n_col;
1100 int equal;
1101
1102 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1103 div1->n_col >= div2->n_col, return -1);
1104
1105 if (div1->n_row == div2->n_row)
1106 return isl_mat_is_equal(div1, div2);
1107
1108 n_row = div1->n_row;
1109 n_col = div1->n_col;
1110 div1->n_row = div2->n_row;
1111 div1->n_col = div2->n_col;
1112
1113 equal = isl_mat_is_equal(div1, div2);
1114
1115 div1->n_row = n_row;
1116 div1->n_col = n_col;
1117
1118 return equal;
1119 }
1120
1121 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1122 {
1123 int li, lj;
1124
1125 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1126 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1127
1128 if (li != lj)
1129 return li - lj;
1130
1131 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1132 }
1133
1134 struct isl_div_sort_info {
1135 isl_mat *div;
1136 int row;
1137 };
1138
1139 static int div_sort_cmp(const void *p1, const void *p2)
1140 {
1141 const struct isl_div_sort_info *i1, *i2;
1142 i1 = (const struct isl_div_sort_info *) p1;
1143 i2 = (const struct isl_div_sort_info *) p2;
1144
1145 return cmp_row(i1->div, i1->row, i2->row);
1146 }
1147
1148 /* Sort divs and remove duplicates.
1149 */
1150 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1151 {
1152 int i;
1153 int skip;
1154 int len;
1155 struct isl_div_sort_info *array = NULL;
1156 int *pos = NULL, *at = NULL;
1157 int *reordering = NULL;
1158 unsigned div_pos;
1159
1160 if (!qp)
1161 return NULL;
1162 if (qp->div->n_row <= 1)
1163 return qp;
1164
1165 div_pos = isl_dim_total(qp->dim);
1166
1167 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1168 qp->div->n_row);
1169 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1171 len = qp->div->n_col - 2;
1172 reordering = isl_alloc_array(qp->div->ctx, int, len);
1173 if (!array || !pos || !at || !reordering)
1174 goto error;
1175
1176 for (i = 0; i < qp->div->n_row; ++i) {
1177 array[i].div = qp->div;
1178 array[i].row = i;
1179 pos[i] = i;
1180 at[i] = i;
1181 }
1182
1183 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1184 div_sort_cmp);
1185
1186 for (i = 0; i < div_pos; ++i)
1187 reordering[i] = i;
1188
1189 for (i = 0; i < qp->div->n_row; ++i) {
1190 if (pos[array[i].row] == i)
1191 continue;
1192 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1193 pos[at[i]] = pos[array[i].row];
1194 at[pos[array[i].row]] = at[i];
1195 at[i] = array[i].row;
1196 pos[array[i].row] = i;
1197 }
1198
1199 skip = 0;
1200 for (i = 0; i < len - div_pos; ++i) {
1201 if (i > 0 &&
1202 isl_seq_eq(qp->div->row[i - skip - 1],
1203 qp->div->row[i - skip], qp->div->n_col)) {
1204 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1205 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1206 2 + div_pos + i - skip);
1207 qp->div = isl_mat_drop_cols(qp->div,
1208 2 + div_pos + i - skip, 1);
1209 skip++;
1210 }
1211 reordering[div_pos + array[i].row] = div_pos + i - skip;
1212 }
1213
1214 qp->upoly = reorder(qp->upoly, reordering);
1215
1216 if (!qp->upoly || !qp->div)
1217 goto error;
1218
1219 free(at);
1220 free(pos);
1221 free(array);
1222 free(reordering);
1223
1224 return qp;
1225 error:
1226 free(at);
1227 free(pos);
1228 free(array);
1229 free(reordering);
1230 isl_qpolynomial_free(qp);
1231 return NULL;
1232 }
1233
1234 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1235 int *exp, int first)
1236 {
1237 int i;
1238 struct isl_upoly_rec *rec;
1239
1240 if (isl_upoly_is_cst(up))
1241 return up;
1242
1243 if (up->var < first)
1244 return up;
1245
1246 if (exp[up->var - first] == up->var - first)
1247 return up;
1248
1249 up = isl_upoly_cow(up);
1250 if (!up)
1251 goto error;
1252
1253 up->var = exp[up->var - first] + first;
1254
1255 rec = isl_upoly_as_rec(up);
1256 if (!rec)
1257 goto error;
1258
1259 for (i = 0; i < rec->n; ++i) {
1260 rec->p[i] = expand(rec->p[i], exp, first);
1261 if (!rec->p[i])
1262 goto error;
1263 }
1264
1265 return up;
1266 error:
1267 isl_upoly_free(up);
1268 return NULL;
1269 }
1270
1271 static __isl_give isl_qpolynomial *with_merged_divs(
1272 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1273 __isl_take isl_qpolynomial *qp2),
1274 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1275 {
1276 int *exp1 = NULL;
1277 int *exp2 = NULL;
1278 isl_mat *div = NULL;
1279
1280 qp1 = isl_qpolynomial_cow(qp1);
1281 qp2 = isl_qpolynomial_cow(qp2);
1282
1283 if (!qp1 || !qp2)
1284 goto error;
1285
1286 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1287 qp1->div->n_col >= qp2->div->n_col, goto error);
1288
1289 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1290 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1291 if (!exp1 || !exp2)
1292 goto error;
1293
1294 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1295 if (!div)
1296 goto error;
1297
1298 isl_mat_free(qp1->div);
1299 qp1->div = isl_mat_copy(div);
1300 isl_mat_free(qp2->div);
1301 qp2->div = isl_mat_copy(div);
1302
1303 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1304 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1305
1306 if (!qp1->upoly || !qp2->upoly)
1307 goto error;
1308
1309 isl_mat_free(div);
1310 free(exp1);
1311 free(exp2);
1312
1313 return fn(qp1, qp2);
1314 error:
1315 isl_mat_free(div);
1316 free(exp1);
1317 free(exp2);
1318 isl_qpolynomial_free(qp1);
1319 isl_qpolynomial_free(qp2);
1320 return NULL;
1321 }
1322
1323 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1324 __isl_take isl_qpolynomial *qp2)
1325 {
1326 qp1 = isl_qpolynomial_cow(qp1);
1327
1328 if (!qp1 || !qp2)
1329 goto error;
1330
1331 if (qp1->div->n_row < qp2->div->n_row)
1332 return isl_qpolynomial_add(qp2, qp1);
1333
1334 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1335 if (!compatible_divs(qp1->div, qp2->div))
1336 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1337
1338 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1339 if (!qp1->upoly)
1340 goto error;
1341
1342 isl_qpolynomial_free(qp2);
1343
1344 return qp1;
1345 error:
1346 isl_qpolynomial_free(qp1);
1347 isl_qpolynomial_free(qp2);
1348 return NULL;
1349 }
1350
1351 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1352 __isl_keep isl_set *dom,
1353 __isl_take isl_qpolynomial *qp1,
1354 __isl_take isl_qpolynomial *qp2)
1355 {
1356 qp1 = isl_qpolynomial_add(qp1, qp2);
1357 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1358 return qp1;
1359 }
1360
1361 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1362 __isl_take isl_qpolynomial *qp2)
1363 {
1364 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1365 }
1366
1367 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1368 __isl_take isl_qpolynomial *qp, isl_int v)
1369 {
1370 if (isl_int_is_zero(v))
1371 return qp;
1372
1373 qp = isl_qpolynomial_cow(qp);
1374 if (!qp)
1375 return NULL;
1376
1377 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1378 if (!qp->upoly)
1379 goto error;
1380
1381 return qp;
1382 error:
1383 isl_qpolynomial_free(qp);
1384 return NULL;
1385
1386 }
1387
1388 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1389 {
1390 if (!qp)
1391 return NULL;
1392
1393 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1394 }
1395
1396 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1397 __isl_take isl_qpolynomial *qp, isl_int v)
1398 {
1399 if (isl_int_is_one(v))
1400 return qp;
1401
1402 if (qp && isl_int_is_zero(v)) {
1403 isl_qpolynomial *zero;
1404 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1405 isl_qpolynomial_free(qp);
1406 return zero;
1407 }
1408
1409 qp = isl_qpolynomial_cow(qp);
1410 if (!qp)
1411 return NULL;
1412
1413 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1414 if (!qp->upoly)
1415 goto error;
1416
1417 return qp;
1418 error:
1419 isl_qpolynomial_free(qp);
1420 return NULL;
1421 }
1422
1423 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1424 __isl_take isl_qpolynomial *qp, isl_int v)
1425 {
1426 return isl_qpolynomial_mul_isl_int(qp, v);
1427 }
1428
1429 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1430 __isl_take isl_qpolynomial *qp2)
1431 {
1432 qp1 = isl_qpolynomial_cow(qp1);
1433
1434 if (!qp1 || !qp2)
1435 goto error;
1436
1437 if (qp1->div->n_row < qp2->div->n_row)
1438 return isl_qpolynomial_mul(qp2, qp1);
1439
1440 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1441 if (!compatible_divs(qp1->div, qp2->div))
1442 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1443
1444 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1445 if (!qp1->upoly)
1446 goto error;
1447
1448 isl_qpolynomial_free(qp2);
1449
1450 return qp1;
1451 error:
1452 isl_qpolynomial_free(qp1);
1453 isl_qpolynomial_free(qp2);
1454 return NULL;
1455 }
1456
1457 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1458 unsigned power)
1459 {
1460 qp = isl_qpolynomial_cow(qp);
1461
1462 if (!qp)
1463 return NULL;
1464
1465 qp->upoly = isl_upoly_pow(qp->upoly, power);
1466 if (!qp->upoly)
1467 goto error;
1468
1469 return qp;
1470 error:
1471 isl_qpolynomial_free(qp);
1472 return NULL;
1473 }
1474
1475 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1476 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1477 {
1478 int i;
1479
1480 if (power == 1)
1481 return pwqp;
1482
1483 pwqp = isl_pw_qpolynomial_cow(pwqp);
1484 if (!pwqp)
1485 return NULL;
1486
1487 for (i = 0; i < pwqp->n; ++i) {
1488 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1489 if (!pwqp->p[i].qp)
1490 return isl_pw_qpolynomial_free(pwqp);
1491 }
1492
1493 return pwqp;
1494 }
1495
1496 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1497 {
1498 if (!dim)
1499 return NULL;
1500 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1501 }
1502
1503 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1504 {
1505 if (!dim)
1506 return NULL;
1507 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1508 }
1509
1510 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1511 {
1512 if (!dim)
1513 return NULL;
1514 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1515 }
1516
1517 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1518 {
1519 if (!dim)
1520 return NULL;
1521 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1522 }
1523
1524 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1525 {
1526 if (!dim)
1527 return NULL;
1528 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1529 }
1530
1531 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1532 isl_int v)
1533 {
1534 struct isl_qpolynomial *qp;
1535 struct isl_upoly_cst *cst;
1536
1537 if (!dim)
1538 return NULL;
1539
1540 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1541 if (!qp)
1542 return NULL;
1543
1544 cst = isl_upoly_as_cst(qp->upoly);
1545 isl_int_set(cst->n, v);
1546
1547 return qp;
1548 }
1549
1550 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1551 isl_int *n, isl_int *d)
1552 {
1553 struct isl_upoly_cst *cst;
1554
1555 if (!qp)
1556 return -1;
1557
1558 if (!isl_upoly_is_cst(qp->upoly))
1559 return 0;
1560
1561 cst = isl_upoly_as_cst(qp->upoly);
1562 if (!cst)
1563 return -1;
1564
1565 if (n)
1566 isl_int_set(*n, cst->n);
1567 if (d)
1568 isl_int_set(*d, cst->d);
1569
1570 return 1;
1571 }
1572
1573 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1574 {
1575 int is_cst;
1576 struct isl_upoly_rec *rec;
1577
1578 if (!up)
1579 return -1;
1580
1581 if (up->var < 0)
1582 return 1;
1583
1584 rec = isl_upoly_as_rec(up);
1585 if (!rec)
1586 return -1;
1587
1588 if (rec->n > 2)
1589 return 0;
1590
1591 isl_assert(up->ctx, rec->n > 1, return -1);
1592
1593 is_cst = isl_upoly_is_cst(rec->p[1]);
1594 if (is_cst < 0)
1595 return -1;
1596 if (!is_cst)
1597 return 0;
1598
1599 return isl_upoly_is_affine(rec->p[0]);
1600 }
1601
1602 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1603 {
1604 if (!qp)
1605 return -1;
1606
1607 if (qp->div->n_row > 0)
1608 return 0;
1609
1610 return isl_upoly_is_affine(qp->upoly);
1611 }
1612
1613 static void update_coeff(__isl_keep isl_vec *aff,
1614 __isl_keep struct isl_upoly_cst *cst, int pos)
1615 {
1616 isl_int gcd;
1617 isl_int f;
1618
1619 if (isl_int_is_zero(cst->n))
1620 return;
1621
1622 isl_int_init(gcd);
1623 isl_int_init(f);
1624 isl_int_gcd(gcd, cst->d, aff->el[0]);
1625 isl_int_divexact(f, cst->d, gcd);
1626 isl_int_divexact(gcd, aff->el[0], gcd);
1627 isl_seq_scale(aff->el, aff->el, f, aff->size);
1628 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1629 isl_int_clear(gcd);
1630 isl_int_clear(f);
1631 }
1632
1633 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1634 __isl_keep isl_vec *aff)
1635 {
1636 struct isl_upoly_cst *cst;
1637 struct isl_upoly_rec *rec;
1638
1639 if (!up || !aff)
1640 return -1;
1641
1642 if (up->var < 0) {
1643 struct isl_upoly_cst *cst;
1644
1645 cst = isl_upoly_as_cst(up);
1646 if (!cst)
1647 return -1;
1648 update_coeff(aff, cst, 0);
1649 return 0;
1650 }
1651
1652 rec = isl_upoly_as_rec(up);
1653 if (!rec)
1654 return -1;
1655 isl_assert(up->ctx, rec->n == 2, return -1);
1656
1657 cst = isl_upoly_as_cst(rec->p[1]);
1658 if (!cst)
1659 return -1;
1660 update_coeff(aff, cst, 1 + up->var);
1661
1662 return isl_upoly_update_affine(rec->p[0], aff);
1663 }
1664
1665 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1666 __isl_keep isl_qpolynomial *qp)
1667 {
1668 isl_vec *aff;
1669 unsigned d;
1670
1671 if (!qp)
1672 return NULL;
1673
1674 d = isl_dim_total(qp->dim);
1675 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1676 if (!aff)
1677 return NULL;
1678
1679 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1680 isl_int_set_si(aff->el[0], 1);
1681
1682 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1683 goto error;
1684
1685 return aff;
1686 error:
1687 isl_vec_free(aff);
1688 return NULL;
1689 }
1690
1691 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1692 __isl_keep isl_qpolynomial *qp2)
1693 {
1694 int equal;
1695
1696 if (!qp1 || !qp2)
1697 return -1;
1698
1699 equal = isl_dim_equal(qp1->dim, qp2->dim);
1700 if (equal < 0 || !equal)
1701 return equal;
1702
1703 equal = isl_mat_is_equal(qp1->div, qp2->div);
1704 if (equal < 0 || !equal)
1705 return equal;
1706
1707 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1708 }
1709
1710 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1711 {
1712 int i;
1713 struct isl_upoly_rec *rec;
1714
1715 if (isl_upoly_is_cst(up)) {
1716 struct isl_upoly_cst *cst;
1717 cst = isl_upoly_as_cst(up);
1718 if (!cst)
1719 return;
1720 isl_int_lcm(*d, *d, cst->d);
1721 return;
1722 }
1723
1724 rec = isl_upoly_as_rec(up);
1725 if (!rec)
1726 return;
1727
1728 for (i = 0; i < rec->n; ++i)
1729 upoly_update_den(rec->p[i], d);
1730 }
1731
1732 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1733 {
1734 isl_int_set_si(*d, 1);
1735 if (!qp)
1736 return;
1737 upoly_update_den(qp->upoly, d);
1738 }
1739
1740 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1741 int pos, int power)
1742 {
1743 struct isl_ctx *ctx;
1744
1745 if (!dim)
1746 return NULL;
1747
1748 ctx = dim->ctx;
1749
1750 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1751 }
1752
1753 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1754 enum isl_dim_type type, unsigned pos)
1755 {
1756 if (!dim)
1757 return NULL;
1758
1759 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1760 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1761
1762 if (type == isl_dim_set)
1763 pos += isl_dim_size(dim, isl_dim_param);
1764
1765 return isl_qpolynomial_var_pow(dim, pos, 1);
1766 error:
1767 isl_dim_free(dim);
1768 return NULL;
1769 }
1770
1771 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1772 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1773 {
1774 int i;
1775 struct isl_upoly_rec *rec;
1776 struct isl_upoly *base, *res;
1777
1778 if (!up)
1779 return NULL;
1780
1781 if (isl_upoly_is_cst(up))
1782 return up;
1783
1784 if (up->var < first)
1785 return up;
1786
1787 rec = isl_upoly_as_rec(up);
1788 if (!rec)
1789 goto error;
1790
1791 isl_assert(up->ctx, rec->n >= 1, goto error);
1792
1793 if (up->var >= first + n)
1794 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1795 else
1796 base = isl_upoly_copy(subs[up->var - first]);
1797
1798 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1799 for (i = rec->n - 2; i >= 0; --i) {
1800 struct isl_upoly *t;
1801 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1802 res = isl_upoly_mul(res, isl_upoly_copy(base));
1803 res = isl_upoly_sum(res, t);
1804 }
1805
1806 isl_upoly_free(base);
1807 isl_upoly_free(up);
1808
1809 return res;
1810 error:
1811 isl_upoly_free(up);
1812 return NULL;
1813 }
1814
1815 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1816 isl_int denom, unsigned len)
1817 {
1818 int i;
1819 struct isl_upoly *up;
1820
1821 isl_assert(ctx, len >= 1, return NULL);
1822
1823 up = isl_upoly_rat_cst(ctx, f[0], denom);
1824 for (i = 0; i < len - 1; ++i) {
1825 struct isl_upoly *t;
1826 struct isl_upoly *c;
1827
1828 if (isl_int_is_zero(f[1 + i]))
1829 continue;
1830
1831 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1832 t = isl_upoly_var_pow(ctx, i, 1);
1833 t = isl_upoly_mul(c, t);
1834 up = isl_upoly_sum(up, t);
1835 }
1836
1837 return up;
1838 }
1839
1840 /* Remove common factor of non-constant terms and denominator.
1841 */
1842 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1843 {
1844 isl_ctx *ctx = qp->div->ctx;
1845 unsigned total = qp->div->n_col - 2;
1846
1847 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1848 isl_int_gcd(ctx->normalize_gcd,
1849 ctx->normalize_gcd, qp->div->row[div][0]);
1850 if (isl_int_is_one(ctx->normalize_gcd))
1851 return;
1852
1853 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1854 ctx->normalize_gcd, total);
1855 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1856 ctx->normalize_gcd);
1857 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1858 ctx->normalize_gcd);
1859 }
1860
1861 /* Replace the integer division identified by "div" by the polynomial "s".
1862 * The integer division is assumed not to appear in the definition
1863 * of any other integer divisions.
1864 */
1865 static __isl_give isl_qpolynomial *substitute_div(
1866 __isl_take isl_qpolynomial *qp,
1867 int div, __isl_take struct isl_upoly *s)
1868 {
1869 int i;
1870 int total;
1871 int *reordering;
1872
1873 if (!qp || !s)
1874 goto error;
1875
1876 qp = isl_qpolynomial_cow(qp);
1877 if (!qp)
1878 goto error;
1879
1880 total = isl_dim_total(qp->dim);
1881 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1882 if (!qp->upoly)
1883 goto error;
1884
1885 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1886 if (!reordering)
1887 goto error;
1888 for (i = 0; i < total + div; ++i)
1889 reordering[i] = i;
1890 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1891 reordering[i] = i - 1;
1892 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1893 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1894 qp->upoly = reorder(qp->upoly, reordering);
1895 free(reordering);
1896
1897 if (!qp->upoly || !qp->div)
1898 goto error;
1899
1900 isl_upoly_free(s);
1901 return qp;
1902 error:
1903 isl_qpolynomial_free(qp);
1904 isl_upoly_free(s);
1905 return NULL;
1906 }
1907
1908 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1909 * divisions because d is equal to 1 by their definition, i.e., e.
1910 */
1911 static __isl_give isl_qpolynomial *substitute_non_divs(
1912 __isl_take isl_qpolynomial *qp)
1913 {
1914 int i, j;
1915 int total;
1916 struct isl_upoly *s;
1917
1918 if (!qp)
1919 return NULL;
1920
1921 total = isl_dim_total(qp->dim);
1922 for (i = 0; qp && i < qp->div->n_row; ++i) {
1923 if (!isl_int_is_one(qp->div->row[i][0]))
1924 continue;
1925 for (j = i + 1; j < qp->div->n_row; ++j) {
1926 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1927 continue;
1928 isl_seq_combine(qp->div->row[j] + 1,
1929 qp->div->ctx->one, qp->div->row[j] + 1,
1930 qp->div->row[j][2 + total + i],
1931 qp->div->row[i] + 1, 1 + total + i);
1932 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1933 normalize_div(qp, j);
1934 }
1935 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1936 qp->div->row[i][0], qp->div->n_col - 1);
1937 qp = substitute_div(qp, i, s);
1938 --i;
1939 }
1940
1941 return qp;
1942 }
1943
1944 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1945 * with d the denominator. When replacing the coefficient e of x by
1946 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1947 * inside the division, so we need to add floor(e/d) * x outside.
1948 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1949 * to adjust the coefficient of x in each later div that depends on the
1950 * current div "div" and also in the affine expression "aff"
1951 * (if it too depends on "div").
1952 */
1953 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1954 __isl_keep isl_vec *aff)
1955 {
1956 int i, j;
1957 isl_int v;
1958 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1959
1960 isl_int_init(v);
1961 for (i = 0; i < 1 + total + div; ++i) {
1962 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1963 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1964 continue;
1965 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1966 isl_int_fdiv_r(qp->div->row[div][1 + i],
1967 qp->div->row[div][1 + i], qp->div->row[div][0]);
1968 if (!isl_int_is_zero(aff->el[1 + total + div]))
1969 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1970 for (j = div + 1; j < qp->div->n_row; ++j) {
1971 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1972 continue;
1973 isl_int_addmul(qp->div->row[j][1 + i],
1974 v, qp->div->row[j][2 + total + div]);
1975 }
1976 }
1977 isl_int_clear(v);
1978 }
1979
1980 /* Check if the last non-zero coefficient is bigger that half of the
1981 * denominator. If so, we will invert the div to further reduce the number
1982 * of distinct divs that may appear.
1983 * If the last non-zero coefficient is exactly half the denominator,
1984 * then we continue looking for earlier coefficients that are bigger
1985 * than half the denominator.
1986 */
1987 static int needs_invert(__isl_keep isl_mat *div, int row)
1988 {
1989 int i;
1990 int cmp;
1991
1992 for (i = div->n_col - 1; i >= 1; --i) {
1993 if (isl_int_is_zero(div->row[row][i]))
1994 continue;
1995 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1996 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1997 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1998 if (cmp)
1999 return cmp > 0;
2000 if (i == 1)
2001 return 1;
2002 }
2003
2004 return 0;
2005 }
2006
2007 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2008 * We only invert the coefficients of e (and the coefficient of q in
2009 * later divs and in "aff"). After calling this function, the
2010 * coefficients of e should be reduced again.
2011 */
2012 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2013 __isl_keep isl_vec *aff)
2014 {
2015 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2016
2017 isl_seq_neg(qp->div->row[div] + 1,
2018 qp->div->row[div] + 1, qp->div->n_col - 1);
2019 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2020 isl_int_add(qp->div->row[div][1],
2021 qp->div->row[div][1], qp->div->row[div][0]);
2022 if (!isl_int_is_zero(aff->el[1 + total + div]))
2023 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2024 isl_mat_col_mul(qp->div, 2 + total + div,
2025 qp->div->ctx->negone, 2 + total + div);
2026 }
2027
2028 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2029 * in the interval [0, d-1], with d the denominator and such that the
2030 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2031 *
2032 * After the reduction, some divs may have become redundant or identical,
2033 * so we call substitute_non_divs and sort_divs. If these functions
2034 * eliminate divs or merge two or more divs into one, the coefficients
2035 * of the enclosing divs may have to be reduced again, so we call
2036 * ourselves recursively if the number of divs decreases.
2037 */
2038 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2039 {
2040 int i;
2041 isl_vec *aff = NULL;
2042 struct isl_upoly *s;
2043 unsigned n_div;
2044
2045 if (!qp)
2046 return NULL;
2047
2048 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2049 aff = isl_vec_clr(aff);
2050 if (!aff)
2051 goto error;
2052
2053 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2054
2055 for (i = 0; i < qp->div->n_row; ++i) {
2056 normalize_div(qp, i);
2057 reduce_div(qp, i, aff);
2058 if (needs_invert(qp->div, i)) {
2059 invert_div(qp, i, aff);
2060 reduce_div(qp, i, aff);
2061 }
2062 }
2063
2064 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2065 qp->div->ctx->one, aff->size);
2066 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2067 isl_upoly_free(s);
2068 if (!qp->upoly)
2069 goto error;
2070
2071 isl_vec_free(aff);
2072
2073 n_div = qp->div->n_row;
2074 qp = substitute_non_divs(qp);
2075 qp = sort_divs(qp);
2076 if (qp && qp->div->n_row < n_div)
2077 return reduce_divs(qp);
2078
2079 return qp;
2080 error:
2081 isl_qpolynomial_free(qp);
2082 isl_vec_free(aff);
2083 return NULL;
2084 }
2085
2086 /* Assumes each div only depends on earlier divs.
2087 */
2088 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2089 int power)
2090 {
2091 struct isl_qpolynomial *qp = NULL;
2092 struct isl_upoly_rec *rec;
2093 struct isl_upoly_cst *cst;
2094 int i, d;
2095 int pos;
2096
2097 if (!div)
2098 return NULL;
2099
2100 d = div->line - div->bmap->div;
2101
2102 pos = isl_dim_total(div->bmap->dim) + d;
2103 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2104 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2105 div->bmap->n_div, &rec->up);
2106 if (!qp)
2107 goto error;
2108
2109 for (i = 0; i < div->bmap->n_div; ++i)
2110 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2111
2112 for (i = 0; i < 1 + power; ++i) {
2113 rec->p[i] = isl_upoly_zero(div->ctx);
2114 if (!rec->p[i])
2115 goto error;
2116 rec->n++;
2117 }
2118 cst = isl_upoly_as_cst(rec->p[power]);
2119 isl_int_set_si(cst->n, 1);
2120
2121 isl_div_free(div);
2122
2123 qp = reduce_divs(qp);
2124
2125 return qp;
2126 error:
2127 isl_qpolynomial_free(qp);
2128 isl_div_free(div);
2129 return NULL;
2130 }
2131
2132 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2133 {
2134 return isl_qpolynomial_div_pow(div, 1);
2135 }
2136
2137 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2138 const isl_int n, const isl_int d)
2139 {
2140 struct isl_qpolynomial *qp;
2141 struct isl_upoly_cst *cst;
2142
2143 if (!dim)
2144 return NULL;
2145
2146 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2147 if (!qp)
2148 return NULL;
2149
2150 cst = isl_upoly_as_cst(qp->upoly);
2151 isl_int_set(cst->n, n);
2152 isl_int_set(cst->d, d);
2153
2154 return qp;
2155 }
2156
2157 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2158 {
2159 struct isl_upoly_rec *rec;
2160 int i;
2161
2162 if (!up)
2163 return -1;
2164
2165 if (isl_upoly_is_cst(up))
2166 return 0;
2167
2168 if (up->var < d)
2169 active[up->var] = 1;
2170
2171 rec = isl_upoly_as_rec(up);
2172 for (i = 0; i < rec->n; ++i)
2173 if (up_set_active(rec->p[i], active, d) < 0)
2174 return -1;
2175
2176 return 0;
2177 }
2178
2179 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2180 {
2181 int i, j;
2182 int d = isl_dim_total(qp->dim);
2183
2184 if (!qp || !active)
2185 return -1;
2186
2187 for (i = 0; i < d; ++i)
2188 for (j = 0; j < qp->div->n_row; ++j) {
2189 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2190 continue;
2191 active[i] = 1;
2192 break;
2193 }
2194
2195 return up_set_active(qp->upoly, active, d);
2196 }
2197
2198 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2199 enum isl_dim_type type, unsigned first, unsigned n)
2200 {
2201 int i;
2202 int *active = NULL;
2203 int involves = 0;
2204
2205 if (!qp)
2206 return -1;
2207 if (n == 0)
2208 return 0;
2209
2210 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2211 return -1);
2212 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2213 type == isl_dim_set, return -1);
2214
2215 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2216 if (set_active(qp, active) < 0)
2217 goto error;
2218
2219 if (type == isl_dim_set)
2220 first += isl_dim_size(qp->dim, isl_dim_param);
2221 for (i = 0; i < n; ++i)
2222 if (active[first + i]) {
2223 involves = 1;
2224 break;
2225 }
2226
2227 free(active);
2228
2229 return involves;
2230 error:
2231 free(active);
2232 return -1;
2233 }
2234
2235 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2236 * of the divs that do appear in the quasi-polynomial.
2237 */
2238 static __isl_give isl_qpolynomial *remove_redundant_divs(
2239 __isl_take isl_qpolynomial *qp)
2240 {
2241 int i, j;
2242 int d;
2243 int len;
2244 int skip;
2245 int *active = NULL;
2246 int *reordering = NULL;
2247 int redundant = 0;
2248 int n_div;
2249 isl_ctx *ctx;
2250
2251 if (!qp)
2252 return NULL;
2253 if (qp->div->n_row == 0)
2254 return qp;
2255
2256 d = isl_dim_total(qp->dim);
2257 len = qp->div->n_col - 2;
2258 ctx = isl_qpolynomial_get_ctx(qp);
2259 active = isl_calloc_array(ctx, int, len);
2260 if (!active)
2261 goto error;
2262
2263 if (up_set_active(qp->upoly, active, len) < 0)
2264 goto error;
2265
2266 for (i = qp->div->n_row - 1; i >= 0; --i) {
2267 if (!active[d + i]) {
2268 redundant = 1;
2269 continue;
2270 }
2271 for (j = 0; j < i; ++j) {
2272 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2273 continue;
2274 active[d + j] = 1;
2275 break;
2276 }
2277 }
2278
2279 if (!redundant) {
2280 free(active);
2281 return qp;
2282 }
2283
2284 reordering = isl_alloc_array(qp->div->ctx, int, len);
2285 if (!reordering)
2286 goto error;
2287
2288 for (i = 0; i < d; ++i)
2289 reordering[i] = i;
2290
2291 skip = 0;
2292 n_div = qp->div->n_row;
2293 for (i = 0; i < n_div; ++i) {
2294 if (!active[d + i]) {
2295 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2296 qp->div = isl_mat_drop_cols(qp->div,
2297 2 + d + i - skip, 1);
2298 skip++;
2299 }
2300 reordering[d + i] = d + i - skip;
2301 }
2302
2303 qp->upoly = reorder(qp->upoly, reordering);
2304
2305 if (!qp->upoly || !qp->div)
2306 goto error;
2307
2308 free(active);
2309 free(reordering);
2310
2311 return qp;
2312 error:
2313 free(active);
2314 free(reordering);
2315 isl_qpolynomial_free(qp);
2316 return NULL;
2317 }
2318
2319 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2320 unsigned first, unsigned n)
2321 {
2322 int i;
2323 struct isl_upoly_rec *rec;
2324
2325 if (!up)
2326 return NULL;
2327 if (n == 0 || up->var < 0 || up->var < first)
2328 return up;
2329 if (up->var < first + n) {
2330 up = replace_by_constant_term(up);
2331 return isl_upoly_drop(up, first, n);
2332 }
2333 up = isl_upoly_cow(up);
2334 if (!up)
2335 return NULL;
2336 up->var -= n;
2337 rec = isl_upoly_as_rec(up);
2338 if (!rec)
2339 goto error;
2340
2341 for (i = 0; i < rec->n; ++i) {
2342 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2343 if (!rec->p[i])
2344 goto error;
2345 }
2346
2347 return up;
2348 error:
2349 isl_upoly_free(up);
2350 return NULL;
2351 }
2352
2353 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2354 __isl_take isl_qpolynomial *qp,
2355 enum isl_dim_type type, unsigned pos, const char *s)
2356 {
2357 qp = isl_qpolynomial_cow(qp);
2358 if (!qp)
2359 return NULL;
2360 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2361 if (!qp->dim)
2362 goto error;
2363 return qp;
2364 error:
2365 isl_qpolynomial_free(qp);
2366 return NULL;
2367 }
2368
2369 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2370 __isl_take isl_qpolynomial *qp,
2371 enum isl_dim_type type, unsigned first, unsigned n)
2372 {
2373 if (!qp)
2374 return NULL;
2375 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2376 return qp;
2377
2378 qp = isl_qpolynomial_cow(qp);
2379 if (!qp)
2380 return NULL;
2381
2382 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2383 goto error);
2384 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2385 type == isl_dim_set, goto error);
2386
2387 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2388 if (!qp->dim)
2389 goto error;
2390
2391 if (type == isl_dim_set)
2392 first += isl_dim_size(qp->dim, isl_dim_param);
2393
2394 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2395 if (!qp->div)
2396 goto error;
2397
2398 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2399 if (!qp->upoly)
2400 goto error;
2401
2402 return qp;
2403 error:
2404 isl_qpolynomial_free(qp);
2405 return NULL;
2406 }
2407
2408 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2409 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2410 {
2411 int i, j, k;
2412 isl_int denom;
2413 unsigned total;
2414 unsigned n_div;
2415 struct isl_upoly *up;
2416
2417 if (!eq)
2418 goto error;
2419 if (eq->n_eq == 0) {
2420 isl_basic_set_free(eq);
2421 return qp;
2422 }
2423
2424 qp = isl_qpolynomial_cow(qp);
2425 if (!qp)
2426 goto error;
2427 qp->div = isl_mat_cow(qp->div);
2428 if (!qp->div)
2429 goto error;
2430
2431 total = 1 + isl_dim_total(eq->dim);
2432 n_div = eq->n_div;
2433 isl_int_init(denom);
2434 for (i = 0; i < eq->n_eq; ++i) {
2435 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2436 if (j < 0 || j == 0 || j >= total)
2437 continue;
2438
2439 for (k = 0; k < qp->div->n_row; ++k) {
2440 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2441 continue;
2442 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2443 &qp->div->row[k][0]);
2444 normalize_div(qp, k);
2445 }
2446
2447 if (isl_int_is_pos(eq->eq[i][j]))
2448 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2449 isl_int_abs(denom, eq->eq[i][j]);
2450 isl_int_set_si(eq->eq[i][j], 0);
2451
2452 up = isl_upoly_from_affine(qp->dim->ctx,
2453 eq->eq[i], denom, total);
2454 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2455 isl_upoly_free(up);
2456 }
2457 isl_int_clear(denom);
2458
2459 if (!qp->upoly)
2460 goto error;
2461
2462 isl_basic_set_free(eq);
2463
2464 qp = substitute_non_divs(qp);
2465 qp = sort_divs(qp);
2466
2467 return qp;
2468 error:
2469 isl_basic_set_free(eq);
2470 isl_qpolynomial_free(qp);
2471 return NULL;
2472 }
2473
2474 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2475 */
2476 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2477 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2478 {
2479 if (!qp || !eq)
2480 goto error;
2481 if (qp->div->n_row > 0)
2482 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2483 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2484 error:
2485 isl_basic_set_free(eq);
2486 isl_qpolynomial_free(qp);
2487 return NULL;
2488 }
2489
2490 static __isl_give isl_basic_set *add_div_constraints(
2491 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2492 {
2493 int i;
2494 unsigned total;
2495
2496 if (!bset || !div)
2497 goto error;
2498
2499 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2500 if (!bset)
2501 goto error;
2502 total = isl_basic_set_total_dim(bset);
2503 for (i = 0; i < div->n_row; ++i)
2504 if (isl_basic_set_add_div_constraints_var(bset,
2505 total - div->n_row + i, div->row[i]) < 0)
2506 goto error;
2507
2508 isl_mat_free(div);
2509 return bset;
2510 error:
2511 isl_mat_free(div);
2512 isl_basic_set_free(bset);
2513 return NULL;
2514 }
2515
2516 /* Look for equalities among the variables shared by context and qp
2517 * and the integer divisions of qp, if any.
2518 * The equalities are then used to eliminate variables and/or integer
2519 * divisions from qp.
2520 */
2521 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2522 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2523 {
2524 isl_basic_set *aff;
2525
2526 if (!qp)
2527 goto error;
2528 if (qp->div->n_row > 0) {
2529 isl_basic_set *bset;
2530 context = isl_set_add_dims(context, isl_dim_set,
2531 qp->div->n_row);
2532 bset = isl_basic_set_universe(isl_set_get_dim(context));
2533 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2534 context = isl_set_intersect(context,
2535 isl_set_from_basic_set(bset));
2536 }
2537
2538 aff = isl_set_affine_hull(context);
2539 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2540 error:
2541 isl_qpolynomial_free(qp);
2542 isl_set_free(context);
2543 return NULL;
2544 }
2545
2546 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2547 __isl_take isl_qpolynomial *qp)
2548 {
2549 isl_set *dom;
2550
2551 if (!qp)
2552 return NULL;
2553 if (isl_qpolynomial_is_zero(qp)) {
2554 isl_dim *dim = isl_qpolynomial_get_dim(qp);
2555 isl_qpolynomial_free(qp);
2556 return isl_pw_qpolynomial_zero(dim);
2557 }
2558
2559 dom = isl_set_universe(isl_qpolynomial_get_dim(qp));
2560 return isl_pw_qpolynomial_alloc(dom, qp);
2561 }
2562
2563 #undef PW
2564 #define PW isl_pw_qpolynomial
2565 #undef EL
2566 #define EL isl_qpolynomial
2567 #undef EL_IS_ZERO
2568 #define EL_IS_ZERO is_zero
2569 #undef ZERO
2570 #define ZERO zero
2571 #undef IS_ZERO
2572 #define IS_ZERO is_zero
2573 #undef FIELD
2574 #define FIELD qp
2575
2576 #include <isl_pw_templ.c>
2577
2578 #undef UNION
2579 #define UNION isl_union_pw_qpolynomial
2580 #undef PART
2581 #define PART isl_pw_qpolynomial
2582 #undef PARTS
2583 #define PARTS pw_qpolynomial
2584
2585 #include <isl_union_templ.c>
2586
2587 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2588 {
2589 if (!pwqp)
2590 return -1;
2591
2592 if (pwqp->n != -1)
2593 return 0;
2594
2595 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2596 return 0;
2597
2598 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2599 }
2600
2601 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2602 __isl_take isl_pw_qpolynomial *pwqp1,
2603 __isl_take isl_pw_qpolynomial *pwqp2)
2604 {
2605 int i, j, n;
2606 struct isl_pw_qpolynomial *res;
2607
2608 if (!pwqp1 || !pwqp2)
2609 goto error;
2610
2611 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2612 goto error);
2613
2614 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2615 isl_pw_qpolynomial_free(pwqp2);
2616 return pwqp1;
2617 }
2618
2619 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2620 isl_pw_qpolynomial_free(pwqp1);
2621 return pwqp2;
2622 }
2623
2624 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2625 isl_pw_qpolynomial_free(pwqp1);
2626 return pwqp2;
2627 }
2628
2629 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2630 isl_pw_qpolynomial_free(pwqp2);
2631 return pwqp1;
2632 }
2633
2634 n = pwqp1->n * pwqp2->n;
2635 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2636
2637 for (i = 0; i < pwqp1->n; ++i) {
2638 for (j = 0; j < pwqp2->n; ++j) {
2639 struct isl_set *common;
2640 struct isl_qpolynomial *prod;
2641 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2642 isl_set_copy(pwqp2->p[j].set));
2643 if (isl_set_plain_is_empty(common)) {
2644 isl_set_free(common);
2645 continue;
2646 }
2647
2648 prod = isl_qpolynomial_mul(
2649 isl_qpolynomial_copy(pwqp1->p[i].qp),
2650 isl_qpolynomial_copy(pwqp2->p[j].qp));
2651
2652 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2653 }
2654 }
2655
2656 isl_pw_qpolynomial_free(pwqp1);
2657 isl_pw_qpolynomial_free(pwqp2);
2658
2659 return res;
2660 error:
2661 isl_pw_qpolynomial_free(pwqp1);
2662 isl_pw_qpolynomial_free(pwqp2);
2663 return NULL;
2664 }
2665
2666 __isl_give struct isl_upoly *isl_upoly_eval(
2667 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2668 {
2669 int i;
2670 struct isl_upoly_rec *rec;
2671 struct isl_upoly *res;
2672 struct isl_upoly *base;
2673
2674 if (isl_upoly_is_cst(up)) {
2675 isl_vec_free(vec);
2676 return up;
2677 }
2678
2679 rec = isl_upoly_as_rec(up);
2680 if (!rec)
2681 goto error;
2682
2683 isl_assert(up->ctx, rec->n >= 1, goto error);
2684
2685 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2686
2687 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2688 isl_vec_copy(vec));
2689
2690 for (i = rec->n - 2; i >= 0; --i) {
2691 res = isl_upoly_mul(res, isl_upoly_copy(base));
2692 res = isl_upoly_sum(res,
2693 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2694 isl_vec_copy(vec)));
2695 }
2696
2697 isl_upoly_free(base);
2698 isl_upoly_free(up);
2699 isl_vec_free(vec);
2700 return res;
2701 error:
2702 isl_upoly_free(up);
2703 isl_vec_free(vec);
2704 return NULL;
2705 }
2706
2707 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2708 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2709 {
2710 isl_vec *ext;
2711 struct isl_upoly *up;
2712 isl_dim *dim;
2713
2714 if (!qp || !pnt)
2715 goto error;
2716 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2717
2718 if (qp->div->n_row == 0)
2719 ext = isl_vec_copy(pnt->vec);
2720 else {
2721 int i;
2722 unsigned dim = isl_dim_total(qp->dim);
2723 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2724 if (!ext)
2725 goto error;
2726
2727 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2728 for (i = 0; i < qp->div->n_row; ++i) {
2729 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2730 1 + dim + i, &ext->el[1+dim+i]);
2731 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2732 qp->div->row[i][0]);
2733 }
2734 }
2735
2736 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2737 if (!up)
2738 goto error;
2739
2740 dim = isl_dim_copy(qp->dim);
2741 isl_qpolynomial_free(qp);
2742 isl_point_free(pnt);
2743
2744 return isl_qpolynomial_alloc(dim, 0, up);
2745 error:
2746 isl_qpolynomial_free(qp);
2747 isl_point_free(pnt);
2748 return NULL;
2749 }
2750
2751 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2752 __isl_keep struct isl_upoly_cst *cst2)
2753 {
2754 int cmp;
2755 isl_int t;
2756 isl_int_init(t);
2757 isl_int_mul(t, cst1->n, cst2->d);
2758 isl_int_submul(t, cst2->n, cst1->d);
2759 cmp = isl_int_sgn(t);
2760 isl_int_clear(t);
2761 return cmp;
2762 }
2763
2764 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2765 __isl_keep isl_qpolynomial *qp2)
2766 {
2767 struct isl_upoly_cst *cst1, *cst2;
2768
2769 if (!qp1 || !qp2)
2770 return -1;
2771 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2772 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2773 if (isl_qpolynomial_is_nan(qp1))
2774 return -1;
2775 if (isl_qpolynomial_is_nan(qp2))
2776 return -1;
2777 cst1 = isl_upoly_as_cst(qp1->upoly);
2778 cst2 = isl_upoly_as_cst(qp2->upoly);
2779
2780 return isl_upoly_cmp(cst1, cst2) <= 0;
2781 }
2782
2783 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2784 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2785 {
2786 struct isl_upoly_cst *cst1, *cst2;
2787 int cmp;
2788
2789 if (!qp1 || !qp2)
2790 goto error;
2791 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2792 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2793 cst1 = isl_upoly_as_cst(qp1->upoly);
2794 cst2 = isl_upoly_as_cst(qp2->upoly);
2795 cmp = isl_upoly_cmp(cst1, cst2);
2796
2797 if (cmp <= 0) {
2798 isl_qpolynomial_free(qp2);
2799 } else {
2800 isl_qpolynomial_free(qp1);
2801 qp1 = qp2;
2802 }
2803 return qp1;
2804 error:
2805 isl_qpolynomial_free(qp1);
2806 isl_qpolynomial_free(qp2);
2807 return NULL;
2808 }
2809
2810 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2811 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2812 {
2813 struct isl_upoly_cst *cst1, *cst2;
2814 int cmp;
2815
2816 if (!qp1 || !qp2)
2817 goto error;
2818 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2819 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2820 cst1 = isl_upoly_as_cst(qp1->upoly);
2821 cst2 = isl_upoly_as_cst(qp2->upoly);
2822 cmp = isl_upoly_cmp(cst1, cst2);
2823
2824 if (cmp >= 0) {
2825 isl_qpolynomial_free(qp2);
2826 } else {
2827 isl_qpolynomial_free(qp1);
2828 qp1 = qp2;
2829 }
2830 return qp1;
2831 error:
2832 isl_qpolynomial_free(qp1);
2833 isl_qpolynomial_free(qp2);
2834 return NULL;
2835 }
2836
2837 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2838 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2839 unsigned first, unsigned n)
2840 {
2841 unsigned total;
2842 unsigned g_pos;
2843 int *exp;
2844
2845 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2846 return qp;
2847
2848 qp = isl_qpolynomial_cow(qp);
2849 if (!qp)
2850 return NULL;
2851
2852 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2853 goto error);
2854
2855 g_pos = pos(qp->dim, type) + first;
2856
2857 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2858 if (!qp->div)
2859 goto error;
2860
2861 total = qp->div->n_col - 2;
2862 if (total > g_pos) {
2863 int i;
2864 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2865 if (!exp)
2866 goto error;
2867 for (i = 0; i < total - g_pos; ++i)
2868 exp[i] = i + n;
2869 qp->upoly = expand(qp->upoly, exp, g_pos);
2870 free(exp);
2871 if (!qp->upoly)
2872 goto error;
2873 }
2874
2875 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2876 if (!qp->dim)
2877 goto error;
2878
2879 return qp;
2880 error:
2881 isl_qpolynomial_free(qp);
2882 return NULL;
2883 }
2884
2885 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2886 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2887 {
2888 unsigned pos;
2889
2890 pos = isl_qpolynomial_dim(qp, type);
2891
2892 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2893 }
2894
2895 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2896 __isl_take isl_pw_qpolynomial *pwqp,
2897 enum isl_dim_type type, unsigned n)
2898 {
2899 unsigned pos;
2900
2901 pos = isl_pw_qpolynomial_dim(pwqp, type);
2902
2903 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2904 }
2905
2906 static int *reordering_move(isl_ctx *ctx,
2907 unsigned len, unsigned dst, unsigned src, unsigned n)
2908 {
2909 int i;
2910 int *reordering;
2911
2912 reordering = isl_alloc_array(ctx, int, len);
2913 if (!reordering)
2914 return NULL;
2915
2916 if (dst <= src) {
2917 for (i = 0; i < dst; ++i)
2918 reordering[i] = i;
2919 for (i = 0; i < n; ++i)
2920 reordering[src + i] = dst + i;
2921 for (i = 0; i < src - dst; ++i)
2922 reordering[dst + i] = dst + n + i;
2923 for (i = 0; i < len - src - n; ++i)
2924 reordering[src + n + i] = src + n + i;
2925 } else {
2926 for (i = 0; i < src; ++i)
2927 reordering[i] = i;
2928 for (i = 0; i < n; ++i)
2929 reordering[src + i] = dst + i;
2930 for (i = 0; i < dst - src; ++i)
2931 reordering[src + n + i] = src + i;
2932 for (i = 0; i < len - dst - n; ++i)
2933 reordering[dst + n + i] = dst + n + i;
2934 }
2935
2936 return reordering;
2937 }
2938
2939 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2940 __isl_take isl_qpolynomial *qp,
2941 enum isl_dim_type dst_type, unsigned dst_pos,
2942 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2943 {
2944 unsigned g_dst_pos;
2945 unsigned g_src_pos;
2946 int *reordering;
2947
2948 qp = isl_qpolynomial_cow(qp);
2949 if (!qp)
2950 return NULL;
2951
2952 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2953 goto error);
2954
2955 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2956 g_src_pos = pos(qp->dim, src_type) + src_pos;
2957 if (dst_type > src_type)
2958 g_dst_pos -= n;
2959
2960 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2961 if (!qp->div)
2962 goto error;
2963 qp = sort_divs(qp);
2964 if (!qp)
2965 goto error;
2966
2967 reordering = reordering_move(qp->dim->ctx,
2968 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2969 if (!reordering)
2970 goto error;
2971
2972 qp->upoly = reorder(qp->upoly, reordering);
2973 free(reordering);
2974 if (!qp->upoly)
2975 goto error;
2976
2977 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2978 if (!qp->dim)
2979 goto error;
2980
2981 return qp;
2982 error:
2983 isl_qpolynomial_free(qp);
2984 return NULL;
2985 }
2986
2987 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2988 isl_int *f, isl_int denom)
2989 {
2990 struct isl_upoly *up;
2991
2992 if (!dim)
2993 return NULL;
2994
2995 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2996
2997 return isl_qpolynomial_alloc(dim, 0, up);
2998 }
2999
3000 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3001 {
3002 isl_ctx *ctx;
3003 struct isl_upoly *up;
3004 isl_qpolynomial *qp;
3005
3006 if (!aff)
3007 return NULL;
3008
3009 ctx = isl_aff_get_ctx(aff);
3010 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3011 aff->v->size - 1);
3012
3013 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
3014 aff->ls->div->n_row, up);
3015 if (!qp)
3016 goto error;
3017
3018 isl_mat_free(qp->div);
3019 qp->div = isl_mat_copy(aff->ls->div);
3020 qp->div = isl_mat_cow(qp->div);
3021 if (!qp->div)
3022 goto error;
3023
3024 isl_aff_free(aff);
3025 qp = reduce_divs(qp);
3026 qp = remove_redundant_divs(qp);
3027 return qp;
3028 error:
3029 isl_aff_free(aff);
3030 return NULL;
3031 }
3032
3033 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3034 __isl_take isl_pw_aff *pwaff)
3035 {
3036 int i;
3037 isl_pw_qpolynomial *pwqp;
3038
3039 if (!pwaff)
3040 return NULL;
3041
3042 pwqp = isl_pw_qpolynomial_alloc_(isl_pw_aff_get_dim(pwaff), pwaff->n);
3043
3044 for (i = 0; i < pwaff->n; ++i) {
3045 isl_set *dom;
3046 isl_qpolynomial *qp;
3047
3048 dom = isl_set_copy(pwaff->p[i].set);
3049 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3050 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3051 }
3052
3053 isl_pw_aff_free(pwaff);
3054 return pwqp;
3055 }
3056
3057 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3058 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3059 {
3060 isl_aff *aff;
3061
3062 aff = isl_constraint_get_bound(c, type, pos);
3063 isl_constraint_free(c);
3064 return isl_qpolynomial_from_aff(aff);
3065 }
3066
3067 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3068 * in "qp" by subs[i].
3069 */
3070 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3071 __isl_take isl_qpolynomial *qp,
3072 enum isl_dim_type type, unsigned first, unsigned n,
3073 __isl_keep isl_qpolynomial **subs)
3074 {
3075 int i;
3076 struct isl_upoly **ups;
3077
3078 if (n == 0)
3079 return qp;
3080
3081 qp = isl_qpolynomial_cow(qp);
3082 if (!qp)
3083 return NULL;
3084 for (i = 0; i < n; ++i)
3085 if (!subs[i])
3086 goto error;
3087
3088 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3089 goto error);
3090
3091 for (i = 0; i < n; ++i)
3092 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3093 goto error);
3094
3095 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3096 for (i = 0; i < n; ++i)
3097 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3098
3099 first += pos(qp->dim, type);
3100
3101 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3102 if (!ups)
3103 goto error;
3104 for (i = 0; i < n; ++i)
3105 ups[i] = subs[i]->upoly;
3106
3107 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3108
3109 free(ups);
3110
3111 if (!qp->upoly)
3112 goto error;
3113
3114 return qp;
3115 error:
3116 isl_qpolynomial_free(qp);
3117 return NULL;
3118 }
3119
3120 /* Extend "bset" with extra set dimensions for each integer division
3121 * in "qp" and then call "fn" with the extended bset and the polynomial
3122 * that results from replacing each of the integer divisions by the
3123 * corresponding extra set dimension.
3124 */
3125 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3126 __isl_keep isl_basic_set *bset,
3127 int (*fn)(__isl_take isl_basic_set *bset,
3128 __isl_take isl_qpolynomial *poly, void *user), void *user)
3129 {
3130 isl_dim *dim;
3131 isl_mat *div;
3132 isl_qpolynomial *poly;
3133
3134 if (!qp || !bset)
3135 goto error;
3136 if (qp->div->n_row == 0)
3137 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3138 user);
3139
3140 div = isl_mat_copy(qp->div);
3141 dim = isl_dim_copy(qp->dim);
3142 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3143 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3144 bset = isl_basic_set_copy(bset);
3145 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3146 bset = add_div_constraints(bset, div);
3147
3148 return fn(bset, poly, user);
3149 error:
3150 return -1;
3151 }
3152
3153 /* Return total degree in variables first (inclusive) up to last (exclusive).
3154 */
3155 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3156 {
3157 int deg = -1;
3158 int i;
3159 struct isl_upoly_rec *rec;
3160
3161 if (!up)
3162 return -2;
3163 if (isl_upoly_is_zero(up))
3164 return -1;
3165 if (isl_upoly_is_cst(up) || up->var < first)
3166 return 0;
3167
3168 rec = isl_upoly_as_rec(up);
3169 if (!rec)
3170 return -2;
3171
3172 for (i = 0; i < rec->n; ++i) {
3173 int d;
3174
3175 if (isl_upoly_is_zero(rec->p[i]))
3176 continue;
3177 d = isl_upoly_degree(rec->p[i], first, last);
3178 if (up->var < last)
3179 d += i;
3180 if (d > deg)
3181 deg = d;
3182 }
3183
3184 return deg;
3185 }
3186
3187 /* Return total degree in set variables.
3188 */
3189 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3190 {
3191 unsigned ovar;
3192 unsigned nvar;
3193
3194 if (!poly)
3195 return -2;
3196
3197 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3198 nvar = isl_dim_size(poly->dim, isl_dim_set);
3199 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3200 }
3201
3202 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3203 unsigned pos, int deg)
3204 {
3205 int i;
3206 struct isl_upoly_rec *rec;
3207
3208 if (!up)
3209 return NULL;
3210
3211 if (isl_upoly_is_cst(up) || up->var < pos) {
3212 if (deg == 0)
3213 return isl_upoly_copy(up);
3214 else
3215 return isl_upoly_zero(up->ctx);
3216 }
3217
3218 rec = isl_upoly_as_rec(up);
3219 if (!rec)
3220 return NULL;
3221
3222 if (up->var == pos) {
3223 if (deg < rec->n)
3224 return isl_upoly_copy(rec->p[deg]);
3225 else
3226 return isl_upoly_zero(up->ctx);
3227 }
3228
3229 up = isl_upoly_copy(up);
3230 up = isl_upoly_cow(up);
3231 rec = isl_upoly_as_rec(up);
3232 if (!rec)
3233 goto error;
3234
3235 for (i = 0; i < rec->n; ++i) {
3236 struct isl_upoly *t;
3237 t = isl_upoly_coeff(rec->p[i], pos, deg);
3238 if (!t)
3239 goto error;
3240 isl_upoly_free(rec->p[i]);
3241 rec->p[i] = t;
3242 }
3243
3244 return up;
3245 error:
3246 isl_upoly_free(up);
3247 return NULL;
3248 }
3249
3250 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3251 */
3252 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3253 __isl_keep isl_qpolynomial *qp,
3254 enum isl_dim_type type, unsigned t_pos, int deg)
3255 {
3256 unsigned g_pos;
3257 struct isl_upoly *up;
3258 isl_qpolynomial *c;
3259
3260 if (!qp)
3261 return NULL;
3262
3263 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3264 return NULL);
3265
3266 g_pos = pos(qp->dim, type) + t_pos;
3267 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3268
3269 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3270 if (!c)
3271 return NULL;
3272 isl_mat_free(c->div);
3273 c->div = isl_mat_copy(qp->div);
3274 if (!c->div)
3275 goto error;
3276 return c;
3277 error:
3278 isl_qpolynomial_free(c);
3279 return NULL;
3280 }
3281
3282 /* Homogenize the polynomial in the variables first (inclusive) up to
3283 * last (exclusive) by inserting powers of variable first.
3284 * Variable first is assumed not to appear in the input.
3285 */
3286 __isl_give struct isl_upoly *isl_upoly_homogenize(
3287 __isl_take struct isl_upoly *up, int deg, int target,
3288 int first, int last)
3289 {
3290 int i;
3291 struct isl_upoly_rec *rec;
3292
3293 if (!up)
3294 return NULL;
3295 if (isl_upoly_is_zero(up))
3296 return up;
3297 if (deg == target)
3298 return up;
3299 if (isl_upoly_is_cst(up) || up->var < first) {
3300 struct isl_upoly *hom;
3301
3302 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3303 if (!hom)
3304 goto error;
3305 rec = isl_upoly_as_rec(hom);
3306 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3307
3308 return hom;
3309 }
3310
3311 up = isl_upoly_cow(up);
3312 rec = isl_upoly_as_rec(up);
3313 if (!rec)
3314 goto error;
3315
3316 for (i = 0; i < rec->n; ++i) {
3317 if (isl_upoly_is_zero(rec->p[i]))
3318 continue;
3319 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3320 up->var < last ? deg + i : i, target,
3321 first, last);
3322 if (!rec->p[i])
3323 goto error;
3324 }
3325
3326 return up;
3327 error:
3328 isl_upoly_free(up);
3329 return NULL;
3330 }
3331
3332 /* Homogenize the polynomial in the set variables by introducing
3333 * powers of an extra set variable at position 0.
3334 */
3335 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3336 __isl_take isl_qpolynomial *poly)
3337 {
3338 unsigned ovar;
3339 unsigned nvar;
3340 int deg = isl_qpolynomial_degree(poly);
3341
3342 if (deg < -1)
3343 goto error;
3344
3345 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3346 poly = isl_qpolynomial_cow(poly);
3347 if (!poly)
3348 goto error;
3349
3350 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3351 nvar = isl_dim_size(poly->dim, isl_dim_set);
3352 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3353 ovar, ovar + nvar);
3354 if (!poly->upoly)
3355 goto error;
3356
3357 return poly;
3358 error:
3359 isl_qpolynomial_free(poly);
3360 return NULL;
3361 }
3362
3363 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3364 __isl_take isl_mat *div)
3365 {
3366 isl_term *term;
3367 int n;
3368
3369 if (!dim || !div)
3370 goto error;
3371
3372 n = isl_dim_total(dim) + div->n_row;
3373
3374 term = isl_calloc(dim->ctx, struct isl_term,
3375 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3376 if (!term)
3377 goto error;
3378
3379 term->ref = 1;
3380 term->dim = dim;
3381 term->div = div;
3382 isl_int_init(term->n);
3383 isl_int_init(term->d);
3384
3385 return term;
3386 error:
3387 isl_dim_free(dim);
3388 isl_mat_free(div);
3389 return NULL;
3390 }
3391
3392 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3393 {
3394 if (!term)
3395 return NULL;
3396
3397 term->ref++;
3398 return term;
3399 }
3400
3401 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3402 {
3403 int i;
3404 isl_term *dup;
3405 unsigned total;
3406
3407 if (term)
3408 return NULL;
3409
3410 total = isl_dim_total(term->dim) + term->div->n_row;
3411
3412 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3413 if (!dup)
3414 return NULL;
3415
3416 isl_int_set(dup->n, term->n);
3417 isl_int_set(dup->d, term->d);
3418
3419 for (i = 0; i < total; ++i)
3420 dup->pow[i] = term->pow[i];
3421
3422 return dup;
3423 }
3424
3425 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3426 {
3427 if (!term)
3428 return NULL;
3429
3430 if (term->ref == 1)
3431 return term;
3432 term->ref--;
3433 return isl_term_dup(term);
3434 }
3435
3436 void isl_term_free(__isl_take isl_term *term)
3437 {
3438 if (!term)
3439 return;
3440
3441 if (--term->ref > 0)
3442 return;
3443
3444 isl_dim_free(term->dim);
3445 isl_mat_free(term->div);
3446 isl_int_clear(term->n);
3447 isl_int_clear(term->d);
3448 free(term);
3449 }
3450
3451 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3452 {
3453 if (!term)
3454 return 0;
3455
3456 switch (type) {
3457 case isl_dim_param:
3458 case isl_dim_in:
3459 case isl_dim_out: return isl_dim_size(term->dim, type);
3460 case isl_dim_div: return term->div->n_row;
3461 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3462 default: return 0;
3463 }
3464 }
3465
3466 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3467 {
3468 return term ? term->dim->ctx : NULL;
3469 }
3470
3471 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3472 {
3473 if (!term)
3474 return;
3475 isl_int_set(*n, term->n);
3476 }
3477
3478 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3479 {
3480 if (!term)
3481 return;
3482 isl_int_set(*d, term->d);
3483 }
3484
3485 int isl_term_get_exp(__isl_keep isl_term *term,
3486 enum isl_dim_type type, unsigned pos)
3487 {
3488 if (!term)
3489 return -1;
3490
3491 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3492
3493 if (type >= isl_dim_set)
3494 pos += isl_dim_size(term->dim, isl_dim_param);
3495 if (type >= isl_dim_div)
3496 pos += isl_dim_size(term->dim, isl_dim_set);
3497
3498 return term->pow[pos];
3499 }
3500
3501 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3502 {
3503 isl_basic_map *bmap;
3504 unsigned total;
3505 int k;
3506
3507 if (!term)
3508 return NULL;
3509
3510 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3511 return NULL);
3512
3513 total = term->div->n_col - term->div->n_row - 2;
3514 /* No nested divs for now */
3515 isl_assert(term->dim->ctx,
3516 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3517 term->div->n_row) == -1,
3518 return NULL);
3519
3520 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3521 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3522 goto error;
3523
3524 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3525
3526 return isl_basic_map_div(bmap, k);
3527 error:
3528 isl_basic_map_free(bmap);
3529 return NULL;
3530 }
3531
3532 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3533 int (*fn)(__isl_take isl_term *term, void *user),
3534 __isl_take isl_term *term, void *user)
3535 {
3536 int i;
3537 struct isl_upoly_rec *rec;
3538
3539 if (!up || !term)
3540 goto error;
3541
3542 if (isl_upoly_is_zero(up))
3543 return term;
3544
3545 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3546 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3547 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3548
3549 if (isl_upoly_is_cst(up)) {
3550 struct isl_upoly_cst *cst;
3551 cst = isl_upoly_as_cst(up);
3552 if (!cst)
3553 goto error;
3554 term = isl_term_cow(term);
3555 if (!term)
3556 goto error;
3557 isl_int_set(term->n, cst->n);
3558 isl_int_set(term->d, cst->d);
3559 if (fn(isl_term_copy(term), user) < 0)
3560 goto error;
3561 return term;
3562 }
3563
3564 rec = isl_upoly_as_rec(up);
3565 if (!rec)
3566 goto error;
3567
3568 for (i = 0; i < rec->n; ++i) {
3569 term = isl_term_cow(term);
3570 if (!term)
3571 goto error;
3572 term->pow[up->var] = i;
3573 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3574 if (!term)
3575 goto error;
3576 }
3577 term->pow[up->var] = 0;
3578
3579 return term;
3580 error:
3581 isl_term_free(term);
3582 return NULL;
3583 }
3584
3585 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3586 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3587 {
3588 isl_term *term;
3589
3590 if (!qp)
3591 return -1;
3592
3593 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3594 if (!term)
3595 return -1;
3596
3597 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3598
3599 isl_term_free(term);
3600
3601 return term ? 0 : -1;
3602 }
3603
3604 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3605 {
3606 struct isl_upoly *up;
3607 isl_qpolynomial *qp;
3608 int i, n;
3609
3610 if (!term)
3611 return NULL;
3612
3613 n = isl_dim_total(term->dim) + term->div->n_row;
3614
3615 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3616 for (i = 0; i < n; ++i) {
3617 if (!term->pow[i])
3618 continue;
3619 up = isl_upoly_mul(up,
3620 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3621 }
3622
3623 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3624 if (!qp)
3625 goto error;
3626 isl_mat_free(qp->div);
3627 qp->div = isl_mat_copy(term->div);
3628 if (!qp->div)
3629 goto error;
3630
3631 isl_term_free(term);
3632 return qp;
3633 error:
3634 isl_qpolynomial_free(qp);
3635 isl_term_free(term);
3636 return NULL;
3637 }
3638
3639 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3640 __isl_take isl_dim *dim)
3641 {
3642 int i;
3643 int extra;
3644 unsigned total;
3645
3646 if (!qp || !dim)
3647 goto error;
3648
3649 if (isl_dim_equal(qp->dim, dim)) {
3650 isl_dim_free(dim);
3651 return qp;
3652 }
3653
3654 qp = isl_qpolynomial_cow(qp);
3655 if (!qp)
3656 goto error;
3657
3658 extra = isl_dim_size(dim, isl_dim_set) -
3659 isl_dim_size(qp->dim, isl_dim_set);
3660 total = isl_dim_total(qp->dim);
3661 if (qp->div->n_row) {
3662 int *exp;
3663
3664 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3665 if (!exp)
3666 goto error;
3667 for (i = 0; i < qp->div->n_row; ++i)
3668 exp[i] = extra + i;
3669 qp->upoly = expand(qp->upoly, exp, total);
3670 free(exp);
3671 if (!qp->upoly)
3672 goto error;
3673 }
3674 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3675 if (!qp->div)
3676 goto error;
3677 for (i = 0; i < qp->div->n_row; ++i)
3678 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3679
3680 isl_dim_free(qp->dim);
3681 qp->dim = dim;
3682
3683 return qp;
3684 error:
3685 isl_dim_free(dim);
3686 isl_qpolynomial_free(qp);
3687 return NULL;
3688 }
3689
3690 /* For each parameter or variable that does not appear in qp,
3691 * first eliminate the variable from all constraints and then set it to zero.
3692 */
3693 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3694 __isl_keep isl_qpolynomial *qp)
3695 {
3696 int *active = NULL;
3697 int i;
3698 int d;
3699 unsigned nparam;
3700 unsigned nvar;
3701
3702 if (!set || !qp)
3703 goto error;
3704
3705 d = isl_dim_total(set->dim);
3706 active = isl_calloc_array(set->ctx, int, d);
3707 if (set_active(qp, active) < 0)
3708 goto error;
3709
3710 for (i = 0; i < d; ++i)
3711 if (!active[i])
3712 break;
3713
3714 if (i == d) {
3715 free(active);
3716 return set;
3717 }
3718
3719 nparam = isl_dim_size(set->dim, isl_dim_param);
3720 nvar = isl_dim_size(set->dim, isl_dim_set);
3721 for (i = 0; i < nparam; ++i) {
3722 if (active[i])
3723 continue;
3724 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3725 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3726 }
3727 for (i = 0; i < nvar; ++i) {
3728 if (active[nparam + i])
3729 continue;
3730 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3731 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3732 }
3733
3734 free(active);
3735
3736 return set;
3737 error:
3738 free(active);
3739 isl_set_free(set);
3740 return NULL;
3741 }
3742
3743 struct isl_opt_data {
3744 isl_qpolynomial *qp;
3745 int first;
3746 isl_qpolynomial *opt;
3747 int max;
3748 };
3749
3750 static int opt_fn(__isl_take isl_point *pnt, void *user)
3751 {
3752 struct isl_opt_data *data = (struct isl_opt_data *)user;
3753 isl_qpolynomial *val;
3754
3755 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3756 if (data->first) {
3757 data->first = 0;
3758 data->opt = val;
3759 } else if (data->max) {
3760 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3761 } else {
3762 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3763 }
3764
3765 return 0;
3766 }
3767
3768 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3769 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3770 {
3771 struct isl_opt_data data = { NULL, 1, NULL, max };
3772
3773 if (!set || !qp)
3774 goto error;
3775
3776 if (isl_upoly_is_cst(qp->upoly)) {
3777 isl_set_free(set);
3778 return qp;
3779 }
3780
3781 set = fix_inactive(set, qp);
3782
3783 data.qp = qp;
3784 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3785 goto error;
3786
3787 if (data.first)
3788 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3789
3790 isl_set_free(set);
3791 isl_qpolynomial_free(qp);
3792 return data.opt;
3793 error:
3794 isl_set_free(set);
3795 isl_qpolynomial_free(qp);
3796 isl_qpolynomial_free(data.opt);
3797 return NULL;
3798 }
3799
3800 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3801 __isl_take isl_morph *morph)
3802 {
3803 int i;
3804 int n_sub;
3805 isl_ctx *ctx;
3806 struct isl_upoly **subs;
3807 isl_mat *mat;
3808
3809 qp = isl_qpolynomial_cow(qp);
3810 if (!qp || !morph)
3811 goto error;
3812
3813 ctx = qp->dim->ctx;
3814 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3815
3816 n_sub = morph->inv->n_row - 1;
3817 if (morph->inv->n_row != morph->inv->n_col)
3818 n_sub += qp->div->n_row;
3819 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3820 if (!subs)
3821 goto error;
3822
3823 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3824 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3825 morph->inv->row[0][0], morph->inv->n_col);
3826 if (morph->inv->n_row != morph->inv->n_col)
3827 for (i = 0; i < qp->div->n_row; ++i)
3828 subs[morph->inv->n_row - 1 + i] =
3829 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3830
3831 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3832
3833 for (i = 0; i < n_sub; ++i)
3834 isl_upoly_free(subs[i]);
3835 free(subs);
3836
3837 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3838 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3839 qp->div = isl_mat_product(qp->div, mat);
3840 isl_dim_free(qp->dim);
3841 qp->dim = isl_dim_copy(morph->ran->dim);
3842
3843 if (!qp->upoly || !qp->div || !qp->dim)
3844 goto error;
3845
3846 isl_morph_free(morph);
3847
3848 return qp;
3849 error:
3850 isl_qpolynomial_free(qp);
3851 isl_morph_free(morph);
3852 return NULL;
3853 }
3854
3855 static int neg_entry(void **entry, void *user)
3856 {
3857 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3858
3859 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3860
3861 return *pwqp ? 0 : -1;
3862 }
3863
3864 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3865 __isl_take isl_union_pw_qpolynomial *upwqp)
3866 {
3867 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3868 if (!upwqp)
3869 return NULL;
3870
3871 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3872 &neg_entry, NULL) < 0)
3873 goto error;
3874
3875 return upwqp;
3876 error:
3877 isl_union_pw_qpolynomial_free(upwqp);
3878 return NULL;
3879 }
3880
3881 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3882 __isl_take isl_union_pw_qpolynomial *upwqp1,
3883 __isl_take isl_union_pw_qpolynomial *upwqp2)
3884 {
3885 return isl_union_pw_qpolynomial_add(upwqp1,
3886 isl_union_pw_qpolynomial_neg(upwqp2));
3887 }
3888
3889 static int mul_entry(void **entry, void *user)
3890 {
3891 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3892 uint32_t hash;
3893 struct isl_hash_table_entry *entry2;
3894 isl_pw_qpolynomial *pwpq = *entry;
3895 int empty;
3896
3897 hash = isl_dim_get_hash(pwpq->dim);
3898 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3899 hash, &has_dim, pwpq->dim, 0);
3900 if (!entry2)
3901 return 0;
3902
3903 pwpq = isl_pw_qpolynomial_copy(pwpq);
3904 pwpq = isl_pw_qpolynomial_mul(pwpq,
3905 isl_pw_qpolynomial_copy(entry2->data));
3906
3907 empty = isl_pw_qpolynomial_is_zero(pwpq);
3908 if (empty < 0) {
3909 isl_pw_qpolynomial_free(pwpq);
3910 return -1;
3911 }
3912 if (empty) {
3913 isl_pw_qpolynomial_free(pwpq);
3914 return 0;
3915 }
3916
3917 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3918
3919 return 0;
3920 }
3921
3922 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3923 __isl_take isl_union_pw_qpolynomial *upwqp1,
3924 __isl_take isl_union_pw_qpolynomial *upwqp2)
3925 {
3926 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3927 }
3928
3929 /* Reorder the columns of the given div definitions according to the
3930 * given reordering.
3931 */
3932 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3933 __isl_take isl_reordering *r)
3934 {
3935 int i, j;
3936 isl_mat *mat;
3937 int extra;
3938
3939 if (!div || !r)
3940 goto error;
3941
3942 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3943 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3944 if (!mat)
3945 goto error;
3946
3947 for (i = 0; i < div->n_row; ++i) {
3948 isl_seq_cpy(mat->row[i], div->row[i], 2);
3949 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3950 for (j = 0; j < r->len; ++j)
3951 isl_int_set(mat->row[i][2 + r->pos[j]],
3952 div->row[i][2 + j]);
3953 }
3954
3955 isl_reordering_free(r);
3956 isl_mat_free(div);
3957 return mat;
3958 error:
3959 isl_reordering_free(r);
3960 isl_mat_free(div);
3961 return NULL;
3962 }
3963
3964 /* Reorder the dimension of "qp" according to the given reordering.
3965 */
3966 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3967 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3968 {
3969 qp = isl_qpolynomial_cow(qp);
3970 if (!qp)
3971 goto error;
3972
3973 r = isl_reordering_extend(r, qp->div->n_row);
3974 if (!r)
3975 goto error;
3976
3977 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3978 if (!qp->div)
3979 goto error;
3980
3981 qp->upoly = reorder(qp->upoly, r->pos);
3982 if (!qp->upoly)
3983 goto error;
3984
3985 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3986
3987 isl_reordering_free(r);
3988 return qp;
3989 error:
3990 isl_qpolynomial_free(qp);
3991 isl_reordering_free(r);
3992 return NULL;
3993 }
3994
3995 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3996 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3997 {
3998 if (!qp || !model)
3999 goto error;
4000
4001 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4002 isl_reordering *exp;
4003
4004 model = isl_dim_drop(model, isl_dim_in,
4005 0, isl_dim_size(model, isl_dim_in));
4006 model = isl_dim_drop(model, isl_dim_out,
4007 0, isl_dim_size(model, isl_dim_out));
4008 exp = isl_parameter_alignment_reordering(qp->dim, model);
4009 exp = isl_reordering_extend_dim(exp,
4010 isl_qpolynomial_get_dim(qp));
4011 qp = isl_qpolynomial_realign(qp, exp);
4012 }
4013
4014 isl_dim_free(model);
4015 return qp;
4016 error:
4017 isl_dim_free(model);
4018 isl_qpolynomial_free(qp);
4019 return NULL;
4020 }
4021
4022 struct isl_split_periods_data {
4023 int max_periods;
4024 isl_pw_qpolynomial *res;
4025 };
4026
4027 /* Create a slice where the integer division "div" has the fixed value "v".
4028 * In particular, if "div" refers to floor(f/m), then create a slice
4029 *
4030 * m v <= f <= m v + (m - 1)
4031 *
4032 * or
4033 *
4034 * f - m v >= 0
4035 * -f + m v + (m - 1) >= 0
4036 */
4037 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
4038 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4039 {
4040 int total;
4041 isl_basic_set *bset = NULL;
4042 int k;
4043
4044 if (!dim || !qp)
4045 goto error;
4046
4047 total = isl_dim_total(dim);
4048 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4049
4050 k = isl_basic_set_alloc_inequality(bset);
4051 if (k < 0)
4052 goto error;
4053 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4054 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4055
4056 k = isl_basic_set_alloc_inequality(bset);
4057 if (k < 0)
4058 goto error;
4059 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4060 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4061 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4062 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4063
4064 isl_dim_free(dim);
4065 return isl_set_from_basic_set(bset);
4066 error:
4067 isl_basic_set_free(bset);
4068 isl_dim_free(dim);
4069 return NULL;
4070 }
4071
4072 static int split_periods(__isl_take isl_set *set,
4073 __isl_take isl_qpolynomial *qp, void *user);
4074
4075 /* Create a slice of the domain "set" such that integer division "div"
4076 * has the fixed value "v" and add the results to data->res,
4077 * replacing the integer division by "v" in "qp".
4078 */
4079 static int set_div(__isl_take isl_set *set,
4080 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4081 struct isl_split_periods_data *data)
4082 {
4083 int i;
4084 int total;
4085 isl_set *slice;
4086 struct isl_upoly *cst;
4087
4088 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4089 set = isl_set_intersect(set, slice);
4090
4091 if (!qp)
4092 goto error;
4093
4094 total = isl_dim_total(qp->dim);
4095
4096 for (i = div + 1; i < qp->div->n_row; ++i) {
4097 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4098 continue;
4099 isl_int_addmul(qp->div->row[i][1],
4100 qp->div->row[i][2 + total + div], v);
4101 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4102 }
4103
4104 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4105 qp = substitute_div(qp, div, cst);
4106
4107 return split_periods(set, qp, data);
4108 error:
4109 isl_set_free(set);
4110 isl_qpolynomial_free(qp);
4111 return -1;
4112 }
4113
4114 /* Split the domain "set" such that integer division "div"
4115 * has a fixed value (ranging from "min" to "max") on each slice
4116 * and add the results to data->res.
4117 */
4118 static int split_div(__isl_take isl_set *set,
4119 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4120 struct isl_split_periods_data *data)
4121 {
4122 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4123 isl_set *set_i = isl_set_copy(set);
4124 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4125
4126 if (set_div(set_i, qp_i, div, min, data) < 0)
4127 goto error;
4128 }
4129 isl_set_free(set);
4130 isl_qpolynomial_free(qp);
4131 return 0;
4132 error:
4133 isl_set_free(set);
4134 isl_qpolynomial_free(qp);
4135 return -1;
4136 }
4137
4138 /* If "qp" refers to any integer division
4139 * that can only attain "max_periods" distinct values on "set"
4140 * then split the domain along those distinct values.
4141 * Add the results (or the original if no splitting occurs)
4142 * to data->res.
4143 */
4144 static int split_periods(__isl_take isl_set *set,
4145 __isl_take isl_qpolynomial *qp, void *user)
4146 {
4147 int i;
4148 isl_pw_qpolynomial *pwqp;
4149 struct isl_split_periods_data *data;
4150 isl_int min, max;
4151 int total;
4152 int r = 0;
4153
4154 data = (struct isl_split_periods_data *)user;
4155
4156 if (!set || !qp)
4157 goto error;
4158
4159 if (qp->div->n_row == 0) {
4160 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4161 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4162 return 0;
4163 }
4164
4165 isl_int_init(min);
4166 isl_int_init(max);
4167 total = isl_dim_total(qp->dim);
4168 for (i = 0; i < qp->div->n_row; ++i) {
4169 enum isl_lp_result lp_res;
4170
4171 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4172 qp->div->n_row) != -1)
4173 continue;
4174
4175 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4176 set->ctx->one, &min, NULL, NULL);
4177 if (lp_res == isl_lp_error)
4178 goto error2;
4179 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4180 continue;
4181 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4182
4183 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4184 set->ctx->one, &max, NULL, NULL);
4185 if (lp_res == isl_lp_error)
4186 goto error2;
4187 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4188 continue;
4189 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4190
4191 isl_int_sub(max, max, min);
4192 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4193 isl_int_add(max, max, min);
4194 break;
4195 }
4196 }
4197
4198 if (i < qp->div->n_row) {
4199 r = split_div(set, qp, i, min, max, data);
4200 } else {
4201 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4202 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4203 }
4204
4205 isl_int_clear(max);
4206 isl_int_clear(min);
4207
4208 return r;
4209 error2:
4210 isl_int_clear(max);
4211 isl_int_clear(min);
4212 error:
4213 isl_set_free(set);
4214 isl_qpolynomial_free(qp);
4215 return -1;
4216 }
4217
4218 /* If any quasi-polynomial in pwqp refers to any integer division
4219 * that can only attain "max_periods" distinct values on its domain
4220 * then split the domain along those distinct values.
4221 */
4222 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4223 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4224 {
4225 struct isl_split_periods_data data;
4226
4227 data.max_periods = max_periods;
4228 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4229
4230 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4231 goto error;
4232
4233 isl_pw_qpolynomial_free(pwqp);
4234
4235 return data.res;
4236 error:
4237 isl_pw_qpolynomial_free(data.res);
4238 isl_pw_qpolynomial_free(pwqp);
4239 return NULL;
4240 }
4241
4242 /* Construct a piecewise quasipolynomial that is constant on the given
4243 * domain. In particular, it is
4244 * 0 if cst == 0
4245 * 1 if cst == 1
4246 * infinity if cst == -1
4247 */
4248 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4249 __isl_take isl_basic_set *bset, int cst)
4250 {
4251 isl_dim *dim;
4252 isl_qpolynomial *qp;
4253
4254 if (!bset)
4255 return NULL;
4256
4257 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4258 dim = isl_basic_set_get_dim(bset);
4259 if (cst < 0)
4260 qp = isl_qpolynomial_infty(dim);
4261 else if (cst == 0)
4262 qp = isl_qpolynomial_zero(dim);
4263 else
4264 qp = isl_qpolynomial_one(dim);
4265 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4266 }
4267
4268 /* Factor bset, call fn on each of the factors and return the product.
4269 *
4270 * If no factors can be found, simply call fn on the input.
4271 * Otherwise, construct the factors based on the factorizer,
4272 * call fn on each factor and compute the product.
4273 */
4274 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4275 __isl_take isl_basic_set *bset,
4276 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4277 {
4278 int i, n;
4279 isl_dim *dim;
4280 isl_set *set;
4281 isl_factorizer *f;
4282 isl_qpolynomial *qp;
4283 isl_pw_qpolynomial *pwqp;
4284 unsigned nparam;
4285 unsigned nvar;
4286
4287 f = isl_basic_set_factorizer(bset);
4288 if (!f)
4289 goto error;
4290 if (f->n_group == 0) {
4291 isl_factorizer_free(f);
4292 return fn(bset);
4293 }
4294
4295 nparam = isl_basic_set_dim(bset, isl_dim_param);
4296 nvar = isl_basic_set_dim(bset, isl_dim_set);
4297
4298 dim = isl_basic_set_get_dim(bset);
4299 dim = isl_dim_domain(dim);
4300 set = isl_set_universe(isl_dim_copy(dim));
4301 qp = isl_qpolynomial_one(dim);
4302 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4303
4304 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4305
4306 for (i = 0, n = 0; i < f->n_group; ++i) {
4307 isl_basic_set *bset_i;
4308 isl_pw_qpolynomial *pwqp_i;
4309
4310 bset_i = isl_basic_set_copy(bset);
4311 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4312 nparam + n + f->len[i], nvar - n - f->len[i]);
4313 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4314 nparam, n);
4315 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4316 n + f->len[i], nvar - n - f->len[i]);
4317 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4318
4319 pwqp_i = fn(bset_i);
4320 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4321
4322 n += f->len[i];
4323 }
4324
4325 isl_basic_set_free(bset);
4326 isl_factorizer_free(f);
4327
4328 return pwqp;
4329 error:
4330 isl_basic_set_free(bset);
4331 return NULL;
4332 }
4333
4334 /* Factor bset, call fn on each of the factors and return the product.
4335 * The function is assumed to evaluate to zero on empty domains,
4336 * to one on zero-dimensional domains and to infinity on unbounded domains
4337 * and will not be called explicitly on zero-dimensional or unbounded domains.
4338 *
4339 * We first check for some special cases and remove all equalities.
4340 * Then we hand over control to compressed_multiplicative_call.
4341 */
4342 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4343 __isl_take isl_basic_set *bset,
4344 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4345 {
4346 int bounded;
4347 isl_morph *morph;
4348 isl_pw_qpolynomial *pwqp;
4349 unsigned orig_nvar, final_nvar;
4350
4351 if (!bset)
4352 return NULL;
4353
4354 if (isl_basic_set_plain_is_empty(bset))
4355 return constant_on_domain(bset, 0);
4356
4357 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4358
4359 if (orig_nvar == 0)
4360 return constant_on_domain(bset, 1);
4361
4362 bounded = isl_basic_set_is_bounded(bset);
4363 if (bounded < 0)
4364 goto error;
4365 if (!bounded)
4366 return constant_on_domain(bset, -1);
4367
4368 if (bset->n_eq == 0)
4369 return compressed_multiplicative_call(bset, fn);
4370
4371 morph = isl_basic_set_full_compression(bset);
4372 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4373
4374 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4375
4376 pwqp = compressed_multiplicative_call(bset, fn);
4377
4378 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4379 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4380 morph = isl_morph_inverse(morph);
4381
4382 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4383
4384 return pwqp;
4385 error:
4386 isl_basic_set_free(bset);
4387 return NULL;
4388 }
4389
4390 /* Drop all floors in "qp", turning each integer division [a/m] into
4391 * a rational division a/m. If "down" is set, then the integer division
4392 * is replaces by (a-(m-1))/m instead.
4393 */
4394 static __isl_give isl_qpolynomial *qp_drop_floors(
4395 __isl_take isl_qpolynomial *qp, int down)
4396 {
4397 int i;
4398 struct isl_upoly *s;
4399
4400 if (!qp)
4401 return NULL;
4402 if (qp->div->n_row == 0)
4403 return qp;
4404
4405 qp = isl_qpolynomial_cow(qp);
4406 if (!qp)
4407 return NULL;
4408
4409 for (i = qp->div->n_row - 1; i >= 0; --i) {
4410 if (down) {
4411 isl_int_sub(qp->div->row[i][1],
4412 qp->div->row[i][1], qp->div->row[i][0]);
4413 isl_int_add_ui(qp->div->row[i][1],
4414 qp->div->row[i][1], 1);
4415 }
4416 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4417 qp->div->row[i][0], qp->div->n_col - 1);
4418 qp = substitute_div(qp, i, s);
4419 if (!qp)
4420 return NULL;
4421 }
4422
4423 return qp;
4424 }
4425
4426 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4427 * a rational division a/m.
4428 */
4429 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4430 __isl_take isl_pw_qpolynomial *pwqp)
4431 {
4432 int i;
4433
4434 if (!pwqp)
4435 return NULL;
4436
4437 if (isl_pw_qpolynomial_is_zero(pwqp))
4438 return pwqp;
4439
4440 pwqp = isl_pw_qpolynomial_cow(pwqp);
4441 if (!pwqp)
4442 return NULL;
4443
4444 for (i = 0; i < pwqp->n; ++i) {
4445 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4446 if (!pwqp->p[i].qp)
4447 goto error;
4448 }
4449
4450 return pwqp;
4451 error:
4452 isl_pw_qpolynomial_free(pwqp);
4453 return NULL;
4454 }
4455
4456 /* Adjust all the integer divisions in "qp" such that they are at least
4457 * one over the given orthant (identified by "signs"). This ensures
4458 * that they will still be non-negative even after subtracting (m-1)/m.
4459 *
4460 * In particular, f is replaced by f' + v, changing f = [a/m]
4461 * to f' = [(a - m v)/m].
4462 * If the constant term k in a is smaller than m,
4463 * the constant term of v is set to floor(k/m) - 1.
4464 * For any other term, if the coefficient c and the variable x have
4465 * the same sign, then no changes are needed.
4466 * Otherwise, if the variable is positive (and c is negative),
4467 * then the coefficient of x in v is set to floor(c/m).
4468 * If the variable is negative (and c is positive),
4469 * then the coefficient of x in v is set to ceil(c/m).
4470 */
4471 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4472 int *signs)
4473 {
4474 int i, j;
4475 int total;
4476 isl_vec *v = NULL;
4477 struct isl_upoly *s;
4478
4479 qp = isl_qpolynomial_cow(qp);
4480 if (!qp)
4481 return NULL;
4482 qp->div = isl_mat_cow(qp->div);
4483 if (!qp->div)
4484 goto error;
4485
4486 total = isl_dim_total(qp->dim);
4487 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4488
4489 for (i = 0; i < qp->div->n_row; ++i) {
4490 isl_int *row = qp->div->row[i];
4491 v = isl_vec_clr(v);
4492 if (!v)
4493 goto error;
4494 if (isl_int_lt(row[1], row[0])) {
4495 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4496 isl_int_sub_ui(v->el[0], v->el[0], 1);
4497 isl_int_submul(row[1], row[0], v->el[0]);
4498 }
4499 for (j = 0; j < total; ++j) {
4500 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4501 continue;
4502 if (signs[j] < 0)
4503 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4504 else
4505 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4506 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4507 }
4508 for (j = 0; j < i; ++j) {
4509 if (isl_int_sgn(row[2 + total + j]) >= 0)
4510 continue;
4511 isl_int_fdiv_q(v->el[1 + total + j],
4512 row[2 + total + j], row[0]);
4513 isl_int_submul(row[2 + total + j],
4514 row[0], v->el[1 + total + j]);
4515 }
4516 for (j = i + 1; j < qp->div->n_row; ++j) {
4517 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4518 continue;
4519 isl_seq_combine(qp->div->row[j] + 1,
4520 qp->div->ctx->one, qp->div->row[j] + 1,
4521 qp->div->row[j][2 + total + i], v->el, v->size);
4522 }
4523 isl_int_set_si(v->el[1 + total + i], 1);
4524 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4525 qp->div->ctx->one, v->size);
4526 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4527 isl_upoly_free(s);
4528 if (!qp->upoly)
4529 goto error;
4530 }
4531
4532 isl_vec_free(v);
4533 return qp;
4534 error:
4535 isl_vec_free(v);
4536 isl_qpolynomial_free(qp);
4537 return NULL;
4538 }
4539
4540 struct isl_to_poly_data {
4541 int sign;
4542 isl_pw_qpolynomial *res;
4543 isl_qpolynomial *qp;
4544 };
4545
4546 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4547 * We first make all integer divisions positive and then split the
4548 * quasipolynomials into terms with sign data->sign (the direction
4549 * of the requested approximation) and terms with the opposite sign.
4550 * In the first set of terms, each integer division [a/m] is
4551 * overapproximated by a/m, while in the second it is underapproximated
4552 * by (a-(m-1))/m.
4553 */
4554 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4555 void *user)
4556 {
4557 struct isl_to_poly_data *data = user;
4558 isl_pw_qpolynomial *t;
4559 isl_qpolynomial *qp, *up, *down;
4560
4561 qp = isl_qpolynomial_copy(data->qp);
4562 qp = make_divs_pos(qp, signs);
4563
4564 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4565 up = qp_drop_floors(up, 0);
4566 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4567 down = qp_drop_floors(down, 1);
4568
4569 isl_qpolynomial_free(qp);
4570 qp = isl_qpolynomial_add(up, down);
4571
4572 t = isl_pw_qpolynomial_alloc(orthant, qp);
4573 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4574
4575 return 0;
4576 }
4577
4578 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4579 * the polynomial will be an overapproximation. If "sign" is negative,
4580 * it will be an underapproximation. If "sign" is zero, the approximation
4581 * will lie somewhere in between.
4582 *
4583 * In particular, is sign == 0, we simply drop the floors, turning
4584 * the integer divisions into rational divisions.
4585 * Otherwise, we split the domains into orthants, make all integer divisions
4586 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4587 * depending on the requested sign and the sign of the term in which
4588 * the integer division appears.
4589 */
4590 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4591 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4592 {
4593 int i;
4594 struct isl_to_poly_data data;
4595
4596 if (sign == 0)
4597 return pwqp_drop_floors(pwqp);
4598
4599 if (!pwqp)
4600 return NULL;
4601
4602 data.sign = sign;
4603 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4604
4605 for (i = 0; i < pwqp->n; ++i) {
4606 if (pwqp->p[i].qp->div->n_row == 0) {
4607 isl_pw_qpolynomial *t;
4608 t = isl_pw_qpolynomial_alloc(
4609 isl_set_copy(pwqp->p[i].set),
4610 isl_qpolynomial_copy(pwqp->p[i].qp));
4611 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4612 continue;
4613 }
4614 data.qp = pwqp->p[i].qp;
4615 if (isl_set_foreach_orthant(pwqp->p[i].set,
4616 &to_polynomial_on_orthant, &data) < 0)
4617 goto error;
4618 }
4619
4620 isl_pw_qpolynomial_free(pwqp);
4621
4622 return data.res;
4623 error:
4624 isl_pw_qpolynomial_free(pwqp);
4625 isl_pw_qpolynomial_free(data.res);
4626 return NULL;
4627 }
4628
4629 static int poly_entry(void **entry, void *user)
4630 {
4631 int *sign = user;
4632 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4633
4634 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4635
4636 return *pwqp ? 0 : -1;
4637 }
4638
4639 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4640 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4641 {
4642 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4643 if (!upwqp)
4644 return NULL;
4645
4646 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4647 &poly_entry, &sign) < 0)
4648 goto error;
4649
4650 return upwqp;
4651 error:
4652 isl_union_pw_qpolynomial_free(upwqp);
4653 return NULL;
4654 }
4655
4656 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4657 __isl_take isl_qpolynomial *qp)
4658 {
4659 int i, k;
4660 isl_dim *dim;
4661 isl_vec *aff = NULL;
4662 isl_basic_map *bmap = NULL;
4663 unsigned pos;
4664 unsigned n_div;
4665
4666 if (!qp)
4667 return NULL;
4668 if (!isl_upoly_is_affine(qp->upoly))
4669 isl_die(qp->dim->ctx, isl_error_invalid,
4670 "input quasi-polynomial not affine", goto error);
4671 aff = isl_qpolynomial_extract_affine(qp);
4672 if (!aff)
4673 goto error;
4674 dim = isl_qpolynomial_get_dim(qp);
4675 dim = isl_dim_from_domain(dim);
4676 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4677 dim = isl_dim_add(dim, isl_dim_out, 1);
4678 n_div = qp->div->n_row;
4679 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4680
4681 for (i = 0; i < n_div; ++i) {
4682 k = isl_basic_map_alloc_div(bmap);
4683 if (k < 0)
4684 goto error;
4685 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4686 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4687 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4688 goto error;
4689 }
4690 k = isl_basic_map_alloc_equality(bmap);
4691 if (k < 0)
4692 goto error;
4693 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4694 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4695 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4696
4697 isl_vec_free(aff);
4698 isl_qpolynomial_free(qp);
4699 bmap = isl_basic_map_finalize(bmap);
4700 return bmap;
4701 error:
4702 isl_vec_free(aff);
4703 isl_qpolynomial_free(qp);
4704 isl_basic_map_free(bmap);
4705 return NULL;
4706 }
Integer set library